LMFDB - Embedded newform 225.2.k.b.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.1
Root			$-0.180407 - 0.673288i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.17731 - 1.25707i) q^{2} +(1.19154 - 1.25707i) q^{3} +(2.16044 + 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(0.445256 + 0.257068i) q^{7} -5.83502i q^{8} +(-0.160442 - 2.99571i) q^{9} +(1.66044 - 2.87597i) q^{11} +(7.27821 + 1.74293i) q^{12} +(1.14392 - 0.660442i) q^{13} +(-0.646305 - 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} -3.32088i q^{17} +(-3.41648 + 6.72426i) q^{18} +1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(-7.23058 + 4.17458i) q^{22} +(-3.57463 + 2.06382i) q^{23} +(-7.33502 - 6.95269i) q^{24} -3.32088 q^{26} +(-3.95698 - 3.36783i) q^{27} +2.22153i q^{28} +(-0.693252 + 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(3.01885 - 1.74293i) q^{32} +(-1.63680 - 5.51414i) q^{33} +(-4.17458 + 7.23058i) q^{34} +(10.8633 - 7.07243i) q^{36} +0.292611i q^{37} +(-2.87597 - 1.66044i) q^{38} +(0.532810 - 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(-2.17731 - 0.521405i) q^{42} +(8.96263 + 5.17458i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(4.21174 + 2.43165i) q^{47} +(2.97122 + 10.0096i) q^{48} +(-3.36783 - 5.83326i) q^{49} +(-4.17458 - 3.95698i) q^{51} +(4.94274 + 2.85369i) q^{52} +5.02827i q^{53} +(4.38197 + 12.3070i) q^{54} +(1.50000 - 2.59808i) q^{56} +(1.57389 - 1.66044i) q^{57} +(3.01885 - 1.74293i) q^{58} +(-2.51414 - 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +21.9627i q^{62} +(0.698664 - 1.37510i) q^{63} +3.29261 q^{64} +(-3.36783 + 14.0635i) q^{66} +(8.18266 - 4.72426i) q^{67} +(12.4267 - 7.17458i) q^{68} +(-1.66498 + 6.95269i) q^{69} +8.99093 q^{71} +(-17.4800 + 0.936184i) q^{72} -6.05655i q^{73} +(0.367832 - 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(1.47864 - 0.853695i) q^{77} +(-3.95698 + 4.17458i) q^{78} +(-4.02827 + 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} -28.5333i q^{82} +(1.33577 + 0.771205i) q^{83} +(2.79261 + 2.64705i) q^{84} +(-13.0096 - 22.5333i) q^{86} +(0.683382 + 2.30221i) q^{87} +(-16.7813 - 9.68872i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(-15.4456 - 8.91751i) q^{92} +(-14.7146 - 3.52374i) q^{93} +(-6.11350 - 10.5889i) q^{94} +(1.40611 - 5.87168i) q^{96} +(10.6134 + 6.12763i) q^{97} +16.9344i q^{98} +(-8.88197 - 4.51277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46}+ \cdots - 44 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−2.17731	−	1.25707i	−1.53959	−	0.888882i	−0.998863	−	0.0476826i	$-0.984816\pi$
$2$	−2.17731	−	1.25707i	−1.53959	−	0.888882i	−0.540726	−	0.841199i	$-0.681850\pi$
$3$	1.19154	−	1.25707i	0.687939	−	0.725769i
$3$	1.19154	−	1.25707i	0.687939	−	0.725769i
$4$	2.16044	+	3.74200i	1.08022	+	1.87100i
$5$		0			0
$5$		0			0
$6$	−4.17458	+	1.23917i	−1.70426	+	0.505889i
$7$	0.445256	+	0.257068i	0.168291	+	0.0971627i	0.581780	−	0.813346i	$-0.302357\pi$
$7$	0.445256	+	0.257068i	0.168291	+	0.0971627i	−0.413489	+	0.910509i	$0.635690\pi$
$8$		−	5.83502i		−	2.06299i
$9$	−0.160442	−	2.99571i	−0.0534807	−	0.998569i
$10$		0			0
$11$	1.66044	−	2.87597i	0.500642	−	0.867138i	−0.499358	−	0.866396i	$-0.666431\pi$
$11$	1.66044	−	2.87597i	0.500642	−	0.867138i	1.00000		0.000741679i	$-0.000236084\pi$
$12$	7.27821	+	1.74293i	2.10104	+	0.503141i
$13$	1.14392	−	0.660442i	0.317266	−	0.183174i	−0.332907	−	0.942960i	$-0.608030\pi$
$13$	1.14392	−	0.660442i	0.317266	−	0.183174i	0.650173	+	0.759786i	$0.274696\pi$
$14$	−0.646305	−	1.11943i	−0.172732	−	0.299181i
$15$		0			0
$16$	−3.01414	+	5.22064i	−0.753534	+	1.30516i
$17$		−	3.32088i		−	0.805433i	−0.915325	−	0.402716i	$-0.868066\pi$
$17$		−	3.32088i		−	0.805433i	0.915325	−	0.402716i	$-0.131934\pi$
$18$	−3.41648	+	6.72426i	−0.805271	+	1.58492i
$19$	1.32088			0.303032			0.151516	−	0.988455i	$-0.451585\pi$
$19$	1.32088			0.303032			0.151516	+	0.988455i	$0.451585\pi$
$20$		0			0
$21$	0.853695	−	0.253408i	0.186291	−	0.0552982i
$22$	−7.23058	+	4.17458i	−1.54157	+	0.890023i
$23$	−3.57463	+	2.06382i	−0.745363	+	0.430335i	−0.824016	−	0.566567i	$-0.808271\pi$
$23$	−3.57463	+	2.06382i	−0.745363	+	0.430335i	0.0786532	+	0.996902i	$0.474938\pi$
$24$	−7.33502	−	6.95269i	−1.49725	−	1.41921i
$25$		0			0
$26$	−3.32088			−0.651279
$27$	−3.95698	−	3.36783i	−0.761522	−	0.648139i
$28$			2.22153i			0.419829i
$29$	−0.693252	+	1.20075i	−0.128734	+	0.222973i	−0.923186	−	0.384353i	$-0.874425\pi$
$29$	−0.693252	+	1.20075i	−0.128734	+	0.222973i	0.794453	+	0.607326i	$0.207758\pi$
$30$		0			0
$31$	−4.36783	−	7.56531i	−0.784486	−	1.35877i	−0.929306	−	0.369311i	$-0.879594\pi$
$31$	−4.36783	−	7.56531i	−0.784486	−	1.35877i	0.144820	−	0.989458i	$-0.453740\pi$
$32$	3.01885	−	1.74293i	0.533662	−	0.308110i
$33$	−1.63680	−	5.51414i	−0.284930	−	0.959888i
$34$	−4.17458	+	7.23058i	−0.715934	+	1.24003i
$35$		0			0
$36$	10.8633	−	7.07243i	1.81055	−	1.17874i
$37$			0.292611i			0.0481049i	0.999711	+	0.0240524i	$0.00765687\pi$
$37$			0.292611i			0.0481049i	−0.999711	+	0.0240524i	$0.992343\pi$
$38$	−2.87597	−	1.66044i	−0.466544	−	0.269359i
$39$	0.532810	−	2.22493i	0.0853179	−	0.356274i
$40$		0			0
$41$	5.67458	+	9.82866i	0.886220	+	1.53498i	0.844308	+	0.535857i	$0.180012\pi$
$41$	5.67458	+	9.82866i	0.886220	+	1.53498i	0.0419119	+	0.999121i	$0.486655\pi$
$42$	−2.17731	−	0.521405i	−0.335966	−	0.0804546i
$43$	8.96263	+	5.17458i	1.36679	+	0.789116i	0.990517	−	0.137393i	$-0.0438724\pi$
$43$	8.96263	+	5.17458i	1.36679	+	0.789116i	0.376272	+	0.926509i	$0.377206\pi$
$44$	14.3492			2.16322
$45$		0			0
$46$	10.3774			1.53007
$47$	4.21174	+	2.43165i	0.614345	+	0.354692i	0.774664	−	0.632373i	$-0.217919\pi$
$47$	4.21174	+	2.43165i	0.614345	+	0.354692i	−0.160319	+	0.987065i	$0.551252\pi$
$48$	2.97122	+	10.0096i	0.428859	+	1.44476i
$49$	−3.36783	−	5.83326i	−0.481119	−	0.833322i
$50$		0			0
$51$	−4.17458	−	3.95698i	−0.584558	−	0.554088i
$52$	4.94274	+	2.85369i	0.685435	+	0.395736i
$53$			5.02827i			0.690687i	0.938476	+	0.345343i	$0.112238\pi$
$53$			5.02827i			0.690687i	−0.938476	+	0.345343i	$0.887762\pi$
$54$	4.38197	+	12.3070i	0.596310	+	1.67477i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	1.57389	−	1.66044i	0.208467	−	0.219931i
$58$	3.01885	−	1.74293i	0.396394	−	0.228858i
$59$	−2.51414	−	4.35461i	−0.327313	−	0.566922i	0.654665	−	0.755919i	$-0.272810\pi$
$59$	−2.51414	−	4.35461i	−0.327313	−	0.566922i	−0.981978	+	0.188997i	$0.939476\pi$
$60$		0			0
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	−0.999430	−	0.0337558i	$-0.989253\pi$
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	0.528948	+	0.848654i	$0.322586\pi$
$62$			21.9627i			2.78926i
$63$	0.698664	−	1.37510i	0.0880234	−	0.173246i
$64$	3.29261			0.411576
$65$		0			0
$66$	−3.36783	+	14.0635i	−0.414551	+	1.73110i
$67$	8.18266	−	4.72426i	0.999670	−	0.577160i	0.0915197	−	0.995803i	$-0.470828\pi$
$67$	8.18266	−	4.72426i	0.999670	−	0.577160i	0.908151	+	0.418643i	$0.137494\pi$
$68$	12.4267	−	7.17458i	1.50696	−	0.870046i
$69$	−1.66498	+	6.95269i	−0.200440	+	0.837005i
$70$		0			0
$71$	8.99093			1.06703			0.533513	−	0.845792i	$-0.320871\pi$
$71$	8.99093			1.06703			0.533513	+	0.845792i	$0.320871\pi$
$72$	−17.4800	+	0.936184i	−2.06004	+	0.110330i
$73$		−	6.05655i		−	0.708865i	−0.935082	−	0.354433i	$-0.884674\pi$
$73$		−	6.05655i		−	0.708865i	0.935082	−	0.354433i	$-0.115326\pi$
$74$	0.367832	−	0.637103i	0.0427596	−	0.0740617i
$75$		0			0
$76$	2.85369	+	4.94274i	0.327341	+	0.566972i
$77$	1.47864	−	0.853695i	0.168507	−	0.0972875i
$78$	−3.95698	+	4.17458i	−0.448040	+	0.472678i
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	−0.998584	−	0.0532036i	$-0.983057\pi$
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	0.545367	+	0.838197i	$0.316390\pi$
$80$		0			0
$81$	−8.94852	+	0.961276i	−0.994280	+	0.106808i
$82$		−	28.5333i		−	3.15098i
