LMFDB - Embedded newform 315.2.be.b.311.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.5
Character	$\chi$	$=$	315.311
Dual form			315.2.be.b.236.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16637 - 0.673405i) q^{2} +(1.48755 + 0.887234i) q^{3} +(-0.0930506 - 0.161168i) q^{4} +1.00000 q^{5} +(-1.13757 - 2.03657i) q^{6} +(2.59059 + 0.537423i) q^{7} +2.94426i q^{8} +(1.42563 + 2.63962i) q^{9} +O(q^{10})$	\(q+(-1.16637 - 0.673405i) q^{2} +(1.48755 + 0.887234i) q^{3} +(-0.0930506 - 0.161168i) q^{4} +1.00000 q^{5} +(-1.13757 - 2.03657i) q^{6} +(2.59059 + 0.537423i) q^{7} +2.94426i q^{8} +(1.42563 + 2.63962i) q^{9} +(-1.16637 - 0.673405i) q^{10} +4.70521i q^{11} +(0.00457626 - 0.322304i) q^{12} +(-4.03894 - 2.33188i) q^{13} +(-2.65969 - 2.37135i) q^{14} +(1.48755 + 0.887234i) q^{15} +(1.79658 - 3.11177i) q^{16} +(2.39024 - 4.14001i) q^{17} +(0.114713 - 4.03880i) q^{18} +(2.17316 - 1.25468i) q^{19} +(-0.0930506 - 0.161168i) q^{20} +(3.37683 + 3.09791i) q^{21} +(3.16852 - 5.48803i) q^{22} +5.40741i q^{23} +(-2.61225 + 4.37975i) q^{24} +1.00000 q^{25} +(3.14060 + 5.43969i) q^{26} +(-0.221252 + 5.19144i) q^{27} +(-0.154441 - 0.467530i) q^{28} +(-0.970704 + 0.560436i) q^{29} +(-1.13757 - 2.03657i) q^{30} +(6.64821 - 3.83834i) q^{31} +(0.908649 - 0.524609i) q^{32} +(-4.17462 + 6.99926i) q^{33} +(-5.57581 + 3.21920i) q^{34} +(2.59059 + 0.537423i) q^{35} +(0.292767 - 0.475385i) q^{36} +(-0.507284 - 0.878641i) q^{37} -3.37962 q^{38} +(-3.93921 - 7.05228i) q^{39} +2.94426i q^{40} +(4.36860 - 7.56663i) q^{41} +(-1.85249 - 5.88729i) q^{42} +(-2.74866 - 4.76082i) q^{43} +(0.758332 - 0.437823i) q^{44} +(1.42563 + 2.63962i) q^{45} +(3.64138 - 6.30705i) q^{46} +(-6.13772 + 10.6308i) q^{47} +(5.43338 - 3.03494i) q^{48} +(6.42235 + 2.78449i) q^{49} +(-1.16637 - 0.673405i) q^{50} +(7.22877 - 4.03779i) q^{51} +0.867933i q^{52} +(-11.6778 - 6.74218i) q^{53} +(3.75401 - 5.90616i) q^{54} +4.70521i q^{55} +(-1.58232 + 7.62739i) q^{56} +(4.34589 + 0.0617053i) q^{57} +1.50960 q^{58} +(-2.57662 - 4.46283i) q^{59} +(0.00457626 - 0.322304i) q^{60} +(2.20711 + 1.27427i) q^{61} -10.3390 q^{62} +(2.27464 + 7.60434i) q^{63} -8.59943 q^{64} +(-4.03894 - 2.33188i) q^{65} +(9.58250 - 5.35252i) q^{66} +(-5.70633 - 9.88366i) q^{67} -0.889653 q^{68} +(-4.79764 + 8.04381i) q^{69} +(-2.65969 - 2.37135i) q^{70} -4.31814i q^{71} +(-7.77173 + 4.19744i) q^{72} +(-3.32607 - 1.92031i) q^{73} +1.36643i q^{74} +(1.48755 + 0.887234i) q^{75} +(-0.404428 - 0.233497i) q^{76} +(-2.52869 + 12.1893i) q^{77} +(-0.154456 + 10.8783i) q^{78} +(-3.20793 + 5.55629i) q^{79} +(1.79658 - 3.11177i) q^{80} +(-4.93514 + 7.52624i) q^{81} +(-10.1908 + 5.88367i) q^{82} +(-1.81854 - 3.14980i) q^{83} +(0.185069 - 0.832500i) q^{84} +(2.39024 - 4.14001i) q^{85} +7.40386i q^{86} +(-1.94121 - 0.0275624i) q^{87} -13.8534 q^{88} +(0.794914 + 1.37683i) q^{89} +(0.114713 - 4.03880i) q^{90} +(-9.21004 - 8.21158i) q^{91} +(0.871504 - 0.503163i) q^{92} +(13.2951 + 0.188771i) q^{93} +(14.3177 - 8.26634i) q^{94} +(2.17316 - 1.25468i) q^{95} +(1.81712 + 0.0258004i) q^{96} +(-3.58634 + 2.07058i) q^{97} +(-5.61576 - 7.57260i) q^{98} +(-12.4200 + 6.70790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.16637	−	0.673405i	−0.824750	−	0.476169i	0.0273019	−	0.999627i	$-0.491308\pi$
$2$	−1.16637	−	0.673405i	−0.824750	−	0.476169i	−0.852052	+	0.523458i	$0.824642\pi$
$3$	1.48755	+	0.887234i	0.858840	+	0.512245i
$3$	1.48755	+	0.887234i	0.858840	+	0.512245i
$4$	−0.0930506	−	0.161168i	−0.0465253	−	0.0805842i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.13757	−	2.03657i	−0.464412	−	0.831427i
$7$	2.59059	+	0.537423i	0.979152	+	0.203127i
$7$	2.59059	+	0.537423i	0.979152	+	0.203127i
$8$			2.94426i			1.04095i
$9$	1.42563	+	2.63962i	0.475211	+	0.879872i
$10$	−1.16637	−	0.673405i	−0.368839	−	0.212949i
$11$			4.70521i			1.41868i	0.704869	+	0.709338i	$0.251006\pi$
$11$			4.70521i			1.41868i	−0.704869	+	0.709338i	$0.748994\pi$
$12$	0.00457626	−	0.322304i	0.00132105	−	0.0930413i
$13$	−4.03894	−	2.33188i	−1.12020	−	0.646748i	−0.178748	−	0.983895i	$-0.557205\pi$
$13$	−4.03894	−	2.33188i	−1.12020	−	0.646748i	−0.941452	+	0.337147i	$0.890538\pi$
$14$	−2.65969	−	2.37135i	−0.710833	−	0.633771i
$15$	1.48755	+	0.887234i	0.384085	+	0.229083i
$16$	1.79658	−	3.11177i	0.449145	−	0.777943i
$17$	2.39024	−	4.14001i	0.579718	−	1.00410i	−0.415794	−	0.909459i	$-0.636496\pi$
$17$	2.39024	−	4.14001i	0.579718	−	1.00410i	0.995511	−	0.0946417i	$-0.0301706\pi$
$18$	0.114713	−	4.03880i	0.0270382	−	0.951955i
$19$	2.17316	−	1.25468i	0.498558	−	0.287842i	−0.229560	−	0.973294i	$-0.573729\pi$
$19$	2.17316	−	1.25468i	0.498558	−	0.287842i	0.728118	+	0.685452i	$0.240395\pi$
$20$	−0.0930506	−	0.161168i	−0.0208068	−	0.0360384i
$21$	3.37683	+	3.09791i	0.736884	+	0.676019i
$22$	3.16852	−	5.48803i	0.675530	−	1.17005i
$23$			5.40741i			1.12752i	0.825938	+	0.563761i	$0.190646\pi$
$23$			5.40741i			1.12752i	−0.825938	+	0.563761i	$0.809354\pi$
$24$	−2.61225	+	4.37975i	−0.533223	+	0.894013i
$25$	1.00000			0.200000
$26$	3.14060	+	5.43969i	0.615923	+	1.06681i
$27$	−0.221252	+	5.19144i	−0.0425799	+	0.999093i
$28$	−0.154441	−	0.467530i	−0.0291866	−	0.0883548i
$29$	−0.970704	+	0.560436i	−0.180255	+	0.104070i	−0.587413	−	0.809288i	$-0.699853\pi$
$29$	−0.970704	+	0.560436i	−0.180255	+	0.104070i	0.407157	+	0.913358i	$0.366520\pi$
$30$	−1.13757	−	2.03657i	−0.207692	−	0.371825i
$31$	6.64821	−	3.83834i	1.19405	−	0.689387i	0.234830	−	0.972036i	$-0.424547\pi$
$31$	6.64821	−	3.83834i	1.19405	−	0.689387i	0.959223	+	0.282649i	$0.0912133\pi$
$32$	0.908649	−	0.524609i	0.160628	−	0.0927386i
$33$	−4.17462	+	6.99926i	−0.726709	+	1.21841i
$34$	−5.57581	+	3.21920i	−0.956244	+	0.552088i
$35$	2.59059	+	0.537423i	0.437890	+	0.0908411i
$36$	0.292767	−	0.475385i	0.0487945	−	0.0792308i
$37$	−0.507284	−	0.878641i	−0.0833969	−	0.144448i	0.821310	−	0.570482i	$-0.193244\pi$
$37$	−0.507284	−	0.878641i	−0.0833969	−	0.144448i	−0.904707	+	0.426034i	$0.859910\pi$
$38$	−3.37962			−0.548247
$39$	−3.93921	−	7.05228i	−0.630779	−	1.12927i
$40$			2.94426i			0.465529i
$41$	4.36860	−	7.56663i	0.682260	−	1.18171i	−0.292029	−	0.956410i	$-0.594330\pi$
$41$	4.36860	−	7.56663i	0.682260	−	1.18171i	0.974289	−	0.225300i	$-0.0723363\pi$
$42$	−1.85249	−	5.88729i	−0.285845	−	0.908428i
$43$	−2.74866	−	4.76082i	−0.419167	−	0.726019i	0.576689	−	0.816964i	$-0.304345\pi$
$43$	−2.74866	−	4.76082i	−0.419167	−	0.726019i	−0.995856	+	0.0909451i	$0.971011\pi$
$44$	0.758332	−	0.437823i	0.114323	−	0.0660043i
$45$	1.42563	+	2.63962i	0.212521	+	0.393491i
$46$	3.64138	−	6.30705i	0.536892	−	0.929924i
$47$	−6.13772	+	10.6308i	−0.895278	+	1.55067i	−0.0618173	+	0.998087i	$0.519690\pi$
$47$	−6.13772	+	10.6308i	−0.895278	+	1.55067i	−0.833460	+	0.552579i	$0.813644\pi$
$48$	5.43338	−	3.03494i	0.784241	−	0.438056i
$49$	6.42235	+	2.78449i	0.917479	+	0.397784i
$50$	−1.16637	−	0.673405i	−0.164950	−	0.0952339i
$51$	7.22877	−	4.03779i	1.01223	−	0.565404i
$52$			0.867933i			0.120361i
$53$	−11.6778	−	6.74218i	−1.60407	−	0.926110i	−0.990662	−	0.136343i	$-0.956465\pi$
$53$	−11.6778	−	6.74218i	−1.60407	−	0.926110i	−0.613407	−	0.789767i	$-0.710201\pi$
$54$	3.75401	−	5.90616i	0.510855	−	0.803726i
$55$			4.70521i			0.634451i
$56$	−1.58232	+	7.62739i	−0.211446	+	1.01925i
$57$	4.34589	+	0.0617053i	0.575627	+	0.00817307i
$58$	1.50960			0.198221
$59$	−2.57662	−	4.46283i	−0.335447	−	0.581011i	0.648124	−	0.761535i	$-0.275554\pi$
$59$	−2.57662	−	4.46283i	−0.335447	−	0.581011i	−0.983571	+	0.180524i	$0.942221\pi$
$60$	0.00457626	−	0.322304i	0.000590792	−	0.0416093i
$61$	2.20711	+	1.27427i	0.282591	+	0.163154i	0.634596	−	0.772844i	$-0.281167\pi$
$61$	2.20711	+	1.27427i	0.282591	+	0.163154i	−0.352005	+	0.935998i	$0.614500\pi$
$62$	−10.3390			−1.31306
$63$	2.27464	+	7.60434i	0.286578	+	0.958057i
$64$	−8.59943			−1.07493
$65$	−4.03894	−	2.33188i	−0.500969	−	0.289234i
$66$	9.58250	−	5.35252i	1.17952	−	0.658850i
$67$	−5.70633	−	9.88366i	−0.697139	−	1.20748i	−0.969454	−	0.245273i	$-0.921122\pi$
$67$	−5.70633	−	9.88366i	−0.697139	−	1.20748i	0.272315	−	0.962208i	$-0.412211\pi$
$68$	−0.889653			−0.107886
$69$	−4.79764	+	8.04381i	−0.577567	+	0.968361i
$70$	−2.65969	−	2.37135i	−0.317894	−	0.283431i
$71$		−	4.31814i		−	0.512469i	−0.966615	−	0.256235i	$-0.917518\pi$
$71$		−	4.31814i		−	0.512469i	0.966615	−	0.256235i	$-0.0824820\pi$
$72$	−7.77173	+	4.19744i	−0.915907	+	0.494673i
$73$	−3.32607	−	1.92031i	−0.389287	−	0.224755i	0.292564	−	0.956246i	$-0.405491\pi$
$73$	−3.32607	−	1.92031i	−0.389287	−	0.224755i	−0.681851	+	0.731491i	$0.738825\pi$
$74$			1.36643i			0.158844i
$75$	1.48755	+	0.887234i	0.171768	+	0.102449i
$76$	−0.404428	−	0.233497i	−0.0463911	−	0.0267839i
$77$	−2.52869	+	12.1893i	−0.288171	+	1.38910i
$78$	−0.154456	+	10.8783i	−0.0174887	+	1.23172i
