LMFDB - Embedded newform 225.2.k.c.124.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.2
Root			$-1.41485 - 0.816862i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41485 - 0.816862i) q^{2} +(-1.36657 + 1.06419i) q^{3} +(0.334526 + 0.579416i) q^{4} +(2.80278 - 0.389365i) q^{6} +(-0.437645 - 0.252674i) q^{7} +2.17440i q^{8} +(0.735010 - 2.90857i) q^{9} +O(q^{10})$	\(q+(-1.41485 - 0.816862i) q^{2} +(-1.36657 + 1.06419i) q^{3} +(0.334526 + 0.579416i) q^{4} +(2.80278 - 0.389365i) q^{6} +(-0.437645 - 0.252674i) q^{7} +2.17440i q^{8} +(0.735010 - 2.90857i) q^{9} +(-1.55010 + 2.68485i) q^{11} +(-1.07376 - 0.435812i) q^{12} +(5.40337 - 3.11964i) q^{13} +(0.412800 + 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} -6.10020i q^{17} +(-3.41582 + 3.51477i) q^{18} +5.57022 q^{19} +(0.866963 - 0.120440i) q^{21} +(4.38631 - 2.53244i) q^{22} +(3.31307 - 1.91280i) q^{23} +(-2.31397 - 2.97146i) q^{24} -10.1932 q^{26} +(2.09082 + 4.75694i) q^{27} -0.338104i q^{28} +(1.22966 - 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(-3.15309 + 1.82044i) q^{32} +(-0.738871 - 5.31863i) q^{33} +(-4.98302 + 8.63085i) q^{34} +(1.93115 - 0.547115i) q^{36} +6.72677i q^{37} +(-7.88101 - 4.55010i) q^{38} +(-4.06419 + 10.0134i) q^{39} +(2.72092 + 4.71278i) q^{41} +(-1.32500 - 0.537785i) q^{42} +(1.14957 + 0.663704i) q^{43} -2.07420 q^{44} -6.24997 q^{46} +(3.21115 + 1.85396i) q^{47} +(1.16555 + 8.38998i) q^{48} +(-3.37231 - 5.84101i) q^{49} +(6.49176 + 8.33633i) q^{51} +(3.61514 + 2.08720i) q^{52} -2.54205i q^{53} +(0.927572 - 8.43825i) q^{54} +(0.549415 - 0.951614i) q^{56} +(-7.61208 + 5.92776i) q^{57} +(-3.47956 + 2.00893i) q^{58} +(1.44116 + 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} +6.90833i q^{62} +(-1.05659 + 1.08720i) q^{63} -3.83276 q^{64} +(-3.29920 + 8.12860i) q^{66} +(2.08411 - 1.20326i) q^{67} +(3.53456 - 2.04068i) q^{68} +(-2.49195 + 6.13969i) q^{69} +5.54205 q^{71} +(6.32439 + 1.59821i) q^{72} +11.7988i q^{73} +(5.49484 - 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(1.35679 - 0.783341i) q^{77} +(13.9298 - 10.8475i) q^{78} +(1.70149 - 2.94707i) q^{79} +(-7.91952 - 4.27565i) q^{81} -8.89047i q^{82} +(-12.0388 - 6.95059i) q^{83} +(0.359807 + 0.462042i) q^{84} +(-1.08431 - 1.87808i) q^{86} +(0.586130 + 4.21915i) q^{87} +(-5.83795 - 3.37054i) q^{88} -3.38513 q^{89} -3.15301 q^{91} +(2.21661 + 1.27976i) q^{92} +(6.78643 + 2.75444i) q^{93} +(-3.02886 - 5.24614i) q^{94} +(2.37162 - 5.84324i) q^{96} +(-9.59173 - 5.53779i) q^{97} +11.0188i q^{98} +(6.66974 + 6.48197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41485	−	0.816862i	−1.00045	−	0.577608i	−0.0920666	−	0.995753i	$-0.529347\pi$
$2$	−1.41485	−	0.816862i	−1.00045	−	0.577608i	−0.908381	+	0.418144i	$0.862681\pi$
$3$	−1.36657	+	1.06419i	−0.788988	+	0.614409i
$3$	−1.36657	+	1.06419i	−0.788988	+	0.614409i
$4$	0.334526	+	0.579416i	0.167263	+	0.289708i
$5$		0			0
$5$		0			0
$6$	2.80278	−	0.389365i	1.14423	−	0.158958i
$7$	−0.437645	−	0.252674i	−0.165414	−	0.0955019i	0.415008	−	0.909818i	$-0.363779\pi$
$7$	−0.437645	−	0.252674i	−0.165414	−	0.0955019i	−0.580422	+	0.814316i	$0.697112\pi$
$8$			2.17440i			0.768767i
$9$	0.735010	−	2.90857i	0.245003	−	0.969522i
$10$		0			0
$11$	−1.55010	+	2.68485i	−0.467373	+	0.809514i	−0.999305	−	0.0372730i	$-0.988133\pi$
$11$	−1.55010	+	2.68485i	−0.467373	+	0.809514i	0.531932	+	0.846787i	$0.321466\pi$
$12$	−1.07376	−	0.435812i	−0.309968	−	0.125808i
$13$	5.40337	−	3.11964i	1.49863	−	0.865232i	0.498627	−	0.866817i	$-0.333838\pi$
$13$	5.40337	−	3.11964i	1.49863	−	0.865232i	0.999999	+	0.00158518i	$0.000504579\pi$
$14$	0.412800	+	0.714990i	0.110325	+	0.191089i
$15$		0			0
$16$	2.44524	−	4.23527i	0.611309	−	1.05882i
$17$		−	6.10020i		−	1.47952i	−0.672873	−	0.739758i	$-0.734940\pi$
$17$		−	6.10020i		−	1.47952i	0.672873	−	0.739758i	$-0.265060\pi$
$18$	−3.41582	+	3.51477i	−0.805117	+	0.828440i
$19$	5.57022			1.27790			0.638948	−	0.769250i	$-0.279370\pi$
$19$	5.57022			1.27790			0.638948	+	0.769250i	$0.279370\pi$
$20$		0			0
$21$	0.866963	−	0.120440i	0.189187	−	0.0262821i
$22$	4.38631	−	2.53244i	0.935164	−	0.539917i
$23$	3.31307	−	1.91280i	0.690822	−	0.398846i	−0.113098	−	0.993584i	$-0.536077\pi$
$23$	3.31307	−	1.91280i	0.690822	−	0.398846i	0.803920	+	0.594738i	$0.202744\pi$
$24$	−2.31397	−	2.97146i	−0.472337	−	0.606547i
$25$		0			0
$26$	−10.1932			−1.99906
$27$	2.09082	+	4.75694i	0.402379	+	0.915473i
$28$		−	0.338104i		−	0.0638957i
$29$	1.22966	−	2.12984i	0.228342	−	0.395501i	−0.728975	−	0.684541i	$-0.760003\pi$
$29$	1.22966	−	2.12984i	0.228342	−	0.395501i	0.957317	+	0.289040i	$0.0933361\pi$
$30$		0			0
$31$	−2.11429	−	3.66206i	−0.379738	−	0.657725i	0.611286	−	0.791409i	$-0.290652\pi$
$31$	−2.11429	−	3.66206i	−0.379738	−	0.657725i	−0.991024	+	0.133685i	$0.957319\pi$
$32$	−3.15309	+	1.82044i	−0.557394	+	0.321811i
$33$	−0.738871	−	5.31863i	−0.128621	−	0.925855i
$34$	−4.98302	+	8.63085i	−0.854581	+	1.48018i
$35$		0			0
$36$	1.93115	−	0.547115i	0.321858	−	0.0911858i
$37$			6.72677i			1.10587i	0.833223	+	0.552937i	$0.186493\pi$
$37$			6.72677i			1.10587i	−0.833223	+	0.552937i	$0.813507\pi$
$38$	−7.88101	−	4.55010i	−1.27847	−	0.738124i
$39$	−4.06419	+	10.0134i	−0.650791	+	1.60343i
$40$		0			0
$41$	2.72092	+	4.71278i	0.424937	+	0.736012i	0.996415	−	0.0846053i	$-0.0269630\pi$
$41$	2.72092	+	4.71278i	0.424937	+	0.736012i	−0.571478	+	0.820618i	$0.693630\pi$
$42$	−1.32500	−	0.537785i	−0.204452	−	0.0829821i
$43$	1.14957	+	0.663704i	0.175308	+	0.101214i	0.585086	−	0.810971i	$-0.301061\pi$
$43$	1.14957	+	0.663704i	0.175308	+	0.101214i	−0.409779	+	0.912185i	$0.634394\pi$
$44$	−2.07420			−0.312697
$45$		0			0
$46$	−6.24997			−0.921508
$47$	3.21115	+	1.85396i	0.468395	+	0.270428i	0.715568	−	0.698544i	$-0.246168\pi$
$47$	3.21115	+	1.85396i	0.468395	+	0.270428i	−0.247173	+	0.968971i	$0.579501\pi$
$48$	1.16555	+	8.38998i	0.168232	+	1.21099i
$49$	−3.37231	−	5.84101i	−0.481759	−	0.834431i
$50$		0			0
$51$	6.49176	+	8.33633i	0.909028	+	1.16732i
$52$	3.61514	+	2.08720i	0.501329	+	0.289443i
$53$		−	2.54205i		−	0.349177i	−0.984641	−	0.174589i	$-0.944140\pi$
$53$		−	2.54205i		−	0.349177i	0.984641	−	0.174589i	$-0.0558596\pi$
$54$	0.927572	−	8.43825i	0.126227	−	1.14830i
$55$		0			0
$56$	0.549415	−	0.951614i	0.0734187	−	0.127165i
$57$	−7.61208	+	5.92776i	−1.00824	+	0.785151i
$58$	−3.47956	+	2.00893i	−0.456889	+	0.263785i
$59$	1.44116	+	2.49616i	0.187623	+	0.324973i	0.944457	−	0.328634i	$-0.106588\pi$
$59$	1.44116	+	2.49616i	0.187623	+	0.324973i	−0.756834	+	0.653607i	$0.773255\pi$
$60$		0			0
$61$	1.42173	−	2.46250i	0.182033	−	0.315291i	−0.760539	−	0.649292i	$-0.775065\pi$
$61$	1.42173	−	2.46250i	0.182033	−	0.315291i	0.942573	+	0.334001i	$0.108399\pi$
$62$			6.90833i			0.877358i
$63$	−1.05659	+	1.08720i	−0.133118	+	0.136974i
$64$	−3.83276			−0.479095
$65$		0			0
$66$	−3.29920	+	8.12860i	−0.406103	+	1.00056i
$67$	2.08411	−	1.20326i	0.254614	−	0.147002i	−0.367261	−	0.930118i	$-0.619704\pi$
$67$	2.08411	−	1.20326i	0.254614	−	0.147002i	0.621875	+	0.783116i	$0.286371\pi$
$68$	3.53456	−	2.04068i	0.428628	−	0.247468i
$69$	−2.49195	+	6.13969i	−0.299995	+	0.739132i
$70$		0			0
$71$	5.54205			0.657720			0.328860	−	0.944379i	$-0.393336\pi$
$71$	5.54205			0.657720			0.328860	+	0.944379i	$0.393336\pi$
$72$	6.32439	+	1.59821i	0.745336	+	0.188350i
$73$			11.7988i			1.38095i	0.723359	+	0.690473i	$0.242597\pi$
$73$			11.7988i			1.38095i	−0.723359	+	0.690473i	$0.757403\pi$
$74$	5.49484	−	9.51734i	0.638762	−	1.10637i
$75$		0			0
$76$	1.86338	+	3.22748i	0.213745	+	0.370217i
$77$	1.35679	−	0.783341i	0.154620	−	0.0892700i
$78$	13.9298	−	10.8475i	1.57723	−	1.22824i
$79$	1.70149	−	2.94707i	0.191433	−	0.331571i	−0.754293	−	0.656538i	$-0.772020\pi$
$79$	1.70149	−	2.94707i	0.191433	−	0.331571i	0.945725	+	0.324967i	$0.105353\pi$
$80$		0			0
$81$	−7.91952	−	4.27565i	−0.879947	−	0.475072i
$82$		−	8.89047i		−	0.981789i
