LMFDB - Embedded newform 325.2.l.a.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(66,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("325.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.l (of order $5$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			131.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	325.131
Dual form			325.2.l.a.196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 + 0.587785i) q^{2} +(2.11803 - 1.53884i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} -3.85410 q^{7} +(1.80902 + 1.31433i) q^{8} +(1.19098 - 3.66547i) q^{9} +O(q^{10})$	\(q+(0.190983 + 0.587785i) q^{2} +(2.11803 - 1.53884i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} -3.85410 q^{7} +(1.80902 + 1.31433i) q^{8} +(1.19098 - 3.66547i) q^{9} +(1.11803 - 0.812299i) q^{10} +(1.30902 + 4.02874i) q^{11} +(1.30902 - 4.02874i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.736068 - 2.26538i) q^{14} +(-4.73607 - 3.44095i) q^{15} +(0.572949 - 1.76336i) q^{16} +(0.618034 + 0.449028i) q^{17} +2.38197 q^{18} +(4.04508 + 2.93893i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-8.16312 + 5.93085i) q^{21} +(-2.11803 + 1.53884i) q^{22} +(-2.19098 - 6.74315i) q^{23} +5.85410 q^{24} +(-4.04508 + 2.93893i) q^{25} -0.618034 q^{26} +(-0.690983 - 2.12663i) q^{27} +(-5.04508 + 3.66547i) q^{28} +(1.11803 - 3.44095i) q^{30} +(-0.927051 - 0.673542i) q^{31} +5.61803 q^{32} +(8.97214 + 6.51864i) q^{33} +(-0.145898 + 0.449028i) q^{34} +(2.66312 + 8.19624i) q^{35} +(-1.92705 - 5.93085i) q^{36} +(-2.73607 + 8.42075i) q^{37} +(-0.954915 + 2.93893i) q^{38} +(0.809017 + 2.48990i) q^{39} +(1.54508 - 4.75528i) q^{40} +(1.04508 - 3.21644i) q^{41} +(-5.04508 - 3.66547i) q^{42} +5.47214 q^{43} +(5.54508 + 4.02874i) q^{44} -8.61803 q^{45} +(3.54508 - 2.57565i) q^{46} +(6.73607 - 4.89404i) q^{47} +(-1.50000 - 4.61653i) q^{48} +7.85410 q^{49} +(-2.50000 - 1.81636i) q^{50} +2.00000 q^{51} +(0.500000 + 1.53884i) q^{52} +(-7.78115 + 5.65334i) q^{53} +(1.11803 - 0.812299i) q^{54} +(7.66312 - 5.56758i) q^{55} +(-6.97214 - 5.06555i) q^{56} +13.0902 q^{57} +(-0.690983 + 2.12663i) q^{59} -9.47214 q^{60} +(4.23607 + 13.0373i) q^{61} +(0.218847 - 0.673542i) q^{62} +(-4.59017 + 14.1271i) q^{63} +(-0.0729490 - 0.224514i) q^{64} +2.23607 q^{65} +(-2.11803 + 6.51864i) q^{66} +(-5.92705 - 4.30625i) q^{67} +1.23607 q^{68} +(-15.0172 - 10.9106i) q^{69} +(-4.30902 + 3.13068i) q^{70} +(-6.35410 + 4.61653i) q^{71} +(6.97214 - 5.06555i) q^{72} +(0.836881 + 2.57565i) q^{73} -5.47214 q^{74} +(-4.04508 + 12.4495i) q^{75} +8.09017 q^{76} +(-5.04508 - 15.5272i) q^{77} +(-1.30902 + 0.951057i) q^{78} +(-3.35410 + 2.43690i) q^{79} -4.14590 q^{80} +(4.61803 + 3.35520i) q^{81} +2.09017 q^{82} +(-13.8992 - 10.0984i) q^{83} +(-5.04508 + 15.5272i) q^{84} +(0.527864 - 1.62460i) q^{85} +(1.04508 + 3.21644i) q^{86} +(-2.92705 + 9.00854i) q^{88} +(-3.45492 - 10.6331i) q^{89} +(-1.64590 - 5.06555i) q^{90} +(1.19098 - 3.66547i) q^{91} +(-9.28115 - 6.74315i) q^{92} -3.00000 q^{93} +(4.16312 + 3.02468i) q^{94} +(3.45492 - 10.6331i) q^{95} +(11.8992 - 8.64527i) q^{96} +(-6.78115 + 4.92680i) q^{97} +(1.50000 + 4.61653i) q^{98} +16.3262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + q^{13} + 6 q^{14} - 10 q^{15} + 9 q^{16} - 2 q^{17} + 14 q^{18} + 5 q^{19} - 5 q^{20} - 17 q^{21} - 4 q^{22} - 11 q^{23} + 10 q^{24} - 5 q^{25} + 2 q^{26} - 5 q^{27} - 9 q^{28} + 3 q^{31} + 18 q^{32} + 18 q^{33} - 14 q^{34} - 5 q^{35} - q^{36} - 2 q^{37} - 15 q^{38} + q^{39} - 5 q^{40} - 7 q^{41} - 9 q^{42} + 4 q^{43} + 11 q^{44} - 30 q^{45} + 3 q^{46} + 18 q^{47} - 6 q^{48} + 18 q^{49} - 10 q^{50} + 8 q^{51} + 2 q^{52} - 11 q^{53} + 15 q^{55} - 10 q^{56} + 30 q^{57} - 5 q^{59} - 20 q^{60} + 8 q^{61} + 21 q^{62} + 4 q^{63} - 7 q^{64} - 4 q^{66} - 17 q^{67} - 4 q^{68} - 31 q^{69} - 15 q^{70} - 12 q^{71} + 10 q^{72} + 19 q^{73} - 4 q^{74} - 5 q^{75} + 10 q^{76} - 9 q^{77} - 3 q^{78} - 30 q^{80} + 14 q^{81} - 14 q^{82} - 31 q^{83} - 9 q^{84} + 20 q^{85} - 7 q^{86} - 5 q^{88} - 25 q^{89} - 20 q^{90} + 7 q^{91} - 17 q^{92} - 12 q^{93} + q^{94} + 25 q^{95} + 23 q^{96} - 7 q^{97} + 6 q^{98} + 34 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + q^13 + 6 * q^14 - 10 * q^15 + 9 * q^16 - 2 * q^17 + 14 * q^18 + 5 * q^19 - 5 * q^20 - 17 * q^21 - 4 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 2 * q^26 - 5 * q^27 - 9 * q^28 + 3 * q^31 + 18 * q^32 + 18 * q^33 - 14 * q^34 - 5 * q^35 - q^36 - 2 * q^37 - 15 * q^38 + q^39 - 5 * q^40 - 7 * q^41 - 9 * q^42 + 4 * q^43 + 11 * q^44 - 30 * q^45 + 3 * q^46 + 18 * q^47 - 6 * q^48 + 18 * q^49 - 10 * q^50 + 8 * q^51 + 2 * q^52 - 11 * q^53 + 15 * q^55 - 10 * q^56 + 30 * q^57 - 5 * q^59 - 20 * q^60 + 8 * q^61 + 21 * q^62 + 4 * q^63 - 7 * q^64 - 4 * q^66 - 17 * q^67 - 4 * q^68 - 31 * q^69 - 15 * q^70 - 12 * q^71 + 10 * q^72 + 19 * q^73 - 4 * q^74 - 5 * q^75 + 10 * q^76 - 9 * q^77 - 3 * q^78 - 30 * q^80 + 14 * q^81 - 14 * q^82 - 31 * q^83 - 9 * q^84 + 20 * q^85 - 7 * q^86 - 5 * q^88 - 25 * q^89 - 20 * q^90 + 7 * q^91 - 17 * q^92 - 12 * q^93 + q^94 + 25 * q^95 + 23 * q^96 - 7 * q^97 + 6 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	0.995597	−	0.0937362i	$-0.0298810\pi$
$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	−0.860552	+	0.509363i	$0.829881\pi$
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.226514	−	0.974008i	$-0.427267\pi$
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.996333	+	0.0855571i	$0.0272670\pi$
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	−3.85410			−1.45671			−0.728357	−	0.685198i	$-0.759716\pi$
$7$	−3.85410			−1.45671			−0.728357	+	0.685198i	$0.759716\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	1.19098	−	3.66547i	0.396994	−	1.22182i
$10$	1.11803	−	0.812299i	0.353553	−	0.256872i
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	0.929208	+	0.369558i	$0.120491\pi$
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	−0.534524	+	0.845153i	$0.679509\pi$
$12$	1.30902	−	4.02874i	0.377881	−	1.16300i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−0.736068	−	2.26538i	−0.196722	−	0.605449i
$15$	−4.73607	−	3.44095i	−1.22285	−	0.888451i
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	0.618034	+	0.449028i	0.149895	+	0.108905i	0.660205	−	0.751085i	$-0.270469\pi$
$17$	0.618034	+	0.449028i	0.149895	+	0.108905i	−0.510310	+	0.859991i	$0.670469\pi$
$18$	2.38197			0.561435
$19$	4.04508	+	2.93893i	0.928006	+	0.674236i	0.945504	−	0.325611i	$-0.105570\pi$
$19$	4.04508	+	2.93893i	0.928006	+	0.674236i	−0.0174977	+	0.999847i	$0.505570\pi$
$20$	−2.92705	−	2.12663i	−0.654508	−	0.475528i
$21$	−8.16312	+	5.93085i	−1.78134	+	1.29422i
$22$	−2.11803	+	1.53884i	−0.451566	+	0.328082i
$23$	−2.19098	−	6.74315i	−0.456852	−	1.40604i	−0.868948	−	0.494904i	$-0.835203\pi$
$23$	−2.19098	−	6.74315i	−0.456852	−	1.40604i	0.412096	−	0.911140i	$-0.364797\pi$
$24$	5.85410			1.19496
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	−0.618034			−0.121206
$27$	−0.690983	−	2.12663i	−0.132980	−	0.409270i
$28$	−5.04508	+	3.66547i	−0.953431	+	0.692708i
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	1.11803	−	3.44095i	0.204124	−	0.628230i
$31$	−0.927051	−	0.673542i	−0.166503	−	0.120972i	0.501413	−	0.865208i	$-0.332814\pi$
$31$	−0.927051	−	0.673542i	−0.166503	−	0.120972i	−0.667916	+	0.744236i	$0.732814\pi$
$32$	5.61803			0.993137
$33$	8.97214	+	6.51864i	1.56185	+	1.13475i
$34$	−0.145898	+	0.449028i	−0.0250213	+	0.0770077i
$35$	2.66312	+	8.19624i	0.450149	+	1.38542i
$36$	−1.92705	−	5.93085i	−0.321175	−	0.988476i
$37$	−2.73607	+	8.42075i	−0.449807	+	1.38436i	0.427318	+	0.904101i	$0.359458\pi$
$37$	−2.73607	+	8.42075i	−0.449807	+	1.38436i	−0.877125	+	0.480262i	$0.840542\pi$
$38$	−0.954915	+	2.93893i	−0.154908	+	0.476757i
$39$	0.809017	+	2.48990i	0.129546	+	0.398703i
$40$	1.54508	−	4.75528i	0.244299	−	0.751876i
$41$	1.04508	−	3.21644i	0.163215	−	0.502324i	−0.835685	−	0.549208i	$-0.814929\pi$
$41$	1.04508	−	3.21644i	0.163215	−	0.502324i	0.998900	+	0.0468847i	$0.0149293\pi$
$42$	−5.04508	−	3.66547i	−0.778474	−	0.565594i
$43$	5.47214			0.834493			0.417246	−	0.908793i	$-0.362995\pi$
$43$	5.47214			0.834493			0.417246	+	0.908793i	$0.362995\pi$
$44$	5.54508	+	4.02874i	0.835953	+	0.607355i
$45$	−8.61803			−1.28470
$46$	3.54508	−	2.57565i	0.522694	−	0.379760i
$47$	6.73607	−	4.89404i	0.982556	−	0.713869i	0.0242780	−	0.999705i	$-0.492271\pi$
$47$	6.73607	−	4.89404i	0.982556	−	0.713869i	0.958279	+	0.285836i	$0.0922713\pi$
$48$	−1.50000	−	4.61653i	−0.216506	−	0.666338i
$49$	7.85410			1.12201
$50$	−2.50000	−	1.81636i	−0.353553	−	0.256872i
$51$	2.00000			0.280056
$52$	0.500000	+	1.53884i	0.0693375	+	0.213399i
$53$	−7.78115	+	5.65334i	−1.06882	+	0.776546i	−0.975700	−	0.219109i	$-0.929685\pi$
$53$	−7.78115	+	5.65334i	−1.06882	+	0.776546i	−0.0931231	+	0.995655i	$0.529685\pi$
$54$	1.11803	−	0.812299i	0.152145	−	0.110540i
$55$	7.66312	−	5.56758i	1.03329	−	0.750733i
$56$	−6.97214	−	5.06555i	−0.931691	−	0.676913i
