LMFDB - Embedded newform 546.2.bi.f.257.14

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			257.14
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.48743 - 0.887438i) q^{3} +1.00000 q^{4} +(0.511132 + 0.295102i) q^{5} +(1.48743 - 0.887438i) q^{6} +(2.62812 + 0.304939i) q^{7} +1.00000 q^{8} +(1.42491 - 2.64001i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.48743 - 0.887438i) q^{3} +1.00000 q^{4} +(0.511132 + 0.295102i) q^{5} +(1.48743 - 0.887438i) q^{6} +(2.62812 + 0.304939i) q^{7} +1.00000 q^{8} +(1.42491 - 2.64001i) q^{9} +(0.511132 + 0.295102i) q^{10} +(-3.05521 + 5.29178i) q^{11} +(1.48743 - 0.887438i) q^{12} +(1.86885 + 3.08341i) q^{13} +(2.62812 + 0.304939i) q^{14} +(1.02216 - 0.0146533i) q^{15} +1.00000 q^{16} -7.64672 q^{17} +(1.42491 - 2.64001i) q^{18} +(-1.97552 - 3.42169i) q^{19} +(0.511132 + 0.295102i) q^{20} +(4.17976 - 1.87872i) q^{21} +(-3.05521 + 5.29178i) q^{22} -8.38604i q^{23} +(1.48743 - 0.887438i) 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} +(1.02216 - 0.0146533i) q^{30} +(1.38966 + 2.40696i) q^{31} +1.00000 q^{32} +(0.151707 + 10.5825i) q^{33} -7.64672 q^{34} +(1.25333 + 0.931429i) q^{35} +(1.42491 - 2.64001i) q^{36} +2.22904i q^{37} +(-1.97552 - 3.42169i) q^{38} +(5.51612 + 2.92787i) q^{39} +(0.511132 + 0.295102i) q^{40} +(-1.36416 + 0.787598i) q^{41} +(4.17976 - 1.87872i) 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} +(1.48743 - 0.887438i) q^{48} +(6.81402 + 1.60283i) q^{49} +(-2.32583 - 4.02845i) q^{50} +(-11.3740 + 6.78599i) 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} +(1.02216 - 0.0146533i) q^{60} +(0.0871190 - 0.0502982i) q^{61} +(1.38966 + 2.40696i) q^{62} +(4.54987 - 6.50374i) q^{63} +1.00000 q^{64} +(0.0453104 + 2.12753i) q^{65} +(0.151707 + 10.5825i) q^{66} +(8.95985 + 5.17297i) q^{67} -7.64672 q^{68} +(-7.44209 - 12.4737i) q^{69} +(1.25333 + 0.931429i) q^{70} +(-0.875991 + 1.51726i) q^{71} +(1.42491 - 2.64001i) 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} +(5.51612 + 2.92787i) q^{78} +(-3.17751 + 5.50361i) q^{79} +(0.511132 + 0.295102i) q^{80} +(-4.93927 - 7.52354i) q^{81} +(-1.36416 + 0.787598i) q^{82} +9.07449i q^{83} +(4.17976 - 1.87872i) 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} +(1.48743 - 0.887438i) 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} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 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} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * 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 + 6 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	1.48743	−	0.887438i	0.858769	−	0.512362i
$3$	1.48743	−	0.887438i	0.858769	−	0.512362i
$4$	1.00000			0.500000
$5$	0.511132	+	0.295102i	0.228585	+	0.131974i	0.609919	−	0.792464i	$-0.291202\pi$
$5$	0.511132	+	0.295102i	0.228585	+	0.131974i	−0.381334	+	0.924437i	$0.624535\pi$
$6$	1.48743	−	0.887438i	0.607242	−	0.362295i
$7$	2.62812	+	0.304939i	0.993336	+	0.115256i
$7$	2.62812	+	0.304939i	0.993336	+	0.115256i
$8$	1.00000			0.353553
$9$	1.42491	−	2.64001i	0.474970	−	0.880002i
$10$	0.511132	+	0.295102i	0.161634	+	0.0933196i
$11$	−3.05521	+	5.29178i	−0.921180	+	1.59553i	−0.123588	+	0.992334i	$0.539440\pi$
$11$	−3.05521	+	5.29178i	−0.921180	+	1.59553i	−0.797592	+	0.603197i	$0.793893\pi$
$12$	1.48743	−	0.887438i	0.429385	−	0.256181i
$13$	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
$15$	1.02216	−	0.0146533i	0.263920	−	0.00378347i
$16$	1.00000			0.250000
$17$	−7.64672			−1.85460			−0.927301	−	0.374316i	$-0.877877\pi$
$17$	−7.64672			−1.85460			−0.927301	+	0.374316i	$0.877877\pi$
$18$	1.42491	−	2.64001i	0.335854	−	0.622256i
$19$	−1.97552	−	3.42169i	−0.453214	−	0.784991i	0.545369	−	0.838196i	$-0.316390\pi$
$19$	−1.97552	−	3.42169i	−0.453214	−	0.784991i	−0.998584	+	0.0532055i	$0.983056\pi$
$20$	0.511132	+	0.295102i	0.114293	+	0.0659869i
$21$	4.17976	−	1.87872i	0.912099	−	0.409969i
$22$	−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	$-0.338682\pi$
$24$	1.48743	−	0.887438i	0.303621	−	0.181147i
$25$	−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	$-0.618991\pi$
$29$	1.39183	−	0.803572i	0.258456	−	0.149220i	0.623630	+	0.781720i	$0.285657\pi$
$30$	1.02216	−	0.0146533i	0.186620	−	0.00267532i
$31$	1.38966	+	2.40696i	0.249590	+	0.432303i	0.963412	−	0.268024i	$-0.0863707\pi$
$31$	1.38966	+	2.40696i	0.249590	+	0.432303i	−0.713822	+	0.700327i	$0.753037\pi$
$32$	1.00000			0.176777
$33$	0.151707	+	10.5825i	0.0264087	+	1.84217i
$34$	−7.64672			−1.31140
$35$	1.25333	+	0.931429i	0.211851	+	0.157440i
$36$	1.42491	−	2.64001i	0.237485	−	0.440001i
$37$			2.22904i			0.366451i	0.983071	+	0.183226i	$0.0586539\pi$
$37$			2.22904i			0.366451i	−0.983071	+	0.183226i	$0.941346\pi$
$38$	−1.97552	−	3.42169i	−0.320471	−	0.555072i
$39$	5.51612	+	2.92787i	0.883286	+	0.468834i
$40$	0.511132	+	0.295102i	0.0808171	+	0.0466598i
$41$	−1.36416	+	0.787598i	−0.213046	+	0.123002i	−0.602726	−	0.797948i	$-0.705919\pi$
$41$	−1.36416	+	0.787598i	−0.213046	+	0.123002i	0.389680	+	0.920950i	$0.372586\pi$
$42$	4.17976	−	1.87872i	0.644952	−	0.289892i
$43$	−2.90674	+	5.03462i	−0.443274	+	0.767773i	−0.997930	−	0.0643067i	$-0.979516\pi$
$43$	−2.90674	+	5.03462i	−0.443274	+	0.767773i	0.554656	+	0.832080i	$0.312850\pi$
$44$	−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	$-0.470073\pi$
$47$	−4.94554	−	2.85531i	−0.721381	−	0.416489i	−0.815261	+	0.579094i	$0.803406\pi$
$48$	1.48743	−	0.887438i	0.214692	−	0.128091i
$49$	6.81402	+	1.60283i	0.973432	+	0.228976i
$50$	−2.32583	−	4.02845i	−0.328922	−	0.569709i
$51$	−11.3740	+	6.78599i	−1.59268	+	0.950228i
$52$	1.86885	+	3.08341i	0.259163	+	0.427591i
$53$	3.30431	−	1.90774i	0.453881	−	0.262049i	−0.255587	−	0.966786i	$-0.582269\pi$
$53$	3.30431	−	1.90774i	0.453881	−	0.262049i	0.709468	+	0.704738i	$0.248935\pi$
$54$	−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	$-0.0942447\pi$
$60$	1.02216	−	0.0146533i	0.131960	−	0.00189174i
$61$	0.0871190	−	0.0502982i	0.0111544	−	0.00644002i	−0.494412	−	0.869227i	$-0.664617\pi$
$61$	0.0871190	−	0.0502982i	0.0111544	−	0.00644002i	0.505567	+	0.862787i	$0.331283\pi$
$62$	1.38966	+	2.40696i	0.176487	+	0.305684i
$63$	4.54987	−	6.50374i	0.573230	−	0.819395i
$64$	1.00000			0.125000
$65$	0.0453104	+	2.12753i	0.00562006	+	0.263888i
$66$	0.151707	+	10.5825i	0.0186738	+	1.30261i
$67$	8.95985	+	5.17297i	1.09462	+	0.631979i	0.934803	−	0.355168i	$-0.115576\pi$
$67$	8.95985	+	5.17297i	1.09462	+	0.631979i	0.159817	+	0.987147i	$0.448910\pi$
$68$	−7.64672			−0.927301
$69$	−7.44209	−	12.4737i	−0.895922	−	1.50165i
$70$	1.25333	+	0.931429i	0.149801	+	0.111327i
$71$	−0.875991	+	1.51726i	−0.103961	+	0.180066i	−0.913313	−	0.407258i	$-0.866485\pi$
$71$	−0.875991	+	1.51726i	−0.103961	+	0.180066i	0.809352	+	0.587324i	$0.199818\pi$
$72$	1.42491	−	2.64001i	0.167927	−	0.311128i
$73$	−5.41081	−	9.37179i	−0.633287	−	1.09689i	−0.986875	−	0.161484i	$-0.948372\pi$
$73$	−5.41081	−	9.37179i	−0.633287	−	1.09689i	0.353588	−	0.935401i	$-0.384961\pi$
