LMFDB - Embedded newform 170.2.k.b.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.3
Root			$-0.923170i$ of defining polynomial
Character	$\chi$	$=$	170.161
Dual form			170.2.k.b.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.0294014 + 0.0709814i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.0294014 - 0.0709814i) q^{6} +(3.48924 - 1.44529i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11715 + 2.11715i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0294014 + 0.0709814i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.0294014 - 0.0709814i) q^{6} +(3.48924 - 1.44529i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11715 + 2.11715i) q^{9} +(0.923880 - 0.382683i) q^{10} +(1.39907 + 3.37765i) q^{11} +(0.0709814 + 0.0294014i) q^{12} -4.29194i q^{13} +(-1.44529 + 3.48924i) q^{14} +(0.0543268 - 0.0543268i) q^{15} -1.00000 q^{16} +(2.96045 + 2.86979i) q^{17} -2.99410 q^{18} +(-2.18510 + 2.18510i) q^{19} +(-0.382683 + 0.923880i) q^{20} +0.290164i q^{21} +(-3.37765 - 1.39907i) q^{22} +(-2.47749 - 5.98120i) q^{23} +(-0.0709814 + 0.0294014i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.03486 + 3.03486i) q^{26} +(-0.425469 + 0.176235i) q^{27} +(-1.44529 - 3.48924i) q^{28} +(2.10291 + 0.871055i) q^{29} +0.0768297i q^{30} +(2.31493 - 5.58873i) q^{31} +(0.707107 - 0.707107i) q^{32} -0.280885 q^{33} +(-4.12261 + 0.0641084i) q^{34} -3.77672 q^{35} +(2.11715 - 2.11715i) q^{36} +(-3.10484 + 7.49575i) q^{37} -3.09019i q^{38} +(0.304648 + 0.126189i) q^{39} +(-0.382683 - 0.923880i) q^{40} +(-7.61607 + 3.15468i) q^{41} +(-0.205177 - 0.205177i) q^{42} +(-7.80465 - 7.80465i) q^{43} +(3.37765 - 1.39907i) q^{44} +(-1.14579 - 2.76619i) q^{45} +(5.98120 + 2.47749i) q^{46} -8.27314i q^{47} +(0.0294014 - 0.0709814i) q^{48} +(5.13617 - 5.13617i) q^{49} -1.00000 q^{50} +(-0.290743 + 0.125761i) q^{51} -4.29194 q^{52} +(-7.36717 + 7.36717i) q^{53} +(0.176235 - 0.425469i) q^{54} -3.65595i q^{55} +(3.48924 + 1.44529i) q^{56} +(-0.0908561 - 0.219346i) q^{57} +(-2.10291 + 0.871055i) q^{58} +(-3.39657 - 3.39657i) q^{59} +(-0.0543268 - 0.0543268i) q^{60} +(-2.56272 + 1.06151i) q^{61} +(2.31493 + 5.58873i) q^{62} +(10.4471 + 4.32734i) q^{63} +1.00000i q^{64} +(-1.64246 + 3.96524i) q^{65} +(0.198616 - 0.198616i) q^{66} +3.43790 q^{67} +(2.86979 - 2.96045i) q^{68} +0.497395 q^{69} +(2.67055 - 2.67055i) q^{70} +(-5.25072 + 12.6764i) q^{71} +2.99410i q^{72} +(10.9486 + 4.53508i) q^{73} +(-3.10484 - 7.49575i) q^{74} +(-0.0709814 + 0.0294014i) q^{75} +(2.18510 + 2.18510i) q^{76} +(9.76337 + 9.76337i) q^{77} +(-0.304648 + 0.126189i) q^{78} +(1.15991 + 2.80028i) q^{79} +(0.923880 + 0.382683i) q^{80} +8.94691i q^{81} +(3.15468 - 7.61607i) q^{82} +(-1.30018 + 1.30018i) q^{83} +0.290164 q^{84} +(-1.63688 - 3.78426i) q^{85} +11.0374 q^{86} +(-0.123657 + 0.123657i) q^{87} +(-1.39907 + 3.37765i) q^{88} -9.64127i q^{89} +(2.76619 + 1.14579i) q^{90} +(-6.20310 - 14.9756i) q^{91} +(-5.98120 + 2.47749i) q^{92} +(0.328633 + 0.328633i) q^{93} +(5.84999 + 5.84999i) q^{94} +(2.85497 - 1.18257i) q^{95} +(0.0294014 + 0.0709814i) q^{96} +(-0.613459 - 0.254103i) q^{97} +7.26364i q^{98} +(-4.18895 + 10.1130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.0294014	+	0.0709814i	−0.0169749	+	0.0409811i	−0.932140	−	0.362099i	$-0.882060\pi$
$3$	−0.0294014	+	0.0709814i	−0.0169749	+	0.0409811i	0.915165	+	0.403080i	$0.132060\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$	−0.0294014	−	0.0709814i	−0.0120031	−	0.0289780i
$7$	3.48924	−	1.44529i	1.31881	−	0.546268i	0.391366	−	0.920235i	$-0.372003\pi$
$7$	3.48924	−	1.44529i	1.31881	−	0.546268i	0.927442	+	0.373967i	$0.122003\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.11715	+	2.11715i	0.705715	+	0.705715i
$10$	0.923880	−	0.382683i	0.292156	−	0.121015i
$11$	1.39907	+	3.37765i	0.421835	+	1.01840i	0.981806	+	0.189888i	$0.0608125\pi$
$11$	1.39907	+	3.37765i	0.421835	+	1.01840i	−0.559970	+	0.828513i	$0.689187\pi$
$12$	0.0709814	+	0.0294014i	0.0204906	+	0.00848746i
$13$		−	4.29194i		−	1.19037i	−0.803588	−	0.595185i	$-0.797079\pi$
$13$		−	4.29194i		−	1.19037i	0.803588	−	0.595185i	$-0.202921\pi$
$14$	−1.44529	+	3.48924i	−0.386270	+	0.932538i
$15$	0.0543268	−	0.0543268i	0.0140271	−	0.0140271i
$16$	−1.00000			−0.250000
$17$	2.96045	+	2.86979i	0.718016	+	0.696027i
$17$	2.96045	+	2.86979i	0.718016	+	0.696027i
$18$	−2.99410			−0.705715
$19$	−2.18510	+	2.18510i	−0.501295	+	0.501295i	−0.911840	−	0.410545i	$-0.865338\pi$
$19$	−2.18510	+	2.18510i	−0.501295	+	0.501295i	0.410545	+	0.911840i	$0.365338\pi$
$20$	−0.382683	+	0.923880i	−0.0855706	+	0.206586i
$21$			0.290164i			0.0633191i
$22$	−3.37765	−	1.39907i	−0.720118	−	0.298283i
$23$	−2.47749	−	5.98120i	−0.516593	−	1.24717i	−0.939984	−	0.341219i	$-0.889160\pi$
$23$	−2.47749	−	5.98120i	−0.516593	−	1.24717i	0.423391	−	0.905947i	$-0.360840\pi$
$24$	−0.0709814	+	0.0294014i	−0.0144890	+	0.00600154i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	3.03486	+	3.03486i	0.595185	+	0.595185i
$27$	−0.425469	+	0.176235i	−0.0818816	+	0.0339165i
$28$	−1.44529	−	3.48924i	−0.273134	−	0.659404i
$29$	2.10291	+	0.871055i	0.390501	+	0.161751i	0.569290	−	0.822137i	$-0.307218\pi$
$29$	2.10291	+	0.871055i	0.390501	+	0.161751i	−0.178789	+	0.983887i	$0.557218\pi$
$30$			0.0768297i			0.0140271i
$31$	2.31493	−	5.58873i	0.415773	−	1.00376i	−0.567786	−	0.823176i	$-0.692200\pi$
$31$	2.31493	−	5.58873i	0.415773	−	1.00376i	0.983559	−	0.180588i	$-0.0578002\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.280885			−0.0488958
$34$	−4.12261	+	0.0641084i	−0.707021	+	0.0109945i
$35$	−3.77672			−0.638383
$36$	2.11715	−	2.11715i	0.352858	−	0.352858i
$37$	−3.10484	+	7.49575i	−0.510433	+	1.23229i	0.433200	+	0.901298i	$0.357384\pi$
$37$	−3.10484	+	7.49575i	−0.510433	+	1.23229i	−0.943632	+	0.330995i	$0.892616\pi$
$38$		−	3.09019i		−	0.501295i
$39$	0.304648	+	0.126189i	0.0487827	+	0.0202065i
$40$	−0.382683	−	0.923880i	−0.0605076	−	0.146078i
$41$	−7.61607	+	3.15468i	−1.18943	+	0.492678i	−0.887570	−	0.460674i	$-0.847608\pi$
$41$	−7.61607	+	3.15468i	−1.18943	+	0.492678i	−0.301861	+	0.953352i	$0.597608\pi$
$42$	−0.205177	−	0.205177i	−0.0316595	−	0.0316595i
$43$	−7.80465	−	7.80465i	−1.19020	−	1.19020i	−0.977011	−	0.213187i	$-0.931616\pi$
$43$	−7.80465	−	7.80465i	−1.19020	−	1.19020i	−0.213187	−	0.977011i	$-0.568384\pi$
$44$	3.37765	−	1.39907i	0.509200	−	0.210918i
$45$	−1.14579	−	2.76619i	−0.170804	−	0.412359i
$46$	5.98120	+	2.47749i	0.881880	+	0.365286i
$47$		−	8.27314i		−	1.20676i	−0.797453	−	0.603381i	$-0.793820\pi$
$47$		−	8.27314i		−	1.20676i	0.797453	−	0.603381i	$-0.206180\pi$
$48$	0.0294014	−	0.0709814i	0.00424373	−	0.0102453i
$49$	5.13617	−	5.13617i	0.733738	−	0.733738i
$50$	−1.00000			−0.141421
$51$	−0.290743	+	0.125761i	−0.0407122	+	0.0176101i
$52$	−4.29194			−0.595185
$53$	−7.36717	+	7.36717i	−1.01196	+	1.01196i	−0.0120310	+	0.999928i	$0.503830\pi$
$53$	−7.36717	+	7.36717i	−1.01196	+	1.01196i	−0.999928	+	0.0120310i	$0.996170\pi$
$54$	0.176235	−	0.425469i	0.0239826	−	0.0578990i
$55$		−	3.65595i		−	0.492968i
$56$	3.48924	+	1.44529i	0.466269	+	0.193135i
$57$	−0.0908561	−	0.219346i	−0.0120342	−	0.0290531i
$58$	−2.10291	+	0.871055i	−0.276126	+	0.114375i
$59$	−3.39657	−	3.39657i	−0.442195	−	0.442195i	0.450554	−	0.892749i	$-0.351227\pi$
$59$	−3.39657	−	3.39657i	−0.442195	−	0.442195i	−0.892749	+	0.450554i	$0.851227\pi$
$60$	−0.0543268	−	0.0543268i	−0.00701356	−	0.00701356i
$61$	−2.56272	+	1.06151i	−0.328123	+	0.135913i	−0.540663	−	0.841239i	$-0.681826\pi$
$61$	−2.56272	+	1.06151i	−0.328123	+	0.135913i	0.212540	+	0.977152i	$0.431826\pi$
$62$	2.31493	+	5.58873i	0.293996	+	0.709769i
$63$	10.4471	+	4.32734i	1.31621	+	0.545193i
$64$			1.00000i			0.125000i
$65$	−1.64246	+	3.96524i	−0.203722	+	0.491827i
$66$	0.198616	−	0.198616i	0.0244479	−	0.0244479i
$67$	3.43790			0.420007			0.210003	−	0.977701i	$-0.432652\pi$
$67$	3.43790			0.420007			0.210003	+	0.977701i	$0.432652\pi$
$68$	2.86979	−	2.96045i	0.348013	−	0.359008i
$69$	0.497395			0.0598794
$70$	2.67055	−	2.67055i	0.319191	−	0.319191i
$71$	−5.25072	+	12.6764i	−0.623145	+	1.50441i	0.224845	+	0.974395i	$0.427812\pi$
$71$	−5.25072	+	12.6764i	−0.623145	+	1.50441i	−0.847990	+	0.530012i	$0.822188\pi$
$72$			2.99410i			0.352858i
$73$	10.9486	+	4.53508i	1.28144	+	0.530791i	0.916424	−	0.400209i	$-0.131063\pi$
$73$	10.9486	+	4.53508i	1.28144	+	0.530791i	0.365019	+	0.931000i	$0.381063\pi$
$74$	−3.10484	−	7.49575i	−0.360930	−	0.871363i
$75$	−0.0709814	+	0.0294014i	−0.00819622	+	0.00339499i
$76$	2.18510	+	2.18510i	0.250648	+	0.250648i
$77$	9.76337	+	9.76337i	1.11264	+	1.11264i
$78$	−0.304648	+	0.126189i	−0.0344946	+	0.0142881i
$79$	1.15991	+	2.80028i	0.130500	+	0.315056i	0.975601	−	0.219552i	$-0.0704595\pi$
$79$	1.15991	+	2.80028i	0.130500	+	0.315056i	−0.845101	+	0.534607i	$0.820459\pi$
