LMFDB - Embedded newform 546.2.by.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	546.19
Dual form			546.2.by.a.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.106603 + 0.0285643i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-1.53649 + 2.15388i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.106603 + 0.0285643i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-1.53649 + 2.15388i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.110364 q^{10} +(-3.35328 - 3.35328i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.58290 + 0.403548i) q^{13} +(2.04160 - 1.68282i) q^{14} +(-0.0285643 - 0.106603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.45251 - 2.51582i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.89114 - 1.89114i) q^{19} +(-0.106603 - 0.0285643i) q^{20} +(-2.15388 - 1.53649i) q^{21} +(2.37113 + 4.10691i) q^{22} +(4.62851 - 2.67227i) q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.31958 + 2.49391i) q^{25} +(3.56526 + 0.537525i) q^{26} -1.00000i q^{27} +(-2.40758 + 1.09707i) q^{28} +(-0.975346 + 1.68935i) q^{29} +0.110364i q^{30} +(2.51818 - 9.39797i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(3.35328 - 3.35328i) q^{33} +(-2.05416 + 2.05416i) q^{34} +(0.102271 - 0.273500i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-1.97621 + 7.37530i) q^{37} +(1.33724 + 2.31616i) q^{38} +(-0.403548 - 3.58290i) q^{39} +(0.0955780 + 0.0551820i) q^{40} +(-6.25225 + 1.67529i) q^{41} +(1.68282 + 2.04160i) q^{42} +(-2.18502 + 1.26152i) q^{43} +(-1.22739 - 4.58067i) q^{44} +(0.106603 - 0.0285643i) q^{45} +(-5.16243 + 1.38327i) q^{46} +(-1.58056 - 5.89873i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-2.27841 - 6.61883i) q^{49} +(4.81786 - 1.29094i) q^{50} +(2.51582 + 1.45251i) q^{51} +(-3.30465 - 1.44197i) q^{52} +(-3.68798 - 6.38777i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(0.453255 + 0.261687i) q^{55} +(2.60949 - 0.436563i) q^{56} +(1.89114 - 1.89114i) q^{57} +(1.37935 - 1.37935i) q^{58} +(-0.816788 - 3.04829i) q^{59} +(0.0285643 - 0.106603i) q^{60} +7.91216i q^{61} +(-4.86475 + 8.42599i) q^{62} +(1.53649 - 2.15388i) q^{63} +1.00000i q^{64} +(0.370422 - 0.145363i) q^{65} +(-4.10691 + 2.37113i) q^{66} +(-5.73824 + 5.73824i) q^{67} +(2.51582 - 1.45251i) q^{68} +(2.67227 + 4.62851i) q^{69} +(-0.169573 + 0.237711i) q^{70} +(-5.73377 - 1.53636i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-5.15941 - 1.38246i) q^{73} +(3.81774 - 6.61251i) q^{74} +(-2.49391 - 4.31958i) q^{75} +(-0.692204 - 2.58334i) q^{76} +(12.3748 - 2.07029i) q^{77} +(-0.537525 + 3.56526i) q^{78} +(-1.92006 + 3.32564i) q^{79} +(-0.0780392 - 0.0780392i) q^{80} +1.00000 q^{81} +6.47281 q^{82} +(8.03572 + 8.03572i) q^{83} +(-1.09707 - 2.40758i) q^{84} +(-0.0829800 + 0.309686i) q^{85} +(2.43707 - 0.653011i) q^{86} +(-1.68935 - 0.975346i) q^{87} +4.74225i q^{88} +(-13.6924 - 3.66888i) q^{89} -0.110364 q^{90} +(4.63588 - 8.33718i) q^{91} +5.34454 q^{92} +(9.39797 + 2.51818i) q^{93} +6.10682i q^{94} +(0.255621 + 0.147583i) q^{95} +(0.965926 - 0.258819i) q^{96} +(-3.07814 + 11.4878i) q^{97} +(0.487697 + 6.98299i) q^{98} +(3.35328 + 3.35328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.106603	+	0.0285643i	−0.0476745	+	0.0127743i	−0.282577	−	0.959244i	$-0.591189\pi$
$5$	−0.106603	+	0.0285643i	−0.0476745	+	0.0127743i	0.234903	+	0.972019i	$0.424523\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	−1.53649	+	2.15388i	−0.580738	+	0.814091i
$7$	−1.53649	+	2.15388i	−0.580738	+	0.814091i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	0.110364			0.0349002
$11$	−3.35328	−	3.35328i	−1.01105	−	1.01105i	−0.999938	−	0.0111138i	$-0.996462\pi$
$11$	−3.35328	−	3.35328i	−1.01105	−	1.01105i	−0.0111138	−	0.999938i	$-0.503538\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.58290	+	0.403548i	−0.993717	+	0.111924i
$13$	−3.58290	+	0.403548i	−0.993717	+	0.111924i
$14$	2.04160	−	1.68282i	0.545640	−	0.449752i
$15$	−0.0285643	−	0.106603i	−0.00737527	−	0.0275249i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.45251	−	2.51582i	0.352286	−	0.610177i	−0.634364	−	0.773035i	$-0.718738\pi$
$17$	1.45251	−	2.51582i	0.352286	−	0.610177i	0.986650	+	0.162858i	$0.0520711\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	−1.89114	−	1.89114i	−0.433857	−	0.433857i	0.456081	−	0.889938i	$-0.349253\pi$
$19$	−1.89114	−	1.89114i	−0.433857	−	0.433857i	−0.889938	+	0.456081i	$0.849253\pi$
$20$	−0.106603	−	0.0285643i	−0.0238373	−	0.00638717i
$21$	−2.15388	−	1.53649i	−0.470015	−	0.335289i
$22$	2.37113	+	4.10691i	0.505526	+	0.875597i
$23$	4.62851	−	2.67227i	0.965111	−	0.557207i	0.0673690	−	0.997728i	$-0.478540\pi$
$23$	4.62851	−	2.67227i	0.965111	−	0.557207i	0.897742	+	0.440521i	$0.145206\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−4.31958	+	2.49391i	−0.863916	+	0.498782i
$26$	3.56526	+	0.537525i	0.699205	+	0.105417i
$27$		−	1.00000i		−	0.192450i
$28$	−2.40758	+	1.09707i	−0.454990	+	0.207327i
$29$	−0.975346	+	1.68935i	−0.181117	+	0.313704i	−0.942261	−	0.334879i	$-0.891305\pi$
$29$	−0.975346	+	1.68935i	−0.181117	+	0.313704i	0.761144	+	0.648583i	$0.224638\pi$
$30$			0.110364i			0.0201496i
$31$	2.51818	−	9.39797i	0.452278	−	1.68793i	−0.243690	−	0.969853i	$-0.578358\pi$
$31$	2.51818	−	9.39797i	0.452278	−	1.68793i	0.695968	−	0.718073i	$-0.254975\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	3.35328	−	3.35328i	0.583731	−	0.583731i
$34$	−2.05416	+	2.05416i	−0.352286	+	0.352286i
$35$	0.102271	−	0.273500i	0.0172869	−	0.0462299i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−1.97621	+	7.37530i	−0.324886	+	1.21249i	0.589540	+	0.807739i	$0.299309\pi$
$37$	−1.97621	+	7.37530i	−0.324886	+	1.21249i	−0.914426	+	0.404753i	$0.867358\pi$
$38$	1.33724	+	2.31616i	0.216928	+	0.375731i
$39$	−0.403548	−	3.58290i	−0.0646193	−	0.573723i
$40$	0.0955780	+	0.0551820i	0.0151122	+	0.00872504i
$41$	−6.25225	+	1.67529i	−0.976438	+	0.261636i	−0.711544	−	0.702642i	$-0.752004\pi$
$41$	−6.25225	+	1.67529i	−0.976438	+	0.261636i	−0.264894	+	0.964278i	$0.585337\pi$
$42$	1.68282	+	2.04160i	0.259664	+	0.315026i
$43$	−2.18502	+	1.26152i	−0.333212	+	0.192380i	−0.657266	−	0.753659i	$-0.728287\pi$
$43$	−2.18502	+	1.26152i	−0.333212	+	0.192380i	0.324054	+	0.946038i	$0.394954\pi$
$44$	−1.22739	−	4.58067i	−0.185035	−	0.690561i
$45$	0.106603	−	0.0285643i	0.0158915	−	0.00425812i
$46$	−5.16243	+	1.38327i	−0.761159	+	0.203952i
$47$	−1.58056	−	5.89873i	−0.230549	−	0.860419i	−0.980105	−	0.198479i	$-0.936400\pi$
$47$	−1.58056	−	5.89873i	−0.230549	−	0.860419i	0.749557	−	0.661940i	$-0.230267\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−2.27841	−	6.61883i	−0.325487	−	0.945546i
$50$	4.81786	−	1.29094i	0.681349	−	0.182567i
$51$	2.51582	+	1.45251i	0.352286	+	0.203392i
$52$	−3.30465	−	1.44197i	−0.458273	−	0.199965i
$53$	−3.68798	−	6.38777i	−0.506583	−	0.877428i	−0.999971	−	0.00761857i	$-0.997575\pi$
$53$	−3.68798	−	6.38777i	−0.506583	−	0.877428i	0.493388	−	0.869810i	$-0.335758\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	0.453255	+	0.261687i	0.0611170	+	0.0352859i
$56$	2.60949	−	0.436563i	0.348707	−	0.0583382i
$57$	1.89114	−	1.89114i	0.250487	−	0.250487i
$58$	1.37935	−	1.37935i	0.181117	−	0.181117i
$59$	−0.816788	−	3.04829i	−0.106337	−	0.396854i	0.892157	−	0.451726i	$-0.149192\pi$
$59$	−0.816788	−	3.04829i	−0.106337	−	0.396854i	−0.998493	+	0.0548721i	$0.982525\pi$
$60$	0.0285643	−	0.106603i	0.00368764	−	0.0137624i
$61$			7.91216i			1.01305i	0.862226	+	0.506524i	$0.169070\pi$
$61$			7.91216i			1.01305i	−0.862226	+	0.506524i	$0.830930\pi$
$62$	−4.86475	+	8.42599i	−0.617824	+	1.07010i
$63$	1.53649	−	2.15388i	0.193579	−	0.271364i
$64$			1.00000i			0.125000i
$65$	0.370422	−	0.145363i	0.0459452	−	0.0180300i
$66$	−4.10691	+	2.37113i	−0.505526	+	0.291866i
$67$	−5.73824	+	5.73824i	−0.701037	+	0.701037i	−0.964633	−	0.263596i	$-0.915091\pi$
$67$	−5.73824	+	5.73824i	−0.701037	+	0.701037i	0.263596	+	0.964633i	$0.415091\pi$
$68$	2.51582	−	1.45251i	0.305089	−	0.176143i
$69$	2.67227	+	4.62851i	0.321704	+	0.557207i
$70$	−0.169573	+	0.237711i	−0.0202678	+	0.0284119i
$71$	−5.73377	−	1.53636i	−0.680473	−	0.182332i	−0.0980050	−	0.995186i	$-0.531246\pi$
$71$	−5.73377	−	1.53636i	−0.680473	−	0.182332i	−0.582468	+	0.812854i	$0.697913\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−5.15941	−	1.38246i	−0.603864	−	0.161805i	−0.0560820	−	0.998426i	$-0.517861\pi$
$73$	−5.15941	−	1.38246i	−0.603864	−	0.161805i	−0.547782	+	0.836621i	$0.684528\pi$
$74$	3.81774	−	6.61251i	0.443803	−	0.768689i
$75$	−2.49391	−	4.31958i	−0.287972	−	0.498782i
$76$	−0.692204	−	2.58334i	−0.0794013	−	0.296330i
$77$	12.3748	−	2.07029i	1.41024	−	0.235932i
$78$	−0.537525	+	3.56526i	−0.0608627	+	0.403686i
$79$	−1.92006	+	3.32564i	−0.216024	+	0.374164i	−0.953589	−	0.301112i	$-0.902642\pi$
$79$	−1.92006	+	3.32564i	−0.216024	+	0.374164i	0.737565	+	0.675276i	$0.235975\pi$
$80$	−0.0780392	−	0.0780392i	−0.00872504	−	0.00872504i
$81$	1.00000			0.111111
$82$	6.47281			0.714802
