LMFDB - Embedded newform 1183.2.e.k.170.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.11
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.k.508.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.294236 + 0.509631i) q^{2} +(-0.386839 - 0.670024i) q^{3} +(0.826851 + 1.43215i) q^{4} +(-1.34801 + 2.33482i) q^{5} +0.455287 q^{6} +(-2.52472 - 0.791073i) q^{7} -2.15010 q^{8} +(1.20071 - 2.07969i) q^{9} +O(q^{10})$	\(q+(-0.294236 + 0.509631i) q^{2} +(-0.386839 - 0.670024i) q^{3} +(0.826851 + 1.43215i) q^{4} +(-1.34801 + 2.33482i) q^{5} +0.455287 q^{6} +(-2.52472 - 0.791073i) q^{7} -2.15010 q^{8} +(1.20071 - 2.07969i) q^{9} +(-0.793264 - 1.37397i) q^{10} +(-1.34641 - 2.33205i) q^{11} +(0.639715 - 1.10802i) q^{12} +(1.14602 - 1.05391i) q^{14} +2.08585 q^{15} +(-1.02107 + 1.76854i) q^{16} +(0.237613 + 0.411557i) q^{17} +(0.706584 + 1.22384i) q^{18} +(0.980747 - 1.69870i) q^{19} -4.45841 q^{20} +(0.446620 + 1.99764i) q^{21} +1.58464 q^{22} +(2.86140 - 4.95610i) q^{23} +(0.831741 + 1.44062i) q^{24} +(-1.13425 - 1.96458i) q^{25} -4.17896 q^{27} +(-0.954632 - 4.26987i) q^{28} +1.40991 q^{29} +(-0.613730 + 1.06301i) q^{30} +(-1.65548 - 2.86737i) q^{31} +(-2.75097 - 4.76481i) q^{32} +(-1.04168 + 1.80425i) q^{33} -0.279656 q^{34} +(5.25035 - 4.82838i) q^{35} +3.97124 q^{36} +(5.44364 - 9.42866i) q^{37} +(0.577141 + 0.999638i) q^{38} +(2.89835 - 5.02009i) q^{40} +11.6603 q^{41} +(-1.14947 - 0.360165i) q^{42} -9.43290 q^{43} +(2.22656 - 3.85651i) q^{44} +(3.23714 + 5.60689i) q^{45} +(1.68385 + 2.91652i) q^{46} +(-4.49357 + 7.78310i) q^{47} +1.57995 q^{48} +(5.74841 + 3.99447i) q^{49} +1.33495 q^{50} +(0.183835 - 0.318412i) q^{51} +(2.15184 + 3.72710i) q^{53} +(1.22960 - 2.12973i) q^{54} +7.25987 q^{55} +(5.42839 + 1.70089i) q^{56} -1.51756 q^{57} +(-0.414845 + 0.718533i) q^{58} +(4.96188 + 8.59422i) q^{59} +(1.72468 + 2.98724i) q^{60} +(4.98418 - 8.63285i) q^{61} +1.94840 q^{62} +(-4.67665 + 4.30079i) q^{63} -0.846536 q^{64} +(-0.613001 - 1.06175i) q^{66} +(-1.70475 - 2.95272i) q^{67} +(-0.392940 + 0.680592i) q^{68} -4.42761 q^{69} +(0.915854 + 4.09643i) q^{70} -5.27688 q^{71} +(-2.58165 + 4.47155i) q^{72} +(-2.10930 - 3.65342i) q^{73} +(3.20343 + 5.54850i) q^{74} +(-0.877543 + 1.51995i) q^{75} +3.24373 q^{76} +(1.55448 + 6.95286i) q^{77} +(7.39741 - 12.8127i) q^{79} +(-2.75281 - 4.76801i) q^{80} +(-1.98555 - 3.43908i) q^{81} +(-3.43088 + 5.94246i) q^{82} -4.99284 q^{83} +(-2.49163 + 2.29138i) q^{84} -1.28121 q^{85} +(2.77550 - 4.80730i) q^{86} +(-0.545407 - 0.944672i) q^{87} +(2.89491 + 5.01413i) q^{88} +(1.83625 - 3.18048i) q^{89} -3.80993 q^{90} +9.46382 q^{92} +(-1.28080 + 2.21842i) q^{93} +(-2.64434 - 4.58013i) q^{94} +(2.64411 + 4.57973i) q^{95} +(-2.12836 + 3.68643i) q^{96} +17.3995 q^{97} +(-3.72709 + 1.75425i) q^{98} -6.46659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.294236	+	0.509631i	−0.208056	+	0.360364i	−0.951102	−	0.308877i	$-0.900047\pi$
$2$	−0.294236	+	0.509631i	−0.208056	+	0.360364i	0.743046	+	0.669240i	$0.233380\pi$
$3$	−0.386839	−	0.670024i	−0.223341	−	0.386839i	0.732479	−	0.680789i	$-0.238363\pi$
$3$	−0.386839	−	0.670024i	−0.223341	−	0.386839i	−0.955821	+	0.293951i	$0.905030\pi$
$4$	0.826851	+	1.43215i	0.413425	+	0.716074i
$5$	−1.34801	+	2.33482i	−0.602847	+	1.04416i	0.389540	+	0.921009i	$0.372634\pi$
$5$	−1.34801	+	2.33482i	−0.602847	+	1.04416i	−0.992388	+	0.123153i	$0.960699\pi$
$6$	0.455287			0.185870
$7$	−2.52472	−	0.791073i	−0.954254	−	0.298998i
$7$	−2.52472	−	0.791073i	−0.954254	−	0.298998i
$8$	−2.15010			−0.760175
$9$	1.20071	−	2.07969i	0.400237	−	0.693231i
$10$	−0.793264	−	1.37397i	−0.250852	−	0.434488i
$11$	−1.34641	−	2.33205i	−0.405957	−	0.703138i	0.588475	−	0.808515i	$-0.299728\pi$
$11$	−1.34641	−	2.33205i	−0.405957	−	0.703138i	−0.994432	+	0.105377i	$0.966395\pi$
$12$	0.639715	−	1.10802i	0.184670	−	0.319858i
$13$		0			0
$13$		0			0
$14$	1.14602	−	1.05391i	0.306286	−	0.281670i
$15$	2.08585			0.538563
$16$	−1.02107	+	1.76854i	−0.255267	+	0.442135i
$17$	0.237613	+	0.411557i	0.0576295	+	0.0998172i	0.893401	−	0.449260i	$-0.148312\pi$
$17$	0.237613	+	0.411557i	0.0576295	+	0.0998172i	−0.835771	+	0.549078i	$0.814979\pi$
$18$	0.706584	+	1.22384i	0.166544	+	0.288462i
$19$	0.980747	−	1.69870i	0.224999	−	0.389709i	−0.731320	−	0.682034i	$-0.761096\pi$
$19$	0.980747	−	1.69870i	0.224999	−	0.389709i	0.956319	+	0.292325i	$0.0944289\pi$
$20$	−4.45841			−0.996930
$21$	0.446620	+	1.99764i	0.0974605	+	0.435921i
$22$	1.58464			0.337847
$23$	2.86140	−	4.95610i	0.596644	−	1.03342i	−0.396669	−	0.917962i	$-0.629834\pi$
$23$	2.86140	−	4.95610i	0.596644	−	1.03342i	0.993313	−	0.115456i	$-0.0368329\pi$
$24$	0.831741	+	1.44062i	0.169778	+	0.294065i
$25$	−1.13425	−	1.96458i	−0.226850	−	0.392916i
$26$		0			0
$27$	−4.17896			−0.804241
$28$	−0.954632	−	4.26987i	−0.180408	−	0.806929i
$29$	1.40991			0.261813			0.130907	−	0.991395i	$-0.458211\pi$
$29$	1.40991			0.261813			0.130907	+	0.991395i	$0.458211\pi$
$30$	−0.613730	+	1.06301i	−0.112051	+	0.194078i
$31$	−1.65548	−	2.86737i	−0.297333	−	0.514995i	0.678192	−	0.734885i	$-0.262764\pi$
$31$	−1.65548	−	2.86737i	−0.297333	−	0.514995i	−0.975525	+	0.219889i	$0.929430\pi$
$32$	−2.75097	−	4.76481i	−0.486307	−	0.842308i
$33$	−1.04168	+	1.80425i	−0.181334	+	0.314080i
$34$	−0.279656			−0.0479607
$35$	5.25035	−	4.82838i	0.887472	−	0.816146i
$36$	3.97124			0.661873
$37$	5.44364	−	9.42866i	0.894929	−	1.55006i	0.0610370	−	0.998136i	$-0.480559\pi$
$37$	5.44364	−	9.42866i	0.894929	−	1.55006i	0.833892	−	0.551927i	$-0.186107\pi$
$38$	0.577141	+	0.999638i	0.0936247	+	0.162163i
$39$		0			0
$40$	2.89835	−	5.02009i	0.458269	−	0.793746i
$41$	11.6603			1.82103			0.910517	−	0.413471i	$-0.135684\pi$
$41$	11.6603			1.82103			0.910517	+	0.413471i	$0.135684\pi$
$42$	−1.14947	−	0.360165i	−0.177367	−	0.0555747i
$43$	−9.43290			−1.43850			−0.719252	−	0.694749i	$-0.755515\pi$
$43$	−9.43290			−1.43850			−0.719252	+	0.694749i	$0.755515\pi$
$44$	2.22656	−	3.85651i	0.335666	−	0.581390i
$45$	3.23714	+	5.60689i	0.482564	+	0.835825i
$46$	1.68385	+	2.91652i	0.248271	+	0.430018i
$47$	−4.49357	+	7.78310i	−0.655455	+	1.13528i	0.326324	+	0.945258i	$0.394190\pi$
$47$	−4.49357	+	7.78310i	−0.655455	+	1.13528i	−0.981779	+	0.190024i	$0.939143\pi$
$48$	1.57995			0.228046
$49$	5.74841	+	3.99447i	0.821201	+	0.570639i
$50$	1.33495			0.188790
$51$	0.183835	−	0.318412i	0.0257421	−	0.0445866i
$52$		0			0
$53$	2.15184	+	3.72710i	0.295578	+	0.511956i	0.975119	−	0.221681i	$-0.0711545\pi$
$53$	2.15184	+	3.72710i	0.295578	+	0.511956i	−0.679541	+	0.733637i	$0.737821\pi$
$54$	1.22960	−	2.12973i	0.167327	−	0.289819i
$55$	7.25987			0.978920
$56$	5.42839	+	1.70089i	0.725399	+	0.227290i
$57$	−1.51756			−0.201006
$58$	−0.414845	+	0.718533i	−0.0544718	+	0.0943480i
$59$	4.96188	+	8.59422i	0.645981	+	1.11887i	0.984074	+	0.177759i	$0.0568849\pi$
$59$	4.96188	+	8.59422i	0.645981	+	1.11887i	−0.338093	+	0.941113i	$0.609782\pi$
$60$	1.72468	+	2.98724i	0.222656	+	0.385651i
$61$	4.98418	−	8.63285i	0.638158	−	1.10532i	−0.347678	−	0.937614i	$-0.613030\pi$
$61$	4.98418	−	8.63285i	0.638158	−	1.10532i	0.985837	−	0.167709i	$-0.0536368\pi$
$62$	1.94840			0.247447
$63$	−4.67665	+	4.30079i	−0.589203	+	0.541849i
$64$	−0.846536			−0.105817
$65$		0			0
$66$	−0.613001	−	1.06175i	−0.0754552	−	0.130692i
$67$	−1.70475	−	2.95272i	−0.208269	−	0.360732i	0.742901	−	0.669402i	$-0.233449\pi$
$67$	−1.70475	−	2.95272i	−0.208269	−	0.360732i	−0.951169	+	0.308670i	$0.900116\pi$
$68$	−0.392940	+	0.680592i	−0.0476510	+	0.0825339i
$69$	−4.42761			−0.533021
$70$	0.915854	+	4.09643i	0.109466	+	0.489616i
$71$	−5.27688			−0.626250			−0.313125	−	0.949712i	$-0.601376\pi$
$71$	−5.27688			−0.626250			−0.313125	+	0.949712i	$0.601376\pi$
$72$	−2.58165	+	4.47155i	−0.304250	+	0.526977i
$73$	−2.10930	−	3.65342i	−0.246875	−	0.427601i	0.715782	−	0.698324i	$-0.246071\pi$
$73$	−2.10930	−	3.65342i	−0.246875	−	0.427601i	−0.962657	+	0.270723i	$0.912737\pi$
$74$	3.20343	+	5.54850i	0.372391	+	0.645000i
$75$	−0.877543	+	1.51995i	−0.101330	+	0.175509i
$76$	3.24373			0.372081
$77$	1.55448	+	6.95286i	0.177149	+	0.792352i
$78$		0			0
