LMFDB - Embedded newform 686.2.g.h.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			373.2
Character	$\chi$	$=$	686.373
Dual form			686.2.g.h.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826239 + 0.563320i) q^{2} +(-0.539257 + 0.500357i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-2.65055 - 0.817585i) q^{5} +(0.163694 - 0.717189i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-0.183750 + 2.45197i) q^{9} +O(q^{10})$	\(q+(-0.826239 + 0.563320i) q^{2} +(-0.539257 + 0.500357i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-2.65055 - 0.817585i) q^{5} +(0.163694 - 0.717189i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-0.183750 + 2.45197i) q^{9} +(2.65055 - 0.817585i) q^{10} +(0.207285 + 2.76602i) q^{11} +(0.268757 + 0.684781i) q^{12} +(-3.14454 - 1.51433i) q^{13} +(1.83841 - 0.885332i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(4.34356 + 0.654686i) q^{17} +(-1.22942 - 2.12942i) q^{18} +(2.26879 - 3.92965i) q^{19} +(-1.72942 + 2.16863i) q^{20} +(-1.72942 - 2.16863i) q^{22} +(-3.18512 + 0.480079i) q^{23} +(-0.607808 - 0.414397i) q^{24} +(2.22576 + 1.51750i) q^{25} +(3.45119 - 0.520184i) q^{26} +(-2.50375 - 3.13960i) q^{27} +(5.83599 - 7.31810i) q^{29} +(-1.02024 + 1.76711i) q^{30} +(-4.56829 - 7.91252i) q^{31} +(0.988831 + 0.149042i) q^{32} +(-1.49578 - 1.38788i) q^{33} +(-3.95761 + 1.90589i) q^{34} +(2.21534 + 1.06685i) q^{36} +(-3.06154 - 7.80067i) q^{37} +(0.339093 + 4.52488i) q^{38} +(2.45342 - 0.756780i) q^{39} +(0.207285 - 2.76602i) q^{40} +(0.176526 + 0.773410i) q^{41} +(0.242866 - 1.06407i) q^{43} +(2.65055 + 0.817585i) q^{44} +(2.49173 - 6.34883i) q^{45} +(2.36123 - 2.19090i) q^{46} +(-2.41018 + 1.64323i) q^{47} +0.735633 q^{48} -2.69384 q^{50} +(-2.66987 + 1.82029i) q^{51} +(-2.55848 + 2.37392i) q^{52} +(3.04900 - 7.76873i) q^{53} +(3.83730 + 1.18365i) q^{54} +(1.71204 - 7.50094i) q^{55} +(0.742771 + 3.25429i) q^{57} +(-0.699489 + 9.33403i) q^{58} +(3.22641 - 0.995216i) q^{59} +(-0.152485 - 2.03478i) q^{60} +(0.144277 + 0.367612i) q^{61} +(8.23178 + 3.96422i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(7.09666 + 6.58473i) q^{65} +(2.01769 + 0.304118i) q^{66} +(5.94527 + 10.2975i) q^{67} +(2.19631 - 3.80412i) q^{68} +(1.47738 - 1.85258i) q^{69} +(4.55451 + 5.71117i) q^{71} +(-2.43138 + 0.366472i) q^{72} +(-7.57967 - 5.16773i) q^{73} +(6.92384 + 4.72059i) q^{74} +(-1.95955 + 0.295354i) q^{75} +(-2.82913 - 3.54762i) q^{76} +(-1.60080 + 2.00734i) q^{78} +(2.66962 - 4.62391i) q^{79} +(1.38689 + 2.40216i) q^{80} +(-4.37306 - 0.659132i) q^{81} +(-0.581530 - 0.539581i) q^{82} +(9.31611 - 4.48640i) q^{83} +(-10.9775 - 5.28650i) q^{85} +(0.398744 + 1.01598i) q^{86} +(0.514567 + 6.86642i) q^{87} +(-2.65055 + 0.817585i) q^{88} +(-0.124404 + 1.66006i) q^{89} +(1.51766 + 6.64929i) q^{90} +(-0.716761 + 3.14033i) q^{92} +(6.42257 + 1.98110i) q^{93} +(1.06572 - 2.71540i) q^{94} +(-9.22635 + 8.56080i) q^{95} +(-0.607808 + 0.414397i) q^{96} -12.6470 q^{97} -6.82029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

Coefficient data

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

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

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

$2$	−0.826239	+	0.563320i	−0.584239	+	0.398327i
$2$	−0.826239	+	0.563320i	−0.584239	+	0.398327i
$3$	−0.539257	+	0.500357i	−0.311340	+	0.288881i	−0.820329	−	0.571892i	$-0.806210\pi$
$3$	−0.539257	+	0.500357i	−0.311340	+	0.288881i	0.508989	+	0.860773i	$0.330019\pi$
$4$	0.365341	−	0.930874i	0.182671	−	0.465437i
$5$	−2.65055	−	0.817585i	−1.18536	−	0.365635i	−0.361470	−	0.932384i	$-0.617725\pi$
$5$	−2.65055	−	0.817585i	−1.18536	−	0.365635i	−0.823891	+	0.566749i	$0.808201\pi$
$6$	0.163694	−	0.717189i	0.0668277	−	0.292791i
$7$		0			0
$7$		0			0
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	−0.183750	+	2.45197i	−0.0612499	+	0.817323i
$10$	2.65055	−	0.817585i	0.838177	−	0.258543i
$11$	0.207285	+	2.76602i	0.0624987	+	0.833987i	0.937081	+	0.349111i	$0.113516\pi$
$11$	0.207285	+	2.76602i	0.0624987	+	0.833987i	−0.874583	+	0.484876i	$0.838865\pi$
$12$	0.268757	+	0.684781i	0.0775834	+	0.197679i
$13$	−3.14454	−	1.51433i	−0.872139	−	0.420000i	−0.0563916	−	0.998409i	$-0.517960\pi$
$13$	−3.14454	−	1.51433i	−0.872139	−	0.420000i	−0.815747	+	0.578409i	$0.803674\pi$
$14$		0			0
$15$	1.83841	−	0.885332i	0.474676	−	0.228592i
$16$	−0.733052	−	0.680173i	−0.183263	−	0.170043i
$17$	4.34356	+	0.654686i	1.05347	+	0.158785i	0.652870	−	0.757470i	$-0.273565\pi$
$17$	4.34356	+	0.654686i	1.05347	+	0.158785i	0.400597	+	0.916254i	$0.368803\pi$
$18$	−1.22942	−	2.12942i	−0.289778	−	0.501910i
$19$	2.26879	−	3.92965i	0.520495	−	0.901524i	−0.479221	−	0.877694i	$-0.659081\pi$
$19$	2.26879	−	3.92965i	0.520495	−	0.901524i	0.999716	−	0.0238296i	$-0.00758590\pi$
$20$	−1.72942	+	2.16863i	−0.386711	+	0.484920i
$21$		0			0
$22$	−1.72942	−	2.16863i	−0.368714	−	0.462353i
$23$	−3.18512	+	0.480079i	−0.664143	+	0.100103i	−0.472458	−	0.881353i	$-0.656633\pi$
$23$	−3.18512	+	0.480079i	−0.664143	+	0.100103i	−0.191685	+	0.981457i	$0.561395\pi$
$24$	−0.607808	−	0.414397i	−0.124068	−	0.0845884i
$25$	2.22576	+	1.51750i	0.445152	+	0.303499i
$26$	3.45119	−	0.520184i	0.676835	−	0.102016i
$27$	−2.50375	−	3.13960i	−0.481847	−	0.604217i
$28$		0			0
$29$	5.83599	−	7.31810i	1.08372	−	1.35894i	0.155099	−	0.987899i	$-0.450430\pi$
$29$	5.83599	−	7.31810i	1.08372	−	1.35894i	0.928618	−	0.371038i	$-0.120998\pi$
$30$	−1.02024	+	1.76711i	−0.186270	+	0.322628i
$31$	−4.56829	−	7.91252i	−0.820490	−	1.42113i	−0.905318	−	0.424734i	$-0.860367\pi$
$31$	−4.56829	−	7.91252i	−0.820490	−	1.42113i	0.0848282	−	0.996396i	$-0.472966\pi$
$32$	0.988831	+	0.149042i	0.174802	+	0.0263472i
$33$	−1.49578	−	1.38788i	−0.260382	−	0.241599i
$34$	−3.95761	+	1.90589i	−0.678725	+	0.326857i
$35$		0			0
$36$	2.21534	+	1.06685i	0.369224	+	0.177809i
$37$	−3.06154	−	7.80067i	−0.503314	−	1.28242i	−0.926471	−	0.376366i	$-0.877173\pi$
$37$	−3.06154	−	7.80067i	−0.503314	−	1.28242i	0.423157	−	0.906056i	$-0.360922\pi$
$38$	0.339093	+	4.52488i	0.0550082	+	0.734033i
$39$	2.45342	−	0.756780i	0.392862	−	0.121182i
$40$	0.207285	−	2.76602i	0.0327746	−	0.437346i
$41$	0.176526	+	0.773410i	0.0275687	+	0.120786i	0.986840	−	0.161700i	$-0.0516978\pi$
$41$	0.176526	+	0.773410i	0.0275687	+	0.120786i	−0.959271	+	0.282487i	$0.908841\pi$
$42$		0			0
$43$	0.242866	−	1.06407i	0.0370367	−	0.162269i	−0.953028	−	0.302883i	$-0.902051\pi$
$43$	0.242866	−	1.06407i	0.0370367	−	0.162269i	0.990064	+	0.140615i	$0.0449079\pi$
$44$	2.65055	+	0.817585i	0.399585	+	0.123256i
$45$	2.49173	−	6.34883i	0.371445	−	0.946427i
$46$	2.36123	−	2.19090i	0.348144	−	0.323031i
$47$	−2.41018	+	1.64323i	−0.351561	+	0.239690i	−0.726204	−	0.687479i	$-0.758717\pi$
$47$	−2.41018	+	1.64323i	−0.351561	+	0.239690i	0.374644	+	0.927169i	$0.377765\pi$
$48$	0.735633			0.106179
$49$		0			0
$50$	−2.69384			−0.380967
$51$	−2.66987	+	1.82029i	−0.373856	+	0.254891i
$52$	−2.55848	+	2.37392i	−0.354797	+	0.329204i
$53$	3.04900	−	7.76873i	0.418813	−	1.06712i	−0.553379	−	0.832930i	$-0.686662\pi$
$53$	3.04900	−	7.76873i	0.418813	−	1.06712i	0.972191	−	0.234188i	$-0.0752430\pi$
$54$	3.83730	+	1.18365i	0.522190	+	0.161074i
$55$	1.71204	−	7.50094i	0.230852	−	1.01143i
$56$		0			0
$57$	0.742771	+	3.25429i	0.0983825	+	0.431042i
$58$	−0.699489	+	9.33403i	−0.0918474	+	1.22562i
$59$	3.22641	−	0.995216i	0.420043	−	0.129566i	−0.0775263	−	0.996990i	$-0.524702\pi$
$59$	3.22641	−	0.995216i	0.420043	−	0.129566i	0.497569	+	0.867424i	$0.334226\pi$
$60$	−0.152485	−	2.03478i	−0.0196858	−	0.262688i
$61$	0.144277	+	0.367612i	0.0184728	+	0.0470679i	0.939813	−	0.341690i	$-0.110999\pi$
$61$	0.144277	+	0.367612i	0.0184728	+	0.0470679i	−0.921340	+	0.388758i	$0.872904\pi$
$62$	8.23178	+	3.96422i	1.04544	+	0.503456i
$63$		0			0
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	7.09666	+	6.58473i	0.880232	+	0.816736i
$66$	2.01769	+	0.304118i	0.248361	+	0.0374343i
$67$	5.94527	+	10.2975i	0.726330	+	1.25804i	0.958424	+	0.285347i	$0.0921088\pi$
$67$	5.94527	+	10.2975i	0.726330	+	1.25804i	−0.232094	+	0.972693i	$0.574558\pi$
$68$	2.19631	−	3.80412i	0.266342	−	0.461317i
$69$	1.47738	−	1.85258i	0.177856	−	0.223025i
$70$		0			0
$71$	4.55451	+	5.71117i	0.540521	+	0.677791i	0.974824	−	0.222975i	$-0.0715769\pi$
$71$	4.55451	+	5.71117i	0.540521	+	0.677791i	−0.434304	+	0.900767i	$0.643005\pi$
$72$	−2.43138	+	0.366472i	−0.286541	+	0.0431891i
$73$	−7.57967	−	5.16773i	−0.887133	−	0.604837i	0.0316941	−	0.999498i	$-0.489910\pi$
$73$	−7.57967	−	5.16773i	−0.887133	−	0.604837i	−0.918827	+	0.394661i	$0.870862\pi$
$74$	6.92384	+	4.72059i	0.804880	+	0.548758i
$75$	−1.95955	+	0.295354i	−0.226269	+	0.0341046i
$76$	−2.82913	−	3.54762i	−0.324523	−	0.406939i
