LMFDB - Embedded newform 441.2.f.h.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.2
Character	$\chi$	$=$	441.148
Dual form			441.2.f.h.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08816 - 1.88474i) q^{2} +(1.68791 + 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(-0.634145 + 1.09837i) q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} +O(q^{10})$	\(q+(-1.08816 - 1.88474i) q^{2} +(1.68791 + 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(-0.634145 + 1.09837i) q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} +2.76019 q^{10} +(2.73867 + 4.74351i) q^{11} +(-3.23009 + 3.46828i) q^{12} +(2.37268 - 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 + 1.71920i) q^{16} -4.81644 q^{17} +(-0.463740 - 6.51244i) q^{18} +5.38119 q^{19} +(-1.73523 - 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(2.70484 + 0.622645i) q^{24} +(1.69572 + 2.93707i) q^{25} -10.3274 q^{26} +(4.04442 + 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(4.65895 + 1.07247i) q^{30} +(0.732093 - 1.26802i) q^{31} +(3.76264 - 6.51709i) q^{32} +(2.77952 + 9.07071i) q^{33} +(5.24103 + 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +1.91834 q^{37} +(-5.85557 - 10.1421i) q^{38} +(5.60164 - 6.01471i) q^{39} +(-1.01621 + 1.76012i) q^{40} +(-1.94808 + 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} -14.9878 q^{44} +(-3.15166 + 2.13168i) q^{45} -11.2653 q^{46} +(-1.57773 - 2.73271i) q^{47} +(1.00739 + 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(-8.12969 - 1.87143i) q^{51} +(6.49243 + 11.2452i) q^{52} -7.14299 q^{53} +(1.74766 - 11.1726i) q^{54} -6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} +(-0.154341 + 0.267327i) q^{59} +(-1.76111 - 5.74723i) q^{60} +(-5.17143 - 8.95719i) q^{61} -3.18652 q^{62} -12.4070 q^{64} +(3.00924 + 5.21216i) q^{65} +(14.0714 - 15.1090i) q^{66} +(-2.23655 + 3.87382i) q^{67} +(6.58968 - 11.4137i) q^{68} +(6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(4.32359 + 2.10193i) q^{72} -10.5503 q^{73} +(-2.08745 - 3.61557i) q^{74} +(1.72102 + 5.61638i) q^{75} +(-7.36235 + 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 + 7.80846i) q^{79} -2.51776 q^{80} +(5.55902 + 7.07794i) q^{81} +8.47926 q^{82} +(-5.08023 - 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(2.04664 + 6.67903i) q^{87} +(4.38866 + 7.60138i) q^{88} +5.19552 q^{89} +(7.44716 + 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(1.72840 - 1.85585i) q^{93} +(-3.43363 + 5.94722i) q^{94} +(-3.41245 + 5.91054i) q^{95} +(8.88321 - 9.53826i) q^{96} +(-2.48521 - 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.08816	−	1.88474i	−0.769442	−	1.33271i	−0.937866	−	0.346998i	$-0.887201\pi$
$2$	−1.08816	−	1.88474i	−0.769442	−	1.33271i	0.168424	−	0.985715i	$-0.446132\pi$
$3$	1.68791	+	0.388551i	0.974513	+	0.224330i
$3$	1.68791	+	0.388551i	0.974513	+	0.224330i
$4$	−1.36816	+	2.36973i	−0.684082	+	1.18487i
$5$	−0.634145	+	1.09837i	−0.283598	+	0.491206i	−0.972268	−	0.233868i	$-0.924862\pi$
$5$	−0.634145	+	1.09837i	−0.283598	+	0.491206i	0.688670	+	0.725075i	$0.258195\pi$
$6$	−1.10439	−	3.60407i	−0.450864	−	1.47136i
$7$		0			0
$7$		0			0
$8$	1.60248			0.566563
$9$	2.69806	+	1.31167i	0.899352	+	0.437225i
$10$	2.76019			0.872849
$11$	2.73867	+	4.74351i	0.825739	+	1.43022i	0.901353	+	0.433084i	$0.142575\pi$
$11$	2.73867	+	4.74351i	0.825739	+	1.43022i	−0.0756148	+	0.997137i	$0.524092\pi$
$12$	−3.23009	+	3.46828i	−0.932448	+	1.00121i
$13$	2.37268	−	4.10960i	0.658062	−	1.13980i	−0.323054	−	0.946380i	$-0.604710\pi$
$13$	2.37268	−	4.10960i	0.658062	−	1.13980i	0.981117	−	0.193417i	$-0.0619570\pi$
$14$		0			0
$15$	−1.49715	+	1.60755i	−0.386562	+	0.415068i
$16$	0.992580	+	1.71920i	0.248145	+	0.429800i
$17$	−4.81644			−1.16816			−0.584079	−	0.811697i	$-0.698544\pi$
$17$	−4.81644			−1.16816			−0.584079	+	0.811697i	$0.698544\pi$
$18$	−0.463740	−	6.51244i	−0.109305	−	1.53500i
$19$	5.38119			1.23453			0.617265	−	0.786756i	$-0.288241\pi$
$19$	5.38119			1.23453			0.617265	+	0.786756i	$0.288241\pi$
$20$	−1.73523	−	3.00550i	−0.388009	−	0.672051i
$21$		0			0
$22$	5.96019	−	10.3233i	1.27072	−	2.20095i
$23$	2.58816	−	4.48282i	0.539668	−	0.934732i	−0.459254	−	0.888305i	$-0.651883\pi$
$23$	2.58816	−	4.48282i	0.539668	−	0.934732i	0.998922	−	0.0464269i	$-0.0147835\pi$
$24$	2.70484	+	0.622645i	0.552123	+	0.127097i
$25$	1.69572	+	2.93707i	0.339144	+	0.587415i
$26$	−10.3274			−2.02536
$27$	4.04442	+	3.26231i	0.778348	+	0.627833i
$28$		0			0
$29$	2.01656	+	3.49278i	0.374466	+	0.648594i	0.990247	−	0.139324i	$-0.0444928\pi$
$29$	2.01656	+	3.49278i	0.374466	+	0.648594i	−0.615781	+	0.787917i	$0.711159\pi$
$30$	4.65895	+	1.07247i	0.850603	+	0.195806i
$31$	0.732093	−	1.26802i	0.131488	−	0.227744i	−0.792763	−	0.609531i	$-0.791358\pi$
$31$	0.732093	−	1.26802i	0.131488	−	0.227744i	0.924250	+	0.381787i	$0.124691\pi$
$32$	3.76264	−	6.51709i	0.665148	−	1.15207i
$33$	2.77952	+	9.07071i	0.483852	+	1.57901i
$34$	5.24103	+	9.07773i	0.898830	+	1.55682i
$35$		0			0
$36$	−6.79970	+	4.59908i	−1.13328	+	0.766514i
$37$	1.91834			0.315373			0.157687	−	0.987489i	$-0.449596\pi$
$37$	1.91834			0.315373			0.157687	+	0.987489i	$0.449596\pi$
$38$	−5.85557	−	10.1421i	−0.949899	−	1.64527i
$39$	5.60164	−	6.01471i	0.896981	−	0.963125i
$40$	−1.01621	+	1.76012i	−0.160676	+	0.278299i
$41$	−1.94808	+	3.37418i	−0.304239	+	0.526958i	−0.977092	−	0.212819i	$-0.931736\pi$
$41$	−1.94808	+	3.37418i	−0.304239	+	0.526958i	0.672852	+	0.739777i	$0.265069\pi$
$42$		0			0
$43$	−1.66016	−	2.87549i	−0.253173	−	0.438508i	0.711225	−	0.702964i	$-0.248141\pi$
$43$	−1.66016	−	2.87549i	−0.253173	−	0.438508i	−0.964398	+	0.264457i	$0.914807\pi$
$44$	−14.9878			−2.25949
$45$	−3.15166	+	2.13168i	−0.469822	+	0.317771i
$46$	−11.2653			−1.66097
$47$	−1.57773	−	2.73271i	−0.230135	−	0.398606i	0.727712	−	0.685882i	$-0.240584\pi$
$47$	−1.57773	−	2.73271i	−0.230135	−	0.398606i	−0.957848	+	0.287276i	$0.907250\pi$
$48$	1.00739	+	3.28752i	0.145404	+	0.474512i
$49$		0			0
$50$	3.69042	−	6.39199i	0.521904	−	0.903964i
$51$	−8.12969	−	1.87143i	−1.13838	−	0.262052i
$52$	6.49243	+	11.2452i	0.900338	+	1.55943i
$53$	−7.14299			−0.981165			−0.490582	−	0.871395i	$-0.663216\pi$
$53$	−7.14299			−0.981165			−0.490582	+	0.871395i	$0.663216\pi$
$54$	1.74766	−	11.1726i	0.237827	−	1.52040i
$55$	−6.94684			−0.936712
$56$		0			0
$57$	9.08294	+	2.09086i	1.20307	+	0.276942i
$58$	4.38866	−	7.60138i	0.576259	−	0.998111i
$59$	−0.154341	+	0.267327i	−0.0200935	+	0.0348030i	−0.875897	−	0.482498i	$-0.839730\pi$
$59$	−0.154341	+	0.267327i	−0.0200935	+	0.0348030i	0.855804	+	0.517301i	$0.173063\pi$
$60$	−1.76111	−	5.74723i	−0.227359	−	0.741965i
$61$	−5.17143	−	8.95719i	−0.662134	−	1.14685i	−0.980054	−	0.198732i	$-0.936318\pi$
$61$	−5.17143	−	8.95719i	−0.662134	−	1.14685i	0.317920	−	0.948118i	$-0.397016\pi$
$62$	−3.18652			−0.404689
$63$		0			0
$64$	−12.4070			−1.55088
$65$	3.00924	+	5.21216i	0.373250	+	0.646489i
$66$	14.0714	−	15.1090i	1.73207	−	1.85979i
$67$	−2.23655	+	3.87382i	−0.273238	+	0.473262i	−0.969689	−	0.244342i	$-0.921428\pi$
$67$	−2.23655	+	3.87382i	−0.273238	+	0.473262i	0.696451	+	0.717604i	$0.254761\pi$
$68$	6.58968	−	11.4137i	0.799116	−	1.38411i
$69$	6.11037	−	6.56095i	0.735602	−	0.789845i
$70$		0			0
$71$	−1.96688			−0.233426			−0.116713	−	0.993166i	$-0.537236\pi$
$71$	−1.96688			−0.233426			−0.116713	+	0.993166i	$0.537236\pi$
$72$	4.32359	+	2.10193i	0.509540	+	0.247715i
$73$	−10.5503			−1.23482			−0.617409	−	0.786642i	$-0.711818\pi$
$73$	−10.5503			−1.23482			−0.617409	+	0.786642i	$0.711818\pi$
$74$	−2.08745	−	3.61557i	−0.242662	−	0.420302i
$75$	1.72102	+	5.61638i	0.198726	+	0.648524i
$76$	−7.36235	+	12.7520i	−0.844520	+	1.46275i
$77$		0			0
$78$	−17.4316	−	4.01270i	−1.97374	−	0.454349i
$79$	4.50822	+	7.80846i	0.507214	+	0.878520i	0.999965	+	0.00835000i	$0.00265792\pi$
$79$	4.50822	+	7.80846i	0.507214	+	0.878520i	−0.492751	+	0.870170i	$0.664009\pi$
$80$	−2.51776			−0.281494
$81$	5.55902	+	7.07794i	0.617669	+	0.786438i
$82$	8.47926			0.936378
$83$	−5.08023	−	8.79921i	−0.557627	−	0.965839i	−0.997694	−	0.0678739i	$-0.978378\pi$
