LMFDB - Embedded newform 930.2.n.g.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 $ x^16 - x^15 + 31x^14 + 20x^13 + 474x^12 + 463x^11 + 6637x^10 + 13567x^9 + 108596x^8 + 172826x^7 + 917001x^6 + 1583565x^5 + 3229491x^4 - 1732290x^3 + 4672960x^2 - 5544800x + 22848400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$-1.17072 + 3.60310i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.g.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.17072 - 3.60310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.17072 - 3.60310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-1.62721 - 5.00804i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-1.08783 + 0.790358i) q^{13} +(-1.17072 + 3.60310i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.54433 + 4.75295i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(0.668127 + 0.485423i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.06498 + 2.22684i) q^{21} +(-1.62721 + 5.00804i) q^{22} +(-2.04174 + 6.28382i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +1.34464 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.06498 - 2.22684i) q^{28} +(3.45527 + 2.51040i) q^{29} +1.00000 q^{30} +(-3.69478 - 4.16517i) q^{31} +1.00000 q^{32} +(4.26009 + 3.09514i) q^{33} +(4.04310 - 2.93749i) q^{34} +(-1.17072 - 3.60310i) q^{35} +1.00000 q^{36} -6.77473 q^{37} +(-0.255202 - 0.785431i) q^{38} +(0.415516 - 1.27883i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-8.05861 - 5.85492i) q^{41} +(-1.17072 - 3.60310i) q^{42} +(-4.41583 - 3.20829i) q^{43} +(4.26009 - 3.09514i) q^{44} +(0.309017 - 0.951057i) q^{45} +(5.34534 - 3.88361i) q^{46} +(-5.45663 + 3.96447i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-5.94862 + 4.32193i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.54433 - 4.75295i) q^{51} +(-1.08783 - 0.790358i) q^{52} +(-1.17898 + 3.62853i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-1.62721 - 5.00804i) q^{55} -3.78852 q^{56} -0.825851 q^{57} +(-1.31979 - 4.06191i) q^{58} +(-6.81009 + 4.94782i) q^{59} +(-0.809017 - 0.587785i) q^{60} +7.30290 q^{61} +(0.540917 + 5.54143i) q^{62} -3.78852 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.08783 + 0.790358i) q^{65} +(-1.62721 - 5.00804i) q^{66} +3.63183 q^{67} -4.99755 q^{68} +(-2.04174 - 6.28382i) q^{69} +(-1.17072 + 3.60310i) q^{70} +(1.40173 - 4.31407i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.630797 - 1.94139i) q^{73} +(5.48087 + 3.98208i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-0.255202 + 0.785431i) q^{76} +(-16.1395 + 11.7260i) q^{77} +(-1.08783 + 0.790358i) q^{78} +(2.10192 - 6.46905i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.07811 + 9.47346i) q^{82} +(0.379511 + 0.275731i) q^{83} +(-1.17072 + 3.60310i) q^{84} +(-1.54433 + 4.75295i) q^{85} +(1.68670 + 5.19112i) q^{86} -4.27094 q^{87} -5.26576 q^{88} +(0.991032 + 3.05008i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(4.12128 + 2.99429i) q^{91} -6.60720 q^{92} +(5.43736 + 1.19795i) q^{93} +6.74477 q^{94} +(0.668127 + 0.485423i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-5.38066 - 16.5600i) q^{97} +7.35290 q^{98} -5.26576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−1.17072	−	3.60310i	−0.442490	−	1.36184i	−0.885213	−	0.465185i	$-0.845988\pi$
$7$	−1.17072	−	3.60310i	−0.442490	−	1.36184i	0.442724	−	0.896658i	$-0.354012\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−1.62721	−	5.00804i	−0.490622	−	1.50998i	−0.823669	−	0.567070i	$-0.808077\pi$
$11$	−1.62721	−	5.00804i	−0.490622	−	1.50998i	0.333047	−	0.942910i	$-0.391923\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	−1.08783	+	0.790358i	−0.301711	+	0.219206i	−0.728332	−	0.685225i	$-0.759704\pi$
$13$	−1.08783	+	0.790358i	−0.301711	+	0.219206i	0.426621	+	0.904431i	$0.359704\pi$
$14$	−1.17072	+	3.60310i	−0.312887	+	0.962969i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.54433	+	4.75295i	−0.374554	+	1.15276i	0.569224	+	0.822182i	$0.307244\pi$
$17$	−1.54433	+	4.75295i	−0.374554	+	1.15276i	−0.943779	+	0.330578i	$0.892756\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	0.668127	+	0.485423i	0.153279	+	0.111364i	0.661781	−	0.749697i	$-0.269801\pi$
$19$	0.668127	+	0.485423i	0.153279	+	0.111364i	−0.508502	+	0.861061i	$0.669801\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	3.06498	+	2.22684i	0.668833	+	0.485936i
$22$	−1.62721	+	5.00804i	−0.346922	+	1.06772i
$23$	−2.04174	+	6.28382i	−0.425732	+	1.31027i	0.476560	+	0.879142i	$0.341883\pi$
$23$	−2.04174	+	6.28382i	−0.425732	+	1.31027i	−0.902292	+	0.431125i	$0.858117\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	1.34464			0.263705
