LMFDB - Embedded newform 804.2.j.b.499.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.20
Character	$\chi$	$=$	804.499
Dual form			804.2.j.b.775.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.315172 - 1.37865i) q^{2} +1.00000 q^{3} +(-1.80133 - 0.869020i) q^{4} +2.49461i q^{5} +(0.315172 - 1.37865i) q^{6} +(1.03268 - 1.78865i) q^{7} +(-1.76580 + 2.20951i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.315172 - 1.37865i) q^{2} +1.00000 q^{3} +(-1.80133 - 0.869020i) q^{4} +2.49461i q^{5} +(0.315172 - 1.37865i) q^{6} +(1.03268 - 1.78865i) q^{7} +(-1.76580 + 2.20951i) q^{8} +1.00000 q^{9} +(3.43919 + 0.786230i) q^{10} +(-1.12863 + 1.95485i) q^{11} +(-1.80133 - 0.869020i) q^{12} +(2.84463 - 1.64235i) q^{13} +(-2.14045 - 1.98743i) q^{14} +2.49461i q^{15} +(2.48961 + 3.13079i) q^{16} +(0.194453 + 0.336802i) q^{17} +(0.315172 - 1.37865i) q^{18} +(7.27526 - 4.20038i) q^{19} +(2.16787 - 4.49363i) q^{20} +(1.03268 - 1.78865i) q^{21} +(2.33933 + 2.17210i) q^{22} +(4.44361 - 2.56552i) q^{23} +(-1.76580 + 2.20951i) q^{24} -1.22308 q^{25} +(-1.36767 - 4.43937i) q^{26} +1.00000 q^{27} +(-3.41458 + 2.32454i) q^{28} +(-1.15724 + 2.00439i) q^{29} +(3.43919 + 0.786230i) q^{30} +(-0.712032 + 1.23328i) q^{31} +(5.10091 - 2.44555i) q^{32} +(-1.12863 + 1.95485i) q^{33} +(0.525617 - 0.161931i) q^{34} +(4.46200 + 2.57614i) q^{35} +(-1.80133 - 0.869020i) q^{36} +(0.330689 + 0.572770i) q^{37} +(-3.49788 - 11.3539i) q^{38} +(2.84463 - 1.64235i) q^{39} +(-5.51187 - 4.40499i) q^{40} +(1.06131 + 0.612750i) q^{41} +(-2.14045 - 1.98743i) q^{42} -6.64380 q^{43} +(3.73184 - 2.54053i) q^{44} +2.49461i q^{45} +(-2.13645 - 6.93475i) q^{46} +(3.37137 + 1.94646i) q^{47} +(2.48961 + 3.13079i) q^{48} +(1.36714 + 2.36796i) q^{49} +(-0.385481 + 1.68620i) q^{50} +(0.194453 + 0.336802i) q^{51} +(-6.55137 + 0.486376i) q^{52} +0.907658i q^{53} +(0.315172 - 1.37865i) q^{54} +(-4.87658 - 2.81549i) q^{55} +(2.12855 + 5.44013i) q^{56} +(7.27526 - 4.20038i) q^{57} +(2.39862 + 2.22715i) q^{58} +2.53002i q^{59} +(2.16787 - 4.49363i) q^{60} +(11.8782 - 6.85789i) q^{61} +(1.47584 + 1.37033i) q^{62} +(1.03268 - 1.78865i) q^{63} +(-1.76389 - 7.80312i) q^{64} +(4.09702 + 7.09625i) q^{65} +(2.33933 + 2.17210i) q^{66} +(-6.14974 + 5.40192i) q^{67} +(-0.0575865 - 0.775676i) q^{68} +(4.44361 - 2.56552i) q^{69} +(4.95787 - 5.33959i) q^{70} +(-13.1632 - 7.59978i) q^{71} +(-1.76580 + 2.20951i) q^{72} +(-4.82904 - 8.36414i) q^{73} +(0.893871 - 0.275382i) q^{74} -1.22308 q^{75} +(-16.7554 + 1.24393i) q^{76} +(2.33103 + 4.03746i) q^{77} +(-1.36767 - 4.43937i) q^{78} +(-6.39671 + 11.0794i) q^{79} +(-7.81011 + 6.21060i) q^{80} +1.00000 q^{81} +(1.17926 - 1.27006i) q^{82} +(-0.879905 + 0.508013i) q^{83} +(-3.41458 + 2.32454i) q^{84} +(-0.840190 + 0.485084i) q^{85} +(-2.09394 + 9.15946i) q^{86} +(-1.15724 + 2.00439i) q^{87} +(-2.32632 - 5.94559i) q^{88} -7.19134 q^{89} +(3.43919 + 0.786230i) q^{90} -6.78409i q^{91} +(-10.2339 + 0.759769i) q^{92} +(-0.712032 + 1.23328i) q^{93} +(3.74604 - 4.03446i) q^{94} +(10.4783 + 18.1490i) q^{95} +(5.10091 - 2.44555i) q^{96} +(-8.05372 + 4.64982i) q^{97} +(3.69547 - 1.13849i) q^{98} +(-1.12863 + 1.95485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.315172	−	1.37865i	0.222860	−	0.974850i
$2$	0.315172	−	1.37865i	0.222860	−	0.974850i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.80133	−	0.869020i	−0.900667	−	0.434510i
$5$			2.49461i			1.11562i	0.829967	+	0.557812i	$0.188359\pi$
$5$			2.49461i			1.11562i	−0.829967	+	0.557812i	$0.811641\pi$
$6$	0.315172	−	1.37865i	0.128668	−	0.562830i
$7$	1.03268	−	1.78865i	0.390316	−	0.676048i	−0.602175	−	0.798364i	$-0.705699\pi$
$7$	1.03268	−	1.78865i	0.390316	−	0.676048i	0.992491	+	0.122316i	$0.0390323\pi$
$8$	−1.76580	+	2.20951i	−0.624305	+	0.781181i
$9$	1.00000			0.333333
$10$	3.43919	+	0.786230i	1.08757	+	0.248628i
$11$	−1.12863	+	1.95485i	−0.340295	+	0.589408i	−0.984487	−	0.175455i	$-0.943860\pi$
$11$	−1.12863	+	1.95485i	−0.340295	+	0.589408i	0.644192	+	0.764863i	$0.277194\pi$
$12$	−1.80133	−	0.869020i	−0.520000	−	0.250865i
$13$	2.84463	−	1.64235i	0.788959	−	0.455506i	−0.0506367	−	0.998717i	$-0.516125\pi$
$13$	2.84463	−	1.64235i	0.788959	−	0.455506i	0.839596	+	0.543211i	$0.182792\pi$
$14$	−2.14045	−	1.98743i	−0.572060	−	0.531164i
$15$			2.49461i			0.644106i
$16$	2.48961	+	3.13079i	0.622402	+	0.782698i
$17$	0.194453	+	0.336802i	0.0471617	+	0.0816865i	0.888643	−	0.458600i	$-0.151649\pi$
$17$	0.194453	+	0.336802i	0.0471617	+	0.0816865i	−0.841481	+	0.540287i	$0.818316\pi$
$18$	0.315172	−	1.37865i	0.0742866	−	0.324950i
$19$	7.27526	−	4.20038i	1.66906	−	0.963632i	0.700914	−	0.713246i	$-0.252776\pi$
$19$	7.27526	−	4.20038i	1.66906	−	0.963632i	0.968146	−	0.250387i	$-0.0805578\pi$
$20$	2.16787	−	4.49363i	0.484750	−	1.00481i
$21$	1.03268	−	1.78865i	0.225349	−	0.390316i
$22$	2.33933	+	2.17210i	0.498747	+	0.463092i
$23$	4.44361	−	2.56552i	0.926557	−	0.534948i	0.0408358	−	0.999166i	$-0.486998\pi$
$23$	4.44361	−	2.56552i	0.926557	−	0.534948i	0.885721	+	0.464218i	$0.153665\pi$
$24$	−1.76580	+	2.20951i	−0.360443	+	0.451015i
$25$	−1.22308			−0.244617
$26$	−1.36767	−	4.43937i	−0.268223	−	0.870631i
$27$	1.00000			0.192450
$28$	−3.41458	+	2.32454i	−0.645295	+	0.439297i
$29$	−1.15724	+	2.00439i	−0.214894	+	0.372207i	−0.953240	−	0.302215i	$-0.902274\pi$
$29$	−1.15724	+	2.00439i	−0.214894	+	0.372207i	0.738346	+	0.674422i	$0.235607\pi$
$30$	3.43919	+	0.786230i	0.627907	+	0.143545i
$31$	−0.712032	+	1.23328i	−0.127885	+	0.221503i	−0.922857	−	0.385143i	$-0.874152\pi$
$31$	−0.712032	+	1.23328i	−0.127885	+	0.221503i	0.794972	+	0.606646i	$0.207485\pi$
$32$	5.10091	−	2.44555i	0.901722	−	0.432317i
$33$	−1.12863	+	1.95485i	−0.196469	+	0.340295i
$34$	0.525617	−	0.161931i	0.0901426	−	0.0277710i
$35$	4.46200	+	2.57614i	0.754215	+	0.435446i
$36$	−1.80133	−	0.869020i	−0.300222	−	0.144837i
$37$	0.330689	+	0.572770i	0.0543649	+	0.0941628i	0.891927	−	0.452179i	$-0.149353\pi$
$37$	0.330689	+	0.572770i	0.0543649	+	0.0941628i	−0.837562	+	0.546342i	$0.816020\pi$
$38$	−3.49788	−	11.3539i	−0.567431	−	1.84184i
$39$	2.84463	−	1.64235i	0.455506	−	0.262986i
$40$	−5.51187	−	4.40499i	−0.871504	−	0.696490i
$41$	1.06131	+	0.612750i	0.165749	+	0.0956954i	0.580580	−	0.814203i	$-0.302826\pi$
$41$	1.06131	+	0.612750i	0.165749	+	0.0956954i	−0.414831	+	0.909899i	$0.636159\pi$
$42$	−2.14045	−	1.98743i	−0.330279	−	0.306668i
$43$	−6.64380			−1.01317			−0.506585	−	0.862190i	$-0.669092\pi$
$43$	−6.64380			−1.01317			−0.506585	+	0.862190i	$0.669092\pi$
$44$	3.73184	−	2.54053i	0.562596	−	0.382999i
$45$			2.49461i			0.371875i
$46$	−2.13645	−	6.93475i	−0.315002	−	1.02247i
$47$	3.37137	+	1.94646i	0.491765	+	0.283921i	0.725306	−	0.688426i	$-0.241698\pi$
$47$	3.37137	+	1.94646i	0.491765	+	0.283921i	−0.233541	+	0.972347i	$0.575031\pi$
$48$	2.48961	+	3.13079i	0.359344	+	0.451891i
$49$	1.36714	+	2.36796i	0.195306	+	0.338280i
$50$	−0.385481	+	1.68620i	−0.0545153	+	0.238465i
$51$	0.194453	+	0.336802i	0.0272288	+	0.0471617i
$52$	−6.55137	+	0.486376i	−0.908512	+	0.0674482i
$53$			0.907658i			0.124676i	0.998055	+	0.0623382i	$0.0198557\pi$
$53$			0.907658i			0.124676i	−0.998055	+	0.0623382i	$0.980144\pi$
$54$	0.315172	−	1.37865i	0.0428894	−	0.187610i
$55$	−4.87658	−	2.81549i	−0.657558	−	0.379641i
$56$	2.12855	+	5.44013i	0.284439	+	0.726968i
$57$	7.27526	−	4.20038i	0.963632	−	0.556353i
$58$	2.39862	+	2.22715i	0.314955	+	0.292439i
$59$			2.53002i			0.329381i	0.986345	+	0.164690i	$0.0526625\pi$
$59$			2.53002i			0.329381i	−0.986345	+	0.164690i	$0.947338\pi$
$60$	2.16787	−	4.49363i	0.279871	−	0.580125i
$61$	11.8782	−	6.85789i	1.52085	−	0.878062i	0.521151	−	0.853464i	$-0.325503\pi$
$61$	11.8782	−	6.85789i	1.52085	−	0.878062i	0.999697	−	0.0245981i	$-0.00783061\pi$
$62$	1.47584	+	1.37033i	0.187432	+	0.174033i
$63$	1.03268	−	1.78865i	0.130105	−	0.225349i
$64$	−1.76389	−	7.80312i	−0.220487	−	0.975390i
$65$	4.09702	+	7.09625i	0.508173	+	0.880182i
$66$	2.33933	+	2.17210i	0.287952	+	0.267366i
$67$	−6.14974	+	5.40192i	−0.751310	+	0.659949i
$67$	−6.14974	+	5.40192i	−0.751310	+	0.659949i
$68$	−0.0575865	−	0.775676i	−0.00698339	−	0.0940645i
$69$	4.44361	−	2.56552i	0.534948	−	0.308852i
$70$	4.95787	−	5.33959i	0.592579	−	0.638203i
$71$	−13.1632	−	7.59978i	−1.56218	−	0.901927i	−0.997036	−	0.0769382i	$-0.975486\pi$
$71$	−13.1632	−	7.59978i	−1.56218	−	0.901927i	−0.565148	−	0.824989i	$-0.691181\pi$
$72$	−1.76580	+	2.20951i	−0.208102	+	0.260394i
$73$	−4.82904	−	8.36414i	−0.565196	−	0.978949i	−0.997031	−	0.0769962i	$-0.975467\pi$
$73$	−4.82904	−	8.36414i	−0.565196	−	0.978949i	0.431835	−	0.901953i	$-0.357866\pi$
$74$	0.893871	−	0.275382i	0.103910	−	0.0320125i
$75$	−1.22308			−0.141230
$76$	−16.7554	+	1.24393i	−1.92198	+	0.142688i
$77$	2.33103	+	4.03746i	0.265645	+	0.460111i
$78$	−1.36767	−	4.43937i	−0.154858	−	0.502659i