$83$	−12.0388	−	6.95059i	−1.32143	−	0.762926i	−0.337470	−	0.941336i	$-0.609571\pi$
$83$	−12.0388	−	6.95059i	−1.32143	−	0.762926i	−0.983956	+	0.178410i	$0.942905\pi$
$84$	0.359807	+	0.462042i	0.0392581	+	0.0504129i
$85$		0			0
$86$	−1.08431	−	1.87808i	−0.116924	−	0.202518i
$87$	0.586130	+	4.21915i	0.0628398	+	0.452341i
$88$	−5.83795	−	3.37054i	−0.622327	−	0.359301i
$89$	−3.38513			−0.358823			−0.179411	−	0.983774i	$-0.557419\pi$
$89$	−3.38513			−0.358823			−0.179411	+	0.983774i	$0.557419\pi$
$90$		0			0
$91$	−3.15301			−0.330525
$92$	2.21661	+	1.27976i	0.231098	+	0.133425i
$93$	6.78643	+	2.75444i	0.703720	+	0.285623i
$94$	−3.02886	−	5.24614i	−0.312403	−	0.541098i
$95$		0			0
$96$	2.37162	−	5.84324i	0.242053	−	0.596373i
$97$	−9.59173	−	5.53779i	−0.973892	−	0.562277i	−0.0734716	−	0.997297i	$-0.523408\pi$
$97$	−9.59173	−	5.53779i	−0.973892	−	0.562277i	−0.900421	+	0.435020i	$0.856741\pi$
$98$			11.0188i			1.11307i
$99$	6.66974	+	6.48197i	0.670334	+	0.651462i
$100$		0			0
$101$	8.68451	−	15.0420i	0.864141	−	1.49674i	−0.00375621	−	0.999993i	$-0.501196\pi$
$101$	8.68451	−	15.0420i	0.864141	−	1.49674i	0.867897	−	0.496744i	$-0.165471\pi$
$102$	−2.37521	−	17.0975i	−0.235181	−	1.69290i
$103$	−0.721188	+	0.416378i	−0.0710608	+	0.0410269i	−0.535109	−	0.844783i	$-0.679730\pi$
$103$	−0.721188	+	0.416378i	−0.0710608	+	0.0410269i	0.464049	+	0.885810i	$0.346396\pi$
$104$	6.78334	+	11.7491i	0.665161	+	1.15209i
$105$		0			0
$106$	−2.07650	+	3.59661i	−0.201688	+	0.349334i
$107$		−	11.0684i		−	1.07002i	−0.844844	−	0.535012i	$-0.820307\pi$
$107$		−	11.0684i		−	1.07002i	0.844844	−	0.535012i	$-0.179693\pi$
$108$	−2.05681	+	2.80278i	−0.197917	+	0.269697i
$109$	4.65836			0.446190			0.223095	−	0.974797i	$-0.428384\pi$
$109$	4.65836			0.446190			0.223095	+	0.974797i	$0.428384\pi$
$110$		0			0
$111$	−7.15854	−	9.19258i	−0.679459	−	0.872521i
$112$	−2.14029	+	1.23570i	−0.202238	+	0.116762i
$113$	10.3873	−	5.99711i	0.977155	−	0.564160i	0.0757447	−	0.997127i	$-0.475867\pi$
$113$	10.3873	−	5.99711i	0.977155	−	0.564160i	0.901410	+	0.432967i	$0.142533\pi$
$114$	15.6121	−	2.16885i	1.46221	−	0.203132i
$115$		0			0
$116$	1.64542			0.152773
$117$	−5.10214	−	18.0090i	−0.471693	−	1.66494i
$118$		−	4.70892i		−	0.433491i
$119$	−1.54136	+	2.66972i	−0.141297	+	0.244733i
$120$		0			0
$121$	0.694371	+	1.20269i	0.0631246	+	0.109335i
$122$	−4.02305	+	2.32271i	−0.364230	+	0.210288i
$123$	−8.73360	−	3.54475i	−0.787483	−	0.319620i
$124$	1.41457	−	2.45011i	0.127032	−	0.220026i
$125$		0			0
$126$	2.38301	−	0.675131i	0.212295	−	0.0601454i
$127$			3.22858i			0.286490i	0.989687	+	0.143245i	$0.0457537\pi$
$127$			3.22858i			0.286490i	−0.989687	+	0.143245i	$0.954246\pi$
$128$	11.7289	+	6.77171i	1.03670	+	0.598540i
$129$	−2.27727	+	0.316361i	−0.200502	+	0.0278540i
$130$		0			0
$131$	4.69256	+	8.12776i	0.409991	+	0.710125i	0.994888	−	0.100982i	$-0.0321985\pi$
$131$	4.69256	+	8.12776i	0.409991	+	0.710125i	−0.584897	+	0.811107i	$0.698865\pi$
$132$	2.83453	−	2.20734i	0.246714	−	0.192124i
$133$	−2.43778	−	1.40745i	−0.211382	−	0.122042i
$134$	−3.93159			−0.339637
$135$		0			0
$136$	13.2643			1.13740
$137$	2.00013	+	1.15478i	0.170883	+	0.0986593i	0.583002	−	0.812471i	$-0.301878\pi$
$137$	2.00013	+	1.15478i	0.170883	+	0.0986593i	−0.412119	+	0.911130i	$0.635211\pi$
$138$	8.54100	−	6.65114i	0.727059	−	0.566183i
$139$	5.44701	+	9.43449i	0.462009	+	0.800223i	0.999061	−	0.0433260i	$-0.0137954\pi$
$139$	5.44701	+	9.43449i	0.462009	+	0.800223i	−0.537052	+	0.843549i	$0.680462\pi$
$140$		0			0
$141$	−6.36122	+	0.883709i	−0.535711	+	0.0744217i
$142$	−7.84115	−	4.52709i	−0.658014	−	0.379905i
$143$			19.3430i			1.61754i
$144$	−10.5213	−	10.2251i	−0.876775	−	0.852092i
$145$		0			0
$146$	9.63799	−	16.6935i	0.797646	−	1.38156i
$147$	10.8244	+	4.39337i	0.892783	+	0.362359i
$148$	−3.89760	+	2.25028i	−0.320381	+	0.184972i
$149$	−8.17151	−	14.1535i	−0.669436	−	1.15950i	−0.978062	−	0.208314i	$-0.933202\pi$
$149$	−8.17151	−	14.1535i	−0.669436	−	1.15950i	0.308626	−	0.951183i	$-0.400131\pi$
$150$		0			0
$151$	−11.3913	+	19.7304i	−0.927015	+	1.60564i	−0.138727	+	0.990331i	$0.544301\pi$
$151$	−11.3913	+	19.7304i	−0.927015	+	1.60564i	−0.788288	+	0.615306i	$0.789032\pi$
$152$			12.1119i			0.982404i
$153$	−17.7428	−	4.48371i	−1.43442	−	0.362486i
$154$	−2.55953			−0.206252
$155$		0			0
$156$	−7.16150	+	0.994885i	−0.573379	+	0.0796545i
$157$	−10.7913	+	6.23035i	−0.861238	+	0.497236i	−0.864427	−	0.502759i	$-0.832318\pi$
$157$	−10.7913	+	6.23035i	−0.861238	+	0.497236i	0.00318877	+	0.999995i	$0.498985\pi$
$158$	−4.81469	+	2.77976i	−0.383036	+	0.221146i
$159$	2.70522	+	3.47388i	0.214538	+	0.275497i
$160$		0			0
$161$	−1.93326			−0.152362
$162$	7.71229	+	12.5185i	0.605935	+	0.983549i
$163$		−	7.57384i		−	0.593229i	−0.954997	−	0.296614i	$-0.904142\pi$
$163$		−	7.57384i		−	0.593229i	0.954997	−	0.296614i	$-0.0958576\pi$
$164$	−1.82044	+	3.15309i	−0.142152	+	0.246215i
$165$		0			0
$166$	11.3553	+	19.6680i	0.881345	+	1.52653i
$167$	2.57793	−	1.48837i	0.199486	−	0.115174i	−0.396929	−	0.917849i	$-0.629924\pi$
$167$	2.57793	−	1.48837i	0.199486	−	0.115174i	0.596416	+	0.802676i	$0.296591\pi$
$168$	0.261884	+	1.88513i	0.0202048	+	0.145441i
$169$	12.9643	−	22.4548i	0.997252	−	1.72729i
$170$		0			0
$171$	4.09417	−	16.2014i	0.313089	−	1.23895i
$172$			0.888105i			0.0677174i
$173$	13.7291	+	7.92649i	1.04380	+	0.602640i	0.920908	−	0.389780i	$-0.127449\pi$
$173$	13.7291	+	7.92649i	1.04380	+	0.602640i	0.122895	+	0.992420i	$0.460782\pi$
$174$	2.61718	−	6.44824i	0.198408	−	0.488840i
$175$		0			0
$176$	7.58073	+	13.1302i	0.571419	+	0.989727i
$177$	−4.62583	−	1.87751i	−0.347699	−	0.141122i
$178$	4.78943	+	2.76518i	0.358983	+	0.207259i
$179$	−17.0841			−1.27693			−0.638463	−	0.769653i	$-0.720429\pi$
$179$	−17.0841			−1.27693			−0.638463	+	0.769653i	$0.720429\pi$
$180$		0			0
$181$	13.3690			0.993712			0.496856	−	0.867833i	$-0.334488\pi$
$181$	13.3690			0.993712			0.496856	+	0.867833i	$0.334488\pi$
$182$	4.46102	+	2.57557i	0.330673	+	0.190914i
$183$	0.677680	+	4.87816i	0.0500956	+	0.360604i
$184$	4.15919	+	7.20393i	0.306620	+	0.531081i
$185$		0			0
$186$	−7.35176	−	9.44069i	−0.539057	−	0.692225i
$187$	16.3782	+	9.45593i	1.19769	+	0.691486i
$188$			2.48079i			0.180930i
$189$	0.286920	−	2.61014i	0.0208703	−	0.189860i
$190$		0			0
$191$	−12.6686	+	21.9427i	−0.916669	+	1.58772i	−0.112230	+	0.993682i	$0.535799\pi$
$191$	−12.6686	+	21.9427i	−0.916669	+	1.58772i	−0.804439	+	0.594035i	$0.797534\pi$
$192$	5.23772	−	4.07877i	0.378000	−	0.294360i
$193$	−8.27879	+	4.77976i	−0.595921	+	0.344055i	−0.767435	−	0.641127i	$-0.778467\pi$
$193$	−8.27879	+	4.77976i	−0.595921	+	0.344055i	0.171515	+	0.985182i	$0.445134\pi$
$194$	9.04721	+	15.6702i	0.649552	+	1.12506i
$195$		0			0
$196$	2.25625	−	3.90794i	0.161161	−	0.279139i
$197$			2.06841i			0.147368i	0.997282	+	0.0736842i	$0.0234757\pi$
$197$			2.06841i			0.147368i	−0.997282	+	0.0736842i	$0.976524\pi$
$198$	−4.14178	−	14.6192i	−0.294344	−	1.03894i
$199$	−13.0970			−0.928419			−0.464210	−	0.885725i	$-0.653662\pi$
$199$	−13.0970			−0.928419			−0.464210	+	0.885725i	$0.653662\pi$
$200$		0			0
$201$	−1.56758	+	3.86221i	−0.110568	+	0.272420i
$202$	−24.5745	+	14.1881i	−1.72906	+	0.998271i
$203$	−1.07631	+	0.621407i	−0.0755421	+	0.0436142i
$204$	−2.65854	+	6.55015i	−0.186135	+	0.458602i
$205$		0			0
$206$	1.36049			0.0947900
$207$	−3.12837	−	11.0422i	−0.217437	−	0.767486i
$208$		−	30.5130i		−	2.11570i
$209$	−8.63441	+	14.9552i	−0.597255	+	1.03448i
$210$		0			0
$211$	−5.55595	−	9.62318i	−0.382487	−	0.662487i	0.608930	−	0.793224i	$-0.291599\pi$
$211$	−5.55595	−	9.62318i	−0.382487	−	0.662487i	−0.991417	+	0.130737i	$0.958266\pi$
$212$	1.47291	−	0.850382i	0.101160	−	0.0584045i
$213$	−7.57358	+	5.89778i	−0.518933	+	0.404109i
$214$	−9.04136	+	15.6601i	−0.618055	+	1.07050i
$215$		0			0
$216$	−10.3435	+	4.54628i	−0.703785	+	0.309335i
$217$			2.13690i			0.145063i