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	3.06498	−	2.22684i	0.579227	−	0.420833i
$29$	3.45527	+	2.51040i	0.641627	+	0.466169i	0.860409	−	0.509605i	$-0.170208\pi$
$29$	3.45527	+	2.51040i	0.641627	+	0.466169i	−0.218782	+	0.975774i	$0.570208\pi$
$30$	1.00000			0.182574
$31$	−3.69478	−	4.16517i	−0.663602	−	0.748086i
$31$	−3.69478	−	4.16517i	−0.663602	−	0.748086i
$32$	1.00000			0.176777
$33$	4.26009	+	3.09514i	0.741587	+	0.538794i
$34$	4.04310	−	2.93749i	0.693386	−	0.503775i
$35$	−1.17072	−	3.60310i	−0.197887	−	0.609035i
$36$	1.00000			0.166667
$37$	−6.77473			−1.11376			−0.556879	−	0.830594i	$-0.688001\pi$
$37$	−6.77473			−1.11376			−0.556879	+	0.830594i	$0.688001\pi$
$38$	−0.255202	−	0.785431i	−0.0413992	−	0.127414i
$39$	0.415516	−	1.27883i	0.0665358	−	0.204776i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−8.05861	−	5.85492i	−1.25854	−	0.914385i	−0.259858	−	0.965647i	$-0.583676\pi$
$41$	−8.05861	−	5.85492i	−1.25854	−	0.914385i	−0.998685	+	0.0512616i	$0.983676\pi$
$42$	−1.17072	−	3.60310i	−0.180646	−	0.555970i
$43$	−4.41583	−	3.20829i	−0.673408	−	0.489259i	0.197756	−	0.980251i	$-0.436635\pi$
$43$	−4.41583	−	3.20829i	−0.673408	−	0.489259i	−0.871164	+	0.490992i	$0.836635\pi$
$44$	4.26009	−	3.09514i	0.642233	−	0.466610i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	5.34534	−	3.88361i	0.788127	−	0.572608i
$47$	−5.45663	+	3.96447i	−0.795931	+	0.578278i	−0.909718	−	0.415227i	$-0.863702\pi$
$47$	−5.45663	+	3.96447i	−0.795931	+	0.578278i	0.113786	+	0.993505i	$0.463702\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−5.94862	+	4.32193i	−0.849803	+	0.617418i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−1.54433	−	4.75295i	−0.216249	−	0.665546i
$52$	−1.08783	−	0.790358i	−0.150855	−	0.109603i
$53$	−1.17898	+	3.62853i	−0.161945	+	0.498416i	−0.998798	−	0.0490114i	$-0.984393\pi$
$53$	−1.17898	+	3.62853i	−0.161945	+	0.498416i	0.836853	+	0.547428i	$0.184393\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−1.62721	−	5.00804i	−0.219413	−	0.675284i
$56$	−3.78852			−0.506263
$57$	−0.825851			−0.109387
$58$	−1.31979	−	4.06191i	−0.173298	−	0.533355i
$59$	−6.81009	+	4.94782i	−0.886598	+	0.644151i	−0.934989	−	0.354677i	$-0.884591\pi$
$59$	−6.81009	+	4.94782i	−0.886598	+	0.644151i	0.0483905	+	0.998828i	$0.484591\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	7.30290			0.935040			0.467520	−	0.883982i	$-0.345148\pi$
$61$	7.30290			0.935040			0.467520	+	0.883982i	$0.345148\pi$
$62$	0.540917	+	5.54143i	0.0686965	+	0.703762i
$63$	−3.78852			−0.477309
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.08783	+	0.790358i	−0.134929	+	0.0980318i
$66$	−1.62721	−	5.00804i	−0.200296	−	0.616447i
$67$	3.63183			0.443699			0.221849	−	0.975081i	$-0.428791\pi$
$67$	3.63183			0.443699			0.221849	+	0.975081i	$0.428791\pi$
$68$	−4.99755			−0.606042
$69$	−2.04174	−	6.28382i	−0.245796	−	0.756483i
$70$	−1.17072	+	3.60310i	−0.139928	+	0.430653i
$71$	1.40173	−	4.31407i	0.166354	−	0.511986i	−0.832779	−	0.553605i	$-0.813252\pi$
$71$	1.40173	−	4.31407i	0.166354	−	0.511986i	0.999134	+	0.0416194i	$0.0132517\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−0.630797	−	1.94139i	−0.0738292	−	0.227223i	0.907332	−	0.420416i	$-0.138116\pi$
$73$	−0.630797	−	1.94139i	−0.0738292	−	0.227223i	−0.981161	+	0.193193i	$0.938116\pi$
$74$	5.48087	+	3.98208i	0.637138	+	0.462908i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	−0.255202	+	0.785431i	−0.0292737	+	0.0900951i
$77$	−16.1395	+	11.7260i	−1.83926	+	1.33630i
$78$	−1.08783	+	0.790358i	−0.123173	+	0.0894904i
$79$	2.10192	−	6.46905i	0.236485	−	0.727825i	−0.760436	−	0.649413i	$-0.775015\pi$
$79$	2.10192	−	6.46905i	0.236485	−	0.727825i	0.996921	−	0.0784127i	$-0.0249852\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.07811	+	9.47346i	0.339921	+	1.04617i
$83$	0.379511	+	0.275731i	0.0416567	+	0.0302654i	0.608419	−	0.793616i	$-0.291804\pi$
$83$	0.379511	+	0.275731i	0.0416567	+	0.0302654i	−0.566762	+	0.823882i	$0.691804\pi$
$84$	−1.17072	+	3.60310i	−0.127736	+	0.393130i
$85$	−1.54433	+	4.75295i	−0.167506	+	0.515530i
$86$	1.68670	+	5.19112i	0.181881	+	0.559773i
$87$	−4.27094			−0.457893
$88$	−5.26576			−0.561332
$89$	0.991032	+	3.05008i	0.105049	+	0.323308i	0.989742	−	0.142866i	$-0.0456319\pi$
$89$	0.991032	+	3.05008i	0.105049	+	0.323308i	−0.884693	+	0.466174i	$0.845632\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	4.12128	+	2.99429i	0.432028	+	0.313887i
$92$	−6.60720			−0.688848
$93$	5.43736	+	1.19795i	0.563828	+	0.124222i
$94$	6.74477			0.695670
