LMFDB - Embedded newform 675.2.k.c.199.7

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			199.7
Root			$1.41485 - 0.816862i$ of defining polynomial
Character	$\chi$	$=$	675.199
Dual form			675.2.k.c.424.7

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

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

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	$-0.470653\pi$
$2$	1.41485	−	0.816862i	1.00045	−	0.577608i	0.908381	+	0.418144i	$0.137319\pi$
$3$		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	−0.580422	−	0.814316i	$-0.697112\pi$
$7$	−0.437645	+	0.252674i	−0.165414	+	0.0955019i	0.415008	+	0.909818i	$0.363779\pi$
$8$			2.17440i			0.768767i
$9$		0			0
$10$		0			0
$11$	1.55010	+	2.68485i	0.467373	+	0.809514i	0.999305	−	0.0372730i	$-0.0118671\pi$
$11$	1.55010	+	2.68485i	0.467373	+	0.809514i	−0.531932	+	0.846787i	$0.678534\pi$
$12$		0			0
$13$	5.40337	+	3.11964i	1.49863	+	0.865232i	0.999999	−	0.00158518i	$-0.000504579\pi$
$13$	5.40337	+	3.11964i	1.49863	+	0.865232i	0.498627	+	0.866817i	$0.333838\pi$
$14$	−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	$-0.265060\pi$
$18$		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	0.113098	−	0.993584i	$-0.463923\pi$
$23$	−3.31307	−	1.91280i	−0.690822	−	0.398846i	−0.803920	+	0.594738i	$0.797256\pi$
$24$		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	0.728975	−	0.684541i	$-0.239997\pi$
$29$	−1.22966	−	2.12984i	−0.228342	−	0.395501i	−0.957317	+	0.289040i	$0.906664\pi$
$30$		0			0
$31$	−2.11429	+	3.66206i	−0.379738	+	0.657725i	−0.991024	−	0.133685i	$-0.957319\pi$
$31$	−2.11429	+	3.66206i	−0.379738	+	0.657725i	0.611286	+	0.791409i	$0.290652\pi$
$32$	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	$-0.813507\pi$
$37$		−	6.72677i		−	1.10587i	0.833223	−	0.552937i	$-0.186493\pi$
$38$	7.88101	−	4.55010i	1.27847	−	0.738124i
$39$		0			0
$40$		0			0
$41$	−2.72092	+	4.71278i	−0.424937	+	0.736012i	−0.996415	−	0.0846053i	$-0.973037\pi$
$41$	−2.72092	+	4.71278i	−0.424937	+	0.736012i	0.571478	+	0.820618i	$0.306370\pi$
$42$		0			0
$43$	1.14957	−	0.663704i	0.175308	−	0.101214i	−0.409779	−	0.912185i	$-0.634394\pi$
$43$	1.14957	−	0.663704i	0.175308	−	0.101214i	0.585086	+	0.810971i	$0.301061\pi$
$44$	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	$-0.753832\pi$
$47$	−3.21115	+	1.85396i	−0.468395	+	0.270428i	0.247173	+	0.968971i	$0.420499\pi$
$48$		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	$-0.944140\pi$
$53$		−	2.54205i		−	0.349177i	0.984641	−	0.174589i	$-0.0558596\pi$
$54$		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	−0.944457	−	0.328634i	$-0.893412\pi$
$59$	−1.44116	+	2.49616i	−0.187623	+	0.324973i	0.756834	+	0.653607i	$0.226745\pi$
$60$		0			0
$61$	1.42173	+	2.46250i	0.182033	+	0.315291i	0.942573	−	0.334001i	$-0.108399\pi$
$61$	1.42173	+	2.46250i	0.182033	+	0.315291i	−0.760539	+	0.649292i	$0.775065\pi$
$62$			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	0.621875	−	0.783116i	$-0.286371\pi$
$67$	2.08411	+	1.20326i	0.254614	+	0.147002i	−0.367261	+	0.930118i	$0.619704\pi$
$68$	−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	$-0.757403\pi$
$73$		−	11.7988i		−	1.38095i	0.723359	−	0.690473i	$-0.242597\pi$