$79$	7.39741	−	12.8127i	0.832274	−	1.44154i	−0.0639570	−	0.997953i	$-0.520372\pi$
$79$	7.39741	−	12.8127i	0.832274	−	1.44154i	0.896231	−	0.443588i	$-0.146295\pi$
$80$	−2.75281	−	4.76801i	−0.307774	−	0.533079i
$81$	−1.98555	−	3.43908i	−0.220617	−	0.382120i
$82$	−3.43088	+	5.94246i	−0.378877	+	0.656235i
$83$	−4.99284			−0.548036			−0.274018	−	0.961725i	$-0.588353\pi$
$83$	−4.99284			−0.548036			−0.274018	+	0.961725i	$0.588353\pi$
$84$	−2.49163	+	2.29138i	−0.271859	+	0.250010i
$85$	−1.28121			−0.138967
$86$	2.77550	−	4.80730i	0.299289	−	0.518385i
$87$	−0.545407	−	0.944672i	−0.0584737	−	0.101279i
$88$	2.89491	+	5.01413i	0.308598	+	0.534508i
$89$	1.83625	−	3.18048i	0.194642	−	0.337130i	−0.752141	−	0.659002i	$-0.770979\pi$
$89$	1.83625	−	3.18048i	0.194642	−	0.337130i	0.946783	+	0.321872i	$0.104312\pi$
$90$	−3.80993			−0.401601
$91$		0			0
$92$	9.46382			0.986671
$93$	−1.28080	+	2.21842i	−0.132813	+	0.230039i
$94$	−2.64434	−	4.58013i	−0.272743	−	0.472404i
$95$	2.64411	+	4.57973i	0.271280	+	0.469871i
$96$	−2.12836	+	3.68643i	−0.217225	+	0.376244i
$97$	17.3995			1.76665			0.883327	−	0.468758i	$-0.155298\pi$
$97$	17.3995			1.76665			0.883327	+	0.468758i	$0.155298\pi$
$98$	−3.72709	+	1.75425i	−0.376493	+	0.177206i
$99$	−6.46659			−0.649917
$100$	1.87571	−	3.24883i	0.187571	−	0.324883i
$101$	−8.48974	−	14.7047i	−0.844761	−	1.46317i	−0.885829	−	0.464013i	$-0.846409\pi$
$101$	−8.48974	−	14.7047i	−0.844761	−	1.46317i	0.0410676	−	0.999156i	$-0.486924\pi$
$102$	0.108182	+	0.187376i	0.0107116	+	0.0185530i
$103$	7.90401	−	13.6901i	0.778805	−	1.34893i	−0.153826	−	0.988098i	$-0.549160\pi$
$103$	7.90401	−	13.6901i	0.778805	−	1.34893i	0.932631	−	0.360832i	$-0.117507\pi$
$104$		0			0
$105$	−5.26617	−	1.65006i	−0.513926	−	0.161029i
$106$	−2.53259			−0.245987
$107$	−0.0292811	+	0.0507164i	−0.00283071	+	0.00490294i	−0.867437	−	0.497547i	$-0.834234\pi$
$107$	−0.0292811	+	0.0507164i	−0.00283071	+	0.00490294i	0.864607	+	0.502449i	$0.167568\pi$
$108$	−3.45537	−	5.98488i	−0.332494	−	0.575896i
$109$	−3.08252	−	5.33907i	−0.295251	−	0.511391i	0.679792	−	0.733405i	$-0.262070\pi$
$109$	−3.08252	−	5.33907i	−0.295251	−	0.511391i	−0.975043	+	0.222015i	$0.928737\pi$
$110$	−2.13611	+	3.69985i	−0.203670	+	0.352767i
$111$	−8.42324			−0.799499
$112$	3.97695	−	3.65732i	0.375786	−	0.345585i
$113$	−5.85802			−0.551076			−0.275538	−	0.961290i	$-0.588856\pi$
$113$	−5.85802			−0.551076			−0.275538	+	0.961290i	$0.588856\pi$
$114$	0.446521	−	0.773397i	0.0418205	−	0.0724353i
$115$	7.71439	+	13.3617i	0.719371	+	1.24599i
$116$	1.16578	+	2.01920i	0.108240	+	0.187478i
$117$		0			0
$118$	−5.83984			−0.537601
$119$	−0.274333	−	1.22703i	−0.0251481	−	0.112482i
$120$	−4.48477			−0.409402
$121$	1.87438	−	3.24652i	0.170398	−	0.295138i
$122$	2.93304	+	5.08018i	0.265545	+	0.459938i
$123$	−4.51066	−	7.81269i	−0.406712	−	0.704446i
$124$	2.73767	−	4.74178i	0.245850	−	0.425824i
$125$	−7.36417			−0.658671
$126$	−0.815779	−	3.64881i	−0.0726754	−	0.325062i
$127$	−20.5054			−1.81956			−0.909781	−	0.415090i	$-0.863750\pi$
$127$	−20.5054			−1.81956			−0.909781	+	0.415090i	$0.863750\pi$
$128$	5.75101	−	9.96105i	0.508323	−	0.880441i
$129$	3.64901	+	6.32027i	0.321277	+	0.556469i
$130$		0			0
$131$	−5.54177	+	9.59863i	−0.484187	+	0.838636i	−0.999835	−	0.0181644i	$-0.994218\pi$
$131$	−5.54177	+	9.59863i	−0.484187	+	0.838636i	0.515648	+	0.856800i	$0.327551\pi$
$132$	−3.44527			−0.299872
$133$	−3.81991	+	3.51291i	−0.331228	+	0.304608i
$134$	2.00639			0.173326
$135$	5.63327	−	9.75711i	0.484834	−	0.839758i
$136$	−0.510890	−	0.884888i	−0.0438085	−	0.0758785i
$137$	−4.81770	−	8.34449i	−0.411603	−	0.712918i	0.583462	−	0.812141i	$-0.301698\pi$
$137$	−4.81770	−	8.34449i	−0.411603	−	0.712918i	−0.995065	+	0.0992224i	$0.968364\pi$
$138$	1.30276	−	2.25645i	0.110898	−	0.192081i
$139$	−4.71596			−0.400003			−0.200001	−	0.979796i	$-0.564095\pi$
$139$	−4.71596			−0.400003			−0.200001	+	0.979796i	$0.564095\pi$
$140$	11.2562	+	3.52693i	0.951324	+	0.298080i
$141$	6.95315			0.585561
$142$	1.55265	−	2.68926i	0.130295	−	0.225678i
$143$		0			0
$144$	2.45201	+	4.24701i	0.204334	+	0.353918i
$145$	−1.90057	+	3.29188i	−0.157833	+	0.273376i
$146$	2.48253			0.205456
$147$	0.452689	−	5.39679i	0.0373372	−	0.445119i
$148$	18.0043			1.47995
$149$	4.72571	−	8.18517i	0.387145	−	0.670555i	−0.604919	−	0.796287i	$-0.706794\pi$
$149$	4.72571	−	8.18517i	0.387145	−	0.670555i	0.992064	+	0.125732i	$0.0401278\pi$
$150$	−0.516409	−	0.894446i	−0.0421646	−	0.0730312i
$151$	−0.448026	−	0.776004i	−0.0364599	−	0.0631503i	0.847220	−	0.531243i	$-0.178275\pi$
$151$	−0.448026	−	0.776004i	−0.0364599	−	0.0631503i	−0.883680	+	0.468092i	$0.844941\pi$
$152$	−2.10870	+	3.65238i	−0.171038	+	0.296247i
$153$	1.14122			0.0922619
$154$	−4.00078	−	1.25357i	−0.322392	−	0.101015i
$155$	8.92639			0.716985
$156$		0			0
$157$	8.35947	+	14.4790i	0.667158	+	1.15555i	0.978695	+	0.205318i	$0.0658229\pi$
$157$	8.35947	+	14.4790i	0.667158	+	1.15555i	−0.311537	+	0.950234i	$0.600844\pi$
$158$	4.35316	+	7.53990i	0.346319	+	0.599842i
$159$	1.66483	−	2.88357i	0.132030	−	0.228682i
$160$	14.8333			1.17268
$161$	−11.1449	+	10.2492i	−0.878339	+	0.807748i
$162$	2.33688			0.183603
$163$	5.55604	−	9.62335i	0.435183	−	0.753759i	−0.562128	−	0.827051i	$-0.690017\pi$
$163$	5.55604	−	9.62335i	0.435183	−	0.753759i	0.997311	+	0.0732915i	$0.0233503\pi$
$164$	9.64134	+	16.6993i	0.752862	+	1.30400i
$165$	−2.80840	−	4.86429i	−0.218633	−	0.378684i
$166$	1.46907	−	2.54451i	0.114022	−	0.197492i
$167$	−15.4628			−1.19655			−0.598275	−	0.801291i	$-0.704147\pi$
$167$	−15.4628			−1.19655			−0.598275	+	0.801291i	$0.704147\pi$
$168$	−0.960277	−	4.29512i	−0.0740870	−	0.331376i
$169$		0			0
$170$	0.376979	−	0.652946i	0.0289130	−	0.0500787i
$171$	−2.35519	−	4.07931i	−0.180106	−	0.311952i
$172$	−7.79960	−	13.5093i	−0.594714	−	1.03008i
$173$	−0.851417	+	1.47470i	−0.0647320	+	0.112119i	−0.896575	−	0.442892i	$-0.853953\pi$
$173$	−0.851417	+	1.47470i	−0.0647320	+	0.112119i	0.831843	+	0.555011i	$0.187286\pi$
$174$	0.641912			0.0486632
$175$	1.30954	+	5.85728i	0.0989916	+	0.442769i
$176$	5.49908			0.414509
$177$	3.83889	−	6.64915i	0.288549	−	0.499781i
$178$	1.08058	+	1.87162i	0.0809930	+	0.140284i
$179$	−5.29384	−	9.16919i	−0.395680	−	0.685338i	0.597508	−	0.801863i	$-0.296158\pi$
$179$	−5.29384	−	9.16919i	−0.395680	−	0.685338i	−0.993188	+	0.116525i	$0.962824\pi$
$180$	−5.35326	+	9.27212i	−0.399008	+	0.691103i
$181$	−18.5361			−1.37777			−0.688887	−	0.724868i	$-0.741901\pi$
$181$	−18.5361			−1.37777			−0.688887	+	0.724868i	$0.741901\pi$
$182$		0			0
$183$	−7.71228			−0.570108
$184$	−6.15230	+	10.6561i	−0.453554	+	0.785578i
$185$	14.6761	+	25.4198i	1.07901	+	1.86890i
$186$	−0.753717	−	1.30548i	−0.0552652	−	0.0957221i
$187$	0.639846	−	1.10825i	0.0467902	−	0.0810430i
$188$	−14.8621			−1.08393
$189$	10.5507	+	3.30586i	0.767450	+	0.240466i
$190$	−3.11196			−0.225766
$191$	−9.74690	+	16.8821i	−0.705261	+	1.22155i	0.261336	+	0.965248i	$0.415837\pi$
$191$	−9.74690	+	16.8821i	−0.705261	+	1.22155i	−0.966597	+	0.256300i	$0.917497\pi$
$192$	0.327473	+	0.567199i	0.0236333	+	0.0409341i
$193$	−3.87886	−	6.71838i	−0.279206	−	0.483600i	0.691981	−	0.721915i	$-0.256738\pi$
$193$	−3.87886	−	6.71838i	−0.279206	−	0.483600i	−0.971188	+	0.238316i	$0.923405\pi$
$194$	−5.11956	+	8.86734i	−0.367563	+	0.636638i
$195$		0			0
$196$	−0.967604	+	11.5354i	−0.0691145	+	0.823957i
$197$	−1.03890			−0.0740184			−0.0370092	−	0.999315i	$-0.511783\pi$
$197$	−1.03890			−0.0740184			−0.0370092	+	0.999315i	$0.511783\pi$
$198$	1.90270	−	3.29557i	0.135219	−	0.234206i
$199$	−6.67052	−	11.5537i	−0.472860	−	0.819018i	0.526657	−	0.850078i	$-0.323445\pi$
$199$	−6.67052	−	11.5537i	−0.472860	−	0.819018i	−0.999518	+	0.0310595i	$0.990112\pi$
$200$	2.43875	+	4.22404i	0.172446	+	0.298685i
$201$	−1.31893	+	2.28445i	−0.0930299	+	0.161133i
$202$	9.99194			0.703030
$203$	−3.55962	−	1.11534i	−0.249836	−	0.0782816i
$204$	0.608018			0.0425697
$205$	−15.7182	+	27.2247i	−1.09781	+	1.90146i
$206$	4.65128	+	8.05625i	0.324070	+	0.561306i
$207$	−6.87144	−	11.9017i	−0.477598	−	0.827225i
$208$		0			0
$209$	−5.28194			−0.365359
$210$	2.39042	−	2.19830i	0.164954	−	0.151697i