$79$	−6.39671	+	11.0794i	−0.719686	+	1.24653i	0.241438	+	0.970416i	$0.422381\pi$
$79$	−6.39671	+	11.0794i	−0.719686	+	1.24653i	−0.961124	+	0.276117i	$0.910952\pi$
$80$	−7.81011	+	6.21060i	−0.873197	+	0.694366i
$81$	1.00000			0.111111
$82$	1.17926	−	1.27006i	0.130228	−	0.140254i
$83$	−0.879905	+	0.508013i	−0.0965821	+	0.0557617i	−0.547513	−	0.836797i	$-0.684425\pi$
$83$	−0.879905	+	0.508013i	−0.0965821	+	0.0557617i	0.450931	+	0.892559i	$0.351092\pi$
$84$	−3.41458	+	2.32454i	−0.372561	+	0.253629i
$85$	−0.840190	+	0.485084i	−0.0911314	+	0.0526147i
$86$	−2.09394	+	9.15946i	−0.225795	+	0.987690i
$87$	−1.15724	+	2.00439i	−0.124069	+	0.214894i
$88$	−2.32632	−	5.94559i	−0.247986	−	0.633802i
$89$	−7.19134			−0.762281			−0.381141	−	0.924517i	$-0.624469\pi$
$89$	−7.19134			−0.762281			−0.381141	+	0.924517i	$0.624469\pi$
$90$	3.43919	+	0.786230i	0.362522	+	0.0828759i
$91$		−	6.78409i		−	0.711166i
$92$	−10.2339	+	0.759769i	−1.06696	+	0.0792114i
$93$	−0.712032	+	1.23328i	−0.0738343	+	0.127885i
$94$	3.74604	−	4.03446i	0.386375	−	0.416123i
$95$	10.4783	+	18.1490i	1.07505	+	1.86204i
$96$	5.10091	−	2.44555i	0.520609	−	0.249598i
$97$	−8.05372	+	4.64982i	−0.817731	+	0.472117i	−0.849633	−	0.527374i	$-0.823177\pi$
$97$	−8.05372	+	4.64982i	−0.817731	+	0.472117i	0.0319022	+	0.999491i	$0.489843\pi$
$98$	3.69547	−	1.13849i	0.373299	−	0.115005i
$99$	−1.12863	+	1.95485i	−0.113432	+	0.196469i
$100$	2.20318	+	1.06288i	0.220318	+	0.106288i
$101$	−3.47005	−	2.00343i	−0.345283	−	0.199349i	0.317323	−	0.948318i	$-0.397216\pi$
$101$	−3.47005	−	2.00343i	−0.345283	−	0.199349i	−0.662606	+	0.748969i	$0.730549\pi$
$102$	0.525617	−	0.161931i	0.0520438	−	0.0160336i
$103$	−12.8920	−	7.44322i	−1.27029	−	0.733402i	−0.295247	−	0.955421i	$-0.595402\pi$
$103$	−12.8920	−	7.44322i	−1.27029	−	0.733402i	−0.975042	+	0.222019i	$0.928735\pi$
$104$	−1.39426	+	9.18532i	−0.136719	+	0.900694i
$105$	4.46200	+	2.57614i	0.435446	+	0.251405i
$106$	1.25134	+	0.286068i	0.121541	+	0.0277854i
$107$			11.9824i			1.15838i	0.815192	+	0.579191i	$0.196631\pi$
$107$			11.9824i			1.15838i	−0.815192	+	0.579191i	$0.803369\pi$
$108$	−1.80133	−	0.869020i	−0.173333	−	0.0836215i
$109$		−	12.7634i		−	1.22251i	−0.791434	−	0.611255i	$-0.790665\pi$
$109$		−	12.7634i		−	1.22251i	0.791434	−	0.611255i	$-0.209335\pi$
$110$	−5.41853	+	5.83572i	−0.516637	+	0.556414i
$111$	0.330689	+	0.572770i	0.0313876	+	0.0543649i
$112$	8.17087	−	1.21994i	0.772075	−	0.115274i
$113$	−3.27862	−	1.89291i	−0.308427	−	0.178070i	0.337795	−	0.941220i	$-0.390319\pi$
$113$	−3.27862	−	1.89291i	−0.308427	−	0.178070i	−0.646222	+	0.763149i	$0.723652\pi$
$114$	−3.49788	−	11.3539i	−0.327606	−	1.06339i
$115$	6.39997	+	11.0851i	0.596801	+	1.03369i
$116$	3.82643	−	2.60492i	0.355275	−	0.241861i
$117$	2.84463	−	1.64235i	0.262986	−	0.151835i
$118$	3.48800	+	0.797390i	0.321097	+	0.0734057i
$119$	0.803230			0.0736320
$120$	−5.51187	−	4.40499i	−0.503163	−	0.402118i
$121$	2.95238	+	5.11368i	0.268399	+	0.464880i
$122$	−5.71093	−	18.5373i	−0.517043	−	1.67829i
$123$	1.06131	+	0.612750i	0.0956954	+	0.0552498i
$124$	2.35435	−	1.60277i	0.211427	−	0.143933i
$125$			9.42194i			0.842724i
$126$	−2.14045	−	1.98743i	−0.190687	−	0.177055i
$127$	−1.02639	−	0.592589i	−0.0910778	−	0.0525838i	0.453769	−	0.891119i	$-0.350079\pi$
$127$	−1.02639	−	0.592589i	−0.0910778	−	0.0525838i	−0.544847	+	0.838535i	$0.683412\pi$
$128$	−11.3137	−	0.0275367i	−0.999997	−	0.00243392i
$129$	−6.64380			−0.584954
$130$	11.0745	−	3.41181i	0.971297	−	0.299236i
$131$		−	8.87034i		−	0.775005i	−0.921869	−	0.387502i	$-0.873338\pi$
$131$		−	8.87034i		−	0.775005i	0.921869	−	0.387502i	$-0.126662\pi$
$132$	3.73184	−	2.54053i	0.324815	−	0.221124i
$133$		−	17.3506i		−	1.50449i
$134$	5.50911	+	10.1808i	0.475915	+	0.879491i
$135$			2.49461i			0.214702i
$136$	−1.08753	−	0.165080i	−0.0932552	−	0.0141555i
$137$			11.9192i			1.01833i	0.860669	+	0.509165i	$0.170046\pi$
$137$			11.9192i			1.01833i	−0.860669	+	0.509165i	$0.829954\pi$
$138$	−2.13645	−	6.93475i	−0.181866	−	0.590325i
$139$	10.3522			0.878062			0.439031	−	0.898472i	$-0.355322\pi$
$139$	10.3522			0.878062			0.439031	+	0.898472i	$0.355322\pi$
$140$	−5.79883	−	8.51805i	−0.490091	−	0.719906i
$141$	3.37137	+	1.94646i	0.283921	+	0.163922i
$142$	−14.6261	+	15.7522i	−1.22739	+	1.32189i
$143$			7.41443i			0.620026i
$144$	2.48961	+	3.13079i	0.207467	+	0.260899i
$145$	−5.00018	−	2.88686i	−0.415243	−	0.239740i
$146$	−13.0532	+	4.02140i	−1.08029	+	0.332814i
$147$	1.36714	+	2.36796i	0.112760	+	0.195306i
$148$	−0.0979323	−	1.31912i	−0.00804999	−	0.108431i
$149$	13.1688			1.07883			0.539414	−	0.842041i	$-0.318646\pi$
$149$	13.1688			1.07883			0.539414	+	0.842041i	$0.318646\pi$
$150$	−0.385481	+	1.68620i	−0.0314744	+	0.137678i
$151$	−9.27090	+	5.35256i	−0.754455	+	0.435585i	−0.827301	−	0.561758i	$-0.810125\pi$
$151$	−9.27090	+	5.35256i	−0.754455	+	0.435585i	0.0728463	+	0.997343i	$0.476792\pi$
$152$	−3.56589	+	23.4918i	−0.289232	+	1.90544i
$153$	0.194453	+	0.336802i	0.0157206	+	0.0272288i
$154$	6.30091	−	1.94117i	0.507742	−	0.156424i
$155$	−3.07654	−	1.77624i	−0.247114	−	0.142671i
$156$	−6.55137	+	0.486376i	−0.524529	+	0.0389413i
$157$	−0.764278	−	1.32377i	−0.0609960	−	0.105648i	0.833915	−	0.551893i	$-0.186094\pi$
$157$	−0.764278	−	1.32377i	−0.0609960	−	0.105648i	−0.894911	+	0.446245i	$0.852761\pi$
$158$	13.2586	+	12.3107i	1.05479	+	0.979389i
$159$			0.907658i			0.0719820i
$160$	6.10070	+	12.7248i	0.482303	+	1.00598i
$161$		−	10.5974i		−	0.835196i
$162$	0.315172	−	1.37865i	0.0247622	−	0.108317i
$163$	0.794906	+	0.458939i	0.0622619	+	0.0359469i	0.530808	−	0.847492i	$-0.321889\pi$
$163$	0.794906	+	0.458939i	0.0622619	+	0.0359469i	−0.468546	+	0.883439i	$0.655222\pi$
$164$	−1.37929	−	2.02607i	−0.107704	−	0.158209i
$165$	−4.87658	−	2.81549i	−0.379641	−	0.219186i
$166$	0.423050	+	1.37319i	0.0328350	+	0.106580i
$167$	−2.33894	−	1.35039i	−0.180993	−	0.104496i	0.406766	−	0.913532i	$-0.366656\pi$
$167$	−2.33894	−	1.35039i	−0.180993	−	0.104496i	−0.587759	+	0.809036i	$0.699990\pi$
$168$	2.12855	+	5.44013i	0.164221	+	0.419715i
$169$	−1.10537	+	1.91456i	−0.0850287	+	0.147274i
$170$	0.403955	+	1.31121i	0.0309820	+	0.100565i
$171$	7.27526	−	4.20038i	0.556353	−	0.321211i
$172$	11.9677	+	5.77360i	0.912529	+	0.440233i
$173$	−6.84556	−	11.8569i	−0.520458	−	0.901460i	−0.999717	−	0.0237862i	$-0.992428\pi$
$173$	−6.84556	−	11.8569i	−0.520458	−	0.901460i	0.479259	−	0.877673i	$-0.340905\pi$
$174$	2.39862	+	2.22715i	0.181839	+	0.168840i
$175$	−1.26305	+	2.18767i	−0.0954779	+	0.165373i
$176$	−8.93006	+	1.33329i	−0.673129	+	0.100501i
$177$			2.53002i			0.190168i
$178$	−2.26651	+	9.91432i	−0.169882	+	0.743110i
$179$	0.990898			0.0740632			0.0370316	−	0.999314i	$-0.488210\pi$
$179$	0.990898			0.0740632			0.0370316	+	0.999314i	$0.488210\pi$
$180$	2.16787	−	4.49363i	0.161583	−	0.334935i
$181$	11.5729	−	20.0448i	0.860203	−	1.48992i	−0.0115290	−	0.999934i	$-0.503670\pi$
$181$	11.5729	−	20.0448i	0.860203	−	1.48992i	0.871732	−	0.489982i	$-0.162997\pi$
$182$	−9.35286	−	2.13815i	−0.693280	−	0.158490i
$183$	11.8782	−	6.85789i	0.878062	−	0.506950i
$184$	−2.17798	+	14.3484i	−0.160563	+	1.05778i
$185$	−1.42884	+	0.824940i	−0.105050	+	0.0606508i
$186$	1.47584	+	1.37033i	0.108214	+	0.100478i
$187$	−0.877861			−0.0641956
$188$	−4.38145	−	6.43602i	−0.319550	−	0.469395i
$189$	1.03268	−	1.78865i	0.0751164	−	0.130105i
$190$	28.3235	−	8.72585i	2.05480	−	0.633039i
$191$	5.87263	+	10.1717i	0.424928	+	0.735997i	0.996414	−	0.0846148i	$-0.0269660\pi$
$191$	5.87263	+	10.1717i	0.424928	+	0.735997i	−0.571485	+	0.820612i	$0.693633\pi$
$192$	−1.76389	−	7.80312i	−0.127298	−	0.563142i
$193$	19.4034			1.39669			0.698343	−	0.715763i	$-0.253921\pi$
$193$	19.4034			1.39669			0.698343	+	0.715763i	$0.253921\pi$
$194$	3.87215	+	12.5687i	0.278004	+	0.902382i
$195$	4.09702	+	7.09625i	0.293394	+	0.508173i
$196$	−0.404875	−	5.45357i	−0.0289196	−	0.389540i
$197$	16.2673	+	9.39193i	1.15900	+	0.669147i	0.951063	−	0.308996i	$-0.0999929\pi$
$197$	16.2673	+	9.39193i	1.15900	+	0.669147i	0.207933	+	0.978143i	$0.433326\pi$
$198$	2.33933	+	2.17210i	0.166249	+	0.154364i
$199$	−9.66739	+	5.58147i	−0.685303	+	0.395660i	−0.801850	−	0.597525i	$-0.796151\pi$
$199$	−9.66739	+	5.58147i	−0.685303	+	0.395660i	0.116547	+	0.993185i	$0.462817\pi$
$200$	2.15972	−	2.70242i	0.152715	−	0.191090i
$201$	−6.14974	+	5.40192i	−0.433769	+	0.381022i
$202$	−3.85569	+	4.15254i	−0.271285	+	0.292172i
$203$	2.39011	+	4.13980i	0.167753	+	0.290557i
$204$	−0.0575865	−	0.775676i	−0.00403186	−	0.0543082i
$205$	−1.52857	+	2.64756i	−0.106760	+	0.184914i
$206$	−14.3248	+	15.4277i	−0.998054	+	1.07490i
$207$	4.44361	−	2.56552i	0.308852	−	0.178316i
$208$	12.2239	+	4.81715i	0.847573	+	0.334009i
$209$			18.9627i			1.31168i
$210$	4.95787	−	5.33959i	0.342126	−	0.368467i
