LMFDB - Embedded newform 675.2.k.c.424.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, 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("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.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:	$5.38990213644$
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:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.7
Root			$1.41485 + 0.816862i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.c.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41485 + 0.816862i) q^{2} +(0.334526 + 0.579416i) q^{4} +(-0.437645 - 0.252674i) q^{7} -2.17440i q^{8} +O(q^{10})$	\(q+(1.41485 + 0.816862i) q^{2} +(0.334526 + 0.579416i) q^{4} +(-0.437645 - 0.252674i) q^{7} -2.17440i q^{8} +(1.55010 - 2.68485i) q^{11} +(5.40337 - 3.11964i) q^{13} +(-0.412800 - 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} +6.10020i q^{17} +5.57022 q^{19} +(4.38631 - 2.53244i) q^{22} +(-3.31307 + 1.91280i) q^{23} +10.1932 q^{26} -0.338104i q^{28} +(-1.22966 + 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(3.15309 - 1.82044i) q^{32} +(-4.98302 + 8.63085i) q^{34} +6.72677i q^{37} +(7.88101 + 4.55010i) q^{38} +(-2.72092 - 4.71278i) q^{41} +(1.14957 + 0.663704i) q^{43} +2.07420 q^{44} -6.24997 q^{46} +(-3.21115 - 1.85396i) q^{47} +(-3.37231 - 5.84101i) q^{49} +(3.61514 + 2.08720i) q^{52} +2.54205i q^{53} +(-0.549415 + 0.951614i) q^{56} +(-3.47956 + 2.00893i) q^{58} +(-1.44116 - 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} -6.90833i q^{62} -3.83276 q^{64} +(2.08411 - 1.20326i) q^{67} +(-3.53456 + 2.04068i) q^{68} -5.54205 q^{71} +11.7988i q^{73} +(-5.49484 + 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(-1.35679 + 0.783341i) q^{77} +(1.70149 - 2.94707i) q^{79} -8.89047i q^{82} +(12.0388 + 6.95059i) q^{83} +(1.08431 + 1.87808i) q^{86} +(-5.83795 - 3.37054i) q^{88} +3.38513 q^{89} -3.15301 q^{91} +(-2.21661 - 1.27976i) q^{92} +(-3.02886 - 5.24614i) q^{94} +(-9.59173 - 5.53779i) q^{97} -11.0188i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.908381	−	0.418144i	$-0.137319\pi$
$2$	1.41485	+	0.816862i	1.00045	+	0.577608i	0.0920666	+	0.995753i	$0.470653\pi$
$3$		0			0
$3$		0			0
$4$	0.334526	+	0.579416i	0.167263	+	0.289708i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−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			0
$10$		0			0
$11$	1.55010	−	2.68485i	0.467373	−	0.809514i	−0.531932	−	0.846787i	$-0.678534\pi$
$11$	1.55010	−	2.68485i	0.467373	−	0.809514i	0.999305	+	0.0372730i	$0.0118671\pi$
$12$		0			0
$13$	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	$0.265060\pi$
$17$			6.10020i			1.47952i	−0.672873	+	0.739758i	$0.734940\pi$
$18$		0			0
$19$	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			0
$22$	4.38631	−	2.53244i	0.935164	−	0.539917i
$23$	−3.31307	+	1.91280i	−0.690822	+	0.398846i	−0.803920	−	0.594738i	$-0.797256\pi$
$23$	−3.31307	+	1.91280i	−0.690822	+	0.398846i	0.113098	+	0.993584i	$0.463923\pi$
$24$		0			0
$25$		0			0
$26$	10.1932			1.99906
$27$		0			0
$28$		−	0.338104i		−	0.0638957i
$29$	−1.22966	+	2.12984i	−0.228342	+	0.395501i	−0.957317	−	0.289040i	$-0.906664\pi$
$29$	−1.22966	+	2.12984i	−0.228342	+	0.395501i	0.728975	+	0.684541i	$0.239997\pi$
$30$		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			0
$34$	−4.98302	+	8.63085i	−0.854581	+	1.48018i
$35$		0			0
$36$		0			0
$37$			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
$39$		0			0
$40$		0			0
$41$	−2.72092	−	4.71278i	−0.424937	−	0.736012i	0.571478	−	0.820618i	$-0.306370\pi$
$41$	−2.72092	−	4.71278i	−0.424937	−	0.736012i	−0.996415	+	0.0846053i	$0.973037\pi$
$42$		0			0
$43$	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	0.247173	−	0.968971i	$-0.420499\pi$
$47$	−3.21115	−	1.85396i	−0.468395	−	0.270428i	−0.715568	+	0.698544i	$0.753832\pi$
$48$		0			0
$49$	−3.37231	−	5.84101i	−0.481759	−	0.834431i
$50$		0			0
$51$		0			0
$52$	3.61514	+	2.08720i	0.501329	+	0.289443i
$53$			2.54205i			0.349177i	0.984641	+	0.174589i	$0.0558596\pi$
$53$			2.54205i			0.349177i	−0.984641	+	0.174589i	$0.944140\pi$
$54$		0			0
$55$		0			0
$56$	−0.549415	+	0.951614i	−0.0734187	+	0.127165i
$57$		0			0
$58$	−3.47956	+	2.00893i	−0.456889	+	0.263785i
$59$	−1.44116	−	2.49616i	−0.187623	−	0.324973i	0.756834	−	0.653607i	$-0.226745\pi$
$59$	−1.44116	−	2.49616i	−0.187623	−	0.324973i	−0.944457	+	0.328634i	$0.893412\pi$
$60$		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
$63$		0			0
