LMFDB - Embedded newform 370.2.m.d.159.5

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			159.5
Root			$0.101618i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.d.249.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.0880035 - 0.0508088i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.11174 - 0.735216i) q^{5} -0.101618i q^{6} +(-1.94895 - 1.12523i) q^{7} -1.00000 q^{8} +(-1.49484 - 2.58913i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.0880035 - 0.0508088i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.11174 - 0.735216i) 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} +(0.148485 + 0.171997i) 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} +(1.69259 - 1.46122i) q^{20} +(0.114343 + 0.198048i) q^{21} +(-1.67560 - 2.90222i) q^{22} +5.63248 q^{23} +(0.0880035 + 0.0508088i) q^{24} +(3.91892 + 3.10517i) q^{25} -4.09868 q^{26} +0.608657i q^{27} +(1.94895 - 1.12523i) q^{28} -7.65373i q^{29} +(-0.0747109 + 0.214590i) q^{30} +1.11203i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.294916 + 0.170270i) q^{33} +(-0.819242 + 1.41897i) q^{34} +(3.28840 + 3.80909i) q^{35} +2.98967 q^{36} +(-3.87021 + 4.69270i) q^{37} -4.77928i q^{38} +(0.360698 - 0.208249i) q^{39} +(2.11174 + 0.735216i) 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} +(-0.729701 + 4.94647i) q^{50} -0.166499i q^{51} +(-2.04934 - 3.54956i) q^{52} +(0.873581 - 0.504362i) q^{53} +(-0.527112 + 0.304328i) q^{54} +(7.07685 + 2.46385i) 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} +(6.93738 - 5.98906i) q^{65} +0.340540i q^{66} +(-12.9564 - 7.48037i) q^{67} -1.63848 q^{68} +(-0.495678 - 0.286180i) q^{69} +(-1.65457 + 4.75238i) 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} +(-5.06028 + 4.36856i) 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} +(6.98355 + 8.08934i) 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} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	$ 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 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^{20} - 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} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 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} - 35 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} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 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} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 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 - 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^20 - 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 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 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 - 35 * 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 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * 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 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.342672\pi$
$3$	−0.0880035	−	0.0508088i	−0.0508088	−	0.0293345i	−0.525189	+	0.850985i	$0.676005\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.11174	−	0.735216i	−0.944400	−	0.328798i
$5$	−2.11174	−	0.735216i	−0.944400	−	0.328798i
$6$		−	0.101618i		−	0.0414852i
$7$	−1.94895	−	1.12523i	−0.736635	−	0.425296i	0.0842099	−	0.996448i	$-0.473163\pi$
$7$	−1.94895	−	1.12523i	−0.736635	−	0.425296i	−0.820844	+	0.571152i	$0.806497\pi$
$8$	−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	0.428341	+	0.903617i	$0.359098\pi$
$13$	−2.04934	+	3.54956i	−0.568385	+	0.984472i	−0.996726	+	0.0808546i	$0.974235\pi$
$14$		−	2.25046i		−	0.601460i
$15$	0.148485	+	0.171997i	0.0383387	+	0.0444094i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.819242	+	1.41897i	0.198695	+	0.344150i	0.948106	−	0.317956i	$-0.102996\pi$
$17$	0.819242	+	1.41897i	0.198695	+	0.344150i	−0.749410	+	0.662106i	$0.769663\pi$
$18$	1.49484	−	2.58913i	0.352336	−	0.610265i
$19$	−4.13898	−	2.38964i	−0.949546	−	0.548221i	−0.0566062	−	0.998397i	$-0.518028\pi$
$19$	−4.13898	−	2.38964i	−0.949546	−	0.548221i	−0.892940	+	0.450176i	$0.851361\pi$
$20$	1.69259	−	1.46122i	0.378474	−	0.326738i
$21$	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	$-0.300220\pi$
$23$	5.63248			1.17445			0.587227	+	0.809422i	$0.300220\pi$
$24$	0.0880035	+	0.0508088i	0.0179636	+	0.0103713i
$25$	3.91892	+	3.10517i	0.783783	+	0.621035i
$26$	−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	$-0.748410\pi$
$29$		−	7.65373i		−	1.42126i	0.703565	−	0.710631i	$-0.251590\pi$
$30$	−0.0747109	+	0.214590i	−0.0136403	+	0.0391787i
$31$			1.11203i			0.199726i	0.995001	+	0.0998631i	$0.0318405\pi$
$31$			1.11203i			0.199726i	−0.995001	+	0.0998631i	$0.968160\pi$
$32$	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
$35$	3.28840	+	3.80909i	0.555841	+	0.643854i
$36$	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
$40$	2.11174	+	0.735216i	0.333896	+	0.116248i
$41$	−2.65378	+	4.59648i	−0.414451	+	0.717850i	−0.995371	−	0.0961110i	$-0.969360\pi$
$41$	−2.65378	+	4.59648i	−0.414451	+	0.717850i	0.580920	+	0.813961i	$0.302693\pi$
$42$	−0.114343	+	0.198048i	−0.0176435	+	0.0305595i
$43$	−3.28419			−0.500835			−0.250417	−	0.968138i	$-0.580568\pi$
$43$	−3.28419			−0.500835			−0.250417	+	0.968138i	$0.580568\pi$
$44$	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
$50$	−0.729701	+	4.94647i	−0.103195	+	0.699536i
$51$		−	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	$-0.644597\pi$
$53$	0.873581	−	0.504362i	0.119996	−	0.0692795i	0.558796	+	0.829305i	$0.311263\pi$
$54$	−0.527112	+	0.304328i	−0.0717309	+	0.0414138i
$55$	7.07685	+	2.46385i	0.954243	+	0.332225i
$56$	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	−0.304467	−	0.952523i	$-0.598478\pi$
$59$	2.82827	−	1.63290i	0.368209	−	0.212585i	0.672676	+	0.739937i	$0.265145\pi$
$60$	−0.223196	+	0.0425936i	−0.0288145	+	0.00549881i
