LMFDB - Embedded newform 896.2.bn.a.533.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			533.15
Character	$\chi$	$=$	896.533
Dual form			896.2.bn.a.701.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.776680 + 1.18185i) q^{2} +(-1.22033 - 1.00150i) q^{3} +(-0.793537 - 1.83584i) q^{4} +(0.109002 + 0.359330i) q^{5} +(2.13142 - 0.664400i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(2.78601 + 0.488017i) q^{8} +(-0.0990695 - 0.498056i) q^{9} +O(q^{10})$	\(q+(-0.776680 + 1.18185i) q^{2} +(-1.22033 - 1.00150i) q^{3} +(-0.793537 - 1.83584i) q^{4} +(0.109002 + 0.359330i) q^{5} +(2.13142 - 0.664400i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(2.78601 + 0.488017i) q^{8} +(-0.0990695 - 0.498056i) q^{9} +(-0.509333 - 0.150261i) q^{10} +(0.212654 - 2.15911i) q^{11} +(-0.870210 + 3.03504i) q^{12} +(-3.72124 - 1.12883i) q^{13} +(0.992324 - 1.00762i) q^{14} +(0.226850 - 0.547664i) q^{15} +(-2.74060 + 2.91361i) q^{16} +(-1.07606 - 2.59784i) q^{17} +(0.665573 + 0.269745i) q^{18} +(2.09195 + 3.91376i) q^{19} +(0.573175 - 0.485251i) q^{20} +(1.00150 + 1.22033i) q^{21} +(2.38658 + 1.92826i) q^{22} +(-2.80201 + 4.19350i) q^{23} +(-2.91109 - 3.38571i) q^{24} +(4.04011 - 2.69952i) q^{25} +(4.22432 - 3.52121i) q^{26} +(-2.61044 + 4.88379i) q^{27} +(0.420135 + 1.95537i) q^{28} +(2.31711 - 0.228215i) q^{29} +(0.471067 + 0.693462i) q^{30} +(2.96716 + 2.96716i) q^{31} +(-1.31488 - 5.50192i) q^{32} +(-2.42185 + 2.42185i) q^{33} +(3.90602 + 0.745949i) q^{34} +(-0.0368053 - 0.373691i) q^{35} +(-0.835735 + 0.577101i) q^{36} +(-1.42485 - 0.761596i) q^{37} +(-6.25025 - 0.567371i) q^{38} +(3.41061 + 5.10434i) q^{39} +(0.128320 + 1.05429i) q^{40} +(1.34795 + 0.900674i) q^{41} +(-2.22008 + 0.235814i) q^{42} +(0.733421 - 0.601903i) q^{43} +(-4.13253 + 1.32294i) q^{44} +(0.168168 - 0.0898875i) q^{45} +(-2.77982 - 6.56856i) q^{46} +(-9.58211 + 3.96904i) q^{47} +(6.26239 - 0.810854i) q^{48} +(0.923880 + 0.382683i) q^{49} +(0.0525485 + 6.87146i) q^{50} +(-1.28858 + 4.24788i) q^{51} +(0.880600 + 7.72737i) q^{52} +(-8.75454 - 0.862247i) q^{53} +(-3.74443 - 6.87828i) q^{54} +(0.799013 - 0.158934i) q^{55} +(-2.63727 - 1.02216i) q^{56} +(1.36675 - 6.87114i) q^{57} +(-1.52993 + 2.91572i) q^{58} +(-9.20152 + 2.79125i) q^{59} +(-1.18544 + 0.0181319i) q^{60} +(-5.74374 + 6.99877i) q^{61} +(-5.81127 + 1.20220i) q^{62} +0.507814i q^{63} +(7.52368 + 2.71924i) q^{64} -1.46020i q^{65} +(-0.981259 - 4.74326i) q^{66} +(-8.67917 + 10.5756i) q^{67} +(-3.91532 + 4.03696i) q^{68} +(7.61913 - 2.31124i) q^{69} +(0.470232 + 0.246740i) q^{70} +(-1.64209 + 8.25533i) q^{71} +(-0.0329484 - 1.43594i) q^{72} +(2.47608 - 0.492524i) q^{73} +(2.00674 - 1.09244i) q^{74} +(-7.63380 - 0.751864i) q^{75} +(5.52499 - 6.94619i) q^{76} +(-0.629790 + 2.07614i) q^{77} +(-8.68152 + 0.0663906i) q^{78} +(-15.7882 - 6.53968i) q^{79} +(-1.34568 - 0.667191i) q^{80} +(6.66919 - 2.76247i) q^{81} +(-2.11139 + 0.893544i) q^{82} +(-0.710749 + 0.379903i) q^{83} +(1.44560 - 2.80696i) q^{84} +(0.816190 - 0.669830i) q^{85} +(0.141726 + 1.33428i) q^{86} +(-3.05618 - 2.04207i) q^{87} +(1.64614 - 5.91152i) q^{88} +(6.39067 + 9.56431i) q^{89} +(-0.0243790 + 0.268563i) q^{90} +(3.42952 + 1.83312i) q^{91} +(9.92208 + 1.81633i) q^{92} +(-0.649305 - 6.59250i) q^{93} +(2.75142 - 14.4073i) q^{94} +(-1.17831 + 1.17831i) q^{95} +(-3.90556 + 8.03097i) q^{96} +(-5.85150 - 5.85150i) q^{97} +(-1.16983 + 0.794664i) q^{98} +(-1.09643 + 0.107989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q+O(q^{10}) $ 752 * q	$ 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) $ 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{32}\right)$

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 $

$2$	−0.776680	+	1.18185i	−0.549196	+	0.835694i
$2$	−0.776680	+	1.18185i	−0.549196	+	0.835694i
$3$	−1.22033	−	1.00150i	−0.704555	−	0.578213i	0.212410	−	0.977181i	$-0.431869\pi$
$3$	−1.22033	−	1.00150i	−0.704555	−	0.578213i	−0.916965	+	0.398967i	$0.869369\pi$
$4$	−0.793537	−	1.83584i	−0.396768	−	0.917919i
$5$	0.109002	+	0.359330i	0.0487470	+	0.160697i	0.977935	−	0.208911i	$-0.0669919\pi$
$5$	0.109002	+	0.359330i	0.0487470	+	0.160697i	−0.929188	+	0.369608i	$0.879492\pi$
$6$	2.13142	−	0.664400i	0.870148	−	0.271240i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$8$	2.78601	+	0.488017i	0.985002	+	0.172540i
$9$	−0.0990695	−	0.498056i	−0.0330232	−	0.166019i
$10$	−0.509333	−	0.150261i	−0.161065	−	0.0475167i
$11$	0.212654	−	2.15911i	0.0641176	−	0.650997i	−0.908390	−	0.418124i	$-0.862688\pi$
$11$	0.212654	−	2.15911i	0.0641176	−	0.650997i	0.972507	−	0.232872i	$-0.0748124\pi$
$12$	−0.870210	+	3.03504i	−0.251208	+	0.876141i
$13$	−3.72124	−	1.12883i	−1.03209	−	0.313080i	−0.271584	−	0.962415i	$-0.587548\pi$
$13$	−3.72124	−	1.12883i	−1.03209	−	0.313080i	−0.760503	+	0.649334i	$0.775048\pi$
$14$	0.992324	−	1.00762i	0.265210	−	0.269297i
$15$	0.226850	−	0.547664i	0.0585724	−	0.141406i
$16$	−2.74060	+	2.91361i	−0.685150	+	0.728402i
$17$	−1.07606	−	2.59784i	−0.260983	−	0.630069i	0.738017	−	0.674783i	$-0.235763\pi$
$17$	−1.07606	−	2.59784i	−0.260983	−	0.630069i	−0.999000	+	0.0447131i	$0.985763\pi$
$18$	0.665573	+	0.269745i	0.156877	+	0.0635795i
$19$	2.09195	+	3.91376i	0.479926	+	0.897878i	0.999067	+	0.0431896i	$0.0137520\pi$
$19$	2.09195	+	3.91376i	0.479926	+	0.897878i	−0.519141	+	0.854689i	$0.673748\pi$
$20$	0.573175	−	0.485251i	0.128166	−	0.108505i
$21$	1.00150	+	1.22033i	0.218544	+	0.266297i
$22$	2.38658	+	1.92826i	0.508821	+	0.411107i
$23$	−2.80201	+	4.19350i	−0.584259	+	0.874405i	−0.999375	−	0.0353633i	$-0.988741\pi$
$23$	−2.80201	+	4.19350i	−0.584259	+	0.874405i	0.415115	+	0.909769i	$0.363741\pi$
$24$	−2.91109	−	3.38571i	−0.594224	−	0.691106i
$25$	4.04011	−	2.69952i	0.808022	−	0.539903i
$26$	4.22432	−	3.52121i	0.828457	−	0.690567i
$27$	−2.61044	+	4.88379i	−0.502379	+	0.939885i
$28$	0.420135	+	1.95537i	0.0793980	+	0.369531i
$29$	2.31711	−	0.228215i	0.430276	−	0.0423785i	0.119438	−	0.992842i	$-0.461891\pi$
$29$	2.31711	−	0.228215i	0.430276	−	0.0423785i	0.310837	+	0.950463i	$0.399391\pi$
$30$	0.471067	+	0.693462i	0.0860046	+	0.126608i
$31$	2.96716	+	2.96716i	0.532918	+	0.532918i	0.921440	−	0.388522i	$-0.127014\pi$
$31$	2.96716	+	2.96716i	0.532918	+	0.532918i	−0.388522	+	0.921440i	$0.627014\pi$
$32$	−1.31488	−	5.50192i	−0.232440	−	0.972611i
$33$	−2.42185	+	2.42185i	−0.421589	+	0.421589i
$34$	3.90602	+	0.745949i	0.669876	+	0.127929i
$35$	−0.0368053	−	0.373691i	−0.00622123	−	0.0631652i
$36$	−0.835735	+	0.577101i	−0.139289	+	0.0961836i
$37$	−1.42485	−	0.761596i	−0.234243	−	0.125206i	0.350100	−	0.936712i	$-0.386148\pi$
$37$	−1.42485	−	0.761596i	−0.234243	−	0.125206i	−0.584343	+	0.811507i	$0.698648\pi$
$38$	−6.25025	−	0.567371i	−1.01392	−	0.0920397i
$39$	3.41061	+	5.10434i	0.546135	+	0.817349i
$40$	0.128320	+	1.05429i	0.0202892	+	0.166698i
$41$	1.34795	+	0.900674i	0.210515	+	0.140662i	0.656358	−	0.754449i	$-0.272096\pi$
$41$	1.34795	+	0.900674i	0.210515	+	0.140662i	−0.445843	+	0.895111i	$0.647096\pi$
$42$	−2.22008	+	0.235814i	−0.342566	+	0.0363869i
$43$	0.733421	−	0.601903i	0.111846	−	0.0917894i	−0.576808	−	0.816880i	$-0.695702\pi$
$43$	0.733421	−	0.601903i	0.111846	−	0.0917894i	0.688654	+	0.725090i	$0.258202\pi$
$44$	−4.13253	+	1.32294i	−0.623002	+	0.199440i
$45$	0.168168	−	0.0898875i	0.0250690	−	0.0133996i
$46$	−2.77982	−	6.56856i	−0.409863	−	0.968481i
$47$	−9.58211	+	3.96904i	−1.39769	+	0.578944i	−0.949152	−	0.314818i	$-0.898057\pi$
$47$	−9.58211	+	3.96904i	−1.39769	+	0.578944i	−0.448542	+	0.893762i	$0.648057\pi$
$48$	6.26239	−	0.810854i	0.903898	−	0.117037i
$49$	0.923880	+	0.382683i	0.131983	+	0.0546691i
$50$	0.0525485	+	6.87146i	0.00743147	+	0.971772i
$51$	−1.28858	+	4.24788i	−0.180438	+	0.594823i
$52$	0.880600	+	7.72737i	0.122117	+	1.07159i
$53$	−8.75454	−	0.862247i	−1.20253	−	0.118439i	−0.523159	−	0.852235i	$-0.675247\pi$
$53$	−8.75454	−	0.862247i	−1.20253	−	0.118439i	−0.679370	+	0.733796i	$0.737747\pi$
$54$	−3.74443	−	6.87828i	−0.509552	−	0.936016i
$55$	0.799013	−	0.158934i	0.107739	−	0.0214306i
$56$	−2.63727	−	1.02216i	−0.352420	−	0.136592i
$57$	1.36675	−	6.87114i	0.181031	−	0.910104i
$58$	−1.52993	+	2.91572i	−0.200890	+	0.382853i
$59$	−9.20152	+	2.79125i	−1.19794	+	0.363390i	−0.825357	−	0.564611i	$-0.809026\pi$
$59$	−9.20152	+	2.79125i	−1.19794	+	0.363390i	−0.372578	+	0.928001i	$0.621526\pi$
$60$	−1.18544	+	0.0181319i	−0.153039	+	0.00234082i
$61$	−5.74374	+	6.99877i	−0.735411	+	0.896101i	−0.997623	−	0.0689094i	$-0.978048\pi$
$61$	−5.74374	+	6.99877i	−0.735411	+	0.896101i	0.262212	+	0.965010i	$0.415548\pi$
$62$	−5.81127	+	1.20220i	−0.738032	+	0.152680i
$63$			0.507814i			0.0639785i
$64$	7.52368	+	2.71924i	0.940460	+	0.339905i
$65$		−	1.46020i		−	0.181115i
$66$	−0.981259	−	4.74326i	−0.120785	−	0.583855i
$67$	−8.67917	+	10.5756i	−1.06033	+	1.29202i	−0.105642	+	0.994404i	$0.533690\pi$
$67$	−8.67917	+	10.5756i	−1.06033	+	1.29202i	−0.954687	+	0.297611i	$0.903810\pi$
$68$	−3.91532	+	4.03696i	−0.474803	+	0.489553i
$69$	7.61913	−	2.31124i	0.917236	−	0.278240i
$70$	0.470232	+	0.246740i	0.0562035	+	0.0294910i
$71$	−1.64209	+	8.25533i	−0.194880	+	0.979727i	0.752250	+	0.658878i	$0.228968\pi$
$71$	−1.64209	+	8.25533i	−0.194880	+	0.979727i	−0.947130	+	0.320850i	$0.896032\pi$
$72$	−0.0329484	−	1.43594i	−0.00388301	−	0.169227i
$73$	2.47608	−	0.492524i	0.289804	−	0.0576455i	−0.0480476	−	0.998845i	$-0.515300\pi$