$83$	−5.08023	−	8.79921i	−0.557627	−	0.965839i	0.440066	−	0.897965i	$-0.354955\pi$
$84$		0			0
$85$	3.05432	−	5.29023i	0.331287	−	0.573806i
$86$	−3.61303	+	6.25796i	−0.389603	+	0.674813i
$87$	2.04664	+	6.67903i	0.219423	+	0.716067i
$88$	4.38866	+	7.60138i	0.467833	+	0.810310i
$89$	5.19552			0.550724			0.275362	−	0.961341i	$-0.411202\pi$
$89$	5.19552			0.550724			0.275362	+	0.961341i	$0.411202\pi$
$90$	7.44716	+	3.62047i	0.784999	+	0.381631i
$91$		0			0
$92$	7.08205	+	12.2665i	0.738354	+	1.27887i
$93$	1.72840	−	1.85585i	0.179226	−	0.192442i
$94$	−3.43363	+	5.94722i	−0.354152	+	0.613409i
$95$	−3.41245	+	5.91054i	−0.350110	+	0.606409i
$96$	8.88321	−	9.53826i	0.906639	−	0.973495i
$97$	−2.48521	−	4.30451i	−0.252335	−	0.437057i	0.711833	−	0.702348i	$-0.247865\pi$
$97$	−2.48521	−	4.30451i	−0.252335	−	0.437057i	−0.964168	+	0.265291i	$0.914532\pi$
$98$		0			0
$99$	1.16714	+	16.3905i	0.117302	+	1.64731i
$100$	−9.28010			−0.928010
$101$	−0.00266904	−	0.00462292i	−0.000265580	−	0.000459997i	0.865893	−	0.500230i	$-0.166751\pi$
$101$	−0.00266904	−	0.00462292i	−0.000265580	−	0.000459997i	−0.866158	+	0.499770i	$0.833418\pi$
$102$	5.31921	+	17.3588i	0.526681	+	1.71877i
$103$	−6.51741	+	11.2885i	−0.642180	+	1.11229i	0.342765	+	0.939421i	$0.388636\pi$
$103$	−6.51741	+	11.2885i	−0.642180	+	1.11229i	−0.984945	+	0.172867i	$0.944697\pi$
$104$	3.80217	−	6.58555i	0.372834	−	0.645767i
$105$		0			0
$106$	7.77268	+	13.4627i	0.754950	+	1.30761i
$107$	9.42162			0.910822			0.455411	−	0.890281i	$-0.349492\pi$
$107$	9.42162			0.910822			0.455411	+	0.890281i	$0.349492\pi$
$108$	−13.2642	+	5.12079i	−1.27635	+	0.492749i
$109$	16.8903			1.61779			0.808896	−	0.587951i	$-0.200065\pi$
$109$	16.8903			1.61779			0.808896	+	0.587951i	$0.200065\pi$
$110$	7.55924	+	13.0930i	0.720746	+	1.24837i
$111$	3.23798	+	0.745372i	0.307335	+	0.0707476i
$112$		0			0
$113$	−3.07313	+	5.32281i	−0.289095	+	0.500728i	−0.973594	−	0.228286i	$-0.926688\pi$
$113$	−3.07313	+	5.32281i	−0.289095	+	0.500728i	0.684499	+	0.729014i	$0.260021\pi$
$114$	−5.94292	−	19.3942i	−0.556605	−	1.81643i
$115$	3.28253	+	5.68551i	0.306098	+	0.530176i
$116$	−11.0359			−1.02466
$117$	11.7921	−	7.97575i	1.09018	−	0.737358i
$118$	0.671790			0.0618432
$119$		0			0
$120$	−2.39915	+	2.57607i	−0.219012	+	0.235162i
$121$	−9.50058	+	16.4555i	−0.863689	+	1.49595i
$122$	−11.2546	+	19.4936i	−1.01895	+	1.76487i
$123$	−4.59922	+	4.93837i	−0.414698	+	0.445278i
$124$	2.00325	+	3.46973i	0.179897	+	0.311591i
$125$	−10.6428			−0.951919
$126$		0			0
$127$	−13.9305			−1.23613			−0.618065	−	0.786127i	$-0.712083\pi$
$127$	−13.9305			−1.23613			−0.618065	+	0.786127i	$0.712083\pi$
$128$	5.97551	+	10.3499i	0.528165	+	0.914809i
$129$	−1.68493	−	5.49861i	−0.148350	−	0.484126i
$130$	6.54905	−	11.3433i	0.574389	−	0.994871i
$131$	0.0895778	−	0.155153i	0.00782645	−	0.0135558i	−0.862086	−	0.506763i	$-0.830842\pi$
$131$	0.0895778	−	0.155153i	0.00782645	−	0.0135558i	0.869912	+	0.493207i	$0.164175\pi$
$132$	−25.2980	−	5.82351i	−2.20191	−	0.506872i
$133$		0			0
$134$	9.73486			0.840964
$135$	−6.14798	+	2.37349i	−0.529134	+	0.204277i
$136$	−7.71825			−0.661835
$137$	−1.57603	−	2.72977i	−0.134649	−	0.233220i	0.790814	−	0.612056i	$-0.209657\pi$
$137$	−1.57603	−	2.72977i	−0.134649	−	0.233220i	−0.925463	+	0.378837i	$0.876324\pi$
$138$	−19.0147	−	4.37712i	−1.61864	−	0.372606i
$139$	9.42857	−	16.3308i	0.799721	−	1.38516i	−0.120077	−	0.992765i	$-0.538314\pi$
$139$	9.42857	−	16.3308i	0.799721	−	1.38516i	0.919798	−	0.392392i	$-0.128352\pi$
$140$		0			0
$141$	−1.60126	−	5.22558i	−0.134851	−	0.440073i
$142$	2.14027	+	3.70706i	0.179608	+	0.311090i
$143$	25.9919			2.17355
$144$	0.423009	+	5.94044i	0.0352507	+	0.495037i
$145$	−5.11516			−0.424791
$146$	11.4804	+	19.8846i	0.950122	+	1.64566i
$147$		0			0
$148$	−2.62461	+	4.54595i	−0.215741	+	0.373675i
$149$	10.6370	−	18.4238i	0.871418	−	1.50934i	0.0108879	−	0.999941i	$-0.496534\pi$
$149$	10.6370	−	18.4238i	0.871418	−	1.50934i	0.860530	−	0.509400i	$-0.170132\pi$
$150$	8.71269	−	9.35516i	0.711388	−	0.763846i
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	0.706965	−	0.707249i	$-0.250064\pi$
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	−0.965978	+	0.258625i	$0.916731\pi$
$152$	8.62326			0.699438
$153$	−12.9950	−	6.31759i	−1.05059	−	0.510747i
$154$		0			0
$155$	0.928506	+	1.60822i	0.0745794	+	0.129175i
$156$	6.58927	+	21.5035i	0.527564	+	1.72166i
$157$	−0.697976	+	1.20893i	−0.0557045	+	0.0964830i	−0.892533	−	0.450982i	$-0.851074\pi$
$157$	−0.697976	+	1.20893i	−0.0557045	+	0.0964830i	0.836828	+	0.547465i	$0.184407\pi$
$158$	9.81128	−	16.9936i	0.780543	−	1.35194i
$159$	−12.0567	−	2.77541i	−0.956158	−	0.220105i
$160$	4.77212	+	8.26556i	0.377269	+	0.653450i
$161$		0			0
$162$	7.29101	−	18.1792i	0.572836	−	1.42829i
$163$	−19.0617			−1.49303			−0.746515	−	0.665369i	$-0.768274\pi$
$163$	−19.0617			−1.49303			−0.746515	+	0.665369i	$0.768274\pi$
$164$	−5.33059	−	9.23286i	−0.416249	−	0.720965i
$165$	−11.7256	−	2.69920i	−0.912838	−	0.210132i
$166$	−11.0562	+	19.1498i	−0.858124	+	1.48631i
$167$	0.872003	−	1.51035i	0.0674776	−	0.116875i	−0.830313	−	0.557298i	$-0.811838\pi$
$167$	0.872003	−	1.51035i	0.0674776	−	0.116875i	0.897790	+	0.440423i	$0.145172\pi$
$168$		0			0
$169$	−4.75919	−	8.24317i	−0.366092	−	0.634090i
$170$	−13.2943			−1.01963
$171$	14.5188	+	7.05837i	1.11028	+	0.539767i
$172$	9.08551			0.692764
$173$	5.03794	+	8.72598i	0.383028	+	0.663424i	0.991493	−	0.130157i	$-0.0415480\pi$
$173$	5.03794	+	8.72598i	0.383028	+	0.663424i	−0.608466	+	0.793580i	$0.708215\pi$
$174$	10.3612	−	11.1252i	0.785478	−	0.843400i
$175$		0			0
$176$	−5.43669	+	9.41662i	−0.409806	+	0.709805i
$177$	−0.364384	+	0.391254i	−0.0273888	+	0.0294084i
$178$	−5.65353	−	9.79221i	−0.423750	−	0.733957i
$179$	−18.5424			−1.38592			−0.692961	−	0.720975i	$-0.743694\pi$
$179$	−18.5424			−1.38592			−0.692961	+	0.720975i	$0.743694\pi$
$180$	−0.739504	−	10.3851i	−0.0551193	−	0.774058i
$181$	−8.80982			−0.654829			−0.327414	−	0.944881i	$-0.606177\pi$
$181$	−8.80982			−0.654829			−0.327414	+	0.944881i	$0.606177\pi$
$182$		0			0
$183$	−5.24858	−	17.1283i	−0.387986	−	1.26616i
$184$	4.14747	−	7.18363i	0.305756	−	0.529584i
$185$	−1.21651	+	2.10705i	−0.0894393	+	0.154913i
$186$	−5.37855	−	1.23813i	−0.394375	−	0.0907838i
$187$	−13.1906	−	22.8468i	−0.964593	−	1.67072i
$188$	8.63437			0.629726
$189$		0			0
$190$	14.8531			1.07756
$191$	−2.45469	−	4.25165i	−0.177615	−	0.307639i	0.763448	−	0.645869i	$-0.223505\pi$
$191$	−2.45469	−	4.25165i	−0.177615	−	0.307639i	−0.941063	+	0.338231i	$0.890172\pi$
$192$	−20.9419	−	4.82077i	−1.51135	−	0.347909i
$193$	4.88380	−	8.45899i	0.351544	−	0.608892i	−0.634976	−	0.772531i	$-0.718990\pi$
$193$	4.88380	−	8.45899i	0.351544	−	0.608892i	0.986520	+	0.163640i	$0.0523235\pi$
$194$	−5.40859	+	9.36796i	−0.388314	+	0.672580i
$195$	3.05413	+	9.96688i	0.218711	+	0.713743i
$196$		0			0
$197$	3.31445			0.236145			0.118073	−	0.993005i	$-0.462328\pi$
$197$	3.31445			0.236145			0.118073	+	0.993005i	$0.462328\pi$
$198$	29.6218	−	20.0352i	2.10513	−	1.42384i
$199$	11.0886			0.786053			0.393026	−	0.919527i	$-0.371428\pi$
$199$	11.0886			0.786053			0.393026	+	0.919527i	$0.371428\pi$
$200$	2.71736	+	4.70661i	0.192146	+	0.332807i
$201$	−5.28026	+	5.66963i	−0.372441	+	0.399905i
$202$	−0.00580866	+	0.0100609i	−0.000408696	+	0.000707883i
$203$		0			0
$204$	15.5575	−	16.7048i	1.08925	−	1.16957i
$205$	−2.47073	−	4.27943i	−0.172563	−	0.298889i
$206$	28.3678			1.97648
$207$	12.8630	−	8.70008i	0.894039	−	0.604697i
$208$	9.42029			0.653180
$209$	14.7373	+	25.5257i	1.01940	+	1.76565i
$210$		0			0
$211$	−3.66118	+	6.34135i	−0.252046	+	0.436557i	−0.964089	−	0.265579i	$-0.914437\pi$
$211$	−3.66118	+	6.34135i	−0.252046	+	0.436557i	0.712043	+	0.702136i	$0.247770\pi$
$212$	9.77278	−	16.9270i	0.671198	−	1.16255i
$213$	−3.31991	−	0.764233i	−0.227477	−	0.0523644i
$214$	−10.2522	−	17.7573i	−0.700825	−	1.21386i
$215$	4.21114			0.287197
$216$	6.48110	+	5.22780i	0.440983	+	0.355707i
$217$		0			0
$218$	−18.3792	−	31.8337i	−1.24480	−	2.15605i
$219$	−17.8079	−	4.09932i	−1.20335	−	0.277007i