$64$	−3.83276			−0.479095
$65$		0			0
$66$		0			0
$67$	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
$69$		0			0
$70$		0			0
$71$	−5.54205			−0.657720			−0.328860	−	0.944379i	$-0.606664\pi$
$71$	−5.54205			−0.657720			−0.328860	+	0.944379i	$0.606664\pi$
$72$		0			0
$73$			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
$78$		0			0
$79$	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
$81$		0			0
$82$		−	8.89047i		−	0.981789i
$83$	12.0388	+	6.95059i	1.32143	+	0.762926i	0.983956	−	0.178410i	$-0.0570955\pi$
$83$	12.0388	+	6.95059i	1.32143	+	0.762926i	0.337470	+	0.941336i	$0.390429\pi$
$84$		0			0
$85$		0			0
$86$	1.08431	+	1.87808i	0.116924	+	0.202518i
$87$		0			0
$88$	−5.83795	−	3.37054i	−0.622327	−	0.359301i
$89$	3.38513			0.358823			0.179411	−	0.983774i	$-0.442581\pi$
$89$	3.38513			0.358823			0.179411	+	0.983774i	$0.442581\pi$
$90$		0			0
$91$	−3.15301			−0.330525
$92$	−2.21661	−	1.27976i	−0.231098	−	0.133425i
$93$		0			0
$94$	−3.02886	−	5.24614i	−0.312403	−	0.541098i
$95$		0			0
$96$		0			0
$97$	−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
$99$		0			0
$100$		0			0
$101$	−8.68451	+	15.0420i	−0.864141	+	1.49674i	0.00375621	+	0.999993i	$0.498804\pi$
$101$	−8.68451	+	15.0420i	−0.864141	+	1.49674i	−0.867897	+	0.496744i	$0.834529\pi$
$102$		0			0
$103$	−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	$0.179693\pi$
$107$			11.0684i			1.07002i	−0.844844	+	0.535012i	$0.820307\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−2.14029	+	1.23570i	−0.202238	+	0.116762i
$113$	−10.3873	+	5.99711i	−0.977155	+	0.564160i	−0.901410	−	0.432967i	$-0.857467\pi$
$113$	−10.3873	+	5.99711i	−0.977155	+	0.564160i	−0.0757447	+	0.997127i	$0.524133\pi$
$114$		0			0
$115$		0			0
$116$	−1.64542			−0.152773
$117$		0			0
$118$		−	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
$123$		0			0
$124$	1.41457	−	2.45011i	0.127032	−	0.220026i
$125$		0			0
$126$		0			0
$127$			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
$129$		0			0
$130$		0			0
$131$	−4.69256	−	8.12776i	−0.409991	−	0.710125i	0.584897	−	0.811107i	$-0.301135\pi$
$131$	−4.69256	−	8.12776i	−0.409991	−	0.710125i	−0.994888	+	0.100982i	$0.967802\pi$
$132$		0			0
$133$	−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	0.412119	−	0.911130i	$-0.364789\pi$
$137$	−2.00013	−	1.15478i	−0.170883	−	0.0986593i	−0.583002	+	0.812471i	$0.698122\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	−7.84115	−	4.52709i	−0.658014	−	0.379905i
$143$		−	19.3430i		−	1.61754i
$144$		0			0
$145$		0			0
$146$	−9.63799	+	16.6935i	−0.797646	+	1.38156i
$147$		0			0
$148$	−3.89760	+	2.25028i	−0.320381	+	0.184972i
$149$	8.17151	+	14.1535i	0.669436	+	1.15950i	0.978062	+	0.208314i	$0.0667975\pi$
$149$	8.17151	+	14.1535i	0.669436	+	1.15950i	−0.308626	+	0.951183i	$0.599869\pi$
$150$		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
$153$		0			0
$154$	−2.55953			−0.206252
$155$		0			0
$156$		0			0
$157$	−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
$159$		0			0
$160$		0			0
$161$	1.93326			0.152362
$162$		0			0
$163$		−	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	−0.596416	−	0.802676i	$-0.703409\pi$
$167$	−2.57793	+	1.48837i	−0.199486	+	0.115174i	0.396929	+	0.917849i	$0.370076\pi$
$168$		0			0
$169$	12.9643	−	22.4548i	0.997252	−	1.72729i
$170$		0			0
$171$		0			0
$172$			0.888105i			0.0677174i
$173$	−13.7291	−	7.92649i	−1.04380	−	0.602640i	−0.122895	−	0.992420i	$-0.539218\pi$
$173$	−13.7291	−	7.92649i	−1.04380	−	0.602640i	−0.920908	+	0.389780i	$0.872551\pi$
$174$		0			0
$175$		0			0
$176$	−7.58073	−	13.1302i	−0.571419	−	0.989727i
$177$		0			0
$178$	4.78943	+	2.76518i	0.358983	+	0.207259i
$179$	17.0841			1.27693			0.638463	−	0.769653i	$-0.279571\pi$
$179$	17.0841			1.27693			0.638463	+	0.769653i	$0.279571\pi$
$180$		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			0
$184$	4.15919	+	7.20393i	0.306620	+	0.531081i
$185$		0			0
$186$		0			0
$187$	16.3782	+	9.45593i	1.19769	+	0.691486i
$188$		−	2.48079i		−	0.180930i
$189$		0			0
$190$		0			0
$191$	12.6686	−	21.9427i	0.916669	−	1.58772i	0.112230	−	0.993682i	$-0.464201\pi$
$191$	12.6686	−	21.9427i	0.916669	−	1.58772i	0.804439	−	0.594035i	$-0.202466\pi$
$192$		0			0
$193$	−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	$-0.976524\pi$
$197$		−	2.06841i		−	0.147368i	0.997282	−	0.0736842i	$-0.0234757\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−24.5745	+	14.1881i	−1.72906	+	0.998271i
