LMFDB - Embedded newform 456.2.u.d.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(11,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("456.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.u (of order $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	456.11
Dual form			456.2.u.d.83.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.954387 + 1.04362i) q^{2} +(-1.35307 - 1.08130i) q^{3} +(-0.178291 - 1.99204i) q^{4} +(-1.99273 + 3.45151i) q^{5} +(2.41982 - 0.380112i) q^{6} +0.938475i q^{7} +(2.24909 + 1.71511i) q^{8} +(0.661584 + 2.92614i) q^{9} +O(q^{10})$	\(q+(-0.954387 + 1.04362i) q^{2} +(-1.35307 - 1.08130i) q^{3} +(-0.178291 - 1.99204i) q^{4} +(-1.99273 + 3.45151i) q^{5} +(2.41982 - 0.380112i) q^{6} +0.938475i q^{7} +(2.24909 + 1.71511i) q^{8} +(0.661584 + 2.92614i) q^{9} +(-1.70023 - 5.37373i) q^{10} -4.53299i q^{11} +(-1.91275 + 2.88815i) q^{12} +(-1.90481 + 1.09974i) q^{13} +(-0.979413 - 0.895668i) q^{14} +(6.42841 - 2.51539i) q^{15} +(-3.93642 + 0.710325i) q^{16} +(3.59371 + 2.07483i) q^{17} +(-3.68519 - 2.10223i) q^{18} +(-3.77512 + 2.17911i) q^{19} +(7.23082 + 3.35422i) q^{20} +(1.01477 - 1.26982i) q^{21} +(4.73072 + 4.32622i) q^{22} +(-2.04022 - 3.53376i) q^{23} +(-1.18863 - 4.75260i) q^{24} +(-5.44194 - 9.42572i) q^{25} +(0.670210 - 3.03747i) q^{26} +(2.26887 - 4.67464i) q^{27} +(1.86948 - 0.167322i) q^{28} +(-2.79078 - 4.83378i) q^{29} +(-3.51008 + 9.10948i) q^{30} -3.09951i q^{31} +(3.01556 - 4.78606i) q^{32} +(-4.90152 + 6.13344i) q^{33} +(-5.59512 + 1.77028i) q^{34} +(-3.23916 - 1.87013i) q^{35} +(5.71103 - 1.83960i) q^{36} -9.54582i q^{37} +(1.32876 - 6.01950i) q^{38} +(3.76648 + 0.571642i) q^{39} +(-10.4015 + 4.34502i) q^{40} +(-9.86165 - 5.69363i) q^{41} +(0.356726 + 2.27094i) q^{42} +(2.21581 - 3.83790i) q^{43} +(-9.02988 + 0.808191i) q^{44} +(-11.4180 - 3.54755i) q^{45} +(5.63506 + 1.24336i) q^{46} +(1.34559 + 2.33064i) q^{47} +(6.09432 + 3.29534i) q^{48} +6.11926 q^{49} +(15.0306 + 3.31646i) q^{50} +(-2.61902 - 6.69325i) q^{51} +(2.53033 + 3.59837i) q^{52} +(3.96153 + 6.86157i) q^{53} +(2.71318 + 6.82925i) q^{54} +(15.6456 + 9.03302i) q^{55} +(-1.60958 + 2.11072i) q^{56} +(7.46425 + 1.13355i) q^{57} +(7.70812 + 1.70077i) q^{58} +(0.471250 + 0.272077i) q^{59} +(-6.15688 - 12.3572i) q^{60} +(-11.1864 + 6.45845i) q^{61} +(3.23472 + 2.95814i) q^{62} +(-2.74611 + 0.620880i) q^{63} +(2.11682 + 7.71486i) q^{64} -8.76594i q^{65} +(-1.72304 - 10.9690i) q^{66} +(-0.848171 - 1.46907i) q^{67} +(3.49241 - 7.52872i) q^{68} +(-1.06050 + 6.98750i) q^{69} +(5.04311 - 1.59563i) q^{70} +(-0.0740547 + 0.128266i) q^{71} +(-3.53068 + 7.71585i) q^{72} +(-1.99938 + 3.46302i) q^{73} +(9.96222 + 9.11041i) q^{74} +(-2.82871 + 18.6380i) q^{75} +(5.01393 + 7.13165i) q^{76} +4.25410 q^{77} +(-4.19126 + 3.38521i) q^{78} +(-6.47368 - 3.73758i) q^{79} +(5.39254 - 15.0021i) q^{80} +(-8.12461 + 3.87178i) q^{81} +(15.3538 - 4.85791i) q^{82} -1.80247i q^{83} +(-2.71045 - 1.79507i) q^{84} +(-14.3226 + 8.26914i) q^{85} +(1.89057 + 5.97531i) q^{86} +(-1.45064 + 9.55809i) q^{87} +(7.77455 - 10.1951i) q^{88} +(7.05692 - 4.07431i) q^{89} +(14.5995 - 8.53030i) q^{90} +(-1.03208 - 1.78761i) q^{91} +(-6.67562 + 4.69422i) q^{92} +(-3.35150 + 4.19385i) q^{93} +(-3.71652 - 0.820039i) q^{94} +(0.00157758 - 17.3722i) q^{95} +(-9.25542 + 3.21514i) q^{96} +(4.31610 - 7.47570i) q^{97} +(-5.84015 + 6.38620i) q^{98} +(13.2642 - 2.99895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.954387	+	1.04362i	−0.674853	+	0.737952i
$2$	−0.954387	+	1.04362i	−0.674853	+	0.737952i
$3$	−1.35307	−	1.08130i	−0.781194	−	0.624288i
$3$	−1.35307	−	1.08130i	−0.781194	−	0.624288i
$4$	−0.178291	−	1.99204i	−0.0891455	−	0.996019i
$5$	−1.99273	+	3.45151i	−0.891176	+	1.54356i	−0.0527086	+	0.998610i	$0.516785\pi$
$5$	−1.99273	+	3.45151i	−0.891176	+	1.54356i	−0.838467	+	0.544952i	$0.816548\pi$
$6$	2.41982	−	0.380112i	0.987886	−	0.155180i
$7$			0.938475i			0.354710i	0.984147	+	0.177355i	$0.0567541\pi$
$7$			0.938475i			0.354710i	−0.984147	+	0.177355i	$0.943246\pi$
$8$	2.24909	+	1.71511i	0.795174	+	0.606382i
$9$	0.661584	+	2.92614i	0.220528	+	0.975381i
$10$	−1.70023	−	5.37373i	−0.537661	−	1.69932i
$11$		−	4.53299i		−	1.36675i	−0.730069	−	0.683374i	$-0.760512\pi$
$11$		−	4.53299i		−	1.36675i	0.730069	−	0.683374i	$-0.239488\pi$
$12$	−1.91275	+	2.88815i	−0.552163	+	0.833736i
$13$	−1.90481	+	1.09974i	−0.528298	+	0.305013i	−0.740323	−	0.672251i	$-0.765328\pi$
$13$	−1.90481	+	1.09974i	−0.528298	+	0.305013i	0.212025	+	0.977264i	$0.431994\pi$
$14$	−0.979413	−	0.895668i	−0.261759	−	0.239377i
$15$	6.42841	−	2.51539i	1.65981	−	0.649470i
$16$	−3.93642	+	0.710325i	−0.984106	+	0.177581i
$17$	3.59371	+	2.07483i	0.871602	+	0.503219i	0.867880	−	0.496774i	$-0.165482\pi$
$17$	3.59371	+	2.07483i	0.871602	+	0.503219i	0.00372152	+	0.999993i	$0.498815\pi$
$18$	−3.68519	−	2.10223i	−0.868608	−	0.495500i
$19$	−3.77512	+	2.17911i	−0.866071	+	0.499921i
$19$	−3.77512	+	2.17911i	−0.866071	+	0.499921i
$20$	7.23082	+	3.35422i	1.61686	+	0.750026i
$21$	1.01477	−	1.26982i	0.221441	−	0.277097i
$22$	4.73072	+	4.32622i	1.00859	+	0.922354i
$23$	−2.04022	−	3.53376i	−0.425414	−	0.736839i	0.571045	−	0.820919i	$-0.306538\pi$
$23$	−2.04022	−	3.53376i	−0.425414	−	0.736839i	−0.996459	+	0.0840797i	$0.973205\pi$
$24$	−1.18863	−	4.75260i	−0.242628	−	0.970119i
$25$	−5.44194	−	9.42572i	−1.08839	−	1.88514i
$26$	0.670210	−	3.03747i	0.131439	−	0.595698i
$27$	2.26887	−	4.67464i	0.436644	−	0.899635i
$28$	1.86948	−	0.167322i	0.353298	−	0.0316208i
$29$	−2.79078	−	4.83378i	−0.518235	−	0.897610i	−0.999776	−	0.0211857i	$-0.993256\pi$
$29$	−2.79078	−	4.83378i	−0.518235	−	0.897610i	0.481540	−	0.876424i	$-0.340077\pi$
$30$	−3.51008	+	9.10948i	−0.640850	+	1.66316i
$31$		−	3.09951i		−	0.556689i	−0.960481	−	0.278345i	$-0.910214\pi$
$31$		−	3.09951i		−	0.556689i	0.960481	−	0.278345i	$-0.0897857\pi$
$32$	3.01556	−	4.78606i	0.533081	−	0.846064i
$33$	−4.90152	+	6.13344i	−0.853244	+	1.06769i
$34$	−5.59512	+	1.77028i	−0.959555	+	0.303601i
$35$	−3.23916	−	1.87013i	−0.547517	−	0.316109i
$36$	5.71103	−	1.83960i	0.951838	−	0.306601i
$37$		−	9.54582i		−	1.56932i	−0.619924	−	0.784662i	$-0.712837\pi$
$37$		−	9.54582i		−	1.56932i	0.619924	−	0.784662i	$-0.287163\pi$
$38$	1.32876	−	6.01950i	0.215553	−	0.976492i
$39$	3.76648	+	0.571642i	0.603120	+	0.0915360i
$40$	−10.4015	+	4.34502i	−1.64463	+	0.687007i
$41$	−9.86165	−	5.69363i	−1.54013	−	0.889195i	−0.998830	−	0.0483668i	$-0.984598\pi$
$41$	−9.86165	−	5.69363i	−1.54013	−	0.889195i	−0.541302	−	0.840828i	$-0.682068\pi$
$42$	0.356726	+	2.27094i	0.0550440	+	0.350413i
$43$	2.21581	−	3.83790i	0.337908	−	0.585274i	−0.646131	−	0.763227i	$-0.723614\pi$
$43$	2.21581	−	3.83790i	0.337908	−	0.585274i	0.984039	+	0.177952i	$0.0569473\pi$
$44$	−9.02988	+	0.808191i	−1.36131	+	0.121839i
$45$	−11.4180	−	3.54755i	−1.70209	−	0.528837i
$46$	5.63506	+	1.24336i	0.830844	+	0.183323i
$47$	1.34559	+	2.33064i	0.196275	+	0.339958i	0.947318	−	0.320295i	$-0.103782\pi$
$47$	1.34559	+	2.33064i	0.196275	+	0.339958i	−0.751043	+	0.660254i	$0.770449\pi$
$48$	6.09432	+	3.29534i	0.879640	+	0.475641i
$49$	6.11926			0.874181
$50$	15.0306	+	3.31646i	2.12565	+	0.469018i
$51$	−2.61902	−	6.69325i	−0.366736	−	0.937243i
$52$	2.53033	+	3.59837i	0.350894	+	0.499004i
$53$	3.96153	+	6.86157i	0.544158	+	0.942509i	0.998659	+	0.0517631i	$0.0164841\pi$
$53$	3.96153	+	6.86157i	0.544158	+	0.942509i	−0.454502	+	0.890746i	$0.650183\pi$
$54$	2.71318	+	6.82925i	0.369216	+	0.929343i
$55$	15.6456	+	9.03302i	2.10966	+	1.21801i
$56$	−1.60958	+	2.11072i	−0.215090	+	0.282056i
$57$	7.46425	+	1.13355i	0.988664	+	0.150142i
$58$	7.70812	+	1.70077i	1.01213	+	0.223322i
$59$	0.471250	+	0.272077i	0.0613516	+	0.0354214i	0.530362	−	0.847771i	$-0.322056\pi$
$59$	0.471250	+	0.272077i	0.0613516	+	0.0354214i	−0.469010	+	0.883193i	$0.655389\pi$
$60$	−6.15688	−	12.3572i	−0.794849	−	1.59530i
$61$	−11.1864	+	6.45845i	−1.43227	+	0.826919i	−0.997293	−	0.0735240i	$-0.976575\pi$
$61$	−11.1864	+	6.45845i	−1.43227	+	0.826919i	−0.434973	+	0.900443i	$0.643242\pi$
$62$	3.23472	+	2.95814i	0.410810	+	0.375684i
$63$	−2.74611	+	0.620880i	−0.345977	+	0.0782235i
$64$	2.11682	+	7.71486i	0.264603	+	0.964357i
$65$		−	8.76594i		−	1.08728i
$66$	−1.72304	−	10.9690i	−0.212092	−	1.35019i
$67$	−0.848171	−	1.46907i	−0.103621	−	0.179476i	0.809553	−	0.587046i	$-0.199709\pi$
$67$	−0.848171	−	1.46907i	−0.103621	−	0.179476i	−0.913174	+	0.407570i	$0.866376\pi$
$68$	3.49241	−	7.52872i	0.423517	−	0.912991i
$69$	−1.06050	+	6.98750i	−0.127669	+	0.841196i
$70$	5.04311	−	1.59563i	0.602767	−	0.190714i
$71$	−0.0740547	+	0.128266i	−0.00878867	+	0.0152224i	−0.870386	−	0.492369i	$-0.836131\pi$
$71$	−0.0740547	+	0.128266i	−0.00878867	+	0.0152224i	0.861598	+	0.507592i	$0.169464\pi$
$72$	−3.53068	+	7.71585i	−0.416095	+	0.909321i
$73$	−1.99938	+	3.46302i	−0.234009	+	0.405316i	−0.958984	−	0.283459i	$-0.908518\pi$
$73$	−1.99938	+	3.46302i	−0.234009	+	0.405316i	0.724975	+	0.688775i	$0.241851\pi$
$74$	9.96222	+	9.11041i	1.15808	+	1.05906i
