LMFDB - Embedded newform 510.2.z.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(53,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 6, 7]))

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

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

chi := DirichletCharacter("510.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.z (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	510.53
Dual form			510.2.z.b.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(1.70711 + 4.12132i) q^{7} -1.00000i q^{8} +(-1.00000 + 2.82843i) q^{9} +(0.707107 + 2.12132i) q^{10} +(0.878680 - 2.12132i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(4.41421 - 4.41421i) q^{13} +(-4.12132 + 1.70711i) q^{14} +(3.12132 + 2.29289i) q^{15} +1.00000 q^{16} +(-2.82843 - 3.00000i) q^{17} +(-2.82843 - 1.00000i) q^{18} +(-3.24264 + 3.24264i) q^{19} +(-2.12132 + 0.707107i) q^{20} +(-4.12132 + 6.53553i) q^{21} +(2.12132 + 0.878680i) q^{22} +(-3.12132 + 1.29289i) q^{23} +(1.41421 - 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} +(4.41421 + 4.41421i) q^{26} +(-5.00000 + 1.41421i) q^{27} +(-1.70711 - 4.12132i) q^{28} +(0.121320 + 0.292893i) q^{29} +(-2.29289 + 3.12132i) q^{30} +(-0.707107 + 0.292893i) q^{31} +1.00000i q^{32} +(3.87868 - 0.878680i) q^{33} +(3.00000 - 2.82843i) q^{34} +(6.53553 + 7.53553i) q^{35} +(1.00000 - 2.82843i) q^{36} +(1.12132 - 2.70711i) q^{37} +(-3.24264 - 3.24264i) q^{38} +(10.6569 + 1.82843i) q^{39} +(-0.707107 - 2.12132i) q^{40} +(-1.12132 - 0.464466i) q^{41} +(-6.53553 - 4.12132i) q^{42} -11.6569 q^{43} +(-0.878680 + 2.12132i) q^{44} +(-0.121320 + 6.70711i) q^{45} +(-1.29289 - 3.12132i) q^{46} +(5.82843 - 5.82843i) q^{47} +(1.00000 + 1.41421i) q^{48} +(-9.12132 + 9.12132i) q^{49} +(3.00000 + 4.00000i) q^{50} +(1.41421 - 7.00000i) q^{51} +(-4.41421 + 4.41421i) q^{52} -1.17157 q^{53} +(-1.41421 - 5.00000i) q^{54} +(0.363961 - 5.12132i) q^{55} +(4.12132 - 1.70711i) q^{56} +(-7.82843 - 1.34315i) q^{57} +(-0.292893 + 0.121320i) q^{58} +(-6.41421 + 6.41421i) q^{59} +(-3.12132 - 2.29289i) q^{60} +(1.05025 - 2.53553i) q^{61} +(-0.292893 - 0.707107i) q^{62} +(-13.3640 + 0.707107i) q^{63} -1.00000 q^{64} +(6.24264 - 12.4853i) q^{65} +(0.878680 + 3.87868i) q^{66} +(-4.41421 + 4.41421i) q^{67} +(2.82843 + 3.00000i) q^{68} +(-4.94975 - 3.12132i) q^{69} +(-7.53553 + 6.53553i) q^{70} +(2.36396 + 5.70711i) q^{71} +(2.82843 + 1.00000i) q^{72} +(3.87868 - 9.36396i) q^{73} +(2.70711 + 1.12132i) q^{74} +(8.24264 + 2.65685i) q^{75} +(3.24264 - 3.24264i) q^{76} +10.2426 q^{77} +(-1.82843 + 10.6569i) q^{78} +(5.87868 - 14.1924i) q^{79} +(2.12132 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(0.464466 - 1.12132i) q^{82} +11.6569 q^{83} +(4.12132 - 6.53553i) q^{84} +(-8.12132 - 4.36396i) q^{85} -11.6569i q^{86} +(-0.292893 + 0.464466i) q^{87} +(-2.12132 - 0.878680i) q^{88} -14.1421i q^{89} +(-6.70711 - 0.121320i) q^{90} +(25.7279 + 10.6569i) q^{91} +(3.12132 - 1.29289i) q^{92} +(-1.12132 - 0.707107i) q^{93} +(5.82843 + 5.82843i) q^{94} +(-4.58579 + 9.17157i) q^{95} +(-1.41421 + 1.00000i) q^{96} +(3.53553 + 1.46447i) q^{97} +(-9.12132 - 9.12132i) q^{98} +(5.12132 + 4.60660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{7} - 4 q^{9} + 12 q^{11} - 4 q^{12} + 12 q^{13} - 8 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{19} - 8 q^{21} - 4 q^{23} + 16 q^{25} + 12 q^{26} - 20 q^{27} - 4 q^{28} - 8 q^{29}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^7 - 4 * q^9 + 12 * q^11 - 4 * q^12 + 12 * q^13 - 8 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^19 - 8 * q^21 - 4 * q^23 + 16 * q^25 + 12 * q^26 - 20 * q^27 - 4 * q^28 - 8 * q^29 - 12 * q^30 + 24 * q^33 + 12 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 + 4 * q^38 + 20 * q^39 + 4 * q^41 - 12 * q^42 - 24 * q^43 - 12 * q^44 + 8 * q^45 - 8 * q^46 + 12 * q^47 + 4 * q^48 - 28 * q^49 + 12 * q^50 - 12 * q^52 - 16 * q^53 - 24 * q^55 + 8 * q^56 - 20 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 + 24 * q^61 - 4 * q^62 - 28 * q^63 - 4 * q^64 + 8 * q^65 + 12 * q^66 - 12 * q^67 - 16 * q^70 - 16 * q^71 + 24 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 + 4 * q^78 + 32 * q^79 - 28 * q^81 + 16 * q^82 + 24 * q^83 + 8 * q^84 - 24 * q^85 - 4 * q^87 - 24 * q^90 + 52 * q^91 + 4 * q^92 + 4 * q^93 + 12 * q^94 - 24 * q^95 - 28 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	−1.00000			−0.500000
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$	−1.41421	+	1.00000i	−0.577350	+	0.408248i
$7$	1.70711	+	4.12132i	0.645226	+	1.55771i	0.819540	+	0.573023i	$0.194229\pi$
$7$	1.70711	+	4.12132i	0.645226	+	1.55771i	−0.174314	+	0.984690i	$0.555771\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	0.707107	+	2.12132i	0.223607	+	0.670820i
$11$	0.878680	−	2.12132i	0.264932	−	0.639602i	−0.734299	−	0.678827i	$-0.762489\pi$
$11$	0.878680	−	2.12132i	0.264932	−	0.639602i	0.999230	+	0.0392245i	$0.0124888\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	4.41421	−	4.41421i	1.22428	−	1.22428i	0.258188	−	0.966095i	$-0.416875\pi$
$13$	4.41421	−	4.41421i	1.22428	−	1.22428i	0.966095	−	0.258188i	$-0.0831253\pi$
$14$	−4.12132	+	1.70711i	−1.10147	+	0.456243i
$15$	3.12132	+	2.29289i	0.805921	+	0.592022i
$16$	1.00000			0.250000
$17$	−2.82843	−	3.00000i	−0.685994	−	0.727607i
$17$	−2.82843	−	3.00000i	−0.685994	−	0.727607i
$18$	−2.82843	−	1.00000i	−0.666667	−	0.235702i
$19$	−3.24264	+	3.24264i	−0.743913	+	0.743913i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$	−3.24264	+	3.24264i	−0.743913	+	0.743913i	0.229416	+	0.973329i	$0.426318\pi$
$20$	−2.12132	+	0.707107i	−0.474342	+	0.158114i
$21$	−4.12132	+	6.53553i	−0.899346	+	1.42617i
$22$	2.12132	+	0.878680i	0.452267	+	0.187335i
$23$	−3.12132	+	1.29289i	−0.650840	+	0.269587i	−0.683578	−	0.729877i	$-0.739577\pi$
$23$	−3.12132	+	1.29289i	−0.650840	+	0.269587i	0.0327381	+	0.999464i	$0.489577\pi$
$24$	1.41421	−	1.00000i	0.288675	−	0.204124i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$	4.41421	+	4.41421i	0.865699	+	0.865699i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	−1.70711	−	4.12132i	−0.322613	−	0.778856i
$29$	0.121320	+	0.292893i	0.0225286	+	0.0543889i	0.934744	−	0.355323i	$-0.115629\pi$
$29$	0.121320	+	0.292893i	0.0225286	+	0.0543889i	−0.912215	+	0.409712i	$0.865629\pi$
$30$	−2.29289	+	3.12132i	−0.418623	+	0.569873i
$31$	−0.707107	+	0.292893i	−0.127000	+	0.0526052i	−0.445279	−	0.895392i	$-0.646895\pi$
$31$	−0.707107	+	0.292893i	−0.127000	+	0.0526052i	0.318278	+	0.947997i	$0.396895\pi$
$32$			1.00000i			0.176777i
$33$	3.87868	−	0.878680i	0.675191	−	0.152958i
$34$	3.00000	−	2.82843i	0.514496	−	0.485071i
$35$	6.53553	+	7.53553i	1.10471	+	1.27374i
$36$	1.00000	−	2.82843i	0.166667	−	0.471405i
$37$	1.12132	−	2.70711i	0.184344	−	0.445046i	−0.804509	−	0.593940i	$-0.797572\pi$
$37$	1.12132	−	2.70711i	0.184344	−	0.445046i	0.988853	+	0.148895i	$0.0475715\pi$
$38$	−3.24264	−	3.24264i	−0.526026	−	0.526026i
$39$	10.6569	+	1.82843i	1.70646	+	0.292783i
$40$	−0.707107	−	2.12132i	−0.111803	−	0.335410i
$41$	−1.12132	−	0.464466i	−0.175121	−	0.0725374i	0.293400	−	0.955990i	$-0.405213\pi$
$41$	−1.12132	−	0.464466i	−0.175121	−	0.0725374i	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−6.53553	−	4.12132i	−1.00845	−	0.635934i
$43$	−11.6569			−1.77765			−0.888827	−	0.458243i	$-0.848479\pi$
$43$	−11.6569			−1.77765			−0.888827	+	0.458243i	$0.848479\pi$
$44$	−0.878680	+	2.12132i	−0.132466	+	0.319801i
$45$	−0.121320	+	6.70711i	−0.0180854	+	0.999836i
$46$	−1.29289	−	3.12132i	−0.190627	−	0.460214i
$47$	5.82843	−	5.82843i	0.850163	−	0.850163i	−0.139990	−	0.990153i	$-0.544707\pi$
$47$	5.82843	−	5.82843i	0.850163	−	0.850163i	0.990153	+	0.139990i	$0.0447069\pi$
$48$	1.00000	+	1.41421i	0.144338	+	0.204124i
$49$	−9.12132	+	9.12132i	−1.30305	+	1.30305i
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$	1.41421	−	7.00000i	0.198030	−	0.980196i
$52$	−4.41421	+	4.41421i	−0.612141	+	0.612141i
$53$	−1.17157			−0.160928			−0.0804640	−	0.996758i	$-0.525640\pi$
$53$	−1.17157			−0.160928			−0.0804640	+	0.996758i	$0.525640\pi$
$54$	−1.41421	−	5.00000i	−0.192450	−	0.680414i
$55$	0.363961	−	5.12132i	0.0490765	−	0.690559i
$56$	4.12132	−	1.70711i	0.550735	−	0.228122i
$57$	−7.82843	−	1.34315i	−1.03690	−	0.177904i
$58$	−0.292893	+	0.121320i	−0.0384588	+	0.0159301i
$59$	−6.41421	+	6.41421i	−0.835059	+	0.835059i	−0.988204	−	0.153144i	$-0.951060\pi$
$59$	−6.41421	+	6.41421i	−0.835059	+	0.835059i	0.153144	+	0.988204i	$0.451060\pi$
$60$	−3.12132	−	2.29289i	−0.402961	−	0.296011i
$61$	1.05025	−	2.53553i	0.134471	−	0.324642i	−0.842273	−	0.539052i	$-0.818783\pi$
$61$	1.05025	−	2.53553i	0.134471	−	0.324642i	0.976744	+	0.214410i	$0.0687828\pi$
$62$	−0.292893	−	0.707107i	−0.0371975	−	0.0898027i
$63$	−13.3640	+	0.707107i	−1.68370	+	0.0890871i
$64$	−1.00000			−0.125000
$65$	6.24264	−	12.4853i	0.774304	−	1.54861i
$66$	0.878680	+	3.87868i	0.108158	+	0.477432i
$67$	−4.41421	+	4.41421i	−0.539282	+	0.539282i	−0.923318	−	0.384036i	$-0.874534\pi$
$67$	−4.41421	+	4.41421i	−0.539282	+	0.539282i	0.384036	+	0.923318i	$0.374534\pi$
$68$	2.82843	+	3.00000i	0.342997	+	0.363803i
$69$	−4.94975	−	3.12132i	−0.595880	−	0.375763i
