LMFDB - Embedded newform 527.2.h.c.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +O(q^{10})$	\(q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +(0.669036 + 2.05908i) q^{10} +(4.41639 - 3.20870i) q^{11} +(0.0382502 + 0.117722i) q^{12} +(0.455967 - 1.40332i) q^{13} +(0.196788 + 0.142975i) q^{14} +(0.131483 - 0.404664i) q^{15} +(-0.833720 + 2.56593i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.10731 - 3.40794i) q^{18} +(-1.73093 - 5.32725i) q^{19} +(-0.744018 + 0.540561i) q^{20} +(-0.0147722 - 0.0454642i) q^{21} +(-5.37778 - 3.90718i) q^{22} +(-7.23855 - 5.25912i) q^{23} +(0.593437 - 0.431157i) q^{24} -1.83872 q^{25} -1.79674 q^{26} +(-1.15054 + 0.835914i) q^{27} +(-0.0319288 + 0.0982668i) q^{28} +(1.55371 + 4.78184i) q^{29} -0.518112 q^{30} +(4.57132 - 3.17853i) q^{31} -2.84513 q^{32} +(0.403691 + 1.24243i) q^{33} +(-0.376285 + 1.15809i) q^{34} +(0.287340 - 0.208765i) q^{35} +1.52211 q^{36} +10.4793 q^{37} +(-5.51810 + 4.00913i) q^{38} +(0.285670 + 0.207552i) q^{39} +(4.40910 + 3.20340i) q^{40} +(-3.45554 - 10.6350i) q^{41} +(-0.0470929 + 0.0342150i) q^{42} +(0.499597 + 1.53760i) q^{43} +(0.872542 - 2.68541i) q^{44} +(-4.23292 - 3.07540i) q^{45} +(-3.36676 + 10.3618i) q^{46} +(0.491048 - 1.51129i) q^{47} +(-0.522339 - 0.379501i) q^{48} +(-2.15079 + 6.61944i) q^{49} +(0.691882 + 2.12939i) q^{50} +(0.193604 - 0.140662i) q^{51} +(-0.235845 - 0.725857i) q^{52} +(-4.61935 - 3.35616i) q^{53} +(1.40099 + 1.01788i) q^{54} +(-7.85235 + 5.70506i) q^{55} +0.612303 q^{56} +1.34046 q^{57} +(4.95315 - 3.59867i) q^{58} +(-0.428033 + 1.31735i) q^{59} +(-0.0680088 - 0.209310i) q^{60} +3.71271 q^{61} +(-5.40113 - 4.09796i) q^{62} -0.587837 q^{63} +(2.73802 + 8.42677i) q^{64} +(-0.810709 + 2.49511i) q^{65} +(1.28694 - 0.935019i) q^{66} -2.38128 q^{67} -0.517242 q^{68} +(1.73224 - 1.25855i) q^{69} +(-0.349889 - 0.254210i) q^{70} +(5.86105 + 4.25830i) q^{71} +(-2.78736 - 8.57861i) q^{72} +(0.160910 - 0.116908i) q^{73} +(-3.94322 - 12.1360i) q^{74} +(0.135973 - 0.418483i) q^{75} +(-2.34395 - 1.70298i) q^{76} +(-0.336976 + 1.03710i) q^{77} +(0.132869 - 0.408930i) q^{78} +(11.3142 + 8.22025i) q^{79} +(1.48235 - 4.56222i) q^{80} +(2.62289 + 8.07244i) q^{81} +(-11.0161 + 8.00363i) q^{82} +(-0.432705 - 1.33173i) q^{83} +(-0.0200039 - 0.0145337i) q^{84} +(1.43843 + 1.04508i) q^{85} +(1.59269 - 1.15715i) q^{86} -1.20322 q^{87} -16.7329 q^{88} +(8.62465 - 6.26618i) q^{89} +(-1.96879 + 6.05932i) q^{90} +(0.0910834 + 0.280326i) q^{91} -4.62795 q^{92} +(0.385367 + 1.27546i) q^{93} -1.93498 q^{94} +(3.07759 + 9.47185i) q^{95} +(0.210398 - 0.647539i) q^{96} +(5.17845 - 3.76236i) q^{97} +8.47521 q^{98} +16.0643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.376285	−	1.15809i	−0.266074	−	0.818892i	−0.991444	−	0.130532i	$-0.958331\pi$
$2$	−0.376285	−	1.15809i	−0.266074	−	0.818892i	0.725370	−	0.688359i	$-0.241669\pi$
$3$	−0.0739502	+	0.227595i	−0.0426952	+	0.131402i	−0.970132	−	0.242578i	$-0.922007\pi$
$3$	−0.0739502	+	0.227595i	−0.0426952	+	0.131402i	0.927437	+	0.373980i	$0.122007\pi$
$4$	0.418458	−	0.304028i	0.209229	−	0.152014i
$5$	−1.77800			−0.795146			−0.397573	−	0.917571i	$-0.630147\pi$
$5$	−1.77800			−0.795146			−0.397573	+	0.917571i	$0.630147\pi$
$6$	0.291402			0.118964
$7$	−0.161608	+	0.117415i	−0.0610822	+	0.0443788i	−0.617907	−	0.786251i	$-0.712019\pi$
$7$	−0.161608	+	0.117415i	−0.0610822	+	0.0443788i	0.556825	+	0.830630i	$0.312019\pi$
$8$	−2.47981	−	1.80168i	−0.876744	−	0.636992i
$9$	2.38072	+	1.72969i	0.793573	+	0.576565i
$10$	0.669036	+	2.05908i	0.211568	+	0.651138i
$11$	4.41639	−	3.20870i	1.33159	−	0.967459i	0.331884	−	0.943320i	$-0.392316\pi$
$11$	4.41639	−	3.20870i	1.33159	−	0.967459i	0.999709	−	0.0241383i	$-0.00768421\pi$
$12$	0.0382502	+	0.117722i	0.0110419	+	0.0339834i
$13$	0.455967	−	1.40332i	0.126462	−	0.389211i	−0.867702	−	0.497084i	$-0.834404\pi$
$13$	0.455967	−	1.40332i	0.126462	−	0.389211i	0.994165	+	0.107873i	$0.0344040\pi$
$14$	0.196788	+	0.142975i	0.0525939	+	0.0382117i
$15$	0.131483	−	0.404664i	0.0339489	−	0.104484i
$16$	−0.833720	+	2.56593i	−0.208430	+	0.641482i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	1.10731	−	3.40794i	0.260995	−	0.803259i
$19$	−1.73093	−	5.32725i	−0.397102	−	1.22215i	−0.927312	−	0.374288i	$-0.877887\pi$
$19$	−1.73093	−	5.32725i	−0.397102	−	1.22215i	0.530210	−	0.847866i	$-0.322113\pi$
$20$	−0.744018	+	0.540561i	−0.166368	+	0.120873i
$21$	−0.0147722	−	0.0454642i	−0.00322356	−	0.00992110i
$22$	−5.37778	−	3.90718i	−1.14655	−	0.833014i
$23$	−7.23855	−	5.25912i	−1.50934	−	1.09660i	−0.966468	−	0.256788i	$-0.917336\pi$
$23$	−7.23855	−	5.25912i	−1.50934	−	1.09660i	−0.542875	−	0.839814i	$-0.682664\pi$
$24$	0.593437	−	0.431157i	0.121135	−	0.0880096i
$25$	−1.83872			−0.367743
$26$	−1.79674			−0.352370
$27$	−1.15054	+	0.835914i	−0.221421	+	0.160872i
$28$	−0.0319288	+	0.0982668i	−0.00603398	+	0.0185707i
$29$	1.55371	+	4.78184i	0.288517	+	0.887965i	0.985322	+	0.170704i	$0.0546043\pi$
$29$	1.55371	+	4.78184i	0.288517	+	0.887965i	−0.696805	+	0.717261i	$0.745396\pi$
$30$	−0.518112			−0.0945939
$31$	4.57132	−	3.17853i	0.821033	−	0.570880i
$31$	4.57132	−	3.17853i	0.821033	−	0.570880i
$32$	−2.84513			−0.502953
$33$	0.403691	+	1.24243i	0.0702736	+	0.216280i
$34$	−0.376285	+	1.15809i	−0.0645324	+	0.198610i
$35$	0.287340	−	0.208765i	0.0485693	−	0.0352877i
$36$	1.52211			0.253684
$37$	10.4793			1.72279			0.861396	−	0.507933i	$-0.169590\pi$
$37$	10.4793			1.72279			0.861396	+	0.507933i	$0.169590\pi$
$38$	−5.51810	+	4.00913i	−0.895153	+	0.650367i
$39$	0.285670	+	0.207552i	0.0457439	+	0.0332349i
$40$	4.40910	+	3.20340i	0.697139	+	0.506501i
$41$	−3.45554	−	10.6350i	−0.539664	−	1.66092i	−0.733349	−	0.679852i	$-0.762044\pi$
$41$	−3.45554	−	10.6350i	−0.539664	−	1.66092i	0.193685	−	0.981064i	$-0.437956\pi$
$42$	−0.0470929	+	0.0342150i	−0.00726660	+	0.00527949i
$43$	0.499597	+	1.53760i	0.0761878	+	0.234482i	0.981896	−	0.189419i	$-0.0606605\pi$
$43$	0.499597	+	1.53760i	0.0761878	+	0.234482i	−0.905709	+	0.423901i	$0.860660\pi$
$44$	0.872542	−	2.68541i	0.131541	−	0.404841i
$45$	−4.23292	−	3.07540i	−0.631007	−	0.458453i
$46$	−3.36676	+	10.3618i	−0.496401	+	1.52777i
$47$	0.491048	−	1.51129i	0.0716267	−	0.220444i	−0.908834	−	0.417157i	$-0.863027\pi$
$47$	0.491048	−	1.51129i	0.0716267	−	0.220444i	0.980461	+	0.196712i	$0.0630265\pi$
$48$	−0.522339	−	0.379501i	−0.0753931	−	0.0547763i
$49$	−2.15079	+	6.61944i	−0.307255	+	0.945635i
$50$	0.691882	+	2.12939i	0.0978469	+	0.301142i
$51$	0.193604	−	0.140662i	0.0271100	−	0.0196966i
$52$	−0.235845	−	0.725857i	−0.0327059	−	0.100658i
$53$	−4.61935	−	3.35616i	−0.634517	−	0.461004i	0.223445	−	0.974717i	$-0.428270\pi$
$53$	−4.61935	−	3.35616i	−0.634517	−	0.461004i	−0.857962	+	0.513713i	$0.828270\pi$
$54$	1.40099	+	1.01788i	0.190651	+	0.138516i
$55$	−7.85235	+	5.70506i	−1.05881	+	0.769271i
$56$	0.612303			0.0818224
$57$	1.34046			0.177548
$58$	4.95315	−	3.59867i	0.650380	−	0.472529i
$59$	−0.428033	+	1.31735i	−0.0557252	+	0.171505i	−0.975045	−	0.222006i	$-0.928740\pi$
$59$	−0.428033	+	1.31735i	−0.0557252	+	0.171505i	0.919320	+	0.393511i	$0.128740\pi$
$60$	−0.0680088	−	0.209310i	−0.00877990	−	0.0270218i
$61$	3.71271			0.475364			0.237682	−	0.971343i	$-0.423612\pi$
$61$	3.71271			0.475364			0.237682	+	0.971343i	$0.423612\pi$
$62$	−5.40113	−	4.09796i	−0.685945	−	0.520441i
$63$	−0.587837			−0.0740605
$64$	2.73802	+	8.42677i	0.342253	+	1.05335i
$65$	−0.810709	+	2.49511i	−0.100556	+	0.309480i
$66$	1.28694	−	0.935019i	0.158412	−	0.115093i
$67$	−2.38128			−0.290920			−0.145460	−	0.989364i	$-0.546466\pi$
$67$	−2.38128			−0.290920			−0.145460	+	0.989364i	$0.546466\pi$
$68$	−0.517242			−0.0627249
$69$	1.73224	−	1.25855i	0.208537	−	0.151511i
$70$	−0.349889	−	0.254210i	−0.0418198	−	0.0303839i
$71$	5.86105	+	4.25830i	0.695579	+	0.505368i	0.878489	−	0.477762i	$-0.158552\pi$
$71$	5.86105	+	4.25830i	0.695579	+	0.505368i	−0.182910	+	0.983130i	$0.558552\pi$
$72$	−2.78736	−	8.57861i	−0.328494	−	1.01100i
$73$	0.160910	−	0.116908i	0.0188331	−	0.0136830i	−0.578329	−	0.815804i	$-0.696295\pi$
$73$	0.160910	−	0.116908i	0.0188331	−	0.0136830i	0.597162	+	0.802121i	$0.296295\pi$
$74$	−3.94322	−	12.1360i	−0.458390	−	1.41078i
$75$	0.135973	−	0.418483i	0.0157008	−	0.0483222i
$76$	−2.34395	−	1.70298i	−0.268870	−	0.195345i
$77$	−0.336976	+	1.03710i	−0.0384020	+	0.118189i
$78$	0.132869	−	0.408930i	0.0150445	−	0.0463022i
$79$	11.3142	+	8.22025i	1.27295	+	0.924850i	0.999316	−	0.0369842i	$-0.0117751\pi$
$79$	11.3142	+	8.22025i	1.27295	+	0.924850i	0.273631	+	0.961835i	$0.411775\pi$
$80$	1.48235	−	4.56222i	0.165732	−	0.510072i
$81$	2.62289	+	8.07244i	0.291433	+	0.896938i
$82$	−11.0161	+	8.00363i	−1.21652	+	0.883853i