$211$	2.17164			0.149502			0.0747510	−	0.997202i	$-0.476184\pi$
$211$	2.17164			0.149502			0.0747510	+	0.997202i	$0.476184\pi$
$212$	−3.55850	+	6.16350i	−0.244399	+	0.423311i
$213$	2.04130	+	3.53563i	0.139868	+	0.242258i
$214$	−0.0172311	−	0.0298451i	−0.00117789	−	0.00204017i
$215$	12.7156	−	22.0241i	0.867199	−	1.50203i
$216$	8.98517			0.611363
$217$	1.91131	+	8.54891i	0.129748	+	0.580338i
$218$	3.62794			0.245715
$219$	−1.63192	+	2.82657i	−0.110275	+	0.191002i
$220$	6.00283	+	10.3972i	0.404711	+	0.700979i
$221$		0			0
$222$	2.47842	−	4.29275i	0.166340	−	0.288110i
$223$	1.36259			0.0912459			0.0456229	−	0.998959i	$-0.485473\pi$
$223$	1.36259			0.0912459			0.0456229	+	0.998959i	$0.485473\pi$
$224$	3.17610	+	14.2060i	0.212212	+	0.949180i
$225$	−5.44763			−0.363175
$226$	1.72364	−	2.98543i	0.114655	−	0.198588i
$227$	3.14026	+	5.43909i	0.208427	+	0.361005i	0.951219	−	0.308516i	$-0.0998324\pi$
$227$	3.14026	+	5.43909i	0.208427	+	0.361005i	−0.742792	+	0.669522i	$0.766499\pi$
$228$	−1.25480	−	2.17337i	−0.0831010	−	0.143935i
$229$	10.1390	−	17.5612i	0.670001	−	1.16048i	−0.307902	−	0.951418i	$-0.599627\pi$
$229$	10.1390	−	17.5612i	0.670001	−	1.16048i	0.977903	−	0.209058i	$-0.0670397\pi$
$230$	−9.07939			−0.598678
$231$	4.05725	−	3.73117i	0.266948	−	0.245493i
$232$	−3.03144			−0.199024
$233$	2.68683	−	4.65373i	0.176020	−	0.304876i	−0.764494	−	0.644631i	$-0.777011\pi$
$233$	2.68683	−	4.65373i	0.176020	−	0.304876i	0.940514	+	0.339755i	$0.110344\pi$
$234$		0			0
$235$	−12.1147	−	20.9834i	−0.790279	−	1.36880i
$236$	−8.20546	+	14.2123i	−0.534130	+	0.925140i
$237$	−11.4464			−0.743525
$238$	0.706053	+	0.221229i	0.0457666	+	0.0143401i
$239$	5.82294			0.376654			0.188327	−	0.982106i	$-0.439693\pi$
$239$	5.82294			0.376654			0.188327	+	0.982106i	$0.439693\pi$
$240$	−2.12979	+	3.68890i	−0.137477	+	0.238117i
$241$	10.7362	+	18.5956i	0.691579	+	1.19785i	0.971320	+	0.237774i	$0.0764179\pi$
$241$	10.7362	+	18.5956i	0.691579	+	1.19785i	−0.279742	+	0.960075i	$0.590249\pi$
$242$	1.10302	+	1.91048i	0.0709046	+	0.122810i
$243$	−7.80461	+	13.5180i	−0.500666	+	0.867179i
$244$	16.4847			1.05532
$245$	−17.0753	+	8.03690i	−1.09090	+	0.513459i
$246$	5.30878			0.338476
$247$		0			0
$248$	3.55944	+	6.16513i	0.226025	+	0.391486i
$249$	1.93142	+	3.34532i	0.122399	+	0.212001i
$250$	2.16680	−	3.75301i	0.137040	−	0.237361i
$251$	14.3859			0.908030			0.454015	−	0.890994i	$-0.349991\pi$
$251$	14.3859			0.908030			0.454015	+	0.890994i	$0.349991\pi$
$252$	−10.0263	−	3.14154i	−0.631595	−	0.197898i
$253$	−15.4105			−0.968847
$254$	6.03342	−	10.4502i	0.378571	−	0.655704i
$255$	0.495623	+	0.858444i	0.0310371	+	0.0537579i
$256$	2.53777	+	4.39555i	0.158611	+	0.274722i
$257$	−4.13309	+	7.15873i	−0.257815	+	0.446549i	−0.965656	−	0.259823i	$-0.916336\pi$
$257$	−4.13309	+	7.15873i	−0.257815	+	0.446549i	0.707841	+	0.706372i	$0.249669\pi$
$258$	−4.29468			−0.267375
$259$	−21.2024	+	19.4984i	−1.31745	+	1.21157i
$260$		0			0
$261$	1.69289	−	2.93218i	0.104787	−	0.181497i
$262$	−3.26117	−	5.64852i	−0.201476	−	0.348966i
$263$	8.27978	+	14.3410i	0.510553	+	0.884304i	0.999925	+	0.0122288i	$0.00389265\pi$
$263$	8.27978	+	14.3410i	0.510553	+	0.884304i	−0.489372	+	0.872075i	$0.662774\pi$
$264$	2.23972	−	3.87931i	0.137845	−	0.238755i
$265$	−11.6028			−0.712753
$266$	−0.666332	−	2.98037i	−0.0408555	−	0.182738i
$267$	−2.84133			−0.173887
$268$	2.81915	−	4.88291i	0.172207	−	0.298271i
$269$	10.2182	+	17.6985i	0.623017	+	1.07910i	0.988921	+	0.148444i	$0.0474264\pi$
$269$	10.2182	+	17.6985i	0.623017	+	1.07910i	−0.365904	+	0.930652i	$0.619240\pi$
$270$	3.31502	+	5.74178i	0.201745	+	0.349433i
$271$	1.45764	−	2.52470i	0.0885452	−	0.153365i	−0.818351	−	0.574718i	$-0.805112\pi$
$271$	1.45764	−	2.52470i	0.0885452	−	0.153365i	0.906896	+	0.421354i	$0.138445\pi$
$272$	−0.970472			−0.0588435
$273$		0			0
$274$	5.67015			0.342546
$275$	−3.05432	+	5.29024i	−0.184183	+	0.319014i
$276$	−3.66097	−	6.34099i	−0.220364	−	0.381682i
$277$	−4.14928	−	7.18677i	−0.249306	−	0.431811i	0.714027	−	0.700118i	$-0.246869\pi$
$277$	−4.14928	−	7.18677i	−0.249306	−	0.431811i	−0.963333	+	0.268307i	$0.913536\pi$
$278$	1.38760	−	2.40340i	0.0832229	−	0.144146i
$279$	−7.95101			−0.476014
$280$	−11.2888	+	10.3815i	−0.674633	+	0.620413i
$281$	13.3030			0.793593			0.396796	−	0.917907i	$-0.370122\pi$
$281$	13.3030			0.793593			0.396796	+	0.917907i	$0.370122\pi$
$282$	−2.04586	+	3.54354i	−0.121829	+	0.211015i
$283$	−4.38781	−	7.59992i	−0.260828	−	0.451768i	0.705634	−	0.708577i	$-0.250662\pi$
$283$	−4.38781	−	7.59992i	−0.260828	−	0.451768i	−0.966462	+	0.256809i	$0.917329\pi$
$284$	−4.36319	−	7.55727i	−0.258908	−	0.448441i
$285$	2.04569	−	3.54323i	0.121176	−	0.209883i
$286$		0			0
$287$	−29.4390	−	9.22416i	−1.73773	−	0.544485i
$288$	−13.2125			−0.778552
$289$	8.38708	−	14.5268i	0.493358	−	0.854521i
$290$	−1.11843	−	1.93718i	−0.0656764	−	0.113755i
$291$	−6.73080	−	11.6581i	−0.394567	−	0.683410i
$292$	3.48816	−	6.04167i	0.204129	−	0.353562i
$293$	−9.29629			−0.543095			−0.271547	−	0.962425i	$-0.587535\pi$
$293$	−9.29629			−0.543095			−0.271547	+	0.962425i	$0.587535\pi$
$294$	2.61717	+	1.81863i	0.152637	+	0.106065i
$295$	−26.7546			−1.55771
$296$	−11.7044	+	20.2726i	−0.680302	+	1.17832i
$297$	5.62658	+	9.74552i	0.326487	+	0.565492i
$298$	2.78095	+	4.81674i	0.161096	+	0.279026i
$299$		0			0
$300$	−2.90239			−0.167570
$301$	23.8154	+	7.46212i	1.37270	+	0.430109i
$302$	0.527301			0.0303428
$303$	−6.56832	+	11.3767i	−0.377340	+	0.653572i
$304$	2.00281	+	3.46898i	0.114869	+	0.198959i
$305$	13.4374	+	23.2743i	0.769424	+	1.33268i
$306$	−0.335787	+	0.581599i	−0.0191956	+	0.0332478i
$307$	6.62280			0.377983			0.188992	−	0.981979i	$-0.439478\pi$
$307$	6.62280			0.377983			0.188992	+	0.981979i	$0.439478\pi$
$308$	−8.67221	+	7.97523i	−0.494145	+	0.454431i
$309$	−12.2303			−0.695757
$310$	−2.62646	+	4.54916i	−0.149173	+	0.258375i
$311$	13.3527	+	23.1275i	0.757161	+	1.31144i	0.944293	+	0.329106i	$0.106747\pi$
$311$	13.3527	+	23.1275i	0.757161	+	1.31144i	−0.187132	+	0.982335i	$0.559919\pi$
$312$		0			0
$313$	−11.7972	+	20.4334i	−0.666818	+	1.15496i	0.311971	+	0.950092i	$0.399011\pi$
$313$	−11.7972	+	20.4334i	−0.666818	+	1.15496i	−0.978789	+	0.204871i	$0.934322\pi$
$314$	−9.83862			−0.555225
$315$	−3.73740	−	16.7166i	−0.210579	−	0.941875i
$316$	24.4662			1.37633
$317$	0.359058	−	0.621907i	0.0201667	−	0.0349298i	−0.855766	−	0.517363i	$-0.826914\pi$
$317$	0.359058	−	0.621907i	0.0201667	−	0.0349298i	0.875933	+	0.482433i	$0.160247\pi$
$318$	0.979704	+	1.69690i	0.0549391	+	0.0951573i
$319$	−1.89831	−	3.28797i	−0.106285	−	0.184091i
$320$	1.14114	−	1.97651i	0.0637915	−	0.110490i
$321$	0.0453082			0.00252886
$322$	−1.94408	−	8.69545i	−0.108339	−	0.484578i
$323$	0.932151			0.0518663
$324$	3.28351	−	5.68721i	0.182417	−	0.315956i
$325$		0			0
$326$	3.26957	+	5.66307i	0.181085	+	0.313648i
$327$	−2.38487	+	4.13072i	−0.131884	+	0.228429i
$328$	−25.0708			−1.38430
$329$	17.5020	−	16.0954i	0.964917	−	0.887367i
$330$	3.30532			0.181952
$331$	4.74555	−	8.21953i	0.260839	−	0.451786i	−0.705626	−	0.708584i	$-0.749334\pi$
$331$	4.74555	−	8.21953i	0.260839	−	0.451786i	0.966465	+	0.256798i	$0.0826676\pi$
$332$	−4.12834	−	7.15049i	−0.226572	−	0.392434i
$333$	−13.0725	−	22.6422i	−0.716368	−	1.24079i
$334$	4.54971	−	7.88034i	0.248949	−	0.431193i
$335$	9.19207			0.502217
$336$	−3.98893	−	1.24986i	−0.217614	−	0.0681853i
$337$	−10.0435			−0.547107			−0.273553	−	0.961857i	$-0.588199\pi$
$337$	−10.0435			−0.547107			−0.273553	+	0.961857i	$0.588199\pi$
$338$		0			0
$339$	2.26611	+	3.92501i	0.123078	+	0.213177i
$340$	−1.05937	−	1.83489i	−0.0574526	−	0.0995108i
$341$	−4.45789	+	7.72130i	−0.241408	+	0.418132i
$342$	2.77192			0.149888
$343$	−11.3532	−	14.6323i	−0.613014	−	0.790072i
$344$	20.2817			1.09351
$345$	5.96845	−	10.3377i	0.321330	−	0.556561i
$346$	−0.501034	−	0.867817i	−0.0269358	−	0.0466541i
$347$	−3.80572	−	6.59170i	−0.204302	−	0.353861i	0.745608	−	0.666385i	$-0.232159\pi$
$347$	−3.80572	−	6.59170i	−0.204302	−	0.353861i	−0.949910	+	0.312523i	$0.898826\pi$
$348$	0.901940	−	1.56221i	0.0483490	−	0.0837430i
