LMFDB - Embedded newform 690.2.i.b.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	690.323
Dual form			690.2.i.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(3.00000 - 3.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(3.00000 - 3.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(1.00000 - 2.00000i) q^{10} +4.24264i q^{11} +(-1.70711 + 0.292893i) q^{12} +(2.00000 + 2.00000i) q^{13} +4.24264 q^{14} +(3.41421 - 1.82843i) q^{15} -1.00000 q^{16} +(4.24264 + 4.24264i) q^{17} +(-2.70711 - 1.29289i) q^{18} +4.00000i q^{19} +(2.12132 - 0.707107i) q^{20} +(6.00000 + 4.24264i) q^{21} +(-3.00000 + 3.00000i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.41421 - 1.00000i) q^{24} +(-4.00000 + 3.00000i) q^{25} +2.82843i q^{26} +(-2.53553 - 4.53553i) q^{27} +(3.00000 + 3.00000i) q^{28} +7.07107 q^{29} +(3.70711 + 1.12132i) q^{30} +2.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.24264 + 1.24264i) q^{33} +6.00000i q^{34} +(-8.48528 - 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 - 6.00000i) q^{37} +(-2.82843 + 2.82843i) q^{38} +(-2.82843 + 4.00000i) q^{39} +(2.00000 + 1.00000i) q^{40} -5.65685i q^{41} +(1.24264 + 7.24264i) q^{42} -4.24264 q^{44} +(4.12132 + 5.29289i) q^{45} -1.00000 q^{46} +(-8.48528 - 8.48528i) q^{47} +(-0.292893 - 1.70711i) q^{48} -11.0000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-6.00000 + 8.48528i) q^{51} +(-2.00000 + 2.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +(1.41421 - 5.00000i) q^{54} +(9.00000 - 3.00000i) q^{55} +4.24264i q^{56} +(-6.82843 + 1.17157i) q^{57} +(5.00000 + 5.00000i) q^{58} -1.41421 q^{59} +(1.82843 + 3.41421i) q^{60} -10.0000 q^{61} +(1.41421 + 1.41421i) q^{62} +(-5.48528 + 11.4853i) q^{63} -1.00000i q^{64} +(2.82843 - 5.65685i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-10.0000 + 10.0000i) q^{67} +(-4.24264 + 4.24264i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(-3.00000 - 9.00000i) q^{70} +5.65685i q^{71} +(1.29289 - 2.70711i) q^{72} +(-1.00000 - 1.00000i) q^{73} +8.48528 q^{74} +(-6.29289 - 5.94975i) q^{75} -4.00000 q^{76} +(12.7279 + 12.7279i) q^{77} +(-4.82843 + 0.828427i) q^{78} -14.0000i q^{79} +(0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} +(8.48528 - 8.48528i) q^{83} +(-4.24264 + 6.00000i) q^{84} +(6.00000 - 12.0000i) q^{85} +(2.07107 + 12.0711i) q^{87} +(-3.00000 - 3.00000i) q^{88} -11.3137 q^{89} +(-0.828427 + 6.65685i) q^{90} +12.0000 q^{91} +(-0.707107 - 0.707107i) q^{92} +(0.585786 + 3.41421i) q^{93} -12.0000i q^{94} +(8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 + 3.00000i) q^{97} +(7.77817 - 7.77817i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} + 12 q^{7}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^6 + 12 * q^7	$ 4 q + 4 q^{3} - 4 q^{6} + 12 q^{7} + 4 q^{10} - 4 q^{12} + 8 q^{13} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{21} - 12 q^{22} - 16 q^{25} + 4 q^{27} + 12 q^{28} + 12 q^{30} + 8 q^{31} - 12 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} - 12 q^{42} + 8 q^{45} - 4 q^{46} - 4 q^{48} - 24 q^{51} - 8 q^{52} + 36 q^{55} - 16 q^{57} + 20 q^{58} - 4 q^{60} - 40 q^{61} + 12 q^{63} - 24 q^{66} - 40 q^{67} - 12 q^{70} + 8 q^{72} - 4 q^{73} - 28 q^{75} - 16 q^{76} - 8 q^{78} + 28 q^{81} + 16 q^{82} + 24 q^{85} - 20 q^{87} - 12 q^{88} + 8 q^{90} + 48 q^{91} + 8 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 + 12 * q^7 + 4 * q^10 - 4 * q^12 + 8 * q^13 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^21 - 12 * q^22 - 16 * q^25 + 4 * q^27 + 12 * q^28 + 12 * q^30 + 8 * q^31 - 12 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 - 12 * q^42 + 8 * q^45 - 4 * q^46 - 4 * q^48 - 24 * q^51 - 8 * q^52 + 36 * q^55 - 16 * q^57 + 20 * q^58 - 4 * q^60 - 40 * q^61 + 12 * q^63 - 24 * q^66 - 40 * q^67 - 12 * q^70 + 8 * q^72 - 4 * q^73 - 28 * q^75 - 16 * q^76 - 8 * q^78 + 28 * q^81 + 16 * q^82 + 24 * q^85 - 20 * q^87 - 12 * q^88 + 8 * q^90 + 48 * q^91 + 8 * q^93 + 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$4$			1.00000i			0.500000i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.144370	−	0.989524i	$-0.453885\pi$
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.989524	−	0.144370i	$-0.0461154\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$			4.24264i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$11$			4.24264i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$12$	−1.70711	+	0.292893i	−0.492799	+	0.0845510i
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	4.24264			1.13389
$15$	3.41421	−	1.82843i	0.881546	−	0.472098i
$16$	−1.00000			−0.250000
$17$	4.24264	+	4.24264i	1.02899	+	1.02899i	0.999567	+	0.0294245i	$0.00936746\pi$
$17$	4.24264	+	4.24264i	1.02899	+	1.02899i	0.0294245	+	0.999567i	$0.490633\pi$
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$	6.00000	+	4.24264i	1.30931	+	0.925820i
$22$	−3.00000	+	3.00000i	−0.639602	+	0.639602i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$	−1.41421	−	1.00000i	−0.288675	−	0.204124i
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$			2.82843i			0.554700i
$27$	−2.53553	−	4.53553i	−0.487964	−	0.872864i
$28$	3.00000	+	3.00000i	0.566947	+	0.566947i
$29$	7.07107			1.31306			0.656532	−	0.754298i	$-0.272023\pi$
$29$	7.07107			1.31306			0.656532	+	0.754298i	$0.272023\pi$
$30$	3.70711	+	1.12132i	0.676822	+	0.204724i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−7.24264	+	1.24264i	−1.26078	+	0.216316i
$34$			6.00000i			1.02899i
$35$	−8.48528	−	4.24264i	−1.43427	−	0.717137i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	6.00000	−	6.00000i	0.986394	−	0.986394i	−0.0135147	−	0.999909i	$-0.504302\pi$
$37$	6.00000	−	6.00000i	0.986394	−	0.986394i	0.999909	+	0.0135147i	$0.00430201\pi$
$38$	−2.82843	+	2.82843i	−0.458831	+	0.458831i
$39$	−2.82843	+	4.00000i	−0.452911	+	0.640513i
$40$	2.00000	+	1.00000i	0.316228	+	0.158114i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	1.24264	+	7.24264i	0.191744	+	1.11756i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	−4.24264			−0.639602
$45$	4.12132	+	5.29289i	0.614370	+	0.789018i
$46$	−1.00000			−0.147442
$47$	−8.48528	−	8.48528i	−1.23771	−	1.23771i	−0.960936	−	0.276769i	$-0.910736\pi$
$47$	−8.48528	−	8.48528i	−1.23771	−	1.23771i	−0.276769	−	0.960936i	$-0.589264\pi$
$48$	−0.292893	−	1.70711i	−0.0422755	−	0.246400i
$49$		−	11.0000i		−	1.57143i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$	−6.00000	+	8.48528i	−0.840168	+	1.18818i
$52$	−2.00000	+	2.00000i	−0.277350	+	0.277350i
$53$	2.82843	−	2.82843i	0.388514	−	0.388514i	−0.485643	−	0.874157i	$-0.661414\pi$
$53$	2.82843	−	2.82843i	0.388514	−	0.388514i	0.874157	+	0.485643i	$0.161414\pi$
$54$	1.41421	−	5.00000i	0.192450	−	0.680414i
$55$	9.00000	−	3.00000i	1.21356	−	0.404520i
$56$			4.24264i			0.566947i
$57$	−6.82843	+	1.17157i	−0.904447	+	0.155179i
$58$	5.00000	+	5.00000i	0.656532	+	0.656532i
$59$	−1.41421			−0.184115			−0.0920575	−	0.995754i	$-0.529344\pi$
$59$	−1.41421			−0.184115			−0.0920575	+	0.995754i	$0.529344\pi$
$60$	1.82843	+	3.41421i	0.236049	+	0.440773i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	1.41421	+	1.41421i	0.179605	+	0.179605i
$63$	−5.48528	+	11.4853i	−0.691080	+	1.44701i
$64$		−	1.00000i		−	0.125000i
$65$	2.82843	−	5.65685i	0.350823	−	0.701646i
$66$	−6.00000	−	4.24264i	−0.738549	−	0.522233i
$67$	−10.0000	+	10.0000i	−1.22169	+	1.22169i	−0.254665	+	0.967029i	$0.581965\pi$
$67$	−10.0000	+	10.0000i	−1.22169	+	1.22169i	−0.967029	+	0.254665i	$0.918035\pi$
$68$	−4.24264	+	4.24264i	−0.514496	+	0.514496i
$69$	−1.41421	−	1.00000i	−0.170251	−	0.120386i
$70$	−3.00000	−	9.00000i	−0.358569	−	1.07571i
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	8.48528			0.986394
$75$	−6.29289	−	5.94975i	−0.726641	−	0.687018i
$76$	−4.00000			−0.458831
$77$	12.7279	+	12.7279i	1.45048	+	1.45048i
$78$	−4.82843	+	0.828427i	−0.546712	+	0.0938009i
$79$		−	14.0000i		−	1.57512i	−0.616236	−	0.787562i	$-0.711343\pi$
$79$		−	14.0000i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$80$	0.707107	+	2.12132i	0.0790569	+	0.237171i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	4.00000	−	4.00000i	0.441726	−	0.441726i
