LMFDB - Embedded newform 1232.2.q.o.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.939795628203.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{7} + 10x^{6} - 26x^{5} + 87x^{4} - 48x^{3} - 65x^{2} + 30x + 36 $ x^10 - x^9 + x^8 - 9x^7 + 10x^6 - 26x^5 + 87x^4 - 48x^3 - 65x^2 + 30*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$-0.574432 - 0.269593i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.o.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29867 + 2.24937i) q^{3} +(-1.07443 - 1.86097i) q^{5} +(-0.726377 + 2.54409i) q^{7} +(-1.87311 - 3.24431i) q^{9} +O(q^{10})$	\(q+(-1.29867 + 2.24937i) q^{3} +(-1.07443 - 1.86097i) q^{5} +(-0.726377 + 2.54409i) q^{7} +(-1.87311 - 3.24431i) q^{9} +(-0.500000 + 0.866025i) q^{11} -0.0931948 q^{13} +5.58135 q^{15} +(-3.02505 + 5.23954i) q^{17} +(-0.679779 - 1.17741i) q^{19} +(-4.77926 - 4.93783i) q^{21} +(-1.83172 - 3.17264i) q^{23} +(0.191191 - 0.331152i) q^{25} +1.93817 q^{27} +0.458323 q^{29} +(-0.118894 + 0.205931i) q^{31} +(-1.29867 - 2.24937i) q^{33} +(5.51491 - 1.38168i) q^{35} +(-4.78759 - 8.29235i) q^{37} +(0.121030 - 0.209629i) q^{39} +5.47985 q^{41} -2.67181 q^{43} +(-4.02505 + 6.97159i) q^{45} +(-1.02505 - 1.77544i) q^{47} +(-5.94475 - 3.69593i) q^{49} +(-7.85711 - 13.6089i) q^{51} +(6.93462 - 12.0111i) q^{53} +2.14886 q^{55} +3.53125 q^{57} +(7.27959 - 12.6086i) q^{59} +(2.01150 + 3.48403i) q^{61} +(9.61440 - 2.40875i) q^{63} +(0.100132 + 0.173433i) q^{65} +(-4.50137 + 7.79660i) q^{67} +9.51525 q^{69} +4.60844 q^{71} +(-4.00937 + 6.94443i) q^{73} +(0.496589 + 0.860117i) q^{75} +(-1.84006 - 1.90110i) q^{77} +(4.62453 + 8.00993i) q^{79} +(3.10227 - 5.37328i) q^{81} -9.85257 q^{83} +13.0008 q^{85} +(-0.595211 + 1.03094i) q^{87} +(-1.28376 - 2.22354i) q^{89} +(0.0676946 - 0.237096i) q^{91} +(-0.308809 - 0.534873i) q^{93} +(-1.46075 + 2.53010i) q^{95} -0.990160 q^{97} +3.74621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.29867	+	2.24937i	−0.749789	+	1.29867i	0.198134	+	0.980175i	$0.436512\pi$
$3$	−1.29867	+	2.24937i	−0.749789	+	1.29867i	−0.947923	+	0.318499i	$0.896821\pi$
$4$		0			0
$5$	−1.07443	−	1.86097i	−0.480501	−	0.832252i	0.519249	−	0.854623i	$-0.326212\pi$
$5$	−1.07443	−	1.86097i	−0.480501	−	0.832252i	−0.999750	+	0.0223714i	$0.992878\pi$
$6$		0			0
$7$	−0.726377	+	2.54409i	−0.274545	+	0.961574i
$7$	−0.726377	+	2.54409i	−0.274545	+	0.961574i
$8$		0			0
$9$	−1.87311	−	3.24431i	−0.624369	−	1.08144i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−0.0931948			−0.0258476			−0.0129238	−	0.999916i	$-0.504114\pi$
$13$	−0.0931948			−0.0258476			−0.0129238	+	0.999916i	$0.504114\pi$
$14$		0			0
$15$	5.58135			1.44110
$16$		0			0
$17$	−3.02505	+	5.23954i	−0.733682	+	1.27078i	0.221617	+	0.975134i	$0.428867\pi$
$17$	−3.02505	+	5.23954i	−0.733682	+	1.27078i	−0.955299	+	0.295641i	$0.904467\pi$
$18$		0			0
$19$	−0.679779	−	1.17741i	−0.155952	−	0.270117i	0.777453	−	0.628941i	$-0.216511\pi$
$19$	−0.679779	−	1.17741i	−0.155952	−	0.270117i	−0.933405	+	0.358824i	$0.883178\pi$
$20$		0			0
$21$	−4.77926	−	4.93783i	−1.04292	−	1.07752i
$22$		0			0
$23$	−1.83172	−	3.17264i	−0.381941	−	0.661541i	0.609399	−	0.792864i	$-0.291411\pi$
$23$	−1.83172	−	3.17264i	−0.381941	−	0.661541i	−0.991340	+	0.131323i	$0.958078\pi$
$24$		0			0
$25$	0.191191	−	0.331152i	0.0382382	−	0.0662304i
$26$		0			0
$27$	1.93817			0.373001
$28$		0			0
$29$	0.458323			0.0851084			0.0425542	−	0.999094i	$-0.486450\pi$
$29$	0.458323			0.0851084			0.0425542	+	0.999094i	$0.486450\pi$
$30$		0			0
$31$	−0.118894	+	0.205931i	−0.0213540	+	0.0369862i	−0.876505	−	0.481393i	$-0.840131\pi$
$31$	−0.118894	+	0.205931i	−0.0213540	+	0.0369862i	0.855151	+	0.518379i	$0.173464\pi$
$32$		0			0
$33$	−1.29867	−	2.24937i	−0.226070	−	0.391565i
$34$		0			0
$35$	5.51491	−	1.38168i	0.932191	−	0.233547i
$36$		0			0
$37$	−4.78759	−	8.29235i	−0.787075	−	1.36325i	−0.927751	−	0.373199i	$-0.878261\pi$
$37$	−4.78759	−	8.29235i	−0.787075	−	1.36325i	0.140676	−	0.990056i	$-0.455072\pi$
$38$		0			0
$39$	0.121030	−	0.209629i	0.0193803	−	0.0335676i
$40$		0			0
$41$	5.47985			0.855808			0.427904	−	0.903824i	$-0.359252\pi$
$41$	5.47985			0.855808			0.427904	+	0.903824i	$0.359252\pi$
$42$		0			0
$43$	−2.67181			−0.407447			−0.203723	−	0.979029i	$-0.565304\pi$
$43$	−2.67181			−0.407447			−0.203723	+	0.979029i	$0.565304\pi$
$44$		0			0
$45$	−4.02505	+	6.97159i	−0.600019	+	1.03926i
$46$		0			0
$47$	−1.02505	−	1.77544i	−0.149519	−	0.258974i	0.781531	−	0.623867i	$-0.214439\pi$
$47$	−1.02505	−	1.77544i	−0.149519	−	0.258974i	−0.931050	+	0.364892i	$0.881106\pi$
$48$		0			0
$49$	−5.94475	−	3.69593i	−0.849250	−	0.527990i
$50$		0			0
$51$	−7.85711	−	13.6089i	−1.10021	−	1.90563i
$52$		0			0
$53$	6.93462	−	12.0111i	0.952543	−	1.64985i	0.212650	−	0.977128i	$-0.431791\pi$
$53$	6.93462	−	12.0111i	0.952543	−	1.64985i	0.739893	−	0.672724i	$-0.234876\pi$
$54$		0			0
$55$	2.14886			0.289753
$56$		0			0
$57$	3.53125			0.467725
$58$		0			0
$59$	7.27959	−	12.6086i	0.947722	−	1.64150i	0.197516	−	0.980300i	$-0.436713\pi$
$59$	7.27959	−	12.6086i	0.947722	−	1.64150i	0.750207	−	0.661203i	$-0.229954\pi$
$60$		0			0
$61$	2.01150	+	3.48403i	0.257547	+	0.446084i	0.965584	−	0.260091i	$-0.0837526\pi$
$61$	2.01150	+	3.48403i	0.257547	+	0.446084i	−0.708037	+	0.706175i	$0.750419\pi$
$62$		0			0
$63$	9.61440	−	2.40875i	1.21130	−	0.303474i
$64$		0			0
$65$	0.100132	+	0.173433i	0.0124198	+	0.0215117i
$66$		0			0
$67$	−4.50137	+	7.79660i	−0.549930	+	0.952506i	0.448349	+	0.893859i	$0.352012\pi$
$67$	−4.50137	+	7.79660i	−0.549930	+	0.952506i	−0.998279	+	0.0586475i	$0.981321\pi$
$68$		0			0
$69$	9.51525			1.14550
$70$		0			0
$71$	4.60844			0.546921			0.273461	−	0.961883i	$-0.411832\pi$
$71$	4.60844			0.546921			0.273461	+	0.961883i	$0.411832\pi$
$72$		0			0
$73$	−4.00937	+	6.94443i	−0.469261	+	0.812784i	−0.999382	−	0.0351378i	$-0.988813\pi$
$73$	−4.00937	+	6.94443i	−0.469261	+	0.812784i	0.530121	+	0.847922i	$0.322146\pi$
$74$		0			0
$75$	0.496589	+	0.860117i	0.0573411	+	0.0993178i
$76$		0			0
$77$	−1.84006	−	1.90110i	−0.209694	−	0.216651i
$78$		0			0
$79$	4.62453	+	8.00993i	0.520301	+	0.901187i	0.999721	+	0.0236019i	$0.00751343\pi$
$79$	4.62453	+	8.00993i	0.520301	+	0.901187i	−0.479421	+	0.877585i	$0.659153\pi$
$80$		0			0
$81$	3.10227	−	5.37328i	0.344696	−	0.597032i
$82$		0			0