$73$	2.47608	−	0.492524i	0.289804	−	0.0576455i	0.337851	+	0.941200i	$0.390300\pi$
$74$	2.00674	−	1.09244i	0.233279	−	0.126993i
$75$	−7.63380	−	0.751864i	−0.881476	−	0.0868178i
$76$	5.52499	−	6.94619i	0.633760	−	0.796783i
$77$	−0.629790	+	2.07614i	−0.0717712	+	0.236598i
$78$	−8.68152	+	0.0663906i	−0.982989	+	0.00751726i
$79$	−15.7882	−	6.53968i	−1.77631	−	0.735772i	−0.993543	−	0.113457i	$-0.963808\pi$
$79$	−15.7882	−	6.53968i	−1.77631	−	0.735772i	−0.782767	−	0.622315i	$-0.786192\pi$
$80$	−1.34568	−	0.667191i	−0.150451	−	0.0745943i
$81$	6.66919	−	2.76247i	0.741022	−	0.306941i
$82$	−2.11139	+	0.893544i	−0.233164	+	0.0986754i
$83$	−0.710749	+	0.379903i	−0.0780149	+	0.0416998i	−0.509943	−	0.860208i	$-0.670333\pi$
$83$	−0.710749	+	0.379903i	−0.0780149	+	0.0416998i	0.431928	+	0.901908i	$0.357833\pi$
$84$	1.44560	−	2.80696i	0.157727	−	0.306264i
$85$	0.816190	−	0.669830i	0.0885283	−	0.0726533i
$86$	0.141726	+	1.33428i	0.0152827	+	0.143879i
$87$	−3.05618	−	2.04207i	−0.327657	−	0.218933i
$88$	1.64614	−	5.91152i	0.175479	−	0.630171i
$89$	6.39067	+	9.56431i	0.677409	+	1.01381i	0.997785	+	0.0665241i	$0.0211909\pi$
$89$	6.39067	+	9.56431i	0.677409	+	1.01381i	−0.320375	+	0.947291i	$0.603809\pi$
$90$	−0.0243790	+	0.268563i	−0.00256977	+	0.0283090i
$91$	3.42952	+	1.83312i	0.359511	+	0.192163i
$92$	9.92208	+	1.81633i	1.03445	+	0.189366i
$93$	−0.649305	−	6.59250i	−0.0673297	−	0.683610i
$94$	2.75142	−	14.4073i	0.283788	−	1.48600i
$95$	−1.17831	+	1.17831i	−0.120892	+	0.120892i
$96$	−3.90556	+	8.03097i	−0.398610	+	0.819658i
$97$	−5.85150	−	5.85150i	−0.594129	−	0.594129i	0.344615	−	0.938744i	$-0.388010\pi$
$97$	−5.85150	−	5.85150i	−0.594129	−	0.594129i	−0.938744	+	0.344615i	$0.888010\pi$
$98$	−1.16983	+	0.794664i	−0.118171	+	0.0802732i
$99$	−1.09643	+	0.107989i	−0.110195	+	0.0108533i
$100$	−8.16185	−	5.27482i	−0.816185	−	0.527482i
$101$	−6.49690	+	12.1548i	−0.646466	+	1.20945i	0.318710	+	0.947852i	$0.396750\pi$
$101$	−6.49690	+	12.1548i	−0.646466	+	1.20945i	−0.965176	+	0.261601i	$0.915750\pi$
$102$	−4.01954	−	4.82216i	−0.397994	−	0.477465i
$103$	15.0777	−	10.0746i	1.48565	−	0.992681i	0.493218	−	0.869906i	$-0.335820\pi$
$103$	15.0777	−	10.0746i	1.48565	−	0.992681i	0.992434	−	0.122776i	$-0.0391796\pi$
$104$	−9.81653	−	4.96095i	−0.962590	−	0.486461i
$105$	−0.329335	+	0.492884i	−0.0321398	+	0.0481006i
$106$	7.81852	−	9.67686i	0.759402	−	0.939900i
$107$	2.03847	+	2.48388i	0.197066	+	0.240126i	0.862163	−	0.506631i	$-0.169110\pi$
$107$	2.03847	+	2.48388i	0.197066	+	0.240126i	−0.665096	+	0.746758i	$0.731610\pi$
$108$	11.0373	+	0.916877i	1.06207	+	0.0882265i
$109$	−0.152700	−	0.285682i	−0.0146260	−	0.0273633i	0.874502	−	0.485022i	$-0.161188\pi$
$109$	−0.152700	−	0.285682i	−0.0146260	−	0.0273633i	−0.889128	+	0.457658i	$0.848688\pi$
$110$	−0.432742	+	1.06775i	−0.0412603	+	0.101806i
$111$	0.976040	+	2.35637i	0.0926417	+	0.223657i
$112$	3.25636	−	2.32296i	0.307697	−	0.219499i
$113$	4.03133	−	9.73249i	0.379236	−	0.915556i	−0.612874	−	0.790181i	$-0.709987\pi$
$113$	4.03133	−	9.73249i	0.379236	−	0.915556i	0.992109	−	0.125375i	$-0.0400134\pi$
$114$	7.05912	+	6.95197i	0.661147	+	0.651112i
$115$	−1.81227	−	0.549747i	−0.168995	−	0.0512642i
$116$	−2.25767	−	4.07273i	−0.209620	−	0.378144i
$117$	−0.193557	+	1.96522i	−0.0178944	+	0.181685i
$118$	3.84780	−	13.0427i	0.354218	−	1.20068i
$119$	0.548572	+	2.75786i	0.0502875	+	0.252812i
$120$	0.899275	−	1.41509i	0.0820922	−	0.129179i
$121$	6.17210	+	1.22771i	0.561100	+	0.111610i
$122$	−3.81044	−	12.2240i	−0.344981	−	1.10671i
$123$	−0.742922	−	2.44909i	−0.0669870	−	0.220827i
$124$	3.09268	−	7.80178i	0.277730	−	0.700620i
$125$	2.86172	+	2.34855i	0.255960	+	0.210061i
$126$	−0.600159	−	0.394409i	−0.0534664	−	0.0351367i
$127$	5.72030			0.507595			0.253797	−	0.967257i	$-0.418320\pi$
$127$	5.72030			0.507595			0.253797	+	0.967257i	$0.418320\pi$
$128$	−9.05722	+	6.77988i	−0.800553	+	0.599262i
$129$	−1.49782			−0.131875
$130$	1.72573	+	1.13411i	0.151357	+	0.0994677i
$131$	8.61128	+	7.06710i	0.752371	+	0.617455i	0.930390	−	0.366572i	$-0.119469\pi$
$131$	8.61128	+	7.06710i	0.752371	+	0.617455i	−0.178019	+	0.984027i	$0.556969\pi$
$132$	6.36794	+	2.52429i	0.554258	+	0.219712i
$133$	−1.28822	−	4.24668i	−0.111702	−	0.368234i
$134$	−5.75783	−	18.4713i	−0.497401	−	1.59568i
$135$	−2.03943	−	0.405668i	−0.175526	−	0.0349144i
$136$	−1.73012	−	7.76275i	−0.148357	−	0.665650i
$137$	2.02466	+	10.1786i	0.172978	+	0.869620i	0.965625	+	0.259939i	$0.0837024\pi$
$137$	2.02466	+	10.1786i	0.172978	+	0.869620i	−0.792647	+	0.609681i	$0.791298\pi$
$138$	−3.18609	+	10.7998i	−0.271218	+	0.919337i
$139$	−1.19382	+	12.1211i	−0.101259	+	1.02810i	0.801514	+	0.597977i	$0.204028\pi$
$139$	−1.19382	+	12.1211i	−0.101259	+	1.02810i	−0.902772	+	0.430119i	$0.858472\pi$
$140$	−0.656829	+	0.364106i	−0.0555122	+	0.0307726i
$141$	15.6683	+	4.75292i	1.31951	+	0.400268i
$142$	−8.48118	−	8.35245i	−0.711725	−	0.700922i
$143$	−3.22860	+	7.79453i	−0.269989	+	0.651812i
$144$	1.72265	+	1.07632i	0.143554	+	0.0896935i
$145$	0.334573	+	0.807730i	0.0277847	+	0.0670783i
$146$	−1.34104	+	3.30889i	−0.110985	+	0.273846i
$147$	−0.744178	−	1.39226i	−0.0613788	−	0.114832i
$148$	−0.267499	+	3.22014i	−0.0219883	+	0.264694i
$149$	−11.4626	−	13.9672i	−0.939053	−	1.14424i	−0.989358	−	0.145505i	$-0.953519\pi$
$149$	−11.4626	−	13.9672i	−0.939053	−	1.14424i	0.0503050	−	0.998734i	$-0.483981\pi$
$150$	6.81761	−	8.43805i	0.556656	−	0.688964i
$151$	8.36740	−	12.5227i	0.680929	−	1.01908i	−0.316581	−	0.948565i	$-0.602535\pi$
$151$	8.36740	−	12.5227i	0.680929	−	1.01908i	0.997511	−	0.0705171i	$-0.0224649\pi$
$152$	3.91820	+	11.9247i	0.317808	+	0.967219i
$153$	−1.18727	+	0.793306i	−0.0959848	+	0.0641350i
$154$	−1.96454	−	2.35681i	−0.158307	−	0.189917i
$155$	−0.742765	+	1.38961i	−0.0596603	+	0.111617i
$156$	6.66430	−	10.3118i	0.533571	−	0.825606i
$157$	−2.34822	+	0.231279i	−0.187408	+	0.0184581i	−0.191286	−	0.981534i	$-0.561266\pi$
$157$	−2.34822	+	0.231279i	−0.187408	+	0.0184581i	0.00387752	+	0.999992i	$0.498766\pi$
$158$	19.9913	−	13.5800i	1.59042	−	1.08037i
$159$	9.81985	+	9.81985i	0.778765	+	0.778765i
$160$	1.83368	−	1.07219i	0.144965	−	0.0847643i
$161$	3.56628	−	3.56628i	0.281062	−	0.281062i
$162$	−1.91500	+	10.0275i	−0.150457	+	0.787838i
$163$	−2.18117	−	22.1458i	−0.170843	−	1.73459i	−0.573467	−	0.819229i	$-0.694402\pi$
$163$	−2.18117	−	22.1458i	−0.170843	−	1.73459i	0.402624	−	0.915365i	$-0.368098\pi$
$164$	0.583841	−	3.18934i	0.0455903	−	0.249046i
$165$	−1.13423	−	0.606257i	−0.0882995	−	0.0471970i
$166$	0.103036	−	1.13506i	0.00799715	−	0.0880979i
$167$	2.14211	+	3.20589i	0.165761	+	0.248080i	0.905046	−	0.425314i	$-0.139836\pi$
$167$	2.14211	+	3.20589i	0.165761	+	0.248080i	−0.739285	+	0.673393i	$0.764836\pi$
$168$	2.19463	+	3.88858i	0.169320	+	0.300011i
$169$	1.76430	+	1.17887i	0.135715	+	0.0906822i
$170$	0.157720	+	1.48486i	0.0120966	+	0.113883i
$171$	1.74202	−	1.42964i	0.133216	−	0.109327i
$172$	−1.68699	−	0.868810i	−0.128632	−	0.0662461i
$173$	−8.31473	+	4.44432i	−0.632157	+	0.337895i	−0.756160	−	0.654387i	$-0.772927\pi$
$173$	−8.31473	+	4.44432i	−0.632157	+	0.337895i	0.124003	+	0.992282i	$0.460427\pi$
$174$	4.78710	−	2.02591i	0.362909	−	0.153584i
$175$	−4.48913	+	1.85946i	−0.339346	+	0.140562i
$176$	5.70801	+	6.53685i	0.430257	+	0.492734i
$177$	14.0243	+	5.80904i	1.05413	+	0.436634i
$178$	−16.2671	+	0.124400i	−1.21927	+	0.00932417i
$179$	2.07963	−	6.85561i	0.155439	−	0.512413i	−0.844286	−	0.535893i	$-0.819975\pi$
$179$	2.07963	−	6.85561i	0.155439	−	0.512413i	0.999724	+	0.0234809i	$0.00747488\pi$
$180$	−0.298466	−	0.237400i	−0.0222464	−	0.0176947i
$181$	2.02079	+	0.199031i	0.150204	+	0.0147938i	0.172840	−	0.984950i	$-0.444706\pi$
$181$	2.02079	+	0.199031i	0.150204	+	0.0147938i	−0.0226354	+	0.999744i	$0.507206\pi$
$182$	−4.83010	+	2.62943i	−0.358031	+	0.194906i
$183$	14.0185	−	2.78845i	1.03628	−	0.206128i
$184$	−9.85292	+	10.3157i	−0.726367	+	0.760483i
$185$	0.118354	−	0.595005i	0.00870154	−	0.0437456i
$186$	8.29564	+	4.35288i	0.608266	+	0.319169i
$187$	−5.83786	+	1.77090i	−0.426907	+	0.129501i
$188$	14.8903	+	14.4416i	1.08598	+	1.05326i
$189$	3.51306	−	4.28067i	0.255537	−	0.311373i
$190$	−0.477414	−	2.30775i	−0.0346352	−	0.167421i
$191$			13.3492i			0.965914i	0.875644	+	0.482957i	$0.160437\pi$
$191$			13.3492i			0.965914i	−0.875644	+	0.482957i	$0.839563\pi$
$192$	−6.45803	−	10.8533i	−0.466068	−	0.783268i
$193$		−	0.0378643i		−	0.00272553i	−0.999999	−	0.00136276i	$-0.999566\pi$
$193$		−	0.0378643i		−	0.00272553i	0.999999	−	0.00136276i	$-0.000433782\pi$
$194$	11.4603	−	2.37085i	0.822804	−	0.170217i
$195$	−1.46238	+	1.78192i	−0.104723	+	0.127606i
$196$	−0.0305876	−	1.99977i	−0.00218483	−	0.142840i
$197$	−4.63003	+	1.40450i	−0.329876	+	0.100067i	−0.450878	−	0.892585i	$-0.648889\pi$
$197$	−4.63003	+	1.40450i	−0.329876	+	0.100067i	0.121002	+	0.992652i	$0.461389\pi$
$198$	0.723946	−	1.37968i	0.0514486	−	0.0980499i
$199$	−0.119532	+	0.600929i	−0.00847341	+	0.0425987i	−0.984791	−	0.173745i	$-0.944413\pi$
$199$	−0.119532	+	0.600929i	−0.00847341	+	0.0425987i	0.976317	+	0.216344i	$0.0694132\pi$
$200$	12.5732	−	5.54923i	0.889059	−	0.392390i
$201$	21.1828	−	4.21353i	1.49412	−	0.297199i
$202$	−9.31919	−	17.1188i	−0.655696	−	1.20447i
$203$	−2.31711	−	0.228215i	−0.162629	−	0.0160176i
$204$	8.82096	−	1.00523i	0.617591	−	0.0703798i
$205$	−0.176710	+	0.582535i	−0.0123420	+	0.0406860i
$206$	0.196111	+	25.6444i	0.0136637	+	1.78673i