$83$	−0.432705	−	1.33173i	−0.0474955	−	0.146176i	0.924496	−	0.381191i	$-0.124486\pi$
$83$	−0.432705	−	1.33173i	−0.0474955	−	0.146176i	−0.971992	+	0.235015i	$0.924486\pi$
$84$	−0.0200039	−	0.0145337i	−0.00218261	−	0.00158576i
$85$	1.43843	+	1.04508i	0.156020	+	0.113355i
$86$	1.59269	−	1.15715i	0.171744	−	0.124779i
$87$	−1.20322			−0.128999
$88$	−16.7329			−1.78373
$89$	8.62465	−	6.26618i	0.914211	−	0.664213i	−0.0278651	−	0.999612i	$-0.508871\pi$
$89$	8.62465	−	6.26618i	0.914211	−	0.664213i	0.942076	+	0.335398i	$0.108871\pi$
$90$	−1.96879	+	6.05932i	−0.207529	+	0.638708i
$91$	0.0910834	+	0.280326i	0.00954814	+	0.0293861i
$92$	−4.62795			−0.482497
$93$	0.385367	+	1.27546i	0.0399607	+	0.132259i
$94$	−1.93498			−0.199578
$95$	3.07759	+	9.47185i	0.315754	+	0.971791i
$96$	0.210398	−	0.647539i	0.0214737	−	0.0660892i
$97$	5.17845	−	3.76236i	0.525791	−	0.382010i	−0.292990	−	0.956116i	$-0.594650\pi$
$97$	5.17845	−	3.76236i	0.525791	−	0.382010i	0.818781	+	0.574106i	$0.194650\pi$
$98$	8.47521			0.856125
$99$	16.0643			1.61452
$100$	−0.769425	+	0.559020i	−0.0769425	+	0.0559020i
$101$	−4.91332	−	3.56974i	−0.488894	−	0.355202i	0.315865	−	0.948804i	$-0.397705\pi$
$101$	−4.91332	−	3.56974i	−0.488894	−	0.355202i	−0.804759	+	0.593602i	$0.797705\pi$
$102$	−0.235749	−	0.171282i	−0.0233426	−	0.0169594i
$103$	0.132155	+	0.406731i	0.0130216	+	0.0400764i	0.957356	−	0.288910i	$-0.0932929\pi$
$103$	0.132155	+	0.406731i	0.0130216	+	0.0400764i	−0.944335	+	0.328987i	$0.893293\pi$
$104$	−3.65905	+	2.65846i	−0.358799	+	0.260683i
$105$	0.0262650	+	0.0808353i	0.00256320	+	0.00788872i
$106$	−2.14853	+	6.61249i	−0.208684	+	0.642262i
$107$	5.38236	+	3.91051i	0.520332	+	0.378044i	0.816729	−	0.577021i	$-0.195785\pi$
$107$	5.38236	+	3.91051i	0.520332	+	0.378044i	−0.296397	+	0.955065i	$0.595785\pi$
$108$	−0.227311	+	0.699590i	−0.0218730	+	0.0673181i
$109$	−5.50617	+	16.9463i	−0.527396	+	1.62316i	0.232133	+	0.972684i	$0.425429\pi$
$109$	−5.50617	+	16.9463i	−0.527396	+	1.62316i	−0.759529	+	0.650473i	$0.774571\pi$
$110$	9.56169	+	6.94697i	0.911671	+	0.662368i
$111$	−0.774949	+	2.38505i	−0.0735549	+	0.226379i
$112$	−0.166543	−	0.512567i	−0.0157368	−	0.0484330i
$113$	4.17928	−	3.03642i	0.393153	−	0.285643i	−0.373593	−	0.927593i	$-0.621874\pi$
$113$	4.17928	−	3.03642i	0.393153	−	0.285643i	0.766746	+	0.641950i	$0.221874\pi$
$114$	−0.504395	−	1.55237i	−0.0472409	−	0.145393i
$115$	12.8701	+	9.35071i	1.20015	+	0.871958i
$116$	2.10397	+	1.52863i	0.195349	+	0.141929i
$117$	3.51285	−	2.55223i	0.324763	−	0.235954i
$118$	1.68667			0.155271
$119$	0.199759			0.0183119
$120$	−1.05513	+	0.766598i	−0.0963198	+	0.0699805i
$121$	5.80960	−	17.8801i	0.528145	−	1.62546i
$122$	−1.39704	−	4.29964i	−0.126482	−	0.389271i
$123$	2.67602			0.241289
$124$	0.946546	−	2.71989i	0.0850024	−	0.244253i
$125$	12.1592			1.08756
$126$	0.221195	+	0.680767i	0.0197056	+	0.0606475i
$127$	−0.781318	+	2.40465i	−0.0693308	+	0.213378i	−0.979719	−	0.200377i	$-0.935783\pi$
$127$	−0.781318	+	2.40465i	−0.0693308	+	0.213378i	0.910388	+	0.413756i	$0.135783\pi$
$128$	4.12513	−	2.99709i	0.364614	−	0.264907i
$129$	−0.386896			−0.0340643
$130$	3.19461			0.280186
$131$	5.15658	−	3.74647i	0.450532	−	0.327331i	−0.339274	−	0.940688i	$-0.610181\pi$
$131$	5.15658	−	3.74647i	0.450532	−	0.327331i	0.789806	+	0.613357i	$0.210181\pi$
$132$	0.546662	+	0.397173i	0.0475808	+	0.0345695i
$133$	0.905233	+	0.657690i	0.0784937	+	0.0570290i
$134$	0.896043	+	2.75774i	0.0774063	+	0.238232i
$135$	2.04565	−	1.48626i	0.176062	−	0.127916i
$136$	0.947202	+	2.91519i	0.0812219	+	0.249975i
$137$	−5.70366	+	17.5541i	−0.487297	+	1.49975i	0.341329	+	0.939944i	$0.389123\pi$
$137$	−5.70366	+	17.5541i	−0.487297	+	1.49975i	−0.828626	+	0.559802i	$0.810877\pi$
$138$	−2.10933	−	1.53251i	−0.179558	−	0.130456i
$139$	4.85167	−	14.9319i	0.411513	−	1.26651i	−0.503819	−	0.863809i	$-0.668072\pi$
$139$	4.85167	−	14.9319i	0.411513	−	1.26651i	0.915333	−	0.402699i	$-0.131928\pi$
$140$	0.0567694	−	0.174718i	0.00479789	−	0.0147664i
$141$	0.307650	+	0.223520i	0.0259088	+	0.0188238i
$142$	2.72606	−	8.38995i	0.228766	−	0.704069i
$143$	−2.48910	−	7.66068i	−0.208149	−	0.640618i
$144$	−6.42312	+	4.66667i	−0.535260	+	0.388889i
$145$	−2.76250	−	8.50211i	−0.229413	−	0.706061i
$146$	−0.195937	−	0.142357i	−0.0162159	−	0.0117815i
$147$	−1.34750	−	0.979018i	−0.111140	−	0.0807481i
$148$	4.38516	−	3.18601i	0.360458	−	0.261888i
$149$	−16.1260			−1.32109			−0.660545	−	0.750786i	$-0.729675\pi$
$149$	−16.1260			−1.32109			−0.660545	+	0.750786i	$0.729675\pi$
$150$	−0.535805			−0.0437483
$151$	−7.22653	+	5.25038i	−0.588087	+	0.427270i	−0.841630	−	0.540054i	$-0.818404\pi$
$151$	−7.22653	+	5.25038i	−0.588087	+	0.427270i	0.253544	+	0.967324i	$0.418404\pi$
$152$	−5.30566	+	16.3291i	−0.430345	+	1.32447i
$153$	−0.909354	−	2.79870i	−0.0735169	−	0.226262i
$154$	1.32786			0.107002
$155$	−8.12781	+	5.65142i	−0.652841	+	0.453933i
$156$	0.182642			0.0146231
$157$	6.36067	+	19.5761i	0.507637	+	1.56234i	0.796292	+	0.604912i	$0.206792\pi$
$157$	6.36067	+	19.5761i	0.507637	+	1.56234i	−0.288656	+	0.957433i	$0.593208\pi$
$158$	5.26240	−	16.1960i	0.418654	−	1.28848i
$159$	1.10545	−	0.803155i	0.0876677	−	0.0636943i
$160$	5.05865			0.399921
$161$	1.78731			0.140860
$162$	8.36164	−	6.07508i	0.656952	−	0.477304i
$163$	14.6234	+	10.6245i	1.14539	+	0.832174i	0.987861	−	0.155340i	$-0.0496473\pi$
$163$	14.6234	+	10.6245i	1.14539	+	0.832174i	0.157529	+	0.987514i	$0.449647\pi$
$164$	−4.67934	−	3.39974i	−0.365395	−	0.265475i
$165$	−0.717763	−	2.20905i	−0.0558778	−	0.171974i
$166$	−1.37944	+	1.00222i	−0.107065	+	0.0777874i
$167$	1.42820	+	4.39554i	0.110517	+	0.340137i	0.990986	−	0.133968i	$-0.0427719\pi$
$167$	1.42820	+	4.39554i	0.110517	+	0.340137i	−0.880469	+	0.474105i	$0.842772\pi$
$168$	−0.0452799	+	0.139357i	−0.00349342	+	0.0107516i
$169$	8.75582	+	6.36147i	0.673524	+	0.489344i
$170$	0.669036	−	2.05908i	0.0513127	−	0.157924i
$171$	5.09366	−	15.6767i	0.389522	−	1.19882i
$172$	0.676533	+	0.491530i	0.0515852	+	0.0374788i
$173$	−4.19524	+	12.9116i	−0.318958	+	0.981653i	0.655136	+	0.755511i	$0.272611\pi$
$173$	−4.19524	+	12.9116i	−0.318958	+	0.981653i	−0.974094	+	0.226142i	$0.927389\pi$
$174$	0.452754	+	1.39343i	0.0343232	+	0.105636i
$175$	0.297152	−	0.215893i	0.0224626	−	0.0163200i
$176$	4.55125	+	14.0073i	0.343063	+	1.05584i
$177$	−0.268170	−	0.194837i	−0.0201569	−	0.0146448i
$178$	−10.5021	−	7.63023i	−0.787167	−	0.571910i
$179$	12.4747	−	9.06339i	0.932402	−	0.677429i	−0.0141780	−	0.999899i	$-0.504513\pi$
$179$	12.4747	−	9.06339i	0.932402	−	0.677429i	0.946580	+	0.322470i	$0.104513\pi$
$180$	−2.70630			−0.201716
$181$	−23.8252			−1.77091			−0.885457	−	0.464722i	$-0.846154\pi$
$181$	−23.8252			−1.77091			−0.885457	+	0.464722i	$0.846154\pi$
$182$	0.290369	−	0.210965i	0.0215236	−	0.0156378i
$183$	−0.274556	+	0.844995i	−0.0202957	+	0.0624638i
$184$	8.47494	+	26.0832i	0.624781	+	1.92288i
$185$	−18.6323			−1.36987
$186$	1.33209	−	0.926227i	0.0976736	−	0.0679143i
$187$	−5.45896			−0.399199
$188$	−0.253991	−	0.781704i	−0.0185242	−	0.0570116i
$189$	0.0877873	−	0.270181i	0.00638559	−	0.0196528i
$190$	9.81118	−	7.12824i	0.711778	−	0.517137i
$191$	11.3763			0.823163			0.411581	−	0.911373i	$-0.364977\pi$
$191$	11.3763			0.823163			0.411581	+	0.911373i	$0.364977\pi$
$192$	−2.12037			−0.153024
$193$	18.1802	−	13.2087i	1.30864	−	0.950780i	0.308637	−	0.951180i	$-0.400127\pi$
$193$	18.1802	−	13.2087i	1.30864	−	0.950780i	1.00000		0.000399665i	$0.000127217\pi$
$194$	−6.30572	−	4.58137i	−0.452724	−	0.328923i
$195$	−0.507922	−	0.369027i	−0.0363730	−	0.0264266i
$196$	1.11248	+	3.42386i	0.0794628	+	0.244561i
$197$	−9.72309	+	7.06424i	−0.692741	+	0.503306i	−0.877560	−	0.479466i	$-0.840830\pi$
$197$	−9.72309	+	7.06424i	−0.692741	+	0.503306i	0.184819	+	0.982773i	$0.440830\pi$
$198$	−6.04475	−	18.6038i	−0.429581	−	1.32212i
$199$	0.546738	−	1.68269i	0.0387572	−	0.119282i	−0.929806	−	0.368050i	$-0.880026\pi$
$199$	0.546738	−	1.68269i	0.0387572	−	0.119282i	0.968563	+	0.248768i	$0.0800255\pi$
$200$	4.55966	+	3.31279i	0.322417	+	0.234249i
$201$	0.176096	−	0.541969i	0.0124209	−	0.0382275i
$202$	−2.28526	+	7.03330i	−0.160790	+	0.494861i
$203$	−0.812554	−	0.590355i	−0.0570301	−	0.0414348i
$204$	0.0382502	−	0.117722i	0.00267805	−	0.00824218i
$205$	6.14395	+	18.9091i	0.429112	+	1.32067i
$206$	0.421302	−	0.306094i	0.0293535	−	0.0213266i
$207$	−8.13630	−	25.0410i	−0.565512	−	1.74047i
$208$	3.22067	+	2.33995i	0.223313	+	0.162247i
$209$	−24.7380	−	17.9732i	−1.71116	−	1.24323i
$210$	0.0837313	−	0.0608343i	0.00577801	−	0.00419797i
$211$	−5.65487			−0.389297			−0.194649	−	0.980873i	$-0.562357\pi$
$211$	−5.65487			−0.389297			−0.194649	+	0.980873i	$0.562357\pi$
$212$	−2.95337			−0.202838
