LMFDB - Embedded newform 225.2.e.b.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

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, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.3
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.2.e.b.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25707 - 2.17731i) q^{2} +(-1.25707 - 1.19154i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(-0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 + 2.99571i) q^{9} +O(q^{10})$	\(q+(1.25707 - 2.17731i) q^{2} +(-1.25707 - 1.19154i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(-0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 + 2.99571i) q^{9} +(1.66044 - 2.87597i) q^{11} +(-1.74293 + 7.27821i) q^{12} +(-0.660442 - 1.14392i) q^{13} +(0.646305 + 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} +3.32088 q^{17} +(6.72426 + 3.41648i) q^{18} -1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(-4.17458 - 7.23058i) q^{22} +(2.06382 + 3.57463i) q^{23} +(7.33502 + 6.95269i) q^{24} -3.32088 q^{26} +(3.36783 - 3.95698i) q^{27} +2.22153 q^{28} +(0.693252 - 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(1.74293 + 3.01885i) q^{32} +(-5.51414 + 1.63680i) q^{33} +(4.17458 - 7.23058i) q^{34} +(10.8633 - 7.07243i) q^{36} -0.292611 q^{37} +(-1.66044 + 2.87597i) q^{38} +(-0.532810 + 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(0.521405 - 2.17731i) q^{42} +(5.17458 - 8.96263i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-2.43165 + 4.21174i) q^{47} +(10.0096 - 2.97122i) q^{48} +(3.36783 + 5.83326i) q^{49} +(-4.17458 - 3.95698i) q^{51} +(-2.85369 + 4.94274i) q^{52} +5.02827 q^{53} +(-4.38197 - 12.3070i) q^{54} +(1.50000 - 2.59808i) q^{56} +(1.66044 + 1.57389i) q^{57} +(-1.74293 - 3.01885i) q^{58} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} -21.9627 q^{62} +(-1.37510 - 0.698664i) q^{63} -3.29261 q^{64} +(-3.36783 + 14.0635i) q^{66} +(4.72426 + 8.18266i) q^{67} +(-7.17458 - 12.4267i) q^{68} +(1.66498 - 6.95269i) q^{69} +8.99093 q^{71} +(-0.936184 - 17.4800i) q^{72} -6.05655 q^{73} +(-0.367832 + 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(0.853695 + 1.47864i) q^{77} +(4.17458 + 3.95698i) q^{78} +(4.02827 - 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} +28.5333 q^{82} +(0.771205 - 1.33577i) q^{83} +(-2.79261 - 2.64705i) q^{84} +(-13.0096 - 22.5333i) q^{86} +(-2.30221 + 0.683382i) q^{87} +(-9.68872 + 16.7813i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(8.91751 - 15.4456i) q^{92} +(-3.52374 + 14.7146i) q^{93} +(6.11350 + 10.5889i) q^{94} +(1.40611 - 5.87168i) q^{96} +(-6.12763 + 10.6134i) q^{97} +16.9344 q^{98} +(8.88197 + 4.51277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9	$ 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) $ 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9 + 2 * q^11 - 17 * q^12 + 4 * q^13 + 9 * q^14 - 5 * q^16 + 4 * q^17 + 23 * q^18 + 8 * q^19 - 4 * q^22 + 3 * q^23 + 15 * q^24 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 7 * q^29 - 8 * q^31 + 17 * q^32 - 20 * q^33 + 4 * q^34 + 10 * q^36 - 12 * q^37 - 2 * q^38 - 14 * q^39 + 13 * q^41 + 33 * q^42 + 10 * q^43 - 44 * q^44 - 6 * q^46 + 13 * q^47 + 10 * q^48 + 2 * q^49 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 5 * q^54 + 9 * q^56 + 2 * q^57 - 17 * q^58 + 2 * q^59 - q^61 - 84 * q^62 - 33 * q^63 - 30 * q^64 - 2 * q^66 + 11 * q^67 - 22 * q^68 + 39 * q^69 - 20 * q^71 - 15 * q^72 + 16 * q^73 + 16 * q^74 + 12 * q^76 + 4 * q^78 - 2 * q^79 - 19 * q^81 + 58 * q^82 - 15 * q^83 - 27 * q^84 - 28 * q^86 + 26 * q^87 - 24 * q^88 - 18 * q^89 + 20 * q^91 + 39 * q^92 + 42 * q^93 + 31 * q^94 + 13 * q^96 - 18 * q^97 + 80 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.25707	−	2.17731i	0.888882	−	1.53959i	0.0476826	−	0.998863i	$-0.484816\pi$
$2$	1.25707	−	2.17731i	0.888882	−	1.53959i	0.841199	−	0.540726i	$-0.181850\pi$
$3$	−1.25707	−	1.19154i	−0.725769	−	0.687939i
$3$	−1.25707	−	1.19154i	−0.725769	−	0.687939i
$4$	−2.16044	−	3.74200i	−1.08022	−	1.87100i
$5$		0			0
$5$		0			0
$6$	−4.17458	+	1.23917i	−1.70426	+	0.505889i
$7$	−0.257068	+	0.445256i	−0.0971627	+	0.168291i	−0.910509	−	0.413489i	$-0.864310\pi$
$7$	−0.257068	+	0.445256i	−0.0971627	+	0.168291i	0.813346	+	0.581780i	$0.197643\pi$
$8$	−5.83502			−2.06299
$9$	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	$-0.000236084\pi$
$12$	−1.74293	+	7.27821i	−0.503141	+	2.10104i
$13$	−0.660442	−	1.14392i	−0.183174	−	0.317266i	0.759786	−	0.650173i	$-0.225304\pi$
$13$	−0.660442	−	1.14392i	−0.183174	−	0.317266i	−0.942960	+	0.332907i	$0.891970\pi$
$14$	0.646305	+	1.11943i	0.172732	+	0.299181i
$15$		0			0
$16$	−3.01414	+	5.22064i	−0.753534	+	1.30516i
$17$	3.32088			0.805433			0.402716	−	0.915325i	$-0.368066\pi$
$17$	3.32088			0.805433			0.402716	+	0.915325i	$0.368066\pi$
$18$	6.72426	+	3.41648i	1.58492	+	0.805271i
$19$	−1.32088			−0.303032			−0.151516	−	0.988455i	$-0.548415\pi$
$19$	−1.32088			−0.303032			−0.151516	+	0.988455i	$0.548415\pi$
$20$		0			0
$21$	0.853695	−	0.253408i	0.186291	−	0.0552982i
$22$	−4.17458	−	7.23058i	−0.890023	−	1.54157i
$23$	2.06382	+	3.57463i	0.430335	+	0.745363i	0.996902	−	0.0786532i	$-0.0250620\pi$
$23$	2.06382	+	3.57463i	0.430335	+	0.745363i	−0.566567	+	0.824016i	$0.691729\pi$
$24$	7.33502	+	6.95269i	1.49725	+	1.41921i
$25$		0			0
$26$	−3.32088			−0.651279
$27$	3.36783	−	3.95698i	0.648139	−	0.761522i
$28$	2.22153			0.419829
$29$	0.693252	−	1.20075i	0.128734	−	0.222973i	−0.794453	−	0.607326i	$-0.792242\pi$
$29$	0.693252	−	1.20075i	0.128734	−	0.222973i	0.923186	+	0.384353i	$0.125575\pi$
$30$		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	$-0.453740\pi$
$32$	1.74293	+	3.01885i	0.308110	+	0.533662i
$33$	−5.51414	+	1.63680i	−0.959888	+	0.284930i
$34$	4.17458	−	7.23058i	0.715934	−	1.24003i
$35$		0			0
$36$	10.8633	−	7.07243i	1.81055	−	1.17874i
$37$	−0.292611			−0.0481049			−0.0240524	−	0.999711i	$-0.507657\pi$
$37$	−0.292611			−0.0481049			−0.0240524	+	0.999711i	$0.507657\pi$
$38$	−1.66044	+	2.87597i	−0.269359	+	0.466544i
$39$	−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	$0.486655\pi$
$42$	0.521405	−	2.17731i	0.0804546	−	0.335966i
$43$	5.17458	−	8.96263i	0.789116	−	1.36679i	−0.137393	−	0.990517i	$-0.543872\pi$
$43$	5.17458	−	8.96263i	0.789116	−	1.36679i	0.926509	−	0.376272i	$-0.122794\pi$
$44$	−14.3492			−2.16322
$45$		0			0
$46$	10.3774			1.53007
$47$	−2.43165	+	4.21174i	−0.354692	+	0.614345i	−0.987065	−	0.160319i	$-0.948748\pi$
$47$	−2.43165	+	4.21174i	−0.354692	+	0.614345i	0.632373	+	0.774664i	$0.282081\pi$
$48$	10.0096	−	2.97122i	1.44476	−	0.428859i
$49$	3.36783	+	5.83326i	0.481119	+	0.833322i
$50$		0			0
$51$	−4.17458	−	3.95698i	−0.584558	−	0.554088i
$52$	−2.85369	+	4.94274i	−0.395736	+	0.685435i
$53$	5.02827			0.690687			0.345343	−	0.938476i	$-0.387762\pi$
$53$	5.02827			0.690687			0.345343	+	0.938476i	$0.387762\pi$
$54$	−4.38197	−	12.3070i	−0.596310	−	1.67477i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	1.66044	+	1.57389i	0.219931	+	0.208467i
$58$	−1.74293	−	3.01885i	−0.228858	−	0.396394i
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	0.981978	−	0.188997i	$-0.0605236\pi$
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	−0.654665	+	0.755919i	$0.727190\pi$
$60$		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	$0.322586\pi$
$62$	−21.9627			−2.78926
$63$	−1.37510	−	0.698664i	−0.173246	−	0.0880234i
$64$	−3.29261			−0.411576
$65$		0			0
$66$	−3.36783	+	14.0635i	−0.414551	+	1.73110i