$83$	1.33577	+	0.771205i	0.146619	+	0.0846508i	0.571515	−	0.820592i	$-0.306356\pi$
$83$	1.33577	+	0.771205i	0.146619	+	0.0846508i	−0.424896	+	0.905242i	$0.639689\pi$
$84$	2.79261	+	2.64705i	0.304699	+	0.288817i
$85$		0			0
$86$	−13.0096	−	22.5333i	−1.40286	−	2.42983i
$87$	0.683382	+	2.30221i	0.0732662	+	0.246823i
$88$	−16.7813	−	9.68872i	−1.78890	−	1.03282i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	0.679116			0.0711906
$92$	−15.4456	−	8.91751i	−1.61031	−	0.929715i
$93$	−14.7146	−	3.52374i	−1.52583	−	0.365395i
$94$	−6.11350	−	10.5889i	−0.630559	−	1.09216i
$95$		0			0
$96$	1.40611	−	5.87168i	0.143510	−	0.599276i
$97$	10.6134	+	6.12763i	1.07762	+	0.622167i	0.930255	−	0.366915i	$-0.119586\pi$
$97$	10.6134	+	6.12763i	1.07762	+	0.622167i	0.147370	+	0.989081i	$0.452919\pi$
$98$			16.9344i			1.71063i
$99$	−8.88197	−	4.51277i	−0.892671	−	0.453551i
$100$		0			0
$101$	−5.83502	+	10.1066i	−0.580606	+	1.00564i	0.414801	+	0.909912i	$0.363851\pi$
$101$	−5.83502	+	10.1066i	−0.580606	+	1.00564i	−0.995408	+	0.0957276i	$0.969482\pi$
$102$	4.11514	+	13.8633i	0.407460	+	1.37267i
$103$	−0.253408	+	0.146305i	−0.0249691	+	0.0144159i	−0.512433	−	0.858727i	$-0.671256\pi$
$103$	−0.253408	+	0.146305i	−0.0249691	+	0.0144159i	0.487464	+	0.873143i	$0.337922\pi$
$104$	−3.85369	−	6.67479i	−0.377886	−	0.654517i
$105$		0			0
$106$	6.32088	−	10.9481i	0.613939	−	1.06337i
$107$			1.87237i			0.181009i	0.995896	+	0.0905043i	$0.0288479\pi$
$107$			1.87237i			0.181009i	−0.995896	+	0.0905043i	$0.971152\pi$
$108$	4.05358	−	22.0830i	0.390056	−	2.12494i
$109$	−5.54787			−0.531390			−0.265695	−	0.964057i	$-0.585601\pi$
$109$	−5.54787			−0.531390			−0.265695	+	0.964057i	$0.585601\pi$
$110$		0			0
$111$	0.367832	+	0.348659i	0.0349130	+	0.0330932i
$112$	−2.68412	+	1.54968i	−0.253626	+	0.146431i
$113$	−6.75611	+	3.90064i	−0.635561	+	0.366942i	−0.782903	−	0.622144i	$-0.786262\pi$
$113$	−6.75611	+	3.90064i	−0.635561	+	0.366942i	0.147341	+	0.989086i	$0.452928\pi$
$114$	−5.51414	+	1.63680i	−0.516446	+	0.153300i
$115$		0			0
$116$	−5.99093			−0.556244
$117$	−2.16202	−	3.32088i	−0.199879	−	0.307016i
$118$			12.6418i			1.16377i
$119$	0.853695	−	1.47864i	0.0782581	−	0.135547i
$120$		0			0
$121$	−0.0141369	−	0.0244859i	−0.00128518	−	0.00222599i
$122$	16.0014	−	9.23840i	1.44870	−	0.836405i
$123$	19.1168	+	4.57795i	1.72370	+	0.412780i
$124$	18.8729	−	32.6888i	1.69484	−	2.93554i
$125$		0			0
$126$	−3.24980	+	2.11575i	−0.289515	+	0.188486i
$127$			17.8916i			1.58762i	0.608166	+	0.793810i	$0.291906\pi$
$127$			17.8916i			1.58762i	−0.608166	+	0.793810i	$0.708094\pi$
$128$	−13.2067	−	7.62490i	−1.16732	−	0.673952i
$129$	17.1842	−	5.10090i	1.51298	−	0.449109i
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	17.0977	−	18.0379i	1.48816	−	1.57000i
$133$	0.588131	+	0.339558i	0.0509974	+	0.0294434i
$134$	−23.7549			−2.05211
$135$		0			0
$136$	−19.3774			−1.66160
$137$	−4.91040	−	2.83502i	−0.419524	−	0.242212i	0.275350	−	0.961344i	$-0.411206\pi$
$137$	−4.91040	−	2.83502i	−0.419524	−	0.242212i	−0.694874	+	0.719132i	$0.744540\pi$
$138$	12.3652	−	13.0451i	1.05259	−	1.11048i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	8.07522	−	2.39703i	0.680056	−	0.201866i
$142$	−19.5760	−	11.3022i	−1.64278	−	0.948460i
$143$		−	4.38650i		−	0.366818i
$144$	16.1231	+	8.19186i	1.34359	+	0.682655i
$145$		0			0
$146$	−7.61350	+	13.1870i	−0.630097	+	1.09136i
$147$	−11.3457	−	2.71699i	−0.935780	−	0.224094i
$148$	−1.09495	+	0.632168i	−0.0900042	+	0.0519639i
$149$	8.83049	+	15.2948i	0.723422	+	1.25300i	0.959620	+	0.281298i	$0.0907650\pi$
$149$	8.83049	+	15.2948i	0.723422	+	1.25300i	−0.236199	+	0.971705i	$0.575902\pi$
$150$		0			0
$151$	−0.632168	+	1.09495i	−0.0514451	+	0.0891056i	−0.890601	−	0.454785i	$-0.849716\pi$
$151$	−0.632168	+	1.09495i	−0.0514451	+	0.0891056i	0.839156	+	0.543891i	$0.183049\pi$
$152$		−	7.70739i		−	0.625152i
$153$	−9.94840	+	0.532810i	−0.804280	+	0.0430752i
$154$	−4.29261			−0.345908
$155$		0			0
$156$	9.47679	−	2.81306i	0.758750	−	0.225225i
$157$	−13.5707	+	7.83502i	−1.08306	+	0.625303i	−0.931719	−	0.363179i	$-0.881691\pi$
$157$	−13.5707	+	7.83502i	−1.08306	+	0.625303i	−0.151337	+	0.988482i	$0.548358\pi$
$158$	17.5416	−	10.1276i	1.39553	−	0.805711i
$159$	6.32088	+	5.99141i	0.501279	+	0.475150i
$160$		0			0
$161$	−2.12217			−0.167250
$162$	20.6921	+	9.15591i	1.62572	+	0.719356i
$163$		−	15.7074i		−	1.23030i	−0.788411	−	0.615149i	$-0.789096\pi$
$163$		−	15.7074i		−	1.23030i	0.788411	−	0.615149i	$-0.210904\pi$
$164$	−24.5192	+	42.4685i	−1.91463	+	3.31623i
$165$		0			0
$166$	−1.93892	−	3.35830i	−0.150489	−	0.260655i
$167$	5.33903	−	3.08249i	0.413146	−	0.238530i	−0.278994	−	0.960293i	$-0.590001\pi$
$167$	5.33903	−	3.08249i	0.413146	−	0.238530i	0.692141	+	0.721763i	$0.256668\pi$
$168$	−1.47864	−	4.98133i	−0.114080	−	0.384318i
$169$	−5.62763	+	9.74734i	−0.432895	+	0.749796i
$170$		0			0
$171$	−0.211926	−	3.95698i	−0.0162064	−	0.302598i
$172$			44.7175i			3.40968i
$173$	7.43502	+	4.29261i	0.565274	+	0.326361i	0.755260	−	0.655426i	$-0.227511\pi$
$173$	7.43502	+	4.29261i	0.565274	+	0.326361i	−0.189986	+	0.981787i	$0.560844\pi$
$174$	1.40611	−	5.87168i	0.106597	−	0.445131i
$175$		0			0
$176$	10.0096	+	17.3371i	0.754502	+	1.30684i
$177$	−8.46975	−	2.02827i	−0.636626	−	0.152454i
$178$	−6.53192	−	3.77121i	−0.489588	−	0.282664i
$179$	1.06562			0.0796482			0.0398241	−	0.999207i	$-0.487320\pi$
$179$	1.06562			0.0796482			0.0398241	+	0.999207i	$0.487320\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$	−1.47864	−	0.853695i	−0.109604	−	0.0632801i
$183$	3.62226	+	12.2029i	0.267765	+	0.902061i
$184$	12.0424	+	20.8581i	0.887778	+	1.53768i
$185$		0			0
$186$	27.6086	+	26.1695i	2.02436	+	1.91884i
$187$	−9.55077	−	5.51414i	−0.698421	−	0.403234i
$188$			21.0137i			1.53258i
$189$	−0.896105	−	2.51676i	−0.0651821	−	0.183067i
$190$		0			0
$191$	8.46719	−	14.6656i	0.612664	−	1.06117i	−0.378125	−	0.925754i	$-0.623431\pi$
$191$	8.46719	−	14.6656i	0.612664	−	1.06117i	0.990789	−	0.135411i	$-0.0432356\pi$
$192$	3.92329	−	4.13904i	0.283139	−	0.298709i
$193$	−23.1380	+	13.3588i	−1.66551	+	0.961585i	−0.695502	+	0.718524i	$0.744818\pi$
$193$	−23.1380	+	13.3588i	−1.66551	+	0.961585i	−0.970011	+	0.243060i	$0.921849\pi$
$194$	−15.4057	−	26.6835i	−1.10607	−	1.91576i
$195$		0			0
$196$	14.5520	−	25.2048i	1.03943	−	1.80034i
$197$		−	14.2553i		−	1.01565i	−0.861462	−	0.507823i	$-0.830450\pi$
$197$		−	14.2553i		−	1.01565i	0.861462	−	0.507823i	$-0.169550\pi$
$198$	13.6659	+	20.9909i	0.971194	+	1.49176i
$199$	24.6610			1.74817			0.874085	−	0.485773i	$-0.161462\pi$
$199$	24.6610			1.74817			0.874085	+	0.485773i	$0.161462\pi$
$200$		0			0
$201$	3.81128	−	15.9153i	0.268827	−	1.12258i
$202$	25.4093	−	14.6700i	1.78779	−	1.03218i
$203$	−0.617349	+	0.356427i	−0.0433294	+	0.0250162i
$204$	5.78807	−	24.1701i	0.405246	−	1.69224i
$205$		0			0
$206$	0.735663			0.0512561
$207$	6.75611	+	10.3774i	0.469582	+	0.721281i
$208$			7.96265i			0.552111i
$209$	2.19325	−	3.79882i	0.151710	−	0.262770i
$210$		0			0
$211$	2.68872	+	4.65699i	0.185099	+	0.320601i	0.943610	−	0.331060i	$-0.107406\pi$
$211$	2.68872	+	4.65699i	0.185099	+	0.320601i	−0.758511	+	0.651660i	$0.774073\pi$
$212$	−18.8158	+	10.8633i	−1.29227	+	0.746094i
$213$	10.7131	−	11.3022i	0.734049	−	0.774415i
$214$	2.35369	−	4.07672i	0.160895	−	0.278679i
$215$		0			0
$216$	−19.6514	+	23.0891i	−1.33711	+	1.57101i
$217$		−	4.49133i		−	0.304891i
$218$	12.0794	+	6.97406i	0.818122	+	0.472343i
$219$	−7.61350	−	7.21665i	−0.514472	−	0.487656i
$220$		0			0
$221$	−2.19325	−	3.79882i	−0.147534	−	0.255537i
$222$	−0.362594	−	1.22153i	−0.0243357	−	0.0819835i
$223$	7.50375	+	4.33229i	0.502488	+	0.290112i	0.729740	−	0.683724i	$-0.239641\pi$
$223$	7.50375	+	4.33229i	0.502488	+	0.290112i	−0.227252	+	0.973836i	$0.572974\pi$
$224$	1.79221			0.119747
