LMFDB - Embedded newform 135.2.q.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$135 = 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	135.q (of order $36$ , degree $12$ , 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.10

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.184358 + 0.263290i) q^{2} +(-1.70366 + 0.312334i) q^{3} +(0.648706 - 1.78231i) q^{4} +(-0.0853346 + 2.23444i) q^{5} +(-0.396317 - 0.390975i) q^{6} +(4.46037 + 2.07991i) q^{7} +(1.20979 - 0.324162i) q^{8} +(2.80490 - 1.06422i) q^{9} +(-0.604038 + 0.389469i) q^{10} +(0.0393995 - 0.0469545i) q^{11} +(-0.548499 + 3.23905i) q^{12} +(-0.0650996 - 0.0455832i) q^{13} +(0.274686 + 1.55782i) q^{14} +(-0.552510 - 3.83337i) q^{15} +(-2.59752 - 2.17957i) q^{16} +(-3.89214 - 1.04290i) q^{17} +(0.797303 + 0.542304i) q^{18} +(-1.80193 - 1.04035i) q^{19} +(3.92710 + 1.60159i) q^{20} +(-8.24857 - 2.15032i) q^{21} +(0.0196263 + 0.00171708i) q^{22} +(2.74553 + 5.88782i) q^{23} +(-1.95982 + 0.930119i) q^{24} +(-4.98544 - 0.381350i) q^{25} -0.0255437i q^{26} +(-4.44619 + 2.68913i) q^{27} +(6.60050 - 6.60050i) q^{28} +(1.24585 - 7.06559i) q^{29} +(0.907430 - 0.852182i) q^{30} +(0.209263 + 0.0761654i) q^{31} +(0.313308 - 3.58112i) q^{32} +(-0.0524578 + 0.0923002i) q^{33} +(-0.442962 - 1.21703i) q^{34} +(-5.02805 + 9.78894i) q^{35} +(-0.0772105 - 5.68955i) q^{36} +(1.69714 - 6.33380i) q^{37} +(-0.0582873 - 0.666227i) q^{38} +(0.125145 + 0.0573254i) q^{39} +(0.621084 + 2.73086i) q^{40} +(-2.22023 + 0.391486i) q^{41} +(-0.954529 - 2.56820i) q^{42} +(-3.71962 + 0.325424i) q^{43} +(-0.0581286 - 0.100682i) q^{44} +(2.13858 + 6.35818i) q^{45} +(-1.04404 + 1.80834i) q^{46} +(-0.591824 + 1.26917i) q^{47} +(5.10603 + 2.90196i) q^{48} +(11.0694 + 13.1920i) q^{49} +(-0.818698 - 1.38292i) q^{50} +(6.95660 + 0.561090i) q^{51} +(-0.123474 + 0.0864573i) q^{52} +(-8.67464 - 8.67464i) q^{53} +(-1.52771 - 0.674876i) q^{54} +(0.101555 + 0.0920427i) q^{55} +(6.07034 + 1.07036i) q^{56} +(3.39481 + 1.20959i) q^{57} +(2.08998 - 0.974575i) q^{58} +(0.888968 - 0.745933i) q^{59} +(-7.19066 - 1.50199i) q^{60} +(-6.77967 + 2.46760i) q^{61} +(0.0185256 + 0.0691385i) q^{62} +(14.7243 + 1.08710i) q^{63} +(-4.87243 + 2.81310i) q^{64} +(0.107408 - 0.141571i) q^{65} +(-0.0339728 + 0.00320464i) q^{66} +(-4.36094 + 6.22807i) q^{67} +(-4.38361 + 6.26045i) q^{68} +(-6.51641 - 9.17330i) q^{69} +(-3.50429 + 0.480832i) q^{70} +(6.33059 - 3.65497i) q^{71} +(3.04835 - 2.19672i) q^{72} +(-1.72056 - 6.42123i) q^{73} +(1.98051 - 0.720846i) q^{74} +(8.61258 - 0.907430i) q^{75} +(-3.02314 + 2.53672i) q^{76} +(0.273398 - 0.127487i) q^{77} +(0.00797816 + 0.0435177i) q^{78} +(6.06016 + 1.06857i) q^{79} +(5.09178 - 5.61800i) q^{80} +(6.73488 - 5.97005i) q^{81} +(-0.512391 - 0.512391i) q^{82} +(-3.30178 + 2.31193i) q^{83} +(-9.18343 + 13.3065i) q^{84} +(2.66242 - 8.60775i) q^{85} +(-0.771422 - 0.919344i) q^{86} +(0.0843133 + 12.4265i) q^{87} +(0.0324443 - 0.0695770i) q^{88} +(5.25350 - 9.09933i) q^{89} +(-1.27978 + 1.73525i) q^{90} +(-0.195560 - 0.338719i) q^{91} +(12.2749 - 1.07392i) q^{92} +(-0.380301 - 0.0643999i) q^{93} +(-0.443268 + 0.0781601i) q^{94} +(2.47836 - 3.93753i) q^{95} +(0.584736 + 6.19886i) q^{96} +(0.855375 + 9.77698i) q^{97} +(-1.43259 + 5.34651i) q^{98} +(0.0605417 - 0.173632i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100})$ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$ .

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.184358	+	0.263290i	0.130361	+	0.186174i	0.879026	−	0.476774i	$-0.158194\pi$
$2$	0.184358	+	0.263290i	0.130361	+	0.186174i	−0.748665	+	0.662948i	$0.769305\pi$
$3$	−1.70366	+	0.312334i	−0.983607	+	0.180326i
$3$	−1.70366	+	0.312334i	−0.983607	+	0.180326i
$4$	0.648706	−	1.78231i	0.324353	−	0.891153i
$5$	−0.0853346	+	2.23444i	−0.0381628	+	0.999272i
$5$	−0.0853346	+	2.23444i	−0.0381628	+	0.999272i
$6$	−0.396317	−	0.390975i	−0.161796	−	0.159615i
$7$	4.46037	+	2.07991i	1.68586	+	0.786130i	0.998192	+	0.0601067i	$0.0191441\pi$
$7$	4.46037	+	2.07991i	1.68586	+	0.786130i	0.687670	+	0.726024i	$0.258634\pi$
$8$	1.20979	−	0.324162i	0.427725	−	0.114609i
$9$	2.80490	−	1.06422i	0.934965	−	0.354740i
$10$	−0.604038	+	0.389469i	−0.191014	+	0.123161i
$11$	0.0393995	−	0.0469545i	0.0118794	−	0.0141573i	−0.760072	−	0.649839i	$-0.774836\pi$
$11$	0.0393995	−	0.0469545i	0.0118794	−	0.0141573i	0.771951	+	0.635682i	$0.219281\pi$
$12$	−0.548499	+	3.23905i	−0.158338	+	0.935034i
$13$	−0.0650996	−	0.0455832i	−0.0180554	−	0.0126425i	0.564514	−	0.825424i	$-0.309064\pi$
$13$	−0.0650996	−	0.0455832i	−0.0180554	−	0.0126425i	−0.582569	+	0.812781i	$0.697953\pi$
$14$	0.274686	+	1.55782i	0.0734128	+	0.416345i
$15$	−0.552510	−	3.83337i	−0.142657	−	0.989772i
$16$	−2.59752	−	2.17957i	−0.649379	−	0.544894i
$17$	−3.89214	−	1.04290i	−0.943982	−	0.252939i	−0.246175	−	0.969225i	$-0.579174\pi$
$17$	−3.89214	−	1.04290i	−0.943982	−	0.252939i	−0.697807	+	0.716286i	$0.745841\pi$
$18$	0.797303	+	0.542304i	0.187926	+	0.127822i
$19$	−1.80193	−	1.04035i	−0.413392	−	0.238672i	0.278854	−	0.960333i	$-0.410045\pi$
$19$	−1.80193	−	1.04035i	−0.413392	−	0.238672i	−0.692246	+	0.721662i	$0.743379\pi$
$20$	3.92710	+	1.60159i	0.878126	+	0.358126i
$21$	−8.24857	−	2.15032i	−1.79998	−	0.469239i
$22$	0.0196263	+	0.00171708i	0.00418434	+	0.000366082i
$23$	2.74553	+	5.88782i	0.572483	+	1.22769i	0.953014	+	0.302926i	$0.0979636\pi$
$23$	2.74553	+	5.88782i	0.572483	+	1.22769i	−0.380531	+	0.924768i	$0.624259\pi$
$24$	−1.95982	+	0.930119i	−0.400047	+	0.189860i
$25$	−4.98544	−	0.381350i	−0.997087	−	0.0762700i
$26$		−	0.0255437i		−	0.00500954i
$27$	−4.44619	+	2.68913i	−0.855669	+	0.517523i
$28$	6.60050	−	6.60050i	1.24738	−	1.24738i
$29$	1.24585	−	7.06559i	0.231349	−	1.31205i	−0.618818	−	0.785534i	$-0.712388\pi$
$29$	1.24585	−	7.06559i	0.231349	−	1.31205i	0.850167	−	0.526512i	$-0.176501\pi$
$30$	0.907430	−	0.852182i	0.165673	−	0.155586i
$31$	0.209263	+	0.0761654i	0.0375847	+	0.0136797i	0.360744	−	0.932665i	$-0.382523\pi$
$31$	0.209263	+	0.0761654i	0.0375847	+	0.0136797i	−0.323159	+	0.946345i	$0.604745\pi$
$32$	0.313308	−	3.58112i	0.0553855	−	0.633059i
$33$	−0.0524578	+	0.0923002i	−0.00913174	+	0.0160674i
$34$	−0.442962	−	1.21703i	−0.0759674	−	0.208719i
$35$	−5.02805	+	9.78894i	−0.849895	+	1.65463i
$36$	−0.0772105	−	5.68955i	−0.0128684	−	0.948258i
$37$	1.69714	−	6.33380i	0.279007	−	1.04127i	−0.674101	−	0.738640i	$-0.735469\pi$
$37$	1.69714	−	6.33380i	0.279007	−	1.04127i	0.953108	−	0.302630i	$-0.0978648\pi$
$38$	−0.0582873	−	0.666227i	−0.00945545	−	0.108076i
$39$	0.125145	+	0.0573254i	0.0200392	+	0.00917941i
$40$	0.621084	+	2.73086i	0.0982020	+	0.431787i
$41$	−2.22023	+	0.391486i	−0.346742	+	0.0611399i	−0.344307	−	0.938857i	$-0.611886\pi$
$41$	−2.22023	+	0.391486i	−0.346742	+	0.0611399i	−0.00243462	+	0.999997i	$0.500775\pi$
$42$	−0.954529	−	2.56820i	−0.147287	−	0.396281i
$43$	−3.71962	+	0.325424i	−0.567236	+	0.0496267i	−0.367167	−	0.930155i	$-0.619672\pi$
$43$	−3.71962	+	0.325424i	−0.567236	+	0.0496267i	−0.200069	+	0.979782i	$0.564117\pi$
$44$	−0.0581286	−	0.100682i	−0.00876322	−	0.0151783i
$45$	2.13858	+	6.35818i	0.318800	+	0.947822i
$46$	−1.04404	+	1.80834i	−0.153936	+	0.266625i
$47$	−0.591824	+	1.26917i	−0.0863264	+	0.185128i	−0.944732	−	0.327844i	$-0.893678\pi$
$47$	−0.591824	+	1.26917i	−0.0863264	+	0.185128i	0.858405	+	0.512972i	$0.171456\pi$
$48$	5.10603	+	2.90196i	0.736992	+	0.418861i
$49$	11.0694	+	13.1920i	1.58134	+	1.88457i
$50$	−0.818698	−	1.38292i	−0.115781	−	0.195575i
$51$	6.95660	+	0.561090i	0.974119	+	0.0785684i
$52$	−0.123474	+	0.0864573i	−0.0171227	+	0.0119895i
$53$	−8.67464	−	8.67464i	−1.19155	−	1.19155i	−0.976631	−	0.214923i	$-0.931050\pi$
$53$	−8.67464	−	8.67464i	−1.19155	−	1.19155i	−0.214923	−	0.976631i	$-0.568950\pi$
$54$	−1.52771	−	0.674876i	−0.207895	−	0.0918390i
$55$	0.101555	+	0.0920427i	0.0136937	+	0.0124110i
$56$	6.07034	+	1.07036i	0.811183	+	0.143033i
$57$	3.39481	+	1.20959i	0.449654	+	0.160214i
$58$	2.08998	−	0.974575i	0.274428	−	0.127968i
$59$	0.888968	−	0.745933i	0.115734	−	0.0971121i	−0.583084	−	0.812412i	$-0.698154\pi$
$59$	0.888968	−	0.745933i	0.115734	−	0.0971121i	0.698818	+	0.715300i	$0.253710\pi$
$60$	−7.19066	−	1.50199i	−0.928310	−	0.193906i
$61$	−6.77967	+	2.46760i	−0.868048	+	0.315944i	−0.737377	−	0.675482i	$-0.763936\pi$
$61$	−6.77967	+	2.46760i	−0.868048	+	0.315944i	−0.130672	+	0.991426i	$0.541713\pi$
$62$	0.0185256	+	0.0691385i	0.00235275	+	0.00878060i
$63$	14.7243	+	1.08710i	1.85509	+	0.136962i
$64$	−4.87243	+	2.81310i	−0.609054	+	0.351637i
$65$	0.107408	−	0.141571i	0.0133224	−	0.0175598i
$66$	−0.0339728	+	0.00320464i	−0.00418176	+	0.000394464i
$67$	−4.36094	+	6.22807i	−0.532774	+	0.760880i	−0.991835	−	0.127524i	$-0.959297\pi$
$67$	−4.36094	+	6.22807i	−0.532774	+	0.760880i	0.459061	+	0.888405i	$0.348186\pi$
$68$	−4.38361	+	6.26045i	−0.531591	+	0.759191i
$69$	−6.51641	−	9.17330i	−0.784484	−	1.10434i
$70$	−3.50429	+	0.480832i	−0.418843	+	0.0574704i
$71$	6.33059	−	3.65497i	0.751303	−	0.433765i	−0.0748614	−	0.997194i	$-0.523851\pi$
$71$	6.33059	−	3.65497i	0.751303	−	0.433765i	0.826165	+	0.563429i	$0.190518\pi$