$67$	4.72426	+	8.18266i	0.577160	+	0.999670i	0.995803	+	0.0915197i	$0.0291724\pi$
$67$	4.72426	+	8.18266i	0.577160	+	0.999670i	−0.418643	+	0.908151i	$0.637494\pi$
$68$	−7.17458	−	12.4267i	−0.870046	−	1.50696i
$69$	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	$0.320871\pi$
$72$	−0.936184	−	17.4800i	−0.110330	−	2.06004i
$73$	−6.05655			−0.708865			−0.354433	−	0.935082i	$-0.615326\pi$
$73$	−6.05655			−0.708865			−0.354433	+	0.935082i	$0.615326\pi$
$74$	−0.367832	+	0.637103i	−0.0427596	+	0.0740617i
$75$		0			0
$76$	2.85369	+	4.94274i	0.327341	+	0.566972i
$77$	0.853695	+	1.47864i	0.0972875	+	0.168507i
$78$	4.17458	+	3.95698i	0.472678	+	0.448040i
$79$	4.02827	−	6.97717i	0.453216	−	0.784994i	−0.545367	−	0.838197i	$-0.683610\pi$
$79$	4.02827	−	6.97717i	0.453216	−	0.784994i	0.998584	+	0.0532036i	$0.0169432\pi$
$80$		0			0
$81$	−8.94852	+	0.961276i	−0.994280	+	0.106808i
$82$	28.5333			3.15098
$83$	0.771205	−	1.33577i	0.0846508	−	0.146619i	−0.820592	−	0.571515i	$-0.806356\pi$
$83$	0.771205	−	1.33577i	0.0846508	−	0.146619i	0.905242	+	0.424896i	$0.139689\pi$
$84$	−2.79261	−	2.64705i	−0.304699	−	0.288817i
$85$		0			0
$86$	−13.0096	−	22.5333i	−1.40286	−	2.42983i
$87$	−2.30221	+	0.683382i	−0.246823	+	0.0732662i
$88$	−9.68872	+	16.7813i	−1.03282	+	1.78890i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	0.679116			0.0711906
$92$	8.91751	−	15.4456i	0.929715	−	1.61031i
$93$	−3.52374	+	14.7146i	−0.365395	+	1.52583i
$94$	6.11350	+	10.5889i	0.630559	+	1.09216i
$95$		0			0
$96$	1.40611	−	5.87168i	0.143510	−	0.599276i
$97$	−6.12763	+	10.6134i	−0.622167	+	1.07762i	0.366915	+	0.930255i	$0.380414\pi$
$97$	−6.12763	+	10.6134i	−0.622167	+	1.07762i	−0.989081	+	0.147370i	$0.952919\pi$
$98$	16.9344			1.71063
$99$	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	$0.969482\pi$
$102$	−13.8633	+	4.11514i	−1.37267	+	0.407460i
$103$	0.146305	+	0.253408i	0.0144159	+	0.0249691i	0.873143	−	0.487464i	$-0.162078\pi$
$103$	0.146305	+	0.253408i	0.0144159	+	0.0249691i	−0.858727	+	0.512433i	$0.828744\pi$
$104$	3.85369	+	6.67479i	0.377886	+	0.654517i
$105$		0			0
$106$	6.32088	−	10.9481i	0.613939	−	1.06337i
$107$	−1.87237			−0.181009			−0.0905043	−	0.995896i	$-0.528848\pi$
$107$	−1.87237			−0.181009			−0.0905043	+	0.995896i	$0.528848\pi$
$108$	−22.0830	−	4.05358i	−2.12494	−	0.390056i
$109$	5.54787			0.531390			0.265695	−	0.964057i	$-0.414399\pi$
$109$	5.54787			0.531390			0.265695	+	0.964057i	$0.414399\pi$
$110$		0			0
$111$	0.367832	+	0.348659i	0.0349130	+	0.0330932i
$112$	−1.54968	−	2.68412i	−0.146431	−	0.253626i
$113$	3.90064	+	6.75611i	0.366942	+	0.635561i	0.989086	−	0.147341i	$-0.0470716\pi$
$113$	3.90064	+	6.75611i	0.366942	+	0.635561i	−0.622144	+	0.782903i	$0.713738\pi$
$114$	5.51414	−	1.63680i	0.516446	−	0.153300i
$115$		0			0
$116$	−5.99093			−0.556244
$117$	3.32088	−	2.16202i	0.307016	−	0.199879i
$118$	12.6418			1.16377
$119$	−0.853695	+	1.47864i	−0.0782581	+	0.135547i
$120$		0			0
$121$	−0.0141369	−	0.0244859i	−0.00128518	−	0.00222599i
$122$	9.23840	+	16.0014i	0.836405	+	1.44870i
$123$	4.57795	−	19.1168i	0.412780	−	1.72370i
$124$	−18.8729	+	32.6888i	−1.69484	+	2.93554i
$125$		0			0
$126$	−3.24980	+	2.11575i	−0.289515	+	0.188486i
$127$	−17.8916			−1.58762			−0.793810	−	0.608166i	$-0.791906\pi$
$127$	−17.8916			−1.58762			−0.793810	+	0.608166i	$0.791906\pi$
$128$	−7.62490	+	13.2067i	−0.673952	+	1.16732i
$129$	−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	$0.748915\pi$
$132$	18.0379	+	17.0977i	1.57000	+	1.48816i
$133$	0.339558	−	0.588131i	0.0294434	−	0.0509974i
$134$	23.7549			2.05211
$135$		0			0
$136$	−19.3774			−1.66160
$137$	2.83502	−	4.91040i	0.242212	−	0.419524i	−0.719132	−	0.694874i	$-0.755460\pi$
$137$	2.83502	−	4.91040i	0.242212	−	0.419524i	0.961344	+	0.275350i	$0.0887936\pi$
$138$	−13.0451	−	12.3652i	−1.11048	−	1.05259i
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$		0			0
$141$	8.07522	−	2.39703i	0.680056	−	0.201866i
$142$	11.3022	−	19.5760i	0.948460	−	1.64278i
$143$	−4.38650			−0.366818
$144$	−16.1231	−	8.19186i	−1.34359	−	0.682655i
$145$		0			0
$146$	−7.61350	+	13.1870i	−0.630097	+	1.09136i
$147$	2.71699	−	11.3457i	0.224094	−	0.935780i
$148$	0.632168	+	1.09495i	0.0519639	+	0.0900042i
$149$	−8.83049	−	15.2948i	−0.723422	−	1.25300i	−0.959620	−	0.281298i	$-0.909235\pi$
$149$	−8.83049	−	15.2948i	−0.723422	−	1.25300i	0.236199	−	0.971705i	$-0.424098\pi$
$150$		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	$0.183049\pi$
$152$	7.70739			0.625152
$153$	0.532810	+	9.94840i	0.0430752	+	0.804280i
$154$	4.29261			0.345908
$155$		0			0
$156$	9.47679	−	2.81306i	0.758750	−	0.225225i
$157$	−7.83502	−	13.5707i	−0.625303	−	1.08306i	−0.988482	−	0.151337i	$-0.951642\pi$
$157$	−7.83502	−	13.5707i	−0.625303	−	1.08306i	0.363179	−	0.931719i	$-0.381691\pi$
$158$	−10.1276	−	17.5416i	−0.805711	−	1.39553i
$159$	−6.32088	−	5.99141i	−0.501279	−	0.475150i
$160$		0			0
$161$	−2.12217			−0.167250
$162$	−9.15591	+	20.6921i	−0.719356	+	1.62572i
$163$	−15.7074			−1.23030			−0.615149	−	0.788411i	$-0.710904\pi$
$163$	−15.7074			−1.23030			−0.615149	+	0.788411i	$0.710904\pi$
$164$	24.5192	−	42.4685i	1.91463	−	3.31623i
$165$		0			0
$166$	−1.93892	−	3.35830i	−0.150489	−	0.260655i
$167$	3.08249	+	5.33903i	0.238530	+	0.413146i	0.960293	−	0.278994i	$-0.0900011\pi$
$167$	3.08249	+	5.33903i	0.238530	+	0.413146i	−0.721763	+	0.692141i	$0.756668\pi$
$168$	−4.98133	+	1.47864i	−0.384318	+	0.114080i
$169$	5.62763	−	9.74734i	0.432895	−	0.749796i
$170$		0			0
$171$	−0.211926	−	3.95698i	−0.0162064	−	0.302598i
$172$	−44.7175			−3.40968
$173$	4.29261	−	7.43502i	0.326361	−	0.565274i	−0.655426	−	0.755260i	$-0.727511\pi$
$173$	4.29261	−	7.43502i	0.326361	−	0.565274i	0.981787	+	0.189986i	$0.0608441\pi$
$174$	−1.40611	+	5.87168i	−0.106597	+	0.445131i
$175$		0			0
$176$	10.0096	+	17.3371i	0.754502	+	1.30684i
$177$	2.02827	−	8.46975i	0.152454	−	0.636626i
$178$	−3.77121	+	6.53192i	−0.282664	+	0.489588i
$179$	−1.06562			−0.0796482			−0.0398241	−	0.999207i	$-0.512680\pi$
$179$	−1.06562			−0.0796482			−0.0398241	+	0.999207i	$0.512680\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$	0.853695	−	1.47864i	0.0632801	−	0.109604i
$183$	12.2029	−	3.62226i	0.902061	−	0.267765i
$184$	−12.0424	−	20.8581i	−0.887778	−	1.53768i
$185$		0			0
$186$	27.6086	+	26.1695i	2.02436	+	1.91884i
$187$	5.51414	−	9.55077i	0.403234	−	0.698421i
$188$	21.0137			1.53258
$189$	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	$-0.0432356\pi$
$192$	4.13904	+	3.92329i	0.298709	+	0.283139i
$193$	13.3588	+	23.1380i	0.961585	+	1.66551i	0.718524	+	0.695502i	$0.244818\pi$
$193$	13.3588	+	23.1380i	0.961585	+	1.66551i	0.243060	+	0.970011i	$0.421849\pi$
$194$	15.4057	+	26.6835i	1.10607	+	1.91576i
$195$		0			0
$196$	14.5520	−	25.2048i	1.03943	−	1.80034i
$197$	14.2553			1.01565			0.507823	−	0.861462i	$-0.330450\pi$
$197$	14.2553			1.01565			0.507823	+	0.861462i	$0.330450\pi$
$198$	20.9909	−	13.6659i	1.49176	−	0.971194i
$199$	−24.6610			−1.74817			−0.874085	−	0.485773i	$-0.838538\pi$
$199$	−24.6610			−1.74817			−0.874085	+	0.485773i	$0.838538\pi$
$200$		0			0
$201$	3.81128	−	15.9153i	0.268827	−	1.12258i
$202$	14.6700	+	25.4093i	1.03218	+	1.78779i
$203$	0.356427	+	0.617349i	0.0250162	+	0.0433294i
$204$	−5.78807	+	24.1701i	−0.405246	+	1.69224i
$205$		0			0
$206$	0.735663			0.0512561
$207$	−10.3774	+	6.75611i	−0.721281	+	0.469582i
$208$	7.96265			0.552111
$209$	−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	$0.774073\pi$