$79$	−3.20793	+	5.55629i	−0.360920	+	0.625132i	−0.988112	−	0.153733i	$-0.950871\pi$
$79$	−3.20793	+	5.55629i	−0.360920	+	0.625132i	0.627193	+	0.778864i	$0.284204\pi$
$80$	1.79658	−	3.11177i	0.200864	−	0.347907i
$81$	−4.93514	+	7.52624i	−0.548349	+	0.836249i
$82$	−10.1908	+	5.88367i	−1.12539	+	0.649743i
$83$	−1.81854	−	3.14980i	−0.199611	−	0.345736i	0.748792	−	0.662806i	$-0.230634\pi$
$83$	−1.81854	−	3.14980i	−0.199611	−	0.345736i	−0.948402	+	0.317070i	$0.897301\pi$
$84$	0.185069	−	0.832500i	0.0201927	−	0.0908332i
$85$	2.39024	−	4.14001i	0.259258	−	0.449048i
$86$			7.40386i			0.798378i
$87$	−1.94121	−	0.0275624i	−0.208120	−	0.00295500i
$88$	−13.8534			−1.47678
$89$	0.794914	+	1.37683i	0.0842608	+	0.145944i	0.905076	−	0.425250i	$-0.139814\pi$
$89$	0.794914	+	1.37683i	0.0842608	+	0.145944i	−0.820815	+	0.571194i	$0.806480\pi$
$90$	0.114713	−	4.03880i	0.0120919	−	0.425727i
$91$	−9.21004	−	8.21158i	−0.965475	−	0.860807i
$92$	0.871504	−	0.503163i	0.0908605	−	0.0524583i
$93$	13.2951	+	0.188771i	1.37864	+	0.0195746i
$94$	14.3177	−	8.26634i	1.47676	−	0.852608i
$95$	2.17316	−	1.25468i	0.222962	−	0.128727i
$96$	1.81712	+	0.0258004i	0.185459	+	0.00263324i
$97$	−3.58634	+	2.07058i	−0.364138	+	0.210235i	−0.670894	−	0.741553i	$-0.734090\pi$
$97$	−3.58634	+	2.07058i	−0.364138	+	0.210235i	0.306756	+	0.951788i	$0.400756\pi$
$98$	−5.61576	−	7.57260i	−0.567278	−	0.764948i
$99$	−12.4200	+	6.70790i	−1.24825	+	0.674170i
$100$	−0.0930506	−	0.161168i	−0.00930506	−	0.0161168i
$101$	−7.61673			−0.757893			−0.378946	−	0.925419i	$-0.623714\pi$
$101$	−7.61673			−0.757893			−0.378946	+	0.925419i	$0.623714\pi$
$102$	−11.1505	−	0.158321i	−1.10406	−	0.0156761i
$103$			10.6677i			1.05112i	0.850756	+	0.525560i	$0.176144\pi$
$103$			10.6677i			1.05112i	−0.850756	+	0.525560i	$0.823856\pi$
$104$	6.86568	−	11.8917i	0.673235	−	1.16608i
$105$	3.37683	+	3.09791i	0.329545	+	0.302325i
$106$	9.08044	+	15.7278i	0.881970	+	1.52762i
$107$	2.04092	−	1.17833i	0.197303	−	0.113913i	−0.398094	−	0.917345i	$-0.630328\pi$
$107$	2.04092	−	1.17833i	0.197303	−	0.113913i	0.595397	+	0.803432i	$0.296995\pi$
$108$	0.857284	−	0.447408i	0.0824922	−	0.0430519i
$109$	−5.07754	+	8.79456i	−0.486340	+	0.842366i	−0.999877	−	0.0157016i	$-0.995002\pi$
$109$	−5.07754	+	8.79456i	−0.486340	+	0.842366i	0.513536	+	0.858068i	$0.328335\pi$
$110$	3.16852	−	5.48803i	0.302106	−	0.523263i
$111$	0.0249484	−	1.75711i	0.00236799	−	0.166777i
$112$	6.32655	−	7.09581i	0.597803	−	0.670491i
$113$	2.08695	+	1.20490i	0.196323	+	0.113347i	0.594939	−	0.803771i	$-0.297176\pi$
$113$	2.08695	+	1.20490i	0.196323	+	0.113347i	−0.398616	+	0.917118i	$0.630509\pi$
$114$	−5.02737	−	2.99851i	−0.470856	−	0.280837i
$115$			5.40741i			0.504243i
$116$	0.180649	+	0.104298i	0.0167729	+	0.00968382i
$117$	0.397232	−	13.9857i	0.0367241	−	1.29297i
$118$			6.94043i			0.638918i
$119$	8.41707	−	9.44052i	0.771592	−	0.865412i
$120$	−2.61225	+	4.37975i	−0.238465	+	0.399815i
$121$	−11.1390			−1.01264
$122$	−1.71621	−	2.97256i	−0.155378	−	0.269123i
$123$	13.2119	−	7.37981i	1.19128	−	0.665415i
$124$	−1.23724	−	0.714321i	−0.111107	−	0.0641479i
$125$	1.00000			0.0894427
$126$	2.46772	−	10.4012i	0.219842	−	0.926617i
$127$	−1.22813			−0.108979			−0.0544895	−	0.998514i	$-0.517353\pi$
$127$	−1.22813			−0.108979			−0.0544895	+	0.998514i	$0.517353\pi$
$128$	8.21283	+	4.74168i	0.725919	+	0.419109i
$129$	0.135180	−	9.52069i	0.0119019	−	0.838250i
$130$	3.14060	+	5.43969i	0.275449	+	0.477092i
$131$	−1.84688			−0.161363			−0.0806813	−	0.996740i	$-0.525710\pi$
$131$	−1.84688			−0.161363			−0.0806813	+	0.996740i	$0.525710\pi$
$132$	1.51651	+	0.0215323i	0.131995	+	0.00187414i
$133$	6.30407	−	2.08245i	0.546632	−	0.180571i
$134$			15.3707i			1.32783i
$135$	−0.221252	+	5.19144i	−0.0190423	+	0.446808i
$136$	12.1893	+	7.03749i	1.04522	+	0.603460i
$137$		−	16.3199i		−	1.39430i	−0.716924	−	0.697152i	$-0.754450\pi$
$137$		−	16.3199i		−	1.39430i	0.716924	−	0.697152i	$-0.245550\pi$
$138$	11.0126	−	6.15132i	0.937452	−	0.523635i
$139$	12.8287	+	7.40667i	1.08812	+	0.628226i	0.933075	−	0.359682i	$-0.117115\pi$
$139$	12.8287	+	7.40667i	1.08812	+	0.628226i	0.155044	+	0.987908i	$0.450448\pi$
$140$	−0.154441	−	0.467530i	−0.0130526	−	0.0395135i
$141$	−18.5622	+	10.3683i	−1.56322	+	0.873173i
$142$	−2.90786	+	5.03656i	−0.244022	+	0.422659i
$143$	10.9720	−	19.0041i	0.917525	−	1.58920i
$144$	10.7751	+	0.306045i	0.897929	+	0.0255037i
$145$	−0.970704	+	0.560436i	−0.0806126	+	0.0465417i
$146$	2.58629	+	4.47958i	0.214043	+	0.370733i
$147$	7.08310	+	9.84021i	0.584204	+	0.811607i
$148$	−0.0944062	+	0.163516i	−0.00776014	+	0.0134410i
$149$			1.20412i			0.0986453i	0.998783	+	0.0493226i	$0.0157063\pi$
$149$			1.20412i			0.0986453i	−0.998783	+	0.0493226i	$0.984294\pi$
$150$	−1.13757	−	2.03657i	−0.0928825	−	0.166285i
$151$	16.2344			1.32114			0.660569	−	0.750765i	$-0.270315\pi$
$151$	16.2344			1.32114			0.660569	+	0.750765i	$0.270315\pi$
$152$	3.69410	+	6.39837i	0.299631	+	0.518976i
$153$	14.3356	+	0.407173i	1.15897	+	0.0329180i
$154$	11.1577	−	12.5144i	0.899115	−	1.00844i
$155$	6.64821	−	3.83834i	0.533997	−	0.308303i
$156$	−0.770059	+	1.29110i	−0.0616541	+	0.103370i
$157$	−15.5096	+	8.95450i	−1.23780	+	0.714647i	−0.968645	−	0.248449i	$-0.920079\pi$
$157$	−15.5096	+	8.95450i	−1.23780	+	0.714647i	−0.269159	+	0.963096i	$0.586746\pi$
$158$	7.48327	−	4.32047i	0.595337	−	0.343718i
$159$	−11.3895	−	20.3903i	−0.903243	−	1.61706i
$160$	0.908649	−	0.524609i	0.0718350	−	0.0414740i
$161$	−2.90607	+	14.0084i	−0.229030	+	1.10402i
$162$	10.8244	−	5.45505i	0.850447	−	0.428589i
$163$	−9.82069	−	17.0099i	−0.769216	−	1.33232i	−0.937988	−	0.346666i	$-0.887314\pi$
$163$	−9.82069	−	17.0099i	−0.769216	−	1.33232i	0.168772	−	0.985655i	$-0.446020\pi$
$164$	−1.62600			−0.126970
$165$	−4.17462	+	6.99926i	−0.324994	+	0.544891i
$166$			4.89846i			0.380194i
$167$	1.88700	−	3.26839i	0.146021	−	0.252915i	−0.783733	−	0.621098i	$-0.786687\pi$
$167$	1.88700	−	3.26839i	0.146021	−	0.252915i	0.929753	+	0.368183i	$0.120020\pi$
$168$	−9.12106	+	9.94227i	−0.703705	+	0.767063i
$169$	4.37535	+	7.57833i	0.336566	+	0.582949i
$170$	−5.57581	+	3.21920i	−0.427645	+	0.246901i
$171$	6.40999	+	3.94761i	0.490184	+	0.301881i
$172$	−0.511530	+	0.885995i	−0.0390038	+	0.0675565i
$173$	8.97117	−	15.5385i	0.682065	−	1.18137i	−0.292284	−	0.956332i	$-0.594415\pi$
$173$	8.97117	−	15.5385i	0.682065	−	1.18137i	0.974349	−	0.225040i	$-0.0722514\pi$
$174$	2.24562	+	1.33937i	0.170240	+	0.101537i
$175$	2.59059	+	0.537423i	0.195830	+	0.0406254i
$176$	14.6415	+	8.45330i	1.10365	+	0.637191i
$177$	0.126719	−	8.92476i	0.00952476	−	0.670826i
$178$		−	2.14120i		−	0.160490i
$179$	0.00419063	+	0.00241946i	0.000313222	+	0.000180839i	0.500157	−	0.865935i	$-0.333276\pi$
$179$	0.00419063	+	0.00241946i	0.000313222	+	0.000180839i	−0.499843	+	0.866116i	$0.666609\pi$
$180$	0.292767	−	0.475385i	0.0218215	−	0.0354331i
$181$		−	16.1981i		−	1.20400i	−0.798497	−	0.601999i	$-0.794371\pi$
$181$		−	16.1981i		−	1.20400i	0.798497	−	0.601999i	$-0.205629\pi$
$182$	5.21262	+	15.7798i	0.386385	+	1.16968i
$183$	2.15261	+	3.85377i	0.159126	+	0.284879i
$184$	−15.9208			−1.17370
$185$	−0.507284	−	0.878641i	−0.0372962	−	0.0645990i
$186$	−15.3799	−	9.17315i	−1.12771	−	0.672608i
$187$	19.4796	+	11.2466i	1.42449	+	0.822431i
$188$	2.28447			0.166612
$189$	−3.36317	+	13.3300i	−0.244635	+	0.969615i
$190$	−3.37962			−0.245184
$191$	−4.23858	−	2.44714i	−0.306693	−	0.177069i	0.338753	−	0.940875i	$-0.389995\pi$
$191$	−4.23858	−	2.44714i	−0.306693	−	0.177069i	−0.645446	+	0.763806i	$0.723328\pi$
$192$	−12.7921	−	7.62970i	−0.923191	−	0.550626i
$193$	3.77032	+	6.53039i	0.271394	+	0.470068i	0.969219	−	0.246200i	$-0.0791821\pi$
$193$	3.77032	+	6.53039i	0.271394	+	0.470068i	−0.697825	+	0.716268i	$0.745849\pi$
$194$	5.57735			0.400430
$195$	−3.93921	−	7.05228i	−0.282093	−	0.505025i
$196$	−0.148832	−	1.29418i	−0.0106309	−	0.0924414i
$197$			6.80985i			0.485182i	0.970129	+	0.242591i	$0.0779973\pi$
$197$			6.80985i			0.485182i	−0.970129	+	0.242591i	$0.922003\pi$
$198$	19.0034	+	0.539751i	1.35051	+	0.0383585i
$199$	8.52636	+	4.92269i	0.604417	+	0.348961i	0.770777	−	0.637105i	$-0.219868\pi$
$199$	8.52636	+	4.92269i	0.604417	+	0.348961i	−0.166360	+	0.986065i	$0.553201\pi$
$200$			2.94426i			0.208191i
$201$	0.280639	−	19.7653i	0.0197948	−	1.39414i
$202$	8.88394	+	5.12915i	0.625072	+	0.360885i
$203$	−2.81589	+	0.930184i	−0.197637	+	0.0652861i
$204$	−1.32341	−	0.789330i	−0.0926570	−	0.0552642i
$205$	4.36860	−	7.56663i	0.305116	−	0.528477i
$206$	7.18369	−	12.4425i	0.500511	−	0.866911i
$207$	−14.2735	+	7.70898i	−0.992076	+	0.535811i
$208$	−14.5126	+	8.37884i	−1.00627	+	0.580968i
$209$	5.90352	+	10.2252i	0.408355	+	0.707291i
$210$	−1.85249	−	5.88729i	−0.127834	−	0.406261i
$211$	12.6023	−	21.8279i	0.867579	−	1.50269i	0.00311607	−	0.999995i	$-0.499008\pi$
