LMFDB - Embedded newform 546.2.bi.e.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (of order $6$, 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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.0248275 - 1.73187i) q^{3} +1.00000 q^{4} +(-0.511132 + 0.295102i) q^{5} +(0.0248275 + 1.73187i) q^{6} +(2.62812 - 0.304939i) q^{7} -1.00000 q^{8} +(-2.99877 + 0.0859963i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.0248275 - 1.73187i) q^{3} +1.00000 q^{4} +(-0.511132 + 0.295102i) q^{5} +(0.0248275 + 1.73187i) q^{6} +(2.62812 - 0.304939i) q^{7} -1.00000 q^{8} +(-2.99877 + 0.0859963i) q^{9} +(0.511132 - 0.295102i) q^{10} +(3.05521 + 5.29178i) q^{11} +(-0.0248275 - 1.73187i) q^{12} +(1.86885 - 3.08341i) q^{13} +(-2.62812 + 0.304939i) q^{14} +(0.523770 + 0.877889i) q^{15} +1.00000 q^{16} +7.64672 q^{17} +(2.99877 - 0.0859963i) q^{18} +(-1.97552 + 3.42169i) q^{19} +(-0.511132 + 0.295102i) q^{20} +(-0.593366 - 4.54400i) q^{21} +(-3.05521 - 5.29178i) q^{22} -8.38604i q^{23} +(0.0248275 + 1.73187i) q^{24} +(-2.32583 + 4.02845i) q^{25} +(-1.86885 + 3.08341i) q^{26} +(0.223387 + 5.19135i) q^{27} +(2.62812 - 0.304939i) q^{28} +(-1.39183 - 0.803572i) q^{29} +(-0.523770 - 0.877889i) q^{30} +(1.38966 - 2.40696i) q^{31} -1.00000 q^{32} +(9.08883 - 5.42261i) q^{33} -7.64672 q^{34} +(-1.25333 + 0.931429i) q^{35} +(-2.99877 + 0.0859963i) q^{36} -2.22904i q^{37} +(1.97552 - 3.42169i) q^{38} +(-5.38647 - 3.16006i) q^{39} +(0.511132 - 0.295102i) q^{40} +(1.36416 + 0.787598i) q^{41} +(0.593366 + 4.54400i) q^{42} +(-2.90674 - 5.03462i) q^{43} +(3.05521 + 5.29178i) q^{44} +(1.50739 - 0.928899i) q^{45} +8.38604i q^{46} +(4.94554 - 2.85531i) q^{47} +(-0.0248275 - 1.73187i) q^{48} +(6.81402 - 1.60283i) q^{49} +(2.32583 - 4.02845i) q^{50} +(-0.189849 - 13.2431i) q^{51} +(1.86885 - 3.08341i) q^{52} +(-3.30431 - 1.90774i) q^{53} +(-0.223387 - 5.19135i) q^{54} +(-3.12323 - 1.80320i) q^{55} +(-2.62812 + 0.304939i) q^{56} +(5.97499 + 3.33639i) q^{57} +(1.39183 + 0.803572i) q^{58} -4.48228i q^{59} +(0.523770 + 0.877889i) q^{60} +(0.0871190 + 0.0502982i) q^{61} +(-1.38966 + 2.40696i) q^{62} +(-7.85489 + 1.14045i) q^{63} +1.00000 q^{64} +(-0.0453104 + 2.12753i) q^{65} +(-9.08883 + 5.42261i) q^{66} +(8.95985 - 5.17297i) q^{67} +7.64672 q^{68} +(-14.5236 + 0.208205i) q^{69} +(1.25333 - 0.931429i) q^{70} +(0.875991 + 1.51726i) q^{71} +(2.99877 - 0.0859963i) q^{72} +(-5.41081 + 9.37179i) q^{73} +2.22904i q^{74} +(7.03452 + 3.92802i) q^{75} +(-1.97552 + 3.42169i) q^{76} +(9.64312 + 12.9758i) q^{77} +(5.38647 + 3.16006i) q^{78} +(-3.17751 - 5.50361i) q^{79} +(-0.511132 + 0.295102i) q^{80} +(8.98521 - 0.515766i) q^{81} +(-1.36416 - 0.787598i) q^{82} +9.07449i q^{83} +(-0.593366 - 4.54400i) q^{84} +(-3.90849 + 2.25657i) q^{85} +(2.90674 + 5.03462i) q^{86} +(-1.35713 + 2.43042i) q^{87} +(-3.05521 - 5.29178i) q^{88} -4.11835i q^{89} +(-1.50739 + 0.928899i) q^{90} +(3.97132 - 8.67345i) q^{91} -8.38604i q^{92} +(-4.20305 - 2.34696i) q^{93} +(-4.94554 + 2.85531i) q^{94} -2.33192i q^{95} +(0.0248275 + 1.73187i) q^{96} +(-2.82580 - 4.89442i) q^{97} +(-6.81402 + 1.60283i) q^{98} +(-9.61693 - 15.6061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.0248275	−	1.73187i	−0.0143342	−	0.999897i
$3$	−0.0248275	−	1.73187i	−0.0143342	−	0.999897i
$4$	1.00000			0.500000
$5$	−0.511132	+	0.295102i	−0.228585	+	0.131974i	−0.609919	−	0.792464i	$-0.708798\pi$
$5$	−0.511132	+	0.295102i	−0.228585	+	0.131974i	0.381334	+	0.924437i	$0.375465\pi$
$6$	0.0248275	+	1.73187i	0.0101358	+	0.707034i
$7$	2.62812	−	0.304939i	0.993336	−	0.115256i
$7$	2.62812	−	0.304939i	0.993336	−	0.115256i
$8$	−1.00000			−0.353553
$9$	−2.99877	+	0.0859963i	−0.999589	+	0.0286654i
$10$	0.511132	−	0.295102i	0.161634	−	0.0933196i
$11$	3.05521	+	5.29178i	0.921180	+	1.59553i	0.797592	+	0.603197i	$0.206107\pi$
$11$	3.05521	+	5.29178i	0.921180	+	1.59553i	0.123588	+	0.992334i	$0.460560\pi$
$12$	−0.0248275	−	1.73187i	−0.00716709	−	0.499949i
$13$	1.86885	−	3.08341i	0.518326	−	0.855183i
$13$	1.86885	−	3.08341i	0.518326	−	0.855183i
$14$	−2.62812	+	0.304939i	−0.702394	+	0.0814984i
$15$	0.523770	+	0.877889i	0.135237	+	0.226670i
$16$	1.00000			0.250000
$17$	7.64672			1.85460			0.927301	−	0.374316i	$-0.122123\pi$
$17$	7.64672			1.85460			0.927301	+	0.374316i	$0.122123\pi$
$18$	2.99877	−	0.0859963i	0.706816	−	0.0202695i
$19$	−1.97552	+	3.42169i	−0.453214	+	0.784991i	−0.998584	−	0.0532055i	$-0.983056\pi$
$19$	−1.97552	+	3.42169i	−0.453214	+	0.784991i	0.545369	+	0.838196i	$0.316390\pi$
$20$	−0.511132	+	0.295102i	−0.114293	+	0.0659869i
$21$	−0.593366	−	4.54400i	−0.129483	−	0.991582i
$22$	−3.05521	−	5.29178i	−0.651373	−	1.12821i
$23$		−	8.38604i		−	1.74861i	−0.485377	−	0.874305i	$-0.661318\pi$
$23$		−	8.38604i		−	1.74861i	0.485377	−	0.874305i	$-0.338682\pi$
$24$	0.0248275	+	1.73187i	0.00506790	+	0.353517i
$25$	−2.32583	+	4.02845i	−0.465166	+	0.805691i
$26$	−1.86885	+	3.08341i	−0.366512	+	0.604706i
$27$	0.223387	+	5.19135i	0.0429908	+	0.999075i
$28$	2.62812	−	0.304939i	0.496668	−	0.0576281i
$29$	−1.39183	−	0.803572i	−0.258456	−	0.149220i	0.365174	−	0.930939i	$-0.381009\pi$
$29$	−1.39183	−	0.803572i	−0.258456	−	0.149220i	−0.623630	+	0.781720i	$0.714343\pi$
$30$	−0.523770	−	0.877889i	−0.0956269	−	0.160280i
$31$	1.38966	−	2.40696i	0.249590	−	0.432303i	−0.713822	−	0.700327i	$-0.753037\pi$
$31$	1.38966	−	2.40696i	0.249590	−	0.432303i	0.963412	+	0.268024i	$0.0863707\pi$
$32$	−1.00000			−0.176777
$33$	9.08883	−	5.42261i	1.58216	−	0.943956i
$34$	−7.64672			−1.31140
$35$	−1.25333	+	0.931429i	−0.211851	+	0.157440i
$36$	−2.99877	+	0.0859963i	−0.499795	+	0.0143327i
$37$		−	2.22904i		−	0.366451i	−0.983071	−	0.183226i	$-0.941346\pi$
$37$		−	2.22904i		−	0.366451i	0.983071	−	0.183226i	$-0.0586539\pi$
$38$	1.97552	−	3.42169i	0.320471	−	0.555072i
$39$	−5.38647	−	3.16006i	−0.862525	−	0.506015i
$40$	0.511132	−	0.295102i	0.0808171	−	0.0466598i
$41$	1.36416	+	0.787598i	0.213046	+	0.123002i	0.602726	−	0.797948i	$-0.294081\pi$
$41$	1.36416	+	0.787598i	0.213046	+	0.123002i	−0.389680	+	0.920950i	$0.627414\pi$
$42$	0.593366	+	4.54400i	0.0915583	+	0.701154i
$43$	−2.90674	−	5.03462i	−0.443274	−	0.767773i	0.554656	−	0.832080i	$-0.312850\pi$
$43$	−2.90674	−	5.03462i	−0.443274	−	0.767773i	−0.997930	+	0.0643067i	$0.979516\pi$
$44$	3.05521	+	5.29178i	0.460590	+	0.797765i
$45$	1.50739	−	0.928899i	0.224708	−	0.138472i
$46$			8.38604i			1.23645i
$47$	4.94554	−	2.85531i	0.721381	−	0.416489i	−0.0938798	−	0.995584i	$-0.529927\pi$
$47$	4.94554	−	2.85531i	0.721381	−	0.416489i	0.815261	+	0.579094i	$0.196594\pi$
$48$	−0.0248275	−	1.73187i	−0.00358355	−	0.249974i
$49$	6.81402	−	1.60283i	0.973432	−	0.228976i
$50$	2.32583	−	4.02845i	0.328922	−	0.569709i
$51$	−0.189849	−	13.2431i	−0.0265842	−	1.85441i
$52$	1.86885	−	3.08341i	0.259163	−	0.427591i
$53$	−3.30431	−	1.90774i	−0.453881	−	0.262049i	0.255587	−	0.966786i	$-0.417731\pi$
$53$	−3.30431	−	1.90774i	−0.453881	−	0.262049i	−0.709468	+	0.704738i	$0.751065\pi$
$54$	−0.223387	−	5.19135i	−0.0303991	−	0.706453i
$55$	−3.12323	−	1.80320i	−0.421136	−	0.243143i
$56$	−2.62812	+	0.304939i	−0.351197	+	0.0407492i
$57$	5.97499	+	3.33639i	0.791406	+	0.441916i
$58$	1.39183	+	0.803572i	0.182756	+	0.105514i
$59$		−	4.48228i		−	0.583543i	−0.956488	−	0.291772i	$-0.905755\pi$
$59$		−	4.48228i		−	0.583543i	0.956488	−	0.291772i	$-0.0942447\pi$
$60$	0.523770	+	0.877889i	0.0676184	+	0.113335i
$61$	0.0871190	+	0.0502982i	0.0111544	+	0.00644002i	0.505567	−	0.862787i	$-0.331283\pi$
$61$	0.0871190	+	0.0502982i	0.0111544	+	0.00644002i	−0.494412	+	0.869227i	$0.664617\pi$
$62$	−1.38966	+	2.40696i	−0.176487	+	0.305684i
$63$	−7.85489	+	1.14045i	−0.989624	+	0.143683i
$64$	1.00000			0.125000
$65$	−0.0453104	+	2.12753i	−0.00562006	+	0.263888i
$66$	−9.08883	+	5.42261i	−1.11876	+	0.667478i
$67$	8.95985	−	5.17297i	1.09462	−	0.631979i	0.159817	−	0.987147i	$-0.448910\pi$
$67$	8.95985	−	5.17297i	1.09462	−	0.631979i	0.934803	+	0.355168i	$0.115576\pi$
$68$	7.64672			0.927301
$69$	−14.5236	+	0.208205i	−1.74843	+	0.0250649i
$70$	1.25333	−	0.931429i	0.149801	−	0.111327i
$71$	0.875991	+	1.51726i	0.103961	+	0.180066i	0.913313	−	0.407258i	$-0.133515\pi$
$71$	0.875991	+	1.51726i	0.103961	+	0.180066i	−0.809352	+	0.587324i	$0.800182\pi$
$72$	2.99877	−	0.0859963i	0.353408	−	0.0101348i
$73$	−5.41081	+	9.37179i	−0.633287	+	1.09689i	0.353588	+	0.935401i	$0.384961\pi$
$73$	−5.41081	+	9.37179i	−0.633287	+	1.09689i	−0.986875	+	0.161484i	$0.948372\pi$
$74$			2.22904i			0.259120i
$75$	7.03452	+	3.92802i	0.812276	+	0.453569i
$76$	−1.97552	+	3.42169i	−0.226607	+	0.392495i
$77$	9.64312	+	12.9758i	1.09894	+	1.47873i
$78$	5.38647	+	3.16006i	0.609897	+	0.357806i
$79$	−3.17751	−	5.50361i	−0.357498	−	0.619205i	0.630044	−	0.776559i	$-0.283037\pi$
$79$	−3.17751	−	5.50361i	−0.357498	−	0.619205i	−0.987542	+	0.157355i	$0.949703\pi$