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	−0.0664117	−	0.997792i	$-0.521155\pi$
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	0.997792	+	0.0664117i	$0.0211551\pi$
$84$	−4.24264	+	6.00000i	−0.462910	+	0.654654i
$85$	6.00000	−	12.0000i	0.650791	−	1.30158i
$86$		0			0
$87$	2.07107	+	12.0711i	0.222042	+	1.29415i
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	−11.3137			−1.19925			−0.599625	−	0.800281i	$-0.704684\pi$
$89$	−11.3137			−1.19925			−0.599625	+	0.800281i	$0.704684\pi$
$90$	−0.828427	+	6.65685i	−0.0873239	+	0.701694i
$91$	12.0000			1.25794
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$	0.585786	+	3.41421i	0.0607432	+	0.354037i
$94$		−	12.0000i		−	1.23771i
$95$	8.48528	−	2.82843i	0.870572	−	0.290191i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$	7.77817	−	7.77817i	0.785714	−	0.785714i
$99$	−4.24264	−	12.0000i	−0.426401	−	1.20605i
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$		−	12.7279i		−	1.26648i	−0.773957	−	0.633238i	$-0.781726\pi$
$101$		−	12.7279i		−	1.26648i	0.773957	−	0.633238i	$-0.218274\pi$
$102$	−10.2426	+	1.75736i	−1.01417	+	0.174005i
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	0.909145	−	0.416480i	$-0.136736\pi$
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	−0.416480	+	0.909145i	$0.636736\pi$
$104$	−2.82843			−0.277350
$105$	4.75736	−	15.7279i	0.464271	−	1.53489i
$106$	4.00000			0.388514
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	0.830481	−	0.557047i	$-0.188066\pi$
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	−0.557047	+	0.830481i	$0.688066\pi$
$108$	4.53553	−	2.53553i	0.436432	−	0.243982i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	8.48528	+	4.24264i	0.809040	+	0.404520i
$111$	12.0000	+	8.48528i	1.13899	+	0.805387i
$112$	−3.00000	+	3.00000i	−0.283473	+	0.283473i
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	−0.877920	−	0.478806i	$-0.841070\pi$
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	0.478806	+	0.877920i	$0.341070\pi$
$114$	−5.65685	−	4.00000i	−0.529813	−	0.374634i
$115$	2.00000	+	1.00000i	0.186501	+	0.0932505i
$116$			7.07107i			0.656532i
$117$	−7.65685	−	3.65685i	−0.707876	−	0.338076i
$118$	−1.00000	−	1.00000i	−0.0920575	−	0.0920575i
$119$	25.4558			2.33353
$120$	−1.12132	+	3.70711i	−0.102362	+	0.338411i
$121$	−7.00000			−0.636364
$122$	−7.07107	−	7.07107i	−0.640184	−	0.640184i
$123$	9.65685	−	1.65685i	0.870729	−	0.149394i
$124$			2.00000i			0.179605i
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$	−12.0000	+	4.24264i	−1.06904	+	0.377964i
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	6.00000	−	2.00000i	0.526235	−	0.175412i
$131$			1.41421i			0.123560i	0.998090	+	0.0617802i	$0.0196778\pi$
$131$			1.41421i			0.123560i	−0.998090	+	0.0617802i	$0.980322\pi$
$132$	−1.24264	−	7.24264i	−0.108158	−	0.630391i
$133$	12.0000	+	12.0000i	1.04053	+	1.04053i
$134$	−14.1421			−1.22169
$135$	−7.82843	+	8.58579i	−0.673764	+	0.738947i
$136$	−6.00000			−0.514496
$137$	1.41421	+	1.41421i	0.120824	+	0.120824i	0.764934	−	0.644109i	$-0.222772\pi$
$137$	1.41421	+	1.41421i	0.120824	+	0.120824i	−0.644109	+	0.764934i	$0.722772\pi$
$138$	−0.292893	−	1.70711i	−0.0249327	−	0.145319i
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$	4.24264	−	8.48528i	0.358569	−	0.717137i
$141$	12.0000	−	16.9706i	1.01058	−	1.42918i
$142$	−4.00000	+	4.00000i	−0.335673	+	0.335673i
$143$	−8.48528	+	8.48528i	−0.709575	+	0.709575i
$144$	2.82843	−	1.00000i	0.235702	−	0.0833333i
$145$	−5.00000	−	15.0000i	−0.415227	−	1.24568i
$146$		−	1.41421i		−	0.117041i
$147$	18.7782	−	3.22183i	1.54880	−	0.265732i
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$	−0.242641	−	8.65685i	−0.0198115	−	0.706829i
$151$	−24.0000			−1.95309			−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000			−1.95309			−0.976546	+	0.215308i	$0.930924\pi$
$152$	−2.82843	−	2.82843i	−0.229416	−	0.229416i
$153$	−16.2426	−	7.75736i	−1.31314	−	0.627145i
$154$			18.0000i			1.45048i
$155$	−1.41421	−	4.24264i	−0.113592	−	0.340777i
$156$	−4.00000	−	2.82843i	−0.320256	−	0.226455i
$157$	−12.0000	+	12.0000i	−0.957704	+	0.957704i	−0.999141	−	0.0414369i	$-0.986806\pi$
$157$	−12.0000	+	12.0000i	−0.957704	+	0.957704i	0.0414369	+	0.999141i	$0.486806\pi$
$158$	9.89949	−	9.89949i	0.787562	−	0.787562i
$159$	5.65685	+	4.00000i	0.448618	+	0.317221i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$			4.24264i			0.334367i
$162$	8.94975	+	0.949747i	0.703159	+	0.0746192i
$163$	16.0000	+	16.0000i	1.25322	+	1.25322i	0.954270	+	0.298947i	$0.0966354\pi$
$163$	16.0000	+	16.0000i	1.25322	+	1.25322i	0.298947	+	0.954270i	$0.403365\pi$
$164$	5.65685			0.441726
$165$	7.75736	+	14.4853i	0.603910	+	1.12768i
$166$	12.0000			0.931381
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$	−7.24264	+	1.24264i	−0.558782	+	0.0958718i
$169$		−	5.00000i		−	0.384615i
$170$	12.7279	−	4.24264i	0.976187	−	0.325396i
$171$	−4.00000	−	11.3137i	−0.305888	−	0.865181i
$172$		0			0
$173$	9.89949	−	9.89949i	0.752645	−	0.752645i	−0.222327	−	0.974972i	$-0.571365\pi$
$173$	9.89949	−	9.89949i	0.752645	−	0.752645i	0.974972	+	0.222327i	$0.0713654\pi$
$174$	−7.07107	+	10.0000i	−0.536056	+	0.758098i
$175$	−3.00000	+	21.0000i	−0.226779	+	1.58745i
$176$		−	4.24264i		−	0.319801i
$177$	−0.414214	−	2.41421i	−0.0311342	−	0.181463i
$178$	−8.00000	−	8.00000i	−0.599625	−	0.599625i
$179$	4.24264			0.317110			0.158555	−	0.987350i	$-0.449317\pi$
$179$	4.24264			0.317110			0.158555	+	0.987350i	$0.449317\pi$
$180$	−5.29289	+	4.12132i	−0.394509	+	0.307185i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	8.48528	+	8.48528i	0.628971	+	0.628971i
$183$	−2.92893	−	17.0711i	−0.216513	−	1.26193i
$184$		−	1.00000i		−	0.0737210i
$185$	−16.9706	−	8.48528i	−1.24770	−	0.623850i
$186$	−2.00000	+	2.82843i	−0.146647	+	0.207390i
$187$	−18.0000	+	18.0000i	−1.31629	+	1.31629i
$188$	8.48528	−	8.48528i	0.618853	−	0.618853i
$189$	−21.2132	−	6.00000i	−1.54303	−	0.436436i
$190$	8.00000	+	4.00000i	0.580381	+	0.290191i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	1.70711	−	0.292893i	0.123200	−	0.0211377i
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.996534	−	0.0831899i	$-0.973489\pi$
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.0831899	−	0.996534i	$-0.526511\pi$
$194$	−4.24264			−0.304604
$195$	10.4853	+	3.17157i	0.750867	+	0.227121i
$196$	11.0000			0.785714
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	0.336966	−	0.941517i	$-0.390599\pi$
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	−0.941517	+	0.336966i	$0.890599\pi$
$198$	5.48528	−	11.4853i	0.389822	−	0.816223i
$199$		−	8.00000i		−	0.567105i	−0.958957	−	0.283552i	$-0.908487\pi$
$199$		−	8.00000i		−	0.567105i	0.958957	−	0.283552i	$-0.0915130\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$	−20.0000	−	14.1421i	−1.41069	−	0.997509i
$202$	9.00000	−	9.00000i	0.633238	−	0.633238i
$203$	21.2132	−	21.2132i	1.48888	−	1.48888i
$204$	−8.48528	−	6.00000i	−0.594089	−	0.420084i
$205$	−12.0000	+	4.00000i	−0.838116	+	0.279372i
$206$			7.07107i			0.492665i
$207$	1.29289	−	2.70711i	0.0898623	−	0.188157i
$208$	−2.00000	−	2.00000i	−0.138675	−	0.138675i
$209$	−16.9706			−1.17388
$210$	14.4853	−	7.75736i	0.999579	−	0.535309i
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.82843	+	2.82843i	0.194257	+	0.194257i
$213$	−9.65685	+	1.65685i	−0.661677	+	0.113526i
$214$			4.00000i			0.273434i
$215$		0			0
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	6.00000	−	6.00000i	0.407307	−	0.407307i
$218$	4.24264	−	4.24264i	0.287348	−	0.287348i
$219$	1.41421	−	2.00000i	0.0955637	−	0.135147i
$220$	3.00000	+	9.00000i	0.202260	+	0.606780i
$221$			16.9706i			1.14156i
$222$	2.48528	+	14.4853i	0.166801	+	0.972188i
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	0.235307	−	0.971921i	$-0.424391\pi$
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	−0.971921	+	0.235307i	$0.924391\pi$
$224$	−4.24264			−0.283473
$225$	8.31371	−	12.4853i	0.554247	−	0.832352i
$226$	−6.00000			−0.399114