$61$	4.44572	+	2.56673i	0.569216	+	0.328637i	0.756836	−	0.653605i	$-0.226744\pi$
$61$	4.44572	+	2.56673i	0.569216	+	0.328637i	−0.187620	+	0.982242i	$0.560077\pi$
$62$	−0.963045	+	0.556014i	−0.122307	+	0.0706139i
$63$			6.72813i			0.847664i
$64$	1.00000			0.125000
$65$	6.93738	−	5.98906i	0.860476	−	0.742851i
$66$			0.340540i			0.0419176i
$67$	−12.9564	−	7.48037i	−1.58287	−	0.913873i	−0.994437	−	0.105330i	$-0.966410\pi$
$67$	−12.9564	−	7.48037i	−1.58287	−	0.913873i	−0.588438	−	0.808543i	$-0.700257\pi$
$68$	−1.63848			−0.198695
$69$	−0.495678	−	0.286180i	−0.0596726	−	0.0344520i
$70$	−1.65457	+	4.75238i	−0.197759	+	0.568018i
$71$	1.50690	−	2.61003i	0.178837	−	0.309754i	−0.762646	−	0.646816i	$-0.776100\pi$
$71$	1.50690	−	2.61003i	0.178837	−	0.309754i	0.941482	+	0.337062i	$0.109433\pi$
$72$	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	0.314139	−	0.949377i	$-0.398284\pi$
$79$	−3.11955	−	1.80107i	−0.350977	−	0.202637i	−0.665115	+	0.746741i	$0.731618\pi$
$80$	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	$-0.812380\pi$
$83$	−6.97386	+	4.02636i	−0.765480	+	0.441950i	0.0657796	+	0.997834i	$0.479047\pi$
$84$	−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	−0.263088	−	0.964772i	$-0.584741\pi$
$89$	4.15930	−	2.40137i	0.440884	−	0.254545i	0.703973	+	0.710227i	$0.251408\pi$
$90$	−5.06028	+	4.36856i	−0.533401	+	0.460486i
$91$	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
$95$	6.98355	+	8.08934i	0.716497	+	0.829949i
$96$	−0.0880035	+	0.0508088i	−0.00898182	+	0.00518565i
$97$	8.86409			0.900012			0.450006	−	0.893026i	$-0.351422\pi$
$97$	8.86409			0.900012			0.450006	+	0.893026i	$0.351422\pi$
$98$	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	$-0.767160\pi$
$103$	−15.1052			−1.48836			−0.744180	+	0.667979i	$0.767160\pi$
$104$	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	$-0.551263\pi$
$107$	−11.3304	−	6.54158i	−1.09535	−	0.632399i	−0.934995	+	0.354661i	$0.884596\pi$
$108$	−0.527112	−	0.304328i	−0.0507214	−	0.0292840i
$109$	−6.20852	+	3.58449i	−0.594668	+	0.343332i	−0.766941	−	0.641718i	$-0.778222\pi$
$109$	−6.20852	+	3.58449i	−0.594668	+	0.343332i	0.172273	+	0.985049i	$0.444889\pi$
$110$	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	−0.999992	−	0.00392776i	$-0.998750\pi$
$113$	−5.35119	−	9.26853i	−0.503398	−	0.871910i	0.496595	−	0.867983i	$-0.334584\pi$
$114$	−0.242829	+	0.420593i	−0.0227431	+	0.0393921i
$115$	−11.8944	−	4.14109i	−1.10915	−	0.386159i
$116$	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
$120$	−0.148485	−	0.171997i	−0.0135548	−	0.0157011i
$121$	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	$-0.509061\pi$
$127$	9.27455	−	5.35466i	0.822983	−	0.475149i	0.851444	+	0.524445i	$0.175727\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.289020	+	0.166866i	0.0254468	+	0.0146917i
$130$	8.65536	+	3.01342i	0.759126	+	0.264294i
$131$	0.971678	−	0.560998i	0.0848959	−	0.0490147i	−0.456951	−	0.889492i	$-0.651059\pi$
$131$	0.971678	−	0.560998i	0.0848959	−	0.0490147i	0.541847	+	0.840477i	$0.317725\pi$
$132$	−0.294916	+	0.170270i	−0.0256692	+	0.0148201i
$133$	5.37778	+	9.31458i	0.466312	+	0.807677i
$134$		−	14.9607i		−	1.29241i
$135$	0.447494	−	1.28533i	0.0385141	−	0.110623i
$136$	−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	−0.970524	−	0.241003i	$-0.922524\pi$
$139$	−8.18187	−	14.1714i	−0.693977	−	1.20200i	0.276547	−	0.961000i	$-0.410810\pi$
$140$	−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
$145$	−5.62714	+	16.1627i	−0.467309	+	1.34224i
$146$	−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	$0.656040\pi$
$150$	0.315540	−	0.398231i	0.0257638	−	0.0325154i
$151$	−4.37838	+	7.58358i	−0.356308	+	0.617143i	−0.987341	−	0.158613i	$-0.949298\pi$
$151$	−4.37838	+	7.58358i	−0.356308	+	0.617143i	0.631033	+	0.775756i	$0.282631\pi$
$152$	4.13898	+	2.38964i	0.335715	+	0.193825i
$153$	2.44926	−	4.24225i	0.198011	−	0.342966i
$154$			7.54171i			0.607728i
$155$	0.817581	−	2.34832i	0.0656697	−	0.188621i
$156$			0.416499i			0.0333466i
$157$	6.51088	−	3.75906i	0.519625	−	0.300005i	−0.217156	−	0.976137i	$-0.569678\pi$
$157$	6.51088	−	3.75906i	0.519625	−	0.300005i	0.736781	+	0.676131i	$0.236345\pi$
$158$		−	3.60215i		−	0.286571i
$159$	−0.102504			−0.00812912
$160$	−1.69259	+	1.46122i	−0.133811	+	0.115519i
$161$	−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	$-0.124288\pi$
$163$	1.69478	+	2.93544i	0.132745	+	0.229921i	−0.791989	+	0.610536i	$0.790954\pi$
$164$	−2.65378	−	4.59648i	−0.207225	−	0.358925i
$165$	−0.497602	−	0.576394i	−0.0387383	−	0.0448722i
$166$	−6.97386	−	4.02636i	−0.541276	−	0.312506i
$167$	9.86808	−	17.0920i	0.763615	−	1.32262i	−0.177361	−	0.984146i	$-0.556756\pi$
$167$	9.86808	−	17.0920i	0.763615	−	1.32262i	0.940976	−	0.338474i	$-0.109911\pi$
$168$	−0.114343	−	0.198048i	−0.00882175	−	0.0152797i
$169$	−1.89960	−	3.29021i	−0.146123	−	0.253093i
$170$	2.77328	−	2.39418i	0.212700	−	0.183625i
$171$			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	$-0.509199\pi$
$173$	10.8160	−	6.24460i	0.822322	−	0.474768i	0.851217	+	0.524814i	$0.175865\pi$
$174$	−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	$-0.692432\pi$
$179$		−	22.0156i		−	1.64552i	0.568387	−	0.822762i	$-0.307568\pi$
$180$	−6.31342	−	2.19806i	−0.470575	−	0.163833i
$181$	3.03685	−	5.25998i	0.225728	−	0.390972i	−0.730810	−	0.682581i	$-0.760857\pi$
$181$	3.03685	−	5.25998i	0.225728	−	0.390972i	0.956537	+	0.291609i	$0.0941908\pi$
$182$	7.98814	+	4.61195i	0.592120	+	0.341861i
$183$	−0.260826	−	0.451763i	−0.0192808	−	0.0333953i
$184$	−5.63248			−0.415232
$185$	11.6230	−	7.06434i	0.854543	−	0.519380i
$186$	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
$190$	−3.51380	+	10.0926i	−0.254918	+	0.732195i
$191$		−	26.4219i		−	1.91182i	−0.293659	−	0.955910i	$-0.594873\pi$
$191$		−	26.4219i		−	1.91182i	0.293659	−	0.955910i	$-0.405127\pi$
