LMFDB - Embedded newform 510.2.w.b.383.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(257,510)]

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, 2, 7]))

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

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

chi := DirichletCharacter("510.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.w (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:	$1$
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			383.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	510.383
Dual form			510.2.w.b.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-0.292893 + 1.70711i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-4.12132 - 1.70711i) q^{7} +1.00000 q^{8} +(-2.82843 - 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} +(-0.878680 - 2.12132i) q^{11} +(-0.292893 + 1.70711i) q^{12} +(-4.41421 + 4.41421i) q^{13} +(-4.12132 - 1.70711i) q^{14} +(2.29289 - 3.12132i) q^{15} +1.00000 q^{16} +(-3.00000 - 2.82843i) q^{17} +(-2.82843 - 1.00000i) q^{18} +(3.24264 + 3.24264i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(4.12132 - 6.53553i) q^{21} +(-0.878680 - 2.12132i) q^{22} +(-1.29289 + 3.12132i) q^{23} +(-0.292893 + 1.70711i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-4.41421 + 4.41421i) q^{26} +(2.53553 - 4.53553i) q^{27} +(-4.12132 - 1.70711i) q^{28} +(0.121320 - 0.292893i) q^{29} +(2.29289 - 3.12132i) q^{30} +(-0.707107 - 0.292893i) q^{31} +1.00000 q^{32} +(3.87868 - 0.878680i) q^{33} +(-3.00000 - 2.82843i) q^{34} +(6.53553 + 7.53553i) q^{35} +(-2.82843 - 1.00000i) q^{36} +(2.70711 - 1.12132i) q^{37} +(3.24264 + 3.24264i) q^{38} +(-6.24264 - 8.82843i) q^{39} +(-2.00000 - 1.00000i) q^{40} +(1.12132 - 0.464466i) q^{41} +(4.12132 - 6.53553i) q^{42} -11.6569i q^{43} +(-0.878680 - 2.12132i) q^{44} +(4.65685 + 4.82843i) q^{45} +(-1.29289 + 3.12132i) q^{46} +(-5.82843 + 5.82843i) q^{47} +(-0.292893 + 1.70711i) q^{48} +(9.12132 + 9.12132i) q^{49} +(3.00000 + 4.00000i) q^{50} +(5.70711 - 4.29289i) q^{51} +(-4.41421 + 4.41421i) q^{52} +1.17157i q^{53} +(2.53553 - 4.53553i) q^{54} +(-0.363961 + 5.12132i) q^{55} +(-4.12132 - 1.70711i) q^{56} +(-6.48528 + 4.58579i) q^{57} +(0.121320 - 0.292893i) q^{58} +(-6.41421 - 6.41421i) q^{59} +(2.29289 - 3.12132i) q^{60} +(1.05025 + 2.53553i) q^{61} +(-0.707107 - 0.292893i) q^{62} +(9.94975 + 8.94975i) q^{63} +1.00000 q^{64} +(13.2426 - 4.41421i) q^{65} +(3.87868 - 0.878680i) q^{66} +(-4.41421 + 4.41421i) q^{67} +(-3.00000 - 2.82843i) q^{68} +(-4.94975 - 3.12132i) q^{69} +(6.53553 + 7.53553i) q^{70} +(-2.36396 + 5.70711i) q^{71} +(-2.82843 - 1.00000i) q^{72} +(-9.36396 + 3.87868i) q^{73} +(2.70711 - 1.12132i) q^{74} +(-7.70711 + 3.94975i) q^{75} +(3.24264 + 3.24264i) q^{76} +10.2426i q^{77} +(-6.24264 - 8.82843i) q^{78} +(-5.87868 - 14.1924i) q^{79} +(-2.00000 - 1.00000i) q^{80} +(7.00000 + 5.65685i) q^{81} +(1.12132 - 0.464466i) q^{82} -11.6569i q^{83} +(4.12132 - 6.53553i) q^{84} +(3.17157 + 8.65685i) q^{85} -11.6569i q^{86} +(0.464466 + 0.292893i) q^{87} +(-0.878680 - 2.12132i) q^{88} +14.1421i q^{89} +(4.65685 + 4.82843i) q^{90} +(25.7279 - 10.6569i) q^{91} +(-1.29289 + 3.12132i) q^{92} +(0.707107 - 1.12132i) q^{93} +(-5.82843 + 5.82843i) q^{94} +(-3.24264 - 9.72792i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(-1.46447 - 3.53553i) q^{97} +(9.12132 + 9.12132i) q^{98} +(0.363961 + 6.87868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 8 q^{7} + 4 q^{8} - 8 q^{10} - 12 q^{11} - 4 q^{12} - 12 q^{13} - 8 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{19} - 8 q^{20} + 8 q^{21} - 12 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 8 * q^7 + 4 * q^8 - 8 * q^10 - 12 * q^11 - 4 * q^12 - 12 * q^13 - 8 * q^14 + 12 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^19 - 8 * q^20 + 8 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 + 12 * q^25 - 12 * q^26 - 4 * q^27 - 8 * q^28 - 8 * q^29 + 12 * q^30 + 4 * q^32 + 24 * q^33 - 12 * q^34 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 8 * q^39 - 8 * q^40 - 4 * q^41 + 8 * q^42 - 12 * q^44 - 4 * q^45 - 8 * q^46 - 12 * q^47 - 4 * q^48 + 28 * q^49 + 12 * q^50 + 20 * q^51 - 12 * q^52 - 4 * q^54 + 24 * q^55 - 8 * q^56 + 8 * q^57 - 8 * q^58 - 20 * q^59 + 12 * q^60 + 24 * q^61 + 20 * q^63 + 4 * q^64 + 36 * q^65 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 12 * q^70 + 16 * q^71 - 12 * q^73 + 8 * q^74 - 28 * q^75 - 4 * q^76 - 8 * q^78 - 32 * q^79 - 8 * q^80 + 28 * q^81 - 4 * q^82 + 8 * q^84 + 24 * q^85 + 16 * q^87 - 12 * q^88 - 4 * q^90 + 52 * q^91 - 8 * q^92 - 12 * q^94 + 4 * q^95 - 4 * q^96 - 20 * q^97 + 28 * q^98 - 24 * q^99

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$	1.00000			0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	−0.292893	+	1.70711i	−0.119573	+	0.696923i
$7$	−4.12132	−	1.70711i	−1.55771	−	0.645226i	−0.573023	−	0.819540i	$-0.694229\pi$
$7$	−4.12132	−	1.70711i	−1.55771	−	0.645226i	−0.984690	+	0.174314i	$0.944229\pi$
$8$	1.00000			0.353553
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$	−2.00000	−	1.00000i	−0.632456	−	0.316228i
$11$	−0.878680	−	2.12132i	−0.264932	−	0.639602i	0.734299	−	0.678827i	$-0.237511\pi$
$11$	−0.878680	−	2.12132i	−0.264932	−	0.639602i	−0.999230	+	0.0392245i	$0.987511\pi$
$12$	−0.292893	+	1.70711i	−0.0845510	+	0.492799i
$13$	−4.41421	+	4.41421i	−1.22428	+	1.22428i	−0.258188	+	0.966095i	$0.583125\pi$
$13$	−4.41421	+	4.41421i	−1.22428	+	1.22428i	−0.966095	+	0.258188i	$0.916875\pi$
$14$	−4.12132	−	1.70711i	−1.10147	−	0.456243i
$15$	2.29289	−	3.12132i	0.592022	−	0.805921i
$16$	1.00000			0.250000
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$18$	−2.82843	−	1.00000i	−0.666667	−	0.235702i
$19$	3.24264	+	3.24264i	0.743913	+	0.743913i	0.973329	−	0.229416i	$-0.0736815\pi$
$19$	3.24264	+	3.24264i	0.743913	+	0.743913i	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	4.12132	−	6.53553i	0.899346	−	1.42617i
$22$	−0.878680	−	2.12132i	−0.187335	−	0.452267i
$23$	−1.29289	+	3.12132i	−0.269587	+	0.650840i	−0.999464	−	0.0327381i	$-0.989577\pi$
$23$	−1.29289	+	3.12132i	−0.269587	+	0.650840i	0.729877	+	0.683578i	$0.239577\pi$
$24$	−0.292893	+	1.70711i	−0.0597866	+	0.348462i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−4.41421	+	4.41421i	−0.865699	+	0.865699i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	−4.12132	−	1.70711i	−0.778856	−	0.322613i
$29$	0.121320	−	0.292893i	0.0225286	−	0.0543889i	−0.912215	−	0.409712i	$-0.865629\pi$
$29$	0.121320	−	0.292893i	0.0225286	−	0.0543889i	0.934744	+	0.355323i	$0.115629\pi$
$30$	2.29289	−	3.12132i	0.418623	−	0.569873i
$31$	−0.707107	−	0.292893i	−0.127000	−	0.0526052i	0.318278	−	0.947997i	$-0.396895\pi$
$31$	−0.707107	−	0.292893i	−0.127000	−	0.0526052i	−0.445279	+	0.895392i	$0.646895\pi$
$32$	1.00000			0.176777
$33$	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
$36$	−2.82843	−	1.00000i	−0.471405	−	0.166667i
$37$	2.70711	−	1.12132i	0.445046	−	0.184344i	−0.148895	−	0.988853i	$-0.547572\pi$
$37$	2.70711	−	1.12132i	0.445046	−	0.184344i	0.593940	+	0.804509i	$0.297572\pi$
$38$	3.24264	+	3.24264i	0.526026	+	0.526026i
$39$	−6.24264	−	8.82843i	−0.999623	−	1.41368i
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$	1.12132	−	0.464466i	0.175121	−	0.0725374i	−0.293400	−	0.955990i	$-0.594787\pi$
$41$	1.12132	−	0.464466i	0.175121	−	0.0725374i	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.12132	−	6.53553i	0.635934	−	1.00845i
$43$		−	11.6569i		−	1.77765i	−0.458243	−	0.888827i	$-0.651521\pi$
$43$		−	11.6569i		−	1.77765i	0.458243	−	0.888827i	$-0.348479\pi$
$44$	−0.878680	−	2.12132i	−0.132466	−	0.319801i
$45$	4.65685	+	4.82843i	0.694203	+	0.719779i
$46$	−1.29289	+	3.12132i	−0.190627	+	0.460214i
$47$	−5.82843	+	5.82843i	−0.850163	+	0.850163i	−0.990153	−	0.139990i	$-0.955293\pi$
$47$	−5.82843	+	5.82843i	−0.850163	+	0.850163i	0.139990	+	0.990153i	$0.455293\pi$
$48$	−0.292893	+	1.70711i	−0.0422755	+	0.246400i
$49$	9.12132	+	9.12132i	1.30305	+	1.30305i
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$	5.70711	−	4.29289i	0.799155	−	0.601125i
$52$	−4.41421	+	4.41421i	−0.612141	+	0.612141i
$53$			1.17157i			0.160928i	0.996758	+	0.0804640i	$0.0256402\pi$
$53$			1.17157i			0.160928i	−0.996758	+	0.0804640i	$0.974360\pi$
$54$	2.53553	−	4.53553i	0.345042	−	0.617208i
$55$	−0.363961	+	5.12132i	−0.0490765	+	0.690559i
$56$	−4.12132	−	1.70711i	−0.550735	−	0.228122i
$57$	−6.48528	+	4.58579i	−0.858997	+	0.607402i
$58$	0.121320	−	0.292893i	0.0159301	−	0.0384588i
$59$	−6.41421	−	6.41421i	−0.835059	−	0.835059i	0.153144	−	0.988204i	$-0.451060\pi$
$59$	−6.41421	−	6.41421i	−0.835059	−	0.835059i	−0.988204	+	0.153144i	$0.951060\pi$
$60$	2.29289	−	3.12132i	0.296011	−	0.402961i
$61$	1.05025	+	2.53553i	0.134471	+	0.324642i	0.976744	−	0.214410i	$-0.0687828\pi$