$227$	−9.89949	−	9.89949i	−0.657053	−	0.657053i	0.297629	−	0.954682i	$-0.403804\pi$
$227$	−9.89949	−	9.89949i	−0.657053	−	0.657053i	−0.954682	+	0.297629i	$0.903804\pi$
$228$	−1.17157	−	6.82843i	−0.0775893	−	0.452224i
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$	0.707107	+	2.12132i	0.0466252	+	0.139876i
$231$	−18.0000	+	25.4558i	−1.18431	+	1.67487i
$232$	−5.00000	+	5.00000i	−0.328266	+	0.328266i
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	−0.832288	−	0.554343i	$-0.812969\pi$
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	0.554343	+	0.832288i	$0.312969\pi$
$234$	−2.82843	−	8.00000i	−0.184900	−	0.522976i
$235$	−12.0000	+	24.0000i	−0.782794	+	1.56559i
$236$		−	1.41421i		−	0.0920575i
$237$	23.8995	−	4.10051i	1.55244	−	0.266356i
$238$	18.0000	+	18.0000i	1.16677	+	1.16677i
$239$	11.3137			0.731823			0.365911	−	0.930650i	$-0.380757\pi$
$239$	11.3137			0.731823			0.365911	+	0.930650i	$0.380757\pi$
$240$	−3.41421	+	1.82843i	−0.220387	+	0.118024i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−4.94975	−	4.94975i	−0.318182	−	0.318182i
$243$	11.7071	+	10.2929i	0.751011	+	0.660289i
$244$		−	10.0000i		−	0.640184i
$245$	−23.3345	+	7.77817i	−1.49079	+	0.496929i
$246$	8.00000	+	5.65685i	0.510061	+	0.360668i
$247$	−8.00000	+	8.00000i	−0.509028	+	0.509028i
$248$	−1.41421	+	1.41421i	−0.0898027	+	0.0898027i
$249$	16.9706	+	12.0000i	1.07547	+	0.760469i
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$			18.3848i			1.16044i	0.814461	+	0.580218i	$0.197033\pi$
$251$			18.3848i			1.16044i	−0.814461	+	0.580218i	$0.802967\pi$
$252$	−11.4853	−	5.48528i	−0.723505	−	0.345540i
$253$	−3.00000	−	3.00000i	−0.188608	−	0.188608i
$254$	−12.7279			−0.798621
$255$	22.2426	+	6.72792i	1.39289	+	0.421319i
$256$	1.00000			0.0625000
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	0.661622	−	0.749838i	$-0.269869\pi$
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	−0.749838	+	0.661622i	$0.769869\pi$
$258$		0			0
$259$		−	36.0000i		−	2.23693i
$260$	5.65685	+	2.82843i	0.350823	+	0.175412i
$261$	−20.0000	+	7.07107i	−1.23797	+	0.437688i
$262$	−1.00000	+	1.00000i	−0.0617802	+	0.0617802i
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.0475824	+	0.998867i	$0.515152\pi$
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.998867	+	0.0475824i	$0.984848\pi$
$264$	4.24264	−	6.00000i	0.261116	−	0.369274i
$265$	−8.00000	−	4.00000i	−0.491436	−	0.245718i
$266$			16.9706i			1.04053i
$267$	−3.31371	−	19.3137i	−0.202796	−	1.18198i
$268$	−10.0000	−	10.0000i	−0.610847	−	0.610847i
$269$	21.2132			1.29339			0.646696	−	0.762748i	$-0.276150\pi$
$269$	21.2132			1.29339			0.646696	+	0.762748i	$0.276150\pi$
$270$	−11.6066	+	0.535534i	−0.706355	+	0.0325916i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	−4.24264	−	4.24264i	−0.257248	−	0.257248i
$273$	3.51472	+	20.4853i	0.212720	+	1.23983i
$274$			2.00000i			0.120824i
$275$	−12.7279	−	16.9706i	−0.767523	−	1.02336i
$276$	1.00000	−	1.41421i	0.0601929	−	0.0851257i
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	−0.576653	−	0.816989i	$-0.695641\pi$
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	0.816989	+	0.576653i	$0.195641\pi$
$278$	8.48528	−	8.48528i	0.508913	−	0.508913i
$279$	−5.65685	+	2.00000i	−0.338667	+	0.119737i
$280$	9.00000	−	3.00000i	0.537853	−	0.179284i
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$	20.4853	−	3.51472i	1.21988	−	0.209298i
$283$	18.0000	+	18.0000i	1.06999	+	1.06999i	0.997359	+	0.0726300i	$0.0231392\pi$
$283$	18.0000	+	18.0000i	1.06999	+	1.06999i	0.0726300	+	0.997359i	$0.476861\pi$
$284$	−5.65685			−0.335673
$285$	7.31371	+	13.6569i	0.433227	+	0.808962i
$286$	−12.0000			−0.709575
$287$	−16.9706	−	16.9706i	−1.00174	−	1.00174i
$288$	2.70711	+	1.29289i	0.159518	+	0.0761845i
$289$			19.0000i			1.11765i
$290$	7.07107	−	14.1421i	0.415227	−	0.830455i
$291$	−6.00000	−	4.24264i	−0.351726	−	0.248708i
$292$	1.00000	−	1.00000i	0.0585206	−	0.0585206i
$293$	11.3137	−	11.3137i	0.660954	−	0.660954i	−0.294651	−	0.955605i	$-0.595203\pi$
$293$	11.3137	−	11.3137i	0.660954	−	0.660954i	0.955605	+	0.294651i	$0.0952034\pi$
$294$	15.5563	+	11.0000i	0.907265	+	0.641533i
$295$	1.00000	+	3.00000i	0.0582223	+	0.174667i
$296$			8.48528i			0.493197i
$297$	19.2426	−	10.7574i	1.11657	−	0.624205i
$298$	1.00000	+	1.00000i	0.0579284	+	0.0579284i
$299$	−2.82843			−0.163572
$300$	5.94975	−	6.29289i	0.343509	−	0.363320i
$301$		0			0
$302$	−16.9706	−	16.9706i	−0.976546	−	0.976546i
$303$	21.7279	−	3.72792i	1.24824	−	0.214164i
$304$		−	4.00000i		−	0.229416i
$305$	7.07107	+	21.2132i	0.404888	+	1.21466i
$306$	−6.00000	−	16.9706i	−0.342997	−	0.970143i
$307$	−2.00000	+	2.00000i	−0.114146	+	0.114146i	−0.761873	−	0.647727i	$-0.775720\pi$
$307$	−2.00000	+	2.00000i	−0.114146	+	0.114146i	0.647727	+	0.761873i	$0.275720\pi$
$308$	−12.7279	+	12.7279i	−0.725241	+	0.725241i
$309$	−7.07107	+	10.0000i	−0.402259	+	0.568880i
$310$	2.00000	−	4.00000i	0.113592	−	0.227185i
$311$		−	22.6274i		−	1.28308i	−0.767088	−	0.641542i	$-0.778295\pi$
$311$		−	22.6274i		−	1.28308i	0.767088	−	0.641542i	$-0.221705\pi$
$312$	−0.828427	−	4.82843i	−0.0469005	−	0.273356i
$313$	7.00000	+	7.00000i	0.395663	+	0.395663i	0.876700	−	0.481037i	$-0.159740\pi$
$313$	7.00000	+	7.00000i	0.395663	+	0.395663i	−0.481037	+	0.876700i	$0.659740\pi$
$314$	−16.9706			−0.957704
$315$	28.2426	+	3.51472i	1.59129	+	0.198032i
$316$	14.0000			0.787562
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	0.666276	−	0.745706i	$-0.267887\pi$
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	−0.745706	+	0.666276i	$0.767887\pi$
$318$	1.17157	+	6.82843i	0.0656985	+	0.382919i
$319$			30.0000i			1.67968i
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$	−4.00000	+	5.65685i	−0.223258	+	0.315735i
$322$	−3.00000	+	3.00000i	−0.167183	+	0.167183i
$323$	−16.9706	+	16.9706i	−0.944267	+	0.944267i
$324$	5.65685	+	7.00000i	0.314270	+	0.388889i
$325$	−14.0000	−	2.00000i	−0.776580	−	0.110940i
$326$			22.6274i			1.25322i
$327$	10.2426	−	1.75736i	0.566419	−	0.0971822i
$328$	4.00000	+	4.00000i	0.220863	+	0.220863i
$329$	−50.9117			−2.80685
$330$	−4.75736	+	15.7279i	−0.261884	+	0.865794i
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$	8.48528	+	8.48528i	0.465690	+	0.465690i
$333$	−10.9706	+	22.9706i	−0.601183	+	1.25878i
$334$			12.0000i			0.656611i
$335$	28.2843	+	14.1421i	1.54533	+	0.772667i
$336$	−6.00000	−	4.24264i	−0.327327	−	0.231455i
$337$	9.00000	−	9.00000i	0.490261	−	0.490261i	−0.418127	−	0.908388i	$-0.637313\pi$
$337$	9.00000	−	9.00000i	0.490261	−	0.490261i	0.908388	+	0.418127i	$0.137313\pi$
$338$	3.53553	−	3.53553i	0.192308	−	0.192308i
$339$	−8.48528	−	6.00000i	−0.460857	−	0.325875i
$340$	12.0000	+	6.00000i	0.650791	+	0.325396i
$341$			8.48528i			0.459504i
$342$	5.17157	−	10.8284i	0.279647	−	0.585534i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$	−1.12132	+	3.70711i	−0.0603699	+	0.199584i
$346$	14.0000			0.752645
$347$	4.24264	+	4.24264i	0.227757	+	0.227757i	0.811755	−	0.583998i	$-0.198512\pi$
$347$	4.24264	+	4.24264i	0.227757	+	0.227757i	−0.583998	+	0.811755i	$0.698512\pi$
$348$	−12.0711	+	2.07107i	−0.647077	+	0.111021i
$349$		−	34.0000i		−	1.81998i	−0.414632	−	0.909989i	$-0.636090\pi$
$349$		−	34.0000i		−	1.81998i	0.414632	−	0.909989i	$-0.363910\pi$
$350$	−16.9706	+	12.7279i	−0.907115	+	0.680336i
$351$	4.00000	−	14.1421i	0.213504	−	0.754851i
$352$	3.00000	−	3.00000i	0.159901	−	0.159901i
$353$	−9.89949	+	9.89949i	−0.526897	+	0.526897i	−0.919646	−	0.392749i	$-0.871524\pi$
$353$	−9.89949	+	9.89949i	−0.526897	+	0.526897i	0.392749	+	0.919646i	$0.371524\pi$
$354$	1.41421	−	2.00000i	0.0751646	−	0.106299i
$355$	12.0000	−	4.00000i	0.636894	−	0.212298i
$356$		−	11.3137i		−	0.599625i
$357$	7.45584	+	43.4558i	0.394605	+	2.29993i
$358$	3.00000	+	3.00000i	0.158555	+	0.158555i
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$	−6.65685	−	0.828427i	−0.350847	−	0.0436619i
$361$	3.00000			0.157895
$362$	4.24264	+	4.24264i	0.222988	+	0.222988i
$363$	−2.05025	−	11.9497i	−0.107610	−	0.627199i
$364$			12.0000i			0.628971i