$192$	−0.0880035	−	0.0508088i	−0.00635110	−	0.00366681i
$193$	−18.4359			−1.32704			−0.663521	−	0.748157i	$-0.730939\pi$
$193$	−18.4359			−1.32704			−0.663521	+	0.748157i	$0.730939\pi$
$194$	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	$-0.428185\pi$
$197$	16.5569	−	9.55916i	1.17963	−	0.681062i	0.955930	+	0.293595i	$0.0948518\pi$
$198$	−5.00948	+	8.67668i	−0.356009	+	0.616625i
$199$			7.75309i			0.549602i	0.961501	+	0.274801i	$0.0886120\pi$
$199$			7.75309i			0.549602i	−0.961501	+	0.274801i	$0.911388\pi$
$200$	−3.91892	−	3.10517i	−0.277109	−	0.219569i
$201$	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
$205$	8.98351	−	7.75549i	0.627435	−	0.541667i
$206$	−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
$210$	0.387071	−	0.334159i	0.0267104	−	0.0230592i
$211$	−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
$215$	6.93537	+	2.41459i	0.472988	+	0.164674i
$216$		−	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
$220$	−5.67218	+	4.89681i	−0.382418	+	0.330143i
$221$	−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
$225$	2.18157	−	14.7883i	0.145438	−	0.985888i
$226$	5.35119	−	9.26853i	0.355956	−	0.616534i
$227$	−11.5695	+	20.0390i	−0.767896	+	1.33003i	0.170806	+	0.985305i	$0.445363\pi$
$227$	−11.5695	+	20.0390i	−0.767896	+	1.33003i	−0.938702	+	0.344730i	$0.887971\pi$
$228$	−0.485659			−0.0321636
$229$	−8.99176	+	15.5742i	−0.594192	+	1.02917i	0.399468	+	0.916747i	$0.369195\pi$
$229$	−8.99176	+	15.5742i	−0.594192	+	1.02917i	−0.993660	+	0.112424i	$0.964139\pi$
$230$	−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
$235$	−2.63527	+	7.56922i	−0.171906	+	0.493762i
$236$			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	−0.512166	−	0.858886i	$-0.671157\pi$
$239$	−0.377703	+	0.218067i	−0.0244316	+	0.0141056i	0.487734	+	0.872992i	$0.337823\pi$
$240$	0.0747109	−	0.214590i	0.00482257	−	0.0138517i
$241$	−4.73639	−	2.73456i	−0.305098	−	0.176148i	0.339633	−	0.940558i	$-0.389697\pi$
$241$	−4.73639	−	2.73456i	−0.305098	−	0.176148i	−0.644731	+	0.764410i	$0.723030\pi$
$242$	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
$250$	5.17766	−	9.90918i	0.327464	−	0.626711i
$251$			22.7700i			1.43723i	0.695407	+	0.718616i	$0.255224\pi$
$251$			22.7700i			1.43723i	−0.695407	+	0.718616i	$0.744776\pi$
$252$	−5.82673	−	3.36406i	−0.367049	−	0.211916i
$253$	−18.8755			−1.18669
$254$	9.27455	+	5.35466i	0.581937	+	0.335981i
$255$	−0.122413	+	0.351603i	−0.00766577	+	0.0220182i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.35026	−	10.9990i	−0.396118	−	0.686097i	0.597125	−	0.802148i	$-0.296310\pi$
$257$	−6.35026	−	10.9990i	−0.396118	−	0.686097i	−0.993243	+	0.116051i	$0.962976\pi$
$258$			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	$-0.305424\pi$
$263$	2.45972	+	1.42012i	0.151673	+	0.0875683i	−0.422243	+	0.906483i	$0.638757\pi$
$264$	−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	0.855633	−	0.517582i	$-0.173168\pi$
$271$	−0.336198	−	0.582312i	−0.0204226	−	0.0353729i	−0.876056	+	0.482209i	$0.839834\pi$
$272$	0.819242	−	1.41897i	0.0496738	−	0.0860376i
$273$	−0.937312			−0.0567287
$274$	−18.7333	+	10.8157i	−1.13172	+	0.653399i
$275$	−13.1330	−	10.4060i	−0.791952	−	0.627507i
$276$	0.495678	−	0.286180i	0.0298363	−	0.0172260i
$277$	−7.62576	+	13.2082i	−0.458187	+	0.793604i	−0.998865	−	0.0476258i	$-0.984834\pi$
$277$	−7.62576	+	13.2082i	−0.458187	+	0.793604i	0.540678	+	0.841230i	$0.318168\pi$
$278$	8.18187	−	14.1714i	0.490716	−	0.849945i
$279$	2.87919	−	1.66230i	0.172373	−	0.0995194i
$280$	−3.28840	−	3.80909i	−0.196519	−	0.227637i
$281$	21.3227	−	12.3107i	1.27201	−	0.734394i	0.296642	−	0.954989i	$-0.404133\pi$
$281$	21.3227	−	12.3107i	1.27201	−	0.734394i	0.975366	+	0.220594i	$0.0707997\pi$
$282$	−0.364233			−0.0216898
$283$	−9.42935	+	16.3321i	−0.560517	+	0.970844i	0.436934	+	0.899493i	$0.356064\pi$
$283$	−9.42935	+	16.3321i	−0.560517	+	0.970844i	−0.997451	+	0.0713504i	$0.977269\pi$
$284$	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	$-0.344383\pi$
$293$	−1.02893	−	0.594054i	−0.0601109	−	0.0347050i	−0.529754	+	0.848151i	$0.677716\pi$
$294$	−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
$300$	0.502648	+	0.0741505i	0.0290204	+	0.00428108i
$301$	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
$305$	−7.50110	−	8.68884i	−0.429512	−	0.497522i
$306$	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	−0.671543	−	0.740966i	$-0.734368\pi$
$311$	−6.44777	+	3.72262i	−0.365619	+	0.211090i	0.305924	+	0.952056i	$0.401035\pi$
$312$	−0.360698	+	0.208249i	−0.0204205	+	0.0117898i
$313$	16.8822	+	29.2408i	0.954237	+	1.65279i	0.736104	+	0.676869i	$0.236664\pi$
$313$	16.8822	+	29.2408i	0.954237	+	1.65279i	0.218134	+	0.975919i	$0.430003\pi$
$314$	6.51088	+	3.75906i	0.367430	+	0.212136i
$315$	4.94663	−	14.2081i	0.278711	−	0.800534i
$316$	3.11955	−	1.80107i	0.175488	−	0.101318i
$317$	−17.0296	+	9.83203i	−0.956477	+	0.552222i	−0.895087	−	0.445892i	$-0.852887\pi$
$317$	−17.0296	+	9.83203i	−0.956477	+	0.552222i	−0.0613897	+	0.998114i	$0.519553\pi$
$318$	−0.0512521	−	0.0887713i	−0.00287408	−	0.00497805i
$319$			25.6491i			1.43607i
$320$	−2.11174	−	0.735216i	−0.118050	−	0.0410998i
$321$	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
$330$	0.250370	−	0.719133i	0.0137824	−	0.0395870i
$331$	29.6384	−	17.1118i	1.62908	−	0.940548i	0.644707	−	0.764430i	$-0.276979\pi$
$331$	29.6384	−	17.1118i	1.62908	−	0.940548i	0.984369	−	0.176118i	$-0.0563541\pi$
$332$		−	8.05272i		−	0.441950i
$333$	17.9354	+	3.00568i	0.982852	+	0.164710i
$334$	19.7362			1.07991
$335$	21.8609	+	25.3224i	1.19439	+	1.38351i
$336$	0.114343	−	0.198048i	0.00623792	−	0.0108044i
$337$	−0.571966	−	0.330225i	−0.0311570	−	0.0179885i	0.484341	−	0.874880i	$-0.339060\pi$
$337$	−0.571966	−	0.330225i	−0.0311570	−	0.0179885i	−0.515498	+	0.856891i	$0.672393\pi$
