LMFDB - Embedded newform 225.2.h.e.181.4

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			181.4
Root			$-1.85090 - 0.438393i$ of defining polynomial
Character	$\chi$	$=$	225.181
Dual form			225.2.h.e.46.4

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	0.847255	+	0.531186i	$0.178253\pi$
$2$	0.670386	+	2.06324i	0.474035	+	1.45893i	−0.373221	+	0.927743i	$0.621747\pi$
$3$		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	0.955463	+	0.295112i	$0.0953569\pi$
$11$	1.18052	+	3.63326i	0.355940	+	1.09547i	−0.599523	+	0.800357i	$0.704643\pi$
$12$		0			0
$13$	0.819443	−	2.52199i	0.227273	−	0.699473i	−0.770780	−	0.637101i	$-0.780133\pi$
$13$	0.819443	−	2.52199i	0.227273	−	0.699473i	0.998053	−	0.0623720i	$-0.0198665\pi$
$14$	−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	0.945649	−	0.325190i	$-0.105428\pi$
$17$	3.82870	+	2.78171i	0.928596	+	0.674664i	−0.0170528	+	0.999855i	$0.505428\pi$
$18$		0			0
$19$	2.95435	+	2.14646i	0.677773	+	0.492431i	0.872618	−	0.488403i	$-0.162420\pi$
$19$	2.95435	+	2.14646i	0.677773	+	0.492431i	−0.194845	+	0.980834i	$0.562420\pi$
$20$	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	−0.997363	−	0.0725682i	$-0.976880\pi$
$23$	−1.11807	−	3.44107i	−0.233134	−	0.717513i	0.764229	−	0.644944i	$-0.223120\pi$
$24$		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	−0.585170	−	0.810911i	$-0.698972\pi$
$29$	0.0281335	−	0.0204402i	0.00522426	−	0.00379565i	0.590394	+	0.807115i	$0.298972\pi$
$30$		0			0
$31$	8.17609	+	5.94028i	1.46847	+	1.06690i	0.981054	+	0.193734i	$0.0620599\pi$
$31$	8.17609	+	5.94028i	1.46847	+	1.06690i	0.487415	+	0.873171i	$0.337940\pi$
$32$	−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	−0.219252	−	0.975668i	$-0.570362\pi$
$37$	3.23366	−	9.95217i	0.531610	−	1.63613i	0.750862	−	0.660459i	$-0.229638\pi$
$38$	−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	−0.986497	−	0.163779i	$-0.947632\pi$
$41$	−0.589966	+	1.81573i	−0.0921371	+	0.283569i	0.894360	+	0.447348i	$0.147632\pi$
$42$		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	−0.497272	−	0.867595i	$-0.665665\pi$
$47$	1.19421	−	0.867645i	0.174194	−	0.126559i	0.671466	+	0.741036i	$0.265665\pi$
$48$		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	−0.960316	−	0.278915i	$-0.910025\pi$
$53$	−7.22046	+	5.24597i	−0.991806	+	0.720589i	−0.0314903	+	0.999504i	$0.510025\pi$
$54$		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	0.311955	+	0.950097i	$0.399016\pi$
$59$	−3.83193	+	11.7935i	−0.498875	+	1.53538i	−0.810830	+	0.585282i	$0.800984\pi$
$60$		0			0
$61$	−1.59967	−	4.92329i	−0.204817	−	0.630363i	−0.999721	−	0.0236271i	$-0.992479\pi$
$61$	−1.59967	−	4.92329i	−0.204817	−	0.630363i	0.794903	−	0.606736i	$-0.207521\pi$
$62$	−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	0.822916	−	0.568162i	$-0.192345\pi$
$67$	4.39437	+	3.19269i	0.536857	+	0.390050i	−0.286059	+	0.958212i	$0.592345\pi$
$68$	−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	0.173530	−	0.984829i	$-0.444483\pi$
$71$	9.80619	−	7.12462i	1.16378	−	0.845536i	0.990251	+	0.139292i	$0.0444828\pi$
$72$		0			0
$73$	3.78817	+	11.6588i	0.443371	+	1.36456i	0.884260	+	0.466995i	$0.154663\pi$