$225$		0			0
$226$	19.6135			1.30467
$227$	−2.87597	−	1.66044i	−0.190885	−	0.110207i	0.401512	−	0.915854i	$-0.368485\pi$
$227$	−2.87597	−	1.66044i	−0.190885	−	0.110207i	−0.592397	+	0.805646i	$0.701818\pi$
$228$	9.61367	+	2.30221i	0.636681	+	0.152468i
$229$	−12.6559	−	21.9207i	−0.836326	−	1.44856i	−0.892946	−	0.450163i	$-0.851366\pi$
$229$	−12.6559	−	21.9207i	−0.836326	−	1.44856i	0.0566206	−	0.998396i	$-0.481967\pi$
$230$		0			0
$231$	0.688716	−	2.87597i	0.0453142	−	0.189225i
$232$	7.00639	+	4.04514i	0.459992	+	0.265577i
$233$		−	27.6327i		−	1.81028i	−0.425116	−	0.905139i	$-0.639767\pi$
$233$		−	27.6327i		−	1.81028i	0.425116	−	0.905139i	$-0.360233\pi$
$234$	0.532810	+	9.94840i	0.0348309	+	0.650347i
$235$		0			0
$236$	10.8633	−	18.8158i	0.707140	−	1.22480i
$237$	3.97092	+	13.3774i	0.257939	+	0.868958i
$238$	−3.71751	+	2.14631i	−0.240970	+	0.139124i
$239$	−2.09936	−	3.63620i	−0.135796	−	0.235206i	0.790105	−	0.612971i	$-0.210026\pi$
$239$	−2.09936	−	3.63620i	−0.135796	−	0.235206i	−0.925901	+	0.377765i	$0.876693\pi$
$240$		0			0
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	−0.918215	−	0.396082i	$-0.870370\pi$
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	0.802125	+	0.597157i	$0.203703\pi$
$242$			0.0710844i			0.00456948i
$243$	−9.45417	+	12.3943i	−0.606485	+	0.795095i
$244$	−31.7549			−2.03290
$245$		0			0
$246$	−35.8684	−	33.9987i	−2.28688	−	2.16768i
$247$	1.51099	−	0.872368i	0.0961417	−	0.0555074i
$248$	−44.1437	+	25.4864i	−2.80313	+	1.61839i
$249$	2.56108	−	0.760225i	0.162302	−	0.0481773i
$250$		0			0
$251$	−6.87783			−0.434125			−0.217062	−	0.976158i	$-0.569648\pi$
$251$	−6.87783			−0.434125			−0.217062	+	0.976158i	$0.569648\pi$
$252$	6.65504	−	0.356427i	0.419228	−	0.0224528i
$253$			13.7074i			0.861776i
$254$	22.4909	−	38.9554i	1.41121	−	2.44428i
$255$		0			0
$256$	15.8774	+	27.5005i	0.992340	+	1.71878i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$	−43.8274	−	10.4955i	−2.72858	−	0.653419i
$259$	−0.0752210	+	0.130287i	−0.00467400	+	0.00809561i
$260$		0			0
$261$	3.70832	+	1.88413i	0.229539	+	0.116625i
$262$		−	15.0848i		−	0.931943i
$263$	5.40059	+	3.11803i	0.333015	+	0.192266i	0.657179	−	0.753735i	$-0.271750\pi$
$263$	5.40059	+	3.11803i	0.333015	+	0.192266i	−0.324164	+	0.946001i	$0.605083\pi$
$264$	−32.1751	+	9.55077i	−1.98024	+	0.587809i
$265$		0			0
$266$	−0.853695	−	1.47864i	−0.0523434	−	0.0906614i
$267$	3.57463	−	3.77121i	0.218764	−	0.230794i
$268$	35.3563	+	20.4130i	2.15973	+	1.24692i
$269$	−9.92345			−0.605044			−0.302522	−	0.953142i	$-0.597828\pi$
$269$	−9.92345			−0.605044			−0.302522	+	0.953142i	$0.597828\pi$
$270$		0			0
$271$	6.60442			0.401190			0.200595	−	0.979674i	$-0.435712\pi$
$271$	6.60442			0.401190			0.200595	+	0.979674i	$0.435712\pi$
$272$	17.3371	+	10.0096i	1.05122	+	0.606921i
$273$	0.809197	−	0.853695i	0.0489748	−	0.0516680i
$274$	7.12763	+	12.3454i	0.430596	+	0.745814i
$275$		0			0
$276$	−29.6140	+	8.79054i	−1.78255	+	0.529128i
$277$	−19.6250	−	11.3305i	−1.17915	−	0.680783i	−0.223333	−	0.974742i	$-0.571694\pi$
$277$	−19.6250	−	11.3305i	−1.17915	−	0.680783i	−0.955818	+	0.293959i	$0.905027\pi$
$278$		−	20.1131i		−	1.20630i
$279$	−21.9627	+	14.2985i	−1.31487	+	0.856031i
$280$		0			0
$281$	7.77394	−	13.4649i	0.463754	−	0.803246i	−0.535390	−	0.844605i	$-0.679835\pi$
$281$	7.77394	−	13.4649i	0.463754	−	0.803246i	0.999144	+	0.0413590i	$0.0131687\pi$
$282$	−20.5955	−	4.93205i	−1.22644	−	0.293699i
$283$	−0.558913	+	0.322689i	−0.0332240	+	0.0191819i	−0.516520	−	0.856275i	$-0.672773\pi$
$283$	−0.558913	+	0.322689i	−0.0332240	+	0.0191819i	0.483296	+	0.875457i	$0.339439\pi$
$284$	19.4244	+	33.6440i	1.15262	+	1.99640i
$285$		0			0
$286$	−5.51414	+	9.55077i	−0.326058	+	0.564749i
$287$			5.83502i			0.344430i
$288$	−5.70566	−	8.76394i	−0.336209	−	0.516420i
$289$	5.97173			0.351278
$290$		0			0
$291$	20.3492	−	6.04039i	1.19289	−	0.354094i
$292$	22.6636	−	13.0848i	1.32629	−	0.765731i
$293$	1.19289	−	0.688716i	0.0696895	−	0.0402352i	−0.464750	−	0.885442i	$-0.653856\pi$
$293$	1.19289	−	0.688716i	0.0696895	−	0.0402352i	0.534440	+	0.845207i	$0.320523\pi$
$294$	21.2877	+	20.1781i	1.24152	+	1.17681i
$295$		0			0
$296$	1.70739			0.0992400
$297$	−16.2561	+	5.78807i	−0.943276	+	0.335858i
$298$		−	44.4021i		−	2.57214i
$299$	−2.72606	+	4.72168i	−0.157652	+	0.273062i
$300$		0			0
$301$	2.66044	+	4.60802i	0.153345	+	0.265602i
$302$	2.75285	−	1.58936i	0.158409	−	0.0914573i
$303$	5.75194	+	19.3774i	0.330440	+	1.11320i
$304$	−3.98133	+	6.89586i	−0.228345	+	0.395505i
$305$		0			0
$306$	22.3305	+	11.3457i	1.27655	+	0.648592i
$307$		−	7.98546i		−	0.455754i	−0.973690	−	0.227877i	$-0.926822\pi$
$307$		−	7.98546i		−	0.455754i	0.973690	−	0.227877i	$-0.0731785\pi$
$308$	6.38904	+	3.68872i	0.364050	+	0.210184i
$309$	−0.118031	+	0.492881i	−0.00671458	+	0.0280390i
$310$		0			0
$311$	−4.81635	−	8.34216i	−0.273110	−	0.473040i	0.696547	−	0.717512i	$-0.254719\pi$
$311$	−4.81635	−	8.34216i	−0.273110	−	0.473040i	−0.969657	+	0.244471i	$0.921386\pi$
$312$	−12.9825	−	3.10896i	−0.734991	−	0.176010i
$313$	−21.2496	−	12.2685i	−1.20110	−	0.693455i	−0.240300	−	0.970699i	$-0.577246\pi$
$313$	−21.2496	−	12.2685i	−1.20110	−	0.693455i	−0.960800	+	0.277244i	$0.910579\pi$
$314$	39.3966			2.22328
$315$		0			0
$316$	−34.8114			−1.95829
$317$	17.6229	+	10.1746i	0.989800	+	0.571461i	0.905215	−	0.424955i	$-0.139710\pi$
$317$	17.6229	+	10.1746i	0.989800	+	0.571461i	0.0845855	+	0.996416i	$0.473043\pi$
$318$	−6.23089	−	20.9909i	−0.349411	−	1.17711i
$319$	2.30221	+	3.98755i	0.128899	+	0.223260i
$320$		0			0
$321$	2.35369	+	2.23101i	0.131370	+	0.124523i
$322$	4.62061	+	2.66771i	0.257497	+	0.148666i
$323$		−	4.38650i		−	0.244072i
$324$	−22.9298	−	31.4085i	−1.27388	−	1.74492i
$325$		0			0
$326$	−19.7453	+	34.1998i	−1.09359	+	1.89415i
$327$	−6.61054	+	6.97406i	−0.365564	+	0.385666i
$328$	57.3504	−	33.1113i	3.16665	−	1.82827i
$329$	1.25020	+	2.16541i	0.0689257	+	0.119383i
$330$		0			0
$331$	−8.22153	+	14.2401i	−0.451896	+	0.782707i	−0.998504	−	0.0546819i	$-0.982586\pi$
$331$	−8.22153	+	14.2401i	−0.451896	+	0.782707i	0.546608	+	0.837389i	$0.315919\pi$
$332$			6.66458i			0.365766i
$333$	0.876576	−	0.0469471i	0.0480360	−	0.00257269i
$334$	−15.4996			−0.848100
$335$		0			0
$336$	−1.25020	+	5.22064i	−0.0682040	+	0.284809i
$337$	4.24096	−	2.44852i	0.231020	−	0.133379i	−0.380023	−	0.924977i	$-0.624084\pi$
$337$	4.24096	−	2.44852i	0.231020	−	0.133379i	0.611042	+	0.791598i	$0.290751\pi$
$338$	24.5062	−	14.1486i	1.33296	−	0.769584i
$339$	−3.14683	+	13.1407i	−0.170913	+	0.713704i
$340$		0			0
$341$	−29.0101			−1.57099
$342$	−4.51277	+	8.88197i	−0.244023	+	0.480282i
$343$		−	7.06201i		−	0.381313i
$344$	30.1938	−	52.2972i	1.62794	−	2.81967i
$345$		0			0
$346$	−10.7922	−	18.6927i	−0.580193	−	1.00492i
$347$	19.2903	−	11.1372i	1.03556	−	0.597878i	0.116984	−	0.993134i	$-0.462677\pi$
$347$	19.2903	−	11.1372i	1.03556	−	0.597878i	0.918571	+	0.395256i	$0.129344\pi$
$348$	−7.13846	+	7.53101i	−0.382662	+	0.403704i
$349$	−1.47173	+	2.54910i	−0.0787797	+	0.136450i	−0.902724	−	0.430221i	$-0.858436\pi$
$349$	−1.47173	+	2.54910i	−0.0787797	+	0.136450i	0.823944	+	0.566671i	$0.191769\pi$
$350$		0			0
$351$	−6.75073	−	1.23917i	−0.360327	−	0.0661420i
$352$		−	11.5761i		−	0.617011i
$353$	16.3069	+	9.41478i	0.867927	+	0.501098i	0.866659	−	0.498901i	$-0.166263\pi$
$353$	16.3069	+	9.41478i	0.867927	+	0.501098i	0.00126845	+	0.999999i	$0.499596\pi$
$354$	15.8916	+	15.0632i	0.844627	+	0.800602i
$355$		0			0
$356$	6.48133	+	11.2260i	0.343510	+	0.594976i
$357$	−0.841540	−	2.83502i	−0.0445390	−	0.150045i
$358$	−2.32018	−	1.33956i	−0.122625	−	0.0707978i
$359$	31.8770			1.68241			0.841203	−	0.540720i	$-0.181848\pi$
$359$	31.8770			1.68241			0.841203	+	0.540720i	$0.181848\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$	27.5866	+	15.9271i	1.44992	+	0.837110i
