LMFDB - Embedded newform 546.2.o.a.265.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.1
Root			$-3.73923i$ of defining polynomial
Character	$\chi$	$=$	546.265
Dual form			546.2.o.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(-1.80230 - 1.80230i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.93693 + 1.80230i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(-1.80230 - 1.80230i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.93693 + 1.80230i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +2.54884 q^{10} +(0.936931 + 0.936931i) q^{11} +1.00000 q^{12} +(2.00000 - 3.00000i) q^{13} +(-2.64404 + 0.0951965i) q^{14} +(1.80230 - 1.80230i) q^{15} -1.00000 q^{16} -0.496594 q^{17} +(0.707107 - 0.707107i) q^{18} +(3.07156 + 3.07156i) q^{19} +(-1.80230 + 1.80230i) q^{20} +(-1.80230 + 1.93693i) q^{21} -1.32502 q^{22} +7.37727i q^{23} +(-0.707107 + 0.707107i) q^{24} +1.49659i q^{25} +(0.707107 + 3.53553i) q^{26} -1.00000i q^{27} +(1.80230 - 1.93693i) q^{28} +7.25113 q^{29} +2.54884i q^{30} +(5.73923 + 5.73923i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.936931 + 0.936931i) q^{33} +(0.351145 - 0.351145i) q^{34} +(-0.242641 - 6.73923i) q^{35} +1.00000i q^{36} +(3.54154 + 3.54154i) q^{37} -4.34384 q^{38} +(3.00000 + 2.00000i) q^{39} -2.54884i q^{40} +(-6.11650 - 6.11650i) q^{41} +(-0.0951965 - 2.64404i) q^{42} +6.85574i q^{43} +(0.936931 - 0.936931i) q^{44} +(1.80230 + 1.80230i) q^{45} +(-5.21652 - 5.21652i) q^{46} +(-5.87386 + 5.87386i) q^{47} -1.00000i q^{48} +(0.503406 + 6.98188i) q^{49} +(-1.05825 - 1.05825i) q^{50} -0.496594i q^{51} +(-3.00000 - 2.00000i) q^{52} -4.26926 q^{53} +(0.707107 + 0.707107i) q^{54} -3.37727i q^{55} +(0.0951965 + 2.64404i) q^{56} +(-3.07156 + 3.07156i) q^{57} +(-5.12732 + 5.12732i) q^{58} +(-1.37727 + 1.37727i) q^{59} +(-1.80230 - 1.80230i) q^{60} -0.496594i q^{61} -8.11650 q^{62} +(-1.93693 - 1.80230i) q^{63} +1.00000i q^{64} +(-9.01152 + 1.80230i) q^{65} -1.32502i q^{66} +(9.11650 - 9.11650i) q^{67} +0.496594i q^{68} -7.37727 q^{69} +(4.93693 + 4.59379i) q^{70} +(11.3773 - 11.3773i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(3.54154 - 3.54154i) q^{73} -5.00849 q^{74} -1.49659 q^{75} +(3.07156 - 3.07156i) q^{76} +(0.126137 + 3.50341i) q^{77} +(-3.53553 + 0.707107i) q^{78} -13.1499 q^{79} +(1.80230 + 1.80230i) q^{80} +1.00000 q^{81} +8.65004 q^{82} +(7.87386 + 7.87386i) q^{83} +(1.93693 + 1.80230i) q^{84} +(0.895013 + 0.895013i) q^{85} +(-4.84774 - 4.84774i) q^{86} +7.25113i q^{87} +1.32502i q^{88} +(10.2177 - 10.2177i) q^{89} -2.54884 q^{90} +(9.28077 - 2.20619i) q^{91} +7.37727 q^{92} +(-5.73923 + 5.73923i) q^{93} -8.30690i q^{94} -11.0718i q^{95} +(0.707107 + 0.707107i) q^{96} +(9.46034 + 9.46034i) q^{97} +(-5.29289 - 4.58097i) q^{98} +(-0.936931 - 0.936931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	−1.80230	−	1.80230i	−0.806015	−	0.806015i	0.178014	−	0.984028i	$-0.443033\pi$
$5$	−1.80230	−	1.80230i	−0.806015	−	0.806015i	−0.984028	+	0.178014i	$0.943033\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	1.93693	+	1.80230i	0.732091	+	0.681207i
$7$	1.93693	+	1.80230i	0.732091	+	0.681207i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	2.54884			0.806015
$11$	0.936931	+	0.936931i	0.282495	+	0.282495i	0.834103	−	0.551608i	$-0.185986\pi$
$11$	0.936931	+	0.936931i	0.282495	+	0.282495i	−0.551608	+	0.834103i	$0.685986\pi$
$12$	1.00000			0.288675
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$	−2.64404	+	0.0951965i	−0.706649	+	0.0254423i
$15$	1.80230	−	1.80230i	0.465353	−	0.465353i
$16$	−1.00000			−0.250000
$17$	−0.496594			−0.120442			−0.0602209	−	0.998185i	$-0.519180\pi$
$17$	−0.496594			−0.120442			−0.0602209	+	0.998185i	$0.519180\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	3.07156	+	3.07156i	0.704664	+	0.704664i	0.965408	−	0.260744i	$-0.0839678\pi$
$19$	3.07156	+	3.07156i	0.704664	+	0.704664i	−0.260744	+	0.965408i	$0.583968\pi$
$20$	−1.80230	+	1.80230i	−0.403007	+	0.403007i
$21$	−1.80230	+	1.93693i	−0.393295	+	0.422673i
$22$	−1.32502			−0.282495
$23$			7.37727i			1.53827i	0.639088	+	0.769133i	$0.279312\pi$
$23$			7.37727i			1.53827i	−0.639088	+	0.769133i	$0.720688\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			1.49659i			0.299319i
$26$	0.707107	+	3.53553i	0.138675	+	0.693375i
$27$		−	1.00000i		−	0.192450i
$28$	1.80230	−	1.93693i	0.340603	−	0.366046i
$29$	7.25113			1.34650			0.673251	−	0.739414i	$-0.264897\pi$
$29$	7.25113			1.34650			0.673251	+	0.739414i	$0.264897\pi$
$30$			2.54884i			0.465353i
$31$	5.73923	+	5.73923i	1.03080	+	1.03080i	0.999510	+	0.0312865i	$0.00996043\pi$
$31$	5.73923	+	5.73923i	1.03080	+	1.03080i	0.0312865	+	0.999510i	$0.490040\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.936931	+	0.936931i	−0.163099	+	0.163099i
$34$	0.351145	−	0.351145i	0.0602209	−	0.0602209i
$35$	−0.242641	−	6.73923i	−0.0410138	−	1.13914i
$36$			1.00000i			0.166667i
$37$	3.54154	+	3.54154i	0.582225	+	0.582225i	0.935514	−	0.353289i	$-0.114937\pi$
$37$	3.54154	+	3.54154i	0.582225	+	0.582225i	−0.353289	+	0.935514i	$0.614937\pi$
$38$	−4.34384			−0.704664
$39$	3.00000	+	2.00000i	0.480384	+	0.320256i
$40$		−	2.54884i		−	0.403007i
$41$	−6.11650	−	6.11650i	−0.955237	−	0.955237i	0.0438029	−	0.999040i	$-0.486053\pi$
$41$	−6.11650	−	6.11650i	−0.955237	−	0.955237i	−0.999040	+	0.0438029i	$0.986053\pi$
$42$	−0.0951965	−	2.64404i	−0.0146891	−	0.407984i
$43$			6.85574i			1.04549i	0.852489	+	0.522745i	$0.175092\pi$
$43$			6.85574i			1.04549i	−0.852489	+	0.522745i	$0.824908\pi$
$44$	0.936931	−	0.936931i	0.141248	−	0.141248i
$45$	1.80230	+	1.80230i	0.268672	+	0.268672i
$46$	−5.21652	−	5.21652i	−0.769133	−	0.769133i
$47$	−5.87386	+	5.87386i	−0.856791	+	0.856791i	−0.990959	−	0.134168i	$-0.957164\pi$
$47$	−5.87386	+	5.87386i	−0.856791	+	0.856791i	0.134168	+	0.990959i	$0.457164\pi$
$48$		−	1.00000i		−	0.144338i
$49$	0.503406	+	6.98188i	0.0719152	+	0.997411i
$50$	−1.05825	−	1.05825i	−0.149659	−	0.149659i
$51$		−	0.496594i		−	0.0695371i
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	−4.26926			−0.586427			−0.293214	−	0.956047i	$-0.594725\pi$
$53$	−4.26926			−0.586427			−0.293214	+	0.956047i	$0.594725\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$		−	3.37727i		−	0.455391i
$56$	0.0951965	+	2.64404i	0.0127212	+	0.353324i
$57$	−3.07156	+	3.07156i	−0.406838	+	0.406838i
$58$	−5.12732	+	5.12732i	−0.673251	+	0.673251i
$59$	−1.37727	+	1.37727i	−0.179305	+	0.179305i	−0.791053	−	0.611748i	$-0.790467\pi$
$59$	−1.37727	+	1.37727i	−0.179305	+	0.179305i	0.611748	+	0.791053i	$0.290467\pi$
$60$	−1.80230	−	1.80230i	−0.232676	−	0.232676i
$61$		−	0.496594i		−	0.0635823i	−0.999495	−	0.0317912i	$-0.989879\pi$
$61$		−	0.496594i		−	0.0635823i	0.999495	−	0.0317912i	$-0.0101211\pi$
$62$	−8.11650			−1.03080
$63$	−1.93693	−	1.80230i	−0.244030	−	0.227069i
$64$			1.00000i			0.125000i
$65$	−9.01152	+	1.80230i	−1.11774	+	0.223548i
$66$		−	1.32502i		−	0.163099i
$67$	9.11650	−	9.11650i	1.11376	−	1.11376i	0.121120	−	0.992638i	$-0.461351\pi$
$67$	9.11650	−	9.11650i	1.11376	−	1.11376i	0.992638	−	0.121120i	$-0.0386487\pi$
$68$			0.496594i			0.0602209i
$69$	−7.37727			−0.888119
$70$	4.93693	+	4.59379i	0.590076	+	0.549062i
$71$	11.3773	−	11.3773i	1.35023	−	1.35023i	0.464837	−	0.885396i	$-0.346113\pi$
$71$	11.3773	−	11.3773i	1.35023	−	1.35023i	0.885396	−	0.464837i	$-0.153887\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	3.54154	−	3.54154i	0.414506	−	0.414506i	−0.468799	−	0.883305i	$-0.655313\pi$
$73$	3.54154	−	3.54154i	0.414506	−	0.414506i	0.883305	+	0.468799i	$0.155313\pi$
$74$	−5.00849			−0.582225
$75$	−1.49659			−0.172812
$76$	3.07156	−	3.07156i	0.352332	−	0.352332i
$77$	0.126137	+	3.50341i	0.0143747	+	0.399250i
$78$	−3.53553	+	0.707107i	−0.400320	+	0.0800641i
$79$	−13.1499			−1.47948			−0.739741	−	0.672891i	$-0.765052\pi$
$79$	−13.1499			−1.47948			−0.739741	+	0.672891i	$0.765052\pi$
$80$	1.80230	+	1.80230i	0.201504	+	0.201504i
$81$	1.00000			0.111111
$82$	8.65004			0.955237
$83$	7.87386	+	7.87386i	0.864269	+	0.864269i	0.991831	−	0.127562i	$-0.0407151\pi$