$207$	2.36619	+	0.980109i	0.164462	+	0.0681223i
$208$	13.4874	−	7.74859i	0.935183	−	0.537268i
$209$	8.89511	−	3.68447i	0.615288	−	0.254860i
$210$	−0.326727	−	0.772038i	−0.0225463	−	0.0532757i
$211$	1.09643	−	0.586053i	0.0754812	−	0.0403455i	−0.433224	−	0.901286i	$-0.642624\pi$
$211$	1.09643	−	0.586053i	0.0754812	−	0.0403455i	0.508705	+	0.860941i	$0.330124\pi$
$212$	5.36410	+	16.7561i	0.368408	+	1.15082i
$213$	10.2716	−	8.42964i	0.703795	−	0.577590i
$214$	−4.51882	+	0.479983i	−0.308900	+	0.0328110i
$215$	0.296226	+	0.197932i	0.0202024	+	0.0134988i
$216$	−9.65607	+	12.3323i	−0.657012	+	0.839108i
$217$	−2.33128	−	3.48901i	−0.158258	−	0.236850i
$218$	0.456232	+	0.0414147i	0.0308999	+	0.00280496i
$219$	−3.51489	−	1.87875i	−0.237514	−	0.126954i
$220$	−0.925822	−	1.34074i	−0.0624189	−	0.0903926i
$221$	1.07177	+	10.8819i	0.0720953	+	0.731995i
$222$	−3.54295	−	0.676612i	−0.237787	−	0.0454113i
$223$	−20.4155	+	20.4155i	−1.36712	+	1.36712i	−0.502608	+	0.864515i	$0.667626\pi$
$223$	−20.4155	+	20.4155i	−1.36712	+	1.36712i	−0.864515	+	0.502608i	$0.832374\pi$
$224$	0.216243	+	5.65272i	0.0144483	+	0.377688i
$225$	−1.74476	−	1.74476i	−0.116318	−	0.116318i
$226$	8.37129	+	12.3235i	0.556850	+	0.819744i
$227$	−23.9365	+	2.35754i	−1.58872	+	0.156476i	−0.853406	−	0.521247i	$-0.825467\pi$
$227$	−23.9365	+	2.35754i	−1.58872	+	0.156476i	−0.735318	+	0.677722i	$0.762967\pi$
$228$	−13.6989	+	2.94336i	−0.907229	+	0.194929i
$229$	1.98686	−	3.71715i	0.131295	−	0.245636i	−0.807680	−	0.589621i	$-0.799277\pi$
$229$	1.98686	−	3.71715i	0.131295	−	0.245636i	0.938975	+	0.343985i	$0.111777\pi$
$230$	2.05727	−	1.71486i	0.135653	−	0.113074i
$231$	2.84779	−	1.90283i	0.187371	−	0.125197i
$232$	6.56685	+	0.494979i	0.431135	+	0.0324970i
$233$	12.0295	−	18.0035i	0.788080	−	1.17945i	−0.192107	−	0.981374i	$-0.561532\pi$
$233$	12.0295	−	18.0035i	0.788080	−	1.17945i	0.980188	−	0.198071i	$-0.0634678\pi$
$234$	−2.17226	−	1.75510i	−0.142005	−	0.114735i
$235$	−2.47066	−	3.01051i	−0.161168	−	0.196384i
$236$	12.4260	+	14.6775i	0.808865	+	0.955426i
$237$	12.7173	+	23.7923i	0.826075	+	1.54548i
$238$	−3.68543	−	1.49364i	−0.238891	−	0.0968184i
$239$	5.55853	+	13.4195i	0.359552	+	0.868034i	0.995363	+	0.0961898i	$0.0306656\pi$
$239$	5.55853	+	13.4195i	0.359552	+	0.868034i	−0.635812	+	0.771844i	$0.719334\pi$
$240$	0.973974	+	2.16188i	0.0628697	+	0.139549i
$241$	4.59738	−	11.0991i	0.296143	−	0.714953i	−0.703846	−	0.710352i	$-0.748536\pi$
$241$	4.59738	−	11.0991i	0.296143	−	0.714953i	0.999989	−	0.00460062i	$-0.00146443\pi$
$242$	−6.24471	+	6.34095i	−0.401425	+	0.407612i
$243$	4.99246	+	1.51445i	0.320266	+	0.0971518i
$244$	17.4065	+	4.99080i	1.11434	+	0.319503i
$245$	−0.0368053	+	0.373691i	−0.00235141	+	0.0238742i
$246$	3.47146	+	1.02413i	0.221332	+	0.0652964i
$247$	−3.36669	−	16.9255i	−0.214218	−	1.07694i
$248$	6.81851	+	9.71456i	0.432976	+	0.616875i
$249$	1.24782	+	0.248206i	0.0790772	+	0.0157294i
$250$	−4.99827	+	1.55805i	−0.316118	+	0.0985396i
$251$	−0.676886	−	2.23140i	−0.0427247	−	0.140844i	0.932983	−	0.359920i	$-0.117196\pi$
$251$	−0.676886	−	2.23140i	−0.0427247	−	0.140844i	−0.975708	+	0.219075i	$0.929696\pi$
$252$	0.932263	−	0.402969i	0.0587271	−	0.0253846i
$253$	8.45838	+	6.94161i	0.531774	+	0.436416i
$254$	−4.44284	+	6.76054i	−0.278769	+	0.424194i
$255$	−1.66685			−0.104382
$256$	−0.978231	−	15.9701i	−0.0611394	−	0.998129i
$257$	−21.2317			−1.32440			−0.662200	−	0.749327i	$-0.730377\pi$
$257$	−21.2317			−1.32440			−0.662200	+	0.749327i	$0.730377\pi$
$258$	1.16332	−	1.77019i	0.0724254	−	0.110207i
$259$	1.24889	+	1.02494i	0.0776021	+	0.0636864i
$260$	−2.68069	+	1.15872i	−0.166249	+	0.0718608i
$261$	−0.343218	−	1.13144i	−0.0212447	−	0.0700344i
$262$	−15.0405	+	4.68837i	−0.929202	+	0.289648i
$263$	7.82089	+	1.55567i	0.482257	+	0.0959269i	0.430231	−	0.902719i	$-0.358432\pi$
$263$	7.82089	+	1.55567i	0.482257	+	0.0959269i	0.0520260	+	0.998646i	$0.483432\pi$
$264$	−7.92919	+	5.56538i	−0.488008	+	0.342526i
$265$	−0.644427	−	3.23976i	−0.0395869	−	0.199017i
$266$	6.01947	+	1.77583i	0.369077	+	0.108883i
$267$	1.77992	−	18.0718i	0.108929	−	1.10598i
$268$	26.3023	+	7.54142i	1.60667	+	0.460666i
$269$	2.96156	+	0.898379i	0.180570	+	0.0547752i	0.379275	−	0.925284i	$-0.376174\pi$
$269$	2.96156	+	0.898379i	0.180570	+	0.0547752i	−0.198705	+	0.980059i	$0.563674\pi$
$270$	2.06342	−	2.09523i	0.125576	−	0.127511i
$271$	7.71986	−	18.6374i	0.468948	−	1.13214i	−0.495675	−	0.868508i	$-0.665079\pi$
$271$	7.71986	−	18.6374i	0.468948	−	1.13214i	0.964623	−	0.263632i	$-0.0849206\pi$
$272$	10.5182	+	3.98442i	0.637757	+	0.241591i
$273$	−2.34927	−	5.67164i	−0.142184	−	0.343263i
$274$	−13.6021	−	5.51270i	−0.821735	−	0.333035i
$275$	−4.96941	−	9.29712i	−0.299667	−	0.560637i
$276$	−10.2891	−	12.1534i	−0.619332	−	0.731551i
$277$	14.0152	+	17.0776i	0.842095	+	1.02610i	0.999258	+	0.0385225i	$0.0122651\pi$
$277$	14.0152	+	17.0776i	0.842095	+	1.02610i	−0.157163	+	0.987573i	$0.550235\pi$
$278$	−13.3981	−	10.8251i	−0.803562	−	0.649247i
$279$	1.18386	−	1.77177i	0.0708757	−	0.106073i
$280$	0.0798276	−	1.05907i	0.00477061	−	0.0632913i
$281$	0.109008	−	0.0728367i	0.00650286	−	0.00434507i	−0.552315	−	0.833636i	$-0.686255\pi$
$281$	0.109008	−	0.0728367i	0.00650286	−	0.00434507i	0.558817	+	0.829291i	$0.311255\pi$
$282$	−17.7865	+	14.8260i	−1.05917	+	0.882878i
$283$	−11.4300	+	21.3841i	−0.679445	+	1.27115i	0.271693	+	0.962384i	$0.412417\pi$
$283$	−11.4300	+	21.3841i	−0.679445	+	1.27115i	−0.951137	+	0.308768i	$0.900083\pi$
$284$	16.4585	−	3.53630i	0.976632	−	0.209841i
$285$	2.61798	−	0.257849i	0.155076	−	0.0152736i
$286$	−6.70438	−	9.86958i	−0.396438	−	0.583600i
$287$	−1.14634	−	1.14634i	−0.0676664	−	0.0676664i
$288$	−2.61000	+	1.19996i	−0.153796	+	0.0707081i
$289$	6.42994	−	6.42994i	0.378232	−	0.378232i
$290$	−1.21447	−	0.231933i	−0.0713162	−	0.0136196i
$291$	1.28048	+	13.0010i	0.0750633	+	0.762131i
$292$	−2.86906	−	4.15485i	−0.167899	−	0.243144i
$293$	−23.5303	−	12.5772i	−1.37466	−	0.734770i	−0.391959	−	0.919983i	$-0.628203\pi$
$293$	−23.5303	−	12.5772i	−1.37466	−	0.734770i	−0.982698	+	0.185213i	$0.940703\pi$
$294$	2.22343	+	0.201833i	0.129673	+	0.0117712i
$295$	−2.00596	−	3.00213i	−0.116791	−	0.174791i
$296$	−3.59796	−	2.81716i	−0.209127	−	0.163744i
$297$	9.98952	+	6.67478i	0.579651	+	0.387310i
$298$	25.4099	−	2.69901i	1.47196	−	0.156349i
$299$	15.1607	−	12.4421i	0.876766	−	0.719543i
$300$	4.67740	+	14.6111i	0.270050	+	0.843570i
$301$	−0.836754	+	0.447255i	−0.0482297	+	0.0257793i
$302$	8.30115	+	19.6151i	0.477678	+	1.12872i
$303$	20.1014	−	8.32625i	1.15479	−	0.478331i
$304$	−17.1364	−	4.63093i	−0.982838	−	0.265602i
$305$	−3.14094	−	1.30102i	−0.179850	−	0.0744963i
$306$	−0.0154424	−	2.01932i	−0.000882784	−	0.115437i
$307$	1.78742	−	5.89232i	0.102013	−	0.336293i	−0.891045	−	0.453915i	$-0.850027\pi$
$307$	1.78742	−	5.89232i	0.102013	−	0.336293i	0.993058	+	0.117622i	$0.0375271\pi$
$308$	4.31121	−	0.491300i	0.245654	−	0.0279944i
$309$	−28.4894	−	2.80596i	−1.62071	−	0.159626i
$310$	−1.06543	−	1.95712i	−0.0605121	−	0.111157i
$311$	−8.83008	+	1.75641i	−0.500708	+	0.0995969i	−0.438981	−	0.898496i	$-0.644661\pi$
$311$	−8.83008	+	1.75641i	−0.500708	+	0.0995969i	−0.0617263	+	0.998093i	$0.519661\pi$
$312$	7.01099	+	15.8852i	0.396919	+	0.899321i
$313$	−1.03352	+	5.19586i	−0.0584180	+	0.293687i	−0.998939	−	0.0460477i	$-0.985337\pi$
$313$	−1.03352	+	5.19586i	−0.0584180	+	0.293687i	0.940521	+	0.339735i	$0.110337\pi$
$314$	1.55048	−	2.95487i	0.0874985	−	0.166753i
$315$	−0.182473	+	0.0553525i	−0.0102812	+	0.00311876i
$316$	0.522712	+	34.1740i	0.0294048	+	1.92244i
$317$	−8.53377	+	10.3984i	−0.479304	+	0.584034i	−0.955383	−	0.295369i	$-0.904558\pi$
$317$	−8.53377	+	10.3984i	−0.479304	+	0.584034i	0.476079	+	0.879402i	$0.342058\pi$
$318$	−19.2325	+	3.97871i	−1.07850	+	0.223115i
$319$		−	5.05142i		−	0.282825i
$320$	−0.157012	+	2.99988i	−0.00877723	+	0.167699i
$321$		−	5.07266i		−	0.283129i
$322$	1.44495	+	6.98466i	0.0805238	+	0.389240i
$323$	7.91627	−	9.64600i	0.440473	−	0.536718i
$324$	−10.3637	−	10.0514i	−0.575761	−	0.558413i
$325$	−18.0815	+	5.48497i	−1.00298	+	0.304251i
$326$	27.8671	+	14.6224i	1.54342	+	0.809859i
$327$	−0.0997651	+	0.501553i	−0.00551702	+	0.0277359i
$328$	3.31587	+	3.16711i	0.183088	+	0.174874i
$329$	10.1723	−	2.02340i	0.560818	−	0.111554i
$330$	1.59744	−	0.869618i	0.0879360	−	0.0478709i
$331$	−20.0891	−	1.97861i	−1.10420	−	0.108754i	−0.470549	−	0.882374i	$-0.655944\pi$
$331$	−20.0891	−	1.97861i	−1.10420	−	0.108754i	−0.633650	+	0.773620i	$0.718444\pi$
$332$	1.26145	+	1.00335i	0.0692309	+	0.0550661i
$333$	−0.238159	+	0.785104i	−0.0130510	+	0.0430234i
$334$	−5.45262	+	0.0416981i	−0.298354	+	0.00228162i
$335$	−4.74617	−	1.96593i	−0.259311	−	0.107410i
$336$	−6.30025	−	0.426458i	−0.343707	−	0.0232652i
$337$	10.2697	−	4.25386i	0.559427	−	0.231722i	−0.0850094	−	0.996380i	$-0.527092\pi$
$337$	10.2697	−	4.25386i	0.559427	−	0.231722i	0.644436	+	0.764658i	$0.277092\pi$
$338$	−2.76354	+	1.16954i	−0.150317	+	0.0636143i
$339$	−14.6666	+	7.83945i	−0.796579	+	0.425780i
$340$	−1.87738	−	0.966858i	−0.101815	−	0.0524352i
$341$	7.03741	−	5.77546i	0.381097	−	0.312758i
$342$	0.336627	+	3.16918i	0.0182027	+	0.171370i
$343$	−0.831470	−	0.555570i	−0.0448951	−	0.0299980i
$344$	2.33706	−	1.31898i	0.126006	−	0.0711149i
$345$	1.66099	+	2.48585i	0.0894249	+	0.133834i
$346$	1.20537	−	13.2786i	0.0648012	−	0.713860i