$211$	12.6023	−	21.8279i	0.867579	−	1.50269i	0.864463	−	0.502696i	$-0.167659\pi$
$212$			2.50946i			0.172350i
$213$	3.83120	−	6.42347i	0.262510	−	0.440129i
$214$	−3.17397			−0.216968
$215$	−2.74866	−	4.76082i	−0.187457	−	0.324685i
$216$	−15.2850	−	0.651424i	−1.04001	−	0.0443238i
$217$	19.2856	−	6.37069i	1.30919	−	0.432471i
$218$	11.8446	−	6.83849i	0.802218	−	0.463161i
$219$	−3.24394	−	5.80756i	−0.219205	−	0.392438i
$220$	0.758332	−	0.437823i	0.0511267	−	0.0295180i
$221$	−19.3081	+	11.1475i	−1.29880	+	0.749863i
$222$	−1.21234	+	2.03264i	−0.0813672	+	0.136422i
$223$	−15.5699	+	8.98931i	−1.04264	+	0.601969i	−0.920580	−	0.390554i	$-0.872283\pi$
$223$	−15.5699	+	8.98931i	−1.04264	+	0.601969i	−0.122060	+	0.992523i	$0.538950\pi$
$224$	2.63588	−	0.870720i	0.176117	−	0.0581774i
$225$	1.42563	+	2.63962i	0.0950422	+	0.175974i
$226$	−1.62277	−	2.81072i	−0.107945	−	0.186966i
$227$	−5.58417			−0.370634			−0.185317	−	0.982679i	$-0.559331\pi$
$227$	−5.58417			−0.370634			−0.185317	+	0.982679i	$0.559331\pi$
$228$	−0.394443	−	0.706162i	−0.0261226	−	0.0467667i
$229$			3.85536i			0.254770i	0.991853	+	0.127385i	$0.0406583\pi$
$229$			3.85536i			0.254770i	−0.991853	+	0.127385i	$0.959342\pi$
$230$	3.64138	−	6.30705i	0.240105	−	0.415875i
$231$	−14.5763	+	15.8887i	−0.959051	+	1.04540i
$232$	−1.65007	−	2.85801i	−0.108333	−	0.187638i
$233$	−20.5385	+	11.8579i	−1.34552	+	0.776837i	−0.987611	−	0.156919i	$-0.949844\pi$
$233$	−20.5385	+	11.8579i	−1.34552	+	0.776837i	−0.357910	+	0.933756i	$0.616510\pi$
$234$	−9.88134	+	16.0450i	−0.645963	+	1.04889i
$235$	−6.13772	+	10.6308i	−0.400380	+	0.693479i
$236$	−0.479512	+	0.830538i	−0.0312135	+	0.0540634i
$237$	−9.70169	+	5.41910i	−0.630193	+	0.352008i
$238$	−16.1747	+	5.34306i	−1.04845	+	0.346339i
$239$	−11.3709	−	6.56500i	−0.735523	−	0.424654i	0.0849163	−	0.996388i	$-0.472938\pi$
$239$	−11.3709	−	6.56500i	−0.735523	−	0.424654i	−0.820439	+	0.571734i	$0.806271\pi$
$240$	5.43338	−	3.03494i	0.350723	−	0.195904i
$241$			14.6916i			0.946372i	0.880962	+	0.473186i	$0.156896\pi$
$241$			14.6916i			0.946372i	−0.880962	+	0.473186i	$0.843104\pi$
$242$	12.9923	+	7.50108i	0.835174	+	0.482188i
$243$	−14.0188	+	6.81706i	−0.899308	+	0.437315i
$244$		−	0.474288i		−	0.0303632i
$245$	6.42235	+	2.78449i	0.410309	+	0.177894i
$246$	−20.3796	−	0.289361i	−1.29936	−	0.0184490i
$247$	−11.7030			−0.744646
$248$	11.3011	+	19.5741i	0.717621	+	1.24296i
$249$	0.0894363	−	6.29897i	0.00566780	−	0.399181i
$250$	−1.16637	−	0.673405i	−0.0737679	−	0.0425899i
$251$	4.11403			0.259675			0.129838	−	0.991535i	$-0.458554\pi$
$251$	4.11403			0.259675			0.129838	+	0.991535i	$0.458554\pi$
$252$	1.01392	−	1.07419i	0.0638711	−	0.0676676i
$253$	−25.4430			−1.59959
$254$	1.43246	+	0.827030i	0.0898804	+	0.0518925i
$255$	7.22877	−	4.03779i	0.452683	−	0.252856i
$256$	2.21328	+	3.83351i	0.138330	+	0.239595i
$257$	8.66694			0.540629			0.270315	−	0.962772i	$-0.412872\pi$
$257$	8.66694			0.540629			0.270315	+	0.962772i	$0.412872\pi$
$258$	−6.56895	+	11.0136i	−0.408965	+	0.685679i
$259$	−0.841964	−	2.54883i	−0.0523171	−	0.158377i
$260$			0.867933i			0.0538269i
$261$	−2.86320	−	1.76331i	−0.177228	−	0.109146i
$262$	2.15415	+	1.24370i	0.133084	+	0.0768360i
$263$			3.17430i			0.195735i	0.995199	+	0.0978677i	$0.0312022\pi$
$263$			3.17430i			0.195735i	−0.995199	+	0.0978677i	$0.968798\pi$
$264$	−20.6077	−	12.2912i	−1.26831	−	0.756471i
$265$	−11.6778	−	6.74218i	−0.717361	−	0.414169i
$266$	−8.75523	−	1.81629i	−0.536817	−	0.111364i
$267$	−0.0390941	+	2.75339i	−0.00239252	+	0.168505i
$268$	−1.06196	+	1.83936i	−0.0648693	+	0.112357i
$269$	−4.82224	+	8.35236i	−0.294017	+	0.509252i	−0.974756	−	0.223274i	$-0.928326\pi$
$269$	−4.82224	+	8.35236i	−0.294017	+	0.509252i	0.680739	+	0.732526i	$0.261659\pi$
$270$	3.75401	−	5.90616i	0.228461	−	0.359437i
$271$	6.26437	−	3.61674i	0.380534	−	0.219701i	−0.297517	−	0.954717i	$-0.596158\pi$
$271$	6.26437	−	3.61674i	0.380534	−	0.219701i	0.678050	+	0.735015i	$0.262825\pi$
$272$	−8.58852	−	14.8757i	−0.520755	−	0.901975i
$273$	−6.41484	−	20.3866i	−0.388244	−	1.23385i
$274$	−10.9899	+	19.0351i	−0.663925	+	1.14995i
$275$			4.70521i			0.283735i
$276$	1.74283	+	0.0247457i	0.104906	+	0.00148952i
$277$	26.5375			1.59448			0.797241	−	0.603661i	$-0.206292\pi$
$277$	26.5375			1.59448			0.797241	+	0.603661i	$0.206292\pi$
$278$	−9.97538	−	17.2779i	−0.598284	−	1.03626i
$279$	19.6097	+	12.0766i	1.17400	+	0.723010i
$280$	−1.58232	+	7.62739i	−0.0945614	+	0.455824i
$281$	−0.835904	+	0.482610i	−0.0498659	+	0.0287901i	−0.524726	−	0.851271i	$-0.675832\pi$
$281$	−0.835904	+	0.482610i	−0.0498659	+	0.0287901i	0.474860	+	0.880061i	$0.342499\pi$
$282$	28.6326	+	0.406541i	1.70504	+	0.0242092i
$283$	25.7731	−	14.8801i	1.53205	−	0.884532i	0.532787	−	0.846249i	$-0.321145\pi$
$283$	25.7731	−	14.8801i	1.53205	−	0.884532i	0.999267	−	0.0382824i	$-0.0121887\pi$
$284$	−0.695948	+	0.401806i	−0.0412969	+	0.0238428i
$285$	4.34589	+	0.0617053i	0.257428	+	0.00365511i
$286$	−25.5949	+	14.7772i	−1.51346	+	0.873795i
$287$	15.3837	−	17.2543i	0.908074	−	1.01849i
$288$	2.68017	+	1.65059i	0.157930	+	0.0972617i
$289$	−2.92647	−	5.06880i	−0.172146	−	0.298165i
$290$	1.50960			0.0886470
$291$	−7.17196	−	0.101832i	−0.420428	−	0.00596947i
$292$			0.714742i			0.0418271i
$293$	0.204632	−	0.354433i	0.0119547	−	0.0207062i	−0.859986	−	0.510317i	$-0.829528\pi$
$293$	0.204632	−	0.354433i	0.0119547	−	0.0207062i	0.871941	+	0.489611i	$0.162861\pi$
$294$	−1.63509	−	16.2471i	−0.0953602	−	0.947553i
$295$	−2.57662	−	4.46283i	−0.150016	−	0.259836i
$296$	2.58695	−	1.49358i	0.150364	−	0.0868124i
$297$	−24.4268	−	1.04104i	−1.41739	−	0.0604071i
$298$	0.810860	−	1.40445i	0.0469719	−	0.0813577i
$299$	12.6094	−	21.8402i	0.729223	−	1.26305i
$300$	0.00457626	−	0.322304i	0.000264210	−	0.0186083i
$301$	−4.56209	−	13.8106i	−0.262955	−	0.796027i
$302$	−18.9354	−	10.9323i	−1.08961	−	0.629086i
$303$	−11.3303	−	6.75782i	−0.650908	−	0.388227i
$304$		−	9.01651i		−	0.517132i
$305$	2.20711	+	1.27427i	0.126379	+	0.0729647i
$306$	−16.4465	−	10.1286i	−0.940184	−	0.579014i
$307$		−	12.8475i		−	0.733244i	−0.930370	−	0.366622i	$-0.880514\pi$
$307$		−	12.8475i		−	0.733244i	0.930370	−	0.366622i	$-0.119486\pi$
$308$	2.19983	−	0.726677i	0.125347	−	0.0414063i
$309$	−9.46475	+	15.8688i	−0.538431	+	0.902744i
$310$	−10.3390			−0.587218
$311$	−3.61081	−	6.25411i	−0.204750	−	0.354638i	0.745303	−	0.666726i	$-0.232305\pi$
$311$	−3.61081	−	6.25411i	−0.204750	−	0.354638i	−0.950053	+	0.312088i	$0.898972\pi$
$312$	20.7638	−	11.5981i	1.17552	−	0.656612i
$313$	20.1751	+	11.6481i	1.14036	+	0.658389i	0.946520	−	0.322644i	$-0.104572\pi$
$313$	20.1751	+	11.6481i	1.14036	+	0.658389i	0.193842	+	0.981033i	$0.437905\pi$
$314$	24.1200			1.36117
$315$	2.27464	+	7.60434i	0.128162	+	0.428456i
$316$	1.19400			0.0671677
$317$	19.6819	+	11.3633i	1.10544	+	0.638228i	0.937645	−	0.347593i	$-0.113001\pi$
$317$	19.6819	+	11.3633i	1.10544	+	0.638228i	0.167798	+	0.985821i	$0.446334\pi$
$318$	−0.446579	+	31.4524i	−0.0250429	+	1.76376i
$319$	−2.63697	−	4.56737i	−0.147642	−	0.255724i
$320$	−8.59943			−0.480722
$321$	4.08143	+	0.0579505i	0.227803	+	0.00323448i
$322$	12.8229	−	14.3820i	0.714591	−	0.801480i
$323$		−	11.9959i		−	0.667470i
$324$	1.67221	+	0.0950678i	0.0929006	+	0.00528155i
$325$	−4.03894	−	2.33188i	−0.224040	−	0.129350i
$326$			26.4532i			1.46511i
$327$	−15.3560	+	8.57742i	−0.849186	+	0.474332i
$328$	22.2782	+	12.8623i	1.23011	+	0.710202i
$329$	−21.6136	+	24.2416i	−1.19160	+	1.33648i
$330$	9.58250	−	5.35252i	0.527499	−	0.294647i
$331$	4.25287	−	7.36619i	0.233759	−	0.404883i	−0.725152	−	0.688589i	$-0.758231\pi$
$331$	4.25287	−	7.36619i	0.233759	−	0.404883i	0.958911	+	0.283706i	$0.0915640\pi$
$332$	−0.338433	+	0.586182i	−0.0185739	+	0.0321709i
$333$	1.59608	−	2.59165i	0.0874644	−	0.142022i
$334$	−4.40190	+	2.54144i	−0.240861	+	0.139061i
$335$	−5.70633	−	9.88366i	−0.311770	−	0.540002i
$336$	15.7067	−	4.94227i	0.856872	−	0.269623i
$337$	10.3959	−	18.0062i	0.566300	−	0.980860i	−0.430628	−	0.902530i	$-0.641708\pi$
$337$	10.3959	−	18.0062i	0.566300	−	0.980860i	0.996927	−	0.0783302i	$-0.0249588\pi$
$338$		−	11.7855i		−	0.641049i
$339$	2.03542	+	3.64396i	0.110549	+	0.197913i
$340$	−0.889653			−0.0482482
$341$	18.0602	+	31.2812i	0.978016	+	1.69397i
$342$	−4.81810	−	8.92090i	−0.260533	−	0.482387i
$343$	15.1413	+	10.6650i	0.817551	+	0.575856i
$344$	14.0171	−	8.09279i	0.755753	−	0.436334i
$345$	−4.79764	+	8.04381i	−0.258296	+	0.433064i
$346$	−20.9274	+	12.0825i	−1.12507	+	0.649557i
$347$	19.9639	−	11.5262i	1.07172	−	0.618757i	0.143069	−	0.989713i	$-0.454303\pi$
$347$	19.9639	−	11.5262i	1.07172	−	0.618757i	0.928651	+	0.370955i	$0.120970\pi$
$348$	0.176189	+	0.315427i	0.00944472	+	0.0169087i
$349$	5.25696	−	3.03511i	0.281399	−	0.162466i	−0.352658	−	0.935752i	$-0.614722\pi$
