LMFDB - Embedded newform 912.2.u.a.685.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(229,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("912.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.u (of order $4$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			685.19
Character	$\chi$	$=$	912.685
Dual form			912.2.u.a.229.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0417641 + 1.41360i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.99651 - 0.118075i) q^{4} +(1.69566 - 1.69566i) q^{5} +(-1.02910 + 0.970032i) q^{6} +4.01648i q^{7} +(0.250293 - 2.81733i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.0417641 + 1.41360i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.99651 - 0.118075i) q^{4} +(1.69566 - 1.69566i) q^{5} +(-1.02910 + 0.970032i) q^{6} +4.01648i q^{7} +(0.250293 - 2.81733i) q^{8} +1.00000i q^{9} +(2.32616 + 2.46780i) q^{10} +(3.12754 - 3.12754i) q^{11} +(-1.32826 - 1.49524i) q^{12} +(3.31631 + 3.31631i) q^{13} +(-5.67769 - 0.167745i) q^{14} +2.39803 q^{15} +(3.97212 + 0.471477i) q^{16} +1.28627 q^{17} +(-1.41360 - 0.0417641i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-3.58562 + 3.18519i) q^{20} +(-2.84008 + 2.84008i) q^{21} +(4.29046 + 4.55170i) q^{22} -8.95781i q^{23} +(2.16914 - 1.81517i) q^{24} -0.750527i q^{25} +(-4.82643 + 4.54943i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.474247 - 8.01895i) q^{28} +(3.81503 + 3.81503i) q^{29} +(-0.100151 + 3.38984i) q^{30} -3.28373 q^{31} +(-0.832370 + 5.59528i) q^{32} +4.42301 q^{33} +(-0.0537201 + 1.81827i) q^{34} +(6.81059 + 6.81059i) q^{35} +(0.118075 - 1.99651i) q^{36} +(-2.41733 + 2.41733i) q^{37} +(1.02910 - 0.970032i) q^{38} +4.68997i q^{39} +(-4.35282 - 5.20165i) q^{40} +11.8121i q^{41} +(-3.89612 - 4.13334i) q^{42} +(0.432575 - 0.432575i) q^{43} +(-6.61345 + 5.87488i) q^{44} +(1.69566 + 1.69566i) q^{45} +(12.6627 + 0.374115i) q^{46} -5.81260 q^{47} +(2.47533 + 3.14210i) q^{48} -9.13213 q^{49} +(1.06094 + 0.0313451i) q^{50} +(0.909533 + 0.909533i) q^{51} +(-6.22948 - 7.01263i) q^{52} +(-8.37304 + 8.37304i) q^{53} +(-0.970032 - 1.02910i) q^{54} -10.6065i q^{55} +(11.3158 + 1.00530i) q^{56} -1.00000i q^{57} +(-5.55224 + 5.23358i) q^{58} +(6.07068 - 6.07068i) q^{59} +(-4.78769 - 0.283147i) q^{60} +(9.39559 + 9.39559i) q^{61} +(0.137142 - 4.64188i) q^{62} -4.01648 q^{63} +(-7.87471 - 1.41032i) q^{64} +11.2467 q^{65} +(-0.184723 + 6.25235i) q^{66} +(-4.53509 - 4.53509i) q^{67} +(-2.56806 - 0.151877i) q^{68} +(6.33413 - 6.33413i) q^{69} +(-9.91187 + 9.34299i) q^{70} +0.435690i q^{71} +(2.81733 + 0.250293i) q^{72} -6.52722i q^{73} +(-3.31617 - 3.51809i) q^{74} +(0.530703 - 0.530703i) q^{75} +(1.32826 + 1.49524i) q^{76} +(12.5617 + 12.5617i) q^{77} +(-6.62973 - 0.195873i) q^{78} +5.60770 q^{79} +(7.53482 - 5.93590i) q^{80} -1.00000 q^{81} +(-16.6976 - 0.493323i) q^{82} +(1.87477 + 1.87477i) q^{83} +(6.00560 - 5.33491i) q^{84} +(2.18108 - 2.18108i) q^{85} +(0.593421 + 0.629553i) q^{86} +5.39526i q^{87} +(-8.02851 - 9.59412i) q^{88} -16.5092i q^{89} +(-2.46780 + 2.32616i) q^{90} +(-13.3199 + 13.3199i) q^{91} +(-1.05770 + 17.8844i) q^{92} +(-2.32195 - 2.32195i) q^{93} +(0.242758 - 8.21667i) q^{94} -2.39803 q^{95} +(-4.54504 + 3.36789i) q^{96} -5.55954 q^{97} +(0.381395 - 12.9092i) q^{98} +(3.12754 + 3.12754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{4}+O(q^{10}) $ 72 * q + 4 * q^4	$ 72 q + 4 q^{4} + 8 q^{11} - 8 q^{12} - 12 q^{14} - 4 q^{16} - 4 q^{18} - 44 q^{20} - 52 q^{26} + 52 q^{28} + 16 q^{29} + 8 q^{30} - 64 q^{31} + 40 q^{34} + 16 q^{37} + 4 q^{40} - 8 q^{42} + 8 q^{43} + 68 q^{44} + 104 q^{47} + 16 q^{48} - 72 q^{49} + 116 q^{50} - 8 q^{52} - 16 q^{53} - 28 q^{56} - 92 q^{58} - 32 q^{59} + 32 q^{60} + 24 q^{62} - 40 q^{63} + 28 q^{64} + 16 q^{65} + 28 q^{66} - 8 q^{67} - 100 q^{68} - 20 q^{70} + 4 q^{72} - 124 q^{74} - 16 q^{75} + 8 q^{76} - 16 q^{77} - 12 q^{78} + 48 q^{79} + 44 q^{80} - 72 q^{81} + 52 q^{82} - 8 q^{84} - 64 q^{85} + 48 q^{86} - 32 q^{88} + 8 q^{90} + 8 q^{91} + 96 q^{92} + 12 q^{94} - 20 q^{96} + 208 q^{98} + 8 q^{99}+O(q^{100}) $ 72 * q + 4 * q^4 + 8 * q^11 - 8 * q^12 - 12 * q^14 - 4 * q^16 - 4 * q^18 - 44 * q^20 - 52 * q^26 + 52 * q^28 + 16 * q^29 + 8 * q^30 - 64 * q^31 + 40 * q^34 + 16 * q^37 + 4 * q^40 - 8 * q^42 + 8 * q^43 + 68 * q^44 + 104 * q^47 + 16 * q^48 - 72 * q^49 + 116 * q^50 - 8 * q^52 - 16 * q^53 - 28 * q^56 - 92 * q^58 - 32 * q^59 + 32 * q^60 + 24 * q^62 - 40 * q^63 + 28 * q^64 + 16 * q^65 + 28 * q^66 - 8 * q^67 - 100 * q^68 - 20 * q^70 + 4 * q^72 - 124 * q^74 - 16 * q^75 + 8 * q^76 - 16 * q^77 - 12 * q^78 + 48 * q^79 + 44 * q^80 - 72 * q^81 + 52 * q^82 - 8 * q^84 - 64 * q^85 + 48 * q^86 - 32 * q^88 + 8 * q^90 + 8 * q^91 + 96 * q^92 + 12 * q^94 - 20 * q^96 + 208 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.0417641	+	1.41360i	−0.0295317	+	0.999564i
$2$	−0.0417641	+	1.41360i	−0.0295317	+	0.999564i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.99651	−	0.118075i	−0.998256	−	0.0590376i
$5$	1.69566	−	1.69566i	0.758322	−	0.758322i	−0.217695	−	0.976017i	$-0.569854\pi$
$5$	1.69566	−	1.69566i	0.758322	−	0.758322i	0.976017	+	0.217695i	$0.0698537\pi$
$6$	−1.02910	+	0.970032i	−0.420126	+	0.396014i
$7$			4.01648i			1.51809i	0.651040	+	0.759044i	$0.274333\pi$
$7$			4.01648i			1.51809i	−0.651040	+	0.759044i	$0.725667\pi$
$8$	0.250293	−	2.81733i	0.0884920	−	0.996077i
$9$			1.00000i			0.333333i
$10$	2.32616	+	2.46780i	0.735597	+	0.780386i
$11$	3.12754	−	3.12754i	0.942989	−	0.942989i	−0.0554715	−	0.998460i	$-0.517666\pi$
$11$	3.12754	−	3.12754i	0.942989	−	0.942989i	0.998460	+	0.0554715i	$0.0176662\pi$
$12$	−1.32826	−	1.49524i	−0.383434	−	0.431638i
$13$	3.31631	+	3.31631i	0.919780	+	0.919780i	0.997013	−	0.0772334i	$-0.0246087\pi$
$13$	3.31631	+	3.31631i	0.919780	+	0.919780i	−0.0772334	+	0.997013i	$0.524609\pi$
$14$	−5.67769	−	0.167745i	−1.51743	−	0.0448317i
$15$	2.39803			0.619168
$16$	3.97212	+	0.471477i	0.993029	+	0.117869i
$17$	1.28627			0.311967			0.155984	−	0.987760i	$-0.450145\pi$
$17$	1.28627			0.311967			0.155984	+	0.987760i	$0.450145\pi$
$18$	−1.41360	−	0.0417641i	−0.333188	−	0.00984389i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−3.58562	+	3.18519i	−0.801769	+	0.712230i
$21$	−2.84008	+	2.84008i	−0.619757	+	0.619757i
$22$	4.29046	+	4.55170i	0.914729	+	0.970426i
$23$		−	8.95781i		−	1.86783i	−0.357492	−	0.933916i	$-0.616368\pi$
$23$		−	8.95781i		−	1.86783i	0.357492	−	0.933916i	$-0.383632\pi$
$24$	2.16914	−	1.81517i	0.442773	−	0.370520i
$25$		−	0.750527i		−	0.150105i
$26$	−4.82643	+	4.54943i	−0.946541	+	0.892216i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.474247	−	8.01895i	0.0896243	−	1.51544i
$29$	3.81503	+	3.81503i	0.708432	+	0.708432i	0.966205	−	0.257773i	$-0.0829887\pi$
$29$	3.81503	+	3.81503i	0.708432	+	0.708432i	−0.257773	+	0.966205i	$0.582989\pi$
$30$	−0.100151	+	3.38984i	−0.0182851	+	0.618898i
$31$	−3.28373			−0.589776			−0.294888	−	0.955532i	$-0.595282\pi$
$31$	−3.28373			−0.589776			−0.294888	+	0.955532i	$0.595282\pi$
$32$	−0.832370	+	5.59528i	−0.147144	+	0.989115i
$33$	4.42301			0.769947
$34$	−0.0537201	+	1.81827i	−0.00921292	+	0.311831i
$35$	6.81059	+	6.81059i	1.15120	+	1.15120i
$36$	0.118075	−	1.99651i	0.0196792	−	0.332752i
$37$	−2.41733	+	2.41733i	−0.397407	+	0.397407i	−0.877317	−	0.479911i	$-0.840669\pi$
$37$	−2.41733	+	2.41733i	−0.397407	+	0.397407i	0.479911	+	0.877317i	$0.340669\pi$
$38$	1.02910	−	0.970032i	0.166941	−	0.157360i
$39$			4.68997i			0.750997i
$40$	−4.35282	−	5.20165i	−0.688242	−	0.822453i
$41$			11.8121i			1.84475i	0.386300	+	0.922373i	$0.373753\pi$
$41$			11.8121i			1.84475i	−0.386300	+	0.922373i	$0.626247\pi$
$42$	−3.89612	−	4.13334i	−0.601184	−	0.637789i
$43$	0.432575	−	0.432575i	0.0659671	−	0.0659671i	−0.673354	−	0.739321i	$-0.735147\pi$
$43$	0.432575	−	0.432575i	0.0659671	−	0.0659671i	0.739321	+	0.673354i	$0.235147\pi$
$44$	−6.61345	+	5.87488i	−0.997016	+	0.885672i
$45$	1.69566	+	1.69566i	0.252774	+	0.252774i
$46$	12.6627	+	0.374115i	1.86702	+	0.0551602i
$47$	−5.81260			−0.847855			−0.423927	−	0.905696i	$-0.639349\pi$
$47$	−5.81260			−0.847855			−0.423927	+	0.905696i	$0.639349\pi$
$48$	2.47533	+	3.14210i	0.357283	+	0.453522i
$49$	−9.13213			−1.30459
$50$	1.06094	+	0.0313451i	0.150040	+	0.00443287i
$51$	0.909533	+	0.909533i	0.127360	+	0.127360i
$52$	−6.22948	−	7.01263i	−0.863874	−	0.972477i
$53$	−8.37304	+	8.37304i	−1.15013	+	1.15013i	−0.163599	+	0.986527i	$0.552310\pi$
$53$	−8.37304	+	8.37304i	−1.15013	+	1.15013i	−0.986527	+	0.163599i	$0.947690\pi$
$54$	−0.970032	−	1.02910i	−0.132005	−	0.140042i
$55$		−	10.6065i		−	1.43018i
$56$	11.3158	+	1.00530i	1.51213	+	0.134339i
$57$		−	1.00000i		−	0.132453i
$58$	−5.55224	+	5.23358i	−0.729045	+	0.687202i
$59$	6.07068	−	6.07068i	0.790335	−	0.790335i	−0.191214	−	0.981548i	$-0.561242\pi$
$59$	6.07068	−	6.07068i	0.790335	−	0.790335i	0.981548	+	0.191214i	$0.0612424\pi$