$83$	7.87386	+	7.87386i	0.864269	+	0.864269i	−0.127562	+	0.991831i	$0.540715\pi$
$84$	1.93693	+	1.80230i	0.211337	+	0.196647i
$85$	0.895013	+	0.895013i	0.0970778	+	0.0970778i
$86$	−4.84774	−	4.84774i	−0.522745	−	0.522745i
$87$			7.25113i			0.777403i
$88$			1.32502i			0.141248i
$89$	10.2177	−	10.2177i	1.08307	−	1.08307i	0.0868533	−	0.996221i	$-0.472319\pi$
$89$	10.2177	−	10.2177i	1.08307	−	1.08307i	0.996221	−	0.0868533i	$-0.0276811\pi$
$90$	−2.54884			−0.268672
$91$	9.28077	−	2.20619i	0.972889	−	0.231271i
$92$	7.37727			0.769133
$93$	−5.73923	+	5.73923i	−0.595131	+	0.595131i
$94$		−	8.30690i		−	0.856791i
$95$		−	11.0718i		−	1.13594i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	9.46034	+	9.46034i	0.960552	+	0.960552i	0.999251	−	0.0386985i	$-0.0123212\pi$
$97$	9.46034	+	9.46034i	0.960552	+	0.960552i	−0.0386985	+	0.999251i	$0.512321\pi$
$98$	−5.29289	−	4.58097i	−0.534663	−	0.462748i
$99$	−0.936931	−	0.936931i	−0.0941651	−	0.0941651i
$100$	1.49659			0.149659
$101$	−4.66465			−0.464150			−0.232075	−	0.972698i	$-0.574551\pi$
$101$	−4.66465			−0.464150			−0.232075	+	0.972698i	$0.574551\pi$
$102$	0.351145	+	0.351145i	0.0347685	+	0.0347685i
$103$	−18.5865			−1.83138			−0.915690	−	0.401885i	$-0.868355\pi$
$103$	−18.5865			−1.83138			−0.915690	+	0.401885i	$0.868355\pi$
$104$	3.53553	−	0.707107i	0.346688	−	0.0693375i
$105$	6.73923	−	0.242641i	0.657682	−	0.0236793i
$106$	3.01882	−	3.01882i	0.293214	−	0.293214i
$107$	6.95694			0.672553			0.336276	−	0.941763i	$-0.390832\pi$
$107$	6.95694			0.672553			0.336276	+	0.941763i	$0.390832\pi$
$108$	−1.00000			−0.0962250
$109$	2.94374	−	2.94374i	0.281959	−	0.281959i	−0.551931	−	0.833890i	$-0.686109\pi$
$109$	2.94374	−	2.94374i	0.281959	−	0.281959i	0.833890	+	0.551931i	$0.186109\pi$
$110$	2.38809	+	2.38809i	0.227695	+	0.227695i
$111$	−3.54154	+	3.54154i	−0.336148	+	0.336148i
$112$	−1.93693	−	1.80230i	−0.183023	−	0.170302i
$113$	−2.93996			−0.276568			−0.138284	−	0.990393i	$-0.544159\pi$
$113$	−2.93996			−0.276568			−0.138284	+	0.990393i	$0.544159\pi$
$114$		−	4.34384i		−	0.406838i
$115$	13.2961	−	13.2961i	1.23987	−	1.23987i
$116$		−	7.25113i		−	0.673251i
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$		−	1.94775i		−	0.179305i
$119$	−0.961868	−	0.895013i	−0.0881743	−	0.0820457i
$120$	2.54884			0.232676
$121$		−	9.24432i		−	0.840393i
$122$	0.351145	+	0.351145i	0.0317912	+	0.0317912i
$123$	6.11650	−	6.11650i	0.551507	−	0.551507i
$124$	5.73923	−	5.73923i	0.515398	−	0.515398i
$125$	−6.31420	+	6.31420i	−0.564759	+	0.564759i
$126$	2.64404	−	0.0951965i	0.235550	−	0.00848077i
$127$		−	19.8376i		−	1.76030i	−0.474692	−	0.880152i	$-0.657441\pi$
$127$		−	19.8376i		−	1.76030i	0.474692	−	0.880152i	$-0.342559\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−6.85574			−0.603614
$130$	5.09768	−	7.64653i	0.447096	−	0.670645i
$131$			5.10801i			0.446289i	0.974785	+	0.223145i	$0.0716322\pi$
$131$			5.10801i			0.446289i	−0.974785	+	0.223145i	$0.928368\pi$
$132$	0.936931	+	0.936931i	0.0815494	+	0.0815494i
$133$	0.413518	+	11.4853i	0.0358566	+	0.995900i
$134$			12.8927i			1.11376i
$135$	−1.80230	+	1.80230i	−0.155118	+	0.155118i
$136$	−0.351145	−	0.351145i	−0.0301104	−	0.0301104i
$137$	3.80230	+	3.80230i	0.324853	+	0.324853i	0.850625	−	0.525773i	$-0.176224\pi$
$137$	3.80230	+	3.80230i	0.324853	+	0.324853i	−0.525773	+	0.850625i	$0.676224\pi$
$138$	5.21652	−	5.21652i	0.444059	−	0.444059i
$139$		−	2.93996i		−	0.249364i	−0.992197	−	0.124682i	$-0.960209\pi$
$139$		−	2.93996i		−	0.249364i	0.992197	−	0.124682i	$-0.0397910\pi$
$140$	−6.73923	+	0.242641i	−0.569569	+	0.0205069i
$141$	−5.87386	−	5.87386i	−0.494668	−	0.494668i
$142$			16.0899i			1.35023i
$143$	4.68466	−	0.936931i	0.391751	−	0.0783501i
$144$	1.00000			0.0833333
$145$	−13.0687	−	13.0687i	−1.08530	−	1.08530i
$146$			5.00849i			0.414506i
$147$	−6.98188	+	0.503406i	−0.575855	+	0.0415202i
$148$	3.54154	−	3.54154i	0.291113	−	0.291113i
$149$	−1.74605	+	1.74605i	−0.143042	+	0.143042i	−0.775001	−	0.631960i	$-0.782251\pi$
$149$	−1.74605	+	1.74605i	−0.143042	+	0.143042i	0.631960	+	0.775001i	$0.282251\pi$
$150$	1.05825	−	1.05825i	0.0864059	−	0.0864059i
$151$	−6.55003	−	6.55003i	−0.533034	−	0.533034i	0.388440	−	0.921474i	$-0.373014\pi$
$151$	−6.55003	−	6.55003i	−0.533034	−	0.533034i	−0.921474	+	0.388440i	$0.873014\pi$
$152$			4.34384i			0.352332i
$153$	0.496594			0.0401472
$154$	−2.56647	−	2.38809i	−0.206812	−	0.192438i
$155$		−	20.6877i		−	1.66167i
$156$	2.00000	−	3.00000i	0.160128	−	0.240192i
$157$			1.70581i			0.136138i	0.997681	+	0.0680691i	$0.0216838\pi$
$157$			1.70581i			0.136138i	−0.997681	+	0.0680691i	$0.978316\pi$
$158$	9.29841	−	9.29841i	0.739741	−	0.739741i
$159$		−	4.26926i		−	0.338574i
$160$	−2.54884			−0.201504
$161$	−13.2961	+	14.2893i	−1.04788	+	1.12615i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−4.23583	−	4.23583i	−0.331776	−	0.331776i	0.521485	−	0.853261i	$-0.325378\pi$
$163$	−4.23583	−	4.23583i	−0.331776	−	0.331776i	−0.853261	+	0.521485i	$0.825378\pi$
$164$	−6.11650	+	6.11650i	−0.477619	+	0.477619i
$165$	3.37727			0.262920
$166$	−11.1353			−0.864269
$167$	8.02001	−	8.02001i	0.620607	−	0.620607i	−0.325080	−	0.945687i	$-0.605391\pi$
$167$	8.02001	−	8.02001i	0.620607	−	0.620607i	0.945687	+	0.325080i	$0.105391\pi$
$168$	−2.64404	+	0.0951965i	−0.203992	+	0.00734457i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−1.26574			−0.0970778
$171$	−3.07156	−	3.07156i	−0.234888	−	0.234888i
$172$	6.85574			0.522745
$173$	4.21603			0.320538			0.160269	−	0.987073i	$-0.448764\pi$
$173$	4.21603			0.320538			0.160269	+	0.987073i	$0.448764\pi$
$174$	−5.12732	−	5.12732i	−0.388701	−	0.388701i
$175$	−2.69732	+	2.89880i	−0.203898	+	0.219129i
$176$	−0.936931	−	0.936931i	−0.0706239	−	0.0706239i
$177$	−1.37727	−	1.37727i	−0.103522	−	0.103522i
$178$			14.4500i			1.08307i
$179$		−	5.33535i		−	0.398783i	−0.979920	−	0.199391i	$-0.936103\pi$
$179$		−	5.33535i		−	0.398783i	0.979920	−	0.199391i	$-0.0638965\pi$
$180$	1.80230	−	1.80230i	0.134336	−	0.134336i
$181$	1.79760			0.133615			0.0668073	−	0.997766i	$-0.478719\pi$
$181$	1.79760			0.133615			0.0668073	+	0.997766i	$0.478719\pi$
$182$	−5.00249	+	8.12251i	−0.370809	+	0.602080i
$183$	0.496594			0.0367093
$184$	−5.21652	+	5.21652i	−0.384567	+	0.384567i
$185$		−	12.7659i		−	0.938564i
$186$		−	8.11650i		−	0.595131i
$187$	−0.465274	−	0.465274i	−0.0340242	−	0.0340242i
$188$	5.87386	+	5.87386i	0.428395	+	0.428395i
$189$	1.80230	−	1.93693i	0.131098	−	0.140891i
$190$	7.82892	+	7.82892i	0.567969	+	0.567969i
$191$	−18.7889			−1.35952			−0.679758	−	0.733437i	$-0.737915\pi$
$191$	−18.7889			−1.35952			−0.679758	+	0.733437i	$0.737915\pi$
$192$	−1.00000			−0.0721688
$193$	1.37046	+	1.37046i	0.0986476	+	0.0986476i	0.754708	−	0.656061i	$-0.227778\pi$
$193$	1.37046	+	1.37046i	0.0986476	+	0.0986476i	−0.656061	+	0.754708i	$0.727778\pi$
$194$	−13.3789			−0.960552
$195$	−1.80230	−	9.01152i	−0.129066	−	0.645328i
$196$	6.98188	−	0.503406i	0.498705	−	0.0359576i
$197$	−2.86537	+	2.86537i	−0.204149	+	0.204149i	−0.801775	−	0.597626i	$-0.796111\pi$
$197$	−2.86537	+	2.86537i	−0.204149	+	0.204149i	0.597626	+	0.801775i	$0.296111\pi$
$198$	1.32502			0.0941651
$199$	−14.0650			−0.997038			−0.498519	−	0.866879i	$-0.666123\pi$
$199$	−14.0650			−0.997038			−0.498519	+	0.866879i	$0.666123\pi$
$200$	−1.05825	+	1.05825i	−0.0748297	+	0.0748297i
$201$	9.11650	+	9.11650i	0.643029	+	0.643029i
$202$	3.29841	−	3.29841i	0.232075	−	0.232075i
$203$	14.0449	+	13.0687i	0.985762	+	0.917246i
$204$	−0.496594			−0.0347685
$205$			22.0476i			1.53987i
$206$	13.1426	−	13.1426i	0.915690	−	0.915690i
$207$		−	7.37727i		−	0.512756i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$			5.75568i			0.398129i
$210$	−4.59379	+	4.93693i	−0.317001	+	0.340681i
$211$	−14.8557			−1.02271			−0.511356	−	0.859369i	$-0.670856\pi$
$211$	−14.8557			−1.02271			−0.511356	+	0.859369i	$0.670856\pi$
$212$			4.26926i			0.293214i
$213$	11.3773	+	11.3773i	0.779558	+	0.779558i
$214$	−4.91930	+	4.91930i	−0.336276	+	0.336276i
$215$	12.3561	−	12.3561i	0.842680	−	0.842680i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	0.772662	+	21.4603i	0.0524517	+	1.45682i
