LMFDB - Embedded newform 546.2.ch.a.137.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.5
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.33512 + 1.10338i) q^{3} -1.00000i q^{4} +(2.13400 + 0.571804i) q^{5} +(0.163866 - 1.72428i) q^{6} +(-2.34532 - 1.22452i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.565101 - 2.94630i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33512 + 1.10338i) q^{3} -1.00000i q^{4} +(2.13400 + 0.571804i) q^{5} +(0.163866 - 1.72428i) q^{6} +(-2.34532 - 1.22452i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.565101 - 2.94630i) q^{9} +(-1.91329 + 1.10464i) q^{10} +(-0.546485 + 2.03951i) q^{11} +(1.10338 + 1.33512i) q^{12} +(-3.42792 - 1.11774i) q^{13} +(2.52426 - 0.792526i) q^{14} +(-3.48007 + 1.59119i) q^{15} -1.00000 q^{16} -4.18923 q^{17} +(1.68376 + 2.48293i) q^{18} +(-0.460929 + 0.123506i) q^{19} +(0.571804 - 2.13400i) q^{20} +(4.48241 - 0.952898i) q^{21} +(-1.05573 - 1.82857i) q^{22} -4.83014 q^{23} +(-1.72428 - 0.163866i) q^{24} +(-0.103127 - 0.0595401i) q^{25} +(3.21427 - 1.63354i) q^{26} +(2.49641 + 4.55719i) q^{27} +(-1.22452 + 2.34532i) q^{28} +(-0.814739 - 0.470390i) q^{29} +(1.33564 - 3.58592i) q^{30} +(-4.28819 + 1.14902i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.52073 - 3.32597i) q^{33} +(2.96223 - 2.96223i) q^{34} +(-4.30474 - 3.95420i) q^{35} +(-2.94630 - 0.565101i) q^{36} +(6.42867 - 6.42867i) q^{37} +(0.238594 - 0.413257i) q^{38} +(5.80999 - 2.28998i) q^{39} +(1.10464 + 1.91329i) q^{40} +(-2.42880 - 9.06440i) q^{41} +(-2.49574 + 3.84334i) q^{42} +(2.32396 - 1.34174i) q^{43} +(2.03951 + 0.546485i) q^{44} +(2.89063 - 5.96427i) q^{45} +(3.41542 - 3.41542i) q^{46} +(-1.08788 + 4.06004i) q^{47} +(1.33512 - 1.10338i) q^{48} +(4.00109 + 5.74380i) q^{49} +(0.115023 - 0.0308202i) q^{50} +(5.59313 - 4.62231i) q^{51} +(-1.11774 + 3.42792i) q^{52} +(-4.82321 - 2.78468i) q^{53} +(-4.98764 - 1.45719i) q^{54} +(-2.33240 + 4.03983i) q^{55} +(-0.792526 - 2.52426i) q^{56} +(0.479123 - 0.673475i) q^{57} +(0.908723 - 0.243492i) q^{58} +(-10.0972 - 10.0972i) q^{59} +(1.59119 + 3.48007i) q^{60} +(2.02149 - 3.50132i) q^{61} +(2.21973 - 3.84468i) q^{62} +(-4.93315 + 6.21804i) q^{63} +1.00000i q^{64} +(-6.67606 - 4.34536i) q^{65} +(3.42714 + 1.27650i) q^{66} +(-2.19711 + 8.19973i) q^{67} +4.18923i q^{68} +(6.44882 - 5.32948i) q^{69} +(5.83995 - 0.247868i) q^{70} +(5.98706 + 1.60423i) q^{71} +(2.48293 - 1.68376i) q^{72} +(-1.80093 - 6.72115i) q^{73} +9.09152i q^{74} +(0.203382 - 0.0342945i) q^{75} +(0.123506 + 0.460929i) q^{76} +(3.77911 - 4.11413i) q^{77} +(-2.48902 + 5.72755i) q^{78} +(-1.77600 - 3.07612i) q^{79} +(-2.13400 - 0.571804i) q^{80} +(-8.36132 - 3.32991i) q^{81} +(8.12692 + 4.69208i) q^{82} +(-7.36931 + 7.36931i) q^{83} +(-0.952898 - 4.48241i) q^{84} +(-8.93981 - 2.39542i) q^{85} +(-0.694536 + 2.59204i) q^{86} +(1.60679 - 0.270940i) q^{87} +(-1.82857 + 1.05573i) q^{88} +(11.1696 + 11.1696i) q^{89} +(2.17339 + 6.26136i) q^{90} +(6.67089 + 6.81904i) q^{91} +4.83014i q^{92} +(4.45745 - 6.26558i) q^{93} +(-2.10163 - 3.64013i) q^{94} -1.05424 q^{95} +(-0.163866 + 1.72428i) q^{96} +(-4.62372 + 17.2560i) q^{97} +(-6.89068 - 1.23229i) q^{98} +(5.70018 + 2.76263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.33512	+	1.10338i	−0.770833	+	0.637037i
$3$	−1.33512	+	1.10338i	−0.770833	+	0.637037i
$4$		−	1.00000i		−	0.500000i
$5$	2.13400	+	0.571804i	0.954354	+	0.255718i	0.702209	−	0.711971i	$-0.252197\pi$
$5$	2.13400	+	0.571804i	0.954354	+	0.255718i	0.252145	+	0.967689i	$0.418864\pi$
$6$	0.163866	−	1.72428i	0.0668979	−	0.703935i
$7$	−2.34532	−	1.22452i	−0.886449	−	0.462826i
$7$	−2.34532	−	1.22452i	−0.886449	−	0.462826i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.565101	−	2.94630i	0.188367	−	0.982099i
$10$	−1.91329	+	1.10464i	−0.605036	+	0.349318i
$11$	−0.546485	+	2.03951i	−0.164771	+	0.614935i	0.833298	+	0.552824i	$0.186450\pi$
$11$	−0.546485	+	2.03951i	−0.164771	+	0.614935i	−0.998069	+	0.0621108i	$0.980217\pi$
$12$	1.10338	+	1.33512i	0.318519	+	0.385417i
$13$	−3.42792	−	1.11774i	−0.950735	−	0.310006i
$13$	−3.42792	−	1.11774i	−0.950735	−	0.310006i
$14$	2.52426	−	0.792526i	0.674638	−	0.211812i
$15$	−3.48007	+	1.59119i	−0.898550	+	0.410843i
$16$	−1.00000			−0.250000
$17$	−4.18923			−1.01604			−0.508018	−	0.861346i	$-0.669622\pi$
$17$	−4.18923			−1.01604			−0.508018	+	0.861346i	$0.669622\pi$
$18$	1.68376	+	2.48293i	0.396866	+	0.585233i
$19$	−0.460929	+	0.123506i	−0.105744	+	0.0283341i	−0.311303	−	0.950311i	$-0.600765\pi$
$19$	−0.460929	+	0.123506i	−0.105744	+	0.0283341i	0.205559	+	0.978645i	$0.434099\pi$
$20$	0.571804	−	2.13400i	0.127859	−	0.477177i
$21$	4.48241	−	0.952898i	0.978142	−	0.207939i
$22$	−1.05573	−	1.82857i	−0.225082	−	0.389853i
$23$	−4.83014			−1.00715			−0.503577	−	0.863951i	$-0.667983\pi$
$23$	−4.83014			−1.00715			−0.503577	+	0.863951i	$0.667983\pi$
$24$	−1.72428	−	0.163866i	−0.351968	−	0.0334490i
$25$	−0.103127	−	0.0595401i	−0.0206253	−	0.0119080i
$26$	3.21427	−	1.63354i	0.630370	−	0.320364i
$27$	2.49641	+	4.55719i	0.480434	+	0.877031i
$28$	−1.22452	+	2.34532i	−0.231413	+	0.443225i
$29$	−0.814739	−	0.470390i	−0.151293	−	0.0873492i	0.422442	−	0.906390i	$-0.361173\pi$
$29$	−0.814739	−	0.470390i	−0.151293	−	0.0873492i	−0.573735	+	0.819041i	$0.694506\pi$
$30$	1.33564	−	3.58592i	0.243853	−	0.654696i
$31$	−4.28819	+	1.14902i	−0.770181	+	0.206369i	−0.622452	−	0.782658i	$-0.713863\pi$
$31$	−4.28819	+	1.14902i	−0.770181	+	0.206369i	−0.147730	+	0.989028i	$0.547197\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.52073	−	3.32597i	−0.264725	−	0.578978i
$34$	2.96223	−	2.96223i	0.508018	−	0.508018i
$35$	−4.30474	−	3.95420i	−0.727633	−	0.668381i
$36$	−2.94630	−	0.565101i	−0.491049	−	0.0941836i
$37$	6.42867	−	6.42867i	1.05687	−	1.05687i	0.0585852	−	0.998282i	$-0.481341\pi$
$37$	6.42867	−	6.42867i	1.05687	−	1.05687i	0.998282	−	0.0585852i	$-0.0186589\pi$
$38$	0.238594	−	0.413257i	0.0387051	−	0.0670392i
$39$	5.80999	−	2.28998i	0.930343	−	0.366691i
$40$	1.10464	+	1.91329i	0.174659	+	0.302518i
$41$	−2.42880	−	9.06440i	−0.379315	−	1.41562i	−0.846937	−	0.531693i	$-0.821556\pi$
$41$	−2.42880	−	9.06440i	−0.379315	−	1.41562i	0.467623	−	0.883928i	$-0.345111\pi$
$42$	−2.49574	+	3.84334i	−0.385101	+	0.593041i
$43$	2.32396	−	1.34174i	0.354401	−	0.204613i	−0.312221	−	0.950010i	$-0.601073\pi$
$43$	2.32396	−	1.34174i	0.354401	−	0.204613i	0.666622	+	0.745396i	$0.267740\pi$
$44$	2.03951	+	0.546485i	0.307467	+	0.0823857i
$45$	2.89063	−	5.96427i	0.430910	−	0.889101i
$46$	3.41542	−	3.41542i	0.503577	−	0.503577i
$47$	−1.08788	+	4.06004i	−0.158684	+	0.592218i	0.840077	+	0.542467i	$0.182510\pi$
$47$	−1.08788	+	4.06004i	−0.158684	+	0.592218i	−0.998762	+	0.0497512i	$0.984157\pi$
$48$	1.33512	−	1.10338i	0.192708	−	0.159259i
$49$	4.00109	+	5.74380i	0.571584	+	0.820544i
$50$	0.115023	−	0.0308202i	0.0162667	−	0.00435864i
$51$	5.59313	−	4.62231i	0.783195	−	0.647253i
$52$	−1.11774	+	3.42792i	−0.155003	+	0.475367i
$53$	−4.82321	−	2.78468i	−0.662518	−	0.382505i	0.130718	−	0.991420i	$-0.458272\pi$
$53$	−4.82321	−	2.78468i	−0.662518	−	0.382505i	−0.793236	+	0.608915i	$0.791605\pi$
$54$	−4.98764	−	1.45719i	−0.678732	−	0.198299i
$55$	−2.33240	+	4.03983i	−0.314500	+	0.544731i
$56$	−0.792526	−	2.52426i	−0.105906	−	0.337319i
$57$	0.479123	−	0.673475i	0.0634613	−	0.0892039i
$58$	0.908723	−	0.243492i	0.119321	−	0.0319720i
$59$	−10.0972	−	10.0972i	−1.31455	−	1.31455i	−0.918024	−	0.396524i	$-0.870216\pi$
$59$	−10.0972	−	10.0972i	−1.31455	−	1.31455i	−0.396524	−	0.918024i	$-0.629784\pi$
$60$	1.59119	+	3.48007i	0.205421	+	0.449275i
$61$	2.02149	−	3.50132i	0.258825	−	0.448298i	−0.707103	−	0.707111i	$-0.749998\pi$
$61$	2.02149	−	3.50132i	0.258825	−	0.448298i	0.965927	+	0.258813i	$0.0833314\pi$
$62$	2.21973	−	3.84468i	0.281906	−	0.488275i
$63$	−4.93315	+	6.21804i	−0.621519	+	0.783399i
$64$			1.00000i			0.125000i
$65$	−6.67606	−	4.34536i	−0.828063	−	0.538976i
$66$	3.42714	+	1.27650i	0.421851	+	0.157126i
$67$	−2.19711	+	8.19973i	−0.268420	+	1.00176i	0.691704	+	0.722181i	$0.256860\pi$
$67$	−2.19711	+	8.19973i	−0.268420	+	1.00176i	−0.960124	+	0.279576i	$0.909806\pi$
$68$			4.18923i			0.508018i
$69$	6.44882	−	5.32948i	0.776347	−	0.641594i
$70$	5.83995	−	0.247868i	0.698007	−	0.0296259i
$71$	5.98706	+	1.60423i	0.710533	+	0.190387i	0.595944	−	0.803026i	$-0.296778\pi$
$71$	5.98706	+	1.60423i	0.710533	+	0.190387i	0.114589	+	0.993413i	$0.463445\pi$
$72$	2.48293	−	1.68376i	0.292616	−	0.198433i
$73$	−1.80093	−	6.72115i	−0.210782	−	0.786651i	−0.987609	−	0.156936i	$-0.949838\pi$
$73$	−1.80093	−	6.72115i	−0.210782	−	0.786651i	0.776826	−	0.629715i	$-0.216828\pi$
$74$			9.09152i			1.05687i
$75$	0.203382	−	0.0342945i	0.0234845	−	0.00395999i
$76$	0.123506	+	0.460929i	0.0141671	+	0.0528722i
$77$	3.77911	−	4.11413i	0.430669	−	0.468848i
$78$	−2.48902	+	5.72755i	−0.281826	+	0.648517i
$79$	−1.77600	−	3.07612i	−0.199816	−	0.346091i	0.748653	−	0.662962i	$-0.230701\pi$
$79$	−1.77600	−	3.07612i	−0.199816	−	0.346091i	−0.948469	+	0.316871i	$0.897368\pi$
$80$	−2.13400	−	0.571804i	−0.238589	−	0.0639296i
$81$	−8.36132	−	3.32991i	−0.929036	−	0.369990i