$338$	1.89960	−	3.29021i	0.103325	−	0.178964i
$339$			1.08755i			0.0590677i
$340$	3.46005	+	1.20464i	0.187648	+	0.0653307i
$341$		−	3.72662i		−	0.201808i
$342$	−12.3742	+	7.14424i	−0.669119	+	0.386316i
$343$			20.1088i			1.08577i
$344$	3.28419			0.177072
$345$	0.836340	+	0.968768i	0.0450271	+	0.0521567i
$346$	10.8160	+	6.24460i	0.581470	+	0.335712i
$347$	−22.4993			−1.20783			−0.603913	−	0.797050i	$-0.706393\pi$
$347$	−22.4993			−1.20783			−0.603913	+	0.797050i	$0.706393\pi$
$348$	−0.388877	−	0.673555i	−0.0208460	−	0.0361063i
$349$	7.95733	+	13.7825i	0.425946	+	0.737760i	0.996508	−	0.0834942i	$-0.0266080\pi$
$349$	7.95733	+	13.7825i	0.425946	+	0.737760i	−0.570562	+	0.821254i	$0.693275\pi$
$350$	6.98805	−	8.81935i	0.373527	−	0.471414i
$351$	−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	−0.712678	−	0.701492i	$-0.752518\pi$
$353$	−18.1091	−	31.3658i	−0.963848	−	1.66943i	−0.251171	−	0.967943i	$-0.580816\pi$
$354$	−0.165931	−	0.287402i	−0.00881916	−	0.0152752i
$355$	−5.10113	+	4.40382i	−0.270740	+	0.233731i
$356$			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
$365$	7.08738	−	20.3569i	0.370971	−	1.06553i
$366$	0.260826	−	0.451763i	0.0136336	−	0.0236140i
$367$	8.72891	+	5.03964i	0.455646	+	0.263067i	0.710212	−	0.703988i	$-0.248599\pi$
$367$	8.72891	+	5.03964i	0.455646	+	0.263067i	−0.254566	+	0.967055i	$0.581933\pi$
$368$	−2.81624	−	4.87787i	−0.146807	−	0.254277i
$369$	15.8679			0.826048
$370$	11.9294	+	6.53368i	0.620181	+	0.339670i
$371$	−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	$-0.179277\pi$
$373$	15.5652	+	8.98657i	0.805935	+	0.465307i	−0.0396070	+	0.999215i	$0.512611\pi$
$374$	2.74543	−	4.75523i	0.141963	−	0.245887i
$375$	0.0478215	+	1.13511i	0.00246949	+	0.0586170i
$376$			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	0.957060	+	0.289888i	$0.0936182\pi$
$379$	14.2034	+	24.6011i	0.729581	+	1.26367i	−0.227479	+	0.973783i	$0.573048\pi$
$380$	−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	$-0.973693\pi$
$383$	−8.35265	+	14.4672i	−0.426800	+	0.739240i	0.569786	+	0.821793i	$0.307026\pi$
$384$		−	0.101618i		−	0.00518565i
$385$	−11.0201	−	12.7650i	−0.561634	−	0.650564i
$386$	−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	−0.183925	−	0.982940i	$-0.558880\pi$
$389$	−22.2307	−	12.8349i	−1.12714	−	0.650754i	−0.943214	+	0.332186i	$0.892214\pi$
$390$	−0.608594	−	0.704960i	−0.0308174	−	0.0356970i
$391$	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
$395$	5.26351	+	6.09695i	0.264836	+	0.306771i
$396$	−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
$400$	0.729701	−	4.94647i	0.0364851	−	0.247323i
$401$		−	5.34305i		−	0.266819i	−0.991061	−	0.133410i	$-0.957407\pi$
$401$		−	5.34305i		−	0.266819i	0.991061	−	0.133410i	$-0.0425926\pi$
$402$	−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
$405$	15.0762	−	13.0153i	0.749141	−	0.646735i
$406$	−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	−0.933699	−	0.358059i	$-0.883439\pi$
$409$	−22.0532	+	12.7324i	−1.09046	+	0.629578i	−0.156761	+	0.987637i	$0.550105\pi$
$410$	11.2082	+	3.90220i	0.553534	+	0.192716i
$411$	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	0.872772	−	0.488129i	$-0.162320\pi$
$419$	0.279488	+	0.484087i	0.0136539	+	0.0236492i	−0.859118	+	0.511778i	$0.828987\pi$
$420$	0.482926	+	0.168134i	0.0235644	+	0.00820408i
$421$		−	20.4640i		−	0.997354i	−0.866788	−	0.498677i	$-0.833819\pi$
$421$		−	20.4640i		−	0.997354i	0.866788	−	0.498677i	$-0.166181\pi$
$422$	−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
$425$	−1.19560	+	8.10470i	−0.0579953	+	0.393136i
$426$	−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	0.760680	−	0.649127i	$-0.224866\pi$
$431$	12.0174	+	6.93826i	0.578859	+	0.334204i	−0.181821	+	0.983332i	$0.558199\pi$
$432$	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
$435$	1.31642	−	1.13647i	0.0631173	−	0.0544894i
$436$		−	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	0.650530	−	0.759481i	$-0.274547\pi$
$439$	6.66420	+	3.84758i	0.318065	+	0.183635i	−0.332465	+	0.943116i	$0.607880\pi$
$440$	−7.07685	−	2.46385i	−0.337376	−	0.117459i
$441$	−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	0.888470	−	0.458935i	$-0.151769\pi$
$449$	19.8177	+	11.4417i	0.935255	+	0.539969i	0.0467850	+	0.998905i	$0.485102\pi$
$450$	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	0.496154	+	0.868234i	$0.334745\pi$
$457$	−10.7708	+	18.6555i	−0.503836	+	0.872669i	−0.999990	+	0.00443501i	$0.998588\pi$
$458$	−17.9835			−0.840315
$459$	−0.863664	+	0.498637i	−0.0403124	+	0.0232744i
$460$	9.53346	−	8.23027i	0.444500	−	0.383738i
$461$	−17.2165	+	9.93992i	−0.801850	+	0.462948i	−0.844118	−	0.536158i	$-0.819875\pi$
$461$	−17.2165	+	9.93992i	−0.801850	+	0.462948i	0.0422676	+	0.999106i	$0.486542\pi$
$462$	0.383185	−	0.663696i	0.0178274	−	0.0308779i
$463$	11.9854	−	20.7594i	0.557010	−	0.964769i	−0.440734	−	0.897638i	$-0.645282\pi$
$463$	11.9854	−	20.7594i	0.557010	−	0.964769i	0.997744	−	0.0671318i	$-0.0213848\pi$
$464$	−6.62832	+	3.82686i	−0.307712	+	0.177658i
$465$	−0.191265	+	0.165120i	−0.00886971	+	0.00765725i
$466$	−11.0598	+	6.38537i	−0.512335	+	0.295797i
$467$	−0.381827			−0.0176688			−0.00883441	−	0.999961i	$-0.502812\pi$
$467$	−0.381827			−0.0176688			−0.00883441	+	0.999961i	$0.502812\pi$
$468$	−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	−0.943397	−	0.331666i	$-0.892389\pi$
$479$	−24.6845	+	14.2516i	−1.12786	+	0.651172i	−0.184467	+	0.982839i	$0.559056\pi$
$480$	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
$485$	−18.7187	−	6.51702i	−0.849971	−	0.295923i
$486$	2.36520	+	1.36555i	0.107288	+	0.0619425i
$487$	−11.6193			−0.526523			−0.263261	−	0.964725i	$-0.584798\pi$
$487$	−11.6193			−0.526523			−0.263261	+	0.964725i	$0.584798\pi$
$488$	−4.44572	−	2.56673i	−0.201248	−	0.116191i
$489$		−	0.344438i		−	0.0155760i