$73$	3.78817	+	11.6588i	0.443371	+	1.36456i	−0.440889	+	0.897562i	$0.645337\pi$
$74$	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	−0.206788	−	0.978386i	$-0.566301\pi$
$79$	5.86453	−	4.26083i	0.659811	−	0.479381i	0.866599	+	0.499005i	$0.166301\pi$
$80$	−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	0.309163	−	0.951009i	$-0.399951\pi$
$83$	−4.55307	−	3.30800i	−0.499764	−	0.363100i	−0.808927	+	0.587909i	$0.799951\pi$
$84$		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	−0.604946	−	0.796266i	$-0.706805\pi$
$89$	−5.50537	−	16.9438i	−0.583568	−	1.79604i	0.0213784	−	0.999771i	$-0.493195\pi$
$90$		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	−0.193383	−	0.981123i	$-0.561946\pi$
$97$	6.69686	−	4.86555i	0.679963	−	0.494022i	0.873345	+	0.487102i	$0.161946\pi$
$98$	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	−0.960621	−	0.277861i	$-0.910374\pi$
$103$	−10.0800	+	7.32352i	−0.993208	+	0.721608i	−0.0325865	+	0.999469i	$0.510374\pi$
$104$	−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	−0.630217	−	0.776419i	$-0.717034\pi$
$109$	3.50801	−	10.7966i	0.336007	−	1.03412i	0.966224	−	0.257704i	$-0.0829659\pi$
$110$	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	−0.302873	−	0.953031i	$-0.597946\pi$
$113$	5.33988	−	16.4345i	0.502334	−	1.54603i	0.805207	−	0.592994i	$-0.202054\pi$
$114$		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	−0.992802	−	0.119767i	$-0.961785\pi$
$127$	−2.93011	−	9.01796i	−0.260005	−	0.800214i	0.732797	−	0.680448i	$-0.238215\pi$
$128$	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	0.873570	−	0.486699i	$-0.161799\pi$
$131$	7.79027	+	5.65996i	0.680639	+	0.494513i	−0.192931	+	0.981212i	$0.561799\pi$
$132$		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	−0.968097	−	0.250574i	$-0.919381\pi$
$137$	−0.440172	+	1.35471i	−0.0376064	+	0.115741i	0.930491	+	0.366315i	$0.119381\pi$
$138$		0			0
$139$	−0.508854	−	1.56609i	−0.0431605	−	0.132834i	0.927154	−	0.374680i	$-0.122247\pi$
$139$	−0.508854	−	1.56609i	−0.0431605	−	0.132834i	−0.970315	+	0.241845i	$0.922247\pi$
$140$	−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	0.689455	+	0.724329i	$0.257850\pi$
$163$	−3.75451	+	11.5552i	−0.294076	+	0.905072i	−0.983530	+	0.180743i	$0.942150\pi$
$164$	−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	0.852393	−	0.522901i	$-0.175150\pi$
$167$	7.99263	+	5.80699i	0.618488	+	0.449358i	−0.233905	+	0.972260i	$0.575150\pi$
$168$		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	0.948835	−	0.315772i	$-0.102263\pi$
$173$	−0.0578028	−	0.177899i	−0.00439467	−	0.0135254i	−0.953230	+	0.302246i	$0.902263\pi$
$174$		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	−0.953739	−	0.300635i	$-0.902801\pi$
$179$	−12.8779	+	9.35635i	−0.962540	+	0.699326i	−0.00880060	+	0.999961i	$0.502801\pi$
$180$		0			0
$181$	10.7058	+	7.77821i	0.795755	+	0.578150i	0.909666	−	0.415341i	$-0.136338\pi$
$181$	10.7058	+	7.77821i	0.795755	+	0.578150i	−0.113910	+	0.993491i	$0.536338\pi$
$182$	−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	−0.917087	−	0.398686i	$-0.869466\pi$
$191$	0.818073	−	2.51777i	0.0591937	−	0.182179i	0.976281	+	0.216507i	$0.0694663\pi$
$192$		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	0.206589	−	0.978428i	$-0.433764\pi$