$72$	3.04835	−	2.19672i	0.359252	−	0.258886i
$73$	−1.72056	−	6.42123i	−0.201377	−	0.751549i	−0.990523	−	0.137344i	$-0.956144\pi$
$73$	−1.72056	−	6.42123i	−0.201377	−	0.751549i	0.789147	−	0.614205i	$-0.210523\pi$
$74$	1.98051	−	0.720846i	0.230229	−	0.0837966i
$75$	8.61258	−	0.907430i	0.994495	−	0.104781i
$76$	−3.02314	+	2.53672i	−0.346778	+	0.290981i
$77$	0.273398	−	0.127487i	0.0311565	−	0.0145285i
$78$	0.00797816	+	0.0435177i	0.000903349	+	0.00492741i
$79$	6.06016	+	1.06857i	0.681821	+	0.120223i	0.503822	−	0.863807i	$-0.331927\pi$
$79$	6.06016	+	1.06857i	0.681821	+	0.120223i	0.177999	+	0.984031i	$0.443038\pi$
$80$	5.09178	−	5.61800i	0.569279	−	0.628111i
$81$	6.73488	−	5.97005i	0.748320	−	0.663338i
$82$	−0.512391	−	0.512391i	−0.0565841	−	0.0565841i
$83$	−3.30178	+	2.31193i	−0.362417	+	0.253767i	−0.740575	−	0.671974i	$-0.765447\pi$
$83$	−3.30178	+	2.31193i	−0.362417	+	0.253767i	0.378158	+	0.925741i	$0.376558\pi$
$84$	−9.18343	+	13.3065i	−1.00199	+	1.45186i
$85$	2.66242	−	8.60775i	0.288780	−	0.933642i
$86$	−0.771422	−	0.919344i	−0.0831845	−	0.0991355i
$87$	0.0843133	+	12.4265i	0.00903933	+	1.33226i
$88$	0.0324443	−	0.0695770i	0.00345857	−	0.00741693i
$89$	5.25350	−	9.09933i	0.556870	−	0.964527i	−0.440886	−	0.897563i	$-0.645336\pi$
$89$	5.25350	−	9.09933i	0.556870	−	0.964527i	0.997755	−	0.0669633i	$-0.0213311\pi$
$90$	−1.27978	+	1.73525i	−0.134901	+	0.182911i
$91$	−0.195560	−	0.338719i	−0.0205002	−	0.0355074i
$92$	12.2749	−	1.07392i	1.27975	−	0.111964i
$93$	−0.380301	−	0.0643999i	−0.0394354	−	0.00667796i
$94$	−0.443268	+	0.0781601i	−0.0457196	+	0.00806160i
$95$	2.47836	−	3.93753i	0.254274	−	0.403982i
$96$	0.584736	+	6.19886i	0.0596794	+	0.632669i
$97$	0.855375	+	9.77698i	0.0868501	+	0.992702i	0.907161	+	0.420784i	$0.138245\pi$
$97$	0.855375	+	9.77698i	0.0868501	+	0.992702i	−0.820311	+	0.571918i	$0.806200\pi$
$98$	−1.43259	+	5.34651i	−0.144714	+	0.540079i
$99$	0.0605417	−	0.173632i	0.00608467	−	0.0174507i
$100$	−3.91377	+	8.63819i	−0.391377	+	0.863819i
$101$	1.28534	+	3.53144i	0.127896	+	0.351391i	0.987069	−	0.160293i	$-0.0512439\pi$
$101$	1.28534	+	3.53144i	0.127896	+	0.351391i	−0.859173	+	0.511684i	$0.829022\pi$
$102$	1.13477	+	1.93505i	0.112359	+	0.191598i
$103$	−0.211590	+	2.41848i	−0.0208485	+	0.238300i	0.978619	+	0.205680i	$0.0659406\pi$
$103$	−0.211590	+	2.41848i	−0.0208485	+	0.238300i	−0.999468	+	0.0326198i	$0.989615\pi$
$104$	−0.0935332	−	0.0340433i	−0.00917169	−	0.00333822i
$105$	5.50865	−	18.2474i	0.537589	−	1.78077i
$106$	0.684711	−	3.88319i	0.0665050	−	0.377168i
$107$	−1.54852	+	1.54852i	−0.149701	+	0.149701i	−0.777984	−	0.628284i	$-0.783758\pi$
$107$	−1.54852	+	1.54852i	−0.149701	+	0.149701i	0.628284	+	0.777984i	$0.283758\pi$
$108$	1.90858	+	9.66892i	0.183653	+	0.930393i
$109$			0.257274i			0.0246424i	0.999924	+	0.0123212i	$0.00392206\pi$
$109$			0.257274i			0.0246424i	−0.999924	+	0.0123212i	$0.996078\pi$
$110$	−0.00551151	+	0.0437072i	−0.000525502	+	0.00416732i
$111$	−0.913080	+	11.3207i	−0.0866657	+	1.07451i
$112$	−7.05257	−	15.1243i	−0.666406	−	1.42911i
$113$	−11.2070	−	0.980488i	−1.05427	−	0.0922366i	−0.453180	−	0.891419i	$-0.649711\pi$
$113$	−11.2070	−	0.980488i	−1.05427	−	0.0922366i	−0.601089	+	0.799182i	$0.705266\pi$
$114$	0.307387	+	1.11682i	0.0287894	+	0.104600i
$115$	−13.3903	+	5.63229i	−1.24865	+	0.525214i
$116$	−11.7848	−	6.80398i	−1.09420	−	0.631734i
$117$	−0.231108	−	0.0585760i	−0.0213660	−	0.00541535i
$118$	0.360285	+	0.0965380i	0.0331669	+	0.00888705i
$119$	−15.1913	−	12.7470i	−1.39258	−	1.16851i
$120$	−1.91105	−	4.45847i	−0.174455	−	0.407001i
$121$	1.90948	+	10.8292i	0.173589	+	0.984471i
$122$	−1.89958	−	1.33010i	−0.171980	−	0.120422i
$123$	3.66024	−	1.36041i	0.330032	−	0.122664i
$124$	0.271500	−	0.323561i	0.0243814	−	0.0290567i
$125$	1.27753	−	11.1071i	0.114266	−	0.993450i
$126$	2.42832	+	4.07719i	0.216332	+	0.363225i
$127$	7.47317	−	2.00243i	0.663137	−	0.177687i	0.0884755	−	0.996078i	$-0.471801\pi$
$127$	7.47317	−	2.00243i	0.663137	−	0.177687i	0.574661	+	0.818391i	$0.305134\pi$
$128$	−8.15493	−	3.80270i	−0.720800	−	0.336115i
$129$	6.23531	−	1.71617i	0.548989	−	0.151101i
$130$	0.0570759	+	0.00217976i	0.00500589	+	0.000191178i
$131$	3.14700	−	8.64630i	0.274954	−	0.755431i	−0.722961	−	0.690889i	$-0.757219\pi$
$131$	3.14700	−	8.64630i	0.274954	−	0.755431i	0.997915	−	0.0645417i	$-0.0205586\pi$
$132$	0.130478	+	0.153372i	0.0113566	+	0.0133493i
$133$	−5.87347	−	8.38818i	−0.509294	−	0.727347i
$134$	−2.44376			−0.211109
$135$	−5.62928	−	10.1642i	−0.484491	−	0.874796i
$136$	−5.04674			−0.432754
$137$	−7.88810	−	11.2654i	−0.673926	−	0.962466i	−0.999854	−	0.0170715i	$-0.994566\pi$
$137$	−7.88810	−	11.2654i	−0.673926	−	0.962466i	0.325928	−	0.945394i	$-0.394323\pi$
$138$	1.21389	−	3.40688i	0.103333	−	0.290013i
$139$	0.364140	−	1.00047i	0.0308860	−	0.0848586i	−0.923291	−	0.384101i	$-0.874512\pi$
$139$	0.364140	−	1.00047i	0.0308860	−	0.0848586i	0.954177	+	0.299242i	$0.0967338\pi$
$140$	14.1852	+	15.3117i	1.19886	+	1.29407i
$141$	0.611861	−	2.34708i	0.0515280	−	0.197660i
$142$	2.12941	+	0.992961i	0.178696	+	0.0833274i
$143$	−0.00470524	+	0.00126076i	−0.000393472	+	0.000105430i
$144$	−9.60530	−	3.34915i	−0.800442	−	0.279096i
$145$	15.6813	+	3.38672i	1.30226	+	0.281252i
$146$	1.37345	−	1.63681i	0.113667	−	0.135464i
$147$	−22.9787	−	19.0173i	−1.89526	−	1.56852i
$148$	−10.1878	−	7.13359i	−0.837434	−	0.586378i
$149$	3.12678	+	17.7328i	0.256156	+	1.45273i	0.793089	+	0.609106i	$0.208472\pi$
$149$	3.12678	+	17.7328i	0.256156	+	1.45273i	−0.536933	+	0.843625i	$0.680417\pi$
$150$	1.82671	+	2.10032i	0.149151	+	0.171490i
$151$	7.30896	+	6.13294i	0.594795	+	0.499092i	0.889768	−	0.456414i	$-0.150866\pi$
$151$	7.30896	+	6.13294i	0.594795	+	0.499092i	−0.294973	+	0.955506i	$0.595311\pi$
$152$	−2.51720	−	0.674482i	−0.204172	−	0.0547077i
$153$	−12.0269	+	1.21688i	−0.972318	+	0.0983785i
$154$	0.0839692	+	0.0484796i	0.00676643	+	0.00390660i
$155$	−0.188044	+	0.461085i	−0.0151041	+	0.0370353i
$156$	0.183354	−	0.185859i	0.0146800	−	0.0148806i
$157$	16.1522	+	1.41313i	1.28908	+	0.112780i	0.710997	−	0.703195i	$-0.248244\pi$
$157$	16.1522	+	1.41313i	1.28908	+	0.112780i	0.578087	+	0.815975i	$0.303799\pi$
$158$	0.835893	+	1.79258i	0.0665001	+	0.142610i
$159$	17.4880	+	12.0692i	1.38689	+	0.957152i
$160$	7.97507	+	1.00566i	0.630484	+	0.0795045i
$161$			31.9723i			2.51977i
$162$	2.81348	+	0.672603i	0.221048	+	0.0528446i
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	−0.943559	−	0.331205i	$-0.892545\pi$
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	0.331205	+	0.943559i	$0.392545\pi$
$164$	−0.742528	+	4.21109i	−0.0579817	+	0.328831i
$165$	−0.201763	−	0.125090i	−0.0157072	−	0.00973826i
$166$	−1.21742	−	0.443103i	−0.0944898	−	0.0343915i
$167$	1.13992	−	13.0293i	0.0882093	−	1.00824i	−0.815121	−	0.579291i	$-0.803329\pi$
$167$	1.13992	−	13.0293i	0.0882093	−	1.00824i	0.903330	−	0.428946i	$-0.141115\pi$
$168$	−10.6761	+	0.0724370i	−0.823678	+	0.00558864i
$169$	−4.44410	−	12.2101i	−0.341854	−	0.939236i
$170$	2.75717	−	0.885917i	0.211466	−	0.0679467i
$171$	−6.16139	−	1.00041i	−0.471173	−	0.0765034i
$172$	−1.83293	+	6.84060i	−0.139760	+	0.521591i
$173$	1.98304	+	22.6663i	0.150768	+	1.72329i	0.575360	+	0.817900i	$0.304862\pi$
$173$	1.98304	+	22.6663i	0.150768	+	1.72329i	−0.424592	+	0.905385i	$0.639582\pi$
$174$	−3.25622	+	2.31311i	−0.246854	+	0.175357i
$175$	−21.4437	−	12.0702i	−1.62099	−	0.912421i
$176$	−0.204682	+	0.0360909i	−0.0154285	+	0.00272046i
$177$	−1.28152	+	1.54847i	−0.0963247	+	0.116390i
$178$	3.36429	−	0.294337i	0.252164	−	0.0220615i
$179$	9.11136	+	15.7813i	0.681015	+	1.17955i	0.974671	+	0.223642i	$0.0717945\pi$
$179$	9.11136	+	15.7813i	0.681015	+	1.17955i	−0.293656	+	0.955911i	$0.594872\pi$
$180$	12.7195	+	0.312993i	0.948058	+	0.0233291i
$181$	6.18809	−	10.7181i	0.459957	−	0.796669i	−0.539001	−	0.842305i	$-0.681198\pi$
$181$	6.18809	−	10.7181i	0.459957	−	0.796669i	0.998958	+	0.0456358i	$0.0145314\pi$
$182$	0.0531285	−	0.113934i	0.00393815	−	0.00844539i
$183$	10.7795	−	6.32146i	0.796846	−	0.467296i
$184$	5.23013	+	6.23302i	0.385570	+	0.459504i
$185$	14.0077	+	4.33264i	1.02986	+	0.318542i
$186$	−0.0531556	−	0.112002i	−0.00389756	−	0.00821240i
$187$	−0.202317	+	0.141664i	−0.0147949	+	0.0103595i
$188$	1.87813	+	1.87813i	0.136977	+	0.136977i
$189$	−25.4248	+	2.74686i	−1.84938	+	0.199804i
$190$	1.49362	−	0.0733872i	0.108358	−	0.00532407i
$191$	12.0893	+	2.13167i	0.874752	+	0.154242i	0.592959	−	0.805233i	$-0.297960\pi$
$191$	12.0893	+	2.13167i	0.874752	+	0.154242i	0.281793	+	0.959475i	$0.409071\pi$
$192$	7.42232	−	6.31438i	0.535660	−	0.455701i
$193$	16.0742	−	7.49551i	1.15704	−	0.539538i	0.253205	−	0.967413i	$-0.418515\pi$
$193$	16.0742	−	7.49551i	1.15704	−	0.539538i	0.903838	+	0.427874i	$0.140737\pi$
$194$	−2.41649	+	2.02767i	−0.173494	+	0.145579i
$195$	−0.138769	+	0.274736i	−0.00993748	+	0.0196743i
$196$	30.6929	−	11.1713i	2.19235	−	0.797951i
$197$	2.35826	+	8.80113i	0.168019	+	0.627055i	0.997636	+	0.0687218i	$0.0218921\pi$
$197$	2.35826	+	8.80113i	0.168019	+	0.627055i	−0.829617	+	0.558333i	$0.811441\pi$
$198$	0.0568770	−	0.0160704i	0.00404207	−	0.00114208i