$218$	−6.59086	−	3.80523i	−0.446389	−	0.257723i
$219$	−12.5561	−	16.1238i	−0.848465	−	1.08955i
$220$		0			0
$221$	−19.0304	−	32.9617i	−1.28012	−	2.21724i
$222$	2.61917	+	18.8536i	0.175787	+	1.26537i
$223$	3.37231	+	1.94701i	0.225827	+	0.130381i	0.608645	−	0.793442i	$-0.291713\pi$
$223$	3.37231	+	1.94701i	0.225827	+	0.130381i	−0.382819	+	0.923824i	$0.625047\pi$
$224$	1.83991			0.122934
$225$		0			0
$226$	−19.5952			−1.30346
$227$	11.0922	+	6.40406i	0.736213	+	0.425053i	0.820691	−	0.571373i	$-0.193589\pi$
$227$	11.0922	+	6.40406i	0.736213	+	0.425053i	−0.0844781	+	0.996425i	$0.526922\pi$
$228$	−5.98108	−	2.42757i	−0.396107	−	0.160770i
$229$	3.32647	+	5.76162i	0.219820	+	0.380739i	0.954753	−	0.297401i	$-0.0961198\pi$
$229$	3.32647	+	5.76162i	0.219820	+	0.380739i	−0.734933	+	0.678140i	$0.762786\pi$
$230$		0			0
$231$	−1.02052	+	2.51436i	−0.0671451	+	0.165433i
$232$	4.63112	+	2.67378i	0.304048	+	0.175542i
$233$		−	3.65836i		−	0.239667i	−0.992794	−	0.119833i	$-0.961764\pi$
$233$		−	3.65836i		−	0.239667i	0.992794	−	0.119833i	$-0.0382360\pi$
$234$	−7.49214	+	29.6477i	−0.489776	+	1.93813i
$235$		0			0
$236$	−0.964212	+	1.67006i	−0.0627648	+	0.108712i
$237$	0.811032	+	5.83807i	0.0526822	+	0.379223i
$238$	4.36158	−	2.51816i	0.282720	−	0.163228i
$239$	−7.84576	−	13.5893i	−0.507500	−	0.879016i	−0.999962	−	0.00868195i	$-0.997236\pi$
$239$	−7.84576	−	13.5893i	−0.507500	−	0.879016i	0.492462	−	0.870334i	$-0.336097\pi$
$240$		0			0
$241$	−5.61248	+	9.72110i	−0.361532	+	0.626191i	−0.988213	−	0.153084i	$-0.951079\pi$
$241$	−5.61248	+	9.72110i	−0.361532	+	0.626191i	0.626681	+	0.779276i	$0.284413\pi$
$242$		−	2.26882i		−	0.145845i
$243$	15.3726	−	2.58489i	0.986156	−	0.165821i
$244$	1.90242			0.121790
$245$		0			0
$246$	9.46113	+	12.1494i	0.603220	+	0.774619i
$247$	30.0980	−	17.3771i	1.91509	−	1.10568i
$248$	7.96278	−	4.59731i	0.505637	−	0.291930i
$249$	23.8485	−	3.31307i	1.51134	−	0.209957i
$250$		0			0
$251$	6.94042			0.438075			0.219038	−	0.975716i	$-0.429708\pi$
$251$	6.94042			0.438075			0.219038	+	0.975716i	$0.429708\pi$
$252$	−0.983399	−	0.248510i	−0.0619483	−	0.0156547i
$253$			11.8601i			0.745640i
$254$	2.63730	−	4.56794i	0.165479	−	0.286618i
$255$		0			0
$256$	−7.23035	−	12.5233i	−0.451897	−	0.782708i
$257$	−15.8766	+	9.16635i	−0.990354	+	0.571781i	−0.905380	−	0.424602i	$-0.860414\pi$
$257$	−15.8766	+	9.16635i	−0.990354	+	0.571781i	−0.0849739	+	0.996383i	$0.527081\pi$
$258$	3.48041	+	1.41261i	0.216681	+	0.0879453i
$259$	1.69968	−	2.94393i	0.105613	−	0.182927i
$260$		0			0
$261$	−5.29096	−	5.14200i	−0.327502	−	0.318282i
$262$		−	15.3327i		−	0.947257i
$263$	−13.9228	−	8.03832i	−0.858515	−	0.495664i	0.00499942	−	0.999988i	$-0.498409\pi$
$263$	−13.9228	−	8.03832i	−0.858515	−	0.495664i	−0.863515	+	0.504323i	$0.831742\pi$
$264$	11.5648	−	1.60660i	0.711766	−	0.0988795i
$265$		0			0
$266$	2.29939	+	3.98265i	0.140984	+	0.244192i
$267$	4.62600	−	3.60241i	0.283107	−	0.220464i
$268$	1.39438	+	0.805043i	0.0851751	+	0.0491758i
$269$	18.2004			1.10970			0.554849	−	0.831951i	$-0.312776\pi$
$269$	18.2004			1.10970			0.554849	+	0.831951i	$0.312776\pi$
$270$		0			0
$271$	−2.48571			−0.150996			−0.0754979	−	0.997146i	$-0.524055\pi$
$271$	−2.48571			−0.150996			−0.0754979	+	0.997146i	$0.524055\pi$
$272$	−25.8360	−	14.9164i	−1.56654	−	0.904442i
$273$	4.30879	−	3.35539i	0.260780	−	0.203077i
$274$	−1.88659	−	3.26766i	−0.113973	−	0.197407i
$275$		0			0
$276$	−4.39106	+	0.610012i	−0.264311	+	0.0367184i
$277$	6.64004	+	3.83363i	0.398962	+	0.230341i	0.686036	−	0.727568i	$-0.259349\pi$
$277$	6.64004	+	3.83363i	0.398962	+	0.230341i	−0.287074	+	0.957908i	$0.592683\pi$
$278$		−	17.7978i		−	1.06744i
$279$	−12.2054	+	3.45790i	−0.730716	+	0.207019i
$280$		0			0
$281$	−0.136615	+	0.236624i	−0.00814978	+	0.0141158i	−0.870072	−	0.492925i	$-0.835928\pi$
$281$	−0.136615	+	0.236624i	−0.00814978	+	0.0141158i	0.861922	+	0.507041i	$0.169261\pi$
$282$	9.72201	+	3.94592i	0.578937	+	0.234976i
$283$	2.91928	−	1.68544i	0.173533	−	0.100189i	−0.410718	−	0.911763i	$-0.634722\pi$
$283$	2.91928	−	1.68544i	0.173533	−	0.100189i	0.584251	+	0.811573i	$0.301389\pi$
$284$	1.85396	+	3.21115i	0.110012	+	0.190547i
$285$		0			0
$286$	15.8006	−	27.3674i	0.934307	−	1.61827i
$287$		−	2.75003i		−	0.162329i
$288$	2.97732	+	10.5090i	0.175440	+	0.619250i
$289$	−20.2125			−1.18897
$290$		0			0
$291$	19.0010	−	2.63964i	1.11386	−	0.154739i
$292$	−6.83642	+	3.94701i	−0.400071	+	0.230981i
$293$	−4.88788	+	2.82202i	−0.285553	+	0.164864i	−0.635935	−	0.771743i	$-0.719385\pi$
$293$	−4.88788	+	2.82202i	−0.285553	+	0.164864i	0.350382	+	0.936607i	$0.386052\pi$
$294$	−11.7261	−	15.0580i	−0.683881	−	0.878200i
$295$		0			0
$296$	−14.6267			−0.850159
$297$	−16.0127	−	1.76019i	−0.929150	−	0.102137i
$298$			26.7000i			1.54669i
$299$	11.9345	−	20.6711i	0.690189	−	1.19544i
$300$		0			0
$301$	−0.335402	−	0.580933i	−0.0193322	−	0.0334844i
$302$	32.2340	−	18.6103i	1.85486	−	1.07090i
$303$	4.13956	+	29.7979i	0.237811	+	1.71184i
$304$	13.6205	−	23.5914i	0.781190	−	1.35306i
$305$		0			0
$306$	21.4408	+	20.8372i	1.22569	+	1.19118i
$307$		−	5.44105i		−	0.310537i	−0.987872	−	0.155269i	$-0.950376\pi$
$307$		−	5.44105i		−	0.310537i	0.987872	−	0.155269i	$-0.0496243\pi$
$308$	0.907761	+	0.524096i	0.0517245	+	0.0298632i
$309$	0.542447	−	1.33649i	0.0308587	−	0.0760301i
$310$		0			0
$311$	9.53985	+	16.5235i	0.540955	+	0.936962i	0.998849	+	0.0479550i	$0.0152704\pi$
$311$	9.53985	+	16.5235i	0.540955	+	0.936962i	−0.457895	+	0.889007i	$0.651396\pi$
$312$	−21.7731	−	8.83717i	−1.23266	−	0.500306i
$313$	7.91747	+	4.57116i	0.447522	+	0.258377i	0.706783	−	0.707430i	$-0.250146\pi$
$313$	7.91747	+	4.57116i	0.447522	+	0.258377i	−0.259261	+	0.965807i	$0.583479\pi$
$314$	20.3573			1.14883
$315$		0			0
$316$	2.27677			0.128078
$317$	12.3294	+	7.11836i	0.692486	+	0.399807i	0.804543	−	0.593895i	$-0.202410\pi$
$317$	12.3294	+	7.11836i	0.692486	+	0.399807i	−0.112056	+	0.993702i	$0.535744\pi$
$318$	−0.989786	−	7.12480i	−0.0555045	−	0.399539i
$319$	3.81220	+	6.60292i	0.213442	+	0.369693i
$320$		0			0
$321$	11.7789	+	15.1257i	0.657432	+	0.844236i
$322$	2.73527	+	1.57921i	0.152430	+	0.0880057i
$323$		−	33.9795i		−	1.89067i
$324$	−0.171906	−	6.01902i	−0.00955032	−	0.334390i
$325$		0			0
$326$	−6.18678	+	10.7158i	−0.342654	+	0.593494i
$327$	−6.36595	+	4.95736i	−0.352038	+	0.274143i
$328$	−10.2475	+	5.91638i	−0.565822	+	0.326677i
$329$	−0.936896	−	1.62275i	−0.0516527	−	0.0894652i
$330$		0			0
$331$	6.10001	−	10.5655i	0.335287	−	0.580734i	−0.648253	−	0.761425i	$-0.724500\pi$
$331$	6.10001	−	10.5655i	0.335287	−	0.580734i	0.983540	+	0.180691i	$0.0578334\pi$
$332$		−	9.30061i		−	0.510437i
$333$	19.5653	+	4.94424i	1.07217	+	0.270943i
$334$	−4.86317			−0.266101
$335$		0			0
$336$	1.60984	−	3.96633i	0.0878237	−	0.216381i
$337$	−3.97494	+	2.29493i	−0.216529	+	0.125013i	−0.604342	−	0.796725i	$-0.706564\pi$
$337$	−3.97494	+	2.29493i	−0.216529	+	0.125013i	0.387813	+	0.921738i	$0.373231\pi$
$338$	−36.6849	+	21.1800i	−1.99540	+	1.15204i
$339$	−7.81289	+	19.2495i	−0.424338	+	1.04549i
$340$		0			0
$341$	13.1094			0.709917
$342$	−19.0269	+	19.5781i	−1.02886	+	1.05866i
$343$			6.94582i			0.375039i
$344$	−1.44316	+	2.49962i	−0.0778099	+	0.134771i
$345$		0			0
$346$	−12.9497	−	22.4295i	−0.696180	−	1.20582i
$347$	−28.9775	+	16.7301i	−1.55559	+	0.898121i	−0.557921	+	0.829894i	$0.688401\pi$
$347$	−28.9775	+	16.7301i	−1.55559	+	0.898121i	−0.997670	+	0.0682272i	$0.978266\pi$
$348$	−2.24857	+	1.75103i	−0.120536	+	0.0938651i
$349$	−14.0408	+	24.3193i	−0.751586	+	1.30178i	0.195468	+	0.980710i	$0.437377\pi$
$349$	−14.0408	+	24.3193i	−0.751586	+	1.30178i	−0.947054	+	0.321074i	$0.895956\pi$
$350$		0			0
$351$	26.1374	+	19.1809i	1.39511	+	1.02380i
$352$		−	11.2875i		−	0.601624i
$353$	1.59496	+	0.920851i	0.0848912	+	0.0490119i	0.541845	−	0.840479i	$-0.317726\pi$
$353$	1.59496	+	0.920851i	0.0848912	+	0.0490119i	−0.456954	+	0.889491i	$0.651059\pi$