$83$	8.03572	+	8.03572i	0.882035	+	0.882035i	0.993741	−	0.111707i	$-0.0356317\pi$
$83$	8.03572	+	8.03572i	0.882035	+	0.882035i	−0.111707	+	0.993741i	$0.535632\pi$
$84$	−1.09707	−	2.40758i	−0.119700	−	0.262688i
$85$	−0.0829800	+	0.309686i	−0.00900045	+	0.0335901i
$86$	2.43707	−	0.653011i	0.262796	−	0.0704159i
$87$	−1.68935	−	0.975346i	−0.181117	−	0.104568i
$88$			4.74225i			0.505526i
$89$	−13.6924	−	3.66888i	−1.45140	−	0.388900i	−0.554887	−	0.831926i	$-0.687239\pi$
$89$	−13.6924	−	3.66888i	−1.45140	−	0.388900i	−0.896509	+	0.443025i	$0.853905\pi$
$90$	−0.110364			−0.0116334
$91$	4.63588	−	8.33718i	0.485973	−	0.873974i
$92$	5.34454			0.557207
$93$	9.39797	+	2.51818i	0.974524	+	0.261123i
$94$			6.10682i			0.629870i
$95$	0.255621	+	0.147583i	0.0262261	+	0.0151417i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	−3.07814	+	11.4878i	−0.312538	+	1.16641i	0.613722	+	0.789522i	$0.289672\pi$
$97$	−3.07814	+	11.4878i	−0.312538	+	1.16641i	−0.926260	+	0.376886i	$0.876995\pi$
$98$	0.487697	+	6.98299i	0.0492648	+	0.705389i
$99$	3.35328	+	3.35328i	0.337017	+	0.337017i
$100$	−4.98782			−0.498782
$101$	−12.9430			−1.28788			−0.643938	−	0.765078i	$-0.722701\pi$
$101$	−12.9430			−1.28788			−0.643938	+	0.765078i	$0.722701\pi$
$102$	−2.05416	−	2.05416i	−0.203392	−	0.203392i
$103$	3.73968	−	6.47732i	0.368482	−	0.638229i	−0.620847	−	0.783932i	$-0.713211\pi$
$103$	3.73968	−	6.47732i	0.368482	−	0.638229i	0.989328	+	0.145703i	$0.0465444\pi$
$104$	2.81884	+	2.24814i	0.276410	+	0.220448i
$105$	0.273500	+	0.102271i	0.0266909	+	0.00998061i
$106$	1.90904	+	7.12464i	0.185422	+	0.692006i
$107$	2.95549	+	5.11907i	0.285718	+	0.494879i	0.972783	−	0.231717i	$-0.0744344\pi$
$107$	2.95549	+	5.11907i	0.285718	+	0.494879i	−0.687065	+	0.726596i	$0.741101\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	11.7740	+	3.15483i	1.12774	+	0.302178i	0.774014	−	0.633169i	$-0.218246\pi$
$109$	11.7740	+	3.15483i	1.12774	+	0.302178i	0.353731	+	0.935347i	$0.384913\pi$
$110$	−0.370082	−	0.370082i	−0.0352859	−	0.0352859i
$111$	−7.37530	−	1.97621i	−0.700033	−	0.187573i
$112$	−2.63356	−	0.253697i	−0.248848	−	0.0239721i
$113$	4.30290	+	7.45284i	0.404783	+	0.701104i	0.994296	−	0.106654i	$-0.0340139\pi$
$113$	4.30290	+	7.45284i	0.404783	+	0.701104i	−0.589514	+	0.807759i	$0.700681\pi$
$114$	−2.31616	+	1.33724i	−0.216928	+	0.125244i
$115$	−0.417084	+	0.417084i	−0.0388933	+	0.0388933i
$116$	−1.68935	+	0.975346i	−0.156852	+	0.0905586i
$117$	3.58290	−	0.403548i	0.331239	−	0.0373080i
$118$			3.15583i			0.290517i
$119$	3.18702	+	6.99407i	0.292154	+	0.641146i
$120$	−0.0551820	+	0.0955780i	−0.00503741	+	0.00872504i
$121$			11.4890i			1.04445i
$122$	2.04782	−	7.64256i	0.185401	−	0.691924i
$123$	−1.67529	−	6.25225i	−0.151055	−	0.563747i
$124$	6.87979	−	6.87979i	0.617824	−	0.617824i
$125$	0.779441	−	0.779441i	0.0697153	−	0.0697153i
$126$	−2.04160	+	1.68282i	−0.181880	+	0.149917i
$127$	16.1064	+	9.29904i	1.42921	+	0.825156i	0.997059	−	0.0766440i	$-0.0244205\pi$
$127$	16.1064	+	9.29904i	1.42921	+	0.825156i	0.432154	+	0.901800i	$0.357754\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−1.26152	−	2.18502i	−0.111071	−	0.192380i
$130$	−0.395423	+	0.0445371i	−0.0346809	+	0.00390617i
$131$	7.41047	+	4.27844i	0.647456	+	0.373809i	0.787481	−	0.616339i	$-0.211385\pi$
$131$	7.41047	+	4.27844i	0.647456	+	0.373809i	−0.140025	+	0.990148i	$0.544718\pi$
$132$	4.58067	−	1.22739i	0.398696	−	0.106830i
$133$	6.97899	−	1.16758i	0.605155	−	0.101242i
$134$	7.02788	−	4.05755i	0.607116	−	0.350519i
$135$	0.0285643	+	0.106603i	0.00245842	+	0.00917497i
$136$	−2.80604	+	0.751875i	−0.240616	+	0.0644728i
$137$	10.8544	−	2.90843i	0.927355	−	0.248484i	0.236629	−	0.971600i	$-0.423958\pi$
$137$	10.8544	−	2.90843i	0.927355	−	0.248484i	0.690726	+	0.723116i	$0.257291\pi$
$138$	−1.38327	−	5.16243i	−0.117752	−	0.439456i
$139$	−3.48145	+	2.01002i	−0.295293	+	0.170487i	−0.640326	−	0.768103i	$-0.721201\pi$
$139$	−3.48145	+	2.01002i	−0.295293	+	0.170487i	0.345034	+	0.938590i	$0.387868\pi$
$140$	0.225319	−	0.185722i	0.0190429	−	0.0156964i
$141$	5.89873	−	1.58056i	0.496763	−	0.133107i
$142$	5.14075	+	2.96802i	0.431402	+	0.249070i
$143$	13.3677	+	10.6612i	1.11786	+	0.891538i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.0557202	−	0.207951i	0.00462731	−	0.0172694i
$146$	4.62580	+	2.67071i	0.382834	+	0.221029i
$147$	6.61883	−	2.27841i	0.545912	−	0.187920i
$148$	−5.39909	+	5.39909i	−0.443803	+	0.443803i
$149$	−13.1240	+	13.1240i	−1.07516	+	1.07516i	−0.0782221	+	0.996936i	$0.524924\pi$
$149$	−13.1240	+	13.1240i	−1.07516	+	1.07516i	−0.996936	+	0.0782221i	$0.975076\pi$
$150$	1.29094	+	4.81786i	0.105405	+	0.393377i
$151$	2.83671	−	10.5867i	0.230848	−	0.861537i	−0.749128	−	0.662425i	$-0.769527\pi$
$151$	2.83671	−	10.5867i	0.230848	−	0.861537i	0.979977	−	0.199112i	$-0.0638059\pi$
$152$			2.67447i			0.216928i
$153$	−1.45251	+	2.51582i	−0.117429	+	0.203392i
$154$	−12.4890	−	1.20310i	−1.00639	−	0.0969482i
$155$			1.07379i			0.0862486i
$156$	1.44197	−	3.30465i	0.115450	−	0.264584i
$157$	19.7395	−	11.3966i	1.57538	−	0.909546i	0.579889	−	0.814696i	$-0.303096\pi$
$157$	19.7395	−	11.3966i	1.57538	−	0.909546i	0.995491	−	0.0948508i	$-0.0302374\pi$
$158$	2.71537	−	2.71537i	0.216024	−	0.216024i
$159$	6.38777	−	3.68798i	0.506583	−	0.292476i
$160$	0.0551820	+	0.0955780i	0.00436252	+	0.00755611i
$161$	−1.35589	+	14.0752i	−0.106859	+	1.10928i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−9.51293	−	9.51293i	−0.745110	−	0.745110i	0.228446	−	0.973557i	$-0.426636\pi$
$163$	−9.51293	−	9.51293i	−0.745110	−	0.745110i	−0.973557	+	0.228446i	$0.926636\pi$
$164$	−6.25225	−	1.67529i	−0.488219	−	0.130818i
$165$	−0.261687	+	0.453255i	−0.0203723	+	0.0352859i
$166$	−5.68211	−	9.84170i	−0.441017	−	0.763864i
$167$	−4.53469	−	16.9237i	−0.350905	−	1.30960i	−0.885560	−	0.464525i	$-0.846225\pi$
$167$	−4.53469	−	16.9237i	−0.350905	−	1.30960i	0.534655	−	0.845071i	$-0.320442\pi$
$168$	0.436563	+	2.60949i	0.0336816	+	0.201326i
$169$	12.6743	−	2.89174i	0.974946	−	0.222441i
$170$	0.160305	−	0.277657i	0.0122948	−	0.0212953i
$171$	1.89114	+	1.89114i	0.144619	+	0.144619i
$172$	−2.52304			−0.192380
$173$	−2.87726			−0.218754			−0.109377	−	0.994000i	$-0.534886\pi$
$173$	−2.87726			−0.218754			−0.109377	+	0.994000i	$0.534886\pi$
$174$	1.37935	+	1.37935i	0.104568	+	0.104568i
$175$	1.26539	−	13.1357i	0.0956548	−	0.992967i
$176$	1.22739	−	4.58067i	0.0925177	−	0.345281i
$177$	3.04829	−	0.816788i	0.229124	−	0.0613935i
$178$	12.2763	+	7.08773i	0.920148	+	0.531248i
$179$		−	2.00519i		−	0.149875i	−0.997188	−	0.0749374i	$-0.976124\pi$
$179$		−	2.00519i		−	0.149875i	0.997188	−	0.0749374i	$-0.0238757\pi$
$180$	0.106603	+	0.0285643i	0.00794575	+	0.00212906i
$181$	−6.98784			−0.519402			−0.259701	−	0.965689i	$-0.583624\pi$
$181$	−6.98784			−0.519402			−0.259701	+	0.965689i	$0.583624\pi$
$182$	−6.63574	+	6.85324i	−0.491874	+	0.507996i
$183$	−7.91216			−0.584883
$184$	−5.16243	−	1.38327i	−0.380580	−	0.101976i
$185$		−	0.842682i		−	0.0619552i
$186$	−8.42599	−	4.86475i	−0.617824	−	0.356701i
$187$	−13.3069	+	3.56558i	−0.973100	+	0.260741i
$188$	1.58056	−	5.89873i	0.115274	−	0.430209i
$189$	2.15388	+	1.53649i	0.156672	+	0.111763i
$190$	−0.208713	−	0.208713i	−0.0151417	−	0.0151417i
$191$	−16.8272			−1.21757			−0.608785	−	0.793335i	$-0.708343\pi$
$191$	−16.8272			−1.21757			−0.608785	+	0.793335i	$0.708343\pi$
$192$	−1.00000			−0.0721688
$193$	8.87988	+	8.87988i	0.639188	+	0.639188i	0.950355	−	0.311167i	$-0.100720\pi$
$193$	8.87988	+	8.87988i	0.639188	+	0.639188i	−0.311167	+	0.950355i	$0.600720\pi$
$194$	5.94652	−	10.2997i	0.426935	−	0.739473i
$195$	0.145363	+	0.370422i	0.0104096	+	0.0265265i
$196$	1.33625	−	6.87128i	0.0954466	−	0.490805i
$197$	5.73136	+	21.3897i	0.408343	+	1.52396i	0.797806	+	0.602914i	$0.205994\pi$
$197$	5.73136	+	21.3897i	0.408343	+	1.52396i	−0.389463	+	0.921042i	$0.627340\pi$
$198$	−2.37113	−	4.10691i	−0.168509	−	0.291866i
$199$	−0.0573426	+	0.0993202i	−0.00406491	+	0.00704062i	−0.868051	−	0.496476i	$-0.834627\pi$
$199$	−0.0573426	+	0.0993202i	−0.00406491	+	0.00704062i	0.863986	+	0.503516i	$0.167961\pi$
$200$	4.81786	+	1.29094i	0.340674	+	0.0912834i
$201$	−5.73824	−	5.73824i	−0.404744	−	0.404744i
$202$	12.5020	+	3.34989i	0.879636	+	0.235698i
$203$	−2.14005	−	4.69645i	−0.150202	−	0.329626i
$204$	1.45251	+	2.51582i	0.101696	+	0.176143i
$205$	0.618658	−	0.357183i	0.0432090	−	0.0249467i
$206$	−5.28871	+	5.28871i	−0.368482	+	0.368482i
$207$	−4.62851	+	2.67227i	−0.321704	+	0.185736i
$208$	−2.14093	−	2.90111i	−0.148447	−	0.201155i
$209$			12.6830i			0.877303i
$210$	−0.237711	−	0.169573i	−0.0164036	−	0.0117016i
$211$	−10.5071	+	18.1989i	−0.723340	+	1.25286i	0.236313	+	0.971677i	$0.424061\pi$
$211$	−10.5071	+	18.1989i	−0.723340	+	1.25286i	−0.959654	+	0.281185i	$0.909272\pi$
$212$		−	7.37597i		−	0.506583i
$213$	1.53636	−	5.73377i	0.105270	−	0.392871i
$214$	−1.52988	−	5.70958i	−0.104580	−	0.390299i
$215$	0.196896	−	0.196896i	0.0134282	−	0.0134282i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	16.3730	+	19.8637i	1.11147	+	1.34844i