$83$	−9.85257			−1.08146			−0.540730	−	0.841196i	$-0.681852\pi$
$83$	−9.85257			−1.08146			−0.540730	+	0.841196i	$0.681852\pi$
$84$		0			0
$85$	13.0008			1.41014
$86$		0			0
$87$	−0.595211	+	1.03094i	−0.0638134	+	0.110528i
$88$		0			0
$89$	−1.28376	−	2.22354i	−0.136078	−	0.235694i	0.789931	−	0.613196i	$-0.210116\pi$
$89$	−1.28376	−	2.22354i	−0.136078	−	0.235694i	−0.926009	+	0.377502i	$0.876783\pi$
$90$		0			0
$91$	0.0676946	−	0.237096i	0.00709632	−	0.0248544i
$92$		0			0
$93$	−0.308809	−	0.534873i	−0.0320220	−	0.0554638i
$94$		0			0
$95$	−1.46075	+	2.53010i	−0.149870	+	0.259583i
$96$		0			0
$97$	−0.990160			−0.100536			−0.0502678	−	0.998736i	$-0.516007\pi$
$97$	−0.990160			−0.100536			−0.0502678	+	0.998736i	$0.516007\pi$
$98$		0			0
$99$	3.74621			0.376508
$100$		0			0
$101$	3.12667	−	5.41555i	0.311115	−	0.538867i	−0.667489	−	0.744620i	$-0.732631\pi$
$101$	3.12667	−	5.41555i	0.311115	−	0.538867i	0.978604	+	0.205753i	$0.0659642\pi$
$102$		0			0
$103$	−0.980588	−	1.69843i	−0.0966203	−	0.167351i	0.813663	−	0.581336i	$-0.197470\pi$
$103$	−0.980588	−	1.69843i	−0.0966203	−	0.167351i	−0.910284	+	0.413985i	$0.864137\pi$
$104$		0			0
$105$	−4.05416	+	14.1994i	−0.395646	+	1.38572i
$106$		0			0
$107$	−9.27340	−	16.0620i	−0.896493	−	1.55277i	−0.831946	−	0.554857i	$-0.812773\pi$
$107$	−9.27340	−	16.0620i	−0.896493	−	1.55277i	−0.0645475	−	0.997915i	$-0.520560\pi$
$108$		0			0
$109$	9.52547	−	16.4986i	0.912375	−	1.58028i	0.101675	−	0.994818i	$-0.467580\pi$
$109$	9.52547	−	16.4986i	0.912375	−	1.58028i	0.810700	−	0.585462i	$-0.199087\pi$
$110$		0			0
$111$	24.8701			2.36056
$112$		0			0
$113$	12.6029			1.18558			0.592789	−	0.805358i	$-0.298027\pi$
$113$	12.6029			1.18558			0.592789	+	0.805358i	$0.298027\pi$
$114$		0			0
$115$	−3.93613	+	6.81757i	−0.367046	+	0.635742i
$116$		0			0
$117$	0.174564	+	0.302353i	0.0161384	+	0.0279526i
$118$		0			0
$119$	−11.1325	−	11.5019i	−1.02052	−	1.05437i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−7.11653	+	12.3262i	−0.641676	+	1.11142i
$124$		0			0
$125$	−11.5660			−1.03450
$126$		0			0
$127$	−2.51185			−0.222890			−0.111445	−	0.993771i	$-0.535548\pi$
$127$	−2.51185			−0.222890			−0.111445	+	0.993771i	$0.535548\pi$
$128$		0			0
$129$	3.46980	−	6.00988i	0.305499	−	0.529140i
$130$		0			0
$131$	−1.45800	−	2.52534i	−0.127386	−	0.220640i	0.795277	−	0.606246i	$-0.207326\pi$
$131$	−1.45800	−	2.52534i	−0.127386	−	0.220640i	−0.922663	+	0.385607i	$0.873992\pi$
$132$		0			0
$133$	3.48922	−	0.874173i	0.302553	−	0.0758004i
$134$		0			0
$135$	−2.08243	−	3.60688i	−0.179227	−	0.310431i
$136$		0			0
$137$	−8.77373	+	15.1965i	−0.749590	+	1.29833i	0.198429	+	0.980115i	$0.436416\pi$
$137$	−8.77373	+	15.1965i	−0.749590	+	1.29833i	−0.948019	+	0.318213i	$0.896917\pi$
$138$		0			0
$139$	−21.4223			−1.81701			−0.908506	−	0.417871i	$-0.862776\pi$
$139$	−21.4223			−1.81701			−0.908506	+	0.417871i	$0.862776\pi$
$140$		0			0
$141$	5.32482			0.448431
$142$		0			0
$143$	0.0465974	−	0.0807091i	0.00389667	−	0.00674923i
$144$		0			0
$145$	−0.492437	−	0.852925i	−0.0408946	−	0.0708316i
$146$		0			0
$147$	16.0338	−	8.57213i	1.32245	−	0.707018i
$148$		0			0
$149$	−8.25344	−	14.2954i	−0.676148	−	1.17112i	−0.976132	−	0.217179i	$-0.930314\pi$
$149$	−8.25344	−	14.2954i	−0.676148	−	1.17112i	0.299983	−	0.953944i	$-0.403019\pi$
$150$		0			0
$151$	6.32168	−	10.9495i	0.514451	−	0.891055i	−0.485408	−	0.874288i	$-0.661329\pi$
$151$	6.32168	−	10.9495i	0.514451	−	0.891055i	0.999859	−	0.0167678i	$-0.00533761\pi$
$152$		0			0
$153$	22.6650			1.83235
$154$		0			0
$155$	0.510975			0.0410425
$156$		0			0
$157$	−7.13594	+	12.3598i	−0.569510	+	0.986421i	0.427104	+	0.904203i	$0.359534\pi$
$157$	−7.13594	+	12.3598i	−0.569510	+	0.986421i	−0.996614	+	0.0822184i	$0.973800\pi$
$158$		0			0
$159$	18.0116	+	31.1970i	1.42841	+	2.47408i
$160$		0			0
$161$	9.40199	−	2.35553i	0.740981	−	0.185642i
$162$		0			0
$163$	−2.38209	−	4.12589i	−0.186579	−	0.323165i	0.757528	−	0.652802i	$-0.226407\pi$
$163$	−2.38209	−	4.12589i	−0.186579	−	0.323165i	−0.944108	+	0.329637i	$0.893073\pi$
$164$		0			0
$165$	−2.79067	+	4.83359i	−0.217254	+	0.376294i
$166$		0			0
$167$	−3.62444			−0.280468			−0.140234	−	0.990118i	$-0.544785\pi$
$167$	−3.62444			−0.280468			−0.140234	+	0.990118i	$0.544785\pi$
$168$		0			0
$169$	−12.9913			−0.999332
$170$		0			0
$171$	−2.54660	+	4.41084i	−0.194743	+	0.337305i
$172$		0			0
$173$	11.9097	+	20.6282i	0.905476	+	1.56833i	0.820277	+	0.571966i	$0.193819\pi$
$173$	11.9097	+	20.6282i	0.905476	+	1.56833i	0.0851982	+	0.996364i	$0.472848\pi$
$174$		0			0
$175$	0.703603	+	0.726947i	0.0531874	+	0.0549520i
$176$		0			0
$177$	18.9076	+	32.7490i	1.42118	+	2.46156i
$178$		0			0
$179$	2.29132	−	3.96869i	0.171261	−	0.296634i	−0.767600	−	0.640930i	$-0.778549\pi$
$179$	2.29132	−	3.96869i	0.171261	−	0.296634i	0.938861	+	0.344296i	$0.111882\pi$
$180$		0			0
$181$	5.14738			0.382602			0.191301	−	0.981531i	$-0.438729\pi$
$181$	5.14738			0.382602			0.191301	+	0.981531i	$0.438729\pi$
$182$		0			0
$183$	−10.4491			−0.772423
$184$		0			0
$185$	−10.2879	+	17.8191i	−0.756381	+	1.31009i
$186$		0			0
$187$	−3.02505	−	5.23954i	−0.221214	−	0.383153i
$188$		0			0
$189$	−1.40784	+	4.93087i	−0.102405	+	0.358668i
$190$		0			0
$191$	−7.84676	−	13.5910i	−0.567771	−	0.983409i	−0.996786	−	0.0801114i	$-0.974472\pi$
$191$	−7.84676	−	13.5910i	−0.567771	−	0.983409i	0.429014	−	0.903298i	$-0.358861\pi$
$192$		0			0
$193$	−12.7866	+	22.1470i	−0.920400	+	1.59418i	−0.121602	+	0.992579i	$0.538803\pi$
$193$	−12.7866	+	22.1470i	−0.920400	+	1.59418i	−0.798798	+	0.601600i	$0.794530\pi$
$194$		0			0
$195$	−0.520153			−0.0372489
$196$		0			0
$197$	−2.35066			−0.167478			−0.0837389	−	0.996488i	$-0.526686\pi$
$197$	−2.35066			−0.167478			−0.0837389	+	0.996488i	$0.526686\pi$
$198$		0			0
$199$	−9.05535	+	15.6843i	−0.641917	+	1.11183i	0.343088	+	0.939303i	$0.388527\pi$
$199$	−9.05535	+	15.6843i	−0.641917	+	1.11183i	−0.985004	+	0.172529i	$0.944806\pi$
$200$		0			0
$201$	−11.6916	−	20.2505i	−0.824663	−	1.42836i
$202$		0			0
$203$	−0.332915	+	1.16601i	−0.0233660	+	0.0818380i
$204$		0			0
$205$	−5.88772	−	10.1978i	−0.411217	−	0.712248i
$206$		0			0
$207$	−6.86203	+	11.8854i	−0.476944	+	0.826091i
$208$		0			0
$209$	1.35956			0.0940426
$210$		0			0
$211$	−21.6460			−1.49017			−0.745085	−	0.666969i	$-0.767591\pi$