$203$	1.07631	−	0.621407i	0.0755421	−	0.0436142i
$204$		0			0
$205$		0			0
$206$	−1.36049			−0.0947900
$207$		0			0
$208$		−	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
$213$		0			0
$214$	−9.04136	+	15.6601i	−0.618055	+	1.07050i
$215$		0			0
$216$		0			0
$217$			2.13690i			0.145063i
$218$	6.59086	+	3.80523i	0.446389	+	0.257723i
$219$		0			0
$220$		0			0
$221$	19.0304	+	32.9617i	1.28012	+	2.21724i
$222$		0			0
$223$	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	0.0844781	−	0.996425i	$-0.473078\pi$
$227$	−11.0922	−	6.40406i	−0.736213	−	0.425053i	−0.820691	+	0.571373i	$0.806411\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	4.63112	+	2.67378i	0.304048	+	0.175542i
$233$			3.65836i			0.239667i	0.992794	+	0.119833i	$0.0382360\pi$
$233$			3.65836i			0.239667i	−0.992794	+	0.119833i	$0.961764\pi$
$234$		0			0
$235$		0			0
$236$	0.964212	−	1.67006i	0.0627648	−	0.108712i
$237$		0			0
$238$	4.36158	−	2.51816i	0.282720	−	0.163228i
$239$	7.84576	+	13.5893i	0.507500	+	0.879016i	0.999962	+	0.00868195i	$0.00276358\pi$
$239$	7.84576	+	13.5893i	0.507500	+	0.879016i	−0.492462	+	0.870334i	$0.663903\pi$
$240$		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
$243$		0			0
$244$	1.90242			0.121790
$245$		0			0
$246$		0			0
$247$	30.0980	−	17.3771i	1.91509	−	1.10568i
$248$	−7.96278	+	4.59731i	−0.505637	+	0.291930i
$249$		0			0
$250$		0			0
$251$	−6.94042			−0.438075			−0.219038	−	0.975716i	$-0.570292\pi$
$251$	−6.94042			−0.438075			−0.219038	+	0.975716i	$0.570292\pi$
$252$		0			0
$253$			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	0.0849739	−	0.996383i	$-0.472919\pi$
$257$	15.8766	−	9.16635i	0.990354	−	0.571781i	0.905380	+	0.424602i	$0.139586\pi$
$258$		0			0
$259$	1.69968	−	2.94393i	0.105613	−	0.182927i
$260$		0			0
$261$		0			0
$262$		−	15.3327i		−	0.947257i
$263$	13.9228	+	8.03832i	0.858515	+	0.495664i	0.863515	−	0.504323i	$-0.168258\pi$
$263$	13.9228	+	8.03832i	0.858515	+	0.495664i	−0.00499942	+	0.999988i	$0.501591\pi$
$264$		0			0
$265$		0			0
$266$	−2.29939	−	3.98265i	−0.140984	−	0.244192i
$267$		0			0
$268$	1.39438	+	0.805043i	0.0851751	+	0.0491758i
$269$	−18.2004			−1.10970			−0.554849	−	0.831951i	$-0.687224\pi$
$269$	−18.2004			−1.10970			−0.554849	+	0.831951i	$0.687224\pi$
$270$		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
$273$		0			0
$274$	−1.88659	−	3.26766i	−0.113973	−	0.197407i
$275$		0			0
$276$		0			0
$277$	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
$279$		0			0
$280$		0			0
$281$	0.136615	−	0.236624i	0.00814978	−	0.0141158i	−0.861922	−	0.507041i	$-0.830739\pi$
$281$	0.136615	−	0.236624i	0.00814978	−	0.0141158i	0.870072	+	0.492925i	$0.164072\pi$
$282$		0			0
$283$	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
$288$		0			0
$289$	−20.2125			−1.18897
$290$		0			0
$291$		0			0
$292$	−6.83642	+	3.94701i	−0.400071	+	0.230981i
$293$	4.88788	−	2.82202i	0.285553	−	0.164864i	−0.350382	−	0.936607i	$-0.613948\pi$
$293$	4.88788	−	2.82202i	0.285553	−	0.164864i	0.635935	+	0.771743i	$0.280615\pi$
$294$		0			0
$295$		0			0
$296$	14.6267			0.850159
$297$		0			0
$298$			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
$303$		0			0
$304$	13.6205	−	23.5914i	0.781190	−	1.35306i
$305$		0			0
$306$		0			0
$307$		−	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			0
$310$		0			0
$311$	−9.53985	−	16.5235i	−0.540955	−	0.936962i	−0.998849	−	0.0479550i	$-0.984730\pi$
$311$	−9.53985	−	16.5235i	−0.540955	−	0.936962i	0.457895	−	0.889007i	$-0.348604\pi$
$312$		0			0
$313$	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	0.112056	−	0.993702i	$-0.464256\pi$
$317$	−12.3294	−	7.11836i	−0.692486	−	0.399807i	−0.804543	+	0.593895i	$0.797590\pi$
$318$		0			0
$319$	3.81220	+	6.60292i	0.213442	+	0.369693i
$320$		0			0
$321$		0			0
$322$	2.73527	+	1.57921i	0.152430	+	0.0880057i
$323$			33.9795i			1.89067i
$324$		0			0
$325$		0			0
$326$	6.18678	−	10.7158i	0.342654	−	0.593494i
$327$		0			0
$328$	−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
$333$		0			0
$334$	−4.86317			−0.266101
$335$		0			0
$336$		0			0
$337$	−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
$339$		0			0
$340$		0			0
$341$	−13.1094			−0.709917
$342$		0			0
$343$			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	$-0.311599\pi$
$347$	28.9775	−	16.7301i	1.55559	−	0.898121i	0.997670	−	0.0682272i	$-0.0217343\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$		−	11.2875i		−	0.601624i