$490$	−3.27592	+	2.82811i	−0.147991	+	0.127761i
$491$	−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	−0.393922	−	0.919144i	$-0.628882\pi$
$499$	−30.9807	−	17.8867i	−1.38689	−	0.800718i	−0.992963	+	0.118425i	$0.962215\pi$
$500$	11.1704	−	0.470602i	0.499557	−	0.0210460i
$501$	−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	0.999536	+	0.0304514i	$0.00969447\pi$
$503$	11.8001	+	20.4383i	0.526140	+	0.911301i	−0.473396	+	0.880849i	$0.656972\pi$
$504$		−	6.72813i		−	0.299695i
$505$	−33.1783	−	11.5512i	−1.47641	−	0.514023i
$506$	−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	0.998485	−	0.0550252i	$-0.0175239\pi$
$509$	10.1883	+	17.6467i	0.451589	+	0.782176i	−0.546896	+	0.837201i	$0.684191\pi$
$510$	−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
$515$	31.8983	+	11.1056i	1.40561	+	0.489371i
$516$	−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
$520$	−6.93738	+	5.98906i	−0.304224	+	0.262638i
$521$	−10.7044	+	18.5405i	−0.468967	+	0.812275i	−0.999371	−	0.0354700i	$-0.988707\pi$
$521$	−10.7044	+	18.5405i	−0.468967	+	0.812275i	0.530403	+	0.847745i	$0.322041\pi$
$522$	−19.8165	−	11.4411i	−0.867346	−	0.500762i
$523$	22.2690	−	38.5711i	0.973756	−	1.68660i	0.289777	−	0.957094i	$-0.406419\pi$
$523$	22.2690	−	38.5711i	0.973756	−	1.68660i	0.683979	−	0.729501i	$-0.260248\pi$
$524$			1.12200i			0.0490147i
$525$	−0.166872	+	1.13119i	−0.00728291	+	0.0493691i
$526$			2.84024i			0.123840i
$527$	−1.57793	+	0.911020i	−0.0687358	+	0.0396846i
$528$		−	0.340540i		−	0.0148201i
$529$	8.72485			0.379341
$530$	−1.47396	−	1.70735i	−0.0640249	−	0.0741627i
$531$	−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
$535$	19.1173	+	22.1444i	0.826514	+	0.957386i
$536$	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
$540$	0.889378	+	1.03020i	0.0382727	+	0.0443329i
$541$		−	38.1217i		−	1.63898i	−0.573094	−	0.819490i	$-0.694257\pi$
$541$		−	38.1217i		−	1.63898i	0.573094	−	0.819490i	$-0.305743\pi$
$542$	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	$-0.852036\pi$
$547$	−41.8128			−1.78778			−0.893892	+	0.448282i	$0.852036\pi$
$548$	−18.7333	−	10.8157i	−0.800248	−	0.462023i
$549$		−	15.3474i		−	0.655011i
$550$	2.44537	−	16.5766i	0.104271	−	0.706827i
$551$	−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
$555$	−1.38180	+	0.0311328i	−0.0586541	+	0.00132151i
$556$	16.3637			0.693977
$557$	−14.6940	−	25.4507i	−0.622604	−	1.07838i	−0.988999	−	0.147922i	$-0.952742\pi$
$557$	−14.6940	−	25.4507i	−0.622604	−	1.07838i	0.366395	−	0.930459i	$-0.380592\pi$
$558$	2.87919	+	1.66230i	0.121886	+	0.0703708i
$559$	6.73043	−	11.6575i	0.284667	−	0.493058i
$560$	1.65457	−	4.75238i	0.0699184	−	0.200825i
$561$			0.557969i			0.0235575i
$562$	21.3227	+	12.3107i	0.899446	+	0.519295i
$563$	10.8601			0.457698			0.228849	−	0.973462i	$-0.426504\pi$
$563$	10.8601			0.457698			0.228849	+	0.973462i	$0.426504\pi$
$564$	−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	$-0.854505\pi$
$569$		−	21.0550i		−	0.882671i	0.897342	−	0.441336i	$-0.145495\pi$
$570$	0.822020	−	0.709652i	0.0344306	−	0.0297241i
$571$	−10.3193	−	17.8735i	−0.431848	−	0.747982i	0.565185	−	0.824964i	$-0.308805\pi$
$571$	−10.3193	−	17.8735i	−0.431848	−	0.747982i	−0.997032	+	0.0769821i	$0.975472\pi$
$572$	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
$575$	22.0732	+	17.4898i	0.920517	+	0.729376i
$576$	−1.49484	−	2.58913i	−0.0622849	−	0.107881i
$577$	−5.46012	−	9.45720i	−0.227308	−	0.393709i	0.729702	−	0.683766i	$-0.239659\pi$
$577$	−5.46012	−	9.45720i	−0.227308	−	0.393709i	−0.957009	+	0.290057i	$0.906326\pi$
$578$	14.3154			0.595441
$579$	1.62242	+	0.936705i	0.0674255	+	0.0389281i
$580$	−11.1837	−	12.9546i	−0.464380	−	0.537910i
$581$	18.1223			0.751839
$582$		−	0.900748i		−	0.0373372i
$583$	−2.92754	+	1.69021i	−0.121246	+	0.0700015i
$584$		−	9.63987i		−	0.398901i
$585$	−25.8767	−	9.00913i	−1.06987	−	0.372482i
$586$		−	1.18811i		−	0.0490803i
$587$	−1.97715	+	3.42453i	−0.0816058	+	0.141345i	−0.903940	−	0.427660i	$-0.859338\pi$
$587$	−1.97715	+	3.42453i	−0.0816058	+	0.141345i	0.822334	+	0.569005i	$0.192672\pi$
$588$	−0.170326	−	0.0983379i	−0.00702414	−	0.00405539i
$589$	2.65735	−	4.60266i	0.109494	−	0.189649i
$590$	−4.77204	−	5.52765i	−0.196462	−	0.227570i
$591$	−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
$595$	−2.71099	+	7.78670i	−0.111140	+	0.319224i
$596$	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	−0.910172	−	0.414231i	$-0.864051\pi$
$599$	−2.35815	+	4.08444i	−0.0963514	+	0.166886i	0.813820	+	0.581116i	$0.197384\pi$
$600$	0.187108	+	0.472382i	0.00763865	+	0.0192849i
$601$	−13.2064	−	22.8742i	−0.538700	−	0.933056i	−0.998974	−	0.0452794i	$-0.985582\pi$
$601$	−13.2064	−	22.8742i	−0.538700	−	0.933056i	0.460274	−	0.887777i	$-0.347751\pi$
$602$			7.39093i			0.301232i
$603$			44.7278i			1.82146i
$604$	−4.37838	−	7.58358i	−0.178154	−	0.308571i
$605$	−0.486714	−	0.169452i	−0.0197877	−	0.00688922i
$606$		−	1.59655i		−	0.0648554i
$607$	−5.89939	−	10.2181i	−0.239449	−	0.414738i	0.721107	−	0.692823i	$-0.243633\pi$
$607$	−5.89939	−	10.2181i	−0.239449	−	0.414738i	−0.960556	+	0.278086i	$0.910300\pi$
$608$	−4.13898	+	2.38964i	−0.167858	+	0.0969126i
$609$	1.51580	−	0.875150i	0.0614235	−	0.0354629i
$610$	3.77421	−	10.8406i	0.152813	−	0.438922i
$611$	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	$-0.776067\pi$
$613$	−14.4502	+	8.34283i	−0.583639	+	0.336964i	0.178939	+	0.983860i	$0.442733\pi$
$614$	−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	$-0.729847\pi$
$617$	−8.48355	+	4.89798i	−0.341535	+	0.197185i	0.319416	+	0.947615i	$0.396513\pi$
$618$			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	$0.656569\pi$
$620$	1.62491	+	1.88220i	0.0652581	+	0.0755912i
$621$			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
$625$	5.71580	+	24.3378i	0.228632	+	0.973513i