$211$	−21.6460			−1.49017			−0.745085	+	0.666969i	$0.767591\pi$
$212$		0			0
$213$	−5.98486	+	10.3661i	−0.410076	+	0.710272i
$214$		0			0
$215$	2.87067	+	4.97215i	0.195778	+	0.339098i
$216$		0			0
$217$	−0.437543	−	0.452060i	−0.0297024	−	0.0306878i
$218$		0			0
$219$	−10.4137	−	18.0371i	−0.703694	−	1.21883i
$220$		0			0
$221$	0.281919	−	0.488298i	0.0189639	−	0.0328465i
$222$		0			0
$223$	−19.6065			−1.31295			−0.656474	−	0.754349i	$-0.727953\pi$
$223$	−19.6065			−1.31295			−0.656474	+	0.754349i	$0.727953\pi$
$224$		0			0
$225$	−1.43248			−0.0954988
$226$		0			0
$227$	4.76883	−	8.25986i	0.316518	−	0.548226i	−0.663241	−	0.748406i	$-0.730819\pi$
$227$	4.76883	−	8.25986i	0.316518	−	0.548226i	0.979759	+	0.200180i	$0.0641528\pi$
$228$		0			0
$229$	−0.749292	−	1.29781i	−0.0495146	−	0.0857618i	0.840206	−	0.542268i	$-0.182434\pi$
$229$	−0.749292	−	1.29781i	−0.0495146	−	0.0857618i	−0.889720	+	0.456506i	$0.849101\pi$
$230$		0			0
$231$	6.66591	−	1.67005i	0.438585	−	0.109881i
$232$		0			0
$233$	−5.81557	−	10.0729i	−0.380991	−	0.659895i	0.610214	−	0.792237i	$-0.291084\pi$
$233$	−5.81557	−	10.0729i	−0.380991	−	0.659895i	−0.991204	+	0.132342i	$0.957750\pi$
$234$		0			0
$235$	−2.20269	+	3.81518i	−0.143688	+	0.248875i
$236$		0			0
$237$	−24.0230			−1.56046
$238$		0			0
$239$	3.45514			0.223494			0.111747	−	0.993737i	$-0.464355\pi$
$239$	3.45514			0.223494			0.111747	+	0.993737i	$0.464355\pi$
$240$		0			0
$241$	−4.03219	+	6.98396i	−0.259736	+	0.449876i	−0.966171	−	0.257902i	$-0.916969\pi$
$241$	−4.03219	+	6.98396i	−0.259736	+	0.449876i	0.706435	+	0.707778i	$0.250302\pi$
$242$		0			0
$243$	10.9649	+	18.9918i	0.703400	+	1.21832i
$244$		0			0
$245$	−0.490787	+	15.0340i	−0.0313552	+	0.960490i
$246$		0			0
$247$	0.0633519	+	0.109729i	0.00403099	+	0.00698187i
$248$		0			0
$249$	12.7953	−	22.1621i	0.810868	−	1.40446i
$250$		0			0
$251$	12.7607			0.805447			0.402723	−	0.915322i	$-0.368064\pi$
$251$	12.7607			0.805447			0.402723	+	0.915322i	$0.368064\pi$
$252$		0			0
$253$	3.66345			0.230319
$254$		0			0
$255$	−16.8839	+	29.2437i	−1.05731	+	1.83131i
$256$		0			0
$257$	−15.3418	−	26.5727i	−0.956992	−	1.65756i	−0.729742	−	0.683723i	$-0.760360\pi$
$257$	−15.3418	−	26.5727i	−0.956992	−	1.65756i	−0.227251	−	0.973836i	$-0.572974\pi$
$258$		0			0
$259$	24.5741	−	6.15668i	1.52696	−	0.382557i
$260$		0			0
$261$	−0.858487	−	1.48694i	−0.0531390	−	0.0920394i
$262$		0			0
$263$	6.07118	−	10.5156i	0.374365	−	0.648419i	−0.615867	−	0.787850i	$-0.711194\pi$
$263$	6.07118	−	10.5156i	0.374365	−	0.648419i	0.990232	+	0.139431i	$0.0445275\pi$
$264$		0			0
$265$	−29.8031			−1.83079
$266$		0			0
$267$	6.66873			0.408120
$268$		0			0
$269$	−14.9709	+	25.9303i	−0.912790	+	1.58100i	−0.102686	+	0.994714i	$0.532744\pi$
$269$	−14.9709	+	25.9303i	−0.912790	+	1.58100i	−0.810104	+	0.586286i	$0.800590\pi$
$270$		0			0
$271$	14.4336	+	24.9998i	0.876780	+	1.51863i	0.854854	+	0.518868i	$0.173646\pi$
$271$	14.4336	+	24.9998i	0.876780	+	1.51863i	0.0219260	+	0.999760i	$0.493020\pi$
$272$		0			0
$273$	0.445402	+	0.460180i	0.0269570	+	0.0278514i
$274$		0			0
$275$	0.191191	+	0.331152i	0.0115292	+	0.0199692i
$276$		0			0
$277$	−5.30004	+	9.17994i	−0.318449	+	0.551569i	−0.980165	−	0.198185i	$-0.936495\pi$
$277$	−5.30004	+	9.17994i	−0.318449	+	0.551569i	0.661716	+	0.749755i	$0.269828\pi$
$278$		0			0
$279$	0.890805			0.0533311
$280$		0			0
$281$	2.10700			0.125693			0.0628465	−	0.998023i	$-0.479982\pi$
$281$	2.10700			0.125693			0.0628465	+	0.998023i	$0.479982\pi$
$282$		0			0
$283$	−6.50140	+	11.2608i	−0.386468	+	0.669383i	−0.991972	−	0.126460i	$-0.959638\pi$
$283$	−6.50140	+	11.2608i	−0.386468	+	0.669383i	0.605503	+	0.795843i	$0.292972\pi$
$284$		0			0
$285$	−3.79408	−	6.57155i	−0.224742	−	0.389265i
$286$		0			0
$287$	−3.98043	+	13.9412i	−0.234958	+	0.822923i
$288$		0			0
$289$	−9.80186	−	16.9773i	−0.576580	−	0.998666i
$290$		0			0
$291$	1.28589	−	2.22723i	0.0753805	−	0.130563i
$292$		0			0
$293$	15.3344			0.895844			0.447922	−	0.894073i	$-0.352164\pi$
$293$	15.3344			0.895844			0.447922	+	0.894073i	$0.352164\pi$
$294$		0			0
$295$	−31.2857			−1.82152
$296$		0			0
$297$	−0.969085	+	1.67850i	−0.0562320	+	0.0973967i
$298$		0			0
$299$	0.170707	+	0.295673i	0.00987225	+	0.0170992i
$300$		0			0
$301$	1.94074	−	6.79731i	0.111862	−	0.391790i
$302$		0			0
$303$	8.12104	+	14.0661i	0.466542	+	0.808074i
$304$		0			0
$305$	4.32245	−	7.48670i	0.247503	−	0.428687i
$306$		0			0
$307$	3.77727			0.215580			0.107790	−	0.994174i	$-0.465623\pi$
$307$	3.77727			0.215580			0.107790	+	0.994174i	$0.465623\pi$
$308$		0			0
$309$	5.09386			0.289779
$310$		0			0
$311$	−5.17593	+	8.96498i	−0.293500	+	0.508357i	−0.974635	−	0.223801i	$-0.928153\pi$
$311$	−5.17593	+	8.96498i	−0.293500	+	0.508357i	0.681135	+	0.732158i	$0.261487\pi$
$312$		0			0
$313$	−6.21381	−	10.7626i	−0.351225	−	0.608340i	0.635239	−	0.772316i	$-0.280902\pi$
$313$	−6.21381	−	10.7626i	−0.351225	−	0.608340i	−0.986464	+	0.163975i	$0.947568\pi$
$314$		0			0
$315$	−14.8126	−	15.3041i	−0.834597	−	0.862287i
$316$		0			0
$317$	−3.58353	−	6.20686i	−0.201271	−	0.348612i	0.747667	−	0.664074i	$-0.231174\pi$
$317$	−3.58353	−	6.20686i	−0.201271	−	0.348612i	−0.948938	+	0.315462i	$0.897841\pi$
$318$		0			0
$319$	−0.229161	+	0.396919i	−0.0128306	+	0.0222232i
$320$		0			0
$321$	48.1725			2.68872
$322$		0			0
$323$	8.22547			0.457677
$324$		0			0
$325$	−0.0178180	+	0.0308617i	−0.000988364	+	0.00171190i
$326$		0			0
$327$	24.7410	+	42.8526i	1.36818	+	2.36975i
$328$		0			0
$329$	5.26144	−	1.31818i	0.290073	−	0.0726736i
$330$		0			0
$331$	1.17993	+	2.04371i	0.0648550	+	0.112332i	0.896630	−	0.442781i	$-0.146008\pi$
$331$	1.17993	+	2.04371i	0.0648550	+	0.112332i	−0.831775	+	0.555113i	$0.812675\pi$
$332$		0			0
$333$	−17.9353	+	31.0649i	−0.982850	+	1.70235i
$334$		0			0
$335$	19.3457			1.05697
$336$		0			0
$337$	−7.81168			−0.425529			−0.212765	−	0.977103i	$-0.568247\pi$
$337$	−7.81168			−0.425529			−0.212765	+	0.977103i	$0.568247\pi$
$338$		0			0
$339$	−16.3670	+	28.3485i	−0.888934	+	1.53968i
$340$		0			0
$341$	−0.118894	−	0.205931i	−0.00643848	−	0.0111518i
$342$		0			0
$343$	13.7209	−	12.4393i	0.740859	−	0.671661i
$344$		0			0
$345$	−10.2235	−	17.7076i	−0.550414	−	0.953345i
$346$		0			0
$347$	1.05962	−	1.83532i	0.0568835	−	0.0985252i	−0.836181	−	0.548453i	$-0.815217\pi$