$347$	−9.67254	−	5.17008i	−0.519249	−	0.277545i	0.190883	−	0.981613i	$-0.438865\pi$
$347$	−9.67254	−	5.17008i	−0.519249	−	0.277545i	−0.710132	+	0.704068i	$0.751365\pi$
$348$	−1.32373	+	7.23111i	−0.0709591	+	0.387628i
$349$	−1.93502	−	19.6466i	−0.103579	−	1.05166i	−0.896714	−	0.442610i	$-0.854053\pi$
$349$	−1.93502	−	19.6466i	−0.103579	−	1.05166i	0.793135	−	0.609046i	$-0.208447\pi$
$350$	1.28902	−	6.74968i	0.0689009	−	0.360786i
$351$	15.2270	−	15.2270i	0.812758	−	0.812758i
$352$	−12.1589	+	1.66897i	−0.648070	+	0.0889562i
$353$	−7.08760	−	7.08760i	−0.377235	−	0.377235i	0.492869	−	0.870104i	$-0.335948\pi$
$353$	−7.08760	−	7.08760i	−0.377235	−	0.377235i	−0.870104	+	0.492869i	$0.835948\pi$
$354$	−17.7578	+	12.0628i	−0.943815	+	0.641131i
$355$	−3.14538	+	0.309793i	−0.166939	+	0.0164421i
$356$	12.4873	−	19.3219i	0.661825	−	1.02406i
$357$	2.09254	−	3.91487i	0.110749	−	0.207197i
$358$	6.48710	+	7.78242i	0.342854	+	0.411314i
$359$	19.3248	−	12.9124i	1.01992	−	0.681492i	0.0711562	−	0.997465i	$-0.477331\pi$
$359$	19.3248	−	12.9124i	1.01992	−	0.681492i	0.948768	+	0.315974i	$0.102331\pi$
$360$	0.512383	−	0.168359i	0.0270050	−	0.00887328i
$361$	−0.385438	+	0.576849i	−0.0202862	+	0.0303605i
$362$	−1.80473	+	2.23369i	−0.0948547	+	0.117400i
$363$	−6.30242	−	7.67952i	−0.330791	−	0.403070i
$364$	0.643854	−	7.75068i	0.0337471	−	0.406246i
$365$	0.446875	+	0.836045i	0.0233905	+	0.0437606i
$366$	−7.59234	+	18.7335i	−0.396858	+	0.979213i
$367$	4.31547	+	10.4185i	0.225266	+	0.543840i	0.995590	−	0.0938127i	$-0.0299055\pi$
$367$	4.31547	+	10.4185i	0.225266	+	0.543840i	−0.770324	+	0.637653i	$0.779905\pi$
$368$	−4.53904	−	19.6567i	−0.236614	−	1.02467i
$369$	0.315045	−	0.760586i	0.0164006	−	0.0395945i
$370$	0.611283	+	0.602004i	0.0317791	+	0.0312967i
$371$	8.41811	+	2.55361i	0.437047	+	0.132577i
$372$	−11.5875	+	6.42341i	−0.600785	+	0.333038i
$373$	2.46064	−	24.9833i	0.127407	−	1.29359i	−0.692637	−	0.721287i	$-0.743551\pi$
$373$	2.46064	−	24.9833i	0.127407	−	1.29359i	0.820044	−	0.572301i	$-0.193949\pi$
$374$	2.44122	−	8.27489i	0.126232	−	0.427885i
$375$	−1.14016	−	5.73199i	−0.0588778	−	0.295999i
$376$	−28.6328	+	6.38154i	−1.47662	+	0.329103i
$377$	−8.88013	−	1.76637i	−0.457350	−	0.0909726i
$378$	2.33059	+	7.47662i	0.119873	+	0.384556i
$379$	−9.38208	−	30.9286i	−0.481925	−	1.58869i	−0.774580	−	0.632476i	$-0.782039\pi$
$379$	−9.38208	−	30.9286i	−0.481925	−	1.58869i	0.292654	−	0.956218i	$-0.405461\pi$
$380$	3.09821	+	1.22815i	0.158935	+	0.0630027i
$381$	−6.98063	−	5.72885i	−0.357628	−	0.293498i
$382$	−15.7767	−	10.3681i	−0.807209	−	0.530476i
$383$	−15.1817			−0.775748			−0.387874	−	0.921712i	$-0.626790\pi$
$383$	−15.1817			−0.775748			−0.387874	+	0.921712i	$0.626790\pi$
$384$	17.8428	+	0.797109i	0.910535	+	0.0406773i
$385$	−0.814667			−0.0415193
$386$	0.0447499	+	0.0294084i	0.00227771	+	0.00149685i
$387$	−0.372441	−	0.305655i	−0.0189323	−	0.0155373i
$388$	−6.09902	+	15.3858i	−0.309631	+	0.781094i
$389$	8.89276	+	29.3155i	0.450881	+	1.48635i	0.828286	+	0.560306i	$0.189316\pi$
$389$	8.89276	+	29.3155i	0.450881	+	1.48635i	−0.377405	+	0.926048i	$0.623184\pi$
$390$	−0.970155	−	3.11229i	−0.0491257	−	0.157597i
$391$	13.9092	+	2.76671i	0.703418	+	0.139919i
$392$	2.38718	+	1.51703i	0.120571	+	0.0766215i
$393$	−3.43090	−	17.2483i	−0.173066	−	0.870062i
$394$	1.93614	−	6.56285i	0.0975413	−	0.330632i
$395$	0.628966	−	6.38600i	0.0316467	−	0.321315i
$396$	1.06830	+	1.92717i	0.0536843	+	0.0968438i
$397$	0.740961	+	0.224768i	0.0371878	+	0.0112808i	0.308824	−	0.951119i	$-0.400065\pi$
$397$	0.740961	+	0.224768i	0.0371878	+	0.0112808i	−0.271636	+	0.962400i	$0.587565\pi$
$398$	−0.617369	−	0.607998i	−0.0309459	−	0.0304762i
$399$	−2.68098	+	6.47247i	−0.134217	+	0.324029i
$400$	−3.20699	+	19.1696i	−0.160350	+	0.958480i
$401$	−9.06254	−	21.8789i	−0.452562	−	1.09258i	−0.971345	−	0.237674i	$-0.923615\pi$
$401$	−9.06254	−	21.8789i	−0.452562	−	1.09258i	0.518783	−	0.854906i	$-0.326385\pi$
$402$	−11.4725	+	28.3075i	−0.572197	+	1.41185i
$403$	−7.69212	−	14.3909i	−0.383172	−	0.716864i
$404$	27.4699	+	2.28194i	1.36668	+	0.113531i
$405$	1.71959	+	2.09533i	0.0854472	+	0.104118i
$406$	2.06937	−	2.56122i	0.102701	−	0.127111i
$407$	−1.94737	+	2.91444i	−0.0965275	+	0.144464i
$408$	−5.66304	+	11.2058i	−0.280362	+	0.554769i
$409$	4.08780	−	2.73138i	0.202129	−	0.135058i	−0.450387	−	0.892834i	$-0.648714\pi$
$409$	4.08780	−	2.73138i	0.202129	−	0.135058i	0.652515	+	0.757776i	$0.273714\pi$
$410$	−0.551222	−	0.661288i	−0.0272229	−	0.0326587i
$411$	7.72312	−	14.4489i	0.380953	−	0.712713i
$412$	−30.4601	−	19.6857i	−1.50066	−	0.969844i
$413$	9.56926	−	0.942490i	0.470872	−	0.0463769i
$414$	−2.99612	+	2.03525i	−0.147251	+	0.100027i
$415$	−0.213983	−	0.213983i	−0.0105040	−	0.0105040i
$416$	−1.31773	+	21.9582i	−0.0646070	+	1.07659i
$417$	13.5960	−	13.5960i	0.665801	−	0.665801i
$418$	−2.55416	+	13.3743i	−0.124928	+	0.654160i
$419$	−0.792445	−	8.04583i	−0.0387135	−	0.393064i	−0.994943	−	0.100445i	$-0.967973\pi$
$419$	−0.792445	−	8.04583i	−0.0387135	−	0.393064i	0.956229	−	0.292619i	$-0.0945268\pi$
$420$	1.16620	+	0.213483i	0.0569045	+	0.0104169i
$421$	18.5078	+	9.89261i	0.902014	+	0.482136i	0.856101	−	0.516809i	$-0.172880\pi$
$421$	18.5078	+	9.89261i	0.902014	+	0.482136i	0.0459129	+	0.998945i	$0.485380\pi$
$422$	−0.158947	+	1.75099i	−0.00773742	+	0.0852367i
$423$	2.92610	+	4.37922i	0.142272	+	0.212925i
$424$	−23.9694	−	6.67460i	−1.16406	−	0.324147i
$425$	−11.3603	−	7.59073i	−0.551057	−	0.368204i
$426$	1.98486	+	18.6866i	0.0961670	+	0.905367i
$427$	6.99877	−	5.74374i	0.338694	−	0.277959i
$428$	2.94241	−	5.71335i	0.142227	−	0.276165i
$429$	11.7461	−	6.27844i	0.567109	−	0.303126i
$430$	−0.463998	+	0.196365i	−0.0223760	+	0.00946955i
$431$	−34.8726	+	14.4447i	−1.67975	+	0.695777i	−0.999314	−	0.0370267i	$-0.988211\pi$
$431$	−34.8726	+	14.4447i	−1.67975	+	0.695777i	−0.680440	+	0.732804i	$0.738211\pi$
$432$	−7.07528	−	20.9903i	−0.340409	−	1.00990i
$433$	2.66283	+	1.10298i	0.127967	+	0.0530059i	0.445748	−	0.895158i	$-0.352938\pi$
$433$	2.66283	+	1.10298i	0.127967	+	0.0530059i	−0.317781	+	0.948164i	$0.602938\pi$
$434$	5.93415	−	0.0453805i	0.284848	−	0.00217833i
$435$	0.400650	−	1.32077i	0.0192097	−	0.0633259i
$436$	−0.403292	+	0.507031i	−0.0193142	+	0.0242824i
$437$	−22.2740	−	2.19380i	−1.06551	−	0.104944i
$438$	4.95034	−	2.69488i	0.236536	−	0.128767i
$439$	18.2657	−	3.63328i	0.871775	−	0.173407i	0.261123	−	0.965306i	$-0.415907\pi$
$439$	18.2657	−	3.63328i	0.871775	−	0.173407i	0.610653	+	0.791899i	$0.290907\pi$
$440$	2.30362	−	0.0528580i	0.109821	−	0.00251990i
$441$	0.0990695	−	0.498056i	0.00471760	−	0.0237170i
$442$	−13.6932	−	7.18507i	−0.651318	−	0.341759i
$443$	−16.5504	+	5.02049i	−0.786331	+	0.238531i	−0.657818	−	0.753177i	$-0.728520\pi$
$443$	−16.5504	+	5.02049i	−0.786331	+	0.238531i	−0.128513	+	0.991708i	$0.541020\pi$
$444$	3.55139	−	3.66172i	0.168541	−	0.173777i
$445$	−2.74015	+	3.33888i	−0.129896	+	0.158278i
$446$	−8.27174	−	39.9843i	−0.391678	−	1.89331i
$447$			28.5243i			1.34915i
$448$	−6.84862	−	4.13479i	−0.323567	−	0.195350i
$449$		−	23.0875i		−	1.08957i	−0.838577	−	0.544784i	$-0.816612\pi$
$449$		−	23.0875i		−	1.08957i	0.838577	−	0.544784i	$-0.183388\pi$
$450$	3.41717	−	0.706925i	0.161087	−	0.0333248i
$451$	2.23130	−	2.71885i	0.105068	−	0.128026i
$452$	−21.0663	+	0.322221i	−0.990874	+	0.0151560i
$453$	−22.7524	+	6.90185i	−1.06900	+	0.324277i
$454$	15.8048	−	30.1204i	0.741755	−	1.41362i
$455$	−0.284871	+	1.43214i	−0.0133549	+	0.0671398i
$456$	7.16102	−	18.4760i	0.335346	−	0.865220i
$457$	−37.7554	+	7.51002i	−1.76612	+	0.351304i	−0.967954	−	0.251128i	$-0.919198\pi$
$457$	−37.7554	+	7.51002i	−1.76612	+	0.351304i	−0.798170	+	0.602432i	$0.794198\pi$
$458$	2.84996	+	5.23520i	0.133170	+	0.244625i
$459$	15.4963	+	1.52625i	0.723305	+	0.0712394i
$460$	0.428859	+	3.76328i	0.0199956	+	0.175464i
$461$	−8.51908	+	28.0837i	−0.396773	+	1.30799i	0.500203	+	0.865908i	$0.333259\pi$
$461$	−8.51908	+	28.0837i	−0.396773	+	1.30799i	−0.896977	+	0.442078i	$0.854241\pi$
$462$	0.0370403	+	4.84355i	0.00172327	+	0.225342i
$463$	−3.53101	−	1.46259i	−0.164100	−	0.0679725i	0.299121	−	0.954215i	$-0.403306\pi$
$463$	−3.53101	−	1.46259i	−0.164100	−	0.0679725i	−0.463221	+	0.886243i	$0.653306\pi$
$464$	−5.68533	+	7.37659i	−0.263935	+	0.342449i
$465$	2.29811	−	0.951907i	0.106572	−	0.0441436i
$466$	11.9343	+	28.2000i	0.552845	+	1.30634i
$467$	7.87338	−	4.20841i	0.364337	−	0.194742i	−0.279062	−	0.960273i	$-0.590024\pi$
$467$	7.87338	−	4.20841i	0.364337	−	0.194742i	0.643399	+	0.765531i	$0.277524\pi$
$468$	3.76142	−	1.20413i	0.173872	−	0.0556611i
$469$	10.5756	−	8.67917i	0.488336	−	0.400767i
$470$	5.47688	−	0.581747i	0.252629	−	0.0268340i
$471$	3.09722	+	2.06949i	0.142712	+	0.0953573i
$472$	−26.9977	+	3.28594i	−1.24267	+	0.151248i
$473$	−1.14361	−	1.71154i	−0.0525833	−	0.0786965i
$474$	−37.9962	−	3.44913i	−1.74522	−	0.158424i
$475$	19.0170	+	10.1648i	0.872558	+	0.466392i
$476$	4.62766	−	3.19555i	0.212109	−	0.146468i
$477$	0.437861	+	4.44568i	0.0200483	+	0.203554i
$478$	−20.1770	−	3.85329i	−0.922875	−	0.176246i
$479$	−6.87294	+	6.87294i	−0.314032	+	0.314032i	−0.846470	−	0.532437i	$-0.821276\pi$
$479$	−6.87294	+	6.87294i	−0.314032	+	0.314032i	0.532437	+	0.846470i	$0.321276\pi$
$480$	−3.31148	−	0.527997i	−0.151148	−	0.0240997i
$481$	4.44249	+	4.44249i	0.202560	+	0.202560i
$482$	9.54672	+	14.0538i	0.434841	+	0.640134i
$483$	−7.92363	+	0.780410i	−0.360538	+	0.0355099i