$211$	−12.0841	+	6.97675i	−0.831902	+	0.480299i	−0.854504	−	0.519446i	$-0.826138\pi$
$211$	−12.0841	+	6.97675i	−0.831902	+	0.480299i	0.0226013	+	0.999745i	$0.492805\pi$
$212$	0.788774	−	1.63500i	0.0541732	−	0.112292i
$213$	−13.1632	−	7.59978i	−0.901927	−	0.520728i
$214$	16.5195	+	3.77651i	1.12925	+	0.258157i
$215$		−	16.5737i		−	1.13032i
$216$	−1.76580	+	2.20951i	−0.120148	+	0.150338i
$217$	1.47060	+	2.54716i	0.0998310	+	0.172912i
$218$	−17.5962	−	4.02265i	−1.19176	−	0.272448i
$219$	−4.82904	−	8.36414i	−0.326316	−	0.565196i
$220$	6.33763	+	9.30949i	0.427283	+	0.627646i
$221$	1.10629	+	0.638719i	0.0744173	+	0.0429649i
$222$	0.893871	−	0.275382i	0.0599927	−	0.0184824i
$223$			5.48935i			0.367594i	0.982964	+	0.183797i	$0.0588389\pi$
$223$			5.48935i			0.367594i	−0.982964	+	0.183797i	$0.941161\pi$
$224$	0.893358	−	11.6492i	0.0596900	−	0.778347i
$225$	−1.22308			−0.0815389
$226$	−3.64299	+	3.92347i	−0.242328	+	0.260986i
$227$	−3.71947	−	2.14744i	−0.246870	−	0.142530i	0.371460	−	0.928449i	$-0.378857\pi$
$227$	−3.71947	−	2.14744i	−0.246870	−	0.142530i	−0.618330	+	0.785919i	$0.712190\pi$
$228$	−16.7554	+	1.24393i	−1.10965	+	0.0823810i
$229$	16.5554	−	9.55826i	1.09401	−	0.631628i	0.159370	−	0.987219i	$-0.449054\pi$
$229$	16.5554	−	9.55826i	1.09401	−	0.631628i	0.934642	+	0.355591i	$0.115720\pi$
$230$	17.2995	−	5.32960i	1.14069	−	0.351423i
$231$	2.33103	+	4.03746i	0.153370	+	0.265645i
$232$	−2.38528	−	6.09629i	−0.156601	−	0.400241i
$233$	−12.1986	−	7.04286i	−0.799156	−	0.461393i	0.0440199	−	0.999031i	$-0.485984\pi$
$233$	−12.1986	−	7.04286i	−0.799156	−	0.461393i	−0.843176	+	0.537638i	$0.819317\pi$
$234$	−1.36767	−	4.43937i	−0.0894076	−	0.290210i
$235$	−4.85567	+	8.41026i	−0.316749	+	0.548625i
$236$	2.19864	−	4.55741i	0.143119	−	0.296662i
$237$	−6.39671	+	11.0794i	−0.415511	+	0.719686i
$238$	0.253155	−	1.10737i	0.0164096	−	0.0717801i
$239$	8.19349	−	14.1915i	0.529993	−	0.917974i	−0.469395	−	0.882988i	$-0.655528\pi$
$239$	8.19349	−	14.1915i	0.529993	−	0.917974i	0.999388	−	0.0349861i	$-0.0111387\pi$
$240$	−7.81011	+	6.21060i	−0.504140	+	0.400893i
$241$	−16.9302			−1.09057			−0.545284	−	0.838252i	$-0.683578\pi$
$241$	−16.9302			−1.09057			−0.545284	+	0.838252i	$0.683578\pi$
$242$	7.98047	−	2.45861i	0.513004	−	0.158045i
$243$	1.00000			0.0641500
$244$	−27.3563	+	2.03094i	−1.75131	+	0.130018i
$245$	−5.90714	+	3.41049i	−0.377394	+	0.217888i
$246$	1.17926	−	1.27006i	0.0751869	−	0.0809758i
$247$	13.7970	−	23.8971i	0.877880	−	1.52053i
$248$	−1.46763	−	3.75096i	−0.0931947	−	0.238186i
$249$	−0.879905	+	0.508013i	−0.0557617	+	0.0321940i
$250$	12.9895	+	2.96953i	0.821530	+	0.187809i
$251$	−7.15767	−	12.3975i	−0.451788	−	0.782520i	0.546709	−	0.837323i	$-0.315880\pi$
$251$	−7.15767	−	12.3975i	−0.451788	−	0.782520i	−0.998497	+	0.0548025i	$0.982547\pi$
$252$	−3.41458	+	2.32454i	−0.215098	+	0.146432i
$253$			11.5821i			0.728160i
$254$	−1.14046	+	1.22827i	−0.0715589	+	0.0770684i
$255$	−0.840190	+	0.485084i	−0.0526147	+	0.0303771i
$256$	−3.60371	+	15.5889i	−0.225232	+	0.974305i
$257$	−14.5021	+	25.1183i	−0.904613	+	1.56684i	−0.0831778	+	0.996535i	$0.526507\pi$
$257$	−14.5021	+	25.1183i	−0.904613	+	1.56684i	−0.821435	+	0.570301i	$0.806826\pi$
$258$	−2.09394	+	9.15946i	−0.130363	+	0.570243i
$259$	1.36598			0.0848780
$260$	−1.21332	−	16.3431i	−0.0752469	−	1.01356i
$261$	−1.15724	+	2.00439i	−0.0716312	+	0.124069i
$262$	−12.2291	−	2.79568i	−0.755514	−	0.172718i
$263$		−	22.9977i		−	1.41810i	−0.705160	−	0.709048i	$-0.749125\pi$
$263$		−	22.9977i		−	1.41810i	0.705160	−	0.709048i	$-0.250875\pi$
$264$	−2.32632	−	5.94559i	−0.143175	−	0.365926i
$265$	−2.26425			−0.139092
$266$	−23.9203	−	5.46841i	−1.46665	−	0.335290i
$267$	−7.19134			−0.440103
$268$	15.7721	−	4.38641i	0.963435	−	0.267943i
$269$	6.00531			0.366150			0.183075	−	0.983099i	$-0.441395\pi$
$269$	6.00531			0.366150			0.183075	+	0.983099i	$0.441395\pi$
$270$	3.43919	+	0.786230i	0.209302	+	0.0478485i
$271$	−18.0788			−1.09821			−0.549103	−	0.835754i	$-0.685031\pi$
$271$	−18.0788			−1.09821			−0.549103	+	0.835754i	$0.685031\pi$
$272$	−0.570346	+	1.44730i	−0.0345823	+	0.0877552i
$273$		−	6.78409i		−	0.410592i
$274$	16.4324	+	3.75660i	0.992719	+	0.226945i
$275$	1.38041	−	2.39094i	0.0832419	−	0.144179i
$276$	−10.2339	+	0.759769i	−0.616009	+	0.0457327i
$277$	−18.1908			−1.09298			−0.546490	−	0.837465i	$-0.684037\pi$
$277$	−18.1908			−1.09298			−0.546490	+	0.837465i	$0.684037\pi$
$278$	3.26272	−	14.2720i	0.195685	−	0.855979i
$279$	−0.712032	+	1.23328i	−0.0426283	+	0.0738343i
$280$	−13.5710	+	5.30990i	−0.811023	+	0.317327i
$281$	0.713941	−	0.412194i	0.0425901	−	0.0245894i	−0.478554	−	0.878058i	$-0.658839\pi$
$281$	0.713941	−	0.412194i	0.0425901	−	0.0245894i	0.521144	+	0.853469i	$0.325505\pi$
$282$	3.74604	−	4.03446i	0.223074	−	0.240249i
$283$			17.7703i			1.05633i	0.849141	+	0.528167i	$0.177120\pi$
$283$			17.7703i			1.05633i	−0.849141	+	0.528167i	$0.822880\pi$
$284$	17.1070	+	25.1288i	1.01511	+	1.49112i
$285$	10.4783	+	18.1490i	0.620681	+	1.07505i
$286$	10.2219	+	2.33682i	0.604432	+	0.138179i
$287$	2.19199	−	1.26555i	0.129389	−	0.0747030i
$288$	5.10091	−	2.44555i	0.300574	−	0.144106i
$289$	8.42438	−	14.5914i	0.495552	−	0.858320i
$290$	−5.55587	+	5.98363i	−0.326252	+	0.351371i
$291$	−8.05372	+	4.64982i	−0.472117	+	0.272577i
$292$	1.43010	+	19.2631i	0.0836904	+	1.12729i
$293$	−14.6021			−0.853064			−0.426532	−	0.904472i	$-0.640265\pi$
$293$	−14.6021			−0.853064			−0.426532	+	0.904472i	$0.640265\pi$
$294$	3.69547	−	1.13849i	0.215524	−	0.0663983i
$295$	−6.31142			−0.367465
$296$	−1.84947	−	0.280736i	−0.107498	−	0.0163175i
$297$	−1.12863	+	1.95485i	−0.0654898	+	0.113432i
$298$	4.15042	−	18.1551i	0.240427	−	1.05170i
$299$	8.42696	−	14.5959i	0.487344	−	0.844104i
$300$	2.20318	+	1.06288i	0.127201	+	0.0613657i
$301$	−6.86093	+	11.8835i	−0.395457	+	0.684952i
$302$	4.45736	+	14.4683i	0.256492	+	0.832555i
$303$	−3.47005	−	2.00343i	−0.199349	−	0.115094i
$304$	31.2631	+	12.3201i	1.79306	+	0.706603i
$305$	17.1078	+	29.6315i	0.979587	+	1.69670i
$306$	0.525617	−	0.161931i	0.0300475	−	0.00925699i
$307$	11.7664	−	6.79332i	0.671542	−	0.387715i	−0.125118	−	0.992142i	$-0.539931\pi$
$307$	11.7664	−	6.79332i	0.671542	−	0.387715i	0.796661	+	0.604427i	$0.206598\pi$
$308$	−0.690326	−	9.29853i	−0.0393350	−	0.529833i
$309$	−12.8920	−	7.44322i	−0.733402	−	0.423430i
$310$	−3.41845	+	3.68165i	−0.194155	+	0.209103i
$311$	14.8187			0.840293			0.420146	−	0.907456i	$-0.361979\pi$
$311$	14.8187			0.840293			0.420146	+	0.907456i	$0.361979\pi$
$312$	−1.39426	+	9.18532i	−0.0789347	+	0.520016i
$313$			17.2743i			0.976402i	0.872731	+	0.488201i	$0.162347\pi$
$313$			17.2743i			0.976402i	−0.872731	+	0.488201i	$0.837653\pi$
$314$	−2.06589	+	0.636455i	−0.116585	+	0.0359172i
$315$	4.46200	+	2.57614i	0.251405	+	0.145149i
$316$	21.1509	−	14.3989i	1.18983	−	0.810000i
$317$	−14.5587	−	25.2164i	−0.817699	−	1.41630i	−0.907374	−	0.420325i	$-0.861916\pi$
$317$	−14.5587	−	25.2164i	−0.817699	−	1.41630i	0.0896748	−	0.995971i	$-0.471417\pi$
$318$	1.25134	+	0.286068i	0.0701717	+	0.0160419i
$319$	−2.61219	−	4.52444i	−0.146254	−	0.253320i
$320$	19.4657	−	4.40023i	1.08817	−	0.245980i
$321$			11.9824i			0.668792i
$322$	−14.6101	−	3.34001i	−0.814191	−	0.186132i
$323$	2.82939	+	1.63355i	0.157431	+	0.0908931i
$324$	−1.80133	−	0.869020i	−0.100074	−	0.0482789i
$325$	−3.47923	+	2.00873i	−0.192993	+	0.111424i
$326$	0.883247	−	0.951250i	0.0489185	−	0.0526849i
$327$		−	12.7634i		−	0.705816i
$328$	−3.22795	+	1.26299i	−0.178234	+	0.0697370i
$329$	6.96310	−	4.02015i	0.383888	−	0.221638i
$330$	−5.41853	+	5.83572i	−0.298280	+	0.321246i
$331$	−17.1462	+	29.6981i	−0.942442	+	1.63236i	−0.181648	+	0.983364i	$0.558143\pi$
$331$	−17.1462	+	29.6981i	−0.942442	+	1.63236i	−0.760794	+	0.648994i	$0.775190\pi$
$332$	2.02648	−	0.150446i	0.111217	−	0.00825681i
$333$	0.330689	+	0.572770i	0.0181216	+	0.0313876i
$334$	−2.59888	+	2.79897i	−0.142204	+	0.153153i
$335$	−13.4757	−	15.3412i	−0.736255	−	0.838180i
$336$	8.17087	−	1.21994i	0.445758	−	0.0665532i
$337$	−21.1429	+	12.2069i	−1.15173	+	0.664951i	−0.949308	−	0.314348i	$-0.898214\pi$
$337$	−21.1429	+	12.2069i	−1.15173	+	0.664951i	−0.202421	+	0.979299i	$0.564881\pi$
$338$	2.29112	+	2.12733i	0.124621	+	0.115712i
$339$	−3.27862	−	1.89291i	−0.178070	−	0.102809i
$340$	1.93501	−	0.143656i	0.104941	−	0.00779083i
$341$	−1.60724	−	2.78383i	−0.0870371	−	0.150753i
$342$	−3.49788	−	11.3539i	−0.189144	−	0.613946i
$343$	20.1048			1.08556
$344$	11.7316	−	14.6796i	0.632528	−	0.791469i
$345$	6.39997	+	11.0851i	0.344563	+	0.596801i
$346$	−18.5039	+	5.70066i	−0.994778	+	0.306469i
$347$	−4.61522	+	7.99379i	−0.247758	+	0.429129i	−0.962903	−	0.269846i	$-0.913027\pi$
$347$	−4.61522	+	7.99379i	−0.247758	+	0.429129i	0.715146	+	0.698976i	$0.246360\pi$
$348$	3.82643	−	2.60492i	0.205118	−	0.139638i
$349$	−8.77567			−0.469751			−0.234875	−	0.972025i	$-0.575468\pi$