$74$			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
$78$	5.51612	+	2.92787i	0.624578	+	0.331516i
$79$	−3.17751	+	5.50361i	−0.357498	+	0.619205i	−0.987542	−	0.157355i	$-0.949703\pi$
$79$	−3.17751	+	5.50361i	−0.357498	+	0.619205i	0.630044	+	0.776559i	$0.283037\pi$
$80$	0.511132	+	0.295102i	0.0571463	+	0.0329934i
$81$	−4.93927	−	7.52354i	−0.548808	−	0.835949i
$82$	−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	$0.834058\pi$
$84$	4.17976	−	1.87872i	0.456050	−	0.204985i
$85$	−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
$96$	1.48743	−	0.887438i	0.151810	−	0.0905737i
$97$	−2.82580	+	4.89442i	−0.286916	+	0.496953i	−0.973072	−	0.230501i	$-0.925963\pi$
$97$	−2.82580	+	4.89442i	−0.286916	+	0.496953i	0.686156	+	0.727455i	$0.259297\pi$
$98$	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	0.406331	+	0.913726i	$0.366808\pi$
$101$	−5.91078	+	10.2378i	−0.588144	+	1.01870i	−0.994475	+	0.104970i	$0.966525\pi$
$102$	−11.3740	+	6.78599i	−1.12619	+	0.671913i
$103$	−3.76608	−	2.17435i	−0.371083	−	0.214245i	0.302848	−	0.953039i	$-0.402062\pi$
$103$	−3.76608	−	2.17435i	−0.371083	−	0.214245i	−0.673932	+	0.738794i	$0.735396\pi$
$104$	1.86885	+	3.08341i	0.183256	+	0.302353i
$105$	2.69083	+	0.273186i	0.262598	+	0.0266602i
$106$	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	0.429816	−	0.902917i	$-0.358579\pi$
$109$	14.8949	−	8.59957i	1.42667	−	0.823690i	0.996857	+	0.0792270i	$0.0252452\pi$
$110$	−3.12323	+	1.80320i	−0.297788	+	0.171928i
$111$	1.97813	+	3.31554i	0.187756	+	0.314697i
$112$	2.62812	+	0.304939i	0.248334	+	0.0288141i
$113$	13.5393	+	7.81690i	1.27367	+	0.735353i	0.975676	−	0.219216i	$-0.0703499\pi$
$113$	13.5393	+	7.81690i	1.27367	+	0.735353i	0.297992	+	0.954568i	$0.403683\pi$
$114$	−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
$117$	10.8032	−	0.540211i	0.998752	−	0.0499425i
$118$		−	4.48228i		−	0.412627i
$119$	−20.0965	−	2.33179i	−1.84224	−	0.213754i
$120$	1.02216	−	0.0146533i	0.0933100	−	0.00133766i
$121$	−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
$126$	4.54987	−	6.50374i	0.405335	−	0.579399i
$127$	2.99064	+	5.17994i	0.265377	+	0.459646i	0.967662	−	0.252250i	$-0.0811704\pi$
$127$	2.99064	+	5.17994i	0.265377	+	0.459646i	−0.702286	+	0.711895i	$0.747837\pi$
$128$	1.00000			0.0883883
$129$	0.144334	+	10.0682i	0.0127079	+	0.886457i
$130$	0.0453104	+	2.12753i	0.00397398	+	0.186597i
$131$	2.79856	−	4.84725i	0.244511	−	0.423506i	−0.717483	−	0.696576i	$-0.754706\pi$
$131$	2.79856	−	4.84725i	0.244511	−	0.423506i	0.961994	+	0.273070i	$0.0880392\pi$
$132$	0.151707	+	10.5825i	0.0132044	+	0.921085i
$133$	−4.14848	−	9.59503i	−0.359719	−	0.831995i
$134$	8.95985	+	5.17297i	0.774013	+	0.446877i
$135$	1.41780	−	2.71939i	0.122025	−	0.234048i
$136$	−7.64672			−0.655701
$137$	21.1472			1.80673			0.903363	−	0.428876i	$-0.141090\pi$
$137$	21.1472			1.80673			0.903363	+	0.428876i	$0.141090\pi$
$138$	−7.44209	−	12.4737i	−0.633513	−	1.06183i
$139$	−9.34314	−	5.39426i	−0.792475	−	0.457535i	0.0483583	−	0.998830i	$-0.484601\pi$
$139$	−9.34314	−	5.39426i	−0.792475	−	0.457535i	−0.840833	+	0.541295i	$0.817934\pi$
$140$	1.25333	+	0.931429i	0.105926	+	0.0787201i
$141$	−9.89006	+	0.141781i	−0.832893	+	0.0119401i
$142$	−0.875991	+	1.51726i	−0.0735115	+	0.127326i
$143$	−22.0264	+	0.469101i	−1.84194	+	0.0392282i
$144$	1.42491	−	2.64001i	0.118742	−	0.220001i
$145$	0.948544			0.0787723
$146$	−5.41081	−	9.37179i	−0.447801	−	0.775615i
$147$	11.5578	−	3.66292i	0.953272	−	0.302112i
$148$			2.22904i			0.183226i
$149$	4.01109	+	6.94741i	0.328601	+	0.569154i	0.982235	−	0.187657i	$-0.0600894\pi$
$149$	4.01109	+	6.94741i	0.328601	+	0.569154i	−0.653633	+	0.756811i	$0.726756\pi$
$150$	−7.03452	−	3.92802i	−0.574366	−	0.320722i
$151$	−7.60834	+	4.39268i	−0.619158	+	0.357471i	−0.776541	−	0.630066i	$-0.783028\pi$
$151$	−7.60834	+	4.39268i	−0.619158	+	0.357471i	0.157383	+	0.987538i	$0.449694\pi$
$152$	−1.97552	−	3.42169i	−0.160236	−	0.277536i
$153$	−10.8959	+	20.1874i	−0.880880	+	1.63205i
$154$	−9.64312	+	12.9758i	−0.777065	+	1.04562i
$155$			1.64037i			0.131758i
$156$	5.51612	+	2.92787i	0.441643	+	0.234417i
$157$	2.49489	−	1.44042i	0.199114	−	0.114958i	−0.397128	−	0.917763i	$-0.629993\pi$
$157$	2.49489	−	1.44042i	0.199114	−	0.114958i	0.596242	+	0.802805i	$0.296660\pi$
$158$	−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
$162$	−4.93927	−	7.52354i	−0.388066	−	0.591105i
$163$	−4.65862	+	2.68966i	−0.364891	+	0.210670i	−0.671224	−	0.741254i	$-0.734231\pi$
$163$	−4.65862	+	2.68966i	−0.364891	+	0.210670i	0.306333	+	0.951924i	$0.400898\pi$
$164$	−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	$-0.883798\pi$
$167$	−14.1115	+	8.14728i	−1.09198	+	0.630455i	−0.157878	+	0.987459i	$0.550465\pi$
$168$	4.17976	−	1.87872i	0.322476	−	0.144946i
$169$	−6.01478	+	11.5249i	−0.462676	+	0.886528i
$170$	−3.90849	−	2.25657i	−0.299767	−	0.173071i
$171$	−11.8482	+	0.339774i	−0.906056	+	0.0259832i
$172$	−2.90674	+	5.03462i	−0.221637	+	0.383886i
$173$	7.20003	+	12.4708i	0.547408	+	0.948138i	0.998451	+	0.0556362i	$0.0177187\pi$
$173$	7.20003	+	12.4708i	0.547408	+	0.948138i	−0.451043	+	0.892502i	$0.648948\pi$
$174$	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
$177$	−3.97774	−	6.66709i	−0.298986	−	0.501129i
$178$		−	4.11835i		−	0.308683i
$179$	9.93300	+	5.73482i	0.742427	+	0.428641i	0.822951	−	0.568112i	$-0.192326\pi$
$179$	9.93300	+	5.73482i	0.742427	+	0.428641i	−0.0805240	+	0.996753i	$0.525659\pi$
$180$	1.50739	−	0.928899i	0.112354	−	0.0692360i
$181$		−	14.7039i		−	1.09293i	−0.837482	−	0.546465i	$-0.815973\pi$
$181$		−	14.7039i		−	1.09293i	0.837482	−	0.546465i	$-0.184027\pi$
$182$	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
$189$	0.995959	−	13.7116i	0.0724454	−	0.997372i
$190$		−	2.33192i		−	0.169175i
$191$	9.40428	−	5.42957i	0.680470	−	0.392870i	−0.119562	−	0.992827i	$-0.538149\pi$
$191$	9.40428	−	5.42957i	0.680470	−	0.392870i	0.800032	+	0.599957i	$0.204816\pi$
$192$	1.48743	−	0.887438i	0.107346	−	0.0640453i
$193$	16.6658	+	9.62200i	1.19963	+	0.692607i	0.960473	−	0.278374i	$-0.0897954\pi$
$193$	16.6658	+	9.62200i	1.19963	+	0.692607i	0.239158	+	0.970981i	$0.423129\pi$
$194$	−2.82580	+	4.89442i	−0.202880	+	0.351399i
$195$	1.95545	+	3.12435i	0.140032	+	0.223739i
$196$	6.81402	+	1.60283i	0.486716	+	0.114488i
$197$	3.97307	+	6.88156i	0.283070	+	0.490291i	0.972139	−	0.234404i	$-0.0753139\pi$
$197$	3.97307	+	6.88156i	0.283070	+	0.490291i	−0.689070	+	0.724695i	$0.741981\pi$
$198$	9.61693	+	15.6061i	0.683446	+	1.10908i
$199$			18.8182i			1.33399i	0.745064	+	0.666993i	$0.232419\pi$
$199$			18.8182i			1.33399i	−0.745064	+	0.666993i	$0.767581\pi$
$200$	−2.32583	−	4.02845i	−0.164461	−	0.284855i
$201$	17.9179	−	0.256864i	1.26383	−	0.0181178i
$202$	−5.91078	+	10.2378i	−0.415881	+	0.720327i
$203$	3.90293	−	1.68746i	0.273932	−	0.118436i
$204$	−11.3740	+	6.78599i	−0.796338	+	0.475114i
$205$	−0.929688			−0.0649322
$206$	−3.76608	−	2.17435i	−0.262395	−	0.151494i