$80$	−0.511132	+	0.295102i	−0.0571463	+	0.0329934i
$81$	8.98521	−	0.515766i	0.998357	−	0.0573073i
$82$	−1.36416	−	0.787598i	−0.150646	−	0.0869756i
$83$			9.07449i			0.996055i	0.867161	+	0.498027i	$0.165942\pi$
$83$			9.07449i			0.996055i	−0.867161	+	0.498027i	$0.834058\pi$
$84$	−0.593366	−	4.54400i	−0.0647415	−	0.495791i
$85$	−3.90849	+	2.25657i	−0.423935	+	0.244759i
$86$	2.90674	+	5.03462i	0.313442	+	0.542897i
$87$	−1.35713	+	2.43042i	−0.145499	+	0.260568i
$88$	−3.05521	−	5.29178i	−0.325686	−	0.564105i
$89$		−	4.11835i		−	0.436544i	−0.975888	−	0.218272i	$-0.929958\pi$
$89$		−	4.11835i		−	0.436544i	0.975888	−	0.218272i	$-0.0700421\pi$
$90$	−1.50739	+	0.928899i	−0.158893	+	0.0979145i
$91$	3.97132	−	8.67345i	0.416307	−	0.909224i
$92$		−	8.38604i		−	0.874305i
$93$	−4.20305	−	2.34696i	−0.435836	−	0.243368i
$94$	−4.94554	+	2.85531i	−0.510093	+	0.294503i
$95$		−	2.33192i		−	0.239250i
$96$	0.0248275	+	1.73187i	0.00253395	+	0.176759i
$97$	−2.82580	−	4.89442i	−0.286916	−	0.496953i	0.686156	−	0.727455i	$-0.259297\pi$
$97$	−2.82580	−	4.89442i	−0.286916	−	0.496953i	−0.973072	+	0.230501i	$0.925963\pi$
$98$	−6.81402	+	1.60283i	−0.688320	+	0.161911i
$99$	−9.61693	−	15.6061i	−0.966538	−	1.56847i
$100$	−2.32583	+	4.02845i	−0.232583	+	0.402845i
$101$	5.91078	+	10.2378i	0.588144	+	1.01870i	0.994475	+	0.104970i	$0.0334747\pi$
$101$	5.91078	+	10.2378i	0.588144	+	1.01870i	−0.406331	+	0.913726i	$0.633192\pi$
$102$	0.189849	+	13.2431i	0.0187979	+	1.31127i
$103$	−3.76608	+	2.17435i	−0.371083	+	0.214245i	−0.673932	−	0.738794i	$-0.735396\pi$
$103$	−3.76608	+	2.17435i	−0.371083	+	0.214245i	0.302848	+	0.953039i	$0.402062\pi$
$104$	−1.86885	+	3.08341i	−0.183256	+	0.302353i
$105$	1.64423	+	2.14748i	0.160461	+	0.209573i
$106$	3.30431	+	1.90774i	0.320943	+	0.185296i
$107$			8.84064i			0.854657i	0.904097	+	0.427328i	$0.140545\pi$
$107$			8.84064i			0.854657i	−0.904097	+	0.427328i	$0.859455\pi$
$108$	0.223387	+	5.19135i	0.0214954	+	0.499538i
$109$	14.8949	+	8.59957i	1.42667	+	0.823690i	0.996857	−	0.0792270i	$-0.0252452\pi$
$109$	14.8949	+	8.59957i	1.42667	+	0.823690i	0.429816	+	0.902917i	$0.358579\pi$
$110$	3.12323	+	1.80320i	0.297788	+	0.171928i
$111$	−3.86041	+	0.0553415i	−0.366414	+	0.00525278i
$112$	2.62812	−	0.304939i	0.248334	−	0.0288141i
$113$	−13.5393	+	7.81690i	−1.27367	+	0.735353i	−0.975676	−	0.219216i	$-0.929650\pi$
$113$	−13.5393	+	7.81690i	−1.27367	+	0.735353i	−0.297992	+	0.954568i	$0.596317\pi$
$114$	−5.97499	−	3.33639i	−0.559609	−	0.312482i
$115$	2.47474	+	4.28638i	0.230771	+	0.399707i
$116$	−1.39183	−	0.803572i	−0.129228	−	0.0746098i
$117$	−5.33909	+	9.40713i	−0.493599	+	0.869690i
$118$			4.48228i			0.412627i
$119$	20.0965	−	2.33179i	1.84224	−	0.213754i
$120$	−0.523770	−	0.877889i	−0.0478134	−	0.0801400i
$121$	−13.1686	+	22.8087i	−1.19715	+	2.07352i
$122$	−0.0871190	−	0.0502982i	−0.00788738	−	0.00455378i
$123$	1.33015	−	2.38210i	0.119936	−	0.214787i
$124$	1.38966	−	2.40696i	0.124795	−	0.216152i
$125$		−	5.69645i		−	0.509506i
$126$	7.85489	−	1.14045i	0.699770	−	0.101599i
$127$	2.99064	−	5.17994i	0.265377	−	0.459646i	−0.702286	−	0.711895i	$-0.747837\pi$
$127$	2.99064	−	5.17994i	0.265377	−	0.459646i	0.967662	+	0.252250i	$0.0811704\pi$
$128$	−1.00000			−0.0883883
$129$	−8.64716	+	5.15910i	−0.761340	+	0.454234i
$130$	0.0453104	−	2.12753i	0.00397398	−	0.186597i
$131$	−2.79856	−	4.84725i	−0.244511	−	0.423506i	0.717483	−	0.696576i	$-0.245294\pi$
$131$	−2.79856	−	4.84725i	−0.244511	−	0.423506i	−0.961994	+	0.273070i	$0.911961\pi$
$132$	9.08883	−	5.42261i	0.791081	−	0.471978i
$133$	−4.14848	+	9.59503i	−0.359719	+	0.831995i
$134$	−8.95985	+	5.17297i	−0.774013	+	0.446877i
$135$	−1.64616	−	2.58754i	−0.141679	−	0.222700i
$136$	−7.64672			−0.655701
$137$	−21.1472			−1.80673			−0.903363	−	0.428876i	$-0.858910\pi$
$137$	−21.1472			−1.80673			−0.903363	+	0.428876i	$0.858910\pi$
$138$	14.5236	−	0.208205i	1.23633	−	0.0177236i
$139$	−9.34314	+	5.39426i	−0.792475	+	0.457535i	−0.840833	−	0.541295i	$-0.817934\pi$
$139$	−9.34314	+	5.39426i	−0.792475	+	0.457535i	0.0483583	+	0.998830i	$0.484601\pi$
$140$	−1.25333	+	0.931429i	−0.105926	+	0.0787201i
$141$	−5.06782	−	8.49415i	−0.426787	−	0.715337i
$142$	−0.875991	−	1.51726i	−0.0735115	−	0.127326i
$143$	22.0264	+	0.469101i	1.84194	+	0.0392282i
$144$	−2.99877	+	0.0859963i	−0.249897	+	0.00716636i
$145$	0.948544			0.0787723
$146$	5.41081	−	9.37179i	0.447801	−	0.775615i
$147$	−2.94508	−	11.7612i	−0.242906	−	0.970050i
$148$		−	2.22904i		−	0.183226i
$149$	−4.01109	+	6.94741i	−0.328601	+	0.569154i	−0.982235	−	0.187657i	$-0.939911\pi$
$149$	−4.01109	+	6.94741i	−0.328601	+	0.569154i	0.653633	+	0.756811i	$0.273244\pi$
$150$	−7.03452	−	3.92802i	−0.574366	−	0.320722i
$151$	−7.60834	−	4.39268i	−0.619158	−	0.357471i	0.157383	−	0.987538i	$-0.449694\pi$
$151$	−7.60834	−	4.39268i	−0.619158	−	0.357471i	−0.776541	+	0.630066i	$0.783028\pi$
$152$	1.97552	−	3.42169i	0.160236	−	0.277536i
$153$	−22.9307	+	0.657590i	−1.85384	+	0.0531630i
$154$	−9.64312	−	12.9758i	−0.777065	−	1.04562i
$155$			1.64037i			0.131758i
$156$	−5.38647	−	3.16006i	−0.431262	−	0.253007i
$157$	2.49489	+	1.44042i	0.199114	+	0.114958i	0.596242	−	0.802805i	$-0.296660\pi$
$157$	2.49489	+	1.44042i	0.199114	+	0.114958i	−0.397128	+	0.917763i	$0.629993\pi$
$158$	3.17751	+	5.50361i	0.252789	+	0.437844i
$159$	−3.22193	+	5.77000i	−0.255516	+	0.457591i
$160$	0.511132	−	0.295102i	0.0404086	−	0.0233299i
$161$	−2.55723	−	22.0395i	−0.201538	−	1.73696i
$162$	−8.98521	+	0.515766i	−0.705945	+	0.0405224i
$163$	−4.65862	−	2.68966i	−0.364891	−	0.210670i	0.306333	−	0.951924i	$-0.400898\pi$
$163$	−4.65862	−	2.68966i	−0.364891	−	0.210670i	−0.671224	+	0.741254i	$0.734231\pi$
$164$	1.36416	+	0.787598i	0.106523	+	0.0615011i
$165$	−3.04537	+	5.45381i	−0.237082	+	0.424578i
$166$		−	9.07449i		−	0.704317i
$167$	14.1115	+	8.14728i	1.09198	+	0.630455i	0.934103	−	0.357003i	$-0.116202\pi$
$167$	14.1115	+	8.14728i	1.09198	+	0.630455i	0.157878	+	0.987459i	$0.449535\pi$
$168$	0.593366	+	4.54400i	0.0457792	+	0.350577i
$169$	−6.01478	−	11.5249i	−0.462676	−	0.886528i
$170$	3.90849	−	2.25657i	0.299767	−	0.173071i
$171$	5.62986	−	10.4308i	0.430526	−	0.797660i
$172$	−2.90674	−	5.03462i	−0.221637	−	0.383886i
$173$	−7.20003	+	12.4708i	−0.547408	+	0.948138i	0.451043	+	0.892502i	$0.351052\pi$
$173$	−7.20003	+	12.4708i	−0.547408	+	0.948138i	−0.998451	+	0.0556362i	$0.982281\pi$
$174$	1.35713	−	2.43042i	0.102884	−	0.184250i
$175$	−4.88412	+	11.2965i	−0.369205	+	0.853935i
$176$	3.05521	+	5.29178i	0.230295	+	0.398883i
$177$	−7.76274	+	0.111284i	−0.583483	+	0.00836462i
$178$			4.11835i			0.308683i
$179$	−9.93300	+	5.73482i	−0.742427	+	0.428641i	−0.822951	−	0.568112i	$-0.807674\pi$
$179$	−9.93300	+	5.73482i	−0.742427	+	0.428641i	0.0805240	+	0.996753i	$0.474341\pi$
$180$	1.50739	−	0.928899i	0.112354	−	0.0692360i
$181$			14.7039i			1.09293i	0.837482	+	0.546465i	$0.184027\pi$
$181$			14.7039i			1.09293i	−0.837482	+	0.546465i	$0.815973\pi$
$182$	−3.97132	+	8.67345i	−0.294373	+	0.642919i
$183$	0.0849471	−	0.152128i	0.00627947	−	0.0112456i
$184$			8.38604i			0.618227i
$185$	0.657794	+	1.13933i	0.0483619	+	0.0837654i
$186$	4.20305	+	2.34696i	0.308183	+	0.172087i
$187$	23.3623	+	40.4647i	1.70842	+	2.95907i
$188$	4.94554	−	2.85531i	0.360690	−	0.208245i
$189$	2.17013	+	13.5754i	0.157854	+	0.987462i
$190$			2.33192i			0.169175i
$191$	−9.40428	−	5.42957i	−0.680470	−	0.392870i	0.119562	−	0.992827i	$-0.461851\pi$
$191$	−9.40428	−	5.42957i	−0.680470	−	0.392870i	−0.800032	+	0.599957i	$0.795184\pi$
$192$	−0.0248275	−	1.73187i	−0.00179177	−	0.124987i
$193$	16.6658	−	9.62200i	1.19963	−	0.692607i	0.239158	−	0.970981i	$-0.423129\pi$
$193$	16.6658	−	9.62200i	1.19963	−	0.692607i	0.960473	+	0.278374i	$0.0897954\pi$
$194$	2.82580	+	4.89442i	0.202880	+	0.351399i
$195$	3.68574	+	0.0256505i	0.263941	+	0.00183687i
$196$	6.81402	−	1.60283i	0.486716	−	0.114488i
$197$	−3.97307	+	6.88156i	−0.283070	+	0.490291i	−0.972139	−	0.234404i	$-0.924686\pi$
$197$	−3.97307	+	6.88156i	−0.283070	+	0.490291i	0.689070	+	0.724695i	$0.258019\pi$
$198$	9.61693	+	15.6061i	0.683446	+	1.10908i
$199$		−	18.8182i		−	1.33399i	−0.745064	−	0.666993i	$-0.767581\pi$
$199$		−	18.8182i		−	1.33399i	0.745064	−	0.666993i	$-0.232419\pi$
$200$	2.32583	−	4.02845i	0.164461	−	0.284855i
$201$	−9.18138	−	15.3889i	−0.647605	−	1.08545i
$202$	−5.91078	−	10.2378i	−0.415881	−	0.720327i
$203$	−3.90293	−	1.68746i	−0.273932	−	0.118436i
$204$	−0.189849	−	13.2431i	−0.0132921	−	0.927206i
$205$	−0.929688			−0.0649322
$206$	3.76608	−	2.17435i	0.262395	−	0.151494i
$207$	0.721168	+	25.1478i	0.0501247	+	1.74789i
$208$	1.86885	−	3.08341i	0.129582	−	0.213796i
$209$	−24.1425			−1.66997
$210$	−1.64423	−	2.14748i	−0.113463	−	0.148190i
$211$	1.28361	−	2.22329i	0.0883677	−	0.153057i	−0.818454	−	0.574573i	$-0.805168\pi$
