LMFDB - Embedded newform 802.2.e.b.45.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, 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:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.11
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.868578 + 0.359777i) q^{3} +1.00000i q^{4} +3.24260 q^{5} +(0.359777 + 0.868578i) q^{6} +(1.17950 - 1.17950i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49633 - 1.49633i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.868578 + 0.359777i) q^{3} +1.00000i q^{4} +3.24260 q^{5} +(0.359777 + 0.868578i) q^{6} +(1.17950 - 1.17950i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49633 - 1.49633i) q^{9} +(2.29286 + 2.29286i) q^{10} +(0.815523 + 0.815523i) q^{11} +(-0.359777 + 0.868578i) q^{12} +(0.661198 - 0.273877i) q^{13} +1.66807 q^{14} +(2.81645 + 1.16661i) q^{15} -1.00000 q^{16} +(2.18723 - 0.905982i) q^{17} -2.11613i q^{18} +(-0.0238666 - 0.0576191i) q^{19} +3.24260i q^{20} +(1.44885 - 0.600134i) q^{21} +1.15332i q^{22} +(1.17749 + 2.84271i) q^{23} +(-0.868578 + 0.359777i) q^{24} +5.51442 q^{25} +(0.661198 + 0.273877i) q^{26} +(-1.84067 - 4.44376i) q^{27} +(1.17950 + 1.17950i) q^{28} -8.40955 q^{29} +(1.16661 + 2.81645i) q^{30} +(1.52502 + 3.68173i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.414940 + 1.00175i) q^{33} +(2.18723 + 0.905982i) q^{34} +(3.82466 - 3.82466i) q^{35} +(1.49633 - 1.49633i) q^{36} +(-4.73714 - 1.96219i) q^{37} +(0.0238666 - 0.0576191i) q^{38} +0.672837 q^{39} +(-2.29286 + 2.29286i) q^{40} -1.79131 q^{41} +(1.44885 + 0.600134i) q^{42} +(1.16247 - 1.16247i) q^{43} +(-0.815523 + 0.815523i) q^{44} +(-4.85200 - 4.85200i) q^{45} +(-1.17749 + 2.84271i) q^{46} +(-1.57436 - 1.57436i) q^{47} +(-0.868578 - 0.359777i) q^{48} +4.21754i q^{49} +(3.89929 + 3.89929i) q^{50} +2.22574 q^{51} +(0.273877 + 0.661198i) q^{52} +(0.844101 - 2.03784i) q^{53} +(1.84067 - 4.44376i) q^{54} +(2.64441 + 2.64441i) q^{55} +1.66807i q^{56} -0.0586334i q^{57} +(-5.94645 - 5.94645i) q^{58} +(-6.62374 + 2.74364i) q^{59} +(-1.16661 + 2.81645i) q^{60} +(0.796763 + 1.92356i) q^{61} +(-1.52502 + 3.68173i) q^{62} -3.52986 q^{63} -1.00000i q^{64} +(2.14400 - 0.888072i) q^{65} +(-0.414940 + 1.00175i) q^{66} +(-1.55204 + 3.74696i) q^{67} +(0.905982 + 2.18723i) q^{68} +2.89275i q^{69} +5.40888 q^{70} +(1.90037 - 4.58789i) q^{71} +2.11613 q^{72} +(-8.96959 + 8.96959i) q^{73} +(-1.96219 - 4.73714i) q^{74} +(4.78971 + 1.98396i) q^{75} +(0.0576191 - 0.0238666i) q^{76} +1.92383 q^{77} +(0.475767 + 0.475767i) q^{78} +(2.66608 + 6.43648i) q^{79} -3.24260 q^{80} +1.82641i q^{81} +(-1.26665 - 1.26665i) q^{82} +6.20305 q^{83} +(0.600134 + 1.44885i) q^{84} +(7.09232 - 2.93773i) q^{85} +1.64398 q^{86} +(-7.30436 - 3.02556i) q^{87} -1.15332 q^{88} +(-0.190326 + 0.190326i) q^{89} -6.86176i q^{90} +(0.456846 - 1.10292i) q^{91} +(-2.84271 + 1.17749i) q^{92} +3.74654i q^{93} -2.22649i q^{94} +(-0.0773897 - 0.186835i) q^{95} +(-0.359777 - 0.868578i) q^{96} +(-2.98750 - 7.21245i) q^{97} +(-2.98225 + 2.98225i) q^{98} -2.44059i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.868578	+	0.359777i	0.501474	+	0.207717i	0.619057	−	0.785346i	$-0.287515\pi$
$3$	0.868578	+	0.359777i	0.501474	+	0.207717i	−0.117583	+	0.993063i	$0.537515\pi$
$4$			1.00000i			0.500000i
$5$	3.24260			1.45013			0.725066	−	0.688679i	$-0.241809\pi$
$5$	3.24260			1.45013			0.725066	+	0.688679i	$0.241809\pi$
$6$	0.359777	+	0.868578i	0.146878	+	0.354596i
$7$	1.17950	−	1.17950i	0.445811	−	0.445811i	−0.448148	−	0.893959i	$-0.647916\pi$
$7$	1.17950	−	1.17950i	0.445811	−	0.445811i	0.893959	+	0.448148i	$0.147916\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.49633	−	1.49633i	−0.498777	−	0.498777i
$10$	2.29286	+	2.29286i	0.725066	+	0.725066i
$11$	0.815523	+	0.815523i	0.245890	+	0.245890i	0.819281	−	0.573392i	$-0.194373\pi$
$11$	0.815523	+	0.815523i	0.245890	+	0.245890i	−0.573392	+	0.819281i	$0.694373\pi$
$12$	−0.359777	+	0.868578i	−0.103859	+	0.250737i
$13$	0.661198	−	0.273877i	0.183383	−	0.0759598i	−0.289102	−	0.957298i	$-0.593357\pi$
$13$	0.661198	−	0.273877i	0.183383	−	0.0759598i	0.472486	+	0.881338i	$0.343357\pi$
$14$	1.66807			0.445811
$15$	2.81645	+	1.16661i	0.727204	+	0.301218i
$16$	−1.00000			−0.250000
$17$	2.18723	−	0.905982i	0.530482	−	0.219733i	−0.101332	−	0.994853i	$-0.532310\pi$
$17$	2.18723	−	0.905982i	0.530482	−	0.219733i	0.631814	+	0.775120i	$0.282310\pi$
$18$		−	2.11613i		−	0.498777i
$19$	−0.0238666	−	0.0576191i	−0.00547538	−	0.0132187i	0.921118	−	0.389283i	$-0.127277\pi$
$19$	−0.0238666	−	0.0576191i	−0.00547538	−	0.0132187i	−0.926594	+	0.376064i	$0.877277\pi$
$20$			3.24260i			0.725066i
$21$	1.44885	−	0.600134i	0.316165	−	0.130960i
$22$			1.15332i			0.245890i
$23$	1.17749	+	2.84271i	0.245523	+	0.592745i	0.997814	−	0.0660860i	$-0.0210512\pi$
$23$	1.17749	+	2.84271i	0.245523	+	0.592745i	−0.752291	+	0.658831i	$0.771051\pi$
$24$	−0.868578	+	0.359777i	−0.177298	+	0.0734392i
$25$	5.51442			1.10288
$26$	0.661198	+	0.273877i	0.129672	+	0.0537117i
$27$	−1.84067	−	4.44376i	−0.354236	−	0.855202i
$28$	1.17950	+	1.17950i	0.222905	+	0.222905i
$29$	−8.40955			−1.56162			−0.780808	−	0.624772i	$-0.785192\pi$
$29$	−8.40955			−1.56162			−0.780808	+	0.624772i	$0.785192\pi$
$30$	1.16661	+	2.81645i	0.212993	+	0.514211i
$31$	1.52502	+	3.68173i	0.273902	+	0.661259i	0.999643	−	0.0267094i	$-0.00850289\pi$
$31$	1.52502	+	3.68173i	0.273902	+	0.661259i	−0.725741	+	0.687968i	$0.758503\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.414940	+	1.00175i	0.0722317	+	0.174383i
$34$	2.18723	+	0.905982i	0.375108	+	0.155375i
$35$	3.82466	−	3.82466i	0.646485	−	0.646485i
$36$	1.49633	−	1.49633i	0.249389	−	0.249389i
$37$	−4.73714	−	1.96219i	−0.778782	−	0.322582i	−0.0423578	−	0.999103i	$-0.513487\pi$
$37$	−4.73714	−	1.96219i	−0.778782	−	0.322582i	−0.736424	+	0.676521i	$0.763487\pi$
$38$	0.0238666	−	0.0576191i	0.00387167	−	0.00934705i
$39$	0.672837			0.107740
$40$	−2.29286	+	2.29286i	−0.362533	+	0.362533i
$41$	−1.79131			−0.279756			−0.139878	−	0.990169i	$-0.544671\pi$
$41$	−1.79131			−0.279756			−0.139878	+	0.990169i	$0.544671\pi$
$42$	1.44885	+	0.600134i	0.223563	+	0.0926026i
$43$	1.16247	−	1.16247i	0.177274	−	0.177274i	−0.612892	−	0.790167i	$-0.709994\pi$
$43$	1.16247	−	1.16247i	0.177274	−	0.177274i	0.790167	+	0.612892i	$0.209994\pi$
$44$	−0.815523	+	0.815523i	−0.122945	+	0.122945i
$45$	−4.85200	−	4.85200i	−0.723293	−	0.723293i
$46$	−1.17749	+	2.84271i	−0.173611	+	0.419134i
$47$	−1.57436	−	1.57436i	−0.229645	−	0.229645i	0.582900	−	0.812544i	$-0.301918\pi$
$47$	−1.57436	−	1.57436i	−0.229645	−	0.229645i	−0.812544	+	0.582900i	$0.801918\pi$
$48$	−0.868578	−	0.359777i	−0.125368	−	0.0519293i
$49$			4.21754i			0.602505i
$50$	3.89929	+	3.89929i	0.551442	+	0.551442i
$51$	2.22574			0.311665
$52$	0.273877	+	0.661198i	0.0379799	+	0.0916916i
$53$	0.844101	−	2.03784i	0.115946	−	0.279919i	−0.855244	−	0.518226i	$-0.826593\pi$
$53$	0.844101	−	2.03784i	0.115946	−	0.279919i	0.971190	+	0.238307i	$0.0765926\pi$
$54$	1.84067	−	4.44376i	0.250483	−	0.604719i
$55$	2.64441	+	2.64441i	0.356572	+	0.356572i
$56$			1.66807i			0.222905i
$57$		−	0.0586334i		−	0.00776618i
$58$	−5.94645	−	5.94645i	−0.780808	−	0.780808i
$59$	−6.62374	+	2.74364i	−0.862338	+	0.357192i	−0.769621	−	0.638500i	$-0.779555\pi$
$59$	−6.62374	+	2.74364i	−0.862338	+	0.357192i	−0.0927166	+	0.995693i	$0.529555\pi$
$60$	−1.16661	+	2.81645i	−0.150609	+	0.363602i
$61$	0.796763	+	1.92356i	0.102015	+	0.246286i	0.966643	−	0.256126i	$-0.0824461\pi$
$61$	0.796763	+	1.92356i	0.102015	+	0.246286i	−0.864628	+	0.502412i	$0.832446\pi$
$62$	−1.52502	+	3.68173i	−0.193678	+	0.467580i
$63$	−3.52986			−0.444720
$64$		−	1.00000i		−	0.125000i
$65$	2.14400	−	0.888072i	0.265930	−	0.110152i
$66$	−0.414940	+	1.00175i	−0.0510755	+	0.123307i
$67$	−1.55204	+	3.74696i	−0.189612	+	0.457763i	−0.989885	−	0.141872i	$-0.954688\pi$
$67$	−1.55204	+	3.74696i	−0.189612	+	0.457763i	0.800273	+	0.599636i	$0.204688\pi$
$68$	0.905982	+	2.18723i	0.109866	+	0.265241i
$69$			2.89275i			0.348246i
$70$	5.40888			0.646485
$71$	1.90037	−	4.58789i	0.225532	−	0.544482i	−0.770092	−	0.637933i	$-0.779790\pi$
$71$	1.90037	−	4.58789i	0.225532	−	0.544482i	0.995624	+	0.0934505i	$0.0297897\pi$
$72$	2.11613			0.249389
$73$	−8.96959	+	8.96959i	−1.04981	+	1.04981i	−0.0511189	+	0.998693i	$0.516279\pi$
$73$	−8.96959	+	8.96959i	−1.04981	+	1.04981i	−0.998693	+	0.0511189i	$0.983721\pi$
$74$	−1.96219	−	4.73714i	−0.228100	−	0.550682i
$75$	4.78971	+	1.98396i	0.553068	+	0.229088i
$76$	0.0576191	−	0.0238666i	0.00660936	−	0.00273769i
$77$	1.92383			0.219240
$78$	0.475767	+	0.475767i	0.0538700	+	0.0538700i
