LMFDB - Embedded newform 96.2.n.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, 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:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	96.13
Dual form			96.2.n.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40823 + 0.129991i) q^{2} +(-0.382683 + 0.923880i) q^{3} +(1.96620 + 0.366115i) q^{4} +(-2.51374 + 1.04122i) q^{5} +(-0.659001 + 1.25129i) q^{6} +(2.01027 - 2.01027i) q^{7} +(2.72127 + 0.771162i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(1.40823 + 0.129991i) q^{2} +(-0.382683 + 0.923880i) q^{3} +(1.96620 + 0.366115i) q^{4} +(-2.51374 + 1.04122i) q^{5} +(-0.659001 + 1.25129i) q^{6} +(2.01027 - 2.01027i) q^{7} +(2.72127 + 0.771162i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.67526 + 1.13951i) q^{10} +(-1.32741 - 3.20465i) q^{11} +(-1.09068 + 1.67643i) q^{12} +(-5.55375 - 2.30044i) q^{13} +(3.09223 - 2.56960i) q^{14} -2.72085i q^{15} +(3.73192 + 1.43971i) q^{16} +4.16447i q^{17} +(-0.903849 - 1.08768i) q^{18} +(4.49866 + 1.86340i) q^{19} +(-5.32373 + 1.12694i) q^{20} +(1.08795 + 2.62654i) q^{21} +(-1.45272 - 4.68542i) q^{22} +(-1.94282 - 1.94282i) q^{23} +(-1.75385 + 2.21901i) q^{24} +(1.69919 - 1.69919i) q^{25} +(-7.52191 - 3.96148i) q^{26} +(0.923880 - 0.382683i) q^{27} +(4.68859 - 3.21661i) q^{28} +(-1.96103 + 4.73434i) q^{29} +(0.353687 - 3.83157i) q^{30} -2.87015 q^{31} +(5.06824 + 2.51256i) q^{32} +3.46869 q^{33} +(-0.541346 + 5.86452i) q^{34} +(-2.96015 + 7.14642i) q^{35} +(-1.13143 - 1.64920i) q^{36} +(6.31049 - 2.61389i) q^{37} +(6.09290 + 3.20888i) q^{38} +(4.25066 - 4.25066i) q^{39} +(-7.64351 + 0.894952i) q^{40} +(0.756366 + 0.756366i) q^{41} +(1.19065 + 3.84019i) q^{42} +(1.53775 + 3.71245i) q^{43} +(-1.43669 - 6.78698i) q^{44} +(2.51374 + 1.04122i) q^{45} +(-2.48338 - 2.98848i) q^{46} +1.08220i q^{47} +(-2.75826 + 2.89689i) q^{48} -1.08236i q^{49} +(2.61372 - 2.17196i) q^{50} +(-3.84747 - 1.59367i) q^{51} +(-10.0776 - 6.55645i) q^{52} +(-2.90450 - 7.01208i) q^{53} +(1.35078 - 0.418809i) q^{54} +(6.67351 + 6.67351i) q^{55} +(7.02073 - 3.92024i) q^{56} +(-3.44312 + 3.44312i) q^{57} +(-3.37700 + 6.41211i) q^{58} +(10.3425 - 4.28402i) q^{59} +(0.996142 - 5.34974i) q^{60} +(-2.97711 + 7.18739i) q^{61} +(-4.04183 - 0.373095i) q^{62} -2.84295 q^{63} +(6.81062 + 4.19708i) q^{64} +16.3559 q^{65} +(4.88470 + 0.450899i) q^{66} +(-3.88805 + 9.38659i) q^{67} +(-1.52467 + 8.18820i) q^{68} +(2.53841 - 1.05145i) q^{69} +(-5.09753 + 9.67899i) q^{70} +(-1.88924 + 1.88924i) q^{71} +(-1.37893 - 2.46952i) q^{72} +(-7.00727 - 7.00727i) q^{73} +(9.22638 - 2.86064i) q^{74} +(0.919594 + 2.22010i) q^{75} +(8.16306 + 5.31086i) q^{76} +(-9.11066 - 3.77376i) q^{77} +(6.53844 - 5.43334i) q^{78} -11.0255i q^{79} +(-10.8801 + 0.266706i) q^{80} +1.00000i q^{81} +(0.966814 + 1.16346i) q^{82} +(-2.30515 - 0.954824i) q^{83} +(1.17752 + 5.56263i) q^{84} +(-4.33615 - 10.4684i) q^{85} +(1.68291 + 5.42786i) q^{86} +(-3.62351 - 3.62351i) q^{87} +(-1.14093 - 9.74436i) q^{88} +(7.65800 - 7.65800i) q^{89} +(3.40456 + 1.79304i) q^{90} +(-15.7890 + 6.54003i) q^{91} +(-3.10868 - 4.53127i) q^{92} +(1.09836 - 2.65168i) q^{93} +(-0.140676 + 1.52398i) q^{94} -13.2487 q^{95} +(-4.26083 + 3.72093i) q^{96} -11.3029 q^{97} +(0.140697 - 1.52421i) q^{98} +(-1.32741 + 3.20465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	1.40823	+	0.129991i	0.995767	+	0.0919178i
$2$	1.40823	+	0.129991i	0.995767	+	0.0919178i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$	1.96620	+	0.366115i	0.983102	+	0.183057i
$5$	−2.51374	+	1.04122i	−1.12418	+	0.465649i	−0.865798	−	0.500394i	$-0.833188\pi$
$5$	−2.51374	+	1.04122i	−1.12418	+	0.465649i	−0.258379	+	0.966044i	$0.583188\pi$
$6$	−0.659001	+	1.25129i	−0.269036	+	0.510835i
$7$	2.01027	−	2.01027i	0.759810	−	0.759810i	−0.216477	−	0.976288i	$-0.569457\pi$
$7$	2.01027	−	2.01027i	0.759810	−	0.759810i	0.976288	+	0.216477i	$0.0694568\pi$
$8$	2.72127	+	0.771162i	0.962114	+	0.272647i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−3.67526	+	1.13951i	−1.16222	+	0.360346i
$11$	−1.32741	−	3.20465i	−0.400229	−	0.966238i	−0.987610	−	0.156928i	$-0.949841\pi$
$11$	−1.32741	−	3.20465i	−0.400229	−	0.966238i	0.587381	−	0.809310i	$-0.300159\pi$
$12$	−1.09068	+	1.67643i	−0.314852	+	0.483944i
$13$	−5.55375	−	2.30044i	−1.54033	−	0.638027i	−0.558798	−	0.829304i	$-0.688737\pi$
$13$	−5.55375	−	2.30044i	−1.54033	−	0.638027i	−0.981536	+	0.191277i	$0.938737\pi$
$14$	3.09223	−	2.56960i	0.826434	−	0.686753i
$15$		−	2.72085i		−	0.702520i
$16$	3.73192	+	1.43971i	0.932980	+	0.359928i
$17$			4.16447i			1.01003i	0.863110	+	0.505016i	$0.168514\pi$
$17$			4.16447i			1.01003i	−0.863110	+	0.505016i	$0.831486\pi$
$18$	−0.903849	−	1.08768i	−0.213039	−	0.256370i
$19$	4.49866	+	1.86340i	1.03206	+	0.427494i	0.833456	−	0.552585i	$-0.186359\pi$
$19$	4.49866	+	1.86340i	1.03206	+	0.427494i	0.198606	+	0.980079i	$0.436359\pi$
$20$	−5.32373	+	1.12694i	−1.19042	+	0.251992i
$21$	1.08795	+	2.62654i	0.237410	+	0.573159i
$22$	−1.45272	−	4.68542i	−0.309720	−	0.998936i
$23$	−1.94282	−	1.94282i	−0.405106	−	0.405106i	0.474922	−	0.880028i	$-0.342476\pi$
$23$	−1.94282	−	1.94282i	−0.405106	−	0.405106i	−0.880028	+	0.474922i	$0.842476\pi$
$24$	−1.75385	+	2.21901i	−0.358002	+	0.452954i
$25$	1.69919	−	1.69919i	0.339838	−	0.339838i
$26$	−7.52191	−	3.96148i	−1.47517	−	0.776910i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	4.68859	−	3.21661i	0.886060	−	0.607882i
$29$	−1.96103	+	4.73434i	−0.364154	+	0.879145i	0.630530	+	0.776165i	$0.282838\pi$
$29$	−1.96103	+	4.73434i	−0.364154	+	0.879145i	−0.994683	+	0.102980i	$0.967162\pi$
$30$	0.353687	−	3.83157i	0.0645741	−	0.699546i
$31$	−2.87015			−0.515495			−0.257747	−	0.966212i	$-0.582980\pi$
$31$	−2.87015			−0.515495			−0.257747	+	0.966212i	$0.582980\pi$
$32$	5.06824	+	2.51256i	0.895947	+	0.444162i
$33$	3.46869			0.603821
$34$	−0.541346	+	5.86452i	−0.0928400	+	1.00576i
$35$	−2.96015	+	7.14642i	−0.500356	+	1.20797i
$36$	−1.13143	−	1.64920i	−0.188572	−	0.274866i
$37$	6.31049	−	2.61389i	1.03744	−	0.429721i	0.202046	−	0.979376i	$-0.435241\pi$
$37$	6.31049	−	2.61389i	1.03744	−	0.429721i	0.835392	+	0.549655i	$0.185241\pi$
$38$	6.09290	+	3.20888i	0.988399	+	0.520549i
$39$	4.25066	−	4.25066i	0.680650	−	0.680650i
$40$	−7.64351	+	0.894952i	−1.20854	+	0.141504i
$41$	0.756366	+	0.756366i	0.118125	+	0.118125i	0.763698	−	0.645574i	$-0.223382\pi$
$41$	0.756366	+	0.756366i	0.118125	+	0.118125i	−0.645574	+	0.763698i	$0.723382\pi$
$42$	1.19065	+	3.84019i	0.183722	+	0.592554i
$43$	1.53775	+	3.71245i	0.234504	+	0.566143i	0.996697	−	0.0812067i	$-0.0258774\pi$
$43$	1.53775	+	3.71245i	0.234504	+	0.566143i	−0.762193	+	0.647350i	$0.775877\pi$
$44$	−1.43669	−	6.78698i	−0.216589	−	1.02318i
$45$	2.51374	+	1.04122i	0.374726	+	0.155216i
$46$	−2.48338	−	2.98848i	−0.366154	−	0.440627i
$47$			1.08220i			0.157855i	0.996880	+	0.0789273i	$0.0251495\pi$
$47$			1.08220i			0.157855i	−0.996880	+	0.0789273i	$0.974851\pi$
$48$	−2.75826	+	2.89689i	−0.398121	+	0.418130i
$49$		−	1.08236i		−	0.154623i
$50$	2.61372	−	2.17196i	0.369636	−	0.307162i
$51$	−3.84747	−	1.59367i	−0.538754	−	0.223159i
$52$	−10.0776	−	6.55645i	−1.39751	−	0.909215i
$53$	−2.90450	−	7.01208i	−0.398963	−	0.963183i	−0.987912	−	0.155013i	$-0.950458\pi$
$53$	−2.90450	−	7.01208i	−0.398963	−	0.963183i	0.588949	−	0.808170i	$-0.299542\pi$
$54$	1.35078	−	0.418809i	0.183818	−	0.0569926i
$55$	6.67351	+	6.67351i	0.899856	+	0.899856i
$56$	7.02073	−	3.92024i	0.938184	−	0.523864i
$57$	−3.44312	+	3.44312i	−0.456053	+	0.456053i
$58$	−3.37700	+	6.41211i	−0.443421	+	0.841951i
$59$	10.3425	−	4.28402i	1.34648	−	0.557732i	0.411172	−	0.911558i	$-0.365120\pi$
$59$	10.3425	−	4.28402i	1.34648	−	0.557732i	0.935311	+	0.353826i	$0.115120\pi$
$60$	0.996142	−	5.34974i	0.128601	−	0.690649i
$61$	−2.97711	+	7.18739i	−0.381180	+	0.920251i	0.610558	+	0.791972i	$0.290945\pi$
$61$	−2.97711	+	7.18739i	−0.381180	+	0.920251i	−0.991738	+	0.128279i	$0.959055\pi$
$62$	−4.04183	−	0.373095i	−0.513312	−	0.0473831i
$63$	−2.84295			−0.358178
$64$	6.81062	+	4.19708i	0.851327	+	0.524635i
$65$	16.3559			2.02870
$66$	4.88470	+	0.450899i	0.601265	+	0.0555019i
$67$	−3.88805	+	9.38659i	−0.475001	+	1.14676i	0.486924	+	0.873444i	$0.338119\pi$
$67$	−3.88805	+	9.38659i	−0.475001	+	1.14676i	−0.961926	+	0.273311i	$0.911881\pi$
$68$	−1.52467	+	8.18820i	−0.184894	+	0.992966i
$69$	2.53841	−	1.05145i	0.305589	−	0.126579i
$70$	−5.09753	+	9.67899i	−0.609271	+	1.15686i
$71$	−1.88924	+	1.88924i	−0.224211	+	0.224211i	−0.810269	−	0.586058i	$-0.800679\pi$
$71$	−1.88924	+	1.88924i	−0.224211	+	0.224211i	0.586058	+	0.810269i	$0.300679\pi$
$72$	−1.37893	−	2.46952i	−0.162509	−	0.291036i
$73$	−7.00727	−	7.00727i	−0.820139	−	0.820139i	0.165989	−	0.986128i	$-0.446918\pi$
$73$	−7.00727	−	7.00727i	−0.820139	−	0.820139i	−0.986128	+	0.165989i	$0.946918\pi$
$74$	9.22638	−	2.86064i	1.07255	−	0.332543i
$75$	0.919594	+	2.22010i	0.106186	+	0.256355i
$76$	8.16306	+	5.31086i	0.936367	+	0.609197i
$77$	−9.11066	−	3.77376i	−1.03826	−	0.430060i
