LMFDB - Embedded newform 370.2.g.e.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.82785 - 1.82785i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.e.327.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.82785	+	1.82785i	−1.05531	+	1.05531i	−0.0569322	+	0.998378i	$0.518132\pi$
$3$	−1.82785	+	1.82785i	−1.05531	+	1.05531i	−0.998378	+	0.0569322i	$0.981868\pi$
$4$	−1.00000			−0.500000
$5$	1.86276	−	1.23698i	0.833051	−	0.553196i
$5$	1.86276	−	1.23698i	0.833051	−	0.553196i
$6$	−1.82785	−	1.82785i	−0.746217	−	0.746217i
$7$	3.41332	−	3.41332i	1.29011	−	1.29011i	0.355399	−	0.934715i	$-0.384345\pi$
$7$	3.41332	−	3.41332i	1.29011	−	1.29011i	0.934715	−	0.355399i	$-0.115655\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	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
$13$		−	4.28763i		−	1.18917i	−0.804031	−	0.594587i	$-0.797316\pi$
$13$		−	4.28763i		−	1.18917i	0.804031	−	0.594587i	$-0.202684\pi$
$14$	3.41332	+	3.41332i	0.912248	+	0.912248i
$15$	−1.14383	+	5.66587i	−0.295335	+	1.46292i
$16$	1.00000			0.250000
$17$	2.57516			0.624569			0.312284	−	0.949989i	$-0.398906\pi$
$17$	2.57516			0.624569			0.312284	+	0.949989i	$0.398906\pi$
$18$	3.68208			0.867874
$19$	−5.24415	+	5.24415i	−1.20309	+	1.20309i	−0.229868	+	0.973222i	$0.573830\pi$
$19$	−5.24415	+	5.24415i	−1.20309	+	1.20309i	−0.973222	+	0.229868i	$0.926170\pi$
$20$	−1.86276	+	1.23698i	−0.416526	+	0.276598i
$21$			12.4781i			2.72294i
$22$	3.97950			0.848433
$23$		−	2.21783i		−	0.462451i	−0.972900	−	0.231225i	$-0.925727\pi$
$23$		−	2.21783i		−	0.462451i	0.972900	−	0.231225i	$-0.0742734\pi$
$24$	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	0.870357	−	0.492422i	$-0.163888\pi$
$29$	2.03524	+	2.03524i	0.377935	+	0.377935i	−0.492422	+	0.870357i	$0.663888\pi$
$30$	−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	$0.384869\pi$
$32$			1.00000i			0.176777i
$33$	7.27394	+	7.27394i	1.26623	+	1.26623i
$34$			2.57516i			0.441637i
$35$	2.13598	−	10.5804i	0.361046	−	1.78842i
$36$			3.68208i			0.613680i
$37$	2.37084	−	5.60171i	0.389764	−	0.920915i
$37$	2.37084	−	5.60171i	0.389764	−	0.920915i
$38$	−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	$0.937265\pi$
$42$	−12.4781			−1.92541
$43$			9.00337i			1.37300i	0.727129	+	0.686501i	$0.240854\pi$
$43$			9.00337i			1.37300i	−0.727129	+	0.686501i	$0.759146\pi$
$44$			3.97950i			0.599933i
$45$	−4.55467	−	6.85883i	−0.678970	−	1.02245i
$46$	2.21783			0.327002
$47$	−0.943466	+	0.943466i	−0.137619	+	0.137619i	−0.772560	−	0.634942i	$-0.781024\pi$
$47$	−0.943466	+	0.943466i	−0.137619	+	0.137619i	0.634942	+	0.772560i	$0.281024\pi$
$48$	−1.82785	+	1.82785i	−0.263828	+	0.263828i
$49$		−	16.3015i		−	2.32879i
$50$	4.60840	+	1.93975i	0.651727	+	0.274321i
$51$	−4.70702	+	4.70702i	−0.659114	+	0.659114i
$52$			4.28763i			0.594587i
$53$	2.84055	+	2.84055i	0.390180	+	0.390180i	0.874751	−	0.484572i	$-0.161025\pi$
$53$	2.84055	+	2.84055i	0.390180	+	0.390180i	−0.484572	+	0.874751i	$0.661025\pi$
$54$	−1.24674	+	1.24674i	−0.169660	+	0.169660i
$55$	−4.92258	−	7.41286i	−0.663760	−	0.999549i
$56$	−3.41332	−	3.41332i	−0.456124	−	0.456124i
$57$		−	19.1710i		−	2.53927i
$58$	−2.03524	+	2.03524i	−0.267240	+	0.267240i
$59$	2.91109	−	2.91109i	0.378991	−	0.378991i	−0.491747	−	0.870738i	$-0.663641\pi$
$59$	2.91109	−	2.91109i	0.378991	−	0.378991i	0.870738	+	0.491747i	$0.163641\pi$
$60$	1.14383	−	5.66587i	0.147667	−	0.731460i
$61$	−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	$-0.214584\pi$
$67$	1.28531	+	1.28531i	0.157026	+	0.157026i	−0.624222	+	0.781247i	$0.714584\pi$
$68$	−2.57516			−0.312284
$69$	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	$0.333831\pi$
$72$	−3.68208			−0.433937
$73$	5.32492	−	5.32492i	0.623235	−	0.623235i	−0.323123	−	0.946357i	$-0.604733\pi$
$73$	5.32492	−	5.32492i	0.623235	−	0.623235i	0.946357	+	0.323123i	$0.104733\pi$
$74$	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	$0.533438\pi$
$79$	−9.77118	+	9.77118i	−1.09934	+	1.09934i	−0.994487	+	0.104856i	$0.966562\pi$
$80$	1.86276	−	1.23698i	0.208263	−	0.138299i
$81$	6.48853			0.720948
$82$	−2.50763			−0.276922
$83$	2.57398	+	2.57398i	0.282531	+	0.282531i	0.834117	−	0.551587i	$-0.185977\pi$
$83$	2.57398	+	2.57398i	0.282531	+	0.282531i	−0.551587	+	0.834117i	$0.685977\pi$
$84$		−	12.4781i		−	1.36147i
$85$	4.79691	−	3.18543i	0.520298	−	0.345509i
$86$	−9.00337			−0.970859
$87$	−7.44024			−0.797678
$88$	−3.97950			−0.424216
$89$	9.42876	+	9.42876i	0.999447	+	0.999447i	1.00000		0.000552868i	$-0.000175983\pi$
$89$	9.42876	+	9.42876i	0.999447	+	0.999447i	−0.000552868		1.00000i	$0.500176\pi$
$90$	6.85883	−	4.55467i	0.722984	−	0.480104i
$91$	−14.6350	−	14.6350i	−1.53417	−	1.53417i
$92$			2.21783i			0.231225i
$93$		−	11.8347i		−	1.22720i
$94$	−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
$97$	5.92246			0.601335			0.300668	−	0.953729i	$-0.402791\pi$
$97$	5.92246			0.601335			0.300668	+	0.953729i	$0.402791\pi$
$98$	16.3015			1.64670
$99$	−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
$103$	−2.79089			−0.274994			−0.137497	−	0.990502i	$-0.543906\pi$
$103$	−2.79089			−0.274994			−0.137497	+	0.990502i	$0.543906\pi$
$104$	−4.28763			−0.420436
$105$	15.4352	+	23.2437i	1.50632	+	2.26835i
$106$	−2.84055	+	2.84055i	−0.275899	+	0.275899i
$107$	−3.77209	+	3.77209i	−0.364662	+	0.364662i	−0.865526	−	0.500864i	$-0.833016\pi$
$107$	−3.77209	+	3.77209i	−0.364662	+	0.364662i	0.500864	+	0.865526i	$0.333016\pi$
$108$	−1.24674	−	1.24674i	−0.119967	−	0.119967i
$109$	−11.9302	+	11.9302i	−1.14271	+	1.14271i	−0.154756	+	0.987953i	$0.549459\pi$