$349$	−29.9682			−1.60416			−0.802080	−	0.597217i	$-0.796273\pi$
$349$	−29.9682			−1.60416			−0.802080	+	0.597217i	$0.796273\pi$
$350$	−3.37036	−	1.05604i	−0.180154	−	0.0564478i
$351$		0			0
$352$	−7.40784	+	12.8308i	−0.394839	+	0.683882i
$353$	−8.86193	−	15.3493i	−0.471673	−	0.816961i	0.527802	−	0.849367i	$-0.323016\pi$
$353$	−8.86193	−	15.3493i	−0.471673	−	0.816961i	−0.999475	+	0.0324062i	$0.989683\pi$
$354$	2.25908	+	3.91283i	0.120069	+	0.207965i
$355$	7.11327	−	12.3205i	0.377533	−	0.653907i
$356$	6.07323			0.321880
$357$	−0.716020	+	0.658474i	−0.0378958	+	0.0348501i
$358$	6.23054			0.329294
$359$	−13.4091	+	23.2252i	−0.707704	+	1.22578i	0.258003	+	0.966144i	$0.416936\pi$
$359$	−13.4091	+	23.2252i	−0.707704	+	1.22578i	−0.965707	+	0.259635i	$0.916398\pi$
$360$	−6.96016	−	12.0554i	−0.366833	−	0.635373i
$361$	7.57627	+	13.1225i	0.398751	+	0.690657i
$362$	5.45397	−	9.44655i	0.286654	−	0.496500i
$363$	−2.90032			−0.152228
$364$		0			0
$365$	11.3734			0.595313
$366$	2.26923	−	3.93042i	0.118614	−	0.205446i
$367$	−8.01241	−	13.8779i	−0.418244	−	0.724420i	0.577519	−	0.816377i	$-0.304021\pi$
$367$	−8.01241	−	13.8779i	−0.418244	−	0.724420i	−0.995763	+	0.0919572i	$0.970688\pi$
$368$	5.84337	+	10.1210i	0.304607	+	0.527594i
$369$	14.0007	−	24.2499i	0.728846	−	1.26240i
$370$	−17.2730			−0.897979
$371$	−2.48438	−	11.1121i	−0.128983	−	0.576913i
$372$	−4.23614			−0.219634
$373$	0.397528	−	0.688539i	0.0205832	−	0.0356512i	−0.855550	−	0.517720i	$-0.826781\pi$
$373$	0.397528	−	0.688539i	0.0205832	−	0.0356512i	0.876134	+	0.482068i	$0.160114\pi$
$374$	0.376531	+	0.652171i	0.0194700	+	0.0337230i
$375$	2.84874	+	4.93417i	0.147108	+	0.254799i
$376$	9.66163	−	16.7344i	0.498260	−	0.863012i
$377$		0			0
$378$	−4.78916	+	4.40426i	−0.246328	+	0.226531i
$379$	−9.67134			−0.496784			−0.248392	−	0.968660i	$-0.579902\pi$
$379$	−9.67134			−0.496784			−0.248392	+	0.968660i	$0.579902\pi$
$380$	−4.37257	+	7.57351i	−0.224308	+	0.388513i
$381$	7.93228	+	13.7391i	0.406383	+	0.703876i
$382$	−5.73577	−	9.93465i	−0.293468	−	0.508301i
$383$	7.02786	−	12.1726i	0.359107	−	0.621991i	−0.628705	−	0.777644i	$-0.716415\pi$
$383$	7.02786	−	12.1726i	0.359107	−	0.621991i	0.987812	+	0.155653i	$0.0497481\pi$
$384$	−8.89885			−0.454118
$385$	−18.3291	−	5.74309i	−0.934139	−	0.292695i
$386$	4.56520			0.232362
$387$	−11.3262	+	19.6176i	−0.575743	+	0.997216i
$388$	14.3868	+	24.9187i	0.730379	+	1.26505i
$389$	−12.9553	−	22.4392i	−0.656858	−	1.13771i	−0.981424	−	0.191849i	$-0.938552\pi$
$389$	−12.9553	−	22.4392i	−0.656858	−	1.13771i	0.324566	−	0.945863i	$-0.394782\pi$
$390$		0			0
$391$	2.71962			0.137537
$392$	−12.3596	−	8.58851i	−0.624256	−	0.433785i
$393$	8.57508			0.432556
$394$	0.305681	−	0.529455i	0.0154000	−	0.0266735i
$395$	19.9435	+	34.5432i	1.00347	+	1.73806i
$396$	−5.34690	−	9.26111i	−0.268692	−	0.465388i
$397$	−6.63042	+	11.4842i	−0.332771	+	0.576377i	−0.983054	−	0.183315i	$-0.941317\pi$
$397$	−6.63042	+	11.4842i	−0.332771	+	0.576377i	0.650283	+	0.759692i	$0.274650\pi$
$398$	7.85082			0.393526
$399$	3.83142	+	1.20050i	0.191811	+	0.0601003i
$400$	4.63258			0.231629
$401$	15.9182	−	27.5711i	0.794917	−	1.37684i	−0.127975	−	0.991777i	$-0.540848\pi$
$401$	15.9182	−	27.5711i	0.794917	−	1.37684i	0.922892	−	0.385059i	$-0.125819\pi$
$402$	−0.776151	−	1.34433i	−0.0387109	−	0.0670492i
$403$		0			0
$404$	14.0395	−	24.3171i	0.698491	−	1.20982i
$405$	10.7062			0.531994
$406$	1.61578	−	1.48592i	0.0801898	−	0.0737450i
$407$	−29.3174			−1.45321
$408$	−0.395264	+	0.684617i	−0.0195685	+	0.0338936i
$409$	6.47910	+	11.2221i	0.320371	+	0.554898i	0.980565	−	0.196197i	$-0.0628592\pi$
$409$	6.47910	+	11.2221i	0.320371	+	0.554898i	−0.660194	+	0.751095i	$0.729526\pi$
$410$	−9.24970	−	16.0210i	−0.456810	−	0.791219i
$411$	−3.72734	+	6.45594i	−0.183856	+	0.318448i
$412$	26.1417			1.28791
$413$	−5.72868	−	25.6232i	−0.281890	−	1.26083i
$414$	8.08730			0.397469
$415$	6.73039	−	11.6574i	0.330382	−	0.572238i
$416$		0			0
$417$	1.82432	+	3.15981i	0.0893371	+	0.154736i
$418$	1.55413	−	2.69184i	0.0760152	−	0.131662i
$419$	−8.51999			−0.416229			−0.208114	−	0.978104i	$-0.566733\pi$
$419$	−8.51999			−0.416229			−0.208114	+	0.978104i	$0.566733\pi$
$420$	−1.99121	−	8.90629i	−0.0971613	−	0.434582i
$421$	−13.1013			−0.638519			−0.319259	−	0.947667i	$-0.603434\pi$
$421$	−13.1013			−0.638519			−0.319259	+	0.947667i	$0.603434\pi$
$422$	−0.638974	+	1.10674i	−0.0311048	+	0.0538751i
$423$	10.7910	+	18.6905i	0.524675	+	0.908764i
$424$	−4.62667	−	8.01362i	−0.224691	−	0.389176i
$425$	0.539024	−	0.933617i	0.0261465	−	0.0452871i
$426$	−2.40249			−0.116401
$427$	−19.4129	+	17.8527i	−0.939454	+	0.863950i
$428$	−0.0968444			−0.00468115
$429$		0			0
$430$	7.48278	+	12.9606i	0.360852	+	0.625014i
$431$	17.6675	+	30.6011i	0.851016	+	1.47400i	0.880292	+	0.474431i	$0.157346\pi$
$431$	17.6675	+	30.6011i	0.851016	+	1.47400i	−0.0292765	+	0.999571i	$0.509320\pi$
$432$	4.26699	−	7.39065i	0.205296	−	0.355583i
$433$	0.385519			0.0185269			0.00926343	−	0.999957i	$-0.497051\pi$
$433$	0.385519			0.0185269			0.00926343	+	0.999957i	$0.497051\pi$
$434$	−4.91917	−	1.54133i	−0.236127	−	0.0739861i
$435$	2.94085			0.141003
$436$	5.09756	−	8.82924i	0.244129	−	0.422844i
$437$	−5.61263	−	9.72136i	−0.268488	−	0.465036i
$438$	−0.960338	−	1.66335i	−0.0458867	−	0.0794782i
$439$	9.41973	−	16.3155i	0.449579	−	0.778694i	−0.548779	−	0.835967i	$-0.684907\pi$
$439$	9.41973	−	16.3155i	0.449579	−	0.778694i	0.998359	+	0.0572731i	$0.0182406\pi$
$440$	−15.6094			−0.744150
$441$	15.2095	−	7.15871i	0.724260	−	0.340891i
$442$		0			0
$443$	8.98415	−	15.5610i	0.426850	−	0.739325i	−0.569741	−	0.821824i	$-0.692957\pi$
$443$	8.98415	−	15.5610i	0.426850	−	0.739325i	0.996591	+	0.0824986i	$0.0262900\pi$
$444$	−6.96476	−	12.0633i	−0.330533	−	0.572500i
$445$	4.95056	+	8.57463i	0.234679	+	0.406476i
$446$	−0.400923	+	0.694419i	−0.0189843	+	0.0328817i
$447$	−7.31235			−0.345862
$448$	2.13726	+	0.669672i	0.100976	+	0.0316390i
$449$	8.02696			0.378816			0.189408	−	0.981899i	$-0.439343\pi$
$449$	8.02696			0.378816			0.189408	+	0.981899i	$0.439343\pi$
$450$	1.60289	−	2.77628i	0.0755608	−	0.130875i
$451$	−15.6995	−	27.1924i	−0.739262	−	1.28044i
$452$	−4.84371	−	8.38955i	−0.227829	−	0.394611i
$453$	−0.346628	+	0.600377i	−0.0162860	+	0.0282082i
$454$	−3.69591			−0.173458
$455$		0			0
$456$	3.26291			0.152800
$457$	0.221156	−	0.383053i	0.0103452	−	0.0179184i	−0.860806	−	0.508932i	$-0.830040\pi$
$457$	0.221156	−	0.383053i	0.0103452	−	0.0179184i	0.871152	+	0.491014i	$0.163374\pi$
$458$	5.96648	+	10.3343i	0.278795	+	0.482888i
$459$	−0.992973	−	1.71988i	−0.0463480	−	0.0802771i
$460$	−12.7573	+	22.0963i	−0.594812	+	1.03024i
$461$	−30.7003			−1.42985			−0.714927	−	0.699199i	$-0.753540\pi$
$461$	−30.7003			−1.42985			−0.714927	+	0.699199i	$0.753540\pi$
$462$	0.707734	+	3.16555i	0.0329268	+	0.147275i
$463$	25.3809			1.17955			0.589776	−	0.807567i	$-0.299216\pi$
$463$	25.3809			1.17955			0.589776	+	0.807567i	$0.299216\pi$
$464$	−1.43961	+	2.49348i	−0.0668322	+	0.115757i
$465$	−3.45307	−	5.98089i	−0.160132	−	0.277357i
$466$	1.58112	+	2.73859i	0.0732442	+	0.126863i
$467$	−12.2401	+	21.2005i	−0.566404	+	0.981040i	0.430514	+	0.902584i	$0.358332\pi$
$467$	−12.2401	+	21.2005i	−0.566404	+	0.981040i	−0.996918	+	0.0784562i	$0.975001\pi$
$468$		0			0
$469$	1.96820	+	8.80336i	0.0908831	+	0.406501i
$470$	14.2584			0.657689
$471$	6.46753	−	11.2021i	0.298008	−	0.516165i
$472$	−10.6685	−	18.4784i	−0.491058	−	0.850538i
$473$	12.7005	+	21.9980i	0.583971	+	1.01147i
$474$	3.36794	−	5.83345i	0.154695	−	0.267939i
$475$	−4.44965			−0.204164
$476$	1.53046	−	1.40746i	0.0701486	−	0.0645108i
$477$	10.3350			0.473205
$478$	−1.71332	+	2.96755i	−0.0783652	+	0.135733i
$479$	5.40857	+	9.36793i	0.247124	+	0.428031i	0.962727	−	0.270476i	$-0.0871811\pi$
$479$	5.40857	+	9.36793i	0.247124	+	0.428031i	−0.715603	+	0.698508i	$0.753848\pi$
$480$	−5.73809	−	9.93866i	−0.261907	−	0.453636i
$481$		0			0
$482$	−12.6359			−0.575549
$483$	11.1785	+	3.50256i	0.508637	+	0.159372i
$484$	6.19932			0.281787
$485$	−23.4547	+	40.6247i	−1.06502	+	1.84467i
$486$	−4.59279	−	7.95495i	−0.208333	−	0.360844i