$199$	−9.38387	+	5.41778i	−0.665205	+	0.384056i	−0.794257	−	0.607581i	$-0.792140\pi$
$199$	−9.38387	+	5.41778i	−0.665205	+	0.384056i	0.129052	+	0.991638i	$0.458807\pi$
$200$	−6.15495	+	1.15474i	−0.435221	+	0.0816522i
$201$	5.48432	−	11.9726i	0.386834	−	0.844480i
$202$	−0.692831	+	0.989466i	−0.0487474	+	0.0696186i
$203$	20.2527	−	28.9239i	1.42146	−	2.03006i
$204$	5.51283	−	12.0348i	0.385975	−	0.842605i
$205$	−0.685290	−	4.99437i	−0.0478627	−	0.348822i
$206$	−0.675770	+	0.390156i	−0.0470831	+	0.0271835i
$207$	13.9669	+	13.5929i	0.970764	+	0.944769i
$208$	0.0697452	+	0.260293i	0.00483596	+	0.0180480i
$209$	−0.119844	+	0.0436198i	−0.00828980	+	0.00301724i
$210$	5.81993	−	1.91368i	0.401613	−	0.132057i
$211$	−1.55684	+	1.30634i	−0.107177	+	0.0899325i	−0.694802	−	0.719202i	$-0.744508\pi$
$211$	−1.55684	+	1.30634i	−0.107177	+	0.0899325i	0.587624	+	0.809134i	$0.300063\pi$
$212$	−21.0882	+	9.83357i	−1.44834	+	0.675372i
$213$	−9.64359	+	8.20407i	−0.660768	+	0.562134i
$214$	−0.693191	−	0.122228i	−0.0473856	−	0.00835535i
$215$	−0.409729	−	8.33903i	−0.0279433	−	0.568717i
$216$	−4.50724	+	4.69457i	−0.306679	+	0.319425i
$217$	0.774973	+	0.774973i	0.0526086	+	0.0526086i
$218$	−0.0677378	+	0.0474305i	−0.00458779	+	0.00321240i
$219$	4.93682	+	10.4022i	0.333599	+	0.702915i
$220$	0.229928	−	0.121293i	0.0155017	−	0.00817759i
$221$	0.205838	+	0.245308i	0.0138462	+	0.0165012i
$222$	−3.14896	+	1.84665i	−0.211344	+	0.123939i
$223$	−1.15123	+	2.46881i	−0.0770918	+	0.165324i	−0.941076	−	0.338195i	$-0.890184\pi$
$223$	−1.15123	+	2.46881i	−0.0770918	+	0.165324i	0.863984	+	0.503519i	$0.167961\pi$
$224$	8.84586	−	15.3215i	0.591039	−	1.02371i
$225$	−14.3895	+	4.23595i	−0.959298	+	0.282397i
$226$	−1.80795	−	3.13146i	−0.120263	−	0.208302i
$227$	14.1158	−	1.23497i	0.936899	−	0.0819680i	0.391531	−	0.920165i	$-0.371946\pi$
$227$	14.1158	−	1.23497i	0.936899	−	0.0819680i	0.545368	+	0.838197i	$0.316390\pi$
$228$	4.35809	−	5.26592i	0.288622	−	0.348744i
$229$	−13.0574	+	2.30237i	−0.862857	+	0.152145i	−0.587527	−	0.809205i	$-0.699898\pi$
$229$	−13.0574	+	2.30237i	−0.862857	+	0.152145i	−0.275330	+	0.961350i	$0.588787\pi$
$230$	−3.95153	−	2.48717i	−0.260556	−	0.163999i
$231$	−0.425957	+	0.302586i	−0.0280259	+	0.0199087i
$232$	−0.783175	−	8.95173i	−0.0514180	−	0.587710i
$233$	−1.75621	+	6.55427i	−0.115053	+	0.429384i	−0.999291	−	0.0376527i	$-0.988012\pi$
$233$	−1.75621	+	6.55427i	−0.115053	+	0.429384i	0.884238	+	0.467037i	$0.154679\pi$
$234$	−0.0271841	−	0.0716475i	−0.00177708	−	0.00468374i
$235$	−2.78538	−	1.43070i	−0.181698	−	0.0933285i
$236$	−0.752801	−	2.06830i	−0.0490032	−	0.134635i
$237$	−10.6582	+	0.0723155i	−0.692323	+	0.00469740i
$238$	0.555528	−	6.34972i	0.0360095	−	0.411591i
$239$	−17.1554	−	6.24407i	−1.10969	−	0.403895i	−0.278812	−	0.960346i	$-0.589941\pi$
$239$	−17.1554	−	6.24407i	−1.10969	−	0.403895i	−0.830881	+	0.556451i	$0.812163\pi$
$240$	−6.91996	+	11.1615i	−0.446682	+	0.720470i
$241$	−2.76886	+	15.7030i	−0.178358	+	1.01152i	0.755839	+	0.654758i	$0.227229\pi$
$241$	−2.76886	+	15.7030i	−0.178358	+	1.01152i	−0.934196	+	0.356759i	$0.883882\pi$
$242$	−2.49919	+	2.49919i	−0.160654	+	0.160654i
$243$	−9.60927	+	12.2744i	−0.616435	+	0.787406i
$244$			13.6842i			0.876041i
$245$	−30.4213	+	23.6081i	−1.94355	+	1.50827i
$246$	1.03298	+	0.712902i	0.0658601	+	0.0454530i
$247$	0.0698828	+	0.149864i	0.00444653	+	0.00953562i
$248$	0.277854	+	0.0243091i	0.0176437	+	0.00154363i
$249$	4.90300	−	4.96999i	0.310715	−	0.314960i
$250$	3.15992	−	1.71132i	0.199851	−	0.108233i
$251$	14.9016	+	8.60342i	0.940578	+	0.543043i	0.890141	−	0.455684i	$-0.150605\pi$
$251$	14.9016	+	8.60342i	0.940578	+	0.543043i	0.0504364	+	0.998727i	$0.483939\pi$
$252$	11.4893	−	25.5381i	0.723760	−	1.60875i
$253$	0.384632	+	0.103062i	0.0241816	+	0.00647945i
$254$	1.90496	+	1.59845i	0.119528	+	0.100296i
$255$	−1.84736	+	15.4962i	−0.115686	+	0.970411i
$256$	1.45175	+	8.23327i	0.0907343	+	0.514580i
$257$	−7.66961	−	5.37032i	−0.478417	−	0.334991i	0.309367	−	0.950943i	$-0.399883\pi$
$257$	−7.66961	−	5.37032i	−0.478417	−	0.334991i	−0.787784	+	0.615952i	$0.788772\pi$
$258$	1.60138	+	1.32531i	0.0996976	+	0.0825100i
$259$	20.7436	−	24.7212i	1.28894	−	1.53610i
$260$	−0.182647	−	0.283273i	−0.0113273	−	0.0175678i
$261$	−4.02484	−	21.1441i	−0.249132	−	1.30879i
$262$	2.85666	−	0.765440i	0.176485	−	0.0472890i
$263$	0.828096	+	0.386147i	0.0510626	+	0.0238109i	0.447982	−	0.894043i	$-0.352143\pi$
$263$	0.828096	+	0.386147i	0.0510626	+	0.0238109i	−0.396919	+	0.917854i	$0.629921\pi$
$264$	−0.0335427	+	0.128669i	−0.00206441	+	0.00791901i
$265$	20.1232	−	18.6427i	1.23616	−	1.14521i
$266$	1.12571	−	3.09285i	0.0690215	−	0.189635i
$267$	−6.10813	+	17.1430i	−0.373812	+	1.04913i
$268$	8.27136	+	11.8127i	0.505254	+	0.721577i
$269$	27.6508			1.68590			0.842951	−	0.537990i	$-0.180816\pi$
$269$	27.6508			1.68590			0.842951	+	0.537990i	$0.180816\pi$
$270$	1.63834	−	3.35599i	0.0997060	−	0.204239i
$271$	−18.0879			−1.09876			−0.549380	−	0.835572i	$-0.685136\pi$
$271$	−18.0879			−1.09876			−0.549380	+	0.835572i	$0.685136\pi$
$272$	7.83682	+	11.1921i	0.475177	+	0.678623i
$273$	0.438960	+	0.515982i	0.0265671	+	0.0312286i
$274$	1.51183	−	4.15372i	0.0913330	−	0.250935i
$275$	−0.214330	+	0.219064i	−0.0129246	+	0.0132100i
$276$	−20.5769	+	5.66346i	−1.23858	+	0.340900i
$277$	4.69280	+	2.18829i	0.281963	+	0.131481i	0.558455	−	0.829535i	$-0.311394\pi$
$277$	4.69280	+	2.18829i	0.281963	+	0.131481i	−0.276492	+	0.961016i	$0.589172\pi$
$278$	0.330545	−	0.0885694i	0.0198248	−	0.00531204i
$279$	0.668017	−	0.00906538i	0.0399931	−	0.000542730i
$280$	−2.90967	+	13.4725i	−0.173886	+	0.805134i
$281$	−4.92653	+	5.87122i	−0.293892	+	0.350247i	−0.892705	−	0.450642i	$-0.851195\pi$
$281$	−4.92653	+	5.87122i	−0.293892	+	0.350247i	0.598812	+	0.800889i	$0.295640\pi$
$282$	0.730764	−	0.271605i	0.0435164	−	0.0161739i
$283$	−7.76215	−	5.43511i	−0.461412	−	0.323084i	0.319652	−	0.947535i	$-0.396434\pi$
$283$	−7.76215	−	5.43511i	−0.461412	−	0.323084i	−0.781064	+	0.624451i	$0.785323\pi$
$284$	−2.40758	−	13.6541i	−0.142863	−	0.810219i
$285$	−2.99245	+	7.48228i	−0.177257	+	0.443212i
$286$	−0.00119939	−	0.00100641i	−7.09216e−5	−	5.95103e-5i
$287$	−10.7173	−	2.87169i	−0.632622	−	0.169511i
$288$	−2.93230	−	10.3781i	−0.172788	−	0.611536i
$289$	−0.661319	−	0.381813i	−0.0389011	−	0.0224596i
$290$	1.99928	+	4.75310i	0.117402	+	0.279112i
$291$	−4.51094	−	16.3895i	−0.264436	−	0.960767i
$292$	−12.5607	−	1.09892i	−0.735062	−	0.0643096i
$293$	−3.61107	−	7.74397i	−0.210961	−	0.452408i	0.772144	−	0.635447i	$-0.219184\pi$
$293$	−3.61107	−	7.74397i	−0.210961	−	0.452408i	−0.983106	+	0.183039i	$0.941406\pi$
$294$	0.770752	−	9.55606i	0.0449512	−	0.557321i
$295$	1.59088	+	2.05000i	0.0926247	+	0.119356i
$296$		−	8.21271i		−	0.477354i
$297$	−0.0489110	+	0.314719i	−0.00283811	+	0.0182619i
$298$	−4.09244	+	4.09244i	−0.237069	+	0.237069i
$299$	0.0896526	−	0.508445i	0.00518474	−	0.0294041i
$300$	3.96972	−	15.9389i	0.229192	−	0.920234i
$301$	−17.2677	−	6.28494i	−0.995295	−	0.362258i
$302$	−0.267281	+	3.05503i	−0.0153803	+	0.175797i
$303$	−3.29276	−	5.61491i	−0.189164	−	0.322568i
$304$	2.41304	+	6.62976i	0.138397	+	0.380243i
$305$	−4.93516	−	15.3593i	−0.282586	−	0.879473i
$306$	−2.53765	−	2.94223i	−0.145068	−	0.168196i
$307$	5.49053	−	20.4909i	0.313361	−	1.16948i	−0.612145	−	0.790746i	$-0.709693\pi$
$307$	5.49053	−	20.4909i	0.313361	−	1.16948i	0.925506	−	0.378734i	$-0.123640\pi$
$308$	−0.0498668	−	0.569980i	−0.00284142	−	0.0324776i
$309$	−0.394896	−	4.18635i	−0.0224649	−	0.238153i
$310$	−0.156067	+	0.0354944i	−0.00886399	+	0.00201595i
$311$	−19.3816	+	3.41750i	−1.09903	+	0.193788i	−0.693616	−	0.720345i	$-0.743983\pi$
$311$	−19.3816	+	3.41750i	−1.09903	+	0.193788i	−0.405413	+	0.914134i	$0.632872\pi$
$312$	0.169981	+	0.0287846i	0.00962330	+	0.00162960i
$313$	4.18556	−	0.366189i	0.236582	−	0.0206983i	0.0317519	−	0.999496i	$-0.489891\pi$
$313$	4.18556	−	0.366189i	0.236582	−	0.0206983i	0.204830	+	0.978798i	$0.434336\pi$
$314$	2.60572	+	4.51323i	0.147049	+	0.254696i
$315$	−3.68557	+	32.8079i	−0.207658	+	1.84852i
$316$	5.83578	−	10.1079i	0.328288	−	0.568612i
$317$	−7.05644	+	15.1326i	−0.396329	+	0.849930i	0.602334	+	0.798244i	$0.294237\pi$
$317$	−7.05644	+	15.1326i	−0.396329	+	0.849930i	−0.998663	+	0.0516863i	$0.983540\pi$
$318$	0.0463379	+	6.82948i	0.00259850	+	0.382978i
$319$	−0.282675	−	0.336879i	−0.0158268	−	0.0188616i
$320$	−5.86991	−	11.1272i	−0.328138	−	0.622029i
$321$	2.15449	−	3.12180i	0.120252	−	0.174242i
$322$	−8.41799	+	5.89434i	−0.469116	+	0.328479i
$323$	5.92840	+	5.92840i	0.329865	+	0.329865i
$324$	−6.27149	−	15.8764i	−0.348416	−	0.882023i
$325$	0.307167	+	0.252078i	0.0170386	+	0.0139828i
$326$	−3.49972	−	0.617095i	−0.193831	−	0.0341777i
$327$	−0.0803555	−	0.438307i	−0.00444367	−	0.0242385i
$328$	−2.55911	+	1.19333i	−0.141303	+	0.0658907i
$329$	−5.27951	+	4.43004i	−0.291069	+	0.244236i
$330$	−0.00426152	−	0.0761835i	−0.000234589	−	0.00419377i
$331$	−12.4570	+	4.53397i	−0.684698	+	0.249210i	−0.660863	−	0.750506i	$-0.729810\pi$
$331$	−12.4570	+	4.53397i	−0.684698	+	0.249210i	−0.0238345	+	0.999716i	$0.507587\pi$
$332$	1.97868	+	7.38454i	0.108594	+	0.405279i