$349$	5.25696	−	3.03511i	0.281399	−	0.162466i	0.634056	+	0.773287i	$0.281389\pi$
$350$	−2.65969	−	2.37135i	−0.142167	−	0.126754i
$351$	12.9995	−	20.4520i	0.693859	−	1.09165i
$352$	2.46840	+	4.27539i	0.131566	+	0.227879i
$353$	−32.5706			−1.73356			−0.866778	−	0.498694i	$-0.833813\pi$
$353$	−32.5706			−1.73356			−0.866778	+	0.498694i	$0.833813\pi$
$354$	−6.15778	+	10.3243i	−0.327282	+	0.548728i
$355$		−	4.31814i		−	0.229183i
$356$	0.147935	−	0.256230i	0.00784052	−	0.0135802i
$357$	20.8968	−	6.57538i	1.10598	−	0.348006i
$358$	−0.00325856	−	0.00564398i	−0.000172220	−	0.000298294i
$359$	−11.5257	+	6.65434i	−0.608301	+	0.351203i	−0.772300	−	0.635258i	$-0.780894\pi$
$359$	−11.5257	+	6.65434i	−0.608301	+	0.351203i	0.163999	+	0.986460i	$0.447560\pi$
$360$	−7.77173	+	4.19744i	−0.409606	+	0.221224i
$361$	−6.35158	+	11.0013i	−0.334293	+	0.579013i
$362$	−10.9079	+	18.8931i	−0.573307	+	0.992997i
$363$	−16.5699	−	9.88292i	−0.869694	−	0.518719i
$364$	−0.466447	+	2.24846i	−0.0244485	+	0.117851i
$365$	−3.32607	−	1.92031i	−0.174094	−	0.100513i
$366$	0.0844035	−	5.94451i	0.00441184	−	0.310725i
$367$		−	8.82209i		−	0.460509i	−0.973130	−	0.230255i	$-0.926044\pi$
$367$		−	8.82209i		−	0.460509i	0.973130	−	0.230255i	$-0.0739559\pi$
$368$	16.8266	+	9.71485i	0.877148	+	0.506422i
$369$	26.2010	+	0.744184i	1.36397	+	0.0387407i
$370$			1.36643i			0.0710373i
$371$	−26.6290	−	23.7422i	−1.38251	−	1.23263i
$372$	−1.20669	−	2.16031i	−0.0625640	−	0.112007i
$373$	−2.74106			−0.141927			−0.0709633	−	0.997479i	$-0.522607\pi$
$373$	−2.74106			−0.141927			−0.0709633	+	0.997479i	$0.522607\pi$
$374$	−15.1470	−	26.2354i	−0.783233	−	1.35660i
$375$	1.48755	+	0.887234i	0.0768169	+	0.0458166i
$376$	−31.3000	−	18.0711i	−1.61417	−	0.931944i
$377$	5.22749			0.269229
$378$	12.8992	−	13.2830i	0.663464	−	0.683202i
$379$	16.9823			0.872321			0.436161	−	0.899869i	$-0.356338\pi$
$379$	16.9823			0.872321			0.436161	+	0.899869i	$0.356338\pi$
$380$	−0.404428	−	0.233497i	−0.0207467	−	0.0119781i
$381$	−1.82691	−	1.08964i	−0.0935955	−	0.0558239i
$382$	3.29584	+	5.70856i	0.168630	+	0.292075i
$383$	17.7149			0.905190			0.452595	−	0.891716i	$-0.350498\pi$
$383$	17.7149			0.905190			0.452595	+	0.891716i	$0.350498\pi$
$384$	8.01005	+	14.3402i	0.408761	+	0.731796i
$385$	−2.52869	+	12.1893i	−0.128874	+	0.621224i
$386$		−	10.1558i		−	0.516918i
$387$	8.64816	−	14.0426i	0.439611	−	0.713825i
$388$	0.667423	+	0.385337i	0.0338833	+	0.0195625i
$389$		−	5.37953i		−	0.272753i	−0.990657	−	0.136377i	$-0.956454\pi$
$389$		−	5.37953i		−	0.272753i	0.990657	−	0.136377i	$-0.0435457\pi$
$390$	−0.154456	+	10.8783i	−0.00782118	+	0.550843i
$391$	22.3867	+	12.9250i	1.13215	+	0.653645i
$392$	−8.19827	+	18.9091i	−0.414075	+	0.955054i
$393$	−2.74733	−	1.63861i	−0.138585	−	0.0826572i
$394$	4.58579	−	7.94282i	0.231029	−	0.400154i
$395$	−3.20793	+	5.55629i	−0.161408	+	0.279567i
$396$	2.23679	+	1.37753i	0.112403	+	0.0692235i
$397$	−29.9736	+	17.3053i	−1.50433	+	0.868527i	−0.504346	+	0.863502i	$0.668266\pi$
$397$	−29.9736	+	17.3053i	−1.50433	+	0.868527i	−0.999987	+	0.00502555i	$0.998400\pi$
$398$	−6.62994	−	11.4834i	−0.332329	−	0.575610i
$399$	11.2253	+	2.49543i	0.561966	+	0.124928i
$400$	1.79658	−	3.11177i	0.0898291	−	0.155589i
$401$			16.4508i			0.821514i	0.911745	+	0.410757i	$0.134736\pi$
$401$			16.4508i			0.821514i	−0.911745	+	0.410757i	$0.865264\pi$
$402$	−13.6374	+	22.8647i	−0.680172	+	1.14039i
$403$	−35.8023			−1.78344
$404$	0.708742	+	1.22758i	0.0352612	+	0.0610742i
$405$	−4.93514	+	7.52624i	−0.245229	+	0.373982i
$406$	3.91077	+	0.811295i	0.194088	+	0.0402639i
$407$	4.13419	−	2.38688i	0.204924	−	0.118313i
$408$	11.8883	+	21.2834i	0.588560	+	1.05369i
$409$	−14.5252	+	8.38610i	−0.718223	+	0.414666i	−0.814098	−	0.580727i	$-0.802768\pi$
$409$	−14.5252	+	8.38610i	−0.718223	+	0.414666i	0.0958755	+	0.995393i	$0.469435\pi$
$410$	−10.1908	+	5.88367i	−0.503289	+	0.290574i
$411$	14.4796	−	24.2767i	0.714225	−	1.19748i
$412$	1.71930	−	0.992637i	0.0847037	−	0.0489037i
$413$	−4.27654	−	12.9461i	−0.210435	−	0.637037i
$414$	21.8395	+	0.620303i	1.07335	+	0.0304862i
$415$	−1.81854	−	3.14980i	−0.0892686	−	0.154618i
$416$	−4.89331			−0.239914
$417$	12.5120	+	22.3999i	0.612714	+	1.09693i
$418$		−	15.9018i		−	0.777784i
$419$	−15.0971	+	26.1490i	−0.737542	+	1.27746i	0.216057	+	0.976381i	$0.430680\pi$
$419$	−15.0971	+	26.1490i	−0.737542	+	1.27746i	−0.953599	+	0.301079i	$0.902653\pi$
$420$	0.185069	−	0.832500i	0.00903044	−	0.0406219i
$421$	−16.0259	−	27.7576i	−0.781053	−	1.35282i	−0.931329	−	0.364179i	$-0.881350\pi$
$421$	−16.0259	−	27.7576i	−0.781053	−	1.35282i	0.150276	−	0.988644i	$-0.451984\pi$
$422$	−29.3980	+	16.9729i	−1.43107	+	0.826229i
$423$	−36.8114	−	1.04555i	−1.78983	−	0.0508364i
$424$	19.8508	−	34.3825i	0.964038	−	1.66976i
$425$	2.39024	−	4.14001i	0.115944	−	0.200820i
$426$	−8.79420	+	4.91220i	−0.426081	+	0.237997i
$427$	5.03289	+	4.48728i	0.243559	+	0.217155i
$428$	−0.379818	−	0.219288i	−0.0183592	−	0.0105997i
$429$	33.1825	−	18.5348i	1.60207	−	0.894871i
$430$			7.40386i			0.357046i
$431$	−31.4516	−	18.1586i	−1.51497	−	0.874668i	−0.999846	−	0.0175515i	$-0.994413\pi$
$431$	−31.4516	−	18.1586i	−1.51497	−	0.874668i	−0.515123	−	0.857116i	$-0.672254\pi$
$432$	15.7571	+	10.0153i	0.758113	+	0.481863i
$433$			8.33139i			0.400381i	0.979757	+	0.200191i	$0.0641561\pi$
$433$			8.33139i			0.400381i	−0.979757	+	0.200191i	$0.935844\pi$
$434$	−26.7843	−	5.55644i	−1.28569	−	0.266718i
$435$	−1.94121	−	0.0275624i	−0.0930740	−	0.00132152i
$436$	1.88987			0.0905086
$437$	6.78455	+	11.7512i	0.324549	+	0.562135i
$438$	−0.127194	+	8.95826i	−0.00607758	+	0.428042i
$439$	−14.5574	−	8.40474i	−0.694788	−	0.401136i	0.110615	−	0.993863i	$-0.464718\pi$
$439$	−14.5574	−	8.40474i	−0.694788	−	0.401136i	−0.805403	+	0.592727i	$0.798051\pi$
$440$	−13.8534			−0.660434
$441$	1.80593	+	20.9222i	0.0859968	+	0.996295i
$442$	30.0272			1.42825
$443$	−9.49850	−	5.48396i	−0.451287	−	0.260551i	0.257086	−	0.966388i	$-0.417237\pi$
$443$	−9.49850	−	5.48396i	−0.451287	−	0.260551i	−0.708374	+	0.705838i	$0.750571\pi$
$444$	−0.285511	+	0.159479i	−0.0135498	+	0.00756853i
$445$	0.794914	+	1.37683i	0.0376826	+	0.0652681i
$446$	24.2138			1.14656
$447$	−1.06834	+	1.79119i	−0.0505305	+	0.0847205i
$448$	−22.2776	−	4.62153i	−1.05252	−	0.218347i
$449$			12.1373i			0.572792i	0.958111	+	0.286396i	$0.0924573\pi$
$449$			12.1373i			0.572792i	−0.958111	+	0.286396i	$0.907543\pi$
$450$	0.114713	−	4.03880i	0.00540765	−	0.190391i
$451$	35.6026	+	20.5552i	1.67646	+	0.967906i
$452$		−	0.448467i		−	0.0210941i
$453$	24.1496	+	14.4037i	1.13465	+	0.676746i
$454$	6.51322	+	3.76041i	0.305681	+	0.176485i
$455$	−9.21004	−	8.21158i	−0.431774	−	0.384965i
$456$	−0.181677	+	12.7954i	−0.00850780	+	0.599201i
$457$	−1.27945	+	2.21607i	−0.0598500	+	0.103663i	−0.894398	−	0.447272i	$-0.852396\pi$
$457$	−1.27945	+	2.21607i	−0.0598500	+	0.103663i	0.834548	+	0.550935i	$0.185729\pi$
$458$	2.59622	−	4.49679i	0.121313	−	0.210121i
$459$	20.9638	+	13.3248i	0.978506	+	0.621947i
$460$	0.871504	−	0.503163i	0.0406341	−	0.0234601i
$461$	1.42204	+	2.46304i	0.0662308	+	0.114715i	0.897239	−	0.441545i	$-0.145569\pi$
$461$	1.42204	+	2.46304i	0.0662308	+	0.114715i	−0.831008	+	0.556260i	$0.812236\pi$
$462$	27.7009	−	8.71636i	1.28876	−	0.405522i
$463$	−1.01405	+	1.75638i	−0.0471268	+	0.0816261i	−0.888627	−	0.458631i	$-0.848340\pi$
$463$	−1.01405	+	1.75638i	−0.0471268	+	0.0816261i	0.841500	+	0.540258i	$0.181673\pi$
$464$			4.02748i			0.186971i
$465$	13.2951	+	0.188771i	0.616544	+	0.00875404i
$466$	31.9407			1.47962
$467$	15.6329	+	27.0770i	0.723405	+	1.25297i	0.959627	+	0.281276i	$0.0907575\pi$
$467$	15.6329	+	27.0770i	0.723405	+	1.25297i	−0.236222	+	0.971699i	$0.575909\pi$
$468$	−2.29101	+	1.23735i	−0.105902	+	0.0571967i
$469$	−9.47109	−	28.6713i	−0.437334	−	1.32392i
$470$	14.3177	−	8.26634i	0.660427	−	0.381298i
$471$	−31.0162	−	0.440385i	−1.42915	−	0.0202919i
$472$	13.1398	−	7.58624i	0.604806	−	0.349185i
$473$	22.4007	−	12.9330i	1.02998	−	0.594662i
$474$	14.9650	+	0.212482i	0.687367	+	0.00975962i
$475$	2.17316	−	1.25468i	0.0997115	−	0.0575685i
$476$	−2.30473	−	0.478120i	−0.105637	−	0.0219146i
$477$	1.14852	−	40.4368i	0.0525871	−	1.85147i
$478$	8.84181	+	15.3145i	0.404415	+	0.700467i
$479$	13.7524			0.628363			0.314181	−	0.949363i	$-0.398270\pi$
$479$	13.7524			0.628363			0.314181	+	0.949363i	$0.398270\pi$
$480$	1.81712	+	0.0258004i	0.0829396	+	0.00117762i
$481$			4.73171i			0.215747i
$482$	9.89343	−	17.1359i	0.450634	−	0.780520i
$483$	−16.7517	+	18.2599i	−0.762227	+	0.830854i
$484$	1.03649	+	1.79526i	0.0471134	+	0.0816027i
$485$	−3.58634	+	2.07058i	−0.162847	+	0.0940200i
$486$	20.9418	+	1.48912i	0.949940	+	0.0675479i
$487$	−18.6366	+	32.2795i	−0.844503	+	1.46272i	0.0415495	+	0.999136i	$0.486771\pi$