$79$	2.66608	+	6.43648i	0.299957	+	0.724161i	0.999950	+	0.0100107i	$0.00318657\pi$
$79$	2.66608	+	6.43648i	0.299957	+	0.724161i	−0.699993	+	0.714150i	$0.746813\pi$
$80$	−3.24260			−0.362533
$81$			1.82641i			0.202935i
$82$	−1.26665	−	1.26665i	−0.139878	−	0.139878i
$83$	6.20305			0.680873			0.340437	−	0.940267i	$-0.389425\pi$
$83$	6.20305			0.680873			0.340437	+	0.940267i	$0.389425\pi$
$84$	0.600134	+	1.44885i	0.0654799	+	0.158083i
$85$	7.09232	−	2.93773i	0.769270	−	0.318642i
$86$	1.64398			0.177274
$87$	−7.30436	−	3.02556i	−0.783109	−	0.324375i
$88$	−1.15332			−0.122945
$89$	−0.190326	+	0.190326i	−0.0201746	+	0.0201746i	−0.717122	−	0.696948i	$-0.754541\pi$
$89$	−0.190326	+	0.190326i	−0.0201746	+	0.0201746i	0.696948	+	0.717122i	$0.254541\pi$
$90$		−	6.86176i		−	0.723293i
$91$	0.456846	−	1.10292i	0.0478905	−	0.115618i
$92$	−2.84271	+	1.17749i	−0.296373	+	0.122762i
$93$			3.74654i			0.388498i
$94$		−	2.22649i		−	0.229645i
$95$	−0.0773897	−	0.186835i	−0.00794002	−	0.0191689i
$96$	−0.359777	−	0.868578i	−0.0367196	−	0.0886489i
$97$	−2.98750	−	7.21245i	−0.303334	−	0.732314i	−0.999890	−	0.0148113i	$-0.995285\pi$
$97$	−2.98750	−	7.21245i	−0.303334	−	0.732314i	0.696556	−	0.717502i	$-0.254715\pi$
$98$	−2.98225	+	2.98225i	−0.301253	+	0.301253i
$99$		−	2.44059i		−	0.245288i
$100$			5.51442i			0.551442i
$101$	−2.63582	+	6.36343i	−0.262274	+	0.633185i	−0.999078	−	0.0429206i	$-0.986334\pi$
$101$	−2.63582	+	6.36343i	−0.262274	+	0.633185i	0.736805	+	0.676106i	$0.236334\pi$
$102$	1.57383	+	1.57383i	0.155833	+	0.155833i
$103$	6.25359	−	6.25359i	0.616184	−	0.616184i	−0.328366	−	0.944551i	$-0.606498\pi$
$103$	6.25359	−	6.25359i	0.616184	−	0.616184i	0.944551	+	0.328366i	$0.106498\pi$
$104$	−0.273877	+	0.661198i	−0.0268558	+	0.0648358i
$105$	4.69804	−	1.94599i	0.458481	−	0.189909i
$106$	2.03784	−	0.844101i	0.197932	−	0.0819863i
$107$	7.29308	−	3.02089i	0.705049	−	0.292041i	−0.00120526	−	0.999999i	$-0.500384\pi$
$107$	7.29308	−	3.02089i	0.705049	−	0.292041i	0.706254	+	0.707959i	$0.250384\pi$
$108$	4.44376	−	1.84067i	0.427601	−	0.177118i
$109$	−3.09913	−	3.09913i	−0.296843	−	0.296843i	0.542933	−	0.839776i	$-0.317314\pi$
$109$	−3.09913	−	3.09913i	−0.296843	−	0.296843i	−0.839776	+	0.542933i	$0.817314\pi$
$110$			3.73976i			0.356572i
$111$	−3.40863	−	3.40863i	−0.323533	−	0.323533i
$112$	−1.17950	+	1.17950i	−0.111453	+	0.111453i
$113$			2.23311i			0.210074i	0.994468	+	0.105037i	$0.0334961\pi$
$113$			2.23311i			0.210074i	−0.994468	+	0.105037i	$0.966504\pi$
$114$	0.0414600	−	0.0414600i	0.00388309	−	0.00388309i
$115$	3.81811	+	9.21774i	0.356041	+	0.859559i
$116$		−	8.40955i		−	0.780808i
$117$	−1.39918	−	0.579560i	−0.129354	−	0.0535803i
$118$	−6.62374	−	2.74364i	−0.609765	−	0.252573i
$119$	1.51124	−	3.64846i	0.138535	−	0.334454i
$120$	−2.81645	+	1.16661i	−0.257105	+	0.106497i
$121$		−	9.66984i		−	0.879077i
$122$	−0.796763	+	1.92356i	−0.0721356	+	0.174151i
$123$	−1.55589	−	0.644472i	−0.140290	−	0.0581101i
$124$	−3.68173	+	1.52502i	−0.330629	+	0.136951i
$125$	1.66806			0.149196
$126$	−2.49599	−	2.49599i	−0.222360	−	0.222360i
$127$	−6.13011	−	14.7994i	−0.543959	−	1.31323i	−0.921909	−	0.387407i	$-0.873371\pi$
$127$	−6.13011	−	14.7994i	−0.543959	−	1.31323i	0.377950	−	0.925826i	$-0.376629\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.42792	−	0.591465i	0.125722	−	0.0520756i
$130$	2.14400	+	0.888072i	0.188041	+	0.0778891i
$131$	−1.29559	+	3.12783i	−0.113196	+	0.273280i	−0.970317	−	0.241835i	$-0.922251\pi$
$131$	−1.29559	+	3.12783i	−0.113196	+	0.273280i	0.857121	+	0.515115i	$0.172251\pi$
$132$	−1.00175	+	0.414940i	−0.0871914	+	0.0361158i
$133$	−0.0961127	−	0.0398112i	−0.00833403	−	0.00345207i
$134$	−3.74696	+	1.55204i	−0.323688	+	0.134076i
$135$	−5.96854	−	14.4093i	−0.513690	−	1.24016i
$136$	−0.905982	+	2.18723i	−0.0776873	+	0.187554i
$137$	−17.2868	−	7.16043i	−1.47691	−	0.611756i	−0.508488	−	0.861069i	$-0.669795\pi$
$137$	−17.2868	−	7.16043i	−1.47691	−	0.611756i	−0.968423	+	0.249313i	$0.919795\pi$
$138$	−2.04548	+	2.04548i	−0.174123	+	0.174123i
$139$	6.40870	−	2.65457i	0.543579	−	0.225158i	−0.0939599	−	0.995576i	$-0.529953\pi$
$139$	6.40870	−	2.65457i	0.543579	−	0.225158i	0.637539	+	0.770418i	$0.279953\pi$
$140$	3.82466	+	3.82466i	0.323242	+	0.323242i
$141$	−0.801039	−	1.93388i	−0.0674596	−	0.162862i
$142$	4.58789	−	1.90037i	0.385007	−	0.159475i
$143$	0.762575	+	0.315869i	0.0637697	+	0.0264143i
$144$	1.49633	+	1.49633i	0.124694	+	0.124694i
$145$	−27.2688			−2.26455
$146$	−12.6849			−1.04981
$147$	−1.51737	+	3.66326i	−0.125151	+	0.302141i
$148$	1.96219	−	4.73714i	0.161291	−	0.389391i
$149$		−	16.2027i		−	1.32738i	−0.748009	−	0.663689i	$-0.768990\pi$
$149$		−	16.2027i		−	1.32738i	0.748009	−	0.663689i	$-0.231010\pi$
$150$	1.98396	+	4.78971i	0.161990	+	0.391078i
$151$	0.644506	+	0.644506i	0.0524491	+	0.0524491i	0.732845	−	0.680396i	$-0.238192\pi$
$151$	0.644506	+	0.644506i	0.0524491	+	0.0524491i	−0.680396	+	0.732845i	$0.738192\pi$
$152$	0.0576191	+	0.0238666i	0.00467353	+	0.00193584i
$153$	−4.62848	−	1.91718i	−0.374190	−	0.154995i
$154$	1.36035	+	1.36035i	0.109620	+	0.109620i
$155$	4.94503	+	11.9384i	0.397195	+	0.958913i
$156$			0.672837i			0.0538700i
$157$	−9.95684	+	4.12426i	−0.794642	+	0.329152i	−0.742808	−	0.669504i	$-0.766507\pi$
$157$	−9.95684	+	4.12426i	−0.794642	+	0.329152i	−0.0518338	+	0.998656i	$0.516507\pi$
$158$	−2.66608	+	6.43648i	−0.212102	+	0.512059i
$159$	1.46634	−	1.46634i	0.116288	−	0.116288i
$160$	−2.29286	−	2.29286i	−0.181267	−	0.181267i
$161$	4.74184	+	1.96413i	0.373709	+	0.154795i
$162$	−1.29147	+	1.29147i	−0.101467	+	0.101467i
$163$	14.5447	−	6.02461i	1.13923	−	0.471884i	0.268320	−	0.963330i	$-0.413531\pi$
$163$	14.5447	−	6.02461i	1.13923	−	0.471884i	0.870908	+	0.491446i	$0.163531\pi$
$164$		−	1.79131i		−	0.139878i
$165$	1.34548	+	3.24828i	0.104746	+	0.252878i
$166$	4.38622	+	4.38622i	0.340437	+	0.340437i
$167$	0.764981	+	1.84683i	0.0591960	+	0.142912i	0.950710	−	0.310081i	$-0.100356\pi$
$167$	0.764981	+	1.84683i	0.0591960	+	0.142912i	−0.891514	+	0.452993i	$0.850356\pi$
$168$	−0.600134	+	1.44885i	−0.0463013	+	0.111781i
$169$	−8.83021	+	8.83021i	−0.679247	+	0.679247i
$170$	7.09232	+	2.93773i	0.543956	+	0.225314i
$171$	−0.0505049	+	0.121930i	−0.00386221	+	0.00932419i
$172$	1.16247	+	1.16247i	0.0886372	+	0.0886372i
$173$	2.85586			0.217127			0.108564	−	0.994089i	$-0.465375\pi$
$173$	2.85586			0.217127			0.108564	+	0.994089i	$0.465375\pi$
$174$	−3.02556	−	7.30436i	−0.229367	−	0.553742i
$175$	6.50429	−	6.50429i	0.491678	−	0.491678i
$176$	−0.815523	−	0.815523i	−0.0614724	−	0.0614724i
$177$	−6.74034			−0.506635
$178$	−0.269162			−0.0201746
$179$		−	1.99976i		−	0.149469i	−0.997203	−	0.0747346i	$-0.976189\pi$
$179$		−	1.99976i		−	0.149469i	0.997203	−	0.0747346i	$-0.0238110\pi$
$180$	4.85200	−	4.85200i	0.361646	−	0.361646i
$181$	12.5908	−	12.5908i	0.935864	−	0.935864i	−0.0621998	−	0.998064i	$-0.519812\pi$
$181$	12.5908	−	12.5908i	0.935864	−	0.935864i	0.998064	+	0.0621998i	$0.0198116\pi$
$182$	1.10292	−	0.456846i	0.0817542	−	0.0338637i
$183$			1.95742i			0.144696i
$184$	−2.84271	−	1.17749i	−0.209567	−	0.0868055i
$185$	−15.3606	−	6.36258i	−1.12934	−	0.467786i
$186$	−2.64921	+	2.64921i	−0.194249	+	0.194249i
$187$	2.52259	+	1.04489i	0.184470	+	0.0764100i
$188$	1.57436	−	1.57436i	0.114822	−	0.114822i
$189$	−7.41251	−	3.07036i	−0.539181	−	0.223336i
$190$	0.0773897	−	0.186835i	0.00561444	−	0.0135545i
$191$	−11.5037	−	4.76499i	−0.832379	−	0.344783i	−0.0745351	−	0.997218i	$-0.523747\pi$
$191$	−11.5037	−	4.76499i	−0.832379	−	0.344783i	−0.757844	+	0.652436i	$0.773747\pi$
$192$	0.359777	−	0.868578i	0.0259647	−	0.0626842i
$193$	18.9644	−	7.85533i	1.36509	−	0.565439i	0.424637	−	0.905364i	$-0.360402\pi$
$193$	18.9644	−	7.85533i	1.36509	−	0.565439i	0.940453	+	0.339925i	$0.110402\pi$
$194$	2.98750	−	7.21245i	0.214490	−	0.517824i
$195$	2.18174			0.156237
$196$	−4.21754			−0.301253
$197$		−	0.359876i		−	0.0256401i	−0.999918	−	0.0128200i	$-0.995919\pi$
$197$		−	0.359876i		−	0.0256401i	0.999918	−	0.0128200i	$-0.00408086\pi$
$198$	1.72576	−	1.72576i	0.122644	−	0.122644i
$199$	8.72368	−	3.61347i	0.618405	−	0.256152i	−0.0514123	−	0.998678i	$-0.516372\pi$
$199$	8.72368	−	3.61347i	0.618405	−	0.256152i	0.669818	+	0.742526i	$0.266372\pi$
$200$	−3.89929	+	3.89929i	−0.275721	+	0.275721i
$201$	−2.69614	+	2.69614i	−0.190171	+	0.190171i
$202$	−6.36343	+	2.63582i	−0.447730	+	0.185456i
$203$	−9.91911	+	9.91911i	−0.696185	+	0.696185i
$204$			2.22574i			0.155833i
$205$	−5.80849			−0.405683
$206$	8.84391			0.616184
$207$	2.49172	−	6.01554i	0.173186	−	0.418109i
$208$	−0.661198	+	0.273877i	−0.0458458	+	0.0189900i