$82$	8.12692	+	4.69208i	0.897468	+	0.518153i
$83$	−7.36931	+	7.36931i	−0.808887	+	0.808887i	−0.984465	−	0.175578i	$-0.943820\pi$
$83$	−7.36931	+	7.36931i	−0.808887	+	0.808887i	0.175578	+	0.984465i	$0.443820\pi$
$84$	−0.952898	−	4.48241i	−0.103970	−	0.489071i
$85$	−8.93981	−	2.39542i	−0.969659	−	0.259819i
$86$	−0.694536	+	2.59204i	−0.0748937	+	0.279507i
$87$	1.60679	−	0.270940i	0.172266	−	0.0290478i
$88$	−1.82857	+	1.05573i	−0.194927	+	0.112541i
$89$	11.1696	+	11.1696i	1.18397	+	1.18397i	0.978707	+	0.205263i	$0.0658050\pi$
$89$	11.1696	+	11.1696i	1.18397	+	1.18397i	0.205263	+	0.978707i	$0.434195\pi$
$90$	2.17339	+	6.26136i	0.229096	+	0.660005i
$91$	6.67089	+	6.81904i	0.699299	+	0.714829i
$92$			4.83014i			0.503577i
$93$	4.45745	−	6.26558i	0.462216	−	0.649710i
$94$	−2.10163	−	3.64013i	−0.216767	−	0.375451i
$95$	−1.05424			−0.108163
$96$	−0.163866	+	1.72428i	−0.0167245	+	0.175984i
$97$	−4.62372	+	17.2560i	−0.469468	+	1.75208i	0.172168	+	0.985068i	$0.444923\pi$
$97$	−4.62372	+	17.2560i	−0.469468	+	1.75208i	−0.641635	+	0.767010i	$0.721744\pi$
$98$	−6.89068	−	1.23229i	−0.696064	−	0.124480i
$99$	5.70018	+	2.76263i	0.572889	+	0.277655i
$100$	−0.0595401	+	0.103127i	−0.00595401	+	0.0103127i
$101$	4.07493	+	7.05798i	0.405470	+	0.702295i	0.994376	−	0.105907i	$-0.0337745\pi$
$101$	4.07493	+	7.05798i	0.405470	+	0.702295i	−0.588906	+	0.808202i	$0.700441\pi$
$102$	−0.686471	+	7.22341i	−0.0679707	+	0.715224i
$103$	−10.9259	+	6.30805i	−1.07656	+	0.621551i	−0.929966	−	0.367646i	$-0.880164\pi$
$103$	−10.9259	+	6.30805i	−1.07656	+	0.621551i	−0.146592	+	0.989197i	$0.546830\pi$
$104$	−1.63354	−	3.21427i	−0.160182	−	0.315185i
$105$	10.1103	+	0.529573i	0.986668	+	0.0516810i
$106$	5.37959	−	1.44146i	0.522512	−	0.140007i
$107$			0.548012i			0.0529783i	0.999649	+	0.0264892i	$0.00843275\pi$
$107$			0.548012i			0.0529783i	−0.999649	+	0.0264892i	$0.991567\pi$
$108$	4.55719	−	2.49641i	0.438515	−	0.240217i
$109$	8.77267	−	2.35063i	0.840270	−	0.225150i	0.187081	−	0.982345i	$-0.440097\pi$
$109$	8.77267	−	2.35063i	0.840270	−	0.225150i	0.653189	+	0.757195i	$0.273431\pi$
$110$	−1.20734	−	4.50585i	−0.115115	−	0.429616i
$111$	−1.48979	+	15.6763i	−0.141404	+	1.48793i
$112$	2.34532	+	1.22452i	0.221612	+	0.115707i
$113$	−5.76556	+	3.32875i	−0.542378	+	0.313142i	−0.746042	−	0.665899i	$-0.768048\pi$
$113$	−5.76556	+	3.32875i	−0.542378	+	0.313142i	0.203664	+	0.979041i	$0.434715\pi$
$114$	0.137428	+	0.815010i	0.0128713	+	0.0763326i
$115$	−10.3075	−	2.76189i	−0.961181	−	0.257548i
$116$	−0.470390	+	0.814739i	−0.0436746	+	0.0756466i
$117$	−5.23032	+	9.46804i	−0.483543	+	0.875320i
$118$	14.2797			1.31455
$119$	9.82509	+	5.12980i	0.900665	+	0.470248i
$120$	−3.58592	−	1.33564i	−0.327348	−	0.121927i
$121$	5.66533	+	3.27088i	0.515030	+	0.297353i
$122$	1.04640	+	3.90521i	0.0947365	+	0.353561i
$123$	13.2442	+	9.42219i	1.19419	+	0.849570i
$124$	1.14902	+	4.28819i	0.103185	+	0.385091i
$125$	−7.99701	−	7.99701i	−0.715275	−	0.715275i
$126$	−0.908552	−	7.88508i	−0.0809403	−	0.702459i
$127$	4.84622	+	2.79797i	0.430033	+	0.248280i	0.699361	−	0.714769i	$-0.253468\pi$
$127$	4.84622	+	2.79797i	0.430033	+	0.248280i	−0.269328	+	0.963049i	$0.586801\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.62232	+	4.35560i	−0.142838	+	0.383489i
$130$	7.79332	−	1.64805i	0.683520	−	0.144544i
$131$	−1.13235	+	0.653760i	−0.0989335	+	0.0571193i	−0.548650	−	0.836052i	$-0.684858\pi$
$131$	−1.13235	+	0.653760i	−0.0989335	+	0.0571193i	0.449717	+	0.893171i	$0.351525\pi$
$132$	−3.32597	+	1.52073i	−0.289489	+	0.132363i
$133$	1.23226	+	0.274757i	0.106851	+	0.0238245i
$134$	−4.24449	−	7.35168i	−0.366669	−	0.635089i
$135$	2.72152	+	11.1525i	0.234231	+	0.959854i
$136$	−2.96223	−	2.96223i	−0.254009	−	0.254009i
$137$	−11.9831	−	11.9831i	−1.02379	−	1.02379i	−0.999710	−	0.0240751i	$-0.992336\pi$
$137$	−11.9831	−	11.9831i	−1.02379	−	1.02379i	−0.0240751	−	0.999710i	$-0.507664\pi$
$138$	−0.791494	+	8.32852i	−0.0673764	+	0.708970i
$139$	0.00803392	+	0.0139152i	0.000681428	+	0.00118027i	0.866366	−	0.499410i	$-0.166450\pi$
$139$	0.00803392	+	0.0139152i	0.000681428	+	0.00118027i	−0.865684	+	0.500590i	$0.833116\pi$
$140$	−3.95420	+	4.30474i	−0.334191	+	0.363817i
$141$	−3.02731	−	6.62100i	−0.254946	−	0.557589i
$142$	−5.36785	+	3.09913i	−0.450460	+	0.260073i
$143$	4.15295	−	6.38045i	0.347287	−	0.533560i
$144$	−0.565101	+	2.94630i	−0.0470918	+	0.245525i
$145$	−1.46968	−	1.46968i	−0.122051	−	0.122051i
$146$	6.02601	+	3.47912i	0.498716	+	0.287934i
$147$	−11.6795	−	3.25396i	−0.963313	−	0.268382i
$148$	−6.42867	−	6.42867i	−0.528434	−	0.528434i
$149$	2.69197	+	10.0466i	0.220535	+	0.823047i	0.984144	+	0.177369i	$0.0567586\pi$
$149$	2.69197	+	10.0466i	0.220535	+	0.823047i	−0.763610	+	0.645678i	$0.776575\pi$
$150$	−0.119563	+	0.168063i	−0.00976226	+	0.0137223i
$151$	−3.95546	−	14.7620i	−0.321891	−	1.20131i	−0.917401	−	0.397964i	$-0.869717\pi$
$151$	−3.95546	−	14.7620i	−0.321891	−	1.20131i	0.595510	−	0.803348i	$-0.296950\pi$
$152$	−0.413257	−	0.238594i	−0.0335196	−	0.0193526i
$153$	−2.36734	+	12.3427i	−0.191388	+	0.997848i
$154$	0.236893	+	5.58136i	0.0190894	+	0.449759i
$155$	−9.80801			−0.787798
$156$	−2.28998	−	5.80999i	−0.183345	−	0.465171i
$157$	−10.4574	+	18.1128i	−0.834592	+	1.44556i	0.0597707	+	0.998212i	$0.480963\pi$
$157$	−10.4574	+	18.1128i	−0.834592	+	1.44556i	−0.894362	+	0.447343i	$0.852370\pi$
$158$	3.43097	+	0.919325i	0.272953	+	0.0731376i
$159$	9.51213	−	1.60395i	0.754361	−	0.127201i
$160$	1.91329	−	1.10464i	0.151259	−	0.0873295i
$161$	11.3282	+	5.91461i	0.892790	+	0.466137i
$162$	8.26695	−	3.55774i	0.649513	−	0.279523i
$163$	−6.57144	−	24.5250i	−0.514715	−	1.92094i	−0.359863	−	0.933005i	$-0.617177\pi$
$163$	−6.57144	−	24.5250i	−0.514715	−	1.92094i	−0.154852	−	0.987938i	$-0.549490\pi$
$164$	−9.06440	+	2.42880i	−0.707811	+	0.189657i
$165$	−1.34344	−	7.96719i	−0.104586	−	0.620245i
$166$		−	10.4218i		−	0.808887i
$167$	−6.53289	+	1.75048i	−0.505530	+	0.135456i	−0.502565	−	0.864539i	$-0.667610\pi$
$167$	−6.53289	+	1.75048i	−0.505530	+	0.135456i	−0.00296472	+	0.999996i	$0.500944\pi$
$168$	3.84334	+	2.49574i	0.296520	+	0.192551i
$169$	10.5013	+	7.66306i	0.807793	+	0.589466i
$170$	8.01522	−	4.62759i	0.614739	−	0.354920i
$171$	0.103412	+	1.42783i	0.00790813	+	0.109189i
$172$	−1.34174	−	2.32396i	−0.102307	−	0.177200i
$173$	3.35697	−	5.81445i	0.255226	−	0.442064i	−0.709731	−	0.704473i	$-0.751183\pi$
$173$	3.35697	−	5.81445i	0.255226	−	0.442064i	0.964957	+	0.262408i	$0.0845168\pi$
$174$	−0.944592	+	1.32776i	−0.0716093	+	0.100657i
$175$	0.168957	+	0.265922i	0.0127719	+	0.0201018i
$176$	0.546485	−	2.03951i	0.0411928	−	0.153734i
$177$	24.6221	+	2.33995i	1.85071	+	0.175881i
$178$	−15.7961			−1.18397
$179$	2.19808	+	3.80718i	0.164292	+	0.284562i	0.936404	−	0.350925i	$-0.114133\pi$
$179$	2.19808	+	3.80718i	0.164292	+	0.284562i	−0.772112	+	0.635487i	$0.780799\pi$
$180$	−5.96427	−	2.89063i	−0.444551	−	0.215455i
$181$			26.8774i			1.99778i	0.0470732	+	0.998891i	$0.485011\pi$
$181$			26.8774i			1.99778i	−0.0470732	+	0.998891i	$0.514989\pi$
$182$	−9.53882	−	0.104755i	−0.707064	−	0.00776498i
$183$	1.16436	+	6.90516i	0.0860716	+	0.510444i
$184$	−3.41542	−	3.41542i	−0.251788	−	0.251788i
$185$	17.3947	−	10.0429i	1.27889	−	0.738366i
$186$	1.27854	+	7.58233i	0.0937472	+	0.555963i
$187$	2.28935	−	8.54396i	0.167414	−	0.624797i
$188$	4.06004	+	1.08788i	0.296109	+	0.0793421i
$189$	−0.274505	−	13.7450i	−0.0199673	−	0.999801i
$190$	0.745463	−	0.745463i	0.0540815	−	0.0540815i
$191$	−4.16967	−	2.40736i	−0.301707	−	0.174191i	0.341503	−	0.939881i	$-0.389064\pi$
$191$	−4.16967	−	2.40736i	−0.301707	−	0.174191i	−0.643209	+	0.765690i	$0.722398\pi$
$192$	−1.10338	−	1.33512i	−0.0796297	−	0.0963541i
$193$	0.812354	+	0.217670i	0.0584745	+	0.0156682i	0.287938	−	0.957649i	$-0.407030\pi$
$193$	0.812354	+	0.217670i	0.0584745	+	0.0156682i	−0.229463	+	0.973317i	$0.573697\pi$
$194$	−8.93234	−	15.4713i	−0.641305	−	1.11077i
$195$	13.7079	−	1.56465i	0.981646	−	0.112047i
$196$	5.74380	−	4.00109i	0.410272	−	0.285792i
$197$	−3.67600	−	13.7190i	−0.261904	−	0.977440i	−0.964118	−	0.265474i	$-0.914472\pi$
$197$	−3.67600	−	13.7190i	−0.261904	−	0.977440i	0.702214	−	0.711966i	$-0.252195\pi$
$198$	−5.98411	+	2.07716i	−0.425272	+	0.147617i
$199$		−	7.14634i		−	0.506590i	−0.967389	−	0.253295i	$-0.918486\pi$
$199$		−	7.14634i		−	0.506590i	0.967389	−	0.253295i	$-0.0815144\pi$
$200$	−0.0308202	−	0.115023i	−0.00217932	−	0.00813333i
$201$	−6.11402	−	13.3719i	−0.431250	−	0.943181i
$202$	−7.87215	−	2.10934i	−0.553883	−	0.148412i
$203$	1.33482	+	2.10088i	0.0936862	+	0.147453i
$204$	−4.62231	−	5.59313i	−0.323627	−	0.391597i
$205$		−	20.7322i		−	1.44800i
$206$	3.26529	−	12.1862i	0.227503	−	0.849054i
$207$	−2.72952	+	14.2310i	−0.189715	+	0.989124i
$208$	3.42792	+	1.11774i	0.237684	+	0.0775014i
$209$		−	1.00756i		−	0.0696945i
$210$	−7.52355	+	6.77462i	−0.519174	+	0.467493i
$211$	6.91083	−	11.9699i	0.475761	−	0.824042i	−0.523854	−	0.851808i	$-0.675506\pi$
$211$	6.91083	−	11.9699i	0.475761	−	0.824042i	0.999614	+	0.0277663i	$0.00883942\pi$
$212$	−2.78468	+	4.82321i	−0.191253	+	0.331259i
$213$	−9.76353	+	4.46417i	−0.668986	+	0.305880i