$80$	0.923880	+	0.382683i	0.103293	+	0.0427853i
$81$			8.94691i			0.994101i
$82$	3.15468	−	7.61607i	0.348376	−	0.841055i
$83$	−1.30018	+	1.30018i	−0.142713	+	0.142713i	−0.774854	−	0.632141i	$-0.782177\pi$
$83$	−1.30018	+	1.30018i	−0.142713	+	0.142713i	0.632141	+	0.774854i	$0.282177\pi$
$84$	0.290164			0.0316595
$85$	−1.63688	−	3.78426i	−0.177545	−	0.410461i
$86$	11.0374			1.19020
$87$	−0.123657	+	0.123657i	−0.0132575	+	0.0132575i
$88$	−1.39907	+	3.37765i	−0.149141	+	0.360059i
$89$		−	9.64127i		−	1.02197i	−0.859589	−	0.510986i	$-0.829280\pi$
$89$		−	9.64127i		−	1.02197i	0.859589	−	0.510986i	$-0.170720\pi$
$90$	2.76619	+	1.14579i	0.291582	+	0.120777i
$91$	−6.20310	−	14.9756i	−0.650262	−	1.56987i
$92$	−5.98120	+	2.47749i	−0.623583	+	0.258297i
$93$	0.328633	+	0.328633i	0.0340777	+	0.0340777i
$94$	5.84999	+	5.84999i	0.603381	+	0.603381i
$95$	2.85497	−	1.18257i	0.292913	−	0.121329i
$96$	0.0294014	+	0.0709814i	0.00300077	+	0.00724450i
$97$	−0.613459	−	0.254103i	−0.0622873	−	0.0258003i	0.351322	−	0.936255i	$-0.385732\pi$
$97$	−0.613459	−	0.254103i	−0.0622873	−	0.0258003i	−0.413610	+	0.910454i	$0.635732\pi$
$98$			7.26364i			0.733738i
$99$	−4.18895	+	10.1130i	−0.421005	+	1.01640i
$100$	0.707107	−	0.707107i	0.0707107	−	0.0707107i
$101$	11.7385			1.16802			0.584011	−	0.811746i	$-0.301482\pi$
$101$	11.7385			1.16802			0.584011	+	0.811746i	$0.301482\pi$
$102$	0.116660	−	0.294513i	0.0115511	−	0.0291611i
$103$	−11.8499			−1.16761			−0.583803	−	0.811896i	$-0.698436\pi$
$103$	−11.8499			−1.16761			−0.583803	+	0.811896i	$0.698436\pi$
$104$	3.03486	−	3.03486i	0.297593	−	0.297593i
$105$	0.111041	−	0.268077i	0.0108365	−	0.0261616i
$106$		−	10.4188i		−	1.01196i
$107$	1.64733	+	0.682347i	0.159254	+	0.0659650i	0.460886	−	0.887459i	$-0.347532\pi$
$107$	1.64733	+	0.682347i	0.159254	+	0.0659650i	−0.301633	+	0.953424i	$0.597532\pi$
$108$	0.176235	+	0.425469i	0.0169582	+	0.0409408i
$109$	−7.61732	+	3.15520i	−0.729607	+	0.302213i	−0.716391	−	0.697699i	$-0.754207\pi$
$109$	−7.61732	+	3.15520i	−0.729607	+	0.302213i	−0.0132167	+	0.999913i	$0.504207\pi$
$110$	2.58514	+	2.58514i	0.246484	+	0.246484i
$111$	−0.440772	−	0.440772i	−0.0418362	−	0.0418362i
$112$	−3.48924	+	1.44529i	−0.329702	+	0.136567i
$113$	−2.46195	−	5.94368i	−0.231601	−	0.559134i	0.764765	−	0.644309i	$-0.222855\pi$
$113$	−2.46195	−	5.94368i	−0.231601	−	0.559134i	−0.996366	+	0.0851751i	$0.972855\pi$
$114$	0.219346	+	0.0908561i	0.0205436	+	0.00850945i
$115$			6.47400i			0.603704i
$116$	0.871055	−	2.10291i	0.0808754	−	0.195251i
$117$	9.08667	−	9.08667i	0.840063	−	0.840063i
$118$	4.80347			0.442195
$119$	14.4774	+	5.73467i	1.32714	+	0.525696i
$120$	0.0768297			0.00701356
$121$	−1.67297	+	1.67297i	−0.152088	+	0.152088i
$122$	1.06151	−	2.56272i	0.0961050	−	0.232018i
$123$		−	0.633351i		−	0.0571074i
$124$	−5.58873	−	2.31493i	−0.501882	−	0.207887i
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$	−10.4471	+	4.32734i	−0.930703	+	0.385510i
$127$	−2.51714	−	2.51714i	−0.223360	−	0.223360i	0.586552	−	0.809912i	$-0.300485\pi$
$127$	−2.51714	−	2.51714i	−0.223360	−	0.223360i	−0.809912	+	0.586552i	$0.800485\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.783453	−	0.324517i	0.0689792	−	0.0285721i
$130$	−1.64246	−	3.96524i	−0.144053	−	0.347774i
$131$	−13.1945	−	5.46533i	−1.15281	−	0.477508i	−0.277333	−	0.960774i	$-0.589450\pi$
$131$	−13.1945	−	5.46533i	−1.15281	−	0.477508i	−0.875474	+	0.483266i	$0.839450\pi$
$132$			0.280885i			0.0244479i
$133$	−4.46622	+	10.7824i	−0.387271	+	0.934954i
$134$	−2.43097	+	2.43097i	−0.210003	+	0.210003i
$135$	0.460524			0.0396356
$136$	0.0641084	+	4.12261i	0.00549725	+	0.353511i
$137$	−7.89423			−0.674450			−0.337225	−	0.941424i	$-0.609488\pi$
$137$	−7.89423			−0.674450			−0.337225	+	0.941424i	$0.609488\pi$
$138$	−0.351712	+	0.351712i	−0.0299397	+	0.0299397i
$139$	1.53396	−	3.70331i	0.130109	−	0.314111i	−0.845378	−	0.534169i	$-0.820625\pi$
$139$	1.53396	−	3.70331i	0.130109	−	0.314111i	0.975487	+	0.220058i	$0.0706247\pi$
$140$			3.77672i			0.319191i
$141$	0.587239	+	0.243242i	0.0494544	+	0.0204847i
$142$	−5.25072	−	12.6764i	−0.440630	−	1.06378i
$143$	14.4967	−	6.00473i	1.21227	−	0.502141i
$144$	−2.11715	−	2.11715i	−0.176429	−	0.176429i
$145$	−1.60950	−	1.60950i	−0.133662	−	0.133662i
$146$	−10.9486	+	4.53508i	−0.906117	+	0.375326i
$147$	0.213561	+	0.515583i	0.0176142	+	0.0425246i
$148$	7.49575	+	3.10484i	0.616147	+	0.255216i
$149$		−	18.2611i		−	1.49601i	−0.663692	−	0.748006i	$-0.731012\pi$
$149$		−	18.2611i		−	1.49601i	0.663692	−	0.748006i	$-0.268988\pi$
$150$	0.0294014	−	0.0709814i	0.00240062	−	0.00579560i
$151$	10.6876	−	10.6876i	0.869743	−	0.869743i	−0.122700	−	0.992444i	$-0.539155\pi$
$151$	10.6876	−	10.6876i	0.869743	−	0.869743i	0.992444	+	0.122700i	$0.0391554\pi$
$152$	−3.09019			−0.250648
$153$	0.191947	+	12.3435i	0.0155180	+	0.997912i
$154$	−13.8075			−1.11264
$155$	−4.27743	+	4.27743i	−0.343571	+	0.343571i
$156$	0.126189	−	0.304648i	0.0101032	−	0.0243914i
$157$		−	12.5469i		−	1.00135i	−0.865634	−	0.500677i	$-0.833084\pi$
$157$		−	12.5469i		−	1.00135i	0.865634	−	0.500677i	$-0.166916\pi$
$158$	−2.80028	−	1.15991i	−0.222778	−	0.0922777i
$159$	−0.306326	−	0.739537i	−0.0242933	−	0.0586491i
$160$	−0.923880	+	0.382683i	−0.0730391	+	0.0302538i
$161$	−17.2891	−	17.2891i	−1.36257	−	1.36257i
$162$	−6.32642	−	6.32642i	−0.497051	−	0.497051i
$163$	13.1151	−	5.43246i	1.02726	−	0.425503i	0.195534	−	0.980697i	$-0.437356\pi$
$163$	13.1151	−	5.43246i	1.02726	−	0.425503i	0.831721	+	0.555194i	$0.187356\pi$
$164$	3.15468	+	7.61607i	0.246339	+	0.594715i
$165$	0.259504	+	0.107490i	0.0202024	+	0.00836809i
$166$		−	1.83873i		−	0.142713i
$167$	−3.75167	+	9.05734i	−0.290313	+	0.700878i	−0.999993	−	0.00364617i	$-0.998839\pi$
$167$	−3.75167	+	9.05734i	−0.290313	+	0.700878i	0.709680	+	0.704524i	$0.248839\pi$
$168$	−0.205177	+	0.205177i	−0.0158298	+	0.0158298i
$169$	−5.42078			−0.416983
$170$	3.83333	+	1.51843i	0.294003	+	0.116458i
$171$	−9.25234			−0.707544
$172$	−7.80465	+	7.80465i	−0.595099	+	0.595099i
$173$	−1.94144	+	4.68705i	−0.147605	+	0.356350i	−0.980338	−	0.197325i	$-0.936775\pi$
$173$	−1.94144	+	4.68705i	−0.147605	+	0.356350i	0.832733	+	0.553674i	$0.186775\pi$
$174$		−	0.174878i		−	0.0132575i
$175$	3.48924	+	1.44529i	0.263762	+	0.109254i
$176$	−1.39907	−	3.37765i	−0.105459	−	0.254600i
$177$	0.340957	−	0.141229i	0.0256279	−	0.0106154i
$178$	6.81741	+	6.81741i	0.510986	+	0.510986i
$179$	3.03854	+	3.03854i	0.227111	+	0.227111i	0.811485	−	0.584373i	$-0.198660\pi$
$179$	3.03854	+	3.03854i	0.227111	+	0.227111i	−0.584373	+	0.811485i	$0.698660\pi$
$180$	−2.76619	+	1.14579i	−0.206179	+	0.0854022i
$181$	6.59363	+	15.9184i	0.490100	+	1.18321i	0.954669	+	0.297670i	$0.0962095\pi$
$181$	6.59363	+	15.9184i	0.490100	+	1.18321i	−0.464568	+	0.885537i	$0.653791\pi$
$182$	14.9756	+	6.20310i	1.11007	+	0.459804i
$183$		−	0.213116i		−	0.0157540i
$184$	2.47749	−	5.98120i	0.182643	−	0.440940i
$185$	5.73700	−	5.73700i	0.421792	−	0.421792i
$186$	−0.464758			−0.0340777
$187$	−5.55128	+	14.0144i	−0.405950	+	1.02484i
$188$	−8.27314			−0.603381
$189$	−1.22985	+	1.22985i	−0.0894586	+	0.0894586i
$190$	−1.18257	+	2.85497i	−0.0857923	+	0.207121i
$191$		−	10.8947i		−	0.788309i	−0.919044	−	0.394155i	$-0.871037\pi$
$191$		−	10.8947i		−	0.788309i	0.919044	−	0.394155i	$-0.128963\pi$
$192$	−0.0709814	−	0.0294014i	−0.00512264	−	0.00212187i
$193$	7.37516	+	17.8052i	0.530875	+	1.28165i	0.930944	+	0.365161i	$0.118986\pi$
$193$	7.37516	+	17.8052i	0.530875	+	1.28165i	−0.400069	+	0.916485i	$0.631014\pi$
$194$	0.613459	−	0.254103i	0.0440438	−	0.0182435i
$195$	−0.233167	−	0.233167i	−0.0166975	−	0.0166975i
$196$	−5.13617	−	5.13617i	−0.366869	−	0.366869i
$197$	−11.9563	+	4.95246i	−0.851850	+	0.352848i	−0.765515	−	0.643418i	$-0.777516\pi$
$197$	−11.9563	+	4.95246i	−0.851850	+	0.352848i	−0.0863354	+	0.996266i	$0.527516\pi$
$198$	−4.18895	−	10.1130i	−0.297696	−	0.718701i
$199$	4.44093	+	1.83950i	0.314810	+	0.130398i	0.534493	−	0.845173i	$-0.320503\pi$
$199$	4.44093	+	1.83950i	0.314810	+	0.130398i	−0.219684	+	0.975571i	$0.570503\pi$
$200$			1.00000i			0.0707107i
$201$	−0.101079	+	0.244027i	−0.00712959	+	0.0172123i
$202$	−8.30036	+	8.30036i	−0.584011	+	0.584011i
$203$	8.59649			0.603355
$204$	0.125761	+	0.290743i	0.00880504	+	0.0203561i
$205$	8.24358			0.575756
$206$	8.37914	−	8.37914i	0.583803	−	0.583803i
$207$	7.41786	−	17.9083i	0.515577	−	1.24471i
$208$			4.29194i			0.297593i
$209$	−10.4376	−	4.32339i	−0.721984	−	0.299055i
$210$	0.111041	+	0.268077i	0.00766256	+	0.0184991i
$211$	−6.83256	+	2.83014i	−0.470373	+	0.194835i	−0.605263	−	0.796026i	$-0.706932\pi$
$211$	−6.83256	+	2.83014i	−0.470373	+	0.194835i	0.134890	+	0.990861i	$0.456932\pi$
$212$	7.36717	+	7.36717i	0.505979	+	0.505979i
$213$	−0.745406	−	0.745406i	−0.0510744	−	0.0510744i