$77$		0			0
$78$	−1.60080	+	2.00734i	−0.181255	+	0.227287i
$79$	2.66962	−	4.62391i	0.300355	−	0.520230i	−0.675861	−	0.737029i	$-0.736228\pi$
$79$	2.66962	−	4.62391i	0.300355	−	0.520230i	0.976216	+	0.216798i	$0.0695614\pi$
$80$	1.38689	+	2.40216i	0.155059	+	0.268570i
$81$	−4.37306	−	0.659132i	−0.485895	−	0.0732369i
$82$	−0.581530	−	0.539581i	−0.0642193	−	0.0595868i
$83$	9.31611	−	4.48640i	1.02258	−	0.492446i	0.154035	−	0.988065i	$-0.450773\pi$
$83$	9.31611	−	4.48640i	1.02258	−	0.492446i	0.868540	+	0.495619i	$0.165059\pi$
$84$		0			0
$85$	−10.9775	−	5.28650i	−1.19068	−	0.573402i
$86$	0.398744	+	1.01598i	0.0429977	+	0.109556i
$87$	0.514567	+	6.86642i	0.0551674	+	0.736157i
$88$	−2.65055	+	0.817585i	−0.282549	+	0.0871549i
$89$	−0.124404	+	1.66006i	−0.0131868	+	0.175966i	0.986721	+	0.162422i	$0.0519305\pi$
$89$	−0.124404	+	1.66006i	−0.0131868	+	0.175966i	−0.999908	+	0.0135444i	$0.995689\pi$
$90$	1.51766	+	6.64929i	0.159975	+	0.700897i
$91$		0			0
$92$	−0.716761	+	3.14033i	−0.0747275	+	0.327402i
$93$	6.42257	+	1.98110i	0.665989	+	0.205431i
$94$	1.06572	−	2.71540i	0.109920	−	0.280073i
$95$	−9.22635	+	8.56080i	−0.946603	+	0.878319i
$96$	−0.607808	+	0.414397i	−0.0620342	+	0.0422942i
$97$	−12.6470			−1.28411			−0.642053	−	0.766660i	$-0.721917\pi$
$97$	−12.6470			−1.28411			−0.642053	+	0.766660i	$0.721917\pi$
$98$		0			0
$99$	−6.82029			−0.685465
$100$	2.22576	−	1.51750i	0.222576	−	0.151750i
$101$	−5.06039	+	4.69536i	−0.503528	+	0.467205i	−0.890563	−	0.454859i	$-0.849690\pi$
$101$	−5.06039	+	4.69536i	−0.503528	+	0.467205i	0.387036	+	0.922065i	$0.373499\pi$
$102$	1.18055	−	3.00798i	0.116891	−	0.297835i
$103$	4.83812	+	1.49236i	0.476714	+	0.147047i	0.523795	−	0.851844i	$-0.324516\pi$
$103$	4.83812	+	1.49236i	0.476714	+	0.147047i	−0.0470811	+	0.998891i	$0.514992\pi$
$104$	0.776637	−	3.40267i	0.0761556	−	0.333659i
$105$		0			0
$106$	1.85708	+	8.13639i	0.180375	+	0.790276i
$107$	1.41587	−	18.8934i	0.136877	−	1.82650i	−0.332052	−	0.943261i	$-0.607741\pi$
$107$	1.41587	−	18.8934i	0.136877	−	1.82650i	0.468929	−	0.883236i	$-0.344640\pi$
$108$	−3.83730	+	1.18365i	−0.369244	+	0.113897i
$109$	−0.754921	−	10.0737i	−0.0723083	−	0.964887i	−0.908888	−	0.417041i	$-0.863067\pi$
$109$	−0.754921	−	10.0737i	−0.0723083	−	0.964887i	0.836579	−	0.547846i	$-0.184552\pi$
$110$	2.81088	+	7.16200i	0.268007	+	0.682870i
$111$	5.55408	+	2.67470i	0.527170	+	0.253872i
$112$		0			0
$113$	−4.13780	+	1.99266i	−0.389252	+	0.187454i	−0.618265	−	0.785969i	$-0.712164\pi$
$113$	−4.13780	+	1.99266i	−0.389252	+	0.187454i	0.229014	+	0.973423i	$0.426450\pi$
$114$	−2.44692	−	2.27041i	−0.229175	−	0.212643i
$115$	8.83481	+	1.33163i	0.823850	+	0.124175i
$116$	−4.68010	−	8.10617i	−0.434537	−	0.752639i
$117$	4.29090	−	7.43206i	0.396694	−	0.687094i
$118$	−2.10516	+	2.63979i	−0.193796	+	0.243012i
$119$		0			0
$120$	1.27222	+	1.59531i	0.116137	+	0.145631i
$121$	3.26923	−	0.492757i	0.297203	−	0.0447961i
$122$	−0.326291	−	0.222461i	−0.0295410	−	0.0201407i
$123$	−0.482174	−	0.328741i	−0.0434762	−	0.0296416i
$124$	−9.03454	+	1.36174i	−0.811326	+	0.122288i
$125$	3.98832	+	5.00119i	0.356726	+	0.447320i
$126$		0			0
$127$	9.13083	−	11.4497i	0.810231	−	1.01600i	−0.189189	−	0.981941i	$-0.560586\pi$
$127$	9.13083	−	11.4497i	0.810231	−	1.01600i	0.999420	−	0.0340563i	$-0.0108426\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.401446	+	0.695325i	0.0353453	+	0.0612199i
$130$	−9.57285	−	1.44287i	−0.839594	−	0.126548i
$131$	0.634678	+	0.588895i	0.0554521	+	0.0514520i	0.707412	−	0.706801i	$-0.249863\pi$
$131$	0.634678	+	0.588895i	0.0554521	+	0.0514520i	−0.651960	+	0.758253i	$0.726053\pi$
$132$	−1.83841	+	0.885332i	−0.160013	+	0.0770582i
$133$		0			0
$134$	−10.7130	−	5.15911i	−0.925462	−	0.445679i
$135$	4.06941	+	10.3687i	0.350239	+	0.892395i
$136$	0.328261	+	4.38034i	0.0281481	+	0.375611i
$137$	−21.0433	+	6.49100i	−1.79785	+	0.554563i	−0.998903	−	0.0468377i	$-0.985086\pi$
$137$	−21.0433	+	6.49100i	−1.79785	+	0.554563i	−0.798947	+	0.601401i	$0.794609\pi$
$138$	−0.177076	+	2.36292i	−0.0150737	+	0.201145i
$139$	1.87674	+	8.22254i	0.159183	+	0.697426i	0.990022	+	0.140913i	$0.0450039\pi$
$139$	1.87674	+	8.22254i	0.159183	+	0.697426i	−0.830839	+	0.556513i	$0.812139\pi$
$140$		0			0
$141$	0.477502	−	2.09207i	0.0402130	−	0.176184i
$142$	−6.98033	−	2.15315i	−0.585776	−	0.180688i
$143$	3.53686	−	9.01176i	0.295767	−	0.753602i
$144$	1.80246	−	1.67244i	0.150205	−	0.139370i
$145$	−21.4517	+	14.6255i	−1.78147	+	1.21459i
$146$	9.17370			0.759221
$147$		0			0
$148$	−8.37994			−0.688827
$149$	2.29640	−	1.56566i	0.188129	−	0.128264i	−0.465593	−	0.884999i	$-0.654159\pi$
$149$	2.29640	−	1.56566i	0.188129	−	0.128264i	0.653722	+	0.756735i	$0.273207\pi$
$150$	1.45267	−	1.34788i	0.118610	−	0.110054i
$151$	−1.60243	+	4.08294i	−0.130404	+	0.332265i	−0.981131	−	0.193343i	$-0.938067\pi$
$151$	−1.60243	+	4.08294i	−0.130404	+	0.332265i	0.850727	+	0.525608i	$0.176162\pi$
$152$	4.33598	+	1.33747i	0.351694	+	0.108483i
$153$	−2.40340	+	10.5300i	−0.194303	+	0.851297i
$154$		0			0
$155$	5.63932	+	24.7075i	0.452961	+	1.98455i
$156$	0.191869	−	2.56031i	0.0153618	−	0.204989i
$157$	−22.5614	+	6.95928i	−1.80060	+	0.555411i	−0.999093	−	0.0425754i	$-0.986444\pi$
$157$	−22.5614	+	6.95928i	−1.80060	+	0.555411i	−0.801506	+	0.597987i	$0.795968\pi$
$158$	0.399001	+	5.32430i	0.0317428	+	0.423579i
$159$	2.24295	+	5.71493i	0.177877	+	0.453224i
$160$	−2.49909	−	1.20350i	−0.197570	−	0.0951448i
$161$		0			0
$162$	3.98449	−	1.91883i	0.313051	−	0.150757i
$163$	−7.02473	−	6.51800i	−0.550219	−	0.510529i	0.355346	−	0.934735i	$-0.384363\pi$
$163$	−7.02473	−	6.51800i	−0.550219	−	0.510529i	−0.905566	+	0.424206i	$0.860553\pi$
$164$	0.784440	+	0.118235i	0.0612544	+	0.00923262i
$165$	2.82992	+	4.90157i	0.220309	+	0.381587i
$166$	−5.17005	+	8.95479i	−0.401274	+	0.695026i
$167$	−9.03558	+	11.3303i	−0.699194	+	0.876762i	−0.996963	−	0.0778764i	$-0.975186\pi$
$167$	−9.03558	+	11.3303i	−0.699194	+	0.876762i	0.297769	+	0.954638i	$0.403757\pi$
$168$		0			0
$169$	−0.510432	−	0.640061i	−0.0392640	−	0.0492355i
$170$	12.0481	−	1.81595i	0.924044	−	0.139277i
$171$	9.21850	+	6.28506i	0.704956	+	0.480631i
$172$	−0.901782	−	0.614825i	−0.0687602	−	0.0468799i
$173$	3.31642	−	0.499869i	0.252142	−	0.0380044i	−0.0217547	−	0.999763i	$-0.506925\pi$
$173$	3.31642	−	0.499869i	0.252142	−	0.0380044i	0.273897	+	0.961759i	$0.411687\pi$
$174$	−4.29315	−	5.38343i	−0.325463	−	0.408117i
$175$		0			0
$176$	1.72942	−	2.16863i	0.130360	−	0.163466i
$177$	−1.24190	+	2.15104i	−0.0933470	+	0.161682i
$178$	−0.832358	−	1.44169i	−0.0623879	−	0.108059i
$179$	4.12559	+	0.621833i	0.308361	+	0.0464780i	0.301400	−	0.953498i	$-0.402546\pi$
$179$	4.12559	+	0.621833i	0.308361	+	0.0464780i	0.00696125	+	0.999976i	$0.497784\pi$
$180$	−4.99963	−	4.63897i	−0.372650	−	0.345769i
$181$	19.3312	−	9.30943i	1.43688	−	0.691965i	0.456617	−	0.889663i	$-0.349061\pi$
$181$	19.3312	−	9.30943i	1.43688	−	0.691965i	0.980263	+	0.197699i	$0.0633467\pi$
$182$		0			0
$183$	−0.261740	−	0.126047i	−0.0193484	−	0.00931768i
$184$	−1.17680	−	2.99843i	−0.0867547	−	0.221047i
$185$	1.73703	+	23.1791i	0.127709	+	1.70416i
$186$	−6.42257	+	1.98110i	−0.470926	+	0.145261i
$187$	−0.910522	+	12.1501i	−0.0665840	+	0.888502i
$188$	0.649104	+	2.84391i	0.0473408	+	0.207414i
$189$		0			0
$190$	2.80070	−	12.2707i	0.203184	−	0.890207i
$191$	−13.4816	−	4.15851i	−0.975491	−	0.300899i	−0.234278	−	0.972170i	$-0.575273\pi$
$191$	−13.4816	−	4.15851i	−0.975491	−	0.300899i	−0.741213	+	0.671270i	$0.765749\pi$
$192$	0.268757	−	0.684781i	0.0193958	−	0.0494198i
$193$	9.05375	−	8.40065i	0.651703	−	0.604692i	−0.283428	−	0.958993i	$-0.591472\pi$
$193$	9.05375	−	8.40065i	0.651703	−	0.604692i	0.935131	+	0.354301i	$0.115281\pi$
$194$	10.4494	−	7.12430i	0.750225	−	0.511495i
$195$	−7.12164			−0.509991
$196$		0			0
$197$	−16.2039			−1.15448			−0.577240	−	0.816575i	$-0.695870\pi$
$197$	−16.2039			−1.15448			−0.577240	+	0.816575i	$0.695870\pi$
$198$	5.63519	−	3.84201i	0.400475	−	0.273039i
$199$	−13.1510	+	12.2023i	−0.932248	+	0.865000i	−0.991080	−	0.133268i	$-0.957453\pi$
$199$	−13.1510	+	12.2023i	−0.932248	+	0.865000i	0.0588319	+	0.998268i	$0.481262\pi$
$200$	−0.984172	+	2.50763i	−0.0695915	+	0.177316i
$201$	−8.35846	−	2.57824i	−0.589560	−	0.181855i
$202$	1.53610	−	6.73011i	0.108080	−	0.473529i
$203$		0			0
$204$	0.719044	+	3.15034i	0.0503431	+	0.220568i
$205$	0.164439	−	2.19429i	0.0114849	−	0.153256i
$206$	−4.83812	+	1.49236i	−0.337088	+	0.103978i
$207$	−0.591875	−	7.89802i	−0.0411381	−	0.548950i
$208$	1.27510	+	3.24891i	0.0884126	+	0.225272i
$209$	11.3398	+	5.46095i	0.784389	+	0.377742i
$210$		0			0
$211$	11.4252	−	5.50207i	0.786540	−	0.378778i	0.00290249	−	0.999996i	$-0.499076\pi$
