LMFDB - Embedded newform 370.2.h.e.117.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			117.9
Root			$1.82785 - 1.82785i$ of defining polynomial
Character	$\chi$	$=$	370.117
Dual form			370.2.h.e.253.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.82785 + 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 + 1.86276i) q^{5} +(-1.82785 - 1.82785i) q^{6} +(3.41332 + 3.41332i) q^{7} -1.00000 q^{8} +3.68208i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.82785 + 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 + 1.86276i) q^{5} +(-1.82785 - 1.82785i) q^{6} +(3.41332 + 3.41332i) q^{7} -1.00000 q^{8} +3.68208i q^{9} +(1.23698 - 1.86276i) q^{10} -3.97950i q^{11} +(1.82785 + 1.82785i) q^{12} -4.28763 q^{13} +(-3.41332 - 3.41332i) q^{14} +(-5.66587 + 1.14383i) q^{15} +1.00000 q^{16} +2.57516i q^{17} -3.68208i q^{18} +(5.24415 - 5.24415i) q^{19} +(-1.23698 + 1.86276i) q^{20} +12.4781i q^{21} +3.97950i q^{22} -2.21783 q^{23} +(-1.82785 - 1.82785i) q^{24} +(-1.93975 - 4.60840i) q^{25} +4.28763 q^{26} +(-1.24674 + 1.24674i) q^{27} +(3.41332 + 3.41332i) q^{28} +(-2.03524 - 2.03524i) q^{29} +(5.66587 - 1.14383i) q^{30} +(-3.23732 + 3.23732i) q^{31} -1.00000 q^{32} +(7.27394 - 7.27394i) q^{33} -2.57516i q^{34} +(-10.5804 + 2.13598i) q^{35} +3.68208i q^{36} +(5.60171 + 2.37084i) q^{37} +(-5.24415 + 5.24415i) q^{38} +(-7.83714 - 7.83714i) q^{39} +(1.23698 - 1.86276i) q^{40} +2.50763i q^{41} -12.4781i q^{42} +9.00337 q^{43} -3.97950i q^{44} +(-6.85883 - 4.55467i) q^{45} +2.21783 q^{46} +(-0.943466 - 0.943466i) q^{47} +(1.82785 + 1.82785i) q^{48} +16.3015i q^{49} +(1.93975 + 4.60840i) q^{50} +(-4.70702 + 4.70702i) q^{51} -4.28763 q^{52} +(2.84055 - 2.84055i) q^{53} +(1.24674 - 1.24674i) q^{54} +(7.41286 + 4.92258i) q^{55} +(-3.41332 - 3.41332i) q^{56} +19.1710 q^{57} +(2.03524 + 2.03524i) q^{58} +(-2.91109 + 2.91109i) q^{59} +(-5.66587 + 1.14383i) q^{60} +(-5.71266 + 5.71266i) q^{61} +(3.23732 - 3.23732i) q^{62} +(-12.5681 + 12.5681i) q^{63} +1.00000 q^{64} +(5.30372 - 7.98682i) q^{65} +(-7.27394 + 7.27394i) q^{66} +(-1.28531 + 1.28531i) q^{67} +2.57516i q^{68} +(-4.05387 - 4.05387i) q^{69} +(10.5804 - 2.13598i) q^{70} +8.40334 q^{71} -3.68208i q^{72} +(-5.32492 - 5.32492i) q^{73} +(-5.60171 - 2.37084i) q^{74} +(4.87791 - 11.9690i) q^{75} +(5.24415 - 5.24415i) q^{76} +(13.5833 - 13.5833i) q^{77} +(7.83714 + 7.83714i) q^{78} +(9.77118 - 9.77118i) q^{79} +(-1.23698 + 1.86276i) q^{80} +6.48853 q^{81} -2.50763i q^{82} +(2.57398 - 2.57398i) q^{83} +12.4781i q^{84} +(-4.79691 - 3.18543i) q^{85} -9.00337 q^{86} -7.44024i q^{87} +3.97950i q^{88} +(-9.42876 - 9.42876i) q^{89} +(6.85883 + 4.55467i) q^{90} +(-14.6350 - 14.6350i) q^{91} -2.21783 q^{92} -11.8347 q^{93} +(0.943466 + 0.943466i) q^{94} +(3.28166 + 16.2555i) q^{95} +(-1.82785 - 1.82785i) q^{96} +5.92246i q^{97} -16.3015i q^{98} +14.6528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.82785	+	1.82785i	1.05531	+	1.05531i	0.998378	+	0.0569322i	$0.0181319\pi$
$3$	1.82785	+	1.82785i	1.05531	+	1.05531i	0.0569322	+	0.998378i	$0.481868\pi$
$4$	1.00000			0.500000
$5$	−1.23698	+	1.86276i	−0.553196	+	0.833051i
$5$	−1.23698	+	1.86276i	−0.553196	+	0.833051i
$6$	−1.82785	−	1.82785i	−0.746217	−	0.746217i
$7$	3.41332	+	3.41332i	1.29011	+	1.29011i	0.934715	+	0.355399i	$0.115655\pi$
$7$	3.41332	+	3.41332i	1.29011	+	1.29011i	0.355399	+	0.934715i	$0.384345\pi$
$8$	−1.00000			−0.353553
$9$			3.68208i			1.22736i
$10$	1.23698	−	1.86276i	0.391168	−	0.589056i
$11$		−	3.97950i		−	1.19987i	−0.800051	−	0.599933i	$-0.795194\pi$
$11$		−	3.97950i		−	1.19987i	0.800051	−	0.599933i	$-0.204806\pi$
$12$	1.82785	+	1.82785i	0.527655	+	0.527655i
$13$	−4.28763			−1.18917			−0.594587	−	0.804031i	$-0.702684\pi$
$13$	−4.28763			−1.18917			−0.594587	+	0.804031i	$0.702684\pi$
$14$	−3.41332	−	3.41332i	−0.912248	−	0.912248i
$15$	−5.66587	+	1.14383i	−1.46292	+	0.295335i
$16$	1.00000			0.250000
$17$			2.57516i			0.624569i	0.949989	+	0.312284i	$0.101094\pi$
$17$			2.57516i			0.624569i	−0.949989	+	0.312284i	$0.898906\pi$
$18$		−	3.68208i		−	0.867874i
$19$	5.24415	−	5.24415i	1.20309	−	1.20309i	0.229868	−	0.973222i	$-0.426170\pi$
$19$	5.24415	−	5.24415i	1.20309	−	1.20309i	0.973222	−	0.229868i	$-0.0738296\pi$
$20$	−1.23698	+	1.86276i	−0.276598	+	0.416526i
$21$			12.4781i			2.72294i
$22$			3.97950i			0.848433i
$23$	−2.21783			−0.462451			−0.231225	−	0.972900i	$-0.574273\pi$
$23$	−2.21783			−0.462451			−0.231225	+	0.972900i	$0.574273\pi$
$24$	−1.82785	−	1.82785i	−0.373109	−	0.373109i
$25$	−1.93975	−	4.60840i	−0.387949	−	0.921681i
$26$	4.28763			0.840873
$27$	−1.24674	+	1.24674i	−0.239935	+	0.239935i
$28$	3.41332	+	3.41332i	0.645057	+	0.645057i
$29$	−2.03524	−	2.03524i	−0.377935	−	0.377935i	0.492422	−	0.870357i	$-0.336112\pi$
$29$	−2.03524	−	2.03524i	−0.377935	−	0.377935i	−0.870357	+	0.492422i	$0.836112\pi$
$30$	5.66587	−	1.14383i	1.03444	−	0.208833i
$31$	−3.23732	+	3.23732i	−0.581439	+	0.581439i	−0.935299	−	0.353859i	$-0.884869\pi$
$31$	−3.23732	+	3.23732i	−0.581439	+	0.581439i	0.353859	+	0.935299i	$0.384869\pi$
$32$	−1.00000			−0.176777
$33$	7.27394	−	7.27394i	1.26623	−	1.26623i
$34$		−	2.57516i		−	0.441637i
$35$	−10.5804	+	2.13598i	−1.78842	+	0.361046i
$36$			3.68208i			0.613680i
$37$	5.60171	+	2.37084i	0.920915	+	0.389764i
$37$	5.60171	+	2.37084i	0.920915	+	0.389764i
$38$	−5.24415	+	5.24415i	−0.850713	+	0.850713i
$39$	−7.83714	−	7.83714i	−1.25495	−	1.25495i
$40$	1.23698	−	1.86276i	0.195584	−	0.294528i
$41$			2.50763i			0.391627i	0.980641	+	0.195813i	$0.0627347\pi$
$41$			2.50763i			0.391627i	−0.980641	+	0.195813i	$0.937265\pi$
$42$		−	12.4781i		−	1.92541i
$43$	9.00337			1.37300			0.686501	−	0.727129i	$-0.259146\pi$
$43$	9.00337			1.37300			0.686501	+	0.727129i	$0.259146\pi$
$44$		−	3.97950i		−	0.599933i
$45$	−6.85883	−	4.55467i	−1.02245	−	0.678970i
$46$	2.21783			0.327002
$47$	−0.943466	−	0.943466i	−0.137619	−	0.137619i	0.634942	−	0.772560i	$-0.281024\pi$
$47$	−0.943466	−	0.943466i	−0.137619	−	0.137619i	−0.772560	+	0.634942i	$0.781024\pi$
$48$	1.82785	+	1.82785i	0.263828	+	0.263828i
$49$			16.3015i			2.32879i
$50$	1.93975	+	4.60840i	0.274321	+	0.651727i
$51$	−4.70702	+	4.70702i	−0.659114	+	0.659114i
$52$	−4.28763			−0.594587
$53$	2.84055	−	2.84055i	0.390180	−	0.390180i	−0.484572	−	0.874751i	$-0.661025\pi$
$53$	2.84055	−	2.84055i	0.390180	−	0.390180i	0.874751	+	0.484572i	$0.161025\pi$
$54$	1.24674	−	1.24674i	0.169660	−	0.169660i
$55$	7.41286	+	4.92258i	0.999549	+	0.663760i
$56$	−3.41332	−	3.41332i	−0.456124	−	0.456124i
$57$	19.1710			2.53927
$58$	2.03524	+	2.03524i	0.267240	+	0.267240i
$59$	−2.91109	+	2.91109i	−0.378991	+	0.378991i	−0.870738	−	0.491747i	$-0.836359\pi$
$59$	−2.91109	+	2.91109i	−0.378991	+	0.378991i	0.491747	+	0.870738i	$0.336359\pi$
$60$	−5.66587	+	1.14383i	−0.731460	+	0.147667i
$61$	−5.71266	+	5.71266i	−0.731431	+	0.731431i	−0.970903	−	0.239472i	$-0.923026\pi$
$61$	−5.71266	+	5.71266i	−0.731431	+	0.731431i	0.239472	+	0.970903i	$0.423026\pi$
$62$	3.23732	−	3.23732i	0.411140	−	0.411140i
$63$	−12.5681	+	12.5681i	−1.58343	+	1.58343i
$64$	1.00000			0.125000
$65$	5.30372	−	7.98682i	0.657846	−	0.990643i
$66$	−7.27394	+	7.27394i	−0.895360	+	0.895360i
$67$	−1.28531	+	1.28531i	−0.157026	+	0.157026i	−0.781247	−	0.624222i	$-0.785416\pi$
$67$	−1.28531	+	1.28531i	−0.157026	+	0.157026i	0.624222	+	0.781247i	$0.285416\pi$
$68$			2.57516i			0.312284i
$69$	−4.05387	−	4.05387i	−0.488029	−	0.488029i
$70$	10.5804	−	2.13598i	1.26460	−	0.255298i
$71$	8.40334			0.997293			0.498646	−	0.866806i	$-0.333831\pi$
$71$	8.40334			0.997293			0.498646	+	0.866806i	$0.333831\pi$
$72$		−	3.68208i		−	0.433937i
$73$	−5.32492	−	5.32492i	−0.623235	−	0.623235i	0.323123	−	0.946357i	$-0.395267\pi$
$73$	−5.32492	−	5.32492i	−0.623235	−	0.623235i	−0.946357	+	0.323123i	$0.895267\pi$
$74$	−5.60171	−	2.37084i	−0.651185	−	0.275605i
$75$	4.87791	−	11.9690i	0.563253	−	1.38207i
$76$	5.24415	−	5.24415i	0.601545	−	0.601545i
$77$	13.5833	−	13.5833i	1.54796	−	1.54796i
$78$	7.83714	+	7.83714i	0.887382	+	0.887382i