$214$	−1.64733	+	0.682347i	−0.112609	+	0.0466443i
$215$	4.22385	+	10.1973i	0.288064	+	0.695448i
$216$	−0.425469	−	0.176235i	−0.0289495	−	0.0119913i
$217$		−	22.8461i		−	1.55090i
$218$	3.15520	−	7.61732i	0.213697	−	0.515910i
$219$	−0.643812	+	0.643812i	−0.0435048	+	0.0435048i
$220$	−3.65595			−0.246484
$221$	12.3170	−	12.7061i	0.828530	−	0.854705i
$222$	0.623345			0.0418362
$223$	−0.994253	+	0.994253i	−0.0665801	+	0.0665801i	−0.739613	−	0.673033i	$-0.764991\pi$
$223$	−0.994253	+	0.994253i	−0.0665801	+	0.0665801i	0.673033	+	0.739613i	$0.264991\pi$
$224$	1.44529	−	3.48924i	0.0965675	−	0.233134i
$225$			2.99410i			0.199606i
$226$	5.94368	+	2.46195i	0.395368	+	0.163767i
$227$	0.538299	+	1.29957i	0.0357282	+	0.0862554i	0.940736	−	0.339139i	$-0.110136\pi$
$227$	0.538299	+	1.29957i	0.0357282	+	0.0862554i	−0.905008	+	0.425394i	$0.860136\pi$
$228$	−0.219346	+	0.0908561i	−0.0145265	+	0.00601709i
$229$	15.9495	+	15.9495i	1.05397	+	1.05397i	0.998458	+	0.0555146i	$0.0176799\pi$
$229$	15.9495	+	15.9495i	1.05397	+	1.05397i	0.0555146	+	0.998458i	$0.482320\pi$
$230$	−4.57781	−	4.57781i	−0.301852	−	0.301852i
$231$	−0.980075	+	0.405960i	−0.0644842	+	0.0267102i
$232$	0.871055	+	2.10291i	0.0571876	+	0.138063i
$233$	11.3088	+	4.68427i	0.740866	+	0.306877i	0.721009	−	0.692926i	$-0.243679\pi$
$233$	11.3088	+	4.68427i	0.740866	+	0.306877i	0.0198572	+	0.999803i	$0.493679\pi$
$234$			12.8505i			0.840063i
$235$	−3.16599	+	7.64338i	−0.206527	+	0.498599i
$236$	−3.39657	+	3.39657i	−0.221098	+	0.221098i
$237$	−0.232871			−0.0151266
$238$	−14.2921	+	6.18205i	−0.926419	+	0.400723i
$239$	−16.6182			−1.07494			−0.537470	−	0.843283i	$-0.680620\pi$
$239$	−16.6182			−1.07494			−0.537470	+	0.843283i	$0.680620\pi$
$240$	−0.0543268	+	0.0543268i	−0.00350678	+	0.00350678i
$241$	−2.21235	+	5.34110i	−0.142510	+	0.344050i	−0.978978	−	0.203966i	$-0.934617\pi$
$241$	−2.21235	+	5.34110i	−0.142510	+	0.344050i	0.836468	+	0.548016i	$0.184617\pi$
$242$		−	2.36594i		−	0.152088i
$243$	−1.91147	−	0.791757i	−0.122621	−	0.0507913i
$244$	1.06151	+	2.56272i	0.0679565	+	0.164061i
$245$	−6.71073	+	2.77967i	−0.428733	+	0.177587i
$246$	0.447847	+	0.447847i	0.0285537	+	0.0285537i
$247$	9.37831	+	9.37831i	0.596727	+	0.596727i
$248$	5.58873	−	2.31493i	0.354884	−	0.146998i
$249$	−0.0540614	−	0.130516i	−0.00342600	−	0.00827109i
$250$	0.923880	+	0.382683i	0.0584313	+	0.0242030i
$251$		−	11.1464i		−	0.703554i	−0.936084	−	0.351777i	$-0.885578\pi$
$251$		−	11.1464i		−	0.703554i	0.936084	−	0.351777i	$-0.114422\pi$
$252$	4.32734	−	10.4471i	0.272597	−	0.658106i
$253$	16.7362	−	16.7362i	1.05220	−	1.05220i
$254$	3.55977			0.223360
$255$	0.316739	−	0.00492543i	0.0198349	−	0.000308442i
$256$	1.00000			0.0625000
$257$	5.90592	−	5.90592i	0.368401	−	0.368401i	−0.498493	−	0.866894i	$-0.666113\pi$
$257$	5.90592	−	5.90592i	0.368401	−	0.368401i	0.866894	+	0.498493i	$0.166113\pi$
$258$	−0.324517	+	0.783453i	−0.0202035	+	0.0487756i
$259$			30.6418i			1.90399i
$260$	3.96524	+	1.64246i	0.245914	+	0.101861i
$261$	2.60802	+	6.29633i	0.161433	+	0.389733i
$262$	13.1945	−	5.46533i	0.815157	−	0.337649i
$263$	−5.85789	−	5.85789i	−0.361213	−	0.361213i	0.503047	−	0.864259i	$-0.332212\pi$
$263$	−5.85789	−	5.85789i	−0.361213	−	0.361213i	−0.864259	+	0.503047i	$0.832212\pi$
$264$	−0.198616	−	0.198616i	−0.0122240	−	0.0122240i
$265$	9.62567	−	3.98708i	0.591300	−	0.244925i
$266$	−4.46622	−	10.7824i	−0.273842	−	0.661112i
$267$	0.684351	+	0.283467i	0.0418816	+	0.0173479i
$268$		−	3.43790i		−	0.210003i
$269$	8.85556	−	21.3792i	0.539933	−	1.30351i	−0.384836	−	0.922985i	$-0.625742\pi$
$269$	8.85556	−	21.3792i	0.539933	−	1.30351i	0.924769	−	0.380529i	$-0.124258\pi$
$270$	−0.325640	+	0.325640i	−0.0198178	+	0.0198178i
$271$	21.1328			1.28373			0.641865	−	0.766818i	$-0.278161\pi$
$271$	21.1328			1.28373			0.641865	+	0.766818i	$0.278161\pi$
$272$	−2.96045	−	2.86979i	−0.179504	−	0.174007i
$273$	1.24537			0.0753732
$274$	5.58207	−	5.58207i	0.337225	−	0.337225i
$275$	−1.39907	+	3.37765i	−0.0843671	+	0.203680i
$276$		−	0.497395i		−	0.0299397i
$277$	−20.2092	−	8.37091i	−1.21425	−	0.502959i	−0.318674	−	0.947864i	$-0.603237\pi$
$277$	−20.2092	−	8.37091i	−1.21425	−	0.502959i	−0.895578	+	0.444905i	$0.853237\pi$
$278$	1.53396	+	3.70331i	0.0920009	+	0.222110i
$279$	16.7332	−	6.93111i	1.00179	−	0.414955i
$280$	−2.67055	−	2.67055i	−0.159596	−	0.159596i
$281$	−5.43059	−	5.43059i	−0.323962	−	0.323962i	0.526323	−	0.850285i	$-0.323570\pi$
$281$	−5.43059	−	5.43059i	−0.323962	−	0.323962i	−0.850285	+	0.526323i	$0.823570\pi$
$282$	−0.587239	+	0.243242i	−0.0349695	+	0.0144849i
$283$	−0.296032	−	0.714685i	−0.0175973	−	0.0424836i	0.914837	−	0.403824i	$-0.132319\pi$
$283$	−0.296032	−	0.714685i	−0.0175973	−	0.0424836i	−0.932434	+	0.361340i	$0.882319\pi$
$284$	12.6764	+	5.25072i	0.752203	+	0.311573i
$285$			0.237418i			0.0140635i
$286$	−6.00473	+	14.4967i	−0.355067	+	0.857208i
$287$	−22.0149	+	22.0149i	−1.29950	+	1.29950i
$288$	2.99410			0.176429
$289$	0.528587	+	16.9918i	0.0310934	+	0.999516i
$290$	2.27618			0.133662
$291$	0.0360732	−	0.0360732i	0.00211465	−	0.00211465i
$292$	4.53508	−	10.9486i	0.265395	−	0.640721i
$293$		−	12.7655i		−	0.745770i	−0.927878	−	0.372885i	$-0.878369\pi$
$293$		−	12.7655i		−	0.745770i	0.927878	−	0.372885i	$-0.121631\pi$
$294$	−0.515583	−	0.213561i	−0.0300694	−	0.0124552i
$295$	1.83821	+	4.43783i	0.107025	+	0.258380i
$296$	−7.49575	+	3.10484i	−0.435681	+	0.180465i
$297$	−1.19052	−	1.19052i	−0.0690811	−	0.0690811i
$298$	12.9126	+	12.9126i	0.748006	+	0.748006i
$299$	−25.6710	+	10.6333i	−1.48459	+	0.614937i
$300$	0.0294014	+	0.0709814i	0.00169749	+	0.00409811i
$301$	−38.5123	−	15.9523i	−2.21981	−	0.919475i
$302$			15.1145i			0.869743i
$303$	−0.345128	+	0.833213i	−0.0198271	+	0.0478668i
$304$	2.18510	−	2.18510i	0.125324	−	0.125324i
$305$	2.77387			0.158831
$306$	−8.86389	−	8.59244i	−0.506715	−	0.491197i
$307$	−5.04815			−0.288113			−0.144056	−	0.989569i	$-0.546015\pi$
$307$	−5.04815			−0.288113			−0.144056	+	0.989569i	$0.546015\pi$
$308$	9.76337	−	9.76337i	0.556320	−	0.556320i
$309$	0.348404	−	0.841122i	0.0198200	−	0.0478498i
$310$		−	6.04919i		−	0.343571i
$311$	30.1017	+	12.4685i	1.70691	+	0.707026i	1.00000		0.000274549i	$-8.73916e-5\pi$
$311$	30.1017	+	12.4685i	1.70691	+	0.707026i	0.706913	+	0.707301i	$0.250087\pi$
$312$	0.126189	+	0.304648i	0.00714406	+	0.0172473i
$313$	−15.2374	+	6.31153i	−0.861267	+	0.356749i	−0.769203	−	0.639004i	$-0.779347\pi$
$313$	−15.2374	+	6.31153i	−0.861267	+	0.356749i	−0.0920643	+	0.995753i	$0.529347\pi$
$314$	8.87202	+	8.87202i	0.500677	+	0.500677i
$315$	−7.99588	−	7.99588i	−0.450517	−	0.450517i
$316$	2.80028	−	1.15991i	0.157528	−	0.0652502i
$317$	6.30266	+	15.2160i	0.353993	+	0.854614i	0.996119	+	0.0880151i	$0.0280524\pi$
$317$	6.30266	+	15.2160i	0.353993	+	0.854614i	−0.642127	+	0.766599i	$0.721948\pi$
$318$	0.739537	+	0.306326i	0.0414712	+	0.0171779i
$319$			8.32158i			0.465919i
$320$	0.382683	−	0.923880i	0.0213927	−	0.0516464i
$321$	−0.0968679	+	0.0968679i	−0.00540664	+	0.00540664i
$322$	24.4505			1.36257
$323$	−12.7396	+	0.198107i	−0.708853	+	0.0110230i
$324$	8.94691			0.497051
$325$	3.03486	−	3.03486i	0.168344	−	0.168344i
$326$	−5.43246	+	13.1151i	−0.300876	+	0.726379i
$327$		−	0.633455i		−	0.0350302i
$328$	−7.61607	−	3.15468i	−0.420527	−	0.174188i
$329$	−11.9571	−	28.8669i	−0.659215	−	1.59149i
$330$	−0.259504	+	0.107490i	−0.0142852	+	0.00591713i
$331$	23.7207	+	23.7207i	1.30381	+	1.30381i	0.925804	+	0.378004i	$0.123390\pi$
$331$	23.7207	+	23.7207i	1.30381	+	1.30381i	0.378004	+	0.925804i	$0.376610\pi$
$332$	1.30018	+	1.30018i	0.0713566	+	0.0713566i
$333$	−22.4430	+	9.29619i	−1.22987	+	0.509428i
$334$	−3.75167	−	9.05734i	−0.205282	−	0.495595i
$335$	−3.17621	−	1.31563i	−0.173535	−	0.0718805i
$336$		−	0.290164i		−	0.0158298i
$337$	−3.67487	+	8.87192i	−0.200183	+	0.483284i	−0.991810	−	0.127720i	$-0.959234\pi$
$337$	−3.67487	+	8.87192i	−0.200183	+	0.483284i	0.791627	+	0.611004i	$0.209234\pi$
$338$	3.83307	−	3.83307i	0.208491	−	0.208491i
$339$	0.494275			0.0268454
$340$	−3.78426	+	1.63688i	−0.205230	+	0.0887724i
$341$	22.1155			1.19762
$342$	6.54239	−	6.54239i	0.353772	−	0.353772i
$343$	0.381034	−	0.919897i	0.0205739	−	0.0496697i
$344$		−	11.0374i		−	0.595099i
$345$	−0.459533	−	0.190345i	−0.0247404	−	0.0102478i
$346$	−1.94144	−	4.68705i	−0.104372	−	0.251977i
$347$	−2.87803	+	1.19212i	−0.154501	+	0.0639962i	−0.458594	−	0.888646i	$-0.651647\pi$
$347$	−2.87803	+	1.19212i	−0.154501	+	0.0639962i	0.304093	+	0.952642i	$0.401647\pi$
$348$	0.123657	+	0.123657i	0.00662873	+	0.00662873i
$349$	−22.6314	−	22.6314i	−1.21143	−	1.21143i	−0.970556	−	0.240876i	$-0.922565\pi$
$349$	−22.6314	−	22.6314i	−1.21143	−	1.21143i	−0.240876	−	0.970556i	$-0.577435\pi$
$350$	−3.48924	+	1.44529i	−0.186508	+	0.0772540i
$351$	0.756391	+	1.82609i	0.0403732	+	0.0974694i