$214$	−0.387503	−	0.387503i	−0.0264892	−	0.0264892i
$215$	5.72655	−	1.53442i	0.390547	−	0.104647i
$216$	−1.45719	+	4.98764i	−0.0991493	+	0.339366i
$217$	11.4642	+	2.55617i	0.778240	+	0.173524i
$218$	−4.54107	+	7.86536i	−0.307560	+	0.532710i
$219$	9.82044	+	6.98644i	0.663604	+	0.472100i
$220$	4.03983	+	2.33240i	0.272365	+	0.157250i
$221$	14.3603	+	4.68247i	0.965981	+	0.314977i
$222$	−10.0314	−	12.1383i	−0.673264	−	0.814668i
$223$	−4.03794	+	1.08196i	−0.270401	+	0.0724536i	−0.391471	−	0.920190i	$-0.628034\pi$
$223$	−4.03794	+	1.08196i	−0.270401	+	0.0724536i	0.121071	+	0.992644i	$0.461367\pi$
$224$	−2.52426	+	0.792526i	−0.168659	+	0.0529529i
$225$	−0.233700	+	0.270195i	−0.0155800	+	0.0180130i
$226$	1.72309	−	6.43065i	0.114618	−	0.427760i
$227$	−7.99215	+	7.99215i	−0.530458	+	0.530458i	−0.920709	−	0.390251i	$-0.872388\pi$
$227$	−7.99215	+	7.99215i	−0.530458	+	0.530458i	0.390251	+	0.920709i	$0.372388\pi$
$228$	−0.673475	−	0.479123i	−0.0446020	−	0.0317307i
$229$	1.91084	+	0.512008i	0.126272	+	0.0338344i	0.321401	−	0.946943i	$-0.395846\pi$
$229$	1.91084	+	0.512008i	0.126272	+	0.0338344i	−0.195130	+	0.980777i	$0.562513\pi$
$230$	9.24147	−	5.33556i	0.609364	−	0.351817i
$231$	−0.506123	+	9.66265i	−0.0333005	+	0.635756i
$232$	−0.243492	−	0.908723i	−0.0159860	−	0.0596606i
$233$	8.36770	+	14.4933i	0.548187	+	0.949487i	0.998399	+	0.0565654i	$0.0180150\pi$
$233$	8.36770	+	14.4933i	0.548187	+	0.949487i	−0.450212	+	0.892922i	$0.648652\pi$
$234$	−2.99652	−	10.3933i	−0.195888	−	0.679432i
$235$	−4.64309	+	8.04207i	−0.302882	+	0.524607i
$236$	−10.0972	+	10.0972i	−0.657274	+	0.657274i
$237$	5.76531	+	2.14739i	0.374497	+	0.139488i
$238$	−10.5747	+	3.32007i	−0.685457	+	0.215208i
$239$	10.8665	−	10.8665i	0.702893	−	0.702893i	−0.262138	−	0.965030i	$-0.584428\pi$
$239$	10.8665	−	10.8665i	0.702893	−	0.702893i	0.965030	+	0.262138i	$0.0844275\pi$
$240$	3.48007	−	1.59119i	0.224637	−	0.102711i
$241$	−19.2521	+	19.2521i	−1.24014	+	1.24014i	−0.280195	+	0.959943i	$0.590399\pi$
$241$	−19.2521	+	19.2521i	−1.24014	+	1.24014i	−0.959943	+	0.280195i	$0.909601\pi$
$242$	−6.31885	+	1.69313i	−0.406191	+	0.108839i
$243$	14.8375	−	4.77988i	0.951829	−	0.306630i
$244$	−3.50132	−	2.02149i	−0.224149	−	0.129412i
$245$	5.25400	+	14.5451i	0.335666	+	0.929254i
$246$	−16.0276	+	2.70259i	−1.02188	+	0.172311i
$247$	1.71808	+	0.0918320i	0.109319	+	0.00584313i
$248$	−3.84468	−	2.21973i	−0.244138	−	0.140953i
$249$	1.70777	−	17.9701i	0.108226	−	1.13881i
$250$	11.3095			0.715275
$251$	9.46986	+	16.4023i	0.597732	+	1.03530i	0.993155	+	0.116804i	$0.0372648\pi$
$251$	9.46986	+	16.4023i	0.597732	+	1.03530i	−0.395423	+	0.918499i	$0.629402\pi$
$252$	6.21804	+	4.93315i	0.391700	+	0.310759i
$253$	2.63960	−	9.85110i	0.165950	−	0.619334i
$254$	−5.40526	+	1.44834i	−0.339156	+	0.0908766i
$255$	14.5788	−	6.66585i	0.912960	−	0.417432i
$256$	1.00000			0.0625000
$257$	14.5992			0.910675			0.455337	−	0.890319i	$-0.349519\pi$
$257$	14.5992			0.910675			0.455337	+	0.890319i	$0.349519\pi$
$258$	−1.93272	−	4.22703i	−0.120326	−	0.263163i
$259$	−22.9494	+	7.20527i	−1.42601	+	0.447713i
$260$	−4.34536	+	6.67606i	−0.269488	+	0.414032i
$261$	−1.84632	+	2.13464i	−0.114284	+	0.132131i
$262$	0.338411	−	1.26297i	0.0209071	−	0.0780264i
$263$	15.2054	−	8.77884i	0.937605	−	0.541326i	0.0483960	−	0.998828i	$-0.484589\pi$
$263$	15.2054	−	8.77884i	0.937605	−	0.541326i	0.889209	+	0.457502i	$0.151256\pi$
$264$	1.27650	−	3.42714i	0.0785631	−	0.210926i
$265$	−8.70044	−	8.70044i	−0.534464	−	0.534464i
$266$	−1.06562	+	0.677058i	−0.0653376	+	0.0415131i
$267$	−27.2370	−	2.58844i	−1.66688	−	0.158410i
$268$	8.19973	+	2.19711i	0.500879	+	0.134210i
$269$		−	11.7089i		−	0.713905i	−0.934123	−	0.356952i	$-0.883816\pi$
$269$		−	11.7089i		−	0.713905i	0.934123	−	0.356952i	$-0.116184\pi$
$270$	−9.81041	−	5.96160i	−0.597043	−	0.362811i
$271$	9.51859	−	9.51859i	0.578213	−	0.578213i	−0.356197	−	0.934411i	$-0.615927\pi$
$271$	9.51859	−	9.51859i	0.578213	−	0.578213i	0.934411	+	0.356197i	$0.115927\pi$
$272$	4.18923			0.254009
$273$	−16.4304	−	1.74371i	−0.994416	−	0.105534i
$274$	16.9467			1.02379
$275$	0.177790	−	0.177790i	0.0107211	−	0.0107211i
$276$	−5.32948	−	6.44882i	−0.320797	−	0.388173i
$277$		−	2.99386i		−	0.179884i	−0.995947	−	0.0899418i	$-0.971332\pi$
$277$		−	2.99386i		−	0.179884i	0.995947	−	0.0899418i	$-0.0286681\pi$
$278$	−0.0155203	−	0.00415866i	−0.000930849	−	0.000249420i
$279$	0.962082	+	13.2836i	0.0575983	+	0.795267i
$280$	−0.247868	−	5.83995i	−0.0148130	−	0.349004i
$281$	−7.79421	−	7.79421i	−0.464964	−	0.464964i	0.435315	−	0.900278i	$-0.356637\pi$
$281$	−7.79421	−	7.79421i	−0.464964	−	0.464964i	−0.900278	+	0.435315i	$0.856637\pi$
$282$	6.82239	+	2.54112i	0.406267	+	0.151322i
$283$	4.83320	−	2.79045i	0.287304	−	0.165875i	−0.349421	−	0.936966i	$-0.613622\pi$
$283$	4.83320	−	2.79045i	0.287304	−	0.165875i	0.636725	+	0.771091i	$0.280288\pi$
$284$	1.60423	−	5.98706i	0.0951934	−	0.355267i
$285$	1.40754	−	1.16323i	0.0833757	−	0.0689039i
$286$	1.57508	+	7.44824i	0.0931364	+	0.440424i
$287$	−5.40324	+	24.2331i	−0.318943	+	1.43043i
$288$	−1.68376	−	2.48293i	−0.0992164	−	0.146308i
$289$	0.549621			0.0323307
$290$	2.07845			0.122051
$291$	−12.8667	−	28.1405i	−0.754257	−	1.64963i
$292$	−6.72115	+	1.80093i	−0.393325	+	0.105391i
$293$	4.48295	−	16.7306i	0.261897	−	0.977412i	−0.702226	−	0.711955i	$-0.747810\pi$
$293$	4.48295	−	16.7306i	0.261897	−	0.977412i	0.964122	−	0.265458i	$-0.0855231\pi$
$294$	10.5596	−	5.95779i	0.615847	−	0.347465i
$295$	−15.7739	−	27.3212i	−0.918391	−	1.59070i
$296$	9.09152			0.528434
$297$	−10.6587	+	2.60101i	−0.618479	+	0.150926i
$298$	−9.00751	−	5.20049i	−0.521791	−	0.301256i
$299$	16.5573	+	5.39884i	0.957535	+	0.312223i
$300$	−0.0342945	−	0.203382i	−0.00197999	−	0.0117423i
$301$	−7.09344	+	0.301071i	−0.408859	+	0.0173534i
$302$	13.2352	+	7.64136i	0.761601	+	0.439711i
$303$	−13.2282	−	4.92707i	−0.759938	−	0.283053i
$304$	0.460929	−	0.123506i	0.0264361	−	0.00708353i
$305$	6.31592	−	6.31592i	0.361649	−	0.361649i
$306$	−7.05365	−	10.4016i	−0.403230	−	0.594618i
$307$	4.71257	−	4.71257i	0.268961	−	0.268961i	−0.559721	−	0.828681i	$-0.689092\pi$
$307$	4.71257	−	4.71257i	0.268961	−	0.268961i	0.828681	+	0.559721i	$0.189092\pi$
$308$	−4.11413	−	3.77911i	−0.234424	−	0.215335i
$309$	7.62718	−	20.4774i	0.433895	−	1.16492i
$310$	6.93531	−	6.93531i	0.393899	−	0.393899i
$311$	−8.67825	+	15.0312i	−0.492098	+	0.852339i	−0.999959	−	0.00910006i	$-0.997103\pi$
$311$	−8.67825	+	15.0312i	−0.492098	+	0.852339i	0.507860	+	0.861440i	$0.330437\pi$
$312$	5.72755	+	2.48902i	0.324258	+	0.140913i
$313$	−0.700926	−	1.21404i	−0.0396187	−	0.0686215i	0.845536	−	0.533918i	$-0.179281\pi$
$313$	−0.700926	−	1.21404i	−0.0396187	−	0.0686215i	−0.885155	+	0.465297i	$0.845948\pi$
$314$	−5.41315	−	20.2022i	−0.305482	−	1.14007i
$315$	−14.0829	+	10.4485i	−0.793479	+	0.588707i
$316$	−3.07612	+	1.77600i	−0.173045	+	0.0999078i
$317$	−24.7414	−	6.62944i	−1.38962	−	0.372346i	−0.515011	−	0.857184i	$-0.672212\pi$
$317$	−24.7414	−	6.62944i	−1.38962	−	0.372346i	−0.874604	+	0.484837i	$0.838879\pi$
$318$	−5.59193	+	7.86025i	−0.313580	+	0.440781i
$319$	1.40461	−	1.40461i	0.0786428	−	0.0786428i
$320$	−0.571804	+	2.13400i	−0.0319648	+	0.119294i
$321$	−0.604666	−	0.731663i	−0.0337492	−	0.0408374i
$322$	−12.1925	+	3.82801i	−0.679463	+	0.213327i
$323$	1.93094	−	0.517393i	0.107440	−	0.0287885i
$324$	−3.32991	+	8.36132i	−0.184995	+	0.464518i
$325$	0.286959	+	0.319368i	0.0159176	+	0.0177153i
$326$	21.9885	+	12.6951i	1.21783	+	0.703114i
$327$	−9.11895	+	12.8180i	−0.504279	+	0.708836i
$328$	4.69208	−	8.12692i	0.259077	−	0.448734i
$329$	7.52305	−	8.18997i	0.414759	−	0.451528i
$330$	6.58361	+	4.68370i	0.362416	+	0.257829i
$331$	4.35240	−	1.16622i	0.239230	−	0.0641014i	−0.137212	−	0.990542i	$-0.543814\pi$
$331$	4.35240	−	1.16622i	0.239230	−	0.0641014i	0.376442	+	0.926440i	$0.377148\pi$
$332$	7.36931	+	7.36931i	0.404444	+	0.404444i
$333$	−15.3079	−	22.5736i	−0.838869	−	1.23703i
$334$	3.38167	−	5.85723i	0.185037	−	0.320493i
$335$	−9.37728	+	16.2419i	−0.512336	+	0.887391i
$336$	−4.48241	+	0.952898i	−0.244535	+	0.0519849i
$337$			34.7055i			1.89053i	0.326303	+	0.945265i	$0.394197\pi$
$337$			34.7055i			1.89053i	−0.326303	+	0.945265i	$0.605803\pi$
$338$	−12.8441	+	2.00694i	−0.698630	+	0.109163i
$339$	4.02485	−	10.8059i	0.218600	−	0.586896i
$340$	−2.39542	+	8.93981i	−0.129910	+	0.484829i
$341$		−	9.37371i		−	0.507615i
$342$	−1.08275	−	0.936502i	−0.0585484	−	0.0506402i
$343$	−2.35043	−	18.3705i	−0.126911	−	0.991914i
$344$	2.59204	+	0.694536i	0.139754	+	0.0374469i
$345$	16.8092	−	7.68566i	0.904977	−	0.413782i
$346$	1.73770	+	6.48518i	0.0934192	+	0.348645i
$347$			15.8381i			0.850232i	0.905139	+	0.425116i	$0.139767\pi$
$347$			15.8381i			0.850232i	−0.905139	+	0.425116i	$0.860233\pi$
$348$	−0.270940	−	1.60679i	−0.0145239	−	0.0861332i
$349$	−7.94079	−	29.6354i	−0.425061	−	1.58635i	−0.763790	−	0.645465i	$-0.776664\pi$
$349$	−7.94079	−	29.6354i	−0.425061	−	1.58635i	0.338729	−	0.940884i	$-0.390003\pi$
$350$	−0.307505	−	0.0685644i	−0.0164369	−	0.00366492i
$351$	−3.46373	−	18.4120i	−0.184880	−	0.982761i
$352$	1.05573	+	1.82857i	0.0562705	+	0.0974633i