$347$	1.05962	−	1.83532i	0.0568835	−	0.0985252i	0.893065	+	0.449928i	$0.148550\pi$
$348$		0			0
$349$	−18.6490			−0.998256			−0.499128	−	0.866528i	$-0.666346\pi$
$349$	−18.6490			−0.998256			−0.499128	+	0.866528i	$0.666346\pi$
$350$		0			0
$351$	−0.180627			−0.00964118
$352$		0			0
$353$	−8.01482	+	13.8821i	−0.426586	+	0.738869i	−0.996567	−	0.0827892i	$-0.973617\pi$
$353$	−8.01482	+	13.8821i	−0.426586	+	0.738869i	0.569981	+	0.821658i	$0.306951\pi$
$354$		0			0
$355$	−4.95146	−	8.57618i	−0.262796	−	0.455176i
$356$		0			0
$357$	40.3295	−	10.1040i	2.13446	−	0.534758i
$358$		0			0
$359$	6.79183	+	11.7638i	0.358459	+	0.620869i	0.987704	−	0.156338i	$-0.0499689\pi$
$359$	6.79183	+	11.7638i	0.358459	+	0.620869i	−0.629245	+	0.777207i	$0.716636\pi$
$360$		0			0
$361$	8.57580	−	14.8537i	0.451358	−	0.781775i
$362$		0			0
$363$	2.59735			0.136325
$364$		0			0
$365$	17.2312			0.901921
$366$		0			0
$367$	13.4219	−	23.2474i	0.700618	−	1.21351i	−0.267631	−	0.963521i	$-0.586241\pi$
$367$	13.4219	−	23.2474i	0.700618	−	1.21351i	0.968250	−	0.249985i	$-0.0804258\pi$
$368$		0			0
$369$	−10.2643	−	17.7783i	−0.534340	−	0.925504i
$370$		0			0
$371$	25.5202	+	26.3669i	1.32494	+	1.36890i
$372$		0			0
$373$	12.7657	+	22.1109i	0.660984	+	1.14486i	0.980357	+	0.197229i	$0.0631944\pi$
$373$	12.7657	+	22.1109i	0.660984	+	1.14486i	−0.319373	+	0.947629i	$0.603472\pi$
$374$		0			0
$375$	15.0205	−	26.0162i	0.775654	−	1.34347i
$376$		0			0
$377$	−0.0427133			−0.00219985
$378$		0			0
$379$	−32.0544			−1.64652			−0.823262	−	0.567662i	$-0.807848\pi$
$379$	−32.0544			−1.64652			−0.823262	+	0.567662i	$0.807848\pi$
$380$		0			0
$381$	3.26207	−	5.65007i	0.167121	−	0.289462i
$382$		0			0
$383$	−1.74976	−	3.03068i	−0.0894088	−	0.154861i	0.817853	−	0.575428i	$-0.195164\pi$
$383$	−1.74976	−	3.03068i	−0.0894088	−	0.154861i	−0.907261	+	0.420567i	$0.861831\pi$
$384$		0			0
$385$	−1.56089	+	5.46690i	−0.0795501	+	0.278619i
$386$		0			0
$387$	5.00458	+	8.66818i	0.254397	+	0.440628i
$388$		0			0
$389$	−14.1143	+	24.4468i	−0.715626	+	1.23950i	0.247092	+	0.968992i	$0.420525\pi$
$389$	−14.1143	+	24.4468i	−0.715626	+	1.23950i	−0.962718	+	0.270508i	$0.912808\pi$
$390$		0			0
$391$	22.1642			1.12089
$392$		0			0
$393$	7.57389			0.382052
$394$		0			0
$395$	9.93749	−	17.2122i	0.500010	−	0.866042i
$396$		0			0
$397$	−6.16333	−	10.6752i	−0.309329	−	0.535773i	0.668887	−	0.743364i	$-0.266771\pi$
$397$	−6.16333	−	10.6752i	−0.309329	−	0.535773i	−0.978216	+	0.207591i	$0.933438\pi$
$398$		0			0
$399$	−2.56502	+	8.98380i	−0.128411	+	0.449752i
$400$		0			0
$401$	12.0964	+	20.9515i	0.604063	+	1.04627i	0.992199	+	0.124666i	$0.0397858\pi$
$401$	12.0964	+	20.9515i	0.604063	+	1.04627i	−0.388136	+	0.921602i	$0.626881\pi$
$402$		0			0
$403$	0.0110803	−	0.0191917i	0.000551950	−	0.000956005i
$404$		0			0
$405$	−13.3327			−0.662507
$406$		0			0
$407$	9.57519			0.474624
$408$		0			0
$409$	11.0852	−	19.2001i	0.548127	−	0.949384i	−0.450276	−	0.892889i	$-0.648674\pi$
$409$	11.0852	−	19.2001i	0.548127	−	0.949384i	0.998403	−	0.0564943i	$-0.0179923\pi$
$410$		0			0
$411$	−22.7884	−	39.4707i	−1.12407	−	1.94695i
$412$		0			0
$413$	26.7897	+	27.6785i	1.31824	+	1.36197i
$414$		0			0
$415$	10.5859	+	18.3354i	0.519642	+	0.900047i
$416$		0			0
$417$	27.8205	−	48.1866i	1.36238	−	2.35971i
$418$		0			0
$419$	30.9675			1.51286			0.756432	−	0.654073i	$-0.226941\pi$
$419$	30.9675			1.51286			0.756432	+	0.654073i	$0.226941\pi$
$420$		0			0
$421$	6.87440			0.335038			0.167519	−	0.985869i	$-0.446425\pi$
$421$	6.87440			0.335038			0.167519	+	0.985869i	$0.446425\pi$
$422$		0			0
$423$	−3.84006	+	6.65117i	−0.186710	+	0.323391i
$424$		0			0
$425$	1.15672	+	2.00350i	0.0561093	+	0.0971842i
$426$		0			0
$427$	−10.3248	+	2.58672i	−0.499651	+	0.125180i
$428$		0			0
$429$	0.121030	+	0.209629i	0.00584337	+	0.0101210i
$430$		0			0
$431$	17.8507	−	30.9184i	0.859840	−	1.48929i	−0.0122411	−	0.999925i	$-0.503897\pi$
$431$	17.8507	−	30.9184i	0.859840	−	1.48929i	0.872081	−	0.489361i	$-0.162770\pi$
$432$		0			0
$433$	24.1741			1.16173			0.580866	−	0.813999i	$-0.302714\pi$
$433$	24.1741			1.16173			0.580866	+	0.813999i	$0.302714\pi$
$434$		0			0
$435$	2.55806			0.122649
$436$		0			0
$437$	−2.49034	+	4.31339i	−0.119129	+	0.206337i
$438$		0			0
$439$	−8.49844	−	14.7197i	−0.405609	−	0.702535i	0.588784	−	0.808291i	$-0.299607\pi$
$439$	−8.49844	−	14.7197i	−0.405609	−	0.702535i	−0.994392	+	0.105756i	$0.966274\pi$
$440$		0			0
$441$	−0.855610	+	26.2095i	−0.0407433	+	1.24807i
$442$		0			0
$443$	19.3363	+	33.4914i	0.918693	+	1.59122i	0.801403	+	0.598125i	$0.204087\pi$
$443$	19.3363	+	33.4914i	0.918693	+	1.59122i	0.117290	+	0.993098i	$0.462579\pi$
$444$		0			0
$445$	−2.75862	+	4.77808i	−0.130771	+	0.226503i
$446$		0			0
$447$	42.8741			2.02788
$448$		0			0
$449$	−0.416411			−0.0196516			−0.00982582	−	0.999952i	$-0.503128\pi$
$449$	−0.416411			−0.0196516			−0.00982582	+	0.999952i	$0.503128\pi$
$450$		0			0
$451$	−2.73992	+	4.74569i	−0.129018	+	0.223466i
$452$		0			0
$453$	16.4196	+	28.4396i	0.771460	+	1.33621i
$454$		0			0
$455$	−0.513961	+	0.128766i	−0.0240949	+	0.00603663i
$456$		0			0
$457$	−4.40257	−	7.62547i	−0.205944	−	0.356705i	0.744489	−	0.667634i	$-0.232693\pi$
$457$	−4.40257	−	7.62547i	−0.205944	−	0.356705i	−0.950433	+	0.310930i	$0.899360\pi$
$458$		0			0
$459$	−5.86306	+	10.1551i	−0.273664	+	0.474000i
$460$		0			0
$461$	−21.0089			−0.978481			−0.489240	−	0.872149i	$-0.662726\pi$
$461$	−21.0089			−0.978481			−0.489240	+	0.872149i	$0.662726\pi$
$462$		0			0
$463$	−10.5927			−0.492283			−0.246142	−	0.969234i	$-0.579163\pi$
$463$	−10.5927			−0.492283			−0.246142	+	0.969234i	$0.579163\pi$
$464$		0			0
$465$	−0.663589	+	1.14937i	−0.0307732	+	0.0533008i
$466$		0			0
$467$	−16.2279	−	28.1076i	−0.750940	−	1.30067i	−0.947368	−	0.320147i	$-0.896268\pi$
$467$	−16.2279	−	28.1076i	−0.750940	−	1.30067i	0.196428	−	0.980518i	$-0.437066\pi$
$468$		0			0
$469$	−16.5655	−	17.1151i	−0.764925	−	0.790304i
$470$		0			0
$471$	−18.5345	−	32.1027i	−0.854026	−	1.47922i
$472$		0			0
$473$	1.33590	−	2.31385i	0.0614249	−	0.106391i
$474$		0			0
$475$	−0.519870			−0.0238533
$476$		0			0
$477$	−51.9571			−2.37895
$478$		0			0
$479$	14.8673	−	25.7508i	0.679302	−	1.17659i	−0.295889	−	0.955222i	$-0.595616\pi$
$479$	14.8673	−	25.7508i	0.679302	−	1.17659i	0.975191	−	0.221364i	$-0.0710508\pi$