$353$	−1.59496	−	0.920851i	−0.0848912	−	0.0490119i	0.456954	−	0.889491i	$-0.348941\pi$
$353$	−1.59496	−	0.920851i	−0.0848912	−	0.0490119i	−0.541845	+	0.840479i	$0.682274\pi$
$354$		0			0
$355$		0			0
$356$	1.13241	+	1.96140i	0.0600178	+	0.103954i
$357$		0			0
$358$	24.1714	+	13.9553i	1.27750	+	0.737563i
$359$	−12.1119			−0.639241			−0.319621	−	0.947546i	$-0.603555\pi$
$359$	−12.1119			−0.639241			−0.319621	+	0.947546i	$0.603555\pi$
$360$		0			0
$361$	12.0274			0.633020
$362$	18.9151	+	10.9206i	0.994156	+	0.573976i
$363$		0			0
$364$	−1.05476	−	1.82690i	−0.0552846	−	0.0957558i
$365$		0			0
$366$		0			0
$367$	−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
$369$		0			0
$370$		0			0
$371$	0.642310	−	1.11251i	0.0333471	−	0.0577589i
$372$		0			0
$373$	−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
$378$		0			0
$379$	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
$381$		0			0
$382$	35.8483	−	20.6970i	1.83416	−	1.05895i
$383$	−1.26908	+	0.732704i	−0.0648470	+	0.0374394i	−0.532073	−	0.846699i	$-0.678587\pi$
$383$	−1.26908	+	0.732704i	−0.0648470	+	0.0374394i	0.467226	+	0.884138i	$0.345253\pi$
$384$		0			0
$385$		0			0
$386$	−15.6176			−0.794916
$387$		0			0
$388$		−	7.41014i		−	0.376193i
$389$	6.45506	−	11.1805i	0.327284	−	0.566873i	−0.654688	−	0.755900i	$-0.727200\pi$
$389$	6.45506	−	11.1805i	0.327284	−	0.566873i	0.981972	+	0.189026i	$0.0605331\pi$
$390$		0			0
$391$	−11.6685	−	20.2104i	−0.590100	−	1.02208i
$392$	−12.7007	+	7.33276i	−0.641483	+	0.370360i
$393$		0			0
$394$	1.68961	−	2.92649i	0.0851212	−	0.147434i
$395$		0			0
$396$		0			0
$397$			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
$399$		0			0
$400$		0			0
$401$	16.7063	+	28.9361i	0.834270	+	1.44500i	0.894623	+	0.446822i	$0.147444\pi$
$401$	16.7063	+	28.9361i	0.834270	+	1.44500i	−0.0603527	+	0.998177i	$0.519223\pi$
$402$		0			0
$403$	−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
$408$		0			0
$409$	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
$411$		0			0
$412$	−0.482512	−	0.278579i	−0.0237717	−	0.0137246i
$413$			1.45658i			0.0716734i
$414$		0			0
$415$		0			0
$416$	11.3582	−	19.6730i	0.556883	−	0.964549i
$417$		0			0
$418$	24.4327	−	14.1062i	1.19504	−	0.689959i
$419$	−5.47880	−	9.48955i	−0.267657	−	0.463595i	0.700600	−	0.713555i	$-0.252916\pi$
$419$	−5.47880	−	9.48955i	−0.267657	−	0.463595i	−0.968256	+	0.249960i	$0.919583\pi$
$420$		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
$423$		0			0
$424$	5.52744			0.268436
$425$		0			0
$426$		0			0
$427$	−1.24442	+	0.718467i	−0.0602218	+	0.0347691i
$428$	−6.41322	+	3.70267i	−0.309995	+	0.178975i
$429$		0			0
$430$		0			0
$431$	37.3529			1.79923			0.899613	−	0.436687i	$-0.143848\pi$
$431$	37.3529			1.79923			0.899613	+	0.436687i	$0.143848\pi$
$432$		0			0
$433$		−	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
$438$		0			0
$439$	−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
$441$		0			0
$442$			62.1809i			2.95764i
$443$	−0.308268	−	0.177979i	−0.0146463	−	0.00845603i	0.492659	−	0.870222i	$-0.336025\pi$
$443$	−0.308268	−	0.177979i	−0.0146463	−	0.00845603i	−0.507305	+	0.861766i	$0.669358\pi$
$444$		0			0
$445$		0			0
$446$	3.18087	+	5.50943i	0.150619	+	0.260879i
$447$		0			0
$448$	1.67738	+	0.968438i	0.0792490	+	0.0457544i
$449$	−7.85632			−0.370762			−0.185381	−	0.982667i	$-0.559352\pi$
$449$	−7.85632			−0.370762			−0.185381	+	0.982667i	$0.559352\pi$
$450$		0			0
$451$	−16.8708			−0.794416
$452$	−6.94964	−	4.01238i	−0.326884	−	0.188726i
$453$		0			0
$454$	−10.4625	−	18.1215i	−0.491028	−	0.850485i
$455$		0			0
$456$		0			0
$457$	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
$459$		0			0
$460$		0			0
$461$	20.4964	−	35.5007i	0.954611	−	1.65343i	0.219355	−	0.975645i	$-0.429605\pi$
$461$	20.4964	−	35.5007i	0.954611	−	1.65343i	0.735256	−	0.677789i	$-0.237062\pi$
$462$		0			0
$463$	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	$-0.825388\pi$
$467$		−	22.5376i		−	1.04292i	0.853276	−	0.521459i	$-0.174612\pi$
$468$		0			0
$469$	−1.21613			−0.0561557
$470$		0			0
$471$		0			0
$472$	−5.42766	+	3.13366i	−0.249828	+	0.144238i
$473$	3.56390	−	2.05762i	0.163868	−	0.0946093i
$474$		0			0
$475$		0			0
$476$	2.06251			0.0945348
$477$		0			0
$478$			25.6356i			1.17255i
$479$	16.6440	−	28.8282i	0.760483	−	1.31720i	−0.182119	−	0.983277i	$-0.558296\pi$
$479$	16.6440	−	28.8282i	0.760483	−	1.31720i	0.942602	−	0.333919i	$-0.108371\pi$
$480$		0			0
$481$	20.9851	+	36.3472i	0.956837	+	1.65729i