$333$	−1.98026	−	19.5718i	−0.108518	−	1.07253i
$334$	3.64064	−	2.10192i	0.199207	−	0.115012i
$335$	−13.5441	−	10.2757i	−0.739994	−	0.561423i
$336$	16.7390	+	23.5639i	0.913187	+	1.28551i
$337$	−12.1886	+	17.4071i	−0.663953	+	0.948223i	0.336027	+	0.941852i	$0.390917\pi$
$337$	−12.1886	+	17.4071i	−0.663953	+	0.948223i	−0.999980	+	0.00637058i	$0.997972\pi$
$338$	2.39549	−	3.42111i	0.130297	−	0.186084i
$339$	19.3992	−	1.82992i	1.05362	−	0.0993875i
$340$	−13.6145	−	10.3292i	−0.738351	−	0.560177i
$341$	0.0118212	−	0.00682495i	0.000640152	−	0.000369592i
$342$	−0.872501	−	1.80667i	−0.0471795	−	0.0976934i
$343$	13.0191	+	48.5880i	0.702966	+	2.62350i
$344$	−4.39446	+	1.59945i	−0.236934	+	0.0862368i
$345$	21.0532	−	13.7777i	1.13347	−	0.741768i
$346$	−5.60222	+	4.70082i	−0.301177	+	0.252718i
$347$	28.5852	−	13.3295i	1.53453	−	0.715565i	0.542327	−	0.840168i	$-0.317544\pi$
$347$	28.5852	−	13.3295i	1.53453	−	0.715565i	0.992207	+	0.124603i	$0.0397657\pi$
$348$	22.2024	+	7.91085i	1.19018	+	0.424066i
$349$	−16.6978	−	2.94427i	−0.893813	−	0.157603i	−0.292168	−	0.956367i	$-0.594377\pi$
$349$	−16.6978	−	2.94427i	−0.893813	−	0.157603i	−0.601645	+	0.798764i	$0.705488\pi$
$350$	−0.775353	−	7.87116i	−0.0414444	−	0.420731i
$351$	0.412024	+	0.0276105i	0.0219922	+	0.00147374i
$352$	−0.155806	−	0.155806i	−0.00830448	−	0.00830448i
$353$	15.5802	−	10.9094i	0.829252	−	0.580648i	−0.0800474	−	0.996791i	$-0.525507\pi$
$353$	15.5802	−	10.9094i	0.829252	−	0.580648i	0.909299	+	0.416143i	$0.136618\pi$
$354$	−0.643954	−	0.0519386i	−0.0342258	−	0.00276051i
$355$	7.62659	+	14.4572i	0.404777	+	0.767310i
$356$	−12.8098	−	15.2661i	−0.678918	−	0.809103i
$357$	29.8620	+	16.9717i	1.58047	+	0.898240i
$358$	−2.47532	+	5.30835i	−0.130825	+	0.280555i
$359$	−15.6916	+	27.1786i	−0.828170	+	1.43443i	0.0713028	+	0.997455i	$0.477284\pi$
$359$	−15.6916	+	27.1786i	−0.828170	+	1.43443i	−0.899473	+	0.436977i	$0.856049\pi$
$360$	4.64831	+	6.99882i	0.244988	+	0.368870i
$361$	−7.33536	−	12.7052i	−0.386072	−	0.668696i
$362$	3.96279	−	0.346699i	0.208280	−	0.0182221i
$363$	−6.63541	−	17.8528i	−0.348269	−	0.937030i
$364$	−0.730562	+	0.128818i	−0.0382919	+	0.00675189i
$365$	14.4947	−	3.29654i	0.758686	−	0.172549i
$366$	3.65167	+	1.67273i	0.190876	+	0.0874351i
$367$	1.56237	+	17.8579i	0.0815549	+	0.932177i	0.921212	+	0.389060i	$0.127200\pi$
$367$	1.56237	+	17.8579i	0.0815549	+	0.932177i	−0.839657	+	0.543117i	$0.817244\pi$
$368$	5.70137	−	21.2778i	0.297204	−	1.10918i
$369$	−5.81088	+	3.46089i	−0.302503	+	0.180167i
$370$	1.44168	+	4.48684i	0.0749494	+	0.233260i
$371$	−20.6497	−	56.7346i	−1.07208	−	2.94551i
$372$	−0.361484	+	0.636036i	−0.0187421	+	0.0329769i
$373$	−0.441145	+	5.04230i	−0.0228416	+	0.261081i	0.976184	+	0.216945i	$0.0696091\pi$
$373$	−0.441145	+	5.04230i	−0.0228416	+	0.261081i	−0.999026	+	0.0441361i	$0.985946\pi$
$374$	−0.0745975	−	0.0271513i	−0.00385734	−	0.00140396i
$375$	1.29265	+	19.3217i	0.0667520	+	0.997770i
$376$	−0.304566	+	1.72728i	−0.0157068	+	0.0890775i
$377$	−0.403177	+	0.403177i	−0.0207647	+	0.0207647i
$378$	−5.41048	−	6.18769i	−0.278285	−	0.318261i
$379$		−	9.89195i		−	0.508115i	−0.967189	−	0.254058i	$-0.918235\pi$
$379$		−	9.89195i		−	0.508115i	0.967189	−	0.254058i	$-0.0817653\pi$
$380$	−5.41016	−	6.97149i	−0.277535	−	0.357630i
$381$	−12.1063	+	5.74558i	−0.620224	+	0.294355i
$382$	1.66751	+	3.57599i	0.0853173	+	0.182963i
$383$	19.1117	+	1.67206i	0.976561	+	0.0854380i	0.564249	−	0.825605i	$-0.309166\pi$
$383$	19.1117	+	1.67206i	0.976561	+	0.0854380i	0.412312	+	0.911043i	$0.364721\pi$
$384$	15.0809	+	3.93145i	0.769595	+	0.200626i
$385$	0.261533	+	0.621769i	0.0133289	+	0.0316883i
$386$	4.93689	+	2.85032i	0.251281	+	0.145077i
$387$	−10.0868	+	4.87127i	−0.512742	+	0.247621i
$388$	17.9805	+	4.81785i	0.912819	+	0.244589i
$389$	−5.65836	−	4.74792i	−0.286890	−	0.240729i	0.487973	−	0.872859i	$-0.337737\pi$
$389$	−5.65836	−	4.74792i	−0.286890	−	0.240729i	−0.774863	+	0.632130i	$0.782181\pi$
$390$	−0.0979186	+	0.0141132i	−0.00495830	+	0.000714647i
$391$	−4.54562	−	25.7795i	−0.229882	−	1.30373i
$392$	17.6680	+	12.3713i	0.892368	+	0.624843i
$393$	−2.66087	+	15.7132i	−0.134223	+	0.792629i
$394$	−1.88249	+	2.24346i	−0.0948384	+	0.113024i
$395$	−2.90479	+	13.4499i	−0.146156	+	0.676736i
$396$	−0.270192	−	0.220540i	−0.0135777	−	0.0110826i
$397$	−12.4735	+	3.34227i	−0.626028	+	0.167744i	−0.557866	−	0.829931i	$-0.688380\pi$
$397$	−12.4735	+	3.34227i	−0.626028	+	0.167744i	−0.0681611	+	0.997674i	$0.521713\pi$
$398$	−3.15644	−	1.47187i	−0.158218	−	0.0737783i
$399$	12.6263	+	12.4561i	0.632105	+	0.623585i
$400$	12.1186	+	11.8567i	0.605928	+	0.592834i
$401$	−2.92360	+	8.03253i	−0.145998	+	0.401125i	−0.991039	−	0.133576i	$-0.957354\pi$
$401$	−2.92360	+	8.03253i	−0.145998	+	0.401125i	0.845041	+	0.534702i	$0.179576\pi$
$402$	4.16334	−	0.763270i	0.207648	−	0.0380684i
$403$	−0.0101511	−	0.0144972i	−0.000505660	−	0.000722158i
$404$	7.12791			0.354627
$405$	12.7650	+	15.5581i	0.634297	+	0.773089i
$406$	11.3491			0.563248
$407$	−0.230534	−	0.329237i	−0.0114272	−	0.0163197i
$408$	8.59791	−	1.57627i	0.425660	−	0.0780368i
$409$	4.56883	−	12.5528i	0.225914	−	0.620694i	−0.774008	−	0.633176i	$-0.781751\pi$
$409$	4.56883	−	12.5528i	0.225914	−	0.620694i	0.999922	+	0.0124819i	$0.00397323\pi$
$410$	1.18863	−	1.10118i	0.0587023	−	0.0543835i
$411$	16.9572	+	16.7286i	0.836436	+	0.825162i
$412$	4.17321	+	1.94600i	0.205599	+	0.0958725i
$413$	5.51659	−	1.47817i	0.271454	−	0.0727359i
$414$	−1.00397	+	6.18329i	−0.0493423	+	0.303892i
$415$	−4.88411	−	7.57490i	−0.239751	−	0.371837i
$416$	−0.183635	+	0.218848i	−0.00900347	+	0.0107299i
$417$	−0.307891	+	1.81819i	−0.0150775	+	0.0890370i
$418$	−0.0335789	−	0.0235122i	−0.00164240	−	0.00115002i
$419$	4.65475	+	26.3984i	0.227399	+	1.28964i	0.858045	+	0.513574i	$0.171679\pi$
$419$	4.65475	+	26.3984i	0.227399	+	1.28964i	−0.630646	+	0.776071i	$0.717210\pi$
$420$	−28.9490	−	21.6553i	−1.41257	−	1.05667i
$421$	19.3371	+	16.2257i	0.942432	+	0.790794i	0.978007	−	0.208573i	$-0.0668818\pi$
$421$	19.3371	+	16.2257i	0.942432	+	0.790794i	−0.0355751	+	0.999367i	$0.511326\pi$
$422$	−0.630963	−	0.169066i	−0.0307148	−	0.00823001i
$423$	−0.309329	+	4.18972i	−0.0150401	+	0.203711i
$424$	−13.3065	−	7.68250i	−0.646220	−	0.373095i
$425$	19.0063	+	6.68355i	0.921941	+	0.324200i
$426$	−3.93792	−	1.02658i	−0.190793	−	0.0497379i
$427$	−35.3722	−	3.09467i	−1.71178	−	0.149762i
$428$	1.75540	+	3.76447i	0.0848504	+	0.181962i
$429$	0.00762233	−	0.00361751i	0.000368010	−	0.000174655i
$430$	2.12005	−	1.64524i	0.102238	−	0.0793406i
$431$		−	23.0274i		−	1.10919i	−0.832121	−	0.554595i	$-0.812873\pi$
$431$		−	23.0274i		−	1.10919i	0.832121	−	0.554595i	$-0.187127\pi$
$432$	17.4102	+	2.70575i	0.837648	+	0.130180i
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	−0.326752	−	0.945110i	$-0.605954\pi$
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	0.945110	+	0.326752i	$0.105954\pi$
$434$	−0.0611705	+	0.346915i	−0.00293628	+	0.0166525i
$435$	−27.7734	−	0.872014i	−1.33163	−	0.0418099i
$436$	0.458542	+	0.166896i	0.0219602	+	0.00799285i
$437$	1.17810	−	13.4658i	0.0563562	−	0.644154i
$438$	−1.82865	+	3.21754i	−0.0873765	+	0.153740i
$439$	−10.8870	−	29.9118i	−0.519609	−	1.42761i	−0.870952	−	0.491367i	$-0.836497\pi$
$439$	−10.8870	−	29.9118i	−0.519609	−	1.42761i	0.351343	−	0.936247i	$-0.385725\pi$
$440$	0.152697	+	0.0784321i	0.00727954	+	0.00373910i
$441$	45.0876	+	25.2219i	2.14703	+	1.20104i
$442$	−0.0266394	+	0.0994197i	−0.00126711	+	0.00472891i
$443$	0.783237	+	8.95244i	0.0372127	+	0.425343i	0.991835	+	0.127525i	$0.0407033\pi$
$443$	0.783237	+	8.95244i	0.0372127	+	0.425343i	−0.954623	+	0.297818i	$0.903741\pi$
$444$	19.5846	+	8.97119i	0.929445	+	0.425754i
$445$	19.8836	+	12.5151i	0.942572	+	0.593273i
$446$	−0.862251	+	0.152038i	−0.0408288	+	0.00719922i
$447$	−10.8655	−	29.2341i	−0.513922	−	1.38272i
$448$	−27.5838	+	2.41327i	−1.30321	+	0.114016i
$449$	−5.30209	−	9.18349i	−0.250221	−	0.433396i	0.713365	−	0.700792i	$-0.247170\pi$
$449$	−5.30209	−	9.18349i	−0.250221	−	0.433396i	−0.963587	+	0.267396i	$0.913837\pi$
$450$	−3.76809	−	3.00768i	−0.177630	−	0.141783i
$451$	−0.0690940	+	0.119674i	−0.00325351	+	0.00563524i
$452$	−9.01760	+	19.3383i	−0.424152	+	0.909598i
$453$	−14.3675	−	8.16560i	−0.675043	−	0.383653i
$454$	2.92752	+	3.48888i	0.137395	+	0.163741i
$455$	0.773535	−	0.408062i	0.0362639	−	0.0191302i
$456$	4.49911	+	0.362879i	0.210690	+	0.0169934i
$457$	27.2519	−	19.0820i	1.27479	−	0.892617i	0.277119	−	0.960836i	$-0.410620\pi$
$457$	27.2519	−	19.0820i	1.27479	−	0.892617i	0.997670	+	0.0682185i	$0.0217315\pi$
$458$	−3.01343	−	3.01343i	−0.140808	−	0.140808i
$459$	20.1097	−	5.82955i	0.938639	−	0.272100i
$460$	1.35213	+	27.5192i	0.0630432	+	1.28309i
$461$	7.72166	+	1.36154i	0.359634	+	0.0634131i	0.350546	−	0.936546i	$-0.385996\pi$
$461$	7.72166	+	1.36154i	0.359634	+	0.0634131i	0.00908790	+	0.999959i	$0.497107\pi$
$462$	−0.158196	−	0.0563663i	−0.00735997	−	0.00262240i
$463$	−16.0360	+	7.47769i	−0.745254	+	0.347518i	−0.757873	−	0.652403i	$-0.773761\pi$
$463$	−16.0360	+	7.47769i	−0.745254	+	0.347518i	0.0126183	+	0.999920i	$0.495983\pi$