$487$	−18.6366	+	32.2795i	−0.844503	+	1.46272i	−0.886052	+	0.463585i	$0.846563\pi$
$488$	−3.75180	+	6.49831i	−0.169836	+	0.294165i
$489$	0.482985	−	34.0165i	0.0218413	−	1.53828i
$490$	−5.61576	−	7.57260i	−0.253694	−	0.342095i
$491$	−16.8271	−	9.71513i	−0.759396	−	0.438438i	0.0696827	−	0.997569i	$-0.477801\pi$
$491$	−16.8271	−	9.71513i	−0.759396	−	0.438438i	−0.829079	+	0.559132i	$0.811135\pi$
$492$	−2.41877	−	1.44265i	−0.109046	−	0.0650395i
$493$			5.35831i			0.241326i
$494$	13.6501	+	7.88088i	0.614146	+	0.354578i
$495$	−12.4200	+	6.70790i	−0.558235	+	0.301498i
$496$		−	27.5836i		−	1.23854i
$497$	2.32067	−	11.1866i	0.104096	−	0.501785i
$498$	−4.34608	+	7.28672i	−0.194752	+	0.326526i
$499$	17.0703			0.764171			0.382086	−	0.924127i	$-0.375206\pi$
$499$	17.0703			0.764171			0.382086	+	0.924127i	$0.375206\pi$
$500$	−0.0930506	−	0.161168i	−0.00416135	−	0.00720767i
$501$	5.70684	−	3.18769i	0.254963	−	0.142415i
$502$	−4.79849	−	2.77041i	−0.214167	−	0.123649i
$503$	26.1131			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$503$	26.1131			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$504$	−22.3892	+	6.69715i	−0.997294	+	0.298315i
$505$	−7.61673			−0.338940
$506$	29.6760	+	17.1335i	1.31926	+	0.761675i
$507$	−0.215181	+	15.1551i	−0.00955653	+	0.673063i
$508$	0.114278	+	0.197936i	0.00507028	+	0.00878199i
$509$	−0.859047			−0.0380766			−0.0190383	−	0.999819i	$-0.506060\pi$
$509$	−0.859047			−0.0380766			−0.0190383	+	0.999819i	$0.506060\pi$
$510$	−11.1505	−	0.158321i	−0.493753	−	0.00701058i
$511$	−7.58447	−	6.76223i	−0.335517	−	0.299144i
$512$		−	24.9285i		−	1.10169i
$513$	6.03276	+	11.5594i	0.266353	+	0.510362i
$514$	−10.1089	−	5.83637i	−0.445884	−	0.257431i
$515$			10.6677i			0.470075i
$516$	−1.54701	+	0.864119i	−0.0681035	+	0.0380407i
$517$	−50.0203	−	28.8793i	−2.19989	−	1.27011i
$518$	−0.734351	+	3.53987i	−0.0322655	+	0.155533i
$519$	27.1314	−	15.1549i	1.19094	−	0.665225i
$520$	6.86568	−	11.8917i	0.301080	−	0.521486i
$521$	3.85811	−	6.68244i	0.169027	−	0.292763i	−0.769051	−	0.639187i	$-0.779271\pi$
$521$	3.85811	−	6.68244i	0.169027	−	0.292763i	0.938078	+	0.346424i	$0.112604\pi$
$522$	2.15214	+	3.98477i	0.0941966	+	0.174409i
$523$	−1.87099	+	1.08022i	−0.0818128	+	0.0472346i	−0.540348	−	0.841441i	$-0.681708\pi$
$523$	−1.87099	+	1.08022i	−0.0818128	+	0.0472346i	0.458536	+	0.888676i	$0.348374\pi$
$524$	0.171853	+	0.297659i	0.00750745	+	0.0130033i
$525$	3.37683	+	3.09791i	0.147377	+	0.135204i
$526$	2.13759	−	3.70241i	0.0932032	−	0.161433i
$527$		−	36.6982i		−	1.59860i
$528$	14.2800	+	25.5652i	0.621459	+	1.11258i
$529$	−6.24006			−0.271307
$530$	9.08044	+	15.7278i	0.394429	+	0.683171i
$531$	8.10685	−	13.1636i	0.351807	−	0.571253i
$532$	−0.922223	−	0.822245i	−0.0399834	−	0.0356488i
$533$	−35.2890	+	20.3741i	−1.52854	+	0.882501i
$534$	1.89974	−	3.18515i	0.0822099	−	0.137835i
$535$	2.04092	−	1.17833i	0.0882367	−	0.0509435i
$536$	29.1001	−	16.8010i	1.25693	−	0.725691i
$537$	0.00408716	+	0.00731715i	0.000176374	+	0.000315758i
$538$	11.2490	−	6.49464i	0.484981	−	0.280004i
$539$	−13.1016	+	30.2185i	−0.564327	+	1.30160i
$540$	0.857284	−	0.447408i	0.0368916	−	0.0192534i
$541$	14.5851	+	25.2621i	0.627061	+	1.08610i	0.988139	+	0.153565i	$0.0490755\pi$
$541$	14.5851	+	25.2621i	0.627061	+	1.08610i	−0.361078	+	0.932536i	$0.617591\pi$
$542$	−9.74212			−0.418460
$543$	14.3715	−	24.0956i	0.616742	−	1.03404i
$544$		−	5.01576i		−	0.215049i
$545$	−5.07754	+	8.79456i	−0.217498	+	0.376718i
$546$	−6.24637	+	28.0982i	−0.267320	+	1.20249i
$547$	13.1363	+	22.7527i	0.561666	+	0.972834i	0.997351	+	0.0727353i	$0.0231728\pi$
$547$	13.1363	+	22.7527i	0.561666	+	0.972834i	−0.435685	+	0.900099i	$0.643494\pi$
$548$	−2.63025	+	1.51858i	−0.112359	+	0.0648704i
$549$	−0.217071	+	7.64256i	−0.00926434	+	0.326177i
$550$	3.16852	−	5.48803i	0.135106	−	0.234010i
$551$	−1.40633	+	2.43584i	−0.0599118	+	0.103770i
$552$	−23.6831	−	14.1255i	−1.00802	−	0.601221i
$553$	−11.2965	+	12.6701i	−0.480377	+	0.538787i
$554$	−30.9526	−	17.8705i	−1.31505	−	0.759244i
$555$	0.0249484	−	1.75711i	0.00105900	−	0.0745850i
$556$		−	2.75678i		−	0.116914i
$557$	−22.1614	−	12.7949i	−0.939008	−	0.542137i	−0.0493589	−	0.998781i	$-0.515718\pi$
$557$	−22.1614	−	12.7949i	−0.939008	−	0.542137i	−0.889649	+	0.456644i	$0.849051\pi$
$558$	−14.7397	−	27.2911i	−0.623980	−	1.15532i
$559$			25.6382i			1.08438i
$560$	6.32655	−	7.09581i	0.267346	−	0.299853i
$561$	18.9987	+	34.0129i	0.802125	+	1.43603i
$562$	1.29997			0.0548358
$563$	−3.92156	−	6.79234i	−0.165274	−	0.286263i	0.771479	−	0.636255i	$-0.219518\pi$
$563$	−3.92156	−	6.79234i	−0.165274	−	0.286263i	−0.936753	+	0.349992i	$0.886184\pi$
$564$	3.39828	+	2.02686i	0.143093	+	0.0853463i
$565$	2.08695	+	1.20490i	0.0877985	+	0.0506905i
$566$	−40.0814			−1.68475
$567$	−16.8297	+	16.8452i	−0.706782	+	0.707431i
$568$	12.7138			0.533457
$569$	32.2359	+	18.6114i	1.35140	+	0.780230i	0.988445	−	0.151578i	$-0.0484355\pi$
$569$	32.2359	+	18.6114i	1.35140	+	0.780230i	0.362952	+	0.931808i	$0.381769\pi$
$570$	−5.02737	−	2.99851i	−0.210573	−	0.125594i
$571$	5.60366	+	9.70583i	0.234506	+	0.406176i	0.959129	−	0.282969i	$-0.0913194\pi$
$571$	5.60366	+	9.70583i	0.234506	+	0.406176i	−0.724623	+	0.689146i	$0.757986\pi$
$572$	−4.08381			−0.170753
$573$	−4.13392	−	7.40087i	−0.172697	−	0.309176i
$574$	−29.5623	+	9.76543i	−1.23391	+	0.407601i
$575$			5.40741i			0.225505i
$576$	−12.2596	−	22.6992i	−0.510817	−	0.945799i
$577$	9.28910	+	5.36306i	0.386710	+	0.223267i	0.680734	−	0.732531i	$-0.261661\pi$
$577$	9.28910	+	5.36306i	0.386710	+	0.223267i	−0.294024	+	0.955798i	$0.594994\pi$
$578$			7.88281i			0.327882i
$579$	−0.185426	+	13.0595i	−0.00770602	+	0.542733i
$580$	0.180649	+	0.104298i	0.00750105	+	0.00433074i
$581$	−3.01832	−	9.13718i	−0.125221	−	0.379074i
$582$	8.29660	+	4.94841i	0.343905	+	0.205118i
$583$	31.7234	−	54.9465i	1.31385	−	2.27565i
$584$	5.65389	−	9.79282i	0.233959	−	0.405230i
$585$	0.397232	−	13.9857i	0.0164235	−	0.578236i
$586$	−0.477354	+	0.275600i	−0.0197193	+	0.0113849i
$587$	13.6023	+	23.5598i	0.561426	+	0.972418i	0.997372	+	0.0724456i	$0.0230804\pi$
$587$	13.6023	+	23.5598i	0.561426	+	0.972418i	−0.435946	+	0.899973i	$0.643586\pi$
$588$	0.926843	−	2.05721i	0.0382224	−	0.0848379i
$589$	9.63176	−	16.6827i	0.396870	−	0.687398i
$590$			6.94043i			0.285733i
$591$	−6.04193	+	10.1300i	−0.248532	+	0.416693i
$592$	−3.64551			−0.149829
$593$	−15.0255	−	26.0249i	−0.617023	−	1.06872i	−0.990026	−	0.140885i	$-0.955005\pi$
$593$	−15.0255	−	26.0249i	−0.617023	−	1.06872i	0.373003	−	0.927830i	$-0.378328\pi$
$594$	27.7897	+	17.6634i	1.14023	+	0.724738i
$595$	8.41707	−	9.44052i	0.345066	−	0.387024i
$596$	0.194066	−	0.112044i	0.00794925	−	0.00458950i
$597$	8.31583	+	14.8876i	0.340344	+	0.609311i
$598$	−29.4146	+	16.9825i	−1.20285	+	0.694467i
$599$	11.7316	−	6.77322i	0.479339	−	0.276746i	−0.240802	−	0.970574i	$-0.577410\pi$
$599$	11.7316	−	6.77322i	0.479339	−	0.276746i	0.720141	+	0.693828i	$0.244077\pi$
$600$	−2.61225	+	4.37975i	−0.106645	+	0.178803i
$601$	32.6100	−	18.8274i	1.33019	−	0.767984i	0.344859	−	0.938654i	$-0.387927\pi$
$601$	32.6100	−	18.8274i	1.33019	−	0.767984i	0.985328	+	0.170670i	$0.0545933\pi$
$602$	−3.97900	+	19.1804i	−0.162172	+	0.781734i
$603$	17.9539	−	29.1530i	0.731141	−	1.18720i
$604$	−1.51062	−	2.61648i	−0.0614664	−	0.106463i
$605$	−11.1390			−0.452866
$606$	8.66459	+	15.5120i	0.351975	+	0.630133i
$607$			16.5099i			0.670114i	0.942198	+	0.335057i	$0.108756\pi$
$607$			16.5099i			0.670114i	−0.942198	+	0.335057i	$0.891244\pi$
$608$	1.31643	−	2.28012i	0.0533882	−	0.0924711i
$609$	−5.01408	−	1.11466i	−0.203181	−	0.0451681i
$610$	−1.71621	−	2.97256i	−0.0694871	−	0.120355i
$611$	49.5797	−	28.6249i	2.00578	−	1.15804i
$612$	−1.26832	−	2.34834i	−0.0512687	−	0.0949261i
$613$	−9.98331	+	17.2916i	−0.403222	+	0.698401i	−0.994113	−	0.108351i	$-0.965443\pi$
$613$	−9.98331	+	17.2916i	−0.403222	+	0.698401i	0.590891	+	0.806752i	$0.298776\pi$
$614$	−8.65156	+	14.9849i	−0.349148	+	0.604743i
$615$	13.2119	−	7.37981i	0.532755	−	0.297583i
$616$	−35.8885	−	7.44513i	−1.44599	−	0.299973i
$617$	−12.8164	−	7.39957i	−0.515970	−	0.297895i	0.219314	−	0.975654i	$-0.429618\pi$
$617$	−12.8164	−	7.39957i	−0.515970	−	0.297895i	−0.735284	+	0.677759i	$0.762951\pi$
$618$	21.7255	−	12.1353i	0.873929	−	0.488153i
$619$		−	6.76016i		−	0.271714i	−0.990728	−	0.135857i	$-0.956621\pi$
$619$		−	6.76016i		−	0.271714i	0.990728	−	0.135857i	$-0.0433787\pi$
$620$	−1.23724	−	0.714321i	−0.0496888	−	0.0286878i
$621$	−28.0722	−	1.19640i	−1.12650	−	0.0480098i
$622$			9.72615i			0.389983i
$623$	1.31936	+	3.99402i	0.0528590	+	0.160017i
$624$	−29.0222	−	0.412074i	−1.16182	−	0.0164961i
$625$	1.00000			0.0400000
$626$	−15.6878	−	27.1720i	−0.627009	−	1.08601i
$627$	−0.290337	+	20.4483i	−0.0115949	+	0.816627i