$487$	4.16463	+	7.21336i	0.188718	+	0.326868i	0.944823	−	0.327582i	$-0.106234\pi$
$487$	4.16463	+	7.21336i	0.188718	+	0.326868i	−0.756105	+	0.654450i	$0.772900\pi$
$488$	−10.7165	+	18.5615i	−0.485112	+	0.840238i
$489$	−8.59717			−0.388777
$490$	0.928299	−	11.0668i	0.0419363	−	0.499948i
$491$	−0.894844			−0.0403837			−0.0201919	−	0.999796i	$-0.506428\pi$
$491$	−0.894844			−0.0403837			−0.0201919	+	0.999796i	$0.506428\pi$
$492$	7.45928	−	12.9199i	0.336290	−	0.582472i
$493$	0.335012	+	0.580257i	0.0150882	+	0.0261335i
$494$		0			0
$495$	8.71701	−	15.0983i	0.391800	−	0.678618i
$496$	6.76141			0.303596
$497$	13.3226	+	4.17440i	0.597602	+	0.187247i
$498$	−2.27317			−0.101863
$499$	−3.30482	+	5.72411i	−0.147944	+	0.256246i	−0.930467	−	0.366375i	$-0.880599\pi$
$499$	−3.30482	+	5.72411i	−0.147944	+	0.256246i	0.782523	+	0.622621i	$0.213932\pi$
$500$	−6.08907	−	10.5466i	−0.272311	−	0.471657i
$501$	5.98162	+	10.3605i	0.267239	+	0.462871i
$502$	−4.23284	+	7.33150i	−0.188921	+	0.327221i
$503$	24.9855			1.11405			0.557025	−	0.830496i	$-0.311943\pi$
$503$	24.9855			1.11405			0.557025	+	0.830496i	$0.311943\pi$
$504$	10.0553	−	9.24712i	0.447897	−	0.411900i
$505$	45.7770			2.03705
$506$	4.53431	−	7.85365i	0.201574	−	0.349137i
$507$		0			0
$508$	−16.9549	−	29.3668i	−0.752253	−	1.30294i
$509$	−4.77634	+	8.27286i	−0.211707	+	0.366688i	−0.952249	−	0.305323i	$-0.901236\pi$
$509$	−4.77634	+	8.27286i	−0.211707	+	0.366688i	0.740542	+	0.672011i	$0.234569\pi$
$510$	−0.583320			−0.0258298
$511$	2.43527	+	10.8925i	0.107730	+	0.481855i
$512$	20.0172			0.884646
$513$	−4.09850	+	7.09881i	−0.180953	+	0.313420i
$514$	−2.43221	−	4.21271i	−0.107280	−	0.185814i
$515$	21.3093	+	36.9088i	0.939001	+	1.62640i
$516$	−6.03437	+	10.4518i	−0.265649	+	0.460117i
$517$	24.2007			1.06435
$518$	−3.69848	−	16.5425i	−0.162502	−	0.726837i
$519$	1.31744			0.0578293
$520$		0			0
$521$	7.67879	+	13.3001i	0.336414	+	0.582686i	0.983755	−	0.179514i	$-0.0574526\pi$
$521$	7.67879	+	13.3001i	0.336414	+	0.582686i	−0.647342	+	0.762200i	$0.724119\pi$
$522$	0.996219	+	1.72550i	0.0436033	+	0.0755232i
$523$	1.54686	−	2.67924i	0.0676395	−	0.117155i	−0.830222	−	0.557432i	$-0.811787\pi$
$523$	1.54686	−	2.67924i	0.0676395	−	0.117155i	0.897862	+	0.440277i	$0.145120\pi$
$524$	−18.3289			−0.800700
$525$	3.41794	−	3.14324i	0.149171	−	0.137182i
$526$	−9.74482			−0.424895
$527$	0.786724	−	1.36265i	0.0342702	−	0.0593578i
$528$	−2.12726	−	3.68452i	−0.0925770	−	0.160348i
$529$	−4.87527	−	8.44422i	−0.211968	−	0.367140i
$530$	3.41395	−	5.91314i	0.148293	−	0.256850i
$531$	23.8311			1.03418
$532$	−8.18949	−	2.56602i	−0.355060	−	0.111251i
$533$		0			0
$534$	0.836021	−	1.44803i	0.0361782	−	0.0626624i
$535$	−0.0789423	−	0.136732i	−0.00341297	−	0.00591144i
$536$	3.66538	+	6.34863i	0.158320	+	0.274219i
$537$	−4.09572	+	7.09399i	−0.176743	+	0.306128i
$538$	−12.0263			−0.518489
$539$	1.57560	−	18.7837i	0.0678660	−	0.809073i
$540$	18.6315			0.801772
$541$	−4.10619	+	7.11213i	−0.176539	+	0.305774i	−0.940693	−	0.339260i	$-0.889823\pi$
$541$	−4.10619	+	7.11213i	−0.176539	+	0.305774i	0.764154	+	0.645034i	$0.223157\pi$
$542$	0.857778	+	1.48572i	0.0368447	+	0.0638169i
$543$	7.17046	+	12.4196i	0.307714	+	0.532976i
$544$	1.30733	−	2.26436i	0.0560512	−	0.0970836i
$545$	16.6210			0.711966
$546$		0			0
$547$	15.2648			0.652674			0.326337	−	0.945254i	$-0.394186\pi$
$547$	15.2648			0.652674			0.326337	+	0.945254i	$0.394186\pi$
$548$	7.96703	−	13.7993i	0.340335	−	0.589477i
$549$	−11.9691	−	20.7311i	−0.510829	−	0.884783i
$550$	−1.79738	−	3.11316i	−0.0766406	−	0.132745i
$551$	1.38276	−	2.39502i	0.0589077	−	0.102031i
$552$	9.51979			0.405189
$553$	−28.8122	+	26.4965i	−1.22522	+	1.12675i
$554$	4.88347			0.207479
$555$	11.3546	−	19.6667i	0.481976	−	0.834806i
$556$	−3.89940	−	6.75395i	−0.165371	−	0.286431i
$557$	−15.5281	−	26.8955i	−0.657948	−	1.13960i	−0.981146	−	0.193268i	$-0.938091\pi$
$557$	−15.5281	−	26.8955i	−0.657948	−	1.13960i	0.323198	−	0.946331i	$-0.395242\pi$
$558$	2.33947	−	4.05208i	0.0990376	−	0.171538i
$559$		0			0
$560$	3.17823	+	14.2156i	0.134305	+	0.600717i
$561$	−0.990069			−0.0418007
$562$	−3.91423	+	6.77964i	−0.165112	+	0.285982i
$563$	−15.7747	−	27.3226i	−0.664824	−	1.15151i	−0.979333	−	0.202255i	$-0.935173\pi$
$563$	−15.7747	−	27.3226i	−0.664824	−	1.15151i	0.314509	−	0.949255i	$-0.398160\pi$
$564$	5.74922	+	9.95794i	0.242086	+	0.419305i
$565$	7.89665	−	13.6774i	0.332215	−	0.575413i
$566$	5.16420			0.217068
$567$	2.29240	+	10.2534i	0.0962717	+	0.430604i
$568$	11.3458			0.476059
$569$	9.73715	−	16.8652i	0.408203	−	0.707028i	−0.586486	−	0.809959i	$-0.699489\pi$
$569$	9.73715	−	16.8652i	0.408203	−	0.707028i	0.994688	+	0.102932i	$0.0328224\pi$
$570$	1.20383	+	2.08509i	0.0504228	+	0.0873348i
$571$	19.6498	+	34.0345i	0.822320	+	1.42430i	0.903950	+	0.427637i	$0.140654\pi$
$571$	19.6498	+	34.0345i	0.822320	+	1.42430i	−0.0816306	+	0.996663i	$0.526013\pi$
$572$		0			0
$573$	15.0819			0.630056
$574$	13.3629	−	12.2890i	0.557758	−	0.512931i
$575$	−12.9822			−0.541395
$576$	−1.01645	+	1.76053i	−0.0423519	+	0.0733556i
$577$	12.7838	+	22.1423i	0.532198	+	0.921795i	0.999293	+	0.0375876i	$0.0119673\pi$
$577$	12.7838	+	22.1423i	0.532198	+	0.921795i	−0.467095	+	0.884207i	$0.654699\pi$
$578$	4.93556	+	8.54863i	0.205292	+	0.355576i
$579$	−3.00098	+	5.19786i	−0.124717	+	0.216016i
$580$	−6.28594			−0.261009
$581$	12.6055	+	3.94970i	0.522965	+	0.163861i
$582$	7.92177			0.328368
$583$	5.79450	−	10.0364i	0.239984	−	0.415664i
$584$	4.53521	+	7.85522i	0.187668	+	0.325051i
$585$		0			0
$586$	2.73530	−	4.73768i	0.112994	−	0.195712i
$587$	10.9912			0.453655			0.226828	−	0.973935i	$-0.427165\pi$
$587$	10.9912			0.453655			0.226828	+	0.973935i	$0.427165\pi$
$588$	8.10330	−	3.81402i	0.334175	−	0.157288i
$589$	−6.49442			−0.267598
$590$	7.87215	−	13.6350i	0.324091	−	0.561343i
$591$	0.401886	+	0.696087i	0.0165314	+	0.0286332i
$592$	11.1166	+	19.2546i	0.456891	+	0.791358i
$593$	−2.07872	+	3.60045i	−0.0853628	+	0.147853i	−0.905546	−	0.424249i	$-0.860538\pi$
$593$	−2.07872	+	3.60045i	−0.0853628	+	0.147853i	0.820183	+	0.572101i	$0.193872\pi$
$594$	−6.62216			−0.271710
$595$	3.23470	+	1.01353i	0.132610	+	0.0415509i
$596$	15.6298			0.640223
$597$	−5.16083	+	8.93881i	−0.211219	+	0.365841i
$598$		0			0
$599$	−3.51368	−	6.08588i	−0.143565	−	0.248662i	0.785272	−	0.619152i	$-0.212523\pi$
$599$	−3.51368	−	6.08588i	−0.143565	−	0.248662i	−0.928837	+	0.370489i	$0.879190\pi$
$600$	1.88680	−	3.26804i	0.0770284	−	0.133417i
$601$	36.3334			1.48207			0.741034	−	0.671467i	$-0.234336\pi$
$601$	36.3334			1.48207			0.741034	+	0.671467i	$0.234336\pi$
$602$	−10.8103	+	9.94146i	−0.440594	+	0.405184i
$603$	−8.18766			−0.333427
$604$	0.740902	−	1.28328i	0.0301469	−	0.0522159i
$605$	5.05335	+	8.75266i	0.205448	+	0.355846i
$606$	−3.86527	−	6.69484i	−0.157016	−	0.271959i
$607$	2.89737	−	5.01840i	0.117601	−	0.203691i	−0.801216	−	0.598376i	$-0.795813\pi$
$607$	2.89737	−	5.01840i	0.117601	−	0.203691i	0.918816	+	0.394685i	$0.129146\pi$
$608$	−10.7920			−0.437674
$609$	0.629693	+	2.81649i	0.0255165	+	0.114130i
$610$	−15.8151			−0.640333
$611$		0			0
$612$	0.943616	+	1.63439i	0.0381434	+	0.0660663i
$613$	−22.4253	−	38.8418i	−0.905751	−	1.56881i	−0.819906	−	0.572498i	$-0.805974\pi$
$613$	−22.4253	−	38.8418i	−0.905751	−	1.56881i	−0.0858447	−	0.996309i	$-0.527359\pi$
$614$	−1.94866	+	3.37519i	−0.0786417	+	0.136211i
$615$	24.3216			0.980742
$616$	−3.34228	−	14.9493i	−0.134664	−	0.602326i
$617$	33.3721			1.34351			0.671754	−	0.740774i	$-0.265541\pi$
$617$	33.3721			1.34351			0.671754	+	0.740774i	$0.265541\pi$
$618$	3.59859	−	6.23294i	0.144756	−	0.250726i
$619$	−5.62337	−	9.73996i	−0.226022	−	0.391482i	0.730603	−	0.682802i	$-0.239239\pi$
$619$	−5.62337	−	9.73996i	−0.226022	−	0.391482i	−0.956626	+	0.291320i	$0.905906\pi$
$620$	7.38079	+	12.7839i	0.296420	+	0.513414i
$621$	−11.9577	+	20.7113i	−0.479845	+	0.831117i
$622$	−15.7153			−0.630127
$623$	−7.15201	+	6.57721i	−0.286539	+	0.263510i
$624$		0			0
$625$	15.5982	−	27.0169i	0.623928	−	1.08068i
$626$	−6.94232	−	12.0245i	−0.277471	−	0.480594i
$627$	2.04326	+	3.53903i	0.0815998	+	0.141335i
$628$	−13.8241	+	23.9440i	−0.551640	+	0.955469i