$60$	−4.78769	−	0.283147i	−0.618088	−	0.0365542i
$61$	9.39559	+	9.39559i	1.20298	+	1.20298i	0.973255	+	0.229728i	$0.0737836\pi$
$61$	9.39559	+	9.39559i	1.20298	+	1.20298i	0.229728	+	0.973255i	$0.426216\pi$
$62$	0.137142	−	4.64188i	0.0174171	−	0.589519i
$63$	−4.01648			−0.506029
$64$	−7.87471	−	1.41032i	−0.984338	−	0.176290i
$65$	11.2467			1.39498
$66$	−0.184723	+	6.25235i	−0.0227378	+	0.769611i
$67$	−4.53509	−	4.53509i	−0.554049	−	0.554049i	0.373558	−	0.927607i	$-0.378138\pi$
$67$	−4.53509	−	4.53509i	−0.554049	−	0.554049i	−0.927607	+	0.373558i	$0.878138\pi$
$68$	−2.56806	−	0.151877i	−0.311423	−	0.0184178i
$69$	6.33413	−	6.33413i	0.762539	−	0.762539i
$70$	−9.91187	+	9.34299i	−1.18469	+	1.11670i
$71$			0.435690i			0.0517069i	0.999666	+	0.0258534i	$0.00823032\pi$
$71$			0.435690i			0.0517069i	−0.999666	+	0.0258534i	$0.991770\pi$
$72$	2.81733	+	0.250293i	0.332026	+	0.0294973i
$73$		−	6.52722i		−	0.763954i	−0.924172	−	0.381977i	$-0.875243\pi$
$73$		−	6.52722i		−	0.763954i	0.924172	−	0.381977i	$-0.124757\pi$
$74$	−3.31617	−	3.51809i	−0.385497	−	0.408970i
$75$	0.530703	−	0.530703i	0.0612803	−	0.0612803i
$76$	1.32826	+	1.49524i	0.152361	+	0.171516i
$77$	12.5617	+	12.5617i	1.43154	+	1.43154i
$78$	−6.62973	−	0.195873i	−0.750669	−	0.0221782i
$79$	5.60770			0.630916			0.315458	−	0.948940i	$-0.397842\pi$
$79$	5.60770			0.630916			0.315458	+	0.948940i	$0.397842\pi$
$80$	7.53482	−	5.93590i	0.842419	−	0.663653i
$81$	−1.00000			−0.111111
$82$	−16.6976	−	0.493323i	−1.84394	−	0.0544785i
$83$	1.87477	+	1.87477i	0.205783	+	0.205783i	0.802472	−	0.596689i	$-0.203518\pi$
$83$	1.87477	+	1.87477i	0.205783	+	0.205783i	−0.596689	+	0.802472i	$0.703518\pi$
$84$	6.00560	−	5.33491i	0.655265	−	0.582087i
$85$	2.18108	−	2.18108i	0.236572	−	0.236572i
$86$	0.593421	+	0.629553i	0.0639902	+	0.0678864i
$87$			5.39526i			0.578433i
$88$	−8.02851	−	9.59412i	−0.855842	−	1.02274i
$89$		−	16.5092i		−	1.74998i	−0.484145	−	0.874988i	$-0.660869\pi$
$89$		−	16.5092i		−	1.74998i	0.484145	−	0.874988i	$-0.339131\pi$
$90$	−2.46780	+	2.32616i	−0.260129	+	0.245199i
$91$	−13.3199	+	13.3199i	−1.39631	+	1.39631i
$92$	−1.05770	+	17.8844i	−0.110272	+	1.86457i
$93$	−2.32195	−	2.32195i	−0.240775	−	0.240775i
$94$	0.242758	−	8.21667i	0.0250386	−	0.847485i
$95$	−2.39803			−0.246032
$96$	−4.54504	+	3.36789i	−0.463876	+	0.343733i
$97$	−5.55954			−0.564486			−0.282243	−	0.959343i	$-0.591078\pi$
$97$	−5.55954			−0.564486			−0.282243	+	0.959343i	$0.591078\pi$
$98$	0.381395	−	12.9092i	0.0385267	−	1.30402i
$99$	3.12754	+	3.12754i	0.314330	+	0.314330i
$100$	−0.0886186	+	1.49844i	−0.00886186	+	0.149844i
$101$	12.0505	−	12.0505i	1.19907	−	1.19907i	0.224619	−	0.974447i	$-0.427886\pi$
$101$	12.0505	−	12.0505i	1.19907	−	1.19907i	0.974447	−	0.224619i	$-0.0721136\pi$
$102$	−1.32370	+	1.24773i	−0.131066	+	0.123543i
$103$		−	0.764345i		−	0.0753131i	−0.999291	−	0.0376566i	$-0.988011\pi$
$103$		−	0.764345i		−	0.0753131i	0.999291	−	0.0376566i	$-0.0119893\pi$
$104$	10.1732	−	8.51310i	0.997564	−	0.834778i
$105$			9.63163i			0.939951i
$106$	−11.4864	−	12.1858i	−1.11566	−	1.18359i
$107$	−2.31480	+	2.31480i	−0.223781	+	0.223781i	−0.810088	−	0.586308i	$-0.800581\pi$
$107$	−2.31480	+	2.31480i	−0.223781	+	0.223781i	0.586308	+	0.810088i	$0.300581\pi$
$108$	1.49524	−	1.32826i	0.143879	−	0.127811i
$109$	−10.8167	−	10.8167i	−1.03606	−	1.03606i	−0.999325	−	0.0367303i	$-0.988306\pi$
$109$	−10.8167	−	10.8167i	−1.03606	−	1.03606i	−0.0367303	−	0.999325i	$-0.511694\pi$
$110$	14.9933	+	0.442971i	1.42956	+	0.0422356i
$111$	−3.41862			−0.324481
$112$	−1.89368	+	15.9539i	−0.178936	+	1.50751i
$113$	−17.7886			−1.67341			−0.836703	−	0.547656i	$-0.815520\pi$
$113$	−17.7886			−1.67341			−0.836703	+	0.547656i	$0.815520\pi$
$114$	1.41360	+	0.0417641i	0.132395	+	0.00391157i
$115$	−15.1894	−	15.1894i	−1.41642	−	1.41642i
$116$	−7.16628	−	8.06720i	−0.665373	−	0.749021i
$117$	−3.31631	+	3.31631i	−0.306593	+	0.306593i
$118$	8.32795	+	8.83502i	0.766650	+	0.813330i
$119$			5.16630i			0.473594i
$120$	0.600210	−	6.75603i	0.0547914	−	0.616739i
$121$		−	8.56301i		−	0.778456i
$122$	−13.6740	+	12.8892i	−1.23798	+	1.16693i
$123$	−8.35245	+	8.35245i	−0.753115	+	0.753115i
$124$	6.55601	+	0.387728i	0.588747	+	0.0348190i
$125$	7.20566	+	7.20566i	0.644494	+	0.644494i
$126$	0.167745	−	5.67769i	0.0149439	−	0.505809i
$127$	14.8617			1.31876			0.659381	−	0.751809i	$-0.270818\pi$
$127$	14.8617			1.31876			0.659381	+	0.751809i	$0.270818\pi$
$128$	2.32250	−	11.0728i	0.205282	−	0.978703i
$129$	0.611754			0.0538619
$130$	−0.469707	+	15.8983i	−0.0411961	+	1.39437i
$131$	−6.76043	−	6.76043i	−0.590661	−	0.590661i	0.347149	−	0.937810i	$-0.387150\pi$
$131$	−6.76043	−	6.76043i	−0.590661	−	0.590661i	−0.937810	+	0.347149i	$0.887150\pi$
$132$	−8.83059	−	0.522248i	−0.768604	−	0.0454558i
$133$	2.84008	−	2.84008i	0.246266	−	0.246266i
$134$	6.60019	−	6.22138i	0.570170	−	0.537445i
$135$			2.39803i			0.206389i
$136$	0.321946	−	3.62386i	0.0276066	−	0.310743i
$137$		−	6.81085i		−	0.581890i	−0.956740	−	0.290945i	$-0.906030\pi$
$137$		−	6.81085i		−	0.581890i	0.956740	−	0.290945i	$-0.0939696\pi$
$138$	8.68936	+	9.21844i	0.739688	+	0.784726i
$139$	3.63392	−	3.63392i	0.308225	−	0.308225i	−0.535996	−	0.844221i	$-0.680064\pi$
$139$	3.63392	−	3.63392i	0.308225	−	0.308225i	0.844221	+	0.535996i	$0.180064\pi$
$140$	−12.7933	−	14.4016i	−1.08123	−	1.21716i
$141$	−4.11013	−	4.11013i	−0.346135	−	0.346135i
$142$	−0.615890	−	0.0181962i	−0.0516843	−	0.00152699i
$143$	20.7438			1.73468
$144$	−0.471477	+	3.97212i	−0.0392897	+	0.331010i
$145$	12.9380			1.07444
$146$	9.22686	+	0.272604i	0.763620	+	0.0225608i
$147$	−6.45739	−	6.45739i	−0.532597	−	0.532597i
$148$	5.11166	−	4.54080i	0.420176	−	0.373252i
$149$	−1.29352	+	1.29352i	−0.105969	+	0.105969i	−0.758104	−	0.652134i	$-0.773874\pi$
$149$	−1.29352	+	1.29352i	−0.105969	+	0.105969i	0.652134	+	0.758104i	$0.273874\pi$
$150$	0.728035	+	0.772364i	0.0594438	+	0.0630633i
$151$			8.77728i			0.714285i	0.934050	+	0.357142i	$0.116249\pi$
$151$			8.77728i			0.714285i	−0.934050	+	0.357142i	$0.883751\pi$
$152$	−2.16914	+	1.81517i	−0.175940	+	0.147230i
$153$			1.28627i			0.103989i
$154$	−18.2818	+	17.2326i	−1.47319	+	1.38864i
$155$	−5.56810	+	5.56810i	−0.447240	+	0.447240i
$156$	0.553770	−	9.36359i	0.0443371	−	0.749687i
$157$	−4.54898	−	4.54898i	−0.363048	−	0.363048i	0.501886	−	0.864934i	$-0.332640\pi$
$157$	−4.54898	−	4.54898i	−0.363048	−	0.363048i	−0.864934	+	0.501886i	$0.832640\pi$
$158$	−0.234201	+	7.92703i	−0.0186320	+	0.630641i
$159$	−11.8413			−0.939074
$160$	8.07628	+	10.8991i	0.638486	+	0.861650i
$161$	35.9789			2.83553
$162$	0.0417641	−	1.41360i	0.00328130	−	0.111063i
$163$	−10.7494	−	10.7494i	−0.841960	−	0.841960i	0.147153	−	0.989114i	$-0.452989\pi$
$163$	−10.7494	−	10.7494i	−0.841960	−	0.841960i	−0.989114	+	0.147153i	$0.952989\pi$
$164$	1.39472	−	23.5831i	0.108909	−	1.84153i
$165$	7.49992	−	7.49992i	0.583868	−	0.583868i
$166$	−2.72847	+	2.57188i	−0.211770	+	0.199616i
$167$		−	1.36066i		−	0.105291i	−0.998613	−	0.0526454i	$-0.983235\pi$
$167$		−	1.36066i		−	0.105291i	0.998613	−	0.0526454i	$-0.0167653\pi$
$168$	7.29060	+	8.71230i	0.562482	+	0.672169i
$169$			8.99586i			0.691989i
$170$	2.99208	+	3.17426i	0.229482	+	0.243455i
$171$	0.707107	−	0.707107i	0.0540738	−	0.0540738i
$172$	−0.914718	+	0.812565i	−0.0697466	+	0.0619575i
$173$	−7.34626	−	7.34626i	−0.558526	−	0.558526i	0.370362	−	0.928888i	$-0.379234\pi$
$173$	−7.34626	−	7.34626i	−0.558526	−	0.558526i	−0.928888	+	0.370362i	$0.879234\pi$
$174$	−7.62672	−	0.225328i	−0.578180	−	0.0170821i
$175$	3.01448			0.227873
$176$	13.8975	−	10.9484i	1.04756	−	0.825266i
$177$	8.58523			0.645305
$178$	23.3374	+	0.689493i	1.74921	+	0.0516797i
$179$	−6.72145	−	6.72145i	−0.502385	−	0.502385i	0.409794	−	0.912178i	$-0.365601\pi$
$179$	−6.72145	−	6.72145i	−0.502385	−	0.502385i	−0.912178	+	0.409794i	$0.865601\pi$
$180$	−3.18519	−	3.58562i	−0.237410	−	0.267256i
$181$	5.39298	−	5.39298i	0.400857	−	0.400857i	−0.477678	−	0.878535i	$-0.658521\pi$
$181$	5.39298	−	5.39298i	0.400857	−	0.400857i	0.878535	+	0.477678i	$0.158521\pi$
$182$	−18.2727	−	19.3853i	−1.35446	−	1.43693i
$183$			13.2874i			0.982231i
$184$	−25.2371	−	2.24208i	−1.86050	−	0.165288i
$185$			8.19794i			0.602725i
$186$	3.37928	−	3.18533i	0.247781	−	0.233560i
$187$	4.02287	−	4.02287i	0.294182	−	0.294182i
$188$	11.6049	+	0.686324i	0.846376	+	0.0500553i
$189$	−2.84008	−	2.84008i	−0.206586	−	0.206586i
$190$	0.100151	−	3.38984i	0.00726575	−	0.245925i
$191$	23.2786			1.68438			0.842190	−	0.539180i	$-0.181266\pi$
$191$	23.2786			1.68438			0.842190	+	0.539180i	$0.181266\pi$
$192$	−4.57101	−	6.56550i	−0.329884	−	0.473824i
$193$	−1.03215			−0.0742961			−0.0371481	−	0.999310i	$-0.511827\pi$
$193$	−1.03215			−0.0742961			−0.0371481	+	0.999310i	$0.511827\pi$
$194$	0.232189	−	7.85895i	0.0166702	−	0.564240i
$195$	7.95260	+	7.95260i	0.569498	+	0.569498i
$196$	18.2324	+	1.07828i	1.30231	+	0.0770199i