$70$	−7.53553	+	6.53553i	−0.900669	+	0.781146i
$71$	2.36396	+	5.70711i	0.280551	+	0.677309i	0.999849	−	0.0173925i	$-0.00553648\pi$
$71$	2.36396	+	5.70711i	0.280551	+	0.677309i	−0.719298	+	0.694701i	$0.755536\pi$
$72$	2.82843	+	1.00000i	0.333333	+	0.117851i
$73$	3.87868	−	9.36396i	0.453965	−	1.09597i	−0.516836	−	0.856084i	$-0.672890\pi$
$73$	3.87868	−	9.36396i	0.453965	−	1.09597i	0.970801	−	0.239885i	$-0.0771096\pi$
$74$	2.70711	+	1.12132i	0.314695	+	0.130351i
$75$	8.24264	+	2.65685i	0.951778	+	0.306787i
$76$	3.24264	−	3.24264i	0.371956	−	0.371956i
$77$	10.2426			1.16726
$78$	−1.82843	+	10.6569i	−0.207029	+	1.20665i
$79$	5.87868	−	14.1924i	0.661403	−	1.59677i	−0.134203	−	0.990954i	$-0.542847\pi$
$79$	5.87868	−	14.1924i	0.661403	−	1.59677i	0.795606	−	0.605815i	$-0.207153\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	0.464466	−	1.12132i	0.0512917	−	0.123829i
$83$	11.6569			1.27951			0.639753	−	0.768581i	$-0.279037\pi$
$83$	11.6569			1.27951			0.639753	+	0.768581i	$0.279037\pi$
$84$	4.12132	−	6.53553i	0.449673	−	0.713085i
$85$	−8.12132	−	4.36396i	−0.880881	−	0.473338i
$86$		−	11.6569i		−	1.25699i
$87$	−0.292893	+	0.464466i	−0.0314014	+	0.0497960i
$88$	−2.12132	−	0.878680i	−0.226134	−	0.0936676i
$89$		−	14.1421i		−	1.49906i	−0.661968	−	0.749532i	$-0.730279\pi$
$89$		−	14.1421i		−	1.49906i	0.661968	−	0.749532i	$-0.269721\pi$
$90$	−6.70711	−	0.121320i	−0.706991	−	0.0127883i
$91$	25.7279	+	10.6569i	2.69702	+	1.11714i
$92$	3.12132	−	1.29289i	0.325420	−	0.134793i
$93$	−1.12132	−	0.707107i	−0.116276	−	0.0733236i
$94$	5.82843	+	5.82843i	0.601156	+	0.601156i
$95$	−4.58579	+	9.17157i	−0.470492	+	0.940984i
$96$	−1.41421	+	1.00000i	−0.144338	+	0.102062i
$97$	3.53553	+	1.46447i	0.358979	+	0.148694i	0.554882	−	0.831929i	$-0.312764\pi$
$97$	3.53553	+	1.46447i	0.358979	+	0.148694i	−0.195902	+	0.980623i	$0.562764\pi$
$98$	−9.12132	−	9.12132i	−0.921392	−	0.921392i
$99$	5.12132	+	4.60660i	0.514712	+	0.462981i
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$			10.8284i			1.07747i	0.842476	+	0.538734i	$0.181097\pi$
$101$			10.8284i			1.07747i	−0.842476	+	0.538734i	$0.818903\pi$
$102$	7.00000	+	1.41421i	0.693103	+	0.140028i
$103$	−1.34315	−	1.34315i	−0.132344	−	0.132344i	0.637832	−	0.770176i	$-0.279832\pi$
$103$	−1.34315	−	1.34315i	−0.132344	−	0.132344i	−0.770176	+	0.637832i	$0.779832\pi$
$104$	−4.41421	−	4.41421i	−0.432849	−	0.432849i
$105$	−4.12132	+	16.7782i	−0.402200	+	1.63738i
$106$		−	1.17157i		−	0.113793i
$107$	2.70711	−	6.53553i	0.261706	−	0.631814i	−0.737338	−	0.675524i	$-0.763918\pi$
$107$	2.70711	−	6.53553i	0.261706	−	0.631814i	0.999044	+	0.0437097i	$0.0139177\pi$
$108$	5.00000	−	1.41421i	0.481125	−	0.136083i
$109$	6.70711	+	2.77817i	0.642424	+	0.266101i	0.680022	−	0.733192i	$-0.261970\pi$
$109$	6.70711	+	2.77817i	0.642424	+	0.266101i	−0.0375973	+	0.999293i	$0.511970\pi$
$110$	5.12132	+	0.363961i	0.488299	+	0.0347023i
$111$	4.94975	−	1.12132i	0.469809	−	0.106431i
$112$	1.70711	+	4.12132i	0.161306	+	0.389428i
$113$	−3.29289	+	1.36396i	−0.309769	+	0.128311i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$	−3.29289	+	1.36396i	−0.309769	+	0.128311i	0.222383	+	0.974959i	$0.428617\pi$
$114$	1.34315	−	7.82843i	0.125797	−	0.733199i
$115$	−5.70711	+	4.94975i	−0.532190	+	0.461566i
$116$	−0.121320	−	0.292893i	−0.0112643	−	0.0271945i
$117$	8.07107	+	16.8995i	0.746170	+	1.56236i
$118$	−6.41421	−	6.41421i	−0.590476	−	0.590476i
$119$	7.53553	−	16.7782i	0.690781	−	1.53805i
$120$	2.29289	−	3.12132i	0.209312	−	0.284936i
$121$	4.05025	+	4.05025i	0.368205	+	0.368205i
$122$	2.53553	+	1.05025i	0.229556	+	0.0950854i
$123$	−0.464466	−	2.05025i	−0.0418795	−	0.184865i
$124$	0.707107	−	0.292893i	0.0635001	−	0.0263026i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$	−0.707107	−	13.3640i	−0.0629941	−	1.19056i
$127$			1.65685i			0.147022i	0.997294	+	0.0735110i	$0.0234204\pi$
$127$			1.65685i			0.147022i	−0.997294	+	0.0735110i	$0.976580\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−11.6569	−	16.4853i	−1.02633	−	1.45145i
$130$	12.4853	+	6.24264i	1.09503	+	0.547516i
$131$	8.53553	−	3.53553i	0.745753	−	0.308901i	0.0227456	−	0.999741i	$-0.492759\pi$
$131$	8.53553	−	3.53553i	0.745753	−	0.308901i	0.723007	+	0.690840i	$0.242759\pi$
$132$	−3.87868	+	0.878680i	−0.337596	+	0.0764792i
$133$	−18.8995	−	7.82843i	−1.63879	−	0.678811i
$134$	−4.41421	−	4.41421i	−0.381330	−	0.381330i
$135$	−9.60660	+	6.53553i	−0.826805	+	0.562489i
$136$	−3.00000	+	2.82843i	−0.257248	+	0.242536i
$137$	7.48528	+	7.48528i	0.639511	+	0.639511i	0.950435	−	0.310924i	$-0.100638\pi$
$137$	7.48528	+	7.48528i	0.639511	+	0.639511i	−0.310924	+	0.950435i	$0.600638\pi$
$138$	3.12132	−	4.94975i	0.265704	−	0.421350i
$139$	−3.12132	−	7.53553i	−0.264747	−	0.639156i	0.734473	−	0.678638i	$-0.237429\pi$
$139$	−3.12132	−	7.53553i	−0.264747	−	0.639156i	−0.999220	+	0.0394819i	$0.987429\pi$
$140$	−6.53553	−	7.53553i	−0.552353	−	0.636869i
$141$	14.0711	+	2.41421i	1.18500	+	0.203313i
$142$	−5.70711	+	2.36396i	−0.478930	+	0.198379i
$143$	−5.48528	−	13.2426i	−0.458702	−	1.10741i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	0.464466	+	0.535534i	0.0385718	+	0.0444737i
$146$	9.36396	+	3.87868i	0.774967	+	0.321002i
$147$	−22.0208	−	3.77817i	−1.81625	−	0.311619i
$148$	−1.12132	+	2.70711i	−0.0921720	+	0.222523i
$149$			22.1421i			1.81395i	0.421180	+	0.906977i	$0.361616\pi$
$149$			22.1421i			1.81395i	−0.421180	+	0.906977i	$0.638384\pi$
$150$	−2.65685	+	8.24264i	−0.216931	+	0.673009i
$151$	6.65685	+	6.65685i	0.541727	+	0.541727i	0.924035	−	0.382308i	$-0.124871\pi$
$151$	6.65685	+	6.65685i	0.541727	+	0.541727i	−0.382308	+	0.924035i	$0.624871\pi$
$152$	3.24264	+	3.24264i	0.263013	+	0.263013i
$153$	11.3137	−	5.00000i	0.914659	−	0.404226i
$154$			10.2426i			0.825376i
$155$	−1.29289	+	1.12132i	−0.103848	+	0.0900666i
$156$	−10.6569	−	1.82843i	−0.853231	−	0.146391i
$157$	−16.0711	−	16.0711i	−1.28261	−	1.28261i	−0.939177	−	0.343434i	$-0.888410\pi$
$157$	−16.0711	−	16.0711i	−1.28261	−	1.28261i	−0.343434	−	0.939177i	$-0.611590\pi$
$158$	14.1924	+	5.87868i	1.12909	+	0.467683i
$159$	−1.17157	−	1.65685i	−0.0929118	−	0.131397i
$160$	0.707107	+	2.12132i	0.0559017	+	0.167705i
$161$	−10.6569	−	10.6569i	−0.839878	−	0.839878i
$162$	5.65685	−	7.00000i	0.444444	−	0.549972i
$163$	−8.12132	+	3.36396i	−0.636111	+	0.263486i	−0.677347	−	0.735664i	$-0.736870\pi$
$163$	−8.12132	+	3.36396i	−0.636111	+	0.263486i	0.0412361	+	0.999149i	$0.486870\pi$
$164$	1.12132	+	0.464466i	0.0875604	+	0.0362687i
$165$	7.60660	−	4.60660i	0.592173	−	0.358623i
$166$			11.6569i			0.904747i
$167$	−3.36396	−	1.39340i	−0.260311	−	0.107824i	0.248711	−	0.968578i	$-0.419993\pi$
$167$	−3.36396	−	1.39340i	−0.260311	−	0.107824i	−0.509022	+	0.860753i	$0.669993\pi$
$168$	6.53553	+	4.12132i	0.504227	+	0.317967i
$169$		−	25.9706i		−	1.99774i
$170$	4.36396	−	8.12132i	0.334701	−	0.622877i
$171$	−5.92893	−	12.4142i	−0.453397	−	0.949339i
$172$	11.6569			0.888827
$173$	−6.29289	+	15.1924i	−0.478440	+	1.15506i	0.481901	+	0.876226i	$0.339947\pi$
$173$	−6.29289	+	15.1924i	−0.478440	+	1.15506i	−0.960340	+	0.278830i	$0.910053\pi$
$174$	−0.464466	−	0.292893i	−0.0352111	−	0.0222042i
$175$	19.1924	+	11.3640i	1.45081	+	0.859035i
$176$	0.878680	−	2.12132i	0.0662330	−	0.159901i
$177$	−15.4853	−	2.65685i	−1.16395	−	0.199701i
$178$	14.1421			1.06000
$179$	1.24264	−	1.24264i	0.0928793	−	0.0928793i	−0.659140	−	0.752020i	$-0.729080\pi$
$179$	1.24264	−	1.24264i	0.0928793	−	0.0928793i	0.752020	+	0.659140i	$0.229080\pi$
$180$	0.121320	−	6.70711i	0.00904268	−	0.499918i
$181$	−3.87868	−	1.60660i	−0.288300	−	0.119418i	0.233847	−	0.972273i	$-0.424869\pi$
$181$	−3.87868	−	1.60660i	−0.288300	−	0.119418i	−0.522147	+	0.852856i	$0.674869\pi$
$182$	−10.6569	+	25.7279i	−0.789939	+	1.90708i
$183$	4.63604	−	1.05025i	0.342706	−	0.0776369i
$184$	1.29289	+	3.12132i	0.0953134	+	0.230107i
$185$	0.464466	−	6.53553i	0.0341482	−	0.480502i
$186$	0.707107	−	1.12132i	0.0518476	−	0.0822192i
$187$	−8.84924	+	3.36396i	−0.647121	+	0.245997i
$188$	−5.82843	+	5.82843i	−0.425082	+	0.425082i
$189$	−14.3640	−	18.1924i	−1.04482	−	1.32330i
$190$	−9.17157	−	4.58579i	−0.665376	−	0.332688i
$191$	17.6569			1.27761			0.638803	−	0.769371i	$-0.279430\pi$
$191$	17.6569			1.27761			0.638803	+	0.769371i	$0.279430\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$	3.43503	+	8.29289i	0.247259	+	0.596936i	0.997969	−	0.0636957i	$-0.0202887\pi$
$193$	3.43503	+	8.29289i	0.247259	+	0.596936i	−0.750711	+	0.660631i	$0.770289\pi$
$194$	−1.46447	+	3.53553i	−0.105143	+	0.253837i
$195$	23.8995	−	3.65685i	1.71148	−	0.261873i
$196$	9.12132	−	9.12132i	0.651523	−	0.651523i
$197$	−2.53553	+	1.05025i	−0.180649	+	0.0748274i	−0.471175	−	0.882040i	$-0.656170\pi$
$197$	−2.53553	+	1.05025i	−0.180649	+	0.0748274i	0.290525	+	0.956867i	$0.406170\pi$
$198$	−4.60660	+	5.12132i	−0.327377	+	0.363956i
$199$	−7.77817	+	3.22183i	−0.551380	+	0.228389i	−0.640938	−	0.767592i	$-0.721455\pi$
$199$	−7.77817	+	3.22183i	−0.551380	+	0.228389i	0.0895581	+	0.995982i	$0.471455\pi$
$200$	−3.00000	−	4.00000i	−0.212132	−	0.282843i
$201$	−10.6569	−	1.82843i	−0.751677	−	0.128967i
$202$	−10.8284			−0.761885