$353$	10.6111	+	2.84322i	0.564769	+	0.151330i	0.529897	−	0.848062i	$-0.322231\pi$
$353$	10.6111	+	2.84322i	0.564769	+	0.151330i	0.0348728	+	0.999392i	$0.488897\pi$
$354$	−19.0651	+	15.7559i	−1.01330	+	0.837416i
$355$	11.8591	+	6.84685i	0.629415	+	0.363393i
$356$	11.1696	−	11.1696i	0.591985	−	0.591985i
$357$	−18.7778	+	3.99191i	−0.993828	+	0.211274i
$358$	−4.24635	−	1.13781i	−0.224427	−	0.0601350i
$359$	−0.843227	+	3.14697i	−0.0445038	+	0.166091i	−0.984601	−	0.174815i	$-0.944067\pi$
$359$	−0.843227	+	3.14697i	−0.0445038	+	0.166091i	0.940097	+	0.340906i	$0.110734\pi$
$360$	6.26136	−	2.17339i	0.330003	−	0.114548i
$361$	−16.2573	+	9.38615i	−0.855646	+	0.494008i
$362$	−19.0052	−	19.0052i	−0.998891	−	0.998891i
$363$	−11.1729	+	1.88399i	−0.586427	+	0.0988840i
$364$	6.81904	−	6.67089i	0.357415	−	0.349650i
$365$		−	15.3727i		−	0.804644i
$366$	−5.70601	−	4.05936i	−0.298258	−	0.212186i
$367$	10.3040	+	17.8470i	0.537863	+	0.931606i	0.999019	+	0.0442870i	$0.0141016\pi$
$367$	10.3040	+	17.8470i	0.537863	+	0.931606i	−0.461156	+	0.887319i	$0.652565\pi$
$368$	4.83014			0.251788
$369$	−28.0789	+	2.03365i	−1.46173	+	0.105868i
$370$	−5.19857	+	19.4013i	−0.270261	+	1.00863i
$371$	7.90208	+	12.4371i	0.410255	+	0.645702i
$372$	−6.26558	−	4.45745i	−0.324855	−	0.231108i
$373$	−0.705053	+	1.22119i	−0.0365063	+	0.0632307i	−0.883701	−	0.468051i	$-0.844956\pi$
$373$	−0.705053	+	1.22119i	−0.0365063	+	0.0632307i	0.847195	+	0.531282i	$0.178290\pi$
$374$	4.42268	+	7.66031i	0.228691	+	0.396105i
$375$	19.5007	+	1.85324i	1.00701	+	0.0957007i
$376$	−3.64013	+	2.10163i	−0.187726	+	0.108383i
$377$	2.26709	+	2.52313i	0.116761	+	0.129948i
$378$	9.91328	+	9.52507i	0.509884	+	0.489917i
$379$	−15.7641	+	4.22399i	−0.809749	+	0.216972i	−0.639860	−	0.768492i	$-0.721008\pi$
$379$	−15.7641	+	4.22399i	−0.809749	+	0.216972i	−0.169889	+	0.985463i	$0.554341\pi$
$380$			1.05424i			0.0540815i
$381$	−9.55753	+	1.61160i	−0.489647	+	0.0825648i
$382$	4.65067	−	1.24614i	0.237949	−	0.0637582i
$383$	−6.43288	−	24.0078i	−0.328705	−	1.22674i	−0.910535	−	0.413432i	$-0.864330\pi$
$383$	−6.43288	−	24.0078i	−0.328705	−	1.22674i	0.581830	−	0.813310i	$-0.302337\pi$
$384$	1.72428	+	0.163866i	0.0879919	+	0.00836224i
$385$	10.4171	−	6.61864i	0.530904	−	0.337317i
$386$	−0.728336	+	0.420505i	−0.0370713	+	0.0214032i
$387$	−2.63989	−	7.60530i	−0.134193	−	0.386599i
$388$	17.2560	+	4.62372i	0.876039	+	0.234734i
$389$	5.33488	−	9.24029i	0.270489	−	0.468501i	−0.698498	−	0.715612i	$-0.746148\pi$
$389$	5.33488	−	9.24029i	0.270489	−	0.468501i	0.968987	+	0.247111i	$0.0794812\pi$
$390$	−8.58660	+	10.7994i	−0.434800	+	0.546847i
$391$	20.2345			1.02330
$392$	−1.23229	+	6.89068i	−0.0622399	+	0.348032i
$393$	0.790474	−	2.12226i	0.0398741	−	0.107054i
$394$	12.3001	+	7.10149i	0.619672	+	0.357768i
$395$	−2.03105	−	7.57997i	−0.102193	−	0.381390i
$396$	2.76263	−	5.70018i	0.138828	−	0.286445i
$397$	5.13972	+	19.1817i	0.257955	+	0.962701i	0.966423	+	0.256958i	$0.0827201\pi$
$397$	5.13972	+	19.1817i	0.257955	+	0.962701i	−0.708468	+	0.705743i	$0.750613\pi$
$398$	5.05322	+	5.05322i	0.253295	+	0.253295i
$399$	−1.94838	+	0.992820i	−0.0975412	+	0.0497032i
$400$	0.103127	+	0.0595401i	0.00515633	+	0.00297701i
$401$	−5.20885	−	5.20885i	−0.260118	−	0.260118i	0.564984	−	0.825102i	$-0.308882\pi$
$401$	−5.20885	−	5.20885i	−0.260118	−	0.260118i	−0.825102	+	0.564984i	$0.808882\pi$
$402$	13.7786	+	5.13210i	0.687215	+	0.255966i
$403$	15.9839	+	0.854346i	0.796214	+	0.0425580i
$404$	7.05798	−	4.07493i	0.351148	−	0.202735i
$405$	−15.9390	−	11.8871i	−0.792016	−	0.590673i
$406$	−2.42941	−	0.541685i	−0.120570	−	0.0268834i
$407$	9.59816	+	16.6245i	0.475763	+	0.824046i
$408$	7.22341	+	0.686471i	0.357612	+	0.0339854i
$409$	−28.5210	−	28.5210i	−1.41028	−	1.41028i	−0.757873	−	0.652402i	$-0.773762\pi$
$409$	−28.5210	−	28.5210i	−1.41028	−	1.41028i	−0.652402	−	0.757873i	$-0.726238\pi$
$410$	14.6599	+	14.6599i	0.724001	+	0.724001i
$411$	29.2208	+	2.77698i	1.44136	+	0.136978i
$412$	6.30805	+	10.9259i	0.310775	+	0.538279i
$413$	11.3170	+	36.0456i	0.556873	+	1.77369i
$414$	−8.13279	−	11.9929i	−0.399705	−	0.589419i
$415$	−19.9399	+	11.5123i	−0.978812	+	0.565117i
$416$	−3.21427	+	1.63354i	−0.157593	+	0.0800911i
$417$	−0.0260800	−	0.00971396i	−0.00127714	−	0.000475695i
$418$	0.712454	+	0.712454i	0.0348473	+	0.0348473i
$419$	13.8736	+	8.00994i	0.677771	+	0.391311i	0.799015	−	0.601312i	$-0.205355\pi$
$419$	13.8736	+	8.00994i	0.677771	+	0.391311i	−0.121244	+	0.992623i	$0.538688\pi$
$420$	0.529573	−	10.1103i	0.0258405	−	0.493334i
$421$	14.1022	+	14.1022i	0.687301	+	0.687301i	0.961635	−	0.274334i	$-0.0884573\pi$
$421$	14.1022	+	14.1022i	0.687301	+	0.687301i	−0.274334	+	0.961635i	$0.588457\pi$
$422$	3.57731	+	13.3507i	0.174141	+	0.649901i
$423$	11.3473	+	5.49957i	0.551725	+	0.267398i
$424$	−1.44146	−	5.37959i	−0.0700033	−	0.261256i
$425$	0.432020	+	0.249427i	0.0209561	+	0.0120990i
$426$	3.74721	−	10.0605i	0.181553	−	0.487433i
$427$	−9.02849	+	5.73637i	−0.436919	+	0.277602i
$428$	0.548012			0.0264892
$429$	1.49537	+	13.1010i	0.0721971	+	0.632520i
$430$	−2.96428	+	5.13428i	−0.142950	+	0.247597i
$431$	30.6067	+	8.20105i	1.47427	+	0.395030i	0.904394	−	0.426698i	$-0.140323\pi$
$431$	30.6067	+	8.20105i	1.47427	+	0.395030i	0.569880	+	0.821728i	$0.306990\pi$
$432$	−2.49641	−	4.55719i	−0.120108	−	0.219258i
$433$	23.8503	−	13.7700i	1.14617	−	0.661744i	0.198222	−	0.980157i	$-0.436483\pi$
$433$	23.8503	−	13.7700i	1.14617	−	0.661744i	0.947952	+	0.318414i	$0.103150\pi$
$434$	−9.91389	+	6.29892i	−0.475882	+	0.302358i
$435$	3.58383	+	0.340586i	0.171831	+	0.0163298i
$436$	−2.35063	−	8.77267i	−0.112575	−	0.420135i
$437$	2.22635	−	0.596548i	0.106501	−	0.0285368i
$438$	−11.8843	+	2.00394i	−0.567852	+	0.0957519i
$439$		−	1.85814i		−	0.0886842i	−0.999016	−	0.0443421i	$-0.985881\pi$
$439$		−	1.85814i		−	0.0886842i	0.999016	−	0.0443421i	$-0.0141192\pi$
$440$	−4.50585	+	1.20734i	−0.214808	+	0.0575576i
$441$	19.1840	−	8.54256i	0.913522	−	0.406788i
$442$	−13.4653	+	6.84329i	−0.640479	+	0.325502i
$443$	−27.1823	+	15.6937i	−1.29147	+	0.745631i	−0.978915	−	0.204269i	$-0.934518\pi$
$443$	−27.1823	+	15.6937i	−1.29147	+	0.745631i	−0.312555	+	0.949900i	$0.601185\pi$
$444$	15.6763	+	1.48979i	0.743966	+	0.0707022i
$445$	17.4490	+	30.2226i	0.827164	+	1.43269i
$446$	2.09019	−	3.62032i	0.0989735	−	0.171427i
$447$	−14.6793	−	10.4431i	−0.694307	−	0.493943i
$448$	1.22452	−	2.34532i	0.0578533	−	0.110806i
$449$	−1.27900	+	4.77331i	−0.0603600	+	0.225266i	−0.989516	−	0.144420i	$-0.953868\pi$
$449$	−1.27900	+	4.77331i	−0.0603600	+	0.225266i	0.929156	+	0.369687i	$0.120535\pi$
$450$	−0.0258061	−	0.356307i	−0.00121651	−	0.0167965i
$451$	19.8142			0.933015
$452$	3.32875	+	5.76556i	0.156571	+	0.271189i
$453$	21.5691	+	15.3447i	1.01340	+	0.720955i
$454$		−	11.3026i		−	0.530458i
$455$	10.3365	+	18.3663i	0.484584	+	0.861024i
$456$	0.815010	−	0.137428i	0.0381663	−	0.00643565i
$457$	1.44665	+	1.44665i	0.0676715	+	0.0676715i	0.740133	−	0.672461i	$-0.234763\pi$
$457$	1.44665	+	1.44665i	0.0676715	+	0.0676715i	−0.672461	+	0.740133i	$0.734763\pi$
$458$	−1.71321	+	0.989123i	−0.0800531	+	0.0462187i
$459$	−10.4580	−	19.0911i	−0.488138	−	0.891096i
$460$	−2.76189	+	10.3075i	−0.128774	+	0.480590i
$461$	−36.8262	−	9.86755i	−1.71517	−	0.459578i	−0.738485	−	0.674270i	$-0.764459\pi$
$461$	−36.8262	−	9.86755i	−1.71517	−	0.459578i	−0.976682	+	0.214692i	$0.931125\pi$
$462$	−6.47465	−	7.19041i	−0.301228	−	0.334528i
$463$	13.6453	−	13.6453i	0.634149	−	0.634149i	−0.314957	−	0.949106i	$-0.601990\pi$
$463$	13.6453	−	13.6453i	0.634149	−	0.634149i	0.949106	+	0.314957i	$0.101990\pi$
$464$	0.814739	+	0.470390i	0.0378233	+	0.0218373i
$465$	13.0949	−	10.8220i	0.607261	−	0.501857i
$466$	−16.1652	−	4.33144i	−0.748837	−	0.200650i
$467$	−4.93246	−	8.54326i	−0.228247	−	0.395335i	0.729042	−	0.684469i	$-0.239966\pi$
$467$	−4.93246	−	8.54326i	−0.228247	−	0.395335i	−0.957289	+	0.289134i	$0.906633\pi$
$468$	9.46804	+	5.23032i	0.437660	+	0.241772i
$469$	15.1937	−	16.5406i	0.701580	−	0.763775i
$470$	−2.40344	−	8.96977i	−0.110863	−	0.413745i
$471$	−6.02336	−	35.7212i	−0.277542	−	1.64595i
$472$		−	14.2797i		−	0.657274i
$473$	1.46648	+	5.47298i	0.0674289	+	0.251648i
$474$	−5.59513	+	2.55825i	−0.256993	+	0.117504i
$475$	0.0548875	+	0.0147071i	0.00251841	+	0.000674806i
$476$	5.12980	−	9.82509i	0.235124	−	0.450332i
$477$	−10.9301	+	12.6370i	−0.500454	+	0.578607i
$478$			15.3675i			0.702893i
$479$	4.05989	−	15.1517i	0.185501	−	0.692300i	−0.809021	−	0.587779i	$-0.800002\pi$
$479$	4.05989	−	15.1517i	0.185501	−	0.692300i	0.994523	−	0.104521i	$-0.0333309\pi$
$480$	−1.33564	+	3.58592i	−0.0609634	+	0.163674i
$481$	−29.2226	+	14.8514i	−1.33244	+	0.677166i
$482$		−	27.2266i		−	1.24014i
$483$	−21.6506	+	4.60263i	−0.985138	+	0.209427i
$484$	3.27088	−	5.66533i	0.148676	−	0.257515i
$485$	−19.7340	+	34.1804i	−0.896077	+	1.55205i
$486$	−7.11184	+	13.8716i	−0.322600	+	0.629229i
$487$	25.8159	+	25.8159i	1.16983	+	1.16983i	0.982249	+	0.187580i	$0.0600642\pi$
$487$	25.8159	+	25.8159i	1.16983	+	1.16983i	0.187580	+	0.982249i	$0.439936\pi$
$488$	3.90521	−	1.04640i	0.176781	−	0.0473682i
$489$	35.8340	+	25.4930i	1.62047	+	1.15283i