$197$	16.8564	−	12.2469i	1.20097	−	0.872555i	0.994380	+	0.105873i	$0.0337637\pi$
$198$		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	0.998068	+	0.0621231i	$0.0197871\pi$
$211$	3.29924	+	10.1540i	0.227129	+	0.699032i	−0.770939	+	0.636909i	$0.780213\pi$
$212$	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	0.956572	−	0.291497i	$-0.0941533\pi$
$223$	0.169512	+	0.521705i	0.0113514	+	0.0349359i	−0.945220	+	0.326433i	$0.894153\pi$
$224$	25.2496			1.68706
$225$		0			0
$226$	37.4880			2.49366
$227$	−1.13841	−	3.50365i	−0.0755586	−	0.232546i	0.906143	−	0.422972i	$-0.139013\pi$
$227$	−1.13841	−	3.50365i	−0.0755586	−	0.232546i	−0.981702	+	0.190426i	$0.939013\pi$
$228$		0			0
$229$	1.39323	−	1.01224i	0.0920673	−	0.0668908i	−0.540799	−	0.841152i	$-0.681878\pi$
$229$	1.39323	−	1.01224i	0.0920673	−	0.0668908i	0.632867	+	0.774261i	$0.281878\pi$
$230$	−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	0.0254662	−	0.999676i	$-0.491893\pi$
$233$	−14.0037	−	10.1743i	−0.917412	−	0.666539i	−0.942879	+	0.333137i	$0.891893\pi$
$234$		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	0.999765	+	0.0216761i	$0.00690025\pi$
$239$	3.14880	+	9.69101i	0.203679	+	0.626860i	−0.796086	+	0.605183i	$0.793100\pi$
$240$		0			0
$241$	3.71188	−	11.4240i	0.239104	−	0.735885i	−0.757447	−	0.652897i	$-0.773554\pi$
$241$	3.71188	−	11.4240i	0.239104	−	0.735885i	0.996551	−	0.0829883i	$-0.0264464\pi$
$242$	−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	−0.998222	−	0.0596022i	$-0.981017\pi$
$263$	−2.52357	+	7.76676i	−0.155610	+	0.478919i	0.842612	+	0.538521i	$0.181017\pi$
$264$		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	0.870910	−	0.491442i	$-0.163530\pi$
$269$	11.0322	+	8.01539i	0.672647	+	0.488707i	−0.198263	+	0.980149i	$0.563530\pi$
$270$		0			0
$271$	0.872330	−	0.633785i	0.0529902	−	0.0384997i	−0.560975	−	0.827833i	$-0.689574\pi$
$271$	0.872330	−	0.633785i	0.0529902	−	0.0384997i	0.613965	+	0.789333i	$0.289574\pi$
$272$	−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	0.970188	+	0.242353i	$0.0779192\pi$
$277$	5.45470	+	16.7878i	0.327741	+	1.00868i	−0.642447	+	0.766330i	$0.722081\pi$
$278$	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	−0.227596	−	0.973756i	$-0.573087\pi$
$281$	−20.5184	−	14.9075i	−1.22402	−	0.889305i	−0.996428	+	0.0844503i	$0.973087\pi$
$282$		0			0
$283$	8.81015	+	6.40095i	0.523709	+	0.380497i	0.817999	−	0.575219i	$-0.195083\pi$
$283$	8.81015	+	6.40095i	0.523709	+	0.380497i	−0.294290	+	0.955716i	$0.595083\pi$
$284$	−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	0.969508	+	0.245060i	$0.0788077\pi$
$311$	5.80554	+	17.8676i	0.329202	+	1.01318i	−0.640306	+	0.768120i	$0.721192\pi$
$312$		0			0
$313$	6.73970	−	20.7427i	0.380950	−	1.17244i	−0.558425	−	0.829555i	$-0.688594\pi$
$313$	6.73970	−	20.7427i	0.380950	−	1.17244i	0.939376	−	0.342890i	$-0.111406\pi$
$314$	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	0.308822	−	0.951120i	$-0.400065\pi$
$317$	−8.90788	−	6.47195i	−0.500316	−	0.363501i	−0.809138	+	0.587619i	$0.800065\pi$
$318$		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	0.375812	−	0.926696i	$-0.377364\pi$