$203$	−1.00000	+	1.00000i	−0.0701862	+	0.0701862i
$204$	−1.41421	+	7.00000i	−0.0990148	+	0.490098i
$205$	−2.70711	−	0.192388i	−0.189073	−	0.0134370i
$206$	1.34315	−	1.34315i	0.0935814	−	0.0935814i
$207$	−0.535534	−	10.1213i	−0.0372222	−	0.703480i
$208$	4.41421	−	4.41421i	0.306071	−	0.306071i
$209$	4.02944	+	9.72792i	0.278722	+	0.672894i
$210$	−16.7782	−	4.12132i	−1.15780	−	0.284398i
$211$	−1.60660	+	3.87868i	−0.110603	+	0.267019i	−0.969483	−	0.245157i	$-0.921161\pi$
$211$	−1.60660	+	3.87868i	−0.110603	+	0.267019i	0.858880	+	0.512176i	$0.171161\pi$
$212$	1.17157			0.0804640
$213$	−5.70711	+	9.05025i	−0.391045	+	0.620113i
$214$	6.53553	+	2.70711i	0.446760	+	0.185054i
$215$	−24.7279	+	8.24264i	−1.68643	+	0.562143i
$216$	1.41421	+	5.00000i	0.0962250	+	0.340207i
$217$	−2.41421	−	2.41421i	−0.163887	−	0.163887i
$218$	−2.77817	+	6.70711i	−0.188162	+	0.454263i
$219$	17.1213	−	3.87868i	1.15695	−	0.262097i
$220$	−0.363961	+	5.12132i	−0.0245382	+	0.345279i
$221$	−25.7279	−	0.757359i	−1.73065	−	0.0509455i
$222$	1.12132	+	4.94975i	0.0752581	+	0.332205i
$223$		−	23.3137i		−	1.56120i	−0.625030	−	0.780601i	$-0.714913\pi$
$223$		−	23.3137i		−	1.56120i	0.625030	−	0.780601i	$-0.285087\pi$
$224$	−4.12132	+	1.70711i	−0.275367	+	0.114061i
$225$	4.48528	+	14.3137i	0.299019	+	0.954247i
$226$	−1.36396	−	3.29289i	−0.0907293	−	0.219040i
$227$	1.87868	+	4.53553i	0.124692	+	0.301034i	0.973882	−	0.227054i	$-0.0729093\pi$
$227$	1.87868	+	4.53553i	0.124692	+	0.301034i	−0.849190	+	0.528088i	$0.822909\pi$
$228$	7.82843	+	1.34315i	0.518450	+	0.0889520i
$229$	11.5858	+	11.5858i	0.765610	+	0.765610i	0.977330	−	0.211720i	$-0.0679065\pi$
$229$	11.5858	+	11.5858i	0.765610	+	0.765610i	−0.211720	+	0.977330i	$0.567906\pi$
$230$	−4.94975	−	5.70711i	−0.326377	−	0.376315i
$231$	10.2426	+	14.4853i	0.673916	+	0.953062i
$232$	0.292893	−	0.121320i	0.0192294	−	0.00796507i
$233$	−7.53553	−	3.12132i	−0.493669	−	0.204484i	0.121938	−	0.992538i	$-0.461089\pi$
$233$	−7.53553	−	3.12132i	−0.493669	−	0.204484i	−0.615607	+	0.788053i	$0.711089\pi$
$234$	−16.8995	+	8.07107i	−1.10475	+	0.527622i
$235$	8.24264	−	16.4853i	0.537691	−	1.07538i
$236$	6.41421	−	6.41421i	0.417530	−	0.417530i
$237$	25.9497	−	5.87868i	1.68562	−	0.381861i
$238$	16.7782	+	7.53553i	1.08757	+	0.488456i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	3.12132	+	2.29289i	0.201480	+	0.148006i
$241$	1.36396	−	0.564971i	0.0878605	−	0.0363930i	−0.338320	−	0.941031i	$-0.609859\pi$
$241$	1.36396	−	0.564971i	0.0878605	−	0.0363930i	0.426181	+	0.904638i	$0.359859\pi$
$242$	−4.05025	+	4.05025i	−0.260360	+	0.260360i
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$	−1.05025	+	2.53553i	−0.0672355	+	0.162321i
$245$	−12.8995	+	25.7990i	−0.824119	+	1.64824i
$246$	2.05025	−	0.464466i	0.130719	−	0.0296133i
$247$			28.6274i			1.82152i
$248$	0.292893	+	0.707107i	0.0185987	+	0.0449013i
$249$	11.6569	+	16.4853i	0.738723	+	1.04471i
$250$	9.19239	+	6.36396i	0.581378	+	0.402492i
$251$	−9.17157			−0.578905			−0.289452	−	0.957192i	$-0.593473\pi$
$251$	−9.17157			−0.578905			−0.289452	+	0.957192i	$0.593473\pi$
$252$	13.3640	−	0.707107i	0.841850	−	0.0445435i
$253$			7.75736i			0.487701i
$254$	−1.65685			−0.103960
$255$	−1.94975	−	15.8492i	−0.122098	−	0.992518i
$256$	1.00000			0.0625000
$257$			3.17157i			0.197837i	0.995096	+	0.0989186i	$0.0315384\pi$
$257$			3.17157i			0.197837i	−0.995096	+	0.0989186i	$0.968462\pi$
$258$	16.4853	−	11.6569i	1.02633	−	0.725724i
$259$	13.0711			0.812197
$260$	−6.24264	+	12.4853i	−0.387152	+	0.774304i
$261$	−0.949747	+	0.0502525i	−0.0587879	+	0.00311055i
$262$	3.53553	+	8.53553i	0.218426	+	0.527327i
$263$			8.00000i			0.493301i	0.969104	+	0.246651i	$0.0793300\pi$
$263$			8.00000i			0.493301i	−0.969104	+	0.246651i	$0.920670\pi$
$264$	−0.878680	−	3.87868i	−0.0540790	−	0.238716i
$265$	−2.48528	+	0.828427i	−0.152670	+	0.0508899i
$266$	7.82843	−	18.8995i	0.479992	−	1.15880i
$267$	20.0000	−	14.1421i	1.22398	−	0.865485i
$268$	4.41421	−	4.41421i	0.269641	−	0.269641i
$269$	−29.0919	+	12.0503i	−1.77376	+	0.734717i	−0.779670	+	0.626191i	$0.784613\pi$
$269$	−29.0919	+	12.0503i	−1.77376	+	0.734717i	−0.994094	+	0.108526i	$0.965387\pi$
$270$	−6.53553	−	9.60660i	−0.397740	−	0.584639i
$271$	−0.686292			−0.0416892			−0.0208446	−	0.999783i	$-0.506636\pi$
$271$	−0.686292			−0.0416892			−0.0208446	+	0.999783i	$0.506636\pi$
$272$	−2.82843	−	3.00000i	−0.171499	−	0.181902i
$273$	10.6569	+	47.0416i	0.644982	+	2.84709i
$274$	−7.48528	+	7.48528i	−0.452202	+	0.452202i
$275$	−2.84924	−	11.1213i	−0.171816	−	0.670641i
$276$	4.94975	+	3.12132i	0.297940	+	0.187881i
$277$	−26.7782	−	11.0919i	−1.60894	−	0.666447i	−0.616300	−	0.787511i	$-0.711369\pi$
$277$	−26.7782	−	11.0919i	−1.60894	−	0.666447i	−0.992645	+	0.121065i	$0.961369\pi$
$278$	7.53553	−	3.12132i	0.451951	−	0.187204i
$279$	−0.121320	−	2.29289i	−0.00726326	−	0.137272i
$280$	7.53553	−	6.53553i	0.450334	−	0.390573i
$281$	2.51472	+	2.51472i	0.150016	+	0.150016i	0.778125	−	0.628109i	$-0.216171\pi$
$281$	2.51472	+	2.51472i	0.150016	+	0.150016i	−0.628109	+	0.778125i	$0.716171\pi$
$282$	−2.41421	+	14.0711i	−0.143764	+	0.837920i
$283$	6.94975	+	16.7782i	0.413120	+	0.997359i	0.984295	+	0.176531i	$0.0564876\pi$
$283$	6.94975	+	16.7782i	0.413120	+	0.997359i	−0.571175	+	0.820828i	$0.693512\pi$
$284$	−2.36396	−	5.70711i	−0.140275	−	0.338654i
$285$	−17.5563	+	2.68629i	−1.03995	+	0.159122i
$286$	13.2426	−	5.48528i	0.783054	−	0.324351i
$287$		−	5.41421i		−	0.319591i
$288$	−2.82843	−	1.00000i	−0.166667	−	0.0589256i
$289$	−1.00000	+	16.9706i	−0.0588235	+	0.998268i
$290$	−0.535534	+	0.464466i	−0.0314476	+	0.0272744i
$291$	1.46447	+	6.46447i	0.0858485	+	0.378954i
$292$	−3.87868	+	9.36396i	−0.226983	+	0.547984i
$293$	−5.58579	−	5.58579i	−0.326325	−	0.326325i	0.524862	−	0.851187i	$-0.324117\pi$
$293$	−5.58579	−	5.58579i	−0.326325	−	0.326325i	−0.851187	+	0.524862i	$0.824117\pi$
$294$	3.77817	−	22.0208i	0.220348	−	1.28428i
$295$	−9.07107	+	18.1421i	−0.528138	+	1.05628i
$296$	−2.70711	−	1.12132i	−0.157347	−	0.0651754i
$297$	−1.39340	+	11.8492i	−0.0808532	+	0.687563i
$298$	−22.1421			−1.28266
$299$	−8.07107	+	19.4853i	−0.466762	+	1.12686i
$300$	−8.24264	−	2.65685i	−0.475889	−	0.153394i
$301$	−19.8995	−	48.0416i	−1.14699	−	2.76907i
$302$	−6.65685	+	6.65685i	−0.383059	+	0.383059i
$303$	−15.3137	+	10.8284i	−0.879750	+	0.622077i
$304$	−3.24264	+	3.24264i	−0.185978	+	0.185978i
$305$	0.435029	−	6.12132i	0.0249097	−	0.350506i
$306$	5.00000	+	11.3137i	0.285831	+	0.646762i
$307$	3.72792	−	3.72792i	0.212764	−	0.212764i	−0.592677	−	0.805440i	$-0.701929\pi$
$307$	3.72792	−	3.72792i	0.212764	−	0.212764i	0.805440	+	0.592677i	$0.201929\pi$
$308$	−10.2426			−0.583629
$309$	0.556349	−	3.24264i	0.0316496	−	0.184467i
$310$	−1.12132	−	1.29289i	−0.0636867	−	0.0734314i
$311$	−25.1924	+	10.4350i	−1.42853	+	0.591716i	−0.956988	−	0.290128i	$-0.906302\pi$
$311$	−25.1924	+	10.4350i	−1.42853	+	0.591716i	−0.471541	+	0.881844i	$0.656302\pi$
$312$	1.82843	−	10.6569i	0.103514	−	0.603326i
$313$	−18.6066	+	7.70711i	−1.05171	+	0.435631i	−0.840501	−	0.541810i	$-0.817739\pi$
$313$	−18.6066	+	7.70711i	−1.05171	+	0.435631i	−0.211206	+	0.977441i	$0.567739\pi$
$314$	16.0711	−	16.0711i	0.906943	−	0.906943i
$315$	−27.8492	+	10.9497i	−1.56913	+	0.616948i
$316$	−5.87868	+	14.1924i	−0.330702	+	0.798384i
$317$	−8.09188	−	19.5355i	−0.454485	−	1.09722i	−0.970598	−	0.240704i	$-0.922622\pi$
$317$	−8.09188	−	19.5355i	−0.454485	−	1.09722i	0.516113	−	0.856520i	$-0.327378\pi$
$318$	1.65685	−	1.17157i	0.0929118	−	0.0656985i
$319$	0.727922			0.0407558
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$	11.9497	−	2.70711i	0.666970	−	0.151096i
$322$	10.6569	−	10.6569i	0.593883	−	0.593883i
$323$	18.8995	+	0.556349i	1.05160	+	0.0309561i
$324$	7.00000	+	5.65685i	0.388889	+	0.314270i
$325$	4.41421	−	30.8995i	0.244857	−	1.71400i
$326$	−3.36396	−	8.12132i	−0.186313	−	0.449798i
$327$	2.77817	+	12.2635i	0.153633	+	0.678171i
$328$	−0.464466	+	1.12132i	−0.0256458	+	0.0619146i
$329$	33.9706	+	14.0711i	1.87286	+	0.775763i
$330$	4.60660	+	7.60660i	0.253585	+	0.418730i
$331$	−4.41421	+	4.41421i	−0.242627	+	0.242627i	−0.817936	−	0.575309i	$-0.804882\pi$
$331$	−4.41421	+	4.41421i	−0.242627	+	0.242627i	0.575309	+	0.817936i	$0.304882\pi$
$332$	−11.6569			−0.639753
$333$	6.53553	+	5.87868i	0.358145	+	0.322150i
$334$	1.39340	−	3.36396i	0.0762434	−	0.184068i
$335$	−6.24264	+	12.4853i	−0.341072	+	0.682144i
$336$	−4.12132	+	6.53553i	−0.224836	+	0.356543i
$337$	2.80761	−	6.77817i	0.152940	−	0.369231i	−0.828776	−	0.559581i	$-0.810962\pi$
$337$	2.80761	−	6.77817i	0.152940	−	0.369231i	0.981716	+	0.190350i	$0.0609622\pi$
$338$	25.9706			1.41261
$339$	−5.22183	−	3.29289i	−0.283611	−	0.178845i
$340$	8.12132	+	4.36396i	0.440440	+	0.236669i
$341$			1.75736i			0.0951663i
$342$	12.4142	−	5.92893i	0.671284	−	0.320600i
$343$	−24.3137	−	10.0711i	−1.31282	−	0.543787i
$344$			11.6569i			0.628495i
$345$	−12.7071	−	3.12132i	−0.684128	−	0.168046i
$346$	−15.1924	−	6.29289i	−0.816748	−	0.338308i
$347$	18.9497	−	7.84924i	1.01728	−	0.421369i	0.189172	−	0.981944i	$-0.439420\pi$
$347$	18.9497	−	7.84924i	1.01728	−	0.421369i	0.828104	+	0.560575i	$0.189420\pi$
$348$	0.292893	−	0.464466i	0.0157007	−	0.0248980i
