LMFDB - Embedded newform 756.2.cf.a.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(155,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 7, 0]))

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

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

chi := DirichletCharacter("756.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	756.239
Dual form			756.2.cf.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41412 + 0.0164052i) q^{2} +(0.147426 - 1.72577i) q^{3} +(1.99946 - 0.0463977i) q^{4} +(-3.09496 - 0.545724i) q^{5} +(-0.180167 + 2.44285i) q^{6} +(0.642788 + 0.766044i) q^{7} +(-2.82671 + 0.0984134i) q^{8} +(-2.95653 - 0.508847i) q^{9} +O(q^{10})$	\(q+(-1.41412 + 0.0164052i) q^{2} +(0.147426 - 1.72577i) q^{3} +(1.99946 - 0.0463977i) q^{4} +(-3.09496 - 0.545724i) q^{5} +(-0.180167 + 2.44285i) q^{6} +(0.642788 + 0.766044i) q^{7} +(-2.82671 + 0.0984134i) q^{8} +(-2.95653 - 0.508847i) q^{9} +(4.38559 + 0.720946i) q^{10} +(0.881478 + 4.99911i) q^{11} +(0.214702 - 3.45744i) q^{12} +(-0.371483 + 0.135209i) q^{13} +(-0.921545 - 1.07273i) q^{14} +(-1.39807 + 5.26071i) q^{15} +(3.99569 - 0.185541i) q^{16} +(3.65557 + 2.11055i) q^{17} +(4.18923 + 0.671067i) q^{18} +(3.95341 - 2.28250i) q^{19} +(-6.21357 - 0.947556i) q^{20} +(1.41678 - 0.996365i) q^{21} +(-1.32853 - 7.05487i) q^{22} +(1.71110 + 1.43578i) q^{23} +(-0.246894 + 4.89275i) q^{24} +(4.58248 + 1.66789i) q^{25} +(0.523102 - 0.197295i) q^{26} +(-1.31402 + 5.02726i) q^{27} +(1.32077 + 1.50185i) q^{28} +(0.798106 - 2.19278i) q^{29} +(1.89073 - 7.46221i) q^{30} +(6.38089 - 7.60445i) q^{31} +(-5.64734 + 0.327927i) q^{32} +(8.75724 - 0.784223i) q^{33} +(-5.20404 - 2.92459i) q^{34} +(-1.57135 - 2.72166i) q^{35} +(-5.93508 - 0.880243i) q^{36} +(-2.81640 + 4.87815i) q^{37} +(-5.55314 + 3.29258i) q^{38} +(0.178572 + 0.661025i) q^{39} +(8.80227 + 1.23802i) q^{40} +(-0.801612 - 2.20241i) q^{41} +(-1.98714 + 1.43222i) q^{42} +(-0.945108 + 0.166648i) q^{43} +(1.99443 + 9.95463i) q^{44} +(8.87265 + 3.18831i) q^{45} +(-2.44325 - 2.00229i) q^{46} +(1.77248 - 1.48729i) q^{47} +(0.268871 - 6.92298i) q^{48} +(-0.173648 + 0.984808i) q^{49} +(-6.50753 - 2.28341i) q^{50} +(4.18124 - 5.99751i) q^{51} +(-0.736492 + 0.287580i) q^{52} -5.41162i q^{53} +(1.77571 - 7.13070i) q^{54} -15.9531i q^{55} +(-1.89237 - 2.10213i) q^{56} +(-3.35622 - 7.15915i) q^{57} +(-1.09264 + 3.11394i) q^{58} +(0.521825 - 2.95942i) q^{59} +(-2.55130 + 10.5835i) q^{60} +(-8.35826 + 7.01341i) q^{61} +(-8.89858 + 10.8583i) q^{62} +(-1.51062 - 2.59191i) q^{63} +(7.98063 - 0.556373i) q^{64} +(1.22351 - 0.215738i) q^{65} +(-12.3709 + 1.25265i) q^{66} +(5.23878 + 14.3934i) q^{67} +(7.40710 + 4.05035i) q^{68} +(2.73008 - 2.74128i) q^{69} +(2.26673 + 3.82297i) q^{70} +(6.57003 - 11.3796i) q^{71} +(8.40735 + 1.14740i) q^{72} +(0.741893 + 1.28500i) q^{73} +(3.90270 - 6.94448i) q^{74} +(3.55396 - 7.66239i) q^{75} +(7.79878 - 4.74720i) q^{76} +(-3.26294 + 3.88862i) q^{77} +(-0.263366 - 0.931838i) q^{78} +(0.0581453 - 0.159753i) q^{79} +(-12.4678 - 1.60631i) q^{80} +(8.48215 + 3.00884i) q^{81} +(1.16971 + 3.10132i) q^{82} +(10.4128 + 3.78994i) q^{83} +(2.78656 - 2.05793i) q^{84} +(-10.1621 - 8.52698i) q^{85} +(1.33376 - 0.251165i) q^{86} +(-3.66656 - 1.70062i) q^{87} +(-2.98366 - 14.0443i) q^{88} +(13.2487 - 7.64915i) q^{89} +(-12.5993 - 4.36309i) q^{90} +(-0.342360 - 0.197662i) q^{91} +(3.48789 + 2.79140i) q^{92} +(-12.1828 - 12.1330i) q^{93} +(-2.48210 + 2.13228i) q^{94} +(-13.4812 + 4.90677i) q^{95} +(-0.266642 + 9.79433i) q^{96} +(2.82765 + 16.0364i) q^{97} +(0.229403 - 1.39548i) q^{98} +(-0.0623368 - 15.2286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q+O(q^{10}) $ 648 * q	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41412	+	0.0164052i	−0.999933	+	0.0116002i
$2$	−1.41412	+	0.0164052i	−0.999933	+	0.0116002i
$3$	0.147426	−	1.72577i	0.0851167	−	0.996371i
$3$	0.147426	−	1.72577i	0.0851167	−	0.996371i
$4$	1.99946	−	0.0463977i	0.999731	−	0.0231989i
$5$	−3.09496	−	0.545724i	−1.38411	−	0.244055i	−0.568510	−	0.822676i	$-0.692480\pi$
$5$	−3.09496	−	0.545724i	−1.38411	−	0.244055i	−0.815597	+	0.578621i	$0.803591\pi$
$6$	−0.180167	+	2.44285i	−0.0735528	+	0.997291i
$7$	0.642788	+	0.766044i	0.242951	+	0.289538i
$7$	0.642788	+	0.766044i	0.242951	+	0.289538i
$8$	−2.82671	+	0.0984134i	−0.999394	+	0.0347944i
$9$	−2.95653	−	0.508847i	−0.985510	−	0.169616i
$10$	4.38559	+	0.720946i	1.38684	+	0.227983i
$11$	0.881478	+	4.99911i	0.265776	+	1.50729i	0.766818	+	0.641865i	$0.221839\pi$
$11$	0.881478	+	4.99911i	0.265776	+	1.50729i	−0.501042	+	0.865423i	$0.667050\pi$
$12$	0.214702	−	3.45744i	0.0619791	−	0.998077i
$13$	−0.371483	+	0.135209i	−0.103031	+	0.0375001i	−0.393021	−	0.919529i	$-0.628570\pi$
$13$	−0.371483	+	0.135209i	−0.103031	+	0.0375001i	0.289990	+	0.957030i	$0.406348\pi$
$14$	−0.921545	−	1.07273i	−0.246293	−	0.286700i
$15$	−1.39807	+	5.26071i	−0.360980	+	1.35831i
$16$	3.99569	−	0.185541i	0.998924	−	0.0463852i
$17$	3.65557	+	2.11055i	0.886607	+	0.511883i	0.872831	−	0.488022i	$-0.162282\pi$
$17$	3.65557	+	2.11055i	0.886607	+	0.511883i	0.0137757	+	0.999905i	$0.495615\pi$
$18$	4.18923	+	0.671067i	0.987412	+	0.158172i
$19$	3.95341	−	2.28250i	0.906974	−	0.523642i	0.0275175	−	0.999621i	$-0.491240\pi$
$19$	3.95341	−	2.28250i	0.906974	−	0.523642i	0.879456	+	0.475980i	$0.157906\pi$
$20$	−6.21357	−	0.947556i	−1.38940	−	0.211880i
$21$	1.41678	−	0.996365i	0.309166	−	0.217425i
$22$	−1.32853	−	7.05487i	−0.283242	−	1.50410i
$23$	1.71110	+	1.43578i	0.356788	+	0.299381i	0.803509	−	0.595293i	$-0.202964\pi$
$23$	1.71110	+	1.43578i	0.356788	+	0.299381i	−0.446721	+	0.894673i	$0.647408\pi$
$24$	−0.246894	+	4.89275i	−0.0503970	+	0.998729i
$25$	4.58248	+	1.66789i	0.916496	+	0.333577i
$26$	0.523102	−	0.197295i	0.102589	−	0.0386928i
$27$	−1.31402	+	5.02726i	−0.252883	+	0.967497i
$28$	1.32077	+	1.50185i	0.249602	+	0.283823i
$29$	0.798106	−	2.19278i	0.148205	−	0.407189i	−0.843270	−	0.537491i	$-0.819372\pi$
$29$	0.798106	−	2.19278i	0.148205	−	0.407189i	0.991474	+	0.130302i	$0.0415946\pi$
$30$	1.89073	−	7.46221i	0.345199	−	1.36241i
$31$	6.38089	−	7.60445i	1.14604	−	1.36580i	0.225930	−	0.974144i	$-0.427458\pi$
$31$	6.38089	−	7.60445i	1.14604	−	1.36580i	0.920112	−	0.391655i	$-0.128097\pi$
$32$	−5.64734	+	0.327927i	−0.998318	+	0.0579698i
$33$	8.75724	−	0.784223i	1.52444	−	0.136516i
$34$	−5.20404	−	2.92459i	−0.892485	−	0.501563i
$35$	−1.57135	−	2.72166i	−0.265607	−	0.460044i
$36$	−5.93508	−	0.880243i	−0.989180	−	0.146707i
$37$	−2.81640	+	4.87815i	−0.463013	+	0.801962i	−0.999109	−	0.0421945i	$-0.986565\pi$
$37$	−2.81640	+	4.87815i	−0.463013	+	0.801962i	0.536096	+	0.844157i	$0.319898\pi$
$38$	−5.55314	+	3.29258i	−0.900838	+	0.534127i
$39$	0.178572	+	0.661025i	0.0285944	+	0.105849i
$40$	8.80227	+	1.23802i	1.39176	+	0.195748i
$41$	−0.801612	−	2.20241i	−0.125191	−	0.343959i	0.861226	−	0.508223i	$-0.169697\pi$
$41$	−0.801612	−	2.20241i	−0.125191	−	0.343959i	−0.986416	+	0.164264i	$0.947475\pi$
$42$	−1.98714	+	1.43222i	−0.306623	+	0.220996i
$43$	−0.945108	+	0.166648i	−0.144128	+	0.0254136i	−0.245246	−	0.969461i	$-0.578869\pi$
$43$	−0.945108	+	0.166648i	−0.144128	+	0.0254136i	0.101119	+	0.994874i	$0.467758\pi$
$44$	1.99443	+	9.95463i	0.300671	+	1.50072i
$45$	8.87265	+	3.18831i	1.32266	+	0.475285i
$46$	−2.44325	−	2.00229i	−0.360237	−	0.295222i
$47$	1.77248	−	1.48729i	0.258543	−	0.216943i	−0.504298	−	0.863530i	$-0.668249\pi$
$47$	1.77248	−	1.48729i	0.258543	−	0.216943i	0.762841	+	0.646587i	$0.223804\pi$
$48$	0.268871	−	6.92298i	0.0388082	−	0.999247i
$49$	−0.173648	+	0.984808i	−0.0248069	+	0.140687i
$50$	−6.50753	−	2.28341i	−0.920304	−	0.322923i
$51$	4.18124	−	5.99751i	0.585490	−	0.839819i
$52$	−0.736492	+	0.287580i	−0.102133	+	0.0398802i
$53$		−	5.41162i		−	0.743344i	−0.928364	−	0.371672i	$-0.878785\pi$
$53$		−	5.41162i		−	0.743344i	0.928364	−	0.371672i	$-0.121215\pi$
$54$	1.77571	−	7.13070i	0.241643	−	0.970365i
$55$		−	15.9531i		−	2.15111i
$56$	−1.89237	−	2.10213i	−0.252878	−	0.280909i
$57$	−3.35622	−	7.15915i	−0.444543	−	0.948253i
$58$	−1.09264	+	3.11394i	−0.143471	+	0.408881i
$59$	0.521825	−	2.95942i	0.0679359	−	0.385283i	−0.931814	−	0.362935i	$-0.881775\pi$
$59$	0.521825	−	2.95942i	0.0679359	−	0.385283i	0.999750	−	0.0223482i	$-0.00711426\pi$
$60$	−2.55130	+	10.5835i	−0.329372	+	1.36632i
$61$	−8.35826	+	7.01341i	−1.07016	+	0.897975i	−0.995067	−	0.0992011i	$-0.968371\pi$
$61$	−8.35826	+	7.01341i	−1.07016	+	0.897975i	−0.0750976	+	0.997176i	$0.523927\pi$
$62$	−8.89858	+	10.8583i	−1.13012	+	1.37900i
$63$	−1.51062	−	2.59191i	−0.190321	−	0.326551i
$64$	7.98063	−	0.556373i	0.997579	−	0.0695466i
$65$	1.22351	−	0.215738i	0.151758	−	0.0267590i
$66$	−12.3709	+	1.25265i	−1.52275	+	0.154190i
$67$	5.23878	+	14.3934i	0.640018	+	1.75844i	0.651668	+	0.758504i	$0.274069\pi$
$67$	5.23878	+	14.3934i	0.640018	+	1.75844i	−0.0116498	+	0.999932i	$0.503708\pi$
$68$	7.40710	+	4.05035i	0.898243	+	0.491177i
$69$	2.73008	−	2.74128i	0.328663	−	0.330011i
$70$	2.26673	+	3.82297i	0.270925	+	0.456932i
$71$	6.57003	−	11.3796i	0.779719	−	1.35051i	−0.152385	−	0.988321i	$-0.548695\pi$
$71$	6.57003	−	11.3796i	0.779719	−	1.35051i	0.932104	−	0.362191i	$-0.117971\pi$
$72$	8.40735	+	1.14740i	0.990815	+	0.135223i
$73$	0.741893	+	1.28500i	0.0868320	+	0.150397i	0.906170	−	0.422913i	$-0.138992\pi$