$75$	−2.82871	+	18.6380i	−0.326631	+	2.15213i
$76$	5.01393	+	7.13165i	0.575137	+	0.818057i
$77$	4.25410			0.484799
$78$	−4.19126	+	3.38521i	−0.474567	+	0.383300i
$79$	−6.47368	−	3.73758i	−0.728346	−	0.420511i	0.0894708	−	0.995989i	$-0.471482\pi$
$79$	−6.47368	−	3.73758i	−0.728346	−	0.420511i	−0.817817	+	0.575479i	$0.804816\pi$
$80$	5.39254	−	15.0021i	0.602904	−	1.67728i
$81$	−8.12461	+	3.87178i	−0.902735	+	0.430198i
$82$	15.3538	−	4.85791i	1.69555	−	0.536466i
$83$		−	1.80247i		−	0.197847i	−0.995095	−	0.0989236i	$-0.968460\pi$
$83$		−	1.80247i		−	0.197847i	0.995095	−	0.0989236i	$-0.0315399\pi$
$84$	−2.71045	−	1.79507i	−0.295735	−	0.195858i
$85$	−14.3226	+	8.26914i	−1.55350	+	0.896914i
$86$	1.89057	+	5.97531i	0.203866	+	0.644334i
$87$	−1.45064	+	9.55809i	−0.155525	+	1.02474i
$88$	7.77455	−	10.1951i	0.828770	−	1.08680i
$89$	7.05692	−	4.07431i	0.748032	−	0.431876i	−0.0769506	−	0.997035i	$-0.524518\pi$
$89$	7.05692	−	4.07431i	0.748032	−	0.431876i	0.824982	+	0.565159i	$0.191185\pi$
$90$	14.5995	−	8.53030i	1.53892	−	0.899172i
$91$	−1.03208	−	1.78761i	−0.108191	−	0.187393i
$92$	−6.67562	+	4.69422i	−0.695982	+	0.489407i
$93$	−3.35150	+	4.19385i	−0.347535	+	0.434882i
$94$	−3.71652	−	0.820039i	−0.383330	−	0.0845806i
$95$	0.00157758	−	17.3722i	0.000161856	−	1.78235i
$96$	−9.25542	+	3.21514i	−0.944628	+	0.328144i
$97$	4.31610	−	7.47570i	0.438233	−	0.759042i	−0.559320	−	0.828952i	$-0.688938\pi$
$97$	4.31610	−	7.47570i	0.438233	−	0.759042i	0.997553	+	0.0699095i	$0.0222710\pi$
$98$	−5.84015	+	6.38620i	−0.589944	+	0.645103i
$99$	13.2642	−	2.99895i	1.33310	−	0.301406i
$100$	−17.8061	+	12.5211i	−1.78061	+	1.25211i
$101$	3.27428	+	5.67121i	0.325803	+	0.564307i	0.981674	−	0.190566i	$-0.0610322\pi$
$101$	3.27428	+	5.67121i	0.325803	+	0.564307i	−0.655872	+	0.754872i	$0.727699\pi$
$102$	9.48478	+	3.65469i	0.939133	+	0.361868i
$103$			4.71495i			0.464578i	0.972647	+	0.232289i	$0.0746216\pi$
$103$			4.71495i			0.464578i	−0.972647	+	0.232289i	$0.925378\pi$
$104$	−6.17025	−	0.793528i	−0.605043	−	0.0778119i
$105$	2.36063	+	6.03290i	0.230374	+	0.588751i
$106$	−10.9417	−	2.41426i	−1.06275	−	0.234493i
$107$			7.86316i			0.760160i	0.924954	+	0.380080i	$0.124104\pi$
$107$			7.86316i			0.760160i	−0.924954	+	0.380080i	$0.875896\pi$
$108$	−9.71657	−	3.68622i	−0.934978	−	0.354707i
$109$	−6.90042	−	3.98396i	−0.660940	−	0.381594i	0.131695	−	0.991290i	$-0.457958\pi$
$109$	−6.90042	−	3.98396i	−0.660940	−	0.381594i	−0.792635	+	0.609696i	$0.791291\pi$
$110$	−24.3591	+	7.70714i	−2.32254	+	0.734847i
$111$	−10.3219	+	12.9161i	−0.979710	+	1.22595i
$112$	−0.666622	−	3.69424i	−0.0629899	−	0.349073i
$113$		−	3.82367i		−	0.359701i	−0.983694	−	0.179850i	$-0.942439\pi$
$113$		−	3.82367i		−	0.359701i	0.983694	−	0.179850i	$-0.0575614\pi$
$114$	−8.30678	+	6.70801i	−0.778001	+	0.628262i
$115$	16.2624			1.51648
$116$	−9.13149	+	6.42116i	−0.847837	+	0.596190i
$117$	−4.47819	−	4.84616i	−0.414008	−	0.448028i
$118$	−0.733700	+	0.232141i	−0.0675426	+	0.0213703i
$119$	−1.94717	+	3.37260i	−0.178497	+	0.309166i
$120$	18.7722	+	5.36807i	1.71366	+	0.490036i
$121$	−9.54797			−0.867997
$122$	3.93594	−	17.8382i	0.356343	−	1.61499i
$123$	7.18697	+	18.3673i	0.648027	+	1.65612i
$124$	−6.17435	+	0.552616i	−0.554473	+	0.0496264i
$125$	23.4500			2.09743
$126$	1.97289	−	3.45846i	0.175759	−	0.308104i
$127$	10.2113	−	5.89552i	0.906109	−	0.523143i	0.0269321	−	0.999637i	$-0.491426\pi$
$127$	10.2113	−	5.89552i	0.906109	−	0.523143i	0.879177	+	0.476495i	$0.158093\pi$
$128$	−10.0717	−	5.15380i	−0.890217	−	0.455536i
$129$	−7.14806	+	2.79698i	−0.629352	+	0.246261i
$130$	9.14833	+	8.36610i	0.802361	+	0.733756i
$131$	−11.2345	−	6.48625i	−0.981564	−	0.566706i	−0.0788221	−	0.996889i	$-0.525116\pi$
$131$	−11.2345	−	6.48625i	−0.981564	−	0.566706i	−0.902742	+	0.430182i	$0.858449\pi$
$132$	13.0919	+	8.67046i	1.13951	+	0.754667i
$133$	−2.04504	−	3.54285i	−0.177327	−	0.307204i
$134$	2.34264	+	0.516897i	0.202373	+	0.0446531i
$135$	11.6133	+	17.1463i	0.999515	+	1.47572i
$136$	4.52402	+	10.8301i	0.387932	+	0.928670i
$137$	−12.8191	+	7.40108i	−1.09521	+	0.632317i	−0.934958	−	0.354759i	$-0.884563\pi$
$137$	−12.8191	+	7.40108i	−1.09521	+	0.632317i	−0.160248	+	0.987077i	$0.551229\pi$
$138$	−6.28017	−	7.77553i	−0.534604	−	0.661897i
$139$	−0.164363	−	0.284686i	−0.0139411	−	0.0241467i	0.858971	−	0.512025i	$-0.171104\pi$
$139$	−0.164363	−	0.284686i	−0.0139411	−	0.0241467i	−0.872912	+	0.487878i	$0.837771\pi$
$140$	−3.14785	+	6.78595i	−0.266042	+	0.573517i
$141$	0.699436	−	4.60850i	0.0589032	−	0.388106i
$142$	−0.0631848	−	0.199701i	−0.00530235	−	0.0167585i
$143$	4.98511	+	8.63446i	0.416876	+	0.722050i
$144$	−4.68279	−	11.0486i	−0.390232	−	0.920716i
$145$	22.2451			1.84735
$146$	−1.70590	−	5.39165i	−0.141182	−	0.446216i
$147$	−8.27978	−	6.61676i	−0.682905	−	0.545741i
$148$	−19.0156	+	1.70193i	−1.56307	+	0.139898i
$149$	−1.98709	+	3.44173i	−0.162788	+	0.281958i	−0.935868	−	0.352352i	$-0.885382\pi$
$149$	−1.98709	+	3.44173i	−0.162788	+	0.281958i	0.773079	+	0.634309i	$0.218715\pi$
$150$	−16.7513	−	20.7400i	−1.36774	−	1.69341i
$151$			0.780445i			0.0635117i	0.999496	+	0.0317559i	$0.0101099\pi$
$151$			0.780445i			0.0635117i	−0.999496	+	0.0317559i	$0.989890\pi$
$152$	−12.2280	−	1.57371i	−0.991820	−	0.127645i
$153$	−3.69370	+	11.8884i	−0.298618	+	0.961117i
$154$	−4.06005	+	4.43966i	−0.327168	+	0.357758i
$155$	10.6980	+	6.17650i	0.859284	+	0.496108i
$156$	0.467203	−	7.60489i	0.0374062	−	0.608878i
$157$	−1.14410	−	0.660548i	−0.0913093	−	0.0527175i	0.453650	−	0.891180i	$-0.350122\pi$
$157$	−1.14410	−	0.660548i	−0.0913093	−	0.0527175i	−0.544959	+	0.838462i	$0.683455\pi$
$158$	10.0790	−	3.18897i	0.801843	−	0.253701i
$159$	2.05919	−	13.5678i	0.163305	−	1.07599i
$160$	10.5099	+	19.9456i	0.830883	+	1.57684i
$161$	3.31634	−	1.91469i	0.261364	−	0.150899i
$162$	3.71335	−	12.1742i	0.291749	−	0.956495i
$163$	−17.0561			−1.33594			−0.667968	−	0.744190i	$-0.732836\pi$
$163$	−17.0561			−1.33594			−0.667968	+	0.744190i	$0.732836\pi$
$164$	−9.58367	+	20.6599i	−0.748359	+	1.61327i
$165$	−11.4022	−	29.1399i	−0.887662	−	2.26854i
$166$	1.88110	+	1.72026i	0.146002	+	0.133518i
$167$	−11.6553	−	20.1876i	−0.901916	−	1.56217i	−0.825004	−	0.565127i	$-0.808827\pi$
$167$	−11.6553	−	20.1876i	−0.901916	−	1.56217i	−0.0769128	−	0.997038i	$-0.524506\pi$
$168$	4.46019	−	1.11550i	0.344111	−	0.0860626i
$169$	−4.08114	+	7.06874i	−0.313934	+	0.543750i
$170$	5.03942	−	22.8393i	0.386506	−	1.75169i
$171$	−8.87393	−	9.60486i	−0.678606	−	0.734502i
$172$	−8.04030	−	3.72972i	−0.613067	−	0.284388i
$173$	5.01142	−	8.68004i	0.381011	−	0.659931i	−0.610196	−	0.792251i	$-0.708909\pi$
$173$	5.01142	−	8.68004i	0.381011	−	0.659931i	0.991207	+	0.132320i	$0.0422425\pi$
$174$	−8.59056	−	10.6360i	−0.651249	−	0.806316i
$175$	8.84581	−	5.10713i	0.668680	−	0.386063i
$176$	3.21989	+	17.8438i	0.242709	+	1.34502i
$177$	−0.343438	−	0.877701i	−0.0258143	−	0.0659720i
$178$	−2.48299	+	11.2532i	−0.186108	+	0.843465i
$179$			6.60415i			0.493617i	0.969064	+	0.246809i	$0.0793819\pi$
$179$			6.60415i			0.493617i	−0.969064	+	0.246809i	$0.920618\pi$
$180$	−5.03112	+	23.3775i	−0.374998	+	1.74246i
$181$	3.48037	−	2.00939i	0.258694	−	0.149357i	−0.365045	−	0.930990i	$-0.618946\pi$
$181$	3.48037	−	2.00939i	0.258694	−	0.149357i	0.623738	+	0.781633i	$0.285613\pi$
$182$	2.85059	+	0.628975i	0.211300	+	0.0466227i
$183$	22.1194	+	3.35708i	1.63511	+	0.248163i
$184$	1.47214	−	11.4469i	0.108527	−	0.843879i
$185$	32.9475	+	19.0222i	2.42235	+	1.39854i
$186$	−1.17816	−	7.50026i	−0.0863872	−	0.549946i
$187$	9.40516	−	16.2902i	0.687774	−	1.19126i
$188$	4.40281	−	3.09601i	0.321108	−	0.225799i
$189$	4.38703	+	2.12927i	0.319110	+	0.154882i
$190$	18.1285	+	16.5815i	1.31518	+	1.20295i
$191$	−16.7504			−1.21202			−0.606008	−	0.795459i	$-0.707230\pi$
$191$	−16.7504			−1.21202			−0.606008	+	0.795459i	$0.707230\pi$
$192$	5.47787	−	12.7276i	0.395331	−	0.918539i
$193$	−2.55238	+	4.42086i	−0.183725	+	0.318220i	−0.943146	−	0.332379i	$-0.892149\pi$
$193$	−2.55238	+	4.42086i	−0.183725	+	0.318220i	0.759421	+	0.650599i	$0.225482\pi$
$194$	3.68257	+	11.6391i	0.264393	+	0.835637i
$195$	−9.47861	+	11.8609i	−0.678777	+	0.849378i
$196$	−1.09101	−	12.1898i	−0.0779293	−	0.870700i
$197$	19.4768			1.38766			0.693831	−	0.720138i	$-0.255921\pi$
$197$	19.4768			1.38766			0.693831	+	0.720138i	$0.255921\pi$
$198$	−9.52937	+	16.7049i	−0.677223	+	1.18717i
$199$	−15.6664	+	9.04499i	−1.11056	+	0.641182i	−0.938975	−	0.343987i	$-0.888223\pi$
$199$	−15.6664	+	9.04499i	−1.11056	+	0.641182i	−0.171586	+	0.985169i	$0.554889\pi$
$200$	3.92669	−	30.5328i	0.277659	−	2.15900i
$201$	−0.440877	+	2.90488i	−0.0310971	+	0.204895i
$202$	−9.04353	−	1.99543i	−0.636300	−	0.140398i
$203$	4.53638	−	2.61908i	0.318391	−	0.183823i
$204$	−12.8663	+	6.41053i	−0.900818	+	0.448827i
$205$	39.3032	−	22.6917i	2.74506	−	1.58486i
$206$	−4.92063	−	4.49989i	−0.342836	−	0.313522i
$207$	8.99050	−	8.30784i	0.624883	−	0.577435i
$208$	6.71695	−	5.68208i	0.465737	−	0.393981i