$212$	−10.8633	−	18.8158i	−0.746094	−	1.29227i
$213$	−11.3022	−	10.7131i	−0.774415	−	0.734049i
$214$	−2.35369	+	4.07672i	−0.160895	+	0.278679i
$215$		0			0
$216$	−19.6514	+	23.0891i	−1.33711	+	1.57101i
$217$	4.49133			0.304891
$218$	6.97406	−	12.0794i	0.472343	−	0.818122i
$219$	7.61350	+	7.21665i	0.514472	+	0.487656i
$220$		0			0
$221$	−2.19325	−	3.79882i	−0.147534	−	0.255537i
$222$	1.22153	−	0.362594i	0.0819835	−	0.0243357i
$223$	4.33229	−	7.50375i	0.290112	−	0.502488i	−0.683724	−	0.729740i	$-0.739641\pi$
$223$	4.33229	−	7.50375i	0.290112	−	0.502488i	0.973836	+	0.227252i	$0.0729743\pi$
$224$	−1.79221			−0.119747
$225$		0			0
$226$	19.6135			1.30467
$227$	1.66044	−	2.87597i	0.110207	−	0.190885i	−0.805646	−	0.592397i	$-0.798182\pi$
$227$	1.66044	−	2.87597i	0.110207	−	0.190885i	0.915854	+	0.401512i	$0.131515\pi$
$228$	2.30221	−	9.61367i	0.152468	−	0.636681i
$229$	12.6559	+	21.9207i	0.836326	+	1.44856i	0.892946	+	0.450163i	$0.148634\pi$
$229$	12.6559	+	21.9207i	0.836326	+	1.44856i	−0.0566206	+	0.998396i	$0.518033\pi$
$230$		0			0
$231$	0.688716	−	2.87597i	0.0453142	−	0.189225i
$232$	−4.04514	+	7.00639i	−0.265577	+	0.459992i
$233$	−27.6327			−1.81028			−0.905139	−	0.425116i	$-0.860233\pi$
$233$	−27.6327			−1.81028			−0.905139	+	0.425116i	$0.860233\pi$
$234$	−0.532810	−	9.94840i	−0.0348309	−	0.650347i
$235$		0			0
$236$	10.8633	−	18.8158i	0.707140	−	1.22480i
$237$	−13.3774	+	3.97092i	−0.868958	+	0.257939i
$238$	2.14631	+	3.71751i	0.139124	+	0.240970i
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	0.925901	−	0.377765i	$-0.123307\pi$
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	−0.790105	+	0.612971i	$0.789974\pi$
$240$		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	$0.203703\pi$
$242$	−0.0710844			−0.00456948
$243$	12.3943	+	9.45417i	0.795095	+	0.606485i
$244$	31.7549			2.03290
$245$		0			0
$246$	−35.8684	−	33.9987i	−2.28688	−	2.16768i
$247$	0.872368	+	1.51099i	0.0555074	+	0.0961417i
$248$	25.4864	+	44.1437i	1.61839	+	2.80313i
$249$	−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	$0.569648\pi$
$252$	0.356427	+	6.65504i	0.0224528	+	0.419228i
$253$	13.7074			0.861776
$254$	−22.4909	+	38.9554i	−1.41121	+	2.44428i
$255$		0			0
$256$	15.8774	+	27.5005i	0.992340	+	1.71878i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	−10.4955	+	43.8274i	−0.653419	+	2.72858i
$259$	0.0752210	−	0.130287i	0.00467400	−	0.00809561i
$260$		0			0
$261$	3.70832	+	1.88413i	0.229539	+	0.116625i
$262$	15.0848			0.931943
$263$	3.11803	−	5.40059i	0.192266	−	0.333015i	−0.753735	−	0.657179i	$-0.771750\pi$
$263$	3.11803	−	5.40059i	0.192266	−	0.333015i	0.946001	+	0.324164i	$0.105083\pi$
$264$	32.1751	−	9.55077i	1.98024	−	0.587809i
$265$		0			0
$266$	−0.853695	−	1.47864i	−0.0523434	−	0.0906614i
$267$	3.77121	+	3.57463i	0.230794	+	0.218764i
$268$	20.4130	−	35.3563i	1.24692	−	2.15973i
$269$	9.92345			0.605044			0.302522	−	0.953142i	$-0.402172\pi$
$269$	9.92345			0.605044			0.302522	+	0.953142i	$0.402172\pi$
$270$		0			0
$271$	6.60442			0.401190			0.200595	−	0.979674i	$-0.435712\pi$
$271$	6.60442			0.401190			0.200595	+	0.979674i	$0.435712\pi$
$272$	−10.0096	+	17.3371i	−0.606921	+	1.05122i
$273$	−0.853695	−	0.809197i	−0.0516680	−	0.0489748i
$274$	−7.12763	−	12.3454i	−0.430596	−	0.745814i
$275$		0			0
$276$	−29.6140	+	8.79054i	−1.78255	+	0.529128i
$277$	11.3305	−	19.6250i	0.680783	−	1.17915i	−0.293959	−	0.955818i	$-0.594973\pi$
$277$	11.3305	−	19.6250i	0.680783	−	1.17915i	0.974742	−	0.223333i	$-0.0716936\pi$
$278$	−20.1131			−1.20630
$279$	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	$0.0131687\pi$
$282$	4.93205	−	20.5955i	0.293699	−	1.22644i
$283$	0.322689	+	0.558913i	0.0191819	+	0.0332240i	0.875457	−	0.483296i	$-0.160561\pi$
$283$	0.322689	+	0.558913i	0.0191819	+	0.0332240i	−0.856275	+	0.516520i	$0.827227\pi$
$284$	−19.4244	−	33.6440i	−1.15262	−	1.99640i
$285$		0			0
$286$	−5.51414	+	9.55077i	−0.326058	+	0.564749i
$287$	−5.83502			−0.344430
$288$	−8.76394	+	5.70566i	−0.516420	+	0.336209i
$289$	−5.97173			−0.351278
$290$		0			0
$291$	20.3492	−	6.04039i	1.19289	−	0.354094i
$292$	13.0848	+	22.6636i	0.765731	+	1.32629i
$293$	−0.688716	−	1.19289i	−0.0402352	−	0.0696895i	0.845207	−	0.534440i	$-0.179477\pi$
$293$	−0.688716	−	1.19289i	−0.0402352	−	0.0696895i	−0.885442	+	0.464750i	$0.846144\pi$
$294$	−21.2877	−	20.1781i	−1.24152	−	1.17681i
$295$		0			0
$296$	1.70739			0.0992400
$297$	−5.78807	−	16.2561i	−0.335858	−	0.943276i
$298$	−44.4021			−2.57214
$299$	2.72606	−	4.72168i	0.157652	−	0.273062i
$300$		0			0
$301$	2.66044	+	4.60802i	0.153345	+	0.265602i
$302$	1.58936	+	2.75285i	0.0914573	+	0.158409i
$303$	19.3774	−	5.75194i	1.11320	−	0.330440i
$304$	3.98133	−	6.89586i	0.228345	−	0.395505i
$305$		0			0
$306$	22.3305	+	11.3457i	1.27655	+	0.648592i
$307$	7.98546			0.455754			0.227877	−	0.973690i	$-0.426822\pi$
$307$	7.98546			0.455754			0.227877	+	0.973690i	$0.426822\pi$
$308$	3.68872	−	6.38904i	0.210184	−	0.364050i
$309$	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	$0.921386\pi$
$312$	3.10896	−	12.9825i	0.176010	−	0.734991i
$313$	−12.2685	+	21.2496i	−0.693455	+	1.20110i	0.277244	+	0.960800i	$0.410579\pi$
$313$	−12.2685	+	21.2496i	−0.693455	+	1.20110i	−0.970699	+	0.240300i	$0.922754\pi$
$314$	−39.3966			−2.22328
$315$		0			0
$316$	−34.8114			−1.95829
$317$	−10.1746	+	17.6229i	−0.571461	+	0.989800i	0.424955	+	0.905215i	$0.360290\pi$
$317$	−10.1746	+	17.6229i	−0.571461	+	0.989800i	−0.996416	+	0.0845855i	$0.973043\pi$
$318$	−20.9909	+	6.23089i	−1.17711	+	0.349411i
$319$	−2.30221	−	3.98755i	−0.128899	−	0.223260i
$320$		0			0
$321$	2.35369	+	2.23101i	0.131370	+	0.124523i
$322$	−2.66771	+	4.62061i	−0.148666	+	0.257497i
$323$	−4.38650			−0.244072
$324$	22.9298	+	31.4085i	1.27388	+	1.74492i
$325$		0			0
$326$	−19.7453	+	34.1998i	−1.09359	+	1.89415i
$327$	−6.97406	−	6.61054i	−0.385666	−	0.365564i
$328$	−33.1113	−	57.3504i	−1.82827	−	3.16665i
$329$	−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	$0.315919\pi$
$332$	−6.66458			−0.365766
$333$	−0.0469471	−	0.876576i	−0.00257269	−	0.0480360i
$334$	15.4996			0.848100
$335$		0			0
$336$	−1.25020	+	5.22064i	−0.0682040	+	0.284809i
$337$	2.44852	+	4.24096i	0.133379	+	0.231020i	0.924977	−	0.380023i	$-0.124084\pi$
$337$	2.44852	+	4.24096i	0.133379	+	0.231020i	−0.791598	+	0.611042i	$0.790751\pi$
$338$	−14.1486	−	24.5062i	−0.769584	−	1.33296i
$339$	3.14683	−	13.1407i	0.170913	−	0.713704i
$340$		0			0
$341$	−29.0101			−1.57099
$342$	−8.88197	−	4.51277i	−0.480282	−	0.244023i
$343$	−7.06201			−0.381313
$344$	−30.1938	+	52.2972i	−1.62794	+	2.81967i
$345$		0			0
$346$	−10.7922	−	18.6927i	−0.580193	−	1.00492i
$347$	11.1372	+	19.2903i	0.597878	+	1.03556i	0.993134	+	0.116984i	$0.0373226\pi$
$347$	11.1372	+	19.2903i	0.597878	+	1.03556i	−0.395256	+	0.918571i	$0.629344\pi$
$348$	7.53101	+	7.13846i	0.403704	+	0.382662i
$349$	1.47173	−	2.54910i	0.0787797	−	0.136450i	−0.823944	−	0.566671i	$-0.808231\pi$
$349$	1.47173	−	2.54910i	0.0787797	−	0.136450i	0.902724	+	0.430221i	$0.141564\pi$
$350$		0			0
$351$	−6.75073	−	1.23917i	−0.360327	−	0.0661420i
$352$	11.5761			0.617011
$353$	9.41478	−	16.3069i	0.501098	−	0.867927i	−0.498901	−	0.866659i	$-0.666263\pi$
$353$	9.41478	−	16.3069i	0.501098	−	0.867927i	0.999999	−	0.00126845i	$-0.000403761\pi$
$354$	−15.8916	−	15.0632i	−0.844627	−	0.800602i
$355$		0			0
$356$	6.48133	+	11.2260i	0.343510	+	0.594976i
$357$	2.83502	−	0.841540i	0.150045	−	0.0445390i