$354$	5.01117	+	6.43505i	0.266341	+	0.342019i
$355$		0			0
$356$	−1.13241	−	1.96140i	−0.0600178	−	0.103954i
$357$	−0.734707	−	5.28865i	−0.0388848	−	0.279905i
$358$	24.1714	+	13.9553i	1.27750	+	0.737563i
$359$	12.1119			0.639241			0.319621	−	0.947546i	$-0.396445\pi$
$359$	12.1119			0.639241			0.319621	+	0.947546i	$0.396445\pi$
$360$		0			0
$361$	12.0274			0.633020
$362$	−18.9151	−	10.9206i	−0.994156	−	0.573976i
$363$	−2.22879	−	0.904610i	−0.116981	−	0.0474797i
$364$	−1.05476	−	1.82690i	−0.0552846	−	0.0957558i
$365$		0			0
$366$	3.02597	−	7.45541i	0.158170	−	0.389701i
$367$	−12.6212	−	7.28688i	−0.658824	−	0.380372i	0.133005	−	0.991115i	$-0.457537\pi$
$367$	−12.6212	−	7.28688i	−0.658824	−	0.380372i	−0.791829	+	0.610743i	$0.790871\pi$
$368$		−	18.7090i		−	0.975274i
$369$	15.7073	−	4.45005i	0.817691	−	0.231660i
$370$		0			0
$371$	−0.642310	+	1.11251i	−0.0333471	+	0.0577589i
$372$	0.674269	+	4.85360i	0.0349592	+	0.251648i
$373$	−8.18087	+	4.72323i	−0.423590	+	0.244560i	−0.696612	−	0.717448i	$-0.745310\pi$
$373$	−8.18087	+	4.72323i	−0.423590	+	0.244560i	0.273022	+	0.962008i	$0.411977\pi$
$374$	−15.4484	−	26.7574i	−0.798817	−	1.38359i
$375$		0			0
$376$	−4.03125	+	6.98233i	−0.207896	+	0.360086i
$377$		−	15.3444i		−	0.790276i
$378$	−2.53807	+	3.45858i	−0.130544	+	0.177890i
$379$	28.5541			1.46673			0.733363	−	0.679837i	$-0.237949\pi$
$379$	28.5541			1.46673			0.733363	+	0.679837i	$0.237949\pi$
$380$		0			0
$381$	−3.43581	−	4.41207i	−0.176022	−	0.226037i
$382$	35.8483	−	20.6970i	1.83416	−	1.05895i
$383$	1.26908	−	0.732704i	0.0648470	−	0.0374394i	−0.467226	−	0.884138i	$-0.654747\pi$
$383$	1.26908	−	0.732704i	0.0648470	−	0.0374394i	0.532073	+	0.846699i	$0.321413\pi$
$384$	−23.2348	+	3.22780i	−1.18569	+	0.164718i
$385$		0			0
$386$	15.6176			0.794916
$387$	2.77537	−	2.85577i	0.141080	−	0.145167i
$388$		−	7.41014i		−	0.376193i
$389$	−6.45506	+	11.1805i	−0.327284	+	0.566873i	−0.981972	−	0.189026i	$-0.939467\pi$
$389$	−6.45506	+	11.1805i	−0.327284	+	0.566873i	0.654688	+	0.755900i	$0.272800\pi$
$390$		0			0
$391$	−11.6685	−	20.2104i	−0.590100	−	1.02208i
$392$	12.7007	−	7.33276i	0.641483	−	0.370360i
$393$	−15.0622	−	6.11336i	−0.759785	−	0.308378i
$394$	1.68961	−	2.92649i	0.0851212	−	0.147434i
$395$		0			0
$396$	−1.52456	+	6.03294i	−0.0766118	+	0.303167i
$397$			0.868386i			0.0435831i	0.999763	+	0.0217915i	$0.00693701\pi$
$397$			0.868386i			0.0435831i	−0.999763	+	0.0217915i	$0.993063\pi$
$398$	18.5302	+	10.6984i	0.928834	+	0.536263i
$399$	4.82918	−	0.670876i	0.241761	−	0.0335858i
$400$		0			0
$401$	−16.7063	−	28.9361i	−0.834270	−	1.44500i	−0.894623	−	0.446822i	$-0.852556\pi$
$401$	−16.7063	−	28.9361i	−0.834270	−	1.44500i	0.0603527	−	0.998177i	$-0.480777\pi$
$402$	5.37277	−	4.18394i	0.267970	−	0.208676i
$403$	−22.8486	−	13.1916i	−1.13817	−	0.657122i
$404$	11.6208			0.578156
$405$		0			0
$406$	2.03042			0.100768
$407$	−18.0604	−	10.4272i	−0.895221	−	0.516856i
$408$	−18.1265	+	14.1157i	−0.897397	+	0.698831i
$409$	2.52767	+	4.37806i	0.124985	+	0.216481i	0.921727	−	0.387839i	$-0.126778\pi$
$409$	2.52767	+	4.37806i	0.124985	+	0.216481i	−0.796742	+	0.604320i	$0.793445\pi$
$410$		0			0
$411$	−3.96221	+	0.550436i	−0.195442	+	0.0271510i
$412$	−0.482512	−	0.278579i	−0.0237717	−	0.0137246i
$413$		−	1.45658i		−	0.0716734i
$414$	−4.59379	+	18.1785i	−0.225772	+	0.893423i
$415$		0			0
$416$	−11.3582	+	19.6730i	−0.556883	+	0.964549i
$417$	−17.4838	−	7.09623i	−0.856184	−	0.347504i
$418$	24.4327	−	14.1062i	1.19504	−	0.689959i
$419$	5.47880	+	9.48955i	0.267657	+	0.463595i	0.968256	−	0.249960i	$-0.0804174\pi$
$419$	5.47880	+	9.48955i	0.267657	+	0.463595i	−0.700600	+	0.713555i	$0.747084\pi$
$420$		0			0
$421$	5.31932	−	9.21333i	0.259248	−	0.449030i	−0.706793	−	0.707421i	$-0.749859\pi$
$421$	5.31932	−	9.21333i	0.259248	−	0.449030i	0.966041	+	0.258390i	$0.0831921\pi$
$422$			18.1538i			0.883711i
$423$	7.75260	−	7.97718i	0.376944	−	0.387864i
$424$	5.52744			0.268436
$425$		0			0
$426$	15.5331	−	2.15788i	0.752582	−	0.104550i
$427$	−1.24442	+	0.718467i	−0.0602218	+	0.0347691i
$428$	6.41322	−	3.70267i	0.309995	−	0.178975i
$429$	−20.5846	−	26.4335i	−0.993834	−	1.27622i
$430$		0			0
$431$	−37.3529			−1.79923			−0.899613	−	0.436687i	$-0.856152\pi$
$431$	−37.3529			−1.79923			−0.899613	+	0.436687i	$0.856152\pi$
$432$	25.2595	+	2.77664i	1.21530	+	0.133591i
$433$		−	17.2125i		−	0.827179i	−0.910464	−	0.413589i	$-0.864275\pi$
$433$		−	17.2125i		−	0.827179i	0.910464	−	0.413589i	$-0.135725\pi$
$434$	1.74556	−	3.02339i	0.0837894	−	0.145127i
$435$		0			0
$436$	1.55834	+	2.69913i	0.0746310	+	0.129265i
$437$	18.4545	−	10.6547i	0.882799	−	0.509684i
$438$	4.59404	+	33.0694i	0.219512	+	1.58012i
$439$	−15.8744	+	27.4952i	−0.757642	+	1.31228i	0.186408	+	0.982473i	$0.440316\pi$
$439$	−15.8744	+	27.4952i	−0.757642	+	1.31228i	−0.944050	+	0.329803i	$0.893018\pi$
$440$		0			0
$441$	−19.4677	+	5.51539i	−0.927032	+	0.262638i
$442$			62.1809i			2.95764i
$443$	0.308268	+	0.177979i	0.0146463	+	0.00845603i	0.507305	−	0.861766i	$-0.330642\pi$
$443$	0.308268	+	0.177979i	0.0146463	+	0.00845603i	−0.492659	+	0.870222i	$0.663975\pi$
$444$	2.93161	−	7.22293i	0.139128	−	0.342785i
$445$		0			0
$446$	−3.18087	−	5.50943i	−0.150619	−	0.260879i
$447$	26.2289	+	10.6456i	1.24058	+	0.503522i
$448$	1.67738	+	0.968438i	0.0792490	+	0.0457544i
$449$	7.85632			0.370762			0.185381	−	0.982667i	$-0.440648\pi$
$449$	7.85632			0.370762			0.185381	+	0.982667i	$0.440648\pi$
$450$		0			0
$451$	−16.8708			−0.794416
$452$	6.94964	+	4.01238i	0.326884	+	0.188726i
$453$	−5.42980	−	39.0854i	−0.255114	−	1.83639i
$454$	−10.4625	−	18.1215i	−0.491028	−	0.850485i
$455$		0			0
$456$	−12.8893	−	16.5517i	−0.603598	−	0.775105i
$457$	18.6118	+	10.7455i	0.870622	+	0.502654i	0.867555	−	0.497341i	$-0.165690\pi$
$457$	18.6118	+	10.7455i	0.870622	+	0.502654i	0.00306742	+	0.999995i	$0.499024\pi$
$458$		−	10.8691i		−	0.507879i
$459$	29.0183	−	12.7544i	1.35446	−	0.595326i
$460$		0			0
$461$	−20.4964	+	35.5007i	−0.954611	+	1.65343i	−0.219355	+	0.975645i	$0.570395\pi$
$461$	−20.4964	+	35.5007i	−0.954611	+	1.65343i	−0.735256	+	0.677789i	$0.762938\pi$
$462$	3.49776	−	2.72382i	0.162731	−	0.126723i
$463$	36.4890	−	21.0669i	1.69579	−	0.979063i	0.746116	−	0.665816i	$-0.231916\pi$
$463$	36.4890	−	21.0669i	1.69579	−	0.979063i	0.949671	−	0.313248i	$-0.101417\pi$
$464$	−6.01363	−	10.4159i	−0.279176	−	0.483546i
$465$		0			0
$466$	−2.98837	+	5.17601i	−0.138434	+	0.239774i
$467$			22.5376i			1.04292i	0.853276	+	0.521459i	$0.174612\pi$
$467$			22.5376i			1.04292i	−0.853276	+	0.521459i	$0.825388\pi$
$468$	8.72792	−	8.98075i	0.403448	−	0.415136i
$469$	−1.21613			−0.0561557
$470$		0			0
$471$	8.11675	−	19.9981i	0.374000	−	0.921465i
$472$	−5.42766	+	3.13366i	−0.249828	+	0.144238i
$473$	−3.56390	+	2.05762i	−0.163868	+	0.0946093i
$474$	3.62141	−	8.92247i	0.166337	−	0.409822i
$475$		0			0
$476$	−2.06251			−0.0945348
$477$	−7.39372	−	1.86843i	−0.338535	−	0.0855496i
$478$			25.6356i			1.17255i
$479$	−16.6440	+	28.8282i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$479$	−16.6440	+	28.8282i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$480$		0			0
$481$	20.9851	+	36.3472i	0.956837	+	1.65729i
$482$	15.8816	−	9.16924i	0.723387	−	0.417647i
$483$	2.64193	−	2.05735i	0.120212	−	0.0936127i
$484$	−0.464570	+	0.804660i	−0.0211168	+	0.0365754i
$485$		0			0
$486$	−23.8614	−	8.90010i	−1.08238	−	0.403717i
$487$		−	23.7703i		−	1.07713i	−0.842583	−	0.538566i	$-0.818966\pi$
$487$		−	23.7703i		−	1.07713i	0.842583	−	0.538566i	$-0.181034\pi$
$488$	5.35447	+	3.09140i	0.242385	+	0.139941i
$489$	8.05999	+	10.3502i	0.364485	+	0.468050i
$490$		0			0
$491$	2.30281	+	3.98859i	0.103925	+	0.180003i	0.913298	−	0.407291i	$-0.133527\pi$
$491$	2.30281	+	3.98859i	0.103925	+	0.180003i	−0.809374	+	0.587294i	$0.800193\pi$
$492$	−0.867731	−	6.24620i	−0.0391203	−	0.281601i
$493$	−12.9924	−	7.50118i	−0.585150	−	0.337836i