$629$	5.17391			0.206297
$630$	9.61899	+	3.01393i	0.383230	+	0.120078i
$631$	−23.2566			−0.925830			−0.462915	−	0.886403i	$-0.653197\pi$
$631$	−23.2566			−0.925830			−0.462915	+	0.886403i	$0.653197\pi$
$632$	−15.9052	+	27.5485i	−0.632673	+	1.09582i
$633$	−0.840075	−	1.45505i	−0.0333900	−	0.0578331i
$634$	0.211295	+	0.365974i	0.00839161	+	0.0145347i
$635$	27.6415	−	47.8764i	1.09692	−	1.89992i
$636$	5.50626			0.218337
$637$		0			0
$638$	2.23420			0.0884529
$639$	−6.33601	+	10.9743i	−0.250649	+	0.434136i
$640$	15.5048	+	26.8551i	0.612882	+	1.06154i
$641$	12.3270	+	21.3510i	0.486886	+	0.843312i	0.999886	−	0.0150766i	$-0.00479922\pi$
$641$	12.3270	+	21.3510i	0.486886	+	0.843312i	−0.513000	+	0.858389i	$0.671466\pi$
$642$	−0.0133313	+	0.0230905i	−0.000526144	+	0.000911309i
$643$	10.8011			0.425955			0.212978	−	0.977057i	$-0.431684\pi$
$643$	10.8011			0.425955			0.212978	+	0.977057i	$0.431684\pi$
$644$	−23.8935	−	7.48657i	−0.941535	−	0.295012i
$645$	−19.6756			−0.774725
$646$	−0.274272	+	0.475053i	−0.0107911	+	0.0186907i
$647$	−15.2648	−	26.4394i	−0.600122	−	1.03944i	−0.992802	−	0.119767i	$-0.961785\pi$
$647$	−15.2648	−	26.4394i	−0.600122	−	1.03944i	0.392680	−	0.919675i	$-0.371548\pi$
$648$	4.26914	+	7.39436i	0.167708	+	0.290478i
$649$	13.3614	−	23.1426i	0.524481	−	0.908428i
$650$		0			0
$651$	4.98860	−	4.58767i	0.195519	−	0.179805i
$652$	18.3761			0.719663
$653$	−15.7037	+	27.1996i	−0.614532	+	1.06440i	0.375934	+	0.926646i	$0.377322\pi$
$653$	−15.7037	+	27.1996i	−0.614532	+	1.06440i	−0.990466	+	0.137755i	$0.956011\pi$
$654$	−1.40343	−	2.43081i	−0.0548784	−	0.0950522i
$655$	−14.9407	−	25.8780i	−0.583781	−	1.01114i
$656$	−11.9059	+	20.6217i	−0.464849	+	0.805142i
$657$	−10.1307			−0.395235
$658$	3.05299	+	13.6554i	0.119018	+	0.532343i
$659$	39.3041			1.53107			0.765536	−	0.643393i	$-0.222474\pi$
$659$	39.3041			1.53107			0.765536	+	0.643393i	$0.222474\pi$
$660$	4.64425	−	8.04408i	0.180777	−	0.313115i
$661$	11.1066	+	19.2372i	0.431998	+	0.748242i	0.997045	−	0.0768164i	$-0.0244755\pi$
$661$	11.1066	+	19.2372i	0.431998	+	0.748242i	−0.565048	+	0.825058i	$0.691142\pi$
$662$	2.79262	+	4.83696i	0.108538	+	0.187994i
$663$		0			0
$664$	10.7351			0.416603
$665$	−3.05273	−	13.6542i	−0.118380	−	0.529488i
$666$	15.3856			0.596179
$667$	4.03432	−	6.98764i	0.156209	−	0.270563i
$668$	−12.7855	−	22.1451i	−0.494684	−	0.856818i
$669$	−0.527103	−	0.912969i	−0.0203790	−	0.0352974i
$670$	−2.70463	+	4.68457i	−0.104489	+	0.180981i
$671$	−26.8429			−1.03626
$672$	8.28974	−	7.62350i	0.319784	−	0.294083i
$673$	8.31502			0.320520			0.160260	−	0.987075i	$-0.448767\pi$
$673$	8.31502			0.320520			0.160260	+	0.987075i	$0.448767\pi$
$674$	2.95517	−	5.11850i	0.113829	−	0.197157i
$675$	4.73998	+	8.20989i	0.182442	+	0.315999i
$676$		0			0
$677$	−11.8415	+	20.5100i	−0.455104	+	0.788263i	−0.998694	−	0.0510875i	$-0.983731\pi$
$677$	−11.8415	+	20.5100i	−0.455104	+	0.788263i	0.543590	+	0.839351i	$0.317065\pi$
$678$	−2.66708			−0.102428
$679$	−43.9289	−	13.7643i	−1.68584	−	0.528225i
$680$	2.75474			0.105639
$681$	2.42955	−	4.20810i	0.0931005	−	0.161255i
$682$	−2.62334	−	4.54376i	−0.100453	−	0.173990i
$683$	−10.4915	−	18.1718i	−0.401445	−	0.695324i	0.592455	−	0.805603i	$-0.298159\pi$
$683$	−10.4915	−	18.1718i	−0.401445	−	0.695324i	−0.993901	+	0.110280i	$0.964825\pi$
$684$	3.89478	−	6.74596i	0.148921	−	0.257938i
$685$	25.9772			0.992536
$686$	10.7976	−	1.48058i	0.412254	−	0.0565288i
$687$	−15.6886			−0.598556
$688$	9.63162	−	16.6825i	0.367202	−	0.636013i
$689$		0			0
$690$	3.51226	+	6.08341i	0.133709	+	0.231592i
$691$	22.7981	−	39.4874i	0.867280	−	1.50217i	0.00251460	−	0.999997i	$-0.499200\pi$
$691$	22.7981	−	39.4874i	0.867280	−	1.50217i	0.864765	−	0.502176i	$-0.167467\pi$
$692$	−2.81598			−0.107047
$693$	16.3263	+	5.11555i	0.620185	+	0.194323i
$694$	4.47911			0.170025
$695$	6.35715	−	11.0109i	0.241141	−	0.417668i
$696$	1.17268	+	2.03114i	0.0444502	+	0.0769901i
$697$	2.77064	+	4.79888i	0.104945	+	0.181771i
$698$	8.81770	−	15.2727i	0.333755	−	0.578081i
$699$	−4.15748			−0.157250
$700$	−7.30570	+	6.71855i	−0.276130	+	0.253937i
$701$	37.7591			1.42614			0.713070	−	0.701092i	$-0.247304\pi$
$701$	37.7591			1.42614			0.713070	+	0.701092i	$0.247304\pi$
$702$		0			0
$703$	−10.6777	−	18.4943i	−0.402716	−	0.697524i
$704$	1.13978	+	1.97416i	0.0429571	+	0.0744039i
$705$	−9.37290	+	16.2343i	−0.353004	+	0.611421i
$706$	10.4300			0.392537
$707$	9.80174	+	43.8412i	0.368632	+	1.64882i
$708$	12.6968			0.477173
$709$	−7.94968	+	13.7693i	−0.298557	+	0.517115i	−0.975806	−	0.218638i	$-0.929838\pi$
$709$	−7.94968	+	13.7693i	−0.298557	+	0.517115i	0.677249	+	0.735754i	$0.263172\pi$
$710$	4.18596	+	7.25029i	0.157096	+	0.272098i
$711$	−17.7643	−	30.7687i	−0.666214	−	1.15392i
$712$	−3.94812	+	6.83835i	−0.147962	+	0.256278i
$713$	−18.9480			−0.709607
$714$	−0.124900	−	0.558652i	−0.00467427	−	0.0209070i
$715$		0			0
$716$	8.75442	−	15.1631i	0.327168	−	0.566672i
$717$	−2.25254	−	3.90151i	−0.0841225	−	0.145704i
$718$	−7.89086	−	13.6674i	−0.294484	−	0.510061i
$719$	11.1479	−	19.3088i	0.415748	−	0.720097i	−0.579759	−	0.814788i	$-0.696853\pi$
$719$	11.1479	−	19.3088i	0.415748	−	0.720097i	0.995507	+	0.0946916i	$0.0301865\pi$
$720$	−13.2213			−0.492730
$721$	−30.7853	+	28.3111i	−1.14650	+	1.05436i
$722$	−8.91683			−0.331850
$723$	8.30634	−	14.3870i	0.308916	−	0.535059i
$724$	−15.3266	−	26.5464i	−0.569607	−	0.986588i
$725$	−1.59919	−	2.76987i	−0.0593923	−	0.102871i
$726$	0.853379	−	1.47810i	0.0316719	−	0.0548573i
$727$	−9.63440			−0.357320			−0.178660	−	0.983911i	$-0.557176\pi$
$727$	−9.63440			−0.357320			−0.178660	+	0.983911i	$0.557176\pi$
$728$		0			0
$729$	0.163177			0.00604360
$730$	−3.34647	+	5.79626i	−0.123858	+	0.214529i
$731$	−2.24138	−	3.88218i	−0.0829003	−	0.143588i
$732$	−6.37691	−	11.0451i	−0.235697	−	0.408240i
$733$	14.5843	−	25.2607i	0.538682	−	0.933025i	−0.460293	−	0.887767i	$-0.652256\pi$
$733$	14.5843	−	25.2607i	0.538682	−	0.933025i	0.998975	−	0.0452577i	$-0.0144109\pi$
$734$	9.43014			0.348073
$735$	11.9903	+	8.33186i	0.442268	+	0.307325i
$736$	−31.4865			−1.16061
$737$	−4.59058	+	7.95111i	−0.169096	+	0.292883i
$738$	8.23899	+	14.2704i	0.303282	+	0.525299i
$739$	4.63065	+	8.02052i	0.170341	+	0.295040i	0.938539	−	0.345173i	$-0.112180\pi$
$739$	4.63065	+	8.02052i	0.170341	+	0.295040i	−0.768198	+	0.640212i	$0.778846\pi$
$740$	−24.2700	+	42.0368i	−0.892182	+	1.54530i
$741$		0			0
$742$	6.39408	+	2.00347i	0.234734	+	0.0735495i
$743$	−18.5977			−0.682285			−0.341142	−	0.940012i	$-0.610814\pi$
$743$	−18.5977			−0.682285			−0.341142	+	0.940012i	$0.610814\pi$
$744$	2.75386	−	4.76982i	0.100961	−	0.174870i
$745$	12.7406	+	22.0674i	0.466779	+	0.808485i
$746$	0.233934	+	0.405185i	0.00856493	+	0.0148349i
$747$	−5.99497	+	10.3836i	−0.219344	+	0.379916i
$748$	2.11623			0.0773770
$749$	0.114047	−	0.104881i	0.00416718	−	0.00383227i
$750$	−3.35281			−0.122427
$751$	17.1465	−	29.6986i	0.625684	−	1.08372i	−0.362724	−	0.931897i	$-0.618153\pi$
$751$	17.1465	−	29.6986i	0.625684	−	1.08372i	0.988408	−	0.151820i	$-0.0485134\pi$
$752$	−9.17647	−	15.8941i	−0.334632	−	0.579599i
$753$	−5.56502	−	9.63890i	−0.202801	−	0.351261i
$754$		0			0
$755$	2.41577			0.0879189
$756$	3.98937	+	17.8436i	0.145092	+	0.648966i
$757$	−13.6364			−0.495625			−0.247813	−	0.968808i	$-0.579712\pi$
$757$	−13.6364			−0.495625			−0.247813	+	0.968808i	$0.579712\pi$
$758$	2.84565	−	4.92882i	0.103359	−	0.179023i
$759$	5.96136	+	10.3254i	0.216384	+	0.374787i
$760$	−5.68509	−	9.84687i	−0.206220	−	0.357184i
$761$	−0.720838	+	1.24853i	−0.0261304	+	0.0452591i	−0.878795	−	0.477200i	$-0.841652\pi$
$761$	−0.720838	+	1.24853i	−0.0261304	+	0.0452591i	0.852665	+	0.522459i	$0.174985\pi$
$762$	−9.33584			−0.338202
$763$	3.55889	+	15.9182i	0.128840	+	0.576276i
$764$	−32.2369			−1.16629
$765$	−1.53837	+	2.66453i	−0.0556198	+	0.0963364i
$766$	4.13569	+	7.16323i	0.149429	+	0.258818i
$767$		0			0
$768$	1.96341	−	3.40073i	0.0708486	−	0.122713i
$769$	−5.01845			−0.180970			−0.0904850	−	0.995898i	$-0.528842\pi$
$769$	−5.01845			−0.180970			−0.0904850	+	0.995898i	$0.528842\pi$
$770$	8.31994	−	7.65127i	0.299830	−	0.275733i