$220$	9.50442	−	16.4621i	0.640788	−	1.10988i
$221$	−11.4278	+	19.7936i	−0.768720	+	1.33146i
$222$	−2.11859	−	6.91383i	−0.142191	−	0.464026i
$223$	2.02765	+	3.51199i	0.135782	+	0.235181i	0.925896	−	0.377779i	$-0.123312\pi$
$223$	2.02765	+	3.51199i	0.135782	+	0.235181i	−0.790114	+	0.612960i	$0.789979\pi$
$224$		0			0
$225$	0.722667	+	10.1486i	0.0481778	+	0.676575i
$226$	13.3762			0.889769
$227$	−0.667087	−	1.15543i	−0.0442761	−	0.0766884i	0.843038	−	0.537854i	$-0.180765\pi$
$227$	−0.667087	−	1.15543i	−0.0442761	−	0.0766884i	−0.887314	+	0.461165i	$0.847431\pi$
$228$	−17.3817	+	18.6635i	−1.15113	+	1.23602i
$229$	7.99832	−	13.8535i	0.528544	−	0.915465i	−0.470902	−	0.882185i	$-0.656072\pi$
$229$	7.99832	−	13.8535i	0.528544	−	0.915465i	0.999446	−	0.0332795i	$-0.0105952\pi$
$230$	7.14381	−	12.3734i	0.471049	−	0.815880i
$231$		0			0
$232$	3.23150	+	5.59712i	0.212158	+	0.367469i
$233$	8.13083			0.532669			0.266334	−	0.963881i	$-0.414187\pi$
$233$	8.13083			0.532669			0.266334	+	0.963881i	$0.414187\pi$
$234$	−27.8638	−	13.5461i	−1.82152	−	0.885539i
$235$	4.00203			0.261064
$236$	−0.422329	−	0.731495i	−0.0274913	−	0.0476163i
$237$	4.57547	+	14.9316i	0.297208	+	0.969913i
$238$		0			0
$239$	11.0509	−	19.1407i	0.714823	−	1.23811i	−0.248204	−	0.968708i	$-0.579840\pi$
$239$	11.0509	−	19.1407i	0.714823	−	1.23811i	0.963028	−	0.269403i	$-0.0868262\pi$
$240$	−4.24974	−	0.978276i	−0.274320	−	0.0631475i
$241$	−13.7973	−	23.8977i	−0.888765	−	1.53939i	−0.841336	−	0.540512i	$-0.818230\pi$
$241$	−13.7973	−	23.8977i	−0.888765	−	1.53939i	−0.0474292	−	0.998875i	$-0.515103\pi$
$242$	41.3524			2.65823
$243$	6.63297	+	14.1069i	0.425505	+	0.904956i
$244$	28.3015			1.81182
$245$		0			0
$246$	14.3122	+	3.29462i	0.912513	+	0.210057i
$247$	12.7678	−	22.1145i	0.812397	−	1.40711i
$248$	1.17317	−	2.03198i	0.0744961	−	0.129031i
$249$	−5.15601	−	16.8262i	−0.326749	−	1.06632i
$250$	11.5810	+	20.0589i	0.732447	+	1.26863i
$251$	−16.5610			−1.04532			−0.522661	−	0.852541i	$-0.675061\pi$
$251$	−16.5610			−1.04532			−0.522661	+	0.852541i	$0.675061\pi$
$252$		0			0
$253$	28.3524			1.78250
$254$	15.1585	+	26.2553i	0.951130	+	1.64741i
$255$	7.21093	−	7.74266i	0.451566	−	0.484864i
$256$	0.597516	−	1.03493i	0.0373448	−	0.0646831i
$257$	−1.03287	+	1.78898i	−0.0644285	+	0.111593i	−0.896440	−	0.443164i	$-0.853856\pi$
$257$	−1.03287	+	1.78898i	−0.0644285	+	0.111593i	0.832012	+	0.554758i	$0.187189\pi$
$258$	−8.53000	+	9.15900i	−0.531054	+	0.570214i
$259$		0			0
$260$	−16.4686			−1.02134
$261$	0.859399	+	12.0688i	0.0531954	+	0.747040i
$262$	−0.389898			−0.0240880
$263$	−5.06482	−	8.77252i	−0.312310	−	0.540937i	0.666552	−	0.745458i	$-0.267769\pi$
$263$	−5.06482	−	8.77252i	−0.312310	−	0.540937i	−0.978862	+	0.204522i	$0.934436\pi$
$264$	4.45413	+	14.5356i	0.274133	+	0.894607i
$265$	4.52969	−	7.84565i	0.278257	−	0.481954i
$266$		0			0
$267$	8.76955	+	2.01872i	0.536688	+	0.123544i
$268$	−6.11994	−	10.6000i	−0.373835	−	0.647501i
$269$	−15.0994			−0.920630			−0.460315	−	0.887756i	$-0.652263\pi$
$269$	−15.0994			−0.920630			−0.460315	+	0.887756i	$0.652263\pi$
$270$	11.1634	+	9.00462i	0.679381	+	0.548003i
$271$	−28.8051			−1.74979			−0.874893	−	0.484317i	$-0.839068\pi$
$271$	−28.8051			−1.74979			−0.874893	+	0.484317i	$0.839068\pi$
$272$	−4.78070	−	8.28041i	−0.289872	−	0.502074i
$273$		0			0
$274$	−3.42993	+	5.94082i	−0.207210	+	0.358898i
$275$	−9.28802	+	16.0873i	−0.560089	+	0.970102i
$276$	7.18769	+	23.4564i	0.432648	+	1.41191i
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	0.903724	−	0.428116i	$-0.140823\pi$
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	−0.822621	+	0.568590i	$0.807489\pi$
$278$	−41.0390			−2.46135
$279$	3.63846	−	2.46093i	0.217829	−	0.147332i
$280$		0			0
$281$	−2.46312	−	4.26626i	−0.146938	−	0.254503i	0.783157	−	0.621825i	$-0.213608\pi$
$281$	−2.46312	−	4.26626i	−0.146938	−	0.254503i	−0.930094	+	0.367321i	$0.880275\pi$
$282$	−8.10644	+	8.70421i	−0.482731	+	0.518328i
$283$	−1.79079	+	3.10173i	−0.106451	+	0.184379i	−0.914330	−	0.404969i	$-0.867282\pi$
$283$	−1.79079	+	3.10173i	−0.106451	+	0.184379i	0.807879	+	0.589348i	$0.200615\pi$
$284$	2.69102	−	4.66098i	0.159682	−	0.276578i
$285$	−8.05644	+	8.65053i	−0.477223	+	0.512413i
$286$	−28.2832	−	48.9879i	−1.67242	−	2.89672i
$287$		0			0
$288$	18.7001	−	12.6481i	1.10192	−	0.745298i
$289$	6.19806			0.364592
$290$	5.56609	+	9.64075i	0.326852	+	0.566125i
$291$	−2.52228	−	8.23124i	−0.147859	−	0.482524i
$292$	14.4345	−	25.0014i	0.844718	−	1.46309i
$293$	12.1955	−	21.1232i	0.712469	−	1.23403i	−0.251459	−	0.967868i	$-0.580910\pi$
$293$	12.1955	−	21.1232i	0.712469	−	1.23403i	0.963928	−	0.266164i	$-0.0857563\pi$
$294$		0			0
$295$	−0.195750	−	0.339048i	−0.0113970	−	0.0197401i
$296$	3.07411			0.178679
$297$	−4.39851	+	28.1191i	−0.255228	+	1.63164i
$298$	−46.2989			−2.68202
$299$	−12.2817	−	21.2726i	−0.710270	−	1.23022i
$300$	−15.6639	−	3.60579i	−0.904358	−	0.208180i
$301$		0			0
$302$	−6.92678	+	11.9975i	−0.398591	+	0.690380i
$303$	−0.00270886	−	0.00884011i	−0.000155620	−	0.000507851i
$304$	5.34126	+	9.25134i	0.306342	+	0.530600i
$305$	13.1177			0.751120
$306$	2.23357	+	31.3668i	0.127685	+	1.79312i
$307$	−23.9025			−1.36419			−0.682094	−	0.731265i	$-0.738930\pi$
$307$	−23.9025			−1.36419			−0.682094	+	0.731265i	$0.738930\pi$
$308$		0			0
$309$	−15.3869	+	16.5216i	−0.875332	+	0.939879i
$310$	2.02072	−	3.49998i	0.114769	−	0.198786i
$311$	6.47082	−	11.2078i	0.366926	−	0.635535i	−0.622157	−	0.782893i	$-0.713743\pi$
$311$	6.47082	−	11.2078i	0.366926	−	0.635535i	0.989083	+	0.147357i	$0.0470768\pi$
$312$	8.97653	−	9.63846i	0.508196	−	0.545671i
$313$	13.4340	+	23.2684i	0.759336	+	1.31521i	0.943189	+	0.332255i	$0.107810\pi$
$313$	13.4340	+	23.2684i	0.759336	+	1.31521i	−0.183853	+	0.982954i	$0.558857\pi$
$314$	3.03802			0.171446
$315$		0			0
$316$	−24.6719			−1.38790
$317$	−4.15584	−	7.19813i	−0.233415	−	0.404287i	0.725396	−	0.688332i	$-0.241657\pi$
$317$	−4.15584	−	7.19813i	−0.233415	−	0.404287i	−0.958811	+	0.284045i	$0.908324\pi$
$318$	7.88863	+	25.7438i	0.442372	+	1.44364i
$319$	−11.0454	+	19.1311i	−0.618422	+	1.07114i
$320$	7.86786	−	13.6275i	0.439827	−	0.761803i
$321$	15.9028	+	3.66078i	0.887608	+	0.204325i
$322$		0			0
$323$	−25.9182			−1.44212
$324$	−24.3785	+	3.48959i	−1.35436	+	0.193866i
$325$	16.0936			0.892712
$326$	20.7421	+	35.9264i	1.14880	+	1.98978i
$327$	28.5092	+	6.56272i	1.57656	+	0.362919i
$328$	−3.12177	+	5.40706i	−0.172371	+	0.298555i
$329$		0			0
$330$	7.67201	+	25.0369i	0.422330	+	1.37824i
$331$	−6.19889	−	10.7368i	−0.340722	−	0.590147i	0.643845	−	0.765156i	$-0.277338\pi$
$331$	−6.19889	−	10.7368i	−0.340722	−	0.590147i	−0.984567	+	0.175009i	$0.944005\pi$
$332$	27.8024			1.52585
$333$	5.17579	+	2.51624i	0.283632	+	0.137889i
$334$	−3.79550			−0.207680
$335$	−2.83659	−	4.91312i	−0.154980	−	0.268433i
$336$		0			0
$337$	−12.9588	+	22.4454i	−0.705913	+	1.22268i	0.260448	+	0.965488i	$0.416130\pi$
$337$	−12.9588	+	22.4454i	−0.705913	+	1.22268i	−0.966361	+	0.257189i	$0.917204\pi$
$338$	−10.3575	+	17.9397i	−0.563373	+	0.975791i
$339$	−7.25533	+	7.79034i	−0.394056	+	0.423113i
$340$	8.35762	+	14.4758i	0.453256	+	0.785062i
$341$	8.01983			0.434298
$342$	−2.49547	−	35.0447i	−0.134940	−	1.89500i
$343$		0			0
$344$	−2.66038	−	4.60792i	−0.143438	−	0.248442i
$345$	3.33150	+	10.8720i	0.179362	+	0.585331i
$346$	10.9641	−	18.9904i	0.589435	−	1.02093i
$347$	8.42415	−	14.5911i	0.452232	−	0.783289i	−0.546292	−	0.837595i	$-0.683961\pi$
$347$	8.42415	−	14.5911i	0.452232	−	0.783289i	0.998524	+	0.0543058i	$0.0172946\pi$
$348$	−18.6276	−	4.28802i	−0.998546	−	0.229862i
$349$	15.5503	+	26.9340i	0.832390	+	1.44174i	0.896138	+	0.443776i	$0.146361\pi$
$349$	15.5503	+	26.9340i	0.832390	+	1.44174i	−0.0637477	+	0.997966i	$0.520305\pi$
$350$		0			0
$351$	23.0029	−	8.88050i	1.22780	−	0.474006i
$352$	41.2185			2.19695
$353$	−1.32969	−	2.30309i	−0.0707722	−	0.122581i	0.828468	−	0.560037i	$-0.189213\pi$
$353$	−1.32969	−	2.30309i	−0.0707722	−	0.122581i	−0.899240	+	0.437456i	$0.855880\pi$
$354$	1.13392	+	0.261024i	0.0602671	+	0.0138733i
$355$	1.24729	−	2.16036i	0.0661991	−	0.114660i