$494$	−56.7787			−2.55459
$495$		0			0
$496$	−20.6797			−0.928548
$497$	−2.42545	−	1.40033i	−0.108796	−	0.0628135i
$498$	−36.4483	−	14.7935i	−1.63329	−	0.662910i
$499$	−9.44878	−	16.3658i	−0.422985	−	0.732632i	0.573245	−	0.819384i	$-0.305684\pi$
$499$	−9.44878	−	16.3658i	−0.422985	−	0.732632i	−0.996230	+	0.0867522i	$0.972351\pi$
$500$		0			0
$501$	−1.93901	+	4.77736i	−0.0866287	+	0.213437i
$502$	−9.81962	−	5.66936i	−0.438271	−	0.253036i
$503$			35.7581i			1.59438i	0.603731	+	0.797188i	$0.293680\pi$
$503$			35.7581i			1.59438i	−0.603731	+	0.797188i	$0.706320\pi$
$504$	−2.36401	−	2.29746i	−0.105301	−	0.102337i
$505$		0			0
$506$	9.68809	−	16.7803i	0.430688	−	0.745974i
$507$	6.17955	+	44.4824i	0.274444	+	1.97553i
$508$	−1.87069	+	1.08004i	−0.0829985	+	0.0479192i
$509$	12.2034	+	21.1368i	0.540904	+	0.936874i	0.998852	+	0.0478949i	$0.0152513\pi$
$509$	12.2034	+	21.1368i	0.540904	+	0.936874i	−0.457948	+	0.888979i	$0.651415\pi$
$510$		0			0
$511$	2.98125	−	5.16368i	0.131883	−	0.228428i
$512$		−	3.46207i		−	0.153003i
$513$	11.6463	+	26.4972i	0.514198	+	1.16988i
$514$	29.9506			1.32106
$515$		0			0
$516$	−0.945110	−	1.21365i	−0.0416062	−	0.0534282i
$517$	−9.95523	+	5.74765i	−0.437830	+	0.252782i
$518$	−4.80957	+	2.77681i	−0.211321	+	0.122006i
$519$	−27.1970	+	3.77824i	−1.19381	+	0.165846i
$520$		0			0
$521$	33.3968			1.46314			0.731571	−	0.681766i	$-0.238788\pi$
$521$	33.3968			1.46314			0.731571	+	0.681766i	$0.238788\pi$
$522$	3.28558	+	11.5971i	0.143806	+	0.507592i
$523$		−	37.3654i		−	1.63388i	−0.576726	−	0.816938i	$-0.695670\pi$
$523$		−	37.3654i		−	1.63388i	0.576726	−	0.816938i	$-0.304330\pi$
$524$	−3.13957	+	5.43789i	−0.137153	+	0.237555i
$525$		0			0
$526$	13.1324	+	22.7460i	0.572600	+	0.991772i
$527$	−22.3393	+	12.8976i	−0.973115	+	0.561828i
$528$	−24.3326	−	9.87599i	−1.05894	−	0.429797i
$529$	−4.18239	+	7.24412i	−0.181843	+	0.314962i
$530$		0			0
$531$	8.31953	−	2.35701i	0.361037	−	0.102285i
$532$		−	1.88332i		−	0.0816521i
$533$	29.4043	+	16.9766i	1.27364	+	0.735338i
$534$	−9.48775	+	1.31805i	−0.410575	+	0.0570376i
$535$		0			0
$536$	2.61637	+	4.53168i	0.113010	+	0.195739i
$537$	23.3466	−	18.1807i	1.00748	−	0.784555i
$538$	−25.7508	−	14.8672i	−1.11019	−	0.640971i
$539$	20.9097			0.900645
$540$		0			0
$541$	28.2560			1.21482			0.607409	−	0.794389i	$-0.292209\pi$
$541$	28.2560			1.21482			0.607409	+	0.794389i	$0.292209\pi$
$542$	3.51689	+	2.03048i	0.151063	+	0.0872165i
$543$	−18.2697	+	14.2271i	−0.784026	+	0.610545i
$544$	11.1051	+	19.2345i	0.476125	+	0.824673i
$545$		0			0
$546$	−8.83717	+	1.22767i	−0.378196	+	0.0525395i
$547$	−33.3811	−	19.2726i	−1.42727	−	0.824036i	−0.430368	−	0.902654i	$-0.641616\pi$
$547$	−33.3811	−	19.2726i	−1.42727	−	0.824036i	−0.996905	+	0.0786172i	$0.974950\pi$
$548$			1.54521i			0.0660082i
$549$	−6.11737	−	5.94515i	−0.261083	−	0.253733i
$550$		0			0
$551$	6.84949	−	11.8637i	0.291798	−	0.505409i
$552$	−13.3502	−	5.41850i	−0.568220	−	0.230626i
$553$	−1.48929	+	0.859845i	−0.0633313	+	0.0365643i
$554$	−6.26309	−	10.8480i	−0.266093	−	0.460887i
$555$		0			0
$556$	−3.64433	+	6.31217i	−0.154554	+	0.267696i
$557$			27.4125i			1.16151i	0.814080	+	0.580753i	$0.197242\pi$
$557$			27.4125i			1.16151i	−0.814080	+	0.580753i	$0.802758\pi$
$558$	20.0933	+	5.07769i	0.850618	+	0.214956i
$559$	8.28206			0.350294
$560$		0			0
$561$	−32.4447	+	4.50727i	−1.36982	+	0.190297i
$562$	0.386579	−	0.223191i	0.0163068	−	0.00941476i
$563$	−23.9363	+	13.8196i	−1.00879	+	0.582427i	−0.910838	−	0.412764i	$-0.864563\pi$
$563$	−23.9363	+	13.8196i	−1.00879	+	0.582427i	−0.0979551	+	0.995191i	$0.531230\pi$
$564$	−2.64003	−	3.39017i	−0.111165	−	0.142752i
$565$		0			0
$566$	−5.50710			−0.231481
$567$	2.38559	+	3.87227i	0.100185	+	0.162620i
$568$			12.0506i			0.505634i
$569$	−7.35807	+	12.7446i	−0.308467	+	0.534280i	−0.978027	−	0.208478i	$-0.933149\pi$
$569$	−7.35807	+	12.7446i	−0.308467	+	0.534280i	0.669561	+	0.742757i	$0.266482\pi$
$570$		0			0
$571$	14.1503	+	24.5090i	0.592172	+	1.02567i	0.993939	+	0.109930i	$0.0350627\pi$
$571$	14.1503	+	24.5090i	0.592172	+	1.02567i	−0.401768	+	0.915742i	$0.631604\pi$
$572$	−11.2077	+	6.47074i	−0.468616	+	0.270555i
$573$	−6.03862	−	43.4679i	−0.252267	−	1.81590i
$574$	−2.24639	+	3.89087i	−0.0937626	+	0.162402i
$575$		0			0
$576$	−2.81711	+	11.1478i	−0.117380	+	0.464493i
$577$			40.7976i			1.69843i	0.528049	+	0.849214i	$0.322924\pi$
$577$			40.7976i			1.69843i	−0.528049	+	0.849214i	$0.677076\pi$
$578$	28.5975	+	16.5108i	1.18950	+	0.686759i
$579$	6.22696	−	15.3421i	0.258784	−	0.637594i
$580$		0			0
$581$	3.51247	+	6.08377i	0.145722	+	0.252397i
$582$	−29.0397	−	11.7865i	−1.20373	−	0.488565i
$583$	6.82504	+	3.94044i	0.282664	+	0.163196i
$584$	−25.6553			−1.06162
$585$		0			0
$586$	9.22080			0.380908
$587$	2.40784	+	1.39016i	0.0993820	+	0.0573782i	0.548867	−	0.835910i	$-0.315059\pi$
$587$	2.40784	+	1.39016i	0.0993820	+	0.0573782i	−0.449485	+	0.893288i	$0.648393\pi$
$588$	1.07547	+	7.74154i	0.0443514	+	0.319256i
$589$	−11.7771	−	20.3985i	−0.485265	−	0.840504i
$590$		0			0
$591$	−2.20118	−	2.82663i	−0.0905445	−	0.116272i
$592$	28.4897	+	16.4485i	1.17092	+	0.676031i
$593$		−	14.8084i		−	0.608109i	−0.952655	−	0.304055i	$-0.901659\pi$
$593$		−	14.8084i		−	0.608109i	0.952655	−	0.304055i	$-0.0983405\pi$
$594$	21.2176	+	15.5705i	0.870570	+	0.638867i
$595$		0			0
$596$	5.46717	−	9.46941i	0.223944	−	0.387882i
$597$	17.8979	−	13.9376i	0.732511	−	0.570429i
$598$	−33.7709	+	19.4976i	−1.38100	+	0.797318i
$599$	−8.17151	−	14.1535i	−0.333879	−	0.578295i	0.649390	−	0.760456i	$-0.275024\pi$
$599$	−8.17151	−	14.1535i	−0.333879	−	0.578295i	−0.983269	+	0.182160i	$0.941691\pi$
$600$		0			0
$601$	3.31185	−	5.73630i	0.135093	−	0.233988i	−0.790540	−	0.612411i	$-0.790200\pi$
$601$	3.31185	−	5.73630i	0.135093	−	0.233988i	0.925633	+	0.378422i	$0.123533\pi$
$602$			1.09591i			0.0446658i
$603$	−1.96792	−	6.94617i	−0.0801400	−	0.282870i
$604$	−15.2428			−0.620221
$605$		0			0
$606$	18.4839	−	45.5408i	0.750857	−	1.84997i
$607$	−26.2487	+	15.1547i	−1.06540	+	0.615110i	−0.926921	−	0.375256i	$-0.877555\pi$
$607$	−26.2487	+	15.1547i	−1.06540	+	0.615110i	−0.138480	+	0.990365i	$0.544222\pi$
$608$	−17.5634	+	10.1403i	−0.712291	+	0.411242i
$609$	0.809554	−	1.99459i	0.0328048	−	0.0808248i
$610$		0			0
$611$	23.1347			0.935931
$612$	−3.33751	−	11.7804i	−0.134911	−	0.476195i
$613$			14.7803i			0.596969i	0.954415	+	0.298484i	$0.0964811\pi$
$613$			14.7803i			0.596969i	−0.954415	+	0.298484i	$0.903519\pi$
$614$	−4.44459	+	7.69825i	−0.179369	+	0.310676i
$615$		0			0
$616$	1.70330	+	2.95020i	0.0686278	+	0.118867i
$617$	29.3160	−	16.9256i	1.18022	−	0.681399i	0.224152	−	0.974554i	$-0.428039\pi$
$617$	29.3160	−	16.9256i	1.18022	−	0.681399i	0.956065	+	0.293155i	$0.0947053\pi$
$618$	−1.85920	+	1.44782i	−0.0747882	+	0.0582399i
$619$	5.84433	−	10.1227i	0.234903	−	0.406865i	−0.724341	−	0.689442i	$-0.757856\pi$
$619$	5.84433	−	10.1227i	0.234903	−	0.406865i	0.959245	+	0.282577i	$0.0911893\pi$
$620$		0			0
$621$	16.0261	+	11.7607i	0.643105	+	0.471942i
$622$		−	31.1709i		−	1.24984i
$623$	1.48148	+	0.855334i	0.0593543	+	0.0342682i
$624$	32.4716	+	41.6981i	1.29990	+	1.66926i
$625$		0			0
$626$	−7.46800	−	12.9350i	−0.298481	−	0.516985i
$627$	−4.11568	−	29.6260i	−0.164364	−	1.18315i
$628$	−7.21993	−	4.16843i	−0.288107	−	0.166338i
$629$	41.0347			1.63616
$630$		0			0
$631$	−38.1357			−1.51816			−0.759078	−	0.650999i	$-0.774350\pi$
$631$	−38.1357			−1.51816			−0.759078	+	0.650999i	$0.774350\pi$
$632$	6.40810	+	3.69972i	0.254901	+	0.147167i
$633$	17.8334	+	7.23815i	0.708816	+	0.287691i
$634$	−11.6294	−	20.1428i	−0.461864	−	0.799972i
$635$		0			0
$636$	−1.10786	+	2.72955i	−0.0439294	+	0.108234i
$637$	−36.4437	−	21.0408i	−1.44395	−	0.833666i
$638$		−	12.4562i		−	0.493144i
$639$	4.07346	−	16.1194i	0.161144	−	0.637675i
$640$		0			0
$641$	17.3827	−	30.1077i	0.686576	−	1.18918i	−0.286363	−	0.958121i	$-0.592446\pi$
