LMFDB - Embedded newform 414.2.e.c.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.1481180578947.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 6x^{8} - 11x^{7} + 22x^{6} - 45x^{5} + 66x^{4} - 99x^{3} + 162x^{2} - 162x + 243 $ x^10 - 2x^9 + 6x^8 - 11x^7 + 22x^6 - 45x^5 + 66x^4 - 99x^3 + 162x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.3
Root			$1.64906 + 0.529718i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.c.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.365780 - 1.69299i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.231157 + 0.400376i) q^{5} +(1.28328 + 1.16327i) q^{6} +(0.165447 - 0.286563i) q^{7} +1.00000 q^{8} +(-2.73241 - 1.23852i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.365780 - 1.69299i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.231157 + 0.400376i) q^{5} +(1.28328 + 1.16327i) q^{6} +(0.165447 - 0.286563i) q^{7} +1.00000 q^{8} +(-2.73241 - 1.23852i) q^{9} -0.462315 q^{10} +(2.28368 - 3.95545i) q^{11} +(-1.64906 + 0.529718i) q^{12} +(-0.380217 - 0.658556i) q^{13} +(0.165447 + 0.286563i) q^{14} +(0.762385 - 0.244897i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.46482 q^{17} +(2.43880 - 1.74707i) q^{18} -8.02193 q^{19} +(0.231157 - 0.400376i) q^{20} +(-0.424630 - 0.384919i) q^{21} +(2.28368 + 3.95545i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.365780 - 1.69299i) q^{24} +(2.39313 - 4.14503i) q^{25} +0.760435 q^{26} +(-3.09626 + 4.17291i) q^{27} -0.330894 q^{28} +(3.24600 - 5.62223i) q^{29} +(-0.169106 + 0.782693i) q^{30} +(-4.49738 - 7.78968i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.86121 - 5.31307i) q^{33} +(-2.73241 + 4.73267i) q^{34} +0.152977 q^{35} +(0.293612 + 2.98560i) q^{36} +5.26535 q^{37} +(4.01096 - 6.94719i) q^{38} +(-1.25400 + 0.402816i) q^{39} +(0.231157 + 0.400376i) q^{40} +(3.11743 + 5.39955i) q^{41} +(0.545664 - 0.175281i) q^{42} +(-0.391880 + 0.678757i) q^{43} -4.56737 q^{44} +(-0.135741 - 1.38029i) q^{45} +1.00000 q^{46} +(3.79812 - 6.57854i) q^{47} +(1.28328 + 1.16327i) q^{48} +(3.44525 + 5.96736i) q^{49} +(2.39313 + 4.14503i) q^{50} +(1.99892 - 9.25187i) q^{51} +(-0.380217 + 0.658556i) q^{52} -6.47523 q^{53} +(-2.06571 - 4.76790i) q^{54} +2.11156 q^{55} +(0.165447 - 0.286563i) q^{56} +(-2.93426 + 13.5810i) q^{57} +(3.24600 + 5.62223i) q^{58} +(6.14839 + 10.6493i) q^{59} +(-0.593279 - 0.537796i) q^{60} +(-5.55142 + 9.61535i) q^{61} +8.99475 q^{62} +(-0.806984 + 0.578097i) q^{63} +1.00000 q^{64} +(0.175780 - 0.304460i) q^{65} +(7.53186 - 2.41942i) q^{66} +(6.83706 + 11.8421i) q^{67} +(-2.73241 - 4.73267i) q^{68} +(-1.64906 + 0.529718i) q^{69} +(-0.0764887 + 0.132482i) q^{70} +3.24298 q^{71} +(-2.73241 - 1.23852i) q^{72} -9.95681 q^{73} +(-2.63267 + 4.55992i) q^{74} +(-6.14212 - 5.56771i) q^{75} +(4.01096 + 6.94719i) q^{76} +(-0.755658 - 1.30884i) q^{77} +(0.278152 - 1.28741i) q^{78} +(1.76884 - 3.06373i) q^{79} -0.462315 q^{80} +(5.93212 + 6.76830i) q^{81} -6.23486 q^{82} +(3.95239 - 6.84573i) q^{83} +(-0.121035 + 0.560200i) q^{84} +(1.26323 + 2.18798i) q^{85} +(-0.391880 - 0.678757i) q^{86} +(-8.33104 - 7.55193i) q^{87} +(2.28368 - 3.95545i) q^{88} +1.01372 q^{89} +(1.26323 + 0.572588i) q^{90} -0.251623 q^{91} +(-0.500000 + 0.866025i) q^{92} +(-14.8329 + 4.76469i) q^{93} +(3.79812 + 6.57854i) q^{94} +(-1.85433 - 3.21179i) q^{95} +(-1.64906 + 0.529718i) q^{96} +(-1.08490 + 1.87910i) q^{97} -6.89051 q^{98} +(-11.1389 + 7.97953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.365780	−	1.69299i	0.211183	−	0.977446i
$3$	0.365780	−	1.69299i	0.211183	−	0.977446i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.231157	+	0.400376i	0.103377	+	0.179054i	0.913074	−	0.407794i	$-0.133702\pi$
$5$	0.231157	+	0.400376i	0.103377	+	0.179054i	−0.809697	+	0.586848i	$0.800369\pi$
$6$	1.28328	+	1.16327i	0.523897	+	0.474902i
$7$	0.165447	−	0.286563i	0.0625331	−	0.108311i	−0.833064	−	0.553177i	$-0.813415\pi$
$7$	0.165447	−	0.286563i	0.0625331	−	0.108311i	0.895597	+	0.444866i	$0.146749\pi$
$8$	1.00000			0.353553
$9$	−2.73241	−	1.23852i	−0.910803	−	0.412841i
$10$	−0.462315			−0.146197
$11$	2.28368	−	3.95545i	0.688556	−	1.19261i	−0.283749	−	0.958899i	$-0.591578\pi$
$11$	2.28368	−	3.95545i	0.688556	−	1.19261i	0.972305	−	0.233716i	$-0.0750885\pi$
$12$	−1.64906	+	0.529718i	−0.476043	+	0.152917i
$13$	−0.380217	−	0.658556i	−0.105453	−	0.182650i	0.808470	−	0.588537i	$-0.200296\pi$
$13$	−0.380217	−	0.658556i	−0.105453	−	0.182650i	−0.913923	+	0.405887i	$0.866963\pi$
$14$	0.165447	+	0.286563i	0.0442176	+	0.0765871i
$15$	0.762385	−	0.244897i	0.196847	−	0.0632321i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.46482			1.32541			0.662707	−	0.748879i	$-0.269408\pi$
$17$	5.46482			1.32541			0.662707	+	0.748879i	$0.269408\pi$
$18$	2.43880	−	1.74707i	0.574830	−	0.411789i
$19$	−8.02193			−1.84036			−0.920178	−	0.391499i	$-0.871957\pi$
$19$	−8.02193			−1.84036			−0.920178	+	0.391499i	$0.871957\pi$
$20$	0.231157	−	0.400376i	0.0516884	−	0.0895269i
$21$	−0.424630	−	0.384919i	−0.0926618	−	0.0839962i
$22$	2.28368	+	3.95545i	0.486883	+	0.843306i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	0.365780	−	1.69299i	0.0746646	−	0.345580i
$25$	2.39313	−	4.14503i	0.478626	−	0.829005i
$26$	0.760435			0.149134
$27$	−3.09626	+	4.17291i	−0.595876	+	0.803076i
$28$	−0.330894			−0.0625331
$29$	3.24600	−	5.62223i	0.602767	−	1.04402i	−0.389634	−	0.920970i	$-0.627398\pi$
$29$	3.24600	−	5.62223i	0.602767	−	1.04402i	0.992400	−	0.123052i	$-0.0392683\pi$
$30$	−0.169106	+	0.782693i	−0.0308743	+	0.142900i
$31$	−4.49738	−	7.78968i	−0.807753	−	1.39907i	−0.914417	−	0.404774i	$-0.867350\pi$
$31$	−4.49738	−	7.78968i	−0.807753	−	1.39907i	0.106664	−	0.994295i	$-0.465983\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−5.86121	−	5.31307i	−1.02031	−	0.924887i
$34$	−2.73241	+	4.73267i	−0.468604	+	0.811647i
$35$	0.152977			0.0258579
$36$	0.293612	+	2.98560i	0.0489354	+	0.497600i
$37$	5.26535			0.865617			0.432809	−	0.901486i	$-0.357523\pi$
$37$	5.26535			0.865617			0.432809	+	0.901486i	$0.357523\pi$
$38$	4.01096	−	6.94719i	0.650664	−	1.12698i
$39$	−1.25400	+	0.402816i	−0.200801	+	0.0645022i
$40$	0.231157	+	0.400376i	0.0365492	+	0.0633051i
$41$	3.11743	+	5.39955i	0.486861	+	0.843267i	0.999886	−	0.0151062i	$-0.00480863\pi$
$41$	3.11743	+	5.39955i	0.486861	+	0.843267i	−0.513025	+	0.858374i	$0.671475\pi$
$42$	0.545664	−	0.175281i	0.0841979	−	0.0270464i
$43$	−0.391880	+	0.678757i	−0.0597612	+	0.103509i	−0.894358	−	0.447352i	$-0.852367\pi$
$43$	−0.391880	+	0.678757i	−0.0597612	+	0.103509i	0.834597	+	0.550861i	$0.185701\pi$
$44$	−4.56737			−0.688556
$45$	−0.135741	−	1.38029i	−0.0202351	−	0.205761i
$46$	1.00000			0.147442
$47$	3.79812	−	6.57854i	0.554013	−	0.959578i	−0.443967	−	0.896043i	$-0.646429\pi$
$47$	3.79812	−	6.57854i	0.554013	−	0.959578i	0.997980	−	0.0635350i	$-0.0202374\pi$
$48$	1.28328	+	1.16327i	0.185225	+	0.167903i
$49$	3.44525	+	5.96736i	0.492179	+	0.852479i
$50$	2.39313	+	4.14503i	0.338440	+	0.586195i
$51$	1.99892	−	9.25187i	0.279905	−	1.29552i
$52$	−0.380217	+	0.658556i	−0.0527267	+	0.0913252i
$53$	−6.47523			−0.889441			−0.444721	−	0.895669i	$-0.646697\pi$
$53$	−6.47523			−0.889441			−0.444721	+	0.895669i	$0.646697\pi$
$54$	−2.06571	−	4.76790i	−0.281108	−	0.648829i
$55$	2.11156			0.284723
$56$	0.165447	−	0.286563i	0.0221088	−	0.0382936i
$57$	−2.93426	+	13.5810i	−0.388653	+	1.79885i
$58$	3.24600	+	5.62223i	0.426220	+	0.738235i
$59$	6.14839	+	10.6493i	0.800452	+	1.38642i	0.919319	+	0.393513i	$0.128740\pi$
$59$	6.14839	+	10.6493i	0.800452	+	1.38642i	−0.118867	+	0.992910i	$0.537926\pi$
$60$	−0.593279	−	0.537796i	−0.0765920	−	0.0694292i
$61$	−5.55142	+	9.61535i	−0.710787	+	1.23112i	0.253775	+	0.967263i	$0.418328\pi$
$61$	−5.55142	+	9.61535i	−0.710787	+	1.23112i	−0.964562	+	0.263856i	$0.915006\pi$
$62$	8.99475			1.14233
$63$	−0.806984	+	0.578097i	−0.101670	+	0.0728334i
$64$	1.00000			0.125000
$65$	0.175780	−	0.304460i	0.0218028	−	0.0377636i
$66$	7.53186	−	2.41942i	0.927108	−	0.297810i
$67$	6.83706	+	11.8421i	0.835279	+	1.44675i	0.893803	+	0.448460i	$0.148027\pi$
$67$	6.83706	+	11.8421i	0.835279	+	1.44675i	−0.0585233	+	0.998286i	$0.518639\pi$
$68$	−2.73241	−	4.73267i	−0.331353	−	0.573921i
$69$	−1.64906	+	0.529718i	−0.198523	+	0.0637706i
$70$	−0.0764887	+	0.132482i	−0.00914215	+	0.0158347i
$71$	3.24298			0.384871			0.192436	−	0.981310i	$-0.438361\pi$
$71$	3.24298			0.384871			0.192436	+	0.981310i	$0.438361\pi$
$72$	−2.73241	−	1.23852i	−0.322018	−	0.145961i
$73$	−9.95681			−1.16536			−0.582678	−	0.812703i	$-0.697995\pi$
$73$	−9.95681			−1.16536			−0.582678	+	0.812703i	$0.697995\pi$
$74$	−2.63267	+	4.55992i	−0.306042	+	0.530080i