$490$	−14.0001	−	6.56982i	−0.632460	−	0.296794i
$491$	16.2655	−	28.1727i	0.734053	−	1.27142i	−0.221084	−	0.975255i	$-0.570960\pi$
$491$	16.2655	−	28.1727i	0.734053	−	1.27142i	0.955138	−	0.296163i	$-0.0957071\pi$
$492$	9.42219	−	13.2442i	0.424785	−	0.597096i
$493$	3.41313	+	1.97057i	0.153719	+	0.0887500i
$494$	−1.27980	+	1.14993i	−0.0575808	+	0.0517377i
$495$	10.5845	+	9.15485i	0.475738	+	0.411480i
$496$	4.28819	−	1.14902i	0.192545	−	0.0515924i
$497$	−12.0772	−	11.0937i	−0.541735	−	0.497621i
$498$	11.4992	+	13.9143i	0.515291	+	0.623517i
$499$	−8.87224	+	33.1116i	−0.397176	+	1.48228i	0.420866	+	0.907123i	$0.361726\pi$
$499$	−8.87224	+	33.1116i	−0.397176	+	1.48228i	−0.818042	+	0.575158i	$0.804941\pi$
$500$	−7.99701	+	7.99701i	−0.357637	+	0.357637i
$501$	6.79075	−	9.54537i	0.303389	−	0.426456i
$502$	−18.2944	−	4.90196i	−0.816518	−	0.218785i
$503$	9.85823	−	5.69165i	0.439557	−	0.253778i	−0.263853	−	0.964563i	$-0.584993\pi$
$503$	9.85823	−	5.69165i	0.439557	−	0.253778i	0.703410	+	0.710785i	$0.251660\pi$
$504$	−7.88508	+	0.908552i	−0.351230	+	0.0404701i
$505$	4.66012	+	17.3918i	0.207372	+	0.773925i
$506$	5.09931	+	8.83226i	0.226692	+	0.392642i
$507$	−22.4758	+	1.35582i	−0.998185	+	0.0602139i
$508$	2.79797	−	4.84622i	0.124140	−	0.215016i
$509$	−19.2634	+	19.2634i	−0.853835	+	0.853835i	−0.990603	−	0.136768i	$-0.956329\pi$
$509$	−19.2634	+	19.2634i	−0.853835	+	0.853835i	0.136768	+	0.990603i	$0.456329\pi$
$510$	−5.59530	+	15.0222i	−0.247764	+	0.665196i
$511$	−4.00644	+	17.9685i	−0.177235	+	0.794881i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.71350	−	1.79222i	−0.0756530	−	0.0791284i
$514$	−10.3232	+	10.3232i	−0.455337	+	0.455337i
$515$	−26.9228	+	7.21394i	−1.18636	+	0.317884i
$516$	4.35560	+	1.62232i	0.191745	+	0.0714188i
$517$	−7.68598	−	4.43750i	−0.338029	−	0.195161i
$518$	11.1328	−	21.3226i	0.489146	−	0.936859i
$519$	1.93358	+	11.4670i	0.0848749	+	0.503346i
$520$	−1.64805	−	7.79332i	−0.0722719	−	0.341760i
$521$	−23.4026	−	13.5115i	−1.02529	−	0.591949i	−0.109655	−	0.993970i	$-0.534975\pi$
$521$	−23.4026	−	13.5115i	−1.02529	−	0.591949i	−0.915631	+	0.402021i	$0.868308\pi$
$522$	−0.203878	−	2.81496i	−0.00892348	−	0.123208i
$523$	−25.5581			−1.11758			−0.558789	−	0.829310i	$-0.688734\pi$
$523$	−25.5581			−1.11758			−0.558789	+	0.829310i	$0.688734\pi$
$524$	0.653760	+	1.13235i	0.0285597	+	0.0494668i
$525$	−0.518991	−	0.168614i	−0.0226506	−	0.00735892i
$526$	−4.54426	+	16.9594i	−0.198139	+	0.739465i
$527$	17.9642	−	4.81349i	0.782532	−	0.209679i
$528$	1.52073	+	3.32597i	0.0661813	+	0.144744i
$529$	0.330220			0.0143574
$530$	12.3043			0.534464
$531$	−35.4554	+	24.0435i	−1.53863	+	1.04340i
$532$	0.274757	−	1.23226i	0.0119122	−	0.0534254i
$533$	−1.80592	+	33.7868i	−0.0782232	+	1.46347i
$534$	21.0898	−	17.4291i	0.912643	−	0.754233i
$535$	−0.313355	+	1.16946i	−0.0135475	+	0.0505601i
$536$	−7.35168	+	4.24449i	−0.317544	+	0.183334i
$537$	−7.13547	−	2.65773i	−0.307918	−	0.114690i
$538$	8.27945	+	8.27945i	0.356952	+	0.356952i
$539$	−13.9011	+	5.02135i	−0.598762	+	0.216285i
$540$	11.1525	−	2.72152i	0.479927	−	0.117116i
$541$	11.3406	+	3.03870i	0.487569	+	0.130644i	0.494225	−	0.869334i	$-0.335452\pi$
$541$	11.3406	+	3.03870i	0.487569	+	0.130644i	−0.00665574	+	0.999978i	$0.502119\pi$
$542$			13.4613i			0.578213i
$543$	−29.6560	−	35.8846i	−1.27266	−	1.53996i
$544$	−2.96223	+	2.96223i	−0.127005	+	0.127005i
$545$	20.0650			0.859490
$546$	12.8511	−	10.3851i	0.549975	−	0.444441i
$547$	40.5275			1.73283			0.866415	−	0.499324i	$-0.166418\pi$
$547$	40.5275			1.73283			0.866415	+	0.499324i	$0.166418\pi$
$548$	−11.9831	+	11.9831i	−0.511893	+	0.511893i
$549$	−9.17357	−	7.93450i	−0.391519	−	0.338636i
$550$			0.251432i			0.0107211i
$551$	0.433632	+	0.116191i	0.0184734	+	0.00494992i
$552$	8.32852	+	0.791494i	0.354485	+	0.0336882i
$553$	0.398514	+	9.38925i	0.0169465	+	0.399272i
$554$	2.11698	+	2.11698i	0.0899418	+	0.0899418i
$555$	−12.1430	+	32.6015i	−0.515442	+	1.38385i
$556$	0.0139152	−	0.00803392i	0.000590134	−	0.000340714i
$557$	8.96108	−	33.4432i	0.379693	−	1.41703i	−0.466672	−	0.884431i	$-0.654547\pi$
$557$	8.96108	−	33.4432i	0.379693	−	1.41703i	0.846365	−	0.532603i	$-0.178786\pi$
$558$	−10.0732	−	8.71262i	−0.426433	−	0.368834i
$559$	−9.46608	+	2.00179i	−0.400373	+	0.0846668i
$560$	4.30474	+	3.95420i	0.181908	+	0.167095i
$561$	6.37069	+	13.9333i	0.268971	+	0.588263i
$562$	11.0227			0.464964
$563$	−31.3297			−1.32039			−0.660195	−	0.751094i	$-0.729526\pi$
$563$	−31.3297			−1.32039			−0.660195	+	0.751094i	$0.729526\pi$
$564$	−6.62100	+	3.02731i	−0.278794	+	0.127473i
$565$	−14.2071	+	3.80678i	−0.597697	+	0.160153i
$566$	−1.44444	+	5.39074i	−0.0607145	+	0.226590i
$567$	15.5325	+	18.0483i	0.652302	+	0.757959i
$568$	3.09913	+	5.36785i	0.130037	+	0.225230i
$569$	−36.3578			−1.52420			−0.762098	−	0.647461i	$-0.775831\pi$
$569$	−36.3578			−1.52420			−0.762098	+	0.647461i	$0.775831\pi$
$570$	−0.172754	+	1.81781i	−0.00723588	+	0.0761398i
$571$	−19.2095	−	11.0906i	−0.803891	−	0.464126i	0.0409392	−	0.999162i	$-0.486965\pi$
$571$	−19.2095	−	11.0906i	−0.803891	−	0.464126i	−0.844830	+	0.535035i	$0.820298\pi$
$572$	−6.38045	−	4.15295i	−0.266780	−	0.173644i
$573$	8.22326	−	1.38662i	0.343532	−	0.0579267i
$574$	−13.3147	−	20.9560i	−0.555745	−	0.874688i
$575$	0.498115	+	0.287587i	0.0207728	+	0.0119932i
$576$	2.94630	+	0.565101i	0.122762	+	0.0235459i
$577$	32.5787	−	8.72943i	1.35627	−	0.363411i	0.493823	−	0.869562i	$-0.335599\pi$
$577$	32.5787	−	8.72943i	1.35627	−	0.363411i	0.862445	+	0.506151i	$0.168932\pi$
$578$	−0.388641	+	0.388641i	−0.0161653	+	0.0161653i
$579$	−1.32476	+	0.605720i	−0.0550553	+	0.0251729i
$580$	−1.46968	+	1.46968i	−0.0610253	+	0.0610253i
$581$	26.3073	−	8.25953i	1.09141	−	0.342663i
$582$	28.9965	+	10.8003i	1.20194	+	0.447685i
$583$	8.31518	−	8.31518i	0.344380	−	0.344380i
$584$	3.47912	−	6.02601i	0.143967	−	0.249358i
$585$	−16.5754	+	17.2141i	−0.685307	+	0.711715i
$586$	8.66040	+	15.0003i	0.357758	+	0.619655i
$587$	−11.4129	−	42.5935i	−0.471061	−	1.75802i	−0.635970	−	0.771714i	$-0.719400\pi$
$587$	−11.4129	−	42.5935i	−0.471061	−	1.75802i	0.164909	−	0.986309i	$-0.447267\pi$
$588$	−3.25396	+	11.6795i	−0.134191	+	0.481656i
$589$	1.83464	−	1.05923i	0.0755950	−	0.0436448i
$590$	30.4728	+	8.16516i	1.25454	+	0.336154i
$591$	20.0452	+	14.2605i	0.824551	+	0.586601i
$592$	−6.42867	+	6.42867i	−0.264217	+	0.264217i
$593$	6.64578	−	24.8024i	0.272909	−	1.01851i	−0.684320	−	0.729182i	$-0.739901\pi$
$593$	6.64578	−	24.8024i	0.272909	−	1.01851i	0.957229	−	0.289330i	$-0.0934325\pi$
$594$	5.69762	−	9.37601i	0.233776	−	0.384702i
$595$	18.0335	+	16.5650i	0.739302	+	0.679100i
$596$	10.0466	−	2.69197i	0.411524	−	0.110267i
$597$	7.88513	+	9.54123i	0.322717	+	0.390497i
$598$	−15.5254	+	7.89024i	−0.634879	+	0.322656i
$599$	0.0523660	+	0.0302335i	0.00213962	+	0.00123531i	0.501069	−	0.865407i	$-0.332940\pi$
$599$	0.0523660	+	0.0302335i	0.00213962	+	0.00123531i	−0.498930	+	0.866642i	$0.666273\pi$
$600$	0.168063	+	0.119563i	0.00686113	+	0.00488113i
$601$	−5.10069	+	8.83465i	−0.208061	+	0.360373i	−0.951104	−	0.308872i	$-0.900049\pi$
$601$	−5.10069	+	8.83465i	−0.208061	+	0.360373i	0.743042	+	0.669244i	$0.233382\pi$
$602$	4.80293	−	5.22871i	0.195753	−	0.213106i
$603$	22.9173	+	11.1070i	0.933263	+	0.452313i
$604$	−14.7620	+	3.95546i	−0.600656	+	0.160945i
$605$	10.2195	+	10.2195i	0.415482	+	0.415482i
$606$	12.8377	−	5.86976i	0.521495	−	0.238443i
$607$	0.263588	−	0.456547i	0.0106987	−	0.0185307i	−0.860626	−	0.509237i	$-0.829928\pi$
$607$	0.263588	−	0.456547i	0.0106987	−	0.0185307i	0.871325	+	0.490706i	$0.163261\pi$
$608$	−0.238594	+	0.413257i	−0.00967628	+	0.0167598i
$609$	−4.10023	−	1.33212i	−0.166150	−	0.0539800i
$610$			8.93206i			0.361649i
$611$	8.26726	−	12.7015i	0.334458	−	0.513849i
$612$	12.3427	+	2.36734i	0.498924	+	0.0956940i
$613$	−2.03809	+	7.60627i	−0.0823179	+	0.307215i	−0.994793	−	0.101918i	$-0.967502\pi$
$613$	−2.03809	+	7.60627i	−0.0823179	+	0.307215i	0.912475	+	0.409133i	$0.134169\pi$
$614$			6.66458i			0.268961i
$615$	22.8755	+	27.6801i	0.922431	+	1.11617i
$616$	5.58136	−	0.236893i	0.224879	−	0.00954469i
$617$	35.0869	+	9.40151i	1.41255	+	0.378491i	0.882833	−	0.469686i	$-0.155633\pi$
$617$	35.0869	+	9.40151i	1.41255	+	0.378491i	0.529713	+	0.848177i	$0.322300\pi$
$618$	9.08649	+	19.8730i	0.365512	+	0.799407i
$619$	−5.72554	−	21.3680i	−0.230129	−	0.858853i	−0.980284	−	0.197591i	$-0.936688\pi$
$619$	−5.72554	−	21.3680i	−0.230129	−	0.858853i	0.750156	−	0.661261i	$-0.229979\pi$
$620$			9.80801i			0.393899i
$621$	−12.0580	−	22.0118i	−0.483870	−	0.883304i
$622$	−4.49219	−	16.7651i	−0.180121	−	0.672219i
$623$	−12.5188	−	39.8736i	−0.501557	−	1.59750i
$624$	−5.80999	+	2.28998i	−0.232586	+	0.0916727i
$625$	−12.1952	−	21.1227i	−0.487808	−	0.844909i
$626$	1.35408	+	0.362826i	0.0541201	+	0.0145014i
$627$	1.11172	+	1.34522i	0.0443980	+	0.0537228i
$628$	18.1128	+	10.4574i	0.722778	+	0.417296i
$629$	−26.9312	+	26.9312i	−1.07382	+	1.07382i
$630$	2.56987	−	17.3463i	0.102386	−	0.691093i
$631$	−2.70265	−	0.724172i	−0.107591	−	0.0288288i	0.204622	−	0.978841i	$-0.434403\pi$