$61$	1.05025	+	2.53553i	0.134471	+	0.324642i	−0.842273	+	0.539052i	$0.818783\pi$
$62$	−0.707107	−	0.292893i	−0.0898027	−	0.0371975i
$63$	9.94975	+	8.94975i	1.25355	+	1.12756i
$64$	1.00000			0.125000
$65$	13.2426	−	4.41421i	1.64255	−	0.547516i
$66$	3.87868	−	0.878680i	0.477432	−	0.108158i
$67$	−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	$0.374534\pi$
$68$	−3.00000	−	2.82843i	−0.363803	−	0.342997i
$69$	−4.94975	−	3.12132i	−0.595880	−	0.375763i
$70$	6.53553	+	7.53553i	0.781146	+	0.900669i
$71$	−2.36396	+	5.70711i	−0.280551	+	0.677309i	−0.999849	−	0.0173925i	$-0.994464\pi$
$71$	−2.36396	+	5.70711i	−0.280551	+	0.677309i	0.719298	+	0.694701i	$0.244464\pi$
$72$	−2.82843	−	1.00000i	−0.333333	−	0.117851i
$73$	−9.36396	+	3.87868i	−1.09597	+	0.453965i	−0.856084	−	0.516836i	$-0.827110\pi$
$73$	−9.36396	+	3.87868i	−1.09597	+	0.453965i	−0.239885	+	0.970801i	$0.577110\pi$
$74$	2.70711	−	1.12132i	0.314695	−	0.130351i
$75$	−7.70711	+	3.94975i	−0.889940	+	0.456078i
$76$	3.24264	+	3.24264i	0.371956	+	0.371956i
$77$			10.2426i			1.16726i
$78$	−6.24264	−	8.82843i	−0.706840	−	0.999623i
$79$	−5.87868	−	14.1924i	−0.661403	−	1.59677i	−0.795606	−	0.605815i	$-0.792847\pi$
$79$	−5.87868	−	14.1924i	−0.661403	−	1.59677i	0.134203	−	0.990954i	$-0.457153\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	1.12132	−	0.464466i	0.123829	−	0.0512917i
$83$		−	11.6569i		−	1.27951i	−0.768581	−	0.639753i	$-0.779037\pi$
$83$		−	11.6569i		−	1.27951i	0.768581	−	0.639753i	$-0.220963\pi$
$84$	4.12132	−	6.53553i	0.449673	−	0.713085i
$85$	3.17157	+	8.65685i	0.344005	+	0.938968i
$86$		−	11.6569i		−	1.25699i
$87$	0.464466	+	0.292893i	0.0497960	+	0.0314014i
$88$	−0.878680	−	2.12132i	−0.0936676	−	0.226134i
$89$			14.1421i			1.49906i	0.661968	+	0.749532i	$0.269721\pi$
$89$			14.1421i			1.49906i	−0.661968	+	0.749532i	$0.730279\pi$
$90$	4.65685	+	4.82843i	0.490876	+	0.508961i
$91$	25.7279	−	10.6569i	2.69702	−	1.11714i
$92$	−1.29289	+	3.12132i	−0.134793	+	0.325420i
$93$	0.707107	−	1.12132i	0.0733236	−	0.116276i
$94$	−5.82843	+	5.82843i	−0.601156	+	0.601156i
$95$	−3.24264	−	9.72792i	−0.332688	−	0.998064i
$96$	−0.292893	+	1.70711i	−0.0298933	+	0.174231i
$97$	−1.46447	−	3.53553i	−0.148694	−	0.358979i	0.831929	−	0.554882i	$-0.187236\pi$
$97$	−1.46447	−	3.53553i	−0.148694	−	0.358979i	−0.980623	+	0.195902i	$0.937236\pi$
$98$	9.12132	+	9.12132i	0.921392	+	0.921392i
$99$	0.363961	+	6.87868i	0.0365795	+	0.691333i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$			10.8284i			1.07747i	0.842476	+	0.538734i	$0.181097\pi$
$101$			10.8284i			1.07747i	−0.842476	+	0.538734i	$0.818903\pi$
$102$	5.70711	−	4.29289i	0.565088	−	0.425060i
$103$	−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
$105$	−14.7782	+	8.94975i	−1.44220	+	0.873406i
$106$			1.17157i			0.113793i
$107$	−6.53553	+	2.70711i	−0.631814	+	0.261706i	−0.675524	−	0.737338i	$-0.736082\pi$
$107$	−6.53553	+	2.70711i	−0.631814	+	0.261706i	0.0437097	+	0.999044i	$0.486082\pi$
$108$	2.53553	−	4.53553i	0.243982	−	0.436432i
$109$	−6.70711	+	2.77817i	−0.642424	+	0.266101i	−0.680022	−	0.733192i	$-0.738030\pi$
$109$	−6.70711	+	2.77817i	−0.642424	+	0.266101i	0.0375973	+	0.999293i	$0.488030\pi$
$110$	−0.363961	+	5.12132i	−0.0347023	+	0.488299i
$111$	1.12132	+	4.94975i	0.106431	+	0.469809i
$112$	−4.12132	−	1.70711i	−0.389428	−	0.161306i
$113$	−1.36396	+	3.29289i	−0.128311	+	0.309769i	−0.974959	−	0.222383i	$-0.928617\pi$
$113$	−1.36396	+	3.29289i	−0.128311	+	0.309769i	0.846649	+	0.532152i	$0.178617\pi$
$114$	−6.48528	+	4.58579i	−0.607402	+	0.429498i
$115$	5.70711	−	4.94975i	0.532190	−	0.461566i
$116$	0.121320	−	0.292893i	0.0112643	−	0.0271945i
$117$	16.8995	−	8.07107i	1.56236	−	0.746170i
$118$	−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
$122$	1.05025	+	2.53553i	0.0950854	+	0.229556i
$123$	0.464466	+	2.05025i	0.0418795	+	0.184865i
$124$	−0.707107	−	0.292893i	−0.0635001	−	0.0263026i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	9.94975	+	8.94975i	0.886394	+	0.797307i
$127$	−1.65685			−0.147022			−0.0735110	−	0.997294i	$-0.523420\pi$
$127$	−1.65685			−0.147022			−0.0735110	+	0.997294i	$0.523420\pi$
$128$	1.00000			0.0883883
$129$	19.8995	+	3.41421i	1.75205	+	0.300605i
$130$	13.2426	−	4.41421i	1.16146	−	0.387152i
$131$	−8.53553	−	3.53553i	−0.745753	−	0.308901i	−0.0227456	−	0.999741i	$-0.507241\pi$
$131$	−8.53553	−	3.53553i	−0.745753	−	0.308901i	−0.723007	+	0.690840i	$0.757241\pi$
$132$	3.87868	−	0.878680i	0.337596	−	0.0764792i
$133$	−7.82843	−	18.8995i	−0.678811	−	1.63879i
$134$	−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	$0.600638\pi$
$138$	−4.94975	−	3.12132i	−0.421350	−	0.265704i
$139$	3.12132	−	7.53553i	0.264747	−	0.639156i	−0.734473	−	0.678638i	$-0.762571\pi$
$139$	3.12132	−	7.53553i	0.264747	−	0.639156i	0.999220	+	0.0394819i	$0.0125707\pi$
$140$	6.53553	+	7.53553i	0.552353	+	0.636869i
$141$	−8.24264	−	11.6569i	−0.694156	−	0.981684i
$142$	−2.36396	+	5.70711i	−0.198379	+	0.478930i
$143$	13.2426	+	5.48528i	1.10741	+	0.458702i
$144$	−2.82843	−	1.00000i	−0.235702	−	0.0833333i
$145$	−0.535534	+	0.464466i	−0.0444737	+	0.0385718i
$146$	−9.36396	+	3.87868i	−0.774967	+	0.321002i
$147$	−18.2426	+	12.8995i	−1.50463	+	1.06393i
$148$	2.70711	−	1.12132i	0.222523	−	0.0921720i
$149$		−	22.1421i		−	1.81395i	−0.421180	−	0.906977i	$-0.638384\pi$
$149$		−	22.1421i		−	1.81395i	0.421180	−	0.906977i	$-0.361616\pi$
$150$	−7.70711	+	3.94975i	−0.629283	+	0.322496i
$151$	6.65685	−	6.65685i	0.541727	−	0.541727i	−0.382308	−	0.924035i	$-0.624871\pi$
$151$	6.65685	−	6.65685i	0.541727	−	0.541727i	0.924035	+	0.382308i	$0.124871\pi$
$152$	3.24264	+	3.24264i	0.263013	+	0.263013i
$153$	5.65685	+	11.0000i	0.457330	+	0.889297i
$154$			10.2426i			0.825376i
$155$	1.12132	+	1.29289i	0.0900666	+	0.103848i
$156$	−6.24264	−	8.82843i	−0.499811	−	0.706840i
$157$	16.0711	+	16.0711i	1.28261	+	1.28261i	0.939177	+	0.343434i	$0.111590\pi$
$157$	16.0711	+	16.0711i	1.28261	+	1.28261i	0.343434	+	0.939177i	$0.388410\pi$
$158$	−5.87868	−	14.1924i	−0.467683	−	1.12909i
$159$	−2.00000	−	0.343146i	−0.158610	−	0.0272132i
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$	10.6569	−	10.6569i	0.839878	−	0.839878i
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$	3.36396	−	8.12132i	0.263486	−	0.636111i	−0.735664	−	0.677347i	$-0.763130\pi$
$163$	3.36396	−	8.12132i	0.263486	−	0.636111i	0.999149	+	0.0412361i	$0.0131296\pi$
$164$	1.12132	−	0.464466i	0.0875604	−	0.0362687i
$165$	−8.63604	−	2.12132i	−0.672315	−	0.165145i
$166$		−	11.6569i		−	0.904747i
$167$	−1.39340	−	3.36396i	−0.107824	−	0.260311i	0.860753	−	0.509022i	$-0.169993\pi$
$167$	−1.39340	−	3.36396i	−0.107824	−	0.260311i	−0.968578	+	0.248711i	$0.919993\pi$
$168$	4.12132	−	6.53553i	0.317967	−	0.504227i
$169$		−	25.9706i		−	1.99774i
$170$	3.17157	+	8.65685i	0.243249	+	0.663950i
$171$	−5.92893	−	12.4142i	−0.453397	−	0.949339i
$172$		−	11.6569i		−	0.888827i
$173$	−15.1924	+	6.29289i	−1.15506	+	0.478440i	−0.876226	−	0.481901i	$-0.839947\pi$
$173$	−15.1924	+	6.29289i	−1.15506	+	0.478440i	−0.278830	+	0.960340i	$0.589947\pi$
$174$	0.464466	+	0.292893i	0.0352111	+	0.0222042i
$175$	−5.53553	−	21.6066i	−0.418447	−	1.63331i
$176$	−0.878680	−	2.12132i	−0.0662330	−	0.159901i
$177$	12.8284	−	9.07107i	0.964244	−	0.681823i
$178$			14.1421i			1.06000i
$179$	1.24264	+	1.24264i	0.0928793	+	0.0928793i	0.752020	−	0.659140i	$-0.229080\pi$
$179$	1.24264	+	1.24264i	0.0928793	+	0.0928793i	−0.659140	+	0.752020i	$0.729080\pi$
$180$	4.65685	+	4.82843i	0.347101	+	0.359890i
$181$	−3.87868	+	1.60660i	−0.288300	+	0.119418i	−0.522147	−	0.852856i	$-0.674869\pi$
$181$	−3.87868	+	1.60660i	−0.288300	+	0.119418i	0.233847	+	0.972273i	$0.424869\pi$
$182$	25.7279	−	10.6569i	1.90708	−	0.789939i
$183$	−4.63604	+	1.05025i	−0.342706	+	0.0776369i
$184$	−1.29289	+	3.12132i	−0.0953134	+	0.230107i
$185$	−6.53553	−	0.464466i	−0.480502	−	0.0341482i
$186$	0.707107	−	1.12132i	0.0518476	−	0.0822192i
$187$	−3.36396	+	8.84924i	−0.245997	+	0.647121i
$188$	−5.82843	+	5.82843i	−0.425082	+	0.425082i
$189$	−18.1924	+	14.3640i	−1.32330	+	1.04482i
$190$	−3.24264	−	9.72792i	−0.235246	−	0.705738i
$191$	−17.6569			−1.27761			−0.638803	−	0.769371i	$-0.720570\pi$
$191$	−17.6569			−1.27761			−0.638803	+	0.769371i	$0.720570\pi$
$192$	−0.292893	+	1.70711i	−0.0211377	+	0.123200i
$193$	8.29289	+	3.43503i	0.596936	+	0.247259i	0.660631	−	0.750711i	$-0.270289\pi$
$193$	8.29289	+	3.43503i	0.596936	+	0.247259i	−0.0636957	+	0.997969i	$0.520289\pi$
$194$	−1.46447	−	3.53553i	−0.105143	−	0.253837i
$195$	3.65685	+	23.8995i	0.261873	+	1.71148i
$196$	9.12132	+	9.12132i	0.651523	+	0.651523i
$197$	1.05025	−	2.53553i	0.0748274	−	0.180649i	−0.882040	−	0.471175i	$-0.843830\pi$
$197$	1.05025	−	2.53553i	0.0748274	−	0.180649i	0.956867	+	0.290525i	$0.0938301\pi$
$198$	0.363961	+	6.87868i	0.0258656	+	0.488846i