$363$	−0.0476252	−	0.0114049i	−0.00249968	−	0.000598604i
$364$	1.46719	+	2.54125i	0.0769016	+	0.133198i
$365$		0			0
$366$	7.45305	−	31.1228i	0.389577	−	1.62681i
$367$	15.8908	+	9.17458i	0.829495	+	0.478909i	0.853680	−	0.520798i	$-0.174366\pi$
$367$	15.8908	+	9.17458i	0.829495	+	0.478909i	−0.0241848	+	0.999708i	$0.507699\pi$
$368$		−	24.8825i		−	1.29709i
$369$	28.5333	−	18.5763i	1.48539	−	0.967044i
$370$		0			0
$371$	−1.29261	+	2.23887i	−0.0671090	+	0.116236i
$372$	−18.6042	−	62.6747i	−0.964582	−	3.24953i
$373$	1.90414	−	1.09936i	0.0985929	−	0.0569226i	−0.449893	−	0.893083i	$-0.648538\pi$
$373$	1.90414	−	1.09936i	0.0985929	−	0.0569226i	0.548486	+	0.836160i	$0.315205\pi$
$374$	13.8633	+	24.0119i	0.716854	+	1.24163i
$375$		0			0
$376$	14.1887	−	24.5756i	0.731727	−	1.26739i
$377$			1.83141i			0.0943226i
$378$	−1.21265	+	6.60623i	−0.0623717	+	0.339788i
$379$	−15.4713			−0.794709			−0.397354	−	0.917665i	$-0.630072\pi$
$379$	−15.4713			−0.794709			−0.397354	+	0.917665i	$0.630072\pi$
$380$		0			0
$381$	22.4909	+	21.3186i	1.15225	+	1.09219i
$382$	−36.8713	+	21.2877i	−1.88650	+	1.08917i
$383$	−6.67479	+	3.85369i	−0.341066	+	0.196915i	−0.660743	−	0.750612i	$-0.729759\pi$
$383$	−6.67479	+	3.85369i	−0.341066	+	0.196915i	0.319677	+	0.947526i	$0.396426\pi$
$384$	−25.3214	+	7.51633i	−1.29218	+	0.383566i
$385$		0			0
$386$	67.1715			3.41894
$387$	14.0635	−	27.6796i	0.714890	−	1.40704i
$388$			52.9536i			2.68831i
$389$	−12.3163	+	21.3325i	−0.624464	+	1.08160i	0.364181	+	0.931328i	$0.381349\pi$
$389$	−12.3163	+	21.3325i	−0.624464	+	1.08160i	−0.988644	+	0.150274i	$0.951984\pi$
$390$		0			0
$391$	6.85369	+	11.8709i	0.346606	+	0.600340i
$392$	−34.0372	+	19.6514i	−1.71914	+	0.992544i
$393$	10.1066	+	2.42024i	0.509808	+	0.122085i
$394$	−17.9198	+	31.0381i	−0.902789	+	1.56368i
$395$		0			0
$396$	−2.30221	−	42.9859i	−0.115690	−	2.16012i
$397$		−	6.77301i		−	0.339928i	−0.985450	−	0.169964i	$-0.945635\pi$
$397$		−	6.77301i		−	0.339928i	0.985450	−	0.169964i	$-0.0543651\pi$
$398$	−53.6945	−	31.0005i	−2.69146	−	1.55392i
$399$	1.12763	−	0.334723i	0.0564522	−	0.0167571i
$400$		0			0
$401$	9.24980	+	16.0211i	0.461913	+	0.800057i	0.999056	−	0.0434343i	$-0.0138299\pi$
$401$	9.24980	+	16.0211i	0.461913	+	0.800057i	−0.537143	+	0.843491i	$0.680497\pi$
$402$	−28.3050	+	29.8615i	−1.41172	+	1.48936i
$403$	−9.99290	−	5.76940i	−0.497782	−	0.287394i
$404$	−50.4249			−2.50873
$405$		0			0
$406$	1.79221			0.0889459
$407$	0.841540	+	0.485863i	0.0417136	+	0.0240833i
$408$	−23.0891	+	24.3588i	−1.14308	+	1.20594i
$409$	−6.70739	−	11.6175i	−0.331659	−	0.574450i	0.651178	−	0.758925i	$-0.274275\pi$
$409$	−6.70739	−	11.6175i	−0.331659	−	0.574450i	−0.982837	+	0.184474i	$0.940942\pi$
$410$		0			0
$411$	−9.41478	+	2.79466i	−0.464397	+	0.137850i
$412$	−1.09495	−	0.632168i	−0.0539442	−	0.0311447i
$413$		−	2.58522i		−	0.127210i
$414$	−1.66498	−	31.0877i	−0.0818292	−	1.52788i
$415$		0			0
$416$	2.30221	−	3.98755i	0.112875	−	0.195506i
$417$	13.4754	+	3.22699i	0.659893	+	0.158026i
$418$	−9.55077	+	5.51414i	−0.467143	+	0.269705i
$419$	−16.5575	−	28.6784i	−0.808886	−	1.40103i	−0.913636	−	0.406532i	$-0.866738\pi$
$419$	−16.5575	−	28.6784i	−0.808886	−	1.40103i	0.104751	−	0.994499i	$-0.466596\pi$
$420$		0			0
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	−0.629480	−	0.777017i	$-0.716732\pi$
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	0.987656	+	0.156637i	$0.0500654\pi$
$422$		−	13.5196i		−	0.658124i
$423$	6.60876	−	13.0073i	0.321329	−	0.632435i
$424$	29.3401			1.42488
$425$		0			0
$426$	−37.5333	+	11.1413i	−1.81850	+	0.539797i
$427$	−3.27225	+	1.88924i	−0.158355	+	0.0914266i
$428$	−7.00639	+	4.04514i	−0.338667	+	0.195529i
$429$	−5.51414	−	5.22672i	−0.266225	−	0.252348i
$430$		0			0
$431$	−32.7549			−1.57775			−0.788873	−	0.614556i	$-0.789335\pi$
$431$	−32.7549			−1.57775			−0.788873	+	0.614556i	$0.789335\pi$
$432$	29.5091	−	10.5069i	1.41976	−	0.505512i
$433$			11.8314i			0.568581i	0.958738	+	0.284291i	$0.0917581\pi$
$433$			11.8314i			0.568581i	−0.958738	+	0.284291i	$0.908242\pi$
$434$	−5.64591	+	9.77900i	−0.271012	+	0.469407i
$435$		0			0
$436$	−11.9859	−	20.7601i	−0.574019	−	0.994230i
$437$	−4.72168	+	2.72606i	−0.225869	+	0.130405i
$438$	7.50509	+	25.2835i	0.358607	+	1.20809i
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	−0.749643	−	0.661842i	$-0.769775\pi$
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	0.947994	+	0.318289i	$0.103108\pi$
$440$		0			0
$441$	−16.9344	+	11.0249i	−0.806399	+	0.524997i
$442$			11.0283i			0.524561i
$443$	−25.2664	−	14.5876i	−1.20044	−	0.693076i	−0.239789	−	0.970825i	$-0.577078\pi$
$443$	−25.2664	−	14.5876i	−1.20044	−	0.693076i	−0.960654	+	0.277750i	$0.910411\pi$
$444$	−0.510000	+	2.12968i	−0.0242035	+	0.101070i
$445$		0			0
$446$	−10.8920	−	18.8654i	−0.515750	−	0.893305i
$447$	29.7486	+	7.12397i	1.40706	+	0.336952i
$448$	1.46605	+	0.846426i	0.0692645	+	0.0399899i
$449$	−18.9717			−0.895331			−0.447666	−	0.894201i	$-0.647744\pi$
$449$	−18.9717			−0.895331			−0.447666	+	0.894201i	$0.647744\pi$
$450$		0			0
$451$	37.6892			1.77472
$452$	−29.1924	−	16.8542i	−1.37309	−	0.792756i
$453$	0.623167	+	2.09936i	0.0292790	+	0.0986365i
$454$	4.17458	+	7.23058i	0.195923	+	0.339348i
$455$		0			0
$456$	−9.68872	−	9.18370i	−0.453716	−	0.430066i
$457$	20.1223	+	11.6176i	0.941283	+	0.543450i	0.890362	−	0.455253i	$-0.150451\pi$
$457$	20.1223	+	11.6176i	0.941283	+	0.543450i	0.0509206	+	0.998703i	$0.483784\pi$
$458$			63.6374i			2.97358i
$459$	−11.1842	+	13.1407i	−0.522033	+	0.613354i
$460$		0			0
$461$	−2.21285	+	3.83277i	−0.103063	+	0.178510i	−0.912945	−	0.408082i	$-0.866198\pi$
$461$	−2.21285	+	3.83277i	−0.103063	+	0.178510i	0.809882	+	0.586592i	$0.199531\pi$
$462$	−5.11484	+	5.39611i	−0.237964	+	0.251050i
$463$	16.8950	−	9.75434i	0.785178	−	0.453322i	−0.0530845	−	0.998590i	$-0.516905\pi$
$463$	16.8950	−	9.75434i	0.785178	−	0.453322i	0.838262	+	0.545268i	$0.183572\pi$
$464$	−4.17912	−	7.23844i	−0.194011	−	0.336036i
$465$		0			0
$466$	−34.7362	+	60.1648i	−1.60912	+	2.78708i
$467$		−	24.5935i		−	1.13805i	−0.822320	−	0.569026i	$-0.807321\pi$
$467$		−	24.5935i		−	1.13805i	0.822320	−	0.569026i	$-0.192679\pi$
$468$	7.75581	−	15.2649i	0.358512	−	0.705619i
$469$	4.85783			0.224314
$470$		0			0
$471$	−6.32088	+	26.3950i	−0.291251	+	1.21622i
$472$	−25.4093	+	14.6700i	−1.16956	+	0.675243i
$473$	29.7639	−	17.1842i	1.36854	−	0.790129i
$474$	8.17044	−	34.1185i	0.375281	−	1.56711i
$475$		0			0
$476$	7.37743			0.338144
$477$	15.0632	−	0.806748i	0.689698	−	0.0369384i
$478$			10.5561i			0.482827i
$479$	16.3774	−	28.3665i	0.748304	−	1.29610i	−0.200331	−	0.979728i	$-0.564202\pi$
$479$	16.3774	−	28.3665i	0.748304	−	1.29610i	0.948635	−	0.316372i	$-0.102465\pi$
$480$		0			0
$481$	0.193252	+	0.334723i	0.00881155	+	0.0152621i
$482$	7.84793	−	4.53101i	0.357464	−	0.206382i
$483$	−2.52866	+	2.66771i	−0.115058	+	0.121385i
$484$	0.0610840	−	0.105801i	0.00277655	−	0.00480912i
$485$		0			0
$486$	36.1651	−	15.1017i	1.64048	−	0.685025i
$487$		−	6.03735i		−	0.273578i	−0.990600	−	0.136789i	$-0.956322\pi$
$487$		−	6.03735i		−	0.273578i	0.990600	−	0.136789i	$-0.0436783\pi$
$488$	37.1373	+	21.4412i	1.68113	+	0.970600i
$489$	−19.7453	−	18.7161i	−0.892912	−	0.846369i
$490$		0			0
$491$	−7.22153	−	12.5081i	−0.325903	−	0.564480i	0.655792	−	0.754942i	$-0.272335\pi$
$491$	−7.22153	−	12.5081i	−0.325903	−	0.564480i	−0.981695	+	0.190461i	$0.939002\pi$
$492$	24.1701	+	81.4254i	1.08967	+	3.67094i
$493$	3.98755	+	2.30221i	0.179590	+	0.103686i
$494$	−4.38650			−0.197358
$495$		0			0
$496$	52.6610			2.36455
$497$	4.00326	+	2.31128i	0.179571	+	0.103675i
$498$	−6.53192	−	1.56422i	−0.292702	−	0.0700942i
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	0.999388	−	0.0349673i	$-0.0111327\pi$