$211$	11.4252	−	5.50207i	0.786540	−	0.378778i	0.783638	+	0.621218i	$0.213362\pi$
$212$	−6.11778	−	5.67647i	−0.420171	−	0.389862i
$213$	−5.31368	−	0.800908i	−0.364087	−	0.0548773i
$214$	9.47321	+	16.4081i	0.647575	+	1.12163i
$215$	−1.51369	+	2.62179i	−0.103233	+	0.178805i
$216$	2.50375	−	3.13960i	0.170359	−	0.213623i
$217$		0			0
$218$	6.29847	+	7.89803i	0.426586	+	0.534922i
$219$	6.67310	−	1.00581i	0.450926	−	0.0679662i
$220$	−6.35695	−	4.33410i	−0.428586	−	0.292205i
$221$	−12.6671	−	8.63627i	−0.852080	−	0.580938i
$222$	−6.09571	+	0.918780i	−0.409117	+	0.0616645i
$223$	−5.76942	−	7.23462i	−0.386349	−	0.484466i	0.550185	−	0.835043i	$-0.314557\pi$
$223$	−5.76942	−	7.23462i	−0.386349	−	0.484466i	−0.936534	+	0.350577i	$0.885986\pi$
$224$		0			0
$225$	−4.12984	+	5.17865i	−0.275323	+	0.345244i
$226$	2.29631	−	3.97732i	0.152748	−	0.264567i
$227$	9.23163	+	15.9897i	0.612725	+	1.06127i	0.990779	+	0.135487i	$0.0432600\pi$
$227$	9.23163	+	15.9897i	0.612725	+	1.06127i	−0.378054	+	0.925784i	$0.623407\pi$
$228$	3.30070	+	0.497501i	0.218594	+	0.0329478i
$229$	−1.83497	−	1.70260i	−0.121258	−	0.112511i	0.617213	−	0.786796i	$-0.288262\pi$
$229$	−1.83497	−	1.70260i	−0.121258	−	0.112511i	−0.738471	+	0.674285i	$0.764452\pi$
$230$	−8.04979	+	3.87658i	−0.530788	+	0.255614i
$231$		0			0
$232$	8.43325	+	4.06124i	0.553670	+	0.266633i
$233$	0.300999	+	0.766932i	0.0197191	+	0.0502434i	0.940394	−	0.340086i	$-0.110456\pi$
$233$	0.300999	+	0.766932i	0.0197191	+	0.0502434i	−0.920675	+	0.390330i	$0.872361\pi$
$234$	0.641319	+	8.55780i	0.0419243	+	0.559441i
$235$	7.73177	−	2.38494i	0.504365	−	0.155576i
$236$	0.252320	−	3.36698i	0.0164246	−	0.219171i
$237$	0.873998	+	3.82924i	0.0567723	+	0.248736i
$238$		0			0
$239$	−5.29042	+	23.1789i	−0.342209	+	1.49932i	0.452191	+	0.891921i	$0.350642\pi$
$239$	−5.29042	+	23.1789i	−0.342209	+	1.49932i	−0.794400	+	0.607395i	$0.792215\pi$
$240$	−1.94983	−	0.601443i	−0.125861	−	0.0388229i
$241$	10.6811	−	27.2149i	0.688027	−	1.75306i	0.0306173	−	0.999531i	$-0.490253\pi$
$241$	10.6811	−	27.2149i	0.688027	−	1.75306i	0.657410	−	0.753533i	$-0.271652\pi$
$242$	−2.42358	+	2.24876i	−0.155794	+	0.144556i
$243$	12.6418	−	8.61903i	0.810971	−	0.552911i
$244$	0.394911			0.0252816
$245$		0			0
$246$	0.583577			0.0372075
$247$	−13.0851	+	8.92126i	−0.832584	+	0.567646i
$248$	6.69759	−	6.21446i	0.425298	−	0.394618i
$249$	−2.77897	+	7.08070i	−0.176110	+	0.448721i
$250$	−6.11257	−	1.88548i	−0.386593	−	0.119248i
$251$	2.15632	−	9.44746i	0.136106	−	0.596319i	−0.860163	−	0.510019i	$-0.829639\pi$
$251$	2.15632	−	9.44746i	0.136106	−	0.596319i	0.996269	−	0.0863000i	$-0.0275043\pi$
$252$		0			0
$253$	−1.98814	−	8.71059i	−0.124993	−	0.547630i
$254$	−1.09440	+	14.6038i	−0.0686688	+	0.916322i
$255$	8.56485	−	2.64191i	0.536352	−	0.165443i
$256$	0.0747301	+	0.997204i	0.00467063	+	0.0623252i
$257$	−1.12898	−	2.87658i	−0.0704235	−	0.179436i	0.891328	−	0.453358i	$-0.149774\pi$
$257$	−1.12898	−	2.87658i	−0.0704235	−	0.179436i	−0.961752	+	0.273922i	$0.911679\pi$
$258$	−0.723381	−	0.348362i	−0.0450357	−	0.0216881i
$259$		0			0
$260$	8.72226	−	4.20042i	0.540931	−	0.260499i
$261$	16.8714	+	15.6544i	1.04431	+	0.968981i
$262$	−0.856132	−	0.129041i	−0.0528920	−	0.00797219i
$263$	−8.84820	−	15.3255i	−0.545604	−	0.945013i	−0.998569	−	0.0534849i	$-0.982967\pi$
$263$	−8.84820	−	15.3255i	−0.545604	−	0.945013i	0.452965	−	0.891528i	$-0.350366\pi$
$264$	1.02024	−	1.76711i	0.0627915	−	0.108758i
$265$	−14.4331	+	18.0986i	−0.886620	+	1.11179i
$266$		0			0
$267$	−0.763538	−	0.957446i	−0.0467277	−	0.0585947i
$268$	11.7577	−	1.77219i	0.718217	−	0.108254i
$269$	−15.8386	−	10.7985i	−0.965694	−	0.658399i	−0.0257287	−	0.999669i	$-0.508191\pi$
$269$	−15.8386	−	10.7985i	−0.965694	−	0.658399i	−0.939965	+	0.341270i	$0.889143\pi$
$270$	−9.20320	−	6.27464i	−0.560089	−	0.381862i
$271$	29.4122	−	4.43317i	1.78666	−	0.269296i	0.829429	−	0.558612i	$-0.188666\pi$
$271$	29.4122	−	4.43317i	1.78666	−	0.269296i	0.957234	+	0.289316i	$0.0934279\pi$
$272$	−2.73875	−	3.43429i	−0.166061	−	0.208234i
$273$		0			0
$274$	13.7303	−	17.2172i	0.829476	−	1.04013i
$275$	−3.73606	+	6.47105i	−0.225293	+	0.390219i
$276$	−1.18477	−	2.05208i	−0.0713148	−	0.123521i
$277$	7.90209	+	1.19105i	0.474790	+	0.0715631i	0.382079	−	0.924130i	$-0.375208\pi$
$277$	7.90209	+	1.19105i	0.474790	+	0.0715631i	0.0927118	+	0.995693i	$0.470446\pi$
$278$	−6.18256	−	5.73657i	−0.370805	−	0.344057i
$279$	20.2407	−	9.74739i	1.21178	−	0.583561i
$280$		0			0
$281$	−11.0645	−	5.32837i	−0.660051	−	0.317864i	0.0737018	−	0.997280i	$-0.476519\pi$
$281$	−11.0645	−	5.32837i	−0.660051	−	0.317864i	−0.733753	+	0.679416i	$0.762233\pi$
$282$	0.783977	+	1.99754i	0.0466851	+	0.118952i
$283$	−0.502656	−	6.70747i	−0.0298798	−	0.398718i	−0.992013	−	0.126138i	$-0.959742\pi$
$283$	−0.502656	−	6.70747i	−0.0298798	−	0.398718i	0.962133	−	0.272580i	$-0.0878771\pi$
$284$	6.98033	−	2.15315i	0.414206	−	0.127766i
$285$	0.691913	−	9.23294i	0.0409854	−	0.546912i
$286$	2.15422	+	9.43825i	0.127382	+	0.558096i
$287$		0			0
$288$	−0.547144	+	2.39720i	−0.0322408	+	0.141256i
$289$	2.19313	+	0.676490i	0.129007	+	0.0397935i
$290$	9.48539	−	24.1684i	0.557002	−	1.41922i
$291$	6.81997	−	6.32801i	0.399794	−	0.370955i
$292$	−7.57967	+	5.16773i	−0.443566	+	0.302418i
$293$	−17.2151			−1.00571			−0.502857	−	0.864369i	$-0.667718\pi$
$293$	−17.2151			−1.00571			−0.502857	+	0.864369i	$0.667718\pi$
$294$		0			0
$295$	−9.36543			−0.545276
$296$	6.92384	−	4.72059i	0.402440	−	0.274379i
$297$	8.16522	−	7.57622i	0.473794	−	0.439617i
$298$	−1.01541	+	2.58722i	−0.0588210	+	0.149874i
$299$	10.7427	+	3.31369i	0.621268	+	0.191636i
$300$	−0.440965	+	1.93200i	−0.0254591	+	0.111544i
$301$		0			0
$302$	−0.976007	−	4.27617i	−0.0561629	−	0.246066i
$303$	0.379495	−	5.06401i	0.0218014	−	0.290920i
$304$	−4.33598	+	1.33747i	−0.248685	+	0.0767093i
$305$	−0.0818590	−	1.09233i	−0.00468723	−	0.0625467i
$306$	−3.94596	−	10.0541i	−0.225576	−	0.574757i
$307$	−4.13864	−	1.99306i	−0.236204	−	0.113750i	0.312038	−	0.950070i	$-0.398988\pi$
$307$	−4.13864	−	1.99306i	−0.236204	−	0.113750i	−0.548242	+	0.836320i	$0.684703\pi$
$308$		0			0
$309$	−3.35570	+	1.61602i	−0.190899	+	0.0919322i
$310$	−18.5776	−	17.2375i	−1.05514	−	0.979026i
$311$	30.9119	+	4.65922i	1.75286	+	0.264200i	0.945443	−	0.325787i	$-0.105629\pi$
$311$	30.9119	+	4.65922i	1.75286	+	0.264200i	0.807412	+	0.589988i	$0.200867\pi$
$312$	1.28374	+	2.22351i	0.0726777	+	0.125881i
$313$	−3.39541	+	5.88102i	−0.191920	+	0.332415i	−0.945886	−	0.324498i	$-0.894805\pi$
$313$	−3.39541	+	5.88102i	−0.191920	+	0.332415i	0.753967	+	0.656913i	$0.228138\pi$
$314$	14.7208	−	18.4593i	0.830745	−	1.04172i
$315$		0			0
$316$	−3.32896	−	4.17438i	−0.187268	−	0.234827i
$317$	−22.0841	+	3.32864i	−1.24036	+	0.186955i	−0.736266	−	0.676692i	$-0.763413\pi$
$317$	−22.0841	+	3.32864i	−1.24036	+	0.186955i	−0.504098	+	0.863647i	$0.668175\pi$
$318$	−5.07255	−	3.45840i	−0.284454	−	0.193938i
$319$	21.4517	+	14.6255i	1.20107	+	0.818874i
$320$	2.74280	−	0.413410i	0.153327	−	0.0231103i
$321$	8.68995	+	10.8969i	0.485026	+	0.608203i
$322$		0			0
$323$	12.4273	−	15.5833i	0.691472	−	0.867079i
$324$	−2.21123	+	3.82995i	−0.122846	+	0.212775i
$325$	−4.70100	−	8.14236i	−0.260764	−	0.451657i
$326$	9.47583	+	1.42825i	0.524817	+	0.0791035i
$327$	5.44755	+	5.05459i	0.301250	+	0.279519i
$328$	−0.714739	+	0.344200i	−0.0394648	+	0.0190053i
$329$		0			0
$330$	−5.09934	−	2.45571i	−0.280710	−	0.135183i
$331$	5.36899	+	13.6800i	0.295106	+	0.751919i	0.999128	+	0.0417409i	$0.0132904\pi$
$331$	5.36899	+	13.6800i	0.295106	+	0.751919i	−0.704022	+	0.710178i	$0.748614\pi$
$332$	−0.772716	−	10.3112i	−0.0424083	−	0.565900i
$333$	19.6896	−	6.07343i	1.07898	−	0.332822i
$334$	1.08298	−	14.4514i	0.0592583	−	0.790746i
$335$	−7.33912	−	32.1548i	−0.400979	−	1.75680i
$336$		0			0
$337$	5.04280	−	22.0940i	0.274699	−	1.20353i	−0.629697	−	0.776841i	$-0.716821\pi$
$337$	5.04280	−	22.0940i	0.274699	−	1.20353i	0.904396	−	0.426694i	$-0.140322\pi$
$338$	0.782298	+	0.241307i	0.0425514	+	0.0131254i
$339$	1.23430	−	3.14494i	0.0670378	−	0.170809i
$340$	−8.93161	+	8.28732i	−0.484385	+	0.449443i
$341$	20.9393	−	14.2761i	1.13392	−	0.773097i
$342$	−11.1572			−0.603311
$343$		0			0
$344$	1.09143			0.0588460
$345$	−5.43052	+	3.70247i	−0.292369	+	0.199334i
$346$	−2.45857	+	2.28122i	−0.132173	+	0.122639i
$347$	2.71511	−	6.91800i	0.145755	−	0.371378i	−0.839288	−	0.543687i	$-0.817028\pi$
$347$	2.71511	−	6.91800i	0.145755	−	0.371378i	0.985043	+	0.172310i	$0.0551230\pi$
$348$	6.57976	+	2.02959i	0.352712	+	0.108797i
$349$	1.31543	−	5.76327i	0.0704132	−	0.308501i	−0.927441	−	0.373968i	$-0.877997\pi$
$349$	1.31543	−	5.76327i	0.0704132	−	0.308501i	0.997855	+	0.0654679i	$0.0208540\pi$
$350$		0			0