$74$	−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	0.945725	−	0.324967i	$-0.105353\pi$
$79$	1.70149	+	2.94707i	0.191433	+	0.331571i	−0.754293	+	0.656538i	$0.772020\pi$
$80$		0			0
$81$		0			0
$82$			8.89047i			0.981789i
$83$	12.0388	−	6.95059i	1.32143	−	0.762926i	0.337470	−	0.941336i	$-0.390429\pi$
$83$	12.0388	−	6.95059i	1.32143	−	0.762926i	0.983956	+	0.178410i	$0.0570955\pi$
$84$		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	−0.900421	−	0.435020i	$-0.856741\pi$
$97$	−9.59173	+	5.53779i	−0.973892	+	0.562277i	−0.0734716	+	0.997297i	$0.523408\pi$
$98$			11.0188i			1.11307i
$99$		0			0
$100$		0			0
$101$	−8.68451	−	15.0420i	−0.864141	−	1.49674i	−0.867897	−	0.496744i	$-0.834529\pi$
$101$	−8.68451	−	15.0420i	−0.864141	−	1.49674i	0.00375621	−	0.999993i	$-0.498804\pi$
$102$		0			0
$103$	−0.721188	−	0.416378i	−0.0710608	−	0.0410269i	0.464049	−	0.885810i	$-0.346396\pi$
$103$	−0.721188	−	0.416378i	−0.0710608	−	0.0410269i	−0.535109	+	0.844783i	$0.679730\pi$
$104$	−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	$-0.179693\pi$
$108$		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	−0.0757447	−	0.997127i	$-0.524133\pi$
$113$	−10.3873	−	5.99711i	−0.977155	−	0.564160i	−0.901410	+	0.432967i	$0.857467\pi$
$114$		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	$-0.954246\pi$
$127$		−	3.22858i		−	0.286490i	0.989687	−	0.143245i	$-0.0457537\pi$
$128$	−11.7289	+	6.77171i	−1.03670	+	0.598540i
$129$		0			0
$130$		0			0
$131$	−4.69256	+	8.12776i	−0.409991	+	0.710125i	−0.994888	−	0.100982i	$-0.967802\pi$
$131$	−4.69256	+	8.12776i	−0.409991	+	0.710125i	0.584897	+	0.811107i	$0.301135\pi$
$132$		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	−0.583002	−	0.812471i	$-0.698122\pi$
$137$	−2.00013	+	1.15478i	−0.170883	+	0.0986593i	0.412119	+	0.911130i	$0.364789\pi$
$138$		0			0
$139$	5.44701	−	9.43449i	0.462009	−	0.800223i	−0.537052	−	0.843549i	$-0.680462\pi$
$139$	5.44701	−	9.43449i	0.462009	−	0.800223i	0.999061	+	0.0433260i	$0.0137954\pi$
$140$		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	−0.308626	−	0.951183i	$-0.599869\pi$
$149$	8.17151	−	14.1535i	0.669436	−	1.15950i	0.978062	−	0.208314i	$-0.0667975\pi$
$150$		0			0
$151$	−11.3913	−	19.7304i	−0.927015	−	1.60564i	−0.788288	−	0.615306i	$-0.789032\pi$
$151$	−11.3913	−	19.7304i	−0.927015	−	1.60564i	−0.138727	−	0.990331i	$-0.544301\pi$
$152$			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	0.00318877	−	0.999995i	$-0.498985\pi$
$157$	−10.7913	−	6.23035i	−0.861238	−	0.497236i	−0.864427	+	0.502759i	$0.832318\pi$
$158$	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	$0.0958576\pi$
$163$			7.57384i			0.593229i	−0.954997	+	0.296614i	$0.904142\pi$
$164$	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	$-0.370076\pi$
$167$	−2.57793	−	1.48837i	−0.199486	−	0.115174i	−0.596416	+	0.802676i	$0.703409\pi$
$168$		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	−0.920908	−	0.389780i	$-0.872551\pi$
$173$	−13.7291	+	7.92649i	−1.04380	+	0.602640i	−0.122895	+	0.992420i	$0.539218\pi$
$174$		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	0.804439	+	0.594035i	$0.202466\pi$
$191$	12.6686	+	21.9427i	0.916669	+	1.58772i	0.112230	+	0.993682i	$0.464201\pi$
$192$		0			0