$197$	−0.216314	+	0.216314i	−0.0154117	+	0.0154117i	−0.714771	−	0.699359i	$-0.753469\pi$
$197$	−0.216314	+	0.216314i	−0.0154117	+	0.0154117i	0.699359	+	0.714771i	$0.253469\pi$
$198$	−4.55170	+	4.29046i	−0.323475	+	0.304910i
$199$			4.75556i			0.337113i	0.985692	+	0.168556i	$0.0539105\pi$
$199$			4.75556i			0.337113i	−0.985692	+	0.168556i	$0.946089\pi$
$200$	−2.11448	−	0.187852i	−0.149517	−	0.0132831i
$201$		−	6.41358i		−	0.452379i
$202$	16.5312	+	17.5378i	1.16313	+	1.23395i
$203$	−15.3230	+	15.3230i	−1.07546	+	1.07546i
$204$	−1.70850	−	1.92329i	−0.119619	−	0.134657i
$205$	20.0294	+	20.0294i	1.39891	+	1.39891i
$206$	1.08047	+	0.0319222i	0.0752803	+	0.00222412i
$207$	8.95781			0.622611
$208$	11.6092	+	14.7363i	0.804954	+	1.02178i
$209$	−4.42301			−0.305946
$210$	−13.6152	−	0.402256i	−0.939541	−	0.0277583i
$211$	−4.44485	−	4.44485i	−0.305996	−	0.305996i	0.537358	−	0.843354i	$-0.319422\pi$
$211$	−4.44485	−	4.44485i	−0.305996	−	0.305996i	−0.843354	+	0.537358i	$0.819422\pi$
$212$	17.7055	−	15.7282i	1.21602	−	1.08022i
$213$	−0.308079	+	0.308079i	−0.0211092	+	0.0211092i
$214$	−3.17552	−	3.36888i	−0.217074	−	0.230292i
$215$		−	1.46700i		−	0.100049i
$216$	1.81517	+	2.16914i	0.123507	+	0.147591i
$217$		−	13.1891i		−	0.895332i
$218$	15.7423	−	14.8388i	1.06620	−	1.00501i
$219$	4.61544	−	4.61544i	0.311883	−	0.311883i
$220$	−1.25236	+	21.1760i	−0.0844343	+	1.42768i
$221$	4.26569	+	4.26569i	0.286941	+	0.286941i
$222$	0.142776	−	4.83255i	0.00958248	−	0.324340i
$223$	24.8496			1.66405			0.832026	−	0.554736i	$-0.187181\pi$
$223$	24.8496			1.66405			0.832026	+	0.554736i	$0.187181\pi$
$224$	−22.4733	−	3.34320i	−1.50156	−	0.223377i
$225$	0.750527			0.0500351
$226$	0.742923	−	25.1458i	0.0494185	−	1.67268i
$227$	−8.39340	−	8.39340i	−0.557089	−	0.557089i	0.371388	−	0.928478i	$-0.378882\pi$
$227$	−8.39340	−	8.39340i	−0.557089	−	0.557089i	−0.928478	+	0.371388i	$0.878882\pi$
$228$	−0.118075	+	1.99651i	−0.00781972	+	0.132222i
$229$	7.87664	−	7.87664i	0.520503	−	0.520503i	−0.397220	−	0.917723i	$-0.630025\pi$
$229$	7.87664	−	7.87664i	0.520503	−	0.520503i	0.917723	+	0.397220i	$0.130025\pi$
$230$	22.1061	−	20.8373i	1.45763	−	1.37397i
$231$			17.7649i			1.16885i
$232$	11.7031	−	9.79331i	0.768344	−	0.642962i
$233$			0.905760i			0.0593383i	0.999560	+	0.0296691i	$0.00944537\pi$
$233$			0.905760i			0.0593383i	−0.999560	+	0.0296691i	$0.990555\pi$
$234$	−4.54943	−	4.82643i	−0.297405	−	0.315514i
$235$	−9.85619	+	9.85619i	−0.642947	+	0.642947i
$236$	−12.8370	+	11.4034i	−0.835615	+	0.742297i
$237$	3.96524	+	3.96524i	0.257570	+	0.257570i
$238$	−7.30306	−	0.215766i	−0.473387	−	0.0139860i
$239$	−15.2167			−0.984287			−0.492143	−	0.870514i	$-0.663786\pi$
$239$	−15.2167			−0.984287			−0.492143	+	0.870514i	$0.663786\pi$
$240$	9.52524	+	1.13061i	0.614851	+	0.0729808i
$241$	25.0035			1.61062			0.805309	−	0.592855i	$-0.201999\pi$
$241$	25.0035			1.61062			0.805309	+	0.592855i	$0.201999\pi$
$242$	12.1046	+	0.357627i	0.778116	+	0.0229891i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−17.6490	−	19.8678i	−1.12986	−	1.27191i
$245$	−15.4850	+	15.4850i	−0.989300	+	0.989300i
$246$	−11.4582	−	12.1558i	−0.730545	−	0.775027i
$247$		−	4.68997i		−	0.298416i
$248$	−0.821896	+	9.25137i	−0.0521905	+	0.587462i
$249$			2.65133i			0.168021i
$250$	−10.4868	+	9.88496i	−0.663246	+	0.625180i
$251$	−1.36247	+	1.36247i	−0.0859986	+	0.0859986i	−0.748797	−	0.662799i	$-0.769368\pi$
$251$	−1.36247	+	1.36247i	−0.0859986	+	0.0859986i	0.662799	+	0.748797i	$0.269368\pi$
$252$	8.01895	+	0.474247i	0.505147	+	0.0298748i
$253$	−28.0159	−	28.0159i	−1.76134	−	1.76134i
$254$	−0.620686	+	21.0085i	−0.0389453	+	1.31819i
$255$	3.08452			0.193160
$256$	15.5554	+	3.74552i	0.972214	+	0.234095i
$257$	5.87061			0.366198			0.183099	−	0.983094i	$-0.441387\pi$
$257$	5.87061			0.366198			0.183099	+	0.983094i	$0.441387\pi$
$258$	−0.0255493	+	0.864773i	−0.00159063	+	0.0538384i
$259$	−9.70917	−	9.70917i	−0.603298	−	0.603298i
$260$	−22.4541	−	1.32795i	−1.39255	−	0.0823562i
$261$	−3.81503	+	3.81503i	−0.236144	+	0.236144i
$262$	9.83886	−	9.27418i	0.607847	−	0.572961i
$263$			1.32677i			0.0818119i	0.999163	+	0.0409060i	$0.0130244\pi$
$263$			1.32677i			0.0818119i	−0.999163	+	0.0409060i	$0.986976\pi$
$264$	1.10705	−	12.4611i	0.0681342	−	0.766927i
$265$			28.3957i			1.74433i
$266$	3.89612	+	4.13334i	0.238886	+	0.253432i
$267$	11.6738	−	11.6738i	0.714425	−	0.714425i
$268$	8.51887	+	9.58984i	0.520373	+	0.585792i
$269$	20.2148	+	20.2148i	1.23252	+	1.23252i	0.962994	+	0.269523i	$0.0868659\pi$
$269$	20.2148	+	20.2148i	1.23252	+	1.23252i	0.269523	+	0.962994i	$0.413134\pi$
$270$	−3.38984	−	0.100151i	−0.206299	−	0.00609502i
$271$	−12.8145			−0.778424			−0.389212	−	0.921148i	$-0.627253\pi$
$271$	−12.8145			−0.778424			−0.389212	+	0.921148i	$0.627253\pi$
$272$	5.10923	+	0.606449i	0.309793	+	0.0367713i
$273$	−18.8372			−1.14008
$274$	9.62779	+	0.284449i	0.581636	+	0.0171842i
$275$	−2.34730	−	2.34730i	−0.141548	−	0.141548i
$276$	−13.3941	+	11.8983i	−0.806228	+	0.716191i
$277$	−20.6791	+	20.6791i	−1.24249	+	1.24249i	−0.283521	+	0.958966i	$0.591503\pi$
$277$	−20.6791	+	20.6791i	−1.24249	+	1.24249i	−0.958966	+	0.283521i	$0.908497\pi$
$278$	4.98513	+	5.28867i	0.298988	+	0.317193i
$279$		−	3.28373i		−	0.196592i
$280$	20.8923	−	17.4830i	1.24856	−	1.04481i
$281$		−	15.8593i		−	0.946085i	−0.881040	−	0.473043i	$-0.843156\pi$
$281$		−	15.8593i		−	0.946085i	0.881040	−	0.473043i	$-0.156844\pi$
$282$	5.98172	−	5.63841i	0.356206	−	0.335762i
$283$	−19.1613	+	19.1613i	−1.13902	+	1.13902i	−0.150393	+	0.988626i	$0.548054\pi$
$283$	−19.1613	+	19.1613i	−1.13902	+	1.13902i	−0.988626	+	0.150393i	$0.951946\pi$
$284$	0.0514442	−	0.869860i	0.00305265	−	0.0516167i
$285$	−1.69566	−	1.69566i	−0.100442	−	0.100442i
$286$	−0.866346	+	29.3234i	−0.0512281	+	1.73393i
$287$	−47.4433			−2.80049
$288$	−5.59528	−	0.832370i	−0.329705	−	0.0490479i
$289$	−15.3455			−0.902676
$290$	−0.540343	+	18.2891i	−0.0317300	+	1.07397i
$291$	−3.93119	−	3.93119i	−0.230450	−	0.230450i
$292$	−0.770703	+	13.0317i	−0.0451020	+	0.762621i
$293$	−11.8736	+	11.8736i	−0.693664	+	0.693664i	−0.963036	−	0.269372i	$-0.913184\pi$
$293$	−11.8736	+	11.8736i	−0.693664	+	0.693664i	0.269372	+	0.963036i	$0.413184\pi$
$294$	9.39784	−	8.85846i	0.548093	−	0.516636i
$295$		−	20.5876i		−	1.19866i
$296$	6.20538	+	7.41546i	0.360680	+	0.431015i
$297$			4.42301i			0.256649i
$298$	−1.77450	−	1.88254i	−0.102794	−	0.109053i
$299$	29.7069	−	29.7069i	1.71799	−	1.71799i
$300$	−1.12222	+	0.996891i	−0.0647912	+	0.0575556i
$301$	1.73743	+	1.73743i	0.100144	+	0.100144i
$302$	−12.4075	−	0.366575i	−0.713973	−	0.0210940i
$303$	17.0419			0.979033
$304$	−2.47533	−	3.14210i	−0.141970	−	0.180212i
$305$	31.8635			1.82450
$306$	−1.81827	−	0.0537201i	−0.103944	−	0.00307097i
$307$	−18.6128	−	18.6128i	−1.06229	−	1.06229i	−0.997927	−	0.0643625i	$-0.979499\pi$
$307$	−18.6128	−	18.6128i	−1.06229	−	1.06229i	−0.0643625	−	0.997927i	$-0.520501\pi$
$308$	−23.5964	−	26.5628i	−1.34453	−	1.51356i
$309$	0.540473	−	0.540473i	0.0307464	−	0.0307464i
$310$	−7.63850	−	8.10359i	−0.433838	−	0.460253i
$311$		−	13.1304i		−	0.744557i	−0.928121	−	0.372278i	$-0.878577\pi$
$311$		−	13.1304i		−	0.744557i	0.928121	−	0.372278i	$-0.121423\pi$
$312$	13.2132	+	1.17387i	0.748051	+	0.0664572i
$313$		−	27.7167i		−	1.56664i	−0.621618	−	0.783320i	$-0.713524\pi$
$313$		−	27.7167i		−	1.56664i	0.621618	−	0.783320i	$-0.286476\pi$
$314$	6.62040	−	6.24043i	0.373611	−	0.352168i
$315$	−6.81059	+	6.81059i	−0.383733	+	0.383733i
$316$	−11.1958	−	0.662131i	−0.629815	−	0.0372478i
$317$	17.1979	+	17.1979i	0.965932	+	0.965932i	0.999439	−	0.0335063i	$-0.0106674\pi$
$317$	17.1979	+	17.1979i	0.965932	+	0.965932i	−0.0335063	+	0.999439i	$0.510667\pi$
$318$	0.494540	−	16.7388i	0.0277324	−	0.938664i
$319$	23.8633			1.33609
$320$	−15.7442	+	10.9614i	−0.880130	+	0.612761i
$321$	−3.27363			−0.182716
$322$	−1.50263	+	50.8596i	−0.0837381	+	2.83430i
$323$	−0.909533	−	0.909533i	−0.0506078	−	0.0506078i
$324$	1.99651	+	0.118075i	0.110917	+	0.00655973i
$325$	2.48898	−	2.48898i	0.138064	−	0.138064i
$326$	15.6443	−	14.7464i	0.866458	−	0.816729i
$327$		−	15.2972i		−	0.845936i
$328$	33.2787	+	2.95650i	1.83751	+	0.163245i
$329$		−	23.3462i		−	1.28712i
$330$	10.2886	+	10.9151i	0.566371	+	0.600856i
$331$	15.8401	−	15.8401i	0.870648	−	0.870648i	−0.121895	−	0.992543i	$-0.538897\pi$
$331$	15.8401	−	15.8401i	0.870648	−	0.870648i	0.992543	+	0.121895i	$0.0388970\pi$
$332$	−3.52164	−	3.96437i	−0.193275	−	0.217573i
$333$	−2.41733	−	2.41733i	−0.132469	−	0.132469i
$334$	1.92342	+	0.0568266i	0.105245	+	0.00310941i
$335$	−15.3799			−0.840296
$336$	−12.6202	+	9.94210i	−0.688487	+	0.542386i
$337$	−7.95821			−0.433512			−0.216756	−	0.976226i	$-0.569548\pi$
$337$	−7.95821			−0.433512			−0.216756	+	0.976226i	$0.569548\pi$
$338$	−12.7165	−	0.375704i	−0.691687	−	0.0204356i
$339$	−12.5784	−	12.5784i	−0.683165	−	0.683165i
