LMFDB - Embedded newform 806.2.k.c.287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [806,2,Mod(157,806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(806, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("806.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 806 = 2 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	806.k (of order $5$, 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:	$6.43594240292$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.1
Character	$\chi$	$=$	806.287
Dual form			806.2.k.c.469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.656869 - 2.02163i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.73248 q^{5} +2.12567 q^{6} +(0.597248 + 0.433926i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.22848 + 0.892540i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.656869 - 2.02163i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.73248 q^{5} +2.12567 q^{6} +(0.597248 + 0.433926i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.22848 + 0.892540i) q^{9} +(0.535366 - 1.64769i) q^{10} +(4.73298 + 3.43871i) q^{11} +(-0.656869 + 2.02163i) q^{12} +(-0.309017 - 0.951057i) q^{13} +(-0.597248 + 0.433926i) q^{14} +(1.13801 + 3.50244i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.465588 - 0.338270i) q^{17} +(-0.469236 - 1.44416i) q^{18} +(0.641527 - 1.97442i) q^{19} +(1.40161 + 1.01833i) q^{20} +(0.484926 - 1.49245i) q^{21} +(-4.73298 + 3.43871i) q^{22} +(1.93718 - 1.40744i) q^{23} +(-1.71970 - 1.24944i) q^{24} -1.99851 q^{25} +1.00000 q^{26} +(-2.54778 - 1.85107i) q^{27} +(-0.228128 - 0.702107i) q^{28} +(2.00285 - 6.16413i) q^{29} -3.68268 q^{30} +(-0.855576 - 5.50164i) q^{31} -1.00000 q^{32} +(3.84287 - 11.8271i) q^{33} +(0.177839 + 0.547332i) q^{34} +(-1.03472 - 0.751768i) q^{35} +1.51848 q^{36} +4.80898 q^{37} +(1.67954 + 1.22026i) q^{38} +(-1.71970 + 1.24944i) q^{39} +(-1.40161 + 1.01833i) q^{40} +(1.24099 - 3.81939i) q^{41} +(1.26955 + 0.922384i) q^{42} +(-1.45663 + 4.48306i) q^{43} +(-1.80784 - 5.56395i) q^{44} +(2.12831 - 1.54631i) q^{45} +(0.739937 + 2.27729i) q^{46} +(0.597723 + 1.83960i) q^{47} +(1.71970 - 1.24944i) q^{48} +(-1.99471 - 6.13907i) q^{49} +(0.617574 - 1.90070i) q^{50} +(-0.989688 - 0.719050i) q^{51} +(-0.309017 + 0.951057i) q^{52} +(1.90555 - 1.38447i) q^{53} +(2.54778 - 1.85107i) q^{54} +(-8.19979 - 5.95750i) q^{55} +0.738239 q^{56} -4.41295 q^{57} +(5.24353 + 3.80964i) q^{58} +(-3.82827 - 11.7822i) q^{59} +(1.13801 - 3.50244i) q^{60} -1.22916 q^{61} +(5.49675 + 0.886398i) q^{62} -1.12100 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.535366 + 1.64769i) q^{65} +(10.0608 + 7.30957i) q^{66} -9.60517 q^{67} -0.575499 q^{68} +(-4.11781 - 2.99176i) q^{69} +(1.03472 - 0.751768i) q^{70} +(10.7591 - 7.81692i) q^{71} +(-0.469236 + 1.44416i) q^{72} +(8.66267 + 6.29380i) q^{73} +(-1.48606 + 4.57361i) q^{74} +(1.31276 + 4.04026i) q^{75} +(-1.67954 + 1.22026i) q^{76} +(1.33461 + 4.10752i) q^{77} +(-0.656869 - 2.02163i) q^{78} +(6.82192 - 4.95641i) q^{79} +(-0.535366 - 1.64769i) q^{80} +(-3.47634 + 10.6991i) q^{81} +(3.24897 + 2.36051i) q^{82} +(2.87682 - 8.85395i) q^{83} +(-1.26955 + 0.922384i) q^{84} +(-0.806622 + 0.586045i) q^{85} +(-3.81352 - 2.77068i) q^{86} -13.7772 q^{87} +5.85028 q^{88} +(-2.24815 - 1.63337i) q^{89} +(0.812942 + 2.50198i) q^{90} +(0.228128 - 0.702107i) q^{91} -2.39449 q^{92} +(-10.5603 + 5.34351i) q^{93} -1.93427 q^{94} +(-1.11143 + 3.42064i) q^{95} +(0.656869 + 2.02163i) q^{96} +(8.73299 + 6.34489i) q^{97} +6.45500 q^{98} -8.88354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8}+O(q^{10}) $ 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8} + 3 q^{10} + 3 q^{11} + q^{12} + 7 q^{13} + q^{14} + 6 q^{15} - 7 q^{16} - 2 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} + 15 q^{21} - 3 q^{22} + 18 q^{23} + 4 q^{24} + 54 q^{25} + 28 q^{26} - 26 q^{27} + 4 q^{28} + 27 q^{29} + 14 q^{30} - 33 q^{31} - 28 q^{32} + 3 q^{33} + 2 q^{34} + 8 q^{35} + 30 q^{36} - 6 q^{37} - 27 q^{38} + 4 q^{39} - 2 q^{40} - 22 q^{41} + 5 q^{42} + q^{43} - 12 q^{44} + 28 q^{45} + 27 q^{46} + 7 q^{47} - 4 q^{48} - 30 q^{49} + q^{50} - 52 q^{51} + 7 q^{52} + q^{53} + 26 q^{54} - 18 q^{55} + 6 q^{56} - 112 q^{57} + 23 q^{58} + 27 q^{59} + 6 q^{60} - 6 q^{61} - 17 q^{62} + 54 q^{63} - 7 q^{64} + 3 q^{65} + 17 q^{66} - 24 q^{67} + 8 q^{68} + 6 q^{69} - 8 q^{70} + 28 q^{71} + 15 q^{72} - 8 q^{73} - 9 q^{74} - 62 q^{75} + 27 q^{76} - 62 q^{77} + q^{78} + 40 q^{79} - 3 q^{80} - 24 q^{81} - 18 q^{82} + 3 q^{83} - 5 q^{84} - q^{85} + 4 q^{86} + 42 q^{87} - 18 q^{88} - 5 q^{89} - 23 q^{90} - 4 q^{91} + 18 q^{92} - 69 q^{93} - 12 q^{94} - 17 q^{95} - q^{96} + 29 q^{97} - 30 q^{98} + 88 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8 + 3 * q^10 + 3 * q^11 + q^12 + 7 * q^13 + q^14 + 6 * q^15 - 7 * q^16 - 2 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 + 15 * q^21 - 3 * q^22 + 18 * q^23 + 4 * q^24 + 54 * q^25 + 28 * q^26 - 26 * q^27 + 4 * q^28 + 27 * q^29 + 14 * q^30 - 33 * q^31 - 28 * q^32 + 3 * q^33 + 2 * q^34 + 8 * q^35 + 30 * q^36 - 6 * q^37 - 27 * q^38 + 4 * q^39 - 2 * q^40 - 22 * q^41 + 5 * q^42 + q^43 - 12 * q^44 + 28 * q^45 + 27 * q^46 + 7 * q^47 - 4 * q^48 - 30 * q^49 + q^50 - 52 * q^51 + 7 * q^52 + q^53 + 26 * q^54 - 18 * q^55 + 6 * q^56 - 112 * q^57 + 23 * q^58 + 27 * q^59 + 6 * q^60 - 6 * q^61 - 17 * q^62 + 54 * q^63 - 7 * q^64 + 3 * q^65 + 17 * q^66 - 24 * q^67 + 8 * q^68 + 6 * q^69 - 8 * q^70 + 28 * q^71 + 15 * q^72 - 8 * q^73 - 9 * q^74 - 62 * q^75 + 27 * q^76 - 62 * q^77 + q^78 + 40 * q^79 - 3 * q^80 - 24 * q^81 - 18 * q^82 + 3 * q^83 - 5 * q^84 - q^85 + 4 * q^86 + 42 * q^87 - 18 * q^88 - 5 * q^89 - 23 * q^90 - 4 * q^91 + 18 * q^92 - 69 * q^93 - 12 * q^94 - 17 * q^95 - q^96 + 29 * q^97 - 30 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/806\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.656869	−	2.02163i	−0.379243	−	1.16719i	−0.940571	−	0.339597i	$-0.889709\pi$
$3$	−0.656869	−	2.02163i	−0.379243	−	1.16719i	0.561328	−	0.827594i	$-0.310291\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.73248			−0.774789			−0.387394	−	0.921914i	$-0.626625\pi$
$5$	−1.73248			−0.774789			−0.387394	+	0.921914i	$0.626625\pi$
$6$	2.12567			0.867802
$7$	0.597248	+	0.433926i	0.225738	+	0.164009i	0.694906	−	0.719101i	$-0.255446\pi$
$7$	0.597248	+	0.433926i	0.225738	+	0.164009i	−0.469168	+	0.883109i	$0.655446\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−1.22848	+	0.892540i	−0.409492	+	0.297513i
$10$	0.535366	−	1.64769i	0.169298	−	0.521044i
$11$	4.73298	+	3.43871i	1.42705	+	1.03681i	0.990557	+	0.137100i	$0.0437783\pi$
$11$	4.73298	+	3.43871i	1.42705	+	1.03681i	0.436489	+	0.899709i	$0.356222\pi$
$12$	−0.656869	+	2.02163i	−0.189622	+	0.583595i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$	−0.597248	+	0.433926i	−0.159621	+	0.115972i
$15$	1.13801	+	3.50244i	0.293833	+	0.904326i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.465588	−	0.338270i	0.112922	−	0.0820424i	−0.529891	−	0.848066i	$-0.677767\pi$
$17$	0.465588	−	0.338270i	0.112922	−	0.0820424i	0.642813	+	0.766023i	$0.277767\pi$
$18$	−0.469236	−	1.44416i	−0.110600	−	0.340392i
$19$	0.641527	−	1.97442i	0.147176	−	0.452963i	−0.850108	−	0.526608i	$-0.823463\pi$
$19$	0.641527	−	1.97442i	0.147176	−	0.452963i	0.997284	+	0.0736458i	$0.0234634\pi$
$20$	1.40161	+	1.01833i	0.313409	+	0.227705i
$21$	0.484926	−	1.49245i	0.105819	−	0.325679i
$22$	−4.73298	+	3.43871i	−1.00907	+	0.733135i
$23$	1.93718	−	1.40744i	0.403930	−	0.293472i	−0.367210	−	0.930138i	$-0.619687\pi$
$23$	1.93718	−	1.40744i	0.403930	−	0.293472i	0.771140	+	0.636666i	$0.219687\pi$
$24$	−1.71970	−	1.24944i	−0.351033	−	0.255041i
$25$	−1.99851			−0.399702
$26$	1.00000			0.196116
$27$	−2.54778	−	1.85107i	−0.490320	−	0.356238i
$28$	−0.228128	−	0.702107i	−0.0431122	−	0.132686i
$29$	2.00285	−	6.16413i	0.371920	−	1.14465i	−0.573614	−	0.819126i	$-0.694459\pi$
$29$	2.00285	−	6.16413i	0.371920	−	1.14465i	0.945533	−	0.325525i	$-0.105541\pi$
$30$	−3.68268			−0.672363
$31$	−0.855576	−	5.50164i	−0.153666	−	0.988123i
$31$	−0.855576	−	5.50164i	−0.153666	−	0.988123i
$32$	−1.00000			−0.176777
$33$	3.84287	−	11.8271i	0.668957	−	2.05884i
$34$	0.177839	+	0.547332i	0.0304991	+	0.0938666i
$35$	−1.03472	−	0.751768i	−0.174900	−	0.127072i
$36$	1.51848			0.253080
$37$	4.80898			0.790591			0.395295	−	0.918554i	$-0.370642\pi$
$37$	4.80898			0.790591			0.395295	+	0.918554i	$0.370642\pi$
$38$	1.67954	+	1.22026i	0.272457	+	0.197952i
$39$	−1.71970	+	1.24944i	−0.275373	+	0.200070i
$40$	−1.40161	+	1.01833i	−0.221613	+	0.161012i
$41$	1.24099	−	3.81939i	0.193811	−	0.596488i	−0.806178	−	0.591674i	$-0.798467\pi$
$41$	1.24099	−	3.81939i	0.193811	−	0.596488i	0.999988	−	0.00481469i	$-0.00153257\pi$
$42$	1.26955	+	0.922384i	0.195896	+	0.142327i
$43$	−1.45663	+	4.48306i	−0.222135	+	0.683660i	0.776435	+	0.630197i	$0.217026\pi$
$43$	−1.45663	+	4.48306i	−0.222135	+	0.683660i	−0.998570	+	0.0534631i	$0.982974\pi$
$44$	−1.80784	−	5.56395i	−0.272542	−	0.838797i
$45$	2.12831	−	1.54631i	0.317270	−	0.230510i
$46$	0.739937	+	2.27729i	0.109098	+	0.335768i
$47$	0.597723	+	1.83960i	0.0871869	+	0.268334i	0.985139	−	0.171760i	$-0.0549453\pi$
$47$	0.597723	+	1.83960i	0.0871869	+	0.268334i	−0.897952	+	0.440094i	$0.854945\pi$
$48$	1.71970	−	1.24944i	0.248218	−	0.180341i