$207$	−22.1392	−	11.9493i	−1.53878	−	0.830537i
$208$	1.86885	+	3.08341i	0.129582	+	0.213796i
$209$	24.1425			1.66997
$210$	2.69083	+	0.273186i	0.185685	+	0.0188516i
$211$	1.28361	+	2.22329i	0.0883677	+	0.153057i	0.906821	−	0.421515i	$-0.138502\pi$
$211$	1.28361	+	2.22329i	0.0883677	+	0.153057i	−0.818454	+	0.574573i	$0.805168\pi$
$212$	3.30431	−	1.90774i	0.226941	−	0.131024i
$213$	0.0434974	+	3.03421i	0.00298039	+	0.207901i
$214$			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
$222$	1.97813	+	3.31554i	0.132763	+	0.222524i
$223$	1.78923	+	3.09905i	0.119816	+	0.207527i	0.919695	−	0.392634i	$-0.128436\pi$
$223$	1.78923	+	3.09905i	0.119816	+	0.207527i	−0.799879	+	0.600162i	$0.795103\pi$
$224$	2.62812	+	0.304939i	0.175599	+	0.0203746i
$225$	−13.9492	+	0.400025i	−0.929949	+	0.0266684i
$226$	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	−0.620905	−	0.783886i	$-0.713235\pi$
$229$	5.57509	−	9.65634i	0.368412	−	0.638109i	0.989318	+	0.145777i	$0.0465681\pi$
$230$	2.47474	−	4.28638i	0.163180	−	0.282635i
$231$	−2.82831	+	27.8582i	−0.186089	+	1.83294i
$232$	1.39183	−	0.803572i	0.0913779	−	0.0527571i
$233$	−13.8355	−	7.98795i	−0.906396	−	0.523308i	−0.0271263	−	0.999632i	$-0.508636\pi$
$233$	−13.8355	−	7.98795i	−0.906396	−	0.523308i	−0.879270	+	0.476324i	$0.841969\pi$
$234$	10.8032	−	0.540211i	0.706224	−	0.0353147i
$235$	−1.68522	−	2.91888i	−0.109931	−	0.190407i
$236$		−	4.48228i		−	0.291772i
$237$	0.157780	+	11.0061i	0.0102489	+	0.714923i
$238$	−20.0965	−	2.33179i	−1.30266	−	0.151147i
$239$	−17.6869			−1.14407			−0.572034	−	0.820230i	$-0.693846\pi$
$239$	−17.6869			−1.14407			−0.572034	+	0.820230i	$0.693846\pi$
$240$	1.02216	−	0.0146533i	0.0659801	−	0.000945869i
$241$	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
$243$	−14.0235	−	6.80745i	−0.899608	−	0.436698i
$244$	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
$249$	8.05305	+	13.4977i	0.510341	+	0.855381i
$250$		−	5.69645i		−	0.360275i
$251$	−1.60381	+	2.77787i	−0.101231	+	0.175338i	−0.912192	−	0.409763i	$-0.865612\pi$
$251$	−1.60381	+	2.77787i	−0.101231	+	0.175338i	0.810961	+	0.585100i	$0.198945\pi$
$252$	4.54987	−	6.50374i	0.286615	−	0.409697i
$253$	44.3770	+	25.6211i	2.78996	+	1.61078i
$254$	2.99064	+	5.17994i	0.187650	+	0.325019i
$255$	−7.81617	+	0.112050i	−0.489467	+	0.00701684i
$256$	1.00000			0.0625000
$257$	−1.18333			−0.0738138			−0.0369069	−	0.999319i	$-0.511751\pi$
$257$	−1.18333			−0.0738138			−0.0369069	+	0.999319i	$0.511751\pi$
$258$	0.144334	+	10.0682i	0.00898587	+	0.626819i
$259$	−0.679720	+	5.85817i	−0.0422358	+	0.364009i
$260$	0.0453104	+	2.12753i	0.00281003	+	0.131944i
$261$	−0.138208	−	4.81945i	−0.00855489	−	0.298316i
$262$	2.79856	−	4.84725i	0.172896	−	0.299464i
$263$	1.16231	+	0.671062i	0.0716713	+	0.0413794i	0.535407	−	0.844594i	$-0.320158\pi$
$263$	1.16231	+	0.671062i	0.0716713	+	0.0413794i	−0.463736	+	0.885973i	$0.653491\pi$
$264$	0.151707	+	10.5825i	0.00933690	+	0.651306i
$265$	2.25192			0.138334
$266$	−4.14848	−	9.59503i	−0.254360	−	0.588309i
$267$	−3.65478	−	6.12577i	−0.223669	−	0.374891i
$268$	8.95985	+	5.17297i	0.547310	+	0.315990i
$269$	6.46592			0.394234			0.197117	−	0.980380i	$-0.436842\pi$
$269$	6.46592			0.394234			0.197117	+	0.980380i	$0.436842\pi$
$270$	1.41780	−	2.71939i	0.0862845	−	0.165497i
$271$	−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
$273$	13.6042	+	9.37687i	0.823364	+	0.567514i
$274$	21.1472			1.27755
$275$	28.4236			1.71401
$276$	−7.44209	−	12.4737i	−0.447961	−	0.750826i
$277$	−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
$279$	8.33453	−	0.239011i	0.498976	−	0.0143092i
$280$	1.25333	+	0.931429i	0.0749007	+	0.0556635i
$281$	21.9950			1.31211			0.656057	−	0.754711i	$-0.272223\pi$
$281$	21.9950			1.31211			0.656057	+	0.754711i	$0.272223\pi$
$282$	−9.89006	+	0.141781i	−0.588945	+	0.00844291i
$283$	−11.1271	−	6.42423i	−0.661437	−	0.381881i	0.131387	−	0.991331i	$-0.458057\pi$
$283$	−11.1271	−	6.42423i	−0.661437	−	0.381881i	−0.792824	+	0.609450i	$0.791390\pi$
$284$	−0.875991	+	1.51726i	−0.0519805	+	0.0900329i
$285$	−2.06943	−	3.46857i	−0.122583	−	0.205460i
$286$	−22.0264	+	0.469101i	−1.30245	+	0.0277385i
$287$	−3.82534	+	1.65392i	−0.225803	+	0.0976275i
$288$	1.42491	−	2.64001i	0.0839635	−	0.155564i
$289$	41.4723			2.43955
$290$	0.948544			0.0557004
$291$	0.140315	+	9.78784i	0.00822542	+	0.573773i
$292$	−5.41081	−	9.37179i	−0.316643	−	0.548443i
$293$	−0.344829	−	0.199087i	−0.0201451	−	0.0116308i	0.489894	−	0.871782i	$-0.337036\pi$
$293$	−0.344829	−	0.199087i	−0.0201451	−	0.0116308i	−0.510039	+	0.860151i	$0.670369\pi$
$294$	11.5578	−	3.66292i	0.674065	−	0.213626i
$295$	1.32273	−	2.29104i	0.0770124	−	0.133389i
$296$			2.22904i			0.129560i
$297$	28.1539	+	14.6785i	1.63366	+	0.851735i
$298$	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
$303$	0.293500	+	20.4734i	0.0168611	+	1.17617i
$304$	−1.97552	−	3.42169i	−0.113304	−	0.196248i
$305$	0.0593724			0.00339966
$306$	−10.8959	+	20.1874i	−0.622876	+	1.15404i
$307$	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
$309$	−7.53139	+	0.107968i	−0.428446	+	0.00614206i
$310$			1.64037i			0.0931666i
$311$	−1.05163	−	1.82148i	−0.0596325	−	0.103287i	0.834668	−	0.550754i	$-0.185660\pi$
$311$	−1.05163	−	1.82148i	−0.0596325	−	0.103287i	−0.894300	+	0.447467i	$0.852326\pi$
$312$	5.51612	+	2.92787i	0.312289	+	0.165758i
$313$	−9.44084	−	5.45067i	−0.533628	−	0.308090i	0.208865	−	0.977945i	$-0.433023\pi$
$313$	−9.44084	−	5.45067i	−0.533628	−	0.308090i	−0.742492	+	0.669854i	$0.766356\pi$
$314$	2.49489	−	1.44042i	0.140795	−	0.0812878i
$315$	4.24486	−	1.98159i	0.239171	−	0.111650i
$316$	−3.17751	+	5.50361i	−0.178749	+	0.309602i
$317$	5.27267	−	9.13253i	0.296143	−	0.512934i	−0.679107	−	0.734039i	$-0.737633\pi$
$317$	5.27267	−	9.13253i	0.296143	−	0.512934i	0.975250	+	0.221105i	$0.0709663\pi$
$318$	3.22193	−	5.77000i	0.180677	−	0.323566i
$319$			9.82032i			0.549832i
$320$	0.511132	+	0.295102i	0.0285732	+	0.0164967i
$321$	7.84551	+	13.1498i	0.437894	+	0.733953i
$322$	2.55723	−	22.0395i	0.142509	−	1.22821i
$323$	15.1062	+	26.1647i	0.840533	+	1.45585i
$324$	−4.93927	−	7.52354i	−0.274404	−	0.417974i
$325$	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	−0.804905	−	0.593404i	$-0.797784\pi$
$331$	−12.6163	+	7.28403i	−0.693455	+	0.400366i	0.111450	+	0.993770i	$0.464450\pi$
$332$			9.07449i			0.498027i
$333$	5.88467	+	3.17617i	0.322478	+	0.174053i
$334$	−14.1115	+	8.14728i	−0.772147	+	0.445799i
$335$	3.05311	+	5.28815i	0.166809	+	0.288922i
$336$	4.17976	−	1.87872i	0.228025	−	0.102492i
$337$	−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
$339$	27.0758	−	0.388149i	1.47055	−	0.0210814i
$340$	−3.90849	−	2.25657i	−0.211967	−	0.122379i
$341$	−16.9828			−0.919671
$342$	−11.8482	+	0.339774i	−0.640679	+	0.0183729i
$343$	17.4193	+	6.29030i	0.940554	+	0.339644i
$344$	−2.90674	+	5.03462i	−0.156721	+	0.271449i
$345$	−0.122883	−	8.57187i	−0.00661582	−	0.461494i
$346$	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	−0.842811	−	0.538210i	$-0.819101\pi$