$73$	0.741893	+	1.28500i	0.0868320	+	0.150397i	−0.819338	+	0.573310i	$0.805659\pi$
$74$	3.90270	−	6.94448i	0.453679	−	0.807279i
$75$	3.55396	−	7.66239i	0.410376	−	0.884777i
$76$	7.79878	−	4.74720i	0.894582	−	0.544541i
$77$	−3.26294	+	3.88862i	−0.371846	+	0.443149i
$78$	−0.263366	−	0.931838i	−0.0298204	−	0.105510i
$79$	0.0581453	−	0.159753i	0.00654185	−	0.0179736i	−0.936379	−	0.350991i	$-0.885845\pi$
$79$	0.0581453	−	0.159753i	0.00654185	−	0.0179736i	0.942921	+	0.333018i	$0.108067\pi$
$80$	−12.4678	−	1.60631i	−1.39394	−	0.179591i
$81$	8.48215	+	3.00884i	0.942461	+	0.334316i
$82$	1.16971	+	3.10132i	0.129172	+	0.342483i
$83$	10.4128	+	3.78994i	1.14295	+	0.416000i	0.842978	−	0.537947i	$-0.180800\pi$
$83$	10.4128	+	3.78994i	1.14295	+	0.416000i	0.299973	+	0.953948i	$0.403022\pi$
$84$	2.78656	−	2.05793i	0.304039	−	0.224539i
$85$	−10.1621	−	8.52698i	−1.10223	−	0.924881i
$86$	1.33376	−	0.251165i	0.143823	−	0.0270838i
$87$	−3.66656	−	1.70062i	−0.393097	−	0.182325i
$88$	−2.98366	−	14.0443i	−0.318060	−	1.49713i
$89$	13.2487	−	7.64915i	1.40436	−	0.810808i	0.409524	−	0.912299i	$-0.365695\pi$
$89$	13.2487	−	7.64915i	1.40436	−	0.810808i	0.994836	+	0.101491i	$0.0323613\pi$
$90$	−12.5993	−	4.36309i	−1.32808	−	0.459910i
$91$	−0.342360	−	0.197662i	−0.0358891	−	0.0207206i
$92$	3.48789	+	2.79140i	0.363637	+	0.291023i
$93$	−12.1828	−	12.1330i	−1.26330	−	1.25813i
$94$	−2.48210	+	2.13228i	−0.256009	+	0.219928i
$95$	−13.4812	+	4.90677i	−1.38315	+	0.503424i
$96$	−0.266642	+	9.79433i	−0.0272141	+	0.999630i
$97$	2.82765	+	16.0364i	0.287104	+	1.62825i	0.697670	+	0.716419i	$0.254220\pi$
$97$	2.82765	+	16.0364i	0.287104	+	1.62825i	−0.410566	+	0.911831i	$0.634669\pi$
$98$	0.229403	−	1.39548i	0.0231732	−	0.140965i
$99$	−0.0623368	−	15.2286i	−0.00626509	−	1.53053i
$100$	9.23988	+	3.12226i	0.923988	+	0.312226i
$101$	7.55873	+	9.00814i	0.752121	+	0.896343i	0.997322	−	0.0731289i	$-0.0232985\pi$
$101$	7.55873	+	9.00814i	0.752121	+	0.896343i	−0.245201	+	0.969472i	$0.578854\pi$
$102$	−5.81437	+	8.54978i	−0.575709	+	0.846555i
$103$	14.9084	+	2.62876i	1.46897	+	0.259019i	0.850161	−	0.526523i	$-0.176505\pi$
$103$	14.9084	+	2.62876i	1.46897	+	0.259019i	0.618809	+	0.785542i	$0.287616\pi$
$104$	1.03677	−	0.418755i	0.101664	−	0.0410623i
$105$	−4.92860	+	2.31054i	−0.480982	+	0.225485i
$106$	0.0887786	+	7.65268i	0.00862294	+	0.743294i
$107$	0.146669			0.0141790			0.00708952	−	0.999975i	$-0.497743\pi$
$107$	0.146669			0.0141790			0.00708952	+	0.999975i	$0.497743\pi$
$108$	−2.39408	+	10.1128i	−0.230370	+	0.973103i
$109$	14.3441			1.37391			0.686956	−	0.726699i	$-0.258947\pi$
$109$	14.3441			1.37391			0.686956	+	0.726699i	$0.258947\pi$
$110$	0.261713	+	22.5595i	0.0249533	+	2.15097i
$111$	8.00332	+	5.57961i	0.759642	+	0.529593i
$112$	2.71052	+	2.94162i	0.256120	+	0.277957i
$113$	−1.17779	−	0.207677i	−0.110798	−	0.0195366i	0.117974	−	0.993017i	$-0.462360\pi$
$113$	−1.17779	−	0.207677i	−0.110798	−	0.0195366i	−0.228772	+	0.973480i	$0.573471\pi$
$114$	4.86354	+	10.0688i	0.455513	+	0.943032i
$115$	−4.51223	−	5.37746i	−0.420767	−	0.501451i
$116$	1.49404	−	4.42141i	0.138718	−	0.410518i
$117$	1.16710	−	0.210721i	0.107898	−	0.0194811i
$118$	−0.689373	+	4.19353i	−0.0634619	+	0.386046i
$119$	0.732985	+	4.15696i	0.0671926	+	0.381068i
$120$	3.43422	−	15.0081i	0.313500	−	1.37005i
$121$	−13.8775	+	5.05098i	−1.26159	+	0.459180i
$122$	11.7045	−	10.0549i	1.05968	−	0.910329i
$123$	−3.91902	+	1.05870i	−0.353366	+	0.0954598i
$124$	12.4055	−	15.5009i	1.11405	−	1.39202i
$125$	0.335928	+	0.193948i	0.0300463	+	0.0173473i
$126$	2.17872	+	3.64049i	0.194096	+	0.324321i
$127$	−10.2761	+	5.93289i	−0.911854	+	0.526459i	−0.881027	−	0.473066i	$-0.843147\pi$
$127$	−10.2761	+	5.93289i	−0.911854	+	0.526459i	−0.0308267	+	0.999525i	$0.509814\pi$
$128$	−11.2764	+	0.917701i	−0.996705	+	0.0811141i
$129$	0.148262	+	1.65560i	0.0130537	+	0.145768i
$130$	−1.72665	+	0.325151i	−0.151437	+	0.0285176i
$131$	9.63366	+	8.08360i	0.841697	+	0.706267i	0.957945	−	0.286953i	$-0.0926423\pi$
$131$	9.63366	+	8.08360i	0.841697	+	0.706267i	−0.116248	+	0.993220i	$0.537087\pi$
$132$	17.4734	−	1.97434i	1.52086	−	0.171844i
$133$	4.28970	+	1.56132i	0.371964	+	0.135384i
$134$	−7.64438	−	20.2681i	−0.660374	−	1.75089i
$135$	6.81033	−	14.8421i	0.586140	−	1.27740i
$136$	−10.5410	−	5.60615i	−0.903881	−	0.480724i
$137$	−0.0834772	+	0.229352i	−0.00713194	+	0.0195948i	−0.943208	−	0.332204i	$-0.892208\pi$
$137$	−0.0834772	+	0.229352i	−0.00713194	+	0.0195948i	0.936076	+	0.351799i	$0.114430\pi$
$138$	−3.81568	+	3.92128i	−0.324813	+	0.333801i
$139$	−2.99326	+	3.56723i	−0.253885	+	0.302569i	−0.877900	−	0.478844i	$-0.841056\pi$
$139$	−2.99326	+	3.56723i	−0.253885	+	0.302569i	0.624015	+	0.781412i	$0.285500\pi$
$140$	−3.26813	−	5.36895i	−0.276208	−	0.453759i
$141$	−2.30540	−	3.27815i	−0.194150	−	0.276070i
$142$	−9.10411	+	16.1999i	−0.764000	+	1.35947i
$143$	−1.00338	−	1.73790i	−0.0839066	−	0.145330i
$144$	−11.9078	−	1.48464i	−0.992317	−	0.123720i
$145$	−3.66676	+	6.35101i	−0.304508	+	0.527423i
$146$	−1.07020	−	1.80497i	−0.0885708	−	0.149380i
$147$	1.67395	+	0.444863i	0.138065	+	0.0366916i
$148$	−5.40495	+	9.88434i	−0.444284	+	0.812488i
$149$	2.20287	+	6.05235i	0.180467	+	0.495828i	0.996633	−	0.0819888i	$-0.0261272\pi$
$149$	2.20287	+	6.05235i	0.180467	+	0.495828i	−0.816167	+	0.577816i	$0.803905\pi$
$150$	−4.90001	+	10.8938i	−0.400084	+	0.889478i
$151$	18.2616	−	3.22001i	1.48611	−	0.262041i	0.629092	−	0.777331i	$-0.283427\pi$
$151$	18.2616	−	3.22001i	1.48611	−	0.262041i	0.857016	+	0.515290i	$0.172316\pi$
$152$	−10.9505	+	6.84105i	−0.888205	+	0.554882i
$153$	−9.73387	−	8.10002i	−0.786937	−	0.654848i
$154$	4.55038	−	5.55249i	0.366680	−	0.447433i
$155$	−23.8985	+	20.0532i	−1.91957	+	1.61071i
$156$	0.387718	+	1.31341i	0.0310423	+	0.105157i
$157$	1.11503	−	6.32364i	0.0889890	−	0.504682i	−0.907435	−	0.420192i	$-0.861963\pi$
$157$	1.11503	−	6.32364i	0.0889890	−	0.504682i	0.996424	−	0.0844899i	$-0.0269261\pi$
$158$	−0.0796035	+	0.226863i	−0.00633292	+	0.0180483i
$159$	−9.33919	−	0.797816i	−0.740646	−	0.0632709i
$160$	17.6572	+	2.06697i	1.39593	+	0.163409i
$161$			2.23368i			0.176038i
$162$	−12.0441	−	4.11571i	−0.946276	−	0.323360i
$163$		−	21.6027i		−	1.69205i	−0.533140	−	0.846027i	$-0.678988\pi$
$163$		−	21.6027i		−	1.69205i	0.533140	−	0.846027i	$-0.321012\pi$
$164$	−1.70498	−	4.36644i	−0.133137	−	0.340962i
$165$	−27.5312	−	2.35190i	−2.14330	−	0.183095i
$166$	−14.7871	−	5.18860i	−1.14770	−	0.402714i
$167$	0.960537	−	5.44748i	0.0743286	−	0.421538i	−0.924825	−	0.380394i	$-0.875788\pi$
$167$	0.960537	−	5.44748i	0.0743286	−	0.421538i	0.999153	−	0.0411446i	$-0.0131004\pi$
$168$	−3.90677	+	2.95587i	−0.301414	+	0.228050i
$169$	−9.83886	+	8.25578i	−0.756835	+	0.635060i
$170$	14.5102	+	11.8915i	1.11289	+	0.912033i
$171$	−12.8498	+	4.73661i	−0.982650	+	0.362217i
$172$	−1.88198	+	0.377057i	−0.143499	+	0.0287504i
$173$	−21.5614	+	3.80186i	−1.63928	+	0.289050i	−0.915903	−	0.401400i	$-0.868524\pi$
$173$	−21.5614	+	3.80186i	−1.63928	+	0.289050i	−0.723380	+	0.690450i	$0.757412\pi$
$174$	5.21285	+	2.34472i	0.395185	+	0.177753i
$175$	1.66789	+	4.58248i	0.126080	+	0.346403i
$176$	4.44965	+	19.8114i	0.335405	+	1.49334i
$177$	−5.03033	−	1.33684i	−0.378103	−	0.100483i
$178$	−18.6098	+	11.0341i	−1.39486	+	0.827044i
$179$	−3.25380	+	5.63574i	−0.243200	+	0.421235i	−0.961624	−	0.274370i	$-0.911531\pi$
$179$	−3.25380	+	5.63574i	−0.243200	+	0.421235i	0.718424	+	0.695606i	$0.244864\pi$
$180$	17.8884	+	5.96323i	1.33333	+	0.444473i
$181$	−6.07868	−	10.5286i	−0.451825	−	0.782584i	0.546675	−	0.837345i	$-0.315894\pi$
$181$	−6.07868	−	10.5286i	−0.451825	−	0.782584i	−0.998499	+	0.0547614i	$0.982560\pi$
$182$	0.487381	+	0.273901i	0.0361271	+	0.0203029i
$183$	10.8713	+	15.4583i	0.803627	+	1.14271i
$184$	−4.97808	−	3.89014i	−0.366989	−	0.286785i
$185$	11.3788	−	13.5607i	0.836583	−	0.997001i
$186$	17.4269	+	16.9577i	1.27781	+	1.24340i
$187$	−7.32854	+	20.1350i	−0.535916	+	1.47242i
$188$	3.47500	−	3.05602i	0.253441	−	0.222883i
$189$	−4.69574	+	2.22486i	−0.341565	+	0.161835i
$190$	18.9836	−	7.15992i	1.37721	−	0.519435i
$191$	−12.2246	−	4.44938i	−0.884538	−	0.321946i	−0.140499	−	0.990081i	$-0.544871\pi$
$191$	−12.2246	−	4.44938i	−0.884538	−	0.321946i	−0.744040	+	0.668135i	$0.767093\pi$
$192$	0.216386	−	13.8547i	0.0156163	−	0.999878i
$193$	15.4310	+	12.9481i	1.11075	+	0.932027i	0.998100	−	0.0616079i	$-0.0196228\pi$
$193$	15.4310	+	12.9481i	1.11075	+	0.932027i	0.112646	+	0.993635i	$0.464067\pi$
$194$	−4.26171	−	22.6310i	−0.305973	−	1.62481i
$195$	−0.191935	−	2.14330i	−0.0137448	−	0.153485i
$196$	−0.301510	+	1.97714i	−0.0215364	+	0.141224i
$197$	−11.5455	+	6.66581i	−0.822585	+	0.474919i	−0.851307	−	0.524668i	$-0.824189\pi$
$197$	−11.5455	+	6.66581i	−0.822585	+	0.474919i	0.0287223	+	0.999587i	$0.490856\pi$
$198$	0.337979	+	21.5340i	0.0240191	+	1.53035i
$199$	−19.3510	−	11.1723i	−1.37175	−	0.791982i	−0.380605	−	0.924738i	$-0.624284\pi$
$199$	−19.3510	−	11.1723i	−1.37175	−	0.791982i	−0.991149	+	0.132756i	$0.957617\pi$
$200$	−13.1175	−	4.26366i	−0.927547	−	0.301486i
$201$	25.6120	−	6.91893i	1.80653	−	0.488024i
$202$	−10.8367	−	12.6146i	−0.762468	−	0.887558i
$203$	2.19278	−	0.798106i	0.153903	−	0.0560161i
$204$	8.08195	−	12.1858i	0.565850	−	0.853176i
$205$	1.27905	+	7.25383i	0.0893324	+	0.506629i