$218$			4.16308i			0.281959i
$219$	3.54154	+	3.54154i	0.239315	+	0.239315i
$220$	−3.37727			−0.227695
$221$	−0.993188	+	1.48978i	−0.0668090	+	0.100214i
$222$		−	5.00849i		−	0.336148i
$223$	6.24945	+	6.24945i	0.418494	+	0.418494i	0.884685	−	0.466190i	$-0.154374\pi$
$223$	6.24945	+	6.24945i	0.418494	+	0.418494i	−0.466190	+	0.884685i	$0.654374\pi$
$224$	2.64404	−	0.0951965i	0.176662	−	0.00636058i
$225$		−	1.49659i		−	0.0997729i
$226$	2.07886	−	2.07886i	0.138284	−	0.138284i
$227$	−5.50341	−	5.50341i	−0.365274	−	0.365274i	0.500476	−	0.865750i	$-0.333158\pi$
$227$	−5.50341	−	5.50341i	−0.365274	−	0.365274i	−0.865750	+	0.500476i	$0.833158\pi$
$228$	3.07156	+	3.07156i	0.203419	+	0.203419i
$229$	−2.50341	+	2.50341i	−0.165430	+	0.165430i	−0.784967	−	0.619537i	$-0.787320\pi$
$229$	−2.50341	+	2.50341i	−0.165430	+	0.165430i	0.619537	+	0.784967i	$0.287320\pi$
$230$			18.8035i			1.23987i
$231$	−3.50341	+	0.126137i	−0.230507	+	0.00829923i
$232$	5.12732	+	5.12732i	0.336625	+	0.336625i
$233$			16.5615i			1.08498i	0.840061	+	0.542491i	$0.182519\pi$
$233$			16.5615i			1.08498i	−0.840061	+	0.542491i	$0.817481\pi$
$234$	−0.707107	−	3.53553i	−0.0462250	−	0.231125i
$235$	21.1730			1.38117
$236$	1.37727	+	1.37727i	0.0896526	+	0.0896526i
$237$		−	13.1499i		−	0.854180i
$238$	1.31301	−	0.0472740i	0.0851100	−	0.00306432i
$239$	−2.41238	+	2.41238i	−0.156044	+	0.156044i	−0.780811	−	0.624767i	$-0.785194\pi$
$239$	−2.41238	+	2.41238i	−0.156044	+	0.156044i	0.624767	+	0.780811i	$0.285194\pi$
$240$	−1.80230	+	1.80230i	−0.116338	+	0.116338i
$241$	−8.37727	+	8.37727i	−0.539627	+	0.539627i	−0.923419	−	0.383792i	$-0.874618\pi$
$241$	−8.37727	+	8.37727i	−0.539627	+	0.539627i	0.383792	+	0.923419i	$0.374618\pi$
$242$	6.53672	+	6.53672i	0.420196	+	0.420196i
$243$			1.00000i			0.0641500i
$244$	−0.496594			−0.0317912
$245$	11.6762	−	13.4907i	0.745963	−	0.861892i
$246$			8.65004i			0.551507i
$247$	15.3578	−	3.07156i	0.977193	−	0.195439i
$248$			8.11650i			0.515398i
$249$	−7.87386	+	7.87386i	−0.498986	+	0.498986i
$250$		−	8.92963i		−	0.564759i
$251$	26.8727			1.69619			0.848096	−	0.529843i	$-0.177749\pi$
$251$	26.8727			1.69619			0.848096	+	0.529843i	$0.177749\pi$
$252$	−1.80230	+	1.93693i	−0.113534	+	0.122015i
$253$	−6.91199	+	6.91199i	−0.434553	+	0.434553i
$254$	14.0273	+	14.0273i	0.880152	+	0.880152i
$255$	−0.895013	+	0.895013i	−0.0560479	+	0.0560479i
$256$	1.00000			0.0625000
$257$	7.98302			0.497967			0.248984	−	0.968508i	$-0.419904\pi$
$257$	7.98302			0.497967			0.248984	+	0.968508i	$0.419904\pi$
$258$	4.84774	−	4.84774i	0.301807	−	0.301807i
$259$	0.476791	+	13.2426i	0.0296263	+	0.822858i
$260$	1.80230	+	9.01152i	0.111774	+	0.558871i
$261$	−7.25113			−0.448834
$262$	−3.61191	−	3.61191i	−0.223145	−	0.223145i
$263$	−2.47166			−0.152409			−0.0762044	−	0.997092i	$-0.524280\pi$
$263$	−2.47166			−0.152409			−0.0762044	+	0.997092i	$0.524280\pi$
$264$	−1.32502			−0.0815494
$265$	7.69449	+	7.69449i	0.472669	+	0.472669i
$266$	−8.41372	−	7.82892i	−0.515878	−	0.480022i
$267$	10.2177	+	10.2177i	0.625313	+	0.625313i
$268$	−9.11650	−	9.11650i	−0.556879	−	0.556879i
$269$		−	5.83761i		−	0.355926i	−0.984037	−	0.177963i	$-0.943049\pi$
$269$		−	5.83761i		−	0.355926i	0.984037	−	0.177963i	$-0.0569507\pi$
$270$		−	2.54884i		−	0.155118i
$271$	−8.57799	+	8.57799i	−0.521076	+	0.521076i	−0.917896	−	0.396820i	$-0.870114\pi$
$271$	−8.57799	+	8.57799i	−0.521076	+	0.521076i	0.396820	+	0.917896i	$0.370114\pi$
$272$	0.496594			0.0301104
$273$	2.20619	+	9.28077i	0.133525	+	0.561698i
$274$	−5.37727			−0.324853
$275$	−1.40221	+	1.40221i	−0.0845562	+	0.0845562i
$276$			7.37727i			0.444059i
$277$			2.66465i			0.160103i	0.996791	+	0.0800516i	$0.0255085\pi$
$277$			2.66465i			0.160103i	−0.996791	+	0.0800516i	$0.974491\pi$
$278$	2.07886	+	2.07886i	0.124682	+	0.124682i
$279$	−5.73923	−	5.73923i	−0.343599	−	0.343599i
$280$	4.59379	−	4.93693i	0.274531	−	0.295038i
$281$	−8.09952	−	8.09952i	−0.483177	−	0.483177i	0.422968	−	0.906145i	$-0.360988\pi$
$281$	−8.09952	−	8.09952i	−0.483177	−	0.483177i	−0.906145	+	0.422968i	$0.860988\pi$
$282$	8.30690			0.494668
$283$	−30.2730			−1.79954			−0.899772	−	0.436360i	$-0.856267\pi$
$283$	−30.2730			−1.79954			−0.899772	+	0.436360i	$0.856267\pi$
$284$	−11.3773	−	11.3773i	−0.675117	−	0.675117i
$285$	11.0718			0.655835
$286$	−2.65004	+	3.97506i	−0.156700	+	0.235050i
$287$	−0.823453	−	22.8710i	−0.0486069	−	1.35003i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−16.7534			−0.985494
$290$	18.4820			1.08530
$291$	−9.46034	+	9.46034i	−0.554575	+	0.554575i
$292$	−3.54154	−	3.54154i	−0.207253	−	0.207253i
$293$	−17.9235	+	17.9235i	−1.04710	+	1.04710i	−0.0482683	+	0.998834i	$0.515370\pi$
$293$	−17.9235	+	17.9235i	−1.04710	+	1.04710i	−0.998834	+	0.0482683i	$0.984630\pi$
$294$	4.58097	−	5.29289i	0.267168	−	0.308688i
$295$	4.96451			0.289045
$296$			5.00849i			0.291113i
$297$	0.936931	−	0.936931i	0.0543663	−	0.0543663i
$298$		−	2.46928i		−	0.143042i
$299$	22.1318	+	14.7545i	1.27992	+	0.853277i
$300$			1.49659i			0.0864059i
$301$	−12.3561	+	13.2791i	−0.712195	+	0.765394i
$302$	9.26314			0.533034
$303$		−	4.66465i		−	0.267977i
$304$	−3.07156	−	3.07156i	−0.176166	−	0.176166i
$305$	−0.895013	+	0.895013i	−0.0512483	+	0.0512483i
$306$	−0.351145	+	0.351145i	−0.0200736	+	0.0200736i
$307$	−5.09157	+	5.09157i	−0.290591	+	0.290591i	−0.837314	−	0.546723i	$-0.815875\pi$
$307$	−5.09157	+	5.09157i	−0.290591	+	0.290591i	0.546723	+	0.837314i	$0.315875\pi$
$308$	3.50341	−	0.126137i	0.199625	−	0.00718734i
$309$		−	18.5865i		−	1.05735i
$310$	14.6284	+	14.6284i	0.830837	+	0.830837i
$311$	−14.0729			−0.798001			−0.399001	−	0.916951i	$-0.630643\pi$
$311$	−14.0729			−0.798001			−0.399001	+	0.916951i	$0.630643\pi$
$312$	0.707107	+	3.53553i	0.0400320	+	0.200160i
$313$		−	28.3059i		−	1.59994i	−0.600037	−	0.799972i	$-0.704847\pi$
$313$		−	28.3059i		−	1.59994i	0.600037	−	0.799972i	$-0.295153\pi$
$314$	−1.20619	−	1.20619i	−0.0680691	−	0.0680691i
$315$	0.242641	+	6.73923i	0.0136713	+	0.379713i
$316$			13.1499i			0.739741i
$317$	20.5119	−	20.5119i	1.15206	−	1.15206i	0.165924	−	0.986138i	$-0.446939\pi$
$317$	20.5119	−	20.5119i	1.15206	−	1.15206i	0.986138	−	0.165924i	$-0.0530608\pi$
$318$	3.01882	+	3.01882i	0.169287	+	0.169287i
$319$	6.79381	+	6.79381i	0.380380	+	0.380380i
$320$	1.80230	−	1.80230i	0.100752	−	0.100752i
$321$			6.95694i			0.388298i
$322$	−0.702290	−	19.5058i	−0.0391371	−	1.08701i
$323$	−1.52532	−	1.52532i	−0.0848709	−	0.0848709i
$324$		−	1.00000i		−	0.0555556i
$325$	4.48978	+	2.99319i	0.249048	+	0.166032i
$326$	5.99037			0.331776
$327$	2.94374	+	2.94374i	0.162789	+	0.162789i
$328$		−	8.65004i		−	0.477619i
$329$	−21.9638	+	0.790787i	−1.21090	+	0.0435975i
$330$	−2.38809	+	2.38809i	−0.131460	+	0.131460i
$331$	−9.65502	+	9.65502i	−0.530688	+	0.530688i	−0.920777	−	0.390089i	$-0.872444\pi$
$331$	−9.65502	+	9.65502i	−0.530688	+	0.530688i	0.390089	+	0.920777i	$0.372444\pi$
$332$	7.87386	−	7.87386i	0.432134	−	0.432134i
$333$	−3.54154	−	3.54154i	−0.194075	−	0.194075i
$334$			11.3420i			0.620607i
$335$	−32.8614			−1.79541
$336$	1.80230	−	1.93693i	0.0983237	−	0.105668i
$337$			7.25113i			0.394994i	0.980303	+	0.197497i	$0.0632813\pi$
$337$			7.25113i			0.394994i	−0.980303	+	0.197497i	$0.936719\pi$
$338$	12.0208	+	4.94975i	0.653846	+	0.269231i
$339$		−	2.93996i		−	0.159677i
$340$	0.895013	−	0.895013i	0.0485389	−	0.0485389i
$341$			10.7545i			0.582391i
$342$	4.34384			0.234888
$343$	−11.6084	+	14.4307i	−0.626794	+	0.779185i
$344$	−4.84774	+	4.84774i	−0.261373	+	0.261373i
$345$	13.2961	+	13.2961i	0.715837	+	0.715837i
$346$	−2.98118	+	2.98118i	−0.160269	+	0.160269i
$347$	29.7647			1.59785			0.798927	−	0.601429i	$-0.205402\pi$
$347$	29.7647			1.59785			0.798927	+	0.601429i	$0.205402\pi$
$348$	7.25113			0.388701
$349$	13.1431	−	13.1431i	0.703535	−	0.703535i	−0.261633	−	0.965168i	$-0.584261\pi$
$349$	13.1431	−	13.1431i	0.703535	−	0.703535i	0.965168	+	0.261633i	$0.0842608\pi$
$350$	−0.142470	−	3.95705i	−0.00761536	−	0.211513i
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$	1.32502			0.0706239
