LMFDB - Embedded newform 370.2.m.c.249.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.4
Root			$-0.101618i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.c.159.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.0880035 - 0.0508088i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.69259 + 1.46122i) q^{5} +0.101618i q^{6} +(1.94895 - 1.12523i) q^{7} +1.00000 q^{8} +(-1.49484 + 2.58913i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.0880035 - 0.0508088i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.69259 + 1.46122i) q^{5} +0.101618i q^{6} +(1.94895 - 1.12523i) q^{7} +1.00000 q^{8} +(-1.49484 + 2.58913i) q^{9} +(-0.419156 - 2.19643i) q^{10} -3.35119 q^{11} +(-0.0880035 - 0.0508088i) q^{12} +(2.04934 + 3.54956i) q^{13} +2.25046i q^{14} +(-0.0747109 + 0.214590i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.819242 + 1.41897i) q^{17} +(-1.49484 - 2.58913i) q^{18} +(-4.13898 + 2.38964i) q^{19} +(2.11174 + 0.735216i) q^{20} +(0.114343 - 0.198048i) q^{21} +(1.67560 - 2.90222i) q^{22} -5.63248 q^{23} +(0.0880035 - 0.0508088i) q^{24} +(0.729701 - 4.94647i) q^{25} -4.09868 q^{26} +0.608657i q^{27} +(-1.94895 - 1.12523i) q^{28} +7.65373i q^{29} +(-0.148485 - 0.171997i) q^{30} -1.11203i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.294916 + 0.170270i) q^{33} +(-0.819242 - 1.41897i) q^{34} +(-1.65457 + 4.75238i) q^{35} +2.98967 q^{36} +(3.87021 + 4.69270i) q^{37} -4.77928i q^{38} +(0.360698 + 0.208249i) q^{39} +(-1.69259 + 1.46122i) q^{40} +(-2.65378 - 4.59648i) q^{41} +(0.114343 + 0.198048i) q^{42} +3.28419 q^{43} +(1.67560 + 2.90222i) q^{44} +(-1.25314 - 6.56661i) q^{45} +(2.81624 - 4.87787i) q^{46} -3.58435i q^{47} +0.101618i q^{48} +(-0.967725 + 1.67615i) q^{49} +(3.91892 + 3.10517i) q^{50} +0.166499i q^{51} +(2.04934 - 3.54956i) q^{52} +(-0.873581 - 0.504362i) q^{53} +(-0.527112 - 0.304328i) q^{54} +(5.67218 - 4.89681i) q^{55} +(1.94895 - 1.12523i) q^{56} +(-0.242829 + 0.420593i) q^{57} +(-6.62832 - 3.82686i) q^{58} +(2.82827 + 1.63290i) q^{59} +(0.223196 - 0.0425936i) q^{60} +(4.44572 - 2.56673i) q^{61} +(0.963045 + 0.556014i) q^{62} +6.72813i q^{63} +1.00000 q^{64} +(-8.65536 - 3.01342i) q^{65} -0.340540i q^{66} +(12.9564 - 7.48037i) q^{67} +1.63848 q^{68} +(-0.495678 + 0.286180i) q^{69} +(-3.28840 - 3.80909i) q^{70} +(1.50690 + 2.61003i) q^{71} +(-1.49484 + 2.58913i) q^{72} +9.63987i q^{73} +(-5.99911 + 1.00535i) q^{74} +(-0.187108 - 0.472382i) q^{75} +(4.13898 + 2.38964i) q^{76} +(-6.53131 + 3.77085i) q^{77} +(-0.360698 + 0.208249i) q^{78} +(-3.11955 + 1.80107i) q^{79} +(-0.419156 - 2.19643i) q^{80} +(-4.45359 - 7.71384i) q^{81} +5.30756 q^{82} +(6.97386 + 4.02636i) q^{83} -0.228686 q^{84} +(-0.686780 - 3.59881i) q^{85} +(-1.64210 + 2.84419i) q^{86} +(0.388877 + 0.673555i) q^{87} -3.35119 q^{88} +(4.15930 + 2.40137i) q^{89} +(6.31342 + 2.19806i) q^{90} +(7.98814 + 4.61195i) q^{91} +(2.81624 + 4.87787i) q^{92} +(-0.0565009 - 0.0978624i) q^{93} +(3.10414 + 1.79217i) q^{94} +(3.51380 - 10.0926i) q^{95} +(-0.0880035 - 0.0508088i) q^{96} -8.86409 q^{97} +(-0.967725 - 1.67615i) q^{98} +(5.00948 - 8.67668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.0880035	−	0.0508088i	0.0508088	−	0.0293345i	−0.474380	−	0.880320i	$-0.657328\pi$
$3$	0.0880035	−	0.0508088i	0.0508088	−	0.0293345i	0.525189	+	0.850985i	$0.323995\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.69259	+	1.46122i	−0.756948	+	0.653475i
$5$	−1.69259	+	1.46122i	−0.756948	+	0.653475i
$6$			0.101618i			0.0414852i
$7$	1.94895	−	1.12523i	0.736635	−	0.425296i	−0.0842099	−	0.996448i	$-0.526837\pi$
$7$	1.94895	−	1.12523i	0.736635	−	0.425296i	0.820844	+	0.571152i	$0.193503\pi$
$8$	1.00000			0.353553
$9$	−1.49484	+	2.58913i	−0.498279	+	0.863045i
$10$	−0.419156	−	2.19643i	−0.132549	−	0.694572i
$11$	−3.35119			−1.01042			−0.505211	−	0.862996i	$-0.668585\pi$
$11$	−3.35119			−1.01042			−0.505211	+	0.862996i	$0.668585\pi$
$12$	−0.0880035	−	0.0508088i	−0.0254044	−	0.0146672i
$13$	2.04934	+	3.54956i	0.568385	+	0.984472i	0.996726	+	0.0808546i	$0.0257649\pi$
$13$	2.04934	+	3.54956i	0.568385	+	0.984472i	−0.428341	+	0.903617i	$0.640902\pi$
$14$			2.25046i			0.601460i
$15$	−0.0747109	+	0.214590i	−0.0192903	+	0.0554070i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.819242	+	1.41897i	−0.198695	+	0.344150i	−0.948106	−	0.317956i	$-0.897004\pi$
$17$	−0.819242	+	1.41897i	−0.198695	+	0.344150i	0.749410	+	0.662106i	$0.230337\pi$
$18$	−1.49484	−	2.58913i	−0.352336	−	0.610265i
$19$	−4.13898	+	2.38964i	−0.949546	+	0.548221i	−0.892940	−	0.450176i	$-0.851361\pi$
$19$	−4.13898	+	2.38964i	−0.949546	+	0.548221i	−0.0566062	+	0.998397i	$0.518028\pi$
$20$	2.11174	+	0.735216i	0.472200	+	0.164399i
$21$	0.114343	−	0.198048i	0.0249517	−	0.0432176i
$22$	1.67560	−	2.90222i	0.357238	−	0.618755i
$23$	−5.63248			−1.17445			−0.587227	−	0.809422i	$-0.699780\pi$
$23$	−5.63248			−1.17445			−0.587227	+	0.809422i	$0.699780\pi$
$24$	0.0880035	−	0.0508088i	0.0179636	−	0.0103713i
$25$	0.729701	−	4.94647i	0.145940	−	0.989293i
$26$	−4.09868			−0.803818
$27$			0.608657i			0.117136i
$28$	−1.94895	−	1.12523i	−0.368317	−	0.212648i
$29$			7.65373i			1.42126i	0.703565	+	0.710631i	$0.251590\pi$
$29$			7.65373i			1.42126i	−0.703565	+	0.710631i	$0.748410\pi$
$30$	−0.148485	−	0.171997i	−0.0271096	−	0.0314022i
$31$		−	1.11203i		−	0.199726i	−0.995001	−	0.0998631i	$-0.968160\pi$
$31$		−	1.11203i		−	0.199726i	0.995001	−	0.0998631i	$-0.0318405\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.294916	+	0.170270i	−0.0513384	+	0.0296402i
$34$	−0.819242	−	1.41897i	−0.140499	−	0.243351i
$35$	−1.65457	+	4.75238i	−0.279673	+	0.803299i
$36$	2.98967			0.498279
$37$	3.87021	+	4.69270i	0.636259	+	0.771475i
$37$	3.87021	+	4.69270i	0.636259	+	0.771475i
$38$		−	4.77928i		−	0.775301i
$39$	0.360698	+	0.208249i	0.0577580	+	0.0333466i
$40$	−1.69259	+	1.46122i	−0.267621	+	0.231038i
$41$	−2.65378	−	4.59648i	−0.414451	−	0.717850i	0.580920	−	0.813961i	$-0.302693\pi$
$41$	−2.65378	−	4.59648i	−0.414451	−	0.717850i	−0.995371	+	0.0961110i	$0.969360\pi$
$42$	0.114343	+	0.198048i	0.0176435	+	0.0305595i
$43$	3.28419			0.500835			0.250417	−	0.968138i	$-0.419432\pi$
$43$	3.28419			0.500835			0.250417	+	0.968138i	$0.419432\pi$
$44$	1.67560	+	2.90222i	0.252606	+	0.437526i
$45$	−1.25314	−	6.56661i	−0.186807	−	0.978893i
$46$	2.81624	−	4.87787i	0.415232	−	0.719203i
$47$		−	3.58435i		−	0.522831i	−0.965226	−	0.261415i	$-0.915811\pi$
$47$		−	3.58435i		−	0.522831i	0.965226	−	0.261415i	$-0.0841893\pi$
$48$			0.101618i			0.0146672i
$49$	−0.967725	+	1.67615i	−0.138246	+	0.239450i
$50$	3.91892	+	3.10517i	0.554218	+	0.439138i
$51$			0.166499i			0.0233145i
$52$	2.04934	−	3.54956i	0.284193	−	0.492236i
$53$	−0.873581	−	0.504362i	−0.119996	−	0.0692795i	0.438801	−	0.898584i	$-0.355403\pi$
$53$	−0.873581	−	0.504362i	−0.119996	−	0.0692795i	−0.558796	+	0.829305i	$0.688737\pi$
$54$	−0.527112	−	0.304328i	−0.0717309	−	0.0414138i
$55$	5.67218	−	4.89681i	0.764837	−	0.660286i
$56$	1.94895	−	1.12523i	0.260440	−	0.150365i
$57$	−0.242829	+	0.420593i	−0.0321636	+	0.0557089i
$58$	−6.62832	−	3.82686i	−0.870341	−	0.502492i
$59$	2.82827	+	1.63290i	0.368209	+	0.212585i	0.672676	−	0.739937i	$-0.265145\pi$
$59$	2.82827	+	1.63290i	0.368209	+	0.212585i	−0.304467	+	0.952523i	$0.598478\pi$
$60$	0.223196	−	0.0425936i	0.0288145	−	0.00549881i
$61$	4.44572	−	2.56673i	0.569216	−	0.328637i	−0.187620	−	0.982242i	$-0.560077\pi$
$61$	4.44572	−	2.56673i	0.569216	−	0.328637i	0.756836	+	0.653605i	$0.226744\pi$
$62$	0.963045	+	0.556014i	0.122307	+	0.0706139i
$63$			6.72813i			0.847664i
$64$	1.00000			0.125000
$65$	−8.65536	−	3.01342i	−1.07357	−	0.373768i
$66$		−	0.340540i		−	0.0419176i
$67$	12.9564	−	7.48037i	1.58287	−	0.913873i	0.588438	−	0.808543i	$-0.299743\pi$
$67$	12.9564	−	7.48037i	1.58287	−	0.913873i	0.994437	−	0.105330i	$-0.0335900\pi$
$68$	1.63848			0.198695
$69$	−0.495678	+	0.286180i	−0.0596726	+	0.0344520i
$70$	−3.28840	−	3.80909i	−0.393039	−	0.455274i
$71$	1.50690	+	2.61003i	0.178837	+	0.309754i	0.941482	−	0.337062i	$-0.109433\pi$
$71$	1.50690	+	2.61003i	0.178837	+	0.309754i	−0.762646	+	0.646816i	$0.776100\pi$
$72$	−1.49484	+	2.58913i	−0.176168	+	0.305132i
$73$			9.63987i			1.12826i	0.825686	+	0.564131i	$0.190789\pi$
$73$			9.63987i			1.12826i	−0.825686	+	0.564131i	$0.809211\pi$
$74$	−5.99911	+	1.00535i	−0.697382	+	0.116870i
$75$	−0.187108	−	0.472382i	−0.0216054	−	0.0545459i
$76$	4.13898	+	2.38964i	0.474773	+	0.274110i
$77$	−6.53131	+	3.77085i	−0.744312	+	0.429729i
$78$	−0.360698	+	0.208249i	−0.0408410	+	0.0235796i
$79$	−3.11955	+	1.80107i	−0.350977	+	0.202637i	−0.665115	−	0.746741i	$-0.731618\pi$