$109$	−11.9302	+	11.9302i	−1.14271	+	1.14271i	−0.987953	+	0.154756i	$0.950541\pi$
$110$	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
$113$	15.5469			1.46253			0.731267	−	0.682091i	$-0.238929\pi$
$113$	15.5469			1.46253			0.731267	+	0.682091i	$0.238929\pi$
$114$	19.1710			1.79553
$115$	−2.74342	−	4.13129i	−0.255826	−	0.385245i
$116$	−2.03524	−	2.03524i	−0.188968	−	0.188968i
$117$	−15.7874			−1.45954
$118$	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
$125$	−2.08724	−	10.9838i	−0.186688	−	0.982419i
$126$	12.5681	−	12.5681i	1.11966	−	1.11966i
$127$	0.0553748	−	0.0553748i	0.00491372	−	0.00491372i	−0.704646	−	0.709559i	$-0.748894\pi$
$127$	0.0553748	−	0.0553748i	0.00491372	−	0.00491372i	0.709559	+	0.704646i	$0.248894\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−16.4568	−	16.4568i	−1.44894	−	1.44894i
$130$	7.98682	−	5.30372i	0.700490	−	0.465167i
$131$	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
$133$			35.7999i			3.10425i
$134$	−1.28531	+	1.28531i	−0.111034	+	0.111034i
$135$	3.86457	+	0.780179i	0.332609	+	0.0671471i
$136$		−	2.57516i		−	0.220818i
$137$	−1.84871	+	1.84871i	−0.157946	+	0.157946i	−0.781656	−	0.623710i	$-0.785625\pi$
$137$	−1.84871	+	1.84871i	−0.157946	+	0.157946i	0.623710	+	0.781656i	$0.285625\pi$
$138$	−4.05387	+	4.05387i	−0.345088	+	0.345088i
$139$	10.9433			0.928195			0.464097	−	0.885784i	$-0.346379\pi$
$139$	10.9433			0.928195			0.464097	+	0.885784i	$0.346379\pi$
$140$	−2.13598	+	10.5804i	−0.180523	+	0.894208i
$141$		−	3.44903i		−	0.290461i
$142$			8.40334i			0.705192i
$143$	−17.0626			−1.42685
$144$		−	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
$148$	−2.37084	+	5.60171i	−0.194882	+	0.460457i
$149$		−	13.0913i		−	1.07248i	−0.844066	−	0.536240i	$-0.819844\pi$
$149$		−	13.0913i		−	1.07248i	0.844066	−	0.536240i	$-0.180156\pi$
$150$	−11.9690	+	4.87791i	−0.977268	+	0.398280i
$151$			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
$153$		−	9.48196i		−	0.766571i
$154$	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	−0.371321	+	0.928504i	$0.621095\pi$
$157$	−16.2868	+	16.2868i	−1.29983	+	1.29983i	−0.928504	+	0.371321i	$0.878905\pi$
$158$	−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
$162$			6.48853i			0.509787i
$163$	−2.14382			−0.167917			−0.0839586	−	0.996469i	$-0.526756\pi$
$163$	−2.14382			−0.167917			−0.0839586	+	0.996469i	$0.526756\pi$
$164$		−	2.50763i		−	0.195813i
$165$	22.5473	+	4.55186i	1.75531	+	0.354362i
$166$	−2.57398	+	2.57398i	−0.199779	+	0.199779i
$167$	20.3382			1.57382			0.786908	−	0.617071i	$-0.211681\pi$
$167$	20.3382			1.57382			0.786908	+	0.617071i	$0.211681\pi$
$168$	12.4781			0.962705
$169$	−5.38374			−0.414134
$170$	3.18543	+	4.79691i	0.244312	+	0.367906i
$171$	19.3094	+	19.3094i	1.47662	+	1.47662i
$172$		−	9.00337i		−	0.686501i
$173$	−13.7435	+	13.7435i	−1.04490	+	1.04490i	−0.0459570	+	0.998943i	$0.514634\pi$
$173$	−13.7435	+	13.7435i	−1.04490	+	1.04490i	−0.998943	+	0.0459570i	$0.985366\pi$
$174$		−	7.44024i		−	0.564043i
$175$	−9.10899	−	22.3509i	−0.688575	−	1.68957i
$176$		−	3.97950i		−	0.299966i
$177$			10.6421i			0.799907i
$178$	−9.42876	+	9.42876i	−0.706716	+	0.706716i
$179$	−13.4168	−	13.4168i	−1.00282	−	1.00282i	−0.999996	−	0.00281938i	$-0.999103\pi$
$179$	−13.4168	−	13.4168i	−1.00282	−	1.00282i	−0.00281938	−	0.999996i	$-0.500897\pi$
$180$	4.55467	+	6.85883i	0.339485	+	0.511227i
$181$	−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
$183$		−	20.8838i		−	1.54377i
$184$	−2.21783			−0.163501
$185$	−2.51291	−	13.3673i	−0.184753	−	0.982785i
$186$	11.8347			0.867760
$187$		−	10.2479i		−	0.749398i
$188$	0.943466	−	0.943466i	0.0688093	−	0.0688093i
$189$	8.51103			0.619087
$190$	−16.2555	−	3.28166i	−1.17930	−	0.238077i
$191$	−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
$193$		−	5.70785i		−	0.410860i	−0.978672	−	0.205430i	$-0.934141\pi$
$193$		−	5.70785i		−	0.410860i	0.978672	−	0.205430i	$-0.0658592\pi$
$194$			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	−0.301670	−	0.953412i	$-0.597544\pi$
$197$	9.14763	−	9.14763i	0.651742	−	0.651742i	0.953412	+	0.301670i	$0.0975442\pi$
$198$		−	14.6528i		−	1.04133i
$199$	6.66896	+	6.66896i	0.472750	+	0.472750i	0.902803	−	0.430053i	$-0.141505\pi$
$199$	6.66896	+	6.66896i	0.472750	+	0.472750i	−0.430053	+	0.902803i	$0.641505\pi$
$200$	−4.60840	−	1.93975i	−0.325863	−	0.137161i
$201$	−4.69872			−0.331422
$202$	1.64079			0.115445
$203$	13.8939			0.975159
$204$	4.70702	−	4.70702i	0.329557	−	0.329557i
$205$	3.10190	+	4.67112i	0.216646	+	0.326245i
$206$		−	2.79089i		−	0.194450i
$207$	−8.16624			−0.567593
$208$		−	4.28763i		−	0.297293i
$209$	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
$217$			22.1000i			1.50025i
$218$	−11.9302	−	11.9302i	−0.808017	−	0.808017i
$219$			19.4663i			1.31541i
$220$	4.92258	+	7.41286i	0.331880	+	0.499775i
$221$		−	11.0413i		−	0.742721i
$222$	−14.5726	+	5.90554i	−0.978051	+	0.396354i
$223$	−6.25546	−	6.25546i	−0.418896	−	0.418896i	0.465927	−	0.884823i	$-0.345721\pi$
$223$	−6.25546	−	6.25546i	−0.418896	−	0.418896i	−0.884823	+	0.465927i	$0.845721\pi$
$224$	3.41332	+	3.41332i	0.228062	+	0.228062i
$225$	−16.9685	−	7.14229i	−1.13123	−	0.476153i
$226$			15.5469i			1.03417i
$227$	9.87949			0.655725			0.327862	−	0.944725i	$-0.393672\pi$
$227$	9.87949			0.655725			0.327862	+	0.944725i	$0.393672\pi$
$228$			19.1710i			1.26963i
$229$			21.9472i			1.45031i	0.688586	+	0.725155i	$0.258232\pi$
$229$			21.9472i			1.45031i	−0.688586	+	0.725155i	$0.741768\pi$