$218$	−10.5563	−	6.09467i	−0.714961	−	0.412783i
$219$	1.38246	−	5.15941i	0.0934180	−	0.348641i
$220$	0.261687	+	0.453255i	0.0176429	+	0.0305585i
$221$	−4.18895	+	9.60010i	−0.281779	+	0.645772i
$222$	6.61251	+	3.81774i	0.443803	+	0.256230i
$223$	−22.4292	+	6.00988i	−1.50197	+	0.402451i	−0.913759	−	0.406257i	$-0.866834\pi$
$223$	−22.4292	+	6.00988i	−1.50197	+	0.402451i	−0.588210	+	0.808708i	$0.700167\pi$
$224$	2.47816	+	0.926668i	0.165579	+	0.0619156i
$225$	4.31958	−	2.49391i	0.287972	−	0.166261i
$226$	−2.22734	−	8.31256i	−0.148161	−	0.552943i
$227$	−14.0233	+	3.75754i	−0.930760	+	0.249396i	−0.692179	−	0.721726i	$-0.743349\pi$
$227$	−14.0233	+	3.75754i	−0.930760	+	0.249396i	−0.238581	+	0.971123i	$0.576682\pi$
$228$	2.58334	−	0.692204i	0.171086	−	0.0458423i
$229$	−6.31689	−	23.5749i	−0.417432	−	1.55788i	−0.779915	−	0.625886i	$-0.784738\pi$
$229$	−6.31689	−	23.5749i	−0.417432	−	1.55788i	0.362483	−	0.931990i	$-0.381929\pi$
$230$	0.510821	−	0.294923i	0.0336825	−	0.0194466i
$231$	2.07029	+	12.3748i	0.136215	+	0.814205i
$232$	1.88422	−	0.504876i	0.123705	−	0.0331468i
$233$	−17.0991	−	9.87216i	−1.12020	−	0.646746i	−0.178746	−	0.983895i	$-0.557204\pi$
$233$	−17.0991	−	9.87216i	−1.12020	−	0.646746i	−0.941451	+	0.337149i	$0.890537\pi$
$234$	−3.56526	−	0.537525i	−0.233068	−	0.0351391i
$235$	0.336987	+	0.583678i	0.0219826	+	0.0380749i
$236$	0.816788	−	3.04829i	0.0531684	−	0.198427i
$237$	−3.32564	−	1.92006i	−0.216024	−	0.124721i
$238$	−1.26823	−	7.58062i	−0.0822069	−	0.491378i
$239$	20.7785	−	20.7785i	1.34405	−	1.34405i	0.452069	−	0.891983i	$-0.350686\pi$
$239$	20.7785	−	20.7785i	1.34405	−	1.34405i	0.891983	−	0.452069i	$-0.149314\pi$
$240$	0.0780392	−	0.0780392i	0.00503741	−	0.00503741i
$241$	−2.79215	−	10.4204i	−0.179858	−	0.671240i	−0.995673	−	0.0929267i	$-0.970378\pi$
$241$	−2.79215	−	10.4204i	−0.179858	−	0.671240i	0.815815	−	0.578313i	$-0.196289\pi$
$242$	2.97357	−	11.0975i	0.191148	−	0.713374i
$243$			1.00000i			0.0641500i
$244$	−3.95608	+	6.85213i	−0.253262	+	0.438663i
$245$	0.431949	+	0.640509i	0.0275962	+	0.0409206i
$246$			6.47281i			0.412691i
$247$	7.53891	+	6.01258i	0.479689	+	0.382572i
$248$	−8.42599	+	4.86475i	−0.535051	+	0.308912i
$249$	−8.03572	+	8.03572i	−0.509243	+	0.509243i
$250$	−0.954616	+	0.551148i	−0.0603752	+	0.0348577i
$251$	4.95719	+	8.58610i	0.312895	+	0.541950i	0.978988	−	0.203919i	$-0.0653679\pi$
$251$	4.95719	+	8.58610i	0.312895	+	0.541950i	−0.666093	+	0.745869i	$0.732035\pi$
$252$	2.40758	−	1.09707i	0.151663	−	0.0691090i
$253$	−24.4816	−	6.55982i	−1.53914	−	0.412412i
$254$	−13.1508	−	13.1508i	−0.825156	−	0.825156i
$255$	−0.309686	−	0.0829800i	−0.0193933	−	0.00519641i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.93180	+	8.54213i	0.307637	+	0.532843i	0.977845	−	0.209330i	$-0.0671284\pi$
$257$	4.93180	+	8.54213i	0.307637	+	0.532843i	−0.670208	+	0.742174i	$0.733795\pi$
$258$	0.653011	+	2.43707i	0.0406547	+	0.151725i
$259$	−12.8491	−	15.5886i	−0.798405	−	0.968627i
$260$	0.393476	+	0.0593234i	0.0244024	+	0.00367908i
$261$	0.975346	−	1.68935i	0.0603724	−	0.104568i
$262$	−6.05062	−	6.05062i	−0.373809	−	0.373809i
$263$	−15.5169			−0.956815			−0.478408	−	0.878138i	$-0.658786\pi$
$263$	−15.5169			−0.956815			−0.478408	+	0.878138i	$0.658786\pi$
$264$	−4.74225			−0.291866
$265$	0.575614	+	0.575614i	0.0353597	+	0.0353597i
$266$	−7.04338	−	0.678505i	−0.431857	−	0.0416018i
$267$	3.66888	−	13.6924i	0.224532	−	0.837964i
$268$	−7.83858	+	2.10034i	−0.478817	+	0.128299i
$269$	−12.8554	−	7.42208i	−0.783809	−	0.452532i	0.0539698	−	0.998543i	$-0.482813\pi$
$269$	−12.8554	−	7.42208i	−0.783809	−	0.452532i	−0.837778	+	0.546011i	$0.816146\pi$
$270$		−	0.110364i		−	0.00671654i
$271$	−6.01472	−	1.61164i	−0.365368	−	0.0979002i	0.0714638	−	0.997443i	$-0.477233\pi$
$271$	−6.01472	−	1.61164i	−0.365368	−	0.0979002i	−0.436832	+	0.899543i	$0.643900\pi$
$272$	2.90502			0.176143
$273$	8.33718	+	4.63588i	0.504589	+	0.280576i
$274$	−11.2373			−0.678871
$275$	22.8475	+	6.12198i	1.37776	+	0.369169i
$276$			5.34454i			0.321704i
$277$	11.6414	+	6.72115i	0.699463	+	0.403835i	0.807147	−	0.590350i	$-0.201010\pi$
$277$	11.6414	+	6.72115i	0.699463	+	0.403835i	−0.107685	+	0.994185i	$0.534344\pi$
$278$	3.88305	−	1.04046i	0.232890	−	0.0624027i
$279$	−2.51818	+	9.39797i	−0.150759	+	0.562642i
$280$	−0.265710	+	0.121077i	−0.0158792	+	0.00723575i
$281$	18.2088	+	18.2088i	1.08625	+	1.08625i	0.995911	+	0.0903356i	$0.0287940\pi$
$281$	18.2088	+	18.2088i	1.08625	+	1.08625i	0.0903356	+	0.995911i	$0.471206\pi$
$282$	−6.10682			−0.363656
$283$	2.42771			0.144312			0.0721561	−	0.997393i	$-0.477012\pi$
$283$	2.42771			0.144312			0.0721561	+	0.997393i	$0.477012\pi$
$284$	−4.19741	−	4.19741i	−0.249070	−	0.249070i
$285$	−0.147583	+	0.255621i	−0.00874205	+	0.0151417i
$286$	−10.1528	−	13.7578i	−0.600350	−	0.813515i
$287$	5.99814	−	16.0407i	0.354059	−	0.946851i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	4.28042	+	7.41390i	0.251789	+	0.436112i
$290$	−0.107643	+	0.186443i	−0.00632102	+	0.0109483i
$291$	−11.4878	−	3.07814i	−0.673426	−	0.180444i
$292$	−3.77695	−	3.77695i	−0.221029	−	0.221029i
$293$	−26.4611	−	7.09023i	−1.54587	−	0.414216i	−0.617716	−	0.786401i	$-0.711942\pi$
$293$	−26.4611	−	7.09023i	−1.54587	−	0.414216i	−0.928158	+	0.372186i	$0.878609\pi$
$294$	−6.98299	+	0.487697i	−0.407256	+	0.0284430i
$295$	0.174145	+	0.301628i	0.0101391	+	0.0175614i
$296$	6.61251	−	3.81774i	0.384345	−	0.221901i
$297$	−3.35328	+	3.35328i	−0.194577	+	0.194577i
$298$	16.0735	−	9.28005i	0.931114	−	0.537579i
$299$	−15.5051	+	11.4423i	−0.896682	+	0.661725i
$300$		−	4.98782i		−	0.287972i
$301$	0.640087	−	6.64457i	0.0368940	−	0.382987i
$302$	−5.48010	+	9.49182i	−0.315344	+	0.546193i
$303$		−	12.9430i		−	0.743556i
$304$	0.692204	−	2.58334i	0.0397006	−	0.148165i
$305$	−0.226005	−	0.843463i	−0.0129410	−	0.0482966i
$306$	2.05416	−	2.05416i	0.117429	−	0.117429i
$307$	18.4157	−	18.4157i	1.05104	−	1.05104i	0.0524157	−	0.998625i	$-0.483308\pi$
$307$	18.4157	−	18.4157i	1.05104	−	1.05104i	0.998625	−	0.0524157i	$-0.0166921\pi$
$308$	11.7521	+	4.39449i	0.669637	+	0.250400i
$309$	6.47732	+	3.73968i	0.368482	+	0.212743i
$310$	0.277916	−	1.03720i	0.0157846	−	0.0589089i
$311$	−10.1803	−	17.6328i	−0.577270	−	0.999862i	−0.995791	−	0.0916542i	$-0.970785\pi$
$311$	−10.1803	−	17.6328i	−0.577270	−	0.999862i	0.418521	−	0.908207i	$-0.362549\pi$
$312$	−2.24814	+	2.81884i	−0.127276	+	0.159585i
$313$	3.12174	+	1.80234i	0.176451	+	0.101874i	0.585624	−	0.810583i	$-0.300849\pi$
$313$	3.12174	+	1.80234i	0.176451	+	0.101874i	−0.409173	+	0.912457i	$0.634183\pi$
$314$	−22.0165	+	5.89931i	−1.24246	+	0.332917i
$315$	−0.102271	+	0.273500i	−0.00576231	+	0.0154100i
$316$	−3.32564	+	1.92006i	−0.187082	+	0.108012i
$317$	−3.86698	−	14.4318i	−0.217191	−	0.810568i	−0.985384	−	0.170350i	$-0.945510\pi$
$317$	−3.86698	−	14.4318i	−0.217191	−	0.810568i	0.768193	−	0.640219i	$-0.221156\pi$
$318$	−7.12464	+	1.90904i	−0.399530	+	0.107054i
$319$	8.93547	−	2.39425i	0.500290	−	0.134052i
$320$	−0.0285643	−	0.106603i	−0.00159679	−	0.00595931i
$321$	−5.11907	+	2.95549i	−0.285718	+	0.164960i
$322$	4.95262	−	13.2446i	0.275999	−	0.738095i
$323$	−7.50467	+	2.01087i	−0.417571	+	0.111888i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	14.4702	−	10.6786i	0.802662	−	0.592341i
$326$	6.72666	+	11.6509i	0.372555	+	0.645284i
$327$	−3.15483	+	11.7740i	−0.174463	+	0.651104i
$328$	5.60562	+	3.23640i	0.309518	+	0.178701i
$329$	15.1337	+	5.65899i	0.834347	+	0.311990i
$330$	0.370082	−	0.370082i	0.0203723	−	0.0203723i
$331$	0.887675	−	0.887675i	0.0487910	−	0.0487910i	−0.682290	−	0.731081i	$-0.739016\pi$
$331$	0.887675	−	0.887675i	0.0487910	−	0.0487910i	0.731081	+	0.682290i	$0.239016\pi$
$332$	2.94128	+	10.9770i	0.161424	+	0.602441i
$333$	1.97621	−	7.37530i	0.108295	−	0.404164i
$334$			17.5207i			0.958691i
$335$	0.447807	−	0.775625i	0.0244663	−	0.0423769i
$336$	0.253697	−	2.63356i	0.0138403	−	0.143672i
$337$		−	23.4908i		−	1.27962i	−0.768532	−	0.639812i	$-0.779012\pi$
$337$		−	23.4908i		−	1.27962i	0.768532	−	0.639812i	$-0.220988\pi$
$338$	−12.9909	−	0.487145i	−0.706610	−	0.0264972i
$339$	−7.45284	+	4.30290i	−0.404783	+	0.233701i
$340$	−0.226706	+	0.226706i	−0.0122948	+	0.0122948i
$341$	−39.9582	+	23.0699i	−2.16386	+	1.24930i
$342$	−1.33724	−	2.31616i	−0.0723094	−	0.125244i
$343$	17.7569	+	5.26232i	0.958783	+	0.284139i
$344$	2.43707	+	0.653011i	0.131398	+	0.0352080i
$345$	−0.417084	−	0.417084i	−0.0224550	−	0.0224550i
$346$	2.77922	+	0.744689i	0.149412	+	0.0400347i
$347$	9.74332	−	16.8759i	0.523049	−	0.905947i	−0.476591	−	0.879125i	$-0.658128\pi$
$347$	9.74332	−	16.8759i	0.523049	−	0.905947i	0.999640	−	0.0268221i	$-0.00853877\pi$
$348$	−0.975346	−	1.68935i	−0.0522841	−	0.0905586i
$349$	4.98912	+	18.6197i	0.267062	+	0.996688i	0.960976	+	0.276630i	$0.0892178\pi$
$349$	4.98912	+	18.6197i	0.267062	+	0.996688i	−0.693915	+	0.720057i	$0.744116\pi$
$350$	−4.62205	+	12.3606i	−0.247059	+	0.660703i