$353$	−13.5531	−	13.5531i	−0.721356	−	0.721356i	0.247525	−	0.968881i	$-0.420383\pi$
$353$	−13.5531	−	13.5531i	−0.721356	−	0.721356i	−0.968881	+	0.247525i	$0.920383\pi$
$354$	1.94775			0.103522
$355$	−41.0106			−2.17662
$356$	−10.2177	−	10.2177i	−0.541537	−	0.541537i
$357$	0.895013	−	0.961868i	0.0473691	−	0.0509075i
$358$	3.77266	+	3.77266i	0.199391	+	0.199391i
$359$	−4.04192	−	4.04192i	−0.213324	−	0.213324i	0.592354	−	0.805678i	$-0.298199\pi$
$359$	−4.04192	−	4.04192i	−0.213324	−	0.213324i	−0.805678	+	0.592354i	$0.798199\pi$
$360$			2.54884i			0.134336i
$361$		−	0.131045i		−	0.00689710i
$362$	−1.27109	+	1.27109i	−0.0668073	+	0.0668073i
$363$	9.24432			0.485201
$364$	−2.20619	−	9.28077i	−0.115636	−	0.486445i
$365$	−12.7659			−0.668195
$366$	−0.351145	+	0.351145i	−0.0183546	+	0.0183546i
$367$			4.26926i			0.222853i	0.993773	+	0.111427i	$0.0355420\pi$
$367$			4.26926i			0.222853i	−0.993773	+	0.111427i	$0.964458\pi$
$368$		−	7.37727i		−	0.384567i
$369$	6.11650	+	6.11650i	0.318412	+	0.318412i
$370$	9.02682	+	9.02682i	0.469282	+	0.469282i
$371$	−8.26926	−	7.69449i	−0.429318	−	0.399478i
$372$	5.73923	+	5.73923i	0.297565	+	0.297565i
$373$	9.67146			0.500769			0.250385	−	0.968146i	$-0.419443\pi$
$373$	9.67146			0.500769			0.250385	+	0.968146i	$0.419443\pi$
$374$	0.657997			0.0340242
$375$	−6.31420	−	6.31420i	−0.326064	−	0.326064i
$376$	−8.30690			−0.428395
$377$	14.5023	−	21.7534i	0.746905	−	1.12036i
$378$	0.0951965	+	2.64404i	0.00489638	+	0.135995i
$379$	−0.746047	+	0.746047i	−0.0383218	+	0.0383218i	−0.726008	−	0.687686i	$-0.758627\pi$
$379$	−0.746047	+	0.746047i	−0.0383218	+	0.0383218i	0.687686	+	0.726008i	$0.258627\pi$
$380$	−11.0718			−0.567969
$381$	19.8376			1.01631
$382$	13.2857	−	13.2857i	0.679758	−	0.679758i
$383$	18.1461	+	18.1461i	0.927225	+	0.927225i	0.997526	−	0.0703012i	$-0.0223960\pi$
$383$	18.1461	+	18.1461i	0.927225	+	0.927225i	−0.0703012	+	0.997526i	$0.522396\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	6.08686	−	6.54154i	0.310215	−	0.333388i
$386$	−1.93812			−0.0986476
$387$		−	6.85574i		−	0.348497i
$388$	9.46034	−	9.46034i	0.480276	−	0.480276i
$389$			6.73756i			0.341608i	0.985305	+	0.170804i	$0.0546364\pi$
$389$			6.73756i			0.341608i	−0.985305	+	0.170804i	$0.945364\pi$
$390$	7.64653	+	5.09768i	0.387197	+	0.258131i
$391$		−	3.66351i		−	0.185271i
$392$	−4.58097	+	5.29289i	−0.231374	+	0.267331i
$393$	−5.10801			−0.257665
$394$		−	4.05225i		−	0.204149i
$395$	23.7002	+	23.7002i	1.19248	+	1.19248i
$396$	−0.936931	+	0.936931i	−0.0470826	+	0.0470826i
$397$	−21.7715	+	21.7715i	−1.09268	+	1.09268i	−0.0974398	+	0.995241i	$0.531065\pi$
$397$	−21.7715	+	21.7715i	−1.09268	+	1.09268i	−0.995241	+	0.0974398i	$0.968935\pi$
$398$	9.94542	−	9.94542i	0.498519	−	0.498519i
$399$	−11.4853	+	0.413518i	−0.574983	+	0.0207018i
$400$		−	1.49659i		−	0.0748297i
$401$	16.5119	+	16.5119i	0.824565	+	0.824565i	0.986759	−	0.162194i	$-0.0518571\pi$
$401$	16.5119	+	16.5119i	0.824565	+	0.824565i	−0.162194	+	0.986759i	$0.551857\pi$
$402$	−12.8927			−0.643029
$403$	28.6962	−	5.73923i	1.42946	−	0.285892i
$404$			4.66465i			0.232075i
$405$	−1.80230	−	1.80230i	−0.0895572	−	0.0895572i
$406$	−19.1723	+	0.690282i	−0.951504	+	0.0342581i
$407$			6.63636i			0.328952i
$408$	0.351145	−	0.351145i	0.0173843	−	0.0173843i
$409$	4.00379	+	4.00379i	0.197975	+	0.197975i	0.799131	−	0.601157i	$-0.205293\pi$
$409$	4.00379	+	4.00379i	0.197975	+	0.197975i	−0.601157	+	0.799131i	$0.705293\pi$
$410$	−15.5900	−	15.5900i	−0.769935	−	0.769935i
$411$	−3.80230	+	3.80230i	−0.187554	+	0.187554i
$412$			18.5865i			0.915690i
$413$	−5.14993	+	0.185419i	−0.253412	+	0.00912388i
$414$	5.21652	+	5.21652i	0.256378	+	0.256378i
$415$		−	28.3822i		−	1.39323i
$416$	−0.707107	−	3.53553i	−0.0346688	−	0.173344i
$417$	2.93996			0.143970
$418$	−4.06988	−	4.06988i	−0.199064	−	0.199064i
$419$			15.1782i			0.741505i	0.928732	+	0.370752i	$0.120900\pi$
$419$			15.1782i			0.741505i	−0.928732	+	0.370752i	$0.879100\pi$
$420$	−0.242641	−	6.73923i	−0.0118397	−	0.328841i
$421$	11.0650	−	11.0650i	0.539273	−	0.539273i	−0.384043	−	0.923315i	$-0.625468\pi$
$421$	11.0650	−	11.0650i	0.539273	−	0.539273i	0.923315	+	0.384043i	$0.125468\pi$
$422$	10.5046	−	10.5046i	0.511356	−	0.511356i
$423$	5.87386	−	5.87386i	0.285597	−	0.285597i
$424$	−3.01882	−	3.01882i	−0.146607	−	0.146607i
$425$		−	0.743199i		−	0.0360505i
$426$	−16.0899			−0.779558
$427$	0.895013	−	0.961868i	0.0433127	−	0.0465481i
$428$		−	6.95694i		−	0.336276i
$429$	0.936931	+	4.68466i	0.0452355	+	0.226177i
$430$			17.4742i			0.842680i
$431$	9.60461	−	9.60461i	0.462638	−	0.462638i	−0.436881	−	0.899519i	$-0.643917\pi$
$431$	9.60461	−	9.60461i	0.462638	−	0.462638i	0.899519	+	0.436881i	$0.143917\pi$
$432$			1.00000i			0.0481125i
$433$	−6.52489			−0.313566			−0.156783	−	0.987633i	$-0.550112\pi$
$433$	−6.52489			−0.313566			−0.156783	+	0.987633i	$0.550112\pi$
$434$	−15.7211	−	14.6284i	−0.754637	−	0.702186i
$435$	13.0687	−	13.0687i	0.626598	−	0.626598i
$436$	−2.94374	−	2.94374i	−0.140980	−	0.140980i
$437$	−22.6597	+	22.6597i	−1.08396	+	1.08396i
$438$	−5.00849			−0.239315
$439$	1.61592			0.0771236			0.0385618	−	0.999256i	$-0.487722\pi$
$439$	1.61592			0.0771236			0.0385618	+	0.999256i	$0.487722\pi$
$440$	2.38809	−	2.38809i	0.113848	−	0.113848i
$441$	−0.503406	−	6.98188i	−0.0239717	−	0.332470i
$442$	−0.351145	−	1.75572i	−0.0167023	−	0.0835113i
$443$	−19.0408			−0.904655			−0.452327	−	0.891852i	$-0.649406\pi$
$443$	−19.0408			−0.904655			−0.452327	+	0.891852i	$0.649406\pi$
$444$	3.54154	+	3.54154i	0.168074	+	0.168074i
$445$	−36.8308			−1.74595
$446$	−8.83806			−0.418494
$447$	−1.74605	−	1.74605i	−0.0825852	−	0.0825852i
$448$	−1.80230	+	1.93693i	−0.0851508	+	0.0915114i
$449$	−10.3408	−	10.3408i	−0.488013	−	0.488013i	0.419666	−	0.907679i	$-0.362147\pi$
$449$	−10.3408	−	10.3408i	−0.488013	−	0.488013i	−0.907679	+	0.419666i	$0.862147\pi$
$450$	1.05825	+	1.05825i	0.0498865	+	0.0498865i
$451$		−	11.4615i		−	0.539700i
$452$			2.93996i			0.138284i
$453$	6.55003	−	6.55003i	0.307747	−	0.307747i
$454$	7.78299			0.365274
$455$	−20.7030	−	12.7505i	−0.970571	−	0.597755i
$456$	−4.34384			−0.203419
$457$	20.0718	−	20.0718i	0.938917	−	0.938917i	−0.0593215	−	0.998239i	$-0.518894\pi$
$457$	20.0718	−	20.0718i	0.938917	−	0.938917i	0.998239	+	0.0593215i	$0.0188937\pi$
$458$		−	3.54035i		−	0.165430i
$459$			0.496594i			0.0231790i
$460$	−13.2961	−	13.2961i	−0.619933	−	0.619933i
$461$	−13.4069	−	13.4069i	−0.624422	−	0.624422i	0.322237	−	0.946659i	$-0.395565\pi$
$461$	−13.4069	−	13.4069i	−0.624422	−	0.624422i	−0.946659	+	0.322237i	$0.895565\pi$
$462$	2.38809	−	2.56647i	0.111104	−	0.119403i
$463$	−17.7592	−	17.7592i	−0.825342	−	0.825342i	0.161526	−	0.986868i	$-0.448358\pi$
$463$	−17.7592	−	17.7592i	−0.825342	−	0.825342i	−0.986868	+	0.161526i	$0.948358\pi$
$464$	−7.25113			−0.336625
$465$	20.6877			0.959368
$466$	−11.7108	−	11.7108i	−0.542491	−	0.542491i
$467$	39.5072			1.82817			0.914087	−	0.405518i	$-0.132909\pi$
$467$	39.5072			1.82817			0.914087	+	0.405518i	$0.132909\pi$
$468$	3.00000	+	2.00000i	0.138675	+	0.0924500i
$469$	34.0887	−	1.22734i	1.57407	−	0.0566732i
$470$	−14.9715	+	14.9715i	−0.690586	+	0.690586i
$471$	−1.70581			−0.0785994
$472$	−1.94775			−0.0896526
$473$	−6.42336	+	6.42336i	−0.295346	+	0.295346i
$474$	9.29841	+	9.29841i	0.427090	+	0.427090i
$475$	−4.59688	+	4.59688i	−0.210919	+	0.210919i
$476$	−0.895013	+	0.961868i	−0.0410228	+	0.0440872i
$477$	4.26926			0.195476
$478$		−	3.41161i		−	0.156044i
$479$	20.1768	−	20.1768i	0.921899	−	0.921899i	−0.0752644	−	0.997164i	$-0.523980\pi$
$479$	20.1768	−	20.1768i	0.921899	−	0.921899i	0.997164	+	0.0752644i	$0.0239801\pi$
$480$		−	2.54884i		−	0.116338i
$481$	17.7077	−	3.54154i	0.807401	−	0.161480i
$482$		−	11.8472i		−	0.539627i
$483$	−14.2893	−	13.2961i	−0.650184	−	0.604992i
$484$	−9.24432			−0.420196
$485$		−	34.1008i		−	1.54844i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−14.5837	+	14.5837i	−0.660849	+	0.660849i	−0.955580	−	0.294731i	$-0.904770\pi$
$487$	−14.5837	+	14.5837i	−0.660849	+	0.660849i	0.294731	+	0.955580i	$0.404770\pi$
$488$	0.351145	−	0.351145i	0.0158956	−	0.0158956i