$209$	9.87786	+	17.1125i	0.683266	+	1.18370i
$210$	−8.54902	−	3.29412i	−0.589939	−	0.227316i
$211$	9.72918	−	16.8514i	0.669785	−	1.16010i	−0.308179	−	0.951328i	$-0.599720\pi$
$211$	9.72918	−	16.8514i	0.669785	−	1.16010i	0.977964	−	0.208773i	$-0.0669469\pi$
$212$	12.9622	−	9.11487i	0.890247	−	0.626012i
$213$	0.238895	−	0.0934779i	0.0163688	−	0.00640500i
$214$	−8.20616	−	7.50450i	−0.560962	−	0.512997i
$215$	8.83103	+	15.2958i	0.602271	+	1.04316i
$216$	13.1204	−	6.62234i	0.892729	−	0.450593i
$217$	2.90882			0.197463
$218$	10.7434	−	3.39919i	0.727636	−	0.230222i
$219$	6.44985	−	2.52378i	0.435841	−	0.170541i
$220$	15.2046	−	32.7772i	1.02510	−	2.20984i
$221$	−9.12709			−0.613954
$222$	−3.62848	−	23.0991i	−0.243528	−	1.55031i
$223$	−13.8338	−	7.98698i	−0.926383	−	0.534848i	−0.0407173	−	0.999171i	$-0.512964\pi$
$223$	−13.8338	−	7.98698i	−0.926383	−	0.534848i	−0.885666	+	0.464323i	$0.846298\pi$
$224$	4.49160	+	2.83003i	0.300108	+	0.189089i
$225$	23.9807	−	22.1598i	1.59871	−	1.47732i
$226$	3.99047	+	3.64926i	0.265442	+	0.242745i
$227$			17.0377i			1.13083i	0.824806	+	0.565416i	$0.191285\pi$
$227$			17.0377i			1.13083i	−0.824806	+	0.565416i	$0.808715\pi$
$228$	0.927265	−	15.0712i	0.0614096	−	0.998113i
$229$		−	7.01176i		−	0.463350i	−0.972793	−	0.231675i	$-0.925579\pi$
$229$		−	7.01176i		−	0.463350i	0.972793	−	0.231675i	$-0.0744207\pi$
$230$	−15.5206	+	16.9718i	−1.02340	+	1.11909i
$231$	−5.75608	−	4.59995i	−0.378722	−	0.302654i
$232$	2.01372	−	15.6581i	0.132207	−	1.02800i
$233$	−2.61490	−	1.50971i	−0.171308	−	0.0989045i	0.411895	−	0.911231i	$-0.364867\pi$
$233$	−2.61490	−	1.50971i	−0.171308	−	0.0989045i	−0.583202	+	0.812327i	$0.698200\pi$
$234$	9.33148	−	0.0484160i	0.610018	−	0.00316505i
$235$	−10.7256			−0.699662
$236$	0.457967	−	0.987257i	0.0298111	−	0.0642650i
$237$	4.71788	+	12.0572i	0.306460	+	0.783198i
$238$	−1.66136	−	5.25088i	−0.107690	−	0.340364i
$239$	−27.9805			−1.80991			−0.904954	−	0.425510i	$-0.860095\pi$
$239$	−27.9805			−1.80991			−0.904954	+	0.425510i	$0.860095\pi$
$240$	−23.5182	+	14.4679i	−1.51809	+	0.933899i
$241$	−2.66442	−	4.61491i	−0.171630	−	0.297273i	0.767360	−	0.641217i	$-0.221570\pi$
$241$	−2.66442	−	4.61491i	−0.171630	−	0.297273i	−0.938990	+	0.343944i	$0.888237\pi$
$242$	9.11246	−	9.96447i	0.585771	−	0.640540i
$243$	15.1797	+	3.54636i	0.973778	+	0.227499i
$244$	14.8599	+	21.1322i	0.951307	+	1.35285i
$245$	−12.1940	+	21.1207i	−0.779049	+	1.34935i
$246$	−26.0276	−	10.0290i	−1.65946	−	0.639426i
$247$	4.79441	−	8.30242i	0.305061	−	0.528271i
$248$	5.31600	−	6.97109i	0.337566	−	0.442665i
$249$	−1.94901	+	2.43887i	−0.123514	+	0.154557i
$250$	−22.3804	+	24.4729i	−1.41546	+	1.54780i
$251$	23.9606	−	13.8337i	1.51238	−	0.873172i	0.512484	−	0.858697i	$-0.328725\pi$
$251$	23.9606	−	13.8337i	1.51238	−	0.873172i	0.999895	−	0.0144756i	$-0.00460789\pi$
$252$	1.72642	+	5.35966i	0.108754	+	0.337627i
$253$	−16.0185	+	9.24827i	−1.00707	+	0.581434i
$254$	−3.59288	+	16.2834i	−0.225437	+	1.02171i
$255$	28.3208	+	4.29828i	1.77352	+	0.269169i
$256$	14.9909	−	5.59228i	0.936930	−	0.349517i
$257$	−22.8219	+	13.1762i	−1.42359	+	0.821909i	−0.996603	−	0.0823498i	$-0.973758\pi$
$257$	−22.8219	+	13.1762i	−1.42359	+	0.821909i	−0.426985	+	0.904259i	$0.640424\pi$
$258$	3.90303	−	10.1293i	0.242992	−	0.630621i
$259$	8.95851			0.556655
$260$	−17.4621	+	1.56289i	−1.08295	+	0.0969263i
$261$	12.2980	−	11.3642i	0.761226	−	0.703425i
$262$	17.4913	−	5.53419i	1.08061	−	0.341903i
$263$	8.51528	−	14.7489i	0.525075	−	0.909456i	−0.474499	−	0.880256i	$-0.657371\pi$
$263$	8.51528	−	14.7489i	0.525075	−	0.909456i	0.999574	−	0.0291998i	$-0.00929591\pi$
$264$	−21.5435	+	5.38804i	−1.32591	+	0.331611i
$265$	−31.5770			−1.93976
$266$	5.64915	+	1.24701i	0.346372	+	0.0764589i
$267$	−13.9540	−	2.11782i	−0.853973	−	0.129608i
$268$	−2.77523	+	1.95151i	−0.169524	+	0.119207i
$269$	−5.68199	+	9.84149i	−0.346437	+	0.600046i	−0.985614	−	0.169014i	$-0.945942\pi$
$269$	−5.68199	+	9.84149i	−0.346437	+	0.600046i	0.639177	+	0.769060i	$0.279275\pi$
$270$	−28.9779	−	4.24430i	−1.76354	−	0.258300i
$271$	−12.5490	−	7.24516i	−0.762297	−	0.440112i	0.0678232	−	0.997697i	$-0.478395\pi$
$271$	−12.5490	−	7.24516i	−0.762297	−	0.440112i	−0.830120	+	0.557585i	$0.811728\pi$
$272$	−15.6202	−	5.61470i	−0.947111	−	0.340441i
$273$	−0.536472	+	3.53475i	−0.0324688	+	0.213933i
$274$	4.51041	−	20.4417i	0.272484	−	1.23493i
$275$	−42.7267	+	24.6683i	−2.57652	+	1.48755i
$276$	14.1084	+	0.866746i	0.849228	+	0.0521720i
$277$			19.1421i			1.15014i	0.818105	+	0.575068i	$0.195025\pi$
$277$			19.1421i			1.15014i	−0.818105	+	0.575068i	$0.804975\pi$
$278$	0.453971	+	0.100167i	0.0272273	+	0.00600763i
$279$	9.06962	−	2.05059i	0.542984	−	0.122766i
$280$	−4.07769	−	9.76158i	−0.243689	−	0.583366i
$281$	−7.05598	+	4.07377i	−0.420924	+	0.243021i	−0.695473	−	0.718552i	$-0.744805\pi$
$281$	−7.05598	+	4.07377i	−0.420924	+	0.243021i	0.274548	+	0.961573i	$0.411472\pi$
$282$	4.14200	+	5.12824i	0.246652	+	0.305382i
$283$	−0.481471	+	0.833933i	−0.0286205	+	0.0495722i	−0.879981	−	0.475009i	$-0.842445\pi$
$283$	−0.481471	+	0.833933i	−0.0286205	+	0.0495722i	0.851360	+	0.524581i	$0.175778\pi$
$284$	0.268715	+	0.124651i	0.0159453	+	0.00739667i
$285$	−18.7867	+	23.5041i	−1.11283	+	1.39226i
$286$	−13.7688	−	3.03805i	−0.814168	−	0.179644i
$287$	5.34333	−	9.25491i	0.315407	−	0.546300i
$288$	15.9997	+	5.65758i	0.942794	+	0.333376i
$289$	0.109814	+	0.190204i	0.00645968	+	0.0111885i
$290$	−21.2304	+	23.2155i	−1.24669	+	1.36326i
$291$	−13.9234	+	5.44814i	−0.816207	+	0.319375i
$292$	7.25494	+	3.36541i	0.424563	+	0.196945i
$293$	−18.5054			−1.08110			−0.540548	−	0.841313i	$-0.681783\pi$
$293$	−18.5054			−1.08110			−0.540548	+	0.841313i	$0.681783\pi$
$294$	14.8075	−	2.32601i	0.863591	−	0.135656i
$295$	−1.87815	+	1.08435i	−0.109350	+	0.0631333i
$296$	16.3721	−	21.4694i	0.951609	−	1.24788i
$297$	−21.1901	−	10.2847i	−1.22957	−	0.596781i
$298$	−1.69542	−	5.35851i	−0.0982129	−	0.310410i
$299$	7.77243	+	4.48742i	0.449491	+	0.259514i
$300$	37.6319	+	2.31190i	2.17268	+	0.133478i
$301$	3.60177	+	2.07949i	0.207603	+	0.119860i
$302$	−0.814489	−	0.744847i	−0.0468686	−	0.0428611i
$303$	1.70196	−	11.2140i	0.0977751	−	0.644228i
$304$	13.3126	−	11.2594i	0.763529	−	0.645774i
$305$		−	51.4798i		−	2.94772i
$306$	−8.88173	−	15.2009i	−0.507735	−	0.868979i
$307$	−1.01939	+	1.76563i	−0.0581794	+	0.100770i	−0.893648	−	0.448768i	$-0.851863\pi$
$307$	−1.01939	+	1.76563i	−0.0581794	+	0.100770i	0.835469	+	0.549538i	$0.185196\pi$
$308$	−0.758467	−	8.47432i	−0.0432177	−	0.482869i
$309$	5.09828	−	6.37965i	0.290031	−	0.362926i
$310$	−16.6560	+	5.26990i	−0.945995	+	0.299310i
$311$	4.69503			0.266230			0.133115	−	0.991101i	$-0.457502\pi$
$311$	4.69503			0.266230			0.133115	+	0.991101i	$0.457502\pi$
$312$	7.49073	+	7.74559i	0.424079	+	0.438508i
$313$	13.6801	+	23.6947i	0.773247	+	1.33930i	0.935775	+	0.352599i	$0.114702\pi$
$313$	13.6801	+	23.6947i	0.773247	+	1.33930i	−0.162528	+	0.986704i	$0.551965\pi$
$314$	1.78128	−	0.563592i	0.100523	−	0.0318053i
$315$	3.32928	−	10.7155i	0.187584	−	0.603749i
$316$	−6.29120	+	13.5622i	−0.353908	+	0.762933i
$317$	2.37648	+	4.11619i	0.133476	+	0.231188i	0.925014	−	0.379932i	$-0.124053\pi$
$317$	2.37648	+	4.11619i	0.133476	+	0.231188i	−0.791538	+	0.611120i	$0.790719\pi$
$318$	12.1943	+	15.0979i	0.683825	+	0.846649i
$319$	−21.9114	+	12.6506i	−1.22681	+	0.708296i
$320$	−30.8462	−	8.06740i	−1.72435	−	0.450981i
$321$	8.50243	−	10.6394i	0.474559	−	0.593833i
$322$	−1.16686	+	5.28836i	−0.0650267	+	0.294709i
$323$	−18.0879	−	0.00164257i	−1.00644	−	9.13952e-5i
$324$	9.16127	+	15.4942i	0.508960	+	0.860790i
$325$	20.7317	+	11.9695i	1.14999	+	0.663946i
$326$	16.2781	−	17.8001i	0.901562	−	0.985857i
$327$	5.02888	+	12.8520i	0.278098	+	0.710716i
$328$	−12.4146	−	29.7193i	−0.685481	−	1.64097i
$329$	−2.18725	+	1.26281i	−0.120587	+	0.0696208i
$330$	41.2932	+	15.9111i	2.27311	+	0.875880i
$331$	3.21824			0.176891			0.0884454	−	0.996081i	$-0.471810\pi$
$331$	3.21824			0.176891			0.0884454	+	0.996081i	$0.471810\pi$
$332$	−3.59059	+	0.321365i	−0.197059	+	0.0176372i
$333$	27.9324	−	6.31536i	1.53069	−	0.346080i
$334$	32.1919	+	7.10305i	1.76146	+	0.388662i
$335$	6.76070			0.369376
$336$	−3.09259	+	5.71937i	−0.168715	+	0.312017i
$337$	6.99055	−	12.1080i	0.380800	−	0.659564i	−0.610377	−	0.792111i	$-0.708982\pi$
$337$	6.99055	−	12.1080i	0.380800	−	0.659564i	0.991177	+	0.132547i	$0.0423154\pi$
$338$	−3.48210	−	11.0055i	−0.189402	−	0.598619i
$339$	−4.13453	+	5.17369i	−0.224557	+	0.280996i
$340$	19.0260	+	27.0568i	1.03183	+	1.46736i
$341$	−14.0501			−0.760853
$342$	18.4930	−	0.0942708i	0.999987	−	0.00509758i
$343$			12.3121i			0.664791i
$344$	11.5660	−	4.83143i	0.623595	−	0.260493i
$345$	−22.0041	−	17.5845i	−1.18466	−	0.946718i
$346$	4.27584	+	13.5141i	0.229870	+	0.726525i
$347$	24.1956	+	13.9693i	1.29889	+	0.749912i	0.980212	−	0.197952i	$-0.0634291\pi$
$347$	24.1956	+	13.9693i	1.29889	+	0.749912i	0.318674	+	0.947864i	$0.396762\pi$
$348$	19.2987	+	1.18561i	1.03452	+	0.0635553i