$351$	0.403548	+	3.58290i	0.0215398	+	0.191241i
$352$	−2.37113	+	4.10691i	−0.126382	+	0.218899i
$353$	6.53074	+	6.53074i	0.347596	+	0.347596i	0.859213	−	0.511617i	$-0.170953\pi$
$353$	6.53074	+	6.53074i	0.347596	+	0.347596i	−0.511617	+	0.859213i	$0.670953\pi$
$354$	−3.15583			−0.167730
$355$	0.655124			0.0347704
$356$	−10.0236	−	10.0236i	−0.531248	−	0.531248i
$357$	−6.99407	+	3.18702i	−0.370166	+	0.168675i
$358$	−0.518981	+	1.93686i	−0.0274290	+	0.102366i
$359$	−6.18788	+	1.65804i	−0.326584	+	0.0875078i	−0.418386	−	0.908269i	$-0.637404\pi$
$359$	−6.18788	+	1.65804i	−0.326584	+	0.0875078i	0.0918021	+	0.995777i	$0.470737\pi$
$360$	−0.0955780	−	0.0551820i	−0.00503741	−	0.00290835i
$361$		−	11.8472i		−	0.623537i
$362$	6.74973	+	1.80859i	0.354758	+	0.0950571i
$363$	−11.4890			−0.603015
$364$	8.18338	−	4.90227i	0.428926	−	0.256949i
$365$	0.589500			0.0308559
$366$	7.64256	+	2.04782i	0.399483	+	0.107041i
$367$		−	20.2346i		−	1.05624i	−0.849171	−	0.528118i	$-0.822898\pi$
$367$		−	20.2346i		−	1.05624i	0.849171	−	0.528118i	$-0.177102\pi$
$368$	4.62851	+	2.67227i	0.241278	+	0.139302i
$369$	6.25225	−	1.67529i	0.325479	−	0.0872119i
$370$	−0.218102	+	0.813968i	−0.0113386	+	0.0423162i
$371$	19.4250	+	1.87126i	1.00850	+	0.0971510i
$372$	6.87979	+	6.87979i	0.356701	+	0.356701i
$373$	28.0274			1.45120			0.725601	−	0.688115i	$-0.241562\pi$
$373$	28.0274			1.45120			0.725601	+	0.688115i	$0.241562\pi$
$374$	13.7764			0.712359
$375$	0.779441	+	0.779441i	0.0402502	+	0.0402502i
$376$	−3.05341	+	5.28866i	−0.157468	+	0.272742i
$377$	2.81283	−	6.44636i	0.144868	−	0.332005i
$378$	−1.68282	−	2.04160i	−0.0865548	−	0.105009i
$379$	−2.68893	−	10.0352i	−0.138121	−	0.515475i	−0.999966	−	0.00830227i	$-0.997357\pi$
$379$	−2.68893	−	10.0352i	−0.138121	−	0.515475i	0.861844	−	0.507173i	$-0.169309\pi$
$380$	0.147583	+	0.255621i	0.00757083	+	0.0131131i
$381$	−9.29904	+	16.1064i	−0.476404	+	0.825156i
$382$	16.2538	+	4.35519i	0.831616	+	0.222831i
$383$	0.424825	+	0.424825i	0.0217075	+	0.0217075i	0.717877	−	0.696170i	$-0.245114\pi$
$383$	0.424825	+	0.424825i	0.0217075	+	0.0217075i	−0.696170	+	0.717877i	$0.745114\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	−1.26006	+	0.574179i	−0.0642188	+	0.0292629i
$386$	−6.27902	−	10.8756i	−0.319594	−	0.553553i
$387$	2.18502	−	1.26152i	0.111071	−	0.0641266i
$388$	−8.40964	+	8.40964i	−0.426935	+	0.426935i
$389$	−3.62894	+	2.09517i	−0.183994	+	0.106229i	−0.589168	−	0.808011i	$-0.700544\pi$
$389$	−3.62894	+	2.09517i	−0.183994	+	0.106229i	0.405174	+	0.914240i	$0.367211\pi$
$390$	−0.0445371	−	0.395423i	−0.00225523	−	0.0200230i
$391$		−	15.5260i		−	0.785185i
$392$	−3.06914	+	6.29130i	−0.155015	+	0.317758i
$393$	−4.27844	+	7.41047i	−0.215819	+	0.373809i
$394$		−	22.1443i		−	1.11561i
$395$	0.109690	−	0.409370i	0.00551912	−	0.0205976i
$396$	1.22739	+	4.58067i	0.0616785	+	0.230187i
$397$	8.75727	−	8.75727i	0.439515	−	0.439515i	−0.452334	−	0.891849i	$-0.649408\pi$
$397$	8.75727	−	8.75727i	0.439515	−	0.439515i	0.891849	+	0.452334i	$0.149408\pi$
$398$	0.0810946	−	0.0810946i	0.00406491	−	0.00406491i
$399$	1.16758	+	6.97899i	0.0584519	+	0.349387i
$400$	−4.31958	−	2.49391i	−0.215979	−	0.124695i
$401$	1.17504	−	4.38530i	0.0586786	−	0.218992i	−0.930360	−	0.366647i	$-0.880506\pi$
$401$	1.17504	−	4.38530i	0.0586786	−	0.218992i	0.989039	+	0.147655i	$0.0471725\pi$
$402$	4.05755	+	7.02788i	0.202372	+	0.350519i
$403$	−5.22985	+	34.6882i	−0.260517	+	1.72794i
$404$	−11.2090	−	6.47150i	−0.557667	−	0.321969i
$405$	−0.106603	+	0.0285643i	−0.00529717	+	0.00141937i
$406$	0.851600	+	5.09030i	0.0422642	+	0.252628i
$407$	31.3582	−	18.1047i	1.55437	−	0.897416i
$408$	−0.751875	−	2.80604i	−0.0372234	−	0.138920i
$409$	−9.85971	+	2.64190i	−0.487531	+	0.130634i	−0.494207	−	0.869344i	$-0.664542\pi$
$409$	−9.85971	+	2.64190i	−0.487531	+	0.130634i	0.00667601	+	0.999978i	$0.497875\pi$
$410$	−0.690024	+	0.184891i	−0.0340778	+	0.00913113i
$411$	2.90843	+	10.8544i	0.143462	+	0.535409i
$412$	6.47732	−	3.73968i	0.319114	−	0.184241i
$413$	7.82065	+	2.92440i	0.384829	+	0.143900i
$414$	5.16243	−	1.38327i	0.253720	−	0.0679840i
$415$	−1.08617	−	0.627101i	−0.0533180	−	0.0307832i
$416$	1.31712	+	3.35637i	0.0645771	+	0.164559i
$417$	−2.01002	−	3.48145i	−0.0984309	−	0.170487i
$418$	3.28261	−	12.2509i	0.160558	−	0.599209i
$419$	17.4518	+	10.0758i	0.852577	+	0.492236i	0.861520	−	0.507724i	$-0.169513\pi$
$419$	17.4518	+	10.0758i	0.852577	+	0.492236i	−0.00894233	+	0.999960i	$0.502846\pi$
$420$	0.185722	+	0.225319i	0.00906233	+	0.0109944i
$421$	−24.1017	+	24.1017i	−1.17464	+	1.17464i	−0.193554	+	0.981090i	$0.562001\pi$
$421$	−24.1017	+	24.1017i	−1.17464	+	1.17464i	−0.981090	+	0.193554i	$0.937999\pi$
$422$	14.8593	−	14.8593i	0.723340	−	0.723340i
$423$	1.58056	+	5.89873i	0.0768495	+	0.286806i
$424$	−1.90904	+	7.12464i	−0.0927112	+	0.346003i
$425$			14.4897i			0.702855i
$426$	−2.96802	+	5.14075i	−0.143801	+	0.249070i
$427$	−17.0418	−	12.1569i	−0.824713	−	0.588315i
$428$			5.91099i			0.285718i
$429$	−10.6612	+	13.3677i	−0.514730	+	0.645397i
$430$	−0.241147	+	0.139226i	−0.0116291	+	0.00671409i
$431$	9.27466	−	9.27466i	0.446745	−	0.446745i	−0.447526	−	0.894271i	$-0.647695\pi$
$431$	9.27466	−	9.27466i	0.446745	−	0.446745i	0.894271	+	0.447526i	$0.147695\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−6.88386	−	11.9232i	−0.330817	−	0.572992i	0.651855	−	0.758344i	$-0.273991\pi$
$433$	−6.88386	−	11.9232i	−0.330817	−	0.572992i	−0.982672	+	0.185351i	$0.940658\pi$
$434$	−10.6740	−	23.4245i	−0.512366	−	1.12441i
$435$	0.207951	+	0.0557202i	0.00997047	+	0.00267158i
$436$	8.61917	+	8.61917i	0.412783	+	0.412783i
$437$	−13.8068	−	3.69952i	−0.660468	−	0.176972i
$438$	−2.67071	+	4.62580i	−0.127611	+	0.221029i
$439$	−9.88793	−	17.1264i	−0.471925	−	0.817399i	0.527559	−	0.849519i	$-0.323107\pi$
$439$	−9.88793	−	17.1264i	−0.471925	−	0.817399i	−0.999484	+	0.0321199i	$0.989774\pi$
$440$	−0.135459	−	0.505541i	−0.00645777	−	0.0241007i
$441$	2.27841	+	6.61883i	0.108496	+	0.315182i
$442$	6.53090	−	8.18880i	0.310643	−	0.389502i
$443$	−4.24346	+	7.34989i	−0.201613	+	0.349204i	−0.949048	−	0.315131i	$-0.897952\pi$
$443$	−4.24346	+	7.34989i	−0.201613	+	0.349204i	0.747435	+	0.664335i	$0.231285\pi$
$444$	−5.39909	−	5.39909i	−0.256230	−	0.256230i
$445$	1.56446			0.0741626
$446$	23.2204			1.09952
$447$	−13.1240	−	13.1240i	−0.620743	−	0.620743i
$448$	−2.15388	−	1.53649i	−0.101761	−	0.0725922i
$449$	−2.00385	+	7.47846i	−0.0945674	+	0.352930i	−0.996954	−	0.0779982i	$-0.975147\pi$
$449$	−2.00385	+	7.47846i	−0.0945674	+	0.352930i	0.902386	+	0.430928i	$0.141814\pi$
$450$	−4.81786	+	1.29094i	−0.227116	+	0.0608556i
$451$	26.5833	+	15.3479i	1.25176	+	0.722702i
$452$			8.60580i			0.404783i
$453$	10.5867	+	2.83671i	0.497409	+	0.133280i
$454$	14.5180			0.681364
$455$	−0.256055	+	1.02119i	−0.0120041	+	0.0478743i
$456$	−2.67447			−0.125244
$457$	33.3765	+	8.94320i	1.56129	+	0.418345i	0.933070	−	0.359694i	$-0.117119\pi$
$457$	33.3765	+	8.94320i	1.56129	+	0.418345i	0.628216	+	0.778039i	$0.283786\pi$
$458$			24.4066i			1.14044i
$459$	−2.51582	−	1.45251i	−0.117429	−	0.0677974i
$460$	−0.569747	+	0.152663i	−0.0265646	+	0.00711796i
$461$	6.83932	−	25.5247i	0.318539	−	1.18880i	−0.602111	−	0.798413i	$-0.705673\pi$
$461$	6.83932	−	25.5247i	0.318539	−	1.18880i	0.920650	−	0.390390i	$-0.127660\pi$
$462$	1.20310	−	12.4890i	0.0559731	−	0.581041i
$463$	−9.03832	−	9.03832i	−0.420046	−	0.420046i	0.465173	−	0.885220i	$-0.345992\pi$
$463$	−9.03832	−	9.03832i	−0.420046	−	0.420046i	−0.885220	+	0.465173i	$0.845992\pi$
$464$	−1.95069			−0.0905586
$465$	−1.07379			−0.0497957
$466$	13.9613	+	13.9613i	0.646746	+	0.646746i
$467$	−10.9859	+	19.0282i	−0.508368	+	0.880520i	0.491585	+	0.870830i	$0.336418\pi$
$467$	−10.9859	+	19.0282i	−0.508368	+	0.880520i	−0.999953	+	0.00969007i	$0.996916\pi$
$468$	3.30465	+	1.44197i	0.152758	+	0.0666549i
$469$	−3.54275	−	21.1762i	−0.163589	−	0.977827i
$470$	−0.174437	−	0.651008i	−0.00804618	−	0.0300288i
$471$	11.3966	+	19.7395i	0.525127	+	0.909546i
$472$	−1.57791	+	2.73303i	−0.0726293	+	0.125798i
$473$	11.5572	+	3.09674i	0.531401	+	0.142388i
$474$	2.71537	+	2.71537i	0.124721	+	0.124721i
$475$	12.8852	+	3.45259i	0.591215	+	0.158416i
$476$	−0.736996	+	7.65055i	−0.0337801	+	0.350663i
$477$	3.68798	+	6.38777i	0.168861	+	0.292476i
$478$	−25.4484	+	14.6926i	−1.16398	+	0.672026i
$479$	7.02988	−	7.02988i	0.321203	−	0.321203i	−0.528025	−	0.849229i	$-0.677067\pi$
$479$	7.02988	−	7.02988i	0.321203	−	0.321203i	0.849229	+	0.528025i	$0.177067\pi$
$480$	−0.0955780	+	0.0551820i	−0.00436252	+	0.00251870i
$481$	4.10426	−	27.2224i	0.187138	−	1.24124i
$482$			10.7880i			0.491382i
$483$	−14.0752	−	1.35589i	−0.640443	−	0.0616953i
$484$	−5.74449	+	9.94975i	−0.261113	+	0.452261i
$485$		−	1.31256i		−	0.0596004i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	3.55636	+	13.2725i	0.161154	+	0.601435i	0.998499	+	0.0547609i	$0.0174396\pi$
$487$	3.55636	+	13.2725i	0.161154	+	0.601435i	−0.837346	+	0.546674i	$0.815894\pi$