$482$	−15.8816	+	9.16924i	−0.723387	+	0.417647i
$483$		0			0
$484$	−0.464570	+	0.804660i	−0.0211168	+	0.0365754i
$485$		0			0
$486$		0			0
$487$		−	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
$489$		0			0
$490$		0			0
$491$	−2.30281	−	3.98859i	−0.103925	−	0.180003i	0.809374	−	0.587294i	$-0.199807\pi$
$491$	−2.30281	−	3.98859i	−0.103925	−	0.180003i	−0.913298	+	0.407291i	$0.866473\pi$
$492$		0			0
$493$	−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
$498$		0			0
$499$	−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
$501$		0			0
$502$	−9.81962	−	5.66936i	−0.438271	−	0.253036i
$503$		−	35.7581i		−	1.59438i	−0.603731	−	0.797188i	$-0.706320\pi$
$503$		−	35.7581i		−	1.59438i	0.603731	−	0.797188i	$-0.293680\pi$
$504$		0			0
$505$		0			0
$506$	−9.68809	+	16.7803i	−0.430688	+	0.745974i
$507$		0			0
$508$	−1.87069	+	1.08004i	−0.0829985	+	0.0479192i
$509$	−12.2034	−	21.1368i	−0.540904	−	0.936874i	−0.998852	−	0.0478949i	$-0.984749\pi$
$509$	−12.2034	−	21.1368i	−0.540904	−	0.936874i	0.457948	−	0.888979i	$-0.348585\pi$
$510$		0			0
$511$	2.98125	−	5.16368i	0.131883	−	0.228428i
$512$			3.46207i			0.153003i
$513$		0			0
$514$	29.9506			1.32106
$515$		0			0
$516$		0			0
$517$	−9.95523	+	5.74765i	−0.437830	+	0.252782i
$518$	4.80957	−	2.77681i	0.211321	−	0.122006i
$519$		0			0
$520$		0			0
$521$	−33.3968			−1.46314			−0.731571	−	0.681766i	$-0.761212\pi$
$521$	−33.3968			−1.46314			−0.731571	+	0.681766i	$0.761212\pi$
$522$		0			0
$523$		−	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
$528$		0			0
$529$	−4.18239	+	7.24412i	−0.181843	+	0.314962i
$530$		0			0
$531$		0			0
$532$		−	1.88332i		−	0.0816521i
$533$	−29.4043	−	16.9766i	−1.27364	−	0.735338i
$534$		0			0
$535$		0			0
$536$	−2.61637	−	4.53168i	−0.113010	−	0.195739i
$537$		0			0
$538$	−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
$543$		0			0
$544$	11.1051	+	19.2345i	0.476125	+	0.824673i
$545$		0			0
$546$		0			0
$547$	−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
$549$		0			0
$550$		0			0
$551$	−6.84949	+	11.8637i	−0.291798	+	0.505409i
$552$		0			0
$553$	−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	$-0.802758\pi$
$557$		−	27.4125i		−	1.16151i	0.814080	−	0.580753i	$-0.197242\pi$
$558$		0			0
$559$	8.28206			0.350294
$560$		0			0
$561$		0			0
$562$	0.386579	−	0.223191i	0.0163068	−	0.00941476i
$563$	23.9363	−	13.8196i	1.00879	−	0.582427i	0.0979551	−	0.995191i	$-0.468770\pi$
$563$	23.9363	−	13.8196i	1.00879	−	0.582427i	0.910838	+	0.412764i	$0.135437\pi$
$564$		0			0
$565$		0			0
$566$	5.50710			0.231481
$567$		0			0
$568$			12.0506i			0.505634i
$569$	7.35807	−	12.7446i	0.308467	−	0.534280i	−0.669561	−	0.742757i	$-0.733518\pi$
$569$	7.35807	−	12.7446i	0.308467	−	0.534280i	0.978027	+	0.208478i	$0.0668509\pi$
$570$		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
$573$		0			0
$574$	−2.24639	+	3.89087i	−0.0937626	+	0.162402i
$575$		0			0
$576$		0			0
$577$			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
$579$		0			0
$580$		0			0
$581$	−3.51247	−	6.08377i	−0.145722	−	0.252397i
$582$		0			0
$583$	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	0.449485	−	0.893288i	$-0.351607\pi$
$587$	−2.40784	−	1.39016i	−0.0993820	−	0.0573782i	−0.548867	+	0.835910i	$0.684941\pi$
$588$		0			0
$589$	−11.7771	−	20.3985i	−0.485265	−	0.840504i
$590$		0			0
$591$		0			0
$592$	28.4897	+	16.4485i	1.17092	+	0.676031i
$593$			14.8084i			0.608109i	0.952655	+	0.304055i	$0.0983405\pi$
$593$			14.8084i			0.608109i	−0.952655	+	0.304055i	$0.901659\pi$
$594$		0			0
$595$		0			0
$596$	−5.46717	+	9.46941i	−0.223944	+	0.387882i
$597$		0			0
$598$	−33.7709	+	19.4976i	−1.38100	+	0.797318i
$599$	8.17151	+	14.1535i	0.333879	+	0.578295i	0.983269	−	0.182160i	$-0.0583090\pi$
$599$	8.17151	+	14.1535i	0.333879	+	0.578295i	−0.649390	+	0.760456i	$0.724976\pi$
$600$		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
$603$		0			0
$604$	−15.2428			−0.620221
$605$		0			0
$606$		0			0
$607$	−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			0
$610$		0			0
$611$	−23.1347			−0.935931
$612$		0			0
$613$			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	−0.956065	−	0.293155i	$-0.905295\pi$
$617$	−29.3160	+	16.9256i	−1.18022	+	0.681399i	−0.224152	+	0.974554i	$0.571961\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$		−	31.1709i		−	1.24984i
$623$	−1.48148	−	0.855334i	−0.0593543	−	0.0342682i
$624$		0			0
$625$		0			0