$211$	1.28361	−	2.22329i	0.0883677	−	0.153057i	0.906821	+	0.421515i	$0.138502\pi$
$212$	−3.30431	−	1.90774i	−0.226941	−	0.131024i
$213$	2.60595	−	1.55477i	0.178557	−	0.106531i
$214$		−	8.84064i		−	0.604333i
$215$	2.97146	+	1.71557i	0.202652	+	0.117001i
$216$	−0.223387	−	5.19135i	−0.0151995	−	0.353227i
$217$	2.91822	−	6.74955i	0.198101	−	0.458189i
$218$	−14.8949	−	8.59957i	−1.00881	−	0.582437i
$219$	16.3651	+	9.13815i	1.10585	+	0.617499i
$220$	−3.12323	−	1.80320i	−0.210568	−	0.121572i
$221$	14.2906	−	23.5779i	0.961289	−	1.58602i
$222$	3.86041	−	0.0553415i	0.259093	−	0.00371428i
$223$	1.78923	−	3.09905i	0.119816	−	0.207527i	−0.799879	−	0.600162i	$-0.795103\pi$
$223$	1.78923	−	3.09905i	0.119816	−	0.207527i	0.919695	+	0.392634i	$0.128436\pi$
$224$	−2.62812	+	0.304939i	−0.175599	+	0.0203746i
$225$	6.62819	−	12.2804i	0.441879	−	0.818694i
$226$	13.5393	−	7.81690i	0.900619	−	0.519973i
$227$		−	11.9739i		−	0.794736i	−0.917659	−	0.397368i	$-0.869924\pi$
$227$		−	11.9739i		−	0.794736i	0.917659	−	0.397368i	$-0.130076\pi$
$228$	5.97499	+	3.33639i	0.395703	+	0.220958i
$229$	5.57509	+	9.65634i	0.368412	+	0.638109i	0.989318	−	0.145777i	$-0.0465681\pi$
$229$	5.57509	+	9.65634i	0.368412	+	0.638109i	−0.620905	+	0.783886i	$0.713235\pi$
$230$	−2.47474	−	4.28638i	−0.163180	−	0.282635i
$231$	22.2330	−	17.0228i	1.46282	−	1.12002i
$232$	1.39183	+	0.803572i	0.0913779	+	0.0527571i
$233$	13.8355	−	7.98795i	0.906396	−	0.523308i	0.0271263	−	0.999632i	$-0.491364\pi$
$233$	13.8355	−	7.98795i	0.906396	−	0.523308i	0.879270	+	0.476324i	$0.158031\pi$
$234$	5.33909	−	9.40713i	0.349027	−	0.614963i
$235$	−1.68522	+	2.91888i	−0.109931	+	0.190407i
$236$		−	4.48228i		−	0.291772i
$237$	−9.45267	+	5.63969i	−0.614017	+	0.366337i
$238$	−20.0965	+	2.33179i	−1.30266	+	0.151147i
$239$	17.6869			1.14407			0.572034	−	0.820230i	$-0.306154\pi$
$239$	17.6869			1.14407			0.572034	+	0.820230i	$0.306154\pi$
$240$	0.523770	+	0.877889i	0.0338092	+	0.0566675i
$241$	24.1671			1.55674			0.778370	−	0.627805i	$-0.216047\pi$
$241$	24.1671			1.55674			0.778370	+	0.627805i	$0.216047\pi$
$242$	13.1686	−	22.8087i	0.846510	−	1.46620i
$243$	−1.11632	−	15.5484i	−0.0716121	−	0.997433i
$244$	0.0871190	+	0.0502982i	0.00557722	+	0.00322001i
$245$	−3.00987	+	2.83009i	−0.192293	+	0.180808i
$246$	−1.33015	+	2.38210i	−0.0848073	+	0.151877i
$247$	6.85852	+	12.4860i	0.436397	+	0.794463i
$248$	−1.38966	+	2.40696i	−0.0882435	+	0.152842i
$249$	15.7159	−	0.225297i	0.995953	−	0.0142776i
$250$			5.69645i			0.360275i
$251$	1.60381	+	2.77787i	0.101231	+	0.175338i	0.912192	−	0.409763i	$-0.134388\pi$
$251$	1.60381	+	2.77787i	0.101231	+	0.175338i	−0.810961	+	0.585100i	$0.801055\pi$
$252$	−7.85489	+	1.14045i	−0.494812	+	0.0718416i
$253$	44.3770	−	25.6211i	2.78996	−	1.61078i
$254$	−2.99064	+	5.17994i	−0.187650	+	0.325019i
$255$	4.00512	+	6.71298i	0.250811	+	0.420383i
$256$	1.00000			0.0625000
$257$	1.18333			0.0738138			0.0369069	−	0.999319i	$-0.488249\pi$
$257$	1.18333			0.0738138			0.0369069	+	0.999319i	$0.488249\pi$
$258$	8.64716	−	5.15910i	0.538349	−	0.321192i
$259$	−0.679720	−	5.85817i	−0.0422358	−	0.364009i
$260$	−0.0453104	+	2.12753i	−0.00281003	+	0.131944i
$261$	4.24287	+	2.29003i	0.262627	+	0.141749i
$262$	2.79856	+	4.84725i	0.172896	+	0.299464i
$263$	−1.16231	+	0.671062i	−0.0716713	+	0.0413794i	−0.535407	−	0.844594i	$-0.679842\pi$
$263$	−1.16231	+	0.671062i	−0.0716713	+	0.0413794i	0.463736	+	0.885973i	$0.346509\pi$
$264$	−9.08883	+	5.42261i	−0.559379	+	0.333739i
$265$	2.25192			0.138334
$266$	4.14848	−	9.59503i	0.254360	−	0.588309i
$267$	−7.13246	+	0.102249i	−0.436500	+	0.00625751i
$268$	8.95985	−	5.17297i	0.547310	−	0.315990i
$269$	−6.46592			−0.394234			−0.197117	−	0.980380i	$-0.563158\pi$
$269$	−6.46592			−0.394234			−0.197117	+	0.980380i	$0.563158\pi$
$270$	1.64616	+	2.58754i	0.100182	+	0.157473i
$271$	−19.2359			−1.16850			−0.584249	−	0.811575i	$-0.698611\pi$
$271$	−19.2359			−1.16850			−0.584249	+	0.811575i	$0.698611\pi$
$272$	7.64672			0.463651
$273$	−15.1199	−	6.66247i	−0.915098	−	0.403231i
$274$	21.1472			1.27755
$275$	−28.4236			−1.71401
$276$	−14.5236	+	0.208205i	−0.874215	+	0.0125325i
$277$	−11.7622			−0.706725			−0.353362	−	0.935487i	$-0.614962\pi$
$277$	−11.7622			−0.706725			−0.353362	+	0.935487i	$0.614962\pi$
$278$	9.34314	−	5.39426i	0.560364	−	0.323526i
$279$	−3.96028	+	7.33742i	−0.237096	+	0.439280i
$280$	1.25333	−	0.931429i	0.0749007	−	0.0556635i
$281$	−21.9950			−1.31211			−0.656057	−	0.754711i	$-0.727777\pi$
$281$	−21.9950			−1.31211			−0.656057	+	0.754711i	$0.727777\pi$
$282$	5.06782	+	8.49415i	0.301784	+	0.505819i
$283$	−11.1271	+	6.42423i	−0.661437	+	0.381881i	−0.792824	−	0.609450i	$-0.791390\pi$
$283$	−11.1271	+	6.42423i	−0.661437	+	0.381881i	0.131387	+	0.991331i	$0.458057\pi$
$284$	0.875991	+	1.51726i	0.0519805	+	0.0900329i
$285$	−4.03859	+	0.0578958i	−0.239225	+	0.00342945i
$286$	−22.0264	−	0.469101i	−1.30245	−	0.0277385i
$287$	3.82534	+	1.65392i	0.225803	+	0.0976275i
$288$	2.99877	−	0.0859963i	0.176704	−	0.00506738i
$289$	41.4723			2.43955
$290$	−0.948544			−0.0557004
$291$	−8.40636	+	5.01544i	−0.492790	+	0.294010i
$292$	−5.41081	+	9.37179i	−0.316643	+	0.548443i
$293$	0.344829	−	0.199087i	0.0201451	−	0.0116308i	−0.489894	−	0.871782i	$-0.662964\pi$
$293$	0.344829	−	0.199087i	0.0201451	−	0.0116308i	0.510039	+	0.860151i	$0.329631\pi$
$294$	2.94508	+	11.7612i	0.171761	+	0.685929i
$295$	1.32273	+	2.29104i	0.0770124	+	0.133389i
$296$			2.22904i			0.129560i
$297$	−26.7890	+	17.0428i	−1.55445	+	0.988922i
$298$	4.01109	−	6.94741i	0.232356	−	0.402453i
$299$	−25.8576	−	15.6723i	−1.49538	−	0.906351i
$300$	7.03452	+	3.92802i	0.406138	+	0.226785i
$301$	−9.17452	−	12.3452i	−0.528810	−	0.711566i
$302$	7.60834	+	4.39268i	0.437811	+	0.252770i
$303$	17.5838	−	10.4909i	1.01016	−	0.602686i
$304$	−1.97552	+	3.42169i	−0.113304	+	0.196248i
$305$	−0.0593724			−0.00339966
$306$	22.9307	−	0.657590i	1.31086	−	0.0375919i
$307$	10.2738			0.586356			0.293178	−	0.956058i	$-0.405287\pi$
$307$	10.2738			0.586356			0.293178	+	0.956058i	$0.405287\pi$
$308$	9.64312	+	12.9758i	0.549468	+	0.739363i
$309$	3.85920	+	6.46839i	0.219542	+	0.367974i
$310$		−	1.64037i		−	0.0931666i
$311$	1.05163	−	1.82148i	0.0596325	−	0.103287i	−0.834668	−	0.550754i	$-0.814340\pi$
$311$	1.05163	−	1.82148i	0.0596325	−	0.103287i	0.894300	+	0.447467i	$0.147674\pi$
$312$	5.38647	+	3.16006i	0.304949	+	0.178903i
$313$	−9.44084	+	5.45067i	−0.533628	+	0.308090i	−0.742492	−	0.669854i	$-0.766356\pi$
$313$	−9.44084	+	5.45067i	−0.533628	+	0.308090i	0.208865	+	0.977945i	$0.433023\pi$
$314$	−2.49489	−	1.44042i	−0.140795	−	0.0812878i
$315$	3.67834	−	2.90092i	0.207251	−	0.163448i
$316$	−3.17751	−	5.50361i	−0.178749	−	0.309602i
$317$	−5.27267	−	9.13253i	−0.296143	−	0.512934i	0.679107	−	0.734039i	$-0.262367\pi$
$317$	−5.27267	−	9.13253i	−0.296143	−	0.512934i	−0.975250	+	0.221105i	$0.929034\pi$
$318$	3.22193	−	5.77000i	0.180677	−	0.323566i
$319$		−	9.82032i		−	0.549832i
$320$	−0.511132	+	0.295102i	−0.0285732	+	0.0164967i
$321$	15.3109	−	0.219491i	0.854569	−	0.0122508i
$322$	2.55723	+	22.0395i	0.142509	+	1.22821i
$323$	−15.1062	+	26.1647i	−0.840533	+	1.45585i
$324$	8.98521	−	0.515766i	0.499178	−	0.0286537i
$325$	8.07473	+	14.7001i	0.447905	+	0.815413i
$326$	4.65862	+	2.68966i	0.258017	+	0.148966i
$327$	14.5236	−	26.0096i	0.803155	−	1.43833i
$328$	−1.36416	−	0.787598i	−0.0753231	−	0.0434878i
$329$	12.1268	−	9.01218i	0.668570	−	0.496858i
$330$	3.04537	−	5.45381i	0.167642	−	0.300222i
$331$	−12.6163	−	7.28403i	−0.693455	−	0.400366i	0.111450	−	0.993770i	$-0.464450\pi$
$331$	−12.6163	−	7.28403i	−0.693455	−	0.400366i	−0.804905	+	0.593404i	$0.797784\pi$
$332$			9.07449i			0.498027i
$333$	0.191689	+	6.68436i	0.0105045	+	0.366301i
$334$	−14.1115	−	8.14728i	−0.772147	−	0.445799i
$335$	−3.05311	+	5.28815i	−0.166809	+	0.288922i
$336$	−0.593366	−	4.54400i	−0.0323708	−	0.247895i
$337$	−31.0830			−1.69320			−0.846599	−	0.532231i	$-0.821354\pi$
$337$	−31.0830			−1.69320			−0.846599	+	0.532231i	$0.821354\pi$
$338$	6.01478	+	11.5249i	0.327161	+	0.626870i
$339$	13.8740	+	23.2542i	0.753534	+	1.26300i
$340$	−3.90849	+	2.25657i	−0.211967	+	0.122379i
$341$	16.9828			0.919671
$342$	−5.62986	+	10.4308i	−0.304428	+	0.564030i
$343$	17.4193	−	6.29030i	0.940554	−	0.339644i
$344$	2.90674	+	5.03462i	0.156721	+	0.271449i
$345$	7.36202	−	4.39236i	0.396358	−	0.236476i
$346$	7.20003	−	12.4708i	0.387076	−	0.670435i
$347$		−	24.6678i		−	1.32424i	−0.749398	−	0.662119i	$-0.769657\pi$
$347$		−	24.6678i		−	1.32424i	0.749398	−	0.662119i	$-0.230343\pi$
$348$	−1.35713	+	2.43042i	−0.0727497	+	0.130284i
$349$	−16.5800	+	28.7175i	−0.887509	+	1.53721i	−0.0446981	+	0.999001i	$0.514233\pi$
$349$	−16.5800	+	28.7175i	−0.887509	+	1.53721i	−0.842811	+	0.538210i	$0.819101\pi$
$350$	4.88412	−	11.2965i	0.261067	−	0.603823i
$351$	16.4245	+	9.01307i	0.876676	+	0.481082i