$488$	5.59474	−	5.59474i	0.253262	−	0.253262i
$489$	9.51293	−	9.51293i	0.430190	−	0.430190i
$490$	−0.251454	−	0.730480i	−0.0113596	−	0.0329997i
$491$	−17.8027	−	10.2784i	−0.803425	−	0.463858i	0.0412423	−	0.999149i	$-0.486868\pi$
$491$	−17.8027	−	10.2784i	−0.803425	−	0.463858i	−0.844667	+	0.535291i	$0.820202\pi$
$492$	1.67529	−	6.25225i	0.0755277	−	0.281873i
$493$	2.83340	+	4.90760i	0.127610	+	0.221027i
$494$	−5.72586	−	7.75892i	−0.257619	−	0.349091i
$495$	−0.453255	−	0.261687i	−0.0203723	−	0.0117620i
$496$	9.39797	−	2.51818i	0.421981	−	0.113070i
$497$	12.1190	−	9.98926i	0.543611	−	0.448079i
$498$	9.84170	−	5.68211i	0.441017	−	0.254621i
$499$	9.51356	+	35.5051i	0.425886	+	1.58943i	0.761981	+	0.647599i	$0.224227\pi$
$499$	9.51356	+	35.5051i	0.425886	+	1.58943i	−0.336096	+	0.941828i	$0.609107\pi$
$500$	1.06474	−	0.285295i	0.0476164	−	0.0127588i
$501$	16.9237	−	4.53469i	0.756095	−	0.202595i
$502$	−2.56603	−	9.57655i	−0.114527	−	0.427422i
$503$	−2.30320	+	1.32976i	−0.102695	+	0.0592909i	−0.550468	−	0.834856i	$-0.685551\pi$
$503$	−2.30320	+	1.32976i	−0.102695	+	0.0592909i	0.447773	+	0.894147i	$0.352217\pi$
$504$	−2.60949	+	0.436563i	−0.116236	+	0.0194461i
$505$	1.37977	−	0.369708i	0.0613989	−	0.0164518i
$506$	21.9496	+	12.6726i	0.975778	+	0.563366i
$507$	2.89174	+	12.6743i	0.128427	+	0.562885i
$508$	9.29904	+	16.1064i	0.412578	+	0.714606i
$509$	10.7618	−	40.1635i	0.477008	−	1.78022i	−0.136621	−	0.990623i	$-0.543624\pi$
$509$	10.7618	−	40.1635i	0.477008	−	1.78022i	0.613629	−	0.789594i	$-0.289709\pi$
$510$	0.277657	+	0.160305i	0.0122948	+	0.00709843i
$511$	10.9050	−	8.98863i	0.482410	−	0.397634i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.89114	+	1.89114i	−0.0834957	+	0.0834957i
$514$	−2.55289	−	9.52751i	−0.112603	−	0.420240i
$515$	−0.213643	+	0.797326i	−0.00941423	+	0.0351344i
$516$		−	2.52304i		−	0.111071i
$517$	−14.4800	+	25.0802i	−0.636832	+	1.10302i
$518$	8.37666	+	18.3830i	0.368049	+	0.807703i
$519$		−	2.87726i		−	0.126298i
$520$	−0.364715	−	0.159141i	−0.0159938	−	0.00697880i
$521$	−18.6983	+	10.7955i	−0.819187	+	0.472958i	−0.850136	−	0.526563i	$-0.823480\pi$
$521$	−18.6983	+	10.7955i	−0.819187	+	0.472958i	0.0309490	+	0.999521i	$0.490147\pi$
$522$	−1.37935	+	1.37935i	−0.0603724	+	0.0603724i
$523$	−18.3784	+	10.6108i	−0.803632	+	0.463977i	−0.844739	−	0.535178i	$-0.820245\pi$
$523$	−18.3784	+	10.6108i	−0.803632	+	0.463977i	0.0411079	+	0.999155i	$0.486911\pi$
$524$	4.27844	+	7.41047i	0.186904	+	0.323728i
$525$	13.1357	+	1.26539i	0.573290	+	0.0552263i
$526$	14.9882	+	4.01608i	0.653517	+	0.175109i
$527$	−19.9860	−	19.9860i	−0.870602	−	0.870602i
$528$	4.58067	+	1.22739i	0.199348	+	0.0534151i
$529$	2.78208	−	4.81870i	0.120960	−	0.209509i
$530$	−0.407021	−	0.704980i	−0.0176798	−	0.0306224i
$531$	0.816788	+	3.04829i	0.0354456	+	0.132285i
$532$	6.62777	+	2.47835i	0.287350	+	0.107450i
$533$	21.7251	−	8.52546i	0.941019	−	0.369279i
$534$	−7.08773	+	12.2763i	−0.306716	+	0.531248i
$535$	−0.461289	−	0.461289i	−0.0199432	−	0.0199432i
$536$	8.11509			0.350519
$537$	2.00519			0.0865303
$538$	10.4964	+	10.4964i	0.452532	+	0.452532i
$539$	−14.5546	+	29.8349i	−0.626912	+	1.28508i
$540$	−0.0285643	+	0.106603i	−0.00122921	+	0.00458748i
$541$	−31.8611	+	8.53716i	−1.36982	+	0.367041i	−0.867411	−	0.497591i	$-0.834218\pi$
$541$	−31.8611	+	8.53716i	−1.36982	+	0.367041i	−0.502405	+	0.864633i	$0.667551\pi$
$542$	5.39265	+	3.11345i	0.231634	+	0.133734i
$543$		−	6.98784i		−	0.299877i
$544$	−2.80604	−	0.751875i	−0.120308	−	0.0322364i
$545$	−1.34526			−0.0576248
$546$	−6.85324	−	6.63574i	−0.293292	−	0.283984i
$547$	−6.03776			−0.258156			−0.129078	−	0.991634i	$-0.541202\pi$
$547$	−6.03776			−0.258156			−0.129078	+	0.991634i	$0.541202\pi$
$548$	10.8544	+	2.90843i	0.463678	+	0.124242i
$549$		−	7.91216i		−	0.337683i
$550$	−20.4845	−	11.8268i	−0.873464	−	0.504295i
$551$	5.03930	−	1.35028i	0.214682	−	0.0575238i
$552$	1.38327	−	5.16243i	0.0588759	−	0.219728i
$553$	−4.21289	−	9.24539i	−0.179150	−	0.393154i
$554$	−9.50515	−	9.50515i	−0.403835	−	0.403835i
$555$	0.842682			0.0357698
$556$	−4.02003			−0.170487
$557$	8.05803	+	8.05803i	0.341430	+	0.341430i	0.856905	−	0.515475i	$-0.172385\pi$
$557$	8.05803	+	8.05803i	0.341430	+	0.341430i	−0.515475	+	0.856905i	$0.672385\pi$
$558$	4.86475	−	8.42599i	0.205941	−	0.356701i
$559$	7.31960	−	5.40165i	0.309586	−	0.228466i
$560$	0.287993	−	0.0481809i	0.0121699	−	0.00203601i
$561$	−3.56558	−	13.3069i	−0.150539	−	0.561820i
$562$	−12.8756	−	22.3012i	−0.543124	−	0.940718i
$563$	−1.62989	+	2.82305i	−0.0686917	+	0.118977i	−0.898326	−	0.439330i	$-0.855216\pi$
$563$	−1.62989	+	2.82305i	−0.0686917	+	0.118977i	0.829634	+	0.558308i	$0.188549\pi$
$564$	5.89873	+	1.58056i	0.248382	+	0.0665536i
$565$	−0.671589	−	0.671589i	−0.0282540	−	0.0282540i
$566$	−2.34498	−	0.628336i	−0.0985670	−	0.0264109i
$567$	−1.53649	+	2.15388i	−0.0645264	+	0.0904545i
$568$	2.96802	+	5.14075i	0.124535	+	0.215701i
$569$	16.3207	−	9.42276i	0.684199	−	0.395023i	−0.117236	−	0.993104i	$-0.537403\pi$
$569$	16.3207	−	9.42276i	0.684199	−	0.395023i	0.801435	+	0.598081i	$0.204070\pi$
$570$	0.208713	−	0.208713i	0.00874205	−	0.00874205i
$571$	−5.26372	+	3.03901i	−0.220280	+	0.127179i	−0.606080	−	0.795404i	$-0.707259\pi$
$571$	−5.26372	+	3.03901i	−0.220280	+	0.127179i	0.385800	+	0.922582i	$0.373925\pi$
$572$	6.24611	+	15.9167i	0.261163	+	0.665513i
$573$		−	16.8272i		−	0.702965i
$574$	−9.94539	+	13.9417i	−0.415113	+	0.581914i
$575$	−13.3288	+	23.0862i	−0.555850	+	0.962760i
$576$		−	1.00000i		−	0.0416667i
$577$	−4.49714	+	16.7835i	−0.187218	+	0.698708i	0.806927	+	0.590652i	$0.201129\pi$
$577$	−4.49714	+	16.7835i	−0.187218	+	0.698708i	−0.994145	+	0.108056i	$0.965537\pi$
$578$	−2.21571	−	8.26913i	−0.0921613	−	0.343951i
$579$	−8.87988	+	8.87988i	−0.369035	+	0.369035i
$580$	0.152230	−	0.152230i	0.00632102	−	0.00632102i
$581$	−29.6548	+	4.96120i	−1.23029	+	0.205825i
$582$	10.2997	+	5.94652i	0.426935	+	0.246491i
$583$	−9.05315	+	33.7868i	−0.374943	+	1.39931i
$584$	2.67071	+	4.62580i	0.110515	+	0.191417i
$585$	−0.370422	+	0.145363i	−0.0153151	+	0.00601000i
$586$	23.7244	+	13.6973i	0.980045	+	0.565829i
$587$	25.1856	−	6.74846i	1.03952	−	0.278539i	0.301606	−	0.953433i	$-0.402477\pi$
$587$	25.1856	−	6.74846i	1.03952	−	0.278539i	0.737915	+	0.674894i	$0.235811\pi$
$588$	6.87128	+	1.33625i	0.283367	+	0.0551061i
$589$	−22.5351	+	13.0106i	−0.928542	+	0.536094i
$590$	−0.0901440	−	0.336422i	−0.00371117	−	0.0138503i
$591$	−21.3897	+	5.73136i	−0.879856	+	0.235757i
$592$	−7.37530	+	1.97621i	−0.303123	+	0.0812216i
$593$	6.54941	+	24.4427i	0.268952	+	1.00374i	0.959787	+	0.280730i	$0.0905766\pi$
$593$	6.54941	+	24.4427i	0.268952	+	1.00374i	−0.690835	+	0.723013i	$0.742757\pi$
$594$	4.10691	−	2.37113i	0.168509	−	0.0972885i
$595$	−0.539528	−	0.654557i	−0.0221185	−	0.0268342i
$596$	−17.9277	+	4.80371i	−0.734347	+	0.196768i
$597$	−0.0993202	−	0.0573426i	−0.00406491	−	0.00234687i
$598$	17.9383	−	7.03940i	0.733550	−	0.287863i
$599$	1.42785	+	2.47311i	0.0583403	+	0.101048i	0.893720	−	0.448624i	$-0.148086\pi$
$599$	1.42785	+	2.47311i	0.0583403	+	0.101048i	−0.835380	+	0.549673i	$0.814752\pi$
$600$	−1.29094	+	4.81786i	−0.0527025	+	0.196688i
$601$	−5.19948	−	3.00192i	−0.212091	−	0.122451i	0.390192	−	0.920734i	$-0.372409\pi$
$601$	−5.19948	−	3.00192i	−0.212091	−	0.122451i	−0.602283	+	0.798283i	$0.705742\pi$
$602$	−2.33802	+	6.25250i	−0.0952906	+	0.254833i
$603$	5.73824	−	5.73824i	0.233679	−	0.233679i
$604$	7.75004	−	7.75004i	0.315344	−	0.315344i
$605$	−0.328175	−	1.22476i	−0.0133422	−	0.0497938i
$606$	−3.34989	+	12.5020i	−0.136080	+	0.507858i
$607$			13.1408i			0.533368i	0.963784	+	0.266684i	$0.0859280\pi$
$607$			13.1408i			0.533368i	−0.963784	+	0.266684i	$0.914072\pi$
$608$	−1.33724	+	2.31616i	−0.0542321	+	0.0939327i
$609$	4.69645	−	2.14005i	0.190310	−	0.0867192i
$610$			0.873217i			0.0353555i
$611$	8.04341	+	20.4967i	0.325401	+	0.829209i
$612$	−2.51582	+	1.45251i	−0.101696	+	0.0587143i
$613$	11.7082	−	11.7082i	0.472891	−	0.472891i	−0.429958	−	0.902849i	$-0.641472\pi$
$613$	11.7082	−	11.7082i	0.472891	−	0.472891i	0.902849	+	0.429958i	$0.141472\pi$
$614$	−22.5546	+	13.0219i	−0.910228	+	0.525521i
$615$	0.357183	+	0.618658i	0.0144030	+	0.0249467i
$616$	−10.2143	−	7.28642i	−0.411544	−	0.293578i
$617$	0.970874	+	0.260145i	0.0390859	+	0.0104730i	0.278309	−	0.960492i	$-0.410226\pi$
$617$	0.970874	+	0.260145i	0.0390859	+	0.0104730i	−0.239223	+	0.970965i	$0.576893\pi$
$618$	−5.28871	−	5.28871i	−0.212743	−	0.212743i
$619$	−29.8975	−	8.01100i	−1.20168	−	0.321989i	−0.398188	−	0.917304i	$-0.630361\pi$
$619$	−29.8975	−	8.01100i	−1.20168	−	0.321989i	−0.803493	+	0.595315i	$0.797027\pi$
$620$	−0.536893	+	0.929926i	−0.0215622	+	0.0373467i
$621$	−2.67227	−	4.62851i	−0.107235	−	0.185736i
$622$	5.26970	+	19.6668i	0.211296	+	0.788566i
$623$	28.9406	−	23.8547i	1.15948	−	0.955719i
$624$	2.90111	−	2.14093i	0.116137	−	0.0857058i
$625$	12.4087	−	21.4925i	0.496349	−	0.859702i
$626$	−2.54889	−	2.54889i	−0.101874	−	0.101874i