$230$	4.13129	−	2.74342i	0.272409	−	0.180896i
$231$	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	$-0.613662\pi$
$233$	8.96601	−	8.96601i	0.587383	−	0.587383i	0.936922	+	0.349539i	$0.113662\pi$
$234$		−	15.7874i		−	1.03205i
$235$	−0.590399	+	2.92450i	−0.0385134	+	0.190773i
$236$	−2.91109	+	2.91109i	−0.189496	+	0.189496i
$237$		−	35.7205i		−	2.32030i
$238$	8.78986	+	8.78986i	0.569762	+	0.569762i
$239$	13.0815	−	13.0815i	0.846174	−	0.846174i	−0.143479	−	0.989653i	$-0.545829\pi$
$239$	13.0815	−	13.0815i	0.846174	−	0.846174i	0.989653	+	0.143479i	$0.0458291\pi$
$240$	−1.14383	+	5.66587i	−0.0738336	+	0.365730i
$241$	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	$0.670717\pi$
$242$		−	4.83644i		−	0.310898i
$243$	−15.6003	+	15.6003i	−1.00076	+	1.00076i
$244$	5.71266	−	5.71266i	0.365716	−	0.365716i
$245$	−20.1647	−	30.3658i	−1.28828	−	1.94000i
$246$	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
$253$	−8.82588			−0.554878
$254$	0.0553748	+	0.0553748i	0.00347453	+	0.00347453i
$255$	−2.94554	+	14.5905i	−0.184457	+	0.913695i
$256$	1.00000			0.0625000
$257$	−5.80813			−0.362301			−0.181151	−	0.983455i	$-0.557982\pi$
$257$	−5.80813			−0.362301			−0.181151	+	0.983455i	$0.557982\pi$
$258$	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	$-0.517635\pi$
$263$	15.2944	−	15.2944i	0.943090	−	0.943090i	0.998466	+	0.0553752i	$0.0176355\pi$
$264$	7.27394	−	7.27394i	0.447680	−	0.447680i
$265$	8.80497	+	1.77755i	0.540885	+	0.109194i
$266$	−35.7999			−2.19503
$267$	−34.4688			−2.10945
$268$	−1.28531	−	1.28531i	−0.0785129	−	0.0785129i
$269$			18.2273i			1.11134i	0.831404	+	0.555668i	$0.187537\pi$
$269$			18.2273i			1.11134i	−0.831404	+	0.555668i	$0.812463\pi$
$270$	−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	$0.799562\pi$
$272$	2.57516			0.156142
$273$	53.5014			3.23805
$274$	−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
$277$		−	0.845623i		−	0.0508086i	−0.999677	−	0.0254043i	$-0.991913\pi$
$277$		−	0.845623i		−	0.0508086i	0.999677	−	0.0254043i	$-0.00808731\pi$
$278$			10.9433i			0.656333i
$279$	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	$0.590610\pi$
$282$	3.44903			0.205387
$283$	6.37857			0.379167			0.189583	−	0.981865i	$-0.439286\pi$
$283$	6.37857			0.379167			0.189583	+	0.981865i	$0.439286\pi$
$284$	−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
$288$	3.68208			0.216969
$289$	−10.3685			−0.609914
$290$	−1.27361	+	6.30873i	−0.0747888	+	0.370461i
$291$	−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	0.492058	−	0.870562i	$-0.336245\pi$
$293$	−6.47894	−	6.47894i	−0.378504	−	0.378504i	−0.870562	+	0.492058i	$0.836245\pi$
$294$	−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
$298$	13.0913			0.758358
$299$	−9.50925			−0.549934
$300$	−4.87791	−	11.9690i	−0.281626	−	0.691033i
$301$	30.7314	+	30.7314i	1.77133	+	1.77133i
$302$	−9.37187			−0.539290
$303$	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	$-0.297005\pi$
$307$	−3.64587	−	3.64587i	−0.208081	−	0.208081i	−0.803451	+	0.595371i	$0.797005\pi$
$308$	13.5833	+	13.5833i	0.773981	+	0.773981i
$309$	5.10132	−	5.10132i	0.290204	−	0.290204i
$310$	−10.0349	−	2.02584i	−0.569941	−	0.115060i
$311$	−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
$313$		−	18.2772i		−	1.03309i	−0.856261	−	0.516543i	$-0.827219\pi$
$313$		−	18.2772i		−	1.03309i	0.856261	−	0.516543i	$-0.172781\pi$
$314$	−16.2868	−	16.2868i	−0.919116	−	0.919116i
$315$	−38.9579	−	7.86483i	−2.19503	−	0.443133i
$316$	9.77118	−	9.77118i	0.549672	−	0.549672i
$317$	4.85997	+	4.85997i	0.272963	+	0.272963i	0.830292	−	0.557329i	$-0.188174\pi$
$317$	4.85997	+	4.85997i	0.272963	+	0.272963i	−0.557329	+	0.830292i	$0.688174\pi$
$318$		−	10.3842i		−	0.582317i
$319$	8.09925	−	8.09925i	0.453471	−	0.453471i
$320$	−1.86276	+	1.23698i	−0.104131	+	0.0691495i
$321$		−	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
$325$	−19.7591	−	8.31690i	−1.09604	−	0.461339i
$326$		−	2.14382i		−	0.118735i
$327$		−	43.6134i		−	2.41182i
$328$	2.50763			0.138461
$329$			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
$333$	−20.6259	−	8.72962i	−1.13029	−	0.478380i
$334$			20.3382i			1.11286i
$335$	3.98413	+	0.804317i	0.217677	+	0.0439446i
$336$			12.4781i			0.680735i
$337$	−6.47001	−	6.47001i	−0.352444	−	0.352444i	0.508574	−	0.861018i	$-0.330173\pi$
$337$	−6.47001	−	6.47001i	−0.352444	−	0.352444i	−0.861018	+	0.508574i	$0.830173\pi$
$338$		−	5.38374i		−	0.292837i
$339$	−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
$347$			6.44807i			0.346151i	0.984909	+	0.173075i	$0.0553704\pi$
$347$			6.44807i			0.346151i	−0.984909	+	0.173075i	$0.944630\pi$
$348$	7.44024			0.398839
$349$		−	4.70014i		−	0.251593i	−0.992056	−	0.125796i	$-0.959851\pi$
$349$		−	4.70014i		−	0.251593i	0.992056	−	0.125796i	$-0.0401486\pi$
$350$	22.3509	−	9.10899i	1.19471	−	0.486896i
$351$	5.34555	−	5.34555i	0.285324	−	0.285324i
$352$	3.97950			0.212108
$353$	−19.6162			−1.04406			−0.522031	−	0.852926i	$-0.674826\pi$
$353$	−19.6162			−1.04406			−0.522031	+	0.852926i	$0.674826\pi$
$354$	−10.6421			−0.565620
$355$	15.6534	−	10.3948i	0.830796	−	0.551698i
$356$	−9.42876	−	9.42876i	−0.499723	−	0.499723i
$357$			32.1331i			1.70066i
$358$	13.4168	−	13.4168i	0.709098	−	0.709098i
$359$		−	7.60520i		−	0.401387i	−0.979654	−	0.200694i	$-0.935680\pi$
$359$		−	7.60520i		−	0.401387i	0.979654	−	0.200694i	$-0.0643196\pi$
$360$	−6.85883	+	4.55467i	−0.361492	+	0.240052i
$361$		−	36.0022i		−	1.89485i
$362$		−	15.3711i		−	0.807885i
$363$	8.84029	−	8.84029i	0.463995	−	0.463995i