$352$	−3.05521	−	5.29178i	−0.162843	−	0.282053i
$353$	−12.5305	+	7.23450i	−0.666933	+	0.385054i	−0.794913	−	0.606723i	$-0.792484\pi$
$353$	−12.5305	+	7.23450i	−0.666933	+	0.385054i	0.127981	+	0.991777i	$0.459150\pi$
$354$	7.76274	−	0.111284i	0.412585	−	0.00591468i
$355$	−0.895494	−	0.517014i	−0.0475279	−	0.0274403i
$356$		−	4.11835i		−	0.218272i
$357$	−4.53730	−	34.7467i	−0.240140	−	1.83899i
$358$	9.93300	−	5.73482i	0.524975	−	0.303095i
$359$	−7.00098	−	12.1261i	−0.369498	−	0.639989i	0.619989	−	0.784610i	$-0.287137\pi$
$359$	−7.00098	−	12.1261i	−0.369498	−	0.639989i	−0.989487	+	0.144621i	$0.953804\pi$
$360$	−1.50739	+	0.928899i	−0.0794464	+	0.0489573i
$361$	1.69467	+	2.93526i	0.0891932	+	0.154487i
$362$		−	14.7039i		−	0.772819i
$363$	39.8287	+	22.2401i	2.09046	+	1.16730i
$364$	3.97132	−	8.67345i	0.208153	−	0.454612i
$365$		−	6.38697i		−	0.334309i
$366$	−0.0849471	+	0.152128i	−0.00444025	+	0.00795185i
$367$	−12.7593	+	7.36659i	−0.666030	+	0.384533i	−0.794571	−	0.607172i	$-0.792304\pi$
$367$	−12.7593	+	7.36659i	−0.666030	+	0.384533i	0.128541	+	0.991704i	$0.458971\pi$
$368$		−	8.38604i		−	0.437153i
$369$	−4.15853	−	2.24451i	−0.216484	−	0.116845i
$370$	−0.657794	−	1.13933i	−0.0341971	−	0.0592310i
$371$	−9.26586	−	4.00616i	−0.481059	−	0.207990i
$372$	−4.20305	−	2.34696i	−0.217918	−	0.121684i
$373$	−7.91499	+	13.7092i	−0.409822	+	0.709833i	−0.994870	−	0.101166i	$-0.967743\pi$
$373$	−7.91499	+	13.7092i	−0.409822	+	0.709833i	0.585047	+	0.810999i	$0.301076\pi$
$374$	−23.3623	−	40.4647i	−1.20804	−	2.09238i
$375$	−9.86553	+	0.141429i	−0.509454	+	0.00730336i
$376$	−4.94554	+	2.85531i	−0.255047	+	0.147251i
$377$	−5.07886	+	2.78981i	−0.261575	+	0.143683i
$378$	−2.17013	−	13.5754i	−0.111620	−	0.698241i
$379$	−11.2444	−	6.49193i	−0.577584	−	0.333468i	0.182589	−	0.983189i	$-0.441552\pi$
$379$	−11.2444	−	6.49193i	−0.577584	−	0.333468i	−0.760173	+	0.649721i	$0.774886\pi$
$380$		−	2.33192i		−	0.119625i
$381$	−9.04525	−	5.05081i	−0.463402	−	0.258761i
$382$	9.40428	+	5.42957i	0.481165	+	0.277801i
$383$	−3.62494	−	2.09286i	−0.185226	−	0.106940i	0.404520	−	0.914529i	$-0.367439\pi$
$383$	−3.62494	−	2.09286i	−0.185226	−	0.106940i	−0.589746	+	0.807589i	$0.700772\pi$
$384$	0.0248275	+	1.73187i	0.00126698	+	0.0883793i
$385$	−8.75809	−	3.78663i	−0.446354	−	0.192984i
$386$	−16.6658	+	9.62200i	−0.848267	+	0.489747i
$387$	9.14960	+	14.8477i	0.465100	+	0.754751i
$388$	−2.82580	−	4.89442i	−0.143458	−	0.248477i
$389$	−19.0201	−	10.9812i	−0.964356	−	0.556771i	−0.0668451	−	0.997763i	$-0.521293\pi$
$389$	−19.0201	−	10.9812i	−0.964356	−	0.556771i	−0.897511	+	0.440992i	$0.854627\pi$
$390$	−3.68574	−	0.0256505i	−0.186635	−	0.00129886i
$391$		−	64.1257i		−	3.24298i
$392$	−6.81402	+	1.60283i	−0.344160	+	0.0809553i
$393$	−8.32533	+	4.96709i	−0.419957	+	0.250557i
$394$	3.97307	−	6.88156i	0.200160	−	0.346688i
$395$	3.24826	+	1.87538i	0.163438	+	0.0943608i
$396$	−9.61693	−	15.6061i	−0.483269	−	0.784235i
$397$	−16.5607	+	28.6839i	−0.831156	+	1.43960i	0.0659662	+	0.997822i	$0.478987\pi$
$397$	−16.5607	+	28.6839i	−0.831156	+	1.43960i	−0.897122	+	0.441783i	$0.854346\pi$
$398$			18.8182i			0.943271i
$399$	16.7204	+	6.94642i	0.837066	+	0.347756i
$400$	−2.32583	+	4.02845i	−0.116291	+	0.201423i
$401$	−6.94374			−0.346754			−0.173377	−	0.984856i	$-0.555468\pi$
$401$	−6.94374			−0.346754			−0.173377	+	0.984856i	$0.555468\pi$
$402$	9.18138	+	15.3889i	0.457926	+	0.767528i
$403$	−4.82457	−	8.78314i	−0.240329	−	0.437519i
$404$	5.91078	+	10.2378i	0.294072	+	0.509348i
$405$	−4.44043	+	2.91518i	−0.220647	+	0.144857i
$406$	3.90293	+	1.68746i	0.193699	+	0.0837472i
$407$	11.7956	−	6.81017i	0.584684	−	0.337568i
$408$	0.189849	+	13.2431i	0.00939894	+	0.655634i
$409$	−0.303545			−0.0150093			−0.00750467	−	0.999972i	$-0.502389\pi$
$409$	−0.303545			−0.0150093			−0.00750467	+	0.999972i	$0.502389\pi$
$410$	0.929688			0.0459140
$411$	0.525033	+	36.6243i	0.0258980	+	1.80654i
$412$	−3.76608	+	2.17435i	−0.185542	+	0.107123i
$413$	−1.36682	−	11.7800i	−0.0672570	−	0.579654i
$414$	−0.721168	−	25.1478i	−0.0354435	−	1.23595i
$415$	−2.67790	−	4.63827i	−0.131453	−	0.227684i
$416$	−1.86885	+	3.08341i	−0.0916280	+	0.151176i
$417$	9.57415	+	16.0472i	0.468848	+	0.785835i
$418$	24.1425			1.18085
$419$	2.85725	−	4.94891i	0.139586	−	0.241770i	−0.787754	−	0.615990i	$-0.788756\pi$
$419$	2.85725	−	4.94891i	0.139586	−	0.241770i	0.927340	+	0.374220i	$0.122089\pi$
$420$	1.64423	+	2.14748i	0.0802304	+	0.104786i
$421$			9.25537i			0.451079i	0.974234	+	0.225540i	$0.0724145\pi$
$421$			9.25537i			0.451079i	−0.974234	+	0.225540i	$0.927585\pi$
$422$	−1.28361	+	2.22329i	−0.0624854	+	0.108228i
$423$	−14.5850	+	8.98770i	−0.709146	+	0.436997i
$424$	3.30431	+	1.90774i	0.160471	+	0.0926481i
$425$	−17.7850	+	30.8045i	−0.862698	+	1.49424i
$426$	−2.60595	+	1.55477i	−0.126259	+	0.0753291i
$427$	0.244297	+	0.105624i	0.0118224	+	0.00511148i
$428$			8.84064i			0.427328i
$429$	0.265561	−	38.1586i	0.0128214	−	1.84232i
$430$	−2.97146	−	1.71557i	−0.143296	−	0.0827322i
$431$	−5.05283	−	8.75176i	−0.243386	−	0.421557i	0.718290	−	0.695743i	$-0.244925\pi$
$431$	−5.05283	−	8.75176i	−0.243386	−	0.421557i	−0.961677	+	0.274186i	$0.911592\pi$
$432$	0.223387	+	5.19135i	0.0107477	+	0.249769i
$433$	32.8655	−	18.9749i	1.57942	−	0.911877i	0.584476	−	0.811411i	$-0.301300\pi$
$433$	32.8655	−	18.9749i	1.57942	−	0.911877i	0.994941	−	0.100466i	$-0.0320333\pi$
$434$	−2.91822	+	6.74955i	−0.140079	+	0.323989i
$435$	−0.0235500	−	1.64276i	−0.00112914	−	0.0787642i
$436$	14.8949	+	8.59957i	0.713336	+	0.411845i
$437$	28.6945	+	16.5668i	1.37264	+	0.792495i
$438$	−16.3651	−	9.13815i	−0.781954	−	0.436638i
$439$		−	28.4483i		−	1.35776i	−0.734248	−	0.678881i	$-0.762465\pi$
$439$		−	28.4483i		−	1.35776i	0.734248	−	0.678881i	$-0.237535\pi$
$440$	3.12323	+	1.80320i	0.148894	+	0.0859641i
$441$	−20.2958	+	5.39251i	−0.966468	+	0.256786i
$442$	−14.2906	+	23.5779i	−0.679734	+	1.12149i
$443$	18.7651	−	10.8340i	0.891555	−	0.514740i	0.0171043	−	0.999854i	$-0.494555\pi$
$443$	18.7651	−	10.8340i	0.891555	−	0.514740i	0.874451	+	0.485114i	$0.161222\pi$
$444$	−3.86041	+	0.0553415i	−0.183207	+	0.00262639i
$445$	1.21534	+	2.10502i	0.0576124	+	0.0997876i
$446$	−1.78923	+	3.09905i	−0.0847227	+	0.146744i
$447$	12.1316	+	6.77421i	0.573806	+	0.320409i
$448$	2.62812	−	0.304939i	0.124167	−	0.0144070i
$449$	−6.23704	−	10.8029i	−0.294344	−	0.509819i	0.680488	−	0.732759i	$-0.261768\pi$
$449$	−6.23704	−	10.8029i	−0.294344	−	0.509819i	−0.974832	+	0.222940i	$0.928434\pi$
$450$	−6.62819	+	12.2804i	−0.312456	+	0.578904i
$451$			9.62510i			0.453228i
$452$	−13.5393	+	7.81690i	−0.636834	+	0.367676i
$453$	−7.41867	+	13.2857i	−0.348559	+	0.624219i
$454$			11.9739i			0.561963i
$455$	0.529687	+	5.60522i	0.0248321	+	0.262777i
$456$	−5.97499	−	3.33639i	−0.279804	−	0.156241i
$457$			9.59213i			0.448701i	0.974509	+	0.224351i	$0.0720261\pi$
$457$			9.59213i			0.448701i	−0.974509	+	0.224351i	$0.927974\pi$
$458$	−5.57509	−	9.65634i	−0.260507	−	0.451211i
$459$	1.70818	+	39.6968i	0.0797308	+	1.85289i
$460$	2.47474	+	4.28638i	0.115385	+	0.199853i
$461$	−4.17780	+	2.41206i	−0.194580	+	0.112341i	−0.594125	−	0.804373i	$-0.702501\pi$
$461$	−4.17780	+	2.41206i	−0.194580	+	0.112341i	0.399545	+	0.916714i	$0.369168\pi$
$462$	−22.2330	+	17.0228i	−1.03437	+	0.791973i
$463$			3.08747i			0.143487i	0.997423	+	0.0717434i	$0.0228563\pi$
$463$			3.08747i			0.143487i	−0.997423	+	0.0717434i	$0.977144\pi$
$464$	−1.39183	−	0.803572i	−0.0646140	−	0.0373049i
$465$	2.84091	−	0.0407263i	0.131744	−	0.00188864i
$466$	−13.8355	+	7.98795i	−0.640919	+	0.370035i
$467$	4.16237	+	7.20943i	0.192611	+	0.333613i	0.946115	−	0.323831i	$-0.104971\pi$
$467$	4.16237	+	7.20943i	0.192611	+	0.333613i	−0.753504	+	0.657444i	$0.771638\pi$
$468$	−5.33909	+	9.40713i	−0.246800	+	0.434845i
$469$	21.9701	−	16.3274i	1.01449	−	0.753929i
$470$	1.68522	−	2.91888i	0.0777332	−	0.134638i
$471$	2.43269	−	4.35659i	0.112092	−	0.200741i
$472$			4.48228i			0.206314i
$473$	17.7614	−	30.7636i	0.816670	−	1.41451i
$474$	9.45267	−	5.63969i	0.434175	−	0.259039i
$475$	−9.18943	−	15.9166i	−0.421640	−	0.730302i
$476$	20.0965	−	2.33179i	0.921121	−	0.106877i
$477$	10.0729	+	5.43672i	0.461207	+	0.248930i
$478$	−17.6869			−0.808979
$479$	−10.4595	+	6.03880i	−0.477907	+	0.275920i	−0.719544	−	0.694447i	$-0.755649\pi$
$479$	−10.4595	+	6.03880i	−0.477907	+	0.275920i	0.241637	+	0.970367i	$0.422316\pi$
$480$	−0.523770	−	0.877889i	−0.0239067	−	0.0400700i
$481$	−6.87302	−	4.16574i	−0.313383	−	0.189941i
$482$	−24.1671			−1.10078
$483$	−38.1061	+	4.97599i	−1.73389	+	0.226415i
$484$	−13.1686	+	22.8087i	−0.598573	+	1.03676i
$485$	2.88871	+	1.66780i	0.131170	+	0.0757308i
$486$	1.11632	+	15.5484i	0.0506374	+	0.705291i
$487$		−	5.59837i		−	0.253686i	−0.991923	−	0.126843i	$-0.959516\pi$
$487$		−	5.59837i		−	0.253686i	0.991923	−	0.126843i	$-0.0404845\pi$