$199$	7.77817	+	3.22183i	0.551380	+	0.228389i	0.640938	−	0.767592i	$-0.278545\pi$
$199$	7.77817	+	3.22183i	0.551380	+	0.228389i	−0.0895581	+	0.995982i	$0.528545\pi$
$200$	3.00000	+	4.00000i	0.212132	+	0.282843i
$201$	−6.24264	−	8.82843i	−0.440322	−	0.622709i
$202$			10.8284i			0.761885i
$203$	−1.00000	+	1.00000i	−0.0701862	+	0.0701862i
$204$	5.70711	−	4.29289i	0.399577	−	0.300563i
$205$	−2.70711	−	0.192388i	−0.189073	−	0.0134370i
$206$	−1.34315	−	1.34315i	−0.0935814	−	0.0935814i
$207$	6.77817	−	7.53553i	0.471116	−	0.523756i
$208$	−4.41421	+	4.41421i	−0.306071	+	0.306071i
$209$	4.02944	−	9.72792i	0.278722	−	0.672894i
$210$	−14.7782	+	8.94975i	−1.01979	+	0.617591i
$211$	−1.60660	−	3.87868i	−0.110603	−	0.267019i	0.858880	−	0.512176i	$-0.171161\pi$
$211$	−1.60660	−	3.87868i	−0.110603	−	0.267019i	−0.969483	+	0.245157i	$0.921161\pi$
$212$			1.17157i			0.0804640i
$213$	−9.05025	−	5.70711i	−0.620113	−	0.391045i
$214$	−6.53553	+	2.70711i	−0.446760	+	0.185054i
$215$	−11.6569	+	23.3137i	−0.794991	+	1.58998i
$216$	2.53553	−	4.53553i	0.172521	−	0.308604i
$217$	2.41421	+	2.41421i	0.163887	+	0.163887i
$218$	−6.70711	+	2.77817i	−0.454263	+	0.188162i
$219$	−3.87868	−	17.1213i	−0.262097	−	1.15695i
$220$	−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
$223$	−23.3137			−1.56120			−0.780601	−	0.625030i	$-0.785087\pi$
$223$	−23.3137			−1.56120			−0.780601	+	0.625030i	$0.785087\pi$
$224$	−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
$227$	4.53553	+	1.87868i	0.301034	+	0.124692i	0.528088	−	0.849190i	$-0.322909\pi$
$227$	4.53553	+	1.87868i	0.301034	+	0.124692i	−0.227054	+	0.973882i	$0.572909\pi$
$228$	−6.48528	+	4.58579i	−0.429498	+	0.303701i
$229$	−11.5858	+	11.5858i	−0.765610	+	0.765610i	−0.977330	−	0.211720i	$-0.932094\pi$
$229$	−11.5858	+	11.5858i	−0.765610	+	0.765610i	0.211720	+	0.977330i	$0.432094\pi$
$230$	5.70711	−	4.94975i	0.376315	−	0.326377i
$231$	−17.4853	−	3.00000i	−1.15045	−	0.197386i
$232$	0.121320	−	0.292893i	0.00796507	−	0.0192294i
$233$	3.12132	+	7.53553i	0.204484	+	0.493669i	0.992538	−	0.121938i	$-0.0389109\pi$
$233$	3.12132	+	7.53553i	0.204484	+	0.493669i	−0.788053	+	0.615607i	$0.788911\pi$
$234$	16.8995	−	8.07107i	1.10475	−	0.527622i
$235$	17.4853	−	5.82843i	1.14061	−	0.380205i
$236$	−6.41421	−	6.41421i	−0.417530	−	0.417530i
$237$	25.9497	−	5.87868i	1.68562	−	0.381861i
$238$	7.53553	+	16.7782i	0.488456	+	1.08757i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	2.29289	−	3.12132i	0.148006	−	0.201480i
$241$	1.36396	+	0.564971i	0.0878605	+	0.0363930i	0.426181	−	0.904638i	$-0.359859\pi$
$241$	1.36396	+	0.564971i	0.0878605	+	0.0363930i	−0.338320	+	0.941031i	$0.609859\pi$
$242$	4.05025	−	4.05025i	0.260360	−	0.260360i
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$	1.05025	+	2.53553i	0.0672355	+	0.162321i
$245$	−9.12132	−	27.3640i	−0.582740	−	1.74822i
$246$	0.464466	+	2.05025i	0.0296133	+	0.130719i
$247$	−28.6274			−1.82152
$248$	−0.707107	−	0.292893i	−0.0449013	−	0.0185987i
$249$	19.8995	+	3.41421i	1.26108	+	0.216367i
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$	9.17157			0.578905			0.289452	−	0.957192i	$-0.406527\pi$
$251$	9.17157			0.578905			0.289452	+	0.957192i	$0.406527\pi$
$252$	9.94975	+	8.94975i	0.626775	+	0.563781i
$253$	7.75736			0.487701
$254$	−1.65685			−0.103960
$255$	−15.7071	+	2.87868i	−0.983617	+	0.180270i
$256$	1.00000			0.0625000
$257$	3.17157			0.197837			0.0989186	−	0.995096i	$-0.468462\pi$
$257$	3.17157			0.197837			0.0989186	+	0.995096i	$0.468462\pi$
$258$	19.8995	+	3.41421i	1.23889	+	0.212560i
$259$	−13.0711			−0.812197
$260$	13.2426	−	4.41421i	0.821274	−	0.273758i
$261$	−0.636039	+	0.707107i	−0.0393698	+	0.0437688i
$262$	−8.53553	−	3.53553i	−0.527327	−	0.218426i
$263$	−8.00000			−0.493301			−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000			−0.493301			−0.246651	+	0.969104i	$0.579330\pi$
$264$	3.87868	−	0.878680i	0.238716	−	0.0540790i
$265$	1.17157	−	2.34315i	0.0719691	−	0.143938i
$266$	−7.82843	−	18.8995i	−0.479992	−	1.15880i
$267$	−24.1421	−	4.14214i	−1.47747	−	0.253495i
$268$	−4.41421	+	4.41421i	−0.269641	+	0.269641i
$269$	−29.0919	−	12.0503i	−1.77376	−	0.734717i	−0.994094	−	0.108526i	$-0.965387\pi$
$269$	−29.0919	−	12.0503i	−1.77376	−	0.734717i	−0.779670	−	0.626191i	$-0.784613\pi$
$270$	−9.60660	+	6.53553i	−0.584639	+	0.397740i
$271$	−0.686292			−0.0416892			−0.0208446	−	0.999783i	$-0.506636\pi$
$271$	−0.686292			−0.0416892			−0.0208446	+	0.999783i	$0.506636\pi$
$272$	−3.00000	−	2.82843i	−0.181902	−	0.171499i
$273$	10.6569	+	47.0416i	0.644982	+	2.84709i
$274$	7.48528	+	7.48528i	0.452202	+	0.452202i
$275$	5.84924	−	9.87868i	0.352723	−	0.595707i
$276$	−4.94975	−	3.12132i	−0.297940	−	0.187881i
$277$	11.0919	+	26.7782i	0.666447	+	1.60894i	0.787511	+	0.616300i	$0.211369\pi$
$277$	11.0919	+	26.7782i	0.666447	+	1.60894i	−0.121065	+	0.992645i	$0.538631\pi$
$278$	3.12132	−	7.53553i	0.187204	−	0.451951i
$279$	1.70711	+	1.53553i	0.102202	+	0.0919300i
$280$	6.53553	+	7.53553i	0.390573	+	0.450334i
$281$	−2.51472	+	2.51472i	−0.150016	+	0.150016i	−0.778125	−	0.628109i	$-0.783829\pi$
$281$	−2.51472	+	2.51472i	−0.150016	+	0.150016i	0.628109	+	0.778125i	$0.283829\pi$
$282$	−8.24264	−	11.6569i	−0.490842	−	0.694156i
$283$	16.7782	+	6.94975i	0.997359	+	0.413120i	0.820828	−	0.571175i	$-0.193512\pi$
$283$	16.7782	+	6.94975i	0.997359	+	0.413120i	0.176531	+	0.984295i	$0.443512\pi$
$284$	−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
$287$	−5.41421			−0.319591
$288$	−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
$291$	6.46447	−	1.46447i	0.378954	−	0.0858485i
$292$	−9.36396	+	3.87868i	−0.547984	+	0.226983i
$293$	5.58579	+	5.58579i	0.326325	+	0.326325i	0.851187	−	0.524862i	$-0.175883\pi$
$293$	5.58579	+	5.58579i	0.326325	+	0.326325i	−0.524862	+	0.851187i	$0.675883\pi$
$294$	−18.2426	+	12.8995i	−1.06393	+	0.752314i
$295$	6.41421	+	19.2426i	0.373450	+	1.12035i
$296$	2.70711	−	1.12132i	0.157347	−	0.0651754i
$297$	−11.8492	−	1.39340i	−0.687563	−	0.0808532i
$298$		−	22.1421i		−	1.28266i
$299$	−8.07107	−	19.4853i	−0.466762	−	1.12686i
$300$	−7.70711	+	3.94975i	−0.444970	+	0.228039i
$301$	−19.8995	+	48.0416i	−1.14699	+	2.76907i
$302$	6.65685	−	6.65685i	0.383059	−	0.383059i
$303$	−18.4853	−	3.17157i	−1.06195	−	0.182202i
$304$	3.24264	+	3.24264i	0.185978	+	0.185978i
$305$	0.435029	−	6.12132i	0.0249097	−	0.350506i
$306$	5.65685	+	11.0000i	0.323381	+	0.628828i
$307$	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	$0.201929\pi$
$308$			10.2426i			0.583629i
$309$	2.68629	−	1.89949i	0.152818	−	0.108058i
$310$	1.12132	+	1.29289i	0.0636867	+	0.0734314i
$311$	25.1924	+	10.4350i	1.42853	+	0.591716i	0.956988	−	0.290128i	$-0.0936978\pi$
$311$	25.1924	+	10.4350i	1.42853	+	0.591716i	0.471541	+	0.881844i	$0.343698\pi$
$312$	−6.24264	−	8.82843i	−0.353420	−	0.499811i
$313$	7.70711	−	18.6066i	0.435631	−	1.05171i	−0.541810	−	0.840501i	$-0.682261\pi$
$313$	7.70711	−	18.6066i	0.435631	−	1.05171i	0.977441	−	0.211206i	$-0.0677392\pi$
$314$	16.0711	+	16.0711i	0.906943	+	0.906943i
$315$	−10.9497	−	27.8492i	−0.616948	−	1.56913i
$316$	−5.87868	−	14.1924i	−0.330702	−	0.798384i
$317$	−19.5355	−	8.09188i	−1.09722	−	0.454485i	−0.240704	−	0.970598i	$-0.577378\pi$
$317$	−19.5355	−	8.09188i	−1.09722	−	0.454485i	−0.856520	+	0.516113i	$0.827378\pi$
$318$	−2.00000	−	0.343146i	−0.112154	−	0.0192427i
$319$	−0.727922			−0.0407558
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	−2.70711	−	11.9497i	−0.151096	−	0.666970i
$322$	10.6569	−	10.6569i	0.593883	−	0.593883i
$323$	−0.556349	−	18.8995i	−0.0309561	−	1.05160i
$324$	7.00000	+	5.65685i	0.388889	+	0.314270i
$325$	−30.8995	−	4.41421i	−1.71400	−	0.244857i
$326$	3.36396	−	8.12132i	0.186313	−	0.449798i
$327$	−2.77817	−	12.2635i	−0.153633	−	0.678171i
$328$	1.12132	−	0.464466i	0.0619146	−	0.0256458i
$329$	33.9706	−	14.0711i	1.87286	−	0.775763i
$330$	−8.63604	−	2.12132i	−0.475398	−	0.116775i
$331$	−4.41421	−	4.41421i	−0.242627	−	0.242627i	0.575309	−	0.817936i	$-0.304882\pi$
$331$	−4.41421	−	4.41421i	−0.242627	−	0.242627i	−0.817936	+	0.575309i	$0.804882\pi$
$332$		−	11.6569i		−	0.639753i
$333$	−8.77817	+	0.464466i	−0.481041	+	0.0254526i
$334$	−1.39340	−	3.36396i	−0.0762434	−	0.184068i
$335$	13.2426	−	4.41421i	0.723523	−	0.241174i
$336$	4.12132	−	6.53553i	0.224836	−	0.356543i
$337$	6.77817	−	2.80761i	0.369231	−	0.152940i	−0.190350	−	0.981716i	$-0.560962\pi$
$337$	6.77817	−	2.80761i	0.369231	−	0.152940i	0.559581	+	0.828776i	$0.310962\pi$
$338$		−	25.9706i		−	1.41261i
$339$	−5.22183	−	3.29289i	−0.283611	−	0.178845i
$340$	3.17157	+	8.65685i	0.172003	+	0.469484i
$341$			1.75736i			0.0951663i
$342$	−5.92893	−	12.4142i	−0.320600	−	0.671284i
$343$	−10.0711	−	24.3137i	−0.543787	−	1.31282i
$344$		−	11.6569i		−	0.628495i
$345$	6.77817	+	11.1924i	0.364925	+	0.602578i