$209$	0.0275259	−	0.0664535i	0.00190401	−	0.00459668i
$210$	4.69804	+	1.94599i	0.324195	+	0.134286i
$211$	−3.15923	+	7.62705i	−0.217490	+	0.525068i	−0.994538	−	0.104374i	$-0.966716\pi$
$211$	−3.15923	+	7.62705i	−0.217490	+	0.525068i	0.777048	+	0.629441i	$0.216716\pi$
$212$	2.03784	+	0.844101i	0.139959	+	0.0579731i
$213$	3.30123	−	3.30123i	0.226197	−	0.226197i
$214$	7.29308	+	3.02089i	0.498545	+	0.206504i
$215$	3.76941	−	3.76941i	0.257071	−	0.257071i
$216$	4.44376	+	1.84067i	0.302360	+	0.125241i
$217$	6.14139	+	2.54385i	0.416905	+	0.172688i
$218$		−	4.38283i		−	0.296843i
$219$	−11.0178	+	4.56374i	−0.744517	+	0.308389i
$220$	−2.64441	+	2.64441i	−0.178286	+	0.178286i
$221$	1.19807	−	1.19807i	0.0805907	−	0.0805907i
$222$		−	4.82053i		−	0.323533i
$223$	4.63906			0.310654			0.155327	−	0.987863i	$-0.450357\pi$
$223$	4.63906			0.310654			0.155327	+	0.987863i	$0.450357\pi$
$224$	−1.66807			−0.111453
$225$	−8.25140	−	8.25140i	−0.550094	−	0.550094i
$226$	−1.57905	+	1.57905i	−0.105037	+	0.105037i
$227$	2.40962	+	5.81734i	0.159932	+	0.386110i	0.983450	−	0.181180i	$-0.0579917\pi$
$227$	2.40962	+	5.81734i	0.159932	+	0.386110i	−0.823518	+	0.567290i	$0.807992\pi$
$228$	0.0586334			0.00388309
$229$	10.4575	+	10.4575i	0.691049	+	0.691049i	0.962463	−	0.271414i	$-0.0874912\pi$
$229$	10.4575	+	10.4575i	0.691049	+	0.691049i	−0.271414	+	0.962463i	$0.587491\pi$
$230$	−3.81811	+	9.21774i	−0.251759	+	0.607800i
$231$	1.67099	+	0.692149i	0.109943	+	0.0455400i
$232$	5.94645	−	5.94645i	0.390404	−	0.390404i
$233$	1.70068	−	4.10579i	0.111415	−	0.268980i	−0.858331	−	0.513097i	$-0.828498\pi$
$233$	1.70068	−	4.10579i	0.111415	−	0.268980i	0.969746	+	0.244117i	$0.0784982\pi$
$234$	−0.579560	−	1.39918i	−0.0378870	−	0.0914673i
$235$	−5.10502	−	5.10502i	−0.333015	−	0.333015i
$236$	−2.74364	−	6.62374i	−0.178596	−	0.431169i
$237$			6.54978i			0.425454i
$238$	3.64846	−	1.51124i	0.236495	−	0.0979593i
$239$	−2.49223	+	2.49223i	−0.161209	+	0.161209i	−0.783102	−	0.621893i	$-0.786364\pi$
$239$	−2.49223	+	2.49223i	−0.161209	+	0.161209i	0.621893	+	0.783102i	$0.286364\pi$
$240$	−2.81645	−	1.16661i	−0.181801	−	0.0753044i
$241$	−0.359431	−	0.359431i	−0.0231530	−	0.0231530i	0.695436	−	0.718589i	$-0.255211\pi$
$241$	−0.359431	−	0.359431i	−0.0231530	−	0.0231530i	−0.718589	+	0.695436i	$0.755211\pi$
$242$	6.83761	−	6.83761i	0.439538	−	0.439538i
$243$	−6.17910	+	14.9177i	−0.396389	+	0.956969i
$244$	−1.92356	+	0.796763i	−0.123143	+	0.0510075i
$245$			13.6758i			0.873713i
$246$	−0.644472	−	1.55589i	−0.0410900	−	0.0992002i
$247$	−0.0315611	−	0.0315611i	−0.00200818	−	0.00200818i
$248$	−3.68173	−	1.52502i	−0.233790	−	0.0968391i
$249$	5.38784	+	2.23172i	0.341440	+	0.141429i
$250$	1.17950	+	1.17950i	0.0745981	+	0.0745981i
$251$	5.24505	+	12.6627i	0.331064	+	0.799260i	0.998508	+	0.0546001i	$0.0173884\pi$
$251$	5.24505	+	12.6627i	0.331064	+	0.799260i	−0.667444	+	0.744660i	$0.732612\pi$
$252$		−	3.52986i		−	0.222360i
$253$	−1.35802	+	3.27856i	−0.0853783	+	0.206121i
$254$	6.13011	−	14.7994i	0.384637	−	0.928596i
$255$	7.21716			0.451956
$256$	1.00000			0.0625000
$257$	1.09545	+	1.09545i	0.0683326	+	0.0683326i	0.740447	−	0.672115i	$-0.234614\pi$
$257$	1.09545	+	1.09545i	0.0683326	+	0.0683326i	−0.672115	+	0.740447i	$0.734614\pi$
$258$	1.42792	+	0.591465i	0.0888985	+	0.0368230i
$259$	−7.90189	+	3.27307i	−0.491000	+	0.203379i
$260$	0.888072	+	2.14400i	0.0550759	+	0.132965i
$261$	12.5835	+	12.5835i	0.778898	+	0.778898i
$262$	−3.12783	+	1.29559i	−0.193238	+	0.0800417i
$263$	9.84101	−	9.84101i	0.606822	−	0.606822i	−0.335292	−	0.942114i	$-0.608835\pi$
$263$	9.84101	−	9.84101i	0.606822	−	0.606822i	0.942114	+	0.335292i	$0.108835\pi$
$264$	−1.00175	−	0.414940i	−0.0616536	−	0.0255378i
$265$	2.73708	−	6.60789i	0.168137	−	0.405919i
$266$	−0.0398112	−	0.0961127i	−0.00244098	−	0.00589305i
$267$	−0.233789	+	0.0968384i	−0.0143076	+	0.00592641i
$268$	−3.74696	−	1.55204i	−0.228882	−	0.0948059i
$269$	2.21333	−	0.916790i	0.134949	−	0.0558977i	−0.314187	−	0.949361i	$-0.601732\pi$
$269$	2.21333	−	0.916790i	0.134949	−	0.0558977i	0.449136	+	0.893463i	$0.351732\pi$
$270$	5.96854	−	14.4093i	0.363234	−	0.876923i
$271$	−2.60909	−	1.08072i	−0.158491	−	0.0656492i	0.302027	−	0.953299i	$-0.402337\pi$
$271$	−2.60909	−	1.08072i	−0.158491	−	0.0656492i	−0.460519	+	0.887650i	$0.652337\pi$
$272$	−2.18723	+	0.905982i	−0.132621	+	0.0549332i
$273$	0.793614	−	0.793614i	0.0480317	−	0.0480317i
$274$	−7.16043	−	17.2868i	−0.432577	−	1.04433i
$275$	4.49714	+	4.49714i	0.271188	+	0.271188i
$276$	−2.89275			−0.174123
$277$	15.3047	−	6.33943i	0.919573	−	0.380899i	0.127859	−	0.991792i	$-0.459189\pi$
$277$	15.3047	−	6.33943i	0.919573	−	0.380899i	0.791713	+	0.610893i	$0.209189\pi$
$278$	6.40870	+	2.65457i	0.384368	+	0.159211i
$279$	3.22715	−	7.79103i	0.193204	−	0.466437i
$280$			5.40888i			0.323242i
$281$	−5.51019	+	2.28239i	−0.328710	+	0.136156i	−0.540934	−	0.841065i	$-0.681929\pi$
$281$	−5.51019	+	2.28239i	−0.328710	+	0.136156i	0.212224	+	0.977221i	$0.431929\pi$
$282$	0.801039	−	1.93388i	0.0477011	−	0.115161i
$283$	−6.86164	−	2.84219i	−0.407882	−	0.168950i	0.169302	−	0.985564i	$-0.445849\pi$
$283$	−6.86164	−	2.84219i	−0.407882	−	0.168950i	−0.577184	+	0.816614i	$0.695849\pi$
$284$	4.58789	+	1.90037i	0.272241	+	0.112766i
$285$		−	0.190124i		−	0.0112620i
$286$	0.315869	+	0.762575i	0.0186777	+	0.0450920i
$287$	−2.11286	+	2.11286i	−0.124718	+	0.124718i
$288$			2.11613i			0.124694i
$289$	−8.05762	+	8.05762i	−0.473978	+	0.473978i
$290$	−19.2819	−	19.2819i	−1.13227	−	1.13227i
$291$		−	7.33941i		−	0.430244i
$292$	−8.96959	−	8.96959i	−0.524906	−	0.524906i
$293$	−8.78260	+	3.63787i	−0.513085	+	0.212527i	−0.624176	−	0.781283i	$-0.714565\pi$
$293$	−8.78260	+	3.63787i	−0.513085	+	0.212527i	0.111091	+	0.993810i	$0.464565\pi$
$294$	−3.66326	+	1.51737i	−0.213646	+	0.0884950i
$295$	−21.4781	+	8.89653i	−1.25050	+	0.517976i
$296$	4.73714	−	1.96219i	0.275341	−	0.114050i
$297$	2.12289	−	5.12510i	0.123182	−	0.297388i
$298$	11.4570	−	11.4570i	0.663689	−	0.663689i
$299$	1.55710	+	1.55710i	0.0900496	+	0.0900496i
$300$	−1.98396	+	4.78971i	−0.114544	+	0.276534i
$301$		−	2.74227i		−	0.158062i
$302$			0.911469i			0.0524491i
$303$	−4.57883	+	4.57883i	−0.263047	+	0.263047i
$304$	0.0238666	+	0.0576191i	0.00136884	+	0.00330468i
$305$	2.58358	+	6.23732i	0.147935	+	0.357148i
$306$	−1.91718	−	4.62848i	−0.109598	−	0.264592i
$307$		−	13.4692i		−	0.768729i	−0.923181	−	0.384364i	$-0.874421\pi$
$307$		−	13.4692i		−	0.768729i	0.923181	−	0.384364i	$-0.125579\pi$
$308$			1.92383i			0.109620i
$309$	7.68163	−	3.18184i	0.436993	−	0.181008i
$310$	−4.94503	+	11.9384i	−0.280859	+	0.678054i
$311$			30.3856i			1.72301i	0.507748	+	0.861506i	$0.330478\pi$
$311$			30.3856i			1.72301i	−0.507748	+	0.861506i	$0.669522\pi$
$312$	−0.475767	+	0.475767i	−0.0269350	+	0.0269350i
$313$	−33.5632			−1.89711			−0.948553	−	0.316617i	$-0.897453\pi$
$313$	−33.5632			−1.89711			−0.948553	+	0.316617i	$0.897453\pi$
$314$	−9.95684	−	4.12426i	−0.561897	−	0.232745i
$315$	−11.4459			−0.644904
$316$	−6.43648	+	2.66608i	−0.362080	+	0.149979i
$317$	4.33197	+	10.4583i	0.243308	+	0.587397i	0.997607	−	0.0691332i	$-0.0220234\pi$
$317$	4.33197	+	10.4583i	0.243308	+	0.587397i	−0.754300	+	0.656530i	$0.772023\pi$
$318$	2.07371			0.116288
$319$	−6.85819	−	6.85819i	−0.383985	−	0.383985i
$320$		−	3.24260i		−	0.181267i
$321$	7.42146			0.414226
$322$	1.96413	+	4.74184i	0.109457	+	0.264252i
$323$	−0.104404	−	0.104404i	−0.00580918	−	0.00580918i
$324$	−1.82641			−0.101467
$325$	3.64612	−	1.51027i	0.202250	−	0.0837749i
$326$	14.5447	+	6.02461i	0.805556	+	0.333672i
$327$	−1.57684	−	3.80683i	−0.0871995	−	0.210518i
$328$	1.26665	−	1.26665i	0.0699389	−	0.0699389i
$329$	−3.71394			−0.204756
$330$	−1.34548	+	3.24828i	−0.0740663	+	0.178812i
$331$	27.3962			1.50583			0.752914	−	0.658118i	$-0.228647\pi$
$331$	27.3962			1.50583			0.752914	+	0.658118i	$0.228647\pi$
$332$			6.20305i			0.340437i
$333$	4.15225	+	10.0244i	0.227542	+	0.549335i
$334$	−0.764981	+	1.84683i	−0.0418579	+	0.101054i
$335$	−5.03264	+	12.1499i	−0.274962	+	0.663818i
$336$	−1.44885	+	0.600134i	−0.0790413	+	0.0327400i
$337$		−	3.61372i		−	0.196852i	−0.995144	−	0.0984258i	$-0.968619\pi$
$337$		−	3.61372i		−	0.196852i	0.995144	−	0.0984258i	$-0.0313807\pi$
$338$	−12.4878			−0.679247
$339$	−0.803423	+	1.93963i	−0.0436359	+	0.105347i
$340$	2.93773	+	7.09232i	0.159321	+	0.384635i
$341$	−1.75885	+	4.24623i	−0.0952469	+	0.229946i
$342$	−0.121930	+	0.0505049i	−0.00659320	+	0.00273099i
$343$	13.2311	+	13.2311i	0.714414	+	0.714414i
$344$			1.64398i			0.0886372i
$345$			9.38000i			0.505002i
$346$	2.01940	+	2.01940i	0.108564	+	0.108564i