$488$	−0.0871190	−	0.0502982i	−0.00394369	−	0.00227689i
$489$	−4.54248	+	8.13492i	−0.205418	+	0.367874i
$490$	3.00987	−	2.83009i	0.135972	−	0.127851i
$491$	−0.451495	−	0.260671i	−0.0203757	−	0.0117639i	0.489778	−	0.871847i	$-0.337078\pi$
$491$	−0.451495	−	0.260671i	−0.0203757	−	0.0117639i	−0.510153	+	0.860084i	$0.670411\pi$
$492$	1.33015	−	2.38210i	0.0599678	−	0.107394i
$493$	−10.6429	−	6.14469i	−0.479333	−	0.276743i
$494$	−6.85852	−	12.4860i	−0.308580	−	0.561770i
$495$	9.52091	+	5.13879i	0.427933	+	0.230971i
$496$	1.38966	−	2.40696i	0.0623976	−	0.108076i
$497$	2.76488	+	3.72042i	0.124022	+	0.166884i
$498$	−15.7159	+	0.225297i	−0.704245	+	0.0100958i
$499$	−28.9603	+	16.7202i	−1.29644	+	0.748501i	−0.979788	−	0.200041i	$-0.935893\pi$
$499$	−28.9603	+	16.7202i	−1.29644	+	0.748501i	−0.316654	+	0.948541i	$0.602559\pi$
$500$		−	5.69645i		−	0.254753i
$501$	13.7597	−	24.6416i	0.614738	−	1.10091i
$502$	−1.60381	−	2.77787i	−0.0715814	−	0.123983i
$503$	−9.16509	−	15.8744i	−0.408651	−	0.707805i	0.586088	−	0.810248i	$-0.300667\pi$
$503$	−9.16509	−	15.8744i	−0.408651	−	0.707805i	−0.994739	+	0.102443i	$0.967334\pi$
$504$	7.85489	−	1.14045i	0.349885	−	0.0507997i
$505$	−6.04238	−	3.48857i	−0.268882	−	0.155239i
$506$	−44.3770	+	25.6211i	−1.97280	+	1.13900i
$507$	−19.8103	+	10.7030i	−0.879805	+	0.475336i
$508$	2.99064	−	5.17994i	0.132688	−	0.229823i
$509$			34.9103i			1.54737i	0.633569	+	0.773686i	$0.281589\pi$
$509$			34.9103i			1.54737i	−0.633569	+	0.773686i	$0.718411\pi$
$510$	−4.00512	−	6.71298i	−0.177350	−	0.297256i
$511$	−11.3624	+	26.2802i	−0.502644	+	1.16257i
$512$	−1.00000			−0.0441942
$513$	−18.2045	−	9.49123i	−0.803749	−	0.419048i
$514$	−1.18333			−0.0521943
$515$	1.28331	−	2.22276i	0.0565495	−	0.0979465i
$516$	−8.64716	+	5.15910i	−0.380670	+	0.227117i
$517$	30.2193	+	17.4471i	1.32904	+	0.767324i
$518$	0.679720	+	5.85817i	0.0298652	+	0.257393i
$519$	21.7766	+	12.1599i	0.955888	+	0.533761i
$520$	0.0453104	−	2.12753i	0.00198699	−	0.0932984i
$521$	15.3561	−	26.5976i	0.672763	−	1.16526i	−0.304354	−	0.952559i	$-0.598441\pi$
$521$	15.3561	−	26.5976i	0.672763	−	1.16526i	0.977117	−	0.212701i	$-0.0682260\pi$
$522$	−4.24287	−	2.29003i	−0.185705	−	0.100232i
$523$		−	31.3290i		−	1.36992i	−0.728581	−	0.684960i	$-0.759820\pi$
$523$		−	31.3290i		−	1.36992i	0.728581	−	0.684960i	$-0.240180\pi$
$524$	−2.79856	−	4.84725i	−0.122256	−	0.211753i
$525$	19.6854	+	8.17822i	0.859139	+	0.356927i
$526$	1.16231	−	0.671062i	0.0506793	−	0.0292597i
$527$	10.6263	−	18.4054i	0.462891	−	0.801750i
$528$	9.08883	−	5.42261i	0.395541	−	0.235989i
$529$	−47.3257			−2.05764
$530$	−2.25192			−0.0978170
$531$	0.385459	+	13.4413i	0.0167275	+	0.583303i
$532$	−4.14848	+	9.59503i	−0.179860	+	0.415997i
$533$	4.97790	−	2.73435i	0.215617	−	0.118438i
$534$	7.13246	−	0.102249i	0.308652	−	0.00442473i
$535$	−2.60889	−	4.51873i	−0.112792	−	0.195362i
$536$	−8.95985	+	5.17297i	−0.387007	+	0.223438i
$537$	10.1786	+	17.0603i	0.439239	+	0.736207i
$538$	6.46592			0.278765
$539$	29.3001	+	31.1613i	1.26204	+	1.34221i
$540$	−1.64616	−	2.58754i	−0.0708394	−	0.111350i
$541$	−18.3221	+	10.5782i	−0.787726	+	0.454794i	−0.839162	−	0.543882i	$-0.816954\pi$
$541$	−18.3221	+	10.5782i	−0.787726	+	0.454794i	0.0514351	+	0.998676i	$0.483620\pi$
$542$	19.2359			0.826252
$543$	25.4652	−	0.365061i	1.09282	−	0.0156663i
$544$	−7.64672			−0.327850
$545$	−10.1510			−0.434822
$546$	15.1199	+	6.66247i	0.647072	+	0.285128i
$547$	−2.57133			−0.109942			−0.0549710	−	0.998488i	$-0.517507\pi$
$547$	−2.57133			−0.109942			−0.0549710	+	0.998488i	$0.517507\pi$
$548$	−21.1472			−0.903363
$549$	−0.265575	−	0.143341i	−0.0113345	−	0.00611763i
$550$	28.4236			1.21199
$551$	5.49916	−	3.17494i	0.234272	−	0.135257i
$552$	14.5236	−	0.208205i	0.618164	−	0.00886178i
$553$	−10.0292	−	13.4952i	−0.426483	−	0.573874i
$554$	11.7622			0.499730
$555$	1.95685	−	1.16750i	0.0830635	−	0.0495577i
$556$	−9.34314	+	5.39426i	−0.396237	+	0.228768i
$557$	7.56444	+	13.1020i	0.320515	+	0.555149i	0.980594	−	0.196047i	$-0.0628106\pi$
$557$	7.56444	+	13.1020i	0.320515	+	0.555149i	−0.660079	+	0.751196i	$0.729477\pi$
$558$	3.96028	−	7.33742i	0.167652	−	0.310618i
$559$	−20.9561	−	0.446305i	−0.886347	−	0.0188767i
$560$	−1.25333	+	0.931429i	−0.0529628	+	0.0393600i
$561$	69.4998	−	41.4652i	2.93428	−	1.75066i
$562$	21.9950			0.927805
$563$	5.82808			0.245624			0.122812	−	0.992430i	$-0.460809\pi$
$563$	5.82808			0.245624			0.122812	+	0.992430i	$0.460809\pi$
$564$	−5.06782	−	8.49415i	−0.213394	−	0.357668i
$565$	4.61357	−	7.99094i	0.194095	−	0.336182i
$566$	11.1271	−	6.42423i	0.467706	−	0.270030i
$567$	23.4569	−	4.09544i	0.985098	−	0.171992i
$568$	−0.875991	−	1.51726i	−0.0367558	−	0.0636628i
$569$			23.1239i			0.969405i	0.874679	+	0.484703i	$0.161072\pi$
$569$			23.1239i			0.969405i	−0.874679	+	0.484703i	$0.838928\pi$
$570$	4.03859	−	0.0578958i	0.169158	−	0.00242499i
$571$	−17.1315	+	29.6727i	−0.716933	+	1.24176i	0.245277	+	0.969453i	$0.421121\pi$
$571$	−17.1315	+	29.6727i	−0.716933	+	1.24176i	−0.962209	+	0.272311i	$0.912212\pi$
$572$	22.0264	+	0.469101i	0.920971	+	0.0196141i
$573$	−9.16983	+	16.4218i	−0.383075	+	0.686032i
$574$	−3.82534	−	1.65392i	−0.159667	−	0.0690331i
$575$	33.7828	+	19.5045i	1.40884	+	0.813394i
$576$	−2.99877	+	0.0859963i	−0.124949	+	0.00358318i
$577$	−7.81628	+	13.5382i	−0.325396	+	0.563602i	−0.981592	−	0.190988i	$-0.938831\pi$
$577$	−7.81628	+	13.5382i	−0.325396	+	0.563602i	0.656196	+	0.754590i	$0.272164\pi$
$578$	−41.4723			−1.72502
$579$	−17.0779	−	28.6242i	−0.709732	−	1.18958i
$580$	0.948544			0.0393861
$581$	2.76717	+	23.8489i	0.114802	+	0.989417i
$582$	8.40636	−	5.01544i	0.348455	−	0.207897i
$583$		−	23.3142i		−	0.965576i
$584$	5.41081	−	9.37179i	0.223901	−	0.387807i
$585$	−0.0470845	−	6.38387i	−0.00194670	−	0.263940i
$586$	−0.344829	+	0.199087i	−0.0142448	+	0.00822421i
$587$	25.9699	+	14.9937i	1.07189	+	0.618856i	0.928697	−	0.370838i	$-0.120930\pi$
$587$	25.9699	+	14.9937i	1.07189	+	0.618856i	0.143193	+	0.989695i	$0.454263\pi$
$588$	−2.94508	−	11.7612i	−0.121453	−	0.485025i
$589$	5.49059	+	9.50998i	0.226236	+	0.391852i
$590$	−1.32273	−	2.29104i	−0.0544560	−	0.0943205i
$591$	12.0166	+	6.71000i	0.494298	+	0.276013i
$592$		−	2.22904i		−	0.0916128i
$593$	−12.0409	+	6.95181i	−0.494460	+	0.285477i	−0.726423	−	0.687248i	$-0.758819\pi$
$593$	−12.0409	+	6.95181i	−0.494460	+	0.285477i	0.231963	+	0.972725i	$0.425485\pi$
$594$	26.7890	−	17.0428i	1.09916	−	0.699273i
$595$	−9.58385	+	7.12237i	−0.392900	+	0.291989i
$596$	−4.01109	+	6.94741i	−0.164301	+	0.284577i
$597$	−32.5907	+	0.467210i	−1.33385	+	0.0191216i
$598$	25.8576	+	15.6723i	1.05739	+	0.640887i
$599$	5.85303	+	3.37925i	0.239148	+	0.138072i	0.614785	−	0.788695i	$-0.289243\pi$
$599$	5.85303	+	3.37925i	0.239148	+	0.138072i	−0.375637	+	0.926767i	$0.622576\pi$
$600$	−7.03452	−	3.92802i	−0.287183	−	0.160361i
$601$	11.3845	+	6.57283i	0.464382	+	0.268111i	0.713885	−	0.700263i	$-0.246934\pi$
$601$	11.3845	+	6.57283i	0.464382	+	0.268111i	−0.249503	+	0.968374i	$0.580267\pi$
$602$	9.17452	+	12.3452i	0.373925	+	0.503153i
$603$	−26.4236	+	16.2831i	−1.07605	+	0.663097i
$604$	−7.60834	−	4.39268i	−0.309579	−	0.178736i
$605$		−	15.5443i		−	0.631967i
$606$	−17.5838	+	10.4909i	−0.714291	+	0.426163i
$607$	−26.4291	−	15.2588i	−1.07272	−	0.619337i	−0.143799	−	0.989607i	$-0.545932\pi$
$607$	−26.4291	−	15.2588i	−1.07272	−	0.619337i	−0.928924	+	0.370270i	$0.879265\pi$
$608$	1.97552	−	3.42169i	0.0801178	−	0.138768i
$609$	−2.82557	+	6.80127i	−0.114498	+	0.275601i
$610$	0.0593724			0.00240392
$611$	0.438408	−	20.5853i	0.0177361	−	0.832790i
$612$	−22.9307	+	0.657590i	−0.926920	+	0.0265815i
$613$	3.14710	−	1.81698i	0.127110	−	0.0733872i	−0.435097	−	0.900384i	$-0.643286\pi$
$613$	3.14710	−	1.81698i	0.127110	−	0.0733872i	0.562207	+	0.826997i	$0.309952\pi$
$614$	−10.2738			−0.414616
$615$	0.0230819	+	1.61010i	0.000930751	+	0.0649255i
$616$	−9.64312	−	12.9758i	−0.388533	−	0.522809i
$617$	17.7255	+	30.7015i	0.713603	+	1.23600i	0.963496	+	0.267723i	$0.0862712\pi$
$617$	17.7255	+	30.7015i	0.713603	+	1.23600i	−0.249893	+	0.968273i	$0.580395\pi$
$618$	−3.85920	−	6.46839i	−0.155240	−	0.260197i
$619$	21.7709	−	37.7083i	0.875046	−	1.51562i	0.0183329	−	0.999832i	$-0.494164\pi$
$619$	21.7709	−	37.7083i	0.875046	−	1.51562i	0.856713	−	0.515793i	$-0.172503\pi$
$620$			1.64037i			0.0658788i
$621$	43.5349	−	1.87333i	1.74699	−	0.0751741i
$622$	−1.05163	+	1.82148i	−0.0421666	+	0.0730347i
$623$	−1.25585	−	10.8235i	−0.0503144	−	0.433635i
$624$	−5.38647	−	3.16006i	−0.215631	−	0.126504i
$625$	−9.94811	−	17.2306i	−0.397924	−	0.689225i
$626$	9.44084	−	5.45067i	0.377332	−	0.217853i
$627$	0.599398	+	41.8117i	0.0239376	+	1.66980i
$628$	2.49489	+	1.44042i	0.0995568	+	0.0574791i
$629$		−	17.0448i		−	0.679621i
$630$	−3.67834	+	2.90092i	−0.146549	+	0.115575i