$75$	−6.14212	−	5.56771i	−0.709230	−	0.642904i
$76$	4.01096	+	6.94719i	0.460089	+	0.796898i
$77$	−0.755658	−	1.30884i	−0.0861152	−	0.149156i
$78$	0.278152	−	1.28741i	0.0314945	−	0.145770i
$79$	1.76884	−	3.06373i	0.199010	−	0.344696i	−0.749197	−	0.662347i	$-0.769561\pi$
$79$	1.76884	−	3.06373i	0.199010	−	0.344696i	0.948208	+	0.317651i	$0.102894\pi$
$80$	−0.462315			−0.0516884
$81$	5.93212	+	6.76830i	0.659125	+	0.752034i
$82$	−6.23486			−0.688525
$83$	3.95239	−	6.84573i	0.433831	−	0.751417i	−0.563369	−	0.826206i	$-0.690495\pi$
$83$	3.95239	−	6.84573i	0.433831	−	0.751417i	0.997199	+	0.0747889i	$0.0238283\pi$
$84$	−0.121035	+	0.560200i	−0.0132060	+	0.0611228i
$85$	1.26323	+	2.18798i	0.137017	+	0.237320i
$86$	−0.391880	−	0.678757i	−0.0422576	−	0.0731922i
$87$	−8.33104	−	7.55193i	−0.893182	−	0.809652i
$88$	2.28368	−	3.95545i	0.243441	−	0.421653i
$89$	1.01372			0.107454			0.0537271	−	0.998556i	$-0.482890\pi$
$89$	1.01372			0.107454			0.0537271	+	0.998556i	$0.482890\pi$
$90$	1.26323	+	0.572588i	0.133157	+	0.0603560i
$91$	−0.251623			−0.0263773
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$	−14.8329	+	4.76469i	−1.53810	+	0.494075i
$94$	3.79812	+	6.57854i	0.391746	+	0.678524i
$95$	−1.85433	−	3.21179i	−0.190250	−	0.329523i
$96$	−1.64906	+	0.529718i	−0.168306	+	0.0540642i
$97$	−1.08490	+	1.87910i	−0.110155	+	0.190793i	−0.915832	−	0.401561i	$-0.868468\pi$
$97$	−1.08490	+	1.87910i	−0.110155	+	0.190793i	0.805678	+	0.592354i	$0.201801\pi$
$98$	−6.89051			−0.696047
$99$	−11.1389	+	7.97953i	−1.11950	+	0.801973i
$100$	−4.78626			−0.478626
$101$	−6.57272	+	11.3843i	−0.654010	+	1.13278i	0.328131	+	0.944632i	$0.393581\pi$
$101$	−6.57272	+	11.3843i	−0.654010	+	1.13278i	−0.982141	+	0.188147i	$0.939752\pi$
$102$	7.01289	+	6.35705i	0.694380	+	0.629442i
$103$	−4.89265	−	8.47432i	−0.482087	−	0.835000i	0.517701	−	0.855561i	$-0.326788\pi$
$103$	−4.89265	−	8.47432i	−0.482087	−	0.835000i	−0.999789	+	0.0205618i	$0.993455\pi$
$104$	−0.380217	−	0.658556i	−0.0372834	−	0.0645767i
$105$	0.0559561	−	0.258989i	0.00546076	−	0.0252747i
$106$	3.23762	−	5.60771i	0.314465	−	0.544669i
$107$	−1.97888			−0.191305			−0.0956526	−	0.995415i	$-0.530494\pi$
$107$	−1.97888			−0.191305			−0.0956526	+	0.995415i	$0.530494\pi$
$108$	5.16198	+	0.594991i	0.496711	+	0.0572530i
$109$	11.7191			1.12249			0.561243	−	0.827651i	$-0.310323\pi$
$109$	11.7191			1.12249			0.561243	+	0.827651i	$0.310323\pi$
$110$	−1.05578	+	1.82867i	−0.100665	+	0.174356i
$111$	1.92596	−	8.91416i	0.182804	−	0.846095i
$112$	0.165447	+	0.286563i	0.0156333	+	0.0270776i
$113$	5.42521	+	9.39674i	0.510361	+	0.883971i	0.999928	+	0.0120051i	$0.00382144\pi$
$113$	5.42521	+	9.39674i	0.510361	+	0.883971i	−0.489567	+	0.871966i	$0.662845\pi$
$114$	−10.2944	−	9.33166i	−0.964157	−	0.873990i
$115$	0.231157	−	0.400376i	0.0215555	−	0.0373353i
$116$	−6.49200			−0.602767
$117$	0.223273	+	2.27035i	0.0206416	+	0.209894i
$118$	−12.2968			−1.13201
$119$	0.904139	−	1.56601i	0.0828823	−	0.143556i
$120$	0.762385	−	0.244897i	0.0695959	−	0.0223559i
$121$	−4.93041	−	8.53973i	−0.448219	−	0.776339i
$122$	−5.55142	−	9.61535i	−0.502602	−	0.870533i
$123$	10.2817	−	3.30272i	0.927066	−	0.297796i
$124$	−4.49738	+	7.78968i	−0.403876	+	0.699534i
$125$	4.52434			0.404669
$126$	−0.0971547	−	0.987917i	−0.00865523	−	0.0880106i
$127$	−8.11851			−0.720401			−0.360200	−	0.932875i	$-0.617292\pi$
$127$	−8.11851			−0.720401			−0.360200	+	0.932875i	$0.617292\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.00578	+	0.911725i	0.0885544	+	0.0802729i
$130$	0.175780	+	0.304460i	0.0154169	+	0.0267029i
$131$	5.50879	+	9.54150i	0.481305	+	0.833644i	0.999770	−	0.0214544i	$-0.00682967\pi$
$131$	5.50879	+	9.54150i	0.481305	+	0.833644i	−0.518465	+	0.855099i	$0.673496\pi$
$132$	−1.67065	+	7.73249i	−0.145412	+	0.673027i
$133$	−1.32721	+	2.29879i	−0.115083	+	0.199330i
$134$	−13.6741			−1.18126
$135$	−2.38646	−	0.275073i	−0.205394	−	0.0236745i
$136$	5.46482			0.468604
$137$	−3.56371	+	6.17252i	−0.304468	+	0.527354i	−0.977143	−	0.212584i	$-0.931812\pi$
$137$	−3.56371	+	6.17252i	−0.304468	+	0.527354i	0.672675	+	0.739938i	$0.265145\pi$
$138$	0.365780	−	1.69299i	0.0311373	−	0.144117i
$139$	6.82958	+	11.8292i	0.579277	+	1.00334i	0.995562	+	0.0941033i	$0.0299984\pi$
$139$	6.82958	+	11.8292i	0.579277	+	1.00334i	−0.416285	+	0.909234i	$0.636668\pi$
$140$	−0.0764887	−	0.132482i	−0.00646447	−	0.0111968i
$141$	−9.74810	−	8.83647i	−0.820938	−	0.744165i
$142$	−1.62149	+	2.80850i	−0.136072	+	0.235684i
$143$	−3.47318			−0.290442
$144$	2.43880	−	1.74707i	0.203233	−	0.145590i
$145$	3.00135			0.249248
$146$	4.97841	−	8.62285i	0.412016	−	0.713632i
$147$	11.3629	−	3.65003i	0.937193	−	0.301049i
$148$	−2.63267	−	4.55992i	−0.216404	−	0.374823i
$149$	6.37759	+	11.0463i	0.522473	+	0.904950i	0.999658	+	0.0261468i	$0.00832373\pi$
$149$	6.37759	+	11.0463i	0.522473	+	0.904950i	−0.477185	+	0.878803i	$0.658343\pi$
$150$	7.89284	−	2.53537i	0.644447	−	0.207012i
$151$	−3.28756	+	5.69422i	−0.267538	+	0.463389i	−0.968225	−	0.250079i	$-0.919543\pi$
$151$	−3.28756	+	5.69422i	−0.267538	+	0.463389i	0.700688	+	0.713468i	$0.252877\pi$
$152$	−8.02193			−0.650664
$153$	−14.9321	−	6.76830i	−1.20719	−	0.547185i
$154$	1.51132			0.121785
$155$	2.07920	−	3.60129i	0.167006	−	0.289262i
$156$	0.975850	+	0.884590i	0.0781305	+	0.0708239i
$157$	−0.124910	−	0.216351i	−0.00996891	−	0.0172667i	0.860998	−	0.508608i	$-0.169840\pi$
$157$	−0.124910	−	0.216351i	−0.00996891	−	0.0172667i	−0.870967	+	0.491342i	$0.836507\pi$
$158$	1.76884	+	3.06373i	0.140722	+	0.243737i
$159$	−2.36851	+	10.9625i	−0.187835	+	0.869381i
$160$	0.231157	−	0.400376i	0.0182746	−	0.0316525i
$161$	−0.330894			−0.0260781
$162$	−8.82758	+	1.75322i	−0.693560	+	0.137746i
$163$	−1.46018			−0.114370			−0.0571852	−	0.998364i	$-0.518213\pi$
$163$	−1.46018			−0.114370			−0.0571852	+	0.998364i	$0.518213\pi$
$164$	3.11743	−	5.39955i	0.243430	−	0.421634i
$165$	0.772368	−	3.57485i	0.0601287	−	0.278301i
$166$	3.95239	+	6.84573i	0.306765	+	0.531332i
$167$	0.136092	+	0.235718i	0.0105311	+	0.0182404i	0.871243	−	0.490852i	$-0.163314\pi$
$167$	0.136092	+	0.235718i	0.0105311	+	0.0182404i	−0.860712	+	0.509092i	$0.829981\pi$
$168$	−0.424630	−	0.384919i	−0.0327609	−	0.0296971i
$169$	6.21087	−	10.7575i	0.477759	−	0.827503i
$170$	−2.52647			−0.193771
$171$	21.9192	+	9.93534i	1.67620	+	0.759775i
$172$	0.783761			0.0597612
$173$	4.94246	−	8.56058i	0.375768	−	0.650849i	−0.614674	−	0.788781i	$-0.710712\pi$
$173$	4.94246	−	8.56058i	0.375768	−	0.650849i	0.990442	+	0.137932i	$0.0440456\pi$
$174$	10.7057	−	3.43893i	0.811596	−	0.260705i
$175$	−0.791874	−	1.37157i	−0.0598600	−	0.103681i
$176$	2.28368	+	3.95545i	0.172139	+	0.298154i
$177$	20.2781	−	6.51383i	1.52420	−	0.489609i
$178$	−0.506861	+	0.877909i	−0.0379908	+	0.0658020i
$179$	−18.4626			−1.37996			−0.689980	−	0.723828i	$-0.742381\pi$
$179$	−18.4626			−1.37996			−0.689980	+	0.723828i	$0.742381\pi$
$180$	−1.12749	+	0.807699i	−0.0840383	+	0.0602023i
$181$	18.7344			1.39252			0.696259	−	0.717791i	$-0.254846\pi$
$181$	18.7344			1.39252			0.696259	+	0.717791i	$0.254846\pi$
$182$	0.125812	−	0.217912i	0.00932579	−	0.0161527i
$183$	14.2481	+	12.9156i	1.05325	+	0.954748i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	1.21712	+	2.10812i	0.0894847	+	0.154992i
$186$	3.29010	−	15.2280i	0.241242	−	1.11657i
$187$	12.4799	−	21.6158i	0.912622	−	1.58071i
$188$	−7.59624			−0.554013
$189$	0.683532	+	1.57767i	0.0497196	+	0.114759i
$190$	3.70866			0.269054
$191$	8.44285	−	14.6234i	0.610903	−	1.05812i	−0.380185	−	0.924910i	$-0.624140\pi$
$191$	8.44285	−	14.6234i	0.610903	−	1.05812i	0.991089	−	0.133205i	$-0.0425268\pi$
$192$	0.365780	−	1.69299i	0.0263979	−	0.122181i
$193$	−6.22934	−	10.7895i	−0.448398	−	0.776648i	0.549884	−	0.835241i	$-0.314672\pi$
$193$	−6.22934	−	10.7895i	−0.448398	−	0.776648i	−0.998282	+	0.0585932i	$0.981339\pi$
$194$	−1.08490	−	1.87910i	−0.0778910	−	0.134911i
$195$	−0.451150	−	0.408959i	−0.0323075	−	0.0292862i
$196$	3.44525	−	5.96736i	0.246090	−	0.426240i
$197$	−10.6470			−0.758570			−0.379285	−	0.925280i	$-0.623830\pi$
$197$	−10.6470			−0.758570			−0.379285	+	0.925280i	$0.623830\pi$
$198$	−1.34104	−	13.6363i	−0.0953033	−	0.969091i
$199$	24.4902			1.73606			0.868031	−	0.496510i	$-0.165385\pi$
$199$	24.4902			1.73606			0.868031	+	0.496510i	$0.165385\pi$
$200$	2.39313	−	4.14503i	0.169220	−	0.293098i
$201$	22.5494	−	7.24343i	1.59051	−	0.510912i
$202$	−6.57272	−	11.3843i	−0.462455	−	0.800996i
$203$	−1.07408	−	1.86036i	−0.0753858	−	0.130572i
$204$	−9.01181	+	2.89481i	−0.630953	+	0.202678i
$205$	−1.44123	+	2.49629i	−0.100660	+	0.174348i
$206$	9.78530			0.681774
$207$	0.293612	+	2.98560i	0.0204075	+	0.207513i
$208$	0.760435			0.0527267