$480$		0			0
$481$	0.446179	+	0.772804i	0.0203440	+	0.0352368i
$482$		0			0
$483$	−6.91165	+	24.2076i	−0.314491	+	1.10148i
$484$		0			0
$485$	1.06386	+	1.84266i	0.0483074	+	0.0836708i
$486$		0			0
$487$	20.0083	−	34.6554i	0.906663	−	1.57039i	0.0879947	−	0.996121i	$-0.471954\pi$
$487$	20.0083	−	34.6554i	0.906663	−	1.57039i	0.818669	−	0.574266i	$-0.194713\pi$
$488$		0			0
$489$	12.3742			0.559581
$490$		0			0
$491$	−27.8325			−1.25606			−0.628032	−	0.778188i	$-0.716139\pi$
$491$	−27.8325			−1.25606			−0.628032	+	0.778188i	$0.716139\pi$
$492$		0			0
$493$	−1.38645	+	2.40140i	−0.0624425	+	0.108154i
$494$		0			0
$495$	−4.02505	−	6.97159i	−0.180913	−	0.313350i
$496$		0			0
$497$	−3.34746	+	11.7243i	−0.150154	+	0.525905i
$498$		0			0
$499$	5.99731	+	10.3876i	0.268476	+	0.465015i	0.968469	−	0.249136i	$-0.0801465\pi$
$499$	5.99731	+	10.3876i	0.268476	+	0.465015i	−0.699992	+	0.714150i	$0.746813\pi$
$500$		0			0
$501$	4.70697	−	8.15270i	0.210292	−	0.364236i
$502$		0			0
$503$	−28.0898			−1.25246			−0.626230	−	0.779638i	$-0.715403\pi$
$503$	−28.0898			−1.25246			−0.626230	+	0.779638i	$0.715403\pi$
$504$		0			0
$505$	−13.4376			−0.597964
$506$		0			0
$507$	16.8715	−	29.2223i	0.749289	−	1.29781i
$508$		0			0
$509$	−7.65068	−	13.2514i	−0.339111	−	0.587357i	0.645155	−	0.764052i	$-0.276793\pi$
$509$	−7.65068	−	13.2514i	−0.339111	−	0.587357i	−0.984266	+	0.176695i	$0.943459\pi$
$510$		0			0
$511$	−14.7549	−	15.2445i	−0.652719	−	0.674375i
$512$		0			0
$513$	−1.31753	−	2.28203i	−0.0581703	−	0.100754i
$514$		0			0
$515$	−2.10715	+	3.64969i	−0.0928522	+	0.160825i
$516$		0			0
$517$	2.05010			0.0901633
$518$		0			0
$519$	−61.8671			−2.71566
$520$		0			0
$521$	−6.27576	+	10.8699i	−0.274946	+	0.476220i	−0.970121	−	0.242620i	$-0.921993\pi$
$521$	−6.27576	+	10.8699i	−0.274946	+	0.476220i	0.695176	+	0.718840i	$0.255327\pi$
$522$		0			0
$523$	−10.6782	−	18.4953i	−0.466927	−	0.808741i	0.532359	−	0.846519i	$-0.321306\pi$
$523$	−10.6782	−	18.4953i	−0.466927	−	0.808741i	−0.999286	+	0.0377773i	$0.987972\pi$
$524$		0			0
$525$	−2.54892	+	0.638596i	−0.111244	+	0.0278706i
$526$		0			0
$527$	−0.719321	−	1.24590i	−0.0313341	−	0.0542723i
$528$		0			0
$529$	4.78957	−	8.29579i	0.208242	−	0.360686i
$530$		0			0
$531$	−54.5418			−2.36691
$532$		0			0
$533$	−0.510693			−0.0221206
$534$		0			0
$535$	−19.9273	+	34.5151i	−0.861531	+	1.49222i
$536$		0			0
$537$	5.95136	+	10.3081i	0.256820	+	0.444825i
$538$		0			0
$539$	6.17315	−	3.30034i	0.265896	−	0.142156i
$540$		0			0
$541$	6.07687	+	10.5255i	0.261265	+	0.452524i	0.966578	−	0.256371i	$-0.0825270\pi$
$541$	6.07687	+	10.5255i	0.261265	+	0.452524i	−0.705313	+	0.708896i	$0.749194\pi$
$542$		0			0
$543$	−6.68477	+	11.5784i	−0.286871	+	0.496875i
$544$		0			0
$545$	−40.9379			−1.75359
$546$		0			0
$547$	43.6138			1.86479			0.932395	−	0.361441i	$-0.117715\pi$
$547$	43.6138			1.86479			0.932395	+	0.361441i	$0.117715\pi$
$548$		0			0
$549$	7.53552	−	13.0519i	0.321608	−	0.557041i
$550$		0			0
$551$	−0.311558	−	0.539635i	−0.0132728	−	0.0229892i
$552$		0			0
$553$	−23.7371	+	5.94699i	−1.00940	+	0.252892i
$554$		0			0
$555$	−26.7212	−	46.2825i	−1.13425	−	1.96458i
$556$		0			0
$557$	13.0915	−	22.6751i	0.554703	−	0.960773i	−0.443224	−	0.896411i	$-0.646165\pi$
$557$	13.0915	−	22.6751i	0.554703	−	0.960773i	0.997927	−	0.0643624i	$-0.0205014\pi$
$558$		0			0
$559$	0.248998			0.0105315
$560$		0			0
$561$	15.7142			0.663454
$562$		0			0
$563$	1.77054	−	3.06667i	0.0746195	−	0.129245i	−0.826301	−	0.563228i	$-0.809559\pi$
$563$	1.77054	−	3.06667i	0.0746195	−	0.129245i	0.900921	+	0.433984i	$0.142892\pi$
$564$		0			0
$565$	−13.5409	−	23.4536i	−0.569671	−	0.986700i
$566$		0			0
$567$	11.4167	+	11.7955i	0.479456	+	0.495363i
$568$		0			0
$569$	6.32225	+	10.9505i	0.265043	+	0.459067i	0.967575	−	0.252585i	$-0.0812807\pi$
$569$	6.32225	+	10.9505i	0.265043	+	0.459067i	−0.702532	+	0.711652i	$0.747947\pi$
$570$		0			0
$571$	−12.9461	+	22.4233i	−0.541777	+	0.938386i	0.457025	+	0.889454i	$0.348915\pi$
$571$	−12.9461	+	22.4233i	−0.541777	+	0.938386i	−0.998802	+	0.0489320i	$0.984418\pi$
$572$		0			0
$573$	40.7615			1.70284
$574$		0			0
$575$	−1.40083			−0.0584189
$576$		0			0
$577$	−6.48504	+	11.2324i	−0.269976	+	0.467611i	−0.968855	−	0.247628i	$-0.920349\pi$
$577$	−6.48504	+	11.2324i	−0.269976	+	0.467611i	0.698880	+	0.715239i	$0.253682\pi$
$578$		0			0
$579$	−33.2112	−	57.5235i	−1.38021	−	2.39060i
$580$		0			0
$581$	7.15668	−	25.0658i	0.296909	−	1.03990i
$582$		0			0
$583$	6.93462	+	12.0111i	0.287203	+	0.497449i
$584$		0			0
$585$	0.375114	−	0.649716i	0.0155090	−	0.0268625i
$586$		0			0
$587$	−34.3535			−1.41792			−0.708960	−	0.705249i	$-0.750835\pi$
$587$	−34.3535			−1.41792			−0.708960	+	0.705249i	$0.750835\pi$
$588$		0			0
$589$	0.323287			0.0133208
$590$		0			0
$591$	3.05274	−	5.28751i	0.125573	−	0.217499i
$592$		0			0
$593$	1.63526	+	2.83236i	0.0671521	+	0.116311i	0.897647	−	0.440716i	$-0.145275\pi$
$593$	1.63526	+	2.83236i	0.0671521	+	0.116311i	−0.830495	+	0.557027i	$0.811942\pi$
$594$		0			0
$595$	−9.44351	+	33.0753i	−0.387146	+	1.35595i
$596$		0			0
$597$	−23.5199	−	40.7376i	−0.962605	−	1.66728i
$598$		0			0
$599$	−9.28998	+	16.0907i	−0.379578	+	0.657449i	−0.991001	−	0.133856i	$-0.957264\pi$
$599$	−9.28998	+	16.0907i	−0.379578	+	0.657449i	0.611423	+	0.791304i	$0.290598\pi$
$600$		0			0
$601$	−35.5056			−1.44830			−0.724151	−	0.689641i	$-0.757768\pi$
$601$	−35.5056			−1.44830			−0.724151	+	0.689641i	$0.757768\pi$
$602$		0			0
$603$	33.7262			1.37344
$604$		0			0
$605$	−1.07443	+	1.86097i	−0.0436819	+	0.0756592i
$606$		0			0
$607$	−12.5379	−	21.7164i	−0.508900	−	0.881440i	−0.999947	−	0.0103071i	$-0.996719\pi$
$607$	−12.5379	−	21.7164i	−0.508900	−	0.881440i	0.491047	−	0.871133i	$-0.336614\pi$
$608$		0			0
$609$	−2.19044	−	2.26312i	−0.0887613	−	0.0917062i
$610$		0			0
$611$	0.0955294	+	0.165462i	0.00386470	+	0.00669386i
$612$		0			0
$613$	−12.6202	+	21.8588i	−0.509724	+	0.882868i	0.490213	+	0.871603i	$0.336919\pi$
$613$	−12.6202	+	21.8588i	−0.509724	+	0.882868i	−0.999937	+	0.0112648i	$0.996414\pi$
$614$		0			0
$615$	30.5849			1.23330
$616$		0			0
$617$	7.56829			0.304688			0.152344	−	0.988328i	$-0.451318\pi$
$617$	7.56829			0.304688			0.152344	+	0.988328i	$0.451318\pi$
$618$		0			0
$619$	−10.3026	+	17.8446i	−0.414096	+	0.717235i	−0.995333	−	0.0964988i	$-0.969236\pi$