$57$	13.0902			1.73384
$58$		0			0
$59$	−0.690983	+	2.12663i	−0.0899583	+	0.276863i	−0.985907	−	0.167294i	$-0.946497\pi$
$59$	−0.690983	+	2.12663i	−0.0899583	+	0.276863i	0.895949	+	0.444158i	$0.146497\pi$
$60$	−9.47214			−1.22285
$61$	4.23607	+	13.0373i	0.542373	+	1.66925i	0.727155	+	0.686473i	$0.240842\pi$
$61$	4.23607	+	13.0373i	0.542373	+	1.66925i	−0.184783	+	0.982779i	$0.559158\pi$
$62$	0.218847	−	0.673542i	0.0277936	−	0.0855399i
$63$	−4.59017	+	14.1271i	−0.578307	+	1.77985i
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$	2.23607			0.277350
$66$	−2.11803	+	6.51864i	−0.260712	+	0.802389i
$67$	−5.92705	−	4.30625i	−0.724105	−	0.526093i	0.163588	−	0.986529i	$-0.447693\pi$
$67$	−5.92705	−	4.30625i	−0.724105	−	0.526093i	−0.887693	+	0.460436i	$0.847693\pi$
$68$	1.23607			0.149895
$69$	−15.0172	−	10.9106i	−1.80786	−	1.31349i
$70$	−4.30902	+	3.13068i	−0.515026	+	0.374188i
$71$	−6.35410	+	4.61653i	−0.754093	+	0.547881i	−0.897093	−	0.441842i	$-0.854325\pi$
$71$	−6.35410	+	4.61653i	−0.754093	+	0.547881i	0.143000	+	0.989723i	$0.454325\pi$
$72$	6.97214	−	5.06555i	0.821674	−	0.596981i
$73$	0.836881	+	2.57565i	0.0979495	+	0.301458i	0.988011	−	0.154383i	$-0.0493388\pi$
$73$	0.836881	+	2.57565i	0.0979495	+	0.301458i	−0.890062	+	0.455840i	$0.849339\pi$
$74$	−5.47214			−0.636123
$75$	−4.04508	+	12.4495i	−0.467086	+	1.43754i
$76$	8.09017			0.928006
$77$	−5.04508	−	15.5272i	−0.574941	−	1.76949i
$78$	−1.30902	+	0.951057i	−0.148217	+	0.107686i
$79$	−3.35410	+	2.43690i	−0.377366	+	0.274172i	−0.760259	−	0.649620i	$-0.774928\pi$
$79$	−3.35410	+	2.43690i	−0.377366	+	0.274172i	0.382893	+	0.923793i	$0.374928\pi$
$80$	−4.14590			−0.463525
$81$	4.61803	+	3.35520i	0.513115	+	0.372800i
$82$	2.09017			0.230821
$83$	−13.8992	−	10.0984i	−1.52563	−	1.10844i	−0.958605	−	0.284740i	$-0.908093\pi$
$83$	−13.8992	−	10.0984i	−1.52563	−	1.10844i	−0.567029	−	0.823698i	$-0.691907\pi$
$84$	−5.04508	+	15.5272i	−0.550464	+	1.69415i
$85$	0.527864	−	1.62460i	0.0572549	−	0.176212i
$86$	1.04508	+	3.21644i	0.112694	+	0.346838i
$87$		0			0
$88$	−2.92705	+	9.00854i	−0.312025	+	0.960313i
$89$	−3.45492	−	10.6331i	−0.366220	−	1.12711i	−0.949213	−	0.314633i	$-0.898119\pi$
$89$	−3.45492	−	10.6331i	−0.366220	−	1.12711i	0.582993	−	0.812477i	$-0.301881\pi$
$90$	−1.64590	−	5.06555i	−0.173493	−	0.533956i
$91$	1.19098	−	3.66547i	0.124849	−	0.384246i
$92$	−9.28115	−	6.74315i	−0.967627	−	0.703022i
$93$	−3.00000			−0.311086
$94$	4.16312	+	3.02468i	0.429393	+	0.311972i
$95$	3.45492	−	10.6331i	0.354467	−	1.09094i
$96$	11.8992	−	8.64527i	1.21446	−	0.882354i
$97$	−6.78115	+	4.92680i	−0.688522	+	0.500240i	−0.876174	−	0.481995i	$-0.839912\pi$
$97$	−6.78115	+	4.92680i	−0.688522	+	0.500240i	0.187652	+	0.982236i	$0.439912\pi$
$98$	1.50000	+	4.61653i	0.151523	+	0.466339i
$99$	16.3262			1.64085
$100$	−2.50000	+	7.69421i	−0.250000	+	0.769421i
$101$	3.70820			0.368980			0.184490	−	0.982834i	$-0.440937\pi$
$101$	3.70820			0.368980			0.184490	+	0.982834i	$0.440937\pi$
$102$	0.381966	+	1.17557i	0.0378203	+	0.116399i
$103$	−5.97214	+	4.33901i	−0.588452	+	0.427535i	−0.841761	−	0.539850i	$-0.818481\pi$
$103$	−5.97214	+	4.33901i	−0.588452	+	0.427535i	0.253309	+	0.967385i	$0.418481\pi$
$104$	−1.80902	+	1.31433i	−0.177389	+	0.128880i
$105$	18.2533	+	13.2618i	1.78134	+	1.29422i
$106$	−4.80902	−	3.49396i	−0.467093	−	0.339363i
$107$	−10.7639			−1.04059			−0.520294	−	0.853987i	$-0.674178\pi$
$107$	−10.7639			−1.04059			−0.520294	+	0.853987i	$0.674178\pi$
$108$	−2.92705	−	2.12663i	−0.281656	−	0.204635i
$109$	4.14590	−	12.7598i	0.397105	−	1.22216i	−0.530205	−	0.847869i	$-0.677885\pi$
$109$	4.14590	−	12.7598i	0.397105	−	1.22216i	0.927310	−	0.374294i	$-0.122115\pi$
$110$	4.73607	+	3.44095i	0.451566	+	0.328082i
$111$	7.16312	+	22.0458i	0.679893	+	2.09250i
$112$	−2.20820	+	6.79615i	−0.208656	+	0.642176i
$113$	2.64590	−	8.14324i	0.248905	−	0.766051i	−0.746064	−	0.665874i	$-0.768059\pi$
$113$	2.64590	−	8.14324i	0.248905	−	0.766051i	0.994970	−	0.100178i	$-0.0319411\pi$
$114$	2.50000	+	7.69421i	0.234146	+	0.720629i
$115$	−12.8262	+	9.31881i	−1.19605	+	0.868983i
$116$		0			0
$117$	3.11803	+	2.26538i	0.288262	+	0.209435i
$118$	−1.38197			−0.127220
$119$	−2.38197	−	1.73060i	−0.218354	−	0.158644i
$120$	−4.04508	−	12.4495i	−0.369264	−	1.13648i
$121$	−5.61803	+	4.08174i	−0.510730	+	0.371067i
$122$	−6.85410	+	4.97980i	−0.620541	+	0.450850i
$123$	−2.73607	−	8.42075i	−0.246703	−	0.759274i
$124$	−1.85410			−0.166503
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$	−9.18034			−0.817850
$127$	−4.80902	−	14.8006i	−0.426731	−	1.31334i	−0.901327	−	0.433140i	$-0.857406\pi$
$127$	−4.80902	−	14.8006i	−0.426731	−	1.31334i	0.474596	−	0.880204i	$-0.342594\pi$
$128$	9.20820	−	6.69015i	0.813898	−	0.591331i
$129$	11.5902	−	8.42075i	1.02046	−	0.741406i
$130$	0.427051	+	1.31433i	0.0374548	+	0.115274i
$131$	5.61803	+	4.08174i	0.490850	+	0.356623i	0.805511	−	0.592581i	$-0.201891\pi$
$131$	5.61803	+	4.08174i	0.490850	+	0.356623i	−0.314661	+	0.949204i	$0.601891\pi$
$132$	17.9443			1.56185
$133$	−15.5902	−	11.3269i	−1.35184	−	0.982169i
$134$	1.39919	−	4.30625i	0.120871	−	0.372004i
$135$	−4.04508	+	2.93893i	−0.348145	+	0.252942i
$136$	0.527864	+	1.62460i	0.0452640	+	0.139308i
$137$	4.60081	−	14.1598i	0.393074	−	1.20976i	−0.537377	−	0.843342i	$-0.680585\pi$
$137$	4.60081	−	14.1598i	0.393074	−	1.20976i	0.930451	−	0.366415i	$-0.119415\pi$
$138$	3.54508	−	10.9106i	0.301778	−	0.928776i
$139$	2.39919	+	7.38394i	0.203496	+	0.626297i	0.999772	+	0.0213632i	$0.00680063\pi$
$139$	2.39919	+	7.38394i	0.203496	+	0.626297i	−0.796275	+	0.604934i	$0.793199\pi$
$140$	11.2812	+	8.19624i	0.953431	+	0.692708i
$141$	6.73607	−	20.7315i	0.567279	−	1.74591i
$142$	−3.92705	−	2.85317i	−0.329551	−	0.239433i
$143$	−4.23607			−0.354238
$144$	−5.78115	−	4.20025i	−0.481763	−	0.350021i
$145$		0			0
$146$	−1.35410	+	0.983813i	−0.112066	+	0.0814209i
$147$	16.6353	−	12.0862i	1.37205	−	0.996855i
$148$	4.42705	+	13.6251i	0.363901	+	1.11997i
$149$	−2.76393			−0.226430			−0.113215	−	0.993571i	$-0.536115\pi$
$149$	−2.76393			−0.226430			−0.113215	+	0.993571i	$0.536115\pi$
$150$	−8.09017			−0.660560
$151$	−8.32624			−0.677580			−0.338790	−	0.940862i	$-0.610018\pi$
$151$	−8.32624			−0.677580			−0.338790	+	0.940862i	$0.610018\pi$
$152$	3.45492	+	10.6331i	0.280231	+	0.862461i
$153$	2.38197	−	1.73060i	0.192571	−	0.139911i
$154$	8.16312	−	5.93085i	0.657803	−	0.477922i
$155$	−0.791796	+	2.43690i	−0.0635986	+	0.195736i
$156$	3.42705	+	2.48990i	0.274384	+	0.199351i
$157$	14.5623			1.16220			0.581099	−	0.813833i	$-0.302623\pi$
$157$	14.5623			1.16220			0.581099	+	0.813833i	$0.302623\pi$
$158$	−2.07295	−	1.50609i	−0.164915	−	0.119818i
$159$	−7.78115	+	23.9479i	−0.617086	+	1.89919i
$160$	−3.88197	−	11.9475i	−0.306896	−	0.944530i
$161$	8.44427	+	25.9888i	0.665502	+	2.04820i
$162$	−1.09017	+	3.35520i	−0.0856518	+	0.263609i
$163$	−6.66312	+	20.5070i	−0.521896	+	1.60623i	0.248478	+	0.968638i	$0.420070\pi$
$163$	−6.66312	+	20.5070i	−0.521896	+	1.60623i	−0.770374	+	0.637592i	$0.779930\pi$
$164$	−1.69098	−	5.20431i	−0.132044	−	0.406388i
$165$	7.66312	−	23.5847i	0.596573	−	1.83606i
$166$	3.28115	−	10.0984i	0.254667	−	0.783784i
$167$	−11.7812	−	8.55951i	−0.911653	−	0.662355i	0.0297794	−	0.999556i	$-0.490520\pi$
$167$	−11.7812	−	8.55951i	−0.911653	−	0.662355i	−0.941432	+	0.337202i	$0.890520\pi$
$168$	−22.5623			−1.74072
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	1.05573			0.0809706
$171$	15.5902	−	11.3269i	1.19221	−	0.866191i
$172$	7.16312	−	5.20431i	0.546183	−	0.396825i
$173$	−3.63525	−	11.1882i	−0.276383	−	0.850620i	−0.988850	−	0.148915i	$-0.952422\pi$
$173$	−3.63525	−	11.1882i	−0.276383	−	0.850620i	0.712467	−	0.701706i	$-0.247578\pi$
$174$		0			0
$175$	15.5902	−	11.3269i	1.17851	−	0.856235i
$176$	7.85410			0.592025
$177$	1.80902	+	5.56758i	0.135974	+	0.418485i
$178$	5.59017	−	4.06150i	0.419001	−	0.304422i
$179$	6.70820	−	4.87380i	0.501395	−	0.364285i	−0.308155	−	0.951336i	$-0.599711\pi$
$179$	6.70820	−	4.87380i	0.501395	−	0.364285i	0.809549	+	0.587052i	$0.199711\pi$
$180$	−11.2812	+	8.19624i	−0.840847	+	0.610911i
$181$	12.5902	+	9.14729i	0.935820	+	0.679913i	0.947411	−	0.320020i	$-0.103690\pi$
$181$	12.5902	+	9.14729i	0.935820	+	0.679913i	−0.0115909	+	0.999933i	$0.503690\pi$
$182$	2.38197			0.176563
$183$	29.0344	+	21.0948i	2.14629	+	1.55937i
$184$	4.89919	−	15.0781i	0.361173	−	1.11158i
$185$	19.7984			1.45561
$186$	−0.572949	−	1.76336i	−0.0420107	−	0.129296i
$187$	−1.00000	+	3.07768i	−0.0731272	+	0.225063i
$188$	4.16312	−	12.8128i	0.303627	−	0.934467i
$189$	2.66312	+	8.19624i	0.193713	+	0.596189i
$190$	6.90983			0.501292
$191$	6.10739	−	18.7966i	0.441915	−	1.36008i	−0.443916	−	0.896068i	$-0.646411\pi$
$191$	6.10739	−	18.7966i	0.441915	−	1.36008i	0.885831	−	0.464007i	$-0.153589\pi$
$192$	−0.500000	−	0.363271i	−0.0360844	−	0.0262168i
$193$	−14.1246			−1.01671			−0.508356	−	0.861147i	$-0.669747\pi$
$193$	−14.1246			−1.01671			−0.508356	+	0.861147i	$0.669747\pi$