$631$	−21.1471	+	12.2093i	−0.841854	+	0.486045i	−0.857894	−	0.513827i	$-0.828227\pi$
$631$	−21.1471	+	12.2093i	−0.841854	+	0.486045i	0.0160399	+	0.999871i	$0.494894\pi$
$632$	3.17751	+	5.50361i	0.126395	+	0.218922i
$633$	−3.88232	−	2.16786i	−0.154308	−	0.0861646i
$634$	5.27267	+	9.13253i	0.209404	+	0.362699i
$635$			3.53018i			0.140091i
$636$	−3.22193	+	5.77000i	−0.127758	+	0.228795i
$637$	7.79222	−	24.0059i	0.308739	−	0.951147i
$638$			9.82032i			0.388790i
$639$	−2.75737	−	4.47458i	−0.109080	−	0.177012i
$640$	0.511132	−	0.295102i	0.0202043	−	0.0116649i
$641$			19.2703i			0.761132i	0.924754	+	0.380566i	$0.124271\pi$
$641$			19.2703i			0.761132i	−0.924754	+	0.380566i	$0.875729\pi$
$642$	−15.3109	+	0.219491i	−0.604271	+	0.00866263i
$643$	15.0498	+	26.0670i	0.593505	+	1.02798i	0.993756	+	0.111575i	$0.0355895\pi$
$643$	15.0498	+	26.0670i	0.593505	+	1.02798i	−0.400251	+	0.916405i	$0.631077\pi$
$644$	−2.55723	−	22.0395i	−0.100769	−	0.868478i
$645$	2.89738	−	5.18878i	0.114084	−	0.204308i
$646$	15.1062	−	26.1647i	0.594346	−	1.02944i
$647$	14.3354	+	24.8296i	0.563582	+	0.976153i	0.997180	+	0.0750466i	$0.0239105\pi$
$647$	14.3354	+	24.8296i	0.563582	+	0.976153i	−0.433598	+	0.901107i	$0.642756\pi$
$648$	−8.98521	+	0.515766i	−0.352972	+	0.0202612i
$649$	23.7192	−	13.6943i	0.931061	−	0.537548i
$650$	−8.07473	−	14.7001i	−0.316717	−	0.576584i
$651$	−11.7618	−	4.88640i	−0.460982	−	0.191513i
$652$	−4.65862	−	2.68966i	−0.182446	−	0.105335i
$653$		−	27.6088i		−	1.08041i	−0.841532	−	0.540207i	$-0.818346\pi$
$653$		−	27.6088i		−	1.08041i	0.841532	−	0.540207i	$-0.181654\pi$
$654$	−14.5236	+	26.0096i	−0.567916	+	1.01705i
$655$	2.86087	+	1.65172i	0.111783	+	0.0645381i
$656$	1.36416	+	0.787598i	0.0532615	+	0.0307505i
$657$	15.4198	−	28.5691i	0.601584	−	1.11459i
$658$	−12.1268	+	9.01218i	−0.472751	+	0.351331i
$659$	−28.9405	+	16.7088i	−1.12736	+	0.650884i	−0.943270	−	0.332025i	$-0.892268\pi$
$659$	−28.9405	+	16.7088i	−1.12736	+	0.650884i	−0.184093	+	0.982909i	$0.558935\pi$
$660$	−3.04537	+	5.45381i	−0.118541	+	0.212289i
$661$	5.20701	+	9.01881i	0.202529	+	0.350791i	0.949343	−	0.314243i	$-0.101751\pi$
$661$	5.20701	+	9.01881i	0.202529	+	0.350791i	−0.746813	+	0.665034i	$0.768417\pi$
$662$	12.6163	+	7.28403i	0.490347	+	0.283102i
$663$	−41.1888	−	24.1641i	−1.59964	−	0.938456i
$664$		−	9.07449i		−	0.352159i
$665$	−0.711093	−	6.12856i	−0.0275750	−	0.237655i
$666$	−0.191689	−	6.68436i	−0.00742779	−	0.259014i
$667$	−6.73879	+	11.6719i	−0.260927	+	0.451939i
$668$	14.1115	+	8.14728i	0.545990	+	0.315228i
$669$	−5.41157	−	3.02179i	−0.209224	−	0.116829i
$670$	3.05311	−	5.28815i	0.117952	−	0.204299i
$671$			0.614686i			0.0237297i
$672$	0.593366	+	4.54400i	0.0228896	+	0.175289i
$673$	−0.105584	+	0.182877i	−0.00406998	+	0.00704941i	−0.868053	−	0.496471i	$-0.834629\pi$
$673$	−0.105584	+	0.182877i	−0.00406998	+	0.00704941i	0.863983	+	0.503521i	$0.167962\pi$
$674$	31.0830			1.19727
$675$	−21.4327	−	11.1743i	−0.824944	−	0.430098i
$676$	−6.01478	−	11.5249i	−0.231338	−	0.443264i
$677$	−11.7820	−	20.4071i	−0.452820	−	0.784307i	0.545740	−	0.837955i	$-0.316249\pi$
$677$	−11.7820	−	20.4071i	−0.452820	−	0.784307i	−0.998560	+	0.0536474i	$0.982915\pi$
$678$	−13.8740	−	23.2542i	−0.532829	−	0.893073i
$679$	−8.91903	−	12.0014i	−0.342281	−	0.460573i
$680$	3.90849	−	2.25657i	0.149884	−	0.0865353i
$681$	−20.7373	+	0.297282i	−0.794654	+	0.0113919i
$682$	−16.9828			−0.650305
$683$	−1.38840			−0.0531255			−0.0265627	−	0.999647i	$-0.508456\pi$
$683$	−1.38840			−0.0531255			−0.0265627	+	0.999647i	$0.508456\pi$
$684$	5.62986	−	10.4308i	0.215263	−	0.398830i
$685$	10.8090	−	6.24059i	0.412991	−	0.238441i
$686$	−17.4193	+	6.29030i	−0.665072	+	0.240165i
$687$	16.5851	−	9.89509i	0.632763	−	0.377521i
$688$	−2.90674	−	5.03462i	−0.110818	−	0.191943i
$689$	−12.0576	+	6.62323i	−0.459358	+	0.252325i
$690$	−7.36202	+	4.39236i	−0.280267	+	0.167214i
$691$	26.2488			0.998552			0.499276	−	0.866443i	$-0.333599\pi$
$691$	26.2488			0.998552			0.499276	+	0.866443i	$0.333599\pi$
$692$	−7.20003	+	12.4708i	−0.273704	+	0.474069i
$693$	−30.0334	−	38.0820i	−1.14087	−	1.44662i
$694$			24.6678i			0.936378i
$695$	3.18372	−	5.51436i	0.120765	−	0.209172i
$696$	1.35713	−	2.43042i	0.0514418	−	0.0921248i
$697$	10.4313	+	6.02254i	0.395115	+	0.228120i
$698$	16.5800	−	28.7175i	0.627564	−	1.08697i
$699$	−14.1776	−	23.7631i	−0.536247	−	0.898802i
$700$	−4.88412	+	11.2965i	−0.184603	+	0.426967i
$701$		−	35.5148i		−	1.34137i	−0.741740	−	0.670687i	$-0.765999\pi$
$701$		−	35.5148i		−	1.34137i	0.741740	−	0.670687i	$-0.234001\pi$
$702$	−16.4245	−	9.01307i	−0.619903	−	0.340176i
$703$	7.62708	+	4.40350i	0.287661	+	0.166081i
$704$	3.05521	+	5.29178i	0.115148	+	0.199441i
$705$	5.09697	+	2.84611i	0.191963	+	0.107191i
$706$	12.5305	−	7.23450i	0.471593	−	0.272274i
$707$	18.6561	+	25.1036i	0.701636	+	0.944120i
$708$	−7.76274	+	0.111284i	−0.291742	+	0.00418231i
$709$	18.7918	+	10.8494i	0.705739	+	0.407459i	0.809482	−	0.587145i	$-0.199748\pi$
$709$	18.7918	+	10.8494i	0.705739	+	0.407459i	−0.103742	+	0.994604i	$0.533082\pi$
$710$	0.895494	+	0.517014i	0.0336073	+	0.0194032i
$711$	10.0019	+	16.2308i	0.375101	+	0.608703i
$712$			4.11835i			0.154342i
$713$	−20.1849	−	11.6537i	−0.755930	−	0.436436i
$714$	4.53730	+	34.7467i	0.169804	+	1.30036i
$715$	−11.3969	+	6.26028i	−0.426218	+	0.234121i
$716$	−9.93300	+	5.73482i	−0.371214	+	0.214320i
$717$	−0.439122	−	30.6314i	−0.0163993	−	1.14395i
$718$	7.00098	+	12.1261i	0.261274	+	0.452541i
$719$	14.7420	−	25.5339i	0.549785	−	0.952255i	−0.448504	−	0.893781i	$-0.648043\pi$
$719$	14.7420	−	25.5339i	0.549785	−	0.952255i	0.998289	−	0.0584744i	$-0.0186236\pi$
$720$	1.50739	−	0.928899i	0.0561771	−	0.0346180i
$721$	−9.23467	+	6.86288i	−0.343917	+	0.255587i
$722$	−1.69467	−	2.93526i	−0.0630691	−	0.109239i
$723$	−0.600010	−	41.8544i	−0.0223146	−	1.55658i
$724$			14.7039i			0.546465i
$725$	6.47431	−	3.73794i	0.240450	−	0.138824i
$726$	−39.8287	−	22.2401i	−1.47818	−	0.825406i
$727$			7.96128i			0.295268i	0.989042	+	0.147634i	$0.0471657\pi$
$727$			7.96128i			0.295268i	−0.989042	+	0.147634i	$0.952834\pi$
$728$	−3.97132	+	8.67345i	−0.147187	+	0.321459i
$729$	−26.9002	+	2.31936i	−0.996304	+	0.0859021i
$730$			6.38697i			0.236392i
$731$	−22.2270	−	38.4984i	−0.822097	−	1.42391i
$732$	0.0849471	−	0.152128i	0.00313973	−	0.00562280i
$733$	−23.6265	−	40.9223i	−0.872665	−	1.51150i	−0.859230	−	0.511590i	$-0.829057\pi$
$733$	−23.6265	−	40.9223i	−0.872665	−	1.51150i	−0.0134348	−	0.999910i	$-0.504277\pi$
$734$	12.7593	−	7.36659i	0.470954	−	0.271906i
$735$	4.97609	+	5.14244i	0.183546	+	0.189682i
$736$			8.38604i			0.309114i
$737$	54.7484	+	31.6090i	2.01668	+	1.16433i
$738$	4.15853	+	2.24451i	0.153077	+	0.0826215i
$739$	18.9360	−	10.9327i	0.696572	−	0.402166i	−0.109498	−	0.993987i	$-0.534924\pi$
$739$	18.9360	−	10.9327i	0.696572	−	0.402166i	0.806069	+	0.591821i	$0.201591\pi$
$740$	0.657794	+	1.13933i	0.0241810	+	0.0418827i
$741$	21.4538	−	12.1881i	0.788126	−	0.447741i
$742$	9.26586	+	4.00616i	0.340160	+	0.147071i
$743$	−5.23639	+	9.06969i	−0.192104	+	0.332735i	−0.945947	−	0.324320i	$-0.894865\pi$
$743$	−5.23639	+	9.06969i	−0.192104	+	0.332735i	0.753843	+	0.657055i	$0.228198\pi$
$744$	4.20305	+	2.34696i	0.154091	+	0.0860436i
$745$		−	4.73473i		−	0.173467i
$746$	7.91499	−	13.7092i	0.289788	−	0.501928i
$747$	−0.780373	−	27.2123i	−0.0285523	−	0.995646i
$748$	23.3623	+	40.4647i	0.854211	+	1.47954i
$749$	2.69586	+	23.2342i	0.0985045	+	0.848961i
$750$	9.86553	−	0.141429i	0.360238	−	0.00516426i
$751$	34.6538			1.26454			0.632268	−	0.774750i	$-0.282124\pi$
$751$	34.6538			1.26454			0.632268	+	0.774750i	$0.282124\pi$
$752$	4.94554	−	2.85531i	0.180345	−	0.104122i
$753$	4.77111	−	2.84656i	0.173869	−	0.103734i
$754$	5.07886	−	2.78981i	0.184961	−	0.101599i
$755$	5.18516			0.188707
$756$	2.17013	+	13.5754i	0.0789270	+	0.493731i
$757$	−12.1846	+	21.1043i	−0.442856	+	0.767050i	−0.997900	−	0.0647715i	$-0.979368\pi$
$757$	−12.1846	+	21.1043i	−0.442856	+	0.767050i	0.555044	+	0.831821i	$0.312701\pi$
$758$	11.2444	+	6.49193i	0.408414	+	0.235798i
$759$	−45.4743	−	76.2193i	−1.65061	−	2.76659i
$760$			2.33192i			0.0845876i
$761$	5.80180	+	3.34967i	0.210315	+	0.121426i	0.601458	−	0.798905i	$-0.294587\pi$
$761$	5.80180	+	3.34967i	0.210315	+	0.121426i	−0.391143	+	0.920330i	$0.627920\pi$
$762$	9.04525	+	5.05081i	0.327675	+	0.182971i
$763$	41.7679	+	18.0587i	1.51210	+	0.653768i
$764$	−9.40428	−	5.42957i	−0.340235	−	0.196435i
$765$	11.5266	−	7.10303i	0.416744	−	0.256811i
$766$	3.62494	+	2.09286i	0.130975	+	0.0756182i
$767$	−13.8207	−	8.37672i	−0.499036	−	0.302466i
$768$	−0.0248275	−	1.73187i	−0.000895887	−	0.0624936i
$769$	−3.97005	+	6.87633i	−0.143164	+	0.247967i	−0.928686	−	0.370866i	$-0.879061\pi$
$769$	−3.97005	+	6.87633i	−0.143164	+	0.247967i	0.785523	+	0.618833i	$0.212394\pi$
$770$	8.75809	+	3.78663i	0.315620	+	0.136461i