$49$	−1.99471	−	6.13907i	−0.284958	−	0.877010i
$50$	0.617574	−	1.90070i	0.0873382	−	0.268799i
$51$	−0.989688	−	0.719050i	−0.138584	−	0.100687i
$52$	−0.309017	+	0.951057i	−0.0428529	+	0.131888i
$53$	1.90555	−	1.38447i	0.261748	−	0.190171i	−0.449169	−	0.893447i	$-0.648280\pi$
$53$	1.90555	−	1.38447i	0.261748	−	0.190171i	0.710917	+	0.703276i	$0.248280\pi$
$54$	2.54778	−	1.85107i	0.346708	−	0.251898i
$55$	−8.19979	−	5.95750i	−1.10566	−	0.803309i
$56$	0.738239			0.0986513
$57$	−4.41295			−0.584509
$58$	5.24353	+	3.80964i	0.688509	+	0.500231i
$59$	−3.82827	−	11.7822i	−0.498399	−	1.53391i	−0.811592	−	0.584225i	$-0.801399\pi$
$59$	−3.82827	−	11.7822i	−0.498399	−	1.53391i	0.313193	−	0.949689i	$-0.398601\pi$
$60$	1.13801	−	3.50244i	0.146917	−	0.452163i
$61$	−1.22916			−0.157378			−0.0786888	−	0.996899i	$-0.525073\pi$
$61$	−1.22916			−0.157378			−0.0786888	+	0.996899i	$0.525073\pi$
$62$	5.49675	+	0.886398i	0.698088	+	0.112573i
$63$	−1.12100			−0.141233
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.535366	+	1.64769i	0.0664040	+	0.204370i
$66$	10.0608	+	7.30957i	1.23839	+	0.899746i
$67$	−9.60517			−1.17346			−0.586729	−	0.809783i	$-0.699585\pi$
$67$	−9.60517			−1.17346			−0.586729	+	0.809783i	$0.699585\pi$
$68$	−0.575499			−0.0697895
$69$	−4.11781	−	2.99176i	−0.495726	−	0.360166i
$70$	1.03472	−	0.751768i	0.123673	−	0.0898534i
$71$	10.7591	−	7.81692i	1.27687	−	0.927698i	0.277413	−	0.960751i	$-0.410523\pi$
$71$	10.7591	−	7.81692i	1.27687	−	0.927698i	0.999454	+	0.0330530i	$0.0105230\pi$
$72$	−0.469236	+	1.44416i	−0.0553000	+	0.170196i
$73$	8.66267	+	6.29380i	1.01389	+	0.736633i	0.965021	−	0.262172i	$-0.0844387\pi$
$73$	8.66267	+	6.29380i	1.01389	+	0.736633i	0.0488678	+	0.998805i	$0.484439\pi$
$74$	−1.48606	+	4.57361i	−0.172750	+	0.531671i
$75$	1.31276	+	4.04026i	0.151584	+	0.466529i
$76$	−1.67954	+	1.22026i	−0.192656	+	0.139973i
$77$	1.33461	+	4.10752i	0.152093	+	0.468096i
$78$	−0.656869	−	2.02163i	−0.0743757	−	0.228905i
$79$	6.82192	−	4.95641i	0.767526	−	0.557640i	−0.133684	−	0.991024i	$-0.542681\pi$
$79$	6.82192	−	4.95641i	0.767526	−	0.557640i	0.901209	+	0.433384i	$0.142681\pi$
$80$	−0.535366	−	1.64769i	−0.0598557	−	0.184217i
$81$	−3.47634	+	10.6991i	−0.386260	+	1.18878i
$82$	3.24897	+	2.36051i	0.358788	+	0.260675i
$83$	2.87682	−	8.85395i	0.315772	−	0.971847i	−0.659663	−	0.751561i	$-0.729301\pi$
$83$	2.87682	−	8.85395i	0.315772	−	0.971847i	0.975435	−	0.220286i	$-0.0706990\pi$
$84$	−1.26955	+	0.922384i	−0.138520	+	0.100640i
$85$	−0.806622	+	0.586045i	−0.0874905	+	0.0635656i
$86$	−3.81352	−	2.77068i	−0.411222	−	0.298770i
$87$	−13.7772			−1.47707
$88$	5.85028			0.623642
$89$	−2.24815	−	1.63337i	−0.238303	−	0.173137i	0.462224	−	0.886763i	$-0.347052\pi$
$89$	−2.24815	−	1.63337i	−0.238303	−	0.173137i	−0.700527	+	0.713626i	$0.747052\pi$
$90$	0.812942	+	2.50198i	0.0856916	+	0.263732i
$91$	0.228128	−	0.702107i	0.0239143	−	0.0736008i
$92$	−2.39449			−0.249642
$93$	−10.5603	+	5.34351i	−1.09505	+	0.554096i
$94$	−1.93427			−0.199505
$95$	−1.11143	+	3.42064i	−0.114031	+	0.350950i
$96$	0.656869	+	2.02163i	0.0670414	+	0.206332i
$97$	8.73299	+	6.34489i	0.886701	+	0.644226i	0.935016	−	0.354606i	$-0.115385\pi$
$97$	8.73299	+	6.34489i	0.886701	+	0.644226i	−0.0483149	+	0.998832i	$0.515385\pi$
$98$	6.45500			0.652054
$99$	−8.88354			−0.892829
$100$	1.61683	+	1.17470i	0.161683	+	0.117470i
$101$	−0.808516	+	0.587421i	−0.0804503	+	0.0584506i	−0.627283	−	0.778791i	$-0.715833\pi$
$101$	−0.808516	+	0.587421i	−0.0804503	+	0.0584506i	0.546833	+	0.837242i	$0.315833\pi$
$102$	0.989688	−	0.719050i	0.0979937	−	0.0711966i
$103$	−2.02352	+	6.22775i	−0.199383	+	0.613639i	0.800514	+	0.599314i	$0.204560\pi$
$103$	−2.02352	+	6.22775i	−0.199383	+	0.613639i	−0.999897	+	0.0143249i	$0.995440\pi$
$104$	−0.809017	−	0.587785i	−0.0793306	−	0.0576371i
$105$	−0.840124	+	2.58564i	−0.0819877	+	0.252332i
$106$	0.727856	+	2.24011i	0.0706957	+	0.217579i
$107$	−0.917142	+	0.666343i	−0.0886635	+	0.0644178i	−0.631234	−	0.775593i	$-0.717451\pi$
$107$	−0.917142	+	0.666343i	−0.0886635	+	0.0644178i	0.542570	+	0.840010i	$0.317451\pi$
$108$	0.973164	+	2.99509i	0.0936428	+	0.288203i
$109$	0.640026	+	1.96980i	0.0613034	+	0.188672i	0.977018	−	0.213157i	$-0.0683745\pi$
$109$	0.640026	+	1.96980i	0.0613034	+	0.188672i	−0.915715	+	0.401829i	$0.868375\pi$
$110$	8.19979	−	5.95750i	0.781819	−	0.568025i
$111$	−3.15887	−	9.72199i	−0.299826	−	0.922770i
$112$	−0.228128	+	0.702107i	−0.0215561	+	0.0663428i
$113$	−2.18514	−	1.58760i	−0.205561	−	0.149348i	0.480242	−	0.877136i	$-0.340549\pi$
$113$	−2.18514	−	1.58760i	−0.205561	−	0.149348i	−0.685803	+	0.727787i	$0.740549\pi$
$114$	1.36368	−	4.19696i	0.127720	−	0.393082i
$115$	−3.35613	+	2.43837i	−0.312960	+	0.227379i
$116$	−5.24353	+	3.80964i	−0.486849	+	0.353717i
$117$	1.22848	+	0.892540i	0.113573	+	0.0825154i
$118$	12.3886			1.14046
$119$	0.424855			0.0389464
$120$	2.97935	+	2.16463i	0.271977	+	0.197603i
$121$	7.17717	+	22.0890i	0.652470	+	2.00810i
$122$	0.379831	−	1.16900i	0.0343883	−	0.105836i
$123$	−8.53658			−0.769717
$124$	−2.54160	+	4.95381i	−0.228243	+	0.444865i
$125$	12.1248			1.08447
$126$	0.346408	−	1.06613i	0.0308605	−	0.0949789i
$127$	5.71739	+	17.5963i	0.507336	+	1.56142i	0.796807	+	0.604234i	$0.206521\pi$
$127$	5.71739	+	17.5963i	0.507336	+	1.56142i	−0.289471	+	0.957187i	$0.593479\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	10.0199			0.882205
$130$	−1.73248			−0.151949
$131$	−1.85974	−	1.35118i	−0.162486	−	0.118053i	0.503571	−	0.863954i	$-0.332019\pi$
$131$	−1.85974	−	1.35118i	−0.162486	−	0.118053i	−0.666057	+	0.745901i	$0.732019\pi$
$132$	−10.0608	+	7.30957i	−0.875676	+	0.636216i
$133$	1.23990	−	0.900841i	0.107513	−	0.0781128i
$134$	2.96816	−	9.13506i	0.256410	−	0.789149i
$135$	4.41397	+	3.20694i	0.379894	+	0.276009i
$136$	0.177839	−	0.547332i	0.0152496	−	0.0469333i
$137$	5.44786	+	16.7668i	0.465442	+	1.43248i	0.858426	+	0.512937i	$0.171443\pi$
$137$	5.44786	+	16.7668i	0.465442	+	1.43248i	−0.392984	+	0.919545i	$0.628557\pi$
$138$	4.11781	−	2.99176i	0.350531	−	0.254676i
$139$	−3.59804	−	11.0736i	−0.305182	−	0.939253i	−0.979609	−	0.200912i	$-0.935610\pi$
$139$	−3.59804	−	11.0736i	−0.305182	−	0.939253i	0.674428	−	0.738341i	$-0.264390\pi$
$140$	0.395228	+	1.21639i	0.0334028	+	0.102803i
$141$	3.32638	−	2.41676i	0.280132	−	0.203528i
$142$	4.10960	+	12.6480i	0.344870	+	1.06140i
$143$	1.80784	−	5.56395i	0.151179	−	0.465281i
$144$	−1.22848	−	0.892540i	−0.102373	−	0.0743783i
$145$	−3.46990	+	10.6792i	−0.288159	+	0.886863i
$146$	−8.66267	+	6.29380i	−0.716928	+	0.520879i
$147$	−11.1007	+	8.06513i	−0.915570	+	0.665201i
$148$	−3.89054	−	2.82665i	−0.319801	−	0.232349i
$149$	10.1842			0.834318			0.417159	−	0.908833i	$-0.363026\pi$
$149$	10.1842			0.834318			0.417159	+	0.908833i	$0.363026\pi$
$150$	−4.24818			−0.346863
$151$	−15.1677	−	11.0200i	−1.23433	−	0.896796i	−0.237126	−	0.971479i	$-0.576205\pi$
$151$	−15.1677	−	11.0200i	−1.23433	−	0.896796i	−0.997207	+	0.0746832i	$0.976205\pi$
$152$	−0.641527	−	1.97442i	−0.0520347	−	0.160146i
$153$	−0.270045	+	0.831112i	−0.0218318	+	0.0671914i
$154$	−4.31890			−0.348027
$155$	1.48227	+	9.53147i	0.119059	+	0.765586i
$156$	2.12567			0.170190
$157$	4.13317	−	12.7206i	0.329863	−	1.01521i	−0.639335	−	0.768929i	$-0.720790\pi$
$157$	4.13317	−	12.7206i	0.329863	−	1.01521i	0.969198	−	0.246285i	$-0.0792099\pi$
$158$	2.60574	+	8.01964i	0.207302	+	0.638009i
$159$	−4.05058	−	2.94292i	−0.321232	−	0.233389i
$160$	1.73248			0.136965
$161$	1.76770			0.139314
$162$	−9.10116	−	6.61238i	−0.715055	−	0.519518i
$163$	2.87996	−	2.09241i	0.225576	−	0.163890i	−0.469257	−	0.883062i	$-0.655478\pi$
$163$	2.87996	−	2.09241i	0.225576	−	0.163890i	0.694833	+	0.719171i	$0.255478\pi$
$164$	−3.24897	+	2.36051i	−0.253702	+	0.184325i
$165$	−6.65769	+	20.4903i	−0.518301	+	1.59517i
$166$	7.53162	+	5.47204i	0.584567	+	0.424713i
$167$	0.405780	−	1.24886i	0.0314002	−	0.0966399i	−0.934128	−	0.356938i	$-0.883821\pi$
$167$	0.405780	−	1.24886i	0.0314002	−	0.0966399i	0.965528	+	0.260298i	$0.0838208\pi$
$168$	−0.484926	−	1.49245i	−0.0374128	−	0.115145i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−0.308102	−	0.948241i	−0.0236304	−	0.0727268i
$171$	0.974146	+	2.99811i	0.0744948	+	0.229272i
$172$	3.81352	−	2.77068i	0.290778	−	0.211263i
$173$	−2.27557	−	7.00348i	−0.173008	−	0.532465i	0.826529	−	0.562895i	$-0.190312\pi$
$173$	−2.27557	−	7.00348i	−0.173008	−	0.532465i	−0.999537	+	0.0304298i	$0.990312\pi$
$174$	4.25740	−	13.1029i	0.322753	−	0.993330i
$175$	−1.19361	−	0.867206i	−0.0902282	−	0.0655546i
$176$	−1.80784	+	5.56395i	−0.136271	+	0.419398i
$177$	−21.3047	+	15.4787i	−1.60136	+	1.16345i
$178$	2.24815	−	1.63337i	0.168506	−	0.122427i
$179$	−16.8161	−	12.2176i	−1.25690	−	0.913188i	−0.258295	−	0.966066i	$-0.583161\pi$
$179$	−16.8161	−	12.2176i	−1.25690	−	0.913188i	−0.998601	+	0.0528782i	$0.983161\pi$
$180$	−2.63074			−0.196084
$181$	15.3756			1.14286			0.571429	−	0.820651i	$-0.306389\pi$
$181$	15.3756			1.14286			0.571429	+	0.820651i	$0.306389\pi$
$182$	0.597248	+	0.433926i	0.0442709	+	0.0321647i
$183$	0.807396	+	2.48491i	0.0596844	+	0.183690i
$184$	0.739937	−	2.27729i	0.0545489	−	0.167884i
$185$	−8.33146			−0.612541
$186$	−1.81867	−	11.6947i	−0.133352	−	0.857495i
$187$	3.36683			0.246207
$188$	0.597723	−	1.83960i	0.0435935	−	0.134167i
$189$	−0.718427	−	2.21109i	−0.0522579	−	0.160833i