$209$	−18.3195	+	31.7304i	−1.26719	+	2.19484i
$210$	0.196313	+	0.177954i	0.0135469	+	0.0122800i
$211$	−7.49049	−	12.9739i	−0.515667	−	0.893161i	−0.999835	−	0.0181857i	$-0.994211\pi$
$211$	−7.49049	−	12.9739i	−0.515667	−	0.893161i	0.484168	−	0.874975i	$-0.339122\pi$
$212$	3.23762	+	5.60771i	0.222360	+	0.385139i
$213$	1.18622	−	5.49033i	0.0812784	−	0.376191i
$214$	0.989438	−	1.71376i	0.0676366	−	0.117150i
$215$	−0.362344			−0.0247117
$216$	−3.09626	+	4.17291i	−0.210674	+	0.283930i
$217$	−2.97631			−0.202045
$218$	−5.85955	+	10.1490i	−0.396859	+	0.687380i
$219$	−3.64201	+	16.8568i	−0.246104	+	1.13907i
$220$	−1.05578	−	1.82867i	−0.0711807	−	0.123289i
$221$	−2.07782	−	3.59889i	−0.139769	−	0.242087i
$222$	6.75691	+	6.12501i	0.453494	+	0.411084i
$223$	5.04416	−	8.73674i	0.337782	−	0.585055i	−0.646233	−	0.763140i	$-0.723657\pi$
$223$	5.04416	−	8.73674i	0.337782	−	0.585055i	0.984015	+	0.178084i	$0.0569900\pi$
$224$	−0.330894			−0.0221088
$225$	−11.6727	+	8.36196i	−0.778182	+	0.557464i
$226$	−10.8504			−0.721759
$227$	−1.39594	+	2.41784i	−0.0926520	+	0.160478i	−0.908626	−	0.417610i	$-0.862868\pi$
$227$	−1.39594	+	2.41784i	−0.0926520	+	0.160478i	0.815974	+	0.578088i	$0.196201\pi$
$228$	13.2286	−	4.24936i	0.876088	−	0.281421i
$229$	−4.90859	−	8.50193i	−0.324369	−	0.561823i	0.657015	−	0.753877i	$-0.271819\pi$
$229$	−4.90859	−	8.50193i	−0.324369	−	0.561823i	−0.981384	+	0.192054i	$0.938485\pi$
$230$	0.231157	+	0.400376i	0.0152421	+	0.0264000i
$231$	−2.49225	+	0.800571i	−0.163978	+	0.0526737i
$232$	3.24600	−	5.62223i	0.213110	−	0.369118i
$233$	20.9665			1.37356			0.686782	−	0.726864i	$-0.259023\pi$
$233$	20.9665			1.37356			0.686782	+	0.726864i	$0.259023\pi$
$234$	−2.07782	−	0.941816i	−0.135831	−	0.0615684i
$235$	3.51185			0.229088
$236$	6.14839	−	10.6493i	0.400226	−	0.693212i
$237$	−4.53984	−	4.11528i	−0.294894	−	0.267316i
$238$	0.904139	+	1.56601i	0.0586066	+	0.101510i
$239$	−7.21920	−	12.5040i	−0.466971	−	0.808818i	0.532317	−	0.846545i	$-0.321321\pi$
$239$	−7.21920	−	12.5040i	−0.466971	−	0.808818i	−0.999288	+	0.0377274i	$0.987988\pi$
$240$	−0.169106	+	0.782693i	−0.0109157	+	0.0505226i
$241$	−5.09582	+	8.82622i	−0.328251	+	0.568547i	−0.982165	−	0.188022i	$-0.939792\pi$
$241$	−5.09582	+	8.82622i	−0.328251	+	0.568547i	0.653914	+	0.756569i	$0.273126\pi$
$242$	9.86083			0.633878
$243$	13.6285	−	7.56729i	0.874269	−	0.485442i
$244$	11.1028			0.710787
$245$	−1.59279	+	2.75880i	−0.101760	+	0.176253i
$246$	−2.28059	+	10.5555i	−0.145405	+	0.672996i
$247$	3.05008	+	5.28289i	0.194072	+	0.336142i
$248$	−4.49738	−	7.78968i	−0.285584	−	0.494645i
$249$	−10.1440	−	9.19537i	−0.642852	−	0.582733i
$250$	−2.26217	+	3.91819i	−0.143072	+	0.247808i
$251$	25.6973			1.62200			0.811000	−	0.585046i	$-0.198924\pi$
$251$	25.6973			1.62200			0.811000	+	0.585046i	$0.198924\pi$
$252$	0.904139	+	0.409820i	0.0569554	+	0.0258162i
$253$	−4.56737			−0.287148
$254$	4.05925	−	7.03083i	0.254700	−	0.441154i
$255$	4.16630	−	1.33832i	0.260904	−	0.0838086i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.72723	−	4.72370i	−0.170120	−	0.294656i	0.768342	−	0.640040i	$-0.221082\pi$
$257$	−2.72723	−	4.72370i	−0.170120	−	0.294656i	−0.938462	+	0.345384i	$0.887749\pi$
$258$	−1.29247	+	0.415173i	−0.0804656	+	0.0258475i
$259$	0.871136	−	1.50885i	0.0541298	−	0.0937555i
$260$	−0.351560			−0.0218028
$261$	−15.8327	+	11.3420i	−0.980017	+	0.702052i
$262$	−11.0176			−0.680668
$263$	8.70499	−	15.0775i	0.536773	−	0.929718i	−0.462303	−	0.886722i	$-0.652977\pi$
$263$	8.70499	−	15.0775i	0.536773	−	0.929718i	0.999075	−	0.0429954i	$-0.0136901\pi$
$264$	−5.86121	−	5.31307i	−0.360732	−	0.326997i
$265$	−1.49680	−	2.59253i	−0.0919476	−	0.159258i
$266$	−1.32721	−	2.29879i	−0.0813762	−	0.140948i
$267$	0.370800	−	1.71622i	0.0226926	−	0.105031i
$268$	6.83706	−	11.8421i	0.417640	−	0.723373i
$269$	−22.4752			−1.37034			−0.685169	−	0.728384i	$-0.740272\pi$
$269$	−22.4752			−1.37034			−0.685169	+	0.728384i	$0.740272\pi$
$270$	1.43145	−	1.92920i	0.0871152	−	0.117407i
$271$	−22.5676			−1.37088			−0.685441	−	0.728128i	$-0.740390\pi$
$271$	−22.5676			−1.37088			−0.685441	+	0.728128i	$0.740390\pi$
$272$	−2.73241	+	4.73267i	−0.165677	+	0.286960i
$273$	−0.0920389	+	0.425995i	−0.00557045	+	0.0257824i
$274$	−3.56371	−	6.17252i	−0.215291	−	0.372896i
$275$	−10.9303	−	18.9319i	−0.659123	−	1.14163i
$276$	1.28328	+	1.16327i	0.0772443	+	0.0700205i
$277$	3.01285	−	5.21841i	0.181024	−	0.313544i	−0.761205	−	0.648511i	$-0.775392\pi$
$277$	3.01285	−	5.21841i	0.181024	−	0.313544i	0.942230	+	0.334967i	$0.108725\pi$
$278$	−13.6592			−0.819221
$279$	2.64097	+	26.8547i	0.158111	+	1.60775i
$280$	0.152977			0.00914215
$281$	−3.54046	+	6.13225i	−0.211206	+	0.365820i	−0.952092	−	0.305811i	$-0.901072\pi$
$281$	−3.54046	+	6.13225i	−0.211206	+	0.365820i	0.740886	+	0.671631i	$0.234406\pi$
$282$	12.5267	−	4.02387i	0.745951	−	0.239618i
$283$	−4.10983	−	7.11843i	−0.244304	−	0.423147i	0.717632	−	0.696423i	$-0.245226\pi$
$283$	−4.10983	−	7.11843i	−0.244304	−	0.423147i	−0.961936	+	0.273276i	$0.911893\pi$
$284$	−1.62149	−	2.80850i	−0.0962178	−	0.166654i
$285$	−6.11580	+	1.96454i	−0.362269	+	0.116370i
$286$	1.73659	−	3.00786i	0.102687	−	0.177859i
$287$	2.06308			0.121780
$288$	0.293612	+	2.98560i	0.0173013	+	0.175928i
$289$	12.8642			0.756720
$290$	−1.50067	+	2.59924i	−0.0881226	+	0.152633i
$291$	2.78445	+	2.52405i	0.163227	+	0.147963i
$292$	4.97841	+	8.62285i	0.291339	+	0.504614i
$293$	13.3751	+	23.1664i	0.781383	+	1.35339i	0.931136	+	0.364671i	$0.118819\pi$
$293$	13.3751	+	23.1664i	0.781383	+	1.35339i	−0.149753	+	0.988723i	$0.547848\pi$
$294$	−2.52041	+	11.6655i	−0.146993	+	0.680348i
$295$	−2.84249	+	4.92334i	−0.165496	+	0.286648i
$296$	5.26535			0.306042
$297$	9.43485	+	21.7767i	0.547466	+	1.26361i
$298$	−12.7552			−0.738888
$299$	−0.380217	+	0.658556i	−0.0219885	+	0.0380853i
$300$	−1.75072	+	8.10308i	−0.101078	+	0.467832i
$301$	0.129671	+	0.224597i	0.00747411	+	0.0129455i
$302$	−3.28756	−	5.69422i	−0.189178	−	0.327665i
$303$	16.8693	+	15.2917i	0.969115	+	0.878484i
$304$	4.01096	−	6.94719i	0.230045	−	0.398449i
$305$	−5.13301			−0.293915
$306$	13.3276	−	9.54745i	0.761887	−	0.545791i
$307$	−15.6388			−0.892553			−0.446276	−	0.894895i	$-0.647250\pi$
$307$	−15.6388			−0.892553			−0.446276	+	0.894895i	$0.647250\pi$
$308$	−0.755658	+	1.30884i	−0.0430576	+	0.0745779i
$309$	−16.1365	+	5.18345i	−0.917976	+	0.294876i
$310$	2.07920	+	3.60129i	0.118091	+	0.204539i
$311$	3.61310	+	6.25807i	0.204880	+	0.354862i	0.950094	−	0.311962i	$-0.100986\pi$
$311$	3.61310	+	6.25807i	0.204880	+	0.354862i	−0.745215	+	0.666825i	$0.767653\pi$
$312$	−1.25400	+	0.402816i	−0.0709939	+	0.0228050i
$313$	2.36744	−	4.10052i	0.133815	−	0.231775i	−0.791329	−	0.611391i	$-0.790610\pi$
$313$	2.36744	−	4.10052i	0.133815	−	0.231775i	0.925144	+	0.379616i	$0.123944\pi$
$314$	0.249820			0.0140982
$315$	−0.417997	−	0.189466i	−0.0235515	−	0.0106752i
$316$	−3.53769			−0.199010
$317$	−6.83798	+	11.8437i	−0.384059	+	0.665210i	−0.991638	−	0.129049i	$-0.958808\pi$
$317$	−6.83798	+	11.8437i	−0.384059	+	0.665210i	0.607579	+	0.794259i	$0.292141\pi$
$318$	−8.30953	−	7.53243i	−0.465975	−	0.422398i
$319$	−14.8257	−	25.6788i	−0.830078	−	1.43774i
$320$	0.231157	+	0.400376i	0.0129221	+	0.0223817i
$321$	−0.723834	+	3.35021i	−0.0404005	+	0.186991i
$322$	0.165447	−	0.286563i	0.00922001	−	0.0159695i
$323$	−43.8384			−2.43923
$324$	2.89546	−	8.52152i	0.160859	−	0.473418i
$325$	−3.63964			−0.201891
$326$	0.730092	−	1.26456i	0.0404361	−	0.0700373i
$327$	4.28662	−	19.8403i	0.237051	−	1.09717i
$328$	3.11743	+	5.39955i	0.172131	+	0.298140i
$329$	−1.25678	−	2.17680i	−0.0692883	−	0.120011i
$330$	2.70972	+	2.45631i	0.149165	+	0.135216i
$331$	−5.11673	+	8.86244i	−0.281241	+	0.487124i	−0.971691	−	0.236257i	$-0.924079\pi$
$331$	−5.11673	+	8.86244i	−0.281241	+	0.487124i	0.690450	+	0.723380i	$0.257413\pi$
$332$	−7.90477			−0.433831
$333$	−14.3871	−	6.52125i	−0.788407	−	0.357362i
$334$	−0.272183			−0.0148932
$335$	−3.16087	+	5.47479i	−0.172697	+	0.299120i
$336$	0.545664	−	0.175281i	0.0297684	−	0.00956235i
$337$	−0.231856	−	0.401586i	−0.0126300	−	0.0218758i	0.859641	−	0.510898i	$-0.170687\pi$
$337$	−0.231856	−	0.401586i	−0.0126300	−	0.0218758i	−0.872271	+	0.489022i	$0.837354\pi$
$338$	6.21087	+	10.7575i	0.337827	+	0.585133i
$339$	17.8930	−	5.74767i	0.971814	−	0.312170i
$340$	1.26323	−	2.18798i	0.0685085	−	0.118660i
$341$	−41.0823			−2.22473
$342$	−19.5639	+	14.0149i	−1.05789	+	0.757839i
$343$	4.59629			0.248176
$344$	−0.391880	+	0.678757i	−0.0211288	+	0.0365961i
$345$	−0.593279	−	0.537796i	−0.0319411	−	0.0289540i
$346$	4.94246	+	8.56058i	0.265708	+	0.460220i
$347$	6.87275	+	11.9040i	0.368949	+	0.639038i	0.989401	−	0.145206i	$-0.0463845\pi$