$193$	−8.27879	−	4.77976i	−0.595921	−	0.344055i	0.171515	−	0.985182i	$-0.445134\pi$
$193$	−8.27879	−	4.77976i	−0.595921	−	0.344055i	−0.767435	+	0.641127i	$0.778467\pi$
$194$	−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	$0.976524\pi$
$198$		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	−0.991417	−	0.130737i	$-0.958266\pi$
$211$	−5.55595	+	9.62318i	−0.382487	+	0.662487i	0.608930	+	0.793224i	$0.291599\pi$
$212$	−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	−0.382819	−	0.923824i	$-0.625047\pi$
$223$	3.37231	−	1.94701i	0.225827	−	0.130381i	0.608645	+	0.793442i	$0.291713\pi$
$224$	−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	$-0.806411\pi$
$227$	−11.0922	+	6.40406i	−0.736213	+	0.425053i	0.0844781	+	0.996425i	$0.473078\pi$
$228$		0			0
$229$	3.32647	−	5.76162i	0.219820	−	0.380739i	−0.734933	−	0.678140i	$-0.762786\pi$
$229$	3.32647	−	5.76162i	0.219820	−	0.380739i	0.954753	+	0.297401i	$0.0961198\pi$
$230$		0			0
$231$		0			0
$232$	4.63112	−	2.67378i	0.304048	−	0.175542i
$233$		−	3.65836i		−	0.239667i	−0.992794	−	0.119833i	$-0.961764\pi$
$233$		−	3.65836i		−	0.239667i	0.992794	−	0.119833i	$-0.0382360\pi$
$234$		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	−0.492462	−	0.870334i	$-0.663903\pi$
$239$	7.84576	−	13.5893i	0.507500	−	0.879016i	0.999962	−	0.00868195i	$-0.00276358\pi$
$240$		0			0
$241$	−5.61248	−	9.72110i	−0.361532	−	0.626191i	0.626681	−	0.779276i	$-0.284413\pi$
$241$	−5.61248	−	9.72110i	−0.361532	−	0.626191i	−0.988213	+	0.153084i	$0.951079\pi$
$242$		−	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	0.905380	−	0.424602i	$-0.139586\pi$
$257$	15.8766	+	9.16635i	0.990354	+	0.571781i	0.0849739	+	0.996383i	$0.472919\pi$
$258$		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	−0.00499942	−	0.999988i	$-0.501591\pi$
$263$	13.9228	−	8.03832i	0.858515	−	0.495664i	0.863515	+	0.504323i	$0.168258\pi$
$264$		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	−0.287074	−	0.957908i	$-0.592683\pi$
$277$	6.64004	−	3.83363i	0.398962	−	0.230341i	0.686036	+	0.727568i	$0.259349\pi$
$278$		−	17.7978i		−	1.06744i
$279$		0			0
$280$		0			0
$281$	0.136615	+	0.236624i	0.00814978	+	0.0141158i	0.870072	−	0.492925i	$-0.164072\pi$
$281$	0.136615	+	0.236624i	0.00814978	+	0.0141158i	−0.861922	+	0.507041i	$0.830739\pi$
$282$		0			0
$283$	2.91928	+	1.68544i	0.173533	+	0.100189i	0.584251	−	0.811573i	$-0.301389\pi$
$283$	2.91928	+	1.68544i	0.173533	+	0.100189i	−0.410718	+	0.911763i	$0.634722\pi$
$284$	−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	0.635935	−	0.771743i	$-0.280615\pi$
$293$	4.88788	+	2.82202i	0.285553	+	0.164864i	−0.350382	+	0.936607i	$0.613948\pi$
$294$		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	$0.0496243\pi$
$307$			5.44105i			0.310537i	−0.987872	+	0.155269i	$0.950376\pi$
$308$	−0.907761	+	0.524096i	−0.0517245	+	0.0298632i
$309$		0			0
$310$		0			0
$311$	−9.53985	+	16.5235i	−0.540955	+	0.936962i	0.457895	+	0.889007i	$0.348604\pi$
$311$	−9.53985	+	16.5235i	−0.540955	+	0.936962i	−0.998849	+	0.0479550i	$0.984730\pi$
$312$		0			0
$313$	7.91747	−	4.57116i	0.447522	−	0.258377i	−0.259261	−	0.965807i	$-0.583479\pi$
$313$	7.91747	−	4.57116i	0.447522	−	0.258377i	0.706783	+	0.707430i	$0.250146\pi$