$489$	4.23583	−	4.23583i	0.191551	−	0.191551i
$490$	1.28310	+	17.7957i	0.0579647	+	0.803928i
$491$			10.3591i			0.467502i	0.972297	+	0.233751i	$0.0751000\pi$
$491$			10.3591i			0.467502i	−0.972297	+	0.233751i	$0.924900\pi$
$492$	−6.11650	−	6.11650i	−0.275753	−	0.275753i
$493$	−3.60087			−0.162175
$494$	−8.68768	+	13.0315i	−0.390877	+	0.586316i
$495$			3.37727i			0.151797i
$496$	−5.73923	−	5.73923i	−0.257699	−	0.257699i
$497$	42.5423	−	1.53170i	1.90828	−	0.0687061i
$498$		−	11.1353i		−	0.498986i
$499$	30.2834	−	30.2834i	1.35567	−	1.35567i	0.476494	−	0.879178i	$-0.341907\pi$
$499$	30.2834	−	30.2834i	1.35567	−	1.35567i	0.879178	−	0.476494i	$-0.158093\pi$
$500$	6.31420	+	6.31420i	0.282380	+	0.282380i
$501$	8.02001	+	8.02001i	0.358307	+	0.358307i
$502$	−19.0019	+	19.0019i	−0.848096	+	0.848096i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$	−0.0951965	−	2.64404i	−0.00424039	−	0.117775i
$505$	8.40711	+	8.40711i	0.374112	+	0.374112i
$506$		−	9.77504i		−	0.434553i
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$	−19.8376			−0.880152
$509$	−27.9685	−	27.9685i	−1.23968	−	1.23968i	−0.960132	−	0.279548i	$-0.909815\pi$
$509$	−27.9685	−	27.9685i	−1.23968	−	1.23968i	−0.279548	−	0.960132i	$-0.590185\pi$
$510$		−	1.26574i		−	0.0560479i
$511$	13.2426	−	0.476791i	0.585820	−	0.0210920i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.07156	−	3.07156i	0.135613	−	0.135613i
$514$	−5.64485	+	5.64485i	−0.248984	+	0.248984i
$515$	33.4985	+	33.4985i	1.47612	+	1.47612i
$516$			6.85574i			0.301807i
$517$	−11.0068			−0.484079
$518$	−9.70110	−	9.02682i	−0.426242	−	0.396616i
$519$			4.21603i			0.185063i
$520$	−7.64653	−	5.09768i	−0.335322	−	0.223548i
$521$		−	18.7160i		−	0.819962i	−0.912094	−	0.409981i	$-0.865535\pi$
$521$		−	18.7160i		−	0.819962i	0.912094	−	0.409981i	$-0.134465\pi$
$522$	5.12732	−	5.12732i	0.224417	−	0.224417i
$523$		−	5.69449i		−	0.249003i	−0.992219	−	0.124501i	$-0.960267\pi$
$523$		−	5.69449i		−	0.249003i	0.992219	−	0.124501i	$-0.0397331\pi$
$524$	5.10801			0.223145
$525$	−2.89880	−	2.69732i	−0.126514	−	0.117721i
$526$	1.74773	−	1.74773i	0.0762044	−	0.0762044i
$527$	−2.85007	−	2.85007i	−0.124151	−	0.124151i
$528$	0.936931	−	0.936931i	0.0407747	−	0.0407747i
$529$	−31.4241			−1.36626
$530$	−10.8817			−0.472669
$531$	1.37727	−	1.37727i	0.0597684	−	0.0597684i
$532$	11.4853	−	0.413518i	0.497950	−	0.0179283i
$533$	−30.5825	+	6.11650i	−1.32468	+	0.264935i
$534$	−14.4500			−0.625313
$535$	−12.5385	−	12.5385i	−0.542087	−	0.542087i
$536$	12.8927			0.556879
$537$	5.33535			0.230237
$538$	4.12782	+	4.12782i	0.177963	+	0.177963i
$539$	−6.06988	+	7.01319i	−0.261448	+	0.302080i
$540$	1.80230	+	1.80230i	0.0775588	+	0.0775588i
$541$	6.48149	+	6.48149i	0.278661	+	0.278661i	0.832574	−	0.553913i	$-0.186866\pi$
$541$	6.48149	+	6.48149i	0.278661	+	0.278661i	−0.553913	+	0.832574i	$0.686866\pi$
$542$		−	12.1311i		−	0.521076i
$543$			1.79760i			0.0771424i
$544$	−0.351145	+	0.351145i	−0.0150552	+	0.0150552i
$545$	−10.6110			−0.454527
$546$	−8.12251	−	5.00249i	−0.347611	−	0.214087i
$547$	39.5294			1.69016			0.845078	−	0.534643i	$-0.179554\pi$
$547$	39.5294			1.69016			0.845078	+	0.534643i	$0.179554\pi$
$548$	3.80230	−	3.80230i	0.162426	−	0.162426i
$549$			0.496594i			0.0211941i
$550$		−	1.98302i		−	0.0845562i
$551$	22.2723	+	22.2723i	0.948831	+	0.948831i
$552$	−5.21652	−	5.21652i	−0.222030	−	0.222030i
$553$	−25.4705	−	23.7002i	−1.08312	−	1.00783i
$554$	−1.88419	−	1.88419i	−0.0800516	−	0.0800516i
$555$	12.7659			0.541880
$556$	−2.93996			−0.124682
$557$	−0.806090	−	0.806090i	−0.0341551	−	0.0341551i	0.689823	−	0.723978i	$-0.257688\pi$
$557$	−0.806090	−	0.806090i	−0.0341551	−	0.0341551i	−0.723978	+	0.689823i	$0.757688\pi$
$558$	8.11650			0.343599
$559$	20.5672	+	13.7115i	0.869900	+	0.579934i
$560$	0.242641	+	6.73923i	0.0102534	+	0.284785i
$561$	0.465274	−	0.465274i	0.0196439	−	0.0196439i
$562$	11.4545			0.483177
$563$	−44.4350			−1.87271			−0.936357	−	0.351050i	$-0.885825\pi$
$563$	−44.4350			−1.87271			−0.936357	+	0.351050i	$0.885825\pi$
$564$	−5.87386	+	5.87386i	−0.247334	+	0.247334i
$565$	5.29869	+	5.29869i	0.222918	+	0.222918i
$566$	21.4063	−	21.4063i	0.899772	−	0.899772i
$567$	1.93693	+	1.80230i	0.0813435	+	0.0756896i
$568$	16.0899			0.675117
$569$		−	5.40826i		−	0.226726i	−0.993554	−	0.113363i	$-0.963838\pi$
$569$		−	5.40826i		−	0.226726i	0.993554	−	0.113363i	$-0.0361623\pi$
$570$	−7.82892	+	7.82892i	−0.327917	+	0.327917i
$571$		−	2.46830i		−	0.103295i	−0.998665	−	0.0516476i	$-0.983553\pi$
$571$		−	2.46830i		−	0.103295i	0.998665	−	0.0516476i	$-0.0164472\pi$
$572$	−0.936931	−	4.68466i	−0.0391751	−	0.195875i
$573$		−	18.7889i		−	0.784917i
$574$	16.7545	+	15.5900i	0.699321	+	0.650714i
$575$	−11.0408			−0.460432
$576$		−	1.00000i		−	0.0416667i
$577$	27.0650	+	27.0650i	1.12673	+	1.12673i	0.990706	+	0.136023i	$0.0434321\pi$
$577$	27.0650	+	27.0650i	1.12673	+	1.12673i	0.136023	+	0.990706i	$0.456568\pi$
$578$	11.8464	−	11.8464i	0.492747	−	0.492747i
$579$	−1.37046	+	1.37046i	−0.0569542	+	0.0569542i
$580$	−13.0687	+	13.0687i	−0.542650	+	0.542650i
$581$	1.06004	+	29.4422i	0.0439780	+	1.22147i
$582$		−	13.3789i		−	0.554575i
$583$	−4.00000	−	4.00000i	−0.165663	−	0.165663i
$584$	5.00849			0.207253
$585$	9.01152	−	1.80230i	0.372580	−	0.0745161i
$586$		−	25.3477i		−	1.04710i
$587$	−10.6533	−	10.6533i	−0.439710	−	0.439710i	0.452204	−	0.891914i	$-0.350638\pi$
$587$	−10.6533	−	10.6533i	−0.439710	−	0.439710i	−0.891914	+	0.452204i	$0.850638\pi$
$588$	0.503406	+	6.98188i	0.0207601	+	0.287928i
$589$			35.2568i			1.45273i
$590$	−3.51044	+	3.51044i	−0.144523	+	0.144523i
$591$	−2.86537	−	2.86537i	−0.117866	−	0.117866i
$592$	−3.54154	−	3.54154i	−0.145556	−	0.145556i
$593$	11.4938	−	11.4938i	0.471993	−	0.471993i	−0.430566	−	0.902559i	$-0.641686\pi$
$593$	11.4938	−	11.4938i	0.471993	−	0.471993i	0.902559	+	0.430566i	$0.141686\pi$
$594$			1.32502i			0.0543663i
$595$	0.120494	+	3.34666i	0.00493977	+	0.137200i
$596$	1.74605	+	1.74605i	0.0715209	+	0.0715209i
$597$		−	14.0650i		−	0.575640i
$598$	−26.0826	+	5.21652i	−1.06660	+	0.213319i
$599$	−30.3149			−1.23863			−0.619317	−	0.785141i	$-0.712591\pi$
$599$	−30.3149			−1.23863			−0.619317	+	0.785141i	$0.712591\pi$
$600$	−1.05825	−	1.05825i	−0.0432029	−	0.0432029i
$601$		−	11.9638i		−	0.488012i	−0.969774	−	0.244006i	$-0.921538\pi$
$601$		−	11.9638i		−	0.488012i	0.969774	−	0.244006i	$-0.0784616\pi$
$602$	−0.652642	−	18.1268i	−0.0265997	−	0.738795i
$603$	−9.11650	+	9.11650i	−0.371253	+	0.371253i
$604$	−6.55003	+	6.55003i	−0.266517	+	0.266517i
$605$	−16.6611	+	16.6611i	−0.677369	+	0.677369i
$606$	3.29841	+	3.29841i	0.133989	+	0.133989i
$607$		−	41.6103i		−	1.68891i	−0.535627	−	0.844454i	$-0.679925\pi$
$607$		−	41.6103i		−	1.68891i	0.535627	−	0.844454i	$-0.320075\pi$
$608$	4.34384			0.176166
$609$	−13.0687	+	14.0449i	−0.529572	+	0.569130i
$610$		−	1.26574i		−	0.0512483i
$611$	5.87386	+	29.3693i	0.237631	+	1.18816i
$612$		−	0.496594i		−	0.0200736i
$613$	−27.9736	+	27.9736i	−1.12984	+	1.12984i	−0.139640	+	0.990202i	$0.544595\pi$
$613$	−27.9736	+	27.9736i	−1.12984	+	1.12984i	−0.990202	+	0.139640i	$0.955405\pi$
$614$		−	7.20056i		−	0.290591i
$615$	−22.0476			−0.889045
$616$	−2.38809	+	2.56647i	−0.0962189	+	0.103406i
$617$	15.7830	−	15.7830i	0.635401	−	0.635401i	−0.314016	−	0.949418i	$-0.601675\pi$
$617$	15.7830	−	15.7830i	0.635401	−	0.635401i	0.949418	+	0.314016i	$0.101675\pi$
$618$	13.1426	+	13.1426i	0.528674	+	0.528674i
$619$	−0.473765	+	0.473765i	−0.0190422	+	0.0190422i	−0.716564	−	0.697522i	$-0.754286\pi$
$619$	−0.473765	+	0.473765i	−0.0190422	+	0.0190422i	0.697522	+	0.716564i	$0.254286\pi$
$620$	−20.6877			−0.830837
$621$	7.37727			0.296040
$622$	9.95105	−	9.95105i	0.399001	−	0.399001i
$623$	38.2064	−	1.37559i	1.53071	−	0.0551119i
$624$	−3.00000	−	2.00000i	−0.120096	−	0.0800641i
$625$	30.2432			1.20973
$626$	20.0153	+	20.0153i	0.799972	+	0.799972i
$627$	−5.75568			−0.229860
$628$	1.70581			0.0680691
$629$	−1.75871	−	1.75871i	−0.0701242	−	0.0701242i
$630$	−4.93693	−	4.59379i	−0.196692	−	0.183021i
$631$	−30.2978	−	30.2978i	−1.20613	−	1.20613i	−0.972269	−	0.233866i	$-0.924862\pi$