$347$	6.87275	+	11.9040i	0.368949	+	0.639038i	−0.620453	+	0.784244i	$0.713051\pi$
$348$	−2.37464	+	10.9909i	−0.127294	+	0.589172i
$349$	−6.73858	+	11.6716i	−0.360708	+	0.624765i	−0.988078	−	0.153957i	$-0.950798\pi$
$349$	−6.73858	+	11.6716i	−0.360708	+	0.624765i	0.627369	+	0.778722i	$0.284132\pi$
$350$	1.58375			0.0846549
$351$	3.92534	+	0.452452i	0.209519	+	0.0241501i
$352$	−4.56737			−0.243441
$353$	10.3062	−	17.8509i	0.548545	−	0.950109i	−0.449829	−	0.893115i	$-0.648515\pi$
$353$	10.3062	−	17.8509i	0.548545	−	0.950109i	0.998375	−	0.0569939i	$-0.0181516\pi$
$354$	−4.49792	+	20.8183i	−0.239062	+	1.10648i
$355$	0.749639	+	1.29841i	0.0397867	+	0.0689126i
$356$	−0.506861	−	0.877909i	−0.0268636	−	0.0465291i
$357$	−2.32053	−	2.10351i	−0.122815	−	0.111330i
$358$	9.23131	−	15.9891i	0.487890	−	0.845050i
$359$	34.2097			1.80552			0.902759	−	0.430147i	$-0.141538\pi$
$359$	34.2097			1.80552			0.902759	+	0.430147i	$0.141538\pi$
$360$	−0.135741	−	1.38029i	−0.00715420	−	0.0727475i
$361$	45.3514			2.38691
$362$	−9.36721	+	16.2245i	−0.492330	+	0.852740i
$363$	−16.2611	+	5.22346i	−0.853486	+	0.274161i
$364$	0.125812	+	0.217912i	0.00659433	+	0.0114217i
$365$	−2.30159	−	3.98647i	−0.120471	−	0.208662i
$366$	−18.3093	+	5.88138i	−0.957040	+	0.307425i
$367$	−12.0295	+	20.8356i	−0.627933	+	1.08761i	0.360033	+	0.932940i	$0.382765\pi$
$367$	−12.0295	+	20.8356i	−0.627933	+	1.08761i	−0.987966	+	0.154672i	$0.950568\pi$
$368$	1.00000			0.0521286
$369$	−1.83063	−	18.6148i	−0.0952989	−	0.969047i
$370$	−2.43425			−0.126551
$371$	−1.07131	+	1.85556i	−0.0556196	+	0.0963359i
$372$	11.5428	+	10.4633i	0.598465	+	0.542498i
$373$	−11.7214	−	20.3021i	−0.606911	−	1.05120i	−0.991746	−	0.128216i	$-0.959075\pi$
$373$	−11.7214	−	20.3021i	−0.606911	−	1.05120i	0.384835	−	0.922985i	$-0.374258\pi$
$374$	12.4799	+	21.6158i	0.645321	+	1.11773i
$375$	1.65491	−	7.65964i	0.0854594	−	0.395542i
$376$	3.79812	−	6.57854i	0.195873	−	0.339262i
$377$	−4.93674			−0.254255
$378$	−1.70807	−	0.196879i	−0.0878535	−	0.0101264i
$379$	−9.99031			−0.513168			−0.256584	−	0.966522i	$-0.582597\pi$
$379$	−9.99031			−0.513168			−0.256584	+	0.966522i	$0.582597\pi$
$380$	−1.85433	+	3.21179i	−0.0951251	+	0.164761i
$381$	−2.96959	+	13.7445i	−0.152137	+	0.704153i
$382$	8.44285	+	14.6234i	0.431974	+	0.748200i
$383$	−7.68298	−	13.3073i	−0.392582	−	0.679972i	0.600207	−	0.799844i	$-0.295085\pi$
$383$	−7.68298	−	13.3073i	−0.392582	−	0.679972i	−0.992789	+	0.119873i	$0.961751\pi$
$384$	1.28328	+	1.16327i	0.0654871	+	0.0593628i
$385$	0.349352	−	0.605095i	0.0178046	−	0.0308385i
$386$	12.4587			0.634130
$387$	1.91143	−	1.36929i	0.0971636	−	0.0696049i
$388$	2.16979			0.110155
$389$	13.2837	−	23.0080i	0.673509	−	1.16655i	−0.303393	−	0.952866i	$-0.598119\pi$
$389$	13.2837	−	23.0080i	0.673509	−	1.16655i	0.976902	−	0.213687i	$-0.0685473\pi$
$390$	0.579744	−	0.186228i	0.0293565	−	0.00943002i
$391$	−2.73241	−	4.73267i	−0.138184	−	0.239342i
$392$	3.44525	+	5.96736i	0.174012	+	0.301397i
$393$	18.1686	−	5.83621i	0.916486	−	0.294398i
$394$	5.32352	−	9.22061i	0.268195	−	0.464528i
$395$	1.63552			0.0822922
$396$	12.4799	+	5.65679i	0.627139	+	0.284264i
$397$	−30.0992			−1.51064			−0.755318	−	0.655358i	$-0.772518\pi$
$397$	−30.0992			−1.51064			−0.755318	+	0.655358i	$0.772518\pi$
$398$	−12.2451	+	21.2091i	−0.613791	+	1.06312i
$399$	3.40635	+	3.08779i	0.170531	+	0.154583i
$400$	2.39313	+	4.14503i	0.119657	+	0.207251i
$401$	6.96076	+	12.0564i	0.347604	+	0.602067i	0.985823	−	0.167787i	$-0.0536622\pi$
$401$	6.96076	+	12.0564i	0.347604	+	0.602067i	−0.638220	+	0.769854i	$0.720329\pi$
$402$	−5.00172	+	23.1501i	−0.249463	+	1.15462i
$403$	−3.41996	+	5.92355i	−0.170360	+	0.295073i
$404$	13.1454			0.654010
$405$	−1.33861	+	3.93963i	−0.0665163	+	0.195762i
$406$	2.14816			0.106612
$407$	12.0244	−	20.8268i	0.596026	−	1.03235i
$408$	1.99892	−	9.25187i	0.0989615	−	0.458036i
$409$	9.28694	+	16.0854i	0.459210	+	0.795374i	0.998919	−	0.0464768i	$-0.0147994\pi$
$409$	9.28694	+	16.0854i	0.459210	+	0.795374i	−0.539710	+	0.841851i	$0.681466\pi$
$410$	−1.44123	−	2.49629i	−0.0711775	−	0.123283i
$411$	9.14646	+	8.29110i	0.451162	+	0.408970i
$412$	−4.89265	+	8.47432i	−0.241044	+	0.417500i
$413$	4.06893			0.200219
$414$	−2.73241	−	1.23852i	−0.134291	−	0.0608701i
$415$	3.65449			0.179392
$416$	−0.380217	+	0.658556i	−0.0186417	+	0.0322884i
$417$	22.5248	−	7.23550i	1.10304	−	0.354324i
$418$	−18.3195	−	31.7304i	−0.896038	−	1.55198i
$419$	−5.27291	−	9.13294i	−0.257598	−	0.446173i	0.708000	−	0.706213i	$-0.249598\pi$
$419$	−5.27291	−	9.13294i	−0.257598	−	0.446173i	−0.965598	+	0.260039i	$0.916264\pi$
$420$	−0.252269	+	0.0810349i	−0.0123095	+	0.00395410i
$421$	−5.91002	+	10.2365i	−0.288037	+	0.498894i	−0.973341	−	0.229363i	$-0.926336\pi$
$421$	−5.91002	+	10.2365i	−0.288037	+	0.498894i	0.685304	+	0.728257i	$0.259669\pi$
$422$	14.9810			0.729263
$423$	−18.5257	+	13.2712i	−0.900750	+	0.645268i
$424$	−6.47523			−0.314465
$425$	13.0780	−	22.6518i	0.634378	−	1.09877i
$426$	4.16165	+	3.77246i	0.201633	+	0.182776i
$427$	1.83693	+	3.18166i	0.0888955	+	0.153971i
$428$	0.989438	+	1.71376i	0.0478263	+	0.0828376i
$429$	−1.27042	+	5.88005i	−0.0613366	+	0.283892i
$430$	0.181172	−	0.313799i	0.00873690	−	0.0151328i
$431$	−12.8272			−0.617864			−0.308932	−	0.951084i	$-0.599972\pi$
$431$	−12.8272			−0.617864			−0.308932	+	0.951084i	$0.599972\pi$
$432$	−2.06571	−	4.76790i	−0.0993865	−	0.229396i
$433$	32.8852			1.58036			0.790180	−	0.612874i	$-0.209987\pi$
$433$	32.8852			1.58036			0.790180	+	0.612874i	$0.209987\pi$
$434$	1.48816	−	2.57756i	0.0714338	−	0.123727i
$435$	1.09783	−	5.08124i	0.0526371	−	0.243627i
$436$	−5.85955	−	10.1490i	−0.280622	−	0.486051i
$437$	4.01096	+	6.94719i	0.191870	+	0.332329i
$438$	−12.7774	−	11.5824i	−0.610527	−	0.553431i
$439$	−10.9058	+	18.8894i	−0.520505	+	0.901541i	0.479211	+	0.877700i	$0.340923\pi$
$439$	−10.9058	+	18.8894i	−0.520505	+	0.901541i	−0.999716	+	0.0238414i	$0.992410\pi$
$440$	2.11156			0.100665
$441$	−2.02314	−	20.5723i	−0.0963400	−	0.979633i
$442$	4.15564			0.197664
$443$	−13.0212	+	22.5534i	−0.618657	+	1.07155i	0.371074	+	0.928603i	$0.378990\pi$
$443$	−13.0212	+	22.5534i	−0.618657	+	1.07155i	−0.989731	+	0.142943i	$0.954344\pi$
$444$	−8.68287	+	2.78915i	−0.412071	+	0.132367i
$445$	0.234329	+	0.405870i	0.0111083	+	0.0192401i
$446$	5.04416	+	8.73674i	0.238848	+	0.413697i
$447$	21.0341	−	6.75666i	0.994877	−	0.319579i
$448$	0.165447	−	0.286563i	0.00781664	−	0.0135388i
$449$	11.0877			0.523262			0.261631	−	0.965168i	$-0.415740\pi$
$449$	11.0877			0.523262			0.261631	+	0.965168i	$0.415740\pi$
$450$	−1.40531	−	14.2899i	−0.0662468	−	0.673630i
$451$	28.4769			1.34092
$452$	5.42521	−	9.39674i	0.255180	−	0.441985i
$453$	8.43771	+	7.64863i	0.396438	+	0.359364i
$454$	−1.39594	−	2.41784i	−0.0655148	−	0.113475i
$455$	−0.0581646	−	0.100744i	−0.00272680	−	0.00472296i
$456$	−2.93426	+	13.5810i	−0.137410	+	0.635990i
$457$	3.97904	−	6.89190i	0.186132	−	0.322389i	−0.757826	−	0.652457i	$-0.773738\pi$
$457$	3.97904	−	6.89190i	0.186132	−	0.322389i	0.943957	+	0.330068i	$0.107072\pi$
$458$	9.81719			0.458727
$459$	−16.9205	+	22.8042i	−0.789782	+	1.06441i
$460$	−0.462315			−0.0215555
$461$	−14.3134	+	24.7915i	−0.666640	+	1.15465i	0.312198	+	0.950017i	$0.398935\pi$
$461$	−14.3134	+	24.7915i	−0.666640	+	1.15465i	−0.978838	+	0.204637i	$0.934399\pi$
$462$	0.552809	−	2.55864i	0.0257190	−	0.119039i
$463$	−9.28647	−	16.0846i	−0.431579	−	0.747516i	0.565431	−	0.824796i	$-0.308710\pi$
$463$	−9.28647	−	16.0846i	−0.431579	−	0.747516i	−0.997009	+	0.0772794i	$0.975377\pi$
$464$	3.24600	+	5.62223i	0.150692	+	0.261006i
$465$	−5.33640	−	4.83735i	−0.247470	−	0.224327i
$466$	−10.4833	+	18.1575i	−0.485628	+	0.841132i
$467$	−22.8820			−1.05885			−0.529427	−	0.848356i	$-0.677593\pi$
$467$	−22.8820			−1.05885			−0.529427	+	0.848356i	$0.677593\pi$
$468$	1.85455	−	1.32854i	0.0857264	−	0.0614116i
$469$	4.52469			0.208931
$470$	−1.75593	+	3.04136i	−0.0809949	+	0.140287i
$471$	−0.411968	+	0.132334i	−0.0189825	+	0.00609764i
$472$	6.14839	+	10.6493i	0.283002	+	0.490175i
$473$	1.78986	+	3.10013i	0.0822979	+	0.142544i
$474$	5.83385	−	1.87398i	0.267958	−	0.0860746i
$475$	−19.1975	+	33.2511i	−0.880844	+	1.52567i
$476$	−1.80828			−0.0828823
$477$	17.6930	+	8.01972i	0.810106	+	0.367198i
$478$	14.4384			0.660397
$479$	−3.69343	+	6.39721i	−0.168757	+	0.292296i	−0.937983	−	0.346681i	$-0.887309\pi$
$479$	−3.69343	+	6.39721i	−0.168757	+	0.292296i	0.769226	+	0.638977i	$0.220642\pi$
$480$	−0.593279	−	0.537796i	−0.0270794	−	0.0245469i
$481$	−2.00198	−	3.46752i	−0.0912822	−	0.158105i
$482$	−5.09582	−	8.82622i	−0.232108	−	0.402023i
$483$	−0.121035	+	0.560200i	−0.00550727	+	0.0254900i