$190$	−2.90977	−	2.11407i	−0.211097	−	0.153371i
$191$	16.6693			1.20615			0.603076	−	0.797684i	$-0.293942\pi$
$191$	16.6693			1.20615			0.603076	+	0.797684i	$0.293942\pi$
$192$	−2.12567			−0.153407
$193$	−4.75310	−	3.45333i	−0.342135	−	0.248576i	0.403427	−	0.915012i	$-0.367819\pi$
$193$	−4.75310	−	3.45333i	−0.342135	−	0.248576i	−0.745562	+	0.666436i	$0.767819\pi$
$194$	−8.73299	+	6.34489i	−0.626992	+	0.455536i
$195$	2.97935	−	2.16463i	0.213356	−	0.155012i
$196$	−1.99471	+	6.13907i	−0.142479	+	0.438505i
$197$	−2.14635	−	1.55941i	−0.152921	−	0.111104i	0.508694	−	0.860948i	$-0.330129\pi$
$197$	−2.14635	−	1.55941i	−0.152921	−	0.111104i	−0.661615	+	0.749844i	$0.730129\pi$
$198$	2.74516	−	8.44874i	0.195090	−	0.600426i
$199$	4.33895	+	13.3539i	0.307580	+	0.946634i	0.978702	+	0.205287i	$0.0658128\pi$
$199$	4.33895	+	13.3539i	0.307580	+	0.946634i	−0.671122	+	0.741347i	$0.734187\pi$
$200$	−1.61683	+	1.17470i	−0.114327	+	0.0830636i
$201$	6.30933	+	19.4181i	0.445026	+	1.36965i
$202$	−0.308825	−	0.950467i	−0.0217289	−	0.0668746i
$203$	3.87097	−	2.81243i	0.271689	−	0.197394i
$204$	0.378027	+	1.16345i	0.0264672	+	0.0814576i
$205$	−2.15000	+	6.61702i	−0.150162	+	0.462152i
$206$	−5.29764	−	3.84896i	−0.369104	−	0.268170i
$207$	−1.12358	+	3.45802i	−0.0780942	+	0.240349i
$208$	0.809017	−	0.587785i	0.0560952	−	0.0407556i
$209$	9.82578	−	7.13885i	0.679664	−	0.493805i
$210$	−2.19947	−	1.59801i	−0.151778	−	0.110273i
$211$	−24.1259			−1.66089			−0.830447	−	0.557097i	$-0.811915\pi$
$211$	−24.1259			−1.66089			−0.830447	+	0.557097i	$0.811915\pi$
$212$	−2.35539			−0.161769
$213$	−22.8702	−	16.6162i	−1.56704	−	1.13852i
$214$	−0.350317	−	1.07817i	−0.0239472	−	0.0737018i
$215$	2.52359	−	7.76681i	0.172107	−	0.529692i
$216$	−3.14923			−0.214278
$217$	1.87631	−	3.65709i	0.127372	−	0.248260i
$218$	−2.07117			−0.140277
$219$	7.03352	−	21.6469i	0.475281	−	1.46277i
$220$	3.13204	+	9.63943i	0.211162	+	0.649890i
$221$	−0.465588	−	0.338270i	−0.0313189	−	0.0227545i
$222$	10.2223			0.686076
$223$	−26.6731			−1.78616			−0.893081	−	0.449896i	$-0.851461\pi$
$223$	−26.6731			−1.78616			−0.893081	+	0.449896i	$0.851461\pi$
$224$	−0.597248	−	0.433926i	−0.0399053	−	0.0289929i
$225$	2.45512	−	1.78375i	0.163675	−	0.118917i
$226$	2.18514	−	1.58760i	0.145353	−	0.105605i
$227$	4.18406	−	12.8772i	0.277706	−	0.854690i	−0.710785	−	0.703409i	$-0.751660\pi$
$227$	4.18406	−	12.8772i	0.277706	−	0.854690i	0.988491	−	0.151281i	$-0.0483398\pi$
$228$	3.57015	+	2.59387i	0.236439	+	0.171783i
$229$	−6.13500	+	18.8816i	−0.405412	+	1.24773i	0.515138	+	0.857107i	$0.327741\pi$
$229$	−6.13500	+	18.8816i	−0.405412	+	1.24773i	−0.920550	+	0.390624i	$0.872259\pi$
$230$	−1.28193	−	3.94536i	−0.0845277	−	0.260150i
$231$	7.42724	−	5.39621i	0.488676	−	0.355044i
$232$	−2.00285	−	6.16413i	−0.131493	−	0.404695i
$233$	3.29092	+	10.1284i	0.215595	+	0.663534i	0.999111	+	0.0421616i	$0.0134244\pi$
$233$	3.29092	+	10.1284i	0.215595	+	0.663534i	−0.783516	+	0.621372i	$0.786576\pi$
$234$	−1.22848	+	0.892540i	−0.0803080	+	0.0583472i
$235$	−1.03554	−	3.18708i	−0.0675514	−	0.207902i
$236$	−3.82827	+	11.7822i	−0.249199	+	0.766957i
$237$	−14.5012	−	10.5357i	−0.941951	−	0.684368i
$238$	−0.131288	+	0.404061i	−0.00851011	+	0.0261914i
$239$	18.4555	−	13.4087i	1.19379	−	0.867336i	0.200127	−	0.979770i	$-0.435865\pi$
$239$	18.4555	−	13.4087i	1.19379	−	0.867336i	0.993659	+	0.112434i	$0.0358646\pi$
$240$	−2.97935	+	2.16463i	−0.192316	+	0.139726i
$241$	−10.8714	−	7.89852i	−0.700288	−	0.508789i	0.179738	−	0.983714i	$-0.442475\pi$
$241$	−10.8714	−	7.89852i	−0.700288	−	0.508789i	−0.880026	+	0.474926i	$0.842475\pi$
$242$	−23.2258			−1.49301
$243$	14.4654			0.927956
$244$	0.994411	+	0.722482i	0.0636606	+	0.0462521i
$245$	3.45579	+	10.6358i	0.220782	+	0.679498i
$246$	2.63795	−	8.11877i	0.168189	−	0.517634i
$247$	−2.07603			−0.132094
$248$	−3.92596	−	3.94802i	−0.249298	−	0.250700i
$249$	−19.7891			−1.25409
$250$	−3.74676	+	11.5314i	−0.236966	+	0.729307i
$251$	7.81861	+	24.0632i	0.493506	+	1.51886i	0.819272	+	0.573406i	$0.194378\pi$
$251$	7.81861	+	24.0632i	0.493506	+	1.51886i	−0.325765	+	0.945451i	$0.605622\pi$
$252$	0.906909	+	0.658908i	0.0571299	+	0.0415073i
$253$	14.0084			0.880702
$254$	−18.5019			−1.16091
$255$	1.71461	+	1.24574i	0.107373	+	0.0780113i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.46593	+	1.06506i	−0.0914421	+	0.0664366i	−0.632567	−	0.774506i	$-0.717999\pi$
$257$	−1.46593	+	1.06506i	−0.0914421	+	0.0664366i	0.541125	+	0.840942i	$0.317999\pi$
$258$	−3.09633	+	9.52951i	−0.192769	+	0.593282i
$259$	2.87215	+	2.08674i	0.178467	+	0.129664i
$260$	0.535366	−	1.64769i	0.0332020	−	0.102185i
$261$	3.04129	+	9.36011i	0.188251	+	0.579377i
$262$	1.85974	−	1.35118i	0.114895	−	0.0834761i
$263$	−1.59077	−	4.89588i	−0.0980910	−	0.301893i	0.889956	−	0.456047i	$-0.150735\pi$
$263$	−1.59077	−	4.89588i	−0.0980910	−	0.301893i	−0.988047	+	0.154154i	$0.950735\pi$
$264$	−3.84287	−	11.8271i	−0.236512	−	0.727909i
$265$	−3.30133	+	2.39856i	−0.202799	+	0.147342i
$266$	0.473600	+	1.45759i	0.0290383	+	0.0893707i
$267$	−1.82535	+	5.61784i	−0.111710	+	0.343807i
$268$	7.77075	+	5.64578i	0.474674	+	0.344871i
$269$	3.60379	−	11.0913i	0.219727	−	0.676251i	−0.779057	−	0.626953i	$-0.784302\pi$
$269$	3.60379	−	11.0913i	0.219727	−	0.676251i	0.998784	−	0.0492977i	$-0.0156983\pi$
$270$	−4.41397	+	3.20694i	−0.268626	+	0.195168i
$271$	−9.29508	+	6.75327i	−0.564636	+	0.410232i	−0.833153	−	0.553043i	$-0.813467\pi$
$271$	−9.29508	+	6.75327i	−0.564636	+	0.410232i	0.268517	+	0.963275i	$0.413467\pi$
$272$	0.465588	+	0.338270i	0.0282304	+	0.0205106i
$273$	−1.56925			−0.0949755
$274$	−17.6296			−1.06504
$275$	−9.45891	−	6.87230i	−0.570394	−	0.414415i
$276$	1.57286	+	4.84077i	0.0946752	+	0.291380i
$277$	−4.61415	+	14.2009i	−0.277238	+	0.853250i	0.711381	+	0.702807i	$0.248070\pi$
$277$	−4.61415	+	14.2009i	−0.277238	+	0.853250i	−0.988619	+	0.150443i	$0.951930\pi$
$278$	11.6435			0.698331
$279$	5.96148	+	5.99499i	0.356905	+	0.358911i
$280$	−1.27898			−0.0764339
$281$	−1.35818	+	4.18004i	−0.0810221	+	0.249361i	−0.983360	−	0.181670i	$-0.941850\pi$
$281$	−1.35818	+	4.18004i	−0.0810221	+	0.249361i	0.902337	+	0.431030i	$0.141850\pi$
$282$	1.27056	+	3.91039i	0.0756610	+	0.232860i
$283$	7.66168	+	5.56654i	0.455440	+	0.330896i	0.791740	−	0.610859i	$-0.209176\pi$
$283$	7.66168	+	5.56654i	0.455440	+	0.330896i	−0.336300	+	0.941755i	$0.609176\pi$
$284$	−13.2989			−0.789147
$285$	7.64535			0.452871
$286$	4.73298	+	3.43871i	0.279867	+	0.203335i
$287$	2.39851	−	1.74262i	0.141580	−	0.102864i
$288$	1.22848	−	0.892540i	0.0723886	−	0.0525934i
$289$	−5.15094	+	15.8530i	−0.302997	+	0.932528i
$290$	−9.08430	−	6.60013i	−0.533449	−	0.387573i
$291$	7.09061	−	21.8227i	0.415659	−	1.27927i
$292$	−3.30885	−	10.1836i	−0.193636	−	0.595949i
$293$	−8.58901	+	6.24028i	−0.501775	+	0.364561i	−0.809695	−	0.586851i	$-0.800367\pi$
$293$	−8.58901	+	6.24028i	−0.501775	+	0.364561i	0.307919	+	0.951412i	$0.400367\pi$
$294$	−4.24009	−	13.0497i	−0.247287	−	0.761071i
$295$	6.63241	+	20.4125i	0.386154	+	1.18846i
$296$	3.89054	−	2.82665i	0.226133	−	0.164295i
$297$	−5.69328	−	17.5221i	−0.330358	−	1.01674i
$298$	−3.14708	+	9.68571i	−0.182305	+	0.561078i
$299$	−1.93718	−	1.40744i	−0.112030	−	0.0813946i
$300$	1.31276	−	4.04026i	0.0757922	−	0.233265i
$301$	−2.81529	+	2.04543i	−0.162270	+	0.117896i
$302$	15.1677	−	11.0200i	0.872805	−	0.634130i
$303$	1.71864	+	1.24866i	0.0987332	+	0.0717339i
$304$	2.07603			0.119068
$305$	2.12949			0.121934
$306$	−0.706986	−	0.513656i	−0.0404157	−	0.0293637i
$307$	−2.77671	−	8.54582i	−0.158475	−	0.487736i	0.840021	−	0.542553i	$-0.182542\pi$
$307$	−2.77671	−	8.54582i	−0.158475	−	0.487736i	−0.998496	+	0.0548174i	$0.982542\pi$
$308$	1.33461	−	4.10752i	0.0760467	−	0.234048i
$309$	13.9194			0.791849
$310$	−9.52302	−	1.53567i	−0.540871	−	0.0872200i
$311$	−3.06228			−0.173646			−0.0868229	−	0.996224i	$-0.527671\pi$
$311$	−3.06228			−0.173646			−0.0868229	+	0.996224i	$0.527671\pi$
$312$	−0.656869	+	2.02163i	−0.0371879	+	0.114452i
$313$	9.35556	+	28.7935i	0.528808	+	1.62750i	0.756661	+	0.653807i	$0.226829\pi$
$313$	9.35556	+	28.7935i	0.528808	+	1.62750i	−0.227854	+	0.973695i	$0.573171\pi$
$314$	10.8208	+	7.86176i	0.610652	+	0.443665i
$315$	1.94211			0.109426
$316$	−8.43235			−0.474357
$317$	18.9148	+	13.7424i	1.06236	+	0.771849i	0.974523	−	0.224286i	$-0.0720050\pi$
$317$	18.9148	+	13.7424i	1.06236	+	0.771849i	0.0878357	+	0.996135i	$0.472005\pi$
$318$	4.05058	−	2.94292i	0.227145	−	0.165031i
$319$	30.6761	−	22.2875i	1.71753	−	1.24786i
$320$	−0.535366	+	1.64769i	−0.0299279	+	0.0921085i
$321$	1.94954	+	1.41643i	0.108813	+	0.0790572i
$322$	−0.546250	+	1.68118i	−0.0304413	+	0.0936888i
$323$	−0.369198	−	1.13627i	−0.0205427	−	0.0632240i
$324$	9.10116	−	6.61238i	0.505620	−	0.367355i
$325$	0.617574	+	1.90070i	0.0342569	+	0.105432i
$326$	1.10005	+	3.38559i	0.0609259	+	0.187511i
$327$	3.56180	−	2.58780i	0.196968	−	0.143106i
$328$	−1.24099	−	3.81939i	−0.0685225	−	0.210890i
$329$	−0.441262	+	1.35807i	−0.0243276	+	0.0748726i
$330$	−17.4301	−	12.6637i	−0.959493	−	0.697113i
$331$	1.35115	−	4.15841i	0.0742659	−	0.228567i	−0.907032	−	0.421061i	$-0.861658\pi$
$331$	1.35115	−	4.15841i	0.0742659	−	0.228567i	0.981298	+	0.192494i	$0.0616577\pi$
$332$	−7.53162	+	5.47204i	−0.413351	+	0.300317i