$194$	−4.19098	−	3.04493i	−0.300895	−	0.218613i
$195$	4.73607	−	3.44095i	0.339157	−	0.246412i
$196$	10.2812	−	7.46969i	0.734368	−	0.533550i
$197$	−4.11803	+	2.99193i	−0.293398	+	0.213166i	−0.724740	−	0.689022i	$-0.758040\pi$
$197$	−4.11803	+	2.99193i	−0.293398	+	0.213166i	0.431342	+	0.902188i	$0.358040\pi$
$198$	3.11803	+	9.59632i	0.221589	+	0.681981i
$199$	−2.56231			−0.181637			−0.0908185	−	0.995867i	$-0.528948\pi$
$199$	−2.56231			−0.181637			−0.0908185	+	0.995867i	$0.528948\pi$
$200$	−11.1803			−0.790569
$201$	−19.1803			−1.35288
$202$	0.708204	+	2.17963i	0.0498291	+	0.153358i
$203$		0			0
$204$	2.61803	−	1.90211i	0.183299	−	0.133175i
$205$	−7.56231			−0.528174
$206$	−3.69098	−	2.68166i	−0.257163	−	0.186840i
$207$	−27.3262			−1.89930
$208$	1.50000	+	1.08981i	0.104006	+	0.0755650i
$209$	−6.54508	+	20.1437i	−0.452733	+	1.39337i
$210$	−4.30902	+	13.2618i	−0.297350	+	0.915150i
$211$	−3.79180	−	11.6699i	−0.261038	−	0.803392i	−0.992580	−	0.121596i	$-0.961199\pi$
$211$	−3.79180	−	11.6699i	−0.261038	−	0.803392i	0.731542	−	0.681797i	$-0.238801\pi$
$212$	−4.80902	+	14.8006i	−0.330285	+	1.01651i
$213$	−6.35410	+	19.5559i	−0.435376	+	1.33995i
$214$	−2.05573	−	6.32688i	−0.140527	−	0.432497i
$215$	−3.78115	−	11.6372i	−0.257872	−	0.793650i
$216$	1.54508	−	4.75528i	0.105130	−	0.323556i
$217$	3.57295	+	2.59590i	0.242548	+	0.176221i
$218$	8.29180			0.561591
$219$	5.73607	+	4.16750i	0.387608	+	0.281613i
$220$	4.73607	−	14.5761i	0.319306	−	0.982722i
$221$	−0.618034	+	0.449028i	−0.0415735	+	0.0302049i
$222$	−11.5902	+	8.42075i	−0.777881	+	0.565164i
$223$	−5.80902	−	17.8783i	−0.389001	−	1.19722i	−0.933536	−	0.358483i	$-0.883294\pi$
$223$	−5.80902	−	17.8783i	−0.389001	−	1.19722i	0.544536	−	0.838738i	$-0.316706\pi$
$224$	−21.6525			−1.44672
$225$	5.95492	+	18.3273i	0.396994	+	1.22182i
$226$	5.29180			0.352005
$227$	4.50000	+	13.8496i	0.298675	+	0.919229i	0.981962	+	0.189078i	$0.0605500\pi$
$227$	4.50000	+	13.8496i	0.298675	+	0.919229i	−0.683287	+	0.730150i	$0.739450\pi$
$228$	17.1353	−	12.4495i	1.13481	−	0.824488i
$229$	−12.2361	+	8.89002i	−0.808582	+	0.587469i	−0.913419	−	0.407020i	$-0.866568\pi$
$229$	−12.2361	+	8.89002i	−0.808582	+	0.587469i	0.104837	+	0.994489i	$0.466568\pi$
$230$	−7.92705	−	5.75934i	−0.522694	−	0.379760i
$231$	−34.5795	−	25.1235i	−2.27517	−	1.65300i
$232$		0			0
$233$	11.4271	+	8.30224i	0.748611	+	0.543898i	0.895396	−	0.445271i	$-0.146893\pi$
$233$	11.4271	+	8.30224i	0.748611	+	0.543898i	−0.146785	+	0.989168i	$0.546893\pi$
$234$	−0.736068	+	2.26538i	−0.0481183	+	0.148093i
$235$	−15.0623	−	10.9434i	−0.982556	−	0.713869i
$236$	1.11803	+	3.44095i	0.0727778	+	0.223987i
$237$	−3.35410	+	10.3229i	−0.217872	+	0.670542i
$238$	0.562306	−	1.73060i	0.0364489	−	0.112178i
$239$	−5.91641	−	18.2088i	−0.382701	−	1.17783i	−0.938135	−	0.346271i	$-0.887448\pi$
$239$	−5.91641	−	18.2088i	−0.382701	−	1.17783i	0.555434	−	0.831561i	$-0.312552\pi$
$240$	−8.78115	+	6.37988i	−0.566821	+	0.411820i
$241$	−7.63525	+	23.4989i	−0.491830	+	1.51370i	0.330009	+	0.943978i	$0.392948\pi$
$241$	−7.63525	+	23.4989i	−0.491830	+	1.51370i	−0.821839	+	0.569719i	$0.807052\pi$
$242$	−3.47214	−	2.52265i	−0.223197	−	0.162162i
$243$	21.6525			1.38901
$244$	17.9443	+	13.0373i	1.14876	+	0.834626i
$245$	−5.42705	−	16.7027i	−0.346722	−	1.06710i
$246$	4.42705	−	3.21644i	0.282258	−	0.205073i
$247$	−4.04508	+	2.93893i	−0.257383	+	0.186999i
$248$	−0.791796	−	2.43690i	−0.0502791	−	0.154743i
$249$	−44.9787			−2.85041
$250$	−2.13525	+	6.57164i	−0.135045	+	0.415627i
$251$	−9.38197			−0.592184			−0.296092	−	0.955159i	$-0.595684\pi$
$251$	−9.38197			−0.592184			−0.296092	+	0.955159i	$0.595684\pi$
$252$	7.42705	+	22.8581i	0.467860	+	1.43993i
$253$	24.2984	−	17.6538i	1.52763	−	1.10989i
$254$	7.78115	−	5.65334i	0.488233	−	0.354722i
$255$	−1.38197	−	4.25325i	−0.0865421	−	0.266349i
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	17.1246			1.06820			0.534102	−	0.845420i	$-0.320650\pi$
$257$	17.1246			1.06820			0.534102	+	0.845420i	$0.320650\pi$
$258$	7.16312	+	5.20431i	0.445956	+	0.324006i
$259$	10.5451	−	32.4544i	0.655240	−	2.01662i
$260$	2.92705	−	2.12663i	0.181528	−	0.131888i
$261$		0			0
$262$	−1.32624	+	4.08174i	−0.0819353	+	0.252171i
$263$	−4.42705	+	13.6251i	−0.272984	+	0.840157i	0.716762	+	0.697318i	$0.245623\pi$
$263$	−4.42705	+	13.6251i	−0.272984	+	0.840157i	−0.989746	+	0.142840i	$0.954377\pi$
$264$	7.66312	+	23.5847i	0.471632	+	1.45154i
$265$	17.3992	+	12.6412i	1.06882	+	0.776546i
$266$	3.68034	−	11.3269i	0.225656	−	0.694498i
$267$	−23.6803	−	17.2048i	−1.44921	−	1.05292i
$268$	−11.8541			−0.724105
$269$	−9.04508	−	6.57164i	−0.551489	−	0.400680i	0.276845	−	0.960914i	$-0.410711\pi$
$269$	−9.04508	−	6.57164i	−0.551489	−	0.400680i	−0.828334	+	0.560235i	$0.810711\pi$
$270$	−2.50000	−	1.81636i	−0.152145	−	0.110540i
$271$	9.92705	−	7.21242i	0.603025	−	0.438124i	−0.243926	−	0.969794i	$-0.578435\pi$
$271$	9.92705	−	7.21242i	0.603025	−	0.438124i	0.846951	+	0.531670i	$0.178435\pi$
$272$	1.14590	−	0.832544i	0.0694803	−	0.0504804i
$273$	−3.11803	−	9.59632i	−0.188712	−	0.580796i
$274$	9.20163			0.555891
$275$	−17.1353	−	12.4495i	−1.03329	−	0.750733i
$276$	−30.0344			−1.80786
$277$	8.87132	+	27.3031i	0.533026	+	1.64049i	0.747876	+	0.663839i	$0.231074\pi$
$277$	8.87132	+	27.3031i	0.533026	+	1.64049i	−0.214850	+	0.976647i	$0.568926\pi$
$278$	−3.88197	+	2.82041i	−0.232825	+	0.169157i
$279$	−3.57295	+	2.59590i	−0.213907	+	0.155412i
$280$	−5.95492	+	18.3273i	−0.355874	+	1.09527i
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	0.903939	−	0.427661i	$-0.140662\pi$
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	−0.127397	+	0.991852i	$0.540662\pi$
$282$	13.4721			0.802254
$283$	−1.33688	−	0.971301i	−0.0794693	−	0.0577378i	0.547341	−	0.836910i	$-0.315640\pi$
$283$	−1.33688	−	0.971301i	−0.0794693	−	0.0577378i	−0.626811	+	0.779172i	$0.715640\pi$
$284$	−3.92705	+	12.0862i	−0.233028	+	0.717185i
$285$	−9.04508	−	27.8379i	−0.535785	−	1.64898i
$286$	−0.809017	−	2.48990i	−0.0478382	−	0.147231i
$287$	−4.02786	+	12.3965i	−0.237757	+	0.731742i
$288$	6.69098	−	20.5927i	0.394270	−	1.21344i
$289$	−5.07295	−	15.6129i	−0.298409	−	0.918408i
$290$		0			0
$291$	−6.78115	+	20.8702i	−0.397518	+	1.22344i
$292$	3.54508	+	2.57565i	0.207460	+	0.150729i
$293$	19.4164			1.13432			0.567159	−	0.823608i	$-0.308042\pi$
$293$	19.4164			1.13432			0.567159	+	0.823608i	$0.308042\pi$
$294$	10.2812	+	7.46969i	0.599609	+	0.435641i
$295$	5.00000			0.291111
$296$	−16.0172	+	11.6372i	−0.930982	+	0.676398i
$297$	7.66312	−	5.56758i	0.444659	−	0.323064i
$298$	−0.527864	−	1.62460i	−0.0305783	−	0.0941105i
$299$	7.09017			0.410035
$300$	6.54508	+	20.1437i	0.377881	+	1.16300i
$301$	−21.0902			−1.21562
$302$	−1.59017	−	4.89404i	−0.0915040	−	0.281620i
$303$	7.85410	−	5.70634i	0.451206	−	0.327821i
$304$	7.50000	−	5.44907i	0.430155	−	0.312526i
$305$	24.7984	−	18.0171i	1.41995	−	1.03165i
$306$	1.47214	+	1.06957i	0.0841564	+	0.0611432i
$307$	12.1246			0.691988			0.345994	−	0.938237i	$-0.387542\pi$
$307$	12.1246			0.691988			0.345994	+	0.938237i	$0.387542\pi$
$308$	−21.3713	−	15.5272i	−1.21774	−	0.884743i
$309$	−5.97214	+	18.3803i	−0.339743	+	1.04562i
$310$	−1.58359			−0.0899420
$311$	2.48936	+	7.66145i	0.141158	+	0.434441i	0.996497	−	0.0836284i	$-0.0266509\pi$
$311$	2.48936	+	7.66145i	0.141158	+	0.434441i	−0.855339	+	0.518069i	$0.826651\pi$
$312$	−1.80902	+	5.56758i	−0.102415	+	0.315202i
$313$	1.79180	−	5.51458i	0.101278	−	0.311703i	−0.887561	−	0.460691i	$-0.847602\pi$
$313$	1.79180	−	5.51458i	0.101278	−	0.311703i	0.988839	+	0.148988i	$0.0476017\pi$
$314$	2.78115	+	8.55951i	0.156950	+	0.483041i
$315$	33.2148			1.87144
$316$	−2.07295	+	6.37988i	−0.116612	+	0.358896i
$317$	9.13525	+	6.63715i	0.513087	+	0.372780i	0.813993	−	0.580874i	$-0.197289\pi$
$317$	9.13525	+	6.63715i	0.513087	+	0.372780i	−0.300906	+	0.953654i	$0.597289\pi$
$318$	−15.5623			−0.872691
$319$		0			0
$320$	−0.427051	+	0.310271i	−0.0238729	+	0.0173447i
$321$	−22.7984	+	16.5640i	−1.27248	+	0.924512i
$322$	−13.6631	+	9.92684i	−0.761416	+	0.553201i
$323$	1.18034	+	3.63271i	0.0656759	+	0.202130i
$324$	9.23607			0.513115
$325$	−1.54508	−	4.75528i	−0.0857059	−	0.263776i
$326$	−13.3262			−0.738072
$327$	−10.8541	−	33.4055i	−0.600233	−	1.84733i
$328$	6.11803	−	4.44501i	0.337812	−	0.245435i
$329$	−25.9615	+	18.8621i	−1.43130	+	1.03990i
$330$	15.3262			0.843682
$331$	−26.1525	−	19.0009i	−1.43747	−	1.04438i	−0.988564	−	0.150804i	$-0.951814\pi$
$331$	−26.1525	−	19.0009i	−1.43747	−	1.04438i	−0.448906	−	0.893579i	$-0.648186\pi$
$332$	−27.7984			−1.52563
$333$	27.6074	+	20.0579i	1.51288	+	1.09917i
$334$	2.78115	−	8.55951i	0.152178	−	0.468355i
$335$	−5.06231	+	15.5802i	−0.276583	+	0.851236i
$336$	5.78115	+	17.7926i	0.315388	+	0.970664i
$337$	−4.90983	+	15.1109i	−0.267455	+	0.823143i	0.723662	+	0.690155i	$0.242457\pi$
$337$	−4.90983	+	15.1109i	−0.267455	+	0.823143i	−0.991118	+	0.132989i	$0.957543\pi$
$338$	0.190983	−	0.587785i	0.0103881	−	0.0319713i
$339$	−6.92705	−	21.3193i	−0.376226	−	1.15790i