$631$	−2.70265	−	0.724172i	−0.107591	−	0.0288288i	−0.312213	+	0.950012i	$0.601070\pi$
$632$	0.919325	−	3.43097i	0.0365688	−	0.136477i
$633$	3.98056	+	23.6066i	0.158213	+	0.938276i
$634$	22.1825	−	12.8071i	0.880981	−	0.508634i
$635$	8.74196	+	8.74196i	0.346914	+	0.346914i
$636$	−1.60395	−	9.51213i	−0.0636006	−	0.377180i
$637$	−7.29533	−	24.1615i	−0.289052	−	0.957314i
$638$			1.98641i			0.0786428i
$639$	8.10982	−	16.7331i	0.320820	−	0.661951i
$640$	−1.10464	−	1.91329i	−0.0436647	−	0.0756295i
$641$	1.86163			0.0735298			0.0367649	−	0.999324i	$-0.488295\pi$
$641$	1.86163			0.0735298			0.0367649	+	0.999324i	$0.488295\pi$
$642$	0.944927	+	0.0898004i	0.0372933	+	0.00354414i
$643$	4.16762	−	15.5538i	0.164355	−	0.613381i	−0.833767	−	0.552117i	$-0.813820\pi$
$643$	4.16762	−	15.5538i	0.164355	−	0.613381i	0.998122	−	0.0612638i	$-0.0195131\pi$
$644$	5.91461	−	11.3282i	0.233068	−	0.446395i
$645$	−5.95259	+	8.36721i	−0.234383	+	0.329459i
$646$	−0.999526	+	1.73123i	−0.0393258	+	0.0681143i
$647$	−0.729257	−	1.26311i	−0.0286701	−	0.0496580i	0.851334	−	0.524623i	$-0.175794\pi$
$647$	−0.729257	−	1.26311i	−0.0286701	−	0.0496580i	−0.880004	+	0.474965i	$0.842461\pi$
$648$	−3.55774	−	8.26695i	−0.139761	−	0.324756i
$649$	26.1114	−	15.0754i	1.02496	−	0.591762i
$650$	−0.428738	−	0.0229163i	−0.0168165	−	0.000898849i
$651$	−18.1265	+	9.23657i	−0.710434	+	0.362010i
$652$	−24.5250	+	6.57144i	−0.960471	+	0.257358i
$653$		−	45.1206i		−	1.76570i	−0.469651	−	0.882852i	$-0.655620\pi$
$653$		−	45.1206i		−	1.76570i	0.469651	−	0.882852i	$-0.344380\pi$
$654$	−2.61561	−	15.5117i	−0.102278	−	0.606557i
$655$	−2.79025	+	0.747645i	−0.109024	+	0.0292129i
$656$	2.42880	+	9.06440i	0.0948286	+	0.353905i
$657$	−20.8202	+	1.50793i	−0.812273	+	0.0588300i
$658$	0.471582	+	11.1108i	0.0183842	+	0.433144i
$659$	−6.23306	+	3.59866i	−0.242805	+	0.140184i	−0.616465	−	0.787382i	$-0.711436\pi$
$659$	−6.23306	+	3.59866i	−0.242805	+	0.140184i	0.373660	+	0.927566i	$0.378103\pi$
$660$	−7.96719	+	1.34344i	−0.310122	+	0.0522932i
$661$	11.2768	+	3.02162i	0.438618	+	0.117527i	0.471369	−	0.881936i	$-0.343760\pi$
$661$	11.2768	+	3.02162i	0.438618	+	0.117527i	−0.0327507	+	0.999464i	$0.510427\pi$
$662$	−2.25297	+	3.90225i	−0.0875641	+	0.151665i
$663$	−24.3394	+	9.59326i	−0.945263	+	0.372571i
$664$	−10.4218			−0.404444
$665$	2.47254	+	1.29095i	0.0958811	+	0.0500607i
$666$	26.7863	+	5.13763i	1.03795	+	0.199079i
$667$	3.93530	+	2.27205i	0.152375	+	0.0879740i
$668$	1.75048	+	6.53289i	0.0677282	+	0.252765i
$669$	4.19733	−	5.89994i	0.162278	−	0.228105i
$670$	−4.85404	−	18.1155i	−0.187528	−	0.699863i
$671$	6.03626	+	6.03626i	0.233027	+	0.233027i
$672$	2.49574	−	3.84334i	0.0962753	−	0.148260i
$673$	10.8414	+	6.25926i	0.417903	+	0.241277i	0.694180	−	0.719802i	$-0.255767\pi$
$673$	10.8414	+	6.25926i	0.417903	+	0.241277i	−0.276276	+	0.961078i	$0.589101\pi$
$674$	−24.5405	−	24.5405i	−0.945265	−	0.945265i
$675$	0.0138897	−	0.618603i	0.000534613	−	0.0238100i
$676$	7.66306	−	10.5013i	0.294733	−	0.403896i
$677$	−26.6494	+	15.3860i	−1.02422	+	0.591333i	−0.915323	−	0.402721i	$-0.868065\pi$
$677$	−26.6494	+	15.3860i	−1.02422	+	0.591333i	−0.108895	+	0.994053i	$0.534731\pi$
$678$	4.79492	+	10.4869i	0.184148	+	0.402748i
$679$	31.9744	−	34.8090i	1.22707	−	1.33585i
$680$	−4.62759	−	8.01522i	−0.177460	−	0.307370i
$681$	1.85211	−	19.4889i	0.0709730	−	0.746816i
$682$	6.62822	+	6.62822i	0.253808	+	0.253808i
$683$	−24.6600	−	24.6600i	−0.943587	−	0.943587i	0.0549048	−	0.998492i	$-0.482514\pi$
$683$	−24.6600	−	24.6600i	−0.943587	−	0.943587i	−0.998492	+	0.0549048i	$0.982514\pi$
$684$	1.42783	−	0.103412i	0.0545943	−	0.00395407i
$685$	−18.7200	−	32.4239i	−0.715253	−	1.23885i
$686$	14.6519	+	11.3279i	0.559413	+	0.432501i
$687$	−3.11614	+	1.42479i	−0.118888	+	0.0543591i
$688$	−2.32396	+	1.34174i	−0.0886002	+	0.0511534i
$689$	13.4210	+	14.9368i	0.511300	+	0.569045i
$690$	−6.45133	+	17.3205i	−0.245598	+	0.659380i
$691$	−29.0405	−	29.0405i	−1.10475	−	1.10475i	−0.993829	−	0.110924i	$-0.964619\pi$
$691$	−29.0405	−	29.0405i	−1.10475	−	1.10475i	−0.110924	−	0.993829i	$-0.535381\pi$
$692$	−5.81445	−	3.35697i	−0.221032	−	0.127613i
$693$	−9.98585	−	13.4593i	−0.379331	−	0.511275i
$694$	−11.1992	−	11.1992i	−0.425116	−	0.425116i
$695$	0.00918766	+	0.0342888i	0.000348508	+	0.00130065i
$696$	1.32776	+	0.944592i	0.0503286	+	0.0358047i
$697$	10.1748	+	37.9728i	0.385398	+	1.43832i
$698$	26.5704	+	15.3404i	1.00571	+	0.580644i
$699$	−27.1635	−	10.1175i	−1.02742	−	0.382681i
$700$	0.265922	−	0.168957i	0.0100509	−	0.00638597i
$701$	33.7188			1.27354			0.636771	−	0.771053i	$-0.280270\pi$
$701$	33.7188			1.27354			0.636771	+	0.771053i	$0.280270\pi$
$702$	15.4685	+	10.5700i	0.583821	+	0.398940i
$703$	−2.16918	+	3.75714i	−0.0818123	+	0.141703i
$704$	−2.03951	−	0.546485i	−0.0768669	−	0.0205964i
$705$	−2.67437	−	15.8603i	−0.100723	−	0.597332i
$706$	−9.51361	+	5.49269i	−0.358049	+	0.206720i
$707$	−0.914366	−	21.5431i	−0.0343883	−	0.810211i
$708$	2.33995	−	24.6221i	0.0879405	−	0.925357i
$709$	2.19359	+	8.18660i	0.0823821	+	0.307454i	0.994806	−	0.101793i	$-0.0324580\pi$
$709$	2.19359	+	8.18660i	0.0823821	+	0.307454i	−0.912424	+	0.409247i	$0.865791\pi$
$710$	−13.2271	+	3.54419i	−0.496404	+	0.133011i
$711$	−10.0668	+	3.49430i	−0.377534	+	0.131046i
$712$			15.7961i			0.591985i
$713$	20.7125	−	5.54991i	0.775690	−	0.207846i
$714$	10.4552	−	16.1006i	0.391277	−	0.602551i
$715$	12.5108	−	11.2412i	0.467876	−	0.420397i
$716$	3.80718	−	2.19808i	0.142281	−	0.0821459i
$717$	−2.51820	+	26.4979i	−0.0940441	+	0.989581i
$718$	−1.62899	−	2.82149i	−0.0607933	−	0.105297i
$719$	0.413728	−	0.716598i	0.0154294	−	0.0267246i	−0.858208	−	0.513303i	$-0.828422\pi$
$719$	0.413728	−	0.716598i	0.0154294	−	0.0267246i	0.873637	+	0.486578i	$0.161755\pi$
$720$	−2.89063	+	5.96427i	−0.107727	+	0.222275i
$721$	33.3491	−	1.41545i	1.24198	−	0.0527142i
$722$	4.85863	−	18.1326i	0.180819	−	0.674827i
$723$	4.46151	−	46.9464i	0.165925	−	1.74595i
$724$	26.8774			0.998891
$725$	0.0560141	+	0.0970193i	0.00208031	+	0.00360321i
$726$	6.56827	−	9.23264i	0.243771	−	0.342655i
$727$		−	4.04016i		−	0.149841i	−0.997190	−	0.0749206i	$-0.976130\pi$
$727$		−	4.04016i		−	0.149841i	0.997190	−	0.0749206i	$-0.0238703\pi$
$728$	−0.104755	+	9.53882i	−0.00388249	+	0.353532i
$729$	−14.5359	+	22.7532i	−0.538367	+	0.842711i
$730$	10.8701	+	10.8701i	0.402322	+	0.402322i
$731$	−9.73560	+	5.62085i	−0.360084	+	0.207895i
$732$	6.90516	−	1.16436i	0.255222	−	0.0430358i
$733$	9.79359	−	36.5502i	0.361735	−	1.35001i	−0.510059	−	0.860139i	$-0.670377\pi$
$733$	9.79359	−	36.5502i	0.361735	−	1.35001i	0.871794	−	0.489873i	$-0.162957\pi$
$734$	−19.9057	−	5.33373i	−0.734735	−	0.196872i
$735$	−23.0635	−	13.6224i	−0.850711	−	0.502468i
$736$	−3.41542	+	3.41542i	−0.125894	+	0.125894i
$737$	−15.5227	−	8.96206i	−0.571787	−	0.330122i
$738$	18.4168	−	21.2928i	0.677931	−	0.783799i
$739$	−37.6065	−	10.0766i	−1.38338	−	0.370675i	−0.511032	−	0.859562i	$-0.670737\pi$
$739$	−37.6065	−	10.0766i	−1.38338	−	0.370675i	−0.872347	+	0.488886i	$0.837403\pi$
$740$	−10.0429	−	17.3947i	−0.369183	−	0.639443i
$741$	−2.39517	+	1.77308i	−0.0879886	+	0.0651359i
$742$	−14.3820	−	3.20675i	−0.527979	−	0.117723i
$743$	−1.98573	−	7.41084i	−0.0728493	−	0.271877i	0.919888	−	0.392182i	$-0.128280\pi$
$743$	−1.98573	−	7.41084i	−0.0728493	−	0.271877i	−0.992737	+	0.120305i	$0.961613\pi$
$744$	7.58233	−	1.27854i	0.277982	−	0.0468736i
$745$			22.9787i			0.841874i
$746$	−0.364962	−	1.36206i	−0.0133622	−	0.0498685i
$747$	17.5478	+	25.8766i	0.642039	+	0.946775i
$748$	−8.54396	−	2.28935i	−0.312398	−	0.0837069i
$749$	0.671053	−	1.28527i	0.0245198	−	0.0469626i
$750$	−15.0995	+	12.4787i	−0.551357	+	0.455657i
$751$			37.2883i			1.36067i	0.732901	+	0.680335i	$0.238166\pi$
$751$			37.2883i			1.36067i	−0.732901	+	0.680335i	$0.761834\pi$
$752$	1.08788	−	4.06004i	0.0396711	−	0.148054i
$753$	−30.7414	−	11.4502i	−1.12028	−	0.417268i
$754$	−3.38719	−	0.181047i	−0.123354	−	0.00659335i
$755$		−	33.7638i		−	1.22879i
$756$	−13.7450	+	0.274505i	−0.499900	+	0.00998365i
$757$	−6.78893	+	11.7588i	−0.246748	+	0.427380i	−0.962622	−	0.270850i	$-0.912695\pi$
$757$	−6.78893	+	11.7588i	−0.246748	+	0.427380i	0.715874	+	0.698230i	$0.246029\pi$
$758$	8.16012	−	14.1337i	0.296389	−	0.513360i
$759$	7.34534	+	16.0649i	0.266619	+	0.583119i
$760$	−0.745463	−	0.745463i	−0.0270408	−	0.0270408i
$761$	−7.59946	+	2.03627i	−0.275480	+	0.0738147i	−0.393914	−	0.919147i	$-0.628879\pi$
$761$	−7.59946	+	2.03627i	−0.275480	+	0.0738147i	0.118434	+	0.992962i	$0.462213\pi$
$762$	5.61862	−	7.89777i	0.203541	−	0.286106i
$763$	−23.4532	−	5.22935i	−0.849061	−	0.189315i
$764$	−2.40736	+	4.16967i	−0.0870953	+	0.150853i
$765$	−12.1095	+	24.9857i	−0.437820	+	0.903359i
$766$	21.5248	+	12.4274i	0.777723	+	0.449019i
$767$	23.3264	+	45.8987i	0.842269	+	1.65730i
$768$	−1.33512	+	1.10338i	−0.0481771	+	0.0398148i
$769$	17.5074	−	4.69109i	0.631333	−	0.169165i	0.0710583	−	0.997472i	$-0.477362\pi$
$769$	17.5074	−	4.69109i	0.631333	−	0.169165i	0.560274	+	0.828307i	$0.310696\pi$
$770$	−2.68591	+	12.0461i	−0.0967936	+	0.434111i
$771$	−19.4917	+	16.1085i	−0.701978	+	0.580134i
$772$	0.217670	−	0.812354i	0.00783410	−	0.0292372i