$349$			10.4481i			0.559274i	0.960106	+	0.279637i	$0.0902141\pi$
$349$			10.4481i			0.559274i	−0.960106	+	0.279637i	$0.909786\pi$
$350$	−3.11241	+	14.1059i	−0.166366	+	0.753989i
$351$	0.819137	+	11.3994i	0.0437223	+	0.608457i
$352$	−21.6952	−	13.6695i	−1.15636	−	0.728587i
$353$			27.0617i			1.44035i	0.693793	+	0.720174i	$0.255938\pi$
$353$			27.0617i			1.44035i	−0.693793	+	0.720174i	$0.744062\pi$
$354$	1.24376	+	0.479247i	0.0661051	+	0.0254717i
$355$	−0.295142	−	0.511201i	−0.0156645	−	0.0271317i
$356$	−9.37437	−	13.3312i	−0.496841	−	0.706554i
$357$	6.28145	−	2.45788i	0.332450	−	0.130085i
$358$	−6.89223	−	6.30291i	−0.364266	−	0.333119i
$359$	−6.52049	+	11.2938i	−0.344138	+	0.596065i	−0.985197	−	0.171427i	$-0.945162\pi$
$359$	−6.52049	+	11.2938i	−0.344138	+	0.596065i	0.641058	+	0.767492i	$0.278496\pi$
$360$	−19.5956	−	27.5618i	−1.03278	−	1.45263i
$361$	9.50299	−	16.4528i	0.500157	−	0.865935i
$362$	−1.22457	+	5.54992i	−0.0643622	+	0.291697i
$363$	12.9191	+	10.3242i	0.678074	+	0.541881i
$364$	−3.37698	+	2.37466i	−0.177002	+	0.124466i
$365$	−7.96843	−	13.8017i	−0.417087	−	0.722415i
$366$	−24.6140	+	19.8803i	−1.28659	+	1.03916i
$367$	−0.398083	+	0.229833i	−0.0207797	+	0.0119972i	−0.510354	−	0.859964i	$-0.670486\pi$
$367$	−0.398083	+	0.229833i	−0.0207797	+	0.0119972i	0.489574	+	0.871962i	$0.337152\pi$
$368$	10.5413	+	12.4612i	0.549502	+	0.649582i
$369$	10.1360	−	32.6234i	0.527662	−	1.69831i
$370$	−51.2967	+	16.2301i	−2.66679	+	0.843764i
$371$	−6.43941	+	3.71780i	−0.334318	+	0.193018i
$372$	8.95186	+	5.92859i	0.464132	+	0.307383i
$373$		−	19.5517i		−	1.01235i	−0.862431	−	0.506175i	$-0.831059\pi$
$373$		−	19.5517i		−	1.01235i	0.862431	−	0.506175i	$-0.168941\pi$
$374$	8.02466	+	25.3626i	0.414945	+	1.31147i
$375$	−31.7294	−	25.3565i	−1.63850	−	1.30940i
$376$	−0.970926	+	7.54965i	−0.0500717	+	0.389344i
$377$	10.6318	+	6.13827i	0.547565	+	0.316137i
$378$	−6.40908	+	2.54625i	−0.329648	+	0.130965i
$379$	−27.3875			−1.40680			−0.703400	−	0.710794i	$-0.748336\pi$
$379$	−27.3875			−1.40680			−0.703400	+	0.710794i	$0.748336\pi$
$380$	−34.6064	+	3.09417i	−1.77527	+	0.158727i
$381$	−20.1914	−	3.06448i	−1.03444	−	0.156998i
$382$	15.9864	−	17.4811i	0.817933	−	0.894409i
$383$	2.58183	−	4.47186i	0.131925	−	0.228502i	−0.792493	−	0.609881i	$-0.791217\pi$
$383$	2.58183	−	4.47186i	0.131925	−	0.228502i	0.924419	+	0.381379i	$0.124551\pi$
$384$	8.05484	+	17.8639i	0.411047	+	0.911614i
$385$	−8.47726	+	14.6830i	−0.432041	+	0.748317i
$386$	−2.17774	−	6.88293i	−0.110844	−	0.350332i
$387$	12.6962	+	3.94469i	0.645384	+	0.200520i
$388$	−15.6614	−	7.26498i	−0.795087	−	0.368823i
$389$	6.79713	+	11.7730i	0.344628	+	0.596914i	0.985286	−	0.170913i	$-0.0546716\pi$
$389$	6.79713	+	11.7730i	0.344628	+	0.596914i	−0.640658	+	0.767827i	$0.721338\pi$
$390$	−3.33204	−	21.2120i	−0.168725	−	1.07411i
$391$		−	16.9324i		−	0.856307i
$392$	13.7628	+	10.4952i	0.695126	+	0.530087i
$393$	8.18748	+	20.9242i	0.413004	+	1.05549i
$394$	−18.5884	+	20.3264i	−0.936469	+	1.02403i
$395$	25.8006	−	14.8960i	1.29817	−	0.749498i
$396$	−8.33891	−	25.8880i	−0.419046	−	1.30092i
$397$	16.7801	+	9.68801i	0.842170	+	0.486227i	0.858001	−	0.513647i	$-0.171706\pi$
$397$	16.7801	+	9.68801i	0.842170	+	0.486227i	−0.0158310	+	0.999875i	$0.505039\pi$
$398$	5.51225	−	24.9822i	0.276304	−	1.25224i
$399$	−1.06381	+	7.00501i	−0.0532570	+	0.350689i
$400$	28.1171	+	33.2381i	1.40586	+	1.66191i
$401$	2.04718	+	1.18194i	0.102231	+	0.0590232i	0.550244	−	0.835004i	$-0.314535\pi$
$401$	2.04718	+	1.18194i	0.102231	+	0.0590232i	−0.448013	+	0.894027i	$0.647868\pi$
$402$	−2.61083	−	3.23249i	−0.130216	−	0.161222i
$403$	3.40866	+	5.90398i	0.169798	+	0.294098i
$404$	10.7135	−	7.53361i	0.533016	−	0.374811i
$405$	2.82668	−	35.7576i	0.140459	−	1.77681i
$406$	−1.59613	+	7.23388i	−0.0792148	+	0.359011i
$407$	−43.2711			−2.14487
$408$	5.58923	−	19.5456i	0.276708	−	0.967653i
$409$	−9.87757	−	17.1085i	−0.488415	−	0.845959i	0.511497	−	0.859285i	$-0.329091\pi$
$409$	−9.87757	−	17.1085i	−0.488415	−	0.845959i	−0.999911	+	0.0133264i	$0.995758\pi$
$410$	−13.8289	+	62.6744i	−0.682961	+	3.09527i
$411$	25.3478	+	3.84707i	1.25032	+	0.189762i
$412$	9.39237	−	0.840634i	0.462729	−	0.0414151i
$413$	−0.255337	+	0.442257i	−0.0125643	+	0.0217620i
$414$	0.0898204	+	17.3116i	0.00441443	+	0.850817i
$415$	6.22125	+	3.59184i	0.305389	+	0.176317i
$416$	−0.480637	+	12.4329i	−0.0235652	+	0.609571i
$417$	−0.0854357	+	0.562925i	−0.00418381	+	0.0275666i
$418$	−27.2863	−	6.02324i	−1.33462	−	0.294607i
$419$		−	23.2346i		−	1.13508i	−0.823345	−	0.567542i	$-0.807895\pi$
$419$		−	23.2346i		−	1.13508i	0.823345	−	0.567542i	$-0.192105\pi$
$420$	11.5969	−	5.77807i	0.565870	−	0.281941i
$421$	6.01517	+	3.47286i	0.293161	+	0.169257i	0.639367	−	0.768902i	$-0.279197\pi$
$421$	6.01517	+	3.47286i	0.293161	+	0.169257i	−0.346205	+	0.938159i	$0.612530\pi$
$422$	8.30112	+	26.2364i	0.404092	+	1.27717i
$423$	−5.92955	+	5.47931i	−0.288305	+	0.266413i
$424$	−2.85848	+	22.2267i	−0.138820	+	1.07943i
$425$		−	45.1644i		−	2.19079i
$426$	−0.130443	+	0.338530i	−0.00631999	+	0.0164019i
$427$	−6.06109	−	10.4981i	−0.293317	−	0.508040i
$428$	15.6637	−	1.40193i	0.757134	−	0.0677649i
$429$	2.59125	−	17.0734i	0.125107	−	0.824312i
$430$	−24.3912	−	5.38186i	−1.17625	−	0.259536i
$431$	7.48379	+	12.9623i	0.360482	+	0.624372i	0.988040	−	0.154197i	$-0.0492790\pi$
$431$	7.48379	+	12.9623i	0.360482	+	0.624372i	−0.627559	+	0.778569i	$0.715946\pi$
$432$	−5.61071	+	20.0130i	−0.269946	+	0.962876i
$433$	−0.184189	−	0.319024i	−0.00885154	−	0.0153313i	0.861566	−	0.507646i	$-0.169484\pi$
$433$	−0.184189	−	0.319024i	−0.00885154	−	0.0153313i	−0.870417	+	0.492315i	$0.836151\pi$
$434$	−2.77614	+	3.03570i	−0.133259	+	0.145718i
$435$	−30.0991	−	24.0536i	−1.44314	−	1.15328i
$436$	−6.70591	+	14.4562i	−0.321155	+	0.692326i
$437$	15.4025	+	8.89449i	0.736801	+	0.425481i
$438$	−3.52179	+	9.13986i	−0.168277	+	0.436720i
$439$	−21.0076	−	12.1288i	−1.00264	−	0.578874i	−0.0936110	−	0.995609i	$-0.529841\pi$
$439$	−21.0076	−	12.1288i	−1.00264	−	0.578874i	−0.909028	+	0.416735i	$0.863174\pi$
$440$	19.6959	+	47.1500i	0.938965	+	2.24779i
$441$	4.04841	+	17.9058i	0.192781	+	0.852659i
$442$	8.71077	−	9.52522i	0.414329	−	0.453069i
$443$	−8.71683	+	5.03266i	−0.414149	+	0.239109i	−0.692571	−	0.721350i	$-0.743522\pi$
$443$	−8.71683	+	5.03266i	−0.414149	+	0.239109i	0.278422	+	0.960459i	$0.410189\pi$
$444$	27.5697	+	18.2588i	1.30840	+	0.866522i
$445$			32.4760i			1.53951i
$446$	21.5382	−	6.81463i	1.01986	−	0.322682i
$447$	6.41021	−	2.50826i	0.303192	−	0.118637i
$448$	−7.24020	+	1.98659i	−0.342067	+	0.0938573i
$449$			2.45970i			0.116080i	0.998314	+	0.0580401i	$0.0184851\pi$
$449$			2.45970i			0.116080i	−0.998314	+	0.0580401i	$0.981515\pi$
$450$	0.239581	+	46.1758i	0.0112940	+	2.17675i
$451$	−25.8091	+	44.7027i	−1.21530	+	2.10497i
$452$	−7.61690	+	0.681726i	−0.358269	+	0.0320657i
$453$	0.843895	−	1.05599i	0.0396496	−	0.0496150i
$454$	−17.7809	−	16.2606i	−0.834500	−	0.763147i
$455$	8.22662			0.385670
$456$	14.8436	+	15.3514i	0.695116	+	0.718897i
$457$	9.04729			0.423214			0.211607	−	0.977355i	$-0.432130\pi$
$457$	9.04729			0.423214			0.211607	+	0.977355i	$0.432130\pi$
$458$	7.31763	+	6.69194i	0.341930	+	0.312694i
$459$	17.8527	−	12.0918i	0.833293	−	0.564395i
$460$	−2.89944	−	32.3953i	−0.135187	−	1.51044i
$461$	12.0074	−	20.7974i	0.559240	−	0.968632i	−0.438320	−	0.898819i	$-0.644426\pi$
$461$	12.0074	−	20.7974i	0.559240	−	0.968632i	0.997560	−	0.0698129i	$-0.0222402\pi$
$462$	10.2941	−	1.61703i	0.478926	−	0.0752312i
$463$			31.2534i			1.45247i	0.687448	+	0.726234i	$0.258731\pi$
$463$			31.2534i			1.45247i	−0.687448	+	0.726234i	$0.741269\pi$
$464$	14.4193	+	17.0454i	0.669397	+	0.791314i
$465$	−7.79648	−	19.9250i	−0.361553	−	0.923998i
$466$	4.07119	−	1.28811i	0.188594	−	0.0596707i
$467$		−	26.8361i		−	1.24183i	−0.783879	−	0.620913i	$-0.786762\pi$
$467$		−	26.8361i		−	1.24183i	0.783879	−	0.620913i	$-0.213238\pi$
$468$	−8.85532	+	9.78474i	−0.409337	+	0.452300i
$469$	1.37869	−	0.795987i	0.0636620	−	0.0367553i
$470$	10.2364	−	11.1935i	0.472170	−	0.516317i
$471$	0.833798	+	2.13088i	0.0384194	+	0.0981859i
$472$	0.593245	+	1.42017i	0.0273063	+	0.0653686i
$473$	−17.3972	−	10.0443i	−0.799922	−	0.461835i
$474$	−17.0858	−	6.58354i	−0.784778	−	0.302392i
$475$	41.0836	+	23.7246i	1.88505	+	1.08856i
$476$	7.06551	+	3.27754i	0.323847	+	0.150226i
$477$	−17.4570	+	16.1315i	−0.799303	+	0.738611i
$478$	26.7042	−	29.2010i	1.22142	−	1.33562i
$479$	−14.7010	−	25.4628i	−0.671705	−	1.16343i	−0.977420	−	0.211304i	$-0.932229\pi$
$479$	−14.7010	−	25.4628i	−0.671705	−	1.16343i	0.305716	−	0.952123i	$-0.401104\pi$
$480$	7.34647	−	38.3521i	0.335319	−	1.75053i
$481$	10.4979	+	18.1829i	0.478664	+	0.829071i
$482$	7.35911	+	1.62377i	0.335198	+	0.0739605i
$483$	−6.55759	−	0.995252i	−0.298381	−	0.0452855i
$484$	1.70232	+	19.0199i	0.0773781	+	0.864542i
$485$	17.2016	+	29.7941i	0.781086	+	1.35288i
$486$	−18.1884	+	12.4573i	−0.825041	+	0.565073i
$487$		−	14.3764i		−	0.651458i	−0.945463	−	0.325729i	$-0.894390\pi$