$78$	6.53844	−	5.43334i	0.740333	−	0.615205i
$79$		−	11.0255i		−	1.24047i	−0.784417	−	0.620234i	$-0.787038\pi$
$79$		−	11.0255i		−	1.24047i	0.784417	−	0.620234i	$-0.212962\pi$
$80$	−10.8801	+	0.266706i	−1.21643	+	0.0298186i
$81$			1.00000i			0.111111i
$82$	0.966814	+	1.16346i	0.106767	+	0.128482i
$83$	−2.30515	−	0.954824i	−0.253023	−	0.104806i	0.252567	−	0.967579i	$-0.418725\pi$
$83$	−2.30515	−	0.954824i	−0.253023	−	0.104806i	−0.505590	+	0.862774i	$0.668725\pi$
$84$	1.17752	+	5.56263i	0.128477	+	0.606933i
$85$	−4.33615	−	10.4684i	−0.470321	−	1.13546i
$86$	1.68291	+	5.42786i	0.181473	+	0.585301i
$87$	−3.62351	−	3.62351i	−0.388481	−	0.388481i
$88$	−1.14093	−	9.74436i	−0.121624	−	1.03875i
$89$	7.65800	−	7.65800i	0.811747	−	0.811747i	−0.173149	−	0.984896i	$-0.555394\pi$
$89$	7.65800	−	7.65800i	0.811747	−	0.811747i	0.984896	+	0.173149i	$0.0553943\pi$
$90$	3.40456	+	1.79304i	0.358872	+	0.189003i
$91$	−15.7890	+	6.54003i	−1.65514	+	0.685582i
$92$	−3.10868	−	4.53127i	−0.324103	−	0.472418i
$93$	1.09836	−	2.65168i	0.113895	−	0.274966i
$94$	−0.140676	+	1.52398i	−0.0145096	+	0.157186i
$95$	−13.2487			−1.35928
$96$	−4.26083	+	3.72093i	−0.434869	+	0.379766i
$97$	−11.3029			−1.14764			−0.573819	−	0.818982i	$-0.694539\pi$
$97$	−11.3029			−1.14764			−0.573819	+	0.818982i	$0.694539\pi$
$98$	0.140697	−	1.52421i	0.0142126	−	0.153968i
$99$	−1.32741	+	3.20465i	−0.133410	+	0.322079i
$100$	3.96305	−	2.71885i	0.396305	−	0.271885i
$101$	3.56392	−	1.47622i	0.354623	−	0.146890i	−0.198258	−	0.980150i	$-0.563528\pi$
$101$	3.56392	−	1.47622i	0.354623	−	0.146890i	0.552881	+	0.833260i	$0.313528\pi$
$102$	−5.21095	−	2.74439i	−0.515961	−	0.271735i
$103$	−1.94329	+	1.94329i	−0.191478	+	0.191478i	−0.796335	−	0.604856i	$-0.793231\pi$
$103$	−1.94329	+	1.94329i	−0.191478	+	0.191478i	0.604856	+	0.796335i	$0.293231\pi$
$104$	−13.3392	−	10.5430i	−1.30802	−	1.03382i
$105$	−5.46964	−	5.46964i	−0.533782	−	0.533782i
$106$	−3.17868	−	10.2522i	−0.308741	−	0.995777i
$107$	−5.35190	−	12.9206i	−0.517388	−	1.24908i	−0.939502	−	0.342542i	$-0.888712\pi$
$107$	−5.35190	−	12.9206i	−0.517388	−	1.24908i	0.422114	−	0.906543i	$-0.361288\pi$
$108$	1.95664	−	0.414188i	0.188278	−	0.0398553i
$109$	12.1425	+	5.02958i	1.16304	+	0.481747i	0.878886	−	0.477032i	$-0.158287\pi$
$109$	12.1425	+	5.02958i	1.16304	+	0.481747i	0.284154	+	0.958779i	$0.408287\pi$
$110$	8.53032	+	10.2653i	0.813334	+	0.978760i
$111$			6.83043i			0.648315i
$112$	10.3964	−	4.60795i	0.982365	−	0.435411i
$113$			13.8394i			1.30190i	0.759121	+	0.650950i	$0.225629\pi$
$113$			13.8394i			1.30190i	−0.759121	+	0.650950i	$0.774371\pi$
$114$	−5.29627	+	4.40112i	−0.496041	+	0.412203i
$115$	6.90664	+	2.86082i	0.644048	+	0.266773i
$116$	−5.58909	+	8.59072i	−0.518934	+	0.797628i
$117$	2.30044	+	5.55375i	0.212676	+	0.513445i
$118$	15.1215	−	4.68843i	1.39205	−	0.431605i
$119$	8.37171	+	8.37171i	0.767433	+	0.767433i
$120$	2.09821	−	7.40416i	0.191540	−	0.675904i
$121$	−0.729588	+	0.729588i	−0.0663262	+	0.0663262i
$122$	−5.12675	+	9.73448i	−0.464154	+	0.881318i
$123$	−0.988240	+	0.409342i	−0.0891066	+	0.0369092i
$124$	−5.64331	−	1.05081i	−0.506784	−	0.0943651i
$125$	2.70404	−	6.52814i	0.241857	−	0.583894i
$126$	−4.00352	−	0.369559i	−0.356662	−	0.0329229i
$127$	−5.47542			−0.485865			−0.242932	−	0.970043i	$-0.578109\pi$
$127$	−5.47542			−0.485865			−0.242932	+	0.970043i	$0.578109\pi$
$128$	9.04531	+	6.79576i	0.799500	+	0.600666i
$129$	−4.01832			−0.353794
$130$	23.0329	+	2.12613i	2.02012	+	0.186474i
$131$	8.03254	−	19.3923i	0.701806	−	1.69431i	−0.0177195	−	0.999843i	$-0.505641\pi$
$131$	8.03254	−	19.3923i	0.701806	−	1.69431i	0.719525	−	0.694466i	$-0.244359\pi$
$132$	6.82015	+	1.26994i	0.593618	+	0.110534i
$133$	12.7894	−	5.29756i	1.10899	−	0.459357i
$134$	−6.69544	+	12.7130i	−0.578398	+	1.09824i
$135$	−1.92393	+	1.92393i	−0.165586	+	0.165586i
$136$	−3.21148	+	11.3327i	−0.275382	+	0.971767i
$137$	−3.73965	−	3.73965i	−0.319500	−	0.319500i	0.529075	−	0.848575i	$-0.322539\pi$
$137$	−3.73965	−	3.73965i	−0.319500	−	0.319500i	−0.848575	+	0.529075i	$0.822539\pi$
$138$	3.71134	−	1.15070i	0.315930	−	0.0979542i
$139$	−4.05949	−	9.80047i	−0.344321	−	0.831265i	−0.997268	−	0.0738616i	$-0.976468\pi$
$139$	−4.05949	−	9.80047i	−0.344321	−	0.831265i	0.652947	−	0.757403i	$-0.273532\pi$
$140$	−8.43666	+	12.9676i	−0.713028	+	1.09596i
$141$	−0.999819	−	0.414139i	−0.0841999	−	0.0348768i
$142$	−2.90606	+	2.41489i	−0.243871	+	0.202653i
$143$			20.8515i			1.74369i
$144$	−1.62084	−	3.65690i	−0.135070	−	0.304741i
$145$		−	13.9427i		−	1.15788i
$146$	−8.95694	−	10.7787i	−0.741282	−	0.892052i
$147$	0.999970	+	0.414201i	0.0824761	+	0.0341627i
$148$	13.3647	−	2.82908i	1.09857	−	0.232549i
$149$	4.32999	+	10.4535i	0.354727	+	0.856386i	0.996023	+	0.0890929i	$0.0283968\pi$
$149$	4.32999	+	10.4535i	0.354727	+	0.856386i	−0.641297	+	0.767293i	$0.721603\pi$
$150$	1.00640	+	3.24594i	0.0821725	+	0.265030i
$151$	12.1795	+	12.1795i	0.991157	+	0.991157i	0.999961	−	0.00880460i	$-0.00280263\pi$
$151$	12.1795	+	12.1795i	0.991157	+	0.991157i	−0.00880460	+	0.999961i	$0.502803\pi$
$152$	10.8051	+	8.54002i	0.876407	+	0.692687i
$153$	2.94473	−	2.94473i	0.238067	−	0.238067i
$154$	−12.3393	−	6.49861i	−0.994330	−	0.523673i
$155$	7.21481	−	2.98847i	0.579507	−	0.240040i
$156$	9.91389	−	6.80144i	0.793747	−	0.544551i
$157$	−5.53996	+	13.3746i	−0.442137	+	1.06741i	0.533061	+	0.846077i	$0.321042\pi$
$157$	−5.53996	+	13.3746i	−0.442137	+	1.06741i	−0.975198	+	0.221336i	$0.928958\pi$
$158$	1.43322	−	15.5264i	0.114021	−	1.23522i
$159$	7.58982			0.601912
$160$	−15.3563	−	1.03874i	−1.21403	−	0.0821196i
$161$	−7.81117			−0.615607
$162$	−0.129991	+	1.40823i	−0.0102131	+	0.110641i
$163$	5.79233	−	13.9839i	0.453690	−	1.09530i	−0.517218	−	0.855854i	$-0.673032\pi$
$163$	5.79233	−	13.9839i	0.453690	−	1.09530i	0.970908	−	0.239451i	$-0.0769675\pi$
$164$	1.21025	+	1.76409i	0.0945049	+	0.137752i
$165$	−8.71936	+	3.61168i	−0.678802	+	0.281169i
$166$	−3.12205	−	1.64426i	−0.242318	−	0.127619i
$167$	4.07626	−	4.07626i	0.315430	−	0.315430i	−0.531579	−	0.847009i	$-0.678401\pi$
$167$	4.07626	−	4.07626i	0.315430	−	0.315430i	0.847009	+	0.531579i	$0.178401\pi$
$168$	0.935114	+	7.98652i	0.0721456	+	0.616173i
$169$	16.3598	+	16.3598i	1.25844	+	1.25844i
$170$	−4.74548	−	15.3055i	−0.363962	−	1.17388i
$171$	−1.86340	−	4.49866i	−0.142498	−	0.344021i
$172$	1.66434	+	7.86242i	0.126905	+	0.599504i
$173$	4.29724	+	1.77998i	0.326713	+	0.135329i	0.540010	−	0.841658i	$-0.318420\pi$
$173$	4.29724	+	1.77998i	0.326713	+	0.135329i	−0.213297	+	0.976987i	$0.568420\pi$
$174$	−4.63169	−	5.57374i	−0.351128	−	0.422544i
$175$		−	6.83165i		−	0.516424i
$176$	−0.340011	−	13.8706i	−0.0256293	−	1.04553i
$177$			11.1947i			0.841443i
$178$	11.7797	−	9.78873i	0.882924	−	0.733696i
$179$	−0.273384	−	0.113240i	−0.0204337	−	0.00846392i	0.372443	−	0.928055i	$-0.378520\pi$
$179$	−0.273384	−	0.113240i	−0.0204337	−	0.00846392i	−0.392877	+	0.919591i	$0.628520\pi$
$180$	4.56131	+	2.96757i	0.339980	+	0.221190i
$181$	4.00336	+	9.66497i	0.297567	+	0.718391i	0.999978	+	0.00661937i	$0.00210703\pi$
$181$	4.00336	+	9.66497i	0.297567	+	0.718391i	−0.702411	+	0.711772i	$0.747893\pi$
$182$	−23.0847	+	7.15741i	−1.71115	+	0.530543i
$183$	−5.50099	−	5.50099i	−0.406645	−	0.406645i
$184$	−3.78871	−	6.78516i	−0.279307	−	0.500209i
$185$	−13.1413	+	13.1413i	−0.966165	+	0.966165i
$186$	1.89143	−	3.59138i	0.138687	−	0.263333i
$187$	13.3457	−	5.52796i	0.975932	−	0.404244i
$188$	−0.396208	+	2.12782i	−0.0288964	+	0.155187i
$189$	1.08795	−	2.62654i	0.0791367	−	0.191053i
$190$	−18.6571	−	1.72221i	−1.35353	−	0.124942i
$191$	15.1625			1.09712			0.548561	−	0.836110i	$-0.315176\pi$
$191$	15.1625			1.09712			0.548561	+	0.836110i	$0.315176\pi$
$192$	−6.48391	+	4.68604i	−0.467936	+	0.338186i
$193$	−18.3549			−1.32122			−0.660608	−	0.750731i	$-0.729701\pi$
$193$	−18.3549			−1.32122			−0.660608	+	0.750731i	$0.729701\pi$
$194$	−15.9171	−	1.46928i	−1.14278	−	0.105488i
$195$	−6.25915	+	15.1109i	−0.448227	+	1.08212i
$196$	0.396268	−	2.12814i	0.0283048	−	0.152010i
$197$	−6.65334	+	2.75590i	−0.474031	+	0.196350i	−0.606891	−	0.794785i	$-0.707584\pi$
$197$	−6.65334	+	2.75590i	−0.474031	+	0.196350i	0.132861	+	0.991135i	$0.457584\pi$
$198$	−2.28587	+	4.34032i	−0.162450	+	0.308453i
$199$	−0.849057	+	0.849057i	−0.0601880	+	0.0601880i	−0.736560	−	0.676372i	$-0.763551\pi$
$199$	−0.849057	+	0.849057i	−0.0601880	+	0.0601880i	0.676372	+	0.736560i	$0.263551\pi$
$200$	5.93430	−	3.31360i	0.419618	−	0.234307i
$201$	−7.18419	−	7.18419i	−0.506734	−	0.506734i
$202$	5.21070	−	1.61558i	0.366624	−	0.113672i
$203$	5.57510	+	13.4595i	0.391295	+	0.944671i
$204$	−6.98145	−	4.54211i	−0.488799	−	0.318011i
$205$	−2.68885	−	1.11376i	−0.187797	−	0.0777883i
$206$	−2.98921	+	2.48398i	−0.208268	+	0.173067i
$207$			2.74756i			0.190969i
$208$	−17.4142	−	16.5809i	−1.20746	−	1.14968i
$209$		−	16.8901i		−	1.16831i
$210$	−6.99148	−	8.41349i	−0.482458	−	0.580586i
$211$	−7.40729	−	3.06820i	−0.509939	−	0.211224i	0.112852	−	0.993612i	$-0.464001\pi$