$464$	−18.6361	+	15.6375i	−0.865159	+	0.725955i
$465$	0.176351	−	0.844264i	0.00817806	−	0.0391518i
$466$	−2.04945	+	0.745938i	−0.0949388	+	0.0345549i
$467$	−4.09572	−	15.2854i	−0.189527	−	0.707325i	−0.993616	−	0.112816i	$-0.964013\pi$
$467$	−4.09572	−	15.2854i	−0.189527	−	0.707325i	0.804089	−	0.594509i	$-0.202654\pi$
$468$	−0.254322	+	0.373907i	−0.0117560	+	0.0172839i
$469$	−32.4052	+	18.7092i	−1.49633	+	0.863909i
$470$	−0.136818	−	0.997125i	−0.00631094	−	0.0459939i
$471$	−27.9591	+	2.63738i	−1.28829	+	0.121524i
$472$	0.833661	−	1.19059i	0.0383724	−	0.0548014i
$473$	−0.131271	+	0.187475i	−0.00603585	+	0.00862009i
$474$	−1.98396	−	2.79286i	−0.0911262	−	0.128280i
$475$	8.58668	+	5.87375i	0.393984	+	0.269506i
$476$	−32.5737	+	18.8064i	−1.49301	+	0.861991i
$477$	−33.5632	−	15.0997i	−1.53675	−	0.691370i
$478$	−1.51874	−	5.66800i	−0.0694654	−	0.259248i
$479$	25.2585	−	9.19333i	1.15409	−	0.420054i	0.307106	−	0.951675i	$-0.400639\pi$
$479$	25.2585	−	9.19333i	1.15409	−	0.420054i	0.846982	+	0.531621i	$0.178417\pi$
$480$	−13.9009	+	0.777581i	−0.634485	+	0.0354915i
$481$	−0.399198	+	0.334967i	−0.0182019	+	0.0152732i
$482$	−4.64490	+	2.16595i	−0.211569	+	0.0986564i
$483$	−9.98602	−	54.4698i	−0.454380	−	2.47846i
$484$	20.5396	+	3.62169i	0.933619	+	0.164622i
$485$	−21.9191	+	1.07697i	−0.995293	+	0.0489026i
$486$	−5.00328	−	0.267139i	−0.226954	−	0.0121177i
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	0.372571	−	0.928004i	$-0.378476\pi$
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	−0.928004	+	0.372571i	$0.878476\pi$
$488$	−7.40208	+	5.18299i	−0.335076	+	0.234623i
$489$	10.8774	−	15.7610i	0.491892	−	0.712739i
$490$	−11.8242	−	3.65728i	−0.534163	−	0.165219i
$491$	8.64628	+	10.3042i	0.390201	+	0.465024i	0.925006	−	0.379952i	$-0.124059\pi$
$491$	8.64628	+	10.3042i	0.390201	+	0.465024i	−0.534805	+	0.844976i	$0.679615\pi$
$492$	−0.0502507	−	7.40617i	−0.00226548	−	0.333896i
$493$	−12.2177	+	26.2010i	−0.550258	+	1.18003i
$494$	−0.0265743	+	0.0460281i	−0.00119563	+	0.00207090i
$495$	0.382805	+	0.150094i	0.0172058	+	0.00674620i
$496$	−0.377555	−	0.653944i	−0.0169527	−	0.0293630i
$497$	35.8388	−	3.13549i	1.60759	−	0.140646i
$498$	2.21246	+	0.374656i	0.0991425	+	0.0167887i
$499$	37.5256	−	6.61678i	1.67988	−	0.296208i	0.749281	−	0.662252i	$-0.230399\pi$
$499$	37.5256	−	6.61678i	1.67988	−	0.296208i	0.930597	+	0.366044i	$0.119288\pi$
$500$	−18.9675	−	9.48221i	−0.848254	−	0.424057i
$501$	2.12746	+	22.5535i	0.0950480	+	1.00762i
$502$	0.482022	+	5.50954i	0.0215137	+	0.245903i
$503$	4.95246	−	18.4828i	0.220819	−	0.824109i	−0.763217	−	0.646142i	$-0.776381\pi$
$503$	4.95246	−	18.4828i	0.220819	−	0.824109i	0.984036	−	0.177967i	$-0.0569521\pi$
$504$	18.1658	−	3.45791i	0.809167	−	0.154028i
$505$	−8.00047	+	2.57066i	−0.356016	+	0.114393i
$506$	0.0437748	+	0.120270i	0.00194603	+	0.00534666i
$507$	11.3848	+	19.4137i	0.505619	+	0.862194i
$508$	1.27895	−	14.6185i	0.0567442	−	0.648590i
$509$	−22.8762	−	8.32625i	−1.01397	−	0.369054i	−0.219013	−	0.975722i	$-0.570284\pi$
$509$	−22.8762	−	8.32625i	−1.01397	−	0.369054i	−0.794956	+	0.606667i	$0.792506\pi$
$510$	−4.42058	+	2.37046i	−0.195747	+	0.104966i
$511$	5.68120	−	32.2197i	0.251322	−	1.42532i
$512$	−14.6251	+	14.6251i	−0.646346	+	0.646346i
$513$	10.8094	−	0.220051i	0.477245	−	0.00971548i
$514$		−	3.00939i		−	0.132739i
$515$	−5.38589	−	0.679164i	−0.237331	−	0.0299275i
$516$	0.986140	−	12.2265i	0.0434124	−	0.538243i
$517$	0.0362758	+	0.0777936i	0.00159541	+	0.00342136i
$518$	10.3331	+	0.904028i	0.454010	+	0.0397207i
$519$	−10.4579	−	37.9962i	−0.459049	−	1.66785i
$520$	0.0840493	−	0.206089i	0.00368581	−	0.00903761i
$521$	23.8927	+	13.7944i	1.04676	+	0.604345i	0.921739	−	0.387810i	$-0.126768\pi$
$521$	23.8927	+	13.7944i	1.04676	+	0.604345i	0.125017	+	0.992155i	$0.460102\pi$
$522$	4.82502	−	4.95778i	0.211185	−	0.216996i
$523$	−12.5250	−	3.35607i	−0.547681	−	0.146751i	−0.0256401	−	0.999671i	$-0.508162\pi$
$523$	−12.5250	−	3.35607i	−0.547681	−	0.146751i	−0.522041	+	0.852921i	$0.674829\pi$
$524$	−13.3689	−	11.2178i	−0.584022	−	0.490053i
$525$	40.3027	+	13.8659i	1.75895	+	0.605157i
$526$	0.0509971	+	0.289219i	0.00222358	+	0.0126105i
$527$	−0.735047	−	0.514685i	−0.0320191	−	0.0224200i
$528$	0.337435	−	0.125416i	0.0146850	−	0.00545801i
$529$	−12.3443	+	14.7114i	−0.536709	+	0.639625i
$530$	8.61831	+	1.86131i	0.374356	+	0.0808503i
$531$	1.69963	−	3.03832i	0.0737575	−	0.131852i
$532$	−18.7605	+	5.02685i	−0.813369	+	0.217942i
$533$	0.162381	+	0.0757196i	0.00703351	+	0.00327978i
$534$	−5.63966	+	1.55223i	−0.244052	+	0.0671715i
$535$	−3.32793	−	3.59221i	−0.143879	−	0.155305i
$536$	−3.25692	+	8.94831i	−0.140677	+	0.386508i
$537$	−20.4517	−	24.0402i	−0.882555	−	1.03741i
$538$	5.09765	+	7.28020i	0.219775	+	0.313872i
$539$	1.05555			0.0454659
$540$	−21.7675	+	3.43951i	−0.936723	+	0.148013i
$541$	37.8477			1.62720			0.813600	−	0.581425i	$-0.197505\pi$
$541$	37.8477			1.62720			0.813600	+	0.581425i	$0.197505\pi$
$542$	−3.33464	−	4.76236i	−0.143235	−	0.204561i
$543$	−7.19477	+	20.1927i	−0.308757	+	0.866552i
$544$	−4.95417	+	13.6115i	−0.212408	+	0.583587i
$545$	−0.574864	−	0.0219544i	−0.0246245	−	0.000940423i
$546$	−0.0549272	+	0.210699i	−0.00235067	+	0.00901709i
$547$	−13.4509	−	6.27224i	−0.575117	−	0.268182i	0.113223	−	0.993570i	$-0.463883\pi$
$547$	−13.4509	−	6.27224i	−0.575117	−	0.268182i	−0.688340	+	0.725388i	$0.741660\pi$
$548$	−25.1954	+	6.75109i	−1.07629	+	0.288392i
$549$	−16.3902	+	14.1364i	−0.699517	+	0.603328i
$550$	−0.0971908	−	0.0160449i	−0.00414423	−	0.000684155i
$551$	−9.59560	+	11.4356i	−0.408786	+	0.487173i
$552$	−10.8571	−	8.98539i	−0.462110	−	0.382443i
$553$	24.8080	+	17.3708i	1.05494	+	0.738680i
$554$	0.288999	+	1.63900i	0.0122784	+	0.0696342i
$555$	−25.2175	−	3.00627i	−1.07042	−	0.127609i
$556$	−1.54692	−	1.29802i	−0.0656040	−	0.0550483i
$557$	13.9965	+	3.75036i	0.593052	+	0.158908i	0.542847	−	0.839831i	$-0.317346\pi$
$557$	13.9965	+	3.75036i	0.593052	+	0.158908i	0.0502041	+	0.998739i	$0.484013\pi$
$558$	0.125541	+	0.174211i	0.00531457	+	0.00737494i
$559$	0.256980	+	0.148367i	0.0108691	+	0.00627527i
$560$	34.3961	−	14.4679i	1.45350	−	0.611381i
$561$	0.300433	−	0.304537i	0.0126843	−	0.0128576i
$562$	−2.45408	−	0.214704i	−0.103519	−	0.00905674i
$563$	14.4812	+	31.0550i	0.610309	+	1.30881i	0.932169	+	0.362025i	$0.117914\pi$
$563$	14.4812	+	31.0550i	0.610309	+	1.30881i	−0.321859	+	0.946787i	$0.604308\pi$
$564$	−3.78630	−	2.61309i	−0.159432	−	0.110031i
$565$	3.14719	−	24.9578i	0.132403	−	1.04998i
$566$		−	3.04570i		−	0.128020i
$567$	42.4572	−	12.6207i	1.78303	−	0.530020i
$568$	6.47388	−	6.47388i	0.271638	−	0.271638i
$569$	−1.25548	+	7.12016i	−0.0526323	+	0.298493i	−0.999749	−	0.0223961i	$-0.992870\pi$
$569$	−1.25548	+	7.12016i	−0.0526323	+	0.298493i	0.947117	+	0.320889i	$0.103982\pi$
$570$	−2.52169	+	0.591534i	−0.105622	+	0.0247766i
$571$	25.3539	+	9.22807i	1.06103	+	0.386183i	0.812815	−	0.582522i	$-0.197934\pi$
$571$	25.3539	+	9.22807i	1.06103	+	0.386183i	0.248214	+	0.968705i	$0.420156\pi$
$572$	−0.000805249		0.00920404i	−3.36691e−5		0.000384840i
$573$	−21.2618	+	0.144261i	−0.888226	+	0.00602659i
$574$	−1.21973	−	3.35118i	−0.0509105	−	0.139876i
$575$	−11.4424	−	30.4003i	−0.477180	−	1.26778i
$576$	−10.6729	+	13.0758i	−0.444704	+	0.544824i
$577$	1.64754	−	6.14870i	0.0685880	−	0.255974i	−0.923115	−	0.384524i	$-0.874366\pi$
$577$	1.64754	−	6.14870i	0.0685880	−	0.255974i	0.991703	+	0.128550i	$0.0410323\pi$
$578$	−0.0213918	−	0.244509i	−0.000889781	−	0.0101702i
$579$	−25.0438	+	17.7903i	−1.04078	+	0.739339i
$580$	16.2087	−	25.7519i	0.673031	−	1.06929i
$581$	−19.5357	+	3.44468i	−0.810479	+	0.142909i
$582$	3.48356	−	4.20921i	0.144398	−	0.174477i
$583$	−0.749091	+	0.0655370i	−0.0310242	+	0.00271426i
$584$	−4.16304	−	7.21060i	−0.172268	−	0.298377i
$585$	0.150606	−	0.511399i	0.00622679	−	0.0211437i
$586$	1.37318	−	2.37842i	0.0567256	−	0.0982517i
$587$	−16.0039	+	34.3204i	−0.660550	+	1.41656i	0.235177	+	0.971952i	$0.424433\pi$
$587$	−16.0039	+	34.3204i	−0.660550	+	1.41656i	−0.895728	+	0.444603i	$0.853345\pi$
$588$	−48.8011	+	28.6185i	−2.01252	+	1.18021i
$589$	−0.297839	−	0.354951i	−0.0122722	−	0.0146255i
$590$	−0.246453	+	0.796797i	−0.0101463	+	0.0328036i
$591$	−6.76655	−	14.2575i	−0.278339	−	0.586477i
$592$	−18.2133	+	12.7531i	−0.748563	+	0.524149i
$593$	3.48236	+	3.48236i	0.143004	+	0.143004i	0.774984	−	0.631981i	$-0.217758\pi$
$593$	3.48236	+	3.48236i	0.143004	+	0.143004i	−0.631981	+	0.774984i	$0.717758\pi$
$594$	−0.0918796	+	0.0451431i	−0.00376987	+	0.00185225i
$595$	29.7787	−	32.8562i	1.22081	−	1.34697i
$596$	33.6337	+	5.93053i	1.37769	+	0.242924i
$597$	14.2947	−	12.1609i	0.585045	−	0.497714i
$598$	0.150397	−	0.0701311i	0.00615018	−	0.00286788i
$599$	7.62357	−	6.39694i	0.311491	−	0.261372i	−0.473617	−	0.880731i	$-0.657052\pi$
$599$	7.62357	−	6.39694i	0.311491	−	0.261372i	0.785108	+	0.619359i	$0.212608\pi$
$600$	10.1253	−	3.88967i	0.413362	−	0.158795i
$601$	−16.6225	+	6.05010i	−0.678046	+	0.246789i	−0.658008	−	0.753011i	$-0.728601\pi$
$601$	−16.6225	+	6.05010i	−0.678046	+	0.246789i	−0.0200379	+	0.999799i	$0.506379\pi$
$602$	−1.52868	−	5.70510i	−0.0623042	−	0.232523i