$356$	−7.10833	+	12.3120i	−0.376741	+	0.652534i
$357$		0			0
$358$	20.1770	+	34.9476i	1.06639	+	1.84704i
$359$	−32.5429			−1.71755			−0.858775	−	0.512353i	$-0.828774\pi$
$359$	−32.5429			−1.71755			−0.858775	+	0.512353i	$0.828774\pi$
$360$	−5.05048	+	3.41597i	−0.266184	+	0.180038i
$361$	9.95719			0.524063
$362$	9.58646	+	16.6042i	0.503853	+	0.872699i
$363$	−22.4299	+	24.0839i	−1.17726	+	1.26407i
$364$		0			0
$365$	6.69042	−	11.5881i	0.350192	−	0.606551i
$366$	−26.5711	+	28.5304i	−1.38889	+	1.49131i
$367$	−7.07678	−	12.2573i	−0.369405	−	0.639828i	0.620068	−	0.784548i	$-0.287105\pi$
$367$	−7.07678	−	12.2573i	−0.369405	−	0.639828i	−0.989473	+	0.144720i	$0.953772\pi$
$368$	10.2758			0.535663
$369$	−9.68186	+	6.54847i	−0.504017	+	0.340900i
$370$	5.29499			0.275273
$371$		0			0
$372$	2.03313	+	6.63494i	0.105413	+	0.344005i
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	−0.898587	−	0.438795i	$-0.855406\pi$
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	0.829301	+	0.558802i	$0.188739\pi$
$374$	−28.7069	+	49.7217i	−1.48440	+	2.57105i
$375$	−17.9640	−	4.13526i	−0.927658	−	0.213544i
$376$	−2.52828	−	4.37911i	−0.130386	−	0.225835i
$377$	19.1386			0.985687
$378$		0			0
$379$	−0.312929			−0.0160741			−0.00803705	−	0.999968i	$-0.502558\pi$
$379$	−0.312929			−0.0160741			−0.00803705	+	0.999968i	$0.502558\pi$
$380$	−9.33759	−	16.1732i	−0.479008	−	0.829667i
$381$	−23.5133	−	5.41270i	−1.20463	−	0.277301i
$382$	−5.34218	+	9.25292i	−0.273330	+	0.473421i
$383$	4.49440	−	7.78453i	0.229653	−	0.397771i	−0.728052	−	0.685522i	$-0.759574\pi$
$383$	4.49440	−	7.78453i	0.229653	−	0.397771i	0.957705	+	0.287751i	$0.0929075\pi$
$384$	6.06465	+	19.7914i	0.309485	+	1.00998i
$385$		0			0
$386$	−21.2573			−1.08197
$387$	−0.707513	−	9.93583i	−0.0359649	−	0.505066i
$388$	13.6007			0.690472
$389$	13.4934	+	23.3713i	0.684144	+	1.18497i	0.973705	+	0.227813i	$0.0731575\pi$
$389$	13.4934	+	23.3713i	0.684144	+	1.18497i	−0.289560	+	0.957160i	$0.593509\pi$
$390$	15.4616	−	16.6018i	0.782929	−	0.840663i
$391$	−12.4657	+	21.5912i	−0.630417	+	1.09191i
$392$		0			0
$393$	0.211484	−	0.227079i	0.0106680	−	0.0114546i
$394$	−3.60664	−	6.24689i	−0.181700	−	0.314714i
$395$	−11.4354			−0.575380
$396$	−40.4379	−	19.6591i	−2.03208	−	0.987906i
$397$	29.5005			1.48059			0.740295	−	0.672282i	$-0.234686\pi$
$397$	29.5005			1.48059			0.740295	+	0.672282i	$0.234686\pi$
$398$	−12.0662	−	20.8992i	−0.604822	−	1.04758i
$399$		0			0
$400$	−3.36628	+	5.83056i	−0.168314	+	0.291528i
$401$	17.1392	−	29.6860i	0.855891	−	1.48245i	−0.0199251	−	0.999801i	$-0.506343\pi$
$401$	17.1392	−	29.6860i	0.855891	−	1.48245i	0.875816	−	0.482645i	$-0.160324\pi$
$402$	16.4315	+	3.78248i	0.819530	+	0.188653i
$403$	−3.47404	−	6.01721i	−0.173054	−	0.299739i
$404$	0.0146068			0.000726713
$405$	−11.2994	+	1.61743i	−0.561473	+	0.0803706i
$406$		0			0
$407$	5.25369	+	9.09966i	0.260416	+	0.451054i
$408$	−13.0277	−	2.99893i	−0.644967	−	0.148469i
$409$	−5.49225	+	9.51286i	−0.271574	+	0.470381i	−0.969265	−	0.246018i	$-0.920878\pi$
$409$	−5.49225	+	9.51286i	−0.271574	+	0.470381i	0.697691	+	0.716399i	$0.254211\pi$
$410$	−5.37708	+	9.31338i	−0.265555	+	0.459955i
$411$	−1.59954	−	5.21996i	−0.0788995	−	0.257481i
$412$	−17.8338	−	30.8890i	−0.878608	−	1.52179i
$413$		0			0
$414$	−30.3943	−	14.7764i	−1.49380	−	0.726218i
$415$	12.8864			0.632568
$416$	−17.8551	−	30.9259i	−0.875417	−	1.51627i
$417$	22.2599	−	23.9013i	1.09007	−	1.17045i
$418$	32.0729	−	55.5519i	1.56874	−	2.71713i
$419$	−3.33207	+	5.77132i	−0.162782	+	0.281947i	−0.935866	−	0.352357i	$-0.885380\pi$
$419$	−3.33207	+	5.77132i	−0.162782	+	0.281947i	0.773083	+	0.634305i	$0.218714\pi$
$420$		0			0
$421$	−17.0430	−	29.5193i	−0.830625	−	1.43868i	−0.897543	−	0.440926i	$-0.854650\pi$
$421$	−17.0430	−	29.5193i	−0.830625	−	1.43868i	0.0669186	−	0.997758i	$-0.478683\pi$
$422$	15.9357			0.775740
$423$	−0.672382	−	9.44246i	−0.0326923	−	0.459108i
$424$	−11.4465			−0.555892
$425$	−8.16733	−	14.1462i	−0.396174	−	0.686193i
$426$	2.17220	+	7.08877i	0.105243	+	0.343452i
$427$		0			0
$428$	−12.8903	+	22.3267i	−0.623077	+	1.07920i
$429$	43.8719	+	10.0992i	2.11815	+	0.487592i
$430$	−4.58237	−	7.93690i	−0.220982	−	0.382751i
$431$	2.25939			0.108831			0.0544155	−	0.998518i	$-0.482670\pi$
$431$	2.25939			0.108831			0.0544155	+	0.998518i	$0.482670\pi$
$432$	−1.59416	+	10.1913i	−0.0766992	+	0.490328i
$433$	34.3904			1.65270			0.826348	−	0.563160i	$-0.190415\pi$
$433$	34.3904			1.65270			0.826348	+	0.563160i	$0.190415\pi$
$434$		0			0
$435$	−8.63392	−	1.98750i	−0.413965	−	0.0952933i
$436$	−23.1086	+	40.0254i	−1.10670	+	1.91687i
$437$	13.9274	−	24.1229i	0.666236	−	1.15395i
$438$	11.6516	+	38.0240i	0.556736	+	1.81686i
$439$	−2.99569	−	5.18869i	−0.142977	−	0.247643i	0.785640	−	0.618684i	$-0.212334\pi$
$439$	−2.99569	−	5.18869i	−0.142977	−	0.247643i	−0.928616	+	0.371042i	$0.879001\pi$
$440$	−11.1322			−0.530706
$441$		0			0
$442$	49.7411			2.36594
$443$	19.7190	+	34.1543i	0.936879	+	1.62272i	0.771249	+	0.636534i	$0.219632\pi$
$443$	19.7190	+	34.1543i	0.936879	+	1.62272i	0.165630	+	0.986188i	$0.447034\pi$
$444$	−6.19642	+	6.65335i	−0.294069	+	0.315754i
$445$	−3.29471	+	5.70661i	−0.156184	+	0.270519i
$446$	4.41280	−	7.64319i	0.208952	−	0.361916i
$447$	25.1129	−	26.9647i	1.18780	−	1.27539i
$448$		0			0
$449$	2.45092			0.115666			0.0578330	−	0.998326i	$-0.481581\pi$
$449$	2.45092			0.115666			0.0578330	+	0.998326i	$0.481581\pi$
$450$	18.3412	−	12.4053i	0.864610	−	0.584793i
$451$	−21.3406			−1.00489
$452$	−8.40909	−	14.5650i	−0.395530	−	0.685078i
$453$	−3.23029	−	10.5417i	−0.151772	−	0.495294i
$454$	−1.45179	+	2.51457i	−0.0681358	+	0.118015i
$455$		0			0
$456$	14.5552	+	3.35057i	0.681612	+	0.156905i
$457$	−5.51058	−	9.54461i	−0.257774	−	0.446478i	0.707871	−	0.706342i	$-0.249656\pi$
$457$	−5.51058	−	9.54461i	−0.257774	−	0.446478i	−0.965645	+	0.259864i	$0.916322\pi$
$458$	−34.8137			−1.62674
$459$	−19.4797	−	15.7127i	−0.909233	−	0.733408i
$460$	−17.9642			−0.837584
$461$	14.6540	+	25.3814i	0.682503	+	1.18213i	0.974215	+	0.225624i	$0.0724420\pi$
$461$	14.6540	+	25.3814i	0.682503	+	1.18213i	−0.291711	+	0.956506i	$0.594225\pi$
$462$		0			0
$463$	0.593566	−	1.02809i	0.0275853	−	0.0477792i	−0.851903	−	0.523699i	$-0.824552\pi$
$463$	0.593566	−	1.02809i	0.0275853	−	0.0477792i	0.879489	+	0.475920i	$0.157885\pi$
$464$	−4.00319	+	6.93374i	−0.185844	+	0.321891i
$465$	0.942356	+	3.07530i	0.0437007	+	0.142613i
$466$	−8.84761	−	15.3245i	−0.409858	−	0.709894i
$467$	22.1147			1.02335			0.511673	−	0.859180i	$-0.329026\pi$
$467$	22.1147			1.02335			0.511673	+	0.859180i	$0.329026\pi$
$468$	2.76688	+	38.8562i	0.127899	+	1.79613i
$469$		0			0
$470$	−4.35483	−	7.54280i	−0.200874	−	0.347923i
$471$	−1.64785	+	1.76936i	−0.0759288	+	0.0815278i
$472$	−0.247329	+	0.428387i	−0.0113842	+	0.0197181i
$473$	9.09327	−	15.7500i	0.418109	−	0.724186i
$474$	23.1634	−	24.8715i	1.06393	−	1.14239i
$475$	9.12499	+	15.8050i	0.418683	+	0.725181i
$476$		0			0
$477$	−19.2722	−	9.36927i	−0.882413	−	0.428990i
$478$	−48.1004			−2.20006
$479$	12.5714	+	21.7743i	0.574402	+	0.994894i	0.996106	+	0.0881606i	$0.0280989\pi$
$479$	12.5714	+	21.7743i	0.574402	+	0.994894i	−0.421704	+	0.906734i	$0.638568\pi$
$480$	4.84331	+	15.8057i	0.221066	+	0.721428i
$481$	4.55160	−	7.88361i	0.207535	−	0.359462i
$482$	−30.0273	+	52.0088i	−1.36771	+	2.36894i
$483$		0			0
$484$	−25.9967	−	45.0276i	−1.18167	−	2.04671i
$485$	6.30393			0.286247
$486$	19.3701	−	27.8519i	0.878645	−	1.26339i
$487$	13.5781			0.615281			0.307641	−	0.951503i	$-0.400461\pi$
$487$	13.5781			0.615281			0.307641	+	0.951503i	$0.400461\pi$
$488$	−8.28713	−	14.3537i	−0.375141	−	0.649763i
$489$	−32.1744	−	7.40644i	−1.45498	−	0.334931i
$490$		0			0
$491$	7.25177	−	12.5604i	0.327268	−	0.566844i	−0.654701	−	0.755888i	$-0.727205\pi$
$491$	7.25177	−	12.5604i	0.327268	−	0.566844i	0.981969	+	0.189044i	$0.0605387\pi$
$492$	−5.41011	−	17.6554i	−0.243907	−	0.795967i
$493$	−9.71263	−	16.8228i	−0.437435	−	0.757659i
$494$	−55.5735			−2.50037
$495$	−18.7430	−	9.11199i	−0.842434	−	0.409554i
$496$	2.90664			0.130512
$497$		0			0