$628$	2.88636	+	1.66644i	0.115178	+	0.0664983i
$629$	−4.85012			−0.193387
$630$	2.46772	−	10.4012i	0.0983164	−	0.414396i
$631$	−7.93650			−0.315947			−0.157974	−	0.987443i	$-0.550496\pi$
$631$	−7.93650			−0.315947			−0.157974	+	0.987443i	$0.550496\pi$
$632$	−16.3592	−	9.44498i	−0.650734	−	0.375701i
$633$	38.1130	−	21.2889i	1.51486	−	0.846158i
$634$	−15.3043	−	26.5077i	−0.607809	−	1.05276i
$635$	−1.22813			−0.0487369
$636$	−2.22647	+	3.73295i	−0.0882855	+	0.148021i
$637$	−19.4464	−	26.2226i	−0.770494	−	1.03898i
$638$			7.10301i			0.281211i
$639$	11.3982	−	6.15608i	0.450907	−	0.243531i
$640$	8.21283	+	4.74168i	0.324641	+	0.187431i
$641$			23.4345i			0.925607i	0.886461	+	0.462804i	$0.153156\pi$
$641$			23.4345i			0.925607i	−0.886461	+	0.462804i	$0.846844\pi$
$642$	−4.72144	−	2.81605i	−0.186341	−	0.111141i
$643$	32.7126	+	18.8866i	1.29006	+	0.744816i	0.978665	−	0.205464i	$-0.0658704\pi$
$643$	32.7126	+	18.8866i	1.29006	+	0.744816i	0.311395	+	0.950281i	$0.399204\pi$
$644$	2.52812	−	0.835124i	0.0996220	−	0.0329085i
$645$	0.135180	−	9.52069i	0.00532271	−	0.374877i
$646$	−8.07810	+	13.9917i	−0.317829	+	0.550495i
$647$	−14.1550	+	24.5172i	−0.556491	+	0.963871i	0.441295	+	0.897362i	$0.354519\pi$
$647$	−14.1550	+	24.5172i	−0.556491	+	0.963871i	−0.997786	+	0.0665087i	$0.978814\pi$
$648$	−22.1593	−	14.5304i	−0.870498	−	0.570807i
$649$	20.9986	−	12.1235i	0.824266	−	0.475890i
$650$	3.14060	+	5.43969i	0.123185	+	0.213362i
$651$	34.3407	+	7.63411i	1.34592	+	0.299204i
$652$	−1.82764	+	3.16557i	−0.0715761	+	0.123973i
$653$			26.3772i			1.03222i	0.856523	+	0.516109i	$0.172620\pi$
$653$			26.3772i			1.03222i	−0.856523	+	0.516109i	$0.827380\pi$
$654$	23.6868	+	0.336319i	0.926228	+	0.0131511i
$655$	−1.84688			−0.0721636
$656$	−15.6971	−	27.1882i	−0.612868	−	1.06152i
$657$	0.327121	−	11.5172i	0.0127622	−	0.449328i
$658$	41.5339	−	13.7201i	1.61916	−	0.534864i
$659$	−33.9313	+	19.5902i	−1.32177	+	0.763127i	−0.984012	−	0.178105i	$-0.943003\pi$
$659$	−33.9313	+	19.5902i	−1.32177	+	0.763127i	−0.337763	+	0.941231i	$0.609670\pi$
$660$	1.51651	+	0.0215323i	0.0590301	+	0.000838142i
$661$	−3.72709	+	2.15184i	−0.144967	+	0.0836967i	−0.570729	−	0.821138i	$-0.693339\pi$
$661$	−3.72709	+	2.15184i	−0.144967	+	0.0836967i	0.425762	+	0.904835i	$0.360006\pi$
$662$	−9.92087	+	5.72782i	−0.385585	+	0.222618i
$663$	−38.6122	−	0.548238i	−1.49957	−	0.0212918i
$664$	9.27385	−	5.35426i	0.359895	−	0.207786i
$665$	6.30407	−	2.08245i	0.244461	−	0.0807539i
$666$	−3.60685	+	1.94803i	−0.139763	+	0.0754845i
$667$	−3.03051	−	5.24899i	−0.117342	−	0.203242i
$668$	−0.702348			−0.0271746
$669$	−31.1367	−	0.442097i	−1.20382	−	0.0170925i
$670$			15.3707i			0.593822i
$671$	−5.99573	+	10.3849i	−0.231463	+	0.400905i
$672$	4.69354	+	1.04340i	0.181057	+	0.0402499i
$673$	9.06463	+	15.7004i	0.349416	+	0.605206i	0.986146	−	0.165881i	$-0.0530468\pi$
$673$	9.06463	+	15.7004i	0.349416	+	0.605206i	−0.636730	+	0.771087i	$0.719713\pi$
$674$	−24.2509	+	14.0013i	−0.934111	+	0.539309i
$675$	−0.221252	+	5.19144i	−0.00851599	+	0.199819i
$676$	0.814259	−	1.41034i	0.0313176	−	0.0542438i
$677$	1.93370	−	3.34927i	0.0743183	−	0.128723i	−0.826471	−	0.562979i	$-0.809655\pi$
$677$	1.93370	−	3.34927i	0.0743183	−	0.128723i	0.900790	+	0.434256i	$0.142989\pi$
$678$	0.0798083	−	5.62088i	0.00306502	−	0.215868i
$679$	−10.4035	+	3.43664i	−0.399251	+	0.131886i
$680$	12.1893	+	7.03749i	0.467438	+	0.269876i
$681$	−8.30675	−	4.95446i	−0.318315	−	0.189855i
$682$		−	48.6474i		−	1.86281i
$683$	19.8471	+	11.4587i	0.759428	+	0.438456i	0.829090	−	0.559115i	$-0.188859\pi$
$683$	19.8471	+	11.4587i	0.759428	+	0.438456i	−0.0696622	+	0.997571i	$0.522192\pi$
$684$	0.0397758	−	1.40042i	0.00152087	−	0.0535462i
$685$		−	16.3199i		−	0.623551i
$686$	−10.4785	−	22.6356i	−0.400070	−	0.864230i
$687$	−3.42061	+	5.73506i	−0.130504	+	0.218806i
$688$	−19.7528			−0.753068
$689$	31.4439	+	54.4625i	1.19792	+	2.07486i
$690$	11.0126	−	6.15132i	0.419241	−	0.234177i
$691$	−18.9249	−	10.9263i	−0.719938	−	0.415656i	0.0947918	−	0.995497i	$-0.469781\pi$
$691$	−18.9249	−	10.9263i	−0.719938	−	0.415656i	−0.814730	+	0.579841i	$0.803115\pi$
$692$	−3.33909			−0.126933
$693$	−35.7800	+	10.7027i	−1.35917	+	0.406561i
$694$	−31.0471			−1.17853
$695$	12.8287	+	7.40667i	0.486621	+	0.280951i
$696$	0.0811511	−	5.71544i	0.00307602	−	0.216643i
$697$	−20.8840	−	36.1721i	−0.791037	−	1.37012i
$698$	−8.17543			−0.309445
$699$	−41.0728	−	0.583175i	−1.55352	−	0.0220577i
$700$	−0.154441	−	0.467530i	−0.00583731	−	0.0176710i
$701$			20.2998i			0.766712i	0.923601	+	0.383356i	$0.125232\pi$
$701$			20.2998i			0.766712i	−0.923601	+	0.383356i	$0.874768\pi$
$702$	−28.9347	+	15.1007i	−1.09207	+	0.569940i
$703$	−2.20482	−	1.27295i	−0.0831564	−	0.0480104i
$704$		−	40.4621i		−	1.52497i
$705$	−18.5622	+	10.3683i	−0.699094	+	0.390495i
$706$	37.9894	+	21.9332i	1.42975	+	0.825467i
$707$	−19.7319	−	4.09341i	−0.742093	−	0.153948i
$708$	−1.45018	+	0.810032i	−0.0545011	+	0.0304429i
$709$	5.82104	−	10.0823i	0.218614	−	0.378650i	−0.735771	−	0.677231i	$-0.763180\pi$
$709$	5.82104	−	10.0823i	0.218614	−	0.378650i	0.954384	+	0.298581i	$0.0965132\pi$
$710$	−2.90786	+	5.03656i	−0.109130	+	0.189019i
$711$	−19.2398	−	0.546465i	−0.721549	−	0.0204940i
$712$	−4.05376	+	2.34044i	−0.151921	+	0.0877116i
$713$	20.7555	+	35.9496i	0.777299	+	1.34632i
$714$	−28.8013	−	6.40268i	−1.07786	−	0.239614i
$715$	10.9720	−	19.0041i	0.410330	−	0.710712i
$716$		0	0.000900529i		0	3.36544e-5i
$717$	−11.0901	−	19.8544i	−0.414169	−	0.741478i
$718$	17.9243			0.668928
$719$	−4.90218	−	8.49082i	−0.182820	−	0.316654i	0.760020	−	0.649900i	$-0.225189\pi$
$719$	−4.90218	−	8.49082i	−0.182820	−	0.316654i	−0.942840	+	0.333246i	$0.891856\pi$
$720$	10.7751	+	0.306045i	0.401566	+	0.0114056i
$721$	−5.73307	+	27.6357i	−0.213511	+	1.02921i
$722$	14.8166	−	8.55437i	0.551417	−	0.318361i
$723$	−13.0349	+	21.8546i	−0.484774	+	0.812782i
$724$	−2.61063	+	1.50725i	−0.0970232	+	0.0560164i
$725$	−0.970704	+	0.560436i	−0.0360511	+	0.0208141i
$726$	12.6715	+	22.6854i	0.470282	+	0.841935i
$727$	−27.0997	+	15.6460i	−1.00507	+	0.580280i	−0.909745	−	0.415166i	$-0.863723\pi$
$727$	−27.0997	+	15.6460i	−1.00507	+	0.580280i	−0.0953281	+	0.995446i	$0.530390\pi$
$728$	24.1771	−	27.1168i	0.896061	−	1.00502i
$729$	−26.9021	−	2.29723i	−0.996374	−	0.0850826i
$730$	2.58629	+	4.47958i	0.0957228	+	0.165797i
$731$	−26.2798			−0.971995
$732$	0.420804	−	0.705529i	0.0155534	−	0.0260771i
$733$		−	30.4217i		−	1.12365i	−0.827255	−	0.561826i	$-0.810099\pi$
$733$		−	30.4217i		−	1.12365i	0.827255	−	0.561826i	$-0.189901\pi$
$734$	−5.94084	+	10.2898i	−0.219280	+	0.379805i
$735$	7.08310	+	9.84021i	0.261264	+	0.362961i
$736$	2.83677	+	4.91344i	0.104565	+	0.181112i
$737$	46.5047	−	26.8495i	1.71302	−	0.989014i
$738$	−30.0590	−	18.5119i	−1.10649	−	0.681433i
$739$	−11.2627	+	19.5076i	−0.414306	+	0.717598i	−0.995355	−	0.0962698i	$-0.969309\pi$
$739$	−11.2627	+	19.5076i	−0.414306	+	0.717598i	0.581050	+	0.813868i	$0.302642\pi$
$740$	−0.0944062	+	0.163516i	−0.00347044	+	0.00601098i
$741$	−17.4089	−	10.3833i	−0.639531	−	0.381441i
$742$	15.0713	+	45.6243i	0.553283	+	1.67492i
$743$	16.3414	+	9.43471i	0.599508	+	0.346126i	0.768848	−	0.639432i	$-0.220830\pi$
$743$	16.3414	+	9.43471i	0.599508	+	0.346126i	−0.169340	+	0.985558i	$0.554164\pi$
$744$	−0.555791	+	39.1442i	−0.0203763	+	1.43510i
$745$			1.20412i			0.0441155i
$746$	3.19709	+	1.84584i	0.117054	+	0.0675811i
$747$	5.72170	−	9.29071i	0.209346	−	0.339929i
$748$		−	4.18601i		−	0.153056i
$749$	5.92046	−	1.95573i	0.216329	−	0.0714607i
$750$	−1.13757	−	2.03657i	−0.0415383	−	0.0743651i
$751$	−41.1785			−1.50262			−0.751312	−	0.659947i	$-0.770579\pi$
$751$	−41.1785			−1.50262			−0.751312	+	0.659947i	$0.770579\pi$
$752$	22.0538	+	38.1983i	0.804220	+	1.39295i
$753$	6.11984	+	3.65010i	0.223019	+	0.133017i
$754$	−6.09720	−	3.52022i	−0.222047	−	0.128199i
$755$	16.2344			0.590831
$756$	2.46132	−	0.698328i	0.0895174	−	0.0253980i
$757$	13.3508			0.485243			0.242621	−	0.970121i	$-0.421993\pi$
$757$	13.3508			0.485243			0.242621	+	0.970121i	$0.421993\pi$
$758$	−19.8077	−	11.4360i	−0.719447	−	0.415373i
$759$	−37.8478	−	22.5739i	−1.37379	−	0.819381i
$760$	3.69410	+	6.39837i	0.133999	+	0.232093i
$761$	36.7218			1.33116			0.665582	−	0.746325i	$-0.268183\pi$
$761$	36.7218			1.33116			0.665582	+	0.746325i	$0.268183\pi$
$762$	1.39709	+	2.50118i	0.0506112	+	0.0906081i
$763$	−17.8803	+	20.0544i	−0.647309	+	0.726016i
$764$			0.910833i			0.0329528i
$765$	14.3356	+	0.407173i	0.518306	+	0.0147214i
$766$	−20.6622	−	11.9293i	−0.746555	−	0.431024i
$767$			24.0335i			0.867798i
$768$	−0.108850	+	7.66625i	−0.00392778	+	0.276632i
$769$	−4.77150	−	2.75483i	−0.172065	−	0.0993416i	0.411494	−	0.911412i	$-0.365007\pi$
$769$	−4.77150	−	2.75483i	−0.172065	−	0.0993416i	−0.583559	+	0.812071i	$0.698340\pi$