$358$	−1.33956	+	2.32018i	−0.0707978	+	0.122625i
$359$	−31.8770			−1.68241			−0.841203	−	0.540720i	$-0.818152\pi$
$359$	−31.8770			−1.68241			−0.841203	+	0.540720i	$0.818152\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$	−15.9271	+	27.5866i	−0.837110	+	1.44992i
$363$	−0.0114049	+	0.0476252i	−0.000598604	+	0.00249968i
$364$	−1.46719	−	2.54125i	−0.0769016	−	0.133198i
$365$		0			0
$366$	7.45305	−	31.1228i	0.389577	−	1.62681i
$367$	−9.17458	+	15.8908i	−0.478909	+	0.829495i	−0.999708	−	0.0241848i	$-0.992301\pi$
$367$	−9.17458	+	15.8908i	−0.478909	+	0.829495i	0.520798	+	0.853680i	$0.325634\pi$
$368$	−24.8825			−1.29709
$369$	−28.5333	+	18.5763i	−1.48539	+	0.967044i
$370$		0			0
$371$	−1.29261	+	2.23887i	−0.0671090	+	0.116236i
$372$	62.6747	−	18.6042i	3.24953	−	0.964582i
$373$	−1.09936	−	1.90414i	−0.0569226	−	0.0985929i	0.836160	−	0.548486i	$-0.184795\pi$
$373$	−1.09936	−	1.90414i	−0.0569226	−	0.0985929i	−0.893083	+	0.449893i	$0.851462\pi$
$374$	−13.8633	−	24.0119i	−0.716854	−	1.24163i
$375$		0			0
$376$	14.1887	−	24.5756i	0.731727	−	1.26739i
$377$	−1.83141			−0.0943226
$378$	6.60623	+	1.21265i	0.339788	+	0.0623717i
$379$	15.4713			0.794709			0.397354	−	0.917665i	$-0.369928\pi$
$379$	15.4713			0.794709			0.397354	+	0.917665i	$0.369928\pi$
$380$		0			0
$381$	22.4909	+	21.3186i	1.15225	+	1.09219i
$382$	−21.2877	−	36.8713i	−1.08917	−	1.88650i
$383$	3.85369	+	6.67479i	0.196915	+	0.341066i	0.947526	−	0.319677i	$-0.103574\pi$
$383$	3.85369	+	6.67479i	0.196915	+	0.341066i	−0.750612	+	0.660743i	$0.770241\pi$
$384$	25.3214	−	7.51633i	1.29218	−	0.383566i
$385$		0			0
$386$	67.1715			3.41894
$387$	27.6796	+	14.0635i	1.40704	+	0.714890i
$388$	52.9536			2.68831
$389$	12.3163	−	21.3325i	0.624464	−	1.08160i	−0.364181	−	0.931328i	$-0.618651\pi$
$389$	12.3163	−	21.3325i	0.624464	−	1.08160i	0.988644	−	0.150274i	$-0.0480157\pi$
$390$		0			0
$391$	6.85369	+	11.8709i	0.346606	+	0.600340i
$392$	−19.6514	−	34.0372i	−0.992544	−	1.71914i
$393$	2.42024	−	10.1066i	0.122085	−	0.509808i
$394$	17.9198	−	31.0381i	0.902789	−	1.56368i
$395$		0			0
$396$	−2.30221	−	42.9859i	−0.115690	−	2.16012i
$397$	6.77301			0.339928			0.169964	−	0.985450i	$-0.445635\pi$
$397$	6.77301			0.339928			0.169964	+	0.985450i	$0.445635\pi$
$398$	−31.0005	+	53.6945i	−1.55392	+	2.69146i
$399$	−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	$0.680497\pi$
$402$	−29.8615	−	28.3050i	−1.48936	−	1.41172i
$403$	−5.76940	+	9.99290i	−0.287394	+	0.497782i
$404$	50.4249			2.50873
$405$		0			0
$406$	1.79221			0.0889459
$407$	−0.485863	+	0.841540i	−0.0240833	+	0.0417136i
$408$	24.3588	+	23.0891i	1.20594	+	1.14308i
$409$	6.70739	+	11.6175i	0.331659	+	0.574450i	0.982837	−	0.184474i	$-0.0590583\pi$
$409$	6.70739	+	11.6175i	0.331659	+	0.574450i	−0.651178	+	0.758925i	$0.725725\pi$
$410$		0			0
$411$	−9.41478	+	2.79466i	−0.464397	+	0.137850i
$412$	0.632168	−	1.09495i	0.0311447	−	0.0539442i
$413$	−2.58522			−0.127210
$414$	1.66498	+	31.0877i	0.0818292	+	1.52788i
$415$		0			0
$416$	2.30221	−	3.98755i	0.112875	−	0.195506i
$417$	−3.22699	+	13.4754i	−0.158026	+	0.659893i
$418$	5.51414	+	9.55077i	0.269705	+	0.467143i
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	0.913636	+	0.406532i	$0.133262\pi$
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	−0.104751	+	0.994499i	$0.533404\pi$
$420$		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	$0.0500654\pi$
$422$	13.5196			0.658124
$423$	−13.0073	−	6.60876i	−0.632435	−	0.321329i
$424$	−29.3401			−1.42488
$425$		0			0
$426$	−37.5333	+	11.1413i	−1.81850	+	0.539797i
$427$	−1.88924	−	3.27225i	−0.0914266	−	0.158355i
$428$	4.04514	+	7.00639i	0.195529	+	0.338667i
$429$	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	$0.789335\pi$
$432$	10.5069	+	29.5091i	0.505512	+	1.41976i
$433$	11.8314			0.568581			0.284291	−	0.958738i	$-0.408242\pi$
$433$	11.8314			0.568581			0.284291	+	0.958738i	$0.408242\pi$
$434$	5.64591	−	9.77900i	0.271012	−	0.469407i
$435$		0			0
$436$	−11.9859	−	20.7601i	−0.574019	−	0.994230i
$437$	−2.72606	−	4.72168i	−0.130405	−	0.225869i
$438$	25.2835	−	7.50509i	1.20809	−	0.358607i
$439$	−4.15591	+	7.19824i	−0.198351	+	0.343553i	−0.947994	−	0.318289i	$-0.896892\pi$
$439$	−4.15591	+	7.19824i	−0.198351	+	0.343553i	0.749643	+	0.661842i	$0.230225\pi$
$440$		0			0
$441$	−16.9344	+	11.0249i	−0.806399	+	0.524997i
$442$	−11.0283			−0.524561
$443$	−14.5876	+	25.2664i	−0.693076	+	1.20044i	0.277750	+	0.960654i	$0.410411\pi$
$443$	−14.5876	+	25.2664i	−0.693076	+	1.20044i	−0.970825	+	0.239789i	$0.922922\pi$
$444$	0.510000	−	2.12968i	0.0242035	−	0.101070i
$445$		0			0
$446$	−10.8920	−	18.8654i	−0.515750	−	0.893305i
$447$	−7.12397	+	29.7486i	−0.336952	+	1.40706i
$448$	0.846426	−	1.46605i	0.0399899	−	0.0692645i
$449$	18.9717			0.895331			0.447666	−	0.894201i	$-0.352256\pi$
$449$	18.9717			0.895331			0.447666	+	0.894201i	$0.352256\pi$
$450$		0			0
$451$	37.6892			1.77472
$452$	16.8542	−	29.1924i	0.792756	−	1.37309i
$453$	2.09936	−	0.623167i	0.0986365	−	0.0292790i
$454$	−4.17458	−	7.23058i	−0.195923	−	0.339348i
$455$		0			0
$456$	−9.68872	−	9.18370i	−0.453716	−	0.430066i
$457$	−11.6176	+	20.1223i	−0.543450	+	0.941283i	0.455253	+	0.890362i	$0.349549\pi$
$457$	−11.6176	+	20.1223i	−0.543450	+	0.941283i	−0.998703	+	0.0509206i	$0.983784\pi$
$458$	63.6374			2.97358
$459$	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	$0.199531\pi$
$462$	−5.39611	−	5.11484i	−0.251050	−	0.237964i
$463$	−9.75434	−	16.8950i	−0.453322	−	0.785178i	0.545268	−	0.838262i	$-0.316428\pi$
$463$	−9.75434	−	16.8950i	−0.453322	−	0.785178i	−0.998590	+	0.0530845i	$0.983095\pi$
$464$	4.17912	+	7.23844i	0.194011	+	0.336036i
$465$		0			0
$466$	−34.7362	+	60.1648i	−1.60912	+	2.78708i
$467$	24.5935			1.13805			0.569026	−	0.822320i	$-0.307321\pi$
$467$	24.5935			1.13805			0.569026	+	0.822320i	$0.307321\pi$
$468$	−15.2649	−	7.75581i	−0.705619	−	0.358512i
$469$	−4.85783			−0.224314
$470$		0			0
$471$	−6.32088	+	26.3950i	−0.291251	+	1.21622i
$472$	−14.6700	−	25.4093i	−0.675243	−	1.16956i
$473$	−17.1842	−	29.7639i	−0.790129	−	1.36854i
$474$	−8.17044	+	34.1185i	−0.375281	+	1.56711i
$475$		0			0
$476$	7.37743			0.338144
$477$	0.806748	+	15.0632i	0.0369384	+	0.689698i
$478$	10.5561			0.482827
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	0.200331	+	0.979728i	$0.435798\pi$
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	−0.948635	+	0.316372i	$0.897535\pi$
$480$		0			0
$481$	0.193252	+	0.334723i	0.00881155	+	0.0152621i
$482$	4.53101	+	7.84793i	0.206382	+	0.357464i
$483$	2.66771	+	2.52866i	0.121385	+	0.115058i
$484$	−0.0610840	+	0.105801i	−0.00277655	+	0.00480912i
$485$		0			0
$486$	36.1651	−	15.1017i	1.64048	−	0.685025i
$487$	6.03735			0.273578			0.136789	−	0.990600i	$-0.456322\pi$
$487$	6.03735			0.273578			0.136789	+	0.990600i	$0.456322\pi$
$488$	21.4412	−	37.1373i	0.970600	−	1.68113i
$489$	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	$0.939002\pi$
$492$	−81.4254	+	24.1701i	−3.67094	+	1.08967i
$493$	2.30221	−	3.98755i	0.103686	−	0.179590i
$494$	4.38650			0.197358
$495$		0			0
$496$	52.6610			2.36455
$497$	−2.31128	+	4.00326i	−0.103675	+	0.179571i
$498$	−1.56422	+	6.53192i	−0.0700942	+	0.292702i
$499$	−10.4859	−	18.1620i	−0.469412	−	0.813045i	0.529977	−	0.848012i	$-0.322201\pi$
$499$	−10.4859	−	18.1620i	−0.469412	−	0.813045i	−0.999388	+	0.0349673i	$0.988867\pi$
$500$		0			0
$501$	2.48679	−	10.3844i	0.111102	−	0.463943i
$502$	−8.64591	+	14.9751i	−0.385886	+	0.668374i