$79$	−3.11955	+	1.80107i	−0.350977	+	0.202637i	0.314139	+	0.949377i	$0.398284\pi$
$80$	−0.419156	−	2.19643i	−0.0468630	−	0.245568i
$81$	−4.45359	−	7.71384i	−0.494843	−	0.857093i
$82$	5.30756			0.586122
$83$	6.97386	+	4.02636i	0.765480	+	0.441950i	0.831260	−	0.555884i	$-0.187620\pi$
$83$	6.97386	+	4.02636i	0.765480	+	0.441950i	−0.0657796	+	0.997834i	$0.520953\pi$
$84$	−0.228686			−0.0249517
$85$	−0.686780	−	3.59881i	−0.0744917	−	0.390346i
$86$	−1.64210	+	2.84419i	−0.177072	+	0.306697i
$87$	0.388877	+	0.673555i	0.0416920	+	0.0722126i
$88$	−3.35119			−0.357238
$89$	4.15930	+	2.40137i	0.440884	+	0.254545i	0.703973	−	0.710227i	$-0.251408\pi$
$89$	4.15930	+	2.40137i	0.440884	+	0.254545i	−0.263088	+	0.964772i	$0.584741\pi$
$90$	6.31342	+	2.19806i	0.665493	+	0.231695i
$91$	7.98814	+	4.61195i	0.837384	+	0.483464i
$92$	2.81624	+	4.87787i	0.293613	+	0.508553i
$93$	−0.0565009	−	0.0978624i	−0.00585887	−	0.0101479i
$94$	3.10414	+	1.79217i	0.320167	+	0.184849i
$95$	3.51380	−	10.0926i	0.360508	−	1.03548i
$96$	−0.0880035	−	0.0508088i	−0.00898182	−	0.00518565i
$97$	−8.86409			−0.900012			−0.450006	−	0.893026i	$-0.648578\pi$
$97$	−8.86409			−0.900012			−0.450006	+	0.893026i	$0.648578\pi$
$98$	−0.967725	−	1.67615i	−0.0977550	−	0.169317i
$99$	5.00948	−	8.67668i	0.503472	−	0.872039i
$100$	−4.64862	+	1.84129i	−0.464862	+	0.184129i
$101$	15.7113			1.56334			0.781668	−	0.623695i	$-0.214369\pi$
$101$	15.7113			1.56334			0.781668	+	0.623695i	$0.214369\pi$
$102$	−0.144192	−	0.0832494i	−0.0142772	−	0.00824292i
$103$	15.1052			1.48836			0.744180	−	0.667979i	$-0.232840\pi$
$103$	15.1052			1.48836			0.744180	+	0.667979i	$0.232840\pi$
$104$	2.04934	+	3.54956i	0.200954	+	0.348063i
$105$	0.0958551	+	0.502293i	0.00935450	+	0.0490188i
$106$	0.873581	−	0.504362i	0.0848497	−	0.0489880i
$107$	11.3304	−	6.54158i	1.09535	−	0.632399i	0.160352	−	0.987060i	$-0.448737\pi$
$107$	11.3304	−	6.54158i	1.09535	−	0.632399i	0.934995	+	0.354661i	$0.115404\pi$
$108$	0.527112	−	0.304328i	0.0507214	−	0.0292840i
$109$	−6.20852	−	3.58449i	−0.594668	−	0.343332i	0.172273	−	0.985049i	$-0.444889\pi$
$109$	−6.20852	−	3.58449i	−0.594668	−	0.343332i	−0.766941	+	0.641718i	$0.778222\pi$
$110$	1.40467	+	7.36066i	0.133930	+	0.701811i
$111$	0.579023	+	0.216333i	0.0549584	+	0.0205334i
$112$			2.25046i			0.212648i
$113$	5.35119	−	9.26853i	0.503398	−	0.871910i	−0.496595	−	0.867983i	$-0.665416\pi$
$113$	5.35119	−	9.26853i	0.503398	−	0.871910i	0.999992	−	0.00392776i	$-0.00125025\pi$
$114$	−0.242829	−	0.420593i	−0.0227431	−	0.0393921i
$115$	9.53346	−	8.23027i	0.889000	−	0.767476i
$116$	6.62832	−	3.82686i	0.615424	−	0.355315i
$117$	−12.2537			−1.13286
$118$	−2.82827	+	1.63290i	−0.260363	+	0.150321i
$119$			3.68733i			0.338017i
$120$	−0.0747109	+	0.214590i	−0.00682014	+	0.0195893i
$121$	0.230480			0.0209527
$122$			5.13347i			0.464763i
$123$	−0.467084	−	0.269671i	−0.0421155	−	0.0243154i
$124$	−0.963045	+	0.556014i	−0.0864840	+	0.0499315i
$125$	5.99277	+	9.43858i	0.536010	+	0.844212i
$126$	−5.82673	−	3.36406i	−0.519086	−	0.299695i
$127$	−9.27455	−	5.35466i	−0.822983	−	0.475149i	0.0284610	−	0.999595i	$-0.490939\pi$
$127$	−9.27455	−	5.35466i	−0.822983	−	0.475149i	−0.851444	+	0.524445i	$0.824273\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.289020	−	0.166866i	0.0254468	−	0.0146917i
$130$	6.93738	−	5.98906i	0.608448	−	0.525275i
$131$	0.971678	+	0.560998i	0.0848959	+	0.0490147i	0.541847	−	0.840477i	$-0.317725\pi$
$131$	0.971678	+	0.560998i	0.0848959	+	0.0490147i	−0.456951	+	0.889492i	$0.651059\pi$
$132$	0.294916	+	0.170270i	0.0256692	+	0.0148201i
$133$	−5.37778	+	9.31458i	−0.466312	+	0.807677i
$134$			14.9607i			1.29241i
$135$	−0.889378	−	1.03020i	−0.0765455	−	0.0886659i
$136$	−0.819242	+	1.41897i	−0.0702494	+	0.121675i
$137$			21.6314i			1.84809i	0.382280	+	0.924046i	$0.375139\pi$
$137$			21.6314i			1.84809i	−0.382280	+	0.924046i	$0.624861\pi$
$138$		−	0.572360i		−	0.0487225i
$139$	−8.18187	+	14.1714i	−0.693977	+	1.20200i	0.276547	+	0.961000i	$0.410810\pi$
$139$	−8.18187	+	14.1714i	−0.693977	+	1.20200i	−0.970524	+	0.241003i	$0.922524\pi$
$140$	4.94297	−	0.943292i	0.417757	−	0.0797227i
$141$	−0.182117	−	0.315435i	−0.0153370	−	0.0265644i
$142$	−3.01381			−0.252913
$143$	−6.86773	−	11.8953i	−0.574309	−	0.994732i
$144$	−1.49484	−	2.58913i	−0.124570	−	0.215761i
$145$	−11.1837	−	12.9546i	−0.928759	−	1.07582i
$146$	−8.34837	−	4.81993i	−0.690916	−	0.398901i
$147$			0.196676i			0.0162216i
$148$	2.12889	−	5.69805i	0.174994	−	0.468377i
$149$	−11.4940			−0.941627			−0.470813	−	0.882233i	$-0.656040\pi$
$149$	−11.4940			−0.941627			−0.470813	+	0.882233i	$0.656040\pi$
$150$	0.502648	+	0.0741505i	0.0410411	+	0.00605437i
$151$	−4.37838	−	7.58358i	−0.356308	−	0.617143i	0.631033	−	0.775756i	$-0.282631\pi$
$151$	−4.37838	−	7.58358i	−0.356308	−	0.617143i	−0.987341	+	0.158613i	$0.949298\pi$
$152$	−4.13898	+	2.38964i	−0.335715	+	0.193825i
$153$	−2.44926	−	4.24225i	−0.198011	−	0.342966i
$154$		−	7.54171i		−	0.607728i
$155$	1.62491	+	1.88220i	0.130516	+	0.151182i
$156$		−	0.416499i		−	0.0333466i
$157$	−6.51088	−	3.75906i	−0.519625	−	0.300005i	0.217156	−	0.976137i	$-0.430322\pi$
$157$	−6.51088	−	3.75906i	−0.519625	−	0.300005i	−0.736781	+	0.676131i	$0.763655\pi$
$158$		−	3.60215i		−	0.286571i
$159$	−0.102504			−0.00812912
$160$	2.11174	+	0.735216i	0.166948	+	0.0581239i
$161$	−10.9774	+	6.33782i	−0.865143	+	0.499491i
$162$	8.90717			0.699813
$163$	−1.69478	+	2.93544i	−0.132745	+	0.229921i	−0.924734	−	0.380615i	$-0.875712\pi$
$163$	−1.69478	+	2.93544i	−0.132745	+	0.229921i	0.791989	+	0.610536i	$0.209046\pi$
$164$	−2.65378	+	4.59648i	−0.207225	+	0.358925i
$165$	0.250370	−	0.719133i	0.0194913	−	0.0559844i
$166$	−6.97386	+	4.02636i	−0.541276	+	0.312506i
$167$	−9.86808	−	17.0920i	−0.763615	−	1.32262i	−0.940976	−	0.338474i	$-0.890089\pi$
$167$	−9.86808	−	17.0920i	−0.763615	−	1.32262i	0.177361	−	0.984146i	$-0.443244\pi$
$168$	0.114343	−	0.198048i	0.00882175	−	0.0152797i
$169$	−1.89960	+	3.29021i	−0.146123	+	0.253093i
$170$	3.46005	+	1.20464i	0.265374	+	0.0923916i
$171$		−	14.2885i		−	1.09267i
$172$	−1.64210	−	2.84419i	−0.125209	−	0.216868i
$173$	−10.8160	−	6.24460i	−0.822322	−	0.474768i	0.0288942	−	0.999582i	$-0.490801\pi$
$173$	−10.8160	−	6.24460i	−0.822322	−	0.474768i	−0.851217	+	0.524814i	$0.824135\pi$
$174$	−0.777754			−0.0589614
$175$	−4.14375	−	10.4615i	−0.313238	−	0.790815i
$176$	1.67560	−	2.90222i	0.126303	−	0.218763i
$177$	0.331863			0.0249443
$178$	−4.15930	+	2.40137i	−0.311752	+	0.179990i
$179$			22.0156i			1.64552i	0.568387	+	0.822762i	$0.307568\pi$
$179$			22.0156i			1.64552i	−0.568387	+	0.822762i	$0.692432\pi$
$180$	−5.06028	+	4.36856i	−0.377171	+	0.325613i
$181$	3.03685	+	5.25998i	0.225728	+	0.390972i	0.956537	−	0.291609i	$-0.0941908\pi$
$181$	3.03685	+	5.25998i	0.225728	+	0.390972i	−0.730810	+	0.682581i	$0.760857\pi$
$182$	−7.98814	+	4.61195i	−0.592120	+	0.341861i
$183$	0.260826	−	0.451763i	0.0192808	−	0.0333953i
$184$	−5.63248			−0.415232
$185$	−13.4077	−	2.28759i	−0.985755	−	0.168187i
$186$	0.113002			0.00828569
$187$	2.74543	−	4.75523i	0.200766	−	0.347737i
$188$	−3.10414	+	1.79217i	−0.226392	+	0.130708i
$189$	0.684877	+	1.18624i	0.0498175	+	0.0862864i
$190$	6.98355	+	8.08934i	0.506640	+	0.586863i
$191$			26.4219i			1.91182i	0.293659	+	0.955910i	$0.405127\pi$
$191$			26.4219i			1.91182i	−0.293659	+	0.955910i	$0.594873\pi$
$192$	0.0880035	−	0.0508088i	0.00635110	−	0.00366681i
$193$	18.4359			1.32704			0.663521	−	0.748157i	$-0.269061\pi$
$193$	18.4359			1.32704			0.663521	+	0.748157i	$0.269061\pi$
$194$	4.43204	−	7.67652i	0.318202	−	0.551142i
$195$	−0.914810	+	0.174578i	−0.0655109	+	0.0125018i
$196$	1.93545			0.138246
$197$	−16.5569	−	9.55916i	−1.17963	−	0.681062i	−0.223704	−	0.974657i	$-0.571815\pi$
$197$	−16.5569	−	9.55916i	−1.17963	−	0.681062i	−0.955930	+	0.293595i	$0.905148\pi$
$198$	5.00948	+	8.67668i	0.356009	+	0.616625i
$199$		−	7.75309i		−	0.549602i	−0.961501	−	0.274801i	$-0.911388\pi$
$199$		−	7.75309i		−	0.549602i	0.961501	−	0.274801i	$-0.0886120\pi$
$200$	0.729701	−	4.94647i	0.0515977	−	0.349768i
$201$	0.760138	−	1.31660i	0.0536160	−	0.0928657i
$202$	−7.85567	+	13.6064i	−0.552723	+	0.957344i
$203$	8.61219	+	14.9167i	0.604457	+	1.04695i
$204$	0.144192	−	0.0832494i	0.0100955	−	0.00582862i
$205$	11.2082	+	3.90220i	0.782815	+	0.272542i
$206$	−7.55261	+	13.0815i	−0.526215	+	0.911431i
$207$	8.41964	−	14.5832i	0.585206	−	1.01361i
$208$	−4.09868			−0.284193
$209$	13.8705	−	8.00814i	0.959442	−	0.553934i
$210$	−0.482926	−	0.168134i	−0.0333251	−	0.0116023i
$211$	−15.4360			−1.06266			−0.531329	−	0.847165i	$-0.678307\pi$
$211$	−15.4360			−1.06266			−0.531329	+	0.847165i	$0.678307\pi$