$770$	11.1577	−	12.5144i	0.402097	−	0.450988i
$771$	12.8925	+	7.68961i	0.464314	+	0.276934i
$772$	0.701662	−	1.21531i	0.0252534	−	0.0437401i
$773$	9.85688	−	17.0726i	0.354527	−	0.614060i	−0.632510	−	0.774553i	$-0.717975\pi$
$773$	9.85688	−	17.0726i	0.354527	−	0.614060i	0.987037	+	0.160493i	$0.0513084\pi$
$774$	−19.5433	+	10.5552i	−0.702471	+	0.379398i
$775$	6.64821	−	3.83834i	0.238811	−	0.137877i
$776$	−6.09632	−	10.5591i	−0.218845	−	0.379051i
$777$	1.00894	−	4.53854i	0.0361955	−	0.162819i
$778$	−3.62261	+	6.27454i	−0.129877	+	0.224953i
$779$		−	21.9247i		−	0.785534i
$780$	−0.770059	+	1.29110i	−0.0275725	+	0.0462287i
$781$	20.3178			0.727027
$782$	−17.4075	−	30.1507i	−0.622492	−	1.07819i
$783$	−2.69470	−	5.16335i	−0.0963008	−	0.184523i
$784$	20.2030	−	14.9823i	0.721535	−	0.535083i
$785$	−15.5096	+	8.95450i	−0.553563	+	0.319600i
$786$	2.10096	+	3.76130i	0.0749388	+	0.134161i
$787$	3.40459	−	1.96564i	0.121361	−	0.0700676i	−0.438091	−	0.898931i	$-0.644345\pi$
$787$	3.40459	−	1.96564i	0.121361	−	0.0700676i	0.559451	+	0.828863i	$0.311012\pi$
$788$	1.09753	−	0.633661i	0.0390980	−	0.0225732i
$789$	−2.81634	+	4.72193i	−0.100264	+	0.168105i
$790$	7.48327	−	4.32047i	0.266243	−	0.153715i
$791$	4.75889	+	4.24298i	0.169207	+	0.150863i
$792$	−19.7498	−	36.5676i	−0.701780	−	1.29937i
$793$	−5.94291	−	10.2934i	−0.211039	−	0.365530i
$794$	46.6139			1.65426
$795$	−11.3895	−	20.3903i	−0.403943	−	0.723169i
$796$		−	1.83224i		−	0.0649420i
$797$	−1.85475	+	3.21252i	−0.0656985	+	0.113793i	−0.897004	−	0.442023i	$-0.854261\pi$
$797$	−1.85475	+	3.21252i	−0.0656985	+	0.113793i	0.831305	+	0.555816i	$0.187594\pi$
$798$	−11.4124	−	10.4698i	−0.403995	−	0.370625i
$799$	29.3412	+	50.8204i	1.03802	+	1.79790i
$800$	0.908649	−	0.524609i	0.0321256	−	0.0185477i
$801$	−2.50105	+	4.06113i	−0.0883703	+	0.143493i
$802$	11.0781	−	19.1878i	0.391180	−	0.677543i
$803$	9.03544	−	15.6498i	0.318854	−	0.552271i
$804$	−3.21166	+	1.79395i	−0.113267	+	0.0632676i
$805$	−2.90607	+	14.0084i	−0.102425	+	0.493731i
$806$	41.7588	+	24.1094i	1.47089	+	0.849219i
$807$	−14.5838	+	8.14613i	−0.513375	+	0.286757i
$808$		−	22.4257i		−	0.788932i
$809$	−29.9373	−	17.2843i	−1.05254	−	0.607684i	−0.129180	−	0.991621i	$-0.541234\pi$
$809$	−29.9373	−	17.2843i	−1.05254	−	0.607684i	−0.923359	+	0.383938i	$0.874568\pi$
$810$	10.8244	−	5.45505i	0.380332	−	0.191671i
$811$		−	7.43429i		−	0.261053i	−0.991445	−	0.130527i	$-0.958333\pi$
$811$		−	7.43429i		−	0.261053i	0.991445	−	0.130527i	$-0.0416668\pi$
$812$	0.411937	+	0.367279i	0.0144562	+	0.0128890i
$813$	12.5275	+	0.177872i	0.439358	+	0.00623825i
$814$	−6.42935			−0.225348
$815$	−9.82069	−	17.0099i	−0.344004	−	0.595832i
$816$	0.422386	−	29.7485i	0.0147865	−	1.04141i
$817$	−11.9466	−	6.89736i	−0.417958	−	0.241308i
$818$	22.5890			0.789805
$819$	8.54528	−	36.0177i	0.298596	−	1.25856i
$820$	−1.62600			−0.0567825
$821$	−13.3265	−	7.69403i	−0.465096	−	0.268523i	0.249088	−	0.968481i	$-0.419869\pi$
$821$	−13.3265	−	7.69403i	−0.465096	−	0.268523i	−0.714185	+	0.699957i	$0.753202\pi$
$822$	−33.2366	+	18.5651i	−1.15926	+	0.647532i
$823$	3.80272	+	6.58650i	0.132554	+	0.229591i	0.924661	−	0.380792i	$-0.124349\pi$
$823$	3.80272	+	6.58650i	0.132554	+	0.229591i	−0.792106	+	0.610383i	$0.791015\pi$
$824$	−31.4085			−1.09417
$825$	−4.17462	+	6.99926i	−0.145342	+	0.243683i
$826$	−3.72994	+	17.9798i	−0.129781	+	0.625598i
$827$		−	41.0586i		−	1.42775i	−0.700274	−	0.713874i	$-0.746939\pi$
$827$		−	41.0586i		−	1.42775i	0.700274	−	0.713874i	$-0.253061\pi$
$828$	2.57060	+	1.58311i	0.0893345	+	0.0550169i
$829$	16.0974	+	9.29382i	0.559085	+	0.322788i	0.752778	−	0.658274i	$-0.228713\pi$
$829$	16.0974	+	9.29382i	0.559085	+	0.322788i	−0.193693	+	0.981062i	$0.562047\pi$
$830$			4.89846i			0.170028i
$831$	39.4759	+	23.5450i	1.36940	+	0.816765i
$832$	34.7326	+	20.0528i	1.20413	+	0.695207i
$833$	26.8788	−	19.9330i	0.931294	−	0.690639i
$834$	0.490592	−	34.5523i	0.0169878	−	1.19645i
$835$	1.88700	−	3.26839i	0.0653024	−	0.113107i
$836$	1.09865	−	1.90292i	0.0379977	−	0.0658139i
$837$	18.4556	+	35.3630i	0.637919	+	1.22232i
$838$	35.2177	−	20.3329i	1.21657	−	0.702390i
$839$	2.86659	+	4.96508i	0.0989657	+	0.171414i	0.911257	−	0.411839i	$-0.135113\pi$
$839$	2.86659	+	4.96508i	0.0989657	+	0.171414i	−0.812291	+	0.583252i	$0.801780\pi$
$840$	−9.12106	+	9.94227i	−0.314706	+	0.343041i
$841$	−13.8718	+	24.0267i	−0.478339	+	0.828507i
$842$			43.1676i			1.48765i
$843$	−1.67164	−	0.0237349i	−0.0575744	−	0.000817473i
$844$	−4.69061			−0.161458
$845$	4.37535	+	7.57833i	0.150517	+	0.260703i
$846$	42.2318	+	26.0085i	1.45196	+	0.894191i
$847$	−28.8567	−	5.98637i	−0.991528	−	0.205694i
$848$	−41.9602	+	24.2258i	−1.44092	+	0.831916i
$849$	51.5411	+	0.731809i	1.76889	+	0.0251156i
$850$	−5.57581	+	3.21920i	−0.191249	+	0.110418i
$851$	4.75117	−	2.74309i	0.162868	−	0.0940319i
$852$	−1.39176	−	0.0197609i	−0.0476808	−	0.000676998i
$853$	−24.5713	+	14.1862i	−0.841305	+	0.485728i	−0.857708	−	0.514138i	$-0.828112\pi$
$853$	−24.5713	+	14.1862i	−0.841305	+	0.485728i	0.0164023	+	0.999865i	$0.494779\pi$
$854$	−2.84847	−	8.62301i	−0.0974727	−	0.295073i
$855$	6.40999	+	3.94761i	0.219217	+	0.135005i
$856$	3.46931	+	6.00901i	0.118578	+	0.205384i
$857$	32.2763			1.10254			0.551269	−	0.834328i	$-0.314144\pi$
$857$	32.2763			1.10254			0.551269	+	0.834328i	$0.314144\pi$
$858$	−51.1846	−	0.726748i	−1.74741	−	0.0248108i
$859$			34.3066i			1.17052i	0.810844	+	0.585262i	$0.199009\pi$
$859$			34.3066i			1.17052i	−0.810844	+	0.585262i	$0.800991\pi$
$860$	−0.511530	+	0.885995i	−0.0174430	+	0.0302122i
$861$	38.1927	−	12.0177i	1.30161	−	0.409562i
$862$	24.4562	+	42.3593i	0.832980	+	1.44276i
$863$	−27.8147	+	16.0588i	−0.946823	+	0.546648i	−0.892092	−	0.451853i	$-0.850763\pi$
$863$	−27.8147	+	16.0588i	−0.946823	+	0.546648i	−0.0547301	+	0.998501i	$0.517430\pi$
$864$	2.52244	+	4.83327i	0.0858150	+	0.164431i
$865$	8.97117	−	15.5385i	0.305029	−	0.528326i
$866$	5.61040	−	9.71750i	0.190649	−	0.330214i
$867$	0.143925	−	10.1366i	0.00488795	−	0.344256i
$868$	−2.82129	−	2.51544i	−0.0957610	−	0.0853795i
$869$	−26.1435	−	15.0940i	−0.886859	−	0.512028i
$870$	2.24562	+	1.33937i	0.0761335	+	0.0454089i
$871$			53.2260i			1.80349i
$872$	−25.8935	−	14.9496i	−0.876865	−	0.506258i
$873$	−10.5783	−	6.51469i	−0.358022	−	0.220489i
$874$		−	18.2750i		−	0.618161i
$875$	2.59059	+	0.537423i	0.0875781	+	0.0181682i
$876$	−0.634144	+	1.06322i	−0.0214257	+	0.0359228i
$877$	−36.7577			−1.24122			−0.620610	−	0.784119i	$-0.713115\pi$
$877$	−36.7577			−1.24122			−0.620610	+	0.784119i	$0.713115\pi$
$878$	11.3196	+	19.6061i	0.382018	+	0.661674i
$879$	0.618866	−	0.345681i	0.0208738	−	0.0116595i
$880$	14.6415	+	8.45330i	0.493566	+	0.284961i
$881$	9.98124			0.336276			0.168138	−	0.985763i	$-0.446225\pi$
$881$	9.98124			0.336276			0.168138	+	0.985763i	$0.446225\pi$
$882$	11.9827	−	25.6192i	0.403480	−	0.862643i
$883$	21.9494			0.738657			0.369329	−	0.929299i	$-0.379588\pi$
$883$	21.9494			0.738657			0.369329	+	0.929299i	$0.379588\pi$
$884$	3.59325	+	2.07457i	0.120854	+	0.0697752i
$885$	0.126719	−	8.92476i	0.00425960	−	0.300003i
$886$	7.38586	+	12.7927i	0.248133	+	0.429778i
$887$	33.2900			1.11777			0.558884	−	0.829246i	$-0.311230\pi$
$887$	33.2900			1.11777			0.558884	+	0.829246i	$0.311230\pi$
$888$	5.17338	+	0.0734546i	0.173607	+	0.00246497i
$889$	−3.18159	−	0.660026i	−0.106707	−	0.0221366i
$890$		−	2.14120i		−	0.0717731i
$891$	−35.4126	−	23.2209i	−1.18637	−	0.777930i
$892$	2.89759	+	1.67292i	0.0970184	+	0.0560136i
$893$			30.8034i			1.03080i
$894$	2.45227	−	1.36977i	0.0820163	−	0.0458121i
$895$	0.00419063	+	0.00241946i	0.000140077	+	8.08737e-5i
$896$	18.7278	+	16.6975i	0.625653	+	0.557825i
$897$	38.1346	−	21.3009i	1.27328	−	0.711218i
$898$	8.17329	−	14.1566i	0.272746	−	0.472410i
$899$	−4.30230	+	7.45180i	−0.143490	+	0.248531i
$900$	0.292767	−	0.475385i	0.00975889	−	0.0158462i
$901$	−55.8254	+	32.2308i	−1.85981	+	1.07376i
$902$	−27.6839	−	47.9500i	−0.921774	−	1.59656i
$903$	5.46683	−	24.5916i	0.181925	−	0.818357i
$904$	−3.54754	+	6.14452i	−0.117989	+	0.204364i
$905$		−	16.1981i		−	0.538444i
$906$	−18.4678	−	33.0626i	−0.613553	−	1.09843i
$907$	−40.8135			−1.35519			−0.677596	−	0.735435i	$-0.736978\pi$
$907$	−40.8135			−1.35519			−0.677596	+	0.735435i	$0.736978\pi$
$908$	0.519611	+	0.899992i	0.0172439	+	0.0298673i
$909$	−10.8587	−	20.1052i	−0.360159	−	0.666849i
$910$	5.21262	+	15.7798i	0.172797	+	0.523097i
$911$	36.6763	−	21.1751i	1.21514	−	0.701562i	0.251266	−	0.967918i	$-0.419153\pi$
$911$	36.6763	−	21.1751i	1.21514	−	0.701562i	0.963875	+	0.266356i	$0.0858197\pi$
$912$	7.99975	−	13.4125i	0.264898	−	0.444134i
$913$	14.8205	−	8.55662i	0.490487	−	0.283183i
$914$	2.98462	−	1.72317i	0.0987225	−	0.0569974i
$915$	2.15261	+	3.85377i	0.0711632	+	0.127402i