$771$	6.39536			0.230323
$772$	6.41448	−	11.1102i	0.230862	−	0.399865i
$773$	1.72969	+	2.99590i	0.0622124	+	0.107755i	0.895454	−	0.445154i	$-0.146851\pi$
$773$	1.72969	+	2.99590i	0.0622124	+	0.107755i	−0.833242	+	0.552909i	$0.813518\pi$
$774$	−6.66514	−	11.5444i	−0.239574	−	0.414954i
$775$	−3.75545	+	6.50463i	−0.134900	+	0.233653i
$776$	−37.4107			−1.34297
$777$	21.2663	+	6.66340i	0.762925	+	0.239048i
$778$	15.2476			0.546653
$779$	11.4358	−	19.8074i	0.409731	−	0.709674i
$780$		0			0
$781$	7.10482	+	12.3059i	0.254231	+	0.440340i
$782$	−0.800210	+	1.38600i	−0.0286154	+	0.0495634i
$783$	−5.89194			−0.210561
$784$	−12.9339	+	6.08765i	−0.461924	+	0.217416i
$785$	−45.0745			−1.60878
$786$	−2.52309	+	4.37013i	−0.0899958	+	0.155877i
$787$	−5.22281	−	9.04618i	−0.186173	−	0.322461i	0.757798	−	0.652489i	$-0.226275\pi$
$787$	−5.22281	−	9.04618i	−0.186173	−	0.322461i	−0.943971	+	0.330028i	$0.892942\pi$
$788$	−0.859014	−	1.48786i	−0.0306011	−	0.0530026i
$789$	6.40588	−	11.0953i	0.228055	−	0.395003i
$790$	−23.4724			−0.835110
$791$	14.7898	+	4.63412i	0.525866	+	0.164770i
$792$	13.9038			0.494050
$793$		0			0
$794$	−3.90181	−	6.75814i	−0.138470	−	0.239837i
$795$	4.48840	+	7.77414i	0.159187	+	0.275720i
$796$	11.0310	−	19.1063i	0.390985	−	0.677206i
$797$	−51.1691			−1.81250			−0.906251	−	0.422741i	$-0.861068\pi$
$797$	−51.1691			−1.81250			−0.906251	+	0.422741i	$0.861068\pi$
$798$	−1.73915	+	1.59938i	−0.0615654	+	0.0566174i
$799$	−4.27092			−0.151094
$800$	−6.24057	+	10.8090i	−0.220637	+	0.382155i
$801$	−4.40962	−	7.63768i	−0.155806	−	0.269864i
$802$	9.36740	+	16.2248i	0.330775	+	0.572918i
$803$	−5.67997	+	9.83799i	−0.200442	+	0.347175i
$804$	−4.36222			−0.153844
$805$	−8.90657	−	39.8372i	−0.313915	−	1.40408i
$806$		0			0
$807$	7.90561	−	13.6929i	0.278291	−	0.482014i
$808$	18.2538	+	31.6165i	0.642166	+	1.11226i
$809$	−11.1527	−	19.3171i	−0.392109	−	0.679153i	0.600618	−	0.799536i	$-0.294921\pi$
$809$	−11.1527	−	19.3171i	−0.392109	−	0.679153i	−0.992728	+	0.120383i	$0.961588\pi$
$810$	−3.15014	+	5.45620i	−0.110685	+	0.191711i
$811$	−21.5392			−0.756345			−0.378172	−	0.925735i	$-0.623447\pi$
$811$	−21.5392			−0.756345			−0.378172	+	0.925735i	$0.623447\pi$
$812$	−1.34594	−	6.02012i	−0.0472333	−	0.211265i
$813$	−2.25548			−0.0791032
$814$	8.62623	−	14.9411i	0.302349	−	0.523684i
$815$	14.9792	+	25.9447i	0.524698	+	0.908803i
$816$	0.375416	+	0.650240i	0.0131422	+	0.0227629i
$817$	−9.25129	+	16.0237i	−0.323662	+	0.560599i
$818$	−7.62552			−0.266620
$819$		0			0
$820$	−51.9864			−1.81544
$821$	−23.5876	+	40.8549i	−0.823212	+	1.42584i	0.0800669	+	0.996789i	$0.474487\pi$
$821$	−23.5876	+	40.8549i	−0.823212	+	1.42584i	−0.903278	+	0.429055i	$0.858847\pi$
$822$	−2.19343	−	3.79914i	−0.0765047	−	0.132510i
$823$	5.37353	+	9.30723i	0.187309	+	0.324430i	0.944352	−	0.328936i	$-0.106690\pi$
$823$	5.37353	+	9.30723i	0.187309	+	0.324430i	−0.757043	+	0.653365i	$0.773357\pi$
$824$	−16.9944	+	29.4351i	−0.592028	+	1.02542i
$825$	4.72612			0.164542
$826$	14.7440	+	4.61974i	0.513008	+	0.160741i
$827$	47.9015			1.66570			0.832849	−	0.553500i	$-0.186708\pi$
$827$	47.9015			1.66570			0.832849	+	0.553500i	$0.186708\pi$
$828$	11.3633	−	19.6818i	0.394903	−	0.683991i
$829$	3.15080	+	5.45735i	0.109432	+	0.189542i	0.915540	−	0.402226i	$-0.131764\pi$
$829$	3.15080	+	5.45735i	0.109432	+	0.189542i	−0.806108	+	0.591768i	$0.798430\pi$
$830$	3.96064	+	6.86003i	0.137476	+	0.238115i
$831$	−3.21020	+	5.56024i	−0.111361	+	0.192882i
$832$		0			0
$833$	−0.278061	+	3.31493i	−0.00963423	+	0.114856i
$834$	−2.14711			−0.0743485
$835$	20.8440	−	36.1029i	0.721337	−	1.24939i
$836$	−4.36737	−	7.56451i	−0.151049	−	0.261624i
$837$	6.91817	+	11.9826i	0.239127	+	0.414180i
$838$	2.50688	−	4.34205i	0.0865989	−	0.149994i
$839$	−17.5158			−0.604712			−0.302356	−	0.953195i	$-0.597773\pi$
$839$	−17.5158			−0.604712			−0.302356	+	0.953195i	$0.597773\pi$
$840$	11.3228	+	3.54778i	0.390673	+	0.122410i
$841$	−27.0122			−0.931454
$842$	3.85487	−	6.67684i	0.132848	−	0.230099i
$843$	−5.14613	−	8.91335i	−0.177242	−	0.306992i
$844$	1.79562	+	3.11011i	0.0618079	+	0.107054i
$845$		0			0
$846$	−12.7004			−0.436647
$847$	−7.30050	+	6.71377i	−0.250848	+	0.230688i
$848$	−8.78868			−0.301805
$849$	−3.39475	+	5.87988i	−0.116508	+	0.201797i
$850$	0.317200	+	0.549407i	0.0108799	+	0.0188445i
$851$	−31.1529	−	53.9584i	−1.06791	−	1.84967i
$852$	−3.37570	+	5.84688i	−0.115650	+	0.200311i
$853$	−1.20324			−0.0411982			−0.0205991	−	0.999788i	$-0.506557\pi$
$853$	−1.20324			−0.0411982			−0.0205991	+	0.999788i	$0.506557\pi$
$854$	−3.38631	−	15.1463i	−0.115877	−	0.518295i
$855$	12.6993			0.434305
$856$	0.0629573	−	0.109045i	0.00215183	−	0.00372709i
$857$	−21.1570	−	36.6450i	−0.722709	−	1.25177i	−0.959910	−	0.280308i	$-0.909563\pi$
$857$	−21.1570	−	36.6450i	−0.722709	−	1.25177i	0.237201	−	0.971460i	$-0.423770\pi$
$858$		0			0
$859$	3.52045	−	6.09760i	0.120116	−	0.208047i	−0.799697	−	0.600404i	$-0.795007\pi$
$859$	3.52045	−	6.09760i	0.120116	−	0.208047i	0.919813	+	0.392356i	$0.128340\pi$
$860$	42.0557			1.43409
$861$	5.20773	+	23.2931i	0.177479	+	0.793827i
$862$	−20.7937			−0.708236
$863$	−1.46004	+	2.52886i	−0.0497002	+	0.0860833i	−0.889805	−	0.456340i	$-0.849160\pi$
$863$	−1.46004	+	2.52886i	−0.0497002	+	0.0860833i	0.840105	+	0.542424i	$0.182493\pi$
$864$	11.4962	+	19.9120i	0.391108	+	0.677418i
$865$	−2.29543	−	3.97581i	−0.0780471	−	0.135181i
$866$	−0.113433	+	0.196472i	−0.00385463	+	0.00667641i
$867$	−12.9778			−0.440749
$868$	−10.6629	+	9.80595i	−0.361923	+	0.332836i
$869$	−39.8397			−1.35147
$870$	−0.865303	+	1.49875i	−0.0293365	+	0.0508123i
$871$		0			0
$872$	6.62771	+	11.4795i	0.224443	+	0.388746i
$873$	20.8918	−	36.1857i	0.707081	−	1.22470i
$874$	6.60574			0.223442
$875$	18.5924	+	5.82560i	0.628539	+	0.196941i
$876$	−5.39742			−0.182362
$877$	−4.34753	+	7.53015i	−0.146806	+	0.254275i	−0.930045	−	0.367445i	$-0.880233\pi$
$877$	−4.34753	+	7.53015i	−0.146806	+	0.254275i	0.783239	+	0.621720i	$0.213566\pi$
$878$	5.54324	+	9.60118i	0.187075	+	0.324024i
$879$	3.59616	+	6.22873i	0.121296	+	0.210090i
$880$	−7.41281	+	12.8394i	−0.249886	+	0.432815i
$881$	54.5460			1.83770			0.918851	−	0.394605i	$-0.129119\pi$
$881$	54.5460			1.83770			0.918851	+	0.394605i	$0.129119\pi$
$882$	−0.826865	+	9.85756i	−0.0278420	+	0.331921i
$883$	−6.72397			−0.226280			−0.113140	−	0.993579i	$-0.536091\pi$
$883$	−6.72397			−0.226280			−0.113140	+	0.993579i	$0.536091\pi$
$884$		0			0
$885$	10.3497	+	17.9262i	0.347902	+	0.602583i
$886$	5.28691	+	9.15720i	0.177617	+	0.307642i
$887$	7.71195	−	13.3575i	0.258942	−	0.448500i	−0.707017	−	0.707197i	$-0.749960\pi$
$887$	7.71195	−	13.3575i	0.258942	−	0.448500i	0.965959	+	0.258696i	$0.0832929\pi$
$888$	18.1108			0.607759
$889$	51.7704	+	16.2213i	1.73632	+	0.544044i
$890$	−5.82653			−0.195306
$891$	−5.34673	+	9.26080i	−0.179122	+	0.310249i
$892$	1.12666	+	1.95143i	0.0377234	+	0.0653388i
$893$	8.81412	+	15.2665i	0.294953	+	0.510874i
$894$	2.15155	−	3.72660i	0.0719587	−	0.124636i
$895$	28.5445			0.954138
$896$	−22.3996	+	20.5994i	−0.748318	+	0.688177i
$897$		0			0
$898$	−2.36182	+	4.09079i	−0.0788149	+	0.136511i
$899$	−2.33407	−	4.04273i	−0.0778456	−	0.134833i
$900$	−4.50438	−	7.80181i	−0.150146	−	0.260060i
$901$	−1.02261	+	1.77121i	−0.0340680	+	0.0590075i
$902$	18.4774			0.615231
$903$	−4.21293	−	18.8435i	−0.140197	−	0.627074i
$904$	12.5953			0.418914
$905$	24.9868	−	43.2783i	0.830588	−	1.43862i
$906$	−0.203980	−	0.353304i	−0.00677679	−	0.0117378i
$907$	25.6958	+	44.5064i	0.853214	+	1.47781i	0.878292	+	0.478125i	$0.158683\pi$
$907$	25.6958	+	44.5064i	0.853214	+	1.47781i	−0.0250777	+	0.999686i	$0.507983\pi$
$908$	−5.19306	+	8.99464i	−0.172338	+	0.298498i
$909$	−40.7749			−1.35242
$910$		0			0
$911$	14.8168			0.490902			0.245451	−	0.969409i	$-0.421064\pi$
$911$	14.8168			0.490902			0.245451	+	0.969409i	$0.421064\pi$
$912$	1.54953	−	2.68387i	0.0513101	−	0.0888718i
$913$	6.72240	+	11.6435i	0.222479	+	0.385345i
$914$	0.130144	+	0.225415i	0.00430477	+	0.00745608i
$915$	10.3962	−	18.0068i	0.343688	−	0.595286i
$916$	33.5336			1.10798
$917$	21.5846	−	19.8499i	0.712787	−	0.655501i