$349$	0.757359	+	0.757359i	0.0405405	+	0.0405405i	0.727086	−	0.686546i	$-0.240874\pi$
$349$	0.757359	+	0.757359i	0.0405405	+	0.0405405i	−0.686546	+	0.727086i	$0.740874\pi$
$350$	−11.3640	+	19.1924i	−0.607429	+	1.02588i
$351$	−15.8284	+	28.3137i	−0.844859	+	1.51127i
$352$	2.12132	+	0.878680i	0.113067	+	0.0468338i
$353$	16.6569	+	16.6569i	0.886555	+	0.886555i	0.994190	−	0.107636i	$-0.0343280\pi$
$353$	16.6569	+	16.6569i	0.886555	+	0.886555i	−0.107636	+	0.994190i	$0.534328\pi$
$354$	2.65685	−	15.4853i	0.141210	−	0.823033i
$355$	9.05025	+	10.4350i	0.480338	+	0.553834i
$356$			14.1421i			0.749532i
$357$	31.2635	−	6.12132i	1.65464	−	0.323975i
$358$	1.24264	+	1.24264i	0.0656756	+	0.0656756i
$359$	8.65685	+	8.65685i	0.456891	+	0.456891i	0.897634	−	0.440742i	$-0.145285\pi$
$359$	8.65685	+	8.65685i	0.456891	+	0.456891i	−0.440742	+	0.897634i	$0.645285\pi$
$360$	6.70711	+	0.121320i	0.353496	+	0.00639414i
$361$		−	2.02944i		−	0.106812i
$362$	1.60660	−	3.87868i	0.0844411	−	0.203859i
$363$	−1.67767	+	9.77817i	−0.0880548	+	0.513221i
$364$	−25.7279	−	10.6569i	−1.34851	−	0.558571i
$365$	1.60660	−	22.6066i	0.0840934	−	1.18328i
$366$	1.05025	+	4.63604i	0.0548976	+	0.242330i
$367$	1.70711	+	4.12132i	0.0891102	+	0.215131i	0.962151	−	0.272515i	$-0.0878555\pi$
$367$	1.70711	+	4.12132i	0.0891102	+	0.215131i	−0.873041	+	0.487646i	$0.837856\pi$
$368$	−3.12132	+	1.29289i	−0.162710	+	0.0673967i
$369$	2.43503	−	2.70711i	0.126763	−	0.140926i
$370$	6.53553	+	0.464466i	0.339766	+	0.0241464i
$371$	−2.00000	−	4.82843i	−0.103835	−	0.250679i
$372$	1.12132	+	0.707107i	0.0581378	+	0.0366618i
$373$	−11.2426	−	11.2426i	−0.582122	−	0.582122i	0.353364	−	0.935486i	$-0.385038\pi$
$373$	−11.2426	−	11.2426i	−0.582122	−	0.582122i	−0.935486	+	0.353364i	$0.885038\pi$
$374$	−3.36396	−	8.84924i	−0.173946	−	0.457583i
$375$	19.3640	−	0.192388i	0.999951	−	0.00993488i
$376$	−5.82843	−	5.82843i	−0.300578	−	0.300578i
$377$	1.82843	+	0.757359i	0.0941688	+	0.0390060i
$378$	18.1924	−	14.3640i	0.935715	−	0.738802i
$379$	34.0919	−	14.1213i	1.75118	−	0.725364i	0.753491	−	0.657459i	$-0.228369\pi$
$379$	34.0919	−	14.1213i	1.75118	−	0.725364i	0.997692	−	0.0679048i	$-0.0216314\pi$
$380$	4.58579	−	9.17157i	0.235246	−	0.470492i
$381$	−2.34315	+	1.65685i	−0.120043	+	0.0848832i
$382$			17.6569i			0.903403i
$383$		−	27.3137i		−	1.39567i	−0.716261	−	0.697833i	$-0.754148\pi$
$383$		−	27.3137i		−	1.39567i	0.716261	−	0.697833i	$-0.245852\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	21.7279	−	7.24264i	1.10736	−	0.369119i
$386$	−8.29289	+	3.43503i	−0.422097	+	0.174838i
$387$	11.6569	−	32.9706i	0.592551	−	1.67599i
$388$	−3.53553	−	1.46447i	−0.179490	−	0.0743470i
$389$	2.41421	+	2.41421i	0.122405	+	0.122405i	0.765656	−	0.643250i	$-0.222415\pi$
$389$	2.41421	+	2.41421i	0.122405	+	0.122405i	−0.643250	+	0.765656i	$0.722415\pi$
$390$	3.65685	+	23.8995i	0.185172	+	1.21020i
$391$	12.7071	+	5.70711i	0.642626	+	0.288621i
$392$	9.12132	+	9.12132i	0.460696	+	0.460696i
$393$	13.5355	+	8.53553i	0.682777	+	0.430561i
$394$	−1.05025	−	2.53553i	−0.0529110	−	0.127738i
$395$	2.43503	−	34.2635i	0.122520	−	1.72398i
$396$	−5.12132	−	4.60660i	−0.257356	−	0.231490i
$397$	10.2929	−	4.26346i	0.516586	−	0.213977i	−0.109131	−	0.994027i	$-0.534807\pi$
$397$	10.2929	−	4.26346i	0.516586	−	0.213977i	0.625716	+	0.780051i	$0.284807\pi$
$398$	−3.22183	−	7.77817i	−0.161496	−	0.389885i
$399$	−7.82843	−	34.5563i	−0.391912	−	1.72998i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	−1.94975	−	0.807612i	−0.0973657	−	0.0403302i	0.333469	−	0.942761i	$-0.391781\pi$
$401$	−1.94975	−	0.807612i	−0.0973657	−	0.0403302i	−0.430835	+	0.902431i	$0.641781\pi$
$402$	1.82843	−	10.6569i	0.0911937	−	0.531516i
$403$	−1.82843	+	4.41421i	−0.0910804	+	0.219888i
$404$		−	10.8284i		−	0.538734i
$405$	−18.8492	−	7.05025i	−0.936626	−	0.350330i
$406$	−1.00000	−	1.00000i	−0.0496292	−	0.0496292i
$407$	−4.75736	−	4.75736i	−0.235814	−	0.235814i
$408$	−7.00000	−	1.41421i	−0.346552	−	0.0700140i
$409$			10.8284i			0.535431i	0.963498	+	0.267716i	$0.0862688\pi$
$409$			10.8284i			0.535431i	−0.963498	+	0.267716i	$0.913731\pi$
$410$	0.192388	−	2.70711i	0.00950137	−	0.133694i
$411$	−3.10051	+	18.0711i	−0.152937	+	0.891380i
$412$	1.34315	+	1.34315i	0.0661720	+	0.0661720i
$413$	−37.3848	−	15.4853i	−1.83958	−	0.761981i
$414$	10.1213	−	0.535534i	0.497436	−	0.0263201i
$415$	24.7279	−	8.24264i	1.21385	−	0.404615i
$416$	4.41421	+	4.41421i	0.216425	+	0.216425i
$417$	7.53553	−	11.9497i	0.369017	−	0.585182i
$418$	−9.72792	+	4.02944i	−0.475808	+	0.197086i
$419$	−13.6066	−	5.63604i	−0.664726	−	0.275339i	0.0246997	−	0.999695i	$-0.492137\pi$
$419$	−13.6066	−	5.63604i	−0.664726	−	0.275339i	−0.689426	+	0.724356i	$0.742137\pi$
$420$	4.12132	−	16.7782i	0.201100	−	0.818691i
$421$			38.1421i			1.85893i	0.368905	+	0.929467i	$0.379733\pi$
$421$			38.1421i			1.85893i	−0.368905	+	0.929467i	$0.620267\pi$
$422$	−3.87868	−	1.60660i	−0.188811	−	0.0782081i
$423$	10.6569	+	22.3137i	0.518154	+	1.08493i
$424$			1.17157i			0.0568966i
$425$	−20.3137	−	3.51472i	−0.985360	−	0.170489i
$426$	−9.05025	−	5.70711i	−0.438486	−	0.276510i
$427$	12.2426			0.592463
$428$	−2.70711	+	6.53553i	−0.130853	+	0.315907i
$429$	13.2426	−	21.0000i	0.639361	−	1.01389i
$430$	−8.24264	−	24.7279i	−0.397495	−	1.19249i
$431$	−13.3934	+	32.3345i	−0.645137	+	1.55750i	0.174525	+	0.984653i	$0.444161\pi$
$431$	−13.3934	+	32.3345i	−0.645137	+	1.55750i	−0.819663	+	0.572847i	$0.805839\pi$
$432$	−5.00000	+	1.41421i	−0.240563	+	0.0680414i
$433$	28.9706			1.39224			0.696118	−	0.717927i	$-0.254909\pi$
$433$	28.9706			1.39224			0.696118	+	0.717927i	$0.254909\pi$
$434$	2.41421	−	2.41421i	0.115886	−	0.115886i
$435$	−0.292893	+	1.19239i	−0.0140432	+	0.0571706i
$436$	−6.70711	−	2.77817i	−0.321212	−	0.133050i
$437$	5.92893	−	14.3137i	0.283619	−	0.684718i
$438$	3.87868	+	17.1213i	0.185330	+	0.818088i
$439$	9.77817	+	23.6066i	0.466687	+	1.12668i	0.965601	+	0.260030i	$0.0837324\pi$
$439$	9.77817	+	23.6066i	0.466687	+	1.12668i	−0.498914	+	0.866652i	$0.666268\pi$
$440$	−5.12132	−	0.363961i	−0.244149	−	0.0173512i
$441$	−16.6777	−	34.9203i	−0.794175	−	1.66287i
$442$	0.757359	−	25.7279i	0.0360239	−	1.22375i
$443$	22.0711	−	22.0711i	1.04863	−	1.04863i	0.0498725	−	0.998756i	$-0.484119\pi$
$443$	22.0711	−	22.0711i	1.04863	−	1.04863i	0.998756	−	0.0498725i	$-0.0158815\pi$
$444$	−4.94975	+	1.12132i	−0.234905	+	0.0532155i
$445$	−10.0000	−	30.0000i	−0.474045	−	1.42214i
$446$	23.3137			1.10394
$447$	−31.3137	+	22.1421i	−1.48109	+	1.04729i
$448$	−1.70711	−	4.12132i	−0.0806532	−	0.194714i
$449$	4.19239	−	10.1213i	0.197851	−	0.477655i	−0.793551	−	0.608503i	$-0.791770\pi$
$449$	4.19239	−	10.1213i	0.197851	−	0.477655i	0.991402	+	0.130849i	$0.0417702\pi$
$450$	−14.3137	+	4.48528i	−0.674755	+	0.211438i
$451$	−1.97056	+	1.97056i	−0.0927902	+	0.0927902i
$452$	3.29289	−	1.36396i	0.154885	−	0.0641553i
$453$	−2.75736	+	16.0711i	−0.129552	+	0.755085i
$454$	−4.53553	+	1.87868i	−0.212863	+	0.0881708i
$455$	62.1127	+	4.41421i	2.91189	+	0.206942i
$456$	−1.34315	+	7.82843i	−0.0628986	+	0.366600i
$457$	−9.65685			−0.451729			−0.225864	−	0.974159i	$-0.572521\pi$
$457$	−9.65685			−0.451729			−0.225864	+	0.974159i	$0.572521\pi$
$458$	−11.5858	+	11.5858i	−0.541368	+	0.541368i
$459$	18.3848	+	11.0000i	0.858128	+	0.513436i
$460$	5.70711	−	4.94975i	0.266095	−	0.230783i
$461$	19.7279	−	19.7279i	0.918821	−	0.918821i	−0.0781228	−	0.996944i	$-0.524893\pi$
$461$	19.7279	−	19.7279i	0.918821	−	0.918821i	0.996944	+	0.0781228i	$0.0248926\pi$
$462$	−14.4853	+	10.2426i	−0.673916	+	0.476531i
$463$	−8.17157	+	8.17157i	−0.379765	+	0.379765i	−0.871017	−	0.491252i	$-0.836539\pi$
$463$	−8.17157	+	8.17157i	−0.379765	+	0.379765i	0.491252	+	0.871017i	$0.336539\pi$
$464$	0.121320	+	0.292893i	0.00563216	+	0.0135972i
$465$	−2.87868	−	0.707107i	−0.133496	−	0.0327913i
$466$	3.12132	−	7.53553i	0.144592	−	0.349077i
$467$	−26.4853			−1.22559			−0.612796	−	0.790241i	$-0.709955\pi$
$467$	−26.4853			−1.22559			−0.612796	+	0.790241i	$0.709955\pi$
$468$	−8.07107	−	16.8995i	−0.373085	−	0.781179i
$469$	−25.7279	−	10.6569i	−1.18801	−	0.492088i
$470$	16.4853	+	8.24264i	0.760409	+	0.380205i
$471$	6.65685	−	38.7990i	0.306732	−	1.78776i
$472$	6.41421	+	6.41421i	0.295238	+	0.295238i
$473$	−10.2426	+	24.7279i	−0.470957	+	1.13699i
$474$	5.87868	+	25.9497i	0.270017	+	1.19191i
$475$	−3.24264	+	22.6985i	−0.148783	+	1.04148i
$476$	−7.53553	+	16.7782i	−0.345391	+	0.769026i
$477$	1.17157	−	3.31371i	0.0536426	−	0.151724i
$478$		−	12.0000i		−	0.548867i
$479$	20.3640	−	8.43503i	0.930453	−	0.385406i	0.134603	−	0.990900i	$-0.457024\pi$
$479$	20.3640	−	8.43503i	0.930453	−	0.385406i	0.795850	+	0.605493i	$0.207024\pi$
$480$	−2.29289	+	3.12132i	−0.104656	+	0.142468i
$481$	−7.00000	−	16.8995i	−0.319173	−	0.770551i
$482$	0.564971	+	1.36396i	0.0257337	+	0.0621267i
$483$	4.41421	−	25.7279i	0.200854	−	1.17066i
$484$	−4.05025	−	4.05025i	−0.184102	−	0.184102i
$485$	8.53553	+	0.606602i	0.387579	+	0.0275444i
$486$	15.5563	+	1.00000i	0.705650	+	0.0453609i
$487$	−8.53553	+	3.53553i	−0.386782	+	0.160210i	−0.567597	−	0.823307i	$-0.692127\pi$
$487$	−8.53553	+	3.53553i	−0.386782	+	0.160210i	0.180815	+	0.983517i	$0.442127\pi$