$503$	5.31728			0.237086			0.118543	−	0.992949i	$-0.462178\pi$
$503$	5.31728			0.237086			0.118543	+	0.992949i	$0.462178\pi$
$504$	8.02374	+	4.07672i	0.357406	+	0.181591i
$505$		0			0
$506$	17.2311	−	29.8452i	0.766017	−	1.32678i
$507$	−18.6887	+	5.54750i	−0.829995	+	0.246373i
$508$	38.6537	+	66.9502i	1.71498	+	2.97043i
$509$	−9.11350	−	15.7850i	−0.403949	−	0.699659i	0.590250	−	0.807221i	$-0.299029\pi$
$509$	−9.11350	−	15.7850i	−0.403949	−	0.699659i	−0.994198	+	0.107561i	$0.965696\pi$
$510$		0			0
$511$	1.55695	−	2.69671i	0.0688753	−	0.119296i
$512$	49.3365			2.18038
$513$	−4.44852	+	5.22672i	−0.196407	+	0.230765i
$514$	−45.2545			−1.99609
$515$		0			0
$516$	56.2130	+	53.2829i	2.47464	+	2.34565i
$517$	8.07522	+	13.9867i	0.355148	+	0.615134i
$518$	−0.189116	−	0.327558i	−0.00830927	−	0.0143921i
$519$	−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	$0.158268\pi$
$522$	8.76394	−	5.70566i	0.383587	−	0.249730i
$523$	−18.9873			−0.830257			−0.415129	−	0.909763i	$-0.636263\pi$
$523$	−18.9873			−0.830257			−0.415129	+	0.909763i	$0.636263\pi$
$524$	12.9627	−	22.4520i	0.566276	−	0.980819i
$525$		0			0
$526$	−7.83916	−	13.5778i	−0.341804	−	0.592021i
$527$	−14.5051	−	25.1235i	−0.631851	−	1.09440i
$528$	8.07522	−	33.7209i	0.351429	−	1.46751i
$529$	2.98133	−	5.16381i	0.129623	−	0.224513i
$530$		0			0
$531$	−12.6418	+	8.23028i	−0.548606	+	0.357164i
$532$	−2.93438			−0.127221
$533$	7.49546	−	12.9825i	0.324665	−	0.562336i
$534$	12.5237	−	3.71751i	0.541955	−	0.160872i
$535$		0			0
$536$	−27.5661	−	47.7460i	−1.19068	−	2.06231i
$537$	1.33956	+	1.26973i	0.0578062	+	0.0547931i
$538$	12.4745	−	21.6064i	0.537812	−	0.931518i
$539$	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	$0.384381\pi$
$542$	8.30221	−	14.3799i	0.356611	−	0.617668i
$543$	15.9271	+	15.0969i	0.683498	+	0.647871i
$544$	5.78807	+	10.0252i	0.248162	+	0.429829i
$545$		0			0
$546$	−2.83502	+	0.841540i	−0.121328	+	0.0360146i
$547$	8.83683	−	15.3058i	0.377835	−	0.654430i	−0.612912	−	0.790151i	$-0.710002\pi$
$547$	8.83683	−	15.3058i	0.377835	−	0.654430i	0.990747	+	0.135721i	$0.0433352\pi$
$548$	−24.4996			−1.04657
$549$	−19.6559	−	9.98682i	−0.838894	−	0.426227i
$550$		0			0
$551$	−0.915706	+	1.58605i	−0.0390104	+	0.0675680i
$552$	−9.71519	+	40.5691i	−0.413506	+	1.72674i
$553$	2.07108	+	3.58722i	0.0880715	+	0.152544i
$554$	−28.4864	−	49.3399i	−1.21027	−	2.09625i
$555$		0			0
$556$	−17.2835	+	29.9360i	−0.732985	+	1.26957i
$557$	−17.3401			−0.734723			−0.367362	−	0.930078i	$-0.619739\pi$
$557$	−17.3401			−0.734723			−0.367362	+	0.930078i	$0.619739\pi$
$558$	−3.52374	−	65.7937i	−0.149172	−	2.78527i
$559$	−13.6700			−0.578181
$560$		0			0
$561$	−18.3118	+	5.43563i	−0.773125	+	0.229492i
$562$	−19.5447	−	33.8525i	−0.824445	−	1.42798i
$563$	6.49727	+	11.2536i	0.273827	+	0.474283i	0.969839	−	0.243748i	$-0.0783770\pi$
$563$	6.49727	+	11.2536i	0.273827	+	0.474283i	−0.696011	+	0.718031i	$0.745044\pi$
$564$	−26.4157	−	25.0388i	−1.11230	−	1.05432i
$565$		0			0
$566$	1.62257			0.0682016
$567$	1.87237	−	4.23149i	0.0786321	−	0.177706i
$568$	−52.4623			−2.20127
$569$	8.34009	−	14.4455i	0.349635	−	0.605585i	−0.636550	−	0.771236i	$-0.719639\pi$
$569$	8.34009	−	14.4455i	0.349635	−	0.605585i	0.986184	+	0.165651i	$0.0529724\pi$
$570$		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	$0.970773\pi$
$572$	9.47679	+	16.4143i	0.396245	+	0.686316i
$573$	−28.1186	+	8.34663i	−1.17467	+	0.348686i
$574$	−7.33502	+	12.7046i	−0.306158	+	0.530281i
$575$		0			0
$576$	−0.528274	−	9.86370i	−0.0220114	−	0.410987i
$577$	23.5953			0.982287			0.491144	−	0.871079i	$-0.336579\pi$
$577$	23.5953			0.982287			0.491144	+	0.871079i	$0.336579\pi$
$578$	−7.50687	+	13.0023i	−0.312245	+	0.540823i
$579$	10.7771	−	45.0037i	0.447883	−	1.87029i
$580$		0			0
$581$	0.396505	+	0.686767i	0.0164498	+	0.0284919i
$582$	12.4285	−	51.8995i	0.515179	−	2.15130i
$583$	8.34916	−	14.4612i	0.345787	−	0.598920i
$584$	35.3401			1.46238
$585$		0			0
$586$	−3.46305			−0.143057
$587$	14.0638	−	24.3592i	0.580476	−	1.00541i	−0.414947	−	0.909846i	$-0.636200\pi$
$587$	14.0638	−	24.3592i	0.580476	−	1.00541i	0.995423	−	0.0955681i	$-0.0304668\pi$
$588$	−48.3255	+	14.3448i	−1.99291	+	0.591570i
$589$	5.76940	+	9.99290i	0.237724	+	0.411750i
$590$		0			0
$591$	−17.9198	−	16.9858i	−0.737124	−	0.698702i
$592$	0.881969	−	1.52761i	0.0362487	−	0.0627846i
$593$	9.17872			0.376925			0.188462	−	0.982080i	$-0.439650\pi$
$593$	9.17872			0.376925			0.188462	+	0.982080i	$0.439650\pi$
$594$	−42.6706	−	7.83265i	−1.75079	−	0.321378i
$595$		0			0
$596$	−38.1555	+	66.0873i	−1.56291	+	2.70704i
$597$	31.0005	+	29.3846i	1.26877	+	1.20263i
$598$	−6.85369	−	11.8709i	−0.280268	−	0.485439i
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	0.984773	+	0.173846i	$0.0556196\pi$
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	−0.341831	+	0.939761i	$0.611047\pi$
$600$		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	$-0.0369265\pi$
$602$	13.3774			0.545223
$603$	−23.7549	+	15.4653i	−0.967373	+	0.629797i
$604$	5.46305			0.222288
$605$		0			0
$606$	11.8350	−	49.4212i	0.480765	−	2.00760i
$607$	−22.1017	−	38.2813i	−0.897080	−	1.55379i	−0.831209	−	0.555960i	$-0.812351\pi$
$607$	−22.1017	−	38.2813i	−0.897080	−	1.55379i	−0.0658708	−	0.997828i	$-0.520983\pi$
$608$	−2.30221	−	3.98755i	−0.0933670	−	0.161716i
$609$	0.287546	−	1.20075i	0.0116520	−	0.0486568i
$610$		0			0
$611$	6.42385			0.259881
$612$	36.0757	−	23.4867i	1.45828	−	0.949394i
$613$	35.1715			1.42056			0.710282	−	0.703918i	$-0.248568\pi$
$613$	35.1715			1.42056			0.710282	+	0.703918i	$0.248568\pi$
$614$	10.0383	−	17.3868i	0.405112	−	0.701674i
$615$		0			0
$616$	−4.98133	−	8.62791i	−0.200703	−	0.347628i
$617$	−3.71285	−	6.43085i	−0.149474	−	0.258896i	0.781559	−	0.623831i	$-0.214425\pi$
$617$	−3.71285	−	6.43085i	−0.149474	−	0.258896i	−0.931033	+	0.364935i	$0.881091\pi$
$618$	−0.924779	−	0.876576i	−0.0372001	−	0.0352610i
$619$	−4.27394	+	7.40268i	−0.171784	+	0.297539i	−0.939044	−	0.343798i	$-0.888286\pi$
$619$	−4.27394	+	7.40268i	−0.171784	+	0.297539i	0.767260	+	0.641337i	$0.221620\pi$
$620$		0			0
$621$	21.0953	+	3.87228i	0.846527	+	0.155389i
$622$	−24.2179			−0.971050
$623$	0.771205	−	1.33577i	0.0308977	−	0.0535164i
$624$	−10.0096	−	9.48786i	−0.400705	−	0.379818i
$625$		0			0
$626$	30.8446	+	53.4245i	1.23280	+	2.13527i
$627$	7.28354	−	2.16202i	0.290876	−	0.0863429i
$628$	−33.8542	+	58.6372i	−1.35093	+	2.33988i
$629$	−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	$0.515011\pi$
$632$	−23.5051	+	40.7120i	−0.934981	+	1.61944i
$633$	2.16912	−	9.05788i	0.0862146	−	0.360019i
$634$	25.5803	+	44.3064i	1.01592	+	1.75963i
$635$		0			0
$636$	−8.76394	+	36.5968i	−0.347513	+	1.45116i
$637$	4.44852	−	7.70506i	0.176257	−	0.305285i
$638$	−11.5761			−0.458304
$639$	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	$0.165830\pi$
$642$	7.81635	−	2.32018i	0.308487	−	0.0915703i
$643$	−11.3232	−	19.6124i	−0.446544	−	0.773437i	0.551614	−	0.834099i	$-0.314012\pi$
$643$	−11.3232	−	19.6124i	−0.446544	−	0.773437i	−0.998158	+	0.0606623i	$0.980679\pi$
$644$	4.58482	+	7.94114i	0.180667	+	0.312925i
$645$		0			0
$646$	−5.51414	+	9.55077i	−0.216951	+	0.375770i
$647$	−46.3912			−1.82383			−0.911913	−	0.410385i	$-0.865394\pi$
$647$	−46.3912			−1.82383			−0.911913	+	0.410385i	$0.865394\pi$
$648$	52.2148	−	5.60907i	2.05119	−	0.220345i
$649$	16.6983			0.655466
$650$		0			0
$651$	−5.64591	−	5.35162i	−0.221280	−	0.209746i
$652$	33.9349	+	58.7770i	1.32899	+	2.30188i