$79$	9.77118	−	9.77118i	1.09934	−	1.09934i	0.104856	−	0.994487i	$-0.466562\pi$
$79$	9.77118	−	9.77118i	1.09934	−	1.09934i	0.994487	−	0.104856i	$-0.0334382\pi$
$80$	−1.23698	+	1.86276i	−0.138299	+	0.208263i
$81$	6.48853			0.720948
$82$		−	2.50763i		−	0.276922i
$83$	2.57398	−	2.57398i	0.282531	−	0.282531i	−0.551587	−	0.834117i	$-0.685977\pi$
$83$	2.57398	−	2.57398i	0.282531	−	0.282531i	0.834117	+	0.551587i	$0.185977\pi$
$84$			12.4781i			1.36147i
$85$	−4.79691	−	3.18543i	−0.520298	−	0.345509i
$86$	−9.00337			−0.970859
$87$		−	7.44024i		−	0.797678i
$88$			3.97950i			0.424216i
$89$	−9.42876	−	9.42876i	−0.999447	−	0.999447i	0.000552868	−	1.00000i	$-0.499824\pi$
$89$	−9.42876	−	9.42876i	−0.999447	−	0.999447i	−1.00000		0.000552868i	$0.999824\pi$
$90$	6.85883	+	4.55467i	0.722984	+	0.480104i
$91$	−14.6350	−	14.6350i	−1.53417	−	1.53417i
$92$	−2.21783			−0.231225
$93$	−11.8347			−1.22720
$94$	0.943466	+	0.943466i	0.0973111	+	0.0973111i
$95$	3.28166	+	16.2555i	0.336692	+	1.66778i
$96$	−1.82785	−	1.82785i	−0.186554	−	0.186554i
$97$			5.92246i			0.601335i	0.953729	+	0.300668i	$0.0972095\pi$
$97$			5.92246i			0.601335i	−0.953729	+	0.300668i	$0.902791\pi$
$98$		−	16.3015i		−	1.64670i
$99$	14.6528			1.47267
$100$	−1.93975	−	4.60840i	−0.193975	−	0.460840i
$101$		−	1.64079i		−	0.163265i	−0.996663	−	0.0816323i	$-0.973987\pi$
$101$		−	1.64079i		−	0.163265i	0.996663	−	0.0816323i	$-0.0260133\pi$
$102$	4.70702	−	4.70702i	0.466064	−	0.466064i
$103$			2.79089i			0.274994i	0.990502	+	0.137497i	$0.0439058\pi$
$103$			2.79089i			0.274994i	−0.990502	+	0.137497i	$0.956094\pi$
$104$	4.28763			0.420436
$105$	−23.2437	−	15.4352i	−2.26835	−	1.50632i
$106$	−2.84055	+	2.84055i	−0.275899	+	0.275899i
$107$	−3.77209	−	3.77209i	−0.364662	−	0.364662i	0.500864	−	0.865526i	$-0.333016\pi$
$107$	−3.77209	−	3.77209i	−0.364662	−	0.364662i	−0.865526	+	0.500864i	$0.833016\pi$
$108$	−1.24674	+	1.24674i	−0.119967	+	0.119967i
$109$	11.9302	−	11.9302i	1.14271	−	1.14271i	0.154756	−	0.987953i	$-0.450541\pi$
$109$	11.9302	−	11.9302i	1.14271	−	1.14271i	0.987953	−	0.154756i	$-0.0494590\pi$
$110$	−7.41286	−	4.92258i	−0.706788	−	0.469349i
$111$	5.90554	+	14.5726i	0.560529	+	1.38317i
$112$	3.41332	+	3.41332i	0.322528	+	0.322528i
$113$		−	15.5469i		−	1.46253i	−0.682091	−	0.731267i	$-0.738929\pi$
$113$		−	15.5469i		−	1.46253i	0.682091	−	0.731267i	$-0.261071\pi$
$114$	−19.1710			−1.79553
$115$	2.74342	−	4.13129i	0.255826	−	0.385245i
$116$	−2.03524	−	2.03524i	−0.188968	−	0.188968i
$117$		−	15.7874i		−	1.45954i
$118$	2.91109	−	2.91109i	0.267987	−	0.267987i
$119$	−8.78986	+	8.78986i	−0.805765	+	0.805765i
$120$	5.66587	−	1.14383i	0.517221	−	0.104417i
$121$	−4.83644			−0.439676
$122$	5.71266	−	5.71266i	0.517200	−	0.517200i
$123$	−4.58358	+	4.58358i	−0.413288	+	0.413288i
$124$	−3.23732	+	3.23732i	−0.290720	+	0.290720i
$125$	10.9838	+	2.08724i	0.982419	+	0.186688i
$126$	12.5681	−	12.5681i	1.11966	−	1.11966i
$127$	0.0553748	+	0.0553748i	0.00491372	+	0.00491372i	0.709559	−	0.704646i	$-0.248894\pi$
$127$	0.0553748	+	0.0553748i	0.00491372	+	0.00491372i	−0.704646	+	0.709559i	$0.748894\pi$
$128$	−1.00000			−0.0883883
$129$	16.4568	+	16.4568i	1.44894	+	1.44894i
$130$	−5.30372	+	7.98682i	−0.465167	+	0.700490i
$131$	3.08937	−	3.08937i	0.269920	−	0.269920i	−0.559148	−	0.829068i	$-0.688872\pi$
$131$	3.08937	−	3.08937i	0.269920	−	0.269920i	0.829068	+	0.559148i	$0.188872\pi$
$132$	7.27394	−	7.27394i	0.633115	−	0.633115i
$133$	35.7999			3.10425
$134$	1.28531	−	1.28531i	0.111034	−	0.111034i
$135$	−0.780179	−	3.86457i	−0.0671471	−	0.332609i
$136$		−	2.57516i		−	0.220818i
$137$	−1.84871	−	1.84871i	−0.157946	−	0.157946i	0.623710	−	0.781656i	$-0.285625\pi$
$137$	−1.84871	−	1.84871i	−0.157946	−	0.157946i	−0.781656	+	0.623710i	$0.785625\pi$
$138$	4.05387	+	4.05387i	0.345088	+	0.345088i
$139$	−10.9433			−0.928195			−0.464097	−	0.885784i	$-0.653621\pi$
$139$	−10.9433			−0.928195			−0.464097	+	0.885784i	$0.653621\pi$
$140$	−10.5804	+	2.13598i	−0.894208	+	0.180523i
$141$		−	3.44903i		−	0.290461i
$142$	−8.40334			−0.705192
$143$			17.0626i			1.42685i
$144$			3.68208i			0.306840i
$145$	6.30873	−	1.27361i	0.523911	−	0.105767i
$146$	5.32492	+	5.32492i	0.440693	+	0.440693i
$147$	−29.7967	+	29.7967i	−2.45759	+	2.45759i
$148$	5.60171	+	2.37084i	0.460457	+	0.194882i
$149$			13.0913i			1.07248i	0.844066	+	0.536240i	$0.180156\pi$
$149$			13.0913i			1.07248i	−0.844066	+	0.536240i	$0.819844\pi$
$150$	−4.87791	+	11.9690i	−0.398280	+	0.977268i
$151$			9.37187i			0.762672i	0.924437	+	0.381336i	$0.124536\pi$
$151$			9.37187i			0.762672i	−0.924437	+	0.381336i	$0.875464\pi$
$152$	−5.24415	+	5.24415i	−0.425357	+	0.425357i
$153$	−9.48196			−0.766571
$154$	−13.5833	+	13.5833i	−1.09457	+	1.09457i
$155$	−2.02584	−	10.0349i	−0.162719	−	0.806019i
$156$	−7.83714	−	7.83714i	−0.627474	−	0.627474i
$157$	−16.2868	−	16.2868i	−1.29983	−	1.29983i	−0.928504	−	0.371321i	$-0.878905\pi$
$157$	−16.2868	−	16.2868i	−1.29983	−	1.29983i	−0.371321	−	0.928504i	$-0.621095\pi$
$158$	−9.77118	+	9.77118i	−0.777353	+	0.777353i
$159$	10.3842			0.823521
$160$	1.23698	−	1.86276i	0.0977921	−	0.147264i
$161$	−7.57018	−	7.57018i	−0.596614	−	0.596614i
$162$	−6.48853			−0.509787
$163$			2.14382i			0.167917i	0.996469	+	0.0839586i	$0.0267564\pi$
$163$			2.14382i			0.167917i	−0.996469	+	0.0839586i	$0.973244\pi$
$164$			2.50763i			0.195813i
$165$	4.55186	+	22.5473i	0.354362	+	1.75531i
$166$	−2.57398	+	2.57398i	−0.199779	+	0.199779i
$167$			20.3382i			1.57382i	0.617071	+	0.786908i	$0.288319\pi$
$167$			20.3382i			1.57382i	−0.617071	+	0.786908i	$0.711681\pi$
$168$		−	12.4781i		−	0.962705i
$169$	5.38374			0.414134
$170$	4.79691	+	3.18543i	0.367906	+	0.244312i
$171$	19.3094	+	19.3094i	1.47662	+	1.47662i
$172$	9.00337			0.686501
$173$	13.7435	+	13.7435i	1.04490	+	1.04490i	0.998943	+	0.0459570i	$0.0146337\pi$
$173$	13.7435	+	13.7435i	1.04490	+	1.04490i	0.0459570	+	0.998943i	$0.485366\pi$
$174$			7.44024i			0.564043i
$175$	9.10899	−	22.3509i	0.688575	−	1.68957i
$176$		−	3.97950i		−	0.299966i
$177$	−10.6421			−0.799907
$178$	9.42876	+	9.42876i	0.706716	+	0.706716i
$179$	13.4168	+	13.4168i	1.00282	+	1.00282i	0.999996	+	0.00281938i	$0.000897436\pi$
$179$	13.4168	+	13.4168i	1.00282	+	1.00282i	0.00281938	+	0.999996i	$0.499103\pi$
$180$	−6.85883	−	4.55467i	−0.511227	−	0.339485i
$181$	−15.3711			−1.14252			−0.571261	−	0.820768i	$-0.693546\pi$
$181$	−15.3711			−1.14252			−0.571261	+	0.820768i	$0.693546\pi$
$182$	14.6350	+	14.6350i	1.08482	+	1.08482i
$183$	−20.8838			−1.54377
$184$	2.21783			0.163501
$185$	−11.3455	+	7.50194i	−0.834139	+	0.551554i
$186$	11.8347			0.867760
$187$	10.2479			0.749398
$188$	−0.943466	−	0.943466i	−0.0688093	−	0.0688093i
$189$	−8.51103			−0.619087
$190$	−3.28166	−	16.2555i	−0.238077	−	1.17930i
$191$	−16.9686	−	16.9686i	−1.22781	−	1.22781i	−0.964791	−	0.263016i	$-0.915283\pi$
$191$	−16.9686	−	16.9686i	−1.22781	−	1.22781i	−0.263016	−	0.964791i	$-0.584717\pi$
$192$	1.82785	+	1.82785i	0.131914	+	0.131914i
$193$	−5.70785			−0.410860			−0.205430	−	0.978672i	$-0.565859\pi$
$193$	−5.70785			−0.410860			−0.205430	+	0.978672i	$0.565859\pi$
$194$		−	5.92246i		−	0.425208i
$195$	24.2931	−	4.90430i	1.73967	−	0.351204i
$196$			16.3015i			1.16439i
$197$	9.14763	+	9.14763i	0.651742	+	0.651742i	0.953412	−	0.301670i	$-0.0975442\pi$
$197$	9.14763	+	9.14763i	0.651742	+	0.651742i	−0.301670	+	0.953412i	$0.597544\pi$
$198$	−14.6528			−1.04133
$199$	−6.66896	−	6.66896i	−0.472750	−	0.472750i	0.430053	−	0.902803i	$-0.358495\pi$
$199$	−6.66896	−	6.66896i	−0.472750	−	0.472750i	−0.902803	+	0.430053i	$0.858495\pi$
$200$	1.93975	+	4.60840i	0.137161	+	0.325863i
$201$	−4.69872			−0.331422
$202$			1.64079i			0.115445i
$203$		−	13.8939i		−	0.975159i
$204$	−4.70702	+	4.70702i	−0.329557	+	0.329557i
$205$	−4.67112	−	3.10190i	−0.326245	−	0.216646i
$206$		−	2.79089i		−	0.194450i
$207$		−	8.16624i		−	0.567593i
$208$	−4.28763			−0.297293
$209$	−20.8691	−	20.8691i	−1.44355	−	1.44355i
$210$	23.2437	+	15.4352i	1.60397	+	1.06513i
$211$	15.1553			1.04334			0.521668	−	0.853149i	$-0.325310\pi$
