LMFDB - Embedded newform 896.2.bn.b.141.44

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:	$784$
Relative dimension:	$49$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			141.44
Character	$\chi$	$=$	896.141
Dual form			896.2.bn.b.197.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30835 - 0.536867i) q^{2} +(-0.445686 - 1.46923i) q^{3} +(1.42355 - 1.40482i) q^{4} +(0.0111242 + 0.112946i) q^{5} +(-1.37189 - 1.68299i) q^{6} +(-0.555570 + 0.831470i) q^{7} +(1.10829 - 2.60225i) q^{8} +(0.534412 - 0.357083i) q^{9} +O(q^{10})$	\(q+(1.30835 - 0.536867i) q^{2} +(-0.445686 - 1.46923i) q^{3} +(1.42355 - 1.40482i) q^{4} +(0.0111242 + 0.112946i) q^{5} +(-1.37189 - 1.68299i) q^{6} +(-0.555570 + 0.831470i) q^{7} +(1.10829 - 2.60225i) q^{8} +(0.534412 - 0.357083i) q^{9} +(0.0751911 + 0.141800i) q^{10} +(1.94760 - 1.04101i) q^{11} +(-2.69845 - 1.46541i) q^{12} +(-4.72026 - 0.464905i) q^{13} +(-0.280490 + 1.38612i) q^{14} +(0.160985 - 0.0666822i) q^{15} +(0.0529711 - 3.99965i) q^{16} +(-4.49190 - 1.86060i) q^{17} +(0.507491 - 0.754097i) q^{18} +(5.80324 - 4.76260i) q^{19} +(0.174504 + 0.145156i) q^{20} +(1.46923 + 0.445686i) q^{21} +(1.98925 - 2.40761i) q^{22} +(-0.312426 + 1.57067i) q^{23} +(-4.31725 - 0.468552i) q^{24} +(4.89129 - 0.972939i) q^{25} +(-6.42534 + 1.92590i) q^{26} +(-4.32332 - 3.54805i) q^{27} +(0.377183 + 1.96411i) q^{28} +(0.0286577 - 0.0536148i) q^{29} +(0.174825 - 0.173671i) q^{30} +(-2.09000 + 2.09000i) q^{31} +(-2.07798 - 5.26137i) q^{32} +(-2.39751 - 2.39751i) q^{33} +(-6.87586 - 0.0227646i) q^{34} +(-0.100091 - 0.0534998i) q^{35} +(0.259124 - 1.25908i) q^{36} +(-0.691058 + 0.842057i) q^{37} +(5.03577 - 9.34670i) q^{38} +(1.42070 + 7.14235i) q^{39} +(0.306241 + 0.0962289i) q^{40} +(8.20175 + 1.63143i) q^{41} +(2.16154 - 0.205669i) q^{42} +(-3.11927 + 10.2829i) q^{43} +(1.31006 - 4.21796i) q^{44} +(0.0462758 + 0.0563872i) q^{45} +(0.434481 + 2.22272i) q^{46} +(-2.58708 + 6.24576i) q^{47} +(-5.90001 + 1.70476i) q^{48} +(-0.382683 - 0.923880i) q^{49} +(5.87717 - 3.89892i) q^{50} +(-0.731679 + 7.42887i) q^{51} +(-7.37262 + 5.96930i) q^{52} +(-5.83727 - 10.9208i) q^{53} +(-7.56124 - 2.32104i) q^{54} +(0.139243 + 0.208392i) q^{55} +(1.54795 + 2.36724i) q^{56} +(-9.58376 - 6.40367i) q^{57} +(0.00871021 - 0.0855322i) q^{58} +(2.25421 - 0.222020i) q^{59} +(0.135493 - 0.321080i) q^{60} +(6.60790 - 2.00448i) q^{61} +(-1.61240 + 3.85650i) q^{62} +0.642732i q^{63} +(-5.54337 - 5.76810i) q^{64} -0.538304i q^{65} +(-4.42391 - 1.84963i) q^{66} +(7.29886 - 2.21408i) q^{67} +(-9.00823 + 3.66164i) q^{68} +(2.44692 - 0.241001i) q^{69} +(-0.159676 - 0.0162607i) q^{70} +(2.81306 + 1.87963i) q^{71} +(-0.336932 - 1.78642i) q^{72} +(-5.81704 - 8.70581i) q^{73} +(-0.452071 + 1.47271i) q^{74} +(-3.60945 - 6.75280i) q^{75} +(1.57060 - 14.9323i) q^{76} +(-0.216457 + 2.19773i) q^{77} +(5.69326 + 8.58194i) q^{78} +(3.99462 + 9.64387i) q^{79} +(0.452332 - 0.0385099i) q^{80} +(-2.54817 + 6.15184i) q^{81} +(11.6066 - 2.26877i) q^{82} +(10.3569 + 12.6199i) q^{83} +(2.71762 - 1.42954i) q^{84} +(0.160178 - 0.528037i) q^{85} +(1.43944 + 15.1282i) q^{86} +(-0.0915448 - 0.0182094i) q^{87} +(-0.550464 - 6.22189i) q^{88} +(1.82155 + 9.15757i) q^{89} +(0.0908173 + 0.0489301i) q^{90} +(3.00899 - 3.66647i) q^{91} +(1.76176 + 2.67483i) q^{92} +(4.00217 + 2.13921i) q^{93} +(-0.0316531 + 9.56054i) q^{94} +(0.602470 + 0.602470i) q^{95} +(-6.80403 + 5.39794i) q^{96} +(-2.80154 + 2.80154i) q^{97} +(-0.996684 - 1.00331i) q^{98} +(0.669093 - 1.25178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q+O(q^{10}) $ 784 * q	$ 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) $ 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{32}\right)$

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 $

$2$	1.30835	−	0.536867i	0.925141	−	0.379623i
$2$	1.30835	−	0.536867i	0.925141	−	0.379623i
$3$	−0.445686	−	1.46923i	−0.257317	−	0.848260i	−0.986475	−	0.163914i	$-0.947588\pi$
$3$	−0.445686	−	1.46923i	−0.257317	−	0.848260i	0.729158	−	0.684345i	$-0.239912\pi$
$4$	1.42355	−	1.40482i	0.711773	−	0.702409i
$5$	0.0111242	+	0.112946i	0.00497488	+	0.0505108i	0.997352	−	0.0727302i	$-0.0231712\pi$
$5$	0.0111242	+	0.112946i	0.00497488	+	0.0505108i	−0.992377	+	0.123241i	$0.960671\pi$
$6$	−1.37189	−	1.68299i	−0.560073	−	0.687077i
$7$	−0.555570	+	0.831470i	−0.209986	+	0.314266i
$7$	−0.555570	+	0.831470i	−0.209986	+	0.314266i
$8$	1.10829	−	2.60225i	0.391841	−	0.920033i
$9$	0.534412	−	0.357083i	0.178137	−	0.119028i
$10$	0.0751911	+	0.141800i	0.0237775	+	0.0448410i
$11$	1.94760	−	1.04101i	0.587224	−	0.313878i	−0.150894	−	0.988550i	$-0.548215\pi$
$11$	1.94760	−	1.04101i	0.587224	−	0.313878i	0.738117	+	0.674672i	$0.235715\pi$
$12$	−2.69845	−	1.46541i	−0.778976	−	0.423027i
$13$	−4.72026	−	0.464905i	−1.30917	−	0.128942i	−0.580752	−	0.814080i	$-0.697242\pi$
$13$	−4.72026	−	0.464905i	−1.30917	−	0.128942i	−0.728413	+	0.685139i	$0.759742\pi$
$14$	−0.280490	+	1.38612i	−0.0749641	+	0.370456i
$15$	0.160985	−	0.0666822i	0.0415661	−	0.0172173i
$16$	0.0529711	−	3.99965i	0.0132428	−	0.999912i
$17$	−4.49190	−	1.86060i	−1.08944	−	0.451263i	−0.235632	−	0.971842i	$-0.575716\pi$
$17$	−4.49190	−	1.86060i	−1.08944	−	0.451263i	−0.853813	+	0.520580i	$0.825716\pi$
$18$	0.507491	−	0.754097i	0.119617	−	0.177742i
$19$	5.80324	−	4.76260i	1.33135	−	1.09261i	0.343182	−	0.939269i	$-0.388495\pi$
$19$	5.80324	−	4.76260i	1.33135	−	1.09261i	0.988173	−	0.153346i	$-0.0490048\pi$
$20$	0.174504	+	0.145156i	0.0390202	+	0.0324578i
$21$	1.46923	+	0.445686i	0.320612	+	0.0972566i
$22$	1.98925	−	2.40761i	0.424110	−	0.513305i
$23$	−0.312426	+	1.57067i	−0.0651454	+	0.327508i	−0.999591	−	0.0285978i	$-0.990896\pi$
$23$	−0.312426	+	1.57067i	−0.0651454	+	0.327508i	0.934446	+	0.356106i	$0.115896\pi$
$24$	−4.31725	−	0.468552i	−0.881254	−	0.0956427i
$25$	4.89129	−	0.972939i	0.978259	−	0.194588i
$26$	−6.42534	+	1.92590i	−1.26011	+	0.377699i
$27$	−4.32332	−	3.54805i	−0.832023	−	0.682823i
$28$	0.377183	+	1.96411i	0.0712810	+	0.371182i
$29$	0.0286577	−	0.0536148i	0.00532160	−	0.00995602i	−0.879246	−	0.476367i	$-0.841953\pi$
$29$	0.0286577	−	0.0536148i	0.00532160	−	0.00995602i	0.884568	+	0.466411i	$0.154453\pi$
$30$	0.174825	−	0.173671i	0.0319185	−	0.0317078i
$31$	−2.09000	+	2.09000i	−0.375375	+	0.375375i	−0.869431	−	0.494055i	$-0.835514\pi$
$31$	−2.09000	+	2.09000i	−0.375375	+	0.375375i	0.494055	+	0.869431i	$0.335514\pi$
$32$	−2.07798	−	5.26137i	−0.367338	−	0.930088i
$33$	−2.39751	−	2.39751i	−0.417352	−	0.417352i
$34$	−6.87586	−	0.0227646i	−1.17920	−	0.00390410i
$35$	−0.100091	−	0.0534998i	−0.0169185	−	0.00904311i
$36$	0.259124	−	1.25908i	0.0431874	−	0.209846i
$37$	−0.691058	+	0.842057i	−0.113609	+	0.138433i	−0.826710	−	0.562628i	$-0.809790\pi$
$37$	−0.691058	+	0.842057i	−0.113609	+	0.138433i	0.713101	+	0.701062i	$0.247290\pi$
$38$	5.03577	−	9.34670i	0.816910	−	1.51624i
$39$	1.42070	+	7.14235i	0.227494	+	1.14369i
$40$	0.306241	+	0.0962289i	0.0484210	+	0.0152151i
$41$	8.20175	+	1.63143i	1.28090	+	0.254786i	0.788203	−	0.615416i	$-0.211012\pi$
$41$	8.20175	+	1.63143i	1.28090	+	0.254786i	0.492695	+	0.870202i	$0.336012\pi$
$42$	2.16154	−	0.205669i	0.333532	−	0.0317354i
$43$	−3.11927	+	10.2829i	−0.475685	+	1.56812i	0.310777	+	0.950483i	$0.399411\pi$
$43$	−3.11927	+	10.2829i	−0.475685	+	1.56812i	−0.786462	+	0.617639i	$0.788089\pi$
$44$	1.31006	−	4.21796i	0.197500	−	0.635881i
$45$	0.0462758	+	0.0563872i	0.00689839	+	0.00840571i
$46$	0.434481	+	2.22272i	0.0640608	+	0.327722i
$47$	−2.58708	+	6.24576i	−0.377364	+	0.911038i	0.615094	+	0.788454i	$0.289118\pi$
$47$	−2.58708	+	6.24576i	−0.377364	+	0.911038i	−0.992458	+	0.122584i	$0.960882\pi$
$48$	−5.90001	+	1.70476i	−0.851593	+	0.246061i
$49$	−0.382683	−	0.923880i	−0.0546691	−	0.131983i
$50$	5.87717	−	3.89892i	0.831158	−	0.551390i
$51$	−0.731679	+	7.42887i	−0.102456	+	1.04025i
$52$	−7.37262	+	5.96930i	−1.02240	+	0.827792i
$53$	−5.83727	−	10.9208i	−0.801811	−	1.50008i	−0.864827	−	0.502070i	$-0.832572\pi$
$53$	−5.83727	−	10.9208i	−0.801811	−	1.50008i	0.0630163	−	0.998013i	$-0.479928\pi$
$54$	−7.56124	−	2.32104i	−1.02895	−	0.315854i
$55$	0.139243	+	0.208392i	0.0187756	+	0.0280996i
$56$	1.54795	+	2.36724i	0.206854	+	0.316336i
$57$	−9.58376	−	6.40367i	−1.26940	−	0.848186i
$58$	0.00871021	−	0.0855322i	0.00114371	−	0.0112309i
$59$	2.25421	−	0.222020i	0.293473	−	0.0289046i	0.0497906	−	0.998760i	$-0.484145\pi$
$59$	2.25421	−	0.222020i	0.293473	−	0.0289046i	0.243682	+	0.969855i	$0.421645\pi$
$60$	0.135493	−	0.321080i	0.0174921	−	0.0414512i
$61$	6.60790	−	2.00448i	0.846055	−	0.256648i	0.162647	−	0.986684i	$-0.447997\pi$
$61$	6.60790	−	2.00448i	0.846055	−	0.256648i	0.683408	+	0.730037i	$0.260497\pi$
$62$	−1.61240	+	3.85650i	−0.204774	+	0.489776i
$63$			0.642732i			0.0809766i
$64$	−5.54337	−	5.76810i	−0.692922	−	0.721013i
$65$		−	0.538304i		−	0.0667684i
$66$	−4.42391	−	1.84963i	−0.544546	−	0.227673i
$67$	7.29886	−	2.21408i	0.891697	−	0.270493i	0.188996	−	0.981978i	$-0.439477\pi$
$67$	7.29886	−	2.21408i	0.891697	−	0.270493i	0.702702	+	0.711485i	$0.251977\pi$
$68$	−9.00823	+	3.66164i	−1.09241	+	0.444039i
$69$	2.44692	−	0.241001i	0.294575	−	0.0290131i
$70$	−0.159676	−	0.0162607i	−0.0190850	−	0.00194352i
$71$	2.81306	+	1.87963i	0.333849	+	0.223070i	0.711184	−	0.703006i	$-0.248159\pi$
$71$	2.81306	+	1.87963i	0.333849	+	0.223070i	−0.377335	+	0.926077i	$0.623159\pi$
$72$	−0.336932	−	1.78642i	−0.0397078	−	0.210532i