$626$	−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	−0.267965	−	0.963429i	$-0.586351\pi$
$631$	10.8619	−	6.27112i	0.432406	−	0.249649i	0.700371	+	0.713779i	$0.253018\pi$
$632$	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	0.996057	−	0.0887201i	$-0.0282777\pi$
$641$	10.6638	+	18.4702i	0.421194	+	0.729530i	−0.574862	+	0.818250i	$0.694944\pi$
$642$	−0.664740	+	1.15136i	−0.0262352	+	0.0454407i
$643$	34.7722			1.37128			0.685641	−	0.727940i	$-0.259522\pi$
$643$	34.7722			1.37128			0.685641	+	0.727940i	$0.259522\pi$
$644$	10.9774	−	6.33782i	0.432571	−	0.249745i
$645$	−0.487654	−	0.564870i	−0.0192014	−	0.0222418i
$646$	6.78164	−	3.91538i	0.266820	−	0.154049i
$647$	7.41831	−	12.8489i	0.291644	−	0.505142i	−0.682555	−	0.730834i	$-0.739131\pi$
$647$	7.41831	−	12.8489i	0.291644	−	0.505142i	0.974199	+	0.225693i	$0.0724645\pi$
$648$	4.45359	−	7.71384i	0.174953	−	0.303028i
$649$	−9.47806	+	5.47216i	−0.372046	+	0.214801i
$650$	−16.0624	−	12.7271i	−0.630019	−	0.499199i
$651$	−0.220235	+	0.127153i	−0.00863169	+	0.00498351i
$652$	−3.38955			−0.132745
$653$	15.8795	−	27.5041i	0.621412	−	1.07632i	−0.367811	−	0.929901i	$-0.619893\pi$
$653$	15.8795	−	27.5041i	0.621412	−	1.07632i	0.989223	−	0.146417i	$-0.0467741\pi$
$654$	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	−0.905037	−	0.425334i	$-0.860157\pi$
$659$	−2.16069	+	3.74243i	−0.0841686	+	0.145784i	0.820868	+	0.571118i	$0.193490\pi$
$660$	0.747973	−	0.142739i	0.0291148	−	0.00555612i
$661$	6.67436	+	3.85345i	0.259603	+	0.149882i	0.624153	−	0.781302i	$-0.285444\pi$
$661$	6.67436	+	3.85345i	0.259603	+	0.149882i	−0.364551	+	0.931184i	$0.618777\pi$
$662$	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
$670$	−10.9994	+	31.5933i	−0.424943	+	1.22055i
$671$	−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	$-0.583948\pi$
$673$	−31.8340	−	18.3793i	−1.22711	−	0.708472i	−0.966424	+	0.256952i	$0.917282\pi$
$674$		−	0.660450i		−	0.0254396i
$675$	−1.88998	+	2.38527i	−0.0727455	+	0.0918092i
$676$	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	$-0.0617876\pi$
$683$	8.45595	+	14.6461i	0.323558	+	0.560419i	−0.657661	+	0.753314i	$0.728454\pi$
$684$	−12.3742	−	7.14424i	−0.473139	−	0.273167i
$685$	15.9037	−	45.6799i	0.607650	−	1.74534i
$686$	−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
$690$	−0.420808	+	1.20868i	−0.0160199	+	0.0460135i
$691$	19.7039	+	34.1282i	0.749573	+	1.29830i	0.948027	+	0.318189i	$0.103075\pi$
$691$	19.7039	+	34.1282i	0.749573	+	1.29830i	−0.198454	+	0.980110i	$0.563592\pi$
$692$			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
$700$	11.1318	+	1.64216i	0.420743	+	0.0620678i
$701$	−19.6847	+	11.3650i	−0.743481	+	0.429249i	−0.823333	−	0.567558i	$-0.807888\pi$
$701$	−19.6847	+	11.3650i	−0.743481	+	0.429249i	0.0798528	+	0.996807i	$0.474555\pi$
$702$		−	2.49469i		−	0.0941560i
$703$	27.2326	−	10.1746i	1.02710	−	0.383741i
$704$	−3.35119			−0.126303
$705$	0.616496	−	0.532223i	0.0232186	−	0.0200447i
$706$	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	$-0.711191\pi$
$709$		−	41.9565i		−	1.57571i	0.615860	−	0.787855i	$-0.288809\pi$
$710$	−6.36439	−	2.21580i	−0.238851	−	0.0831575i
$711$			10.7692i			0.403878i
$712$	−4.15930	+	2.40137i	−0.155876	+	0.0899952i
$713$			6.26348i			0.234569i
$714$	−0.374698			−0.0140227
$715$	−23.2485	+	20.0705i	−0.869444	+	0.750593i
$716$	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	0.908658	−	0.417541i	$-0.137108\pi$
$719$	2.48642	+	4.30661i	0.0927278	+	0.160609i	−0.815930	+	0.578150i	$0.803775\pi$
$720$	5.06028	−	4.36856i	0.188586	−	0.162806i
$721$	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
$725$	23.7662	−	29.9943i	0.882653	−	1.11396i
$726$		−	0.0234208i		−	0.000869228i
$727$	15.1011	−	26.1558i	0.560068	−	0.970066i	−0.437422	−	0.899256i	$-0.644108\pi$
$727$	15.1011	−	26.1558i	0.560068	−	0.970066i	0.997490	−	0.0708095i	$-0.0225582\pi$
$728$	−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	$-0.600398\pi$
$733$	−34.8879	−	20.1425i	−1.28861	−	0.743981i	−0.978407	+	0.206689i	$0.933731\pi$
$734$			10.0793i			0.372033i
$735$	0.144599	−	0.415329i	0.00533362	−	0.0153196i
$736$	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	$0.132101\pi$
$740$	0.306372	+	13.5980i	0.0112625	+	0.499873i
$741$	−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	$-0.182103\pi$
$743$	21.5964	+	12.4687i	0.792294	+	0.457431i	−0.0484753	+	0.998824i	$0.515436\pi$
$744$	−0.0565009	+	0.0978624i	−0.00207142	+	0.00358781i
$745$	24.2724	+	8.45059i	0.889272	+	0.309605i
$746$			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
$755$	14.8216	−	12.7955i	0.539412	−	0.465676i
$756$	0.684877	+	1.18624i	0.0249087	+	0.0431432i
$757$	21.0518	+	36.4628i	0.765142	+	1.32526i	0.940172	+	0.340701i	$0.110664\pi$
$757$	21.0518	+	36.4628i	0.765142	+	1.32526i	−0.175030	+	0.984563i	$0.556002\pi$
$758$	−14.2034	+	24.6011i	−0.515892	+	0.893551i
$759$	1.66111	+	0.959043i	0.0602945	+	0.0348111i
$760$	−6.98355	−	8.08934i	−0.253320	−	0.293431i
$761$	17.5778	+	30.4456i	0.637195	+	1.10365i	0.986046	+	0.166476i	$0.0532387\pi$
$761$	17.5778	+	30.4456i	0.637195	+	1.10365i	−0.348851	+	0.937178i	$0.613428\pi$
$762$	−0.544128	−	0.942458i	−0.0197117	−	0.0341416i
$763$	16.1335			0.584071
$764$	22.8820	+	13.2109i	0.827843	+	0.477955i
$765$	−8.29119	+	7.15781i	−0.299769	+	0.258791i
$766$	−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	$-0.697879\pi$
$769$		−	45.0857i		−	1.62583i	0.582381	−	0.812916i	$-0.302121\pi$
$770$	5.54478	−	15.9261i	0.199820	−	0.573938i
$771$			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	$-0.382500\pi$
$773$	−7.40864	−	4.27738i	−0.266470	−	0.153847i	−0.627283	+	0.778792i	$0.715833\pi$
$774$	−4.90933	+	8.50321i	−0.176462	+	0.305642i
$775$	−3.45304	+	4.35795i	−0.124037	+	0.156542i
$776$	−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