$487$		−	14.3764i		−	0.651458i	0.945463	−	0.325729i	$-0.105610\pi$
$488$	−36.2361	−	4.66015i	−1.64033	−	0.210955i
$489$	23.0781	+	18.4427i	1.04363	+	0.834010i
$490$	−10.4042	−	32.8833i	−0.470013	−	1.48552i
$491$	−0.314071	−	0.181329i	−0.0141738	−	0.00818326i	0.492896	−	0.870088i	$-0.335938\pi$
$491$	−0.314071	−	0.181329i	−0.0141738	−	0.00818326i	−0.507070	+	0.861905i	$0.669272\pi$
$492$	35.3069	−	17.5914i	1.59176	−	0.793083i
$493$		−	23.1616i		−	1.04314i
$494$	4.08886	+	12.9273i	0.183967	+	0.581626i
$495$	−16.0810	+	51.7575i	−0.722786	+	2.32633i
$496$	2.20166	+	12.2010i	0.0988576	+	0.547841i
$497$	−0.120375	−	0.0694985i	−0.00539955	−	0.00311743i
$498$	−0.685143	−	4.36166i	−0.0307020	−	0.195451i
$499$	−9.72893	+	16.8510i	−0.435527	+	0.754354i	−0.997338	−	0.0729107i	$-0.976771\pi$
$499$	−9.72893	+	16.8510i	−0.435527	+	0.754354i	0.561812	+	0.827265i	$0.310105\pi$
$500$	−4.18092	−	46.7133i	−0.186977	−	2.08908i
$501$	−6.05841	+	39.9181i	−0.270670	+	1.78341i
$502$	−8.43058	+	38.2084i	−0.376275	+	1.70533i
$503$	−0.168799	−	0.292369i	−0.00752638	−	0.0130361i	0.862238	−	0.506504i	$-0.169062\pi$
$503$	−0.168799	−	0.292369i	−0.00752638	−	0.0130361i	−0.869764	+	0.493468i	$0.835729\pi$
$504$	−7.24113	−	3.31346i	−0.322546	−	0.147593i
$505$	−26.0990			−1.16139
$506$	5.63613	−	25.5437i	0.250557	−	1.13555i
$507$	13.1655	−	5.15155i	0.584700	−	0.228789i
$508$	−13.5647	−	19.2902i	−0.601835	−	0.855866i
$509$	−3.33230	−	5.77172i	−0.147702	−	0.255827i	0.782676	−	0.622429i	$-0.213854\pi$
$509$	−3.33230	−	5.77172i	−0.147702	−	0.255827i	−0.930378	+	0.366602i	$0.880521\pi$
$510$	−31.5148	+	25.4540i	−1.39550	+	1.12712i
$511$	−3.24996	−	1.87636i	−0.143770	−	0.0830055i
$512$	−8.47088	+	20.9820i	−0.374363	+	0.927282i
$513$	1.62130	+	22.5914i	0.0715822	+	0.997435i
$514$	8.02991	−	36.3926i	0.354184	−	1.60521i
$515$	−16.2737	−	9.39563i	−0.717105	−	0.414021i
$516$	6.84613	+	13.7405i	0.301384	+	0.604893i
$517$	10.5647	−	6.09956i	0.464637	−	0.268258i
$518$	−8.54989	+	9.34930i	−0.375661	+	0.410784i
$519$	−16.1665	+	6.32583i	−0.709631	+	0.277673i
$520$	15.0345	−	19.7154i	0.659307	−	0.864578i
$521$			28.7060i			1.25763i	0.777554	+	0.628817i	$0.216460\pi$
$521$			28.7060i			1.25763i	−0.777554	+	0.628817i	$0.783540\pi$
$522$	0.122864	+	23.6802i	0.00537761	+	1.03646i
$523$	19.1174	+	33.1123i	0.835945	+	1.44790i	0.893259	+	0.449542i	$0.148413\pi$
$523$	19.1174	+	33.1123i	0.835945	+	1.44790i	−0.0573143	+	0.998356i	$0.518254\pi$
$524$	−10.9178	+	23.5360i	−0.476948	+	1.02818i
$525$	−17.4913	−	2.65467i	−0.763383	−	0.115859i
$526$	7.26539	+	22.9629i	0.316786	+	1.00123i
$527$	6.43096	−	11.1387i	0.280137	−	0.485211i
$528$	14.9377	−	27.6255i	0.650080	−	1.20224i
$529$	3.17504	−	5.49933i	0.138045	−	0.239101i
$530$	30.1367	−	32.9545i	1.30905	−	1.43145i
$531$	−0.484363	+	1.55895i	−0.0210196	+	0.0676526i
$532$	−6.69288	+	4.70545i	−0.290173	+	0.204007i
$533$	25.0461			1.08486
$534$	15.5278	−	12.5415i	0.671952	−	0.542724i
$535$	−27.1398	−	15.6692i	−1.17335	−	0.677437i
$536$	0.612006	−	4.75879i	0.0264346	−	0.205548i
$537$	7.14106	−	8.93586i	0.308159	−	0.385611i
$538$	−4.84797	−	15.3224i	−0.209011	−	0.660597i
$539$		−	27.7385i		−	1.19478i
$540$	32.0855	−	26.1912i	1.38074	−	1.12709i
$541$	−2.32825	+	1.34421i	−0.100099	+	0.0577923i	−0.549214	−	0.835682i	$-0.685073\pi$
$541$	−2.32825	+	1.34421i	−0.100099	+	0.0577923i	0.449115	+	0.893474i	$0.351739\pi$
$542$	19.5378	−	6.18170i	0.839220	−	0.265527i
$543$	−6.88192	−	1.04448i	−0.295332	−	0.0448228i
$544$	20.7673	−	10.9429i	0.890390	−	0.469174i
$545$	27.5013	−	15.8779i	1.17803	−	0.680135i
$546$	−3.17694	−	3.93339i	−0.135960	−	0.168334i
$547$	−2.59577	−	4.49601i	−0.110987	−	0.192236i	0.805181	−	0.593029i	$-0.202068\pi$
$547$	−2.59577	−	4.49601i	−0.110987	−	0.192236i	−0.916169	+	0.400793i	$0.868735\pi$
$548$	17.0288	+	24.2165i	0.727433	+	1.03448i
$549$	−26.2991	−	28.4601i	−1.12242	−	1.21465i
$550$	15.0335	−	68.1335i	0.641029	−	2.90522i
$551$	21.0688	+	12.1666i	0.897562	+	0.518317i
$552$	−14.3695	+	13.8966i	−0.611605	+	0.591481i
$553$	3.50763	−	6.07539i	0.149159	−	0.258352i
$554$	−19.9771	−	18.2690i	−0.848745	−	0.776174i
$555$	−24.0114	−	61.3645i	−1.01923	−	2.60478i
$556$	−0.537800	+	0.378175i	−0.0228078	+	0.0160382i
$557$	−5.34483	−	9.25752i	−0.226468	−	0.392254i	0.730291	−	0.683136i	$-0.239384\pi$
$557$	−5.34483	−	9.25752i	−0.226468	−	0.392254i	−0.956759	+	0.290882i	$0.906051\pi$
$558$	−6.51589	+	11.4223i	−0.275840	+	0.483545i
$559$			9.74728i			0.412266i
$560$	14.0791	+	5.06076i	0.594950	+	0.213856i
$561$	−30.3404	+	11.8720i	−1.28097	+	0.501235i
$562$	2.48266	−	11.2517i	0.104725	−	0.474625i
$563$		−	18.0128i		−	0.759151i	−0.925161	−	0.379575i	$-0.876070\pi$
$563$		−	18.0128i		−	0.759151i	0.925161	−	0.379575i	$-0.123930\pi$
$564$	−9.30501	−	0.571649i	−0.391811	−	0.0240708i
$565$	13.1974	+	7.61955i	0.555220	+	0.320557i
$566$	−0.410800	−	1.29837i	−0.0172672	−	0.0545745i
$567$	−3.63357	−	7.62475i	−0.152595	−	0.320209i
$568$	−0.386546	+	0.161471i	−0.0162191	+	0.00677519i
$569$		−	12.0148i		−	0.503689i	−0.967768	−	0.251844i	$-0.918963\pi$
$569$		−	12.0148i		−	0.503689i	0.967768	−	0.251844i	$-0.0810371\pi$
$570$	−6.59958	−	42.0382i	−0.276426	−	1.76079i
$571$	14.1250			0.591114			0.295557	−	0.955325i	$-0.404495\pi$
$571$	14.1250			0.591114			0.295557	+	0.955325i	$0.404495\pi$
$572$	16.3114	−	11.4700i	0.682013	−	0.479584i
$573$	22.6644	+	18.1122i	0.946820	+	0.756648i
$574$	4.55902	+	14.4092i	0.190290	+	0.601428i
$575$	−22.2055	+	38.4610i	−0.926032	+	1.60394i
$576$	−21.1743	+	11.2982i	−0.882263	+	0.470756i
$577$	44.0935			1.83564			0.917818	−	0.397002i	$-0.129949\pi$
$577$	44.0935			1.83564			0.917818	+	0.397002i	$0.129949\pi$
$578$	−0.303307	−	0.0669237i	−0.0126159	−	0.00278366i
$579$	8.23382	−	3.22183i	0.342186	−	0.133895i
$580$	−3.96610	−	44.3131i	−0.164683	−	1.84000i
$581$	1.69158			0.0701784
$582$	7.60256	−	19.7304i	0.315136	−	0.817853i
$583$	31.1034	−	17.9576i	1.28817	−	0.743726i
$584$	−10.4362	+	4.35951i	−0.431854	+	0.180398i
$585$	25.6504	−	5.79941i	1.06051	−	0.239776i
$586$	17.6613	−	19.3126i	0.729581	−	0.797797i
$587$	−22.8072	−	13.1678i	−0.941355	−	0.543491i	−0.0509700	−	0.998700i	$-0.516231\pi$
$587$	−22.8072	−	13.1678i	−0.941355	−	0.543491i	−0.890385	+	0.455209i	$0.849565\pi$
$588$	−11.7046	+	17.6733i	−0.482690	+	0.728836i
$589$	6.75417	+	11.7010i	0.278301	+	0.482132i
$590$	0.660831	−	2.99497i	0.0272060	−	0.123301i
$591$	−26.3534	−	21.0602i	−1.08403	−	0.866301i
$592$	6.78063	+	37.5764i	0.278682	+	1.54438i
$593$	−10.7780	+	6.22270i	−0.442601	+	0.255536i	−0.704700	−	0.709505i	$-0.748918\pi$
$593$	−10.7780	+	6.22270i	−0.442601	+	0.255536i	0.262100	+	0.965041i	$0.415585\pi$
$594$	30.9569	−	12.2988i	1.27018	−	0.504625i
$595$	−7.76038	−	13.4414i	−0.318145	−	0.551043i
$596$	7.21034	+	3.34472i	0.295347	+	0.137005i
$597$	30.9780	+	4.70156i	1.26785	+	0.192422i
$598$	−12.1011	+	3.82874i	−0.494850	+	0.156569i
$599$	−20.3324	−	35.2167i	−0.830758	−	1.43891i	−0.897438	−	0.441140i	$-0.854574\pi$
$599$	−20.3324	−	35.2167i	−0.830758	−	1.43891i	0.0666803	−	0.997774i	$-0.478759\pi$
$600$	−38.3282	+	37.0671i	−1.56474	+	1.51326i
$601$	18.7903			0.766474			0.383237	−	0.923650i	$-0.374809\pi$
$601$	18.7903			0.766474			0.383237	+	0.923650i	$0.374809\pi$
$602$	−5.60768	+	1.77425i	−0.228552	+	0.0723132i
$603$	3.73758	−	3.45378i	0.152206	−	0.140649i
$604$	1.55468	−	0.139146i	0.0632589	−	0.00566178i
$605$	19.0265	−	32.9549i	0.773538	−	1.33981i
$606$	10.0788	+	12.4787i	0.409425	+	0.506913i
$607$			35.5431i			1.44265i	0.692598	+	0.721324i	$0.256466\pi$
$607$			35.5431i			1.44265i	−0.692598	+	0.721324i	$0.743534\pi$
$608$	−0.954756	+	24.6392i	−0.0387205	+	0.999250i
$609$	−8.97003	−	1.36139i	−0.363484	−	0.0551663i
$610$	53.7254	+	49.1316i	2.17528	+	1.98928i
$611$	−5.12619	−	2.95961i	−0.207384	−	0.119733i
$612$	24.3406	+	5.23840i	0.983911	+	0.211750i
$613$	−16.7781	−	9.68682i	−0.677660	−	0.391247i	0.121313	−	0.992614i	$-0.461290\pi$
$613$	−16.7781	−	9.68682i	−0.677660	−	0.391247i	−0.798973	+	0.601367i	$0.794623\pi$
$614$	−0.869758	−	2.74894i	−0.0351006	−	0.110938i
$615$	−77.7165	−	11.7951i	−3.13383	−	0.475624i
$616$	9.56785	+	7.29622i	0.385500	+	0.293973i
$617$	−1.25415	+	0.724082i	−0.0504900	+	0.0291504i	−0.525033	−	0.851082i	$-0.675947\pi$
$617$	−1.25415	+	0.724082i	−0.0504900	+	0.0291504i	0.474542	+	0.880233i	$0.342614\pi$
$618$	1.79221	+	11.4093i	0.0720934	+	0.458950i
$619$	−17.5178			−0.704098			−0.352049	−	0.935982i	$-0.614515\pi$
$619$	−17.5178			−0.704098			−0.352049	+	0.935982i	$0.614515\pi$
$620$	10.3965	−	22.4120i	0.417532	−	0.900089i
$621$	−21.1480	+	1.51965i	−0.848641	+	0.0609813i
$622$	−4.48087	+	4.89983i	−0.179667	+	0.196465i
$623$	3.82364	+	6.62274i	0.153191	+	0.265335i
$624$	−15.2325	+	0.425197i	−0.609789	+	0.0170215i
$625$	−19.5198	+	33.8093i	−0.780792	+	1.35237i
$626$	−37.7844	−	8.33702i	−1.51017	−	0.333214i
$627$	5.13837	−	33.8354i	0.205207	−	1.35125i
$628$	−1.11185	+	2.39686i	−0.0443678	+	0.0956453i
$629$	19.8059	−	34.3049i	0.789714	−	1.36782i