$73$	−5.81704	−	8.70581i	−0.680833	−	1.01894i	−0.997518	−	0.0704079i	$-0.977570\pi$
$73$	−5.81704	−	8.70581i	−0.680833	−	1.01894i	0.316685	−	0.948531i	$-0.397430\pi$
$74$	−0.452071	+	1.47271i	−0.0525522	+	0.171199i
$75$	−3.60945	−	6.75280i	−0.416783	−	0.779747i
$76$	1.57060	−	14.9323i	0.180160	−	1.71285i
$77$	−0.216457	+	2.19773i	−0.0246676	+	0.250454i
$78$	5.69326	+	8.58194i	0.644635	+	0.971714i
$79$	3.99462	+	9.64387i	0.449430	+	1.08502i	0.972536	+	0.232753i	$0.0747732\pi$
$79$	3.99462	+	9.64387i	0.449430	+	1.08502i	−0.523106	+	0.852268i	$0.675227\pi$
$80$	0.452332	−	0.0385099i	0.0505722	−	0.00430554i
$81$	−2.54817	+	6.15184i	−0.283130	+	0.683537i
$82$	11.6066	−	2.26877i	1.28173	−	0.250544i
$83$	10.3569	+	12.6199i	1.13681	+	1.38521i	0.911689	+	0.410881i	$0.134779\pi$
$83$	10.3569	+	12.6199i	1.13681	+	1.38521i	0.225124	+	0.974330i	$0.427721\pi$
$84$	2.71762	−	1.42954i	0.296517	−	0.155976i
$85$	0.160178	−	0.528037i	0.0173738	−	0.0572737i
$86$	1.43944	+	15.1282i	0.155219	+	1.63132i
$87$	−0.0915448	−	0.0182094i	−0.00981463	−	0.00195225i
$88$	−0.550464	−	6.22189i	−0.0586796	−	0.663255i
$89$	1.82155	+	9.15757i	0.193084	+	0.970700i	0.948819	+	0.315822i	$0.102280\pi$
$89$	1.82155	+	9.15757i	0.193084	+	0.970700i	−0.755734	+	0.654878i	$0.772720\pi$
$90$	0.0908173	+	0.0489301i	0.00957298	+	0.00515769i
$91$	3.00899	−	3.66647i	0.315428	−	0.384350i
$92$	1.76176	+	2.67483i	0.183676	+	0.278870i
$93$	4.00217	+	2.13921i	0.415006	+	0.221825i
$94$	−0.0316531	+	9.56054i	−0.00326477	+	0.986095i
$95$	0.602470	+	0.602470i	0.0618122	+	0.0618122i
$96$	−6.80403	+	5.39794i	−0.694433	+	0.550925i
$97$	−2.80154	+	2.80154i	−0.284453	+	0.284453i	−0.834882	−	0.550429i	$-0.814464\pi$
$97$	−2.80154	+	2.80154i	−0.284453	+	0.284453i	0.550429	+	0.834882i	$0.314464\pi$
$98$	−0.996684	−	1.00331i	−0.100680	−	0.101349i
$99$	0.669093	−	1.25178i	0.0672464	−	0.125809i
$100$	5.59618	−	8.25640i	0.559618	−	0.825640i
$101$	4.31768	+	3.54343i	0.429626	+	0.352585i	0.824219	−	0.566271i	$-0.191615\pi$
$101$	4.31768	+	3.54343i	0.429626	+	0.352585i	−0.394593	+	0.918856i	$0.629115\pi$
$102$	3.03102	+	10.1124i	0.300116	+	1.00127i
$103$	−14.9418	+	2.97212i	−1.47226	+	0.292851i	−0.865049	−	0.501687i	$-0.832713\pi$
$103$	−14.9418	+	2.97212i	−1.47226	+	0.292851i	−0.607214	+	0.794538i	$0.707713\pi$
$104$	−6.44123	+	11.7680i	−0.631615	+	1.15395i
$105$	−0.0339943	+	0.170901i	−0.00331750	+	0.0166782i
$106$	−13.5002	−	11.1543i	−1.31125	−	1.08340i
$107$	11.8842	+	3.60504i	1.14889	+	0.348512i	0.806609	−	0.591085i	$-0.201300\pi$
$107$	11.8842	+	3.60504i	1.14889	+	0.348512i	0.342281	+	0.939597i	$0.388800\pi$
$108$	−11.1388	+	1.02265i	−1.07183	+	0.0984048i
$109$	11.9819	−	9.83331i	1.14766	−	0.941861i	0.148766	−	0.988872i	$-0.452470\pi$
$109$	11.9819	−	9.83331i	1.14766	−	0.941861i	0.998894	+	0.0470118i	$0.0149698\pi$
$110$	0.294058	+	0.197895i	0.0280373	+	0.0188685i
$111$	1.54517	+	0.640030i	0.146661	+	0.0607489i
$112$	3.29616	+	2.26613i	0.311458	+	0.214129i
$113$	6.73023	−	2.78775i	0.633126	−	0.262250i	−0.0429544	−	0.999077i	$-0.513677\pi$
$113$	6.73023	−	2.78775i	0.633126	−	0.262250i	0.676081	+	0.736827i	$0.263677\pi$
$114$	−15.9768	−	3.23301i	−1.49637	−	0.302799i
$115$	−0.180876	−	0.0178147i	−0.0168668	−	0.00166123i
$116$	−0.0345235	−	0.116582i	−0.00320542	−	0.0108244i
$117$	−2.68857	+	1.43707i	−0.248559	+	0.132857i
$118$	2.83009	−	1.50069i	0.260531	−	0.138150i
$119$	4.04260	−	2.70118i	0.370584	−	0.247617i
$120$	0.00489509	−	0.492826i	0.000446859	−	0.0449886i
$121$	−3.40183	+	5.09121i	−0.309258	+	0.462837i
$122$	7.56929	−	6.17013i	0.685291	−	0.558617i
$123$	−1.25846	−	12.7773i	−0.113471	−	1.15209i
$124$	−0.0391427	+	5.91129i	−0.00351512	+	0.530849i
$125$	0.329026	+	1.08465i	0.0294290	+	0.0970143i
$126$	0.345062	+	0.840917i	0.0307405	+	0.0749148i
$127$	16.4147			1.45657			0.728286	−	0.685273i	$-0.240317\pi$
$127$	16.4147			1.45657			0.728286	+	0.685273i	$0.240317\pi$
$128$	−10.3494	−	4.57063i	−0.914763	−	0.403990i
$129$	16.4981			1.45258
$130$	−0.288998	−	0.704289i	−0.0253468	−	0.0617702i
$131$	−0.0293800	−	0.0968528i	−0.00256694	−	0.00846207i	0.955648	−	0.294513i	$-0.0951574\pi$
$131$	−0.0293800	−	0.0968528i	−0.00256694	−	0.00846207i	−0.958214	+	0.286051i	$0.907657\pi$
$132$	−6.78102	−	0.0449018i	−0.590212	−	0.00390820i
$133$	0.735847	+	7.47118i	0.0638060	+	0.647833i
$134$	8.36077	−	6.81531i	0.722261	−	0.588753i
$135$	0.352644	−	0.527769i	0.0303507	−	0.0454231i
$136$	−9.82009	+	9.62693i	−0.842065	+	0.825502i
$137$	5.04810	−	3.37303i	0.431288	−	0.288178i	−0.320916	−	0.947108i	$-0.603991\pi$
$137$	5.04810	−	3.37303i	0.431288	−	0.288178i	0.752204	+	0.658930i	$0.228991\pi$
$138$	3.07204	−	1.62899i	0.261509	−	0.138669i
$139$	15.3897	−	8.22595i	1.30534	−	0.697716i	0.335630	−	0.941994i	$-0.391051\pi$
$139$	15.3897	−	8.22595i	1.30534	−	0.697716i	0.969705	+	0.244278i	$0.0785509\pi$
$140$	−0.217642	+	0.0644503i	−0.0183941	+	0.00544704i
$141$	10.3295	+	1.01736i	0.869898	+	0.0856775i
$142$	4.68957	+	0.948964i	0.393540	+	0.0796353i
$143$	−9.67716	+	4.00841i	−0.809245	+	0.335200i
$144$	−1.39990	−	2.15638i	−0.116658	−	0.179698i
$145$	0.00637435	+	0.00264034i	0.000529361	+	0.000219268i
$146$	−12.2846	−	8.26725i	−1.01668	−	0.684203i
$147$	−1.18683	+	0.974009i	−0.0978884	+	0.0803349i
$148$	0.199183	+	2.16952i	0.0163728	+	0.178333i
$149$	−20.2147	−	6.13205i	−1.65605	−	0.502357i	−0.682510	−	0.730877i	$-0.739111\pi$
$149$	−20.2147	−	6.13205i	−1.65605	−	0.502357i	−0.973539	+	0.228520i	$0.926611\pi$
$150$	−8.34777	−	6.89722i	−0.681593	−	0.563156i
$151$	−0.255826	+	1.28613i	−0.0208189	+	0.104663i	−0.989798	−	0.142481i	$-0.954492\pi$
$151$	−0.255826	+	1.28613i	−0.0208189	+	0.104663i	0.968979	+	0.247144i	$0.0794921\pi$
$152$	−5.96176	−	20.3798i	−0.483563	−	1.65302i
$153$	−3.06491	+	0.609649i	−0.247783	+	0.0492872i
$154$	0.896687	+	2.99160i	0.0722571	+	0.241070i
$155$	−0.259306	−	0.212807i	−0.0208280	−	0.0170931i
$156$	12.0561	+	8.17164i	0.965263	+	0.654255i
$157$	5.31884	−	9.95086i	0.424490	−	0.794165i	−0.575226	−	0.817994i	$-0.695086\pi$
$157$	5.31884	−	9.95086i	0.424490	−	0.794165i	0.999716	+	0.0238296i	$0.00758591\pi$
$158$	10.4038	+	10.4730i	0.827685	+	0.833183i
$159$	−13.4435	+	13.4435i	−1.06614	+	1.06614i
$160$	0.571133	−	0.293227i	0.0451520	−	0.0231816i
$161$	−1.13239	−	1.13239i	−0.0892451	−	0.0892451i
$162$	−0.0311771	+	9.41677i	−0.00244950	+	0.739852i
$163$	8.02134	+	4.28750i	0.628280	+	0.335823i	0.754618	−	0.656165i	$-0.227822\pi$
$163$	8.02134	+	4.28750i	0.628280	+	0.335823i	−0.126338	+	0.991987i	$0.540322\pi$
$164$	13.9674	−	9.19955i	1.09067	−	0.718364i
$165$	0.244117	−	0.297458i	0.0190045	−	0.0231571i
$166$	20.3256	+	10.9509i	1.57757	+	0.849956i
$167$	−3.51597	−	17.6760i	−0.272074	−	1.36781i	−0.839041	−	0.544068i	$-0.816883\pi$
$167$	−3.51597	−	17.6760i	−0.272074	−	1.36781i	0.566967	−	0.823740i	$-0.308117\pi$
$168$	2.78812	−	3.32934i	0.215108	−	0.256865i
$169$	9.31453	+	1.85277i	0.716502	+	0.142521i
$170$	−0.0739170	−	0.776851i	−0.00566918	−	0.0595817i
$171$	1.40068	−	4.61742i	0.107113	−	0.353103i
$172$	10.0051	+	19.0201i	0.762883	+	1.45027i
$173$	−8.48140	−	10.3346i	−0.644829	−	0.785726i	0.343321	−	0.939218i	$-0.388448\pi$
$173$	−8.48140	−	10.3346i	−0.644829	−	0.785726i	−0.988150	+	0.153492i	$0.950948\pi$
$174$	−0.129548	+	0.0253232i	−0.00982104	+	0.00191975i
$175$	−1.90849	+	4.60750i	−0.144268	+	0.348294i
$176$	−4.06053	−	7.84486i	−0.306074	−	0.591329i
$177$	−1.33087	−	3.21300i	−0.100034	−	0.241504i
$178$	7.29962	+	11.0033i	0.547130	+	0.824736i
$179$	−1.62992	+	16.5489i	−0.121826	+	1.23692i	0.718767	+	0.695251i	$0.244707\pi$
$179$	−1.62992	+	16.5489i	−0.121826	+	1.23692i	−0.840593	+	0.541668i	$0.817793\pi$
$180$	0.145090	+	0.0152608i	0.0108143	+	0.00113747i
$181$	5.62431	+	10.5223i	0.418052	+	0.782120i	0.999505	−	0.0314599i	$-0.0100156\pi$
$181$	5.62431	+	10.5223i	0.418052	+	0.782120i	−0.581453	+	0.813580i	$0.697516\pi$
$182$	1.96840	−	6.41244i	0.145908	−	0.475322i
$183$	−5.89009	−	8.81514i	−0.435408	−	0.651634i
$184$	3.74102	+	2.55378i	0.275792	+	0.188267i
$185$	−0.102794	−	0.0686848i	−0.00755757	−	0.00504980i
$186$	6.38471	+	0.650189i	0.468149	+	0.0476742i
$187$	−10.6853	+	1.05241i	−0.781389	+	0.0769601i
$188$	5.09133	+	12.5255i	0.371323	+	0.913516i
$189$	5.35201	−	1.62351i	0.389301	−	0.118093i
$190$	1.11169	+	0.464794i	0.0806503	+	0.0337197i
$191$			17.8861i			1.29419i	0.762408	+	0.647097i	$0.224017\pi$
$191$			17.8861i			1.29419i	−0.762408	+	0.647097i	$0.775983\pi$
$192$	−6.00406	+	10.7152i	−0.433306	+	0.773306i
$193$			3.13324i			0.225536i	0.993621	+	0.112768i	$0.0359716\pi$
$193$			3.13324i			0.225536i	−0.993621	+	0.112768i	$0.964028\pi$
$194$	−2.16133	+	5.16944i	−0.155174	+	0.371144i
$195$	−0.790892	+	0.239914i	−0.0566370	+	0.0171806i
$196$	−1.84265	−	0.777585i	−0.131618	−	0.0555418i
$197$	2.11558	−	0.208366i	0.150729	−	0.0148455i	−0.0223714	−	0.999750i	$-0.507122\pi$
$197$	2.11558	−	0.208366i	0.150729	−	0.0148455i	0.173100	+	0.984904i	$0.444622\pi$
$198$	0.203364	−	1.99698i	0.0144524	−	0.141919i
$199$	20.2444	+	13.5269i	1.43509	+	0.958894i	0.998237	+	0.0593601i	$0.0189060\pi$
$199$	20.2444	+	13.5269i	1.43509	+	0.958894i	0.436850	+	0.899534i	$0.356094\pi$
$200$	2.88916	−	13.8067i	0.204294	−	0.976278i
$201$	−6.50599	−	9.73690i	−0.458897	−	0.686788i
$202$	7.55138	+	2.31802i	0.531313	+	0.163095i
$203$	0.0286577	+	0.0536148i	0.00201138	+	0.00376302i
$204$	9.39463	+	11.6032i	0.657755	+	0.812388i
$205$	−0.0930250	+	0.944499i	−0.00649715	+	0.0659667i