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	−0.529977	+	0.848012i	$0.677799\pi$
$500$		0			0
$501$	2.48679	−	10.3844i	0.111102	−	0.463943i
$502$	14.9751	+	8.64591i	0.668374	+	0.385886i
$503$			5.31728i			0.237086i	0.992949	+	0.118543i	$0.0378223\pi$
$503$			5.31728i			0.237086i	−0.992949	+	0.118543i	$0.962178\pi$
$504$	−8.02374	−	4.07672i	−0.357406	−	0.181591i
$505$		0			0
$506$	17.2311	−	29.8452i	0.766017	−	1.32678i
$507$	5.54750	+	18.6887i	0.246373	+	0.829995i
$508$	−66.9502	+	38.6537i	−2.97043	+	1.71498i
$509$	9.11350	+	15.7850i	0.403949	+	0.699659i	0.994198	−	0.107561i	$-0.0343041\pi$
$509$	9.11350	+	15.7850i	0.403949	+	0.699659i	−0.590250	+	0.807221i	$0.700971\pi$
$510$		0			0
$511$	1.55695	−	2.69671i	0.0688753	−	0.119296i
$512$		−	49.3365i		−	2.18038i
$513$	−5.22672	−	4.44852i	−0.230765	−	0.196407i
$514$	45.2545			1.99609
$515$		0			0
$516$	56.2130	+	53.2829i	2.47464	+	2.34565i
$517$	13.9867	−	8.07522i	0.615134	−	0.355148i
$518$	0.327558	−	0.189116i	0.0143921	−	0.00830927i
$519$	14.2553	−	4.23149i	0.625737	−	0.185742i
$520$		0			0
$521$	40.1232			1.75783			0.878915	−	0.476978i	$-0.158268\pi$
$521$	40.1232			1.75783			0.878915	+	0.476978i	$0.158268\pi$
$522$	−5.70566	−	8.76394i	−0.249730	−	0.383587i
$523$		−	18.9873i		−	0.830257i	−0.909763	−	0.415129i	$-0.863737\pi$
$523$		−	18.9873i		−	0.830257i	0.909763	−	0.415129i	$-0.136263\pi$
$524$	−12.9627	+	22.4520i	−0.566276	+	0.980819i
$525$		0			0
$526$	−7.83916	−	13.5778i	−0.341804	−	0.592021i
$527$	−25.1235	+	14.5051i	−1.09440	+	0.631851i
$528$	33.7209	+	8.07522i	1.46751	+	0.351429i
$529$	−2.98133	+	5.16381i	−0.129623	+	0.224513i
$530$		0			0
$531$	−12.6418	+	8.23028i	−0.548606	+	0.357164i
$532$			2.93438i			0.127221i
$533$	12.9825	+	7.49546i	0.562336	+	0.324665i
$534$	−12.5237	+	3.71751i	−0.541955	+	0.160872i
$535$		0			0
$536$	−27.5661	−	47.7460i	−1.19068	−	2.06231i
$537$	1.26973	−	1.33956i	0.0547931	−	0.0578062i
$538$	21.6064	+	12.4745i	0.931518	+	0.537812i
$539$	−22.3684			−0.963473
$540$		0			0
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$	−14.3799	−	8.30221i	−0.617668	−	0.356611i
$543$	−15.0969	+	15.9271i	−0.647871	+	0.683498i
$544$	−5.78807	−	10.0252i	−0.248162	−	0.429829i
$545$		0			0
$546$	−2.83502	+	0.841540i	−0.121328	+	0.0360146i
$547$	−15.3058	−	8.83683i	−0.654430	−	0.377835i	0.135721	−	0.990747i	$-0.456665\pi$
$547$	−15.3058	−	8.83683i	−0.654430	−	0.377835i	−0.790151	+	0.612912i	$0.789998\pi$
$548$		−	24.4996i		−	1.04657i
$549$	19.6559	+	9.98682i	0.838894	+	0.426227i
$550$		0			0
$551$	−0.915706	+	1.58605i	−0.0390104	+	0.0675680i
$552$	40.5691	+	9.71519i	1.72674	+	0.413506i
$553$	−3.58722	+	2.07108i	−0.152544	+	0.0880715i
$554$	28.4864	+	49.3399i	1.21027	+	2.09625i
$555$		0			0
$556$	−17.2835	+	29.9360i	−0.732985	+	1.26957i
$557$			17.3401i			0.734723i	0.930078	+	0.367362i	$0.119739\pi$
$557$			17.3401i			0.734723i	−0.930078	+	0.367362i	$0.880261\pi$
$558$	65.7937	−	3.52374i	2.78527	−	0.149172i
$559$	13.6700			0.578181
$560$		0			0
$561$	−18.3118	+	5.43563i	−0.773125	+	0.229492i
$562$	−33.8525	+	19.5447i	−1.42798	+	0.824445i
$563$	−11.2536	+	6.49727i	−0.474283	+	0.273827i	−0.718031	−	0.696011i	$-0.754956\pi$
$563$	−11.2536	+	6.49727i	−0.474283	+	0.273827i	0.243748	+	0.969839i	$0.421623\pi$
$564$	26.4157	+	25.0388i	1.11230	+	1.05432i
$565$		0			0
$566$	1.62257			0.0682016
$567$	−4.23149	−	1.87237i	−0.177706	−	0.0786321i
$568$		−	52.4623i		−	2.20127i
$569$	−8.34009	+	14.4455i	−0.349635	+	0.605585i	−0.986184	−	0.165651i	$-0.947028\pi$
$569$	−8.34009	+	14.4455i	−0.349635	+	0.605585i	0.636550	+	0.771236i	$0.280361\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	16.4143	−	9.47679i	0.686316	−	0.396245i
$573$	−8.34663	−	28.1186i	−0.348686	−	1.17467i
$574$	7.33502	−	12.7046i	0.306158	−	0.530281i
$575$		0			0
$576$	−0.528274	−	9.86370i	−0.0220114	−	0.410987i
$577$		−	23.5953i		−	0.982287i	−0.871079	−	0.491144i	$-0.836579\pi$
$577$		−	23.5953i		−	0.982287i	0.871079	−	0.491144i	$-0.163421\pi$
$578$	−13.0023	−	7.50687i	−0.540823	−	0.312245i
$579$	−10.7771	+	45.0037i	−0.447883	+	1.87029i
$580$		0			0
$581$	0.396505	+	0.686767i	0.0164498	+	0.0284919i
$582$	−51.8995	−	12.4285i	−2.15130	−	0.515179i
$583$	14.4612	+	8.34916i	0.598920	+	0.345787i
$584$	−35.3401			−1.46238
$585$		0			0
$586$	−3.46305			−0.143057
$587$	−24.3592	−	14.0638i	−1.00541	−	0.580476i	−0.0955681	−	0.995423i	$-0.530467\pi$
$587$	−24.3592	−	14.0638i	−1.00541	−	0.580476i	−0.909846	+	0.414947i	$0.863800\pi$
$588$	−14.3448	−	48.3255i	−0.591570	−	1.99291i
$589$	−5.76940	−	9.99290i	−0.237724	−	0.411750i
$590$		0			0
$591$	−17.9198	−	16.9858i	−0.737124	−	0.698702i
$592$	−1.52761	−	0.881969i	−0.0627846	−	0.0362487i
$593$			9.17872i			0.376925i	0.982080	+	0.188462i	$0.0603503\pi$
$593$			9.17872i			0.376925i	−0.982080	+	0.188462i	$0.939650\pi$
$594$	42.6706	+	7.83265i	1.75079	+	0.321378i
$595$		0			0
$596$	−38.1555	+	66.0873i	−1.56291	+	2.70704i
$597$	29.3846	−	31.0005i	1.20263	−	1.26877i
$598$	11.8709	−	6.85369i	0.485439	−	0.280268i
$599$	−15.7357	−	27.2550i	−0.642942	−	1.11361i	−0.984773	−	0.173846i	$-0.944380\pi$
$599$	−15.7357	−	27.2550i	−0.642942	−	1.11361i	0.341831	−	0.939761i	$-0.388953\pi$
$600$		0			0
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	−0.396398	−	0.918079i	$-0.629740\pi$
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	0.993279	−	0.115748i	$-0.0369265\pi$
$602$		−	13.3774i		−	0.545223i
$603$	−15.4653	−	23.7549i	−0.629797	−	0.967373i
$604$	−5.46305			−0.222288
$605$		0			0
$606$	11.8350	−	49.4212i	0.480765	−	2.00760i
$607$	−38.2813	+	22.1017i	−1.55379	+	0.897080i	−0.555960	+	0.831209i	$0.687649\pi$
$607$	−38.2813	+	22.1017i	−1.55379	+	0.897080i	−0.997828	+	0.0658708i	$0.979017\pi$
$608$	3.98755	−	2.30221i	0.161716	−	0.0933670i
$609$	−0.287546	+	1.20075i	−0.0116520	+	0.0486568i
$610$		0			0
$611$	6.42385			0.259881
$612$	−23.4867	−	36.0757i	−0.949394	−	1.45828i
$613$			35.1715i			1.42056i	0.703918	+	0.710282i	$0.251432\pi$
$613$			35.1715i			1.42056i	−0.703918	+	0.710282i	$0.748568\pi$
$614$	−10.0383	+	17.3868i	−0.405112	+	0.701674i
$615$		0			0
$616$	−4.98133	−	8.62791i	−0.200703	−	0.347628i
$617$	−6.43085	+	3.71285i	−0.258896	+	0.149474i	−0.623831	−	0.781559i	$-0.714425\pi$
$617$	−6.43085	+	3.71285i	−0.258896	+	0.149474i	0.364935	+	0.931033i	$0.381091\pi$
$618$	0.876576	−	0.924779i	0.0352610	−	0.0372001i
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	−0.767260	−	0.641337i	$-0.778380\pi$
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	0.939044	+	0.343798i	$0.111714\pi$
$620$		0			0
$621$	21.0953	+	3.87228i	0.846527	+	0.155389i
$622$			24.2179i			0.971050i
$623$	1.33577	+	0.771205i	0.0535164	+	0.0308977i
$624$	10.0096	+	9.48786i	0.400705	+	0.379818i
$625$		0			0
$626$	30.8446	+	53.4245i	1.23280	+	2.13527i
$627$	−2.16202	−	7.28354i	−0.0863429	−	0.290876i
$628$	−58.6372	−	33.8542i	−2.33988	−	1.35093i
$629$	0.971726			0.0387453
$630$		0			0
$631$	−2.36836			−0.0942829			−0.0471415	−	0.998888i	$-0.515011\pi$
$631$	−2.36836			−0.0942829			−0.0471415	+	0.998888i	$0.515011\pi$
$632$	40.7120	+	23.5051i	1.61944	+	0.934981i
$633$	9.05788	+	2.16912i	0.360019	+	0.0862146i
$634$	−25.5803	−	44.3064i	−1.01592	−	1.75963i
$635$		0			0
$636$	−8.76394	+	36.5968i	−0.347513	+	1.45116i
$637$	−7.70506	−	4.44852i	−0.305285	−	0.176257i
$638$		−	11.5761i		−	0.458304i
$639$	−1.44252	−	26.9342i	−0.0570654	−	1.06550i
$640$		0			0
$641$	0.0665480	−	0.115265i	0.00262849	−	0.00455268i	−0.864708	−	0.502275i	$-0.832497\pi$
$641$	0.0665480	−	0.115265i	0.00262849	−	0.00455268i	0.867337	+	0.497722i	$0.165830\pi$
$642$	−2.32018	−	7.81635i	−0.0915703	−	0.308487i
$643$	19.6124	−	11.3232i	0.773437	−	0.446544i	−0.0606623	−	0.998158i	$-0.519321\pi$
$643$	19.6124	−	11.3232i	0.773437	−	0.446544i	0.834099	+	0.551614i	$0.185988\pi$