$627$	−12.6830			−0.506511
$628$	22.7932			0.909546
$629$	15.6845	+	15.6845i	0.625382	+	0.625382i
$630$	0.169573	−	0.237711i	0.00675595	−	0.00947063i
$631$	6.97463	−	26.0297i	0.277656	−	1.03622i	−0.676385	−	0.736548i	$-0.736454\pi$
$631$	6.97463	−	26.0297i	0.277656	−	1.03622i	0.954041	−	0.299677i	$-0.0968788\pi$
$632$	3.70927	−	0.993896i	0.147547	−	0.0395351i
$633$	−18.1989	−	10.5071i	−0.723340	−	0.417621i
$634$			14.9409i			0.593377i
$635$	−1.98262	−	0.531241i	−0.0786778	−	0.0210817i
$636$	7.37597			0.292476
$637$	10.8343	+	22.7951i	0.429271	+	0.903176i
$638$	−9.25068			−0.366238
$639$	5.73377	+	1.53636i	0.226824	+	0.0607774i
$640$			0.110364i			0.00436252i
$641$	−35.9977	−	20.7833i	−1.42183	−	0.820891i	−0.425370	−	0.905019i	$-0.639856\pi$
$641$	−35.9977	−	20.7833i	−1.42183	−	0.820891i	−0.996455	+	0.0841281i	$0.973189\pi$
$642$	5.70958	−	1.52988i	0.225339	−	0.0603794i
$643$	4.08448	−	15.2435i	0.161076	−	0.601145i	−0.837432	−	0.546542i	$-0.815944\pi$
$643$	4.08448	−	15.2435i	0.161076	−	0.601145i	0.998508	−	0.0546032i	$-0.0173894\pi$
$644$	−8.21183	+	11.5115i	−0.323591	+	0.453617i
$645$	0.196896	+	0.196896i	0.00775277	+	0.00775277i
$646$	7.76940			0.305683
$647$	−4.19392			−0.164880			−0.0824401	−	0.996596i	$-0.526271\pi$
$647$	−4.19392			−0.164880			−0.0824401	+	0.996596i	$0.526271\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−7.48286	+	12.9607i	−0.293728	+	0.508752i
$650$	−16.7410	+	6.56955i	−0.656634	+	0.257679i
$651$	−19.8637	+	16.3730i	−0.778521	+	0.641707i
$652$	−3.48197	−	12.9949i	−0.136365	−	0.508920i
$653$	−15.4562	−	26.7709i	−0.604846	−	1.04762i	−0.992076	−	0.125641i	$-0.959901\pi$
$653$	−15.4562	−	26.7709i	−0.604846	−	1.04762i	0.387230	−	0.921983i	$-0.373432\pi$
$654$	6.09467	−	10.5563i	0.238320	−	0.412783i
$655$	−0.912192	−	0.244421i	−0.0356423	−	0.00955033i
$656$	−4.57697	−	4.57697i	−0.178701	−	0.178701i
$657$	5.15941	+	1.38246i	0.201288	+	0.0539349i
$658$	−13.1534	−	9.38305i	−0.512771	−	0.365790i
$659$	−22.3340	−	38.6836i	−0.870009	−	1.50690i	−0.861986	−	0.506932i	$-0.830779\pi$
$659$	−22.3340	−	38.6836i	−0.870009	−	1.50690i	−0.00802347	−	0.999968i	$-0.502554\pi$
$660$	−0.453255	+	0.261687i	−0.0176429	+	0.0101862i
$661$	27.6979	−	27.6979i	1.07732	−	1.07732i	0.0805758	−	0.996748i	$-0.474324\pi$
$661$	27.6979	−	27.6979i	1.07732	−	1.07732i	0.996748	−	0.0805758i	$-0.0256759\pi$
$662$	−1.08718	+	0.627681i	−0.0422543	+	0.0243955i
$663$	−9.60010	−	4.18895i	−0.372837	−	0.162685i
$664$		−	11.3642i		−	0.441017i
$665$	−0.710634	+	0.323818i	−0.0275572	+	0.0125571i
$666$	−3.81774	+	6.61251i	−0.147934	+	0.256230i
$667$			10.4256i			0.403679i
$668$	4.53469	−	16.9237i	0.175453	−	0.654798i
$669$	−6.00988	−	22.4292i	−0.232355	−	0.867162i
$670$	−0.633295	+	0.633295i	−0.0244663	+	0.0244663i
$671$	26.5317	−	26.5317i	1.02424	−	1.02424i
$672$	−0.926668	+	2.47816i	−0.0357470	+	0.0955972i
$673$	−37.7573	−	21.7992i	−1.45544	−	0.840298i	−0.456656	−	0.889643i	$-0.650953\pi$
$673$	−37.7573	−	21.7992i	−1.45544	−	0.840298i	−0.998782	+	0.0493454i	$0.984286\pi$
$674$	−6.07986	+	22.6903i	−0.234187	+	0.873999i
$675$	2.49391	+	4.31958i	0.0959906	+	0.166261i
$676$	12.4221	+	3.83283i	0.477774	+	0.147417i
$677$	16.6756	+	9.62769i	0.640897	+	0.370022i	0.784960	−	0.619547i	$-0.212683\pi$
$677$	16.6756	+	9.62769i	0.640897	+	0.370022i	−0.144063	+	0.989569i	$0.546017\pi$
$678$	8.31256	−	2.22734i	0.319242	−	0.0855406i
$679$	−20.0138	−	24.2808i	−0.768059	−	0.931812i
$680$	0.277657	−	0.160305i	0.0106476	−	0.00614742i
$681$	−3.75754	−	14.0233i	−0.143989	−	0.537375i
$682$	44.5676	−	11.9418i	1.70658	−	0.457277i
$683$	−21.9611	+	5.88445i	−0.840316	+	0.225162i	−0.653209	−	0.757177i	$-0.726578\pi$
$683$	−21.9611	+	5.88445i	−0.840316	+	0.225162i	−0.187107	+	0.982340i	$0.559911\pi$
$684$	0.692204	+	2.58334i	0.0264671	+	0.0987765i
$685$	−1.07404	+	0.620098i	−0.0410370	+	0.0236927i
$686$	−15.7899	−	9.67884i	−0.602860	−	0.369540i
$687$	23.5749	−	6.31689i	0.899440	−	0.241004i
$688$	−2.18502	−	1.26152i	−0.0833030	−	0.0480950i
$689$	15.7914	+	21.3985i	0.601606	+	0.815216i
$690$	0.294923	+	0.510821i	0.0112275	+	0.0194466i
$691$	−7.03903	+	26.2700i	−0.267777	+	0.999359i	0.692751	+	0.721177i	$0.256399\pi$
$691$	−7.03903	+	26.2700i	−0.267777	+	0.999359i	−0.960528	+	0.278182i	$0.910268\pi$
$692$	−2.49178	−	1.43863i	−0.0947232	−	0.0546885i
$693$	−12.3748	+	2.07029i	−0.470081	+	0.0786439i
$694$	−13.7791	+	13.7791i	−0.523049	+	0.523049i
$695$	0.313720	−	0.313720i	0.0119001	−	0.0119001i
$696$	0.504876	+	1.88422i	0.0191373	+	0.0714213i
$697$	−4.86675	+	18.1629i	−0.184341	+	0.687971i
$698$		−	19.2765i		−	0.729626i
$699$	9.87216	−	17.0991i	0.373399	−	0.646746i
$700$	7.66373	−	10.7432i	0.289662	−	0.406054i
$701$		−	6.14164i		−	0.231966i	−0.993251	−	0.115983i	$-0.962998\pi$
$701$		−	6.14164i		−	0.231966i	0.993251	−	0.115983i	$-0.0370019\pi$
$702$	0.537525	−	3.56526i	0.0202876	−	0.134562i
$703$	17.6850	−	10.2104i	0.667002	−	0.385094i
$704$	3.35328	−	3.35328i	0.126382	−	0.126382i
$705$	−0.583678	+	0.336987i	−0.0219826	+	0.0126916i
$706$	−4.61793	−	7.99849i	−0.173798	−	0.301027i
$707$	19.8868	−	27.8777i	0.747918	−	1.04845i
$708$	3.04829	+	0.816788i	0.114562	+	0.0306968i
$709$	0.0948186	+	0.0948186i	0.00356099	+	0.00356099i	0.708885	−	0.705324i	$-0.249198\pi$
$709$	0.0948186	+	0.0948186i	0.00356099	+	0.00356099i	−0.705324	+	0.708885i	$0.749198\pi$
$710$	−0.632801	−	0.169559i	−0.0237486	−	0.00636342i
$711$	1.92006	−	3.32564i	0.0720079	−	0.124721i
$712$	7.08773	+	12.2763i	0.265624	+	0.460074i
$713$	−13.4585	−	50.2279i	−0.504026	−	1.88105i
$714$	7.58062	−	1.26823i	0.283697	−	0.0474622i
$715$	−1.72957	−	0.754688i	−0.0646823	−	0.0282237i
$716$	1.00259	−	1.73654i	0.0374687	−	0.0648977i
$717$	20.7785	+	20.7785i	0.775989	+	0.775989i
$718$	6.40616			0.239076
$719$	32.6420			1.21734			0.608671	−	0.793423i	$-0.291703\pi$
$719$	32.6420			1.21734			0.608671	+	0.793423i	$0.291703\pi$
$720$	0.0780392	+	0.0780392i	0.00290835	+	0.00290835i
$721$	8.20540	+	18.0071i	0.305585	+	0.670621i
$722$	−3.06628	+	11.4435i	−0.114115	+	0.425884i
$723$	10.4204	−	2.79215i	0.387541	−	0.103841i
$724$	−6.05164	−	3.49392i	−0.224908	−	0.129850i
$725$		−	9.72970i		−	0.361352i
$726$	11.0975	+	2.97357i	0.411867	+	0.110359i
$727$	−22.6381			−0.839601			−0.419801	−	0.907616i	$-0.637900\pi$
$727$	−22.6381			−0.839601			−0.419801	+	0.907616i	$0.637900\pi$
$728$	−9.17334	+	2.61721i	−0.339987	+	0.0970003i
$729$	−1.00000			−0.0370370
$730$	−0.569414	−	0.152574i	−0.0210749	−	0.00564701i
$731$			7.32949i			0.271091i
$732$	−6.85213	−	3.95608i	−0.253262	−	0.146221i
$733$	−25.1255	+	6.73236i	−0.928032	+	0.248665i	−0.691015	−	0.722840i	$-0.742836\pi$
$733$	−25.1255	+	6.73236i	−0.928032	+	0.248665i	−0.237017	+	0.971506i	$0.576170\pi$
$734$	−5.23709	+	19.5451i	−0.193305	+	0.721423i
$735$	−0.640509	+	0.431949i	−0.0236255	+	0.0159327i
$736$	−3.77916	−	3.77916i	−0.139302	−	0.139302i
$737$	38.4838			1.41757
$738$	−6.47281			−0.238267
$739$	−4.69165	−	4.69165i	−0.172585	−	0.172585i	0.615529	−	0.788114i	$-0.288942\pi$
$739$	−4.69165	−	4.69165i	−0.172585	−	0.172585i	−0.788114	+	0.615529i	$0.788942\pi$
$740$	0.421341	−	0.729784i	0.0154888	−	0.0268274i
$741$	−6.01258	+	7.53891i	−0.220878	+	0.276949i
$742$	−18.2788	−	6.83507i	−0.671037	−	0.250923i
$743$	1.05610	+	3.94142i	0.0387446	+	0.144597i	0.982589	−	0.185795i	$-0.0594859\pi$
$743$	1.05610	+	3.94142i	0.0387446	+	0.144597i	−0.943844	+	0.330391i	$0.892819\pi$
$744$	−4.86475	−	8.42599i	−0.178350	−	0.308912i
$745$	1.02418	−	1.77394i	0.0375232	−	0.0649921i
$746$	−27.0724	−	7.25402i	−0.991190	−	0.265589i
$747$	−8.03572	−	8.03572i	−0.294012	−	0.294012i
$748$	−13.3069	−	3.56558i	−0.486550	−	0.130371i
$749$	−15.5669	−	1.49960i	−0.568804	−	0.0547942i
$750$	−0.551148	−	0.954616i	−0.0201251	−	0.0348577i
$751$	30.1341	−	17.3979i	1.09961	−	0.634860i	0.163491	−	0.986545i	$-0.447724\pi$
$751$	30.1341	−	17.3979i	1.09961	−	0.634860i	0.936118	+	0.351685i	$0.114391\pi$
$752$	4.31817	−	4.31817i	0.157468	−	0.157468i
$753$	−8.58610	+	4.95719i	−0.312895	+	0.180650i
$754$	−4.38543	+	5.49869i	−0.159708	+	0.200251i
$755$			1.20961i			0.0440223i
$756$	1.09707	+	2.40758i	0.0399001	+	0.0875628i
$757$	−12.4183	+	21.5092i	−0.451352	+	0.781765i	−0.998470	−	0.0552903i	$-0.982392\pi$
$757$	−12.4183	+	21.5092i	−0.451352	+	0.781765i	0.547118	+	0.837055i	$0.315725\pi$
$758$			10.3892i			0.377354i
$759$	6.55982	−	24.4816i	0.238106	−	0.888625i
$760$	−0.0763944	−	0.285108i	−0.00277112	−	0.0103420i
$761$	27.3063	−	27.3063i	0.989854	−	0.989854i	−0.0100950	−	0.999949i	$-0.503213\pi$
$761$	27.3063	−	27.3063i	0.989854	−	0.989854i	0.999949	+	0.0100950i	$0.00321340\pi$
$762$	13.1508	−	13.1508i	0.476404	−	0.476404i
$763$	−24.8857	+	20.5124i	−0.900924	+	0.742600i
$764$	−14.5728	−	8.41358i	−0.527224	−	0.304393i
$765$	0.0829800	−	0.309686i	0.00300015	−	0.0111967i
$766$	−0.300396	−	0.520302i	−0.0108538	−	0.0187993i
$767$	4.15660	+	10.5921i	0.150086	+	0.382459i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−21.1183	+	5.65864i	−0.761547	+	0.204056i	−0.618634	−	0.785680i	$-0.712314\pi$