$484$	−2.64391	−	12.3052i	−0.120178	−	0.559327i
$485$	1.46480	−	2.74044i	0.0665129	−	0.124437i
$486$	−5.66739	+	4.72410i	−0.257078	+	0.214289i
$487$	−8.72754	+	5.83156i	−0.395483	+	0.264253i	−0.737372	−	0.675487i	$-0.763933\pi$
$487$	−8.72754	+	5.83156i	−0.395483	+	0.264253i	0.341889	+	0.939740i	$0.388933\pi$
$488$	−19.4176	+	16.6956i	−0.878995	+	0.755774i
$489$	−19.5172	+	29.2095i	−0.882598	+	1.32090i
$490$	−0.413060	−	0.333736i	−0.0186602	−	0.0150767i
$491$	−6.71917	−	8.18734i	−0.303232	−	0.369489i	0.598993	−	0.800754i	$-0.295568\pi$
$491$	−6.71917	−	8.18734i	−0.303232	−	0.369489i	−0.902226	+	0.431265i	$0.858068\pi$
$492$	−3.90659	+	3.30732i	−0.176123	+	0.149106i
$493$	−3.08622	−	5.77390i	−0.138996	−	0.260044i
$494$	22.6182	+	9.16678i	1.01764	+	0.412433i
$495$	−0.158316	−	0.382208i	−0.00711576	−	0.0171790i
$496$	−16.7769	+	0.513347i	−0.753307	+	0.0230499i
$497$	3.22107	−	7.77635i	0.144485	−	0.348817i
$498$	−1.26250	+	1.28195i	−0.0565738	+	0.0574458i
$499$	10.0410	+	3.04590i	0.449496	+	0.136353i	0.506913	−	0.861997i	$-0.330786\pi$
$499$	10.0410	+	3.04590i	0.449496	+	0.136353i	−0.0574169	+	0.998350i	$0.518286\pi$
$500$	2.04068	−	7.11731i	0.0912620	−	0.318296i
$501$	0.596616	−	6.05755i	0.0266548	−	0.270631i
$502$	3.16290	+	0.933102i	0.141167	+	0.0416464i
$503$	1.00939	+	5.07455i	0.0450065	+	0.226263i	0.996742	−	0.0806567i	$-0.0257017\pi$
$503$	1.00939	+	5.07455i	0.0450065	+	0.226263i	−0.951735	+	0.306920i	$0.900702\pi$
$504$	−0.247822	+	1.41477i	−0.0110389	+	0.0630190i
$505$	−5.07577	−	1.00963i	−0.225869	−	0.0449281i
$506$	−14.7734	+	4.60512i	−0.656758	+	0.204723i
$507$	−0.972390	−	3.20554i	−0.0431854	−	0.142363i
$508$	−4.53927	−	10.5015i	−0.201398	−	0.465931i
$509$	−24.6216	−	20.2064i	−1.09133	−	0.895634i	−0.0963170	−	0.995351i	$-0.530706\pi$
$509$	−24.6216	−	20.2064i	−1.09133	−	0.895634i	−0.995016	+	0.0997170i	$0.968206\pi$
$510$	1.29461	−	1.96996i	0.0573262	−	0.0872315i
$511$	−2.52459			−0.111681
$512$	19.6340	+	11.2475i	0.867708	+	0.497074i
$513$	−24.5749			−1.08501
$514$	16.4903	−	25.0927i	0.727354	−	1.10679i
$515$	5.26361	+	4.31973i	0.231942	+	0.190350i
$516$	1.18857	+	2.74975i	0.0523239	+	0.121051i
$517$	6.53193	+	21.5329i	0.287274	+	0.947015i
$518$	−2.18131	+	0.679950i	−0.0958410	+	0.0298753i
$519$	14.5976	+	2.90365i	0.640765	+	0.127456i
$520$	0.712602	−	4.06812i	0.0312497	−	0.178399i
$521$	2.84960	+	14.3259i	0.124843	+	0.627628i	0.991647	+	0.128980i	$0.0411702\pi$
$521$	2.84960	+	14.3259i	0.124843	+	0.627628i	−0.866804	+	0.498649i	$0.833830\pi$
$522$	1.60376	+	0.473134i	0.0701948	+	0.0207085i
$523$	4.11868	−	41.8177i	0.180097	−	1.82856i	−0.302998	−	0.952991i	$-0.597987\pi$
$523$	4.11868	−	41.8177i	0.180097	−	1.82856i	0.483095	−	0.875568i	$-0.339513\pi$
$524$	6.14067	−	21.4169i	0.268257	−	0.935602i
$525$	7.34044	+	2.22670i	0.320363	+	0.0971811i
$526$	−7.91290	+	8.03486i	−0.345019	+	0.350336i
$527$	4.51537	−	10.9011i	0.196693	−	0.474858i
$528$	−0.419002	−	13.6936i	−0.0182347	−	0.595939i
$529$	−0.932486	−	2.25122i	−0.0405429	−	0.0978791i
$530$	4.32942	+	1.75464i	0.188058	+	0.0762165i
$531$	2.30179	+	4.30634i	0.0998891	+	0.186879i
$532$	−6.77396	+	5.73485i	−0.293689	+	0.248637i
$533$	−3.99936	−	4.87324i	−0.173232	−	0.211083i
$534$	19.9757	+	16.1396i	0.864434	+	0.698428i
$535$	−0.670337	+	1.00323i	−0.0289812	+	0.0433734i
$536$	−29.3413	+	25.2281i	−1.26735	+	1.08969i
$537$	−9.40368	+	6.28334i	−0.405799	+	0.271146i
$538$	−3.36193	+	2.80237i	−0.144943	+	0.120819i
$539$	1.02272	−	1.91338i	0.0440518	−	0.0824151i
$540$	0.873623	+	4.06598i	0.0375947	+	0.174972i
$541$	20.5726	−	2.02622i	0.884483	−	0.0871140i	0.354434	−	0.935081i	$-0.384674\pi$
$541$	20.5726	−	2.02622i	0.884483	−	0.0871140i	0.530049	+	0.847967i	$0.322174\pi$
$542$	16.0307	+	23.5990i	0.688579	+	1.01366i
$543$	−2.26670	−	2.26670i	−0.0972733	−	0.0972733i
$544$	−12.8782	+	9.33625i	−0.552149	+	0.400288i
$545$	0.0860094	−	0.0860094i	0.00368424	−	0.00368424i
$546$	8.52766	+	1.62857i	0.364950	+	0.0696962i
$547$	1.21003	+	12.2856i	0.0517370	+	0.525295i	0.985769	+	0.168105i	$0.0537649\pi$
$547$	1.21003	+	12.2856i	0.0517370	+	0.525295i	−0.934032	+	0.357189i	$0.883735\pi$
$548$	17.0797	−	11.7941i	0.729608	−	0.503817i
$549$	4.05481	+	2.16734i	0.173055	+	0.0924999i
$550$	14.8474	+	1.34779i	0.633097	+	0.0574698i
$551$	5.74044	+	8.59118i	0.244551	+	0.365997i
$552$	22.3549	−	2.72086i	0.951487	−	0.115807i
$553$	14.2090	+	9.49415i	0.604228	+	0.403732i
$554$	−31.0685	+	3.30006i	−1.31998	+	0.140206i
$555$	−0.740324	+	0.607568i	−0.0314250	+	0.0257898i
$556$	23.1997	−	7.42685i	0.983884	−	0.314969i
$557$	1.61294	−	0.862136i	0.0683426	−	0.0365299i	−0.436871	−	0.899524i	$-0.643914\pi$
$557$	1.61294	−	0.862136i	0.0683426	−	0.0365299i	0.505214	+	0.862994i	$0.331414\pi$
$558$	1.17448	+	2.77524i	0.0497199	+	0.117485i
$559$	−3.40868	+	1.41192i	−0.144172	+	0.0597180i
$560$	1.18966	+	0.916900i	0.0502722	+	0.0387461i
$561$	8.89764	+	3.68552i	0.375658	+	0.155603i
$562$	0.00141783	+	0.185402i	5.98076e−5	+	0.00782070i
$563$	−11.2155	+	36.9726i	−0.472677	+	1.55821i	0.319298	+	0.947654i	$0.396553\pi$
$563$	−11.2155	+	36.9726i	−0.472677	+	1.55821i	−0.791975	+	0.610553i	$0.790947\pi$
$564$	−3.70776	−	32.5360i	−0.156125	−	1.37001i
$565$	3.93660	+	0.387721i	0.165614	+	0.0163115i
$566$	−16.3953	−	30.1172i	−0.689146	−	1.26592i
$567$	−7.07998	+	1.40830i	−0.297331	+	0.0591429i
$568$	−8.60361	+	22.1980i	−0.360999	+	0.931409i
$569$	−8.25085	+	41.4798i	−0.345894	+	1.73892i	0.280898	+	0.959738i	$0.409368\pi$
$569$	−8.25085	+	41.4798i	−0.345894	+	1.73892i	−0.626792	+	0.779187i	$0.715632\pi$
$570$	−1.72860	+	3.29433i	−0.0724029	+	0.137984i
$571$	−19.9365	+	6.04768i	−0.834318	+	0.253088i	−0.678409	−	0.734684i	$-0.737330\pi$
$571$	−19.9365	+	6.04768i	−0.834318	+	0.253088i	−0.155908	+	0.987772i	$0.549830\pi$
$572$	16.8715	−	0.258060i	0.705433	−	0.0107900i
$573$	13.3692	−	16.2904i	0.558505	−	0.680540i
$574$	2.24514	−	0.464462i	0.0937104	−	0.0193863i
$575$			24.5063i			1.02198i
$576$	0.608967	−	4.01661i	0.0253736	−	0.167359i
$577$		−	13.0051i		−	0.541408i	−0.962663	−	0.270704i	$-0.912744\pi$
$577$		−	13.0051i		−	0.541408i	0.962663	−	0.270704i	$-0.0872565\pi$
$578$	2.60521	+	12.5932i	0.108363	+	0.523809i
$579$	−0.0379209	+	0.0462067i	−0.00157594	+	0.00192029i
$580$	1.21736	−	1.25518i	0.0505483	−	0.0521187i
$581$	0.771208	−	0.233943i	0.0319951	−	0.00970560i
$582$	−16.3597	−	8.58426i	−0.678132	−	0.355829i
$583$	−3.72338	+	18.7187i	−0.154206	+	0.775248i
$584$	7.13875	−	0.163803i	0.295403	−	0.00677822i
$585$	−0.727261	+	0.144661i	−0.0300685	+	0.00598100i
$586$	33.1399	−	18.0408i	1.36900	−	0.745260i
$587$	25.3700	+	2.49872i	1.04713	+	0.103133i	0.606922	−	0.794762i	$-0.292404\pi$
$587$	25.3700	+	2.49872i	1.04713	+	0.103133i	0.440209	+	0.897895i	$0.354904\pi$
$588$	−1.96543	+	2.47100i	−0.0810529	+	0.101902i
$589$	−5.40561	+	17.8199i	−0.222734	+	0.734257i
$590$	5.10605	−	0.0390478i	0.210213	−	0.00160757i
$591$	7.05675	+	2.92300i	0.290276	+	0.120236i
$592$	6.12392	−	2.06421i	0.251692	−	0.0848386i
$593$	−17.8949	+	7.41231i	−0.734855	+	0.304387i	−0.718545	−	0.695480i	$-0.755192\pi$
$593$	−17.8949	+	7.41231i	−0.734855	+	0.304387i	−0.0163096	+	0.999867i	$0.505192\pi$
$594$	−15.6472	+	6.62194i	−0.642014	+	0.271701i
$595$	−0.931185	+	0.497729i	−0.0381749	+	0.0204049i
$596$	−16.5455	+	32.1270i	−0.677732	+	1.31597i
$597$	0.747695	−	0.613617i	0.0306011	−	0.0251137i
$598$	2.92964	+	27.5812i	0.119802	+	1.12788i
$599$	12.5212	+	8.36640i	0.511602	+	0.341842i	0.784426	−	0.620222i	$-0.212958\pi$
$599$	12.5212	+	8.36640i	0.511602	+	0.341842i	−0.272824	+	0.962064i	$0.587958\pi$
$600$	−20.9009	−	5.82013i	−0.853276	−	0.237606i
$601$	3.14551	+	4.70759i	0.128308	+	0.192027i	0.890062	−	0.455840i	$-0.150661\pi$
$601$	3.14551	+	4.70759i	0.128308	+	0.192027i	−0.761753	+	0.647867i	$0.775661\pi$
$602$	0.121303	−	1.33629i	0.00494393	−	0.0544632i
$603$	6.12708	+	3.27499i	0.249514	+	0.133368i
$604$	−29.6295	−	5.42397i	−1.20561	−	0.220698i
$605$	0.231616	+	2.35164i	0.00941654	+	0.0956078i
$606$	−5.77194	+	30.2236i	−0.234469	+	1.22775i
$607$	−0.612489	+	0.612489i	−0.0248602	+	0.0248602i	−0.719428	−	0.694567i	$-0.755596\pi$
$607$	−0.612489	+	0.612489i	−0.0248602	+	0.0248602i	0.694567	+	0.719428i	$0.255596\pi$
$608$	18.7825	−	16.6558i	0.761732	−	0.675484i
$609$	2.59907	+	2.59907i	0.105319	+	0.105319i
$610$	3.97712	−	2.70165i	0.161029	−	0.109386i
$611$	40.1377	−	3.95322i	1.62380	−	0.159930i
$612$	2.39852	+	1.55011i	0.0969545	+	0.0626595i
$613$	−14.8919	+	27.8608i	−0.601479	+	1.12529i	0.378390	+	0.925646i	$0.376478\pi$
$613$	−14.8919	+	27.8608i	−0.601479	+	1.12529i	−0.979869	+	0.199642i	$0.936022\pi$
$614$	5.57559	+	6.68891i	0.225012	+	0.269942i
$615$	0.799050	−	0.533908i	0.0322208	−	0.0215293i
$616$	−2.76779	+	5.47679i	−0.111517	+	0.220666i
$617$	13.3745	−	20.0164i	0.538439	−	0.805830i	−0.458105	−	0.888898i	$-0.651472\pi$
$617$	13.3745	−	20.0164i	0.538439	−	0.805830i	0.996544	+	0.0830677i	$0.0264718\pi$
$618$	25.4434	−	31.4909i	1.02348	−	1.26675i
$619$	−25.2529	−	30.7708i	−1.01500	−	1.23678i	−0.971330	−	0.237737i	$-0.923594\pi$
$619$	−25.2529	−	30.7708i	−1.01500	−	1.23678i	−0.0436718	−	0.999046i	$-0.513906\pi$
$620$	3.14052	+	0.260885i	0.126126	+	0.0104774i
$621$	−13.1657	−	24.6313i	−0.528321	−	0.988419i
$622$	4.78233	−	11.8000i	0.191754	−	0.473136i
$623$	−4.40197	−	10.6273i	−0.176361	−	0.425773i
$624$	−24.2192	−	4.05177i	−0.969543	−	0.162201i