$352$	3.37765	+	1.39907i	0.180030	+	0.0745707i
$353$			17.6226i			0.937954i	0.883210	+	0.468977i	$0.155377\pi$
$353$			17.6226i			0.937954i	−0.883210	+	0.468977i	$0.844623\pi$
$354$	−0.141229	+	0.340957i	−0.00750623	+	0.0181217i
$355$	9.70206	−	9.70206i	0.514932	−	0.514932i
$356$	−9.64127			−0.510986
$357$	−0.832711	+	0.859019i	−0.0440718	+	0.0454641i
$358$	−4.29715			−0.227111
$359$	−6.00531	+	6.00531i	−0.316948	+	0.316948i	−0.847594	−	0.530646i	$-0.821949\pi$
$359$	−6.00531	+	6.00531i	−0.316948	+	0.316948i	0.530646	+	0.847594i	$0.321949\pi$
$360$	1.14579	−	2.76619i	0.0603885	−	0.145791i
$361$			9.45071i			0.497406i
$362$	−15.9184	−	6.59363i	−0.836654	−	0.346553i
$363$	−0.0695620	−	0.167938i	−0.00365106	−	0.00881444i
$364$	−14.9756	+	6.20310i	−0.784935	+	0.325131i
$365$	−8.37973	−	8.37973i	−0.438615	−	0.438615i
$366$	0.150695	+	0.150695i	0.00787698	+	0.00787698i
$367$	15.8984	−	6.58534i	0.829891	−	0.343752i	0.0730312	−	0.997330i	$-0.476733\pi$
$367$	15.8984	−	6.58534i	0.829891	−	0.343752i	0.756859	+	0.653578i	$0.226733\pi$
$368$	2.47749	+	5.98120i	0.129148	+	0.311792i
$369$	−22.8033	−	9.44542i	−1.18709	−	0.491709i
$370$			8.11334i			0.421792i
$371$	−15.0581	+	36.3535i	−0.781778	+	1.88738i
$372$	0.328633	−	0.328633i	0.0170388	−	0.0170388i
$373$	−20.1236			−1.04196			−0.520980	−	0.853569i	$-0.674433\pi$
$373$	−20.1236			−1.04196			−0.520980	+	0.853569i	$0.674433\pi$
$374$	−5.98435	−	13.8350i	−0.309443	−	0.715393i
$375$	0.0768297			0.00396747
$376$	5.84999	−	5.84999i	0.301690	−	0.301690i
$377$	3.73852	−	9.02558i	0.192544	−	0.464841i
$378$		−	1.73927i		−	0.0894586i
$379$	4.53043	+	1.87657i	0.232713	+	0.0963927i	0.495993	−	0.868327i	$-0.334804\pi$
$379$	4.53043	+	1.87657i	0.232713	+	0.0963927i	−0.263280	+	0.964719i	$0.584804\pi$
$380$	−1.18257	−	2.85497i	−0.0606643	−	0.146457i
$381$	0.252677	−	0.104662i	0.0129450	−	0.00536201i
$382$	7.70368	+	7.70368i	0.394155	+	0.394155i
$383$	−7.64225	−	7.64225i	−0.390501	−	0.390501i	0.484365	−	0.874866i	$-0.339051\pi$
$383$	−7.64225	−	7.64225i	−0.390501	−	0.390501i	−0.874866	+	0.484365i	$0.839051\pi$
$384$	0.0709814	−	0.0294014i	0.00362225	−	0.00150039i
$385$	−5.28390	−	12.7565i	−0.269292	−	0.650130i
$386$	−17.8052	−	7.37516i	−0.906261	−	0.375386i
$387$		−	33.0472i		−	1.67988i
$388$	−0.254103	+	0.613459i	−0.0129001	+	0.0311437i
$389$	2.32107	−	2.32107i	0.117683	−	0.117683i	−0.645813	−	0.763496i	$-0.723481\pi$
$389$	2.32107	−	2.32107i	0.117683	−	0.117683i	0.763496	+	0.645813i	$0.223481\pi$
$390$	0.329749			0.0166975
$391$	9.83029	−	24.8170i	0.497139	−	1.25505i
$392$	7.26364			0.366869
$393$	0.775873	−	0.775873i	0.0391376	−	0.0391376i
$394$	4.95246	−	11.9563i	0.249501	−	0.602349i
$395$		−	3.03100i		−	0.152506i
$396$	10.1130	+	4.18895i	0.508199	+	0.210503i
$397$	5.38710	+	13.0056i	0.270371	+	0.652733i	0.999499	−	0.0316442i	$-0.0100744\pi$
$397$	5.38710	+	13.0056i	0.270371	+	0.652733i	−0.729129	+	0.684377i	$0.760074\pi$
$398$	−4.44093	+	1.83950i	−0.222604	+	0.0922056i
$399$	−0.634037	−	0.634037i	−0.0317415	−	0.0317415i
$400$	−0.707107	−	0.707107i	−0.0353553	−	0.0353553i
$401$	18.3144	−	7.58609i	0.914579	−	0.378831i	0.124771	−	0.992186i	$-0.460180\pi$
$401$	18.3144	−	7.58609i	0.914579	−	0.378831i	0.789808	+	0.613354i	$0.210180\pi$
$402$	−0.101079	−	0.244027i	−0.00504138	−	0.0121710i
$403$	−23.9865	−	9.93553i	−1.19485	−	0.494924i
$404$		−	11.7385i		−	0.584011i
$405$	3.42383	−	8.26587i	0.170132	−	0.410734i
$406$	−6.07864	+	6.07864i	−0.301678	+	0.301678i
$407$	−29.6619			−1.47029
$408$	−0.294513	−	0.116660i	−0.0145806	−	0.00577554i
$409$	33.6048			1.66165			0.830826	−	0.556533i	$-0.187869\pi$
$409$	33.6048			1.66165			0.830826	+	0.556533i	$0.187869\pi$
$410$	−5.82909	+	5.82909i	−0.287878	+	0.287878i
$411$	0.232102	−	0.560343i	0.0114487	−	0.0276397i
$412$			11.8499i			0.583803i
$413$	−16.7604	−	6.94241i	−0.824728	−	0.341613i
$414$	7.41786	+	17.9083i	0.364568	+	0.880144i
$415$	1.69877	−	0.703652i	0.0833892	−	0.0345409i
$416$	−3.03486	−	3.03486i	−0.148796	−	0.148796i
$417$	0.217765	+	0.217765i	0.0106640	+	0.0106640i
$418$	10.4376	−	4.32339i	0.510520	−	0.211464i
$419$	−5.83251	−	14.0809i	−0.284937	−	0.687898i	0.715000	−	0.699124i	$-0.246426\pi$
$419$	−5.83251	−	14.0809i	−0.284937	−	0.687898i	−0.999937	+	0.0112263i	$0.996426\pi$
$420$	−0.268077	−	0.111041i	−0.0130808	−	0.00541825i
$421$			37.9005i			1.84716i	0.383408	+	0.923579i	$0.374750\pi$
$421$			37.9005i			1.84716i	−0.383408	+	0.923579i	$0.625250\pi$
$422$	2.83014	−	6.83256i	0.137769	−	0.332604i
$423$	17.5154	−	17.5154i	0.851630	−	0.851630i
$424$	−10.4188			−0.505979
$425$	0.0641084	+	4.12261i	0.00310971	+	0.199976i
$426$	1.05416			0.0510744
$427$	−7.40775	+	7.40775i	−0.358486	+	0.358486i
$428$	0.682347	−	1.64733i	0.0329825	−	0.0796268i
$429$			1.20554i			0.0582042i
$430$	−10.1973	−	4.22385i	−0.491756	−	0.203692i
$431$	5.38469	+	12.9998i	0.259371	+	0.626177i	0.998897	−	0.0469506i	$-0.0149503\pi$
$431$	5.38469	+	12.9998i	0.259371	+	0.626177i	−0.739526	+	0.673128i	$0.764950\pi$
$432$	0.425469	−	0.176235i	0.0204704	−	0.00847911i
$433$	−18.2145	−	18.2145i	−0.875332	−	0.875332i	0.117715	−	0.993047i	$-0.462443\pi$
$433$	−18.2145	−	18.2145i	−0.875332	−	0.875332i	−0.993047	+	0.117715i	$0.962443\pi$
$434$	16.1547	+	16.1547i	0.775448	+	0.775448i
$435$	0.161566	−	0.0669229i	0.00774650	−	0.00320871i
$436$	3.15520	+	7.61732i	0.151107	+	0.364804i
$437$	18.4831	+	7.65593i	0.884164	+	0.366233i
$438$		−	0.910488i		−	0.0435048i
$439$	−1.95058	+	4.70912i	−0.0930962	+	0.224754i	−0.963568	−	0.267465i	$-0.913814\pi$
$439$	−1.95058	+	4.70912i	−0.0930962	+	0.224754i	0.870471	+	0.492219i	$0.163814\pi$
$440$	2.58514	−	2.58514i	0.123242	−	0.123242i
$441$	21.7480			1.03562
$442$	0.275150	+	17.6940i	0.0130875	+	0.841618i
$443$	13.3938			0.636357			0.318178	−	0.948031i	$-0.396929\pi$
$443$	13.3938			0.636357			0.318178	+	0.948031i	$0.396929\pi$
$444$	−0.440772	+	0.440772i	−0.0209181	+	0.0209181i
$445$	−3.68955	+	8.90737i	−0.174902	+	0.422250i
$446$		−	1.40609i		−	0.0665801i
$447$	1.29620	+	0.536904i	0.0613082	+	0.0253947i
$448$	1.44529	+	3.48924i	0.0682835	+	0.164851i
$449$	35.9141	−	14.8761i	1.69489	−	0.702046i	0.695032	−	0.718978i	$-0.255390\pi$
$449$	35.9141	−	14.8761i	1.69489	−	0.702046i	0.999857	+	0.0169324i	$0.00539000\pi$
$450$	−2.11715	−	2.11715i	−0.0998032	−	0.0998032i
$451$	−21.3108	−	21.3108i	−1.00349	−	1.00349i
$452$	−5.94368	+	2.46195i	−0.279567	+	0.115800i
$453$	0.444389	+	1.07285i	0.0208792	+	0.0504069i
$454$	−1.29957	−	0.538299i	−0.0609918	−	0.0252636i
$455$			16.2095i			0.759912i
$456$	0.0908561	−	0.219346i	0.00425473	−	0.0102718i
$457$	−15.7065	+	15.7065i	−0.734718	+	0.734718i	−0.971550	−	0.236832i	$-0.923891\pi$
$457$	−15.7065	+	15.7065i	−0.734718	+	0.734718i	0.236832	+	0.971550i	$0.423891\pi$
$458$	−22.5560			−1.05397
$459$	−1.76534	−	0.699272i	−0.0823990	−	0.0326392i
$460$	6.47400			0.301852
$461$	−3.31355	+	3.31355i	−0.154328	+	0.154328i	−0.780048	−	0.625720i	$-0.784805\pi$
$461$	−3.31355	+	3.31355i	−0.154328	+	0.154328i	0.625720	+	0.780048i	$0.284805\pi$
$462$	0.405960	−	0.980075i	0.0188870	−	0.0455972i
$463$			28.3054i			1.31547i	0.753252	+	0.657733i	$0.228484\pi$
$463$			28.3054i			1.31547i	−0.753252	+	0.657733i	$0.771516\pi$
$464$	−2.10291	−	0.871055i	−0.0976253	−	0.0404377i
$465$	−0.177855	−	0.429380i	−0.00824783	−	0.0199120i
$466$	−11.3088	+	4.68427i	−0.523871	+	0.216995i
$467$	15.2361	+	15.2361i	0.705041	+	0.705041i	0.965488	−	0.260447i	$-0.0838699\pi$
$467$	15.2361	+	15.2361i	0.705041	+	0.705041i	−0.260447	+	0.965488i	$0.583870\pi$
$468$	−9.08667	−	9.08667i	−0.420032	−	0.420032i
$469$	11.9957	−	4.96877i	0.553908	−	0.229436i
$470$	−3.16599	−	7.64338i	−0.146036	−	0.352563i
$471$	0.890598	+	0.368898i	0.0410366	+	0.0169979i
$472$		−	4.80347i		−	0.221098i
$473$	15.4422	−	37.2807i	0.710031	−	1.71417i
$474$	0.164664	−	0.164664i	0.00756328	−	0.00756328i
$475$	−3.09019			−0.141788
$476$	5.73467	−	14.4774i	0.262848	−	0.663571i
$477$	−31.1948			−1.42831
$478$	11.7508	−	11.7508i	0.537470	−	0.537470i
$479$	−0.866176	+	2.09113i	−0.0395766	+	0.0955464i	−0.942432	−	0.334398i	$-0.891467\pi$
$479$	−0.866176	+	2.09113i	−0.0395766	+	0.0955464i	0.902855	+	0.429945i	$0.141467\pi$
$480$		−	0.0768297i		−	0.00350678i
$481$	32.1713	+	13.3258i	1.46689	+	0.607604i
$482$	−2.21235	−	5.34110i	−0.100770	−	0.243280i
$483$	1.73553	−	0.718880i	0.0789694	−	0.0327102i
$484$	1.67297	+	1.67297i	0.0760442	+	0.0760442i
$485$	0.469521	+	0.469521i	0.0213199	+	0.0213199i
$486$	1.91147	−	0.791757i	0.0867061	−	0.0359148i
$487$	−11.1821	−	26.9960i	−0.506709	−	1.22330i	−0.945767	−	0.324845i	$-0.894688\pi$
$487$	−11.1821	−	26.9960i	−0.506709	−	1.22330i	0.439058	−	0.898459i	$-0.355312\pi$
$488$	−2.56272	−	1.06151i	−0.116009	−	0.0480525i
$489$			1.09065i			0.0493209i
$490$	2.77967	−	6.71073i	0.125573	−	0.303160i