$630$	8.00547	+	13.7012i	0.318946	+	0.545870i
$631$	25.7962	−	14.8935i	1.02693	−	0.592899i	0.110828	−	0.993840i	$-0.464650\pi$
$631$	25.7962	−	14.8935i	1.02693	−	0.592899i	0.916104	+	0.400940i	$0.131317\pi$
$632$	−8.14955	−	19.5092i	−0.324172	−	0.776035i
$633$	−31.3857	+	12.2810i	−1.24747	+	0.488125i
$634$	−6.56382	−	1.44829i	−0.260683	−	0.0575189i
$635$			46.9927i			1.86485i
$636$	−27.3946	−	1.68298i	−1.08627	−	0.0667344i
$637$	−11.6560	+	6.72960i	−0.461828	+	0.266637i
$638$	7.70958	−	34.9408i	0.305225	−	1.38332i
$639$	−0.424319	−	0.131835i	−0.0167858	−	0.00521533i
$640$	37.8585	−	24.4923i	1.49649	−	0.968143i
$641$	−22.4678	−	12.9718i	−0.887424	−	0.512355i	−0.0143253	−	0.999897i	$-0.504560\pi$
$641$	−22.4678	−	12.9718i	−0.887424	−	0.512355i	−0.873099	+	0.487543i	$0.837893\pi$
$642$	2.98889	+	19.0274i	0.117962	+	0.750952i
$643$	3.61466	−	6.26077i	0.142548	−	0.246901i	−0.785907	−	0.618344i	$-0.787804\pi$
$643$	3.61466	−	6.26077i	0.142548	−	0.246901i	0.928456	+	0.371444i	$0.121137\pi$
$644$	−4.40541	−	6.26491i	−0.173598	−	0.246872i
$645$	4.59035	−	30.2452i	0.180745	−	1.19091i
$646$	17.2646	−	18.8754i	0.679266	−	0.742642i
$647$	17.4038			0.684215			0.342108	−	0.939661i	$-0.388859\pi$
$647$	17.4038			0.684215			0.342108	+	0.939661i	$0.388859\pi$
$648$	−24.9135	−	5.22659i	−0.978695	−	0.205320i
$649$	1.23332	−	2.13617i	0.0484120	−	0.0838521i
$650$	−32.2776	+	10.2126i	−1.26603	+	0.400569i
$651$	−3.93583	−	3.14530i	−0.154257	−	0.123274i
$652$	3.04095	+	33.9764i	0.119093	+	1.33062i
$653$	5.52428			0.216182			0.108091	−	0.994141i	$-0.465526\pi$
$653$	5.52428			0.216182			0.108091	+	0.994141i	$0.465526\pi$
$654$	−18.2121	−	7.01751i	−0.712149	−	0.274407i
$655$	44.7747	−	25.8507i	1.74949	−	1.01007i
$656$	42.8640	+	15.4076i	1.67356	+	0.601564i
$657$	−11.4560	−	3.55938i	−0.446943	−	0.138865i
$658$	0.769586	−	3.48786i	0.0300016	−	0.135971i
$659$	9.67926	−	5.58833i	0.377051	−	0.217690i	−0.299484	−	0.954101i	$-0.596814\pi$
$659$	9.67926	−	5.58833i	0.377051	−	0.217690i	0.676534	+	0.736411i	$0.263481\pi$
$660$	−56.0149	+	27.9090i	−2.18038	+	1.08636i
$661$	−25.1909	+	14.5440i	−0.979812	+	0.565695i	−0.902213	−	0.431290i	$-0.858059\pi$
$661$	−25.1909	+	14.5440i	−0.979812	+	0.565695i	−0.0775985	+	0.996985i	$0.524725\pi$
$662$	−3.07145	+	3.35863i	−0.119375	+	0.130537i
$663$	12.3496	+	9.86911i	0.479617	+	0.383284i
$664$	3.09143	−	4.05393i	0.119971	−	0.157323i
$665$	16.3034	+	0.00148052i	0.632218	+	5.74120e-5i
$666$	−20.0675	+	35.1782i	−0.777600	+	1.36313i
$667$	−11.3876	+	19.7239i	−0.440929	+	0.763712i
$668$	−38.1365	+	26.8171i	−1.47554	+	1.03759i
$669$	10.0818	+	25.7655i	0.389786	+	0.996150i
$670$	−6.45232	+	7.05561i	−0.249275	+	0.272582i
$671$	29.2761	+	50.7076i	1.13019	+	1.95755i
$672$	−3.01733	−	8.68598i	−0.116396	−	0.335069i
$673$	−43.7214			−1.68533			−0.842667	−	0.538435i	$-0.819016\pi$
$673$	−43.7214			−1.68533			−0.842667	+	0.538435i	$0.819016\pi$
$674$	5.96447	+	18.8512i	0.229743	+	0.726121i
$675$	−56.4089	+	4.05341i	−2.17118	+	0.156016i
$676$	14.8088	+	6.86949i	0.569571	+	0.264211i
$677$	−30.0509			−1.15495			−0.577474	−	0.816409i	$-0.695962\pi$
$677$	−30.0509			−1.15495			−0.577474	+	0.816409i	$0.695962\pi$
$678$	−1.45343	−	9.25259i	−0.0558185	−	0.355343i
$679$	7.01576	+	4.05055i	0.269240	+	0.155446i
$680$	−46.3952	−	5.96668i	−1.77918	−	0.228812i
$681$	18.4229	−	23.0532i	0.705966	−	0.883400i
$682$	13.4092	−	14.6629i	0.513465	−	0.561473i
$683$			45.1875i			1.72905i	0.502589	+	0.864525i	$0.332381\pi$
$683$			45.1875i			1.72905i	−0.502589	+	0.864525i	$0.667619\pi$
$684$	−17.5511	+	19.3897i	−0.671083	+	0.741382i
$685$		−	58.9934i		−	2.25402i
$686$	−12.8492	−	11.7505i	−0.490584	−	0.448637i
$687$	−7.58182	+	9.48739i	−0.289264	+	0.361967i
$688$	−5.99622	+	16.6816i	−0.228604	+	0.635978i
$689$	−15.0919	−	8.71331i	−0.574955	−	0.331951i
$690$	39.3520	−	6.18154i	1.49811	−	0.235327i
$691$	−10.1999			−0.388024			−0.194012	−	0.980999i	$-0.562150\pi$
$691$	−10.1999			−0.388024			−0.194012	+	0.980999i	$0.562150\pi$
$692$	−18.1845	−	8.43537i	−0.691269	−	0.320665i
$693$	2.81444	+	12.4481i	0.106912	+	0.472864i
$694$	−37.6706	+	11.9189i	−1.42996	+	0.452434i
$695$	1.31013			0.0496960
$696$	−19.6558	+	19.0090i	−0.745050	+	0.720535i
$697$	−23.6266	−	40.9224i	−0.894921	−	1.55005i
$698$	−10.9039	−	9.97153i	−0.412717	−	0.377428i
$699$	1.90568	+	4.87023i	0.0720795	+	0.184209i
$700$	−11.7507	−	16.7106i	−0.444135	−	0.631602i
$701$	−13.2861	+	23.0122i	−0.501810	+	0.869161i	0.498188	+	0.867069i	$0.333999\pi$
$701$	−13.2861	+	23.0122i	−0.501810	+	0.869161i	−0.999998	+	0.00209145i	$0.999334\pi$
$702$	−12.6785	−	10.0246i	−0.478518	−	0.378355i
$703$	20.8014	+	36.0366i	0.784538	+	1.35914i
$704$	34.9714	−	9.59553i	1.31803	−	0.361645i
$705$	14.5125	+	11.5976i	0.546572	+	0.436791i
$706$	−28.2422	−	25.8273i	−1.06291	−	0.972024i
$707$	−5.32229	+	3.07283i	−0.200165	+	0.115566i
$708$	−1.68718	+	0.840627i	−0.0634081	+	0.0315927i
$709$	32.4162	−	18.7155i	1.21742	−	0.702877i	0.253053	−	0.967452i	$-0.418565\pi$
$709$	32.4162	−	18.7155i	1.21742	−	0.702877i	0.964365	+	0.264576i	$0.0852320\pi$
$710$	0.815180	+	0.179867i	0.0305931	+	0.00675029i
$711$	6.65381	−	21.4156i	0.249537	−	0.803149i
$712$	22.8595	+	2.93986i	0.856697	+	0.110176i
$713$	−10.9529	+	6.32368i	−0.410191	+	0.236824i
$714$	−3.42984	+	8.90123i	−0.128358	+	0.333120i
$715$	−39.7359			−1.48604
$716$	13.1557	−	1.17746i	0.491652	−	0.0440037i
$717$	37.8595	+	30.2553i	1.41389	+	1.12990i
$718$	−5.56340	−	17.5836i	−0.207624	−	0.656214i
$719$	15.7524	−	27.2840i	0.587466	−	1.01752i	−0.407097	−	0.913385i	$-0.633459\pi$
$719$	15.7524	−	27.2840i	0.587466	−	1.01752i	0.994563	−	0.104137i	$-0.0332079\pi$
$720$	47.4659	+	5.85419i	1.76895	+	0.218173i
$721$	−4.42487			−0.164791
$722$	8.10092	+	25.6198i	0.301485	+	0.953471i
$723$	−1.38496	+	9.12532i	−0.0515072	+	0.339374i
$724$	−4.62330	−	6.57476i	−0.171824	−	0.244349i
$725$	−30.3746	+	52.6103i	−1.12808	+	1.95390i
$726$	−23.1043	+	3.62930i	−0.857483	+	0.134696i
$727$	−14.3021	−	8.25732i	−0.530436	−	0.306247i	0.210758	−	0.977538i	$-0.432407\pi$
$727$	−14.3021	−	8.25732i	−0.530436	−	0.306247i	−0.741194	+	0.671291i	$0.765740\pi$
$728$	0.744707	−	5.79063i	0.0276007	−	0.214615i
$729$	−16.7045	−	21.2123i	−0.618685	−	0.785639i
$730$	22.0087	+	4.85616i	0.814580	+	0.179735i
$731$	15.9260	−	9.19486i	0.589043	−	0.340084i
$732$	2.74374	−	44.6612i	0.101412	−	1.65073i
$733$		−	43.2155i		−	1.59620i	−0.602525	−	0.798100i	$-0.705839\pi$
$733$		−	43.2155i		−	1.59620i	0.602525	−	0.798100i	$-0.294161\pi$
$734$	0.140066	−	0.634797i	0.00516994	−	0.0234308i
$735$	39.3372	−	15.3923i	1.45097	−	0.567755i
$736$	−23.0652	−	0.891667i	−0.850194	−	0.0328673i
$737$	−6.65930	+	3.84475i	−0.245298	+	0.141623i
$738$	24.3728	+	41.7136i	0.897174	+	1.53550i
$739$	−14.3268	+	24.8147i	−0.527019	+	0.912824i	0.472485	+	0.881339i	$0.343357\pi$
$739$	−14.3268	+	24.8147i	−0.527019	+	0.912824i	−0.999504	+	0.0314850i	$0.989976\pi$
$740$	32.0188	−	69.0241i	1.17703	−	2.53738i
$741$	−15.4646	+	6.04955i	−0.568105	+	0.222236i
$742$	2.26572	−	10.2685i	0.0831772	−	0.376969i
$743$	−13.1181	+	22.7213i	−0.481258	+	0.833563i	−0.999769	−	0.0215083i	$-0.993153\pi$
$743$	−13.1181	+	22.7213i	−0.481258	+	0.833563i	0.518511	+	0.855071i	$0.326486\pi$
$744$	−14.7307	+	3.68418i	−0.540055	+	0.135068i
$745$	−7.91945	−	13.7169i	−0.290146	−	0.502548i
$746$	20.4046	+	18.6599i	0.747066	+	0.683188i
$747$	5.27429	−	1.19249i	0.192976	−	0.0436309i
$748$	−34.1276	−	15.8310i	−1.24783	−	0.578840i
$749$	−7.37938			−0.269637
$750$	56.7447	−	8.91364i	2.07202	−	0.325480i
$751$	22.3626	−	12.9111i	0.816023	−	0.471131i	−0.0330198	−	0.999455i	$-0.510512\pi$
$751$	22.3626	−	12.9111i	0.816023	−	0.471131i	0.849043	+	0.528323i	$0.177179\pi$
$752$	−6.95234	−	8.21857i	−0.253526	−	0.299700i
$753$	−47.3786	−	7.19070i	−1.72657	−	0.262044i
$754$	−16.5529	+	5.23728i	−0.602820	+	0.190731i
$755$	−2.69371	−	1.55522i	−0.0980343	−	0.0566001i
$756$	3.45943	−	9.11876i	0.125818	−	0.331646i
$757$	28.0486	+	16.1939i	1.01945	+	0.588577i	0.913943	−	0.405842i	$-0.133022\pi$
$757$	28.0486	+	16.1939i	1.01945	+	0.588577i	0.105502	+	0.994419i	$0.466355\pi$
$758$	26.1383	−	28.5822i	0.949384	−	1.03815i
$759$	31.6742	+	4.80723i	1.14970	+	0.174491i
$760$	29.7987	−	39.0690i	1.08091	−	1.41718i
$761$			38.8275i			1.40749i	0.710451	+	0.703747i	$0.248491\pi$
$761$			38.8275i			1.40749i	−0.710451	+	0.703747i	$0.751509\pi$
$762$	22.4686	−	18.1475i	0.813952	−	0.657416i
$763$	3.73884	−	6.47587i	0.135355	−	0.234442i
$764$	2.98645	+	33.3674i	0.108046	+	1.20719i
$765$	−33.6723	−	36.4391i	−1.21742	−	1.31746i
$766$	2.20287	+	6.96234i	0.0795928	+	0.251560i
$767$	−1.19685			−0.0432159
$768$	−26.3306	−	8.64289i	−0.950124	−	0.311873i
$769$	14.3300	+	24.8204i	0.516754	+	0.895045i	0.999811	+	0.0194557i	$0.00619333\pi$
$769$	14.3300	+	24.8204i	0.516754	+	0.895045i	−0.483056	+	0.875589i	$0.660473\pi$
$770$	−7.23295	−	22.8604i	−0.260658	−	0.823830i
$771$	45.1269	+	6.84896i	1.62521	+	0.246659i
$772$	9.26158	+	4.29625i	0.333332	+	0.154625i