$333$	−5.90771	+	4.29220i	−0.323741	+	0.235211i
$334$	1.06235	+	0.771839i	0.0581290	+	0.0422332i
$335$	16.6408			0.909182
$336$	1.56925			0.0856098
$337$	−19.4463	−	14.1286i	−1.05931	−	0.769632i	−0.0853476	−	0.996351i	$-0.527200\pi$
$337$	−19.4463	−	14.1286i	−1.05931	−	0.769632i	−0.973960	+	0.226719i	$0.927200\pi$
$338$	−0.309017	−	0.951057i	−0.0168083	−	0.0517307i
$339$	−1.77419	+	5.46039i	−0.0963607	+	0.296568i
$340$	0.997040			0.0540721
$341$	14.8691	−	28.9812i	0.805207	−	1.56942i
$342$	−3.15240			−0.170462
$343$	3.06947	−	9.44685i	0.165736	−	0.510082i
$344$	1.45663	+	4.48306i	0.0785365	+	0.241710i
$345$	7.13402	+	5.18317i	0.384083	+	0.279052i
$346$	7.36390			0.395886
$347$	18.9931			1.01960			0.509802	−	0.860292i	$-0.329719\pi$
$347$	18.9931			1.01960			0.509802	+	0.860292i	$0.329719\pi$
$348$	11.1460	+	8.09805i	0.597489	+	0.434101i
$349$	7.56573	−	5.49682i	0.404984	−	0.294238i	−0.366584	−	0.930385i	$-0.619473\pi$
$349$	7.56573	−	5.49682i	0.404984	−	0.294238i	0.771568	+	0.636147i	$0.219473\pi$
$350$	1.19361	−	0.867206i	0.0638010	−	0.0463541i
$351$	−0.973164	+	2.99509i	−0.0519437	+	0.159866i
$352$	−4.73298	−	3.43871i	−0.252269	−	0.183284i
$353$	5.03663	−	15.5011i	0.268073	−	0.825042i	−0.722897	−	0.690956i	$-0.757190\pi$
$353$	5.03663	−	15.5011i	0.268073	−	0.825042i	0.990970	−	0.134087i	$-0.0428100\pi$
$354$	−8.13765	−	25.0451i	−0.432511	−	1.33113i
$355$	−18.6399	+	13.5427i	−0.989302	+	0.718770i
$356$	0.858716	+	2.64286i	0.0455119	+	0.140071i
$357$	−0.279074	−	0.858902i	−0.0147702	−	0.0454579i
$358$	16.8161	−	12.2176i	0.888759	−	0.645721i
$359$	7.62747	+	23.4749i	0.402562	+	1.23896i	0.922913	+	0.385007i	$0.125801\pi$
$359$	7.62747	+	23.4749i	0.402562	+	1.23896i	−0.520351	+	0.853953i	$0.674199\pi$
$360$	0.812942	−	2.50198i	0.0428458	−	0.131866i
$361$	11.8846	+	8.63463i	0.625503	+	0.454454i
$362$	−4.75132	+	14.6231i	−0.249724	+	0.768571i
$363$	39.9415	−	29.0192i	2.09639	−	1.52311i
$364$	−0.597248	+	0.433926i	−0.0313043	+	0.0227439i
$365$	−15.0079	−	10.9039i	−0.785550	−	0.570735i
$366$	−2.61279			−0.136573
$367$	−8.60709			−0.449287			−0.224643	−	0.974441i	$-0.572122\pi$
$367$	−8.60709			−0.449287			−0.224643	+	0.974441i	$0.572122\pi$
$368$	1.93718	+	1.40744i	0.100982	+	0.0733681i
$369$	1.88443	+	5.79967i	0.0980993	+	0.301919i
$370$	2.57456	−	7.92369i	0.133845	−	0.411933i
$371$	1.73884			0.0902762
$372$	11.6843	+	1.88419i	0.605802	+	0.0976908i
$373$	11.5196			0.596463			0.298232	−	0.954494i	$-0.403603\pi$
$373$	11.5196			0.596463			0.298232	+	0.954494i	$0.403603\pi$
$374$	−1.04041	+	3.20205i	−0.0537982	+	0.165574i
$375$	−7.96439	−	24.5119i	−0.411279	−	1.26579i
$376$	1.56486	+	1.13694i	0.0807015	+	0.0586331i
$377$	−6.48135			−0.333807
$378$	2.32488			0.119579
$379$	−17.8442	−	12.9645i	−0.916593	−	0.665944i	0.0260808	−	0.999660i	$-0.491697\pi$
$379$	−17.8442	−	12.9645i	−0.916593	−	0.665944i	−0.942674	+	0.333716i	$0.891697\pi$
$380$	2.90977	−	2.11407i	0.149268	−	0.108450i
$381$	31.8177	−	23.1169i	1.63007	−	1.18432i
$382$	−5.15111	+	15.8535i	−0.263554	+	0.811135i
$383$	12.3415	+	8.96660i	0.630620	+	0.458172i	0.856615	−	0.515956i	$-0.172563\pi$
$383$	12.3415	+	8.96660i	0.630620	+	0.458172i	−0.225995	+	0.974128i	$0.572563\pi$
$384$	0.656869	−	2.02163i	0.0335207	−	0.103166i
$385$	−2.31219	−	7.11620i	−0.117840	−	0.362675i
$386$	4.75310	−	3.45333i	0.241926	−	0.175770i
$387$	−2.21187	−	6.80744i	−0.112436	−	0.346041i
$388$	−3.33571	−	10.2662i	−0.169345	−	0.521190i
$389$	6.20745	−	4.50998i	0.314730	−	0.228665i	−0.419193	−	0.907897i	$-0.637687\pi$
$389$	6.20745	−	4.50998i	0.314730	−	0.228665i	0.733924	+	0.679232i	$0.237687\pi$
$390$	1.13801	+	3.50244i	0.0576255	+	0.177353i
$391$	0.425833	−	1.31058i	0.0215353	−	0.0662788i
$392$	−5.22221	−	3.79416i	−0.263761	−	0.191634i
$393$	−1.50998	+	4.64726i	−0.0761687	+	0.234423i
$394$	2.14635	−	1.55941i	0.108132	−	0.0785622i
$395$	−11.8188	+	8.58689i	−0.594670	+	0.432053i
$396$	7.18693	+	5.22161i	0.361157	+	0.262396i
$397$	24.5831			1.23379			0.616895	−	0.787045i	$-0.288390\pi$
$397$	24.5831			1.23379			0.616895	+	0.787045i	$0.288390\pi$
$398$	−14.0411			−0.703819
$399$	−2.63562	−	1.91489i	−0.131946	−	0.0958645i
$400$	−0.617574	−	1.90070i	−0.0308787	−	0.0950349i
$401$	5.32663	−	16.3937i	0.265999	−	0.818661i	−0.725463	−	0.688262i	$-0.758374\pi$
$401$	5.32663	−	16.3937i	0.265999	−	0.818661i	0.991462	−	0.130399i	$-0.0416259\pi$
$402$	−20.4174			−1.01833
$403$	−4.96798	+	2.51380i	−0.247473	+	0.125221i
$404$	0.999380			0.0497210
$405$	6.02268	−	18.5359i	0.299270	−	0.921057i
$406$	1.47858	+	4.55060i	0.0733807	+	0.225843i
$407$	22.7608	+	16.5367i	1.12821	+	0.819692i
$408$	−1.22332			−0.0605634
$409$	−20.2921			−1.00338			−0.501691	−	0.865047i	$-0.667289\pi$
$409$	−20.2921			−1.00338			−0.501691	+	0.865047i	$0.667289\pi$
$410$	−5.62877	−	4.08954i	−0.277985	−	0.201968i
$411$	30.3178	−	22.0271i	1.49546	−	1.08652i
$412$	5.29764	−	3.84896i	0.260996	−	0.189625i
$413$	2.82618	−	8.69809i	0.139067	−	0.428005i
$414$	−2.94157	−	2.13717i	−0.144570	−	0.105036i
$415$	−4.98404	+	15.3393i	−0.244657	+	0.752976i
$416$	0.309017	+	0.951057i	0.0151508	+	0.0466294i
$417$	−20.0234	+	14.5478i	−0.980549	+	0.712411i
$418$	3.75312	+	11.5509i	0.183571	+	0.564973i
$419$	−1.25760	−	3.87048i	−0.0614376	−	0.189085i	0.915627	−	0.402029i	$-0.131695\pi$
$419$	−1.25760	−	3.87048i	−0.0614376	−	0.189085i	−0.977064	+	0.212944i	$0.931695\pi$
$420$	2.19947	−	1.59801i	0.107323	−	0.0779750i
$421$	9.19427	+	28.2971i	0.448101	+	1.37911i	0.879047	+	0.476736i	$0.158180\pi$
$421$	9.19427	+	28.2971i	0.448101	+	1.37911i	−0.430945	+	0.902378i	$0.641820\pi$
$422$	7.45531	−	22.9451i	0.362919	−	1.11695i
$423$	−2.37621	−	1.72642i	−0.115535	−	0.0839413i
$424$	0.727856	−	2.24011i	0.0353478	−	0.108789i
$425$	−0.930484	+	0.676036i	−0.0451351	+	0.0327926i
$426$	22.8702	−	16.6162i	1.10807	−	0.805058i
$427$	−0.734112	−	0.533364i	−0.0355262	−	0.0258113i
$428$	1.13365			0.0547970
$429$	−12.4358			−0.600405
$430$	6.60685	+	4.80015i	0.318610	+	0.231484i
$431$	8.19198	+	25.2123i	0.394594	+	1.21443i	0.929278	+	0.369382i	$0.120431\pi$
$431$	8.19198	+	25.2123i	0.394594	+	1.21443i	−0.534684	+	0.845052i	$0.679569\pi$
$432$	0.973164	−	2.99509i	0.0468214	−	0.144101i
$433$	10.0380			0.482396			0.241198	−	0.970476i	$-0.422460\pi$
$433$	10.0380			0.482396			0.241198	+	0.970476i	$0.422460\pi$
$434$	2.89829	+	2.91458i	0.139122	+	0.139904i
$435$	23.8688			1.14442
$436$	0.640026	−	1.96980i	0.0306517	−	0.0943362i
$437$	−1.53613	−	4.72772i	−0.0734830	−	0.226157i
$438$	18.4140	+	13.3786i	0.879855	+	0.639252i
$439$	29.1780			1.39259			0.696294	−	0.717757i	$-0.254831\pi$
$439$	29.1780			1.39259			0.696294	+	0.717757i	$0.254831\pi$
$440$	−10.1355			−0.483191
$441$	7.92982	+	5.76135i	0.377610	+	0.274350i
$442$	0.465588	−	0.338270i	0.0221458	−	0.0160898i
$443$	−26.4651	+	19.2280i	−1.25740	+	0.913551i	−0.998627	−	0.0523879i	$-0.983317\pi$
$443$	−26.4651	+	19.2280i	−1.25740	+	0.913551i	−0.258769	+	0.965939i	$0.583317\pi$
$444$	−3.15887	+	9.72199i	−0.149913	+	0.461385i
$445$	3.89487	+	2.82979i	0.184635	+	0.134145i
$446$	8.24244	−	25.3676i	0.390291	−	1.20119i
$447$	−6.68965	−	20.5886i	−0.316410	−	0.973809i
$448$	0.597248	−	0.433926i	0.0282173	−	0.0205011i
$449$	5.73994	+	17.6657i	0.270884	+	0.833696i	0.990279	+	0.139095i	$0.0444193\pi$
$449$	5.73994	+	17.6657i	0.270884	+	0.833696i	−0.719395	+	0.694601i	$0.755581\pi$
$450$	0.937774	+	2.88617i	0.0442071	+	0.136055i
$451$	19.0074	−	13.8097i	0.895022	−	0.650272i
$452$	0.834649	+	2.56878i	0.0392586	+	0.120825i
$453$	−12.3152	+	37.9023i	−0.578619	+	1.78081i
$454$	10.9540	+	7.95855i	0.514097	+	0.373513i
$455$	−0.395228	+	1.21639i	−0.0185286	+	0.0570251i
$456$	−3.57015	+	2.59387i	−0.167188	+	0.121469i
$457$	−1.92465	+	1.39834i	−0.0900313	+	0.0654115i	−0.631890	−	0.775058i	$-0.717721\pi$
$457$	−1.92465	+	1.39834i	−0.0900313	+	0.0654115i	0.541859	+	0.840469i	$0.317721\pi$
$458$	−16.0616	−	11.6695i	−0.750512	−	0.545279i
$459$	−1.81237			−0.0845944
$460$	4.14840			0.193420
$461$	−1.09747	−	0.797356i	−0.0511141	−	0.0371366i	0.561935	−	0.827182i	$-0.310057\pi$
$461$	−1.09747	−	0.797356i	−0.0511141	−	0.0371366i	−0.613049	+	0.790045i	$0.710057\pi$
$462$	2.83695	+	8.73124i	0.131987	+	0.406214i
$463$	−3.59676	+	11.0697i	−0.167155	+	0.514452i	−0.999189	−	0.0402742i	$-0.987177\pi$
$463$	−3.59676	+	11.0697i	−0.167155	+	0.514452i	0.832033	+	0.554726i	$0.187177\pi$
$464$	6.48135			0.300889
$465$	18.2955	−	9.25753i	0.848433	−	0.429308i
$466$	−10.6496			−0.493335
$467$	−10.5505	+	32.4710i	−0.488218	+	1.50258i	0.339048	+	0.940769i	$0.389895\pi$
$467$	−10.5505	+	32.4710i	−0.488218	+	1.50258i	−0.827266	+	0.561810i	$0.810105\pi$
$468$	−0.469236	−	1.44416i	−0.0216904	−	0.0667563i
$469$	−5.73666	−	4.16793i	−0.264895	−	0.192457i
$470$	3.35109			0.154574
$471$	−28.4313			−1.31005
$472$	−10.0226	−	7.28181i	−0.461325	−	0.335172i
$473$	−22.3102	+	16.2093i	−1.02582	+	0.745303i
$474$	14.5012	−	10.5357i	0.666060	−	0.483921i
$475$	−1.28210	+	3.94590i	−0.0588268	+	0.181050i
$476$	−0.343715	−	0.249724i	−0.0157542	−	0.0114461i
$477$	−1.10524	+	3.40156i	−0.0506053	+	0.155747i
$478$	7.04937	+	21.6957i	0.322431	+	0.992339i
$479$	−14.3460	+	10.4230i	−0.655485	+	0.476238i	−0.865135	−	0.501539i	$-0.832767\pi$
$479$	−14.3460	+	10.4230i	−0.655485	+	0.476238i	0.209650	+	0.977776i	$0.432767\pi$
$480$	−1.13801	−	3.50244i	−0.0519429	−	0.159864i