$364$	14.6350	+	14.6350i	0.767085	+	0.767085i
$365$	3.33221	−	16.5059i	0.174416	−	0.863957i
$366$	20.8838			1.09161
$367$	−10.3061	+	10.3061i	−0.537975	+	0.537975i	−0.922934	−	0.384959i	$-0.874216\pi$
$367$	−10.3061	+	10.3061i	−0.537975	+	0.537975i	0.384959	+	0.922934i	$0.374216\pi$
$368$		−	2.21783i		−	0.115613i
$369$	9.23331			0.480667
$370$	13.3673	−	2.51291i	0.694934	−	0.130640i
$371$	19.3914			1.00675
$372$			11.8347i			0.613599i
$373$	−0.690871	+	0.690871i	−0.0357719	+	0.0357719i	−0.724767	−	0.688995i	$-0.758052\pi$
$373$	−0.690871	+	0.690871i	−0.0357719	+	0.0357719i	0.688995	+	0.724767i	$0.258052\pi$
$374$	10.2479			0.529905
$375$	23.8919	+	16.2616i	1.23377	+	0.839743i
$376$	0.943466	+	0.943466i	0.0486555	+	0.0486555i
$377$	8.72636	−	8.72636i	0.449430	−	0.449430i
$378$			8.51103i			0.437760i
$379$			0.266778i			0.0137035i	0.999977	+	0.00685174i	$0.00218099\pi$
$379$			0.266778i			0.0137035i	−0.999977	+	0.00685174i	$0.997819\pi$
$380$	3.28166	−	16.2555i	0.168346	−	0.833890i
$381$			0.202434i			0.0103710i
$382$	16.9686	−	16.9686i	0.868191	−	0.868191i
$383$			32.6980i			1.67079i	0.549650	+	0.835395i	$0.314761\pi$
$383$			32.6980i			1.67079i	−0.549650	+	0.835395i	$0.685239\pi$
$384$	1.82785	+	1.82785i	0.0932771	+	0.0932771i
$385$	−42.1048	−	8.50012i	−2.14586	−	0.433206i
$386$	5.70785			0.290522
$387$	33.1511			1.68517
$388$	−5.92246			−0.300668
$389$	−24.7831	+	24.7831i	−1.25655	+	1.25655i	−0.303825	+	0.952728i	$0.598264\pi$
$389$	−24.7831	+	24.7831i	−1.25655	+	1.25655i	−0.952728	+	0.303825i	$0.901736\pi$
$390$	−4.90430	+	24.2931i	−0.248339	+	1.23013i
$391$		−	5.71129i		−	0.288832i
$392$	−16.3015			−0.823351
$393$			11.2938i			0.569698i
$394$	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	$-0.117462\pi$
$397$	11.3967	+	11.3967i	0.571984	+	0.571984i	−0.360698	+	0.932683i	$0.617462\pi$
$398$	−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	$0.423438\pi$
$402$		−	4.69872i		−	0.234351i
$403$	13.8804	+	13.8804i	0.691432	+	0.691432i
$404$			1.64079i			0.0816323i
$405$	12.0866	−	8.02621i	0.600587	−	0.398825i
$406$			13.8939i			0.689541i
$407$	−22.2920	−	9.43477i	−1.10497	−	0.467664i
$408$	4.70702	+	4.70702i	0.233032	+	0.233032i
$409$	10.7756	+	10.7756i	0.532819	+	0.532819i	0.921410	−	0.388591i	$-0.127038\pi$
$409$	10.7756	+	10.7756i	0.532819	+	0.532819i	−0.388591	+	0.921410i	$0.627038\pi$
$410$	−4.67112	+	3.10190i	−0.230690	+	0.153192i
$411$		−	6.75833i		−	0.333364i
$412$	2.79089			0.137497
$413$		−	19.8730i		−	0.977884i
$414$		−	8.16624i		−	0.401349i
$415$	7.97866	+	1.61073i	0.391657	+	0.0790678i
$416$	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	$0.200298\pi$
$419$			24.0943i			1.17709i	−0.808466	+	0.588543i	$0.799702\pi$
$420$	−15.4352	−	23.2437i	−0.753160	−	1.13417i
$421$	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	$-0.0179267\pi$
$422$			15.1553i			0.737750i
$423$	3.47392	+	3.47392i	0.168908	+	0.168908i
$424$	2.84055	−	2.84055i	0.137949	−	0.137949i
$425$	4.99516	−	11.8674i	0.242301	−	0.575653i
$426$	−15.3600	−	15.3600i	−0.744197	−	0.744197i
$427$			38.9983i			1.88726i
$428$	3.77209	−	3.77209i	0.182331	−	0.182331i
$429$	31.1879	−	31.1879i	1.50577	−	1.50577i
$430$	−16.7711	+	11.1370i	−0.808775	+	0.537075i
$431$	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	0.336872	−	0.941550i	$-0.390631\pi$
$433$	−12.5825	−	12.5825i	−0.604678	−	0.604678i	−0.941550	+	0.336872i	$0.890631\pi$
$434$	−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
$438$	−19.4663			−0.930137
$439$	13.6362	+	13.6362i	0.650822	+	0.650822i	0.953191	−	0.302369i	$-0.0977774\pi$
$439$	13.6362	+	13.6362i	0.650822	+	0.650822i	−0.302369	+	0.953191i	$0.597777\pi$
$440$	−7.41286	+	4.92258i	−0.353394	+	0.234675i
$441$	−60.0235			−2.85826
$442$	11.0413			0.525183
$443$	23.2157	−	23.2157i	1.10301	−	1.10301i	0.108963	−	0.994046i	$-0.465247\pi$
$443$	23.2157	−	23.2157i	1.10301	−	1.10301i	0.994046	−	0.108963i	$-0.0347531\pi$
$444$	−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	−0.976248	−	0.216654i	$-0.930486\pi$
$449$	−16.0955	+	16.0955i	−0.759594	+	0.759594i	0.216654	+	0.976248i	$0.430486\pi$
$450$	7.14229	−	16.9685i	0.336691	−	0.799903i
$451$	9.97914			0.469899
$452$	−15.5469			−0.731267
$453$	−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
$457$	3.34685			0.156559			0.0782794	−	0.996931i	$-0.475057\pi$
$457$	3.34685			0.156559			0.0782794	+	0.996931i	$0.475057\pi$
$458$	−21.9472			−1.02552
$459$	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	$0.491562\pi$
$462$			49.6566i			2.31023i
$463$		−	10.8598i		−	0.504696i	−0.967637	−	0.252348i	$-0.918797\pi$
$463$		−	10.8598i		−	0.504696i	0.967637	−	0.252348i	$-0.0812027\pi$
$464$	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
$467$	−12.9597			−0.599702			−0.299851	−	0.953986i	$-0.596937\pi$
$467$	−12.9597			−0.599702			−0.299851	+	0.953986i	$0.596937\pi$
$468$	15.7874			0.729772
$469$	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
$473$	35.8289			1.64742
$474$	35.7205			1.64070
$475$	13.9948	+	34.3395i	0.642127	+	1.57560i
$476$	−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	−0.635734	−	0.771908i	$-0.719302\pi$
$479$	2.98032	−	2.98032i	0.136174	−	0.136174i	0.771908	+	0.635734i	$0.219302\pi$
$480$	−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
$483$	27.6743			1.25923
$484$	4.83644			0.219838
$485$	11.0321	−	7.32599i	0.500943	−	0.332656i
$486$	−15.6003	−	15.6003i	−0.707643	−	0.707643i
$487$	4.69219			0.212624			0.106312	−	0.994333i	$-0.466096\pi$