$206$	−21.1254	−	3.47280i	−1.47188	−	0.241961i
$207$	−4.32832	−	5.11561i	−0.300839	−	0.355560i
$208$	−1.45924	+	0.609178i	−0.101180	+	0.0422389i
$209$	14.8953	+	17.7515i	1.03033	+	1.22790i
$210$	6.93172	−	3.34823i	0.478334	−	0.231050i
$211$	−27.3386	−	4.82053i	−1.88206	−	0.331859i	−0.889835	−	0.456282i	$-0.849181\pi$
$211$	−27.3386	−	4.82053i	−1.88206	−	0.331859i	−0.992229	+	0.124423i	$0.960292\pi$
$212$	−0.251087	−	10.8203i	−0.0172447	−	0.743144i
$213$	−18.6700	−	13.0160i	−1.27924	−	0.891840i
$214$	−0.207407	+	0.00240613i	−0.0141781	+	0.000164480i
$215$	3.01601			0.205690
$216$	3.21961	−	14.3399i	0.219067	−	0.975710i
$217$	9.92690			0.673882
$218$	−20.2842	+	0.235317i	−1.37382	+	0.0159377i
$219$	2.32698	−	1.09089i	0.157242	−	0.0737155i
$220$	−0.740186	−	31.8975i	−0.0499033	−	2.15053i
$221$	−1.64335	−	0.289766i	−0.110543	−	0.0194918i
$222$	−11.4092	−	7.75893i	−0.765734	−	0.520746i
$223$	−6.17475	−	7.35878i	−0.413492	−	0.492780i	0.518593	−	0.855021i	$-0.326456\pi$
$223$	−6.17475	−	7.35878i	−0.413492	−	0.492780i	−0.932084	+	0.362241i	$0.882012\pi$
$224$	−3.88125	−	4.11533i	−0.259327	−	0.274967i
$225$	−12.6995	−	7.26294i	−0.846636	−	0.484196i
$226$	1.66895	+	0.274358i	0.111017	+	0.0182500i
$227$	1.23474	+	7.00256i	0.0819526	+	0.464776i	0.997973	+	0.0636438i	$0.0202722\pi$
$227$	1.23474	+	7.00256i	0.0819526	+	0.464776i	−0.916020	+	0.401132i	$0.868617\pi$
$228$	−7.04281	−	14.1587i	−0.466421	−	0.937685i
$229$	5.12543	−	1.86550i	0.338698	−	0.123276i	−0.167071	−	0.985945i	$-0.553431\pi$
$229$	5.12543	−	1.86550i	0.338698	−	0.123276i	0.505769	+	0.862669i	$0.331209\pi$
$230$	6.46904	+	7.53035i	0.426556	+	0.496536i
$231$	6.22980	+	6.20435i	0.409890	+	0.408216i
$232$	−2.04022	+	6.27691i	−0.133947	+	0.412099i
$233$	9.85508	+	5.68983i	0.645628	+	0.372753i	0.786779	−	0.617235i	$-0.211747\pi$
$233$	9.85508	+	5.68983i	0.645628	+	0.372753i	−0.141151	+	0.989988i	$0.545080\pi$
$234$	−1.64696	+	0.317131i	−0.107665	+	0.0207315i
$235$	−6.29740	+	3.63581i	−0.410797	+	0.237174i
$236$	0.906060	−	5.94146i	0.0589795	−	0.386756i
$237$	−0.267124	−	0.123897i	−0.0173515	−	0.00804797i
$238$	−1.10472	−	5.86642i	−0.0716086	−	0.380263i
$239$	13.2755	+	11.1395i	0.858723	+	0.720555i	0.961693	−	0.274130i	$-0.0883899\pi$
$239$	13.2755	+	11.1395i	0.858723	+	0.720555i	−0.102969	+	0.994685i	$0.532834\pi$
$240$	−4.61018	+	21.2796i	−0.297586	+	1.37359i
$241$	20.0737	+	7.30624i	1.29306	+	0.470636i	0.894731	−	0.446605i	$-0.147367\pi$
$241$	20.0737	+	7.30624i	1.29306	+	0.470636i	0.398331	+	0.917242i	$0.369589\pi$
$242$	19.5415	−	7.37035i	1.25618	−	0.473784i
$243$	6.44305	−	14.1946i	0.413322	−	0.910585i
$244$	−16.3866	+	14.4108i	−1.04904	+	0.922560i
$245$	1.07487	−	2.95317i	0.0686707	−	0.188671i
$246$	5.52459	−	1.56142i	0.352235	−	0.0995525i
$247$	−1.16001	+	1.38244i	−0.0738096	+	0.0879628i
$248$	−17.2886	+	22.1236i	−1.09783	+	1.40485i
$249$	8.07567	−	17.4113i	0.511775	−	1.10340i
$250$	−0.478224	−	0.268755i	−0.0302455	−	0.0169975i
$251$	7.41945	+	12.8509i	0.468312	+	0.811139i	0.999344	−	0.0362120i	$-0.0115292\pi$
$251$	7.41945	+	12.8509i	0.468312	+	0.811139i	−0.531033	+	0.847351i	$0.678196\pi$
$252$	−3.14069	−	5.11234i	−0.197845	−	0.322047i
$253$	−5.66933	+	9.81956i	−0.356427	+	0.617351i
$254$	14.4343	−	8.55839i	0.905685	−	0.537001i
$255$	−16.2137	+	16.2802i	−1.01534	+	1.01951i
$256$	15.9311	−	1.48273i	0.995697	−	0.0926706i
$257$	1.48081	+	4.06848i	0.0923701	+	0.253785i	0.977271	−	0.211995i	$-0.0679961\pi$
$257$	1.48081	+	4.06848i	0.0923701	+	0.253785i	−0.884901	+	0.465780i	$0.845774\pi$
$258$	−0.236820	−	2.33879i	−0.0147438	−	0.145607i
$259$	−5.54722	+	0.978125i	−0.344688	+	0.0607777i
$260$	2.43635	−	0.488127i	0.151096	−	0.0302724i
$261$	−3.47541	+	6.07691i	−0.215123	+	0.376151i
$262$	−13.7557	−	11.2731i	−0.849833	−	0.696456i
$263$	−7.14963	+	5.99926i	−0.440865	+	0.369930i	−0.836033	−	0.548679i	$-0.815131\pi$
$263$	−7.14963	+	5.99926i	−0.440865	+	0.369930i	0.395168	+	0.918609i	$0.370686\pi$
$264$	−24.6770	+	3.07860i	−1.51877	+	0.189475i
$265$	−2.95326	+	16.7487i	−0.181417	+	1.02887i
$266$	−6.09175	−	2.13752i	−0.373509	−	0.131060i
$267$	−11.2474	−	23.9919i	−0.688331	−	1.46828i
$268$	11.1426	+	28.5360i	0.680640	+	1.74312i
$269$		−	16.1098i		−	0.982235i	−0.871093	−	0.491117i	$-0.836589\pi$
$269$		−	16.1098i		−	0.982235i	0.871093	−	0.491117i	$-0.163411\pi$
$270$	−9.38713	+	21.1002i	−0.571283	+	1.28411i
$271$		−	16.0309i		−	0.973807i	−0.873456	−	0.486904i	$-0.838126\pi$
$271$		−	16.0309i		−	0.973807i	0.873456	−	0.486904i	$-0.161874\pi$
$272$	14.9981	+	7.75484i	0.909396	+	0.470206i
$273$	−0.391591	+	0.561693i	−0.0237002	+	0.0339952i
$274$	0.114284	−	0.325700i	0.00690415	−	0.0196762i
$275$	−4.29859	+	24.3785i	−0.259215	+	1.47008i
$276$	5.33150	−	5.60775i	0.320919	−	0.337547i
$277$	−11.9080	+	9.99199i	−0.715481	+	0.600360i	−0.926131	−	0.377201i	$-0.876886\pi$
$277$	−11.9080	+	9.99199i	−0.715481	+	0.600360i	0.210650	+	0.977562i	$0.432442\pi$
$278$	4.17431	−	5.09359i	0.250358	−	0.305493i
$279$	−22.7348	+	19.2359i	−1.36110	+	1.15162i
$280$	4.70961	+	7.53871i	0.281453	+	0.450524i
$281$	−7.73152	+	1.36328i	−0.461224	+	0.0813262i	−0.399432	−	0.916763i	$-0.630793\pi$
$281$	−7.73152	+	1.36328i	−0.461224	+	0.0813262i	−0.0617920	+	0.998089i	$0.519682\pi$
$282$	3.31389	+	4.59788i	0.197339	+	0.273800i
$283$	1.00485	+	2.76079i	0.0597318	+	0.164112i	0.965969	−	0.258658i	$-0.0832802\pi$
$283$	1.00485	+	2.76079i	0.0597318	+	0.164112i	−0.906237	+	0.422770i	$0.861058\pi$
$284$	12.6085	−	23.0579i	0.748178	−	1.36824i
$285$	6.48044	+	23.9888i	0.383868	+	1.42098i
$286$	1.44740	+	2.44113i	0.0855868	+	0.144347i
$287$	1.17188	−	2.02975i	0.0691738	−	0.119813i
$288$	16.8634	+	1.90410i	0.993686	+	0.112200i
$289$	0.408810	+	0.708080i	0.0240477	+	0.0416518i
$290$	5.08104	−	9.04124i	0.298369	−	0.530920i
$291$	28.0919	−	2.51567i	1.64678	−	0.147471i
$292$	1.54301	+	2.53488i	0.0902976	+	0.148342i
$293$	0.453631	−	0.540617i	0.0265014	−	0.0315832i	−0.752631	−	0.658443i	$-0.771216\pi$
$293$	0.453631	−	0.540617i	0.0265014	−	0.0315832i	0.779132	+	0.626859i	$0.215660\pi$
$294$	−2.37446	−	0.601627i	−0.138481	−	0.0350876i
$295$	−3.23005	+	8.87450i	−0.188061	+	0.516693i
$296$	7.48108	−	14.0663i	0.434829	−	0.817587i
$297$	−26.2901	−	2.13751i	−1.52551	−	0.124031i
$298$	−3.21442	−	8.52260i	−0.186206	−	0.493701i
$299$	−0.829772	−	0.302012i	−0.0479870	−	0.0174658i
$300$	6.75049	−	15.4856i	0.389739	−	0.894059i
$301$	−0.735164	−	0.616876i	−0.0423741	−	0.0355561i
$302$	−25.7712	+	4.85306i	−1.48297	+	0.279262i
$303$	16.6603	−	11.7165i	0.957108	−	0.673098i
$304$	15.3731	−	9.85369i	0.881708	−	0.565148i
$305$	29.6958	−	17.1449i	1.70038	−	0.981714i
$306$	13.8977	+	11.2947i	0.794480	+	0.645675i
$307$	−1.52068	−	0.877965i	−0.0867898	−	0.0501081i	0.455977	−	0.889992i	$-0.349290\pi$
$307$	−1.52068	−	0.877965i	−0.0867898	−	0.0501081i	−0.542767	+	0.839883i	$0.682623\pi$
$308$	−6.34369	+	7.92653i	−0.361465	+	0.451656i
$309$	6.73451	−	25.3409i	0.383113	−	1.44159i
$310$	33.4663	−	28.7497i	1.90076	−	1.63287i
$311$	19.2288	−	6.99871i	1.09036	−	0.396860i	0.266609	−	0.963805i	$-0.414097\pi$
$311$	19.2288	−	6.99871i	1.09036	−	0.396860i	0.823756	+	0.566944i	$0.191875\pi$
$312$	−0.569826	−	1.85096i	−0.0322600	−	0.104790i
$313$	−0.0782110	−	0.443557i	−0.00442075	−	0.0250713i	0.982518	−	0.186170i	$-0.0596074\pi$
$313$	−0.0782110	−	0.443557i	−0.00442075	−	0.0250713i	−0.986938	+	0.161098i	$0.948496\pi$
$314$	−1.47304	+	8.96067i	−0.0831286	+	0.505680i
$315$	3.26084	+	8.84625i	0.183728	+	0.498430i
$316$	0.108847	−	0.322117i	0.00612313	−	0.0181205i
$317$	−13.1686	−	15.6937i	−0.739622	−	0.881448i	0.256756	−	0.966476i	$-0.417346\pi$
$317$	−13.1686	−	15.6937i	−0.739622	−	0.881448i	−0.996379	+	0.0850285i	$0.972902\pi$
$318$	13.2198	+	0.974996i	0.741330	+	0.0546750i
$319$	11.6655	+	2.05693i	0.653140	+	0.115166i
$320$	−25.0033	−	2.63327i	−1.39773	−	0.147204i
$321$	0.0216229	−	0.253116i	0.00120687	−	0.0141276i
$322$	−0.0366438	−	3.15868i	−0.00204208	−	0.176027i
$323$	19.2693			1.07217
$324$	17.0993	+	5.62251i	0.949963	+	0.312362i
$325$	−1.92782			−0.106936
$326$	0.354396	+	30.5488i	0.0196282	+	1.69194i
$327$	2.11469	−	24.7545i	0.116943	−	1.36893i
$328$	2.48268	+	6.14670i	0.137083	+	0.339395i
$329$	2.27866	+	0.401789i	0.125627	+	0.0221513i
$330$	38.9710	+	2.87421i	2.14528	+	0.158220i
$331$	20.4269	+	24.3438i	1.12276	+	1.33806i	0.934509	+	0.355938i	$0.115839\pi$
$331$	20.4269	+	24.3438i	1.12276	+	1.33806i	0.188255	+	0.982120i	$0.439717\pi$
$332$	20.9958	+	7.09472i	1.15229	+	0.389373i
$333$	10.8090	−	12.9893i	0.592330	−	0.711808i
$334$	−1.26895	+	7.71913i	−0.0694337	+	0.422372i
$335$	−8.35895	−	47.4059i	−0.456698	−	2.59006i
$336$	5.47614	−	4.24404i	0.298748	−	0.231531i
$337$	24.4353	−	8.89373i	1.33108	−	0.484472i	0.424086	−	0.905622i	$-0.360595\pi$
$337$	24.4353	−	8.89373i	1.33108	−	0.484472i	0.906991	+	0.421150i	$0.138373\pi$
$338$	13.7779	−	11.8361i	0.749418	−	0.643797i
$339$	−0.532039	+	2.00198i	−0.0288964	+	0.108733i
$340$	−20.7143	−	16.5779i	−1.12339	−	0.899062i
$341$	43.6401	+	25.1956i	2.36324	+	1.36442i
$342$	18.0935	−	6.90892i	0.978382	−	0.373592i
$343$	−0.866025	+	0.500000i	−0.0467610	+	0.0269975i
$344$	2.65515	−	0.564078i	0.143156	−	0.0304130i
$345$	−9.94546	+	6.99426i	−0.535446	+	0.376559i
$346$	30.4280	−	5.72999i	1.63582	−	0.308046i