$314$	−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	$-0.797590\pi$
$317$	−12.3294	+	7.11836i	−0.692486	+	0.399807i	0.112056	+	0.993702i	$0.464256\pi$
$318$		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	0.983540	−	0.180691i	$-0.0578334\pi$
$331$	6.10001	+	10.5655i	0.335287	+	0.580734i	−0.648253	+	0.761425i	$0.724500\pi$
$332$		−	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	0.387813	−	0.921738i	$-0.373231\pi$
$337$	−3.97494	−	2.29493i	−0.216529	−	0.125013i	−0.604342	+	0.796725i	$0.706564\pi$
$338$	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	0.997670	+	0.0682272i	$0.0217343\pi$
$347$	28.9775	+	16.7301i	1.55559	+	0.898121i	0.557921	+	0.829894i	$0.311599\pi$
$348$		0			0
$349$	−14.0408	−	24.3193i	−0.751586	−	1.30178i	−0.947054	−	0.321074i	$-0.895956\pi$
$349$	−14.0408	−	24.3193i	−0.751586	−	1.30178i	0.195468	−	0.980710i	$-0.437377\pi$
$350$		0			0
$351$		0			0
$352$			11.2875i			0.601624i
$353$	−1.59496	+	0.920851i	−0.0848912	+	0.0490119i	−0.541845	−	0.840479i	$-0.682274\pi$
$353$	−1.59496	+	0.920851i	−0.0848912	+	0.0490119i	0.456954	+	0.889491i	$0.348941\pi$
$354$		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	−0.791829	−	0.610743i	$-0.790871\pi$
$367$	−12.6212	+	7.28688i	−0.658824	+	0.380372i	0.133005	+	0.991115i	$0.457537\pi$
$368$		−	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	0.273022	−	0.962008i	$-0.411977\pi$
$373$	−8.18087	−	4.72323i	−0.423590	−	0.244560i	−0.696612	+	0.717448i	$0.745310\pi$
$374$	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	0.467226	−	0.884138i	$-0.345253\pi$
$383$	−1.26908	−	0.732704i	−0.0648470	−	0.0374394i	−0.532073	+	0.846699i	$0.678587\pi$
$384$		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	0.981972	−	0.189026i	$-0.0605331\pi$
$389$	6.45506	+	11.1805i	0.327284	+	0.566873i	−0.654688	+	0.755900i	$0.727200\pi$
$390$		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	$-0.993063\pi$
$397$		−	0.868386i		−	0.0435831i	0.999763	−	0.0217915i	$-0.00693701\pi$
$398$	−18.5302	+	10.6984i	−0.928834	+	0.536263i
$399$		0			0
$400$		0			0
$401$	16.7063	−	28.9361i	0.834270	−	1.44500i	−0.0603527	−	0.998177i	$-0.519223\pi$
$401$	16.7063	−	28.9361i	0.834270	−	1.44500i	0.894623	−	0.446822i	$-0.147444\pi$
$402$		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	−0.796742	−	0.604320i	$-0.793445\pi$
$409$	2.52767	−	4.37806i	0.124985	−	0.216481i	0.921727	+	0.387839i	$0.126778\pi$
$410$		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	−0.968256	−	0.249960i	$-0.919583\pi$
$419$	−5.47880	+	9.48955i	−0.267657	+	0.463595i	0.700600	+	0.713555i	$0.252916\pi$
$420$		0			0
$421$	5.31932	+	9.21333i	0.259248	+	0.449030i	0.966041	−	0.258390i	$-0.0831921\pi$
$421$	5.31932	+	9.21333i	0.259248	+	0.449030i	−0.706793	+	0.707421i	$0.749859\pi$
$422$			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	$0.135725\pi$
$433$			17.2125i			0.827179i	−0.910464	+	0.413589i	$0.864275\pi$
$434$	−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	−0.944050	−	0.329803i	$-0.893018\pi$
$439$	−15.8744	−	27.4952i	−0.757642	−	1.31228i	0.186408	−	0.982473i	$-0.440316\pi$
$440$		0			0
$441$		0			0
$442$		−	62.1809i		−	2.95764i
$443$	−0.308268	+	0.177979i	−0.0146463	+	0.00845603i	−0.507305	−	0.861766i	$-0.669358\pi$