$484$	−4.93041	+	8.53973i	−0.224110	+	0.388169i
$485$	−1.00313			−0.0455497
$486$	−0.260783	+	15.5863i	−0.0118293	+	0.707008i
$487$	−29.1373			−1.32034			−0.660168	−	0.751118i	$-0.729515\pi$
$487$	−29.1373			−1.32034			−0.660168	+	0.751118i	$0.729515\pi$
$488$	−5.55142	+	9.61535i	−0.251301	+	0.435266i
$489$	−0.534107	+	2.47207i	−0.0241531	+	0.111791i
$490$	−1.59279	−	2.75880i	−0.0719550	−	0.124630i
$491$	3.52986	+	6.11389i	0.159300	+	0.275916i	0.934617	−	0.355657i	$-0.115743\pi$
$491$	3.52986	+	6.11389i	0.159300	+	0.275916i	−0.775316	+	0.631573i	$0.782410\pi$
$492$	−8.00107	−	7.25281i	−0.360716	−	0.326982i
$493$	17.7388	−	30.7245i	0.798915	−	1.38376i
$494$	−6.10015			−0.274459
$495$	−5.76965	−	2.61522i	−0.259326	−	0.117545i
$496$	8.99475			0.403876
$497$	0.536542	−	0.929318i	0.0240672	−	0.0416856i
$498$	13.0354	−	4.18730i	0.584132	−	0.187637i
$499$	8.01005	+	13.8738i	0.358579	+	0.621078i	0.987724	−	0.156211i	$-0.0499279\pi$
$499$	8.01005	+	13.8738i	0.358579	+	0.621078i	−0.629144	+	0.777288i	$0.716595\pi$
$500$	−2.26217	−	3.91819i	−0.101167	−	0.175227i
$501$	0.448847	−	0.144181i	0.0200530	−	0.00644151i
$502$	−12.8487	+	22.2545i	−0.573463	+	0.993268i
$503$	25.9060			1.15509			0.577545	−	0.816359i	$-0.304011\pi$
$503$	25.9060			1.15509			0.577545	+	0.816359i	$0.304011\pi$
$504$	−0.806984	+	0.578097i	−0.0359459	+	0.0257505i
$505$	−6.07733			−0.270438
$506$	2.28368	−	3.95545i	0.101522	−	0.175841i
$507$	−15.9406	−	14.4498i	−0.707945	−	0.641739i
$508$	4.05925	+	7.03083i	0.180100	+	0.311943i
$509$	0.664666	+	1.15123i	0.0294608	+	0.0510276i	0.880380	−	0.474269i	$-0.157288\pi$
$509$	0.664666	+	1.15123i	0.0294608	+	0.0510276i	−0.850919	+	0.525297i	$0.823954\pi$
$510$	−0.924132	+	4.27728i	−0.0409213	+	0.189401i
$511$	−1.64733	+	2.85325i	−0.0728734	+	0.126220i
$512$	1.00000			0.0441942
$513$	24.8380	−	33.4748i	1.09663	−	1.47795i
$514$	5.45446			0.240586
$515$	2.26195	−	3.91780i	0.0996732	−	0.172639i
$516$	0.286684	−	1.32690i	0.0126206	−	0.0584134i
$517$	−17.3474	−	30.0466i	−0.762938	−	1.32145i
$518$	0.871136	+	1.50885i	0.0382755	+	0.0662952i
$519$	−12.6851	−	11.4988i	−0.556814	−	0.504742i
$520$	0.175780	−	0.304460i	0.00770847	−	0.0133515i
$521$	−10.3015			−0.451318			−0.225659	−	0.974206i	$-0.572454\pi$
$521$	−10.3015			−0.451318			−0.225659	+	0.974206i	$0.572454\pi$
$522$	−1.90613	−	19.3825i	−0.0834291	−	0.848348i
$523$	2.63399			0.115176			0.0575881	−	0.998340i	$-0.481659\pi$
$523$	2.63399			0.115176			0.0575881	+	0.998340i	$0.481659\pi$
$524$	5.50879	−	9.54150i	0.240652	−	0.416822i
$525$	−2.61169	+	0.838940i	−0.113984	+	0.0366144i
$526$	8.70499	+	15.0775i	0.379556	+	0.657410i
$527$	−24.5773	−	42.5692i	−1.07061	−	1.85434i
$528$	7.53186	−	2.41942i	0.327782	−	0.105292i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	2.99360			0.130033
$531$	−3.61049	−	36.7132i	−0.156682	−	1.59322i
$532$	2.65441			0.115083
$533$	2.37060	−	4.10600i	0.102682	−	0.177851i
$534$	1.30089	+	1.17923i	0.0562949	+	0.0510303i
$535$	−0.457432	−	0.792296i	−0.0197765	−	0.0342539i
$536$	6.83706	+	11.8421i	0.295316	+	0.511502i
$537$	−6.75326	+	31.2570i	−0.291425	+	1.34884i
$538$	11.2376	−	19.4641i	0.484488	−	0.839158i
$539$	31.4715			1.35557
$540$	0.955009	+	2.20427i	0.0410970	+	0.0948567i
$541$	−12.9690			−0.557581			−0.278791	−	0.960352i	$-0.589934\pi$
$541$	−12.9690			−0.557581			−0.278791	+	0.960352i	$0.589934\pi$
$542$	11.2838	−	19.5441i	0.484680	−	0.839490i
$543$	6.85268	−	31.7171i	0.294077	−	1.36111i
$544$	−2.73241	−	4.73267i	−0.117151	−	0.202912i
$545$	2.70896	+	4.69205i	0.116039	+	0.200985i
$546$	−0.322903	−	0.292706i	−0.0138190	−	0.0125266i
$547$	2.00516	−	3.47305i	0.0857346	−	0.148497i	−0.819969	−	0.572407i	$-0.806010\pi$
$547$	2.00516	−	3.47305i	0.0857346	−	0.148497i	0.905704	+	0.423911i	$0.139343\pi$
$548$	7.12741			0.304468
$549$	27.0776	−	19.3975i	1.15564	−	0.827865i
$550$	21.8606			0.932140
$551$	−26.0392	+	45.1012i	−1.10931	+	1.92137i
$552$	−1.64906	+	0.529718i	−0.0701886	+	0.0225463i
$553$	−0.585300	−	1.01377i	−0.0248895	−	0.0431098i
$554$	3.01285	+	5.21841i	0.128004	+	0.221709i
$555$	4.01422	−	1.28947i	0.170394	−	0.0547348i
$556$	6.82958	−	11.8292i	0.289639	−	0.501669i
$557$	−3.91047			−0.165692			−0.0828461	−	0.996562i	$-0.526401\pi$
$557$	−3.91047			−0.165692			−0.0828461	+	0.996562i	$0.526401\pi$
$558$	−24.5773	−	11.1402i	−1.04044	−	0.471603i
$559$	0.595999			0.0252081
$560$	−0.0764887	+	0.132482i	−0.00323224	+	0.00559840i
$561$	−32.0304	−	29.0350i	−1.35233	−	1.22586i
$562$	−3.54046	−	6.13225i	−0.149345	−	0.258674i
$563$	−14.6134	−	25.3112i	−0.615882	−	1.06674i	−0.990229	−	0.139450i	$-0.955467\pi$
$563$	−14.6134	−	25.3112i	−0.615882	−	1.06674i	0.374347	−	0.927289i	$-0.377867\pi$
$564$	−2.77856	+	12.8603i	−0.116998	+	0.541518i
$565$	−2.50815	+	4.34425i	−0.105519	+	0.182764i
$566$	8.21966			0.345498
$567$	2.92100	−	0.580130i	0.122670	−	0.0243632i
$568$	3.24298			0.136072
$569$	−6.03334	+	10.4500i	−0.252931	+	0.438089i	−0.964331	−	0.264698i	$-0.914728\pi$
$569$	−6.03334	+	10.4500i	−0.252931	+	0.438089i	0.711401	+	0.702787i	$0.248061\pi$
$570$	1.35655	−	6.27871i	0.0568198	−	0.262986i
$571$	17.5275	+	30.3585i	0.733502	+	1.27046i	0.955377	+	0.295388i	$0.0954489\pi$
$571$	17.5275	+	30.3585i	0.733502	+	1.27046i	−0.221875	+	0.975075i	$0.571218\pi$
$572$	1.73659	+	3.00786i	0.0726105	+	0.125765i
$573$	−21.6691	−	19.6426i	−0.905238	−	0.820581i
$574$	−1.03154	+	1.78668i	−0.0430556	+	0.0745745i
$575$	−4.78626			−0.199601
$576$	−2.73241	−	1.23852i	−0.113850	−	0.0516051i
$577$	34.1506			1.42171			0.710855	−	0.703339i	$-0.248308\pi$
$577$	34.1506			1.42171			0.710855	+	0.703339i	$0.248308\pi$
$578$	−6.43212	+	11.1408i	−0.267541	+	0.463395i
$579$	−20.5451	+	6.59959i	−0.853826	+	0.274270i
$580$	−1.50067	−	2.59924i	−0.0623121	−	0.107928i
$581$	−1.30782	−	2.26521i	−0.0542576	−	0.0939769i
$582$	−3.57812	+	1.14938i	−0.148318	+	0.0476433i
$583$	−14.7874	+	25.6125i	−0.612430	+	1.06076i
$584$	−9.95681			−0.412016
$585$	−0.857384	+	0.614202i	−0.0354485	+	0.0253941i
$586$	−26.7502			−1.10504
$587$	14.6722	−	25.4131i	0.605588	−	1.04891i	−0.386370	−	0.922344i	$-0.626271\pi$
$587$	14.6722	−	25.4131i	0.605588	−	1.04891i	0.991958	−	0.126566i	$-0.0403955\pi$
$588$	−8.84245	−	8.01551i	−0.364656	−	0.330554i
$589$	36.0776	+	62.4883i	1.48655	+	2.57479i
$590$	−2.84249	−	4.92334i	−0.117023	−	0.202691i
$591$	−3.89448	+	18.0253i	−0.160197	+	0.741462i
$592$	−2.63267	+	4.55992i	−0.108202	+	0.187412i
$593$	−30.3173			−1.24498			−0.622491	−	0.782627i	$-0.713879\pi$
$593$	−30.3173			−1.24498			−0.622491	+	0.782627i	$0.713879\pi$
$594$	−23.5766	−	2.71754i	−0.967361	−	0.111502i
$595$	0.835994			0.0342724
$596$	6.37759	−	11.0463i	0.261236	−	0.452475i
$597$	8.95802	−	41.4615i	0.366627	−	1.69691i
$598$	−0.380217	−	0.658556i	−0.0155482	−	0.0269303i
$599$	−12.6599	−	21.9277i	−0.517271	−	0.895940i	−0.999799	−	0.0200595i	$-0.993614\pi$
$599$	−12.6599	−	21.9277i	−0.517271	−	0.895940i	0.482527	−	0.875881i	$-0.339719\pi$
$600$	−6.14212	−	5.56771i	−0.250751	−	0.227301i
$601$	−23.7790	+	41.1865i	−0.969967	+	1.68003i	−0.274333	+	0.961635i	$0.588457\pi$
$601$	−23.7790	+	41.1865i	−0.969967	+	1.68003i	−0.695633	+	0.718397i	$0.744876\pi$
$602$	−0.259342			−0.0105700
$603$	−4.01489	−	40.8254i	−0.163499	−	1.66254i
$604$	6.57512			0.267538
$605$	2.27940	−	3.94804i	0.0926710	−	0.160511i
$606$	−21.6776	+	6.96338i	−0.880593	+	0.282868i
$607$	22.2047	+	38.4597i	0.901262	+	1.56103i	0.825857	+	0.563879i	$0.190692\pi$
$607$	22.2047	+	38.4597i	0.901262	+	1.56103i	0.0754049	+	0.997153i	$0.475975\pi$
$608$	4.01096	+	6.94719i	0.162666	+	0.281746i
$609$	−3.54245	+	1.13792i	−0.143547	+	0.0461109i
$610$	2.56651	−	4.44532i	0.103915	−	0.179986i
$611$	−5.77644			−0.233690
$612$	1.60454	+	16.3157i	0.0648596	+	0.659525i
$613$	−8.95266			−0.361595			−0.180797	−	0.983520i	$-0.557868\pi$
$613$	−8.95266			−0.361595			−0.180797	+	0.983520i	$0.557868\pi$
$614$	7.81939	−	13.5436i	0.315565	−	0.546575i
$615$	3.69901	+	3.35308i	0.149159	+	0.135209i
$616$	−0.755658	−	1.30884i	−0.0304463	−	0.0527346i
$617$	−19.1451	−	33.1603i	−0.770753	−	1.33498i	−0.937151	−	0.348925i	$-0.886547\pi$
$617$	−19.1451	−	33.1603i	−0.770753	−	1.33498i	0.166397	−	0.986059i	$-0.446787\pi$
$618$	3.57927	−	16.5664i	0.143979	−	0.666398i
$619$	−7.57988	+	13.1287i	−0.304661	+	0.527688i	−0.977186	−	0.212386i	$-0.931877\pi$
$619$	−7.57988	+	13.1287i	−0.304661	+	0.527688i	0.672525	+	0.740075i	$0.265210\pi$
$620$	−4.15841			−0.167006
$621$	5.16198	+	0.594991i	0.207143	+	0.0238762i
$622$	−7.22619			−0.289744
$623$	0.167717	−	0.290495i	0.00671945	−	0.0116384i
$624$	0.278152	−	1.28741i	0.0111350	−	0.0515375i
$625$	−10.9198	−	18.9137i	−0.436793	−	0.756548i