$95$	0.668127	+	0.485423i	0.0685484	+	0.0498033i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−5.38066	−	16.5600i	−0.546323	−	1.68141i	−0.717824	−	0.696225i	$-0.754862\pi$
$97$	−5.38066	−	16.5600i	−0.546323	−	1.68141i	0.171501	−	0.985184i	$-0.445138\pi$
$98$	7.35290			0.742755
$99$	−5.26576			−0.529229
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−4.95681	+	15.2555i	−0.493221	+	1.51798i	0.326490	+	0.945200i	$0.394134\pi$
$101$	−4.95681	+	15.2555i	−0.493221	+	1.51798i	−0.819711	+	0.572777i	$0.805866\pi$
$102$	−1.54433	+	4.75295i	−0.152911	+	0.470612i
$103$	−13.2793	−	9.64795i	−1.30844	−	0.950641i	−0.308445	−	0.951242i	$-0.599809\pi$
$103$	−13.2793	−	9.64795i	−1.30844	−	0.950641i	−1.00000		0.000601277i	$0.999809\pi$
$104$	0.415516	+	1.27883i	0.0407447	+	0.125399i
$105$	3.06498	+	2.22684i	0.299111	+	0.217317i
$106$	3.08661	−	2.24255i	0.299798	−	0.217816i
$107$	−1.44283	+	4.44057i	−0.139484	+	0.429287i	−0.996260	−	0.0864009i	$-0.972463\pi$
$107$	−1.44283	+	4.44057i	−0.139484	+	0.429287i	0.856777	+	0.515687i	$0.172463\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	5.35543	−	3.89095i	0.512957	−	0.372685i	−0.300987	−	0.953628i	$-0.597316\pi$
$109$	5.35543	−	3.89095i	0.512957	−	0.372685i	0.813944	+	0.580943i	$0.197316\pi$
$110$	−1.62721	+	5.00804i	−0.155148	+	0.477498i
$111$	5.48087	−	3.98208i	0.520221	−	0.377963i
$112$	3.06498	+	2.22684i	0.289613	+	0.210416i
$113$	1.48844	+	4.58095i	0.140021	+	0.430940i	0.996337	−	0.0855119i	$-0.0272526\pi$
$113$	1.48844	+	4.58095i	0.140021	+	0.430940i	−0.856316	+	0.516452i	$0.827253\pi$
$114$	0.668127	+	0.485423i	0.0625759	+	0.0454640i
$115$	−2.04174	+	6.28382i	−0.190393	+	0.585969i
$116$	−1.31979	+	4.06191i	−0.122540	+	0.377139i
$117$	0.415516	+	1.27883i	0.0384144	+	0.118228i
$118$	8.41774			0.774915
$119$	18.9333			1.73561
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−13.5335	+	9.83263i	−1.23031	+	0.893876i
$122$	−5.90817	−	4.29254i	−0.534900	−	0.388628i
$123$	9.96099			0.898152
$124$	2.81956	−	4.80105i	0.253204	−	0.431147i
$125$	1.00000			0.0894427
$126$	3.06498	+	2.22684i	0.273050	+	0.198382i
$127$	4.84152	−	3.51757i	0.429615	−	0.312134i	−0.351880	−	0.936045i	$-0.614457\pi$
$127$	4.84152	−	3.51757i	0.429615	−	0.312134i	0.781495	+	0.623911i	$0.214457\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	5.45827			0.480574
$130$	1.34464			0.117932
$131$	−5.15122	−	15.8538i	−0.450064	−	1.38516i	−0.876833	−	0.480795i	$-0.840348\pi$
$131$	−5.15122	−	15.8538i	−0.450064	−	1.38516i	0.426769	−	0.904361i	$-0.359652\pi$
$132$	−1.62721	+	5.00804i	−0.141631	+	0.435894i
$133$	0.966838	−	2.97562i	0.0838355	−	0.258019i
$134$	−2.93821	−	2.13474i	−0.253823	−	0.184413i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	4.04310	+	2.93749i	0.346693	+	0.251887i
$137$	−12.8558	+	9.34029i	−1.09835	+	0.797995i	−0.980789	−	0.195071i	$-0.937506\pi$
$137$	−12.8558	+	9.34029i	−1.09835	+	0.797995i	−0.117556	+	0.993066i	$0.537506\pi$
$138$	−2.04174	+	6.28382i	−0.173804	+	0.534914i
$139$	5.46466	−	3.97031i	0.463506	−	0.336757i	−0.331399	−	0.943491i	$-0.607521\pi$
$139$	5.46466	−	3.97031i	0.463506	−	0.336757i	0.794905	+	0.606734i	$0.207521\pi$
$140$	3.06498	−	2.22684i	0.259038	−	0.188202i
$141$	2.08425	−	6.41465i	0.175525	−	0.540211i
$142$	−3.66977	+	2.66624i	−0.307960	+	0.223746i
$143$	5.72828	+	4.16184i	0.479023	+	0.348030i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	3.45527	+	2.51040i	0.286944	+	0.208477i
$146$	−0.630797	+	1.94139i	−0.0522052	+	0.160671i
$147$	2.27217	−	6.99302i	0.187405	−	0.576775i
$148$	−2.09351	−	6.44315i	−0.172085	−	0.529624i
$149$	−16.0548			−1.31526			−0.657630	−	0.753341i	$-0.728441\pi$
$149$	−16.0548			−1.31526			−0.657630	+	0.753341i	$0.728441\pi$
$150$	1.00000			0.0816497
$151$	3.06420	+	9.43063i	0.249361	+	0.767453i	0.994889	+	0.100979i	$0.0321975\pi$
$151$	3.06420	+	9.43063i	0.249361	+	0.767453i	−0.745528	+	0.666474i	$0.767803\pi$
$152$	0.668127	−	0.485423i	0.0541923	−	0.0393730i
$153$	4.04310	+	2.93749i	0.326865	+	0.237482i
$154$	19.9495			1.60757
$155$	−3.69478	−	4.16517i	−0.296772	−	0.334554i
$156$	1.34464			0.107657
$157$	−16.5406	−	12.0175i	−1.32009	−	0.959099i	−0.999931	−	0.0117346i	$-0.996265\pi$
$157$	−16.5406	−	12.0175i	−1.32009	−	0.959099i	−0.320156	−	0.947365i	$-0.603735\pi$
$158$	−5.50291	+	3.99809i	−0.437788	+	0.318071i
$159$	−1.17898	−	3.62853i	−0.0934992	−	0.287761i
$160$	1.00000			0.0790569
$161$	25.0315			1.97276
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	2.98547	−	9.18833i	0.233840	−	0.719685i	−0.763433	−	0.645887i	$-0.776488\pi$
$163$	2.98547	−	9.18833i	0.233840	−	0.719685i	0.997273	−	0.0737985i	$-0.0235122\pi$