$340$	−4.61209	+	4.09703i	−0.250126	+	0.222192i
$341$	−10.2700	+	10.2700i	−0.556152	+	0.556152i
$342$	0.970032	+	1.02910i	0.0524533	+	0.0556471i
$343$		−	8.56367i		−	0.462395i
$344$	−1.11044	−	1.32698i	−0.0598707	−	0.0715459i
$345$		−	21.4811i		−	1.15650i
$346$	10.6915	−	10.0778i	0.574776	−	0.541788i
$347$	10.8017	−	10.8017i	0.579868	−	0.579868i	−0.354999	−	0.934867i	$-0.615519\pi$
$347$	10.8017	−	10.8017i	0.579868	−	0.579868i	0.934867	+	0.354999i	$0.115519\pi$
$348$	0.637046	−	10.7717i	0.0341493	−	0.577424i
$349$	1.23770	+	1.23770i	0.0662523	+	0.0662523i	0.739457	−	0.673204i	$-0.235083\pi$
$349$	1.23770	+	1.23770i	0.0662523	+	0.0662523i	−0.673204	+	0.739457i	$0.735083\pi$
$350$	−0.125897	+	4.26126i	−0.00672948	+	0.227774i
$351$	−4.68997			−0.250332
$352$	14.8962	+	20.1027i	0.793970	+	1.07148i
$353$	−22.3824			−1.19130			−0.595648	−	0.803245i	$-0.703105\pi$
$353$	−22.3824			−1.19130			−0.595648	+	0.803245i	$0.703105\pi$
$354$	−0.358554	+	12.1361i	−0.0190570	+	0.645024i
$355$	0.738782	+	0.738782i	0.0392105	+	0.0392105i
$356$	−1.94933	+	32.9609i	−0.103314	+	1.74692i
$357$	−3.65312	+	3.65312i	−0.193344	+	0.193344i
$358$	9.78213	−	9.22070i	0.517002	−	0.487329i
$359$			13.9486i			0.736180i	0.929790	+	0.368090i	$0.119988\pi$
$359$			13.9486i			0.736180i	−0.929790	+	0.368090i	$0.880012\pi$
$360$	5.20165	−	4.35282i	0.274151	−	0.229414i
$361$			1.00000i			0.0526316i
$362$	7.39827	+	7.84874i	0.388844	+	0.412520i
$363$	6.05496	−	6.05496i	0.317803	−	0.317803i
$364$	28.1661	−	25.0206i	1.47631	−	1.31144i
$365$	−11.0680	−	11.0680i	−0.579323	−	0.579323i
$366$	−18.7830	−	0.554935i	−0.981803	−	0.0290069i
$367$	4.51862			0.235870			0.117935	−	0.993021i	$-0.462373\pi$
$367$	4.51862			0.235870			0.117935	+	0.993021i	$0.462373\pi$
$368$	4.22340	−	35.5815i	0.220160	−	1.85481i
$369$	−11.8121			−0.614916
$370$	−11.5886	−	0.342380i	−0.602462	−	0.0177995i
$371$	−33.6302	−	33.6302i	−1.74599	−	1.74599i
$372$	4.36164	+	4.90997i	0.226140	+	0.254570i
$373$	4.30193	−	4.30193i	0.222745	−	0.222745i	−0.586908	−	0.809654i	$-0.699655\pi$
$373$	4.30193	−	4.30193i	0.222745	−	0.222745i	0.809654	+	0.586908i	$0.199655\pi$
$374$	5.51871	+	5.85473i	0.285366	+	0.302741i
$375$			10.1903i			0.526227i
$376$	−1.45485	+	16.3760i	−0.0750284	+	0.844529i
$377$			25.3036i			1.30320i
$378$	4.13334	−	3.89612i	0.212596	−	0.200395i
$379$	−11.6200	+	11.6200i	−0.596881	+	0.596881i	−0.939481	−	0.342600i	$-0.888692\pi$
$379$	−11.6200	+	11.6200i	−0.596881	+	0.596881i	0.342600	+	0.939481i	$0.388692\pi$
$380$	4.78769	+	0.283147i	0.245603	+	0.0145252i
$381$	10.5088	+	10.5088i	0.538383	+	0.538383i
$382$	−0.972210	+	32.9066i	−0.0497426	+	1.68365i
$383$	−32.1857			−1.64461			−0.822307	−	0.569044i	$-0.807313\pi$
$383$	−32.1857			−1.64461			−0.822307	+	0.569044i	$0.807313\pi$
$384$	9.47188	−	6.18737i	0.483360	−	0.315748i
$385$	42.6008			2.17114
$386$	0.0431070	−	1.45905i	0.00219409	−	0.0742637i
$387$	0.432575	+	0.432575i	0.0219890	+	0.0219890i
$388$	11.0997	+	0.656444i	0.563502	+	0.0333259i
$389$	2.93023	−	2.93023i	0.148569	−	0.148569i	−0.628910	−	0.777478i	$-0.716499\pi$
$389$	2.93023	−	2.93023i	0.148569	−	0.148569i	0.777478	+	0.628910i	$0.216499\pi$
$390$	−11.5739	+	10.9096i	−0.586068	+	0.552431i
$391$		−	11.5222i		−	0.582702i
$392$	−2.28571	+	25.7282i	−0.115446	+	1.29947i
$393$		−	9.56069i		−	0.482273i
$394$	−0.296746	−	0.314814i	−0.0149499	−	0.0158601i
$395$	9.50876	−	9.50876i	0.478438	−	0.478438i
$396$	−5.87488	−	6.61345i	−0.295224	−	0.332339i
$397$	−22.9846	−	22.9846i	−1.15356	−	1.15356i	−0.985833	−	0.167732i	$-0.946356\pi$
$397$	−22.9846	−	22.9846i	−1.15356	−	1.15356i	−0.167732	−	0.985833i	$-0.553644\pi$
$398$	−6.72244	−	0.198612i	−0.336966	−	0.00995550i
$399$	4.01648			0.201076
$400$	0.353856	−	2.98118i	0.0176928	−	0.149059i
$401$	24.6947			1.23319			0.616597	−	0.787279i	$-0.288511\pi$
$401$	24.6947			1.23319			0.616597	+	0.787279i	$0.288511\pi$
$402$	9.06622	+	0.267858i	0.452182	+	0.0133595i
$403$	−10.8899	−	10.8899i	−0.542464	−	0.542464i
$404$	−25.4817	+	22.6360i	−1.26776	+	1.12618i
$405$	−1.69566	+	1.69566i	−0.0842580	+	0.0842580i
$406$	−21.0206	−	22.3005i	−1.04323	−	1.10675i
$407$			15.1206i			0.749500i
$408$	2.79011	−	2.33481i	0.138131	−	0.115590i
$409$			10.9815i			0.543003i	0.962438	+	0.271501i	$0.0875201\pi$
$409$			10.9815i			0.543003i	−0.962438	+	0.271501i	$0.912480\pi$
$410$	−29.1500	+	27.4770i	−1.43961	+	1.35699i
$411$	4.81600	−	4.81600i	0.237556	−	0.237556i
$412$	−0.0902501	+	1.52602i	−0.00444631	+	0.0751817i
$413$	24.3828	+	24.3828i	1.19980	+	1.19980i
$414$	−0.374115	+	12.6627i	−0.0183867	+	0.622339i
$415$	6.35796			0.312100
$416$	−21.3161	+	15.7953i	−1.04511	+	0.774428i
$417$	5.13914			0.251665
$418$	0.184723	−	6.25235i	0.00903510	−	0.305813i
$419$	−10.6608	−	10.6608i	−0.520812	−	0.520812i	0.397004	−	0.917817i	$-0.370050\pi$
$419$	−10.6608	−	10.6608i	−0.520812	−	0.520812i	−0.917817	+	0.397004i	$0.870050\pi$
$420$	1.13726	−	19.2297i	0.0554924	−	0.938311i
$421$	−16.4338	+	16.4338i	−0.800936	+	0.800936i	−0.983242	−	0.182306i	$-0.941644\pi$
$421$	−16.4338	+	16.4338i	−0.800936	+	0.800936i	0.182306	+	0.983242i	$0.441644\pi$
$422$	6.46886	−	6.09759i	0.314899	−	0.296826i
$423$		−	5.81260i		−	0.282618i
$424$	21.4939	+	25.6853i	1.04384	+	1.24739i
$425$		−	0.965383i		−	0.0468280i
$426$	−0.422633	−	0.448366i	−0.0204766	−	0.0217234i
$427$	−37.7372	+	37.7372i	−1.82623	+	1.82623i
$428$	4.89485	−	4.34821i	0.236602	−	0.210179i
$429$	14.6681	+	14.6681i	0.708182	+	0.708182i
$430$	2.07375	+	0.0612680i	0.100005	+	0.00295460i
$431$	−13.4823			−0.649421			−0.324711	−	0.945813i	$-0.605267\pi$
$431$	−13.4823			−0.649421			−0.324711	+	0.945813i	$0.605267\pi$
$432$	−3.14210	+	2.47533i	−0.151174	+	0.119094i
$433$	−8.44894			−0.406030			−0.203015	−	0.979176i	$-0.565074\pi$
$433$	−8.44894			−0.406030			−0.203015	+	0.979176i	$0.565074\pi$
$434$	18.6440	+	0.550829i	0.894941	+	0.0264407i
$435$	9.14853	+	9.14853i	0.438638	+	0.438638i
$436$	20.3186	+	22.8729i	0.973082	+	1.09541i
$437$	−6.33413	+	6.33413i	−0.303002	+	0.303002i
$438$	6.33162	+	6.71714i	0.302536	+	0.320957i
$439$			16.1013i			0.768472i	0.923235	+	0.384236i	$0.125535\pi$
$439$			16.1013i			0.768472i	−0.923235	+	0.384236i	$0.874465\pi$
$440$	−29.8820	−	2.65473i	−1.42457	−	0.126559i
$441$		−	9.13213i		−	0.434863i
$442$	−6.20811	+	5.85181i	−0.295290	+	0.278342i
$443$	0.593689	−	0.593689i	0.0282070	−	0.0282070i	−0.692863	−	0.721070i	$-0.743651\pi$
$443$	0.593689	−	0.593689i	0.0282070	−	0.0282070i	0.721070	+	0.692863i	$0.243651\pi$
$444$	6.82532	+	0.403655i	0.323915	+	0.0191566i
$445$	−27.9941	−	27.9941i	−1.32705	−	1.32705i
$446$	−1.03782	+	35.1273i	−0.0491423	+	1.66333i
$447$	−1.82932			−0.0865237
$448$	5.66452	−	31.6286i	0.267623	−	1.49431i
$449$	−0.130798			−0.00617274			−0.00308637	−	0.999995i	$-0.500982\pi$
$449$	−0.130798			−0.00617274			−0.00308637	+	0.999995i	$0.500982\pi$
$450$	−0.0313451	+	1.06094i	−0.00147762	+	0.0500133i
$451$	36.9429	+	36.9429i	1.73958	+	1.73958i
$452$	35.5151	+	2.10039i	1.67049	+	0.0987939i
$453$	−6.20647	+	6.20647i	−0.291606	+	0.291606i
$454$	12.2154	−	11.5143i	0.573298	−	0.540395i
$455$			45.1721i			2.11770i
$456$	−2.81733	−	0.250293i	−0.131934	−	0.0117211i
$457$		−	26.9457i		−	1.26047i	−0.776405	−	0.630234i	$-0.782959\pi$
$457$		−	26.9457i		−	1.26047i	0.776405	−	0.630234i	$-0.217041\pi$
$458$	10.8054	+	11.4634i	0.504905	+	0.535647i
$459$	−0.909533	+	0.909533i	−0.0424534	+	0.0424534i
$460$	28.5323	+	32.1193i	1.33033	+	1.49757i
$461$	−24.3607	−	24.3607i	−1.13459	−	1.13459i	−0.989404	−	0.145186i	$-0.953622\pi$
$461$	−24.3607	−	24.3607i	−1.13459	−	1.13459i	−0.145186	−	0.989404i	$-0.546378\pi$
$462$	−25.1125	−	0.741937i	−1.16834	−	0.0345180i
$463$	0.882356			0.0410066			0.0205033	−	0.999790i	$-0.493473\pi$
$463$	0.882356			0.0410066			0.0205033	+	0.999790i	$0.493473\pi$
$464$	13.3550	+	16.9524i	0.619992	+	0.786996i
$465$	−7.87448			−0.365170
$466$	−1.28038	−	0.0378282i	−0.0593124	−	0.00175236i
$467$	6.15276	+	6.15276i	0.284716	+	0.284716i	0.834986	−	0.550271i	$-0.185475\pi$
$467$	6.15276	+	6.15276i	0.284716	+	0.284716i	−0.550271	+	0.834986i	$0.685475\pi$
$468$	7.01263	−	6.22948i	0.324159	−	0.287958i
$469$	18.2151	−	18.2151i	0.841095	−	0.841095i
$470$	−13.5210	−	14.3443i	−0.623680	−	0.661654i
$471$		−	6.43322i		−	0.296427i
$472$	−15.5837	−	18.6225i	−0.717296	−	0.857172i
$473$		−	2.70579i		−	0.124412i
$474$	−5.77086	+	5.43965i	−0.265064	+	0.249851i
$475$	−0.530703	+	0.530703i	−0.0243503	+	0.0243503i
$476$	0.610011	−	10.3146i	0.0279598	−	0.472768i
$477$	−8.37304	−	8.37304i	−0.383375	−	0.383375i
$478$	0.635512	−	21.5103i	0.0290676	−	0.983858i
$479$	6.39674			0.292274			0.146137	−	0.989264i	$-0.453316\pi$
$479$	6.39674			0.292274			0.146137	+	0.989264i	$0.453316\pi$
$480$	−1.99605	+	13.4176i	−0.0911066	+	0.612428i
$481$	−16.0333			−0.731053
$482$	−1.04425	+	35.3449i	−0.0475643	+	1.60992i
$483$	25.4409	+	25.4409i	1.15760	+	1.15760i