$443$	−0.308268	+	0.177979i	−0.0146463	+	0.00845603i	0.492659	+	0.870222i	$0.336025\pi$
$444$		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	0.00306742	−	0.999995i	$-0.499024\pi$
$457$	18.6118	−	10.7455i	0.870622	−	0.502654i	0.867555	+	0.497341i	$0.165690\pi$
$458$		−	10.8691i		−	0.507879i
$459$		0			0
$460$		0			0
$461$	20.4964	+	35.5007i	0.954611	+	1.65343i	0.735256	+	0.677789i	$0.237062\pi$
$461$	20.4964	+	35.5007i	0.954611	+	1.65343i	0.219355	+	0.975645i	$0.429605\pi$
$462$		0			0
$463$	36.4890	+	21.0669i	1.69579	+	0.979063i	0.949671	+	0.313248i	$0.101417\pi$
$463$	36.4890	+	21.0669i	1.69579	+	0.979063i	0.746116	+	0.665816i	$0.231916\pi$
$464$	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	$0.825388\pi$
$468$		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	0.942602	+	0.333919i	$0.108371\pi$
$479$	16.6440	+	28.8282i	0.760483	+	1.31720i	−0.182119	+	0.983277i	$0.558296\pi$
$480$		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	$0.181034\pi$
$487$			23.7703i			1.07713i	−0.842583	+	0.538566i	$0.818966\pi$
$488$	−5.35447	+	3.09140i	−0.242385	+	0.139941i
$489$		0			0
$490$		0			0
$491$	−2.30281	+	3.98859i	−0.103925	+	0.180003i	−0.913298	−	0.407291i	$-0.866473\pi$
$491$	−2.30281	+	3.98859i	−0.103925	+	0.180003i	0.809374	+	0.587294i	$0.199807\pi$
$492$		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	−0.996230	−	0.0867522i	$-0.972351\pi$
$499$	−9.44878	+	16.3658i	−0.422985	+	0.732632i	0.573245	+	0.819384i	$0.305684\pi$
$500$		0			0
$501$		0			0
$502$	−9.81962	+	5.66936i	−0.438271	+	0.253036i
$503$			35.7581i			1.59438i	0.603731	+	0.797188i	$0.293680\pi$
$503$			35.7581i			1.59438i	−0.603731	+	0.797188i	$0.706320\pi$
$504$		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	0.457948	+	0.888979i	$0.348585\pi$
$509$	−12.2034	+	21.1368i	−0.540904	+	0.936874i	−0.998852	+	0.0478949i	$0.984749\pi$
$510$		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	$0.304330\pi$
$523$			37.3654i			1.63388i	−0.576726	+	0.816938i	$0.695670\pi$
$524$	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	−0.996905	−	0.0786172i	$-0.974950\pi$
$547$	−33.3811	+	19.2726i	−1.42727	+	0.824036i	−0.430368	+	0.902654i	$0.641616\pi$
$548$			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	$0.197242\pi$
$557$			27.4125i			1.16151i	−0.814080	+	0.580753i	$0.802758\pi$
$558$		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	0.910838	−	0.412764i	$-0.135437\pi$
$563$	23.9363	+	13.8196i	1.00879	+	0.582427i	0.0979551	+	0.995191i	$0.468770\pi$
$564$		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	0.978027	−	0.208478i	$-0.0668509\pi$
$569$	7.35807	+	12.7446i	0.308467	+	0.534280i	−0.669561	+	0.742757i	$0.733518\pi$
$570$		0			0
$571$	14.1503	−	24.5090i	0.592172	−	1.02567i	−0.401768	−	0.915742i	$-0.631604\pi$
$571$	14.1503	−	24.5090i	0.592172	−	1.02567i	0.993939	−	0.109930i	$-0.0350627\pi$
$572$	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	$-0.677076\pi$
$577$		−	40.7976i		−	1.69843i	0.528049	−	0.849214i	$-0.322924\pi$
$578$	−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	−0.548867	−	0.835910i	$-0.684941\pi$
$587$	−2.40784	+	1.39016i	−0.0993820	+	0.0573782i	0.449485	+	0.893288i	$0.351607\pi$