$365$	−1.41421	+	2.82843i	−0.0740233	+	0.148047i
$366$	10.0000	−	14.1421i	0.522708	−	0.739221i
$367$	17.0000	−	17.0000i	0.887393	−	0.887393i	−0.106879	−	0.994272i	$-0.534086\pi$
$367$	17.0000	−	17.0000i	0.887393	−	0.887393i	0.994272	+	0.106879i	$0.0340858\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	5.65685	+	16.0000i	0.294484	+	0.832927i
$370$	−6.00000	−	18.0000i	−0.311925	−	0.935775i
$371$		−	16.9706i		−	0.881068i
$372$	−3.41421	+	0.585786i	−0.177019	+	0.0303716i
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	0.158854	−	0.987302i	$-0.449220\pi$
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	−0.987302	+	0.158854i	$0.949220\pi$
$374$	−25.4558			−1.31629
$375$	−8.17157	+	17.5563i	−0.421978	+	0.906606i
$376$	12.0000			0.618853
$377$	14.1421	+	14.1421i	0.728357	+	0.728357i
$378$	−10.7574	−	19.2426i	−0.553299	−	0.989735i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	2.82843	+	8.48528i	0.145095	+	0.435286i
$381$	−18.0000	−	12.7279i	−0.922168	−	0.652071i
$382$	2.00000	−	2.00000i	0.102329	−	0.102329i
$383$	−5.65685	+	5.65685i	−0.289052	+	0.289052i	−0.836705	−	0.547653i	$-0.815521\pi$
$383$	−5.65685	+	5.65685i	−0.289052	+	0.289052i	0.547653	+	0.836705i	$0.315521\pi$
$384$	1.41421	+	1.00000i	0.0721688	+	0.0510310i
$385$	18.0000	−	36.0000i	0.917365	−	1.83473i
$386$		−	21.2132i		−	1.07972i
$387$		0			0
$388$	−3.00000	−	3.00000i	−0.152302	−	0.152302i
$389$	−1.41421			−0.0717035			−0.0358517	−	0.999357i	$-0.511414\pi$
$389$	−1.41421			−0.0717035			−0.0358517	+	0.999357i	$0.511414\pi$
$390$	5.17157	+	9.65685i	0.261873	+	0.488994i
$391$	−6.00000			−0.303433
$392$	7.77817	+	7.77817i	0.392857	+	0.392857i
$393$	−2.41421	+	0.414214i	−0.121781	+	0.0208943i
$394$		−	12.0000i		−	0.604551i
$395$	−29.6985	+	9.89949i	−1.49429	+	0.498098i
$396$	12.0000	−	4.24264i	0.603023	−	0.213201i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	5.65685	−	5.65685i	0.283552	−	0.283552i
$399$	−16.9706	+	24.0000i	−0.849591	+	1.20150i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$			22.6274i			1.12996i	0.825105	+	0.564980i	$0.191116\pi$
$401$			22.6274i			1.12996i	−0.825105	+	0.564980i	$0.808884\pi$
$402$	−4.14214	−	24.1421i	−0.206591	−	1.20410i
$403$	4.00000	+	4.00000i	0.199254	+	0.199254i
$404$	12.7279			0.633238
$405$	−16.9497	−	10.8492i	−0.842240	−	0.539103i
$406$	30.0000			1.48888
$407$	25.4558	+	25.4558i	1.26180	+	1.26180i
$408$	−1.75736	−	10.2426i	−0.0870023	−	0.507086i
$409$		−	8.00000i		−	0.395575i	−0.980245	−	0.197787i	$-0.936624\pi$
$409$		−	8.00000i		−	0.395575i	0.980245	−	0.197787i	$-0.0633755\pi$
$410$	−11.3137	−	5.65685i	−0.558744	−	0.279372i
$411$	−2.00000	+	2.82843i	−0.0986527	+	0.139516i
$412$	−5.00000	+	5.00000i	−0.246332	+	0.246332i
$413$	−4.24264	+	4.24264i	−0.208767	+	0.208767i
$414$	2.82843	−	1.00000i	0.139010	−	0.0491473i
$415$	−24.0000	−	12.0000i	−1.17811	−	0.589057i
$416$		−	2.82843i		−	0.138675i
$417$	20.4853	−	3.51472i	1.00317	−	0.172117i
$418$	−12.0000	−	12.0000i	−0.586939	−	0.586939i
$419$	24.0416			1.17451			0.587255	−	0.809402i	$-0.300208\pi$
$419$	24.0416			1.17451			0.587255	+	0.809402i	$0.300208\pi$
$420$	15.7279	+	4.75736i	0.767444	+	0.232135i
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$	−2.82843	−	2.82843i	−0.137686	−	0.137686i
$423$	32.4853	+	15.5147i	1.57949	+	0.754351i
$424$			4.00000i			0.194257i
$425$	−29.6985	−	4.24264i	−1.44059	−	0.205798i
$426$	−8.00000	−	5.65685i	−0.387601	−	0.274075i
$427$	−30.0000	+	30.0000i	−1.45180	+	1.45180i
$428$	−2.82843	+	2.82843i	−0.136717	+	0.136717i
$429$	−16.9706	−	12.0000i	−0.819346	−	0.579365i
$430$		0			0
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$	2.53553	+	4.53553i	0.121991	+	0.218216i
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.999957	+	0.00923827i	$0.00294067\pi$
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.00923827	+	0.999957i	$0.497059\pi$
$434$	8.48528			0.407307
$435$	24.1421	−	12.9289i	1.15753	−	0.619895i
$436$	6.00000			0.287348
$437$	−2.82843	−	2.82843i	−0.135302	−	0.135302i
$438$	2.41421	−	0.414214i	0.115356	−	0.0197919i
$439$			8.00000i			0.381819i	0.981608	+	0.190910i	$0.0611437\pi$
$439$			8.00000i			0.381819i	−0.981608	+	0.190910i	$0.938856\pi$
$440$	−4.24264	+	8.48528i	−0.202260	+	0.404520i
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$	−12.0000	+	12.0000i	−0.570782	+	0.570782i
$443$	−21.2132	+	21.2132i	−1.00787	+	1.00787i	−0.00790092	+	0.999969i	$0.502515\pi$
$443$	−21.2132	+	21.2132i	−1.00787	+	1.00787i	−0.999969	+	0.00790092i	$0.997485\pi$
$444$	−8.48528	+	12.0000i	−0.402694	+	0.569495i
$445$	8.00000	+	24.0000i	0.379236	+	1.13771i
$446$		−	15.5563i		−	0.736614i
$447$	0.414214	+	2.41421i	0.0195916	+	0.114188i
$448$	−3.00000	−	3.00000i	−0.141737	−	0.141737i
$449$	−2.82843			−0.133482			−0.0667409	−	0.997770i	$-0.521260\pi$
$449$	−2.82843			−0.133482			−0.0667409	+	0.997770i	$0.521260\pi$
$450$	14.7071	−	2.94975i	0.693300	−	0.139052i
$451$	24.0000			1.13012
$452$	−4.24264	−	4.24264i	−0.199557	−	0.199557i
$453$	−7.02944	−	40.9706i	−0.330272	−	1.92496i
$454$		−	14.0000i		−	0.657053i
$455$	−8.48528	−	25.4558i	−0.397796	−	1.19339i
$456$	4.00000	−	5.65685i	0.187317	−	0.264906i
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	−0.263099	−	0.964769i	$-0.584744\pi$
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	0.964769	+	0.263099i	$0.0847444\pi$
$458$	7.07107	−	7.07107i	0.330409	−	0.330409i
$459$	8.48528	−	30.0000i	0.396059	−	1.40028i
$460$	−1.00000	+	2.00000i	−0.0466252	+	0.0932505i
$461$			12.7279i			0.592798i	0.955064	+	0.296399i	$0.0957859\pi$
$461$			12.7279i			0.592798i	−0.955064	+	0.296399i	$0.904214\pi$
$462$	−30.7279	+	5.27208i	−1.42959	+	0.245279i
$463$	−13.0000	−	13.0000i	−0.604161	−	0.604161i	0.337253	−	0.941414i	$-0.390502\pi$
$463$	−13.0000	−	13.0000i	−0.604161	−	0.604161i	−0.941414	+	0.337253i	$0.890502\pi$
$464$	−7.07107			−0.328266
$465$	6.82843	−	3.65685i	0.316661	−	0.169583i
$466$	−6.00000			−0.277945
$467$	14.1421	+	14.1421i	0.654420	+	0.654420i	0.954054	−	0.299634i	$-0.0968646\pi$
$467$	14.1421	+	14.1421i	0.654420	+	0.654420i	−0.299634	+	0.954054i	$0.596865\pi$
$468$	3.65685	−	7.65685i	0.169038	−	0.353938i
$469$			60.0000i			2.77054i
$470$	−25.4558	+	8.48528i	−1.17419	+	0.391397i
$471$	−24.0000	−	16.9706i	−1.10586	−	0.781962i
$472$	1.00000	−	1.00000i	0.0460287	−	0.0460287i
$473$		0			0
$474$	19.7990	+	14.0000i	0.909398	+	0.643041i
$475$	−12.0000	−	16.0000i	−0.550598	−	0.734130i
$476$			25.4558i			1.16677i
$477$	−5.17157	+	10.8284i	−0.236790	+	0.495800i
$478$	8.00000	+	8.00000i	0.365911	+	0.365911i
$479$	−2.82843			−0.129234			−0.0646171	−	0.997910i	$-0.520583\pi$
$479$	−2.82843			−0.129234			−0.0646171	+	0.997910i	$0.520583\pi$
$480$	−3.70711	−	1.12132i	−0.169206	−	0.0511810i
$481$	24.0000			1.09431
$482$		0			0
$483$	−7.24264	+	1.24264i	−0.329552	+	0.0565421i
$484$		−	7.00000i		−	0.318182i
$485$	8.48528	+	4.24264i	0.385297	+	0.192648i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	−9.00000	+	9.00000i	−0.407829	+	0.407829i	−0.880981	−	0.473152i	$-0.843116\pi$
$487$	−9.00000	+	9.00000i	−0.407829	+	0.407829i	0.473152	+	0.880981i	$0.343116\pi$
$488$	7.07107	−	7.07107i	0.320092	−	0.320092i
$489$	−22.6274	+	32.0000i	−1.02325	+	1.44709i
$490$	−22.0000	−	11.0000i	−0.993859	−	0.496929i
$491$		−	32.5269i		−	1.46792i	−0.679193	−	0.733959i	$-0.737670\pi$
$491$		−	32.5269i		−	1.46792i	0.679193	−	0.733959i	$-0.262330\pi$
$492$	1.65685	+	9.65685i	0.0746968	+	0.435365i
$493$	30.0000	+	30.0000i	1.35113	+	1.35113i
$494$	−11.3137			−0.509028
$495$	−22.4558	+	17.4853i	−1.00932	+	0.785905i
$496$	−2.00000			−0.0898027
$497$	16.9706	+	16.9706i	0.761234	+	0.761234i
$498$	3.51472	+	20.4853i	0.157498	+	0.917967i
$499$			8.00000i			0.358129i	0.983837	+	0.179065i	$0.0573071\pi$
$499$			8.00000i			0.358129i	−0.983837	+	0.179065i	$0.942693\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$	−12.0000	+	16.9706i	−0.536120	+	0.758189i
$502$	−13.0000	+	13.0000i	−0.580218	+	0.580218i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$	−4.24264	−	12.0000i	−0.188982	−	0.534522i