$213$	−1.40260	+	1.01905i	−0.0961043	+	0.0698238i
$214$	2.50341	−	7.70471i	0.171130	−	0.526683i
$215$	−0.888283	−	2.73385i	−0.0605804	−	0.186447i
$216$	4.35916			0.296603
$217$	−0.365556	+	1.05042i	−0.0248156	+	0.0713071i
$218$	21.6971			1.46952
$219$	0.0147083	+	0.0452676i	0.000993898	+	0.00305890i
$220$	−1.55138	+	4.77466i	−0.104594	+	0.321907i
$221$	−1.19374	+	0.867300i	−0.0802994	+	0.0583409i
$222$	3.05370			0.204951
$223$	−7.32415			−0.490461			−0.245231	−	0.969465i	$-0.578864\pi$
$223$	−7.32415			−0.490461			−0.245231	+	0.969465i	$0.578864\pi$
$224$	0.459797	−	0.334062i	0.0307215	−	0.0223205i
$225$	−4.37747	−	3.18042i	−0.291831	−	0.212028i
$226$	−5.08904	−	3.69741i	−0.338518	−	0.245948i
$227$	2.73057	+	8.40382i	0.181234	+	0.557781i	0.999863	−	0.0165414i	$-0.00526554\pi$
$227$	2.73057	+	8.40382i	0.181234	+	0.557781i	−0.818629	+	0.574323i	$0.805266\pi$
$228$	0.560926	−	0.407536i	0.0371482	−	0.0269897i
$229$	2.09978	+	6.46245i	0.138757	+	0.427051i	0.996155	−	0.0876027i	$-0.0279206\pi$
$229$	2.09978	+	6.46245i	0.138757	+	0.427051i	−0.857398	+	0.514653i	$0.827921\pi$
$230$	5.98609	−	18.4233i	0.394711	−	1.21480i
$231$	−0.211121	−	0.153388i	−0.0138907	−	0.0100922i
$232$	4.76246	−	14.6573i	0.312670	−	0.962301i
$233$	5.90586	−	18.1764i	0.386906	−	1.19077i	−0.548182	−	0.836359i	$-0.684680\pi$
$233$	5.90586	−	18.1764i	0.386906	−	1.19077i	0.935088	−	0.354415i	$-0.115320\pi$
$234$	−4.27754	−	3.10781i	−0.279632	−	0.203164i
$235$	−0.873084	+	2.68708i	−0.0569537	+	0.175285i
$236$	0.221397	+	0.681390i	0.0144117	+	0.0443547i
$237$	−2.70758	+	1.96717i	−0.175876	+	0.127781i
$238$	−0.0751664	−	0.231338i	−0.00487231	−	0.0149954i
$239$	2.34985	+	1.70726i	0.151999	+	0.110434i	0.661185	−	0.750223i	$-0.270054\pi$
$239$	2.34985	+	1.70726i	0.151999	+	0.110434i	−0.509187	+	0.860656i	$0.670054\pi$
$240$	0.928719	+	0.674754i	0.0599485	+	0.0435552i
$241$	−12.1666	+	8.83958i	−0.783722	+	0.569408i	−0.906094	−	0.423077i	$-0.860950\pi$
$241$	−12.1666	+	8.83958i	−0.783722	+	0.569408i	0.122371	+	0.992484i	$0.460950\pi$
$242$	−22.8928			−1.47161
$243$	−6.29764			−0.403994
$244$	1.55361	−	1.12877i	0.0994599	−	0.0722618i
$245$	3.82410	−	11.7694i	0.244313	−	0.751918i
$246$	−1.00695	−	3.09907i	−0.0642007	−	0.197590i
$247$	−8.26508			−0.525895
$248$	−17.0627	−	0.353951i	−1.08348	−	0.0224759i
$249$	0.335094			0.0212357
$250$	−4.57534	−	14.0815i	−0.289370	−	0.890590i
$251$	−7.70800	+	23.7228i	−0.486525	+	1.49737i	0.343236	+	0.939249i	$0.388477\pi$
$251$	−7.70800	+	23.7228i	−0.486525	+	1.49737i	−0.829761	+	0.558120i	$0.811523\pi$
$252$	−0.245985	+	0.178719i	−0.0154956	+	0.0112582i
$253$	−48.8432			−3.07075
$254$	3.07879			0.193181
$255$	−0.344228	+	0.250096i	−0.0215564	+	0.0156616i
$256$	9.31336	+	6.76655i	0.582085	+	0.422909i
$257$	−16.7731	−	12.1863i	−1.04627	−	0.760163i	−0.0747739	−	0.997201i	$-0.523823\pi$
$257$	−16.7731	−	12.1863i	−1.04627	−	0.760163i	−0.971500	+	0.237038i	$0.923823\pi$
$258$	0.145583	+	0.448059i	0.00906362	+	0.0278949i
$259$	−1.69355	+	1.23044i	−0.105232	+	0.0764555i
$260$	0.419333	+	1.29057i	0.0260059	+	0.0800380i
$261$	−4.57216	+	14.0717i	−0.283010	+	0.871014i
$262$	−6.27909	−	4.56203i	−0.387924	−	0.281843i
$263$	−4.32462	+	13.3098i	−0.266667	+	0.820717i	0.724637	+	0.689130i	$0.242007\pi$
$263$	−4.32462	+	13.3098i	−0.266667	+	0.820717i	−0.991305	+	0.131587i	$0.957993\pi$
$264$	1.23740	−	3.80832i	0.0761566	−	0.234386i
$265$	8.21321	+	5.96725i	0.504534	+	0.366565i
$266$	0.421037	−	1.29582i	0.0258154	−	0.0794517i
$267$	0.788357	+	2.42631i	0.0482467	+	0.148488i
$268$	−0.996467	+	0.723976i	−0.0608689	+	0.0442239i
$269$	6.69581	+	20.6076i	0.408251	+	1.25647i	0.918150	+	0.396233i	$0.129683\pi$
$269$	6.69581	+	20.6076i	0.408251	+	1.25647i	−0.509899	+	0.860234i	$0.670317\pi$
$270$	−2.49096	−	1.80979i	−0.151595	−	0.110140i
$271$	−25.7994	−	18.7444i	−1.56720	−	1.13864i	−0.929774	−	0.368132i	$-0.879998\pi$
$271$	−25.7994	−	18.7444i	−1.56720	−	1.13864i	−0.637430	−	0.770508i	$-0.720002\pi$
$272$	2.18271	−	1.58583i	0.132346	−	0.0961551i
$273$	−0.0705365			−0.00426906
$274$	22.4754			1.35779
$275$	−8.12049	+	5.89988i	−0.489684	+	0.355776i
$276$	0.342237	−	1.05330i	0.0206003	−	0.0634011i
$277$	−4.06760	−	12.5188i	−0.244398	−	0.752180i	−0.995735	−	0.0922613i	$-0.970591\pi$
$277$	−4.06760	−	12.5188i	−0.244398	−	0.752180i	0.751337	−	0.659919i	$-0.229409\pi$
$278$	−19.1181			−1.14663
$279$	16.3809	+	0.339808i	0.980700	+	0.0203438i
$280$	−1.08867			−0.0650608
$281$	−8.04158	−	24.7494i	−0.479721	−	1.47643i	−0.839484	−	0.543385i	$-0.817143\pi$
$281$	−8.04158	−	24.7494i	−0.479721	−	1.47643i	0.359763	−	0.933044i	$-0.382857\pi$
$282$	0.143092	−	0.440393i	0.00852102	−	0.0262250i
$283$	21.5688	−	15.6706i	1.28213	−	0.931523i	0.282516	−	0.959263i	$-0.408831\pi$
$283$	21.5688	−	15.6706i	1.28213	−	0.931523i	0.999615	+	0.0277396i	$0.00883094\pi$
$284$	3.74725			0.222358
$285$	−2.38334			−0.141177
$286$	−7.93512	+	5.76520i	−0.469213	+	0.340904i
$287$	1.80716	+	1.31298i	0.106673	+	0.0775028i
$288$	−6.77347	−	4.92121i	−0.399130	−	0.289985i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−8.80669	+	6.39844i	−0.517147	+	0.375729i
$291$	0.473348	+	1.45682i	0.0277482	+	0.0854001i
$292$	0.0317908	−	0.0978420i	0.00186042	−	0.00572577i
$293$	20.3866	+	14.8117i	1.19100	+	0.865309i	0.993369	−	0.114969i	$-0.0366768\pi$
$293$	20.3866	+	14.8117i	1.19100	+	0.865309i	0.197626	+	0.980277i	$0.436677\pi$
$294$	−0.626743	+	1.92892i	−0.0365524	+	0.112497i
$295$	0.761043	−	2.34225i	0.0443097	−	0.136371i
$296$	−25.9867	−	18.8805i	−1.51045	−	1.09740i
$297$	−2.39903	+	7.38345i	−0.139206	+	0.428431i
$298$	6.06796	+	18.6753i	0.351508	+	1.08183i
$299$	−10.6808	+	7.76003i	−0.617685	+	0.448774i
$300$	−0.0703312	−	0.216457i	−0.00406057	−	0.0124972i
$301$	−0.261277	−	0.189829i	−0.0150598	−	0.0109416i
$302$	8.79964	+	6.39331i	0.506362	+	0.367894i
$303$	1.17580	−	0.854266i	0.0675477	−	0.0490763i
$304$	15.1124			0.866758
$305$	−6.60120			−0.377984
$306$	−2.89897	+	2.10622i	−0.165723	+	0.120405i
$307$	6.18208	−	19.0265i	0.352830	−	1.08590i	−0.604427	−	0.796660i	$-0.706598\pi$
$307$	6.18208	−	19.0265i	0.352830	−	1.08590i	0.957257	−	0.289238i	$-0.0934020\pi$
$308$	0.174298	+	0.536435i	0.00993156	+	0.0305662i
$309$	−0.102343			−0.00582208
$310$	9.60321	+	7.28617i	0.545426	+	0.413827i
$311$	2.88523			0.163607			0.0818033	−	0.996648i	$-0.473932\pi$
$311$	2.88523			0.163607			0.0818033	+	0.996648i	$0.473932\pi$
$312$	−0.334464	−	1.02938i	−0.0189353	−	0.0582769i
$313$	5.41701	−	16.6718i	0.306187	−	0.942348i	−0.673044	−	0.739602i	$-0.735014\pi$
$313$	5.41701	−	16.6718i	0.306187	−	0.942348i	0.979231	−	0.202746i	$-0.0649865\pi$
$314$	20.2774	−	14.7324i	1.14432	−	0.831399i
$315$	1.04517			0.0588889
$316$	7.23370			0.406927
$317$	−13.4919	+	9.80247i	−0.757783	+	0.550561i	−0.898229	−	0.439527i	$-0.855146\pi$
$317$	−13.4919	+	9.80247i	−0.757783	+	0.550561i	0.140447	+	0.990088i	$0.455146\pi$
$318$	−1.34609	−	0.977990i	−0.0754848	−	0.0548429i
$319$	22.2053	+	16.1331i	1.24326	+	0.903279i
$320$	−4.86820	−	14.9828i	−0.272141	−	0.837564i
$321$	−1.28804	+	0.935816i	−0.0718914	+	0.0522322i
$322$	−0.672540	−	2.06986i	−0.0374792	−	0.115349i
$323$	−1.73093	+	5.32725i	−0.0963114	+	0.296416i
$324$	3.55181	+	2.58054i	0.197323	+	0.143364i
$325$	−0.838393	+	2.58031i	−0.0465057	+	0.143130i
$326$	6.80153	−	20.9330i	0.376702	−	1.15937i
$327$	−3.44971	−	2.50636i	−0.190769	−	0.138602i
$328$	−10.5919	+	32.5987i	−0.584842	+	1.79996i
$329$	0.0980913	+	0.301894i	0.00540795	+	0.0166440i
$330$	−2.28819	+	1.66246i	−0.125961	+	0.0915157i
$331$	3.12470	+	9.61684i	0.171749	+	0.528589i	0.999470	−	0.0325506i	$-0.0103630\pi$
$331$	3.12470	+	9.61684i	0.171749	+	0.528589i	−0.827721	+	0.561140i	$0.810363\pi$
$332$	−0.585951	−	0.425718i	−0.0321582	−	0.0233643i
$333$	24.9484	+	18.1261i	1.36716	+	0.993302i
$334$	4.55301	−	3.30795i	0.249129	−	0.181003i
$335$	4.23392			0.231324
$336$	0.128974			0.00703609
$337$	0.137700	−	0.100045i	0.00750101	−	0.00544980i	−0.584028	−	0.811733i	$-0.698524\pi$
$337$	0.137700	−	0.100045i	0.00750101	−	0.00544980i	0.591529	+	0.806283i	$0.298524\pi$
$338$	4.07246	−	12.5337i	0.221512	−	0.681745i
$339$	0.382017	+	1.17573i	0.0207483	+	0.0638567i
$340$	0.919657			0.0498754
$341$	9.98982	−	28.7056i	0.540979	−	1.55450i
$342$	−20.0716			−1.08535
$343$	−0.861742	−	2.65217i	−0.0465297	−	0.143204i
$344$	1.53137	−	4.71307i	0.0825659	−	0.254112i
$345$	−3.07993	+	2.23770i	−0.165818	+	0.120474i
$346$	16.5314			0.888734
$347$	15.4448			0.829120			0.414560	−	0.910022i	$-0.363936\pi$
$347$	15.4448			0.829120			0.414560	+	0.910022i	$0.363936\pi$
$348$	−0.503497	+	0.365812i	−0.0269903	+	0.0196096i
$349$	−5.12666	−	3.72474i	−0.274424	−	0.199381i	0.442058	−	0.896987i	$-0.354249\pi$