$487$	4.69219			0.212624			0.106312	+	0.994333i	$0.466096\pi$
$488$	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
$495$	−27.2947	+	18.1253i	−1.22681	+	0.814672i
$496$	−3.23732	+	3.23732i	−0.145360	+	0.145360i
$497$	28.6833	−	28.6833i	1.28662	−	1.28662i
$498$		−	9.40969i		−	0.421658i
$499$	24.3133	+	24.3133i	1.08841	+	1.08841i	0.995692	+	0.0927210i	$0.0295565\pi$
$499$	24.3133	+	24.3133i	1.08841	+	1.08841i	0.0927210	+	0.995692i	$0.470444\pi$
$500$	2.08724	+	10.9838i	0.0933442	+	0.491210i
$501$	−37.1752	+	37.1752i	−1.66086	+	1.66086i
$502$	2.34715	+	2.34715i	0.104759	+	0.104759i
$503$			15.7435i			0.701968i	0.936381	+	0.350984i	$0.114153\pi$
$503$			15.7435i			0.701968i	−0.936381	+	0.350984i	$0.885847\pi$
$504$	−12.5681	+	12.5681i	−0.559828	+	0.559828i
$505$	−2.02963	−	3.05639i	−0.0903173	−	0.136008i
$506$		−	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	$-0.239950\pi$
$509$	32.8974			1.45815			0.729077	+	0.684432i	$0.239950\pi$
$510$	−14.5905	−	2.94554i	−0.646080	−	0.130431i
$511$		−	36.3513i		−	1.60809i
$512$			1.00000i			0.0441942i
$513$	−13.0762			−0.577327
$514$		−	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
$518$	27.2129	−	11.0280i	1.19566	−	0.484542i
$519$		−	50.2422i		−	2.20539i
$520$	−7.98682	+	5.30372i	−0.350245	+	0.232584i
$521$			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
$523$		−	20.7364i		−	0.906739i	−0.891323	−	0.453369i	$-0.850222\pi$
$523$		−	20.7364i		−	0.906739i	0.891323	−	0.453369i	$-0.149778\pi$
$524$	−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
$532$		−	35.7999i		−	1.55212i
$533$	10.7518			0.465712
$534$		−	34.4688i		−	1.49161i
$535$	−2.36048	+	11.6925i	−0.102053	+	0.505511i
$536$	1.28531	−	1.28531i	0.0555170	−	0.0555170i
$537$	49.0477			2.11656
$538$	−18.2273			−0.785833
$539$	−64.8719			−2.79423
$540$	−3.86457	−	0.780179i	−0.166304	−	0.0335736i
$541$	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	$0.715527\pi$
$542$		−	26.6096i		−	1.14298i
$543$	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
$547$		−	10.3831i		−	0.443950i	−0.975052	−	0.221975i	$-0.928750\pi$
$547$		−	10.3831i		−	0.443950i	0.975052	−	0.221975i	$-0.0712504\pi$
$548$	1.84871	−	1.84871i	0.0789729	−	0.0789729i
$549$	21.0345	+	21.0345i	0.897729	+	0.897729i
$550$	7.71922	−	18.3392i	0.329149	−	0.781984i
$551$	−21.3462			−0.909380
$552$	4.05387	−	4.05387i	0.172544	−	0.172544i
$553$			66.7043i			2.83656i
$554$	0.845623			0.0359271
$555$	29.0267	+	19.8402i	1.23211	+	0.842172i
$556$	−10.9433			−0.464097
$557$			4.73501i			0.200629i	0.994956	+	0.100314i	$0.0319849\pi$
$557$			4.73501i			0.200629i	−0.994956	+	0.100314i	$0.968015\pi$
$558$	−11.9201	+	11.9201i	−0.504616	+	0.504616i
$559$	38.6031			1.63274
$560$	2.13598	−	10.5804i	0.0902614	−	0.447104i
$561$	18.7316	+	18.7316i	0.790848	+	0.790848i
$562$	−11.3809	+	11.3809i	−0.480074	+	0.480074i
$563$			3.05563i			0.128779i	0.997925	+	0.0643897i	$0.0205101\pi$
$563$			3.05563i			0.128779i	−0.997925	+	0.0643897i	$0.979490\pi$
$564$			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
$568$		−	8.40334i		−	0.352596i
$569$	−29.4912	−	29.4912i	−1.23633	−	1.23633i	−0.961488	−	0.274845i	$-0.911373\pi$
$569$	−29.4912	−	29.4912i	−1.23633	−	1.23633i	−0.274845	−	0.961488i	$-0.588627\pi$
$570$	35.7110	−	23.7143i	1.49577	−	0.993281i
$571$	14.8841			0.622881			0.311440	−	0.950266i	$-0.399189\pi$
$571$	14.8841			0.622881			0.311440	+	0.950266i	$0.399189\pi$
$572$	17.0626			0.713424
$573$	62.0323			2.59144
$574$	−8.55936	+	8.55936i	−0.357261	+	0.357261i
$575$	−10.2207	−	4.30203i	−0.426232	−	0.179407i
$576$			3.68208i			0.153420i
$577$	9.65939			0.402126			0.201063	−	0.979578i	$-0.435560\pi$
$577$	9.65939			0.402126			0.201063	+	0.979578i	$0.435560\pi$
$578$		−	10.3685i		−	0.431274i
$579$	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
$587$			0.789320i			0.0325787i	0.999867	+	0.0162894i	$0.00518529\pi$
$587$			0.789320i			0.0325787i	−0.999867	+	0.0162894i	$0.994815\pi$
$588$	−29.7967	−	29.7967i	−1.22880	−	1.22880i
$589$		−	33.9539i		−	1.39905i
$590$	9.02362	+	1.82169i	0.371497	+	0.0749978i
$591$			33.4410i			1.37558i
$592$	2.37084	−	5.60171i	0.0974410	−	0.230229i
$593$	4.13138	+	4.13138i	0.169656	+	0.169656i	0.786828	−	0.617172i	$-0.211722\pi$
$593$	4.13138	+	4.13138i	0.169656	+	0.169656i	−0.617172	+	0.786828i	$0.711722\pi$
$594$	4.96140	+	4.96140i	0.203569	+	0.203569i
$595$	5.50049	−	27.2463i	0.225498	−	1.11699i
$596$			13.0913i			0.536240i
$597$	−24.3797			−0.997796
$598$		−	9.50925i		−	0.388862i
$599$		−	38.0949i		−	1.55652i	−0.627944	−	0.778258i	$-0.716104\pi$
$599$		−	38.0949i		−	1.55652i	0.627944	−	0.778258i	$-0.283896\pi$
$600$	11.9690	−	4.87791i	0.488634	−	0.199140i
$601$	−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
$605$	−9.00912	+	5.98259i	−0.366273	+	0.243227i
$606$	−2.99912	+	2.99912i	−0.121831	+	0.121831i
$607$			4.59751i			0.186607i	0.995638	+	0.0933036i	$0.0297427\pi$
$607$			4.59751i			0.186607i	−0.995638	+	0.0933036i	$0.970257\pi$
$608$	−5.24415	−	5.24415i	−0.212678	−	0.212678i
$609$	−25.3959	+	25.3959i	−1.02909	+	1.02909i
$610$	−17.7078	−	3.57485i	−0.716967	−	0.144741i
$611$	4.04523	+	4.04523i	0.163652	+	0.163652i
$612$			9.48196i			0.383285i
$613$	−9.19983	+	9.19983i	−0.371578	+	0.371578i	−0.868052	−	0.496474i	$-0.834628\pi$
$613$	−9.19983	+	9.19983i	−0.371578	+	0.371578i	0.496474	+	0.868052i	$0.334628\pi$
$614$	3.64587	−	3.64587i	0.147135	−	0.147135i
$615$	−14.2079	−	2.86830i	−0.572919	−	0.115661i
$616$	−13.5833	+	13.5833i	−0.547287	+	0.547287i