$206$	−17.9535	+	11.9103i	−1.25088	+	0.829833i
$207$	0.393896	+	0.950949i	0.0273777	+	0.0660955i
$208$	−2.10950	+	18.8548i	−0.146267	+	1.30734i
$209$	6.34446	−	15.3169i	0.438856	−	1.05949i
$210$	0.0472747	+	0.241848i	0.00326226	+	0.0166891i
$211$	−11.8944	−	14.4933i	−0.818843	−	0.997763i	−0.999898	−	0.0142898i	$-0.995451\pi$
$211$	−11.8944	−	14.4933i	−0.818843	−	0.997763i	0.181055	−	0.983473i	$-0.442049\pi$
$212$	−23.6513	−	7.34592i	−1.62438	−	0.504520i
$213$	1.50786	−	4.97075i	0.103317	−	0.340590i
$214$	17.4841	−	1.66361i	1.19519	−	0.113722i
$215$	−1.19610	−	0.237920i	−0.0815735	−	0.0162260i
$216$	−14.0244	+	7.31805i	−0.954240	+	0.497930i
$217$	−0.576630	−	2.89892i	−0.0391442	−	0.196791i
$218$	10.3973	−	19.2981i	0.704197	−	1.30703i
$219$	−10.1983	+	12.4266i	−0.689135	+	0.839713i
$220$	0.490973	+	0.101045i	0.0331014	+	0.00681244i
$221$	20.3379	+	10.8708i	1.36808	+	0.731252i
$222$	2.36523	+	0.00783081i	0.158744	+	0.000525569i
$223$	11.9512	+	11.9512i	0.800309	+	0.800309i	0.983144	−	0.182835i	$-0.0585274\pi$
$223$	11.9512	+	11.9512i	0.800309	+	0.800309i	−0.182835	+	0.983144i	$0.558527\pi$
$224$	5.52913	+	1.19529i	0.369431	+	0.0798634i
$225$	2.26655	−	2.26655i	0.151103	−	0.151103i
$226$	7.30882	−	7.26059i	0.486176	−	0.482967i
$227$	−0.885811	+	1.65724i	−0.0587933	+	0.109995i	−0.909601	−	0.415482i	$-0.863613\pi$
$227$	−0.885811	+	1.65724i	−0.0587933	+	0.109995i	0.850808	+	0.525477i	$0.176113\pi$
$228$	−22.6389	+	4.34753i	−1.49930	+	0.287922i
$229$	2.53478	+	2.08024i	0.167503	+	0.137466i	0.714410	−	0.699727i	$-0.246695\pi$
$229$	2.53478	+	2.08024i	0.167503	+	0.137466i	−0.546907	+	0.837193i	$0.684195\pi$
$230$	−0.246213	+	0.0737986i	−0.0162348	+	0.00486614i
$231$	3.32544	−	0.661470i	0.218798	−	0.0435216i
$232$	−0.107758	−	0.133995i	−0.00707465	−	0.00879723i
$233$	0.155944	−	0.783984i	0.0102162	−	0.0513605i	−0.975341	−	0.220704i	$-0.929165\pi$
$233$	0.155944	−	0.783984i	0.0102162	−	0.0513605i	0.985557	+	0.169343i	$0.0541646\pi$
$234$	−2.74607	+	3.32360i	−0.179516	+	0.217270i
$235$	−0.734210	−	0.222720i	−0.0478946	−	0.0145287i
$236$	2.89707	−	3.48281i	0.188583	−	0.226712i
$237$	12.3887	−	10.1671i	0.804733	−	0.660427i
$238$	3.83895	−	5.70442i	0.248842	−	0.369763i
$239$	−9.72952	−	4.03010i	−0.629350	−	0.260685i	0.0451268	−	0.998981i	$-0.485631\pi$
$239$	−9.72952	−	4.03010i	−0.629350	−	0.260685i	−0.674477	+	0.738296i	$0.735631\pi$
$240$	−0.258178	−	0.647416i	−0.0166653	−	0.0417905i
$241$	−26.5419	+	10.9940i	−1.70972	+	0.708188i	−0.709723	+	0.704481i	$0.751180\pi$
$241$	−26.5419	+	10.9940i	−1.70972	+	0.708188i	−0.999993	+	0.00370691i	$0.998820\pi$
$242$	−1.71748	+	8.48740i	−0.110404	+	0.545591i
$243$	−6.52356	−	0.642515i	−0.418487	−	0.0412173i
$244$	6.59072	−	12.1364i	0.421927	−	0.776952i
$245$	0.100091	−	0.0534998i	0.00639458	−	0.00341798i
$246$	−8.50624	−	16.0416i	−0.542338	−	1.02277i
$247$	−29.6070	+	19.7827i	−1.88385	+	1.25875i
$248$	3.12237	+	7.75503i	0.198270	+	0.492445i
$249$	13.9256	−	20.8411i	0.882497	−	1.32075i
$250$	1.01279	+	1.24246i	0.0640547	+	0.0785800i
$251$	1.12974	+	11.4705i	0.0713088	+	0.724010i	0.962663	+	0.270703i	$0.0872560\pi$
$251$	1.12974	+	11.4705i	0.0713088	+	0.724010i	−0.891354	+	0.453307i	$0.850244\pi$
$252$	0.902921	+	0.914959i	0.0568787	+	0.0576370i
$253$	1.02661	+	3.38429i	0.0645425	+	0.212768i
$254$	21.4762	−	8.81253i	1.34754	−	0.552948i
$255$	−0.847197			−0.0530535
$256$	−15.9944	−	0.423732i	−0.999649	−	0.0264832i
$257$	0.750530			0.0468168			0.0234084	−	0.999726i	$-0.492548\pi$
$257$	0.750530			0.0468168			0.0234084	+	0.999726i	$0.492548\pi$
$258$	21.5852	−	8.85729i	1.34384	−	0.551431i
$259$	−0.316213	−	1.04242i	−0.0196485	−	0.0647725i
$260$	−0.756220	−	0.766301i	−0.0468988	−	0.0475240i
$261$	−0.00382989	−	0.0388856i	−0.000237065	−	0.00240696i
$262$	−0.0904363	−	0.110944i	−0.00558717	−	0.00685414i
$263$	−8.69683	+	13.0157i	−0.536270	+	0.802584i	−0.996356	−	0.0852899i	$-0.972818\pi$
$263$	−8.69683	+	13.0157i	−0.536270	+	0.802584i	0.460087	+	0.887874i	$0.347818\pi$
$264$	−8.89604	+	3.58176i	−0.547513	+	0.220442i
$265$	1.16852	−	0.780778i	0.0717814	−	0.0479628i
$266$	4.97377	+	9.37984i	0.304962	+	0.575115i
$267$	12.6427	−	6.75767i	0.773722	−	0.413563i
$268$	7.27988	−	13.4054i	0.444689	−	0.818866i
$269$	−15.3488	−	1.51172i	−0.935832	−	0.0921714i	−0.381409	−	0.924406i	$-0.624561\pi$
$269$	−15.3488	−	1.51172i	−0.935832	−	0.0921714i	−0.554423	+	0.832235i	$0.687061\pi$
$270$	0.178039	−	0.879828i	0.0108351	−	0.0535446i
$271$	−2.09477	+	0.867681i	−0.127248	+	0.0527079i	−0.445399	−	0.895332i	$-0.646938\pi$
$271$	−2.09477	+	0.867681i	−0.127248	+	0.0527079i	0.318151	+	0.948040i	$0.396938\pi$
$272$	−7.67970	+	17.8674i	−0.465650	+	1.08337i
$273$	−6.72794	−	2.78680i	−0.407194	−	0.168665i
$274$	4.79380	−	7.12326i	0.289604	−	0.430332i
$275$	8.51344	−	6.98680i	0.513380	−	0.421320i
$276$	3.14475	−	3.78056i	0.189292	−	0.227563i
$277$	21.3032	+	6.46225i	1.27998	+	0.388279i	0.855805	−	0.517299i	$-0.173063\pi$
$277$	21.3032	+	6.46225i	1.27998	+	0.388279i	0.424179	+	0.905578i	$0.360563\pi$
$278$	15.7188	−	19.0246i	0.942751	−	1.14102i
$279$	−0.370619	+	1.86323i	−0.0221884	+	0.111548i
$280$	−0.250150	+	0.201168i	−0.0149493	+	0.0120221i
$281$	−31.2628	+	6.21856i	−1.86498	+	0.370968i	−0.992955	−	0.118489i	$-0.962195\pi$
$281$	−31.2628	+	6.21856i	−1.86498	+	0.370968i	−0.872027	+	0.489458i	$0.837195\pi$
$282$	14.0607	−	4.21449i	0.837304	−	0.250969i
$283$	0.807096	+	0.662367i	0.0479769	+	0.0393736i	0.658076	−	0.752951i	$-0.271370\pi$
$283$	0.807096	+	0.662367i	0.0479769	+	0.0393736i	−0.610099	+	0.792325i	$0.708870\pi$
$284$	6.64505	−	1.27610i	0.394311	−	0.0757227i
$285$	0.616654	−	1.15368i	0.0365274	−	0.0683380i
$286$	−10.5091	+	10.4397i	−0.621416	+	0.617315i
$287$	−5.91313	+	5.91313i	−0.349041	+	0.349041i
$288$	−2.98924	−	2.06973i	−0.176143	−	0.121960i
$289$	4.69446	+	4.69446i	0.276145	+	0.276145i
$290$	0.00975738		3.23048e-5i	0.000572973		1.89700e-6i
$291$	5.36470	+	2.86749i	0.314484	+	0.168095i
$292$	−20.5109	−	4.22125i	−1.20031	−	0.247030i
$293$	−10.0806	+	12.2833i	−0.588916	+	0.717596i	−0.979154	−	0.203118i	$-0.934892\pi$
$293$	−10.0806	+	12.2833i	−0.588916	+	0.717596i	0.390239	+	0.920714i	$0.372392\pi$
$294$	−1.02988	+	1.91151i	−0.0600637	+	0.111482i
$295$	0.0501524	+	0.252133i	0.00291998	+	0.0146798i
$296$	1.42534	+	2.73155i	0.0828465	+	0.158768i
$297$	−12.1137	−	2.40956i	−0.702906	−	0.139817i
$298$	−29.7399	+	2.82974i	−1.72279	+	0.163922i
$299$	2.20495	−	7.26874i	0.127516	−	0.420362i
$300$	−14.6247	−	4.54231i	−0.844356	−	0.262251i
$301$	−6.81691	−	8.30643i	−0.392920	−	0.478775i
$302$	0.355769	+	1.82004i	0.0204722	+	0.104732i
$303$	3.28178	−	7.92292i	0.188533	−	0.455160i
$304$	−18.7413	−	23.4632i	−1.07489	−	1.34571i
$305$	0.299905	+	0.724034i	0.0171725	+	0.0414581i
$306$	−3.68267	+	2.44308i	−0.210524	+	0.139662i
$307$	1.54093	−	15.6453i	0.0879454	−	0.892924i	−0.845445	−	0.534062i	$-0.820665\pi$
$307$	1.54093	−	15.6453i	0.0879454	−	0.892924i	0.933391	−	0.358862i	$-0.116835\pi$
$308$	2.77927	+	3.43265i	0.158364	+	0.195593i
$309$	11.0261	+	20.6283i	0.627252	+	1.17351i
$310$	−0.453511	−	0.139212i	−0.0257577	−	0.00790674i
$311$	−17.8589	−	26.7278i	−1.01269	−	1.51559i	−0.848523	−	0.529159i	$-0.822508\pi$
$311$	−17.8589	−	26.7278i	−1.01269	−	1.51559i	−0.164163	−	0.986433i	$-0.552492\pi$
$312$	20.1607	+	4.21880i	1.14137	+	0.238842i
$313$	2.87515	+	1.92111i	0.162513	+	0.108588i	0.634167	−	0.773196i	$-0.281343\pi$
$313$	2.87515	+	1.92111i	0.162513	+	0.108588i	−0.471654	+	0.881784i	$0.656343\pi$
$314$	1.61661	−	15.8747i	0.0912304	−	0.895861i
$315$	−0.0725937	+	0.00714985i	−0.00409019	+	0.000402849i
$316$	19.2344	+	8.11678i	1.08202	+	0.456605i
$317$	10.4618	−	3.17356i	0.587595	−	0.178245i	0.0175323	−	0.999846i	$-0.494419\pi$
$317$	10.4618	−	3.17356i	0.587595	−	0.178245i	0.570062	+	0.821601i	$0.306919\pi$
$318$	−10.3714	+	24.8062i	−0.581599	+	1.39106i
$319$		−	0.134253i		−	0.00751675i
$320$	0.589816	−	0.690265i	0.0329717	−	0.0385870i
$321$		−	19.0673i		−	1.06424i
$322$	−2.08951	−	0.873619i	−0.116444	−	0.0486849i
$323$	−34.9289	+	10.5956i	−1.94349	+	0.589552i
$324$	5.01477	+	12.3372i	0.278598	+	0.685397i
$325$	−23.5405	+	2.31854i	−1.30579	+	0.128609i
$326$	12.7965	+	1.30314i	0.708734	+	0.0721742i
$327$	−19.7876	−	13.2216i	−1.09425	−	0.731157i
$328$	13.3353	−	19.5349i	0.736320	−	1.07863i
$329$	−3.75586	−	5.62103i	−0.207067	−	0.309898i
$330$	0.159695	−	0.520237i	0.00879092	−	0.0286381i
$331$	−16.2163	−	30.3386i	−0.891330	−	1.66756i	−0.733058	−	0.680167i	$-0.761907\pi$
$331$	−16.2163	−	30.3386i	−0.891330	−	1.66756i	−0.158273	−	0.987395i	$-0.550593\pi$
$332$	32.4721	+	3.41547i	1.78214	+	0.187448i
$333$	−0.0686259	+	0.696770i	−0.00376067	+	0.0381828i
$334$	−14.0898	−	21.2387i	−0.770958	−	1.16213i
$335$	0.331265	+	0.799744i	0.0180989	+	0.0436947i
$336$	1.86041	−	5.85279i	0.101494	−	0.319296i
$337$	−12.8709	+	31.0731i	−0.701122	+	1.69266i	0.0199527	+	0.999801i	$0.493648\pi$
$337$	−12.8709	+	31.0731i	−0.701122	+	1.69266i	−0.721075	+	0.692857i	$0.756352\pi$
$338$	13.1813	−	2.57659i	0.716970	−	0.140148i
$339$	−7.09541	−	8.64578i	−0.385370	−	0.469574i
$340$	−0.513775	−	0.976707i	−0.0278634	−	0.0529694i
$341$	−1.89477	+	6.24621i	−0.102607	+	0.338251i
$342$	−0.646368	−	6.79318i	−0.0349516	−	0.367333i
$343$	0.980785	+	0.195090i	0.0529574	+	0.0105339i
$344$	23.3015	+	19.5135i	1.25633	+	1.05210i
$345$	0.0544400	+	0.273688i	0.00293095	+	0.0147349i
$346$	−16.6449	−	8.96788i	−0.894838	−	0.482116i