$340$	−0.854102	−	2.62866i	−0.0463202	−	0.142559i
$341$	1.50000	−	4.61653i	0.0812296	−	0.249999i
$342$	9.63525	+	7.00042i	0.521015	+	0.378539i
$343$	−3.29180			−0.177740
$344$	9.89919	+	7.19218i	0.533728	+	0.387776i
$345$	−12.8262	+	39.4751i	−0.690541	+	2.12527i
$346$	5.88197	−	4.27350i	0.316216	−	0.229745i
$347$	−6.51722	+	4.73504i	−0.349863	+	0.254190i	−0.748811	−	0.662783i	$-0.769375\pi$
$347$	−6.51722	+	4.73504i	−0.349863	+	0.254190i	0.398949	+	0.916973i	$0.369375\pi$
$348$		0			0
$349$	17.7639			0.950881			0.475441	−	0.879748i	$-0.342289\pi$
$349$	17.7639			0.950881			0.475441	+	0.879748i	$0.342289\pi$
$350$	9.63525	+	7.00042i	0.515026	+	0.374188i
$351$	2.23607			0.119352
$352$	7.35410	+	22.6336i	0.391975	+	1.20637i
$353$	14.2533	−	10.3556i	0.758626	−	0.551174i	−0.139863	−	0.990171i	$-0.544666\pi$
$353$	14.2533	−	10.3556i	0.758626	−	0.551174i	0.898489	+	0.438997i	$0.144666\pi$
$354$	−2.92705	+	2.12663i	−0.155571	+	0.113029i
$355$	14.2082	+	10.3229i	0.754093	+	0.547881i
$356$	−14.6353	−	10.6331i	−0.775667	−	0.563555i
$357$	−7.70820			−0.407961
$358$	4.14590	+	3.01217i	0.219118	+	0.159198i
$359$	−4.30902	+	13.2618i	−0.227421	+	0.699931i	0.770616	+	0.637300i	$0.219949\pi$
$359$	−4.30902	+	13.2618i	−0.227421	+	0.699931i	−0.998037	+	0.0626303i	$0.980051\pi$
$360$	−15.5902	−	11.3269i	−0.821674	−	0.596981i
$361$	1.85410	+	5.70634i	0.0975843	+	0.300334i
$362$	−2.97214	+	9.14729i	−0.156212	+	0.480771i
$363$	−5.61803	+	17.2905i	−0.294870	+	0.907518i
$364$	−1.92705	−	5.93085i	−0.101005	−	0.310861i
$365$	4.89919	−	3.55947i	0.256435	−	0.186311i
$366$	−6.85410	+	21.0948i	−0.358270	+	1.10264i
$367$	27.6525	+	20.0907i	1.44345	+	1.04873i	0.987308	+	0.158818i	$0.0507682\pi$
$367$	27.6525	+	20.0907i	1.44345	+	1.04873i	0.456140	+	0.889908i	$0.349232\pi$
$368$	−13.1459			−0.685277
$369$	−10.5451	−	7.66145i	−0.548955	−	0.398839i
$370$	3.78115	+	11.6372i	0.196573	+	0.604989i
$371$	29.9894	−	21.7885i	1.55697	−	1.13120i
$372$	−3.92705	+	2.85317i	−0.203608	+	0.147930i
$373$	−3.24671	−	9.99235i	−0.168108	−	0.517384i	0.831144	−	0.556058i	$-0.187687\pi$
$373$	−3.24671	−	9.99235i	−0.168108	−	0.517384i	−0.999252	+	0.0386737i	$0.987687\pi$
$374$	−2.00000			−0.103418
$375$	29.2705			1.51152
$376$	18.6180			0.960152
$377$		0			0
$378$	−4.30902	+	3.13068i	−0.221632	+	0.161025i
$379$	26.3435	−	19.1396i	1.35317	−	0.983137i	0.354326	−	0.935122i	$-0.384710\pi$
$379$	26.3435	−	19.1396i	1.35317	−	0.983137i	0.998847	−	0.0480155i	$-0.0152897\pi$
$380$	−5.59017	−	17.2048i	−0.286770	−	0.882586i
$381$	−32.9615	−	23.9479i	−1.68867	−	1.22689i
$382$	12.2148			0.624963
$383$	5.14590	+	3.73871i	0.262943	+	0.191039i	0.711444	−	0.702743i	$-0.248042\pi$
$383$	5.14590	+	3.73871i	0.262943	+	0.191039i	−0.448500	+	0.893783i	$0.648042\pi$
$384$	9.20820	−	28.3399i	0.469904	−	1.44622i
$385$	−29.5344	+	21.4580i	−1.50521	+	1.09360i
$386$	−2.69756	−	8.30224i	−0.137302	−	0.422573i
$387$	6.51722	−	20.0579i	0.331289	−	1.01960i
$388$	−4.19098	+	12.8985i	−0.212765	+	0.654823i
$389$	−2.72542	−	8.38800i	−0.138185	−	0.425288i	0.857887	−	0.513838i	$-0.171777\pi$
$389$	−2.72542	−	8.38800i	−0.138185	−	0.425288i	−0.996072	+	0.0885498i	$0.971777\pi$
$390$	2.92705	+	2.12663i	0.148217	+	0.107686i
$391$	1.67376	−	5.15131i	0.0846458	−	0.260513i
$392$	14.2082	+	10.3229i	0.717623	+	0.521383i
$393$	18.1803			0.917077
$394$	−2.54508	−	1.84911i	−0.128220	−	0.0931569i
$395$	7.50000	+	5.44907i	0.377366	+	0.274172i
$396$	21.3713	−	15.5272i	1.07395	−	0.780270i
$397$	2.85410	−	2.07363i	0.143243	−	0.104072i	−0.513856	−	0.857877i	$-0.671783\pi$
$397$	2.85410	−	2.07363i	0.143243	−	0.104072i	0.657099	+	0.753804i	$0.271783\pi$
$398$	−0.489357	−	1.50609i	−0.0245292	−	0.0754933i
$399$	−50.4508			−2.52570
$400$	2.86475	+	8.81678i	0.143237	+	0.440839i
$401$	11.4721			0.572891			0.286446	−	0.958097i	$-0.407526\pi$
$401$	11.4721			0.572891			0.286446	+	0.958097i	$0.407526\pi$
$402$	−3.66312	−	11.2739i	−0.182700	−	0.562292i
$403$	0.927051	−	0.673542i	0.0461797	−	0.0335515i
$404$	4.85410	−	3.52671i	0.241501	−	0.175460i
$405$	3.94427	−	12.1392i	0.195992	−	0.603203i
$406$		0			0
$407$	−37.5066			−1.85913
$408$	3.61803	+	2.62866i	0.179119	+	0.130138i
$409$	−2.56231	+	7.88597i	−0.126698	+	0.389936i	−0.994207	−	0.107486i	$-0.965720\pi$
$409$	−2.56231	+	7.88597i	−0.126698	+	0.389936i	0.867509	+	0.497422i	$0.165720\pi$
$410$	−1.44427	−	4.44501i	−0.0713275	−	0.219523i
$411$	−12.0451	−	37.0710i	−0.594140	−	1.82858i
$412$	−3.69098	+	11.3597i	−0.181842	+	0.559651i
$413$	2.66312	−	8.19624i	0.131044	−	0.403310i
$414$	−5.21885	−	16.0620i	−0.256492	−	0.789402i
$415$	−11.8713	+	36.5362i	−0.582740	+	1.79349i
$416$	−1.73607	+	5.34307i	−0.0851177	+	0.261965i
$417$	16.4443	+	11.9475i	0.805279	+	0.585070i
$418$	−13.0902			−0.640261
$419$	−15.7533	−	11.4454i	−0.769599	−	0.559146i	0.132241	−	0.991218i	$-0.457783\pi$
$419$	−15.7533	−	11.4454i	−0.769599	−	0.559146i	−0.901839	+	0.432072i	$0.857783\pi$
$420$	36.5066			1.78134
$421$	3.01722	−	2.19214i	0.147050	−	0.106838i	−0.511828	−	0.859088i	$-0.671031\pi$
$421$	3.01722	−	2.19214i	0.147050	−	0.106838i	0.658878	+	0.752250i	$0.271031\pi$
$422$	6.13525	−	4.45752i	0.298660	−	0.216989i
$423$	−9.91641	−	30.5196i	−0.482152	−	1.48391i
$424$	−21.5066			−1.04445
$425$	−3.81966			−0.185281
$426$	−12.7082			−0.615714
$427$	−16.3262	−	50.2470i	−0.790082	−	2.43162i
$428$	−14.0902	+	10.2371i	−0.681074	+	0.494829i
$429$	−8.97214	+	6.51864i	−0.433179	+	0.314723i
$430$	6.11803	−	4.44501i	0.295038	−	0.214358i
$431$	−8.85410	−	6.43288i	−0.426487	−	0.309861i	0.353756	−	0.935338i	$-0.384904\pi$
$431$	−8.85410	−	6.43288i	−0.426487	−	0.309861i	−0.780243	+	0.625477i	$0.784904\pi$
$432$	−4.14590			−0.199470
$433$	−11.5000	−	8.35524i	−0.552655	−	0.401527i	0.276109	−	0.961126i	$-0.410955\pi$
$433$	−11.5000	−	8.35524i	−0.552655	−	0.401527i	−0.828763	+	0.559599i	$0.810955\pi$
$434$	−0.843459	+	2.59590i	−0.0404873	+	0.124607i
$435$		0			0
$436$	−6.70820	−	20.6457i	−0.321265	−	0.988751i
$437$	10.9549	−	33.7158i	0.524045	−	1.61284i
$438$	−1.35410	+	4.16750i	−0.0647015	+	0.199131i
$439$	0.263932	+	0.812299i	0.0125968	+	0.0387689i	0.957157	−	0.289568i	$-0.0935117\pi$
$439$	0.263932	+	0.812299i	0.0125968	+	0.0387689i	−0.944561	+	0.328337i	$0.893512\pi$
$440$	21.1803			1.00973
$441$	9.35410	−	28.7890i	0.445433	−	1.37090i
$442$	−0.381966	−	0.277515i	−0.0181683	−	0.0132000i
$443$	−31.0344			−1.47449			−0.737245	−	0.675625i	$-0.763874\pi$
$443$	−31.0344			−1.47449			−0.737245	+	0.675625i	$0.763874\pi$
$444$	30.3435	+	22.0458i	1.44004	+	1.04625i
$445$	−20.2254	+	14.6946i	−0.958777	+	0.696592i
$446$	9.39919	−	6.82891i	0.445064	−	0.323358i
$447$	−5.85410	+	4.25325i	−0.276890	+	0.201172i
$448$	0.281153	+	0.865300i	0.0132832	+	0.0408816i
$449$	35.1246			1.65763			0.828816	−	0.559521i	$-0.189015\pi$
$449$	35.1246			1.65763			0.828816	+	0.559521i	$0.189015\pi$
$450$	−9.63525	+	7.00042i	−0.454210	+	0.330003i
$451$	14.3262			0.674596
$452$	−4.28115	−	13.1760i	−0.201368	−	0.619749i
$453$	−17.6353	+	12.8128i	−0.828577	+	0.601996i
$454$	−7.28115	+	5.29007i	−0.341721	+	0.248275i
$455$	−8.61803			−0.404020
$456$	23.6803	+	17.2048i	1.10893	+	0.805687i
$457$	−5.76393			−0.269625			−0.134813	−	0.990871i	$-0.543043\pi$
$457$	−5.76393			−0.269625			−0.134813	+	0.990871i	$0.543043\pi$
$458$	−7.56231	−	5.49434i	−0.353363	−	0.256734i
$459$	0.527864	−	1.62460i	0.0246386	−	0.0758298i
$460$	−7.92705	+	24.3970i	−0.369601	+	1.13751i
$461$	9.43769	+	29.0462i	0.439557	+	1.35282i	0.888344	+	0.459179i	$0.151856\pi$
$461$	9.43769	+	29.0462i	0.439557	+	1.35282i	−0.448786	+	0.893639i	$0.648144\pi$
$462$	8.16312	−	25.1235i	0.379783	−	1.16885i
$463$	8.56231	−	26.3521i	0.397924	−	1.22468i	−0.528737	−	0.848786i	$-0.677334\pi$
$463$	8.56231	−	26.3521i	0.397924	−	1.22468i	0.926661	−	0.375899i	$-0.122666\pi$
$464$		0			0
$465$	2.07295	+	6.37988i	0.0961307	+	0.295860i
$466$	−2.69756	+	8.30224i	−0.124962	+	0.384594i
$467$	25.4164	+	18.4661i	1.17613	+	0.854509i	0.991730	−	0.128342i	$-0.0409655\pi$
$467$	25.4164	+	18.4661i	1.17613	+	0.854509i	0.184401	+	0.982851i	$0.440965\pi$
$468$	6.23607			0.288262
$469$	22.8435	+	16.5967i	1.05481	+	0.766366i
$470$	3.55573	−	10.9434i	0.164014	−	0.504782i
$471$	30.8435	−	22.4091i	1.42119	−	1.03256i
$472$	−4.04508	+	2.93893i	−0.186190	+	0.135275i
$473$	7.16312	+	22.0458i	0.329361	+	1.01367i
$474$	−6.70820			−0.308118
$475$	−25.0000			−1.14708
$476$	−4.76393			−0.218354
$477$	11.4549	+	35.2546i	0.524485	+	1.61420i
$478$	9.57295	−	6.95515i	0.437856	−	0.318121i
$479$	−8.35410	+	6.06961i	−0.381709	+	0.277328i	−0.762049	−	0.647519i	$-0.775807\pi$
$479$	−8.35410	+	6.06961i	−0.381709	+	0.277328i	0.380341	+	0.924846i	$0.375807\pi$
$480$	−26.6074	−	19.3314i	−1.21446	−	0.882354i
$481$	−7.16312	−	5.20431i	−0.326610	−	0.237296i
$482$	−15.2705			−0.695553
$483$	57.8779	+	42.0508i	2.63354	+	1.91338i
$484$	−3.47214	+	10.6861i	−0.157824	+	0.485733i
$485$	15.1631	+	11.0167i	0.688522	+	0.500240i