$211$	−7.40729	−	3.06820i	−0.509939	−	0.211224i	−0.622791	+	0.782388i	$0.714001\pi$
$212$	−3.14361	−	14.8506i	−0.215904	−	1.01994i
$213$	−1.02245	−	2.46841i	−0.0700570	−	0.169133i
$214$	−5.85712	−	18.8909i	−0.400384	−	1.29135i
$215$	−7.73098	−	7.73098i	−0.527248	−	0.527248i
$216$	2.80924	−	0.328924i	0.191144	−	0.0223804i
$217$	−5.76978	+	5.76978i	−0.391678	+	0.391678i
$218$	16.4456	+	8.66121i	1.11384	+	0.586611i
$219$	9.15544	−	3.79231i	0.618667	−	0.256260i
$220$	10.6782	+	15.5648i	0.719925	+	1.04938i
$221$	9.58012	−	23.1285i	0.644429	−	1.55579i
$222$	−0.887896	+	9.61879i	−0.0595917	+	0.645571i
$223$	0.188370			0.0126142			0.00630710	−	0.999980i	$-0.497992\pi$
$223$	0.188370			0.0126142			0.00630710	+	0.999980i	$0.497992\pi$
$224$	15.2394	−	5.13760i	1.01823	−	0.343271i
$225$	−2.40301			−0.160201
$226$	−1.79900	+	19.4890i	−0.119668	+	1.29639i
$227$	−0.106761	+	0.257744i	−0.00708599	+	0.0171071i	−0.927383	−	0.374113i	$-0.877947\pi$
$227$	−0.106761	+	0.257744i	−0.00708599	+	0.0171071i	0.920297	+	0.391221i	$0.127947\pi$
$228$	−8.03046	+	5.50930i	−0.531830	+	0.364863i
$229$	2.03685	−	0.843689i	0.134599	−	0.0557526i	−0.314367	−	0.949301i	$-0.601792\pi$
$229$	2.03685	−	0.843689i	0.134599	−	0.0557526i	0.448966	+	0.893549i	$0.351792\pi$
$230$	9.35423	+	4.92649i	0.616800	+	0.324843i
$231$	6.97299	−	6.97299i	0.458789	−	0.458789i
$232$	−8.98743	+	11.3711i	−0.590054	+	0.746552i
$233$	−4.32675	−	4.32675i	−0.283455	−	0.283455i	0.551030	−	0.834485i	$-0.314235\pi$
$233$	−4.32675	−	4.32675i	−0.283455	−	0.283455i	−0.834485	+	0.551030i	$0.814235\pi$
$234$	2.51760	+	8.11998i	0.164581	+	0.530820i
$235$	−1.12681	−	2.72036i	−0.0735049	−	0.177456i
$236$	21.9040	−	4.63670i	1.42583	−	0.301824i
$237$	10.1863	+	4.21928i	0.661668	+	0.274072i
$238$	10.7010	+	12.8775i	0.693644	+	0.834725i
$239$			8.26905i			0.534880i	0.963575	+	0.267440i	$0.0861777\pi$
$239$			8.26905i			0.534880i	−0.963575	+	0.267440i	$0.913822\pi$
$240$	3.91724	−	10.1540i	0.252857	−	0.655437i
$241$			22.7291i			1.46411i	0.681244	+	0.732057i	$0.261439\pi$
$241$			22.7291i			1.46411i	−0.681244	+	0.732057i	$0.738561\pi$
$242$	−1.12227	+	0.932585i	−0.0721419	+	0.0599488i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	−8.48503	+	13.0419i	−0.543198	+	0.834923i
$245$	1.12698	+	2.72077i	0.0720000	+	0.173823i
$246$	−1.44488	+	0.447984i	−0.0921220	+	0.0285624i
$247$	−20.6978	−	20.6978i	−1.31697	−	1.31697i
$248$	−7.81046	−	2.21335i	−0.495965	−	0.140548i
$249$	1.76429	−	1.76429i	0.111807	−	0.111807i
$250$	4.65651	−	8.84159i	0.294503	−	0.559191i
$251$	−12.3335	+	5.10871i	−0.778485	+	0.322459i	−0.736304	−	0.676651i	$-0.763431\pi$
$251$	−12.3335	+	5.10871i	−0.778485	+	0.322459i	−0.0421812	+	0.999110i	$0.513431\pi$
$252$	−5.58982	−	1.04085i	−0.352126	−	0.0655671i
$253$	−3.64714	+	8.80497i	−0.229294	+	0.553564i
$254$	−7.71063	−	0.711757i	−0.483808	−	0.0446596i
$255$	11.3309			0.709568
$256$	11.8545	+	10.7458i	0.740903	+	0.671612i
$257$	15.9974			0.997893			0.498947	−	0.866633i	$-0.333720\pi$
$257$	15.9974			0.997893			0.498947	+	0.866633i	$0.333720\pi$
$258$	−5.65871	−	0.522348i	−0.352296	−	0.0325199i
$259$	7.43116	−	17.9404i	0.461750	−	1.11476i
$260$	32.1591	+	5.98815i	1.99442	+	0.371369i
$261$	4.73434	−	1.96103i	0.293048	−	0.121385i
$262$	13.8325	−	26.2645i	0.854572	−	1.62263i
$263$	−4.44583	+	4.44583i	−0.274141	+	0.274141i	−0.830765	−	0.556623i	$-0.812097\pi$
$263$	−4.44583	+	4.44583i	−0.274141	+	0.274141i	0.556623	+	0.830765i	$0.312097\pi$
$264$	9.43923	+	2.67492i	0.580945	+	0.164630i
$265$	14.6023	+	14.6023i	0.897011	+	0.897011i
$266$	18.6991	−	5.79765i	1.14651	−	0.355477i
$267$	4.14448	+	10.0057i	0.253638	+	0.612336i
$268$	−11.0813	+	17.0325i	−0.676897	+	1.04042i
$269$	−11.1204	−	4.60621i	−0.678021	−	0.280846i	0.0169781	−	0.999856i	$-0.494595\pi$
$269$	−11.1204	−	4.60621i	−0.678021	−	0.280846i	−0.695000	+	0.719010i	$0.744595\pi$
$270$	−2.95942	+	2.45924i	−0.180105	+	0.149664i
$271$		−	18.7073i		−	1.13638i	−0.822896	−	0.568192i	$-0.807643\pi$
$271$		−	18.7073i		−	1.13638i	0.822896	−	0.568192i	$-0.192357\pi$
$272$	−5.99564	+	15.5415i	−0.363539	+	0.942341i
$273$		−	17.0899i		−	1.03433i
$274$	−4.78015	−	5.75240i	−0.288780	−	0.347515i
$275$	−7.70082	−	3.18978i	−0.464377	−	0.192351i
$276$	5.37599	−	1.13801i	0.323597	−	0.0684999i
$277$	−4.13646	−	9.98630i	−0.248536	−	0.600019i	0.749544	−	0.661954i	$-0.230273\pi$
$277$	−4.13646	−	9.98630i	−0.248536	−	0.600019i	−0.998080	+	0.0619354i	$0.980273\pi$
$278$	−4.44270	−	14.3290i	−0.266456	−	0.859395i
$279$	2.02950	+	2.02950i	0.121503	+	0.121503i
$280$	−13.5664	+	17.1646i	−0.810748	+	1.02578i
$281$	−13.2105	+	13.2105i	−0.788071	+	0.788071i	−0.981178	−	0.193106i	$-0.938144\pi$
$281$	−13.2105	+	13.2105i	−0.788071	+	0.788071i	0.193106	+	0.981178i	$0.438144\pi$
$282$	−1.35414	−	0.713169i	−0.0806377	−	0.0424686i
$283$	−21.9884	+	9.10789i	−1.30707	+	0.541408i	−0.924029	−	0.382321i	$-0.875125\pi$
$283$	−21.9884	+	9.10789i	−1.30707	+	0.541408i	−0.383045	+	0.923730i	$0.625125\pi$
$284$	−4.40631	+	3.02295i	−0.261466	+	0.179379i
$285$	5.07004	−	12.2402i	0.300323	−	0.725044i
$286$	−2.71051	+	29.3636i	−0.160276	+	1.73630i
$287$	3.04100			0.179504
$288$	−1.80714	−	5.36043i	−0.106487	−	0.315867i
$289$	−0.342832			−0.0201666
$290$	1.81244	−	19.6345i	0.106430	−	1.15298i
$291$	4.32544	−	10.4425i	0.253562	−	0.612152i
$292$	−11.2123	−	16.3432i	−0.656148	−	0.956413i
$293$	−18.8878	+	7.82359i	−1.10344	+	0.457059i	−0.858673	−	0.512524i	$-0.828711\pi$
$293$	−18.8878	+	7.82359i	−1.10344	+	0.457059i	−0.244764	+	0.969583i	$0.578711\pi$
$294$	1.35434	+	0.713277i	0.0789868	+	0.0415991i
$295$	−21.5378	+	21.5378i	−1.25398	+	1.25398i
$296$	19.1883	−	2.24669i	1.11530	−	0.130586i
$297$	−2.45273	−	2.45273i	−0.142322	−	0.142322i
$298$	4.73874	+	15.2838i	0.274508	+	0.885366i
$299$	6.32060	+	15.2593i	0.365530	+	0.882466i
$300$	0.995300	+	4.70184i	0.0574637	+	0.271461i
$301$	10.5543	+	4.37173i	0.608340	+	0.251983i
$302$	15.5683	+	18.7348i	0.895856	+	1.07807i
$303$			3.85756i			0.221611i
$304$	14.1059	+	13.4308i	0.809026	+	0.770312i
$305$		−	21.1670i		−	1.21202i
$306$	4.52963	−	3.76405i	0.258942	−	0.215177i
$307$	10.7709	+	4.46145i	0.614728	+	0.254629i	0.668249	−	0.743938i	$-0.267044\pi$
$307$	10.7709	+	4.46145i	0.614728	+	0.254629i	−0.0535206	+	0.998567i	$0.517044\pi$
$308$	−16.5318	−	10.7555i	−0.941986	−	0.612853i
$309$	−1.05170	−	2.53903i	−0.0598292	−	0.144440i
$310$	10.5486	−	3.27058i	0.599118	−	0.185757i
$311$	−6.79085	−	6.79085i	−0.385074	−	0.385074i	0.487852	−	0.872926i	$-0.337780\pi$
$311$	−6.79085	−	6.79085i	−0.385074	−	0.385074i	−0.872926	+	0.487852i	$0.837780\pi$
$312$	14.8451	−	8.28924i	0.840440	−	0.469286i
$313$	12.7080	−	12.7080i	0.718300	−	0.718300i	−0.249957	−	0.968257i	$-0.580417\pi$
$313$	12.7080	−	12.7080i	0.718300	−	0.718300i	0.968257	+	0.249957i	$0.0804166\pi$
$314$	−9.54011	+	18.1144i	−0.538379	+	1.02225i
$315$	7.14642	−	2.96015i	0.402655	−	0.166785i
$316$	4.03661	−	21.6784i	0.227077	−	1.21951i
$317$	−6.89303	+	16.6412i	−0.387151	+	0.934665i	0.603390	+	0.797446i	$0.293816\pi$
$317$	−6.89303	+	16.6412i	−0.387151	+	0.934665i	−0.990541	+	0.137219i	$0.956184\pi$
$318$	10.6882	+	0.986611i	0.599363	+	0.0553264i
$319$	17.7750			0.995208
$320$	−21.4902	−	3.45897i	−1.20134	−	0.193363i
$321$	13.9852			0.780577
$322$	−10.9999	−	1.01539i	−0.613001	−	0.0565852i
$323$	−7.76010	+	18.7345i	−0.431783	+	1.04242i
$324$	−0.366115	+	1.96620i	−0.0203397	+	0.109234i
$325$	−13.3457	+	5.52799i	−0.740289	+	0.306638i
$326$	9.97470	−	18.9396i	0.552447	−	1.04897i
$327$	−9.29346	+	9.29346i	−0.513930	+	0.513930i
$328$	1.47500	+	2.64156i	0.0814430	+	0.145856i
$329$	2.17550	+	2.17550i	0.119939	+	0.119939i
$330$	−12.7483	+	3.95262i	−0.701772	+	0.217585i
$331$	0.259261	+	0.625913i	0.0142503	+	0.0344033i	0.930845	−	0.365415i	$-0.119073\pi$
$331$	0.259261	+	0.625913i	0.0142503	+	0.0344033i	−0.916594	+	0.399819i	$0.869073\pi$
$332$	−4.18282	−	2.72133i	−0.229562	−	0.149352i
$333$	−6.31049	−	2.61389i	−0.345813	−	0.143240i
$334$	6.27017	−	5.21042i	0.343089	−	0.285101i
$335$		−	27.6438i		−	1.51034i
$336$	0.278675	+	11.3684i	0.0152029	+	0.620196i
$337$		−	24.3244i		−	1.32504i	−0.749046	−	0.662518i	$-0.769488\pi$
$337$		−	24.3244i		−	1.32504i	0.749046	−	0.662518i	$-0.230512\pi$
$338$	20.9116	+	25.1649i	1.13744	+	1.36879i
$339$	−12.7859	−	5.29611i	−0.694436	−	0.287645i
$340$	−4.69312	−	22.1705i	−0.254520	−	1.20236i
$341$	3.80987	+	9.19783i	0.206316	+	0.498091i
$342$	−2.03931	−	6.57735i	−0.110273	−	0.355663i
$343$	11.8960	+	11.8960i	0.642326	+	0.642326i
$344$	1.32172	+	11.2884i	0.0712626	+	0.608631i
$345$	−5.28611	+	5.28611i	−0.284595	+	0.284595i
$346$	5.82011	+	3.06521i	0.312891	+	0.164787i
$347$	6.95491	−	2.88082i	0.373359	−	0.154650i	−0.188110	−	0.982148i	$-0.560236\pi$
$347$	6.95491	−	2.88082i	0.373359	−	0.154650i	0.561469	+	0.827498i	$0.310236\pi$
$348$	−5.79794	−	8.45117i	−0.310802	−	0.453031i
$349$	11.9159	−	28.7676i	0.637845	−	1.53989i	−0.191700	−	0.981454i	$-0.561400\pi$
$349$	11.9159	−	28.7676i	0.637845	−	1.53989i	0.829545	−	0.558440i	$-0.188600\pi$