$347$	−3.29977	+	4.02078i	−0.177141	+	0.215847i	−0.854010	−	0.520257i	$-0.825836\pi$
$347$	−3.29977	+	4.02078i	−0.177141	+	0.215847i	0.676869	+	0.736103i	$0.263336\pi$
$348$	−0.155899	+	0.102682i	−0.00835707	+	0.00550432i
$349$	24.4862	+	13.0882i	1.31072	+	0.700593i	0.970806	−	0.239865i	$-0.0771032\pi$
$349$	24.4862	+	13.0882i	1.31072	+	0.700593i	0.339911	+	0.940458i	$0.389603\pi$
$350$	−0.0233505	+	7.05281i	−0.00124814	+	0.376989i
$351$	18.7577	+	18.7577i	1.00121	+	1.00121i
$352$	−9.52423	−	8.08384i	−0.507643	−	0.430870i
$353$	−3.06829	+	3.06829i	−0.163309	+	0.163309i	−0.784031	−	0.620722i	$-0.786840\pi$
$353$	−3.06829	+	3.06829i	−0.163309	+	0.163309i	0.620722	+	0.784031i	$0.286840\pi$
$354$	−3.46619	−	3.48922i	−0.184226	−	0.185450i
$355$	−0.181002	+	0.338632i	−0.00960661	+	0.0179727i
$356$	15.4578	+	10.4773i	0.819261	+	0.555294i
$357$	−5.77038	−	4.73563i	−0.305401	−	0.250636i
$358$	6.75204	+	22.5267i	0.356856	+	1.19057i
$359$	−18.1623	+	3.61270i	−0.958568	+	0.190671i	−0.649494	−	0.760367i	$-0.725019\pi$
$359$	−18.1623	+	3.61270i	−0.958568	+	0.190671i	−0.309074	+	0.951038i	$0.600019\pi$
$360$	0.198021	−	0.0579275i	0.0104366	−	0.00305304i
$361$	7.28856	−	36.6421i	0.383608	−	1.92853i
$362$	13.0077	+	10.7474i	0.683668	+	0.564870i
$363$	8.99629	+	2.72900i	0.472183	+	0.143235i
$364$	−0.867279	−	9.44647i	−0.0454578	−	0.495130i
$365$	0.918573	−	0.753854i	0.0480803	−	0.0394585i
$366$	−12.4388	−	8.37107i	−0.650189	−	0.437563i
$367$	11.0517	+	4.57775i	0.576893	+	0.238957i	0.652000	−	0.758219i	$-0.273930\pi$
$367$	11.0517	+	4.57775i	0.576893	+	0.238957i	−0.0751076	+	0.997175i	$0.523930\pi$
$368$	6.26560	+	1.33280i	0.326617	+	0.0694768i
$369$	4.96567	−	2.05685i	0.258502	−	0.107075i
$370$	−0.171365	−	0.0346768i	−0.00890884	−	0.00180276i
$371$	12.3233	+	1.21374i	0.639794	+	0.0630142i
$372$	8.70248	−	2.57707i	0.451203	−	0.133615i
$373$	−2.92485	+	1.56336i	−0.151443	+	0.0809480i	−0.545377	−	0.838191i	$-0.683614\pi$
$373$	−2.92485	+	1.56336i	−0.151443	+	0.0809480i	0.393934	+	0.919139i	$0.371114\pi$
$374$	−13.4151	+	7.11353i	−0.693680	+	0.367832i
$375$	1.44696	−	0.966828i	0.0747207	−	0.0499268i
$376$	13.3858	+	13.6543i	0.690318	+	0.704169i
$377$	−0.160198	+	0.239753i	−0.00825060	+	0.0123479i
$378$	6.13067	−	4.99744i	0.315328	−	0.257040i
$379$	−1.15376	−	11.7144i	−0.0592649	−	0.601726i	−0.978249	−	0.207432i	$-0.933489\pi$
$379$	−1.15376	−	11.7144i	−0.0592649	−	0.601726i	0.918984	−	0.394294i	$-0.129011\pi$
$380$	1.70401	+	0.0112834i	0.0874137	+	0.000578825i
$381$	−7.31581	−	24.1170i	−0.374800	−	1.23555i
$382$	9.60247	+	23.4013i	0.491305	+	1.19731i
$383$	−19.4130			−0.991956			−0.495978	−	0.868335i	$-0.665190\pi$
$383$	−19.4130			−0.991956			−0.495978	+	0.868335i	$0.665190\pi$
$384$	−2.10273	+	17.2426i	−0.107305	+	0.879910i
$385$	−0.250631			−0.0127734
$386$	1.68214	+	4.09937i	0.0856184	+	0.208652i
$387$	2.00486	+	6.60912i	0.101913	+	0.335961i
$388$	−0.0524687	+	7.92377i	−0.00266369	+	0.402268i
$389$	−0.547880	−	5.56272i	−0.0277786	−	0.282041i	−0.999032	−	0.0439924i	$-0.985992\pi$
$389$	−0.547880	−	5.56272i	−0.0277786	−	0.282041i	0.971253	−	0.238049i	$-0.0765077\pi$
$390$	−0.905959	+	0.738496i	−0.0458750	+	0.0373952i
$391$	4.32579	−	6.47400i	0.218765	−	0.327404i
$392$	−2.82829	−	0.0280925i	−0.142850	−	0.00141889i
$393$	−0.129205	+	0.0863318i	−0.00651751	+	0.00435486i
$394$	2.65604	−	1.40840i	0.133810	−	0.0709541i
$395$	−1.04480	+	0.558455i	−0.0525694	+	0.0280989i
$396$	−0.806045	−	2.72193i	−0.0405053	−	0.136782i
$397$	22.9941	+	2.26472i	1.15404	+	0.113663i	0.656881	−	0.753995i	$-0.271876\pi$
$397$	22.9941	+	2.26472i	1.15404	+	0.113663i	0.497162	+	0.867658i	$0.334376\pi$
$398$	33.7488	+	6.82929i	1.69168	+	0.342322i
$399$	10.6489	−	4.41092i	0.533112	−	0.220822i
$400$	−3.63232	−	19.6150i	−0.181616	−	0.980750i
$401$	−31.5998	−	13.0890i	−1.57802	−	0.653636i	−0.589919	−	0.807463i	$-0.700840\pi$
$401$	−31.5998	−	13.0890i	−1.57802	−	0.653636i	−0.988098	+	0.153827i	$0.950840\pi$
$402$	−13.7395	−	9.24640i	−0.685265	−	0.461169i
$403$	10.8370	−	8.89370i	0.539830	−	0.443027i
$404$	11.1243	−	1.02132i	0.553455	−	0.0508126i
$405$	−0.723169	−	0.219371i	−0.0359346	−	0.0109006i
$406$	0.0662783	+	0.0547614i	0.00328934	+	0.00271776i
$407$	−0.469312	+	2.35939i	−0.0232629	+	0.116951i
$408$	18.5208	+	10.1374i	0.916917	+	0.501875i
$409$	−13.7453	+	2.73411i	−0.679662	+	0.135193i	−0.522836	−	0.852433i	$-0.675126\pi$
$409$	−13.7453	+	2.73411i	−0.679662	+	0.135193i	−0.156826	+	0.987626i	$0.550126\pi$
$410$	0.385362	+	1.28568i	0.0190317	+	0.0634950i
$411$	−7.20562	−	5.91350i	−0.355427	−	0.291691i
$412$	−17.0951	+	25.2215i	−0.842216	+	1.24257i
$413$	−1.06777	+	1.99765i	−0.0525414	+	0.0982981i
$414$	1.02589	+	1.03270i	0.0504196	+	0.0507545i
$415$	−1.31015	+	1.31015i	−0.0643126	+	0.0643126i
$416$	7.36256	+	25.8011i	0.360979	+	1.26500i
$417$	−18.9448	−	18.9448i	−0.927729	−	0.927729i
$418$	0.0776250	−	23.4460i	0.00379676	−	1.14678i
$419$	−9.72450	−	5.19785i	−0.475073	−	0.253932i	0.216440	−	0.976296i	$-0.430555\pi$
$419$	−9.72450	−	5.19785i	−0.475073	−	0.253932i	−0.691513	+	0.722364i	$0.743055\pi$
$420$	0.191692	+	0.291041i	0.00935361	+	0.0142013i
$421$	11.9468	−	14.5572i	0.582250	−	0.709474i	−0.395684	−	0.918387i	$-0.629493\pi$
$421$	11.9468	−	14.5572i	0.582250	−	0.709474i	0.977934	+	0.208913i	$0.0669926\pi$
$422$	−23.3430	−	12.5766i	−1.13632	−	0.612221i
$423$	0.847687	+	4.26161i	0.0412159	+	0.207206i
$424$	−34.8879	+	3.08661i	−1.69431	+	0.149899i
$425$	−23.7814	−	4.73042i	−1.15357	−	0.229459i
$426$	−0.695828	−	7.31299i	−0.0337130	−	0.354315i
$427$	−2.00448	+	6.60790i	−0.0970038	+	0.319779i
$428$	21.9822	−	11.5632i	1.06255	−	0.558929i
$429$	10.2022	+	12.4315i	0.492569	+	0.600197i
$430$	−1.69265	+	0.330867i	−0.0816268	+	0.0159558i
$431$	1.34949	−	3.25795i	0.0650024	−	0.156930i	−0.888040	−	0.459766i	$-0.847933\pi$
$431$	1.34949	−	3.25795i	0.0650024	−	0.156930i	0.953043	+	0.302836i	$0.0979334\pi$
$432$	−14.4200	+	17.1038i	−0.693782	+	0.822907i
$433$	1.45928	+	3.52300i	0.0701283	+	0.169305i	0.955057	−	0.296421i	$-0.0957932\pi$
$433$	1.45928	+	3.52300i	0.0701283	+	0.169305i	−0.884929	+	0.465726i	$0.845793\pi$
$434$	−2.31077	−	3.48322i	−0.110920	−	0.167200i
$435$	0.00103831	−	0.0105421i	4.97832e−5	−	0.000505457i
$436$	3.24282	−	30.8306i	0.155303	−	1.47652i
$437$	5.66740	+	10.6030i	0.271109	+	0.507208i
$438$	−6.67142	+	21.7334i	−0.318773	+	1.03846i
$439$	−7.54253	−	11.2882i	−0.359985	−	0.538756i	0.606631	−	0.794983i	$-0.292520\pi$
$439$	−7.54253	−	11.2882i	−0.359985	−	0.538756i	−0.966617	+	0.256227i	$0.917520\pi$
$440$	0.696611	−	0.131386i	0.0332096	−	0.00626357i
$441$	−0.534412	−	0.357083i	−0.0254482	−	0.0170039i
$442$	32.4453	+	3.30408i	1.54326	+	0.157159i
$443$	−16.3800	+	1.61329i	−0.778237	+	0.0766497i	−0.479333	−	0.877633i	$-0.659121\pi$
$443$	−16.3800	+	1.61329i	−0.778237	+	0.0766497i	−0.298905	+	0.954283i	$0.596621\pi$
$444$	3.09875	−	1.25957i	0.147060	−	0.0597765i
$445$	−1.01404	+	0.307607i	−0.0480703	+	0.0145820i
$446$	22.0525	+	9.22008i	1.04421	+	0.436584i
$447$			32.4329i			1.53402i
$448$	7.87574	−	1.40456i	0.372094	−	0.0663592i
$449$		−	1.20416i		−	0.0568279i	−0.999596	−	0.0284140i	$-0.990954\pi$
$449$		−	1.20416i		−	0.0568279i	0.999596	−	0.0284140i	$-0.00904566\pi$
$450$	1.74860	−	4.18226i	0.0824296	−	0.197154i
$451$	17.6721	−	5.36076i	0.832145	−	0.252428i
$452$	5.66451	−	13.4232i	0.266436	−	0.631376i
$453$	2.00363	−	0.197340i	0.0941388	−	0.00927186i
$454$	−0.269233	+	2.64380i	−0.0126357	+	0.124080i
$455$	0.447584	+	0.299066i	0.0209830	+	0.0140204i
$456$	−27.2855	+	17.8422i	−1.27776	+	0.835537i
$457$	9.03140	+	13.5164i	0.422471	+	0.632273i	0.980261	−	0.197710i	$-0.0633504\pi$
$457$	9.03140	+	13.5164i	0.422471	+	0.632273i	−0.557790	+	0.829982i	$0.688350\pi$
$458$	4.43319	+	1.36084i	0.207149	+	0.0635877i
$459$	12.8184	+	23.9815i	0.598310	+	1.11936i
$460$	−0.282512	+	0.228738i	−0.0131722	+	0.0106650i
$461$	0.353751	−	3.59170i	0.0164758	−	0.167282i	−0.983426	−	0.181311i	$-0.941966\pi$
$461$	0.353751	−	3.59170i	0.0164758	−	0.167282i	0.999902	+	0.0140293i	$0.00446583\pi$
$462$	3.99570	−	2.65075i	0.185897	−	0.123324i
$463$	−4.37715	−	10.5674i	−0.203424	−	0.491108i	0.788938	−	0.614473i	$-0.210631\pi$
$463$	−4.37715	−	10.5674i	−0.203424	−	0.491108i	−0.992361	+	0.123365i	$0.960631\pi$
$464$	−0.212922	−	0.117461i	−0.00988468	−	0.00545298i
$465$	−0.197093	+	0.475825i	−0.00913997	+	0.0220658i
$466$	−0.216866	−	1.10945i	−0.0100461	−	0.0513941i
$467$	−4.21463	−	5.13554i	−0.195030	−	0.237645i	0.666309	−	0.745676i	$-0.267873\pi$
$467$	−4.21463	−	5.13554i	−0.195030	−	0.237645i	−0.861338	+	0.508032i	$0.830373\pi$
$468$	−1.80848	+	5.82270i	−0.0835972	+	0.269154i
$469$	−2.21408	+	7.29886i	−0.102237	+	0.337030i
$470$	−1.08017	+	0.102778i	−0.0498247	+	0.00474079i
$471$	−16.9906	−	3.37964i	−0.782886	−	0.155726i
$472$	1.92057	−	6.11207i	0.0884015	−	0.281331i
$473$	4.62951	+	23.2741i	0.212865	+	1.07015i
$474$	10.7503	−	19.9533i	0.493779	−	0.916483i
$475$	23.7516	−	28.9415i	1.08980	−	1.32793i
$476$	1.96016	−	9.52437i	0.0898440	−	0.436549i
$477$	−7.01912	−	3.75180i	−0.321384	−	0.171783i
$478$	−14.8932	−	0.0493085i	−0.681200	−	0.00225532i
$479$	1.20837	+	1.20837i	0.0552117	+	0.0552117i	0.734174	−	0.678962i	$-0.237570\pi$
$479$	1.20837	+	1.20837i	0.0552117	+	0.0552117i	−0.678962	+	0.734174i	$0.737570\pi$
$480$	−0.685362	−	0.708437i	−0.0312824	−	0.0323356i
$481$	3.65345	−	3.65345i	0.166583	−	0.166583i
$482$	−28.8237	+	28.6335i	−1.31289	+	1.30422i