$498$	−26.1024	+	28.0272i	−1.16968	+	1.25593i
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	−0.979047	−	0.203633i	$-0.934725\pi$
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	0.665875	+	0.746063i	$0.268058\pi$
$500$	14.5611	−	25.2205i	0.651191	−	1.12790i
$501$	2.05871	−	2.21052i	0.0919763	−	0.0987587i
$502$	18.0209	+	31.2132i	0.804314	+	1.39311i
$503$	28.4011			1.26634			0.633171	−	0.774012i	$-0.281753\pi$
$503$	28.4011			1.26634			0.633171	+	0.774012i	$0.281753\pi$
$504$		0			0
$505$	0.00677023			0.000301271
$506$	−30.8518	−	53.4369i	−1.37153	−	2.37556i
$507$	−4.83019	−	15.7629i	−0.214516	−	0.700054i
$508$	19.0592	−	33.0115i	0.845615	−	1.46465i
$509$	1.72997	−	2.99639i	0.0766794	−	0.132813i	−0.825136	−	0.564934i	$-0.808902\pi$
$509$	1.72997	−	2.99639i	0.0766794	−	0.132813i	0.901815	+	0.432122i	$0.142235\pi$
$510$	−22.4395	−	5.16550i	−0.993639	−	0.228732i
$511$		0			0
$512$	21.3013			0.941392
$513$	21.7638	+	17.5551i	0.960894	+	0.775078i
$514$	4.49568			0.198296
$515$	−8.26597	−	14.3171i	−0.364242	−	0.630886i
$516$	15.3355	+	3.53018i	0.675107	+	0.155408i
$517$	8.64174	−	14.9679i	0.380063	−	0.658289i
$518$		0			0
$519$	5.11310	+	16.6861i	0.224440	+	0.732440i
$520$	4.82225	+	8.35239i	0.211470	+	0.366276i
$521$	7.13594			0.312631			0.156316	−	0.987707i	$-0.450038\pi$
$521$	7.13594			0.312631			0.156316	+	0.987707i	$0.450038\pi$
$522$	21.8114	−	14.7525i	0.954659	−	0.645698i
$523$	−13.0647			−0.571280			−0.285640	−	0.958337i	$-0.592206\pi$
$523$	−13.0647			−0.571280			−0.285640	+	0.958337i	$0.592206\pi$
$524$	0.245114	+	0.424551i	0.0107079	+	0.0185466i
$525$		0			0
$526$	−11.0226	+	19.0917i	−0.480609	+	0.832439i
$527$	−3.52608	+	6.10735i	−0.153598	+	0.266040i
$528$	−12.8355	+	13.7820i	−0.558592	+	0.599782i
$529$	−1.89710	−	3.28587i	−0.0824825	−	0.142864i
$530$	−19.7160			−0.856409
$531$	−0.767068	+	0.518818i	−0.0332879	+	0.0225148i
$532$		0			0
$533$	9.24434	+	16.0117i	0.400417	+	0.693542i
$534$	−5.73787	−	18.7250i	−0.248302	−	0.810311i
$535$	−5.97467	+	10.3484i	−0.258308	+	0.447402i
$536$	−3.58403	+	6.20772i	−0.154807	+	0.268133i
$537$	−31.2978	−	7.20465i	−1.35060	−	0.310904i
$538$	16.4305	+	28.4585i	0.708371	+	1.22693i
$539$		0			0
$540$	2.78691	−	17.8164i	0.119930	−	0.766695i
$541$	4.93577			0.212205			0.106103	−	0.994355i	$-0.466163\pi$
$541$	4.93577			0.212205			0.106103	+	0.994355i	$0.466163\pi$
$542$	31.3444	+	54.2901i	1.34636	+	2.33196i
$543$	−14.8702	−	3.42306i	−0.638139	−	0.146898i
$544$	−18.1225	+	31.3892i	−0.776997	+	1.34580i
$545$	−10.7109	+	18.5518i	−0.458803	+	0.794670i
$546$		0			0
$547$	0.559964	+	0.969887i	0.0239423	+	0.0414694i	0.877748	−	0.479122i	$-0.159045\pi$
$547$	0.559964	+	0.969887i	0.0239423	+	0.0414694i	−0.853806	+	0.520591i	$0.825712\pi$
$548$	8.62508			0.368445
$549$	−2.20391	−	30.9502i	−0.0940607	−	1.32092i
$550$	40.4273			1.72382
$551$	10.8515	+	18.7953i	0.462289	+	0.800708i
$552$	9.79175	−	10.5138i	0.416764	−	0.447497i
$553$		0			0
$554$	2.93762	−	5.08811i	0.124808	−	0.216173i
$555$	−2.87204	+	3.08383i	−0.121911	+	0.130901i
$556$	25.7997	+	44.6863i	1.09415	+	1.89512i
$557$	−10.9566			−0.464248			−0.232124	−	0.972686i	$-0.574567\pi$
$557$	−10.9566			−0.464248			−0.232124	+	0.972686i	$0.574567\pi$
$558$	−8.59742	−	4.17968i	−0.363958	−	0.176940i
$559$	−15.7561			−0.666413
$560$		0			0
$561$	−13.3874	−	43.6885i	−0.565215	−	1.84453i
$562$	−5.36052	+	9.28470i	−0.226120	+	0.391651i
$563$	2.38048	−	4.12311i	0.100325	−	0.173768i	−0.811493	−	0.584361i	$-0.801345\pi$
$563$	2.38048	−	4.12311i	0.100325	−	0.173768i	0.911819	+	0.410593i	$0.134678\pi$
$564$	14.5740	+	3.35489i	0.613677	+	0.141266i
$565$	−3.89761	−	6.75087i	−0.163974	−	0.284011i
$566$	7.79462			0.327632
$567$		0			0
$568$	−3.15189			−0.132250
$569$	−1.74988	−	3.03088i	−0.0733588	−	0.127061i	0.827013	−	0.562183i	$-0.190038\pi$
$569$	−1.74988	−	3.03088i	−0.0733588	−	0.127061i	−0.900371	+	0.435122i	$0.856705\pi$
$570$	25.0707	+	5.77119i	1.05009	+	0.241728i
$571$	−3.53051	+	6.11501i	−0.147747	+	0.255905i	−0.930394	−	0.366560i	$-0.880535\pi$
$571$	−3.53051	+	6.11501i	−0.147747	+	0.255905i	0.782647	+	0.622465i	$0.213869\pi$
$572$	−35.5612	+	61.5937i	−1.48689	+	2.57536i
$573$	−2.49131	−	8.13017i	−0.104076	−	0.339643i
$574$		0			0
$575$	17.5552			0.732101
$576$	−33.4749	−	16.2740i	−1.39479	−	0.678084i
$577$	12.8830			0.536326			0.268163	−	0.963374i	$-0.413584\pi$
$577$	12.8830			0.536326			0.268163	+	0.963374i	$0.413584\pi$
$578$	−6.74445	−	11.6817i	−0.280532	−	0.485896i
$579$	11.5301	−	12.3804i	0.479176	−	0.514511i
$580$	6.99838	−	12.1216i	0.290592	−	0.503320i
$581$		0			0
$582$	−12.7691	+	13.7107i	−0.529297	+	0.568328i
$583$	−19.5623	−	33.8828i	−0.810186	−	1.40328i
$584$	−16.9067			−0.699603
$585$	1.28245	+	18.0098i	0.0530228	+	0.744615i
$586$	−53.0824			−2.19281
$587$	−19.5044	−	33.7826i	−0.805034	−	1.39436i	−0.916268	−	0.400565i	$-0.868814\pi$
$587$	−19.5044	−	33.7826i	−0.805034	−	1.39436i	0.111235	−	0.993794i	$-0.464519\pi$
$588$		0			0
$589$	3.93953	−	6.82347i	0.162326	−	0.281156i
$590$	−0.426012	+	0.737874i	−0.0175386	+	0.0303778i
$591$	5.59449	+	1.28783i	0.230127	+	0.0529744i
$592$	1.90411	+	3.29801i	0.0782583	+	0.135547i
$593$	40.3026			1.65503			0.827515	−	0.561444i	$-0.189754\pi$
$593$	40.3026			1.65503			0.827515	+	0.561444i	$0.189754\pi$
$594$	57.7835	−	22.3079i	2.37089	−	0.915304i
$595$		0			0
$596$	29.1064	+	50.4137i	1.19224	+	2.06503i
$597$	18.7166	+	4.30850i	0.766019	+	0.176335i
$598$	−26.7288	+	46.2957i	−1.09302	+	1.89317i
$599$	6.39103	−	11.0696i	0.261130	−	0.452291i	−0.705412	−	0.708797i	$-0.749238\pi$
$599$	6.39103	−	11.0696i	0.261130	−	0.452291i	0.966543	+	0.256506i	$0.0825715\pi$
$600$	2.75790	+	9.00015i	0.112591	+	0.367429i
$601$	−4.86311	−	8.42316i	−0.198371	−	0.343588i	0.749630	−	0.661858i	$-0.230232\pi$
$601$	−4.86311	−	8.42316i	−0.198371	−	0.343588i	−0.948000	+	0.318270i	$0.896898\pi$
$602$		0			0
$603$	−11.1155	+	7.51816i	−0.452659	+	0.306163i
$604$	17.4184			0.708745
$605$	−12.0495	−	20.8703i	−0.489881	−	0.848499i
$606$	−0.0137137	+	0.0147249i	−0.000557079	+	0.000598158i
$607$	−20.7437	+	35.9291i	−0.841959	+	1.45832i	0.0462763	+	0.998929i	$0.485265\pi$
$607$	−20.7437	+	35.9291i	−0.841959	+	1.45832i	−0.888236	+	0.459388i	$0.848069\pi$
$608$	20.2475	−	35.0697i	0.821145	−	1.42226i
$609$		0			0
$610$	−14.2742	−	24.7236i	−0.577943	−	1.00103i
$611$	−14.9738			−0.605774
$612$	32.7503	−	22.1512i	1.32385	−	0.895409i
$613$	15.2957			0.617785			0.308893	−	0.951097i	$-0.400042\pi$
$613$	15.2957			0.617785			0.308893	+	0.951097i	$0.400042\pi$
$614$	26.0096	+	45.0500i	1.04966	+	1.81807i
$615$	−2.50759	−	8.18329i	−0.101116	−	0.329982i
$616$		0			0
$617$	−2.66563	+	4.61700i	−0.107314	+	0.185873i	−0.914681	−	0.404176i	$-0.867558\pi$
$617$	−2.66563	+	4.61700i	−0.107314	+	0.185873i	0.807367	+	0.590049i	$0.200892\pi$
$618$	47.8822	+	11.0223i	1.92611	+	0.443383i
$619$	6.34205	+	10.9847i	0.254908	+	0.441514i	0.964871	−	0.262726i	$-0.0846214\pi$
$619$	6.34205	+	10.9847i	0.254908	+	0.441514i	−0.709962	+	0.704240i	$0.751288\pi$
$620$	−5.08140			−0.204074
$621$	25.0919	−	9.68700i	1.00690	−	0.388726i
$622$	−28.1650			−1.12931
$623$		0			0
$624$	15.9006	+	3.66026i	0.636532	+	0.146528i
$625$	−1.72954	+	2.99566i	−0.0691817	+	0.119826i
$626$	29.2366	−	50.6393i	1.16853	−	2.02395i
$627$	14.9571	+	48.8112i	0.597330	+	1.94933i
$628$	−1.90989	−	3.30803i	−0.0762129	−	0.132005i
$629$	−9.23957			−0.368406
$630$		0			0
$631$	0.123764			0.00492698			0.00246349	−	0.999997i	$-0.499216\pi$
$631$	0.123764			0.00492698			0.00246349	+	0.999997i	$0.499216\pi$
$632$	7.22433	+	12.5129i	0.287369	+	0.497737i
$633$	−8.64367	+	9.28105i	−0.343555	+	0.368889i
$634$	−9.04441	+	15.6654i	−0.359199	+	0.622151i
$635$	8.83394	−	15.3008i	0.350564	−	0.607195i
$636$	23.0725	−	24.7739i	0.914885	−	0.982349i
$637$		0			0
$638$	48.0763			1.90336
$639$	−5.30676	−	2.57991i	−0.209932	−	0.102060i
$640$	−15.1574			−0.599147
$641$	−2.96588	−	5.13706i	−0.117145	−	0.202902i	0.801490	−	0.598008i	$-0.204041\pi$
$641$	−2.96588	−	5.13706i	−0.117145	−	0.202902i	−0.918635	+	0.395107i	$0.870708\pi$
$642$	−10.4051	−	33.9562i	−0.410657	−	1.34014i