$491$	−9.60728	+	9.60728i	−0.433570	+	0.433570i	−0.889841	−	0.456271i	$-0.849185\pi$
$491$	−9.60728	+	9.60728i	−0.433570	+	0.433570i	0.456271	+	0.889841i	$0.349185\pi$
$492$	−0.633351			−0.0285537
$493$	3.72583	+	8.61364i	0.167803	+	0.387939i
$494$	−13.2629			−0.596727
$495$	7.74017	−	7.74017i	0.347895	−	0.347895i
$496$	−2.31493	+	5.58873i	−0.103943	+	0.250941i
$497$			51.8196i			2.32443i
$498$	0.130516	+	0.0540614i	0.00584855	+	0.00242255i
$499$	12.0527	+	29.0977i	0.539551	+	1.30259i	0.925036	+	0.379878i	$0.124034\pi$
$499$	12.0527	+	29.0977i	0.539551	+	1.30259i	−0.385485	+	0.922714i	$0.625966\pi$
$500$	−0.923880	+	0.382683i	−0.0413171	+	0.0171141i
$501$	−0.532597	−	0.532597i	−0.0237947	−	0.0237947i
$502$	7.88169	+	7.88169i	0.351777	+	0.351777i
$503$	31.6549	−	13.1119i	1.41142	−	0.584631i	0.458733	−	0.888574i	$-0.348303\pi$
$503$	31.6549	−	13.1119i	1.41142	−	0.584631i	0.952690	+	0.303943i	$0.0983033\pi$
$504$	4.32734	+	10.4471i	0.192755	+	0.465352i
$505$	−10.8449	−	4.49212i	−0.482594	−	0.199897i
$506$			23.6686i			1.05220i
$507$	0.159379	−	0.384774i	0.00707825	−	0.0170884i
$508$	−2.51714	+	2.51714i	−0.111680	+	0.111680i
$509$	8.79968			0.390039			0.195020	−	0.980799i	$-0.437523\pi$
$509$	8.79968			0.390039			0.195020	+	0.980799i	$0.437523\pi$
$510$	−0.220485	+	0.227451i	−0.00976325	+	0.0100717i
$511$	44.7569			1.97993
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.544600	−	1.31478i	0.0240447	−	0.0580490i
$514$			8.35223i			0.368401i
$515$	10.9479	+	4.53476i	0.482421	+	0.199825i
$516$	−0.324517	−	0.783453i	−0.0142861	−	0.0344896i
$517$	27.9438	−	11.5747i	1.22897	−	0.509055i
$518$	−21.6670	−	21.6670i	−0.951995	−	0.951995i
$519$	−0.275612	−	0.275612i	−0.0120980	−	0.0120980i
$520$	−3.96524	+	1.64246i	−0.173887	+	0.0720264i
$521$	2.45379	+	5.92397i	0.107502	+	0.259534i	0.968472	−	0.249123i	$-0.0801423\pi$
$521$	2.45379	+	5.92397i	0.107502	+	0.259534i	−0.860970	+	0.508657i	$0.830142\pi$
$522$	−6.29633	−	2.60802i	−0.275583	−	0.114150i
$523$		−	27.5457i		−	1.20449i	−0.798312	−	0.602245i	$-0.794273\pi$
$523$		−	27.5457i		−	1.20449i	0.798312	−	0.602245i	$-0.205727\pi$
$524$	−5.46533	+	13.1945i	−0.238754	+	0.576403i
$525$	−0.205177	+	0.205177i	−0.00895467	+	0.00895467i
$526$	8.28430			0.361213
$527$	22.8917	−	9.90182i	0.997179	−	0.431330i
$528$	0.280885			0.0122240
$529$	−13.3733	+	13.3733i	−0.581448	+	0.581448i
$530$	−3.98708	+	9.62567i	−0.173188	+	0.418112i
$531$		−	14.3821i		−	0.624128i
$532$	10.7824	+	4.46622i	0.467477	+	0.193635i
$533$	13.5397	+	32.6878i	0.586470	+	1.41586i
$534$	−0.684351	+	0.283467i	−0.0296147	+	0.0122668i
$535$	−1.26081	−	1.26081i	−0.0545097	−	0.0545097i
$536$	2.43097	+	2.43097i	0.105002	+	0.105002i
$537$	−0.305018	+	0.126342i	−0.0131625	+	0.00545208i
$538$	8.85556	+	21.3792i	0.381790	+	0.921724i
$539$	24.5341	+	10.1623i	1.05676	+	0.437723i
$540$		−	0.460524i		−	0.0198178i
$541$	5.58521	−	13.4839i	0.240127	−	0.579718i	−0.757168	−	0.653220i	$-0.773418\pi$
$541$	5.58521	−	13.4839i	0.240127	−	0.579718i	0.997295	+	0.0735024i	$0.0234176\pi$
$542$	−14.9432	+	14.9432i	−0.641865	+	0.641865i
$543$	−1.32377			−0.0568086
$544$	4.12261	−	0.0641084i	0.176755	−	0.00274862i
$545$	8.24493			0.353174
$546$	−0.880609	+	0.880609i	−0.0376866	+	0.0376866i
$547$	15.0445	−	36.3206i	0.643256	−	1.55296i	−0.179006	−	0.983848i	$-0.557288\pi$
$547$	15.0445	−	36.3206i	0.643256	−	1.55296i	0.822262	−	0.569109i	$-0.192712\pi$
$548$			7.89423i			0.337225i
$549$	−7.67304	−	3.17828i	−0.327477	−	0.135646i
$550$	−1.39907	−	3.37765i	−0.0596565	−	0.144024i
$551$	−6.49841	+	2.69173i	−0.276841	+	0.114671i
$552$	0.351712	+	0.351712i	0.0149698	+	0.0149698i
$553$	8.09442	+	8.09442i	0.344210	+	0.344210i
$554$	20.2092	−	8.37091i	0.858605	−	0.355646i
$555$	0.238544	+	0.575896i	0.0101256	+	0.0244454i
$556$	−3.70331	−	1.53396i	−0.157055	−	0.0650544i
$557$		−	19.4304i		−	0.823293i	−0.911344	−	0.411646i	$-0.864954\pi$
$557$		−	19.4304i		−	0.823293i	0.911344	−	0.411646i	$-0.135046\pi$
$558$	−6.93111	+	16.7332i	−0.293417	+	0.708372i
$559$	−33.4971	+	33.4971i	−1.41678	+	1.41678i
$560$	3.77672			0.159596
$561$	−0.831548	−	0.806082i	−0.0351080	−	0.0340328i
$562$	7.68001			0.323962
$563$	−16.6810	+	16.6810i	−0.703022	+	0.703022i	−0.965058	−	0.262036i	$-0.915606\pi$
$563$	−16.6810	+	16.6810i	−0.703022	+	0.703022i	0.262036	+	0.965058i	$0.415606\pi$
$564$	0.243242	−	0.587239i	0.0102423	−	0.0247272i
$565$			6.43339i			0.270655i
$566$	0.714685	+	0.296032i	0.0300405	+	0.0124432i
$567$	12.9309	+	31.2179i	0.543046	+	1.31103i
$568$	−12.6764	+	5.25072i	−0.531888	+	0.220315i
$569$	−29.3815	−	29.3815i	−1.23173	−	1.23173i	−0.963297	−	0.268437i	$-0.913493\pi$
$569$	−29.3815	−	29.3815i	−1.23173	−	1.23173i	−0.268437	−	0.963297i	$-0.586507\pi$
$570$	−0.167880	−	0.167880i	−0.00703173	−	0.00703173i
$571$	−21.5455	+	8.92444i	−0.901651	+	0.373476i	−0.784855	−	0.619680i	$-0.787262\pi$
$571$	−21.5455	+	8.92444i	−0.901651	+	0.373476i	−0.116796	+	0.993156i	$0.537262\pi$
$572$	−6.00473	−	14.4967i	−0.251070	−	0.606137i
$573$	0.773317	+	0.320318i	0.0323058	+	0.0133815i
$574$		−	31.1337i		−	1.29950i
$575$	2.47749	−	5.98120i	0.103319	−	0.249433i
$576$	−2.11715	+	2.11715i	−0.0882144	+	0.0882144i
$577$	19.7415			0.821850			0.410925	−	0.911669i	$-0.365206\pi$
$577$	19.7415			0.821850			0.410925	+	0.911669i	$0.365206\pi$
$578$	−12.3888	−	11.6412i	−0.515305	−	0.484212i
$579$	−1.48068			−0.0615349
$580$	−1.60950	+	1.60950i	−0.0668309	+	0.0668309i
$581$	−2.65750	+	6.41577i	−0.110252	+	0.266171i
$582$			0.0510151i			0.00211465i
$583$	−35.1909	−	14.5766i	−1.45746	−	0.603699i
$584$	4.53508	+	10.9486i	0.187663	+	0.453058i
$585$	−11.8723	+	4.91767i	−0.490860	+	0.203321i
$586$	9.02659	+	9.02659i	0.372885	+	0.372885i
$587$	27.3477	+	27.3477i	1.12876	+	1.12876i	0.990379	+	0.138379i	$0.0441893\pi$
$587$	27.3477	+	27.3477i	1.12876	+	1.12876i	0.138379	+	0.990379i	$0.455811\pi$
$588$	0.515583	−	0.213561i	0.0212623	−	0.00880712i
$589$	7.15357	+	17.2702i	0.294758	+	0.711608i
$590$	−4.43783	−	1.83821i	−0.182703	−	0.0756779i
$591$		−	0.994283i		−	0.0408993i
$592$	3.10484	−	7.49575i	0.127608	−	0.308073i
$593$	−8.92401	+	8.92401i	−0.366465	+	0.366465i	−0.866186	−	0.499721i	$-0.833436\pi$
$593$	−8.92401	+	8.92401i	−0.366465	+	0.366465i	0.499721	+	0.866186i	$0.333436\pi$
$594$	1.68365			0.0690811
$595$	−11.1808	−	10.8384i	−0.458369	−	0.444331i
$596$	−18.2611			−0.748006
$597$	−0.261140	+	0.261140i	−0.0106877	+	0.0106877i
$598$	10.6333	−	25.6710i	0.434826	−	1.04976i
$599$		−	37.9702i		−	1.55142i	−0.631090	−	0.775710i	$-0.717392\pi$
$599$		−	37.9702i		−	1.55142i	0.631090	−	0.775710i	$-0.282608\pi$
$600$	−0.0709814	−	0.0294014i	−0.00289780	−	0.00120031i
$601$	−12.1056	−	29.2254i	−0.493796	−	1.19213i	−0.952774	−	0.303682i	$-0.901784\pi$
$601$	−12.1056	−	29.2254i	−0.493796	−	1.19213i	0.458977	−	0.888448i	$-0.348216\pi$
$602$	38.5123	−	15.9523i	1.56964	−	0.650167i
$603$	7.27855	+	7.27855i	0.296405	+	0.296405i
$604$	−10.6876	−	10.6876i	−0.434872	−	0.434872i
$605$	2.18584	−	0.905406i	0.0888671	−	0.0368100i
$606$	−0.345128	−	0.833213i	−0.0140199	−	0.0338470i
$607$	−25.2002	−	10.4383i	−1.02285	−	0.423676i	−0.192720	−	0.981254i	$-0.561731\pi$
$607$	−25.2002	−	10.4383i	−1.02285	−	0.423676i	−0.830125	+	0.557577i	$0.811731\pi$
$608$			3.09019i			0.125324i
$609$	−0.252749	+	0.610191i	−0.0102419	+	0.0247262i
$610$	−1.96142	+	1.96142i	−0.0794157	+	0.0794157i
$611$	−35.5078			−1.43649
$612$	12.3435	−	0.191947i	0.498956	−	0.00775899i
$613$	29.8129			1.20413			0.602066	−	0.798446i	$-0.294344\pi$
$613$	29.8129			1.20413			0.602066	+	0.798446i	$0.294344\pi$
$614$	3.56958	−	3.56958i	0.144056	−	0.144056i
$615$	−0.242373	+	0.585140i	−0.00977343	+	0.0235951i
$616$			13.8075i			0.556320i
$617$	−31.5300	−	13.0602i	−1.26935	−	0.525782i	−0.356584	−	0.934263i	$-0.616059\pi$
$617$	−31.5300	−	13.0602i	−1.26935	−	0.525782i	−0.912767	+	0.408481i	$0.866059\pi$
$618$	0.348404	+	0.841122i	0.0140149	+	0.0338349i
$619$	32.3460	−	13.3981i	1.30009	−	0.538517i	0.378116	−	0.925758i	$-0.376572\pi$
$619$	32.3460	−	13.3981i	1.30009	−	0.538517i	0.921978	+	0.387242i	$0.126572\pi$
$620$	4.27743	+	4.27743i	0.171786	+	0.171786i
$621$	2.10819	+	2.10819i	0.0845989	+	0.0845989i
$622$	−30.1017	+	12.4685i	−1.20697	+	0.499943i
$623$	−13.9344	−	33.6407i	−0.558271	−	1.34779i
$624$	−0.304648	−	0.126189i	−0.0121957	−	0.00505162i
$625$			1.00000i			0.0400000i
$626$	6.31153	−	15.2374i	0.252259	−	0.609008i
$627$	0.613761	−	0.613761i	0.0245112	−	0.0245112i
$628$	−12.5469			−0.500677
$629$	−30.7030	+	13.2806i	−1.22421	+	0.529531i
$630$	11.3079			0.450517
$631$	19.8109	−	19.8109i	0.788658	−	0.788658i	−0.192616	−	0.981274i	$-0.561697\pi$
$631$	19.8109	−	19.8109i	0.788658	−	0.788658i	0.981274	+	0.192616i	$0.0616971\pi$
$632$	−1.15991	+	2.80028i	−0.0461388	+	0.111389i