$631$	−30.2978	−	30.2978i	−1.20613	−	1.20613i	−0.233866	−	0.972269i	$-0.575138\pi$
$632$	−9.29841	−	9.29841i	−0.369871	−	0.369871i
$633$		−	14.8557i		−	0.590463i
$634$			29.0082i			1.15206i
$635$	−35.7534	+	35.7534i	−1.41883	+	1.41883i
$636$	−4.26926			−0.169287
$637$	21.9524	+	12.4535i	0.869787	+	0.493427i
$638$	−9.60790			−0.380380
$639$	−11.3773	+	11.3773i	−0.450078	+	0.450078i
$640$			2.54884i			0.100752i
$641$		−	5.40556i		−	0.213507i	−0.994286	−	0.106753i	$-0.965954\pi$
$641$		−	5.40556i		−	0.213507i	0.994286	−	0.106753i	$-0.0340456\pi$
$642$	−4.91930	−	4.91930i	−0.194149	−	0.194149i
$643$	9.08518	+	9.08518i	0.358285	+	0.358285i	0.863180	−	0.504896i	$-0.168469\pi$
$643$	9.08518	+	9.08518i	0.358285	+	0.358285i	−0.504896	+	0.863180i	$0.668469\pi$
$644$	14.2893	+	13.2961i	0.563076	+	0.523939i
$645$	12.3561	+	12.3561i	0.486522	+	0.486522i
$646$	2.15712			0.0848709
$647$	15.0468			0.591552			0.295776	−	0.955257i	$-0.404422\pi$
$647$	15.0468			0.591552			0.295776	+	0.955257i	$0.404422\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−2.58081			−0.101306
$650$	−5.29126	+	1.05825i	−0.207540	+	0.0415080i
$651$	−21.4603	+	0.772662i	−0.841097	+	0.0302830i
$652$	−4.23583	+	4.23583i	−0.165888	+	0.165888i
$653$	6.17411			0.241611			0.120806	−	0.992676i	$-0.461452\pi$
$653$	6.17411			0.241611			0.120806	+	0.992676i	$0.461452\pi$
$654$	−4.16308			−0.162789
$655$	9.20619	−	9.20619i	0.359716	−	0.359716i
$656$	6.11650	+	6.11650i	0.238809	+	0.238809i
$657$	−3.54154	+	3.54154i	−0.138169	+	0.138169i
$658$	14.9715	−	16.0899i	0.583652	−	0.627249i
$659$	2.70131			0.105228			0.0526140	−	0.998615i	$-0.483245\pi$
$659$	2.70131			0.105228			0.0526140	+	0.998615i	$0.483245\pi$
$660$		−	3.37727i		−	0.131460i
$661$	15.1148	−	15.1148i	0.587899	−	0.587899i	−0.349163	−	0.937062i	$-0.613534\pi$
$661$	15.1148	−	15.1148i	0.587899	−	0.587899i	0.937062	+	0.349163i	$0.113534\pi$
$662$		−	13.6543i		−	0.530688i
$663$	−1.48978	−	0.993188i	−0.0578583	−	0.0385722i
$664$			11.1353i			0.432134i
$665$	19.9547	−	21.4452i	0.773809	−	0.831611i
$666$	5.00849			0.194075
$667$			53.4935i			2.07128i
$668$	−8.02001	−	8.02001i	−0.310303	−	0.310303i
$669$	−6.24945	+	6.24945i	−0.241618	+	0.241618i
$670$	23.2365	−	23.2365i	0.897705	−	0.897705i
$671$	0.465274	−	0.465274i	0.0179617	−	0.0179617i
$672$	0.0951965	+	2.64404i	0.00367228	+	0.101996i
$673$		−	18.7262i		−	0.721844i	−0.932596	−	0.360922i	$-0.882462\pi$
$673$		−	18.7262i		−	0.721844i	0.932596	−	0.360922i	$-0.117538\pi$
$674$	−5.12732	−	5.12732i	−0.197497	−	0.197497i
$675$	1.49659			0.0576039
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$		−	25.6884i		−	0.987287i	−0.869664	−	0.493644i	$-0.835665\pi$
$677$		−	25.6884i		−	0.987287i	0.869664	−	0.493644i	$-0.164335\pi$
$678$	2.07886	+	2.07886i	0.0798383	+	0.0798383i
$679$	1.27363	+	35.3744i	0.0488774	+	1.35755i
$680$			1.26574i			0.0485389i
$681$	5.50341	−	5.50341i	0.210891	−	0.210891i
$682$	−7.60461	−	7.60461i	−0.291195	−	0.291195i
$683$	10.6677	+	10.6677i	0.408187	+	0.408187i	0.881106	−	0.472919i	$-0.156800\pi$
$683$	10.6677	+	10.6677i	0.408187	+	0.408187i	−0.472919	+	0.881106i	$0.656800\pi$
$684$	−3.07156	+	3.07156i	−0.117444	+	0.117444i
$685$		−	13.7058i		−	0.523672i
$686$	−1.99567	−	18.4124i	−0.0761952	−	0.702990i
$687$	−2.50341	−	2.50341i	−0.0955109	−	0.0955109i
$688$		−	6.85574i		−	0.261373i
$689$	−8.53851	+	12.8078i	−0.325291	+	0.487937i
$690$	−18.8035			−0.715837
$691$	−18.7630	−	18.7630i	−0.713779	−	0.713779i	0.253544	−	0.967324i	$-0.418404\pi$
$691$	−18.7630	−	18.7630i	−0.713779	−	0.713779i	−0.967324	+	0.253544i	$0.918404\pi$
$692$		−	4.21603i		−	0.160269i
$693$	−0.126137	−	3.50341i	−0.00479156	−	0.133083i
$694$	−21.0468	+	21.0468i	−0.798927	+	0.798927i
$695$	−5.29869	+	5.29869i	−0.200991	+	0.200991i
$696$	−5.12732	+	5.12732i	−0.194351	+	0.194351i
$697$	3.03742	+	3.03742i	0.115050	+	0.115050i
$698$			18.5872i			0.703535i
$699$	−16.5615			−0.626415
$700$	2.89880	+	2.69732i	0.109564	+	0.101949i
$701$			30.4354i			1.14953i	0.818319	+	0.574765i	$0.194906\pi$
$701$			30.4354i			1.14953i	−0.818319	+	0.574765i	$0.805094\pi$
$702$	3.53553	−	0.707107i	0.133440	−	0.0266880i
$703$			21.7561i			0.820546i
$704$	−0.936931	+	0.936931i	−0.0353119	+	0.0353119i
$705$			21.1730i			0.797420i
$706$	19.1669			0.721356
$707$	−9.03511	−	8.40711i	−0.339800	−	0.316182i
$708$	−1.37727	+	1.37727i	−0.0517609	+	0.0517609i
$709$	−31.7070	−	31.7070i	−1.19078	−	1.19078i	−0.976849	−	0.213932i	$-0.931373\pi$
$709$	−31.7070	−	31.7070i	−1.19078	−	1.19078i	−0.213932	−	0.976849i	$-0.568627\pi$
$710$	28.9989	−	28.9989i	1.08831	−	1.08831i
$711$	13.1499			0.493161
$712$	14.4500			0.541537
$713$	−42.3399	+	42.3399i	−1.58564	+	1.58564i
$714$	0.0472740	+	1.31301i	0.00176918	+	0.0491383i
$715$	−10.1318	−	6.75454i	−0.378908	−	0.252605i
$716$	−5.33535			−0.199391
$717$	−2.41238	−	2.41238i	−0.0900918	−	0.0900918i
$718$	5.71614			0.213324
$719$	−0.575169			−0.0214502			−0.0107251	−	0.999942i	$-0.503414\pi$
$719$	−0.575169			−0.0214502			−0.0107251	+	0.999942i	$0.503414\pi$
$720$	−1.80230	−	1.80230i	−0.0671679	−	0.0671679i
$721$	−36.0007	−	33.4985i	−1.34074	−	1.24755i
$722$	0.0926627	+	0.0926627i	0.00344855	+	0.00344855i
$723$	−8.37727	−	8.37727i	−0.311554	−	0.311554i
$724$		−	1.79760i		−	0.0668073i
$725$			10.8520i			0.403033i
$726$	−6.53672	+	6.53672i	−0.242600	+	0.242600i
$727$	32.1850			1.19368			0.596838	−	0.802361i	$-0.296423\pi$
$727$	32.1850			1.19368			0.596838	+	0.802361i	$0.296423\pi$
$728$	8.12251	+	5.00249i	0.301040	+	0.185404i
$729$	−1.00000			−0.0370370
$730$	9.02682	−	9.02682i	0.334098	−	0.334098i
$731$		−	3.40452i		−	0.125921i
$732$		−	0.496594i		−	0.0183546i
$733$	−31.3478	−	31.3478i	−1.15786	−	1.15786i	−0.984935	−	0.172923i	$-0.944679\pi$
$733$	−31.3478	−	31.3478i	−1.15786	−	1.15786i	−0.172923	−	0.984935i	$-0.555321\pi$
$734$	−3.01882	−	3.01882i	−0.111427	−	0.111427i
$735$	13.4907	+	11.6762i	0.497614	+	0.430682i
$736$	5.21652	+	5.21652i	0.192283	+	0.192283i
$737$	17.0831			0.629263
$738$	−8.65004			−0.318412
$739$	18.7211	+	18.7211i	0.688667	+	0.688667i	0.961937	−	0.273270i	$-0.0881053\pi$
$739$	18.7211	+	18.7211i	0.688667	+	0.688667i	−0.273270	+	0.961937i	$0.588105\pi$
$740$	−12.7659			−0.469282
$741$	3.07156	+	15.3578i	0.112837	+	0.564183i
$742$	11.2881	−	0.406418i	0.414398	−	0.0149201i
$743$	20.3172	−	20.3172i	0.745367	−	0.745367i	−0.228239	−	0.973605i	$-0.573297\pi$
$743$	20.3172	−	20.3172i	0.745367	−	0.745367i	0.973605	+	0.228239i	$0.0732966\pi$
$744$	−8.11650			−0.297565
$745$	6.29381			0.230587
$746$	−6.83876	+	6.83876i	−0.250385	+	0.250385i
$747$	−7.87386	−	7.87386i	−0.288090	−	0.288090i
$748$	−0.465274	+	0.465274i	−0.0170121	+	0.0170121i
$749$	13.4751	+	12.5385i	0.492370	+	0.458147i
$750$	8.92963			0.326064
$751$			37.6220i			1.37285i	0.727202	+	0.686423i	$0.240820\pi$
$751$			37.6220i			1.37285i	−0.727202	+	0.686423i	$0.759180\pi$
$752$	5.87386	−	5.87386i	0.214198	−	0.214198i
$753$			26.8727i			0.979296i
$754$	5.12732	+	25.6366i	0.186726	+	0.933631i
$755$			23.6103i			0.859266i
$756$	−1.93693	−	1.80230i	−0.0704455	−	0.0655491i
$757$	18.5249			0.673299			0.336649	−	0.941630i	$-0.390706\pi$
$757$	18.5249			0.673299			0.336649	+	0.941630i	$0.390706\pi$
$758$		−	1.05507i		−	0.0383218i
$759$	−6.91199	−	6.91199i	−0.250890	−	0.250890i
$760$	7.82892	−	7.82892i	0.283985	−	0.283985i
$761$	20.0153	−	20.0153i	0.725554	−	0.725554i	−0.244177	−	0.969731i	$-0.578518\pi$
$761$	20.0153	−	20.0153i	0.725554	−	0.725554i	0.969731	+	0.244177i	$0.0785177\pi$
$762$	−14.0273	+	14.0273i	−0.508156	+	0.508156i
$763$	11.0073	−	0.396311i	0.398493	−	0.0143474i
$764$			18.7889i			0.679758i
$765$	−0.895013	−	0.895013i	−0.0323593	−	0.0323593i
$766$	−25.6625			−0.927225
$767$	1.37727	+	6.88634i	0.0497303	+	0.248651i
$768$			1.00000i			0.0360844i
$769$	22.3493	+	22.3493i	0.805937	+	0.805937i	0.984016	−	0.178079i	$-0.0569884\pi$
$769$	22.3493	+	22.3493i	0.805937	+	0.805937i	−0.178079	+	0.984016i	$0.556988\pi$
$770$	0.321504	+	8.92963i	0.0115862	+	0.321801i
$771$			7.98302i			0.287501i