$643$	−23.4140	+	40.5542i	−0.923358	+	1.59930i	−0.129178	+	0.991621i	$0.541234\pi$
$643$	−23.4140	+	40.5542i	−0.923358	+	1.59930i	−0.794180	+	0.607682i	$0.792100\pi$
$644$		0			0
$645$	7.10801	+	1.63624i	0.279877	+	0.0644269i
$646$	28.2030	+	48.8490i	1.10963	+	1.92194i
$647$	−39.1401			−1.53876			−0.769379	−	0.638793i	$-0.779434\pi$
$647$	−39.1401			−1.53876			−0.769379	+	0.638793i	$0.779434\pi$
$648$	8.90823	+	11.3423i	0.349948	+	0.445567i
$649$	−1.69076			−0.0663680
$650$	−17.5123	−	30.3322i	−0.686890	−	1.18973i
$651$		0			0
$652$	26.0796	−	45.1711i	1.02135	−	1.76904i
$653$	−21.6640	+	37.5232i	−0.847779	+	1.46840i	0.0354068	+	0.999373i	$0.488727\pi$
$653$	−21.6640	+	37.5232i	−0.847779	+	1.46840i	−0.883186	+	0.469023i	$0.844606\pi$
$654$	−18.6534	−	60.8736i	−0.729405	−	2.38035i
$655$	0.113611	+	0.196779i	0.00443913	+	0.00768881i
$656$	−7.73451			−0.301982
$657$	−28.4653	−	13.8386i	−1.11054	−	0.539893i
$658$		0			0
$659$	3.43895	+	5.95643i	0.133962	+	0.232030i	0.925201	−	0.379478i	$-0.123897\pi$
$659$	3.43895	+	5.95643i	0.133962	+	0.232030i	−0.791238	+	0.611508i	$0.790563\pi$
$660$	22.4390	−	24.0936i	0.873435	−	0.937842i
$661$	−19.3835	+	33.5733i	−0.753932	+	1.30585i	0.191971	+	0.981401i	$0.438512\pi$
$661$	−19.3835	+	33.5733i	−0.753932	+	1.30585i	−0.945903	+	0.324449i	$0.894821\pi$
$662$	−13.4907	+	23.3666i	−0.524331	+	0.908168i
$663$	−26.9800	+	28.9695i	−1.04781	+	1.12508i
$664$	−8.14097	−	14.1006i	−0.315931	−	0.547209i
$665$		0			0
$666$	−0.889611	−	12.4931i	−0.0344717	−	0.484097i
$667$	20.8767			0.808348
$668$	2.38609	+	4.13282i	0.0923205	+	0.159904i
$669$	2.05790	+	6.71576i	0.0795629	+	0.259646i
$670$	−6.17331	+	10.6925i	−0.238496	+	0.413087i
$671$	28.3257	−	49.0615i	1.09350	−	1.89400i
$672$		0			0
$673$	17.9897	+	31.1591i	0.693452	+	1.20109i	0.970700	+	0.240295i	$0.0772443\pi$
$673$	17.9897	+	31.1591i	0.693452	+	1.20109i	−0.277248	+	0.960798i	$0.589422\pi$
$674$	56.4049			2.17264
$675$	−2.72346	+	17.4107i	−0.104826	+	0.670139i
$676$	26.0454			1.00175
$677$	−2.23329	−	3.86817i	−0.0858322	−	0.148666i	0.819913	−	0.572488i	$-0.194022\pi$
$677$	−2.23329	−	3.86817i	−0.0858322	−	0.148666i	−0.905746	+	0.423822i	$0.860688\pi$
$678$	22.5777	+	5.19731i	0.867092	+	0.199602i
$679$		0			0
$680$	4.89449	−	8.47750i	0.187695	−	0.325097i
$681$	−0.677038	−	2.20945i	−0.0259441	−	0.0846664i
$682$	−8.72682	−	15.1153i	−0.334167	−	0.578795i
$683$	−26.6713			−1.02055			−0.510274	−	0.860012i	$-0.670456\pi$
$683$	−26.6713			−1.02055			−0.510274	+	0.860012i	$0.670456\pi$
$684$	−36.5905	+	24.7485i	−1.39907	+	0.946284i
$685$	3.99773			0.152745
$686$		0			0
$687$	18.8832	−	20.2757i	0.720439	−	0.773565i
$688$	3.29569	−	5.70831i	0.125647	−	0.217627i
$689$	−16.9480	+	29.3548i	−0.645668	+	1.11833i
$690$	16.8658	−	18.1095i	0.642069	−	0.689416i
$691$	20.5220	+	35.5452i	0.780694	+	1.35220i	0.931538	+	0.363644i	$0.118468\pi$
$691$	20.5220	+	35.5452i	0.780694	+	1.35220i	−0.150844	+	0.988558i	$0.548199\pi$
$692$	−27.5709			−1.04809
$693$		0			0
$694$	−36.6671			−1.39187
$695$	11.9582	+	20.7121i	0.453599	+	0.785656i
$696$	3.27970	+	10.7030i	0.124317	+	0.405697i
$697$	9.38281	−	16.2515i	0.355399	−	0.615570i
$698$	33.8424	−	58.6167i	1.28095	−	2.21867i
$699$	13.7241	+	3.15924i	0.519093	+	0.119493i
$700$		0			0
$701$	9.63355			0.363854			0.181927	−	0.983312i	$-0.441767\pi$
$701$	9.63355			0.363854			0.181927	+	0.983312i	$0.441767\pi$
$702$	−41.7682	−	33.6911i	−1.57644	−	1.27159i
$703$	10.3230			0.389338
$704$	−33.9788	−	58.8529i	−1.28062	−	2.21810i
$705$	6.75506	+	1.55499i	0.254410	+	0.0585644i
$706$	−2.89382	+	5.01224i	−0.108910	+	0.188638i
$707$		0			0
$708$	−0.428629	−	1.39879i	−0.0161089	−	0.0525698i
$709$	5.07131	+	8.78376i	0.190457	+	0.329881i	0.945402	−	0.325907i	$-0.105670\pi$
$709$	5.07131	+	8.78376i	0.190457	+	0.329881i	−0.754945	+	0.655788i	$0.772336\pi$
$710$	−5.42897			−0.203746
$711$	1.92127	+	26.9810i	0.0720532	+	1.01187i
$712$	8.32572			0.312020
$713$	−3.78954	−	6.56368i	−0.141919	−	0.245812i
$714$		0			0
$715$	−16.4826	+	28.5487i	−0.616415	+	1.06766i
$716$	25.3690	−	43.9404i	0.948085	−	1.64213i
$717$	26.0900	−	28.0139i	0.974350	−	1.04620i
$718$	35.4118	+	61.3350i	1.32156	+	2.28900i
$719$	−41.3688			−1.54279			−0.771397	−	0.636354i	$-0.780442\pi$
$719$	−41.3688			−1.54279			−0.771397	+	0.636354i	$0.780442\pi$
$720$	−6.79305	−	3.30248i	−0.253162	−	0.123076i
$721$		0			0
$722$	−10.8350	−	18.7667i	−0.403236	−	0.698425i
$723$	−14.0032	−	45.6981i	−0.520783	−	1.69953i
$724$	12.0533	−	20.8769i	0.447957	−	0.775884i
$725$	−6.83904	+	11.8456i	−0.253996	+	0.439934i
$726$	69.7990	+	16.0675i	2.59048	+	0.596321i
$727$	−4.86372	−	8.42422i	−0.180386	−	0.312437i	0.761626	−	0.648016i	$-0.224401\pi$
$727$	−4.86372	−	8.42422i	−0.180386	−	0.312437i	−0.942012	+	0.335580i	$0.891068\pi$
$728$		0			0
$729$	5.71460	+	26.3883i	0.211652	+	0.977345i
$730$	−29.1209			−1.07781
$731$	7.99607	+	13.8496i	0.295745	+	0.512246i
$732$	47.7703	+	10.9966i	1.76564	+	0.406445i
$733$	−14.4554	+	25.0375i	−0.533922	+	0.924780i	0.465292	+	0.885157i	$0.345949\pi$
$733$	−14.4554	+	25.0375i	−0.533922	+	0.924780i	−0.999215	+	0.0396234i	$0.987384\pi$
$734$	−15.4013	+	26.6758i	−0.568471	+	0.984621i
$735$		0			0
$736$	−19.4766	−	33.7345i	−0.717918	−	1.24347i
$737$	−24.5007			−0.902493
$738$	22.8775	+	11.1220i	0.842134	+	0.409408i
$739$	−13.3493			−0.491063			−0.245532	−	0.969389i	$-0.578963\pi$
$739$	−13.3493			−0.491063			−0.245532	+	0.969389i	$0.578963\pi$
$740$	−3.32876	−	5.76558i	−0.122368	−	0.211947i
$741$	30.1435	−	32.3663i	1.10735	−	1.18901i
$742$		0			0
$743$	19.9100	−	34.4851i	0.730425	−	1.26513i	−0.226276	−	0.974063i	$-0.572655\pi$
$743$	19.9100	−	34.4851i	0.730425	−	1.26513i	0.956702	−	0.291071i	$-0.0940115\pi$
$744$	2.76972	−	2.97396i	0.101543	−	0.109031i
$745$	13.4908	+	23.3668i	0.494265	+	0.856092i
$746$	5.82442			0.213247
$747$	−2.16504	−	30.4044i	−0.0792148	−	1.11244i
$748$	72.1877			2.63944
$749$		0			0
$750$	11.7538	+	38.3573i	0.429186	+	1.40061i
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	−0.266780	−	0.963757i	$-0.585960\pi$
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	0.968029	−	0.250840i	$-0.0807069\pi$
$752$	3.13204	−	5.42486i	0.114214	−	0.197824i
$753$	−27.9534	−	6.43479i	−1.01868	−	0.234497i
$754$	−20.8258	−	36.0713i	−0.758429	−	1.31364i
$755$	8.07344			0.293823
$756$		0			0
$757$	−5.66698			−0.205970			−0.102985	−	0.994683i	$-0.532839\pi$
$757$	−5.66698			−0.205970			−0.102985	+	0.994683i	$0.532839\pi$
$758$	0.340516	+	0.589791i	0.0123681	+	0.0214222i
$759$	47.8561	+	11.0163i	1.73707	+	0.399867i
$760$	−5.46839	+	9.47153i	−0.198359	+	0.343569i
$761$	−26.1661	+	45.3210i	−0.948519	+	1.64288i	−0.199973	+	0.979801i	$0.564085\pi$
$761$	−26.1661	+	45.3210i	−0.948519	+	1.64288i	−0.748546	+	0.663082i	$0.769248\pi$
$762$	15.3846	+	50.2064i	0.557327	+	1.81879i
$763$		0			0
$764$	13.4337			0.486014
$765$	15.1798	−	10.2671i	0.548826	−	0.371207i
$766$	−19.5624			−0.706819
$767$	0.732404	+	1.26856i	0.0264456	+	0.0458051i
$768$	1.41067	−	1.51470i	0.0509033	−	0.0546569i
$769$	1.17360	−	2.03274i	0.0423212	−	0.0733025i	−0.844089	−	0.536203i	$-0.819858\pi$
$769$	1.17360	−	2.03274i	0.0423212	−	0.0733025i	0.886410	+	0.462901i	$0.153191\pi$
$770$		0			0
$771$	−2.43849	+	2.61831i	−0.0878201	+	0.0942960i
$772$	13.3637	+	23.1466i	0.480970	+	0.833064i
$773$	36.3629			1.30788			0.653941	−	0.756545i	$-0.273114\pi$
$773$	36.3629			1.30788			0.653941	+	0.756545i	$0.273114\pi$
$774$	−17.9566	+	12.1452i	−0.645436	+	0.436550i
$775$	4.96570			0.178373
$776$	−3.98251	−	6.89790i	−0.142964	−	0.247620i
$777$		0			0
$778$	29.3659	−	50.8633i	1.05282	−	1.82354i
$779$	−10.4830	+	18.1571i	−0.375592	+	0.650545i
$780$	−27.7974	−	6.39887i	−0.995306	−	0.229116i
$781$	−5.38663	−	9.32991i	−0.192749	−	0.333851i
$782$	54.2584			1.94028
$783$	−3.23875	+	20.7049i	−0.115744	+	0.739934i
$784$		0			0
$785$	−0.885235	−	1.53327i	−0.0315954	−	0.0547248i
$786$	−0.658112	−	0.151495i	−0.0234741	−	0.00540366i
$787$	15.8846	−	27.5129i	0.566224	−	0.980729i	−0.430711	−	0.902490i	$-0.641737\pi$