$349$	−5.12666	−	3.72474i	−0.274424	−	0.199381i	−0.716482	+	0.697606i	$0.754249\pi$
$350$	−0.361837	−	0.262890i	−0.0193410	−	0.0140521i
$351$	0.648449	+	1.99572i	0.0346117	+	0.106524i
$352$	−12.5652	+	9.12917i	−0.669729	+	0.486586i
$353$	0.581150	+	1.78859i	0.0309315	+	0.0951973i	0.965330	−	0.261031i	$-0.0840625\pi$
$353$	0.581150	+	1.78859i	0.0309315	+	0.0951973i	−0.934399	+	0.356228i	$0.884063\pi$
$354$	−0.124730	+	0.383878i	−0.00662930	+	0.0204029i
$355$	−10.4210	−	7.57127i	−0.553087	−	0.401841i
$356$	1.70396	−	5.24426i	0.0903099	−	0.277945i
$357$	−0.0147722	+	0.0454642i	−0.000781828	+	0.00240622i
$358$	−15.1902	−	11.0364i	−0.802829	−	0.583289i
$359$	6.21907	−	19.1403i	0.328230	−	1.01019i	−0.641731	−	0.766930i	$-0.721784\pi$
$359$	6.21907	−	19.1403i	0.328230	−	1.01019i	0.969961	−	0.243259i	$-0.0782164\pi$
$360$	4.95593	+	15.2528i	0.261200	+	0.803892i
$361$	−10.0121	+	7.27424i	−0.526954	+	0.382855i
$362$	8.96508	+	27.5917i	0.471194	+	1.45019i
$363$	3.63981	+	2.64447i	0.191040	+	0.138799i
$364$	0.123341	+	0.0896128i	0.00646485	+	0.00469699i
$365$	−0.286098	+	0.207862i	−0.0149750	+	0.0108800i
$366$	1.08189			0.0565513
$367$	−20.6712			−1.07903			−0.539513	−	0.841977i	$-0.681392\pi$
$367$	−20.6712			−1.07903			−0.539513	+	0.841977i	$0.681392\pi$
$368$	19.5294	−	14.1890i	1.01804	−	0.739651i
$369$	10.1687	−	31.2961i	0.529362	−	1.62921i
$370$	7.01105	+	21.5778i	0.364487	+	1.12178i
$371$	1.14059			0.0592165
$372$	0.549036	+	0.416566i	0.0284662	+	0.0215979i
$373$	−17.0920			−0.884991			−0.442496	−	0.896771i	$-0.645907\pi$
$373$	−17.0920			−0.884991			−0.442496	+	0.896771i	$0.645907\pi$
$374$	2.05413	+	6.32196i	0.106216	+	0.326901i
$375$	−0.899178	+	2.76738i	−0.0464333	+	0.142907i
$376$	−3.94057	+	2.86300i	−0.203220	+	0.147648i
$377$	7.41889			0.382092
$378$	−0.345927			−0.0177926
$379$	21.5113	−	15.6289i	1.10496	−	0.802801i	0.123098	−	0.992394i	$-0.460717\pi$
$379$	21.5113	−	15.6289i	1.10496	−	0.802801i	0.981863	+	0.189593i	$0.0607169\pi$
$380$	4.16754	+	3.02790i	0.213790	+	0.155328i
$381$	−0.489508	−	0.355649i	−0.0250783	−	0.0182204i
$382$	−4.28075	−	13.1748i	−0.219022	−	0.674081i
$383$	−4.49859	+	3.26841i	−0.229867	+	0.167008i	−0.696757	−	0.717307i	$-0.745374\pi$
$383$	−4.49859	+	3.26841i	−0.229867	+	0.167008i	0.466890	+	0.884315i	$0.345374\pi$
$384$	0.377068	+	1.16050i	0.0192422	+	0.0592213i
$385$	0.599143	−	1.84397i	0.0305352	−	0.0939775i
$386$	−22.1377	−	16.0840i	−1.12678	−	0.818654i
$387$	−1.47018	+	4.52475i	−0.0747334	+	0.230006i
$388$	1.02310	−	3.14878i	0.0519401	−	0.159855i
$389$	−2.78238	−	2.02152i	−0.141072	−	0.102495i	0.515011	−	0.857184i	$-0.327788\pi$
$389$	−2.78238	−	2.02152i	−0.141072	−	0.102495i	−0.656083	+	0.754689i	$0.727788\pi$
$390$	−0.236242	+	0.727078i	−0.0119626	+	0.0368170i
$391$	2.76488	+	8.50943i	0.139826	+	0.430340i
$392$	17.2597	−	12.5399i	0.871746	−	0.633361i
$393$	0.471350	+	1.45067i	0.0237764	+	0.0731764i
$394$	11.8397	+	8.60202i	0.596474	+	0.433363i
$395$	−20.1167	−	14.6156i	−1.01218	−	0.735391i
$396$	6.72222	−	4.88398i	0.337804	−	0.245429i
$397$	−13.9725			−0.701259			−0.350629	−	0.936514i	$-0.614032\pi$
$397$	−13.9725			−0.701259			−0.350629	+	0.936514i	$0.614032\pi$
$398$	−2.15443			−0.107992
$399$	−0.216629	+	0.157390i	−0.0108450	+	0.00787938i
$400$	1.53297	−	4.71801i	0.0766487	−	0.235900i
$401$	5.12275	+	15.7662i	0.255818	+	0.787326i	0.993667	+	0.112361i	$0.0358414\pi$
$401$	5.12275	+	15.7662i	0.255818	+	0.787326i	−0.737850	+	0.674965i	$0.764159\pi$
$402$	−0.693910			−0.0346091
$403$	−2.37612	−	7.86433i	−0.118363	−	0.391750i
$404$	−3.14132			−0.156286
$405$	−4.66351	−	14.3528i	−0.231732	−	0.713196i
$406$	−0.377931	+	1.16315i	−0.0187564	+	0.0577262i
$407$	46.2809	−	33.6250i	2.29406	−	1.66673i
$408$	−0.733528			−0.0363151
$409$	−8.15547			−0.403262			−0.201631	−	0.979462i	$-0.564624\pi$
$409$	−8.15547			−0.403262			−0.201631	+	0.979462i	$0.564624\pi$
$410$	19.5865	−	14.2305i	0.967310	−	0.702792i
$411$	−3.57344	−	2.59625i	−0.176265	−	0.128064i
$412$	0.178959	+	0.130021i	0.00881666	+	0.00640568i
$413$	−0.0855035	−	0.263153i	−0.00420735	−	0.0129489i
$414$	−25.9381	+	18.8451i	−1.27479	+	0.926186i
$415$	0.769349	+	2.36781i	0.0377659	+	0.116231i
$416$	−1.29729	+	3.99264i	−0.0636047	+	0.195755i
$417$	3.03965	+	2.20843i	0.148852	+	0.108147i
$418$	−11.5060	+	35.4118i	−0.562776	+	1.73205i
$419$	4.70716	−	14.4872i	0.229960	−	0.707744i	−0.767790	−	0.640701i	$-0.778644\pi$
$419$	4.70716	−	14.4872i	0.229960	−	0.707744i	0.997750	−	0.0670425i	$-0.0213563\pi$
$420$	0.0355670	+	0.0258409i	0.00173549	+	0.00126091i
$421$	1.15327	−	3.54940i	0.0562070	−	0.172987i	−0.919012	−	0.394230i	$-0.871011\pi$
$421$	1.15327	−	3.54940i	0.0562070	−	0.172987i	0.975219	+	0.221243i	$0.0710113\pi$
$422$	2.12784	+	6.54883i	0.103582	+	0.318792i
$423$	3.78312	−	2.74860i	0.183942	−	0.133641i
$424$	5.40837	+	16.6452i	0.262653	+	0.808364i
$425$	1.48755	+	1.08077i	0.0721569	+	0.0524250i
$426$	1.70792	+	1.24088i	0.0827490	+	0.0601207i
$427$	−0.600005	+	0.435929i	−0.0290363	+	0.0210961i
$428$	3.44119			0.166336
$429$	1.92760			0.0930655
$430$	−2.83179	+	2.05742i	−0.136561	+	0.0992176i
$431$	−5.55882	+	17.1083i	−0.267759	+	0.824077i	0.723286	+	0.690548i	$0.242631\pi$
$431$	−5.55882	+	17.1083i	−0.267759	+	0.824077i	−0.991045	+	0.133528i	$0.957369\pi$
$432$	−1.18567	−	3.64911i	−0.0570455	−	0.175568i
$433$	16.8123			0.807945			0.403973	−	0.914771i	$-0.367629\pi$
$433$	16.8123			0.807945			0.403973	+	0.914771i	$0.367629\pi$
$434$	1.35403	+	0.0280883i	0.0649956	+	0.00134828i
$435$	2.13933			0.102573
$436$	2.84803	+	8.76533i	0.136396	+	0.419783i
$437$	−15.4872	+	47.6647i	−0.740854	+	2.28011i
$438$	0.0468894	−	0.0340671i	0.00224046	−	0.00162779i
$439$	23.2212			1.10829			0.554144	−	0.832421i	$-0.313046\pi$
$439$	23.2212			1.10829			0.554144	+	0.832421i	$0.313046\pi$
$440$	29.7510			1.41832
$441$	−16.5700	+	12.0388i	−0.789050	+	0.573278i
$442$	1.45360	+	1.05610i	0.0691405	+	0.0502335i
$443$	−6.26858	−	4.55439i	−0.297829	−	0.216386i	0.428827	−	0.903386i	$-0.358927\pi$
$443$	−6.26858	−	4.55439i	−0.297829	−	0.216386i	−0.726657	+	0.687001i	$0.758927\pi$
$444$	0.400836	+	1.23365i	0.0190229	+	0.0585463i
$445$	−15.3346	+	11.1413i	−0.726931	+	0.528147i
$446$	2.75597	+	8.48200i	0.130499	+	0.401635i
$447$	1.19252	−	3.67019i	0.0564041	−	0.173594i
$448$	−1.43192	−	1.04035i	−0.0676518	−	0.0491519i
$449$	−1.59431	+	4.90679i	−0.0752402	+	0.231566i	−0.981603	−	0.190936i	$-0.938848\pi$
$449$	−1.59431	+	4.90679i	−0.0752402	+	0.231566i	0.906362	+	0.422501i	$0.138848\pi$
$450$	−2.03602	+	6.26623i	−0.0959790	+	0.295393i
$451$	−49.3857	−	35.8808i	−2.32548	−	1.68956i
$452$	0.825696	−	2.54123i	0.0388375	−	0.119529i
$453$	−0.660559	−	2.03299i	−0.0310358	−	0.0955182i
$454$	8.70489	−	6.32447i	0.408541	−	0.296822i
$455$	−0.161946	−	0.498420i	−0.00759216	−	0.0233663i
$456$	−3.32408	−	2.41508i	−0.155664	−	0.113097i
$457$	19.4922	+	14.1619i	0.911807	+	0.662467i	0.941471	−	0.337093i	$-0.109444\pi$
$457$	19.4922	+	14.1619i	0.911807	+	0.662467i	−0.0296642	+	0.999560i	$0.509444\pi$
$458$	6.69397	−	4.86345i	0.312789	−	0.227254i
$459$	1.42214			0.0663799
$460$	8.22849			0.383655
$461$	16.1297	−	11.7189i	0.751233	−	0.545803i	−0.144976	−	0.989435i	$-0.546310\pi$
$461$	16.1297	−	11.7189i	0.751233	−	0.545803i	0.896209	+	0.443632i	$0.146310\pi$
$462$	−0.0981953	+	0.302214i	−0.00456846	+	0.0140603i
$463$	3.89284	+	11.9809i	0.180916	+	0.556802i	0.999854	−	0.0170799i	$-0.00543698\pi$
$463$	3.89284	+	11.9809i	0.180916	+	0.556802i	−0.818938	+	0.573882i	$0.805437\pi$
$464$	−13.5652			−0.629749
$465$	−0.685183	−	2.26777i	−0.0317746	−	0.105166i
$466$	−23.2721			−1.07806
$467$	0.536439	+	1.65099i	0.0248234	+	0.0763986i	0.962701	−	0.270568i	$-0.0872116\pi$
$467$	0.536439	+	1.65099i	0.0248234	+	0.0763986i	−0.937877	+	0.346967i	$0.887212\pi$
$468$	0.694030	−	2.13600i	0.0320815	−	0.0987368i
$469$	0.384836	−	0.279599i	0.0177701	−	0.0129107i
$470$	3.44040			0.158694
$471$	−4.92580			−0.226969
$472$	3.43489	−	2.49559i	0.158104	−	0.114869i
$473$	7.14011	+	5.18759i	0.328303	+	0.238526i
$474$	3.29698	+	2.39539i	0.151435	+	0.110024i
$475$	3.18268	+	9.79529i	0.146032	+	0.449439i
$476$	0.0835907	−	0.0607322i	0.00383137	−	0.00278366i
$477$	−5.19226	−	15.9801i	−0.237737	−	0.731680i
$478$	1.09295	−	3.36375i	0.0499902	−	0.153854i
$479$	33.6753	+	24.4665i	1.53866	+	1.11790i	0.951168	+	0.308675i	$0.0998855\pi$
$479$	33.6753	+	24.4665i	1.53866	+	1.11790i	0.587494	+	0.809228i	$0.300115\pi$
$480$	−0.374088	+	1.15132i	−0.0170747	+	0.0525505i
$481$	4.77823	−	14.7059i	0.217868	−	0.670530i
$482$	14.8151	+	10.7638i	0.674811	+	0.490279i
$483$	−0.132172	+	0.406784i	−0.00601404	+	0.0185093i