$211$	15.1553			1.04334			0.521668	+	0.853149i	$0.325310\pi$
$212$	2.84055	−	2.84055i	0.195090	−	0.195090i
$213$	15.3600	+	15.3600i	1.05245	+	1.05245i
$214$	3.77209	+	3.77209i	0.257855	+	0.257855i
$215$	−11.1370	+	16.7711i	−0.759539	+	1.14378i
$216$	1.24674	−	1.24674i	0.0848298	−	0.0848298i
$217$	−22.1000			−1.50025
$218$	−11.9302	+	11.9302i	−0.808017	+	0.808017i
$219$		−	19.4663i		−	1.31541i
$220$	7.41286	+	4.92258i	0.499775	+	0.331880i
$221$		−	11.0413i		−	0.742721i
$222$	−5.90554	−	14.5726i	−0.396354	−	0.978051i
$223$	−6.25546	+	6.25546i	−0.418896	+	0.418896i	−0.884823	−	0.465927i	$-0.845721\pi$
$223$	−6.25546	+	6.25546i	−0.418896	+	0.418896i	0.465927	+	0.884823i	$0.345721\pi$
$224$	−3.41332	−	3.41332i	−0.228062	−	0.228062i
$225$	16.9685	−	7.14229i	1.13123	−	0.476153i
$226$			15.5469i			1.03417i
$227$			9.87949i			0.655725i	0.944725	+	0.327862i	$0.106328\pi$
$227$			9.87949i			0.655725i	−0.944725	+	0.327862i	$0.893672\pi$
$228$	19.1710			1.26963
$229$		−	21.9472i		−	1.45031i	−0.688586	−	0.725155i	$-0.741768\pi$
$229$		−	21.9472i		−	1.45031i	0.688586	−	0.725155i	$-0.258232\pi$
$230$	−2.74342	+	4.13129i	−0.180896	+	0.272409i
$231$	49.6566			3.26716
$232$	2.03524	+	2.03524i	0.133620	+	0.133620i
$233$	−8.96601	−	8.96601i	−0.587383	−	0.587383i	0.349539	−	0.936922i	$-0.386338\pi$
$233$	−8.96601	−	8.96601i	−0.587383	−	0.587383i	−0.936922	+	0.349539i	$0.886338\pi$
$234$			15.7874i			1.03205i
$235$	2.92450	−	0.590399i	0.190773	−	0.0385134i
$236$	−2.91109	+	2.91109i	−0.189496	+	0.189496i
$237$	35.7205			2.32030
$238$	8.78986	−	8.78986i	0.569762	−	0.569762i
$239$	−13.0815	+	13.0815i	−0.846174	+	0.846174i	−0.989653	−	0.143479i	$-0.954171\pi$
$239$	−13.0815	+	13.0815i	−0.846174	+	0.846174i	0.143479	+	0.989653i	$0.454171\pi$
$240$	−5.66587	+	1.14383i	−0.365730	+	0.0738336i
$241$	5.41196	+	5.41196i	0.348615	+	0.348615i	0.859594	−	0.510978i	$-0.170717\pi$
$241$	5.41196	+	5.41196i	0.348615	+	0.348615i	−0.510978	+	0.859594i	$0.670717\pi$
$242$	4.83644			0.310898
$243$	15.6003	+	15.6003i	1.00076	+	1.00076i
$244$	−5.71266	+	5.71266i	−0.365716	+	0.365716i
$245$	−30.3658	−	20.1647i	−1.94000	−	1.28828i
$246$	4.58358	−	4.58358i	0.292239	−	0.292239i
$247$	−22.4849	+	22.4849i	−1.43068	+	1.43068i
$248$	3.23732	−	3.23732i	0.205570	−	0.205570i
$249$	9.40969			0.596315
$250$	−10.9838	−	2.08724i	−0.694675	−	0.132009i
$251$	2.34715	−	2.34715i	0.148151	−	0.148151i	−0.629141	−	0.777292i	$-0.716593\pi$
$251$	2.34715	−	2.34715i	0.148151	−	0.148151i	0.777292	+	0.629141i	$0.216593\pi$
$252$	−12.5681	+	12.5681i	−0.791717	+	0.791717i
$253$			8.82588i			0.554878i
$254$	−0.0553748	−	0.0553748i	−0.00347453	−	0.00347453i
$255$	−2.94554	−	14.5905i	−0.184457	−	0.913695i
$256$	1.00000			0.0625000
$257$		−	5.80813i		−	0.362301i	−0.983455	−	0.181151i	$-0.942018\pi$
$257$		−	5.80813i		−	0.362301i	0.983455	−	0.181151i	$-0.0579822\pi$
$258$	−16.4568	−	16.4568i	−1.02456	−	1.02456i
$259$	11.0280	+	27.2129i	0.685245	+	1.69092i
$260$	5.30372	−	7.98682i	0.328923	−	0.495321i
$261$	7.49392	−	7.49392i	0.463862	−	0.463862i
$262$	−3.08937	+	3.08937i	−0.190862	+	0.190862i
$263$	−15.2944	−	15.2944i	−0.943090	−	0.943090i	0.0553752	−	0.998466i	$-0.482365\pi$
$263$	−15.2944	−	15.2944i	−0.943090	−	0.943090i	−0.998466	+	0.0553752i	$0.982365\pi$
$264$	−7.27394	+	7.27394i	−0.447680	+	0.447680i
$265$	1.77755	+	8.80497i	0.109194	+	0.540885i
$266$	−35.7999			−2.19503
$267$		−	34.4688i		−	2.10945i
$268$	−1.28531	+	1.28531i	−0.0785129	+	0.0785129i
$269$		−	18.2273i		−	1.11134i	−0.831404	−	0.555668i	$-0.812463\pi$
$269$		−	18.2273i		−	1.11134i	0.831404	−	0.555668i	$-0.187537\pi$
$270$	0.780179	+	3.86457i	0.0474802	+	0.235190i
$271$	−26.6096			−1.61642			−0.808208	−	0.588898i	$-0.799562\pi$
$271$	−26.6096			−1.61642			−0.808208	+	0.588898i	$0.799562\pi$
$272$			2.57516i			0.156142i
$273$		−	53.5014i		−	3.23805i
$274$	1.84871	+	1.84871i	0.111685	+	0.111685i
$275$	−18.3392	+	7.71922i	−1.10589	+	0.465487i
$276$	−4.05387	−	4.05387i	−0.244014	−	0.244014i
$277$	0.845623			0.0508086			0.0254043	−	0.999677i	$-0.491913\pi$
$277$	0.845623			0.0508086			0.0254043	+	0.999677i	$0.491913\pi$
$278$	10.9433			0.656333
$279$	−11.9201	−	11.9201i	−0.713635	−	0.713635i
$280$	10.5804	−	2.13598i	0.632301	−	0.127649i
$281$	11.3809	+	11.3809i	0.678927	+	0.678927i	0.959757	−	0.280830i	$-0.0906098\pi$
$281$	11.3809	+	11.3809i	0.678927	+	0.678927i	−0.280830	+	0.959757i	$0.590610\pi$
$282$			3.44903i			0.205387i
$283$		−	6.37857i		−	0.379167i	−0.981865	−	0.189583i	$-0.939286\pi$
$283$		−	6.37857i		−	0.379167i	0.981865	−	0.189583i	$-0.0607137\pi$
$284$	8.40334			0.498646
$285$	−23.7143	+	35.7110i	−1.40471	+	2.11534i
$286$		−	17.0626i		−	1.00893i
$287$	−8.55936	+	8.55936i	−0.505243	+	0.505243i
$288$		−	3.68208i		−	0.216969i
$289$	10.3685			0.609914
$290$	−6.30873	+	1.27361i	−0.370461	+	0.0747888i
$291$	−10.8254	+	10.8254i	−0.634595	+	0.634595i
$292$	−5.32492	−	5.32492i	−0.311617	−	0.311617i
$293$	−6.47894	+	6.47894i	−0.378504	+	0.378504i	−0.870562	−	0.492058i	$-0.836245\pi$
$293$	−6.47894	+	6.47894i	−0.378504	+	0.378504i	0.492058	+	0.870562i	$0.336245\pi$
$294$	29.7967	−	29.7967i	1.73778	−	1.73778i
$295$	−1.82169	−	9.02362i	−0.106063	−	0.525376i
$296$	−5.60171	−	2.37084i	−0.325593	−	0.137802i
$297$	4.96140	+	4.96140i	0.287889	+	0.287889i
$298$		−	13.0913i		−	0.758358i
$299$	9.50925			0.549934
$300$	4.87791	−	11.9690i	0.281626	−	0.691033i
$301$	30.7314	+	30.7314i	1.77133	+	1.77133i
$302$		−	9.37187i		−	0.539290i
$303$	2.99912	−	2.99912i	0.172295	−	0.172295i
$304$	5.24415	−	5.24415i	0.300773	−	0.300773i
$305$	−3.57485	−	17.7078i	−0.204695	−	1.01394i
$306$	9.48196			0.542047
$307$	3.64587	−	3.64587i	0.208081	−	0.208081i	−0.595371	−	0.803451i	$-0.702995\pi$
$307$	3.64587	−	3.64587i	0.208081	−	0.208081i	0.803451	+	0.595371i	$0.202995\pi$
$308$	13.5833	−	13.5833i	0.773981	−	0.773981i
$309$	−5.10132	+	5.10132i	−0.290204	+	0.290204i
$310$	2.02584	+	10.0349i	0.115060	+	0.569941i
$311$	−0.480637	+	0.480637i	−0.0272545	+	0.0272545i	−0.720603	−	0.693348i	$-0.756135\pi$
$311$	−0.480637	+	0.480637i	−0.0272545	+	0.0272545i	0.693348	+	0.720603i	$0.256135\pi$
$312$	7.83714	+	7.83714i	0.443691	+	0.443691i
$313$	−18.2772			−1.03309			−0.516543	−	0.856261i	$-0.672781\pi$
$313$	−18.2772			−1.03309			−0.516543	+	0.856261i	$0.672781\pi$
$314$	16.2868	+	16.2868i	0.919116	+	0.919116i
$315$	−7.86483	−	38.9579i	−0.443133	−	2.19503i
$316$	9.77118	−	9.77118i	0.549672	−	0.549672i
$317$	−4.85997	+	4.85997i	−0.272963	+	0.272963i	−0.830292	−	0.557329i	$-0.811826\pi$
$317$	−4.85997	+	4.85997i	−0.272963	+	0.272963i	0.557329	+	0.830292i	$0.311826\pi$
$318$	−10.3842			−0.582317
$319$	−8.09925	+	8.09925i	−0.453471	+	0.453471i
$320$	−1.23698	+	1.86276i	−0.0691495	+	0.104131i
$321$		−	13.7896i		−	0.769662i
$322$	7.57018	+	7.57018i	0.421870	+	0.421870i
$323$	13.5045	+	13.5045i	0.751413	+	0.751413i
$324$	6.48853			0.360474
$325$	8.31690	+	19.7591i	0.461339	+	1.09604i
$326$		−	2.14382i		−	0.118735i
$327$	43.6134			2.41182
$328$		−	2.50763i		−	0.138461i
$329$		−	6.44070i		−	0.355088i
$330$	−4.55186	−	22.5473i	−0.250571	−	1.24119i
$331$	−20.7472	−	20.7472i	−1.14037	−	1.14037i	−0.988383	−	0.151986i	$-0.951433\pi$
$331$	−20.7472	−	20.7472i	−1.14037	−	1.14037i	−0.151986	−	0.988383i	$-0.548567\pi$
$332$	2.57398	−	2.57398i	0.141265	−	0.141265i
$333$	−8.72962	+	20.6259i	−0.478380	+	1.13029i
$334$		−	20.3382i		−	1.11286i
$335$	−0.804317	−	3.98413i	−0.0439446	−	0.217677i
$336$			12.4781i			0.680735i
$337$	6.47001	−	6.47001i	0.352444	−	0.352444i	−0.508574	−	0.861018i	$-0.669827\pi$
$337$	6.47001	−	6.47001i	0.352444	−	0.352444i	0.861018	+	0.508574i	$0.169827\pi$
$338$	−5.38374			−0.292837
$339$	28.4175	−	28.4175i	1.54343	−	1.54343i
$340$	−4.79691	−	3.18543i	−0.260149	−	0.172754i
$341$	12.8829	+	12.8829i	0.697649	+	0.697649i
$342$	−19.3094	−	19.3094i	−1.04413	−	1.04413i
$343$	−31.7491	+	31.7491i	−1.71429	+	1.71429i
$344$	−9.00337			−0.485429
$345$	12.5660	−	2.53682i	0.676528	−	0.136578i
$346$	−13.7435	−	13.7435i	−0.738856	−	0.738856i