$349$	−8.77567			−0.469751			−0.234875	+	0.972025i	$0.575468\pi$
$350$	2.61795	+	2.43080i	0.139935	+	0.129932i
$351$	2.84463	−	1.64235i	0.151835	−	0.0876622i
$352$	−0.976364	+	12.7316i	−0.0520404	+	0.678597i
$353$	−21.8820	+	12.6336i	−1.16466	+	0.672417i	−0.952416	−	0.304800i	$-0.901410\pi$
$353$	−21.8820	+	12.6336i	−1.16466	+	0.672417i	−0.212244	+	0.977217i	$0.568077\pi$
$354$	3.48800	+	0.797390i	0.185385	+	0.0423808i
$355$	18.9585	−	32.8371i	1.00621	−	1.74281i
$356$	12.9540	+	6.24942i	0.686561	+	0.331219i
$357$	0.803230			0.0425114
$358$	0.312303	−	1.36610i	0.0165057	−	0.0722005i
$359$			7.74007i			0.408505i	0.978918	+	0.204253i	$0.0654764\pi$
$359$			7.74007i			0.408505i	−0.978918	+	0.204253i	$0.934524\pi$
$360$	−5.51187	−	4.40499i	−0.290501	−	0.232163i
$361$	25.7863	−	44.6632i	1.35717	−	2.35070i
$362$	−23.9872	−	22.2724i	−1.26074	−	1.17061i
$363$	2.95238	+	5.11368i	0.154960	+	0.268399i
$364$	−5.89551	+	12.2204i	−0.309009	+	0.640523i
$365$	20.8653	−	12.0466i	1.09214	−	0.630547i
$366$	−5.71093	−	18.5373i	−0.298515	−	0.968958i
$367$	7.16145	−	12.4040i	0.373824	−	0.647483i	−0.616326	−	0.787491i	$-0.711380\pi$
$367$	7.16145	−	12.4040i	0.373824	−	0.647483i	0.990150	+	0.140008i	$0.0447129\pi$
$368$	19.0949	+	7.52488i	0.995393	+	0.392261i
$369$	1.06131	+	0.612750i	0.0552498	+	0.0318985i
$370$	0.686972	+	2.22986i	0.0357140	+	0.115925i
$371$	1.62349	+	0.937321i	0.0842873	+	0.0486633i
$372$	2.35435	−	1.60277i	0.122067	−	0.0830998i
$373$	−10.3087	−	5.95175i	−0.533766	−	0.308170i	0.208783	−	0.977962i	$-0.433050\pi$
$373$	−10.3087	−	5.95175i	−0.533766	−	0.308170i	−0.742549	+	0.669792i	$0.766383\pi$
$374$	−0.276677	+	1.21026i	−0.0143066	+	0.0625811i
$375$			9.42194i			0.486547i
$376$	−10.2539	+	4.01202i	−0.528805	+	0.206904i
$377$			7.60235i			0.391541i
$378$	−2.14045	−	1.98743i	−0.110093	−	0.102223i
$379$	−4.09150	−	7.08669i	−0.210166	−	0.364019i	0.741600	−	0.670842i	$-0.234067\pi$
$379$	−4.09150	−	7.08669i	−0.210166	−	0.364019i	−0.951766	+	0.306823i	$0.900734\pi$
$380$	−3.10311	−	41.7982i	−0.159186	−	2.14420i
$381$	−1.02639	−	0.592589i	−0.0525838	−	0.0303593i
$382$	15.8740	−	4.89045i	0.812187	−	0.250217i
$383$	5.20951	+	9.02314i	0.266194	+	0.461061i	0.967876	−	0.251429i	$-0.0809006\pi$
$383$	5.20951	+	9.02314i	0.266194	+	0.461061i	−0.701682	+	0.712490i	$0.747567\pi$
$384$	−11.3137	−	0.0275367i	−0.577349	−	0.00140522i
$385$	−10.0719	+	5.81501i	−0.513311	+	0.296360i
$386$	6.11539	−	26.7504i	0.311265	−	1.36156i
$387$	−6.64380			−0.337724
$388$	18.5482	−	1.37703i	0.941643	−	0.0699079i
$389$	−10.4878	−	18.1653i	−0.531751	−	0.921019i	−0.999313	−	0.0370593i	$-0.988201\pi$
$389$	−10.4878	−	18.1653i	−0.531751	−	0.921019i	0.467562	−	0.883960i	$-0.345132\pi$
$390$	11.0745	−	3.41181i	0.560779	−	0.172764i
$391$	1.72814	+	0.997744i	0.0873960	+	0.0504581i
$392$	−7.64615	−	1.16063i	−0.386189	−	0.0586206i
$393$		−	8.87034i		−	0.447449i
$394$	18.0751	−	19.4668i	0.910612	−	0.980723i
$395$	−27.6389	−	15.9573i	−1.39066	−	0.802899i
$396$	3.73184	−	2.54053i	0.187532	−	0.127666i
$397$	−28.3080			−1.42074			−0.710369	−	0.703830i	$-0.751472\pi$
$397$	−28.3080			−1.42074			−0.710369	+	0.703830i	$0.751472\pi$
$398$	4.64799	+	15.0870i	0.232983	+	0.756245i
$399$		−	17.3506i		−	0.868615i
$400$	−3.04500	−	3.82922i	−0.152250	−	0.191461i
$401$		−	27.8739i		−	1.39196i	−0.718062	−	0.695979i	$-0.754971\pi$
$401$		−	27.8739i		−	1.39196i	0.718062	−	0.695979i	$-0.245029\pi$
$402$	5.50911	+	10.1808i	0.274770	+	0.507775i
$403$			4.67762i			0.233009i
$404$	4.50969	+	6.62439i	0.224365	+	0.329576i
$405$			2.49461i			0.123958i
$406$	6.46061	−	1.99037i	0.320635	−	0.0987806i
$407$	−1.49290			−0.0740004
$408$	−1.08753	−	0.165080i	−0.0538409	−	0.00817266i
$409$	5.22660	+	3.01758i	0.258439	+	0.149210i	0.623622	−	0.781726i	$-0.285660\pi$
$409$	5.22660	+	3.01758i	0.258439	+	0.149210i	−0.365183	+	0.930936i	$0.618994\pi$
$410$	3.16829	+	2.94180i	0.156471	+	0.145285i
$411$			11.9192i			0.587933i
$412$	16.7545	+	24.6112i	0.825437	+	1.21250i
$413$	4.52533	+	2.61270i	0.222677	+	0.128563i
$414$	−2.13645	−	6.93475i	−0.105001	−	0.340824i
$415$	−1.26730	−	2.19502i	−0.0622091	−	0.107749i
$416$	10.4938	−	15.3342i	0.514499	−	0.751820i
$417$	10.3522			0.506950
$418$	26.1429	+	5.97650i	1.27869	+	0.292320i
$419$	−10.4893	+	6.05598i	−0.512434	+	0.295854i	−0.733834	−	0.679329i	$-0.762271\pi$
$419$	−10.4893	+	6.05598i	−0.512434	+	0.295854i	0.221400	+	0.975183i	$0.428937\pi$
$420$	−5.79883	−	8.51805i	−0.282954	−	0.415638i
$421$	−13.7185	−	23.7612i	−0.668599	−	1.15805i	−0.978296	−	0.207213i	$-0.933561\pi$
$421$	−13.7185	−	23.7612i	−0.668599	−	1.15805i	0.309697	−	0.950835i	$-0.399772\pi$
$422$	5.80991	+	18.8585i	0.282822	+	0.918020i
$423$	3.37137	+	1.94646i	0.163922	+	0.0946402i
$424$	−2.00548	−	1.60274i	−0.0973948	−	0.0778361i
$425$	−0.237832	−	0.411937i	−0.0115365	−	0.0199819i
$426$	−14.6261	+	15.7522i	−0.708635	+	0.763195i
$427$		−	28.3280i		−	1.37089i
$428$	10.4129	−	21.5843i	0.503329	−	1.04332i
$429$			7.41443i			0.357972i
$430$	−22.8493	−	5.22356i	−1.10189	−	0.251902i
$431$	27.0073	+	15.5927i	1.30090	+	0.751072i	0.980558	−	0.196231i	$-0.0628702\pi$
$431$	27.0073	+	15.5927i	1.30090	+	0.751072i	0.320338	+	0.947303i	$0.396204\pi$
$432$	2.48961	+	3.13079i	0.119781	+	0.150630i
$433$	−0.994728	−	0.574306i	−0.0478036	−	0.0275994i	0.475908	−	0.879495i	$-0.342120\pi$
$433$	−0.994728	−	0.574306i	−0.0478036	−	0.0275994i	−0.523711	+	0.851896i	$0.675453\pi$
$434$	3.97513	−	1.22465i	0.190812	−	0.0587851i
$435$	−5.00018	−	2.88686i	−0.239740	−	0.138414i
$436$	−11.0916	+	22.9911i	−0.531193	+	1.10107i
$437$	21.5523	−	37.3297i	1.03099	−	1.78572i
$438$	−13.0532	+	4.02140i	−0.623705	+	0.192150i
$439$	33.6228	−	19.4121i	1.60473	−	0.926489i	0.614203	−	0.789148i	$-0.289478\pi$
$439$	33.6228	−	19.4121i	1.60473	−	0.926489i	0.990524	−	0.137342i	$-0.0438558\pi$
$440$	14.8319	−	5.80326i	0.707085	−	0.276660i
$441$	1.36714	+	2.36796i	0.0651021	+	0.112760i
$442$	1.22924	−	1.32388i	0.0584690	−	0.0629706i
$443$	14.8274	−	25.6819i	0.704472	−	1.22018i	−0.262410	−	0.964957i	$-0.584517\pi$
$443$	14.8274	−	25.6819i	0.704472	−	1.22018i	0.966882	−	0.255225i	$-0.0821495\pi$
$444$	−0.0979323	−	1.31912i	−0.00464766	−	0.0626029i
$445$		−	17.9396i		−	0.850419i
$446$	7.56787	+	1.73009i	0.358349	+	0.0819219i
$447$	13.1688			0.622861
$448$	−15.7786	−	4.90313i	−0.745470	−	0.231651i
$449$	−7.01987	+	12.1588i	−0.331288	+	0.573808i	−0.982765	−	0.184861i	$-0.940817\pi$
$449$	−7.01987	+	12.1588i	−0.331288	+	0.573808i	0.651476	+	0.758669i	$0.274150\pi$
$450$	−0.385481	+	1.68620i	−0.0181718	+	0.0794883i
$451$	−2.39566	+	1.38314i	−0.112807	+	0.0651293i
$452$	4.26092	+	6.25896i	0.200417	+	0.294397i
$453$	−9.27090	+	5.35256i	−0.435585	+	0.251485i
$454$	−4.13282	+	4.45102i	−0.193963	+	0.208897i
$455$	16.9237			0.793394
$456$	−3.56589	+	23.4918i	−0.166988	+	1.10011i
$457$	2.62718	−	4.55041i	0.122894	−	0.212859i	−0.798014	−	0.602639i	$-0.794116\pi$
$457$	2.62718	−	4.55041i	0.122894	−	0.212859i	0.920908	+	0.389780i	$0.127449\pi$
$458$	−7.95968	−	25.8365i	−0.371931	−	1.20726i
$459$	0.194453	+	0.336802i	0.00907627	+	0.0157206i
$460$	−1.89533	−	25.5296i	−0.0883702	−	1.19033i
$461$	23.2741			1.08398			0.541992	−	0.840384i	$-0.317670\pi$
$461$	23.2741			1.08398			0.541992	+	0.840384i	$0.317670\pi$
$462$	6.30091	−	1.94117i	0.293145	−	0.0903116i
$463$	−17.9191	−	31.0367i	−0.832769	−	1.44240i	−0.895834	−	0.444389i	$-0.853421\pi$
$463$	−17.9191	−	31.0367i	−0.832769	−	1.44240i	0.0630646	−	0.998009i	$-0.479913\pi$
$464$	−9.15641	+	1.36708i	−0.425075	+	0.0634653i
$465$	−3.07654	−	1.77624i	−0.142671	−	0.0823713i
$466$	−13.5543	+	14.5978i	−0.627889	+	0.676232i
$467$	−26.7771	+	15.4598i	−1.23910	+	0.715393i	−0.968910	−	0.247415i	$-0.920419\pi$
$467$	−26.7771	+	15.4598i	−1.23910	+	0.715393i	−0.270187	+	0.962808i	$0.587086\pi$
$468$	−6.55137	+	0.486376i	−0.302837	+	0.0224827i
$469$	3.31145	+	16.5782i	0.152909	+	0.765511i
$470$	10.0644	+	9.34492i	0.464237	+	0.431049i
$471$	−0.764278	−	1.32377i	−0.0352161	−	0.0609960i
$472$	−5.59011	−	4.46751i	−0.257306	−	0.205634i
$473$	7.49840	−	12.9876i	0.344777	−	0.597171i
$474$	13.2586	+	12.3107i	0.608986	+	0.565450i
$475$	−8.89826	+	5.13741i	−0.408280	+	0.235721i
$476$	−1.44688	−	0.698023i	−0.0663179	−	0.0319938i
$477$			0.907658i			0.0415588i
$478$	−16.9828	−	15.7687i	−0.776774	−	0.721243i
$479$	17.4485	−	10.0739i	0.797244	−	0.460289i	−0.0452626	−	0.998975i	$-0.514412\pi$
$479$	17.4485	−	10.0739i	0.797244	−	0.460289i	0.842507	+	0.538686i	$0.181079\pi$
$480$	6.10070	+	12.7248i	0.278458	+	0.580804i
$481$	1.88138	+	1.08621i	0.0857834	+	0.0495271i
$482$	−5.33590	+	23.3407i	−0.243044	+	1.06314i
$483$		−	10.5974i		−	0.482200i
$484$	−0.874338	−	11.7771i	−0.0397427	−	0.535324i
$485$	−11.5995	−	20.0909i	−0.526705	−	0.912281i