$351$	3.11875	+	13.6641i	0.166466	+	0.729337i
$352$	−0.207285	+	2.76602i	−0.0110483	+	0.147429i
$353$	−5.15576	+	1.59034i	−0.274413	+	0.0846453i	−0.428908	−	0.903348i	$-0.641101\pi$
$353$	−5.15576	+	1.59034i	−0.274413	+	0.0846453i	0.154494	+	0.987994i	$0.450625\pi$
$354$	−0.185615	−	2.47686i	−0.00986531	−	0.131643i
$355$	−7.40256	−	18.8614i	−0.392887	−	1.00106i
$356$	1.49986	+	0.722293i	0.0794923	+	0.0382815i
$357$		0			0
$358$	−3.75902	+	1.81025i	−0.198670	+	0.0956745i
$359$	12.9056	+	11.9747i	0.681132	+	0.631999i	0.942878	−	0.333138i	$-0.108108\pi$
$359$	12.9056	+	11.9747i	0.681132	+	0.631999i	−0.261746	+	0.965137i	$0.584298\pi$
$360$	6.74411	+	1.01651i	0.355446	+	0.0535749i
$361$	−0.794772	−	1.37659i	−0.0418301	−	0.0724519i
$362$	−10.7280	+	18.5815i	−0.563853	+	0.976621i
$363$	−1.51640	+	1.90150i	−0.0795903	+	0.0998031i
$364$		0			0
$365$	15.8652	+	19.8943i	0.830423	+	1.04132i
$366$	0.287264	−	0.0432982i	0.0150156	−	0.00226323i
$367$	1.07709	+	0.734348i	0.0562237	+	0.0383326i	0.591106	−	0.806594i	$-0.298692\pi$
$367$	1.07709	+	0.734348i	0.0562237	+	0.0383326i	−0.534882	+	0.844927i	$0.679644\pi$
$368$	2.66139	+	1.81451i	0.138735	+	0.0945877i
$369$	−1.92881	+	0.290722i	−0.100410	+	0.0151344i
$370$	−14.4925	−	18.1730i	−0.753427	−	0.944768i
$371$		0			0
$372$	4.19058	−	5.25482i	0.217272	−	0.272450i
$373$	−2.02796	+	3.51254i	−0.105004	+	0.181872i	−0.913740	−	0.406300i	$-0.866819\pi$
$373$	−2.02796	+	3.51254i	−0.105004	+	0.181872i	0.808736	+	0.588172i	$0.200152\pi$
$374$	−6.09207	−	10.5518i	−0.315014	−	0.545620i
$375$	−4.65311	−	0.701343i	−0.240286	−	0.0362172i
$376$	−2.13835	−	1.98410i	−0.110277	−	0.102322i
$377$	−29.4335	+	14.1744i	−1.51590	+	0.730021i
$378$		0			0
$379$	−16.2392	−	7.82039i	−0.834152	−	0.401706i	−0.0324813	−	0.999472i	$-0.510341\pi$
$379$	−16.2392	−	7.82039i	−0.834152	−	0.401706i	−0.801671	+	0.597766i	$0.796055\pi$
$380$	4.59826	+	11.7162i	0.235886	+	0.601027i
$381$	0.805077	+	10.7430i	0.0412454	+	0.550381i
$382$	13.4816	−	4.15851i	0.689776	−	0.212768i
$383$	0.683001	−	9.11402i	0.0348997	−	0.465705i	−0.952187	−	0.305516i	$-0.901171\pi$
$383$	0.683001	−	9.11402i	0.0348997	−	0.465705i	0.987087	−	0.160188i	$-0.0512101\pi$
$384$	0.163694	+	0.717189i	0.00835346	+	0.0365989i
$385$		0			0
$386$	−2.74830	+	12.0411i	−0.139885	+	0.612876i
$387$	2.56443	+	0.791022i	0.130357	+	0.0402099i
$388$	−4.62046	+	11.7727i	−0.234568	+	0.597671i
$389$	15.7401	−	14.6047i	0.798054	−	0.740486i	−0.171547	−	0.985176i	$-0.554877\pi$
$389$	15.7401	−	14.6047i	0.798054	−	0.740486i	0.969601	+	0.244690i	$0.0786861\pi$
$390$	5.88418	−	4.01176i	0.297957	−	0.203144i
$391$	−14.1490			−0.715547
$392$		0			0
$393$	−0.636913			−0.0321280
$394$	13.3883	−	9.12798i	0.674492	−	0.459861i
$395$	−10.8564	+	10.0733i	−0.546244	+	0.506840i
$396$	−2.49173	+	6.34883i	−0.125214	+	0.319041i
$397$	−24.0480	−	7.41783i	−1.20694	−	0.372290i	−0.374928	−	0.927054i	$-0.622332\pi$
$397$	−24.0480	−	7.41783i	−1.20694	−	0.372290i	−0.832008	+	0.554764i	$0.812809\pi$
$398$	3.99203	−	17.4902i	0.200103	−	0.876707i
$399$		0			0
$400$	−0.599437	−	2.62630i	−0.0299718	−	0.131315i
$401$	−0.620916	+	8.28555i	−0.0310071	+	0.413761i	0.960004	+	0.279985i	$0.0903294\pi$
$401$	−0.620916	+	8.28555i	−0.0310071	+	0.413761i	−0.991012	+	0.133776i	$0.957290\pi$
$402$	8.35846	−	2.57824i	0.416882	−	0.128591i
$403$	2.38302	+	31.7991i	0.118706	+	1.58403i
$404$	2.52202	+	6.42599i	0.125475	+	0.319705i
$405$	11.0521	+	5.32241i	0.549183	+	0.264473i
$406$		0			0
$407$	20.9422	−	10.0852i	1.03807	−	0.499907i
$408$	−2.36875	−	2.19788i	−0.117271	−	0.108811i
$409$	16.1111	+	2.42836i	0.796643	+	0.120075i	0.534737	−	0.845019i	$-0.320411\pi$
$409$	16.1111	+	2.42836i	0.796643	+	0.120075i	0.261906	+	0.965093i	$0.415649\pi$
$410$	1.10022	+	1.90564i	0.0543359	+	0.0941126i
$411$	8.09992	−	14.0295i	0.399540	−	0.692023i
$412$	3.15676	−	3.95846i	0.155523	−	0.195019i
$413$		0			0
$414$	4.93814	+	6.19224i	0.242697	+	0.304332i
$415$	−28.3608	+	4.27470i	−1.39218	+	0.209837i
$416$	−2.88372	−	1.96609i	−0.141386	−	0.0963953i
$417$	−5.12625	−	3.49502i	−0.251034	−	0.171152i
$418$	−12.4456	+	1.87588i	−0.608736	+	0.0917522i
$419$	7.39478	+	9.27277i	0.361259	+	0.453004i	0.928932	−	0.370250i	$-0.120728\pi$
$419$	7.39478	+	9.27277i	0.361259	+	0.453004i	−0.567674	+	0.823254i	$0.692156\pi$
$420$		0			0
$421$	−15.5238	+	19.4662i	−0.756583	+	0.948724i	−0.999774	−	0.0212538i	$-0.993234\pi$
$421$	−15.5238	+	19.4662i	−0.756583	+	0.948724i	0.243192	+	0.969978i	$0.421806\pi$
$422$	−6.34048	+	10.9820i	−0.308650	+	0.534597i
$423$	−3.58628	−	6.21163i	−0.174371	−	0.302020i
$424$	8.25242	+	1.24385i	0.400773	+	0.0604068i
$425$	8.67422	+	8.04850i	0.420762	+	0.390410i
$426$	4.84153	−	2.33156i	0.234573	−	0.112964i
$427$		0			0
$428$	−17.0701	−	8.22054i	−0.825116	−	0.397355i
$429$	2.60183	+	6.62935i	0.125617	+	0.320068i
$430$	−0.226237	−	3.01892i	−0.0109101	−	0.145585i
$431$	4.33336	−	1.33666i	0.208731	−	0.0643849i	−0.188627	−	0.982049i	$-0.560404\pi$
$431$	4.33336	−	1.33666i	0.208731	−	0.0643849i	0.397357	+	0.917664i	$0.369927\pi$
$432$	−0.300094	+	4.00448i	−0.0144383	+	0.192665i
$433$	−2.66189	−	11.6625i	−0.127922	−	0.560463i	−0.997746	−	0.0671013i	$-0.978625\pi$
$433$	−2.66189	−	11.6625i	−0.127922	−	0.560463i	0.869824	−	0.493362i	$-0.164232\pi$
$434$		0			0
$435$	4.25000	−	18.6205i	0.203772	−	0.892783i
$436$	−9.65316	−	2.97761i	−0.462303	−	0.142601i
$437$	−5.33980	+	13.6056i	−0.255437	+	0.650844i
$438$	−4.94698	+	4.59013i	−0.236376	+	0.219325i
$439$	−4.96288	+	3.38363i	−0.236865	+	0.161492i	−0.675936	−	0.736961i	$-0.736260\pi$
$439$	−4.96288	+	3.38363i	−0.236865	+	0.161492i	0.439070	+	0.898453i	$0.355308\pi$
$440$	7.69384			0.366790
$441$		0			0
$442$	15.3310			0.729222
$443$	−9.84107	+	6.70953i	−0.467563	+	0.318779i	−0.774082	−	0.633085i	$-0.781788\pi$
$443$	−9.84107	+	6.70953i	−0.467563	+	0.318779i	0.306519	+	0.951865i	$0.400836\pi$
$444$	4.51894	−	4.19297i	0.214460	−	0.198989i
$445$	1.68698	−	4.29836i	0.0799706	−	0.203762i
$446$	8.84232	+	2.72750i	0.418696	+	0.129151i
$447$	−0.454961	+	1.99331i	−0.0215189	+	0.0942805i
$448$		0			0
$449$	−0.464022	−	2.03301i	−0.0218985	−	0.0959438i	0.962798	−	0.270223i	$-0.0870975\pi$
$449$	−0.464022	−	2.03301i	−0.0218985	−	0.0959438i	−0.984696	+	0.174280i	$0.944240\pi$
$450$	0.494993	−	6.60522i	0.0233342	−	0.311373i
$451$	−2.10268	+	0.648591i	−0.0990113	+	0.0305409i
$452$	0.343206	+	4.57977i	0.0161431	+	0.215414i
$453$	−1.17880	−	3.00354i	−0.0553850	−	0.141119i
$454$	−16.6348	−	8.01091i	−0.780711	−	0.375971i
$455$		0			0
$456$	−3.00742	+	1.44830i	−0.140835	+	0.0678227i
$457$	−5.40669	−	5.01668i	−0.252914	−	0.234670i	0.543519	−	0.839397i	$-0.317092\pi$
$457$	−5.40669	−	5.01668i	−0.252914	−	0.234670i	−0.796433	+	0.604727i	$0.793282\pi$
$458$	2.47523	+	0.373081i	0.115660	+	0.0174329i
$459$	−8.81973	−	15.2762i	−0.411670	−	0.713033i
$460$	4.46730	−	7.73759i	0.208289	−	0.360767i
$461$	−8.41818	+	10.5561i	−0.392074	+	0.491645i	−0.938217	−	0.346047i	$-0.887524\pi$
$461$	−8.41818	+	10.5561i	−0.392074	+	0.491645i	0.546143	+	0.837692i	$0.316095\pi$
$462$		0			0
$463$	−2.05688	−	2.57924i	−0.0955912	−	0.119868i	0.731735	−	0.681589i	$-0.238711\pi$
$463$	−2.05688	−	2.57924i	−0.0955912	−	0.119868i	−0.827326	+	0.561721i	$0.810139\pi$
$464$	−9.25566	+	1.39507i	−0.429683	+	0.0647643i
$465$	−15.4036	−	10.5020i	−0.714325	−	0.487018i
$466$	−0.680725	−	0.464110i	−0.0315340	−	0.0214995i
$467$	−27.3681	+	4.12508i	−1.26645	+	0.190886i	−0.747696	−	0.664041i	$-0.768840\pi$
$467$	−27.3681	+	4.12508i	−1.26645	+	0.190886i	−0.518749	+	0.854927i	$0.673602\pi$
$468$	−5.35067	−	6.70952i	−0.247335	−	0.310148i
$469$		0			0
$470$	−5.04481	+	6.32599i	−0.232700	+	0.291796i
$471$	8.68429	−	15.0416i	0.400151	−	0.693081i
$472$	1.68821	+	2.92406i	0.0777061	+	0.134591i
$473$	2.99357	+	0.451208i	0.137645	+	0.0207466i
$474$	−2.87922	−	2.67152i	−0.132247	−	0.122707i
$475$	11.0130	−	5.30358i	0.505311	−	0.243345i
$476$		0			0
$477$	18.4884	+	8.90356i	0.846527	+	0.407666i
$478$	−8.68596	−	22.1315i	−0.397287	−	1.01227i
$479$	−1.98568	−	26.4970i	−0.0907278	−	1.21068i	−0.837816	−	0.545953i	$-0.816168\pi$
$479$	−1.98568	−	26.4970i	−0.0907278	−	1.21068i	0.747088	−	0.664726i	$-0.231452\pi$
$480$	1.94983	−	0.601443i	0.0889971	−	0.0274520i
$481$	−2.18567	+	29.1657i	−0.0996579	+	1.32984i
$482$	6.50559	+	28.5028i	0.296321	+	1.29827i
$483$		0			0
$484$	0.735689	−	3.22326i	0.0334404	−	0.146512i
$485$	33.5214	+	10.3400i	1.52213	+	0.469515i
$486$	−5.58987	+	14.2428i	−0.253562	+	0.646064i
$487$	−11.5520	+	10.7187i	−0.523473	+	0.485712i	−0.897076	−	0.441877i	$-0.854313\pi$
$487$	−11.5520	+	10.7187i	−0.523473	+	0.485712i	0.373603	+	0.927589i	$0.378122\pi$
$488$	−0.326291	+	0.222461i	−0.0147705	+	0.0100703i