$347$	−6.44807			−0.346151			−0.173075	−	0.984909i	$-0.555370\pi$
$347$	−6.44807			−0.346151			−0.173075	+	0.984909i	$0.555370\pi$
$348$		−	7.44024i		−	0.398839i
$349$			4.70014i			0.251593i	0.992056	+	0.125796i	$0.0401486\pi$
$349$			4.70014i			0.251593i	−0.992056	+	0.125796i	$0.959851\pi$
$350$	−9.10899	+	22.3509i	−0.486896	+	1.19471i
$351$	5.34555	−	5.34555i	0.285324	−	0.285324i
$352$			3.97950i			0.212108i
$353$			19.6162i			1.04406i	0.852926	+	0.522031i	$0.174826\pi$
$353$			19.6162i			1.04406i	−0.852926	+	0.522031i	$0.825174\pi$
$354$	10.6421			0.565620
$355$	−10.3948	+	15.6534i	−0.551698	+	0.830796i
$356$	−9.42876	−	9.42876i	−0.499723	−	0.499723i
$357$	−32.1331			−1.70066
$358$	−13.4168	−	13.4168i	−0.709098	−	0.709098i
$359$			7.60520i			0.401387i	0.979654	+	0.200694i	$0.0643196\pi$
$359$			7.60520i			0.401387i	−0.979654	+	0.200694i	$0.935680\pi$
$360$	6.85883	+	4.55467i	0.361492	+	0.240052i
$361$		−	36.0022i		−	1.89485i
$362$	15.3711			0.807885
$363$	−8.84029	−	8.84029i	−0.463995	−	0.463995i
$364$	−14.6350	−	14.6350i	−0.767085	−	0.767085i
$365$	16.5059	−	3.33221i	0.863957	−	0.174416i
$366$	20.8838			1.09161
$367$	−10.3061	−	10.3061i	−0.537975	−	0.537975i	0.384959	−	0.922934i	$-0.374216\pi$
$367$	−10.3061	−	10.3061i	−0.537975	−	0.537975i	−0.922934	+	0.384959i	$0.874216\pi$
$368$	−2.21783			−0.115613
$369$	−9.23331			−0.480667
$370$	11.3455	−	7.50194i	0.589826	−	0.390007i
$371$	19.3914			1.00675
$372$	−11.8347			−0.613599
$373$	0.690871	+	0.690871i	0.0357719	+	0.0357719i	0.724767	−	0.688995i	$-0.241948\pi$
$373$	0.690871	+	0.690871i	0.0357719	+	0.0357719i	−0.688995	+	0.724767i	$0.741948\pi$
$374$	−10.2479			−0.529905
$375$	16.2616	+	23.8919i	0.839743	+	1.23377i
$376$	0.943466	+	0.943466i	0.0486555	+	0.0486555i
$377$	8.72636	+	8.72636i	0.449430	+	0.449430i
$378$	8.51103			0.437760
$379$		−	0.266778i		−	0.0137035i	−0.999977	−	0.00685174i	$-0.997819\pi$
$379$		−	0.266778i		−	0.0137035i	0.999977	−	0.00685174i	$-0.00218099\pi$
$380$	3.28166	+	16.2555i	0.168346	+	0.833890i
$381$			0.202434i			0.0103710i
$382$	16.9686	+	16.9686i	0.868191	+	0.868191i
$383$	32.6980			1.67079			0.835395	−	0.549650i	$-0.185239\pi$
$383$	32.6980			1.67079			0.835395	+	0.549650i	$0.185239\pi$
$384$	−1.82785	−	1.82785i	−0.0932771	−	0.0932771i
$385$	8.50012	+	42.1048i	0.433206	+	2.14586i
$386$	5.70785			0.290522
$387$			33.1511i			1.68517i
$388$			5.92246i			0.300668i
$389$	24.7831	−	24.7831i	1.25655	−	1.25655i	0.303825	−	0.952728i	$-0.401736\pi$
$389$	24.7831	−	24.7831i	1.25655	−	1.25655i	0.952728	−	0.303825i	$-0.0982639\pi$
$390$	−24.2931	+	4.90430i	−1.23013	+	0.248339i
$391$		−	5.71129i		−	0.288832i
$392$		−	16.3015i		−	0.823351i
$393$	11.2938			0.569698
$394$	−9.14763	−	9.14763i	−0.460851	−	0.460851i
$395$	6.11457	+	30.2881i	0.307658	+	1.52396i
$396$	14.6528			0.736333
$397$	−11.3967	+	11.3967i	−0.571984	+	0.571984i	−0.932683	−	0.360698i	$-0.882538\pi$
$397$	−11.3967	+	11.3967i	−0.571984	+	0.571984i	0.360698	+	0.932683i	$0.382538\pi$
$398$	6.66896	+	6.66896i	0.334285	+	0.334285i
$399$	65.4369	+	65.4369i	3.27594	+	3.27594i
$400$	−1.93975	−	4.60840i	−0.0969873	−	0.230420i
$401$	−14.6783	+	14.6783i	−0.733000	+	0.733000i	−0.971213	−	0.238213i	$-0.923438\pi$
$401$	−14.6783	+	14.6783i	−0.733000	+	0.733000i	0.238213	+	0.971213i	$0.423438\pi$
$402$	4.69872			0.234351
$403$	13.8804	−	13.8804i	0.691432	−	0.691432i
$404$		−	1.64079i		−	0.0816323i
$405$	−8.02621	+	12.0866i	−0.398825	+	0.600587i
$406$			13.8939i			0.689541i
$407$	9.43477	−	22.2920i	0.467664	−	1.10497i
$408$	4.70702	−	4.70702i	0.233032	−	0.233032i
$409$	−10.7756	−	10.7756i	−0.532819	−	0.532819i	0.388591	−	0.921410i	$-0.372962\pi$
$409$	−10.7756	−	10.7756i	−0.532819	−	0.532819i	−0.921410	+	0.388591i	$0.872962\pi$
$410$	4.67112	+	3.10190i	0.230690	+	0.153192i
$411$		−	6.75833i		−	0.333364i
$412$			2.79089i			0.137497i
$413$	−19.8730			−0.977884
$414$			8.16624i			0.401349i
$415$	1.61073	+	7.97866i	0.0790678	+	0.391657i
$416$	4.28763			0.210218
$417$	−20.0026	−	20.0026i	−0.979533	−	0.979533i
$418$	20.8691	+	20.8691i	1.02074	+	1.02074i
$419$		−	24.0943i		−	1.17709i	−0.808466	−	0.588543i	$-0.799702\pi$
$419$		−	24.0943i		−	1.17709i	0.808466	−	0.588543i	$-0.200298\pi$
$420$	−23.2437	−	15.4352i	−1.13417	−	0.753160i
$421$	21.6407	−	21.6407i	1.05470	−	1.05470i	0.0562888	−	0.998415i	$-0.482073\pi$
$421$	21.6407	−	21.6407i	1.05470	−	1.05470i	0.998415	−	0.0562888i	$-0.0179267\pi$
$422$	−15.1553			−0.737750
$423$	3.47392	−	3.47392i	0.168908	−	0.168908i
$424$	−2.84055	+	2.84055i	−0.137949	+	0.137949i
$425$	11.8674	−	4.99516i	0.575653	−	0.242301i
$426$	−15.3600	−	15.3600i	−0.744197	−	0.744197i
$427$	−38.9983			−1.88726
$428$	−3.77209	−	3.77209i	−0.182331	−	0.182331i
$429$	−31.1879	+	31.1879i	−1.50577	+	1.50577i
$430$	11.1370	−	16.7711i	0.537075	−	0.808775i
$431$	1.23281	−	1.23281i	0.0593825	−	0.0593825i	−0.676792	−	0.736174i	$-0.736630\pi$
$431$	1.23281	−	1.23281i	0.0593825	−	0.0593825i	0.736174	+	0.676792i	$0.236630\pi$
$432$	−1.24674	+	1.24674i	−0.0599837	+	0.0599837i
$433$	−12.5825	+	12.5825i	−0.604678	+	0.604678i	−0.941550	−	0.336872i	$-0.890631\pi$
$433$	−12.5825	+	12.5825i	−0.604678	+	0.604678i	0.336872	+	0.941550i	$0.390631\pi$
$434$	22.1000			1.06083
$435$	13.8594	+	9.20345i	0.664506	+	0.441272i
$436$	11.9302	−	11.9302i	0.571354	−	0.571354i
$437$	−11.6307	+	11.6307i	−0.556370	+	0.556370i
$438$			19.4663i			0.930137i
$439$	−13.6362	−	13.6362i	−0.650822	−	0.650822i	0.302369	−	0.953191i	$-0.402223\pi$
$439$	−13.6362	−	13.6362i	−0.650822	−	0.650822i	−0.953191	+	0.302369i	$0.902223\pi$
$440$	−7.41286	−	4.92258i	−0.353394	−	0.234675i
$441$	−60.0235			−2.85826
$442$			11.0413i			0.525183i
$443$	−23.2157	−	23.2157i	−1.10301	−	1.10301i	−0.994046	−	0.108963i	$-0.965247\pi$
$443$	−23.2157	−	23.2157i	−1.10301	−	1.10301i	−0.108963	−	0.994046i	$-0.534753\pi$
$444$	5.90554	+	14.5726i	0.280265	+	0.691586i
$445$	29.2267	−	5.90030i	1.38548	−	0.279701i
$446$	6.25546	−	6.25546i	0.296204	−	0.296204i
$447$	−23.9289	+	23.9289i	−1.13180	+	1.13180i
$448$	3.41332	+	3.41332i	0.161264	+	0.161264i
$449$	16.0955	−	16.0955i	0.759594	−	0.759594i	−0.216654	−	0.976248i	$-0.569514\pi$
$449$	16.0955	−	16.0955i	0.759594	−	0.759594i	0.976248	+	0.216654i	$0.0695144\pi$
$450$	−16.9685	+	7.14229i	−0.799903	+	0.336691i
$451$	9.97914			0.469899
$452$		−	15.5469i		−	0.731267i
$453$	−17.1304	+	17.1304i	−0.804855	+	0.804855i
$454$		−	9.87949i		−	0.463668i
$455$	45.3649	−	9.15826i	2.12674	−	0.429346i
$456$	−19.1710			−0.897766
$457$			3.34685i			0.156559i	0.996931	+	0.0782794i	$0.0249426\pi$
$457$			3.34685i			0.156559i	−0.996931	+	0.0782794i	$0.975057\pi$
$458$			21.9472i			1.02552i
$459$	−3.21055	−	3.21055i	−0.149856	−	0.149856i
$460$	2.74342	−	4.13129i	0.127913	−	0.192623i
$461$	22.0325	+	22.0325i	1.02616	+	1.02616i	0.999649	+	0.0265068i	$0.00843837\pi$
$461$	22.0325	+	22.0325i	1.02616	+	1.02616i	0.0265068	+	0.999649i	$0.491562\pi$
$462$	−49.6566			−2.31023
$463$	−10.8598			−0.504696			−0.252348	−	0.967637i	$-0.581203\pi$
$463$	−10.8598			−0.504696			−0.252348	+	0.967637i	$0.581203\pi$
$464$	−2.03524	−	2.03524i	−0.0944838	−	0.0944838i
$465$	14.6393	−	22.0451i	0.678881	−	1.02232i
$466$	8.96601	+	8.96601i	0.415342	+	0.415342i
$467$		−	12.9597i		−	0.599702i	−0.953986	−	0.299851i	$-0.903063\pi$
$467$		−	12.9597i		−	0.599702i	0.953986	−	0.299851i	$-0.0969371\pi$
$468$		−	15.7874i		−	0.729772i
$469$	−8.77436			−0.405162
$470$	−2.92450	+	0.590399i	−0.134897	+	0.0272331i
$471$		−	59.5396i		−	2.74344i
$472$	2.91109	−	2.91109i	0.133994	−	0.133994i
$473$		−	35.8289i		−	1.64742i
$474$	−35.7205			−1.64070
$475$	−34.3395	−	13.9948i	−1.57560	−	0.642127i
$476$	−8.78986	+	8.78986i	−0.402883	+	0.402883i
$477$	10.4591	+	10.4591i	0.478891	+	0.478891i
$478$	13.0815	−	13.0815i	0.598335	−	0.598335i
$479$	−2.98032	+	2.98032i	−0.136174	+	0.136174i	−0.771908	−	0.635734i	$-0.780698\pi$
$479$	−2.98032	+	2.98032i	−0.136174	+	0.136174i	0.635734	+	0.771908i	$0.280698\pi$
$480$	5.66587	−	1.14383i	0.258610	−	0.0522083i
$481$	−24.0180	−	10.1653i	−1.09513	−	0.463497i