$484$	−3.00497	−	9.24835i	−0.136590	−	0.420380i
$485$	−9.20728	+	6.68948i	−0.418081	+	0.303754i
$486$	2.36971	+	7.29322i	0.107492	+	0.330827i
$487$	0.0580922	+	0.0422065i	0.00263241	+	0.00191256i	0.589101	−	0.808060i	$-0.299482\pi$
$487$	0.0580922	+	0.0422065i	0.00263241	+	0.00191256i	−0.586468	+	0.809972i	$0.699482\pi$
$488$	−9.20680	−	6.68913i	−0.416772	−	0.302803i
$489$	−3.49948	+	2.54252i	−0.158252	+	0.114977i
$490$	−15.0689			−0.680744
$491$	28.2983			1.27708			0.638542	−	0.769587i	$-0.279538\pi$
$491$	28.2983			1.27708			0.638542	+	0.769587i	$0.279538\pi$
$492$	1.11980	−	0.813585i	0.0504846	−	0.0366792i
$493$	1.55371	−	4.78184i	0.0699757	−	0.215363i
$494$	3.11003	+	9.57169i	0.139927	+	0.430651i
$495$	−28.5623			−1.28378
$496$	4.34466	+	14.3797i	0.195081	+	0.645667i
$497$	−1.44719			−0.0649152
$498$	−0.126091	−	0.388068i	−0.00565027	−	0.0173897i
$499$	7.54410	−	23.2184i	0.337720	−	1.03940i	−0.627646	−	0.778499i	$-0.715981\pi$
$499$	7.54410	−	23.2184i	0.337720	−	1.03940i	0.965366	−	0.260898i	$-0.0840186\pi$
$500$	5.08813	−	3.69674i	0.227548	−	0.165323i
$501$	−1.10602			−0.0494133
$502$	30.3735			1.35563
$503$	30.5047	−	22.1630i	1.36014	−	0.988197i	0.361701	−	0.932294i	$-0.382196\pi$
$503$	30.5047	−	22.1630i	1.36014	−	0.988197i	0.998436	−	0.0559030i	$-0.0178038\pi$
$504$	1.45772	+	1.05910i	0.0649321	+	0.0471759i
$505$	8.73589	+	6.34699i	0.388742	+	0.282438i
$506$	18.3790	+	56.5647i	0.817046	+	2.51461i
$507$	−2.09534	+	1.52235i	−0.0930571	+	0.0676099i
$508$	0.404131	+	1.24379i	0.0179304	+	0.0551841i
$509$	−8.63231	+	26.5675i	−0.382620	+	1.17758i	0.555571	+	0.831469i	$0.312500\pi$
$509$	−8.63231	+	26.5675i	−0.382620	+	1.17758i	−0.938192	+	0.346116i	$0.887500\pi$
$510$	0.419161	+	0.304539i	0.0185608	+	0.0134852i
$511$	−0.0122776	+	0.0377866i	−0.000543129	+	0.00167158i
$512$	7.48310	−	23.0306i	0.330709	−	1.01782i
$513$	6.44462	+	4.68229i	0.284537	+	0.206728i
$514$	−7.80139	+	24.0102i	−0.344104	+	1.05904i
$515$	−0.234971	−	0.723167i	−0.0103541	−	0.0318666i
$516$	−0.161900	+	0.117627i	−0.00712723	+	0.00517824i
$517$	−2.68061	−	8.25008i	−0.117893	−	0.362838i
$518$	2.06221	+	1.49828i	0.0906083	+	0.0658308i
$519$	−2.62839	−	1.90963i	−0.115373	−	0.0838237i
$520$	6.50579	−	4.72674i	0.285298	−	0.207281i
$521$	−17.7074			−0.775774			−0.387887	−	0.921707i	$-0.626795\pi$
$521$	−17.7074			−0.775774			−0.387887	+	0.921707i	$0.626795\pi$
$522$	18.0167			0.788568
$523$	3.89900	−	2.83279i	0.170491	−	0.123869i	−0.499267	−	0.866448i	$-0.666397\pi$
$523$	3.89900	−	2.83279i	0.170491	−	0.123869i	0.669759	+	0.742579i	$0.266397\pi$
$524$	1.01878	−	3.13548i	0.0445056	−	0.136974i
$525$	0.0271619	+	0.0835957i	0.00118544	+	0.00364842i
$526$	17.0412			0.743032
$527$	−5.56657	−	0.115474i	−0.242483	−	0.00503012i
$528$	−3.52456			−0.153387
$529$	17.6310	+	54.2625i	0.766563	+	2.35924i
$530$	3.82008	−	11.7570i	0.165934	−	0.510692i
$531$	−3.29764	+	2.39588i	−0.143106	+	0.103972i
$532$	0.578758			0.0250923
$533$	−16.5000			−0.714694
$534$	2.51324	−	1.82597i	0.108758	−	0.0790176i
$535$	−9.56984	−	6.95289i	−0.413740	−	0.300600i
$536$	5.90512	+	4.29032i	0.255063	+	0.185314i
$537$	1.14028	+	3.50942i	0.0492067	+	0.151443i
$538$	21.3459	−	15.5087i	0.920286	−	0.668627i
$539$	11.7411	+	36.1353i	0.505724	+	1.55646i
$540$	0.404158	−	1.24387i	0.0173922	−	0.0535277i
$541$	−9.16307	−	6.65736i	−0.393951	−	0.286222i	0.373122	−	0.927782i	$-0.378287\pi$
$541$	−9.16307	−	6.65736i	−0.393951	−	0.286222i	−0.767073	+	0.641560i	$0.778287\pi$
$542$	−11.9997	+	36.9312i	−0.515431	+	1.58633i
$543$	1.76188	−	5.42250i	0.0756094	−	0.232702i
$544$	2.30176	+	1.67233i	0.0986872	+	0.0717005i
$545$	9.78998	−	30.1305i	0.419357	−	1.29065i
$546$	0.0265419	+	0.0816874i	0.00113589	+	0.00349590i
$547$	−30.7609	+	22.3491i	−1.31524	+	0.955579i	−0.315263	+	0.949004i	$0.602093\pi$
$547$	−30.7609	+	22.3491i	−1.31524	+	0.955579i	−0.999978	+	0.00657462i	$0.997907\pi$
$548$	2.95018	+	9.07971i	0.126025	+	0.387866i
$549$	8.83892	+	6.42185i	0.377236	+	0.274078i
$550$	9.88820	+	7.18420i	0.421634	+	0.306335i
$551$	22.7847	−	16.5540i	0.970659	−	0.705225i
$552$	−6.56313			−0.279345
$553$	−2.79365			−0.118798
$554$	−12.9673	+	9.42127i	−0.550926	+	0.400271i
$555$	1.37786	−	4.24061i	0.0584869	−	0.180004i
$556$	−2.50949	−	7.72342i	−0.106426	−	0.327546i
$557$	−42.6565			−1.80741			−0.903707	−	0.428151i	$-0.859165\pi$
$557$	−42.6565			−1.80741			−0.903707	+	0.428151i	$0.859165\pi$
$558$	−5.77037	−	19.0984i	−0.244279	−	0.808500i
$559$	2.38555			0.100898
$560$	0.296114	+	0.911344i	0.0125131	+	0.0385113i
$561$	0.403691	−	1.24243i	0.0170439	−	0.0524556i
$562$	−25.6361	+	18.6257i	−1.08139	+	0.785678i
$563$	−26.8921			−1.13337			−0.566683	−	0.823936i	$-0.691773\pi$
$563$	−26.8921			−1.13337			−0.566683	+	0.823936i	$0.691773\pi$
$564$	0.196695			0.00828234
$565$	−7.43075	+	5.39876i	−0.312614	+	0.227128i
$566$	−26.2640	−	19.0819i	−1.10396	−	0.802072i
$567$	−1.37171	−	0.996606i	−0.0576064	−	0.0418535i
$568$	−6.86215	−	21.1195i	−0.287930	−	0.886156i
$569$	−21.6052	+	15.6971i	−0.905739	+	0.658058i	−0.939934	−	0.341358i	$-0.889113\pi$
$569$	−21.6052	+	15.6971i	−0.905739	+	0.658058i	0.0341949	+	0.999415i	$0.489113\pi$
$570$	0.896814	+	2.76011i	0.0375634	+	0.115608i
$571$	−3.20136	+	9.85277i	−0.133973	+	0.412326i	−0.995429	−	0.0955064i	$-0.969553\pi$
$571$	−3.20136	+	9.85277i	−0.133973	+	0.412326i	0.861456	+	0.507832i	$0.169553\pi$
$572$	−3.37064	−	2.44891i	−0.140934	−	0.102394i
$573$	−0.841282	+	2.58920i	−0.0351451	+	0.108165i
$574$	0.840537	−	2.58691i	0.0350833	−	0.107975i
$575$	13.3096	+	9.67002i	0.555050	+	0.403268i
$576$	−8.05727	+	24.7977i	−0.335719	+	1.03324i
$577$	11.2257	+	34.5492i	0.467333	+	1.43830i	0.856024	+	0.516936i	$0.172927\pi$
$577$	11.2257	+	34.5492i	0.467333	+	1.43830i	−0.388691	+	0.921368i	$0.627073\pi$
$578$	0.985128	−	0.715737i	0.0409759	−	0.0297708i
$579$	1.66180	+	5.11450i	0.0690621	+	0.212551i
$580$	−3.74086	−	2.71790i	−0.155331	−	0.112855i
$581$	0.226294	+	0.164412i	0.00938826	+	0.00682097i
$582$	1.50901	−	1.09636i	0.0625504	−	0.0454455i
$583$	−31.1698			−1.29092
$584$	−0.609656			−0.0252277
$585$	−6.24584	+	4.53787i	−0.258234	+	0.187618i
$586$	9.48208	−	29.1828i	0.391701	−	1.20553i
$587$	8.85084	+	27.2401i	0.365313	+	1.12432i	0.949785	+	0.312904i	$0.101302\pi$
$587$	8.85084	+	27.2401i	0.365313	+	1.12432i	−0.584471	+	0.811414i	$0.698698\pi$
$588$	−0.861522			−0.0355286
$589$	−24.8454	−	18.8508i	−1.02374	−	0.776732i
$590$	−2.99890			−0.123463
$591$	−0.888763	−	2.73533i	−0.0365588	−	0.112516i
$592$	−8.73684	+	26.8892i	−0.359082	+	1.10514i
$593$	32.1665	−	23.3703i	1.32092	−	0.959705i	0.321001	−	0.947079i	$-0.395981\pi$
$593$	32.1665	−	23.3703i	1.32092	−	0.959705i	0.999920	−	0.0126262i	$-0.00401915\pi$
$594$	9.45340			0.387878
$595$	−0.355171			−0.0145606
$596$	−6.74804	+	4.90274i	−0.276410	+	0.200824i
$597$	0.342540	+	0.248870i	0.0140192	+	0.0101856i
$598$	13.0058	+	9.44928i	0.531847	+	0.386410i
$599$	0.0942623	+	0.290110i	0.00385145	+	0.0118536i	0.952964	−	0.303084i	$-0.0980163\pi$
$599$	0.0942623	+	0.290110i	0.00385145	+	0.0118536i	−0.949112	+	0.314938i	$0.898016\pi$
$600$	−1.09116	+	0.792775i	−0.0445465	+	0.0323649i
$601$	−11.3033	−	34.7881i	−0.461072	−	1.41903i	−0.863856	−	0.503739i	$-0.831957\pi$
$601$	−11.3033	−	34.7881i	−0.461072	−	1.41903i	0.402784	−	0.915295i	$-0.368043\pi$
$602$	−0.121524	+	0.374011i	−0.00495294	+	0.0152436i
$603$	−5.66917	−	4.11889i	−0.230867	−	0.167734i
$604$	−1.42774	+	4.39413i	−0.0580939	+	0.178795i
$605$	−10.3295	+	31.7908i	−0.419953	+	1.29248i
$606$	−1.43175	−	1.04023i	−0.0581609	−	0.0422563i
$607$	7.87786	−	24.2456i	0.319752	−	0.984097i	−0.654002	−	0.756493i	$-0.726911\pi$
$607$	7.87786	−	24.2456i	0.319752	−	0.984097i	0.973754	−	0.227603i	$-0.0730890\pi$
$608$	4.92472	+	15.1567i	0.199724	+	0.614687i
$609$	0.194451	−	0.141277i	0.00787953	−	0.00572482i
$610$	2.48394	+	7.64477i	0.100572	+	0.309528i
$611$	−1.89693	−	1.37820i	−0.0767414	−	0.0557559i
$612$	−1.23141	−	0.894671i	−0.0497768	−	0.0361649i
$613$	−1.60620	+	1.16697i	−0.0648737	+	0.0471335i	−0.619749	−	0.784800i	$-0.712766\pi$
$613$	−1.60620	+	1.16697i	−0.0648737	+	0.0471335i	0.554876	+	0.831933i	$0.312766\pi$
$614$	−24.3606			−0.983112
$615$	−4.75797			−0.191860
$616$	2.70417	−	1.96470i	0.108954	−	0.0791598i
$617$	2.32028	−	7.14110i	0.0934111	−	0.287490i	−0.893425	−	0.449212i	$-0.851705\pi$
$617$	2.32028	−	7.14110i	0.0934111	−	0.287490i	0.986836	+	0.161722i	$0.0517048\pi$
$618$	0.0385101	+	0.118522i	0.00154910	+	0.00476765i
$619$	−25.3824			−1.02020			−0.510102	−	0.860114i	$-0.670392\pi$
$619$	−25.3824			−1.02020			−0.510102	+	0.860114i	$0.670392\pi$
$620$	−1.68296	+	4.83596i	−0.0675893	+	0.194217i
$621$	12.7244			0.510612