$347$	−19.7461	−	16.5689i	−1.06002	−	0.889465i	−0.0659118	−	0.997825i	$-0.520996\pi$
$347$	−19.7461	−	16.5689i	−1.06002	−	0.889465i	−0.994112	+	0.108360i	$0.965440\pi$
$348$	−7.41005	−	3.23020i	−0.397220	−	0.173157i
$349$	−3.12298	−	1.13667i	−0.167169	−	0.0608446i	0.257080	−	0.966390i	$-0.417240\pi$
$349$	−3.12298	−	1.13667i	−0.167169	−	0.0608446i	−0.424249	+	0.905546i	$0.639462\pi$
$350$	−2.43376	−	6.45281i	−0.130090	−	0.344917i
$351$	−0.191593	−	2.04521i	−0.0102265	−	0.109165i
$352$	−6.61735	−	27.9426i	−0.352706	−	1.48935i
$353$	8.18952	−	22.5005i	0.435884	−	1.19758i	−0.506262	−	0.862380i	$-0.668973\pi$
$353$	8.18952	−	22.5005i	0.435884	−	1.19758i	0.942146	−	0.335203i	$-0.108805\pi$
$354$	7.13541	+	1.80793i	0.379243	+	0.0960905i
$355$	−26.5441	+	31.6340i	−1.40881	+	1.67896i
$356$	26.1354	−	15.9089i	1.38517	−	0.843169i
$357$	7.28201	−	0.652114i	0.385405	−	0.0345135i
$358$	4.50880	−	8.02299i	0.238298	−	0.424028i
$359$	4.53726	+	7.85877i	0.239468	+	0.414770i	0.960562	−	0.278067i	$-0.0896938\pi$
$359$	4.53726	+	7.85877i	0.239468	+	0.414770i	−0.721094	+	0.692837i	$0.756360\pi$
$360$	−25.3942	−	8.13925i	−1.33839	−	0.428976i
$361$	0.919616	−	1.59282i	0.0484009	−	0.0838328i
$362$	8.76870	+	14.7889i	0.460873	+	0.777290i
$363$	6.67091	+	24.6939i	0.350132	+	1.29609i
$364$	−0.693707	−	0.379333i	−0.0363601	−	0.0198824i
$365$	−1.59487	−	4.38187i	−0.0834794	−	0.229358i
$366$	−15.6269	−	21.6816i	−0.816829	−	1.13331i
$367$	7.46588	−	1.31644i	0.389716	−	0.0687174i	0.0246429	−	0.999696i	$-0.492155\pi$
$367$	7.46588	−	1.31644i	0.389716	−	0.0687174i	0.365073	+	0.930979i	$0.381044\pi$
$368$	7.10341	+	5.41946i	0.370291	+	0.282509i
$369$	1.24930	+	6.91939i	0.0650360	+	0.360209i
$370$	−15.8684	+	19.3631i	−0.824961	+	1.00664i
$371$	4.14555	−	3.47853i	0.215226	−	0.180596i
$372$	−24.9219	−	23.6942i	−1.29214	−	1.22849i
$373$	2.62876	−	14.9084i	0.136112	−	0.771929i	−0.837967	−	0.545721i	$-0.816256\pi$
$373$	2.62876	−	14.9084i	0.136112	−	0.771929i	0.974079	−	0.226208i	$-0.0726331\pi$
$374$	10.0331	−	28.5935i	0.518800	−	1.47854i
$375$	0.384234	−	0.551140i	0.0198417	−	0.0284607i
$376$	−4.86393	+	4.37858i	−0.250838	+	0.225808i
$377$			0.922491i			0.0475107i
$378$	6.60383	−	3.22325i	0.339665	−	0.165786i
$379$			22.3722i			1.14918i	0.818441	+	0.574591i	$0.194839\pi$
$379$			22.3722i			1.14918i	−0.818441	+	0.574591i	$0.805161\pi$
$380$	−26.7276	+	10.4364i	−1.37109	+	0.535376i
$381$	8.72381	+	18.6087i	0.446935	+	0.953355i
$382$	17.3600	+	6.09140i	0.888214	+	0.311663i
$383$	−5.47134	+	31.0295i	−0.279573	+	1.58554i	0.444479	+	0.895789i	$0.353389\pi$
$383$	−5.47134	+	31.0295i	−0.279573	+	1.58554i	−0.724052	+	0.689746i	$0.757722\pi$
$384$	−0.0787068	+	19.5958i	−0.00401649	+	0.999992i
$385$	12.2208	−	10.2544i	0.622828	−	0.522614i
$386$	−22.0337	−	18.0571i	−1.12148	−	0.919080i
$387$	2.87904	−	0.0117851i	0.146350	−	0.000599071i
$388$	6.39783	+	31.9330i	0.324801	+	1.62115i
$389$	−18.7022	+	3.29769i	−0.948237	+	0.167200i	−0.626318	−	0.779568i	$-0.715439\pi$
$389$	−18.7022	+	3.29769i	−0.948237	+	0.167200i	−0.321919	+	0.946767i	$0.604328\pi$
$390$	0.306580	+	3.02773i	0.0155243	+	0.153315i
$391$	3.22476	+	8.85994i	0.163083	+	0.448067i
$392$	0.393936	−	2.80086i	0.0198968	−	0.141465i
$393$	15.3706	−	15.4337i	0.775347	−	0.778527i
$394$	16.2174	−	9.61565i	0.817020	−	0.484430i
$395$	−0.267138	+	0.462697i	−0.0134412	+	0.0232808i
$396$	−0.831210	−	30.4460i	−0.0417699	−	1.52997i
$397$	−14.5100	−	25.1320i	−0.728234	−	1.26134i	−0.957629	−	0.288005i	$-0.907008\pi$
$397$	−14.5100	−	25.1320i	−0.728234	−	1.26134i	0.229395	−	0.973333i	$-0.426325\pi$
$398$	27.5478	+	15.4815i	1.38085	+	0.776016i
$399$	3.32689	−	7.17283i	0.166553	−	0.359091i
$400$	18.6196	+	5.81413i	0.930982	+	0.290706i
$401$	−9.85491	+	11.7446i	−0.492131	+	0.586499i	−0.953758	−	0.300575i	$-0.902821\pi$
$401$	−9.85491	+	11.7446i	−0.492131	+	0.586499i	0.461627	+	0.887074i	$0.347266\pi$
$402$	−36.1049	+	10.2044i	−1.80075	+	0.508947i
$403$	−1.34220	+	3.68767i	−0.0668599	+	0.183696i
$404$	15.5313	+	17.6607i	0.772713	+	0.878654i
$405$	−24.6099	−	13.9411i	−1.22288	−	0.692741i
$406$	−3.08776	+	1.16459i	−0.153243	+	0.0577976i
$407$	−26.8690	−	9.77951i	−1.33185	−	0.484752i
$408$	−11.2289	+	17.3647i	−0.555914	+	0.859683i
$409$	−21.9428	−	18.4122i	−1.08500	−	0.910423i	−0.0886736	−	0.996061i	$-0.528263\pi$
$409$	−21.9428	−	18.4122i	−1.08500	−	0.910423i	−0.996326	+	0.0856377i	$0.972707\pi$
$410$	−1.92772	−	10.2368i	−0.0952034	−	0.505559i
$411$	0.383500	+	0.177874i	0.0189167	+	0.00877390i
$412$	29.9308	+	4.56438i	1.47458	+	0.224871i
$413$	2.60247	−	1.50254i	0.128059	−	0.0739350i
$414$	6.20467	+	7.16308i	0.304943	+	0.352046i
$415$	−30.1588	−	17.4122i	−1.48044	−	0.854732i
$416$	2.05355	−	0.885389i	0.100684	−	0.0434097i
$417$	5.71492	+	5.69157i	0.279861	+	0.278717i
$418$	−21.3549	−	24.8584i	−1.04450	−	1.21586i
$419$	11.1876	−	4.07194i	0.546549	−	0.198928i	−0.0539636	−	0.998543i	$-0.517185\pi$
$419$	11.1876	−	4.07194i	0.546549	−	0.198928i	0.600512	+	0.799615i	$0.294963\pi$
$420$	−9.74735	+	4.84851i	−0.475622	+	0.236583i
$421$	2.65035	+	15.0309i	0.129170	+	0.732559i	0.978743	+	0.205089i	$0.0657483\pi$
$421$	2.65035	+	15.0309i	0.129170	+	0.732559i	−0.849573	+	0.527470i	$0.823141\pi$
$422$	38.7391	+	6.36830i	1.88579	+	0.310004i
$423$	−5.99720	+	3.49529i	−0.291594	+	0.169947i
$424$	0.532576	+	15.2971i	0.0258642	+	0.742894i
$425$	13.2314	+	15.7686i	0.641819	+	0.764890i
$426$	26.6151	+	18.0998i	1.28950	+	0.876941i
$427$	−10.7452	−	1.89466i	−0.519995	−	0.0916892i
$428$	0.293259	−	0.00680511i	0.0141752	−	0.000328937i
$429$	−3.14713	+	1.47538i	−0.151945	+	0.0712320i
$430$	−4.26500	+	0.0494782i	−0.205677	+	0.00238605i
$431$	7.21924			0.347739			0.173869	−	0.984769i	$-0.444373\pi$
$431$	7.21924			0.347739			0.173869	+	0.984769i	$0.444373\pi$
$432$	−4.31766	+	20.3312i	−0.207734	+	0.978185i
$433$	−37.2734			−1.79125			−0.895623	−	0.444813i	$-0.853270\pi$
$433$	−37.2734			−1.79125			−0.895623	+	0.444813i	$0.853270\pi$
$434$	−14.0378	+	0.162852i	−0.673837	+	0.00781717i
$435$	10.4198	+	7.26427i	0.499590	+	0.348295i
$436$	28.6804	−	0.665531i	1.37354	−	0.0318732i
$437$	10.0418	+	1.77064i	0.480366	+	0.0847014i
$438$	−3.27272	+	1.58082i	−0.156377	+	0.0755346i
$439$	−5.82016	−	6.93620i	−0.277781	−	0.331047i	0.609057	−	0.793126i	$-0.291548\pi$
$439$	−5.82016	−	6.93620i	−0.277781	−	0.331047i	−0.886839	+	0.462079i	$0.847103\pi$
$440$	1.56999	+	45.0948i	0.0748466	+	2.14981i
$441$	1.01451	−	2.82325i	0.0483101	−	0.134441i
$442$	2.32864	+	0.382804i	0.110762	+	0.0182082i
$443$	−0.0259702	−	0.147284i	−0.00123388	−	0.00699769i	0.984185	−	0.177146i	$-0.0566865\pi$
$443$	−0.0259702	−	0.147284i	−0.00123388	−	0.00699769i	−0.985418	+	0.170148i	$0.945575\pi$
$444$	16.2612	+	10.7849i	0.771723	+	0.511828i
$445$	−45.1785	+	16.4436i	−2.14167	+	0.779503i
$446$	8.85255	+	10.3049i	0.419180	+	0.487951i
$447$	10.7697	−	2.90937i	0.509389	−	0.137608i
$448$	5.55606	+	5.75589i	0.262499	+	0.271940i
$449$	8.74597	+	5.04949i	0.412748	+	0.238300i	0.691970	−	0.721927i	$-0.256743\pi$
$449$	8.74597	+	5.04949i	0.412748	+	0.238300i	−0.279222	+	0.960227i	$0.590077\pi$
$450$	18.0778	+	10.0623i	0.852196	+	0.474342i
$451$	10.3035	−	5.94872i	0.485172	−	0.280114i
$452$	−2.36459	−	0.360595i	−0.111221	−	0.0169610i
$453$	−2.86474	−	31.9899i	−0.134597	−	1.50302i
$454$	−1.86095	−	9.88219i	−0.0873386	−	0.463794i
$455$	0.951722	+	0.798589i	0.0446174	+	0.0374384i
$456$	10.1916	+	19.9066i	0.477267	+	0.932211i
$457$	−26.0641	−	9.48656i	−1.21923	−	0.443763i	−0.349332	−	0.936999i	$-0.613592\pi$
$457$	−26.0641	−	9.48656i	−1.21923	−	0.443763i	−0.869895	+	0.493236i	$0.835814\pi$
$458$	−7.21735	+	2.72212i	−0.337245	+	0.127197i
$459$	−15.4138	+	15.6042i	−0.719453	+	0.728343i
$460$	−9.27153	−	10.5427i	−0.432287	−	0.491555i
$461$	2.61046	−	7.17217i	0.121581	−	0.334041i	−0.863940	−	0.503595i	$-0.832010\pi$
$461$	2.61046	−	7.17217i	0.121581	−	0.334041i	0.985521	+	0.169554i	$0.0542326\pi$
$462$	−8.91145	−	8.67148i	−0.414598	−	0.403434i
$463$	−6.07771	+	7.24313i	−0.282455	+	0.336617i	−0.888554	−	0.458773i	$-0.848289\pi$
$463$	−6.07771	+	7.24313i	−0.282455	+	0.336617i	0.606099	+	0.795389i	$0.292734\pi$
$464$	2.78214	−	8.90976i	0.129158	−	0.413625i
$465$	31.0839	+	44.1996i	1.44148	+	2.04971i
$466$	−14.0296	−	7.88442i	−0.649908	−	0.365239i
$467$	−0.185247	−	0.320857i	−0.00857220	−	0.0148475i	0.861707	−	0.507405i	$-0.169395\pi$
$467$	−0.185247	−	0.320857i	−0.00857220	−	0.0148475i	−0.870280	+	0.492558i	$0.836062\pi$
$468$	2.32380	−	0.475479i	0.107418	−	0.0219790i
$469$	−7.65858	+	13.2650i	−0.353640	+	0.612523i
$470$	8.84563	−	5.24477i	0.408018	−	0.241923i
$471$	−10.7487	−	2.85655i	−0.495276	−	0.131623i
$472$	−1.18380	+	8.41679i	−0.0544890	+	0.387414i
$473$	−1.66618	−	4.57780i	−0.0766112	−	0.210488i
$474$	0.379777	+	0.170823i	0.0174437	+	0.00784614i
$475$	21.9234	−	3.86568i	1.00591	−	0.177370i
$476$	1.65845	+	8.27768i	0.0760149	+	0.379407i
$477$	−2.75369	+	15.9996i	−0.126083	+	0.732573i
$478$	−18.9559	−	15.5348i	−0.867024	−	0.710545i
$479$	−20.7077	+	17.3758i	−0.946157	+	0.793920i	−0.978646	−	0.205552i	$-0.934101\pi$
$479$	−20.7077	+	17.3758i	−0.946157	+	0.793920i	0.0324888	+	0.999472i	$0.489657\pi$
$480$	6.17025	−	30.1675i	0.281632	−	1.37695i
$481$	0.386676	−	2.19295i	0.0176309	−	0.0999899i
$482$	−28.5065	−	10.0026i	−1.29844	−	0.455605i
$483$	3.85480	+	0.329303i	0.175400	+	0.0149838i