$617$	−8.47786	−	8.47786i	−0.341306	−	0.341306i	0.515552	−	0.856858i	$-0.327587\pi$
$617$	−8.47786	−	8.47786i	−0.341306	−	0.341306i	−0.856858	+	0.515552i	$0.827587\pi$
$618$	5.10132	+	5.10132i	0.205205	+	0.205205i
$619$	12.3858			0.497827			0.248914	−	0.968526i	$-0.419926\pi$
$619$	12.3858			0.497827			0.248914	+	0.968526i	$0.419926\pi$
$620$	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
$623$	64.3668			2.57880
$624$	7.83714	+	7.83714i	0.313737	+	0.313737i
$625$	−17.4748	−	17.8783i	−0.698991	−	0.715130i
$626$	18.2772			0.730502
$627$	−76.2912			−3.04678
$628$	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
$635$	0.0346523	−	0.171648i	0.00137513	−	0.00681163i
$636$	10.3842			0.411761
$637$	−69.8948			−2.76933
$638$	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	$0.496125\pi$
$642$	13.7896			0.544233
$643$	−42.0640			−1.65884			−0.829422	−	0.558622i	$-0.811330\pi$
$643$	−42.0640			−1.65884			−0.829422	+	0.558622i	$0.811330\pi$
$644$	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
$647$			35.3320i			1.38904i	0.719472	+	0.694521i	$0.244384\pi$
$647$			35.3320i			1.38904i	−0.719472	+	0.694521i	$0.755616\pi$
$648$		−	6.48853i		−	0.254894i
$649$	−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
$652$	2.14382			0.0839586
$653$	−12.3601			−0.483687			−0.241844	−	0.970315i	$-0.577752\pi$
$653$	−12.3601			−0.483687			−0.241844	+	0.970315i	$0.577752\pi$
$654$	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
$658$	−6.44070			−0.251085
$659$	37.7706			1.47133			0.735667	−	0.677344i	$-0.236869\pi$
$659$	37.7706			1.47133			0.735667	+	0.677344i	$0.236869\pi$
$660$	−22.5473	−	4.55186i	−0.877654	−	0.177181i
$661$	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
$668$	−20.3382			−0.786908
$669$	22.8681			0.884131
$670$	−0.804317	+	3.98413i	−0.0310735	+	0.153921i
$671$	22.7335	+	22.7335i	0.877619	+	0.877619i
$672$	−12.4781			−0.481353
$673$	−0.303990	−	0.303990i	−0.0117180	−	0.0117180i	0.701224	−	0.712941i	$-0.252637\pi$
$673$	−0.303990	−	0.303990i	−0.0117180	−	0.0117180i	−0.712941	+	0.701224i	$0.752637\pi$
$674$	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	$-0.424756\pi$
$677$	−19.2022	−	19.2022i	−0.738000	−	0.738000i	−0.972191	+	0.234191i	$0.924756\pi$
$678$	−28.4175	−	28.4175i	−1.09137	−	1.09137i
$679$	20.2153	−	20.2153i	0.775791	−	0.775791i
$680$	−3.18543	−	4.79691i	−0.122156	−	0.183953i
$681$	−18.0582	+	18.0582i	−0.691993	+	0.691993i
$682$	−12.8829	+	12.8829i	−0.493312	+	0.493312i
$683$		−	16.4834i		−	0.630719i	−0.948972	−	0.315359i	$-0.897875\pi$
$683$		−	16.4834i		−	0.630719i	0.948972	−	0.315359i	$-0.102125\pi$
$684$	−19.3094	−	19.3094i	−0.738312	−	0.738312i
$685$	−1.15688	+	5.73052i	−0.0442020	+	0.218952i
$686$	31.7491	−	31.7491i	1.21218	−	1.21218i
$687$	−40.1161	−	40.1161i	−1.53053	−	1.53053i
$688$			9.00337i			0.343250i
$689$	12.1792	−	12.1792i	0.463991	−	0.463991i
$690$	−2.53682	+	12.5660i	−0.0965750	+	0.478378i
$691$		−	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
$695$	20.3846	−	13.5366i	0.773234	−	0.513473i
$696$			7.44024i			0.282022i
$697$			6.45757i			0.244598i
$698$	4.70014			0.177903
$699$			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
$703$	16.9431	+	41.8092i	0.639023	+	1.57686i
$704$			3.97950i			0.149983i
$705$	−4.26639	−	6.42471i	−0.160682	−	0.241969i
$706$		−	19.6162i		−	0.738264i
$707$	−5.60054	−	5.60054i	−0.210630	−	0.210630i
$708$		−	10.6421i		−	0.399953i
$709$	−25.3783	+	25.3783i	−0.953101	+	0.953101i	−0.998948	−	0.0458470i	$-0.985401\pi$
$709$	−25.3783	+	25.3783i	−0.953101	+	0.953101i	0.0458470	+	0.998948i	$0.485401\pi$
$710$	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
$717$			47.8222i			1.78595i
$718$	7.60520			0.283824
$719$		−	0.372987i		−	0.0139101i	−0.999976	−	0.00695503i	$-0.997786\pi$
$719$		−	0.372987i		−	0.0139101i	0.999976	−	0.00695503i	$-0.00221387\pi$
$720$	−4.55467	−	6.85883i	−0.169743	−	0.255613i
$721$	−9.52619	+	9.52619i	−0.354774	+	0.354774i
$722$	36.0022			1.33986
$723$	−19.7845			−0.735794
$724$	15.3711			0.571261
$725$	13.3271	−	5.43137i	0.494955	−	0.201716i
$726$	8.84029	+	8.84029i	0.328094	+	0.328094i
$727$			14.7295i			0.546286i	0.961973	+	0.273143i	$0.0880632\pi$
$727$			14.7295i			0.546286i	−0.961973	+	0.273143i	$0.911937\pi$
$728$	−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
$732$			20.8838i			0.771887i
$733$	−10.6225	+	10.6225i	−0.392351	+	0.392351i	−0.875525	−	0.483173i	$-0.839484\pi$
$733$	−10.6225	+	10.6225i	−0.392351	+	0.392351i	0.483173	+	0.875525i	$0.339484\pi$
$734$	−10.3061	−	10.3061i	−0.380406	−	0.380406i
$735$	92.3622	+	18.6461i	3.40683	+	0.687772i
$736$	2.21783			0.0817505
$737$	5.11490	−	5.11490i	0.188410	−	0.188410i
$738$			9.23331i			0.339883i
$739$	−27.4110			−1.00833			−0.504165	−	0.863608i	$-0.668200\pi$
$739$	−27.4110			−1.00833			−0.504165	+	0.863608i	$0.668200\pi$
$740$	2.51291	+	13.3673i	0.0923764	+	0.491393i
$741$	−82.1983			−3.01963
$742$			19.3914i			0.711881i
$743$	−31.6154	+	31.6154i	−1.15986	+	1.15986i	−0.175349	+	0.984506i	$0.556105\pi$
$743$	−31.6154	+	31.6154i	−1.15986	+	1.15986i	−0.984506	+	0.175349i	$0.943895\pi$
$744$	−11.8347			−0.433880
$745$	−16.1937	−	24.3859i	−0.593291	−	0.893431i
$746$	−0.690871	−	0.690871i	−0.0252946	−	0.0252946i
$747$	9.47758	−	9.47758i	0.346767	−	0.346767i
$748$			10.2479i			0.374699i
$749$			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
$753$			8.58049i			0.312690i
$754$	8.72636	+	8.72636i	0.317795	+	0.317795i
$755$	11.5928	+	17.4575i	0.421907	+	0.635345i
$756$	−8.51103			−0.309543