$350$	0.888055	−	9.62051i	0.0474685	−	0.514238i
$351$	−6.01134			−0.320862
$352$	1.32424	−	19.5771i	0.0705824	−	1.04346i
$353$	−22.1334			−1.17804			−0.589021	−	0.808118i	$-0.700486\pi$
$353$	−22.1334			−1.17804			−0.589021	+	0.808118i	$0.700486\pi$
$354$	−1.45521	+	15.7646i	−0.0773436	+	0.837881i
$355$	2.78193	−	6.71616i	0.147649	−	0.356457i
$356$	17.8609	−	12.2535i	0.946626	−	0.649434i
$357$	−10.9382	+	4.53074i	−0.578909	+	0.239792i
$358$	−0.370267	−	0.195005i	−0.0195692	−	0.0103063i
$359$	−10.1669	+	10.1669i	−0.536586	+	0.536586i	−0.922524	−	0.385939i	$-0.873878\pi$
$359$	−10.1669	+	10.1669i	−0.536586	+	0.536586i	0.385939	+	0.922524i	$0.373878\pi$
$360$	6.03760	+	4.77195i	0.318210	+	0.251504i
$361$	3.33060	+	3.33060i	0.175295	+	0.175295i
$362$	4.38128	+	14.1309i	0.230275	+	0.742702i
$363$	−0.394850	−	0.953252i	−0.0207243	−	0.0500328i
$364$	−33.4389	+	7.07845i	−1.75267	+	0.371011i
$365$	24.9106	+	10.3183i	1.30388	+	0.540084i
$366$	−7.03156	−	8.46172i	−0.367546	−	0.442301i
$367$			9.77761i			0.510387i	0.966890	+	0.255194i	$0.0821392\pi$
$367$			9.77761i			0.510387i	−0.966890	+	0.255194i	$0.917861\pi$
$368$	−4.45334	−	10.0475i	−0.232147	−	0.523764i
$369$		−	1.06966i		−	0.0556844i
$370$	−20.2141	+	16.7976i	−1.05088	+	0.873267i
$371$	−19.9350	−	8.25734i	−1.03497	−	0.428700i
$372$	3.13042	−	4.81161i	0.162305	−	0.249470i
$373$	−2.04735	−	4.94275i	−0.106008	−	0.255926i	0.861971	−	0.506958i	$-0.169230\pi$
$373$	−2.04735	−	4.94275i	−0.106008	−	0.255926i	−0.967979	+	0.251032i	$0.919230\pi$
$374$	19.5123	−	6.04980i	1.00896	−	0.312828i
$375$	4.99642	+	4.99642i	0.258014	+	0.258014i
$376$	−0.834549	+	2.94495i	−0.0430386	+	0.151874i
$377$	21.7821	−	21.7821i	1.12184	−	1.12184i
$378$	1.87351	−	3.55734i	0.0963628	−	0.182970i
$379$	−29.0333	+	12.0260i	−1.49134	+	0.617733i	−0.971608	−	0.236596i	$-0.923968\pi$
$379$	−29.0333	+	12.0260i	−1.49134	+	0.617733i	−0.519732	+	0.854329i	$0.673968\pi$
$380$	−26.0496	−	4.85053i	−1.33631	−	0.248827i
$381$	2.09535	−	5.05863i	0.107348	−	0.259161i
$382$	21.3523	+	1.97100i	1.09248	+	0.100845i
$383$	2.47568			0.126501			0.0632507	−	0.997998i	$-0.479853\pi$
$383$	2.47568			0.126501			0.0632507	+	0.997998i	$0.479853\pi$
$384$	−9.73995	+	5.75615i	−0.497040	+	0.293742i
$385$	26.8311			1.36744
$386$	−25.8479	−	2.38598i	−1.31562	−	0.121443i
$387$	1.53775	−	3.71245i	0.0781680	−	0.188714i
$388$	−22.2238	−	4.13816i	−1.12824	−	0.210083i
$389$	−9.49742	+	3.93396i	−0.481538	+	0.199460i	−0.610229	−	0.792225i	$-0.708923\pi$
$389$	−9.49742	+	3.93396i	−0.481538	+	0.199460i	0.128691	+	0.991685i	$0.458923\pi$
$390$	−10.7786	+	20.4660i	−0.545795	+	1.03633i
$391$	8.09081	−	8.09081i	0.409170	−	0.409170i
$392$	0.834675	−	2.94539i	0.0421574	−	0.148765i
$393$	14.8422	+	14.8422i	0.748689	+	0.748689i
$394$	−9.72766	+	3.01606i	−0.490072	+	0.151947i
$395$	11.4800	+	27.7153i	0.577623	+	1.39451i
$396$	−3.78323	+	5.81501i	−0.190114	+	0.292215i
$397$	−13.8666	−	5.74373i	−0.695944	−	0.288269i	0.00653022	−	0.999979i	$-0.497921\pi$
$397$	−13.8666	−	5.74373i	−0.695944	−	0.288269i	−0.702474	+	0.711709i	$0.747921\pi$
$398$	−1.30603	+	1.08529i	−0.0654656	+	0.0544009i
$399$			13.8432i			0.693027i
$400$	8.78757	−	3.89489i	0.439379	−	0.194745i
$401$			21.9112i			1.09419i	0.837069	+	0.547097i	$0.184267\pi$
$401$			21.9112i			1.09419i	−0.837069	+	0.547097i	$0.815733\pi$
$402$	−9.18308	−	11.0508i	−0.458011	−	0.551166i
$403$	15.9401	+	6.60262i	0.794034	+	0.328900i
$404$	7.54786	−	1.59775i	0.375520	−	0.0794913i
$405$	−1.04122	−	2.51374i	−0.0517388	−	0.124909i
$406$	6.10139	+	19.6787i	0.302807	+	0.976639i
$407$	−16.7532	−	16.7532i	−0.830426	−	0.830426i
$408$	−9.24103	−	7.30384i	−0.457499	−	0.361594i
$409$	13.0005	−	13.0005i	0.642835	−	0.642835i	−0.308417	−	0.951251i	$-0.599799\pi$
$409$	13.0005	−	13.0005i	0.642835	−	0.642835i	0.951251	+	0.308417i	$0.0997991\pi$
$410$	−3.64173	−	1.91795i	−0.179852	−	0.0947209i
$411$	4.88609	−	2.02388i	0.241013	−	0.0998308i
$412$	−4.53237	+	3.10944i	−0.223294	+	0.153191i
$413$	12.1792	−	29.4033i	0.599301	−	1.44684i
$414$	−0.357159	+	3.86919i	−0.0175534	+	0.190160i
$415$	6.78872			0.333245
$416$	−22.3678	−	25.6133i	−1.09667	−	1.25580i
$417$	10.6080			0.519474
$418$	2.19557	−	23.7851i	0.107389	−	1.16337i
$419$	−7.98199	+	19.2702i	−0.389946	+	0.941412i	0.600005	+	0.799997i	$0.295165\pi$
$419$	−7.98199	+	19.2702i	−0.389946	+	0.941412i	−0.989950	+	0.141416i	$0.954835\pi$
$420$	−8.75191	−	12.7569i	−0.427049	−	0.622475i
$421$	−5.11481	+	2.11863i	−0.249281	+	0.103255i	−0.503825	−	0.863806i	$-0.668074\pi$
$421$	−5.11481	+	2.11863i	−0.249281	+	0.103255i	0.254545	+	0.967061i	$0.418074\pi$
$422$	−10.0323	−	5.28361i	−0.488365	−	0.257202i
$423$	0.765228	−	0.765228i	0.0372067	−	0.0372067i
$424$	−2.49647	−	21.3216i	−0.121239	−	1.03547i
$425$	7.07622	+	7.07622i	0.343247	+	0.343247i
$426$	−1.11897	−	3.60899i	−0.0542141	−	0.174856i
$427$	8.46379	+	20.4334i	0.409591	+	0.988841i
$428$	−5.79250	−	27.3640i	−0.279991	−	1.32269i
$429$	−19.2642	−	7.97951i	−0.930086	−	0.385254i
$430$	−9.88201	−	11.8919i	−0.476553	−	0.573480i
$431$			5.20156i			0.250551i	0.992122	+	0.125275i	$0.0399814\pi$
$431$			5.20156i			0.250551i	−0.992122	+	0.125275i	$0.960019\pi$
$432$	3.99880	−	0.0980231i	0.192392	−	0.00471614i
$433$		−	6.44939i		−	0.309938i	−0.987919	−	0.154969i	$-0.950472\pi$
$433$		−	6.44939i		−	0.309938i	0.987919	−	0.154969i	$-0.0495278\pi$
$434$	−8.87518	+	7.37514i	−0.426022	+	0.354018i
$435$	12.8814	+	5.33566i	0.617617	+	0.255825i
$436$	22.0332	+	14.3347i	1.05520	+	0.686509i
$437$	−5.11982	−	12.3603i	−0.244914	−	0.591275i
$438$	13.3859	−	4.15030i	0.639603	−	0.198309i
$439$	−20.5461	−	20.5461i	−0.980610	−	0.980610i	0.0192051	−	0.999816i	$-0.493886\pi$
$439$	−20.5461	−	20.5461i	−0.980610	−	0.980610i	−0.999816	+	0.0192051i	$0.993886\pi$
$440$	13.0141	+	23.3068i	0.620421	+	1.11111i
$441$	−0.765344	+	0.765344i	−0.0364450	+	0.0364450i
$442$	16.4975	−	31.3248i	0.784705	−	1.48997i
$443$	−16.1487	+	6.68902i	−0.767249	+	0.317805i	−0.731757	−	0.681565i	$-0.761300\pi$
$443$	−16.1487	+	6.68902i	−0.767249	+	0.317805i	−0.0354912	+	0.999370i	$0.511300\pi$
$444$	−2.50072	+	13.4300i	−0.118679	+	0.637360i
$445$	−11.2765	+	27.2239i	−0.534557	+	1.29054i
$446$	0.265268	+	0.0244865i	0.0125608	+	0.00115947i
$447$	−11.3148			−0.535172
$448$	22.1284	−	5.25391i	1.04547	−	0.248224i
$449$	−0.794308			−0.0374857			−0.0187428	−	0.999824i	$-0.505966\pi$
$449$	−0.794308			−0.0374857			−0.0187428	+	0.999824i	$0.505966\pi$
$450$	−3.38399	−	0.312371i	−0.159523	−	0.0147253i
$451$	1.41988	−	3.42790i	0.0668596	−	0.161413i
$452$	−5.06680	+	27.2111i	−0.238322	+	1.27990i
$453$	−15.9133	+	6.59152i	−0.747674	+	0.309697i
$454$	−0.183848	+	0.349084i	−0.00862844	+	0.0163833i
$455$	32.8798	−	32.8798i	1.54143	−	1.54143i
$456$	−12.0249	+	6.71446i	−0.563116	+	0.314433i
$457$	21.2796	+	21.2796i	0.995420	+	0.995420i	0.999990	−	0.00456968i	$-0.00145458\pi$
$457$	21.2796	+	21.2796i	0.995420	+	0.995420i	−0.00456968	+	0.999990i	$0.501455\pi$
$458$	2.97801	−	0.923333i	0.139153	−	0.0431445i
$459$	1.59367	+	3.84747i	0.0743864	+	0.179585i
$460$	12.5325	+	8.15359i	0.584330	+	0.380163i
$461$	−0.541763	−	0.224405i	−0.0252324	−	0.0104516i	0.370032	−	0.929019i	$-0.379347\pi$
$461$	−0.541763	−	0.224405i	−0.0252324	−	0.0104516i	−0.395264	+	0.918568i	$0.629347\pi$
$462$	10.7260	−	8.91313i	0.499018	−	0.414676i
$463$			13.0365i			0.605859i	0.953013	+	0.302929i	$0.0979646\pi$
$463$			13.0365i			0.605859i	−0.953013	+	0.302929i	$0.902035\pi$
$464$	−14.1345	+	14.8449i	−0.656177	+	0.689155i
$465$			7.80925i			0.362145i
$466$	−5.53061	−	6.65549i	−0.256200	−	0.308310i
$467$	36.1793	+	14.9860i	1.67418	+	0.693467i	0.999022	−	0.0442081i	$-0.0140765\pi$
$467$	36.1793	+	14.9860i	1.67418	+	0.693467i	0.675156	+	0.737675i	$0.264076\pi$
$468$	2.48982	+	11.7620i	0.115092	+	0.543700i
$469$	11.0535	+	26.6856i	0.510405	+	1.23223i
$470$	−1.23318	−	3.97735i	−0.0568823	−	0.183462i
$471$	−10.2365	−	10.2365i	−0.471674	−	0.471674i
$472$	31.4485	−	3.68220i	1.44753	−	0.169487i
$473$	9.85587	−	9.85587i	0.453174	−	0.453174i
$474$	13.7961	+	7.26583i	0.633675	+	0.333731i
$475$	10.8103	−	4.47779i	0.496012	−	0.205455i
$476$	13.3955	+	19.5255i	0.613981	+	0.894950i
$477$	−2.90450	+	7.01208i	−0.132988	+	0.321061i
$478$	−1.07490	+	11.6447i	−0.0491650	+	0.532616i
$479$	27.6976			1.26554			0.632768	−	0.774341i	$-0.281919\pi$
$479$	27.6976			1.26554			0.632768	+	0.774341i	$0.281919\pi$
$480$	6.83629	−	13.7899i	0.312033	−	0.629420i
$481$	−41.0600			−1.87217
$482$	−2.95459	+	32.0078i	−0.134578	+	1.45792i
$483$	2.98921	−	7.21658i	0.136014	−	0.328366i
$484$	−1.70163	+	1.16741i	−0.0773469	+	0.0530639i
$485$	28.4125	−	11.7689i	1.29015	−	0.534396i
$486$	−1.25129	−	0.659001i	−0.0567595	−	0.0298929i
$487$	22.8658	−	22.8658i	1.03615	−	1.03615i	0.0368273	−	0.999322i	$-0.488275\pi$
$487$	22.8658	−	22.8658i	1.03615	−	1.03615i	0.999322	−	0.0368273i	$-0.0117251\pi$
$488$	−13.6442	+	17.2630i	−0.617643	+	0.781459i
$489$	10.7028	+	10.7028i	0.483999	+	0.483999i