$484$	−27.5131	+	10.7431i	−1.25060	+	0.488324i
$485$		−	51.1751i		−	2.32374i
$486$	−8.87837	+	20.1786i	−0.402731	+	0.915318i
$487$			16.5180i			0.748503i	0.927327	+	0.374251i	$0.122100\pi$
$487$			16.5180i			0.748503i	−0.927327	+	0.374251i	$0.877900\pi$
$488$	22.9362	−	20.6475i	1.03827	−	0.934667i
$489$	−37.2812	−	3.18481i	−1.68591	−	0.144022i
$490$	−1.47154	+	4.19377i	−0.0664775	+	0.189455i
$491$	3.06984	−	17.4099i	0.138540	−	0.785699i	−0.833789	−	0.552083i	$-0.813833\pi$
$491$	3.06984	−	17.4099i	0.138540	−	0.785699i	0.972329	−	0.233616i	$-0.0750558\pi$
$492$	−7.78682	+	2.29867i	−0.351057	+	0.103632i
$493$	7.54550	−	6.33143i	0.339832	−	0.285153i
$494$	1.61771	−	1.97397i	0.0727842	−	0.0888131i
$495$	−8.11766	+	47.1657i	−0.364862	+	2.11994i
$496$	24.0851	−	31.5690i	1.08146	−	1.41749i
$497$	12.9404	−	2.28175i	0.580457	−	0.102350i
$498$	−11.1343	+	24.7541i	−0.498941	+	1.10926i
$499$	−2.08157	−	5.71908i	−0.0931840	−	0.256021i	0.884341	−	0.466842i	$-0.154608\pi$
$499$	−2.08157	−	5.71908i	−0.0931840	−	0.256021i	−0.977525	+	0.210821i	$0.932386\pi$
$500$	0.680674	+	0.372206i	0.0304407	+	0.0166455i
$501$	−9.25946	−	2.46076i	−0.413682	−	0.109939i
$502$	−10.7028	−	18.0509i	−0.477689	−	0.805652i
$503$	10.2415	−	17.7388i	0.456646	−	0.790934i	−0.542135	−	0.840291i	$-0.682384\pi$
$503$	10.2415	−	17.7388i	0.456646	−	0.790934i	0.998781	+	0.0493572i	$0.0157173\pi$
$504$	4.52518	+	7.17794i	0.201567	+	0.319731i
$505$	−18.4780	−	32.0048i	−0.822259	−	1.42419i
$506$	7.85601	−	13.9790i	0.349242	−	0.621444i
$507$	12.7970	+	18.1967i	0.568336	+	0.808143i
$508$	−20.2713	+	12.3394i	−0.899395	+	0.547471i
$509$	8.94266	−	10.6574i	0.396376	−	0.472383i	−0.530535	−	0.847663i	$-0.678009\pi$
$509$	8.94266	−	10.6574i	0.396376	−	0.472383i	0.926912	+	0.375280i	$0.122453\pi$
$510$	22.6611	−	23.2882i	1.00345	−	1.03122i
$511$	−0.507484	+	1.39430i	−0.0224498	+	0.0616803i
$512$	−22.5042	+	2.35811i	−0.994555	+	0.104215i
$513$	6.27987	+	22.8741i	0.277263	+	1.00991i
$514$	−2.16078	−	5.72902i	−0.0953079	−	0.252696i
$515$	−44.7063	−	16.2718i	−1.97000	−	0.717020i
$516$	0.373260	+	3.30344i	0.0164318	+	0.145426i
$517$	8.99752	+	7.54982i	0.395711	+	0.332041i
$518$	7.82838	−	1.47419i	0.343959	−	0.0647721i
$519$	3.38239	+	37.7704i	0.148471	+	1.65794i
$520$	−3.43728	+	0.730239i	−0.150735	+	0.0320231i
$521$	0.586899	−	0.338846i	0.0257125	−	0.0148451i	−0.487089	−	0.873353i	$-0.661941\pi$
$521$	0.586899	−	0.338846i	0.0257125	−	0.0148451i	0.512801	+	0.858507i	$0.328608\pi$
$522$	4.81496	−	8.65048i	0.210745	−	0.378621i
$523$	−15.9122	−	9.18689i	−0.695790	−	0.401714i	0.109988	−	0.993933i	$-0.464919\pi$
$523$	−15.9122	−	9.18689i	−0.695790	−	0.401714i	−0.805777	+	0.592219i	$0.798252\pi$
$524$	19.6372	+	15.7159i	0.857855	+	0.686551i
$525$	8.15417	−	2.20280i	0.355877	−	0.0961381i
$526$	10.0120	−	8.60095i	0.436544	−	0.375019i
$527$	39.3753	−	14.3315i	1.71522	−	0.624288i
$528$	34.8458	−	4.75834i	1.51647	−	0.207080i
$529$	−3.12752	−	17.7371i	−0.135979	−	0.771177i
$530$	3.90149	−	23.7332i	0.169470	−	1.03090i
$531$	−3.04868	+	8.48408i	−0.132302	+	0.368178i
$532$	8.64953	+	2.92277i	0.375005	+	0.126718i
$533$	0.595570	+	0.709773i	0.0257970	+	0.0307437i
$534$	16.2988	+	33.7428i	0.705317	+	1.46019i
$535$	−0.453934	−	0.0800409i	−0.0196253	−	0.00346047i
$536$	−16.2250	−	40.1705i	−0.700815	−	1.73510i
$537$	9.24627	+	6.44615i	0.399006	+	0.278172i
$538$	0.264285	+	22.7812i	0.0113941	+	0.982169i
$539$	−5.07623			−0.218649
$540$	12.9284	−	29.9921i	0.556348	−	1.29066i
$541$	9.83573			0.422871			0.211436	−	0.977392i	$-0.432186\pi$
$541$	9.83573			0.422871			0.211436	+	0.977392i	$0.432186\pi$
$542$	0.262990	+	22.6696i	0.0112964	+	0.973742i
$543$	−19.0660	+	8.93819i	−0.818202	+	0.383574i
$544$	−21.3364	−	10.7202i	−0.914790	−	0.459625i
$545$	−44.3942	−	7.82790i	−1.90164	−	0.335310i
$546$	0.544541	−	0.800724i	0.0233042	−	0.0342678i
$547$	−8.20047	−	9.77293i	−0.350627	−	0.417860i	0.561689	−	0.827349i	$-0.310152\pi$
$547$	−8.20047	−	9.77293i	−0.350627	−	0.417860i	−0.912315	+	0.409488i	$0.865707\pi$
$548$	−0.156268	+	0.462453i	−0.00667544	+	0.0197550i
$549$	28.2802	−	16.4823i	1.20697	−	0.703447i
$550$	5.67878	−	34.5446i	0.242144	−	1.47299i
$551$	−1.84978	−	10.4906i	−0.0788033	−	0.446916i
$552$	−7.44738	+	8.01749i	−0.316981	+	0.341247i
$553$	0.159753	−	0.0581453i	0.00679338	−	0.00247259i
$554$	16.6754	−	14.3252i	0.708469	−	0.608620i
$555$	−21.7250	−	21.6363i	−0.922175	−	0.918408i
$556$	−5.81940	+	7.27142i	−0.246798	+	0.308377i
$557$	−32.4381	−	18.7282i	−1.37445	−	0.793538i	−0.382963	−	0.923764i	$-0.625096\pi$
$557$	−32.4381	−	18.7282i	−1.37445	−	0.793538i	−0.991484	+	0.130226i	$0.958430\pi$
$558$	31.8341	−	27.5748i	1.34765	−	1.16733i
$559$	0.328559	−	0.189694i	0.0138966	−	0.00802319i
$560$	−6.78362	−	10.5834i	−0.286660	−	0.447229i
$561$	33.6679	+	15.6158i	1.42146	+	0.659299i
$562$	10.9109	−	2.05467i	0.460250	−	0.0866710i
$563$	9.38032	+	7.87102i	0.395333	+	0.331724i	0.818687	−	0.574241i	$-0.194703\pi$
$563$	9.38032	+	7.87102i	0.395333	+	0.331724i	−0.423353	+	0.905965i	$0.639147\pi$
$564$	−4.76166	−	6.44758i	−0.200502	−	0.271492i
$565$	3.53189	+	1.28550i	0.148588	+	0.0540815i
$566$	−1.46626	−	3.88760i	−0.0616316	−	0.163408i
$567$	3.14731	+	8.43175i	0.132175	+	0.354100i
$568$	−17.4517	+	32.8135i	−0.732256	+	1.37682i
$569$	13.7711	−	37.8358i	0.577314	−	1.58616i	−0.215375	−	0.976532i	$-0.569097\pi$
$569$	13.7711	−	37.8358i	0.577314	−	1.58616i	0.792689	−	0.609626i	$-0.208681\pi$
$570$	−9.55765	−	33.8167i	−0.400326	−	1.41643i
$571$	10.4156	−	12.4128i	0.435877	−	0.519458i	−0.502731	−	0.864443i	$-0.667671\pi$
$571$	10.4156	−	12.4128i	0.435877	−	0.519458i	0.938608	+	0.344985i	$0.112116\pi$
$572$	−2.08685	−	3.42831i	−0.0872555	−	0.143345i
$573$	−9.48080	+	20.4408i	−0.396066	+	0.853926i
$574$	−1.62388	+	2.88954i	−0.0677793	+	0.120607i
$575$	5.44634	+	9.43334i	0.227128	+	0.393398i
$576$	−23.8781	−	2.41598i	−0.994920	−	0.100666i
$577$	−15.4762	+	26.8057i	−0.644285	+	1.11593i	0.340182	+	0.940360i	$0.389511\pi$
$577$	−15.4762	+	26.8057i	−0.644285	+	1.11593i	−0.984466	+	0.175574i	$0.943822\pi$
$578$	−0.589722	−	0.994603i	−0.0245292	−	0.0413700i
$579$	24.6204	−	24.7214i	1.02319	−	1.02738i
$580$	−7.03687	+	12.8687i	−0.292190	+	0.534345i
$581$	3.78994	+	10.4128i	0.157233	+	0.431995i
$582$	−39.6841	+	4.01831i	−1.64496	+	0.166564i
$583$	27.0533	−	4.77023i	1.12043	−	0.197563i
$584$	−2.22358	−	3.55930i	−0.0920124	−	0.147285i
$585$	−3.72712	+	0.0152567i	−0.154098	+	0.000630785i
$586$	−0.632620	+	0.771938i	−0.0261333	+	0.0318885i
$587$	−7.04811	+	5.91406i	−0.290906	+	0.244100i	−0.776547	−	0.630059i	$-0.783031\pi$
$587$	−7.04811	+	5.91406i	−0.290906	+	0.244100i	0.485641	+	0.874158i	$0.338586\pi$
$588$	3.36763	+	0.811818i	0.138879	+	0.0334788i
$589$	7.86910	−	44.6279i	0.324240	−	1.83886i
$590$	4.42209	−	12.6026i	0.182055	−	0.518840i
$591$	9.80151	+	20.9076i	0.403180	+	0.860023i
$592$	−10.3484	+	20.0141i	−0.425316	+	0.822576i
$593$			28.9526i			1.18894i	0.804118	+	0.594469i	$0.202638\pi$
$593$			28.9526i			1.18894i	−0.804118	+	0.594469i	$0.797362\pi$
$594$	37.2124	+	2.59140i	1.52684	+	0.106326i
$595$		−	13.2656i		−	0.543838i
$596$	4.68538	+	11.9992i	0.191921	+	0.491508i
$597$	−22.1336	+	31.7481i	−0.905867	+	1.29936i
$598$	1.17835	+	0.413469i	0.0481864	+	0.0169080i
$599$	−0.444579	+	2.52133i	−0.0181650	+	0.103019i	−0.992542	−	0.121901i	$-0.961101\pi$
$599$	−0.444579	+	2.52133i	−0.0181650	+	0.103019i	0.974377	+	0.224920i	$0.0722121\pi$
$600$	−9.29194	+	22.0092i	−0.379342	+	0.898520i
$601$	27.4075	−	22.9976i	1.11798	−	0.938093i	0.119476	−	0.992837i	$-0.461879\pi$
$601$	27.4075	−	22.9976i	1.11798	−	0.938093i	0.998500	+	0.0547440i	$0.0174343\pi$
$602$	1.04973	+	0.860275i	0.0427837	+	0.0350622i
$603$	−8.16456	−	45.2203i	−0.332487	−	1.84151i
$604$	36.3640	−	7.28559i	1.47963	−	0.296446i
$605$	45.7066	−	8.05931i	1.85824	−	0.327657i
$606$	−23.3674	+	16.8419i	−0.949236	+	0.684155i
$607$	5.16639	+	14.1946i	0.209697	+	0.576139i	0.999297	−	0.0374831i	$-0.0119340\pi$
$607$	5.16639	+	14.1946i	0.209697	+	0.576139i	−0.789600	+	0.613622i	$0.789712\pi$
$608$	−21.5777	+	14.1865i	−0.875093	+	0.575338i
$609$	−1.05407	−	3.90188i	−0.0427131	−	0.158112i
$610$	−41.7122	+	24.7321i	−1.68888	+	1.00137i
$611$	−0.457352	+	0.792157i	−0.0185025	+	0.0320472i
$612$	−19.8383	−	15.7441i	−0.801917	−	0.636416i
$613$	15.7415	+	27.2650i	0.635792	+	1.10122i	0.986347	+	0.164681i	$0.0526596\pi$
$613$	15.7415	+	27.2650i	0.635792	+	1.10122i	−0.350555	+	0.936542i	$0.614007\pi$
$614$	2.16482	+	1.21660i	0.0873652	+	0.0490980i
$615$	12.7070	−	1.13793i	0.512394	−	0.0458856i
$616$	8.84070	−	11.3131i	0.356202	−	0.455819i
$617$	−7.21958	+	8.60396i	−0.290649	+	0.346382i	−0.891534	−	0.452953i	$-0.850371\pi$
$617$	−7.21958	+	8.60396i	−0.290649	+	0.346382i	0.600885	+	0.799336i	$0.294815\pi$
$618$	−9.10767	+	35.9455i	−0.366364	+	1.44594i
$619$	15.7877	−	43.3765i	0.634563	−	1.74345i	−0.0336035	−	0.999435i	$-0.510698\pi$
$619$	15.7877	−	43.3765i	0.634563	−	1.74345i	0.668166	−	0.744012i	$-0.267079\pi$
$620$	−46.8537	+	41.2045i	−1.88169	+	1.65481i
$621$	−9.46645	+	6.71548i	−0.379876	+	0.269483i
$622$	−27.0770	+	10.2125i	−1.08569	+	0.409482i
$623$	14.3757	+	5.23233i	0.575950	+	0.209629i
$624$	0.836167	+	2.60812i	0.0334734	+	0.104408i
$625$	−19.6122	−	16.4566i	−0.784488	−	0.658263i