$486$	4.13525	+	12.7270i	0.187579	+	0.577309i
$487$	4.01064	−	12.3435i	0.181740	−	0.559337i	−0.818137	−	0.575023i	$-0.804993\pi$
$487$	4.01064	−	12.3435i	0.181740	−	0.559337i	0.999877	+	0.0156859i	$0.00499317\pi$
$488$	−9.47214	+	29.1522i	−0.428783	+	1.31966i
$489$	17.4443	+	53.6879i	0.788857	+	2.42785i
$490$	8.78115	−	6.37988i	0.396692	−	0.288214i
$491$	−1.29180	+	3.97574i	−0.0582979	+	0.179423i	−0.975965	−	0.217928i	$-0.930070\pi$
$491$	−1.29180	+	3.97574i	−0.0582979	+	0.179423i	0.917667	+	0.397350i	$0.130070\pi$
$492$	−11.5902	−	8.42075i	−0.522525	−	0.379637i
$493$		0			0
$494$	−2.50000	−	1.81636i	−0.112480	−	0.0817217i
$495$	−11.2812	−	34.7198i	−0.507050	−	1.56054i
$496$	−1.71885	+	1.24882i	−0.0771785	+	0.0560735i
$497$	24.4894	−	17.7926i	1.09850	−	0.798105i
$498$	−8.59017	−	26.4378i	−0.384935	−	1.18471i
$499$	−23.5410			−1.05384			−0.526920	−	0.849915i	$-0.676653\pi$
$499$	−23.5410			−1.05384			−0.526920	+	0.849915i	$0.676653\pi$
$500$	18.0902			0.809017
$501$	−38.1246			−1.70328
$502$	−1.79180	−	5.51458i	−0.0799718	−	0.246128i
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	−0.402526	−	0.915409i	$-0.631868\pi$
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	0.746218	+	0.665702i	$0.231868\pi$
$504$	−26.8713	+	19.5232i	−1.19694	+	0.869631i
$505$	−2.56231	−	7.88597i	−0.114021	−	0.350921i
$506$	15.0172	+	10.9106i	0.667597	+	0.485038i
$507$	−2.61803			−0.116271
$508$	−20.3713	−	14.8006i	−0.903831	−	0.656672i
$509$	4.83688	−	14.8864i	0.214391	−	0.659828i	−0.784805	−	0.619742i	$-0.787237\pi$
$509$	4.83688	−	14.8864i	0.214391	−	0.659828i	0.999196	−	0.0400852i	$-0.0127629\pi$
$510$	2.23607	−	1.62460i	0.0990148	−	0.0719384i
$511$	−3.22542	−	9.92684i	−0.142684	−	0.439137i
$512$	5.78115	−	17.7926i	0.255493	−	0.786327i
$513$	3.45492	−	10.6331i	0.152538	−	0.469464i
$514$	3.27051	+	10.0656i	0.144256	+	0.443974i
$515$	13.3541	+	9.70232i	0.588452	+	0.427535i
$516$	7.16312	−	22.0458i	0.315339	−	0.970513i
$517$	28.5344	+	20.7315i	1.25494	+	0.911770i
$518$	21.0902			0.926649
$519$	−24.9164	−	18.1028i	−1.09371	−	0.794626i
$520$	4.04508	+	2.93893i	0.177389	+	0.128880i
$521$	−14.1180	+	10.2574i	−0.618522	+	0.449383i	−0.852405	−	0.522882i	$-0.824857\pi$
$521$	−14.1180	+	10.2574i	−0.618522	+	0.449383i	0.233883	+	0.972265i	$0.424857\pi$
$522$		0			0
$523$	−3.04508	−	9.37181i	−0.133152	−	0.409801i	0.862146	−	0.506660i	$-0.169120\pi$
$523$	−3.04508	−	9.37181i	−0.133152	−	0.409801i	−0.995298	+	0.0968598i	$0.969120\pi$
$524$	11.2361			0.490850
$525$	15.5902	−	47.9816i	0.680411	−	2.09409i
$526$	−8.85410			−0.386057
$527$	−0.270510	−	0.832544i	−0.0117836	−	0.0362662i
$528$	16.6353	−	12.0862i	0.723957	−	0.525985i
$529$	−22.0623	+	16.0292i	−0.959231	+	0.696922i
$530$	−4.10739	+	12.6412i	−0.178414	+	0.549101i
$531$	6.97214	+	5.06555i	0.302565	+	0.219826i
$532$	−31.1803			−1.35184
$533$	2.73607	+	1.98787i	0.118512	+	0.0861042i
$534$	5.59017	−	17.2048i	0.241910	−	0.744523i
$535$	7.43769	+	22.8909i	0.321560	+	0.989659i
$536$	−5.06231	−	15.5802i	−0.218658	−	0.672961i
$537$	6.70820	−	20.6457i	0.289480	−	0.890929i
$538$	2.13525	−	6.57164i	0.0920574	−	0.283323i
$539$	10.2812	+	31.6421i	0.442841	+	1.36292i
$540$	−2.50000	+	7.69421i	−0.107583	+	0.331106i
$541$	8.87132	−	27.3031i	0.381408	−	1.17385i	−0.557645	−	0.830080i	$-0.688295\pi$
$541$	8.87132	−	27.3031i	0.381408	−	1.17385i	0.939053	−	0.343773i	$-0.111705\pi$
$542$	6.13525	+	4.45752i	0.263532	+	0.191467i
$543$	40.7426			1.74843
$544$	3.47214	+	2.52265i	0.148867	+	0.108158i
$545$	−30.0000			−1.28506
$546$	5.04508	−	3.66547i	0.215910	−	0.156868i
$547$	22.0623	−	16.0292i	0.943316	−	0.685359i	−0.00590052	−	0.999983i	$-0.501878\pi$
$547$	22.0623	−	16.0292i	0.943316	−	0.685359i	0.949217	+	0.314623i	$0.101878\pi$
$548$	−7.44427	−	22.9111i	−0.318004	−	0.978714i
$549$	52.8328			2.25485
$550$	4.04508	−	12.4495i	0.172483	−	0.530848i
$551$		0			0
$552$	−12.8262	−	39.4751i	−0.545921	−	1.68017i
$553$	12.9271	−	9.39205i	0.549714	−	0.399391i
$554$	−14.3541	+	10.4289i	−0.609847	+	0.443080i
$555$	41.9336	−	30.4666i	1.77998	−	1.29323i
$556$	10.1631	+	7.38394i	0.431012	+	0.313149i
$557$	−16.7426			−0.709409			−0.354704	−	0.934979i	$-0.615418\pi$
$557$	−16.7426			−0.709409			−0.354704	+	0.934979i	$0.615418\pi$
$558$	−2.20820	−	1.60435i	−0.0934807	−	0.0679177i
$559$	−1.69098	+	5.20431i	−0.0715210	+	0.220119i
$560$	15.9787			0.675224
$561$	2.61803	+	8.05748i	0.110533	+	0.340187i
$562$	−3.07295	+	9.45756i	−0.129625	+	0.398943i
$563$	−8.79837	+	27.0786i	−0.370807	+	1.14123i	0.575457	+	0.817832i	$0.304824\pi$
$563$	−8.79837	+	27.0786i	−0.370807	+	1.14123i	−0.946264	+	0.323395i	$0.895176\pi$
$564$	−10.8992	−	33.5442i	−0.458939	−	1.41247i
$565$	−19.1459			−0.805474
$566$	0.315595	−	0.971301i	0.0132654	−	0.0408268i
$567$	−17.7984	−	12.9313i	−0.747461	−	0.543063i
$568$	−17.5623			−0.736898
$569$	−14.7361	−	10.7064i	−0.617768	−	0.448835i	0.234373	−	0.972147i	$-0.424696\pi$
$569$	−14.7361	−	10.7064i	−0.617768	−	0.448835i	−0.852141	+	0.523312i	$0.824696\pi$
$570$	14.6353	−	10.6331i	0.613003	−	0.445373i
$571$	26.6353	−	19.3516i	1.11465	−	0.809841i	0.131261	−	0.991348i	$-0.458097\pi$
$571$	26.6353	−	19.3516i	1.11465	−	0.809841i	0.983390	+	0.181507i	$0.0580974\pi$
$572$	−5.54508	+	4.02874i	−0.231852	+	0.168450i
$573$	−15.9894	−	49.2102i	−0.667965	−	2.05578i
$574$	−8.05573			−0.336240
$575$	28.6803	+	20.8375i	1.19605	+	0.868983i
$576$	−0.909830			−0.0379096
$577$	−5.33688	−	16.4252i	−0.222177	−	0.683791i	−0.998566	−	0.0535368i	$-0.982951\pi$
$577$	−5.33688	−	16.4252i	−0.222177	−	0.683791i	0.776389	−	0.630254i	$-0.217049\pi$
$578$	8.20820	−	5.96361i	0.341416	−	0.248053i
$579$	−29.9164	+	21.7355i	−1.24328	+	0.903298i
$580$		0			0
$581$	53.5689	+	38.9201i	2.22241	+	1.61468i
$582$	−13.5623			−0.562176
$583$	−32.9615	−	23.9479i	−1.36513	−	0.991822i
$584$	−1.87132	+	5.75934i	−0.0774359	+	0.238323i
$585$	2.66312	−	8.19624i	0.110106	−	0.338873i
$586$	3.70820	+	11.4127i	0.153184	+	0.471453i
$587$	−1.29180	+	3.97574i	−0.0533181	+	0.164096i	−0.974170	−	0.225817i	$-0.927495\pi$
$587$	−1.29180	+	3.97574i	−0.0533181	+	0.164096i	0.920852	+	0.389913i	$0.127495\pi$
$588$	10.2812	−	31.6421i	0.423988	−	1.30490i
$589$	−1.77051	−	5.44907i	−0.0729526	−	0.224525i
$590$	0.954915	+	2.93893i	0.0393132	+	0.120994i
$591$	−4.11803	+	12.6740i	−0.169393	+	0.521339i
$592$	13.2812	+	9.64932i	0.545852	+	0.396585i
$593$	18.2361			0.748866			0.374433	−	0.927254i	$-0.377837\pi$
$593$	18.2361			0.748866			0.374433	+	0.927254i	$0.377837\pi$
$594$	4.73607	+	3.44095i	0.194323	+	0.141184i
$595$	−2.03444	+	6.26137i	−0.0834040	+	0.256691i
$596$	−3.61803	+	2.62866i	−0.148200	+	0.107674i
$597$	−5.42705	+	3.94298i	−0.222114	+	0.161376i
$598$	1.35410	+	4.16750i	0.0553733	+	0.170422i
$599$	−8.61803			−0.352123			−0.176062	−	0.984379i	$-0.556336\pi$
$599$	−8.61803			−0.352123			−0.176062	+	0.984379i	$0.556336\pi$
$600$	−23.6803	+	17.2048i	−0.966746	+	0.702382i
$601$	−42.2705			−1.72425			−0.862125	−	0.506696i	$-0.830867\pi$
$601$	−42.2705			−1.72425			−0.862125	+	0.506696i	$0.830867\pi$
$602$	−4.02786	−	12.3965i	−0.164163	−	0.505243i
$603$	−22.8435	+	16.5967i	−0.930258	+	0.675872i
$604$	−10.8992	+	7.91872i	−0.443482	+	0.322208i
$605$	12.5623	+	9.12705i	0.510730	+	0.371067i
$606$	4.85410	+	3.52671i	0.197184	+	0.143263i
$607$	15.6180			0.633916			0.316958	−	0.948440i	$-0.397338\pi$
$607$	15.6180			0.633916			0.316958	+	0.948440i	$0.397338\pi$
$608$	22.7254	+	16.5110i	0.921638	+	0.669609i
$609$		0			0
$610$	15.3262	+	11.1352i	0.620541	+	0.450850i
$611$	2.57295	+	7.91872i	0.104090	+	0.320357i
$612$	1.47214	−	4.53077i	0.0595076	−	0.183145i
$613$	−7.41641	+	22.8254i	−0.299546	+	0.921907i	0.682111	+	0.731249i	$0.261062\pi$
$613$	−7.41641	+	22.8254i	−0.299546	+	0.921907i	−0.981656	+	0.190658i	$0.938938\pi$
$614$	2.31559	+	7.12667i	0.0934498	+	0.287609i
$615$	−16.0172	+	11.6372i	−0.645877	+	0.469257i
$616$	11.2812	−	34.7198i	0.454531	−	1.39890i
$617$	31.2705	+	22.7194i	1.25890	+	0.914647i	0.998703	−	0.0509079i	$-0.0162115\pi$
$617$	31.2705	+	22.7194i	1.25890	+	0.914647i	0.260200	+	0.965555i	$0.416212\pi$
$618$	−11.9443			−0.480469
$619$	2.23607	+	1.62460i	0.0898752	+	0.0652981i	0.631815	−	0.775119i	$-0.282310\pi$
$619$	2.23607	+	1.62460i	0.0898752	+	0.0652981i	−0.541940	+	0.840417i	$0.682310\pi$
$620$	1.28115	+	3.94298i	0.0514523	+	0.158354i
$621$	−12.8262	+	9.31881i	−0.514699	+	0.373951i
$622$	−4.02786	+	2.92641i	−0.161503	+	0.117339i
$623$	13.3156	+	40.9812i	0.533478	+	1.64188i
$624$	4.85410			0.194320
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	3.58359			0.143229
$627$	17.1353	+	52.7369i	0.684316	+	2.10611i
$628$	19.0623	−	13.8496i	0.760669	−	0.552658i
$629$	−5.47214	+	3.97574i	−0.218188	+	0.158523i
$630$	6.34346	+	19.5232i	0.252729	+	0.777821i
$631$	−7.14590	−	5.19180i	−0.284474	−	0.206682i	0.436393	−	0.899756i	$-0.356256\pi$
$631$	−7.14590	−	5.19180i	−0.284474	−	0.206682i	−0.720866	+	0.693074i	$0.756256\pi$
$632$	−9.27051			−0.368761
$633$	−25.9894	−	18.8824i	−1.03298	−	0.750507i