$484$	−1.01108	+	17.0962i	−0.0459582	+	0.777098i
$485$	−9.42710	+	9.42710i	−0.428062	+	0.428062i
$486$	1.02910	−	0.970032i	0.0466807	−	0.0440016i
$487$			9.88627i			0.447990i	0.974590	+	0.223995i	$0.0719099\pi$
$487$			9.88627i			0.447990i	−0.974590	+	0.223995i	$0.928090\pi$
$488$	28.8222	−	24.1188i	1.30472	−	1.09181i
$489$		−	15.2020i		−	0.687458i
$490$	−21.2428	−	22.5363i	−0.959653	−	1.01808i
$491$	−22.5224	+	22.5224i	−1.01642	+	1.01642i	−0.0165575	+	0.999863i	$0.505271\pi$
$491$	−22.5224	+	22.5224i	−1.01642	+	1.01642i	−0.999863	+	0.0165575i	$0.994729\pi$
$492$	17.6620	−	15.6895i	0.796263	−	0.707339i
$493$	4.90717	+	4.90717i	0.221008	+	0.221008i
$494$	6.62973	+	0.195873i	0.298286	+	0.00881272i
$495$	10.6065			0.476726
$496$	−13.0434	−	1.54821i	−0.585665	−	0.0695165i
$497$	−1.74994			−0.0784956
$498$	−3.74791	−	0.110730i	−0.167948	−	0.00496195i
$499$	4.34873	+	4.34873i	0.194676	+	0.194676i	0.797713	−	0.603037i	$-0.206043\pi$
$499$	4.34873	+	4.34873i	0.194676	+	0.194676i	−0.603037	+	0.797713i	$0.706043\pi$
$500$	−13.5354	−	15.2370i	−0.605320	−	0.681419i
$501$	0.962130	−	0.962130i	0.0429848	−	0.0429848i
$502$	−1.86909	−	1.98289i	−0.0834214	−	0.0885008i
$503$		−	20.8300i		−	0.928764i	−0.885635	−	0.464382i	$-0.846276\pi$
$503$		−	20.8300i		−	0.928764i	0.885635	−	0.464382i	$-0.153724\pi$
$504$	−1.00530	+	11.3158i	−0.0447795	+	0.504044i
$505$		−	40.8670i		−	1.81856i
$506$	40.7733	−	38.4331i	1.81259	−	1.70856i
$507$	−6.36103	+	6.36103i	−0.282503	+	0.282503i
$508$	−29.6716	−	1.75480i	−1.31646	−	0.0778566i
$509$	27.4431	+	27.4431i	1.21639	+	1.21639i	0.968885	+	0.247509i	$0.0796121\pi$
$509$	27.4431	+	27.4431i	1.21639	+	1.21639i	0.247509	+	0.968885i	$0.420388\pi$
$510$	−0.128822	+	4.36026i	−0.00570434	+	0.193076i
$511$	26.2165			1.15975
$512$	−5.94432	+	21.8327i	−0.262704	+	0.964876i
$513$	1.00000			0.0441511
$514$	−0.245181	+	8.29867i	−0.0108145	+	0.366039i
$515$	−1.29607	−	1.29607i	−0.0571116	−	0.0571116i
$516$	−1.22137	−	0.0722329i	−0.0537680	−	0.00317988i
$517$	−18.1791	+	18.1791i	−0.799518	+	0.799518i
$518$	14.1303	−	13.3194i	0.620852	−	0.585219i
$519$		−	10.3892i		−	0.456034i
$520$	2.81497	−	31.6856i	0.123444	−	1.38951i
$521$			3.86912i			0.169509i	0.996402	+	0.0847545i	$0.0270106\pi$
$521$			3.86912i			0.169509i	−0.996402	+	0.0847545i	$0.972989\pi$
$522$	−5.23358	−	5.55224i	−0.229067	−	0.243015i
$523$	−21.4819	+	21.4819i	−0.939339	+	0.939339i	−0.998262	−	0.0589238i	$-0.981233\pi$
$523$	−21.4819	+	21.4819i	−0.939339	+	0.939339i	0.0589238	+	0.998262i	$0.481233\pi$
$524$	12.6990	+	14.2955i	0.554760	+	0.624502i
$525$	2.13156	+	2.13156i	0.0930288	+	0.0930288i
$526$	−1.87551	−	0.0554112i	−0.0817763	−	0.00241604i
$527$	−4.22378			−0.183991
$528$	17.5687	+	2.08535i	0.764580	+	0.0907531i
$529$	−57.2423			−2.48880
$530$	−40.1400	−	1.18592i	−1.74357	−	0.0515131i
$531$	6.07068	+	6.07068i	0.263445	+	0.263445i
$532$	−6.00560	+	5.33491i	−0.260376	+	0.231298i
$533$	−39.1728	+	39.1728i	−1.69676	+	1.69676i
$534$	16.0145	+	16.9896i	0.693015	+	0.735211i
$535$			7.85024i			0.339396i
$536$	−13.9119	+	11.6417i	−0.600904	+	0.502847i
$537$		−	9.50556i		−	0.410195i
$538$	−29.4198	+	27.7313i	−1.26838	+	1.19558i
$539$	−28.5611	+	28.5611i	−1.23021	+	1.23021i
$540$	0.283147	−	4.78769i	0.0121847	−	0.206029i
$541$	−11.1589	−	11.1589i	−0.479758	−	0.479758i	0.425296	−	0.905054i	$-0.360170\pi$
$541$	−11.1589	−	11.1589i	−0.479758	−	0.479758i	−0.905054	+	0.425296i	$0.860170\pi$
$542$	0.535185	−	18.1145i	0.0229882	−	0.778085i
$543$	7.62683			0.327299
$544$	−1.07066	+	7.19706i	−0.0459040	+	0.308572i
$545$	−36.6830			−1.57133
$546$	0.786719	−	26.6282i	0.0336685	−	1.13958i
$547$	19.5951	+	19.5951i	0.837828	+	0.837828i	0.988573	−	0.150745i	$-0.0481672\pi$
$547$	19.5951	+	19.5951i	0.837828	+	0.837828i	−0.150745	+	0.988573i	$0.548167\pi$
$548$	−0.804192	+	13.5979i	−0.0343534	+	0.580875i
$549$	−9.39559	+	9.39559i	−0.400994	+	0.400994i
$550$	3.41617	−	3.22011i	0.145666	−	0.137306i
$551$		−	5.39526i		−	0.229846i
$552$	−16.2599	−	19.4307i	−0.692069	−	0.827026i
$553$			22.5232i			0.957786i
$554$	−28.3683	−	30.0956i	−1.20525	−	1.27864i
$555$	−5.79682	+	5.79682i	−0.246061	+	0.246061i
$556$	−7.68425	+	6.82609i	−0.325885	+	0.289491i
$557$	16.7111	+	16.7111i	0.708072	+	0.708072i	0.966130	−	0.258058i	$-0.0830824\pi$
$557$	16.7111	+	16.7111i	0.708072	+	0.708072i	−0.258058	+	0.966130i	$0.583082\pi$
$558$	4.64188	+	0.137142i	0.196506	+	0.00580569i
$559$	2.86911			0.121350
$560$	23.8414	+	30.2635i	1.00748	+	1.27887i
$561$	5.68920			0.240198
$562$	22.4186	+	0.662349i	0.945673	+	0.0279395i
$563$	−3.31748	−	3.31748i	−0.139815	−	0.139815i	0.633735	−	0.773550i	$-0.281521\pi$
$563$	−3.31748	−	3.31748i	−0.139815	−	0.139815i	−0.773550	+	0.633735i	$0.781521\pi$
$564$	7.72062	+	8.69122i	0.325097	+	0.365967i
$565$	−30.1633	+	30.1633i	−1.26898	+	1.26898i
$566$	−26.2861	−	27.8866i	−1.10489	−	1.17216i
$567$		−	4.01648i		−	0.168676i
$568$	1.22748	+	0.109050i	0.0515040	+	0.00457565i
$569$			13.1634i			0.551838i	0.961181	+	0.275919i	$0.0889821\pi$
$569$			13.1634i			0.551838i	−0.961181	+	0.275919i	$0.911018\pi$
$570$	2.46780	−	2.32616i	0.103365	−	0.0974322i
$571$	−3.02144	+	3.02144i	−0.126443	+	0.126443i	−0.767497	−	0.641053i	$-0.778498\pi$
$571$	−3.02144	+	3.02144i	−0.126443	+	0.126443i	0.641053	+	0.767497i	$0.278498\pi$
$572$	−41.4152	−	2.44933i	−1.73166	−	0.102412i
$573$	16.4605	+	16.4605i	0.687646	+	0.687646i
$574$	1.98143	−	67.0656i	0.0827031	−	2.79927i
$575$	−6.72308			−0.280372
$576$	1.41032	−	7.87471i	0.0587632	−	0.328113i
$577$	19.6283			0.817138			0.408569	−	0.912727i	$-0.366028\pi$
$577$	19.6283			0.817138			0.408569	+	0.912727i	$0.366028\pi$
$578$	0.640891	−	21.6923i	0.0266576	−	0.902283i
$579$	−0.729844	−	0.729844i	−0.0303313	−	0.0303313i
$580$	−25.8308	−	1.52765i	−1.07257	−	0.0634324i
$581$	−7.52999	+	7.52999i	−0.312397	+	0.312397i
$582$	5.72130	−	5.39294i	0.237156	−	0.223544i
$583$			52.3740i			2.16911i
$584$	−18.3893	−	1.63372i	−0.760957	−	0.0676038i
$585$			11.2467i			0.464993i
$586$	−16.2886	−	17.2804i	−0.672877	−	0.713847i
$587$	6.02246	−	6.02246i	0.248573	−	0.248573i	−0.571812	−	0.820385i	$-0.693759\pi$
$587$	6.02246	−	6.02246i	0.248573	−	0.248573i	0.820385	+	0.571812i	$0.193759\pi$
$588$	12.1298	+	13.6547i	0.500224	+	0.563111i
$589$	2.32195	+	2.32195i	0.0956743	+	0.0956743i
$590$	29.1026	+	0.859823i	1.19813	+	0.0353983i
$591$	−0.305914			−0.0125836
$592$	−10.7416	+	8.46220i	−0.441479	+	0.347794i
$593$	16.3953			0.673276			0.336638	−	0.941634i	$-0.390710\pi$
$593$	16.3953			0.673276			0.336638	+	0.941634i	$0.390710\pi$
$594$	−6.25235	−	0.184723i	−0.256537	−	0.00757928i
$595$	8.76028	+	8.76028i	0.359137	+	0.359137i
$596$	2.73526	−	2.42980i	0.112041	−	0.0995284i
$597$	−3.36269	+	3.36269i	−0.137626	+	0.137626i
$598$	40.7529	+	43.2343i	1.66651	+	1.76798i
$599$		−	42.0979i		−	1.72007i	−0.510233	−	0.860036i	$-0.670441\pi$
$599$		−	42.0979i		−	1.72007i	0.510233	−	0.860036i	$-0.329559\pi$
$600$	−1.36233	−	1.62800i	−0.0556171	−	0.0664627i
$601$			9.90486i			0.404028i	0.979383	+	0.202014i	$0.0647486\pi$
$601$			9.90486i			0.404028i	−0.979383	+	0.202014i	$0.935251\pi$
$602$	−2.52859	+	2.38346i	−0.103058	+	0.0971427i
$603$	4.53509	−	4.53509i	0.184683	−	0.184683i
$604$	1.03638	−	17.5239i	0.0421697	−	0.713039i
$605$	−14.5200	−	14.5200i	−0.590320	−	0.590320i
$606$	−0.711740	+	24.0904i	−0.0289125	+	0.978606i
$607$	−31.9170			−1.29547			−0.647736	−	0.761865i	$-0.724284\pi$
$607$	−31.9170			−1.29547			−0.647736	+	0.761865i	$0.724284\pi$
$608$	4.54504	−	3.36789i	0.184326	−	0.136586i
$609$	−21.6700			−0.878111
$610$	−1.33075	+	45.0421i	−0.0538805	+	1.82370i
$611$	−19.2764	−	19.2764i	−0.779840	−	0.779840i
$612$	0.151877	−	2.56806i	0.00613927	−	0.103808i
$613$	7.28805	−	7.28805i	0.294362	−	0.294362i	−0.544439	−	0.838801i	$-0.683257\pi$
$613$	7.28805	−	7.28805i	0.294362	−	0.294362i	0.838801	+	0.544439i	$0.183257\pi$
$614$	27.0884	−	25.5337i	1.09320	−	1.03045i
$615$			28.3258i			1.14221i
$616$	38.5346	−	32.2464i	1.55260	−	1.29924i
$617$		−	24.2635i		−	0.976811i	−0.872617	−	0.488406i	$-0.837579\pi$
$617$		−	24.2635i		−	0.976811i	0.872617	−	0.488406i	$-0.162421\pi$
$618$	0.741439	+	0.786584i	0.0298250	+	0.0316410i
$619$	−23.3844	+	23.3844i	−0.939898	+	0.939898i	−0.998294	−	0.0583957i	$-0.981401\pi$
$619$	−23.3844	+	23.3844i	−0.939898	+	0.939898i	0.0583957	+	0.998294i	$0.481401\pi$
$620$	11.7742	−	10.4593i	0.472864	−	0.420056i
$621$	6.33413	+	6.33413i	0.254180	+	0.254180i
$622$	18.5611	+	0.548379i	0.744232	+	0.0219880i
$623$	66.3091			2.65662
$624$	−2.21122	+	18.6291i	−0.0885194	+	0.745762i
$625$	28.1893			1.12757
$626$	39.1802	+	1.15756i	1.56596	+	0.0462655i
$627$	−3.12754	−	3.12754i	−0.124902	−	0.124902i
$628$	8.54496	+	9.61921i	0.340981	+	0.383848i
$629$	−3.10935	+	3.10935i	−0.123978	+	0.123978i
$630$	−9.34299	−	9.91187i	−0.372234	−	0.394898i
$631$		−	18.7187i		−	0.745179i	−0.927996	−	0.372589i	$-0.878470\pi$