$490$	1.23336	+	3.97795i	0.0557177	+	0.179706i
$491$	−10.1610	−	24.5308i	−0.458559	−	1.10706i	−0.968981	−	0.247135i	$-0.920511\pi$
$491$	−10.1610	−	24.5308i	−0.458559	−	1.10706i	0.510423	−	0.859924i	$-0.329489\pi$
$492$	−2.09295	+	0.443042i	−0.0943574	+	0.0199739i
$493$	−19.7160	−	8.16665i	−0.887965	−	0.367807i
$494$	−26.4566	−	31.8377i	−1.19034	−	1.43245i
$495$		−	9.43777i		−	0.424196i
$496$	−10.7112	−	4.13220i	−0.480946	−	0.185541i
$497$			7.59575i			0.340716i
$498$	2.71386	−	2.25517i	0.121611	−	0.101057i
$499$	−11.6135	−	4.81046i	−0.519890	−	0.215346i	0.107278	−	0.994229i	$-0.465786\pi$
$499$	−11.6135	−	4.81046i	−0.519890	−	0.215346i	−0.627169	+	0.778883i	$0.715786\pi$
$500$	7.70675	−	11.8457i	0.344656	−	0.529754i
$501$	2.20606	+	5.32589i	0.0985593	+	0.237943i
$502$	−18.0325	+	5.59097i	−0.804829	+	0.249537i
$503$	12.9948	+	12.9948i	0.579412	+	0.579412i	0.934741	−	0.355330i	$-0.115631\pi$
$503$	12.9948	+	12.9948i	0.579412	+	0.579412i	−0.355330	+	0.934741i	$0.615631\pi$
$504$	−7.73643	−	2.19237i	−0.344608	−	0.0976561i
$505$	−7.42167	+	7.42167i	−0.330260	+	0.330260i
$506$	−6.28056	+	11.9253i	−0.279205	+	0.530144i
$507$	−21.3751	+	8.85384i	−0.949300	+	0.393213i
$508$	−10.7658	−	2.00463i	−0.477655	−	0.0889411i
$509$	−13.3636	+	32.2627i	−0.592333	+	1.43002i	0.288911	+	0.957356i	$0.406707\pi$
$509$	−13.3636	+	32.2627i	−0.592333	+	1.43002i	−0.881244	+	0.472662i	$0.843293\pi$
$510$	15.9565	+	1.47292i	0.706564	+	0.0652219i
$511$	−28.1730			−1.24630
$512$	15.2969	+	16.6735i	0.676034	+	0.736871i
$513$	4.86931			0.214985
$514$	22.5280	+	2.07953i	0.993669	+	0.0917242i
$515$	2.86152	−	6.90832i	0.126094	−	0.304417i
$516$	−7.90085	−	1.47117i	−0.347815	−	0.0647645i
$517$	3.46806	−	1.43652i	0.152525	−	0.0631780i
$518$	12.7969	−	24.2982i	0.562261	−	1.06760i
$519$	−3.28896	+	3.28896i	−0.144370	+	0.144370i
$520$	44.5089	+	12.6131i	1.95185	+	0.553120i
$521$	1.74966	+	1.74966i	0.0766541	+	0.0766541i	0.744394	−	0.667740i	$-0.232738\pi$
$521$	1.74966	+	1.74966i	0.0766541	+	0.0766541i	−0.667740	+	0.744394i	$0.732738\pi$
$522$	6.92194	−	2.14615i	0.302965	−	0.0939344i
$523$	7.05117	+	17.0230i	0.308326	+	0.744366i	0.999760	+	0.0219253i	$0.00697960\pi$
$523$	7.05117	+	17.0230i	0.308326	+	0.744366i	−0.691433	+	0.722440i	$0.743020\pi$
$524$	22.8934	−	35.1883i	1.00010	−	1.53721i
$525$	6.31162	+	2.61436i	0.275462	+	0.114100i
$526$	−6.83865	+	5.68281i	−0.298179	+	0.247782i
$527$		−	11.9527i		−	0.520667i
$528$	12.9449	+	4.99391i	0.563353	+	0.217332i
$529$		−	15.4509i		−	0.671779i
$530$	18.6651	+	22.4615i	0.810762	+	0.975665i
$531$	−10.3425	−	4.28402i	−0.448828	−	0.185911i
$532$	27.0862	−	5.73369i	1.17434	−	0.248587i
$533$	−2.46070	−	5.94064i	−0.106585	−	0.257318i
$534$	4.53572	+	14.6290i	0.196280	+	0.633058i
$535$	26.9065	+	26.9065i	1.16327	+	1.16327i
$536$	−17.8190	+	22.5451i	−0.769665	+	0.973802i
$537$	0.209239	−	0.209239i	0.00902935	−	0.00902935i
$538$	−15.0612	−	7.93214i	−0.649336	−	0.341979i
$539$	−3.46858	+	1.43673i	−0.149402	+	0.0618845i
$540$	−4.48722	+	3.07846i	−0.193099	+	0.132476i
$541$	7.86315	−	18.9833i	0.338063	−	0.816157i	−0.659838	−	0.751408i	$-0.729375\pi$
$541$	7.86315	−	18.9833i	0.338063	−	0.816157i	0.997902	−	0.0647494i	$-0.0206248\pi$
$542$	2.43178	−	26.3441i	0.104454	−	1.13157i
$543$	−10.4613			−0.448937
$544$	−10.4635	+	21.1065i	−0.448618	+	0.904936i
$545$	−35.7599			−1.53179
$546$	2.22154	−	24.0665i	0.0950733	−	1.02995i
$547$	−0.832145	+	2.00898i	−0.0355799	+	0.0858976i	−0.940671	−	0.339321i	$-0.889803\pi$
$547$	−0.832145	+	2.00898i	−0.0355799	+	0.0858976i	0.905091	+	0.425219i	$0.139803\pi$
$548$	−5.98377	−	8.72206i	−0.255614	−	0.372588i
$549$	7.18739	−	2.97711i	0.306750	−	0.127060i
$550$	−10.4299	−	5.49298i	−0.444730	−	0.234221i
$551$	−17.6440	+	17.6440i	−0.751659	+	0.751659i
$552$	7.71855	−	0.903739i	0.328523	−	0.0384657i
$553$	−22.1643	−	22.1643i	−0.942520	−	0.942520i
$554$	−4.52694	−	14.6007i	−0.192331	−	0.620324i
$555$	−7.11200	−	17.1699i	−0.301888	−	0.728821i
$556$	−4.39369	−	20.7560i	−0.186334	−	0.880249i
$557$	27.8685	+	11.5435i	1.18083	+	0.489115i	0.884758	−	0.466051i	$-0.154324\pi$
$557$	27.8685	+	11.5435i	1.18083	+	0.489115i	0.296070	+	0.955166i	$0.404324\pi$
$558$	2.59418	+	3.12182i	0.109821	+	0.132157i
$559$		−	24.1555i		−	1.02167i
$560$	−21.3358	+	22.4081i	−0.901603	+	0.946916i
$561$			14.4453i			0.609879i
$562$	−20.3206	+	16.8861i	−0.857173	+	0.712297i
$563$	−17.3847	−	7.20096i	−0.732676	−	0.303484i	−0.0150247	−	0.999887i	$-0.504783\pi$
$563$	−17.3847	−	7.20096i	−0.732676	−	0.303484i	−0.717651	+	0.696403i	$0.754783\pi$
$564$	−1.81423	−	1.18033i	−0.0763927	−	0.0497008i
$565$	−14.4099	−	34.7886i	−0.606229	−	1.46357i
$566$	−32.1486	+	9.96768i	−1.35131	+	0.418973i
$567$	2.01027	+	2.01027i	0.0844233	+	0.0844233i
$568$	−6.59804	+	3.68422i	−0.276847	+	0.154586i
$569$	−5.37251	+	5.37251i	−0.225227	+	0.225227i	−0.810695	−	0.585468i	$-0.800911\pi$
$569$	−5.37251	+	5.37251i	−0.225227	+	0.225227i	0.585468	+	0.810695i	$0.300911\pi$
$570$	8.73088	−	16.5779i	0.365696	−	0.694370i
$571$	37.6829	−	15.6087i	1.57698	−	0.653206i	0.589047	−	0.808099i	$-0.299503\pi$
$571$	37.6829	−	15.6087i	1.57698	−	0.653206i	0.987931	+	0.154893i	$0.0495033\pi$
$572$	−7.63402	+	40.9982i	−0.319195	+	1.71422i
$573$	−5.80245	+	14.0084i	−0.242401	+	0.585207i
$574$	4.28241	+	0.395303i	0.178745	+	0.0164996i
$575$	−6.60243			−0.275340
$576$	−1.84805	−	7.78362i	−0.0770021	−	0.324317i
$577$	28.6100			1.19105			0.595525	−	0.803337i	$-0.296944\pi$
$577$	28.6100			1.19105			0.595525	+	0.803337i	$0.296944\pi$
$578$	−0.482786	−	0.0445653i	−0.0200812	−	0.00185367i
$579$	7.02413	−	16.9577i	0.291913	−	0.704740i
$580$	5.10464	−	27.4143i	0.211959	−	1.13832i
$581$	−6.55342	+	2.71452i	−0.271882	+	0.112617i
$582$	7.44864	−	14.1432i	0.308756	−	0.586254i
$583$	−18.6158	+	18.6158i	−0.770987	+	0.770987i
$584$	−13.6649	−	24.4724i	−0.565459	−	1.01268i
$585$	−11.5654	−	11.5654i	−0.478170	−	0.478170i
$586$	−27.6153	+	8.56213i	−1.14078	+	0.353698i
$587$	−14.0646	−	33.9550i	−0.580509	−	1.40147i	−0.892353	−	0.451339i	$-0.850947\pi$
$587$	−14.0646	−	33.9550i	−0.580509	−	1.40147i	0.311844	−	0.950133i	$-0.399053\pi$
$588$	1.81450	+	1.18051i	0.0748287	+	0.0486833i
$589$	−12.9118	−	5.34826i	−0.532023	−	0.220371i
$590$	−33.1298	+	27.5303i	−1.36393	+	1.13341i
$591$		−	7.20152i		−	0.296231i
$592$	27.3135	−	0.669539i	1.12258	−	0.0275179i
$593$		−	28.6736i		−	1.17749i	−0.808321	−	0.588743i	$-0.799623\pi$
$593$		−	28.6736i		−	1.17749i	0.808321	−	0.588743i	$-0.200377\pi$
$594$	−3.13517	−	3.77284i	−0.128638	−	0.154801i
$595$	−29.7611	−	12.3274i	−1.22009	−	0.505376i
$596$	4.68646	+	22.1390i	0.191965	+	0.906850i
$597$	−0.459506	−	1.10935i	−0.0188063	−	0.0454025i
$598$	6.91726	+	22.3101i	0.282868	+	0.912329i
$599$	−28.5413	−	28.5413i	−1.16617	−	1.16617i	−0.983100	−	0.183067i	$-0.941397\pi$
$599$	−28.5413	−	28.5413i	−1.16617	−	1.16617i	−0.183067	−	0.983100i	$-0.558603\pi$
$600$	0.790409	+	6.75063i	0.0322683	+	0.275593i
$601$	−29.9824	+	29.9824i	−1.22301	+	1.22301i	−0.256448	+	0.966558i	$0.582552\pi$
$601$	−29.9824	+	29.9824i	−1.22301	+	1.22301i	−0.966558	+	0.256448i	$0.917448\pi$
$602$	14.2946	+	7.52836i	0.582603	+	0.306833i
$603$	9.38659	−	3.88805i	0.382252	−	0.158334i
$604$	19.4884	+	28.4066i	0.792970	+	1.15585i
$605$	1.07433	−	2.59365i	0.0436776	−	0.105447i
$606$	−0.501449	+	5.43232i	−0.0203700	+	0.220673i
$607$	−20.2791			−0.823105			−0.411552	−	0.911386i	$-0.635013\pi$
$607$	−20.2791			−0.823105			−0.411552	+	0.911386i	$0.635013\pi$
$608$	18.1184	+	20.7473i	0.734796	+	0.841415i
$609$	−14.5684			−0.590343
$610$	2.75153	−	29.8080i	0.111406	−	1.20689i
$611$	2.48953	−	6.01025i	0.100715	−	0.243149i
$612$	6.86804	−	4.71183i	0.277624	−	0.190464i
$613$	−22.4278	+	9.28988i	−0.905849	+	0.375215i	−0.786466	−	0.617633i	$-0.788092\pi$
$613$	−22.4278	+	9.28988i	−0.905849	+	0.375215i	−0.119383	+	0.992848i	$0.538092\pi$
$614$	14.5879	+	7.68286i	0.588721	+	0.310055i
$615$	2.05796	−	2.05796i	0.0829848	−	0.0829848i
$616$	−21.8824	−	17.2952i	−0.881666	−	0.696844i
$617$	−28.6181	−	28.6181i	−1.15212	−	1.15212i	−0.986127	−	0.165993i	$-0.946917\pi$
$617$	−28.6181	−	28.6181i	−1.15212	−	1.15212i	−0.165993	−	0.986127i	$-0.553083\pi$
$618$	−1.15098	−	3.71224i	−0.0462993	−	0.149328i
$619$	−0.706861	−	1.70651i	−0.0284111	−	0.0685905i	0.909037	−	0.416715i	$-0.136819\pi$
$619$	−0.706861	−	1.70651i	−0.0284111	−	0.0685905i	−0.937448	+	0.348124i	$0.886819\pi$
$620$	15.2799	−	3.23450i	0.613656	−	0.129901i
$621$	−2.53841	−	1.05145i	−0.101863	−	0.0421931i
$622$	−8.68031	−	10.4458i	−0.348049	−	0.418839i
$623$		−	30.7893i		−	1.23355i
$624$	21.9828	−	9.74339i	0.880018	−	0.390048i
$625$			31.2406i			1.24962i
$626$	19.5477	−	16.2438i	0.781283	−	0.649234i
$627$	15.6044	+	6.46357i	0.623181	+	0.258130i
$628$	−15.7893	+	24.2690i	−0.630064	+	0.968440i
$629$	10.8855	+	26.2799i	0.434032	+	1.04785i
$630$	10.4486	−	3.23958i	0.416281	−	0.129068i
$631$	24.6361	+	24.6361i	0.980748	+	0.980748i	0.999818	−	0.0190703i	$-0.00607062\pi$