$486$	0.315172	−	1.37865i	0.0142965	−	0.0625367i
$487$	−9.65114	−	16.7163i	−0.437335	−	0.757486i	0.560148	−	0.828392i	$-0.310744\pi$
$487$	−9.65114	−	16.7163i	−0.437335	−	0.757486i	−0.997483	+	0.0709064i	$0.977411\pi$
$488$	−5.82197	+	38.3547i	−0.263548	+	1.73624i
$489$	0.794906	+	0.458939i	0.0359469	+	0.0207540i
$490$	2.84010	+	9.21875i	0.128303	+	0.416461i
$491$		−	6.56439i		−	0.296247i	−0.988969	−	0.148123i	$-0.952677\pi$
$491$		−	6.56439i		−	0.296247i	0.988969	−	0.148123i	$-0.0473232\pi$
$492$	−1.37929	−	2.02607i	−0.0621831	−	0.0913423i
$493$	−0.900112			−0.0405390
$494$	−28.5972	−	26.5528i	−1.28665	−	1.19467i
$495$	−4.87658	−	2.81549i	−0.219186	−	0.126547i
$496$	−5.63381	+	0.841148i	−0.252966	+	0.0377687i
$497$	−27.1867	+	15.6963i	−1.21949	+	0.704074i
$498$	0.423050	+	1.37319i	0.0189573	+	0.0615341i
$499$	−3.13468	−	5.42943i	−0.140328	−	0.243055i	0.787292	−	0.616580i	$-0.211482\pi$
$499$	−3.13468	−	5.42943i	−0.140328	−	0.243055i	−0.927620	+	0.373525i	$0.878149\pi$
$500$	8.18785	−	16.9721i	0.366172	−	0.759013i
$501$	−2.33894	−	1.35039i	−0.104496	−	0.0603310i
$502$	−19.3476	+	5.96058i	−0.863526	+	0.266034i
$503$	−15.0499	+	26.0673i	−0.671044	+	1.16228i	0.306564	+	0.951850i	$0.400821\pi$
$503$	−15.0499	+	26.0673i	−0.671044	+	1.16228i	−0.977608	+	0.210432i	$0.932513\pi$
$504$	2.12855	+	5.44013i	0.0948130	+	0.242323i
$505$	4.99778	−	8.65642i	0.222399	−	0.385206i
$506$	15.9676	+	3.65035i	0.709847	+	0.162278i
$507$	−1.10537	+	1.91456i	−0.0490914	+	0.0850287i
$508$	1.33391	+	1.95941i	0.0591826	+	0.0869347i
$509$	−44.9484			−1.99230			−0.996152	−	0.0876435i	$-0.972066\pi$
$509$	−44.9484			−1.99230			−0.996152	+	0.0876435i	$0.972066\pi$
$510$	0.403955	+	1.31121i	0.0178874	+	0.0580613i
$511$	−19.9474			−0.882422
$512$	20.3558	+	9.88142i	0.899607	+	0.436701i
$513$	7.27526	−	4.20038i	0.321211	−	0.185451i
$514$	30.0586	+	27.9098i	1.32583	+	1.23105i
$515$	18.5679	−	32.1606i	0.818201	−	1.41717i
$516$	11.9677	+	5.77360i	0.526849	+	0.254169i
$517$	−7.61007	+	4.39367i	−0.334690	+	0.193234i
$518$	0.430519	−	1.88321i	0.0189159	−	0.0827434i
$519$	−6.84556	−	11.8569i	−0.300487	−	0.520458i
$520$	−22.9138	−	3.47815i	−1.00484	−	0.152527i
$521$		−	14.4215i		−	0.631819i	−0.948789	−	0.315910i	$-0.897690\pi$
$521$		−	14.4215i		−	0.631819i	0.948789	−	0.315910i	$-0.102310\pi$
$522$	2.39862	+	2.22715i	0.104985	+	0.0974797i
$523$	20.4782	−	11.8231i	0.895449	−	0.516988i	0.0197281	−	0.999805i	$-0.493720\pi$
$523$	20.4782	−	11.8231i	0.895449	−	0.516988i	0.875721	+	0.482818i	$0.160387\pi$
$524$	−7.70850	+	15.9784i	−0.336747	+	0.698021i
$525$	−1.26305	+	2.18767i	−0.0551242	+	0.0954779i
$526$	−31.7056	−	7.24821i	−1.38243	−	0.316037i
$527$	−0.553826			−0.0241251
$528$	−8.93006	+	1.33329i	−0.388631	+	0.0580240i
$529$	1.66378	−	2.88175i	0.0723382	−	0.125293i
$530$	−0.713628	+	3.12161i	−0.0309980	+	0.135594i
$531$			2.53002i			0.109794i
$532$	−15.0780	+	31.2542i	−0.653714	+	1.35504i
$533$	4.02540			0.174359
$534$	−2.26651	+	9.91432i	−0.0980813	+	0.429035i
$535$	−29.8914			−1.29232
$536$	−1.07639	−	23.1266i	−0.0464929	−	0.998919i
$537$	0.990898			0.0427604
$538$	1.89270	−	8.27920i	0.0816002	−	0.356942i
$539$	−6.17200			−0.265847
$540$	2.16787	−	4.49363i	0.0932902	−	0.193375i
$541$			16.6509i			0.715880i	0.933745	+	0.357940i	$0.116521\pi$
$541$			16.6509i			0.715880i	−0.933745	+	0.357940i	$0.883479\pi$
$542$	−5.69791	+	24.9242i	−0.244746	+	1.07059i
$543$	11.5729	−	20.0448i	0.496639	−	0.860203i
$544$	1.81555	+	1.24245i	0.0778412	+	0.0532697i
$545$	31.8396			1.36386
$546$	−9.35286	−	2.13815i	−0.400266	−	0.0915044i
$547$	−12.4484	+	21.5613i	−0.532257	+	0.921896i	0.467034	+	0.884240i	$0.345323\pi$
$547$	−12.4484	+	21.5613i	−0.532257	+	0.921896i	−0.999291	+	0.0376567i	$0.988011\pi$
$548$	10.3581	−	21.4705i	0.442474	−	0.917175i
$549$	11.8782	−	6.85789i	0.506950	−	0.292687i
$550$	−2.86120	−	2.65665i	−0.122002	−	0.113280i
$551$			19.4433i			0.828314i
$552$	−2.17798	+	14.3484i	−0.0927012	+	0.610709i
$553$	13.2115	+	22.8830i	0.561811	+	0.973085i
$554$	−5.73323	+	25.0787i	−0.243582	+	1.06549i
$555$	−1.42884	+	0.824940i	−0.0606508	+	0.0350167i
$556$	−18.6478	−	8.99627i	−0.790842	−	0.381527i
$557$	12.6210	−	21.8601i	0.534767	−	0.926243i	−0.464408	−	0.885622i	$-0.653733\pi$
$557$	12.6210	−	21.8601i	0.534767	−	0.926243i	0.999175	−	0.0406219i	$-0.0129339\pi$
$558$	1.47584	+	1.37033i	0.0624773	+	0.0580109i
$559$	−18.8992	+	10.9115i	−0.799351	+	0.461505i
$560$	3.04328	+	20.3831i	0.128602	+	0.861345i
$561$	−0.877861			−0.0370633
$562$	−0.343256	−	1.11418i	−0.0144794	−	0.0469990i
$563$	23.2457			0.979688			0.489844	−	0.871810i	$-0.337054\pi$
$563$	23.2457			0.979688			0.489844	+	0.871810i	$0.337054\pi$
$564$	−4.38145	−	6.43602i	−0.184492	−	0.271005i
$565$	4.72209	−	8.17889i	0.198660	−	0.344089i
$566$	24.4989	+	5.60068i	1.02977	+	0.235414i
$567$	1.03268	−	1.78865i	0.0433685	−	0.0751164i
$568$	40.0354	−	15.6646i	1.67985	−	0.657270i
$569$	−14.0617	+	24.3556i	−0.589499	+	1.02104i	0.404799	+	0.914405i	$0.367341\pi$
$569$	−14.0617	+	24.3556i	−0.589499	+	1.02104i	−0.994298	+	0.106636i	$0.965992\pi$
$570$	28.3235	−	8.72585i	1.18634	−	0.365485i
$571$	15.5162	+	8.95825i	0.649331	+	0.374891i	0.788200	−	0.615419i	$-0.211013\pi$
$571$	15.5162	+	8.95825i	0.649331	+	0.374891i	−0.138869	+	0.990311i	$0.544347\pi$
$572$	6.44329	−	13.3559i	0.269407	−	0.558437i
$573$	5.87263	+	10.1717i	0.245332	+	0.424928i
$574$	−1.05389	−	3.42085i	−0.0439885	−	0.142784i
$575$	−5.43491	+	3.13785i	−0.226651	+	0.130857i
$576$	−1.76389	−	7.80312i	−0.0734955	−	0.325130i
$577$	37.2768	+	21.5218i	1.55185	+	0.895963i	0.997991	+	0.0633541i	$0.0201797\pi$
$577$	37.2768	+	21.5218i	1.55185	+	0.895963i	0.553862	+	0.832609i	$0.313154\pi$
$578$	−17.4613	−	16.2130i	−0.726296	−	0.674374i
$579$	19.4034			0.806377
$580$	6.49826	+	9.54545i	0.269826	+	0.396353i
$581$			2.09846i			0.0870588i
$582$	3.87215	+	12.5687i	0.160506	+	0.520990i
$583$	−1.77433	−	1.02441i	−0.0734853	−	0.0424268i
$584$	27.0078	+	4.09959i	1.11759	+	0.169642i
$585$	4.09702	+	7.09625i	0.169391	+	0.293394i
$586$	−4.60217	+	20.1312i	−0.190114	+	0.831610i
$587$	14.7673	+	25.5778i	0.609513	+	1.05571i	0.991321	+	0.131466i	$0.0419684\pi$
$587$	14.7673	+	25.5778i	0.609513	+	1.05571i	−0.381807	+	0.924242i	$0.624698\pi$
$588$	−0.404875	−	5.45357i	−0.0166968	−	0.224901i
$589$			11.9632i			0.492936i
$590$	−1.98918	+	8.70122i	−0.0818932	+	0.358223i
$591$	16.2673	+	9.39193i	0.669147	+	0.386332i
$592$	−0.969937	+	2.46129i	−0.0398642	+	0.101158i
$593$	15.8142	−	9.13032i	0.649411	−	0.374937i	−0.138820	−	0.990318i	$-0.544331\pi$
$593$	15.8142	−	9.13032i	0.649411	−	0.374937i	0.788230	+	0.615380i	$0.210998\pi$
$594$	2.33933	+	2.17210i	0.0959839	+	0.0891221i
$595$			2.00375i			0.0821456i
$596$	−23.7213	−	11.4439i	−0.971664	−	0.468761i
$597$	−9.66739	+	5.58147i	−0.395660	+	0.228434i
$598$	−17.4667	−	16.2180i	−0.714266	−	0.663204i
$599$	−19.6705	+	34.0704i	−0.803716	+	1.39208i	0.113438	+	0.993545i	$0.463814\pi$
$599$	−19.6705	+	34.0704i	−0.803716	+	1.39208i	−0.917154	+	0.398532i	$0.869520\pi$
$600$	2.15972	−	2.70242i	0.0881703	−	0.110326i
$601$	21.8749	+	37.8884i	0.892295	+	1.54550i	0.837117	+	0.547024i	$0.184240\pi$
$601$	21.8749	+	37.8884i	0.892295	+	1.54550i	0.0551788	+	0.998476i	$0.482427\pi$
$602$	14.2207	+	13.2041i	0.579594	+	0.538160i
$603$	−6.14974	+	5.40192i	−0.250437	+	0.219983i
$604$	21.3515	−	1.58514i	0.868779	−	0.0644985i
$605$	−12.7566	+	7.36505i	−0.518631	+	0.299432i
$606$	−3.85569	+	4.15254i	−0.156627	+	0.168686i
$607$	6.66072	+	3.84557i	0.270350	+	0.156087i	0.629047	−	0.777367i	$-0.283445\pi$
$607$	6.66072	+	3.84557i	0.270350	+	0.156087i	−0.358697	+	0.933454i	$0.616779\pi$
$608$	26.8382	−	39.2178i	1.08843	−	1.59049i
$609$	2.39011	+	4.13980i	0.0968522	+	0.167753i
$610$	46.2433	−	14.2466i	1.87233	−	0.576826i
$611$	12.7871			0.517310
$612$	−0.0575865	−	0.775676i	−0.00232780	−	0.0313548i
$613$	1.81251	+	3.13936i	0.0732066	+	0.126797i	0.900305	−	0.435260i	$-0.143343\pi$
$613$	1.81251	+	3.13936i	0.0732066	+	0.126797i	−0.827098	+	0.562057i	$0.810010\pi$
$614$	−5.65716	−	18.3627i	−0.228304	−	0.741060i
$615$	−1.52857	+	2.64756i	−0.0616380	+	0.106760i
$616$	−13.0370	−	1.97892i	−0.525274	−	0.0797328i
$617$	−14.9049			−0.600048			−0.300024	−	0.953932i	$-0.596995\pi$
$617$	−14.9049			−0.600048			−0.300024	+	0.953932i	$0.596995\pi$
$618$	−14.3248	+	15.4277i	−0.576227	+	0.620592i
$619$	9.87052	−	5.69875i	0.396730	−	0.229052i	−0.288342	−	0.957527i	$-0.593104\pi$
$619$	9.87052	−	5.69875i	0.396730	−	0.229052i	0.685072	+	0.728475i	$0.259771\pi$
$620$	3.99829	+	5.87319i	0.160575	+	0.235873i
$621$	4.44361	−	2.56552i	0.178316	−	0.102951i
$622$	4.67044	−	20.4298i	0.187268	−	0.819160i
$623$	−7.42636	+	12.8628i	−0.297531	+	0.515338i
$624$	12.2239	+	4.81715i	0.489347	+	0.192840i
$625$	−29.6195			−1.18478