$626$	0.117876	+	0.625959i	0.00471128	+	0.0250183i
$627$	32.8309	−	23.0888i	1.31114	−	0.922076i
$628$	1.93605	−	12.6956i	0.0772570	−	0.506610i
$629$	−20.5911	+	11.8883i	−0.821021	+	0.474017i
$630$	−4.75634	−	12.4561i	−0.189497	−	0.496265i
$631$	−8.72866	−	5.03949i	−0.347482	−	0.200619i	0.316094	−	0.948728i	$-0.397629\pi$
$631$	−8.72866	−	5.03949i	−0.347482	−	0.200619i	−0.663576	+	0.748109i	$0.730962\pi$
$632$	−0.148638	+	0.457298i	−0.00591251	+	0.0181903i
$633$	−12.3495	+	46.4693i	−0.490850	+	1.84699i
$634$	18.8794	+	21.9768i	0.749798	+	0.872809i
$635$	35.0417	−	12.7541i	1.39059	−	0.506133i
$636$	−18.7104	−	1.16189i	−0.741915	−	0.0460718i
$637$	−0.0686472	−	0.389318i	−0.00271990	−	0.0154253i
$638$	−16.5301	−	2.71738i	−0.654432	−	0.107582i
$639$	−25.2150	+	30.3011i	−0.997489	+	1.19869i
$640$	35.4009	+	3.31358i	1.39934	+	0.130981i
$641$	19.3363	+	23.0441i	0.763739	+	0.910189i	0.998078	−	0.0619660i	$-0.0197370\pi$
$641$	19.3363	+	23.0441i	0.763739	+	0.910189i	−0.234339	+	0.972155i	$0.575293\pi$
$642$	−0.0264249	+	0.358291i	−0.00104291	+	0.0141406i
$643$	38.2382	+	6.74243i	1.50797	+	0.265896i	0.865692	−	0.500577i	$-0.166879\pi$
$643$	38.2382	+	6.74243i	1.50797	+	0.265896i	0.642277	+	0.766473i	$0.277990\pi$
$644$	0.103637	+	4.46615i	0.00408389	+	0.175991i
$645$	0.444640	−	5.20493i	0.0175077	−	0.204944i
$646$	−27.2491	+	0.316116i	−1.07210	+	0.0124374i
$647$	43.9740			1.72880			0.864398	−	0.502808i	$-0.167700\pi$
$647$	43.9740			1.72880			0.864398	+	0.502808i	$0.167700\pi$
$648$	−24.2727	−	7.67038i	−0.953523	−	0.301321i
$649$	15.2544			0.598789
$650$	2.72617	−	0.0316263i	0.106929	−	0.00124048i
$651$	1.46349	−	17.1315i	0.0573586	−	0.671436i
$652$	−1.00232	−	43.1938i	−0.0392537	−	1.69160i
$653$	−29.4634	−	5.19519i	−1.15299	−	0.203304i	−0.435710	−	0.900087i	$-0.643503\pi$
$653$	−29.4634	−	5.19519i	−1.15299	−	0.203304i	−0.717282	+	0.696783i	$0.754614\pi$
$654$	−2.58432	+	35.0404i	−0.101055	+	1.37019i
$655$	−25.4043	−	30.2757i	−0.992630	−	1.18297i
$656$	−3.61163	−	8.65143i	−0.141011	−	0.337782i
$657$	−1.53956	−	4.17664i	−0.0600641	−	0.162946i
$658$	−3.22888	−	0.530795i	−0.125875	−	0.0206926i
$659$	−3.21235	−	18.2182i	−0.125136	−	0.709679i	−0.981227	−	0.192855i	$-0.938225\pi$
$659$	−3.21235	−	18.2182i	−0.125136	−	0.709679i	0.856092	−	0.516824i	$-0.172886\pi$
$660$	−55.1568	−	3.42515i	−2.14698	−	0.133324i
$661$	7.80059	−	2.83918i	0.303408	−	0.110431i	−0.185830	−	0.982582i	$-0.559497\pi$
$661$	7.80059	−	2.83918i	0.303408	−	0.110431i	0.489238	+	0.872151i	$0.337275\pi$
$662$	−29.2854	−	34.0900i	−1.13821	−	1.32494i
$663$	−0.742341	+	2.79331i	−0.0288301	+	0.108483i
$664$	−29.8069	−	9.68833i	−1.15673	−	0.375980i
$665$	−12.4244	−	7.17322i	−0.481797	−	0.278165i
$666$	−15.0721	+	18.5457i	−0.584033	+	0.718631i
$667$	4.51398	−	2.60615i	0.174782	−	0.100911i
$668$	1.66781	−	10.9366i	0.0645294	−	0.423149i
$669$	−13.6098	+	9.57129i	−0.526187	+	0.370047i
$670$	12.5982	+	66.9005i	0.486713	+	2.58459i
$671$	−42.4284	−	35.6017i	−1.63793	−	1.37439i
$672$	−7.67429	+	6.09141i	−0.296042	+	0.234981i
$673$	29.6873	+	10.8053i	1.14436	+	0.416513i	0.843486	−	0.537151i	$-0.180500\pi$
$673$	29.6873	+	10.8053i	1.14436	+	0.416513i	0.300874	+	0.953664i	$0.402722\pi$
$674$	−34.4085	+	12.9777i	−1.32537	+	0.499881i
$675$	−14.4064	+	20.8457i	−0.554501	+	0.802351i
$676$	−19.2894	+	16.9636i	−0.741899	+	0.652447i
$677$	−11.2770	+	30.9832i	−0.433409	+	1.19078i	0.510297	+	0.859998i	$0.329535\pi$
$677$	−11.2770	+	30.9832i	−0.433409	+	1.19078i	−0.943706	+	0.330784i	$0.892687\pi$
$678$	0.719524	−	2.83976i	0.0276331	−	0.109060i
$679$	−10.4670	+	12.4741i	−0.401687	+	0.478712i
$680$	29.5644	+	23.1033i	1.13374	+	0.885970i
$681$	12.2668	−	1.09851i	0.470065	−	0.0420950i
$682$	−62.1256	−	34.9136i	−2.37891	−	1.33691i
$683$	−17.4605	−	30.2424i	−0.668107	−	1.15719i	−0.978433	−	0.206565i	$-0.933772\pi$
$683$	−17.4605	−	30.2424i	−0.668107	−	1.15719i	0.310326	−	0.950630i	$-0.399562\pi$
$684$	−25.4729	+	10.0669i	−0.973982	+	0.384916i
$685$	0.383521	−	0.664278i	0.0146536	−	0.0253808i
$686$	1.21646	−	0.721266i	0.0464447	−	0.0275381i
$687$	−2.46380	−	9.12030i	−0.0939997	−	0.347961i
$688$	−3.74544	+	0.841231i	−0.142794	+	0.0320716i
$689$	0.731699	+	2.01033i	0.0278755	+	0.0765873i
$690$	13.9493	−	10.0539i	0.531041	−	0.382744i
$691$	−0.124765	+	0.0219995i	−0.00474629	+	0.000836899i	−0.176021	−	0.984386i	$-0.556323\pi$
$691$	−0.124765	+	0.0219995i	−0.00474629	+	0.000836899i	0.171275	+	0.985223i	$0.445211\pi$
$692$	−42.9348	+	8.60206i	−1.63214	+	0.327001i
$693$	11.6257	−	9.83648i	0.441623	−	0.373657i
$694$	28.1951	+	23.1065i	1.07027	+	0.877109i
$695$	11.2107	−	9.40693i	0.425248	−	0.356825i
$696$	10.5317	+	4.44632i	0.399202	+	0.168537i
$697$	1.71794	−	9.74291i	0.0650716	−	0.369039i
$698$	4.43491	+	1.55615i	0.167864	+	0.0589013i
$699$	11.2722	−	16.1687i	0.426354	−	0.611557i
$700$	3.54749	+	9.08511i	0.134083	+	0.343385i
$701$			48.7288i			1.84046i	0.391378	+	0.920230i	$0.371998\pi$
$701$			48.7288i			1.84046i	−0.391378	+	0.920230i	$0.628002\pi$
$702$	0.304488	+	2.88902i	0.0114921	+	0.109039i
$703$			25.7137i			0.969812i
$704$	9.81612	+	39.4056i	0.369959	+	1.48515i
$705$	5.34615	+	11.4039i	0.201348	+	0.429494i
$706$	−11.2118	+	31.9528i	−0.421963	+	1.20256i
$707$	−2.04198	+	11.5806i	−0.0767965	+	0.435535i
$708$	−10.1200	−	2.43957i	−0.380332	−	0.0916848i
$709$	−26.9530	+	22.6162i	−1.01224	+	0.849370i	−0.988633	−	0.150351i	$-0.951960\pi$
$709$	−26.9530	+	22.6162i	−1.01224	+	0.849370i	−0.0236073	+	0.999721i	$0.507515\pi$
$710$	37.0175	−	45.1697i	1.38924	−	1.69519i
$711$	−0.253198	+	0.442727i	−0.00949567	+	0.0166036i
$712$	−36.6976	+	22.9258i	−1.37530	+	0.859181i
$713$	21.8366	−	3.85039i	0.817788	−	0.144198i
$714$	−10.2869	+	1.04163i	−0.384978	+	0.0389820i
$715$	2.15699	+	5.92629i	0.0806670	+	0.221631i
$716$	−6.24436	+	11.4194i	−0.233363	+	0.426764i
$717$	21.1813	−	21.2682i	0.791031	−	0.794276i
$718$	−6.54515	−	11.0388i	−0.244263	−	0.411964i
$719$	−15.2222	+	26.3656i	−0.567692	+	0.983272i	0.429101	+	0.903256i	$0.358830\pi$
$719$	−15.2222	+	26.3656i	−0.567692	+	0.983272i	−0.996794	+	0.0800157i	$0.974503\pi$
$720$	36.0439	+	11.0933i	1.34328	+	0.413422i
$721$	7.56920	+	13.1102i	0.281892	+	0.488251i
$722$	−1.27432	+	2.26753i	−0.0474251	+	0.0843886i
$723$	15.5683	−	33.5654i	0.578989	−	1.24831i
$724$	−12.6426	−	20.7695i	−0.469858	−	0.771891i
$725$	7.31461	−	8.71722i	0.271658	−	0.323749i
$726$	−9.83856	−	34.8106i	−0.365143	−	1.29194i
$727$	7.57236	−	20.8049i	0.280843	−	0.771611i	−0.716419	−	0.697670i	$-0.754220\pi$
$727$	7.57236	−	20.8049i	0.280843	−	0.771611i	0.997263	−	0.0739408i	$-0.0235576\pi$
$728$	0.987207	+	0.525041i	0.0365883	+	0.0194593i
$729$	−23.5467	−	13.2118i	−0.872100	−	0.489328i
$730$	2.32722	+	6.17033i	0.0861344	+	0.228374i
$731$	−3.80663	−	1.38550i	−0.140793	−	0.0512446i
$732$	22.4539	+	30.4040i	0.829921	+	1.12376i
$733$	−13.7232	−	11.5152i	−0.506879	−	0.425322i	0.353150	−	0.935567i	$-0.385110\pi$
$733$	−13.7232	−	11.5152i	−0.506879	−	0.425322i	−0.860029	+	0.510245i	$0.829555\pi$
$734$	−10.5360	+	1.98408i	−0.388893	+	0.0732336i
$735$	−4.93802	−	2.29034i	−0.182142	−	0.0844806i
$736$	−10.1340	−	7.54722i	−0.373543	−	0.278194i
$737$	−67.3364	+	38.8767i	−2.48037	+	1.43204i
$738$	−1.88017	−	9.76435i	−0.0692102	−	0.359431i
$739$	16.5451	+	9.55230i	0.608620	+	0.351387i	0.772425	−	0.635106i	$-0.219043\pi$
$739$	16.5451	+	9.55230i	0.608620	+	0.351387i	−0.163805	+	0.986493i	$0.552377\pi$
$740$	22.1222	−	27.6420i	0.813228	−	1.01614i
$741$	2.21476	+	2.20571i	0.0813612	+	0.0810288i
$742$	−5.80523	+	4.98706i	−0.213117	+	0.183081i
$743$	27.6893	−	10.0781i	1.01582	−	0.369729i	0.220156	−	0.975465i	$-0.429343\pi$
$743$	27.6893	−	10.0781i	1.01582	−	0.369729i	0.795666	+	0.605736i	$0.207121\pi$
$744$	35.6313	+	33.0976i	1.30631	+	1.21342i
$745$	−3.51489	−	19.9339i	−0.128776	−	0.730322i
$746$	−3.47280	+	21.1254i	−0.127148	+	0.773456i
$747$	−28.8572	−	16.5036i	−1.05583	−	0.603835i
$748$	−13.7189	+	40.5992i	−0.501614	+	1.48445i
$749$	0.0942770	+	0.112355i	0.00344481	+	0.00410536i
$750$	−0.534310	+	0.785681i	−0.0195103	+	0.0286890i
$751$	−37.7811	−	6.66182i	−1.37865	−	0.243093i	−0.565309	−	0.824879i	$-0.691243\pi$
$751$	−37.7811	−	6.66182i	−1.37865	−	0.243093i	−0.813342	+	0.581786i	$0.802354\pi$
$752$	6.80634	−	6.27162i	0.248202	−	0.228702i
$753$	23.2714	−	10.9097i	0.848057	−	0.397571i
$754$	−0.0151336	−	1.30451i	−0.000551134	−	0.0475075i
$755$	−58.2761			−2.12088
$756$	−9.28573	+	4.66640i	−0.337719	+	0.169715i
$757$	9.27962			0.337274			0.168637	−	0.985678i	$-0.446064\pi$
$757$	9.27962			0.337274			0.168637	+	0.985678i	$0.446064\pi$
$758$	−0.367019	−	31.6369i	−0.0133307	−	1.14910i
$759$	16.1104	+	11.2316i	0.584772	+	0.407681i
$760$	37.6247	−	15.1968i	1.36479	−	0.551245i
$761$	−40.9849	−	7.22674i	−1.48570	−	0.261969i	−0.628847	−	0.777529i	$-0.716473\pi$
$761$	−40.9849	−	7.22674i	−1.48570	−	0.261969i	−0.856853	+	0.515560i	$0.827584\pi$
$762$	−12.6418	−	26.1719i	−0.457964	−	0.948106i
$763$	9.22018	+	10.9882i	0.333793	+	0.397799i
$764$	−24.6490	−	8.32917i	−0.891769	−	0.301339i
$765$	25.7055	+	30.3812i	0.929385	+	1.09844i
$766$	7.22808	−	43.9692i	0.261161	−	1.58867i
$767$	0.206290	+	1.16993i	0.00744870	+	0.0422437i
$768$	−0.210171	−	27.7120i	−0.00758389	−	0.999971i
$769$	42.0679	−	15.3115i	1.51701	−	0.552146i	0.556609	−	0.830775i	$-0.312102\pi$