$631$	24.6361	+	24.6361i	0.980748	+	0.980748i	−0.0190703	+	0.999818i	$0.506071\pi$
$632$	8.50246	−	30.0034i	0.338210	−	1.19347i
$633$	5.66930	−	5.66930i	0.225334	−	0.225334i
$634$	−11.8702	+	22.5386i	−0.471424	+	0.895122i
$635$	13.7638	−	5.70114i	0.546198	−	0.226243i
$636$	14.9231	+	2.77874i	0.591741	+	0.110184i
$637$	−2.48990	+	6.01116i	−0.0986536	+	0.238171i
$638$	25.0312	+	2.31060i	0.990995	+	0.0914773i
$639$	2.67179			0.105694
$640$	−29.8134	−	7.66456i	−1.17848	−	0.302968i
$641$	0.278463			0.0109986			0.00549931	−	0.999985i	$-0.498250\pi$
$641$	0.278463			0.0109986			0.00549931	+	0.999985i	$0.498250\pi$
$642$	19.6943	+	1.81795i	0.777273	+	0.0717489i
$643$	−5.39050	+	13.0138i	−0.212581	+	0.513215i	−0.993818	−	0.111019i	$-0.964589\pi$
$643$	−5.39050	+	13.0138i	−0.212581	+	0.513215i	0.781238	+	0.624234i	$0.214589\pi$
$644$	−15.3584	−	2.85979i	−0.605204	−	0.112691i
$645$	10.1010	−	4.18397i	0.397727	−	0.164744i
$646$	−13.3633	+	25.3737i	−0.525772	+	0.998316i
$647$	17.8303	−	17.8303i	0.700980	−	0.700980i	−0.263641	−	0.964621i	$-0.584923\pi$
$647$	17.8303	−	17.8303i	0.700980	−	0.700980i	0.964621	+	0.263641i	$0.0849233\pi$
$648$	−0.771162	+	2.72127i	−0.0302941	+	0.106902i
$649$	−27.4575	−	27.4575i	−1.07780	−	1.07780i
$650$	−19.5124	+	6.04983i	−0.765340	+	0.237294i
$651$	−3.12258	−	7.53858i	−0.122384	−	0.295460i
$652$	16.5086	−	25.3746i	0.646527	−	0.993745i
$653$	31.3223	+	12.9741i	1.22574	+	0.507716i	0.899229	−	0.437478i	$-0.144128\pi$
$653$	31.3223	+	12.9741i	1.22574	+	0.507716i	0.326507	+	0.945195i	$0.394128\pi$
$654$	−14.2954	+	11.8792i	−0.558993	+	0.464515i
$655$			57.1107i			2.23150i
$656$	1.73375	+	3.91165i	0.0676915	+	0.152724i
$657$			9.90978i			0.386617i
$658$	2.78081	+	3.34640i	0.108407	+	0.130456i
$659$	38.2358	+	15.8378i	1.48946	+	0.616953i	0.971199	−	0.238271i	$-0.0765807\pi$
$659$	38.2358	+	15.8378i	1.48946	+	0.616953i	0.518258	+	0.855224i	$0.326581\pi$
$660$	−18.4663	+	3.90901i	−0.718801	+	0.152158i
$661$	−7.49776	−	18.1012i	−0.291629	−	0.704055i	0.708369	−	0.705842i	$-0.249431\pi$
$661$	−7.49776	−	18.1012i	−0.291629	−	0.704055i	−0.999998	+	0.00178728i	$0.999431\pi$
$662$	0.283736	+	0.915129i	0.0110277	+	0.0355675i
$663$	17.7018	+	17.7018i	0.687479	+	0.687479i
$664$	−5.53661	−	4.37598i	−0.214862	−	0.169821i
$665$	−26.6334	+	26.6334i	−1.03280	+	1.03280i
$666$	−8.54682	−	4.50126i	−0.331182	−	0.174420i
$667$	13.0079	−	5.38804i	0.503667	−	0.208626i
$668$	9.50714	−	6.52238i	0.367842	−	0.252358i
$669$	−0.0720861	+	0.174031i	−0.00278701	+	0.00672844i
$670$	3.59345	−	38.9287i	0.138827	−	1.50395i
$671$	26.9849			1.04174
$672$	−1.08535	+	16.0455i	−0.0418685	+	0.618968i
$673$	18.3856			0.708711			0.354356	−	0.935111i	$-0.384700\pi$
$673$	18.3856			0.708711			0.354356	+	0.935111i	$0.384700\pi$
$674$	3.16197	−	34.2543i	0.121794	−	1.31943i
$675$	0.919594	−	2.22010i	0.0353952	−	0.0854515i
$676$	26.1771	+	38.1562i	1.00681	+	1.46755i
$677$	34.2111	−	14.1707i	1.31484	−	0.544624i	0.388546	−	0.921429i	$-0.372977\pi$
$677$	34.2111	−	14.1707i	1.31484	−	0.544624i	0.926293	+	0.376805i	$0.122977\pi$
$678$	−17.3170	−	9.12018i	−0.665057	−	0.350258i
$679$	−22.7219	+	22.7219i	−0.871986	+	0.871986i
$680$	−3.72700	−	31.8312i	−0.142924	−	1.22067i
$681$	−0.197269	−	0.197269i	−0.00755936	−	0.00755936i
$682$	4.16952	+	13.4479i	0.159659	+	0.514946i
$683$	9.51662	+	22.9752i	0.364143	+	0.879120i	0.994685	+	0.102964i	$0.0328328\pi$
$683$	9.51662	+	22.9752i	0.364143	+	0.879120i	−0.630542	+	0.776155i	$0.717167\pi$
$684$	−2.01681	−	9.52750i	−0.0771147	−	0.364293i
$685$	13.2943	+	5.50668i	0.507949	+	0.210399i
$686$	15.2059	+	18.2987i	0.580566	+	0.698648i
$687$			2.20467i			0.0841133i
$688$	0.393889	+	16.0685i	0.0150169	+	0.612605i
$689$			45.6250i			1.73817i
$690$	−8.13120	+	6.75690i	−0.309549	+	0.257231i
$691$	18.8902	+	7.82459i	0.718618	+	0.297661i	0.711866	−	0.702316i	$-0.247851\pi$
$691$	18.8902	+	7.82459i	0.718618	+	0.297661i	0.00675270	+	0.999977i	$0.497851\pi$
$692$	7.79758	+	5.07308i	0.296419	+	0.192849i
$693$	3.77376	+	9.11066i	0.143353	+	0.346085i
$694$	10.1686	−	3.15276i	0.385993	−	0.119677i
$695$	20.4090	+	20.4090i	0.774156	+	0.774156i
$696$	−7.06623	−	12.6549i	−0.267845	−	0.479681i
$697$	−3.14987	+	3.14987i	−0.119310	+	0.119310i
$698$	20.5199	−	38.9623i	0.776688	−	1.47475i
$699$	5.65317	−	2.34162i	0.213823	−	0.0885683i
$700$	2.50117	−	13.4324i	0.0945352	−	0.507698i
$701$	−5.48707	+	13.2470i	−0.207244	+	0.500331i	−0.992987	−	0.118222i	$-0.962281\pi$
$701$	−5.48707	+	13.2470i	−0.207244	+	0.500331i	0.785743	+	0.618552i	$0.212281\pi$
$702$	−8.46533	−	0.781422i	−0.319503	−	0.0294929i
$703$	33.2595			1.25440
$704$	4.40969	−	27.3969i	0.166197	−	1.03256i
$705$	2.94449			0.110896
$706$	−31.1688	−	2.87715i	−1.17305	−	0.108283i
$707$	4.19683	−	10.1320i	0.157838	−	0.381055i
$708$	−4.09854	+	22.0110i	−0.154032	+	0.827225i
$709$	3.85647	−	1.59740i	0.144833	−	0.0599917i	−0.309090	−	0.951033i	$-0.600024\pi$
$709$	3.85647	−	1.59740i	0.144833	−	0.0599917i	0.453922	+	0.891041i	$0.350024\pi$
$710$	4.79063	−	9.09626i	0.179789	−	0.341376i
$711$	−7.79622	+	7.79622i	−0.292381	+	0.292381i
$712$	26.7450	−	14.9339i	1.00231	−	0.559673i
$713$	5.57619	+	5.57619i	0.208830	+	0.208830i
$714$	−15.9924	+	4.95844i	−0.598499	+	0.185565i
$715$	−21.7110	−	52.4151i	−0.811946	−	1.96021i
$716$	−0.496071	−	0.322742i	−0.0185390	−	0.0120614i
$717$	−7.63960	−	3.16443i	−0.285306	−	0.118178i
$718$	−15.6388	+	12.9956i	−0.583636	+	0.484993i
$719$		−	8.78550i		−	0.327644i	−0.986490	−	0.163822i	$-0.947618\pi$
$719$		−	8.78550i		−	0.327644i	0.986490	−	0.163822i	$-0.0523823\pi$
$720$	7.88200	+	7.50482i	0.293745	+	0.279688i
$721$			7.81307i			0.290974i
$722$	4.25729	+	5.12319i	0.158440	+	0.190665i
$723$	−20.9990	−	8.69807i	−0.780961	−	0.323485i
$724$	4.33294	+	20.4690i	0.161032	+	0.760724i
$725$	4.71238	+	11.3767i	0.175013	+	0.422520i
$726$	−0.432124	−	1.39372i	−0.0160376	−	0.0517259i
$727$	−10.0533	−	10.0533i	−0.372858	−	0.372858i	0.495659	−	0.868517i	$-0.334927\pi$
$727$	−10.0533	−	10.0533i	−0.372858	−	0.372858i	−0.868517	+	0.495659i	$0.834927\pi$
$728$	−48.0097	+	5.62129i	−1.77936	+	0.208339i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	33.7384	+	17.7686i	1.24871	+	0.657647i
$731$	−15.4604	+	6.40390i	−0.571823	+	0.236857i
$732$	−8.80208	−	12.8301i	−0.325334	−	0.474213i
$733$	10.3759	−	25.0496i	0.383242	−	0.925228i	−0.608093	−	0.793866i	$-0.708065\pi$
$733$	10.3759	−	25.0496i	0.383242	−	0.925228i	0.991334	−	0.131362i	$-0.0419350\pi$
$734$	−1.27100	+	13.7691i	−0.0469136	+	0.508226i
$735$	−2.94494			−0.108626
$736$	−4.96522	−	14.7281i	−0.183021	−	0.542885i
$737$	35.2418			1.29815
$738$	0.139047	−	1.50633i	0.00511839	−	0.0554487i
$739$	−12.3459	+	29.8057i	−0.454153	+	1.09642i	0.516575	+	0.856242i	$0.327207\pi$
$739$	−12.3459	+	29.8057i	−0.454153	+	1.09642i	−0.970728	+	0.240180i	$0.922793\pi$
$740$	−30.6496	+	21.0272i	−1.12670	+	0.772975i
$741$	27.0429	−	11.2016i	0.993447	−	0.411499i
$742$	−26.9996	−	14.2196i	−0.991186	−	0.522017i
$743$	16.0222	−	16.0222i	0.587799	−	0.587799i	−0.349236	−	0.937035i	$-0.613559\pi$
$743$	16.0222	−	16.0222i	0.587799	−	0.587799i	0.937035	+	0.349236i	$0.113559\pi$
$744$	5.03381	−	6.36891i	0.184548	−	0.233496i
$745$	−21.7689	−	21.7689i	−0.797551	−	0.797551i
$746$	−2.24062	−	7.22665i	−0.0820351	−	0.264586i
$747$	0.954824	+	2.30515i	0.0349352	+	0.0843410i
$748$	28.2642	−	5.98305i	1.03344	−	0.218762i
$749$	−36.7327	−	15.2152i	−1.34218	−	0.555951i
$750$	6.38660	+	7.68558i	0.233206	+	0.280638i
$751$			26.5917i			0.970346i	0.874418	+	0.485173i	$0.161243\pi$
$751$			26.5917i			0.970346i	−0.874418	+	0.485173i	$0.838757\pi$
$752$	−1.55805	+	4.03867i	−0.0568163	+	0.147275i
$753$		−	13.3497i		−	0.486491i
$754$	33.5057	−	27.8427i	1.22020	−	1.01397i
$755$	−43.2978	−	17.9345i	−1.57577	−	0.652704i
$756$	3.10075	−	4.76601i	0.112773	−	0.173338i
$757$	5.33084	+	12.8698i	0.193753	+	0.467760i	0.990662	−	0.136338i	$-0.0435334\pi$
$757$	5.33084	+	12.8698i	0.193753	+	0.467760i	−0.796910	+	0.604098i	$0.793533\pi$
$758$	−42.4487	+	13.1612i	−1.54181	+	0.478037i
$759$	−6.73903	−	6.73903i	−0.244611	−	0.244611i
$760$	−36.0532	−	10.2169i	−1.30779	−	0.370604i
$761$	11.8263	−	11.8263i	0.428704	−	0.428704i	−0.459483	−	0.888187i	$-0.651965\pi$
$761$	11.8263	−	11.8263i	0.428704	−	0.428704i	0.888187	+	0.459483i	$0.151965\pi$
$762$	3.60831	−	6.85132i	0.130715	−	0.248197i
$763$	34.5205	−	14.2989i	1.24973	−	0.517653i
$764$	29.8126	+	5.55122i	1.07858	+	0.200836i
$765$	−4.33615	+	10.4684i	−0.156774	+	0.378485i
$766$	3.48632	+	0.321817i	0.125966	+	0.0116277i
$767$	−67.2950			−2.42988
$768$	−14.4643	+	6.83986i	−0.521936	+	0.246812i
$769$	39.2000			1.41359			0.706795	−	0.707419i	$-0.250140\pi$
$769$	39.2000			1.41359			0.706795	+	0.707419i	$0.250140\pi$
$770$	37.7843	+	3.48781i	1.36165	+	0.125692i
$771$	−6.12196	+	14.7797i	−0.220477	+	0.532278i
$772$	−36.0895	−	6.72001i	−1.29889	−	0.241858i
$773$	39.7946	−	16.4834i	1.43131	−	0.592868i	0.473636	−	0.880721i	$-0.342941\pi$
$773$	39.7946	−	16.4834i	1.43131	−	0.592868i	0.957675	+	0.287852i	$0.0929412\pi$