$918$	1.16867			0.0385719
$919$	1.71292	−	2.96687i	0.0565041	−	0.0978680i	−0.836390	−	0.548135i	$-0.815338\pi$
$919$	1.71292	−	2.96687i	0.0565041	−	0.0978680i	0.892894	+	0.450267i	$0.148671\pi$
$920$	−16.5867	−	28.7290i	−0.546847	−	0.947167i
$921$	−2.56195	−	4.43744i	−0.0844193	−	0.146218i
$922$	9.03311	−	15.6458i	0.297490	−	0.515267i
$923$		0			0
$924$	8.69834	+	2.72546i	0.286154	+	0.0896611i
$925$	−24.6978			−0.812059
$926$	−7.46798	+	12.9349i	−0.245413	+	0.425068i
$927$	−18.9809	−	32.8758i	−0.623414	−	1.07978i
$928$	−3.87861	−	6.71795i	−0.127322	−	0.220527i
$929$	−4.82923	+	8.36448i	−0.158442	+	0.274430i	−0.934307	−	0.356469i	$-0.883980\pi$
$929$	−4.82923	+	8.36448i	−0.158442	+	0.274430i	0.775865	+	0.630899i	$0.217314\pi$
$930$	4.06406			0.133266
$931$	12.4232	−	5.84727i	0.407153	−	0.191636i
$932$	8.88644			0.291085
$933$	10.3307	−	17.8932i	0.338211	−	0.585798i
$934$	−7.20294	−	12.4759i	−0.235687	−	0.408223i
$935$	1.72504	+	2.98785i	0.0564147	+	0.0977131i
$936$		0			0
$937$	−50.9972			−1.66601			−0.833003	−	0.553269i	$-0.813380\pi$
$937$	−50.9972			−1.66601			−0.833003	+	0.553269i	$0.813380\pi$
$938$	−5.06558	−	1.58720i	−0.165397	−	0.0518241i
$939$	18.2545			0.595712
$940$	20.0342	−	34.7002i	0.653443	−	1.13180i
$941$	−1.74937	−	3.03001i	−0.0570280	−	0.0987754i	0.836102	−	0.548574i	$-0.184829\pi$
$941$	−1.74937	−	3.03001i	−0.0570280	−	0.0987754i	−0.893130	+	0.449799i	$0.851496\pi$
$942$	3.80596	+	6.59211i	0.124005	+	0.214783i
$943$	33.3649	−	57.7896i	1.08651	−	1.88189i
$944$	−20.2656			−0.659590
$945$	−21.9410	+	20.1776i	−0.713741	+	0.656378i
$946$	−14.9478			−0.485995
$947$	−20.8990	+	36.1980i	−0.679125	+	1.17628i	0.296120	+	0.955151i	$0.404307\pi$
$947$	−20.8990	+	36.1980i	−0.679125	+	1.17628i	−0.975245	+	0.221128i	$0.929026\pi$
$948$	−9.46448	−	16.3930i	−0.307392	−	0.532418i
$949$		0			0
$950$	1.30925	−	2.26768i	0.0424775	−	0.0735732i
$951$	−0.555590			−0.0180162
$952$	0.589843	+	2.63824i	0.0191169	+	0.0855060i
$953$	52.4011			1.69744			0.848720	−	0.528843i	$-0.177374\pi$
$953$	52.4011			1.69744			0.848720	+	0.528843i	$0.177374\pi$
$954$	−3.04091	+	5.26702i	−0.0984532	+	0.170526i
$955$	−26.2778	−	45.5145i	−0.850329	−	1.47281i
$956$	4.81470	+	8.33930i	0.155719	+	0.269712i
$957$	−1.46868	+	2.54383i	−0.0474756	+	0.0822302i
$958$	−6.36558			−0.205663
$959$	5.56222	+	24.8786i	0.179613	+	0.803373i
$960$	−1.76574			−0.0569891
$961$	10.0188	−	17.3531i	0.323187	−	0.559776i
$962$		0			0
$963$	0.0703163	+	0.121791i	0.00226591	+	0.00392468i
$964$	−17.7545	+	30.7516i	−0.571833	+	0.990443i
$965$	20.9149			0.673276
$966$	−5.07411	+	4.66631i	−0.163257	+	0.150136i
$967$	28.3865			0.912847			0.456424	−	0.889763i	$-0.349130\pi$
$967$	28.3865			0.912847			0.456424	+	0.889763i	$0.349130\pi$
$968$	−4.03009	+	6.98033i	−0.129532	+	0.224356i
$969$	−0.360592	−	0.624563i	−0.0115839	−	0.0200639i
$970$	−13.8024	−	23.9065i	−0.443169	−	0.767591i
$971$	3.53431	−	6.12160i	0.113421	−	0.196451i	−0.803726	−	0.594999i	$-0.797152\pi$
$971$	3.53431	−	6.12160i	0.113421	−	0.196451i	0.917148	+	0.398548i	$0.130486\pi$
$972$	−25.8130			−0.827953
$973$	11.9065	+	3.73067i	0.381704	+	0.119600i
$974$	−4.90153			−0.157055
$975$		0			0
$976$	10.1783	+	17.6294i	0.325801	+	0.564304i
$977$	−16.5871	−	28.7297i	−0.530669	−	0.919146i	−0.999360	−	0.0357834i	$-0.988607\pi$
$977$	−16.5871	−	28.7297i	−0.530669	−	0.919146i	0.468690	−	0.883362i	$-0.344726\pi$
$978$	2.52959	−	4.38138i	0.0808875	−	0.140101i
$979$	−9.88937			−0.316066
$980$	−25.6287	−	17.8090i	−0.818680	−	0.568887i
$981$	−14.8049			−0.472683
$982$	0.263295	−	0.456040i	0.00840208	−	0.0145528i
$983$	6.88095	+	11.9182i	0.219468	+	0.380130i	0.954646	−	0.297745i	$-0.0962344\pi$
$983$	6.88095	+	11.9182i	0.219468	+	0.380130i	−0.735177	+	0.677875i	$0.762901\pi$
$984$	9.69836	+	16.7980i	0.309172	+	0.535502i
$985$	1.40044	−	2.42564i	0.0446218	−	0.0772872i
$986$	−0.394290			−0.0125567
$987$	−17.5547	−	5.50045i	−0.558774	−	0.175081i
$988$		0			0
$989$	−26.9914	+	46.7504i	−0.858275	+	1.48658i
$990$	5.12971	+	8.88492i	0.163033	+	0.282381i
$991$	−3.15910	−	5.47172i	−0.100352	−	0.173815i	0.811478	−	0.584383i	$-0.198664\pi$
$991$	−3.15910	−	5.47172i	−0.100352	−	0.173815i	−0.911830	+	0.410569i	$0.865330\pi$
$992$	−9.10832	+	15.7761i	−0.289190	+	0.500891i
$993$	−7.34304			−0.233024
$994$	−6.04739	+	5.56137i	−0.191812	+	0.176396i
$995$	35.9676			1.14025
$996$	−3.19400	+	5.53217i	−0.101206	+	0.175293i
$997$	−0.370208	−	0.641219i	−0.0117246	−	0.0203076i	0.860104	−	0.510119i	$-0.170399\pi$
$997$	−0.370208	−	0.641219i	−0.0117246	−	0.0203076i	−0.871828	+	0.489812i	$0.837065\pi$
$998$	−1.94479	−	3.36848i	−0.0615613	−	0.106627i
$999$	−22.7487	+	39.4020i	−0.719739	+	1.24662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.k.170.11	✓	48
7.2	even	3		8281.2.a.cv.1.14		24
7.4	even	3	inner	1183.2.e.k.508.11	yes	48
7.5	odd	6		8281.2.a.cw.1.14		24
13.12	even	2		1183.2.e.l.170.14	yes	48
91.12	odd	6		8281.2.a.ct.1.11		24
91.25	even	6		1183.2.e.l.508.14	yes	48
91.51	even	6		8281.2.a.cu.1.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.11	✓	48	1.1	even	1	trivial
1183.2.e.k.508.11	yes	48	7.4	even	3	inner
1183.2.e.l.170.14	yes	48	13.12	even	2
1183.2.e.l.508.14	yes	48	91.25	even	6
8281.2.a.ct.1.11		24	91.12	odd	6
8281.2.a.cu.1.11		24	91.51	even	6
8281.2.a.cv.1.14		24	7.2	even	3
8281.2.a.cw.1.14		24	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.294236 + 0.509631i) q^{2} +(-0.386839 - 0.670024i) q^{3} +(0.826851 + 1.43215i) q^{4} +(-1.34801 + 2.33482i) q^{5} +0.455287 q^{6} +(-2.52472 - 0.791073i) q^{7} -2.15010 q^{8} +(1.20071 - 2.07969i) q^{9} +O(q^{10})\)	\(q+(-0.294236 + 0.509631i) q^{2} +(-0.386839 - 0.670024i) q^{3} +(0.826851 + 1.43215i) q^{4} +(-1.34801 + 2.33482i) q^{5} +0.455287 q^{6} +(-2.52472 - 0.791073i) q^{7} -2.15010 q^{8} +(1.20071 - 2.07969i) q^{9} +(-0.793264 - 1.37397i) q^{10} +(-1.34641 - 2.33205i) q^{11} +(0.639715 - 1.10802i) q^{12} +(1.14602 - 1.05391i) q^{14} +2.08585 q^{15} +(-1.02107 + 1.76854i) q^{16} +(0.237613 + 0.411557i) q^{17} +(0.706584 + 1.22384i) q^{18} +(0.980747 - 1.69870i) q^{19} -4.45841 q^{20} +(0.446620 + 1.99764i) q^{21} +1.58464 q^{22} +(2.86140 - 4.95610i) q^{23} +(0.831741 + 1.44062i) q^{24} +(-1.13425 - 1.96458i) q^{25} -4.17896 q^{27} +(-0.954632 - 4.26987i) q^{28} +1.40991 q^{29} +(-0.613730 + 1.06301i) q^{30} +(-1.65548 - 2.86737i) q^{31} +(-2.75097 - 4.76481i) q^{32} +(-1.04168 + 1.80425i) q^{33} -0.279656 q^{34} +(5.25035 - 4.82838i) q^{35} +3.97124 q^{36} +(5.44364 - 9.42866i) q^{37} +(0.577141 + 0.999638i) q^{38} +(2.89835 - 5.02009i) q^{40} +11.6603 q^{41} +(-1.14947 - 0.360165i) q^{42} -9.43290 q^{43} +(2.22656 - 3.85651i) q^{44} +(3.23714 + 5.60689i) q^{45} +(1.68385 + 2.91652i) q^{46} +(-4.49357 + 7.78310i) q^{47} +1.57995 q^{48} +(5.74841 + 3.99447i) q^{49} +1.33495 q^{50} +(0.183835 - 0.318412i) q^{51} +(2.15184 + 3.72710i) q^{53} +(1.22960 - 2.12973i) q^{54} +7.25987 q^{55} +(5.42839 + 1.70089i) q^{56} -1.51756 q^{57} +(-0.414845 + 0.718533i) q^{58} +(4.96188 + 8.59422i) q^{59} +(1.72468 + 2.98724i) q^{60} +(4.98418 - 8.63285i) q^{61} +1.94840 q^{62} +(-4.67665 + 4.30079i) q^{63} -0.846536 q^{64} +(-0.613001 - 1.06175i) q^{66} +(-1.70475 - 2.95272i) q^{67} +(-0.392940 + 0.680592i) q^{68} -4.42761 q^{69} +(0.915854 + 4.09643i) q^{70} -5.27688 q^{71} +(-2.58165 + 4.47155i) q^{72} +(-2.10930 - 3.65342i) q^{73} +(3.20343 + 5.54850i) q^{74} +(-0.877543 + 1.51995i) q^{75} +3.24373 q^{76} +(1.55448 + 6.95286i) q^{77} +(7.39741 - 12.8127i) q^{79} +(-2.75281 - 4.76801i) q^{80} +(-1.98555 - 3.43908i) q^{81} +(-3.43088 + 5.94246i) q^{82} -4.99284 q^{83} +(-2.49163 + 2.29138i) q^{84} -1.28121 q^{85} +(2.77550 - 4.80730i) q^{86} +(-0.545407 - 0.944672i) q^{87} +(2.89491 + 5.01413i) q^{88} +(1.83625 - 3.18048i) q^{89} -3.80993 q^{90} +9.46382 q^{92} +(-1.28080 + 2.21842i) q^{93} +(-2.64434 - 4.58013i) q^{94} +(2.64411 + 4.57973i) q^{95} +(-2.12836 + 3.68643i) q^{96} +17.3995 q^{97} +(-3.72709 + 1.75425i) q^{98} -6.46659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Introduction

L-functions

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