$481$	−1.48606	−	4.57361i	−0.0677583	−	0.208539i
$482$	10.8714	−	7.89852i	0.495178	−	0.359768i
$483$	−1.16115	−	3.57365i	−0.0528341	−	0.162607i
$484$	7.17717	−	22.0890i	0.326235	−	1.00405i
$485$	−15.1297	−	10.9924i	−0.687006	−	0.499139i
$486$	−4.47006	+	13.7574i	−0.202766	+	0.624049i
$487$	3.43458	−	2.49537i	0.155636	−	0.113076i	−0.507242	−	0.861804i	$-0.669335\pi$
$487$	3.43458	−	2.49537i	0.155636	−	0.113076i	0.662878	+	0.748728i	$0.269335\pi$
$488$	−0.994411	+	0.722482i	−0.0450149	+	0.0327052i
$489$	−6.12185	−	4.44778i	−0.276839	−	0.201136i
$490$	−11.1832			−0.505204
$491$	10.6953			0.482671			0.241336	−	0.970442i	$-0.422415\pi$
$491$	10.6953			0.482671			0.241336	+	0.970442i	$0.422415\pi$
$492$	6.90624	+	5.01767i	0.311357	+	0.226214i
$493$	−1.15264	−	3.54745i	−0.0519121	−	0.159769i
$494$	0.641527	−	1.97442i	0.0288637	−	0.0888333i
$495$	15.3906			0.691754
$496$	4.96798	−	2.51380i	0.223069	−	0.112873i
$497$	9.81779			0.440388
$498$	6.11518	−	18.8206i	0.274028	−	0.843371i
$499$	−7.15586	−	22.0235i	−0.320340	−	0.985906i	−0.973500	−	0.228686i	$-0.926557\pi$
$499$	−7.15586	−	22.0235i	−0.320340	−	0.985906i	0.653160	−	0.757220i	$-0.273443\pi$
$500$	−9.80916	−	7.12677i	−0.438679	−	0.318719i
$501$	−2.79129			−0.124705
$502$	−25.3016			−1.12926
$503$	−11.8983	−	8.64459i	−0.530517	−	0.385443i	0.290034	−	0.957016i	$-0.406333\pi$
$503$	−11.8983	−	8.64459i	−0.530517	−	0.385443i	−0.820551	+	0.571573i	$0.806333\pi$
$504$	−0.906909	+	0.658908i	−0.0403969	+	0.0293501i
$505$	1.40074	−	1.01770i	0.0623320	−	0.0452868i
$506$	−4.32884	+	13.3228i	−0.192440	+	0.592271i
$507$	1.71970	+	1.24944i	0.0763748	+	0.0554895i
$508$	5.71739	−	17.5963i	0.253668	−	0.780710i
$509$	−5.62723	−	17.3188i	−0.249423	−	0.767644i	−0.994878	−	0.101088i	$-0.967768\pi$
$509$	−5.62723	−	17.3188i	−0.249423	−	0.767644i	0.745455	−	0.666556i	$-0.232232\pi$
$510$	−1.71461	+	1.24574i	−0.0759244	+	0.0551623i
$511$	2.44272	+	7.51791i	0.108059	+	0.332573i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−5.28925	+	3.84286i	−0.233526	+	0.169667i
$514$	−0.559935	−	1.72330i	−0.0246977	−	0.0760116i
$515$	3.50571	−	10.7895i	0.154480	−	0.475440i
$516$	−8.10629	−	5.88956i	−0.356859	−	0.259274i
$517$	−3.49685	+	10.7622i	−0.153791	+	0.473321i
$518$	−2.87215	+	2.08674i	−0.126195	+	0.0916861i
$519$	−12.6637	+	9.20074i	−0.555876	+	0.403868i
$520$	1.40161	+	1.01833i	0.0614645	+	0.0446566i
$521$	−0.674620			−0.0295556			−0.0147778	−	0.999891i	$-0.504704\pi$
$521$	−0.674620			−0.0295556			−0.0147778	+	0.999891i	$0.504704\pi$
$522$	−9.84181			−0.430764
$523$	−25.5045	−	18.5301i	−1.11523	−	0.810265i	−0.131754	−	0.991282i	$-0.542061\pi$
$523$	−25.5045	−	18.5301i	−1.11523	−	0.810265i	−0.983480	+	0.181018i	$0.942061\pi$
$524$	0.710357	+	2.18625i	0.0310321	+	0.0955069i
$525$	−0.969130	+	2.98268i	−0.0422963	+	0.130175i
$526$	5.14784			0.224456
$527$	−2.25938	−	2.27208i	−0.0984202	−	0.0989734i
$528$	12.4358			0.541198
$529$	−5.33562	+	16.4214i	−0.231984	+	0.713972i
$530$	−1.26100	−	3.88095i	−0.0547742	−	0.168578i
$531$	15.2190	+	11.0573i	0.660450	+	0.479845i
$532$	−1.53260			−0.0664467
$533$	−4.01594			−0.173950
$534$	−4.77882	−	3.47202i	−0.206800	−	0.150249i
$535$	1.58893	−	1.15443i	0.0686955	−	0.0499102i
$536$	−7.77075	+	5.64578i	−0.335645	+	0.243860i
$537$	−13.6536	+	42.0214i	−0.589196	+	1.81336i
$538$	9.43486	+	6.85482i	0.406766	+	0.295532i
$539$	11.6696	−	35.9153i	0.502645	−	1.54698i
$540$	−1.68599	−	5.18894i	−0.0725533	−	0.223296i
$541$	22.3732	−	16.2550i	0.961897	−	0.698859i	0.00830646	−	0.999966i	$-0.497356\pi$
$541$	22.3732	−	16.2550i	0.961897	−	0.698859i	0.953591	+	0.301106i	$0.0973559\pi$
$542$	−3.55041	−	10.9270i	−0.152503	−	0.469356i
$543$	−10.0997	−	31.0838i	−0.433422	−	1.33393i
$544$	−0.465588	+	0.338270i	−0.0199619	+	0.0145032i
$545$	−1.10883	−	3.41264i	−0.0474972	−	0.146181i
$546$	0.484926	−	1.49245i	0.0207529	−	0.0638709i
$547$	−5.63409	−	4.09341i	−0.240896	−	0.175022i	0.460786	−	0.887511i	$-0.347568\pi$
$547$	−5.63409	−	4.09341i	−0.240896	−	0.175022i	−0.701683	+	0.712490i	$0.747568\pi$
$548$	5.44786	−	16.7668i	0.232721	−	0.716241i
$549$	1.50999	−	1.09707i	0.0644449	−	0.0468220i
$550$	9.45891	−	6.87230i	0.403329	−	0.293036i
$551$	−10.8857	−	7.90892i	−0.463746	−	0.336931i
$552$	−5.08989			−0.216640
$553$	6.22509			0.264718
$554$	−12.0800	−	8.77664i	−0.513231	−	0.372884i
$555$	5.47267	+	16.8432i	0.232302	+	0.714952i
$556$	−3.59804	+	11.0736i	−0.152591	+	0.469626i
$557$	−25.7759			−1.09216			−0.546080	−	0.837733i	$-0.683881\pi$
$557$	−25.7759			−1.09216			−0.546080	+	0.837733i	$0.683881\pi$
$558$	−7.54378	+	3.81715i	−0.319354	+	0.161593i
$559$	4.71377			0.199371
$560$	0.395228	−	1.21639i	0.0167014	−	0.0514017i
$561$	−2.21156	−	6.80650i	−0.0933723	−	0.287371i
$562$	−3.55576	−	2.58341i	−0.149991	−	0.108975i
$563$	−27.3881			−1.15427			−0.577136	−	0.816648i	$-0.695830\pi$
$563$	−27.3881			−1.15427			−0.577136	+	0.816648i	$0.695830\pi$
$564$	−4.11163			−0.173131
$565$	3.78571	+	2.75048i	0.159266	+	0.115714i
$566$	−7.66168	+	5.56654i	−0.322044	+	0.233979i
$567$	−6.71883	+	4.88152i	−0.282164	+	0.205004i
$568$	4.10960	−	12.6480i	0.172435	−	0.530700i
$569$	1.75638	+	1.27608i	0.0736311	+	0.0534962i	0.623992	−	0.781431i	$-0.285510\pi$
$569$	1.75638	+	1.27608i	0.0736311	+	0.0534962i	−0.550361	+	0.834927i	$0.685510\pi$
$570$	−2.36254	+	7.27116i	−0.0989560	+	0.304555i
$571$	−8.73879	−	26.8952i	−0.365707	−	1.12553i	−0.949537	−	0.313655i	$-0.898447\pi$
$571$	−8.73879	−	26.8952i	−0.365707	−	1.12553i	0.583830	−	0.811876i	$-0.301553\pi$
$572$	−4.73298	+	3.43871i	−0.197896	+	0.143780i
$573$	−10.9496	−	33.6993i	−0.457425	−	1.40781i
$574$	0.916150	+	2.81962i	0.0382394	+	0.117689i
$575$	−3.87148	+	2.81279i	−0.161452	+	0.117302i
$576$	0.469236	+	1.44416i	0.0195515	+	0.0601733i
$577$	−2.57374	+	7.92117i	−0.107146	+	0.329762i	−0.990228	−	0.139456i	$-0.955464\pi$
$577$	−2.57374	+	7.92117i	−0.107146	+	0.329762i	0.883082	+	0.469219i	$0.155464\pi$
$578$	−13.4853	−	9.79768i	−0.560916	−	0.407530i
$579$	−3.85920	+	11.8774i	−0.160383	+	0.493608i
$580$	9.08430	−	6.60013i	0.377205	−	0.274056i
$581$	5.56013	−	4.03967i	0.230673	−	0.167594i
$582$	18.5635	+	13.4872i	0.769481	+	0.559060i
$583$	13.7797			0.570697
$584$	10.7077			0.443086
$585$	−2.12831	−	1.54631i	−0.0879948	−	0.0639320i
$586$	−3.28071	−	10.0970i	−0.135525	−	0.417103i
$587$	12.4420	−	38.2924i	0.513534	−	1.58050i	−0.272399	−	0.962184i	$-0.587817\pi$
$587$	12.4420	−	38.2924i	0.513534	−	1.58050i	0.785933	−	0.618312i	$-0.212183\pi$
$588$	13.7212			0.565854
$589$	−11.4114	−	1.84019i	−0.470199	−	0.0758235i
$590$	−21.4629			−0.883615
$591$	−1.74270	+	5.36347i	−0.0716849	+	0.220623i
$592$	1.48606	+	4.57361i	0.0610765	+	0.187974i
$593$	−10.0104	−	7.27302i	−0.411080	−	0.298667i	0.362959	−	0.931805i	$-0.381767\pi$
$593$	−10.0104	−	7.27302i	−0.411080	−	0.298667i	−0.774039	+	0.633138i	$0.781767\pi$
$594$	18.4239			0.755940
$595$	−0.736054			−0.0301753
$596$	−8.23915	−	5.98610i	−0.337489	−	0.245200i
$597$	24.1466	−	17.5435i	0.988255	−	0.718009i
$598$	1.93718	−	1.40744i	0.0792172	−	0.0575546i
$599$	−13.2094	+	40.6542i	−0.539720	+	1.66109i	0.193503	+	0.981100i	$0.438015\pi$
$599$	−13.2094	+	40.6542i	−0.539720	+	1.66109i	−0.733223	+	0.679988i	$0.761985\pi$
$600$	3.43685	+	2.49702i	0.140309	+	0.101940i
$601$	−10.6336	+	32.7270i	−0.433755	+	1.33496i	0.460602	+	0.887607i	$0.347634\pi$
$601$	−10.6336	+	32.7270i	−0.433755	+	1.33496i	−0.894357	+	0.447354i	$0.852366\pi$
$602$	−1.07534	−	3.30957i	−0.0438277	−	0.134888i
$603$	11.7997	−	8.57300i	0.480522	−	0.349120i
$604$	5.79356	+	17.8308i	0.235737	+	0.725523i
$605$	−12.4343	−	38.2688i	−0.505526	−	1.55585i
$606$	−1.71864	+	1.24866i	−0.0698149	+	0.0507235i
$607$	11.6499	+	35.8548i	0.472855	+	1.45530i	0.848828	+	0.528669i	$0.177309\pi$
$607$	11.6499	+	35.8548i	0.472855	+	1.45530i	−0.375973	+	0.926631i	$0.622691\pi$
$608$	−0.641527	+	1.97442i	−0.0260174	+	0.0800732i
$609$	−8.22842	−	5.97830i	−0.333432	−	0.242253i
$610$	−0.658050	+	2.02527i	−0.0266437	+	0.0820007i
$611$	1.56486	−	1.13694i	0.0633075	−	0.0459956i
$612$	0.706986	−	0.513656i	0.0285782	−	0.0207633i
$613$	−2.38397	−	1.73206i	−0.0962876	−	0.0699571i	0.538600	−	0.842562i	$-0.318954\pi$
$613$	−2.38397	−	1.73206i	−0.0962876	−	0.0699571i	−0.634887	+	0.772605i	$0.718954\pi$
$614$	8.98561			0.362630
$615$	14.7894			0.596368
$616$	3.49407	+	2.53859i	0.140780	+	0.102283i
$617$	12.8569	+	39.5693i	0.517597	+	1.59300i	0.778506	+	0.627638i	$0.215978\pi$
$617$	12.8569	+	39.5693i	0.517597	+	1.59300i	−0.260908	+	0.965364i	$0.584022\pi$
$618$	−4.30134	+	13.2382i	−0.173025	+	0.532517i
$619$	10.9504			0.440136			0.220068	−	0.975485i	$-0.429372\pi$
$619$	10.9504			0.440136			0.220068	+	0.975485i	$0.429372\pi$
$620$	4.40328	−	8.58238i	0.176840	−	0.344677i
$621$	−7.54078			−0.302601
$622$	0.946295	−	2.91240i	0.0379430	−	0.116776i
$623$	−0.633937	−	1.95106i	−0.0253982	−	0.0781675i
$624$	−1.71970	−	1.24944i	−0.0688433	−	0.0500176i
$625$	−11.0134			−0.440535
$626$	−30.2752			−1.21004
$627$	−20.8864	−	15.1748i	−0.834122	−	0.606025i
$628$	−10.8208	+	7.86176i	−0.431796	+	0.313718i
$629$	2.23900	−	1.62673i	0.0892749	−	0.0648620i
$630$	−0.600145	+	1.84706i	−0.0239104	+	0.0735885i
$631$	31.8461	+	23.1376i	1.26777	+	0.921092i	0.999112	−	0.0421428i	$-0.0134184\pi$
$631$	31.8461	+	23.1376i	1.26777	+	0.921092i	0.268662	+	0.963234i	$0.413418\pi$