$622$	−1.08567	−	3.34135i	−0.0435315	−	0.133976i
$623$	−0.658071	+	2.02533i	−0.0263650	+	0.0811433i
$624$	−0.770732	+	0.559969i	−0.0308540	+	0.0224167i
$625$	−12.4255			−0.497022
$626$	−21.3458			−0.853149
$627$	5.91999	−	4.30113i	0.236422	−	0.171770i
$628$	8.61335	+	6.25797i	0.343710	+	0.249720i
$629$	−8.47796	−	6.15960i	−0.338039	−	0.245599i
$630$	−0.393284	−	1.21040i	−0.0156688	−	0.0482236i
$631$	33.6782	−	24.4686i	1.34071	−	0.974081i	0.341290	−	0.939958i	$-0.389136\pi$
$631$	33.6782	−	24.4686i	1.34071	−	0.974081i	0.999418	−	0.0341228i	$-0.0108637\pi$
$632$	−13.2467	−	40.7693i	−0.526927	−	1.62171i
$633$	0.418178	−	1.28702i	0.0166211	−	0.0511545i
$634$	16.4289	+	11.9363i	0.652476	+	0.474052i
$635$	1.38918	−	4.27547i	0.0551281	−	0.169667i
$636$	0.218402	−	0.672173i	0.00866021	−	0.0266534i
$637$	8.30852	+	6.03649i	0.329196	+	0.239175i
$638$	10.3280	−	31.7863i	0.408889	−	1.25843i
$639$	6.58796	+	20.2757i	0.260616	+	0.802093i
$640$	−7.33449	+	5.32882i	−0.289921	+	0.210640i
$641$	−14.8672	−	45.7566i	−0.587220	−	1.80728i	−0.590166	−	0.807282i	$-0.700938\pi$
$641$	−14.8672	−	45.7566i	−0.587220	−	1.80728i	0.00294610	−	0.999996i	$-0.499062\pi$
$642$	1.56843	+	1.13953i	0.0619009	+	0.0449736i
$643$	−23.8302	−	17.3137i	−0.939772	−	0.682784i	0.00859384	−	0.999963i	$-0.497264\pi$
$643$	−23.8302	−	17.3137i	−0.939772	−	0.682784i	−0.948366	+	0.317179i	$0.897264\pi$
$644$	0.747915	−	0.543392i	0.0294720	−	0.0214126i
$645$	0.687901			0.0270861
$646$	6.82074			0.268359
$647$	16.2427	−	11.8010i	0.638568	−	0.463947i	−0.220790	−	0.975321i	$-0.570864\pi$
$647$	16.2427	−	11.8010i	0.638568	−	0.463947i	0.859358	+	0.511375i	$0.170864\pi$
$648$	8.03972	−	24.7437i	0.315830	−	0.972025i
$649$	2.33662	+	7.19137i	0.0917203	+	0.282286i
$650$	3.30370			0.129582
$651$	−0.212038	−	0.160878i	−0.00831041	−	0.00630529i
$652$	9.34940			0.366151
$653$	9.08720	+	27.9675i	0.355610	+	1.09445i	0.955655	+	0.294488i	$0.0951490\pi$
$653$	9.08720	+	27.9675i	0.355610	+	1.09445i	−0.600046	+	0.799966i	$0.704851\pi$
$654$	−1.60451	+	4.93817i	−0.0627412	+	0.193098i
$655$	−9.16840	+	6.66123i	−0.358239	+	0.260276i
$656$	30.1697			1.17793
$657$	0.585296			0.0228346
$658$	0.312709	−	0.227197i	0.0121907	−	0.00885705i
$659$	14.5674	+	10.5838i	0.567465	+	0.412288i	0.834184	−	0.551487i	$-0.185939\pi$
$659$	14.5674	+	10.5838i	0.567465	+	0.412288i	−0.266718	+	0.963775i	$0.585939\pi$
$660$	−0.971965	−	0.706174i	−0.0378337	−	0.0274878i
$661$	−1.68569	−	5.18803i	−0.0655658	−	0.201791i	0.912907	−	0.408169i	$-0.133832\pi$
$661$	−1.68569	−	5.18803i	−0.0655658	−	0.201791i	−0.978472	+	0.206378i	$0.933832\pi$
$662$	9.96136	−	7.23735i	0.387159	−	0.281288i
$663$	−0.109116	−	0.335826i	−0.00423773	−	0.0130424i
$664$	−1.32633	+	4.08203i	−0.0514716	+	0.158413i
$665$	−1.60950	−	1.16937i	−0.0624139	−	0.0453464i
$666$	11.6038	−	35.7130i	0.449640	−	1.38385i
$667$	13.9016	−	42.7847i	0.538272	−	1.65663i
$668$	1.93400	+	1.40514i	0.0748289	+	0.0543664i
$669$	0.541622	−	1.66694i	0.0209403	−	0.0644477i
$670$	−1.59316	−	4.90325i	−0.0615493	−	0.189429i
$671$	16.3968	−	11.9130i	0.632991	−	0.459895i
$672$	0.0420289	+	0.129352i	0.00162130	+	0.00498985i
$673$	−18.2484	−	13.2582i	−0.703422	−	0.511066i	0.177623	−	0.984099i	$-0.443159\pi$
$673$	−18.2484	−	13.2582i	−0.703422	−	0.511066i	−0.881045	+	0.473032i	$0.843159\pi$
$674$	−0.167676	−	0.121823i	−0.00645862	−	0.00469246i
$675$	2.11551	−	1.53701i	0.0814260	−	0.0591595i
$676$	5.59800			0.215308
$677$	−23.4823			−0.902499			−0.451250	−	0.892398i	$-0.649022\pi$
$677$	−23.4823			−0.902499			−0.451250	+	0.892398i	$0.649022\pi$
$678$	1.21785	−	0.884818i	0.0467712	−	0.0339812i
$679$	−0.395121	+	1.21606i	−0.0151634	+	0.0466680i
$680$	−1.68412	−	5.18320i	−0.0645832	−	0.198767i
$681$	−2.11460			−0.0810315
$682$	−37.0026	−	0.767589i	−1.41690	−	0.0293925i
$683$	−9.42895			−0.360789			−0.180394	−	0.983594i	$-0.557737\pi$
$683$	−9.42895			−0.360789			−0.180394	+	0.983594i	$0.557737\pi$
$684$	−2.63466	−	8.10863i	−0.100739	−	0.310041i
$685$	10.1411	−	31.2111i	0.387472	−	1.19252i
$686$	−2.74718	+	1.99594i	−0.104888	+	0.0762055i
$687$	−1.62610			−0.0620396
$688$	−4.36189			−0.166296
$689$	−6.81604	+	4.95214i	−0.259670	+	0.188662i
$690$	3.75038	+	2.72481i	0.142775	+	0.103732i
$691$	14.9873	+	10.8889i	0.570143	+	0.414233i	0.835157	−	0.550011i	$-0.185377\pi$
$691$	14.9873	+	10.8889i	0.570143	+	0.414233i	−0.265014	+	0.964245i	$0.585377\pi$
$692$	2.16996	+	6.67844i	0.0824894	+	0.253876i
$693$	−2.59612	+	1.88619i	−0.0986184	+	0.0716505i
$694$	−5.81165	−	17.8864i	−0.220607	−	0.678959i
$695$	−8.62627	+	26.5489i	−0.327213	+	1.00706i
$696$	2.98375	+	2.16782i	0.113099	+	0.0821712i
$697$	−3.45554	+	10.6350i	−0.130888	+	0.402831i
$698$	−2.38448	+	7.33868i	−0.0902540	+	0.277773i
$699$	3.70012	+	2.68829i	0.139951	+	0.101681i
$700$	0.0587080	−	0.180685i	0.00221895	−	0.00682924i
$701$	−2.78210	−	8.56241i	−0.105078	−	0.323398i	0.884671	−	0.466217i	$-0.154383\pi$
$701$	−2.78210	−	8.56241i	−0.105078	−	0.323398i	−0.989749	+	0.142819i	$0.954383\pi$
$702$	2.06722	−	1.50192i	0.0780221	−	0.0566864i
$703$	−18.1390	−	55.8260i	−0.684124	−	2.10552i
$704$	39.1311	+	28.4304i	1.47481	+	1.07151i
$705$	−0.547001	−	0.397419i	−0.0206012	−	0.0149677i
$706$	1.85267	−	1.34604i	0.0697262	−	0.0506590i
$707$	1.21318			0.0456262
$708$	−0.171453			−0.00644362
$709$	−6.79383	+	4.93601i	−0.255148	+	0.185376i	−0.708005	−	0.706207i	$-0.750405\pi$
$709$	−6.79383	+	4.93601i	−0.255148	+	0.185376i	0.452857	+	0.891583i	$0.350405\pi$
$710$	−4.84694	+	14.9173i	−0.181902	+	0.559838i
$711$	12.7174	+	39.1402i	0.476941	+	1.46787i
$712$	−32.6771			−1.22463
$713$	−49.8060	−	1.03318i	−1.86525	−	0.0386930i
$714$	0.0582101			0.00217846
$715$	4.42563	+	13.6207i	0.165509	+	0.509385i
$716$	2.46461	−	7.58529i	0.0921069	−	0.283476i
$717$	−0.562336	+	0.408561i	−0.0210008	+	0.0152580i
$718$	−24.5063			−0.914568
$719$	46.9970			1.75269			0.876345	−	0.481683i	$-0.159974\pi$
$719$	46.9970			1.75269			0.876345	+	0.481683i	$0.159974\pi$
$720$	11.4203	−	8.29734i	0.425610	−	0.309224i
$721$	−0.0691138	−	0.0502141i	−0.00257393	−	0.00187007i
$722$	12.1916	+	8.85774i	0.453725	+	0.329651i
$723$	−1.11212	−	3.42276i	−0.0413603	−	0.127294i
$724$	−9.96985	+	7.24352i	−0.370526	+	0.269203i
$725$	−2.85684	−	8.79244i	−0.106100	−	0.326543i
$726$	1.69293	−	5.21029i	0.0628304	−	0.193372i
$727$	−21.7076	−	15.7715i	−0.805092	−	0.584933i	0.107312	−	0.994225i	$-0.465776\pi$
$727$	−21.7076	−	15.7715i	−0.805092	−	0.584933i	−0.912403	+	0.409292i	$0.865776\pi$
$728$	0.279190	−	0.859258i	0.0103475	−	0.0318462i
$729$	−7.40297	+	22.7840i	−0.274184	+	0.843852i
$730$	0.348377	+	0.253111i	0.0128940	+	0.00936804i
$731$	0.499597	−	1.53760i	0.0184783	−	0.0568702i
$732$	0.142012	+	0.437067i	0.00524891	+	0.0161545i
$733$	8.33003	−	6.05212i	0.307677	−	0.223540i	−0.423222	−	0.906026i	$-0.639101\pi$
$733$	8.33003	−	6.05212i	0.307677	−	0.223540i	0.730899	+	0.682486i	$0.239101\pi$
$734$	7.77826	+	23.9390i	0.287101	+	0.883605i
$735$	2.39586	+	1.74069i	0.0883726	+	0.0642065i
$736$	20.5947	+	14.9629i	0.759129	+	0.551539i
$737$	−10.5167	+	7.64082i	−0.387387	+	0.281453i
$738$	−40.0700			−1.47500
$739$	11.7142			0.430912			0.215456	−	0.976514i	$-0.430876\pi$
$739$	11.7142			0.430912			0.215456	+	0.976514i	$0.430876\pi$
$740$	−7.79682	+	5.66472i	−0.286617	+	0.208239i
$741$	0.611204	−	1.88109i	0.0224532	−	0.0691037i
$742$	−0.429188	−	1.32090i	−0.0157560	−	0.0484919i
$743$	39.0027			1.43087			0.715434	−	0.698680i	$-0.246229\pi$
$743$	39.0027			1.43087			0.715434	+	0.698680i	$0.246229\pi$
$744$	1.34235	−	3.85721i	0.0492128	−	0.141412i
$745$	28.6720			1.05046
$746$	6.43148	+	19.7941i	0.235473	+	0.724712i
$747$	1.27333	−	3.91892i	0.0465889	−	0.143386i
$748$	−2.28435	+	1.65967i	−0.0835240	+	0.0606837i
$749$	−1.32899			−0.0485602
$750$	3.54322			0.129380
$751$	8.28352	−	6.01833i	0.302270	−	0.219612i	−0.426303	−	0.904581i	$-0.640184\pi$
$751$	8.28352	−	6.01833i	0.302270	−	0.219612i	0.728573	+	0.684969i	$0.240184\pi$
$752$	3.46847	+	2.51999i	0.126482	+	0.0918945i
$753$	−4.82918	−	3.50861i	−0.175985	−	0.127861i
$754$	−2.79162	−	8.59173i	−0.101665	−	0.312892i
$755$	12.8488	−	9.33518i	0.467615	−	0.339742i
$756$	−0.0454073	−	0.139749i	−0.00165145	−	0.00508263i
$757$	13.0225	−	40.0791i	0.473311	−	1.45670i	−0.374911	−	0.927061i	$-0.622327\pi$
$757$	13.0225	−	40.0791i	0.473311	−	1.45670i	0.848222	−	0.529641i	$-0.177673\pi$
$758$	−26.1940	−	19.0311i	−0.951409	−	0.691239i
$759$	3.61196	−	11.1165i	0.131106	−	0.403503i
$760$	9.43346	−	29.0332i	0.342187	−	1.05314i
$761$	29.2235	+	21.2321i	1.05935	+	0.769662i	0.973968	−	0.226686i	$-0.0727891\pi$
$761$	29.2235	+	21.2321i	1.05935	+	0.769662i	0.0853814	+	0.996348i	$0.472789\pi$
$762$	−0.227677	+	0.700719i	−0.00824788	+	0.0253844i