$505$	−27.0000	+	9.00000i	−1.20148	+	0.400495i
$506$		−	4.24264i		−	0.188608i
$507$	8.53553	−	1.46447i	0.379076	−	0.0650392i
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	−21.2132			−0.940259			−0.470129	−	0.882598i	$-0.655793\pi$
$509$	−21.2132			−0.940259			−0.470129	+	0.882598i	$0.655793\pi$
$510$	10.9706	+	20.4853i	0.485785	+	0.907104i
$511$	−6.00000			−0.265424
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	18.1421	−	10.1421i	0.800995	−	0.447786i
$514$		−	2.00000i		−	0.0882162i
$515$	7.07107	−	14.1421i	0.311588	−	0.623177i
$516$		0			0
$517$	36.0000	−	36.0000i	1.58328	−	1.58328i
$518$	25.4558	−	25.4558i	1.11847	−	1.11847i
$519$	19.7990	+	14.0000i	0.869079	+	0.614532i
$520$	2.00000	+	6.00000i	0.0877058	+	0.263117i
$521$		−	28.2843i		−	1.23916i	−0.784935	−	0.619578i	$-0.787304\pi$
$521$		−	28.2843i		−	1.23916i	0.784935	−	0.619578i	$-0.212696\pi$
$522$	−19.1421	−	9.14214i	−0.837829	−	0.400140i
$523$	18.0000	+	18.0000i	0.787085	+	0.787085i	0.981015	−	0.193930i	$-0.0621236\pi$
$523$	18.0000	+	18.0000i	0.787085	+	0.787085i	−0.193930	+	0.981015i	$0.562124\pi$
$524$	−1.41421			−0.0617802
$525$	−36.7279	+	1.02944i	−1.60294	+	0.0449283i
$526$	−24.0000			−1.04645
$527$	8.48528	+	8.48528i	0.369625	+	0.369625i
$528$	7.24264	−	1.24264i	0.315195	−	0.0540790i
$529$		−	1.00000i		−	0.0434783i
$530$	−2.82843	−	8.48528i	−0.122859	−	0.368577i
$531$	4.00000	−	1.41421i	0.173585	−	0.0613716i
$532$	−12.0000	+	12.0000i	−0.520266	+	0.520266i
$533$	11.3137	−	11.3137i	0.490051	−	0.490051i
$534$	11.3137	−	16.0000i	0.489592	−	0.692388i
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$		−	14.1421i		−	0.610847i
$537$	1.24264	+	7.24264i	0.0536239	+	0.312543i
$538$	15.0000	+	15.0000i	0.646696	+	0.646696i
$539$	46.6690			2.01018
$540$	−8.58579	−	7.82843i	−0.369473	−	0.336882i
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	11.3137	+	11.3137i	0.485965	+	0.485965i
$543$	1.75736	+	10.2426i	0.0754155	+	0.439554i
$544$		−	6.00000i		−	0.257248i
$545$	−12.7279	+	4.24264i	−0.545204	+	0.181735i
$546$	−12.0000	+	16.9706i	−0.513553	+	0.726273i
$547$	−18.0000	+	18.0000i	−0.769624	+	0.769624i	−0.978040	−	0.208416i	$-0.933169\pi$
$547$	−18.0000	+	18.0000i	−0.769624	+	0.769624i	0.208416	+	0.978040i	$0.433169\pi$
$548$	−1.41421	+	1.41421i	−0.0604122	+	0.0604122i
$549$	28.2843	−	10.0000i	1.20714	−	0.426790i
$550$	3.00000	−	21.0000i	0.127920	−	0.895443i
$551$			28.2843i			1.20495i
$552$	1.70711	−	0.292893i	0.0726593	−	0.0124664i
$553$	−42.0000	−	42.0000i	−1.78602	−	1.78602i
$554$	5.65685			0.240337
$555$	9.51472	−	31.4558i	0.403877	−	1.33523i
$556$	12.0000			0.508913
$557$	−16.9706	−	16.9706i	−0.719066	−	0.719066i	0.249348	−	0.968414i	$-0.419784\pi$
$557$	−16.9706	−	16.9706i	−0.719066	−	0.719066i	−0.968414	+	0.249348i	$0.919784\pi$
$558$	−5.41421	−	2.58579i	−0.229202	−	0.109465i
$559$		0			0
$560$	8.48528	+	4.24264i	0.358569	+	0.179284i
$561$	−36.0000	−	25.4558i	−1.51992	−	1.07475i
$562$	−4.00000	+	4.00000i	−0.168730	+	0.168730i
$563$	−4.24264	+	4.24264i	−0.178806	+	0.178806i	−0.790835	−	0.612029i	$-0.790353\pi$
$563$	−4.24264	+	4.24264i	−0.178806	+	0.178806i	0.612029	+	0.790835i	$0.290353\pi$
$564$	16.9706	+	12.0000i	0.714590	+	0.505291i
$565$	12.0000	+	6.00000i	0.504844	+	0.252422i
$566$			25.4558i			1.06999i
$567$	4.02944	−	37.9706i	0.169220	−	1.59461i
$568$	−4.00000	−	4.00000i	−0.167836	−	0.167836i
$569$	5.65685			0.237148			0.118574	−	0.992945i	$-0.462168\pi$
$569$	5.65685			0.237148			0.118574	+	0.992945i	$0.462168\pi$
$570$	−4.48528	+	14.8284i	−0.187868	+	0.621094i
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$	−8.48528	−	8.48528i	−0.354787	−	0.354787i
$573$	4.82843	−	0.828427i	0.201710	−	0.0346080i
$574$		−	24.0000i		−	1.00174i
$575$	0.707107	−	4.94975i	0.0294884	−	0.206419i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	−0.494502	−	0.869177i	$-0.664649\pi$
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	0.869177	+	0.494502i	$0.164649\pi$
$578$	−13.4350	+	13.4350i	−0.558824	+	0.558824i
$579$	21.2132	−	30.0000i	0.881591	−	1.24676i
$580$	15.0000	−	5.00000i	0.622841	−	0.207614i
$581$		−	50.9117i		−	2.11217i
$582$	−1.24264	−	7.24264i	−0.0515091	−	0.300217i
$583$	12.0000	+	12.0000i	0.496989	+	0.496989i
$584$	1.41421			0.0585206
$585$	−2.34315	+	18.8284i	−0.0968772	+	0.778460i
$586$	16.0000			0.660954
$587$	−8.48528	−	8.48528i	−0.350225	−	0.350225i	0.509968	−	0.860193i	$-0.329657\pi$
$587$	−8.48528	−	8.48528i	−0.350225	−	0.350225i	−0.860193	+	0.509968i	$0.829657\pi$
$588$	3.22183	+	18.7782i	0.132866	+	0.774399i
$589$			8.00000i			0.329634i
$590$	−1.41421	+	2.82843i	−0.0582223	+	0.116445i
$591$	12.0000	−	16.9706i	0.493614	−	0.698076i
$592$	−6.00000	+	6.00000i	−0.246598	+	0.246598i
$593$	18.3848	−	18.3848i	0.754972	−	0.754972i	−0.220430	−	0.975403i	$-0.570746\pi$
$593$	18.3848	−	18.3848i	0.754972	−	0.754972i	0.975403	+	0.220430i	$0.0707462\pi$
$594$	21.2132	+	6.00000i	0.870388	+	0.246183i
$595$	−18.0000	−	54.0000i	−0.737928	−	2.21378i
$596$			1.41421i			0.0579284i
$597$	13.6569	−	2.34315i	0.558938	−	0.0958986i
$598$	−2.00000	−	2.00000i	−0.0817861	−	0.0817861i
$599$	19.7990			0.808965			0.404482	−	0.914546i	$-0.367452\pi$
$599$	19.7990			0.808965			0.404482	+	0.914546i	$0.367452\pi$
$600$	8.65685	−	0.242641i	0.353415	−	0.00990576i
$601$	6.00000			0.244745			0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000			0.244745			0.122373	+	0.992484i	$0.460950\pi$
$602$		0			0
$603$	18.2843	−	38.2843i	0.744593	−	1.55906i
$604$		−	24.0000i		−	0.976546i
$605$	4.94975	+	14.8492i	0.201236	+	0.603708i
$606$	18.0000	+	12.7279i	0.731200	+	0.517036i
$607$	−27.0000	+	27.0000i	−1.09590	+	1.09590i	−0.101011	+	0.994885i	$0.532208\pi$
$607$	−27.0000	+	27.0000i	−1.09590	+	1.09590i	−0.994885	+	0.101011i	$0.967792\pi$
$608$	2.82843	−	2.82843i	0.114708	−	0.114708i
$609$	42.4264	+	30.0000i	1.71920	+	1.21566i
$610$	−10.0000	+	20.0000i	−0.404888	+	0.809776i
$611$		−	33.9411i		−	1.37311i
$612$	7.75736	−	16.2426i	0.313573	−	0.656570i
$613$	−26.0000	−	26.0000i	−1.05013	−	1.05013i	−0.998675	−	0.0514548i	$-0.983614\pi$
$613$	−26.0000	−	26.0000i	−1.05013	−	1.05013i	−0.0514548	−	0.998675i	$-0.516386\pi$
$614$	−2.82843			−0.114146
$615$	−10.3431	−	19.3137i	−0.417076	−	0.778804i
$616$	−18.0000			−0.725241
$617$	−29.6985	−	29.6985i	−1.19562	−	1.19562i	−0.975466	−	0.220150i	$-0.929345\pi$
$617$	−29.6985	−	29.6985i	−1.19562	−	1.19562i	−0.220150	−	0.975466i	$-0.570655\pi$
$618$	−12.0711	+	2.07107i	−0.485570	+	0.0833106i
$619$			44.0000i			1.76851i	0.467005	+	0.884255i	$0.345333\pi$
$619$			44.0000i			1.76851i	−0.467005	+	0.884255i	$0.654667\pi$
$620$	4.24264	−	1.41421i	0.170389	−	0.0567962i
$621$	5.00000	+	1.41421i	0.200643	+	0.0567504i
$622$	16.0000	−	16.0000i	0.641542	−	0.641542i
$623$	−33.9411	+	33.9411i	−1.35982	+	1.35982i
$624$	2.82843	−	4.00000i	0.113228	−	0.160128i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			9.89949i			0.395663i
$627$	−4.97056	−	28.9706i	−0.198505	−	1.15697i
$628$	−12.0000	−	12.0000i	−0.478852	−	0.478852i
$629$	50.9117			2.02998
$630$	17.4853	+	22.4558i	0.696630	+	0.894662i
$631$	−38.0000			−1.51276			−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000			−1.51276			−0.756378	+	0.654135i	$0.773033\pi$
$632$	9.89949	+	9.89949i	0.393781	+	0.393781i
$633$	−1.17157	−	6.82843i	−0.0465658	−	0.271406i
$634$		−	2.00000i		−	0.0794301i
$635$	25.4558	+	12.7279i	1.01018	+	0.505092i
$636$	−4.00000	+	5.65685i	−0.158610	+	0.224309i
$637$	22.0000	−	22.0000i	0.871672	−	0.871672i
$638$	−21.2132	+	21.2132i	−0.839839	+	0.839839i
$639$	−5.65685	−	16.0000i	−0.223782	−	0.632950i
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$		−	14.1421i		−	0.558581i	−0.960207	−	0.279290i	$-0.909901\pi$
$641$		−	14.1421i		−	0.558581i	0.960207	−	0.279290i	$-0.0900992\pi$
$642$	−6.82843	+	1.17157i	−0.269497	+	0.0462383i
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	0.815448	−	0.578831i	$-0.196491\pi$
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	−0.578831	+	0.815448i	$0.696491\pi$
$644$	−4.24264			−0.167183
$645$		0			0