$212$			1.00872i			0.0692795i
$213$	0.265226	+	0.153128i	0.0181730	+	0.0104922i
$214$			13.0832i			0.894347i
$215$	−5.55878	+	4.79891i	−0.379106	+	0.327283i
$216$			0.608657i			0.0414138i
$217$	−1.25129	−	2.16729i	−0.0849428	−	0.147125i
$218$	6.20852	−	3.58449i	0.420494	−	0.242772i
$219$	0.489790	+	0.848342i	0.0330970	+	0.0573256i
$220$	−7.07685	−	2.46385i	−0.477121	−	0.166113i
$221$	−6.71562			−0.451742
$222$	−0.476861	+	0.393282i	−0.0320048	+	0.0263954i
$223$		−	14.6392i		−	0.980312i	−0.871635	−	0.490156i	$-0.836940\pi$
$223$		−	14.6392i		−	0.980312i	0.871635	−	0.490156i	$-0.163060\pi$
$224$	−1.94895	−	1.12523i	−0.130220	−	0.0751824i
$225$	11.7163	+	9.28346i	0.781085	+	0.618897i
$226$	5.35119	+	9.26853i	0.355956	+	0.616534i
$227$	11.5695	+	20.0390i	0.767896	+	1.33003i	0.938702	+	0.344730i	$0.112029\pi$
$227$	11.5695	+	20.0390i	0.767896	+	1.33003i	−0.170806	+	0.985305i	$0.554637\pi$
$228$	0.485659			0.0321636
$229$	−8.99176	−	15.5742i	−0.594192	−	1.02917i	−0.993660	−	0.112424i	$-0.964139\pi$
$229$	−8.99176	−	15.5742i	−0.594192	−	1.02917i	0.399468	−	0.916747i	$-0.369195\pi$
$230$	2.36089	+	12.3714i	0.155672	+	0.815743i
$231$	−0.383185	+	0.663696i	−0.0252117	+	0.0436680i
$232$			7.65373i			0.502492i
$233$			12.7707i			0.836639i	0.908300	+	0.418319i	$0.137381\pi$
$233$			12.7707i			0.836639i	−0.908300	+	0.418319i	$0.862619\pi$
$234$	6.12686	−	10.6120i	0.400526	−	0.693731i
$235$	5.23750	+	6.06682i	0.341657	+	0.395756i
$236$		−	3.26580i		−	0.212585i
$237$	−0.183021	+	0.317001i	−0.0118885	+	0.0205915i
$238$	−3.19332	−	1.84367i	−0.206992	−	0.119507i
$239$	−0.377703	−	0.218067i	−0.0244316	−	0.0141056i	0.487734	−	0.872992i	$-0.337823\pi$
$239$	−0.377703	−	0.218067i	−0.0244316	−	0.0141056i	−0.512166	+	0.858886i	$0.671157\pi$
$240$	−0.148485	−	0.171997i	−0.00958468	−	0.0111023i
$241$	−4.73639	+	2.73456i	−0.305098	+	0.176148i	−0.644731	−	0.764410i	$-0.723030\pi$
$241$	−4.73639	+	2.73456i	−0.305098	+	0.176148i	0.339633	+	0.940558i	$0.389697\pi$
$242$	−0.115240	+	0.199601i	−0.00740790	+	0.0128309i
$243$	−2.36520	−	1.36555i	−0.151728	−	0.0875999i
$244$	−4.44572	−	2.56673i	−0.284608	−	0.164318i
$245$	−0.811255	−	4.25108i	−0.0518292	−	0.271592i
$246$	0.467084	−	0.269671i	0.0297802	−	0.0171936i
$247$	−16.9643	−	9.79437i	−1.07942	−	0.623201i
$248$		−	1.11203i		−	0.0706139i
$249$	0.818298			0.0518575
$250$	−11.1704	+	0.470602i	−0.706480	+	0.0297635i
$251$		−	22.7700i		−	1.43723i	−0.695407	−	0.718616i	$-0.744776\pi$
$251$		−	22.7700i		−	1.43723i	0.695407	−	0.718616i	$-0.255224\pi$
$252$	5.82673	−	3.36406i	0.367049	−	0.211916i
$253$	18.8755			1.18669
$254$	9.27455	−	5.35466i	0.581937	−	0.335981i
$255$	−0.243291	−	0.281814i	−0.0152354	−	0.0176479i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.35026	−	10.9990i	0.396118	−	0.686097i	−0.597125	−	0.802148i	$-0.703690\pi$
$257$	6.35026	−	10.9990i	0.396118	−	0.686097i	0.993243	+	0.116051i	$0.0370237\pi$
$258$			0.333732i			0.0207772i
$259$	12.8232	+	4.79098i	0.796796	+	0.297697i
$260$	1.71799	+	9.00247i	0.106545	+	0.558310i
$261$	−19.8165	−	11.4411i	−1.22661	−	0.708185i
$262$	−0.971678	+	0.560998i	−0.0600305	+	0.0346586i
$263$	−2.45972	+	1.42012i	−0.151673	+	0.0875683i	−0.573916	−	0.818914i	$-0.694576\pi$
$263$	−2.45972	+	1.42012i	−0.151673	+	0.0875683i	0.422243	+	0.906483i	$0.361243\pi$
$264$	−0.294916	+	0.170270i	−0.0181509	+	0.0104794i
$265$	2.21559	−	0.422813i	0.136103	−	0.0259732i
$266$	−5.37778	−	9.31458i	−0.329733	−	0.571114i
$267$	0.488043			0.0298678
$268$	−12.9564	−	7.48037i	−0.791437	−	0.456937i
$269$	6.29960			0.384093			0.192047	−	0.981386i	$-0.438487\pi$
$269$	6.29960			0.384093			0.192047	+	0.981386i	$0.438487\pi$
$270$	1.33687	−	0.255122i	0.0813594	−	0.0155262i
$271$	−0.336198	+	0.582312i	−0.0204226	+	0.0353729i	−0.876056	−	0.482209i	$-0.839834\pi$
$271$	−0.336198	+	0.582312i	−0.0204226	+	0.0353729i	0.855633	+	0.517582i	$0.173168\pi$
$272$	−0.819242	−	1.41897i	−0.0496738	−	0.0860376i
$273$	0.937312			0.0567287
$274$	−18.7333	−	10.8157i	−1.13172	−	0.653399i
$275$	−2.44537	+	16.5766i	−0.147461	+	0.999604i
$276$	0.495678	+	0.286180i	0.0298363	+	0.0172260i
$277$	7.62576	+	13.2082i	0.458187	+	0.793604i	0.998865	−	0.0476258i	$-0.0151655\pi$
$277$	7.62576	+	13.2082i	0.458187	+	0.793604i	−0.540678	+	0.841230i	$0.681832\pi$
$278$	−8.18187	−	14.1714i	−0.490716	−	0.849945i
$279$	2.87919	+	1.66230i	0.172373	+	0.0995194i
$280$	−1.65457	+	4.75238i	−0.0988795	+	0.284009i
$281$	21.3227	+	12.3107i	1.27201	+	0.734394i	0.975366	−	0.220594i	$-0.0707997\pi$
$281$	21.3227	+	12.3107i	1.27201	+	0.734394i	0.296642	+	0.954989i	$0.404133\pi$
$282$	0.364233			0.0216898
$283$	9.42935	+	16.3321i	0.560517	+	0.970844i	0.997451	+	0.0713504i	$0.0227308\pi$
$283$	9.42935	+	16.3321i	0.560517	+	0.970844i	−0.436934	+	0.899493i	$0.643936\pi$
$284$	1.50690	−	2.61003i	0.0894183	−	0.154877i
$285$	−0.203567	−	1.06672i	−0.0120583	−	0.0631868i
$286$	13.7355			0.812195
$287$	−10.3442	−	5.97221i	−0.610597	−	0.352529i
$288$	2.98967			0.176168
$289$	7.15769	+	12.3975i	0.421040	+	0.729263i
$290$	16.8109	−	3.20810i	0.987169	−	0.188386i
$291$	−0.780070	+	0.450374i	−0.0457285	+	0.0264014i
$292$	8.34837	−	4.81993i	0.488551	−	0.282065i
$293$	1.02893	−	0.594054i	0.0601109	−	0.0347050i	−0.469643	−	0.882856i	$-0.655617\pi$
$293$	1.02893	−	0.594054i	0.0601109	−	0.0347050i	0.529754	+	0.848151i	$0.322284\pi$
$294$	−0.170326	−	0.0983379i	−0.00993363	−	0.00573518i
$295$	−7.17310	+	1.36888i	−0.417634	+	0.0796992i
$296$	3.87021	+	4.69270i	0.224952	+	0.272758i
$297$		−	2.03972i		−	0.118357i
$298$	5.74701	−	9.95411i	0.332915	−	0.576626i
$299$	−11.5429	−	19.9929i	−0.667542	−	1.15622i
$300$	−0.315540	+	0.398231i	−0.0182177	+	0.0229919i
$301$	6.40073	−	3.69547i	0.368932	−	0.213003i
$302$	8.75676			0.503895
$303$	1.38265	−	0.798275i	0.0794313	−	0.0458597i
$304$		−	4.77928i		−	0.274110i
$305$	−3.77421	+	10.8406i	−0.216111	+	0.620729i
$306$	4.89853			0.280030
$307$			14.2001i			0.810441i	0.914219	+	0.405221i	$0.132805\pi$
$307$			14.2001i			0.810441i	−0.914219	+	0.405221i	$0.867195\pi$
$308$	6.53131	+	3.77085i	0.372156	+	0.214864i
$309$	1.32931	−	0.767478i	0.0756219	−	0.0436603i
$310$	−2.44249	+	0.466113i	−0.138724	+	0.0264735i
$311$	−6.44777	−	3.72262i	−0.365619	−	0.211090i	0.305924	−	0.952056i	$-0.401035\pi$
$311$	−6.44777	−	3.72262i	−0.365619	−	0.211090i	−0.671543	+	0.740966i	$0.734368\pi$
$312$	0.360698	+	0.208249i	0.0204205	+	0.0117898i
$313$	−16.8822	+	29.2408i	−0.954237	+	1.65279i	−0.218134	+	0.975919i	$0.569997\pi$
$313$	−16.8822	+	29.2408i	−0.954237	+	1.65279i	−0.736104	+	0.676869i	$0.763336\pi$
$314$	6.51088	−	3.75906i	0.367430	−	0.212136i
$315$	−9.83124	−	11.3879i	−0.553928	−	0.641638i
$316$	3.11955	+	1.80107i	0.175488	+	0.101318i
$317$	17.0296	+	9.83203i	0.956477	+	0.552222i	0.895087	−	0.445892i	$-0.147113\pi$
$317$	17.0296	+	9.83203i	0.956477	+	0.552222i	0.0613897	+	0.998114i	$0.480447\pi$
$318$	0.0512521	−	0.0887713i	0.00287408	−	0.00497805i
$319$		−	25.6491i		−	1.43607i
$320$	−1.69259	+	1.46122i	−0.0946185	+	0.0816844i
$321$	0.664740	−	1.15136i	0.0371022	−	0.0642629i
$322$		−	12.6756i		−	0.706386i
$323$		−	7.83077i		−	0.435715i
$324$	−4.45359	+	7.71384i	−0.247421	+	0.428546i
$325$	19.0532	−	7.54688i	1.05688	−	0.418626i
$326$	−1.69478	−	2.93544i	−0.0938649	−	0.162579i
$327$	−0.728495			−0.0402858
$328$	−2.65378	−	4.59648i	−0.146530	−	0.253798i
$329$	−4.03321	−	6.98572i	−0.222358	−	0.385135i
$330$	0.497602	+	0.576394i	0.0273921	+	0.0317294i
$331$	29.6384	+	17.1118i	1.62908	+	0.940548i	0.984369	+	0.176118i	$0.0563541\pi$
$331$	29.6384	+	17.1118i	1.62908	+	0.940548i	0.644707	+	0.764430i	$0.276979\pi$
$332$		−	8.05272i		−	0.441950i
$333$	−17.9354	+	3.00568i	−0.982852	+	0.164710i
$334$	19.7362			1.07991
$335$	−10.9994	+	31.5933i	−0.600960	+	1.72612i
$336$	0.114343	+	0.198048i	0.00623792	+	0.0108044i
$337$	0.571966	−	0.330225i	0.0311570	−	0.0179885i	−0.484341	−	0.874880i	$-0.660940\pi$
$337$	0.571966	−	0.330225i	0.0311570	−	0.0179885i	0.515498	+	0.856891i	$0.327607\pi$
$338$	−1.89960	−	3.29021i	−0.103325	−	0.178964i
$339$		−	1.08755i		−	0.0590677i
$340$	−2.77328	+	2.39418i	−0.150402	+	0.129842i
$341$			3.72662i			0.201808i
$342$	12.3742	+	7.14424i	0.669119	+	0.386316i
$343$			20.1088i			1.08577i
$344$	3.28419			0.177072
$345$	0.420808	−	1.20868i	0.0226555	−	0.0650729i
$346$	10.8160	−	6.24460i	0.581470	−	0.335712i
$347$	22.4993			1.20783			0.603913	−	0.797050i	$-0.293607\pi$
$347$	22.4993			1.20783			0.603913	+	0.797050i	$0.293607\pi$
$348$	0.388877	−	0.673555i	0.0208460	−	0.0361063i
$349$	7.95733	−	13.7825i	0.425946	−	0.737760i	−0.570562	−	0.821254i	$-0.693275\pi$