$347$	1.18296	−	2.85592i	0.0635046	−	0.153314i	−0.888942	−	0.458021i	$-0.848559\pi$
$347$	1.18296	−	2.85592i	0.0635046	−	0.153314i	0.952446	+	0.304707i	$0.0985586\pi$
$348$	3.02556	−	7.30436i	0.162187	−	0.391555i
$349$	−8.83087	−	21.3196i	−0.472706	−	1.14121i	−0.962963	−	0.269635i	$-0.913097\pi$
$349$	−8.83087	−	21.3196i	−0.472706	−	1.14121i	0.490257	−	0.871578i	$-0.336903\pi$
$350$	9.19845			0.491678
$351$	−2.43409	−	2.43409i	−0.129922	−	0.129922i
$352$		−	1.15332i		−	0.0614724i
$353$	7.64254	+	3.16564i	0.406771	+	0.168490i	0.576681	−	0.816969i	$-0.304348\pi$
$353$	7.64254	+	3.16564i	0.406771	+	0.168490i	−0.169910	+	0.985460i	$0.554348\pi$
$354$	−4.76614	−	4.76614i	−0.253318	−	0.253318i
$355$	6.16212	−	14.8767i	0.327051	−	0.789572i
$356$	−0.190326	−	0.190326i	−0.0100873	−	0.0100873i
$357$	2.62527	−	2.62527i	0.138944	−	0.138944i
$358$	1.41404	−	1.41404i	0.0747346	−	0.0747346i
$359$	8.78693	+	3.63966i	0.463756	+	0.192094i	0.602312	−	0.798260i	$-0.294246\pi$
$359$	8.78693	+	3.63966i	0.463756	+	0.192094i	−0.138556	+	0.990355i	$0.544246\pi$
$360$	6.86176			0.361646
$361$	13.4323	−	13.4323i	0.706962	−	0.706962i
$362$	17.8060			0.935864
$363$	3.47899	−	8.39902i	0.182599	−	0.440834i
$364$	1.10292	+	0.456846i	0.0578090	+	0.0239453i
$365$	−29.0848	+	29.0848i	−1.52237	+	1.52237i
$366$	−1.38410	+	1.38410i	−0.0723482	+	0.0723482i
$367$	15.0135	+	6.21878i	0.783697	+	0.324618i	0.738406	−	0.674356i	$-0.235579\pi$
$367$	15.0135	+	6.21878i	0.783697	+	0.324618i	0.0452905	+	0.998974i	$0.485579\pi$
$368$	−1.17749	−	2.84271i	−0.0613808	−	0.148186i
$369$	2.68039	+	2.68039i	0.139536	+	0.139536i
$370$	−6.36258	−	15.3606i	−0.330775	−	0.798561i
$371$	−1.40802	−	3.39926i	−0.0731008	−	0.176481i
$372$	−3.74654			−0.194249
$373$	−10.6914	−	10.6914i	−0.553578	−	0.553578i	0.373894	−	0.927471i	$-0.378022\pi$
$373$	−10.6914	−	10.6914i	−0.553578	−	0.553578i	−0.927471	+	0.373894i	$0.878022\pi$
$374$	1.04489	+	2.52259i	0.0540300	+	0.130440i
$375$	1.44884	+	0.600131i	0.0748180	+	0.0309906i
$376$	2.22649			0.114822
$377$	−5.56038	+	2.30318i	−0.286374	+	0.118620i
$378$	−3.07036	−	7.41251i	−0.157922	−	0.381258i
$379$		−	30.4044i		−	1.56177i	−0.624675	−	0.780885i	$-0.714769\pi$
$379$		−	30.4044i		−	1.56177i	0.624675	−	0.780885i	$-0.285231\pi$
$380$	0.186835	−	0.0773897i	0.00958445	−	0.00397001i
$381$		−	15.0599i		−	0.771542i
$382$	−4.76499	−	11.5037i	−0.243798	−	0.588581i
$383$			34.7155i			1.77388i	0.461884	+	0.886940i	$0.347174\pi$
$383$			34.7155i			1.77388i	−0.461884	+	0.886940i	$0.652826\pi$
$384$	0.868578	−	0.359777i	0.0443245	−	0.0183598i
$385$	6.23819			0.317928
$386$	18.9644	+	7.85533i	0.965264	+	0.399826i
$387$	−3.47887			−0.176841
$388$	7.21245	−	2.98750i	0.366157	−	0.151667i
$389$	−8.06599	+	19.4730i	−0.408962	+	0.987321i	0.576450	+	0.817133i	$0.304438\pi$
$389$	−8.06599	+	19.4730i	−0.408962	+	0.987321i	−0.985412	+	0.170188i	$0.945562\pi$
$390$	1.54272	+	1.54272i	0.0781187	+	0.0781187i
$391$	5.15088	+	5.15088i	0.260491	+	0.260491i
$392$	−2.98225	−	2.98225i	−0.150626	−	0.150626i
$393$	−2.25064	+	2.25064i	−0.113530	+	0.113530i
$394$	0.254471	−	0.254471i	0.0128200	−	0.0128200i
$395$	8.64501	+	20.8709i	0.434978	+	1.05013i
$396$	2.44059			0.122644
$397$			25.8171i			1.29572i	0.761759	+	0.647860i	$0.224336\pi$
$397$			25.8171i			1.29572i	−0.761759	+	0.647860i	$0.775664\pi$
$398$	8.72368	+	3.61347i	0.437279	+	0.181127i
$399$	−0.0691583	−	0.0691583i	−0.00346225	−	0.00346225i
$400$	−5.51442			−0.275721
$401$	−6.36245	+	18.9873i	−0.317726	+	0.948183i
$401$	−6.36245	+	18.9873i	−0.317726	+	0.948183i
$402$	−3.81291			−0.190171
$403$	2.01668	+	2.01668i	0.100458	+	0.100458i
$404$	−6.36343	−	2.63582i	−0.316593	−	0.131137i
$405$			5.92231i			0.294282i
$406$	−14.0277			−0.696185
$407$	−2.26304	−	5.46346i	−0.112175	−	0.270814i
$408$	−1.57383	+	1.57383i	−0.0779164	+	0.0779164i
$409$	22.9315	−	22.9315i	1.13389	−	1.13389i	0.144365	−	0.989524i	$-0.453886\pi$
$409$	22.9315	−	22.9315i	1.13389	−	1.13389i	0.989524	−	0.144365i	$-0.0461141\pi$
$410$	−4.10723	−	4.10723i	−0.202841	−	0.202841i
$411$	−12.4388	−	12.4388i	−0.613560	−	0.613560i
$412$	6.25359	+	6.25359i	0.308092	+	0.308092i
$413$	−4.57660	+	11.0489i	−0.225200	+	0.543680i
$414$	6.01554	−	2.49172i	0.295648	−	0.122461i
$415$	20.1140			0.987357
$416$	−0.661198	−	0.273877i	−0.0324179	−	0.0134279i
$417$	6.52151			0.319360
$418$	0.0664535	−	0.0275259i	0.00325035	−	0.00134634i
$419$			21.5229i			1.05146i	0.850650	+	0.525732i	$0.176208\pi$
$419$			21.5229i			1.05146i	−0.850650	+	0.525732i	$0.823792\pi$
$420$	1.94599	+	4.69804i	0.0949546	+	0.229241i
$421$			19.7294i			0.961551i	0.876844	+	0.480775i	$0.159645\pi$
$421$			19.7294i			0.961551i	−0.876844	+	0.480775i	$0.840355\pi$
$422$	−7.62705	+	3.15923i	−0.371279	+	0.153789i
$423$			4.71154i			0.229083i
$424$	0.844101	+	2.03784i	0.0409932	+	0.0989662i
$425$	12.0613	−	4.99597i	0.585061	−	0.242340i
$426$	4.66865			0.226197
$427$	3.20863	+	1.32906i	0.155276	+	0.0643176i
$428$	3.02089	+	7.29308i	0.146020	+	0.352524i
$429$	0.548714	+	0.548714i	0.0264922	+	0.0264922i
$430$	5.33075			0.257071
$431$	13.0724	+	31.5595i	0.629674	+	1.52017i	0.840029	+	0.542542i	$0.182538\pi$
$431$	13.0724	+	31.5595i	0.629674	+	1.52017i	−0.210355	+	0.977625i	$0.567462\pi$
$432$	1.84067	+	4.44376i	0.0885591	+	0.213801i
$433$	7.15230	+	7.15230i	0.343718	+	0.343718i	0.857763	−	0.514045i	$-0.171854\pi$
$433$	7.15230	+	7.15230i	0.343718	+	0.343718i	−0.514045	+	0.857763i	$0.671854\pi$
$434$	2.54385	+	6.14139i	0.122109	+	0.294796i
$435$	−23.6851	−	9.81068i	−1.13561	−	0.470386i
$436$	3.09913	−	3.09913i	0.148421	−	0.148421i
$437$	0.135691	−	0.135691i	0.00649100	−	0.00649100i
$438$	−11.0178	−	4.56374i	−0.526453	−	0.218064i
$439$	3.39448	−	8.19501i	0.162010	−	0.391126i	−0.821939	−	0.569575i	$-0.807108\pi$
$439$	3.39448	−	8.19501i	0.162010	−	0.391126i	0.983949	+	0.178449i	$0.0571078\pi$
$440$	−3.73976			−0.178286
$441$	6.31083	−	6.31083i	0.300516	−	0.300516i
$442$	1.69432			0.0805907
$443$	38.0579	+	15.7641i	1.80819	+	0.748975i	0.982869	+	0.184305i	$0.0590033\pi$
$443$	38.0579	+	15.7641i	1.80819	+	0.748975i	0.825317	+	0.564670i	$0.190997\pi$
$444$	3.40863	−	3.40863i	0.161766	−	0.161766i
$445$	−0.617152	+	0.617152i	−0.0292558	+	0.0292558i
$446$	3.28031	+	3.28031i	0.155327	+	0.155327i
$447$	5.82936	−	14.0733i	0.275719	−	0.665645i
$448$	−1.17950	−	1.17950i	−0.0557264	−	0.0557264i
$449$	−15.9849	−	6.62117i	−0.754375	−	0.312472i	−0.0278495	−	0.999612i	$-0.508866\pi$
$449$	−15.9849	−	6.62117i	−0.754375	−	0.312472i	−0.726525	+	0.687140i	$0.758866\pi$
$450$		−	11.6692i		−	0.550094i
$451$	−1.46086	−	1.46086i	−0.0687890	−	0.0687890i
$452$	−2.23311			−0.105037
$453$	0.327925	+	0.791682i	0.0154073	+	0.0371965i
$454$	−2.40962	+	5.81734i	−0.113089	+	0.273021i
$455$	1.48137	−	3.57634i	0.0694476	−	0.167661i
$456$	0.0414600	+	0.0414600i	0.00194154	+	0.00194154i
$457$			10.2407i			0.479039i	0.970892	+	0.239519i	$0.0769899\pi$
$457$			10.2407i			0.479039i	−0.970892	+	0.239519i	$0.923010\pi$
$458$			14.7891i			0.691049i
$459$	−8.05194	−	8.05194i	−0.375832	−	0.375832i
$460$	−9.21774	+	3.81811i	−0.429780	+	0.178021i
$461$	0.956416	−	2.30899i	0.0445448	−	0.107541i	−0.900041	−	0.435805i	$-0.856464\pi$
$461$	0.956416	−	2.30899i	0.0445448	−	0.107541i	0.944586	+	0.328264i	$0.106464\pi$
$462$	0.692149	+	1.67099i	0.0322017	+	0.0777417i
$463$	−0.115463	+	0.278753i	−0.00536604	+	0.0129548i	−0.926540	−	0.376197i	$-0.877232\pi$
$463$	−0.115463	+	0.278753i	−0.00536604	+	0.0129548i	0.921174	+	0.389151i	$0.127232\pi$
$464$	8.40955			0.390404
$465$			12.1485i			0.563374i
$466$	4.10579	−	1.70068i	0.190197	−	0.0787823i
$467$	−1.34936	+	3.25764i	−0.0624410	+	0.150746i	−0.952020	−	0.306035i	$-0.900998\pi$
$467$	−1.34936	+	3.25764i	−0.0624410	+	0.150746i	0.889579	+	0.456781i	$0.150998\pi$
$468$	0.579560	−	1.39918i	0.0267902	−	0.0646772i
$469$	2.58891	+	6.25019i	0.119545	+	0.288607i
$470$		−	7.21959i		−	0.333015i
$471$	−10.1321			−0.466863
$472$	2.74364	−	6.62374i	0.126286	−	0.304883i
$473$	1.89604			0.0871799
$474$	−4.63140	+	4.63140i	−0.212727	+	0.212727i
$475$	−0.131611	−	0.317736i	−0.00603871	−	0.0145787i
$476$	3.64846	+	1.51124i	0.167227	+	0.0692677i
$477$	−4.31234	+	1.78623i	−0.197448	+	0.0817858i
$478$	−3.52454			−0.161209
$479$	3.66910	+	3.66910i	0.167645	+	0.167645i	0.785944	−	0.618298i	$-0.212178\pi$
$479$	3.66910	+	3.66910i	0.167645	+	0.167645i	−0.618298	+	0.785944i	$0.712178\pi$
$480$	−1.16661	−	2.81645i	−0.0532483	−	0.128553i
$481$	−3.66959			−0.167319
$482$		−	0.508313i		−	0.0231530i
$483$	3.41201	+	3.41201i	0.155252	+	0.155252i
$484$	9.66984			0.439538
$485$	−9.68724	−	23.3871i	−0.439875	−	1.06195i