$646$	−24.0000			−0.944267
$647$	−22.6274	−	22.6274i	−0.889576	−	0.889576i	0.104907	−	0.994482i	$-0.466546\pi$
$647$	−22.6274	−	22.6274i	−0.889576	−	0.889576i	−0.994482	+	0.104907i	$0.966546\pi$
$648$	−0.949747	+	8.94975i	−0.0373096	+	0.351579i
$649$		−	6.00000i		−	0.235521i
$650$	−8.48528	−	11.3137i	−0.332820	−	0.443760i
$651$	12.0000	+	8.48528i	0.470317	+	0.332564i
$652$	−16.0000	+	16.0000i	−0.626608	+	0.626608i
$653$	−24.0416	+	24.0416i	−0.940822	+	0.940822i	−0.998344	−	0.0575225i	$-0.981680\pi$
$653$	−24.0416	+	24.0416i	−0.940822	+	0.940822i	0.0575225	+	0.998344i	$0.481680\pi$
$654$	8.48528	+	6.00000i	0.331801	+	0.234619i
$655$	3.00000	−	1.00000i	0.117220	−	0.0390732i
$656$			5.65685i			0.220863i
$657$	3.82843	+	1.82843i	0.149361	+	0.0713337i
$658$	−36.0000	−	36.0000i	−1.40343	−	1.40343i
$659$	−43.8406			−1.70779			−0.853894	−	0.520447i	$-0.825765\pi$
$659$	−43.8406			−1.70779			−0.853894	+	0.520447i	$0.825765\pi$
$660$	−14.4853	+	7.75736i	−0.563839	+	0.301955i
$661$	26.0000			1.01128			0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000			1.01128			0.505641	+	0.862744i	$0.331256\pi$
$662$	2.82843	+	2.82843i	0.109930	+	0.109930i
$663$	−28.9706	+	4.97056i	−1.12512	+	0.193041i
$664$			12.0000i			0.465690i
$665$	16.9706	−	33.9411i	0.658090	−	1.31618i
$666$	−24.0000	+	8.48528i	−0.929981	+	0.328798i
$667$	−5.00000	+	5.00000i	−0.193601	+	0.193601i
$668$	−8.48528	+	8.48528i	−0.328305	+	0.328305i
$669$	15.5563	−	22.0000i	0.601443	−	0.850569i
$670$	10.0000	+	30.0000i	0.386334	+	1.15900i
$671$		−	42.4264i		−	1.63785i
$672$	−1.24264	−	7.24264i	−0.0479359	−	0.279391i
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	0.858963	−	0.512038i	$-0.171109\pi$
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	−0.512038	+	0.858963i	$0.671109\pi$
$674$	12.7279			0.490261
$675$	23.7487	+	10.5355i	0.914089	+	0.405513i
$676$	5.00000			0.192308
$677$	−4.24264	−	4.24264i	−0.163058	−	0.163058i	0.620862	−	0.783920i	$-0.286783\pi$
$677$	−4.24264	−	4.24264i	−0.163058	−	0.163058i	−0.783920	+	0.620862i	$0.786783\pi$
$678$	−1.75736	−	10.2426i	−0.0674910	−	0.393366i
$679$			18.0000i			0.690777i
$680$	4.24264	+	12.7279i	0.162698	+	0.488094i
$681$	14.0000	−	19.7990i	0.536481	−	0.758699i
$682$	−6.00000	+	6.00000i	−0.229752	+	0.229752i
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	−0.850559	−	0.525879i	$-0.823736\pi$
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	0.525879	+	0.850559i	$0.323736\pi$
$684$	11.3137	−	4.00000i	0.432590	−	0.152944i
$685$	2.00000	−	4.00000i	0.0764161	−	0.152832i
$686$		−	16.9706i		−	0.647939i
$687$	17.0711	−	2.92893i	0.651302	−	0.111746i
$688$		0			0
$689$	11.3137			0.431018
$690$	−3.41421	+	1.82843i	−0.129977	+	0.0696070i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	9.89949	+	9.89949i	0.376322	+	0.376322i
$693$	−48.7279	−	23.2721i	−1.85102	−	0.884033i
$694$			6.00000i			0.227757i
$695$	−25.4558	+	8.48528i	−0.965595	+	0.321865i
$696$	−10.0000	−	7.07107i	−0.379049	−	0.268028i
$697$	24.0000	−	24.0000i	0.909065	−	0.909065i
$698$	24.0416	−	24.0416i	0.909989	−	0.909989i
$699$	−8.48528	−	6.00000i	−0.320943	−	0.226941i
$700$	−21.0000	−	3.00000i	−0.793725	−	0.113389i
$701$			43.8406i			1.65584i	0.560848	+	0.827919i	$0.310475\pi$
$701$			43.8406i			1.65584i	−0.560848	+	0.827919i	$0.689525\pi$
$702$	12.8284	−	7.17157i	0.484178	−	0.270674i
$703$	24.0000	+	24.0000i	0.905177	+	0.905177i
$704$	4.24264			0.159901
$705$	−44.4853	−	13.4558i	−1.67541	−	0.506776i
$706$	−14.0000			−0.526897
$707$	−38.1838	−	38.1838i	−1.43605	−	1.43605i
$708$	2.41421	−	0.414214i	0.0907317	−	0.0155671i
$709$		−	18.0000i		−	0.676004i	−0.941145	−	0.338002i	$-0.890249\pi$
$709$		−	18.0000i		−	0.676004i	0.941145	−	0.338002i	$-0.109751\pi$
$710$	11.3137	+	5.65685i	0.424596	+	0.212298i
$711$	14.0000	+	39.5980i	0.525041	+	1.48504i
$712$	8.00000	−	8.00000i	0.299813	−	0.299813i
$713$	−1.41421	+	1.41421i	−0.0529627	+	0.0529627i
$714$	−25.4558	+	36.0000i	−0.952661	+	1.34727i
$715$	24.0000	+	12.0000i	0.897549	+	0.448775i
$716$			4.24264i			0.158555i
$717$	3.31371	+	19.3137i	0.123753	+	0.721284i
$718$	8.00000	+	8.00000i	0.298557	+	0.298557i
$719$	−31.1127			−1.16031			−0.580154	−	0.814507i	$-0.697008\pi$
$719$	−31.1127			−1.16031			−0.580154	+	0.814507i	$0.697008\pi$
$720$	−4.12132	−	5.29289i	−0.153593	−	0.197254i
$721$	30.0000			1.11726
$722$	2.12132	+	2.12132i	0.0789474	+	0.0789474i
$723$		0			0
$724$			6.00000i			0.222988i
$725$	−28.2843	+	21.2132i	−1.05045	+	0.787839i
$726$	7.00000	−	9.89949i	0.259794	−	0.367405i
$727$	−27.0000	+	27.0000i	−1.00137	+	1.00137i	−0.00137552	+	0.999999i	$0.500438\pi$
$727$	−27.0000	+	27.0000i	−1.00137	+	1.00137i	−0.999999	+	0.00137552i	$0.999562\pi$
$728$	−8.48528	+	8.48528i	−0.314485	+	0.314485i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−3.00000	+	1.00000i	−0.111035	+	0.0370117i
$731$		0			0
$732$	17.0711	−	2.92893i	0.630965	−	0.108256i
$733$	14.0000	+	14.0000i	0.517102	+	0.517102i	0.916693	−	0.399592i	$-0.130848\pi$
$733$	14.0000	+	14.0000i	0.517102	+	0.517102i	−0.399592	+	0.916693i	$0.630848\pi$
$734$	24.0416			0.887393
$735$	−20.1127	−	37.5563i	−0.741868	−	1.38529i
$736$	1.00000			0.0368605
$737$	−42.4264	−	42.4264i	−1.56280	−	1.56280i
$738$	−7.31371	+	15.3137i	−0.269221	+	0.563705i
$739$			24.0000i			0.882854i	0.897297	+	0.441427i	$0.145528\pi$
$739$			24.0000i			0.882854i	−0.897297	+	0.441427i	$0.854472\pi$
$740$	8.48528	−	16.9706i	0.311925	−	0.623850i
$741$	−16.0000	−	11.3137i	−0.587775	−	0.415619i
$742$	12.0000	−	12.0000i	0.440534	−	0.440534i
$743$	−31.1127	+	31.1127i	−1.14141	+	1.14141i	−0.153222	+	0.988192i	$0.548965\pi$
$743$	−31.1127	+	31.1127i	−1.14141	+	1.14141i	−0.988192	+	0.153222i	$0.951035\pi$
$744$	−2.82843	−	2.00000i	−0.103695	−	0.0733236i
$745$	−1.00000	−	3.00000i	−0.0366372	−	0.109911i
$746$		−	22.6274i		−	0.828449i
$747$	−15.5147	+	32.4853i	−0.567654	+	1.18857i
$748$	−18.0000	−	18.0000i	−0.658145	−	0.658145i
$749$	16.9706			0.620091
$750$	−18.1924	+	6.63604i	−0.664292	+	0.242314i
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$	8.48528	+	8.48528i	0.309426	+	0.309426i
$753$	−31.3848	+	5.38478i	−1.14372	+	0.196232i
$754$			20.0000i			0.728357i
$755$	16.9706	+	50.9117i	0.617622	+	1.85287i
$756$	6.00000	−	21.2132i	0.218218	−	0.771517i
$757$	10.0000	−	10.0000i	0.363456	−	0.363456i	−0.501628	−	0.865084i	$-0.667265\pi$
$757$	10.0000	−	10.0000i	0.363456	−	0.363456i	0.865084	+	0.501628i	$0.167265\pi$
$758$		0			0
$759$	4.24264	−	6.00000i	0.153998	−	0.217786i
$760$	−4.00000	+	8.00000i	−0.145095	+	0.290191i
$761$		−	25.4558i		−	0.922774i	−0.887199	−	0.461387i	$-0.847352\pi$
$761$		−	25.4558i		−	0.922774i	0.887199	−	0.461387i	$-0.152648\pi$
$762$	−3.72792	−	21.7279i	−0.135048	−	0.787120i
$763$	−18.0000	−	18.0000i	−0.651644	−	0.651644i
$764$	2.82843			0.102329
$765$	−4.97056	+	39.9411i	−0.179711	+	1.44407i
$766$	−8.00000			−0.289052
$767$	−2.82843	−	2.82843i	−0.102129	−	0.102129i
$768$	0.292893	+	1.70711i	0.0105689	+	0.0615999i
$769$		−	18.0000i		−	0.649097i	−0.945869	−	0.324548i	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$	38.1838	−	12.7279i	1.37605	−	0.458682i
$771$	2.00000	−	2.82843i	0.0720282	−	0.101863i
$772$	15.0000	−	15.0000i	0.539862	−	0.539862i
$773$	−15.5563	+	15.5563i	−0.559523	+	0.559523i	−0.929172	−	0.369649i	$-0.879478\pi$
$773$	−15.5563	+	15.5563i	−0.559523	+	0.559523i	0.369649	+	0.929172i	$0.379478\pi$
$774$		0			0
$775$	−8.00000	+	6.00000i	−0.287368	+	0.215526i
$776$		−	4.24264i		−	0.152302i
$777$	61.4558	−	10.5442i	2.20472	−	0.378269i
$778$	−1.00000	−	1.00000i	−0.0358517	−	0.0358517i
$779$	22.6274			0.810711
$780$	−3.17157	+	10.4853i	−0.113561	+	0.375433i
$781$	−24.0000			−0.858788
$782$	−4.24264	−	4.24264i	−0.151717	−	0.151717i
$783$	−17.9289	−	32.0711i	−0.640728	−	1.14613i
$784$			11.0000i			0.392857i
$785$	33.9411	+	16.9706i	1.21141	+	0.605705i
$786$	−2.00000	−	1.41421i	−0.0713376	−	0.0504433i
$787$	18.0000	−	18.0000i	0.641631	−	0.641631i	−0.309326	−	0.950956i	$-0.600103\pi$
$787$	18.0000	−	18.0000i	0.641631	−	0.641631i	0.950956	+	0.309326i	$0.100103\pi$