$625$	8.76532	−	21.1614i	0.350613	−	0.846454i
$626$	−5.33801	−	5.25699i	−0.213350	−	0.210111i
$627$	−14.5449	−	4.41215i	−0.580868	−	0.176204i
$628$	2.28799	+	4.12742i	0.0913007	+	0.164702i
$629$	−0.445284	+	4.52105i	−0.0177547	+	0.180266i
$630$	0.0763045	−	0.258646i	0.00304005	−	0.0103047i
$631$	−0.509922	−	2.56355i	−0.0202997	−	0.102053i	0.969307	−	0.245853i	$-0.0790680\pi$
$631$	−0.509922	−	2.56355i	−0.0202997	−	0.102053i	−0.989607	+	0.143799i	$0.954068\pi$
$632$	−40.7945	−	25.9245i	−1.62272	−	1.03122i
$633$	−1.92493	−	0.382892i	−0.0765090	−	0.0152186i
$634$	−5.66137	−	18.1619i	−0.224842	−	0.721300i
$635$	0.623522	+	2.05548i	0.0247437	+	0.0815691i
$636$	10.2352	−	25.8201i	0.405854	−	1.02383i
$637$	−3.00600	−	2.46696i	−0.119102	−	0.0977445i
$638$	5.97002	+	3.92334i	0.236355	+	0.155326i
$639$	4.27430			0.169089
$640$	−3.42346	−	2.51551i	−0.135324	−	0.0994344i
$641$	−30.9318			−1.22173			−0.610867	−	0.791733i	$-0.709179\pi$
$641$	−30.9318			−1.22173			−0.610867	+	0.791733i	$0.709179\pi$
$642$	5.99513	+	3.93984i	0.236609	+	0.155493i
$643$	3.43894	+	2.82226i	0.135619	+	0.111299i	0.699757	−	0.714381i	$-0.253292\pi$
$643$	3.43894	+	2.82226i	0.135619	+	0.111299i	−0.564138	+	0.825680i	$0.690792\pi$
$644$	−9.37708	−	3.71714i	−0.369509	−	0.146476i
$645$	−0.163264	−	0.538210i	−0.00642852	−	0.0211920i
$646$	5.25172	+	16.8477i	0.206626	+	0.662864i
$647$	38.9643	+	7.75049i	1.53185	+	0.304703i	0.887781	−	0.460267i	$-0.152246\pi$
$647$	38.9643	+	7.75049i	1.53185	+	0.304703i	0.644066	+	0.764970i	$0.277246\pi$
$648$	19.9286	−	4.44158i	0.782868	−	0.174482i
$649$	4.06988	+	20.4607i	0.159757	+	0.803152i
$650$	7.56115	−	25.6297i	0.296573	−	1.00528i
$651$	−0.649305	+	6.59250i	−0.0254483	+	0.258380i
$652$	−38.9253	+	21.5778i	−1.52443	+	0.845052i
$653$	38.0459	+	11.5411i	1.48885	+	0.451638i	0.926828	−	0.375485i	$-0.122524\pi$
$653$	38.0459	+	11.5411i	1.48885	+	0.451638i	0.562021	+	0.827123i	$0.310024\pi$
$654$	−0.515274	−	0.507453i	−0.0201488	−	0.0198430i
$655$	−1.60078	+	3.86461i	−0.0625475	+	0.151003i
$656$	−6.31841	+	1.45902i	−0.246693	+	0.0569653i
$657$	−0.490609	−	1.18443i	−0.0191405	−	0.0462092i
$658$	−5.50928	+	13.5937i	−0.214774	+	0.529937i
$659$	−13.6259	−	25.4924i	−0.530791	−	0.993041i	−0.994266	−	0.106931i	$-0.965898\pi$
$659$	−13.6259	−	25.4924i	−0.530791	−	0.993041i	0.463475	−	0.886110i	$-0.346602\pi$
$660$	−0.212939	+	2.56334i	−0.00828863	+	0.0997780i
$661$	−3.29334	−	4.01295i	−0.128096	−	0.156086i	0.705013	−	0.709195i	$-0.250941\pi$
$661$	−3.29334	−	4.01295i	−0.128096	−	0.156086i	−0.833109	+	0.553109i	$0.813441\pi$
$662$	17.9413	−	22.2056i	0.697307	−	0.863045i
$663$	9.59025	−	14.3528i	0.372455	−	0.557418i
$664$	−2.16555	+	0.711556i	−0.0840397	+	0.0276137i
$665$	1.38554	−	0.925789i	0.0537290	−	0.0359005i
$666$	−0.742902	−	0.891242i	−0.0287869	−	0.0345349i
$667$	−5.53553	+	10.3562i	−0.214337	+	0.400995i
$668$	4.18566	−	6.47656i	0.161948	−	0.250586i
$669$	45.3596	−	4.46753i	1.75370	−	0.172725i
$670$	6.00969	−	4.08236i	0.232175	−	0.157715i
$671$	13.8897	+	13.8897i	0.536206	+	0.536206i
$672$	5.39728	−	7.11472i	0.208205	−	0.274456i
$673$	−7.86646	+	7.86646i	−0.303230	+	0.303230i	−0.842276	−	0.539046i	$-0.818785\pi$
$673$	−7.86646	+	7.86646i	−0.303230	+	0.303230i	0.539046	+	0.842276i	$0.318785\pi$
$674$	−2.94886	+	15.4411i	−0.113586	+	0.594771i
$675$	2.63740	+	26.7780i	0.101514	+	1.03068i
$676$	0.764173	−	4.17445i	0.0293913	−	0.160556i
$677$	−18.6459	−	9.96645i	−0.716621	−	0.383042i	0.0724270	−	0.997374i	$-0.476926\pi$
$677$	−18.6459	−	9.96645i	−0.716621	−	0.383042i	−0.789048	+	0.614332i	$0.789426\pi$
$678$	2.12619	−	23.4224i	0.0816557	−	0.899533i
$679$	4.59749	+	6.88063i	0.176436	+	0.264054i
$680$	2.60080	−	1.46784i	0.0997362	−	0.0562890i
$681$	31.5714	+	21.0954i	1.20982	+	0.808376i
$682$	1.35990	+	12.8028i	0.0520733	+	0.490246i
$683$	15.5918	−	12.7959i	0.596604	−	0.489620i	−0.286953	−	0.957945i	$-0.592642\pi$
$683$	15.5918	−	12.7959i	0.596604	−	0.489620i	0.883556	+	0.468325i	$0.155142\pi$
$684$	−4.00695	−	2.06360i	−0.153210	−	0.0789037i
$685$	−3.43680	+	1.83701i	−0.131313	+	0.0701884i
$686$	1.30239	−	0.551172i	0.0497253	−	0.0210438i
$687$	−6.14732	+	2.54630i	−0.234535	+	0.0971476i
$688$	−0.256303	+	3.78648i	−0.00977147	+	0.144358i
$689$	31.6045	+	13.0910i	1.20403	+	0.498727i
$690$	−4.22797	+	0.0323327i	−0.160956	+	0.00123089i
$691$	13.1804	−	43.4501i	0.501408	−	1.65292i	−0.231685	−	0.972791i	$-0.574424\pi$
$691$	13.1804	−	43.4501i	0.501408	−	1.65292i	0.733093	−	0.680129i	$-0.238076\pi$
$692$	14.7571	+	11.7378i	0.560980	+	0.446203i
$693$	1.09643	+	0.107989i	0.0416498	+	0.00410215i
$694$	13.6227	−	7.41599i	0.517112	−	0.281507i
$695$	−4.48559	+	0.892239i	−0.170148	+	0.0338446i
$696$	−7.51797	−	7.18070i	−0.284968	−	0.272184i
$697$	0.889328	−	4.47095i	0.0336857	−	0.169349i
$698$	24.7222	+	12.9722i	0.935747	+	0.491004i
$699$	−32.7103	+	9.92256i	−1.23722	+	0.375306i
$700$	6.97595	+	6.76577i	0.263666	+	0.255722i
$701$	1.30787	−	1.59364i	0.0493976	−	0.0601911i	−0.747726	−	0.664008i	$-0.768854\pi$
$701$	1.30787	−	1.59364i	0.0493976	−	0.0601911i	0.797123	+	0.603817i	$0.206354\pi$
$702$	6.16953	+	29.8226i	0.232854	+	1.12558i
$703$		−	7.16972i		−	0.270411i
$704$	7.47108	−	15.6662i	0.281577	−	0.590442i
$705$			6.14815i			0.231553i
$706$	13.8813	−	2.87168i	0.522429	−	0.108077i
$707$	8.74336	−	10.6538i	0.328828	−	0.400678i
$708$	−0.464312	−	30.3560i	−0.0174499	−	1.14085i
$709$	2.52276	−	0.765270i	0.0947441	−	0.0287403i	−0.242557	−	0.970137i	$-0.577986\pi$
$709$	2.52276	−	0.765270i	0.0947441	−	0.0287403i	0.337301	+	0.941397i	$0.390486\pi$
$710$	2.07682	−	3.95797i	0.0779418	−	0.148540i
$711$	−1.69300	+	8.51129i	−0.0634925	+	0.319198i
$712$	13.1369	+	29.7650i	0.492326	+	1.11549i
$713$	−20.7568	+	4.12879i	−0.777348	+	0.154624i
$714$	3.00155	+	5.51367i	0.112330	+	0.206344i
$715$	−3.15273	−	0.310517i	−0.117905	−	0.0116127i
$716$	−14.2361	+	1.62232i	−0.532026	+	0.0606290i
$717$	6.65633	−	21.9430i	0.248585	−	0.819475i
$718$	0.251352	+	32.8678i	0.00938036	+	1.22662i
$719$	−18.6694	−	7.73313i	−0.696252	−	0.288397i	0.00634996	−	0.999980i	$-0.497979\pi$
$719$	−18.6694	−	7.73313i	−0.696252	−	0.288397i	−0.702602	+	0.711583i	$0.747979\pi$
$720$	−0.198983	+	0.736321i	−0.00741567	+	0.0274410i
$721$	−16.7535	+	6.93952i	−0.623932	+	0.258441i
$722$	−0.382386	−	0.903556i	−0.0142309	−	0.0336269i
$723$	−16.7259	+	8.94021i	−0.622045	+	0.332490i
$724$	−1.23819	−	3.86779i	−0.0460168	−	0.143745i
$725$	8.74530	−	7.17708i	0.324792	−	0.266550i
$726$	13.9710	−	1.48398i	0.518513	−	0.0550758i
$727$	−35.4564	−	23.6912i	−1.31501	−	0.878659i	−0.317432	−	0.948281i	$-0.602821\pi$
$727$	−35.4564	−	23.6912i	−1.31501	−	0.878659i	−0.997573	+	0.0696221i	$0.977821\pi$
$728$	8.66007	+	6.78074i	0.320964	+	0.251311i
$729$	−16.6072	−	24.8544i	−0.615080	−	0.920533i
$730$	−1.33516	−	0.121200i	−0.0494164	−	0.00448581i
$731$	−2.35286	−	1.25763i	−0.0870236	−	0.0465151i
$732$	−16.2433	−	23.5229i	−0.600370	−	0.869431i
$733$	1.84257	+	18.7080i	0.0680570	+	0.690994i	0.967315	+	0.253576i	$0.0816069\pi$
$733$	1.84257	+	18.7080i	0.0680570	+	0.690994i	−0.899258	+	0.437418i	$0.855893\pi$
$734$	−15.6648	−	2.99158i	−0.578199	−	0.110421i
$735$	0.419164	−	0.419164i	0.0154611	−	0.0154611i
$736$	26.7566	+	9.90247i	0.986261	+	0.365010i
$737$	20.9882	+	20.9882i	0.773112	+	0.773112i
$738$	0.654209	+	0.963068i	0.0240818	+	0.0354510i
$739$	16.2536	−	1.60084i	0.597899	−	0.0588879i	0.205459	−	0.978666i	$-0.434131\pi$
$739$	16.2536	−	1.60084i	0.597899	−	0.0588879i	0.392440	+	0.919778i	$0.371631\pi$
$740$	−1.18625	+	0.254880i	−0.0436074	+	0.00936956i
$741$	−12.8424	+	24.0263i	−0.471776	+	0.882630i
$742$	−9.55616	+	7.96561i	−0.350817	+	0.292427i
$743$	21.0686	−	14.0776i	0.772931	−	0.516456i	−0.105445	−	0.994425i	$-0.533627\pi$
$743$	21.0686	−	14.0776i	0.772931	−	0.516456i	0.878377	+	0.477969i	$0.158627\pi$
$744$	1.40829	−	18.6836i	0.0516303	−	0.684975i
$745$	3.76940	−	5.64130i	0.138100	−	0.206681i
$746$	27.6154	+	22.3122i	1.01107	+	0.816906i
$747$	0.259627	+	0.316356i	0.00949925	+	0.0115749i
$748$	7.88364	+	9.31210i	0.288254	+	0.340484i
$749$	−1.51472	−	2.83384i	−0.0553467	−	0.103546i
$750$	7.65989	+	3.10442i	0.279700	+	0.113357i
$751$	4.02362	+	9.71387i	0.146824	+	0.354464i	0.980132	−	0.198344i	$-0.0635563\pi$
$751$	4.02362	+	9.71387i	0.146824	+	0.354464i	−0.833309	+	0.552808i	$0.813556\pi$
$752$	14.6965	−	38.7961i	0.535926	−	1.41475i
$753$	−1.40871	+	3.40093i	−0.0513362	+	0.123937i
$754$	8.98460	−	9.12308i	0.327200	−	0.332243i
$755$	5.41184	+	1.64166i	0.196957	+	0.0597462i
$756$	−10.6464	−	3.05253i	−0.387204	−	0.111020i
$757$	−1.51777	+	15.4102i	−0.0551644	+	0.560094i	0.927387	+	0.374103i	$0.122049\pi$
$757$	−1.51777	+	15.4102i	−0.0551644	+	0.560094i	−0.982552	+	0.185990i	$0.940451\pi$
$758$	43.8398	+	12.9334i	1.59233	+	0.469762i
$759$	−3.36998	−	16.9421i	−0.122323	−	0.614958i
$760$	−3.85780	+	2.70773i	−0.139937	+	0.0982199i
$761$	−30.9220	−	6.15077i	−1.12092	−	0.222965i	−0.400361	−	0.916357i	$-0.631115\pi$
$761$	−30.9220	−	6.15077i	−1.12092	−	0.222965i	−0.720560	+	0.693392i	$0.756115\pi$
$762$	12.1924	−	3.80057i	0.441683	−	0.137680i
$763$	0.0940322	+	0.309983i	0.00340419	+	0.0112221i
$764$	24.5070	−	10.5931i	0.886631	−	0.383244i
$765$	−0.414473	−	0.340149i	−0.0149853	−	0.0122981i
$766$	11.7913	−	17.9425i	0.426038	−	0.648288i
$767$	37.3919			1.35014
$768$	−14.8002	+	20.4684i	−0.534056	+	0.738589i