$653$	18.2029	+	31.5283i	0.712333	+	1.23380i	0.963979	+	0.265977i	$0.0856946\pi$
$653$	18.2029	+	31.5283i	0.712333	+	1.23380i	−0.251647	+	0.967819i	$0.580972\pi$
$654$	−23.1600	+	6.87476i	−0.905629	+	0.268824i
$655$		0			0
$656$	−68.4158			−2.67119
$657$	−0.971726	−	18.1436i	−0.0379106	−	0.707851i
$658$	−6.28635			−0.245067
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	−0.989998	−	0.141079i	$-0.954943\pi$
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	0.617177	+	0.786824i	$0.288276\pi$
$660$		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	$-0.449474\pi$
$662$	20.6700	+	35.8016i	0.803364	+	1.39147i
$663$	−1.76940	+	7.38874i	−0.0687178	+	0.286955i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$		0			0
$666$	−1.96759	−	0.999697i	−0.0762425	−	0.0387375i
$667$	5.72298			0.221595
$668$	13.3191	−	23.0693i	0.515331	−	0.892579i
$669$	−14.3870	+	4.27061i	−0.556235	+	0.165111i
$670$		0			0
$671$	12.2029	+	21.1360i	0.471086	+	0.815945i
$672$	2.25293	+	2.13550i	0.0869087	+	0.0823787i
$673$	11.8254	−	20.4822i	0.455836	−	0.789532i	−0.542899	−	0.839798i	$-0.682674\pi$
$673$	11.8254	−	20.4822i	0.455836	−	0.789532i	0.998736	+	0.0502658i	$0.0160068\pi$
$674$	12.3118			0.474233
$675$		0			0
$676$	−48.6327			−1.87049
$677$	−7.40157	+	12.8199i	−0.284465	+	0.492709i	−0.972479	−	0.232989i	$-0.925149\pi$
$677$	−7.40157	+	12.8199i	−0.284465	+	0.492709i	0.688014	+	0.725697i	$0.258483\pi$
$678$	−24.6555	−	23.3704i	−0.946889	−	0.897533i
$679$	−3.15044	−	5.45673i	−0.120903	−	0.209410i
$680$		0			0
$681$	−5.51414	+	1.63680i	−0.211302	+	0.0627223i
$682$	−36.4677	+	63.1639i	−1.39642	+	2.41867i
$683$	4.95252			0.189503			0.0947515	−	0.995501i	$-0.469794\pi$
$683$	4.95252			0.189503			0.0947515	+	0.995501i	$0.469794\pi$
$684$	−14.3492	+	9.34186i	−0.548654	+	0.357195i
$685$		0			0
$686$	−8.87743	+	15.3762i	−0.338942	+	0.587065i
$687$	10.2101	−	42.6359i	0.389540	−	1.62666i
$688$	31.1938	+	54.0292i	1.18925	+	2.05984i
$689$	−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	$0.0476093\pi$
$692$	−37.0957			−1.41017
$693$	−4.29261	+	2.79466i	−0.163063	+	0.106160i
$694$	56.0011			2.12577
$695$		0			0
$696$	13.4335	−	3.98755i	0.509194	−	0.151148i
$697$	18.8446	+	32.6398i	0.713791	+	1.23632i
$698$	−3.70012	−	6.40880i	−0.140052	−	0.242577i
$699$	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	$0.686995\pi$
$702$	−11.1842	+	13.1407i	−0.422120	+	0.495963i
$703$	0.386505			0.0145773
$704$	−5.46719	+	9.46945i	−0.206052	+	0.356893i
$705$		0			0
$706$	−23.6700	−	40.9977i	−0.890834	−	1.54297i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$	−36.0757	+	10.7086i	−1.35581	+	0.402455i
$709$	−19.3633	+	33.5382i	−0.727204	+	1.25955i	0.230857	+	0.972988i	$0.425847\pi$
$709$	−19.3633	+	33.5382i	−0.727204	+	1.25955i	−0.958060	+	0.286566i	$0.907486\pi$
$710$		0			0
$711$	21.5479	+	10.9481i	0.808108	+	0.410586i
$712$	17.5051			0.656030
$713$	18.0288	−	31.2268i	0.675184	−	1.16945i
$714$	1.73153	−	7.23058i	0.0648008	−	0.270598i
$715$		0			0
$716$	2.30221	+	3.98755i	0.0860377	+	0.149022i
$717$	1.69365	−	7.07243i	0.0632506	−	0.264125i
$718$	−40.0716	+	69.4061i	−1.49546	+	2.59021i
$719$	−15.0848			−0.562569			−0.281284	−	0.959624i	$-0.590760\pi$
$719$	−15.0848			−0.562569			−0.281284	+	0.959624i	$0.590760\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$	−21.6910	+	37.5700i	−0.807257	+	1.39821i
$723$	5.98494	−	1.77655i	0.222582	−	0.0660706i
$724$	27.3729	+	47.4112i	1.01731	+	1.76203i
$725$		0			0
$726$	0.0893579	+	0.0847002i	0.00331638	+	0.00314352i
$727$	6.17277	−	10.6916i	0.228936	−	0.396528i	−0.728557	−	0.684985i	$-0.759809\pi$
$727$	6.17277	−	10.6916i	0.228936	−	0.396528i	0.957493	+	0.288457i	$0.0931422\pi$
$728$	−3.96265			−0.146866
$729$	−4.31542	−	26.6529i	−0.159830	−	0.987144i
$730$		0			0
$731$	17.1842	−	29.7639i	0.635580	−	1.10086i
$732$	−39.9180	−	37.8373i	−1.47541	−	1.39851i
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	23.0661	+	39.9517i	0.851387	+	1.47465i
$735$		0			0
$736$	−7.19418	+	12.4607i	−0.265181	+	0.459307i
$737$	31.3774			1.15580
$738$	4.57795	+	85.4775i	0.168517	+	3.14647i
$739$	29.7266			1.09351			0.546755	−	0.837293i	$-0.315863\pi$
$739$	29.7266			1.09351			0.546755	+	0.837293i	$0.315863\pi$
$740$		0			0
$741$	0.703781	−	2.93888i	0.0258540	−	0.107962i
$742$	3.24980	+	5.62882i	0.119304	+	0.206640i
$743$	24.1824	+	41.8851i	0.887165	+	1.53662i	0.843212	+	0.537582i	$0.180662\pi$
$743$	24.1824	+	41.8851i	0.887165	+	1.53662i	0.0439537	+	0.999034i	$0.486005\pi$
$744$	20.5611	−	85.8599i	0.753806	−	3.14778i
$745$		0			0
$746$	−5.52787			−0.202390
$747$	4.12530	+	2.09599i	0.150937	+	0.0766883i
$748$	−47.6519			−1.74233
$749$	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	$0.636162\pi$
$752$	−14.6586	−	25.3895i	−0.534546	−	0.925860i
$753$	8.64591	+	8.19524i	0.315074	+	0.298651i
$754$	−2.30221	+	3.98755i	−0.0838416	+	0.145218i
$755$		0			0
$756$	7.48173	−	8.79054i	0.272108	−	0.319709i
$757$	−4.94531			−0.179740			−0.0898701	−	0.995953i	$-0.528645\pi$
$757$	−4.94531			−0.179740			−0.0898701	+	0.995953i	$0.528645\pi$
$758$	19.4485	−	33.6858i	0.706402	−	1.22352i
$759$	−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	$-0.388593\pi$
$762$	74.6898	−	22.1707i	2.70572	−	0.803160i
$763$	−1.42618	+	2.47022i	−0.0516313	+	0.0894281i
$764$	−73.1715			−2.64725
$765$		0			0
$766$	19.3774			0.700135
$767$	3.32088	−	5.75194i	0.119910	−	0.207691i
$768$	12.8091	−	53.4887i	0.462208	−	1.93011i
$769$	−24.7125	−	42.8032i	−0.891154	−	1.54352i	−0.838494	−	0.544911i	$-0.816563\pi$
$769$	−24.7125	−	42.8032i	−0.891154	−	1.54352i	−0.0526602	−	0.998612i	$-0.516770\pi$
$770$		0			0
$771$	−7.26073	+	30.3197i	−0.261489	+	1.09194i
$772$	57.7217	−	99.9768i	2.07745	−	3.59825i
$773$	−12.6599			−0.455345			−0.227673	−	0.973738i	$-0.573112\pi$
$773$	−12.6599			−0.455345			−0.227673	+	0.973738i	$0.573112\pi$
$774$	65.4158	−	42.5882i	2.35132	−	1.53080i
$775$		0			0
$776$	35.7549	−	61.9292i	1.28352	−	2.22313i
$777$	−0.249800	+	0.0741499i	−0.00896153	+	0.00266011i
$778$	−30.9650	−	53.6329i	−1.11015	−	1.92283i
$779$	−7.49546	−	12.9825i	−0.268553	−	0.465147i
$780$		0			0
$781$	14.9289	−	25.8576i	0.534199	−	0.925259i
$782$	34.4623			1.23237
$783$	−2.41658	−	6.78711i	−0.0863616	−	0.242551i
$784$	−40.6044			−1.45016
$785$		0			0
$786$	−18.9627	−	17.9742i	−0.676375	−	0.641120i
$787$	15.4672	+	26.7900i	0.551346	+	0.954959i	0.998178	+	0.0603410i	$0.0192188\pi$
$787$	15.4672	+	26.7900i	0.551346	+	0.954959i	−0.446832	+	0.894618i	$0.647448\pi$
$788$	−30.7977	−	53.3431i	−1.09712	−	1.90027i
$789$	−10.3546	+	3.07364i	−0.368634	+	0.109424i
$790$		0			0
$791$	−4.01093			−0.142612
$792$	−51.8265	−	26.3321i	−1.84157	−	0.935671i
$793$	9.70739			0.344720
$794$	8.51414	−	14.7469i	0.302155	−	0.523349i
$795$		0			0
$796$	53.2786	+	92.2812i	1.88841	+	3.27082i
$797$	−15.2967	−	26.4947i	−0.541839	−	0.938492i	−0.998799	−	0.0490047i	$-0.984395\pi$
$797$	−15.2967	−	26.4947i	−0.541839	−	0.938492i	0.456960	−	0.889487i	$-0.348938\pi$
$798$	−0.688716	+	2.87597i	−0.0243803	+	0.101808i
$799$	−8.07522	+	13.9867i	−0.285681	+	0.494814i
$800$		0			0
$801$	−0.481327	−	8.98712i	−0.0170068	−	0.317544i
$802$	46.5105			1.64234
$803$	−10.0565	+	17.4185i	−0.354888	+	0.614684i
$804$	−67.7891	+	20.1223i	−2.39074	+	0.709660i
$805$		0			0
$806$	14.5051	+	25.1235i	0.510919	+	0.884938i
$807$	−12.4745	−	11.8242i	−0.439122	−	0.416233i
$808$	34.0475	−	58.9720i	1.19779	−	2.07463i
$809$	−2.89703			−0.101854			−0.0509271	−	0.998702i	$-0.516218\pi$