$489$	7.04946			0.318788
$490$		0			0
$491$	16.4499			0.742375			0.371188	−	0.928558i	$-0.378951\pi$
$491$	16.4499			0.742375			0.371188	+	0.928558i	$0.378951\pi$
$492$	−0.482174	+	0.328741i	−0.0217381	+	0.0148208i
$493$	30.1400	−	27.9658i	1.35744	−	1.25952i
$494$	5.78588	−	14.7422i	0.260319	−	0.663282i
$495$	18.0775	+	5.57617i	0.812523	+	0.250630i
$496$	−2.03308	+	8.90751i	−0.0912881	+	0.399959i
$497$		0			0
$498$	−1.69261	−	7.41580i	−0.0758476	−	0.332310i
$499$	0.527686	−	7.04147i	0.0236224	−	0.315220i	−0.972859	−	0.231401i	$-0.925669\pi$
$499$	0.527686	−	7.04147i	0.0236224	−	0.315220i	0.996481	−	0.0838190i	$-0.0267118\pi$
$500$	6.11257	−	1.88548i	0.273363	−	0.0843212i
$501$	−0.796678	−	10.6309i	−0.0355930	−	0.474955i
$502$	3.54031	+	9.02056i	0.158012	+	0.402607i
$503$	24.4480	+	11.7735i	1.09008	+	0.524955i	0.890526	−	0.454932i	$-0.150336\pi$
$503$	24.4480	+	11.7735i	1.09008	+	0.524955i	0.199554	+	0.979887i	$0.436051\pi$
$504$		0			0
$505$	17.2517	−	8.30796i	0.767689	−	0.369699i
$506$	6.54952	+	6.07707i	0.291162	+	0.270159i
$507$	0.595513	+	0.0897592i	0.0264477	+	0.00398635i
$508$	−7.32236	−	12.6827i	−0.324877	−	0.562704i
$509$	1.85002	−	3.20432i	0.0820005	−	0.142029i	−0.822109	−	0.569331i	$-0.807202\pi$
$509$	1.85002	−	3.20432i	0.0820005	−	0.142029i	0.904109	+	0.427302i	$0.140536\pi$
$510$	−5.58837	+	7.00760i	−0.247457	+	0.310302i
$511$		0			0
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−18.0180	+	2.71578i	−0.795515	+	0.119905i
$514$	2.55324	+	1.74077i	0.112619	+	0.0767820i
$515$	−11.6035	−	7.91115i	−0.511313	−	0.348607i
$516$	0.793924	−	0.119665i	0.0349506	−	0.00526795i
$517$	−5.04481	−	6.32599i	−0.221870	−	0.278217i
$518$		0			0
$519$	−1.53829	+	1.92895i	−0.0675233	+	0.0846715i
$520$	−4.84049	+	8.38397i	−0.212269	+	0.367661i
$521$	7.48520	+	12.9647i	0.327932	+	0.567996i	0.982101	−	0.188353i	$-0.0603148\pi$
$521$	7.48520	+	12.9647i	0.327932	+	0.567996i	−0.654169	+	0.756348i	$0.726981\pi$
$522$	−22.7582	−	3.43025i	−0.996100	−	0.150138i
$523$	19.3080	+	17.9152i	0.844282	+	0.783379i	0.978211	−	0.207612i	$-0.0665692\pi$
$523$	19.3080	+	17.9152i	0.844282	+	0.783379i	−0.133930	+	0.990991i	$0.542760\pi$
$524$	0.780061	−	0.375658i	0.0340771	−	0.0164107i
$525$		0			0
$526$	15.9439	+	7.67818i	0.695188	+	0.334785i
$527$	−14.6624	−	37.3593i	−0.638705	−	1.62739i
$528$	0.152485	+	2.03478i	0.00663607	+	0.0885523i
$529$	−12.0637	+	3.72115i	−0.524508	+	0.161789i
$530$	1.72992	−	23.0842i	0.0751430	−	1.00271i
$531$	1.84739	+	8.09393i	0.0801698	+	0.351247i
$532$		0			0
$533$	0.616106	−	2.69934i	0.0266865	−	0.116921i
$534$	1.17021	+	0.360963i	0.0506401	+	0.0156204i
$535$	−19.1998	+	48.9203i	−0.830081	+	2.11501i
$536$	−8.71638	+	8.08762i	−0.376490	+	0.349332i
$537$	−2.53589	+	1.72894i	−0.109432	+	0.0746094i
$538$	19.1695			0.826455
$539$		0			0
$540$	11.1387			0.479332
$541$	19.1979	−	13.0889i	0.825381	−	0.562735i	−0.0753278	−	0.997159i	$-0.524000\pi$
$541$	19.1979	−	13.0889i	0.825381	−	0.562735i	0.900709	+	0.434424i	$0.143048\pi$
$542$	−21.8042	+	20.2313i	−0.936570	+	0.869010i
$543$	−5.76646	+	14.6927i	−0.247463	+	0.630524i
$544$	4.19747	+	1.29475i	0.179965	+	0.0555118i
$545$	−6.23517	+	27.3181i	−0.267085	+	1.17018i
$546$		0			0
$547$	1.77209	+	7.76401i	0.0757689	+	0.331965i	0.998579	−	0.0532896i	$-0.0169707\pi$
$547$	1.77209	+	7.76401i	0.0757689	+	0.331965i	−0.922810	+	0.385255i	$0.874114\pi$
$548$	−1.64568	+	21.9601i	−0.0703000	+	0.938088i
$549$	−0.927884	+	0.286214i	−0.0396011	+	0.0122153i
$550$	−0.558393	−	7.45123i	−0.0238099	−	0.317722i
$551$	−15.5170	−	39.5366i	−0.661045	−	1.68432i
$552$	2.13488	+	1.02811i	0.0908667	+	0.0437591i
$553$		0			0
$554$	−7.19995	+	3.46731i	−0.305897	+	0.147312i
$555$	−12.5345	−	11.6304i	−0.532062	−	0.493681i
$556$	8.33979	+	1.25702i	0.353686	+	0.0533096i
$557$	−8.68751	−	15.0472i	−0.368101	−	0.637570i	0.621167	−	0.783678i	$-0.286659\pi$
$557$	−8.68751	−	15.0472i	−0.368101	−	0.637570i	−0.989269	+	0.146108i	$0.953325\pi$
$558$	−11.2327	+	19.4556i	−0.475519	+	0.823623i
$559$	−2.37505	+	2.97822i	−0.100454	+	0.125965i
$560$		0			0
$561$	−5.58837	−	7.00760i	−0.235941	−	0.295861i
$562$	12.1435	−	1.83033i	0.512242	−	0.0772080i
$563$	−3.77085	−	2.57092i	−0.158923	−	0.108352i	0.481248	−	0.876585i	$-0.340184\pi$
$563$	−3.77085	−	2.57092i	−0.158923	−	0.108352i	−0.640170	+	0.768233i	$0.721136\pi$
$564$	−1.77301	−	1.20882i	−0.0746570	−	0.0509003i
$565$	12.5966	−	1.89863i	0.529943	−	0.0798761i
$566$	4.19377	+	5.25882i	0.176277	+	0.221045i
$567$		0			0
$568$	−4.55451	+	5.71117i	−0.191103	+	0.239635i
$569$	16.6665	−	28.8672i	0.698695	−	1.21017i	−0.270225	−	0.962797i	$-0.587098\pi$
$569$	16.6665	−	28.8672i	0.698695	−	1.21017i	0.968919	−	0.247377i	$-0.0795687\pi$
$570$	4.62941	+	8.01838i	0.193905	+	0.335853i
$571$	−13.1959	−	1.98897i	−0.552233	−	0.0832358i	−0.133003	−	0.991116i	$-0.542462\pi$
$571$	−13.1959	−	1.98897i	−0.552233	−	0.0832358i	−0.419230	+	0.907880i	$0.637700\pi$
$572$	−7.09666	−	6.58473i	−0.296726	−	0.275322i
$573$	9.35076	−	4.50309i	0.390634	−	0.188119i
$574$		0			0
$575$	−7.81782	−	3.76486i	−0.326026	−	0.157006i
$576$	−0.898317	−	2.28887i	−0.0374299	−	0.0953697i
$577$	1.76693	+	23.5780i	0.0735581	+	0.981564i	0.904851	+	0.425729i	$0.139982\pi$
$577$	1.76693	+	23.5780i	0.0735581	+	0.981564i	−0.831293	+	0.555835i	$0.812399\pi$
$578$	−2.19313	+	0.676490i	−0.0912221	+	0.0281383i
$579$	−0.678970	+	9.06022i	−0.0282170	+	0.376530i
$580$	5.77734	+	25.3122i	0.239891	+	1.05103i
$581$		0			0
$582$	−2.07023	+	9.07028i	−0.0858138	+	0.375975i
$583$	22.1205	+	6.82327i	0.916137	+	0.282591i
$584$	3.35153	−	8.53956i	0.138687	−	0.353369i
$585$	−17.4496	+	16.1908i	−0.721451	+	0.669409i
$586$	14.2238	−	9.69759i	0.587578	−	0.400604i
$587$	0.145628			0.00601071			0.00300535	−	0.999995i	$-0.499043\pi$
$587$	0.145628			0.00601071			0.00300535	+	0.999995i	$0.499043\pi$
$588$		0			0
$589$	−41.4579			−1.70824
$590$	7.73808	−	5.27573i	0.318572	−	0.217199i
$591$	8.73806	−	8.10774i	0.359436	−	0.333508i
$592$	−3.06154	+	7.80067i	−0.125828	+	0.320606i
$593$	−17.0771	−	5.26757i	−0.701271	−	0.216313i	−0.0764406	−	0.997074i	$-0.524356\pi$
$593$	−17.0771	−	5.26757i	−0.701271	−	0.216313i	−0.624830	+	0.780761i	$0.714832\pi$
$594$	−2.47859	+	10.8594i	−0.101698	+	0.445567i
$595$		0			0
$596$	−0.618462	−	2.70966i	−0.0253332	−	0.110992i
$597$	0.986234	−	13.1604i	0.0403639	−	0.538618i
$598$	−10.7427	+	3.31369i	−0.439303	+	0.135507i
$599$	1.87957	+	25.0811i	0.0767972	+	1.02479i	0.893891	+	0.448283i	$0.147964\pi$
$599$	1.87957	+	25.0811i	0.0767972	+	1.02479i	−0.817094	+	0.576504i	$0.804416\pi$
$600$	−0.723989	−	1.84469i	−0.0295567	−	0.0753093i
$601$	−36.5839	−	17.6179i	−1.49229	−	0.718647i	−0.502953	−	0.864314i	$-0.667753\pi$
$601$	−36.5839	−	17.6179i	−1.49229	−	0.718647i	−0.989334	+	0.145666i	$0.953467\pi$
$602$		0			0
$603$	−26.3416	+	12.6854i	−1.07271	+	0.516591i
$604$	3.21526	+	2.98333i	0.130827	+	0.121390i
$605$	−9.06811	−	1.36680i	−0.368671	−	0.0555683i
$606$	2.53910	+	4.39786i	0.103144	+	0.178651i
$607$	−18.1557	+	31.4466i	−0.736918	+	1.27638i	0.216959	+	0.976181i	$0.430386\pi$
$607$	−18.1557	+	31.4466i	−0.736918	+	1.27638i	−0.953877	+	0.300199i	$0.902947\pi$
$608$	2.82913	−	3.54762i	0.114736	−	0.143875i
$609$		0			0
$610$	0.682967	+	0.856414i	0.0276525	+	0.0346752i
$611$	10.0673	−	1.51740i	0.407279	−	0.0613875i
$612$	8.92401	+	6.08429i	0.360732	+	0.245943i
$613$	2.72169	+	1.85561i	0.109928	+	0.0749475i	0.617036	−	0.786935i	$-0.288333\pi$
$613$	2.72169	+	1.85561i	0.109928	+	0.0749475i	−0.507108	+	0.861882i	$0.669286\pi$
$614$	4.54223	−	0.684632i	0.183310	−	0.0276295i
$615$	1.00925	+	1.26556i	0.0406970	+	0.0510324i
$616$		0			0
$617$	17.5702	−	22.0323i	0.707349	−	0.886987i	−0.290200	−	0.956966i	$-0.593722\pi$
$617$	17.5702	−	22.0323i	0.707349	−	0.886987i	0.997548	+	0.0699788i	$0.0222931\pi$
$618$	1.86227	−	3.22555i	0.0749117	−	0.129751i
$619$	−8.07778	−	13.9911i	−0.324674	−	0.562351i	0.656773	−	0.754089i	$-0.271921\pi$
$619$	−8.07778	−	13.9911i	−0.324674	−	0.562351i	−0.981446	+	0.191737i	$0.938588\pi$
$620$	25.0598	+	3.77716i	1.00643	+	0.151694i
$621$	9.48200	+	8.79801i	0.380499	+	0.353052i
$622$	−28.1653	+	13.5637i	−1.12932	+	0.543854i
$623$		0			0
$624$	−2.31323	−	1.11399i	−0.0926032	−	0.0445953i
$625$	−11.4032	−	29.0548i	−0.456127	−	1.16219i
$626$	−0.507478	−	6.77183i	−0.0202829	−	0.270657i
$627$	−8.84749	+	2.72909i	−0.353335	+	0.108989i
$628$	−1.76441	+	23.5444i	−0.0704075	+	0.939523i
$629$	−8.19097	−	35.8870i	−0.326595	−	1.43091i
$630$		0			0
$631$	−7.34291	+	32.1714i	−0.292317	+	1.28072i	0.588976	+	0.808151i	$0.299531\pi$
$631$	−7.34291	+	32.1714i	−0.292317	+	1.28072i	−0.881292	+	0.472572i	$0.843326\pi$
$632$	5.10202	+	1.57377i	0.202948	+	0.0626010i