$483$	−1.15905	+	2.16843i	−0.0527387	+	0.0986672i
$484$	2.30955	+	12.0265i	0.104979	+	0.546660i
$485$	−0.347586	−	0.285256i	−0.0157831	−	0.0129528i
$486$	−8.88003	+	2.66165i	−0.402806	+	0.120735i
$487$	13.7198	−	2.72904i	0.621704	−	0.123665i	0.125820	−	0.992053i	$-0.459844\pi$
$487$	13.7198	−	2.72904i	0.621704	−	0.123665i	0.495885	+	0.868388i	$0.334844\pi$
$488$	2.10733	−	19.4169i	0.0953941	−	0.878963i
$489$	2.72432	−	13.6961i	0.123198	−	0.619357i
$490$	0.102232	−	0.123732i	0.00461835	−	0.00558964i
$491$	−11.6536	−	3.53509i	−0.525921	−	0.159537i	0.0161490	−	0.999870i	$-0.494859\pi$
$491$	−11.6536	−	3.53509i	−0.525921	−	0.159537i	−0.542070	+	0.840333i	$0.682359\pi$
$492$	−19.7413	−	16.4212i	−0.890008	−	0.740327i
$493$	−0.228483	+	0.187512i	−0.0102904	+	0.00844509i
$494$	−28.1155	+	41.7777i	−1.26498	+	1.87967i
$495$	0.148827	+	0.0616460i	0.00668926	+	0.00277078i
$496$	8.24857	+	8.46998i	0.370372	+	0.380314i
$497$	−3.12570	+	1.29471i	−0.140207	+	0.0580756i
$498$	7.03059	−	34.7436i	0.315048	−	1.55690i
$499$	−16.2975	−	1.60516i	−0.729577	−	0.0718570i	−0.273593	−	0.961845i	$-0.588212\pi$
$499$	−16.2975	−	1.60516i	−0.729577	−	0.0718570i	−0.455983	+	0.889988i	$0.650712\pi$
$500$	1.99212	+	1.08183i	0.0890904	+	0.0483810i
$501$	−24.4030	+	13.0437i	−1.09025	+	0.582749i
$502$	7.63622	+	14.4008i	0.340821	+	0.642741i
$503$	22.5054	−	15.0376i	1.00347	−	0.670495i	0.0587121	−	0.998275i	$-0.481301\pi$
$503$	22.5054	−	15.0376i	1.00347	−	0.670495i	0.944754	+	0.327780i	$0.106301\pi$
$504$	1.67255	+	0.712335i	0.0745011	+	0.0317299i
$505$	−0.352184	+	0.527081i	−0.0156720	+	0.0234548i
$506$	3.16008	+	3.87667i	0.140483	+	0.172339i
$507$	−1.42920	−	14.5109i	−0.0634730	−	0.644453i
$508$	23.3671	−	23.0597i	1.03675	−	1.02311i
$509$	10.9392	+	36.0618i	0.484873	+	1.59841i	0.768748	+	0.639551i	$0.220880\pi$
$509$	10.9392	+	36.0618i	0.484873	+	1.59841i	−0.283875	+	0.958861i	$0.591620\pi$
$510$	−1.10843	+	0.454832i	−0.0490820	+	0.0201403i
$511$	10.4704			0.463183
$512$	−21.1537	+	8.03248i	−0.934871	+	0.354989i
$513$	−41.9872			−1.85378
$514$	0.981954	−	0.402935i	0.0433121	−	0.0177727i
$515$	−0.501903	−	1.65455i	−0.0221165	−	0.0729083i
$516$	23.4858	−	23.1768i	1.03390	−	1.02030i
$517$	1.46333	+	14.8574i	0.0643571	+	0.653429i
$518$	−0.973356	−	1.19408i	−0.0427668	−	0.0524647i
$519$	−11.4039	+	17.0671i	−0.500575	+	0.749163i
$520$	−1.40080	−	0.596599i	−0.0614292	−	0.0261626i
$521$	23.2656	−	15.5456i	1.01929	−	0.681065i	0.0706717	−	0.997500i	$-0.477486\pi$
$521$	23.2656	−	15.5456i	1.01929	−	0.681065i	0.948614	+	0.316434i	$0.102486\pi$
$522$	−0.0258872	−	0.0488197i	−0.00113305	−	0.00213678i
$523$	25.0274	−	13.3774i	1.09437	−	0.584953i	0.177493	−	0.984122i	$-0.443201\pi$
$523$	25.0274	−	13.3774i	1.09437	−	0.584953i	0.916877	+	0.399169i	$0.130701\pi$
$524$	−0.177884	−	0.0966009i	−0.00777091	−	0.00422003i
$525$	7.62005	+	0.750510i	0.332566	+	0.0327549i
$526$	−4.39076	+	21.6981i	−0.191446	+	0.946084i
$527$	13.2767	−	5.49940i	0.578344	−	0.239558i
$528$	−9.71618	+	9.46218i	−0.422842	+	0.411789i
$529$	18.8798	+	7.82028i	0.820862	+	0.340012i
$530$	1.10965	−	1.64887i	0.0482002	−	0.0716222i
$531$	1.12540	−	0.923589i	0.0488380	−	0.0400803i
$532$	11.5432	+	9.60184i	0.500459	+	0.416292i
$533$	−37.9559	−	11.5138i	−1.64405	−	0.498718i
$534$	12.9131	−	15.6289i	0.558804	−	0.676327i
$535$	−0.274971	+	1.38237i	−0.0118880	+	0.0597652i
$536$	2.32768	−	21.4473i	0.100540	−	0.926381i
$537$	25.0405	−	4.98086i	1.08058	−	0.214940i
$538$	−20.8931	+	6.26240i	−0.900768	+	0.269991i
$539$	−1.70709	−	1.40097i	−0.0735294	−	0.0603440i
$540$	−0.239414	−	1.24670i	−0.0103027	−	0.0536496i
$541$	−16.9651	+	31.7394i	−0.729385	+	1.36458i	0.194113	+	0.980979i	$0.437817\pi$
$541$	−16.9651	+	31.7394i	−0.729385	+	1.36458i	−0.923498	+	0.383604i	$0.874683\pi$
$542$	−2.27485	+	2.25984i	−0.0977133	+	0.0970684i
$543$	12.9531	−	12.9531i	0.555869	−	0.555869i
$544$	−0.455272	+	27.4998i	−0.0195196	+	1.17904i
$545$	1.24392	+	1.24392i	0.0532836	+	0.0532836i
$546$	−10.2986	−	0.0340967i	−0.440741	−	0.00145921i
$547$	15.4771	+	8.27267i	0.661752	+	0.353714i	0.767839	−	0.640643i	$-0.221332\pi$
$547$	15.4771	+	8.27267i	0.661752	+	0.353714i	−0.106087	+	0.994357i	$0.533832\pi$
$548$	2.44771	−	11.8933i	0.104561	−	0.508058i
$549$	2.81557	−	3.43079i	0.120166	−	0.146422i
$550$	7.38756	−	13.7118i	0.315006	−	0.584671i
$551$	−0.0890381	−	0.447625i	−0.00379315	−	0.0190695i
$552$	2.08476	−	6.63460i	0.0887334	−	0.282387i
$553$	−10.2379	−	2.03644i	−0.435359	−	0.0865983i
$554$	31.3413	−	2.98211i	1.33157	−	0.126698i
$555$	−0.0550998	+	0.181640i	−0.00233886	+	0.00771018i
$556$	10.3520	−	33.3297i	0.439021	−	1.41350i
$557$	−26.3709	−	32.1330i	−1.11737	−	1.36152i	−0.924897	−	0.380219i	$-0.875849\pi$
$557$	−26.3709	−	32.1330i	−1.11737	−	1.36152i	−0.192474	−	0.981302i	$-0.561651\pi$
$558$	0.515407	+	2.63672i	0.0218189	+	0.111621i
$559$	19.5043	−	47.0876i	0.824946	−	1.99159i
$560$	−0.219282	+	0.397495i	−0.00926637	+	0.0167972i
$561$	6.30854	+	15.2302i	0.266347	+	0.643018i
$562$	−37.5641	+	24.9200i	−1.58454	+	1.05119i
$563$	−2.74449	+	27.8652i	−0.115666	+	1.17438i	0.745660	+	0.666327i	$0.232135\pi$
$563$	−2.74449	+	27.8652i	−0.115666	+	1.17438i	−0.861326	+	0.508053i	$0.830365\pi$
$564$	16.1337	−	13.0628i	0.679351	−	0.550042i
$565$	0.389732	+	0.729138i	0.0163962	+	0.0306751i
$566$	1.41156	+	0.433302i	0.0593325	+	0.0182130i
$567$	−3.69938	−	5.53651i	−0.155359	−	0.232511i
$568$	8.00894	−	5.23710i	0.336048	−	0.219744i
$569$	−27.3641	−	18.2841i	−1.14716	−	0.766510i	−0.171371	−	0.985207i	$-0.554820\pi$
$569$	−27.3641	−	18.2841i	−1.14716	−	0.766510i	−0.975793	+	0.218696i	$0.929820\pi$
$570$	0.187426	−	1.84047i	0.00785039	−	0.0770890i
$571$	−27.8352	+	2.74153i	−1.16487	+	0.114729i	−0.661911	−	0.749583i	$-0.730254\pi$
$571$	−27.8352	+	2.74153i	−1.16487	+	0.114729i	−0.502956	+	0.864312i	$0.667754\pi$
$572$	−8.14480	+	19.3008i	−0.340551	+	0.807007i
$573$	26.2788	−	7.97158i	1.09781	−	0.333018i
$574$	−4.56186	+	10.9110i	−0.190408	+	0.455416i
$575$			7.98660i			0.333064i
$576$	−5.02213	−	1.10310i	−0.209256	−	0.0459625i
$577$			14.1565i			0.589343i	0.955599	+	0.294672i	$0.0952103\pi$
$577$			14.1565i			0.589343i	−0.955599	+	0.294672i	$0.904790\pi$
$578$	8.66229	+	3.62169i	0.360304	+	0.150642i
$579$	4.60345	−	1.39644i	0.191313	−	0.0580341i
$580$	0.0127834	−	0.00519615i	0.000530801	−	0.000215758i
$581$	−16.2470	+	1.60019i	−0.674039	+	0.0663871i
$582$	8.55836	+	0.871544i	0.354755	+	0.0361267i
$583$	−22.7373	−	15.1926i	−0.941685	−	0.629214i
$584$	−29.1017	+	5.48878i	−1.20424	+	0.227127i
$585$	−0.192219	−	0.287676i	−0.00794728	−	0.0118939i
$586$	−6.59446	+	21.4827i	−0.272415	+	0.887443i
$587$	−9.76021	−	18.2601i	−0.402847	−	0.753674i	0.595934	−	0.803033i	$-0.296782\pi$
$587$	−9.76021	−	18.2601i	−0.402847	−	0.753674i	−0.998781	+	0.0493596i	$0.984282\pi$
$588$	−0.321207	+	3.05383i	−0.0132464	+	0.125938i
$589$	−2.17495	+	22.0826i	−0.0896172	+	0.909899i
$590$	0.200979	+	0.302952i	0.00827416	+	0.0124724i
$591$	−1.24902	−	3.01540i	−0.0513778	−	0.124037i
$592$	3.33133	+	2.80859i	0.136917	+	0.115433i
$593$	3.60373	−	8.70018i	0.147988	−	0.357274i	−0.832451	−	0.554099i	$-0.813063\pi$
$593$	3.60373	−	8.70018i	0.147988	−	0.357274i	0.980439	+	0.196825i	$0.0630631\pi$
$594$	−17.1425	+	3.35089i	−0.703365	+	0.137489i
$595$	0.350057	+	0.426545i	0.0143509	+	0.0174867i
$596$	−37.3909	+	19.6687i	−1.53159	+	0.805660i
$597$	10.8514	−	35.7724i	0.444119	−	1.46407i
$598$	−1.01751	−	10.6938i	−0.0416091	−	0.437302i
$599$	43.4256	+	8.63788i	1.77432	+	0.352934i	0.970344	−	0.241727i	$-0.0777140\pi$
$599$	43.4256	+	8.63788i	1.77432	+	0.352934i	0.803976	+	0.594662i	$0.202714\pi$
$600$	−21.5728	+	1.90859i	−0.880705	+	0.0779179i
$601$	−2.53163	−	12.7274i	−0.103267	−	0.519159i	−0.997444	−	0.0714463i	$-0.977239\pi$
$601$	−2.53163	−	12.7274i	−0.103267	−	0.519159i	0.894177	−	0.447713i	$-0.147761\pi$
$602$	−13.3783	−	7.20792i	−0.545261	−	0.293773i
$603$	3.10999	−	3.78953i	0.126648	−	0.154322i
$604$	1.44259	+	2.19025i	0.0586982	+	0.0891200i
$605$	−0.612872	−	0.327587i	−0.0249168	−	0.0133183i
$606$	0.0401528	−	12.1278i	0.00163110	−	0.492659i
$607$	−7.14071	−	7.14071i	−0.289832	−	0.289832i	0.547182	−	0.837014i	$-0.315701\pi$
$607$	−7.14071	−	7.14071i	−0.289832	−	0.289832i	−0.837014	+	0.547182i	$0.815701\pi$
$608$	−37.1168	−	20.6364i	−1.50528	−	0.836918i
$609$	0.0660001	−	0.0660001i	0.00267446	−	0.00267446i
$610$	0.781090	+	0.786280i	0.0316254	+	0.0318355i
$611$	15.1154	−	28.2789i	0.611502	−	1.14404i
$612$	−3.50660	+	5.17351i	−0.141746	+	0.209127i
$613$	−7.47223	−	6.13230i	−0.301801	−	0.247681i	0.471288	−	0.881979i	$-0.343789\pi$
$613$	−7.47223	−	6.13230i	−0.301801	−	0.247681i	−0.773089	+	0.634298i	$0.781289\pi$
$614$	−6.38338	−	21.2968i	−0.257612	−	0.859467i
$615$	1.42915	−	0.284275i	0.0576287	−	0.0114631i
$616$	5.47913	+	2.99900i	0.220760	+	0.120833i
$617$	5.57526	−	28.0287i	0.224451	−	1.12839i	−0.690035	−	0.723776i	$-0.742405\pi$
$617$	5.57526	−	28.0287i	0.224451	−	1.12839i	0.914486	−	0.404617i	$-0.132595\pi$
$618$	25.5006	+	21.0695i	1.02579	+	0.847540i
$619$	14.6276	+	4.43723i	0.587932	+	0.178347i	0.570215	−	0.821496i	$-0.306860\pi$
$619$	14.6276	+	4.43723i	0.587932	+	0.178347i	0.0177176	+	0.999843i	$0.494360\pi$
$620$	−0.668089	+	0.0613372i	−0.0268311	+	0.00246336i
$621$	6.92356	−	5.68201i	0.277833	−	0.228011i
$622$	−37.7149	−	25.3813i	−1.51223	−	1.01770i
$623$	−8.62624	−	3.57311i	−0.345603	−	0.143153i