$349$	7.95733	−	13.7825i	0.425946	−	0.737760i	0.996508	+	0.0834942i	$0.0266080\pi$
$350$	11.1318	+	1.64216i	0.595020	+	0.0877772i
$351$	−2.16047	+	1.24735i	−0.115317	+	0.0665784i
$352$	1.67560	+	2.90222i	0.0893095	+	0.154689i
$353$	18.1091	−	31.3658i	0.963848	−	1.66943i	0.251171	−	0.967943i	$-0.419184\pi$
$353$	18.1091	−	31.3658i	0.963848	−	1.66943i	0.712678	−	0.701492i	$-0.247482\pi$
$354$	−0.165931	+	0.287402i	−0.00881916	+	0.0152752i
$355$	−6.36439	−	2.21580i	−0.337787	−	0.117602i
$356$		−	4.80274i		−	0.254545i
$357$	0.187349	+	0.324498i	0.00991556	+	0.0171743i
$358$	−19.0661	−	11.0078i	−1.00767	−	0.581780i
$359$	27.6477			1.45919			0.729595	−	0.683880i	$-0.239709\pi$
$359$	27.6477			1.45919			0.729595	+	0.683880i	$0.239709\pi$
$360$	−1.25314	−	6.56661i	−0.0660462	−	0.346091i
$361$	1.92075	−	3.32683i	0.101092	−	0.175096i
$362$	−6.07371			−0.319227
$363$	0.0202830	−	0.0117104i	0.00106458	−	0.000614637i
$364$		−	9.22390i		−	0.483464i
$365$	−14.0859	−	16.3163i	−0.737291	−	0.854035i
$366$	0.260826	+	0.451763i	0.0136336	+	0.0236140i
$367$	−8.72891	+	5.03964i	−0.455646	+	0.263067i	−0.710212	−	0.703988i	$-0.751401\pi$
$367$	−8.72891	+	5.03964i	−0.455646	+	0.263067i	0.254566	+	0.967055i	$0.418067\pi$
$368$	2.81624	−	4.87787i	0.146807	−	0.254277i
$369$	15.8679			0.826048
$370$	8.68497	−	10.4676i	0.451510	−	0.544186i
$371$	−2.27009			−0.117857
$372$	−0.0565009	+	0.0978624i	−0.00292943	+	0.00507393i
$373$	−15.5652	+	8.98657i	−0.805935	+	0.465307i	−0.845542	−	0.533908i	$-0.820723\pi$
$373$	−15.5652	+	8.98657i	−0.805935	+	0.465307i	0.0396070	+	0.999215i	$0.487389\pi$
$374$	2.74543	+	4.75523i	0.141963	+	0.245887i
$375$	1.00695	+	0.526142i	0.0519985	+	0.0271698i
$376$		−	3.58435i		−	0.184849i
$377$	−27.1674	+	15.6851i	−1.39919	+	0.807824i
$378$	−1.36975			−0.0704526
$379$	14.2034	−	24.6011i	0.729581	−	1.26367i	−0.227479	−	0.973783i	$-0.573048\pi$
$379$	14.2034	−	24.6011i	0.729581	−	1.26367i	0.957060	−	0.289888i	$-0.0936182\pi$
$380$	−10.4974	+	2.00326i	−0.538503	+	0.102765i
$381$	−1.08826			−0.0557531
$382$	−22.8820	−	13.2109i	−1.17075	−	0.675931i
$383$	8.35265	+	14.4672i	0.426800	+	0.739240i	0.996587	−	0.0825529i	$-0.0263073\pi$
$383$	8.35265	+	14.4672i	0.426800	+	0.739240i	−0.569786	+	0.821793i	$0.692974\pi$
$384$			0.101618i			0.00518565i
$385$	5.54478	−	15.9261i	0.282588	−	0.811671i
$386$	−9.21793	+	15.9659i	−0.469180	+	0.812644i
$387$	−4.90933	+	8.50321i	−0.249555	+	0.432243i
$388$	4.43204	+	7.67652i	0.225003	+	0.389717i
$389$	−22.2307	+	12.8349i	−1.12714	+	0.650754i	−0.943214	−	0.332186i	$-0.892214\pi$
$389$	−22.2307	+	12.8349i	−1.12714	+	0.650754i	−0.183925	+	0.982940i	$0.558880\pi$
$390$	0.306216	−	0.879538i	0.0155059	−	0.0445371i
$391$	4.61436	−	7.99231i	0.233358	−	0.404189i
$392$	−0.967725	+	1.67615i	−0.0488775	+	0.0846583i
$393$	0.114015			0.00575128
$394$	16.5569	−	9.55916i	0.834127	−	0.481583i
$395$	2.64835	−	7.60681i	0.133253	−	0.382740i
$396$	−10.0190			−0.503472
$397$			24.6533i			1.23731i	0.785662	+	0.618657i	$0.212323\pi$
$397$			24.6533i			1.23731i	−0.785662	+	0.618657i	$0.787677\pi$
$398$	6.71437	+	3.87654i	0.336561	+	0.194314i
$399$			1.09295i			0.0547161i
$400$	3.91892	+	3.10517i	0.195946	+	0.155259i
$401$			5.34305i			0.266819i	0.991061	+	0.133410i	$0.0425926\pi$
$401$			5.34305i			0.266819i	−0.991061	+	0.133410i	$0.957407\pi$
$402$	0.760138	+	1.31660i	0.0379122	+	0.0656659i
$403$	3.94722	−	2.27893i	0.196625	−	0.113521i
$404$	−7.85567	−	13.6064i	−0.390834	−	0.676944i
$405$	18.8097	+	6.54869i	0.934659	+	0.325407i
$406$	−17.2244			−0.854831
$407$	−12.9698	−	15.7261i	−0.642890	−	0.779516i
$408$			0.166499i			0.00824292i
$409$	−22.0532	−	12.7324i	−1.09046	−	0.629578i	−0.156761	−	0.987637i	$-0.550105\pi$
$409$	−22.0532	−	12.7324i	−1.09046	−	0.629578i	−0.933699	+	0.358059i	$0.883439\pi$
$410$	−8.98351	+	7.75549i	−0.443664	+	0.383016i
$411$	1.09906	+	1.90364i	0.0542129	+	0.0938994i
$412$	−7.55261	−	13.0815i	−0.372090	−	0.644479i
$413$	7.34954			0.361647
$414$	8.41964	+	14.5832i	0.413803	+	0.716727i
$415$	−17.6872	+	3.37534i	−0.868232	+	0.165689i
$416$	2.04934	−	3.54956i	0.100477	−	0.174032i
$417$			1.66284i			0.0814299i
$418$			16.0163i			0.783381i
$419$	0.279488	−	0.484087i	0.0136539	−	0.0236492i	−0.859118	−	0.511778i	$-0.828987\pi$
$419$	0.279488	−	0.484087i	0.0136539	−	0.0236492i	0.872772	+	0.488129i	$0.162320\pi$
$420$	0.387071	−	0.334159i	0.0188871	−	0.0163053i
$421$			20.4640i			0.997354i	0.866788	+	0.498677i	$0.166181\pi$
$421$			20.4640i			0.997354i	−0.866788	+	0.498677i	$0.833819\pi$
$422$	7.71800	−	13.3680i	0.375707	−	0.650743i
$423$	9.28036	+	5.35802i	0.451226	+	0.260516i
$424$	−0.873581	−	0.504362i	−0.0424249	−	0.0244940i
$425$	6.42108	+	5.08777i	0.311468	+	0.246793i
$426$	−0.265226	+	0.153128i	−0.0128502	+	0.00741908i
$427$	5.77632	−	10.0049i	0.279536	−	0.484170i
$428$	−11.3304	−	6.54158i	−0.547673	−	0.316199i
$429$	−1.20877	−	0.697883i	−0.0583599	−	0.0336941i
$430$	−1.37659	−	7.21350i	−0.0663850	−	0.347866i
$431$	12.0174	−	6.93826i	0.578859	−	0.334204i	−0.181821	−	0.983332i	$-0.558199\pi$
$431$	12.0174	−	6.93826i	0.578859	−	0.334204i	0.760680	+	0.649127i	$0.224866\pi$
$432$	−0.527112	−	0.304328i	−0.0253607	−	0.0146420i
$433$		−	14.6035i		−	0.701798i	−0.936413	−	0.350899i	$-0.885876\pi$
$433$		−	14.6035i		−	0.701798i	0.936413	−	0.350899i	$-0.114124\pi$
$434$	2.50257			0.120127
$435$	−1.64242	−	0.571817i	−0.0787478	−	0.0274165i
$436$			7.16898i			0.343332i
$437$	23.3127	−	13.4596i	1.11520	−	0.643860i
$438$	−0.979581			−0.0468062
$439$	6.66420	−	3.84758i	0.318065	−	0.183635i	−0.332465	−	0.943116i	$-0.607880\pi$
$439$	6.66420	−	3.84758i	0.318065	−	0.183635i	0.650530	+	0.759481i	$0.274547\pi$
$440$	5.67218	−	4.89681i	0.270411	−	0.233446i
$441$	−2.89318	−	5.01114i	−0.137771	−	0.238626i
$442$	3.35781	−	5.81590i	0.159715	−	0.276634i
$443$			3.37925i			0.160553i	0.996773	+	0.0802766i	$0.0255803\pi$
$443$			3.37925i			0.160553i	−0.996773	+	0.0802766i	$0.974420\pi$
$444$	−0.102162	−	0.609615i	−0.00484838	−	0.0289310i
$445$	−10.5489	+	2.01310i	−0.500065	+	0.0954299i
$446$	12.6779	+	7.31959i	0.600316	+	0.346593i
$447$	−1.01151	+	0.583998i	−0.0478430	+	0.0276221i
$448$	1.94895	−	1.12523i	0.0920793	−	0.0531620i
$449$	19.8177	−	11.4417i	0.935255	−	0.539969i	0.0467850	−	0.998905i	$-0.485102\pi$
$449$	19.8177	−	11.4417i	0.935255	−	0.539969i	0.888470	+	0.458935i	$0.151769\pi$
$450$	−13.8978	+	5.50487i	−0.655151	+	0.259502i
$451$	8.89332	+	15.4037i	0.418770	+	0.725331i
$452$	−10.7024			−0.503398
$453$	−0.770625	−	0.444921i	−0.0362071	−	0.0209042i
$454$	−23.1390			−1.08597
$455$	−20.2597	+	3.86625i	−0.949788	+	0.181253i
$456$	−0.242829	+	0.420593i	−0.0113715	+	0.0196961i
$457$	10.7708	+	18.6555i	0.503836	+	0.872669i	0.999990	+	0.00443501i	$0.00141171\pi$
$457$	10.7708	+	18.6555i	0.503836	+	0.872669i	−0.496154	+	0.868234i	$0.665255\pi$
$458$	17.9835			0.840315
$459$	−0.863664	−	0.498637i	−0.0403124	−	0.0232744i
$460$	−11.8944	−	4.14109i	−0.554577	−	0.193079i
$461$	−17.2165	−	9.93992i	−0.801850	−	0.462948i	0.0422676	−	0.999106i	$-0.486542\pi$
$461$	−17.2165	−	9.93992i	−0.801850	−	0.462948i	−0.844118	+	0.536158i	$0.819875\pi$
$462$	−0.383185	−	0.663696i	−0.0178274	−	0.0308779i
$463$	−11.9854	−	20.7594i	−0.557010	−	0.964769i	−0.997744	−	0.0671318i	$-0.978615\pi$
$463$	−11.9854	−	20.7594i	−0.557010	−	0.964769i	0.440734	−	0.897638i	$-0.354718\pi$
$464$	−6.62832	−	3.82686i	−0.307712	−	0.177658i
$465$	0.238631	+	0.0830806i	0.0110662	+	0.00385277i
$466$	−11.0598	−	6.38537i	−0.512335	−	0.295797i
$467$	0.381827			0.0176688			0.00883441	−	0.999961i	$-0.497188\pi$
$467$	0.381827			0.0176688			0.00883441	+	0.999961i	$0.497188\pi$
$468$	6.12686	+	10.6120i	0.283214	+	0.490542i
$469$	16.8343	−	29.1578i	0.777333	−	1.34638i
$470$	−7.87277	+	1.50240i	−0.363144	+	0.0693006i
$471$	−0.763973			−0.0352020
$472$	2.82827	+	1.63290i	0.130181	+	0.0751603i
$473$	−11.0060			−0.506054
$474$	−0.183021	−	0.317001i	−0.00840642	−	0.0145604i
$475$	8.80005	+	22.2170i	0.403774	+	1.01939i
$476$	3.19332	−	1.84367i	0.146366	−	0.0845043i
$477$	2.61172	−	1.50788i	0.119583	−	0.0690410i
$478$	0.377703	−	0.218067i	0.0172758	−	0.00997416i
$479$	−24.6845	−	14.2516i	−1.12786	−	0.651172i	−0.184467	−	0.982839i	$-0.559056\pi$
$479$	−24.6845	−	14.2516i	−1.12786	−	0.651172i	−0.943397	+	0.331666i	$0.892389\pi$
$480$	0.223196	−	0.0425936i	0.0101875	−	0.00194412i
$481$	−8.72565	+	23.3545i	−0.397855	+	1.06487i
$482$		−	5.46911i		−	0.249111i
$483$	−0.644035	+	1.11550i	−0.0293046	+	0.0507571i
$484$	−0.115240	−	0.199601i	−0.00523818	−	0.00907279i
$485$	15.0032	−	12.9523i	0.681262	−	0.588135i
$486$	2.36520	−	1.36555i	0.107288	−	0.0619425i