$763$	−1.09991	−	3.38517i	−0.0398193	−	0.122551i
$764$	4.76052	−	3.45872i	0.172229	−	0.125132i
$765$	1.61683	+	4.97610i	0.0584567	+	0.179911i
$766$	5.47786	+	3.97990i	0.197923	+	0.143800i
$767$	1.65350	+	1.20134i	0.0597043	+	0.0433777i
$768$	−2.22876	+	1.61929i	−0.0804234	+	0.0584310i
$769$	29.8738			1.07728			0.538638	−	0.842537i	$-0.318939\pi$
$769$	29.8738			1.07728			0.538638	+	0.842537i	$0.318939\pi$
$770$	−2.36093			−0.0850820
$771$	4.01392	−	2.91629i	0.144558	−	0.105027i
$772$	3.59184	−	11.0545i	0.129273	−	0.397862i
$773$	−1.55429	−	4.78360i	−0.0559038	−	0.172054i	0.919206	−	0.393777i	$-0.128832\pi$
$773$	−1.55429	−	4.78360i	−0.0559038	−	0.172054i	−0.975110	+	0.221723i	$0.928832\pi$
$774$	5.79326			0.208234
$775$	−8.40536	+	5.84440i	−0.301929	+	0.209937i
$776$	−19.6201			−0.704322
$777$	−0.154803	−	0.476435i	−0.00555353	−	0.0170920i
$778$	−1.29413	+	3.98291i	−0.0463967	+	0.142794i
$779$	−50.6743	+	36.8170i	−1.81559	+	1.31911i
$780$	−0.324738			−0.0116275
$781$	39.5483			1.41515
$782$	8.81428	−	6.40395i	0.315198	−	0.229005i
$783$	−5.78481	−	4.20291i	−0.206732	−	0.150200i
$784$	−15.1919	−	11.0375i	−0.542566	−	0.394198i
$785$	−11.3093	−	34.8063i	−0.403645	−	1.24229i
$786$	1.50264	−	1.09173i	0.0535972	−	0.0389407i
$787$	5.62690	+	17.3178i	0.200577	+	0.617313i	0.999866	+	0.0163662i	$0.00520975\pi$
$787$	5.62690	+	17.3178i	0.200577	+	0.617313i	−0.799289	+	0.600947i	$0.794790\pi$
$788$	−1.92098	+	5.91217i	−0.0684321	+	0.210612i
$789$	−2.70944	−	1.96852i	−0.0964587	−	0.0700813i
$790$	−9.35655	+	28.7965i	−0.332891	+	1.02453i
$791$	−0.318884	+	0.981423i	−0.0113382	+	0.0348954i
$792$	−39.8363	−	28.9427i	−1.41552	−	1.02844i
$793$	1.69287	−	5.21012i	0.0601156	−	0.185017i
$794$	5.25764	+	16.1814i	0.186587	+	0.574255i
$795$	−1.96549	+	1.42801i	−0.0697086	+	0.0506463i
$796$	−0.282796	−	0.870357i	−0.0100234	−	0.0308490i
$797$	−3.39850	−	2.46915i	−0.120381	−	0.0874618i	0.525966	−	0.850506i	$-0.323704\pi$
$797$	−3.39850	−	2.46915i	−0.120381	−	0.0874618i	−0.646347	+	0.763044i	$0.723704\pi$
$798$	0.263786	+	0.191652i	0.00933794	+	0.00678441i
$799$	−1.28558	+	0.934029i	−0.0454806	+	0.0330436i
$800$	5.23139			0.184958
$801$	31.3715			1.10846
$802$	16.3310	−	11.8652i	0.576668	−	0.418974i
$803$	0.335519	−	1.03262i	0.0118402	−	0.0364404i
$804$	−0.0910845	−	0.280329i	−0.00321230	−	0.00988646i
$805$	−3.17784			−0.112004
$806$	−8.21349	+	5.71099i	−0.289308	+	0.201161i
$807$	−5.18535			−0.182533
$808$	5.75255	+	17.7045i	0.202374	+	0.622843i
$809$	3.68437	−	11.3393i	0.129535	−	0.398669i	−0.865165	−	0.501488i	$-0.832786\pi$
$809$	3.68437	−	11.3393i	0.129535	−	0.398669i	0.994700	+	0.102819i	$0.0327862\pi$
$810$	−14.8670	+	10.8015i	−0.522373	+	0.379526i
$811$	−1.88461			−0.0661775			−0.0330888	−	0.999452i	$-0.510534\pi$
$811$	−1.88461			−0.0661775			−0.0330888	+	0.999452i	$0.510534\pi$
$812$	−0.519504			−0.0182310
$813$	6.17400	−	4.48568i	0.216532	−	0.157320i
$814$	−56.3555	−	40.9447i	−1.97526	−	1.43511i
$815$	−26.0003	−	18.8903i	−0.910752	−	0.661700i
$816$	0.199516	+	0.614046i	0.00698445	+	0.0214959i
$817$	7.32641	−	5.32295i	0.256319	−	0.186226i
$818$	3.06878	+	9.44475i	0.107298	+	0.330228i
$819$	−0.268034	+	0.824924i	−0.00936587	+	0.0288252i
$820$	8.31988	+	6.04474i	0.290543	+	0.211092i
$821$	−2.25465	+	6.93910i	−0.0786878	+	0.242176i	−0.982660	−	0.185414i	$-0.940637\pi$
$821$	−2.25465	+	6.93910i	−0.0786878	+	0.242176i	0.903973	+	0.427590i	$0.140637\pi$
$822$	−1.66206	+	5.11528i	−0.0579709	+	0.178416i
$823$	4.35320	+	3.16279i	0.151743	+	0.110248i	0.661066	−	0.750328i	$-0.270104\pi$
$823$	4.35320	+	3.16279i	0.151743	+	0.110248i	−0.509323	+	0.860575i	$0.670104\pi$
$824$	0.405082	−	1.24671i	0.0141117	−	0.0434314i
$825$	−0.742273	−	2.28448i	−0.0258426	−	0.0795355i
$826$	−0.272580	+	0.198041i	−0.00948428	+	0.00689073i
$827$	0.825976	+	2.54209i	0.0287220	+	0.0883972i	0.964390	−	0.264485i	$-0.0852018\pi$
$827$	0.825976	+	2.54209i	0.0287220	+	0.0883972i	−0.935668	+	0.352882i	$0.885202\pi$
$828$	−11.0178	−	8.00493i	−0.382897	−	0.278191i
$829$	8.10596	+	5.88933i	0.281532	+	0.204545i	0.719585	−	0.694404i	$-0.244332\pi$
$829$	8.10596	+	5.88933i	0.281532	+	0.204545i	−0.438054	+	0.898949i	$0.644332\pi$
$830$	2.45264	−	1.78195i	0.0851324	−	0.0618523i
$831$	3.15001			0.109273
$832$	13.0739			0.453256
$833$	5.63084	−	4.09104i	0.195097	−	0.141746i
$834$	1.41378	−	4.35118i	0.0489553	−	0.150669i
$835$	−2.53933	−	7.81526i	−0.0878773	−	0.270458i
$836$	−15.8161			−0.547013
$837$	−2.60250	+	7.47824i	−0.0899555	+	0.258486i
$838$	−18.5486			−0.640752
$839$	3.66837	+	11.2901i	0.126646	+	0.389777i	0.994197	−	0.107571i	$-0.0343073\pi$
$839$	3.66837	+	11.2901i	0.126646	+	0.389777i	−0.867551	+	0.497348i	$0.834307\pi$
$840$	0.0805077	−	0.247777i	0.00277778	−	0.00854913i
$841$	3.00955	−	2.18657i	0.103778	−	0.0753989i
$842$	−4.54448			−0.156613
$843$	6.22753			0.214488
$844$	−2.36632	+	1.71923i	−0.0814522	+	0.0591785i
$845$	−15.5678	−	11.3107i	−0.535550	−	0.389100i
$846$	−4.60665	−	3.34693i	−0.158380	−	0.115070i
$847$	1.16052	+	3.57171i	0.0398759	+	0.122725i
$848$	12.4629	−	9.05483i	0.427978	−	0.310944i
$849$	1.97155	+	6.06780i	0.0676633	+	0.208246i
$850$	0.691882	−	2.12939i	0.0237314	−	0.0730376i
$851$	−75.8552	−	55.1121i	−2.60028	−	1.88922i
$852$	−0.277109	+	0.852855i	−0.00949361	+	0.0292183i
$853$	−1.42040	+	4.37153i	−0.0486335	+	0.149678i	−0.972424	−	0.233220i	$-0.925074\pi$
$853$	−1.42040	+	4.37153i	−0.0486335	+	0.149678i	0.923791	+	0.382898i	$0.125074\pi$
$854$	0.730617	+	0.530825i	0.0250012	+	0.0181644i
$855$	−9.05652	+	27.8731i	−0.309726	+	0.953240i
$856$	−6.30170	−	19.3946i	−0.215388	−	0.662895i
$857$	−12.4143	+	9.01949i	−0.424063	+	0.308100i	−0.779271	−	0.626688i	$-0.784410\pi$
$857$	−12.4143	+	9.01949i	−0.424063	+	0.308100i	0.355208	+	0.934787i	$0.384410\pi$
$858$	−0.725329	−	2.23233i	−0.0247623	−	0.0762106i
$859$	−42.6265	−	30.9700i	−1.45440	−	1.05668i	−0.984779	−	0.173814i	$-0.944391\pi$
$859$	−42.6265	−	30.9700i	−1.45440	−	1.05668i	−0.469620	−	0.882869i	$-0.655609\pi$
$860$	−1.20288	−	0.873940i	−0.0410177	−	0.0298011i
$861$	−0.432468	+	0.314206i	−0.0147385	+	0.0107081i
$862$	21.9046			0.746073
$863$	−52.3577			−1.78228			−0.891139	−	0.453731i	$-0.850093\pi$
$863$	−52.3577			−1.78228			−0.891139	+	0.453731i	$0.850093\pi$
$864$	3.27343	−	2.37829i	0.111364	−	0.0809110i
$865$	7.45914	−	22.9569i	0.253618	−	0.780557i
$866$	−6.32621	−	19.4701i	−0.214973	−	0.661620i
$867$	−0.239308			−0.00812732
$868$	0.166387	+	0.550696i	0.00564753	+	0.0186918i
$869$	76.3443			2.58980
$870$	−0.804997	−	2.47753i	−0.0272920	−	0.0839960i
$871$	−1.08579	+	3.34171i	−0.0367905	+	0.113229i
$872$	44.1861	−	32.1031i	1.49633	−	1.08715i
$873$	18.8362			0.637508
$874$	61.0275			2.06429
$875$	−1.96503	+	1.42768i	−0.0664303	+	0.0482644i
$876$	0.0199174	+	0.0144709i	0.000672948	+	0.000488925i
$877$	9.38770	+	6.82056i	0.317000	+	0.230314i	0.734894	−	0.678182i	$-0.237232\pi$
$877$	9.38770	+	6.82056i	0.317000	+	0.230314i	−0.417894	+	0.908496i	$0.637232\pi$
$878$	−8.73781	−	26.8922i	−0.294887	−	0.907568i
$879$	−4.87866	+	3.54455i	−0.164553	+	0.119555i
$880$	−8.09212	−	24.9050i	−0.272785	−	0.839547i
$881$	0.157970	−	0.486180i	0.00532213	−	0.0163798i	−0.948360	−	0.317195i	$-0.897259\pi$
$881$	0.157970	−	0.486180i	0.00532213	−	0.0163798i	0.953682	+	0.300816i	$0.0972589\pi$
$882$	20.1771	+	14.6595i	0.679398	+	0.493612i
$883$	−4.53642	+	13.9617i	−0.152663	+	0.469848i	−0.997917	−	0.0645173i	$-0.979449\pi$
$883$	−4.53642	+	13.9617i	−0.152663	+	0.469848i	0.845254	+	0.534365i	$0.179449\pi$
$884$	−0.235845	+	0.725857i	−0.00793234	+	0.0244132i
$885$	0.476806	+	0.346420i	0.0160277	+	0.0116448i
$886$	−2.91561	+	8.97331i	−0.0979517	+	0.301464i
$887$	−8.98206	−	27.6439i	−0.301588	−	0.928192i	−0.980928	−	0.194369i	$-0.937734\pi$
$887$	−8.98206	−	27.6439i	−0.301588	−	0.928192i	0.679341	−	0.733823i	$-0.262266\pi$
$888$	6.21883	−	4.51824i	0.208690	−	0.151622i
$889$	−0.156075	−	0.480351i	−0.00523460	−	0.0161104i
$890$	18.6728	+	13.5666i	0.625912	+	0.454752i
$891$	37.4857	+	27.2350i	1.25582	+	0.912406i
$892$	−3.06485	+	2.22674i	−0.102619	+	0.0745568i
$893$	−8.90099			−0.297860
$894$	−4.69913			−0.157162
$895$	−22.1800	+	16.1147i	−0.741395	+	0.538655i
$896$	−0.314752	+	0.968708i	−0.0105151	+	0.0323623i
$897$	−0.976302	−	3.00475i	−0.0325978	−	0.100326i
$898$	6.28241			0.209647
$899$	22.3017	+	16.9208i	0.743804	+	0.564340i
$900$	−2.79872			−0.0932907
$901$	1.76444	+	5.43038i	0.0587819	+	0.180912i
$902$	−22.9700	+	70.6943i	−0.764817	+	2.35386i
$903$	0.0625256	−	0.0454275i	0.00208072	−	0.00151173i
$904$	−15.8345			−0.526647
$905$	42.3612			1.40813
$906$	−2.10582	+	1.52997i	−0.0699613	+	0.0508298i