$771$	−0.0293791	−	2.04937i	−0.00105806	−	0.0738062i
$772$	16.6658	−	9.62200i	0.599815	−	0.346304i
$773$			14.9695i			0.538417i	0.963082	+	0.269208i	$0.0867621\pi$
$773$			14.9695i			0.538417i	−0.963082	+	0.269208i	$0.913238\pi$
$774$	−9.14960	−	14.8477i	−0.328876	−	0.533689i
$775$	6.46422	+	11.1964i	0.232202	+	0.402185i
$776$	2.82580	+	4.89442i	0.101440	+	0.175700i
$777$	−10.1287	+	1.32263i	−0.363366	+	0.0474492i
$778$	19.0201	+	10.9812i	0.681903	+	0.393697i
$779$	−5.38984	+	3.11182i	−0.193111	+	0.111493i
$780$	3.68574	+	0.0256505i	0.131971	+	0.000918434i
$781$	−5.35267	+	9.27110i	−0.191534	+	0.331746i
$782$			64.1257i			2.29313i
$783$	3.86071	−	7.40497i	0.137970	−	0.264632i
$784$	6.81402	−	1.60283i	0.243358	−	0.0572441i
$785$	−1.70029			−0.0606859
$786$	8.32533	−	4.96709i	0.296955	−	0.177170i
$787$	−17.6111			−0.627769			−0.313884	−	0.949461i	$-0.601630\pi$
$787$	−17.6111			−0.627769			−0.313884	+	0.949461i	$0.601630\pi$
$788$	−3.97307	+	6.88156i	−0.141535	+	0.245145i
$789$	1.19105	+	1.99632i	0.0424025	+	0.0710708i
$790$	−3.24826	−	1.87538i	−0.115568	−	0.0667231i
$791$	−33.1992	+	24.6724i	−1.18043	+	0.877250i
$792$	9.61693	+	15.6061i	0.341723	+	0.554538i
$793$	0.317902	−	0.174623i	0.0112890	−	0.00620106i
$794$	16.5607	−	28.6839i	0.587716	−	1.01795i
$795$	−0.0559096	−	3.90003i	−0.00198291	−	0.138320i
$796$		−	18.8182i		−	0.666993i
$797$	−0.00976904	−	0.0169205i	−0.000346037	−	0.000599354i	0.865852	−	0.500300i	$-0.166777\pi$
$797$	−0.00976904	−	0.0169205i	−0.000346037	−	0.000599354i	−0.866198	+	0.499700i	$0.833443\pi$
$798$	−16.7204	−	6.94642i	−0.591895	−	0.245901i
$799$	37.8172	−	21.8337i	1.33787	−	0.772422i
$800$	2.32583	−	4.02845i	0.0822305	−	0.142427i
$801$	0.354163	+	12.3500i	0.0125137	+	0.436365i
$802$	6.94374			0.245192
$803$	−66.1246			−2.33349
$804$	−9.18138	−	15.3889i	−0.323802	−	0.542724i
$805$	7.81100	+	10.5105i	0.275301	+	0.370445i
$806$	4.82457	+	8.78314i	0.169938	+	0.309373i
$807$	0.160533	+	11.1981i	0.00565102	+	0.394193i
$808$	−5.91078	−	10.2378i	−0.207940	−	0.360163i
$809$	−5.64352	+	3.25829i	−0.198416	+	0.114555i	−0.595916	−	0.803047i	$-0.703211\pi$
$809$	−5.64352	+	3.25829i	−0.198416	+	0.114555i	0.397501	+	0.917602i	$0.369878\pi$
$810$	4.44043	−	2.91518i	0.156021	−	0.102429i
$811$	7.01415			0.246300			0.123150	−	0.992388i	$-0.460700\pi$
$811$	7.01415			0.246300			0.123150	+	0.992388i	$0.460700\pi$
$812$	−3.90293	−	1.68746i	−0.136966	−	0.0592182i
$813$	0.477580	+	33.3141i	0.0167495	+	1.16838i
$814$	−11.7956	+	6.81017i	−0.413434	+	0.238696i
$815$	3.17490			0.111212
$816$	−0.189849	−	13.2431i	−0.00664606	−	0.463603i
$817$	22.9693			0.803592
$818$	0.303545			0.0106132
$819$	−11.1632	+	26.3512i	−0.390073	+	0.920784i
$820$	−0.929688			−0.0324661
$821$	12.6481			0.441420			0.220710	−	0.975339i	$-0.429163\pi$
$821$	12.6481			0.441420			0.220710	+	0.975339i	$0.429163\pi$
$822$	−0.525033	−	36.6243i	−0.0183126	−	1.27742i
$823$	−43.5737			−1.51888			−0.759441	−	0.650576i	$-0.774528\pi$
$823$	−43.5737			−1.51888			−0.759441	+	0.650576i	$0.774528\pi$
$824$	3.76608	−	2.17435i	0.131198	−	0.0757471i
$825$	0.705688	+	49.2260i	0.0245689	+	1.71383i
$826$	1.36682	+	11.7800i	0.0475579	+	0.409877i
$827$	−25.1546			−0.874712			−0.437356	−	0.899288i	$-0.644085\pi$
$827$	−25.1546			−0.874712			−0.437356	+	0.899288i	$0.644085\pi$
$828$	0.721168	+	25.1478i	0.0250623	+	0.873946i
$829$	42.1390	−	24.3289i	1.46355	−	0.844979i	0.464374	−	0.885639i	$-0.346280\pi$
$829$	42.1390	−	24.3289i	1.46355	−	0.844979i	0.999173	+	0.0406604i	$0.0129462\pi$
$830$	2.67790	+	4.63827i	0.0929514	+	0.160997i
$831$	0.292028	+	20.3707i	0.0101303	+	0.706652i
$832$	1.86885	−	3.08341i	0.0647908	−	0.106898i
$833$	52.1049	−	12.2564i	1.80533	−	0.424660i
$834$	−9.57415	−	16.0472i	−0.331526	−	0.555669i
$835$	−9.61713			−0.332814
$836$	−24.1425			−0.834984
$837$	12.8058	+	6.67653i	0.442634	+	0.230775i
$838$	−2.85725	+	4.94891i	−0.0987022	+	0.170957i
$839$	−18.3244	+	10.5796i	−0.632630	+	0.365249i	−0.781770	−	0.623567i	$-0.785683\pi$
$839$	−18.3244	+	10.5796i	−0.632630	+	0.365249i	0.149140	+	0.988816i	$0.452350\pi$
$840$	−1.64423	−	2.14748i	−0.0567314	−	0.0740951i
$841$	−13.2085	−	22.8779i	−0.455467	−	0.788892i
$842$		−	9.25537i		−	0.318961i
$843$	0.546083	+	38.0926i	0.0188081	+	1.31198i
$844$	1.28361	−	2.22329i	0.0441838	−	0.0765286i
$845$	6.47536	+	4.11575i	0.222759	+	0.141586i
$846$	14.5850	−	8.98770i	0.501442	−	0.309004i
$847$	−27.6534	+	63.9596i	−0.950182	+	2.19768i
$848$	−3.30431	−	1.90774i	−0.113470	−	0.0655121i
$849$	11.4022	+	19.1112i	0.391323	+	0.655895i
$850$	17.7850	−	30.8045i	0.610019	−	1.05658i
$851$	−18.6928			−0.640780
$852$	2.60595	−	1.55477i	0.0892785	−	0.0532657i
$853$	53.6426			1.83669			0.918344	−	0.395782i	$-0.129527\pi$
$853$	53.6426			1.83669			0.918344	+	0.395782i	$0.129527\pi$
$854$	−0.244297	−	0.105624i	−0.00835967	−	0.00361436i
$855$	0.200536	+	6.99288i	0.00685820	+	0.239151i
$856$		−	8.84064i		−	0.302167i
$857$	12.3135	−	21.3277i	0.420623	−	0.728540i	−0.575378	−	0.817888i	$-0.695145\pi$
$857$	12.3135	−	21.3277i	0.420623	−	0.728540i	0.996000	+	0.0893479i	$0.0284783\pi$
$858$	−0.265561	+	38.1586i	−0.00906609	+	1.30271i
$859$	1.35293	−	0.781117i	0.0461615	−	0.0266514i	−0.476742	−	0.879043i	$-0.658182\pi$
$859$	1.35293	−	0.781117i	0.0461615	−	0.0266514i	0.522903	+	0.852392i	$0.324849\pi$
$860$	2.97146	+	1.71557i	0.101326	+	0.0585005i
$861$	2.76940	−	6.66607i	0.0943808	−	0.227179i
$862$	5.05283	+	8.75176i	0.172100	+	0.298086i
$863$	−13.1821	−	22.8320i	−0.448723	−	0.777210i	0.549581	−	0.835441i	$-0.314788\pi$
$863$	−13.1821	−	22.8320i	−0.448723	−	0.777210i	−0.998303	+	0.0582303i	$0.981454\pi$
$864$	−0.223387	−	5.19135i	−0.00759977	−	0.176613i
$865$		−	8.49898i		−	0.288974i
$866$	−32.8655	+	18.9749i	−1.11682	+	0.644794i
$867$	−1.02966	−	71.8248i	−0.0349690	−	2.43930i
$868$	2.91822	−	6.74955i	0.0990507	−	0.229094i
$869$	19.4159	−	33.6294i	0.658640	−	1.14080i
$870$	0.0235500	+	1.64276i	0.000798420	+	0.0556947i
$871$	0.794265	−	37.2944i	0.0269126	−	1.26367i
$872$	−14.8949	−	8.59957i	−0.504405	−	0.291218i
$873$	8.89481	+	14.4342i	0.301044	+	0.488525i
$874$	−28.6945	−	16.5668i	−0.970605	−	0.560379i
$875$	−1.73707	−	14.9710i	−0.0587238	−	0.506111i
$876$	16.3651	+	9.13815i	0.552925	+	0.308749i
$877$	−20.1923	−	11.6580i	−0.681846	−	0.393664i	0.118704	−	0.992930i	$-0.462126\pi$
$877$	−20.1923	−	11.6580i	−0.681846	−	0.393664i	−0.800550	+	0.599265i	$0.795459\pi$
$878$			28.4483i			0.960083i
$879$	−0.353355	−	0.592257i	−0.0119184	−	0.0199763i
$880$	−3.12323	−	1.80320i	−0.105284	−	0.0607858i
$881$	7.67467	−	13.2929i	0.258566	−	0.447850i	−0.707292	−	0.706922i	$-0.750083\pi$
$881$	7.67467	−	13.2929i	0.258566	−	0.447850i	0.965858	+	0.259072i	$0.0834167\pi$
$882$	20.2958	−	5.39251i	0.683396	−	0.181575i
$883$	34.2457			1.15246			0.576230	−	0.817287i	$-0.304523\pi$
$883$	34.2457			1.15246			0.576230	+	0.817287i	$0.304523\pi$
$884$	14.2906	−	23.5779i	0.480645	−	0.793012i
$885$	3.93495	−	2.34768i	0.132272	−	0.0789165i
$886$	−18.7651	+	10.8340i	−0.630425	+	0.363976i
$887$	43.6681			1.46623			0.733116	−	0.680104i	$-0.238065\pi$
$887$	43.6681			1.46623			0.733116	+	0.680104i	$0.238065\pi$
$888$	3.86041	−	0.0553415i	0.129547	−	0.00185714i
$889$	6.28019	−	14.5255i	0.210631	−	0.487169i
$890$	−1.21534	−	2.10502i	−0.0407381	−	0.0705605i
$891$	30.1810	+	45.9719i	1.01110	+	1.54012i
$892$	1.78923	−	3.09905i	0.0599080	−	0.103764i
$893$			22.5628i			0.755036i
$894$	−12.1316	−	6.77421i	−0.405742	−	0.226564i
$895$	3.38472	−	5.86250i	0.113139	−	0.195962i
$896$	−2.62812	+	0.304939i	−0.0877993	+	0.0101873i
$897$	−26.5004	+	45.1711i	−0.884822	+	1.50822i
$898$	6.23704	+	10.8029i	0.208133	+	0.360496i
$899$	−3.86833	+	2.23338i	−0.129016	+	0.0744875i
$900$	6.62819	−	12.2804i	0.220940	−	0.409347i
$901$	−25.2671	−	14.5880i	−0.841769	−	0.485996i
$902$		−	9.62510i		−	0.320481i
$903$	−21.1526	+	16.1956i	−0.703913	+	0.538956i
$904$	13.5393	−	7.81690i	0.450310	−	0.259986i
$905$	−4.33915	−	7.51563i	−0.144238	−	0.249828i
$906$	7.41867	−	13.2857i	0.246469	−	0.441389i
$907$	−11.6509	−	20.1799i	−0.386861	−	0.670063i	0.605164	−	0.796101i	$-0.293107\pi$
$907$	−11.6509	−	20.1799i	−0.386861	−	0.670063i	−0.992026	+	0.126037i	$0.959774\pi$
$908$		−	11.9739i		−	0.397368i
$909$	−18.6055	−	30.1924i	−0.617104	−	1.00142i
$910$	−0.529687	−	5.60522i	−0.0175589	−	0.185811i
$911$			48.4817i			1.60627i	0.595796	+	0.803136i	$0.296837\pi$
$911$			48.4817i			1.60627i	−0.595796	+	0.803136i	$0.703163\pi$
$912$	5.97499	+	3.33639i	0.197852	+	0.110479i
$913$	−48.0202	+	27.7245i	−1.58924	+	0.917546i
$914$		−	9.59213i		−	0.317280i
$915$	0.00147407	+	0.102825i	4.87313e−5	+	0.00339931i
$916$	5.57509	+	9.65634i	0.184206	+	0.319054i
$917$	−8.83306	−	11.8857i	−0.291693	−	0.392502i
$918$	−1.70818	−	39.6968i	−0.0563782	−	1.31019i