$626$	7.46800	+	12.9350i	0.298481	+	0.516985i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−11.6294	−	20.1428i	−0.461864	−	0.799972i
$635$		0			0
$636$		0			0
$637$	−36.4437	−	21.0408i	−1.44395	−	0.833666i
$638$			12.4562i			0.493144i
$639$		0			0
$640$		0			0
$641$	−17.3827	+	30.1077i	−0.686576	+	1.18918i	0.286363	+	0.958121i	$0.407554\pi$
$641$	−17.3827	+	30.1077i	−0.686576	+	1.18918i	−0.972939	+	0.231063i	$0.925780\pi$
$642$		0			0
$643$	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	$0.293218\pi$
$647$			40.5103i			1.59262i	−0.604887	+	0.796311i	$0.706782\pi$
$648$		0			0
$649$	−8.93578			−0.350760
$650$		0			0
$651$		0			0
$652$	4.38841	−	2.53365i	0.171863	−	0.0992253i
$653$	−11.5488	+	6.66772i	−0.451941	+	0.260928i	−0.708650	−	0.705561i	$-0.750695\pi$
$653$	−11.5488	+	6.66772i	−0.451941	+	0.260928i	0.256709	+	0.966489i	$0.417362\pi$
$654$		0			0
$655$		0			0
$656$	−26.6132			−1.03907
$657$		0			0
$658$			3.06126i			0.119340i
$659$	−15.5772	+	26.9804i	−0.606800	+	1.05101i	0.384965	+	0.922931i	$0.374214\pi$
$659$	−15.5772	+	26.9804i	−0.606800	+	1.05101i	−0.991764	+	0.128077i	$0.959120\pi$
$660$		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
$663$		0			0
$664$	15.1134	−	26.1771i	0.586512	−	1.01587i
$665$		0			0
$666$		0			0
$667$		−	9.40838i		−	0.364294i
$668$	−1.72477	−	0.995798i	−0.0667334	−	0.0385286i
$669$		0			0
$670$		0			0
$671$	−4.40764	−	7.63426i	−0.170155	−	0.294717i
$672$		0			0
$673$	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	−0.209788	−	0.977747i	$-0.567278\pi$
$677$	−30.2197	−	17.4473i	−1.16144	−	0.670556i	−0.951648	+	0.307191i	$0.900611\pi$
$678$		0			0
$679$	2.79851	+	4.84716i	0.107397	+	0.186017i
$680$		0			0
$681$		0			0
$682$	−18.5479	−	10.7086i	−0.710234	−	0.410054i
$683$		−	26.0958i		−	0.998528i	−0.866450	−	0.499264i	$-0.833604\pi$
$683$		−	26.0958i		−	0.998528i	0.866450	−	0.499264i	$-0.166396\pi$
$684$		0			0
$685$		0			0
$686$	−5.67378	+	9.82727i	−0.216626	+	0.375207i
$687$		0			0
$688$	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
$693$		0			0
$694$	54.6648			2.07505
$695$		0			0
$696$		0			0
$697$	28.7489	−	16.5982i	1.08894	−	0.628701i
$698$	−39.7311	+	22.9387i	−1.50384	+	0.868244i
$699$		0			0
$700$		0			0
$701$	−15.3891			−0.581239			−0.290620	−	0.956839i	$-0.593861\pi$
$701$	−15.3891			−0.581239			−0.290620	+	0.956839i	$0.593861\pi$
$702$		0			0
$703$			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			0
$709$	−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
$711$		0			0
$712$		−	7.36062i		−	0.275851i
$713$	14.0096	+	8.08842i	0.524662	+	0.302914i
$714$		0			0
$715$		0			0
$716$	5.71508	+	9.89880i	0.213582	+	0.369936i
$717$		0			0
$718$	−17.1365	−	9.89374i	−0.639527	−	0.369231i
$719$	−15.1316			−0.564313			−0.282156	−	0.959368i	$-0.591050\pi$
$719$	−15.1316			−0.564313			−0.282156	+	0.959368i	$0.591050\pi$
$720$		0			0
$721$	0.420832			0.0156726
$722$	17.0169	+	9.82470i	0.633303	+	0.365638i
$723$		0			0
$724$	4.47229	+	7.74623i	0.166211	+	0.287886i
$725$		0			0
$726$		0			0
$727$	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
$729$		0			0
$730$		0			0
$731$	−4.04873	+	7.01260i	−0.149748	+	0.259370i
$732$		0			0
$733$	−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
$738$		0			0
$739$	−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
$741$		0			0
$742$	1.81754	−	1.04936i	0.0667240	−	0.0385231i
$743$	−5.16743	+	2.98342i	−0.189575	+	0.109451i	−0.591783	−	0.806097i	$-0.701576\pi$
$743$	−5.16743	+	2.98342i	−0.189575	+	0.109451i	0.402209	+	0.915548i	$0.368243\pi$
$744$		0			0
$745$		0			0
$746$	−15.4329			−0.565039
$747$		0			0
$748$			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
$753$		0			0
$754$	−12.5342	+	21.7099i	−0.456470	+	0.790630i
$755$		0			0
$756$		0			0
$757$		−	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
$759$		0			0
$760$		0			0
$761$	14.1298	+	24.4735i	0.512204	+	0.887164i	0.999900	+	0.0141502i	$0.00450429\pi$
$761$	14.1298	+	24.4735i	0.512204	+	0.887164i	−0.487696	+	0.873014i	$0.662162\pi$
$762$		0			0
$763$	−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
$768$		0			0
$769$	−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
$771$		0			0
$772$	−5.53894	−	3.19791i	−0.199351	−	0.115095i
$773$		−	9.19641i		−	0.330772i	−0.986229	−	0.165386i	$-0.947113\pi$
$773$		−	9.19641i		−	0.330772i	0.986229	−	0.165386i	$-0.0528870\pi$
$774$		0			0
$775$		0			0
$776$	−12.0414	+	20.8563i	−0.432260	+	0.748696i
$777$		0			0