$788$	8.48528	−	8.48528i	0.302276	−	0.302276i
$789$	−33.9411	−	24.0000i	−1.20834	−	0.854423i
$790$	−28.0000	−	14.0000i	−0.996195	−	0.498098i
$791$			25.4558i			0.905106i
$792$	11.4853	+	5.48528i	0.408112	+	0.194911i
$793$	−20.0000	−	20.0000i	−0.710221	−	0.710221i
$794$		0			0
$795$	4.48528	−	14.8284i	0.159077	−	0.525910i
$796$	8.00000			0.283552
$797$	1.41421	+	1.41421i	0.0500940	+	0.0500940i	0.731710	−	0.681616i	$-0.238723\pi$
$797$	1.41421	+	1.41421i	0.0500940	+	0.0500940i	−0.681616	+	0.731710i	$0.738723\pi$
$798$	−28.9706	+	4.97056i	−1.02555	+	0.175956i
$799$		−	72.0000i		−	2.54718i
$800$	4.94975	+	0.707107i	0.175000	+	0.0250000i
$801$	32.0000	−	11.3137i	1.13066	−	0.399750i
$802$	−16.0000	+	16.0000i	−0.564980	+	0.564980i
$803$	4.24264	−	4.24264i	0.149720	−	0.149720i
$804$	14.1421	−	20.0000i	0.498755	−	0.705346i
$805$	9.00000	−	3.00000i	0.317208	−	0.105736i
$806$			5.65685i			0.199254i
$807$	6.21320	+	36.2132i	0.218715	+	1.27477i
$808$	9.00000	+	9.00000i	0.316619	+	0.316619i
$809$	−5.65685			−0.198884			−0.0994422	−	0.995043i	$-0.531706\pi$
$809$	−5.65685			−0.198884			−0.0994422	+	0.995043i	$0.531706\pi$
$810$	−4.31371	−	19.6569i	−0.151568	−	0.690671i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	21.2132	+	21.2132i	0.744438	+	0.744438i
$813$	4.68629	+	27.3137i	0.164355	+	0.957934i
$814$			36.0000i			1.26180i
$815$	22.6274	−	45.2548i	0.792604	−	1.58521i
$816$	6.00000	−	8.48528i	0.210042	−	0.297044i
$817$		0			0
$818$	5.65685	−	5.65685i	0.197787	−	0.197787i
$819$	−33.9411	+	12.0000i	−1.18600	+	0.419314i
$820$	−4.00000	−	12.0000i	−0.139686	−	0.419058i
$821$		−	38.1838i		−	1.33262i	−0.745674	−	0.666311i	$-0.767872\pi$
$821$		−	38.1838i		−	1.33262i	0.745674	−	0.666311i	$-0.232128\pi$
$822$	−3.41421	+	0.585786i	−0.119084	+	0.0204316i
$823$	13.0000	+	13.0000i	0.453152	+	0.453152i	0.896399	−	0.443248i	$-0.146174\pi$
$823$	13.0000	+	13.0000i	0.453152	+	0.453152i	−0.443248	+	0.896399i	$0.646174\pi$
$824$	−7.07107			−0.246332
$825$	25.2426	−	26.6985i	0.878836	−	0.929522i
$826$	−6.00000			−0.208767
$827$	−4.24264	−	4.24264i	−0.147531	−	0.147531i	0.629483	−	0.777014i	$-0.283267\pi$
$827$	−4.24264	−	4.24264i	−0.147531	−	0.147531i	−0.777014	+	0.629483i	$0.783267\pi$
$828$	2.70711	+	1.29289i	0.0940785	+	0.0449311i
$829$		−	30.0000i		−	1.04194i	−0.853574	−	0.520972i	$-0.825570\pi$
$829$		−	30.0000i		−	1.04194i	0.853574	−	0.520972i	$-0.174430\pi$
$830$	−8.48528	−	25.4558i	−0.294528	−	0.883585i
$831$	8.00000	+	5.65685i	0.277517	+	0.196234i
$832$	2.00000	−	2.00000i	0.0693375	−	0.0693375i
$833$	46.6690	−	46.6690i	1.61699	−	1.61699i
$834$	16.9706	+	12.0000i	0.587643	+	0.415526i
$835$	12.0000	−	24.0000i	0.415277	−	0.830554i
$836$		−	16.9706i		−	0.586939i
$837$	−5.07107	−	9.07107i	−0.175282	−	0.313542i
$838$	17.0000	+	17.0000i	0.587255	+	0.587255i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	7.75736	+	14.4853i	0.267654	+	0.499790i
$841$	21.0000			0.724138
$842$	−21.2132	−	21.2132i	−0.731055	−	0.731055i
$843$	−9.65685	+	1.65685i	−0.332600	+	0.0570651i
$844$		−	4.00000i		−	0.137686i
$845$	−10.6066	+	3.53553i	−0.364878	+	0.121626i
$846$	12.0000	+	33.9411i	0.412568	+	1.16692i
$847$	−21.0000	+	21.0000i	−0.721569	+	0.721569i
$848$	−2.82843	+	2.82843i	−0.0971286	+	0.0971286i
$849$	−25.4558	+	36.0000i	−0.873642	+	1.23552i
$850$	−18.0000	−	24.0000i	−0.617395	−	0.823193i
$851$			8.48528i			0.290872i
$852$	−1.65685	−	9.65685i	−0.0567629	−	0.330838i
$853$	12.0000	+	12.0000i	0.410872	+	0.410872i	0.882042	−	0.471170i	$-0.156168\pi$
$853$	12.0000	+	12.0000i	0.410872	+	0.410872i	−0.471170	+	0.882042i	$0.656168\pi$
$854$	−42.4264			−1.45180
$855$	−21.1716	+	16.4853i	−0.724053	+	0.563785i
$856$	−4.00000			−0.136717
$857$	29.6985	+	29.6985i	1.01448	+	1.01448i	0.999894	+	0.0145873i	$0.00464345\pi$
$857$	29.6985	+	29.6985i	1.01448	+	1.01448i	0.0145873	+	0.999894i	$0.495357\pi$
$858$	−3.51472	−	20.4853i	−0.119991	−	0.699356i
$859$			32.0000i			1.09183i	0.837842	+	0.545913i	$0.183817\pi$
$859$			32.0000i			1.09183i	−0.837842	+	0.545913i	$0.816183\pi$
$860$		0			0
$861$	24.0000	−	33.9411i	0.817918	−	1.15671i
$862$	−4.00000	+	4.00000i	−0.136241	+	0.136241i
$863$	31.1127	−	31.1127i	1.05909	−	1.05909i	0.0609476	−	0.998141i	$-0.480588\pi$
$863$	31.1127	−	31.1127i	1.05909	−	1.05909i	0.998141	−	0.0609476i	$-0.0194123\pi$
$864$	−1.41421	+	5.00000i	−0.0481125	+	0.170103i
$865$	−28.0000	−	14.0000i	−0.952029	−	0.476014i
$866$			29.6985i			1.00920i
$867$	−32.4350	+	5.56497i	−1.10155	+	0.188996i
$868$	6.00000	+	6.00000i	0.203653	+	0.203653i
$869$	59.3970			2.01490
$870$	26.2132	+	7.92893i	0.888711	+	0.268816i
$871$	−40.0000			−1.35535
$872$	4.24264	+	4.24264i	0.143674	+	0.143674i
$873$	5.48528	−	11.4853i	0.185649	−	0.388718i
$874$		−	4.00000i		−	0.135302i
$875$	46.6690	−	8.48528i	1.57770	−	0.286855i
$876$	2.00000	+	1.41421i	0.0675737	+	0.0477818i
$877$	14.0000	−	14.0000i	0.472746	−	0.472746i	−0.430056	−	0.902802i	$-0.641506\pi$
$877$	14.0000	−	14.0000i	0.472746	−	0.472746i	0.902802	+	0.430056i	$0.141506\pi$
$878$	−5.65685	+	5.65685i	−0.190910	+	0.190910i
$879$	22.6274	+	16.0000i	0.763204	+	0.539667i
$880$	−9.00000	+	3.00000i	−0.303390	+	0.101130i
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$	−14.2218	+	29.7782i	−0.478874	+	1.00268i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−16.9706			−0.570782
$885$	−4.82843	+	2.58579i	−0.162306	+	0.0869203i
$886$	−30.0000			−1.00787
$887$	−19.7990	−	19.7990i	−0.664785	−	0.664785i	0.291719	−	0.956504i	$-0.405773\pi$
$887$	−19.7990	−	19.7990i	−0.664785	−	0.664785i	−0.956504	+	0.291719i	$0.905773\pi$
$888$	−14.4853	+	2.48528i	−0.486094	+	0.0834006i
$889$			54.0000i			1.81110i
$890$	−11.3137	+	22.6274i	−0.379236	+	0.758473i
$891$	24.0000	+	29.6985i	0.804030	+	0.994937i
$892$	11.0000	−	11.0000i	0.368307	−	0.368307i
$893$	33.9411	−	33.9411i	1.13580	−	1.13580i
$894$	−1.41421	+	2.00000i	−0.0472984	+	0.0668900i
$895$	−3.00000	−	9.00000i	−0.100279	−	0.300837i
$896$		−	4.24264i		−	0.141737i
$897$	−0.828427	−	4.82843i	−0.0276604	−	0.161216i
$898$	−2.00000	−	2.00000i	−0.0667409	−	0.0667409i
$899$	14.1421			0.471667
$900$	12.4853	+	8.31371i	0.416176	+	0.277124i
$901$	24.0000			0.799556
$902$	16.9706	+	16.9706i	0.565058	+	0.565058i
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$	−4.24264	−	12.7279i	−0.141030	−	0.423090i
$906$	24.0000	−	33.9411i	0.797347	−	1.12762i
$907$	32.0000	−	32.0000i	1.06254	−	1.06254i	0.0646335	−	0.997909i	$-0.479412\pi$
$907$	32.0000	−	32.0000i	1.06254	−	1.06254i	0.997909	−	0.0646335i	$-0.0205878\pi$
$908$	9.89949	−	9.89949i	0.328526	−	0.328526i
$909$	12.7279	+	36.0000i	0.422159	+	1.19404i
$910$	12.0000	−	24.0000i	0.397796	−	0.795592i
$911$			50.9117i			1.68678i	0.537302	+	0.843390i	$0.319443\pi$
$911$			50.9117i			1.68678i	−0.537302	+	0.843390i	$0.680557\pi$
$912$	6.82843	−	1.17157i	0.226112	−	0.0387947i
$913$	36.0000	+	36.0000i	1.19143	+	1.19143i
$914$	21.2132			0.701670
$915$	−34.1421	+	18.2843i	−1.12870	+	0.604459i
$916$	10.0000			0.330409
$917$	4.24264	+	4.24264i	0.140104	+	0.140104i
$918$	27.2132	−	15.2132i	0.898170	−	0.502111i
$919$			34.0000i			1.12156i	0.827966	+	0.560778i	$0.189498\pi$
$919$			34.0000i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$920$	−2.12132	+	0.707107i	−0.0699379	+	0.0233126i
$921$	−4.00000	−	2.82843i	−0.131804	−	0.0931998i
$922$	−9.00000	+	9.00000i	−0.296399	+	0.296399i
$923$	−11.3137	+	11.3137i	−0.372395	+	0.372395i
$924$	−25.4558	−	18.0000i	−0.837436	−	0.592157i
$925$	−6.00000	+	42.0000i	−0.197279	+	1.38095i
$926$		−	18.3848i		−	0.604161i
$927$	−19.1421	−	9.14214i	−0.628710	−	0.300267i
$928$	−5.00000	−	5.00000i	−0.164133	−	0.164133i
$929$	−2.82843			−0.0927977			−0.0463988	−	0.998923i	$-0.514775\pi$
$929$	−2.82843			−0.0927977			−0.0463988	+	0.998923i	$0.514775\pi$
$930$	7.41421	+	2.24264i	0.243122	+	0.0735391i
$931$	44.0000			1.44204
$932$	−4.24264	−	4.24264i	−0.138972	−	0.138972i
$933$	38.6274	−	6.62742i	1.26460	−	0.216972i
$934$			20.0000i			0.654420i
$935$	50.9117	+	25.4558i	1.66499	+	0.832495i
$936$	8.00000	−	2.82843i	0.261488	−	0.0924500i