$634$	−2.15654	+	6.63715i	−0.0856472	+	0.263595i
$635$	−28.1525	+	20.4540i	−1.11720	+	0.811691i
$636$	12.5902	+	38.7486i	0.499233	+	1.53648i
$637$	−2.42705	+	7.46969i	−0.0961633	+	0.295960i
$638$		0			0
$639$	9.35410	+	28.7890i	0.370043	+	1.13887i
$640$	−20.5902	−	14.9596i	−0.813898	−	0.591331i
$641$	1.08359	−	3.33495i	0.0427993	−	0.131723i	−0.927374	−	0.374137i	$-0.877939\pi$
$641$	1.08359	−	3.33495i	0.0427993	−	0.131723i	0.970173	+	0.242414i	$0.0779391\pi$
$642$	−14.0902	−	10.2371i	−0.556095	−	0.404026i
$643$	−10.0557			−0.396559			−0.198280	−	0.980145i	$-0.563535\pi$
$643$	−10.0557			−0.396559			−0.198280	+	0.980145i	$0.563535\pi$
$644$	35.7705	+	25.9888i	1.40956	+	1.02410i
$645$	−25.9164	−	18.8294i	−1.02046	−	0.741406i
$646$	−1.90983	+	1.38757i	−0.0751413	+	0.0545933i
$647$	1.63525	−	1.18808i	0.0642885	−	0.0467083i	−0.555177	−	0.831732i	$-0.687349\pi$
$647$	1.63525	−	1.18808i	0.0642885	−	0.0467083i	0.619465	+	0.785024i	$0.287349\pi$
$648$	3.94427	+	12.1392i	0.154946	+	0.476874i
$649$	−9.47214			−0.371814
$650$	2.50000	−	1.81636i	0.0980581	−	0.0712434i
$651$	11.5623			0.453162
$652$	10.7812	+	33.1810i	0.422223	+	1.29947i
$653$	−32.8435	+	23.8622i	−1.28526	+	0.933799i	−0.999698	−	0.0245603i	$-0.992181\pi$
$653$	−32.8435	+	23.8622i	−1.28526	+	0.933799i	−0.285566	+	0.958359i	$0.592181\pi$
$654$	17.5623	−	12.7598i	0.686741	−	0.498946i
$655$	4.79837	−	14.7679i	0.187488	−	0.577029i
$656$	−5.07295	−	3.68571i	−0.198065	−	0.143903i
$657$	10.4377			0.407213
$658$	−16.0451	−	11.6574i	−0.625503	−	0.454454i
$659$	3.35410	−	10.3229i	0.130657	−	0.402122i	−0.864232	−	0.503093i	$-0.832195\pi$
$659$	3.35410	−	10.3229i	0.130657	−	0.402122i	0.994889	+	0.100972i	$0.0321952\pi$
$660$	−12.3992	−	38.1608i	−0.482638	−	1.48541i
$661$	11.3713	+	34.9973i	0.442293	+	1.36124i	0.885425	+	0.464782i	$0.153867\pi$
$661$	11.3713	+	34.9973i	0.442293	+	1.36124i	−0.443132	+	0.896456i	$0.646133\pi$
$662$	6.17376	−	19.0009i	0.239950	−	0.738490i
$663$	−0.618034	+	1.90211i	−0.0240025	+	0.0738719i
$664$	−11.8713	−	36.5362i	−0.460697	−	1.41788i
$665$	−13.3156	+	40.9812i	−0.516357	+	1.58918i
$666$	−6.51722	+	20.0579i	−0.252537	+	0.777230i
$667$		0			0
$668$	−23.5623			−0.911653
$669$	−39.8156	−	28.9277i	−1.53936	−	1.11841i
$670$	−10.1246			−0.391148
$671$	−46.9787	+	34.1320i	−1.81359	+	1.31765i
$672$	−45.8607	+	33.3197i	−1.76911	+	1.28534i
$673$	−1.07295	−	3.30220i	−0.0413591	−	0.127290i	0.928245	−	0.371969i	$-0.121317\pi$
$673$	−1.07295	−	3.30220i	−0.0413591	−	0.127290i	−0.969604	+	0.244679i	$0.921317\pi$
$674$	−9.81966			−0.378239
$675$	9.04508	+	6.57164i	0.348145	+	0.252942i
$676$	−1.61803			−0.0622321
$677$	9.33688	+	28.7360i	0.358845	+	1.10441i	0.953746	+	0.300614i	$0.0971914\pi$
$677$	9.33688	+	28.7360i	0.358845	+	1.10441i	−0.594901	+	0.803799i	$0.702809\pi$
$678$	11.2082	−	8.14324i	0.430448	−	0.312739i
$679$	26.1353	−	18.9884i	1.00298	−	0.728707i
$680$	3.09017	−	2.24514i	0.118503	−	0.0860972i
$681$	30.8435	+	22.4091i	1.18192	+	0.858718i
$682$	3.00000			0.114876
$683$	−1.76393	−	1.28157i	−0.0674950	−	0.0490380i	0.553526	−	0.832832i	$-0.313282\pi$
$683$	−1.76393	−	1.28157i	−0.0674950	−	0.0490380i	−0.621021	+	0.783794i	$0.713282\pi$
$684$	9.63525	−	29.6543i	0.368413	−	1.13386i
$685$	−33.2918			−1.27201
$686$	−0.628677	−	1.93487i	−0.0240030	−	0.0738736i
$687$	−12.2361	+	37.6587i	−0.466835	+	1.43677i
$688$	3.13525	−	9.64932i	0.119530	−	0.367877i
$689$	−2.97214	−	9.14729i	−0.113229	−	0.348484i
$690$	−25.6525			−0.976573
$691$	−8.79180	+	27.0584i	−0.334456	+	1.02935i	0.632534	+	0.774533i	$0.282015\pi$
$691$	−8.79180	+	27.0584i	−0.334456	+	1.02935i	−0.966990	+	0.254816i	$0.917985\pi$
$692$	−15.3992	−	11.1882i	−0.585389	−	0.425310i
$693$	−62.9230			−2.39025
$694$	−4.02786	−	2.92641i	−0.152896	−	0.111085i
$695$	14.0451	−	10.2044i	0.532760	−	0.387073i
$696$		0			0
$697$	2.09017	−	1.51860i	0.0791708	−	0.0575210i
$698$	3.39261	+	10.4414i	0.128412	+	0.395212i
$699$	36.9787			1.39866
$700$	9.63525	−	29.6543i	0.364178	−	1.12083i
$701$	8.38197			0.316582			0.158291	−	0.987392i	$-0.449402\pi$
$701$	8.38197			0.316582			0.158291	+	0.987392i	$0.449402\pi$
$702$	0.427051	+	1.31433i	0.0161180	+	0.0496061i
$703$	−35.8156	+	26.0216i	−1.35081	+	0.981421i
$704$	0.809017	−	0.587785i	0.0304910	−	0.0221530i
$705$	−48.7426			−1.83575
$706$	8.80902	+	6.40013i	0.331532	+	0.240872i
$707$	−14.2918			−0.537498
$708$	7.66312	+	5.56758i	0.287998	+	0.209243i
$709$	4.10739	−	12.6412i	0.154256	−	0.474752i	−0.843828	−	0.536613i	$-0.819704\pi$
$709$	4.10739	−	12.6412i	0.154256	−	0.474752i	0.998085	+	0.0618609i	$0.0197035\pi$
$710$	−3.35410	+	10.3229i	−0.125877	+	0.387410i
$711$	4.93769	+	15.1967i	0.185178	+	0.569919i
$712$	7.72542	−	23.7764i	0.289523	−	0.891059i
$713$	−2.51064	+	7.72696i	−0.0940243	+	0.289377i
$714$	−1.47214	−	4.53077i	−0.0550933	−	0.169560i
$715$	2.92705	+	9.00854i	0.109466	+	0.336900i
$716$	4.14590	−	12.7598i	0.154939	−	0.476855i
$717$	−40.5517	−	29.4625i	−1.51443	−	1.10030i
$718$	−8.61803			−0.321622
$719$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$719$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$720$	−4.93769	+	15.1967i	−0.184017	+	0.566346i
$721$	23.0172	−	16.7230i	0.857206	−	0.622797i
$722$	−3.00000	+	2.17963i	−0.111648	+	0.0811173i
$723$	19.9894	+	61.5209i	0.743412	+	2.28799i
$724$	25.1803			0.935820
$725$		0			0
$726$	−11.2361			−0.417010
$727$	6.10739	+	18.7966i	0.226511	+	0.697128i	0.998135	+	0.0610492i	$0.0194447\pi$
$727$	6.10739	+	18.7966i	0.226511	+	0.697128i	−0.771624	+	0.636079i	$0.780555\pi$
$728$	6.97214	−	5.06555i	0.258405	−	0.187742i
$729$	32.0066	−	23.2541i	1.18543	−	0.861264i
$730$	3.02786	+	2.19987i	0.112066	+	0.0814209i
$731$	3.38197	+	2.45714i	0.125087	+	0.0908807i
$732$	58.0689			2.14629
$733$	8.13525	+	5.91061i	0.300482	+	0.218313i	0.727802	−	0.685787i	$-0.240542\pi$
$733$	8.13525	+	5.91061i	0.300482	+	0.218313i	−0.427319	+	0.904101i	$0.640542\pi$
$734$	−6.52786	+	20.0907i	−0.240948	+	0.741561i
$735$	−37.1976	−	27.0256i	−1.37205	−	0.996855i
$736$	−12.3090	−	37.8833i	−0.453716	−	1.39640i
$737$	9.59017	−	29.5155i	0.353258	−	1.08722i
$738$	2.48936	−	7.66145i	0.0916345	−	0.282022i
$739$	13.7812	+	42.4140i	0.506948	+	1.56023i	0.797471	+	0.603357i	$0.206171\pi$
$739$	13.7812	+	42.4140i	0.506948	+	1.56023i	−0.290523	+	0.956868i	$0.593829\pi$
$740$	25.9164	−	18.8294i	0.952706	−	0.692181i
$741$	−4.04508	+	12.4495i	−0.148600	+	0.457343i
$742$	18.5344	+	13.4661i	0.680421	+	0.494355i
$743$	34.0902			1.25065			0.625324	−	0.780366i	$-0.284967\pi$
$743$	34.0902			1.25065			0.625324	+	0.780366i	$0.284967\pi$
$744$	−5.42705	−	3.94298i	−0.198965	−	0.144557i
$745$	1.90983	+	5.87785i	0.0699708	+	0.215348i
$746$	5.25329	−	3.81674i	0.192337	−	0.139741i
$747$	−53.5689	+	38.9201i	−1.95998	+	1.42401i
$748$	1.61803	+	4.97980i	0.0591612	+	0.182079i
$749$	41.4853			1.51584
$750$	5.59017	+	17.2048i	0.204124	+	0.628230i
$751$	−37.6738			−1.37474			−0.687368	−	0.726310i	$-0.741234\pi$
$751$	−37.6738			−1.37474			−0.687368	+	0.726310i	$0.741234\pi$
$752$	−4.77051	−	14.6821i	−0.173963	−	0.535402i
$753$	−19.8713	+	14.4374i	−0.724151	+	0.526127i
$754$		0			0
$755$	5.75329	+	17.7068i	0.209384	+	0.644417i
$756$	11.2812	+	8.19624i	0.410292	+	0.298094i
$757$	−41.8673			−1.52169			−0.760846	−	0.648933i	$-0.775216\pi$
$757$	−41.8673			−1.52169			−0.760846	+	0.648933i	$0.775216\pi$
$758$	16.2812	+	11.8290i	0.591358	+	0.429647i
$759$	24.2984	−	74.7827i	0.881975	−	2.71444i
$760$	20.2254	−	14.6946i	0.733653	−	0.533030i
$761$	−10.7016	−	32.9362i	−0.387934	−	1.19394i	−0.934330	−	0.356410i	$-0.884001\pi$
$761$	−10.7016	−	32.9362i	−0.387934	−	1.19394i	0.546396	−	0.837527i	$-0.315999\pi$
$762$	7.78115	−	23.9479i	0.281881	−	0.867542i
$763$	−15.9787	+	49.1774i	−0.578468	+	1.78034i
$764$	−9.88197	−	30.4136i	−0.357517	−	1.10032i
$765$	−5.32624	−	3.86974i	−0.192571	−	0.139911i
$766$	−1.21478	+	3.73871i	−0.0438918	+	0.135085i
$767$	−1.80902	−	1.31433i	−0.0653198	−	0.0474576i
$768$	17.1803			0.619942
$769$	−1.70820	−	1.24108i	−0.0615994	−	0.0447546i	0.556559	−	0.830808i	$-0.312121\pi$
$769$	−1.70820	−	1.24108i	−0.0615994	−	0.0447546i	−0.618159	+	0.786053i	$0.712121\pi$
$770$	−18.2533	−	13.2618i	−0.657803	−	0.477922i
$771$	36.2705	−	26.3521i	1.30625	−	0.949047i
$772$	−18.4894	+	13.4333i	−0.665447	+	0.483475i
$773$	1.30244	+	4.00850i	0.0468455	+	0.144176i	0.971743	−	0.236040i	$-0.0758497\pi$
$773$	1.30244	+	4.00850i	0.0468455	+	0.144176i	−0.924898	+	0.380216i	$0.875850\pi$
$774$	13.0344			0.468513
$775$	5.72949			0.205809
$776$	−18.7426			−0.672822
$777$	−27.6074	−	84.9668i	−0.990410	−	3.04817i
$778$	4.40983	−	3.20393i	0.158100	−	0.114866i
$779$	13.6803	−	9.93935i	0.490149	−	0.356114i
$780$	2.92705	−	9.00854i	0.104805	−	0.322557i
$781$	−26.9164	−	19.5559i	−0.963145	−	0.699766i
$782$	3.34752			0.119707
$783$		0			0
$784$	4.50000	−	13.8496i	0.160714	−	0.494628i
$785$	−10.0623	−	30.9686i	−0.359139	−	1.10532i
$786$	3.47214	+	10.6861i	0.123847	+	0.381162i