$773$	−10.0326	−	17.3770i	−0.360849	−	0.625009i	0.627252	−	0.778817i	$-0.284180\pi$
$773$	−10.0326	−	17.3770i	−0.360849	−	0.625009i	−0.988101	+	0.153808i	$0.950846\pi$
$774$	−16.2338	+	9.48525i	−0.583513	+	0.340940i
$775$	−29.2152	+	16.8674i	−1.04944	+	0.605894i
$776$	22.5289	−	9.41097i	0.808741	−	0.337834i
$777$	−12.1215	−	9.68683i	−0.434855	−	0.347513i
$778$	−18.7736	−	4.14235i	−0.673067	−	0.148510i
$779$	49.6359	+	0.00450746i	1.77839	+	0.000161496i
$780$	25.3173	+	16.7670i	0.906506	+	0.600356i
$781$	0.581430	+	0.335689i	0.0208052	+	0.0120119i
$782$	17.6710	+	16.1600i	0.631913	+	0.577882i
$783$	−28.9281	+	2.07870i	−1.03380	+	0.0742867i
$784$	−24.0880	+	4.34667i	−0.860287	+	0.155238i
$785$	4.55977	−	2.63259i	0.162745	−	0.0939611i
$786$	−29.6510	−	11.4252i	−1.05762	−	0.407522i
$787$	24.1320			0.860212			0.430106	−	0.902778i	$-0.358476\pi$
$787$	24.1320			0.860212			0.430106	+	0.902778i	$0.358476\pi$
$788$	−3.47253	−	38.7984i	−0.123704	−	1.38214i
$789$	−27.4697	+	10.7487i	−0.977948	+	0.382663i
$790$	−9.07799	+	41.1426i	−0.322980	+	1.46379i
$791$	3.58842			0.127590
$792$	34.9758	+	16.0045i	1.24281	+	0.568696i
$793$	14.2052	−	24.6042i	0.504443	−	0.873720i
$794$	−26.1253	+	8.26599i	−0.927154	+	0.293349i
$795$	42.7259	+	34.1442i	1.51533	+	1.21097i
$796$	20.8111	+	29.5954i	0.737631	+	1.04898i
$797$	43.4528			1.53918			0.769589	−	0.638540i	$-0.220461\pi$
$797$	43.4528			1.53918			0.769589	+	0.638540i	$0.220461\pi$
$798$	−6.29530	−	7.79571i	−0.222851	−	0.275965i
$799$			11.1675i			0.395078i
$800$	−61.5226	−	2.37838i	−2.17515	−	0.0840884i
$801$	16.5908	+	17.9540i	0.586206	+	0.634375i
$802$	−3.18729	+	1.00845i	−0.112547	+	0.0356096i
$803$	15.6978	+	9.06314i	0.553964	+	0.319831i
$804$	5.86524	+	0.360329i	0.206851	+	0.0127078i
$805$			15.2619i			0.537910i
$806$	−9.41470	−	2.07733i	−0.331619	−	0.0731707i
$807$	18.3297	−	7.17227i	0.645236	−	0.252476i
$808$	−2.36259	+	18.3708i	−0.0831155	+	0.646283i
$809$		−	44.4857i		−	1.56404i	−0.623256	−	0.782018i	$-0.714191\pi$
$809$		−	44.4857i		−	1.56404i	0.623256	−	0.782018i	$-0.285809\pi$
$810$	34.6196	+	37.0766i	1.21641	+	1.30274i
$811$	−22.4726	−	38.9237i	−0.789119	−	1.36679i	−0.926507	−	0.376278i	$-0.877204\pi$
$811$	−22.4726	−	38.9237i	−0.789119	−	1.36679i	0.137388	−	0.990517i	$-0.456129\pi$
$812$	−6.02610	−	8.56967i	−0.211475	−	0.300737i
$813$	9.14544	+	23.3724i	0.320745	+	0.819706i
$814$	41.2974	−	45.1586i	1.44747	−	1.58281i
$815$	33.9882	−	58.8693i	1.19055	−	2.06210i
$816$	15.0640	+	24.4871i	0.527344	+	0.857221i
$817$	−0.00175419	+	19.3170i	−6.13712e−5	+	0.675817i
$818$	27.2818	+	6.01964i	0.953885	+	0.210472i
$819$	4.54800	−	4.20267i	0.158920	−	0.146853i
$820$	−52.2102	−	74.2477i	−1.82326	−	2.59284i
$821$	−22.1580	−	38.3788i	−0.773320	−	1.33943i	−0.935734	−	0.352706i	$-0.885261\pi$
$821$	−22.1580	−	38.3788i	−0.773320	−	1.33943i	0.162414	−	0.986723i	$-0.448072\pi$
$822$	−28.2065	+	22.7820i	−0.983815	+	0.794612i
$823$	9.13248	−	5.27264i	0.318338	−	0.183793i	−0.332313	−	0.943169i	$-0.607829\pi$
$823$	9.13248	−	5.27264i	0.318338	−	0.183793i	0.650652	+	0.759376i	$0.274496\pi$
$824$	−8.08665	+	10.6044i	−0.281712	+	0.369421i
$825$	84.4859	+	12.8225i	2.94142	+	0.446422i
$826$	−0.217858	−	0.688559i	−0.00758026	−	0.0239580i
$827$	−20.1676	+	11.6437i	−0.701295	+	0.404893i	−0.807830	−	0.589416i	$-0.799358\pi$
$827$	−20.1676	+	11.6437i	−0.701295	+	0.404893i	0.106535	+	0.994309i	$0.466025\pi$
$828$	−18.1524	−	16.4282i	−0.630841	−	0.570919i
$829$			15.9017i			0.552288i	0.961116	+	0.276144i	$0.0890566\pi$
$829$			15.9017i			0.552288i	−0.961116	+	0.276144i	$0.910943\pi$
$830$	−9.68601	+	3.06463i	−0.336206	+	0.106375i
$831$	20.6983	−	25.9005i	0.718017	−	0.898480i
$832$	−12.5165	−	12.3674i	−0.433931	−	0.428761i
$833$	21.9908	+	12.6964i	0.761937	+	0.439905i
$834$	−0.505942	−	0.626411i	−0.0175193	−	0.0216908i
$835$	92.9037			3.21506
$836$	32.3277	−	22.7281i	1.11808	−	0.786067i
$837$	−14.4891	−	7.03239i	−0.500817	−	0.243075i
$838$	24.2481	+	22.1748i	0.837637	+	0.766015i
$839$	22.4304	−	38.8506i	0.774383	−	1.34127i	−0.160758	−	0.986994i	$-0.551394\pi$
$839$	22.4304	−	38.8506i	0.774383	−	1.34127i	0.935141	−	0.354277i	$-0.115273\pi$
$840$	−5.03780	+	17.6173i	−0.173821	+	0.607854i
$841$	−1.07692	+	1.86528i	−0.0371353	+	0.0643202i
$842$	−9.36515	+	2.96311i	−0.322744	+	0.102115i
$843$	13.9522	+	2.11754i	0.480539	+	0.0729318i
$844$	−35.3033	−	16.3764i	−1.21519	−	0.563700i
$845$	−16.2652	−	28.1722i	−0.559541	−	0.969153i
$846$	−0.0592397	−	11.4176i	−0.00203670	−	0.392545i
$847$		−	8.96053i		−	0.307888i
$848$	−20.4682	−	24.1961i	−0.702881	−	0.830897i
$849$	1.55319	−	0.607753i	0.0533055	−	0.0208580i
$850$	47.1345	+	43.1043i	1.61670	+	1.47846i
$851$	−33.7326	+	19.4755i	−1.15634	+	0.667613i
$852$	−0.228804	−	0.459222i	−0.00783871	−	0.0157327i
$853$	−45.7334	−	26.4042i	−1.56588	−	0.904063i	−0.996641	−	0.0818919i	$-0.973904\pi$
$853$	−45.7334	−	26.4042i	−1.56588	−	0.904063i	−0.569241	−	0.822171i	$-0.692763\pi$
$854$	16.7407	+	3.69378i	0.572855	+	0.126399i
$855$	50.8346	−	11.4886i	1.73851	−	0.392901i
$856$	−13.4862	+	17.6850i	−0.460947	+	0.604460i
$857$	13.8910	+	8.01999i	0.474508	+	0.273958i	0.718125	−	0.695914i	$-0.245001\pi$
$857$	13.8910	+	8.01999i	0.474508	+	0.273958i	−0.243617	+	0.969872i	$0.578334\pi$
$858$	15.3451	+	18.9989i	0.523874	+	0.648612i
$859$	22.0938	+	38.2675i	0.753829	+	1.30567i	0.945954	+	0.324300i	$0.105129\pi$
$859$	22.0938	+	38.2675i	0.753829	+	1.30567i	−0.192125	+	0.981371i	$0.561538\pi$
$860$	28.8953	−	20.3189i	0.985322	−	0.692867i
$861$	−17.2372	+	6.74479i	−0.587443	+	0.229862i
$862$	−20.6702	−	4.56081i	−0.704029	−	0.155342i
$863$	−22.0809			−0.751642			−0.375821	−	0.926692i	$-0.622639\pi$
$863$	−22.0809			−0.751642			−0.375821	+	0.926692i	$0.622639\pi$
$864$	−15.5312	−	24.9556i	−0.528382	−	0.849007i
$865$	19.9728	+	34.5939i	0.679096	+	1.17623i
$866$	0.508728	+	0.112249i	0.0172873	+	0.00381438i
$867$	0.0570813	−	0.376102i	0.00193858	−	0.0127731i
$868$	−0.518616	−	5.79447i	−0.0176030	−	0.196677i
$869$	−16.9424	+	29.3451i	−0.574732	+	0.995465i
$870$	53.8291	−	8.45564i	1.82498	−	0.286673i
$871$	3.23120	+	1.86554i	0.109485	+	0.0632112i
$872$	−8.68676	−	20.7952i	−0.294171	−	0.704215i
$873$	24.7304	+	7.68371i	0.836998	+	0.260054i
$874$	−23.9824	+	7.58557i	−0.811217	+	0.256586i
$875$			22.0072i			0.743981i
$876$	−6.17741	−	12.3984i	−0.208715	−	0.418902i
$877$	2.71290	+	1.56630i	0.0916082	+	0.0528900i	0.545104	−	0.838368i	$-0.316490\pi$
$877$	2.71290	+	1.56630i	0.0916082	+	0.0528900i	−0.453496	+	0.891258i	$0.649823\pi$
$878$	32.7072	−	10.3485i	1.10382	−	0.349244i
$879$	25.0390	+	20.0099i	0.844545	+	0.674916i
$880$	−68.0043	−	24.4443i	−2.29242	−	0.824017i
$881$		−	14.0763i		−	0.474242i	−0.971480	−	0.237121i	$-0.923796\pi$
$881$		−	14.0763i		−	0.474242i	0.971480	−	0.237121i	$-0.0762038\pi$
$882$	−22.5507	−	12.8641i	−0.759320	−	0.433157i
$883$	−20.2613	−	35.0935i	−0.681846	−	1.18099i	−0.974417	−	0.224748i	$-0.927844\pi$
$883$	−20.2613	−	35.0935i	−0.681846	−	1.18099i	0.292571	−	0.956244i	$-0.405489\pi$
$884$	1.62728	+	18.1815i	0.0547313	+	0.611510i
$885$	3.71377	+	0.563643i	0.124837	+	0.0189466i
$886$	3.06703	−	13.9002i	0.103039	−	0.466986i
$887$	3.18313	+	5.51335i	0.106879	+	0.185120i	0.914504	−	0.404576i	$-0.132581\pi$
$887$	3.18313	+	5.51335i	0.106879	+	0.185120i	−0.807625	+	0.589696i	$0.799248\pi$
$888$	−45.3674	+	11.3464i	−1.52243	+	0.380762i
$889$	5.53280	+	9.58308i	0.185564	+	0.321406i
$890$	−33.8927	−	30.9947i	−1.13608	−	1.03894i
$891$	17.5507	+	36.8288i	0.587971	+	1.23381i
$892$	−13.4439	+	28.9815i	−0.450135	+	0.970374i
$893$	−10.1585	−	5.86623i	−0.339941	−	0.196306i
$894$	−3.50014	+	9.08368i	−0.117062	+	0.303804i
$895$	−22.7943	−	13.1603i	−0.761928	−	0.439900i
$896$	4.83671	−	9.45200i	0.161583	−	0.315769i
$897$	−5.66439	−	14.4761i	−0.189128	−	0.483343i
$898$	−2.56699	−	2.34750i	−0.0856616	−	0.0783372i
$899$	−14.9824	+	8.65007i	−0.499690	+	0.288496i
$900$	−48.4187	−	43.8196i	−1.61396	−	1.46065i
$901$			32.8780i			1.09532i
$902$	−22.0208	−	69.5987i	−0.733213	−	2.31738i
$903$	−2.62490	−	6.70828i	−0.0873511	−	0.223238i
$904$	6.55800	−	8.59979i	0.218116	−	0.286025i
$905$			16.0167i			0.532413i
$906$	0.296657	+	1.88853i	0.00985576	+	0.0627423i
$907$	6.76564	−	11.7184i	0.224649	−	0.389104i	−0.731565	−	0.681772i	$-0.761210\pi$
$907$	6.76564	−	11.7184i	0.224649	−	0.389104i	0.956214	+	0.292668i	$0.0945430\pi$
$908$	33.9398	−	3.03767i	1.12633	−	0.100809i
$909$	−14.4286	+	13.3330i	−0.478565	+	0.442227i
$910$	−7.85138	+	8.58548i	−0.260271	+	0.284606i
$911$	36.3642			1.20480			0.602400	−	0.798195i	$-0.294211\pi$
$911$	36.3642			1.20480			0.602400	+	0.798195i	$0.294211\pi$
$912$	−30.1877	+	0.839908i	−0.999613	+	0.0278121i
$913$	−8.17059			−0.270407
$914$	−8.63461	+	9.44194i	−0.285608	+	0.312312i
$915$	−55.6650	+	69.6556i	−1.84023	+	2.30274i
$916$	−13.9677	+	1.25013i	−0.461506	+	0.0413056i
$917$	6.08718	−	10.5433i	0.201017	−	0.348171i
$918$	−4.41916	+	30.1717i	−0.145854	+	0.995814i
$919$		−	17.2143i		−	0.567847i	−0.958847	−	0.283924i	$-0.908364\pi$