$631$		−	18.7187i		−	0.745179i	0.927996	−	0.372589i	$-0.121530\pi$
$632$	1.40357	−	15.7988i	0.0558310	−	0.628441i
$633$		−	6.28597i		−	0.249845i
$634$	−25.0292	+	23.5927i	−0.994036	+	0.936985i
$635$	25.2004	−	25.2004i	1.00005	−	1.00005i
$636$	23.6412	+	1.39816i	0.937436	+	0.0554407i
$637$	−30.2850	−	30.2850i	−1.19994	−	1.19994i
$638$	−0.996629	+	33.7331i	−0.0394569	+	1.33550i
$639$	−0.435690			−0.0172356
$640$	−14.8375	−	22.7138i	−0.586502	−	0.897842i
$641$	25.7211			1.01592			0.507961	−	0.861380i	$-0.330399\pi$
$641$	25.7211			1.01592			0.507961	+	0.861380i	$0.330399\pi$
$642$	0.136720	−	4.62759i	0.00539591	−	0.182636i
$643$	0.280088	+	0.280088i	0.0110456	+	0.0110456i	0.712608	−	0.701562i	$-0.247514\pi$
$643$	0.280088	+	0.280088i	0.0110456	+	0.0110456i	−0.701562	+	0.712608i	$0.747514\pi$
$644$	−71.8323	−	4.24821i	−2.83059	−	0.167403i
$645$	1.03733	−	1.03733i	0.0408447	−	0.0408447i
$646$	1.32370	−	1.24773i	0.0520802	−	0.0490912i
$647$		−	15.8259i		−	0.622182i	−0.950380	−	0.311091i	$-0.899306\pi$
$647$		−	15.8259i		−	0.622182i	0.950380	−	0.311091i	$-0.100694\pi$
$648$	−0.250293	+	2.81733i	−0.00983245	+	0.110675i
$649$		−	37.9726i		−	1.49055i
$650$	3.41447	+	3.62237i	0.133926	+	0.142081i
$651$	9.32607	−	9.32607i	0.365518	−	0.365518i
$652$	20.1921	+	22.7306i	0.790784	+	0.890199i
$653$	−33.1534	−	33.1534i	−1.29739	−	1.29739i	−0.930109	−	0.367282i	$-0.880288\pi$
$653$	−33.1534	−	33.1534i	−1.29739	−	1.29739i	−0.367282	−	0.930109i	$-0.619712\pi$
$654$	21.6240	+	0.638873i	0.845567	+	0.0249819i
$655$	−22.9268			−0.895824
$656$	−5.56915	+	46.9192i	−0.217439	+	1.83189i
$657$	6.52722			0.254651
$658$	33.0021	+	0.975033i	1.28656	+	0.0380108i
$659$	11.0625	+	11.0625i	0.430935	+	0.430935i	0.888946	−	0.458011i	$-0.151438\pi$
$659$	11.0625	+	11.0625i	0.430935	+	0.430935i	−0.458011	+	0.888946i	$0.651438\pi$
$660$	−15.8592	+	14.0881i	−0.617320	+	0.548379i
$661$	25.4579	−	25.4579i	0.990197	−	0.990197i	−0.00975499	−	0.999952i	$-0.503105\pi$
$661$	25.4579	−	25.4579i	0.990197	−	0.990197i	0.999952	+	0.00975499i	$0.00310516\pi$
$662$	21.7299	+	23.0530i	0.844557	+	0.895980i
$663$			6.03259i			0.234286i
$664$	5.75110	−	4.81261i	0.223186	−	0.186766i
$665$		−	9.63163i		−	0.373499i
$666$	3.51809	−	3.31617i	0.136323	−	0.128499i
$667$	34.1743	−	34.1743i	1.32323	−	1.32323i
$668$	−0.160660	+	2.71657i	−0.00621612	+	0.105107i
$669$	17.5713	+	17.5713i	0.679347	+	0.679347i
$670$	0.642329	−	21.7410i	0.0248153	−	0.839929i
$671$	58.7702			2.26880
$672$	−13.5271	−	18.2551i	−0.521817	−	0.704204i
$673$	38.3367			1.47777			0.738885	−	0.673831i	$-0.235352\pi$
$673$	38.3367			1.47777			0.738885	+	0.673831i	$0.235352\pi$
$674$	0.332368	−	11.2497i	0.0128023	−	0.433322i
$675$	0.530703	+	0.530703i	0.0204268	+	0.0204268i
$676$	1.06219	−	17.9603i	0.0408534	−	0.690782i
$677$	5.32310	−	5.32310i	0.204583	−	0.204583i	−0.597377	−	0.801960i	$-0.703790\pi$
$677$	5.32310	−	5.32310i	0.204583	−	0.204583i	0.801960	+	0.597377i	$0.203790\pi$
$678$	18.3061	−	17.2555i	0.703042	−	0.662692i
$679$		−	22.3298i		−	0.856939i
$680$	−5.59892	−	6.69074i	−0.214709	−	0.256578i
$681$		−	11.8701i		−	0.454862i
$682$	−14.0887	−	14.9466i	−0.539486	−	0.572334i
$683$	19.6537	−	19.6537i	0.752027	−	0.752027i	−0.222830	−	0.974857i	$-0.571529\pi$
$683$	19.6537	−	19.6537i	0.752027	−	0.752027i	0.974857	+	0.222830i	$0.0715295\pi$
$684$	−1.49524	+	1.32826i	−0.0571719	+	0.0507871i
$685$	−11.5489	−	11.5489i	−0.441260	−	0.441260i
$686$	12.1056	+	0.357654i	0.462193	+	0.0136553i
$687$	11.1393			0.424989
$688$	1.92219	−	1.51429i	0.0732827	−	0.0577318i
$689$	−55.5353			−2.11572
$690$	30.3655	+	0.897137i	1.15600	+	0.0341534i
$691$	−10.8763	−	10.8763i	−0.413756	−	0.413756i	0.469289	−	0.883045i	$-0.344510\pi$
$691$	−10.8763	−	10.8763i	−0.413756	−	0.413756i	−0.883045	+	0.469289i	$0.844510\pi$
$692$	13.7995	+	15.5343i	0.524578	+	0.590526i
$693$	−12.5617	+	12.5617i	−0.477180	+	0.477180i
$694$	14.8182	+	15.7204i	0.562491	+	0.596740i
$695$		−	12.3238i		−	0.467468i
$696$	15.2002	+	1.35040i	0.576163	+	0.0511867i
$697$			15.1936i			0.575500i
$698$	−1.80129	+	1.69791i	−0.0681799	+	0.0642669i
$699$	−0.640469	+	0.640469i	−0.0242248	+	0.0242248i
$700$	−6.01844	−	0.355935i	−0.227476	−	0.0134531i
$701$	8.26463	+	8.26463i	0.312151	+	0.312151i	0.845742	−	0.533592i	$-0.179158\pi$
$701$	8.26463	+	8.26463i	0.312151	+	0.312151i	−0.533592	+	0.845742i	$0.679158\pi$
$702$	0.195873	−	6.62973i	0.00739273	−	0.250223i
$703$	3.41862			0.128936
$704$	−29.0393	+	20.2176i	−1.09446	+	0.761981i
$705$	−13.9388			−0.524964
$706$	0.934782	−	31.6397i	0.0351810	−	1.19078i
$707$	48.4004	+	48.4004i	1.82029	+	1.82029i
$708$	−17.1405	−	1.01370i	−0.644180	−	0.0380973i
$709$	16.3112	−	16.3112i	0.612578	−	0.612578i	−0.331039	−	0.943617i	$-0.607399\pi$
$709$	16.3112	−	16.3112i	0.612578	−	0.612578i	0.943617	+	0.331039i	$0.107399\pi$
$710$	−1.07519	+	1.01349i	−0.0403513	+	0.0380354i
$711$			5.60770i			0.210305i
$712$	−46.5120	−	4.13215i	−1.74311	−	0.154859i
$713$			29.4151i			1.10160i
$714$	−5.01147	−	5.31661i	−0.187550	−	0.198969i
$715$	35.1744	−	35.1744i	1.31545	−	1.31545i
$716$	12.6258	+	14.2131i	0.471849	+	0.531168i
$717$	−10.7598	−	10.7598i	−0.401833	−	0.401833i
$718$	−19.7177	−	0.582552i	−0.735859	−	0.0217406i
$719$	0.245598			0.00915926			0.00457963	−	0.999990i	$-0.498542\pi$
$719$	0.245598			0.00915926			0.00457963	+	0.999990i	$0.498542\pi$
$720$	5.93590	+	7.53482i	0.221218	+	0.280806i
$721$	3.06998			0.114332
$722$	−1.41360	−	0.0417641i	−0.0526086	−	0.00155430i
$723$	17.6802	+	17.6802i	0.657532	+	0.657532i
$724$	−11.4039	+	10.1304i	−0.423824	+	0.376492i
$725$	2.86328	−	2.86328i	0.106340	−	0.106340i
$726$	8.30640	+	8.81216i	0.308279	+	0.327050i
$727$		−	38.3023i		−	1.42055i	−0.703922	−	0.710277i	$-0.748569\pi$
$727$		−	38.3023i		−	1.42055i	0.703922	−	0.710277i	$-0.251431\pi$
$728$	34.1927	+	40.8605i	1.26727	+	1.51439i
$729$		−	1.00000i		−	0.0370370i
$730$	16.1079	−	15.1834i	0.596179	−	0.561962i
$731$	0.556410	−	0.556410i	0.0205796	−	0.0205796i
$732$	1.56891	−	26.5284i	0.0579886	−	0.980518i
$733$	0.600974	+	0.600974i	0.0221975	+	0.0221975i	0.718118	−	0.695921i	$-0.245004\pi$
$733$	0.600974	+	0.600974i	0.0221975	+	0.0221975i	−0.695921	+	0.718118i	$0.745004\pi$
$734$	−0.188716	+	6.38750i	−0.00696564	+	0.235767i
$735$	−21.8991			−0.807760
$736$	50.1214	+	7.45621i	1.84750	+	0.274840i
$737$	−28.3673			−1.04492
$738$	0.493323	−	16.6976i	0.0181595	−	0.614647i
$739$	12.1952	+	12.1952i	0.448608	+	0.448608i	0.894892	−	0.446284i	$-0.147253\pi$
$739$	12.1952	+	12.1952i	0.448608	+	0.448608i	−0.446284	+	0.894892i	$0.647253\pi$
$740$	0.967974	−	16.3673i	0.0355834	−	0.601674i
$741$	3.31631	−	3.31631i	0.121828	−	0.121828i
$742$	48.9440	−	46.1350i	1.79679	−	1.69367i
$743$		−	4.20499i		−	0.154266i	−0.997021	−	0.0771330i	$-0.975423\pi$
$743$		−	4.20499i		−	0.154266i	0.997021	−	0.0771330i	$-0.0245766\pi$
$744$	−7.12287	+	5.96054i	−0.261137	+	0.218524i
$745$			4.38675i			0.160718i
$746$	5.90153	+	6.26086i	0.216070	+	0.229226i
$747$	−1.87477	+	1.87477i	−0.0685944	+	0.0685944i
$748$	−8.50671	+	7.55671i	−0.311036	+	0.276301i
$749$	−9.29737	−	9.29737i	−0.339719	−	0.339719i
$750$	−14.4050	−	0.425591i	−0.525998	−	0.0155404i
$751$	30.0536			1.09667			0.548336	−	0.836258i	$-0.315262\pi$
$751$	30.0536			1.09667			0.548336	+	0.836258i	$0.315262\pi$
$752$	−23.0883	−	2.74051i	−0.841945	−	0.0999360i
$753$	−1.92683			−0.0702176
$754$	−35.7691	−	1.05678i	−1.30263	−	0.0384858i
$755$	14.8833	+	14.8833i	0.541658	+	0.541658i
$756$	5.33491	+	6.00560i	0.194029	+	0.218422i
$757$	8.70096	−	8.70096i	0.316242	−	0.316242i	−0.531080	−	0.847322i	$-0.678214\pi$
$757$	8.70096	−	8.70096i	0.316242	−	0.316242i	0.847322	+	0.531080i	$0.178214\pi$
$758$	−15.9407	−	16.9113i	−0.578994	−	0.614248i
$759$		−	39.6205i		−	1.43813i
$760$	−0.600210	+	6.75603i	−0.0217719	+	0.245067i
$761$			37.3646i			1.35447i	0.735768	+	0.677233i	$0.236821\pi$
$761$			37.3646i			1.35447i	−0.735768	+	0.677233i	$0.763179\pi$
$762$	−15.2941	+	14.4163i	−0.554047	+	0.522248i
$763$	43.4452	−	43.4452i	1.57282	−	1.57282i
$764$	−46.4760	−	2.74863i	−1.68144	−	0.0994418i
$765$	2.18108	+	2.18108i	0.0788572	+	0.0788572i
$766$	1.34421	−	45.4977i	0.0485682	−	1.64390i
$767$	40.2645			1.45387
$768$	8.35086	+	13.6478i	0.301336	+	0.492474i
$769$	20.1253			0.725738			0.362869	−	0.931840i	$-0.381797\pi$
$769$	20.1253			0.725738			0.362869	+	0.931840i	$0.381797\pi$
$770$	−1.77918	+	60.2203i	−0.0641173	+	2.17019i
$771$	4.15114	+	4.15114i	0.149500	+	0.149500i
$772$	2.06071	+	0.121872i	0.0741665	+	0.00438627i
$773$	5.22606	−	5.22606i	0.187968	−	0.187968i	−0.606849	−	0.794817i	$-0.707567\pi$
$773$	5.22606	−	5.22606i	0.187968	−	0.187968i	0.794817	+	0.606849i	$0.207567\pi$
$774$	−0.629553	+	0.593421i	−0.0226288	+	0.0213301i
$775$			2.46453i			0.0885286i
$776$	−1.39152	+	15.6631i	−0.0499525	+	0.562272i
$777$		−	13.7308i		−	0.492591i