$757$	14.8725			0.540552			0.270276	−	0.962783i	$-0.412885\pi$
$757$	14.8725			0.540552			0.270276	+	0.962783i	$0.412885\pi$
$758$	−0.266778			−0.00968982
$759$	16.1324	−	16.1324i	0.585569	−	0.585569i
$760$	16.2555	+	3.28166i	0.589649	+	0.119038i
$761$			41.3732i			1.49978i	0.661564	+	0.749888i	$0.269893\pi$
$761$			41.3732i			1.49978i	−0.661564	+	0.749888i	$0.730107\pi$
$762$	−0.202434			−0.00733341
$763$			81.4434i			2.94845i
$764$	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	0.691962	−	0.721934i	$-0.256747\pi$
$769$	−0.831140	−	0.831140i	−0.0299717	−	0.0299717i	−0.721934	+	0.691962i	$0.756747\pi$
$770$	8.50012	−	42.1048i	0.306323	−	1.51735i
$771$	10.6164	−	10.6164i	0.382340	−	0.382340i
$772$			5.70785i			0.205430i
$773$	−24.1870	−	24.1870i	−0.869946	−	0.869946i	0.122520	−	0.992466i	$-0.460903\pi$
$773$	−24.1870	−	24.1870i	−0.869946	−	0.869946i	−0.992466	+	0.122520i	$0.960903\pi$
$774$			33.1511i			1.19159i
$775$	8.63930	+	21.1984i	0.310333	+	0.761470i
$776$		−	5.92246i		−	0.212604i
$777$	69.8986	+	29.5835i	2.50760	+	1.06130i
$778$	−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
$782$	5.71129			0.204235
$783$			5.07483i			0.181360i
$784$		−	16.3015i		−	0.582197i
$785$	−10.1919	+	50.4848i	−0.363764	+	1.80188i
$786$	−11.2938			−0.402837
$787$	17.1870	−	17.1870i	0.612650	−	0.612650i	−0.330986	−	0.943636i	$-0.607381\pi$
$787$	17.1870	−	17.1870i	0.612650	−	0.612650i	0.943636	+	0.330986i	$0.107381\pi$
$788$	−9.14763	+	9.14763i	−0.325871	+	0.325871i
$789$			55.9116i			1.99051i
$790$	−30.2881	−	6.11457i	−1.07760	−	0.217547i
$791$	53.0667	−	53.0667i	1.88684	−	1.88684i
$792$			14.6528i			0.520666i
$793$	24.4938	+	24.4938i	0.869799	+	0.869799i
$794$	−11.3967	+	11.3967i	−0.404454	+	0.404454i
$795$	−19.3433	+	12.8451i	−0.686035	+	0.455568i
$796$	−6.66896	−	6.66896i	−0.236375	−	0.236375i
$797$		−	10.6790i		−	0.378270i	−0.981951	−	0.189135i	$-0.939432\pi$
$797$		−	10.6790i		−	0.378270i	0.981951	−	0.189135i	$-0.0605683\pi$
$798$	65.4369	−	65.4369i	2.31644	−	2.31644i
$799$	−2.42958	+	2.42958i	−0.0859523	+	0.0859523i
$800$	4.60840	+	1.93975i	0.162932	+	0.0685804i
$801$	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
$808$	−1.64079			−0.0577227
$809$	9.53144	+	9.53144i	0.335108	+	0.335108i	0.854522	−	0.519415i	$-0.173850\pi$
$809$	9.53144	+	9.53144i	0.335108	+	0.335108i	−0.519415	+	0.854522i	$0.673850\pi$
$810$	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	$0.326013\pi$
$812$	−13.8939			−0.487579
$813$	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
$820$	−3.10190	−	4.67112i	−0.108323	−	0.163123i
$821$	−24.3165			−0.848651			−0.424325	−	0.905510i	$-0.639489\pi$
$821$	−24.3165			−0.848651			−0.424325	+	0.905510i	$0.639489\pi$
$822$	6.75833			0.235724
$823$	−35.9075	−	35.9075i	−1.25166	−	1.25166i	−0.954976	−	0.296682i	$-0.904120\pi$
$823$	−35.9075	−	35.9075i	−1.25166	−	1.25166i	−0.296682	−	0.954976i	$-0.595880\pi$
$824$			2.79089i			0.0972251i
$825$	47.6308	−	19.4117i	1.65829	−	0.675827i
$826$	19.8730			0.691468
$827$	−7.03825			−0.244744			−0.122372	−	0.992484i	$-0.539050\pi$
$827$	−7.03825			−0.244744			−0.122372	+	0.992484i	$0.539050\pi$
$828$	8.16624			0.283797
$829$	−12.4360	−	12.4360i	−0.431920	−	0.431920i	0.457361	−	0.889281i	$-0.348795\pi$
$829$	−12.4360	−	12.4360i	−0.431920	−	0.431920i	−0.889281	+	0.457361i	$0.848795\pi$
$830$	−1.61073	+	7.97866i	−0.0559094	+	0.276943i
$831$	1.54567	+	1.54567i	0.0536188	+	0.0536188i
$832$			4.28763i			0.148647i
$833$		−	41.9791i		−	1.45449i
$834$	−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
$837$	−8.07217			−0.279015
$838$	−24.0943			−0.832325
$839$	−21.4518			−0.740598			−0.370299	−	0.928913i	$-0.620745\pi$
$839$	−21.4518			−0.740598			−0.370299	+	0.928913i	$0.620745\pi$
$840$	23.2437	−	15.4352i	0.801983	−	0.532564i
$841$		−	20.7156i		−	0.714330i
$842$	21.6407	+	21.6407i	0.745788	+	0.745788i
$843$	−41.6051			−1.43296
$844$	−15.1553			−0.521668
$845$	−10.0286	+	6.65959i	−0.344995	+	0.229097i
$846$	−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
$853$	−9.13898			−0.312913			−0.156456	−	0.987685i	$-0.550007\pi$
$853$	−9.13898			−0.312913			−0.156456	+	0.987685i	$0.550007\pi$
$854$	−38.9983			−1.33449
$855$	59.8541	+	12.0833i	2.04697	+	0.413242i
$856$	3.77209	+	3.77209i	0.128927	+	0.128927i
$857$	−13.4472			−0.459346			−0.229673	−	0.973268i	$-0.573766\pi$
$857$	−13.4472			−0.459346			−0.229673	+	0.973268i	$0.573766\pi$
$858$	31.1879	+	31.1879i	1.06474	+	1.06474i
$859$	29.5713	−	29.5713i	1.00896	−	1.00896i	0.00900160	−	0.999959i	$-0.497135\pi$
$859$	29.5713	−	29.5713i	1.00896	−	1.00896i	0.999959	−	0.00900160i	$-0.00286534\pi$
$860$	−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	0.850516	−	0.525950i	$-0.176290\pi$
$863$	9.53473	+	9.53473i	0.324566	+	0.324566i	−0.525950	+	0.850516i	$0.676290\pi$
$864$	−1.24674	+	1.24674i	−0.0424149	+	0.0424149i
$865$	−8.60037	+	42.6014i	−0.292421	+	1.44849i
$866$	12.5825	−	12.5825i	0.427572	−	0.427572i
$867$	18.9521	−	18.9521i	0.643648	−	0.643648i
$868$		−	22.1000i		−	0.750123i
$869$	38.8844	+	38.8844i	1.31906	+	1.31906i
$870$	−9.20345	−	13.8594i	−0.312026	−	0.469877i
$871$	5.51094	−	5.51094i	0.186731	−	0.186731i
$872$	11.9302	+	11.9302i	0.404008	+	0.404008i
$873$		−	21.8070i		−	0.738054i
$874$	−11.6307	+	11.6307i	−0.393413	+	0.393413i
$875$	−44.6156	−	30.3667i	−1.50828	−	1.02658i
$876$		−	19.4663i		−	0.657706i
$877$	−7.17655	+	7.17655i	−0.242335	+	0.242335i	−0.817815	−	0.575481i	$-0.804815\pi$
$877$	−7.17655	+	7.17655i	−0.242335	+	0.242335i	0.575481	+	0.817815i	$0.304815\pi$