$773$	−19.8144	+	19.8144i	−0.712675	+	0.712675i	−0.967094	−	0.254419i	$-0.918116\pi$
$773$	−19.8144	+	19.8144i	−0.712675	+	0.712675i	0.254419	+	0.967094i	$0.418116\pi$
$774$	7.24444	+	3.51108i	0.260396	+	0.126203i
$775$	0.510638	+	0.136825i	0.0183427	+	0.00491490i
$776$	−15.4713	+	8.93234i	−0.555386	+	0.320652i
$777$	22.6901	−	34.9418i	0.814002	−	1.25353i
$778$	2.76154	+	10.3062i	0.0990059	+	0.369495i
$779$	2.23901	+	3.87807i	0.0802207	+	0.138946i
$780$	−1.56465	−	13.7079i	−0.0560235	−	0.490823i
$781$	−6.54367	+	11.3340i	−0.234151	+	0.405561i
$782$	−14.3080	+	14.3080i	−0.511652	+	0.511652i
$783$	0.109734	−	4.88720i	0.00392156	−	0.174654i
$784$	−4.00109	−	5.74380i	−0.142896	−	0.205136i
$785$	−32.6731	+	32.6731i	−1.16615	+	1.16615i
$786$	0.941714	+	2.05961i	0.0335898	+	0.0734640i
$787$	19.7840	−	19.7840i	0.705225	−	0.705225i	−0.260303	−	0.965527i	$-0.583822\pi$
$787$	19.7840	−	19.7840i	0.705225	−	0.705225i	0.965527	+	0.260303i	$0.0838223\pi$
$788$	−13.7190	+	3.67600i	−0.488720	+	0.130952i
$789$	−10.6147	+	28.4982i	−0.377892	+	1.01456i
$790$	6.79601	+	3.92368i	0.241791	+	0.139598i
$791$	17.5982	−	0.746932i	0.625721	−	0.0265579i
$792$	2.07716	+	5.98411i	0.0738085	+	0.212636i
$793$	−10.8431	+	9.74275i	−0.385049	+	0.345975i
$794$	−17.1978	−	9.92917i	−0.610328	−	0.352373i
$795$	21.2160	+	2.01625i	0.752455	+	0.0715090i
$796$	−7.14634			−0.253295
$797$	−10.0633	−	17.4302i	−0.356462	−	0.617410i	0.630905	−	0.775860i	$-0.282684\pi$
$797$	−10.0633	−	17.4302i	−0.356462	−	0.617410i	−0.987367	+	0.158450i	$0.949350\pi$
$798$	0.675685	−	2.07974i	0.0239190	−	0.0736222i
$799$	4.55740	−	17.0084i	0.161229	−	0.601715i
$800$	−0.115023	+	0.0308202i	−0.00406667	+	0.00108966i
$801$	39.2207	−	26.5969i	1.38580	−	0.939754i
$802$	7.36643			0.260118
$803$	14.6920			0.518470
$804$	−13.3719	+	6.11402i	−0.471590	+	0.215625i
$805$	20.7925	+	19.0993i	0.732838	+	0.673162i
$806$	−11.9064	+	10.6982i	−0.419386	+	0.376828i
$807$	12.9194	+	15.6328i	0.454784	+	0.550301i
$808$	−2.10934	+	7.87215i	−0.0742062	+	0.276941i
$809$	−12.7031	+	7.33412i	−0.446616	+	0.257854i	−0.706400	−	0.707813i	$-0.749682\pi$
$809$	−12.7031	+	7.33412i	−0.446616	+	0.257854i	0.259784	+	0.965667i	$0.416349\pi$
$810$	19.6760	−	2.86515i	0.691345	−	0.100671i
$811$	−28.5937	−	28.5937i	−1.00406	−	1.00406i	−0.999992	−	0.00406780i	$-0.998705\pi$
$811$	−28.5937	−	28.5937i	−1.00406	−	1.00406i	−0.00406780	−	0.999992i	$-0.501295\pi$
$812$	2.10088	−	1.33482i	0.0737265	−	0.0468431i
$813$	−2.20585	+	23.2111i	−0.0773625	+	0.814049i
$814$	−18.5422	−	4.96838i	−0.649905	−	0.174141i
$815$		−	56.0939i		−	1.96488i
$816$	−5.59313	+	4.62231i	−0.195799	+	0.161813i
$817$	−0.905469	+	0.905469i	−0.0316783	+	0.0316783i
$818$	40.3349			1.41028
$819$	23.8606	−	15.8010i	0.833758	−	0.552130i
$820$	−20.7322			−0.724001
$821$	−9.31639	+	9.31639i	−0.325144	+	0.325144i	−0.850737	−	0.525592i	$-0.823844\pi$
$821$	−9.31639	+	9.31639i	−0.325144	+	0.325144i	0.525592	+	0.850737i	$0.323844\pi$
$822$	−22.6259	+	18.6986i	−0.789168	+	0.652189i
$823$		−	55.1345i		−	1.92187i	−0.276775	−	0.960935i	$-0.589266\pi$
$823$		−	55.1345i		−	1.92187i	0.276775	−	0.960935i	$-0.410734\pi$
$824$	−12.1862	−	3.26529i	−0.424527	−	0.113752i
$825$	−0.0412012	+	0.433540i	−0.00143444	+	0.0150939i
$826$	−33.4904	−	17.4858i	−1.16528	−	0.608407i
$827$	−38.4155	−	38.4155i	−1.33584	−	1.33584i	−0.900048	−	0.435790i	$-0.856469\pi$
$827$	−38.4155	−	38.4155i	−1.33584	−	1.33584i	−0.435790	−	0.900048i	$-0.643531\pi$
$828$	14.2310	+	2.72952i	0.494562	+	0.0948573i
$829$	18.2784	−	10.5531i	0.634836	−	0.366523i	−0.147786	−	0.989019i	$-0.547215\pi$
$829$	18.2784	−	10.5531i	0.634836	−	0.366523i	0.782623	+	0.622496i	$0.213881\pi$
$830$	5.95921	−	22.2401i	0.206847	−	0.771965i
$831$	3.30337	+	3.99717i	0.114593	+	0.138660i
$832$	1.11774	−	3.42792i	0.0387507	−	0.118842i
$833$	−16.7615	−	24.0621i	−0.580750	−	0.833702i
$834$	0.0253101	−	0.0115725i	0.000876419	−	0.000400724i
$835$	−14.9421			−0.517093
$836$	−1.00756			−0.0348473
$837$	−15.9413	−	16.6737i	−0.551013	−	0.576326i
$838$	−15.4740	+	4.14625i	−0.534541	+	0.143230i
$839$	−7.06393	+	26.3630i	−0.243874	+	0.910151i	0.730072	+	0.683370i	$0.239487\pi$
$839$	−7.06393	+	26.3630i	−0.243874	+	0.910151i	−0.973946	+	0.226780i	$0.927180\pi$
$840$	6.77462	+	7.52355i	0.233747	+	0.259587i
$841$	−14.0575	−	24.3482i	−0.484740	−	0.839595i
$842$	−19.9436			−0.687301
$843$	19.0062	+	1.80624i	0.654609	+	0.0622102i
$844$	−11.9699	−	6.91083i	−0.412021	−	0.237880i
$845$	18.0280	+	22.3577i	0.620183	+	0.769127i
$846$	−11.9125	+	4.13498i	−0.409562	+	0.142164i
$847$	−9.28177	−	14.6086i	−0.318925	−	0.501957i
$848$	4.82321	+	2.78468i	0.165630	+	0.0956263i
$849$	−3.37399	+	9.05846i	−0.115795	+	0.310885i
$850$	−0.481856	+	0.129113i	−0.0165275	+	0.00442854i
$851$	−31.0514	+	31.0514i	−1.06443	+	1.06443i
$852$	4.46417	+	9.76353i	0.152940	+	0.334493i
$853$	8.20742	−	8.20742i	0.281017	−	0.281017i	−0.552498	−	0.833514i	$-0.686325\pi$
$853$	8.20742	−	8.20742i	0.281017	−	0.281017i	0.833514	+	0.552498i	$0.186325\pi$
$854$	2.32788	−	10.4403i	0.0796584	−	0.357261i
$855$	−0.595754	+	3.10611i	−0.0203744	+	0.106227i
$856$	−0.387503	+	0.387503i	−0.0132446	+	0.0132446i
$857$	−17.4389	+	30.2051i	−0.595702	+	1.03179i	0.397745	+	0.917496i	$0.369793\pi$
$857$	−17.4389	+	30.2051i	−0.595702	+	1.03179i	−0.993447	+	0.114290i	$0.963541\pi$
$858$	−10.3212	−	8.20639i	−0.352359	−	0.280162i
$859$	−11.1504	−	19.3130i	−0.380445	−	0.658950i	0.610681	−	0.791877i	$-0.290896\pi$
$859$	−11.1504	−	19.3130i	−0.380445	−	0.658950i	−0.991126	+	0.132927i	$0.957563\pi$
$860$	−1.53442	−	5.72655i	−0.0523234	−	0.195274i
$861$	−19.5243	−	38.3159i	−0.665387	−	1.30580i
$862$	−27.4412	+	15.8432i	−0.934652	+	0.539622i
$863$	36.9321	+	9.89593i	1.25718	+	0.336861i	0.825107	−	0.564976i	$-0.191115\pi$
$863$	36.9321	+	9.89593i	1.25718	+	0.336861i	0.432076	+	0.901837i	$0.357781\pi$
$864$	4.98764	+	1.45719i	0.169683	+	0.0495746i
$865$	10.4885	−	10.4885i	0.356620	−	0.356620i
$866$	−7.12787	+	26.6016i	−0.242215	+	0.903959i
$867$	−0.733811	+	0.606442i	−0.0249215	+	0.0205958i
$868$	2.55617	−	11.4642i	0.0867620	−	0.389120i
$869$	7.24433	−	1.94111i	0.245747	−	0.0658478i
$870$	−2.77498	+	2.29332i	−0.0940806	+	0.0777507i
$871$	16.6967	−	25.6523i	0.565747	−	0.869193i
$872$	7.86536	+	4.54107i	0.266355	+	0.153780i
$873$	48.2283	+	23.3742i	1.63228	+	0.791097i
$874$	−1.15244	+	1.99609i	−0.0389820	+	0.0675188i
$875$	8.96306	+	28.5481i	0.303007	+	0.965102i
$876$	6.98644	−	9.82044i	0.236050	−	0.331802i
$877$	−32.0340	+	8.58349i	−1.08171	+	0.289844i	−0.755297	−	0.655383i	$-0.772507\pi$
$877$	−32.0340	+	8.58349i	−1.08171	+	0.289844i	−0.326415	+	0.945227i	$0.605841\pi$
$878$	1.31390	+	1.31390i	0.0443421	+	0.0443421i
$879$	12.4749	+	27.2838i	0.420769	+	0.920260i
$880$	2.33240	−	4.03983i	0.0786251	−	0.136183i
$881$	14.7724	−	25.5866i	0.497695	−	0.862034i	−0.502301	−	0.864693i	$-0.667513\pi$
$881$	14.7724	−	25.5866i	0.497695	−	0.862034i	0.999996	+	0.00265902i	$0.000846393\pi$
$882$	−7.52461	+	19.6056i	−0.253367	+	0.660155i
$883$		−	35.1158i		−	1.18174i	−0.806767	−	0.590870i	$-0.798785\pi$
$883$		−	35.1158i		−	1.18174i	0.806767	−	0.590870i	$-0.201215\pi$
$884$	4.68247	−	14.3603i	0.157489	−	0.482991i
$885$	51.2057	+	19.0725i	1.72126	+	0.641114i
$886$	8.12366	−	30.3179i	0.272920	−	1.01855i
$887$			27.6100i			0.927053i	0.886083	+	0.463527i	$0.153416\pi$
$887$			27.6100i			0.927053i	−0.886083	+	0.463527i	$0.846584\pi$
$888$	−12.1383	+	10.0314i	−0.407334	+	0.336632i
$889$	−7.93979	−	12.4965i	−0.266292	−	0.419118i
$890$	−33.7090	−	9.03229i	−1.12993	−	0.302763i
$891$	11.3607	−	15.2332i	0.380598	−	0.510333i
$892$	1.08196	+	4.03794i	0.0362268	+	0.135200i
$893$		−	2.00575i		−	0.0671198i
$894$	17.7642	−	2.99543i	0.594125	−	0.100182i
$895$	2.51374	+	9.38139i	0.0840249	+	0.313585i
$896$	0.792526	+	2.52426i	0.0264764	+	0.0843297i
$897$	−28.0630	+	11.0609i	−0.936998	+	0.369314i
$898$	−2.47085	−	4.27963i	−0.0824532	−	0.142813i
$899$	4.03424	+	1.08097i	0.134549	+	0.0360524i
$900$	0.270195	+	0.233700i	0.00900650	+	0.00778999i
$901$	20.2055	+	11.6657i	0.673143	+	0.388639i
$902$	−14.0108	+	14.0108i	−0.466508	+	0.466508i
$903$	9.13841	−	8.22873i	0.304107	−	0.273835i
$904$	−6.43065	−	1.72309i	−0.213880	−	0.0573090i
$905$	−15.3686	+	57.3564i	−0.510870	+	1.90659i
$906$	−26.1020	+	4.40134i	−0.867180	+	0.146225i
$907$	−48.3711	+	27.9271i	−1.60614	+	0.927304i	−0.615914	+	0.787813i	$0.711213\pi$
$907$	−48.3711	+	27.9271i	−1.60614	+	0.927304i	−0.990223	+	0.139491i	$0.955453\pi$
$908$	7.99215	+	7.99215i	0.265229	+	0.265229i
$909$	23.0976	−	8.01746i	0.766100	−	0.265922i
$910$	−20.2959	−	5.67788i	−0.672804	−	0.188220i
$911$		−	15.1436i		−	0.501729i	−0.968022	−	0.250864i	$-0.919285\pi$
$911$		−	15.1436i		−	0.501729i	0.968022	−	0.250864i	$-0.0807148\pi$
$912$	−0.479123	+	0.673475i	−0.0158653	+	0.0223010i
$913$	−11.0026	−	19.0570i	−0.364132	−	0.630694i
$914$	−2.04587			−0.0676715
$915$	−1.46366	+	15.4014i	−0.0483871	+	0.509154i
$916$	0.512008	−	1.91084i	0.0169172	−	0.0631359i
$917$	3.45626	−	0.146696i	0.114136	−	0.00484434i
$918$	20.8944	+	6.10450i	0.689617	+	0.201479i