$787$	15.8846	−	27.5129i	0.566224	−	0.980729i	0.996935	−	0.0782386i	$-0.0249296\pi$
$788$	−4.53472	+	7.85437i	−0.161543	+	0.279800i
$789$	−5.14037	−	16.7751i	−0.183002	−	0.597210i
$790$	12.4435	+	21.5528i	0.442721	+	0.766816i
$791$		0			0
$792$	1.87032	+	26.2655i	0.0664589	+	0.933302i
$793$	−49.0806			−1.74290
$794$	−32.1012	−	55.6009i	−1.13923	−	1.97320i
$795$	10.6941	−	11.4827i	0.379281	−	0.407250i
$796$	−15.1711	+	26.2771i	−0.537725	+	0.931367i
$797$	−7.45306	+	12.9091i	−0.264001	+	0.457263i	−0.967301	−	0.253630i	$-0.918375\pi$
$797$	−7.45306	+	12.9091i	−0.264001	+	0.457263i	0.703301	+	0.710893i	$0.251709\pi$
$798$		0			0
$799$	7.59903	+	13.1619i	0.268834	+	0.465635i
$800$	25.5216			0.902324
$801$	14.0178	+	6.81483i	0.495295	+	0.240790i
$802$	−74.6005			−2.63423
$803$	−28.8937	−	50.0454i	−1.01964	−	1.76606i
$804$	−6.21123	−	20.2698i	−0.219053	−	0.714860i
$805$		0			0
$806$	−7.56059	+	13.0953i	−0.266311	+	0.461263i
$807$	−25.4865	−	5.86690i	−0.897166	−	0.206525i
$808$	−0.00427709	−	0.00740814i	−0.000150467	−	0.000260617i
$809$	47.8037			1.68069			0.840344	−	0.542053i	$-0.182353\pi$
$809$	47.8037			1.68069			0.840344	+	0.542053i	$0.182353\pi$
$810$	15.3440	+	19.5365i	0.539132	+	0.686442i
$811$	−32.1131			−1.12764			−0.563821	−	0.825897i	$-0.690669\pi$
$811$	−32.1131			−1.12764			−0.563821	+	0.825897i	$0.690669\pi$
$812$		0			0
$813$	−48.6203	−	11.1922i	−1.70519	−	0.392529i
$814$	11.4337	−	19.8037i	0.400750	−	0.694119i
$815$	12.0879	−	20.9368i	0.423420	−	0.733385i
$816$	−4.85201	−	15.8341i	−0.169854	−	0.554305i
$817$	−8.93366	−	15.4735i	−0.312549	−	0.541351i
$818$	23.9057			0.835843
$819$		0			0
$820$	13.5215			0.472190
$821$	−23.5535	−	40.7958i	−0.822023	−	1.42378i	−0.904174	−	0.427165i	$-0.859512\pi$
$821$	−23.5535	−	40.7958i	−0.822023	−	1.42378i	0.0821512	−	0.996620i	$-0.473821\pi$
$822$	−8.09771	+	8.69484i	−0.282440	+	0.303267i
$823$	−16.8955	+	29.2639i	−0.588941	+	1.02008i	0.405431	+	0.914126i	$0.367122\pi$
$823$	−16.8955	+	29.2639i	−0.588941	+	1.02008i	−0.994372	+	0.105950i	$0.966212\pi$
$824$	−10.4440	+	18.0896i	−0.363835	+	0.630181i
$825$	−21.9281	+	23.5450i	−0.763437	+	0.819733i
$826$		0			0
$827$	2.98023			0.103633			0.0518164	−	0.998657i	$-0.483499\pi$
$827$	2.98023			0.103633			0.0518164	+	0.998657i	$0.483499\pi$
$828$	3.01816	+	42.3850i	0.104888	+	1.47298i
$829$	6.07957			0.211152			0.105576	−	0.994411i	$-0.466331\pi$
$829$	6.07957			0.211152			0.105576	+	0.994411i	$0.466331\pi$
$830$	−14.0224	−	24.2875i	−0.486725	−	0.843032i
$831$	1.36995	+	4.47071i	0.0475231	+	0.155087i
$832$	−29.4379	+	50.9880i	−1.02058	+	1.76769i
$833$		0			0
$834$	−69.2700	−	15.9457i	−2.39862	−	0.552155i
$835$	1.10595	+	1.91557i	0.0382731	+	0.0662909i
$836$	−80.6521			−2.78941
$837$	7.09758	−	2.74009i	0.245328	−	0.0947114i
$838$	14.5033			0.501007
$839$	1.85858	+	3.21915i	0.0641653	+	0.111138i	0.896323	−	0.443401i	$-0.146228\pi$
$839$	1.85858	+	3.21915i	0.0641653	+	0.111138i	−0.832158	+	0.554538i	$0.812895\pi$
$840$		0			0
$841$	6.36697	−	11.0279i	0.219551	−	0.380273i
$842$	−37.0909	+	64.2433i	−1.27824	+	2.21397i
$843$	−2.49987	−	8.15809i	−0.0861000	−	0.280980i
$844$	−10.0182	−	17.3520i	−0.344841	−	0.597281i
$845$	12.0721			0.415292
$846$	−17.0649	+	11.5421i	−0.586705	+	0.396827i
$847$		0			0
$848$	−7.08999	−	12.2802i	−0.243471	−	0.421705i
$849$	−4.22786	+	4.53963i	−0.145100	+	0.155800i
$850$	−17.7747	+	30.7866i	−0.609666	+	1.05597i
$851$	4.96496	−	8.59957i	0.170197	−	0.294789i
$852$	6.35321	−	6.82170i	0.217657	−	0.233708i
$853$	−0.553861	−	0.959315i	−0.0189638	−	0.0328463i	0.856388	−	0.516333i	$-0.172703\pi$
$853$	−0.553861	−	0.959315i	−0.0189638	−	0.0328463i	−0.875352	+	0.483487i	$0.839370\pi$
$854$		0			0
$855$	−16.9597	+	11.4709i	−0.580009	+	0.392298i
$856$	15.0980			0.516038
$857$	19.2597	+	33.3589i	0.657900	+	1.13952i	0.981158	+	0.193206i	$0.0618885\pi$
$857$	19.2597	+	33.3589i	0.657900	+	1.13952i	−0.323258	+	0.946311i	$0.604778\pi$
$858$	−28.7051	−	93.6765i	−0.979976	−	3.19806i
$859$	17.4437	−	30.2134i	0.595171	−	1.03087i	−0.398352	−	0.917233i	$-0.630418\pi$
$859$	17.4437	−	30.2134i	0.595171	−	1.03087i	0.993523	−	0.113634i	$-0.0362491\pi$
$860$	−5.76153	+	9.97926i	−0.196467	+	0.340290i
$861$		0			0
$862$	−2.45857	−	4.25836i	−0.0837391	−	0.145040i
$863$	2.15849			0.0734758			0.0367379	−	0.999325i	$-0.488303\pi$
$863$	2.15849			0.0734758			0.0367379	+	0.999325i	$0.488303\pi$
$864$	36.4785	−	14.0829i	1.24102	−	0.479110i
$865$	−12.7791			−0.434504
$866$	−37.4221	−	64.8169i	−1.27165	−	2.20257i
$867$	10.4617	+	2.40826i	0.355299	+	0.0817888i
$868$		0			0
$869$	−24.6930	+	42.7695i	−0.837652	+	1.45086i
$870$	5.64912	+	18.4354i	0.191523	+	0.625019i
$871$	10.6132	+	18.3826i	0.359615	+	0.622872i
$872$	27.0663			0.916581
$873$	−1.05912	−	14.8736i	−0.0358459	−	0.503395i
$874$	−60.6205			−2.05052
$875$		0			0
$876$	34.0785	−	36.5914i	1.15140	−	1.23631i
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	−0.980227	−	0.197875i	$-0.936596\pi$
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	0.661478	+	0.749965i	$0.269929\pi$
$878$	−6.51956	+	11.2922i	−0.220025	+	0.381094i
$879$	28.7923	−	30.9155i	0.971140	−	1.04275i
$880$	−6.89530	−	11.9430i	−0.232440	−	0.402599i
$881$	−18.7203			−0.630704			−0.315352	−	0.948975i	$-0.602123\pi$
$881$	−18.7203			−0.630704			−0.315352	+	0.948975i	$0.602123\pi$
$882$		0			0
$883$	−13.3717			−0.449993			−0.224996	−	0.974360i	$-0.572237\pi$
$883$	−13.3717			−0.449993			−0.224996	+	0.974360i	$0.572237\pi$
$884$	−31.2704	−	54.1618i	−1.05174	−	1.82166i
$885$	−0.198670	−	0.648340i	−0.00667820	−	0.0217937i
$886$	42.9147	−	74.3305i	1.44175	−	2.49718i
$887$	−20.6284	+	35.7294i	−0.692633	+	1.19968i	0.278339	+	0.960483i	$0.410216\pi$
$887$	−20.6284	+	35.7294i	−0.692633	+	1.19968i	−0.970972	+	0.239193i	$0.923117\pi$
$888$	5.18880	+	1.19445i	0.174125	+	0.0400830i
$889$		0			0
$890$	14.3406			0.480699
$891$	−18.3500	+	45.7534i	−0.614747	+	1.53280i
$892$	−11.0966			−0.371543
$893$	−8.49006	−	14.7052i	−0.284109	−	0.492091i
$894$	−78.1482	−	17.9895i	−2.61367	−	0.601658i
$895$	11.7585	−	20.3664i	0.393045	−	0.680774i
$896$		0			0
$897$	−12.4649	−	40.6782i	−0.416192	−	1.35820i
$898$	−2.66698	−	4.61934i	−0.0889982	−	0.154149i
$899$	5.90524			0.196951
$900$	−25.0382	−	12.1725i	−0.834608	−	0.405749i
$901$	34.4037			1.14616
$902$	23.2219	+	40.2215i	0.773204	+	1.33923i
$903$		0			0
$904$	−4.92463	+	8.52971i	−0.163791	+	0.283694i
$905$	5.58670	−	9.67645i	0.185708	−	0.321656i
$906$	−16.3534	+	17.5593i	−0.543305	+	0.583369i
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	0.833764	−	0.552121i	$-0.186181\pi$
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	−0.895033	+	0.446001i	$0.852848\pi$
$908$	3.65074			0.121154
$909$	−0.00113747	−	0.0159738i	−3.77274e−5	−	0.000529818i
$910$		0			0
$911$	−3.43831	−	5.95533i	−0.113916	−	0.197309i	0.803430	−	0.595400i	$-0.203006\pi$
$911$	−3.43831	−	5.95533i	−0.113916	−	0.197309i	−0.917346	+	0.398091i	$0.869673\pi$
$912$	5.42094	+	17.6907i	0.179505	+	0.585799i
$913$	27.8261	−	48.1962i	0.920909	−	1.59506i
$914$	−11.9927	+	20.7720i	−0.396685	+	0.687078i
$915$	22.1415	+	5.09691i	0.731977	+	0.168499i
$916$	21.8860	+	37.9077i	0.723135	+	1.25251i
$917$		0			0
$918$	−8.41751	+	53.8120i	−0.277819	+	1.77606i
$919$	37.2947			1.23024			0.615119	−	0.788435i	$-0.289108\pi$
$919$	37.2947			1.23024			0.615119	+	0.788435i	$0.289108\pi$
$920$	5.26019	+	9.11092i	0.173423	+	0.300378i
$921$	−40.3452	−	9.28733i	−1.32942	−	0.306028i
$922$	31.8916	−	55.2378i	1.05029	−	1.81916i
$923$	−4.66677	+	8.08309i	−0.153609	+	0.266058i
$924$		0			0
$925$	3.25297	+	5.63431i	0.106957	+	0.185255i
$926$	−2.58357			−0.0849013
$927$	−32.3912	+	21.9083i	−1.06387	+	0.719562i
$928$	30.3504			0.996300
$929$	8.98933	+	15.5700i	0.294930	+	0.510834i	0.974969	−	0.222342i	$-0.0713702\pi$
$929$	8.98933	+	15.5700i	0.294930	+	0.510834i	−0.680038	+	0.733177i	$0.738037\pi$
$930$	4.77070	−	5.12250i	0.156438	−	0.167973i
$931$		0			0
$932$	−11.1243	+	19.2679i	−0.364389	+	0.631141i
$933$	15.2769	−	16.4035i	0.500144	−	0.537025i
$934$	−24.0642	−	41.6804i	−0.787405	−	1.36383i
$935$	33.4590			1.09423