$487$	11.6193			0.526523			0.263261	−	0.964725i	$-0.415202\pi$
$487$	11.6193			0.526523			0.263261	+	0.964725i	$0.415202\pi$
$488$	4.44572	−	2.56673i	0.201248	−	0.116191i
$489$			0.344438i			0.0155760i
$490$	4.08717	+	1.42297i	0.184640	+	0.0642834i
$491$	−26.4852			−1.19526			−0.597629	−	0.801773i	$-0.703890\pi$
$491$	−26.4852			−1.19526			−0.597629	+	0.801773i	$0.703890\pi$
$492$			0.539342i			0.0243154i
$493$	−10.8604	−	6.27025i	−0.489128	−	0.282398i
$494$	16.9643	−	9.79437i	0.763262	−	0.440670i
$495$	4.19951	+	22.0060i	0.188754	+	0.989095i
$496$	0.963045	+	0.556014i	0.0432420	+	0.0249658i
$497$	5.87377	+	3.39122i	0.263474	+	0.152117i
$498$	−0.409149	+	0.708667i	−0.0183344	+	0.0317561i
$499$	−30.9807	+	17.8867i	−1.38689	+	0.800718i	−0.992963	−	0.118425i	$-0.962215\pi$
$499$	−30.9807	+	17.8867i	−1.38689	+	0.800718i	−0.393922	+	0.919144i	$0.628882\pi$
$500$	5.17766	−	9.90918i	0.231552	−	0.443152i
$501$	−1.73685	−	1.00277i	−0.0775968	−	0.0448005i
$502$	19.7194	+	11.3850i	0.880122	+	0.508139i
$503$	−11.8001	+	20.4383i	−0.526140	+	0.911301i	0.473396	+	0.880849i	$0.343028\pi$
$503$	−11.8001	+	20.4383i	−0.526140	+	0.911301i	−0.999536	+	0.0304514i	$0.990306\pi$
$504$			6.72813i			0.299695i
$505$	−26.5928	+	22.9576i	−1.18336	+	1.02160i
$506$	−9.43776	+	16.3467i	−0.419560	+	0.726699i
$507$			0.386066i			0.0171458i
$508$			10.7093i			0.475149i
$509$	10.1883	−	17.6467i	0.451589	−	0.782176i	−0.546896	−	0.837201i	$-0.684191\pi$
$509$	10.1883	−	17.6467i	0.451589	−	0.782176i	0.998485	+	0.0550252i	$0.0175239\pi$
$510$	0.365703	−	0.0697889i	0.0161936	−	0.00309031i
$511$	10.8470	+	18.7876i	0.479845	+	0.831116i
$512$	1.00000			0.0441942
$513$	−1.45447	−	2.51921i	−0.0642164	−	0.111226i
$514$	6.35026	+	10.9990i	0.280098	+	0.485144i
$515$	−25.5669	+	22.0720i	−1.12661	+	0.972607i
$516$	−0.289020	−	0.166866i	−0.0127234	−	0.00734587i
$517$			12.0118i			0.528280i
$518$	−10.5607	+	8.70974i	−0.464011	+	0.382684i
$519$	−1.26912			−0.0557083
$520$	−8.65536	−	3.01342i	−0.379563	−	0.132147i
$521$	−10.7044	−	18.5405i	−0.468967	−	0.812275i	0.530403	−	0.847745i	$-0.322041\pi$
$521$	−10.7044	−	18.5405i	−0.468967	−	0.812275i	−0.999371	+	0.0354700i	$0.988707\pi$
$522$	19.8165	−	11.4411i	0.867346	−	0.500762i
$523$	−22.2690	−	38.5711i	−0.973756	−	1.68660i	−0.683979	−	0.729501i	$-0.739752\pi$
$523$	−22.2690	−	38.5711i	−0.973756	−	1.68660i	−0.289777	−	0.957094i	$-0.593581\pi$
$524$		−	1.12200i		−	0.0490147i
$525$	−0.896201	−	0.710110i	−0.0391134	−	0.0309917i
$526$		−	2.84024i		−	0.123840i
$527$	1.57793	+	0.911020i	0.0687358	+	0.0396846i
$528$		−	0.340540i		−	0.0148201i
$529$	8.72485			0.379341
$530$	−0.741630	+	2.13017i	−0.0322144	+	0.0925286i
$531$	−8.45559	+	4.88184i	−0.366941	+	0.211854i
$532$	10.7556			0.466312
$533$	10.8770	−	18.8395i	0.471135	−	0.816030i
$534$	−0.244022	+	0.422658i	−0.0105598	+	0.0182902i
$535$	−9.61895	+	27.6283i	−0.415864	+	1.19447i
$536$	12.9564	−	7.48037i	0.559631	−	0.323103i
$537$	1.11859	+	1.93745i	0.0482706	+	0.0836071i
$538$	−3.14980	+	5.45562i	−0.135798	+	0.235208i
$539$	3.24303	−	5.61709i	0.139687	−	0.241945i
$540$	−0.447494	+	1.28533i	−0.0192571	+	0.0553116i
$541$			38.1217i			1.63898i	0.573094	+	0.819490i	$0.305743\pi$
$541$			38.1217i			1.63898i	−0.573094	+	0.819490i	$0.694257\pi$
$542$	−0.336198	−	0.582312i	−0.0144409	−	0.0250124i
$543$	0.534507	+	0.308598i	0.0229379	+	0.0132432i
$544$	1.63848			0.0702494
$545$	15.7462	−	3.00492i	0.674491	−	0.128717i
$546$	−0.468656	+	0.811736i	−0.0200566	+	0.0347391i
$547$	41.8128			1.78778			0.893892	−	0.448282i	$-0.147964\pi$
$547$	41.8128			1.78778			0.893892	+	0.448282i	$0.147964\pi$
$548$	18.7333	−	10.8157i	0.800248	−	0.462023i
$549$			15.3474i			0.655011i
$550$	−13.1330	−	10.4060i	−0.559994	−	0.443715i
$551$	−18.2896	−	31.6786i	−0.779165	−	1.34955i
$552$	−0.495678	+	0.286180i	−0.0210975	+	0.0121806i
$553$	−4.05323	+	7.02041i	−0.172361	+	0.298538i
$554$	−15.2515			−0.647975
$555$	−1.29616	+	0.479915i	−0.0550187	+	0.0203712i
$556$	16.3637			0.693977
$557$	14.6940	−	25.4507i	0.622604	−	1.07838i	−0.366395	−	0.930459i	$-0.619408\pi$
$557$	14.6940	−	25.4507i	0.622604	−	1.07838i	0.988999	−	0.147922i	$-0.0472584\pi$
$558$	−2.87919	+	1.66230i	−0.121886	+	0.0703708i
$559$	6.73043	+	11.6575i	0.284667	+	0.493058i
$560$	−3.28840	−	3.80909i	−0.138960	−	0.160964i
$561$		−	0.557969i		−	0.0235575i
$562$	−21.3227	+	12.3107i	−0.899446	+	0.519295i
$563$	−10.8601			−0.457698			−0.228849	−	0.973462i	$-0.573496\pi$
$563$	−10.8601			−0.457698			−0.228849	+	0.973462i	$0.573496\pi$
$564$	−0.182117	+	0.315435i	−0.00766849	+	0.0132822i
$565$	4.48597	+	23.5070i	0.188726	+	0.988949i
$566$	−18.8587			−0.792691
$567$	−17.3596	−	10.0226i	−0.729037	−	0.420909i
$568$	1.50690	+	2.61003i	0.0632283	+	0.109515i
$569$			21.0550i			0.882671i	0.897342	+	0.441336i	$0.145495\pi$
$569$			21.0550i			0.882671i	−0.897342	+	0.441336i	$0.854505\pi$
$570$	1.02559	+	0.357064i	0.0429571	+	0.0149558i
$571$	−10.3193	+	17.8735i	−0.431848	+	0.747982i	−0.997032	−	0.0769821i	$-0.975472\pi$
$571$	−10.3193	+	17.8735i	−0.431848	+	0.747982i	0.565185	+	0.824964i	$0.308805\pi$
$572$	−6.86773	+	11.8953i	−0.287154	+	0.497366i
$573$	1.34246	+	2.32522i	0.0560823	+	0.0971374i
$574$	10.3442	−	5.97221i	0.431758	−	0.249275i
$575$	−4.11003	+	27.8609i	−0.171400	+	1.16188i
$576$	−1.49484	+	2.58913i	−0.0622849	+	0.107881i
$577$	5.46012	−	9.45720i	0.227308	−	0.393709i	−0.729702	−	0.683766i	$-0.760341\pi$
$577$	5.46012	−	9.45720i	0.227308	−	0.393709i	0.957009	+	0.290057i	$0.0936743\pi$
$578$	−14.3154			−0.595441
$579$	1.62242	−	0.936705i	0.0674255	−	0.0389281i
$580$	−5.62714	+	16.1627i	−0.233654	+	0.671120i
$581$	18.1223			0.751839
$582$		−	0.900748i		−	0.0373372i
$583$	2.92754	+	1.69021i	0.121246	+	0.0700015i
$584$			9.63987i			0.398901i
$585$	20.7405	−	17.9053i	0.857514	−	0.740294i
$586$			1.18811i			0.0490803i
$587$	1.97715	+	3.42453i	0.0816058	+	0.141345i	0.903940	−	0.427660i	$-0.140662\pi$
$587$	1.97715	+	3.42453i	0.0816058	+	0.141345i	−0.822334	+	0.569005i	$0.807328\pi$
$588$	0.170326	−	0.0983379i	0.00702414	−	0.00405539i
$589$	2.65735	+	4.60266i	0.109494	+	0.189649i
$590$	2.40107	−	6.89653i	0.0988504	−	0.283926i
$591$	−1.94276			−0.0799144
$592$	−5.99911	+	1.00535i	−0.246562	+	0.0413197i
$593$		−	39.0638i		−	1.60416i	−0.597217	−	0.802079i	$-0.703727\pi$
$593$		−	39.0638i		−	1.60416i	0.597217	−	0.802079i	$-0.296273\pi$
$594$	1.76645	+	1.01986i	0.0724785	+	0.0418455i
$595$	−5.38799	−	6.24113i	−0.220886	−	0.255861i
$596$	5.74701	+	9.95411i	0.235407	+	0.407736i
$597$	−0.393925	−	0.682299i	−0.0161223	−	0.0279246i
$598$	23.0858			0.944047
$599$	−2.35815	−	4.08444i	−0.0963514	−	0.166886i	0.813820	−	0.581116i	$-0.197384\pi$
$599$	−2.35815	−	4.08444i	−0.0963514	−	0.166886i	−0.910172	+	0.414231i	$0.864051\pi$
$600$	−0.187108	−	0.472382i	−0.00763865	−	0.0192849i
$601$	−13.2064	+	22.8742i	−0.538700	+	0.933056i	0.460274	+	0.887777i	$0.347751\pi$
$601$	−13.2064	+	22.8742i	−0.538700	+	0.933056i	−0.998974	+	0.0452794i	$0.985582\pi$
$602$			7.39093i			0.301232i
$603$			44.7278i			1.82146i
$604$	−4.37838	+	7.58358i	−0.178154	+	0.308571i
$605$	−0.390107	+	0.336781i	−0.0158601	+	0.0136921i
$606$			1.59655i			0.0648554i
$607$	5.89939	−	10.2181i	0.239449	−	0.414738i	−0.721107	−	0.692823i	$-0.756367\pi$
$607$	5.89939	−	10.2181i	0.239449	−	0.414738i	0.960556	+	0.278086i	$0.0896999\pi$
$608$	4.13898	+	2.38964i	0.167858	+	0.0969126i
$609$	1.51580	+	0.875150i	0.0614235	+	0.0354629i
$610$	−7.50110	−	8.68884i	−0.303711	−	0.351801i
$611$	12.7229	−	7.34555i	0.514712	−	0.297169i
$612$	−2.44926	+	4.24225i	−0.0990057	+	0.171483i
$613$	14.4502	+	8.34283i	0.583639	+	0.336964i	0.762578	−	0.646896i	$-0.223933\pi$
$613$	14.4502	+	8.34283i	0.583639	+	0.336964i	−0.178939	+	0.983860i	$0.557267\pi$
$614$	−12.2976	−	7.10004i	−0.496292	−	0.286534i
$615$	1.18463	−	0.226068i	0.0477688	−	0.00911595i
$616$	−6.53131	+	3.77085i	−0.263154	+	0.151932i
$617$	8.48355	+	4.89798i	0.341535	+	0.197185i	0.660950	−	0.750430i	$-0.270153\pi$
$617$	8.48355	+	4.89798i	0.341535	+	0.197185i	−0.319416	+	0.947615i	$0.603487\pi$
$618$			1.53496i			0.0617450i
$619$	−23.5005			−0.944563			−0.472282	−	0.881448i	$-0.656569\pi$
$619$	−23.5005			−0.944563			−0.472282	+	0.881448i	$0.656569\pi$
$620$	0.817581	−	2.34832i	0.0328348	−	0.0943107i
$621$		−	3.42825i		−	0.137571i
$622$	6.44777	−	3.72262i	0.258532	−	0.149263i
$623$	10.8084			0.433028
$624$	−0.360698	+	0.208249i	−0.0144395	+	0.00833664i
$625$	−23.9351	−	7.21889i	−0.957403	−	0.288755i
$626$	−16.8822	−	29.2408i	−0.674748	−	1.16870i
$627$	0.813768	−	1.40949i	0.0324988	−	0.0562895i
$628$			7.51811i			0.300005i