$919$	1.33990	−	2.32077i	0.0441991	−	0.0765552i	−0.843079	−	0.537789i	$-0.819260\pi$
$919$	1.33990	−	2.32077i	0.0441991	−	0.0765552i	0.887279	+	0.461234i	$0.152593\pi$
$920$	−5.33556	−	9.24147i	−0.175908	−	0.304682i
$921$	−1.09210	+	11.4916i	−0.0359858	+	0.378661i
$922$	33.0175	−	19.0626i	1.08737	−	0.627795i
$923$	−18.7301	−	12.1912i	−0.616507	−	0.401277i
$924$	9.66265	+	0.506123i	0.317878	+	0.0166502i
$925$	−1.04573	+	0.280203i	−0.0343834	+	0.00921301i
$926$			19.2973i			0.634149i
$927$	12.4112	+	35.7555i	0.407636	+	1.17437i
$928$	−0.908723	+	0.243492i	−0.0298303	+	0.00799300i
$929$	−5.75319	−	21.4712i	−0.188756	−	0.704447i	−0.993795	−	0.111225i	$-0.964523\pi$
$929$	−5.75319	−	21.4712i	−0.188756	−	0.704447i	0.805039	−	0.593221i	$-0.202144\pi$
$930$	−1.60720	+	16.9118i	−0.0527020	+	0.554559i
$931$	−2.55361	−	2.15333i	−0.0836911	−	0.0705725i
$932$	14.4933	−	8.36770i	0.474743	−	0.274093i
$933$	−4.99858	−	29.6439i	−0.163646	−	0.970496i
$934$	9.52877	+	2.55323i	0.311791	+	0.0835441i
$935$	9.77094	−	16.9238i	0.319544	−	0.553466i
$936$	−10.3933	+	2.99652i	−0.339716	+	0.0979442i
$937$	−51.8315			−1.69326			−0.846631	−	0.532180i	$-0.821373\pi$
$937$	−51.8315			−1.69326			−0.846631	+	0.532180i	$0.821373\pi$
$938$	0.952415	+	22.4396i	0.0310975	+	0.732677i
$939$	2.27537	+	0.847502i	0.0742538	+	0.0276572i
$940$	8.04207	+	4.64309i	0.262304	+	0.151441i
$941$	4.80156	+	17.9196i	0.156526	+	0.584164i	0.998970	+	0.0453793i	$0.0144496\pi$
$941$	4.80156	+	17.9196i	0.156526	+	0.584164i	−0.842444	+	0.538785i	$0.818884\pi$
$942$	29.5179	+	20.9996i	0.961745	+	0.684203i
$943$	11.7314	+	43.7823i	0.382028	+	1.42575i
$944$	10.0972	+	10.0972i	0.328637	+	0.328637i
$945$	7.27364	−	29.4888i	0.236612	−	0.959270i
$946$	−4.90694	−	2.83302i	−0.159538	−	0.0921095i
$947$	−6.47922	−	6.47922i	−0.210546	−	0.210546i	0.593953	−	0.804500i	$-0.297566\pi$
$947$	−6.47922	−	6.47922i	−0.210546	−	0.210546i	−0.804500	+	0.593953i	$0.797566\pi$
$948$	2.14739	−	5.76531i	0.0697441	−	0.187249i
$949$	−1.33907	+	25.0525i	−0.0434681	+	0.813240i
$950$	−0.0492108	+	0.0284119i	−0.00159661	+	0.000921803i
$951$	40.3476	−	18.4481i	1.30836	−	0.598220i
$952$	3.32007	+	10.5747i	0.107604	+	0.342728i
$953$	−17.2880	−	29.9437i	−0.560013	−	0.969972i	−0.997495	−	0.0707440i	$-0.977463\pi$
$953$	−17.2880	−	29.9437i	−0.560013	−	0.969972i	0.437481	−	0.899228i	$-0.355871\pi$
$954$	−1.20694	−	16.6644i	−0.0390763	−	0.539531i
$955$	−7.52155	−	7.52155i	−0.243392	−	0.243392i
$956$	−10.8665	−	10.8665i	−0.351446	−	0.351446i
$957$	−0.325505	+	3.42514i	−0.0105221	+	0.110719i
$958$	7.84311	+	13.5847i	0.253399	+	0.438901i
$959$	13.4307	+	42.7778i	0.433699	+	1.38137i
$960$	−1.59119	−	3.48007i	−0.0513554	−	0.112319i
$961$	−9.77847	+	5.64560i	−0.315435	+	0.182116i
$962$	10.1620	−	31.1650i	0.327635	−	1.00480i
$963$	1.61461	+	0.309682i	0.0520299	+	0.00997938i
$964$	19.2521	+	19.2521i	0.620069	+	0.620069i
$965$	1.60910	+	0.929014i	0.0517987	+	0.0299060i
$966$	12.0548	−	18.5639i	0.387856	−	0.597283i
$967$	9.72642	+	9.72642i	0.312781	+	0.312781i	0.845986	−	0.533205i	$-0.179013\pi$
$967$	9.72642	+	9.72642i	0.312781	+	0.312781i	−0.533205	+	0.845986i	$0.679013\pi$
$968$	1.69313	+	6.31885i	0.0544193	+	0.203096i
$969$	−2.00715	+	2.82134i	−0.0644790	+	0.0906345i
$970$	−10.2151	−	38.1233i	−0.327987	−	1.22406i
$971$	−7.96758	−	4.60009i	−0.255692	−	0.147624i	0.366676	−	0.930349i	$-0.380496\pi$
$971$	−7.96758	−	4.60009i	−0.255692	−	0.147624i	−0.622368	+	0.782725i	$0.713829\pi$
$972$	−4.77988	−	14.8375i	−0.153315	−	0.475914i
$973$	−0.00180272	−	0.0424733i	−5.77925e−5	−	0.00136163i
$974$	−36.5092			−1.16983
$975$	−0.735510	−	0.109770i	−0.0235552	−	0.00351544i
$976$	−2.02149	+	3.50132i	−0.0647062	+	0.112074i
$977$	43.9572	+	11.7783i	1.40631	+	0.376821i	0.880608	−	0.473845i	$-0.157134\pi$
$977$	43.9572	+	11.7783i	1.40631	+	0.376821i	0.525706	+	0.850666i	$0.323801\pi$
$978$	−43.3648	+	7.31222i	−1.38665	+	0.233819i
$979$	−28.8844	+	16.6764i	−0.923149	+	0.532980i
$980$	14.5451	−	5.25400i	0.464627	−	0.167833i
$981$	−1.96820	−	27.1752i	−0.0628399	−	0.867638i
$982$	8.41966	+	31.4226i	0.268682	+	1.00274i
$983$	−1.51625	+	0.406277i	−0.0483607	+	0.0129582i	−0.282918	−	0.959144i	$-0.591303\pi$
$983$	−1.51625	+	0.406277i	−0.0483607	+	0.0129582i	0.234558	+	0.972102i	$0.424636\pi$
$984$	2.70259	+	16.0276i	0.0861554	+	0.510940i
$985$		−	31.3784i		−	0.999798i
$986$	−3.80685	+	1.02004i	−0.121235	+	0.0324847i
$987$	−1.00754	+	19.2354i	−0.0320703	+	0.612270i
$988$	0.0918320	−	1.71808i	0.00292157	−	0.0546593i
$989$	−11.2251	+	6.48079i	−0.356936	+	0.206077i
$990$	−13.9578	+	1.01091i	−0.443609	+	0.0321290i
$991$	−3.97292	−	6.88130i	−0.126204	−	0.218592i	0.795999	−	0.605298i	$-0.206946\pi$
$991$	−3.97292	−	6.88130i	−0.126204	−	0.218592i	−0.922203	+	0.386706i	$0.873613\pi$
$992$	−2.21973	+	3.84468i	−0.0704765	+	0.122069i
$993$	−4.52420	+	6.35940i	−0.143571	+	0.201810i
$994$	16.3843	−	0.695408i	0.519678	−	0.0220570i
$995$	4.08630	−	15.2503i	0.129545	−	0.483467i
$996$	−17.9701	−	1.70777i	−0.569404	−	0.0541128i
$997$	57.2142			1.81199			0.905996	−	0.423287i	$-0.139124\pi$
$997$	57.2142			1.81199			0.905996	+	0.423287i	$0.139124\pi$
$998$	−17.1398	−	29.6871i	−0.542552	−	0.939728i
$999$	45.3453	+	13.2481i	1.43466	+	0.419151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.5	yes	152
3.2	odd	2	inner	546.2.ch.a.137.36	yes	152
7.2	even	3		546.2.bw.a.527.28	yes	152
13.2	odd	12		546.2.bw.a.431.9	✓	152
21.2	odd	6		546.2.bw.a.527.9	yes	152
39.2	even	12		546.2.bw.a.431.28	yes	152
91.2	odd	12	inner	546.2.ch.a.275.36	yes	152
273.2	even	12	inner	546.2.ch.a.275.5	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.9	✓	152	13.2	odd	12
546.2.bw.a.431.28	yes	152	39.2	even	12
546.2.bw.a.527.9	yes	152	21.2	odd	6
546.2.bw.a.527.28	yes	152	7.2	even	3
546.2.ch.a.137.5	yes	152	1.1	even	1	trivial
546.2.ch.a.137.36	yes	152	3.2	odd	2	inner
546.2.ch.a.275.5	yes	152	273.2	even	12	inner
546.2.ch.a.275.36	yes	152	91.2	odd	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33512 + 1.10338i) q^{3} -1.00000i q^{4} +(2.13400 + 0.571804i) q^{5} +(0.163866 - 1.72428i) q^{6} +(-2.34532 - 1.22452i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.565101 - 2.94630i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33512 + 1.10338i) q^{3} -1.00000i q^{4} +(2.13400 + 0.571804i) q^{5} +(0.163866 - 1.72428i) q^{6} +(-2.34532 - 1.22452i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.565101 - 2.94630i) q^{9} +(-1.91329 + 1.10464i) q^{10} +(-0.546485 + 2.03951i) q^{11} +(1.10338 + 1.33512i) q^{12} +(-3.42792 - 1.11774i) q^{13} +(2.52426 - 0.792526i) q^{14} +(-3.48007 + 1.59119i) q^{15} -1.00000 q^{16} -4.18923 q^{17} +(1.68376 + 2.48293i) q^{18} +(-0.460929 + 0.123506i) q^{19} +(0.571804 - 2.13400i) q^{20} +(4.48241 - 0.952898i) q^{21} +(-1.05573 - 1.82857i) q^{22} -4.83014 q^{23} +(-1.72428 - 0.163866i) q^{24} +(-0.103127 - 0.0595401i) q^{25} +(3.21427 - 1.63354i) q^{26} +(2.49641 + 4.55719i) q^{27} +(-1.22452 + 2.34532i) q^{28} +(-0.814739 - 0.470390i) q^{29} +(1.33564 - 3.58592i) q^{30} +(-4.28819 + 1.14902i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.52073 - 3.32597i) q^{33} +(2.96223 - 2.96223i) q^{34} +(-4.30474 - 3.95420i) q^{35} +(-2.94630 - 0.565101i) q^{36} +(6.42867 - 6.42867i) q^{37} +(0.238594 - 0.413257i) q^{38} +(5.80999 - 2.28998i) q^{39} +(1.10464 + 1.91329i) q^{40} +(-2.42880 - 9.06440i) q^{41} +(-2.49574 + 3.84334i) q^{42} +(2.32396 - 1.34174i) q^{43} +(2.03951 + 0.546485i) q^{44} +(2.89063 - 5.96427i) q^{45} +(3.41542 - 3.41542i) q^{46} +(-1.08788 + 4.06004i) q^{47} +(1.33512 - 1.10338i) q^{48} +(4.00109 + 5.74380i) q^{49} +(0.115023 - 0.0308202i) q^{50} +(5.59313 - 4.62231i) q^{51} +(-1.11774 + 3.42792i) q^{52} +(-4.82321 - 2.78468i) q^{53} +(-4.98764 - 1.45719i) q^{54} +(-2.33240 + 4.03983i) q^{55} +(-0.792526 - 2.52426i) q^{56} +(0.479123 - 0.673475i) q^{57} +(0.908723 - 0.243492i) q^{58} +(-10.0972 - 10.0972i) q^{59} +(1.59119 + 3.48007i) q^{60} +(2.02149 - 3.50132i) q^{61} +(2.21973 - 3.84468i) q^{62} +(-4.93315 + 6.21804i) q^{63} +1.00000i q^{64} +(-6.67606 - 4.34536i) q^{65} +(3.42714 + 1.27650i) q^{66} +(-2.19711 + 8.19973i) q^{67} +4.18923i q^{68} +(6.44882 - 5.32948i) q^{69} +(5.83995 - 0.247868i) q^{70} +(5.98706 + 1.60423i) q^{71} +(2.48293 - 1.68376i) q^{72} +(-1.80093 - 6.72115i) q^{73} +9.09152i q^{74} +(0.203382 - 0.0342945i) q^{75} +(0.123506 + 0.460929i) q^{76} +(3.77911 - 4.11413i) q^{77} +(-2.48902 + 5.72755i) q^{78} +(-1.77600 - 3.07612i) q^{79} +(-2.13400 - 0.571804i) q^{80} +(-8.36132 - 3.32991i) q^{81} +(8.12692 + 4.69208i) q^{82} +(-7.36931 + 7.36931i) q^{83} +(-0.952898 - 4.48241i) q^{84} +(-8.93981 - 2.39542i) q^{85} +(-0.694536 + 2.59204i) q^{86} +(1.60679 - 0.270940i) q^{87} +(-1.82857 + 1.05573i) q^{88} +(11.1696 + 11.1696i) q^{89} +(2.17339 + 6.26136i) q^{90} +(6.67089 + 6.81904i) q^{91} +4.83014i q^{92} +(4.45745 - 6.26558i) q^{93} +(-2.10163 - 3.64013i) q^{94} -1.05424 q^{95} +(-0.163866 + 1.72428i) q^{96} +(-4.62372 + 17.2560i) q^{97} +(-6.89068 - 1.23229i) q^{98} +(5.70018 + 2.76263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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