$641$	17.3827	−	30.1077i	0.686576	−	1.18918i	0.972939	−	0.231063i	$-0.0742204\pi$
$642$	−4.30966	−	31.0223i	−0.170089	−	1.22435i
$643$	2.32541	−	1.34258i	0.0917053	−	0.0529461i	−0.453446	−	0.891284i	$-0.649806\pi$
$643$	2.32541	−	1.34258i	0.0917053	−	0.0529461i	0.545151	+	0.838338i	$0.316472\pi$
$644$	−0.646726	−	1.12016i	−0.0254846	−	0.0441406i
$645$		0			0
$646$	−27.7565	+	48.0757i	−1.09207	+	1.89151i
$647$		−	40.5103i		−	1.59262i	−0.604887	−	0.796311i	$-0.706782\pi$
$647$		−	40.5103i		−	1.59262i	0.604887	−	0.796311i	$-0.293218\pi$
$648$	9.29698	−	17.2202i	0.365220	−	0.676474i
$649$	−8.93578			−0.350760
$650$		0			0
$651$	−2.27407	−	2.92022i	−0.0891277	−	0.114453i
$652$	4.38841	−	2.53365i	0.171863	−	0.0992253i
$653$	11.5488	−	6.66772i	0.451941	−	0.260928i	−0.256709	−	0.966489i	$-0.582638\pi$
$653$	11.5488	−	6.66772i	0.451941	−	0.260928i	0.708650	+	0.705561i	$0.249305\pi$
$654$	13.0563	−	1.81380i	0.510543	−	0.0709253i
$655$		0			0
$656$	26.6132			1.03907
$657$	34.3176	+	8.67223i	1.33886	+	0.338336i
$658$			3.06126i			0.119340i
$659$	15.5772	−	26.9804i	0.606800	−	1.05101i	−0.384965	−	0.922931i	$-0.625786\pi$
$659$	15.5772	−	26.9804i	0.606800	−	1.05101i	0.991764	−	0.128077i	$-0.0408803\pi$
$660$		0			0
$661$	−3.15894	−	5.47145i	−0.122869	−	0.212815i	0.798029	−	0.602619i	$-0.205876\pi$
$661$	−3.15894	−	5.47145i	−0.122869	−	0.212815i	−0.920898	+	0.389804i	$0.872543\pi$
$662$	−17.2612	+	9.96574i	−0.670874	+	0.387329i
$663$	61.0837	+	24.7924i	2.37230	+	0.962856i
$664$	15.1134	−	26.1771i	0.586512	−	1.01587i
$665$		0			0
$666$	−23.6431	−	22.9775i	−0.916150	−	0.890358i
$667$		−	9.40838i		−	0.364294i
$668$	1.72477	+	0.995798i	0.0667334	+	0.0385286i
$669$	−6.68047	+	0.928060i	−0.258282	+	0.0358809i
$670$		0			0
$671$	4.40764	+	7.63426i	0.170155	+	0.294717i
$672$	−2.51436	+	1.95801i	−0.0969937	+	0.0755320i
$673$	5.70901	+	3.29610i	0.220066	+	0.127055i	0.605981	−	0.795479i	$-0.292781\pi$
$673$	5.70901	+	3.29610i	0.220066	+	0.127055i	−0.385915	+	0.922534i	$0.626114\pi$
$674$	7.49857			0.288834
$675$		0			0
$676$	17.3476			0.667214
$677$	30.2197	+	17.4473i	1.16144	+	0.670556i	0.951648	−	0.307191i	$-0.0993891\pi$
$677$	30.2197	+	17.4473i	1.16144	+	0.670556i	0.209788	+	0.977747i	$0.432722\pi$
$678$	26.7782	−	20.8530i	1.02841	−	0.800855i
$679$	2.79851	+	4.84716i	0.107397	+	0.186017i
$680$		0			0
$681$	−21.9733	+	3.05256i	−0.842019	+	0.116974i
$682$	−18.5479	−	10.7086i	−0.710234	−	0.410054i
$683$			26.0958i			0.998528i	0.866450	+	0.499264i	$0.166396\pi$
$683$			26.0958i			0.998528i	−0.866450	+	0.499264i	$0.833604\pi$
$684$	10.7569	−	3.04755i	0.411302	−	0.116526i
$685$		0			0
$686$	5.67378	−	9.82727i	0.216626	−	0.375207i
$687$	−10.6773	−	4.33365i	−0.407364	−	0.165339i
$688$	5.62194	−	3.24583i	0.214334	−	0.123746i
$689$	−7.93028	−	13.7356i	−0.302119	−	0.523286i
$690$		0			0
$691$	14.6529	−	25.3796i	0.557423	−	0.965485i	−0.440288	−	0.897857i	$-0.645124\pi$
$691$	14.6529	−	25.3796i	0.557423	−	0.965485i	0.997711	−	0.0676282i	$-0.0215432\pi$
$692$			10.6065i			0.403197i
$693$	−1.28115	−	4.52207i	−0.0486668	−	0.171779i
$694$	54.6648			2.07505
$695$		0			0
$696$	−9.17413	+	1.27448i	−0.347745	+	0.0483091i
$697$	28.7489	−	16.5982i	1.08894	−	0.628701i
$698$	39.7311	−	22.9387i	1.50384	−	0.868244i
$699$	3.89318	+	4.99939i	0.147253	+	0.189094i
$700$		0			0
$701$	15.3891			0.581239			0.290620	−	0.956839i	$-0.406139\pi$
$701$	15.3891			0.581239			0.290620	+	0.956839i	$0.406139\pi$
$702$	−21.3123	−	48.4887i	−0.804379	−	1.83009i
$703$			37.4696i			1.41319i
$704$	5.94116	−	10.2904i	0.223916	−	0.387834i
$705$		0			0
$706$	−1.50442	−	2.60572i	−0.0566194	−	0.0980677i
$707$	−7.60146	+	4.38870i	−0.285882	+	0.165054i
$708$	−0.459601	−	3.30836i	−0.0172729	−	0.124336i
$709$	−3.86996	+	6.70296i	−0.145339	+	0.251735i	−0.929499	−	0.368823i	$-0.879761\pi$
$709$	−3.86996	+	6.70296i	−0.145339	+	0.251735i	0.784160	+	0.620558i	$0.213094\pi$
$710$		0			0
$711$	−7.32113	−	7.11502i	−0.274564	−	0.266834i
$712$		−	7.36062i		−	0.275851i
$713$	−14.0096	−	8.08842i	−0.524662	−	0.302914i
$714$	−3.28060	+	8.08278i	−0.122773	+	0.302490i
$715$		0			0
$716$	−5.71508	−	9.89880i	−0.213582	−	0.369936i
$717$	25.1833	+	10.2213i	0.940486	+	0.381720i
$718$	−17.1365	−	9.89374i	−0.639527	−	0.369231i
$719$	15.1316			0.564313			0.282156	−	0.959368i	$-0.408950\pi$
$719$	15.1316			0.564313			0.282156	+	0.959368i	$0.408950\pi$
$720$		0			0
$721$	0.420832			0.0156726
$722$	−17.0169	−	9.82470i	−0.633303	−	0.365638i
$723$	−2.67525	−	19.2573i	−0.0994934	−	0.716185i
$724$	4.47229	+	7.74623i	0.166211	+	0.287886i
$725$		0			0
$726$	2.41445	+	3.10049i	0.0896086	+	0.115070i
$727$	0.140189	+	0.0809381i	0.00519932	+	0.00300183i	0.502597	−	0.864521i	$-0.332378\pi$
$727$	0.140189	+	0.0809381i	0.00519932	+	0.00300183i	−0.497398	+	0.867522i	$0.665711\pi$
$728$		−	6.85590i		−	0.254097i
$729$	−18.2569	+	19.8918i	−0.676183	+	0.736734i
$730$		0			0
$731$	4.04873	−	7.01260i	0.149748	−	0.259370i
$732$	−2.59978	+	2.02453i	−0.0960907	+	0.0748288i
$733$	−43.3300	+	25.0166i	−1.60043	+	0.924009i	−0.609029	+	0.793148i	$0.708441\pi$
$733$	−43.3300	+	25.0166i	−1.60043	+	0.924009i	−0.991401	+	0.130861i	$0.958226\pi$
$734$	11.9047	+	20.6196i	0.439412	+	0.761084i
$735$		0			0
$736$	−6.96427	+	12.0625i	−0.256707	+	0.444629i
$737$			7.46070i			0.274818i
$738$	−25.8585	−	6.53458i	−0.951866	−	0.240541i
$739$	−30.5505			−1.12382			−0.561909	−	0.827199i	$-0.689933\pi$
$739$	−30.5505			−1.12382			−0.561909	+	0.827199i	$0.689933\pi$
$740$		0			0
$741$	−22.6384	+	55.7768i	−0.831643	+	2.04901i
$742$	1.81754	−	1.04936i	0.0667240	−	0.0385231i
$743$	5.16743	−	2.98342i	0.189575	−	0.109451i	−0.402209	−	0.915548i	$-0.631757\pi$
$743$	5.16743	−	2.98342i	0.189575	−	0.109451i	0.591783	+	0.806097i	$0.298424\pi$
$744$	−5.98927	+	14.7564i	−0.219577	+	0.540997i
$745$		0			0
$746$	15.4329			0.565039
$747$	−29.0649	+	29.9068i	−1.06343	+	1.09423i
$748$			12.6530i			0.462640i
$749$	−2.79670	+	4.84403i	−0.102189	+	0.176997i
$750$		0			0
$751$	−17.1988	−	29.7892i	−0.627593	−	1.08702i	−0.988033	−	0.154240i	$-0.950707\pi$
$751$	−17.1988	−	29.7892i	−0.627593	−	1.08702i	0.360441	−	0.932782i	$-0.382626\pi$
$752$	15.7041	−	9.06674i	0.572668	−	0.330630i
$753$	−9.48454	+	7.38591i	−0.345636	+	0.269157i
$754$	−12.5342	+	21.7099i	−0.456470	+	0.790630i
$755$		0			0
$756$	1.60834	−	0.706916i	0.0584948	−	0.0257103i
$757$		−	40.6873i		−	1.47881i	−0.673263	−	0.739403i	$-0.735108\pi$
$757$		−	40.6873i		−	1.47881i	0.673263	−	0.739403i	$-0.264892\pi$
$758$	−40.3997	−	23.3248i	−1.46738	−	0.847194i
$759$	−12.6214	−	16.2077i	−0.458128	−	0.588301i
$760$		0			0
$761$	−14.1298	−	24.4735i	−0.512204	−	0.887164i	−0.999900	−	0.0141502i	$-0.995496\pi$
$761$	−14.1298	−	24.4735i	−0.512204	−	0.887164i	0.487696	−	0.873014i	$-0.337838\pi$
$762$	1.25710	+	9.04898i	0.0455398	+	0.327810i
$763$	−2.03870	−	1.17705i	−0.0738060	−	0.0426119i
$764$	−16.9519			−0.613299
$765$		0			0
$766$	−2.39407			−0.0865013
$767$	15.5743	+	8.99180i	0.562354	+	0.324675i
$768$	23.2079	+	9.41952i	0.837444	+	0.339898i
$769$	−23.4518	−	40.6197i	−0.845694	−	1.46478i	−0.885017	−	0.465558i	$-0.845854\pi$
$769$	−23.4518	−	40.6197i	−0.845694	−	1.46478i	0.0393235	−	0.999227i	$-0.487480\pi$
$770$		0			0
$771$	11.9417	−	29.4221i	0.430070	−	1.05961i
$772$	−5.53894	−	3.19791i	−0.199351	−	0.115095i
$773$			9.19641i			0.330772i	0.986229	+	0.165386i	$0.0528870\pi$
$773$			9.19641i			0.330772i	−0.986229	+	0.165386i	$0.947113\pi$
$774$	−6.25949	+	1.77338i	−0.224993	+	0.0637428i
$775$		0			0
$776$	12.0414	−	20.8563i	0.432260	−	0.748696i
$777$	0.810170	+	5.83186i	0.0290647	+	0.209217i
$778$	18.2658	−	10.5458i	0.654862	−	0.378085i
$779$	15.1562	+	26.2512i	0.543025	+	0.940548i
$780$		0			0
$781$	−8.59074	+	14.8796i	−0.307401	+	0.532434i
$782$			38.1261i			1.36339i
$783$	12.7025	+	1.39632i	0.453950	+	0.0499004i
$784$	−32.9844			−1.17801
$785$		0			0
$786$	16.3169	+	20.9532i	0.582003	+	0.747374i