$878$	−13.6362	+	13.6362i	−0.460201	+	0.460201i
$879$	23.6851			0.798878
$880$	−4.92258	−	7.41286i	−0.165940	−	0.249887i
$881$		−	10.0748i		−	0.339428i	−0.985493	−	0.169714i	$-0.945716\pi$
$881$		−	10.0748i		−	0.339428i	0.985493	−	0.169714i	$-0.0542844\pi$
$882$		−	60.0235i		−	2.02110i
$883$	−33.1203			−1.11459			−0.557293	−	0.830316i	$-0.688160\pi$
$883$	−33.1203			−1.11459			−0.557293	+	0.830316i	$0.688160\pi$
$884$			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	$-0.479848\pi$
$887$	−27.8387	−	27.8387i	−0.934731	−	0.934731i	−0.997997	+	0.0632658i	$0.979848\pi$
$888$	14.5726	−	5.90554i	0.489025	−	0.198177i
$889$		−	0.378024i		−	0.0126785i
$890$	−5.90030	+	29.2267i	−0.197778	+	0.979683i
$891$		−	25.8211i		−	0.865040i
$892$	6.25546	+	6.25546i	0.209448	+	0.209448i
$893$		−	9.89535i		−	0.331135i
$894$	−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
$902$			9.97914i			0.332269i
$903$	−112.345			−3.73860
$904$		−	15.5469i		−	0.517084i
$905$	−28.6326	+	19.0138i	−0.951780	+	0.632039i
$906$	17.1304	−	17.1304i	0.569119	−	0.569119i
$907$	11.8792			0.394444			0.197222	−	0.980359i	$-0.436808\pi$
$907$	11.8792			0.394444			0.197222	+	0.980359i	$0.436808\pi$
$908$	−9.87949			−0.327862
$909$	−6.04151			−0.200384
$910$	9.15826	−	45.3649i	0.303593	−	1.50383i
$911$	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	$0.531732\pi$
$912$		−	19.1710i		−	0.634817i
$913$	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
$917$		−	21.0900i		−	0.696454i
$918$	−3.21055	+	3.21055i	−0.105964	+	0.105964i
$919$	39.7559	+	39.7559i	1.31143	+	1.31143i	0.920364	+	0.391062i	$0.127892\pi$
$919$	39.7559	+	39.7559i	1.31143	+	1.31143i	0.391062	+	0.920364i	$0.372108\pi$
$920$	−4.13129	+	2.74342i	−0.136205	+	0.0904480i
$921$	13.3282			0.439179
$922$	−22.0325	+	22.0325i	−0.725601	+	0.725601i
$923$		−	36.0304i		−	1.18595i
$924$	−49.6566			−1.63358
$925$	−21.2161	−	21.7917i	−0.697581	−	0.716506i
$926$	10.8598			0.356874
$927$			10.2763i			0.337517i
$928$	−2.03524	+	2.03524i	−0.0668101	+	0.0668101i
$929$	−28.8922			−0.947923			−0.473961	−	0.880546i	$-0.657176\pi$
$929$	−28.8922			−0.947923			−0.473961	+	0.880546i	$0.657176\pi$
$930$	22.0451	−	14.6393i	0.722889	−	0.480041i
$931$	85.4876	+	85.4876i	2.80174	+	2.80174i
$932$	−8.96601	+	8.96601i	−0.293691	+	0.293691i
$933$		−	1.75707i		−	0.0575238i
$934$		−	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	−0.0236021	−	0.999721i	$-0.507513\pi$
$937$	29.8795	−	29.8795i	0.976119	−	0.976119i	0.999721	+	0.0236021i	$0.00751348\pi$
$938$			8.77436i			0.286493i
$939$	33.4079	+	33.4079i	1.09023	+	1.09023i
$940$	0.590399	−	2.92450i	0.0192567	−	0.0953867i
$941$	−29.7963			−0.971333			−0.485666	−	0.874144i	$-0.661423\pi$
$941$	−29.7963			−0.971333			−0.485666	+	0.874144i	$0.661423\pi$
$942$	59.5396			1.93990
$943$	5.56152			0.181108
$944$	2.91109	−	2.91109i	0.0947478	−	0.0947478i
$945$	15.8540	−	10.5280i	0.515731	−	0.342476i
$946$			35.8289i			1.16490i
$947$	−41.7971			−1.35822			−0.679112	−	0.734035i	$-0.737635\pi$
$947$	−41.7971			−1.35822			−0.679112	+	0.734035i	$0.737635\pi$
$948$			35.7205i			1.16015i
$949$	−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	$-0.796349\pi$
$953$	−6.33457	+	6.33457i	−0.205197	+	0.205197i	0.597025	+	0.802222i	$0.296349\pi$
$954$	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
$957$			29.6085i			0.957105i
$958$	2.98032	+	2.98032i	0.0962898	+	0.0962898i
$959$			12.6205i			0.407536i
$960$	1.14383	−	5.66587i	0.0369168	−	0.182865i
$961$			10.0396i			0.323856i
$962$	10.1653	−	24.0180i	0.327742	−	0.774372i
$963$	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
$967$	39.3087			1.26408			0.632041	−	0.774935i	$-0.282217\pi$
$967$	39.3087			1.26408			0.632041	+	0.774935i	$0.282217\pi$
$968$			4.83644i			0.155449i
$969$		−	49.3686i		−	1.58595i
$970$	7.32599	+	11.0321i	0.235223	+	0.354220i
$971$	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
$975$	51.3188	−	20.9147i	1.64352	−	0.669805i
$976$	−5.71266	+	5.71266i	−0.182858	+	0.182858i
$977$			0.684369i			0.0218949i	0.999940	+	0.0109474i	$0.00348475\pi$
$977$			0.684369i			0.0218949i	−0.999940	+	0.0109474i	$0.996515\pi$
$978$	3.91859	+	3.91859i	0.125303	+	0.125303i
$979$	37.5218	−	37.5218i	1.19920	−	1.19920i
$980$	20.1647	+	30.3658i	0.644138	+	0.970000i
$981$	43.9280	+	43.9280i	1.40251	+	1.40251i
$982$		−	4.44735i		−	0.141921i
$983$	31.2059	−	31.2059i	0.995314	−	0.995314i	−0.00467471	−	0.999989i	$-0.501488\pi$
$983$	31.2059	−	31.2059i	0.995314	−	0.995314i	0.999989	+	0.00467471i	$0.00148801\pi$
$984$	−4.58358	+	4.58358i	−0.146119	+	0.146119i
$985$	5.72437	−	28.3553i	0.182394	−	0.903475i
$986$	−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
$993$	75.8455			2.40688
$994$	28.6833	+	28.6833i	0.909779	+	0.909779i
$995$	20.6721	+	4.17328i	0.655348	+	0.132302i
$996$	9.40969			0.298157
$997$	−26.5817			−0.841852			−0.420926	−	0.907095i	$-0.638295\pi$
$997$	−26.5817			−0.841852			−0.420926	+	0.907095i	$0.638295\pi$
$998$	−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.g.e.43.2	✓	20
5.2	odd	4		370.2.h.e.117.9	yes	20
37.31	odd	4		370.2.h.e.253.9	yes	20
185.142	even	4	inner	370.2.g.e.327.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.2	✓	20	1.1	even	1	trivial
370.2.g.e.327.2	yes	20	185.142	even	4	inner
370.2.h.e.117.9	yes	20	5.2	odd	4
370.2.h.e.253.9	yes	20	37.31	odd	4

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.g (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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