$331$	−7.08443	−	5.14714i	−0.389395	−	0.282912i	−0.765208	+	0.643784i	$0.777364\pi$
$332$	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	0.272593	+	0.962129i	$0.412119\pi$
$337$	−9.42596	+	29.0101i	−0.513465	+	1.58028i	−0.786058	+	0.618153i	$0.787881\pi$
$338$	−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	−0.276083	−	0.961134i	$-0.589036\pi$
$347$	10.2956	−	7.48018i	0.552696	−	0.401557i	0.828778	+	0.559577i	$0.189036\pi$
$348$		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	−0.157933	−	0.987450i	$-0.550483\pi$
$353$	13.7602	−	9.99740i	0.732384	−	0.532108i	0.890317	+	0.455342i	$0.150483\pi$
$354$		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	−0.639668	−	0.768651i	$-0.720928\pi$
$359$	6.24572	−	19.2223i	0.329636	−	1.01452i	0.969304	−	0.245865i	$-0.0790719\pi$
$360$		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	0.236051	−	0.971741i	$-0.424147\pi$
$367$	−11.7853	−	8.56250i	−0.615186	−	0.446959i	−0.851237	+	0.524782i	$0.824147\pi$
$368$	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	0.895417	−	0.445228i	$-0.146877\pi$
$373$	−1.75150	−	5.39055i	−0.0906891	−	0.279112i	−0.986106	+	0.166116i	$0.946877\pi$
$374$	−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	−0.758685	−	0.651457i	$-0.774158\pi$
$379$	−7.27243	+	5.28373i	−0.373560	+	0.271407i	0.385126	+	0.922864i	$0.374158\pi$
$380$	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	−0.00665004	−	0.999978i	$-0.502117\pi$
$383$	−18.7825	−	13.6463i	−0.959741	−	0.697292i	−0.953090	+	0.302686i	$0.902117\pi$
$384$		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	0.999107	−	0.0422493i	$-0.0134524\pi$
$389$	3.27362	+	10.0752i	0.165979	+	0.510831i	−0.833128	+	0.553080i	$0.813452\pi$
$390$		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	−0.531382	−	0.847133i	$-0.678327\pi$
$397$	2.19339	−	1.59359i	0.110083	−	0.0799802i	0.641465	+	0.767152i	$0.278327\pi$
$398$	−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	−0.750288	−	0.661111i	$-0.770085\pi$
$409$	4.96087	−	15.2680i	0.245299	−	0.754954i	0.995587	−	0.0938422i	$-0.0299149\pi$
$410$	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	−0.100068	−	0.994981i	$-0.531906\pi$
$419$	−22.0512	−	16.0212i	−1.07727	−	0.782685i	−0.977205	+	0.212296i	$0.931906\pi$
$420$		0			0
$421$	−2.42210	+	1.75976i	−0.118046	+	0.0857653i	−0.645242	−	0.763978i	$-0.723243\pi$
$421$	−2.42210	+	1.75976i	−0.118046	+	0.0857653i	0.527196	+	0.849744i	$0.323243\pi$
$422$	−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	−0.999612	−	0.0278621i	$-0.991130\pi$
$431$	−27.7155	−	20.1365i	−1.33501	−	0.969940i	−0.335395	−	0.942077i	$-0.608870\pi$
$432$		0			0
$433$	8.32935	+	6.05163i	0.400283	+	0.290823i	0.769656	−	0.638458i	$-0.220428\pi$
$433$	8.32935	+	6.05163i	0.400283	+	0.290823i	−0.369373	+	0.929281i	$0.620428\pi$
$434$	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	−0.619630	−	0.784894i	$-0.712717\pi$
$439$	−12.1458	−	37.3810i	−0.579688	−	1.78410i	0.0399418	−	0.999202i	$-0.487283\pi$
$440$	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	0.704121	+	0.710080i	$0.251341\pi$
$461$	11.8487	+	36.4666i	0.551850	+	1.69842i	−0.152271	+	0.988339i	$0.548659\pi$
$462$		0			0
$463$	4.66531	−	14.3583i	0.216815	−	0.667289i	−0.782204	−	0.623022i	$-0.785905\pi$