$809$	−2.89703			−0.101854			−0.0509271	+	0.998702i	$0.516218\pi$
$810$		0			0
$811$	−14.8861			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$811$	−14.8861			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$812$	1.54008	−	2.66749i	0.0540462	−	0.0936107i
$813$	−8.30221	−	7.86946i	−0.291171	−	0.275994i
$814$	1.22153	+	2.11575i	0.0428145	+	0.0741568i
$815$		0			0
$816$	33.2407	−	9.86708i	1.16366	−	0.345417i
$817$	−6.83502	+	11.8386i	−0.239127	+	0.414180i
$818$	33.7266			1.17922
$819$	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	$0.116739\pi$
$822$	−5.75020	+	24.0119i	−0.200561	+	0.837512i
$823$	1.49727	+	2.59334i	0.0521915	+	0.0903983i	0.890941	−	0.454119i	$-0.150046\pi$
$823$	1.49727	+	2.59334i	0.0521915	+	0.0903983i	−0.838749	+	0.544518i	$0.816713\pi$
$824$	−0.853695	−	1.47864i	−0.0297399	−	0.0515110i
$825$		0			0
$826$	−3.24980	+	5.62882i	−0.113075	+	0.195852i
$827$	−31.9663			−1.11158			−0.555788	−	0.831324i	$-0.687583\pi$
$827$	−31.9663			−1.11158			−0.555788	+	0.831324i	$0.687583\pi$
$828$	47.7012	+	24.2361i	1.65773	+	0.842263i
$829$	22.7458			0.789994			0.394997	−	0.918682i	$-0.370746\pi$
$829$	22.7458			0.789994			0.394997	+	0.918682i	$0.370746\pi$
$830$		0			0
$831$	−37.6272	+	11.1692i	−1.30527	+	0.387454i
$832$	2.17458	+	3.76648i	0.0753900	+	0.130579i
$833$	11.1842	+	19.3716i	0.387509	+	0.671185i
$834$	25.2835	+	23.9657i	0.875497	+	0.829863i
$835$		0			0
$836$	18.9536			0.655523
$837$	−44.6459	−	8.19524i	−1.54319	−	0.283269i
$838$	83.2555			2.87601
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	−0.592331	−	0.805695i	$-0.701792\pi$
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	0.993918	+	0.110126i	$0.0351254\pi$
$840$		0			0
$841$	13.5388	+	23.4499i	0.466855	+	0.808617i
$842$	−18.4768	−	32.0027i	−0.636752	−	1.10289i
$843$	−25.8163	+	7.66325i	−0.889162	+	0.263936i
$844$	11.6176	−	20.1223i	0.399895	−	0.692639i
$845$		0			0
$846$	−30.7403	+	20.0131i	−1.05687	+	0.688066i
$847$	0.0145366			0.000499485
$848$	−15.1559	+	26.2508i	−0.520456	+	0.901456i
$849$	0.260328	−	1.08709i	0.00893445	−	0.0373089i
$850$		0			0
$851$	−0.603895	−	1.04598i	−0.0207012	−	0.0358556i
$852$	−15.6706	+	65.4378i	−0.536865	+	2.24186i
$853$	5.49546	−	9.51842i	0.188161	−	0.325905i	−0.756476	−	0.654021i	$-0.773081\pi$
$853$	5.49546	−	9.51842i	0.188161	−	0.325905i	0.944637	+	0.328117i	$0.106414\pi$
$854$	−9.49960			−0.325070
$855$		0			0
$856$	10.9253			0.373419
$857$	−8.07522	+	13.9867i	−0.275844	+	0.477776i	−0.970348	−	0.241713i	$-0.922291\pi$
$857$	−8.07522	+	13.9867i	−0.275844	+	0.477776i	0.694503	+	0.719489i	$0.255624\pi$
$858$	18.3118	−	5.43563i	0.625155	−	0.185569i
$859$	−14.2594	−	24.6980i	−0.486524	−	0.842685i	0.513356	−	0.858176i	$-0.328402\pi$
$859$	−14.2594	−	24.6980i	−0.486524	−	0.842685i	−0.999880	+	0.0154909i	$0.995069\pi$
$860$		0			0
$861$	7.33502	+	6.95269i	0.249977	+	0.236947i
$862$	−41.1751	+	71.3174i	−1.40243	+	2.42908i
$863$	−12.2890			−0.418322			−0.209161	−	0.977881i	$-0.567073\pi$
$863$	−12.2890			−0.418322			−0.209161	+	0.977881i	$0.567073\pi$
$864$	17.8154	+	3.27022i	0.606093	+	0.111255i
$865$		0			0
$866$	14.8729	−	25.7606i	0.505402	−	0.875381i
$867$	7.50687	+	7.11558i	0.254947	+	0.241658i
$868$	−9.70325	−	16.8065i	−0.329350	−	0.570451i
$869$	−13.3774	−	23.1704i	−0.453798	−	0.786002i
$870$		0			0
$871$	6.24020	−	10.8083i	0.211441	−	0.366227i
$872$	−32.3720			−1.09625
$873$	−32.7777	−	16.6538i	−1.10936	−	0.563644i
$874$	−13.7074			−0.463659
$875$		0			0
$876$	10.5561	−	44.0808i	0.356659	−	1.48935i
$877$	−19.8501	−	34.3814i	−0.670290	−	1.16098i	−0.977822	−	0.209438i	$-0.932836\pi$
$877$	−19.8501	−	34.3814i	−0.670290	−	1.16098i	0.307532	−	0.951538i	$-0.400497\pi$
$878$	10.4485	+	18.0974i	0.352620	+	0.610756i
$879$	−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	$0.318119\pi$
$882$	2.71699	+	50.7304i	0.0914858	+	1.70818i
$883$	−13.5051			−0.454482			−0.227241	−	0.973839i	$-0.572970\pi$
$883$	−13.5051			−0.454482			−0.227241	+	0.973839i	$0.572970\pi$
$884$	−9.47679	+	16.4143i	−0.318739	+	0.552072i
$885$		0			0
$886$	36.6751	+	63.5231i	1.23212	+	2.13410i
$887$	17.5611	+	30.4167i	0.589643	+	1.02129i	0.994279	+	0.106814i	$0.0340651\pi$
$887$	17.5611	+	30.4167i	0.589643	+	1.02129i	−0.404635	+	0.914478i	$0.632602\pi$
$888$	−2.14631	−	2.03443i	−0.0720253	−	0.0682710i
$889$	4.59936	−	7.96632i	0.154258	−	0.267182i
$890$		0			0
$891$	−12.0939	+	27.3318i	−0.405161	+	0.915650i
$892$	−37.4386			−1.25354
$893$	3.21193	−	5.56322i	0.107483	−	0.186166i
$894$	55.8165	+	52.9071i	1.86678	+	1.76948i
$895$		0			0
$896$	−3.92024	−	6.79006i	−0.130966	−	0.226840i
$897$	−9.05294	+	2.68725i	−0.302269	+	0.0897246i
$898$	23.8488	−	41.3073i	0.795843	−	1.37844i
$899$	−12.1120			−0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$	47.3780	−	82.0610i	1.57751	−	2.73233i
$903$	2.14631	−	8.96263i	0.0714246	−	0.298258i
$904$	−22.7603	−	39.4220i	−0.756997	−	1.31116i
$905$		0			0
$906$	1.28221	−	5.35431i	0.0425986	−	0.177885i
$907$	7.55928	−	13.0931i	0.251002	−	0.434748i	−0.712800	−	0.701367i	$-0.752573\pi$
$907$	7.55928	−	13.0931i	0.251002	−	0.434748i	0.963802	+	0.266619i	$0.0859067\pi$
$908$	−14.3492			−0.476194
$909$	−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	$0.830377\pi$
$912$	−13.2215	+	3.92464i	−0.437808	+	0.129958i
$913$	−2.56108	−	4.43593i	−0.0847595	−	0.146808i
$914$	29.2083	+	50.5903i	0.966125	+	1.67338i
$915$		0			0
$916$	54.6847	−	94.7167i	1.80683	−	3.12953i
$917$	−3.08482			−0.101870
$918$	−14.5520	−	40.8701i	−0.480288	−	1.34892i
$919$	−54.5489			−1.79940			−0.899702	−	0.436505i	$-0.856216\pi$
$919$	−54.5489			−1.79940			−0.899702	+	0.436505i	$0.856216\pi$
$920$		0			0
$921$	−10.0383	−	9.51504i	−0.330772	−	0.313531i
$922$	5.56342	+	9.63612i	0.183221	+	0.317349i
$923$	−5.93799	−	10.2849i	−0.195451	−	0.338532i
$924$	−12.2498	+	3.63620i	−0.402989	+	0.119622i
$925$		0			0
$926$	−49.0475			−1.61180
$927$	−0.735663	+	0.478945i	−0.0241624	+	0.0157306i
$928$	4.83317			0.158656
$929$	−10.1896	+	17.6490i	−0.334311	+	0.579044i	−0.983352	−	0.181709i	$-0.941837\pi$
$929$	−10.1896	+	17.6490i	−0.334311	+	0.579044i	0.649041	+	0.760753i	$0.275170\pi$
$930$		0			0
$931$	−4.44852	−	7.70506i	−0.145794	−	0.252523i
$932$	59.6988	+	103.401i	1.95550	+	3.38703i
$933$	−3.88558	+	16.2256i	−0.127208	+	0.531201i
$934$	30.9157	−	53.5476i	1.01159	−	1.75213i
$935$		0			0
$936$	−19.3774	+	12.6155i	−0.633371	+	0.412349i
$937$	−49.1979			−1.60723			−0.803613	−	0.595152i	$-0.797092\pi$
$937$	−49.1979			−1.60723			−0.803613	+	0.595152i	$0.797092\pi$
$938$	−6.10663	+	10.5770i	−0.199388	+	0.345351i
$939$	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	$0.709686\pi$
$942$	49.5243	+	46.9429i	1.61359	+	1.52948i
$943$	−23.4226	+	40.5691i	−0.762744	+	1.32111i
$944$	−30.3118			−0.986565
$945$		0			0
$946$	−86.4068			−2.80933
$947$	18.5821	−	32.1851i	0.603837	−	1.04588i	−0.388397	−	0.921492i	$-0.626971\pi$
$947$	18.5821	−	32.1851i	0.603837	−	1.04588i	0.992234	−	0.124384i	$-0.0396955\pi$
$948$	43.7603	+	41.4794i	1.42127	+	1.34719i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$	33.7886	−	10.0297i	1.09567	−	0.325236i
$952$	4.98133	−	8.62791i	0.161446	−	0.279632i
$953$	23.5761			0.763706			0.381853	−	0.924223i	$-0.375286\pi$
$953$	23.5761			0.763706			0.381853	+	0.924223i	$0.375286\pi$
$954$	33.8114	+	17.1790i	1.09468	+	0.556190i
$955$		0			0
$956$	9.07108	−	15.7116i	0.293380	−	0.508149i
$957$	−1.85730	+	7.75581i	−0.0600381	+	0.250710i