$626$	2.36744	+	4.10052i	0.0946218	+	0.163890i
$627$	47.0182	+	42.6211i	1.87773	+	1.70212i
$628$	−0.124910	+	0.216351i	−0.00498445	+	0.00863333i
$629$	28.7742			1.14730
$630$	0.373081	−	0.267263i	0.0148639	−	0.0106480i
$631$	−41.9087			−1.66836			−0.834180	−	0.551493i	$-0.814058\pi$
$631$	−41.9087			−1.66836			−0.834180	+	0.551493i	$0.814058\pi$
$632$	1.76884	−	3.06373i	0.0703608	−	0.121868i
$633$	−24.7045	+	7.93570i	−0.981917	+	0.315416i
$634$	−6.83798	−	11.8437i	−0.271571	−	0.470375i
$635$	−1.87665	−	3.25046i	−0.0744727	−	0.128991i
$636$	10.6780	−	3.43005i	0.423412	−	0.136010i
$637$	2.61989	−	4.53778i	0.103804	−	0.179794i
$638$	29.6513			1.17391
$639$	−8.86115	−	4.01651i	−0.350542	−	0.158891i
$640$	−0.462315			−0.0182746
$641$	6.98287	−	12.0947i	0.275807	−	0.477712i	−0.694531	−	0.719462i	$-0.744388\pi$
$641$	6.98287	−	12.0947i	0.275807	−	0.477712i	0.970338	+	0.241751i	$0.0777216\pi$
$642$	−2.53945	−	2.30197i	−0.100224	−	0.0908513i
$643$	−2.04476	−	3.54163i	−0.0806376	−	0.139668i	0.822886	−	0.568206i	$-0.192362\pi$
$643$	−2.04476	−	3.54163i	−0.0806376	−	0.139668i	−0.903524	+	0.428538i	$0.859029\pi$
$644$	0.165447	+	0.286563i	0.00651953	+	0.0112922i
$645$	−0.132538	+	0.613444i	−0.00521870	+	0.0241543i
$646$	21.9192	−	37.9652i	0.862399	−	1.49372i
$647$	47.5565			1.86964			0.934819	−	0.355125i	$-0.115562\pi$
$647$	47.5565			1.86964			0.934819	+	0.355125i	$0.115562\pi$
$648$	5.93212	+	6.76830i	0.233036	+	0.265884i
$649$	56.1639			2.20462
$650$	1.81982	−	3.15202i	0.0713792	−	0.123632i
$651$	−1.08868	+	5.03886i	−0.0426686	+	0.197488i
$652$	0.730092	+	1.26456i	0.0285926	+	0.0495238i
$653$	−12.1621	−	21.0653i	−0.475939	−	0.824350i	0.523681	−	0.851914i	$-0.324558\pi$
$653$	−12.1621	−	21.0653i	−0.475939	−	0.824350i	−0.999620	+	0.0275643i	$0.991225\pi$
$654$	15.0389	+	13.6325i	0.588067	+	0.533072i
$655$	−2.54679	+	4.41118i	−0.0995115	+	0.172359i
$656$	−6.23486			−0.243430
$657$	27.2061	+	12.3317i	1.06141	+	0.481107i
$658$	2.51355			0.0979885
$659$	9.51939	−	16.4881i	0.370823	−	0.642284i	−0.618870	−	0.785494i	$-0.712409\pi$
$659$	9.51939	−	16.4881i	0.370823	−	0.642284i	0.989692	+	0.143210i	$0.0457424\pi$
$660$	−3.48209	+	1.11853i	−0.135540	+	0.0435388i
$661$	−11.5945	−	20.0823i	−0.450974	−	0.781110i	0.547473	−	0.836823i	$-0.315590\pi$
$661$	−11.5945	−	20.0823i	−0.450974	−	0.781110i	−0.998447	+	0.0557138i	$0.982257\pi$
$662$	−5.11673	−	8.86244i	−0.198867	−	0.344448i
$663$	−6.85290	+	2.20132i	−0.266144	+	0.0854921i
$664$	3.95239	−	6.84573i	0.153382	−	0.265666i
$665$	−1.22717			−0.0475878
$666$	12.8411	−	9.19895i	0.497583	−	0.356452i
$667$	−6.49200			−0.251371
$668$	0.136092	−	0.235718i	0.00526555	−	0.00912020i
$669$	−12.9461	−	11.7354i	−0.500526	−	0.453718i
$670$	−3.16087	−	5.47479i	−0.122115	−	0.211510i
$671$	25.3554	+	43.9168i	0.978834	+	1.69539i
$672$	−0.121035	+	0.560200i	−0.00466901	+	0.0216102i
$673$	14.6135	−	25.3114i	0.563310	−	0.975682i	−0.433894	−	0.900964i	$-0.642861\pi$
$673$	14.6135	−	25.3114i	0.563310	−	0.975682i	0.997205	−	0.0747182i	$-0.0238057\pi$
$674$	0.463712			0.0178615
$675$	9.88704	+	22.8204i	0.380552	+	0.878358i
$676$	−12.4217			−0.477759
$677$	6.08808	−	10.5449i	0.233984	−	0.405272i	−0.724993	−	0.688756i	$-0.758157\pi$
$677$	6.08808	−	10.5449i	0.233984	−	0.405272i	0.958977	+	0.283484i	$0.0914903\pi$
$678$	−3.96887	+	18.3696i	−0.152424	+	0.705481i
$679$	0.358986	+	0.621782i	0.0137766	+	0.0238618i
$680$	1.26323	+	2.18798i	0.0484428	+	0.0839054i
$681$	3.58277	+	3.24771i	0.137292	+	0.124453i
$682$	20.5412	−	35.5783i	0.786562	−	1.36236i
$683$	7.93647			0.303680			0.151840	−	0.988405i	$-0.451480\pi$
$683$	7.93647			0.303680			0.151840	+	0.988405i	$0.451480\pi$
$684$	−2.35534	−	23.9503i	−0.0900586	−	0.915761i
$685$	−3.29511			−0.125900
$686$	−2.29814	+	3.98050i	−0.0877436	+	0.151976i
$687$	−16.1891	+	5.20034i	−0.617654	+	0.198405i
$688$	−0.391880	−	0.678757i	−0.0149403	−	0.0258774i
$689$	2.46199	+	4.26430i	0.0937945	+	0.162457i
$690$	0.762385	−	0.244897i	0.0290235	−	0.00932306i
$691$	1.67921	−	2.90848i	0.0638802	−	0.110644i	−0.832317	−	0.554301i	$-0.812986\pi$
$691$	1.67921	−	2.90848i	0.0638802	−	0.110644i	0.896197	+	0.443657i	$0.146319\pi$
$692$	−9.88491			−0.375768
$693$	0.443741	+	4.51218i	0.0168563	+	0.171403i
$694$	−13.7455			−0.521772
$695$	−3.15741	+	5.46880i	−0.119768	+	0.207444i
$696$	−8.33104	−	7.55193i	−0.315787	−	0.286255i
$697$	17.0362	+	29.5075i	0.645292	+	1.11768i
$698$	−6.73858	−	11.6716i	−0.255059	−	0.441775i
$699$	7.66915	−	35.4961i	0.290074	−	1.34258i
$700$	−0.791874	+	1.37157i	−0.0299300	+	0.0518403i
$701$	41.1752			1.55517			0.777583	−	0.628781i	$-0.216446\pi$
$701$	41.1752			1.55517			0.777583	+	0.628781i	$0.216446\pi$
$702$	−2.35451	+	3.17322i	−0.0888651	+	0.119766i
$703$	−42.2382			−1.59304
$704$	2.28368	−	3.95545i	0.0860695	−	0.149077i
$705$	1.28457	−	5.94552i	0.0483796	−	0.223921i
$706$	10.3062	+	17.8509i	0.387880	+	0.671828i
$707$	2.17488	+	3.76700i	0.0817946	+	0.141672i
$708$	−15.7802	−	14.3044i	−0.593056	−	0.537594i
$709$	−9.34605	+	16.1878i	−0.350998	+	0.607947i	−0.986425	−	0.164215i	$-0.947491\pi$
$709$	−9.34605	+	16.1878i	−0.350998	+	0.607947i	0.635426	+	0.772161i	$0.280824\pi$
$710$	−1.49928			−0.0562669
$711$	−8.62770	+	6.18060i	−0.323564	+	0.231791i
$712$	1.01372			0.0379908
$713$	−4.49738	+	7.78968i	−0.168428	+	0.291726i
$714$	2.98196	−	0.957878i	0.111597	−	0.0358477i
$715$	−0.802852	−	1.39058i	−0.0300250	−	0.0520048i
$716$	9.23131	+	15.9891i	0.344990	+	0.597541i
$717$	−23.8098	+	7.64828i	−0.889193	+	0.285630i
$718$	−17.1048	+	29.6265i	−0.638347	+	1.10565i
$719$	−3.02473			−0.112803			−0.0564017	−	0.998408i	$-0.517963\pi$
$719$	−3.02473			−0.112803			−0.0564017	+	0.998408i	$0.517963\pi$
$720$	1.26323	+	0.572588i	0.0470779	+	0.0213391i
$721$	−3.23790			−0.120586
$722$	−22.6757	+	39.2754i	−0.843901	+	1.46168i
$723$	13.0787	+	11.8556i	0.486403	+	0.440915i
$724$	−9.36721	−	16.2245i	−0.348130	−	0.602978i
$725$	−15.5362	−	26.9095i	−0.577000	−	0.999394i
$726$	3.60690	−	16.6943i	0.133865	−	0.619582i
$727$	7.82638	−	13.5557i	0.290264	−	0.502753i	−0.683608	−	0.729850i	$-0.739590\pi$
$727$	7.82638	−	13.5557i	0.290264	−	0.502753i	0.973872	+	0.227097i	$0.0729234\pi$
$728$	−0.251623			−0.00932579
$729$	−7.82629	−	25.8408i	−0.289863	−	0.957068i
$730$	4.60318			0.170371
$731$	−2.14156	+	3.70928i	−0.0792083	+	0.137193i
$732$	4.06120	−	18.7970i	0.150106	−	0.694756i
$733$	7.04905	+	12.2093i	0.260363	+	0.450961i	0.966338	−	0.257275i	$-0.0828245\pi$
$733$	7.04905	+	12.2093i	0.260363	+	0.450961i	−0.705976	+	0.708236i	$0.749491\pi$
$734$	−12.0295	−	20.8356i	−0.444016	−	0.769058i
$735$	4.08800	+	3.70569i	0.150788	+	0.136686i
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	62.4547			2.30055
$738$	17.0362	+	7.72201i	0.627111	+	0.284251i
$739$	20.2291			0.744141			0.372070	−	0.928205i	$-0.378648\pi$
$739$	20.2291			0.744141			0.372070	+	0.928205i	$0.378648\pi$
$740$	1.21712	−	2.10812i	0.0447424	−	0.0774960i
$741$	10.0595	−	3.23136i	0.369546	−	0.118707i
$742$	−1.07131	−	1.85556i	−0.0393290	−	0.0681198i
$743$	2.06026	+	3.56848i	0.0755836	+	0.130915i	0.901340	−	0.433112i	$-0.142585\pi$
$743$	2.06026	+	3.56848i	0.0755836	+	0.130915i	−0.825756	+	0.564027i	$0.809251\pi$
$744$	−14.8329	+	4.76469i	−0.543800	+	0.174682i
$745$	−2.94846	+	5.10688i	−0.108023	+	0.187101i
$746$	23.4428			0.858302
$747$	−19.2781	+	13.8102i	−0.705350	+	0.505290i
$748$	−24.9598			−0.912622
$749$	−0.327400	+	0.567073i	−0.0119629	+	0.0207204i
$750$	5.80599	+	5.26302i	0.212005	+	0.192178i
$751$	21.4180	+	37.0971i	0.781555	+	1.35369i	0.931036	+	0.364928i	$0.118906\pi$
$751$	21.4180	+	37.0971i	0.781555	+	1.35369i	−0.149481	+	0.988765i	$0.547760\pi$
$752$	3.79812	+	6.57854i	0.138503	+	0.239895i
$753$	9.39957	−	43.5052i	0.342539	−	1.58542i
$754$	2.46837	−	4.27534i	0.0898927	−	0.155699i
$755$	−3.03977			−0.110629
$756$	1.02454	−	1.38079i	0.0372620	−	0.0502189i
$757$	48.7258			1.77097			0.885484	−	0.464670i	$-0.153827\pi$
$757$	48.7258			1.77097			0.885484	+	0.464670i	$0.153827\pi$
$758$	4.99516	−	8.65186i	0.181432	−	0.314250i
$759$	−1.67065	+	7.73249i	−0.0606409	+	0.280672i
$760$	−1.85433	−	3.21179i	−0.0672636	−	0.116504i
$761$	1.79282	+	3.10525i	0.0649896	+	0.112565i	0.896689	−	0.442660i	$-0.145965\pi$
$761$	1.79282	+	3.10525i	0.0649896	+	0.112565i	−0.831700	+	0.555226i	$0.812632\pi$
$762$	−10.4183	−	9.44400i	−0.377416	−	0.342120i
$763$	1.93889	−	3.35826i	0.0701926	−	0.121577i
$764$	−16.8857			−0.610903
$765$	−0.741802	−	7.54301i	−0.0268199	−	0.272718i
$766$	15.3660			0.555195
$767$	4.67545	−	8.09811i	0.168821	−	0.292406i
$768$	−1.64906	+	0.529718i	−0.0595053	+	0.0191146i
$769$	1.52772	+	2.64609i	0.0550909	+	0.0954203i	0.892256	−	0.451531i	$-0.149122\pi$