$778$	4.01979	+	4.26454i	0.144116	+	0.152891i
$779$	8.35245	−	8.35245i	0.299257	−	0.299257i
$780$	−14.9385	−	16.8165i	−0.534883	−	0.602126i
$781$	1.36264	+	1.36264i	0.0487590	+	0.0487590i
$782$	16.2877	+	0.481214i	0.582448	+	0.0172082i
$783$	−5.39526			−0.192811
$784$	−36.2739	−	4.30559i	−1.29550	−	0.153771i
$785$	−15.4270			−0.550615
$786$	13.5150	+	0.399294i	0.482063	+	0.0142423i
$787$	20.5710	+	20.5710i	0.733275	+	0.733275i	0.971267	−	0.237992i	$-0.0764891\pi$
$787$	20.5710	+	20.5710i	0.733275	+	0.733275i	−0.237992	+	0.971267i	$0.576489\pi$
$788$	0.457414	−	0.406331i	0.0162947	−	0.0144750i
$789$	−0.938166	+	0.938166i	−0.0333996	+	0.0333996i
$790$	13.0444	+	13.8387i	0.464100	+	0.492358i
$791$		−	71.4474i		−	2.54038i
$792$	9.59412	−	8.02851i	0.340912	−	0.285281i
$793$			62.3175i			2.21296i
$794$	33.4509	−	31.5310i	1.18713	−	1.11899i
$795$	−20.0788	+	20.0788i	−0.712121	+	0.712121i
$796$	0.561514	−	9.49453i	0.0199023	−	0.336525i
$797$	−13.2341	−	13.2341i	−0.468774	−	0.468774i	0.432743	−	0.901517i	$-0.357546\pi$
$797$	−13.2341	−	13.2341i	−0.468774	−	0.468774i	−0.901517	+	0.432743i	$0.857546\pi$
$798$	−0.167745	+	5.67769i	−0.00593810	+	0.200988i
$799$	−7.47660			−0.264503
$800$	4.19941	+	0.624716i	0.148472	+	0.0220871i
$801$	16.5092			0.583325
$802$	−1.03135	+	34.9084i	−0.0364183	+	1.23266i
$803$	−20.4142	−	20.4142i	−0.720400	−	0.720400i
$804$	−0.757285	+	12.8048i	−0.0267074	+	0.451590i
$805$	61.0080	−	61.0080i	2.15025	−	2.15025i
$806$	15.8487	−	14.9391i	0.558247	−	0.526208i
$807$			28.5880i			1.00635i
$808$	−30.9340	−	36.9663i	−1.08825	−	1.30047i
$809$		−	52.0893i		−	1.83136i	−0.401906	−	0.915681i	$-0.631652\pi$
$809$		−	52.0893i		−	1.83136i	0.401906	−	0.915681i	$-0.368348\pi$
$810$	−2.32616	−	2.46780i	−0.0817330	−	0.0867096i
$811$	−26.8313	+	26.8313i	−0.942173	+	0.942173i	−0.998417	−	0.0562438i	$-0.982088\pi$
$811$	−26.8313	+	26.8313i	−0.942173	+	0.942173i	0.0562438	+	0.998417i	$0.482088\pi$
$812$	32.4018	−	28.7832i	1.13708	−	1.01009i
$813$	−9.06121	−	9.06121i	−0.317790	−	0.317790i
$814$	−21.3744	−	0.631498i	−0.749173	−	0.0221340i
$815$	−36.4548			−1.27695
$816$	3.18395	+	4.04159i	0.111460	+	0.141484i
$817$	−0.611754			−0.0214026
$818$	−15.5235	−	0.458634i	−0.542766	−	0.0160358i
$819$	−13.3199	−	13.3199i	−0.465435	−	0.465435i
$820$	−37.6239	−	42.3539i	−1.31388	−	1.47906i
$821$	−23.7140	+	23.7140i	−0.827626	+	0.827626i	−0.987188	−	0.159562i	$-0.948992\pi$
$821$	−23.7140	+	23.7140i	−0.827626	+	0.827626i	0.159562	+	0.987188i	$0.448992\pi$
$822$	6.60674	+	7.00901i	0.230437	+	0.244467i
$823$			41.1179i			1.43328i	0.697444	+	0.716640i	$0.254321\pi$
$823$			41.1179i			1.43328i	−0.697444	+	0.716640i	$0.745679\pi$
$824$	−2.15341	−	0.191310i	−0.0750176	−	0.00666461i
$825$		−	3.31959i		−	0.115573i
$826$	−35.4857	+	33.4491i	−1.23471	+	1.16384i
$827$	11.7188	−	11.7188i	0.407502	−	0.407502i	−0.473364	−	0.880867i	$-0.656961\pi$
$827$	11.7188	−	11.7188i	0.407502	−	0.407502i	0.880867	+	0.473364i	$0.156961\pi$
$828$	−17.8844	−	1.05770i	−0.621525	−	0.0367574i
$829$	−2.46585	−	2.46585i	−0.0856426	−	0.0856426i	0.662988	−	0.748630i	$-0.269288\pi$
$829$	−2.46585	−	2.46585i	−0.0856426	−	0.0856426i	−0.748630	+	0.662988i	$0.769288\pi$
$830$	−0.265534	+	8.98759i	−0.00921683	+	0.311964i
$831$	−29.2447			−1.01449
$832$	−21.4379	−	30.7920i	−0.743227	−	1.06752i
$833$	−11.7464			−0.406989
$834$	−0.214632	+	7.26468i	−0.00743209	+	0.251555i
$835$	−2.30721	−	2.30721i	−0.0798444	−	0.0798444i
$836$	8.83059	+	0.522248i	0.305412	+	0.0180623i
$837$	2.32195	−	2.32195i	0.0802584	−	0.0802584i
$838$	15.5153	−	14.6248i	0.535966	−	0.505205i
$839$			44.0220i			1.51981i	0.650035	+	0.759904i	$0.274754\pi$
$839$			44.0220i			1.51981i	−0.650035	+	0.759904i	$0.725246\pi$
$840$	27.1355	+	2.41073i	0.936263	+	0.0831781i
$841$			0.108832i			0.00375284i
$842$	−22.5445	−	23.9172i	−0.776934	−	0.824240i
$843$	11.2142	−	11.2142i	0.386238	−	0.386238i
$844$	8.34937	+	9.39903i	0.287397	+	0.323528i
$845$	15.2539	+	15.2539i	0.524751	+	0.524751i
$846$	8.21667	+	0.242758i	0.282495	+	0.00834619i
$847$	34.3932			1.18176
$848$	−37.2064	+	29.3110i	−1.27767	+	1.00654i
$849$	−27.0981			−0.930006
$850$	1.36466	+	0.0403184i	0.0468075	+	0.00138291i
$851$	21.6540	+	21.6540i	0.742289	+	0.742289i
$852$	0.651460	−	0.578707i	0.0223187	−	0.0198262i
$853$	−29.1868	+	29.1868i	−0.999338	+	0.999338i	−1.00000		0.000661680i	$-0.999789\pi$
$853$	−29.1868	+	29.1868i	−0.999338	+	0.999338i	0.000661680		1.00000i	$0.499789\pi$
$854$	−51.7692	−	54.9213i	−1.77150	−	1.87937i
$855$		−	2.39803i		−	0.0820107i
$856$	5.94219	+	7.10095i	0.203100	+	0.242705i
$857$			16.2847i			0.556273i	0.960541	+	0.278137i	$0.0897168\pi$
$857$			16.2847i			0.556273i	−0.960541	+	0.278137i	$0.910283\pi$
$858$	−21.3474	+	20.1222i	−0.728787	+	0.686959i
$859$	−5.05121	+	5.05121i	−0.172345	+	0.172345i	−0.788009	−	0.615664i	$-0.788888\pi$
$859$	−5.05121	+	5.05121i	−0.172345	+	0.172345i	0.615664	+	0.788009i	$0.288888\pi$
$860$	−0.173216	+	2.92888i	−0.00590663	+	0.0998741i
$861$	−33.5474	−	33.5474i	−1.14329	−	1.14329i
$862$	0.563077	−	19.0586i	0.0191785	−	0.649138i
$863$	−21.4536			−0.730290			−0.365145	−	0.930951i	$-0.618981\pi$
$863$	−21.4536			−0.730290			−0.365145	+	0.930951i	$0.618981\pi$
$864$	−3.36789	−	4.54504i	−0.114578	−	0.154625i
$865$	−24.9135			−0.847085
$866$	0.352862	−	11.9434i	0.0119907	−	0.405853i
$867$	−10.8509	−	10.8509i	−0.368516	−	0.368516i
$868$	−1.55730	+	26.3321i	−0.0528582	+	0.893770i
$869$	17.5383	−	17.5383i	0.594947	−	0.594947i
$870$	−13.3144	+	12.5502i	−0.451401	+	0.425493i
$871$		−	30.0795i		−	1.01921i
$872$	−33.1817	+	27.7670i	−1.12367	+	0.940308i
$873$		−	5.55954i		−	0.188162i
$874$	−8.68936	−	9.21844i	−0.293922	−	0.311818i
$875$	−28.9414	+	28.9414i	−0.978398	+	0.978398i
$876$	−9.75976	+	8.66982i	−0.329752	+	0.292926i
$877$	−14.2382	−	14.2382i	−0.480788	−	0.480788i	0.424595	−	0.905383i	$-0.360416\pi$
$877$	−14.2382	−	14.2382i	−0.480788	−	0.480788i	−0.905383	+	0.424595i	$0.860416\pi$
$878$	−22.7607	−	0.672455i	−0.768137	−	0.0226943i
$879$	−16.7918			−0.566374
$880$	5.00072	−	42.1302i	0.168574	−	1.42021i
$881$	−2.11101			−0.0711218			−0.0355609	−	0.999368i	$-0.511322\pi$
$881$	−2.11101			−0.0711218			−0.0355609	+	0.999368i	$0.511322\pi$
$882$	12.9092	+	0.381395i	0.434674	+	0.0128422i
$883$	20.1411	+	20.1411i	0.677803	+	0.677803i	0.959503	−	0.281699i	$-0.0908981\pi$
$883$	20.1411	+	20.1411i	0.677803	+	0.677803i	−0.281699	+	0.959503i	$0.590898\pi$
$884$	−8.01282	−	9.02016i	−0.269500	−	0.303381i
$885$	14.5576	−	14.5576i	0.489350	−	0.489350i
$886$	0.814442	+	0.864032i	0.0273617	+	0.0290277i
$887$			11.4072i			0.383015i	0.981491	+	0.191507i	$0.0613376\pi$
$887$			11.4072i			0.383015i	−0.981491	+	0.191507i	$0.938662\pi$
$888$	−0.855658	+	9.63139i	−0.0287140	+	0.323208i
$889$			59.6918i			2.00200i
$890$	40.7415	−	38.4032i	1.36566	−	1.28728i
$891$	−3.12754	+	3.12754i	−0.104777	+	0.104777i
$892$	−49.6125	−	2.93412i	−1.66115	−	0.0982417i
$893$	4.11013	+	4.11013i	0.137540	+	0.137540i
$894$	0.0763998	−	2.58592i	0.00255519	−	0.0864860i
$895$	−22.7946			−0.761939
$896$	44.4735	+	9.32828i	1.48576	+	0.311636i
$897$	42.0119			1.40274
$898$	0.00546266	−	0.184896i	0.000182291	−	0.00617005i
$899$	−12.5275	−	12.5275i	−0.417816	−	0.417816i
$900$	−1.49844	−	0.0886186i	−0.0499479	−	0.00295395i
$901$	−10.7700	+	10.7700i	−0.358802	+	0.358802i
$902$	−53.7653	+	50.6795i	−1.79019	+	1.68744i
$903$			2.45710i			0.0817671i
$904$	−4.45236	+	50.1162i	−0.148083	+	1.66684i
$905$		−	18.2893i		−	0.607958i
$906$	−8.51424	−	9.03266i	−0.282867	−	0.300090i
$907$	−8.90535	+	8.90535i	−0.295697	+	0.295697i	−0.839326	−	0.543629i	$-0.817050\pi$
$907$	−8.90535	+	8.90535i	−0.295697	+	0.295697i	0.543629	+	0.839326i	$0.317050\pi$
$908$	15.7665	+	17.7486i	0.523229	+	0.589007i
$909$	12.0505	+	12.0505i	0.399688	+	0.399688i
$910$	−63.8551	−	1.88657i	−2.11678	−	0.0625392i
$911$	−27.3847			−0.907297			−0.453649	−	0.891181i	$-0.649878\pi$
$911$	−27.3847			−0.907297			−0.453649	+	0.891181i	$0.649878\pi$
$912$	0.471477	−	3.97212i	0.0156122	−	0.131530i
$913$	11.7269			0.388102
$914$	38.0904	+	1.12537i	1.25992	+	0.0372238i
$915$	22.5309	+	22.5309i	0.744848	+	0.744848i
$916$	−16.6558	+	14.7958i	−0.550324	+	0.488866i
$917$	27.1531	−	27.1531i	0.896676	−	0.896676i
$918$	−1.24773	−	1.32370i	−0.0411811	−	0.0436886i
$919$		−	16.7701i		−	0.553195i	−0.960986	−	0.276597i	$-0.910793\pi$
$919$		−	16.7701i		−	0.553195i	0.960986	−	0.276597i	$-0.0892068\pi$
$920$	−46.5954	+	38.9918i	−1.53620	+	1.28552i
$921$		−	26.3225i		−	0.867355i
$922$	35.4536	−	33.4188i	1.16760	−	1.10059i
$923$	−1.44488	+	1.44488i	−0.0475589	+	0.0475589i
$924$	2.09760	−	35.4679i	0.0690059	−	1.16681i
$925$	1.81427	+	1.81427i	0.0596529	+	0.0596529i
$926$	−0.0368508	+	1.24730i	−0.00121099	+	0.0409887i
$927$	0.764345			0.0251044
$928$	−24.5216	+	18.1706i	−0.804963	+	0.596480i
$929$	−14.2388			−0.467159			−0.233580	−	0.972338i	$-0.575044\pi$