$346$	−15.1924	+	6.29289i	−0.816748	+	0.338308i
$347$	−7.84924	+	18.9497i	−0.421369	+	1.01728i	0.560575	+	0.828104i	$0.310580\pi$
$347$	−7.84924	+	18.9497i	−0.421369	+	1.01728i	−0.981944	+	0.189172i	$0.939420\pi$
$348$	0.464466	+	0.292893i	0.0248980	+	0.0157007i
$349$	−0.757359	+	0.757359i	−0.0405405	+	0.0405405i	−0.727086	−	0.686546i	$-0.759126\pi$
$349$	−0.757359	+	0.757359i	−0.0405405	+	0.0405405i	0.686546	+	0.727086i	$0.259126\pi$
$350$	−5.53553	−	21.6066i	−0.295887	−	1.15492i
$351$	8.82843	+	31.2132i	0.471227	+	1.66604i
$352$	−0.878680	−	2.12132i	−0.0468338	−	0.113067i
$353$	−16.6569	−	16.6569i	−0.886555	−	0.886555i	0.107636	−	0.994190i	$-0.465672\pi$
$353$	−16.6569	−	16.6569i	−0.886555	−	0.886555i	−0.994190	+	0.107636i	$0.965672\pi$
$354$	12.8284	−	9.07107i	0.681823	−	0.482122i
$355$	10.4350	−	9.05025i	0.553834	−	0.480338i
$356$			14.1421i			0.749532i
$357$	−30.8492	+	7.94975i	−1.63272	+	0.420745i
$358$	1.24264	+	1.24264i	0.0656756	+	0.0656756i
$359$	8.65685	−	8.65685i	0.456891	−	0.456891i	−0.440742	−	0.897634i	$-0.645285\pi$
$359$	8.65685	−	8.65685i	0.456891	−	0.456891i	0.897634	+	0.440742i	$0.145285\pi$
$360$	4.65685	+	4.82843i	0.245438	+	0.254480i
$361$			2.02944i			0.106812i
$362$	−3.87868	+	1.60660i	−0.203859	+	0.0844411i
$363$	5.72792	+	8.10051i	0.300638	+	0.425166i
$364$	25.7279	−	10.6569i	1.34851	−	0.558571i
$365$	22.6066	+	1.60660i	1.18328	+	0.0840934i
$366$	−4.63604	+	1.05025i	−0.242330	+	0.0548976i
$367$	−4.12132	−	1.70711i	−0.215131	−	0.0891102i	0.272515	−	0.962151i	$-0.412144\pi$
$367$	−4.12132	−	1.70711i	−0.215131	−	0.0891102i	−0.487646	+	0.873041i	$0.662144\pi$
$368$	−1.29289	+	3.12132i	−0.0673967	+	0.162710i
$369$	−3.63604	+	0.192388i	−0.189285	+	0.0100153i
$370$	−6.53553	−	0.464466i	−0.339766	−	0.0241464i
$371$	2.00000	−	4.82843i	0.103835	−	0.250679i
$372$	0.707107	−	1.12132i	0.0366618	−	0.0581378i
$373$	−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
$377$	0.757359	+	1.82843i	0.0390060	+	0.0941688i
$378$	−18.1924	+	14.3640i	−0.935715	+	0.738802i
$379$	−34.0919	−	14.1213i	−1.75118	−	0.725364i	−0.997692	−	0.0679048i	$-0.978369\pi$
$379$	−34.0919	−	14.1213i	−1.75118	−	0.725364i	−0.753491	−	0.657459i	$-0.771631\pi$
$380$	−3.24264	−	9.72792i	−0.166344	−	0.499032i
$381$	0.485281	−	2.82843i	0.0248617	−	0.144905i
$382$	−17.6569			−0.903403
$383$	27.3137			1.39567			0.697833	−	0.716261i	$-0.254148\pi$
$383$	27.3137			1.39567			0.697833	+	0.716261i	$0.254148\pi$
$384$	−0.292893	+	1.70711i	−0.0149466	+	0.0871154i
$385$	10.2426	−	20.4853i	0.522013	−	1.04403i
$386$	8.29289	+	3.43503i	0.422097	+	0.174838i
$387$	−11.6569	+	32.9706i	−0.592551	+	1.67599i
$388$	−1.46447	−	3.53553i	−0.0743470	−	0.179490i
$389$	2.41421	−	2.41421i	0.122405	−	0.122405i	−0.643250	−	0.765656i	$-0.722415\pi$
$389$	2.41421	−	2.41421i	0.122405	−	0.122405i	0.765656	+	0.643250i	$0.222415\pi$
$390$	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
$393$	8.53553	−	13.5355i	0.430561	−	0.682777i
$394$	1.05025	−	2.53553i	0.0529110	−	0.127738i
$395$	−2.43503	+	34.2635i	−0.122520	+	1.72398i
$396$	0.363961	+	6.87868i	0.0182897	+	0.345667i
$397$	4.26346	−	10.2929i	0.213977	−	0.516586i	−0.780051	−	0.625716i	$-0.784807\pi$
$397$	4.26346	−	10.2929i	0.213977	−	0.516586i	0.994027	+	0.109131i	$0.0348068\pi$
$398$	7.77817	+	3.22183i	0.389885	+	0.161496i
$399$	34.5563	−	7.82843i	1.72998	−	0.391912i
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	1.94975	−	0.807612i	0.0973657	−	0.0403302i	−0.333469	−	0.942761i	$-0.608219\pi$
$401$	1.94975	−	0.807612i	0.0973657	−	0.0403302i	0.430835	+	0.902431i	$0.358219\pi$
$402$	−6.24264	−	8.82843i	−0.311355	−	0.440322i
$403$	4.41421	−	1.82843i	0.219888	−	0.0910804i
$404$			10.8284i			0.538734i
$405$	−8.34315	−	18.3137i	−0.414574	−	0.910015i
$406$	−1.00000	+	1.00000i	−0.0496292	+	0.0496292i
$407$	−4.75736	−	4.75736i	−0.235814	−	0.235814i
$408$	5.70711	−	4.29289i	0.282544	−	0.212530i
$409$			10.8284i			0.535431i	0.963498	+	0.267716i	$0.0862688\pi$
$409$			10.8284i			0.535431i	−0.963498	+	0.267716i	$0.913731\pi$
$410$	−2.70711	−	0.192388i	−0.133694	−	0.00950137i
$411$	−14.9706	+	10.5858i	−0.738443	+	0.522158i
$412$	−1.34315	−	1.34315i	−0.0661720	−	0.0661720i
$413$	15.4853	+	37.3848i	0.761981	+	1.83958i
$414$	6.77817	−	7.53553i	0.333129	−	0.370351i
$415$	−11.6569	+	23.3137i	−0.572212	+	1.14442i
$416$	−4.41421	+	4.41421i	−0.216425	+	0.216425i
$417$	11.9497	+	7.53553i	0.585182	+	0.369017i
$418$	4.02944	−	9.72792i	0.197086	−	0.475808i
$419$	−13.6066	+	5.63604i	−0.664726	+	0.275339i	−0.689426	−	0.724356i	$-0.742137\pi$
$419$	−13.6066	+	5.63604i	−0.664726	+	0.275339i	0.0246997	+	0.999695i	$0.492137\pi$
$420$	−14.7782	+	8.94975i	−0.721101	+	0.436703i
$421$		−	38.1421i		−	1.85893i	−0.368905	−	0.929467i	$-0.620267\pi$
$421$		−	38.1421i		−	1.85893i	0.368905	−	0.929467i	$-0.379733\pi$
$422$	−1.60660	−	3.87868i	−0.0782081	−	0.188811i
$423$	22.3137	−	10.6569i	1.08493	−	0.518154i
$424$			1.17157i			0.0568966i
$425$	2.31371	−	20.4853i	0.112231	−	0.993682i
$426$	−9.05025	−	5.70711i	−0.438486	−	0.276510i
$427$		−	12.2426i		−	0.592463i
$428$	−6.53553	+	2.70711i	−0.315907	+	0.130853i
$429$	−13.2426	+	21.0000i	−0.639361	+	1.01389i
$430$	−11.6569	+	23.3137i	−0.562143	+	1.12429i
$431$	13.3934	+	32.3345i	0.645137	+	1.55750i	0.819663	+	0.572847i	$0.194161\pi$
$431$	13.3934	+	32.3345i	0.645137	+	1.55750i	−0.174525	+	0.984653i	$0.555839\pi$
$432$	2.53553	−	4.53553i	0.121991	−	0.218216i
$433$			28.9706i			1.39224i	0.717927	+	0.696118i	$0.245091\pi$
$433$			28.9706i			1.39224i	−0.717927	+	0.696118i	$0.754909\pi$
$434$	2.41421	+	2.41421i	0.115886	+	0.115886i
$435$	−0.636039	−	1.05025i	−0.0304957	−	0.0503558i
$436$	−6.70711	+	2.77817i	−0.321212	+	0.133050i
$437$	−14.3137	+	5.92893i	−0.684718	+	0.283619i
$438$	−3.87868	−	17.1213i	−0.185330	−	0.818088i
$439$	−9.77817	+	23.6066i	−0.466687	+	1.12668i	0.498914	+	0.866652i	$0.333732\pi$
$439$	−9.77817	+	23.6066i	−0.466687	+	1.12668i	−0.965601	+	0.260030i	$0.916268\pi$
$440$	−0.363961	+	5.12132i	−0.0173512	+	0.244149i
$441$	−16.6777	−	34.9203i	−0.794175	−	1.66287i
$442$	25.7279	−	0.757359i	1.22375	−	0.0360239i
$443$	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	$-0.0158815\pi$
$444$	1.12132	+	4.94975i	0.0532155	+	0.234905i
$445$	14.1421	−	28.2843i	0.670402	−	1.34080i
$446$	−23.3137			−1.10394
$447$	37.7990	+	6.48528i	1.78783	+	0.306743i
$448$	−4.12132	−	1.70711i	−0.194714	−	0.0806532i
$449$	4.19239	+	10.1213i	0.197851	+	0.477655i	0.991402	−	0.130849i	$-0.0417702\pi$
$449$	4.19239	+	10.1213i	0.197851	+	0.477655i	−0.793551	+	0.608503i	$0.791770\pi$
$450$	−4.48528	−	14.3137i	−0.211438	−	0.674755i
$451$	−1.97056	−	1.97056i	−0.0927902	−	0.0927902i
$452$	−1.36396	+	3.29289i	−0.0641553	+	0.154885i
$453$	9.41421	+	13.3137i	0.442318	+	0.625533i
$454$	4.53553	+	1.87868i	0.212863	+	0.0881708i
$455$	−62.1127	−	4.41421i	−2.91189	−	0.206942i
$456$	−6.48528	+	4.58579i	−0.303701	+	0.214749i
$457$			9.65685i			0.451729i	0.974159	+	0.225864i	$0.0725206\pi$
$457$			9.65685i			0.451729i	−0.974159	+	0.225864i	$0.927479\pi$
$458$	−11.5858	+	11.5858i	−0.541368	+	0.541368i
$459$	−20.4350	+	6.43503i	−0.953825	+	0.300361i
$460$	5.70711	−	4.94975i	0.266095	−	0.230783i
$461$	−19.7279	−	19.7279i	−0.918821	−	0.918821i	0.0781228	−	0.996944i	$-0.475107\pi$
$461$	−19.7279	−	19.7279i	−0.918821	−	0.918821i	−0.996944	+	0.0781228i	$0.975107\pi$
$462$	−17.4853	−	3.00000i	−0.813489	−	0.139573i
$463$	8.17157	−	8.17157i	0.379765	−	0.379765i	−0.491252	−	0.871017i	$-0.663461\pi$
$463$	8.17157	−	8.17157i	0.379765	−	0.379765i	0.871017	+	0.491252i	$0.163461\pi$
$464$	0.121320	−	0.292893i	0.00563216	−	0.0135972i
$465$	−2.53553	+	1.53553i	−0.117583	+	0.0712087i
$466$	3.12132	+	7.53553i	0.144592	+	0.349077i
$467$		−	26.4853i		−	1.22559i	−0.790241	−	0.612796i	$-0.790045\pi$
$467$		−	26.4853i		−	1.22559i	0.790241	−	0.612796i	$-0.209955\pi$
$468$	16.8995	−	8.07107i	0.781179	−	0.373085i
$469$	25.7279	−	10.6569i	1.18801	−	0.492088i
$470$	17.4853	−	5.82843i	0.806536	−	0.268845i
$471$	−32.1421	+	22.7279i	−1.48103	+	1.04725i
$472$	−6.41421	−	6.41421i	−0.295238	−	0.295238i
$473$	−24.7279	+	10.2426i	−1.13699	+	0.470957i
$474$	25.9497	−	5.87868i	1.19191	−	0.270017i
$475$	−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
$478$	−12.0000			−0.548867
$479$	20.3640	+	8.43503i	0.930453	+	0.385406i	0.795850	−	0.605493i	$-0.207024\pi$
$479$	20.3640	+	8.43503i	0.930453	+	0.385406i	0.134603	+	0.990900i	$0.457024\pi$
$480$	2.29289	−	3.12132i	0.104656	−	0.142468i
$481$	−7.00000	+	16.8995i	−0.319173	+	0.770551i
$482$	1.36396	+	0.564971i	0.0621267	+	0.0257337i
$483$	15.0711	+	21.3137i	0.685757	+	0.969807i
$484$	4.05025	−	4.05025i	0.184102	−	0.184102i
$485$	−0.606602	+	8.53553i	−0.0275444	+	0.387579i