$769$	42.0679	−	15.3115i	1.51701	−	0.552146i	0.960399	+	0.278629i	$0.0898800\pi$
$770$	−17.1134	+	14.7015i	−0.616723	+	0.529804i
$771$	7.23955	−	1.95572i	0.260726	−	0.0704336i
$772$	31.4544	+	25.1733i	1.13207	+	0.906008i
$773$	17.6939	+	10.2156i	0.636407	+	0.367430i	0.783229	−	0.621733i	$-0.213571\pi$
$773$	17.6939	+	10.2156i	0.636407	+	0.367430i	−0.146822	+	0.989163i	$0.546904\pi$
$774$	−4.07111	+	0.0638967i	−0.146333	+	0.00229672i
$775$	41.9236	−	24.2046i	1.50594	−	0.869456i
$776$	−9.57116	−	45.0521i	−0.343585	−	1.61727i
$777$	0.870207	+	9.71741i	0.0312185	+	0.348610i
$778$	26.3930	−	4.97014i	0.946234	−	0.178188i
$779$	−8.19610	−	6.87735i	−0.293656	−	0.246407i
$780$	−0.483211	−	4.27653i	−0.0173017	−	0.153124i
$781$	62.6793	+	22.8134i	2.24284	+	0.816327i
$782$	−4.70554	−	12.4761i	−0.168270	−	0.446145i
$783$	9.97495	+	6.89365i	0.356475	+	0.246359i
$784$	−0.511123	+	3.96721i	−0.0182544	+	0.141686i
$785$	−6.90193	+	18.9629i	−0.246340	+	0.676815i
$786$	−21.4827	+	22.0772i	−0.766263	+	0.787469i
$787$	−11.8029	+	14.0661i	−0.420727	+	0.501402i	−0.934223	−	0.356689i	$-0.883905\pi$
$787$	−11.8029	+	14.0661i	−0.420727	+	0.501402i	0.513496	+	0.858092i	$0.328350\pi$
$788$	−22.7756	+	13.8637i	−0.811346	+	0.493875i
$789$	9.29926	+	13.2230i	0.331062	+	0.470753i
$790$	0.370174	−	0.658690i	0.0131702	−	0.0234352i
$791$	−0.597982	−	1.03573i	−0.0212618	−	0.0368265i
$792$	1.67490	+	43.0406i	0.0595150	+	1.52938i
$793$	2.15667	−	3.73547i	0.0765857	−	0.132650i
$794$	20.9311	+	35.3016i	0.742817	+	1.25281i
$795$	28.4690	+	7.56583i	1.00969	+	0.268332i
$796$	−39.2099	−	21.4407i	−1.38976	−	0.759946i
$797$	9.56773	+	26.2871i	0.338906	+	0.931138i	0.985706	+	0.168477i	$0.0538850\pi$
$797$	9.56773	+	26.2871i	0.338906	+	0.931138i	−0.646799	+	0.762660i	$0.723893\pi$
$798$	−4.58695	+	10.1978i	−0.162376	+	0.360999i
$799$	9.61843	−	1.69599i	0.340276	−	0.0599998i
$800$	−26.4258	−	7.91640i	−0.934292	−	0.279887i
$801$	−43.0625	+	15.8734i	−1.52154	+	0.560858i
$802$	13.7433	−	16.7700i	0.485294	−	0.592168i
$803$	−5.76987	+	4.84150i	−0.203614	+	0.170853i
$804$	50.8892	−	15.0225i	1.79472	−	0.529802i
$805$	1.21897	−	6.91313i	0.0429631	−	0.243656i
$806$	1.83754	−	5.23682i	0.0647245	−	0.184459i
$807$	−27.8018	−	2.37502i	−0.978670	−	0.0836045i
$808$	−22.2529	−	24.7196i	−0.782854	−	0.869631i
$809$			30.9338i			1.08758i	0.839223	+	0.543788i	$0.183010\pi$
$809$			30.9338i			1.08758i	−0.839223	+	0.543788i	$0.816990\pi$
$810$	35.0300	+	19.3107i	1.23083	+	0.678509i
$811$			6.22420i			0.218561i	0.994011	+	0.109281i	$0.0348547\pi$
$811$			6.22420i			0.218561i	−0.994011	+	0.109281i	$0.965145\pi$
$812$	4.34735	−	1.69752i	0.152562	−	0.0595714i
$813$	−27.6656	−	2.36338i	−0.970273	−	0.0828872i
$814$	38.1563	+	13.3886i	1.33738	+	0.469270i
$815$	−11.7891	+	66.8594i	−0.412955	+	2.34198i
$816$	15.5942	−	24.7400i	0.545905	−	0.866074i
$817$	−3.35602	+	2.81604i	−0.117412	+	0.0985207i
$818$	31.3317	+	25.6770i	1.09549	+	0.897776i
$819$	0.911619	+	0.758602i	0.0318546	+	0.0265077i
$820$	2.89396	+	14.4444i	0.101062	+	0.504420i
$821$	−12.5330	+	2.20991i	−0.437406	+	0.0771265i	−0.388015	−	0.921653i	$-0.626839\pi$
$821$	−12.5330	+	2.20991i	−0.437406	+	0.0771265i	−0.0493911	+	0.998780i	$0.515728\pi$
$822$	−0.545233	−	0.245244i	−0.0190172	−	0.00855387i
$823$	−4.65653	−	12.7937i	−0.162316	−	0.445960i	0.831696	−	0.555232i	$-0.187370\pi$
$823$	−4.65653	−	12.7937i	−0.162316	−	0.445960i	−0.994012	+	0.109271i	$0.965148\pi$
$824$	−42.4005	−	5.96355i	−1.47709	−	0.207750i
$825$	41.4379	+	11.0124i	1.44268	+	0.383402i
$826$	−3.65555	+	2.16746i	−0.127193	+	0.0754155i
$827$	16.9113	−	29.2912i	0.588062	−	1.01855i	−0.406424	−	0.913685i	$-0.633224\pi$
$827$	16.9113	−	29.2912i	0.588062	−	1.01855i	0.994486	−	0.104869i	$-0.0334424\pi$
$828$	−8.89165	−	10.0276i	−0.309006	−	0.348485i
$829$	−5.97371	−	10.3468i	−0.207475	−	0.359358i	0.743443	−	0.668799i	$-0.233191\pi$
$829$	−5.97371	−	10.3468i	−0.207475	−	0.359358i	−0.950919	+	0.309441i	$0.899858\pi$
$830$	42.9338	+	24.1282i	1.49026	+	0.837501i
$831$	15.4883	+	22.0235i	0.537282	+	0.763986i
$832$	−2.88944	+	1.28573i	−0.100173	+	0.0445748i
$833$	−2.71327	+	3.23354i	−0.0940091	+	0.112036i
$834$	−8.17494	−	7.95480i	−0.283075	−	0.275452i
$835$	−5.94564	+	16.3355i	−0.205757	+	0.565314i
$836$	30.6062	+	34.8024i	1.05854	+	1.20367i
$837$	29.8449	+	42.0708i	1.03159	+	1.45418i
$838$	−15.7538	+	5.94175i	−0.544204	+	0.205254i
$839$	−41.4114	−	15.0725i	−1.42968	−	0.520362i	−0.492842	−	0.870119i	$-0.664042\pi$
$839$	−41.4114	−	15.0725i	−1.42968	−	0.520362i	−0.936840	+	0.349757i	$0.886264\pi$
$840$	13.7044	−	7.01627i	0.472846	−	0.242084i
$841$	18.0440	+	15.1407i	0.622206	+	0.522093i
$842$	−3.99449	−	21.2119i	−0.137659	−	0.731011i
$843$	1.21286	+	13.5438i	0.0417733	+	0.466472i
$844$	−54.8861	−	8.37001i	−1.88926	−	0.288108i
$845$	34.9562	−	20.1820i	1.20253	−	0.694281i
$846$	8.42341	−	5.04114i	0.289603	−	0.173318i
$847$	−12.7895	−	7.38404i	−0.439454	−	0.253719i
$848$	−1.00408	−	21.6232i	−0.0344802	−	0.742544i
$849$	4.91261	−	1.32711i	0.168601	−	0.0455464i
$850$	−18.9695	−	22.0816i	−0.650649	−	0.757393i
$851$	−11.8231	+	4.30325i	−0.405290	+	0.147513i
$852$	−37.9338	−	25.1587i	−1.29959	−	0.861923i
$853$	0.404525	+	2.29417i	0.0138507	+	0.0785510i	0.990950	−	0.134235i	$-0.0428576\pi$
$853$	0.404525	+	2.29417i	0.0138507	+	0.0785510i	−0.977099	+	0.212786i	$0.931746\pi$
$854$	15.2260	+	2.50300i	0.521024	+	0.0856509i
$855$	42.3545	−	7.64713i	1.44849	−	0.261526i
$856$	−0.414592	+	0.0144342i	−0.0141704	+	0.000493351i
$857$	3.25613	+	3.88051i	0.111227	+	0.132556i	0.818786	−	0.574099i	$-0.194648\pi$
$857$	3.25613	+	3.88051i	0.111227	+	0.132556i	−0.707558	+	0.706655i	$0.750203\pi$
$858$	4.42621	−	2.13799i	0.151108	−	0.0729898i
$859$	−3.74070	−	0.659586i	−0.127631	−	0.0225048i	0.109468	−	0.993990i	$-0.465085\pi$
$859$	−3.74070	−	0.659586i	−0.127631	−	0.0225048i	−0.237099	+	0.971486i	$0.576196\pi$
$860$	6.03040	−	0.139936i	0.205635	−	0.00477178i
$861$	−3.33011	−	2.32163i	−0.113490	−	0.0791208i
$862$	−10.2089	+	0.118433i	−0.347715	+	0.00403384i
$863$	54.7986			1.86537			0.932683	−	0.360697i	$-0.117461\pi$
$863$	54.7986			1.86537			0.932683	+	0.360697i	$0.117461\pi$
$864$	5.77215	−	28.8216i	0.196372	−	0.980529i
$865$	68.8064			2.33949
$866$	52.7090	−	0.611477i	1.79113	−	0.0207788i
$867$	1.28225	−	0.601121i	0.0435475	−	0.0204151i
$868$	19.8485	−	0.460585i	0.673701	−	0.0156333i
$869$	0.849875	+	0.149856i	0.0288300	+	0.00508352i
$870$	−14.8540	−	10.1016i	−0.503597	−	0.342476i
$871$	−3.89223	−	4.63858i	−0.131883	−	0.157172i
$872$	−40.5466	+	1.41165i	−1.37308	+	0.0478044i
$873$	−0.199967	−	48.8510i	−0.00676787	−	1.65335i
$874$	−14.2294	−	2.33916i	−0.481316	−	0.0791234i
$875$	0.0673575	+	0.382003i	0.00227710	+	0.0129141i
$876$	4.60208	−	2.28916i	0.155490	−	0.0773435i
$877$	3.41604	−	1.24334i	0.115352	−	0.0419845i	−0.283700	−	0.958913i	$-0.591562\pi$
$877$	3.41604	−	1.24334i	0.115352	−	0.0419845i	0.399051	+	0.916929i	$0.369340\pi$
$878$	8.34419	+	9.71313i	0.281603	+	0.327802i
$879$	−0.866100	−	0.862562i	−0.0292128	−	0.0290935i
$880$	−2.95995	−	63.7436i	−0.0997798	−	2.14880i
$881$	−30.4693	−	17.5914i	−1.02654	−	0.592671i	−0.110545	−	0.993871i	$-0.535260\pi$
$881$	−30.4693	−	17.5914i	−1.02654	−	0.592671i	−0.915990	+	0.401200i	$0.868593\pi$
$882$	−1.38832	+	4.00906i	−0.0467473	+	0.134992i
$883$	−16.2975	+	9.40934i	−0.548453	+	0.316649i	−0.748498	−	0.663137i	$-0.769225\pi$
$883$	−16.2975	+	9.40934i	−0.548453	+	0.316649i	0.200045	+	0.979787i	$0.435891\pi$
$884$	−3.29925	−	0.503129i	−0.110966	−	0.0169221i
$885$	14.8391	+	6.88265i	0.498811	+	0.231358i
$886$	0.0391412	+	0.207851i	0.00131497	+	0.00698291i
$887$	−27.4961	−	23.0720i	−0.923229	−	0.774681i	0.0513600	−	0.998680i	$-0.483644\pi$
$887$	−27.4961	−	23.0720i	−0.923229	−	0.774681i	−0.974589	+	0.223999i	$0.928089\pi$
$888$	−23.1722	−	14.9843i	−0.777609	−	0.502841i
$889$	−11.1502	−	4.05834i	−0.373965	−	0.136112i
$890$	63.6180	−	23.9944i	2.13248	−	0.804294i
$891$	−7.56470	+	45.0554i	−0.253427	+	1.50941i
$892$	−12.6876	−	14.4271i	−0.424812	−	0.483055i
$893$	3.61260	−	9.92555i	0.120891	−	0.332146i
$894$	−15.1819	+	4.29087i	−0.507758	+	0.143508i
$895$	13.1459	−	15.6667i	0.439420	−	0.523680i
$896$	−7.95135	−	8.04836i	−0.265636	−	0.268877i
$897$	−0.643533	+	1.38747i	−0.0214869	+	0.0463262i
$898$	−12.4507	−	6.99709i	−0.415484	−	0.233496i
$899$	−11.5822	−	20.0610i	−0.386290	−	0.669073i
$900$	−25.7292	−	13.9327i	−0.857641	−	0.464424i
$901$	11.4215	−	19.7826i	0.380505	−	0.659054i
$902$	−14.4728	+	8.58123i	−0.481890	+	0.285724i
$903$	−1.17296	+	1.17778i	−0.0390338	+	0.0391939i
$904$	3.34972	+	0.471132i	0.111410	+	0.0156696i
$905$	13.0676	+	35.9028i	0.434380	+	1.19345i
$906$	4.57589	+	45.1906i	0.152024	+	1.50136i
$907$	16.4919	−	2.90797i	0.547605	−	0.0965575i	0.107001	−	0.994259i	$-0.465875\pi$
$907$	16.4919	−	2.90797i	0.547605	−	0.0965575i	0.440604	+	0.897701i	$0.354764\pi$
$908$	2.79372	+	13.9441i	0.0927128	+	0.462750i
$909$	−17.7638	−	30.4791i	−0.589190	−	1.01093i
$910$	−1.35895	−	1.11369i	−0.0450487	−	0.0369183i
$911$	−5.26224	+	4.41554i	−0.174346	+	0.146294i	−0.725785	−	0.687922i	$-0.758523\pi$
$911$	−5.26224	+	4.41554i	−0.174346	+	0.146294i	0.551439	+	0.834215i	$0.314079\pi$
$912$	−14.7388	−	27.9831i	−0.488049	−	0.926612i
$913$	−9.76770	+	55.3954i	−0.323264	+	1.83332i