$769$	−26.9008			−0.970068			−0.485034	−	0.874495i	$-0.661193\pi$
$769$	−26.9008			−0.970068			−0.485034	+	0.874495i	$0.661193\pi$
$770$	0.632735	−	0.962813i	0.0228022	−	0.0346974i
$771$	25.9096	+	21.2635i	0.933113	+	0.765786i
$772$	−0.0695127	+	0.0300467i	−0.00250182	+	0.00108140i
$773$	−3.01319	−	9.93315i	−0.108377	−	0.357271i	0.885931	−	0.463817i	$-0.153521\pi$
$773$	−3.01319	−	9.93315i	−0.108377	−	0.357271i	−0.994308	+	0.106547i	$0.966021\pi$
$774$	0.650506	−	0.202774i	0.0233819	−	0.00728855i
$775$	19.9976	+	3.97776i	0.718334	+	0.142885i
$776$	−13.4467	−	19.1579i	−0.482708	−	0.687730i
$777$	−0.497581	−	2.50151i	−0.0178506	−	0.0897411i
$778$	−41.5533	−	12.2589i	−1.48976	−	0.439501i
$779$	−0.705172	+	7.15973i	−0.0252654	+	0.256524i
$780$	4.43176	+	1.27068i	0.158683	+	0.0454976i
$781$	17.4750	+	5.30098i	0.625304	+	0.189684i
$782$	−14.0728	+	14.2897i	−0.503243	+	0.510999i
$783$	−4.93411	+	11.9120i	−0.176331	+	0.425700i
$784$	−3.64697	+	1.64304i	−0.130249	+	0.0586801i
$785$	−0.339065	−	0.818576i	−0.0121018	−	0.0292162i
$786$	23.0496	+	9.34161i	0.822153	+	0.333204i
$787$	9.59130	+	17.9441i	0.341893	+	0.639637i	0.992835	−	0.119490i	$-0.0381260\pi$
$787$	9.59130	+	17.9441i	0.341893	+	0.639637i	−0.650942	+	0.759127i	$0.725626\pi$
$788$	6.25254	+	7.38546i	0.222738	+	0.263096i
$789$	−7.98604	−	9.73101i	−0.284310	−	0.346433i
$790$	7.05879	+	5.70322i	0.251140	+	0.202912i
$791$	−5.85258	+	8.75901i	−0.208094	+	0.311435i
$792$	−3.10735	−	0.234218i	−0.110415	−	0.00832258i
$793$	29.2743	−	19.5604i	1.03956	−	0.694612i
$794$	−0.841132	+	0.701132i	−0.0298506	+	0.0248822i
$795$	−2.45819	+	4.59895i	−0.0871829	+	0.163108i
$796$	1.19806	−	0.257417i	0.0424641	−	0.00912391i
$797$	−11.1348	+	1.09668i	−0.394414	+	0.0388464i	−0.293280	−	0.956026i	$-0.594747\pi$
$797$	−11.1348	+	1.09668i	−0.394414	+	0.0388464i	−0.101134	+	0.994873i	$0.532247\pi$
$798$	−5.56722	−	8.19556i	−0.197077	−	0.290120i
$799$	20.6219	+	20.6219i	0.729550	+	0.729550i
$800$	−20.1648	−	18.6788i	−0.712932	−	0.660396i
$801$	4.13044	−	4.13044i	0.145942	−	0.145942i
$802$	32.8963	+	6.28235i	1.16161	+	0.221837i
$803$	−0.536865	−	5.45088i	−0.0189455	−	0.192357i
$804$	−24.5447	−	35.5446i	−0.865625	−	1.25356i
$805$	1.67020	+	0.892741i	0.0588668	+	0.0314650i
$806$	22.9822	+	2.08623i	0.809515	+	0.0734843i
$807$	−2.71434	−	4.06230i	−0.0955494	−	0.143000i
$808$	−24.0322	+	30.6929i	−0.845450	+	1.07977i
$809$	−14.2688	−	9.53411i	−0.501664	−	0.335201i	0.278855	−	0.960333i	$-0.410045\pi$
$809$	−14.2688	−	9.53411i	−0.501664	−	0.335201i	−0.780519	+	0.625132i	$0.785045\pi$
$810$	−3.81193	+	0.404899i	−0.133938	+	0.0142267i
$811$	−0.663452	+	0.544481i	−0.0232969	+	0.0191193i	−0.645970	−	0.763363i	$-0.723547\pi$
$811$	−0.663452	+	0.544481i	−0.0232969	+	0.0191193i	0.622673	+	0.782482i	$0.286047\pi$
$812$	1.41974	+	4.43493i	0.0498232	+	0.155635i
$813$	−28.0860	+	15.0123i	−0.985018	+	0.526503i
$814$	−1.93195	−	4.56509i	−0.0677149	−	0.160006i
$815$	7.71990	−	3.19769i	0.270416	−	0.112010i
$816$	−8.84519	−	15.3962i	−0.309643	−	0.538974i
$817$	3.88998	+	1.61128i	0.136093	+	0.0563717i
$818$	0.0531687	+	6.95257i	0.00185900	+	0.243091i
$819$	0.573234	−	1.88970i	0.0200304	−	0.0660314i
$820$	1.20967	−	0.137852i	0.0422434	−	0.00481400i
$821$	−54.3494	−	5.35295i	−1.89681	−	0.186819i	−0.918705	−	0.394946i	$-0.870763\pi$
$821$	−54.3494	−	5.35295i	−1.89681	−	0.186819i	−0.978102	+	0.208126i	$0.933263\pi$
$822$	11.0781	+	20.3498i	0.386392	+	0.709779i
$823$	−36.8101	+	7.32198i	−1.28312	+	0.255228i	−0.789123	−	0.614236i	$-0.789464\pi$
$823$	−36.8101	+	7.32198i	−1.28312	+	0.255228i	−0.493996	+	0.869464i	$0.664464\pi$
$824$	46.9233	−	20.7098i	1.63465	−	0.721459i
$825$	−3.24672	+	16.3223i	−0.113036	+	0.568271i
$826$	−6.31837	+	12.0414i	−0.219844	+	0.418975i
$827$	−36.7924	+	11.1608i	−1.27940	+	0.388101i	−0.855591	−	0.517652i	$-0.826806\pi$
$827$	−36.7924	+	11.1608i	−1.27940	+	0.388101i	−0.423806	+	0.905753i	$0.639306\pi$
$828$	−0.0783394	−	5.12170i	−0.00272248	−	0.177991i
$829$	11.8922	−	14.4907i	0.413033	−	0.503282i	−0.524389	−	0.851479i	$-0.675706\pi$
$829$	11.8922	−	14.4907i	0.413033	−	0.503282i	0.937421	+	0.348197i	$0.113206\pi$
$830$	0.419093	−	0.0866996i	0.0145469	−	0.00300939i
$831$		−	34.8765i		−	1.20985i
$832$	−24.9279	−	18.6119i	−0.864219	−	0.645251i
$833$		−	2.81188i		−	0.0974260i
$834$	5.50870	+	26.6282i	0.190751	+	0.922061i
$835$	−0.918480	+	1.11917i	−0.0317853	+	0.0387305i
$836$	−13.8227	−	13.4062i	−0.478068	−	0.463663i
$837$	−22.2366	+	6.74539i	−0.768608	+	0.233155i
$838$	10.1244	+	5.31248i	0.349743	+	0.183517i
$839$	−0.976475	+	4.90907i	−0.0337117	+	0.169480i	−0.993973	−	0.109621i	$-0.965036\pi$
$839$	−0.976475	+	4.90907i	−0.0337117	+	0.169480i	0.960262	+	0.279101i	$0.0900364\pi$
$840$	−1.15807	+	1.21246i	−0.0399571	+	0.0418338i
$841$	−23.1259	+	4.60002i	−0.797444	+	0.158621i
$842$	−26.0662	+	14.1900i	−0.898300	+	0.489020i
$843$	−0.205971	−	0.0202863i	−0.00709401	−	0.000698699i
$844$	−1.94595	−	1.54781i	−0.0669824	−	0.0532778i
$845$	−0.231291	+	0.762465i	−0.00795666	+	0.0262296i
$846$	−7.44822	+	0.0569591i	−0.256075	+	0.00195829i
$847$	−5.81399	−	2.40823i	−0.199771	−	0.0827478i
$848$	26.5049	−	23.1442i	0.910184	−	0.794776i
$849$	35.3644	−	14.6484i	1.21370	−	0.502732i
$850$	17.7944	−	7.53063i	0.610344	−	0.258299i
$851$	7.18618	−	3.84109i	0.246339	−	0.131671i
$852$	−23.6263	−	12.1677i	−0.809424	−	0.416857i
$853$	8.31906	−	6.82728i	0.284839	−	0.233762i	−0.481114	−	0.876658i	$-0.659768\pi$
$853$	8.31906	−	6.82728i	0.284839	−	0.233762i	0.765953	+	0.642897i	$0.222268\pi$
$854$	1.35244	+	12.7325i	0.0462794	+	0.435699i
$855$	0.703596	+	0.470128i	0.0240625	+	0.0160780i
$856$	4.46702	+	7.91493i	0.152679	+	0.270527i
$857$	18.0429	+	27.0030i	0.616332	+	0.922406i	0.999999	−	0.00106529i	$-0.000339093\pi$
$857$	18.0429	+	27.0030i	0.616332	+	0.922406i	−0.383667	+	0.923471i	$0.625339\pi$
$858$	−1.70282	+	18.7585i	−0.0581332	+	0.640404i
$859$	19.5098	+	10.4282i	0.665666	+	0.355806i	0.769371	−	0.638802i	$-0.220570\pi$
$859$	19.5098	+	10.4282i	0.665666	+	0.355806i	−0.103705	+	0.994608i	$0.533070\pi$
$860$	0.128305	−	0.700889i	0.00437515	−	0.0239001i
$861$	0.250854	+	2.54696i	0.00854908	+	0.0868003i
$862$	10.0134	−	52.4331i	0.341057	−	1.78588i
$863$	−8.33203	+	8.33203i	−0.283626	+	0.283626i	−0.834553	−	0.550928i	$-0.814274\pi$
$863$	−8.33203	+	8.33203i	−0.283626	+	0.283626i	0.550928	+	0.834553i	$0.314274\pi$
$864$	30.3026	+	7.94083i	1.03092	+	0.270152i
$865$	−2.50329	−	2.50329i	−0.0851145	−	0.0851145i
$866$	−3.37172	+	2.29040i	−0.114576	+	0.0778310i
$867$	−14.2862	+	1.40706i	−0.485184	+	0.0477864i
$868$	−4.55530	+	7.04852i	−0.154617	+	0.239242i
$869$	−17.4773	+	32.6978i	−0.592878	+	1.10920i
$870$	1.24977	+	1.49932i	0.0423712	+	0.0508317i
$871$	44.2353	−	29.5571i	1.49886	−	1.00150i
$872$	−0.286006	−	0.870431i	−0.00968538	−	0.0294765i
$873$	−2.33467	+	3.49408i	−0.0790166	+	0.118257i
$874$	19.8925	−	24.6207i	0.672875	−	0.832806i
$875$	−2.34855	−	2.86172i	−0.0793955	−	0.0967437i
$876$	−0.659882	+	7.94362i	−0.0222953	+	0.268390i
$877$	20.8191	+	38.9499i	0.703012	+	1.31524i	0.939144	+	0.343522i	$0.111620\pi$
$877$	20.8191	+	38.9499i	0.703012	+	1.31524i	−0.236132	+	0.971721i	$0.575880\pi$
$878$	−9.89263	+	24.4092i	−0.333860	+	0.823772i
$879$	16.1186	+	38.9138i	0.543668	+	1.31253i
$880$	−1.72670	+	2.76358i	−0.0582072	+	0.0931604i
$881$	10.8603	−	26.2191i	0.365894	−	0.883345i	−0.628520	−	0.777793i	$-0.716339\pi$
$881$	10.8603	−	26.2191i	0.365894	−	0.883345i	0.994414	−	0.105552i	$-0.0336610\pi$
$882$	0.511682	+	0.503915i	0.0172292	+	0.0169677i
$883$	35.8182	+	10.8653i	1.20538	+	0.365647i	0.828167	−	0.560481i	$-0.189384\pi$
$883$	35.8182	+	10.8653i	1.20538	+	0.365647i	0.377209	+	0.926128i	$0.376884\pi$
$884$	19.1269	−	10.6028i	0.643307	−	0.356610i
$885$	−0.558696	+	5.67253i	−0.0187804	+	0.190680i
$886$	6.92086	−	23.4593i	0.232511	−	0.788132i
$887$	−8.54937	−	42.9806i	−0.287060	−	1.44315i	−0.807813	−	0.589439i	$-0.799349\pi$
$887$	−8.54937	−	42.9806i	−0.287060	−	1.44315i	0.520753	−	0.853707i	$-0.325651\pi$
$888$	1.56931	+	7.04119i	0.0526625	+	0.236287i
$889$	−5.61039	−	1.11598i	−0.188166	−	0.0374286i
$890$	−1.81784	−	5.83169i	−0.0609340	−	0.195479i
$891$	−4.54625	−	14.9870i	−0.152305	−	0.502083i
$892$	53.6800	+	21.2791i	1.79734	+	0.712476i
$893$	−35.5791	−	29.1991i	−1.19061	−	0.977109i
$894$	−33.7114	−	22.1542i	−1.12748	−	0.740949i
$895$	2.69011			0.0899204
$896$	10.2059	−	4.88263i	0.340954	−	0.163117i
$897$	−30.9616			−1.03378
$898$	27.2860	+	17.9316i	0.910545	+	0.598386i
$899$	7.55238	+	6.19808i	0.251886	+	0.206717i
$900$	−1.81857	+	4.58763i	−0.0606189	+	0.152921i
$901$	7.18045	+	23.6708i	0.239215	+	0.788587i
$902$	1.48026	+	4.74874i	0.0492874	+	0.158116i
$903$	1.46904	+	0.292209i	0.0488864	+	0.00972412i
$904$	15.9809	−	25.1474i	0.531518	−	0.836391i
$905$	0.148752	+	0.747826i	0.00494468	+	0.0248586i
$906$	9.51435	−	32.2504i	0.316093	−	1.07145i
$907$	4.43401	−	45.0192i	0.147229	−	1.49484i	−0.583467	−	0.812137i	$-0.698304\pi$
$907$	4.43401	−	45.0192i	0.147229	−	1.49484i	0.730696	−	0.682703i	$-0.239196\pi$
$908$	23.3226	+	42.0728i	0.773987	+	1.39624i
$909$	6.69744	+	2.03165i	0.222140	+	0.0673855i
$910$	−1.47132	−	1.44899i	−0.0487738	−	0.0480335i
$911$	19.0461	−	45.9813i	0.631025	−	1.52343i	−0.207310	−	0.978275i	$-0.566471\pi$
$911$	19.0461	−	45.9813i	0.631025	−	1.52343i	0.838336	−	0.545154i	$-0.183529\pi$
$912$	16.2741	+	22.8132i	0.538889	+	0.755421i