$929$	−14.2388			−0.467159			−0.233580	+	0.972338i	$0.575044\pi$
$930$	0.328871	−	11.1313i	0.0107841	−	0.365011i
$931$	6.45739	+	6.45739i	0.211632	+	0.211632i
$932$	0.106948	−	1.80836i	0.00350319	−	0.0592348i
$933$	9.28460	−	9.28460i	0.303964	−	0.303964i
$934$	−8.95448	+	8.44055i	−0.293000	+	0.276183i
$935$		−	13.6429i		−	0.446169i
$936$	8.51310	+	10.1732i	0.278259	+	0.332521i
$937$		−	6.09698i		−	0.199180i	−0.995029	−	0.0995899i	$-0.968247\pi$
$937$		−	6.09698i		−	0.199180i	0.995029	−	0.0995899i	$-0.0317531\pi$
$938$	24.9881	+	26.5095i	0.815889	+	0.865567i
$939$	19.5987	−	19.5987i	0.639578	−	0.639578i
$940$	20.8418	−	18.5142i	0.679784	−	0.603868i
$941$	32.6743	+	32.6743i	1.06515	+	1.06515i	0.997724	+	0.0674282i	$0.0214794\pi$
$941$	32.6743	+	32.6743i	1.06515	+	1.06515i	0.0674282	+	0.997724i	$0.478521\pi$
$942$	9.09399	+	0.268678i	0.296298	+	0.00875400i
$943$	105.811			3.44568
$944$	26.9756	−	21.2512i	0.877981	−	0.691669i
$945$	−9.63163			−0.313317
$946$	3.82490	+	0.113005i	0.124358	+	0.00367411i
$947$	−1.79605	−	1.79605i	−0.0583638	−	0.0583638i	0.677322	−	0.735686i	$-0.263140\pi$
$947$	−1.79605	−	1.79605i	−0.0583638	−	0.0583638i	−0.735686	+	0.677322i	$0.763140\pi$
$948$	−7.44846	−	8.38485i	−0.241915	−	0.272327i
$949$	21.6463	−	21.6463i	0.702669	−	0.702669i
$950$	−0.728035	−	0.772364i	−0.0236206	−	0.0250588i
$951$			24.3216i			0.788680i
$952$	14.5552	+	1.29309i	0.471736	+	0.0419093i
$953$			11.4900i			0.372198i	0.982531	+	0.186099i	$0.0595846\pi$
$953$			11.4900i			0.372198i	−0.982531	+	0.186099i	$0.940415\pi$
$954$	12.1858	−	11.4864i	0.394530	−	0.371886i
$955$	39.4726	−	39.4726i	1.27730	−	1.27730i
$956$	30.3803	+	1.79672i	0.982570	+	0.0581099i
$957$	16.8739	+	16.8739i	0.545455	+	0.545455i
$958$	−0.267154	+	9.04241i	−0.00863136	+	0.292147i
$959$	27.3556			0.883360
$960$	−18.8837	−	3.38198i	−0.609470	−	0.109153i
$961$	−20.2171			−0.652164
$962$	0.669614	−	22.6646i	0.0215892	−	0.730735i
$963$	−2.31480	−	2.31480i	−0.0745935	−	0.0745935i
$964$	−49.9198	−	2.95230i	−1.60781	−	0.0950871i
$965$	−1.75018	+	1.75018i	−0.0563404	+	0.0563404i
$966$	−37.0257	+	34.9007i	−1.19128	+	1.12291i
$967$			55.1485i			1.77346i	0.462290	+	0.886729i	$0.347028\pi$
$967$			55.1485i			1.77346i	−0.462290	+	0.886729i	$0.652972\pi$
$968$	−24.1248	−	2.14326i	−0.775402	−	0.0688871i
$969$		−	1.28627i		−	0.0413211i
$970$	−12.9324	−	13.7198i	−0.415234	−	0.440517i
$971$	3.12816	−	3.12816i	0.100387	−	0.100387i	−0.655129	−	0.755517i	$-0.727386\pi$
$971$	3.12816	−	3.12816i	0.100387	−	0.100387i	0.755517	+	0.655129i	$0.227386\pi$
$972$	1.32826	+	1.49524i	0.0426038	+	0.0479598i
$973$	14.5956	+	14.5956i	0.467913	+	0.467913i
$974$	−13.9752	−	0.412891i	−0.447794	−	0.0132299i
$975$	3.51995			0.112729
$976$	32.8906	+	41.7502i	1.05280	+	1.33639i
$977$	−28.6613			−0.916957			−0.458479	−	0.888705i	$-0.651605\pi$
$977$	−28.6613			−0.916957			−0.458479	+	0.888705i	$0.651605\pi$
$978$	21.4895	+	0.634897i	0.687158	+	0.0203018i
$979$	−51.6333	−	51.6333i	−1.65021	−	1.65021i
$980$	32.7444	−	29.0876i	1.04598	−	0.929168i
$981$	10.8167	−	10.8167i	0.345352	−	0.345352i
$982$	−30.8969	−	32.7782i	−0.985960	−	1.04599i
$983$			25.4672i			0.812278i	0.913811	+	0.406139i	$0.133125\pi$
$983$			25.4672i			0.812278i	−0.913811	+	0.406139i	$0.866875\pi$
$984$	21.4410	+	25.6222i	0.683515	+	0.816805i
$985$			0.733589i			0.0233741i
$986$	−7.14170	+	6.73181i	−0.227438	+	0.214385i
$987$	16.5083	−	16.5083i	0.525464	−	0.525464i
$988$	−0.553770	+	9.36359i	−0.0176178	+	0.297895i
$989$	−3.87493	−	3.87493i	−0.123215	−	0.123215i
$990$	−0.442971	+	14.9933i	−0.0140785	+	0.476518i
$991$	49.6542			1.57732			0.788659	−	0.614831i	$-0.210776\pi$
$991$	49.6542			1.57732			0.788659	+	0.614831i	$0.210776\pi$
$992$	2.73328	−	18.3734i	0.0867818	−	0.583356i
$993$	22.4012			0.710881
$994$	0.0730847	−	2.47371i	0.00231811	−	0.0784613i
$995$	8.06381	+	8.06381i	0.255640	+	0.255640i
$996$	0.313056	−	5.29341i	0.00991957	−	0.167728i
$997$	15.3984	−	15.3984i	0.487672	−	0.487672i	−0.419899	−	0.907571i	$-0.637934\pi$
$997$	15.3984	−	15.3984i	0.487672	−	0.487672i	0.907571	+	0.419899i	$0.137934\pi$
$998$	−6.32898	+	5.96574i	−0.200340	+	0.188842i
$999$		−	3.41862i		−	0.108160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.u.a.685.19	yes	72
16.5	even	4	inner	912.2.u.a.229.19	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.u.a.229.19	✓	72	16.5	even	4	inner
912.2.u.a.685.19	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0417641 + 1.41360i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.99651 - 0.118075i) q^{4} +(1.69566 - 1.69566i) q^{5} +(-1.02910 + 0.970032i) q^{6} +4.01648i q^{7} +(0.250293 - 2.81733i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.0417641 + 1.41360i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.99651 - 0.118075i) q^{4} +(1.69566 - 1.69566i) q^{5} +(-1.02910 + 0.970032i) q^{6} +4.01648i q^{7} +(0.250293 - 2.81733i) q^{8} +1.00000i q^{9} +(2.32616 + 2.46780i) q^{10} +(3.12754 - 3.12754i) q^{11} +(-1.32826 - 1.49524i) q^{12} +(3.31631 + 3.31631i) q^{13} +(-5.67769 - 0.167745i) q^{14} +2.39803 q^{15} +(3.97212 + 0.471477i) q^{16} +1.28627 q^{17} +(-1.41360 - 0.0417641i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-3.58562 + 3.18519i) q^{20} +(-2.84008 + 2.84008i) q^{21} +(4.29046 + 4.55170i) q^{22} -8.95781i q^{23} +(2.16914 - 1.81517i) q^{24} -0.750527i q^{25} +(-4.82643 + 4.54943i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.474247 - 8.01895i) q^{28} +(3.81503 + 3.81503i) q^{29} +(-0.100151 + 3.38984i) q^{30} -3.28373 q^{31} +(-0.832370 + 5.59528i) q^{32} +4.42301 q^{33} +(-0.0537201 + 1.81827i) q^{34} +(6.81059 + 6.81059i) q^{35} +(0.118075 - 1.99651i) q^{36} +(-2.41733 + 2.41733i) q^{37} +(1.02910 - 0.970032i) q^{38} +4.68997i q^{39} +(-4.35282 - 5.20165i) q^{40} +11.8121i q^{41} +(-3.89612 - 4.13334i) q^{42} +(0.432575 - 0.432575i) q^{43} +(-6.61345 + 5.87488i) q^{44} +(1.69566 + 1.69566i) q^{45} +(12.6627 + 0.374115i) q^{46} -5.81260 q^{47} +(2.47533 + 3.14210i) q^{48} -9.13213 q^{49} +(1.06094 + 0.0313451i) q^{50} +(0.909533 + 0.909533i) q^{51} +(-6.22948 - 7.01263i) q^{52} +(-8.37304 + 8.37304i) q^{53} +(-0.970032 - 1.02910i) q^{54} -10.6065i q^{55} +(11.3158 + 1.00530i) q^{56} -1.00000i q^{57} +(-5.55224 + 5.23358i) q^{58} +(6.07068 - 6.07068i) q^{59} +(-4.78769 - 0.283147i) q^{60} +(9.39559 + 9.39559i) q^{61} +(0.137142 - 4.64188i) q^{62} -4.01648 q^{63} +(-7.87471 - 1.41032i) q^{64} +11.2467 q^{65} +(-0.184723 + 6.25235i) q^{66} +(-4.53509 - 4.53509i) q^{67} +(-2.56806 - 0.151877i) q^{68} +(6.33413 - 6.33413i) q^{69} +(-9.91187 + 9.34299i) q^{70} +0.435690i q^{71} +(2.81733 + 0.250293i) q^{72} -6.52722i q^{73} +(-3.31617 - 3.51809i) q^{74} +(0.530703 - 0.530703i) q^{75} +(1.32826 + 1.49524i) q^{76} +(12.5617 + 12.5617i) q^{77} +(-6.62973 - 0.195873i) q^{78} +5.60770 q^{79} +(7.53482 - 5.93590i) q^{80} -1.00000 q^{81} +(-16.6976 - 0.493323i) q^{82} +(1.87477 + 1.87477i) q^{83} +(6.00560 - 5.33491i) q^{84} +(2.18108 - 2.18108i) q^{85} +(0.593421 + 0.629553i) q^{86} +5.39526i q^{87} +(-8.02851 - 9.59412i) q^{88} -16.5092i q^{89} +(-2.46780 + 2.32616i) q^{90} +(-13.3199 + 13.3199i) q^{91} +(-1.05770 + 17.8844i) q^{92} +(-2.32195 - 2.32195i) q^{93} +(0.242758 - 8.21667i) q^{94} -2.39803 q^{95} +(-4.54504 + 3.36789i) q^{96} -5.55954 q^{97} +(0.381395 - 12.9092i) q^{98} +(3.12754 + 3.12754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{4}+O(q^{10}) \) 72 * q + 4 * q^4	\( 72 q + 4 q^{4} + 8 q^{11} - 8 q^{12} - 12 q^{14} - 4 q^{16} - 4 q^{18} - 44 q^{20} - 52 q^{26} + 52 q^{28} + 16 q^{29} + 8 q^{30} - 64 q^{31} + 40 q^{34} + 16 q^{37} + 4 q^{40} - 8 q^{42} + 8 q^{43} + 68 q^{44} + 104 q^{47} + 16 q^{48} - 72 q^{49} + 116 q^{50} - 8 q^{52} - 16 q^{53} - 28 q^{56} - 92 q^{58} - 32 q^{59} + 32 q^{60} + 24 q^{62} - 40 q^{63} + 28 q^{64} + 16 q^{65} + 28 q^{66} - 8 q^{67} - 100 q^{68} - 20 q^{70} + 4 q^{72} - 124 q^{74} - 16 q^{75} + 8 q^{76} - 16 q^{77} - 12 q^{78} + 48 q^{79} + 44 q^{80} - 72 q^{81} + 52 q^{82} - 8 q^{84} - 64 q^{85} + 48 q^{86} - 32 q^{88} + 8 q^{90} + 8 q^{91} + 96 q^{92} + 12 q^{94} - 20 q^{96} + 208 q^{98} + 8 q^{99}+O(q^{100}) \) 72 * q + 4 * q^4 + 8 * q^11 - 8 * q^12 - 12 * q^14 - 4 * q^16 - 4 * q^18 - 44 * q^20 - 52 * q^26 + 52 * q^28 + 16 * q^29 + 8 * q^30 - 64 * q^31 + 40 * q^34 + 16 * q^37 + 4 * q^40 - 8 * q^42 + 8 * q^43 + 68 * q^44 + 104 * q^47 + 16 * q^48 - 72 * q^49 + 116 * q^50 - 8 * q^52 - 16 * q^53 - 28 * q^56 - 92 * q^58 - 32 * q^59 + 32 * q^60 + 24 * q^62 - 40 * q^63 + 28 * q^64 + 16 * q^65 + 28 * q^66 - 8 * q^67 - 100 * q^68 - 20 * q^70 + 4 * q^72 - 124 * q^74 - 16 * q^75 + 8 * q^76 - 16 * q^77 - 12 * q^78 + 48 * q^79 + 44 * q^80 - 72 * q^81 + 52 * q^82 - 8 * q^84 - 64 * q^85 + 48 * q^86 - 32 * q^88 + 8 * q^90 + 8 * q^91 + 96 * q^92 + 12 * q^94 - 20 * q^96 + 208 * q^98 + 8 * q^99

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