$772$	1.37046	−	1.37046i	0.0493238	−	0.0493238i
$773$	27.6399	+	27.6399i	0.994139	+	0.994139i	0.999983	−	0.00584422i	$-0.00186029\pi$
$773$	27.6399	+	27.6399i	0.994139	+	0.994139i	−0.00584422	+	0.999983i	$0.501860\pi$
$774$	4.84774	+	4.84774i	0.174248	+	0.174248i
$775$	−8.58930	+	8.58930i	−0.308537	+	0.308537i
$776$			13.3789i			0.480276i
$777$	−13.2426	+	0.476791i	−0.475077	+	0.0171048i
$778$	−4.76417	−	4.76417i	−0.170804	−	0.170804i
$779$		−	37.5744i		−	1.34624i
$780$	−9.01152	+	1.80230i	−0.322664	+	0.0645328i
$781$	21.3194			0.762870
$782$	2.59049	+	2.59049i	0.0926357	+	0.0926357i
$783$		−	7.25113i		−	0.259134i
$784$	−0.503406	−	6.98188i	−0.0179788	−	0.249353i
$785$	3.07438	−	3.07438i	0.109729	−	0.109729i
$786$	3.61191	−	3.61191i	0.128833	−	0.128833i
$787$	29.7592	−	29.7592i	1.06080	−	1.06080i	0.0627747	−	0.998028i	$-0.480005\pi$
$787$	29.7592	−	29.7592i	1.06080	−	1.06080i	0.998028	−	0.0627747i	$-0.0199949\pi$
$788$	2.86537	+	2.86537i	0.102075	+	0.102075i
$789$		−	2.47166i		−	0.0879933i
$790$	−33.5171			−1.19248
$791$	−5.69449	−	5.29869i	−0.202473	−	0.188400i
$792$		−	1.32502i		−	0.0470826i
$793$	−1.48978	−	0.993188i	−0.0529037	−	0.0352691i
$794$		−	30.7896i		−	1.09268i
$795$	−7.69449	+	7.69449i	−0.272896	+	0.272896i
$796$			14.0650i			0.498519i
$797$	−19.9732			−0.707486			−0.353743	−	0.935343i	$-0.615091\pi$
$797$	−19.9732			−0.707486			−0.353743	+	0.935343i	$0.615091\pi$
$798$	7.82892	−	8.41372i	0.277141	−	0.297843i
$799$	2.91692	−	2.91692i	0.103193	−	0.103193i
$800$	1.05825	+	1.05825i	0.0374148	+	0.0374148i
$801$	−10.2177	+	10.2177i	−0.361025	+	0.361025i
$802$	−23.3513			−0.824565
$803$	6.63636			0.234192
$804$	9.11650	−	9.11650i	0.321514	−	0.321514i
$805$	49.7171	−	1.79003i	1.75230	−	0.0630901i
$806$	−16.2330	+	24.3495i	−0.571783	+	0.857675i
$807$	5.83761			0.205494
$808$	−3.29841	−	3.29841i	−0.116037	−	0.116037i
$809$	1.89084			0.0664785			0.0332393	−	0.999447i	$-0.489418\pi$
$809$	1.89084			0.0664785			0.0332393	+	0.999447i	$0.489418\pi$
$810$	2.54884			0.0895572
$811$	−7.61007	−	7.61007i	−0.267226	−	0.267226i	0.560756	−	0.827981i	$-0.310511\pi$
$811$	−7.61007	−	7.61007i	−0.267226	−	0.267226i	−0.827981	+	0.560756i	$0.810511\pi$
$812$	13.0687	−	14.0449i	0.458623	−	0.492881i
$813$	−8.57799	−	8.57799i	−0.300843	−	0.300843i
$814$	−4.69261	−	4.69261i	−0.164476	−	0.164476i
$815$			15.2685i			0.534832i
$816$			0.496594i			0.0173843i
$817$	−21.0578	+	21.0578i	−0.736719	+	0.736719i
$818$	−5.66221			−0.197975
$819$	−9.28077	+	2.20619i	−0.324296	+	0.0770904i
$820$	22.0476			0.769935
$821$	32.0304	−	32.0304i	1.11787	−	1.11787i	0.125814	−	0.992054i	$-0.459846\pi$
$821$	32.0304	−	32.0304i	1.11787	−	1.11787i	0.992054	−	0.125814i	$-0.0401543\pi$
$822$		−	5.37727i		−	0.187554i
$823$			54.2791i			1.89205i	0.324094	+	0.946025i	$0.394940\pi$
$823$			54.2791i			1.89205i	−0.324094	+	0.946025i	$0.605060\pi$
$824$	−13.1426	−	13.1426i	−0.457845	−	0.457845i
$825$	−1.40221	−	1.40221i	−0.0488185	−	0.0488185i
$826$	3.51044	−	3.77266i	0.122144	−	0.131268i
$827$	27.2462	+	27.2462i	0.947443	+	0.947443i	0.998686	−	0.0512430i	$-0.0163183\pi$
$827$	27.2462	+	27.2462i	0.947443	+	0.947443i	−0.0512430	+	0.998686i	$0.516318\pi$
$828$	−7.37727			−0.256378
$829$	41.4649			1.44013			0.720067	−	0.693904i	$-0.244111\pi$
$829$	41.4649			1.44013			0.720067	+	0.693904i	$0.244111\pi$
$830$	20.0692	+	20.0692i	0.696613	+	0.696613i
$831$	−2.66465			−0.0924357
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$	−0.249988	−	3.46716i	−0.00866158	−	0.120130i
$834$	−2.07886	+	2.07886i	−0.0719851	+	0.0719851i
$835$	−28.9090			−1.00044
$836$	5.75568			0.199064
$837$	5.73923	−	5.73923i	0.198377	−	0.198377i
$838$	−10.7326	−	10.7326i	−0.370752	−	0.370752i
$839$	0.0702127	−	0.0702127i	0.00242401	−	0.00242401i	−0.705894	−	0.708318i	$-0.749454\pi$
$839$	0.0702127	−	0.0702127i	0.00242401	−	0.00242401i	0.708318	+	0.705894i	$0.249454\pi$
$840$	4.93693	+	4.59379i	0.170340	+	0.158501i
$841$	23.5789			0.813066
$842$			15.6482i			0.539273i
$843$	8.09952	−	8.09952i	0.278962	−	0.278962i
$844$			14.8557i			0.511356i
$845$	−12.6161	+	30.6392i	−0.434008	+	1.05402i
$846$			8.30690i			0.285597i
$847$	16.6611	−	17.9056i	0.572481	−	0.615244i
$848$	4.26926			0.146607
$849$		−	30.2730i		−	1.03897i
$850$	0.525521	+	0.525521i	0.0180252	+	0.0180252i
$851$	−26.1269	+	26.1269i	−0.895618	+	0.895618i
$852$	11.3773	−	11.3773i	0.389779	−	0.389779i
$853$	27.4773	−	27.4773i	0.940806	−	0.940806i	−0.0575376	−	0.998343i	$-0.518325\pi$
$853$	27.4773	−	27.4773i	0.940806	−	0.940806i	0.998343	+	0.0575376i	$0.0183249\pi$
$854$	0.0472740	+	1.31301i	0.00161768	+	0.0449304i
$855$			11.0718i			0.378646i
$856$	4.91930	+	4.91930i	0.168138	+	0.168138i
$857$	−50.2104			−1.71515			−0.857577	−	0.514356i	$-0.828031\pi$
$857$	−50.2104			−1.71515			−0.857577	+	0.514356i	$0.828031\pi$
$858$	−3.97506	−	2.65004i	−0.135706	−	0.0904709i
$859$		−	41.3127i		−	1.40957i	−0.709420	−	0.704786i	$-0.751043\pi$
$859$		−	41.3127i		−	1.40957i	0.709420	−	0.704786i	$-0.248957\pi$
$860$	−12.3561	−	12.3561i	−0.421340	−	0.421340i
$861$	22.8710	−	0.823453i	0.779443	−	0.0280632i
$862$			13.5830i			0.462638i
$863$	−12.8421	+	12.8421i	−0.437151	+	0.437151i	−0.891052	−	0.453901i	$-0.850032\pi$
$863$	−12.8421	+	12.8421i	−0.437151	+	0.437151i	0.453901	+	0.891052i	$0.350032\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−7.59856	−	7.59856i	−0.258359	−	0.258359i
$866$	4.61379	−	4.61379i	0.156783	−	0.156783i
$867$		−	16.7534i		−	0.568975i
$868$	21.4603	−	0.772662i	0.728412	−	0.0262259i
$869$	−12.3206	−	12.3206i	−0.417947	−	0.417947i
$870$			18.4820i			0.626598i
$871$	−9.11650	−	45.5825i	−0.308901	−	1.54450i
$872$	4.16308			0.140980
$873$	−9.46034	−	9.46034i	−0.320184	−	0.320184i
$874$		−	32.0457i		−	1.08396i
$875$	−23.6103	+	0.850069i	−0.798173	+	0.0287376i
$876$	3.54154	−	3.54154i	0.119657	−	0.119657i
$877$	12.9294	−	12.9294i	0.436595	−	0.436595i	−0.454269	−	0.890864i	$-0.650100\pi$
$877$	12.9294	−	12.9294i	0.436595	−	0.436595i	0.890864	+	0.454269i	$0.150100\pi$
$878$	−1.14263	+	1.14263i	−0.0385618	+	0.0385618i
$879$	−17.9235	−	17.9235i	−0.604545	−	0.604545i
$880$			3.37727i			0.113848i
$881$	42.1888			1.42138			0.710688	−	0.703507i	$-0.248384\pi$
$881$	42.1888			1.42138			0.710688	+	0.703507i	$0.248384\pi$
$882$	5.29289	+	4.58097i	0.178221	+	0.154249i
$883$			15.6635i			0.527119i	0.964643	+	0.263559i	$0.0848965\pi$
$883$			15.6635i			0.527119i	−0.964643	+	0.263559i	$0.915103\pi$
$884$	1.48978	+	0.993188i	0.0501068	+	0.0334045i
$885$			4.96451i			0.166880i
$886$	13.4639	−	13.4639i	0.452327	−	0.452327i
$887$			25.2662i			0.848356i	0.905579	+	0.424178i	$0.139437\pi$
$887$			25.2662i			0.848356i	−0.905579	+	0.424178i	$0.860563\pi$
$888$	−5.00849			−0.168074
$889$	35.7534	−	38.4241i	1.19913	−	1.28870i
$890$	26.0433	−	26.0433i	0.872974	−	0.872974i
$891$	0.936931	+	0.936931i	0.0313884	+	0.0313884i
$892$	6.24945	−	6.24945i	0.209247	−	0.209247i
$893$	−36.0838			−1.20750
$894$	2.46928			0.0825852
$895$	−9.61592	+	9.61592i	−0.321425	+	0.321425i
$896$	−0.0951965	−	2.64404i	−0.00318029	−	0.0883311i
$897$	−14.7545	+	22.1318i	−0.492640	+	0.738960i
$898$	14.6241			0.488013
$899$	41.6159	+	41.6159i	1.38797	+	1.38797i
$900$	−1.49659			−0.0498865
$901$	2.12009			0.0706303
$902$	8.10450	+	8.10450i	0.269850	+	0.269850i
$903$	−13.2791	−	12.3561i	−0.441901	−	0.411186i
$904$	−2.07886	−	2.07886i	−0.0691420	−	0.0691420i
$905$	−3.23982	−	3.23982i	−0.107695	−	0.107695i
$906$			9.26314i			0.307747i
$907$			8.71829i			0.289486i	0.989469	+	0.144743i	$0.0462355\pi$
$907$			8.71829i			0.289486i	−0.989469	+	0.144743i	$0.953764\pi$
$908$	−5.50341	+	5.50341i	−0.182637	+	0.182637i
$909$	4.66465			0.154717
$910$	23.6552	−	5.62322i	0.784163	−	0.186408i
$911$	−53.1847			−1.76209			−0.881044	−	0.473035i	$-0.843158\pi$
$911$	−53.1847			−1.76209			−0.881044	+	0.473035i	$0.843158\pi$
$912$	3.07156	−	3.07156i	0.101709	−	0.101709i
$913$			14.7545i			0.488304i
$914$			28.3858i			0.938917i
$915$	−0.895013	−	0.895013i	−0.0295882	−	0.0295882i
$916$	2.50341	+	2.50341i	0.0827149	+	0.0827149i
$917$	−9.20619	+	9.89387i	−0.304015	+	0.326724i