$907$	16.4368	+	11.9420i	0.545774	+	0.396528i	0.826225	−	0.563340i	$-0.190484\pi$
$907$	16.4368	+	11.9420i	0.545774	+	0.396528i	−0.280451	+	0.959868i	$0.590484\pi$
$908$	3.69762	+	2.68648i	0.122710	+	0.0891539i
$909$	−5.52269	−	16.9971i	−0.183176	−	0.563758i
$910$	−0.516276	+	0.375096i	−0.0171144	+	0.0124343i
$911$	9.03153	+	27.7962i	0.299228	+	0.920929i	0.981768	+	0.190081i	$0.0608751\pi$
$911$	9.03153	+	27.7962i	0.299228	+	0.920929i	−0.682540	+	0.730848i	$0.739125\pi$
$912$	−1.11757	+	3.43952i	−0.0370064	+	0.113894i
$913$	−6.18411	−	4.49302i	−0.204664	−	0.148697i
$914$	9.06611	−	27.9026i	0.299880	−	0.922936i
$915$	0.488160	−	1.50240i	0.0161381	−	0.0496679i
$916$	2.84343	+	2.06587i	0.0939496	+	0.0682584i
$917$	−0.393453	+	1.21092i	−0.0129930	+	0.0399882i
$918$	−0.535131	−	1.64696i	−0.0176620	−	0.0543579i
$919$	−24.7421	+	17.9762i	−0.816166	+	0.592979i	−0.915612	−	0.402064i	$-0.868293\pi$
$919$	−24.7421	+	17.9762i	−0.816166	+	0.592979i	0.0994455	+	0.995043i	$0.468293\pi$
$920$	−15.0684	−	46.3759i	−0.496792	−	1.52897i
$921$	3.87317	+	2.81402i	0.127625	+	0.0927252i
$922$	−19.6408	−	14.2699i	−0.646837	−	0.469954i
$923$	8.64821	−	6.28329i	0.284659	−	0.206817i
$924$	−0.134979			−0.00444049
$925$	−19.2685			−0.633545
$926$	12.4102	−	9.01651i	0.407823	−	0.296301i
$927$	−0.388896	+	1.19690i	−0.0127730	+	0.0393113i
$928$	−4.42052	−	13.6050i	−0.145111	−	0.446605i
$929$	12.1310			0.398006			0.199003	−	0.979999i	$-0.436230\pi$
$929$	12.1310			0.398006			0.199003	+	0.979999i	$0.436230\pi$
$930$	−2.36846	+	1.64683i	−0.0776647	+	0.0540018i
$931$	38.9863			1.27772
$932$	−3.05476	−	9.40159i	−0.100062	−	0.307959i
$933$	−0.213364	+	0.656666i	−0.00698521	+	0.0214983i
$934$	1.71014	−	1.24249i	0.0559573	−	0.0406554i
$935$	9.70603			0.317421
$936$	−13.3095			−0.435034
$937$	13.8325	−	10.0499i	0.451887	−	0.328315i	−0.338453	−	0.940983i	$-0.609904\pi$
$937$	13.8325	−	10.0499i	0.451887	−	0.328315i	0.790340	+	0.612668i	$0.209904\pi$
$938$	−0.468609	−	0.340464i	−0.0153006	−	0.0111165i
$939$	3.39384	+	2.46577i	0.110754	+	0.0804674i
$940$	0.451596	+	1.38987i	0.0147294	+	0.0453326i
$941$	−43.7488	+	31.7854i	−1.42617	+	1.03617i	−0.435458	+	0.900209i	$0.643413\pi$
$941$	−43.7488	+	31.7854i	−1.42617	+	1.03617i	−0.990714	+	0.135965i	$0.956587\pi$
$942$	1.85351	+	5.70451i	0.0603906	+	0.185863i
$943$	−30.9179	+	95.1555i	−1.00682	+	3.09869i
$944$	−3.02337	−	2.19660i	−0.0984022	−	0.0714934i
$945$	−0.156086	+	0.480383i	−0.00507747	+	0.0156269i
$946$	3.32097	−	10.2209i	0.107974	−	0.332310i
$947$	−3.76957	−	2.73875i	−0.122495	−	0.0889975i	0.524851	−	0.851194i	$-0.324121\pi$
$947$	−3.76957	−	2.73875i	−0.122495	−	0.0889975i	−0.647346	+	0.762197i	$0.724121\pi$
$948$	−0.534933	+	1.64636i	−0.0173738	+	0.0534711i
$949$	−0.0906897	−	0.279114i	−0.00294391	−	0.00906043i
$950$	10.1462	−	7.37165i	0.329186	−	0.239168i
$951$	−1.23326	−	3.79559i	−0.0399913	−	0.123081i
$952$	−0.495364	−	0.359903i	−0.0160548	−	0.0116645i
$953$	−13.2486	−	9.62568i	−0.429164	−	0.311806i	0.352150	−	0.935943i	$-0.385451\pi$
$953$	−13.2486	−	9.62568i	−0.429164	−	0.311806i	−0.781315	+	0.624137i	$0.785451\pi$
$954$	−16.5526	+	12.0262i	−0.535911	+	0.389362i
$955$	−20.2271			−0.654534
$956$	1.50237			0.0485900
$957$	−5.31389	+	3.86077i	−0.171774	+	0.124801i
$958$	15.6628	−	48.2053i	0.506044	−	1.55744i
$959$	−1.13936	−	3.50658i	−0.0367918	−	0.113234i
$960$	3.77002			0.121677
$961$	10.7940	−	29.0601i	0.348192	−	0.937423i
$962$	−18.8287			−0.607061
$963$	6.04990	+	18.6197i	0.194955	+	0.600011i
$964$	−2.40375	+	7.39799i	−0.0774196	+	0.238273i
$965$	−32.3243	+	23.4850i	−1.04056	+	0.756009i
$966$	0.520826			0.0167573
$967$	57.6946			1.85533			0.927667	−	0.373409i	$-0.121811\pi$
$967$	57.6946			1.85533			0.927667	+	0.373409i	$0.121811\pi$
$968$	−46.6210	+	33.8721i	−1.49846	+	1.08869i
$969$	−1.08445	−	0.787902i	−0.0348377	−	0.0253111i
$970$	11.2116	+	8.14568i	0.359982	+	0.261542i
$971$	12.0699	+	37.1472i	0.387340	+	1.19211i	0.934768	+	0.355258i	$0.115607\pi$
$971$	12.0699	+	37.1472i	0.387340	+	1.19211i	−0.547428	+	0.836853i	$0.684393\pi$
$972$	−2.63530	+	1.91466i	−0.0845272	+	0.0614126i
$973$	0.969165	+	2.98278i	0.0310700	+	0.0956236i
$974$	0.0270195	−	0.0831575i	0.000865761	−	0.00266454i
$975$	−0.525267	−	0.381628i	−0.0168220	−	0.0122219i
$976$	−3.09536	+	9.52654i	−0.0990801	+	0.304937i
$977$	8.72001	−	26.8374i	0.278978	−	0.858605i	−0.709162	−	0.705046i	$-0.750926\pi$
$977$	8.72001	−	26.8374i	0.278978	−	0.858605i	0.988139	−	0.153559i	$-0.0490736\pi$
$978$	4.26127	+	3.09599i	0.136260	+	0.0989990i
$979$	17.9836	−	55.3478i	0.574758	−	1.76892i
$980$	−1.97799	−	6.08762i	−0.0631845	−	0.194462i
$981$	−42.4205	+	30.8203i	−1.35438	+	0.984017i
$982$	−10.6482	−	32.7719i	−0.339799	−	1.04579i
$983$	4.66913	+	3.39232i	0.148922	+	0.108198i	0.659751	−	0.751484i	$-0.270662\pi$
$983$	4.66913	+	3.39232i	0.148922	+	0.108198i	−0.510829	+	0.859682i	$0.670662\pi$
$984$	−6.63602	−	4.82135i	−0.211549	−	0.153699i
$985$	17.2877	−	12.5602i	0.550831	−	0.400202i
$986$	−6.12243			−0.194978
$987$	−0.0759635			−0.00241794
$988$	−3.45859	+	2.51281i	−0.110032	+	0.0799432i
$989$	4.47006	−	13.7574i	0.142140	−	0.437461i
$990$	10.7476	+	33.0776i	0.341580	+	1.05127i
$991$	−6.30092			−0.200155			−0.100078	−	0.994980i	$-0.531909\pi$
$991$	−6.30092			−0.200155			−0.100078	+	0.994980i	$0.531909\pi$
$992$	−13.0060	+	9.04333i	−0.412942	+	0.287126i
$993$	−2.41982			−0.0767906
$994$	0.544555	+	1.67597i	0.0172722	+	0.0531585i
$995$	−0.972100	+	2.99182i	−0.0308176	+	0.0948469i
$996$	0.140223	−	0.101878i	0.00444312	−	0.00322812i
$997$	28.6119			0.906147			0.453073	−	0.891473i	$-0.350328\pi$
$997$	28.6119			0.906147			0.453073	+	0.891473i	$0.350328\pi$
$998$	−29.7276			−0.941012
$999$	−12.0569	+	8.75983i	−0.381462	+	0.277149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.8	✓	96
31.8	even	5	inner	527.2.h.c.256.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.8	✓	96	1.1	even	1	trivial
527.2.h.c.256.8	yes	96	31.8	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:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +O(q^{10})\)	\(q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +(0.669036 + 2.05908i) q^{10} +(4.41639 - 3.20870i) q^{11} +(0.0382502 + 0.117722i) q^{12} +(0.455967 - 1.40332i) q^{13} +(0.196788 + 0.142975i) q^{14} +(0.131483 - 0.404664i) q^{15} +(-0.833720 + 2.56593i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.10731 - 3.40794i) q^{18} +(-1.73093 - 5.32725i) q^{19} +(-0.744018 + 0.540561i) q^{20} +(-0.0147722 - 0.0454642i) q^{21} +(-5.37778 - 3.90718i) q^{22} +(-7.23855 - 5.25912i) q^{23} +(0.593437 - 0.431157i) q^{24} -1.83872 q^{25} -1.79674 q^{26} +(-1.15054 + 0.835914i) q^{27} +(-0.0319288 + 0.0982668i) q^{28} +(1.55371 + 4.78184i) q^{29} -0.518112 q^{30} +(4.57132 - 3.17853i) q^{31} -2.84513 q^{32} +(0.403691 + 1.24243i) q^{33} +(-0.376285 + 1.15809i) q^{34} +(0.287340 - 0.208765i) q^{35} +1.52211 q^{36} +10.4793 q^{37} +(-5.51810 + 4.00913i) q^{38} +(0.285670 + 0.207552i) q^{39} +(4.40910 + 3.20340i) q^{40} +(-3.45554 - 10.6350i) q^{41} +(-0.0470929 + 0.0342150i) q^{42} +(0.499597 + 1.53760i) q^{43} +(0.872542 - 2.68541i) q^{44} +(-4.23292 - 3.07540i) q^{45} +(-3.36676 + 10.3618i) q^{46} +(0.491048 - 1.51129i) q^{47} +(-0.522339 - 0.379501i) q^{48} +(-2.15079 + 6.61944i) q^{49} +(0.691882 + 2.12939i) q^{50} +(0.193604 - 0.140662i) q^{51} +(-0.235845 - 0.725857i) q^{52} +(-4.61935 - 3.35616i) q^{53} +(1.40099 + 1.01788i) q^{54} +(-7.85235 + 5.70506i) q^{55} +0.612303 q^{56} +1.34046 q^{57} +(4.95315 - 3.59867i) q^{58} +(-0.428033 + 1.31735i) q^{59} +(-0.0680088 - 0.209310i) q^{60} +3.71271 q^{61} +(-5.40113 - 4.09796i) q^{62} -0.587837 q^{63} +(2.73802 + 8.42677i) q^{64} +(-0.810709 + 2.49511i) q^{65} +(1.28694 - 0.935019i) q^{66} -2.38128 q^{67} -0.517242 q^{68} +(1.73224 - 1.25855i) q^{69} +(-0.349889 - 0.254210i) q^{70} +(5.86105 + 4.25830i) q^{71} +(-2.78736 - 8.57861i) q^{72} +(0.160910 - 0.116908i) q^{73} +(-3.94322 - 12.1360i) q^{74} +(0.135973 - 0.418483i) q^{75} +(-2.34395 - 1.70298i) q^{76} +(-0.336976 + 1.03710i) q^{77} +(0.132869 - 0.408930i) q^{78} +(11.3142 + 8.22025i) q^{79} +(1.48235 - 4.56222i) q^{80} +(2.62289 + 8.07244i) q^{81} +(-11.0161 + 8.00363i) q^{82} +(-0.432705 - 1.33173i) q^{83} +(-0.0200039 - 0.0145337i) q^{84} +(1.43843 + 1.04508i) q^{85} +(1.59269 - 1.15715i) q^{86} -1.20322 q^{87} -16.7329 q^{88} +(8.62465 - 6.26618i) q^{89} +(-1.96879 + 6.05932i) q^{90} +(0.0910834 + 0.280326i) q^{91} -4.62795 q^{92} +(0.385367 + 1.27546i) q^{93} -1.93498 q^{94} +(3.07759 + 9.47185i) q^{95} +(0.210398 - 0.647539i) q^{96} +(5.17845 - 3.76236i) q^{97} +8.47521 q^{98} +16.0643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more