$919$	−1.25071	+	2.16629i	−0.0412570	+	0.0714593i	−0.885917	−	0.463845i	$-0.846470\pi$
$919$	−1.25071	+	2.16629i	−0.0412570	+	0.0714593i	0.844660	+	0.535304i	$0.179803\pi$
$920$	−2.47474	−	4.28638i	−0.0815898	−	0.141318i
$921$	−0.255073	−	17.7929i	−0.00840493	−	0.586296i
$922$	4.17780	−	2.41206i	0.137589	−	0.0794368i
$923$	6.31543	+	0.134501i	0.207875	+	0.00442715i
$924$	22.2330	−	17.0228i	0.731411	−	0.560010i
$925$	8.97957	+	5.18436i	0.295246	+	0.170461i
$926$		−	3.08747i		−	0.101460i
$927$	11.1066	−	6.84424i	0.364789	−	0.224794i
$928$	1.39183	+	0.803572i	0.0456890	+	0.0263785i
$929$	25.6324	+	14.7989i	0.840971	+	0.485535i	0.857594	−	0.514327i	$-0.171958\pi$
$929$	25.6324	+	14.7989i	0.840971	+	0.485535i	−0.0166234	+	0.999862i	$0.505292\pi$
$930$	−2.84091	+	0.0407263i	−0.0931571	+	0.00133547i
$931$	−7.97681	+	26.4819i	−0.261429	+	0.867910i
$932$	13.8355	−	7.98795i	0.453198	−	0.261654i
$933$	−3.18068	−	1.77607i	−0.104131	−	0.0581459i
$934$	−4.16237	−	7.20943i	−0.136197	−	0.235900i
$935$	−23.8825	−	13.7886i	−0.781041	−	0.450934i
$936$	5.33909	−	9.40713i	0.174514	−	0.307482i
$937$			27.0251i			0.882873i	0.897293	+	0.441436i	$0.145531\pi$
$937$			27.0251i			0.882873i	−0.897293	+	0.441436i	$0.854469\pi$
$938$	−21.9701	+	16.3274i	−0.717350	+	0.533108i
$939$	9.67426	+	16.2150i	0.315708	+	0.529157i
$940$	−1.68522	+	2.91888i	−0.0549657	+	0.0952034i
$941$	32.5113	+	18.7704i	1.05984	+	0.611898i	0.925387	−	0.379022i	$-0.123740\pi$
$941$	32.5113	+	18.7704i	1.05984	+	0.611898i	0.134451	+	0.990920i	$0.457073\pi$
$942$	−2.43269	+	4.35659i	−0.0792612	+	0.141945i
$943$	6.60483	−	11.4399i	0.215083	−	0.372534i
$944$		−	4.48228i		−	0.145886i
$945$	−5.11535	−	6.29840i	−0.166402	−	0.204887i
$946$	−17.7614	+	30.7636i	−0.577473	+	1.00021i
$947$	−31.4328			−1.02143			−0.510714	−	0.859750i	$-0.670619\pi$
$947$	−31.4328			−1.02143			−0.510714	+	0.859750i	$0.670619\pi$
$948$	−9.45267	+	5.63969i	−0.307008	+	0.183169i
$949$	18.7850	+	34.1982i	0.609788	+	1.11012i
$950$	9.18943	+	15.9166i	0.298144	+	0.516401i
$951$	−15.6855	+	9.35833i	−0.508636	+	0.303465i
$952$	−20.0965	+	2.33179i	−0.651331	+	0.0755736i
$953$	47.5409	−	27.4478i	1.54000	−	0.889120i	0.541163	−	0.840918i	$-0.317984\pi$
$953$	47.5409	−	27.4478i	1.54000	−	0.889120i	0.998838	−	0.0482023i	$-0.0153492\pi$
$954$	−10.0729	−	5.43672i	−0.326122	−	0.176020i
$955$	6.40911			0.207394
$956$	17.6869			0.572034
$957$	−17.0075	+	0.243814i	−0.549776	+	0.00788140i
$958$	10.4595	−	6.03880i	0.337931	−	0.195105i
$959$	−55.5774	+	6.44861i	−1.79469	+	0.208236i
$960$	0.523770	+	0.877889i	0.0169046	+	0.0283338i
$961$	11.6377	+	20.1571i	0.375409	+	0.650228i
$962$	6.87302	+	4.16574i	0.221595	+	0.134309i
$963$	−0.760262	−	26.5110i	−0.0244991	−	0.854305i
$964$	24.1671			0.778370
$965$	−5.67895	+	9.83623i	−0.182812	+	0.316640i
$966$	38.1061	−	4.97599i	1.22605	−	0.160100i
$967$			11.5256i			0.370639i	0.982678	+	0.185320i	$0.0593321\pi$
$967$			11.5256i			0.370639i	−0.982678	+	0.185320i	$0.940668\pi$
$968$	13.1686	−	22.8087i	0.423255	−	0.733099i
$969$	45.6891	+	25.5124i	1.46774	+	0.819578i
$970$	−2.88871	−	1.66780i	−0.0927509	−	0.0535498i
$971$	−24.9898	+	43.2836i	−0.801962	+	1.38904i	0.116362	+	0.993207i	$0.462877\pi$
$971$	−24.9898	+	43.2836i	−0.801962	+	1.38904i	−0.918323	+	0.395831i	$0.870456\pi$
$972$	−1.11632	−	15.5484i	−0.0358060	−	0.498716i
$973$	−22.9100	+	17.0259i	−0.734460	+	0.545824i
$974$			5.59837i			0.179383i
$975$	25.2582	−	14.3494i	0.808909	−	0.459548i
$976$	0.0871190	+	0.0502982i	0.00278861	+	0.00161000i
$977$	−2.18839	−	3.79041i	−0.0700129	−	0.121266i	0.828894	−	0.559406i	$-0.188971\pi$
$977$	−2.18839	−	3.79041i	−0.0700129	−	0.121266i	−0.898907	+	0.438140i	$0.855637\pi$
$978$	4.54248	−	8.13492i	0.145253	−	0.260126i
$979$	21.7934	−	12.5824i	0.696520	−	0.402136i
$980$	−3.00987	+	2.83009i	−0.0961467	+	0.0904041i
$981$	−45.4059	−	24.5072i	−1.44970	−	0.782455i
$982$	0.451495	+	0.260671i	0.0144078	+	0.00831833i
$983$	22.4448	+	12.9585i	0.715879	+	0.413313i	0.813234	−	0.581937i	$-0.197705\pi$
$983$	22.4448	+	12.9585i	0.715879	+	0.413313i	−0.0973553	+	0.995250i	$0.531038\pi$
$984$	−1.33015	+	2.38210i	−0.0424037	+	0.0759387i
$985$		−	4.68985i		−	0.149431i
$986$	10.6429	+	6.14469i	0.338940	+	0.195687i
$987$	−15.9090	−	20.7783i	−0.506390	−	0.661380i
$988$	6.85852	+	12.4860i	0.218199	+	0.397231i
$989$	−42.2205	+	24.3760i	−1.34254	+	0.775113i
$990$	−9.52091	−	5.13879i	−0.302594	−	0.163321i
$991$	−11.5787	−	20.0549i	−0.367810	−	0.637066i	0.621413	−	0.783483i	$-0.286559\pi$
$991$	−11.5787	−	20.0549i	−0.367810	−	0.637066i	−0.989223	+	0.146418i	$0.953226\pi$
$992$	−1.38966	+	2.40696i	−0.0441218	+	0.0764211i
$993$	−12.3018	+	22.0307i	−0.390385	+	0.699123i
$994$	−2.76488	−	3.72042i	−0.0876967	−	0.118005i
$995$	5.55329	+	9.61859i	0.176051	+	0.304930i
$996$	15.7159	−	0.225297i	0.497976	−	0.00713882i
$997$			9.63696i			0.305206i	0.988288	+	0.152603i	$0.0487655\pi$
$997$			9.63696i			0.305206i	−0.988288	+	0.152603i	$0.951234\pi$
$998$	28.9603	−	16.7202i	0.916722	−	0.529270i
$999$	11.5717	−	0.497937i	0.366112	−	0.0157540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.17.9	✓	34
3.2	odd	2		546.2.bi.f.17.14	yes	34
7.5	odd	6		546.2.bn.f.173.5	yes	34
13.10	even	6		546.2.bn.e.101.13	yes	34
21.5	even	6		546.2.bn.e.173.13	yes	34
39.23	odd	6		546.2.bn.f.101.5	yes	34
91.75	odd	6		546.2.bi.f.257.14	yes	34
273.257	even	6	inner	546.2.bi.e.257.9	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.9	✓	34	1.1	even	1	trivial
546.2.bi.e.257.9	yes	34	273.257	even	6	inner
546.2.bi.f.17.14	yes	34	3.2	odd	2
546.2.bi.f.257.14	yes	34	91.75	odd	6
546.2.bn.e.101.13	yes	34	13.10	even	6
546.2.bn.e.173.13	yes	34	21.5	even	6
546.2.bn.f.101.5	yes	34	39.23	odd	6
546.2.bn.f.173.5	yes	34	7.5	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.0248275 - 1.73187i) q^{3} +1.00000 q^{4} +(-0.511132 + 0.295102i) q^{5} +(0.0248275 + 1.73187i) q^{6} +(2.62812 - 0.304939i) q^{7} -1.00000 q^{8} +(-2.99877 + 0.0859963i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.0248275 - 1.73187i) q^{3} +1.00000 q^{4} +(-0.511132 + 0.295102i) q^{5} +(0.0248275 + 1.73187i) q^{6} +(2.62812 - 0.304939i) q^{7} -1.00000 q^{8} +(-2.99877 + 0.0859963i) q^{9} +(0.511132 - 0.295102i) q^{10} +(3.05521 + 5.29178i) q^{11} +(-0.0248275 - 1.73187i) q^{12} +(1.86885 - 3.08341i) q^{13} +(-2.62812 + 0.304939i) q^{14} +(0.523770 + 0.877889i) q^{15} +1.00000 q^{16} +7.64672 q^{17} +(2.99877 - 0.0859963i) q^{18} +(-1.97552 + 3.42169i) q^{19} +(-0.511132 + 0.295102i) q^{20} +(-0.593366 - 4.54400i) q^{21} +(-3.05521 - 5.29178i) q^{22} -8.38604i q^{23} +(0.0248275 + 1.73187i) q^{24} +(-2.32583 + 4.02845i) q^{25} +(-1.86885 + 3.08341i) q^{26} +(0.223387 + 5.19135i) q^{27} +(2.62812 - 0.304939i) q^{28} +(-1.39183 - 0.803572i) q^{29} +(-0.523770 - 0.877889i) q^{30} +(1.38966 - 2.40696i) q^{31} -1.00000 q^{32} +(9.08883 - 5.42261i) q^{33} -7.64672 q^{34} +(-1.25333 + 0.931429i) q^{35} +(-2.99877 + 0.0859963i) q^{36} -2.22904i q^{37} +(1.97552 - 3.42169i) q^{38} +(-5.38647 - 3.16006i) q^{39} +(0.511132 - 0.295102i) q^{40} +(1.36416 + 0.787598i) q^{41} +(0.593366 + 4.54400i) q^{42} +(-2.90674 - 5.03462i) q^{43} +(3.05521 + 5.29178i) q^{44} +(1.50739 - 0.928899i) q^{45} +8.38604i q^{46} +(4.94554 - 2.85531i) q^{47} +(-0.0248275 - 1.73187i) q^{48} +(6.81402 - 1.60283i) q^{49} +(2.32583 - 4.02845i) q^{50} +(-0.189849 - 13.2431i) q^{51} +(1.86885 - 3.08341i) q^{52} +(-3.30431 - 1.90774i) q^{53} +(-0.223387 - 5.19135i) q^{54} +(-3.12323 - 1.80320i) q^{55} +(-2.62812 + 0.304939i) q^{56} +(5.97499 + 3.33639i) q^{57} +(1.39183 + 0.803572i) q^{58} -4.48228i q^{59} +(0.523770 + 0.877889i) q^{60} +(0.0871190 + 0.0502982i) q^{61} +(-1.38966 + 2.40696i) q^{62} +(-7.85489 + 1.14045i) q^{63} +1.00000 q^{64} +(-0.0453104 + 2.12753i) q^{65} +(-9.08883 + 5.42261i) q^{66} +(8.95985 - 5.17297i) q^{67} +7.64672 q^{68} +(-14.5236 + 0.208205i) q^{69} +(1.25333 - 0.931429i) q^{70} +(0.875991 + 1.51726i) q^{71} +(2.99877 - 0.0859963i) q^{72} +(-5.41081 + 9.37179i) q^{73} +2.22904i q^{74} +(7.03452 + 3.92802i) q^{75} +(-1.97552 + 3.42169i) q^{76} +(9.64312 + 12.9758i) q^{77} +(5.38647 + 3.16006i) q^{78} +(-3.17751 - 5.50361i) q^{79} +(-0.511132 + 0.295102i) q^{80} +(8.98521 - 0.515766i) q^{81} +(-1.36416 - 0.787598i) q^{82} +9.07449i q^{83} +(-0.593366 - 4.54400i) q^{84} +(-3.90849 + 2.25657i) q^{85} +(2.90674 + 5.03462i) q^{86} +(-1.35713 + 2.43042i) q^{87} +(-3.05521 - 5.29178i) q^{88} -4.11835i q^{89} +(-1.50739 + 0.928899i) q^{90} +(3.97132 - 8.67345i) q^{91} -8.38604i q^{92} +(-4.20305 - 2.34696i) q^{93} +(-4.94554 + 2.85531i) q^{94} -2.33192i q^{95} +(0.0248275 + 1.73187i) q^{96} +(-2.82580 - 4.89442i) q^{97} +(-6.81402 + 1.60283i) q^{98} +(-9.61693 - 15.6061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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