$644$	−4.58482	−	7.94114i	−0.180667	−	0.312925i
$645$		0			0
$646$	−5.51414	+	9.55077i	−0.216951	+	0.375770i
$647$			46.3912i			1.82383i	0.410385	+	0.911913i	$0.365394\pi$
$647$			46.3912i			1.82383i	−0.410385	+	0.911913i	$0.634606\pi$
$648$	5.60907	+	52.2148i	0.220345	+	2.05119i
$649$	−16.6983			−0.655466
$650$		0			0
$651$	−5.64591	−	5.35162i	−0.221280	−	0.209746i
$652$	58.7770	−	33.9349i	2.30188	−	1.32899i
$653$	−31.5283	+	18.2029i	−1.23380	+	0.712333i	−0.967819	−	0.251647i	$-0.919028\pi$
$653$	−31.5283	+	18.2029i	−1.23380	+	0.712333i	−0.265977	+	0.963979i	$0.585695\pi$
$654$	23.1600	−	6.87476i	0.905629	−	0.268824i
$655$		0			0
$656$	−68.4158			−2.67119
$657$	−18.1436	+	0.971726i	−0.707851	+	0.0379106i
$658$		−	6.28635i		−	0.245067i
$659$	9.57068	−	16.5769i	0.372821	−	0.645745i	−0.617177	−	0.786824i	$-0.711724\pi$
$659$	9.57068	−	16.5769i	0.372821	−	0.645745i	0.989998	+	0.141079i	$0.0450572\pi$
$660$		0			0
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	−0.934172	−	0.356824i	$-0.883860\pi$
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	0.158067	−	0.987428i	$-0.449474\pi$
$662$	35.8016	−	20.6700i	1.39147	−	0.803364i
$663$	−7.38874	−	1.76940i	−0.286955	−	0.0687178i
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$		0			0
$666$	−1.96759	−	0.999697i	−0.0762425	−	0.0387375i
$667$		−	5.72298i		−	0.221595i
$668$	23.0693	+	13.3191i	0.892579	+	0.515331i
$669$	14.3870	−	4.27061i	0.556235	−	0.165111i
$670$		0			0
$671$	12.2029	+	21.1360i	0.471086	+	0.815945i
$672$	2.13550	−	2.25293i	0.0823787	−	0.0869087i
$673$	20.4822	+	11.8254i	0.789532	+	0.455836i	0.839798	−	0.542899i	$-0.182674\pi$
$673$	20.4822	+	11.8254i	0.789532	+	0.455836i	−0.0502658	+	0.998736i	$0.516007\pi$
$674$	−12.3118			−0.474233
$675$		0			0
$676$	−48.6327			−1.87049
$677$	12.8199	+	7.40157i	0.492709	+	0.284465i	0.725697	−	0.688014i	$-0.241517\pi$
$677$	12.8199	+	7.40157i	0.492709	+	0.284465i	−0.232989	+	0.972479i	$0.574851\pi$
$678$	23.3704	−	24.6555i	0.897533	−	0.946889i
$679$	3.15044	+	5.45673i	0.120903	+	0.209410i
$680$		0			0
$681$	−5.51414	+	1.63680i	−0.211302	+	0.0627223i
$682$	63.1639	+	36.4677i	2.41867	+	1.39642i
$683$			4.95252i			0.189503i	0.995501	+	0.0947515i	$0.0302057\pi$
$683$			4.95252i			0.189503i	−0.995501	+	0.0947515i	$0.969794\pi$
$684$	14.3492	−	9.34186i	0.548654	−	0.357195i
$685$		0			0
$686$	−8.87743	+	15.3762i	−0.338942	+	0.587065i
$687$	−42.6359	−	10.2101i	−1.62666	−	0.389540i
$688$	−54.0292	+	31.1938i	−2.05984	+	1.18925i
$689$	3.32088	+	5.75194i	0.126516	+	0.219131i
$690$		0			0
$691$	9.60442	−	16.6353i	0.365369	−	0.632838i	−0.623466	−	0.781851i	$-0.714276\pi$
$691$	9.60442	−	16.6353i	0.365369	−	0.632838i	0.988835	+	0.149012i	$0.0476093\pi$
$692$			37.0957i			1.41017i
$693$	−2.79466	−	4.29261i	−0.106160	−	0.163063i
$694$	−56.0011			−2.12577
$695$		0			0
$696$	13.4335	−	3.98755i	0.509194	−	0.151148i
$697$	32.6398	−	18.8446i	1.23632	−	0.713791i
$698$	6.40880	−	3.70012i	0.242577	−	0.140052i
$699$	−34.7362	−	32.9256i	−1.31384	−	1.24536i
$700$		0			0
$701$	−29.3492			−1.10850			−0.554251	−	0.832349i	$-0.686995\pi$
$701$	−29.3492			−1.10850			−0.554251	+	0.832349i	$0.686995\pi$
$702$	13.1407	+	11.1842i	0.495963	+	0.422120i
$703$			0.386505i			0.0145773i
$704$	5.46719	−	9.46945i	0.206052	−	0.356893i
$705$		0			0
$706$	−23.6700	−	40.9977i	−0.890834	−	1.54297i
$707$	−5.19615	+	3.00000i	−0.195421	+	0.112827i
$708$	−10.7086	−	36.0757i	−0.402455	−	1.35581i
$709$	19.3633	−	33.5382i	0.727204	−	1.25955i	−0.230857	−	0.972988i	$-0.574153\pi$
$709$	19.3633	−	33.5382i	0.727204	−	1.25955i	0.958060	−	0.286566i	$-0.0925138\pi$
$710$		0			0
$711$	21.5479	+	10.9481i	0.808108	+	0.410586i
$712$		−	17.5051i		−	0.656030i
$713$	31.2268	+	18.0288i	1.16945	+	0.675184i
$714$	−1.73153	+	7.23058i	−0.0648008	+	0.270598i
$715$		0			0
$716$	2.30221	+	3.98755i	0.0860377	+	0.149022i
$717$	−7.07243	−	1.69365i	−0.264125	−	0.0632506i
$718$	−69.4061	−	40.0716i	−2.59021	−	1.49546i
$719$	15.0848			0.562569			0.281284	−	0.959624i	$-0.409240\pi$
$719$	15.0848			0.562569			0.281284	+	0.959624i	$0.409240\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$	37.5700	+	21.6910i	1.39821	+	0.807257i
$723$	1.77655	+	5.98494i	0.0660706	+	0.222582i
$724$	−27.3729	−	47.4112i	−1.01731	−	1.76203i
$725$		0			0
$726$	0.0893579	+	0.0847002i	0.00331638	+	0.00314352i
$727$	−10.6916	−	6.17277i	−0.396528	−	0.228936i	0.288457	−	0.957493i	$-0.406858\pi$
$727$	−10.6916	−	6.17277i	−0.396528	−	0.228936i	−0.684985	+	0.728557i	$0.740191\pi$
$728$		−	3.96265i		−	0.146866i
$729$	4.31542	+	26.6529i	0.159830	+	0.987144i
$730$		0			0
$731$	17.1842	−	29.7639i	0.635580	−	1.10086i
$732$	−37.8373	+	39.9180i	−1.39851	+	1.47541i
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$	−23.0661	−	39.9517i	−0.851387	−	1.47465i
$735$		0			0
$736$	−7.19418	+	12.4607i	−0.265181	+	0.459307i
$737$		−	31.3774i		−	1.15580i
$738$	−85.4775	+	4.57795i	−3.14647	+	0.168517i
$739$	−29.7266			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$739$	−29.7266			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$740$		0			0
$741$	0.703781	−	2.93888i	0.0258540	−	0.107962i
$742$	5.62882	−	3.24980i	0.206640	−	0.119304i
$743$	−41.8851	+	24.1824i	−1.53662	+	0.887165i	−0.537582	+	0.843212i	$0.680662\pi$
$743$	−41.8851	+	24.1824i	−1.53662	+	0.887165i	−0.999034	+	0.0439537i	$0.986005\pi$
$744$	−20.5611	+	85.8599i	−0.753806	+	3.14778i
$745$		0			0
$746$	−5.52787			−0.202390
$747$	2.09599	−	4.12530i	0.0766883	−	0.150937i
$748$		−	47.6519i		−	1.74233i
$749$	−0.481327	+	0.833682i	−0.0175873	+	0.0304621i
$750$		0			0
$751$	15.9102	+	27.5573i	0.580573	+	1.00558i	0.995411	+	0.0956869i	$0.0305047\pi$
$751$	15.9102	+	27.5573i	0.580573	+	1.00558i	−0.414838	+	0.909895i	$0.636162\pi$
$752$	−25.3895	+	14.6586i	−0.925860	+	0.534546i
$753$	−8.19524	+	8.64591i	−0.298651	+	0.315074i
$754$	2.30221	−	3.98755i	0.0838416	−	0.145218i
$755$		0			0
$756$	7.48173	−	8.79054i	0.272108	−	0.319709i
$757$			4.94531i			0.179740i	0.995953	+	0.0898701i	$0.0286452\pi$
$757$			4.94531i			0.179740i	−0.995953	+	0.0898701i	$0.971355\pi$
$758$	33.6858	+	19.4485i	1.22352	+	0.706402i
$759$	17.2311	+	16.3330i	0.625450	+	0.592849i
$760$		0			0
$761$	−17.7125	−	30.6789i	−0.642076	−	1.11211i	−0.984969	−	0.172734i	$-0.944740\pi$
$761$	−17.7125	−	30.6789i	−0.642076	−	1.11211i	0.342893	−	0.939375i	$-0.388593\pi$
$762$	−22.1707	−	74.6898i	−0.803160	−	2.70572i
$763$	−2.47022	−	1.42618i	−0.0894281	−	0.0516313i
$764$	73.1715			2.64725
$765$		0			0
$766$	19.3774			0.700135
$767$	−5.75194	−	3.32088i	−0.207691	−	0.119910i
$768$	53.4887	+	12.8091i	1.93011	+	0.462208i
$769$	24.7125	+	42.8032i	0.891154	+	1.54352i	0.838494	+	0.544911i	$0.183437\pi$
$769$	24.7125	+	42.8032i	0.891154	+	1.54352i	0.0526602	+	0.998612i	$0.483230\pi$
$770$		0			0
$771$	−7.26073	+	30.3197i	−0.261489	+	1.09194i
$772$	−99.9768	−	57.7217i	−3.59825	−	2.07745i
$773$		−	12.6599i		−	0.455345i	−0.973738	−	0.227673i	$-0.926888\pi$
$773$		−	12.6599i		−	0.455345i	0.973738	−	0.227673i	$-0.0731116\pi$
$774$	−65.4158	+	42.5882i	−2.35132	+	1.53080i
$775$		0			0
$776$	35.7549	−	61.9292i	1.28352	−	2.22313i
$777$	0.0741499	+	0.249800i	0.00266011	+	0.00896153i
$778$	53.6329	−	30.9650i	1.92283	−	1.11015i
$779$	7.49546	+	12.9825i	0.268553	+	0.465147i
$780$		0			0
$781$	14.9289	−	25.8576i	0.534199	−	0.925259i
$782$		−	34.4623i		−	1.23237i
$783$	6.78711	−	2.41658i	0.242551	−	0.0863616i
$784$	40.6044			1.45016
$785$		0			0
$786$	−18.9627	−	17.9742i	−0.676375	−	0.641120i
$787$	26.7900	−	15.4672i	0.954959	−	0.551346i	0.0603410	−	0.998178i	$-0.480781\pi$
$787$	26.7900	−	15.4672i	0.954959	−	0.551346i	0.894618	+	0.446832i	$0.147448\pi$
$788$	53.3431	−	30.7977i	1.90027	−	1.09712i
$789$	10.3546	−	3.07364i	0.368634	−	0.109424i
$790$		0			0
$791$	−4.01093			−0.142612
$792$	−26.3321	+	51.8265i	−0.935671	+	1.84157i