$780$	0.306216	−	0.879538i	0.0109643	−	0.0314925i
$781$	−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
$790$	−2.64835	+	7.60681i	−0.0942242	+	0.270638i
$791$			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
$795$	0.216463	+	0.0753627i	0.00767714	+	0.00267284i
$796$	−6.71437	−	3.87654i	−0.237985	−	0.137400i
$797$	0.764938	+	1.32491i	0.0270955	+	0.0469307i	0.879255	−	0.476351i	$-0.158041\pi$
$797$	0.764938	+	1.32491i	0.0270955	+	0.0469307i	−0.852160	+	0.523282i	$0.824708\pi$
$798$	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
$805$	18.5218	+	21.4546i	0.652809	+	0.756177i
$806$		−	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	0.540989	−	0.841030i	$-0.318050\pi$
$809$	2.36448	+	1.36513i	0.0831308	+	0.0479956i	−0.457858	+	0.889025i	$0.651383\pi$
$810$	18.8097	+	6.54869i	0.660904	+	0.230098i
$811$	7.65057	−	13.2512i	0.268648	−	0.465312i	−0.699865	−	0.714275i	$-0.746757\pi$
$811$	7.65057	−	13.2512i	0.268648	−	0.465312i	0.968513	+	0.248963i	$0.0800898\pi$
$812$	−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	−0.764209	−	0.644969i	$-0.776870\pi$
$821$	5.05599	−	8.75724i	0.176455	−	0.305630i	0.940664	+	0.339339i	$0.110204\pi$
$822$	2.19813			0.0766686
$823$	−11.6477	+	6.72480i	−0.406013	+	0.234412i	−0.689075	−	0.724690i	$-0.741983\pi$
$823$	−11.6477	+	6.72480i	−0.406013	+	0.234412i	0.283062	+	0.959102i	$0.408650\pi$
$824$	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	$-0.832788\pi$
$827$	0.0492539	−	0.0853103i	0.00171273	−	0.00296653i	0.866880	+	0.498516i	$0.166121\pi$
$828$	16.8393			0.585206
$829$	−4.93962	+	2.85189i	−0.171560	+	0.0990503i	−0.583321	−	0.812241i	$-0.698247\pi$
$829$	−4.93962	+	2.85189i	−0.171560	+	0.0990503i	0.411761	+	0.911292i	$0.364914\pi$
$830$	11.7668	+	13.6299i	0.408430	+	0.473102i
$831$	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
$835$	−33.4052	+	28.8388i	−1.15603	+	0.998007i
$836$	−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	−0.975879	−	0.218311i	$-0.929945\pi$
$839$	−19.6097	−	33.9650i	−0.677002	−	1.17260i	0.298877	−	0.954292i	$-0.403388\pi$
$840$	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	−0.965203	−	0.261501i	$-0.915782\pi$
$853$	−20.7092	−	35.8693i	−0.709068	−	1.22814i	0.256135	−	0.966641i	$-0.417551\pi$
$854$	5.77632	−	10.0049i	0.197662	−	0.342360i
$855$	10.5051	−	30.1736i	0.359267	−	1.03192i
$856$	11.3304	+	6.54158i	0.387264	+	0.223587i
$857$	−10.8579			−0.370898			−0.185449	−	0.982654i	$-0.559374\pi$
$857$	−10.8579			−0.370898			−0.185449	+	0.982654i	$0.559374\pi$
$858$	−1.20877	−	0.697883i	−0.0412667	−	0.0238253i
$859$			43.4697i			1.48317i	0.670861	+	0.741583i	$0.265925\pi$
$859$			43.4697i			1.48317i	−0.670861	+	0.741583i	$0.734075\pi$
$860$	−5.55878	+	4.79891i	−0.189553	+	0.163642i
$861$	−1.21376			−0.0413650
$862$			13.8765i			0.472636i
$863$	19.4209	−	11.2127i	0.661095	−	0.381684i	−0.131599	−	0.991303i	$-0.542011\pi$
$863$	19.4209	−	11.2127i	0.661095	−	0.381684i	0.792694	+	0.609619i	$0.208678\pi$
$864$	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
$870$	1.64242	+	0.571817i	0.0556831	+	0.0193864i
$871$	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
$875$	1.05907	+	25.1386i	0.0358031	+	0.849838i
$876$	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	−0.777634	−	0.628717i	$-0.783580\pi$
$881$	4.62049	−	8.00293i	0.155668	−	0.269626i	0.933302	+	0.359092i	$0.116914\pi$
$882$	−5.78636			−0.194837
$883$	12.9574	−	22.4429i	0.436052	−	0.755264i	−0.561329	−	0.827593i	$-0.689710\pi$
$883$	12.9574	−	22.4429i	0.436052	−	0.755264i	0.997381	+	0.0723291i	$0.0230432\pi$
$884$	3.35781	−	5.81590i	0.112935	−	0.195610i
$885$	0.700809	+	0.243991i	0.0235574	+	0.00820166i
$886$	−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
$890$	−7.01784	−	8.12906i	−0.235238	−	0.272487i
$891$	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
$895$	−16.1862	+	46.4913i	−0.541046	+	1.55403i
$896$		−	2.25046i		−	0.0751824i
$897$	2.03163	−	1.17296i	0.0678340	−	0.0391640i
$898$			22.8835i			0.763632i
$899$	8.51116			0.283863
$900$	11.7163	+	9.28346i	0.390543	+	0.309449i
$901$	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
$905$	−10.2803	+	8.87499i	−0.341728	+	0.295015i
$906$	0.770625	+	0.444921i	0.0256023	+	0.0147815i
$907$	2.43179	−	4.21198i	0.0807463	−	0.139857i	−0.822824	−	0.568296i	$-0.807603\pi$
$907$	2.43179	−	4.21198i	0.0807463	−	0.139857i	0.903571	+	0.428439i	$0.140936\pi$
$908$	−11.5695	−	20.0390i	−0.383948	−	0.665017i
$909$	−23.4859	−	40.6787i	−0.778978	−	1.34923i
$910$	−13.4781	−	15.6123i	−0.446795	−	0.517541i
$911$			52.5164i			1.73995i	0.493098	+	0.869974i	$0.335864\pi$
$911$			52.5164i			1.73995i	−0.493098	+	0.869974i	$0.664136\pi$
$912$	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	$-0.959156\pi$
$919$		−	7.75847i		−	0.255928i	0.991779	−	0.127964i	$-0.0408443\pi$
$920$	11.8944	+	4.14109i	0.392145	+	0.136528i
$921$	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
$925$	−29.7387	+	6.37261i	−0.977802	+	0.209530i
$926$	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	−0.970298	−	0.241911i	$-0.922226\pi$
$929$	−8.40161	+	14.5520i	−0.275648	+	0.477436i	0.694651	+	0.719347i	$0.255559\pi$
$930$	−0.238631	−	0.0830806i	−0.00782500	−	0.00272432i
$931$			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	$-0.818110\pi$
$937$	−24.2840	+	14.0204i	−0.793323	+	0.458025i	0.0478083	+	0.998857i	$0.484776\pi$
$938$	−16.8343	+	29.1578i	−0.549658	+	0.952035i
$939$		−	3.43106i		−	0.111968i
$940$	−5.23750	−	6.06682i	−0.170829	−	0.197878i
$941$	14.8474	+	25.7165i	0.484012	+	0.838334i	0.999831	−	0.0183636i	$-0.00584564\pi$
$941$	14.8474	+	25.7165i	0.484012	+	0.838334i	−0.515819	+	0.856698i	$0.672512\pi$
$942$	−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
$945$	−2.31843	+	2.00151i	−0.0754185	+	0.0651090i
$946$	5.50298	+	9.53144i	0.178917	+	0.309894i