$633$	−3.40810	+	8.68369i	−0.135460	+	0.345146i
$634$	16.3716	−	15.1906i	0.650200	−	0.603297i
$635$	−33.5628	+	22.8827i	−1.33190	+	0.908074i
$636$	6.13932			0.243440
$637$		0			0
$638$	−25.9631			−1.02789
$639$	−14.8405	+	10.1181i	−0.587081	+	0.400265i
$640$	−2.03332	+	1.88665i	−0.0803742	+	0.0745763i
$641$	−7.89589	+	20.1184i	−0.311869	+	0.794629i	0.685889	+	0.727706i	$0.259413\pi$
$641$	−7.89589	+	20.1184i	−0.311869	+	0.794629i	−0.997758	+	0.0669230i	$0.978682\pi$
$642$	−13.3184	−	4.10818i	−0.525635	−	0.162137i
$643$	6.63944	−	29.0893i	0.261834	−	1.14717i	−0.657426	−	0.753519i	$-0.728355\pi$
$643$	6.63944	−	29.0893i	0.261834	−	1.14717i	0.919260	−	0.393651i	$-0.128788\pi$
$644$		0			0
$645$	−0.495564	−	2.17121i	−0.0195128	−	0.0854912i
$646$	−1.48951	+	19.8761i	−0.0586038	+	0.782014i
$647$	7.14063	−	2.20259i	0.280727	−	0.0865928i	−0.151194	−	0.988504i	$-0.548312\pi$
$647$	7.14063	−	2.20259i	0.280727	−	0.0865928i	0.431921	+	0.901911i	$0.357836\pi$
$648$	−0.330490	−	4.41008i	−0.0129829	−	0.173244i
$649$	3.42158	+	8.71803i	0.134309	+	0.342213i
$650$	8.47090	+	4.07937i	0.332256	+	0.160006i
$651$		0			0
$652$	−8.63386	+	4.15785i	−0.338128	+	0.162834i
$653$	19.9187	+	18.4818i	0.779478	+	0.723250i	0.965814	−	0.259236i	$-0.0834708\pi$
$653$	19.9187	+	18.4818i	0.779478	+	0.723250i	−0.186336	+	0.982486i	$0.559661\pi$
$654$	−7.34833	−	1.10758i	−0.287343	−	0.0433099i
$655$	−1.20077	−	2.07980i	−0.0469181	−	0.0812645i
$656$	0.396650	−	0.687018i	0.0154866	−	0.0268235i
$657$	14.0639	−	17.6355i	0.548684	−	0.688028i
$658$		0			0
$659$	−15.2150	−	19.0790i	−0.592692	−	0.743212i	0.391527	−	0.920166i	$-0.371947\pi$
$659$	−15.2150	−	19.0790i	−0.592692	−	0.743212i	−0.984219	+	0.176955i	$0.943375\pi$
$660$	5.59663	−	0.843556i	0.217848	−	0.0328354i
$661$	−3.37953	−	2.30413i	−0.131449	−	0.0896201i	0.495811	−	0.868431i	$-0.334871\pi$
$661$	−3.37953	−	2.30413i	−0.131449	−	0.0896201i	−0.627259	+	0.778811i	$0.715823\pi$
$662$	−12.1423	−	8.27846i	−0.471923	−	0.321751i
$663$	11.1520	−	1.68090i	0.433109	−	0.0652806i
$664$	6.44695	+	8.08421i	0.250190	+	0.313728i
$665$		0			0
$666$	−12.8470	+	16.1096i	−0.497811	+	0.624235i
$667$	−15.0750	+	26.1107i	−0.583708	+	1.01101i
$668$	7.24597	+	12.5504i	0.280355	+	0.485589i
$669$	6.73109	+	1.01455i	0.260239	+	0.0392247i
$670$	24.1773	+	22.4333i	0.934050	+	0.866672i
$671$	−0.986917	+	0.475274i	−0.0380995	+	0.0183477i
$672$		0			0
$673$	35.1549	+	16.9297i	1.35512	+	0.652591i	0.963543	−	0.267554i	$-0.0862154\pi$
$673$	35.1549	+	16.9297i	1.35512	+	0.652591i	0.391577	+	0.920145i	$0.371930\pi$
$674$	8.27941	+	21.0956i	0.318911	+	0.812572i
$675$	−0.808406	−	10.7874i	−0.0311156	−	0.415209i
$676$	−0.782298	+	0.241307i	−0.0300884	+	0.00928104i
$677$	−1.73824	+	23.1952i	−0.0668060	+	0.891464i	0.858639	+	0.512581i	$0.171311\pi$
$677$	−1.73824	+	23.1952i	−0.0668060	+	0.891464i	−0.925445	+	0.378883i	$0.876308\pi$
$678$	0.751782	+	3.29377i	0.0288720	+	0.126497i
$679$		0			0
$680$	2.71123	−	11.8787i	0.103971	−	0.455526i
$681$	−12.9788	−	4.00342i	−0.497347	−	0.153411i
$682$	−9.25879	+	23.5910i	−0.354537	+	0.903346i
$683$	5.36871	−	4.98143i	0.205428	−	0.190609i	−0.570749	−	0.821125i	$-0.693347\pi$
$683$	5.36871	−	4.98143i	0.205428	−	0.190609i	0.776177	+	0.630516i	$0.217156\pi$
$684$	9.21850	−	6.28506i	0.352478	−	0.240315i
$685$	61.0832			2.33387
$686$		0			0
$687$	1.84143			0.0702548
$688$	−0.901782	+	0.614825i	−0.0343801	+	0.0234400i
$689$	−21.3521	+	19.8119i	−0.813452	+	0.754773i
$690$	2.40123	−	6.11824i	0.0914134	−	0.232918i
$691$	−46.5723	−	14.3657i	−1.77170	−	0.546496i	−0.775321	−	0.631568i	$-0.782412\pi$
$691$	−46.5723	−	14.3657i	−1.77170	−	0.546496i	−0.996375	+	0.0850721i	$0.972888\pi$
$692$	0.746308	−	3.26979i	0.0283704	−	0.124299i
$693$		0			0
$694$	1.65371	+	7.24540i	0.0627741	+	0.275031i
$695$	1.74824	−	23.3286i	0.0663144	−	0.884905i
$696$	−6.57976	+	2.02959i	−0.249405	+	0.0769313i
$697$	0.260409	+	3.47492i	0.00986370	+	0.131622i
$698$	2.15971	+	5.50284i	0.0817461	+	0.208286i
$699$	−0.546056	−	0.262967i	−0.0206537	−	0.00994631i
$700$		0			0
$701$	−31.4246	+	15.1333i	−1.18689	+	0.571576i	−0.919911	−	0.392127i	$-0.871739\pi$
$701$	−31.4246	+	15.1333i	−1.18689	+	0.571576i	−0.266978	+	0.963703i	$0.586025\pi$
$702$	−10.2741	−	9.53297i	−0.387771	−	0.359799i
$703$	−37.5999	−	5.66727i	−1.41811	−	0.213745i
$704$	−1.38689	−	2.40216i	−0.0522703	−	0.0905349i
$705$	−2.97609	+	5.15474i	−0.112086	+	0.194139i
$706$	3.36402	−	4.21834i	0.126606	−	0.158759i
$707$		0			0
$708$	1.54863	+	1.94191i	0.0582009	+	0.0729816i
$709$	42.8585	−	6.45988i	1.60958	−	0.242606i	0.718195	−	0.695842i	$-0.244969\pi$
$709$	42.8585	−	6.45988i	1.60958	−	0.242606i	0.891390	+	0.453237i	$0.149731\pi$
$710$	16.7413	+	11.4140i	0.628290	+	0.428361i
$711$	10.8471	+	7.39546i	0.406800	+	0.277351i
$712$	−1.64612	+	0.248113i	−0.0616910	+	0.00929843i
$713$	18.3492	+	23.0091i	0.687182	+	0.861699i
$714$		0			0
$715$	−16.7425	+	20.9944i	−0.626134	+	0.785147i
$716$	2.08610	−	3.61322i	0.0779611	−	0.135033i
$717$	−8.74481	−	15.1465i	−0.326581	−	0.565655i
$718$	−17.4087	−	2.62394i	−0.649686	−	0.0979245i
$719$	−6.54579	−	6.07360i	−0.244117	−	0.226507i	0.548619	−	0.836072i	$-0.315154\pi$
$719$	−6.54579	−	6.07360i	−0.244117	−	0.226507i	−0.792736	+	0.609565i	$0.791344\pi$
$720$	−6.14487	+	2.95921i	−0.229006	+	0.110283i
$721$		0			0
$722$	1.43213	+	0.689678i	0.0532984	+	0.0256671i
$723$	7.85733	+	20.0202i	0.292217	+	0.744557i
$724$	−1.60341	−	21.3961i	−0.0595904	−	0.795178i
$725$	24.0947	−	7.43223i	0.894855	−	0.276026i
$726$	0.181752	−	2.42532i	0.00674546	−	0.0900119i
$727$	7.19300	+	31.5146i	0.266774	+	1.16881i	0.913742	+	0.406295i	$0.133179\pi$
$727$	7.19300	+	31.5146i	0.266774	+	1.16881i	−0.646969	+	0.762517i	$0.723964\pi$
$728$		0			0
$729$	0.447683	−	1.96143i	0.0165809	−	0.0726455i
$730$	−24.3153	−	7.50028i	−0.899950	−	0.277598i
$731$	1.75153	−	4.46283i	0.0647827	−	0.165064i
$732$	−0.212958	+	0.197596i	−0.00787117	+	0.00730338i
$733$	17.0438	−	11.6203i	0.629528	−	0.429205i	−0.206077	−	0.978536i	$-0.566070\pi$
$733$	17.0438	−	11.6203i	0.629528	−	0.429205i	0.835605	+	0.549331i	$0.185117\pi$
$734$	−1.30361			−0.0481170
$735$		0			0
$736$	−3.22109			−0.118731
$737$	−27.2508	+	18.5793i	−1.00379	+	0.684376i
$738$	1.42989	−	1.32675i	0.0526351	−	0.0488382i
$739$	0.742329	−	1.89142i	0.0273070	−	0.0695771i	−0.916570	−	0.399874i	$-0.869054\pi$
$739$	0.742329	−	1.89142i	0.0273070	−	0.0695771i	0.943877	+	0.330297i	$0.107149\pi$
$740$	22.2114	+	6.85132i	0.816509	+	0.251860i
$741$	2.59240	−	11.3581i	0.0952343	−	0.417249i
$742$		0			0
$743$	−3.11438	−	13.6450i	−0.114255	−	0.500586i	−0.999379	−	0.0352303i	$-0.988784\pi$
$743$	−3.11438	−	13.6450i	−0.114255	−	0.500586i	0.885124	−	0.465356i	$-0.154074\pi$
$744$	−0.502274	+	6.70238i	−0.0184143	+	0.245721i
$745$	−7.36678	+	2.27235i	−0.269898	+	0.0832525i
$746$	−0.303100	−	4.04459i	−0.0110973	−	0.148083i
$747$	9.28868	+	23.6672i	0.339855	+	0.865937i
$748$	10.9775	+	5.28650i	0.401379	+	0.193294i
$749$		0			0
$750$	4.23966	−	2.04171i	0.154810	−	0.0745528i
$751$	4.24526	+	3.93902i	0.154912	+	0.143737i	0.753821	−	0.657080i	$-0.228209\pi$
$751$	4.24526	+	3.93902i	0.154912	+	0.143737i	−0.598909	+	0.800817i	$0.704399\pi$
$752$	2.88447	+	0.434764i	0.105186	+	0.0158542i
$753$	3.56430	+	6.17354i	0.129890	+	0.224976i
$754$	16.3344	−	28.2920i	0.594863	−	1.03033i
$755$	7.58548	−	9.51189i	0.276064	−	0.346173i
$756$		0			0
$757$	4.41708	+	5.53885i	0.160542	+	0.201313i	0.855596	−	0.517645i	$-0.173191\pi$
$757$	4.41708	+	5.53885i	0.160542	+	0.201313i	−0.695054	+	0.718957i	$0.744620\pi$
$758$	17.8228	−	2.68636i	0.647355	−	0.0975731i
$759$	5.43052	+	3.70247i	0.197115	+	0.134391i
$760$	−10.3992	−	7.09007i	−0.377219	−	0.257184i
$761$	−32.1371	+	4.84389i	−1.16497	+	0.175591i	−0.702924	−	0.711265i	$-0.748122\pi$
$761$	−32.1371	+	4.84389i	−1.16497	+	0.175591i	−0.462046	+	0.886856i	$0.652884\pi$
$762$	−6.71694	−	8.42278i	−0.243329	−	0.305125i
$763$		0			0
$764$	−8.79641	+	11.0304i	−0.318243	+	0.399064i
$765$	14.9795	−	25.9452i	0.541584	−	0.938050i
$766$	4.56979	+	7.91510i	0.165113	+	0.285984i
$767$	−11.6527	−	1.75636i	−0.420753	−	0.0634184i
$768$	−0.539257	−	0.500357i	−0.0194588	−	0.0180551i
$769$	18.7846	−	9.04618i	0.677389	−	0.326213i	−0.0633642	−	0.997990i	$-0.520183\pi$
$769$	18.7846	−	9.04618i	0.677389	−	0.326213i	0.740753	+	0.671777i	$0.234469\pi$
$770$		0			0
$771$	2.04813	+	0.986326i	0.0737615	+	0.0355217i
$772$	−4.51224	−	11.4970i	−0.162399	−	0.413786i
$773$	−1.67286	−	22.3228i	−0.0601686	−	0.802894i	−0.942913	−	0.333040i	$-0.891926\pi$
$773$	−1.67286	−	22.3228i	−0.0601686	−	0.802894i	0.882744	−	0.469854i	$-0.155693\pi$
$774$	−2.56443	+	0.791022i	−0.0921766	+	0.0284327i
$775$	1.83930	−	24.5437i	0.0660695	−	0.881637i