$919$		−	17.2143i		−	0.567847i	0.958847	−	0.283924i	$-0.0916362\pi$
$920$	36.5756	+	27.8917i	1.20586	+	0.919563i
$921$	3.28847	−	1.28675i	0.108359	−	0.0423999i
$922$	10.2449	+	32.3799i	0.337399	+	1.06638i
$923$		−	0.325764i		−	0.0107226i
$924$	−8.13701	+	12.2865i	−0.267688	+	0.404195i
$925$	−89.9763	+	51.9478i	−2.95840	+	1.70803i
$926$	−32.6167	−	29.8278i	−1.07185	−	0.980203i
$927$	−13.7966	+	3.11934i	−0.453141	+	0.102453i
$928$	−31.5505	−	1.21970i	−1.03570	−	0.0400386i
$929$	23.8112	+	13.7474i	0.781219	+	0.451037i	0.836862	−	0.547414i	$-0.184388\pi$
$929$	23.8112	+	13.7474i	0.781219	+	0.451037i	−0.0556433	+	0.998451i	$0.517721\pi$
$930$	28.2350	+	10.8795i	0.925861	+	0.356754i
$931$	−23.1009	+	13.3345i	−0.757102	+	0.437022i
$932$	−2.54119	+	5.47814i	−0.0832394	+	0.179442i
$933$	−6.35269	−	5.07673i	−0.207978	−	0.166205i
$934$	28.0067	+	25.6120i	0.916408	+	0.838051i
$935$	37.4839	+	64.9240i	1.22585	+	2.12324i
$936$	−1.76017	−	18.5800i	−0.0575328	−	0.607307i
$937$	4.42032	+	7.65623i	0.144406	+	0.250118i	0.929151	−	0.369700i	$-0.120540\pi$
$937$	4.42032	+	7.65623i	0.144406	+	0.250118i	−0.784745	+	0.619818i	$0.787206\pi$
$938$	−0.485095	+	2.19851i	−0.0158389	+	0.0717839i
$939$	7.11090	−	46.8528i	0.232055	−	1.52898i
$940$	1.91228	+	21.3658i	0.0623718	+	0.696877i
$941$	25.6283	+	44.3894i	0.835457	+	1.44705i	0.893658	+	0.448749i	$0.148130\pi$
$941$	25.6283	+	44.3894i	0.835457	+	1.44705i	−0.0582006	+	0.998305i	$0.518536\pi$
$942$	−3.01960	−	1.16352i	−0.0983839	−	0.0379095i
$943$			46.4649i			1.51311i
$944$	−2.04830	−	0.736268i	−0.0666666	−	0.0239635i
$945$	−16.0914	+	10.8988i	−0.523453	+	0.354538i
$946$	27.0860	−	8.56994i	0.880642	−	0.278633i
$947$	5.79566	+	3.34613i	0.188334	+	0.108735i	0.591202	−	0.806523i	$-0.298653\pi$
$947$	5.79566	+	3.34613i	0.188334	+	0.108735i	−0.402869	+	0.915258i	$0.631987\pi$
$948$	23.1772	−	11.5479i	0.752761	−	0.375058i
$949$		−	8.79518i		−	0.285504i
$950$	−63.9692	+	20.2333i	−2.07543	+	0.656454i
$951$	1.23529	−	8.13917i	0.0400570	−	0.263931i
$952$	−10.1637	+	4.24568i	−0.329409	+	0.137603i
$953$	2.84919	+	1.64498i	0.0922944	+	0.0532862i	0.545437	−	0.838152i	$-0.316364\pi$
$953$	2.84919	+	1.64498i	0.0922944	+	0.0532862i	−0.453142	+	0.891438i	$0.649697\pi$
$954$	−0.174406	−	33.6142i	−0.00564661	−	1.08830i
$955$	33.3790	−	57.8141i	1.08012	−	1.87082i
$956$	4.98867	+	55.7382i	0.161345	+	1.80270i
$957$	43.3267	+	6.57574i	1.40055	+	0.212563i
$958$	40.6040	+	8.95915i	1.31185	+	0.289457i
$959$	−6.94573	−	12.0304i	−0.224289	−	0.388481i
$960$	33.0137	+	44.2697i	1.06551	+	1.42880i
$961$	21.3930			0.690097
$962$	−28.9952	−	6.39770i	−0.934842	−	0.206270i
$963$	−23.0087	+	5.20214i	−0.741446	+	0.167637i
$964$	−8.71803	+	6.13042i	−0.280789	+	0.197448i
$965$	−10.1724	−	17.6192i	−0.327462	−	0.567181i
$966$	7.29715	−	5.89379i	0.234782	−	0.189629i
$967$	13.3653	+	7.71645i	0.429799	+	0.248144i	0.699261	−	0.714867i	$-0.253513\pi$
$967$	13.3653	+	7.71645i	0.429799	+	0.248144i	−0.269462	+	0.963011i	$0.586846\pi$
$968$	−21.4743	−	16.3758i	−0.690209	−	0.526338i
$969$	24.4724	+	19.5607i	0.786167	+	0.628380i
$970$	−47.5108	−	10.4831i	−1.52548	−	0.336592i
$971$	47.8060	+	27.6008i	1.53417	+	0.885753i	0.999163	+	0.0409045i	$0.0130239\pi$
$971$	47.8060	+	27.6008i	1.53417	+	0.885753i	0.535006	+	0.844848i	$0.320309\pi$
$972$	4.35808	−	30.8708i	0.139785	−	0.990182i
$973$	0.267171	−	0.154251i	0.00856510	−	0.00494506i
$974$	15.0035	+	13.7207i	0.480744	+	0.439638i
$975$	−15.1088	−	38.6127i	−0.483870	−	1.23659i
$976$	39.4467	−	33.3691i	1.26266	−	1.06812i
$977$		−	18.4069i		−	0.588889i	−0.955669	−	0.294444i	$-0.904865\pi$
$977$		−	18.4069i		−	0.588889i	0.955669	−	0.294444i	$-0.0951345\pi$
$978$	−41.2726	+	6.48324i	−1.31975	+	0.207311i
$979$	−18.4688	−	31.9889i	−0.590266	−	1.02237i
$980$	44.2473	+	20.5254i	1.41343	+	0.655658i
$981$	7.09242	−	22.8273i	0.226444	−	0.728820i
$982$	0.488984	−	0.154713i	0.0156041	−	0.00493710i
$983$	−28.0594	+	48.6003i	−0.894956	+	1.55011i	−0.0610962	+	0.998132i	$0.519460\pi$
$983$	−28.0594	+	48.6003i	−0.894956	+	1.55011i	−0.833859	+	0.551977i	$0.813874\pi$
$984$	−15.3377	+	53.6361i	−0.488947	+	1.70985i
$985$	−38.8119	+	67.2242i	−1.23665	+	2.14194i
$986$	24.1719	+	22.1051i	0.769790	+	0.703969i
$987$	4.32496	+	0.656404i	0.137665	+	0.0208936i
$988$	−17.3935	−	8.07040i	−0.553362	−	0.256754i
$989$	−18.0829			−0.575004
$990$	−38.6677	−	66.1791i	−1.22894	−	2.10331i
$991$	17.3227	+	10.0013i	0.550273	+	0.317700i	0.749232	−	0.662308i	$-0.230423\pi$
$991$	17.3227	+	10.0013i	0.550273	+	0.317700i	−0.198959	+	0.980008i	$0.563756\pi$
$992$	−14.8345	−	9.34678i	−0.470995	−	0.296761i
$993$	−4.35450	−	3.47989i	−0.138186	−	0.110431i
$994$	0.187414	−	0.0592974i	0.00594442	−	0.00188080i
$995$		−	72.0969i		−	2.28563i
$996$	5.20581	+	3.44768i	0.164952	+	0.109244i
$997$	−1.79606	+	1.03695i	−0.0568817	+	0.0328407i	−0.528171	−	0.849138i	$-0.677122\pi$
$997$	−1.79606	+	1.03695i	−0.0568817	+	0.0328407i	0.471289	+	0.881979i	$0.343789\pi$
$998$	−8.30090	−	26.2357i	−0.262760	−	0.830476i
$999$	−44.6233	−	21.6582i	−1.41182	−	0.685235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.u.d.11.20	✓	136
3.2	odd	2	inner	456.2.u.d.11.49	yes	136
8.3	odd	2	inner	456.2.u.d.11.43	yes	136
19.7	even	3	inner	456.2.u.d.83.26	yes	136
24.11	even	2	inner	456.2.u.d.11.26	yes	136
57.26	odd	6	inner	456.2.u.d.83.43	yes	136
152.83	odd	6	inner	456.2.u.d.83.49	yes	136
456.83	even	6	inner	456.2.u.d.83.20	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.u.d.11.20	✓	136	1.1	even	1	trivial
456.2.u.d.11.26	yes	136	24.11	even	2	inner
456.2.u.d.11.43	yes	136	8.3	odd	2	inner
456.2.u.d.11.49	yes	136	3.2	odd	2	inner
456.2.u.d.83.20	yes	136	456.83	even	6	inner
456.2.u.d.83.26	yes	136	19.7	even	3	inner
456.2.u.d.83.43	yes	136	57.26	odd	6	inner
456.2.u.d.83.49	yes	136	152.83	odd	6	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.954387 + 1.04362i) q^{2} +(-1.35307 - 1.08130i) q^{3} +(-0.178291 - 1.99204i) q^{4} +(-1.99273 + 3.45151i) q^{5} +(2.41982 - 0.380112i) q^{6} +0.938475i q^{7} +(2.24909 + 1.71511i) q^{8} +(0.661584 + 2.92614i) q^{9} +O(q^{10})\)	\(q+(-0.954387 + 1.04362i) q^{2} +(-1.35307 - 1.08130i) q^{3} +(-0.178291 - 1.99204i) q^{4} +(-1.99273 + 3.45151i) q^{5} +(2.41982 - 0.380112i) q^{6} +0.938475i q^{7} +(2.24909 + 1.71511i) q^{8} +(0.661584 + 2.92614i) q^{9} +(-1.70023 - 5.37373i) q^{10} -4.53299i q^{11} +(-1.91275 + 2.88815i) q^{12} +(-1.90481 + 1.09974i) q^{13} +(-0.979413 - 0.895668i) q^{14} +(6.42841 - 2.51539i) q^{15} +(-3.93642 + 0.710325i) q^{16} +(3.59371 + 2.07483i) q^{17} +(-3.68519 - 2.10223i) q^{18} +(-3.77512 + 2.17911i) q^{19} +(7.23082 + 3.35422i) q^{20} +(1.01477 - 1.26982i) q^{21} +(4.73072 + 4.32622i) q^{22} +(-2.04022 - 3.53376i) q^{23} +(-1.18863 - 4.75260i) q^{24} +(-5.44194 - 9.42572i) q^{25} +(0.670210 - 3.03747i) q^{26} +(2.26887 - 4.67464i) q^{27} +(1.86948 - 0.167322i) q^{28} +(-2.79078 - 4.83378i) q^{29} +(-3.51008 + 9.10948i) q^{30} -3.09951i q^{31} +(3.01556 - 4.78606i) q^{32} +(-4.90152 + 6.13344i) q^{33} +(-5.59512 + 1.77028i) q^{34} +(-3.23916 - 1.87013i) q^{35} +(5.71103 - 1.83960i) q^{36} -9.54582i q^{37} +(1.32876 - 6.01950i) q^{38} +(3.76648 + 0.571642i) q^{39} +(-10.4015 + 4.34502i) q^{40} +(-9.86165 - 5.69363i) q^{41} +(0.356726 + 2.27094i) q^{42} +(2.21581 - 3.83790i) q^{43} +(-9.02988 + 0.808191i) q^{44} +(-11.4180 - 3.54755i) q^{45} +(5.63506 + 1.24336i) q^{46} +(1.34559 + 2.33064i) q^{47} +(6.09432 + 3.29534i) q^{48} +6.11926 q^{49} +(15.0306 + 3.31646i) q^{50} +(-2.61902 - 6.69325i) q^{51} +(2.53033 + 3.59837i) q^{52} +(3.96153 + 6.86157i) q^{53} +(2.71318 + 6.82925i) q^{54} +(15.6456 + 9.03302i) q^{55} +(-1.60958 + 2.11072i) q^{56} +(7.46425 + 1.13355i) q^{57} +(7.70812 + 1.70077i) q^{58} +(0.471250 + 0.272077i) q^{59} +(-6.15688 - 12.3572i) q^{60} +(-11.1864 + 6.45845i) q^{61} +(3.23472 + 2.95814i) q^{62} +(-2.74611 + 0.620880i) q^{63} +(2.11682 + 7.71486i) q^{64} -8.76594i q^{65} +(-1.72304 - 10.9690i) q^{66} +(-0.848171 - 1.46907i) q^{67} +(3.49241 - 7.52872i) q^{68} +(-1.06050 + 6.98750i) q^{69} +(5.04311 - 1.59563i) q^{70} +(-0.0740547 + 0.128266i) q^{71} +(-3.53068 + 7.71585i) q^{72} +(-1.99938 + 3.46302i) q^{73} +(9.96222 + 9.11041i) q^{74} +(-2.82871 + 18.6380i) q^{75} +(5.01393 + 7.13165i) q^{76} +4.25410 q^{77} +(-4.19126 + 3.38521i) q^{78} +(-6.47368 - 3.73758i) q^{79} +(5.39254 - 15.0021i) q^{80} +(-8.12461 + 3.87178i) q^{81} +(15.3538 - 4.85791i) q^{82} -1.80247i q^{83} +(-2.71045 - 1.79507i) q^{84} +(-14.3226 + 8.26914i) q^{85} +(1.89057 + 5.97531i) q^{86} +(-1.45064 + 9.55809i) q^{87} +(7.77455 - 10.1951i) q^{88} +(7.05692 - 4.07431i) q^{89} +(14.5995 - 8.53030i) q^{90} +(-1.03208 - 1.78761i) q^{91} +(-6.67562 + 4.69422i) q^{92} +(-3.35150 + 4.19385i) q^{93} +(-3.71652 - 0.820039i) q^{94} +(0.00157758 - 17.3722i) q^{95} +(-9.25542 + 3.21514i) q^{96} +(4.31610 - 7.47570i) q^{97} +(-5.84015 + 6.38620i) q^{98} +(13.2642 - 2.99895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more