$349$	−16.5800	−	28.7175i	−0.887509	−	1.53721i	−0.0446981	−	0.999001i	$-0.514233\pi$
$350$	−4.88412	−	11.2965i	−0.261067	−	0.603823i
$351$	15.5896	−	10.3907i	0.832109	−	0.554612i
$352$	−3.05521	+	5.29178i	−0.162843	+	0.282053i
$353$	12.5305	+	7.23450i	0.666933	+	0.385054i	0.794913	−	0.606723i	$-0.207516\pi$
$353$	12.5305	+	7.23450i	0.666933	+	0.385054i	−0.127981	+	0.991777i	$0.540850\pi$
$354$	−3.97774	−	6.66709i	−0.211415	−	0.354352i
$355$	−0.895494	+	0.517014i	−0.0475279	+	0.0274403i
$356$		−	4.11835i		−	0.218272i
$357$	−31.9615	+	14.3660i	−1.69158	+	0.760330i
$358$	9.93300	+	5.73482i	0.524975	+	0.303095i
$359$	7.00098	−	12.1261i	0.369498	−	0.639989i	−0.619989	−	0.784610i	$-0.712863\pi$
$359$	7.00098	−	12.1261i	0.369498	−	0.639989i	0.989487	+	0.144621i	$0.0461964\pi$
$360$	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	0.128541	−	0.991704i	$-0.458971\pi$
$367$	−12.7593	−	7.36659i	−0.666030	−	0.384533i	−0.794571	+	0.607172i	$0.792304\pi$
$368$		−	8.38604i		−	0.437153i
$369$	0.135461	+	4.72364i	0.00705182	+	0.245903i
$370$	−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	0.585047	−	0.810999i	$-0.301076\pi$
$373$	−7.91499	−	13.7092i	−0.409822	−	0.709833i	−0.994870	+	0.101166i	$0.967743\pi$
$374$	23.3623	−	40.4647i	1.20804	−	2.09238i
$375$	−5.05525	−	8.47309i	−0.261052	−	0.437548i
$376$	−4.94554	−	2.85531i	−0.255047	−	0.147251i
$377$	5.07886	+	2.78981i	0.261575	+	0.143683i
$378$	0.995959	−	13.7116i	0.0512266	−	0.705249i
$379$	−11.2444	+	6.49193i	−0.577584	+	0.333468i	−0.760173	−	0.649721i	$-0.774886\pi$
$379$	−11.2444	+	6.49193i	−0.577584	+	0.333468i	0.182589	+	0.983189i	$0.441552\pi$
$380$		−	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	$-0.632561\pi$
$383$	3.62494	−	2.09286i	0.185226	−	0.106940i	0.589746	+	0.807589i	$0.299228\pi$
$384$	1.48743	−	0.887438i	0.0759052	−	0.0452869i
$385$	−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	$-0.478707\pi$
$389$	19.0201	−	10.9812i	0.964356	−	0.556771i	0.897511	+	0.440992i	$0.145373\pi$
$390$	1.95545	+	3.12435i	0.0990179	+	0.158207i
$391$			64.1257i			3.24298i
$392$	6.81402	+	1.60283i	0.344160	+	0.0809553i
$393$	−0.138963	−	9.69349i	−0.00700974	−	0.488972i
$394$	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	−0.897122	−	0.441783i	$-0.854346\pi$
$397$	−16.5607	−	28.6839i	−0.831156	−	1.43960i	0.0659662	−	0.997822i	$-0.478987\pi$
$398$			18.8182i			0.943271i
$399$	−14.6856	−	10.5904i	−0.735199	−	0.530185i
$400$	−2.32583	−	4.02845i	−0.116291	−	0.201423i
$401$	6.94374			0.346754			0.173377	−	0.984856i	$-0.444532\pi$
$401$	6.94374			0.346754			0.173377	+	0.984856i	$0.444532\pi$
$402$	17.9179	−	0.256864i	0.893662	−	0.0128112i
$403$	−4.82457	+	8.78314i	−0.240329	+	0.437519i
$404$	−5.91078	+	10.2378i	−0.294072	+	0.509348i
$405$	−0.304407	−	5.30311i	−0.0151261	−	0.263514i
$406$	3.90293	−	1.68746i	0.193699	−	0.0837472i
$407$	−11.7956	−	6.81017i	−0.584684	−	0.337568i
$408$	−11.3740	+	6.78599i	−0.563096	+	0.335957i
$409$	−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
$411$	31.4550	−	18.7668i	1.55156	−	0.925699i
$412$	−3.76608	−	2.17435i	−0.185542	−	0.107123i
$413$	1.36682	−	11.7800i	0.0672570	−	0.579654i
$414$	−22.1392	−	11.9493i	−1.08808	−	0.587278i
$415$	−2.67790	+	4.63827i	−0.131453	+	0.227684i
$416$	1.86885	+	3.08341i	0.0916280	+	0.151176i
$417$	−18.6844	+	0.267853i	−0.914977	+	0.0131168i
$418$	24.1425			1.18085
$419$	−2.85725	−	4.94891i	−0.139586	−	0.241770i	0.787754	−	0.615990i	$-0.211244\pi$
$419$	−2.85725	−	4.94891i	−0.139586	−	0.241770i	−0.927340	+	0.374220i	$0.877911\pi$
$420$	2.69083	+	0.273186i	0.131299	+	0.0133301i
$421$		−	9.25537i		−	0.451079i	−0.974234	−	0.225540i	$-0.927585\pi$
$421$		−	9.25537i		−	0.451079i	0.974234	−	0.225540i	$-0.0724145\pi$
$422$	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
$426$	0.0434974	+	3.03421i	0.00210746	+	0.147008i
$427$	0.244297	−	0.105624i	0.0118224	−	0.00511148i
$428$			8.84064i			0.427328i
$429$	−32.3465	+	20.2448i	−1.56170	+	0.977430i
$430$	−2.97146	+	1.71557i	−0.143296	+	0.0827322i
$431$	5.05283	−	8.75176i	0.243386	−	0.421557i	−0.718290	−	0.695743i	$-0.755075\pi$
$431$	5.05283	−	8.75176i	0.243386	−	0.421557i	0.961677	+	0.274186i	$0.0884084\pi$
$432$	−0.223387	−	5.19135i	−0.0107477	−	0.249769i
$433$	32.8655	+	18.9749i	1.57942	+	0.911877i	0.994941	+	0.100466i	$0.0320333\pi$
$433$	32.8655	+	18.9749i	1.57942	+	0.911877i	0.584476	+	0.811411i	$0.301300\pi$
$434$	2.91822	+	6.74955i	0.140079	+	0.323989i
$435$	1.41089	−	0.841774i	0.0676472	−	0.0403600i
$436$	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	$0.237535\pi$
$439$			28.4483i			1.35776i	−0.734248	+	0.678881i	$0.762465\pi$
$440$	−3.12323	+	1.80320i	−0.148894	+	0.0859641i
$441$	13.9409	−	15.7052i	0.663850	−	0.747866i
$442$	−14.2906	−	23.5779i	−0.679734	−	1.12149i
$443$	−18.7651	−	10.8340i	−0.891555	−	0.514740i	−0.0171043	−	0.999854i	$-0.505445\pi$
$443$	−18.7651	−	10.8340i	−0.891555	−	0.514740i	−0.874451	+	0.485114i	$0.838778\pi$
$444$	1.97813	+	3.31554i	0.0938779	+	0.157349i
$445$	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	$-0.738232\pi$
$449$	6.23704	−	10.8029i	0.294344	−	0.509819i	0.974832	+	0.222940i	$0.0715656\pi$
$450$	−13.9492	+	0.400025i	−0.657574	+	0.0188574i
$451$		−	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	$-0.927974\pi$
$457$		−	9.59213i		−	0.448701i	0.974509	−	0.224351i	$-0.0720261\pi$
$458$	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	$-0.297499\pi$
$461$	4.17780	+	2.41206i	0.194580	+	0.112341i	−0.399545	+	0.916714i	$0.630832\pi$
$462$	−2.82831	+	27.8582i	−0.131585	+	1.29608i
$463$		−	3.08747i		−	0.143487i	−0.997423	−	0.0717434i	$-0.977144\pi$
$463$		−	3.08747i		−	0.143487i	0.997423	−	0.0717434i	$-0.0228563\pi$
$464$	1.39183	−	0.803572i	0.0646140	−	0.0373049i
$465$	1.45572	+	2.43994i	0.0675076	+	0.113149i
$466$	−13.8355	−	7.98795i	−0.640919	−	0.370035i
$467$	−4.16237	+	7.20943i	−0.192611	+	0.333613i	−0.946115	−	0.323831i	$-0.895029\pi$
$467$	−4.16237	+	7.20943i	−0.192611	+	0.333613i	0.753504	+	0.657444i	$0.228362\pi$
$468$	10.8032	−	0.540211i	0.499376	−	0.0249713i
$469$	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
$474$	0.157780	+	11.0061i	0.00724706	+	0.505527i
$475$	−9.18943	+	15.9166i	−0.421640	+	0.730302i
$476$	−20.0965	−	2.33179i	−0.921121	−	0.106877i
$477$	−0.328118	−	11.4417i	−0.0150235	−	0.523882i
$478$	−17.6869			−0.808979
$479$	10.4595	+	6.03880i	0.477907	+	0.275920i	0.719544	−	0.694447i	$-0.244351\pi$
$479$	10.4595	+	6.03880i	0.477907	+	0.275920i	−0.241637	+	0.970367i	$0.577684\pi$
$480$	1.02216	−	0.0146533i	0.0466550	−	0.000668830i
$481$	−6.87302	+	4.16574i	−0.313383	+	0.189941i
$482$	24.1671			1.10078
$483$	−15.7550	−	35.0517i	−0.716877	−	1.59491i
$484$	−13.1686	−	22.8087i	−0.598573	−	1.03676i
$485$	−2.88871	+	1.66780i	−0.131170	+	0.0757308i
$486$	−14.0235	−	6.80745i	−0.636119	−	0.308792i
$487$			5.59837i			0.253686i	0.991923	+	0.126843i	$0.0404845\pi$