$164$	3.07811	−	9.47346i	0.240360	−	0.739753i
$165$	4.26009	+	3.09514i	0.331648	+	0.240956i
$166$	−0.144960	−	0.446142i	−0.0112511	−	0.0346273i
$167$	3.82856	+	2.78161i	0.296263	+	0.215248i	0.725980	−	0.687716i	$-0.241387\pi$
$167$	3.82856	+	2.78161i	0.296263	+	0.215248i	−0.429717	+	0.902964i	$0.641387\pi$
$168$	3.06498	−	2.22684i	0.236468	−	0.171804i
$169$	−3.45850	+	10.6442i	−0.266039	+	0.818783i
$170$	4.04310	−	2.93749i	0.310092	−	0.225295i
$171$	0.668127	−	0.485423i	0.0510930	−	0.0371212i
$172$	1.68670	−	5.19112i	0.128609	−	0.395819i
$173$	9.45979	−	6.87294i	0.719214	−	0.522540i	−0.166919	−	0.985971i	$-0.553382\pi$
$173$	9.45979	−	6.87294i	0.719214	−	0.522540i	0.886133	+	0.463431i	$0.153382\pi$
$174$	3.45527	+	2.51040i	0.261943	+	0.190313i
$175$	−1.17072	−	3.60310i	−0.0884979	−	0.272369i
$176$	4.26009	+	3.09514i	0.321117	+	0.233305i
$177$	2.60122	−	8.00574i	0.195520	−	0.601748i
$178$	0.991032	−	3.05008i	0.0742810	−	0.228613i
$179$	0.278926	+	0.858447i	0.0208479	+	0.0641633i	0.960939	−	0.276759i	$-0.0892605\pi$
$179$	0.278926	+	0.858447i	0.0208479	+	0.0641633i	−0.940091	+	0.340923i	$0.889261\pi$
$180$	1.00000			0.0745356
$181$	0.992901			0.0738018			0.0369009	−	0.999319i	$-0.488251\pi$
$181$	0.992901			0.0738018			0.0369009	+	0.999319i	$0.488251\pi$
$182$	−1.57419	−	4.84486i	−0.116687	−	0.359125i
$183$	−5.90817	+	4.29254i	−0.436744	+	0.317313i
$184$	5.34534	+	3.88361i	0.394063	+	0.286304i
$185$	−6.77473			−0.498088
$186$	−3.69478	−	4.16517i	−0.270914	−	0.305405i
$187$	26.3159			1.92441
$188$	−5.45663	−	3.96447i	−0.397966	−	0.289139i
$189$	3.06498	−	2.22684i	0.222944	−	0.161979i
$190$	−0.255202	−	0.785431i	−0.0185143	−	0.0569811i
$191$	20.7711			1.50294			0.751471	−	0.659766i	$-0.229345\pi$
$191$	20.7711			1.50294			0.751471	+	0.659766i	$0.229345\pi$
$192$	1.00000			0.0721688
$193$	8.10942	+	24.9582i	0.583729	+	1.79653i	0.604317	+	0.796744i	$0.293446\pi$
$193$	8.10942	+	24.9582i	0.583729	+	1.79653i	−0.0205885	+	0.999788i	$0.506554\pi$
$194$	−5.38066	+	16.5600i	−0.386309	+	1.18894i
$195$	0.415516	−	1.27883i	0.0297557	−	0.0915786i
$196$	−5.94862	−	4.32193i	−0.424901	−	0.308709i
$197$	−1.86113	−	5.72798i	−0.132600	−	0.408102i	0.862609	−	0.505872i	$-0.168829\pi$
$197$	−1.86113	−	5.72798i	−0.132600	−	0.408102i	−0.995209	+	0.0977700i	$0.968829\pi$
$198$	4.26009	+	3.09514i	0.302752	+	0.219962i
$199$	3.39114	−	2.46381i	0.240392	−	0.174655i	−0.461066	−	0.887366i	$-0.652533\pi$
$199$	3.39114	−	2.46381i	0.240392	−	0.174655i	0.701458	+	0.712711i	$0.252533\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	−2.93821	+	2.13474i	−0.207245	+	0.150573i
$202$	12.9771	−	9.42841i	0.913065	−	0.663380i
$203$	5.00007	−	15.3886i	0.350936	−	1.08007i
$204$	4.04310	−	2.93749i	0.283074	−	0.205665i
$205$	−8.05861	−	5.85492i	−0.562838	−	0.408926i
$206$	5.07223	+	15.6107i	0.353399	+	1.08765i
$207$	5.34534	+	3.88361i	0.371527	+	0.269930i
$208$	0.415516	−	1.27883i	0.0288108	−	0.0886706i
$209$	1.34383	−	4.13589i	0.0929549	−	0.286086i
$210$	−1.17072	−	3.60310i	−0.0807872	−	0.248637i
$211$	−3.28602			−0.226219			−0.113109	−	0.993583i	$-0.536081\pi$
$211$	−3.28602			−0.226219			−0.113109	+	0.993583i	$0.536081\pi$
$212$	−3.81526			−0.262033
$213$	1.40173	+	4.31407i	0.0960447	+	0.295595i
$214$	3.77738	−	2.74443i	0.258216	−	0.187605i
$215$	−4.41583	−	3.20829i	−0.301157	−	0.218803i
$216$	1.00000			0.0680414
$217$	−10.6820	+	18.1889i	−0.725139	+	1.23474i
$218$	−6.61967			−0.448341
$219$	1.65145	+	1.19985i	0.111595	+	0.0810782i
$220$	4.26009	−	3.09514i	0.287215	−	0.208674i
$221$	−2.07656	−	6.39099i	−0.139685	−	0.429905i
$222$	−6.77473			−0.454690
$223$	20.9568			1.40337			0.701686	−	0.712486i	$-0.252431\pi$
$223$	20.9568			1.40337			0.701686	+	0.712486i	$0.252431\pi$
$224$	−1.17072	−	3.60310i	−0.0782219	−	0.240742i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	1.48844	−	4.58095i	0.0990097	−	0.304720i
$227$	−16.3479	−	11.8775i	−1.08505	−	0.788335i	−0.106493	−	0.994313i	$-0.533962\pi$
$227$	−16.3479	−	11.8775i	−1.08505	−	0.788335i	−0.978557	+	0.205978i	$0.933962\pi$
$228$	−0.255202	−	0.785431i	−0.0169012	−	0.0520164i
$229$	−4.15148	−	3.01623i	−0.274337	−	0.199318i	0.442106	−	0.896963i	$-0.354231\pi$
$229$	−4.15148	−	3.01623i	−0.274337	−	0.199318i	−0.716444	+	0.697645i	$0.754231\pi$
$230$	5.34534	−	3.88361i	0.352461	−	0.256078i
$231$	6.16472	−	18.9731i	0.405609	−	1.24834i
$232$	3.45527	−	2.51040i	0.226849	−	0.164816i
$233$	19.8233	−	14.4025i	1.29867	−	0.943537i	0.298725	−	0.954339i	$-0.403439\pi$
$233$	19.8233	−	14.4025i	1.29867	−	0.943537i	0.999942	+	0.0108025i	$0.00343862\pi$
$234$	0.415516	−	1.27883i	0.0271631	−	0.0835995i