$769$	1.52772	+	2.64609i	0.0550909	+	0.0954203i	−0.837165	+	0.546951i	$0.815788\pi$
$770$	0.349352	+	0.605095i	0.0125898	+	0.0218061i
$771$	−8.99473	+	2.88933i	−0.323937	+	0.104057i
$772$	−6.22934	+	10.7895i	−0.224199	+	0.388324i
$773$	−19.0622			−0.685618			−0.342809	−	0.939405i	$-0.611378\pi$
$773$	−19.0622			−0.685618			−0.342809	+	0.939405i	$0.611378\pi$
$774$	0.230122	+	2.33999i	0.00827157	+	0.0841094i
$775$	−43.0513			−1.54645
$776$	−1.08490	+	1.87910i	−0.0389455	+	0.0674556i
$777$	−2.23582	−	2.02673i	−0.0802097	−	0.0727086i
$778$	13.2837	+	23.0080i	0.476243	+	0.824877i
$779$	−25.0078	−	43.3148i	−0.895997	−	1.55191i
$780$	−0.128594	+	0.595187i	−0.00460440	+	0.0213111i
$781$	7.40594	−	12.8275i	0.265005	−	0.459003i
$782$	5.46482			0.195422
$783$	13.4106	+	30.9532i	0.479255	+	1.10618i
$784$	−6.89051			−0.246090
$785$	0.0577478	−	0.100022i	0.00206111	−	0.00356994i
$786$	−4.03001	+	18.6526i	−0.143746	+	0.665316i
$787$	25.0789	+	43.4380i	0.893968	+	1.54840i	0.835077	+	0.550133i	$0.185423\pi$
$787$	25.0789	+	43.4380i	0.893968	+	1.54840i	0.0588904	+	0.998264i	$0.481244\pi$
$788$	5.32352	+	9.22061i	0.189643	+	0.328471i
$789$	−22.3419	−	20.2525i	−0.795392	−	0.721008i
$790$	−0.817762	+	1.41641i	−0.0290947	+	0.0503935i
$791$	3.59034			0.127658
$792$	−11.1389	+	7.97953i	−0.395803	+	0.283540i
$793$	8.44299			0.299819
$794$	15.0496	−	26.0667i	0.534091	−	0.925072i
$795$	−4.93662	+	1.58576i	−0.175084	+	0.0562412i
$796$	−12.2451	−	21.2091i	−0.434015	−	0.751737i
$797$	26.0511	+	45.1218i	0.922777	+	1.59830i	0.795097	+	0.606482i	$0.207420\pi$
$797$	26.0511	+	45.1218i	0.922777	+	1.59830i	0.127680	+	0.991815i	$0.459247\pi$
$798$	−4.37728	+	1.40609i	−0.154954	+	0.0497750i
$799$	20.7560	−	35.9505i	0.734296	−	1.27184i
$800$	−4.78626			−0.169220
$801$	−2.76990	−	1.25552i	−0.0978697	−	0.0443615i
$802$	−13.9215			−0.491586
$803$	−22.7382	+	39.3837i	−0.802414	+	1.38982i
$804$	−17.5477	−	15.9067i	−0.618860	−	0.560985i
$805$	−0.0764887	−	0.132482i	−0.00269587	−	0.00466939i
$806$	−3.41996	−	5.92355i	−0.120463	−	0.208648i
$807$	−8.22100	+	38.0503i	−0.289393	+	1.33943i
$808$	−6.57272	+	11.3843i	−0.231228	+	0.400498i
$809$	28.3367			0.996264			0.498132	−	0.867101i	$-0.334020\pi$
$809$	28.3367			0.996264			0.498132	+	0.867101i	$0.334020\pi$
$810$	−2.74251	−	3.12909i	−0.0963619	−	0.109945i
$811$	17.4870			0.614051			0.307026	−	0.951701i	$-0.400666\pi$
$811$	17.4870			0.614051			0.307026	+	0.951701i	$0.400666\pi$
$812$	−1.07408	+	1.86036i	−0.0376929	+	0.0652860i
$813$	−8.25477	+	38.2066i	−0.289507	+	1.33996i
$814$	12.0244	+	20.8268i	0.421454	+	0.729980i
$815$	−0.337532	−	0.584623i	−0.0118232	−	0.0204785i
$816$	7.01289	+	6.35705i	0.245500	+	0.222541i
$817$	3.14364	−	5.44494i	0.109982	−	0.190494i
$818$	−18.5739			−0.649420
$819$	0.687538	+	0.311641i	0.0240245	+	0.0108896i
$820$	2.88247			0.100660
$821$	−3.58074	+	6.20202i	−0.124969	+	0.216452i	−0.921721	−	0.387854i	$-0.873216\pi$
$821$	−3.58074	+	6.20202i	−0.124969	+	0.216452i	0.796752	+	0.604306i	$0.206550\pi$
$822$	−11.7535	+	3.77552i	−0.409952	+	0.131686i
$823$	−7.51324	−	13.0133i	−0.261895	−	0.453615i	0.704850	−	0.709356i	$-0.251014\pi$
$823$	−7.51324	−	13.0133i	−0.261895	−	0.453615i	−0.966745	+	0.255740i	$0.917681\pi$
$824$	−4.89265	−	8.47432i	−0.170444	−	0.295217i
$825$	−36.0495	+	11.5800i	−1.25508	+	0.403163i
$826$	−2.03447	+	3.52380i	−0.0707881	+	0.122609i
$827$	−25.4995			−0.886703			−0.443351	−	0.896348i	$-0.646211\pi$
$827$	−25.4995			−0.886703			−0.443351	+	0.896348i	$0.646211\pi$
$828$	2.43880	−	1.74707i	0.0847541	−	0.0607150i
$829$	−20.6854			−0.718434			−0.359217	−	0.933254i	$-0.616956\pi$
$829$	−20.6854			−0.718434			−0.359217	+	0.933254i	$0.616956\pi$
$830$	−1.82725	+	3.16488i	−0.0634247	+	0.109855i
$831$	−7.73265	−	7.00950i	−0.268243	−	0.243157i
$832$	−0.380217	−	0.658556i	−0.0131817	−	0.0228313i
$833$	18.8277	+	32.6105i	0.652341	+	1.12989i
$834$	−4.99625	+	23.1248i	−0.173006	+	0.800745i
$835$	−0.0629172	+	0.108976i	−0.00217734	+	0.00377127i
$836$	36.6391			1.26719
$837$	46.4307	+	5.35180i	1.60488	+	0.184985i
$838$	10.5458			0.364299
$839$	17.0416	−	29.5169i	0.588342	−	1.01904i	−0.406108	−	0.913825i	$-0.633114\pi$
$839$	17.0416	−	29.5169i	0.588342	−	1.01904i	0.994450	−	0.105213i	$-0.0335524\pi$
$840$	0.0559561	−	0.258989i	0.00193067	−	0.00893596i
$841$	−6.57300	−	11.3848i	−0.226655	−	0.392578i
$842$	−5.91002	−	10.2365i	−0.203673	−	0.352771i
$843$	9.08680	+	8.23701i	0.312966	+	0.283698i
$844$	−7.49049	+	12.9739i	−0.257833	+	0.446580i
$845$	5.74276			0.197557
$846$	−2.23035	−	22.6793i	−0.0766810	−	0.779731i
$847$	−3.26289			−0.112114
$848$	3.23762	−	5.60771i	0.111180	−	0.192570i
$849$	−13.5547	+	4.35410i	−0.465196	+	0.149432i
$850$	13.0780	+	22.6518i	0.448573	+	0.776951i
$851$	−2.63267	−	4.55992i	−0.0902469	−	0.156312i
$852$	−5.34787	+	1.71787i	−0.183215	+	0.0588532i
$853$	−27.0666	+	46.8807i	−0.926741	+	1.60516i	−0.138005	+	0.990432i	$0.544069\pi$
$853$	−27.0666	+	46.8807i	−0.926741	+	1.60516i	−0.788736	+	0.614731i	$0.789264\pi$
$854$	−3.67387			−0.125717
$855$	1.08891	+	11.0726i	0.0372399	+	0.378674i
$856$	−1.97888			−0.0676366
$857$	−11.9091	+	20.6271i	−0.406806	+	0.704609i	−0.994530	−	0.104453i	$-0.966691\pi$
$857$	−11.9091	+	20.6271i	−0.406806	+	0.704609i	0.587724	+	0.809062i	$0.300024\pi$
$858$	−4.45706	−	4.04024i	−0.152162	−	0.137932i
$859$	5.76931	+	9.99274i	0.196846	+	0.340948i	0.947504	−	0.319743i	$-0.103597\pi$
$859$	5.76931	+	9.99274i	0.196846	+	0.340948i	−0.750658	+	0.660691i	$0.770263\pi$
$860$	0.181172	+	0.313799i	0.00617792	+	0.0107005i
$861$	0.754634	−	3.49277i	0.0257178	−	0.119033i
$862$	6.41360	−	11.1087i	0.218448	−	0.378363i
$863$	14.9530			0.509007			0.254503	−	0.967072i	$-0.418088\pi$
$863$	14.9530			0.509007			0.254503	+	0.967072i	$0.418088\pi$
$864$	5.16198	+	0.594991i	0.175614	+	0.0202420i
$865$	4.56994			0.155383
$866$	−16.4426	+	28.4794i	−0.558742	+	0.967769i
$867$	4.70549	−	21.7790i	0.159807	−	0.739654i
$868$	1.48816	+	2.57756i	0.0505113	+	0.0874882i
$869$	−8.07895	−	13.9932i	−0.274060	−	0.474685i
$870$	3.85157	+	3.49137i	0.130580	+	0.118369i
$871$	5.19913	−	9.00517i	0.176166	−	0.305128i
$872$	11.7191			0.396859
$873$	5.29168	−	3.79079i	0.179096	−	0.128299i
$874$	−8.02193			−0.271346
$875$	0.748538	−	1.29651i	0.0253052	−	0.0438299i
$876$	16.4194	−	5.27431i	0.554760	−	0.178202i
$877$	−25.9199	−	44.8946i	−0.875252	−	1.51598i	−0.856494	−	0.516158i	$-0.827362\pi$
$877$	−25.9199	−	44.8946i	−0.875252	−	1.51598i	−0.0187587	−	0.999824i	$-0.505971\pi$
$878$	−10.9058	−	18.8894i	−0.368053	−	0.637486i
$879$	44.1127	−	14.1701i	1.48789	−	0.477945i
$880$	−1.05578	+	1.82867i	−0.0355904	+	0.0616443i
$881$	−17.0034			−0.572861			−0.286430	−	0.958101i	$-0.592469\pi$
$881$	−17.0034			−0.572861			−0.286430	+	0.958101i	$0.592469\pi$
$882$	18.8277	+	8.53405i	0.633961	+	0.287356i
$883$	−53.8730			−1.81297			−0.906485	−	0.422238i	$-0.861245\pi$
$883$	−53.8730			−1.81297			−0.906485	+	0.422238i	$0.861245\pi$
$884$	−2.07782	+	3.59889i	−0.0698846	+	0.121044i
$885$	7.29542	+	6.61316i	0.245233	+	0.222299i
$886$	−13.0212	−	22.5534i	−0.437457	−	0.757697i
$887$	2.39035	+	4.14020i	0.0802599	+	0.139014i	0.903362	−	0.428880i	$-0.141092\pi$
$887$	2.39035	+	4.14020i	0.0802599	+	0.139014i	−0.823102	+	0.567894i	$0.807758\pi$
$888$	1.92596	−	8.91416i	0.0646310	−	0.299140i
$889$	−1.34318	+	2.32646i	−0.0450489	+	0.0780270i
$890$	−0.468659			−0.0157095
$891$	40.3188	−	8.00758i	1.35073	−	0.268264i
$892$	−10.0883			−0.337782
$893$	−30.4682	+	52.7726i	−1.01958	+	1.76597i
$894$	−4.66560	+	21.5944i	−0.156041	+	0.722224i
$895$	−4.26777	−	7.39200i	−0.142656	−	0.247087i
$896$	0.165447	+	0.286563i	0.00552720	+	0.00957339i
$897$	0.975850	+	0.884590i	0.0325827	+	0.0295356i
$898$	−5.54386	+	9.60225i	−0.185001	+	0.320431i
$899$	−58.3939			−1.94755
$900$	13.0780	+	5.92790i	0.435935	+	0.197597i
$901$	−35.3860			−1.17888
$902$	−14.2384	+	24.6617i	−0.474088	+	0.821145i
$903$	0.427671	−	0.137378i	0.0142320	−	0.00457166i
$904$	5.42521	+	9.39674i	0.180440	+	0.312531i
$905$	4.33060	+	7.50082i	0.143954	+	0.249336i
$906$	−10.8428	+	3.48296i	−0.360227	+	0.115714i
$907$	−11.3507	+	19.6601i	−0.376895	+	0.652802i	−0.990609	−	0.136727i	$-0.956342\pi$
$907$	−11.3507	+	19.6601i	−0.376895	+	0.652802i	0.613714	+	0.789529i	$0.289675\pi$
$908$	2.79188			0.0926520
$909$	32.0591	−	22.9661i	1.06333	−	0.761736i
$910$	0.116329			0.00385628
$911$	−12.0719	+	20.9092i	−0.399961	+	0.692752i	−0.993721	−	0.111890i	$-0.964310\pi$
$911$	−12.0719	+	20.9092i	−0.399961	+	0.692752i	0.593760	+	0.804642i	$0.297643\pi$
$912$	−10.2944	−	9.33166i	−0.340881	−	0.309002i
$913$	−18.0520	−	31.2670i	−0.597434	−	1.03479i