$487$			5.59837i			0.253686i	−0.991923	+	0.126843i	$0.959516\pi$
$488$	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	$-0.662922\pi$
$491$	0.451495	−	0.260671i	0.0203757	−	0.0117639i	0.510153	+	0.860084i	$0.329589\pi$
$492$	−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
$495$	0.310137	+	10.8147i	0.0139396	+	0.486087i
$496$	1.38966	+	2.40696i	0.0623976	+	0.108076i
$497$	−2.76488	+	3.72042i	−0.124022	+	0.166884i
$498$	8.05305	+	13.4977i	0.360866	+	0.604846i
$499$	−28.9603	−	16.7202i	−1.29644	−	0.748501i	−0.316654	−	0.948541i	$-0.602559\pi$
$499$	−28.9603	−	16.7202i	−1.29644	−	0.748501i	−0.979788	+	0.200041i	$0.935893\pi$
$500$		−	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	$-0.699333\pi$
$503$	9.16509	−	15.8744i	0.408651	−	0.707805i	0.994739	+	0.102443i	$0.0326659\pi$
$504$	4.54987	−	6.50374i	0.202667	−	0.289700i
$505$	−6.04238	+	3.48857i	−0.268882	+	0.155239i
$506$	44.3770	+	25.6211i	1.97280	+	1.13900i
$507$	1.28101	+	22.4802i	0.0568919	+	0.998380i
$508$	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	$0.718411\pi$
$510$	−7.81617	+	0.112050i	−0.346106	+	0.00496166i
$511$	−11.3624	−	26.2802i	−0.502644	−	1.16257i
$512$	1.00000			0.0441942
$513$	−17.3219	+	11.0200i	−0.764781	+	0.486543i
$514$	−1.18333			−0.0521943
$515$	−1.28331	−	2.22276i	−0.0565495	−	0.0979465i
$516$	0.144334	+	10.0682i	0.00635397	+	0.443228i
$517$	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	−0.977117	−	0.212701i	$-0.931774\pi$
$521$	−15.3561	−	26.5976i	−0.672763	−	1.16526i	0.304354	−	0.952559i	$-0.401559\pi$
$522$	−0.138208	−	4.81945i	−0.00604922	−	0.210942i
$523$			31.3290i			1.36992i	0.728581	+	0.684960i	$0.240180\pi$
$523$			31.3290i			1.36992i	−0.728581	+	0.684960i	$0.759820\pi$
$524$	2.79856	−	4.84725i	0.122256	−	0.211753i
$525$	−17.2897	−	12.4684i	−0.754586	−	0.544166i
$526$	1.16231	+	0.671062i	0.0506793	+	0.0292597i
$527$	−10.6263	−	18.4054i	−0.462891	−	0.801750i
$528$	0.151707	+	10.5825i	0.00660219	+	0.460543i
$529$	−47.3257			−2.05764
$530$	2.25192			0.0978170
$531$	−11.8332	−	6.38684i	−0.513519	−	0.277165i
$532$	−4.14848	−	9.59503i	−0.179860	−	0.415997i
$533$	−4.97790	−	2.73435i	−0.215617	−	0.118438i
$534$	−3.65478	−	6.12577i	−0.158158	−	0.265088i
$535$	−2.60889	+	4.51873i	−0.112792	+	0.195362i
$536$	8.95985	+	5.17297i	0.387007	+	0.223438i
$537$	19.8640	−	0.284763i	0.857193	−	0.0122884i
$538$	6.46592			0.278765
$539$	−29.3001	+	31.1613i	−1.26204	+	1.34221i
$540$	1.41780	−	2.71939i	0.0610124	−	0.117024i
$541$	−18.3221	−	10.5782i	−0.787726	−	0.454794i	0.0514351	−	0.998676i	$-0.483620\pi$
$541$	−18.3221	−	10.5782i	−0.787726	−	0.454794i	−0.839162	+	0.543882i	$0.816954\pi$
$542$	−19.2359			−0.826252
$543$	−13.0488	−	21.8710i	−0.559977	−	0.938575i
$544$	−7.64672			−0.327850
$545$	10.1510			0.434822
$546$	13.6042	+	9.37687i	0.582206	+	0.401293i
$547$	−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
$549$	−0.00865091	−	0.301665i	−0.000369212	−	0.0128747i
$550$	28.4236			1.21199
$551$	−5.49916	−	3.17494i	−0.234272	−	0.135257i
$552$	−7.44209	−	12.4737i	−0.316756	−	0.530914i
$553$	−10.0292	+	13.4952i	−0.426483	+	0.573874i
$554$	−11.7622			−0.499730
$555$	0.0326628	+	2.27843i	0.00138646	+	0.0967140i
$556$	−9.34314	−	5.39426i	−0.396237	−	0.228768i
$557$	−7.56444	+	13.1020i	−0.320515	+	0.555149i	−0.980594	−	0.196047i	$-0.937189\pi$
$557$	−7.56444	+	13.1020i	−0.320515	+	0.555149i	0.660079	+	0.751196i	$0.270523\pi$
$558$	8.33453	−	0.239011i	0.352829	−	0.0101182i
$559$	−20.9561	+	0.446305i	−0.886347	+	0.0188767i
$560$	1.25333	+	0.931429i	0.0529628	+	0.0393600i
$561$	−1.16006	−	80.9212i	−0.0489777	−	3.41649i
$562$	21.9950			0.927805
$563$	−5.82808			−0.245624			−0.122812	−	0.992430i	$-0.539191\pi$
$563$	−5.82808			−0.245624			−0.122812	+	0.992430i	$0.539191\pi$
$564$	−9.89006	+	0.141781i	−0.416447	+	0.00597004i
$565$	4.61357	+	7.99094i	0.194095	+	0.336182i
$566$	−11.1271	−	6.42423i	−0.467706	−	0.270030i
$567$	−10.6868	−	21.2789i	−0.448802	−	0.893631i
$568$	−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	$0.838928\pi$
$570$	−2.06943	−	3.46857i	−0.0866790	−	0.145282i
$571$	−17.1315	−	29.6727i	−0.716933	−	1.24176i	−0.962209	−	0.272311i	$-0.912212\pi$
$571$	−17.1315	−	29.6727i	−0.716933	−	1.24176i	0.245277	−	0.969453i	$-0.421121\pi$
$572$	−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
$576$	1.42491	−	2.64001i	0.0593712	−	0.110000i
$577$	−7.81628	−	13.5382i	−0.325396	−	0.563602i	0.656196	−	0.754590i	$-0.272164\pi$
$577$	−7.81628	−	13.5382i	−0.325396	−	0.563602i	−0.981592	+	0.190988i	$0.938831\pi$
$578$	41.4723			1.72502
$579$	33.3282	−	0.477781i	1.38507	−	0.0198559i
$580$	0.948544			0.0393861
$581$	−2.76717	+	23.8489i	−0.114802	+	0.989417i
$582$	0.140315	+	9.78784i	0.00581625	+	0.405719i
$583$			23.3142i			0.965576i
$584$	−5.41081	−	9.37179i	−0.223901	−	0.387807i
$585$	5.68126	+	2.91192i	0.234891	+	0.120393i
$586$	−0.344829	−	0.199087i	−0.0142448	−	0.00822421i
$587$	−25.9699	+	14.9937i	−1.07189	+	0.618856i	−0.928697	−	0.370838i	$-0.879070\pi$
$587$	−25.9699	+	14.9937i	−1.07189	+	0.618856i	−0.143193	+	0.989695i	$0.545737\pi$
$588$	11.5578	−	3.66292i	0.476636	−	0.151056i
$589$	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	$-0.241181\pi$
$593$	12.0409	+	6.95181i	0.494460	+	0.285477i	−0.231963	+	0.972725i	$0.574515\pi$
$594$	28.1539	+	14.6785i	1.15517	+	0.602268i
$595$	−9.58385	−	7.12237i	−0.392900	−	0.291989i
$596$	4.01109	+	6.94741i	0.164301	+	0.284577i
$597$	16.7000	+	27.9908i	0.683484	+	1.14559i
$598$	25.8576	−	15.6723i	1.05739	−	0.640887i
$599$	−5.85303	+	3.37925i	−0.239148	+	0.138072i	−0.614785	−	0.788695i	$-0.710757\pi$
$599$	−5.85303	+	3.37925i	−0.239148	+	0.138072i	0.375637	+	0.926767i	$0.377424\pi$
$600$	−7.03452	−	3.92802i	−0.287183	−	0.160361i
$601$	11.3845	−	6.57283i	0.464382	−	0.268111i	−0.249503	−	0.968374i	$-0.580267\pi$
$601$	11.3845	−	6.57283i	0.464382	−	0.268111i	0.713885	+	0.700263i	$0.246934\pi$
$602$	−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
$606$	0.293500	+	20.4734i	0.0119226	+	0.831676i
$607$	−26.4291	+	15.2588i	−1.07272	+	0.619337i	−0.928924	−	0.370270i	$-0.879265\pi$
$607$	−26.4291	+	15.2588i	−1.07272	+	0.619337i	−0.143799	+	0.989607i	$0.545932\pi$
$608$	−1.97552	−	3.42169i	−0.0801178	−	0.138768i
$609$	4.30783	−	5.97359i	0.174562	−	0.242062i
$610$	0.0593724			0.00240392
$611$	−0.438408	−	20.5853i	−0.0177361	−	0.832790i
$612$	−10.8959	+	20.1874i	−0.440440	+	0.816027i
$613$	3.14710	+	1.81698i	0.127110	+	0.0733872i	0.562207	−	0.826997i	$-0.309952\pi$
$613$	3.14710	+	1.81698i	0.127110	+	0.0733872i	−0.435097	+	0.900384i	$0.643286\pi$
$614$	10.2738			0.414616
$615$	−1.38285	+	0.825040i	−0.0557618	+	0.0332688i
$616$	−9.64312	+	12.9758i	−0.388533	+	0.522809i
$617$	−17.7255	+	30.7015i	−0.713603	+	1.23600i	0.249893	+	0.968273i	$0.419605\pi$
$617$	−17.7255	+	30.7015i	−0.713603	+	1.23600i	−0.963496	+	0.267723i	$0.913729\pi$
$618$	−7.53139	+	0.107968i	−0.302957	+	0.00434309i
$619$	21.7709	+	37.7083i	0.875046	+	1.51562i	0.856713	+	0.515793i	$0.172503\pi$