$626$	23.8152	+	5.44437i	0.951846	+	0.217601i
$627$			18.9627i			0.757297i
$628$	0.226338	+	3.04872i	0.00903188	+	0.121657i
$629$	−0.128607	+	0.222753i	−0.00512788	+	0.00888175i
$630$	4.95787	−	5.33959i	0.197526	−	0.212734i
$631$	2.57643	+	4.46251i	0.102566	+	0.177650i	0.912741	−	0.408538i	$-0.133961\pi$
$631$	2.57643	+	4.46251i	0.102566	+	0.177650i	−0.810175	+	0.586188i	$0.800628\pi$
$632$	−13.1848	−	33.6977i	−0.524464	−	1.34042i
$633$	−12.0841	+	6.97675i	−0.480299	+	0.277301i
$634$	−39.3530	+	12.1238i	−1.56291	+	0.481499i
$635$	1.47828	−	2.56046i	0.0586637	−	0.101609i
$636$	0.788774	−	1.63500i	0.0312769	−	0.0648318i
$637$	7.77804	+	4.49066i	0.308177	+	0.177926i
$638$	−7.06089	+	2.17531i	−0.279543	+	0.0861213i
$639$	−13.1632	−	7.59978i	−0.520728	−	0.300642i
$640$	0.0686933	−	28.2232i	0.00271534	−	1.11562i
$641$	20.4967	+	11.8338i	0.809570	+	0.467405i	0.846806	−	0.531901i	$-0.178522\pi$
$641$	20.4967	+	11.8338i	0.809570	+	0.467405i	−0.0372366	+	0.999306i	$0.511856\pi$
$642$	16.5195	+	3.77651i	0.651972	+	0.149047i
$643$		−	7.95078i		−	0.313548i	−0.987634	−	0.156774i	$-0.949891\pi$
$643$		−	7.95078i		−	0.313548i	0.987634	−	0.156774i	$-0.0501094\pi$
$644$	−9.20939	+	19.0895i	−0.362901	+	0.752233i
$645$		−	16.5737i		−	0.652589i
$646$	3.14383	−	3.38588i	0.123692	−	0.133216i
$647$	−0.715259	−	1.23886i	−0.0281197	−	0.0487048i	0.851623	−	0.524155i	$-0.175619\pi$
$647$	−0.715259	−	1.23886i	−0.0281197	−	0.0487048i	−0.879743	+	0.475450i	$0.842285\pi$
$648$	−1.76580	+	2.20951i	−0.0693672	+	0.0867979i
$649$	−4.94580	−	2.85546i	−0.194140	−	0.112087i
$650$	1.67278	+	5.42972i	0.0656118	+	0.212971i
$651$	1.47060	+	2.54716i	0.0576375	+	0.0998310i
$652$	−1.03306	−	1.51749i	−0.0404579	−	0.0594296i
$653$	5.84079	−	3.37218i	0.228568	−	0.131964i	−0.381343	−	0.924433i	$-0.624538\pi$
$653$	5.84079	−	3.37218i	0.228568	−	0.131964i	0.609911	+	0.792470i	$0.291205\pi$
$654$	−17.5962	−	4.02265i	−0.688065	−	0.157298i
$655$	22.1280			0.864614
$656$	0.723862	+	4.84826i	0.0282621	+	0.189293i
$657$	−4.82904	−	8.36414i	−0.188399	−	0.326316i
$658$	−3.34779	−	10.8667i	−0.130510	−	0.423627i
$659$	−8.15178	−	4.70644i	−0.317548	−	0.183337i	0.332751	−	0.943015i	$-0.392023\pi$
$659$	−8.15178	−	4.70644i	−0.317548	−	0.183337i	−0.650299	+	0.759678i	$0.725357\pi$
$660$	6.33763	+	9.30949i	0.246692	+	0.362372i
$661$			29.6515i			1.15331i	0.816988	+	0.576654i	$0.195642\pi$
$661$			29.6515i			1.15331i	−0.816988	+	0.576654i	$0.804358\pi$
$662$	35.5392	+	32.9986i	1.38127	+	1.28253i
$663$	1.10629	+	0.638719i	0.0429649	+	0.0248058i
$664$	0.431275	−	2.84121i	0.0167367	−	0.110260i
$665$	43.2829			1.67844
$666$	0.893871	−	0.275382i	0.0346368	−	0.0106708i
$667$			11.8757i			0.459827i
$668$	3.03970	+	4.46509i	0.117610	+	0.172760i
$669$			5.48935i			0.212230i
$670$	−25.3973	+	13.7431i	−0.981182	+	0.530942i
$671$			30.9601i			1.19520i
$672$	0.893358	−	11.6492i	0.0344621	−	0.449379i
$673$			19.6014i			0.755578i	0.925892	+	0.377789i	$0.123315\pi$
$673$			19.6014i			0.755578i	−0.925892	+	0.377789i	$0.876685\pi$
$674$	10.1653	+	32.9959i	0.391554	+	1.27095i
$675$	−1.22308			−0.0470765
$676$	3.65494	−	2.48817i	0.140575	−	0.0956990i
$677$	3.35730	+	1.93834i	0.129032	+	0.0744964i	0.563126	−	0.826371i	$-0.309598\pi$
$677$	3.35730	+	1.93834i	0.129032	+	0.0744964i	−0.434095	+	0.900867i	$0.642932\pi$
$678$	−3.64299	+	3.92347i	−0.139908	+	0.150680i
$679$			19.2071i			0.737101i
$680$	0.411809	−	2.71297i	0.0157922	−	0.104038i
$681$	−3.71947	−	2.14744i	−0.142530	−	0.0822899i
$682$	−4.34447	+	1.33844i	−0.166358	+	0.0512514i
$683$	−10.9958	−	19.0453i	−0.420744	−	0.728749i	0.575269	−	0.817964i	$-0.304897\pi$
$683$	−10.9958	−	19.0453i	−0.420744	−	0.728749i	−0.996012	+	0.0892152i	$0.971564\pi$
$684$	−16.7554	+	1.24393i	−0.640658	+	0.0475627i
$685$	−29.7339			−1.13607
$686$	6.33646	−	27.7174i	0.241927	−	1.05826i
$687$	16.5554	−	9.55826i	0.631628	−	0.364670i
$688$	−16.5405	−	20.8004i	−0.630599	−	0.793007i
$689$	1.49069	+	2.58196i	0.0567909	+	0.0983647i
$690$	17.2995	−	5.32960i	0.658581	−	0.202894i
$691$	41.9163	+	24.2004i	1.59457	+	0.920626i	0.992508	+	0.122178i	$0.0389880\pi$
$691$	41.9163	+	24.2004i	1.59457	+	0.920626i	0.602064	+	0.798448i	$0.294345\pi$
$692$	2.02729	+	27.3071i	0.0770659	+	1.03806i
$693$	2.33103	+	4.03746i	0.0885485	+	0.153370i
$694$	9.56603	+	8.88217i	0.363121	+	0.337162i
$695$			25.8247i			0.979587i
$696$	−2.38528	−	6.09629i	−0.0904139	−	0.231079i
$697$			0.476603i			0.0180526i
$698$	−2.76584	+	12.0985i	−0.104689	+	0.457937i
$699$	−12.1986	−	7.04286i	−0.461393	−	0.266385i
$700$	4.17632	−	2.84311i	0.157850	−	0.107460i
$701$	−25.5809	−	14.7691i	−0.966178	−	0.557823i	−0.0681089	−	0.997678i	$-0.521697\pi$
$701$	−25.5809	−	14.7691i	−0.966178	−	0.557823i	−0.898069	+	0.439855i	$0.855030\pi$
$702$	−1.36767	−	4.43937i	−0.0516195	−	0.167553i
$703$	4.81170	+	2.77803i	0.181477	+	0.104776i
$704$	17.2447	+	5.35870i	0.649933	+	0.201964i
$705$	−4.85567	+	8.41026i	−0.182875	+	0.316749i
$706$	10.5207	+	34.1493i	0.395950	+	1.28522i
$707$	−7.16690	+	4.13781i	−0.269539	+	0.155618i
$708$	2.19864	−	4.55741i	0.0826299	−	0.171278i
$709$	−3.73516	−	6.46949i	−0.140277	−	0.242967i	0.787324	−	0.616540i	$-0.211466\pi$
$709$	−3.73516	−	6.46949i	−0.140277	−	0.242967i	−0.927601	+	0.373573i	$0.878133\pi$
$710$	−39.2955	−	36.4864i	−1.47474	−	1.36931i
$711$	−6.39671	+	11.0794i	−0.239895	+	0.415511i
$712$	12.6985	−	15.8894i	0.475896	−	0.595479i
$713$			7.30693i			0.273647i
$714$	0.253155	−	1.10737i	0.00947409	−	0.0414423i
$715$	−18.4961			−0.691715
$716$	−1.78494	−	0.861111i	−0.0667063	−	0.0321812i
$717$	8.19349	−	14.1915i	0.305991	−	0.529993i
$718$	10.6708	+	2.43945i	0.398231	+	0.0910394i
$719$	−23.9470	+	13.8258i	−0.893071	+	0.515615i	−0.874946	−	0.484221i	$-0.839103\pi$
$719$	−23.9470	+	13.8258i	−0.893071	+	0.515615i	−0.0181255	+	0.999836i	$0.505770\pi$
$720$	−7.81011	+	6.21060i	−0.291066	+	0.231455i
$721$	−26.6267	+	15.3729i	−0.991630	+	0.572518i
$722$	−53.4477	−	49.6268i	−1.98912	−	1.84692i
$723$	−16.9302			−0.629639
$724$	−38.2659	+	26.0503i	−1.42214	+	0.968151i
$725$	1.41540	−	2.45154i	0.0525666	−	0.0910480i
$726$	7.98047	−	2.45861i	0.296183	−	0.0912476i
$727$	−10.9599	−	18.9831i	−0.406480	−	0.704045i	0.588012	−	0.808852i	$-0.299911\pi$
$727$	−10.9599	−	18.9831i	−0.406480	−	0.704045i	−0.994493	+	0.104807i	$0.966577\pi$
$728$	14.9895	+	11.9794i	0.555549	+	0.443984i
$729$	1.00000			0.0370370
$730$	−10.0318	−	32.5626i	−0.371295	−	1.20520i
$731$	−1.29191	−	2.23765i	−0.0477829	−	0.0827623i
$732$	−27.3563	+	2.03094i	−1.01112	+	0.0750657i
$733$	−20.5284	−	11.8521i	−0.758233	−	0.437766i	0.0704281	−	0.997517i	$-0.477563\pi$
$733$	−20.5284	−	11.8521i	−0.758233	−	0.437766i	−0.828661	+	0.559751i	$0.810897\pi$
$734$	−14.8436	−	13.7825i	−0.547889	−	0.508721i
$735$	−5.90714	+	3.41049i	−0.217888	+	0.125798i
$736$	16.3923	−	23.9536i	0.604230	−	0.882940i
$737$	−3.61913	−	18.1186i	−0.133312	−	0.667406i
$738$	1.17926	−	1.27006i	0.0434092	−	0.0467514i
$739$	−4.00161	−	6.93100i	−0.147202	−	0.254961i	0.782990	−	0.622034i	$-0.213693\pi$
$739$	−4.00161	−	6.93100i	−0.147202	−	0.254961i	−0.930192	+	0.367073i	$0.880360\pi$
$740$	3.29070	−	0.244303i	0.120969	−	0.00898076i
$741$	13.7970	−	23.8971i	0.506845	−	0.877880i
$742$	1.80391	−	1.94280i	0.0662237	−	0.0713224i
$743$	−21.7817	+	12.5757i	−0.799093	+	0.461357i	−0.843154	−	0.537672i	$-0.819304\pi$
$743$	−21.7817	+	12.5757i	−0.799093	+	0.461357i	0.0440607	+	0.999029i	$0.485971\pi$
$744$	−1.46763	−	3.75096i	−0.0538060	−	0.137517i
$745$			32.8509i			1.20357i
$746$	−11.4544	+	12.3363i	−0.419374	+	0.451663i
$747$	−0.879905	+	0.508013i	−0.0321940	+	0.0185872i
$748$	1.58132	+	0.762879i	0.0578188	+	0.0278936i
$749$	21.4324	+	12.3740i	0.783121	+	0.452135i
$750$	12.9895	+	2.96953i	0.474310	+	0.108432i
$751$			38.1245i			1.39118i	0.718438	+	0.695591i	$0.244857\pi$
$751$			38.1245i			1.39118i	−0.718438	+	0.695591i	$0.755143\pi$
$752$	2.29942	+	15.4010i	0.0838513	+	0.561616i
$753$	−7.15767	−	12.3975i	−0.260840	−	0.451788i
$754$	10.4810	+	2.39605i	0.381694	+	0.0872588i
$755$	−13.3525	−	23.1273i	−0.485949	−	0.841688i
$756$	−3.41458	+	2.32454i	−0.124187	+	0.0845428i
$757$	4.09129	+	2.36211i	0.148701	+	0.0858524i	0.572504	−	0.819902i	$-0.305972\pi$
$757$	4.09129	+	2.36211i	0.148701	+	0.0858524i	−0.423804	+	0.905754i	$0.639305\pi$
$758$	−11.0596	+	3.40721i	−0.401701	+	0.123756i
$759$			11.5821i			0.420403i
$760$	−58.6029	−	8.89550i	−2.12575	−	0.322674i
$761$	37.8980			1.37380			0.686901	−	0.726751i	$-0.258971\pi$
$761$	37.8980			1.37380			0.686901	+	0.726751i	$0.258971\pi$
$762$	−1.14046	+	1.22827i	−0.0413146	+	0.0444955i
$763$	−22.8293	−	13.1805i	−0.826475	−	0.477165i
$764$	−1.73916	−	23.4260i	−0.0629205	−	0.847524i
$765$	−0.840190	+	0.485084i	−0.0303771	+	0.0175382i
$766$	14.0816	−	4.33824i	0.508789	−	0.156747i
$767$	4.15518	+	7.19698i	0.150035	+	0.259868i