$603$	−5.60396	+	22.1101i	−0.228211	+	0.900392i
$604$	15.6721	−	9.04832i	0.637691	−	0.368171i
$605$	−24.3601	+	3.34251i	−0.990379	+	0.135892i
$606$	0.871303	−	1.90210i	0.0353943	−	0.0772677i
$607$	8.36932	−	11.9526i	0.339700	−	0.485142i	−0.612563	−	0.790422i	$-0.709861\pi$
$607$	8.36932	−	11.9526i	0.339700	−	0.485142i	0.952263	+	0.305280i	$0.0987501\pi$
$608$	−4.29017	+	6.12699i	−0.173989	+	0.248482i
$609$	−25.4698	+	55.6020i	−1.03209	+	2.25311i
$610$	3.13413	−	4.13099i	0.126897	−	0.167259i
$611$	0.0963805	−	0.0556453i	0.00389914	−	0.00225117i
$612$	−5.63309	+	22.2250i	−0.227704	+	0.898394i
$613$	−9.82295	−	36.6597i	−0.396745	−	1.48067i	−0.818787	−	0.574097i	$-0.805353\pi$
$613$	−9.82295	−	36.6597i	−0.396745	−	1.48067i	0.422042	−	0.906576i	$-0.361313\pi$
$614$	6.40729	−	2.33206i	0.258577	−	0.0941143i
$615$	2.72741	+	8.29466i	0.109980	+	0.334473i
$616$	0.289427	−	0.242858i	0.0116613	−	0.00978503i
$617$	4.95529	−	2.31069i	0.199493	−	0.0930249i	−0.320305	−	0.947315i	$-0.603785\pi$
$617$	4.95529	−	2.31069i	0.199493	−	0.0930249i	0.519797	+	0.854290i	$0.326007\pi$
$618$	1.02942	−	0.875758i	0.0414094	−	0.0352282i
$619$	−35.6556	−	6.28705i	−1.43312	−	0.252698i	−0.597440	−	0.801913i	$-0.703816\pi$
$619$	−35.6556	−	6.28705i	−1.43312	−	0.252698i	−0.835681	+	0.549215i	$0.814927\pi$
$620$	0.699809	+	0.634261i	0.0281050	+	0.0254726i
$621$	−28.0402	−	18.7952i	−1.12522	−	0.754227i
$622$	−4.47294	−	4.47294i	−0.179349	−	0.179349i
$623$	42.3583	−	29.6596i	1.69705	−	1.18829i
$624$	−0.200120	−	0.421666i	−0.00801121	−	0.0168801i
$625$	24.7091	+	3.80239i	0.988366	+	0.152096i
$626$	0.868056	+	1.03451i	0.0346945	+	0.0413473i
$627$	0.190550	−	0.111745i	0.00760982	−	0.00446265i
$628$	12.9967	−	27.8714i	0.518623	−	1.11219i
$629$	−13.2110	+	22.8821i	−0.526756	+	0.912368i
$630$	−9.31746	+	5.07802i	−0.371217	+	0.202313i
$631$	8.04151	+	13.9283i	0.320128	+	0.554477i	0.980514	−	0.196449i	$-0.0629409\pi$
$631$	8.04151	+	13.9283i	0.320128	+	0.554477i	−0.660387	+	0.750926i	$0.729608\pi$
$632$	7.67791	−	0.671730i	0.305411	−	0.0267200i
$633$	2.24431	−	2.71182i	0.0892032	−	0.107785i
$634$	−5.28517	+	0.931918i	−0.209901	+	0.0370112i
$635$	3.83659	+	16.8692i	0.152250	+	0.669435i
$636$	32.8556	−	23.3396i	1.30281	−	0.925474i
$637$	−0.119280	−	1.36337i	−0.00472603	−	0.0540188i
$638$	0.0365836	−	0.136532i	0.00144836	−	0.00540535i
$639$	13.8670	−	16.9889i	0.548569	−	0.672072i
$640$	9.19281	−	17.8972i	0.363378	−	0.707448i
$641$	12.7590	+	35.0551i	0.503951	+	1.38459i	0.887387	+	0.461026i	$0.152518\pi$
$641$	12.7590	+	35.0551i	0.503951	+	1.38459i	−0.383436	+	0.923567i	$0.625259\pi$
$642$	1.21914	−	0.00827181i	0.0481155	−	0.000326462i
$643$	−1.25970	+	14.3985i	−0.0496779	+	0.567821i	0.930043	+	0.367452i	$0.119770\pi$
$643$	−1.25970	+	14.3985i	−0.0496779	+	0.567821i	−0.979720	+	0.200369i	$0.935786\pi$
$644$	56.9844	+	20.7406i	2.24550	+	0.817295i
$645$	3.30260	+	14.0789i	0.130040	+	0.554355i
$646$	−0.467943	+	2.65384i	−0.0184110	+	0.104414i
$647$	−18.6385	+	18.6385i	−0.732757	+	0.732757i	−0.971165	−	0.238408i	$-0.923374\pi$
$647$	−18.6385	+	18.6385i	−0.732757	+	0.732757i	0.238408	+	0.971165i	$0.423374\pi$
$648$	6.21252	−	9.40569i	0.244051	−	0.369491i
$649$		−	0.0711305i		−	0.00279212i
$650$	−0.00974110	+	0.127347i	−0.000382077	+	0.00499494i
$651$	−1.56234	−	1.07824i	−0.0612328	−	0.0422595i
$652$	8.86250	+	19.0057i	0.347082	+	0.744320i
$653$	−15.1018	−	1.32123i	−0.590977	−	0.0517038i	−0.212255	−	0.977214i	$-0.568081\pi$
$653$	−15.1018	−	1.32123i	−0.590977	−	0.0517038i	−0.378722	+	0.925510i	$0.623636\pi$
$654$	0.100588	−	0.101962i	0.00393330	−	0.00398704i
$655$	19.0511	+	7.76960i	0.744388	+	0.303583i
$656$	6.62035	+	3.82226i	0.258481	+	0.149234i
$657$	−11.6596	−	16.1798i	−0.454884	−	0.631235i
$658$	−2.13970	−	0.573332i	−0.0834144	−	0.0223508i
$659$	−14.6857	−	12.3228i	−0.572075	−	0.480028i	0.310258	−	0.950652i	$-0.399584\pi$
$659$	−14.6857	−	12.3228i	−0.572075	−	0.480028i	−0.882334	+	0.470624i	$0.844029\pi$
$660$	−0.353834	+	0.278456i	−0.0137730	+	0.0108389i
$661$	3.24511	+	18.4039i	0.126220	+	0.715829i	0.980576	+	0.196141i	$0.0628409\pi$
$661$	3.24511	+	18.4039i	0.126220	+	0.715829i	−0.854356	+	0.519689i	$0.826048\pi$
$662$	−3.49029	−	2.44393i	−0.135654	−	0.0949860i
$663$	−0.427296	−	0.353631i	−0.0165948	−	0.0137339i
$664$	−3.24502	+	3.86726i	−0.125931	+	0.150079i
$665$	19.2441	−	12.4081i	0.746253	−	0.481165i
$666$	4.78798	−	4.12959i	0.185530	−	0.160018i
$667$	45.0214	−	12.0634i	1.74324	−	0.467099i
$668$	−22.4827	−	10.4839i	−0.869883	−	0.405633i
$669$	1.19020	−	4.56557i	0.0460158	−	0.176515i
$670$	0.208538	−	5.46044i	0.00805651	−	0.210955i
$671$	−0.151251	+	0.415559i	−0.00583898	+	0.0160425i
$672$	−10.2849	+	28.8654i	−0.396749	+	1.11351i
$673$	−4.69863	−	6.71034i	−0.181119	−	0.258665i	0.718318	−	0.695715i	$-0.244912\pi$
$673$	−4.69863	−	6.71034i	−0.181119	−	0.258665i	−0.899437	+	0.437050i	$0.856023\pi$
$674$	−6.83016			−0.263088
$675$	23.1917	−	11.7109i	0.892648	−	0.450754i
$676$	−24.6450			−0.947884
$677$	−22.9922	−	32.8363i	−0.883663	−	1.26200i	−0.964180	−	0.265249i	$-0.914546\pi$
$677$	−22.9922	−	32.8363i	−0.883663	−	1.26200i	0.0805166	−	0.996753i	$-0.474343\pi$
$678$	4.05819	+	4.77026i	0.155854	+	0.183201i
$679$	−16.5199	+	45.3880i	−0.633976	+	1.74183i
$680$	0.430661	−	11.2766i	0.0165151	−	0.432439i
$681$	−23.6628	+	6.51281i	−0.906759	+	0.249572i
$682$	0.00397627	+	0.00185416i	0.000152259	+	7.09996e-5i
$683$	−0.912231	+	0.244432i	−0.0349056	+	0.00935292i	−0.276230	−	0.961092i	$-0.589085\pi$
$683$	−0.912231	+	0.244432i	−0.0349056	+	0.00935292i	0.241324	+	0.970445i	$0.422418\pi$
$684$	−5.77997	+	10.3325i	−0.221003	+	0.395073i
$685$	25.8449	−	16.6642i	0.987484	−	0.636705i
$686$	−10.3926	+	12.3854i	−0.396790	+	0.472876i
$687$	21.5262	−	8.00072i	0.821277	−	0.305246i
$688$	10.3710	+	7.26189i	0.395393	+	0.276857i
$689$	0.169298	+	0.960134i	0.00644972	+	0.0365782i
$690$	7.50887	+	3.00308i	0.285858	+	0.114325i
$691$	−19.0181	−	15.9581i	−0.723481	−	0.607073i	0.204865	−	0.978790i	$-0.434325\pi$
$691$	−19.0181	−	15.9581i	−0.723481	−	0.607073i	−0.928346	+	0.371717i	$0.878769\pi$
$692$	41.6847	+	11.1694i	1.58461	+	0.424596i
$693$	0.631177	−	0.648544i	0.0239764	−	0.0246361i
$694$	8.77943	+	5.06881i	0.333263	+	0.192409i
$695$	2.20441	+	0.899024i	0.0836180	+	0.0341019i
$696$	4.13019	+	15.0061i	0.156554	+	0.568804i
$697$	9.04972	+	0.791748i	0.342783	+	0.0299896i
$698$	−2.30317	−	4.93917i	−0.0871763	−	0.186950i
$699$	0.944863	−	11.7148i	0.0357380	−	0.443093i
$700$	−35.4235	+	30.3893i	−1.33888	+	1.14861i
$701$		−	30.1877i		−	1.14018i	−0.821584	−	0.570088i	$-0.806909\pi$
$701$		−	30.1877i		−	1.14018i	0.821584	−	0.570088i	$-0.193091\pi$
$702$	0.0686903	+	0.113572i	0.00259255	+	0.00428651i
$703$	−9.64747	+	9.64747i	−0.363861	+	0.363861i
$704$	−0.0598837	+	0.339617i	−0.00225695	+	0.0127998i
$705$	5.19219	+	1.56745i	0.195549	+	0.0590337i
$706$	5.74467	+	2.09089i	0.216204	+	0.0786917i
$707$	−1.61197	+	18.4249i	−0.0606244	+	0.692940i
$708$	1.92852	+	3.28856i	0.0724781	+	0.123591i
$709$	17.1846	+	47.2142i	0.645379	+	1.77317i	0.634127	+	0.773229i	$0.281360\pi$
$709$	17.1846	+	47.2142i	0.645379	+	1.77317i	0.0112523	+	0.999937i	$0.496418\pi$
$710$	−2.40042	+	4.67331i	−0.0900863	+	0.175386i
$711$	18.1353	−	3.45211i	0.680127	−	0.129464i
$712$	3.40597	−	12.7113i	0.127644	−	0.476374i
$713$	0.126090	+	1.44121i	0.00472211	+	0.0539739i
$714$	1.03680	+	10.9912i	0.0388013	+	0.411337i
$715$	−0.00241558	−	0.0106211i	−9.03376e−5	−	0.000397208i
$716$	34.0378	−	6.00178i	1.27205	−	0.224297i
$717$	31.1772	+	5.27953i	1.16433	+	0.197168i
$718$	−10.0487	+	0.879150i	−0.375015	+	0.0328096i
$719$	−6.68387	−	11.5768i	−0.249266	−	0.431742i	0.714056	−	0.700089i	$-0.246856\pi$
$719$	−6.68387	−	11.5768i	−0.249266	−	0.431742i	−0.963322	+	0.268346i	$0.913523\pi$
$720$	8.30314	−	21.1767i	0.309440	−	0.789208i
$721$	−5.97397	+	10.3472i	−0.222482	+	0.385351i
$722$	1.99283	−	4.27363i	0.0741654	−	0.159048i
$723$	−0.187383	−	27.6173i	−0.00696884	−	1.02710i
$724$	−15.0887	−	17.9820i	−0.560766	−	0.668295i
$725$	−8.90558	+	34.7499i	−0.330745	+	1.29058i
$726$	3.47718	−	5.03835i	0.129050	−	0.186991i
$727$	−19.5460	+	13.6862i	−0.724920	+	0.507595i	−0.876830	−	0.480800i	$-0.840346\pi$
$727$	−19.5460	+	13.6862i	−0.724920	+	0.507595i	0.151910	+	0.988394i	$0.451458\pi$
$728$	−0.346386	−	0.346386i	−0.0128379	−	0.0128379i
$729$	12.5372	−	23.9127i	0.464340	−	0.885657i
$730$	3.54015	+	3.20856i	0.131027	+	0.118754i
$731$	14.8167	+	2.61258i	0.548014	+	0.0966296i
$732$	−4.27404	−	23.3132i	−0.157973	−	0.861680i
$733$	−21.1646	+	9.86921i	−0.781732	+	0.364527i	−0.772161	−	0.635427i	$-0.780824\pi$
$733$	−21.1646	+	9.86921i	−0.781732	+	0.364527i	−0.00957046	+	0.999954i	$0.503046\pi$
$734$	−4.41379	+	3.70361i	−0.162916	+	0.136703i
$735$	44.4538	−	49.7218i	1.63970	−	1.83402i
$736$	21.9452	−	7.98740i	0.808910	−	0.294419i
$737$	0.120617	+	0.450149i	0.00444299	+	0.0165815i
$738$	−1.98250	−	0.891907i	−0.0729768	−	0.0328316i
$739$	3.52276	−	2.03387i	0.129587	−	0.0748169i	−0.433805	−	0.901007i	$-0.642829\pi$
$739$	3.52276	−	2.03387i	0.129587	−	0.0748169i	0.563392	+	0.826190i	$0.309496\pi$