$619$	21.7709	+	37.7083i	0.875046	+	1.51562i	0.0183329	+	0.999832i	$0.494164\pi$
$620$			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
$624$	5.51612	+	2.92787i	0.220822	+	0.117208i
$625$	−9.94811	+	17.2306i	−0.397924	+	0.689225i
$626$	−9.44084	−	5.45067i	−0.377332	−	0.217853i
$627$	35.9103	−	21.4249i	1.43412	−	0.855629i
$628$	2.49489	−	1.44042i	0.0995568	−	0.0574791i
$629$		−	17.0448i		−	0.679621i
$630$	4.24486	−	1.98159i	0.169119	−	0.0789486i
$631$	−21.1471	−	12.2093i	−0.841854	−	0.486045i	0.0160399	−	0.999871i	$-0.494894\pi$
$631$	−21.1471	−	12.2093i	−0.841854	−	0.486045i	−0.857894	+	0.513827i	$0.828227\pi$
$632$	−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	$0.875729\pi$
$642$	7.84551	+	13.1498i	0.309638	+	0.518983i
$643$	15.0498	−	26.0670i	0.593505	−	1.02798i	−0.400251	−	0.916405i	$-0.631077\pi$
$643$	15.0498	−	26.0670i	0.593505	−	1.02798i	0.993756	−	0.111575i	$-0.0355895\pi$
$644$	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	0.433598	+	0.901107i	$0.357244\pi$
$647$	−14.3354	+	24.8296i	−0.563582	+	0.976153i	−0.997180	+	0.0750466i	$0.976089\pi$
$648$	−4.93927	−	7.52354i	−0.194033	−	0.295552i
$649$	23.7192	+	13.6943i	0.931061	+	0.537548i
$650$	8.07473	−	14.7001i	0.316717	−	0.576584i
$651$	10.3304	+	7.44976i	0.404882	+	0.291979i
$652$	−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
$657$	−32.4515	+	0.930619i	−1.26605	+	0.0363069i
$658$	−12.1268	−	9.01218i	−0.472751	−	0.351331i
$659$	28.9405	+	16.7088i	1.12736	+	0.650884i	0.943270	−	0.332025i	$-0.107732\pi$
$659$	28.9405	+	16.7088i	1.12736	+	0.650884i	0.184093	+	0.982909i	$0.441065\pi$
$660$	−3.04537	+	5.45381i	−0.118541	+	0.212289i
$661$	5.20701	−	9.01881i	0.202529	−	0.350791i	−0.746813	−	0.665034i	$-0.768417\pi$
$661$	5.20701	−	9.01881i	0.202529	−	0.350791i	0.949343	+	0.314243i	$0.101751\pi$
$662$	−12.6163	+	7.28403i	−0.490347	+	0.283102i
$663$	−42.1802	−	22.3886i	−1.63814	−	0.869500i
$664$			9.07449i			0.352159i
$665$	0.711093	−	6.12856i	0.0275750	−	0.237655i
$666$	5.88467	+	3.17617i	0.228026	+	0.123074i
$667$	−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
$672$	4.17976	−	1.87872i	0.161238	−	0.0724730i
$673$	−0.105584	−	0.182877i	−0.00406998	−	0.00704941i	0.863983	−	0.503521i	$-0.167962\pi$
$673$	−0.105584	−	0.182877i	−0.00406998	−	0.00704941i	−0.868053	+	0.496471i	$0.834629\pi$
$674$	−31.0830			−1.19727
$675$	−20.3936	+	12.9741i	−0.784948	+	0.499373i
$676$	−6.01478	+	11.5249i	−0.231338	+	0.443264i
$677$	11.7820	−	20.4071i	0.452820	−	0.784307i	−0.545740	−	0.837955i	$-0.683751\pi$
$677$	11.7820	−	20.4071i	0.452820	−	0.784307i	0.998560	+	0.0536474i	$0.0170847\pi$
$678$	27.0758	−	0.388149i	1.03984	−	0.0149068i
$679$	−8.91903	+	12.0014i	−0.342281	+	0.460573i
$680$	−3.90849	−	2.25657i	−0.149884	−	0.0865353i
$681$	−10.6261	−	17.8104i	−0.407193	−	0.682495i
$682$	−16.9828			−0.650305
$683$	1.38840			0.0531255			0.0265627	−	0.999647i	$-0.491544\pi$
$683$	1.38840			0.0531255			0.0265627	+	0.999647i	$0.491544\pi$
$684$	−11.8482	+	0.339774i	−0.453028	+	0.0129916i
$685$	10.8090	+	6.24059i	0.412991	+	0.238441i
$686$	17.4193	+	6.29030i	0.665072	+	0.240165i
$687$	−0.276832	−	19.3107i	−0.0105618	−	0.736749i
$688$	−2.90674	+	5.03462i	−0.110818	+	0.191943i
$689$	12.0576	+	6.62323i	0.459358	+	0.252325i
$690$	−0.122883	−	8.57187i	−0.00467809	−	0.326326i
$691$	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
$693$	20.5155	+	43.9472i	0.779321	+	1.66942i
$694$		−	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
$699$	−27.6682	+	0.396642i	−1.04651	+	0.0150024i
$700$	−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	$-0.234001\pi$
$702$	15.5896	−	10.3907i	0.588390	−	0.392170i
$703$	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
$708$	−3.97774	−	6.66709i	−0.149493	−	0.250564i
$709$	18.7918	−	10.8494i	0.705739	−	0.407459i	−0.103742	−	0.994604i	$-0.533082\pi$
$709$	18.7918	−	10.8494i	0.705739	−	0.407459i	0.809482	+	0.587145i	$0.199748\pi$
$710$	−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
$714$	−31.9615	+	14.3660i	−1.19613	+	0.537635i
$715$	−11.3969	−	6.26028i	−0.426218	−	0.234121i
$716$	9.93300	+	5.73482i	0.371214	+	0.214320i
$717$	−26.3080	+	15.6960i	−0.982491	+	0.586178i
$718$	7.00098	−	12.1261i	0.261274	−	0.452541i
$719$	−14.7420	−	25.5339i	−0.549785	−	0.952255i	−0.998289	−	0.0584744i	$-0.981376\pi$
$719$	−14.7420	−	25.5339i	−0.549785	−	0.952255i	0.448504	−	0.893781i	$-0.351957\pi$
$720$	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
$723$	35.9469	−	21.4468i	1.33688	−	0.797615i
$724$		−	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	$-0.952834\pi$
$727$		−	7.96128i		−	0.295268i	0.989042	−	0.147634i	$-0.0471657\pi$
$728$	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	−0.0134348	+	0.999910i	$0.504277\pi$
$733$	−23.6265	+	40.9223i	−0.872665	+	1.51150i	−0.859230	+	0.511590i	$0.829057\pi$
$734$	−12.7593	−	7.36659i	−0.470954	−	0.271906i
$735$	6.98851	+	1.53850i	0.257775	+	0.0567486i
$736$		−	8.38604i		−	0.309114i
$737$	−54.7484	+	31.6090i	−2.01668	+	1.16433i
$738$	0.135461	+	4.72364i	0.00498639	+	0.173880i
$739$	18.9360	+	10.9327i	0.696572	+	0.402166i	0.806069	−	0.591821i	$-0.201591\pi$
$739$	18.9360	+	10.9327i	0.696572	+	0.402166i	−0.109498	+	0.993987i	$0.534924\pi$
$740$	−0.657794	+	1.13933i	−0.0241810	+	0.0418827i
$741$	−0.878922	−	24.6585i	−0.0322880	−	0.905854i
$742$	9.26586	−	4.00616i	0.340160	−	0.147071i
$743$	5.23639	+	9.06969i	0.192104	+	0.332735i	0.945947	−	0.324320i	$-0.105135\pi$
$743$	5.23639	+	9.06969i	0.192104	+	0.332735i	−0.753843	+	0.657055i	$0.771802\pi$
$744$	4.20305	+	2.34696i	0.154091	+	0.0860436i
$745$			4.73473i			0.173467i
$746$	−7.91499	−	13.7092i	−0.289788	−	0.501928i
$747$	23.9567	+	12.9303i	0.876531	+	0.473096i
$748$	23.3623	−	40.4647i	0.854211	−	1.47954i
$749$	−2.69586	+	23.2342i	−0.0985045	+	0.848961i
$750$	−5.05525	−	8.47309i	−0.184592	−	0.309393i
$751$	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
$753$	0.0796371	+	5.55518i	0.00290214	+	0.202442i
$754$	5.07886	+	2.78981i	0.184961	+	0.101599i
$755$	−5.18516			−0.188707
$756$	0.995959	−	13.7116i	0.0362227	−	0.498686i
$757$	−12.1846	−	21.1043i	−0.442856	−	0.767050i	0.555044	−	0.831821i	$-0.312701\pi$
$757$	−12.1846	−	21.1043i	−0.442856	−	0.767050i	−0.997900	+	0.0647715i	$0.979368\pi$
$758$	−11.2444	+	6.49193i	−0.408414	+	0.235798i
$759$	88.7450	−	1.27222i	3.22124	−	0.0461786i
$760$		−	2.33192i		−	0.0845876i
$761$	−5.80180	+	3.34967i	−0.210315	+	0.121426i	−0.601458	−	0.798905i	$-0.705413\pi$
$761$	−5.80180	+	3.34967i	−0.210315	+	0.121426i	0.391143	+	0.920330i	$0.372080\pi$
$762$	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
$768$	1.48743	−	0.887438i	0.0536731	−	0.0320227i
$769$	−3.97005	−	6.87633i	−0.143164	−	0.247967i	0.785523	−	0.618833i	$-0.212394\pi$
$769$	−3.97005	−	6.87633i	−0.143164	−	0.247967i	−0.928686	+	0.370866i	$0.879061\pi$
$770$	−8.75809	+	3.78663i	−0.315620	+	0.136461i
$771$	−1.76012	+	1.05013i	−0.0633890	+	0.0378194i