$778$	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
$783$		0			0
$784$	−32.9844			−1.17801
$785$		0			0
$786$		0			0
$787$	−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
$789$		0			0
$790$		0			0
$791$	6.06126			0.215514
$792$		0			0
$793$		−	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	−0.604569	−	0.796553i	$-0.706655\pi$
$797$	−6.12670	+	3.53725i	−0.217019	+	0.125296i	0.387550	+	0.921849i	$0.373321\pi$
$798$		0			0
$799$	11.3095	−	19.5887i	0.400103	−	0.692998i
$800$		0			0
$801$		0			0
$802$			54.5868i			1.92753i
$803$	31.6781	+	18.2893i	1.11789	+	0.645417i
$804$		0			0
$805$		0			0
$806$	−21.5515	−	37.3282i	−0.759118	−	1.31483i
$807$		0			0
$808$	32.7074	+	18.8836i	1.15064	+	0.664323i
$809$	38.1075			1.33979			0.669894	−	0.742457i	$-0.266340\pi$
$809$	38.1075			1.33979			0.669894	+	0.742457i	$0.266340\pi$
$810$		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
$813$		0			0
$814$	17.0351	+	29.5057i	0.597081	+	1.03417i
$815$		0			0
$816$		0			0
$817$	6.40335	+	3.69698i	0.224025	+	0.129341i
$818$			8.25904i			0.288771i
$819$		0			0
$820$		0			0
$821$	11.2571	−	19.4979i	0.392876	−	0.680482i	−0.599951	−	0.800037i	$-0.704813\pi$
$821$	11.2571	−	19.4979i	0.392876	−	0.680482i	0.992828	+	0.119555i	$0.0381467\pi$
$822$		0			0
$823$	−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	$0.160664\pi$
$827$			27.8133i			0.967164i	−0.875299	+	0.483582i	$0.839336\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	−20.7098	+	11.9568i	−0.717983	+	0.414528i
$833$	35.6314	−	20.5718i	1.23455	−	0.712770i
$834$		0			0
$835$		0			0
$836$	11.5537			0.399595
$837$		0			0
$838$		−	17.9017i		−	0.618403i
$839$	−9.07253	+	15.7141i	−0.313218	+	0.542510i	−0.979057	−	0.203585i	$-0.934741\pi$
$839$	−9.07253	+	15.7141i	−0.313218	+	0.542510i	0.665839	+	0.746096i	$0.268074\pi$
$840$		0			0
$841$	11.4759	+	19.8768i	0.395720	+	0.685406i
$842$	15.0520	−	8.69029i	0.518727	−	0.299487i
$843$		0			0
$844$	3.71722	−	6.43841i	0.127952	−	0.221619i
$845$		0			0
$846$		0			0
$847$		−	0.701798i		−	0.0241141i
$848$	10.7663	+	6.21591i	0.369716	+	0.213455i
$849$		0			0
$850$		0			0
$851$	−12.8670	−	22.2862i	−0.441074	−	0.763962i
$852$		0			0
$853$	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	0.628387	−	0.777901i	$-0.283715\pi$
$857$	7.87192	+	4.54485i	0.268900	+	0.155249i	−0.359488	+	0.933150i	$0.617049\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	52.8486	+	30.5122i	1.80003	+	1.03925i
$863$		−	23.7967i		−	0.810050i	−0.914306	−	0.405025i	$-0.867263\pi$
$863$		−	23.7967i		−	0.810050i	0.914306	−	0.405025i	$-0.132737\pi$
$864$		0			0
$865$		0			0
$866$	14.0602	−	24.3530i	0.477785	−	0.827549i
$867$		0			0
$868$	−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
$873$		0			0
$874$	−34.8137			−1.17759
$875$		0			0
$876$		0			0
$877$	−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
$879$		0			0
$880$		0			0
$881$	35.4575			1.19459			0.597297	−	0.802020i	$-0.296241\pi$
$881$	35.4575			1.19459			0.597297	+	0.802020i	$0.296241\pi$
$882$		0			0
$883$		−	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	0.491280	−	0.871002i	$-0.336529\pi$
$887$	44.4126	−	25.6416i	1.49123	−	0.860962i	0.999950	+	0.0100402i	$0.00319595\pi$
$888$		0			0
$889$	0.815778	−	1.41297i	0.0273603	−	0.0473895i
$890$		0			0
$891$		0			0
$892$			2.60530i			0.0872318i
$893$	−17.8868	−	10.3270i	−0.598560	−	0.345579i
$894$		0			0
$895$		0			0
$896$	3.42207	+	5.92720i	0.114323	+	0.198014i
$897$		0			0
$898$	−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
$903$		0			0
$904$	13.0401	+	22.5861i	0.433708	+	0.751204i
$905$		0			0
$906$		0			0
$907$	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
$909$		0			0
$910$		0			0
$911$	9.02153	−	15.6258i	0.298897	−	0.517704i	−0.676987	−	0.735995i	$-0.736715\pi$
$911$	9.02153	−	15.6258i	0.298897	−	0.517704i	0.975884	+	0.218291i	$0.0700481\pi$
$912$		0			0
$913$	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
$918$		0			0
$919$	−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
$921$		0			0
$922$	57.9984	−	33.4854i	1.91008	−	1.10278i
$923$	−29.9458	+	17.2892i	−0.985676	+	0.569081i
$924$		0			0
$925$		0			0
$926$	68.8351			2.26206
$927$		0			0
$928$			8.95410i			0.293933i
$929$	18.0108	−	31.1956i	0.590915	−	1.02349i	−0.403194	−	0.915114i	$-0.632100\pi$
$929$	18.0108	−	31.1956i	0.590915	−	1.02349i	0.994109	−	0.108381i	$-0.0345665\pi$
$930$		0			0
$931$	−18.7845	−	32.5358i	−0.615638	−	1.06632i
$932$	−2.11971	+	1.22382i	−0.0694334	+	0.0400874i