$629$	−9.82943	+	1.64725i	−0.391925	+	0.0656803i
$630$	14.7779	−	2.82013i	0.588764	−	0.112357i
$631$	10.8619	+	6.27112i	0.432406	+	0.249649i	0.700371	−	0.713779i	$-0.253018\pi$
$631$	10.8619	+	6.27112i	0.432406	+	0.249649i	−0.267965	+	0.963429i	$0.586351\pi$
$632$	−3.11955	+	1.80107i	−0.124089	+	0.0716428i
$633$	−1.35842	+	0.784285i	−0.0539924	+	0.0311725i
$634$	−17.0296	+	9.83203i	−0.676331	+	0.390480i
$635$	23.5223	−	4.48888i	0.933454	−	0.178136i
$636$	0.0512521	+	0.0887713i	0.00203228	+	0.00352001i
$637$	−7.93279			−0.314309
$638$	22.2128	+	12.8246i	0.879412	+	0.507729i
$639$	−9.01030			−0.356442
$640$	−0.419156	−	2.19643i	−0.0165686	−	0.0868216i
$641$	10.6638	−	18.4702i	0.421194	−	0.729530i	−0.574862	−	0.818250i	$-0.694944\pi$
$641$	10.6638	−	18.4702i	0.421194	−	0.729530i	0.996057	+	0.0887201i	$0.0282777\pi$
$642$	0.664740	+	1.15136i	0.0262352	+	0.0454407i
$643$	−34.7722			−1.37128			−0.685641	−	0.727940i	$-0.740478\pi$
$643$	−34.7722			−1.37128			−0.685641	+	0.727940i	$0.740478\pi$
$644$	10.9774	+	6.33782i	0.432571	+	0.249745i
$645$	−0.245365	+	0.704756i	−0.00966124	+	0.0277497i
$646$	6.78164	+	3.91538i	0.266820	+	0.154049i
$647$	−7.41831	−	12.8489i	−0.291644	−	0.505142i	0.682555	−	0.730834i	$-0.260869\pi$
$647$	−7.41831	−	12.8489i	−0.291644	−	0.505142i	−0.974199	+	0.225693i	$0.927536\pi$
$648$	−4.45359	−	7.71384i	−0.174953	−	0.303028i
$649$	−9.47806	−	5.47216i	−0.372046	−	0.214801i
$650$	−2.99081	+	20.2740i	−0.117309	+	0.795212i
$651$	−0.220235	−	0.127153i	−0.00863169	−	0.00498351i
$652$	3.38955			0.132745
$653$	−15.8795	−	27.5041i	−0.621412	−	1.07632i	−0.989223	−	0.146417i	$-0.953226\pi$
$653$	−15.8795	−	27.5041i	−0.621412	−	1.07632i	0.367811	−	0.929901i	$-0.380107\pi$
$654$	0.364247	−	0.630895i	0.0142432	−	0.0246699i
$655$	−2.46439	+	0.470292i	−0.0962916	+	0.0183758i
$656$	5.30756			0.207225
$657$	−24.9589	−	14.4100i	−0.973739	−	0.562189i
$658$	8.06642			0.314462
$659$	−2.16069	−	3.74243i	−0.0841686	−	0.145784i	0.820868	−	0.571118i	$-0.193490\pi$
$659$	−2.16069	−	3.74243i	−0.0841686	−	0.145784i	−0.905037	+	0.425334i	$0.860157\pi$
$660$	−0.747973	+	0.142739i	−0.0291148	+	0.00555612i
$661$	6.67436	−	3.85345i	0.259603	−	0.149882i	−0.364551	−	0.931184i	$-0.618777\pi$
$661$	6.67436	−	3.85345i	0.259603	−	0.149882i	0.624153	+	0.781302i	$0.285444\pi$
$662$	−29.6384	+	17.1118i	−1.15193	+	0.665068i
$663$	−0.590998	+	0.341213i	−0.0229525	+	0.0132516i
$664$	6.97386	+	4.02636i	0.270638	+	0.156253i
$665$	−4.50825	−	23.6238i	−0.174823	−	0.916093i
$666$	6.36469	−	17.0353i	0.246627	−	0.660105i
$667$		−	43.1095i		−	1.66921i
$668$	−9.86808	+	17.0920i	−0.381807	+	0.661310i
$669$	−0.743800	−	1.28830i	−0.0287570	−	0.0498085i
$670$	−21.8609	−	25.3224i	−0.844559	−	0.978288i
$671$	−14.8984	+	8.60162i	−0.575148	+	0.332062i
$672$	−0.228686			−0.00882175
$673$	31.8340	−	18.3793i	1.22711	−	0.708472i	0.260685	−	0.965424i	$-0.416052\pi$
$673$	31.8340	−	18.3793i	1.22711	−	0.708472i	0.966424	+	0.256952i	$0.0827183\pi$
$674$			0.660450i			0.0254396i
$675$	3.01070	+	0.444137i	0.115882	+	0.0170949i
$676$	3.79920			0.146123
$677$			30.1563i			1.15900i	0.814972	+	0.579501i	$0.196752\pi$
$677$			30.1563i			1.15900i	−0.814972	+	0.579501i	$0.803248\pi$
$678$	0.941847	+	0.543775i	0.0361714	+	0.0208836i
$679$	−17.2757	+	9.97412i	−0.662980	+	0.382771i
$680$	−0.686780	−	3.59881i	−0.0263368	−	0.138008i
$681$	2.03631	+	1.17567i	0.0780317	+	0.0450517i
$682$	−3.22735	−	1.86331i	−0.123582	−	0.0713498i
$683$	−8.45595	+	14.6461i	−0.323558	+	0.560419i	−0.981219	−	0.192895i	$-0.938212\pi$
$683$	−8.45595	+	14.6461i	−0.323558	+	0.560419i	0.657661	+	0.753314i	$0.271546\pi$
$684$	−12.3742	+	7.14424i	−0.473139	+	0.273167i
$685$	−31.6081	−	36.6130i	−1.20768	−	1.39891i
$686$	−17.4148	−	10.0544i	−0.664899	−	0.383879i
$687$	−1.58261	−	0.913722i	−0.0603804	−	0.0348607i
$688$	−1.64210	+	2.84419i	−0.0626043	+	0.108434i
$689$		−	4.13444i		−	0.157510i
$690$	0.836340	+	0.968768i	0.0318389	+	0.0368804i
$691$	19.7039	−	34.1282i	0.749573	−	1.29830i	−0.198454	−	0.980110i	$-0.563592\pi$
$691$	19.7039	−	34.1282i	0.749573	−	1.29830i	0.948027	−	0.318189i	$-0.103075\pi$
$692$			12.4892i			0.474768i
$693$		−	22.5472i		−	0.856499i
$694$	−11.2497	+	19.4850i	−0.427031	+	0.739640i
$695$	−6.85896	−	35.9418i	−0.260175	−	1.36335i
$696$	0.388877	+	0.673555i	0.0147403	+	0.0255310i
$697$	8.69635			0.329398
$698$	7.95733	+	13.7825i	0.301189	+	0.521675i
$699$	0.648866	+	1.12387i	0.0245424	+	0.0425086i
$700$	−6.98805	+	8.81935i	−0.264124	+	0.333340i
$701$	−19.6847	−	11.3650i	−0.743481	−	0.429249i	0.0798528	−	0.996807i	$-0.474555\pi$
$701$	−19.6847	−	11.3650i	−0.743481	−	0.429249i	−0.823333	+	0.567558i	$0.807888\pi$
$702$		−	2.49469i		−	0.0941560i
$703$	−27.2326	−	10.1746i	−1.02710	−	0.383741i
$704$	−3.35119			−0.126303
$705$	0.769167	+	0.267790i	0.0289685	+	0.0100856i
$706$	18.1091	+	31.3658i	0.681544	+	1.18047i
$707$	30.6206	−	17.6788i	1.15161	−	0.664881i
$708$	−0.165931	−	0.287402i	−0.00623609	−	0.0108012i
$709$			41.9565i			1.57571i	0.615860	+	0.787855i	$0.288809\pi$
$709$			41.9565i			1.57571i	−0.615860	+	0.787855i	$0.711191\pi$
$710$	5.10113	−	4.40382i	0.191442	−	0.165272i
$711$		−	10.7692i		−	0.403878i
$712$	4.15930	+	2.40137i	0.155876	+	0.0899952i
$713$			6.26348i			0.234569i
$714$	−0.374698			−0.0140227
$715$	29.0058	+	10.0985i	1.08475	+	0.377664i
$716$	19.0661	−	11.0078i	0.712532	−	0.411381i
$717$	−0.0443190			−0.00165512
$718$	−13.8238	+	23.9436i	−0.515901	+	0.893567i
$719$	2.48642	−	4.30661i	0.0927278	−	0.160609i	−0.815930	−	0.578150i	$-0.803775\pi$
$719$	2.48642	−	4.30661i	0.0927278	−	0.160609i	0.908658	+	0.417541i	$0.137108\pi$
$720$	6.31342	+	2.19806i	0.235287	+	0.0819167i
$721$	29.4393	−	16.9968i	1.09638	−	0.632994i
$722$	1.92075	+	3.32683i	0.0714828	+	0.123812i
$723$	−0.277879	+	0.481301i	−0.0103344	+	0.0178998i
$724$	3.03685	−	5.25998i	0.112864	−	0.195486i
$725$	37.8589	+	5.58493i	1.40604	+	0.207419i
$726$			0.0234208i			0.000869228i
$727$	−15.1011	−	26.1558i	−0.560068	−	0.970066i	−0.997490	−	0.0708095i	$-0.977442\pi$
$727$	−15.1011	−	26.1558i	−0.560068	−	0.970066i	0.437422	−	0.899256i	$-0.355892\pi$
$728$	7.98814	+	4.61195i	0.296060	+	0.170930i
$729$	26.4440			0.979407
$730$	21.1733	−	4.04061i	0.783659	−	0.149550i
$731$	−2.69055	+	4.66016i	−0.0995135	+	0.172362i
$732$	−0.521651			−0.0192808
$733$	34.8879	−	20.1425i	1.28861	−	0.743981i	0.310206	−	0.950669i	$-0.399602\pi$
$733$	34.8879	−	20.1425i	1.28861	−	0.743981i	0.978407	+	0.206689i	$0.0662687\pi$
$734$		−	10.0793i		−	0.372033i
$735$	−0.287386	−	0.332891i	−0.0106004	−	0.0122789i
$736$	2.81624	+	4.87787i	0.103808	+	0.179801i
$737$	−43.4193	+	25.0682i	−1.59937	+	0.923398i
$738$	−7.93394	+	13.7420i	−0.292052	+	0.505849i
$739$	49.7539			1.83023			0.915113	−	0.403198i	$-0.132101\pi$
$739$	49.7539			1.83023			0.915113	+	0.403198i	$0.132101\pi$
$740$	4.72275	+	12.7552i	0.173612	+	0.468891i
$741$	−1.99056			−0.0731251
$742$	1.13505	−	1.96596i	0.0416688	−	0.0721725i
$743$	−21.5964	+	12.4687i	−0.792294	+	0.457431i	−0.840770	−	0.541393i	$-0.817897\pi$
$743$	−21.5964	+	12.4687i	−0.792294	+	0.457431i	0.0484753	+	0.998824i	$0.484564\pi$
$744$	−0.0565009	−	0.0978624i	−0.00207142	−	0.00358781i
$745$	19.4546	−	16.7952i	0.712762	−	0.615330i
$746$		−	17.9731i		−	0.658043i
$747$	−20.8496	+	12.0375i	−0.762846	+	0.440429i
$748$	−5.49087			−0.200766
$749$	14.7215	−	25.4985i	0.537914	−	0.931694i
$750$	−0.959126	+	0.608971i	−0.0350223	+	0.0222365i
$751$	−2.78747			−0.101716			−0.0508581	−	0.998706i	$-0.516196\pi$
$751$	−2.78747			−0.101716			−0.0508581	+	0.998706i	$0.516196\pi$
$752$	3.10414	+	1.79217i	0.113196	+	0.0653539i
$753$	−1.15692	−	2.00384i	−0.0421605	−	0.0730241i
$754$		−	31.3702i		−	1.14244i
$755$	18.4920	+	6.43811i	0.672994	+	0.234307i
$756$	0.684877	−	1.18624i	0.0249087	−	0.0431432i
$757$	−21.0518	+	36.4628i	−0.765142	+	1.32526i	0.175030	+	0.984563i	$0.443998\pi$
$757$	−21.0518	+	36.4628i	−0.765142	+	1.32526i	−0.940172	+	0.340701i	$0.889336\pi$
$758$	14.2034	+	24.6011i	0.515892	+	0.893551i
$759$	1.66111	−	0.959043i	0.0602945	−	0.0348111i
$760$	3.51380	−	10.0926i	0.127459	−	0.366097i
$761$	17.5778	−	30.4456i	0.637195	−	1.10365i	−0.348851	−	0.937178i	$-0.613428\pi$
$761$	17.5778	−	30.4456i	0.637195	−	1.10365i	0.986046	−	0.166476i	$-0.0532387\pi$
$762$	0.544128	−	0.942458i	0.0197117	−	0.0341416i
$763$	−16.1335			−0.584071
$764$	22.8820	−	13.2109i	0.827843	−	0.477955i
$765$	10.3444	+	3.60148i	0.374004	+	0.130212i
$766$	−16.7053			−0.603587
$767$			13.3855i			0.483322i
$768$	−0.0880035	−	0.0508088i	−0.00317555	−	0.00183341i
$769$			45.0857i			1.62583i	0.582381	+	0.812916i	$0.302121\pi$