$619$	−10.3026	+	17.8446i	−0.414096	+	0.717235i	0.581237	+	0.813734i	$0.302569\pi$
$620$		0			0
$621$	−3.55019	−	6.14911i	−0.142464	−	0.246755i
$622$		0			0
$623$	6.58936	−	1.65087i	0.263997	−	0.0661407i
$624$		0			0
$625$	11.4709	+	19.8682i	0.458838	+	0.794730i
$626$		0			0
$627$	−1.76562	+	3.05815i	−0.0705122	+	0.122131i
$628$		0			0
$629$	57.9308			2.30985
$630$		0			0
$631$	−6.47940			−0.257941			−0.128970	−	0.991648i	$-0.541167\pi$
$631$	−6.47940			−0.257941			−0.128970	+	0.991648i	$0.541167\pi$
$632$		0			0
$633$	28.1111	−	48.6898i	1.11731	−	1.93525i
$634$		0			0
$635$	2.69881	+	4.67448i	0.107099	+	0.185501i
$636$		0			0
$637$	0.554020	+	0.344442i	0.0219511	+	0.0136473i
$638$		0			0
$639$	−8.63210	−	14.9512i	−0.341480	−	0.591461i
$640$		0			0
$641$	13.1067	−	22.7015i	0.517684	−	0.896654i	−0.482105	−	0.876113i	$-0.660128\pi$
$641$	13.1067	−	22.7015i	0.517684	−	0.896654i	0.999789	−	0.0205410i	$-0.00653888\pi$
$642$		0			0
$643$	8.13092			0.320652			0.160326	−	0.987064i	$-0.448745\pi$
$643$	8.13092			0.320652			0.160326	+	0.987064i	$0.448745\pi$
$644$		0			0
$645$	−14.9123			−0.587170
$646$		0			0
$647$	16.2785	−	28.1952i	0.639973	−	1.10847i	−0.345465	−	0.938432i	$-0.612279\pi$
$647$	16.2785	−	28.1952i	0.639973	−	1.10847i	0.985438	−	0.170034i	$-0.0543879\pi$
$648$		0			0
$649$	7.27959	+	12.6086i	0.285749	+	0.494932i
$650$		0			0
$651$	1.58508	−	0.397118i	0.0621240	−	0.0155643i
$652$		0			0
$653$	1.52514	+	2.64162i	0.0596834	+	0.103375i	0.894323	−	0.447421i	$-0.147658\pi$
$653$	1.52514	+	2.64162i	0.0596834	+	0.103375i	−0.834640	+	0.550796i	$0.814324\pi$
$654$		0			0
$655$	−3.13305	+	5.42661i	−0.122419	+	0.212035i
$656$		0			0
$657$	30.0399			1.17197
$658$		0			0
$659$	−22.9174			−0.892737			−0.446368	−	0.894849i	$-0.647283\pi$
$659$	−22.9174			−0.892737			−0.446368	+	0.894849i	$0.647283\pi$
$660$		0			0
$661$	11.5054	−	19.9280i	0.447510	−	0.775110i	−0.550714	−	0.834694i	$-0.685644\pi$
$661$	11.5054	−	19.9280i	0.447510	−	0.775110i	0.998223	+	0.0595847i	$0.0189776\pi$
$662$		0			0
$663$	0.732241	+	1.26828i	0.0284379	+	0.0492559i
$664$		0			0
$665$	−5.37574	−	5.55409i	−0.208462	−	0.215378i
$666$		0			0
$667$	−0.839521	−	1.45409i	−0.0325064	−	0.0563027i
$668$		0			0
$669$	25.4624	−	44.1022i	0.984435	−	1.70509i
$670$		0			0
$671$	−4.02301			−0.155306
$672$		0			0
$673$	−28.0303			−1.08049			−0.540244	−	0.841509i	$-0.681668\pi$
$673$	−28.0303			−1.08049			−0.540244	+	0.841509i	$0.681668\pi$
$674$		0			0
$675$	0.370560	−	0.641829i	0.0142629	−	0.0247040i
$676$		0			0
$677$	9.75571	+	16.8974i	0.374943	+	0.649419i	0.990318	−	0.138814i	$-0.0443291\pi$
$677$	9.75571	+	16.8974i	0.374943	+	0.649419i	−0.615376	+	0.788234i	$0.710996\pi$
$678$		0			0
$679$	0.719229	−	2.51905i	0.0276015	−	0.0966724i
$680$		0			0
$681$	12.3863	+	21.4537i	0.474644	+	0.822108i
$682$		0			0
$683$	−9.29098	+	16.0924i	−0.355509	+	0.615760i	−0.987205	−	0.159456i	$-0.949026\pi$
$683$	−9.29098	+	16.0924i	−0.355509	+	0.615760i	0.631696	+	0.775217i	$0.282359\pi$
$684$		0			0
$685$	37.7071			1.44071
$686$		0			0
$687$	3.89234			0.148502
$688$		0			0
$689$	−0.646270	+	1.11937i	−0.0246209	+	0.0426447i
$690$		0			0
$691$	8.47364	+	14.6768i	0.322352	+	0.558331i	0.980973	−	0.194145i	$-0.0621931\pi$
$691$	8.47364	+	14.6768i	0.322352	+	0.558331i	−0.658621	+	0.752475i	$0.728860\pi$
$692$		0			0
$693$	−2.72116	+	9.53069i	−0.103368	+	0.362041i
$694$		0			0
$695$	23.0168	+	39.8662i	0.873076	+	1.51221i
$696$		0			0
$697$	−16.5768	+	28.7119i	−0.627892	+	1.08754i
$698$		0			0
$699$	30.2101			1.14265
$700$		0			0
$701$	−32.3538			−1.22198			−0.610992	−	0.791637i	$-0.709229\pi$
$701$	−32.3538			−1.22198			−0.610992	+	0.791637i	$0.709229\pi$
$702$		0			0
$703$	−6.50901	+	11.2739i	−0.245492	+	0.425205i
$704$		0			0
$705$	−5.72116	−	9.90934i	−0.215471	−	0.373207i
$706$		0			0
$707$	11.5065	+	11.8882i	0.432746	+	0.447103i
$708$		0			0
$709$	11.9809	+	20.7515i	0.449952	+	0.779339i	0.998382	−	0.0568567i	$-0.0181078\pi$
$709$	11.9809	+	20.7515i	0.449952	+	0.779339i	−0.548430	+	0.836196i	$0.684774\pi$
$710$		0			0
$711$	17.3245	−	30.0069i	0.649719	−	1.12535i
$712$		0			0
$713$	0.871125			0.0326239
$714$		0			0
$715$	−0.200263			−0.00748941
$716$		0			0
$717$	−4.48709	+	7.77187i	−0.167574	+	0.290246i
$718$		0			0
$719$	−11.7424	−	20.3384i	−0.437918	−	0.758496i	0.559611	−	0.828755i	$-0.310951\pi$
$719$	−11.7424	−	20.3384i	−0.437918	−	0.758496i	−0.997529	+	0.0702598i	$0.977617\pi$
$720$		0			0
$721$	5.03323	−	1.26100i	0.187447	−	0.0469622i
$722$		0			0
$723$	−10.4730	−	18.1398i	−0.389495	−	0.674625i
$724$		0			0
$725$	0.0876271	−	0.151775i	0.00325439	−	0.00563676i
$726$		0			0
$727$	−5.59409			−0.207473			−0.103737	−	0.994605i	$-0.533080\pi$
$727$	−5.59409			−0.207473			−0.103737	+	0.994605i	$0.533080\pi$
$728$		0			0
$729$	−38.3458			−1.42021
$730$		0			0
$731$	8.08235	−	13.9990i	0.298936	−	0.517773i
$732$		0			0
$733$	7.72216	+	13.3752i	0.285225	+	0.494023i	0.972664	−	0.232219i	$-0.0745985\pi$
$733$	7.72216	+	13.3752i	0.285225	+	0.494023i	−0.687439	+	0.726242i	$0.741265\pi$
$734$		0			0
$735$	−33.1797	−	20.6283i	−1.22385	−	0.760885i
$736$		0			0
$737$	−4.50137	−	7.79660i	−0.165810	−	0.287191i
$738$		0			0
$739$	10.3949	−	18.0045i	0.382383	−	0.662306i	−0.609020	−	0.793155i	$-0.708437\pi$
$739$	10.3949	−	18.0045i	0.382383	−	0.662306i	0.991402	+	0.130849i	$0.0417703\pi$
$740$		0			0
$741$	−0.329094			−0.0120896
$742$		0			0
$743$	−7.19748			−0.264050			−0.132025	−	0.991246i	$-0.542148\pi$
$743$	−7.19748			−0.264050			−0.132025	+	0.991246i	$0.542148\pi$
$744$		0			0
$745$	−17.7355	+	30.7188i	−0.649780	+	1.12545i
$746$		0			0
$747$	18.4549	+	31.9648i	0.675230	+	1.16953i
$748$		0			0
$749$	47.5991	−	11.9253i	1.73923	−	0.435740i
$750$		0			0
$751$	−14.0533	−	24.3411i	−0.512814	−	0.888220i	−0.999890	−	0.0148600i	$-0.995270\pi$
$751$	−14.0533	−	24.3411i	−0.512814	−	0.888220i	0.487076	−	0.873360i	$-0.338064\pi$
$752$		0			0
$753$	−16.5720	+	28.7035i	−0.603916	+	1.04601i
$754$		0			0
$755$	−27.1689			−0.988776
$756$		0			0
$757$	−17.0424			−0.619417			−0.309708	−	0.950832i	$-0.600231\pi$
$757$	−17.0424			−0.619417			−0.309708	+	0.950832i	$0.600231\pi$
$758$		0			0
$759$	−4.75762	+	8.24044i	−0.172691	+	0.299109i
$760$		0			0
$761$	3.22898	+	5.59277i	0.117051	+	0.202738i	0.918598	−	0.395194i	$-0.129323\pi$