$776$	−2.81422	−	12.3299i	−0.101025	−	0.442618i
$777$		0			0
$778$	−4.77797	+	20.9337i	−0.171299	+	0.750508i
$779$	3.43973	+	1.06102i	0.123241	+	0.0380149i
$780$	−2.60183	+	6.62935i	−0.0931604	+	0.237369i
$781$	−14.8531	+	13.7817i	−0.531487	+	0.493148i
$782$	11.6905	−	7.97043i	0.418051	−	0.285022i
$783$	−37.5878			−1.34328
$784$		0			0
$785$	65.4900			2.33744
$786$	0.526242	−	0.358786i	0.0187704	−	0.0127975i
$787$	9.80348	−	9.09630i	0.349456	−	0.324248i	−0.485840	−	0.874048i	$-0.661486\pi$
$787$	9.80348	−	9.09630i	0.349456	−	0.324248i	0.835297	+	0.549800i	$0.185296\pi$
$788$	−5.91995	+	15.0838i	−0.210889	+	0.537337i
$789$	12.4397	+	3.83714i	0.442865	+	0.136606i
$790$	3.29550	−	14.4385i	0.117249	−	0.513700i
$791$		0			0
$792$	−1.51766	−	6.64929i	−0.0539276	−	0.236272i
$793$	0.103001	−	1.37445i	0.00365768	−	0.0488083i
$794$	24.0480	−	7.41783i	0.853432	−	0.263249i
$795$	−1.27259	−	16.9815i	−0.0451340	−	0.602272i
$796$	6.55423	+	16.6999i	0.232309	+	0.591913i
$797$	−27.5763	−	13.2801i	−0.976804	−	0.470404i	−0.123799	−	0.992307i	$-0.539508\pi$
$797$	−27.5763	−	13.2801i	−0.976804	−	0.470404i	−0.853005	+	0.521903i	$0.825222\pi$
$798$		0			0
$799$	−11.5445	+	5.55956i	−0.408417	+	0.196683i
$800$	1.97473	+	1.83228i	0.0698172	+	0.0647809i
$801$	−4.04756	−	0.610071i	−0.143013	−	0.0215558i
$802$	−4.15439	−	7.19562i	−0.146697	−	0.254086i
$803$	12.7229	−	22.0367i	0.448981	−	0.777659i
$804$	−5.45370	+	6.83873i	−0.192337	+	0.241183i
$805$		0			0
$806$	−19.8820	−	24.9313i	−0.700315	−	0.878167i
$807$	13.9442	−	2.10175i	0.490859	−	0.0739850i
$808$	−5.70368	−	3.88870i	−0.200655	−	0.136804i
$809$	−13.1299	−	8.95184i	−0.461624	−	0.314730i	0.310082	−	0.950710i	$-0.399644\pi$
$809$	−13.1299	−	8.95184i	−0.461624	−	0.314730i	−0.771705	+	0.635980i	$0.780596\pi$
$810$	−12.1299	+	1.82829i	−0.426201	+	0.0642394i
$811$	17.3645	+	21.7744i	0.609751	+	0.764604i	0.986862	−	0.161564i	$-0.0516539\pi$
$811$	17.3645	+	21.7744i	0.609751	+	0.764604i	−0.377111	+	0.926168i	$0.623082\pi$
$812$		0			0
$813$	−13.6425	+	17.1072i	−0.478465	+	0.599976i
$814$	−11.6221	+	20.1300i	−0.407353	+	0.705556i
$815$	13.2904	+	23.0196i	0.465541	+	0.806341i
$816$	3.19526	+	0.481608i	0.111857	+	0.0168597i
$817$	−3.63040	−	3.36852i	−0.127012	−	0.117849i
$818$	−14.6796	+	7.06930i	−0.513259	+	0.247172i
$819$		0			0
$820$	−1.98253	−	0.954734i	−0.0692328	−	0.0333408i
$821$	4.40800	+	11.2314i	0.153840	+	0.391979i	0.986928	−	0.161162i	$-0.0515243\pi$
$821$	4.40800	+	11.2314i	0.153840	+	0.391979i	−0.833088	+	0.553141i	$0.813429\pi$
$822$	1.21062	+	16.1545i	0.0422251	+	0.563455i
$823$	21.2771	−	6.56313i	0.741675	−	0.228776i	0.0991833	−	0.995069i	$-0.468377\pi$
$823$	21.2771	−	6.56313i	0.741675	−	0.228776i	0.642492	+	0.766293i	$0.277901\pi$
$824$	−0.378363	+	5.04890i	−0.0131809	+	0.175887i
$825$	−1.22314	−	5.35893i	−0.0425843	−	0.186574i
$826$		0			0
$827$	−0.179160	+	0.784951i	−0.00623000	+	0.0272954i	−0.977947	−	0.208851i	$-0.933027\pi$
$827$	−0.179160	+	0.784951i	−0.00623000	+	0.0272954i	0.971717	+	0.236147i	$0.0758846\pi$
$828$	−7.56830	−	2.33451i	−0.263017	−	0.0811298i
$829$	14.2845	−	36.3964i	0.496122	−	1.26410i	−0.435342	−	0.900265i	$-0.643373\pi$
$829$	14.2845	−	36.3964i	0.496122	−	1.26410i	0.931464	−	0.363833i	$-0.118532\pi$
$830$	21.0248	−	19.5081i	0.729780	−	0.677137i
$831$	−4.85720	+	3.31159i	−0.168495	+	0.114878i
$832$	3.49018			0.121000
$833$		0			0
$834$	6.20432			0.214838
$835$	33.2127	−	22.6440i	1.14937	−	0.783629i
$836$	9.22635	−	8.56080i	0.319100	−	0.296081i
$837$	−13.4043	+	34.1536i	−0.463320	+	1.18052i
$838$	−11.3334	−	3.49589i	−0.391506	−	0.120763i
$839$	−11.0750	+	48.5229i	−0.382353	+	1.67520i	0.307735	+	0.951472i	$0.400429\pi$
$839$	−11.0750	+	48.5229i	−0.382353	+	1.67520i	−0.690088	+	0.723725i	$0.742428\pi$
$840$		0			0
$841$	−13.0427	−	57.1438i	−0.449749	−	1.97048i
$842$	1.86065	−	24.8286i	0.0641221	−	0.855649i
$843$	8.63268	−	2.66283i	0.297325	−	0.0917127i
$844$	−0.947650	−	12.6455i	−0.0326195	−	0.435276i
$845$	0.829619	+	2.11383i	0.0285398	+	0.0727181i
$846$	6.46226	+	3.11206i	0.222177	+	0.106995i
$847$		0			0
$848$	−7.51916	+	3.62104i	−0.258209	+	0.124347i
$849$	3.62719	+	3.36554i	0.124485	+	0.115505i
$850$	−11.7009	−	1.76362i	−0.401336	−	0.0604917i
$851$	13.4963	+	23.3763i	0.462647	+	0.801328i
$852$	−2.68685	+	4.65376i	−0.0920499	+	0.159435i
$853$	10.7506	−	13.4808i	0.368092	−	0.461573i	−0.562947	−	0.826493i	$-0.690332\pi$
$853$	10.7506	−	13.4808i	0.368092	−	0.461573i	0.931039	+	0.364920i	$0.118904\pi$
$854$		0			0
$855$	−19.2955	−	24.1958i	−0.659891	−	0.827478i
$856$	18.7348	−	2.82382i	0.640342	−	0.0965161i
$857$	37.1984	+	25.3614i	1.27067	+	0.866330i	0.995472	−	0.0950568i	$-0.0303033\pi$
$857$	37.1984	+	25.3614i	1.27067	+	0.866330i	0.275201	+	0.961387i	$0.411256\pi$
$858$	−5.88418	−	4.01176i	−0.200882	−	0.136959i
$859$	45.2419	−	6.81912i	1.54363	−	0.232665i	0.678649	−	0.734463i	$-0.262566\pi$
$859$	45.2419	−	6.81912i	1.54363	−	0.232665i	0.864985	+	0.501798i	$0.167328\pi$
$860$	1.88754	+	2.36691i	0.0643647	+	0.0807108i
$861$		0			0
$862$	−2.82742	+	3.54547i	−0.0963023	+	0.120759i
$863$	13.5983	−	23.5529i	0.462891	−	0.801750i	−0.536213	−	0.844083i	$-0.680146\pi$
$863$	13.5983	−	23.5529i	0.462891	−	0.801750i	0.999104	+	0.0423325i	$0.0134789\pi$
$864$	−2.00785	−	3.47770i	−0.0683085	−	0.118314i
$865$	−9.19900	−	1.38653i	−0.312775	−	0.0471433i
$866$	8.76907	+	8.13651i	0.297985	+	0.276490i
$867$	−1.52115	+	0.732545i	−0.0516608	+	0.0248785i
$868$		0			0
$869$	13.3432	+	6.42575i	0.452637	+	0.217979i
$870$	6.97777	+	17.7791i	0.236568	+	0.602767i
$871$	−3.10130	−	41.3840i	−0.105084	−	1.40224i
$872$	9.65316	−	2.97761i	0.326897	−	0.100834i
$873$	2.32388	−	31.0100i	0.0786514	−	1.04953i
$874$	−3.25235	−	14.2495i	−0.110012	−	0.481996i
$875$		0			0
$876$	1.50168	−	6.57927i	0.0507369	−	0.222293i
$877$	−19.4727	−	6.00654i	−0.657547	−	0.202826i	−0.0520139	−	0.998646i	$-0.516564\pi$
$877$	−19.4727	−	6.00654i	−0.657547	−	0.202826i	−0.605533	+	0.795820i	$0.707040\pi$
$878$	2.19445	−	5.59138i	0.0740592	−	0.188700i
$879$	9.28334	−	8.61368i	0.313119	−	0.290532i
$880$	−6.35695	+	4.33410i	−0.214293	+	0.146102i
$881$	−2.16278			−0.0728658			−0.0364329	−	0.999336i	$-0.511600\pi$
$881$	−2.16278			−0.0728658			−0.0364329	+	0.999336i	$0.511600\pi$
$882$		0			0
$883$	52.2159			1.75721			0.878603	−	0.477554i	$-0.158476\pi$
$883$	52.2159			1.75721			0.878603	+	0.477554i	$0.158476\pi$
$884$	−12.6671	+	8.63627i	−0.426040	+	0.290469i
$885$	5.05037	−	4.68606i	0.169766	−	0.157520i
$886$	4.35146	−	11.0873i	0.146190	−	0.372487i
$887$	−19.5721	−	6.03720i	−0.657167	−	0.202709i	−0.0518025	−	0.998657i	$-0.516497\pi$
$887$	−19.5721	−	6.03720i	−0.657167	−	0.202709i	−0.605365	+	0.795948i	$0.706973\pi$
$888$	−1.37174	+	6.01000i	−0.0460327	+	0.201682i
$889$		0			0
$890$	1.02750	+	4.50178i	0.0344419	+	0.150900i
$891$	0.916706	−	12.2326i	0.0307108	−	0.409807i
$892$	−8.84232	+	2.72750i	−0.296063	+	0.0913233i
$893$	0.989151	+	13.1993i	0.0331007	+	0.441698i
$894$	−0.746968	−	1.90324i	−0.0249823	−	0.0636539i
$895$	−10.4267	−	5.02122i	−0.348525	−	0.167841i
$896$		0			0
$897$	−7.45112	+	3.58827i	−0.248786	+	0.119809i
$898$	1.52863	+	1.41836i	0.0510110	+	0.0473313i
$899$	−84.5651	−	12.7461i	−2.82040	−	0.425108i
$900$	3.31187	+	5.73633i	0.110396	+	0.191211i
$901$	18.3296	−	31.7478i	0.610647	−	1.05767i
$902$	1.37195	−	1.72037i	0.0456810	−	0.0572821i
$903$		0			0
$904$	−2.86345	−	3.59065i	−0.0952369	−	0.119423i
$905$	−58.8496	+	8.87015i	−1.95623	+	0.294854i
$906$	2.66593	+	1.81760i	0.0885695	+	0.0603857i
$907$	−19.9151	−	13.5779i	−0.661269	−	0.450846i	0.185615	−	0.982622i	$-0.440572\pi$
$907$	−19.9151	−	13.5779i	−0.661269	−	0.450846i	−0.846885	+	0.531777i	$0.821525\pi$
$908$	18.2570	−	2.75181i	0.605881	−	0.0913219i
$909$	−10.5830	−	13.2707i	−0.351017	−	0.440161i
$910$		0			0
$911$	17.9317	−	22.4856i	0.594103	−	0.744981i	−0.390343	−	0.920670i	$-0.627644\pi$
$911$	17.9317	−	22.4856i	0.594103	−	0.744981i	0.984446	+	0.175688i	$0.0562150\pi$
$912$	1.66899	−	2.89078i	0.0552659	−	0.0957233i
$913$	14.3406	+	24.8386i	0.474604	+	0.822037i
$914$	7.29321	+	1.09927i	0.241238	+	0.0363608i
$915$	0.590699	+	0.548089i	0.0195279	+	0.0181193i
$916$	−2.25529	+	1.08609i	−0.0745170	+	0.0358855i
$917$		0			0
$918$	15.8926	+	7.65347i	0.524534	+	0.252602i
$919$	6.35853	+	16.2013i	0.209749	+	0.534431i	0.996570	−	0.0827494i	$-0.0263701\pi$
$919$	6.35853	+	16.2013i	0.209749	+	0.534431i	−0.786822	+	0.617180i	$0.788275\pi$
$920$	0.667683	+	8.90961i	0.0220129	+	0.293741i
$921$	3.22903	−	0.996024i	0.106400	−	0.0328201i
$922$	1.00898	−	13.4640i	0.0332291	−	0.443412i
$923$	−5.67323	−	24.8560i	−0.186737	−	0.818147i
$924$		0			0
$925$	5.02325	−	22.0083i	0.165163	−	0.723628i