$933$		0			0
$934$	18.4101	−	31.8873i	0.602398	−	1.04338i
$935$		0			0
$936$		0			0
$937$		−	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
$939$		0			0
$940$		0			0
$941$	8.33380	+	14.4346i	0.271674	+	0.470553i	0.969291	−	0.245918i	$-0.0790894\pi$
$941$	8.33380	+	14.4346i	0.271674	+	0.470553i	−0.697616	+	0.716471i	$0.745756\pi$
$942$		0			0
$943$	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	0.834666	−	0.550756i	$-0.185661\pi$
$947$	23.8503	+	13.7700i	0.775031	+	0.447464i	−0.0596355	+	0.998220i	$0.518994\pi$
$948$		0			0
$949$	36.8080	+	63.7533i	1.19484	+	2.06952i
$950$		0			0
$951$		0			0
$952$	−5.80504	−	3.35154i	−0.188142	−	0.108624i
$953$			18.1344i			0.587432i	0.955893	+	0.293716i	$0.0948920\pi$
$953$			18.1344i			0.587432i	−0.955893	+	0.293716i	$0.905108\pi$
$954$		0			0
$955$		0			0
$956$	−5.24922	+	9.09192i	−0.169772	+	0.294054i
$957$		0			0
$958$	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
$963$		0			0
$964$	−7.51009			−0.241884
$965$		0			0
$966$		0			0
$967$	−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
$969$		0			0
$970$		0			0
$971$	34.6173			1.11092			0.555461	−	0.831542i	$-0.312542\pi$
$971$	34.6173			1.11092			0.555461	+	0.831542i	$0.312542\pi$
$972$		0			0
$973$		−	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	−0.848860	−	0.528618i	$-0.822710\pi$
$977$	−25.4898	+	14.7166i	−0.815492	+	0.470825i	0.0333671	+	0.999443i	$0.489377\pi$
$978$		0			0
$979$	5.24729	−	9.08857i	0.167704	−	0.290472i
$980$		0			0
$981$		0			0
$982$		−	7.52432i		−	0.240111i
$983$	21.2099	+	12.2456i	0.676492	+	0.390573i	0.798532	−	0.601953i	$-0.205610\pi$
$983$	21.2099	+	12.2456i	0.676492	+	0.390573i	−0.122040	+	0.992525i	$0.538944\pi$
$984$		0			0
$985$		0			0
$986$	−12.2549	−	21.2260i	−0.390274	−	0.675975i
$987$		0			0
$988$	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
$993$		0			0
$994$	2.28776	+	3.96251i	0.0725632	+	0.125683i
$995$		0			0
$996$		0			0
$997$	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.4	✓	8	45.32	even	12
225.2.e.c.151.4	yes	8	15.2	even	4
225.2.e.e.76.1	yes	8	45.23	even	12
225.2.e.e.151.1	yes	8	15.8	even	4
225.2.k.c.49.2		16	45.14	odd	6
225.2.k.c.49.7		16	9.5	odd	6
225.2.k.c.124.2		16	3.2	odd	2
225.2.k.c.124.7		16	15.14	odd	2
675.2.e.c.226.4		8	45.13	odd	12
675.2.e.c.451.4		8	5.3	odd	4
675.2.e.e.226.1		8	45.22	odd	12
675.2.e.e.451.1		8	5.2	odd	4
675.2.k.c.199.2		16	9.4	even	3	inner
675.2.k.c.199.7		16	45.4	even	6	inner
675.2.k.c.424.2		16	5.4	even	2	inner
675.2.k.c.424.7		16	1.1	even	1	trivial
2025.2.a.p.1.4		4	45.7	odd	12
2025.2.a.q.1.4		4	45.38	even	12
2025.2.a.y.1.1		4	45.2	even	12
2025.2.a.z.1.1		4	45.43	odd	12
2025.2.b.n.649.2		8	45.29	odd	6
2025.2.b.n.649.7		8	9.2	odd	6
2025.2.b.o.649.2		8	9.7	even	3
2025.2.b.o.649.7		8	45.34	even	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41485 + 0.816862i) q^{2} +(0.334526 + 0.579416i) q^{4} +(-0.437645 - 0.252674i) q^{7} -2.17440i q^{8} +O(q^{10})\)	\(q+(1.41485 + 0.816862i) q^{2} +(0.334526 + 0.579416i) q^{4} +(-0.437645 - 0.252674i) q^{7} -2.17440i q^{8} +(1.55010 - 2.68485i) q^{11} +(5.40337 - 3.11964i) q^{13} +(-0.412800 - 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} +6.10020i q^{17} +5.57022 q^{19} +(4.38631 - 2.53244i) q^{22} +(-3.31307 + 1.91280i) q^{23} +10.1932 q^{26} -0.338104i q^{28} +(-1.22966 + 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(3.15309 - 1.82044i) q^{32} +(-4.98302 + 8.63085i) q^{34} +6.72677i q^{37} +(7.88101 + 4.55010i) q^{38} +(-2.72092 - 4.71278i) q^{41} +(1.14957 + 0.663704i) q^{43} +2.07420 q^{44} -6.24997 q^{46} +(-3.21115 - 1.85396i) q^{47} +(-3.37231 - 5.84101i) q^{49} +(3.61514 + 2.08720i) q^{52} +2.54205i q^{53} +(-0.549415 + 0.951614i) q^{56} +(-3.47956 + 2.00893i) q^{58} +(-1.44116 - 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} -6.90833i q^{62} -3.83276 q^{64} +(2.08411 - 1.20326i) q^{67} +(-3.53456 + 2.04068i) q^{68} -5.54205 q^{71} +11.7988i q^{73} +(-5.49484 + 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(-1.35679 + 0.783341i) q^{77} +(1.70149 - 2.94707i) q^{79} -8.89047i q^{82} +(12.0388 + 6.95059i) q^{83} +(1.08431 + 1.87808i) q^{86} +(-5.83795 - 3.37054i) q^{88} +3.38513 q^{89} -3.15301 q^{91} +(-2.21661 - 1.27976i) q^{92} +(-3.02886 - 5.24614i) q^{94} +(-9.59173 - 5.53779i) q^{97} -11.0188i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Introduction

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