$740$	16.8089	−	22.1553i	0.617909	−	0.814446i
$741$	−0.165864	−	0.233490i	−0.00609316	−	0.00857748i
$742$	11.1307	−	15.8963i	0.408622	−	0.583572i
$743$	−28.8659	+	41.2248i	−1.05899	+	1.51239i	−0.214569	+	0.976709i	$0.568835\pi$
$743$	−28.8659	+	41.2248i	−1.05899	+	1.51239i	−0.844419	+	0.535683i	$0.820054\pi$
$744$	−0.480960	+	0.0453688i	−0.0176329	+	0.00166330i
$745$	−39.8898	+	5.47337i	−1.46145	+	0.200529i
$746$	−1.40892	+	0.813439i	−0.0515842	+	0.0297821i
$747$	−6.80074	+	9.99853i	−0.248826	+	0.365827i
$748$	0.121244	+	0.452489i	0.00443313	+	0.0165447i
$749$	−10.1277	+	3.68619i	−0.370059	+	0.134691i
$750$	−4.84891	+	3.90245i	−0.177057	+	0.142497i
$751$	2.00167	−	1.67960i	0.0730419	−	0.0612895i	−0.605536	−	0.795818i	$-0.707041\pi$
$751$	2.00167	−	1.67960i	0.0730419	−	0.0612895i	0.678578	+	0.734529i	$0.262597\pi$
$752$	4.30353	−	2.00677i	0.156933	−	0.0731793i
$753$	−28.0743	−	10.0030i	−1.02308	−	0.364530i
$754$	−0.180481	−	0.0318237i	−0.00657274	−	0.00115895i
$755$	−14.3274	+	15.8081i	−0.521427	+	0.575315i
$756$	−11.5975	+	47.0966i	−0.421796	+	1.71289i
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.998990	+	0.0449357i	$0.0143083\pi$
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.0449357	+	0.998990i	$0.485692\pi$
$758$	2.60445	−	1.82366i	0.0945980	−	0.0662383i
$759$	−0.687472	−	0.0554486i	−0.0249536	−	0.00201266i
$760$	1.72189	−	5.56697i	0.0624596	−	0.201935i
$761$	3.22815	+	3.84716i	0.117020	+	0.139459i	0.821374	−	0.570389i	$-0.193208\pi$
$761$	3.22815	+	3.84716i	0.117020	+	0.139459i	−0.704354	+	0.709849i	$0.748763\pi$
$762$	−3.74464	−	2.12823i	−0.135654	−	0.0770975i
$763$	−0.535106	+	1.14754i	−0.0193722	+	0.0415437i
$764$	11.6417	−	20.1640i	0.421182	−	0.729509i
$765$	−1.69272	−	26.9772i	−0.0612005	−	0.975364i
$766$	3.08315	+	5.34017i	0.111399	+	0.192948i
$767$	−0.0918735	+	0.00803789i	−0.00331736	+	0.000290231i
$768$	−5.04481	−	13.5732i	−0.182039	−	0.489782i
$769$	41.2856	−	7.27976i	1.48880	−	0.262515i	0.630709	−	0.776019i	$-0.282764\pi$
$769$	41.2856	−	7.27976i	1.48880	−	0.262515i	0.858087	+	0.513504i	$0.171653\pi$
$770$	−0.115490	+	0.183487i	−0.00416198	+	0.00661241i
$771$	14.7437	+	6.75370i	0.530982	+	0.243229i
$772$	−2.93187	−	33.5115i	−0.105520	−	1.20610i
$773$	−1.57609	+	5.88204i	−0.0566879	+	0.211562i	−0.988460	−	0.151481i	$-0.951596\pi$
$773$	−1.57609	+	5.88204i	−0.0566879	+	0.211562i	0.931772	+	0.363043i	$0.118262\pi$
$774$	−3.14214	−	1.75770i	−0.112942	−	0.0631793i
$775$	−1.01422	−	0.459520i	−0.0364319	−	0.0165064i
$776$	4.20415	+	11.5508i	0.150920	+	0.414650i
$777$	−27.6186	+	48.5954i	−0.990813	+	1.74335i
$778$	0.206920	−	2.36511i	0.00741844	−	0.0847932i
$779$	4.40798	+	1.60437i	0.157932	+	0.0574827i
$780$	0.399643	+	0.425553i	0.0143095	+	0.0152372i
$781$	0.0778050	−	0.441254i	0.00278408	−	0.0157893i
$782$	5.94947	−	5.94947i	0.212753	−	0.212753i
$783$	13.4610	+	34.7652i	0.481056	+	1.24241i
$784$		−	58.3929i		−	2.08546i
$785$	−4.53590	+	35.9705i	−0.161893	+	1.28384i
$786$	−4.62770	+	2.19628i	−0.165065	+	0.0783387i
$787$	−1.76535	−	3.78582i	−0.0629281	−	0.134950i	0.872328	−	0.488920i	$-0.162609\pi$
$787$	−1.76535	−	3.78582i	−0.0629281	−	0.134950i	−0.935257	+	0.353971i	$0.884831\pi$
$788$	17.2161	+	1.50622i	0.613299	+	0.0536567i
$789$	−1.53140	−	0.399220i	−0.0545192	−	0.0142126i
$790$	−4.07674	+	1.71478i	−0.145044	+	0.0610093i
$791$	−47.9482	−	27.6829i	−1.70484	−	0.984291i
$792$	0.0169577	−	0.229684i	0.000602564	−	0.00816146i
$793$	0.553835	+	0.148400i	0.0196673	+	0.00526983i
$794$	−3.17958	−	2.66798i	−0.112839	−	0.0946831i
$795$	−28.4603	+	38.0459i	−1.00938	+	1.34935i
$796$	3.56877	+	20.2395i	0.126492	+	0.717369i
$797$	−35.6551	−	24.9660i	−1.26297	−	0.884339i	−0.266140	−	0.963934i	$-0.585748\pi$
$797$	−35.6551	−	24.9660i	−1.26297	−	0.884339i	−0.996827	+	0.0795948i	$0.974637\pi$
$798$	−0.951815	+	5.62076i	−0.0336939	+	0.198973i
$799$	3.62708	−	4.32258i	0.128317	−	0.152922i
$800$	−2.92764	+	17.7340i	−0.103508	+	0.626991i
$801$	5.05184	−	31.1135i	0.178498	−	1.09934i
$802$	−2.65388	+	0.711104i	−0.0937116	+	0.0251100i
$803$	−0.369296	−	0.172205i	−0.0130322	−	0.00607699i
$804$	−17.7811	−	17.5414i	−0.627090	−	0.618638i
$805$	−71.4401	−	2.72834i	−2.51793	−	0.0961614i
$806$	0.00194555	−	0.00534535i	6.85290e−5	−	0.000188282i
$807$	−47.1076	+	8.63629i	−1.65826	+	0.304012i
$808$	2.69975	+	3.85564i	0.0949768	+	0.135641i
$809$	−16.9733			−0.596751			−0.298375	−	0.954449i	$-0.596445\pi$
$809$	−16.9733			−0.596751			−0.298375	+	0.954449i	$0.596445\pi$
$810$	−1.74298	+	6.22916i	−0.0612420	+	0.218870i
$811$	−40.1642			−1.41036			−0.705178	−	0.709030i	$-0.749133\pi$
$811$	−40.1642			−1.41036			−0.705178	+	0.709030i	$0.749133\pi$
$812$	−38.4131	−	54.8597i	−1.34804	−	1.92520i
$813$	30.8155	−	5.64945i	1.08075	−	0.198135i
$814$	0.0441841	−	0.121395i	0.00154865	−	0.00425489i
$815$	−16.8017	−	18.1360i	−0.588539	−	0.635277i
$816$	−16.8469	−	16.6199i	−0.589761	−	0.581812i
$817$	7.04105	+	3.28330i	0.246335	+	0.114868i
$818$	4.14732	−	1.11127i	0.145008	−	0.0388547i
$819$	−0.908996	−	0.741954i	−0.0317629	−	0.0259260i
$820$	−9.34606	−	2.01849i	−0.326378	−	0.0704886i
$821$	10.6701	−	12.7162i	0.372390	−	0.443797i	−0.547007	−	0.837128i	$-0.684233\pi$
$821$	10.6701	−	12.7162i	0.372390	−	0.443797i	0.919397	+	0.393331i	$0.128677\pi$
$822$	−1.27829	+	7.54871i	−0.0445856	+	0.263291i
$823$	7.03825	+	4.92823i	0.245338	+	0.171787i	0.689778	−	0.724021i	$-0.257708\pi$
$823$	7.03825	+	4.92823i	0.245338	+	0.171787i	−0.444440	+	0.895809i	$0.646597\pi$
$824$	0.528001	+	2.99444i	0.0183938	+	0.104316i
$825$	0.296724	−	0.440152i	0.0103306	−	0.0153241i
$826$	1.40621	+	1.17995i	0.0489285	+	0.0410558i
$827$	−8.98430	−	2.40734i	−0.312415	−	0.0837113i	0.0992048	−	0.995067i	$-0.468370\pi$
$827$	−8.98430	−	2.40734i	−0.312415	−	0.0837113i	−0.411620	+	0.911356i	$0.635037\pi$
$828$	33.2870	−	16.0754i	1.15680	−	0.558660i
$829$	−36.4376	−	21.0373i	−1.26553	−	0.730655i	−0.291392	−	0.956604i	$-0.594118\pi$
$829$	−36.4376	−	21.0373i	−1.26553	−	0.730655i	−0.974139	+	0.225949i	$0.927452\pi$
$830$	1.09398	−	2.68243i	0.0379724	−	0.0931085i
$831$	−8.67839	−	2.26237i	−0.301050	−	0.0784808i
$832$	0.445423	+	0.0389695i	0.0154423	+	0.00135102i
$833$	−29.3257	−	62.8893i	−1.01608	−	2.17898i
$834$	−0.535473	+	0.254132i	−0.0185419	+	0.00879988i
$835$	29.0159	+	3.65892i	1.00414	+	0.126622i
$836$			0.241896i			0.00836613i
$837$	−1.13524	+	0.224088i	−0.0392396	+	0.00774563i
$838$	−6.09230	+	6.09230i	−0.210455	+	0.210455i
$839$	−6.54601	+	37.1243i	−0.225993	+	1.28167i	0.634783	+	0.772690i	$0.281089\pi$
$839$	−6.54601	+	37.1243i	−0.225993	+	1.28167i	−0.860777	+	0.508983i	$0.830022\pi$
$840$	0.749183	−	23.8612i	0.0258493	−	0.823291i
$841$	−21.1193	−	7.68679i	−0.728251	−	0.265062i
$842$	−0.707136	+	8.08261i	−0.0243695	+	0.278545i
$843$	6.55935	−	11.5413i	0.225916	−	0.397502i
$844$	1.31837	+	3.62220i	0.0453803	+	0.124681i
$845$	27.6619	−	8.88813i	0.951598	−	0.305761i
$846$	−1.16014	+	0.690965i	−0.0398865	+	0.0237559i
$847$	−14.0067	+	52.2737i	−0.481276	+	1.79615i
$848$	3.62549	+	41.4395i	0.124500	+	1.42304i
$849$	14.9216	+	6.83519i	0.512108	+	0.234583i
$850$	1.74425	+	6.23634i	0.0598271	+	0.213905i
$851$	41.9518	−	7.39723i	1.43809	−	0.253574i
$852$	8.36631	+	22.5099i	0.286625	+	0.771175i
$853$	40.4116	−	3.53555i	1.38367	−	0.121055i	0.629123	−	0.777306i	$-0.283414\pi$
$853$	40.4116	−	3.53555i	1.38367	−	0.121055i	0.754543	+	0.656251i	$0.227859\pi$
$854$	−5.70635	−	9.88369i	−0.195267	−	0.338213i
$855$	2.76114	−	13.6819i	0.0944289	−	0.467910i
$856$	−1.37141	+	2.37535i	−0.0468738	+	0.0811879i
$857$	15.2865	−	32.7821i	0.522178	−	1.11982i	−0.451580	−	0.892231i	$-0.649139\pi$
$857$	15.2865	−	32.7821i	0.522178	−	1.11982i	0.973758	−	0.227585i	$-0.0730828\pi$
$858$	0.00235769	+	0.00133997i	8.04903e−5	+	4.57458e-5i
$859$	−26.6915	−	31.8097i	−0.910701	−	1.08533i	−0.996034	−	0.0889788i	$-0.971640\pi$
$859$	−26.6915	−	31.8097i	−0.910701	−	1.08533i	0.0853324	−	0.996353i	$-0.472805\pi$
$860$	−15.1285	−	4.67932i	−0.515877	−	0.159563i
$861$	19.1555	+	1.54500i	0.652819	+	0.0526536i
$862$	6.06288	−	4.24528i	0.206503	−	0.144595i
$863$	1.97436	+	1.97436i	0.0672079	+	0.0672079i	0.739912	−	0.672704i	$-0.234867\pi$
$863$	1.97436	+	1.97436i	0.0672079	+	0.0672079i	−0.672704	+	0.739912i	$0.734867\pi$
$864$	8.23707	+	16.7649i	0.280231	+	0.570353i
$865$	−50.8156	+	2.49677i	−1.72778	+	0.0848927i
$866$	5.75997	+	1.01564i	0.195732	+	0.0345128i
$867$	1.24591	+	0.443926i	0.0423135	+	0.0150765i
$868$	1.88397	−	0.878509i	0.0639460	−	0.0298185i
$869$	0.288942	−	0.242451i	0.00980167	−	0.00822458i
$870$	−4.89064	−	7.47322i	−0.165808	−	0.253366i
$871$	0.567792	−	0.206659i	0.0192389	−	0.00700238i
$872$	0.0833986	+	0.311248i	0.00282423	+	0.0105402i
$873$	12.8041	+	26.5131i	0.433353	+	0.897332i
$874$	3.76259	−	2.17233i	0.127272	−	0.0734803i
$875$	28.8000	−	46.8847i	0.973618	−	1.58499i
$876$	21.7424	−	2.05096i	0.734609	−	0.0692954i
$877$	21.7084	−	31.0028i	0.733042	−	1.04689i	−0.263570	−	0.964640i	$-0.584900\pi$
$877$	21.7084	−	31.0028i	0.733042	−	1.04689i	0.996612	−	0.0822516i	$-0.0262111\pi$
$878$	5.86839	−	8.38093i	0.198049	−	0.282843i
$879$	8.57073	+	12.0652i	0.289084	+	0.406949i