$235$	−5.45663	+	3.96447i	−0.355951	+	0.258614i
$236$	−6.81009	−	4.94782i	−0.443299	−	0.322076i
$237$	2.10192	+	6.46905i	0.136535	+	0.420210i
$238$	−15.3174	−	11.1287i	−0.992878	−	0.721368i
$239$	4.73751	−	14.5805i	0.306444	−	0.943137i	−0.672691	−	0.739924i	$-0.734862\pi$
$239$	4.73751	−	14.5805i	0.306444	−	0.943137i	0.979135	−	0.203213i	$-0.0651385\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−3.70554	−	11.4045i	−0.238695	−	0.734627i	−0.996610	−	0.0822735i	$-0.973782\pi$
$241$	−3.70554	−	11.4045i	−0.238695	−	0.734627i	0.757915	−	0.652353i	$-0.226218\pi$
$242$	16.7283			1.07533
$243$	1.00000			0.0641500
$244$	2.25672	+	6.94547i	0.144472	+	0.444638i
$245$	−5.94862	+	4.32193i	−0.380043	+	0.276118i
$246$	−8.05861	−	5.85492i	−0.513798	−	0.373296i
$247$	−1.11047			−0.0706575
$248$	−5.10306	+	2.22684i	−0.324044	+	0.141404i
$249$	−0.469101			−0.0297281
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−6.46003	+	4.69349i	−0.407753	+	0.296250i	−0.772692	−	0.634782i	$-0.781090\pi$
$251$	−6.46003	+	4.69349i	−0.407753	+	0.296250i	0.364938	+	0.931032i	$0.381090\pi$
$252$	−1.17072	−	3.60310i	−0.0737483	−	0.226974i
$253$	34.7920			2.18735
$254$	−5.98445			−0.375498
$255$	−1.54433	−	4.75295i	−0.0967095	−	0.297641i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.34512	−	19.5283i	0.395798	−	1.21814i	−0.532541	−	0.846404i	$-0.678763\pi$
$257$	6.34512	−	19.5283i	0.395798	−	1.21814i	0.928339	−	0.371736i	$-0.121237\pi$
$258$	−4.41583	−	3.20829i	−0.274918	−	0.199739i
$259$	7.93129	+	24.4100i	0.492827	+	1.51676i
$260$	−1.08783	−	0.790358i	−0.0674646	−	0.0490159i
$261$	3.45527	−	2.51040i	0.213876	−	0.155390i
$262$	−5.15122	+	15.8538i	−0.318244	+	0.979453i
$263$	−4.00331	+	2.90857i	−0.246854	+	0.179350i	−0.704332	−	0.709871i	$-0.748753\pi$
$263$	−4.00331	+	2.90857i	−0.246854	+	0.179350i	0.457477	+	0.889221i	$0.348753\pi$
$264$	4.26009	−	3.09514i	0.262191	−	0.190493i
$265$	−1.17898	+	3.62853i	−0.0724241	+	0.222899i
$266$	−2.53122	+	1.83904i	−0.155199	+	0.112758i
$267$	−2.59456	−	1.88506i	−0.158784	−	0.115363i
$268$	1.12230	+	3.45407i	0.0685552	+	0.210991i
$269$	−15.5666	−	11.3098i	−0.949112	−	0.689570i	0.00148452	−	0.999999i	$-0.499527\pi$
$269$	−15.5666	−	11.3098i	−0.949112	−	0.689570i	−0.950597	+	0.310429i	$0.899527\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−1.31649	+	4.05173i	−0.0799710	+	0.246125i	−0.983046	−	0.183356i	$-0.941304\pi$
$271$	−1.31649	+	4.05173i	−0.0799710	+	0.246125i	0.903076	+	0.429482i	$0.141304\pi$
$272$	−1.54433	−	4.75295i	−0.0936386	−	0.288190i
$273$	−5.09419			−0.308314
$274$	15.8906			0.959989
$275$	−1.62721	−	5.00804i	−0.0981245	−	0.301996i
$276$	5.34534	−	3.88361i	0.321751	−	0.233766i
$277$	−13.6649	−	9.92813i	−0.821044	−	0.596524i	0.0959671	−	0.995385i	$-0.469406\pi$
$277$	−13.6649	−	9.92813i	−0.821044	−	0.596524i	−0.917011	+	0.398861i	$0.869406\pi$
$278$	−6.75469			−0.405119
$279$	−5.10306	+	2.22684i	−0.305512	+	0.133317i
$280$	−3.78852			−0.226407
$281$	17.3972	+	12.6398i	1.03783	+	0.754027i	0.969861	−	0.243660i	$-0.0783482\pi$
$281$	17.3972	+	12.6398i	1.03783	+	0.754027i	0.0679687	+	0.997687i	$0.478348\pi$
$282$	−5.45663	+	3.96447i	−0.324938	+	0.236081i
$283$	5.78102	+	17.7922i	0.343646	+	1.05763i	0.962305	+	0.271974i	$0.0876765\pi$
$283$	5.78102	+	17.7922i	0.343646	+	1.05763i	−0.618658	+	0.785660i	$0.712324\pi$
$284$	4.53608			0.269167
$285$	−0.825851			−0.0489192
$286$	−2.18801	−	6.73400i	−0.129380	−	0.398190i
$287$	−11.6615	+	35.8904i	−0.688357	+	2.11854i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−6.45230	−	4.68787i	−0.379547	−	0.275757i
$290$	−1.31979	−	4.06191i	−0.0775010	−	0.238524i
$291$	14.0867	+	10.2346i	0.825779	+	0.599964i
$292$	1.65145	−	1.19985i	0.0966437	−	0.0702158i
$293$	7.28905	−	22.4334i	0.425831	−	1.31057i	−0.476365	−	0.879247i	$-0.658046\pi$
$293$	7.28905	−	22.4334i	0.425831	−	1.31057i	0.902196	−	0.431326i	$-0.141954\pi$
$294$	−5.94862	+	4.32193i	−0.346931	+	0.252060i
$295$	−6.81009	+	4.94782i	−0.396499	+	0.288073i
$296$	−2.09351	+	6.44315i	−0.121683	+	0.374500i
$297$	4.26009	−	3.09514i	0.247196	−	0.179598i
$298$	12.9886	+	9.43677i	0.752409	+	0.546657i
$299$	−2.74540	−	8.44946i	−0.158770	−	0.488645i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	−6.39009	+	19.6667i	−0.368319	+	1.13357i
$302$	3.06420	−	9.43063i	0.176325	−	0.542672i
$303$	−4.95681	−	15.2555i	−0.284761	−	0.876405i
$304$	−0.825851			−0.0473658
$305$	7.30290			0.418163
$306$	−1.54433	−	4.75295i	−0.0882833	−	0.271708i
$307$	−16.7585	+	12.1757i	−0.956456	+	0.694906i	−0.952325	−	0.305085i	$-0.901315\pi$