$947$	−6.99859	−	12.1219i	−0.227424	−	0.393909i	0.729620	−	0.683853i	$-0.239697\pi$
$947$	−6.99859	−	12.1219i	−0.227424	−	0.393909i	−0.957044	+	0.289943i	$0.906364\pi$
$948$	−0.366042			−0.0118885
$949$	−34.2173	−	19.7554i	−1.11074	−	0.641287i
$950$	14.8405	−	18.7296i	0.481489	−	0.607668i
$951$	1.99822			0.0647966
$952$			3.68733i			0.119507i
$953$	−11.0450	+	6.37686i	−0.357784	+	0.206567i	−0.668108	−	0.744064i	$-0.732896\pi$
$953$	−11.0450	+	6.37686i	−0.357784	+	0.206567i	0.310324	+	0.950631i	$0.399562\pi$
$954$		−	3.01576i		−	0.0976388i
$955$	−19.4258	+	55.7962i	−0.628604	+	1.80552i
$956$		−	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
$960$	0.148485	+	0.171997i	0.00479234	+	0.00555117i
$961$	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
$965$	38.9318	+	13.5543i	1.25326	+	0.436330i
$966$	−0.644035	+	1.11550i	−0.0207215	+	0.0358907i
$967$	19.9159	−	34.4954i	0.640453	−	1.10930i	−0.344878	−	0.938647i	$-0.612080\pi$
$967$	19.9159	−	34.4954i	0.640453	−	1.10930i	0.985332	−	0.170650i	$-0.0545869\pi$
$968$	−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	−0.830217	−	0.557441i	$-0.811783\pi$
$971$	−27.9783	−	48.4598i	−0.897866	−	1.55515i	−0.0676495	−	0.997709i	$-0.521550\pi$
$972$			2.73110i			0.0875999i
$973$			36.8259i			1.18058i
$974$	−5.80967	−	10.0626i	−0.186154	−	0.322428i
$975$	2.06020	+	0.303920i	0.0659791	+	0.00973321i
$976$		−	5.13347i		−	0.164318i
$977$	−19.4233	−	33.6421i	−0.621406	−	1.07631i	−0.989224	−	0.146409i	$-0.953229\pi$
$977$	−19.4233	−	33.6421i	−0.621406	−	1.07631i	0.367818	−	0.929898i	$-0.380105\pi$
$978$	0.298292	−	0.172219i	0.00953834	−	0.00550696i
$979$	−13.9386	+	8.04745i	−0.445479	+	0.257198i
$980$	−4.08717	−	1.42297i	−0.130560	−	0.0454552i
$981$	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	$-0.349488\pi$
$983$	45.5913	−	26.3221i	1.45414	−	0.839545i	0.998712	+	0.0507300i	$0.0161548\pi$
$984$	−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
$990$	16.9580	−	14.6399i	0.538960	−	0.465285i
$991$			5.54551i			0.176159i	0.996113	+	0.0880794i	$0.0280729\pi$
$991$			5.54551i			0.176159i	−0.996113	+	0.0880794i	$0.971927\pi$
$992$	0.963045	+	0.556014i	0.0305767	+	0.0176535i
$993$	−3.47771			−0.110362
$994$	−5.87377	−	3.39122i	−0.186305	−	0.107563i
$995$	5.70019	−	16.3725i	0.180708	−	0.519044i
$996$	−0.409149	+	0.708667i	−0.0129644	+	0.0224550i
$997$	2.48179	+	4.29859i	0.0785992	+	0.136138i	0.902646	−	0.430384i	$-0.141622\pi$
$997$	2.48179	+	4.29859i	0.0785992	+	0.136138i	−0.824047	+	0.566522i	$0.808289\pi$
$998$		−	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.d.159.5	yes	16
5.4	even	2		370.2.m.c.159.4	✓	16
37.27	even	6		370.2.m.c.249.4	yes	16
185.64	even	6	inner	370.2.m.d.249.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.4	✓	16	5.4	even	2
370.2.m.c.249.4	yes	16	37.27	even	6
370.2.m.d.159.5	yes	16	1.1	even	1	trivial
370.2.m.d.249.5	yes	16	185.64	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.0880035 - 0.0508088i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.11174 - 0.735216i) q^{5} -0.101618i q^{6} +(-1.94895 - 1.12523i) q^{7} -1.00000 q^{8} +(-1.49484 - 2.58913i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.0880035 - 0.0508088i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.11174 - 0.735216i) 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} +(0.148485 + 0.171997i) 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} +(1.69259 - 1.46122i) q^{20} +(0.114343 + 0.198048i) q^{21} +(-1.67560 - 2.90222i) q^{22} +5.63248 q^{23} +(0.0880035 + 0.0508088i) q^{24} +(3.91892 + 3.10517i) q^{25} -4.09868 q^{26} +0.608657i q^{27} +(1.94895 - 1.12523i) q^{28} -7.65373i q^{29} +(-0.0747109 + 0.214590i) q^{30} +1.11203i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.294916 + 0.170270i) q^{33} +(-0.819242 + 1.41897i) q^{34} +(3.28840 + 3.80909i) q^{35} +2.98967 q^{36} +(-3.87021 + 4.69270i) q^{37} -4.77928i q^{38} +(0.360698 - 0.208249i) q^{39} +(2.11174 + 0.735216i) 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} +(-0.729701 + 4.94647i) q^{50} -0.166499i q^{51} +(-2.04934 - 3.54956i) q^{52} +(0.873581 - 0.504362i) q^{53} +(-0.527112 + 0.304328i) q^{54} +(7.07685 + 2.46385i) 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} +(6.93738 - 5.98906i) q^{65} +0.340540i q^{66} +(-12.9564 - 7.48037i) q^{67} -1.63848 q^{68} +(-0.495678 - 0.286180i) q^{69} +(-1.65457 + 4.75238i) 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} +(-5.06028 + 4.36856i) 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} +(6.98355 + 8.08934i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{28} - 9 q^{30} + 8 q^{32} + 6 q^{33} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 7 q^{41} + 6 q^{42} - 22 q^{43} + 3 q^{44} + 4 q^{45} - 11 q^{46} + 4 q^{49} + 6 q^{50} - 6 q^{52} + 3 q^{53} + 9 q^{54} - 35 q^{55} + 12 q^{56} + 18 q^{57} + 36 q^{58} + 15 q^{59} - 18 q^{60} + 12 q^{61} - 33 q^{62} + 16 q^{64} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 q^{70} - 4 q^{71} - 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} - 24 q^{77} + 15 q^{78} + 6 q^{80} + 10 q^{81} + 14 q^{82} + 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} + 50 q^{87} + 6 q^{88} + 9 q^{89} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 q^{95} - 3 q^{96} + 68 q^{97} - 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 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^20 - 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 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 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 - 35 * 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 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * 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 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

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