$624$	28.6421	−	5.30397i	1.14660	−	0.212329i
$625$	22.9186	−	9.49321i	0.916746	−	0.379728i
$626$	4.79308	+	0.969910i	0.191570	+	0.0387654i
$627$	−25.3317	−	2.49495i	−1.01165	−	0.0996387i
$628$	−6.40752	−	21.6375i	−0.255688	−	0.863431i
$629$	4.67089	−	2.49665i	0.186241	−	0.0995478i
$630$	−0.0911393	+	0.0483277i	−0.00363108	+	0.00192542i
$631$	11.8138	−	7.89376i	0.470302	−	0.314246i	−0.297738	−	0.954648i	$-0.596232\pi$
$631$	11.8138	−	7.89376i	0.470302	−	0.314246i	0.768040	+	0.640402i	$0.221232\pi$
$632$	29.5229	+	0.293243i	1.17436	+	0.0116646i
$633$	−15.9929	+	23.9350i	−0.635660	+	0.951332i
$634$	11.9839	−	9.76873i	0.475942	−	0.387966i
$635$	0.182600	+	1.85397i	0.00724627	+	0.0735726i
$636$	−0.251777	+	38.0232i	−0.00998362	+	1.50772i
$637$	1.37685	+	4.53886i	0.0545528	+	0.179836i
$638$	−0.0720763	−	0.175650i	−0.00285353	−	0.00695405i
$639$	2.17451			0.0860224
$640$	0.401104	−	1.21976i	0.0158550	−	0.0482152i
$641$	−13.3276			−0.526409			−0.263205	−	0.964740i	$-0.584779\pi$
$641$	−13.3276			−0.526409			−0.263205	+	0.964740i	$0.584779\pi$
$642$	−10.2366	−	24.9467i	−0.404008	−	0.984568i
$643$	7.13572	+	23.5233i	0.281405	+	0.927669i	0.977717	+	0.209929i	$0.0673232\pi$
$643$	7.13572	+	23.5233i	0.281405	+	0.927669i	−0.696311	+	0.717740i	$0.745177\pi$
$644$	−3.20282	−	0.0212081i	−0.126209	−	0.000835714i
$645$	0.183527	+	1.86339i	0.00722639	+	0.0733707i
$646$	−40.0107	+	32.6148i	−1.57420	+	1.28321i
$647$	−15.4936	+	23.1878i	−0.609115	+	0.911605i	−0.999961	−	0.00885112i	$-0.997183\pi$
$647$	−15.4936	+	23.1878i	−0.609115	+	0.911605i	0.390846	+	0.920456i	$0.372183\pi$
$648$	13.1845	+	13.4490i	0.517935	+	0.528327i
$649$	4.15917	−	2.77907i	0.163262	−	0.109088i
$650$	−29.5544	+	15.6716i	−1.15922	+	0.614690i
$651$	−4.00217	+	2.13921i	−0.156858	+	0.0838421i
$652$	17.4419	−	5.16508i	0.683078	−	0.202280i
$653$	5.91394	+	0.582472i	0.231430	+	0.0227939i	0.213067	−	0.977038i	$-0.431655\pi$
$653$	5.91394	+	0.582472i	0.231430	+	0.0227939i	0.0183628	+	0.999831i	$0.494155\pi$
$654$	−32.9873	−	6.67518i	−1.28990	−	0.261020i
$655$	0.0106123	−	0.00439574i	0.000414655	−	0.000171756i
$656$	6.95960	−	32.7177i	0.271727	−	1.27741i
$657$	−6.21739	−	2.57533i	−0.242564	−	0.100473i
$658$	−7.93171	−	5.33787i	−0.309210	−	0.208092i
$659$	−26.1846	+	21.4891i	−1.02001	+	0.837097i	−0.986733	−	0.162349i	$-0.948093\pi$
$659$	−26.1846	+	21.4891i	−1.02001	+	0.837097i	−0.0332724	+	0.999446i	$0.510593\pi$
$660$	−0.0703618	−	0.766386i	−0.00273883	−	0.0298315i
$661$	−44.4579	−	13.4862i	−1.72921	−	0.524551i	−0.740201	−	0.672385i	$-0.765270\pi$
$661$	−44.4579	−	13.4862i	−1.72921	−	0.524551i	−0.989012	+	0.147834i	$0.952770\pi$
$662$	−37.5044	−	30.9875i	−1.45765	−	1.20436i
$663$	6.90744	−	34.7260i	0.268263	−	1.34865i
$664$	44.3185	−	12.9646i	1.71989	−	0.503124i
$665$	−0.835650	+	0.166221i	−0.0324051	+	0.00644578i
$666$	0.284287	+	0.948460i	0.0110159	+	0.0367521i
$667$	0.0752580	+	0.0617626i	0.00291400	+	0.00239146i
$668$	−29.8367	−	20.2233i	−1.15442	−	0.782462i
$669$	12.2325	−	22.8854i	0.472937	−	0.884802i
$670$	0.862766	+	0.868497i	0.0333315	+	0.0335530i
$671$	10.7829	−	10.7829i	0.416267	−	0.416267i
$672$	−0.708106	−	8.65628i	−0.0273158	−	0.333923i
$673$	6.20470	+	6.20470i	0.239174	+	0.239174i	0.816508	−	0.577334i	$-0.195907\pi$
$673$	6.20470	+	6.20470i	0.239174	+	0.239174i	−0.577334	+	0.816508i	$0.695907\pi$
$674$	−0.157476	+	47.5643i	−0.00606576	+	1.83211i
$675$	−24.5987	−	13.1483i	−0.946803	−	0.506076i
$676$	15.8625	−	10.4477i	0.610095	−	0.401835i
$677$	−24.1086	+	29.3764i	−0.926569	+	1.12903i	0.0647965	+	0.997898i	$0.479360\pi$
$677$	−24.1086	+	29.3764i	−0.926569	+	1.12903i	−0.991365	+	0.131129i	$0.958140\pi$
$678$	−13.9249	−	7.50239i	−0.534782	−	0.288128i
$679$	−0.772942	−	3.88584i	−0.0296628	−	0.149125i
$680$	−1.19656	−	1.00204i	−0.0458859	−	0.0384266i
$681$	2.82965	+	0.562853i	0.108432	+	0.0215686i
$682$	0.874373	+	9.18945i	0.0334815	+	0.351882i
$683$	5.03543	−	16.5996i	0.192675	−	0.635166i	−0.806367	−	0.591415i	$-0.798569\pi$
$683$	5.03543	−	16.5996i	0.192675	−	0.635166i	0.999042	−	0.0437503i	$-0.0139306\pi$
$684$	−4.49271	−	8.54082i	−0.171783	−	0.326566i
$685$	0.437125	+	0.532638i	0.0167017	+	0.0203511i
$686$	1.38795	−	0.271306i	0.0529920	−	0.0103585i
$687$	1.92663	−	4.65130i	0.0735056	−	0.177458i
$688$	40.9626	+	13.0207i	1.56168	+	0.496409i
$689$	22.4763	+	54.2626i	0.856280	+	2.06724i
$690$	0.218161	+	0.328852i	0.00830523	+	0.0125192i
$691$	−1.75737	+	17.8429i	−0.0668536	+	0.678776i	0.902099	+	0.431529i	$0.142026\pi$
$691$	−1.75737	+	17.8429i	−0.0668536	+	0.678776i	−0.968953	+	0.247247i	$0.920474\pi$
$692$	−26.5919	−	2.79698i	−1.01087	−	0.106325i
$693$	0.669093	+	1.25178i	0.0254167	+	0.0475514i
$694$	−2.15862	+	7.03212i	−0.0819401	+	0.266936i
$695$	1.10028	+	1.64669i	0.0417361	+	0.0624625i
$696$	−0.148844	+	0.218041i	−0.00564191	+	0.00826481i
$697$	−33.8059	−	22.5884i	−1.28049	−	0.855597i
$698$	39.0631	+	3.97800i	1.47856	+	0.150570i
$699$	−1.22135	+	0.120293i	−0.0461959	+	0.00454989i
$700$	3.75587	+	9.24007i	0.141959	+	0.349242i
$701$	5.17664	−	1.57032i	0.195519	−	0.0593100i	−0.191007	−	0.981589i	$-0.561175\pi$
$701$	5.17664	−	1.57032i	0.195519	−	0.0593100i	0.386525	+	0.922279i	$0.373675\pi$
$702$	34.6119	+	14.4712i	1.30634	+	0.546179i
$703$			8.17789i			0.308435i
$704$	−16.8010	−	5.46323i	−0.633210	−	0.205903i
$705$			1.17799i			0.0443655i
$706$	−2.36713	+	5.66166i	−0.0890880	+	0.213079i
$707$	−5.34503	+	1.62140i	−0.201021	+	0.0609789i
$708$	−6.40823	−	2.70422i	−0.240836	−	0.101631i
$709$	2.78267	−	0.274069i	0.104505	−	0.0102929i	−0.0456293	−	0.998958i	$-0.514529\pi$
$709$	2.78267	−	0.274069i	0.104505	−	0.0102929i	0.150135	+	0.988666i	$0.452029\pi$
$710$	−0.0550138	+	0.540222i	−0.00206463	+	0.0202742i
$711$	5.57843	+	3.72739i	0.209208	+	0.139788i
$712$	25.8491	+	5.40914i	0.968735	+	0.202716i
$713$	−2.62974	−	3.93568i	−0.0984845	−	0.147393i
$714$	−10.0921	−	3.09792i	−0.377686	−	0.115937i
$715$	−0.560382	−	1.04840i	−0.0209571	−	0.0392080i
$716$	20.9279	+	25.8478i	0.782111	+	0.965978i
$717$	−1.58483	+	16.0910i	−0.0591865	+	0.600931i
$718$	−21.8230	+	14.4774i	−0.814428	+	0.540291i
$719$	10.3156	+	24.9042i	0.384708	+	0.928768i	0.991041	+	0.133557i	$0.0426400\pi$
$719$	10.3156	+	24.9042i	0.384708	+	0.928768i	−0.606333	+	0.795211i	$0.707360\pi$
$720$	0.227980	−	0.182100i	0.00849632	−	0.00678647i
$721$	5.83002	−	14.0749i	0.217121	−	0.524177i
$722$	−10.1360	−	51.8536i	−0.377221	−	1.92979i
$723$	27.9821	+	34.0963i	1.04067	+	1.26805i
$724$	22.7885	+	7.07792i	0.846926	+	0.263049i
$725$	0.0880094	−	0.290128i	0.00326859	−	0.0107751i
$726$	13.2354	−	1.25934i	0.491211	−	0.0467385i
$727$	−15.9892	−	3.18044i	−0.593005	−	0.117956i	−0.110541	−	0.993872i	$-0.535258\pi$
$727$	−15.9892	−	3.18044i	−0.593005	−	0.117956i	−0.482465	+	0.875916i	$0.660258\pi$
$728$	−6.20621	−	11.8937i	−0.230017	−	0.440808i
$729$	5.86060	+	29.4632i	0.217059	+	1.09123i
$730$	0.797094	−	1.47945i	0.0295018	−	0.0547571i
$731$	33.1438	−	40.3858i	1.22587	−	1.49372i
$732$	−20.7685	−	4.27426i	−0.767626	−	0.157981i
$733$	42.1583	+	22.5341i	1.55715	+	0.832316i	0.999998	+	0.00190799i	$0.000607333\pi$
$733$	42.1583	+	22.5341i	1.55715	+	0.832316i	0.557156	+	0.830408i	$0.311893\pi$
$734$	16.9171	+	0.0560091i	0.624421	+	0.00206733i
$735$	−0.123213	−	0.123213i	−0.00454476	−	0.00454476i
$736$	8.91311	−	1.62003i	0.328542	−	0.0597152i
$737$	11.9104	−	11.9104i	0.438724	−	0.438724i
$738$	5.39256	−	5.35697i	0.198503	−	0.197193i
$739$	−23.7104	+	44.3590i	−0.872200	+	1.63177i	−0.101264	+	0.994860i	$0.532289\pi$
$739$	−23.7104	+	44.3590i	−0.872200	+	1.63177i	−0.770936	+	0.636912i	$0.780211\pi$
$740$	−0.242822	+	0.0466309i	−0.00892630	+	0.00171419i
$741$	42.2608	+	34.6825i	1.55249	+	1.27409i
$742$	16.7748	−	5.02798i	0.615821	−	0.184583i
$743$	−7.21527	+	1.43521i	−0.264703	+	0.0526526i	−0.325657	−	0.945488i	$-0.605586\pi$
$743$	−7.21527	+	1.43521i	−0.264703	+	0.0526526i	0.0609546	+	0.998141i	$0.480586\pi$
$744$	10.0023	−	8.04378i	0.366703	−	0.294899i
$745$	0.467716	−	2.35137i	0.0171358	−	0.0861475i
$746$	−2.98740	+	3.61568i	−0.109377	+	0.132379i
$747$	10.0412	+	3.04595i	0.367387	+	0.111446i
$748$	−13.7326	+	16.5091i	−0.502114	+	0.603633i
$749$	−9.59999	+	7.87851i	−0.350776	+	0.287875i
$750$	1.37407	−	2.04177i	0.0501739	−	0.0745550i
$751$	−17.5901	−	7.28608i	−0.641873	−	0.265873i	0.0379150	−	0.999281i	$-0.487928\pi$
$751$	−17.5901	−	7.28608i	−0.641873	−	0.265873i	−0.679788	+	0.733408i	$0.737928\pi$
$752$	24.8438	+	10.6782i	0.905960	+	0.389396i
$753$	16.3492	−	6.77208i	0.595799	−	0.246788i
$754$	−0.0808788	+	0.399685i	−0.00294543	+	0.0145557i
$755$	−0.148108	−	0.0145874i	−0.00539020	−	0.000530889i
$756$	5.33809	−	9.82974i	0.194144	−	0.357504i
$757$	23.2747	−	12.4406i	0.845933	−	0.452160i	0.00932080	−	0.999957i	$-0.497033\pi$
$757$	23.2747	−	12.4406i	0.845933	−	0.452160i	0.836612	+	0.547796i	$0.184533\pi$
$758$	−7.79858	−	14.7070i	−0.283257	−	0.534184i
$759$	4.51474	−	3.01666i	0.163875	−	0.109498i
$760$	2.23549	−	0.900063i	0.0810897	−	0.0326487i
$761$	−3.16403	+	4.73531i	−0.114696	+	0.171655i	−0.884376	−	0.466775i	$-0.845416\pi$
$761$	−3.16403	+	4.73531i	−0.114696	+	0.171655i	0.769680	+	0.638430i	$0.220416\pi$
$762$	−22.5193	−	27.6258i	−0.815786	−	1.00078i
$763$	1.51930	+	15.4257i	0.0550023	+	0.558448i
$764$	25.1267	+	25.4617i	0.909054	+	0.921173i
$765$	−0.102952	−	0.339386i	−0.00372223	−	0.0122705i
$766$	−25.3989	+	10.4222i	−0.917700	+	0.376569i
$767$	−10.7437			−0.387931