$307$	−16.7585	+	12.1757i	−0.956456	+	0.694906i	−0.00413119	+	0.999991i	$0.501315\pi$
$308$	−16.1395	−	11.7260i	−0.919631	−	0.668151i
$309$	16.4141			0.933764
$310$	0.540917	+	5.54143i	0.0307220	+	0.314732i
$311$	15.3352			0.869579			0.434790	−	0.900532i	$-0.356823\pi$
$311$	15.3352			0.869579			0.434790	+	0.900532i	$0.356823\pi$
$312$	−1.08783	−	0.790358i	−0.0615865	−	0.0447452i
$313$	−7.24716	+	5.26537i	−0.409634	+	0.297616i	−0.773453	−	0.633853i	$-0.781472\pi$
$313$	−7.24716	+	5.26537i	−0.409634	+	0.297616i	0.363820	+	0.931469i	$0.381472\pi$
$314$	6.31796	+	19.4447i	0.356543	+	1.09733i
$315$	−3.78852			−0.213459
$316$	6.80196			0.382640
$317$	9.80482	+	30.1761i	0.550693	+	1.69486i	0.707054	+	0.707160i	$0.250024\pi$
$317$	9.80482	+	30.1761i	0.550693	+	1.69486i	−0.156360	+	0.987700i	$0.549976\pi$
$318$	−1.17898	+	3.62853i	−0.0661139	+	0.203478i
$319$	6.94973	−	21.3891i	0.389110	−	1.19756i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	−1.44283	−	4.44057i	−0.0805309	−	0.247849i
$322$	−20.2509	−	14.7132i	−1.12854	−	0.819932i
$323$	−3.33900	+	2.42592i	−0.185787	+	0.134982i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−1.08783	+	0.790358i	−0.0603422	+	0.0438412i
$326$	−7.81606	+	5.67870i	−0.432891	+	0.314514i
$327$	−2.04559	+	6.29568i	−0.113121	+	0.348152i
$328$	−8.05861	+	5.85492i	−0.444962	+	0.323284i
$329$	20.6726	+	15.0195i	1.13972	+	0.828052i
$330$	−1.62721	−	5.00804i	−0.0895750	−	0.275683i
$331$	−1.95247	−	1.41856i	−0.107318	−	0.0779709i	0.532832	−	0.846221i	$-0.321128\pi$
$331$	−1.95247	−	1.41856i	−0.107318	−	0.0779709i	−0.640150	+	0.768250i	$0.721128\pi$
$332$	−0.144960	+	0.446142i	−0.00795572	+	0.0244852i
$333$	−2.09351	+	6.44315i	−0.114723	+	0.353082i
$334$	−1.46238	−	4.50074i	−0.0800179	−	0.246270i
$335$	3.63183			0.198428
$336$	−3.78852			−0.206681
$337$	9.46082	+	29.1174i	0.515364	+	1.58613i	0.782619	+	0.622501i	$0.213883\pi$
$337$	9.46082	+	29.1174i	0.515364	+	1.58613i	−0.267256	+	0.963626i	$0.586117\pi$
$338$	9.05448	−	6.57846i	0.492499	−	0.357821i
$339$	−3.89679	−	2.83118i	−0.211645	−	0.153769i
$340$	−4.99755			−0.271030
$341$	−14.8471	+	25.2812i	−0.804017	+	1.36905i
$342$	−0.825851			−0.0446569
$343$	1.08163	+	0.785849i	0.0584025	+	0.0424319i
$344$	−4.41583	+	3.20829i	−0.238086	+	0.172979i
$345$	−2.04174	−	6.28382i	−0.109923	−	0.338310i
$346$	−11.6929			−0.628617
$347$	−5.98647			−0.321371			−0.160685	−	0.987006i	$-0.551370\pi$
$347$	−5.98647			−0.321371			−0.160685	+	0.987006i	$0.551370\pi$
$348$	−1.31979	−	4.06191i	−0.0707484	−	0.217741i
$349$	6.77990	−	20.8664i	0.362920	−	1.11695i	−0.588354	−	0.808603i	$-0.700224\pi$
$349$	6.77990	−	20.8664i	0.362920	−	1.11695i	0.951274	−	0.308348i	$-0.0997762\pi$
$350$	−1.17072	+	3.60310i	−0.0625775	+	0.192594i
$351$	−1.08783	−	0.790358i	−0.0580643	−	0.0421862i
$352$	−1.62721	−	5.00804i	−0.0867306	−	0.266929i
$353$	21.8706	+	15.8899i	1.16405	+	0.845734i	0.990285	−	0.139053i	$-0.0444057\pi$
$353$	21.8706	+	15.8899i	1.16405	+	0.845734i	0.173768	+	0.984787i	$0.444406\pi$
$354$	−6.81009	+	4.94782i	−0.361952	+	0.262974i
$355$	1.40173	−	4.31407i	0.0743959	−	0.228967i
$356$	−2.59456	+	1.88506i	−0.137511	+	0.0999077i
$357$	−15.3174	+	11.1287i	−0.810682	+	0.588995i
$358$	0.278926	−	0.858447i	0.0147417	−	0.0453703i
$359$	0.895277	−	0.650457i	0.0472509	−	0.0343298i	−0.563909	−	0.825837i	$-0.690703\pi$
$359$	0.895277	−	0.650457i	0.0472509	−	0.0343298i	0.611160	+	0.791507i	$0.290703\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	−5.66056	−	17.4214i	−0.297924	−	0.916917i
$362$	−0.803274	−	0.583613i	−0.0422191	−	0.0306740i
$363$	5.16932	−	15.9095i	0.271319	−	0.835034i
$364$	−1.57419	+	4.84486i	−0.0825100	+	0.253940i
$365$	−0.630797	−	1.94139i	−0.0330174	−	0.101617i
$366$	7.30290			0.381729
$367$	1.57945			0.0824467			0.0412233	−	0.999150i	$-0.486874\pi$
$367$	1.57945			0.0824467			0.0412233	+	0.999150i	$0.486874\pi$
$368$	−2.04174	−	6.28382i	−0.106433	−	0.327567i
$369$	−8.05861	+	5.85492i	−0.419514	+	0.304795i
$370$	5.48087	+	3.98208i	0.284937	+	0.207019i
$371$	14.4542			0.750424
$372$	0.540917	+	5.54143i	0.0280452	+	0.287310i
$373$	−31.0660			−1.60854			−0.804269	−	0.594265i	$-0.797443\pi$
$373$	−31.0660			−1.60854			−0.804269	+	0.594265i	$0.797443\pi$
$374$	−21.2900	−	15.4681i	−1.10088	−	0.799837i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	2.08425	+	6.41465i	0.107487	+	0.330811i
$377$	−5.74287			−0.295773
$378$	−3.78852			−0.194861
$379$	−3.22507	−	9.92576i	−0.165661	−	0.509852i	0.833423	−	0.552635i	$-0.186378\pi$
$379$	−3.22507	−	9.92576i	−0.165661	−	0.509852i	−0.999084	+	0.0427830i	$0.986378\pi$
$380$	−0.255202	+	0.785431i	−0.0130916	+	0.0402917i