$772$	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
$777$	4.18772	+	9.31684i	0.150234	+	0.334240i
$778$	19.0201	−	10.9812i	0.681903	−	0.393697i
$779$	5.38984	+	3.11182i	0.193111	+	0.111493i
$780$	1.95545	+	3.12435i	0.0700162	+	0.111870i
$781$	−5.35267	−	9.27110i	−0.191534	−	0.331746i
$782$			64.1257i			2.29313i
$783$	−4.48254	−	7.04595i	−0.160193	−	0.251802i
$784$	6.81402	+	1.60283i	0.243358	+	0.0572441i
$785$	1.70029			0.0606859
$786$	−0.138963	−	9.69349i	−0.00495663	−	0.345755i
$787$	−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
$789$	2.32439	−	0.0333216i	0.0827504	−	0.00118628i
$790$	−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
$795$	3.34957	−	1.99844i	0.118797	−	0.0708772i
$796$			18.8182i			0.666993i
$797$	0.00976904	−	0.0169205i	0.000346037	−	0.000599354i	−0.865852	−	0.500300i	$-0.833223\pi$
$797$	0.00976904	−	0.0169205i	0.000346037	−	0.000599354i	0.866198	+	0.499700i	$0.166557\pi$
$798$	−14.6856	−	10.5904i	−0.519864	−	0.374898i
$799$	37.8172	+	21.8337i	1.33787	+	0.772422i
$800$	−2.32583	−	4.02845i	−0.0822305	−	0.142427i
$801$	−10.8725	−	5.86827i	−0.384160	−	0.207345i
$802$	6.94374			0.245192
$803$	66.1246			2.33349
$804$	17.9179	−	0.256864i	0.631914	−	0.00905891i
$805$	7.81100	−	10.5105i	0.275301	−	0.370445i
$806$	−4.82457	+	8.78314i	−0.169938	+	0.309373i
$807$	9.61761	−	5.73810i	0.338556	−	0.201991i
$808$	−5.91078	+	10.2378i	−0.207940	+	0.360163i
$809$	5.64352	+	3.25829i	0.198416	+	0.114555i	0.595916	−	0.803047i	$-0.296789\pi$
$809$	5.64352	+	3.25829i	0.198416	+	0.114555i	−0.397501	+	0.917602i	$0.630122\pi$
$810$	−0.304407	−	5.30311i	−0.0106958	−	0.186332i
$811$	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
$813$	−28.6121	+	17.0707i	−1.00347	+	0.598694i
$814$	−11.7956	−	6.81017i	−0.413434	−	0.238696i
$815$	−3.17490			−0.111212
$816$	−11.3740	+	6.78599i	−0.398169	+	0.237557i
$817$	22.9693			0.803592
$818$	−0.303545			−0.0106132
$819$	28.5567	+	1.87457i	0.997852	+	0.0655027i
$820$	−0.929688			−0.0324661
$821$	−12.6481			−0.441420			−0.220710	−	0.975339i	$-0.570837\pi$
$821$	−12.6481			−0.441420			−0.220710	+	0.975339i	$0.570837\pi$
$822$	31.4550	−	18.7668i	1.09712	−	0.654568i
$823$	−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
$825$	42.2781	−	25.2242i	1.47194	−	0.878192i
$826$	1.36682	−	11.7800i	0.0475579	−	0.409877i
$827$	25.1546			0.874712			0.437356	−	0.899288i	$-0.355915\pi$
$827$	25.1546			0.874712			0.437356	+	0.899288i	$0.355915\pi$
$828$	−22.1392	−	11.9493i	−0.769390	−	0.415268i
$829$	42.1390	+	24.3289i	1.46355	+	0.844979i	0.999173	−	0.0406604i	$-0.0129462\pi$
$829$	42.1390	+	24.3289i	1.46355	+	0.844979i	0.464374	+	0.885639i	$0.346280\pi$
$830$	−2.67790	+	4.63827i	−0.0929514	+	0.160997i
$831$	−17.4955	+	10.4383i	−0.606914	+	0.362099i
$832$	1.86885	+	3.08341i	0.0647908	+	0.106898i
$833$	−52.1049	−	12.2564i	−1.80533	−	0.424660i
$834$	−18.6844	+	0.267853i	−0.646986	+	0.00927498i
$835$	−9.61713			−0.332814
$836$	24.1425			0.834984
$837$	12.1849	−	7.75189i	0.421173	−	0.267945i
$838$	−2.85725	−	4.94891i	−0.0987022	−	0.170957i
$839$	18.3244	+	10.5796i	0.632630	+	0.365249i	0.781770	−	0.623567i	$-0.214317\pi$
$839$	18.3244	+	10.5796i	0.632630	+	0.365249i	−0.149140	+	0.988816i	$0.547650\pi$
$840$	2.69083	+	0.273186i	0.0928423	+	0.00942581i
$841$	−13.2085	+	22.8779i	−0.455467	+	0.788892i
$842$		−	9.25537i		−	0.318961i
$843$	32.7161	−	19.5192i	1.12680	−	0.672278i
$844$	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
$849$	−22.2519	+	0.318996i	−0.763683	+	0.0109479i
$850$	17.7850	+	30.8045i	0.610019	+	1.05658i
$851$	18.6928			0.640780
$852$	0.0434974	+	3.03421i	0.00149020	+	0.103950i
$853$	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
$855$	−6.15628	−	3.32277i	−0.210540	−	0.113636i
$856$			8.84064i			0.302167i
$857$	−12.3135	−	21.3277i	−0.420623	−	0.728540i	0.575378	−	0.817888i	$-0.304855\pi$
$857$	−12.3135	−	21.3277i	−0.420623	−	0.728540i	−0.996000	+	0.0893479i	$0.971522\pi$
$858$	−32.3465	+	20.2448i	−1.10429	+	0.691147i
$859$	1.35293	+	0.781117i	0.0461615	+	0.0266514i	0.522903	−	0.852392i	$-0.324849\pi$
$859$	1.35293	+	0.781117i	0.0461615	+	0.0266514i	−0.476742	+	0.879043i	$0.658182\pi$
$860$	−2.97146	+	1.71557i	−0.101326	+	0.0585005i
$861$	−4.22219	+	5.85484i	−0.143892	+	0.199532i
$862$	5.05283	−	8.75176i	0.172100	−	0.298086i
$863$	13.1821	−	22.8320i	0.448723	−	0.777210i	−0.549581	−	0.835441i	$-0.685212\pi$
$863$	13.1821	−	22.8320i	0.448723	−	0.777210i	0.998303	+	0.0582303i	$0.0185458\pi$
$864$	−0.223387	−	5.19135i	−0.00759977	−	0.176613i
$865$			8.49898i			0.288974i
$866$	32.8655	+	18.9749i	1.11682	+	0.644794i
$867$	61.6873	−	36.8041i	2.09501	−	1.24993i
$868$	2.91822	+	6.74955i	0.0990507	+	0.229094i
$869$	−19.4159	−	33.6294i	−0.658640	−	1.14080i
$870$	1.41089	−	0.841774i	0.0478338	−	0.0285388i
$871$	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	−0.800550	−	0.599265i	$-0.795459\pi$
$877$	−20.1923	+	11.6580i	−0.681846	+	0.393664i	0.118704	+	0.992930i	$0.462126\pi$
$878$			28.4483i			0.960083i
$879$	−0.689587	+	0.00988569i	−0.0232592	+	0.000333436i
$880$	−3.12323	+	1.80320i	−0.105284	+	0.0607858i
$881$	−7.67467	−	13.2929i	−0.258566	−	0.447850i	0.707292	−	0.706922i	$-0.249917\pi$
$881$	−7.67467	−	13.2929i	−0.258566	−	0.447850i	−0.965858	+	0.259072i	$0.916583\pi$
$882$	13.9409	−	15.7052i	0.469413	−	0.528821i
$883$	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
$885$	−0.0656803	−	4.58160i	−0.00220782	−	0.154009i
$886$	−18.7651	−	10.8340i	−0.630425	−	0.363976i
$887$	−43.6681			−1.46623			−0.733116	−	0.680104i	$-0.761935\pi$
$887$	−43.6681			−1.46623			−0.733116	+	0.680104i	$0.761935\pi$
$888$	1.97813	+	3.31554i	0.0663817	+	0.111262i
$889$	6.28019	+	14.5255i	0.210631	+	0.487169i
$890$	1.21534	−	2.10502i	0.0407381	−	0.0705605i
$891$	54.9034	−	3.15154i	1.83933	−	0.105581i
$892$	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
$897$	24.5532	−	46.2584i	0.819808	−	1.54452i
$898$	6.23704	−	10.8029i	0.208133	−	0.360496i
$899$	3.86833	+	2.23338i	0.129016	+	0.0744875i
$900$	−13.9492	+	0.400025i	−0.464975	+	0.0133342i
$901$	−25.2671	+	14.5880i	−0.841769	+	0.485996i
$902$		−	9.62510i		−	0.320481i
$903$	−2.69086	+	26.5045i	−0.0895464	+	0.882014i
$904$	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	−0.992026	−	0.126037i	$-0.959774\pi$
$907$	−11.6509	+	20.1799i	−0.386861	+	0.670063i	0.605164	+	0.796101i	$0.293107\pi$
$908$		−	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
$915$	0.0883124	−	0.0526893i	0.00291952	−	0.00174186i
$916$	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	0.844660	−	0.535304i	$-0.179803\pi$
$919$	−1.25071	−	2.16629i	−0.0412570	−	0.0714593i	−0.885917	+	0.463845i	$0.846470\pi$
$920$	2.47474	−	4.28638i	0.0815898	−	0.141318i
$921$	15.2816	−	9.11734i	0.503544	−	0.300427i
$922$	4.17780	+	2.41206i	0.137589	+	0.0794368i
$923$	−6.31543	+	0.134501i	−0.207875	+	0.00442715i
$924$	−2.82831	+	27.8582i	−0.0930444	+	0.916469i
$925$	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	$-0.828042\pi$