$787$	−4.97651	+	2.87319i	−0.177393	+	0.102418i	−0.586067	−	0.810262i	$-0.699325\pi$
$787$	−4.97651	+	2.87319i	−0.177393	+	0.102418i	0.408674	+	0.912680i	$0.365991\pi$
$788$	−1.19847	+	0.691939i	−0.0426938	+	0.0246493i
$789$	27.5807	−	3.83155i	0.981899	−	0.136407i
$790$		0			0
$791$	−6.06126			−0.215514
$792$	−14.0944	+	14.5027i	−0.500823	+	0.515330i
$793$		−	17.7411i		−	0.630004i
$794$	0.709351	−	1.22863i	0.0251739	−	0.0436025i
$795$		0			0
$796$	−4.38128	−	7.58859i	−0.155290	−	0.268971i
$797$	6.12670	−	3.53725i	0.217019	−	0.125296i	−0.387550	−	0.921849i	$-0.626679\pi$
$797$	6.12670	−	3.53725i	0.217019	−	0.125296i	0.604569	+	0.796553i	$0.293345\pi$
$798$	−7.38056	−	2.99558i	−0.261269	−	0.106043i
$799$	11.3095	−	19.5887i	0.400103	−	0.692998i
$800$		0			0
$801$	−2.48810	+	9.84586i	−0.0879127	+	0.347886i
$802$			54.5868i			1.92753i
$803$	−31.6781	−	18.2893i	−1.11789	−	0.645417i
$804$	−2.76222	+	0.383732i	−0.0974162	+	0.0135332i
$805$		0			0
$806$	21.5515	+	37.3282i	0.759118	+	1.31483i
$807$	−24.8721	+	19.3686i	−0.875538	+	0.681809i
$808$	32.7074	+	18.8836i	1.15064	+	0.664323i
$809$	−38.1075			−1.33979			−0.669894	−	0.742457i	$-0.733660\pi$
$809$	−38.1075			−1.33979			−0.669894	+	0.742457i	$0.733660\pi$
$810$		0			0
$811$	−1.44105			−0.0506022			−0.0253011	−	0.999680i	$-0.508054\pi$
$811$	−1.44105			−0.0506022			−0.0253011	+	0.999680i	$0.508054\pi$
$812$	−0.720107	−	0.415754i	−0.0252708	−	0.0145901i
$813$	3.39688	−	2.64526i	0.119134	−	0.0927732i
$814$	17.0351	+	29.5057i	0.597081	+	1.03417i
$815$		0			0
$816$	51.1806	−	7.11007i	1.79168	−	0.248902i
$817$	6.40335	+	3.69698i	0.224025	+	0.129341i
$818$		−	8.25904i		−	0.288771i
$819$	−2.31749	+	9.17073i	−0.0809797	+	0.320451i
$820$		0			0
$821$	−11.2571	+	19.4979i	−0.392876	+	0.680482i	−0.992828	−	0.119555i	$-0.961853\pi$
$821$	−11.2571	+	19.4979i	−0.392876	+	0.680482i	0.599951	+	0.800037i	$0.295187\pi$
$822$	6.05555	+	2.45780i	0.211212	+	0.0857256i
$823$	−35.9045	+	20.7295i	−1.25155	+	0.722583i	−0.971417	−	0.237378i	$-0.923712\pi$
$823$	−35.9045	+	20.7295i	−1.25155	+	0.722583i	−0.280134	+	0.959961i	$0.590379\pi$
$824$	−0.905373	−	1.56815i	−0.0315402	−	0.0546291i
$825$		0			0
$826$	−1.18982	+	2.06083i	−0.0413992	+	0.0717055i
$827$		−	27.8133i		−	0.967164i	−0.875299	−	0.483582i	$-0.839336\pi$
$827$		−	27.8133i		−	0.967164i	0.875299	−	0.483582i	$-0.160664\pi$
$828$	5.35151	−	5.50653i	0.185978	−	0.191365i
$829$	−20.7232			−0.719745			−0.359872	−	0.933002i	$-0.617180\pi$
$829$	−20.7232			−0.719745			−0.359872	+	0.933002i	$0.617180\pi$
$830$		0			0
$831$	−13.1538	+	1.82734i	−0.456299	+	0.0633897i
$832$	−20.7098	+	11.9568i	−0.717983	+	0.414528i
$833$	−35.6314	+	20.5718i	−1.23455	+	0.712770i
$834$	18.9402	+	24.3219i	0.655846	+	0.842198i
$835$		0			0
$836$	−11.5537			−0.399595
$837$	12.9996	−	17.7142i	0.449331	−	0.612294i
$838$		−	17.9017i		−	0.618403i
$839$	9.07253	−	15.7141i	0.313218	−	0.542510i	−0.665839	−	0.746096i	$-0.731926\pi$
$839$	9.07253	−	15.7141i	0.313218	−	0.542510i	0.979057	+	0.203585i	$0.0652595\pi$
$840$		0			0
$841$	11.4759	+	19.8768i	0.395720	+	0.685406i
$842$	−15.0520	+	8.69029i	−0.518727	+	0.299487i
$843$	−0.0651190	−	0.468747i	−0.00224282	−	0.0161445i
$844$	3.71722	−	6.43841i	0.127952	−	0.221619i
$845$		0			0
$846$	−17.4850	+	4.95368i	−0.601146	+	0.170311i
$847$		−	0.701798i		−	0.0241141i
$848$	−10.7663	−	6.21591i	−0.369716	−	0.213455i
$849$	−2.19576	+	5.40993i	−0.0753581	+	0.185668i
$850$		0			0
$851$	12.8670	+	22.2862i	0.441074	+	0.763962i
$852$	−5.95083	−	2.41529i	−0.203872	−	0.0827466i
$853$	3.47023	+	2.00354i	0.118819	+	0.0685999i	0.558231	−	0.829685i	$-0.311480\pi$
$853$	3.47023	+	2.00354i	0.118819	+	0.0685999i	−0.439413	+	0.898285i	$0.644813\pi$
$854$	2.34755			0.0803316
$855$		0			0
$856$	24.0672			0.822599
$857$	−7.87192	−	4.54485i	−0.268900	−	0.155249i	0.359488	−	0.933150i	$-0.382951\pi$
$857$	−7.87192	−	4.54485i	−0.268900	−	0.155249i	−0.628387	+	0.777901i	$0.716285\pi$
$858$	7.53150	+	54.2141i	0.257121	+	1.85084i
$859$	8.19348	+	14.1915i	0.279558	+	0.484208i	0.971275	−	0.237960i	$-0.0764788\pi$
$859$	8.19348	+	14.1915i	0.279558	+	0.484208i	−0.691717	+	0.722169i	$0.743145\pi$
$860$		0			0
$861$	2.92655	+	3.75810i	0.0997364	+	0.128076i
$862$	52.8486	+	30.5122i	1.80003	+	1.03925i
$863$			23.7967i			0.810050i	0.914306	+	0.405025i	$0.132737\pi$
$863$			23.7967i			0.810050i	−0.914306	+	0.405025i	$0.867263\pi$
$864$	−15.2523	−	11.1929i	−0.518893	−	0.380789i
$865$		0			0
$866$	−14.0602	+	24.3530i	−0.477785	+	0.827549i
$867$	27.6217	−	21.5099i	0.938082	−	0.730513i
$868$	−1.23816	+	0.714850i	−0.0420258	+	0.0242636i
$869$	5.27496	+	9.13650i	0.178941	+	0.309935i
$870$		0			0
$871$	7.50747	−	13.0033i	0.254381	−	0.440600i
$872$			10.1291i			0.343016i
$873$	−23.1570	+	23.8278i	−0.783747	+	0.806450i
$874$	−34.8137			−1.17759
$875$		0			0
$876$	5.14206	−	12.6691i	0.173734	−	0.428048i
$877$	−31.2413	+	18.0372i	−1.05495	+	0.609073i	−0.924030	−	0.382321i	$-0.875125\pi$
$877$	−31.2413	+	18.0372i	−1.05495	+	0.609073i	−0.130916	+	0.991394i	$0.541792\pi$
$878$	44.9196	−	25.9343i	1.51596	−	0.875241i
$879$	3.67646	−	9.05811i	0.124004	−	0.305522i
$880$		0			0
$881$	−35.4575			−1.19459			−0.597297	−	0.802020i	$-0.703759\pi$
$881$	−35.4575			−1.19459			−0.597297	+	0.802020i	$0.703759\pi$
$882$	32.0491	+	8.09896i	1.07915	+	0.272706i
$883$		−	39.1320i		−	1.31690i	−0.752626	−	0.658448i	$-0.771213\pi$
$883$		−	39.1320i		−	1.31690i	0.752626	−	0.658448i	$-0.228787\pi$
$884$	12.7323	−	22.0531i	0.428235	−	0.741725i
$885$		0			0
$886$	−0.290768	−	0.503625i	−0.00976855	−	0.0169196i
$887$	−44.4126	+	25.6416i	−1.49123	+	0.860962i	−0.999950	−	0.0100402i	$-0.996804\pi$
$887$	−44.4126	+	25.6416i	−1.49123	+	0.860962i	−0.491280	+	0.871002i	$0.663471\pi$
$888$	19.9884	−	15.5655i	0.670765	−	0.522345i
$889$	0.815778	−	1.41297i	0.0273603	−	0.0473895i
$890$		0			0
$891$	23.7556	−	14.6351i	0.795841	−	0.490293i
$892$			2.60530i			0.0872318i
$893$	17.8868	+	10.3270i	0.598560	+	0.345579i
$894$	−28.4138	−	36.4873i	−0.950299	−	1.22032i
$895$		0			0
$896$	−3.42207	−	5.92720i	−0.114323	−	0.198014i
$897$	5.68869	+	40.9490i	0.189940	+	1.36725i
$898$	−11.1155	−	6.41752i	−0.370928	−	0.214156i
$899$	−10.3994			−0.346841
$900$		0			0
$901$	−15.5070			−0.516614
$902$	23.8696	+	13.7811i	0.794772	+	0.458862i
$903$	1.07657	+	0.436953i	0.0358260	+	0.0145409i
$904$	13.0401	+	22.5861i	0.433708	+	0.751204i
$905$		0			0
$906$	−24.2451	+	59.7353i	−0.805488	+	1.98457i
$907$	41.4470	+	23.9294i	1.37622	+	0.794563i	0.991703	−	0.128552i	$-0.0410331\pi$
$907$	41.4470	+	23.9294i	1.37622	+	0.794563i	0.384522	+	0.923116i	$0.374366\pi$
$908$			8.56930i			0.284382i
$909$	−37.3675	−	36.3155i	−1.23940	−	1.20451i
$910$		0			0
$911$	−9.02153	+	15.6258i	−0.298897	+	0.517704i	−0.975884	−	0.218291i	$-0.929952\pi$
$911$	−9.02153	+	15.6258i	−0.298897	+	0.517704i	0.676987	+	0.735995i	$0.263285\pi$
$912$	6.49235	+	46.7340i	0.214983	+	1.54752i
$913$	37.3226	−	21.5482i	1.23520	−	0.713142i
$914$	−17.5552	−	30.4065i	−0.580675	−	1.00576i
$915$		0			0
$916$	−2.22559	+	3.85483i	−0.0735354	+	0.127367i
$917$		−	4.74276i		−	0.156620i
$918$	−51.4750	−	5.65838i	−1.69893	−	0.186754i
$919$	−10.3976			−0.342984			−0.171492	−	0.985185i	$-0.554859\pi$
$919$	−10.3976			−0.342984			−0.171492	+	0.985185i	$0.554859\pi$
$920$		0			0
$921$	5.79030	+	7.43556i	0.190797	+	0.245010i
$922$	57.9984	−	33.4854i	1.91008	−	1.10278i
$923$	29.9458	−	17.2892i	0.985676	−	0.569081i
$924$	−1.79825	+	0.249816i	−0.0591582	+	0.00821833i
$925$		0			0
$926$	−68.8351			−2.26206
$927$	0.680983	+	2.40367i	0.0223664	+	0.0789467i
$928$			8.95410i			0.293933i
$929$	−18.0108	+	31.1956i	−0.590915	+	1.02349i	0.403194	+	0.915114i	$0.367900\pi$
$929$	−18.0108	+	31.1956i	−0.590915	+	1.02349i	−0.994109	+	0.108381i	$0.965433\pi$
$930$		0			0
$931$	−18.7845	−	32.5358i	−0.615638	−	1.06632i
$932$	2.11971	−	1.22382i	0.0694334	−	0.0400874i