$463$	4.66531	−	14.3583i	0.216815	−	0.667289i	0.999020	−	0.0442671i	$-0.0140953\pi$
$464$	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	0.478387	−	0.878149i	$-0.341222\pi$
$467$	−4.51552	−	3.28072i	−0.208953	−	0.151814i	−0.687340	+	0.726336i	$0.741222\pi$
$468$		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	−0.640848	−	0.767667i	$-0.721417\pi$
$479$	−2.38091	+	1.72983i	−0.108786	+	0.0790380i	0.532062	+	0.846705i	$0.321417\pi$
$480$		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	−0.983042	−	0.183382i	$-0.941295\pi$
$487$	−1.76445	+	5.43042i	−0.0799549	+	0.246076i	0.903087	+	0.429458i	$0.141295\pi$
$488$	−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	−0.0591157	−	0.998251i	$-0.518828\pi$
$491$	12.7515	−	39.2451i	0.575467	−	1.77111i	0.634583	−	0.772855i	$-0.281172\pi$
$492$		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	−0.965108	−	0.261852i	$-0.915667\pi$
$503$	−22.7485	+	16.5278i	−1.01431	+	0.736937i	−0.0491992	+	0.998789i	$0.515667\pi$
$504$		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	−0.458824	−	0.888527i	$-0.651729\pi$
$509$	9.80583	−	30.1792i	0.434636	−	1.33767i	0.893459	−	0.449144i	$-0.148271\pi$
$510$		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	−0.564272	−	0.825589i	$-0.690843\pi$
$521$	1.06229	−	0.771800i	0.0465398	−	0.0338132i	0.610812	+	0.791776i	$0.290843\pi$
$522$		0			0
$523$	−0.223533	−	0.687963i	−0.00977441	−	0.0300825i	0.946050	−	0.324020i	$-0.105034\pi$
$523$	−0.223533	−	0.687963i	−0.00977441	−	0.0300825i	−0.955825	+	0.293937i	$0.905034\pi$
$524$	−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	0.0311714	+	0.999514i	$0.490076\pi$
$541$	−13.5264	+	41.6301i	−0.581546	+	1.78982i	−0.612718	+	0.790302i	$0.709924\pi$
$542$	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	−0.131993	−	0.991251i	$-0.542138\pi$
$547$	18.0077	−	13.0834i	0.769954	−	0.559405i	0.901947	+	0.431846i	$0.142138\pi$
$548$	−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	0.330195	+	0.943913i	$0.392885\pi$
$563$	−11.6682	+	35.9110i	−0.491756	+	1.51347i	−0.821952	+	0.569557i	$0.807115\pi$
$564$		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	0.944634	−	0.328126i	$-0.106417\pi$
$569$	22.0522	+	16.0218i	0.924476	+	0.671671i	−0.0201584	+	0.999797i	$0.506417\pi$
$570$		0			0
$571$	32.4321	−	23.5633i	1.35724	−	0.986094i	0.358628	−	0.933481i	$-0.383245\pi$
$571$	32.4321	−	23.5633i	1.35724	−	0.986094i	0.998615	−	0.0526136i	$-0.0167552\pi$
$572$	−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	0.999229	+	0.0392614i	$0.0125005\pi$
$577$	5.13837	+	15.8143i	0.213913	+	0.658357i	−0.785316	+	0.619095i	$0.787500\pi$
$578$	−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	−0.859144	−	0.511735i	$-0.829003\pi$
$587$	3.31218	−	10.1938i	0.136708	−	0.420745i	0.995852	+	0.0909899i	$0.0290031\pi$
$588$		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	−0.967313	−	0.253587i	$-0.918390\pi$
$613$	−0.883537	+	2.71925i	−0.0356857	+	0.109829i	0.931627	+	0.363416i	$0.118390\pi$
$614$	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	−0.293012	−	0.956109i	$-0.594658\pi$
$617$	−32.1143	−	23.3324i	−1.29287	−	0.939326i	−0.999859	+	0.0167825i	$0.994658\pi$