$381$	−1.84930	+	5.69155i	−0.0947423	+	0.291587i
$382$	−16.8041	−	12.2089i	−0.859775	−	0.624663i
$383$	−7.18366	−	22.1090i	−0.367068	−	1.12972i	−0.948676	−	0.316249i	$-0.897576\pi$
$383$	−7.18366	−	22.1090i	−0.367068	−	1.12972i	0.581608	−	0.813469i	$-0.302424\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−16.1395	+	11.7260i	−0.822543	+	0.597612i
$386$	8.10942	−	24.9582i	0.412758	−	1.27034i
$387$	−4.41583	+	3.20829i	−0.224469	+	0.163086i
$388$	14.0867	−	10.2346i	0.715146	−	0.519584i
$389$	9.95958	−	30.6524i	0.504971	−	1.55414i	−0.295849	−	0.955235i	$-0.595602\pi$
$389$	9.95958	−	30.6524i	0.504971	−	1.55414i	0.800820	−	0.598906i	$-0.204398\pi$
$390$	−1.08783	+	0.790358i	−0.0550846	+	0.0400213i
$391$	−26.7136	−	19.4086i	−1.35096	−	0.981533i
$392$	2.27217	+	6.99302i	0.114762	+	0.353201i
$393$	13.4861	+	9.79821i	0.680282	+	0.494254i
$394$	−1.86113	+	5.72798i	−0.0937625	+	0.288571i
$395$	2.10192	−	6.46905i	0.105759	−	0.325493i
$396$	−1.62721	−	5.00804i	−0.0817704	−	0.251663i
$397$	24.1365			1.21138			0.605688	−	0.795702i	$-0.292898\pi$
$397$	24.1365			1.21138			0.605688	+	0.795702i	$0.292898\pi$
$398$	−4.19168			−0.210110
$399$	0.966838	+	2.97562i	0.0484024	+	0.148967i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	31.7702	+	23.0824i	1.58653	+	1.15268i	0.908692	+	0.417468i	$0.137082\pi$
$401$	31.7702	+	23.0824i	1.58653	+	1.15268i	0.677837	+	0.735212i	$0.262918\pi$
$402$	3.63183			0.181139
$403$	7.31128	+	1.61081i	0.364201	+	0.0802402i
$404$	−16.0406			−0.798048
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−13.0904	+	9.51070i	−0.649663	+	0.472008i
$407$	11.0239	+	33.9281i	0.546435	+	1.68175i
$408$	−4.99755			−0.247415
$409$	4.52654			0.223823			0.111911	−	0.993718i	$-0.464303\pi$
$409$	4.52654			0.223823			0.111911	+	0.993718i	$0.464303\pi$
$410$	3.07811	+	9.47346i	0.152017	+	0.467861i
$411$	4.91048	−	15.1129i	0.242216	−	0.745465i
$412$	5.07223	−	15.6107i	0.249891	−	0.769085i
$413$	25.8002	+	18.7449i	1.26954	+	0.922378i
$414$	−2.04174	−	6.28382i	−0.100346	−	0.308833i
$415$	0.379511	+	0.275731i	0.0186294	+	0.0135351i
$416$	−1.08783	+	0.790358i	−0.0533355	+	0.0387505i
$417$	−2.08731	+	6.42409i	−0.102216	+	0.314589i
$418$	−3.51820	+	2.55612i	−0.172081	+	0.125024i
$419$	4.51349	−	3.27924i	0.220498	−	0.160201i	−0.472053	−	0.881570i	$-0.656487\pi$
$419$	4.51349	−	3.27924i	0.220498	−	0.160201i	0.692551	+	0.721369i	$0.256487\pi$
$420$	−1.17072	+	3.60310i	−0.0571252	+	0.175813i
$421$	−11.8782	+	8.62999i	−0.578906	+	0.420600i	−0.838330	−	0.545164i	$-0.816467\pi$
$421$	−11.8782	+	8.62999i	−0.578906	+	0.420600i	0.259423	+	0.965764i	$0.416467\pi$
$422$	2.65844	+	1.93147i	0.129411	+	0.0940226i
$423$	2.08425	+	6.41465i	0.101340	+	0.311891i
$424$	3.08661	+	2.24255i	0.149899	+	0.108908i
$425$	−1.54433	+	4.75295i	−0.0749109	+	0.230552i
$426$	1.40173	−	4.31407i	0.0679138	−	0.209017i
$427$	−8.54963	−	26.3131i	−0.413746	−	1.27338i
$428$	−4.66910			−0.225689
$429$	−7.08054			−0.341852
$430$	1.68670	+	5.19112i	0.0813398	+	0.250338i
$431$	5.23962	−	3.80681i	0.252384	−	0.183367i	−0.454399	−	0.890798i	$-0.650146\pi$
$431$	5.23962	−	3.80681i	0.252384	−	0.183367i	0.706783	+	0.707431i	$0.250146\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−5.79073			−0.278285			−0.139142	−	0.990272i	$-0.544435\pi$
$433$	−5.79073			−0.278285			−0.139142	+	0.990272i	$0.544435\pi$
$434$	19.3330	−	8.43642i	0.928016	−	0.404961i
$435$	−4.27094			−0.204776
$436$	5.35543	+	3.89095i	0.256479	+	0.186343i
$437$	−4.41445	+	3.20729i	−0.211172	+	0.153425i
$438$	−0.630797	−	1.94139i	−0.0301407	−	0.0927634i
$439$	−27.5147			−1.31320			−0.656601	−	0.754238i	$-0.728007\pi$
$439$	−27.5147			−1.31320			−0.656601	+	0.754238i	$0.728007\pi$
$440$	−5.26576			−0.251035
$441$	2.27217	+	6.99302i	0.108199	+	0.333001i
$442$	−2.07656	+	6.39099i	−0.0987719	+	0.303989i
$443$	3.71016	−	11.4187i	0.176275	−	0.542519i	−0.823414	−	0.567441i	$-0.807934\pi$
$443$	3.71016	−	11.4187i	0.176275	−	0.542519i	0.999689	+	0.0249216i	$0.00793362\pi$
$444$	5.48087	+	3.98208i	0.260111	+	0.188981i
$445$	0.991032	+	3.05008i	0.0469794	+	0.144588i
$446$	−16.9544	−	12.3181i	−0.802815	−	0.583280i
$447$	12.9886	−	9.43677i	0.614340	−	0.446344i
$448$	−1.17072	+	3.60310i	−0.0553112	+	0.170230i
$449$	−13.3487	+	9.69843i	−0.629966	+	0.457697i	−0.856388	−	0.516332i	$-0.827297\pi$
$449$	−13.3487	+	9.69843i	−0.629966	+	0.457697i	0.226422	+	0.974029i	$0.427297\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−16.2086	+	49.8850i	−0.763234	+	2.34899i
$452$	−3.89679	+	2.83118i	−0.183290	+	0.133168i
$453$	−8.02217	−	5.82845i	−0.376914	−	0.273844i