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	−3.53553	+	8.53553i	−0.160210	+	0.386782i	−0.983517	−	0.180815i	$-0.942127\pi$
$487$	−3.53553	+	8.53553i	−0.160210	+	0.386782i	0.823307	+	0.567597i	$0.192127\pi$
$488$	1.05025	+	2.53553i	0.0475427	+	0.114778i
$489$	12.8787	+	8.12132i	0.582394	+	0.367259i
$490$	−9.12132	−	27.3640i	−0.412059	−	1.23618i
$491$	18.4142	+	18.4142i	0.831022	+	0.831022i	0.987657	−	0.156635i	$-0.0500646\pi$
$491$	18.4142	+	18.4142i	0.831022	+	0.831022i	−0.156635	+	0.987657i	$0.550065\pi$
$492$	0.464466	+	2.05025i	0.0209397	+	0.0924325i
$493$	−1.19239	+	0.535534i	−0.0537025	+	0.0241192i
$494$	−28.6274			−1.28801
$495$	6.15076	−	14.1213i	0.276456	−	0.634706i
$496$	−0.707107	−	0.292893i	−0.0317500	−	0.0131513i
$497$	19.4853	−	19.4853i	0.874034	−	0.874034i
$498$	19.8995	+	3.41421i	0.891718	+	0.152995i
$499$	13.0208	+	31.4350i	0.582892	+	1.40723i	0.890180	+	0.455609i	$0.150578\pi$
$499$	13.0208	+	31.4350i	0.582892	+	1.40723i	−0.307288	+	0.951616i	$0.599422\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	6.15076	−	1.39340i	0.274796	−	0.0622524i
$502$	9.17157			0.409347
$503$	22.6066	+	9.36396i	1.00798	+	0.417518i	0.824717	−	0.565546i	$-0.191334\pi$
$503$	22.6066	+	9.36396i	1.00798	+	0.417518i	0.183262	+	0.983064i	$0.441334\pi$
$504$	9.94975	+	8.94975i	0.443197	+	0.398653i
$505$	10.8284	−	21.6569i	0.481859	−	0.963717i
$506$	7.75736			0.344857
$507$	44.3345	+	7.60660i	1.96897	+	0.337821i
$508$	−1.65685			−0.0735110
$509$	35.6569			1.58046			0.790231	−	0.612809i	$-0.209960\pi$
$509$	35.6569			1.58046			0.790231	+	0.612809i	$0.209960\pi$
$510$	−15.7071	+	2.87868i	−0.695522	+	0.127470i
$511$	45.2132			2.00011
$512$	1.00000			0.0441942
$513$	22.9289	−	6.48528i	1.01234	−	0.286332i
$514$	3.17157			0.139892
$515$	1.34315	+	4.02944i	0.0591861	+	0.177558i
$516$	19.8995	+	3.41421i	0.876026	+	0.150302i
$517$	17.4853	+	7.24264i	0.769002	+	0.318531i
$518$	−13.0711			−0.574310
$519$	−6.29289	−	27.7782i	−0.276227	−	1.21933i
$520$	13.2426	−	4.41421i	0.580728	−	0.193576i
$521$	9.70711	+	23.4350i	0.425276	+	1.02671i	0.980767	+	0.195184i	$0.0625305\pi$
$521$	9.70711	+	23.4350i	0.425276	+	1.02671i	−0.555490	+	0.831523i	$0.687469\pi$
$522$	−0.636039	+	0.707107i	−0.0278387	+	0.0309492i
$523$	−8.41421	+	8.41421i	−0.367928	+	0.367928i	−0.866721	−	0.498793i	$-0.833777\pi$
$523$	−8.41421	+	8.41421i	−0.367928	+	0.367928i	0.498793	+	0.866721i	$0.333777\pi$
$524$	−8.53553	−	3.53553i	−0.372877	−	0.154451i
$525$	38.5061	−	3.12132i	1.68054	−	0.136226i
$526$	−8.00000			−0.348817
$527$	1.29289	+	2.87868i	0.0563193	+	0.125397i
$528$	3.87868	−	0.878680i	0.168798	−	0.0382396i
$529$	8.19239	+	8.19239i	0.356191	+	0.356191i
$530$	1.17157	−	2.34315i	0.0508899	−	0.101780i
$531$	11.7279	+	24.5563i	0.508948	+	1.06565i
$532$	−7.82843	−	18.8995i	−0.339405	−	0.819397i
$533$	−2.89949	+	7.00000i	−0.125591	+	0.303204i
$534$	−24.1421	−	4.14214i	−1.04473	−	0.179248i
$535$	15.7782	+	1.12132i	0.682150	+	0.0484789i
$536$	−4.41421	+	4.41421i	−0.190665	+	0.190665i
$537$	−2.48528	+	1.75736i	−0.107248	+	0.0758357i
$538$	−29.0919	−	12.0503i	−1.25424	−	0.519523i
$539$	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	−0.582810	−	0.812609i	$-0.698047\pi$
$541$	−36.5061	−	15.1213i	−1.56952	−	0.650116i	−0.986710	+	0.162492i	$0.948047\pi$
$542$	−0.686292			−0.0294787
$543$	−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
$546$	10.6569	+	47.0416i	0.456071	+	2.01320i
$547$	27.3640	−	11.3345i	1.17000	−	0.484629i	0.288806	−	0.957388i	$-0.406742\pi$
$547$	27.3640	−	11.3345i	1.17000	−	0.484629i	0.881192	+	0.472758i	$0.156742\pi$
$548$	7.48528	+	7.48528i	0.319755	+	0.319755i
$549$	−0.435029	−	8.22183i	−0.0185666	−	0.350899i
$550$	5.84924	−	9.87868i	0.249413	−	0.421228i
$551$	1.34315	−	0.556349i	0.0572199	−	0.0237013i
$552$	−4.94975	−	3.12132i	−0.210675	−	0.132852i
$553$			68.5269i			2.91406i
$554$	11.0919	+	26.7782i	0.471249	+	1.13770i
$555$	2.70711	−	11.0208i	0.114910	−	0.467808i
$556$	3.12132	−	7.53553i	0.132373	−	0.319578i
$557$	−10.8995	+	10.8995i	−0.461826	+	0.461826i	−0.899254	−	0.437427i	$-0.855890\pi$
$557$	−10.8995	+	10.8995i	−0.461826	+	0.461826i	0.437427	+	0.899254i	$0.355890\pi$
$558$	1.70711	+	1.53553i	0.0722676	+	0.0650043i
$559$	51.4558	+	51.4558i	2.17635	+	2.17635i
$560$	6.53553	+	7.53553i	0.276177	+	0.318434i
$561$	−14.1213	−	8.33452i	−0.596203	−	0.351884i
$562$	−2.51472	+	2.51472i	−0.106077	+	0.106077i
$563$		−	5.02944i		−	0.211966i	−0.994368	−	0.105983i	$-0.966201\pi$
$563$		−	5.02944i		−	0.211966i	0.994368	−	0.105983i	$-0.0337988\pi$
$564$	−8.24264	−	11.6569i	−0.347078	−	0.490842i
$565$	6.02082	−	5.22183i	0.253298	−	0.219684i
$566$	16.7782	+	6.94975i	0.705239	+	0.292120i
$567$	−19.1924	−	35.2635i	−0.806005	−	1.48093i
$568$	−2.36396	+	5.70711i	−0.0991896	+	0.239465i
$569$	8.65685	+	8.65685i	0.362914	+	0.362914i	0.864885	−	0.501971i	$-0.167391\pi$
$569$	8.65685	+	8.65685i	0.362914	+	0.362914i	−0.501971	+	0.864885i	$0.667391\pi$
$570$	17.5563	−	2.68629i	0.735355	−	0.112516i
$571$	−4.29289	−	10.3640i	−0.179652	−	0.433718i	0.808242	−	0.588851i	$-0.200419\pi$
$571$	−4.29289	−	10.3640i	−0.179652	−	0.433718i	−0.987894	+	0.155133i	$0.950419\pi$
$572$	13.2426	+	5.48528i	0.553703	+	0.229351i
$573$	5.17157	−	30.1421i	0.216046	−	1.25921i
$574$	−5.41421			−0.225985
$575$	−16.3640	+	4.19239i	−0.682424	+	0.174835i
$576$	−2.82843	−	1.00000i	−0.117851	−	0.0416667i
$577$	−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	$0.364628\pi$
$578$	1.00000	+	16.9706i	0.0415945	+	0.705882i
$579$	−8.29289	+	13.1508i	−0.344641	+	0.546527i
$580$	−0.535534	+	0.464466i	−0.0222368	+	0.0192859i
$581$	−19.8995	+	48.0416i	−0.825570	+	1.99310i
$582$	6.46447	−	1.46447i	0.267961	−	0.0607041i
$583$	2.48528	−	1.02944i	0.102930	−	0.0426349i
$584$	−9.36396	+	3.87868i	−0.387483	+	0.160501i
$585$	−41.8701	−	0.757359i	−1.73111	−	0.0313130i
$586$	5.58579	+	5.58579i	0.230747	+	0.230747i
$587$		−	36.8284i		−	1.52007i	−0.649881	−	0.760036i	$-0.725181\pi$
$587$		−	36.8284i		−	1.52007i	0.649881	−	0.760036i	$-0.274819\pi$
$588$	−18.2426	+	12.8995i	−0.752314	+	0.531966i
$589$	−1.34315	−	3.24264i	−0.0553434	−	0.133611i
$590$	6.41421	+	19.2426i	0.264069	+	0.792207i
$591$	4.02082	+	2.53553i	0.165394	+	0.104298i
$592$	2.70711	−	1.12132i	0.111261	−	0.0460860i
$593$		−	22.1421i		−	0.909269i	−0.890678	−	0.454634i	$-0.849770\pi$
$593$		−	22.1421i		−	0.909269i	0.890678	−	0.454634i	$-0.150230\pi$
$594$	−11.8492	−	1.39340i	−0.486180	−	0.0571718i
$595$	1.70711	−	41.0919i	0.0699846	−	1.68460i
$596$		−	22.1421i		−	0.906977i
$597$	−7.77817	+	12.3345i	−0.318339	+	0.504818i
$598$	−8.07107	−	19.4853i	−0.330051	−	0.796812i
$599$		−	14.9706i		−	0.611681i	−0.952083	−	0.305840i	$-0.901063\pi$
$599$		−	14.9706i		−	0.611681i	0.952083	−	0.305840i	$-0.0989374\pi$
$600$	−7.70711	+	3.94975i	−0.314641	+	0.161248i
$601$	−0.778175	+	0.322330i	−0.0317424	+	0.0131481i	−0.398498	−	0.917169i	$-0.630468\pi$
$601$	−0.778175	+	0.322330i	−0.0317424	+	0.0131481i	0.366756	+	0.930317i	$0.380468\pi$
$602$	−19.8995	+	48.0416i	−0.811043	+	1.95803i
$603$	16.8995	−	8.07107i	0.688201	−	0.328679i
$604$	6.65685	−	6.65685i	0.270864	−	0.270864i
$605$	−12.1508	+	4.05025i	−0.493999	+	0.164666i
$606$	−18.4853	−	3.17157i	−0.750913	−	0.128836i
$607$	1.19239	+	2.87868i	0.0483975	+	0.116842i	0.946229	−	0.323497i	$-0.104858\pi$
$607$	1.19239	+	2.87868i	0.0483975	+	0.116842i	−0.897832	+	0.440339i	$0.854858\pi$
$608$	3.24264	+	3.24264i	0.131506	+	0.131506i
$609$	−1.41421	−	2.00000i	−0.0573068	−	0.0810441i
$610$	0.435029	−	6.12132i	0.0176138	−	0.247845i
$611$		−	51.4558i		−	2.08168i
$612$	5.65685	+	11.0000i	0.228665	+	0.444649i
$613$	−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
$615$	1.12132	−	4.56497i	0.0452160	−	0.184077i
$616$			10.2426i			0.412688i
$617$	−40.4350	+	16.7487i	−1.62785	+	0.674279i	−0.994989	−	0.0999842i	$-0.968121\pi$
$617$	−40.4350	+	16.7487i	−1.62785	+	0.674279i	−0.632864	+	0.774263i	$0.718121\pi$
$618$	2.68629	−	1.89949i	0.108058	−	0.0764089i
$619$	−20.6777	+	8.56497i	−0.831106	+	0.344255i	−0.757340	−	0.653020i	$-0.773502\pi$
$619$	−20.6777	+	8.56497i	−0.831106	+	0.344255i	−0.0737654	+	0.997276i	$0.523502\pi$
$620$	1.12132	+	1.29289i	0.0450333	+	0.0519238i
$621$	10.8787	+	13.7782i	0.436546	+	0.552899i
$622$	25.1924	+	10.4350i	1.01012	+	0.418407i
$623$	24.1421	−	58.2843i	0.967234	−	2.33511i
$624$	−6.24264	−	8.82843i	−0.249906	−	0.353420i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	7.70711	−	18.6066i	0.308038	−	0.743669i
$627$	15.4264	+	9.72792i	0.616071	+	0.388496i
$628$	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	−0.983566	−	0.180548i	$-0.942213\pi$
$631$	−20.1716	+	20.1716i	−0.803018	+	0.803018i	0.180548	+	0.983566i	$0.442213\pi$
$632$	−5.87868	−	14.1924i	−0.233841	−	0.564543i
$633$	7.09188	−	1.60660i	0.281877	−	0.0638567i
$634$	−19.5355	−	8.09188i	−0.775855	−	0.321370i