$768$	6.50591	+	23.6883i	0.234762	+	0.854777i
$769$	7.64501			0.275686			0.137843	−	0.990454i	$-0.455983\pi$
$769$	7.64501			0.275686			0.137843	+	0.990454i	$0.455983\pi$
$770$	−0.327913	+	0.134556i	−0.0118172	+	0.00484906i
$771$	−0.334500	−	1.10270i	−0.0120467	−	0.0397128i
$772$	4.40164	+	4.46032i	0.158418	+	0.160530i
$773$	−2.19320	−	22.2679i	−0.0788839	−	0.800922i	−0.950498	−	0.310730i	$-0.899427\pi$
$773$	−2.19320	−	22.2679i	−0.0788839	−	0.800922i	0.871614	−	0.490192i	$-0.163073\pi$
$774$	6.17127	+	7.57069i	0.221822	+	0.272123i
$775$	−8.18937	+	12.2563i	−0.294171	+	0.440258i
$776$	4.18536	+	10.3952i	0.150246	+	0.373166i
$777$	−1.39061	+	0.929179i	−0.0498880	+	0.0333341i
$778$	−3.70326	−	6.98383i	−0.132768	−	0.250382i
$779$	55.3666	−	29.5940i	1.98371	−	1.06032i
$780$	−0.788836	+	1.45259i	−0.0282448	+	0.0520110i
$781$	7.43543	+	0.732326i	0.266061	+	0.0262047i
$782$	2.18396	−	10.7926i	0.0780981	−	0.385943i
$783$	−0.314125	+	0.130115i	−0.0112259	+	0.00464992i
$784$	−3.71547	+	1.48166i	−0.132695	+	0.0529164i
$785$	1.18307	+	0.490045i	0.0422257	+	0.0174905i
$786$	−0.122696	+	0.182318i	−0.00437642	+	0.00650306i
$787$	18.5422	−	15.2172i	0.660957	−	0.542434i	−0.243016	−	0.970022i	$-0.578137\pi$
$787$	18.5422	−	15.2172i	0.660957	−	0.542434i	0.903973	+	0.427589i	$0.140637\pi$
$788$	2.71891	−	3.26862i	0.0968570	−	0.116440i
$789$	22.9991	+	6.97671i	0.818791	+	0.248377i
$790$	−1.06714	+	1.29157i	−0.0379671	+	0.0459520i
$791$	−1.42118	+	7.14477i	−0.0505315	+	0.254039i
$792$	−2.51590	−	3.12849i	−0.0893987	−	0.111166i
$793$	−32.1229	+	6.38964i	−1.14072	+	0.226903i
$794$	31.3002	−	9.38175i	1.11080	−	0.332946i
$795$	−1.66793	−	1.36884i	−0.0591555	−	0.0485477i
$796$	47.8216	−	9.18356i	1.69499	−	0.325503i
$797$	−14.0190	+	26.2276i	−0.496577	+	0.929030i	0.501385	+	0.865224i	$0.332824\pi$
$797$	−14.0190	+	26.2276i	−0.496577	+	0.929030i	−0.997962	+	0.0638059i	$0.979676\pi$
$798$	11.5644	−	11.4881i	0.409375	−	0.406673i
$799$	23.2418	−	23.2418i	0.822235	−	0.822235i
$800$	−15.2830	−	23.7132i	−0.540335	−	0.838387i
$801$	4.24347	+	4.24347i	0.149936	+	0.149936i
$802$	−48.3706	−	0.160145i	−1.70802	−	0.00565493i
$803$	−20.3921	−	10.8998i	−0.719623	−	0.384647i
$804$	−22.9402	−	4.72120i	−0.809037	−	0.166504i
$805$	0.115302	−	0.140496i	0.00406385	−	0.00495182i
$806$	9.40384	−	17.4541i	0.331236	−	0.614794i
$807$	4.61967	+	23.2246i	0.162620	+	0.817546i
$808$	14.0061	−	7.30852i	0.492734	−	0.257113i
$809$	−46.2070	−	9.19115i	−1.62455	−	0.323144i	−0.702938	−	0.711251i	$-0.748129\pi$
$809$	−46.2070	−	9.19115i	−1.62455	−	0.323144i	−0.921614	+	0.388107i	$0.873129\pi$
$810$	−1.06393	+	0.101232i	−0.0373827	+	0.00355695i
$811$	13.3990	−	44.1707i	0.470504	−	1.55104i	−0.325373	−	0.945586i	$-0.605490\pi$
$811$	13.3990	−	44.1707i	0.470504	−	1.55104i	0.795877	−	0.605458i	$-0.207010\pi$
$812$	0.116115	+	0.0360643i	0.00407483	+	0.00126561i
$813$	2.20843	+	2.69098i	0.0774530	+	0.0943767i
$814$	0.652657	+	3.33886i	0.0228756	+	0.117027i
$815$	−0.395023	+	0.953670i	−0.0138371	+	0.0334056i
$816$	29.6741	+	3.31998i	1.03880	+	0.116222i
$817$	30.8712	+	74.5298i	1.08005	+	2.60747i
$818$	−16.5158	+	10.9566i	−0.577461	+	0.383088i
$819$	0.298809	−	3.03386i	0.0104412	−	0.106012i
$820$	1.19442	+	1.47522i	0.0417111	+	0.0515170i
$821$	−11.5199	−	21.5522i	−0.402047	−	0.752177i	0.596687	−	0.802474i	$-0.296483\pi$
$821$	−11.5199	−	21.5522i	−0.402047	−	0.752177i	−0.998734	+	0.0502967i	$0.983983\pi$
$822$	−12.6022	−	3.86845i	−0.439553	−	0.134928i
$823$	−3.78020	−	5.65747i	−0.131770	−	0.197207i	0.759717	−	0.650253i	$-0.225337\pi$
$823$	−3.78020	−	5.65747i	−0.131770	−	0.197207i	−0.891487	+	0.453046i	$0.850337\pi$
$824$	−8.82575	+	42.1763i	−0.307460	+	1.46928i
$825$	−14.0595	−	9.39428i	−0.489490	−	0.327067i
$826$	−0.324537	+	3.18687i	−0.0112921	+	0.110886i
$827$	−5.73765	+	0.565109i	−0.199517	+	0.0196508i	−0.197282	−	0.980347i	$-0.563212\pi$
$827$	−5.73765	+	0.565109i	−0.199517	+	0.0196508i	−0.00223529	+	0.999998i	$0.500712\pi$
$828$	1.89664	+	0.800368i	0.0659128	+	0.0278147i
$829$	29.3221	−	8.89475i	1.01840	−	0.308927i	0.263422	−	0.964681i	$-0.415149\pi$
$829$	29.3221	−	8.89475i	1.01840	−	0.308927i	0.754975	+	0.655753i	$0.227649\pi$
$830$	−1.01075	+	2.41750i	−0.0350837	+	0.0839127i
$831$		−	34.1794i		−	1.18567i
$832$	23.4846	+	29.8041i	0.814180	+	1.03327i
$833$			4.86199i			0.168458i
$834$	−34.9572	−	14.6155i	−1.21047	−	0.506094i
$835$	1.95731	−	0.593744i	0.0677355	−	0.0205473i
$836$	−12.4858	−	30.7171i	−0.431831	−	1.06237i
$837$	16.4512	−	1.62030i	0.568636	−	0.0560058i
$838$	−15.5136	−	1.57983i	−0.535908	−	0.0545744i
$839$	9.82297	+	6.56350i	0.339127	+	0.226597i	0.713458	−	0.700698i	$-0.247128\pi$
$839$	9.82297	+	6.56350i	0.339127	+	0.226597i	−0.374332	+	0.927295i	$0.622128\pi$
$840$	0.407050	+	0.277870i	0.0140446	+	0.00958741i
$841$	16.1095	+	24.1095i	0.555499	+	0.831364i
$842$	7.81525	−	25.4597i	0.269331	−	0.877399i
$843$	23.0699	+	43.1607i	0.794568	+	1.48653i
$844$	−37.2927	−	3.92251i	−1.28367	−	0.135018i
$845$	−0.105646	+	1.07264i	−0.00363434	+	0.0369001i
$846$	3.39699	+	5.12057i	0.116791	+	0.176049i
$847$	−2.34322	−	5.65704i	−0.0805141	−	0.194378i
$848$	−43.9884	+	22.7685i	−1.51057	+	0.781875i
$849$	0.613457	−	1.48102i	0.0210538	−	0.0508283i
$850$	−33.6540	+	6.57844i	−1.15432	+	0.225639i
$851$	−1.10669	−	1.34851i	−0.0379369	−	0.0462262i
$852$	−4.83649	−	9.19436i	−0.165695	−	0.314994i
$853$	10.0246	−	33.0465i	0.343234	−	1.13149i	−0.600177	−	0.799867i	$-0.704903\pi$
$853$	10.0246	−	33.0465i	0.343234	−	1.13149i	0.943411	−	0.331624i	$-0.107597\pi$
$854$	0.925003	+	9.72157i	0.0316530	+	0.332665i
$855$	0.537099	+	0.106836i	0.0183684	+	0.00365370i
$856$	22.5524	−	26.9302i	0.770825	−	0.920456i
$857$	−5.09716	−	25.6252i	−0.174116	−	0.875339i	−0.964774	−	0.263081i	$-0.915261\pi$
$857$	−5.09716	−	25.6252i	−0.174116	−	0.875339i	0.790658	−	0.612258i	$-0.209739\pi$
$858$	20.0221	+	10.7874i	0.683544	+	0.368277i
$859$	−5.15158	+	6.27721i	−0.175770	+	0.214176i	−0.853442	−	0.521188i	$-0.825489\pi$
$859$	−5.15158	+	6.27721i	−0.175770	+	0.214176i	0.677672	+	0.735364i	$0.262989\pi$
$860$	−2.03694	+	1.34162i	−0.0694592	+	0.0457488i
$861$	11.3231	+	6.05234i	0.385891	+	0.206263i
$862$	0.0165110	−	4.98702i	0.000562368	−	0.169859i
$863$	26.4097	+	26.4097i	0.898998	+	0.898998i	0.995348	−	0.0963496i	$-0.0307167\pi$
$863$	26.4097	+	26.4097i	0.898998	+	0.898998i	−0.0963496	+	0.995348i	$0.530717\pi$
$864$	−9.68388	+	30.1193i	−0.329452	+	1.02468i
$865$	1.07290	−	1.07290i	0.0364797	−	0.0364797i
$866$	3.80063	+	3.82588i	0.129151	+	0.130009i
$867$	4.80498	−	8.98949i	0.163186	−	0.305299i
$868$	−4.89331	−	3.31668i	−0.166090	−	0.112576i
$869$	17.8193	+	14.6240i	0.604480	+	0.496084i
$870$	−0.00430126	−	0.0143502i	−0.000145826	−	0.000486518i
$871$	−35.4819	+	7.05778i	−1.20226	+	0.239144i
$872$	−12.3092	−	42.0781i	−0.416843	−	1.42494i
$873$	−0.496794	+	2.49755i	−0.0168139	+	0.0845294i
$874$	13.1073	+	10.8297i	0.443361	+	0.366321i
$875$	−1.08465	−	0.329026i	−0.0366679	−	0.0111231i
$876$	2.93944	+	32.0166i	0.0993144	+	1.08174i
$877$	−18.5080	+	15.1891i	−0.624971	+	0.512901i	−0.892734	−	0.450584i	$-0.851216\pi$
$877$	−18.5080	+	15.1891i	−0.624971	+	0.512901i	0.267763	+	0.963485i	$0.413716\pi$
$878$	−15.9285	−	10.7195i	−0.537561	−	0.361767i
$879$	22.5397	+	9.33625i	0.760245	+	0.314904i
$880$	0.840873	−	0.545886i	0.0283458	−	0.0184018i
$881$	−38.3273	+	15.8757i	−1.29128	+	0.534866i	−0.919367	−	0.393402i	$-0.871298\pi$
$881$	−38.3273	+	15.8757i	−1.29128	+	0.534866i	−0.371913	+	0.928267i	$0.621298\pi$
$882$	−0.890903	−	0.180280i	−0.0299982	−	0.00607034i
$883$	−22.3773	−	2.20398i	−0.753057	−	0.0741697i	−0.285798	−	0.958290i	$-0.592259\pi$
$883$	−22.3773	−	2.20398i	−0.753057	−	0.0741697i	−0.467259	+	0.884120i	$0.654759\pi$
$884$	44.2235	−	13.0959i	1.48740	−	0.440464i
$885$	0.348089	−	0.186057i	0.0117009	−	0.00625425i
$886$	−20.5646	+	10.9046i	−0.690882	+	0.366348i
$887$	−12.5261	+	8.36966i	−0.420585	+	0.281026i	−0.747800	−	0.663924i	$-0.768890\pi$
$887$	−12.5261	+	8.36966i	−0.420585	+	0.281026i	0.327215	+	0.944950i	$0.393890\pi$
$888$	3.37801	−	3.31157i	0.113359	−	0.111129i
$889$	−9.11954	+	13.6484i	−0.305859	+	0.457751i
$890$	−1.16158	+	0.946863i	−0.0389362	+	0.0317389i
$891$	1.44132	+	14.6340i	0.0482862	+	0.490258i
$892$	33.8022	+	0.223828i	1.13178	+	0.00749430i
$893$	14.7326	+	48.5669i	0.493007	+	1.62523i
$894$	17.4122	+	42.4335i	0.582350	+	1.41919i
$895$	−1.88725			−0.0630838
$896$	9.55014	−	6.06588i	0.319048	−	0.202647i
$897$	−11.6622			−0.389388
$898$	−0.646475	−	1.57546i	−0.0215732	−	0.0525739i
$899$	0.0521604	+	0.171950i	0.00173965	+	0.00573485i
$900$	0.0424491	−	6.41062i	0.00141497	−	0.213687i
$901$	5.90119	+	59.9158i	0.196597	+	1.99608i
$902$	20.2432	−	16.5013i	0.674024	−	0.549433i
$903$	−9.16585	+	13.7177i	−0.305020	+	0.456495i
$904$	0.204647	−	20.6034i	0.00680646	−	0.685257i
$905$	−1.12589	+	0.752293i	−0.0374257	+	0.0250071i
$906$	2.51550	−	1.33387i	0.0835719	−	0.0443150i
$907$	33.3724	−	17.8379i	1.10811	−	0.592299i	0.187300	−	0.982303i	$-0.440026\pi$
$907$	33.3724	−	17.8379i	1.10811	−	0.592299i	0.920813	+	0.390004i	$0.127526\pi$
$908$	1.06712	+	3.60356i	0.0354137	+	0.119588i
$909$	3.57272	+	0.351882i	0.118500	+	0.0116712i
$910$	0.746154	+	0.150989i	0.0247348	+	0.00500524i
$911$	40.8601	−	16.9248i	1.35376	−	0.560744i	0.416421	−	0.909172i	$-0.363284\pi$
$911$	40.8601	−	16.9248i	1.35376	−	0.560744i	0.937336	+	0.348428i	$0.113284\pi$
$912$	−26.1201	+	37.9925i	−0.864922	+	1.25806i