$761$	3.22898	+	5.59277i	0.117051	+	0.202738i	−0.801547	+	0.597932i	$0.795989\pi$
$762$		0			0
$763$	35.0548	+	36.2178i	1.26907	+	1.31117i
$764$		0			0
$765$	−24.3520	−	42.1788i	−0.880447	−	1.52498i
$766$		0			0
$767$	−0.678420	+	1.17506i	−0.0244963	+	0.0424289i
$768$		0			0
$769$	25.0009			0.901555			0.450777	−	0.892636i	$-0.351147\pi$
$769$	25.0009			0.901555			0.450777	+	0.892636i	$0.351147\pi$
$770$		0			0
$771$	79.6957			2.87017
$772$		0			0
$773$	21.0413	−	36.4445i	0.756802	−	1.31082i	−0.187672	−	0.982232i	$-0.560094\pi$
$773$	21.0413	−	36.4445i	0.756802	−	1.31082i	0.944474	−	0.328587i	$-0.106572\pi$
$774$		0			0
$775$	0.0454629	+	0.0787441i	0.00163308	+	0.00282857i
$776$		0			0
$777$	−18.0651	+	63.2716i	−0.648080	+	2.26986i
$778$		0			0
$779$	−3.72509	−	6.45204i	−0.133465	−	0.231168i
$780$		0			0
$781$	−2.30422	+	3.99103i	−0.0824515	+	0.142810i
$782$		0			0
$783$	0.888307			0.0317455
$784$		0			0
$785$	30.6684			1.09460
$786$		0			0
$787$	7.69274	−	13.3242i	0.274217	−	0.474957i	−0.695721	−	0.718313i	$-0.744915\pi$
$787$	7.69274	−	13.3242i	0.274217	−	0.474957i	0.969937	+	0.243355i	$0.0782481\pi$
$788$		0			0
$789$	15.7689	+	27.3126i	0.561389	+	0.972355i
$790$		0			0
$791$	−9.15443	+	32.0628i	−0.325494	+	1.14002i
$792$		0			0
$793$	−0.187462	−	0.324693i	−0.00665696	−	0.0115302i
$794$		0			0
$795$	38.7045	−	67.0382i	1.37271	−	2.37760i
$796$		0			0
$797$	−31.8002			−1.12642			−0.563210	−	0.826313i	$-0.690434\pi$
$797$	−31.8002			−1.12642			−0.563210	+	0.826313i	$0.690434\pi$
$798$		0			0
$799$	12.4033			0.438798
$800$		0			0
$801$	−4.80923	+	8.32983i	−0.169926	+	0.294320i
$802$		0			0
$803$	−4.00937	−	6.94443i	−0.141488	−	0.245064i
$804$		0			0
$805$	−14.4854	−	14.9660i	−0.510543	−	0.527481i
$806$		0			0
$807$	−38.8846	−	67.3500i	−1.36880	−	2.37083i
$808$		0			0
$809$	0.243702	−	0.422104i	0.00856810	−	0.0148404i	−0.861710	−	0.507402i	$-0.830606\pi$
$809$	0.243702	−	0.422104i	0.00856810	−	0.0148404i	0.870278	+	0.492561i	$0.163939\pi$
$810$		0			0
$811$	34.5753			1.21410			0.607051	−	0.794663i	$-0.292352\pi$
$811$	34.5753			1.21410			0.607051	+	0.794663i	$0.292352\pi$
$812$		0			0
$813$	−74.9783			−2.62960
$814$		0			0
$815$	−5.11878	+	8.86599i	−0.179303	+	0.310562i
$816$		0			0
$817$	1.81624	+	3.14582i	0.0635422	+	0.110058i
$818$		0			0
$819$	−0.896012	+	0.224483i	−0.0313092	+	0.00784407i
$820$		0			0
$821$	−8.50567	−	14.7322i	−0.296850	−	0.514159i	0.678564	−	0.734542i	$-0.262603\pi$
$821$	−8.50567	−	14.7322i	−0.296850	−	0.514159i	−0.975413	+	0.220383i	$0.929269\pi$
$822$		0			0
$823$	6.49785	−	11.2546i	0.226501	−	0.392311i	−0.730268	−	0.683161i	$-0.760605\pi$
$823$	6.49785	−	11.2546i	0.226501	−	0.392311i	0.956769	+	0.290850i	$0.0939381\pi$
$824$		0			0
$825$	−0.993178			−0.0345780
$826$		0			0
$827$	54.1619			1.88339			0.941697	−	0.336462i	$-0.109230\pi$
$827$	54.1619			1.88339			0.941697	+	0.336462i	$0.109230\pi$
$828$		0			0
$829$	5.64495	−	9.77733i	0.196057	−	0.339581i	−0.751189	−	0.660087i	$-0.770520\pi$
$829$	5.64495	−	9.77733i	0.196057	−	0.339581i	0.947247	+	0.320506i	$0.103853\pi$
$830$		0			0
$831$	−13.7660	−	23.8435i	−0.477539	−	0.827122i
$832$		0			0
$833$	37.3482	−	19.9674i	1.29404	−	0.691829i
$834$		0			0
$835$	3.89422	+	6.74498i	0.134765	+	0.233420i
$836$		0			0
$837$	−0.230437	+	0.399129i	−0.00796507	+	0.0137959i
$838$		0			0
$839$	−20.7528			−0.716468			−0.358234	−	0.933632i	$-0.616621\pi$
$839$	−20.7528			−0.716468			−0.358234	+	0.933632i	$0.616621\pi$
$840$		0			0
$841$	−28.7899			−0.992757
$842$		0			0
$843$	−2.73630	+	4.73941i	−0.0942432	+	0.163234i
$844$		0			0
$845$	13.9583	+	24.1765i	0.480180	+	0.831696i
$846$		0			0
$847$	2.56643	−	0.642983i	0.0881836	−	0.0220931i
$848$		0			0
$849$	−16.8864	−	29.2481i	−0.579540	−	1.00379i
$850$		0			0
$851$	−17.5391	+	30.3786i	−0.601233	+	1.04137i
$852$		0			0
$853$	16.1019			0.551318			0.275659	−	0.961255i	$-0.411104\pi$
$853$	16.1019			0.551318			0.275659	+	0.961255i	$0.411104\pi$
$854$		0			0
$855$	10.9446			0.374297
$856$		0			0
$857$	−14.1111	+	24.4411i	−0.482025	+	0.834892i	−0.999787	−	0.0206326i	$-0.993432\pi$
$857$	−14.1111	+	24.4411i	−0.482025	+	0.834892i	0.517762	+	0.855525i	$0.326765\pi$
$858$		0			0
$859$	−10.6642	−	18.4710i	−0.363858	−	0.630221i	0.624734	−	0.780838i	$-0.285207\pi$
$859$	−10.6642	−	18.4710i	−0.363858	−	0.630221i	−0.988592	+	0.150617i	$0.951874\pi$
$860$		0			0
$861$	−26.1896	−	27.0585i	−0.892540	−	0.922153i
$862$		0			0
$863$	13.5696	+	23.5032i	0.461914	+	0.800059i	0.999056	−	0.0434328i	$-0.0138295\pi$
$863$	13.5696	+	23.5032i	0.461914	+	0.800059i	−0.537142	+	0.843492i	$0.680496\pi$
$864$		0			0
$865$	25.5923	−	44.3271i	0.870163	−	1.50717i
$866$		0			0
$867$	50.9177			1.72925
$868$		0			0
$869$	−9.24907			−0.313753
$870$		0			0
$871$	0.419504	−	0.726602i	0.0142144	−	0.0246200i
$872$		0			0
$873$	1.85467	+	3.21239i	0.0627712	+	0.108723i
$874$		0			0
$875$	8.40128	−	29.4249i	0.284015	−	0.994744i
$876$		0			0
$877$	−10.3564	−	17.9378i	−0.349710	−	0.605715i	0.636488	−	0.771287i	$-0.280387\pi$
$877$	−10.3564	−	17.9378i	−0.349710	−	0.605715i	−0.986198	+	0.165571i	$0.947053\pi$
$878$		0			0
$879$	−19.9144	+	34.4927i	−0.671694	+	1.16341i
$880$		0			0
$881$	−29.1875			−0.983352			−0.491676	−	0.870778i	$-0.663615\pi$
$881$	−29.1875			−0.983352			−0.491676	+	0.870778i	$0.663615\pi$
$882$		0			0
$883$	−38.7380			−1.30364			−0.651819	−	0.758374i	$-0.725994\pi$
$883$	−38.7380			−1.30364			−0.651819	+	0.758374i	$0.725994\pi$
$884$		0			0
$885$	40.6299	−	70.3731i	1.36576	−	2.36557i
$886$		0			0
$887$	−2.84612	−	4.92963i	−0.0955635	−	0.165521i	0.814280	−	0.580472i	$-0.197132\pi$
$887$	−2.84612	−	4.92963i	−0.0955635	−	0.165521i	−0.909844	+	0.414951i	$0.863799\pi$
$888$		0			0
$889$	1.82455	−	6.39036i	0.0611934	−	0.214326i
$890$		0			0
$891$	3.10227	+	5.37328i	0.103930	+	0.180012i
$892$		0			0
$893$	−1.39362	+	2.41381i	−0.0466356	+	0.0807752i
$894$		0			0
$895$	−9.84748			−0.329165
$896$		0			0
$897$	−0.886772			−0.0296084
$898$		0			0
$899$	−0.0544919	+	0.0943827i	−0.00181741	+	0.00314784i
$900$		0			0
$901$	41.9551	+	72.6684i	1.39773	+	2.42094i
$902$		0			0
$903$	12.7693	+	13.1929i	0.424934	+	0.439033i
$904$		0			0
$905$	−5.53051	−	9.57913i	−0.183840	−	0.318421i
$906$		0			0
$907$	−10.5823	+	18.3291i	−0.351379	+	0.608607i	−0.986491	−	0.163813i	$-0.947621\pi$