$635$	3.31371	+	1.65685i	0.131501	+	0.0657503i
$636$	−2.00000	−	0.343146i	−0.0793052	−	0.0136066i
$637$	−80.5269			−3.19059
$638$	−0.727922			−0.0288187
$639$	12.3934	−	13.7782i	0.490275	−	0.545056i
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	3.94975	+	1.63604i	0.156006	+	0.0646197i	0.459320	−	0.888271i	$-0.348093\pi$
$641$	3.94975	+	1.63604i	0.156006	+	0.0646197i	−0.303314	+	0.952891i	$0.598093\pi$
$642$	−2.70711	−	11.9497i	−0.106841	−	0.471619i
$643$	−10.3345	−	24.9497i	−0.407554	−	0.983922i	−0.985779	−	0.168045i	$-0.946255\pi$
$643$	−10.3345	−	24.9497i	−0.407554	−	0.983922i	0.578225	−	0.815877i	$-0.303745\pi$
$644$	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	$0.890263\pi$
$648$	7.00000	+	5.65685i	0.274986	+	0.222222i
$649$	−7.97056	+	19.2426i	−0.312872	+	0.755340i
$650$	−30.8995	−	4.41421i	−1.21198	−	0.173140i
$651$	−4.82843	+	3.41421i	−0.189241	+	0.133814i
$652$	3.36396	−	8.12132i	0.131743	−	0.318055i
$653$	25.7782	+	10.6777i	1.00878	+	0.417849i	0.825009	−	0.565120i	$-0.191170\pi$
$653$	25.7782	+	10.6777i	1.00878	+	0.417849i	0.183769	+	0.982969i	$0.441170\pi$
$654$	−2.77817	−	12.2635i	−0.108635	−	0.479539i
$655$	13.5355	+	15.6066i	0.528877	+	0.609800i
$656$	1.12132	−	0.464466i	0.0437802	−	0.0181344i
$657$	30.3640	−	1.60660i	1.18461	−	0.0626795i
$658$	33.9706	−	14.0711i	1.32431	−	0.548547i
$659$			17.5147i			0.682277i	0.940013	+	0.341138i	$0.110812\pi$
$659$			17.5147i			0.682277i	−0.940013	+	0.341138i	$0.889188\pi$
$660$	−8.63604	−	2.12132i	−0.336157	−	0.0825723i
$661$	−6.41421	+	6.41421i	−0.249484	+	0.249484i	−0.820759	−	0.571275i	$-0.806449\pi$
$661$	−6.41421	+	6.41421i	−0.249484	+	0.249484i	0.571275	+	0.820759i	$0.306449\pi$
$662$	−4.41421	−	4.41421i	−0.171563	−	0.171563i
$663$	−6.24264	+	44.1421i	−0.242444	+	1.71434i
$664$		−	11.6569i		−	0.452374i
$665$	−3.24264	+	45.6274i	−0.125744	+	1.76936i
$666$	−8.77817	+	0.464466i	−0.340147	+	0.0179977i
$667$	0.757359	+	0.757359i	0.0293251	+	0.0293251i
$668$	−1.39340	−	3.36396i	−0.0539122	−	0.130156i
$669$	6.82843	−	39.7990i	0.264002	−	1.53872i
$670$	13.2426	−	4.41421i	0.511608	−	0.170536i
$671$	4.45584	−	4.45584i	0.172016	−	0.172016i
$672$	4.12132	−	6.53553i	0.158983	−	0.252114i
$673$	−0.636039	+	1.53553i	−0.0245175	+	0.0591905i	−0.935664	−	0.352892i	$-0.885198\pi$
$673$	−0.636039	+	1.53553i	−0.0245175	+	0.0591905i	0.911147	+	0.412082i	$0.135198\pi$
$674$	6.77817	−	2.80761i	0.261086	−	0.108145i
$675$	25.7487	−	3.46447i	0.991069	−	0.133347i
$676$		−	25.9706i		−	0.998868i
$677$	1.19239	+	2.87868i	0.0458272	+	0.110637i	0.945136	−	0.326679i	$-0.105929\pi$
$677$	1.19239	+	2.87868i	0.0458272	+	0.110637i	−0.899308	+	0.437315i	$0.855929\pi$
$678$	−5.22183	−	3.29289i	−0.200543	−	0.126463i
$679$			17.0711i			0.655127i
$680$	3.17157	+	8.65685i	0.121624	+	0.331975i
$681$	−4.53553	+	7.19239i	−0.173802	+	0.275613i
$682$			1.75736i			0.0672928i
$683$	−41.8492	+	17.3345i	−1.60132	+	0.663287i	−0.991601	−	0.129333i	$-0.958716\pi$
$683$	−41.8492	+	17.3345i	−1.60132	+	0.663287i	−0.609716	+	0.792620i	$0.708716\pi$
$684$	−5.92893	−	12.4142i	−0.226698	−	0.474669i
$685$	−7.48528	−	22.4558i	−0.285998	−	0.857994i
$686$	−10.0711	−	24.3137i	−0.384515	−	0.928302i
$687$	−16.3848	−	23.1716i	−0.625118	−	0.884051i
$688$		−	11.6569i		−	0.444413i
$689$	−5.17157	−	5.17157i	−0.197021	−	0.197021i
$690$	6.77817	+	11.1924i	0.258041	+	0.426087i
$691$	−15.7071	+	6.50610i	−0.597527	+	0.247504i	−0.660885	−	0.750487i	$-0.729819\pi$
$691$	−15.7071	+	6.50610i	−0.597527	+	0.247504i	0.0633584	+	0.997991i	$0.479819\pi$
$692$	−15.1924	+	6.29289i	−0.577528	+	0.239220i
$693$	10.2426	−	28.9706i	0.389086	−	1.10050i
$694$	−7.84924	+	18.9497i	−0.297953	+	0.719323i
$695$	−13.7782	+	11.9497i	−0.522636	+	0.453280i
$696$	0.464466	+	0.292893i	0.0176055	+	0.0111021i
$697$	−4.67767	−	1.77817i	−0.177179	−	0.0673532i
$698$	−0.757359	+	0.757359i	−0.0286665	+	0.0286665i
$699$	−13.7782	+	3.12132i	−0.521138	+	0.118059i
$700$	−5.53553	−	21.6066i	−0.209224	−	0.816653i
$701$	−12.3431			−0.466194			−0.233097	−	0.972453i	$-0.574886\pi$
$701$	−12.3431			−0.466194			−0.233097	+	0.972453i	$0.574886\pi$
$702$	8.82843	+	31.2132i	0.333208	+	1.17807i
$703$	12.4142	+	5.14214i	0.468211	+	0.193939i
$704$	−0.878680	−	2.12132i	−0.0331165	−	0.0799503i
$705$	4.82843	+	31.5563i	0.181849	+	1.18848i
$706$	−16.6569	−	16.6569i	−0.626889	−	0.626889i
$707$	18.4853	−	44.6274i	0.695211	−	1.67839i
$708$	12.8284	−	9.07107i	0.482122	−	0.340912i
$709$	−10.3640	−	4.29289i	−0.389227	−	0.161223i	0.179483	−	0.983761i	$-0.442557\pi$
$709$	−10.3640	−	4.29289i	−0.389227	−	0.161223i	−0.568710	+	0.822538i	$0.692557\pi$
$710$	10.4350	−	9.05025i	0.391620	−	0.339650i
$711$	2.43503	+	46.0208i	0.0913207	+	1.72592i
$712$			14.1421i			0.529999i
$713$	1.82843	−	1.82843i	0.0684751	−	0.0684751i
$714$	−30.8492	+	7.94975i	−1.15450	+	0.297512i
$715$	−21.0000	−	24.2132i	−0.785355	−	0.905522i
$716$	1.24264	+	1.24264i	0.0464397	+	0.0464397i
$717$	3.51472	−	20.4853i	0.131260	−	0.765037i
$718$	8.65685	−	8.65685i	0.323071	−	0.323071i
$719$	−15.3345	+	37.0208i	−0.571881	+	1.38064i	0.328070	+	0.944653i	$0.393602\pi$
$719$	−15.3345	+	37.0208i	−0.571881	+	1.38064i	−0.899951	+	0.435990i	$0.856398\pi$
$720$	4.65685	+	4.82843i	0.173551	+	0.179945i
$721$	3.24264	+	7.82843i	0.120762	+	0.291546i
$722$			2.02944i			0.0755278i
$723$	−1.36396	+	2.16295i	−0.0507263	+	0.0804410i
$724$	−3.87868	+	1.60660i	−0.144150	+	0.0597089i
$725$	1.53553	−	0.393398i	0.0570283	−	0.0146104i
$726$	5.72792	+	8.10051i	0.212583	+	0.300638i
$727$	−20.6569	−	20.6569i	−0.766120	−	0.766120i	0.211301	−	0.977421i	$-0.432230\pi$
$727$	−20.6569	−	20.6569i	−0.766120	−	0.766120i	−0.977421	+	0.211301i	$0.932230\pi$
$728$	25.7279	−	10.6569i	0.953540	−	0.394969i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	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
$733$	47.2548			1.74540			0.872699	−	0.488259i	$-0.162368\pi$
$733$	47.2548			1.74540			0.872699	+	0.488259i	$0.162368\pi$
$734$	−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
$737$	13.2426	+	5.48528i	0.487799	+	0.202053i
$738$	−3.63604	+	0.192388i	−0.133844	+	0.00708191i
$739$	13.9289	−	13.9289i	0.512384	−	0.512384i	−0.402872	−	0.915256i	$-0.631988\pi$
$739$	13.9289	−	13.9289i	0.512384	−	0.512384i	0.915256	+	0.402872i	$0.131988\pi$
$740$	−6.53553	−	0.464466i	−0.240251	−	0.0170741i
$741$	8.38478	−	48.8701i	0.308022	−	1.79529i
$742$	2.00000	−	4.82843i	0.0734223	−	0.177257i
$743$	−13.1924	−	31.8492i	−0.483982	−	1.16844i	−0.957702	−	0.287760i	$-0.907089\pi$
$743$	−13.1924	−	31.8492i	−0.483982	−	1.16844i	0.473721	−	0.880675i	$-0.342911\pi$
$744$	0.707107	−	1.12132i	0.0259238	−	0.0411096i
$745$	−22.1421	+	44.2843i	−0.811225	+	1.62245i
$746$	−11.2426	−	11.2426i	−0.411622	−	0.411622i
$747$	−11.6569	+	32.9706i	−0.426502	+	1.20633i
$748$	−3.36396	+	8.84924i	−0.122999	+	0.323560i
$749$	31.5563			1.15304
$750$	19.3640	−	0.192388i	0.707072	−	0.00702502i
$751$	−5.05025	−	2.09188i	−0.184286	−	0.0763339i	0.288632	−	0.957440i	$-0.406800\pi$
$751$	−5.05025	−	2.09188i	−0.184286	−	0.0763339i	−0.472919	+	0.881106i	$0.656800\pi$
$752$	−5.82843	+	5.82843i	−0.212541	+	0.212541i
$753$	−2.68629	+	15.6569i	−0.0978939	+	0.570567i
$754$	0.757359	+	1.82843i	0.0275814	+	0.0665874i
$755$	−19.9706	+	6.65685i	−0.726803	+	0.242268i
$756$	−18.1924	+	14.3640i	−0.661651	+	0.522412i
$757$	13.3137			0.483895			0.241947	−	0.970289i	$-0.422214\pi$
$757$	13.3137			0.483895			0.241947	+	0.970289i	$0.422214\pi$
$758$	−34.0919	−	14.1213i	−1.23827	−	0.512909i
$759$	−2.27208	+	13.2426i	−0.0824712	+	0.480677i
$760$	−3.24264	−	9.72792i	−0.117623	−	0.352869i
$761$	−26.9706			−0.977682			−0.488841	−	0.872373i	$-0.662580\pi$
$761$	−26.9706			−0.977682			−0.488841	+	0.872373i	$0.662580\pi$
$762$	0.485281	−	2.82843i	0.0175799	−	0.102463i
$763$	32.3848			1.17241
$764$	−17.6569			−0.638803
$765$	−0.313708	−	27.6569i	−0.0113422	−	0.999936i
$766$	27.3137			0.986884
$767$	56.6274			2.04470
$768$	−0.292893	+	1.70711i	−0.0105689	+	0.0615999i
$769$	−48.6274			−1.75355			−0.876775	−	0.480901i	$-0.840310\pi$
$769$	−48.6274			−1.75355			−0.876775	+	0.480901i	$0.840310\pi$
$770$	10.2426	−	20.4853i	0.369119	−	0.738238i
$771$	−0.928932	+	5.41421i	−0.0334547	+	0.194988i
$772$	8.29289	+	3.43503i	0.298468	+	0.123629i
$773$	−46.0000			−1.65451			−0.827253	−	0.561830i	$-0.810097\pi$
$773$	−46.0000			−1.65451			−0.827253	+	0.561830i	$0.810097\pi$
$774$	−11.6569	+	32.9706i	−0.418997	+	1.18510i
$775$	−0.949747	−	3.70711i	−0.0341159	−	0.133163i
$776$	−1.46447	−	3.53553i	−0.0525713	−	0.126918i
$777$	3.82843	−	22.3137i	0.137344	−	0.800500i
$778$	2.41421	−	2.41421i	0.0865537	−	0.0865537i
$779$	5.14214	+	2.12994i	0.184236	+	0.0763131i
$780$	3.65685	+	23.8995i	0.130936	+	0.855739i
$781$	14.1838			0.507535
$782$	12.7071	−	5.70711i	0.454405	−	0.204086i