$793$			9.70739i			0.344720i
$794$	−8.51414	+	14.7469i	−0.302155	+	0.523349i
$795$		0			0
$796$	53.2786	+	92.2812i	1.88841	+	3.27082i
$797$	−26.4947	+	15.2967i	−0.938492	+	0.541839i	−0.889487	−	0.456960i	$-0.848938\pi$
$797$	−26.4947	+	15.2967i	−0.938492	+	0.541839i	−0.0490047	+	0.998799i	$0.515605\pi$
$798$	−2.87597	−	0.688716i	−0.101808	−	0.0243803i
$799$	8.07522	−	13.9867i	0.285681	−	0.494814i
$800$		0			0
$801$	−0.481327	−	8.98712i	−0.0170068	−	0.317544i
$802$		−	46.5105i		−	1.64234i
$803$	−17.4185	−	10.0565i	−0.614684	−	0.354888i
$804$	67.7891	−	20.1223i	2.39074	−	0.709660i
$805$		0			0
$806$	14.5051	+	25.1235i	0.510919	+	0.884938i
$807$	−11.8242	+	12.4745i	−0.416233	+	0.439122i
$808$	58.9720	+	34.0475i	2.07463	+	1.19779i
$809$	2.89703			0.101854			0.0509271	−	0.998702i	$-0.483782\pi$
$809$	2.89703			0.101854			0.0509271	+	0.998702i	$0.483782\pi$
$810$		0			0
$811$	−14.8861			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$811$	−14.8861			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$812$	−2.66749	−	1.54008i	−0.0936107	−	0.0540462i
$813$	7.86946	−	8.30221i	0.275994	−	0.291171i
$814$	−1.22153	−	2.11575i	−0.0428145	−	0.0741568i
$815$		0			0
$816$	33.2407	−	9.86708i	1.16366	−	0.345417i
$817$	11.8386	+	6.83502i	0.414180	+	0.239127i
$818$			33.7266i			1.17922i
$819$	−0.108959	−	2.03443i	−0.00380733	−	0.0710888i
$820$		0			0
$821$	4.47586	−	7.75242i	0.156209	−	0.270561i	−0.777290	−	0.629143i	$-0.783406\pi$
$821$	4.47586	−	7.75242i	0.156209	−	0.270561i	0.933498	+	0.358581i	$0.116739\pi$
$822$	24.0119	+	5.75020i	0.837512	+	0.200561i
$823$	−2.59334	+	1.49727i	−0.0903983	+	0.0521915i	−0.544518	−	0.838749i	$-0.683287\pi$
$823$	−2.59334	+	1.49727i	−0.0903983	+	0.0521915i	0.454119	+	0.890941i	$0.349954\pi$
$824$	0.853695	+	1.47864i	0.0297399	+	0.0515110i
$825$		0			0
$826$	−3.24980	+	5.62882i	−0.113075	+	0.195852i
$827$			31.9663i			1.11158i	0.831324	+	0.555788i	$0.187583\pi$
$827$			31.9663i			1.11158i	−0.831324	+	0.555788i	$0.812417\pi$
$828$	−24.2361	+	47.7012i	−0.842263	+	1.65773i
$829$	−22.7458			−0.789994			−0.394997	−	0.918682i	$-0.629254\pi$
$829$	−22.7458			−0.789994			−0.394997	+	0.918682i	$0.629254\pi$
$830$		0			0
$831$	−37.6272	+	11.1692i	−1.30527	+	0.387454i
$832$	3.76648	−	2.17458i	0.130579	−	0.0753900i
$833$	−19.3716	+	11.1842i	−0.671185	+	0.387509i
$834$	−25.2835	−	23.9657i	−0.875497	−	0.829863i
$835$		0			0
$836$	18.9536			0.655523
$837$	−8.19524	+	44.6459i	−0.283269	+	1.54319i
$838$			83.2555i			2.87601i
$839$	−11.6322	+	20.1475i	−0.401587	+	0.695569i	−0.993918	−	0.110126i	$-0.964875\pi$
$839$	−11.6322	+	20.1475i	−0.401587	+	0.695569i	0.592331	+	0.805695i	$0.298208\pi$
$840$		0			0
$841$	13.5388	+	23.4499i	0.466855	+	0.808617i
$842$	−32.0027	+	18.4768i	−1.10289	+	0.636752i
$843$	−7.66325	−	25.8163i	−0.263936	−	0.889162i
$844$	−11.6176	+	20.1223i	−0.399895	+	0.692639i
$845$		0			0
$846$	−30.7403	+	20.0131i	−1.05687	+	0.688066i
$847$		−	0.0145366i		−	0.000499485i
$848$	−26.2508	−	15.1559i	−0.901456	−	0.520456i
$849$	−0.260328	+	1.08709i	−0.00893445	+	0.0373089i
$850$		0			0
$851$	−0.603895	−	1.04598i	−0.0207012	−	0.0358556i
$852$	65.4378	+	15.6706i	2.24186	+	0.536865i
$853$	9.51842	+	5.49546i	0.325905	+	0.188161i	0.654021	−	0.756476i	$-0.273081\pi$
$853$	9.51842	+	5.49546i	0.325905	+	0.188161i	−0.328117	+	0.944637i	$0.606414\pi$
$854$	9.49960			0.325070
$855$		0			0
$856$	10.9253			0.373419
$857$	13.9867	+	8.07522i	0.477776	+	0.275844i	0.719489	−	0.694503i	$-0.244376\pi$
$857$	13.9867	+	8.07522i	0.477776	+	0.275844i	−0.241713	+	0.970348i	$0.577709\pi$
$858$	5.43563	+	18.3118i	0.185569	+	0.625155i
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	0.999880	−	0.0154909i	$-0.00493111\pi$
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	−0.513356	+	0.858176i	$0.671598\pi$
$860$		0			0
$861$	7.33502	+	6.95269i	0.249977	+	0.236947i
$862$	71.3174	+	41.1751i	2.42908	+	1.40243i
$863$		−	12.2890i		−	0.418322i	−0.977881	−	0.209161i	$-0.932927\pi$
$863$		−	12.2890i		−	0.418322i	0.977881	−	0.209161i	$-0.0670734\pi$
$864$	−17.8154	−	3.27022i	−0.606093	−	0.111255i
$865$		0			0
$866$	14.8729	−	25.7606i	0.505402	−	0.875381i
$867$	7.11558	−	7.50687i	0.241658	−	0.254947i
$868$	16.8065	−	9.70325i	0.570451	−	0.329350i
$869$	13.3774	+	23.1704i	0.453798	+	0.786002i
$870$		0			0
$871$	6.24020	−	10.8083i	0.211441	−	0.366227i
$872$			32.3720i			1.09625i
$873$	16.6538	−	32.7777i	0.563644	−	1.10936i
$874$	13.7074			0.463659
$875$		0			0
$876$	10.5561	−	44.0808i	0.356659	−	1.48935i
$877$	−34.3814	+	19.8501i	−1.16098	+	0.670290i	−0.951538	−	0.307532i	$-0.900497\pi$
$877$	−34.3814	+	19.8501i	−1.16098	+	0.670290i	−0.209438	+	0.977822i	$0.567164\pi$
$878$	−18.0974	+	10.4485i	−0.610756	+	0.352620i
$879$	0.555620	−	2.32018i	0.0187406	−	0.0782578i
$880$		0			0
$881$	32.1040			1.08161			0.540806	−	0.841147i	$-0.318119\pi$
$881$	32.1040			1.08161			0.540806	+	0.841147i	$0.318119\pi$
$882$	50.7304	−	2.71699i	1.70818	−	0.0914858i
$883$		−	13.5051i		−	0.454482i	−0.973839	−	0.227241i	$-0.927030\pi$
$883$		−	13.5051i		−	0.454482i	0.973839	−	0.227241i	$-0.0729704\pi$
$884$	9.47679	−	16.4143i	0.318739	−	0.552072i
$885$		0			0
$886$	36.6751	+	63.5231i	1.23212	+	2.13410i
$887$	30.4167	−	17.5611i	1.02129	−	0.589643i	0.106814	−	0.994279i	$-0.465935\pi$
$887$	30.4167	−	17.5611i	1.02129	−	0.589643i	0.914478	+	0.404635i	$0.132602\pi$
$888$	2.03443	−	2.14631i	0.0682710	−	0.0720253i
$889$	−4.59936	+	7.96632i	−0.154258	+	0.267182i
$890$		0			0
$891$	−12.0939	+	27.3318i	−0.405161	+	0.915650i
$892$			37.4386i			1.25354i
$893$	5.56322	+	3.21193i	0.186166	+	0.107483i
$894$	−55.8165	−	52.9071i	−1.86678	−	1.76948i
$895$		0			0
$896$	−3.92024	−	6.79006i	−0.130966	−	0.226840i
$897$	2.68725	+	9.05294i	0.0897246	+	0.302269i
$898$	41.3073	+	23.8488i	1.37844	+	0.795843i
$899$	12.1120			0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$	−82.0610	−	47.3780i	−2.73233	−	1.57751i
$903$	8.96263	+	2.14631i	0.298258	+	0.0714246i
$904$	22.7603	+	39.4220i	0.756997	+	1.31116i
$905$		0			0
$906$	1.28221	−	5.35431i	0.0425986	−	0.177885i
$907$	−13.0931	−	7.55928i	−0.434748	−	0.251002i	0.266619	−	0.963802i	$-0.414093\pi$
$907$	−13.0931	−	7.55928i	−0.434748	−	0.251002i	−0.701367	+	0.712800i	$0.747427\pi$
$908$		−	14.3492i		−	0.476194i
$909$	31.2125	+	15.8585i	1.03525	+	0.525993i
$910$		0			0
$911$	−26.2781	+	45.5150i	−0.870631	+	1.50798i	−0.00928675	+	0.999957i	$0.502956\pi$
$911$	−26.2781	+	45.5150i	−0.870631	+	1.50798i	−0.861345	+	0.508021i	$0.830377\pi$
$912$	3.92464	+	13.2215i	0.129958	+	0.437808i
$913$	4.43593	−	2.56108i	0.146808	−	0.0847595i
$914$	−29.2083	−	50.5903i	−0.966125	−	1.67338i
$915$		0			0
$916$	54.6847	−	94.7167i	1.80683	−	3.12953i
$917$			3.08482i			0.101870i
$918$	40.8701	−	14.5520i	1.34892	−	0.480288i
$919$	54.5489			1.79940			0.899702	−	0.436505i	$-0.143784\pi$
$919$	54.5489			1.79940			0.899702	+	0.436505i	$0.143784\pi$
$920$		0			0
$921$	−10.0383	−	9.51504i	−0.330772	−	0.313531i
$922$	9.63612	−	5.56342i	0.317349	−	0.183221i
$923$	10.2849	−	5.93799i	0.338532	−	0.195451i
$924$	12.2498	−	3.63620i	0.402989	−	0.119622i
$925$		0			0
$926$	−49.0475			−1.61180
$927$	0.478945	+	0.735663i	0.0157306	+	0.0241624i
$928$			4.83317i			0.158656i
$929$	10.1896	−	17.6490i	0.334311	−	0.579044i	−0.649041	−	0.760753i	$-0.724830\pi$
$929$	10.1896	−	17.6490i	0.334311	−	0.579044i	0.983352	+	0.181709i	$0.0581630\pi$
$930$		0			0
$931$	−4.44852	−	7.70506i	−0.145794	−	0.252523i
$932$	103.401	−	59.6988i	3.38703	−	1.95550i
$933$	−16.2256	−	3.88558i	−0.531201	−	0.127208i
$934$	−30.9157	+	53.5476i	−1.01159	+	1.75213i
$935$		0			0
$936$	−19.3774	+	12.6155i	−0.633371	+	0.412349i
$937$			49.1979i			1.60723i	0.595152	+	0.803613i	$0.297092\pi$
$937$			49.1979i			1.60723i	−0.595152	+	0.803613i	$0.702908\pi$