$633$		−	0.568195i		−	0.0225837i
$634$	−15.2160	−	6.30266i	−0.604303	−	0.250311i
$635$	1.36226	+	3.28880i	0.0540598	+	0.130512i
$636$	−0.739537	+	0.306326i	−0.0293246	+	0.0121466i
$637$	−22.0441	−	22.0441i	−0.873421	−	0.873421i
$638$	−5.88424	−	5.88424i	−0.232959	−	0.232959i
$639$	−37.9542	+	15.7212i	−1.50145	+	0.621919i
$640$	0.382683	+	0.923880i	0.0151269	+	0.0365195i
$641$	7.49564	+	3.10480i	0.296060	+	0.122632i	0.525769	−	0.850627i	$-0.323778\pi$
$641$	7.49564	+	3.10480i	0.296060	+	0.122632i	−0.229709	+	0.973259i	$0.573778\pi$
$642$		−	0.136992i		−	0.00540664i
$643$	2.30152	−	5.55636i	0.0907631	−	0.219121i	−0.871979	−	0.489544i	$-0.837163\pi$
$643$	2.30152	−	5.55636i	0.0907631	−	0.219121i	0.962742	+	0.270422i	$0.0871633\pi$
$644$	−17.2891	+	17.2891i	−0.681287	+	0.681287i
$645$	−0.848003			−0.0333901
$646$	8.86821	−	9.14837i	0.348915	−	0.359938i
$647$	−39.5004			−1.55292			−0.776460	−	0.630167i	$-0.782986\pi$
$647$	−39.5004			−1.55292			−0.776460	+	0.630167i	$0.782986\pi$
$648$	−6.32642	+	6.32642i	−0.248525	+	0.248525i
$649$	6.72039	−	16.2245i	0.263798	−	0.636866i
$650$			4.29194i			0.168344i
$651$	1.62165	+	0.671709i	0.0635574	+	0.0263264i
$652$	−5.43246	−	13.1151i	−0.212752	−	0.513628i
$653$	35.3140	−	14.6275i	1.38194	−	0.572420i	0.436944	−	0.899489i	$-0.356061\pi$
$653$	35.3140	−	14.6275i	1.38194	−	0.572420i	0.945001	+	0.327069i	$0.106061\pi$
$654$	0.447921	+	0.447921i	0.0175151	+	0.0175151i
$655$	10.0986	+	10.0986i	0.394585	+	0.394585i
$656$	7.61607	−	3.15468i	0.297358	−	0.123170i
$657$	13.5785	+	32.7813i	0.529746	+	1.27892i
$658$	28.8669	+	11.9571i	1.12535	+	0.466135i
$659$			11.1500i			0.434341i	0.976134	+	0.217170i	$0.0696827\pi$
$659$			11.1500i			0.434341i	−0.976134	+	0.217170i	$0.930317\pi$
$660$	0.107490	−	0.259504i	0.00418405	−	0.0101012i
$661$	−10.8663	+	10.8663i	−0.422650	+	0.422650i	−0.886115	−	0.463465i	$-0.846606\pi$
$661$	−10.8663	+	10.8663i	−0.422650	+	0.422650i	0.463465	+	0.886115i	$0.346606\pi$
$662$	−33.5462			−1.30381
$663$	0.539759	+	1.24785i	0.0209625	+	0.0484626i
$664$	−1.83873			−0.0713566
$665$	8.25250	−	8.25250i	0.320018	−	0.320018i
$666$	9.29619	−	22.4430i	0.360220	−	0.869648i
$667$		−	14.7360i		−	0.570579i
$668$	9.05734	+	3.75167i	0.350439	+	0.145157i
$669$	−0.0413410	−	0.0998059i	−0.00159833	−	0.00385872i
$670$	3.17621	−	1.31563i	0.122708	−	0.0508272i
$671$	−7.17085	−	7.17085i	−0.276828	−	0.276828i
$672$	0.205177	+	0.205177i	0.00791488	+	0.00791488i
$673$	−16.1225	+	6.67817i	−0.621478	+	0.257425i	−0.671127	−	0.741342i	$-0.734190\pi$
$673$	−16.1225	+	6.67817i	−0.621478	+	0.257425i	0.0496494	+	0.998767i	$0.484190\pi$
$674$	−3.67487	−	8.87192i	−0.141551	−	0.341733i
$675$	−0.425469	−	0.176235i	−0.0163763	−	0.00678329i
$676$			5.42078i			0.208491i
$677$	5.69814	−	13.7565i	0.218997	−	0.528706i	−0.775753	−	0.631036i	$-0.782630\pi$
$677$	5.69814	−	13.7565i	0.218997	−	0.528706i	0.994750	+	0.102330i	$0.0326298\pi$
$678$	−0.349505	+	0.349505i	−0.0134227	+	0.0134227i
$679$	−2.50776			−0.0962389
$680$	1.51843	−	3.83333i	0.0582289	−	0.147001i
$681$	−0.108072			−0.00414133
$682$	−15.6380	+	15.6380i	−0.598811	+	0.598811i
$683$	−2.48109	+	5.98987i	−0.0949361	+	0.229196i	−0.964213	−	0.265130i	$-0.914585\pi$
$683$	−2.48109	+	5.98987i	−0.0949361	+	0.229196i	0.869277	+	0.494326i	$0.164585\pi$
$684$			9.25234i			0.353772i
$685$	7.29332	+	3.02099i	0.278663	+	0.115426i
$686$	0.381034	+	0.919897i	0.0145479	+	0.0351218i
$687$	−1.60106	+	0.663179i	−0.0610841	+	0.0253018i
$688$	7.80465	+	7.80465i	0.297550	+	0.297550i
$689$	31.6195	+	31.6195i	1.20461	+	1.20461i
$690$	0.459533	−	0.190345i	0.0174941	−	0.00724631i
$691$	−18.7413	−	45.2454i	−0.712951	−	1.72122i	−0.692493	−	0.721425i	$-0.743487\pi$
$691$	−18.7413	−	45.2454i	−0.712951	−	1.72122i	−0.0204584	−	0.999791i	$-0.506513\pi$
$692$	4.68705	+	1.94144i	0.178175	+	0.0738025i
$693$			41.3410i			1.57041i
$694$	1.19212	−	2.87803i	0.0452522	−	0.109248i
$695$	−2.83439	+	2.83439i	−0.107515	+	0.107515i
$696$	−0.174878			−0.00662873
$697$	−31.6003	−	12.5173i	−1.19695	−	0.474125i
$698$	32.0057			1.21143
$699$	−0.664991	+	0.664991i	−0.0251523	+	0.0251523i
$700$	1.44529	−	3.48924i	0.0546268	−	0.131881i
$701$		−	7.64686i		−	0.288818i	−0.989518	−	0.144409i	$-0.953872\pi$
$701$		−	7.64686i		−	0.288818i	0.989518	−	0.144409i	$-0.0461281\pi$
$702$	−1.82609	−	0.756391i	−0.0689213	−	0.0285481i
$703$	−9.59455	−	23.1633i	−0.361865	−	0.873620i
$704$	−3.37765	+	1.39907i	−0.127300	+	0.0527294i
$705$	−0.449453	−	0.449453i	−0.0169274	−	0.0169274i
$706$	−12.4610	−	12.4610i	−0.468977	−	0.468977i
$707$	40.9583	−	16.9655i	1.54040	−	0.638053i
$708$	−0.141229	−	0.340957i	−0.00530771	−	0.0128139i
$709$	0.149541	+	0.0619419i	0.00561613	+	0.00232628i	0.385490	−	0.922712i	$-0.374033\pi$
$709$	0.149541	+	0.0619419i	0.00561613	+	0.00232628i	−0.379874	+	0.925038i	$0.624033\pi$
$710$			13.7208i			0.514932i
$711$	−3.47289	+	8.38430i	−0.130244	+	0.314436i
$712$	6.81741	−	6.81741i	0.255493	−	0.255493i
$713$	−39.1625			−1.46665
$714$	−0.0186020	−	1.19623i	−0.000696161	−	0.0447679i
$715$	−15.6911			−0.586814
$716$	3.03854	−	3.03854i	0.113556	−	0.113556i
$717$	0.488598	−	1.17958i	0.0182470	−	0.0440522i
$718$		−	8.49279i		−	0.316948i
$719$	7.07071	+	2.92878i	0.263693	+	0.109225i	0.510613	−	0.859811i	$-0.329418\pi$
$719$	7.07071	+	2.92878i	0.263693	+	0.109225i	−0.246920	+	0.969036i	$0.579418\pi$
$720$	1.14579	+	2.76619i	0.0427011	+	0.103090i
$721$	−41.3471	+	17.1265i	−1.53985	+	0.637825i
$722$	−6.68266	−	6.68266i	−0.248703	−	0.248703i
$723$	−0.314072	−	0.314072i	−0.0116805	−	0.0116805i
$724$	15.9184	−	6.59363i	0.591604	−	0.245050i
$725$	0.871055	+	2.10291i	0.0323502	+	0.0781002i
$726$	0.167938	+	0.0695620i	0.00623275	+	0.00258169i
$727$		−	10.5486i		−	0.391226i	−0.980681	−	0.195613i	$-0.937330\pi$
$727$		−	10.5486i		−	0.391226i	0.980681	−	0.195613i	$-0.0626696\pi$
$728$	6.20310	−	14.9756i	0.229902	−	0.555033i
$729$	−18.8669	+	18.8669i	−0.698773	+	0.698773i
$730$	11.8507			0.438615
$731$	−0.707593	−	45.5030i	−0.0261713	−	1.68299i
$732$	−0.213116			−0.00787698
$733$	8.68304	−	8.68304i	0.320715	−	0.320715i	−0.528326	−	0.849042i	$-0.677180\pi$
$733$	8.68304	−	8.68304i	0.320715	−	0.320715i	0.849042	+	0.528326i	$0.177180\pi$
$734$	−6.58534	+	15.8984i	−0.243069	+	0.586821i
$735$		−	0.558063i		−	0.0205845i
$736$	−5.98120	−	2.47749i	−0.220470	−	0.0913216i
$737$	4.80987	+	11.6120i	0.177174	+	0.427735i
$738$	22.8033	−	9.44542i	0.839400	−	0.347691i
$739$	0.773850	+	0.773850i	0.0284665	+	0.0284665i	0.721197	−	0.692730i	$-0.243592\pi$
$739$	0.773850	+	0.773850i	0.0284665	+	0.0284665i	−0.692730	+	0.721197i	$0.743592\pi$
$740$	−5.73700	−	5.73700i	−0.210896	−	0.210896i
$741$	−0.941421	+	0.389949i	−0.0345840	+	0.0143251i
$742$	−15.0581	−	36.3535i	−0.552801	−	1.33458i
$743$	19.6436	+	8.13666i	0.720655	+	0.298505i	0.712706	−	0.701463i	$-0.247470\pi$
$743$	19.6436	+	8.13666i	0.720655	+	0.298505i	0.00794943	+	0.999968i	$0.497470\pi$
$744$			0.464758i			0.0170388i
$745$	−6.98824	+	16.8711i	−0.256029	+	0.618109i
$746$	14.2295	−	14.2295i	0.520980	−	0.520980i
$747$	−5.50534			−0.201430
$748$	14.0144	+	5.55128i	0.512418	+	0.202975i
$749$	6.73412			0.246059
$750$	−0.0543268	+	0.0543268i	−0.00198373	+	0.00198373i
$751$	−15.8710	+	38.3159i	−0.579139	+	1.39817i	0.314447	+	0.949275i	$0.398181\pi$
$751$	−15.8710	+	38.3159i	−0.579139	+	1.39817i	−0.893586	+	0.448891i	$0.851819\pi$
$752$			8.27314i			0.301690i
$753$	0.791186	+	0.327720i	0.0288324	+	0.0119428i
$754$	3.73852	+	9.02558i	0.136149	+	0.328692i
$755$	−13.9640	+	5.78408i	−0.508202	+	0.210504i
$756$	1.22985	+	1.22985i	0.0447293	+	0.0447293i
$757$	23.4753	+	23.4753i	0.853224	+	0.853224i	0.990529	−	0.137305i	$-0.0438440\pi$
$757$	23.4753	+	23.4753i	0.853224	+	0.853224i	−0.137305	+	0.990529i	$0.543844\pi$
$758$	−4.53043	+	1.87657i	−0.164553	+	0.0681599i
$759$	0.695891	+	1.68003i	0.0252592	+	0.0609812i
$760$	2.85497	+	1.18257i	0.103560	+	0.0428962i
$761$			37.4747i			1.35846i	0.733927	+	0.679228i	$0.237685\pi$
$761$			37.4747i			1.35846i	−0.733927	+	0.679228i	$0.762315\pi$
$762$	−0.104662	+	0.252677i	−0.00379151	+	0.00915352i
$763$	−22.0185	+	22.0185i	−0.797122	+	0.797122i
$764$	−10.8947			−0.394155
$765$	4.54631	−	11.4773i	0.164372	−	0.414964i
$766$	10.8078			0.390501
$767$	−14.5779	+	14.5779i	−0.526376	+	0.526376i
$768$	−0.0294014	+	0.0709814i	−0.00106093	+	0.00256132i
$769$			44.3763i			1.60025i	0.599832	+	0.800126i	$0.295234\pi$
$769$			44.3763i			1.60025i	−0.599832	+	0.800126i	$0.704766\pi$
$770$	12.7565	+	5.28390i	0.459711	+	0.190419i
$771$	0.245567	+	0.592852i	0.00884390	+	0.0213511i
$772$	17.8052	−	7.37516i	0.640823	−	0.265438i
$773$	13.4791	+	13.4791i	0.484810	+	0.484810i	0.906664	−	0.421854i	$-0.138620\pi$
$773$	13.4791	+	13.4791i	0.484810	+	0.484810i	−0.421854	+	0.906664i	$0.638620\pi$
$774$	23.3679	+	23.3679i	0.839941	+	0.839941i