$482$	−5.41196	−	5.41196i	−0.246508	−	0.246508i
$483$		−	27.6743i		−	1.25923i
$484$	−4.83644			−0.219838
$485$	−11.0321	−	7.32599i	−0.500943	−	0.332656i
$486$	−15.6003	−	15.6003i	−0.707643	−	0.707643i
$487$			4.69219i			0.212624i	0.994333	+	0.106312i	$0.0339042\pi$
$487$			4.69219i			0.212624i	−0.994333	+	0.106312i	$0.966096\pi$
$488$	5.71266	−	5.71266i	0.258600	−	0.258600i
$489$	−3.91859	+	3.91859i	−0.177205	+	0.177205i
$490$	30.3658	+	20.1647i	1.37179	+	0.910948i
$491$	−4.44735			−0.200706			−0.100353	−	0.994952i	$-0.531997\pi$
$491$	−4.44735			−0.200706			−0.100353	+	0.994952i	$0.531997\pi$
$492$	−4.58358	+	4.58358i	−0.206644	+	0.206644i
$493$	5.24108	−	5.24108i	0.236047	−	0.236047i
$494$	22.4849	−	22.4849i	1.01165	−	1.01165i
$495$	−18.1253	+	27.2947i	−0.814672	+	1.22681i
$496$	−3.23732	+	3.23732i	−0.145360	+	0.145360i
$497$	28.6833	+	28.6833i	1.28662	+	1.28662i
$498$	−9.40969			−0.421658
$499$	−24.3133	−	24.3133i	−1.08841	−	1.08841i	−0.995692	−	0.0927210i	$-0.970444\pi$
$499$	−24.3133	−	24.3133i	−1.08841	−	1.08841i	−0.0927210	−	0.995692i	$-0.529556\pi$
$500$	10.9838	+	2.08724i	0.491210	+	0.0933442i
$501$	−37.1752	+	37.1752i	−1.66086	+	1.66086i
$502$	−2.34715	+	2.34715i	−0.104759	+	0.104759i
$503$	15.7435			0.701968			0.350984	−	0.936381i	$-0.385847\pi$
$503$	15.7435			0.701968			0.350984	+	0.936381i	$0.385847\pi$
$504$	12.5681	−	12.5681i	0.559828	−	0.559828i
$505$	3.05639	+	2.02963i	0.136008	+	0.0903173i
$506$		−	8.82588i		−	0.392358i
$507$	9.84067	+	9.84067i	0.437040	+	0.437040i
$508$	0.0553748	+	0.0553748i	0.00245686	+	0.00245686i
$509$	−32.8974			−1.45815			−0.729077	−	0.684432i	$-0.760050\pi$
$509$	−32.8974			−1.45815			−0.729077	+	0.684432i	$0.760050\pi$
$510$	2.94554	+	14.5905i	0.130431	+	0.646080i
$511$		−	36.3513i		−	1.60809i
$512$	−1.00000			−0.0441942
$513$			13.0762i			0.577327i
$514$			5.80813i			0.256186i
$515$	−5.19875	−	3.45228i	−0.229084	−	0.152126i
$516$	16.4568	+	16.4568i	0.724471	+	0.724471i
$517$	−3.75453	+	3.75453i	−0.165124	+	0.165124i
$518$	−11.0280	−	27.2129i	−0.484542	−	1.19566i
$519$			50.2422i			2.20539i
$520$	−5.30372	+	7.98682i	−0.232584	+	0.350245i
$521$			21.7965i			0.954920i	0.878653	+	0.477460i	$0.158442\pi$
$521$			21.7965i			0.954920i	−0.878653	+	0.477460i	$0.841558\pi$
$522$	−7.49392	+	7.49392i	−0.328000	+	0.328000i
$523$	−20.7364			−0.906739			−0.453369	−	0.891323i	$-0.649778\pi$
$523$	−20.7364			−0.906739			−0.453369	+	0.891323i	$0.649778\pi$
$524$	3.08937	−	3.08937i	0.134960	−	0.134960i
$525$	57.5040	−	24.2043i	2.50968	−	1.05636i
$526$	15.2944	+	15.2944i	0.666866	+	0.666866i
$527$	−8.33662	−	8.33662i	−0.363149	−	0.363149i
$528$	7.27394	−	7.27394i	0.316557	−	0.316557i
$529$	−18.0812			−0.786140
$530$	−1.77755	−	8.80497i	−0.0772118	−	0.382464i
$531$	−10.7189	−	10.7189i	−0.465159	−	0.465159i
$532$	35.7999			1.55212
$533$		−	10.7518i		−	0.465712i
$534$			34.4688i			1.49161i
$535$	11.6925	−	2.36048i	0.505511	−	0.102053i
$536$	1.28531	−	1.28531i	0.0555170	−	0.0555170i
$537$			49.0477i			2.11656i
$538$			18.2273i			0.785833i
$539$	64.8719			2.79423
$540$	−0.780179	−	3.86457i	−0.0335736	−	0.166304i
$541$	3.55548	+	3.55548i	0.152862	+	0.152862i	0.779395	−	0.626533i	$-0.215527\pi$
$541$	3.55548	+	3.55548i	0.152862	+	0.152862i	−0.626533	+	0.779395i	$0.715527\pi$
$542$	26.6096			1.14298
$543$	−28.0960	−	28.0960i	−1.20572	−	1.20572i
$544$		−	2.57516i		−	0.110409i
$545$	7.46565	+	36.9806i	0.319793	+	1.58408i
$546$			53.5014i			2.28965i
$547$	10.3831			0.443950			0.221975	−	0.975052i	$-0.428750\pi$
$547$	10.3831			0.443950			0.221975	+	0.975052i	$0.428750\pi$
$548$	−1.84871	−	1.84871i	−0.0789729	−	0.0789729i
$549$	−21.0345	−	21.0345i	−0.897729	−	0.897729i
$550$	18.3392	−	7.71922i	0.781984	−	0.329149i
$551$	−21.3462			−0.909380
$552$	4.05387	+	4.05387i	0.172544	+	0.172544i
$553$	66.7043			2.83656
$554$	−0.845623			−0.0359271
$555$	−34.4504	−	7.02549i	−1.46234	−	0.298216i
$556$	−10.9433			−0.464097
$557$	−4.73501			−0.200629			−0.100314	−	0.994956i	$-0.531985\pi$
$557$	−4.73501			−0.200629			−0.100314	+	0.994956i	$0.531985\pi$
$558$	11.9201	+	11.9201i	0.504616	+	0.504616i
$559$	−38.6031			−1.63274
$560$	−10.5804	+	2.13598i	−0.447104	+	0.0902614i
$561$	18.7316	+	18.7316i	0.790848	+	0.790848i
$562$	−11.3809	−	11.3809i	−0.480074	−	0.480074i
$563$	3.05563			0.128779			0.0643897	−	0.997925i	$-0.479490\pi$
$563$	3.05563			0.128779			0.0643897	+	0.997925i	$0.479490\pi$
$564$		−	3.44903i		−	0.145230i
$565$	28.9602	+	19.2313i	1.21837	+	0.809068i
$566$			6.37857i			0.268111i
$567$	22.1474	+	22.1474i	0.930105	+	0.930105i
$568$	−8.40334			−0.352596
$569$	29.4912	+	29.4912i	1.23633	+	1.23633i	0.961488	+	0.274845i	$0.0886266\pi$
$569$	29.4912	+	29.4912i	1.23633	+	1.23633i	0.274845	+	0.961488i	$0.411373\pi$
$570$	23.7143	−	35.7110i	0.993281	−	1.49577i
$571$	14.8841			0.622881			0.311440	−	0.950266i	$-0.399189\pi$
$571$	14.8841			0.622881			0.311440	+	0.950266i	$0.399189\pi$
$572$			17.0626i			0.713424i
$573$		−	62.0323i		−	2.59144i
$574$	8.55936	−	8.55936i	0.357261	−	0.357261i
$575$	4.30203	+	10.2207i	0.179407	+	0.426232i
$576$			3.68208i			0.153420i
$577$			9.65939i			0.402126i	0.979578	+	0.201063i	$0.0644395\pi$
$577$			9.65939i			0.402126i	−0.979578	+	0.201063i	$0.935560\pi$
$578$	−10.3685			−0.431274
$579$	−10.4331	−	10.4331i	−0.433584	−	0.433584i
$580$	6.30873	−	1.27361i	0.261956	−	0.0528836i
$581$	17.5716			0.728993
$582$	10.8254	−	10.8254i	0.448726	−	0.448726i
$583$	−11.3040	−	11.3040i	−0.468163	−	0.468163i
$584$	5.32492	+	5.32492i	0.220347	+	0.220347i
$585$	29.4081	+	19.5287i	1.21587	+	0.807413i
$586$	6.47894	−	6.47894i	0.267643	−	0.267643i
$587$	−0.789320			−0.0325787			−0.0162894	−	0.999867i	$-0.505185\pi$
$587$	−0.789320			−0.0325787			−0.0162894	+	0.999867i	$0.505185\pi$
$588$	−29.7967	+	29.7967i	−1.22880	+	1.22880i
$589$			33.9539i			1.39905i
$590$	1.82169	+	9.02362i	0.0749978	+	0.371497i
$591$			33.4410i			1.37558i
$592$	5.60171	+	2.37084i	0.230229	+	0.0974410i
$593$	4.13138	−	4.13138i	0.169656	−	0.169656i	−0.617172	−	0.786828i	$-0.711722\pi$
$593$	4.13138	−	4.13138i	0.169656	−	0.169656i	0.786828	+	0.617172i	$0.211722\pi$
$594$	−4.96140	−	4.96140i	−0.203569	−	0.203569i
$595$	−5.50049	−	27.2463i	−0.225498	−	1.11699i
$596$			13.0913i			0.536240i
$597$		−	24.3797i		−	0.997796i
$598$	−9.50925			−0.388862
$599$			38.0949i			1.55652i	0.627944	+	0.778258i	$0.283896\pi$
$599$			38.0949i			1.55652i	−0.627944	+	0.778258i	$0.716104\pi$
$600$	−4.87791	+	11.9690i	−0.199140	+	0.488634i
$601$	−43.6207			−1.77933			−0.889663	−	0.456617i	$-0.849061\pi$
$601$	−43.6207			−1.77933			−0.889663	+	0.456617i	$0.849061\pi$
$602$	−30.7314	−	30.7314i	−1.25252	−	1.25252i
$603$	−4.73262	−	4.73262i	−0.192727	−	0.192727i
$604$			9.37187i			0.381336i
$605$	5.98259	−	9.00912i	0.243227	−	0.366273i
$606$	−2.99912	+	2.99912i	−0.121831	+	0.121831i
$607$	−4.59751			−0.186607			−0.0933036	−	0.995638i	$-0.529743\pi$
$607$	−4.59751			−0.186607			−0.0933036	+	0.995638i	$0.529743\pi$
$608$	−5.24415	+	5.24415i	−0.212678	+	0.212678i
$609$	25.3959	−	25.3959i	1.02909	−	1.02909i
$610$	3.57485	+	17.7078i	0.144741	+	0.716967i
$611$	4.04523	+	4.04523i	0.163652	+	0.163652i
$612$	−9.48196			−0.383285
$613$	9.19983	+	9.19983i	0.371578	+	0.371578i	0.868052	−	0.496474i	$-0.165372\pi$
$613$	9.19983	+	9.19983i	0.371578	+	0.371578i	−0.496474	+	0.868052i	$0.665372\pi$
$614$	−3.64587	+	3.64587i	−0.147135	+	0.147135i
$615$	−2.86830	−	14.2079i	−0.115661	−	0.572919i
$616$	−13.5833	+	13.5833i	−0.547287	+	0.547287i
$617$	8.47786	−	8.47786i	0.341306	−	0.341306i	−0.515552	−	0.856858i	$-0.672413\pi$
$617$	8.47786	−	8.47786i	0.341306	−	0.341306i	0.856858	+	0.515552i	$0.172413\pi$
$618$	5.10132	−	5.10132i	0.205205	−	0.205205i
$619$	−12.3858			−0.497827			−0.248914	−	0.968526i	$-0.580074\pi$
$619$	−12.3858			−0.497827			−0.248914	+	0.968526i	$0.580074\pi$
$620$	−2.02584	−	10.0349i	−0.0813596	−	0.403009i
$621$	2.76506	−	2.76506i	0.110958	−	0.110958i
$622$	0.480637	−	0.480637i	0.0192718	−	0.0192718i
$623$		−	64.3668i		−	2.57880i
$624$	−7.83714	−	7.83714i	−0.313737	−	0.313737i