$938$	−10.5770	−	6.10663i	−0.345351	−	0.199388i
$939$	−40.7422	+	12.0938i	−1.32957	+	0.394666i
$940$		0			0
$941$	11.6186	+	20.1239i	0.378754	+	0.656022i	0.990881	−	0.134738i	$-0.0430192\pi$
$941$	11.6186	+	20.1239i	0.378754	+	0.656022i	−0.612127	+	0.790759i	$0.709686\pi$
$942$	46.9429	−	49.5243i	1.52948	−	1.61359i
$943$	−40.5691	−	23.4226i	−1.32111	−	0.762744i
$944$	30.3118			0.986565
$945$		0			0
$946$	−86.4068			−2.80933
$947$	−32.1851	−	18.5821i	−1.04588	−	0.603837i	−0.124384	−	0.992234i	$-0.539695\pi$
$947$	−32.1851	−	18.5821i	−1.04588	−	0.603837i	−0.921492	+	0.388397i	$0.873029\pi$
$948$	−41.4794	+	43.7603i	−1.34719	+	1.42127i
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$	33.7886	−	10.0297i	1.09567	−	0.325236i
$952$	−8.62791	−	4.98133i	−0.279632	−	0.161446i
$953$			23.5761i			0.763706i	0.924223	+	0.381853i	$0.124714\pi$
$953$			23.5761i			0.763706i	−0.924223	+	0.381853i	$0.875286\pi$
$954$	−33.8114	−	17.1790i	−1.09468	−	0.556190i
$955$		0			0
$956$	9.07108	−	15.7116i	0.293380	−	0.508149i
$957$	7.75581	+	1.85730i	0.250710	+	0.0600381i
$958$	−71.3174	+	41.1751i	−2.30416	+	1.33031i
$959$	−1.45759	−	2.52462i	−0.0470680	−	0.0815242i
$960$		0			0
$961$	−22.6559	+	39.2412i	−0.730836	+	1.26584i
$962$		−	0.971726i		−	0.0313297i
$963$	5.60907	−	0.300407i	0.180750	−	0.00968048i
$964$	−15.5743			−0.501614
$965$		0			0
$966$	8.85916	−	2.62973i	0.285039	−	0.0846101i
$967$	7.25980	−	4.19145i	0.233459	−	0.134788i	−0.378708	−	0.925516i	$-0.623631\pi$
$967$	7.25980	−	4.19145i	0.233459	−	0.134788i	0.612167	+	0.790729i	$0.290298\pi$
$968$	−0.142876	+	0.0824893i	−0.00459220	+	0.00265131i
$969$	−5.51414	−	5.22672i	−0.177140	−	0.167906i
$970$		0			0
$971$	13.2078			0.423858			0.211929	−	0.977285i	$-0.432025\pi$
$971$	13.2078			0.423858			0.211929	+	0.977285i	$0.432025\pi$
$972$	−66.8046	−	8.60029i	−2.14276	−	0.275854i
$973$			4.11310i			0.131860i
$974$	−7.58936	+	13.1452i	−0.243179	+	0.421198i
$975$		0			0
$976$	−22.1514	−	38.3673i	−0.709048	−	1.22811i
$977$	−12.4110	+	7.16551i	−0.397064	+	0.229245i	−0.685216	−	0.728340i	$-0.740292\pi$
$977$	−12.4110	+	7.16551i	−0.397064	+	0.229245i	0.288153	+	0.957585i	$0.406959\pi$
$978$	19.4641	+	65.5717i	0.622394	+	2.09675i
$979$	4.98133	−	8.62791i	0.159204	−	0.275749i
$980$		0			0
$981$	0.890114	+	16.6198i	0.0284191	+	0.530630i
$982$			36.3118i			1.15876i
$983$	−27.9797	−	16.1541i	−0.892415	−	0.515236i	−0.0176831	−	0.999844i	$-0.505629\pi$
$983$	−27.9797	−	16.1541i	−0.892415	−	0.515236i	−0.874732	+	0.484608i	$0.838962\pi$
$984$	26.7125	−	111.547i	0.851562	−	3.55599i
$985$		0			0
$986$	−5.78807	−	10.0252i	−0.184330	−	0.319269i
$987$	4.21174	+	1.00860i	0.134061	+	0.0321040i
$988$	6.52879	+	3.76940i	0.207709	+	0.119921i
$989$	−42.7175			−1.35834
$990$		0			0
$991$	−39.6700			−1.26016			−0.630080	−	0.776530i	$-0.716978\pi$
$991$	−39.6700			−1.26016			−0.630080	+	0.776530i	$0.716978\pi$
$992$	−26.3716	−	15.2257i	−0.837300	−	0.483415i
$993$	8.10447	+	27.3027i	0.257187	+	0.866426i
$994$	−5.81088	−	10.0647i	−0.184310	−	0.319234i
$995$		0			0
$996$	8.37783	+	7.94114i	0.265462	+	0.251625i
$997$	−33.5043	−	19.3437i	−1.06109	−	0.612621i	−0.135357	−	0.990797i	$-0.543218\pi$
$997$	−33.5043	−	19.3437i	−1.06109	−	0.612621i	−0.925734	+	0.378176i	$0.876551\pi$
$998$		−	52.7258i		−	1.66901i
$999$	0.985463	−	1.15786i	0.0311787	−	0.0366329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.b.124.1		12
3.2	odd	2		675.2.k.b.424.6		12
5.2	odd	4		225.2.e.b.151.3		6
5.3	odd	4		45.2.e.b.16.1	✓	6
5.4	even	2	inner	225.2.k.b.124.6		12
9.2	odd	6		2025.2.b.m.649.1		6
9.4	even	3	inner	225.2.k.b.49.6		12
9.5	odd	6		675.2.k.b.199.1		12
9.7	even	3		2025.2.b.l.649.6		6
15.2	even	4		675.2.e.b.451.1		6
15.8	even	4		135.2.e.b.46.3		6
15.14	odd	2		675.2.k.b.424.1		12
20.3	even	4		720.2.q.i.241.1		6
45.2	even	12		2025.2.a.o.1.3		3
45.4	even	6	inner	225.2.k.b.49.1		12
45.7	odd	12		2025.2.a.n.1.1		3
45.13	odd	12		45.2.e.b.31.1	yes	6
45.14	odd	6		675.2.k.b.199.6		12
45.22	odd	12		225.2.e.b.76.3		6
45.23	even	12		135.2.e.b.91.3		6
45.29	odd	6		2025.2.b.m.649.6		6
45.32	even	12		675.2.e.b.226.1		6
45.34	even	6		2025.2.b.l.649.1		6
45.38	even	12		405.2.a.i.1.1		3
45.43	odd	12		405.2.a.j.1.3		3
60.23	odd	4		2160.2.q.k.721.1		6
180.23	odd	12		2160.2.q.k.1441.1		6
180.43	even	12		6480.2.a.bv.1.3		3
180.83	odd	12		6480.2.a.bs.1.3		3
180.103	even	12		720.2.q.i.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	5.3	odd	4
45.2.e.b.31.1	yes	6	45.13	odd	12
135.2.e.b.46.3		6	15.8	even	4
135.2.e.b.91.3		6	45.23	even	12
225.2.e.b.76.3		6	45.22	odd	12
225.2.e.b.151.3		6	5.2	odd	4
225.2.k.b.49.1		12	45.4	even	6	inner
225.2.k.b.49.6		12	9.4	even	3	inner
225.2.k.b.124.1		12	1.1	even	1	trivial
225.2.k.b.124.6		12	5.4	even	2	inner
405.2.a.i.1.1		3	45.38	even	12
405.2.a.j.1.3		3	45.43	odd	12
675.2.e.b.226.1		6	45.32	even	12
675.2.e.b.451.1		6	15.2	even	4
675.2.k.b.199.1		12	9.5	odd	6
675.2.k.b.199.6		12	45.14	odd	6
675.2.k.b.424.1		12	15.14	odd	2
675.2.k.b.424.6		12	3.2	odd	2
720.2.q.i.241.1		6	20.3	even	4
720.2.q.i.481.1		6	180.103	even	12
2025.2.a.n.1.1		3	45.7	odd	12
2025.2.a.o.1.3		3	45.2	even	12
2025.2.b.l.649.1		6	45.34	even	6
2025.2.b.l.649.6		6	9.7	even	3
2025.2.b.m.649.1		6	9.2	odd	6
2025.2.b.m.649.6		6	45.29	odd	6
2160.2.q.k.721.1		6	60.23	odd	4
2160.2.q.k.1441.1		6	180.23	odd	12
6480.2.a.bs.1.3		3	180.83	odd	12
6480.2.a.bv.1.3		3	180.43	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.17731 - 1.25707i) q^{2} +(1.19154 - 1.25707i) q^{3} +(2.16044 + 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(0.445256 + 0.257068i) q^{7} -5.83502i q^{8} +(-0.160442 - 2.99571i) q^{9} +(1.66044 - 2.87597i) q^{11} +(7.27821 + 1.74293i) q^{12} +(1.14392 - 0.660442i) q^{13} +(-0.646305 - 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} -3.32088i q^{17} +(-3.41648 + 6.72426i) q^{18} +1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(-7.23058 + 4.17458i) q^{22} +(-3.57463 + 2.06382i) q^{23} +(-7.33502 - 6.95269i) q^{24} -3.32088 q^{26} +(-3.95698 - 3.36783i) q^{27} +2.22153i q^{28} +(-0.693252 + 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(3.01885 - 1.74293i) q^{32} +(-1.63680 - 5.51414i) q^{33} +(-4.17458 + 7.23058i) q^{34} +(10.8633 - 7.07243i) q^{36} +0.292611i q^{37} +(-2.87597 - 1.66044i) q^{38} +(0.532810 - 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(-2.17731 - 0.521405i) q^{42} +(8.96263 + 5.17458i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(4.21174 + 2.43165i) q^{47} +(2.97122 + 10.0096i) q^{48} +(-3.36783 - 5.83326i) q^{49} +(-4.17458 - 3.95698i) q^{51} +(4.94274 + 2.85369i) q^{52} +5.02827i q^{53} +(4.38197 + 12.3070i) q^{54} +(1.50000 - 2.59808i) q^{56} +(1.57389 - 1.66044i) q^{57} +(3.01885 - 1.74293i) q^{58} +(-2.51414 - 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +21.9627i q^{62} +(0.698664 - 1.37510i) q^{63} +3.29261 q^{64} +(-3.36783 + 14.0635i) q^{66} +(8.18266 - 4.72426i) q^{67} +(12.4267 - 7.17458i) q^{68} +(-1.66498 + 6.95269i) q^{69} +8.99093 q^{71} +(-17.4800 + 0.936184i) q^{72} -6.05655i q^{73} +(0.367832 - 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(1.47864 - 0.853695i) q^{77} +(-3.95698 + 4.17458i) q^{78} +(-4.02827 + 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} -28.5333i q^{82} +(1.33577 + 0.771205i) q^{83} +(2.79261 + 2.64705i) q^{84} +(-13.0096 - 22.5333i) q^{86} +(0.683382 + 2.30221i) q^{87} +(-16.7813 - 9.68872i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(-15.4456 - 8.91751i) q^{92} +(-14.7146 - 3.52374i) q^{93} +(-6.11350 - 10.5889i) q^{94} +(1.40611 - 5.87168i) q^{96} +(10.6134 + 6.12763i) q^{97} +16.9344i q^{98} +(-8.88197 - 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46}+ \cdots - 44 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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