$769$			45.0857i			1.62583i	−0.582381	+	0.812916i	$0.697879\pi$
$770$	11.0201	+	12.7650i	0.397135	+	0.460018i
$771$		−	1.29060i		−	0.0464797i
$772$	−9.21793	−	15.9659i	−0.331761	−	0.574626i
$773$	7.40864	−	4.27738i	0.266470	−	0.153847i	−0.360812	−	0.932638i	$-0.617500\pi$
$773$	7.40864	−	4.27738i	0.266470	−	0.153847i	0.627283	+	0.778792i	$0.284167\pi$
$774$	−4.90933	−	8.50321i	−0.176462	−	0.305642i
$775$	−5.50061	−	0.811449i	−0.197588	−	0.0291481i
$776$	−8.86409			−0.318202
$777$	1.37191	−	0.229910i	0.0492171	−	0.00824798i
$778$		−	25.6698i		−	0.920305i
$779$	21.9679	+	12.6832i	0.787080	+	0.454421i
$780$	0.608594	+	0.704960i	0.0217912	+	0.0252416i
$781$	−5.04992	−	8.74672i	−0.180700	−	0.312982i
$782$	4.61436	+	7.99231i	0.165009	+	0.285804i
$783$	−4.65849			−0.166481
$784$	−0.967725	−	1.67615i	−0.0345616	−	0.0598624i
$785$	16.5130	−	3.15126i	0.589375	−	0.112473i
$786$	−0.0570073	+	0.0987396i	−0.00203338	+	0.00352193i
$787$			4.22589i			0.150637i	0.997160	+	0.0753183i	$0.0239973\pi$
$787$			4.22589i			0.150637i	−0.997160	+	0.0753183i	$0.976003\pi$
$788$			19.1183i			0.681062i
$789$	−0.144309	+	0.249951i	−0.00513754	+	0.00889848i
$790$	5.26351	+	6.09695i	0.187267	+	0.216920i
$791$		−	24.0852i		−	0.856372i
$792$	5.00948	−	8.67668i	0.178004	−	0.308312i
$793$	18.2216	+	10.5202i	0.647067	+	0.373584i
$794$	−21.3504	−	12.3266i	−0.757696	−	0.437456i
$795$	0.173497	−	0.149781i	0.00615332	−	0.00531218i
$796$	−6.71437	+	3.87654i	−0.237985	+	0.137400i
$797$	−0.764938	+	1.32491i	−0.0270955	+	0.0469307i	−0.879255	−	0.476351i	$-0.841959\pi$
$797$	−0.764938	+	1.32491i	−0.0270955	+	0.0469307i	0.852160	+	0.523282i	$0.175292\pi$
$798$	−0.946526	−	0.546477i	−0.0335067	−	0.0193451i
$799$	5.08608	+	2.93645i	0.179932	+	0.103884i
$800$	−4.64862	+	1.84129i	−0.164353	+	0.0650996i
$801$	−12.4349	+	7.17931i	−0.439367	+	0.253669i
$802$	−4.62722	−	2.67153i	−0.163393	−	0.0943348i
$803$		−	32.3050i		−	1.14002i
$804$	−1.52028			−0.0536160
$805$	9.31934	−	26.7677i	0.328463	−	0.943438i
$806$			4.55785i			0.160543i
$807$	0.554387	−	0.320075i	0.0195153	−	0.0112672i
$808$	15.7113			0.552723
$809$	2.36448	−	1.36513i	0.0831308	−	0.0479956i	−0.457858	−	0.889025i	$-0.651383\pi$
$809$	2.36448	−	1.36513i	0.0831308	−	0.0479956i	0.540989	+	0.841030i	$0.318050\pi$
$810$	−15.0762	+	13.0153i	−0.529722	+	0.457311i
$811$	7.65057	+	13.2512i	0.268648	+	0.465312i	0.968513	−	0.248963i	$-0.0800898\pi$
$811$	7.65057	+	13.2512i	0.268648	+	0.465312i	−0.699865	+	0.714275i	$0.746757\pi$
$812$	8.61219	−	14.9167i	0.302229	−	0.523475i
$813$			0.0683273i			0.00239634i
$814$	20.1041	−	3.36913i	0.704650	−	0.118088i
$815$	−1.42075	−	7.44491i	−0.0497667	−	0.260784i
$816$	−0.144192	−	0.0832494i	−0.00504774	−	0.00291431i
$817$	−13.5932	+	7.84804i	−0.475566	+	0.274568i
$818$	22.0532	−	12.7324i	0.771072	−	0.445179i
$819$	−23.8819	+	13.7882i	−0.834502	+	0.481800i
$820$	−2.22469	−	11.6577i	−0.0776897	−	0.407104i
$821$	5.05599	+	8.75724i	0.176455	+	0.305630i	0.940664	−	0.339339i	$-0.110204\pi$
$821$	5.05599	+	8.75724i	0.176455	+	0.305630i	−0.764209	+	0.644969i	$0.776870\pi$
$822$	−2.19813			−0.0766686
$823$	11.6477	+	6.72480i	0.406013	+	0.234412i	0.689075	−	0.724690i	$-0.258017\pi$
$823$	11.6477	+	6.72480i	0.406013	+	0.234412i	−0.283062	+	0.959102i	$0.591350\pi$
$824$	15.1052			0.526215
$825$	0.627034	+	1.58304i	0.0218305	+	0.0551144i
$826$	−3.67477	+	6.36489i	−0.127862	+	0.221463i
$827$	−0.0492539	−	0.0853103i	−0.00171273	−	0.00296653i	0.865168	−	0.501483i	$-0.167212\pi$
$827$	−0.0492539	−	0.0853103i	−0.00171273	−	0.00296653i	−0.866880	+	0.498516i	$0.833879\pi$
$828$	−16.8393			−0.585206
$829$	−4.93962	−	2.85189i	−0.171560	−	0.0990503i	0.411761	−	0.911292i	$-0.364914\pi$
$829$	−4.93962	−	2.85189i	−0.171560	−	0.0990503i	−0.583321	+	0.812241i	$0.698247\pi$
$830$	5.92048	−	17.0053i	0.205503	−	0.590261i
$831$	1.34219	+	0.774912i	0.0465599	+	0.0268814i
$832$	2.04934	+	3.54956i	0.0710481	+	0.123059i
$833$	−1.58560	−	2.74634i	−0.0549378	−	0.0951551i
$834$	−1.44007	−	0.831422i	−0.0498654	−	0.0287898i
$835$	41.6777	+	14.5103i	1.44232	+	0.502151i
$836$	−13.8705	−	8.00814i	−0.479721	−	0.276967i
$837$	0.676843			0.0233951
$838$	0.279488	+	0.484087i	0.00965474	+	0.0167225i
$839$	−19.6097	+	33.9650i	−0.677002	+	1.17260i	0.298877	+	0.954292i	$0.403388\pi$
$839$	−19.6097	+	33.9650i	−0.677002	+	1.17260i	−0.975879	+	0.218311i	$0.929945\pi$
$840$	0.0958551	+	0.502293i	0.00330731	+	0.0173308i
$841$	−29.5796			−1.01998
$842$	−17.7223	−	10.2320i	−0.610752	−	0.352618i
$843$	2.50197			0.0861723
$844$	7.71800	+	13.3680i	0.265665	+	0.460145i
$845$	−1.59246	−	8.34469i	−0.0547822	−	0.287066i
$846$	−9.28036	+	5.35802i	−0.319065	+	0.184212i
$847$	0.449194	−	0.259342i	0.0154345	−	0.00891111i
$848$	0.873581	−	0.504362i	0.0299989	−	0.0173199i
$849$	1.65963	+	0.958189i	0.0569584	+	0.0328850i
$850$	−7.61668	+	3.01693i	−0.261250	+	0.103480i
$851$	−21.7989	−	26.4316i	−0.747257	−	0.906062i
$852$		−	0.306256i		−	0.0104922i
$853$	20.7092	−	35.8693i	0.709068	−	1.22814i	−0.256135	−	0.966641i	$-0.582449\pi$
$853$	20.7092	−	35.8693i	0.709068	−	1.22814i	0.965203	−	0.261501i	$-0.0842175\pi$
$854$	5.77632	+	10.0049i	0.197662	+	0.342360i
$855$	20.8785	+	24.1845i	0.714031	+	0.827092i
$856$	11.3304	−	6.54158i	0.387264	−	0.223587i
$857$	10.8579			0.370898			0.185449	−	0.982654i	$-0.440626\pi$
$857$	10.8579			0.370898			0.185449	+	0.982654i	$0.440626\pi$
$858$	1.20877	−	0.697883i	0.0412667	−	0.0238253i
$859$		−	43.4697i		−	1.48317i	−0.670861	−	0.741583i	$-0.734075\pi$
$859$		−	43.4697i		−	1.48317i	0.670861	−	0.741583i	$-0.265925\pi$
$860$	6.93537	+	2.41459i	0.236494	+	0.0823369i
$861$	−1.21376			−0.0413650
$862$			13.8765i			0.472636i
$863$	−19.4209	−	11.2127i	−0.661095	−	0.381684i	0.131599	−	0.991303i	$-0.457989\pi$
$863$	−19.4209	−	11.2127i	−0.661095	−	0.381684i	−0.792694	+	0.609619i	$0.791322\pi$
$864$	0.527112	−	0.304328i	0.0179327	−	0.0103535i
$865$	27.4317	−	5.23492i	0.932704	−	0.177993i
$866$	12.6470	+	7.30173i	0.429762	+	0.248123i
$867$	1.25980	+	0.727347i	0.0427851	+	0.0247020i
$868$	−1.25129	+	2.16729i	−0.0424714	+	0.0735626i
$869$	10.4542	−	6.03574i	0.354635	−	0.204748i
$870$	1.31642	−	1.13647i	0.0446307	−	0.0385298i
$871$	53.1041	+	30.6597i	1.79936	+	1.03886i
$872$	−6.20852	−	3.58449i	−0.210247	−	0.121386i
$873$	13.2504	−	22.9503i	0.448457	−	0.776750i
$874$			26.9192i			0.910555i
$875$	22.3002	+	11.6521i	0.753883	+	0.393913i
$876$	0.489790	−	0.848342i	0.0165485	−	0.0286628i
$877$			17.3357i			0.585386i	0.956206	+	0.292693i	$0.0945514\pi$
$877$			17.3357i			0.585386i	−0.956206	+	0.292693i	$0.905449\pi$
$878$			7.69516i			0.259699i
$879$	0.0603664	−	0.104558i	0.00203611	−	0.00352664i
$880$	1.40467	+	7.36066i	0.0473515	+	0.248128i
$881$	4.62049	+	8.00293i	0.155668	+	0.269626i	0.933302	−	0.359092i	$-0.116914\pi$
$881$	4.62049	+	8.00293i	0.155668	+	0.269626i	−0.777634	+	0.628717i	$0.783580\pi$
$882$	5.78636			0.194837
$883$	−12.9574	−	22.4429i	−0.436052	−	0.755264i	0.561329	−	0.827593i	$-0.310290\pi$
$883$	−12.9574	−	22.4429i	−0.436052	−	0.755264i	−0.997381	+	0.0723291i	$0.976957\pi$
$884$	3.35781	+	5.81590i	0.112935	+	0.195610i
$885$	−0.561707	+	0.484923i	−0.0188816	+	0.0163005i
$886$	−2.92652	−	1.68963i	−0.0983183	−	0.0567641i
$887$			36.3577i			1.22077i	0.792104	+	0.610386i	$0.208986\pi$
$887$			36.3577i			1.22077i	−0.792104	+	0.610386i	$0.791014\pi$
$888$	0.579023	+	0.216333i	0.0194307	+	0.00725966i
$889$	−24.1009			−0.808317
$890$	3.53105	−	10.1422i	0.118361	−	0.339966i
$891$	14.9248	+	25.8505i	0.500000	+	0.866026i
$892$	−12.6779	+	7.31959i	−0.424488	+	0.245078i
$893$	8.56530	+	14.8355i	0.286627	+	0.496452i
$894$		−	1.16800i		−	0.0390636i
$895$	−32.1695	−	37.2633i	−1.07531	−	1.24558i
$896$			2.25046i			0.0751824i
$897$	−2.03163	−	1.17296i	−0.0678340	−	0.0391640i
$898$			22.8835i			0.763632i
$899$	8.51116			0.283863
$900$	2.18157	−	14.7883i	0.0727190	−	0.492944i
$901$	1.43135	−	0.826389i	0.0476851	−	0.0275310i
$902$	−17.7866			−0.592230
$903$	0.375525	−	0.650428i	0.0124967	−	0.0216449i
$904$	5.35119	−	9.26853i	0.177978	−	0.308267i
$905$	−12.8261	−	4.46548i	−0.426354	−	0.148438i
$906$	0.770625	−	0.444921i	0.0256023	−	0.0147815i
$907$	−2.43179	−	4.21198i	−0.0807463	−	0.139857i	0.822824	−	0.568296i	$-0.192397\pi$
$907$	−2.43179	−	4.21198i	−0.0807463	−	0.139857i	−0.903571	+	0.428439i	$0.859064\pi$
$908$	11.5695	−	20.0390i	0.383948	−	0.665017i
$909$	−23.4859	+	40.6787i	−0.778978	+	1.34923i
$910$	6.78156	−	19.4785i	0.224807	−	0.645706i
$911$		−	52.5164i		−	1.73995i	−0.493098	−	0.869974i	$-0.664136\pi$
$911$		−	52.5164i		−	1.73995i	0.493098	−	0.869974i	$-0.335864\pi$