$588$		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	$-0.901659\pi$
$593$		−	14.8084i		−	0.608109i	0.952655	−	0.304055i	$-0.0983405\pi$
$594$		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	−0.649390	−	0.760456i	$-0.724976\pi$
$599$	8.17151	−	14.1535i	0.333879	−	0.578295i	0.983269	+	0.182160i	$0.0583090\pi$
$600$		0			0
$601$	3.31185	+	5.73630i	0.135093	+	0.233988i	0.925633	−	0.378422i	$-0.123533\pi$
$601$	3.31185	+	5.73630i	0.135093	+	0.233988i	−0.790540	+	0.612411i	$0.790200\pi$
$602$			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	−0.138480	−	0.990365i	$-0.544222\pi$
$607$	−26.2487	−	15.1547i	−1.06540	−	0.615110i	−0.926921	+	0.375256i	$0.877555\pi$
$608$	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	$-0.903519\pi$
$613$		−	14.7803i		−	0.596969i	0.954415	−	0.298484i	$-0.0964811\pi$
$614$	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	$-0.571961\pi$
$617$	−29.3160	−	16.9256i	−1.18022	−	0.681399i	−0.956065	+	0.293155i	$0.905295\pi$
$618$		0			0
$619$	5.84433	+	10.1227i	0.234903	+	0.406865i	0.959245	−	0.282577i	$-0.0911893\pi$
$619$	5.84433	+	10.1227i	0.234903	+	0.406865i	−0.724341	+	0.689442i	$0.757856\pi$
$620$		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	−0.972939	−	0.231063i	$-0.925780\pi$
$641$	−17.3827	−	30.1077i	−0.686576	−	1.18918i	0.286363	−	0.958121i	$-0.407554\pi$
$642$		0			0
$643$	2.32541	+	1.34258i	0.0917053	+	0.0529461i	0.545151	−	0.838338i	$-0.316472\pi$
$643$	2.32541	+	1.34258i	0.0917053	+	0.0529461i	−0.453446	+	0.891284i	$0.649806\pi$
$644$	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	$-0.293218\pi$
$648$		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	0.256709	−	0.966489i	$-0.417362\pi$
$653$	−11.5488	−	6.66772i	−0.451941	−	0.260928i	−0.708650	+	0.705561i	$0.750695\pi$
$654$		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	−0.991764	−	0.128077i	$-0.959120\pi$
$659$	−15.5772	−	26.9804i	−0.606800	−	1.05101i	0.384965	−	0.922931i	$-0.374214\pi$
$660$		0			0
$661$	−3.15894	+	5.47145i	−0.122869	+	0.212815i	−0.920898	−	0.389804i	$-0.872543\pi$
$661$	−3.15894	+	5.47145i	−0.122869	+	0.212815i	0.798029	+	0.602619i	$0.205876\pi$
$662$	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	−0.385915	−	0.922534i	$-0.626114\pi$
$673$	5.70901	−	3.29610i	0.220066	−	0.127055i	0.605981	+	0.795479i	$0.292781\pi$
$674$	−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	$-0.900611\pi$
$677$	−30.2197	+	17.4473i	−1.16144	+	0.670556i	−0.209788	+	0.977747i	$0.567278\pi$
$678$		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	$0.166396\pi$
$683$			26.0958i			0.998528i	−0.866450	+	0.499264i	$0.833604\pi$
$684$		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	0.997711	+	0.0676282i	$0.0215432\pi$
$691$	14.6529	+	25.3796i	0.557423	+	0.965485i	−0.440288	+	0.897857i	$0.645124\pi$
$692$			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	0.784160	−	0.620558i	$-0.213094\pi$
$709$	−3.86996	−	6.70296i	−0.145339	−	0.251735i	−0.929499	+	0.368823i	$0.879761\pi$
$710$		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	−0.497398	−	0.867522i	$-0.665711\pi$
$727$	0.140189	−	0.0809381i	0.00519932	−	0.00300183i	0.502597	+	0.864521i	$0.332378\pi$
$728$		−	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	−0.991401	−	0.130861i	$-0.958226\pi$