$916$	0.621363	−	0.358744i	0.0205304	−	0.0118532i
$917$	−4.78452	−	0.992556i	−0.157999	−	0.0327771i
$918$	−15.4786	−	29.6588i	−0.510870	−	0.978885i
$919$	19.2773	+	33.3892i	0.635898	+	1.10141i	0.986324	+	0.164818i	$0.0527036\pi$
$919$	19.2773	+	33.3892i	0.635898	+	1.10141i	−0.350426	+	0.936591i	$0.613963\pi$
$920$	−15.9208			−0.524895
$921$	11.3987	−	19.1113i	0.375600	−	0.629739i
$922$		−	3.83043i		−	0.126148i
$923$	−10.0694	+	17.4407i	−0.331438	+	0.574068i
$924$	3.91709	+	0.870789i	0.128863	+	0.0286469i
$925$	−0.507284	−	0.878641i	−0.0166794	−	0.0288895i
$926$	2.36552	−	1.36573i	0.0777357	−	0.0448807i
$927$	−28.1586	+	15.2082i	−0.924851	+	0.499504i
$928$	−0.588020	+	1.01848i	−0.0193027	+	0.0334332i
$929$	19.1492	−	33.1674i	0.628265	−	1.08819i	−0.359635	−	0.933093i	$-0.617099\pi$
$929$	19.1492	−	33.1674i	0.628265	−	1.08819i	0.987900	−	0.155094i	$-0.0495680\pi$
$930$	−15.3799	−	9.17315i	−0.504326	−	0.300799i
$931$	17.4504	−	2.00682i	0.571915	−	0.0657710i
$932$	3.82224	+	2.20677i	0.125202	+	0.0722852i
$933$	0.177581	−	12.5069i	0.00581373	−	0.409459i
$934$		−	42.1092i		−	1.37785i
$935$	19.4796	+	11.2466i	0.637053	+	0.367802i
$936$	41.1775	+	1.16956i	1.34593	+	0.0382282i
$937$		−	22.6052i		−	0.738480i	−0.929334	−	0.369240i	$-0.879618\pi$
$937$		−	22.6052i		−	0.738480i	0.929334	−	0.369240i	$-0.120382\pi$
$938$	−8.26057	+	39.8192i	−0.269717	+	1.30014i
$939$	19.6769	+	35.2272i	0.642133	+	1.14960i
$940$	2.28447			0.0745113
$941$	2.64351	+	4.57869i	0.0861760	+	0.149261i	0.905892	−	0.423509i	$-0.139202\pi$
$941$	2.64351	+	4.57869i	0.0861760	+	0.149261i	−0.819716	+	0.572771i	$0.805869\pi$
$942$	35.8798	+	21.4001i	1.16903	+	0.697253i
$943$	40.9159	+	23.6228i	1.33240	+	0.769264i
$944$	−18.5164			−0.602658
$945$	−3.36317	+	13.3300i	−0.109404	+	0.433625i
$946$	−34.8367			−1.13264
$947$	−37.7773	−	21.8107i	−1.22760	−	0.708754i	−0.261071	−	0.965320i	$-0.584076\pi$
$947$	−37.7773	−	21.8107i	−1.22760	−	0.708754i	−0.966527	+	0.256566i	$0.917409\pi$
$948$	1.77614	+	1.05936i	0.0576862	+	0.0344063i
$949$	8.95585	+	15.5120i	0.290719	+	0.503541i
$950$	−3.37962			−0.109649
$951$	19.1959	+	34.3660i	0.622470	+	1.11439i
$952$	27.7954	+	24.7821i	0.900854	+	0.803192i
$953$			31.9493i			1.03494i	0.855701	+	0.517470i	$0.173126\pi$
$953$			31.9493i			1.03494i	−0.855701	+	0.517470i	$0.826874\pi$
$954$	−28.5699	+	46.3909i	−0.924986	+	1.50196i
$955$	−4.23858	−	2.44714i	−0.137157	−	0.0791877i
$956$			2.44351i			0.0790287i
$957$	0.129687	−	9.13382i	0.00419219	−	0.295254i
$958$	−16.0404	−	9.26093i	−0.518242	−	0.299207i
$959$	8.77069	−	42.2782i	0.283220	−	1.36524i
$960$	−12.7921	−	7.62970i	−0.412863	−	0.246248i
$961$	13.9658	−	24.1894i	0.450509	−	0.780305i
$962$	3.18636	−	5.51893i	0.102732	−	0.177937i
$963$	6.01993	+	3.70739i	0.193990	+	0.119469i
$964$	2.36783	−	1.36707i	0.0762627	−	0.0440303i
$965$	3.77032	+	6.53039i	0.121371	+	0.210221i
$966$	31.8350	−	10.0172i	1.02427	−	0.322297i
$967$	−21.3910	+	37.0503i	−0.687888	+	1.19146i	0.284632	+	0.958637i	$0.408129\pi$
$967$	−21.3910	+	37.0503i	−0.687888	+	1.19146i	−0.972520	+	0.232820i	$0.925205\pi$
$968$		−	32.7962i		−	1.05411i
$969$	10.6432	−	17.8445i	0.341908	−	0.573249i
$970$	5.57735			0.179078
$971$	5.32225	+	9.21841i	0.170799	+	0.295833i	0.938700	−	0.344736i	$-0.112032\pi$
$971$	5.32225	+	9.21841i	0.170799	+	0.295833i	−0.767900	+	0.640569i	$0.778698\pi$
$972$	2.40316	+	1.62506i	0.0770813	+	0.0521239i
$973$	29.2535	+	26.0821i	0.937825	+	0.836155i
$974$	43.4743	−	25.0999i	1.39301	−	0.804253i
$975$	−3.93921	−	7.05228i	−0.126156	−	0.225854i
$976$	7.93050	−	4.57868i	0.253849	−	0.146560i
$977$	33.9002	−	19.5723i	1.08456	−	0.626173i	0.152439	−	0.988313i	$-0.451287\pi$
$977$	33.9002	−	19.5723i	1.08456	−	0.626173i	0.932124	+	0.362140i	$0.117954\pi$
$978$	−23.4702	+	39.3506i	−0.750494	+	1.25829i
$979$	−6.47829	+	3.74024i	−0.207047	+	0.119539i
$980$	−0.148832	−	1.29418i	−0.00475427	−	0.0413410i
$981$	−30.4530	−	0.864951i	−0.972289	−	0.0276158i
$982$	13.0844	+	22.6629i	0.417541	+	0.723202i
$983$	38.7711			1.23661			0.618303	−	0.785940i	$-0.287820\pi$
$983$	38.7711			1.23661			0.618303	+	0.785940i	$0.287820\pi$
$984$	21.7281	+	38.8993i	0.692667	+	1.24007i
$985$			6.80985i			0.216980i
$986$	3.60831	−	6.24978i	0.114912	−	0.199033i
$987$	−53.6594	+	16.8844i	−1.70800	+	0.537437i
$988$	1.08897	+	1.88616i	0.0346449	+	0.0600067i
$989$	25.7437	−	14.8631i	0.818603	−	0.472620i
$990$	19.0034	+	0.539751i	0.603969	+	0.0171544i
$991$	14.1898	−	24.5775i	0.450755	−	0.780730i	−0.547678	−	0.836689i	$-0.684488\pi$
$991$	14.1898	−	24.5775i	0.450755	−	0.780730i	0.998433	+	0.0559589i	$0.0178216\pi$
$992$	4.02726	−	6.97542i	0.127866	−	0.221470i
$993$	12.8619	−	7.18431i	0.408160	−	0.227987i
$994$	−10.2398	+	11.4849i	−0.324788	+	0.364280i
$995$	8.52636	+	4.92269i	0.270304	+	0.156060i
$996$	−1.02352	+	0.571709i	−0.0324314	+	0.0181153i
$997$		−	44.9380i		−	1.42320i	−0.702584	−	0.711601i	$-0.747970\pi$
$997$		−	44.9380i		−	1.42320i	0.702584	−	0.711601i	$-0.252030\pi$
$998$	−19.9103	−	11.4952i	−0.630250	−	0.363875i
$999$	4.67365	−	2.43913i	0.147868	−	0.0771707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.311.5	yes	30
3.2	odd	2		945.2.be.b.206.11		30
7.5	odd	6		315.2.t.b.131.11	yes	30
9.2	odd	6		315.2.t.b.101.5	✓	30
9.7	even	3		945.2.t.b.521.11		30
21.5	even	6		945.2.t.b.341.5		30
63.47	even	6	inner	315.2.be.b.236.5	yes	30
63.61	odd	6		945.2.be.b.656.11		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.5	✓	30	9.2	odd	6
315.2.t.b.131.11	yes	30	7.5	odd	6
315.2.be.b.236.5	yes	30	63.47	even	6	inner
315.2.be.b.311.5	yes	30	1.1	even	1	trivial
945.2.t.b.341.5		30	21.5	even	6
945.2.t.b.521.11		30	9.7	even	3
945.2.be.b.206.11		30	3.2	odd	2
945.2.be.b.656.11		30	63.61	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16637 - 0.673405i) q^{2} +(1.48755 + 0.887234i) q^{3} +(-0.0930506 - 0.161168i) q^{4} +1.00000 q^{5} +(-1.13757 - 2.03657i) q^{6} +(2.59059 + 0.537423i) q^{7} +2.94426i q^{8} +(1.42563 + 2.63962i) q^{9} +O(q^{10})\)	\(q+(-1.16637 - 0.673405i) q^{2} +(1.48755 + 0.887234i) q^{3} +(-0.0930506 - 0.161168i) q^{4} +1.00000 q^{5} +(-1.13757 - 2.03657i) q^{6} +(2.59059 + 0.537423i) q^{7} +2.94426i q^{8} +(1.42563 + 2.63962i) q^{9} +(-1.16637 - 0.673405i) q^{10} +4.70521i q^{11} +(0.00457626 - 0.322304i) q^{12} +(-4.03894 - 2.33188i) q^{13} +(-2.65969 - 2.37135i) q^{14} +(1.48755 + 0.887234i) q^{15} +(1.79658 - 3.11177i) q^{16} +(2.39024 - 4.14001i) q^{17} +(0.114713 - 4.03880i) q^{18} +(2.17316 - 1.25468i) q^{19} +(-0.0930506 - 0.161168i) q^{20} +(3.37683 + 3.09791i) q^{21} +(3.16852 - 5.48803i) q^{22} +5.40741i q^{23} +(-2.61225 + 4.37975i) q^{24} +1.00000 q^{25} +(3.14060 + 5.43969i) q^{26} +(-0.221252 + 5.19144i) q^{27} +(-0.154441 - 0.467530i) q^{28} +(-0.970704 + 0.560436i) q^{29} +(-1.13757 - 2.03657i) q^{30} +(6.64821 - 3.83834i) q^{31} +(0.908649 - 0.524609i) q^{32} +(-4.17462 + 6.99926i) q^{33} +(-5.57581 + 3.21920i) q^{34} +(2.59059 + 0.537423i) q^{35} +(0.292767 - 0.475385i) q^{36} +(-0.507284 - 0.878641i) q^{37} -3.37962 q^{38} +(-3.93921 - 7.05228i) q^{39} +2.94426i q^{40} +(4.36860 - 7.56663i) q^{41} +(-1.85249 - 5.88729i) q^{42} +(-2.74866 - 4.76082i) q^{43} +(0.758332 - 0.437823i) q^{44} +(1.42563 + 2.63962i) q^{45} +(3.64138 - 6.30705i) q^{46} +(-6.13772 + 10.6308i) q^{47} +(5.43338 - 3.03494i) q^{48} +(6.42235 + 2.78449i) q^{49} +(-1.16637 - 0.673405i) q^{50} +(7.22877 - 4.03779i) q^{51} +0.867933i q^{52} +(-11.6778 - 6.74218i) q^{53} +(3.75401 - 5.90616i) q^{54} +4.70521i q^{55} +(-1.58232 + 7.62739i) q^{56} +(4.34589 + 0.0617053i) q^{57} +1.50960 q^{58} +(-2.57662 - 4.46283i) q^{59} +(0.00457626 - 0.322304i) q^{60} +(2.20711 + 1.27427i) q^{61} -10.3390 q^{62} +(2.27464 + 7.60434i) q^{63} -8.59943 q^{64} +(-4.03894 - 2.33188i) q^{65} +(9.58250 - 5.35252i) q^{66} +(-5.70633 - 9.88366i) q^{67} -0.889653 q^{68} +(-4.79764 + 8.04381i) q^{69} +(-2.65969 - 2.37135i) q^{70} -4.31814i q^{71} +(-7.77173 + 4.19744i) q^{72} +(-3.32607 - 1.92031i) q^{73} +1.36643i q^{74} +(1.48755 + 0.887234i) q^{75} +(-0.404428 - 0.233497i) q^{76} +(-2.52869 + 12.1893i) q^{77} +(-0.154456 + 10.8783i) q^{78} +(-3.20793 + 5.55629i) q^{79} +(1.79658 - 3.11177i) q^{80} +(-4.93514 + 7.52624i) q^{81} +(-10.1908 + 5.88367i) q^{82} +(-1.81854 - 3.14980i) q^{83} +(0.185069 - 0.832500i) q^{84} +(2.39024 - 4.14001i) q^{85} +7.40386i q^{86} +(-1.94121 - 0.0275624i) q^{87} -13.8534 q^{88} +(0.794914 + 1.37683i) q^{89} +(0.114713 - 4.03880i) q^{90} +(-9.21004 - 8.21158i) q^{91} +(0.871504 - 0.503163i) q^{92} +(13.2951 + 0.188771i) q^{93} +(14.3177 - 8.26634i) q^{94} +(2.17316 - 1.25468i) q^{95} +(1.81712 + 0.0258004i) q^{96} +(-3.58634 + 2.07058i) q^{97} +(-5.61576 - 7.57260i) q^{98} +(-12.4200 + 6.70790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more