$768$	−3.60371	+	15.5889i	−0.130038	+	0.562515i
$769$	−2.65973	−	1.53559i	−0.0959122	−	0.0553749i	0.451277	−	0.892384i	$-0.350969\pi$
$769$	−2.65973	−	1.53559i	−0.0959122	−	0.0553749i	−0.547189	+	0.837009i	$0.684302\pi$
$770$	4.84247	+	15.7183i	0.174511	+	0.566449i
$771$	−14.5021	+	25.1183i	−0.522279	+	0.904613i
$772$	−34.9520	−	16.8619i	−1.25795	−	0.606874i
$773$	10.9388	−	18.9465i	0.393440	−	0.681458i	−0.599461	−	0.800404i	$-0.704618\pi$
$773$	10.9388	−	18.9465i	0.393440	−	0.681458i	0.992901	+	0.118946i	$0.0379516\pi$
$774$	−2.09394	+	9.15946i	−0.0752650	+	0.329230i
$775$	0.870875	−	1.50840i	0.0312828	−	0.0541833i
$776$	3.94744	−	26.0054i	0.141705	−	0.933541i
$777$	1.36598			0.0490044
$778$	−28.3490	+	8.73373i	−1.01636	+	0.313119i
$779$	10.2951			0.368861
$780$	−1.21332	−	16.3431i	−0.0434438	−	0.585178i
$781$	29.7128	−	17.1547i	1.06321	−	0.613843i
$782$	1.92020	−	2.06804i	0.0686662	−	0.0739529i
$783$	−1.15724	+	2.00439i	−0.0413563	+	0.0716312i
$784$	−4.00994	+	10.1755i	−0.143212	+	0.363412i
$785$	3.30229	−	1.90658i	0.117864	−	0.0680486i
$786$	−12.2291	−	2.79568i	−0.436196	−	0.0997185i
$787$	−11.4305	−	19.7981i	−0.407452	−	0.705728i	0.587151	−	0.809477i	$-0.300249\pi$
$787$	−11.4305	−	19.7981i	−0.407452	−	0.705728i	−0.994603	+	0.103749i	$0.966916\pi$
$788$	−21.1411	−	31.0546i	−0.753119	−	1.10627i
$789$		−	22.9977i		−	0.818738i
$790$	−30.7105	+	33.0750i	−1.09263	+	1.17675i
$791$	−6.77154	+	3.90955i	−0.240768	+	0.139008i
$792$	−2.32632	−	5.94559i	−0.0826622	−	0.211267i
$793$	22.5261	−	39.0163i	0.799925	−	1.38551i
$794$	−8.92187	+	39.0267i	−0.316625	+	1.38501i
$795$	−2.26425			−0.0803048
$796$	22.2646	−	1.65293i	0.789148	−	0.0585866i
$797$	11.2651	−	19.5116i	0.399029	−	0.691138i	−0.594578	−	0.804038i	$-0.702681\pi$
$797$	11.2651	−	19.5116i	0.399029	−	0.691138i	0.993606	+	0.112900i	$0.0360141\pi$
$798$	−23.9203	−	5.46841i	−0.846770	−	0.193580i
$799$			1.51398i			0.0535607i
$800$	−6.23884	+	2.99112i	−0.220576	+	0.105752i
$801$	−7.19134			−0.254094
$802$	−38.4283	−	8.78507i	−1.35695	−	0.310212i
$803$	21.8008			0.769334
$804$	15.7721	−	4.38641i	0.556239	−	0.154697i
$805$	26.4365			0.931764
$806$	6.44879	+	1.47425i	0.227149	+	0.0519284i
$807$	6.00531			0.211397
$808$	10.5540	−	4.12945i	0.371289	−	0.145274i
$809$		−	4.91430i		−	0.172777i	−0.996262	−	0.0863887i	$-0.972467\pi$
$809$		−	4.91430i		−	0.172777i	0.996262	−	0.0863887i	$-0.0275327\pi$
$810$	3.43919	+	0.786230i	0.120841	+	0.0276253i
$811$	−24.6961	+	42.7748i	−0.867196	+	1.50203i	−0.00234658	+	0.999997i	$0.500747\pi$
$811$	−24.6961	+	42.7748i	−0.867196	+	1.50203i	−0.864850	+	0.502031i	$0.832586\pi$
$812$	−0.707823	−	9.53421i	−0.0248397	−	0.334585i
$813$	−18.0788			−0.634050
$814$	−0.470520	+	2.05818i	−0.0164917	+	0.0721393i
$815$	−1.14488	+	1.98298i	−0.0401032	+	0.0694608i
$816$	−0.570346	+	1.44730i	−0.0199661	+	0.0506655i
$817$	−48.3354	+	27.9065i	−1.69104	+	0.976324i
$818$	5.80745	−	6.25458i	0.203053	−	0.218686i
$819$		−	6.78409i		−	0.237055i
$820$	5.05426	−	3.44079i	0.176502	−	0.120157i
$821$	2.97748	+	5.15715i	0.103915	+	0.179986i	0.913294	−	0.407300i	$-0.133530\pi$
$821$	2.97748	+	5.15715i	0.103915	+	0.179986i	−0.809379	+	0.587286i	$0.800196\pi$
$822$	16.4324	+	3.75660i	0.573146	+	0.131027i
$823$	−16.1847	+	9.34427i	−0.564165	+	0.325721i	−0.754815	−	0.655937i	$-0.772274\pi$
$823$	−16.1847	+	9.34427i	−0.564165	+	0.325721i	0.190651	+	0.981658i	$0.438940\pi$
$824$	39.2106	−	15.3419i	1.36597	−	0.534459i
$825$	1.38041	−	2.39094i	0.0480597	−	0.0832419i
$826$	5.02825	−	5.41539i	0.174955	−	0.188425i
$827$	18.6662	−	10.7769i	0.649087	−	0.374750i	−0.139019	−	0.990290i	$-0.544395\pi$
$827$	18.6662	−	10.7769i	0.649087	−	0.374750i	0.788106	+	0.615539i	$0.211062\pi$
$828$	−10.2339	+	0.759769i	−0.355653	+	0.0264038i
$829$	51.9633			1.80476			0.902379	−	0.430943i	$-0.141819\pi$
$829$	51.9633			1.80476			0.902379	+	0.430943i	$0.141819\pi$
$830$	−3.42557	+	1.05534i	−0.118903	+	0.0366316i
$831$	−18.1908			−0.631033
$832$	−17.8331	−	19.3001i	−0.618251	−	0.669110i
$833$	−0.531689	+	0.920913i	−0.0184219	+	0.0319078i
$834$	3.26272	−	14.2720i	0.112979	−	0.494200i
$835$	3.36870	−	5.83475i	0.116579	−	0.201920i
$836$	16.4790	−	34.1581i	0.569937	−	1.18138i
$837$	−0.712032	+	1.23328i	−0.0246114	+	0.0426283i
$838$	5.04314	+	16.3697i	0.174212	+	0.565480i
$839$	−22.2435	−	12.8423i	−0.767932	−	0.443366i	0.0642041	−	0.997937i	$-0.479549\pi$
$839$	−22.2435	−	12.8423i	−0.767932	−	0.443366i	−0.832137	+	0.554571i	$0.812882\pi$
$840$	−13.5710	+	5.30990i	−0.468244	+	0.183209i
$841$	11.8216	+	20.4756i	0.407642	+	0.706056i
$842$	−37.0819	+	11.4241i	−1.27793	+	0.393702i
$843$	0.713941	−	0.412194i	0.0245894	−	0.0141967i
$844$	27.8304	−	2.06614i	0.957962	−	0.0711194i
$845$	−4.77609	−	2.75748i	−0.164302	−	0.0948601i
$846$	3.74604	−	4.03446i	0.128792	−	0.138708i
$847$	12.1955			0.419042
$848$	−2.84169	+	2.25971i	−0.0975840	+	0.0775989i
$849$			17.7703i			0.609874i
$850$	−0.642874	+	0.198055i	−0.0220504	+	0.00679325i
$851$	2.93890	+	1.69678i	0.100744	+	0.0581648i
$852$	17.1070	+	25.1288i	0.586075	+	0.860899i
$853$	−18.0462	−	31.2570i	−0.617892	−	1.07022i	−0.989870	−	0.141978i	$-0.954654\pi$
$853$	−18.0462	−	31.2570i	−0.617892	−	1.07022i	0.371978	−	0.928242i	$-0.378680\pi$
$854$	−39.0543	−	8.92818i	−1.33641	−	0.305516i
$855$	10.4783	+	18.1490i	0.358350	+	0.620681i
$856$	−26.4752	−	21.1585i	−0.904905	−	0.723183i
$857$			43.8546i			1.49804i	0.662545	+	0.749022i	$0.269476\pi$
$857$			43.8546i			1.49804i	−0.662545	+	0.749022i	$0.730524\pi$
$858$	10.2219	+	2.33682i	0.348969	+	0.0797776i
$859$	38.8297	+	22.4183i	1.32485	+	0.764903i	0.984498	−	0.175395i	$-0.0561202\pi$
$859$	38.8297	+	22.4183i	1.32485	+	0.764903i	0.340353	+	0.940298i	$0.389453\pi$
$860$	−14.4029	+	29.8548i	−0.491134	+	1.01804i
$861$	2.19199	−	1.26555i	0.0747030	−	0.0431298i
$862$	30.0087	−	32.3192i	1.02210	−	1.10079i
$863$		−	20.6020i		−	0.701301i	−0.936506	−	0.350650i	$-0.885961\pi$
$863$		−	20.6020i		−	0.701301i	0.936506	−	0.350650i	$-0.114039\pi$
$864$	5.10091	−	2.44555i	0.173536	−	0.0831994i
$865$	29.5782	−	17.0770i	1.00569	−	0.580635i
$866$	−1.10528	+	1.19037i	−0.0375588	+	0.0404505i
$867$	8.42438	−	14.5914i	0.286107	−	0.495552i
$868$	−0.435514	−	5.86627i	−0.0147823	−	0.199114i
$869$	−14.4391	−	25.0092i	−0.489811	−	0.848378i
$870$	−5.55587	+	5.98363i	−0.188362	+	0.202864i
$871$	−8.62192	+	25.4665i	−0.292142	+	0.862899i
$872$	28.2008	+	22.5376i	0.955001	+	0.763219i
$873$	−8.05372	+	4.64982i	−0.272577	+	0.157372i
$874$	−44.6718	−	41.4782i	−1.51104	−	1.40302i
$875$	16.8526	+	9.72985i	0.569721	+	0.328929i
$876$	1.43010	+	19.2631i	0.0483187	+	0.650841i
$877$	17.9030	+	31.0088i	0.604540	+	1.04709i	0.992124	+	0.125259i	$0.0399763\pi$
$877$	17.9030	+	31.0088i	0.604540	+	1.04709i	−0.387584	+	0.921834i	$0.626690\pi$
$878$	−16.1655	−	52.4721i	−0.545559	−	1.77085i
$879$	−14.6021			−0.492517
$880$	−3.32604	−	22.2770i	−0.112121	−	0.750959i
$881$	−26.8223	−	46.4575i	−0.903665	−	1.56519i	−0.822699	−	0.568478i	$-0.807533\pi$
$881$	−26.8223	−	46.4575i	−0.903665	−	1.56519i	−0.0809667	−	0.996717i	$-0.525801\pi$
$882$	3.69547	−	1.13849i	0.124433	−	0.0383351i
$883$	14.6639	−	25.3986i	0.493480	−	0.854733i	−0.506492	−	0.862245i	$-0.669058\pi$
$883$	14.6639	−	25.3986i	0.493480	−	0.854733i	0.999972	+	0.00751225i	$0.00239125\pi$
$884$	−1.43774	−	2.11194i	−0.0483566	−	0.0710321i
$885$	−6.31142			−0.212156
$886$	−30.7330	−	28.5360i	−1.03250	−	0.958685i
$887$	−11.2730	+	6.50848i	−0.378511	+	0.218533i	−0.677170	−	0.735827i	$-0.736794\pi$
$887$	−11.2730	+	6.50848i	−0.378511	+	0.218533i	0.298659	+	0.954360i	$0.403461\pi$
$888$	−1.84947	−	0.280736i	−0.0620642	−	0.00942090i
$889$	−2.11987	+	1.22391i	−0.0710983	+	0.0410486i
$890$	−24.7324	−	5.65405i	−0.829031	−	0.189524i
$891$	−1.12863	+	1.95485i	−0.0378106	+	0.0654898i
$892$	4.77035	−	9.88814i	0.159723	−	0.331080i
$893$	32.7035			1.09438
$894$	4.15042	−	18.1551i	0.138811	−	0.607197i
$895$			2.47191i			0.0826267i
$896$	−11.7327	+	20.2078i	−0.391961	+	0.675096i
$897$	8.42696	−	14.5959i	0.281368	−	0.487344i
$898$	14.5502	+	13.5100i	0.485546	+	0.450835i
$899$	−1.64798	−	2.85439i	−0.0549632	−	0.0951991i
$900$	2.20318	+	1.06288i	0.0734394	+	0.0354295i
$901$	−0.305701	+	0.176497i	−0.0101844	+	0.00587995i
$902$	1.15181	+	3.73870i	0.0383511	+	0.124485i
$903$	−6.86093	+	11.8835i	−0.228317	+	0.395457i
$904$	9.97182	−	3.90165i	0.331658	−	0.129767i
$905$	50.0039	+	28.8698i	1.66219	+	0.959663i
$906$	4.45736	+	14.4683i	0.148086	+	0.480676i
$907$	42.0215	+	24.2611i	1.39530	+	0.805578i	0.993896	−	0.110322i	$-0.0351882\pi$
$907$	42.0215	+	24.2611i	1.39530	+	0.805578i	0.401406	+	0.915900i	$0.368522\pi$
$908$	4.83384	+	7.10054i	0.160416	+	0.235640i
$909$	−3.47005	−	2.00343i	−0.115094	−	0.0664497i
$910$	5.33386	−	23.3318i	0.176816	−	0.773440i