$488$	−2.53553	−	1.05025i	−0.114778	−	0.0475427i
$489$	−12.8787	−	8.12132i	−0.582394	−	0.367259i
$490$	−25.7990	−	12.8995i	−1.16548	−	0.582740i
$491$	−18.4142	+	18.4142i	−0.831022	+	0.831022i	−0.987657	−	0.156635i	$-0.949935\pi$
$491$	−18.4142	+	18.4142i	−0.831022	+	0.831022i	0.156635	+	0.987657i	$0.449935\pi$
$492$	0.464466	+	2.05025i	0.0209397	+	0.0924325i
$493$	0.535534	−	1.19239i	0.0241192	−	0.0537025i
$494$	−28.6274			−1.28801
$495$	14.1213	+	6.15076i	0.634706	+	0.276456i
$496$	−0.707107	+	0.292893i	−0.0317500	+	0.0131513i
$497$	−19.4853	+	19.4853i	−0.874034	+	0.874034i
$498$	−16.4853	+	11.6569i	−0.738723	+	0.522356i
$499$	−13.0208	+	31.4350i	−0.582892	+	1.40723i	0.307288	+	0.951616i	$0.400578\pi$
$499$	−13.0208	+	31.4350i	−0.582892	+	1.40723i	−0.890180	+	0.455609i	$0.849422\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$	−1.39340	−	6.15076i	−0.0622524	−	0.274796i
$502$		−	9.17157i		−	0.409347i
$503$	−9.36396	−	22.6066i	−0.417518	−	1.00798i	−0.983064	−	0.183262i	$-0.941334\pi$
$503$	−9.36396	−	22.6066i	−0.417518	−	1.00798i	0.565546	−	0.824717i	$-0.308666\pi$
$504$	0.707107	+	13.3640i	0.0314970	+	0.595278i
$505$	7.65685	+	22.9706i	0.340726	+	1.02218i
$506$	−7.75736			−0.344857
$507$	36.7279	−	25.9706i	1.63114	−	1.15339i
$508$		−	1.65685i		−	0.0735110i
$509$	35.6569			1.58046			0.790231	−	0.612809i	$-0.209960\pi$
$509$	35.6569			1.58046			0.790231	+	0.612809i	$0.209960\pi$
$510$	15.8492	−	1.94975i	0.701816	−	0.0863363i
$511$	45.2132			2.00011
$512$			1.00000i			0.0441942i
$513$	11.6274	−	20.7990i	0.513363	−	0.918298i
$514$	−3.17157			−0.139892
$515$	−3.79899	−	1.89949i	−0.167403	−	0.0837017i
$516$	11.6569	+	16.4853i	0.513164	+	0.725724i
$517$	−7.24264	−	17.4853i	−0.318531	−	0.769002i
$518$			13.0711i			0.574310i
$519$	−27.7782	+	6.29289i	−1.21933	+	0.276227i
$520$	−12.4853	−	6.24264i	−0.547516	−	0.273758i
$521$	−9.70711	+	23.4350i	−0.425276	+	1.02671i	0.555490	+	0.831523i	$0.312531\pi$
$521$	−9.70711	+	23.4350i	−0.425276	+	1.02671i	−0.980767	+	0.195184i	$0.937469\pi$
$522$	−0.0502525	−	0.949747i	−0.00219949	−	0.0415693i
$523$	8.41421	−	8.41421i	0.367928	−	0.367928i	−0.498793	−	0.866721i	$-0.666223\pi$
$523$	8.41421	−	8.41421i	0.367928	−	0.367928i	0.866721	+	0.498793i	$0.166223\pi$
$524$	−8.53553	+	3.53553i	−0.372877	+	0.154451i
$525$	3.12132	+	38.5061i	0.136226	+	1.68054i
$526$	−8.00000			−0.348817
$527$	2.87868	+	1.29289i	0.125397	+	0.0563193i
$528$	3.87868	−	0.878680i	0.168798	−	0.0382396i
$529$	−8.19239	+	8.19239i	−0.356191	+	0.356191i
$530$	−0.828427	−	2.48528i	−0.0359846	−	0.107954i
$531$	−11.7279	−	24.5563i	−0.508948	−	1.06565i
$532$	18.8995	+	7.82843i	0.819397	+	0.339405i
$533$	−7.00000	+	2.89949i	−0.303204	+	0.125591i
$534$	14.1421	+	20.0000i	0.611990	+	0.865485i
$535$	1.12132	−	15.7782i	0.0484789	−	0.682150i
$536$	4.41421	+	4.41421i	0.190665	+	0.190665i
$537$	3.00000	+	0.514719i	0.129460	+	0.0222117i
$538$	−12.0503	−	29.0919i	−0.519523	−	1.25424i
$539$	11.3345	+	27.3640i	0.488213	+	1.17865i
$540$	9.60660	−	6.53553i	0.413402	−	0.281245i
$541$	−36.5061	+	15.1213i	−1.56952	+	0.650116i	−0.986710	−	0.162492i	$-0.948047\pi$
$541$	−36.5061	+	15.1213i	−1.56952	+	0.650116i	−0.582810	+	0.812609i	$0.698047\pi$
$542$		−	0.686292i		−	0.0294787i
$543$	−1.60660	−	7.09188i	−0.0689459	−	0.304342i
$544$	3.00000	−	2.82843i	0.128624	−	0.121268i
$545$	16.1924	+	1.15076i	0.693606	+	0.0492930i
$546$	−47.0416	+	10.6569i	−2.01320	+	0.456071i
$547$	11.3345	−	27.3640i	0.484629	−	1.17000i	−0.472758	−	0.881192i	$-0.656742\pi$
$547$	11.3345	−	27.3640i	0.484629	−	1.17000i	0.957388	−	0.288806i	$-0.0932584\pi$
$548$	−7.48528	−	7.48528i	−0.319755	−	0.319755i
$549$	6.12132	+	5.50610i	0.261252	+	0.234994i
$550$	11.1213	−	2.84924i	0.474215	−	0.121492i
$551$	−1.34315	−	0.556349i	−0.0572199	−	0.0237013i
$552$	−3.12132	+	4.94975i	−0.132852	+	0.210675i
$553$	68.5269			2.91406
$554$	11.0919	−	26.7782i	0.471249	−	1.13770i
$555$	9.70711	−	5.87868i	0.412044	−	0.249536i
$556$	3.12132	+	7.53553i	0.132373	+	0.319578i
$557$	10.8995	−	10.8995i	0.461826	−	0.461826i	−0.437427	−	0.899254i	$-0.644110\pi$
$557$	10.8995	−	10.8995i	0.461826	−	0.461826i	0.899254	+	0.437427i	$0.144110\pi$
$558$	2.29289	−	0.121320i	0.0970659	−	0.00513590i
$559$	−51.4558	+	51.4558i	−2.17635	+	2.17635i
$560$	6.53553	+	7.53553i	0.276177	+	0.318434i
$561$	−13.6066	−	9.15076i	−0.574471	−	0.386345i
$562$	−2.51472	+	2.51472i	−0.106077	+	0.106077i
$563$	5.02944			0.211966			0.105983	−	0.994368i	$-0.466201\pi$
$563$	5.02944			0.211966			0.105983	+	0.994368i	$0.466201\pi$
$564$	−14.0711	−	2.41421i	−0.592499	−	0.101657i
$565$	−6.02082	+	5.22183i	−0.253298	+	0.219684i
$566$	−16.7782	+	6.94975i	−0.705239	+	0.292120i
$567$	11.3640	−	38.5061i	0.477242	−	1.61710i
$568$	5.70711	−	2.36396i	0.239465	−	0.0991896i
$569$	8.65685	−	8.65685i	0.362914	−	0.362914i	−0.501971	−	0.864885i	$-0.667391\pi$
$569$	8.65685	−	8.65685i	0.362914	−	0.362914i	0.864885	+	0.501971i	$0.167391\pi$
$570$	−2.68629	−	17.5563i	−0.112516	−	0.735355i
$571$	−4.29289	+	10.3640i	−0.179652	+	0.433718i	−0.987894	−	0.155133i	$-0.950419\pi$
$571$	−4.29289	+	10.3640i	−0.179652	+	0.433718i	0.808242	+	0.588851i	$0.200419\pi$
$572$	5.48528	+	13.2426i	0.229351	+	0.553703i
$573$	17.6569	+	24.9706i	0.737626	+	1.04316i
$574$	5.41421			0.225985
$575$	−8.60660	+	14.5355i	−0.358920	+	0.606174i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	−11.9706	+	11.9706i	−0.498341	+	0.498341i	−0.910921	−	0.412580i	$-0.864628\pi$
$577$	−11.9706	+	11.9706i	−0.498341	+	0.498341i	0.412580	+	0.910921i	$0.364628\pi$
$578$	−16.9706	−	1.00000i	−0.705882	−	0.0415945i
$579$	−8.29289	+	13.1508i	−0.344641	+	0.546527i
$580$	−0.464466	−	0.535534i	−0.0192859	−	0.0222368i
$581$	19.8995	+	48.0416i	0.825570	+	1.99310i
$582$	−6.46447	+	1.46447i	−0.267961	+	0.0607041i
$583$	−1.02944	+	2.48528i	−0.0426349	+	0.102930i
$584$	−9.36396	−	3.87868i	−0.387483	−	0.160501i
$585$	29.0711	+	30.1421i	1.20194	+	1.24622i
$586$	5.58579	−	5.58579i	0.230747	−	0.230747i
$587$	−36.8284			−1.52007			−0.760036	−	0.649881i	$-0.774819\pi$
$587$	−36.8284			−1.52007			−0.760036	+	0.649881i	$0.774819\pi$
$588$	22.0208	+	3.77817i	0.908123	+	0.155809i
$589$	1.34315	−	3.24264i	0.0553434	−	0.133611i
$590$	−18.1421	−	9.07107i	−0.746900	−	0.373450i
$591$	−4.02082	−	2.53553i	−0.165394	−	0.104298i
$592$	1.12132	−	2.70711i	0.0460860	−	0.111261i
$593$	22.1421			0.909269			0.454634	−	0.890678i	$-0.349770\pi$
$593$	22.1421			0.909269			0.454634	+	0.890678i	$0.349770\pi$
$594$	−11.8492	−	1.39340i	−0.486180	−	0.0571718i
$595$	4.12132	−	40.9203i	0.168958	−	1.67757i
$596$		−	22.1421i		−	0.906977i
$597$	−12.3345	−	7.77817i	−0.504818	−	0.318339i
$598$	−19.4853	−	8.07107i	−0.796812	−	0.330051i
$599$			14.9706i			0.611681i	0.952083	+	0.305840i	$0.0989374\pi$
$599$			14.9706i			0.611681i	−0.952083	+	0.305840i	$0.901063\pi$
$600$	2.65685	−	8.24264i	0.108466	−	0.336504i
$601$	−0.778175	−	0.322330i	−0.0317424	−	0.0131481i	0.366756	−	0.930317i	$-0.380468\pi$
$601$	−0.778175	−	0.322330i	−0.0317424	−	0.0131481i	−0.398498	+	0.917169i	$0.630468\pi$
$602$	48.0416	−	19.8995i	1.95803	−	0.811043i
$603$	−8.07107	−	16.8995i	−0.328679	−	0.688201i
$604$	−6.65685	−	6.65685i	−0.270864	−	0.270864i
$605$	11.4558	+	5.72792i	0.465746	+	0.232873i
$606$	−10.8284	−	15.3137i	−0.439875	−	0.622077i
$607$	−2.87868	−	1.19239i	−0.116842	−	0.0483975i	0.323497	−	0.946229i	$-0.395142\pi$
$607$	−2.87868	−	1.19239i	−0.116842	−	0.0483975i	−0.440339	+	0.897832i	$0.645142\pi$
$608$	−3.24264	−	3.24264i	−0.131506	−	0.131506i
$609$	−2.41421	−	0.414214i	−0.0978289	−	0.0167848i
$610$	6.12132	+	0.435029i	0.247845	+	0.0176138i
$611$		−	51.4558i		−	2.08168i
$612$	−11.3137	+	5.00000i	−0.457330	+	0.202113i
$613$	−14.0711	−	14.0711i	−0.568325	−	0.568325i	0.363334	−	0.931659i	$-0.381638\pi$
$613$	−14.0711	−	14.0711i	−0.568325	−	0.568325i	−0.931659	+	0.363334i	$0.881638\pi$
$614$	3.72792	+	3.72792i	0.150447	+	0.150447i
$615$	−2.43503	−	4.02082i	−0.0981898	−	0.162135i
$616$		−	10.2426i		−	0.412688i
$617$	16.7487	−	40.4350i	0.674279	−	1.62785i	−0.0999842	−	0.994989i	$-0.531879\pi$
$617$	16.7487	−	40.4350i	0.674279	−	1.62785i	0.774263	−	0.632864i	$-0.218121\pi$
$618$	3.24264	+	0.556349i	0.130438	+	0.0223796i
$619$	20.6777	+	8.56497i	0.831106	+	0.344255i	0.757340	−	0.653020i	$-0.226498\pi$
$619$	20.6777	+	8.56497i	0.831106	+	0.344255i	0.0737654	+	0.997276i	$0.476498\pi$
$620$	1.29289	−	1.12132i	0.0519238	−	0.0450333i
$621$	13.7782	−	10.8787i	0.552899	−	0.436546i
$622$	−10.4350	−	25.1924i	−0.418407	−	1.01012i
$623$	58.2843	−	24.1421i	2.33511	−	0.967234i
$624$	10.6569	+	1.82843i	0.426616	+	0.0731957i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−7.70711	−	18.6066i	−0.308038	−	0.743669i
$627$	−9.72792	+	15.4264i	−0.388496	+	0.616071i
$628$	16.0711	+	16.0711i	0.641305	+	0.641305i
$629$	−11.2929	+	4.29289i	−0.450277	+	0.171169i
$630$	−10.9497	−	27.8492i	−0.436248	−	1.10954i
$631$	−20.1716	−	20.1716i	−0.803018	−	0.803018i	0.180548	−	0.983566i	$-0.442213\pi$
$631$	−20.1716	−	20.1716i	−0.803018	−	0.803018i	−0.983566	+	0.180548i	$0.942213\pi$
$632$	−14.1924	−	5.87868i	−0.564543	−	0.233841i