$775$	5.58873	−	2.31493i	0.200753	−	0.0831546i
$776$	−0.254103	−	0.613459i	−0.00912177	−	0.0220219i
$777$	−2.17500	−	0.900914i	−0.0780277	−	0.0323201i
$778$			3.28249i			0.117683i
$779$	9.74857	−	23.5351i	0.349279	−	0.843233i
$780$	−0.233167	+	0.233167i	−0.00834873	+	0.00834873i
$781$	−50.1624			−1.79495
$782$	10.5972	+	24.4993i	0.378954	+	0.876093i
$783$	−1.04824			−0.0374609
$784$	−5.13617	+	5.13617i	−0.183435	+	0.183435i
$785$	−4.80150	+	11.5918i	−0.171373	+	0.413731i
$786$			1.09725i			0.0391376i
$787$	−10.2624	−	4.25085i	−0.365817	−	0.151526i	0.192200	−	0.981356i	$-0.438438\pi$
$787$	−10.2624	−	4.25085i	−0.365817	−	0.151526i	−0.558017	+	0.829829i	$0.688438\pi$
$788$	4.95246	+	11.9563i	0.176424	+	0.425925i
$789$	0.588031	−	0.243570i	0.0209345	−	0.00867134i
$790$	2.14324	+	2.14324i	0.0762530	+	0.0762530i
$791$	−17.1807	−	17.1807i	−0.610874	−	0.610874i
$792$	−10.1130	+	4.18895i	−0.359351	+	0.148848i
$793$	4.55596	+	10.9991i	0.161787	+	0.390588i
$794$	−13.0056	−	5.38710i	−0.461552	−	0.191181i
$795$			0.800469i			0.0283897i
$796$	1.83950	−	4.44093i	0.0651992	−	0.157405i
$797$	23.4995	−	23.4995i	0.832395	−	0.832395i	−0.155449	−	0.987844i	$-0.549682\pi$
$797$	23.4995	−	23.4995i	0.832395	−	0.832395i	0.987844	+	0.155449i	$0.0496824\pi$
$798$	0.896664			0.0317415
$799$	23.7422	−	24.4923i	0.839938	−	0.866474i
$800$	1.00000			0.0353553
$801$	20.4120	−	20.4120i	0.721222	−	0.721222i
$802$	−7.58609	+	18.3144i	−0.267874	+	0.646705i
$803$			43.3256i			1.52893i
$804$	0.244027	+	0.101079i	0.00860617	+	0.00356479i
$805$	9.35681	+	22.5893i	0.329784	+	0.796169i
$806$	23.9865	−	9.93553i	0.844888	−	0.349964i
$807$	1.25716	+	1.25716i	0.0442541	+	0.0442541i
$808$	8.30036	+	8.30036i	0.292006	+	0.292006i
$809$	14.2590	−	5.90626i	0.501319	−	0.207653i	−0.117670	−	0.993053i	$-0.537543\pi$
$809$	14.2590	−	5.90626i	0.501319	−	0.207653i	0.618989	+	0.785400i	$0.287543\pi$
$810$	3.42383	+	8.26587i	0.120301	+	0.290433i
$811$	−23.3130	−	9.65655i	−0.818629	−	0.339087i	−0.0662381	−	0.997804i	$-0.521100\pi$
$811$	−23.3130	−	9.65655i	−0.818629	−	0.339087i	−0.752391	+	0.658716i	$0.771100\pi$
$812$		−	8.59649i		−	0.301678i
$813$	−0.621336	+	1.50004i	−0.0217912	+	0.0526086i
$814$	20.9741	−	20.9741i	0.735143	−	0.735143i
$815$	−14.1957			−0.497254
$816$	0.290743	−	0.125761i	0.0101781	−	0.00440252i
$817$	34.1078			1.19328
$818$	−23.7622	+	23.7622i	−0.830826	+	0.830826i
$819$	18.5727	−	44.8384i	0.648982	−	1.56678i
$820$		−	8.24358i		−	0.287878i
$821$	22.3490	+	9.25726i	0.779985	+	0.323081i	0.736910	−	0.675991i	$-0.236284\pi$
$821$	22.3490	+	9.25726i	0.779985	+	0.323081i	0.0430758	+	0.999072i	$0.486284\pi$
$822$	0.232102	+	0.560343i	0.00809548	+	0.0195442i
$823$	21.9537	−	9.09353i	0.765258	−	0.316980i	0.0343083	−	0.999411i	$-0.489077\pi$
$823$	21.9537	−	9.09353i	0.765258	−	0.316980i	0.730950	+	0.682431i	$0.239077\pi$
$824$	−8.37914	−	8.37914i	−0.291901	−	0.291901i
$825$	−0.198616	−	0.198616i	−0.00691491	−	0.00691491i
$826$	16.7604	−	6.94241i	0.583171	−	0.241557i
$827$	11.8863	+	28.6960i	0.413326	+	0.997858i	0.984238	+	0.176847i	$0.0565898\pi$
$827$	11.8863	+	28.6960i	0.413326	+	0.997858i	−0.570912	+	0.821011i	$0.693410\pi$
$828$	−17.9083	−	7.41786i	−0.622356	−	0.257788i
$829$		−	38.0637i		−	1.32201i	−0.750383	−	0.661003i	$-0.770131\pi$
$829$		−	38.0637i		−	1.32201i	0.750383	−	0.661003i	$-0.229869\pi$
$830$	−0.703652	+	1.69877i	−0.0244241	+	0.0589650i
$831$	1.18836	−	1.18836i	0.0412237	−	0.0412237i
$832$	4.29194			0.148796
$833$	29.9451	−	0.465660i	1.03754	−	0.0161342i
$834$	−0.307967			−0.0106640
$835$	6.93218	−	6.93218i	0.239898	−	0.239898i
$836$	−4.32339	+	10.4376i	−0.149528	+	0.360992i
$837$			2.78580i			0.0962914i
$838$	14.0809	+	5.83251i	0.486417	+	0.201481i
$839$	−0.354422	−	0.855650i	−0.0122360	−	0.0295403i	0.917643	−	0.397405i	$-0.130089\pi$
$839$	−0.354422	−	0.855650i	−0.0122360	−	0.0295403i	−0.929879	+	0.367864i	$0.880089\pi$
$840$	0.268077	−	0.111041i	0.00924953	−	0.00383128i
$841$	−16.8426	−	16.8426i	−0.580779	−	0.580779i
$842$	−26.7997	−	26.7997i	−0.923579	−	0.923579i
$843$	0.545138	−	0.225803i	0.0187755	−	0.00777708i
$844$	2.83014	+	6.83256i	0.0974174	+	0.235186i
$845$	5.00815	+	2.07444i	0.172285	+	0.0713630i
$846$			24.7706i			0.851630i
$847$	−3.41947	+	8.25532i	−0.117494	+	0.283656i
$848$	7.36717	−	7.36717i	0.252990	−	0.252990i
$849$	0.0594331			0.00203974
$850$	−2.96045	−	2.86979i	−0.101543	−	0.0984331i
$851$	52.5258			1.80056
$852$	−0.745406	+	0.745406i	−0.0255372	+	0.0255372i
$853$	3.01176	−	7.27102i	0.103121	−	0.248955i	−0.863895	−	0.503672i	$-0.831982\pi$
$853$	3.01176	−	7.27102i	0.103121	−	0.248955i	0.967016	+	0.254717i	$0.0819822\pi$
$854$		−	10.4761i		−	0.358486i
$855$	8.54804	+	3.54072i	0.292337	+	0.121090i
$856$	0.682347	+	1.64733i	0.0233222	+	0.0563047i
$857$	9.21337	−	3.81630i	0.314723	−	0.130362i	−0.219730	−	0.975561i	$-0.570518\pi$
$857$	9.21337	−	3.81630i	0.314723	−	0.130362i	0.534453	+	0.845198i	$0.320518\pi$
$858$	−0.852448	−	0.852448i	−0.0291021	−	0.0291021i
$859$	−18.1801	−	18.1801i	−0.620298	−	0.620298i	0.325310	−	0.945608i	$-0.394532\pi$
$859$	−18.1801	−	18.1801i	−0.620298	−	0.620298i	−0.945608	+	0.325310i	$0.894532\pi$
$860$	10.1973	−	4.22385i	0.347724	−	0.144032i
$861$	−0.915376	−	2.20991i	−0.0311959	−	0.0753136i
$862$	−12.9998	−	5.38469i	−0.442774	−	0.183403i
$863$			24.1592i			0.822390i	0.911547	+	0.411195i	$0.134888\pi$
$863$			24.1592i			0.822390i	−0.911547	+	0.411195i	$0.865112\pi$
$864$	−0.176235	+	0.425469i	−0.00599564	+	0.0144748i
$865$	3.58731	−	3.58731i	0.121972	−	0.121972i
$866$	25.7592			0.875332
$867$	−1.22164	−	0.462063i	−0.0414891	−	0.0156925i
$868$	−22.8461			−0.775448
$869$	−7.83556	+	7.83556i	−0.265803	+	0.265803i
$870$	−0.0669229	+	0.161566i	−0.00226890	+	0.00547760i
$871$		−	14.7553i		−	0.499964i
$872$	−7.61732	−	3.15520i	−0.257955	−	0.106849i
$873$	−0.760809	−	1.83676i	−0.0257495	−	0.0621648i
$874$	−18.4831	+	7.65593i	−0.625199	+	0.258966i
$875$	−2.67055	−	2.67055i	−0.0902810	−	0.0902810i
$876$	0.643812	+	0.643812i	0.0217524	+	0.0217524i
$877$	4.68078	−	1.93884i	0.158059	−	0.0654700i	−0.302251	−	0.953228i	$-0.597738\pi$
$877$	4.68078	−	1.93884i	0.158059	−	0.0654700i	0.460310	+	0.887758i	$0.347738\pi$
$878$	−1.95058	−	4.70912i	−0.0658289	−	0.158925i
$879$	0.906114	+	0.375325i	0.0305625	+	0.0126594i
$880$			3.65595i			0.123242i
$881$	0.00740638	−	0.0178806i	0.000249527	−	0.000602412i	−0.923755	−	0.382985i	$-0.874896\pi$
$881$	0.00740638	−	0.0178806i	0.000249527	−	0.000602412i	0.924004	+	0.382382i	$0.124896\pi$
$882$	−15.3782	+	15.3782i	−0.517810	+	0.517810i
$883$	39.4367			1.32715			0.663575	−	0.748110i	$-0.269038\pi$
$883$	39.4367			1.32715			0.663575	+	0.748110i	$0.269038\pi$
$884$	−12.7061	−	12.3170i	−0.427353	−	0.414265i
$885$	−0.369049			−0.0124054
$886$	−9.47082	+	9.47082i	−0.318178	+	0.318178i
$887$	−2.91160	+	7.02922i	−0.0977619	+	0.236018i	−0.965193	−	0.261540i	$-0.915770\pi$
$887$	−2.91160	+	7.02922i	−0.0977619	+	0.236018i	0.867431	+	0.497558i	$0.165770\pi$
$888$		−	0.623345i		−	0.0209181i
$889$	−12.4209	−	5.14489i	−0.416583	−	0.172554i
$890$	−3.68955	−	8.90737i	−0.123674	−	0.298576i
$891$	−30.2196	+	12.5174i	−1.01239	+	0.419347i
$892$	0.994253	+	0.994253i	0.0332901	+	0.0332901i
$893$	18.0776	+	18.0776i	0.604944	+	0.604944i
$894$	−1.29620	+	0.536904i	−0.0433514	+	0.0179568i
$895$	−1.64445	−	3.97005i	−0.0549678	−	0.132704i
$896$	−3.48924	−	1.44529i	−0.116567	−	0.0482837i
$897$		−	2.13479i		−	0.0712787i
$898$	−14.8761	+	35.9141i	−0.496422	+	1.19847i
$899$	9.73618	−	9.73618i	0.324720	−	0.324720i
$900$	2.99410			0.0998032
$901$	−42.9524	+	0.667929i	−1.43095	+	0.0222520i
$902$	30.1381			1.00349
$903$	2.26463	−	2.26463i	0.0753622	−	0.0753622i
$904$	2.46195	−	5.94368i	0.0818833	−	0.197684i
$905$		−	17.2300i		−	0.572744i
$906$	−1.07285	−	0.444389i	−0.0356430	−	0.0147638i
$907$	3.19234	+	7.70699i	0.106000	+	0.255906i	0.967976	−	0.251042i	$-0.0807733\pi$
$907$	3.19234	+	7.70699i	0.106000	+	0.255906i	−0.861976	+	0.506949i	$0.830773\pi$
$908$	1.29957	−	0.538299i	0.0431277	−	0.0178641i
$909$	24.8521	+	24.8521i	0.824291	+	0.824291i
$910$	−11.4618	−	11.4618i	−0.379956	−	0.379956i
$911$	11.5320	−	4.77672i	0.382073	−	0.158260i	−0.183376	−	0.983043i	$-0.558703\pi$
$911$	11.5320	−	4.77672i	0.382073	−	0.158260i	0.565450	+	0.824783i	$0.308703\pi$
$912$	0.0908561	+	0.219346i	0.00300855	+	0.00726327i
$913$	−6.21060	−	2.57251i	−0.205541	−	0.0851378i
$914$		−	22.2123i		−	0.734718i
$915$	−0.0815558	+	0.196893i	−0.00269615	+	0.00650908i
$916$	15.9495	−	15.9495i	0.526986	−	0.526986i
$917$	−53.9376			−1.78118
$918$	1.74274	−	0.753824i	0.0575191	−	0.0248799i
$919$	−35.0036			−1.15466			−0.577331	−	0.816511i	$-0.695906\pi$
$919$	−35.0036			−1.15466			−0.577331	+	0.816511i	$0.695906\pi$
$920$	−4.57781	+	4.57781i	−0.150926	+	0.150926i