$733$	−43.3300	−	25.0166i	−1.60043	−	0.924009i	−0.609029	−	0.793148i	$-0.708441\pi$
$734$	−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	0.402209	−	0.915548i	$-0.368243\pi$
$743$	−5.16743	−	2.98342i	−0.189575	−	0.109451i	−0.591783	+	0.806097i	$0.701576\pi$
$744$		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	0.360441	+	0.932782i	$0.382626\pi$
$751$	−17.1988	+	29.7892i	−0.627593	+	1.08702i	−0.988033	+	0.154240i	$0.950707\pi$
$752$	−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	$0.264892\pi$
$757$			40.6873i			1.47881i	−0.673263	+	0.739403i	$0.735108\pi$
$758$	40.3997	−	23.3248i	1.46738	−	0.847194i
$759$		0			0
$760$		0			0
$761$	14.1298	−	24.4735i	0.512204	−	0.887164i	−0.487696	−	0.873014i	$-0.662162\pi$
$761$	14.1298	−	24.4735i	0.512204	−	0.887164i	0.999900	−	0.0141502i	$-0.00450429\pi$
$762$		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	0.0393235	+	0.999227i	$0.487480\pi$
$769$	−23.4518	+	40.6197i	−0.845694	+	1.46478i	−0.885017	+	0.465558i	$0.845854\pi$
$770$		0			0
$771$		0			0
$772$	−5.53894	+	3.19791i	−0.199351	+	0.115095i
$773$			9.19641i			0.330772i	0.986229	+	0.165386i	$0.0528870\pi$
$773$			9.19641i			0.330772i	−0.986229	+	0.165386i	$0.947113\pi$
$774$		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	0.408674	−	0.912680i	$-0.365991\pi$
$787$	−4.97651	−	2.87319i	−0.177393	−	0.102418i	−0.586067	+	0.810262i	$0.699325\pi$
$788$	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	0.387550	−	0.921849i	$-0.373321\pi$
$797$	−6.12670	−	3.53725i	−0.217019	−	0.125296i	−0.604569	+	0.796553i	$0.706655\pi$
$798$		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	0.992828	−	0.119555i	$-0.0381467\pi$
$821$	11.2571	+	19.4979i	0.392876	+	0.680482i	−0.599951	+	0.800037i	$0.704813\pi$
$822$		0			0
$823$	−35.9045	−	20.7295i	−1.25155	−	0.722583i	−0.280134	−	0.959961i	$-0.590379\pi$
$823$	−35.9045	−	20.7295i	−1.25155	−	0.722583i	−0.971417	+	0.237378i	$0.923712\pi$
$824$	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	$-0.160664\pi$
$828$		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	0.665839	−	0.746096i	$-0.268074\pi$
$839$	−9.07253	−	15.7141i	−0.313218	−	0.542510i	−0.979057	+	0.203585i	$0.934741\pi$
$840$		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	−0.439413	−	0.898285i	$-0.644813\pi$
$853$	3.47023	−	2.00354i	0.118819	−	0.0685999i	0.558231	+	0.829685i	$0.311480\pi$
$854$	−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	$-0.617049\pi$
$857$	7.87192	−	4.54485i	0.268900	−	0.155249i	0.628387	+	0.777901i	$0.283715\pi$
$858$		0			0
$859$	8.19348	−	14.1915i	0.279558	−	0.484208i	−0.691717	−	0.722169i	$-0.743145\pi$
$859$	8.19348	−	14.1915i	0.279558	−	0.484208i	0.971275	+	0.237960i	$0.0764788\pi$
$860$		0			0
$861$		0			0
$862$	52.8486	−	30.5122i	1.80003	−	1.03925i
$863$			23.7967i			0.810050i	0.914306	+	0.405025i	$0.132737\pi$
$863$			23.7967i			0.810050i	−0.914306	+	0.405025i	$0.867263\pi$
$864$		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	−0.130916	−	0.991394i	$-0.541792\pi$
$877$	−31.2413	−	18.0372i	−1.05495	−	0.609073i	−0.924030	+	0.382321i	$0.875125\pi$
$878$	−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	$0.228787\pi$