$914$	37.0134	+	12.9875i	1.22429	+	0.429589i
$915$	−25.2101	−	53.7756i	−0.833421	−	1.77777i
$916$	10.1615	−	3.96781i	0.335747	−	0.131100i
$917$			12.5758i			0.415291i
$918$	21.5409	−	22.3191i	0.710956	−	0.736639i
$919$			32.1421i			1.06027i	0.847914	+	0.530134i	$0.177859\pi$
$919$			32.1421i			1.06027i	−0.847914	+	0.530134i	$0.822141\pi$
$920$	13.2840	+	14.7565i	0.437960	+	0.486507i
$921$	−1.73935	+	2.49490i	−0.0573135	+	0.0822098i
$922$	−3.57384	+	10.1851i	−0.117698	+	0.335429i
$923$	−0.902028	+	5.11566i	−0.0296906	+	0.168384i
$924$	12.7441	+	12.1163i	0.419250	+	0.398597i
$925$	−21.0423	+	17.6566i	−0.691866	+	0.580544i
$926$	8.47577	−	10.3423i	0.278531	−	0.339871i
$927$	−42.7396	−	15.3581i	−1.40375	−	0.504426i
$928$	−3.78811	+	12.6451i	−0.124351	+	0.415096i
$929$	−14.8524	+	2.61887i	−0.487291	+	0.0859225i	−0.411895	−	0.911231i	$-0.635133\pi$
$929$	−14.8524	+	2.61887i	−0.487291	+	0.0859225i	−0.0753954	+	0.997154i	$0.524022\pi$
$930$	−44.6814	−	61.9935i	−1.46516	−	2.03285i
$931$	1.56132	+	4.28970i	0.0511703	+	0.140589i
$932$	19.9688	+	10.9193i	0.654101	+	0.357675i
$933$	−9.24330	−	34.2162i	−0.302612	−	1.12019i
$934$	0.267225	+	0.450691i	0.00874386	+	0.0147470i
$935$	33.6697	−	58.3176i	1.10112	−	1.90719i
$936$	−3.27832	+	0.710506i	−0.107155	+	0.0232236i
$937$	7.52811	+	13.0391i	0.245933	+	0.425968i	0.962393	−	0.271659i	$-0.0875724\pi$
$937$	7.52811	+	13.0391i	0.245933	+	0.425968i	−0.716461	+	0.697627i	$0.754239\pi$
$938$	10.6125	−	18.8840i	0.346511	−	0.616584i
$939$	−0.777005	+	0.0695819i	−0.0253566	+	0.00227072i
$940$	−12.4227	+	7.56184i	−0.405185	+	0.246640i
$941$	2.65428	−	3.16325i	0.0865270	−	0.103119i	−0.721044	−	0.692889i	$-0.756337\pi$
$941$	2.65428	−	3.16325i	0.0865270	−	0.103119i	0.807571	+	0.589771i	$0.200782\pi$
$942$	15.2468	+	3.86316i	0.496769	+	0.125869i
$943$	1.79054	−	4.91947i	0.0583081	−	0.160200i
$944$	1.53596	−	11.9218i	0.0499913	−	0.388020i
$945$	15.7473	−	4.32327i	0.512259	−	0.140636i
$946$	2.43128	+	6.44622i	0.0790478	+	0.209585i
$947$	−7.79817	−	2.83830i	−0.253407	−	0.0922324i	0.212194	−	0.977228i	$-0.431939\pi$
$947$	−7.79817	−	2.83830i	−0.253407	−	0.0922324i	−0.465600	+	0.884995i	$0.654161\pi$
$948$	−0.539852	−	0.235333i	−0.0175336	−	0.00764326i
$949$	−0.449343	−	0.377043i	−0.0145863	−	0.0122393i
$950$	−30.9388	+	5.82618i	−1.00379	+	0.189026i
$951$	−29.0251	+	20.4122i	−0.941203	+	0.661912i
$952$	−2.48104	−	11.6784i	−0.0804110	−	0.378500i
$953$	−4.05358	+	2.34033i	−0.131308	+	0.0758108i	−0.564215	−	0.825628i	$-0.690821\pi$
$953$	−4.05358	+	2.34033i	−0.131308	+	0.0758108i	0.432907	+	0.901439i	$0.357488\pi$
$954$	3.63156	−	22.6706i	0.117576	−	0.733986i
$955$	35.4064	+	20.4419i	1.14572	+	0.661484i
$956$	27.0608	+	21.6571i	0.875208	+	0.700439i
$957$	5.26958	−	19.8286i	0.170341	−	0.640967i
$958$	28.9980	−	24.9111i	0.936884	−	0.804843i
$959$	−0.229352	+	0.0834772i	−0.00740615	+	0.00269562i
$960$	−8.23056	+	42.7617i	−0.265640	+	1.38013i
$961$	−11.7288	−	66.5172i	−0.378348	−	2.14572i
$962$	−0.510830	+	3.10743i	−0.0164698	+	0.100188i
$963$	−0.433632	−	0.0746320i	−0.0139736	−	0.00240498i
$964$	40.4756	+	13.6772i	1.30363	+	0.440512i
$965$	−40.6921	−	48.4950i	−1.30993	−	1.56111i
$966$	−5.45655	−	0.402435i	−0.175562	−	0.0129481i
$967$	32.0027	+	5.64293i	1.02914	+	0.181464i	0.662627	−	0.748950i	$-0.269442\pi$
$967$	32.0027	+	5.64293i	1.02914	+	0.181464i	0.366509	+	0.930414i	$0.380553\pi$
$968$	38.7305	−	15.6434i	1.24485	−	0.502798i
$969$	2.84080	−	33.2543i	0.0912597	−	1.06828i
$970$	0.839536	+	72.3677i	0.0269559	+	2.32359i
$971$	10.3035			0.330656			0.165328	−	0.986239i	$-0.447132\pi$
$971$	10.3035			0.330656			0.165328	+	0.986239i	$0.447132\pi$
$972$	12.2240	−	28.6805i	0.392086	−	0.919929i
$973$	−4.65669			−0.149287
$974$	−0.270981	−	23.3584i	−0.00868278	−	0.748452i
$975$	−0.284212	+	3.32697i	−0.00910207	+	0.106548i
$976$	−32.0958	+	29.5742i	−1.02736	+	0.946648i
$977$	−16.6437	−	2.93474i	−0.532480	−	0.0938906i	−0.0990581	−	0.995082i	$-0.531583\pi$
$977$	−16.6437	−	2.93474i	−0.532480	−	0.0938906i	−0.433422	+	0.901191i	$0.642694\pi$
$978$	52.7723	+	3.89209i	1.68747	+	0.124455i
$979$	49.9174	+	59.4892i	1.59537	+	1.90128i
$980$	2.01214	−	5.95463i	0.0642753	−	0.190214i
$981$	−42.4086	−	7.29892i	−1.35400	−	0.233037i
$982$	−4.05550	+	24.6701i	−0.129416	+	0.787253i
$983$	2.18509	+	12.3923i	0.0696936	+	0.395252i	0.999622	+	0.0275101i	$0.00875786\pi$
$983$	2.18509	+	12.3923i	0.0696936	+	0.395252i	−0.929928	+	0.367742i	$0.880131\pi$
$984$	10.9738	−	3.37833i	0.349831	−	0.107697i
$985$	39.3706	−	14.3297i	1.25445	−	0.456583i
$986$	−10.5664	+	9.07717i	−0.336501	+	0.289076i
$987$	1.02933	−	3.87320i	0.0327639	−	0.123285i
$988$	−2.25525	+	2.81797i	−0.0717491	+	0.0896514i
$989$	−1.85644	−	1.07182i	−0.0590314	−	0.0340818i
$990$	10.7056	−	66.8311i	0.340246	−	2.12403i
$991$	7.25472	−	4.18851i	0.230454	−	0.133052i	−0.380328	−	0.924852i	$-0.624189\pi$
$991$	7.25472	−	4.18851i	0.230454	−	0.133052i	0.610781	+	0.791799i	$0.290855\pi$
$992$	−33.5414	+	45.0374i	−1.06494	+	1.42994i
$993$	45.0232	−	31.6631i	1.42877	−	1.00480i
$994$	−18.2619	+	3.43895i	−0.579231	+	0.109077i
$995$	53.7934	+	45.1380i	1.70537	+	1.43097i
$996$	15.3392	−	35.1879i	0.486040	−	1.11497i
$997$	−42.7763	−	15.5693i	−1.35474	−	0.493085i	−0.440315	−	0.897843i	$-0.645133\pi$
$997$	−42.7763	−	15.5693i	−1.35474	−	0.493085i	−0.914424	+	0.404759i	$0.867356\pi$
$998$	3.03741	+	8.05330i	0.0961477	+	0.254923i
$999$	−20.8229	−	20.5688i	−0.658808	−	0.650767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.239.2	yes	648
4.3	odd	2	inner	756.2.cf.a.239.83	yes	648
27.20	odd	18	inner	756.2.cf.a.155.83	yes	648
108.47	even	18	inner	756.2.cf.a.155.2	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.155.2	✓	648	108.47	even	18	inner
756.2.cf.a.155.83	yes	648	27.20	odd	18	inner
756.2.cf.a.239.2	yes	648	1.1	even	1	trivial
756.2.cf.a.239.83	yes	648	4.3	odd	2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41412 + 0.0164052i) q^{2} +(0.147426 - 1.72577i) q^{3} +(1.99946 - 0.0463977i) q^{4} +(-3.09496 - 0.545724i) q^{5} +(-0.180167 + 2.44285i) q^{6} +(0.642788 + 0.766044i) q^{7} +(-2.82671 + 0.0984134i) q^{8} +(-2.95653 - 0.508847i) q^{9} +O(q^{10})\)	\(q+(-1.41412 + 0.0164052i) q^{2} +(0.147426 - 1.72577i) q^{3} +(1.99946 - 0.0463977i) q^{4} +(-3.09496 - 0.545724i) q^{5} +(-0.180167 + 2.44285i) q^{6} +(0.642788 + 0.766044i) q^{7} +(-2.82671 + 0.0984134i) q^{8} +(-2.95653 - 0.508847i) q^{9} +(4.38559 + 0.720946i) q^{10} +(0.881478 + 4.99911i) q^{11} +(0.214702 - 3.45744i) q^{12} +(-0.371483 + 0.135209i) q^{13} +(-0.921545 - 1.07273i) q^{14} +(-1.39807 + 5.26071i) q^{15} +(3.99569 - 0.185541i) q^{16} +(3.65557 + 2.11055i) q^{17} +(4.18923 + 0.671067i) q^{18} +(3.95341 - 2.28250i) q^{19} +(-6.21357 - 0.947556i) q^{20} +(1.41678 - 0.996365i) q^{21} +(-1.32853 - 7.05487i) q^{22} +(1.71110 + 1.43578i) q^{23} +(-0.246894 + 4.89275i) q^{24} +(4.58248 + 1.66789i) q^{25} +(0.523102 - 0.197295i) q^{26} +(-1.31402 + 5.02726i) q^{27} +(1.32077 + 1.50185i) q^{28} +(0.798106 - 2.19278i) q^{29} +(1.89073 - 7.46221i) q^{30} +(6.38089 - 7.60445i) q^{31} +(-5.64734 + 0.327927i) q^{32} +(8.75724 - 0.784223i) q^{33} +(-5.20404 - 2.92459i) q^{34} +(-1.57135 - 2.72166i) q^{35} +(-5.93508 - 0.880243i) q^{36} +(-2.81640 + 4.87815i) q^{37} +(-5.55314 + 3.29258i) q^{38} +(0.178572 + 0.661025i) q^{39} +(8.80227 + 1.23802i) q^{40} +(-0.801612 - 2.20241i) q^{41} +(-1.98714 + 1.43222i) q^{42} +(-0.945108 + 0.166648i) q^{43} +(1.99443 + 9.95463i) q^{44} +(8.87265 + 3.18831i) q^{45} +(-2.44325 - 2.00229i) q^{46} +(1.77248 - 1.48729i) q^{47} +(0.268871 - 6.92298i) q^{48} +(-0.173648 + 0.984808i) q^{49} +(-6.50753 - 2.28341i) q^{50} +(4.18124 - 5.99751i) q^{51} +(-0.736492 + 0.287580i) q^{52} -5.41162i q^{53} +(1.77571 - 7.13070i) q^{54} -15.9531i q^{55} +(-1.89237 - 2.10213i) q^{56} +(-3.35622 - 7.15915i) q^{57} +(-1.09264 + 3.11394i) q^{58} +(0.521825 - 2.95942i) q^{59} +(-2.55130 + 10.5835i) q^{60} +(-8.35826 + 7.01341i) q^{61} +(-8.89858 + 10.8583i) q^{62} +(-1.51062 - 2.59191i) q^{63} +(7.98063 - 0.556373i) q^{64} +(1.22351 - 0.215738i) q^{65} +(-12.3709 + 1.25265i) q^{66} +(5.23878 + 14.3934i) q^{67} +(7.40710 + 4.05035i) q^{68} +(2.73008 - 2.74128i) q^{69} +(2.26673 + 3.82297i) q^{70} +(6.57003 - 11.3796i) q^{71} +(8.40735 + 1.14740i) q^{72} +(0.741893 + 1.28500i) q^{73} +(3.90270 - 6.94448i) q^{74} +(3.55396 - 7.66239i) q^{75} +(7.79878 - 4.74720i) q^{76} +(-3.26294 + 3.88862i) q^{77} +(-0.263366 - 0.931838i) q^{78} +(0.0581453 - 0.159753i) q^{79} +(-12.4678 - 1.60631i) q^{80} +(8.48215 + 3.00884i) q^{81} +(1.16971 + 3.10132i) q^{82} +(10.4128 + 3.78994i) q^{83} +(2.78656 - 2.05793i) q^{84} +(-10.1621 - 8.52698i) q^{85} +(1.33376 - 0.251165i) q^{86} +(-3.66656 - 1.70062i) q^{87} +(-2.98366 - 14.0443i) q^{88} +(13.2487 - 7.64915i) q^{89} +(-12.5993 - 4.36309i) q^{90} +(-0.342360 - 0.197662i) q^{91} +(3.48789 + 2.79140i) q^{92} +(-12.1828 - 12.1330i) q^{93} +(-2.48210 + 2.13228i) q^{94} +(-13.4812 + 4.90677i) q^{95} +(-0.266642 + 9.79433i) q^{96} +(2.82765 + 16.0364i) q^{97} +(0.229403 - 1.39548i) q^{98} +(-0.0623368 - 15.2286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q+O(q^{10}) \) 648 * q	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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