$936$	18.8966	−	12.7810i	0.617654	−	0.417760i
$937$	34.7312			1.13462			0.567310	−	0.823504i	$-0.307984\pi$
$937$	34.7312			1.13462			0.567310	+	0.823504i	$0.307984\pi$
$938$		0			0
$939$	13.6344	+	44.4947i	0.444943	+	1.45203i
$940$	−5.47544	+	9.48374i	−0.178589	+	0.309326i
$941$	−21.6512	+	37.5010i	−0.705810	+	1.22250i	0.260588	+	0.965450i	$0.416083\pi$
$941$	−21.6512	+	37.5010i	−0.705810	+	1.22250i	−0.966398	+	0.257049i	$0.917250\pi$
$942$	5.12790	+	1.18043i	0.167076	+	0.0384604i
$943$	10.0839	+	17.4658i	0.328376	+	0.568764i
$944$	−0.612785			−0.0199444
$945$		0			0
$946$	−39.5796			−1.28684
$947$	−19.1295	−	33.1333i	−0.621626	−	1.07669i	−0.989183	−	0.146687i	$-0.953139\pi$
$947$	−19.1295	−	33.1333i	−0.621626	−	1.07669i	0.367557	−	0.930001i	$-0.380194\pi$
$948$	−41.6439	−	9.58629i	−1.35253	−	0.311348i
$949$	−25.0325	+	43.3575i	−0.812588	+	1.40744i
$950$	19.8588	−	34.3965i	0.644305	−	1.11597i
$951$	−4.21784	−	13.7645i	−0.136773	−	0.446345i
$952$		0			0
$953$	−47.8757			−1.55085			−0.775423	−	0.631442i	$-0.782463\pi$
$953$	−47.8757			−1.55085			−0.775423	+	0.631442i	$0.782463\pi$
$954$	3.31249	+	46.5183i	0.107246	+	1.50609i
$955$	6.22652			0.201486
$956$	30.2389	+	52.3753i	0.977996	+	1.69394i
$957$	−26.0770	+	27.9999i	−0.842948	+	0.905108i
$958$	27.3593	−	47.3877i	0.883939	−	1.53103i
$959$		0			0
$960$	18.5752	−	19.9450i	0.599512	−	0.643721i
$961$	14.4281	+	24.9902i	0.465422	+	0.806134i
$962$	−19.8114			−0.638745
$963$	25.4201	+	12.3581i	0.819150	+	0.398234i
$964$	75.5082			2.43195
$965$	6.19407	+	10.7284i	0.199394	+	0.345361i
$966$		0			0
$967$	15.5575	−	26.9463i	0.500294	−	0.866535i	−0.499706	−	0.866195i	$-0.666559\pi$
$967$	15.5575	−	26.9463i	0.500294	−	0.866535i	1.00000		0.000339469i	$-0.000108056\pi$
$968$	−15.2245	+	26.3696i	−0.489334	+	0.847551i
$969$	−43.7474	−	10.0705i	−1.40537	−	0.323511i
$970$	−6.85966	−	11.8813i	−0.220250	−	0.381485i
$971$	30.2624			0.971167			0.485583	−	0.874190i	$-0.338607\pi$
$971$	30.2624			0.971167			0.485583	+	0.874190i	$0.338607\pi$
$972$	−42.5045	−	3.58216i	−1.36333	−	0.114898i
$973$		0			0
$974$	−14.7751	−	25.5911i	−0.473423	−	0.819993i
$975$	27.1645	+	6.25317i	0.869960	+	0.200262i
$976$	10.2661	−	17.7815i	0.328611	−	0.569170i
$977$	−19.1101	+	33.0996i	−0.611385	+	1.05895i	0.379622	+	0.925142i	$0.376054\pi$
$977$	−19.1101	+	33.0996i	−0.611385	+	1.05895i	−0.991007	+	0.133808i	$0.957279\pi$
$978$	21.0515	+	68.6998i	0.673154	+	2.19678i
$979$	14.2288	+	24.6450i	0.454754	+	0.787657i
$980$		0			0
$981$	45.5709	+	22.1545i	1.45497	+	0.707339i
$982$	−31.5642			−1.00725
$983$	−18.6964	−	32.3832i	−0.596324	−	1.03286i	−0.993359	−	0.115059i	$-0.963294\pi$
$983$	−18.6964	−	32.3832i	−0.596324	−	1.03286i	0.397035	−	0.917803i	$-0.370039\pi$
$984$	−7.37016	+	7.91364i	−0.234952	+	0.252278i
$985$	−2.10184	+	3.64050i	−0.0669703	+	0.115996i
$986$	−21.1377	+	36.6116i	−0.673162	+	1.16595i
$987$		0			0
$988$	34.9370	+	60.5126i	1.11149	+	1.92516i
$989$	−17.1871			−0.546516
$990$	3.22153	+	45.2409i	0.102387	+	1.43785i
$991$	−23.8597			−0.757930			−0.378965	−	0.925411i	$-0.623720\pi$
$991$	−23.8597			−0.757930			−0.378965	+	0.925411i	$0.623720\pi$
$992$	−5.50921	−	9.54223i	−0.174918	−	0.302966i
$993$	−6.29136	−	20.5313i	−0.199650	−	0.651540i
$994$		0			0
$995$	−7.03180	+	12.1794i	−0.222923	+	0.386114i
$996$	46.9278	+	10.8026i	1.48696	+	0.342294i
$997$	25.8413	+	44.7585i	0.818403	+	1.41751i	0.906859	+	0.421435i	$0.138473\pi$
$997$	25.8413	+	44.7585i	0.818403	+	1.41751i	−0.0884560	+	0.996080i	$0.528193\pi$
$998$	30.4498			0.963872
$999$	7.75857	+	6.25823i	0.245470	+	0.198002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.h.148.2	yes	24
3.2	odd	2		1323.2.f.h.442.12		24
7.2	even	3		441.2.g.h.67.1		24
7.3	odd	6		441.2.h.h.373.12		24
7.4	even	3		441.2.h.h.373.11		24
7.5	odd	6		441.2.g.h.67.2		24
7.6	odd	2	inner	441.2.f.h.148.1	✓	24
9.2	odd	6		1323.2.f.h.883.12		24
9.4	even	3		3969.2.a.bh.1.12		12
9.5	odd	6		3969.2.a.bi.1.1		12
9.7	even	3	inner	441.2.f.h.295.2	yes	24
21.2	odd	6		1323.2.g.h.361.11		24
21.5	even	6		1323.2.g.h.361.12		24
21.11	odd	6		1323.2.h.h.226.2		24
21.17	even	6		1323.2.h.h.226.1		24
21.20	even	2		1323.2.f.h.442.11		24
63.2	odd	6		1323.2.h.h.802.2		24
63.11	odd	6		1323.2.g.h.667.11		24
63.13	odd	6		3969.2.a.bh.1.11		12
63.16	even	3		441.2.h.h.214.11		24
63.20	even	6		1323.2.f.h.883.11		24
63.25	even	3		441.2.g.h.79.1		24
63.34	odd	6	inner	441.2.f.h.295.1	yes	24
63.38	even	6		1323.2.g.h.667.12		24
63.41	even	6		3969.2.a.bi.1.2		12
63.47	even	6		1323.2.h.h.802.1		24
63.52	odd	6		441.2.g.h.79.2		24
63.61	odd	6		441.2.h.h.214.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.1	✓	24	7.6	odd	2	inner
441.2.f.h.148.2	yes	24	1.1	even	1	trivial
441.2.f.h.295.1	yes	24	63.34	odd	6	inner
441.2.f.h.295.2	yes	24	9.7	even	3	inner
441.2.g.h.67.1		24	7.2	even	3
441.2.g.h.67.2		24	7.5	odd	6
441.2.g.h.79.1		24	63.25	even	3
441.2.g.h.79.2		24	63.52	odd	6
441.2.h.h.214.11		24	63.16	even	3
441.2.h.h.214.12		24	63.61	odd	6
441.2.h.h.373.11		24	7.4	even	3
441.2.h.h.373.12		24	7.3	odd	6
1323.2.f.h.442.11		24	21.20	even	2
1323.2.f.h.442.12		24	3.2	odd	2
1323.2.f.h.883.11		24	63.20	even	6
1323.2.f.h.883.12		24	9.2	odd	6
1323.2.g.h.361.11		24	21.2	odd	6
1323.2.g.h.361.12		24	21.5	even	6
1323.2.g.h.667.11		24	63.11	odd	6
1323.2.g.h.667.12		24	63.38	even	6
1323.2.h.h.226.1		24	21.17	even	6
1323.2.h.h.226.2		24	21.11	odd	6
1323.2.h.h.802.1		24	63.47	even	6
1323.2.h.h.802.2		24	63.2	odd	6
3969.2.a.bh.1.11		12	63.13	odd	6
3969.2.a.bh.1.12		12	9.4	even	3
3969.2.a.bi.1.1		12	9.5	odd	6
3969.2.a.bi.1.2		12	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08816 - 1.88474i) q^{2} +(1.68791 + 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(-0.634145 + 1.09837i) q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} +O(q^{10})\)	\(q+(-1.08816 - 1.88474i) q^{2} +(1.68791 + 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(-0.634145 + 1.09837i) q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} +2.76019 q^{10} +(2.73867 + 4.74351i) q^{11} +(-3.23009 + 3.46828i) q^{12} +(2.37268 - 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 + 1.71920i) q^{16} -4.81644 q^{17} +(-0.463740 - 6.51244i) q^{18} +5.38119 q^{19} +(-1.73523 - 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(2.70484 + 0.622645i) q^{24} +(1.69572 + 2.93707i) q^{25} -10.3274 q^{26} +(4.04442 + 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(4.65895 + 1.07247i) q^{30} +(0.732093 - 1.26802i) q^{31} +(3.76264 - 6.51709i) q^{32} +(2.77952 + 9.07071i) q^{33} +(5.24103 + 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +1.91834 q^{37} +(-5.85557 - 10.1421i) q^{38} +(5.60164 - 6.01471i) q^{39} +(-1.01621 + 1.76012i) q^{40} +(-1.94808 + 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} -14.9878 q^{44} +(-3.15166 + 2.13168i) q^{45} -11.2653 q^{46} +(-1.57773 - 2.73271i) q^{47} +(1.00739 + 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(-8.12969 - 1.87143i) q^{51} +(6.49243 + 11.2452i) q^{52} -7.14299 q^{53} +(1.74766 - 11.1726i) q^{54} -6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} +(-0.154341 + 0.267327i) q^{59} +(-1.76111 - 5.74723i) q^{60} +(-5.17143 - 8.95719i) q^{61} -3.18652 q^{62} -12.4070 q^{64} +(3.00924 + 5.21216i) q^{65} +(14.0714 - 15.1090i) q^{66} +(-2.23655 + 3.87382i) q^{67} +(6.58968 - 11.4137i) q^{68} +(6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(4.32359 + 2.10193i) q^{72} -10.5503 q^{73} +(-2.08745 - 3.61557i) q^{74} +(1.72102 + 5.61638i) q^{75} +(-7.36235 + 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 + 7.80846i) q^{79} -2.51776 q^{80} +(5.55902 + 7.07794i) q^{81} +8.47926 q^{82} +(-5.08023 - 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(2.04664 + 6.67903i) q^{87} +(4.38866 + 7.60138i) q^{88} +5.19552 q^{89} +(7.44716 + 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(1.72840 - 1.85585i) q^{93} +(-3.43363 + 5.94722i) q^{94} +(-3.41245 + 5.91054i) q^{95} +(8.88321 - 9.53826i) q^{96} +(-2.48521 - 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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