$486$	−14.9177	+	6.17910i	−0.676679	+	0.280290i
$487$	−21.7752			−0.986730			−0.493365	−	0.869822i	$-0.664233\pi$
$487$	−21.7752			−0.986730			−0.493365	+	0.869822i	$0.664233\pi$
$488$	−1.92356	−	0.796763i	−0.0870753	−	0.0360678i
$489$	14.8007			0.669312
$490$	−9.67023	+	9.67023i	−0.436856	+	0.436856i
$491$		−	1.60989i		−	0.0726535i	−0.999340	−	0.0363268i	$-0.988434\pi$
$491$		−	1.60989i		−	0.0726535i	0.999340	−	0.0363268i	$-0.0115657\pi$
$492$	0.644472	−	1.55589i	0.0290551	−	0.0701451i
$493$	−18.3937	+	7.61891i	−0.828409	+	0.343138i
$494$		−	0.0446341i		−	0.00200818i
$495$		−	7.91383i		−	0.355700i
$496$	−1.52502	−	3.68173i	−0.0684756	−	0.165315i
$497$	−3.16995	−	7.65293i	−0.142192	−	0.343281i
$498$	2.23172	+	5.38784i	0.100006	+	0.241435i
$499$	25.7626	−	25.7626i	1.15329	−	1.15329i	0.167403	−	0.985888i	$-0.446462\pi$
$499$	25.7626	−	25.7626i	1.15329	−	1.15329i	0.985888	−	0.167403i	$-0.0535382\pi$
$500$			1.66806i			0.0745981i
$501$			1.87934i			0.0839626i
$502$	−5.24505	+	12.6627i	−0.234098	+	0.565162i
$503$	21.3052	+	21.3052i	0.949950	+	0.949950i	0.998806	−	0.0488560i	$-0.0155576\pi$
$503$	21.3052	+	21.3052i	0.949950	+	0.949950i	−0.0488560	+	0.998806i	$0.515558\pi$
$504$	2.49599	−	2.49599i	0.111180	−	0.111180i
$505$	−8.54690	+	20.6340i	−0.380332	+	0.918202i
$506$	−3.27856	+	1.35802i	−0.145750	+	0.0603716i
$507$	−10.8466	+	4.49283i	−0.481716	+	0.199533i
$508$	14.7994	−	6.13011i	0.656617	−	0.271980i
$509$	−24.4366	+	10.1220i	−1.08313	+	0.448649i	−0.851608	−	0.524180i	$-0.824372\pi$
$509$	−24.4366	+	10.1220i	−1.08313	+	0.448649i	−0.231526	+	0.972829i	$0.574372\pi$
$510$	5.10330	+	5.10330i	0.225978	+	0.225978i
$511$			21.1594i			0.936035i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.212115	+	0.212115i	−0.00936511	+	0.00936511i
$514$			1.54921i			0.0683326i
$515$	20.2779	−	20.2779i	0.893549	−	0.893549i
$516$	0.591465	+	1.42792i	0.0260378	+	0.0628608i
$517$		−	2.56786i		−	0.112934i
$518$	−7.90189	−	3.27307i	−0.347189	−	0.143810i
$519$	2.48054	+	1.02747i	0.108884	+	0.0451011i
$520$	−0.888072	+	2.14400i	−0.0389445	+	0.0940204i
$521$	−22.3024	+	9.23794i	−0.977084	+	0.404722i	−0.813345	−	0.581782i	$-0.802356\pi$
$521$	−22.3024	+	9.23794i	−0.977084	+	0.404722i	−0.163739	+	0.986504i	$0.552356\pi$
$522$			17.7957i			0.778898i
$523$	12.0193	−	29.0172i	0.525568	−	1.26883i	−0.408833	−	0.912609i	$-0.634064\pi$
$523$	12.0193	−	29.0172i	0.525568	−	1.26883i	0.934401	−	0.356224i	$-0.115936\pi$
$524$	−3.12783	−	1.29559i	−0.136640	−	0.0565980i
$525$	7.98958	−	3.30939i	0.348694	−	0.144434i
$526$	13.9173			0.606822
$527$	6.67117	+	6.67117i	0.290601	+	0.290601i
$528$	−0.414940	−	1.00175i	−0.0180579	−	0.0435957i
$529$	9.56896	−	9.56896i	0.416042	−	0.416042i
$530$	6.60789	−	2.73708i	0.287028	−	0.118891i
$531$	14.0167	+	5.80591i	0.608274	+	0.251955i
$532$	0.0398112	−	0.0961127i	0.00172603	−	0.00416702i
$533$	−1.18441	+	0.490599i	−0.0513025	+	0.0212502i
$534$	−0.233789	−	0.0968384i	−0.0101170	−	0.00419061i
$535$	23.6485	−	9.79553i	1.02241	−	0.423498i
$536$	−1.55204	−	3.74696i	−0.0670379	−	0.161844i
$537$	0.719468	−	1.73695i	0.0310473	−	0.0749549i
$538$	2.21333	+	0.916790i	0.0954233	+	0.0395256i
$539$	−3.43950	+	3.43950i	−0.148150	+	0.148150i
$540$	14.4093	−	5.96854i	0.620078	−	0.256845i
$541$	−3.52225	−	3.52225i	−0.151433	−	0.151433i	0.627325	−	0.778758i	$-0.284150\pi$
$541$	−3.52225	−	3.52225i	−0.151433	−	0.151433i	−0.778758	+	0.627325i	$0.784150\pi$
$542$	−1.08072	−	2.60909i	−0.0464210	−	0.112070i
$543$	15.4659	−	6.40620i	0.663707	−	0.274916i
$544$	−2.18723	−	0.905982i	−0.0937769	−	0.0388437i
$545$	−10.0492	−	10.0492i	−0.430461	−	0.430461i
$546$	1.12234			0.0480317
$547$	−20.9728			−0.896734			−0.448367	−	0.893850i	$-0.647994\pi$
$547$	−20.9728			−0.896734			−0.448367	+	0.893850i	$0.647994\pi$
$548$	7.16043	−	17.2868i	0.305878	−	0.738455i
$549$	1.68606	−	4.07050i	0.0719591	−	0.173725i
$550$			6.35992i			0.271188i
$551$	0.200708	+	0.484551i	0.00855043	+	0.0206426i
$552$	−2.04548	−	2.04548i	−0.0870614	−	0.0870614i
$553$	10.7365	+	4.44721i	0.456563	+	0.189115i
$554$	15.3047	+	6.33943i	0.650236	+	0.269337i
$555$	−11.0528	−	11.0528i	−0.469166	−	0.469166i
$556$	2.65457	+	6.40870i	0.112579	+	0.271789i
$557$			15.5633i			0.659438i	0.944079	+	0.329719i	$0.106954\pi$
$557$			15.5633i			0.659438i	−0.944079	+	0.329719i	$0.893046\pi$
$558$	7.79103	−	3.22715i	0.329821	−	0.136616i
$559$	0.450247	−	1.08699i	0.0190434	−	0.0459749i
$560$	−3.82466	+	3.82466i	−0.161621	+	0.161621i
$561$	1.81514	+	1.81514i	0.0766353	+	0.0766353i
$562$	−5.51019	−	2.28239i	−0.232433	−	0.0962770i
$563$	−18.9856	+	18.9856i	−0.800150	+	0.800150i	−0.983119	−	0.182969i	$-0.941429\pi$
$563$	−18.9856	+	18.9856i	−0.800150	+	0.800150i	0.182969	+	0.983119i	$0.441429\pi$
$564$	1.93388	−	0.801039i	0.0814310	−	0.0337298i
$565$			7.24108i			0.304635i
$566$	−2.84219	−	6.86164i	−0.119466	−	0.288416i
$567$	2.15426	+	2.15426i	0.0904704	+	0.0904704i
$568$	1.90037	+	4.58789i	0.0797376	+	0.192504i
$569$	2.16044	−	5.21578i	0.0905706	−	0.218657i	−0.872103	−	0.489323i	$-0.837244\pi$
$569$	2.16044	−	5.21578i	0.0905706	−	0.218657i	0.962673	+	0.270666i	$0.0872440\pi$
$570$	0.134438	−	0.134438i	0.00563099	−	0.00563099i
$571$	30.1569	+	12.4914i	1.26203	+	0.522749i	0.910531	−	0.413441i	$-0.135673\pi$
$571$	30.1569	+	12.4914i	1.26203	+	0.522749i	0.351496	+	0.936189i	$0.385673\pi$
$572$	−0.315869	+	0.762575i	−0.0132071	+	0.0318849i
$573$	−8.27754	−	8.27754i	−0.345799	−	0.345799i
$574$	−2.98803			−0.124718
$575$	6.49316	+	15.6759i	0.270784	+	0.653729i
$576$	−1.49633	+	1.49633i	−0.0623471	+	0.0623471i
$577$	2.20392	+	2.20392i	0.0917502	+	0.0917502i	0.751492	−	0.659742i	$-0.229334\pi$
$577$	2.20392	+	2.20392i	0.0917502	+	0.0917502i	−0.659742	+	0.751492i	$0.729334\pi$
$578$	−11.3952			−0.473978
$579$	19.2983			0.802009
$580$		−	27.2688i		−	1.13227i
$581$	7.31653	−	7.31653i	0.303541	−	0.303541i
$582$	5.18975	−	5.18975i	0.215122	−	0.215122i
$583$	2.35029	−	0.973522i	0.0973390	−	0.0403192i
$584$		−	12.6849i		−	0.524906i
$585$	−4.53698	−	1.87928i	−0.187581	−	0.0776986i
$586$	−8.78260	−	3.63787i	−0.362806	−	0.150279i
$587$	−11.3597	+	11.3597i	−0.468864	+	0.468864i	−0.901546	−	0.432682i	$-0.857567\pi$
$587$	−11.3597	+	11.3597i	−0.468864	+	0.468864i	0.432682	+	0.901546i	$0.357567\pi$
$588$	−3.66326	−	1.51737i	−0.151070	−	0.0625754i
$589$	0.175741	−	0.175741i	0.00724128	−	0.00724128i
$590$	−21.4781	−	8.89653i	−0.884240	−	0.366264i
$591$	0.129475	−	0.312580i	0.00532589	−	0.0128578i
$592$	4.73714	+	1.96219i	0.194695	+	0.0806455i
$593$	7.23854	−	17.4754i	0.297251	−	0.717628i	−0.702730	−	0.711457i	$-0.748036\pi$
$593$	7.23854	−	17.4754i	0.297251	−	0.717628i	0.999981	−	0.00617103i	$-0.00196431\pi$
$594$	5.12510	−	2.12289i	0.210285	−	0.0871030i
$595$	4.90035	−	11.8305i	0.200895	−	0.485003i
$596$	16.2027			0.663689
$597$	8.87724			0.363321
$598$			2.20208i			0.0900496i
$599$	1.79441	−	1.79441i	0.0733176	−	0.0733176i	−0.669497	−	0.742815i	$-0.733490\pi$
$599$	1.79441	−	1.79441i	0.0733176	−	0.0733176i	0.742815	+	0.669497i	$0.233490\pi$
$600$	−4.78971	+	1.98396i	−0.195539	+	0.0809949i
$601$	−12.3197	+	12.3197i	−0.502529	+	0.502529i	−0.912223	−	0.409694i	$-0.865636\pi$
$601$	−12.3197	+	12.3197i	−0.502529	+	0.502529i	0.409694	+	0.912223i	$0.365636\pi$
$602$	1.93908	−	1.93908i	0.0790309	−	0.0790309i
$603$	7.92905	−	3.28432i	0.322896	−	0.133748i
$604$	−0.644506	+	0.644506i	−0.0262246	+	0.0262246i
$605$		−	31.3554i		−	1.27478i
$606$	−6.47545			−0.263047
$607$	−18.8549			−0.765297			−0.382649	−	0.923894i	$-0.624988\pi$
$607$	−18.8549			−0.765297			−0.382649	+	0.923894i	$0.624988\pi$
$608$	−0.0238666	+	0.0576191i	−0.000967919	+	0.00233676i
$609$	−12.1842	+	5.04686i	−0.493728	+	0.204509i
$610$	−2.58358	+	6.23732i	−0.104606	+	0.252542i
$611$	−1.47215	−	0.609783i	−0.0595567	−	0.0246692i
$612$	1.91718	−	4.62848i	0.0774973	−	0.187095i
$613$	36.7260	+	15.2124i	1.48335	+	0.614423i	0.969858	−	0.243671i	$-0.0783519\pi$
$613$	36.7260	+	15.2124i	1.48335	+	0.614423i	0.513491	+	0.858095i	$0.328352\pi$
$614$	9.52418	−	9.52418i	0.384364	−	0.384364i
$615$	−5.04513	−	2.08976i	−0.203439	−	0.0842674i
$616$	−1.36035	+	1.36035i	−0.0548101	+	0.0548101i
$617$	9.33495	+	3.86666i	0.375811	+	0.155666i	0.562590	−	0.826736i	$-0.309805\pi$
$617$	9.33495	+	3.86666i	0.375811	+	0.155666i	−0.186779	+	0.982402i	$0.559805\pi$
$618$	7.68163	+	3.18184i	0.309000	+	0.127992i
$619$		−	17.7265i		−	0.712488i	−0.934393	−	0.356244i	$-0.884057\pi$
$619$		−	17.7265i		−	0.712488i	0.934393	−	0.356244i	$-0.115943\pi$
$620$	−11.9384	+	4.94503i	−0.479456	+	0.198597i
$621$	10.4649	−	10.4649i	0.419944	−	0.419944i