$625$	−17.4748	+	17.8783i	−0.698991	+	0.715130i
$626$	18.2772			0.730502
$627$		−	76.2912i		−	3.04678i
$628$	−16.2868	−	16.2868i	−0.649913	−	0.649913i
$629$	−6.10530	+	14.4253i	−0.243434	+	0.575175i
$630$	7.86483	+	38.9579i	0.313342	+	1.55212i
$631$	−19.2781	+	19.2781i	−0.767448	+	0.767448i	−0.977657	−	0.210208i	$-0.932586\pi$
$631$	−19.2781	+	19.2781i	−0.767448	+	0.767448i	0.210208	+	0.977657i	$0.432586\pi$
$632$	−9.77118	+	9.77118i	−0.388677	+	0.388677i
$633$	27.7017	+	27.7017i	1.10104	+	1.10104i
$634$	4.85997	−	4.85997i	0.193014	−	0.193014i
$635$	−0.171648	+	0.0346523i	−0.00681163	+	0.00137513i
$636$	10.3842			0.411761
$637$		−	69.8948i		−	2.76933i
$638$	8.09925	−	8.09925i	0.320653	−	0.320653i
$639$			30.9417i			1.22404i
$640$	1.23698	−	1.86276i	0.0488961	−	0.0736320i
$641$	0.616340			0.0243440			0.0121720	−	0.999926i	$-0.496125\pi$
$641$	0.616340			0.0243440			0.0121720	+	0.999926i	$0.496125\pi$
$642$			13.7896i			0.544233i
$643$			42.0640i			1.65884i	0.558622	+	0.829422i	$0.311330\pi$
$643$			42.0640i			1.65884i	−0.558622	+	0.829422i	$0.688670\pi$
$644$	−7.57018	−	7.57018i	−0.298307	−	0.298307i
$645$	−51.0119	+	10.2983i	−2.00859	+	0.405495i
$646$	−13.5045	−	13.5045i	−0.531329	−	0.531329i
$647$	−35.3320			−1.38904			−0.694521	−	0.719472i	$-0.744384\pi$
$647$	−35.3320			−1.38904			−0.694521	+	0.719472i	$0.744384\pi$
$648$	−6.48853			−0.254894
$649$	11.5847	+	11.5847i	0.454738	+	0.454738i
$650$	−8.31690	−	19.7591i	−0.326216	−	0.775016i
$651$	−40.3955	−	40.3955i	−1.58323	−	1.58323i
$652$			2.14382i			0.0839586i
$653$			12.3601i			0.483687i	0.970315	+	0.241844i	$0.0777521\pi$
$653$			12.3601i			0.483687i	−0.970315	+	0.241844i	$0.922248\pi$
$654$	−43.6134			−1.70542
$655$	1.93326	+	9.57626i	0.0755385	+	0.374175i
$656$			2.50763i			0.0979067i
$657$	19.6068	−	19.6068i	0.764933	−	0.764933i
$658$			6.44070i			0.251085i
$659$	−37.7706			−1.47133			−0.735667	−	0.677344i	$-0.763131\pi$
$659$	−37.7706			−1.47133			−0.735667	+	0.677344i	$0.763131\pi$
$660$	4.55186	+	22.5473i	0.177181	+	0.877654i
$661$	25.3521	−	25.3521i	0.986082	−	0.986082i	−0.0138228	−	0.999904i	$-0.504400\pi$
$661$	25.3521	−	25.3521i	0.986082	−	0.986082i	0.999904	+	0.0138228i	$0.00440006\pi$
$662$	20.7472	+	20.7472i	0.806362	+	0.806362i
$663$	20.1819	−	20.1819i	0.783801	−	0.783801i
$664$	−2.57398	+	2.57398i	−0.0998896	+	0.0998896i
$665$	−44.2839	+	66.6866i	−1.71726	+	2.58600i
$666$	8.72962	−	20.6259i	0.338266	−	0.799238i
$667$	4.51383	+	4.51383i	0.174776	+	0.174776i
$668$			20.3382i			0.786908i
$669$	−22.8681			−0.884131
$670$	0.804317	+	3.98413i	0.0310735	+	0.153921i
$671$	22.7335	+	22.7335i	0.877619	+	0.877619i
$672$		−	12.4781i		−	0.481353i
$673$	−0.303990	+	0.303990i	−0.0117180	+	0.0117180i	−0.712941	−	0.701224i	$-0.752637\pi$
$673$	−0.303990	+	0.303990i	−0.0117180	+	0.0117180i	0.701224	+	0.712941i	$0.252637\pi$
$674$	−6.47001	+	6.47001i	−0.249215	+	0.249215i
$675$	8.16383	+	3.32712i	0.314226	+	0.128061i
$676$	5.38374			0.207067
$677$	19.2022	−	19.2022i	0.738000	−	0.738000i	−0.234191	−	0.972191i	$-0.575244\pi$
$677$	19.2022	−	19.2022i	0.738000	−	0.738000i	0.972191	+	0.234191i	$0.0752440\pi$
$678$	−28.4175	+	28.4175i	−1.09137	+	1.09137i
$679$	−20.2153	+	20.2153i	−0.775791	+	0.775791i
$680$	4.79691	+	3.18543i	0.183953	+	0.122156i
$681$	−18.0582	+	18.0582i	−0.691993	+	0.691993i
$682$	−12.8829	−	12.8829i	−0.493312	−	0.493312i
$683$	−16.4834			−0.630719			−0.315359	−	0.948972i	$-0.602125\pi$
$683$	−16.4834			−0.630719			−0.315359	+	0.948972i	$0.602125\pi$
$684$	19.3094	+	19.3094i	0.738312	+	0.738312i
$685$	5.73052	−	1.15688i	0.218952	−	0.0442020i
$686$	31.7491	−	31.7491i	1.21218	−	1.21218i
$687$	40.1161	−	40.1161i	1.53053	−	1.53053i
$688$	9.00337			0.343250
$689$	−12.1792	+	12.1792i	−0.463991	+	0.463991i
$690$	−12.5660	+	2.53682i	−0.478378	+	0.0965750i
$691$		−	27.8853i		−	1.06081i	−0.847745	−	0.530403i	$-0.822041\pi$
$691$		−	27.8853i		−	1.06081i	0.847745	−	0.530403i	$-0.177959\pi$
$692$	13.7435	+	13.7435i	0.522450	+	0.522450i
$693$	50.0148	+	50.0148i	1.89991	+	1.89991i
$694$	6.44807			0.244765
$695$	13.5366	−	20.3846i	0.513473	−	0.773234i
$696$			7.44024i			0.282022i
$697$	−6.45757			−0.244598
$698$		−	4.70014i		−	0.177903i
$699$		−	32.7771i		−	1.23974i
$700$	9.10899	−	22.3509i	0.344287	−	0.844786i
$701$	5.25849	+	5.25849i	0.198610	+	0.198610i	0.799404	−	0.600794i	$-0.205149\pi$
$701$	5.25849	+	5.25849i	0.198610	+	0.198610i	−0.600794	+	0.799404i	$0.705149\pi$
$702$	−5.34555	+	5.34555i	−0.201755	+	0.201755i
$703$	41.8092	−	16.9431i	1.57686	−	0.639023i
$704$		−	3.97950i		−	0.149983i
$705$	6.42471	+	4.26639i	0.241969	+	0.160682i
$706$		−	19.6162i		−	0.738264i
$707$	5.60054	−	5.60054i	0.210630	−	0.210630i
$708$	−10.6421			−0.399953
$709$	25.3783	−	25.3783i	0.953101	−	0.953101i	−0.0458470	−	0.998948i	$-0.514599\pi$
$709$	25.3783	−	25.3783i	0.953101	−	0.953101i	0.998948	+	0.0458470i	$0.0145987\pi$
$710$	10.3948	−	15.6534i	0.390109	−	0.587461i
$711$	35.9783	+	35.9783i	1.34929	+	1.34929i
$712$	9.42876	+	9.42876i	0.353358	+	0.353358i
$713$	7.17984	−	7.17984i	0.268887	−	0.268887i
$714$	32.1331			1.20255
$715$	−31.7836	−	21.1062i	−1.18864	−	0.789326i
$716$	13.4168	+	13.4168i	0.501408	+	0.501408i
$717$	−47.8222			−1.78595
$718$		−	7.60520i		−	0.283824i
$719$			0.372987i			0.0139101i	0.999976	+	0.00695503i	$0.00221387\pi$
$719$			0.372987i			0.0139101i	−0.999976	+	0.00695503i	$0.997786\pi$
$720$	−6.85883	−	4.55467i	−0.255613	−	0.169743i
$721$	−9.52619	+	9.52619i	−0.354774	+	0.354774i
$722$			36.0022i			1.33986i
$723$			19.7845i			0.735794i
$724$	−15.3711			−0.571261
$725$	−5.43137	+	13.3271i	−0.201716	+	0.494955i
$726$	8.84029	+	8.84029i	0.328094	+	0.328094i
$727$	−14.7295			−0.546286			−0.273143	−	0.961973i	$-0.588063\pi$
$727$	−14.7295			−0.546286			−0.273143	+	0.961973i	$0.588063\pi$
$728$	14.6350	+	14.6350i	0.542411	+	0.542411i
$729$			37.5644i			1.39127i
$730$	−16.5059	+	3.33221i	−0.610910	+	0.123331i
$731$			23.1852i			0.857534i
$732$	−20.8838			−0.771887
$733$	10.6225	+	10.6225i	0.392351	+	0.392351i	0.875525	−	0.483173i	$-0.160516\pi$
$733$	10.6225	+	10.6225i	0.392351	+	0.392351i	−0.483173	+	0.875525i	$0.660516\pi$
$734$	10.3061	+	10.3061i	0.380406	+	0.380406i
$735$	−18.6461	−	92.3622i	−0.687772	−	3.40683i
$736$	2.21783			0.0817505
$737$	5.11490	+	5.11490i	0.188410	+	0.188410i
$738$	9.23331			0.339883
$739$	27.4110			1.00833			0.504165	−	0.863608i	$-0.331800\pi$
$739$	27.4110			1.00833			0.504165	+	0.863608i	$0.331800\pi$
$740$	−11.3455	+	7.50194i	−0.417070	+	0.275777i
$741$	−82.1983			−3.01963
$742$	−19.3914			−0.711881
$743$	31.6154	+	31.6154i	1.15986	+	1.15986i	0.984506	+	0.175349i	$0.0561053\pi$
$743$	31.6154	+	31.6154i	1.15986	+	1.15986i	0.175349	+	0.984506i	$0.443895\pi$
$744$	11.8347			0.433880
$745$	−24.3859	−	16.1937i	−0.893431	−	0.593291i
$746$	−0.690871	−	0.690871i	−0.0252946	−	0.0252946i
$747$	9.47758	+	9.47758i	0.346767	+	0.346767i
$748$	10.2479			0.374699
$749$		−	25.7507i		−	0.940910i
$750$	−16.2616	−	23.8919i	−0.593788	−	0.872408i
$751$		−	25.5768i		−	0.933311i	−0.884439	−	0.466655i	$-0.845459\pi$
$751$		−	25.5768i		−	0.933311i	0.884439	−	0.466655i	$-0.154541\pi$
$752$	−0.943466	−	0.943466i	−0.0344047	−	0.0344047i
$753$	8.58049			0.312690
$754$	−8.72636	−	8.72636i	−0.317795	−	0.317795i
$755$	−17.4575	−	11.5928i	−0.635345	−	0.421907i
$756$	−8.51103			−0.309543
$757$			14.8725i			0.540552i	0.962783	+	0.270276i	$0.0871149\pi$
$757$			14.8725i			0.540552i	−0.962783	+	0.270276i	$0.912885\pi$
$758$			0.266778i			0.00968982i
$759$	−16.1324	+	16.1324i	−0.585569	+	0.585569i
$760$	−3.28166	−	16.2555i	−0.119038	−	0.589649i
$761$			41.3732i			1.49978i	0.661564	+	0.749888i	$0.269893\pi$
$761$			41.3732i			1.49978i	−0.661564	+	0.749888i	$0.730107\pi$
$762$		−	0.202434i		−	0.00733341i
$763$	81.4434			2.94845
$764$	−16.9686	−	16.9686i	−0.613904	−	0.613904i
$765$	11.7290	−	17.6626i	0.424064	−	0.638593i
$766$	−32.6980			−1.18143
$767$	12.4817	−	12.4817i	0.450686	−	0.450686i
$768$	1.82785	+	1.82785i	0.0659569	+	0.0659569i