$783$	−1.02082	−	1.29289i	−0.0364810	−	0.0462042i
$784$	9.12132	+	9.12132i	0.325761	+	0.325761i
$785$	−16.0711	−	48.2132i	−0.573601	−	1.72080i
$786$	8.53553	−	13.5355i	0.304452	−	0.482797i
$787$	−8.67767	−	20.9497i	−0.309326	−	0.746778i	−0.999727	−	0.0233517i	$-0.992566\pi$
$787$	−8.67767	−	20.9497i	−0.309326	−	0.746778i	0.690402	−	0.723426i	$-0.257434\pi$
$788$	1.05025	−	2.53553i	0.0374137	−	0.0903247i
$789$	2.34315	−	13.6569i	0.0834182	−	0.486197i
$790$	−2.43503	+	34.2635i	−0.0866344	+	1.21904i
$791$	11.2426	−	11.2426i	0.399742	−	0.399742i
$792$	0.363961	+	6.87868i	0.0129328	+	0.244423i
$793$	−15.8284	−	6.55635i	−0.562084	−	0.232823i
$794$	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
$797$	−8.34315			−0.295529			−0.147765	−	0.989023i	$-0.547208\pi$
$797$	−8.34315			−0.295529			−0.147765	+	0.989023i	$0.547208\pi$
$798$	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
$801$	14.1421	−	40.0000i	0.499688	−	1.41333i
$802$	1.94975	−	0.807612i	0.0688480	−	0.0285178i
$803$	16.4558	+	16.4558i	0.580714	+	0.580714i
$804$	−6.24264	−	8.82843i	−0.220161	−	0.311355i
$805$	−31.9706	+	10.6569i	−1.12681	+	0.375605i
$806$	4.41421	−	1.82843i	0.155484	−	0.0644036i
$807$	29.0919	−	46.1335i	1.02408	−	1.62398i
$808$			10.8284i			0.380943i
$809$	11.7071	+	28.2635i	0.411600	+	0.993690i	0.984708	+	0.174211i	$0.0557374\pi$
$809$	11.7071	+	28.2635i	0.411600	+	0.993690i	−0.573108	+	0.819480i	$0.694263\pi$
$810$	−8.34315	−	18.3137i	−0.293148	−	0.643478i
$811$	1.80761	−	4.36396i	0.0634738	−	0.153239i	−0.888960	−	0.457985i	$-0.848571\pi$
$811$	1.80761	−	4.36396i	0.0634738	−	0.153239i	0.952434	+	0.304745i	$0.0985714\pi$
$812$	−1.00000	+	1.00000i	−0.0350931	+	0.0350931i
$813$	0.201010	−	1.17157i	0.00704973	−	0.0410889i
$814$	−4.75736	−	4.75736i	−0.166745	−	0.166745i
$815$	−14.8492	+	12.8787i	−0.520146	+	0.451120i
$816$	5.70711	−	4.29289i	0.199789	−	0.150281i
$817$	37.7990	−	37.7990i	1.32242	−	1.32242i
$818$			10.8284i			0.378607i
$819$	−83.4264	+	4.41421i	−2.91515	+	0.154245i
$820$	−2.70711	−	0.192388i	−0.0945363	−	0.00671849i
$821$	31.3345	+	12.9792i	1.09358	+	0.452977i	0.855255	−	0.518208i	$-0.173401\pi$
$821$	31.3345	+	12.9792i	1.09358	+	0.452977i	0.238328	+	0.971185i	$0.423401\pi$
$822$	−14.9706	+	10.5858i	−0.522158	+	0.369222i
$823$	17.7782	−	42.9203i	0.619708	−	1.49611i	−0.232335	−	0.972636i	$-0.574636\pi$
$823$	17.7782	−	42.9203i	0.619708	−	1.49611i	0.852043	−	0.523472i	$-0.175364\pi$
$824$	−1.34315	−	1.34315i	−0.0467907	−	0.0467907i
$825$	15.1508	+	12.8787i	0.527482	+	0.448378i
$826$	15.4853	+	37.3848i	0.538802	+	1.30078i
$827$	20.1924	+	8.36396i	0.702158	+	0.290843i	0.705055	−	0.709152i	$-0.250922\pi$
$827$	20.1924	+	8.36396i	0.702158	+	0.290843i	−0.00289711	+	0.999996i	$0.500922\pi$
$828$	6.77817	−	7.53553i	0.235558	−	0.261878i
$829$	−20.3431			−0.706547			−0.353273	−	0.935520i	$-0.614931\pi$
$829$	−20.3431			−0.706547			−0.353273	+	0.935520i	$0.614931\pi$
$830$	−11.6569	+	23.3137i	−0.404615	+	0.809231i
$831$	−48.9619	+	11.0919i	−1.69847	+	0.384773i
$832$	−4.41421	+	4.41421i	−0.153035	+	0.153035i
$833$	−1.56497	−	53.1630i	−0.0542230	−	1.84199i
$834$	11.9497	+	7.53553i	0.413786	+	0.260934i
$835$	−0.577164	+	8.12132i	−0.0199736	+	0.281050i
$836$	4.02944	−	9.72792i	0.139361	−	0.336447i
$837$	−3.12132	+	2.46447i	−0.107889	+	0.0851844i
$838$	−13.6066	+	5.63604i	−0.470032	+	0.194694i
$839$	−38.0208	+	15.7487i	−1.31262	+	0.543707i	−0.925649	−	0.378383i	$-0.876480\pi$
$839$	−38.0208	+	15.7487i	−1.31262	+	0.543707i	−0.386975	+	0.922090i	$0.626480\pi$
$840$	−14.7782	+	8.94975i	−0.509895	+	0.308796i
$841$	20.4350	+	20.4350i	0.704656	+	0.704656i
$842$		−	38.1421i		−	1.31446i
$843$	−3.55635	−	5.02944i	−0.122487	−	0.173223i
$844$	−1.60660	−	3.87868i	−0.0553015	−	0.133510i
$845$	−25.9706	+	51.9411i	−0.893415	+	1.78683i
$846$	22.3137	−	10.6569i	0.767161	−	0.366390i
$847$	−23.6066	+	9.77817i	−0.811132	+	0.335982i
$848$			1.17157i			0.0402320i
$849$	−16.7782	+	26.6066i	−0.575825	+	0.913136i
$850$	2.31371	−	20.4853i	0.0793595	−	0.702639i
$851$			9.89949i			0.339350i
$852$	−9.05025	−	5.70711i	−0.310057	−	0.195522i
$853$	3.92031	+	9.46447i	0.134229	+	0.324057i	0.976675	−	0.214724i	$-0.0688851\pi$
$853$	3.92031	+	9.46447i	0.134229	+	0.324057i	−0.842446	+	0.538781i	$0.818885\pi$
$854$		−	12.2426i		−	0.418935i
$855$	−0.556349	+	30.7574i	−0.0190267	+	1.05188i
$856$	−6.53553	+	2.70711i	−0.223380	+	0.0925270i
$857$	−18.3345	+	44.2635i	−0.626295	+	1.51201i	0.217898	+	0.975972i	$0.430080\pi$
$857$	−18.3345	+	44.2635i	−0.626295	+	1.51201i	−0.844193	+	0.536039i	$0.819920\pi$
$858$	−13.2426	+	21.0000i	−0.452096	+	0.716928i
$859$	−17.7279	+	17.7279i	−0.604869	+	0.604869i	−0.941601	−	0.336732i	$-0.890678\pi$
$859$	−17.7279	+	17.7279i	−0.604869	+	0.604869i	0.336732	+	0.941601i	$0.390678\pi$
$860$	−11.6569	+	23.3137i	−0.397495	+	0.794991i
$861$	1.58579	−	9.24264i	0.0540435	−	0.314988i
$862$	13.3934	+	32.3345i	0.456181	+	1.10132i
$863$	6.51472	+	6.51472i	0.221764	+	0.221764i	0.809241	−	0.587477i	$-0.199879\pi$
$863$	6.51472	+	6.51472i	0.221764	+	0.221764i	−0.587477	+	0.809241i	$0.699879\pi$
$864$	2.53553	−	4.53553i	0.0862606	−	0.154302i
$865$	36.6777	+	2.60660i	1.24708	+	0.0886271i
$866$			28.9706i			0.984460i
$867$	−29.2635	−	3.26346i	−0.993839	−	0.110833i
$868$	2.41421	+	2.41421i	0.0819437	+	0.0819437i
$869$	−24.9411	+	24.9411i	−0.846070	+	0.846070i
$870$	−0.636039	−	1.05025i	−0.0215637	−	0.0356069i
$871$		−	38.9706i		−	1.32047i
$872$	−6.70711	+	2.77817i	−0.227131	+	0.0940809i
$873$	0.606602	+	11.4645i	0.0205304	+	0.388013i
$874$	−14.3137	+	5.92893i	−0.484168	+	0.200549i
$875$	−10.5355	+	48.7487i	−0.356166	+	1.64801i
$876$	−3.87868	−	17.1213i	−0.131048	−	0.578476i
$877$	−40.7487	−	16.8787i	−1.37599	−	0.569953i	−0.432582	−	0.901595i	$-0.642397\pi$
$877$	−40.7487	−	16.8787i	−1.37599	−	0.569953i	−0.943405	+	0.331642i	$0.892397\pi$
$878$	−9.77817	+	23.6066i	−0.329997	+	0.796684i
$879$	−11.1716	+	7.89949i	−0.376808	+	0.266443i
$880$	−0.363961	+	5.12132i	−0.0122691	+	0.172640i
$881$	2.73654	−	6.60660i	0.0921965	−	0.222582i	−0.871054	−	0.491188i	$-0.836563\pi$
$881$	2.73654	−	6.60660i	0.0921965	−	0.222582i	0.963250	+	0.268606i	$0.0865629\pi$
$882$	−16.6777	−	34.9203i	−0.561566	−	1.17583i
$883$	−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
$887$	1.92031	+	4.63604i	0.0644777	+	0.155663i	0.952834	−	0.303492i	$-0.0981524\pi$
$887$	1.92031	+	4.63604i	0.0644777	+	0.155663i	−0.888356	+	0.459155i	$0.848152\pi$
$888$	1.12132	+	4.94975i	0.0376290	+	0.166103i
$889$	6.82843	+	2.82843i	0.229018	+	0.0948624i
$890$	14.1421	−	28.2843i	0.474045	−	0.948091i
$891$	5.84924	−	19.8198i	0.195957	−	0.663988i
$892$	−23.3137			−0.780601
$893$	−37.7990			−1.26489
$894$	37.7990	+	6.48528i	1.26419	+	0.216900i
$895$	−1.24264	−	3.72792i	−0.0415369	−	0.124611i
$896$	−4.12132	−	1.70711i	−0.137684	−	0.0570304i
$897$	35.6274	−	8.07107i	1.18956	−	0.269485i
$898$	4.19239	+	10.1213i	0.139902	+	0.337753i
$899$	−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
$903$	−76.1838	−	48.0416i	−2.53524	−	1.59873i
$904$	−1.36396	+	3.29289i	−0.0453647	+	0.109520i
$905$	9.36396	+	0.665476i	0.311269	+	0.0221212i
$906$	9.41421	+	13.3137i	0.312766	+	0.442318i
$907$	−17.3223	+	41.8198i	−0.575179	+	1.38860i	0.321917	+	0.946768i	$0.395673\pi$
$907$	−17.3223	+	41.8198i	−0.575179	+	1.38860i	−0.897096	+	0.441836i	$0.854327\pi$
$908$	4.53553	+	1.87868i	0.150517	+	0.0623462i
$909$	10.8284	−	30.6274i	0.359156	−	1.01585i
$910$	−62.1127	−	4.41421i	−2.05902	−	0.146330i
$911$	−5.87868	+	2.43503i	−0.194769	+	0.0806761i	−0.477936	−	0.878395i	$-0.658615\pi$
$911$	−5.87868	+	2.43503i	−0.194769	+	0.0806761i	0.283167	+	0.959071i	$0.408615\pi$
$912$	−6.48528	+	4.58579i	−0.214749	+	0.151851i
$913$	−24.7279	+	10.2426i	−0.818375	+	0.338982i
$914$			9.65685i			0.319420i
$915$	10.3223	+	2.53553i	0.341246	+	0.0838222i
$916$	−11.5858	+	11.5858i	−0.382805	+	0.382805i
$917$	29.1421	+	29.1421i	0.962358	+	0.962358i
$918$	−20.4350	+	6.43503i	−0.674456	+	0.212388i
$919$		−	18.6863i		−	0.616404i	−0.951321	−	0.308202i	$-0.900273\pi$
$919$		−	18.6863i		−	0.616404i	0.951321	−	0.308202i	$-0.0997272\pi$
$920$	5.70711	−	4.94975i	0.188158	−	0.163188i
$921$	5.27208	+	7.45584i	0.173721	+	0.245678i
$922$	−19.7279	−	19.7279i	−0.649705	−	0.649705i
$923$	−14.7574	−	35.6274i	−0.485744	−	1.17269i
$924$	−17.4853	−	3.00000i	−0.575224	−	0.0986928i
$925$	12.6066	+	7.46447i	0.414503	+	0.245430i
$926$	8.17157	−	8.17157i	0.268535	−	0.268535i
$927$	2.45584	+	5.14214i	0.0806605	+	0.168890i
$928$	0.121320	−	0.292893i	0.00398254	−	0.00961469i
$929$	−23.0208	+	9.53553i	−0.755288	+	0.312851i	−0.726897	−	0.686746i	$-0.759038\pi$
$929$	−23.0208	+	9.53553i	−0.755288	+	0.312851i	−0.0283911	+	0.999597i	$0.509038\pi$
$930$	−2.53553	+	1.53553i	−0.0831434	+	0.0503521i