$632$	2.60574	−	8.01964i	0.103651	−	0.319004i
$633$	15.8475	+	48.7737i	0.629883	+	1.93858i
$634$	−18.9148	+	13.7424i	−0.751201	+	0.545780i
$635$	−9.90527	−	30.4853i	−0.393078	−	1.20977i
$636$	1.54718	+	4.76174i	0.0613498	+	0.188815i
$637$	−5.22221	+	3.79416i	−0.206911	+	0.150330i
$638$	11.7172	+	36.0619i	0.463890	+	1.42771i
$639$	−6.24034	+	19.2058i	−0.246864	+	0.759770i
$640$	−1.40161	−	1.01833i	−0.0554033	−	0.0402529i
$641$	11.0023	−	33.8615i	0.434563	−	1.33745i	−0.458971	−	0.888451i	$-0.651782\pi$
$641$	11.0023	−	33.8615i	0.434563	−	1.33745i	0.893534	−	0.448996i	$-0.148218\pi$
$642$	−1.94954	+	1.41643i	−0.0769423	+	0.0559019i
$643$	−32.3037	+	23.4700i	−1.27393	+	0.925566i	−0.999352	−	0.0359976i	$-0.988539\pi$
$643$	−32.3037	+	23.4700i	−1.27393	+	0.925566i	−0.274581	+	0.961564i	$0.588539\pi$
$644$	−1.43010	−	1.03903i	−0.0563539	−	0.0409435i
$645$	−17.3593			−0.683522
$646$	1.19475			0.0470068
$647$	−15.3067	−	11.1210i	−0.601769	−	0.437211i	0.244737	−	0.969589i	$-0.421298\pi$
$647$	−15.3067	−	11.1210i	−0.601769	−	0.437211i	−0.846506	+	0.532379i	$0.821298\pi$
$648$	3.47634	+	10.6991i	0.136563	+	0.420299i
$649$	22.3965	−	68.9293i	0.879139	−	2.70571i
$650$	−1.99851			−0.0783881
$651$	−8.62580	−	1.39098i	−0.338072	−	0.0545169i
$652$	−3.55982			−0.139413
$653$	−1.02298	+	3.14842i	−0.0400324	+	0.123207i	−0.969075	−	0.246764i	$-0.920633\pi$
$653$	−1.02298	+	3.14842i	−0.0400324	+	0.123207i	0.929043	+	0.369972i	$0.120633\pi$
$654$	1.36049	+	4.18714i	0.0531992	+	0.163730i
$655$	3.22196	+	2.34089i	0.125892	+	0.0914661i
$656$	4.01594			0.156796
$657$	−16.2594			−0.634338
$658$	−1.15524	−	0.839331i	−0.0450360	−	0.0327205i
$659$	13.0787	−	9.50223i	0.509473	−	0.370154i	−0.303150	−	0.952943i	$-0.598038\pi$
$659$	13.0787	−	9.50223i	0.509473	−	0.370154i	0.812624	+	0.582789i	$0.198038\pi$
$660$	17.4301	−	12.6637i	0.678464	−	0.492933i
$661$	−11.5495	+	35.5458i	−0.449225	+	1.38257i	0.428558	+	0.903514i	$0.359022\pi$
$661$	−11.5495	+	35.5458i	−0.449225	+	1.38257i	−0.877783	+	0.479058i	$0.840978\pi$
$662$	3.53736	+	2.57004i	0.137483	+	0.0998875i
$663$	−0.378027	+	1.16345i	−0.0146814	+	0.0451846i
$664$	−2.87682	−	8.85395i	−0.111642	−	0.343600i
$665$	−2.14810	+	1.56069i	−0.0832999	+	0.0605209i
$666$	−2.25655	−	6.94493i	−0.0874394	−	0.269111i
$667$	−4.79579	−	14.7599i	−0.185694	−	0.571507i
$668$	−1.06235	+	0.771839i	−0.0411034	+	0.0298634i
$669$	17.5207	+	53.9232i	0.677390	+	2.08479i
$670$	−5.14228	+	15.8263i	−0.198664	+	0.611424i
$671$	−5.81758	−	4.22672i	−0.224585	−	0.163171i
$672$	−0.484926	+	1.49245i	−0.0187064	+	0.0575724i
$673$	−19.1081	+	13.8829i	−0.736565	+	0.535146i	−0.891633	−	0.452758i	$-0.850440\pi$
$673$	−19.1081	+	13.8829i	−0.736565	+	0.535146i	0.155068	+	0.987904i	$0.450440\pi$
$674$	19.4463	−	14.1286i	0.749044	−	0.544212i
$675$	5.09176	+	3.69938i	0.195982	+	0.142389i
$676$	1.00000			0.0384615
$677$	−21.4389			−0.823962			−0.411981	−	0.911192i	$-0.635163\pi$
$677$	−21.4389			−0.823962			−0.411981	+	0.911192i	$0.635163\pi$
$678$	−4.64489	−	3.37471i	−0.178386	−	0.129605i
$679$	2.46255	+	7.57894i	0.0945039	+	0.290853i
$680$	−0.308102	+	0.948241i	−0.0118152	+	0.0363634i
$681$	−28.7814			−1.10290
$682$	22.9679	+	23.0970i	0.879488	+	0.884431i
$683$	−21.6218			−0.827335			−0.413668	−	0.910428i	$-0.635752\pi$
$683$	−21.6218			−0.827335			−0.413668	+	0.910428i	$0.635752\pi$
$684$	0.974146	−	2.99811i	0.0372474	−	0.114636i
$685$	−9.43830	−	29.0481i	−0.360619	−	1.10987i
$686$	8.03597	+	5.83847i	0.306815	+	0.222914i
$687$	42.2016			1.61009
$688$	−4.71377			−0.179711
$689$	−1.90555	−	1.38447i	−0.0725958	−	0.0527439i
$690$	−7.13402	+	5.18317i	−0.271588	+	0.197320i
$691$	11.2294	−	8.15864i	0.427187	−	0.310369i	−0.353336	−	0.935496i	$-0.614953\pi$
$691$	11.2294	−	8.15864i	0.427187	−	0.310369i	0.780523	+	0.625127i	$0.214953\pi$
$692$	−2.27557	+	7.00348i	−0.0865042	+	0.266233i
$693$	−5.30567	−	3.85480i	−0.201546	−	0.146432i
$694$	−5.86920	+	18.0635i	−0.222792	+	0.685682i
$695$	6.23353	+	19.1848i	0.236451	+	0.727722i
$696$	−11.1460	+	8.09805i	−0.422489	+	0.306956i
$697$	−0.714191	−	2.19805i	−0.0270519	−	0.0832572i
$698$	2.88985	+	8.89405i	0.109382	+	0.336645i
$699$	18.3142	−	13.3061i	0.692707	−	0.503281i
$700$	0.455917	+	1.40317i	0.0172321	+	0.0530348i
$701$	9.35697	−	28.7978i	0.353408	−	1.08768i	−0.603519	−	0.797348i	$-0.706235\pi$
$701$	9.35697	−	28.7978i	0.353408	−	1.08768i	0.956927	−	0.290329i	$-0.0937646\pi$
$702$	−2.54778	−	1.85107i	−0.0961596	−	0.0698641i
$703$	3.08509	−	9.49493i	0.116356	−	0.358108i
$704$	4.73298	−	3.43871i	0.178381	−	0.129601i
$705$	−5.76289	+	4.18698i	−0.217043	+	0.157691i
$706$	13.1861	+	9.58023i	0.496264	+	0.360557i
$707$	−0.737781			−0.0277471
$708$	26.3340			0.989692
$709$	−31.0466	−	22.5567i	−1.16598	−	0.847133i	−0.175457	−	0.984487i	$-0.556140\pi$
$709$	−31.0466	−	22.5567i	−1.16598	−	0.847133i	−0.990522	+	0.137354i	$0.956140\pi$
$710$	−7.11980	−	21.9125i	−0.267201	−	0.822361i
$711$	−3.95676	+	12.1777i	−0.148390	+	0.456698i
$712$	−2.77886			−0.104142
$713$	−9.40065	−	9.45348i	−0.352057	−	0.354036i
$714$	0.903103			0.0337978
$715$	−3.13204	+	9.63943i	−0.117132	+	0.360494i
$716$	6.42318	+	19.7685i	0.240046	+	0.738785i
$717$	−39.2303	−	28.5025i	−1.46508	−	1.06444i
$718$	−24.6830			−0.921162
$719$	−27.3720			−1.02080			−0.510401	−	0.859936i	$-0.670503\pi$
$719$	−27.3720			−1.02080			−0.510401	+	0.859936i	$0.670503\pi$
$720$	2.12831	+	1.54631i	0.0793175	+	0.0576275i
$721$	−3.91093	+	2.84145i	−0.145650	+	0.105821i
$722$	−11.8846	+	8.63463i	−0.442297	+	0.321348i
$723$	−8.82685	+	27.1663i	−0.328274	+	1.01032i
$724$	−12.4391	−	9.03755i	−0.462296	−	0.335878i
$725$	−4.00272	+	12.3191i	−0.148657	+	0.457520i
$726$	15.2563	+	46.9541i	0.566214	+	1.74263i
$727$	32.1550	−	23.3620i	1.19256	−	0.866447i	0.199029	−	0.979994i	$-0.436221\pi$
$727$	32.1550	−	23.3620i	1.19256	−	0.866447i	0.993533	+	0.113546i	$0.0362211\pi$
$728$	−0.228128	−	0.702107i	−0.00845500	−	0.0260218i
$729$	0.927136	+	2.85343i	0.0343384	+	0.105683i
$730$	15.0079	−	10.9039i	0.555468	−	0.403571i
$731$	0.838291	+	2.57999i	0.0310053	+	0.0954246i
$732$	0.807396	−	2.48491i	0.0298422	−	0.0918449i
$733$	27.4581	+	19.9494i	1.01419	+	0.736850i	0.965083	−	0.261944i	$-0.0843636\pi$
$733$	27.4581	+	19.9494i	1.01419	+	0.736850i	0.0491035	+	0.998794i	$0.484364\pi$
$734$	2.65974	−	8.18583i	0.0981727	−	0.302145i
$735$	19.2317	−	13.9727i	0.709373	−	0.515390i
$736$	−1.93718	+	1.40744i	−0.0714054	+	0.0518791i
$737$	−45.4611	−	33.0294i	−1.67458	−	1.21665i
$738$	−6.09813			−0.224475
$739$	−52.4901			−1.93088			−0.965439	−	0.260630i	$-0.916070\pi$
$739$	−52.4901			−1.93088			−0.965439	+	0.260630i	$0.916070\pi$
$740$	6.74029	+	4.89711i	0.247778	+	0.180021i
$741$	1.36368	+	4.19696i	0.0500959	+	0.154179i
$742$	−0.537332	+	1.65374i	−0.0197261	+	0.0607106i
$743$	23.0426			0.845351			0.422675	−	0.906281i	$-0.361091\pi$
$743$	23.0426			0.845351			0.422675	+	0.906281i	$0.361091\pi$
$744$	−5.40262	+	10.5302i	−0.198070	+	0.386055i
$745$	−17.6438			−0.646420
$746$	−3.55976	+	10.9558i	−0.130332	+	0.401121i
$747$	4.36840	+	13.4445i	0.159831	+	0.491910i
$748$	−2.72382	−	1.97897i	−0.0995928	−	0.0723584i
$749$	−0.836904			−0.0305798
$750$	25.7733			0.941108
$751$	−25.2422	−	18.3396i	−0.921102	−	0.669220i	0.0226958	−	0.999742i	$-0.492775\pi$
$751$	−25.2422	−	18.3396i	−0.921102	−	0.669220i	−0.943798	+	0.330522i	$0.892775\pi$
$752$	−1.56486	+	1.13694i	−0.0570646	+	0.0414598i
$753$	43.5112	−	31.6127i	1.58564	−	1.15203i
$754$	2.00285	−	6.16413i	0.0729394	−	0.224485i
$755$	26.2778	+	19.0919i	0.956348	+	0.694827i
$756$	−0.718427	+	2.21109i	−0.0261290	+	0.0804166i
$757$	5.25174	+	16.1632i	0.190878	+	0.587461i	1.00000		0.000179197i	$-5.70402e-5\pi$
$757$	5.25174	+	16.1632i	0.190878	+	0.587461i	−0.809122	+	0.587640i	$0.800057\pi$
$758$	17.8442	−	12.9645i	0.648129	−	0.470893i
$759$	−9.20169	−	28.3199i	−0.334000	−	1.02795i
$760$	1.11143	+	3.42064i	0.0403159	+	0.124080i
$761$	−14.5875	+	10.5984i	−0.528795	+	0.384192i	−0.819907	−	0.572497i	$-0.805975\pi$
$761$	−14.5875	+	10.5984i	−0.528795	+	0.384192i	0.291112	+	0.956689i	$0.405975\pi$
$762$	12.1533	+	37.4040i	0.440267	+	1.35500i
$763$	−0.472492	+	1.45418i	−0.0171054	+	0.0526449i
$764$	−13.4858	−	9.79799i	−0.487898	−	0.354479i
$765$	0.467847	−	1.43989i	0.0169151	−	0.0520592i
$766$	−12.3415	+	8.96660i	−0.445915	+	0.323977i
$767$	−10.0226	+	7.28181i	−0.361893	+	0.262931i
$768$	1.71970	+	1.24944i	0.0620545	+	0.0450852i
$769$	28.5196			1.02844			0.514222	−	0.857657i	$-0.328081\pi$
$769$	28.5196			1.02844			0.514222	+	0.857657i	$0.328081\pi$
$770$	7.48242			0.269648
$771$	3.11608	+	2.26397i	0.112223	+	0.0815347i
$772$	1.81552	+	5.58760i	0.0653420	+	0.201102i
$773$	2.79626	−	8.60600i	0.100574	−	0.309536i	−0.888092	−	0.459666i	$-0.847969\pi$
$773$	2.79626	−	8.60600i	0.100574	−	0.309536i	0.988666	+	0.150130i	$0.0479691\pi$
$774$	7.15776			0.257280
$775$	1.70988	+	10.9951i	0.0614206	+	0.394955i
$776$	10.7946			0.387502
$777$	2.33200	−	7.17715i	0.0836599	−	0.257479i
$778$	2.37103	+	7.29729i	0.0850057	+	0.261621i
$779$	−6.74494	−	4.90048i	−0.241662	−	0.175578i
$780$	−3.68268			−0.131861
$781$	77.8025			2.78399
$782$	1.11484	+	0.809982i	0.0398668	+	0.0289649i
$783$	−16.5130	+	11.9974i	−0.590128	+	0.428753i
$784$	5.22221	−	3.79416i	0.186507	−	0.135506i