$769$	0.831140	+	0.831140i	0.0299717	+	0.0299717i	0.721934	−	0.691962i	$-0.243253\pi$
$769$	0.831140	+	0.831140i	0.0299717	+	0.0299717i	−0.691962	+	0.721934i	$0.743253\pi$
$770$	−8.50012	−	42.1048i	−0.306323	−	1.51735i
$771$	10.6164	−	10.6164i	0.382340	−	0.382340i
$772$	−5.70785			−0.205430
$773$	−24.1870	+	24.1870i	−0.869946	+	0.869946i	−0.992466	−	0.122520i	$-0.960903\pi$
$773$	−24.1870	+	24.1870i	−0.869946	+	0.869946i	0.122520	+	0.992466i	$0.460903\pi$
$774$		−	33.1511i		−	1.19159i
$775$	21.1984	+	8.63930i	0.761470	+	0.310333i
$776$		−	5.92246i		−	0.212604i
$777$	−29.5835	+	69.8986i	−1.06130	+	2.50760i
$778$	−24.7831	+	24.7831i	−0.888517	+	0.888517i
$779$	13.1504	+	13.1504i	0.471162	+	0.471162i
$780$	24.2931	−	4.90430i	0.869833	−	0.175602i
$781$		−	33.4411i		−	1.19662i
$782$			5.71129i			0.204235i
$783$	5.07483			0.181360
$784$			16.3015i			0.582197i
$785$	50.4848	−	10.1919i	1.80188	−	0.363764i
$786$	−11.2938			−0.402837
$787$	17.1870	+	17.1870i	0.612650	+	0.612650i	0.943636	−	0.330986i	$-0.107381\pi$
$787$	17.1870	+	17.1870i	0.612650	+	0.612650i	−0.330986	+	0.943636i	$0.607381\pi$
$788$	9.14763	+	9.14763i	0.325871	+	0.325871i
$789$		−	55.9116i		−	1.99051i
$790$	−6.11457	−	30.2881i	−0.217547	−	1.07760i
$791$	53.0667	−	53.0667i	1.88684	−	1.88684i
$792$	−14.6528			−0.520666
$793$	24.4938	−	24.4938i	0.869799	−	0.869799i
$794$	11.3967	−	11.3967i	0.404454	−	0.404454i
$795$	−12.8451	+	19.3433i	−0.455568	+	0.686035i
$796$	−6.66896	−	6.66896i	−0.236375	−	0.236375i
$797$	10.6790			0.378270			0.189135	−	0.981951i	$-0.439432\pi$
$797$	10.6790			0.378270			0.189135	+	0.981951i	$0.439432\pi$
$798$	−65.4369	−	65.4369i	−2.31644	−	2.31644i
$799$	2.42958	−	2.42958i	0.0859523	−	0.0859523i
$800$	1.93975	+	4.60840i	0.0685804	+	0.162932i
$801$	34.7175	−	34.7175i	1.22668	−	1.22668i
$802$	14.6783	−	14.6783i	0.518309	−	0.518309i
$803$	−21.1905	+	21.1905i	−0.747797	+	0.747797i
$804$	−4.69872			−0.165711
$805$	23.4656	−	4.73724i	0.827054	−	0.166966i
$806$	−13.8804	+	13.8804i	−0.488917	+	0.488917i
$807$	33.3167	−	33.3167i	1.17280	−	1.17280i
$808$			1.64079i			0.0577227i
$809$	−9.53144	−	9.53144i	−0.335108	−	0.335108i	0.519415	−	0.854522i	$-0.326150\pi$
$809$	−9.53144	−	9.53144i	−0.335108	−	0.335108i	−0.854522	+	0.519415i	$0.826150\pi$
$810$	8.02621	−	12.0866i	0.282012	−	0.424679i
$811$	29.6048			1.03956			0.519782	−	0.854299i	$-0.326013\pi$
$811$	29.6048			1.03956			0.519782	+	0.854299i	$0.326013\pi$
$812$		−	13.8939i		−	0.487579i
$813$	−48.6383	−	48.6383i	−1.70582	−	1.70582i
$814$	−9.43477	+	22.2920i	−0.330688	+	0.781334i
$815$	−3.99343	−	2.65187i	−0.139884	−	0.0928911i
$816$	−4.70702	+	4.70702i	−0.164779	+	0.164779i
$817$	47.2150	−	47.2150i	1.65184	−	1.65184i
$818$	10.7756	+	10.7756i	0.376760	+	0.376760i
$819$	53.8874	−	53.8874i	1.88298	−	1.88298i
$820$	−4.67112	−	3.10190i	−0.163123	−	0.108323i
$821$	−24.3165			−0.848651			−0.424325	−	0.905510i	$-0.639489\pi$
$821$	−24.3165			−0.848651			−0.424325	+	0.905510i	$0.639489\pi$
$822$			6.75833i			0.235724i
$823$	−35.9075	+	35.9075i	−1.25166	+	1.25166i	−0.296682	+	0.954976i	$0.595880\pi$
$823$	−35.9075	+	35.9075i	−1.25166	+	1.25166i	−0.954976	+	0.296682i	$0.904120\pi$
$824$		−	2.79089i		−	0.0972251i
$825$	−47.6308	−	19.4117i	−1.65829	−	0.675827i
$826$	19.8730			0.691468
$827$		−	7.03825i		−	0.244744i	−0.992484	−	0.122372i	$-0.960950\pi$
$827$		−	7.03825i		−	0.244744i	0.992484	−	0.122372i	$-0.0390501\pi$
$828$		−	8.16624i		−	0.283797i
$829$	12.4360	+	12.4360i	0.431920	+	0.431920i	0.889281	−	0.457361i	$-0.151205\pi$
$829$	12.4360	+	12.4360i	0.431920	+	0.431920i	−0.457361	+	0.889281i	$0.651205\pi$
$830$	−1.61073	−	7.97866i	−0.0559094	−	0.276943i
$831$	1.54567	+	1.54567i	0.0536188	+	0.0536188i
$832$	−4.28763			−0.148647
$833$	−41.9791			−1.45449
$834$	20.0026	+	20.0026i	0.692635	+	0.692635i
$835$	−37.8851	−	25.1580i	−1.31107	−	0.870628i
$836$	−20.8691	−	20.8691i	−0.721773	−	0.721773i
$837$		−	8.07217i		−	0.279015i
$838$			24.0943i			0.832325i
$839$	21.4518			0.740598			0.370299	−	0.928913i	$-0.379255\pi$
$839$	21.4518			0.740598			0.370299	+	0.928913i	$0.379255\pi$
$840$	23.2437	+	15.4352i	0.801983	+	0.532564i
$841$		−	20.7156i		−	0.714330i
$842$	−21.6407	+	21.6407i	−0.745788	+	0.745788i
$843$			41.6051i			1.43296i
$844$	15.1553			0.521668
$845$	−6.65959	+	10.0286i	−0.229097	+	0.344995i
$846$	−3.47392	+	3.47392i	−0.119436	+	0.119436i
$847$	−16.5083	−	16.5083i	−0.567232	−	0.567232i
$848$	2.84055	−	2.84055i	0.0975449	−	0.0975449i
$849$	11.6591	−	11.6591i	0.400139	−	0.400139i
$850$	−11.8674	+	4.99516i	−0.407048	+	0.171333i
$851$	−12.4237	−	5.25813i	−0.425878	−	0.180246i
$852$	15.3600	+	15.3600i	0.526227	+	0.526227i
$853$			9.13898i			0.312913i	0.987685	+	0.156456i	$0.0500071\pi$
$853$			9.13898i			0.312913i	−0.987685	+	0.156456i	$0.949993\pi$
$854$	38.9983			1.33449
$855$	−59.8541	+	12.0833i	−2.04697	+	0.413242i
$856$	3.77209	+	3.77209i	0.128927	+	0.128927i
$857$		−	13.4472i		−	0.459346i	−0.973268	−	0.229673i	$-0.926234\pi$
$857$		−	13.4472i		−	0.459346i	0.973268	−	0.229673i	$-0.0737657\pi$
$858$	31.1879	−	31.1879i	1.06474	−	1.06474i
$859$	−29.5713	+	29.5713i	−1.00896	+	1.00896i	−0.00900160	+	0.999959i	$0.502865\pi$
$859$	−29.5713	+	29.5713i	−1.00896	+	1.00896i	−0.999959	+	0.00900160i	$0.997135\pi$
$860$	−11.1370	+	16.7711i	−0.379769	+	0.571890i
$861$	−31.2905			−1.06638
$862$	−1.23281	+	1.23281i	−0.0419898	+	0.0419898i
$863$	9.53473	−	9.53473i	0.324566	−	0.324566i	−0.525950	−	0.850516i	$-0.676290\pi$
$863$	9.53473	−	9.53473i	0.324566	−	0.324566i	0.850516	+	0.525950i	$0.176290\pi$
$864$	1.24674	−	1.24674i	0.0424149	−	0.0424149i
$865$	−42.6014	+	8.60037i	−1.44849	+	0.292421i
$866$	12.5825	−	12.5825i	0.427572	−	0.427572i
$867$	18.9521	+	18.9521i	0.643648	+	0.643648i
$868$	−22.1000			−0.750123
$869$	−38.8844	−	38.8844i	−1.31906	−	1.31906i
$870$	−13.8594	−	9.20345i	−0.469877	−	0.312026i
$871$	5.51094	−	5.51094i	0.186731	−	0.186731i
$872$	−11.9302	+	11.9302i	−0.404008	+	0.404008i
$873$	−21.8070			−0.738054
$874$	11.6307	−	11.6307i	0.393413	−	0.393413i
$875$	30.3667	+	44.6156i	1.02658	+	1.50828i
$876$		−	19.4663i		−	0.657706i
$877$	−7.17655	−	7.17655i	−0.242335	−	0.242335i	0.575481	−	0.817815i	$-0.304815\pi$
$877$	−7.17655	−	7.17655i	−0.242335	−	0.242335i	−0.817815	+	0.575481i	$0.804815\pi$
$878$	13.6362	+	13.6362i	0.460201	+	0.460201i
$879$	−23.6851			−0.798878
$880$	7.41286	+	4.92258i	0.249887	+	0.165940i
$881$		−	10.0748i		−	0.339428i	−0.985493	−	0.169714i	$-0.945716\pi$
$881$		−	10.0748i		−	0.339428i	0.985493	−	0.169714i	$-0.0542844\pi$
$882$	60.0235			2.02110
$883$			33.1203i			1.11459i	0.830316	+	0.557293i	$0.188160\pi$
$883$			33.1203i			1.11459i	−0.830316	+	0.557293i	$0.811840\pi$
$884$		−	11.0413i		−	0.371360i
$885$	13.1641	−	19.8236i	0.442505	−	0.666364i
$886$	23.2157	+	23.2157i	0.779945	+	0.779945i
$887$	27.8387	−	27.8387i	0.934731	−	0.934731i	−0.0632658	−	0.997997i	$-0.520152\pi$
$887$	27.8387	−	27.8387i	0.934731	−	0.934731i	0.997997	+	0.0632658i	$0.0201516\pi$
$888$	−5.90554	−	14.5726i	−0.198177	−	0.489025i
$889$			0.378024i			0.0126785i
$890$	−29.2267	+	5.90030i	−0.979683	+	0.197778i
$891$		−	25.8211i		−	0.865040i
$892$	−6.25546	+	6.25546i	−0.209448	+	0.209448i
$893$	−9.89535			−0.331135
$894$	23.9289	−	23.9289i	0.800303	−	0.800303i
$895$	−41.5885	+	8.39589i	−1.39015	+	0.280644i
$896$	−3.41332	−	3.41332i	−0.114031	−	0.114031i
$897$	17.3815	+	17.3815i	0.580351	+	0.580351i
$898$	−16.0955	+	16.0955i	−0.537114	+	0.537114i
$899$	13.1775			0.439493
$900$	16.9685	−	7.14229i	0.565617	−	0.238076i
$901$	7.31488	+	7.31488i	0.243694	+	0.243694i
$902$	−9.97914			−0.332269
$903$			112.345i			3.73860i
$904$			15.5469i			0.517084i
$905$	19.0138	−	28.6326i	0.632039	−	0.951780i
$906$	17.1304	−	17.1304i	0.569119	−	0.569119i
$907$			11.8792i			0.394444i	0.980359	+	0.197222i	$0.0631920\pi$
$907$			11.8792i			0.394444i	−0.980359	+	0.197222i	$0.936808\pi$
$908$			9.87949i			0.327862i
$909$	6.04151			0.200384
$910$	−45.3649	+	9.15826i	−1.50383	+	0.303593i
$911$	27.0290	+	27.0290i	0.895512	+	0.895512i	0.995035	−	0.0995236i	$-0.0317319\pi$