$769$	−21.1183	+	5.65864i	−0.761547	+	0.204056i	−0.142913	+	0.989735i	$0.545647\pi$
$770$	1.36574	−	0.228486i	0.0492178	−	0.00823406i
$771$	−8.54213	+	4.93180i	−0.307637	+	0.177614i
$772$	3.25026	+	12.1301i	0.116980	+	0.436573i
$773$	−16.9279	+	4.53581i	−0.608853	+	0.163142i	−0.550055	−	0.835128i	$-0.685393\pi$
$773$	−16.9279	+	4.53581i	−0.608853	+	0.163142i	−0.0587975	+	0.998270i	$0.518727\pi$
$774$	−2.43707	+	0.653011i	−0.0875986	+	0.0234720i
$775$	12.5602	+	46.8754i	0.451177	+	1.68381i
$776$	10.2997	−	5.94652i	0.369737	−	0.213467i
$777$	15.5886	−	12.8491i	0.559237	−	0.460959i
$778$	4.04755	−	1.08454i	0.145112	−	0.0388826i
$779$	14.9921	+	8.65567i	0.537146	+	0.310122i
$780$	−0.0593234	+	0.393476i	−0.00212412	+	0.0140887i
$781$	14.0751	+	24.3788i	0.503646	+	0.872341i
$782$	−4.01843	+	14.9970i	−0.143699	+	0.536291i
$783$	1.68935	+	0.975346i	0.0603724	+	0.0348560i
$784$	4.59287	−	5.28257i	0.164031	−	0.188663i
$785$	−1.77876	+	1.77876i	−0.0634866	+	0.0634866i
$786$	6.05062	−	6.05062i	0.215819	−	0.215819i
$787$	8.85324	+	33.0407i	0.315584	+	1.17778i	0.923445	+	0.383732i	$0.125361\pi$
$787$	8.85324	+	33.0407i	0.315584	+	1.17778i	−0.607861	+	0.794044i	$0.707972\pi$
$788$	−5.73136	+	21.3897i	−0.204171	+	0.761978i
$789$		−	15.5169i		−	0.552417i
$790$	−0.211906	+	0.367031i	−0.00753926	+	0.0130584i
$791$	−22.6639	−	2.18326i	−0.805835	−	0.0776279i
$792$		−	4.74225i		−	0.168509i
$793$	−3.19293	−	28.3484i	−0.113384	−	1.00668i
$794$	−10.7254	+	6.19233i	−0.380631	+	0.219758i
$795$	−0.575614	+	0.575614i	−0.0204149	+	0.0204149i
$796$	−0.0993202	+	0.0573426i	−0.00352031	+	0.00203245i
$797$	−6.45737	−	11.1845i	−0.228732	−	0.396175i	0.728701	−	0.684832i	$-0.240125\pi$
$797$	−6.45737	−	11.1845i	−0.228732	−	0.396175i	−0.957432	+	0.288657i	$0.906791\pi$
$798$	0.678505	−	7.04338i	0.0240188	−	0.249333i
$799$	−17.1360	−	4.59157i	−0.606227	−	0.162438i
$800$	3.52692	+	3.52692i	0.124695	+	0.124695i
$801$	13.6924	+	3.66888i	0.483799	+	0.129633i
$802$	−2.27000	+	3.93175i	−0.0801565	+	0.138835i
$803$	12.6652	+	21.9367i	0.446944	+	0.774131i
$804$	−2.10034	−	7.83858i	−0.0740733	−	0.276445i
$805$	−0.257505	−	1.53919i	−0.00907585	−	0.0542494i
$806$	14.0296	−	32.1526i	0.494172	−	1.13253i
$807$	7.42208	−	12.8554i	0.261270	−	0.452532i
$808$	9.15208	+	9.15208i	0.321969	+	0.321969i
$809$	−45.9264			−1.61469			−0.807344	−	0.590082i	$-0.799096\pi$
$809$	−45.9264			−1.61469			−0.807344	+	0.590082i	$0.799096\pi$
$810$	0.110364			0.00387780
$811$	−1.64402	−	1.64402i	−0.0577294	−	0.0577294i	0.677653	−	0.735382i	$-0.262997\pi$
$811$	−1.64402	−	1.64402i	−0.0577294	−	0.0577294i	−0.735382	+	0.677653i	$0.762997\pi$
$812$	0.494885	−	5.13727i	0.0173671	−	0.180283i
$813$	1.61164	−	6.01472i	0.0565227	−	0.210946i
$814$	−34.9756	+	9.37167i	−1.22589	+	0.328477i
$815$	1.28584	+	0.742381i	0.0450411	+	0.0260045i
$816$			2.90502i			0.101696i
$817$	6.51787	+	1.74646i	0.228031	+	0.0611008i
$818$	10.2075			0.356898
$819$	−4.63588	+	8.33718i	−0.161991	+	0.291325i
$820$	0.714365			0.0249467
$821$	−54.3482	−	14.5625i	−1.89676	−	0.508236i	−0.997486	−	0.0708581i	$-0.977426\pi$
$821$	−54.3482	−	14.5625i	−1.89676	−	0.508236i	−0.899278	−	0.437378i	$-0.855907\pi$
$822$		−	11.2373i		−	0.391946i
$823$	−8.32151	−	4.80442i	−0.290070	−	0.167472i	0.347904	−	0.937530i	$-0.386894\pi$
$823$	−8.32151	−	4.80442i	−0.290070	−	0.167472i	−0.637973	+	0.770059i	$0.720227\pi$
$824$	−7.22451	+	1.93580i	−0.251678	+	0.0674368i
$825$	−6.12198	+	22.8475i	−0.213140	+	0.795449i
$826$	−6.79727	−	4.84889i	−0.236507	−	0.168714i
$827$	19.7507	+	19.7507i	0.686798	+	0.686798i	0.961523	−	0.274725i	$-0.0885868\pi$
$827$	19.7507	+	19.7507i	0.686798	+	0.686798i	−0.274725	+	0.961523i	$0.588587\pi$
$828$	−5.34454			−0.185736
$829$	23.6987			0.823090			0.411545	−	0.911389i	$-0.364989\pi$
$829$	23.6987			0.823090			0.411545	+	0.911389i	$0.364989\pi$
$830$	0.886854	+	0.886854i	0.0307832	+	0.0307832i
$831$	−6.72115	+	11.6414i	−0.233154	+	0.403835i
$832$	−0.403548	−	3.58290i	−0.0139905	−	0.124215i
$833$	−19.9612	−	3.88184i	−0.691615	−	0.134498i
$834$	1.04046	+	3.88305i	0.0360282	+	0.134459i
$835$	0.966828	+	1.67460i	0.0334585	+	0.0579518i
$836$	−6.34151	+	10.9838i	−0.219326	+	0.379883i
$837$	−9.39797	−	2.51818i	−0.324841	−	0.0870410i
$838$	−14.2494	−	14.2494i	−0.492236	−	0.492236i
$839$	29.6146	+	7.93522i	1.02241	+	0.273954i	0.730806	−	0.682585i	$-0.239144\pi$
$839$	29.6146	+	7.93522i	1.02241	+	0.273954i	0.291604	+	0.956539i	$0.405811\pi$
$840$	−0.121077	−	0.265710i	−0.00417756	−	0.00916787i
$841$	12.5974	+	21.8193i	0.434393	+	0.752391i
$842$	29.5184	−	17.0425i	1.01727	−	0.587322i
$843$	−18.2088	+	18.2088i	−0.627145	+	0.627145i
$844$	−18.1989	+	10.5071i	−0.626431	+	0.361670i
$845$	−1.26852	+	0.670302i	−0.0436385	+	0.0230591i
$846$		−	6.10682i		−	0.209957i
$847$	−24.7459	−	17.6527i	−0.850279	−	0.606553i
$848$	3.68798	−	6.38777i	0.126646	−	0.219357i
$849$			2.42771i			0.0833186i
$850$	3.75022	−	13.9960i	0.128631	−	0.480059i
$851$	10.5619	+	39.4176i	0.362058	+	1.35122i
$852$	4.19741	−	4.19741i	0.143801	−	0.143801i
$853$	1.34197	−	1.34197i	0.0459482	−	0.0459482i	−0.683759	−	0.729708i	$-0.739656\pi$
$853$	1.34197	−	1.34197i	0.0459482	−	0.0459482i	0.729708	+	0.683759i	$0.239656\pi$
$854$	13.3147	+	16.1534i	0.455620	+	0.552760i
$855$	−0.255621	−	0.147583i	−0.00874205	−	0.00504722i
$856$	1.52988	−	5.70958i	0.0522901	−	0.195149i
$857$	−9.21153	−	15.9548i	−0.314660	−	0.545007i	0.664705	−	0.747106i	$-0.268557\pi$
$857$	−9.21153	−	15.9548i	−0.314660	−	0.545007i	−0.979365	+	0.202099i	$0.935224\pi$
$858$	13.7578	−	10.1528i	0.469683	−	0.346612i
$859$	7.23497	+	4.17711i	0.246854	+	0.142521i	0.618323	−	0.785924i	$-0.287812\pi$
$859$	7.23497	+	4.17711i	0.246854	+	0.142521i	−0.371469	+	0.928445i	$0.621146\pi$
$860$	0.268965	−	0.0720689i	0.00917162	−	0.00245753i
$861$	16.0407	+	5.99814i	0.546665	+	0.204416i
$862$	−11.3591	+	6.55818i	−0.386892	+	0.223372i
$863$	9.77062	+	36.4645i	0.332596	+	1.24126i	0.906452	+	0.422309i	$0.138780\pi$
$863$	9.77062	+	36.4645i	0.332596	+	1.24126i	−0.573856	+	0.818956i	$0.694553\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	0.306726	−	0.0821869i	0.0104290	−	0.00279444i
$866$	3.56335	+	13.2986i	0.121088	+	0.451905i
$867$	−7.41390	+	4.28042i	−0.251789	+	0.145371i
$868$	4.24754	+	25.3890i	0.144171	+	0.861758i
$869$	17.5903	−	4.71331i	0.596710	−	0.159888i
$870$	−0.186443	−	0.107643i	−0.00632102	−	0.00364944i
$871$	18.2439	−	22.8752i	0.618170	−	0.775095i
$872$	−6.09467	−	10.5563i	−0.206392	−	0.357481i
$873$	3.07814	−	11.4878i	0.104179	−	0.388803i
$874$	12.3788	+	7.14692i	0.418720	+	0.241748i
$875$	0.481222	+	2.87643i	0.0162683	+	0.0972409i
$876$	3.77695	−	3.77695i	0.127611	−	0.127611i
$877$	3.59110	−	3.59110i	0.121263	−	0.121263i	−0.643871	−	0.765134i	$-0.722673\pi$
$877$	3.59110	−	3.59110i	0.121263	−	0.121263i	0.765134	+	0.643871i	$0.222673\pi$
$878$	5.11837	+	19.1020i	0.172737	+	0.644662i
$879$	7.09023	−	26.4611i	0.239148	−	0.892511i
$880$			0.523374i			0.0176429i
$881$	12.8099	−	22.1873i	0.431575	−	0.747510i	−0.565434	−	0.824793i	$-0.691291\pi$
$881$	12.8099	−	22.1873i	0.431575	−	0.747510i	0.997009	+	0.0772835i	$0.0246247\pi$
$882$	−0.487697	−	6.98299i	−0.0164216	−	0.235130i
$883$		−	56.3748i		−	1.89716i	−0.316533	−	0.948582i	$-0.602519\pi$
$883$		−	56.3748i		−	1.89716i	0.316533	−	0.948582i	$-0.397481\pi$
$884$	−8.42778	+	6.21946i	−0.283457	+	0.209183i
$885$	−0.301628	+	0.174145i	−0.0101391	+	0.00585381i
$886$	6.00116	−	6.00116i	0.201613	−	0.201613i
$887$	39.5933	−	22.8592i	1.32941	−	0.767536i	0.344203	−	0.938895i	$-0.388149\pi$
$887$	39.5933	−	22.8592i	1.32941	−	0.767536i	0.985209	+	0.171359i	$0.0548158\pi$
$888$	3.81774	+	6.61251i	0.128115	+	0.221901i
$889$	−44.7763	+	20.4034i	−1.50175	+	0.684309i
$890$	−1.51115	−	0.404912i	−0.0506540	−	0.0135727i
$891$	−3.35328	−	3.35328i	−0.112339	−	0.112339i
$892$	−22.4292	−	6.00988i	−0.750984	−	0.201226i
$893$	−8.16626	+	14.1444i	−0.273273	+	0.473323i
$894$	9.28005	+	16.0735i	0.310371	+	0.537579i
$895$	0.0572768	+	0.213760i	0.00191455	+	0.00714521i
$896$	1.68282	+	2.04160i	0.0562190	+	0.0682050i
$897$	−11.4423	−	15.5051i	−0.382047	−	0.517700i
$898$	3.87113	−	6.70500i	0.129181	−	0.223749i
$899$	13.4204	+	13.4204i	0.447594	+	0.447594i
$900$	4.98782			0.166261
$901$	−21.4274			−0.713849
$902$	−21.7051	−	21.7051i	−0.722702	−	0.722702i
$903$	6.64457	+	0.640087i	0.221118	+	0.0213008i
$904$	2.22734	−	8.31256i	0.0740804	−	0.276472i
$905$	0.744928	−	0.199603i	0.0247622	−	0.00663502i
$906$	−9.49182	−	5.48010i	−0.315344	−	0.182064i
$907$			0.00876367i			0.000290993i	1.00000		0.000145496i	$4.63129e-5\pi$
$907$			0.00876367i			0.000290993i	−1.00000		0.000145496i	$0.999954\pi$
$908$	−14.0233	−	3.75754i	−0.465380	−	0.124698i
$909$	12.9430			0.429292
$910$	0.511635	−	0.920125i	0.0169605	−	0.0305018i
$911$	53.0131			1.75640			0.878201	−	0.478291i	$-0.158744\pi$
$911$	53.0131			1.75640			0.878201	+	0.478291i	$0.158744\pi$