$787$	3.74671	−	11.5312i	0.133556	−	0.411043i	−0.861807	−	0.507237i	$-0.830667\pi$
$787$	3.74671	−	11.5312i	0.133556	−	0.411043i	0.995363	+	0.0961942i	$0.0306670\pi$
$788$	−2.54508	+	7.83297i	−0.0906649	+	0.279038i
$789$	11.5902	+	35.6709i	0.412621	+	1.26992i
$790$	−1.77051	+	5.44907i	−0.0629919	+	0.193869i
$791$	−10.1976	+	31.3849i	−0.362584	+	1.11592i
$792$	29.5344	+	21.4580i	1.04946	+	0.762478i
$793$	−13.7082			−0.486793
$794$	1.76393	+	1.28157i	0.0625996	+	0.0454813i
$795$	56.3050			1.99693
$796$	−3.35410	+	2.43690i	−0.118883	+	0.0863735i
$797$	−5.50000	+	3.99598i	−0.194820	+	0.141545i	−0.680919	−	0.732359i	$-0.738419\pi$
$797$	−5.50000	+	3.99598i	−0.194820	+	0.141545i	0.486099	+	0.873904i	$0.338419\pi$
$798$	−9.63525	−	29.6543i	−0.341084	−	1.04975i
$799$	6.36068			0.225025
$800$	−22.7254	+	16.5110i	−0.803465	+	0.583752i
$801$	−43.0902			−1.52252
$802$	2.19098	+	6.74315i	0.0773663	+	0.238109i
$803$	−9.28115	+	6.74315i	−0.327525	+	0.237961i
$804$	−25.1074	+	18.2416i	−0.885469	+	0.643331i
$805$	49.4336	−	35.9156i	1.74231	−	1.26586i
$806$	0.572949	+	0.416272i	0.0201813	+	0.0146625i
$807$	−29.2705			−1.03037
$808$	6.70820	+	4.87380i	0.235994	+	0.171460i
$809$	−4.14590	+	12.7598i	−0.145762	+	0.448609i	−0.997108	−	0.0759949i	$-0.975787\pi$
$809$	−4.14590	+	12.7598i	−0.145762	+	0.448609i	0.851346	+	0.524604i	$0.175787\pi$
$810$	7.88854			0.277175
$811$	−5.82624	−	17.9313i	−0.204587	−	0.629654i	−0.999730	−	0.0232320i	$-0.992604\pi$
$811$	−5.82624	−	17.9313i	−0.204587	−	0.629654i	0.795143	−	0.606422i	$-0.207396\pi$
$812$		0			0
$813$	9.92705	−	30.5523i	0.348157	−	1.07152i
$814$	−7.16312	−	22.0458i	−0.251067	−	0.772705i
$815$	48.2148			1.68889
$816$	1.14590	−	3.52671i	0.0401145	−	0.123460i
$817$	22.1353	+	16.0822i	0.774415	+	0.562645i
$818$	−5.12461			−0.179178
$819$	−12.0172	−	8.73102i	−0.419916	−	0.305087i
$820$	−9.89919	+	7.19218i	−0.345695	+	0.251162i
$821$	−20.1353	+	14.6291i	−0.702725	+	0.510560i	−0.880819	−	0.473454i	$-0.843007\pi$
$821$	−20.1353	+	14.6291i	−0.702725	+	0.510560i	0.178093	+	0.984014i	$0.443007\pi$
$822$	19.4894	−	14.1598i	0.679769	−	0.493881i
$823$	7.54508	+	23.2214i	0.263005	+	0.809447i	0.992146	+	0.125083i	$0.0399198\pi$
$823$	7.54508	+	23.2214i	0.263005	+	0.809447i	−0.729141	+	0.684363i	$0.760080\pi$
$824$	−16.5066			−0.575034
$825$	−55.4508			−1.93055
$826$	5.32624			0.185324
$827$	−8.59017	−	26.4378i	−0.298709	−	0.919333i	−0.981950	−	0.189140i	$-0.939430\pi$
$827$	−8.59017	−	26.4378i	−0.298709	−	0.919333i	0.683241	−	0.730193i	$-0.260570\pi$
$828$	−35.7705	+	25.9888i	−1.24311	+	0.903173i
$829$	27.1353	−	19.7149i	0.942446	−	0.684727i	−0.00656193	−	0.999978i	$-0.502089\pi$
$829$	27.1353	−	19.7149i	0.942446	−	0.684727i	0.949008	+	0.315251i	$0.102089\pi$
$830$	−23.7426			−0.824119
$831$	60.8050	+	44.1774i	2.10930	+	1.53250i
$832$	0.236068			0.00818418
$833$	4.85410	+	3.52671i	0.168185	+	0.122193i
$834$	−3.88197	+	11.9475i	−0.134421	+	0.413707i
$835$	−10.0623	+	30.9686i	−0.348220	+	1.07171i
$836$	10.5902	+	32.5932i	0.366269	+	1.12726i
$837$	−0.791796	+	2.43690i	−0.0273685	+	0.0842315i
$838$	3.71885	−	11.4454i	0.128465	−	0.395376i
$839$	0.489357	+	1.50609i	0.0168945	+	0.0519958i	0.959148	−	0.282904i	$-0.0912976\pi$
$839$	0.489357	+	1.50609i	0.0168945	+	0.0519958i	−0.942254	+	0.334899i	$0.891298\pi$
$840$	15.5902	+	47.9816i	0.537912	+	1.65552i
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$	1.86475	+	1.35482i	0.0642634	+	0.0466901i
$843$	42.1246			1.45085
$844$	−16.0623	−	11.6699i	−0.552887	−	0.401696i
$845$	−0.690983	+	2.12663i	−0.0237705	+	0.0731582i
$846$	16.0451	−	11.6574i	0.551641	−	0.400791i
$847$	21.6525	−	15.7314i	0.743988	−	0.540539i
$848$	5.51064	+	16.9600i	0.189236	+	0.582409i
$849$	−4.32624			−0.148476
$850$	−0.729490	−	2.24514i	−0.0250213	−	0.0770077i
$851$	62.7771			2.15197
$852$	10.2812	+	31.6421i	0.352226	+	1.08404i
$853$	31.6525	−	22.9969i	1.08376	−	0.787398i	0.105425	−	0.994427i	$-0.466380\pi$
$853$	31.6525	−	22.9969i	1.08376	−	0.787398i	0.978335	+	0.207029i	$0.0663796\pi$
$854$	26.4164	−	19.1926i	0.903951	−	0.656759i
$855$	−34.8607	−	25.3278i	−1.19221	−	0.866191i
$856$	−19.4721	−	14.1473i	−0.665544	−	0.483546i
$857$	30.0902			1.02786			0.513930	−	0.857832i	$-0.328189\pi$
$857$	30.0902			1.02786			0.513930	+	0.857832i	$0.328189\pi$
$858$	−5.54508	−	4.02874i	−0.189306	−	0.137539i
$859$	−3.29180	+	10.1311i	−0.112315	+	0.345669i	−0.991377	−	0.131037i	$-0.958169\pi$
$859$	−3.29180	+	10.1311i	−0.112315	+	0.345669i	0.879063	+	0.476706i	$0.158169\pi$
$860$	−16.0172	−	11.6372i	−0.546183	−	0.396825i
$861$	10.5451	+	32.4544i	0.359376	+	1.10604i
$862$	2.09017	−	6.43288i	0.0711915	−	0.219105i
$863$	5.20820	−	16.0292i	0.177289	−	0.545640i	−0.822441	−	0.568850i	$-0.807388\pi$
$863$	5.20820	−	16.0292i	0.177289	−	0.545640i	0.999731	+	0.0232096i	$0.00738849\pi$
$864$	−3.88197	−	11.9475i	−0.132067	−	0.406461i
$865$	−21.2812	+	15.4617i	−0.723581	+	0.525712i
$866$	2.71478	−	8.35524i	0.0922520	−	0.283923i
$867$	−34.7705	−	25.2623i	−1.18087	−	0.857951i
$868$	7.14590			0.242548
$869$	−14.2082	−	10.3229i	−0.481980	−	0.350179i
$870$		0			0
$871$	5.92705	−	4.30625i	0.200830	−	0.145912i
$872$	24.2705	−	17.6336i	0.821903	−	0.597148i
$873$	9.98278	+	30.7238i	0.337866	+	1.03984i
$874$	21.9098			0.741111
$875$	−34.8607	−	25.3278i	−1.17851	−	0.856235i
$876$	11.4721			0.387608
$877$	17.1631	+	52.8226i	0.579557	+	1.78369i	0.620108	+	0.784517i	$0.287089\pi$
$877$	17.1631	+	52.8226i	0.579557	+	1.78369i	−0.0405505	+	0.999177i	$0.512911\pi$
$878$	−0.427051	+	0.310271i	−0.0144123	+	0.0104711i
$879$	41.1246	−	29.8788i	1.38710	−	1.00779i
$880$	−5.42705	−	16.7027i	−0.182946	−	0.563049i
$881$	−27.7984	−	20.1967i	−0.936551	−	0.680444i	0.0110370	−	0.999939i	$-0.496487\pi$
$881$	−27.7984	−	20.1967i	−0.936551	−	0.680444i	−0.947588	+	0.319495i	$0.896487\pi$
$882$	18.7082			0.629938
$883$	−22.4164	−	16.2865i	−0.754372	−	0.548083i	0.142807	−	0.989751i	$-0.454387\pi$
$883$	−22.4164	−	16.2865i	−0.754372	−	0.548083i	−0.897179	+	0.441667i	$0.854387\pi$
$884$	−0.381966	+	1.17557i	−0.0128469	+	0.0395387i
$885$	10.5902	−	7.69421i	0.355985	−	0.258638i
$886$	−5.92705	−	18.2416i	−0.199123	−	0.612838i
$887$	−5.56231	+	17.1190i	−0.186764	+	0.574800i	−0.999974	−	0.00716953i	$-0.997718\pi$
$887$	−5.56231	+	17.1190i	−0.186764	+	0.574800i	0.813210	+	0.581970i	$0.197718\pi$
$888$	−16.0172	+	49.2959i	−0.537503	+	1.65426i
$889$	18.5344	+	57.0431i	0.621625	+	1.91317i
$890$	−12.5000	−	9.08178i	−0.419001	−	0.304422i
$891$	−7.47214	+	22.9969i	−0.250326	+	0.770424i
$892$	−24.6074	−	17.8783i	−0.823916	−	0.598610i
$893$	41.6312			1.39313
$894$	−3.61803	−	2.62866i	−0.121005	−	0.0879154i
$895$	−15.0000	−	10.8981i	−0.501395	−	0.364285i
$896$	−35.4894	+	25.7845i	−1.18562	+	0.861401i
$897$	15.0172	−	10.9106i	0.501410	−	0.364296i
$898$	6.70820	+	20.6457i	0.223856	+	0.688957i
$899$		0			0
$900$	25.2254	+	18.3273i	0.840847	+	0.610911i
$901$	−7.34752			−0.244782
$902$	2.73607	+	8.42075i	0.0911011	+	0.280380i
$903$	−44.6697	+	32.4544i	−1.48651	+	1.08002i
$904$	15.4894	−	11.2537i	0.515168	−	0.374292i
$905$	10.7533	−	33.0952i	0.357451	−	1.10012i
$906$	−10.8992	−	7.91872i	−0.362101	−	0.263082i
$907$	36.4721			1.21104			0.605519	−	0.795831i	$-0.292966\pi$
$907$	36.4721			1.21104			0.605519	+	0.795831i	$0.292966\pi$
$908$	19.0623	+	13.8496i	0.632605	+	0.459614i
$909$	4.41641	−	13.5923i	0.146483	−	0.450828i
$910$	−1.64590	−	5.06555i	−0.0545610	−	0.167921i
$911$	−17.5967	−	54.1572i	−0.583006	−	1.79431i	−0.607133	−	0.794600i	$-0.707681\pi$
$911$	−17.5967	−	54.1572i	−0.583006	−	1.79431i	0.0241272	−	0.999709i	$-0.492319\pi$
$912$	7.50000	−	23.0826i	0.248350	−	0.764342i
$913$	22.4894	−	69.2151i	0.744289	−	2.29069i
$914$	−1.10081	−	3.38795i	−0.0364117	−	0.112064i
$915$	24.7984	−	76.3215i	0.819809	−	2.52311i
$916$	−7.56231	+	23.2744i	−0.249866	+	0.769007i
$917$	−21.6525	−	15.7314i	−0.715028	−	0.519498i
$918$	1.05573			0.0348442
$919$	14.2082	+	10.3229i	0.468685	+	0.340520i	0.796929	−	0.604073i	$-0.206457\pi$
$919$	14.2082	+	10.3229i	0.468685	+	0.340520i	−0.328243	+	0.944593i	$0.606457\pi$
$920$	−35.4508			−1.16878
$921$	25.6803	−	18.6579i	0.846196	−	0.614797i
$922$	−15.2705	+	11.0947i	−0.502907	+	0.365384i
$923$	−2.42705	−	7.46969i	−0.0798874	−	0.245868i
$924$	−69.1591			−2.27517
$925$	−13.6803	−	42.1038i	−0.449807	−	1.38436i
$926$	17.1246			0.562750
$927$	8.79180	+	27.0584i	0.288760	+	0.888713i
$928$		0			0
$929$	16.2812	−	11.8290i	0.534167	−	0.388095i	−0.287747	−	0.957706i	$-0.592906\pi$
$929$	16.2812	−	11.8290i	0.534167	−	0.388095i	0.821914	+	0.569611i	$0.192906\pi$
$930$	−3.35410	+	2.43690i	−0.109985	+	0.0799090i
$931$	31.7705	+	23.0826i	1.04124	+	0.756503i
$932$	22.8541			0.748611
$933$	17.0623	+	12.3965i	0.558595	+	0.405843i
$934$	−6.00000	+	18.4661i	−0.196326	+	0.604229i
$935$	7.23607			0.236645
$936$	2.66312	+	8.19624i	0.0870468	+	0.267902i
$937$	7.81559	−	24.0539i	0.255324	−	0.785808i	−0.738441	−	0.674318i	$-0.764438\pi$