$622$	−21.4859	+	21.4859i	−0.861506	+	0.861506i
$623$			0.448982i			0.0179881i
$624$	−0.672837			−0.0269350
$625$	−22.1633			−0.886530
$626$	−23.7328	−	23.7328i	−0.948553	−	0.948553i
$627$	0.0478169	−	0.0478169i	0.00190962	−	0.00190962i
$628$	−4.12426	−	9.95684i	−0.164576	−	0.397321i
$629$	−12.1390			−0.484012
$630$	−8.09348	−	8.09348i	−0.322452	−	0.322452i
$631$	−10.3991	+	25.1056i	−0.413981	+	0.999439i	0.570077	+	0.821591i	$0.306913\pi$
$631$	−10.3991	+	25.1056i	−0.413981	+	0.999439i	−0.984058	+	0.177847i	$0.943087\pi$
$632$	−6.43648	−	2.66608i	−0.256029	−	0.106051i
$633$	−5.48808	+	5.48808i	−0.218131	+	0.218131i
$634$	−4.33197	+	10.4583i	−0.172045	+	0.415353i
$635$	−19.8775	−	47.9884i	−0.788813	−	1.90436i
$636$	1.46634	+	1.46634i	0.0581440	+	0.0581440i
$637$	1.15509	+	2.78863i	0.0457662	+	0.110489i
$638$		−	9.69894i		−	0.383985i
$639$	−9.70858	+	4.02143i	−0.384066	+	0.159085i
$640$	2.29286	−	2.29286i	0.0906333	−	0.0906333i
$641$	−7.76417	−	3.21602i	−0.306666	−	0.127025i	0.224043	−	0.974579i	$-0.428074\pi$
$641$	−7.76417	−	3.21602i	−0.306666	−	0.127025i	−0.530709	+	0.847554i	$0.678074\pi$
$642$	5.24777	+	5.24777i	0.207113	+	0.207113i
$643$	14.6487	−	14.6487i	0.577689	−	0.577689i	−0.356577	−	0.934266i	$-0.616056\pi$
$643$	14.6487	−	14.6487i	0.577689	−	0.577689i	0.934266	+	0.356577i	$0.116056\pi$
$644$	−1.96413	+	4.74184i	−0.0773977	+	0.186855i
$645$	4.63017	−	1.91788i	0.182313	−	0.0755165i
$646$		−	0.147649i		−	0.00580918i
$647$	−10.0444	−	24.2493i	−0.394886	−	0.953339i	−0.988859	−	0.148854i	$-0.952441\pi$
$647$	−10.0444	−	24.2493i	−0.394886	−	0.953339i	0.593973	−	0.804485i	$-0.297559\pi$
$648$	−1.29147	−	1.29147i	−0.0507336	−	0.0507336i
$649$	−7.63932	−	3.16431i	−0.299870	−	0.124210i
$650$	3.64612	+	1.51027i	0.143013	+	0.0592378i
$651$	4.41906	+	4.41906i	0.173197	+	0.173197i
$652$	6.02461	+	14.5447i	0.235942	+	0.569614i
$653$			12.2265i			0.478461i	0.970963	+	0.239230i	$0.0768951\pi$
$653$			12.2265i			0.478461i	−0.970963	+	0.239230i	$0.923105\pi$
$654$	1.57684	−	3.80683i	0.0616594	−	0.148859i
$655$	−4.20107	+	10.1423i	−0.164149	+	0.396292i
$656$	1.79131			0.0699389
$657$	26.8430			1.04724
$658$	−2.62615	−	2.62615i	−0.102378	−	0.102378i
$659$	−6.33701	−	2.62488i	−0.246855	−	0.102251i	0.255826	−	0.966723i	$-0.417653\pi$
$659$	−6.33701	−	2.62488i	−0.246855	−	0.102251i	−0.502680	+	0.864472i	$0.667653\pi$
$660$	−3.24828	+	1.34548i	−0.126439	+	0.0523728i
$661$	−10.9510	−	26.4381i	−0.425945	−	1.02832i	−0.980561	−	0.196216i	$-0.937135\pi$
$661$	−10.9510	−	26.4381i	−0.425945	−	1.02832i	0.554616	−	0.832107i	$-0.312865\pi$
$662$	19.3720	+	19.3720i	0.752914	+	0.752914i
$663$	1.47165	−	0.609578i	0.0571542	−	0.0236740i
$664$	−4.38622	+	4.38622i	−0.170218	+	0.170218i
$665$	−0.311655	−	0.129092i	−0.0120855	−	0.00500596i
$666$	−4.15225	+	10.0244i	−0.160896	+	0.388438i
$667$	−9.90214	−	23.9059i	−0.383413	−	0.925640i
$668$	−1.84683	+	0.764981i	−0.0714559	+	0.0295980i
$669$	4.02939	+	1.66903i	0.155785	+	0.0645283i
$670$	−12.1499	+	5.03264i	−0.469390	+	0.194428i
$671$	−0.918926	+	2.21848i	−0.0354748	+	0.0856437i
$672$	−1.44885	−	0.600134i	−0.0558906	−	0.0231507i
$673$	−13.4372	+	5.56585i	−0.517964	+	0.214548i	−0.626322	−	0.779564i	$-0.715441\pi$
$673$	−13.4372	+	5.56585i	−0.517964	+	0.214548i	0.108358	+	0.994112i	$0.465441\pi$
$674$	2.55528	−	2.55528i	0.0984258	−	0.0984258i
$675$	−10.1502	−	24.5048i	−0.390682	−	0.943189i
$676$	−8.83021	−	8.83021i	−0.339624	−	0.339624i
$677$	−1.09175			−0.0419594			−0.0209797	−	0.999780i	$-0.506679\pi$
$677$	−1.09175			−0.0419594			−0.0209797	+	0.999780i	$0.506679\pi$
$678$	−1.93963	+	0.803423i	−0.0744912	+	0.0308553i
$679$	−12.0309	−	4.98336i	−0.461703	−	0.191244i
$680$	−2.93773	+	7.09232i	−0.112657	+	0.271978i
$681$			5.91974i			0.226845i
$682$	−4.24623	+	1.75885i	−0.162597	+	0.0673497i
$683$	13.5118	−	32.6203i	0.517014	−	1.24818i	−0.422715	−	0.906263i	$-0.638923\pi$
$683$	13.5118	−	32.6203i	0.517014	−	1.24818i	0.939729	−	0.341920i	$-0.111077\pi$
$684$	−0.121930	−	0.0505049i	−0.00466209	−	0.00193110i
$685$	−56.0541	−	23.2184i	−2.14172	−	0.887128i
$686$			18.7117i			0.714414i
$687$	5.32078	+	12.8455i	0.203000	+	0.490086i
$688$	−1.16247	+	1.16247i	−0.0443186	+	0.0443186i
$689$		−	1.57859i		−	0.0601396i
$690$	−6.63266	+	6.63266i	−0.252501	+	0.252501i
$691$	−34.7708	−	34.7708i	−1.32274	−	1.32274i	−0.911547	−	0.411195i	$-0.865111\pi$
$691$	−34.7708	−	34.7708i	−1.32274	−	1.32274i	−0.411195	−	0.911547i	$-0.634889\pi$
$692$			2.85586i			0.108564i
$693$	−2.87868	−	2.87868i	−0.109352	−	0.109352i
$694$	2.85592	−	1.18296i	0.108409	−	0.0449045i
$695$	20.7808	−	8.60770i	0.788262	−	0.326509i
$696$	7.30436	−	3.02556i	0.276871	−	0.114684i
$697$	−3.91802	+	1.62290i	−0.148405	+	0.0614715i
$698$	8.83087	−	21.3196i	0.334254	−	0.806959i
$699$	2.95434	−	2.95434i	0.111743	−	0.111743i
$700$	6.50429	+	6.50429i	0.245839	+	0.245839i
$701$	−0.103765	+	0.250510i	−0.00391913	+	0.00946162i	−0.925827	−	0.377948i	$-0.876630\pi$
$701$	−0.103765	+	0.250510i	−0.00391913	+	0.00946162i	0.921908	+	0.387409i	$0.126630\pi$
$702$		−	3.44232i		−	0.129922i
$703$			0.319781i			0.0120608i
$704$	0.815523	−	0.815523i	0.0307362	−	0.0307362i
$705$	−2.59744	−	6.27078i	−0.0978254	−	0.236171i
$706$	3.16564	+	7.64254i	0.119141	+	0.287631i
$707$	4.39674	+	10.6147i	0.165356	+	0.399205i
$708$		−	6.74034i		−	0.253318i
$709$		−	7.51384i		−	0.282188i	−0.989996	−	0.141094i	$-0.954938\pi$
$709$		−	7.51384i		−	0.282188i	0.989996	−	0.141094i	$-0.0450620\pi$
$710$	14.8767	−	6.16212i	0.558312	−	0.231260i
$711$	5.64177	−	13.6204i	0.211583	−	0.510807i
$712$		−	0.269162i		−	0.0100873i
$713$	−8.67039	+	8.67039i	−0.324709	+	0.324709i
$714$	3.71269			0.138944
$715$	2.47272	+	1.02424i	0.0924746	+	0.0383042i
$716$	1.99976			0.0747346
$717$	−3.06134	+	1.26805i	−0.114328	+	0.0473561i
$718$	3.63966	+	8.78693i	0.135831	+	0.327925i
$719$	12.4058			0.462658			0.231329	−	0.972876i	$-0.425693\pi$
$719$	12.4058			0.462658			0.231329	+	0.972876i	$0.425693\pi$
$720$	4.85200	+	4.85200i	0.180823	+	0.180823i
$721$		−	14.7523i		−	0.549403i
$722$	18.9961			0.706962
$723$	−0.182879	−	0.441509i	−0.00680135	−	0.0164199i
$724$	12.5908	+	12.5908i	0.467932	+	0.467932i
$725$	−46.3738			−1.72228
$726$	8.39902	−	3.47899i	0.311717	−	0.129117i
$727$	33.8786	+	14.0330i	1.25649	+	0.520454i	0.908829	−	0.417168i	$-0.136977\pi$
$727$	33.8786	+	14.0330i	1.25649	+	0.520454i	0.347657	+	0.937622i	$0.386977\pi$
$728$	0.456846	+	1.10292i	0.0169319	+	0.0408771i
$729$	−6.85966	+	6.85966i	−0.254062	+	0.254062i
$730$	−41.1321			−1.52237
$731$	1.48941	−	3.59576i	0.0550879	−	0.132994i
$732$	−1.95742			−0.0723482
$733$			20.3890i			0.753084i	0.926400	+	0.376542i	$0.122887\pi$
$733$			20.3890i			0.753084i	−0.926400	+	0.376542i	$0.877113\pi$
$734$	6.21878	+	15.0135i	0.229539	+	0.554157i
$735$	−4.92023	+	11.8785i	−0.181485	+	0.438144i
$736$	1.17749	−	2.84271i	0.0434028	−	0.104784i
$737$	−4.32145	+	1.79000i	−0.159183	+	0.0659357i
$738$			3.79065i			0.139536i
$739$	32.9763			1.21305			0.606527	−	0.795063i	$-0.292562\pi$
$739$	32.9763			1.21305			0.606527	+	0.795063i	$0.292562\pi$
$740$	6.36258	−	15.3606i	0.233893	−	0.564668i
$741$	−0.0160583	−	0.0387682i	−0.000589917	−	0.00142419i
$742$	1.40802	−	3.39926i	0.0516900	−	0.124791i
$743$	−19.2919	+	7.99096i	−0.707750	+	0.293160i	−0.707373	−	0.706840i	$-0.750120\pi$
$743$	−19.2919	+	7.99096i	−0.707750	+	0.293160i	−0.000376985		1.00000i	$0.500120\pi$
$744$	−2.64921	−	2.64921i	−0.0971246	−	0.0971246i
$745$		−	52.5388i		−	1.92487i
$746$		−	15.1199i		−	0.553578i
$747$	−9.28182	−	9.28182i	−0.339604	−	0.339604i
$748$	−1.04489	+	2.52259i	−0.0382050	+	0.0922351i
$749$	5.03907	−	12.1654i	0.184123	−	0.444513i
$750$	0.600131	+	1.44884i	0.0219137	+	0.0529043i
$751$	−22.5993			−0.824659			−0.412330	−	0.911035i	$-0.635285\pi$
$751$	−22.5993			−0.824659			−0.412330	+	0.911035i	$0.635285\pi$
$752$	1.57436	+	1.57436i	0.0574111	+	0.0574111i
$753$			12.8856i			0.469576i
$754$	−5.56038	−	2.30318i	−0.202497	−	0.0838770i
$755$	2.08987	+	2.08987i	0.0760582	+	0.0760582i
$756$	3.07036	−	7.41251i	0.111668	−	0.269590i
$757$	8.20209	+	8.20209i	0.298110	+	0.298110i	0.840273	−	0.542163i	$-0.182395\pi$
$757$	8.20209	+	8.20209i	0.298110	+	0.298110i	−0.542163	+	0.840273i	$0.682395\pi$
$758$	21.4992	−	21.4992i	0.780885	−	0.780885i
$759$	−2.35910	+	2.35910i	−0.0856300	+	0.0856300i
$760$	0.186835	+	0.0773897i	0.00677723	+	0.00280722i
$761$	25.1370			0.911215			0.455608	−	0.890181i	$-0.349422\pi$
$761$	25.1370			0.911215			0.455608	+	0.890181i	$0.349422\pi$
$762$	10.6490	−	10.6490i	0.385771	−	0.385771i
$763$	−7.31087			−0.264671
$764$	4.76499	−	11.5037i	0.172391	−	0.416190i