$633$	−7.09188	+	1.60660i	−0.281877	+	0.0638567i
$634$	19.5355	−	8.09188i	0.775855	−	0.321370i
$635$	1.17157	+	3.51472i	0.0464925	+	0.139477i
$636$	1.17157	+	1.65685i	0.0464559	+	0.0656985i
$637$			80.5269i			3.19059i
$638$			0.727922i			0.0288187i
$639$	−18.5061	+	0.979185i	−0.732090	+	0.0387359i
$640$	−0.707107	−	2.12132i	−0.0279508	−	0.0838525i
$641$	−3.94975	+	1.63604i	−0.156006	+	0.0646197i	−0.459320	−	0.888271i	$-0.651907\pi$
$641$	−3.94975	+	1.63604i	−0.156006	+	0.0646197i	0.303314	+	0.952891i	$0.401907\pi$
$642$	2.70711	+	11.9497i	0.106841	+	0.471619i
$643$	−24.9497	−	10.3345i	−0.983922	−	0.407554i	−0.168045	−	0.985779i	$-0.553745\pi$
$643$	−24.9497	−	10.3345i	−0.983922	−	0.407554i	−0.815877	+	0.578225i	$0.803745\pi$
$644$	10.6569	+	10.6569i	0.419939	+	0.419939i
$645$	−36.3848	−	26.7279i	−1.43265	−	1.05241i
$646$	−0.556349	+	18.8995i	−0.0218893	+	0.743591i
$647$	−15.3431	−	15.3431i	−0.603201	−	0.603201i	0.337959	−	0.941161i	$-0.390263\pi$
$647$	−15.3431	−	15.3431i	−0.603201	−	0.603201i	−0.941161	+	0.337959i	$0.890263\pi$
$648$	−5.65685	+	7.00000i	−0.222222	+	0.274986i
$649$	7.97056	+	19.2426i	0.312872	+	0.755340i
$650$	30.8995	+	4.41421i	1.21198	+	0.173140i
$651$	1.00000	−	5.82843i	0.0391931	−	0.228434i
$652$	8.12132	−	3.36396i	0.318055	−	0.131743i
$653$	−10.6777	−	25.7782i	−0.417849	−	1.00878i	−0.982969	−	0.183769i	$-0.941170\pi$
$653$	−10.6777	−	25.7782i	−0.417849	−	1.00878i	0.565120	−	0.825009i	$-0.308830\pi$
$654$	−12.2635	+	2.77817i	−0.479539	+	0.108635i
$655$	15.6066	−	13.5355i	0.609800	−	0.528877i
$656$	−1.12132	−	0.464466i	−0.0437802	−	0.0181344i
$657$	22.6066	+	20.3345i	0.881968	+	0.793325i
$658$	−14.0711	+	33.9706i	−0.548547	+	1.32431i
$659$		−	17.5147i		−	0.682277i	−0.940013	−	0.341138i	$-0.889188\pi$
$659$		−	17.5147i		−	0.682277i	0.940013	−	0.341138i	$-0.110812\pi$
$660$	−7.60660	+	4.60660i	−0.296087	+	0.179312i
$661$	−6.41421	−	6.41421i	−0.249484	−	0.249484i	0.571275	−	0.820759i	$-0.306449\pi$
$661$	−6.41421	−	6.41421i	−0.249484	−	0.249484i	−0.820759	+	0.571275i	$0.806449\pi$
$662$	−4.41421	−	4.41421i	−0.171563	−	0.171563i
$663$	−24.6569	−	37.1421i	−0.957593	−	1.44248i
$664$		−	11.6569i		−	0.452374i
$665$	−45.6274	−	3.24264i	−1.76936	−	0.125744i
$666$	−5.87868	+	6.53553i	−0.227794	+	0.253247i
$667$	−0.757359	−	0.757359i	−0.0293251	−	0.0293251i
$668$	3.36396	+	1.39340i	0.130156	+	0.0539122i
$669$	32.9706	−	23.3137i	1.27472	−	0.901360i
$670$	−12.4853	−	6.24264i	−0.482349	−	0.241174i
$671$	−4.45584	−	4.45584i	−0.172016	−	0.172016i
$672$	−6.53553	−	4.12132i	−0.252114	−	0.158983i
$673$	1.53553	−	0.636039i	0.0591905	−	0.0245175i	−0.352892	−	0.935664i	$-0.614802\pi$
$673$	1.53553	−	0.636039i	0.0591905	−	0.0245175i	0.412082	+	0.911147i	$0.364802\pi$
$674$	6.77817	+	2.80761i	0.261086	+	0.108145i
$675$	−15.7574	+	20.6569i	−0.606501	+	0.795083i
$676$			25.9706i			0.998868i
$677$	2.87868	+	1.19239i	0.110637	+	0.0458272i	0.437315	−	0.899308i	$-0.355929\pi$
$677$	2.87868	+	1.19239i	0.110637	+	0.0458272i	−0.326679	+	0.945136i	$0.605929\pi$
$678$	3.29289	−	5.22183i	0.126463	−	0.200543i
$679$			17.0711i			0.655127i
$680$	−4.36396	+	8.12132i	−0.167350	+	0.311438i
$681$	−4.53553	+	7.19239i	−0.173802	+	0.275613i
$682$	−1.75736			−0.0672928
$683$	−17.3345	+	41.8492i	−0.663287	+	1.60132i	0.129333	+	0.991601i	$0.458716\pi$
$683$	−17.3345	+	41.8492i	−0.663287	+	1.60132i	−0.792620	+	0.609716i	$0.791284\pi$
$684$	5.92893	+	12.4142i	0.226698	+	0.474669i
$685$	21.1716	+	10.5858i	0.808924	+	0.404462i
$686$	10.0711	−	24.3137i	0.384515	−	0.928302i
$687$	−4.79899	+	27.9706i	−0.183093	+	1.06714i
$688$	−11.6569			−0.444413
$689$	−5.17157	+	5.17157i	−0.197021	+	0.197021i
$690$	3.12132	−	12.7071i	0.118827	−	0.483751i
$691$	−15.7071	−	6.50610i	−0.597527	−	0.247504i	0.0633584	−	0.997991i	$-0.479819\pi$
$691$	−15.7071	−	6.50610i	−0.597527	−	0.247504i	−0.660885	+	0.750487i	$0.729819\pi$
$692$	6.29289	−	15.1924i	0.239220	−	0.577528i
$693$	−10.2426	+	28.9706i	−0.389086	+	1.10050i
$694$	7.84924	+	18.9497i	0.297953	+	0.719323i
$695$	−11.9497	−	13.7782i	−0.453280	−	0.522636i
$696$	0.464466	+	0.292893i	0.0176055	+	0.0111021i
$697$	1.77817	+	4.67767i	0.0673532	+	0.177179i
$698$	−0.757359	+	0.757359i	−0.0286665	+	0.0286665i
$699$	−3.12132	−	13.7782i	−0.118059	−	0.521138i
$700$	−19.1924	−	11.3640i	−0.725404	−	0.429517i
$701$	12.3431			0.466194			0.233097	−	0.972453i	$-0.425114\pi$
$701$	12.3431			0.466194			0.233097	+	0.972453i	$0.425114\pi$
$702$	−28.3137	−	15.8284i	−1.06863	−	0.597405i
$703$	5.14214	+	12.4142i	0.193939	+	0.468211i
$704$	−0.878680	+	2.12132i	−0.0331165	+	0.0799503i
$705$	31.5563	−	4.82843i	1.18848	−	0.181849i
$706$	−16.6569	+	16.6569i	−0.626889	+	0.626889i
$707$	−44.6274	+	18.4853i	−1.67839	+	0.695211i
$708$	15.4853	+	2.65685i	0.581973	+	0.0998507i
$709$	10.3640	−	4.29289i	0.389227	−	0.161223i	−0.179483	−	0.983761i	$-0.557443\pi$
$709$	10.3640	−	4.29289i	0.389227	−	0.161223i	0.568710	+	0.822538i	$0.307443\pi$
$710$	−10.4350	+	9.05025i	−0.391620	+	0.339650i
$711$	34.2635	+	30.8198i	1.28498	+	1.15583i
$712$	−14.1421			−0.529999
$713$	1.82843	−	1.82843i	0.0684751	−	0.0684751i
$714$	6.12132	+	31.2635i	0.229085	+	1.17001i
$715$	−21.0000	−	24.2132i	−0.785355	−	0.905522i
$716$	−1.24264	+	1.24264i	−0.0464397	+	0.0464397i
$717$	−12.0000	−	16.9706i	−0.448148	−	0.633777i
$718$	−8.65685	+	8.65685i	−0.323071	+	0.323071i
$719$	−15.3345	−	37.0208i	−0.571881	−	1.38064i	−0.899951	−	0.435990i	$-0.856398\pi$
$719$	−15.3345	−	37.0208i	−0.571881	−	1.38064i	0.328070	−	0.944653i	$-0.393602\pi$
$720$	−0.121320	+	6.70711i	−0.00452134	+	0.249959i
$721$	3.24264	−	7.82843i	0.120762	−	0.291546i
$722$	2.02944			0.0755278
$723$	2.16295	+	1.36396i	0.0804410	+	0.0507263i
$724$	3.87868	+	1.60660i	0.144150	+	0.0597089i
$725$	1.36396	+	0.807612i	0.0506562	+	0.0299940i
$726$	−9.77817	−	1.67767i	−0.362902	−	0.0622642i
$727$	20.6569	+	20.6569i	0.766120	+	0.766120i	0.977421	−	0.211301i	$-0.0677700\pi$
$727$	20.6569	+	20.6569i	0.766120	+	0.766120i	−0.211301	+	0.977421i	$0.567770\pi$
$728$	10.6569	−	25.7279i	0.394969	−	0.953540i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	22.6066	+	1.60660i	0.836708	+	0.0594630i
$731$	32.9706	+	34.9706i	1.21946	+	1.29343i
$732$	−4.63604	+	1.05025i	−0.171353	+	0.0388185i
$733$			47.2548i			1.74540i	0.488259	+	0.872699i	$0.337632\pi$
$733$			47.2548i			1.74540i	−0.488259	+	0.872699i	$0.662368\pi$
$734$	−4.12132	+	1.70711i	−0.152121	+	0.0630105i
$735$	−49.3848	+	7.55635i	−1.82158	+	0.278720i
$736$	−1.29289	−	3.12132i	−0.0476567	−	0.115053i
$737$	5.48528	+	13.2426i	0.202053	+	0.487799i
$738$	2.70711	+	2.43503i	0.0996500	+	0.0896347i
$739$	−13.9289	−	13.9289i	−0.512384	−	0.512384i	0.402872	−	0.915256i	$-0.368012\pi$
$739$	−13.9289	−	13.9289i	−0.512384	−	0.512384i	−0.915256	+	0.402872i	$0.868012\pi$
$740$	−0.464466	+	6.53553i	−0.0170741	+	0.240251i
$741$	−40.4853	+	28.6274i	−1.48726	+	1.05165i
$742$	4.82843	−	2.00000i	0.177257	−	0.0734223i
$743$	31.8492	+	13.1924i	1.16844	+	0.483982i	0.880675	−	0.473721i	$-0.157089\pi$
$743$	31.8492	+	13.1924i	1.16844	+	0.483982i	0.287760	+	0.957702i	$0.407089\pi$
$744$	−0.707107	+	1.12132i	−0.0259238	+	0.0411096i
$745$	15.6569	+	46.9706i	0.573623	+	1.72087i
$746$	11.2426	−	11.2426i	0.411622	−	0.411622i
$747$	−11.6569	+	32.9706i	−0.426502	+	1.20633i
$748$	8.84924	−	3.36396i	0.323560	−	0.122999i
$749$	31.5563			1.15304
$750$	0.192388	+	19.3640i	0.00702502	+	0.707072i
$751$	−5.05025	+	2.09188i	−0.184286	+	0.0763339i	−0.472919	−	0.881106i	$-0.656800\pi$
$751$	−5.05025	+	2.09188i	−0.184286	+	0.0763339i	0.288632	+	0.957440i	$0.406800\pi$
$752$	5.82843	−	5.82843i	0.212541	−	0.212541i
$753$	−9.17157	−	12.9706i	−0.334231	−	0.472674i
$754$	−0.757359	+	1.82843i	−0.0275814	+	0.0665874i
$755$	18.8284	+	9.41421i	0.685237	+	0.342618i
$756$	14.3640	+	18.1924i	0.522412	+	0.661651i
$757$		−	13.3137i		−	0.483895i	−0.970289	−	0.241947i	$-0.922214\pi$
$757$		−	13.3137i		−	0.483895i	0.970289	−	0.241947i	$-0.0777862\pi$
$758$	14.1213	+	34.0919i	0.512909	+	1.23827i
$759$	−10.9706	+	7.75736i	−0.398206	+	0.281574i
$760$	9.17157	+	4.58579i	0.332688	+	0.166344i
$761$	26.9706			0.977682			0.488841	−	0.872373i	$-0.337420\pi$
$761$	26.9706			0.977682			0.488841	+	0.872373i	$0.337420\pi$
$762$	−1.65685	−	2.34315i	−0.0600215	−	0.0848832i
$763$			32.3848i			1.17241i
$764$	−17.6569			−0.638803
$765$	20.4645	−	18.6066i	0.739894	−	0.672723i
$766$	27.3137			0.986884
$767$			56.6274i			2.04470i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	48.6274			1.75355			0.876775	−	0.480901i	$-0.159690\pi$
$769$	48.6274			1.75355			0.876775	+	0.480901i	$0.159690\pi$
$770$	7.24264	+	21.7279i	0.261007	+	0.783020i
$771$	−4.48528	+	3.17157i	−0.161533	+	0.114221i
$772$	−3.43503	−	8.29289i	−0.123629	−	0.298468i
$773$			46.0000i			1.65451i	0.561830	+	0.827253i	$0.310097\pi$
$773$			46.0000i			1.65451i	−0.561830	+	0.827253i	$0.689903\pi$
$774$	32.9706	+	11.6569i	1.18510	+	0.418997i
$775$	−1.94975	+	3.29289i	−0.0700370	+	0.118284i
$776$	1.46447	−	3.53553i	0.0525713	−	0.126918i
$777$	13.0711	+	18.4853i	0.468922	+	0.663156i
$778$	−2.41421	+	2.41421i	−0.0865537	+	0.0865537i
$779$	5.14214	−	2.12994i	0.184236	−	0.0763131i