$785$	−7.16063	+	22.0382i	−0.255574	+	0.786576i
$786$	−3.95319	−	2.87216i	−0.141006	−	0.102447i
$787$	−4.24246	+	13.0570i	−0.151228	+	0.465430i	−0.997759	−	0.0669080i	$-0.978687\pi$
$787$	−4.24246	+	13.0570i	−0.151228	+	0.465430i	0.846532	+	0.532338i	$0.178687\pi$
$788$	0.819833	+	2.52319i	0.0292053	+	0.0898848i
$789$	−8.85276	+	6.43190i	−0.315166	+	0.228982i
$790$	−4.51439	−	13.8939i	−0.160615	−	0.494322i
$791$	−0.616170	−	1.89638i	−0.0219085	−	0.0674274i
$792$	−7.18693	+	5.22161i	−0.255376	+	0.185542i
$793$	0.379831	+	1.16900i	0.0134882	+	0.0415124i
$794$	−7.59660	+	23.3799i	−0.269593	+	0.829722i
$795$	7.01755	+	5.09855i	0.248887	+	0.180827i
$796$	4.33895	−	13.3539i	0.153790	−	0.473317i
$797$	2.62053	−	1.90392i	0.0928239	−	0.0674405i	−0.540405	−	0.841405i	$-0.681729\pi$
$797$	2.62053	−	1.90392i	0.0928239	−	0.0674405i	0.633229	+	0.773964i	$0.281729\pi$
$798$	2.63562	−	1.91489i	0.0933001	−	0.0677865i
$799$	0.900575	+	0.654306i	0.0318600	+	0.0231477i
$800$	1.99851			0.0706581
$801$	4.21965			0.149094
$802$	13.9453	+	10.1318i	0.492425	+	0.357768i
$803$	19.3577	+	59.5768i	0.683118	+	2.10242i
$804$	6.30933	−	19.4181i	0.222513	−	0.684825i
$805$	−3.06251			−0.107939
$806$	−0.855576	−	5.50164i	−0.0301364	−	0.193787i
$807$	−24.7898			−0.872644
$808$	−0.308825	+	0.950467i	−0.0108644	+	0.0334373i
$809$	4.11440	+	12.6628i	0.144654	+	0.445201i	0.996966	−	0.0778331i	$-0.0248001\pi$
$809$	4.11440	+	12.6628i	0.144654	+	0.445201i	−0.852312	+	0.523034i	$0.824800\pi$
$810$	15.7676	+	11.4558i	0.554017	+	0.402517i
$811$	−36.2484			−1.27285			−0.636427	−	0.771337i	$-0.719588\pi$
$811$	−36.2484			−1.27285			−0.636427	+	0.771337i	$0.719588\pi$
$812$	−4.78479			−0.167913
$813$	19.7583	+	14.3552i	0.692954	+	0.503460i
$814$	−22.7608	+	16.5367i	−0.797765	+	0.579610i
$815$	−4.98947	+	3.62506i	−0.174774	+	0.126980i
$816$	0.378027	−	1.16345i	0.0132336	−	0.0407288i
$817$	7.91696	+	5.75201i	0.276979	+	0.201237i
$818$	6.27062	−	19.2990i	0.219247	−	0.674773i
$819$	0.346408	+	1.06613i	0.0121045	+	0.0372538i
$820$	5.62877	−	4.08954i	0.196565	−	0.142813i
$821$	1.85639	+	5.71339i	0.0647885	+	0.199399i	0.978211	−	0.207615i	$-0.0665701\pi$
$821$	1.85639	+	5.71339i	0.0647885	+	0.199399i	−0.913422	+	0.407014i	$0.866570\pi$
$822$	11.5804	+	35.6407i	0.403911	+	1.24311i
$823$	4.62757	−	3.36213i	0.161307	−	0.117196i	−0.504204	−	0.863585i	$-0.668214\pi$
$823$	4.62757	−	3.36213i	0.161307	−	0.117196i	0.665511	+	0.746388i	$0.268214\pi$
$824$	2.02352	+	6.22775i	0.0704927	+	0.216954i
$825$	−7.68002	+	23.6367i	−0.267384	+	0.822923i
$826$	7.39904	+	5.37571i	0.257445	+	0.187045i
$827$	−17.2870	+	53.2039i	−0.601128	+	1.85008i	−0.0796407	+	0.996824i	$0.525377\pi$
$827$	−17.2870	+	53.2039i	−0.601128	+	1.85008i	−0.521488	+	0.853259i	$0.674623\pi$
$828$	2.94157	−	2.13717i	0.102227	−	0.0742720i
$829$	16.4092	−	11.9220i	0.569915	−	0.414068i	−0.265159	−	0.964205i	$-0.585425\pi$
$829$	16.4092	−	11.9220i	0.569915	−	0.414068i	0.835074	+	0.550137i	$0.185425\pi$
$830$	−13.0484	−	9.48020i	−0.452916	−	0.329063i
$831$	31.7399			1.10105
$832$	−1.00000			−0.0346688
$833$	−3.00537	−	2.18353i	−0.104130	−	0.0756549i
$834$	−7.64825	−	23.5389i	−0.264837	−	0.815085i
$835$	−0.703006	+	2.16363i	−0.0243285	+	0.0748755i
$836$	−12.1453			−0.420055
$837$	−8.00409	+	15.6007i	−0.276662	+	0.539238i
$838$	4.06967			0.140584
$839$	0.508485	−	1.56496i	0.0175549	−	0.0540283i	−0.941895	−	0.335906i	$-0.890957\pi$
$839$	0.508485	−	1.56496i	0.0175549	−	0.0540283i	0.959450	+	0.281878i	$0.0909574\pi$
$840$	0.840124	+	2.58564i	0.0289870	+	0.0892130i
$841$	−10.5237	−	7.64588i	−0.362885	−	0.263651i
$842$	−29.7533			−1.02537
$843$	9.34266			0.321778
$844$	19.5183	+	14.1808i	0.671846	+	0.488125i
$845$	1.40161	−	1.01833i	0.0482167	−	0.0350315i
$846$	2.37621	−	1.72642i	0.0816957	−	0.0593554i
$847$	−5.29846	+	16.3070i	−0.182057	+	0.560315i
$848$	1.90555	+	1.38447i	0.0654370	+	0.0475427i
$849$	6.22078	−	19.1456i	0.213497	−	0.657075i
$850$	−0.355413	−	1.09385i	−0.0121906	−	0.0375187i
$851$	9.31585	−	6.76836i	0.319343	−	0.232017i
$852$	8.73566	+	26.8856i	0.299279	+	0.921085i
$853$	−12.7867	−	39.3534i	−0.437808	−	1.34743i	−0.890182	−	0.455605i	$-0.849423\pi$
$853$	−12.7867	−	39.3534i	−0.437808	−	1.34743i	0.452374	−	0.891828i	$-0.350577\pi$
$854$	0.734112	−	0.533364i	0.0251208	−	0.0182513i
$855$	−1.68769	−	5.19417i	−0.0577178	−	0.177637i
$856$	−0.350317	+	1.07817i	−0.0119736	+	0.0368509i
$857$	18.5984	+	13.5125i	0.635309	+	0.461579i	0.858236	−	0.513256i	$-0.171561\pi$
$857$	18.5984	+	13.5125i	0.635309	+	0.461579i	−0.222926	+	0.974835i	$0.571561\pi$
$858$	3.84287	−	11.8271i	0.131193	−	0.403772i
$859$	−6.72743	+	4.88776i	−0.229537	+	0.166768i	−0.696609	−	0.717451i	$-0.745309\pi$
$859$	−6.72743	+	4.88776i	−0.229537	+	0.166768i	0.467072	+	0.884219i	$0.345309\pi$
$860$	−6.60685	+	4.80015i	−0.225292	+	0.163684i
$861$	−5.09845	−	3.70424i	−0.173755	−	0.126240i
$862$	−26.5098			−0.902927
$863$	7.72243			0.262875			0.131437	−	0.991324i	$-0.458041\pi$
$863$	7.72243			0.262875			0.131437	+	0.991324i	$0.458041\pi$
$864$	2.54778	+	1.85107i	0.0866771	+	0.0629746i
$865$	3.94238	+	12.1334i	0.134045	+	0.412548i
$866$	−3.10192	+	9.54672i	−0.105407	+	0.324411i
$867$	35.4324			1.20335
$868$	−3.66755	+	1.85578i	−0.124485	+	0.0629894i
$869$	49.3316			1.67346
$870$	−7.37586	+	22.7006i	−0.250065	+	0.769621i
$871$	2.96816	+	9.13506i	0.100572	+	0.309530i
$872$	1.67561	+	1.21740i	0.0567433	+	0.0412264i
$873$	−16.3913			−0.554763
$874$	4.97101			0.168147
$875$	7.24150	+	5.26126i	0.244807	+	0.177863i
$876$	−18.4140	+	13.3786i	−0.622151	+	0.452019i
$877$	1.29872	−	0.943576i	0.0438547	−	0.0318623i	−0.565642	−	0.824651i	$-0.691372\pi$
$877$	1.29872	−	0.943576i	0.0438547	−	0.0318623i	0.609497	+	0.792789i	$0.291372\pi$
$878$	−9.01648	+	27.7499i	−0.304292	+	0.936513i
$879$	18.2574	+	13.2648i	0.615807	+	0.447410i
$880$	3.13204	−	9.63943i	0.105581	−	0.324945i
$881$	0.807726	+	2.48593i	0.0272130	+	0.0837530i	0.963741	−	0.266841i	$-0.0859798\pi$
$881$	0.807726	+	2.48593i	0.0272130	+	0.0837530i	−0.936528	+	0.350594i	$0.885980\pi$
$882$	−7.92982	+	5.76135i	−0.267011	+	0.193995i
$883$	2.49369	+	7.67478i	0.0839193	+	0.258277i	0.984208	−	0.177016i	$-0.0566446\pi$
$883$	2.49369	+	7.67478i	0.0839193	+	0.258277i	−0.900289	+	0.435294i	$0.856645\pi$
$884$	0.177839	+	0.547332i	0.00598137	+	0.0184088i
$885$	36.9099	−	26.8166i	1.24071	−	0.901430i
$886$	−10.1088	−	31.1116i	−0.339611	−	1.04521i
$887$	−3.18530	+	9.80335i	−0.106952	+	0.329164i	−0.990184	−	0.139773i	$-0.955363\pi$
$887$	−3.18530	+	9.80335i	−0.106952	+	0.329164i	0.883232	+	0.468937i	$0.155363\pi$
$888$	−8.27002	−	6.00852i	−0.277524	−	0.201633i
$889$	−4.22080	+	12.9903i	−0.141561	+	0.435680i
$890$	−3.89487	+	2.82979i	−0.130556	+	0.0948548i
$891$	−53.2444	+	38.6843i	−1.78375	+	1.29597i
$892$	21.5790	+	15.6780i	0.722518	+	0.524940i
$893$	4.01560			0.134377
$894$	21.6482			0.724023
$895$	29.1336	+	21.1668i	0.973828	+	0.707528i
$896$	0.228128	+	0.702107i	0.00762123	+	0.0234557i
$897$	−1.57286	+	4.84077i	−0.0525164	+	0.161629i
$898$	−18.5748			−0.619850
$899$	−35.6264	−	5.74506i	−1.18821	−	0.191608i
$900$	−3.03470			−0.101157
$901$	0.418880	−	1.28918i	0.0139549	−	0.0429489i
$902$	7.26017	+	22.3445i	0.241737	+	0.743990i
$903$	5.98438	+	4.34790i	0.199148	+	0.144689i
$904$	−2.70098			−0.0898333
$905$	−26.6379			−0.885474
$906$	−32.2416	−	23.4249i	−1.07116	−	0.778241i
$907$	7.40806	−	5.38227i	0.245981	−	0.178715i	−0.457963	−	0.888971i	$-0.651421\pi$
$907$	7.40806	−	5.38227i	0.245981	−	0.178715i	0.703944	+	0.710256i	$0.251421\pi$
$908$	−10.9540	+	7.95855i	−0.363521	+	0.264114i
$909$	0.468945	−	1.44327i	0.0155539	−	0.0478701i
$910$	−1.03472	−	0.751768i	−0.0343006	−	0.0249209i
$911$	3.80341	−	11.7057i	0.126013	−	0.387827i	−0.868072	−	0.496439i	$-0.834641\pi$
$911$	3.80341	−	11.7057i	0.126013	−	0.387827i	0.994084	+	0.108612i	$0.0346407\pi$
$912$	−1.36368	−	4.19696i	−0.0451558	−	0.138975i
$913$	44.0621	−	32.0130i	1.45824	−	1.05948i
$914$	−0.735150	−	2.26256i	−0.0243166	−	0.0748388i
$915$	−1.39880	−	4.30506i	−0.0462428	−	0.142321i
$916$	16.0616	−	11.6695i	0.530692	−	0.385570i
$917$	−0.524413	−	1.61398i	−0.0173176	−	0.0532982i
$918$	0.560055	−	1.72367i	0.0184846	−	0.0568896i
$919$	8.21616	+	5.96939i	0.271026	+	0.196912i	0.714994	−	0.699131i	$-0.246430\pi$
$919$	8.21616	+	5.96939i	0.271026	+	0.196912i	−0.443968	+	0.896043i	$0.646430\pi$
$920$	−1.28193	+	3.94536i	−0.0422638	+	0.130075i
$921$	−15.4526	+	11.2270i	−0.509180	+	0.369941i
$922$	1.09747	−	0.797356i	0.0361431	−	0.0262595i
$923$	−10.7591	−	7.81692i	−0.354139	−	0.257297i
$924$	−9.18057			−0.302019
$925$	−9.61080			−0.316001
$926$	−9.41643	−	6.84144i	−0.309443	−	0.224824i
$927$	−3.07267	−	9.45672i	−0.100920	−	0.310599i
$928$	−2.00285	+	6.16413i	−0.0657467	+	0.202348i
$929$	27.8864			0.914924			0.457462	−	0.889229i	$-0.348758\pi$
$929$	27.8864			0.914924			0.457462	+	0.889229i	$0.348758\pi$
$930$	3.15081	+	20.2608i	0.103319	+	0.664377i
$931$	−13.4008			−0.439192
$932$	3.29092	−	10.1284i	0.107798	−	0.331767i
$933$	2.01151	+	6.19080i	0.0658540	+	0.202678i
$934$	−27.6215	−	20.0682i	−0.903803	−	0.656651i
$935$	−5.83297			−0.190758
$936$	1.51848			0.0496331
$937$	3.83506	+	2.78633i	0.125286	+	0.0910255i	0.648664	−	0.761075i	$-0.275328\pi$
$937$	3.83506	+	2.78633i	0.125286	+	0.0910255i	−0.523378	+	0.852101i	$0.675328\pi$