$765$	−15.0083	−	6.21663i	−0.542625	−	0.224763i
$766$	−24.5476	+	24.5476i	−0.886940	+	0.886940i
$767$	−3.62818	+	3.62818i	−0.131006	+	0.131006i
$768$	0.868578	+	0.359777i	0.0313421	+	0.0129823i
$769$	−17.1893	−	41.4987i	−0.619864	−	1.49648i	−0.851862	−	0.523767i	$-0.824526\pi$
$769$	−17.1893	−	41.4987i	−0.619864	−	1.49648i	0.231998	−	0.972716i	$-0.425474\pi$
$770$	4.41107	+	4.41107i	0.158964	+	0.158964i
$771$	0.557369	+	1.34561i	0.0200731	+	0.0484609i
$772$	7.85533	+	18.9644i	0.282719	+	0.682545i
$773$	23.4335			0.842844			0.421422	−	0.906865i	$-0.361531\pi$
$773$	23.4335			0.842844			0.421422	+	0.906865i	$0.361531\pi$
$774$	−2.45993	−	2.45993i	−0.0884204	−	0.0884204i
$775$	8.40962	+	20.3026i	0.302083	+	0.729292i
$776$	7.21245	+	2.98750i	0.258912	+	0.107245i
$777$	−8.04099			−0.288469
$778$	−19.4730	+	8.06599i	−0.698141	+	0.289180i
$779$	0.0427525	+	0.103214i	0.00153177	+	0.00369801i
$780$			2.18174i			0.0781187i
$781$	5.29133	−	2.19174i	0.189339	−	0.0784266i
$782$			7.28445i			0.260491i
$783$	15.4792	+	37.3701i	0.553181	+	1.33550i
$784$		−	4.21754i		−	0.150626i
$785$	−32.2860	+	13.3733i	−1.15234	+	0.477313i
$786$	−3.18289			−0.113530
$787$	39.3050	+	16.2807i	1.40107	+	0.580343i	0.950030	−	0.312159i	$-0.101052\pi$
$787$	39.3050	+	16.2807i	1.40107	+	0.580343i	0.451042	+	0.892503i	$0.351052\pi$
$788$	0.359876			0.0128200
$789$	12.0883	−	5.00712i	0.430353	−	0.178258i
$790$	−8.64501	+	20.8709i	−0.307576	+	0.742553i
$791$	2.63397	+	2.63397i	0.0936531	+	0.0936531i
$792$	1.72576	+	1.72576i	0.0613220	+	0.0613220i
$793$	1.05364	+	1.05364i	0.0374157	+	0.0374157i
$794$	−18.2554	+	18.2554i	−0.647860	+	0.647860i
$795$	4.75473	−	4.75473i	0.168633	−	0.168633i
$796$	3.61347	+	8.72368i	0.128076	+	0.309203i
$797$	−34.3124			−1.21541			−0.607703	−	0.794164i	$-0.707909\pi$
$797$	−34.3124			−1.21541			−0.607703	+	0.794164i	$0.707909\pi$
$798$		−	0.0978046i		−	0.00346225i
$799$	−4.86985	−	2.01716i	−0.172283	−	0.0713619i
$800$	−3.89929	−	3.89929i	−0.137861	−	0.137861i
$801$	0.569583			0.0201252
$802$	−17.9250	+	8.92715i	−0.632954	+	0.315228i
$803$	−14.6298			−0.516275
$804$	−2.69614	−	2.69614i	−0.0950854	−	0.0950854i
$805$	15.3759	+	6.36889i	0.541928	+	0.224474i
$806$			2.85202i			0.100458i
$807$	2.25229			0.0792843
$808$	−2.63582	−	6.36343i	−0.0927278	−	0.223865i
$809$	−3.87675	+	3.87675i	−0.136299	+	0.136299i	−0.771965	−	0.635665i	$-0.780726\pi$
$809$	−3.87675	+	3.87675i	−0.136299	+	0.136299i	0.635665	+	0.771965i	$0.280726\pi$
$810$	−4.18771	+	4.18771i	−0.147141	+	0.147141i
$811$	2.99259	+	2.99259i	0.105084	+	0.105084i	0.757694	−	0.652610i	$-0.226326\pi$
$811$	2.99259	+	2.99259i	0.105084	+	0.105084i	−0.652610	+	0.757694i	$0.726326\pi$
$812$	−9.91911	−	9.91911i	−0.348092	−	0.348092i
$813$	−1.87738	−	1.87738i	−0.0658427	−	0.0658427i
$814$	2.26304	−	5.46346i	0.0793195	−	0.191494i
$815$	47.1626	−	19.5354i	1.65203	−	0.684294i
$816$	−2.22574			−0.0779164
$817$	−0.0947244	−	0.0392361i	−0.00331399	−	0.00137270i
$818$	32.4300			1.13389
$819$	−2.33393	+	0.966747i	−0.0815543	+	0.0337809i
$820$		−	5.80849i		−	0.202841i
$821$	2.78736	+	6.72927i	0.0972794	+	0.234853i	0.965026	−	0.262153i	$-0.0844325\pi$
$821$	2.78736	+	6.72927i	0.0972794	+	0.234853i	−0.867747	+	0.497006i	$0.834433\pi$
$822$		−	17.5911i		−	0.613560i
$823$	−51.1260	+	21.1771i	−1.78214	+	0.738187i	−0.789995	+	0.613114i	$0.789917\pi$
$823$	−51.1260	+	21.1771i	−1.78214	+	0.738187i	−0.992147	+	0.125074i	$0.960083\pi$
$824$			8.84391i			0.308092i
$825$	2.28815	+	5.52409i	0.0796632	+	0.192324i
$826$	−11.0489	+	4.57660i	−0.384440	+	0.159240i
$827$	−41.8953			−1.45684			−0.728421	−	0.685130i	$-0.759745\pi$
$827$	−41.8953			−1.45684			−0.728421	+	0.685130i	$0.759745\pi$
$828$	6.01554	+	2.49172i	0.209054	+	0.0865932i
$829$	−10.2194	−	24.6718i	−0.354935	−	0.856888i	−0.995996	−	0.0893982i	$-0.971506\pi$
$829$	−10.2194	−	24.6718i	−0.354935	−	0.856888i	0.641061	−	0.767490i	$-0.278494\pi$
$830$	14.2227	+	14.2227i	0.493678	+	0.493678i
$831$	15.5741			0.540261
$832$	−0.273877	−	0.661198i	−0.00949498	−	0.0229229i
$833$	3.82101	+	9.22475i	0.132390	+	0.319618i
$834$	4.61141	+	4.61141i	0.159680	+	0.159680i
$835$	2.48052	+	5.98851i	0.0858420	+	0.207241i
$836$	0.0664535	+	0.0275259i	0.00229834	+	0.000952004i
$837$	13.5537	−	13.5537i	0.468484	−	0.468484i
$838$	−15.2190	+	15.2190i	−0.525732	+	0.525732i
$839$	−7.96382	−	3.29872i	−0.274941	−	0.113884i	0.240953	−	0.970537i	$-0.422540\pi$
$839$	−7.96382	−	3.29872i	−0.274941	−	0.113884i	−0.515894	+	0.856652i	$0.672540\pi$
$840$	−1.94599	+	4.69804i	−0.0671430	+	0.162098i
$841$	41.7206			1.43864
$842$	−13.9508	+	13.9508i	−0.480775	+	0.480775i
$843$	−5.60718			−0.193122
$844$	−7.62705	−	3.15923i	−0.262534	−	0.108745i
$845$	−28.6328	+	28.6328i	−0.984999	+	0.984999i
$846$	−3.33156	+	3.33156i	−0.114541	+	0.114541i
$847$	−11.4056	−	11.4056i	−0.391902	−	0.391902i
$848$	−0.844101	+	2.03784i	−0.0289865	+	0.0699797i
$849$	−4.93732	−	4.93732i	−0.169448	−	0.169448i
$850$	12.0613	+	4.99597i	0.413700	+	0.171360i
$851$		−	15.7768i		−	0.540820i
$852$	3.30123	+	3.30123i	0.113098	+	0.113098i
$853$	57.6598			1.97423			0.987116	−	0.160005i	$-0.0511509\pi$
$853$	57.6598			1.97423			0.987116	+	0.160005i	$0.0511509\pi$
$854$	1.32906	+	3.20863i	0.0454794	+	0.109797i
$855$	−0.163767	+	0.395368i	−0.00560071	+	0.0135213i
$856$	−3.02089	+	7.29308i	−0.103252	+	0.249272i
$857$	7.12427	+	7.12427i	0.243360	+	0.243360i	0.818239	−	0.574878i	$-0.194951\pi$
$857$	7.12427	+	7.12427i	0.243360	+	0.243360i	−0.574878	+	0.818239i	$0.694951\pi$
$858$			0.775999i			0.0264922i
$859$		−	7.92653i		−	0.270450i	−0.990815	−	0.135225i	$-0.956824\pi$
$859$		−	7.92653i		−	0.270450i	0.990815	−	0.135225i	$-0.0431757\pi$
$860$	3.76941	+	3.76941i	0.128536	+	0.128536i
$861$	−2.59534	+	1.07503i	−0.0884490	+	0.0366368i
$862$	−13.0724	+	31.5595i	−0.445247	+	1.07492i
$863$	1.70306	+	4.11155i	0.0579728	+	0.139959i	0.950212	−	0.311605i	$-0.100866\pi$
$863$	1.70306	+	4.11155i	0.0579728	+	0.139959i	−0.892239	+	0.451563i	$0.850866\pi$
$864$	−1.84067	+	4.44376i	−0.0626207	+	0.151180i
$865$	9.26041			0.314863
$866$			10.1149i			0.343718i
$867$	−9.89763	+	4.09973i	−0.336141	+	0.139234i
$868$	−2.54385	+	6.14139i	−0.0863438	+	0.208452i
$869$	−3.07485	+	7.42335i	−0.104307	+	0.251820i
$870$	−9.81068	−	23.6851i	−0.332613	−	0.802999i
$871$			2.90255i			0.0983490i
$872$	4.38283			0.148421
$873$	−6.32194	+	15.2625i	−0.213965	+	0.516558i
$874$	0.191897			0.00649100
$875$	1.96749	−	1.96749i	0.0665133	−	0.0665133i
$876$	−4.56374	−	11.0178i	−0.154195	−	0.372259i
$877$	−23.6116	−	9.78024i	−0.797307	−	0.330255i	−0.0534295	−	0.998572i	$-0.517015\pi$
$877$	−23.6116	−	9.78024i	−0.797307	−	0.330255i	−0.743877	+	0.668316i	$0.767015\pi$
$878$	8.19501	−	3.39448i	0.276568	−	0.114558i
$879$	−8.93720			−0.301444
$880$	−2.64441	−	2.64441i	−0.0891431	−	0.0891431i
$881$	−6.44025	−	15.5481i	−0.216978	−	0.523830i	0.777487	−	0.628898i	$-0.216494\pi$
$881$	−6.44025	−	15.5481i	−0.216978	−	0.523830i	−0.994465	+	0.105068i	$0.966494\pi$
$882$	8.92487			0.300516
$883$		−	3.28503i		−	0.110550i	−0.998471	−	0.0552750i	$-0.982396\pi$
$883$		−	3.28503i		−	0.110550i	0.998471	−	0.0552750i	$-0.0176036\pi$
$884$	1.19807	+	1.19807i	0.0402953	+	0.0402953i
$885$	−21.8562			−0.734688
$886$	15.7641	+	38.0579i	0.529605	+	1.27858i
$887$	6.38774	−	2.64589i	0.214479	−	0.0888402i	−0.272857	−	0.962055i	$-0.587969\pi$
$887$	6.38774	−	2.64589i	0.214479	−	0.0888402i	0.487336	+	0.873214i	$0.337969\pi$
$888$	4.82053			0.161766
$889$	−24.6864	−	10.2255i	−0.827956	−	0.342951i
$890$	−0.872784			−0.0292558
$891$	−1.48948	+	1.48948i	−0.0498995	+	0.0498995i
$892$			4.63906i			0.155327i
$893$	−0.0531387	+	0.128288i	−0.00177822	+	0.00429300i
$894$	14.0733	−	5.82936i	0.470682	−	0.194963i
$895$		−	6.48442i		−	0.216750i
$896$		−	1.66807i		−	0.0557264i
$897$	0.792256	+	1.91268i	0.0264527	+	0.0638624i
$898$	−6.62117	−	15.9849i	−0.220951	−	0.533423i
$899$	−12.8248	−	30.9617i	−0.427730	−	1.03263i
$900$	8.25140	−	8.25140i	0.275047	−	0.275047i
$901$		−	5.22197i		−	0.173969i
$902$		−	2.06596i		−	0.0687890i
$903$	0.986605	−	2.38188i	0.0328322	−	0.0792639i
$904$	−1.57905	−	1.57905i	−0.0525184	−	0.0525184i
$905$	40.8267	−	40.8267i	1.35713	−	1.35713i
$906$	−0.327925	+	0.791682i	−0.0108946	+	0.0263019i
$907$	−18.0122	+	7.46092i	−0.598087	+	0.247736i	−0.661125	−	0.750275i	$-0.729921\pi$
$907$	−18.0122	+	7.46092i	−0.598087	+	0.247736i	0.0630386	+	0.998011i	$0.479921\pi$
$908$	−5.81734	+	2.40962i	−0.193055	+	0.0799661i
$909$	13.4659	−	5.57774i	0.446634	−	0.185002i
$910$	3.57634	−	1.48137i	0.118554	−	0.0491069i
$911$	−40.3402	−	40.3402i	−1.33653	−	1.33653i	−0.899396	−	0.437135i	$-0.855993\pi$