$911$	27.0290	+	27.0290i	0.895512	+	0.895512i	−0.0995236	+	0.995035i	$0.531732\pi$
$912$	19.1710			0.634817
$913$	−10.2431	−	10.2431i	−0.338999	−	0.338999i
$914$		−	3.34685i		−	0.110704i
$915$	25.8329	−	38.9015i	0.854009	−	1.28604i
$916$		−	21.9472i		−	0.725155i
$917$	21.0900			0.696454
$918$	3.21055	+	3.21055i	0.105964	+	0.105964i
$919$	−39.7559	−	39.7559i	−1.31143	−	1.31143i	−0.920364	−	0.391062i	$-0.872108\pi$
$919$	−39.7559	−	39.7559i	−1.31143	−	1.31143i	−0.391062	−	0.920364i	$-0.627892\pi$
$920$	−2.74342	+	4.13129i	−0.0904480	+	0.136205i
$921$	13.3282			0.439179
$922$	−22.0325	−	22.0325i	−0.725601	−	0.725601i
$923$	−36.0304			−1.18595
$924$	49.6566			1.63358
$925$	0.0599082	−	30.4138i	0.00196977	−	0.999998i
$926$	10.8598			0.356874
$927$	−10.2763			−0.337517
$928$	2.03524	+	2.03524i	0.0668101	+	0.0668101i
$929$	28.8922			0.947923			0.473961	−	0.880546i	$-0.342824\pi$
$929$	28.8922			0.947923			0.473961	+	0.880546i	$0.342824\pi$
$930$	−14.6393	+	22.0451i	−0.480041	+	0.722889i
$931$	85.4876	+	85.4876i	2.80174	+	2.80174i
$932$	−8.96601	−	8.96601i	−0.293691	−	0.293691i
$933$	−1.75707			−0.0575238
$934$			12.9597i			0.424054i
$935$	−12.6764	+	19.0893i	−0.414564	+	0.624287i
$936$			15.7874i			0.516027i
$937$	29.8795	+	29.8795i	0.976119	+	0.976119i	0.999721	−	0.0236021i	$-0.00751348\pi$
$937$	29.8795	+	29.8795i	0.976119	+	0.976119i	−0.0236021	+	0.999721i	$0.507513\pi$
$938$	8.77436			0.286493
$939$	−33.4079	−	33.4079i	−1.09023	−	1.09023i
$940$	2.92450	−	0.590399i	0.0953867	−	0.0192567i
$941$	−29.7963			−0.971333			−0.485666	−	0.874144i	$-0.661423\pi$
$941$	−29.7963			−0.971333			−0.485666	+	0.874144i	$0.661423\pi$
$942$			59.5396i			1.93990i
$943$		−	5.56152i		−	0.181108i
$944$	−2.91109	+	2.91109i	−0.0947478	+	0.0947478i
$945$	10.5280	−	15.8540i	0.342476	−	0.515731i
$946$			35.8289i			1.16490i
$947$		−	41.7971i		−	1.35822i	−0.734035	−	0.679112i	$-0.762365\pi$
$947$		−	41.7971i		−	1.35822i	0.734035	−	0.679112i	$-0.237635\pi$
$948$	35.7205			1.16015
$949$	22.8313	+	22.8313i	0.741134	+	0.741134i
$950$	34.3395	+	13.9948i	1.11412	+	0.454053i
$951$	−17.7666			−0.576121
$952$	8.78986	−	8.78986i	0.284881	−	0.284881i
$953$	6.33457	+	6.33457i	0.205197	+	0.205197i	0.802222	−	0.597025i	$-0.203651\pi$
$953$	6.33457	+	6.33457i	0.205197	+	0.205197i	−0.597025	+	0.802222i	$0.703651\pi$
$954$	−10.4591	−	10.4591i	−0.338627	−	0.338627i
$955$	52.5984	−	10.6186i	1.70204	−	0.343609i
$956$	−13.0815	+	13.0815i	−0.423087	+	0.423087i
$957$	−29.6085			−0.957105
$958$	2.98032	−	2.98032i	0.0962898	−	0.0962898i
$959$		−	12.6205i		−	0.407536i
$960$	−5.66587	+	1.14383i	−0.182865	+	0.0369168i
$961$			10.0396i			0.323856i
$962$	24.0180	+	10.1653i	0.774372	+	0.327742i
$963$	13.8891	−	13.8891i	0.447571	−	0.447571i
$964$	5.41196	+	5.41196i	0.174308	+	0.174308i
$965$	7.06051	−	10.6323i	0.227286	−	0.342267i
$966$			27.6743i			0.890407i
$967$			39.3087i			1.26408i	0.774935	+	0.632041i	$0.217783\pi$
$967$			39.3087i			1.26408i	−0.774935	+	0.632041i	$0.782217\pi$
$968$	4.83644			0.155449
$969$			49.3686i			1.58595i
$970$	11.0321	+	7.32599i	0.354220	+	0.235223i
$971$	23.7788			0.763098			0.381549	−	0.924349i	$-0.375391\pi$
$971$	23.7788			0.763098			0.381549	+	0.924349i	$0.375391\pi$
$972$	15.6003	+	15.6003i	0.500379	+	0.500379i
$973$	−37.3528	−	37.3528i	−1.19748	−	1.19748i
$974$		−	4.69219i		−	0.150348i
$975$	−20.9147	+	51.3188i	−0.669805	+	1.64352i
$976$	−5.71266	+	5.71266i	−0.182858	+	0.182858i
$977$	−0.684369			−0.0218949			−0.0109474	−	0.999940i	$-0.503485\pi$
$977$	−0.684369			−0.0218949			−0.0109474	+	0.999940i	$0.503485\pi$
$978$	3.91859	−	3.91859i	0.125303	−	0.125303i
$979$	−37.5218	+	37.5218i	−1.19920	+	1.19920i
$980$	−30.3658	−	20.1647i	−0.970000	−	0.644138i
$981$	43.9280	+	43.9280i	1.40251	+	1.40251i
$982$	4.44735			0.141921
$983$	−31.2059	−	31.2059i	−0.995314	−	0.995314i	0.00467471	−	0.999989i	$-0.498512\pi$
$983$	−31.2059	−	31.2059i	−0.995314	−	0.995314i	−0.999989	+	0.00467471i	$0.998512\pi$
$984$	4.58358	−	4.58358i	0.146119	−	0.146119i
$985$	−28.3553	+	5.72437i	−0.903475	+	0.182394i
$986$	−5.24108	+	5.24108i	−0.166910	+	0.166910i
$987$	11.7726	−	11.7726i	0.374728	−	0.374728i
$988$	−22.4849	+	22.4849i	−0.715342	+	0.715342i
$989$	−19.9680			−0.634945
$990$	18.1253	−	27.2947i	0.576060	−	0.867483i
$991$	−13.0082	+	13.0082i	−0.413219	+	0.413219i	−0.882858	−	0.469639i	$-0.844384\pi$
$991$	−13.0082	+	13.0082i	−0.413219	+	0.413219i	0.469639	+	0.882858i	$0.344384\pi$
$992$	3.23732	−	3.23732i	0.102785	−	0.102785i
$993$		−	75.8455i		−	2.40688i
$994$	−28.6833	−	28.6833i	−0.909779	−	0.909779i
$995$	20.6721	−	4.17328i	0.655348	−	0.132302i
$996$	9.40969			0.298157
$997$		−	26.5817i		−	0.841852i	−0.907095	−	0.420926i	$-0.861705\pi$
$997$		−	26.5817i		−	0.841852i	0.907095	−	0.420926i	$-0.138295\pi$
$998$	24.3133	+	24.3133i	0.769624	+	0.769624i
$999$	−9.93968	+	4.02804i	−0.314478	+	0.127442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.117.9	yes	20
5.3	odd	4		370.2.g.e.43.2	✓	20
37.31	odd	4		370.2.g.e.327.2	yes	20
185.68	even	4	inner	370.2.h.e.253.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.2	✓	20	5.3	odd	4
370.2.g.e.327.2	yes	20	37.31	odd	4
370.2.h.e.117.9	yes	20	1.1	even	1	trivial
370.2.h.e.253.9	yes	20	185.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.82785 + 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 + 1.86276i) q^{5} +(-1.82785 - 1.82785i) q^{6} +(3.41332 + 3.41332i) q^{7} -1.00000 q^{8} +3.68208i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.82785 + 1.82785i) q^{3} +1.00000 q^{4} +(-1.23698 + 1.86276i) q^{5} +(-1.82785 - 1.82785i) q^{6} +(3.41332 + 3.41332i) q^{7} -1.00000 q^{8} +3.68208i q^{9} +(1.23698 - 1.86276i) q^{10} -3.97950i q^{11} +(1.82785 + 1.82785i) q^{12} -4.28763 q^{13} +(-3.41332 - 3.41332i) q^{14} +(-5.66587 + 1.14383i) q^{15} +1.00000 q^{16} +2.57516i q^{17} -3.68208i q^{18} +(5.24415 - 5.24415i) q^{19} +(-1.23698 + 1.86276i) q^{20} +12.4781i q^{21} +3.97950i q^{22} -2.21783 q^{23} +(-1.82785 - 1.82785i) q^{24} +(-1.93975 - 4.60840i) q^{25} +4.28763 q^{26} +(-1.24674 + 1.24674i) q^{27} +(3.41332 + 3.41332i) q^{28} +(-2.03524 - 2.03524i) q^{29} +(5.66587 - 1.14383i) q^{30} +(-3.23732 + 3.23732i) q^{31} -1.00000 q^{32} +(7.27394 - 7.27394i) q^{33} -2.57516i q^{34} +(-10.5804 + 2.13598i) q^{35} +3.68208i q^{36} +(5.60171 + 2.37084i) q^{37} +(-5.24415 + 5.24415i) q^{38} +(-7.83714 - 7.83714i) q^{39} +(1.23698 - 1.86276i) q^{40} +2.50763i q^{41} -12.4781i q^{42} +9.00337 q^{43} -3.97950i q^{44} +(-6.85883 - 4.55467i) q^{45} +2.21783 q^{46} +(-0.943466 - 0.943466i) q^{47} +(1.82785 + 1.82785i) q^{48} +16.3015i q^{49} +(1.93975 + 4.60840i) q^{50} +(-4.70702 + 4.70702i) q^{51} -4.28763 q^{52} +(2.84055 - 2.84055i) q^{53} +(1.24674 - 1.24674i) q^{54} +(7.41286 + 4.92258i) q^{55} +(-3.41332 - 3.41332i) q^{56} +19.1710 q^{57} +(2.03524 + 2.03524i) q^{58} +(-2.91109 + 2.91109i) q^{59} +(-5.66587 + 1.14383i) q^{60} +(-5.71266 + 5.71266i) q^{61} +(3.23732 - 3.23732i) q^{62} +(-12.5681 + 12.5681i) q^{63} +1.00000 q^{64} +(5.30372 - 7.98682i) q^{65} +(-7.27394 + 7.27394i) q^{66} +(-1.28531 + 1.28531i) q^{67} +2.57516i q^{68} +(-4.05387 - 4.05387i) q^{69} +(10.5804 - 2.13598i) q^{70} +8.40334 q^{71} -3.68208i q^{72} +(-5.32492 - 5.32492i) q^{73} +(-5.60171 - 2.37084i) q^{74} +(4.87791 - 11.9690i) q^{75} +(5.24415 - 5.24415i) q^{76} +(13.5833 - 13.5833i) q^{77} +(7.83714 + 7.83714i) q^{78} +(9.77118 - 9.77118i) q^{79} +(-1.23698 + 1.86276i) q^{80} +6.48853 q^{81} -2.50763i q^{82} +(2.57398 - 2.57398i) q^{83} +12.4781i q^{84} +(-4.79691 - 3.18543i) q^{85} -9.00337 q^{86} -7.44024i q^{87} +3.97950i q^{88} +(-9.42876 - 9.42876i) q^{89} +(6.85883 + 4.55467i) q^{90} +(-14.6350 - 14.6350i) q^{91} -2.21783 q^{92} -11.8347 q^{93} +(0.943466 + 0.943466i) q^{94} +(3.28166 + 16.2555i) q^{95} +(-1.82785 - 1.82785i) q^{96} +5.92246i q^{97} -16.3015i q^{98} +14.6528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

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