$938$	5.73666	−	4.16793i	0.187309	−	0.136088i
$939$	52.0645	−	37.8270i	1.69906	−	1.23444i
$940$	−1.03554	+	3.18708i	−0.0337757	+	0.103951i
$941$	33.5350	+	24.3646i	1.09321	+	0.794263i	0.979938	−	0.199301i	$-0.0638673\pi$
$941$	33.5350	+	24.3646i	1.09321	+	0.794263i	0.113271	+	0.993564i	$0.463867\pi$
$942$	8.78576	−	27.0398i	0.286256	−	0.881004i
$943$	−2.97154	−	9.14547i	−0.0967668	−	0.297818i
$944$	10.0226	−	7.28181i	0.326206	−	0.237003i
$945$	1.24466	+	3.83067i	0.0404888	+	0.124612i
$946$	−8.52172	−	26.2272i	−0.277065	−	0.852719i
$947$	10.6700	−	7.75220i	0.346728	−	0.251913i	−0.400767	−	0.916180i	$-0.631256\pi$
$947$	10.6700	−	7.75220i	0.346728	−	0.251913i	0.747495	+	0.664267i	$0.231256\pi$
$948$	5.53895	+	17.0471i	0.179897	+	0.553665i
$949$	3.30885	−	10.1836i	0.107410	−	0.330573i
$950$	−3.35658	−	2.43870i	−0.108902	−	0.0791219i
$951$	15.3575	−	47.2657i	0.498003	−	1.53269i
$952$	0.343715	−	0.249724i	0.0111399	−	0.00809359i
$953$	4.44176	−	3.22713i	0.143883	−	0.104537i	−0.513515	−	0.858080i	$-0.671657\pi$
$953$	4.44176	−	3.22713i	0.143883	−	0.104537i	0.657398	+	0.753544i	$0.271657\pi$
$954$	−2.89354	−	2.10228i	−0.0936819	−	0.0680639i
$955$	−28.8793			−0.934512
$956$	−22.8122			−0.737800
$957$	−65.2073	−	47.3759i	−2.10785	−	1.53145i
$958$	−5.47968	−	16.8647i	−0.177040	−	0.544875i
$959$	−4.02182	+	12.3779i	−0.129871	+	0.399703i
$960$	3.68268			0.118858
$961$	−29.5360	+	9.41413i	−0.952774	+	0.303682i
$962$	4.80898			0.155048
$963$	0.531949	−	1.63717i	0.0171418	−	0.0527571i
$964$	4.15250	+	12.7801i	0.133743	+	0.411619i
$965$	8.23465	+	5.98282i	0.265083	+	0.192594i
$966$	3.75755			0.120897
$967$	38.1804			1.22780			0.613900	−	0.789384i	$-0.289600\pi$
$967$	38.1804			1.22780			0.613900	+	0.789384i	$0.289600\pi$
$968$	18.7901	+	13.6518i	0.603936	+	0.438785i
$969$	−2.05462	+	1.49277i	−0.0660038	+	0.0479546i
$970$	15.1297	−	10.9924i	0.485786	−	0.352945i
$971$	7.24827	−	22.3079i	0.232608	−	0.715894i	−0.764822	−	0.644242i	$-0.777173\pi$
$971$	7.24827	−	22.3079i	0.232608	−	0.715894i	0.997430	−	0.0716520i	$-0.0228271\pi$
$972$	−11.7028	−	8.50255i	−0.375366	−	0.272719i
$973$	2.65621	−	8.17498i	0.0851542	−	0.262078i
$974$	1.31189	+	4.03759i	0.0420357	+	0.129373i
$975$	3.43685	−	2.49702i	0.110067	−	0.0799686i
$976$	−0.379831	−	1.16900i	−0.0121581	−	0.0374188i
$977$	6.11725	+	18.8270i	0.195708	+	0.602328i	0.999968	+	0.00804957i	$0.00256229\pi$
$977$	6.11725	+	18.8270i	0.195708	+	0.602328i	−0.804259	+	0.594278i	$0.797438\pi$
$978$	6.12185	−	4.44778i	0.195755	−	0.142224i
$979$	−5.02373	−	15.4615i	−0.160559	−	0.494150i
$980$	3.45579	−	10.6358i	0.110391	−	0.339749i
$981$	−2.54438	−	1.84860i	−0.0812358	−	0.0590213i
$982$	−3.30502	+	10.1718i	−0.105468	+	0.324596i
$983$	−20.2003	+	14.6764i	−0.644289	+	0.468103i	−0.861321	−	0.508061i	$-0.830362\pi$
$983$	−20.2003	+	14.6764i	−0.644289	+	0.468103i	0.217032	+	0.976164i	$0.430362\pi$
$984$	−6.90624	+	5.01767i	−0.220163	+	0.159958i
$985$	3.71851	+	2.70166i	0.118482	+	0.0860819i
$986$	3.73001			0.118788
$987$	3.03536			0.0966167
$988$	1.67954	+	1.22026i	0.0534333	+	0.0388216i
$989$	3.48789	+	10.7346i	0.110908	+	0.341341i
$990$	−4.75594	+	14.6373i	−0.151154	+	0.465203i
$991$	−43.0007			−1.36596			−0.682981	−	0.730436i	$-0.739317\pi$
$991$	−43.0007			−1.36596			−0.682981	+	0.730436i	$0.739317\pi$
$992$	0.855576	+	5.50164i	0.0271646	+	0.174677i
$993$	−9.29432			−0.294946
$994$	−3.03386	+	9.33727i	−0.0962283	+	0.296160i
$995$	−7.51715	−	23.1354i	−0.238310	−	0.733441i
$996$	16.0097	+	11.6318i	0.507288	+	0.368566i
$997$	−39.4393			−1.24905			−0.624527	−	0.781003i	$-0.714708\pi$
$997$	−39.4393			−1.24905			−0.624527	+	0.781003i	$0.714708\pi$
$998$	23.1569			0.733017
$999$	−12.2522	−	8.90174i	−0.387642	−	0.281639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	806.2.k.c.287.1	✓	28
31.4	even	5	inner	806.2.k.c.469.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
806.2.k.c.287.1	✓	28	1.1	even	1	trivial
806.2.k.c.469.1	yes	28	31.4	even	5	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:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.656869 - 2.02163i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.73248 q^{5} +2.12567 q^{6} +(0.597248 + 0.433926i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.22848 + 0.892540i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.656869 - 2.02163i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.73248 q^{5} +2.12567 q^{6} +(0.597248 + 0.433926i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-1.22848 + 0.892540i) q^{9} +(0.535366 - 1.64769i) q^{10} +(4.73298 + 3.43871i) q^{11} +(-0.656869 + 2.02163i) q^{12} +(-0.309017 - 0.951057i) q^{13} +(-0.597248 + 0.433926i) q^{14} +(1.13801 + 3.50244i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.465588 - 0.338270i) q^{17} +(-0.469236 - 1.44416i) q^{18} +(0.641527 - 1.97442i) q^{19} +(1.40161 + 1.01833i) q^{20} +(0.484926 - 1.49245i) q^{21} +(-4.73298 + 3.43871i) q^{22} +(1.93718 - 1.40744i) q^{23} +(-1.71970 - 1.24944i) q^{24} -1.99851 q^{25} +1.00000 q^{26} +(-2.54778 - 1.85107i) q^{27} +(-0.228128 - 0.702107i) q^{28} +(2.00285 - 6.16413i) q^{29} -3.68268 q^{30} +(-0.855576 - 5.50164i) q^{31} -1.00000 q^{32} +(3.84287 - 11.8271i) q^{33} +(0.177839 + 0.547332i) q^{34} +(-1.03472 - 0.751768i) q^{35} +1.51848 q^{36} +4.80898 q^{37} +(1.67954 + 1.22026i) q^{38} +(-1.71970 + 1.24944i) q^{39} +(-1.40161 + 1.01833i) q^{40} +(1.24099 - 3.81939i) q^{41} +(1.26955 + 0.922384i) q^{42} +(-1.45663 + 4.48306i) q^{43} +(-1.80784 - 5.56395i) q^{44} +(2.12831 - 1.54631i) q^{45} +(0.739937 + 2.27729i) q^{46} +(0.597723 + 1.83960i) q^{47} +(1.71970 - 1.24944i) q^{48} +(-1.99471 - 6.13907i) q^{49} +(0.617574 - 1.90070i) q^{50} +(-0.989688 - 0.719050i) q^{51} +(-0.309017 + 0.951057i) q^{52} +(1.90555 - 1.38447i) q^{53} +(2.54778 - 1.85107i) q^{54} +(-8.19979 - 5.95750i) q^{55} +0.738239 q^{56} -4.41295 q^{57} +(5.24353 + 3.80964i) q^{58} +(-3.82827 - 11.7822i) q^{59} +(1.13801 - 3.50244i) q^{60} -1.22916 q^{61} +(5.49675 + 0.886398i) q^{62} -1.12100 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.535366 + 1.64769i) q^{65} +(10.0608 + 7.30957i) q^{66} -9.60517 q^{67} -0.575499 q^{68} +(-4.11781 - 2.99176i) q^{69} +(1.03472 - 0.751768i) q^{70} +(10.7591 - 7.81692i) q^{71} +(-0.469236 + 1.44416i) q^{72} +(8.66267 + 6.29380i) q^{73} +(-1.48606 + 4.57361i) q^{74} +(1.31276 + 4.04026i) q^{75} +(-1.67954 + 1.22026i) q^{76} +(1.33461 + 4.10752i) q^{77} +(-0.656869 - 2.02163i) q^{78} +(6.82192 - 4.95641i) q^{79} +(-0.535366 - 1.64769i) q^{80} +(-3.47634 + 10.6991i) q^{81} +(3.24897 + 2.36051i) q^{82} +(2.87682 - 8.85395i) q^{83} +(-1.26955 + 0.922384i) q^{84} +(-0.806622 + 0.586045i) q^{85} +(-3.81352 - 2.77068i) q^{86} -13.7772 q^{87} +5.85028 q^{88} +(-2.24815 - 1.63337i) q^{89} +(0.812942 + 2.50198i) q^{90} +(0.228128 - 0.702107i) q^{91} -2.39449 q^{92} +(-10.5603 + 5.34351i) q^{93} -1.93427 q^{94} +(-1.11143 + 3.42064i) q^{95} +(0.656869 + 2.02163i) q^{96} +(8.73299 + 6.34489i) q^{97} +6.45500 q^{98} -8.88354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8}+O(q^{10}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8} + 3 q^{10} + 3 q^{11} + q^{12} + 7 q^{13} + q^{14} + 6 q^{15} - 7 q^{16} - 2 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} + 15 q^{21} - 3 q^{22} + 18 q^{23} + 4 q^{24} + 54 q^{25} + 28 q^{26} - 26 q^{27} + 4 q^{28} + 27 q^{29} + 14 q^{30} - 33 q^{31} - 28 q^{32} + 3 q^{33} + 2 q^{34} + 8 q^{35} + 30 q^{36} - 6 q^{37} - 27 q^{38} + 4 q^{39} - 2 q^{40} - 22 q^{41} + 5 q^{42} + q^{43} - 12 q^{44} + 28 q^{45} + 27 q^{46} + 7 q^{47} - 4 q^{48} - 30 q^{49} + q^{50} - 52 q^{51} + 7 q^{52} + q^{53} + 26 q^{54} - 18 q^{55} + 6 q^{56} - 112 q^{57} + 23 q^{58} + 27 q^{59} + 6 q^{60} - 6 q^{61} - 17 q^{62} + 54 q^{63} - 7 q^{64} + 3 q^{65} + 17 q^{66} - 24 q^{67} + 8 q^{68} + 6 q^{69} - 8 q^{70} + 28 q^{71} + 15 q^{72} - 8 q^{73} - 9 q^{74} - 62 q^{75} + 27 q^{76} - 62 q^{77} + q^{78} + 40 q^{79} - 3 q^{80} - 24 q^{81} - 18 q^{82} + 3 q^{83} - 5 q^{84} - q^{85} + 4 q^{86} + 42 q^{87} - 18 q^{88} - 5 q^{89} - 23 q^{90} - 4 q^{91} + 18 q^{92} - 69 q^{93} - 12 q^{94} - 17 q^{95} - q^{96} + 29 q^{97} - 30 q^{98} + 88 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8 + 3 * q^10 + 3 * q^11 + q^12 + 7 * q^13 + q^14 + 6 * q^15 - 7 * q^16 - 2 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 + 15 * q^21 - 3 * q^22 + 18 * q^23 + 4 * q^24 + 54 * q^25 + 28 * q^26 - 26 * q^27 + 4 * q^28 + 27 * q^29 + 14 * q^30 - 33 * q^31 - 28 * q^32 + 3 * q^33 + 2 * q^34 + 8 * q^35 + 30 * q^36 - 6 * q^37 - 27 * q^38 + 4 * q^39 - 2 * q^40 - 22 * q^41 + 5 * q^42 + q^43 - 12 * q^44 + 28 * q^45 + 27 * q^46 + 7 * q^47 - 4 * q^48 - 30 * q^49 + q^50 - 52 * q^51 + 7 * q^52 + q^53 + 26 * q^54 - 18 * q^55 + 6 * q^56 - 112 * q^57 + 23 * q^58 + 27 * q^59 + 6 * q^60 - 6 * q^61 - 17 * q^62 + 54 * q^63 - 7 * q^64 + 3 * q^65 + 17 * q^66 - 24 * q^67 + 8 * q^68 + 6 * q^69 - 8 * q^70 + 28 * q^71 + 15 * q^72 - 8 * q^73 - 9 * q^74 - 62 * q^75 + 27 * q^76 - 62 * q^77 + q^78 + 40 * q^79 - 3 * q^80 - 24 * q^81 - 18 * q^82 + 3 * q^83 - 5 * q^84 - q^85 + 4 * q^86 + 42 * q^87 - 18 * q^88 - 5 * q^89 - 23 * q^90 - 4 * q^91 + 18 * q^92 - 69 * q^93 - 12 * q^94 - 17 * q^95 - q^96 + 29 * q^97 - 30 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more