$918$	−0.351145	−	0.351145i	−0.0115895	−	0.0115895i
$919$	−37.9468			−1.25175			−0.625874	−	0.779924i	$-0.715258\pi$
$919$	−37.9468			−1.25175			−0.625874	+	0.779924i	$0.715258\pi$
$920$	18.8035			0.619933
$921$	−5.09157	−	5.09157i	−0.167773	−	0.167773i
$922$	18.9602			0.624422
$923$	−11.3773	−	56.8863i	−0.374487	−	1.87244i
$924$	0.126137	+	3.50341i	0.00414961	+	0.115254i
$925$	−5.30024	+	5.30024i	−0.174271	+	0.174271i
$926$	25.1154			0.825342
$927$	18.5865			0.610460
$928$	5.12732	−	5.12732i	0.168313	−	0.168313i
$929$	3.27439	+	3.27439i	0.107429	+	0.107429i	0.758778	−	0.651349i	$-0.225797\pi$
$929$	3.27439	+	3.27439i	0.107429	+	0.107429i	−0.651349	+	0.758778i	$0.725797\pi$
$930$	−14.6284	+	14.6284i	−0.479684	+	0.479684i
$931$	−19.8990	+	22.9915i	−0.652163	+	0.753516i
$932$	16.5615			0.542491
$933$		−	14.0729i		−	0.460726i
$934$	−27.9358	+	27.9358i	−0.914087	+	0.914087i
$935$			1.67713i			0.0548481i
$936$	−3.53553	+	0.707107i	−0.115563	+	0.0231125i
$937$			50.1699i			1.63898i	0.573094	+	0.819490i	$0.305743\pi$
$937$			50.1699i			1.63898i	−0.573094	+	0.819490i	$0.694257\pi$
$938$	−23.2365	+	24.9722i	−0.758699	+	0.815373i
$939$	28.3059			0.923729
$940$		−	21.1730i		−	0.690586i
$941$	4.98020	+	4.98020i	0.162350	+	0.162350i	0.783607	−	0.621257i	$-0.213378\pi$
$941$	4.98020	+	4.98020i	0.162350	+	0.162350i	−0.621257	+	0.783607i	$0.713378\pi$
$942$	1.20619	−	1.20619i	0.0392997	−	0.0392997i
$943$	45.1231	−	45.1231i	1.46941	−	1.46941i
$944$	1.37727	−	1.37727i	0.0448263	−	0.0448263i
$945$	−6.73923	+	0.242641i	−0.219227	+	0.00789310i
$946$		−	9.08400i		−	0.295346i
$947$	4.66768	+	4.66768i	0.151679	+	0.151679i	0.778868	−	0.627188i	$-0.215794\pi$
$947$	4.66768	+	4.66768i	0.151679	+	0.151679i	−0.627188	+	0.778868i	$0.715794\pi$
$948$	−13.1499			−0.427090
$949$	−3.54154	−	17.7077i	−0.114963	−	0.574816i
$950$		−	6.50097i		−	0.210919i
$951$	20.5119	+	20.5119i	0.665144	+	0.665144i
$952$	−0.0472740	−	1.31301i	−0.00153216	−	0.0425550i
$953$		−	16.3818i		−	0.530658i	−0.964158	−	0.265329i	$-0.914520\pi$
$953$		−	16.3818i		−	0.530658i	0.964158	−	0.265329i	$-0.0854805\pi$
$954$	−3.01882	+	3.01882i	−0.0977379	+	0.0977379i
$955$	33.8633	+	33.8633i	1.09579	+	1.09579i
$956$	2.41238	+	2.41238i	0.0780218	+	0.0780218i
$957$	−6.79381	+	6.79381i	−0.219613	+	0.219613i
$958$			28.5342i			0.921899i
$959$	0.511897	+	14.2177i	0.0165300	+	0.459114i
$960$	1.80230	+	1.80230i	0.0581691	+	0.0581691i
$961$			34.8776i			1.12508i
$962$	−10.0170	+	15.0255i	−0.322960	+	0.484441i
$963$	−6.95694			−0.224184
$964$	8.37727	+	8.37727i	0.269814	+	0.269814i
$965$		−	4.93996i		−	0.159023i
$966$	19.5058	−	0.702290i	0.627588	−	0.0225958i
$967$	−37.7762	+	37.7762i	−1.21480	+	1.21480i	−0.245373	+	0.969429i	$0.578910\pi$
$967$	−37.7762	+	37.7762i	−1.21480	+	1.21480i	−0.969429	+	0.245373i	$0.921090\pi$
$968$	6.53672	−	6.53672i	0.210098	−	0.210098i
$969$	1.52532	−	1.52532i	0.0490003	−	0.0490003i
$970$	24.1129	+	24.1129i	0.774219	+	0.774219i
$971$		−	23.3617i		−	0.749714i	−0.927083	−	0.374857i	$-0.877692\pi$
$971$		−	23.3617i		−	0.749714i	0.927083	−	0.374857i	$-0.122308\pi$
$972$	1.00000			0.0320750
$973$	5.29869	−	5.69449i	0.169868	−	0.182557i
$974$		−	20.6244i		−	0.660849i
$975$	−2.99319	+	4.48978i	−0.0958587	+	0.143788i
$976$			0.496594i			0.0158956i
$977$	−29.3537	+	29.3537i	−0.939107	+	0.939107i	−0.998250	−	0.0591422i	$-0.981163\pi$
$977$	−29.3537	+	29.3537i	−0.939107	+	0.939107i	0.0591422	+	0.998250i	$0.481163\pi$
$978$			5.99037i			0.191551i
$979$	19.1466			0.611927
$980$	−13.4907	−	11.6762i	−0.430946	−	0.372981i
$981$	−2.94374	+	2.94374i	−0.0939865	+	0.0939865i
$982$	−7.32502	−	7.32502i	−0.233751	−	0.233751i
$983$	−19.8845	+	19.8845i	−0.634216	+	0.634216i	−0.949123	−	0.314907i	$-0.898027\pi$
$983$	−19.8845	+	19.8845i	−0.634216	+	0.634216i	0.314907	+	0.949123i	$0.398027\pi$
$984$	8.65004			0.275753
$985$	10.3285			0.329095
$986$	2.54620	−	2.54620i	0.0810875	−	0.0810875i
$987$	−0.790787	−	21.9638i	−0.0251710	−	0.699114i
$988$	−3.07156	−	15.3578i	−0.0977193	−	0.488597i
$989$	−50.5766			−1.60824
$990$	−2.38809	−	2.38809i	−0.0758985	−	0.0758985i
$991$	17.8399			0.566703			0.283352	−	0.959016i	$-0.408554\pi$
$991$	17.8399			0.566703			0.283352	+	0.959016i	$0.408554\pi$
$992$	8.11650			0.257699
$993$	−9.65502	−	9.65502i	−0.306393	−	0.306393i
$994$	−28.9989	+	31.1650i	−0.919788	+	0.988494i
$995$	25.3493	+	25.3493i	0.803627	+	0.803627i
$996$	7.87386	+	7.87386i	0.249493	+	0.249493i
$997$		−	24.4660i		−	0.774846i	−0.921902	−	0.387423i	$-0.873365\pi$
$997$		−	24.4660i		−	0.774846i	0.921902	−	0.387423i	$-0.126635\pi$
$998$			42.8272i			1.35567i
$999$	3.54154	−	3.54154i	0.112049	−	0.112049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.a.265.1	✓	8
3.2	odd	2		1638.2.x.d.811.4		8
7.6	odd	2		546.2.o.d.265.2	yes	8
13.8	odd	4		546.2.o.d.307.2	yes	8
21.20	even	2		1638.2.x.b.811.3		8
39.8	even	4		1638.2.x.b.307.3		8
91.34	even	4	inner	546.2.o.a.307.1	yes	8
273.125	odd	4		1638.2.x.d.307.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.1	✓	8	1.1	even	1	trivial
546.2.o.a.307.1	yes	8	91.34	even	4	inner
546.2.o.d.265.2	yes	8	7.6	odd	2
546.2.o.d.307.2	yes	8	13.8	odd	4
1638.2.x.b.307.3		8	39.8	even	4
1638.2.x.b.811.3		8	21.20	even	2
1638.2.x.d.307.4		8	273.125	odd	4
1638.2.x.d.811.4		8	3.2	odd	2

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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(-1.80230 - 1.80230i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.93693 + 1.80230i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(-1.80230 - 1.80230i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.93693 + 1.80230i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +2.54884 q^{10} +(0.936931 + 0.936931i) q^{11} +1.00000 q^{12} +(2.00000 - 3.00000i) q^{13} +(-2.64404 + 0.0951965i) q^{14} +(1.80230 - 1.80230i) q^{15} -1.00000 q^{16} -0.496594 q^{17} +(0.707107 - 0.707107i) q^{18} +(3.07156 + 3.07156i) q^{19} +(-1.80230 + 1.80230i) q^{20} +(-1.80230 + 1.93693i) q^{21} -1.32502 q^{22} +7.37727i q^{23} +(-0.707107 + 0.707107i) q^{24} +1.49659i q^{25} +(0.707107 + 3.53553i) q^{26} -1.00000i q^{27} +(1.80230 - 1.93693i) q^{28} +7.25113 q^{29} +2.54884i q^{30} +(5.73923 + 5.73923i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.936931 + 0.936931i) q^{33} +(0.351145 - 0.351145i) q^{34} +(-0.242641 - 6.73923i) q^{35} +1.00000i q^{36} +(3.54154 + 3.54154i) q^{37} -4.34384 q^{38} +(3.00000 + 2.00000i) q^{39} -2.54884i q^{40} +(-6.11650 - 6.11650i) q^{41} +(-0.0951965 - 2.64404i) q^{42} +6.85574i q^{43} +(0.936931 - 0.936931i) q^{44} +(1.80230 + 1.80230i) q^{45} +(-5.21652 - 5.21652i) q^{46} +(-5.87386 + 5.87386i) q^{47} -1.00000i q^{48} +(0.503406 + 6.98188i) q^{49} +(-1.05825 - 1.05825i) q^{50} -0.496594i q^{51} +(-3.00000 - 2.00000i) q^{52} -4.26926 q^{53} +(0.707107 + 0.707107i) q^{54} -3.37727i q^{55} +(0.0951965 + 2.64404i) q^{56} +(-3.07156 + 3.07156i) q^{57} +(-5.12732 + 5.12732i) q^{58} +(-1.37727 + 1.37727i) q^{59} +(-1.80230 - 1.80230i) q^{60} -0.496594i q^{61} -8.11650 q^{62} +(-1.93693 - 1.80230i) q^{63} +1.00000i q^{64} +(-9.01152 + 1.80230i) q^{65} -1.32502i q^{66} +(9.11650 - 9.11650i) q^{67} +0.496594i q^{68} -7.37727 q^{69} +(4.93693 + 4.59379i) q^{70} +(11.3773 - 11.3773i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(3.54154 - 3.54154i) q^{73} -5.00849 q^{74} -1.49659 q^{75} +(3.07156 - 3.07156i) q^{76} +(0.126137 + 3.50341i) q^{77} +(-3.53553 + 0.707107i) q^{78} -13.1499 q^{79} +(1.80230 + 1.80230i) q^{80} +1.00000 q^{81} +8.65004 q^{82} +(7.87386 + 7.87386i) q^{83} +(1.93693 + 1.80230i) q^{84} +(0.895013 + 0.895013i) q^{85} +(-4.84774 - 4.84774i) q^{86} +7.25113i q^{87} +1.32502i q^{88} +(10.2177 - 10.2177i) q^{89} -2.54884 q^{90} +(9.28077 - 2.20619i) q^{91} +7.37727 q^{92} +(-5.73923 + 5.73923i) q^{93} -8.30690i q^{94} -11.0718i q^{95} +(0.707107 + 0.707107i) q^{96} +(9.46034 + 9.46034i) q^{97} +(-5.29289 - 4.58097i) q^{98} +(-0.936931 - 0.936931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Introduction

L-functions

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