$931$			59.1543i			1.93870i
$932$	3.12132	+	7.53553i	0.102242	+	0.246835i
$933$	−25.1924	+	39.9497i	−0.824762	+	1.30790i
$934$		−	26.4853i		−	0.866625i
$935$	15.5772	−	14.3345i	0.509428	−	0.468789i
$936$	16.8995	−	8.07107i	0.552377	−	0.263811i
$937$		−	17.6569i		−	0.576824i	−0.957506	−	0.288412i	$-0.906873\pi$
$937$		−	17.6569i		−	0.576824i	0.957506	−	0.288412i	$-0.0931273\pi$
$938$	25.7279	−	10.6569i	0.840046	−	0.347959i
$939$	29.5061	+	18.6066i	0.962895	+	0.607203i
$940$	17.4853	−	5.82843i	0.570307	−	0.190102i
$941$	3.29289	+	7.94975i	0.107345	+	0.259154i	0.968420	−	0.249324i	$-0.0802083\pi$
$941$	3.29289	+	7.94975i	0.107345	+	0.259154i	−0.861075	+	0.508478i	$0.830208\pi$
$942$	−32.1421	+	22.7279i	−1.04725	+	0.740516i
$943$			4.10051i			0.133531i
$944$	−6.41421	−	6.41421i	−0.208765	−	0.208765i
$945$	50.7487	−	10.5355i	1.65086	−	0.342721i
$946$	−24.7279	+	10.2426i	−0.803974	+	0.333017i
$947$	4.29289	−	1.77817i	0.139500	−	0.0577829i	−0.311841	−	0.950134i	$-0.600946\pi$
$947$	4.29289	−	1.77817i	0.139500	−	0.0577829i	0.451341	+	0.892351i	$0.350946\pi$
$948$	25.9497	−	5.87868i	0.842809	−	0.190931i
$949$	24.2132	−	58.4558i	0.785994	−	1.89756i
$950$	−3.24264	+	22.6985i	−0.105205	+	0.736436i
$951$	19.5355	−	30.9792i	0.633483	−	1.00457i
$952$	7.53553	+	16.7782i	0.244228	+	0.543784i
$953$	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	$0.0159642\pi$
$954$	1.17157	−	3.31371i	0.0379311	−	0.107285i
$955$	35.3137	+	17.6569i	1.14272	+	0.571362i
$956$	−12.0000			−0.388108
$957$	0.213203	−	1.24264i	0.00689189	−	0.0401689i
$958$	20.3640	+	8.43503i	0.657930	+	0.272523i
$959$	−18.0711	−	43.6274i	−0.583545	−	1.40880i
$960$	2.29289	−	3.12132i	0.0740028	−	0.100740i
$961$	−21.5061	−	21.5061i	−0.693745	−	0.693745i
$962$	−7.00000	+	16.8995i	−0.225689	+	0.544862i
$963$	21.1924	−	1.12132i	0.682915	−	0.0361340i
$964$	1.36396	+	0.564971i	0.0439302	+	0.0181965i
$965$	−13.1508	−	15.1630i	−0.423338	−	0.488113i
$966$	15.0711	+	21.3137i	0.484904	+	0.685757i
$967$		−	23.9411i		−	0.769895i	−0.922939	−	0.384947i	$-0.874220\pi$
$967$		−	23.9411i		−	0.769895i	0.922939	−	0.384947i	$-0.125780\pi$
$968$	4.05025	−	4.05025i	0.130180	−	0.130180i
$969$	32.4264	+	4.58579i	1.04169	+	0.147317i
$970$	−0.606602	+	8.53553i	−0.0194768	+	0.274059i
$971$	7.72792	+	7.72792i	0.248001	+	0.248001i	0.820150	−	0.572149i	$-0.193890\pi$
$971$	7.72792	+	7.72792i	0.248001	+	0.248001i	−0.572149	+	0.820150i	$0.693890\pi$
$972$	−11.7071	+	10.2929i	−0.375506	+	0.330145i
$973$	−25.7279	+	25.7279i	−0.824799	+	0.824799i
$974$	−3.53553	+	8.53553i	−0.113286	+	0.273496i
$975$	16.5858	−	51.4558i	0.531170	−	1.64791i
$976$	1.05025	+	2.53553i	0.0336178	+	0.0811605i
$977$		−	6.54416i		−	0.209366i	−0.994506	−	0.104683i	$-0.966617\pi$
$977$		−	6.54416i		−	0.209366i	0.994506	−	0.104683i	$-0.0333828\pi$
$978$	12.8787	+	8.12132i	0.411815	+	0.259691i
$979$	30.0000	−	12.4264i	0.958804	−	0.397150i
$980$	−9.12132	−	27.3640i	−0.291370	−	0.874110i
$981$	21.7487	−	1.15076i	0.694384	−	0.0367409i
$982$	18.4142	+	18.4142i	0.587621	+	0.587621i
$983$	37.6777	−	15.6066i	1.20173	−	0.497773i	0.310173	−	0.950680i	$-0.399613\pi$
$983$	37.6777	−	15.6066i	1.20173	−	0.497773i	0.891558	+	0.452907i	$0.149613\pi$
$984$	0.464466	+	2.05025i	0.0148066	+	0.0653597i
$985$	−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
$988$	−28.6274			−0.910759
$989$	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	−0.988693	−	0.149952i	$-0.952088\pi$
$991$	−5.77817	+	13.9497i	−0.183550	+	0.443128i	0.805144	+	0.593080i	$0.202088\pi$
$992$	−0.707107	−	0.292893i	−0.0224507	−	0.00929937i
$993$	8.82843	−	6.24264i	0.280162	−	0.198104i
$994$	19.4853	−	19.4853i	0.618036	−	0.618036i
$995$	−12.3345	−	14.2218i	−0.391031	−	0.450862i
$996$	19.8995	+	3.41421i	0.630540	+	0.108183i
$997$	23.0919	−	55.7487i	0.731327	−	1.76558i	0.0932026	−	0.995647i	$-0.470290\pi$
$997$	23.0919	−	55.7487i	0.731327	−	1.76558i	0.638125	−	0.769933i	$-0.279710\pi$
$998$	13.0208	+	31.4350i	0.412167	+	0.995058i
$999$	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.w.b.383.1	yes	4
3.2	odd	2		510.2.w.a.383.1	yes	4
5.2	odd	4		510.2.z.a.77.1	yes	4
15.2	even	4		510.2.z.b.77.1	yes	4
17.2	even	8		510.2.z.b.53.1	yes	4
51.2	odd	8		510.2.z.a.53.1	yes	4
85.2	odd	8		510.2.w.a.257.1	✓	4
255.2	even	8	inner	510.2.w.b.257.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.w.a.257.1	✓	4	85.2	odd	8
510.2.w.a.383.1	yes	4	3.2	odd	2
510.2.w.b.257.1	yes	4	255.2	even	8	inner
510.2.w.b.383.1	yes	4	1.1	even	1	trivial
510.2.z.a.53.1	yes	4	51.2	odd	8
510.2.z.a.77.1	yes	4	5.2	odd	4
510.2.z.b.53.1	yes	4	17.2	even	8
510.2.z.b.77.1	yes	4	15.2	even	4

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.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.292893 + 1.70711i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-4.12132 - 1.70711i) q^{7} +1.00000 q^{8} +(-2.82843 - 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} +(-0.878680 - 2.12132i) q^{11} +(-0.292893 + 1.70711i) q^{12} +(-4.41421 + 4.41421i) q^{13} +(-4.12132 - 1.70711i) q^{14} +(2.29289 - 3.12132i) q^{15} +1.00000 q^{16} +(-3.00000 - 2.82843i) q^{17} +(-2.82843 - 1.00000i) q^{18} +(3.24264 + 3.24264i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(4.12132 - 6.53553i) q^{21} +(-0.878680 - 2.12132i) q^{22} +(-1.29289 + 3.12132i) q^{23} +(-0.292893 + 1.70711i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-4.41421 + 4.41421i) q^{26} +(2.53553 - 4.53553i) q^{27} +(-4.12132 - 1.70711i) q^{28} +(0.121320 - 0.292893i) q^{29} +(2.29289 - 3.12132i) q^{30} +(-0.707107 - 0.292893i) q^{31} +1.00000 q^{32} +(3.87868 - 0.878680i) q^{33} +(-3.00000 - 2.82843i) q^{34} +(6.53553 + 7.53553i) q^{35} +(-2.82843 - 1.00000i) q^{36} +(2.70711 - 1.12132i) q^{37} +(3.24264 + 3.24264i) q^{38} +(-6.24264 - 8.82843i) q^{39} +(-2.00000 - 1.00000i) q^{40} +(1.12132 - 0.464466i) q^{41} +(4.12132 - 6.53553i) q^{42} -11.6569i q^{43} +(-0.878680 - 2.12132i) q^{44} +(4.65685 + 4.82843i) q^{45} +(-1.29289 + 3.12132i) q^{46} +(-5.82843 + 5.82843i) q^{47} +(-0.292893 + 1.70711i) q^{48} +(9.12132 + 9.12132i) q^{49} +(3.00000 + 4.00000i) q^{50} +(5.70711 - 4.29289i) q^{51} +(-4.41421 + 4.41421i) q^{52} +1.17157i q^{53} +(2.53553 - 4.53553i) q^{54} +(-0.363961 + 5.12132i) q^{55} +(-4.12132 - 1.70711i) q^{56} +(-6.48528 + 4.58579i) q^{57} +(0.121320 - 0.292893i) q^{58} +(-6.41421 - 6.41421i) q^{59} +(2.29289 - 3.12132i) q^{60} +(1.05025 + 2.53553i) q^{61} +(-0.707107 - 0.292893i) q^{62} +(9.94975 + 8.94975i) q^{63} +1.00000 q^{64} +(13.2426 - 4.41421i) q^{65} +(3.87868 - 0.878680i) q^{66} +(-4.41421 + 4.41421i) q^{67} +(-3.00000 - 2.82843i) q^{68} +(-4.94975 - 3.12132i) q^{69} +(6.53553 + 7.53553i) q^{70} +(-2.36396 + 5.70711i) q^{71} +(-2.82843 - 1.00000i) q^{72} +(-9.36396 + 3.87868i) q^{73} +(2.70711 - 1.12132i) q^{74} +(-7.70711 + 3.94975i) q^{75} +(3.24264 + 3.24264i) q^{76} +10.2426i q^{77} +(-6.24264 - 8.82843i) q^{78} +(-5.87868 - 14.1924i) q^{79} +(-2.00000 - 1.00000i) q^{80} +(7.00000 + 5.65685i) q^{81} +(1.12132 - 0.464466i) q^{82} -11.6569i q^{83} +(4.12132 - 6.53553i) q^{84} +(3.17157 + 8.65685i) q^{85} -11.6569i q^{86} +(0.464466 + 0.292893i) q^{87} +(-0.878680 - 2.12132i) q^{88} +14.1421i q^{89} +(4.65685 + 4.82843i) q^{90} +(25.7279 - 10.6569i) q^{91} +(-1.29289 + 3.12132i) q^{92} +(0.707107 - 1.12132i) q^{93} +(-5.82843 + 5.82843i) q^{94} +(-3.24264 - 9.72792i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(-1.46447 - 3.53553i) q^{97} +(9.12132 + 9.12132i) q^{98} +(0.363961 + 6.87868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 8 q^{7} + 4 q^{8} - 8 q^{10} - 12 q^{11} - 4 q^{12} - 12 q^{13} - 8 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{19} - 8 q^{20} + 8 q^{21} - 12 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 8 * q^7 + 4 * q^8 - 8 * q^10 - 12 * q^11 - 4 * q^12 - 12 * q^13 - 8 * q^14 + 12 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^19 - 8 * q^20 + 8 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 + 12 * q^25 - 12 * q^26 - 4 * q^27 - 8 * q^28 - 8 * q^29 + 12 * q^30 + 4 * q^32 + 24 * q^33 - 12 * q^34 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 8 * q^39 - 8 * q^40 - 4 * q^41 + 8 * q^42 - 12 * q^44 - 4 * q^45 - 8 * q^46 - 12 * q^47 - 4 * q^48 + 28 * q^49 + 12 * q^50 + 20 * q^51 - 12 * q^52 - 4 * q^54 + 24 * q^55 - 8 * q^56 + 8 * q^57 - 8 * q^58 - 20 * q^59 + 12 * q^60 + 24 * q^61 + 20 * q^63 + 4 * q^64 + 36 * q^65 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 12 * q^70 + 16 * q^71 - 12 * q^73 + 8 * q^74 - 28 * q^75 - 4 * q^76 - 8 * q^78 - 32 * q^79 - 8 * q^80 + 28 * q^81 - 4 * q^82 + 8 * q^84 + 24 * q^85 + 16 * q^87 - 12 * q^88 - 4 * q^90 + 52 * q^91 - 8 * q^92 - 12 * q^94 + 4 * q^95 - 4 * q^96 - 20 * q^97 + 28 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more