$929$	−25.6324	+	14.7989i	−0.840971	+	0.485535i	0.0166234	+	0.999862i	$0.494708\pi$
$930$	1.45572	+	2.43994i	0.0477351	+	0.0800086i
$931$	−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
$936$	10.8032	−	0.540211i	0.353112	−	0.0176574i
$937$		−	27.0251i		−	0.882873i	−0.897293	−	0.441436i	$-0.854469\pi$
$937$		−	27.0251i		−	0.882873i	0.897293	−	0.441436i	$-0.145531\pi$
$938$	21.9701	+	16.3274i	0.717350	+	0.533108i
$939$	−18.8797	+	0.270654i	−0.616117	+	0.00883244i
$940$	−1.68522	−	2.91888i	−0.0549657	−	0.0952034i
$941$	−32.5113	+	18.7704i	−1.05984	+	0.611898i	−0.925387	−	0.379022i	$-0.876260\pi$
$941$	−32.5113	+	18.7704i	−1.05984	+	0.611898i	−0.134451	+	0.990920i	$0.542927\pi$
$942$	2.43269	−	4.35659i	0.0792612	−	0.141945i
$943$	6.60483	+	11.4399i	0.215083	+	0.372534i
$944$		−	4.48228i		−	0.145886i
$945$	4.55539	−	6.71453i	0.148187	−	0.218424i
$946$	−17.7614	−	30.7636i	−0.577473	−	1.00021i
$947$	31.4328			1.02143			0.510714	−	0.859750i	$-0.329381\pi$
$947$	31.4328			1.02143			0.510714	+	0.859750i	$0.329381\pi$
$948$	0.157780	+	11.0061i	0.00512445	+	0.357461i
$949$	18.7850	−	34.1982i	0.609788	−	1.11012i
$950$	−9.18943	+	15.9166i	−0.298144	+	0.516401i
$951$	−0.261815	−	18.2632i	−0.00848993	−	0.592224i
$952$	−20.0965	−	2.33179i	−0.651331	−	0.0755736i
$953$	−47.5409	−	27.4478i	−1.54000	−	0.889120i	−0.998838	−	0.0482023i	$-0.984651\pi$
$953$	−47.5409	−	27.4478i	−1.54000	−	0.889120i	−0.541163	−	0.840918i	$-0.682016\pi$
$954$	−0.328118	−	11.4417i	−0.0106232	−	0.370440i
$955$	6.40911			0.207394
$956$	−17.6869			−0.572034
$957$	8.71492	+	14.6071i	0.281713	+	0.472179i
$958$	10.4595	+	6.03880i	0.337931	+	0.195105i
$959$	55.5774	+	6.44861i	1.79469	+	0.208236i
$960$	1.02216	−	0.0146533i	0.0329901	−	0.000472934i
$961$	11.6377	−	20.1571i	0.375409	−	0.650228i
$962$	−6.87302	+	4.16574i	−0.221595	+	0.134309i
$963$	23.3393	+	12.5971i	0.752100	+	0.405936i
$964$	24.1671			0.778370
$965$	5.67895	+	9.83623i	0.182812	+	0.316640i
$966$	−15.7550	−	35.0517i	−0.506908	−	1.12777i
$967$		−	11.5256i		−	0.370639i	−0.982678	−	0.185320i	$-0.940668\pi$
$967$		−	11.5256i		−	0.370639i	0.982678	−	0.185320i	$-0.0593321\pi$
$968$	−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	0.918323	+	0.395831i	$0.129544\pi$
$971$	24.9898	+	43.2836i	0.801962	+	1.38904i	−0.116362	+	0.993207i	$0.537123\pi$
$972$	−14.0235	−	6.80745i	−0.449804	−	0.218349i
$973$	−22.9100	−	17.0259i	−0.734460	−	0.545824i
$974$			5.59837i			0.179383i
$975$	−1.03478	−	29.0312i	−0.0331394	−	0.929741i
$976$	0.0871190	−	0.0502982i	0.00278861	−	0.00161000i
$977$	2.18839	−	3.79041i	0.0700129	−	0.121266i	−0.828894	−	0.559406i	$-0.811029\pi$
$977$	2.18839	−	3.79041i	0.0700129	−	0.121266i	0.898907	+	0.438140i	$0.144363\pi$
$978$	−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
$981$	−1.47906	−	51.5762i	−0.0472228	−	1.64670i
$982$	0.451495	−	0.260671i	0.0144078	−	0.00831833i
$983$	−22.4448	+	12.9585i	−0.715879	+	0.413313i	−0.813234	−	0.581937i	$-0.802295\pi$
$983$	−22.4448	+	12.9585i	−0.715879	+	0.413313i	0.0973553	+	0.995250i	$0.468962\pi$
$984$	−1.33015	+	2.38210i	−0.0424037	+	0.0759387i
$985$			4.68985i			0.149431i
$986$	−10.6429	+	6.14469i	−0.338940	+	0.195687i
$987$	−26.0355	−	2.64325i	−0.828719	−	0.0841356i
$988$	6.85852	−	12.4860i	0.218199	−	0.397231i
$989$	42.2205	+	24.3760i	1.34254	+	0.775113i
$990$	0.310137	+	10.8147i	0.00985680	+	0.343715i
$991$	−11.5787	+	20.0549i	−0.367810	+	0.637066i	−0.989223	−	0.146418i	$-0.953226\pi$
$991$	−11.5787	+	20.0549i	−0.367810	+	0.637066i	0.621413	+	0.783483i	$0.286559\pi$
$992$	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
$996$	8.05305	+	13.4977i	0.255171	+	0.427691i
$997$		−	9.63696i		−	0.305206i	−0.988288	−	0.152603i	$-0.951234\pi$
$997$		−	9.63696i		−	0.305206i	0.988288	−	0.152603i	$-0.0487655\pi$
$998$	−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.f.257.14	yes	34
3.2	odd	2		546.2.bi.e.257.9	yes	34
7.3	odd	6		546.2.bn.e.101.13	yes	34
13.4	even	6		546.2.bn.f.173.5	yes	34
21.17	even	6		546.2.bn.f.101.5	yes	34
39.17	odd	6		546.2.bn.e.173.13	yes	34
91.17	odd	6		546.2.bi.e.17.9	✓	34
273.17	even	6	inner	546.2.bi.f.17.14	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.9	✓	34	91.17	odd	6
546.2.bi.e.257.9	yes	34	3.2	odd	2
546.2.bi.f.17.14	yes	34	273.17	even	6	inner
546.2.bi.f.257.14	yes	34	1.1	even	1	trivial
546.2.bn.e.101.13	yes	34	7.3	odd	6
546.2.bn.e.173.13	yes	34	39.17	odd	6
546.2.bn.f.101.5	yes	34	21.17	even	6
546.2.bn.f.173.5	yes	34	13.4	even	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.48743 - 0.887438i) q^{3} +1.00000 q^{4} +(0.511132 + 0.295102i) q^{5} +(1.48743 - 0.887438i) q^{6} +(2.62812 + 0.304939i) q^{7} +1.00000 q^{8} +(1.42491 - 2.64001i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.48743 - 0.887438i) q^{3} +1.00000 q^{4} +(0.511132 + 0.295102i) q^{5} +(1.48743 - 0.887438i) q^{6} +(2.62812 + 0.304939i) q^{7} +1.00000 q^{8} +(1.42491 - 2.64001i) q^{9} +(0.511132 + 0.295102i) q^{10} +(-3.05521 + 5.29178i) q^{11} +(1.48743 - 0.887438i) q^{12} +(1.86885 + 3.08341i) q^{13} +(2.62812 + 0.304939i) q^{14} +(1.02216 - 0.0146533i) q^{15} +1.00000 q^{16} -7.64672 q^{17} +(1.42491 - 2.64001i) q^{18} +(-1.97552 - 3.42169i) q^{19} +(0.511132 + 0.295102i) q^{20} +(4.17976 - 1.87872i) q^{21} +(-3.05521 + 5.29178i) q^{22} -8.38604i q^{23} +(1.48743 - 0.887438i) 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} +(1.02216 - 0.0146533i) q^{30} +(1.38966 + 2.40696i) q^{31} +1.00000 q^{32} +(0.151707 + 10.5825i) q^{33} -7.64672 q^{34} +(1.25333 + 0.931429i) q^{35} +(1.42491 - 2.64001i) q^{36} +2.22904i q^{37} +(-1.97552 - 3.42169i) q^{38} +(5.51612 + 2.92787i) q^{39} +(0.511132 + 0.295102i) q^{40} +(-1.36416 + 0.787598i) q^{41} +(4.17976 - 1.87872i) 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} +(1.48743 - 0.887438i) q^{48} +(6.81402 + 1.60283i) q^{49} +(-2.32583 - 4.02845i) q^{50} +(-11.3740 + 6.78599i) 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} +(1.02216 - 0.0146533i) q^{60} +(0.0871190 - 0.0502982i) q^{61} +(1.38966 + 2.40696i) q^{62} +(4.54987 - 6.50374i) q^{63} +1.00000 q^{64} +(0.0453104 + 2.12753i) q^{65} +(0.151707 + 10.5825i) q^{66} +(8.95985 + 5.17297i) q^{67} -7.64672 q^{68} +(-7.44209 - 12.4737i) q^{69} +(1.25333 + 0.931429i) q^{70} +(-0.875991 + 1.51726i) q^{71} +(1.42491 - 2.64001i) 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} +(5.51612 + 2.92787i) q^{78} +(-3.17751 + 5.50361i) q^{79} +(0.511132 + 0.295102i) q^{80} +(-4.93927 - 7.52354i) q^{81} +(-1.36416 + 0.787598i) q^{82} +9.07449i q^{83} +(4.17976 - 1.87872i) 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} +(1.48743 - 0.887438i) q^{96} +(-2.82580 + 4.89442i) q^{97} +(6.81402 + 1.60283i) q^{98} +(9.61693 + 15.6061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * 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 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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