$880$	−0.0631765	−	0.460429i	−0.00212968	−	0.0155211i
$881$	−14.1727	+	8.18263i	−0.477491	+	0.275680i	−0.719370	−	0.694627i	$-0.755570\pi$
$881$	−14.1727	+	8.18263i	−0.477491	+	0.275680i	0.241879	+	0.970306i	$0.422236\pi$
$882$	1.67158	+	16.5210i	0.0562851	+	0.556291i
$883$	0.217699	+	0.812463i	0.00732615	+	0.0273416i	0.969492	−	0.245122i	$-0.0788281\pi$
$883$	0.217699	+	0.812463i	0.00732615	+	0.0273416i	−0.962166	+	0.272464i	$0.912161\pi$
$884$	0.570743	−	0.207734i	0.0191962	−	0.00698683i
$885$	−3.35060	−	2.99561i	−0.112629	−	0.100696i
$886$	−2.21269	+	1.85667i	−0.0743369	+	0.0623761i
$887$	−22.8678	+	10.6634i	−0.767825	+	0.358043i	−0.766741	−	0.641957i	$-0.778123\pi$
$887$	−22.8678	+	10.6634i	−0.767825	+	0.358043i	−0.00108401	+	0.999999i	$0.500345\pi$
$888$	2.56511	+	13.9916i	0.0860793	+	0.469529i
$889$	37.4980	+	6.61191i	1.25764	+	0.221756i
$890$	0.370588	+	7.54241i	0.0124221	+	0.252822i
$891$	−0.0149698	−	0.551450i	−0.000501506	−	0.0184743i
$892$	3.65337	+	3.65337i	0.122324	+	0.122324i
$893$	2.38680	−	1.67126i	0.0798714	−	0.0559265i
$894$	5.69391	−	8.25032i	0.190433	−	0.275932i
$895$	−36.0400	+	19.0121i	−1.20468	+	0.635504i
$896$	−28.4647	−	33.9229i	−0.950940	−	1.13329i
$897$	0.00606725	+	0.894217i	0.000202579	+	0.0298570i
$898$	1.44044	−	3.08904i	0.0480682	−	0.103083i
$899$	0.798864	−	1.38367i	0.0266436	−	0.0461481i
$900$	−1.78478	+	28.3943i	−0.0594927	+	0.946477i
$901$	24.7162	+	42.8097i	0.823415	+	1.42620i
$902$	−0.0442471	+	0.00387112i	−0.00147327	+	0.000128894i
$903$	31.3813	+	5.31409i	1.04430	+	0.176842i
$904$	−13.8760	+	2.44671i	−0.461509	+	0.0813764i
$905$	23.4209	+	14.7415i	0.778536	+	0.490025i
$906$	−0.498835	−	5.28821i	−0.0165727	−	0.175689i
$907$	0.265160	+	3.03079i	0.00880450	+	0.100636i	0.999325	−	0.0367266i	$-0.0116931\pi$
$907$	0.265160	+	3.03079i	0.00880450	+	0.100636i	−0.990521	+	0.137362i	$0.956138\pi$
$908$	6.95591	−	25.9598i	0.230840	−	0.861507i
$909$	7.36347	+	8.53744i	0.244231	+	0.283169i
$910$	0.250046	+	0.128435i	0.00828894	+	0.00425758i
$911$	−16.0677	−	44.1456i	−0.532346	−	1.46261i	−0.856272	−	0.516526i	$-0.827225\pi$
$911$	−16.0677	−	44.1456i	−0.532346	−	1.46261i	0.323926	−	0.946082i	$-0.394997\pi$
$912$	−6.18168	−	10.5412i	−0.204696	−	0.349053i
$913$	−0.0215329	+	0.246122i	−0.000712635	+	0.00814546i
$914$	10.0482	+	3.65724i	0.332365	+	0.120971i
$915$	13.2051	+	24.6256i	0.436546	+	0.814098i
$916$	−4.36689	+	24.7658i	−0.144286	+	0.818287i
$917$	32.0203	−	32.0203i	1.05740	−	1.05740i
$918$	5.24224	+	4.21995i	0.173020	+	0.139279i
$919$			57.4802i			1.89610i	0.318128	+	0.948048i	$0.396946\pi$
$919$			57.4802i			1.89610i	−0.318128	+	0.948048i	$0.603054\pi$
$920$	−14.3736	+	11.1545i	−0.473884	+	0.367753i
$921$	−2.95397	+	36.6244i	−0.0973367	+	1.20682i
$922$	1.06507	+	2.28405i	0.0350762	+	0.0752211i
$923$	−0.578725	−	0.0506318i	−0.0190490	−	0.00166657i
$924$	0.262980	+	0.955475i	0.00865140	+	0.0314328i
$925$	−10.8764	+	30.9295i	−0.357612	+	1.01696i
$926$	−4.92516	−	2.84354i	−0.161851	−	0.0934446i
$927$	1.98030	+	7.00876i	0.0650417	+	0.230198i
$928$	−24.9124	−	6.67526i	−0.817790	−	0.219126i
$929$	40.6798	+	34.1344i	1.33466	+	1.11991i	0.982963	+	0.183802i	$0.0588404\pi$
$929$	40.6798	+	34.1344i	1.33466	+	1.11991i	0.351699	+	0.936113i	$0.385604\pi$
$930$	0.254798	−	0.109215i	0.00835516	−	0.00358131i
$931$	−6.22206	−	35.2871i	−0.203920	−	1.15649i
$932$	10.5424	+	7.38190i	0.345329	+	0.241802i
$933$	31.9522	−	11.8758i	1.04607	−	0.388795i
$934$	3.26943	−	3.89635i	0.106979	−	0.127492i
$935$	−0.299275	−	0.464154i	−0.00978734	−	0.0151795i
$936$	−0.298580	+	0.00405191i	−0.00975941	+	0.000132441i
$937$	−27.8763	+	7.46943i	−0.910679	+	0.244016i	−0.683597	−	0.729860i	$-0.739585\pi$
$937$	−27.8763	+	7.46943i	−0.910679	+	0.244016i	−0.227082	+	0.973876i	$0.572919\pi$
$938$	−10.9001	−	5.08280i	−0.355901	−	0.165959i
$939$	−7.01639	+	1.93115i	−0.228971	+	0.0630208i
$940$	−4.35684	+	4.03630i	−0.142104	+	0.131650i
$941$	4.85822	−	13.3478i	0.158373	−	0.435127i	−0.834973	−	0.550291i	$-0.814517\pi$
$941$	4.85822	−	13.3478i	0.158373	−	0.435127i	0.993347	+	0.115163i	$0.0367392\pi$
$942$	−5.84888	−	6.87515i	−0.190567	−	0.224004i
$943$	−8.40071	−	11.9975i	−0.273565	−	0.390691i
$944$	−3.93492			−0.128071
$945$	−3.96807	−	57.0445i	−0.129081	−	1.85566i
$946$	−0.0735611			−0.00239168
$947$	1.16551	+	1.66453i	0.0378741	+	0.0540898i	0.837643	−	0.546219i	$-0.183933\pi$
$947$	1.16551	+	1.66453i	0.0378741	+	0.0540898i	−0.799768	+	0.600309i	$0.795044\pi$
$948$	−6.78514	+	19.0431i	−0.220371	+	0.618490i
$949$	−0.180693	+	0.496449i	−0.00586553	+	0.0161154i
$950$	0.0365221	+	3.34366i	0.00118493	+	0.108483i
$951$	7.29534	−	27.9847i	0.236567	−	0.907466i
$952$	−22.5103	−	10.4967i	−0.729564	−	0.340201i
$953$	−23.1836	+	6.21202i	−0.750990	+	0.201227i	−0.613957	−	0.789339i	$-0.710423\pi$
$953$	−23.1836	+	6.21202i	−0.750990	+	0.201227i	−0.137033	+	0.990567i	$0.543757\pi$
$954$	−2.21202	−	11.6206i	−0.0716168	−	0.376231i
$955$	−5.79473	+	26.8309i	−0.187513	+	0.868228i
$956$	−22.2577	+	26.5257i	−0.719865	+	0.857901i
$957$	0.586801	+	0.485638i	0.0189686	+	0.0156984i
$958$	7.07711	+	4.95544i	0.228651	+	0.160103i
$959$	−11.7529	−	66.6543i	−0.379522	−	2.15238i
$960$	13.4757	+	17.1236i	0.434927	+	0.552661i
$961$	−23.7094	−	19.8945i	−0.764819	−	0.641759i
$962$	−0.161789	−	0.0433512i	−0.00521628	−	0.00139770i
$963$	−2.69547	+	5.99139i	−0.0868603	+	0.193070i
$964$	26.1913	+	15.1216i	0.843566	+	0.487033i
$965$	15.3766	+	36.5564i	0.494989	+	1.17679i
$966$	12.5004	−	12.6712i	0.402193	−	0.407688i
$967$	9.40347	+	0.822697i	0.302395	+	0.0264561i	0.237344	−	0.971426i	$-0.423723\pi$
$967$	9.40347	+	0.822697i	0.302395	+	0.0264561i	0.0650515	+	0.997882i	$0.479279\pi$
$968$	5.82048	+	12.4821i	0.187077	+	0.401189i
$969$	−11.9516	−	8.24832i	−0.383941	−	0.264974i
$970$	−4.32450	−	5.57253i	−0.138851	−	0.178923i
$971$			16.0188i			0.514066i	0.966403	+	0.257033i	$0.0827450\pi$
$971$			16.0188i			0.514066i	−0.966403	+	0.257033i	$0.917255\pi$
$972$	15.6432	+	25.0892i	0.501756	+	0.804736i
$973$	3.70508	−	3.70508i	0.118779	−	0.118779i
$974$	0.967501	−	5.48697i	0.0310007	−	0.175814i
$975$	−0.602039	−	0.333516i	−0.0192807	−	0.0106811i
$976$	22.9886	+	8.36718i	0.735848	+	0.267827i
$977$	−1.38013	+	15.7750i	−0.0441544	+	0.504687i	0.941627	+	0.336657i	$0.109296\pi$
$977$	−1.38013	+	15.7750i	−0.0441544	+	0.504687i	−0.985782	+	0.168030i	$0.946259\pi$
$978$	6.15506	−	0.0417620i	0.196817	−	0.00133540i
$979$	−0.220269	−	0.605185i	−0.00703984	−	0.0193418i
$980$	22.3425	+	69.5348i	0.713704	+	2.22121i
$981$	0.273796	+	0.721628i	0.00874164	+	0.0230398i
$982$	−1.11900	+	4.17615i	−0.0357086	+	0.133266i
$983$	−3.78597	−	43.2738i	−0.120754	−	1.38022i	−0.778814	−	0.627255i	$-0.784178\pi$
$983$	−3.78597	−	43.2738i	−0.120754	−	1.38022i	0.658060	−	0.752965i	$-0.271377\pi$
$984$	3.98712	−	2.83232i	0.127105	−	0.0902911i
$985$	−19.8668	+	4.51834i	−0.633010	+	0.143966i
$986$	−9.15088	+	1.61355i	−0.291424	+	0.0513858i
$987$	7.61083	−	9.19623i	0.242255	−	0.292719i
$988$	0.312437	−	0.0273347i	0.00993995	−	0.000869633i
$989$	−12.1284	−	21.0070i	−0.385660	−	0.667982i
$990$	0.0310548	+	0.128460i	0.000986988	+	0.00408271i
$991$	−5.77036	+	9.99455i	−0.183301	+	0.317487i	−0.943003	−	0.332785i	$-0.892012\pi$
$991$	−5.77036	+	9.99455i	−0.183301	+	0.317487i	0.759701	+	0.650272i	$0.225345\pi$
$992$	0.338321	−	0.725532i	0.0107417	−	0.0230357i
$993$	19.8063	−	11.6151i	0.628534	−	0.368593i
$994$	7.43270	+	8.85795i	0.235751	+	0.280957i
$995$	−11.3049	−	21.4300i	−0.358391	−	0.679377i
$996$	−5.67743	−	11.9627i	−0.179896	−	0.379053i
$997$	19.9126	−	13.9430i	0.630639	−	0.441579i	−0.214059	−	0.976821i	$-0.568669\pi$
$997$	19.9126	−	13.9430i	0.630639	−	0.441579i	0.844699	+	0.535242i	$0.179780\pi$
$998$	8.66028	+	8.66028i	0.274136	+	0.274136i
$999$	9.48660	+	32.7251i	0.300143	+	1.03538i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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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

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.2.10	✓	192
3.2	odd	2		405.2.r.a.332.7		192
5.2	odd	4		675.2.ba.b.218.7		192
5.3	odd	4	inner	135.2.q.a.83.10	yes	192
5.4	even	2		675.2.ba.b.407.7		192
15.8	even	4		405.2.r.a.8.7		192
27.13	even	9		405.2.r.a.152.7		192
27.14	odd	18	inner	135.2.q.a.122.10	yes	192
135.13	odd	36		405.2.r.a.233.7		192
135.14	odd	18		675.2.ba.b.257.7		192
135.68	even	36	inner	135.2.q.a.68.10	yes	192
135.122	even	36		675.2.ba.b.68.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.10	✓	192	1.1	even	1	trivial
135.2.q.a.68.10	yes	192	135.68	even	36	inner
135.2.q.a.83.10	yes	192	5.3	odd	4	inner
135.2.q.a.122.10	yes	192	27.14	odd	18	inner
405.2.r.a.8.7		192	15.8	even	4
405.2.r.a.152.7		192	27.13	even	9
405.2.r.a.233.7		192	135.13	odd	36
405.2.r.a.332.7		192	3.2	odd	2
675.2.ba.b.68.7		192	135.122	even	36
675.2.ba.b.218.7		192	5.2	odd	4
675.2.ba.b.257.7		192	135.14	odd	18
675.2.ba.b.407.7		192	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	135.2.q.a.2.10

Level	$135$
Weight	$2$
Character	135.2
Analytic conductor	$1.078$
Analytic rank	$0$
Dimension	$192$
Inner twists	$4$