$914$	3.97904	+	6.89190i	0.131615	+	0.227964i
$915$	−1.87756	+	8.69012i	−0.0620701	+	0.287287i
$916$	−4.90859	+	8.50193i	−0.162184	+	0.280912i
$917$	3.64565			0.120390
$918$	−11.2887	−	26.0557i	−0.372584	−	0.859966i
$919$	29.1903			0.962898			0.481449	−	0.876474i	$-0.340111\pi$
$919$	29.1903			0.962898			0.481449	+	0.876474i	$0.340111\pi$
$920$	0.231157	−	0.400376i	0.00762104	−	0.0132000i
$921$	−5.72036	+	26.4763i	−0.188492	+	0.872422i
$922$	−14.3134	−	24.7915i	−0.471386	−	0.816464i
$923$	−1.23304	−	2.13568i	−0.0405859	−	0.0702969i
$924$	1.93944	+	1.75807i	0.0638029	+	0.0578361i
$925$	12.6007	−	21.8250i	0.414307	−	0.717602i
$926$	18.5729			0.610345
$927$	2.87309	+	29.2150i	0.0943646	+	0.959546i
$928$	−6.49200			−0.213110
$929$	10.0069	−	17.3325i	0.328316	−	0.568660i	−0.653862	−	0.756614i	$-0.726852\pi$
$929$	10.0069	−	17.3325i	0.328316	−	0.568660i	0.982178	+	0.187954i	$0.0601855\pi$
$930$	6.85746	−	2.20279i	0.224865	−	0.0722322i
$931$	−27.6376	−	47.8697i	−0.905785	−	1.56887i
$932$	−10.4833	−	18.1575i	−0.343391	−	0.594770i
$933$	11.9164	−	3.82785i	0.390126	−	0.125318i
$934$	11.4410	−	19.8164i	0.374361	−	0.648413i
$935$	11.5393			0.377375
$936$	0.223273	+	2.27035i	0.00729791	+	0.0742088i
$937$	−26.5109			−0.866073			−0.433036	−	0.901376i	$-0.642558\pi$
$937$	−26.5109			−0.866073			−0.433036	+	0.901376i	$0.642558\pi$
$938$	−2.26234	+	3.91849i	−0.0738681	+	0.127943i
$939$	−6.07616	−	5.50793i	−0.198288	−	0.179744i
$940$	−1.75593	−	3.04136i	−0.0572720	−	0.0991981i
$941$	−2.10102	−	3.63907i	−0.0684913	−	0.118630i	0.829746	−	0.558141i	$-0.188485\pi$
$941$	−2.10102	−	3.63907i	−0.0684913	−	0.118630i	−0.898237	+	0.439511i	$0.855152\pi$
$942$	0.0913793	−	0.422942i	0.00297730	−	0.0137802i
$943$	3.11743	−	5.39955i	0.101517	−	0.175833i
$944$	−12.2968			−0.400226
$945$	−0.473658	+	0.638360i	−0.0154081	+	0.0207659i
$946$	−3.57972			−0.116387
$947$	22.2960	−	38.6179i	0.724524	−	1.25491i	−0.234645	−	0.972081i	$-0.575393\pi$
$947$	22.2960	−	38.6179i	0.724524	−	1.25491i	0.959170	−	0.282832i	$-0.0912737\pi$
$948$	−1.29402	+	5.98925i	−0.0420277	+	0.194522i
$949$	3.78575	+	6.55712i	0.122891	+	0.212853i
$950$	−19.1975	−	33.2511i	−0.622850	−	1.07881i
$951$	17.5501	+	15.9088i	0.569101	+	0.515879i
$952$	0.904139	−	1.56601i	0.0293033	−	0.0507548i
$953$	54.5654			1.76755			0.883774	−	0.467915i	$-0.154995\pi$
$953$	54.5654			1.76755			0.883774	+	0.467915i	$0.154995\pi$
$954$	−15.7918	+	11.3127i	−0.511277	+	0.366263i
$955$	7.80651			0.252613
$956$	−7.21920	+	12.5040i	−0.233486	+	0.404409i
$957$	−48.8968	+	15.7068i	−1.58061	+	0.507730i
$958$	−3.69343	−	6.39721i	−0.119329	−	0.206684i
$959$	1.17921	+	2.04245i	0.0380787	+	0.0659542i
$960$	0.762385	−	0.244897i	0.0246059	−	0.00790401i
$961$	−24.9528	+	43.2195i	−0.804929	+	1.39418i
$962$	4.00395			0.129093
$963$	5.40710	+	2.45088i	0.174241	+	0.0789786i
$964$	10.1916			0.328251
$965$	2.87992	−	4.98816i	0.0927078	−	0.160575i
$966$	−0.424630	−	0.384919i	−0.0136622	−	0.0123846i
$967$	−2.80469	−	4.85786i	−0.0901926	−	0.156218i	0.817399	−	0.576071i	$-0.195415\pi$
$967$	−2.80469	−	4.85786i	−0.0901926	−	0.156218i	−0.907592	+	0.419853i	$0.862082\pi$
$968$	−4.93041	−	8.53973i	−0.158470	−	0.274477i
$969$	−16.0352	+	74.2178i	−0.515126	+	2.38422i
$970$	0.501564	−	0.868734i	0.0161042	−	0.0278934i
$971$	−43.0420			−1.38128			−0.690642	−	0.723197i	$-0.742672\pi$
$971$	−43.0420			−1.38128			−0.690642	+	0.723197i	$0.742672\pi$
$972$	−13.3677	−	8.01898i	−0.428770	−	0.257209i
$973$	4.51974			0.144896
$974$	14.5686	−	25.2336i	0.466809	−	0.808537i
$975$	−1.33131	+	6.16187i	−0.0426360	+	0.197338i
$976$	−5.55142	−	9.61535i	−0.177697	−	0.307780i
$977$	−8.55987	−	14.8261i	−0.273855	−	0.474330i	0.695991	−	0.718051i	$-0.254965\pi$
$977$	−8.55987	−	14.8261i	−0.273855	−	0.474330i	−0.969845	+	0.243721i	$0.921632\pi$
$978$	−1.87382	−	1.69859i	−0.0599183	−	0.0543148i
$979$	2.31502	−	4.00973i	0.0739883	−	0.128152i
$980$	3.18559			0.101760
$981$	−32.0214	−	14.5144i	−1.02236	−	0.463408i
$982$	−7.05971			−0.225284
$983$	−23.7876	+	41.2014i	−0.758708	+	1.31412i	0.184802	+	0.982776i	$0.440836\pi$
$983$	−23.7876	+	41.2014i	−0.758708	+	1.31412i	−0.943510	+	0.331344i	$0.892498\pi$
$984$	10.2817	−	3.30272i	0.327767	−	0.105287i
$985$	−2.46114	−	4.26283i	−0.0784185	−	0.135825i
$986$	17.7388	+	30.7245i	0.564918	+	0.978467i
$987$	−4.14500	+	1.33147i	−0.131937	+	0.0423813i
$988$	3.05008	−	5.28289i	0.0970359	−	0.168071i
$989$	0.783761			0.0249221
$990$	5.14967	−	3.68905i	0.163667	−	0.117246i
$991$	22.9326			0.728478			0.364239	−	0.931306i	$-0.381329\pi$
$991$	22.9326			0.728478			0.364239	+	0.931306i	$0.381329\pi$
$992$	−4.49738	+	7.78968i	−0.142792	+	0.247323i
$993$	13.1324	+	11.9043i	0.416744	+	0.377770i
$994$	0.536542	+	0.929318i	0.0170181	+	0.0294762i
$995$	5.66108	+	9.80529i	0.179468	+	0.310848i
$996$	−2.89141	+	13.3827i	−0.0916178	+	0.424046i
$997$	18.2124	−	31.5448i	0.576793	−	0.999035i	−0.419051	−	0.907963i	$-0.637637\pi$
$997$	18.2124	−	31.5448i	0.576793	−	0.999035i	0.995844	−	0.0910723i	$-0.0290294\pi$
$998$	−16.0201			−0.507108
$999$	−16.3029	+	21.9718i	−0.515801	+	0.695157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.c.277.3	yes	10
3.2	odd	2		1242.2.e.c.829.4		10
9.2	odd	6		3726.2.a.s.1.2		5
9.4	even	3	inner	414.2.e.c.139.3	✓	10
9.5	odd	6		1242.2.e.c.415.4		10
9.7	even	3		3726.2.a.t.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.c.139.3	✓	10	9.4	even	3	inner
414.2.e.c.277.3	yes	10	1.1	even	1	trivial
1242.2.e.c.415.4		10	9.5	odd	6
1242.2.e.c.829.4		10	3.2	odd	2
3726.2.a.s.1.2		5	9.2	odd	6
3726.2.a.t.1.4		5	9.7	even	3

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.365780 - 1.69299i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.231157 + 0.400376i) q^{5} +(1.28328 + 1.16327i) q^{6} +(0.165447 - 0.286563i) q^{7} +1.00000 q^{8} +(-2.73241 - 1.23852i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.365780 - 1.69299i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.231157 + 0.400376i) q^{5} +(1.28328 + 1.16327i) q^{6} +(0.165447 - 0.286563i) q^{7} +1.00000 q^{8} +(-2.73241 - 1.23852i) q^{9} -0.462315 q^{10} +(2.28368 - 3.95545i) q^{11} +(-1.64906 + 0.529718i) q^{12} +(-0.380217 - 0.658556i) q^{13} +(0.165447 + 0.286563i) q^{14} +(0.762385 - 0.244897i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.46482 q^{17} +(2.43880 - 1.74707i) q^{18} -8.02193 q^{19} +(0.231157 - 0.400376i) q^{20} +(-0.424630 - 0.384919i) q^{21} +(2.28368 + 3.95545i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.365780 - 1.69299i) q^{24} +(2.39313 - 4.14503i) q^{25} +0.760435 q^{26} +(-3.09626 + 4.17291i) q^{27} -0.330894 q^{28} +(3.24600 - 5.62223i) q^{29} +(-0.169106 + 0.782693i) q^{30} +(-4.49738 - 7.78968i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.86121 - 5.31307i) q^{33} +(-2.73241 + 4.73267i) q^{34} +0.152977 q^{35} +(0.293612 + 2.98560i) q^{36} +5.26535 q^{37} +(4.01096 - 6.94719i) q^{38} +(-1.25400 + 0.402816i) q^{39} +(0.231157 + 0.400376i) q^{40} +(3.11743 + 5.39955i) q^{41} +(0.545664 - 0.175281i) q^{42} +(-0.391880 + 0.678757i) q^{43} -4.56737 q^{44} +(-0.135741 - 1.38029i) q^{45} +1.00000 q^{46} +(3.79812 - 6.57854i) q^{47} +(1.28328 + 1.16327i) q^{48} +(3.44525 + 5.96736i) q^{49} +(2.39313 + 4.14503i) q^{50} +(1.99892 - 9.25187i) q^{51} +(-0.380217 + 0.658556i) q^{52} -6.47523 q^{53} +(-2.06571 - 4.76790i) q^{54} +2.11156 q^{55} +(0.165447 - 0.286563i) q^{56} +(-2.93426 + 13.5810i) q^{57} +(3.24600 + 5.62223i) q^{58} +(6.14839 + 10.6493i) q^{59} +(-0.593279 - 0.537796i) q^{60} +(-5.55142 + 9.61535i) q^{61} +8.99475 q^{62} +(-0.806984 + 0.578097i) q^{63} +1.00000 q^{64} +(0.175780 - 0.304460i) q^{65} +(7.53186 - 2.41942i) q^{66} +(6.83706 + 11.8421i) q^{67} +(-2.73241 - 4.73267i) q^{68} +(-1.64906 + 0.529718i) q^{69} +(-0.0764887 + 0.132482i) q^{70} +3.24298 q^{71} +(-2.73241 - 1.23852i) q^{72} -9.95681 q^{73} +(-2.63267 + 4.55992i) q^{74} +(-6.14212 - 5.56771i) q^{75} +(4.01096 + 6.94719i) q^{76} +(-0.755658 - 1.30884i) q^{77} +(0.278152 - 1.28741i) q^{78} +(1.76884 - 3.06373i) q^{79} -0.462315 q^{80} +(5.93212 + 6.76830i) q^{81} -6.23486 q^{82} +(3.95239 - 6.84573i) q^{83} +(-0.121035 + 0.560200i) q^{84} +(1.26323 + 2.18798i) q^{85} +(-0.391880 - 0.678757i) q^{86} +(-8.33104 - 7.55193i) q^{87} +(2.28368 - 3.95545i) q^{88} +1.01372 q^{89} +(1.26323 + 0.572588i) q^{90} -0.251623 q^{91} +(-0.500000 + 0.866025i) q^{92} +(-14.8329 + 4.76469i) q^{93} +(3.79812 + 6.57854i) q^{94} +(-1.85433 - 3.21179i) q^{95} +(-1.64906 + 0.529718i) q^{96} +(-1.08490 + 1.87910i) q^{97} -6.89051 q^{98} +(-11.1389 + 7.97953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

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