$913$	33.3085	+	13.7968i	1.10235	+	0.456608i
$914$	19.0727	+	12.8355i	0.630870	+	0.424562i
$915$	0.930109	−	0.763321i	0.0307484	−	0.0252346i
$916$	6.53074	−	0.599586i	0.215782	−	0.0198109i
$917$	0.0968528	+	0.0293800i	0.00319836	+	0.000970212i
$918$	29.6457	+	24.4943i	0.978455	+	0.808434i
$919$	1.34532	−	6.76338i	0.0443780	−	0.223103i	−0.952232	−	0.305376i	$-0.901218\pi$
$919$	1.34532	−	6.76338i	0.0443780	−	0.223103i	0.996610	+	0.0822727i	$0.0262178\pi$
$920$	−0.246822	+	0.450940i	−0.00813748	+	0.0148671i
$921$	−23.6733	+	4.70891i	−0.780061	+	0.155164i
$922$	−1.46544	−	4.88911i	−0.0482615	−	0.161014i
$923$	−12.4045	−	10.1801i	−0.408300	−	0.335083i
$924$	3.80467	−	5.61327i	0.125164	−	0.184663i
$925$	−2.56090	+	4.79110i	−0.0842018	+	0.157531i
$926$	−11.4001	−	11.4759i	−0.374631	−	0.377120i
$927$	−6.92381	+	6.92381i	−0.227408	+	0.227408i
$928$	−0.341637	−	0.0393685i	−0.0112148	−	0.00129233i
$929$	19.2447	+	19.2447i	0.631398	+	0.631398i	0.948419	−	0.317021i	$-0.102683\pi$
$929$	19.2447	+	19.2447i	0.631398	+	0.631398i	−0.317021	+	0.948419i	$0.602683\pi$
$930$	−0.00241145	+	0.728357i	−7.90745e−5	+	0.0238838i
$931$	−6.62087	−	3.53893i	−0.216990	−	0.115984i
$932$	−0.879362	−	1.33511i	−0.0288044	−	0.0437330i
$933$	−31.3097	+	38.1510i	−1.02503	+	1.24901i
$934$	−8.27131	−	4.45638i	−0.270645	−	0.145817i
$935$	−0.237731	−	1.19515i	−0.00777463	−	0.0390857i
$936$	0.759890	+	8.58903i	0.0248378	+	0.280741i
$937$	36.9501	+	7.34983i	1.20711	+	0.240108i	0.757330	−	0.653033i	$-0.226504\pi$
$937$	36.9501	+	7.34983i	1.20711	+	0.240108i	0.449777	+	0.893141i	$0.351504\pi$
$938$	1.02173	+	10.7381i	0.0333606	+	0.350612i
$939$	1.54114	−	5.08046i	0.0502933	−	0.165795i
$940$	−1.35806	+	0.714379i	−0.0442951	+	0.0233005i
$941$	−23.6778	−	28.8515i	−0.771874	−	0.940531i	0.227574	−	0.973761i	$-0.426921\pi$
$941$	−23.6778	−	28.8515i	−0.771874	−	0.940531i	−0.999448	+	0.0332298i	$0.989421\pi$
$942$	−24.0441	+	4.69996i	−0.783398	+	0.153133i
$943$	−5.12489	+	12.3726i	−0.166889	+	0.402906i
$944$	−0.768595	−	9.02780i	−0.0250156	−	0.293830i
$945$	0.242905	+	0.586425i	0.00790171	+	0.0190764i
$946$	18.5521	+	27.9652i	0.603182	+	0.909227i
$947$	−0.790056	+	8.02158i	−0.0256734	+	0.260666i	0.973777	+	0.227506i	$0.0730571\pi$
$947$	−0.790056	+	8.02158i	−0.0256734	+	0.260666i	−0.999450	+	0.0331602i	$0.989443\pi$
$948$	3.35291	−	31.8773i	0.108897	−	1.03533i
$949$	23.4106	+	43.7981i	0.759939	+	1.42175i
$950$	15.5377	−	50.6170i	0.504109	−	1.64223i
$951$	−9.32537	−	13.9564i	−0.302396	−	0.452567i
$952$	−2.54875	−	13.5135i	−0.0826054	−	0.437976i
$953$	13.4229	+	8.96891i	0.434811	+	0.290531i	0.753648	−	0.657278i	$-0.228292\pi$
$953$	13.4229	+	8.96891i	0.434811	+	0.290531i	−0.318837	+	0.947810i	$0.603292\pi$
$954$	−11.1977	−	1.14032i	−0.362538	−	0.0369192i
$955$	−2.02016	+	0.198968i	−0.0653708	+	0.00643846i
$956$	−19.5120	+	7.93117i	−0.631062	+	0.256512i
$957$	−0.197249	+	0.0598348i	−0.00637615	+	0.00193418i
$958$	2.22970	+	0.932231i	0.0720382	+	0.0301190i
$959$			6.07130i			0.196052i
$960$	−1.27703	−	0.558934i	−0.0412159	−	0.0180395i
$961$			22.2638i			0.718187i
$962$	2.81857	−	6.74140i	0.0908742	−	0.217352i
$963$	7.63836	−	2.31707i	0.246143	−	0.0746666i
$964$	−22.3391	+	52.9371i	−0.719493	+	1.70499i
$965$	−0.353886	+	0.0348547i	−0.0113920	+	0.00112201i
$966$	−0.352282	+	3.45932i	−0.0113345	+	0.111302i
$967$	9.42448	+	6.29724i	0.303071	+	0.202505i	0.697801	−	0.716292i	$-0.254162\pi$
$967$	9.42448	+	6.29724i	0.303071	+	0.202505i	−0.394730	+	0.918797i	$0.629162\pi$
$968$	9.47834	+	14.4950i	0.304645	+	0.465886i
$969$	31.1346	+	46.5962i	1.00019	+	1.49689i
$970$	−0.607908	−	0.186607i	−0.0195187	−	0.00599159i
$971$	15.4206	+	28.8500i	0.494871	+	0.925839i	0.998096	+	0.0616834i	$0.0196469\pi$
$971$	15.4206	+	28.8500i	0.494871	+	0.925839i	−0.503224	+	0.864156i	$0.667853\pi$
$972$	−10.1892	+	8.24977i	−0.326819	+	0.264611i
$973$	−1.71042	+	17.3661i	−0.0548334	+	0.556733i
$974$	16.4852	−	10.9363i	0.528219	−	0.350420i
$975$	13.8981	+	33.5531i	0.445096	+	1.07456i
$976$	−7.66720	−	26.5355i	−0.245421	−	0.849379i
$977$	1.62768	−	3.92957i	0.0520741	−	0.125718i	−0.895702	−	0.444656i	$-0.853326\pi$
$977$	1.62768	−	3.92957i	0.0520741	−	0.125718i	0.947776	+	0.318938i	$0.103326\pi$
$978$	−3.78862	−	19.3818i	−0.121147	−	0.619762i
$979$	13.0808	+	15.9390i	0.418065	+	0.509413i
$980$	0.0673268	−	0.216769i	0.00215068	−	0.00692444i
$981$	2.89198	−	9.53358i	0.0923338	−	0.304384i
$982$	−17.1449	+	1.63133i	−0.547115	+	0.0520578i
$983$	49.8136	+	9.90854i	1.58881	+	0.316033i	0.908819	−	0.417190i	$-0.136985\pi$
$983$	49.8136	+	9.90854i	1.58881	+	0.316033i	0.679988	+	0.733224i	$0.261985\pi$
$984$	−34.6445	−	10.8862i	−1.10443	−	0.347040i
$985$	0.0470680	+	0.236627i	0.00149971	+	0.00753956i
$986$	−0.198267	+	0.367996i	−0.00631411	+	0.0117194i
$987$	−6.58465	+	8.02342i	−0.209592	+	0.255388i
$988$	−14.3557	+	69.7541i	−0.456717	+	2.21917i
$989$	−15.1765	−	8.11200i	−0.482584	−	0.257947i
$990$	0.227813		0.000754243i	0.00724036		2.39714e-5i
$991$	30.1693	+	30.1693i	0.958359	+	0.958359i	0.999167	−	0.0408078i	$-0.0129931\pi$
$991$	30.1693	+	30.1693i	0.958359	+	0.958359i	−0.0408078	+	0.999167i	$0.512993\pi$
$992$	15.3392	+	6.65330i	0.487022	+	0.211242i
$993$	−37.3470	+	37.3470i	−1.18517	+	1.18517i
$994$	−3.39442	+	3.37202i	−0.107664	+	0.106954i
$995$	−1.30260	+	2.43699i	−0.0412951	+	0.0772577i
$996$	−9.45424	−	49.2312i	−0.299569	−	1.55995i
$997$	−8.15088	−	6.68925i	−0.258141	−	0.211851i	0.496417	−	0.868084i	$-0.334649\pi$
$997$	−8.15088	−	6.68925i	−0.258141	−	0.211851i	−0.754558	+	0.656233i	$0.772149\pi$
$998$	−22.1846	+	6.64949i	−0.702240	+	0.210486i
$999$	5.97533	−	1.18857i	0.189051	−	0.0376046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.b.141.44	✓	784
128.69	even	32	inner	896.2.bn.b.197.44	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.b.141.44	✓	784	1.1	even	1	trivial
896.2.bn.b.197.44	yes	784	128.69	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)

\(f(q)\)	\(=\)	\(q+(1.30835 - 0.536867i) q^{2} +(-0.445686 - 1.46923i) q^{3} +(1.42355 - 1.40482i) q^{4} +(0.0111242 + 0.112946i) q^{5} +(-1.37189 - 1.68299i) q^{6} +(-0.555570 + 0.831470i) q^{7} +(1.10829 - 2.60225i) q^{8} +(0.534412 - 0.357083i) q^{9} +O(q^{10})\)	\(q+(1.30835 - 0.536867i) q^{2} +(-0.445686 - 1.46923i) q^{3} +(1.42355 - 1.40482i) q^{4} +(0.0111242 + 0.112946i) q^{5} +(-1.37189 - 1.68299i) q^{6} +(-0.555570 + 0.831470i) q^{7} +(1.10829 - 2.60225i) q^{8} +(0.534412 - 0.357083i) q^{9} +(0.0751911 + 0.141800i) q^{10} +(1.94760 - 1.04101i) q^{11} +(-2.69845 - 1.46541i) q^{12} +(-4.72026 - 0.464905i) q^{13} +(-0.280490 + 1.38612i) q^{14} +(0.160985 - 0.0666822i) q^{15} +(0.0529711 - 3.99965i) q^{16} +(-4.49190 - 1.86060i) q^{17} +(0.507491 - 0.754097i) q^{18} +(5.80324 - 4.76260i) q^{19} +(0.174504 + 0.145156i) q^{20} +(1.46923 + 0.445686i) q^{21} +(1.98925 - 2.40761i) q^{22} +(-0.312426 + 1.57067i) q^{23} +(-4.31725 - 0.468552i) q^{24} +(4.89129 - 0.972939i) q^{25} +(-6.42534 + 1.92590i) q^{26} +(-4.32332 - 3.54805i) q^{27} +(0.377183 + 1.96411i) q^{28} +(0.0286577 - 0.0536148i) q^{29} +(0.174825 - 0.173671i) q^{30} +(-2.09000 + 2.09000i) q^{31} +(-2.07798 - 5.26137i) q^{32} +(-2.39751 - 2.39751i) q^{33} +(-6.87586 - 0.0227646i) q^{34} +(-0.100091 - 0.0534998i) q^{35} +(0.259124 - 1.25908i) q^{36} +(-0.691058 + 0.842057i) q^{37} +(5.03577 - 9.34670i) q^{38} +(1.42070 + 7.14235i) q^{39} +(0.306241 + 0.0962289i) q^{40} +(8.20175 + 1.63143i) q^{41} +(2.16154 - 0.205669i) q^{42} +(-3.11927 + 10.2829i) q^{43} +(1.31006 - 4.21796i) q^{44} +(0.0462758 + 0.0563872i) q^{45} +(0.434481 + 2.22272i) q^{46} +(-2.58708 + 6.24576i) q^{47} +(-5.90001 + 1.70476i) q^{48} +(-0.382683 - 0.923880i) q^{49} +(5.87717 - 3.89892i) q^{50} +(-0.731679 + 7.42887i) q^{51} +(-7.37262 + 5.96930i) q^{52} +(-5.83727 - 10.9208i) q^{53} +(-7.56124 - 2.32104i) q^{54} +(0.139243 + 0.208392i) q^{55} +(1.54795 + 2.36724i) q^{56} +(-9.58376 - 6.40367i) q^{57} +(0.00871021 - 0.0855322i) q^{58} +(2.25421 - 0.222020i) q^{59} +(0.135493 - 0.321080i) q^{60} +(6.60790 - 2.00448i) q^{61} +(-1.61240 + 3.85650i) q^{62} +0.642732i q^{63} +(-5.54337 - 5.76810i) q^{64} -0.538304i q^{65} +(-4.42391 - 1.84963i) q^{66} +(7.29886 - 2.21408i) q^{67} +(-9.00823 + 3.66164i) q^{68} +(2.44692 - 0.241001i) q^{69} +(-0.159676 - 0.0162607i) q^{70} +(2.81306 + 1.87963i) q^{71} +(-0.336932 - 1.78642i) q^{72} +(-5.81704 - 8.70581i) q^{73} +(-0.452071 + 1.47271i) q^{74} +(-3.60945 - 6.75280i) q^{75} +(1.57060 - 14.9323i) q^{76} +(-0.216457 + 2.19773i) q^{77} +(5.69326 + 8.58194i) q^{78} +(3.99462 + 9.64387i) q^{79} +(0.452332 - 0.0385099i) q^{80} +(-2.54817 + 6.15184i) q^{81} +(11.6066 - 2.26877i) q^{82} +(10.3569 + 12.6199i) q^{83} +(2.71762 - 1.42954i) q^{84} +(0.160178 - 0.528037i) q^{85} +(1.43944 + 15.1282i) q^{86} +(-0.0915448 - 0.0182094i) q^{87} +(-0.550464 - 6.22189i) q^{88} +(1.82155 + 9.15757i) q^{89} +(0.0908173 + 0.0489301i) q^{90} +(3.00899 - 3.66647i) q^{91} +(1.76176 + 2.67483i) q^{92} +(4.00217 + 2.13921i) q^{93} +(-0.0316531 + 9.56054i) q^{94} +(0.602470 + 0.602470i) q^{95} +(-6.80403 + 5.39794i) q^{96} +(-2.80154 + 2.80154i) q^{97} +(-0.996684 - 1.00331i) q^{98} +(0.669093 - 1.25178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q+O(q^{10}) \) 784 * q	\( 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) \) 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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