$926$	3.15241	+	0.972390i	0.103595	+	0.0319547i
$927$	−4.54823	+	11.5887i	−0.149383	+	0.380623i
$928$	6.86151	−	6.36655i	0.225240	−	0.208992i
$929$	7.27006	−	4.95665i	0.238523	−	0.162622i	−0.438159	−	0.898897i	$-0.644369\pi$
$929$	7.27006	−	4.95665i	0.238523	−	0.162622i	0.676682	+	0.736275i	$0.263417\pi$
$930$	18.6430			0.611329
$931$		0			0
$932$	0.823884			0.0269872
$933$	−19.0008	+	12.9545i	−0.622057	+	0.424111i
$934$	20.2889	−	18.8253i	0.663872	−	0.615983i
$935$	12.3471	−	31.4599i	0.403794	−	1.02885i
$936$	8.20054	+	2.52953i	0.268043	+	0.0826803i
$937$	−2.63156	+	11.5296i	−0.0859693	+	0.376656i	−0.999550	−	0.0300016i	$-0.990449\pi$
$937$	−2.63156	+	11.5296i	−0.0859693	+	0.376656i	0.913581	+	0.406658i	$0.133306\pi$
$938$		0			0
$939$	−1.11161	−	4.87030i	−0.0362761	−	0.158936i
$940$	0.604660	−	8.06862i	0.0197218	−	0.263169i
$941$	8.03412	−	2.47820i	0.261905	−	0.0807869i	−0.161022	−	0.986951i	$-0.551479\pi$
$941$	8.03412	−	2.47820i	0.261905	−	0.0807869i	0.422927	+	0.906164i	$0.361003\pi$
$942$	1.29795	+	17.3200i	0.0422897	+	0.564316i
$943$	−0.933553	−	2.37866i	−0.0304007	−	0.0774597i
$944$	−3.04205	−	1.46497i	−0.0990102	−	0.0476808i
$945$		0			0
$946$	−2.72758	+	1.31353i	−0.0886813	+	0.0427067i
$947$	0.306434	+	0.284329i	0.00995777	+	0.00923946i	0.685136	−	0.728415i	$-0.259743\pi$
$947$	0.306434	+	0.284329i	0.00995777	+	0.00923946i	−0.675178	+	0.737655i	$0.735933\pi$
$948$	3.88384	+	0.585395i	0.126141	+	0.0190128i
$949$	16.0089	+	27.7283i	0.519671	+	0.900097i
$950$	−6.11175	+	10.5859i	−0.198292	+	0.343451i
$951$	10.2435	−	12.8449i	0.332167	−	0.416525i
$952$		0			0
$953$	−1.59018	−	1.99403i	−0.0515111	−	0.0645929i	0.755409	−	0.655254i	$-0.227438\pi$
$953$	−1.59018	−	1.99403i	−0.0515111	−	0.0645929i	−0.806920	+	0.590661i	$0.798867\pi$
$954$	−20.2914	+	3.05844i	−0.656959	+	0.0990206i
$955$	32.3336	+	22.0446i	1.04629	+	0.713348i
$956$	19.6438	+	13.3929i	0.635325	+	0.433157i
$957$	−18.8860	+	2.84661i	−0.610498	+	0.0920177i
$958$	16.5669	+	20.7743i	0.535253	+	0.671187i
$959$		0			0
$960$	−1.27222	+	1.59531i	−0.0410607	+	0.0514885i
$961$	−26.2386	+	45.4466i	−0.846407	+	1.46602i
$962$	−14.6237	−	25.3291i	−0.471488	−	0.816642i
$963$	46.0660	+	6.94333i	1.48445	+	0.223746i
$964$	−21.4314	−	19.8854i	−0.690259	−	0.640466i
$965$	−30.8656	+	14.8641i	−0.993600	+	0.478493i
$966$		0			0
$967$	17.2984	+	8.33045i	0.556278	+	0.267889i	0.690830	−	0.723017i	$-0.257245\pi$
$967$	17.2984	+	8.33045i	0.556278	+	0.267889i	−0.134552	+	0.990906i	$0.542960\pi$
$968$	1.20787	+	3.07761i	0.0388225	+	0.0989182i
$969$	1.09573	+	14.6215i	0.0351999	+	0.469710i
$970$	−33.5214	+	10.3400i	−1.07631	+	0.331997i
$971$	0.0160945	−	0.214767i	0.000516499	−	0.00689220i	−0.996940	−	0.0781757i	$-0.975090\pi$
$971$	0.0160945	−	0.214767i	0.000516499	−	0.00689220i	0.997456	+	0.0712835i	$0.0227095\pi$
$972$	−3.40466	−	14.9168i	−0.109205	−	0.478457i
$973$		0			0
$974$	3.50667	−	15.3637i	0.112361	−	0.492285i
$975$	6.60914	+	2.03865i	0.211662	+	0.0652890i
$976$	0.144277	−	0.367612i	0.00461820	−	0.0117670i
$977$	−7.21459	+	6.69416i	−0.230815	+	0.214165i	−0.787098	−	0.616828i	$-0.788418\pi$
$977$	−7.21459	+	6.69416i	−0.230815	+	0.214165i	0.556283	+	0.830993i	$0.312227\pi$
$978$	−5.82454	+	3.97110i	−0.186248	+	0.126982i
$979$	−4.61755			−0.147578
$980$		0			0
$981$	24.8392			0.793053
$982$	−13.5916	+	9.26658i	−0.433725	+	0.295709i
$983$	20.7417	−	19.2455i	0.661557	−	0.613835i	−0.276211	−	0.961097i	$-0.589079\pi$
$983$	20.7417	−	19.2455i	0.661557	−	0.613835i	0.937768	+	0.347262i	$0.112889\pi$
$984$	0.213205	−	0.543237i	0.00679672	−	0.0173178i
$985$	42.9492	+	13.2481i	1.36847	+	0.422119i
$986$	−9.14912	+	40.0849i	−0.291367	+	1.27656i
$987$		0			0
$988$	3.52405	+	15.4399i	0.112115	+	0.491207i
$989$	−0.262721	+	3.50577i	−0.00835404	+	0.111477i
$990$	−18.0775	+	5.57617i	−0.574541	+	0.177222i
$991$	−4.51781	−	60.2859i	−0.143513	−	1.91505i	−0.350262	−	0.936652i	$-0.613907\pi$
$991$	−4.51781	−	60.2859i	−0.143513	−	1.91505i	0.206749	−	0.978394i	$-0.433712\pi$
$992$	−3.33797	−	8.50501i	−0.105981	−	0.270034i
$993$	−9.74014	−	4.69060i	−0.309094	−	0.148852i
$994$		0			0
$995$	44.8337	−	21.5908i	1.42132	−	0.684474i
$996$	5.57597	+	5.17374i	0.176681	+	0.163936i
$997$	−5.16866	−	0.779050i	−0.163693	−	0.0246728i	0.0666843	−	0.997774i	$-0.478758\pi$
$997$	−5.16866	−	0.779050i	−0.163693	−	0.0246728i	−0.230377	+	0.973101i	$0.573996\pi$
$998$	3.53061	+	6.11519i	0.111759	+	0.193573i
$999$	−16.8257	+	29.1429i	−0.532341	+	0.922042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.h.373.2		36
7.2	even	3		98.2.e.b.29.2	✓	18
7.3	odd	6		686.2.g.g.459.2		36
7.4	even	3	inner	686.2.g.h.459.2		36
7.5	odd	6		686.2.e.b.197.2		18
7.6	odd	2		686.2.g.g.373.2		36
21.2	odd	6		882.2.u.g.127.1		18
28.23	odd	6		784.2.u.d.225.2		18
49.2	even	21		4802.2.a.d.1.5		9
49.4	even	21	inner	686.2.g.h.263.2		36
49.22	even	7	inner	686.2.g.h.275.2		36
49.23	even	21		98.2.e.b.71.2	yes	18
49.26	odd	42		686.2.e.b.491.2		18
49.27	odd	14		686.2.g.g.275.2		36
49.45	odd	42		686.2.g.g.263.2		36
49.47	odd	42		4802.2.a.c.1.5		9
147.23	odd	42		882.2.u.g.757.1		18
196.23	odd	42		784.2.u.d.561.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.29.2	✓	18	7.2	even	3
98.2.e.b.71.2	yes	18	49.23	even	21
686.2.e.b.197.2		18	7.5	odd	6
686.2.e.b.491.2		18	49.26	odd	42
686.2.g.g.263.2		36	49.45	odd	42
686.2.g.g.275.2		36	49.27	odd	14
686.2.g.g.373.2		36	7.6	odd	2
686.2.g.g.459.2		36	7.3	odd	6
686.2.g.h.263.2		36	49.4	even	21	inner
686.2.g.h.275.2		36	49.22	even	7	inner
686.2.g.h.373.2		36	1.1	even	1	trivial
686.2.g.h.459.2		36	7.4	even	3	inner
784.2.u.d.225.2		18	28.23	odd	6
784.2.u.d.561.2		18	196.23	odd	42
882.2.u.g.127.1		18	21.2	odd	6
882.2.u.g.757.1		18	147.23	odd	42
4802.2.a.c.1.5		9	49.47	odd	42
4802.2.a.d.1.5		9	49.2	even	21

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.826239 + 0.563320i) q^{2} +(-0.539257 + 0.500357i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-2.65055 - 0.817585i) q^{5} +(0.163694 - 0.717189i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-0.183750 + 2.45197i) q^{9} +O(q^{10})\)	\(q+(-0.826239 + 0.563320i) q^{2} +(-0.539257 + 0.500357i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-2.65055 - 0.817585i) q^{5} +(0.163694 - 0.717189i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-0.183750 + 2.45197i) q^{9} +(2.65055 - 0.817585i) q^{10} +(0.207285 + 2.76602i) q^{11} +(0.268757 + 0.684781i) q^{12} +(-3.14454 - 1.51433i) q^{13} +(1.83841 - 0.885332i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(4.34356 + 0.654686i) q^{17} +(-1.22942 - 2.12942i) q^{18} +(2.26879 - 3.92965i) q^{19} +(-1.72942 + 2.16863i) q^{20} +(-1.72942 - 2.16863i) q^{22} +(-3.18512 + 0.480079i) q^{23} +(-0.607808 - 0.414397i) q^{24} +(2.22576 + 1.51750i) q^{25} +(3.45119 - 0.520184i) q^{26} +(-2.50375 - 3.13960i) q^{27} +(5.83599 - 7.31810i) q^{29} +(-1.02024 + 1.76711i) q^{30} +(-4.56829 - 7.91252i) q^{31} +(0.988831 + 0.149042i) q^{32} +(-1.49578 - 1.38788i) q^{33} +(-3.95761 + 1.90589i) q^{34} +(2.21534 + 1.06685i) q^{36} +(-3.06154 - 7.80067i) q^{37} +(0.339093 + 4.52488i) q^{38} +(2.45342 - 0.756780i) q^{39} +(0.207285 - 2.76602i) q^{40} +(0.176526 + 0.773410i) q^{41} +(0.242866 - 1.06407i) q^{43} +(2.65055 + 0.817585i) q^{44} +(2.49173 - 6.34883i) q^{45} +(2.36123 - 2.19090i) q^{46} +(-2.41018 + 1.64323i) q^{47} +0.735633 q^{48} -2.69384 q^{50} +(-2.66987 + 1.82029i) q^{51} +(-2.55848 + 2.37392i) q^{52} +(3.04900 - 7.76873i) q^{53} +(3.83730 + 1.18365i) q^{54} +(1.71204 - 7.50094i) q^{55} +(0.742771 + 3.25429i) q^{57} +(-0.699489 + 9.33403i) q^{58} +(3.22641 - 0.995216i) q^{59} +(-0.152485 - 2.03478i) q^{60} +(0.144277 + 0.367612i) q^{61} +(8.23178 + 3.96422i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(7.09666 + 6.58473i) q^{65} +(2.01769 + 0.304118i) q^{66} +(5.94527 + 10.2975i) q^{67} +(2.19631 - 3.80412i) q^{68} +(1.47738 - 1.85258i) q^{69} +(4.55451 + 5.71117i) q^{71} +(-2.43138 + 0.366472i) q^{72} +(-7.57967 - 5.16773i) q^{73} +(6.92384 + 4.72059i) q^{74} +(-1.95955 + 0.295354i) q^{75} +(-2.82913 - 3.54762i) q^{76} +(-1.60080 + 2.00734i) q^{78} +(2.66962 - 4.62391i) q^{79} +(1.38689 + 2.40216i) q^{80} +(-4.37306 - 0.659132i) q^{81} +(-0.581530 - 0.539581i) q^{82} +(9.31611 - 4.48640i) q^{83} +(-10.9775 - 5.28650i) q^{85} +(0.398744 + 1.01598i) q^{86} +(0.514567 + 6.86642i) q^{87} +(-2.65055 + 0.817585i) q^{88} +(-0.124404 + 1.66006i) q^{89} +(1.51766 + 6.64929i) q^{90} +(-0.716761 + 3.14033i) q^{92} +(6.42257 + 1.98110i) q^{93} +(1.06572 - 2.71540i) q^{94} +(-9.22635 + 8.56080i) q^{95} +(-0.607808 + 0.414397i) q^{96} -12.6470 q^{97} -6.82029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

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