$911$	−40.3402	−	40.3402i	−1.33653	−	1.33653i	−0.437135	−	0.899396i	$-0.644007\pi$
$912$			0.0586334i			0.00194154i
$913$	5.05873	+	5.05873i	0.167420	+	0.167420i
$914$	−7.24126	+	7.24126i	−0.239519	+	0.239519i
$915$			6.34711i			0.209829i
$916$	−10.4575	+	10.4575i	−0.345524	+	0.345524i
$917$	2.16113	+	5.21744i	0.0713669	+	0.172295i
$918$		−	11.3872i		−	0.375832i
$919$	−1.10036	−	0.455782i	−0.0362974	−	0.0150349i	0.364461	−	0.931219i	$-0.381253\pi$
$919$	−1.10036	−	0.455782i	−0.0362974	−	0.0150349i	−0.400758	+	0.916184i	$0.631253\pi$
$920$	−9.21774	−	3.81811i	−0.303900	−	0.125880i
$921$	4.84591	−	11.6991i	0.159678	−	0.385498i
$922$	2.30899	−	0.956416i	0.0760426	−	0.0314979i
$923$		−	3.55397i		−	0.116980i
$924$	−0.692149	+	1.67099i	−0.0227700	+	0.0549717i
$925$	−26.1226	−	10.8203i	−0.858906	−	0.355771i
$926$	−0.278753	+	0.115463i	−0.00916040	+	0.00379436i
$927$	−18.7149			−0.614677
$928$	5.94645	+	5.94645i	0.195202	+	0.195202i
$929$	−9.97182	−	24.0741i	−0.327165	−	0.789845i	−0.998801	−	0.0489640i	$-0.984408\pi$
$929$	−9.97182	−	24.0741i	−0.327165	−	0.789845i	0.671636	−	0.740881i	$-0.265592\pi$
$930$	−8.59030	+	8.59030i	−0.281687	+	0.281687i
$931$	0.243011	−	0.100658i	0.00796435	−	0.00329894i
$932$	4.10579	+	1.70068i	0.134490	+	0.0557075i
$933$	−10.9321	+	26.3923i	−0.357899	+	0.864046i
$934$	−3.25764	+	1.34936i	−0.106593	+	0.0441524i
$935$	8.17974	+	3.38816i	0.267506	+	0.110805i
$936$	1.39918	−	0.579560i	0.0457337	−	0.0189435i
$937$	−20.3762	−	49.1925i	−0.665662	−	1.60705i	−0.788793	−	0.614659i	$-0.789294\pi$
$937$	−20.3762	−	49.1925i	−0.665662	−	1.60705i	0.123132	−	0.992390i	$-0.460706\pi$
$938$	−2.58891	+	6.25019i	−0.0845310	+	0.204076i
$939$	−29.1523	−	12.0753i	−0.951350	−	0.394062i
$940$	5.10502	−	5.10502i	0.166508	−	0.166508i
$941$	4.92579	−	2.04033i	0.160576	−	0.0665128i	−0.300948	−	0.953641i	$-0.597303\pi$
$941$	4.92579	−	2.04033i	0.160576	−	0.0665128i	0.461524	+	0.887128i	$0.347303\pi$
$942$	−7.16448	−	7.16448i	−0.233431	−	0.233431i
$943$	−2.10925	−	5.09217i	−0.0686865	−	0.165824i
$944$	6.62374	−	2.74364i	0.215585	−	0.0892980i
$945$	−24.0358	−	9.95594i	−0.781884	−	0.323867i
$946$	1.34070	+	1.34070i	0.0435899	+	0.0435899i
$947$	−29.8571			−0.970227			−0.485113	−	0.874451i	$-0.661222\pi$
$947$	−29.8571			−0.970227			−0.485113	+	0.874451i	$0.661222\pi$
$948$	−6.54978			−0.212727
$949$	−3.47411	+	8.38724i	−0.112774	+	0.272261i
$950$	0.131611	−	0.317736i	0.00427001	−	0.0103087i
$951$			10.6424i			0.345104i
$952$	1.51124	+	3.64846i	0.0489797	+	0.118247i
$953$	9.46861	+	9.46861i	0.306718	+	0.306718i	0.843635	−	0.536917i	$-0.180411\pi$
$953$	9.46861	+	9.46861i	0.306718	+	0.306718i	−0.536917	+	0.843635i	$0.680411\pi$
$954$	−4.31234	−	1.78623i	−0.139617	−	0.0578313i
$955$	−37.3019	−	15.4509i	−1.20706	−	0.499981i
$956$	−2.49223	−	2.49223i	−0.0806043	−	0.0806043i
$957$	−3.48946	−	8.42429i	−0.112798	−	0.272319i
$958$			5.18889i			0.167645i
$959$	−28.8356	+	11.9441i	−0.931150	+	0.385695i
$960$	1.16661	−	2.81645i	0.0376522	−	0.0909005i
$961$	10.6909	−	10.6909i	0.344866	−	0.344866i
$962$	−2.59479	−	2.59479i	−0.0836594	−	0.0836594i
$963$	−15.4331	−	6.39261i	−0.497325	−	0.205999i
$964$	0.359431	−	0.359431i	0.0115765	−	0.0115765i
$965$	61.4940	−	25.4716i	1.97956	−	0.819961i
$966$			4.82531i			0.155252i
$967$	14.9070	+	35.9887i	0.479377	+	1.15732i	0.959901	+	0.280338i	$0.0904465\pi$
$967$	14.9070	+	35.9887i	0.479377	+	1.15732i	−0.480524	+	0.876982i	$0.659554\pi$
$968$	6.83761	+	6.83761i	0.219769	+	0.219769i
$969$	−0.0531208	−	0.128245i	−0.00170649	−	0.00411982i
$970$	9.68724	−	23.3871i	0.311039	−	0.750913i
$971$	11.5575	−	11.5575i	0.370899	−	0.370899i	−0.496906	−	0.867804i	$-0.665531\pi$
$971$	11.5575	−	11.5575i	0.370899	−	0.370899i	0.867804	+	0.496906i	$0.165531\pi$
$972$	−14.9177	−	6.17910i	−0.478484	−	0.198195i
$973$	4.42801	−	10.6902i	0.141956	−	0.342711i
$974$	−15.3974	−	15.3974i	−0.493365	−	0.493365i
$975$	3.71031			0.118825
$976$	−0.796763	−	1.92356i	−0.0255038	−	0.0615716i
$977$	−6.52101	+	6.52101i	−0.208625	+	0.208625i	−0.803683	−	0.595058i	$-0.797129\pi$
$977$	−6.52101	+	6.52101i	−0.208625	+	0.208625i	0.595058	+	0.803683i	$0.297129\pi$
$978$	10.4657	+	10.4657i	0.334656	+	0.334656i
$979$	−0.310431			−0.00992143
$980$	−13.6758			−0.436856
$981$			9.27465i			0.296117i
$982$	1.13837	−	1.13837i	0.0363268	−	0.0363268i
$983$	13.0257	−	13.0257i	0.415454	−	0.415454i	−0.468179	−	0.883634i	$-0.655090\pi$
$983$	13.0257	−	13.0257i	0.415454	−	0.415454i	0.883634	+	0.468179i	$0.155090\pi$
$984$	1.55589	−	0.644472i	0.0496001	−	0.0205450i
$985$		−	1.16693i		−	0.0371815i
$986$	−18.3937	−	7.61891i	−0.585774	−	0.242635i
$987$	−3.22585	−	1.33619i	−0.102680	−	0.0425314i
$988$	0.0315611	−	0.0315611i	0.00100409	−	0.00100409i
$989$	4.67334	+	1.93576i	0.148604	+	0.0615536i
$990$	5.59593	−	5.59593i	0.177850	−	0.177850i
$991$	25.5597	+	10.5872i	0.811931	+	0.336313i	0.749724	−	0.661750i	$-0.230186\pi$
$991$	25.5597	+	10.5872i	0.811931	+	0.336313i	0.0622070	+	0.998063i	$0.480186\pi$
$992$	1.52502	−	3.68173i	0.0484195	−	0.116895i
$993$	23.7957	+	9.85651i	0.755134	+	0.312787i
$994$	3.16995	−	7.65293i	0.100545	−	0.242736i
$995$	28.2874	−	11.7170i	0.896770	−	0.371454i
$996$	−2.23172	+	5.38784i	−0.0707146	+	0.170720i
$997$	24.3353			0.770708			0.385354	−	0.922769i	$-0.374079\pi$
$997$	24.3353			0.770708			0.385354	+	0.922769i	$0.374079\pi$
$998$	36.4338			1.15329
$999$			24.6625i			0.780286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.11	✓	68
401.303	even	8	inner	802.2.e.b.303.11	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.11	✓	68	1.1	even	1	trivial
802.2.e.b.303.11	yes	68	401.303	even	8	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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.868578 + 0.359777i) q^{3} +1.00000i q^{4} +3.24260 q^{5} +(0.359777 + 0.868578i) q^{6} +(1.17950 - 1.17950i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49633 - 1.49633i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.868578 + 0.359777i) q^{3} +1.00000i q^{4} +3.24260 q^{5} +(0.359777 + 0.868578i) q^{6} +(1.17950 - 1.17950i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49633 - 1.49633i) q^{9} +(2.29286 + 2.29286i) q^{10} +(0.815523 + 0.815523i) q^{11} +(-0.359777 + 0.868578i) q^{12} +(0.661198 - 0.273877i) q^{13} +1.66807 q^{14} +(2.81645 + 1.16661i) q^{15} -1.00000 q^{16} +(2.18723 - 0.905982i) q^{17} -2.11613i q^{18} +(-0.0238666 - 0.0576191i) q^{19} +3.24260i q^{20} +(1.44885 - 0.600134i) q^{21} +1.15332i q^{22} +(1.17749 + 2.84271i) q^{23} +(-0.868578 + 0.359777i) q^{24} +5.51442 q^{25} +(0.661198 + 0.273877i) q^{26} +(-1.84067 - 4.44376i) q^{27} +(1.17950 + 1.17950i) q^{28} -8.40955 q^{29} +(1.16661 + 2.81645i) q^{30} +(1.52502 + 3.68173i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.414940 + 1.00175i) q^{33} +(2.18723 + 0.905982i) q^{34} +(3.82466 - 3.82466i) q^{35} +(1.49633 - 1.49633i) q^{36} +(-4.73714 - 1.96219i) q^{37} +(0.0238666 - 0.0576191i) q^{38} +0.672837 q^{39} +(-2.29286 + 2.29286i) q^{40} -1.79131 q^{41} +(1.44885 + 0.600134i) q^{42} +(1.16247 - 1.16247i) q^{43} +(-0.815523 + 0.815523i) q^{44} +(-4.85200 - 4.85200i) q^{45} +(-1.17749 + 2.84271i) q^{46} +(-1.57436 - 1.57436i) q^{47} +(-0.868578 - 0.359777i) q^{48} +4.21754i q^{49} +(3.89929 + 3.89929i) q^{50} +2.22574 q^{51} +(0.273877 + 0.661198i) q^{52} +(0.844101 - 2.03784i) q^{53} +(1.84067 - 4.44376i) q^{54} +(2.64441 + 2.64441i) q^{55} +1.66807i q^{56} -0.0586334i q^{57} +(-5.94645 - 5.94645i) q^{58} +(-6.62374 + 2.74364i) q^{59} +(-1.16661 + 2.81645i) q^{60} +(0.796763 + 1.92356i) q^{61} +(-1.52502 + 3.68173i) q^{62} -3.52986 q^{63} -1.00000i q^{64} +(2.14400 - 0.888072i) q^{65} +(-0.414940 + 1.00175i) q^{66} +(-1.55204 + 3.74696i) q^{67} +(0.905982 + 2.18723i) q^{68} +2.89275i q^{69} +5.40888 q^{70} +(1.90037 - 4.58789i) q^{71} +2.11613 q^{72} +(-8.96959 + 8.96959i) q^{73} +(-1.96219 - 4.73714i) q^{74} +(4.78971 + 1.98396i) q^{75} +(0.0576191 - 0.0238666i) q^{76} +1.92383 q^{77} +(0.475767 + 0.475767i) q^{78} +(2.66608 + 6.43648i) q^{79} -3.24260 q^{80} +1.82641i q^{81} +(-1.26665 - 1.26665i) q^{82} +6.20305 q^{83} +(0.600134 + 1.44885i) q^{84} +(7.09232 - 2.93773i) q^{85} +1.64398 q^{86} +(-7.30436 - 3.02556i) q^{87} -1.15332 q^{88} +(-0.190326 + 0.190326i) q^{89} -6.86176i q^{90} +(0.456846 - 1.10292i) q^{91} +(-2.84271 + 1.17749i) q^{92} +3.74654i q^{93} -2.22649i q^{94} +(-0.0773897 - 0.186835i) q^{95} +(-0.359777 - 0.868578i) q^{96} +(-2.98750 - 7.21245i) q^{97} +(-2.98225 + 2.98225i) q^{98} -2.44059i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more