$618$		0			0
$619$	−17.5615	−	12.7592i	−0.705857	−	0.512835i	0.175978	−	0.984394i	$-0.443691\pi$
$619$	−17.5615	−	12.7592i	−0.705857	−	0.512835i	−0.881834	+	0.471559i	$0.843691\pi$
$620$	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	0.653932	−	0.756553i	$-0.273118\pi$
$631$	3.42841	+	2.49089i	0.136483	+	0.0991606i	−0.517449	+	0.855714i	$0.673118\pi$
$632$	−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	−0.659609	−	0.751609i	$-0.729278\pi$
$641$	7.99569	−	24.6082i	0.315811	−	0.971965i	0.975419	−	0.220356i	$-0.0707220\pi$
$642$		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	−0.688518	−	0.725219i	$-0.741738\pi$
$647$	−5.38122	+	3.90969i	−0.211558	+	0.153706i	0.476960	+	0.878925i	$0.341738\pi$
$648$		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	−0.853767	−	0.520654i	$-0.825688\pi$
$653$	−15.9053	+	11.5559i	−0.622424	+	0.452218i	0.231343	+	0.972872i	$0.425688\pi$
$654$		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	−0.949531	−	0.313673i	$-0.898441\pi$
$659$	0.0777271	−	0.239219i	0.00302782	−	0.00931866i	0.952559	+	0.304354i	$0.0984406\pi$
$660$		0			0
$661$	−14.5495	−	44.7788i	−0.565911	−	1.74169i	−0.665230	−	0.746638i	$-0.731667\pi$
$661$	−14.5495	−	44.7788i	−0.565911	−	1.74169i	0.0993193	−	0.995056i	$-0.468333\pi$
$662$	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	0.999809	−	0.0195655i	$-0.00622828\pi$
$673$	4.65524	+	14.3273i	0.179446	+	0.552278i	−0.820362	+	0.571844i	$0.806228\pi$
$674$	−66.1738			−2.54892
$675$		0			0
$676$	−16.1518			−0.621225
$677$	1.91183	+	5.88401i	0.0734776	+	0.226141i	0.981050	−	0.193755i	$-0.0620666\pi$
$677$	1.91183	+	5.88401i	0.0734776	+	0.226141i	−0.907572	+	0.419896i	$0.862067\pi$
$678$		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	0.378166	−	0.925738i	$-0.376555\pi$
$683$	−10.0722	−	7.31789i	−0.385403	−	0.280011i	−0.763569	+	0.645726i	$0.776555\pi$
$684$		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	0.651900	+	0.758305i	$0.273972\pi$
$691$	−8.44383	+	25.9875i	−0.321219	+	0.988609i	−0.973119	+	0.230304i	$0.926028\pi$
$692$	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	−0.893667	−	0.448731i	$-0.851876\pi$
$709$	2.47850	−	7.62803i	0.0930819	−	0.286477i	0.986749	+	0.162254i	$0.0518763\pi$
$710$	−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	0.802763	−	0.596298i	$-0.203362\pi$
$719$	12.9705	+	9.42361i	0.483717	+	0.351441i	−0.319046	+	0.947739i	$0.603362\pi$
$720$		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	0.926999	−	0.375063i	$-0.122379\pi$
$727$	−1.17061	−	3.60278i	−0.0434157	−	0.133620i	−0.970415	+	0.241444i	$0.922379\pi$
$728$	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	0.999155	−	0.0411091i	$-0.0130891\pi$
$733$	34.3518	+	24.9581i	1.26881	+	0.921847i	0.269659	+	0.962956i	$0.413089\pi$
$734$	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	0.944295	−	0.329101i	$-0.106746\pi$
$739$	−0.356025	−	1.09573i	−0.0130966	−	0.0403072i	−0.957391	+	0.288794i	$0.906746\pi$
$740$	−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	0.999435	+	0.0336159i	$0.0107023\pi$
$761$	5.81060	+	17.8832i	0.210634	+	0.648265i	−0.788801	+	0.614649i	$0.789298\pi$