$780$	−23.8995	+	3.65685i	−0.855739	+	0.130936i
$781$	14.1838			0.507535
$782$	−5.70711	+	12.7071i	−0.204086	+	0.454405i
$783$	−1.02082	−	1.29289i	−0.0364810	−	0.0462042i
$784$	−9.12132	+	9.12132i	−0.325761	+	0.325761i
$785$	−45.4558	−	22.7279i	−1.62239	−	0.811194i
$786$	−8.53553	+	13.5355i	−0.304452	+	0.482797i
$787$	20.9497	+	8.67767i	0.746778	+	0.309326i	0.723426	−	0.690402i	$-0.242566\pi$
$787$	20.9497	+	8.67767i	0.746778	+	0.309326i	0.0233517	+	0.999727i	$0.492566\pi$
$788$	2.53553	−	1.05025i	0.0903247	−	0.0374137i
$789$	−11.3137	+	8.00000i	−0.402779	+	0.284808i
$790$	34.2635	+	2.43503i	1.21904	+	0.0866344i
$791$	−11.2426	−	11.2426i	−0.399742	−	0.399742i
$792$	4.60660	−	5.12132i	0.163688	−	0.181978i
$793$	−6.55635	−	15.8284i	−0.232823	−	0.562084i
$794$	4.26346	+	10.2929i	0.151304	+	0.365281i
$795$	−3.65685	−	2.68629i	−0.129695	−	0.0952729i
$796$	7.77817	−	3.22183i	0.275690	−	0.114195i
$797$		−	8.34315i		−	0.295529i	−0.989023	−	0.147765i	$-0.952792\pi$
$797$		−	8.34315i		−	0.295529i	0.989023	−	0.147765i	$-0.0472078\pi$
$798$	34.5563	−	7.82843i	1.22328	−	0.277123i
$799$	−33.9706	−	1.00000i	−1.20179	−	0.0353775i
$800$	3.00000	+	4.00000i	0.106066	+	0.141421i
$801$	40.0000	+	14.1421i	1.41333	+	0.499688i
$802$	0.807612	−	1.94975i	0.0285178	−	0.0688480i
$803$	−16.4558	−	16.4558i	−0.580714	−	0.580714i
$804$	10.6569	+	1.82843i	0.375838	+	0.0644837i
$805$	−30.1421	−	15.0711i	−1.06237	−	0.531185i
$806$	−4.41421	−	1.82843i	−0.155484	−	0.0644036i
$807$	−46.1335	−	29.0919i	−1.62398	−	1.02408i
$808$	10.8284			0.380943
$809$	11.7071	−	28.2635i	0.411600	−	0.993690i	−0.573108	−	0.819480i	$-0.694263\pi$
$809$	11.7071	−	28.2635i	0.411600	−	0.993690i	0.984708	−	0.174211i	$-0.0557374\pi$
$810$	7.05025	−	18.8492i	0.247721	−	0.662295i
$811$	1.80761	+	4.36396i	0.0634738	+	0.153239i	0.952434	−	0.304745i	$-0.0985714\pi$
$811$	1.80761	+	4.36396i	0.0634738	+	0.153239i	−0.888960	+	0.457985i	$0.848571\pi$
$812$	1.00000	−	1.00000i	0.0350931	−	0.0350931i
$813$	−0.686292	−	0.970563i	−0.0240693	−	0.0340391i
$814$	4.75736	−	4.75736i	0.166745	−	0.166745i
$815$	−14.8492	+	12.8787i	−0.520146	+	0.451120i
$816$	1.41421	−	7.00000i	0.0495074	−	0.245049i
$817$	37.7990	−	37.7990i	1.32242	−	1.32242i
$818$	−10.8284			−0.378607
$819$	−55.8701	+	62.1127i	−1.95226	+	2.17039i
$820$	2.70711	+	0.192388i	0.0945363	+	0.00671849i
$821$	−31.3345	+	12.9792i	−1.09358	+	0.452977i	−0.855255	−	0.518208i	$-0.826599\pi$
$821$	−31.3345	+	12.9792i	−1.09358	+	0.452977i	−0.238328	+	0.971185i	$0.576599\pi$
$822$	−18.0711	−	3.10051i	−0.630301	−	0.108143i
$823$	−42.9203	+	17.7782i	−1.49611	+	0.619708i	−0.972636	−	0.232335i	$-0.925364\pi$
$823$	−42.9203	+	17.7782i	−1.49611	+	0.619708i	−0.523472	+	0.852043i	$0.675364\pi$
$824$	−1.34315	+	1.34315i	−0.0467907	+	0.0467907i
$825$	12.8787	−	15.1508i	0.448378	−	0.527482i
$826$	15.4853	−	37.3848i	0.538802	−	1.30078i
$827$	8.36396	+	20.1924i	0.290843	+	0.702158i	0.999996	−	0.00289711i	$-0.000922181\pi$
$827$	8.36396	+	20.1924i	0.290843	+	0.702158i	−0.709152	+	0.705055i	$0.750922\pi$
$828$	0.535534	+	10.1213i	0.0186111	+	0.351740i
$829$	20.3431			0.706547			0.353273	−	0.935520i	$-0.385069\pi$
$829$	20.3431			0.706547			0.353273	+	0.935520i	$0.385069\pi$
$830$	8.24264	+	24.7279i	0.286106	+	0.858319i
$831$	−11.0919	−	48.9619i	−0.384773	−	1.69847i
$832$	−4.41421	+	4.41421i	−0.153035	+	0.153035i
$833$	53.1630	+	1.56497i	1.84199	+	0.0542230i
$834$	11.9497	+	7.53553i	0.413786	+	0.260934i
$835$	−8.12132	−	0.577164i	−0.281050	−	0.0199736i
$836$	−4.02944	−	9.72792i	−0.139361	−	0.336447i
$837$	3.12132	−	2.46447i	0.107889	−	0.0851844i
$838$	5.63604	−	13.6066i	0.194694	−	0.470032i
$839$	−38.0208	−	15.7487i	−1.31262	−	0.543707i	−0.386975	−	0.922090i	$-0.626480\pi$
$839$	−38.0208	−	15.7487i	−1.31262	−	0.543707i	−0.925649	+	0.378383i	$0.876480\pi$
$840$	16.7782	+	4.12132i	0.578902	+	0.142199i
$841$	20.4350	−	20.4350i	0.704656	−	0.704656i
$842$	−38.1421			−1.31446
$843$	−1.04163	+	6.07107i	−0.0358757	+	0.209099i
$844$	1.60660	−	3.87868i	0.0553015	−	0.133510i
$845$	−18.3640	−	55.0919i	−0.631739	−	1.89522i
$846$	−22.3137	+	10.6569i	−0.767161	+	0.366390i
$847$	−9.77817	+	23.6066i	−0.335982	+	0.811132i
$848$	−1.17157			−0.0402320
$849$	−16.7782	+	26.6066i	−0.575825	+	0.913136i
$850$	3.51472	−	20.3137i	0.120554	−	0.696754i
$851$			9.89949i			0.339350i
$852$	5.70711	−	9.05025i	0.195522	−	0.310057i
$853$	9.46447	+	3.92031i	0.324057	+	0.134229i	0.538781	−	0.842446i	$-0.318885\pi$
$853$	9.46447	+	3.92031i	0.324057	+	0.134229i	−0.214724	+	0.976675i	$0.568885\pi$
$854$			12.2426i			0.418935i
$855$	−21.3553	−	22.1421i	−0.730337	−	0.757245i
$856$	−6.53553	−	2.70711i	−0.223380	−	0.0925270i
$857$	44.2635	−	18.3345i	1.51201	−	0.626295i	0.536039	−	0.844193i	$-0.319920\pi$
$857$	44.2635	−	18.3345i	1.51201	−	0.626295i	0.975972	+	0.217898i	$0.0699199\pi$
$858$	21.0000	+	13.2426i	0.716928	+	0.452096i
$859$	17.7279	+	17.7279i	0.604869	+	0.604869i	0.941601	−	0.336732i	$-0.109322\pi$
$859$	17.7279	+	17.7279i	0.604869	+	0.604869i	−0.336732	+	0.941601i	$0.609322\pi$
$860$	24.7279	−	8.24264i	0.843215	−	0.281072i
$861$	7.65685	−	5.41421i	0.260945	−	0.184516i
$862$	−32.3345	−	13.3934i	−1.10132	−	0.456181i
$863$	−6.51472	−	6.51472i	−0.221764	−	0.221764i	0.587477	−	0.809241i	$-0.300121\pi$
$863$	−6.51472	−	6.51472i	−0.221764	−	0.221764i	−0.809241	+	0.587477i	$0.800121\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	−2.60660	+	36.6777i	−0.0886271	+	1.24708i
$866$			28.9706i			0.984460i
$867$	−25.0000	+	15.5563i	−0.849045	+	0.528321i
$868$	2.41421	+	2.41421i	0.0819437	+	0.0819437i
$869$	−24.9411	−	24.9411i	−0.846070	−	0.846070i
$870$	−1.19239	−	0.292893i	−0.0404257	−	0.00993001i
$871$			38.9706i			1.32047i
$872$	2.77817	−	6.70711i	0.0940809	−	0.227131i
$873$	−7.67767	+	8.53553i	−0.259850	+	0.288884i
$874$	14.3137	+	5.92893i	0.484168	+	0.200549i
$875$	48.7487	+	10.5355i	1.64801	+	0.356166i
$876$	−17.1213	+	3.87868i	−0.578476	+	0.131048i
$877$	16.8787	+	40.7487i	0.569953	+	1.37599i	0.901595	+	0.432582i	$0.142397\pi$
$877$	16.8787	+	40.7487i	0.569953	+	1.37599i	−0.331642	+	0.943405i	$0.607603\pi$
$878$	−23.6066	+	9.77817i	−0.796684	+	0.329997i
$879$	2.31371	−	13.4853i	0.0780395	−	0.454847i
$880$	0.363961	−	5.12132i	0.0122691	−	0.172640i
$881$	−2.73654	−	6.60660i	−0.0921965	−	0.222582i	0.871054	−	0.491188i	$-0.163437\pi$
$881$	−2.73654	−	6.60660i	−0.0921965	−	0.222582i	−0.963250	+	0.268606i	$0.913437\pi$
$882$	34.9203	−	16.6777i	1.17583	−	0.561566i
$883$	−18.8995	−	18.8995i	−0.636019	−	0.636019i	0.313552	−	0.949571i	$-0.398481\pi$
$883$	−18.8995	−	18.8995i	−0.636019	−	0.636019i	−0.949571	+	0.313552i	$0.898481\pi$
$884$	25.7279	+	0.757359i	0.865324	+	0.0254728i
$885$	−34.7279	+	5.31371i	−1.16737	+	0.178618i
$886$	22.0711	+	22.0711i	0.741492	+	0.741492i
$887$	4.63604	+	1.92031i	0.155663	+	0.0644777i	0.459155	−	0.888356i	$-0.348152\pi$
$887$	4.63604	+	1.92031i	0.155663	+	0.0644777i	−0.303492	+	0.952834i	$0.598152\pi$
$888$	−1.12132	−	4.94975i	−0.0376290	−	0.166103i
$889$	−6.82843	+	2.82843i	−0.229018	+	0.0948624i
$890$	30.0000	−	10.0000i	1.00560	−	0.335201i
$891$	−18.1508	+	9.87868i	−0.608073	+	0.330948i
$892$			23.3137i			0.780601i
$893$			37.7990i			1.26489i
$894$	−22.1421	−	31.3137i	−0.740544	−	1.04729i
$895$	1.75736	−	3.51472i	0.0587420	−	0.117484i
$896$	4.12132	−	1.70711i	0.137684	−	0.0570304i
$897$	−35.6274	+	8.07107i	−1.18956	+	0.269485i
$898$	10.1213	+	4.19239i	0.337753	+	0.139902i
$899$	−0.171573	−	0.171573i	−0.00572228	−	0.00572228i
$900$	−4.48528	−	14.3137i	−0.149509	−	0.477124i
$901$	3.31371	+	3.51472i	0.110396	+	0.117092i
$902$	−1.97056	−	1.97056i	−0.0656126	−	0.0656126i
$903$	48.0416	−	76.1838i	1.59873	−	2.53524i
$904$	1.36396	+	3.29289i	0.0453647	+	0.109520i
$905$	−9.36396	−	0.665476i	−0.311269	−	0.0221212i
$906$	−16.0711	−	2.75736i	−0.533925	−	0.0916071i
$907$	−41.8198	+	17.3223i	−1.38860	+	0.575179i	−0.946768	−	0.321917i	$-0.895673\pi$
$907$	−41.8198	+	17.3223i	−1.38860	+	0.575179i	−0.441836	+	0.897096i	$0.645673\pi$
$908$	−1.87868	−	4.53553i	−0.0623462	−	0.150517i
$909$	−30.6274	−	10.8284i	−1.01585	−	0.359156i
$910$	−4.41421	+	62.1127i	−0.146330	+	2.05902i
$911$	5.87868	+	2.43503i	0.194769	+	0.0806761i	0.477936	−	0.878395i	$-0.341385\pi$
$911$	5.87868	+	2.43503i	0.194769	+	0.0806761i	−0.283167	+	0.959071i	$0.591385\pi$
$912$	−7.82843	−	1.34315i	−0.259225	−	0.0444760i
$913$	10.2426	−	24.7279i	0.338982	−	0.818375i
$914$		−	9.65685i		−	0.319420i
$915$	9.09188	−	5.50610i	0.300568	−	0.182026i
$916$	−11.5858	−	11.5858i	−0.382805	−	0.382805i
$917$	29.1421	+	29.1421i	0.962358	+	0.962358i
$918$	−11.0000	+	18.3848i	−0.363054	+	0.606788i
$919$		−	18.6863i		−	0.616404i	−0.951321	−	0.308202i	$-0.900273\pi$
$919$		−	18.6863i		−	0.616404i	0.951321	−	0.308202i	$-0.0997272\pi$
$920$	4.94975	+	5.70711i	0.163188	+	0.188158i
$921$	9.00000	+	1.54416i	0.296560	+	0.0508817i
$922$	19.7279	+	19.7279i	0.649705	+	0.649705i
$923$	35.6274	+	14.7574i	1.17269	+	0.485744i
$924$	−10.2426	−	14.4853i	−0.336958	−	0.476531i
$925$	−3.63604	−	14.1924i	−0.119552	−	0.466643i
$926$	−8.17157	−	8.17157i	−0.268535	−	0.268535i
$927$	5.14214	−	2.45584i	0.168890	−	0.0806605i