$911$			53.6780i			1.77843i	0.457487	+	0.889216i	$0.348750\pi$
$911$			53.6780i			1.77843i	−0.457487	+	0.889216i	$0.651250\pi$
$912$	31.2631	+	12.3201i	1.03522	+	0.407958i
$913$		−	2.29344i		−	0.0759017i
$914$	−5.44539	−	5.05611i	−0.180118	−	0.167241i
$915$	17.1078	+	29.6315i	0.565565	+	0.979587i
$916$	−38.1281	+	2.83065i	−1.25979	+	0.0935272i
$917$	−15.8660	−	9.16022i	−0.523940	−	0.302497i
$918$	0.525617	−	0.161931i	0.0173479	−	0.00534453i
$919$	15.0535	+	26.0734i	0.496568	+	0.860081i	0.999992	−	0.00395863i	$-0.00126007\pi$
$919$	15.0535	+	26.0734i	0.496568	+	0.860081i	−0.503424	+	0.864039i	$0.667927\pi$
$920$	−35.7937	−	5.43322i	−1.18008	−	0.179128i
$921$	11.7664	−	6.79332i	0.387715	−	0.223847i
$922$	7.33534	−	32.0868i	0.241577	−	1.05672i
$923$	−49.9260			−1.64333
$924$	−0.690326	−	9.29853i	−0.0227101	−	0.305899i
$925$	−0.404460	−	0.700545i	−0.0132986	−	0.0230338i
$926$	−48.4362	+	14.9222i	−1.59171	+	0.490373i
$927$	−12.8920	−	7.44322i	−0.423430	−	0.244467i
$928$	−1.00111	+	13.0543i	−0.0328631	+	0.428529i
$929$		−	39.1131i		−	1.28326i	−0.767015	−	0.641630i	$-0.778259\pi$
$929$		−	39.1131i		−	1.28326i	0.767015	−	0.641630i	$-0.221741\pi$
$930$	−3.41845	+	3.68165i	−0.112095	+	0.120726i
$931$	19.8927	+	11.4850i	0.651956	+	0.376407i
$932$	15.8533	+	23.2874i	0.519294	+	0.762803i
$933$	14.8187			0.485143
$934$	12.8742	+	41.7886i	0.421256	+	1.36737i
$935$		−	2.18992i		−	0.0716181i
$936$	−1.39426	+	9.18532i	−0.0455730	+	0.300231i
$937$			2.23750i			0.0730959i	0.999332	+	0.0365480i	$0.0116362\pi$
$937$			2.23750i			0.0730959i	−0.999332	+	0.0365480i	$0.988364\pi$
$938$	23.8992	+	0.659659i	0.780336	+	0.0215386i
$939$			17.2743i			0.563726i
$940$	16.0554	−	10.9300i	0.523668	−	0.356498i
$941$		−	6.95279i		−	0.226655i	−0.993558	−	0.113327i	$-0.963849\pi$
$941$		−	6.95279i		−	0.226655i	0.993558	−	0.113327i	$-0.0361509\pi$
$942$	−2.06589	+	0.636455i	−0.0673102	+	0.0207368i
$943$	6.28808			0.204768
$944$	−7.92097	+	6.29876i	−0.257806	+	0.205007i
$945$	4.46200	+	2.57614i	0.145149	+	0.0838017i
$946$	−15.5420	−	14.4310i	−0.505316	−	0.469191i
$947$		−	23.1862i		−	0.753449i	−0.926325	−	0.376724i	$-0.877050\pi$
$947$		−	23.1862i		−	0.753449i	0.926325	−	0.376724i	$-0.122950\pi$
$948$	21.1509	−	14.3989i	0.686948	−	0.467654i
$949$	−27.4737	−	15.8619i	−0.891834	−	0.514901i
$950$	4.27820	+	13.8867i	0.138803	+	0.450545i
$951$	−14.5587	−	25.2164i	−0.472099	−	0.817699i
$952$	−1.41834	+	1.77475i	−0.0459688	+	0.0575199i
$953$	0.401543			0.0130073			0.00650363	−	0.999979i	$-0.497930\pi$
$953$	0.401543			0.0130073			0.00650363	+	0.999979i	$0.497930\pi$
$954$	1.25134	+	0.286068i	0.0405136	+	0.00926179i
$955$	−25.3744	+	14.6499i	−0.821096	+	0.474060i
$956$	−27.0919	+	18.4434i	−0.876216	+	0.596502i
$957$	−2.61219	−	4.52444i	−0.0844400	−	0.146254i
$958$	−8.38909	−	27.2304i	−0.271039	−	0.879774i
$959$	21.3194	+	12.3088i	0.688439	+	0.397471i
$960$	19.4657	−	4.40023i	0.628254	−	0.142017i
$961$	14.4860	+	25.0905i	0.467291	+	0.809372i
$962$	2.09046	−	2.25141i	0.0673992	−	0.0725884i
$963$			11.9824i			0.386127i
$964$	30.4969	+	14.7127i	0.982238	+	0.473863i
$965$			48.4039i			1.55818i
$966$	−14.6101	−	3.34001i	−0.470073	−	0.107463i
$967$	20.1367	+	11.6259i	0.647552	+	0.373864i	0.787518	−	0.616292i	$-0.211366\pi$
$967$	20.1367	+	11.6259i	0.647552	+	0.373864i	−0.139966	+	0.990156i	$0.544699\pi$
$968$	−16.5121	−	2.50641i	−0.530718	−	0.0805591i
$969$	2.82939	+	1.63355i	0.0908931	+	0.0524772i
$970$	−31.3541	+	9.65951i	−1.00672	+	0.310148i
$971$	0.160936	+	0.0929162i	0.00516467	+	0.00298182i	0.502580	−	0.864531i	$-0.332384\pi$
$971$	0.160936	+	0.0929162i	0.00516467	+	0.00298182i	−0.497415	+	0.867512i	$0.665718\pi$
$972$	−1.80133	−	0.869020i	−0.0577778	−	0.0278738i
$973$	10.6905	−	18.5165i	0.342722	−	0.593612i
$974$	−26.0876	+	8.03702i	−0.835900	+	0.257523i
$975$	−3.47923	+	2.00873i	−0.111424	+	0.0643309i
$976$	51.0427	+	20.1147i	1.63384	+	0.643857i
$977$	−30.8644	−	53.4587i	−0.987439	−	1.71030i	−0.630550	−	0.776148i	$-0.717171\pi$
$977$	−30.8644	−	53.4587i	−0.987439	−	1.71030i	−0.356889	−	0.934147i	$-0.616163\pi$
$978$	0.883247	−	0.951250i	0.0282431	−	0.0304176i
$979$	8.11637	−	14.0580i	0.259400	−	0.449295i
$980$	13.6045	−	1.01000i	0.434581	−	0.0322634i
$981$		−	12.7634i		−	0.407503i
$982$	−9.04997	−	2.06891i	−0.288796	−	0.0660215i
$983$	45.6857			1.45715			0.728574	−	0.684967i	$-0.240184\pi$
$983$	45.6857			1.45715			0.728574	+	0.684967i	$0.240184\pi$
$984$	−3.22795	+	1.26299i	−0.102903	+	0.0402627i
$985$	−23.4292	+	40.5806i	−0.746517	+	1.29300i
$986$	−0.283690	+	1.24094i	−0.00903452	+	0.0395195i
$987$	6.96310	−	4.02015i	0.221638	−	0.127963i
$988$	−45.6200	+	31.0567i	−1.45137	+	0.988046i
$989$	−29.5225	+	17.0448i	−0.938760	+	0.541993i
$990$	−5.41853	+	5.83572i	−0.172212	+	0.185471i
$991$	61.2928			1.94703			0.973515	−	0.228623i	$-0.0734222\pi$
$991$	61.2928			1.94703			0.973515	+	0.228623i	$0.0734222\pi$
$992$	−0.615970	+	8.03214i	−0.0195571	+	0.255021i
$993$	−17.1462	+	29.6981i	−0.544119	+	0.942442i
$994$	13.0711	+	42.4279i	0.414591	+	1.34573i
$995$	−13.9236	−	24.1164i	−0.441408	−	0.764541i
$996$	2.02648	−	0.150446i	0.0642113	−	0.00476707i
$997$	−2.02578			−0.0641570			−0.0320785	−	0.999485i	$-0.510213\pi$
$997$	−2.02578			−0.0641570			−0.0320785	+	0.999485i	$0.510213\pi$
$998$	−8.47323	+	2.61042i	−0.268215	+	0.0826314i
$999$	0.330689	+	0.572770i	0.0104625	+	0.0181216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.b.499.20	yes	68
4.3	odd	2		804.2.j.a.499.32	✓	68
67.38	odd	6		804.2.j.a.775.32	yes	68
268.239	even	6	inner	804.2.j.b.775.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.32	✓	68	4.3	odd	2
804.2.j.a.775.32	yes	68	67.38	odd	6
804.2.j.b.499.20	yes	68	1.1	even	1	trivial
804.2.j.b.775.20	yes	68	268.239	even	6	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.315172 - 1.37865i) q^{2} +1.00000 q^{3} +(-1.80133 - 0.869020i) q^{4} +2.49461i q^{5} +(0.315172 - 1.37865i) q^{6} +(1.03268 - 1.78865i) q^{7} +(-1.76580 + 2.20951i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.315172 - 1.37865i) q^{2} +1.00000 q^{3} +(-1.80133 - 0.869020i) q^{4} +2.49461i q^{5} +(0.315172 - 1.37865i) q^{6} +(1.03268 - 1.78865i) q^{7} +(-1.76580 + 2.20951i) q^{8} +1.00000 q^{9} +(3.43919 + 0.786230i) q^{10} +(-1.12863 + 1.95485i) q^{11} +(-1.80133 - 0.869020i) q^{12} +(2.84463 - 1.64235i) q^{13} +(-2.14045 - 1.98743i) q^{14} +2.49461i q^{15} +(2.48961 + 3.13079i) q^{16} +(0.194453 + 0.336802i) q^{17} +(0.315172 - 1.37865i) q^{18} +(7.27526 - 4.20038i) q^{19} +(2.16787 - 4.49363i) q^{20} +(1.03268 - 1.78865i) q^{21} +(2.33933 + 2.17210i) q^{22} +(4.44361 - 2.56552i) q^{23} +(-1.76580 + 2.20951i) q^{24} -1.22308 q^{25} +(-1.36767 - 4.43937i) q^{26} +1.00000 q^{27} +(-3.41458 + 2.32454i) q^{28} +(-1.15724 + 2.00439i) q^{29} +(3.43919 + 0.786230i) q^{30} +(-0.712032 + 1.23328i) q^{31} +(5.10091 - 2.44555i) q^{32} +(-1.12863 + 1.95485i) q^{33} +(0.525617 - 0.161931i) q^{34} +(4.46200 + 2.57614i) q^{35} +(-1.80133 - 0.869020i) q^{36} +(0.330689 + 0.572770i) q^{37} +(-3.49788 - 11.3539i) q^{38} +(2.84463 - 1.64235i) q^{39} +(-5.51187 - 4.40499i) q^{40} +(1.06131 + 0.612750i) q^{41} +(-2.14045 - 1.98743i) q^{42} -6.64380 q^{43} +(3.73184 - 2.54053i) q^{44} +2.49461i q^{45} +(-2.13645 - 6.93475i) q^{46} +(3.37137 + 1.94646i) q^{47} +(2.48961 + 3.13079i) q^{48} +(1.36714 + 2.36796i) q^{49} +(-0.385481 + 1.68620i) q^{50} +(0.194453 + 0.336802i) q^{51} +(-6.55137 + 0.486376i) q^{52} +0.907658i q^{53} +(0.315172 - 1.37865i) q^{54} +(-4.87658 - 2.81549i) q^{55} +(2.12855 + 5.44013i) q^{56} +(7.27526 - 4.20038i) q^{57} +(2.39862 + 2.22715i) q^{58} +2.53002i q^{59} +(2.16787 - 4.49363i) q^{60} +(11.8782 - 6.85789i) q^{61} +(1.47584 + 1.37033i) q^{62} +(1.03268 - 1.78865i) q^{63} +(-1.76389 - 7.80312i) q^{64} +(4.09702 + 7.09625i) q^{65} +(2.33933 + 2.17210i) q^{66} +(-6.14974 + 5.40192i) q^{67} +(-0.0575865 - 0.775676i) q^{68} +(4.44361 - 2.56552i) q^{69} +(4.95787 - 5.33959i) q^{70} +(-13.1632 - 7.59978i) q^{71} +(-1.76580 + 2.20951i) q^{72} +(-4.82904 - 8.36414i) q^{73} +(0.893871 - 0.275382i) q^{74} -1.22308 q^{75} +(-16.7554 + 1.24393i) q^{76} +(2.33103 + 4.03746i) q^{77} +(-1.36767 - 4.43937i) q^{78} +(-6.39671 + 11.0794i) q^{79} +(-7.81011 + 6.21060i) q^{80} +1.00000 q^{81} +(1.17926 - 1.27006i) q^{82} +(-0.879905 + 0.508013i) q^{83} +(-3.41458 + 2.32454i) q^{84} +(-0.840190 + 0.485084i) q^{85} +(-2.09394 + 9.15946i) q^{86} +(-1.15724 + 2.00439i) q^{87} +(-2.32632 - 5.94559i) q^{88} -7.19134 q^{89} +(3.43919 + 0.786230i) q^{90} -6.78409i q^{91} +(-10.2339 + 0.759769i) q^{92} +(-0.712032 + 1.23328i) q^{93} +(3.74604 - 4.03446i) q^{94} +(10.4783 + 18.1490i) q^{95} +(5.10091 - 2.44555i) q^{96} +(-8.05372 + 4.64982i) q^{97} +(3.69547 - 1.13849i) q^{98} +(-1.12863 + 1.95485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more