$921$	0.148423	−	0.358324i	0.00489070	−	0.0118072i
$922$		−	4.68607i		−	0.154328i
$923$	54.4062	+	22.5358i	1.79080	+	0.741774i
$924$	0.405960	+	0.980075i	0.0133551	+	0.0322421i
$925$	−7.49575	+	3.10484i	−0.246459	+	0.102087i
$926$	−20.0150	−	20.0150i	−0.657733	−	0.657733i
$927$	−25.0880	−	25.0880i	−0.823997	−	0.823997i
$928$	2.10291	−	0.871055i	0.0690315	−	0.0285938i
$929$	−2.46116	−	5.94175i	−0.0807479	−	0.194943i	0.878349	−	0.478019i	$-0.158645\pi$
$929$	−2.46116	−	5.94175i	−0.0807479	−	0.194943i	−0.959097	+	0.283076i	$0.908645\pi$
$930$	0.429380	+	0.177855i	0.0140799	+	0.00583210i
$931$			22.4460i			0.735639i
$932$	4.68427	−	11.3088i	0.153438	−	0.370433i
$933$	−1.77007	+	1.77007i	−0.0579494	+	0.0579494i
$934$	−21.5471			−0.705041
$935$	10.4918	−	10.8233i	0.343119	−	0.353959i
$936$	12.8505			0.420032
$937$	28.2723	−	28.2723i	0.923616	−	0.923616i	−0.0736668	−	0.997283i	$-0.523470\pi$
$937$	28.2723	−	28.2723i	0.923616	−	0.923616i	0.997283	+	0.0736668i	$0.0234701\pi$
$938$	−4.96877	+	11.9957i	−0.162236	+	0.391672i
$939$		−	1.26714i		−	0.0413515i
$940$	7.64338	+	3.16599i	0.249300	+	0.103263i
$941$	−9.77539	−	23.5999i	−0.318669	−	0.769334i	−0.999325	−	0.0367316i	$-0.988305\pi$
$941$	−9.77539	−	23.5999i	−0.318669	−	0.769334i	0.680656	−	0.732603i	$-0.261695\pi$
$942$	−0.890598	+	0.368898i	−0.0290172	+	0.0120193i
$943$	37.7375	+	37.7375i	1.22890	+	1.22890i
$944$	3.39657	+	3.39657i	0.110549	+	0.110549i
$945$	1.60688	−	0.665591i	0.0522718	−	0.0216517i
$946$	15.4422	+	37.2807i	0.502068	+	1.21210i
$947$	42.3254	+	17.5318i	1.37539	+	0.569705i	0.943245	−	0.332098i	$-0.107757\pi$
$947$	42.3254	+	17.5318i	1.37539	+	0.569705i	0.432146	+	0.901804i	$0.357757\pi$
$948$			0.232871i			0.00756328i
$949$	19.4643	−	46.9910i	0.631838	−	1.52539i
$950$	2.18510	−	2.18510i	0.0708939	−	0.0708939i
$951$	−1.26536			−0.0410320
$952$	6.18205	+	14.2921i	0.200361	+	0.463210i
$953$	−34.6245			−1.12160			−0.560799	−	0.827952i	$-0.689506\pi$
$953$	−34.6245			−1.12160			−0.560799	+	0.827952i	$0.689506\pi$
$954$	22.0580	−	22.0580i	0.714155	−	0.714155i
$955$	−4.16920	+	10.0653i	−0.134912	+	0.325707i
$956$			16.6182i			0.537470i
$957$	−0.590677	−	0.244666i	−0.0190939	−	0.00790894i
$958$	−0.866176	−	2.09113i	−0.0279849	−	0.0675615i
$959$	−27.5449	+	11.4095i	−0.889470	+	0.368430i
$960$	0.0543268	+	0.0543268i	0.00175339	+	0.00175339i
$961$	−3.95467	−	3.95467i	−0.127570	−	0.127570i
$962$	−32.1713	+	13.3258i	−1.03725	+	0.429641i
$963$	2.04301	+	4.93227i	0.0658352	+	0.158940i
$964$	5.34110	+	2.21235i	0.172025	+	0.0712551i
$965$		−	19.2722i		−	0.620395i
$966$	−0.718880	+	1.73553i	−0.0231296	+	0.0558398i
$967$	−30.7087	+	30.7087i	−0.987526	+	0.987526i	−0.999923	−	0.0123972i	$-0.996054\pi$
$967$	−30.7087	+	30.7087i	−0.987526	+	0.987526i	0.0123972	+	0.999923i	$0.496054\pi$
$968$	−2.36594			−0.0760442
$969$	0.360502	−	0.910102i	0.0115810	−	0.0292367i
$970$	−0.664003			−0.0213199
$971$	−25.5571	+	25.5571i	−0.820166	+	0.820166i	−0.986132	−	0.165966i	$-0.946926\pi$
$971$	−25.5571	+	25.5571i	−0.820166	+	0.820166i	0.165966	+	0.986132i	$0.446926\pi$
$972$	−0.791757	+	1.91147i	−0.0253956	+	0.0613105i
$973$		−	15.1387i		−	0.485326i
$974$	26.9960	+	11.1821i	0.865007	+	0.358297i
$975$	0.126189	+	0.304648i	0.00404129	+	0.00975654i
$976$	2.56272	−	1.06151i	0.0820307	−	0.0339782i
$977$	−12.3224	−	12.3224i	−0.394228	−	0.394228i	0.481963	−	0.876191i	$-0.339924\pi$
$977$	−12.3224	−	12.3224i	−0.394228	−	0.394228i	−0.876191	+	0.481963i	$0.839924\pi$
$978$	−0.771207	−	0.771207i	−0.0246605	−	0.0246605i
$979$	32.5649	−	13.4888i	1.04078	−	0.431104i
$980$	2.77967	+	6.71073i	0.0887934	+	0.214366i
$981$	−22.8070	−	9.44697i	−0.728172	−	0.301619i
$982$		−	13.5867i		−	0.433570i
$983$	−17.9454	+	43.3241i	−0.572371	+	1.38183i	0.327161	+	0.944969i	$0.393908\pi$
$983$	−17.9454	+	43.3241i	−0.572371	+	1.38183i	−0.899531	+	0.436856i	$0.856092\pi$
$984$	0.447847	−	0.447847i	0.0142768	−	0.0142768i
$985$	12.9414			0.412347
$986$	−8.72533	−	3.45620i	−0.277871	−	0.110068i
$987$	2.40057			0.0764110
$988$	9.37831	−	9.37831i	0.298364	−	0.298364i
$989$	−27.3452	+	66.0171i	−0.869527	+	2.09922i
$990$			10.9463i			0.347895i
$991$	−17.5404	−	7.26548i	−0.557190	−	0.230796i	0.0862749	−	0.996271i	$-0.472504\pi$
$991$	−17.5404	−	7.26548i	−0.557190	−	0.230796i	−0.643465	+	0.765476i	$0.722504\pi$
$992$	−2.31493	−	5.58873i	−0.0734990	−	0.177442i
$993$	−2.38115	+	0.986305i	−0.0755636	+	0.0312994i
$994$	−36.6420	−	36.6420i	−1.16221	−	1.16221i
$995$	−3.39894	−	3.39894i	−0.107754	−	0.107754i
$996$	−0.130516	+	0.0540614i	−0.00413555	+	0.00171300i
$997$	9.74593	+	23.5288i	0.308657	+	0.745164i	0.999749	+	0.0223970i	$0.00712979\pi$
$997$	9.74593	+	23.5288i	0.308657	+	0.745164i	−0.691092	+	0.722766i	$0.742870\pi$
$998$	−29.0977	−	12.0527i	−0.921072	−	0.381521i
$999$		−	3.73639i		−	0.118214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.161.3	yes	16
5.2	odd	4		850.2.o.j.399.2		16
5.3	odd	4		850.2.o.g.399.3		16
5.4	even	2		850.2.l.e.501.2		16
17.6	odd	16		2890.2.b.r.2311.9		16
17.7	odd	16		2890.2.a.bj.1.4		8
17.10	odd	16		2890.2.a.bi.1.5		8
17.11	odd	16		2890.2.b.r.2311.8		16
17.15	even	8	inner	170.2.k.b.151.3	✓	16
85.32	odd	8		850.2.o.g.49.3		16
85.49	even	8		850.2.l.e.151.2		16
85.83	odd	8		850.2.o.j.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.151.3	✓	16	17.15	even	8	inner
170.2.k.b.161.3	yes	16	1.1	even	1	trivial
850.2.l.e.151.2		16	85.49	even	8
850.2.l.e.501.2		16	5.4	even	2
850.2.o.g.49.3		16	85.32	odd	8
850.2.o.g.399.3		16	5.3	odd	4
850.2.o.j.49.2		16	85.83	odd	8
850.2.o.j.399.2		16	5.2	odd	4
2890.2.a.bi.1.5		8	17.10	odd	16
2890.2.a.bj.1.4		8	17.7	odd	16
2890.2.b.r.2311.8		16	17.11	odd	16
2890.2.b.r.2311.9		16	17.6	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0294014 + 0.0709814i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.0294014 - 0.0709814i) q^{6} +(3.48924 - 1.44529i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11715 + 2.11715i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0294014 + 0.0709814i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.0294014 - 0.0709814i) q^{6} +(3.48924 - 1.44529i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.11715 + 2.11715i) q^{9} +(0.923880 - 0.382683i) q^{10} +(1.39907 + 3.37765i) q^{11} +(0.0709814 + 0.0294014i) q^{12} -4.29194i q^{13} +(-1.44529 + 3.48924i) q^{14} +(0.0543268 - 0.0543268i) q^{15} -1.00000 q^{16} +(2.96045 + 2.86979i) q^{17} -2.99410 q^{18} +(-2.18510 + 2.18510i) q^{19} +(-0.382683 + 0.923880i) q^{20} +0.290164i q^{21} +(-3.37765 - 1.39907i) q^{22} +(-2.47749 - 5.98120i) q^{23} +(-0.0709814 + 0.0294014i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.03486 + 3.03486i) q^{26} +(-0.425469 + 0.176235i) q^{27} +(-1.44529 - 3.48924i) q^{28} +(2.10291 + 0.871055i) q^{29} +0.0768297i q^{30} +(2.31493 - 5.58873i) q^{31} +(0.707107 - 0.707107i) q^{32} -0.280885 q^{33} +(-4.12261 + 0.0641084i) q^{34} -3.77672 q^{35} +(2.11715 - 2.11715i) q^{36} +(-3.10484 + 7.49575i) q^{37} -3.09019i q^{38} +(0.304648 + 0.126189i) q^{39} +(-0.382683 - 0.923880i) q^{40} +(-7.61607 + 3.15468i) q^{41} +(-0.205177 - 0.205177i) q^{42} +(-7.80465 - 7.80465i) q^{43} +(3.37765 - 1.39907i) q^{44} +(-1.14579 - 2.76619i) q^{45} +(5.98120 + 2.47749i) q^{46} -8.27314i q^{47} +(0.0294014 - 0.0709814i) q^{48} +(5.13617 - 5.13617i) q^{49} -1.00000 q^{50} +(-0.290743 + 0.125761i) q^{51} -4.29194 q^{52} +(-7.36717 + 7.36717i) q^{53} +(0.176235 - 0.425469i) q^{54} -3.65595i q^{55} +(3.48924 + 1.44529i) q^{56} +(-0.0908561 - 0.219346i) q^{57} +(-2.10291 + 0.871055i) q^{58} +(-3.39657 - 3.39657i) q^{59} +(-0.0543268 - 0.0543268i) q^{60} +(-2.56272 + 1.06151i) q^{61} +(2.31493 + 5.58873i) q^{62} +(10.4471 + 4.32734i) q^{63} +1.00000i q^{64} +(-1.64246 + 3.96524i) q^{65} +(0.198616 - 0.198616i) q^{66} +3.43790 q^{67} +(2.86979 - 2.96045i) q^{68} +0.497395 q^{69} +(2.67055 - 2.67055i) q^{70} +(-5.25072 + 12.6764i) q^{71} +2.99410i q^{72} +(10.9486 + 4.53508i) q^{73} +(-3.10484 - 7.49575i) q^{74} +(-0.0709814 + 0.0294014i) q^{75} +(2.18510 + 2.18510i) q^{76} +(9.76337 + 9.76337i) q^{77} +(-0.304648 + 0.126189i) q^{78} +(1.15991 + 2.80028i) q^{79} +(0.923880 + 0.382683i) q^{80} +8.94691i q^{81} +(3.15468 - 7.61607i) q^{82} +(-1.30018 + 1.30018i) q^{83} +0.290164 q^{84} +(-1.63688 - 3.78426i) q^{85} +11.0374 q^{86} +(-0.123657 + 0.123657i) q^{87} +(-1.39907 + 3.37765i) q^{88} -9.64127i q^{89} +(2.76619 + 1.14579i) q^{90} +(-6.20310 - 14.9756i) q^{91} +(-5.98120 + 2.47749i) q^{92} +(0.328633 + 0.328633i) q^{93} +(5.84999 + 5.84999i) q^{94} +(2.85497 - 1.18257i) q^{95} +(0.0294014 + 0.0709814i) q^{96} +(-0.613459 - 0.254103i) q^{97} +7.26364i q^{98} +(-4.18895 + 10.1130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

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