$883$			39.1320i			1.31690i	−0.752626	+	0.658448i	$0.771213\pi$
$884$	−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	$-0.00319595\pi$
$887$	44.4126	+	25.6416i	1.49123	+	0.860962i	0.491280	+	0.871002i	$0.336529\pi$
$888$		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	0.384522	−	0.923116i	$-0.374366\pi$
$907$	41.4470	−	23.9294i	1.37622	−	0.794563i	0.991703	+	0.128552i	$0.0410331\pi$
$908$			8.56930i			0.284382i
$909$		0			0
$910$		0			0
$911$	9.02153	+	15.6258i	0.298897	+	0.517704i	0.975884	−	0.218291i	$-0.0700481\pi$
$911$	9.02153	+	15.6258i	0.298897	+	0.517704i	−0.676987	+	0.735995i	$0.736715\pi$
$912$		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	0.994109	+	0.108381i	$0.0345665\pi$
$929$	18.0108	+	31.1956i	0.590915	+	1.02349i	−0.403194	+	0.915114i	$0.632100\pi$
$930$		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	$0.128409\pi$
$937$			24.0326i			0.785111i	−0.919728	+	0.392555i	$0.871591\pi$
$938$	−1.72064	+	0.993410i	−0.0561808	+	0.0324360i
$939$		0			0
$940$		0			0
$941$	8.33380	−	14.4346i	0.271674	−	0.470553i	−0.697616	−	0.716471i	$-0.745756\pi$
$941$	8.33380	−	14.4346i	0.271674	−	0.470553i	0.969291	+	0.245918i	$0.0790894\pi$
$942$		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	−0.0596355	−	0.998220i	$-0.518994\pi$
$947$	23.8503	−	13.7700i	0.775031	−	0.447464i	0.834666	+	0.550756i	$0.185661\pi$
$948$		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	$-0.905108\pi$
$953$		−	18.1344i		−	0.587432i	0.955893	−	0.293716i	$-0.0948920\pi$
$954$		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	−0.0972552	−	0.995259i	$-0.531006\pi$
$967$	−31.3393	−	18.0937i	−1.00780	−	0.581855i	−0.910548	+	0.413404i	$0.864340\pi$
$968$	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	0.0333671	−	0.999443i	$-0.489377\pi$
$977$	−25.4898	−	14.7166i	−0.815492	−	0.470825i	−0.848860	+	0.528618i	$0.822710\pi$
$978$		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	−0.122040	−	0.992525i	$-0.538944\pi$
$983$	21.2099	−	12.2456i	0.676492	−	0.390573i	0.798532	+	0.601953i	$0.205610\pi$
$984$		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	0.144627	−	0.989486i	$-0.453802\pi$
$997$	33.9075	−	19.5765i	1.07386	−	0.619994i	0.929234	+	0.369492i	$0.120468\pi$
$998$			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.199.7		16
3.2	odd	2		225.2.k.c.49.2		16
5.2	odd	4		675.2.e.c.226.4		8
5.3	odd	4		675.2.e.e.226.1		8
5.4	even	2	inner	675.2.k.c.199.2		16
9.2	odd	6		225.2.k.c.124.7		16
9.4	even	3		2025.2.b.o.649.7		8
9.5	odd	6		2025.2.b.n.649.2		8
9.7	even	3	inner	675.2.k.c.424.2		16
15.2	even	4		225.2.e.e.76.1	yes	8
15.8	even	4		225.2.e.c.76.4	✓	8
15.14	odd	2		225.2.k.c.49.7		16
45.2	even	12		225.2.e.e.151.1	yes	8
45.4	even	6		2025.2.b.o.649.2		8
45.7	odd	12		675.2.e.c.451.4		8
45.13	odd	12		2025.2.a.p.1.4		4
45.14	odd	6		2025.2.b.n.649.7		8
45.22	odd	12		2025.2.a.z.1.1		4
45.23	even	12		2025.2.a.y.1.1		4
45.29	odd	6		225.2.k.c.124.2		16
45.32	even	12		2025.2.a.q.1.4		4
45.34	even	6	inner	675.2.k.c.424.7		16
45.38	even	12		225.2.e.c.151.4	yes	8
45.43	odd	12		675.2.e.e.451.1		8

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

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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