$762$		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	0.946159	−	0.323701i	$-0.104927\pi$
$769$	25.8086	+	18.7510i	0.930681	+	0.676179i	−0.0154785	+	0.999880i	$0.504927\pi$
$770$	−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	0.918821	−	0.394674i	$-0.129143\pi$
$773$	−1.57099	−	4.83500i	−0.0565045	−	0.173903i	−0.975326	+	0.220771i	$0.929143\pi$
$774$		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	0.613422	+	0.789755i	$0.289793\pi$
$787$	−9.73607	+	29.9645i	−0.347053	+	1.06812i	−0.960475	+	0.278365i	$0.910207\pi$
$788$	−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	−0.810527	−	0.585701i	$-0.800819\pi$
$797$	−14.2273	+	10.3368i	−0.503958	+	0.366147i	0.306569	+	0.951849i	$0.400819\pi$
$798$		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	−0.841300	−	0.540569i	$-0.818209\pi$
$809$	4.46737	−	13.7491i	0.157064	−	0.483394i	0.998364	+	0.0571746i	$0.0182092\pi$
$810$		0			0
$811$	7.90971	+	24.3436i	0.277748	+	0.854819i	0.988479	+	0.151356i	$0.0483640\pi$
$811$	7.90971	+	24.3436i	0.277748	+	0.854819i	−0.710732	+	0.703463i	$0.751636\pi$
$812$	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	−0.738011	−	0.674789i	$-0.764235\pi$
$821$	−9.29237	+	6.75130i	−0.324306	+	0.235622i	0.413705	+	0.910411i	$0.364235\pi$
$822$		0			0
$823$	−17.2352	−	53.0444i	−0.600781	−	1.84901i	−0.523542	−	0.852000i	$-0.675390\pi$
$823$	−17.2352	−	53.0444i	−0.600781	−	1.84901i	−0.0772383	−	0.997013i	$-0.524610\pi$
$824$	19.0929			0.665132
$825$		0			0
$826$	89.4316			3.11172
$827$	1.60407	+	4.93680i	0.0557788	+	0.171670i	0.975065	−	0.221921i	$-0.0712327\pi$
$827$	1.60407	+	4.93680i	0.0557788	+	0.171670i	−0.919286	+	0.393591i	$0.871233\pi$
$828$		0			0
$829$	−24.1809	+	17.5685i	−0.839838	+	0.610178i	−0.922325	−	0.386414i	$-0.873714\pi$
$829$	−24.1809	+	17.5685i	−0.839838	+	0.610178i	0.0824876	+	0.996592i	$0.473714\pi$
$830$	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	−0.875845	−	0.482592i	$-0.839695\pi$
$839$	−13.0615	−	40.1991i	−0.450932	−	1.38783i	0.424913	−	0.905234i	$-0.360305\pi$
$840$		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	−0.507780	−	0.861487i	$-0.669534\pi$
$853$	4.51616	−	3.28118i	0.154630	−	0.112346i	0.662410	+	0.749141i	$0.269534\pi$
$854$	−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	−0.912354	−	0.409403i	$-0.865737\pi$
$859$	1.94601	−	5.98920i	0.0663970	−	0.204349i	0.978751	+	0.205054i	$0.0657370\pi$
$860$	−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	−0.798534	−	0.601950i	$-0.794391\pi$
$863$	5.91389	−	18.2011i	0.201311	−	0.619572i	0.999845	−	0.0176217i	$-0.00560946\pi$
$864$		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	0.996201	−	0.0870840i	$-0.0277549\pi$
$877$	4.11847	+	12.6753i	0.139071	+	0.428016i	−0.857130	+	0.515100i	$0.827755\pi$
$878$	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	0.0423910	−	0.999101i	$-0.486502\pi$
$881$	−26.5565	−	19.2944i	−0.894711	−	0.650046i	−0.937102	+	0.349055i	$0.886502\pi$
$882$		0			0
$883$	5.89651	+	4.28406i	0.198433	+	0.144170i	0.682565	−	0.730825i	$-0.260864\pi$
$883$	5.89651	+	4.28406i	0.198433	+	0.144170i	−0.484132	+	0.874995i	$0.660864\pi$
$884$	−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	0.638166	+	0.769899i	$0.279693\pi$