$774$	2.64808	−	5.02807i	0.0951833	−	0.180730i
$775$	−4.87693	+	4.87693i	−0.175184	+	0.175184i
$776$	−30.7583	−	8.71638i	−1.10416	−	0.312900i
$777$	13.7310	+	13.7310i	0.492596	+	0.492596i
$778$	−13.8859	+	4.30532i	−0.497833	+	0.154353i
$779$	1.99321	+	4.81205i	0.0714143	+	0.172409i
$780$	−17.8391	+	27.4196i	−0.638742	+	0.981779i
$781$	8.56214	+	3.54655i	0.306377	+	0.126906i
$782$	12.4454	−	10.3420i	0.445048	−	0.369828i
$783$			5.12441i			0.183132i
$784$	1.55829	−	4.03928i	0.0556531	−	0.144260i
$785$		−	39.3887i		−	1.40584i
$786$	18.9718	+	22.8305i	0.676702	+	0.814338i
$787$	3.18736	+	1.32025i	0.113617	+	0.0470618i	0.438768	−	0.898600i	$-0.355415\pi$
$787$	3.18736	+	1.32025i	0.113617	+	0.0470618i	−0.325151	+	0.945662i	$0.605415\pi$
$788$	−14.0908	+	2.98279i	−0.501964	+	0.106257i
$789$	−2.40606	−	5.80875i	−0.0856581	−	0.206797i
$790$	12.5637	+	40.5217i	0.446998	+	1.44170i
$791$	27.8209	+	27.8209i	0.989197	+	0.989197i
$792$	−6.08354	+	7.69707i	−0.216169	+	0.273503i
$793$	33.0683	−	33.0683i	1.17429	−	1.17429i
$794$	−18.7807	−	9.89101i	−0.666501	−	0.351019i
$795$	−19.0788	+	7.90269i	−0.676655	+	0.280280i
$796$	−1.98027	+	1.35857i	−0.0701888	+	0.0481531i
$797$	−9.15542	+	22.1031i	−0.324302	+	0.782934i	0.674693	+	0.738099i	$0.264276\pi$
$797$	−9.15542	+	22.1031i	−0.324302	+	0.782934i	−0.998994	+	0.0448349i	$0.985724\pi$
$798$	−1.79950	+	19.4944i	−0.0637015	+	0.690093i
$799$	−4.50678			−0.159438
$800$	12.8812	−	4.34258i	0.455419	−	0.153533i
$801$	−10.8300			−0.382661
$802$	−2.84827	+	30.8560i	−0.100576	+	1.08956i
$803$	−13.1543	+	31.7574i	−0.464206	+	1.12069i
$804$	−11.4953	−	16.7558i	−0.405410	−	0.590932i
$805$	19.6352	−	8.13318i	0.692051	−	0.286657i
$806$	21.5890	+	11.3701i	0.760441	+	0.400493i
$807$	8.51117	−	8.51117i	0.299607	−	0.299607i
$808$	10.8368	−	1.26884i	0.381237	−	0.0446378i
$809$	−1.21564	−	1.21564i	−0.0427396	−	0.0427396i	0.685414	−	0.728154i	$-0.259621\pi$
$809$	−1.21564	−	1.21564i	−0.0427396	−	0.0427396i	−0.728154	+	0.685414i	$0.759621\pi$
$810$	−1.13951	−	3.67526i	−0.0400385	−	0.129135i
$811$	−6.74157	−	16.2756i	−0.236728	−	0.571513i	0.760212	−	0.649675i	$-0.225095\pi$
$811$	−6.74157	−	16.2756i	−0.236728	−	0.571513i	−0.996941	+	0.0781619i	$0.975095\pi$
$812$	6.03408	+	28.5052i	0.211755	+	1.00034i
$813$	17.2832	+	7.15896i	0.606150	+	0.251076i
$814$	−21.4145	−	25.7701i	−0.750579	−	0.903241i
$815$			41.1830i			1.44258i
$816$	−12.0640	−	11.4867i	−0.422325	−	0.402116i
$817$			19.5665i			0.684544i
$818$	19.9976	−	16.6177i	0.699201	−	0.581026i
$819$	15.7890	+	6.54003i	0.551714	+	0.228527i
$820$	−4.87907	−	3.17430i	−0.170384	−	0.110852i
$821$	2.00047	+	4.82956i	0.0698169	+	0.168553i	0.954936	−	0.296811i	$-0.0959233\pi$
$821$	2.00047	+	4.82956i	0.0698169	+	0.168553i	−0.885119	+	0.465364i	$0.845923\pi$
$822$	7.14381	−	2.21494i	0.249169	−	0.0772548i
$823$	−13.5268	−	13.5268i	−0.471516	−	0.471516i	0.430889	−	0.902405i	$-0.358200\pi$
$823$	−13.5268	−	13.5268i	−0.471516	−	0.471516i	−0.902405	+	0.430889i	$0.858200\pi$
$824$	−6.78681	+	3.78963i	−0.236430	+	0.132018i
$825$	5.89395	−	5.89395i	0.205201	−	0.205201i
$826$	20.9733	−	39.8233i	0.729755	−	1.38563i
$827$	−22.3808	+	9.27041i	−0.778255	+	0.322364i	−0.736211	−	0.676752i	$-0.763387\pi$
$827$	−22.3808	+	9.27041i	−0.778255	+	0.322364i	−0.0420440	+	0.999116i	$0.513387\pi$
$828$	−1.00592	+	5.40227i	−0.0349582	+	0.187742i
$829$	1.75314	−	4.23245i	0.0608890	−	0.146999i	−0.890507	−	0.454970i	$-0.849650\pi$
$829$	1.75314	−	4.23245i	0.0608890	−	0.146999i	0.951396	+	0.307971i	$0.0996500\pi$
$830$	9.56006	+	0.882475i	0.331835	+	0.0306312i
$831$	10.8091			0.374963
$832$	−28.1694	−	38.9770i	−0.976597	−	1.35128i
$833$	4.50746			0.156174
$834$	14.9384	+	1.37894i	0.517275	+	0.0477489i
$835$	−6.00234	+	14.4909i	−0.207720	+	0.501479i
$836$	6.18372	−	33.2094i	0.213868	−	1.14857i
$837$	−2.65168	+	1.09836i	−0.0916553	+	0.0379649i
$838$	−13.7454	+	26.0993i	−0.474827	+	0.901584i
$839$	−23.6794	+	23.6794i	−0.817503	+	0.817503i	−0.985746	−	0.168242i	$-0.946191\pi$
$839$	−23.6794	+	23.6794i	−0.817503	+	0.817503i	0.168242	+	0.985746i	$0.446191\pi$
$840$	−10.6664	−	19.1023i	−0.368025	−	0.659093i
$841$	1.93775	+	1.93775i	0.0668190	+	0.0668190i
$842$	−7.47822	+	2.31862i	−0.257716	+	0.0799050i
$843$	−7.14946	−	17.2603i	−0.246241	−	0.594477i
$844$	−13.4409	−	8.74463i	−0.462656	−	0.301003i
$845$	−58.1583	−	24.0900i	−2.00071	−	0.828720i
$846$	1.17709	−	0.978142i	0.0404691	−	0.0336292i
$847$			2.93333i			0.100791i
$848$	−0.743977	−	30.3501i	−0.0255483	−	1.04223i
$849$		−	23.8001i		−	0.816816i
$850$	9.04507	+	10.8848i	0.310243	+	0.373344i
$851$	−17.3385	−	7.18182i	−0.594354	−	0.246190i
$852$	−1.10662	−	5.22773i	−0.0379122	−	0.179099i
$853$	1.47996	+	3.57295i	0.0506730	+	0.122335i	0.947189	−	0.320676i	$-0.103910\pi$
$853$	1.47996	+	3.57295i	0.0506730	+	0.122335i	−0.896516	+	0.443011i	$0.853910\pi$
$854$	9.26276	+	29.8751i	0.316965	+	1.02230i
$855$	9.36821	+	9.36821i	0.320386	+	0.320386i
$856$	−4.60007	−	39.2877i	−0.157227	−	1.34283i
$857$	−1.99585	+	1.99585i	−0.0681769	+	0.0681769i	−0.740373	−	0.672196i	$-0.765351\pi$
$857$	−1.99585	+	1.99585i	−0.0681769	+	0.0681769i	0.672196	+	0.740373i	$0.265351\pi$
$858$	−26.0911	−	13.7411i	−0.890737	−	0.469115i
$859$	28.4574	−	11.7874i	0.970953	−	0.402182i	0.159886	−	0.987135i	$-0.448887\pi$
$859$	28.4574	−	11.7874i	0.970953	−	0.402182i	0.811067	+	0.584954i	$0.198887\pi$
$860$	−12.3703	−	18.0311i	−0.421822	−	0.614855i
$861$	−1.16374	+	2.80952i	−0.0396601	+	0.0957480i
$862$	−0.676158	+	7.32498i	−0.0230300	+	0.249490i
$863$	−56.7230			−1.93087			−0.965436	−	0.260639i	$-0.916067\pi$
$863$	−56.7230			−1.93087			−0.965436	+	0.260639i	$0.916067\pi$
$864$	5.64396	+	0.381771i	0.192011	+	0.0129881i
$865$	−12.6555			−0.430299
$866$	0.838365	−	9.08220i	0.0284888	−	0.308626i
$867$	0.131196	−	0.316736i	0.00445566	−	0.0107569i
$868$	−13.4570	+	9.23216i	−0.456759	+	0.313360i
$869$	−35.3329	+	14.6354i	−1.19859	+	0.496471i
$870$	17.4464	+	9.18829i	0.591487	+	0.311512i
$871$	43.1866	−	43.1866i	1.46332	−	1.46332i
$872$	29.1644	+	23.0507i	0.987630	+	0.780595i
$873$	7.99237	+	7.99237i	0.270501	+	0.270501i
$874$	−5.60312	−	18.0717i	−0.189529	−	0.611283i
$875$	−7.68746	−	18.5592i	−0.259883	−	0.627414i
$876$	19.3899	−	4.10451i	0.655123	−	0.138679i
$877$	35.4309	+	14.6760i	1.19642	+	0.495572i	0.889839	−	0.456274i	$-0.150816\pi$
$877$	35.4309	+	14.6760i	1.19642	+	0.495572i	0.306577	+	0.951846i	$0.400816\pi$
$878$	−26.2627	−	31.6043i	−0.886324	−	1.06659i
$879$		−	20.4440i		−	0.689560i
$880$	15.2971	+	34.5130i	0.515664	+	1.16343i
$881$			16.0453i			0.540579i	0.962779	+	0.270290i	$0.0871194\pi$
$881$			16.0453i			0.540579i	−0.962779	+	0.270290i	$0.912881\pi$
$882$	−1.17727	+	0.978290i	−0.0396406	+	0.0329407i
$883$	−3.76841	−	1.56093i	−0.126817	−	0.0525294i	0.318373	−	0.947966i	$-0.396864\pi$
$883$	−3.76841	−	1.56093i	−0.126817	−	0.0525294i	−0.445190	+	0.895436i	$0.646864\pi$
$884$	27.3041	−	41.9678i	0.918338	−	1.41153i
$885$	−11.6562	−	28.1405i	−0.391818	−	0.945931i
$886$	−23.6106	+	7.32046i	−0.793212	+	0.245936i
$887$	41.9135	+	41.9135i	1.40732	+	1.40732i	0.773396	+	0.633923i	$0.218556\pi$
$887$	41.9135	+	41.9135i	1.40732	+	1.40732i	0.633923	+	0.773396i	$0.281444\pi$
$888$	−5.26736	+	18.5874i	−0.176761	+	0.623753i
$889$	−11.0071	+	11.0071i	−0.369165	+	0.369165i
$890$	−19.4187	+	36.8715i	−0.650918	+	1.23594i
$891$	3.20465	−	1.32741i	0.107360	−	0.0444699i
$892$	0.370374	+	0.0689650i	0.0124010	+	0.00230912i
$893$	−2.01657	+	4.86843i	−0.0674819	+	0.162916i
$894$	−15.9338	−	1.47083i	−0.532907	−	0.0491918i
$895$	0.805124			0.0269123
$896$	31.8448	−	4.52220i	1.06386	−	0.151076i
$897$	−16.5165			−0.551470
$898$	−1.11857	−	0.103253i	−0.0373270	−	0.00344560i
$899$	5.62845	−	13.5883i	0.187719	−	0.453195i
$900$	−4.72482	−	0.879779i	−0.157494	−	0.0293260i
$901$	29.2016	−	12.0957i	0.972846	−	0.402966i
$902$	2.44511	−	4.64268i	0.0814133	−	0.154584i
$903$	−8.07791	+	8.07791i	−0.268816	+	0.268816i
$904$	−10.6724	+	37.6607i	−0.354959	+	1.25258i
$905$	−20.1268	−	20.1268i	−0.669037	−	0.669037i
$906$	−23.2664	+	7.21375i	−0.772975	+	0.239661i
$907$	−8.10967	−	19.5785i	−0.269277	−	0.650093i	0.730173	−	0.683263i	$-0.239440\pi$
$907$	−8.10967	−	19.5785i	−0.269277	−	0.650093i	−0.999450	+	0.0331702i	$0.989440\pi$
$908$	−0.304278	+	0.467691i	−0.0100978	+	0.0155209i
$909$	−3.56392	−	1.47622i	−0.118208	−	0.0489632i
$910$	50.5764	−	42.0282i	1.67659	−	1.39322i
$911$			32.2546i			1.06864i	0.845282	+	0.534321i	$0.179433\pi$
$911$			32.2546i			1.06864i	−0.845282	+	0.534321i	$0.820567\pi$
$912$	−17.8066	+	7.89235i	−0.589634	+	0.261342i
$913$			8.65464i			0.286427i
$914$	27.2004	+	32.7327i	0.899709	+	1.08270i
$915$	19.5558	+	8.10028i	0.646495	+	0.267787i
$916$	4.31374	−	0.913146i	0.142530	−	0.0301712i
$917$	−22.8361	−	55.1312i	−0.754114	−	1.82059i
$918$	1.74412	+	5.62528i	0.0575644	+	0.185662i
$919$	−31.0572	−	31.0572i	−1.02448	−	1.02448i	−0.999693	−	0.0247905i	$-0.992108\pi$
$919$	−31.0572	−	31.0572i	−1.02448	−	1.02448i	−0.0247905	−	0.999693i	$-0.507892\pi$