$933$	−30.6209	−	12.4283i	−1.00248	−	0.406884i
$934$	18.4101	−	31.8873i	0.602398	−	1.04338i
$935$		0			0
$936$	39.1588	−	11.0941i	1.27995	−	0.362622i
$937$		−	24.0326i		−	0.785111i	−0.919728	−	0.392555i	$-0.871591\pi$
$937$		−	24.0326i		−	0.785111i	0.919728	−	0.392555i	$-0.128409\pi$
$938$	1.72064	+	0.993410i	0.0561808	+	0.0324360i
$939$	−15.6843	+	2.17889i	−0.511839	+	0.0711053i
$940$		0			0
$941$	−8.33380	−	14.4346i	−0.271674	−	0.470553i	0.697616	−	0.716471i	$-0.254244\pi$
$941$	−8.33380	−	14.4346i	−0.271674	−	0.470553i	−0.969291	+	0.245918i	$0.920911\pi$
$942$	−27.8197	+	21.6640i	−0.906413	+	0.705852i
$943$	18.0292	+	10.4092i	0.587112	+	0.338969i
$944$	14.0959			0.458783
$945$		0			0
$946$	6.72315			0.218589
$947$	−23.8503	−	13.7700i	−0.775031	−	0.447464i	0.0596355	−	0.998220i	$-0.481006\pi$
$947$	−23.8503	−	13.7700i	−0.775031	−	0.447464i	−0.834666	+	0.550756i	$0.814339\pi$
$948$	−3.11136	+	2.42291i	−0.101052	+	0.0786925i
$949$	36.8080	+	63.7533i	1.19484	+	2.06952i
$950$		0			0
$951$	−24.4242	+	3.39304i	−0.792008	+	0.110027i
$952$	−5.80504	−	3.35154i	−0.188142	−	0.108624i
$953$		−	18.1344i		−	0.587432i	−0.955893	−	0.293716i	$-0.905108\pi$
$953$		−	18.1344i		−	0.587432i	0.955893	−	0.293716i	$-0.0948920\pi$
$954$	8.93473	+	8.68319i	0.289273	+	0.281129i
$955$		0			0
$956$	5.24922	−	9.09192i	0.169772	−	0.294054i
$957$	−12.2364	−	4.96644i	−0.395546	−	0.160542i
$958$	47.0974	−	27.1917i	1.52165	−	0.878523i
$959$	−0.583565	−	1.01076i	−0.0188443	−	0.0326393i
$960$		0			0
$961$	6.55956	−	11.3615i	0.211599	−	0.366500i
$962$		−	68.5676i		−	2.21071i
$963$	−32.1932	−	8.13539i	−1.03741	−	0.262159i
$964$	−7.51009			−0.241884
$965$		0			0
$966$	−5.41850	+	0.752745i	−0.174337	+	0.0242192i
$967$	−31.3393	+	18.0937i	−1.00780	+	0.581855i	−0.910548	−	0.413404i	$-0.864340\pi$
$967$	−31.3393	+	18.0937i	−1.00780	+	0.581855i	−0.0972552	+	0.995259i	$0.531006\pi$
$968$	−2.61512	+	1.50984i	−0.0840532	+	0.0485281i
$969$	36.1605	+	46.4352i	1.16164	+	1.49171i
$970$		0			0
$971$	−34.6173			−1.11092			−0.555461	−	0.831542i	$-0.687458\pi$
$971$	−34.6173			−1.11092			−0.555461	+	0.831542i	$0.687458\pi$
$972$	6.64028	+	8.04245i	0.212987	+	0.257962i
$973$		−	5.50527i		−	0.176491i
$974$	−19.4170	+	33.6312i	−0.622161	+	1.07761i
$975$		0			0
$976$	−6.95292	−	12.0428i	−0.222557	−	0.385481i
$977$	25.4898	−	14.7166i	0.815492	−	0.470825i	−0.0333671	−	0.999443i	$-0.510623\pi$
$977$	25.4898	−	14.7166i	0.815492	−	0.470825i	0.848860	+	0.528618i	$0.177290\pi$
$978$	−2.94899	−	21.2278i	−0.0942983	−	0.678789i
$979$	5.24729	−	9.08857i	0.167704	−	0.290472i
$980$		0			0
$981$	3.42394	−	13.5491i	0.109318	−	0.432591i
$982$		−	7.52432i		−	0.240111i
$983$	−21.2099	−	12.2456i	−0.676492	−	0.390573i	0.122040	−	0.992525i	$-0.461056\pi$
$983$	−21.2099	−	12.2456i	−0.676492	−	0.390573i	−0.798532	+	0.601953i	$0.794390\pi$
$984$	7.70771	−	18.9904i	0.245713	−	0.605390i
$985$		0			0
$986$	12.2549	+	21.2260i	0.390274	+	0.675975i
$987$	3.00724	+	1.22057i	0.0957216	+	0.0388510i
$988$	20.1371	+	11.6262i	0.640647	+	0.369878i
$989$	5.07813			0.161475
$990$		0			0
$991$	−13.2821			−0.421919			−0.210959	−	0.977495i	$-0.567659\pi$
$991$	−13.2821			−0.421919			−0.210959	+	0.977495i	$0.567659\pi$
$992$	13.3331	+	7.69787i	0.423327	+	0.244408i
$993$	2.90763	+	20.9301i	0.0922709	+	0.664196i
$994$	2.28776	+	3.96251i	0.0725632	+	0.125683i
$995$		0			0
$996$	9.89759	+	12.7099i	0.313617	+	0.402729i
$997$	33.9075	+	19.5765i	1.07386	+	0.619994i	0.929234	−	0.369492i	$-0.120468\pi$
$997$	33.9075	+	19.5765i	1.07386	+	0.619994i	0.144627	+	0.989486i	$0.453802\pi$
$998$			30.8734i			0.977280i
$999$	−31.9988	+	14.0645i	−1.01240	+	0.444980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.c.124.2		16
3.2	odd	2		675.2.k.c.424.7		16
5.2	odd	4		225.2.e.c.151.4	yes	8
5.3	odd	4		225.2.e.e.151.1	yes	8
5.4	even	2	inner	225.2.k.c.124.7		16
9.2	odd	6		2025.2.b.o.649.2		8
9.4	even	3	inner	225.2.k.c.49.7		16
9.5	odd	6		675.2.k.c.199.2		16
9.7	even	3		2025.2.b.n.649.7		8
15.2	even	4		675.2.e.e.451.1		8
15.8	even	4		675.2.e.c.451.4		8
15.14	odd	2		675.2.k.c.424.2		16
45.2	even	12		2025.2.a.p.1.4		4
45.4	even	6	inner	225.2.k.c.49.2		16
45.7	odd	12		2025.2.a.y.1.1		4
45.13	odd	12		225.2.e.e.76.1	yes	8
45.14	odd	6		675.2.k.c.199.7		16
45.22	odd	12		225.2.e.c.76.4	✓	8
45.23	even	12		675.2.e.c.226.4		8
45.29	odd	6		2025.2.b.o.649.7		8
45.32	even	12		675.2.e.e.226.1		8
45.34	even	6		2025.2.b.n.649.2		8
45.38	even	12		2025.2.a.z.1.1		4
45.43	odd	12		2025.2.a.q.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.4	✓	8	45.22	odd	12
225.2.e.c.151.4	yes	8	5.2	odd	4
225.2.e.e.76.1	yes	8	45.13	odd	12
225.2.e.e.151.1	yes	8	5.3	odd	4
225.2.k.c.49.2		16	45.4	even	6	inner
225.2.k.c.49.7		16	9.4	even	3	inner
225.2.k.c.124.2		16	1.1	even	1	trivial
225.2.k.c.124.7		16	5.4	even	2	inner
675.2.e.c.226.4		8	45.23	even	12
675.2.e.c.451.4		8	15.8	even	4
675.2.e.e.226.1		8	45.32	even	12
675.2.e.e.451.1		8	15.2	even	4
675.2.k.c.199.2		16	9.5	odd	6
675.2.k.c.199.7		16	45.14	odd	6
675.2.k.c.424.2		16	15.14	odd	2
675.2.k.c.424.7		16	3.2	odd	2
2025.2.a.p.1.4		4	45.2	even	12
2025.2.a.q.1.4		4	45.43	odd	12
2025.2.a.y.1.1		4	45.7	odd	12
2025.2.a.z.1.1		4	45.38	even	12
2025.2.b.n.649.2		8	45.34	even	6
2025.2.b.n.649.7		8	9.7	even	3
2025.2.b.o.649.2		8	9.2	odd	6
2025.2.b.o.649.7		8	45.29	odd	6

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41485 - 0.816862i) q^{2} +(-1.36657 + 1.06419i) q^{3} +(0.334526 + 0.579416i) q^{4} +(2.80278 - 0.389365i) q^{6} +(-0.437645 - 0.252674i) q^{7} +2.17440i q^{8} +(0.735010 - 2.90857i) q^{9} +O(q^{10})\)	\(q+(-1.41485 - 0.816862i) q^{2} +(-1.36657 + 1.06419i) q^{3} +(0.334526 + 0.579416i) q^{4} +(2.80278 - 0.389365i) q^{6} +(-0.437645 - 0.252674i) q^{7} +2.17440i q^{8} +(0.735010 - 2.90857i) q^{9} +(-1.55010 + 2.68485i) q^{11} +(-1.07376 - 0.435812i) q^{12} +(5.40337 - 3.11964i) q^{13} +(0.412800 + 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} -6.10020i q^{17} +(-3.41582 + 3.51477i) q^{18} +5.57022 q^{19} +(0.866963 - 0.120440i) q^{21} +(4.38631 - 2.53244i) q^{22} +(3.31307 - 1.91280i) q^{23} +(-2.31397 - 2.97146i) q^{24} -10.1932 q^{26} +(2.09082 + 4.75694i) q^{27} -0.338104i q^{28} +(1.22966 - 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(-3.15309 + 1.82044i) q^{32} +(-0.738871 - 5.31863i) q^{33} +(-4.98302 + 8.63085i) q^{34} +(1.93115 - 0.547115i) q^{36} +6.72677i q^{37} +(-7.88101 - 4.55010i) q^{38} +(-4.06419 + 10.0134i) q^{39} +(2.72092 + 4.71278i) q^{41} +(-1.32500 - 0.537785i) q^{42} +(1.14957 + 0.663704i) q^{43} -2.07420 q^{44} -6.24997 q^{46} +(3.21115 + 1.85396i) q^{47} +(1.16555 + 8.38998i) q^{48} +(-3.37231 - 5.84101i) q^{49} +(6.49176 + 8.33633i) q^{51} +(3.61514 + 2.08720i) q^{52} -2.54205i q^{53} +(0.927572 - 8.43825i) q^{54} +(0.549415 - 0.951614i) q^{56} +(-7.61208 + 5.92776i) q^{57} +(-3.47956 + 2.00893i) q^{58} +(1.44116 + 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} +6.90833i q^{62} +(-1.05659 + 1.08720i) q^{63} -3.83276 q^{64} +(-3.29920 + 8.12860i) q^{66} +(2.08411 - 1.20326i) q^{67} +(3.53456 - 2.04068i) q^{68} +(-2.49195 + 6.13969i) q^{69} +5.54205 q^{71} +(6.32439 + 1.59821i) q^{72} +11.7988i q^{73} +(5.49484 - 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(1.35679 - 0.783341i) q^{77} +(13.9298 - 10.8475i) q^{78} +(1.70149 - 2.94707i) q^{79} +(-7.91952 - 4.27565i) q^{81} -8.89047i q^{82} +(-12.0388 - 6.95059i) q^{83} +(0.359807 + 0.462042i) q^{84} +(-1.08431 - 1.87808i) q^{86} +(0.586130 + 4.21915i) q^{87} +(-5.83795 - 3.37054i) q^{88} -3.38513 q^{89} -3.15301 q^{91} +(2.21661 + 1.27976i) q^{92} +(6.78643 + 2.75444i) q^{93} +(-3.02886 - 5.24614i) q^{94} +(2.37162 - 5.84324i) q^{96} +(-9.59173 - 5.53779i) q^{97} +11.0188i q^{98} +(6.66974 + 6.48197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Introduction

L-functions

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