$937$	−35.0000	+	35.0000i	−1.14340	+	1.14340i	−0.155576	+	0.987824i	$0.549723\pi$
$937$	−35.0000	+	35.0000i	−1.14340	+	1.14340i	−0.987824	+	0.155576i	$0.950277\pi$
$938$	−42.4264	+	42.4264i	−1.38527	+	1.38527i
$939$	−9.89949	+	14.0000i	−0.323058	+	0.456873i
$940$	−24.0000	−	12.0000i	−0.782794	−	0.391397i
$941$		−	32.5269i		−	1.06035i	−0.847889	−	0.530174i	$-0.822127\pi$
$941$		−	32.5269i		−	1.06035i	0.847889	−	0.530174i	$-0.177873\pi$
$942$	−4.97056	−	28.9706i	−0.161950	−	0.943912i
$943$	4.00000	+	4.00000i	0.130258	+	0.130258i
$944$	1.41421			0.0460287
$945$	2.27208	+	49.2426i	0.0739107	+	1.60186i
$946$		0			0
$947$	−12.7279	−	12.7279i	−0.413602	−	0.413602i	0.469389	−	0.882991i	$-0.344474\pi$
$947$	−12.7279	−	12.7279i	−0.413602	−	0.413602i	−0.882991	+	0.469389i	$0.844474\pi$
$948$	4.10051	+	23.8995i	0.133178	+	0.776220i
$949$		−	4.00000i		−	0.129845i
$950$	2.82843	−	19.7990i	0.0917663	−	0.642364i
$951$	2.00000	−	2.82843i	0.0648544	−	0.0917180i
$952$	−18.0000	+	18.0000i	−0.583383	+	0.583383i
$953$	−24.0416	+	24.0416i	−0.778785	+	0.778785i	−0.979624	−	0.200839i	$-0.935633\pi$
$953$	−24.0416	+	24.0416i	−0.778785	+	0.778785i	0.200839	+	0.979624i	$0.435633\pi$
$954$	−11.3137	+	4.00000i	−0.366295	+	0.129505i
$955$	−6.00000	+	2.00000i	−0.194155	+	0.0647185i
$956$			11.3137i			0.365911i
$957$	−51.2132	+	8.78680i	−1.65549	+	0.284037i
$958$	−2.00000	−	2.00000i	−0.0646171	−	0.0646171i
$959$	8.48528			0.274004
$960$	−1.82843	−	3.41421i	−0.0590122	−	0.110193i
$961$	−27.0000			−0.870968
$962$	16.9706	+	16.9706i	0.547153	+	0.547153i
$963$	−10.8284	−	5.17157i	−0.348941	−	0.166652i
$964$		0			0
$965$	−21.2132	+	42.4264i	−0.682877	+	1.36575i
$966$	−6.00000	−	4.24264i	−0.193047	−	0.136505i
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.0632081	−	0.998000i	$-0.479867\pi$
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.998000	−	0.0632081i	$-0.0201332\pi$
$968$	4.94975	−	4.94975i	0.159091	−	0.159091i
$969$	−33.9411	−	24.0000i	−1.09035	−	0.770991i
$970$	3.00000	+	9.00000i	0.0963242	+	0.288973i
$971$			32.5269i			1.04384i	0.852995	+	0.521919i	$0.174784\pi$
$971$			32.5269i			1.04384i	−0.852995	+	0.521919i	$0.825216\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$	−36.0000	−	36.0000i	−1.15411	−	1.15411i
$974$	−12.7279			−0.407829
$975$	−0.686292	−	24.4853i	−0.0219789	−	0.784157i
$976$	10.0000			0.320092
$977$	24.0416	+	24.0416i	0.769160	+	0.769160i	0.977959	−	0.208799i	$-0.0669554\pi$
$977$	24.0416	+	24.0416i	0.769160	+	0.769160i	−0.208799	+	0.977959i	$0.566955\pi$
$978$	−38.6274	+	6.62742i	−1.23517	+	0.211921i
$979$		−	48.0000i		−	1.53409i
$980$	−7.77817	−	23.3345i	−0.248465	−	0.745394i
$981$	6.00000	+	16.9706i	0.191565	+	0.541828i
$982$	23.0000	−	23.0000i	0.733959	−	0.733959i
$983$	−42.4264	+	42.4264i	−1.35319	+	1.35319i	−0.471127	+	0.882066i	$0.656153\pi$
$983$	−42.4264	+	42.4264i	−1.35319	+	1.35319i	−0.882066	+	0.471127i	$0.843847\pi$
$984$	−5.65685	+	8.00000i	−0.180334	+	0.255031i
$985$	−12.0000	+	24.0000i	−0.382352	+	0.764704i
$986$			42.4264i			1.35113i
$987$	−14.9117	−	86.9117i	−0.474644	−	2.76643i
$988$	−8.00000	−	8.00000i	−0.254514	−	0.254514i
$989$		0			0
$990$	−28.2426	−	3.51472i	−0.897610	−	0.111705i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−1.41421	−	1.41421i	−0.0449013	−	0.0449013i
$993$	1.17157	+	6.82843i	0.0371787	+	0.216694i
$994$			24.0000i			0.761234i
$995$	−16.9706	+	5.65685i	−0.538003	+	0.179334i
$996$	−12.0000	+	16.9706i	−0.380235	+	0.537733i
$997$	−14.0000	+	14.0000i	−0.443384	+	0.443384i	−0.893148	−	0.449763i	$-0.851508\pi$
$997$	−14.0000	+	14.0000i	−0.443384	+	0.443384i	0.449763	+	0.893148i	$0.351508\pi$
$998$	−5.65685	+	5.65685i	−0.179065	+	0.179065i
$999$	−42.4264	−	12.0000i	−1.34231	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.b.323.2	yes	4
3.2	odd	2	inner	690.2.i.b.323.1	yes	4
5.2	odd	4	inner	690.2.i.b.47.1	✓	4
15.2	even	4	inner	690.2.i.b.47.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.b.47.1	✓	4	5.2	odd	4	inner
690.2.i.b.47.2	yes	4	15.2	even	4	inner
690.2.i.b.323.1	yes	4	3.2	odd	2	inner
690.2.i.b.323.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(3.00000 - 3.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(3.00000 - 3.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(1.00000 - 2.00000i) q^{10} +4.24264i q^{11} +(-1.70711 + 0.292893i) q^{12} +(2.00000 + 2.00000i) q^{13} +4.24264 q^{14} +(3.41421 - 1.82843i) q^{15} -1.00000 q^{16} +(4.24264 + 4.24264i) q^{17} +(-2.70711 - 1.29289i) q^{18} +4.00000i q^{19} +(2.12132 - 0.707107i) q^{20} +(6.00000 + 4.24264i) q^{21} +(-3.00000 + 3.00000i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.41421 - 1.00000i) q^{24} +(-4.00000 + 3.00000i) q^{25} +2.82843i q^{26} +(-2.53553 - 4.53553i) q^{27} +(3.00000 + 3.00000i) q^{28} +7.07107 q^{29} +(3.70711 + 1.12132i) q^{30} +2.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.24264 + 1.24264i) q^{33} +6.00000i q^{34} +(-8.48528 - 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 - 6.00000i) q^{37} +(-2.82843 + 2.82843i) q^{38} +(-2.82843 + 4.00000i) q^{39} +(2.00000 + 1.00000i) q^{40} -5.65685i q^{41} +(1.24264 + 7.24264i) q^{42} -4.24264 q^{44} +(4.12132 + 5.29289i) q^{45} -1.00000 q^{46} +(-8.48528 - 8.48528i) q^{47} +(-0.292893 - 1.70711i) q^{48} -11.0000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-6.00000 + 8.48528i) q^{51} +(-2.00000 + 2.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +(1.41421 - 5.00000i) q^{54} +(9.00000 - 3.00000i) q^{55} +4.24264i q^{56} +(-6.82843 + 1.17157i) q^{57} +(5.00000 + 5.00000i) q^{58} -1.41421 q^{59} +(1.82843 + 3.41421i) q^{60} -10.0000 q^{61} +(1.41421 + 1.41421i) q^{62} +(-5.48528 + 11.4853i) q^{63} -1.00000i q^{64} +(2.82843 - 5.65685i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-10.0000 + 10.0000i) q^{67} +(-4.24264 + 4.24264i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(-3.00000 - 9.00000i) q^{70} +5.65685i q^{71} +(1.29289 - 2.70711i) q^{72} +(-1.00000 - 1.00000i) q^{73} +8.48528 q^{74} +(-6.29289 - 5.94975i) q^{75} -4.00000 q^{76} +(12.7279 + 12.7279i) q^{77} +(-4.82843 + 0.828427i) q^{78} -14.0000i q^{79} +(0.707107 + 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} +(8.48528 - 8.48528i) q^{83} +(-4.24264 + 6.00000i) q^{84} +(6.00000 - 12.0000i) q^{85} +(2.07107 + 12.0711i) q^{87} +(-3.00000 - 3.00000i) q^{88} -11.3137 q^{89} +(-0.828427 + 6.65685i) q^{90} +12.0000 q^{91} +(-0.707107 - 0.707107i) q^{92} +(0.585786 + 3.41421i) q^{93} -12.0000i q^{94} +(8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-3.00000 + 3.00000i) q^{97} +(7.77817 - 7.77817i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} + 12 q^{7}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^6 + 12 * q^7	\( 4 q + 4 q^{3} - 4 q^{6} + 12 q^{7} + 4 q^{10} - 4 q^{12} + 8 q^{13} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{21} - 12 q^{22} - 16 q^{25} + 4 q^{27} + 12 q^{28} + 12 q^{30} + 8 q^{31} - 12 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} - 12 q^{42} + 8 q^{45} - 4 q^{46} - 4 q^{48} - 24 q^{51} - 8 q^{52} + 36 q^{55} - 16 q^{57} + 20 q^{58} - 4 q^{60} - 40 q^{61} + 12 q^{63} - 24 q^{66} - 40 q^{67} - 12 q^{70} + 8 q^{72} - 4 q^{73} - 28 q^{75} - 16 q^{76} - 8 q^{78} + 28 q^{81} + 16 q^{82} + 24 q^{85} - 20 q^{87} - 12 q^{88} + 8 q^{90} + 48 q^{91} + 8 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 + 12 * q^7 + 4 * q^10 - 4 * q^12 + 8 * q^13 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^21 - 12 * q^22 - 16 * q^25 + 4 * q^27 + 12 * q^28 + 12 * q^30 + 8 * q^31 - 12 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 - 12 * q^42 + 8 * q^45 - 4 * q^46 - 4 * q^48 - 24 * q^51 - 8 * q^52 + 36 * q^55 - 16 * q^57 + 20 * q^58 - 4 * q^60 - 40 * q^61 + 12 * q^63 - 24 * q^66 - 40 * q^67 - 12 * q^70 + 8 * q^72 - 4 * q^73 - 28 * q^75 - 16 * q^76 - 8 * q^78 + 28 * q^81 + 16 * q^82 + 24 * q^85 - 20 * q^87 - 12 * q^88 + 8 * q^90 + 48 * q^91 + 8 * q^93 + 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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