$920$	16.5887	+	13.1112i	0.546912	+	0.432264i
$921$	−8.24369	+	8.24369i	−0.271639	+	0.271639i
$922$	−0.733754	−	0.386438i	−0.0241649	−	0.0127267i
$923$	14.8384	−	6.14628i	0.488413	−	0.202307i
$924$	16.2632	−	11.1574i	0.535022	−	0.367052i
$925$	6.28122	−	15.1642i	0.206525	−	0.498596i
$926$	−1.69464	+	18.3584i	−0.0556892	+	0.603294i
$927$	2.74823			0.0902637
$928$	−21.8343	+	19.0676i	−0.716745	+	0.625924i
$929$	−32.4744			−1.06545			−0.532725	−	0.846288i	$-0.678832\pi$
$929$	−32.4744			−1.06545			−0.532725	+	0.846288i	$0.678832\pi$
$930$	−1.01514	+	10.9972i	−0.0332876	+	0.360612i
$931$	2.01687	−	4.86916i	0.0661004	−	0.159580i
$932$	−6.92319	−	10.0914i	−0.226777	−	0.330554i
$933$	8.87268	−	3.67518i	0.290478	−	0.120320i
$934$	49.0006	+	25.8066i	1.60335	+	0.844418i
$935$	−27.7917	+	27.7917i	−0.908884	+	0.908884i
$936$	1.97727	+	16.8873i	0.0646292	+	0.551978i
$937$	−29.6117	−	29.6117i	−0.967373	−	0.967373i	0.0321113	−	0.999484i	$-0.489777\pi$
$937$	−29.6117	−	29.6117i	−0.967373	−	0.967373i	−0.999484	+	0.0321113i	$0.989777\pi$
$938$	12.0970	+	39.0163i	0.394981	+	1.27393i
$939$	6.87753	+	16.6038i	0.224440	+	0.541845i
$940$	−1.21957	−	5.76132i	−0.0397781	−	0.187913i
$941$	7.86542	+	3.25796i	0.256405	+	0.106207i	0.507184	−	0.861838i	$-0.330687\pi$
$941$	7.86542	+	3.25796i	0.256405	+	0.106207i	−0.250778	+	0.968045i	$0.580687\pi$
$942$	−13.0847	−	15.7460i	−0.426322	−	0.513032i
$943$		−	2.93896i		−	0.0957058i
$944$	44.7653	−	1.09734i	1.45699	−	0.0357153i
$945$			7.73523i			0.251627i
$946$	15.1605	−	12.5981i	0.492910	−	0.409600i
$947$	48.5504	+	20.1102i	1.57767	+	0.653494i	0.988043	−	0.154178i	$-0.0492730\pi$
$947$	48.5504	+	20.1102i	1.57767	+	0.653494i	0.589631	+	0.807672i	$0.299273\pi$
$948$	18.4835	+	12.0253i	0.600317	+	0.390564i
$949$	22.7968	+	55.0364i	0.740017	+	1.78656i
$950$	15.8055	−	4.90049i	0.512797	−	0.158993i
$951$	−12.7367	−	12.7367i	−0.413014	−	0.413014i
$952$	16.3257	+	29.2376i	0.529120	+	0.947597i
$953$	−17.0094	+	17.0094i	−0.550988	+	0.550988i	−0.926726	−	0.375738i	$-0.877389\pi$
$953$	−17.0094	+	17.0094i	−0.550988	+	0.550988i	0.375738	+	0.926726i	$0.377389\pi$
$954$	−5.00170	+	9.49703i	−0.161936	+	0.307478i
$955$	−38.1146	+	15.7876i	−1.23336	+	0.510874i
$956$	−3.02742	+	16.2586i	−0.0979137	+	0.525842i
$957$	−6.80219	+	16.4219i	−0.219884	+	0.530846i
$958$	39.0045	+	3.60045i	1.26018	+	0.116325i
$959$	−15.0354			−0.485518
$960$	11.4196	−	18.5307i	0.368567	−	0.598074i
$961$	−22.7622			−0.734265
$962$	−57.8218	−	5.33745i	−1.86425	−	0.172086i
$963$	−5.35190	+	12.9206i	−0.172463	+	0.416362i
$964$	−8.32147	+	44.6902i	−0.268017	+	1.43937i
$965$	46.1394	−	19.1116i	1.48528	−	0.615223i
$966$	5.14757	−	9.77401i	0.165620	−	0.314474i
$967$	28.7386	−	28.7386i	0.924170	−	0.924170i	−0.0731512	−	0.997321i	$-0.523306\pi$
$967$	28.7386	−	28.7386i	0.924170	−	0.924170i	0.997321	+	0.0731512i	$0.0233056\pi$
$968$	−2.54804	+	1.42277i	−0.0818970	+	0.0457297i
$969$	−14.3388	−	14.3388i	−0.460628	−	0.460628i
$970$	41.5412	−	12.8798i	1.33381	−	0.413547i
$971$	−12.3179	−	29.7379i	−0.395299	−	0.954336i	−0.988765	−	0.149477i	$-0.952241\pi$
$971$	−12.3179	−	29.7379i	−0.395299	−	0.954336i	0.593466	−	0.804859i	$-0.297759\pi$
$972$	−1.67643	−	1.09068i	−0.0537715	−	0.0349836i
$973$	−27.8622	−	11.5409i	−0.893222	−	0.369985i
$974$	35.1726	−	29.2279i	1.12700	−	0.936522i
$975$		−	14.4453i		−	0.462621i
$976$	−21.4581	+	22.5366i	−0.686858	+	0.721378i
$977$		−	13.3790i		−	0.428032i	−0.976830	−	0.214016i	$-0.931345\pi$
$977$		−	13.3790i		−	0.428032i	0.976830	−	0.214016i	$-0.0686545\pi$
$978$	13.6807	+	16.4633i	0.437461	+	0.526438i
$979$	−34.7065	−	14.3759i	−1.10922	−	0.459456i
$980$	1.21976	+	5.76219i	0.0389637	+	0.184066i
$981$	−5.02958	−	12.1425i	−0.160582	−	0.387680i
$982$	−11.1202	−	35.8657i	−0.354859	−	1.14452i
$983$	−13.7710	−	13.7710i	−0.439227	−	0.439227i	0.452525	−	0.891752i	$-0.350523\pi$
$983$	−13.7710	−	13.7710i	−0.439227	−	0.439227i	−0.891752	+	0.452525i	$0.850523\pi$
$984$	−3.00494	+	0.351838i	−0.0957939	+	0.0112162i
$985$	13.8552	−	13.8552i	0.441464	−	0.441464i
$986$	−26.7030	−	14.0634i	−0.850398	−	0.447870i
$987$	−2.84243	+	1.17737i	−0.0904757	+	0.0374763i
$988$	−33.1183	−	48.2738i	−1.05363	−	1.53579i
$989$	4.22505	−	10.2002i	0.134349	−	0.324347i
$990$	1.22683	−	13.2905i	0.0389912	−	0.422400i
$991$	8.30842			0.263926			0.131963	−	0.991255i	$-0.457872\pi$
$991$	8.30842			0.263926			0.131963	+	0.991255i	$0.457872\pi$
$992$	−14.5466	−	7.21143i	−0.461856	−	0.228963i
$993$	−0.677483			−0.0214993
$994$	−0.987382	+	10.6965i	−0.0313179	+	0.339274i
$995$	1.25025	−	3.01836i	0.0396355	−	0.0956885i
$996$	4.11488	−	2.82301i	0.130385	−	0.0894506i
$997$	−25.3066	+	10.4823i	−0.801468	+	0.331979i	−0.745544	−	0.666456i	$-0.767810\pi$
$997$	−25.3066	+	10.4823i	−0.801468	+	0.331979i	−0.0559236	+	0.998435i	$0.517810\pi$
$998$	−15.7291	−	8.28386i	−0.497895	−	0.262221i
$999$	4.82984	−	4.82984i	0.152809	−	0.152809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.13.8	✓	32
3.2	odd	2		288.2.v.d.109.1		32
4.3	odd	2		384.2.n.a.145.6		32
8.3	odd	2		768.2.n.b.289.3		32
8.5	even	2		768.2.n.a.289.7		32
12.11	even	2		1152.2.v.c.145.7		32
32.5	even	8	inner	96.2.n.a.37.8	yes	32
32.11	odd	8		768.2.n.b.481.3		32
32.21	even	8		768.2.n.a.481.7		32
32.27	odd	8		384.2.n.a.241.6		32
96.5	odd	8		288.2.v.d.37.1		32
96.59	even	8		1152.2.v.c.1009.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.8	✓	32	1.1	even	1	trivial
96.2.n.a.37.8	yes	32	32.5	even	8	inner
288.2.v.d.37.1		32	96.5	odd	8
288.2.v.d.109.1		32	3.2	odd	2
384.2.n.a.145.6		32	4.3	odd	2
384.2.n.a.241.6		32	32.27	odd	8
768.2.n.a.289.7		32	8.5	even	2
768.2.n.a.481.7		32	32.21	even	8
768.2.n.b.289.3		32	8.3	odd	2
768.2.n.b.481.3		32	32.11	odd	8
1152.2.v.c.145.7		32	12.11	even	2
1152.2.v.c.1009.7		32	96.59	even	8

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40823 + 0.129991i) q^{2} +(-0.382683 + 0.923880i) q^{3} +(1.96620 + 0.366115i) q^{4} +(-2.51374 + 1.04122i) q^{5} +(-0.659001 + 1.25129i) q^{6} +(2.01027 - 2.01027i) q^{7} +(2.72127 + 0.771162i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(1.40823 + 0.129991i) q^{2} +(-0.382683 + 0.923880i) q^{3} +(1.96620 + 0.366115i) q^{4} +(-2.51374 + 1.04122i) q^{5} +(-0.659001 + 1.25129i) q^{6} +(2.01027 - 2.01027i) q^{7} +(2.72127 + 0.771162i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.67526 + 1.13951i) q^{10} +(-1.32741 - 3.20465i) q^{11} +(-1.09068 + 1.67643i) q^{12} +(-5.55375 - 2.30044i) q^{13} +(3.09223 - 2.56960i) q^{14} -2.72085i q^{15} +(3.73192 + 1.43971i) q^{16} +4.16447i q^{17} +(-0.903849 - 1.08768i) q^{18} +(4.49866 + 1.86340i) q^{19} +(-5.32373 + 1.12694i) q^{20} +(1.08795 + 2.62654i) q^{21} +(-1.45272 - 4.68542i) q^{22} +(-1.94282 - 1.94282i) q^{23} +(-1.75385 + 2.21901i) q^{24} +(1.69919 - 1.69919i) q^{25} +(-7.52191 - 3.96148i) q^{26} +(0.923880 - 0.382683i) q^{27} +(4.68859 - 3.21661i) q^{28} +(-1.96103 + 4.73434i) q^{29} +(0.353687 - 3.83157i) q^{30} -2.87015 q^{31} +(5.06824 + 2.51256i) q^{32} +3.46869 q^{33} +(-0.541346 + 5.86452i) q^{34} +(-2.96015 + 7.14642i) q^{35} +(-1.13143 - 1.64920i) q^{36} +(6.31049 - 2.61389i) q^{37} +(6.09290 + 3.20888i) q^{38} +(4.25066 - 4.25066i) q^{39} +(-7.64351 + 0.894952i) q^{40} +(0.756366 + 0.756366i) q^{41} +(1.19065 + 3.84019i) q^{42} +(1.53775 + 3.71245i) q^{43} +(-1.43669 - 6.78698i) q^{44} +(2.51374 + 1.04122i) q^{45} +(-2.48338 - 2.98848i) q^{46} +1.08220i q^{47} +(-2.75826 + 2.89689i) q^{48} -1.08236i q^{49} +(2.61372 - 2.17196i) q^{50} +(-3.84747 - 1.59367i) q^{51} +(-10.0776 - 6.55645i) q^{52} +(-2.90450 - 7.01208i) q^{53} +(1.35078 - 0.418809i) q^{54} +(6.67351 + 6.67351i) q^{55} +(7.02073 - 3.92024i) q^{56} +(-3.44312 + 3.44312i) q^{57} +(-3.37700 + 6.41211i) q^{58} +(10.3425 - 4.28402i) q^{59} +(0.996142 - 5.34974i) q^{60} +(-2.97711 + 7.18739i) q^{61} +(-4.04183 - 0.373095i) q^{62} -2.84295 q^{63} +(6.81062 + 4.19708i) q^{64} +16.3559 q^{65} +(4.88470 + 0.450899i) q^{66} +(-3.88805 + 9.38659i) q^{67} +(-1.52467 + 8.18820i) q^{68} +(2.53841 - 1.05145i) q^{69} +(-5.09753 + 9.67899i) q^{70} +(-1.88924 + 1.88924i) q^{71} +(-1.37893 - 2.46952i) q^{72} +(-7.00727 - 7.00727i) q^{73} +(9.22638 - 2.86064i) q^{74} +(0.919594 + 2.22010i) q^{75} +(8.16306 + 5.31086i) q^{76} +(-9.11066 - 3.77376i) q^{77} +(6.53844 - 5.43334i) q^{78} -11.0255i q^{79} +(-10.8801 + 0.266706i) q^{80} +1.00000i q^{81} +(0.966814 + 1.16346i) q^{82} +(-2.30515 - 0.954824i) q^{83} +(1.17752 + 5.56263i) q^{84} +(-4.33615 - 10.4684i) q^{85} +(1.68291 + 5.42786i) q^{86} +(-3.62351 - 3.62351i) q^{87} +(-1.14093 - 9.74436i) q^{88} +(7.65800 - 7.65800i) q^{89} +(3.40456 + 1.79304i) q^{90} +(-15.7890 + 6.54003i) q^{91} +(-3.10868 - 4.53127i) q^{92} +(1.09836 - 2.65168i) q^{93} +(-0.140676 + 1.52398i) q^{94} -13.2487 q^{95} +(-4.26083 + 3.72093i) q^{96} -11.3029 q^{97} +(0.140697 - 1.52421i) q^{98} +(-1.32741 + 3.20465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

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