$887$	−9.84779	+	30.3084i	−0.330656	+	1.01766i	−0.968822	+	0.247757i	$0.920307\pi$
$888$		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	−0.993248	−	0.116011i	$-0.962989\pi$
$911$	−7.78362	−	23.9555i	−0.257883	−	0.793682i	0.735365	−	0.677671i	$-0.237011\pi$
$912$		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	0.619447	−	0.785039i	$-0.287357\pi$
$919$	1.94774	+	1.41512i	0.0642500	+	0.0466804i	−0.555197	+	0.831719i	$0.687357\pi$
$920$	−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	−0.431590	−	0.902070i	$-0.642047\pi$
$929$	8.92928	−	6.48750i	0.292960	−	0.212848i	0.724551	+	0.689222i	$0.242047\pi$
$930$		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	−0.942696	−	0.333654i	$-0.891718\pi$
$937$	0.492148	−	1.51468i	0.0160778	−	0.0494823i	0.958774	+	0.284171i	$0.0917184\pi$
$938$	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	−0.983299	−	0.181996i	$-0.941744\pi$
$941$	−2.47918	+	7.63013i	−0.0808189	+	0.248735i	0.902480	+	0.430731i	$0.141744\pi$
$942$		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	−0.424611	−	0.905376i	$-0.639589\pi$
$947$	9.39328	−	6.82462i	0.305241	−	0.221770i	0.729852	+	0.683606i	$0.239589\pi$
$948$		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	−0.575685	−	0.817672i	$-0.695264\pi$
$953$	0.743091	−	0.539888i	0.0240711	−	0.0174887i	0.599756	+	0.800183i	$0.295264\pi$
$954$		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	0.254526	−	0.967066i	$-0.418080\pi$
$967$	−18.2399	−	13.2521i	−0.586555	−	0.426157i	−0.841081	+	0.540909i	$0.818080\pi$
$968$	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	0.474231	−	0.880401i	$-0.342726\pi$
$971$	45.4353	−	33.0106i	1.45809	−	1.05936i	0.983856	−	0.178962i	$-0.0572738\pi$
$972$		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	−0.823915	−	0.566713i	$-0.808215\pi$
$977$	−15.3303	−	47.1818i	−0.490459	−	1.50948i	0.333456	−	0.942766i	$-0.391785\pi$
$978$		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	0.985775	+	0.168069i	$0.0537530\pi$
$983$	45.4691	+	33.0352i	1.45024	+	1.05366i	0.464464	+	0.885592i	$0.346247\pi$
$984$		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	−0.999319	−	0.0369060i	$-0.988250\pi$
$991$	−5.32519	+	16.3892i	−0.169160	+	0.520621i	0.830159	+	0.557527i	$0.188250\pi$
$992$	−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	−0.608005	−	0.793933i	$-0.708030\pi$
$997$	−1.28873	+	0.936317i	−0.0408145	+	0.0296535i	0.567191	+	0.823586i	$0.308030\pi$
$998$	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.181.4	yes	16
3.2	odd	2	inner	225.2.h.e.181.1	yes	16
25.11	even	5		5625.2.a.w.1.8		8
25.14	even	10		5625.2.a.v.1.1		8
25.21	even	5	inner	225.2.h.e.46.4	yes	16
75.11	odd	10		5625.2.a.w.1.1		8
75.14	odd	10		5625.2.a.v.1.8		8
75.71	odd	10	inner	225.2.h.e.46.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.h.e.46.1	✓	16	75.71	odd	10	inner
225.2.h.e.46.4	yes	16	25.21	even	5	inner
225.2.h.e.181.1	yes	16	3.2	odd	2	inner
225.2.h.e.181.4	yes	16	1.1	even	1	trivial
5625.2.a.v.1.1		8	25.14	even	10
5625.2.a.v.1.8		8	75.14	odd	10
5625.2.a.w.1.1		8	75.11	odd	10
5625.2.a.w.1.8		8	25.11	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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