$912$	2.58334	+	0.692204i	0.0855430	+	0.0229212i
$913$		−	53.8920i		−	1.78357i
$914$	−29.9245	−	17.2769i	−0.989816	−	0.571470i
$915$	0.843463	−	0.226005i	0.0278840	−	0.00747150i
$916$	6.31689	−	23.5749i	0.208716	−	0.778938i
$917$	−20.6013	+	9.38751i	−0.680316	+	0.310003i
$918$	2.05416	+	2.05416i	0.0677974	+	0.0677974i
$919$	0.352346			0.0116228			0.00581142	−	0.999983i	$-0.498150\pi$
$919$	0.352346			0.0116228			0.00581142	+	0.999983i	$0.498150\pi$
$920$	0.589845			0.0194466
$921$	18.4157	+	18.4157i	0.606819	+	0.606819i
$922$	−13.2125	+	22.8848i	−0.435132	+	0.753671i
$923$	21.1635	+	3.19076i	0.696605	+	0.105025i
$924$	−4.39449	+	11.7521i	−0.144568	+	0.386615i
$925$	−9.85696	−	36.7867i	−0.324095	−	1.20954i
$926$	6.39106	+	11.0696i	0.210023	+	0.363771i
$927$	−3.73968	+	6.47732i	−0.122827	+	0.212743i
$928$	1.88422	+	0.504876i	0.0618527	+	0.0165734i
$929$	−8.30708	−	8.30708i	−0.272547	−	0.272547i	0.557578	−	0.830125i	$-0.311731\pi$
$929$	−8.30708	−	8.30708i	−0.272547	−	0.272547i	−0.830125	+	0.557578i	$0.811731\pi$
$930$	1.03720	+	0.277916i	0.0340111	+	0.00911324i
$931$	−8.20832	+	16.8259i	−0.269017	+	0.551446i
$932$	−9.87216	−	17.0991i	−0.323373	−	0.560099i
$933$	17.6328	−	10.1803i	0.577270	−	0.333287i
$934$	15.5365	−	15.5365i	0.508368	−	0.508368i
$935$	1.31672	−	0.760207i	0.0430613	−	0.0248614i
$936$	−2.81884	−	2.24814i	−0.0921367	−	0.0734827i
$937$		−	16.5324i		−	0.540089i	−0.962848	−	0.270045i	$-0.912962\pi$
$937$		−	16.5324i		−	0.540089i	0.962848	−	0.270045i	$-0.0870385\pi$
$938$	−2.05877	+	21.3716i	−0.0672214	+	0.697807i
$939$	−1.80234	+	3.12174i	−0.0588170	+	0.101874i
$940$			0.673973i			0.0219826i
$941$	9.08618	−	33.9101i	0.296201	−	1.10544i	−0.644058	−	0.764977i	$-0.722750\pi$
$941$	9.08618	−	33.9101i	0.296201	−	1.10544i	0.940259	−	0.340460i	$-0.110583\pi$
$942$	−5.89931	−	22.0165i	−0.192210	−	0.717337i
$943$	−24.4618	+	24.4618i	−0.796586	+	0.796586i
$944$	2.23151	−	2.23151i	0.0726293	−	0.0726293i
$945$	−0.273500	−	0.102271i	−0.00889695	−	0.00332687i
$946$	−10.3619	−	5.98245i	−0.336894	−	0.194506i
$947$	−13.7473	+	51.3055i	−0.446726	+	1.66720i	0.264613	+	0.964355i	$0.414756\pi$
$947$	−13.7473	+	51.3055i	−0.446726	+	1.66720i	−0.711339	+	0.702849i	$0.751911\pi$
$948$	−1.92006	−	3.32564i	−0.0623606	−	0.108012i
$949$	19.0435	+	2.87114i	0.618179	+	0.0932013i
$950$	−11.5526	−	6.66989i	−0.374815	−	0.216400i
$951$	14.4318	−	3.86698i	0.467982	−	0.125395i
$952$	2.69199	−	7.19912i	0.0872480	−	0.233325i
$953$	−34.7257	+	20.0489i	−1.12488	+	0.649447i	−0.942641	−	0.333808i	$-0.891666\pi$
$953$	−34.7257	+	20.0489i	−1.12488	+	0.649447i	−0.182234	+	0.983255i	$0.558333\pi$
$954$	−1.90904	−	7.12464i	−0.0618075	−	0.230669i
$955$	1.79383	−	0.480656i	0.0580471	−	0.0155537i
$956$	28.3840	−	7.60547i	0.918005	−	0.245979i
$957$	2.39425	+	8.93547i	0.0773952	+	0.288843i
$958$	−8.60981	+	4.97087i	−0.278170	+	0.160602i
$959$	−10.4133	+	27.8479i	−0.336262	+	0.899255i
$960$	0.106603	−	0.0285643i	0.00344061	−	0.000921909i
$961$	−55.1339	−	31.8316i	−1.77851	−	1.02682i
$962$	−11.0101	+	25.2326i	−0.354980	+	0.813531i
$963$	−2.95549	−	5.11907i	−0.0952395	−	0.164960i
$964$	2.79215	−	10.4204i	0.0899291	−	0.335620i
$965$	−1.20027	−	0.692978i	−0.0386382	−	0.0223078i
$966$	13.2446	+	4.95262i	0.426140	+	0.159348i
$967$	−30.1394	+	30.1394i	−0.969218	+	0.969218i	−0.999540	−	0.0303221i	$-0.990347\pi$
$967$	−30.1394	+	30.1394i	−0.969218	+	0.969218i	0.0303221	+	0.999540i	$0.490347\pi$
$968$	8.12393	−	8.12393i	0.261113	−	0.261113i
$969$	−2.01087	−	7.50467i	−0.0645984	−	0.241085i
$970$	−0.339716	+	1.26784i	−0.0109076	+	0.0407078i
$971$		−	46.6604i		−	1.49740i	−0.662907	−	0.748701i	$-0.730678\pi$
$971$		−	46.6604i		−	1.49740i	0.662907	−	0.748701i	$-0.269322\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	1.01987	−	10.5870i	0.0326955	−	0.339404i
$974$		−	13.7407i		−	0.440281i
$975$	10.6786	+	14.4702i	0.341988	+	0.463417i
$976$	−6.85213	+	3.95608i	−0.219331	+	0.126631i
$977$	11.3147	−	11.3147i	0.361988	−	0.361988i	−0.502556	−	0.864544i	$-0.667607\pi$
$977$	11.3147	−	11.3147i	0.361988	−	0.361988i	0.864544	+	0.502556i	$0.167607\pi$
$978$	−11.6509	+	6.72666i	−0.372555	+	0.215095i
$979$	33.6118	+	58.2174i	1.07424	+	1.86064i
$980$	0.0538242	+	0.770671i	0.00171935	+	0.0246182i
$981$	−11.7740	−	3.15483i	−0.375915	−	0.100726i
$982$	14.5359	+	14.5359i	0.463858	+	0.463858i
$983$	−4.37523	−	1.17234i	−0.139548	−	0.0373918i	0.188369	−	0.982098i	$-0.439680\pi$
$983$	−4.37523	−	1.17234i	−0.139548	−	0.0373918i	−0.327917	+	0.944707i	$0.606347\pi$
$984$	−3.23640	+	5.60562i	−0.103173	+	0.178701i
$985$	−1.22197	−	2.11651i	−0.0389351	−	0.0674376i
$986$	−1.46668	−	5.47372i	−0.0467085	−	0.174319i
$987$	−5.65899	+	15.1337i	−0.180128	+	0.481711i
$988$	3.52260	+	8.97651i	0.112069	+	0.285581i
$989$	−6.74225	+	11.6779i	−0.214391	+	0.371336i
$990$	0.370082	+	0.370082i	0.0117620	+	0.0117620i
$991$	−39.2811			−1.24781			−0.623903	−	0.781502i	$-0.714454\pi$
$991$	−39.2811			−1.24781			−0.623903	+	0.781502i	$0.714454\pi$
$992$	−9.72950			−0.308912
$993$	0.887675	+	0.887675i	0.0281695	+	0.0281695i
$994$	−14.2915	+	6.51225i	−0.453298	+	0.206556i
$995$	0.00327590	−	0.0122258i	0.000103853	−	0.000387585i
$996$	−10.9770	+	2.94128i	−0.347819	+	0.0931979i
$997$	52.8810	+	30.5309i	1.67476	+	0.966923i	0.964914	+	0.262565i	$0.0845684\pi$
$997$	52.8810	+	30.5309i	1.67476	+	0.966923i	0.709845	+	0.704358i	$0.248765\pi$
$998$		−	36.7576i		−	1.16354i
$999$	7.37530	+	1.97621i	0.233344	+	0.0625244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.19.3	✓	32
7.3	odd	6		546.2.cg.a.409.7	yes	32
13.11	odd	12		546.2.cg.a.271.7	yes	32
91.24	even	12	inner	546.2.by.a.115.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.3	✓	32	1.1	even	1	trivial
546.2.by.a.115.3	yes	32	91.24	even	12	inner
546.2.cg.a.271.7	yes	32	13.11	odd	12
546.2.cg.a.409.7	yes	32	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.106603 + 0.0285643i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-1.53649 + 2.15388i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.106603 + 0.0285643i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-1.53649 + 2.15388i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.110364 q^{10} +(-3.35328 - 3.35328i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.58290 + 0.403548i) q^{13} +(2.04160 - 1.68282i) q^{14} +(-0.0285643 - 0.106603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.45251 - 2.51582i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.89114 - 1.89114i) q^{19} +(-0.106603 - 0.0285643i) q^{20} +(-2.15388 - 1.53649i) q^{21} +(2.37113 + 4.10691i) q^{22} +(4.62851 - 2.67227i) q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.31958 + 2.49391i) q^{25} +(3.56526 + 0.537525i) q^{26} -1.00000i q^{27} +(-2.40758 + 1.09707i) q^{28} +(-0.975346 + 1.68935i) q^{29} +0.110364i q^{30} +(2.51818 - 9.39797i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(3.35328 - 3.35328i) q^{33} +(-2.05416 + 2.05416i) q^{34} +(0.102271 - 0.273500i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-1.97621 + 7.37530i) q^{37} +(1.33724 + 2.31616i) q^{38} +(-0.403548 - 3.58290i) q^{39} +(0.0955780 + 0.0551820i) q^{40} +(-6.25225 + 1.67529i) q^{41} +(1.68282 + 2.04160i) q^{42} +(-2.18502 + 1.26152i) q^{43} +(-1.22739 - 4.58067i) q^{44} +(0.106603 - 0.0285643i) q^{45} +(-5.16243 + 1.38327i) q^{46} +(-1.58056 - 5.89873i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-2.27841 - 6.61883i) q^{49} +(4.81786 - 1.29094i) q^{50} +(2.51582 + 1.45251i) q^{51} +(-3.30465 - 1.44197i) q^{52} +(-3.68798 - 6.38777i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(0.453255 + 0.261687i) q^{55} +(2.60949 - 0.436563i) q^{56} +(1.89114 - 1.89114i) q^{57} +(1.37935 - 1.37935i) q^{58} +(-0.816788 - 3.04829i) q^{59} +(0.0285643 - 0.106603i) q^{60} +7.91216i q^{61} +(-4.86475 + 8.42599i) q^{62} +(1.53649 - 2.15388i) q^{63} +1.00000i q^{64} +(0.370422 - 0.145363i) q^{65} +(-4.10691 + 2.37113i) q^{66} +(-5.73824 + 5.73824i) q^{67} +(2.51582 - 1.45251i) q^{68} +(2.67227 + 4.62851i) q^{69} +(-0.169573 + 0.237711i) q^{70} +(-5.73377 - 1.53636i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-5.15941 - 1.38246i) q^{73} +(3.81774 - 6.61251i) q^{74} +(-2.49391 - 4.31958i) q^{75} +(-0.692204 - 2.58334i) q^{76} +(12.3748 - 2.07029i) q^{77} +(-0.537525 + 3.56526i) q^{78} +(-1.92006 + 3.32564i) q^{79} +(-0.0780392 - 0.0780392i) q^{80} +1.00000 q^{81} +6.47281 q^{82} +(8.03572 + 8.03572i) q^{83} +(-1.09707 - 2.40758i) q^{84} +(-0.0829800 + 0.309686i) q^{85} +(2.43707 - 0.653011i) q^{86} +(-1.68935 - 0.975346i) q^{87} +4.74225i q^{88} +(-13.6924 - 3.66888i) q^{89} -0.110364 q^{90} +(4.63588 - 8.33718i) q^{91} +5.34454 q^{92} +(9.39797 + 2.51818i) q^{93} +6.10682i q^{94} +(0.255621 + 0.147583i) q^{95} +(0.965926 - 0.258819i) q^{96} +(-3.07814 + 11.4878i) q^{97} +(0.487697 + 6.98299i) q^{98} +(3.35328 + 3.35328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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