$937$	7.81559	−	24.0539i	0.255324	−	0.785808i	0.993766	−	0.111490i	$-0.0355622\pi$
$938$	−5.39261	+	16.5967i	−0.176075	+	0.541903i
$939$	−4.69098	−	14.4374i	−0.153084	−	0.471145i
$940$	−30.1246			−0.982556
$941$	2.62868	−	8.09024i	0.0856924	−	0.263734i	−0.899024	−	0.437899i	$-0.855723\pi$
$941$	2.62868	−	8.09024i	0.0856924	−	0.263734i	0.984716	+	0.174165i	$0.0557226\pi$
$942$	19.0623	+	13.8496i	0.621083	+	0.451244i
$943$	−23.9787			−0.780854
$944$	3.35410	+	2.43690i	0.109167	+	0.0793143i
$945$	15.5902	−	11.3269i	0.507148	−	0.368465i
$946$	−11.5902	+	8.42075i	−0.376829	+	0.273782i
$947$	37.3885	−	27.1644i	1.21496	−	0.882723i	0.219292	−	0.975659i	$-0.429625\pi$
$947$	37.3885	−	27.1644i	1.21496	−	0.882723i	0.995672	+	0.0929359i	$0.0296252\pi$
$948$	5.42705	+	16.7027i	0.176262	+	0.542480i
$949$	−2.70820			−0.0879120
$950$	−4.77458	−	14.6946i	−0.154908	−	0.476757i
$951$	29.5623			0.958623
$952$	−2.03444	−	6.26137i	−0.0659366	−	0.202932i
$953$	48.7877	−	35.4464i	1.58039	−	1.14822i	0.664143	−	0.747606i	$-0.268797\pi$
$953$	48.7877	−	35.4464i	1.58039	−	1.14822i	0.916247	−	0.400615i	$-0.131203\pi$
$954$	−18.5344	+	13.4661i	−0.600075	+	0.435980i
$955$	−44.1935			−1.43007
$956$	−25.0623	−	18.2088i	−0.810573	−	0.588916i
$957$		0			0
$958$	−5.16312	−	3.75123i	−0.166813	−	0.121197i
$959$	−17.7320	+	54.5735i	−0.572596	+	1.76227i
$960$	−0.427051	+	1.31433i	−0.0137830	+	0.0424197i
$961$	−9.17376	−	28.2339i	−0.295928	−	0.910772i
$962$	1.69098	−	5.20431i	0.0545195	−	0.167794i
$963$	−12.8197	+	39.4549i	−0.413108	+	1.27141i
$964$	12.3541	+	38.0220i	0.397899	+	1.22461i
$965$	9.75987	+	30.0378i	0.314181	+	0.966950i
$966$	−13.6631	+	42.0508i	−0.439604	+	1.35296i
$967$	−21.3541	−	15.5147i	−0.686702	−	0.498918i	0.188873	−	0.982002i	$-0.439517\pi$
$967$	−21.3541	−	15.5147i	−0.686702	−	0.498918i	−0.875574	+	0.483084i	$0.839517\pi$
$968$	−15.5279			−0.499084
$969$	8.09017	+	5.87785i	0.259894	+	0.188824i
$970$	−3.57953	+	11.0167i	−0.114932	+	0.353723i
$971$	−12.0451	+	8.75127i	−0.386545	+	0.280842i	−0.764038	−	0.645171i	$-0.776786\pi$
$971$	−12.0451	+	8.75127i	−0.386545	+	0.280842i	0.377493	+	0.926012i	$0.376786\pi$
$972$	28.3435	−	20.5927i	0.909117	−	0.660512i
$973$	−9.24671	−	28.4585i	−0.296436	−	0.912336i
$974$	8.02129			0.257019
$975$	−10.5902	−	7.69421i	−0.339157	−	0.246412i
$976$	25.4164			0.813559
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	0.938782	−	0.344513i	$-0.111956\pi$
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	−0.961990	+	0.273085i	$0.911956\pi$
$978$	−28.2254	+	20.5070i	−0.902550	+	0.655741i
$979$	38.3156	−	27.8379i	1.22457	−	0.889703i
$980$	−22.9894	−	16.7027i	−0.734368	−	0.533550i
$981$	−41.8328	−	30.3933i	−1.33562	−	0.970384i
$982$	−2.58359			−0.0824457
$983$	−35.1803	−	25.5600i	−1.12208	−	0.815238i	−0.137556	−	0.990494i	$-0.543925\pi$
$983$	−35.1803	−	25.5600i	−1.12208	−	0.815238i	−0.984523	+	0.175256i	$0.943925\pi$
$984$	6.11803	−	18.8294i	0.195036	−	0.600258i
$985$	9.20820	+	6.69015i	0.293398	+	0.213166i
$986$		0			0
$987$	−25.9615	+	79.9013i	−0.826363	+	2.54329i
$988$	−2.50000	+	7.69421i	−0.0795356	+	0.244785i
$989$	−11.9894	−	36.8994i	−0.381239	−	1.17333i
$990$	18.2533	−	13.2618i	0.580128	−	0.421487i
$991$	10.2533	−	31.5564i	0.325706	−	1.00242i	−0.645414	−	0.763833i	$-0.723315\pi$
$991$	10.2533	−	31.5564i	0.325706	−	1.00242i	0.971121	−	0.238589i	$-0.0766848\pi$
$992$	−5.20820	−	3.78398i	−0.165361	−	0.120142i
$993$	−84.6312			−2.68569
$994$	15.1353	+	10.9964i	0.480061	+	0.348785i
$995$	1.77051	+	5.44907i	0.0561289	+	0.172747i
$996$	−58.8779	+	42.7773i	−1.86562	+	1.35545i
$997$	−4.90983	+	3.56720i	−0.155496	+	0.112974i	−0.662813	−	0.748785i	$-0.730637\pi$
$997$	−4.90983	+	3.56720i	−0.155496	+	0.112974i	0.507317	+	0.861760i	$0.330637\pi$
$998$	−4.49593	−	13.8371i	−0.142316	−	0.438005i
$999$	19.7984			0.626393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.l.a.131.1	✓	4
25.11	even	5		8125.2.a.a.1.2		2
25.14	even	10		8125.2.a.b.1.1		2
25.21	even	5	inner	325.2.l.a.196.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.l.a.131.1	✓	4	1.1	even	1	trivial
325.2.l.a.196.1	yes	4	25.21	even	5	inner
8125.2.a.a.1.2		2	25.11	even	5
8125.2.a.b.1.1		2	25.14	even	10

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.587785i) q^{2} +(2.11803 - 1.53884i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} -3.85410 q^{7} +(1.80902 + 1.31433i) q^{8} +(1.19098 - 3.66547i) q^{9} +O(q^{10})\)	\(q+(0.190983 + 0.587785i) q^{2} +(2.11803 - 1.53884i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} -3.85410 q^{7} +(1.80902 + 1.31433i) q^{8} +(1.19098 - 3.66547i) q^{9} +(1.11803 - 0.812299i) q^{10} +(1.30902 + 4.02874i) q^{11} +(1.30902 - 4.02874i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.736068 - 2.26538i) q^{14} +(-4.73607 - 3.44095i) q^{15} +(0.572949 - 1.76336i) q^{16} +(0.618034 + 0.449028i) q^{17} +2.38197 q^{18} +(4.04508 + 2.93893i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-8.16312 + 5.93085i) q^{21} +(-2.11803 + 1.53884i) q^{22} +(-2.19098 - 6.74315i) q^{23} +5.85410 q^{24} +(-4.04508 + 2.93893i) q^{25} -0.618034 q^{26} +(-0.690983 - 2.12663i) q^{27} +(-5.04508 + 3.66547i) q^{28} +(1.11803 - 3.44095i) q^{30} +(-0.927051 - 0.673542i) q^{31} +5.61803 q^{32} +(8.97214 + 6.51864i) q^{33} +(-0.145898 + 0.449028i) q^{34} +(2.66312 + 8.19624i) q^{35} +(-1.92705 - 5.93085i) q^{36} +(-2.73607 + 8.42075i) q^{37} +(-0.954915 + 2.93893i) q^{38} +(0.809017 + 2.48990i) q^{39} +(1.54508 - 4.75528i) q^{40} +(1.04508 - 3.21644i) q^{41} +(-5.04508 - 3.66547i) q^{42} +5.47214 q^{43} +(5.54508 + 4.02874i) q^{44} -8.61803 q^{45} +(3.54508 - 2.57565i) q^{46} +(6.73607 - 4.89404i) q^{47} +(-1.50000 - 4.61653i) q^{48} +7.85410 q^{49} +(-2.50000 - 1.81636i) q^{50} +2.00000 q^{51} +(0.500000 + 1.53884i) q^{52} +(-7.78115 + 5.65334i) q^{53} +(1.11803 - 0.812299i) q^{54} +(7.66312 - 5.56758i) q^{55} +(-6.97214 - 5.06555i) q^{56} +13.0902 q^{57} +(-0.690983 + 2.12663i) q^{59} -9.47214 q^{60} +(4.23607 + 13.0373i) q^{61} +(0.218847 - 0.673542i) q^{62} +(-4.59017 + 14.1271i) q^{63} +(-0.0729490 - 0.224514i) q^{64} +2.23607 q^{65} +(-2.11803 + 6.51864i) q^{66} +(-5.92705 - 4.30625i) q^{67} +1.23607 q^{68} +(-15.0172 - 10.9106i) q^{69} +(-4.30902 + 3.13068i) q^{70} +(-6.35410 + 4.61653i) q^{71} +(6.97214 - 5.06555i) q^{72} +(0.836881 + 2.57565i) q^{73} -5.47214 q^{74} +(-4.04508 + 12.4495i) q^{75} +8.09017 q^{76} +(-5.04508 - 15.5272i) q^{77} +(-1.30902 + 0.951057i) q^{78} +(-3.35410 + 2.43690i) q^{79} -4.14590 q^{80} +(4.61803 + 3.35520i) q^{81} +2.09017 q^{82} +(-13.8992 - 10.0984i) q^{83} +(-5.04508 + 15.5272i) q^{84} +(0.527864 - 1.62460i) q^{85} +(1.04508 + 3.21644i) q^{86} +(-2.92705 + 9.00854i) q^{88} +(-3.45492 - 10.6331i) q^{89} +(-1.64590 - 5.06555i) q^{90} +(1.19098 - 3.66547i) q^{91} +(-9.28115 - 6.74315i) q^{92} -3.00000 q^{93} +(4.16312 + 3.02468i) q^{94} +(3.45492 - 10.6331i) q^{95} +(11.8992 - 8.64527i) q^{96} +(-6.78115 + 4.92680i) q^{97} +(1.50000 + 4.61653i) q^{98} +16.3262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + q^{13} + 6 q^{14} - 10 q^{15} + 9 q^{16} - 2 q^{17} + 14 q^{18} + 5 q^{19} - 5 q^{20} - 17 q^{21} - 4 q^{22} - 11 q^{23} + 10 q^{24} - 5 q^{25} + 2 q^{26} - 5 q^{27} - 9 q^{28} + 3 q^{31} + 18 q^{32} + 18 q^{33} - 14 q^{34} - 5 q^{35} - q^{36} - 2 q^{37} - 15 q^{38} + q^{39} - 5 q^{40} - 7 q^{41} - 9 q^{42} + 4 q^{43} + 11 q^{44} - 30 q^{45} + 3 q^{46} + 18 q^{47} - 6 q^{48} + 18 q^{49} - 10 q^{50} + 8 q^{51} + 2 q^{52} - 11 q^{53} + 15 q^{55} - 10 q^{56} + 30 q^{57} - 5 q^{59} - 20 q^{60} + 8 q^{61} + 21 q^{62} + 4 q^{63} - 7 q^{64} - 4 q^{66} - 17 q^{67} - 4 q^{68} - 31 q^{69} - 15 q^{70} - 12 q^{71} + 10 q^{72} + 19 q^{73} - 4 q^{74} - 5 q^{75} + 10 q^{76} - 9 q^{77} - 3 q^{78} - 30 q^{80} + 14 q^{81} - 14 q^{82} - 31 q^{83} - 9 q^{84} + 20 q^{85} - 7 q^{86} - 5 q^{88} - 25 q^{89} - 20 q^{90} + 7 q^{91} - 17 q^{92} - 12 q^{93} + q^{94} + 25 q^{95} + 23 q^{96} - 7 q^{97} + 6 q^{98} + 34 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + q^13 + 6 * q^14 - 10 * q^15 + 9 * q^16 - 2 * q^17 + 14 * q^18 + 5 * q^19 - 5 * q^20 - 17 * q^21 - 4 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 2 * q^26 - 5 * q^27 - 9 * q^28 + 3 * q^31 + 18 * q^32 + 18 * q^33 - 14 * q^34 - 5 * q^35 - q^36 - 2 * q^37 - 15 * q^38 + q^39 - 5 * q^40 - 7 * q^41 - 9 * q^42 + 4 * q^43 + 11 * q^44 - 30 * q^45 + 3 * q^46 + 18 * q^47 - 6 * q^48 + 18 * q^49 - 10 * q^50 + 8 * q^51 + 2 * q^52 - 11 * q^53 + 15 * q^55 - 10 * q^56 + 30 * q^57 - 5 * q^59 - 20 * q^60 + 8 * q^61 + 21 * q^62 + 4 * q^63 - 7 * q^64 - 4 * q^66 - 17 * q^67 - 4 * q^68 - 31 * q^69 - 15 * q^70 - 12 * q^71 + 10 * q^72 + 19 * q^73 - 4 * q^74 - 5 * q^75 + 10 * q^76 - 9 * q^77 - 3 * q^78 - 30 * q^80 + 14 * q^81 - 14 * q^82 - 31 * q^83 - 9 * q^84 + 20 * q^85 - 7 * q^86 - 5 * q^88 - 25 * q^89 - 20 * q^90 + 7 * q^91 - 17 * q^92 - 12 * q^93 + q^94 + 25 * q^95 + 23 * q^96 - 7 * q^97 + 6 * q^98 + 34 * q^99

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