$913$	0.669110	+	1.61537i	0.0221443	+	0.0534611i
$914$	20.4482	−	50.4541i	0.676365	−	1.66887i
$915$	2.53001	+	4.73331i	0.0836395	+	0.156478i
$916$	−8.40073	−	0.697854i	−0.277568	−	0.0230578i
$917$	−7.06710	−	8.61128i	−0.233376	−	0.284370i
$918$	−13.8395	+	17.1289i	−0.456770	+	0.565337i
$919$	−17.6201	+	26.3704i	−0.581234	+	0.869879i	−0.999256	−	0.0385581i	$-0.987724\pi$
$919$	−17.6201	+	26.3704i	−0.581234	+	0.869879i	0.418022	+	0.908437i	$0.362724\pi$
$920$	−4.78072	−	2.41602i	−0.157616	−	0.0796538i
$921$	−8.08236	+	5.40046i	−0.266323	+	0.177951i
$922$	−26.5741	−	31.8803i	−0.875170	−	1.04992i
$923$	15.4294	−	28.8665i	0.507866	−	0.950151i
$924$	−5.75312	−	3.71811i	−0.189264	−	0.122317i
$925$	−7.81247	+	0.769462i	−0.256873	+	0.0252997i
$926$	4.47103	−	3.03716i	0.146927	−	0.0998072i
$927$	−6.51147	−	6.51147i	−0.213865	−	0.213865i
$928$	−4.30233	−	12.4484i	−0.141231	−	0.408640i
$929$	−7.39610	+	7.39610i	−0.242658	+	0.242658i	−0.817949	−	0.575291i	$-0.804889\pi$
$929$	−7.39610	+	7.39610i	−0.242658	+	0.242658i	0.575291	+	0.817949i	$0.304889\pi$
$930$	−0.659883	+	3.45534i	−0.0216384	+	0.113305i
$931$	0.434977	+	4.41640i	0.0142558	+	0.144742i
$932$	−42.5973	−	7.79785i	−1.39532	−	0.255427i
$933$	12.5346	+	6.69988i	0.410364	+	0.219344i
$934$	−1.14139	+	12.5737i	−0.0373474	+	0.411425i
$935$	−1.27267	−	1.90469i	−0.0416208	−	0.0622900i
$936$	−1.49831	+	5.38066i	−0.0489739	+	0.175872i
$937$	44.5468	+	29.7652i	1.45528	+	0.972387i	0.996479	+	0.0838482i	$0.0267211\pi$
$937$	44.5468	+	29.7652i	1.45528	+	0.972387i	0.458801	+	0.888539i	$0.348279\pi$
$938$	2.04362	+	19.2397i	0.0667265	+	0.628199i
$939$	6.46486	−	5.30557i	0.210973	−	0.173141i
$940$	−3.56624	+	6.92468i	−0.116318	+	0.225858i
$941$	−24.7517	+	13.2301i	−0.806882	+	0.431288i	−0.822622	−	0.568588i	$-0.807490\pi$
$941$	−24.7517	+	13.2301i	−0.806882	+	0.431288i	0.0157397	+	0.999876i	$0.494990\pi$
$942$	−4.85138	+	2.05311i	−0.158066	+	0.0668939i
$943$	−7.55396	+	3.12895i	−0.245991	+	0.101893i
$944$	17.0851	−	34.4593i	0.556071	−	1.12156i
$945$	1.92110	+	0.795747i	0.0624935	+	0.0258856i
$946$	2.91100	−	0.0222614i	0.0946447	−	0.000723781i
$947$	−4.34752	+	14.3319i	−0.141275	+	0.465723i	−0.998814	−	0.0486977i	$-0.984493\pi$
$947$	−4.34752	+	14.3319i	−0.141275	+	0.465723i	0.857538	+	0.514420i	$0.171993\pi$
$948$	33.5872	−	42.2269i	1.09086	−	1.37147i
$949$	−9.77008	−	0.962269i	−0.317150	−	0.0312366i
$950$	−26.7833	+	14.5804i	−0.868966	+	0.473051i
$951$	20.8279	−	4.14294i	0.675392	−	0.134344i
$952$	0.182443	+	7.95112i	0.00591302	+	0.257697i
$953$	0.282661	−	1.42103i	0.00915628	−	0.0460317i	−0.975937	−	0.218052i	$-0.930030\pi$
$953$	0.282661	−	1.42103i	0.00915628	−	0.0460317i	0.985093	+	0.172021i	$0.0550296\pi$
$954$	−5.59420	−	2.93538i	−0.181119	−	0.0950365i
$955$	−4.79677	+	1.45508i	−0.155220	+	0.0470854i
$956$	20.2251	−	20.8534i	0.654126	−	0.674448i
$957$	−5.05897	+	6.16438i	−0.163533	+	0.199266i
$958$	−2.78470	−	13.4608i	−0.0899697	−	0.434900i
$959$		−	10.3781i		−	0.335125i
$960$	3.19597	−	3.50359i	0.103150	−	0.113078i
$961$		−	13.3919i		−	0.431997i
$962$	−8.70074	+	1.79996i	−0.280523	+	0.0580331i
$963$	1.03516	−	1.26135i	0.0333577	−	0.0406464i
$964$	−24.0243	+	0.367465i	−0.773769	+	0.0118353i
$965$	0.0136058	−	0.00412726i	0.000437985	−	0.000132861i
$966$	5.23180	−	9.97067i	0.168330	−	0.320801i
$967$	2.67513	−	13.4488i	0.0860262	−	0.432483i	−0.913637	−	0.406531i	$-0.866738\pi$
$967$	2.67513	−	13.4488i	0.0860262	−	0.432483i	0.999663	−	0.0259520i	$-0.00826172\pi$
$968$	16.5964	+	6.43249i	0.533427	+	0.206748i
$969$	−19.3208	+	3.84316i	−0.620675	+	0.123460i
$970$	2.10111	+	3.85961i	0.0674626	+	0.123925i
$971$	8.38899	+	0.826244i	0.269216	+	0.0265154i	0.231724	−	0.972782i	$-0.425563\pi$
$971$	8.38899	+	0.826244i	0.269216	+	0.0265154i	0.0374914	+	0.999297i	$0.488063\pi$
$972$	−1.18142	−	10.3671i	−0.0378941	−	0.332525i
$973$	3.53559	−	11.6553i	0.113346	−	0.373651i
$974$	−0.113516	−	14.8439i	−0.00363730	−	0.475629i
$975$	27.5585	+	11.4151i	0.882579	+	0.365576i
$976$	−4.65038	−	35.9159i	−0.148855	−	1.14964i
$977$	35.0911	−	14.5352i	1.12267	−	0.465023i	0.257384	−	0.966309i	$-0.417140\pi$
$977$	35.0911	−	14.5352i	1.12267	−	0.465023i	0.865282	+	0.501286i	$0.167140\pi$
$978$	−19.3627	−	45.7528i	−0.619150	−	1.46301i
$979$	22.0094	−	11.7643i	0.703424	−	0.375988i
$980$	0.715242	−	0.228969i	0.0228476	−	0.00731413i
$981$	−0.127158	+	0.104356i	−0.00405983	+	0.00333182i
$982$	14.8948	−	1.58211i	0.475314	−	0.0504872i
$983$	−10.2478	−	6.84733i	−0.326853	−	0.218396i	0.381307	−	0.924449i	$-0.375474\pi$
$983$	−10.2478	−	6.84733i	−0.326853	−	0.218396i	−0.708159	+	0.706053i	$0.750474\pi$
$984$	−0.874590	−	7.18573i	−0.0278809	−	0.229073i
$985$	−1.00936	−	1.51062i	−0.0321609	−	0.0481322i
$986$	9.22089	+	0.837032i	0.293653	+	0.0266565i
$987$	−14.4400	−	7.71832i	−0.459629	−	0.245677i
$988$	−28.4009	+	19.6117i	−0.903553	+	0.623932i
$989$	0.469030	+	4.76214i	0.0149143	+	0.151427i
$990$	0.574673	+	0.109748i	0.0182643	+	0.00348802i
$991$	−25.0431	+	25.0431i	−0.795519	+	0.795519i	−0.982385	−	0.186866i	$-0.940167\pi$
$991$	−25.0431	+	25.0431i	−0.795519	+	0.795519i	0.186866	+	0.982385i	$0.440167\pi$
$992$	12.4236	−	20.2265i	0.394450	−	0.642193i
$993$	22.5337	+	22.5337i	0.715086	+	0.715086i
$994$	6.68874	+	9.84655i	0.212154	+	0.312314i
$995$	−0.228961	+	0.0225507i	−0.00725854	+	0.000714904i
$996$	−0.534522	−	2.48775i	−0.0169370	−	0.0788273i
$997$	−2.70682	+	5.06410i	−0.0857258	+	0.160382i	−0.921131	−	0.389253i	$-0.872733\pi$
$997$	−2.70682	+	5.06410i	−0.0857258	+	0.160382i	0.835405	+	0.549635i	$0.185233\pi$
$998$	−11.3984	+	9.50125i	−0.360811	+	0.300757i
$999$	7.43894	−	4.97054i	0.235358	−	0.157261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.a.533.15	✓	752
128.61	even	32	inner	896.2.bn.a.701.15	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.a.533.15	✓	752	1.1	even	1	trivial
896.2.bn.a.701.15	yes	752	128.61	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.776680 + 1.18185i) q^{2} +(-1.22033 - 1.00150i) q^{3} +(-0.793537 - 1.83584i) q^{4} +(0.109002 + 0.359330i) q^{5} +(2.13142 - 0.664400i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(2.78601 + 0.488017i) q^{8} +(-0.0990695 - 0.498056i) q^{9} +O(q^{10})\)	\(q+(-0.776680 + 1.18185i) q^{2} +(-1.22033 - 1.00150i) q^{3} +(-0.793537 - 1.83584i) q^{4} +(0.109002 + 0.359330i) q^{5} +(2.13142 - 0.664400i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(2.78601 + 0.488017i) q^{8} +(-0.0990695 - 0.498056i) q^{9} +(-0.509333 - 0.150261i) q^{10} +(0.212654 - 2.15911i) q^{11} +(-0.870210 + 3.03504i) q^{12} +(-3.72124 - 1.12883i) q^{13} +(0.992324 - 1.00762i) q^{14} +(0.226850 - 0.547664i) q^{15} +(-2.74060 + 2.91361i) q^{16} +(-1.07606 - 2.59784i) q^{17} +(0.665573 + 0.269745i) q^{18} +(2.09195 + 3.91376i) q^{19} +(0.573175 - 0.485251i) q^{20} +(1.00150 + 1.22033i) q^{21} +(2.38658 + 1.92826i) q^{22} +(-2.80201 + 4.19350i) q^{23} +(-2.91109 - 3.38571i) q^{24} +(4.04011 - 2.69952i) q^{25} +(4.22432 - 3.52121i) q^{26} +(-2.61044 + 4.88379i) q^{27} +(0.420135 + 1.95537i) q^{28} +(2.31711 - 0.228215i) q^{29} +(0.471067 + 0.693462i) q^{30} +(2.96716 + 2.96716i) q^{31} +(-1.31488 - 5.50192i) q^{32} +(-2.42185 + 2.42185i) q^{33} +(3.90602 + 0.745949i) q^{34} +(-0.0368053 - 0.373691i) q^{35} +(-0.835735 + 0.577101i) q^{36} +(-1.42485 - 0.761596i) q^{37} +(-6.25025 - 0.567371i) q^{38} +(3.41061 + 5.10434i) q^{39} +(0.128320 + 1.05429i) q^{40} +(1.34795 + 0.900674i) q^{41} +(-2.22008 + 0.235814i) q^{42} +(0.733421 - 0.601903i) q^{43} +(-4.13253 + 1.32294i) q^{44} +(0.168168 - 0.0898875i) q^{45} +(-2.77982 - 6.56856i) q^{46} +(-9.58211 + 3.96904i) q^{47} +(6.26239 - 0.810854i) q^{48} +(0.923880 + 0.382683i) q^{49} +(0.0525485 + 6.87146i) q^{50} +(-1.28858 + 4.24788i) q^{51} +(0.880600 + 7.72737i) q^{52} +(-8.75454 - 0.862247i) q^{53} +(-3.74443 - 6.87828i) q^{54} +(0.799013 - 0.158934i) q^{55} +(-2.63727 - 1.02216i) q^{56} +(1.36675 - 6.87114i) q^{57} +(-1.52993 + 2.91572i) q^{58} +(-9.20152 + 2.79125i) q^{59} +(-1.18544 + 0.0181319i) q^{60} +(-5.74374 + 6.99877i) q^{61} +(-5.81127 + 1.20220i) q^{62} +0.507814i q^{63} +(7.52368 + 2.71924i) q^{64} -1.46020i q^{65} +(-0.981259 - 4.74326i) q^{66} +(-8.67917 + 10.5756i) q^{67} +(-3.91532 + 4.03696i) q^{68} +(7.61913 - 2.31124i) q^{69} +(0.470232 + 0.246740i) q^{70} +(-1.64209 + 8.25533i) q^{71} +(-0.0329484 - 1.43594i) q^{72} +(2.47608 - 0.492524i) q^{73} +(2.00674 - 1.09244i) q^{74} +(-7.63380 - 0.751864i) q^{75} +(5.52499 - 6.94619i) q^{76} +(-0.629790 + 2.07614i) q^{77} +(-8.68152 + 0.0663906i) q^{78} +(-15.7882 - 6.53968i) q^{79} +(-1.34568 - 0.667191i) q^{80} +(6.66919 - 2.76247i) q^{81} +(-2.11139 + 0.893544i) q^{82} +(-0.710749 + 0.379903i) q^{83} +(1.44560 - 2.80696i) q^{84} +(0.816190 - 0.669830i) q^{85} +(0.141726 + 1.33428i) q^{86} +(-3.05618 - 2.04207i) q^{87} +(1.64614 - 5.91152i) q^{88} +(6.39067 + 9.56431i) q^{89} +(-0.0243790 + 0.268563i) q^{90} +(3.42952 + 1.83312i) q^{91} +(9.92208 + 1.81633i) q^{92} +(-0.649305 - 6.59250i) q^{93} +(2.75142 - 14.4073i) q^{94} +(-1.17831 + 1.17831i) q^{95} +(-3.90556 + 8.03097i) q^{96} +(-5.85150 - 5.85150i) q^{97} +(-1.16983 + 0.794664i) q^{98} +(-1.09643 + 0.107989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q+O(q^{10}) \) 752 * q	\( 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) \) 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more