$912$	−0.242829	−	0.420593i	−0.00804089	−	0.0139272i
$913$	−23.3707	−	13.4931i	−0.773458	−	0.446556i
$914$	−21.5416			−0.712532
$915$	0.218653	+	1.14577i	0.00722845	+	0.0378780i
$916$	−8.99176	+	15.5742i	−0.297096	+	0.514586i
$917$	2.52500			0.0833830
$918$	0.863664	−	0.498637i	0.0285052	−	0.0164575i
$919$			7.75847i			0.255928i	0.991779	+	0.127964i	$0.0408443\pi$
$919$			7.75847i			0.255928i	−0.991779	+	0.127964i	$0.959156\pi$
$920$	9.53346	−	8.23027i	0.314309	−	0.271344i
$921$	0.721489	+	1.24966i	0.0237739	+	0.0411776i
$922$	17.2165	−	9.93992i	0.566994	−	0.327354i
$923$	−6.17632	+	10.6977i	−0.203296	+	0.352119i
$924$	0.766370			0.0252117
$925$	26.0364	−	15.7196i	0.856071	−	0.516858i
$926$	23.9708			0.787731
$927$	−22.5798	+	39.1094i	−0.741619	+	1.28452i
$928$	6.62832	−	3.82686i	0.217585	−	0.125623i
$929$	−8.40161	−	14.5520i	−0.275648	−	0.477436i	0.694651	−	0.719347i	$-0.255559\pi$
$929$	−8.40161	−	14.5520i	−0.275648	−	0.477436i	−0.970298	+	0.241911i	$0.922226\pi$
$930$	−0.191265	+	0.165120i	−0.00627183	+	0.00541449i
$931$		−	9.25005i		−	0.303158i
$932$	11.0598	−	6.38537i	0.362275	−	0.209160i
$933$	−0.756568			−0.0247689
$934$	−0.190913	+	0.330672i	−0.00624687	+	0.0108199i
$935$	2.30153	+	12.0603i	0.0752681	+	0.394414i
$936$	−12.2537			−0.400526
$937$	24.2840	+	14.0204i	0.793323	+	0.458025i	0.841131	−	0.540831i	$-0.181890\pi$
$937$	24.2840	+	14.0204i	0.793323	+	0.458025i	−0.0478083	+	0.998857i	$0.515224\pi$
$938$	16.8343	+	29.1578i	0.549658	+	0.952035i
$939$			3.43106i			0.111968i
$940$	2.63527	−	7.56922i	0.0859530	−	0.246881i
$941$	14.8474	−	25.7165i	0.484012	−	0.838334i	−0.515819	−	0.856698i	$-0.672512\pi$
$941$	14.8474	−	25.7165i	0.484012	−	0.838334i	0.999831	+	0.0183636i	$0.00584564\pi$
$942$	0.381987	−	0.661620i	0.0124458	−	0.0215567i
$943$	14.9474	+	25.8896i	0.486753	+	0.843081i
$944$	−2.82827	+	1.63290i	−0.0920522	+	0.0531464i
$945$	−2.89257	−	1.00707i	−0.0940953	−	0.0327598i
$946$	5.50298	−	9.53144i	0.178917	−	0.309894i
$947$	6.99859	−	12.1219i	0.227424	−	0.393909i	−0.729620	−	0.683853i	$-0.760303\pi$
$947$	6.99859	−	12.1219i	0.227424	−	0.393909i	0.957044	+	0.289943i	$0.0936365\pi$
$948$	0.366042			0.0118885
$949$	−34.2173	+	19.7554i	−1.11074	+	0.641287i
$950$	−23.6405	−	3.48744i	−0.767000	−	0.113148i
$951$	1.99822			0.0647966
$952$			3.68733i			0.119507i
$953$	11.0450	+	6.37686i	0.357784	+	0.206567i	0.668108	−	0.744064i	$-0.267104\pi$
$953$	11.0450	+	6.37686i	0.357784	+	0.206567i	−0.310324	+	0.950631i	$0.600438\pi$
$954$			3.01576i			0.0976388i
$955$	−38.6081	−	44.7213i	−1.24933	−	1.44715i
$956$			0.436134i			0.0141056i
$957$	−1.30320	−	2.25721i	−0.0421265	−	0.0729652i
$958$	24.6845	−	14.2516i	0.797520	−	0.460448i
$959$	24.3402	+	42.1585i	0.785987	+	1.36137i
$960$	−0.0747109	+	0.214590i	−0.00241128	+	0.00692587i
$961$	29.7634			0.960109
$962$	−15.8628	−	19.2339i	−0.511437	−	0.620126i
$963$			39.1144i			1.26044i
$964$	4.73639	+	2.73456i	0.152549	+	0.0880741i
$965$	−31.2043	+	26.9388i	−1.00450	+	0.867189i
$966$	−0.644035	−	1.11550i	−0.0207215	−	0.0358907i
$967$	−19.9159	−	34.4954i	−0.640453	−	1.10930i	−0.985332	−	0.170650i	$-0.945413\pi$
$967$	−19.9159	−	34.4954i	−0.640453	−	1.10930i	0.344878	−	0.938647i	$-0.387920\pi$
$968$	0.230480			0.00740790
$969$	−0.397872	−	0.689135i	−0.0127815	−	0.0221382i
$970$	3.71543	+	19.4694i	0.119295	+	0.625123i
$971$	−27.9783	+	48.4598i	−0.897866	+	1.55515i	−0.0676495	+	0.997709i	$0.521550\pi$
$971$	−27.9783	+	48.4598i	−0.897866	+	1.55515i	−0.830217	+	0.557441i	$0.811783\pi$
$972$			2.73110i			0.0875999i
$973$			36.8259i			1.18058i
$974$	−5.80967	+	10.0626i	−0.186154	+	0.322428i
$975$	1.29330	−	1.63222i	0.0414188	−	0.0522730i
$976$			5.13347i			0.164318i
$977$	19.4233	−	33.6421i	0.621406	−	1.07631i	−0.367818	−	0.929898i	$-0.619895\pi$
$977$	19.4233	−	33.6421i	0.621406	−	1.07631i	0.989224	−	0.146409i	$-0.0467714\pi$
$978$	−0.298292	−	0.172219i	−0.00953834	−	0.00550696i
$979$	−13.9386	−	8.04745i	−0.445479	−	0.257198i
$980$	−3.27592	+	2.82811i	−0.104645	+	0.0903406i
$981$	18.5614	−	10.7165i	0.592621	−	0.342150i
$982$	13.2426	−	22.9368i	0.422588	−	0.731943i
$983$	−45.5913	−	26.3221i	−1.45414	−	0.839545i	−0.455423	−	0.890275i	$-0.650512\pi$
$983$	−45.5913	−	26.3221i	−1.45414	−	0.839545i	−0.998712	+	0.0507300i	$0.983845\pi$
$984$	−0.467084	−	0.269671i	−0.0148901	−	0.00859679i
$985$	41.9921	−	8.01355i	1.33798	−	0.255333i
$986$	10.8604	−	6.27025i	0.345865	−	0.199685i
$987$	−0.709873	−	0.409845i	−0.0225955	−	0.0130455i
$988$			19.5887i			0.623201i
$989$	−18.4982			−0.588207
$990$	−21.1575	−	7.36610i	−0.672429	−	0.234110i
$991$		−	5.54551i		−	0.176159i	−0.996113	−	0.0880794i	$-0.971927\pi$
$991$		−	5.54551i		−	0.176159i	0.996113	−	0.0880794i	$-0.0280729\pi$
$992$	−0.963045	+	0.556014i	−0.0305767	+	0.0176535i
$993$	3.47771			0.110362
$994$	−5.87377	+	3.39122i	−0.186305	+	0.107563i
$995$	11.3289	+	13.1228i	0.359151	+	0.416020i
$996$	−0.409149	−	0.708667i	−0.0129644	−	0.0224550i
$997$	−2.48179	+	4.29859i	−0.0785992	+	0.136138i	−0.902646	−	0.430384i	$-0.858378\pi$
$997$	−2.48179	+	4.29859i	−0.0785992	+	0.136138i	0.824047	+	0.566522i	$0.191711\pi$
$998$		−	35.7734i		−	1.13239i
$999$	−2.85624	+	2.35563i	−0.0903675	+	0.0745289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.249.4	yes	16
5.4	even	2		370.2.m.d.249.5	yes	16
37.11	even	6		370.2.m.d.159.5	yes	16
185.159	even	6	inner	370.2.m.c.159.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.4	✓	16	185.159	even	6	inner
370.2.m.c.249.4	yes	16	1.1	even	1	trivial
370.2.m.d.159.5	yes	16	37.11	even	6
370.2.m.d.249.5	yes	16	5.4	even	2

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.0880035 - 0.0508088i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.69259 + 1.46122i) q^{5} +0.101618i q^{6} +(1.94895 - 1.12523i) q^{7} +1.00000 q^{8} +(-1.49484 + 2.58913i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.0880035 - 0.0508088i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.69259 + 1.46122i) q^{5} +0.101618i q^{6} +(1.94895 - 1.12523i) q^{7} +1.00000 q^{8} +(-1.49484 + 2.58913i) q^{9} +(-0.419156 - 2.19643i) q^{10} -3.35119 q^{11} +(-0.0880035 - 0.0508088i) q^{12} +(2.04934 + 3.54956i) q^{13} +2.25046i q^{14} +(-0.0747109 + 0.214590i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.819242 + 1.41897i) q^{17} +(-1.49484 - 2.58913i) q^{18} +(-4.13898 + 2.38964i) q^{19} +(2.11174 + 0.735216i) q^{20} +(0.114343 - 0.198048i) q^{21} +(1.67560 - 2.90222i) q^{22} -5.63248 q^{23} +(0.0880035 - 0.0508088i) q^{24} +(0.729701 - 4.94647i) q^{25} -4.09868 q^{26} +0.608657i q^{27} +(-1.94895 - 1.12523i) q^{28} +7.65373i q^{29} +(-0.148485 - 0.171997i) q^{30} -1.11203i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.294916 + 0.170270i) q^{33} +(-0.819242 - 1.41897i) q^{34} +(-1.65457 + 4.75238i) q^{35} +2.98967 q^{36} +(3.87021 + 4.69270i) q^{37} -4.77928i q^{38} +(0.360698 + 0.208249i) q^{39} +(-1.69259 + 1.46122i) q^{40} +(-2.65378 - 4.59648i) q^{41} +(0.114343 + 0.198048i) q^{42} +3.28419 q^{43} +(1.67560 + 2.90222i) q^{44} +(-1.25314 - 6.56661i) q^{45} +(2.81624 - 4.87787i) q^{46} -3.58435i q^{47} +0.101618i q^{48} +(-0.967725 + 1.67615i) q^{49} +(3.91892 + 3.10517i) q^{50} +0.166499i q^{51} +(2.04934 - 3.54956i) q^{52} +(-0.873581 - 0.504362i) q^{53} +(-0.527112 - 0.304328i) q^{54} +(5.67218 - 4.89681i) q^{55} +(1.94895 - 1.12523i) q^{56} +(-0.242829 + 0.420593i) q^{57} +(-6.62832 - 3.82686i) q^{58} +(2.82827 + 1.63290i) q^{59} +(0.223196 - 0.0425936i) q^{60} +(4.44572 - 2.56673i) q^{61} +(0.963045 + 0.556014i) q^{62} +6.72813i q^{63} +1.00000 q^{64} +(-8.65536 - 3.01342i) q^{65} -0.340540i q^{66} +(12.9564 - 7.48037i) q^{67} +1.63848 q^{68} +(-0.495678 + 0.286180i) q^{69} +(-3.28840 - 3.80909i) q^{70} +(1.50690 + 2.61003i) q^{71} +(-1.49484 + 2.58913i) q^{72} +9.63987i q^{73} +(-5.99911 + 1.00535i) q^{74} +(-0.187108 - 0.472382i) q^{75} +(4.13898 + 2.38964i) q^{76} +(-6.53131 + 3.77085i) q^{77} +(-0.360698 + 0.208249i) q^{78} +(-3.11955 + 1.80107i) q^{79} +(-0.419156 - 2.19643i) q^{80} +(-4.45359 - 7.71384i) q^{81} +5.30756 q^{82} +(6.97386 + 4.02636i) q^{83} -0.228686 q^{84} +(-0.686780 - 3.59881i) q^{85} +(-1.64210 + 2.84419i) q^{86} +(0.388877 + 0.673555i) q^{87} -3.35119 q^{88} +(4.15930 + 2.40137i) q^{89} +(6.31342 + 2.19806i) q^{90} +(7.98814 + 4.61195i) q^{91} +(2.81624 + 4.87787i) q^{92} +(-0.0565009 - 0.0978624i) q^{93} +(3.10414 + 1.79217i) q^{94} +(3.51380 - 10.0926i) q^{95} +(-0.0880035 - 0.0508088i) q^{96} -8.86409 q^{97} +(-0.967725 - 1.67615i) q^{98} +(5.00948 - 8.67668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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