$928$	−0.292893	+	0.121320i	−0.00961469	+	0.00398254i
$929$	−23.0208	−	9.53553i	−0.755288	−	0.312851i	−0.0283911	−	0.999597i	$-0.509038\pi$
$929$	−23.0208	−	9.53553i	−0.755288	−	0.312851i	−0.726897	+	0.686746i	$0.759038\pi$
$930$	0.707107	−	2.87868i	0.0231869	−	0.0943956i
$931$		−	59.1543i		−	1.93870i
$932$	7.53553	+	3.12132i	0.246835	+	0.102242i
$933$	−39.9497	−	25.1924i	−1.30790	−	0.824762i
$934$		−	26.4853i		−	0.866625i
$935$	−16.3934	+	13.3934i	−0.536121	+	0.438011i
$936$	16.8995	−	8.07107i	0.552377	−	0.263811i
$937$	17.6569			0.576824			0.288412	−	0.957506i	$-0.406873\pi$
$937$	17.6569			0.576824			0.288412	+	0.957506i	$0.406873\pi$
$938$	10.6569	−	25.7279i	0.347959	−	0.840046i
$939$	−29.5061	−	18.6066i	−0.962895	−	0.607203i
$940$	−8.24264	+	16.4853i	−0.268845	+	0.537691i
$941$	−3.29289	+	7.94975i	−0.107345	+	0.259154i	−0.968420	−	0.249324i	$-0.919792\pi$
$941$	−3.29289	+	7.94975i	−0.107345	+	0.259154i	0.861075	+	0.508478i	$0.169792\pi$
$942$	38.7990	+	6.65685i	1.26414	+	0.216892i
$943$	4.10051			0.133531
$944$	−6.41421	+	6.41421i	−0.208765	+	0.208765i
$945$	−43.3345	−	28.4350i	−1.40967	−	0.924992i
$946$	−24.7279	−	10.2426i	−0.803974	−	0.333017i
$947$	−1.77817	+	4.29289i	−0.0577829	+	0.139500i	−0.950134	−	0.311841i	$-0.899054\pi$
$947$	−1.77817	+	4.29289i	−0.0577829	+	0.139500i	0.892351	+	0.451341i	$0.149054\pi$
$948$	−25.9497	+	5.87868i	−0.842809	+	0.190931i
$949$	−24.2132	−	58.4558i	−0.785994	−	1.89756i
$950$	−22.6985	−	3.24264i	−0.736436	−	0.105205i
$951$	19.5355	−	30.9792i	0.633483	−	1.00457i
$952$	−16.7782	−	7.53553i	−0.543784	−	0.244228i
$953$	29.2843	−	29.2843i	0.948611	−	0.948611i	−0.0501320	−	0.998743i	$-0.515964\pi$
$953$	29.2843	−	29.2843i	0.948611	−	0.948611i	0.998743	+	0.0501320i	$0.0159642\pi$
$954$	3.31371	+	1.17157i	0.107285	+	0.0379311i
$955$	37.4558	−	12.4853i	1.21204	−	0.404014i
$956$	12.0000			0.388108
$957$	0.727922	+	1.02944i	0.0235304	+	0.0332770i
$958$	8.43503	+	20.3640i	0.272523	+	0.657930i
$959$	−18.0711	+	43.6274i	−0.583545	+	1.40880i
$960$	−3.12132	−	2.29289i	−0.100740	−	0.0740028i
$961$	−21.5061	+	21.5061i	−0.693745	+	0.693745i
$962$	16.8995	−	7.00000i	0.544862	−	0.225689i
$963$	15.7782	+	14.1924i	0.508445	+	0.457343i
$964$	−1.36396	+	0.564971i	−0.0439302	+	0.0181965i
$965$	13.1508	+	15.1630i	0.423338	+	0.488113i
$966$	25.7279	+	4.41421i	0.827782	+	0.142025i
$967$	23.9411			0.769895			0.384947	−	0.922939i	$-0.374220\pi$
$967$	23.9411			0.769895			0.384947	+	0.922939i	$0.374220\pi$
$968$	4.05025	−	4.05025i	0.130180	−	0.130180i
$969$	18.1127	+	27.2843i	0.581864	+	0.876497i
$970$	−0.606602	+	8.53553i	−0.0194768	+	0.274059i
$971$	−7.72792	+	7.72792i	−0.248001	+	0.248001i	−0.820150	−	0.572149i	$-0.806110\pi$
$971$	−7.72792	+	7.72792i	−0.248001	+	0.248001i	0.572149	+	0.820150i	$0.306110\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	25.7279	−	25.7279i	0.824799	−	0.824799i
$974$	−3.53553	−	8.53553i	−0.113286	−	0.273496i
$975$	48.1127	−	24.6569i	1.54084	−	0.789651i
$976$	1.05025	−	2.53553i	0.0336178	−	0.0811605i
$977$	−6.54416			−0.209366			−0.104683	−	0.994506i	$-0.533383\pi$
$977$	−6.54416			−0.209366			−0.104683	+	0.994506i	$0.533383\pi$
$978$	8.12132	−	12.8787i	0.259691	−	0.411815i
$979$	−30.0000	−	12.4264i	−0.958804	−	0.397150i
$980$	12.8995	−	25.7990i	0.412059	−	0.824119i
$981$	−14.5650	+	16.1924i	−0.465024	+	0.516983i
$982$	−18.4142	−	18.4142i	−0.587621	−	0.587621i
$983$	15.6066	−	37.6777i	0.497773	−	1.20173i	−0.452907	−	0.891558i	$-0.649613\pi$
$983$	15.6066	−	37.6777i	0.497773	−	1.20173i	0.950680	−	0.310173i	$-0.100387\pi$
$984$	−2.05025	+	0.464466i	−0.0653597	+	0.0148066i
$985$	−4.63604	+	4.02082i	−0.147716	+	0.128114i
$986$	1.19239	+	0.535534i	0.0379734	+	0.0170549i
$987$	14.0711	+	62.1127i	0.447887	+	1.97707i
$988$		−	28.6274i		−	0.910759i
$989$	36.3848	−	15.0711i	1.15697	−	0.479232i
$990$	−6.15076	+	14.1213i	−0.195484	+	0.448805i
$991$	−5.77817	−	13.9497i	−0.183550	−	0.443128i	0.805144	−	0.593080i	$-0.202088\pi$
$991$	−5.77817	−	13.9497i	−0.183550	−	0.443128i	−0.988693	+	0.149952i	$0.952088\pi$
$992$	−0.292893	−	0.707107i	−0.00929937	−	0.0224507i
$993$	−10.6569	−	1.82843i	−0.338185	−	0.0580234i
$994$	−19.4853	−	19.4853i	−0.618036	−	0.618036i
$995$	−14.2218	+	12.3345i	−0.450862	+	0.391031i
$996$	−11.6569	−	16.4853i	−0.369362	−	0.522356i
$997$	55.7487	−	23.0919i	1.76558	−	0.731327i	0.769933	−	0.638125i	$-0.220290\pi$
$997$	55.7487	−	23.0919i	1.76558	−	0.731327i	0.995647	−	0.0932026i	$-0.0297104\pi$
$998$	−31.4350	−	13.0208i	−0.995058	−	0.412167i
$999$	−1.77817	+	15.1213i	−0.0562590	+	0.478417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.z.b.53.1	yes	4
3.2	odd	2		510.2.z.a.53.1	yes	4
5.2	odd	4		510.2.w.a.257.1	✓	4
15.2	even	4		510.2.w.b.257.1	yes	4
17.9	even	8		510.2.w.b.383.1	yes	4
51.26	odd	8		510.2.w.a.383.1	yes	4
85.77	odd	8		510.2.z.a.77.1	yes	4
255.77	even	8	inner	510.2.z.b.77.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.w.a.257.1	✓	4	5.2	odd	4
510.2.w.a.383.1	yes	4	51.26	odd	8
510.2.w.b.257.1	yes	4	15.2	even	4
510.2.w.b.383.1	yes	4	17.9	even	8
510.2.z.a.53.1	yes	4	3.2	odd	2
510.2.z.a.77.1	yes	4	85.77	odd	8
510.2.z.b.53.1	yes	4	1.1	even	1	trivial
510.2.z.b.77.1	yes	4	255.77	even	8	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(1.70711 + 4.12132i) q^{7} -1.00000i q^{8} +(-1.00000 + 2.82843i) q^{9} +(0.707107 + 2.12132i) q^{10} +(0.878680 - 2.12132i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(4.41421 - 4.41421i) q^{13} +(-4.12132 + 1.70711i) q^{14} +(3.12132 + 2.29289i) q^{15} +1.00000 q^{16} +(-2.82843 - 3.00000i) q^{17} +(-2.82843 - 1.00000i) q^{18} +(-3.24264 + 3.24264i) q^{19} +(-2.12132 + 0.707107i) q^{20} +(-4.12132 + 6.53553i) q^{21} +(2.12132 + 0.878680i) q^{22} +(-3.12132 + 1.29289i) q^{23} +(1.41421 - 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} +(4.41421 + 4.41421i) q^{26} +(-5.00000 + 1.41421i) q^{27} +(-1.70711 - 4.12132i) q^{28} +(0.121320 + 0.292893i) q^{29} +(-2.29289 + 3.12132i) q^{30} +(-0.707107 + 0.292893i) q^{31} +1.00000i q^{32} +(3.87868 - 0.878680i) q^{33} +(3.00000 - 2.82843i) q^{34} +(6.53553 + 7.53553i) q^{35} +(1.00000 - 2.82843i) q^{36} +(1.12132 - 2.70711i) q^{37} +(-3.24264 - 3.24264i) q^{38} +(10.6569 + 1.82843i) q^{39} +(-0.707107 - 2.12132i) q^{40} +(-1.12132 - 0.464466i) q^{41} +(-6.53553 - 4.12132i) q^{42} -11.6569 q^{43} +(-0.878680 + 2.12132i) q^{44} +(-0.121320 + 6.70711i) q^{45} +(-1.29289 - 3.12132i) q^{46} +(5.82843 - 5.82843i) q^{47} +(1.00000 + 1.41421i) q^{48} +(-9.12132 + 9.12132i) q^{49} +(3.00000 + 4.00000i) q^{50} +(1.41421 - 7.00000i) q^{51} +(-4.41421 + 4.41421i) q^{52} -1.17157 q^{53} +(-1.41421 - 5.00000i) q^{54} +(0.363961 - 5.12132i) q^{55} +(4.12132 - 1.70711i) q^{56} +(-7.82843 - 1.34315i) q^{57} +(-0.292893 + 0.121320i) q^{58} +(-6.41421 + 6.41421i) q^{59} +(-3.12132 - 2.29289i) q^{60} +(1.05025 - 2.53553i) q^{61} +(-0.292893 - 0.707107i) q^{62} +(-13.3640 + 0.707107i) q^{63} -1.00000 q^{64} +(6.24264 - 12.4853i) q^{65} +(0.878680 + 3.87868i) q^{66} +(-4.41421 + 4.41421i) q^{67} +(2.82843 + 3.00000i) q^{68} +(-4.94975 - 3.12132i) q^{69} +(-7.53553 + 6.53553i) q^{70} +(2.36396 + 5.70711i) q^{71} +(2.82843 + 1.00000i) q^{72} +(3.87868 - 9.36396i) q^{73} +(2.70711 + 1.12132i) q^{74} +(8.24264 + 2.65685i) q^{75} +(3.24264 - 3.24264i) q^{76} +10.2426 q^{77} +(-1.82843 + 10.6569i) q^{78} +(5.87868 - 14.1924i) q^{79} +(2.12132 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(0.464466 - 1.12132i) q^{82} +11.6569 q^{83} +(4.12132 - 6.53553i) q^{84} +(-8.12132 - 4.36396i) q^{85} -11.6569i q^{86} +(-0.292893 + 0.464466i) q^{87} +(-2.12132 - 0.878680i) q^{88} -14.1421i q^{89} +(-6.70711 - 0.121320i) q^{90} +(25.7279 + 10.6569i) q^{91} +(3.12132 - 1.29289i) q^{92} +(-1.12132 - 0.707107i) q^{93} +(5.82843 + 5.82843i) q^{94} +(-4.58579 + 9.17157i) q^{95} +(-1.41421 + 1.00000i) q^{96} +(3.53553 + 1.46447i) q^{97} +(-9.12132 - 9.12132i) q^{98} +(5.12132 + 4.60660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{7} - 4 q^{9} + 12 q^{11} - 4 q^{12} + 12 q^{13} - 8 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{19} - 8 q^{21} - 4 q^{23} + 16 q^{25} + 12 q^{26} - 20 q^{27} - 4 q^{28} - 8 q^{29}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^7 - 4 * q^9 + 12 * q^11 - 4 * q^12 + 12 * q^13 - 8 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^19 - 8 * q^21 - 4 * q^23 + 16 * q^25 + 12 * q^26 - 20 * q^27 - 4 * q^28 - 8 * q^29 - 12 * q^30 + 24 * q^33 + 12 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 + 4 * q^38 + 20 * q^39 + 4 * q^41 - 12 * q^42 - 24 * q^43 - 12 * q^44 + 8 * q^45 - 8 * q^46 + 12 * q^47 + 4 * q^48 - 28 * q^49 + 12 * q^50 - 12 * q^52 - 16 * q^53 - 24 * q^55 + 8 * q^56 - 20 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 + 24 * q^61 - 4 * q^62 - 28 * q^63 - 4 * q^64 + 8 * q^65 + 12 * q^66 - 12 * q^67 - 16 * q^70 - 16 * q^71 + 24 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 + 4 * q^78 + 32 * q^79 - 28 * q^81 + 16 * q^82 + 24 * q^83 + 8 * q^84 - 24 * q^85 - 4 * q^87 - 24 * q^90 + 52 * q^91 + 4 * q^92 + 4 * q^93 + 12 * q^94 - 24 * q^95 - 28 * q^98 + 12 * q^99

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