$958$	41.1751	+	71.3174i	1.33031	+	2.30416i
$959$	1.45759	+	2.52462i	0.0470680	+	0.0815242i
$960$		0			0
$961$	−22.6559	+	39.2412i	−0.730836	+	1.26584i
$962$	0.971726			0.0313297
$963$	−0.300407	−	5.60907i	−0.00968048	−	0.180750i
$964$	15.5743			0.501614
$965$		0			0
$966$	8.85916	−	2.62973i	0.285039	−	0.0846101i
$967$	4.19145	+	7.25980i	0.134788	+	0.233459i	0.925516	−	0.378708i	$-0.123631\pi$
$967$	4.19145	+	7.25980i	0.134788	+	0.233459i	−0.790729	+	0.612167i	$0.790298\pi$
$968$	0.0824893	+	0.142876i	0.00265131	+	0.00459220i
$969$	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	$0.432025\pi$
$972$	8.60029	−	66.8046i	0.275854	−	2.14276i
$973$	4.11310			0.131860
$974$	7.58936	−	13.1452i	0.243179	−	0.421198i
$975$		0			0
$976$	−22.1514	−	38.3673i	−0.709048	−	1.22811i
$977$	−7.16551	−	12.4110i	−0.229245	−	0.397064i	0.728340	−	0.685216i	$-0.240292\pi$
$977$	−7.16551	−	12.4110i	−0.229245	−	0.397064i	−0.957585	+	0.288153i	$0.906959\pi$
$978$	65.5717	−	19.4641i	2.09675	−	0.622394i
$979$	−4.98133	+	8.62791i	−0.159204	+	0.275749i
$980$		0			0
$981$	0.890114	+	16.6198i	0.0284191	+	0.530630i
$982$	−36.3118			−1.15876
$983$	−16.1541	+	27.9797i	−0.515236	+	0.892415i	0.484608	+	0.874732i	$0.338962\pi$
$983$	−16.1541	+	27.9797i	−0.515236	+	0.892415i	−0.999844	+	0.0176831i	$0.994371\pi$
$984$	−26.7125	+	111.547i	−0.851562	+	3.55599i
$985$		0			0
$986$	−5.78807	−	10.0252i	−0.184330	−	0.319269i
$987$	−1.00860	+	4.21174i	−0.0321040	+	0.134061i
$988$	3.76940	−	6.52879i	0.119921	−	0.207709i
$989$	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	$0.716978\pi$
$992$	15.2257	−	26.3716i	0.483415	−	0.837300i
$993$	27.3027	−	8.10447i	0.866426	−	0.257187i
$994$	5.81088	+	10.0647i	0.184310	+	0.319234i
$995$		0			0
$996$	8.37783	+	7.94114i	0.265462	+	0.251625i
$997$	19.3437	−	33.5043i	0.612621	−	1.06109i	−0.378176	−	0.925734i	$-0.623449\pi$
$997$	19.3437	−	33.5043i	0.612621	−	1.06109i	0.990797	−	0.135357i	$-0.0432181\pi$
$998$	−52.7258			−1.66901
$999$	−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.e.b.151.3		6
3.2	odd	2		675.2.e.b.451.1		6
5.2	odd	4		225.2.k.b.124.6		12
5.3	odd	4		225.2.k.b.124.1		12
5.4	even	2		45.2.e.b.16.1	✓	6
9.2	odd	6		2025.2.a.o.1.3		3
9.4	even	3	inner	225.2.e.b.76.3		6
9.5	odd	6		675.2.e.b.226.1		6
9.7	even	3		2025.2.a.n.1.1		3
15.2	even	4		675.2.k.b.424.1		12
15.8	even	4		675.2.k.b.424.6		12
15.14	odd	2		135.2.e.b.46.3		6
20.19	odd	2		720.2.q.i.241.1		6
45.2	even	12		2025.2.b.m.649.6		6
45.4	even	6		45.2.e.b.31.1	yes	6
45.7	odd	12		2025.2.b.l.649.1		6
45.13	odd	12		225.2.k.b.49.6		12
45.14	odd	6		135.2.e.b.91.3		6
45.22	odd	12		225.2.k.b.49.1		12
45.23	even	12		675.2.k.b.199.1		12
45.29	odd	6		405.2.a.i.1.1		3
45.32	even	12		675.2.k.b.199.6		12
45.34	even	6		405.2.a.j.1.3		3
45.38	even	12		2025.2.b.m.649.1		6
45.43	odd	12		2025.2.b.l.649.6		6
60.59	even	2		2160.2.q.k.721.1		6
180.59	even	6		2160.2.q.k.1441.1		6
180.79	odd	6		6480.2.a.bv.1.3		3
180.119	even	6		6480.2.a.bs.1.3		3
180.139	odd	6		720.2.q.i.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	5.4	even	2
45.2.e.b.31.1	yes	6	45.4	even	6
135.2.e.b.46.3		6	15.14	odd	2
135.2.e.b.91.3		6	45.14	odd	6
225.2.e.b.76.3		6	9.4	even	3	inner
225.2.e.b.151.3		6	1.1	even	1	trivial
225.2.k.b.49.1		12	45.22	odd	12
225.2.k.b.49.6		12	45.13	odd	12
225.2.k.b.124.1		12	5.3	odd	4
225.2.k.b.124.6		12	5.2	odd	4
405.2.a.i.1.1		3	45.29	odd	6
405.2.a.j.1.3		3	45.34	even	6
675.2.e.b.226.1		6	9.5	odd	6
675.2.e.b.451.1		6	3.2	odd	2
675.2.k.b.199.1		12	45.23	even	12
675.2.k.b.199.6		12	45.32	even	12
675.2.k.b.424.1		12	15.2	even	4
675.2.k.b.424.6		12	15.8	even	4
720.2.q.i.241.1		6	20.19	odd	2
720.2.q.i.481.1		6	180.139	odd	6
2025.2.a.n.1.1		3	9.7	even	3
2025.2.a.o.1.3		3	9.2	odd	6
2025.2.b.l.649.1		6	45.7	odd	12
2025.2.b.l.649.6		6	45.43	odd	12
2025.2.b.m.649.1		6	45.38	even	12
2025.2.b.m.649.6		6	45.2	even	12
2160.2.q.k.721.1		6	60.59	even	2
2160.2.q.k.1441.1		6	180.59	even	6
6480.2.a.bs.1.3		3	180.119	even	6
6480.2.a.bv.1.3		3	180.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25707 - 2.17731i) q^{2} +(-1.25707 - 1.19154i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(-0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 + 2.99571i) q^{9} +O(q^{10})\)	\(q+(1.25707 - 2.17731i) q^{2} +(-1.25707 - 1.19154i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(-0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 + 2.99571i) q^{9} +(1.66044 - 2.87597i) q^{11} +(-1.74293 + 7.27821i) q^{12} +(-0.660442 - 1.14392i) q^{13} +(0.646305 + 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} +3.32088 q^{17} +(6.72426 + 3.41648i) q^{18} -1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(-4.17458 - 7.23058i) q^{22} +(2.06382 + 3.57463i) q^{23} +(7.33502 + 6.95269i) q^{24} -3.32088 q^{26} +(3.36783 - 3.95698i) q^{27} +2.22153 q^{28} +(0.693252 - 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(1.74293 + 3.01885i) q^{32} +(-5.51414 + 1.63680i) q^{33} +(4.17458 - 7.23058i) q^{34} +(10.8633 - 7.07243i) q^{36} -0.292611 q^{37} +(-1.66044 + 2.87597i) q^{38} +(-0.532810 + 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(0.521405 - 2.17731i) q^{42} +(5.17458 - 8.96263i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-2.43165 + 4.21174i) q^{47} +(10.0096 - 2.97122i) q^{48} +(3.36783 + 5.83326i) q^{49} +(-4.17458 - 3.95698i) q^{51} +(-2.85369 + 4.94274i) q^{52} +5.02827 q^{53} +(-4.38197 - 12.3070i) q^{54} +(1.50000 - 2.59808i) q^{56} +(1.66044 + 1.57389i) q^{57} +(-1.74293 - 3.01885i) q^{58} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} -21.9627 q^{62} +(-1.37510 - 0.698664i) q^{63} -3.29261 q^{64} +(-3.36783 + 14.0635i) q^{66} +(4.72426 + 8.18266i) q^{67} +(-7.17458 - 12.4267i) q^{68} +(1.66498 - 6.95269i) q^{69} +8.99093 q^{71} +(-0.936184 - 17.4800i) q^{72} -6.05655 q^{73} +(-0.367832 + 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(0.853695 + 1.47864i) q^{77} +(4.17458 + 3.95698i) q^{78} +(4.02827 - 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} +28.5333 q^{82} +(0.771205 - 1.33577i) q^{83} +(-2.79261 - 2.64705i) q^{84} +(-13.0096 - 22.5333i) q^{86} +(-2.30221 + 0.683382i) q^{87} +(-9.68872 + 16.7813i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(8.91751 - 15.4456i) q^{92} +(-3.52374 + 14.7146i) q^{93} +(6.11350 + 10.5889i) q^{94} +(1.40611 - 5.87168i) q^{96} +(-6.12763 + 10.6134i) q^{97} +16.9344 q^{98} +(8.88197 + 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9	\( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9 + 2 * q^11 - 17 * q^12 + 4 * q^13 + 9 * q^14 - 5 * q^16 + 4 * q^17 + 23 * q^18 + 8 * q^19 - 4 * q^22 + 3 * q^23 + 15 * q^24 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 7 * q^29 - 8 * q^31 + 17 * q^32 - 20 * q^33 + 4 * q^34 + 10 * q^36 - 12 * q^37 - 2 * q^38 - 14 * q^39 + 13 * q^41 + 33 * q^42 + 10 * q^43 - 44 * q^44 - 6 * q^46 + 13 * q^47 + 10 * q^48 + 2 * q^49 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 5 * q^54 + 9 * q^56 + 2 * q^57 - 17 * q^58 + 2 * q^59 - q^61 - 84 * q^62 - 33 * q^63 - 30 * q^64 - 2 * q^66 + 11 * q^67 - 22 * q^68 + 39 * q^69 - 20 * q^71 - 15 * q^72 + 16 * q^73 + 16 * q^74 + 12 * q^76 + 4 * q^78 - 2 * q^79 - 19 * q^81 + 58 * q^82 - 15 * q^83 - 27 * q^84 - 28 * q^86 + 26 * q^87 - 24 * q^88 - 18 * q^89 + 20 * q^91 + 39 * q^92 + 42 * q^93 + 31 * q^94 + 13 * q^96 - 18 * q^97 + 80 * q^98 + 22 * q^99

Introduction

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