$907$	−10.5823	+	18.3291i	−0.351379	+	0.608607i	0.635112	+	0.772420i	$0.280954\pi$
$908$		0			0
$909$	−23.4263			−0.777002
$910$		0			0
$911$	11.3432			0.375817			0.187909	−	0.982187i	$-0.439829\pi$
$911$	11.3432			0.375817			0.187909	+	0.982187i	$0.439829\pi$
$912$		0			0
$913$	4.92629	−	8.53258i	0.163036	−	0.282387i
$914$		0			0
$915$	11.2269	+	19.4456i	0.371150	+	0.642850i
$916$		0			0
$917$	7.48374	−	1.87494i	0.247135	−	0.0619161i
$918$		0			0
$919$	−8.86408	−	15.3530i	−0.292399	−	0.506450i	0.681977	−	0.731373i	$-0.261120\pi$
$919$	−8.86408	−	15.3530i	−0.292399	−	0.506450i	−0.974377	+	0.224923i	$0.927787\pi$
$920$		0			0
$921$	−4.90544	+	8.49647i	−0.161640	+	0.279968i
$922$		0			0
$923$	−0.429483			−0.0141366
$924$		0			0
$925$	−3.66137			−0.120385
$926$		0			0
$927$	−3.67349	+	6.36267i	−0.120653	+	0.208978i
$928$		0			0
$929$	−9.07658	−	15.7211i	−0.297793	−	0.515793i	0.677838	−	0.735212i	$-0.262917\pi$
$929$	−9.07658	−	15.7211i	−0.297793	−	0.515793i	−0.975631	+	0.219419i	$0.929584\pi$
$930$		0			0
$931$	−0.310514	+	9.51184i	−0.0101767	+	0.311738i
$932$		0			0
$933$	−13.4437	−	23.2852i	−0.440127	−	0.762322i
$934$		0			0
$935$	−6.50042	+	11.2591i	−0.212587	+	0.368211i
$936$		0			0
$937$	33.0007			1.07809			0.539043	−	0.842279i	$-0.318786\pi$
$937$	33.0007			1.07809			0.539043	+	0.842279i	$0.318786\pi$
$938$		0			0
$939$	32.2788			1.05338
$940$		0			0
$941$	26.1238	−	45.2477i	0.851610	−	1.47503i	−0.0281445	−	0.999604i	$-0.508960\pi$
$941$	26.1238	−	45.2477i	0.851610	−	1.47503i	0.879755	−	0.475428i	$-0.157707\pi$
$942$		0			0
$943$	−10.0376	−	17.3856i	−0.326868	−	0.566152i
$944$		0			0
$945$	10.6888	−	2.67794i	0.347708	−	0.0871132i
$946$		0			0
$947$	13.8830	+	24.0460i	0.451136	+	0.781390i	0.998457	−	0.0555329i	$-0.0176858\pi$
$947$	13.8830	+	24.0460i	0.451136	+	0.781390i	−0.547321	+	0.836923i	$0.684352\pi$
$948$		0			0
$949$	0.373652	−	0.647185i	0.0121293	−	0.0210085i
$950$		0			0
$951$	18.6153			0.603644
$952$		0			0
$953$	21.2642			0.688816			0.344408	−	0.938820i	$-0.388080\pi$
$953$	21.2642			0.688816			0.344408	+	0.938820i	$0.388080\pi$
$954$		0			0
$955$	−16.8616	+	29.2052i	−0.545629	+	0.945057i
$956$		0			0
$957$	−0.595211	−	1.03094i	−0.0192405	−	0.0333254i
$958$		0			0
$959$	−32.2883	−	33.3595i	−1.04264	−	1.07724i
$960$		0			0
$961$	15.4717	+	26.7978i	0.499088	+	0.864446i
$962$		0			0
$963$	−34.7401	+	60.1716i	−1.11948	+	1.93900i
$964$		0			0
$965$	54.9533			1.76901
$966$		0			0
$967$	−26.0490			−0.837679			−0.418840	−	0.908060i	$-0.637563\pi$
$967$	−26.0490			−0.837679			−0.418840	+	0.908060i	$0.637563\pi$
$968$		0			0
$969$	−10.6822	+	18.5021i	−0.343162	+	0.594373i
$970$		0			0
$971$	10.7104	+	18.5509i	0.343713	+	0.595328i	0.985119	−	0.171873i	$-0.0549820\pi$
$971$	10.7104	+	18.5509i	0.343713	+	0.595328i	−0.641406	+	0.767201i	$0.721649\pi$
$972$		0			0
$973$	15.5606	−	54.5001i	0.498851	−	1.74719i
$974$		0			0
$975$	−0.0462795	−	0.0801584i	−0.00148213	−	0.00256712i
$976$		0			0
$977$	9.04668	−	15.6693i	0.289429	−	0.501306i	−0.684245	−	0.729253i	$-0.739868\pi$
$977$	9.04668	−	15.6693i	0.289429	−	0.501306i	0.973674	+	0.227947i	$0.0732013\pi$
$978$		0			0
$979$	2.56752			0.0820582
$980$		0			0
$981$	−71.3689			−2.27863
$982$		0			0
$983$	−16.7430	+	28.9997i	−0.534018	+	0.924947i	0.465192	+	0.885210i	$0.345985\pi$
$983$	−16.7430	+	28.9997i	−0.534018	+	0.924947i	−0.999210	+	0.0397369i	$0.987348\pi$
$984$		0			0
$985$	2.52563	+	4.37452i	0.0804732	+	0.139384i
$986$		0			0
$987$	−3.86783	+	13.5468i	−0.123114	+	0.431200i
$988$		0			0
$989$	4.89401	+	8.47668i	0.155621	+	0.269543i
$990$		0			0
$991$	−12.9498	+	22.4297i	−0.411363	+	0.712502i	−0.995039	−	0.0994847i	$-0.968281\pi$
$991$	−12.9498	+	22.4297i	−0.411363	+	0.712502i	0.583676	+	0.811987i	$0.301614\pi$
$992$		0			0
$993$	−6.12939			−0.194510
$994$		0			0
$995$	38.9174			1.23377
$996$		0			0
$997$	−9.79384	+	16.9634i	−0.310174	+	0.537237i	−0.978400	−	0.206721i	$-0.933721\pi$
$997$	−9.79384	+	16.9634i	−0.310174	+	0.537237i	0.668226	+	0.743958i	$0.267054\pi$
$998$		0			0
$999$	−9.27917	−	16.0720i	−0.293580	−	0.508495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.o.529.1		10
4.3	odd	2		616.2.q.f.529.5	yes	10
7.2	even	3	inner	1232.2.q.o.177.1		10
7.3	odd	6		8624.2.a.db.1.1		5
7.4	even	3		8624.2.a.dc.1.5		5
28.3	even	6		4312.2.a.bg.1.5		5
28.11	odd	6		4312.2.a.bf.1.1		5
28.23	odd	6		616.2.q.f.177.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.f.177.5	✓	10	28.23	odd	6
616.2.q.f.529.5	yes	10	4.3	odd	2
1232.2.q.o.177.1		10	7.2	even	3	inner
1232.2.q.o.529.1		10	1.1	even	1	trivial
4312.2.a.bf.1.1		5	28.11	odd	6
4312.2.a.bg.1.5		5	28.3	even	6
8624.2.a.db.1.1		5	7.3	odd	6
8624.2.a.dc.1.5		5	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29867 + 2.24937i) q^{3} +(-1.07443 - 1.86097i) q^{5} +(-0.726377 + 2.54409i) q^{7} +(-1.87311 - 3.24431i) q^{9} +O(q^{10})\)	\(q+(-1.29867 + 2.24937i) q^{3} +(-1.07443 - 1.86097i) q^{5} +(-0.726377 + 2.54409i) q^{7} +(-1.87311 - 3.24431i) q^{9} +(-0.500000 + 0.866025i) q^{11} -0.0931948 q^{13} +5.58135 q^{15} +(-3.02505 + 5.23954i) q^{17} +(-0.679779 - 1.17741i) q^{19} +(-4.77926 - 4.93783i) q^{21} +(-1.83172 - 3.17264i) q^{23} +(0.191191 - 0.331152i) q^{25} +1.93817 q^{27} +0.458323 q^{29} +(-0.118894 + 0.205931i) q^{31} +(-1.29867 - 2.24937i) q^{33} +(5.51491 - 1.38168i) q^{35} +(-4.78759 - 8.29235i) q^{37} +(0.121030 - 0.209629i) q^{39} +5.47985 q^{41} -2.67181 q^{43} +(-4.02505 + 6.97159i) q^{45} +(-1.02505 - 1.77544i) q^{47} +(-5.94475 - 3.69593i) q^{49} +(-7.85711 - 13.6089i) q^{51} +(6.93462 - 12.0111i) q^{53} +2.14886 q^{55} +3.53125 q^{57} +(7.27959 - 12.6086i) q^{59} +(2.01150 + 3.48403i) q^{61} +(9.61440 - 2.40875i) q^{63} +(0.100132 + 0.173433i) q^{65} +(-4.50137 + 7.79660i) q^{67} +9.51525 q^{69} +4.60844 q^{71} +(-4.00937 + 6.94443i) q^{73} +(0.496589 + 0.860117i) q^{75} +(-1.84006 - 1.90110i) q^{77} +(4.62453 + 8.00993i) q^{79} +(3.10227 - 5.37328i) q^{81} -9.85257 q^{83} +13.0008 q^{85} +(-0.595211 + 1.03094i) q^{87} +(-1.28376 - 2.22354i) q^{89} +(0.0676946 - 0.237096i) q^{91} +(-0.308809 - 0.534873i) q^{93} +(-1.46075 + 2.53010i) q^{95} -0.990160 q^{97} +3.74621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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