$454$	6.24435	+	19.2181i	0.293062	+	0.901952i
$455$	4.12128	+	2.99429i	0.193209	+	0.140374i
$456$	−0.255202	+	0.785431i	−0.0119509	+	0.0367812i
$457$	10.5262	−	32.3962i	0.492393	−	1.51543i	−0.328586	−	0.944474i	$-0.606572\pi$
$457$	10.5262	−	32.3962i	0.492393	−	1.51543i	0.820980	−	0.570957i	$-0.193428\pi$
$458$	1.58572	+	4.88036i	0.0740960	+	0.228044i
$459$	−4.99755			−0.233266
$460$	−6.60720			−0.308062
$461$	−8.42830	−	25.9396i	−0.392545	−	1.20813i	−0.930857	−	0.365383i	$-0.880938\pi$
$461$	−8.42830	−	25.9396i	−0.392545	−	1.20813i	0.538312	−	0.842745i	$-0.319062\pi$
$462$	−16.1395	+	11.7260i	−0.750875	+	0.545543i
$463$	27.1575	+	19.7311i	1.26212	+	0.916981i	0.998860	−	0.0477452i	$-0.0152036\pi$
$463$	27.1575	+	19.7311i	1.26212	+	0.916981i	0.263256	+	0.964726i	$0.415204\pi$
$464$	−4.27094			−0.198274
$465$	5.43736	+	1.19795i	0.252152	+	0.0555537i
$466$	−24.5029			−1.13508
$467$	−31.0181	−	22.5359i	−1.43534	−	1.04284i	−0.988990	−	0.147983i	$-0.952722\pi$
$467$	−31.0181	−	22.5359i	−1.43534	−	1.04284i	−0.446355	−	0.894856i	$-0.647278\pi$
$468$	−1.08783	+	0.790358i	−0.0502852	+	0.0365343i
$469$	−4.25185	−	13.0858i	−0.196332	−	0.604248i
$470$	6.74477			0.311113
$471$	20.4454			0.942073
$472$	2.60122	+	8.00574i	0.119731	+	0.368494i
$473$	−8.88175	+	27.3352i	−0.408383	+	1.25687i
$474$	2.10192	−	6.46905i	0.0965445	−	0.297133i
$475$	0.668127	+	0.485423i	0.0306558	+	0.0222727i
$476$	5.85072	+	18.0067i	0.268167	+	0.825334i
$477$	3.08661	+	2.24255i	0.141326	+	0.102679i
$478$	−12.4030	+	9.01127i	−0.567298	+	0.412166i
$479$	−3.39046	+	10.4348i	−0.154914	+	0.476777i	−0.998152	−	0.0607637i	$-0.980646\pi$
$479$	−3.39046	+	10.4348i	−0.154914	+	0.476777i	0.843238	+	0.537540i	$0.180646\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	7.36978	−	5.35446i	0.336033	−	0.244142i
$482$	−3.70554	+	11.4045i	−0.168783	+	0.519459i
$483$	−20.2509	+	14.7132i	−0.921449	+	0.669472i
$484$	−13.5335	−	9.83263i	−0.615157	−	0.446938i
$485$	−5.38066	−	16.5600i	−0.244323	−	0.751949i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	4.43976	−	13.6642i	0.201185	−	0.619183i	−0.798664	−	0.601777i	$-0.794459\pi$
$487$	4.43976	−	13.6642i	0.201185	−	0.619183i	0.999849	−	0.0174053i	$-0.00554056\pi$
$488$	2.25672	−	6.94547i	0.102157	−	0.314407i
$489$	2.98547	+	9.18833i	0.135008	+	0.415510i
$490$	7.35290			0.332170
$491$	−24.1830			−1.09136			−0.545682	−	0.837992i	$-0.683730\pi$
$491$	−24.1830			−1.09136			−0.545682	+	0.837992i	$0.683730\pi$
$492$	3.07811	+	9.47346i	0.138772	+	0.427097i
$493$	−17.2679	+	12.5458i	−0.777705	+	0.565036i
$494$	0.898389	+	0.652718i	0.0404204	+	0.0293672i
$495$	−5.26576			−0.236678
$496$	5.43736	+	1.19795i	0.244145	+	0.0537897i
$497$	−17.1850			−0.770854
$498$	0.379511	+	0.275731i	0.0170063	+	0.0123558i
$499$	7.15226	−	5.19642i	0.320179	−	0.232624i	−0.416073	−	0.909331i	$-0.636594\pi$
$499$	7.15226	−	5.19642i	0.320179	−	0.232624i	0.736252	+	0.676707i	$0.236594\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−4.73236			−0.211426
$502$	7.98503			0.356390
$503$	1.22358	+	3.76579i	0.0545567	+	0.167908i	0.974622	−	0.223857i	$-0.0718647\pi$
$503$	1.22358	+	3.76579i	0.0545567	+	0.167908i	−0.920065	+	0.391765i	$0.871865\pi$
$504$	−1.17072	+	3.60310i	−0.0521479	+	0.160495i
$505$	−4.95681	+	15.2555i	−0.220575	+	0.678860i
$506$	−28.1473	−	20.4502i	−1.25130	−	0.909122i
$507$	−3.45850	−	10.6442i	−0.153598	−	0.472725i
$508$	4.84152	+	3.51757i	0.214808	+	0.156067i
$509$	−4.31087	+	3.13203i	−0.191076	+	0.138825i	−0.679210	−	0.733944i	$-0.737678\pi$
$509$	−4.31087	+	3.13203i	−0.191076	+	0.138825i	0.488134	+	0.872768i	$0.337678\pi$
$510$	−1.54433	+	4.75295i	−0.0683840	+	0.210464i
$511$	−6.25655	+	4.54565i	−0.276773	+	0.201088i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.255202	+	0.785431i	−0.0112674	+	0.0346776i
$514$	−16.6117	+	12.0691i	−0.732712	+	0.532347i
$515$	−13.2793	−	9.64795i	−0.585154	−	0.425140i
$516$	1.68670	+	5.19112i	0.0742527	+	0.228526i
$517$	28.7333	+	20.8760i	1.26369	+	0.918125i
$518$	7.93129	−	24.4100i	0.348481	−	1.07251i
$519$	−3.61332	+	11.1206i	−0.158607	+	0.488142i
$520$	0.415516	+	1.27883i	0.0182216	+	0.0560802i
$521$	−26.3009			−1.15227			−0.576133	−	0.817356i	$-0.695439\pi$
$521$	−26.3009			−1.15227			−0.576133	+	0.817356i	$0.695439\pi$
$522$	−4.27094			−0.186934
$523$	10.2516	+	31.5511i	0.448270	+	1.37963i	0.878857	+	0.477085i	$0.158306\pi$
$523$	10.2516	+	31.5511i	0.448270	+	1.37963i	−0.430587	+	0.902549i	$0.641694\pi$
$524$	13.4861	−	9.79821i	0.589142	−	0.428037i
$525$	3.06498	+	2.22684i	0.133767	+	0.0971872i
$526$	4.94836			0.215759
$527$	25.5028	−	11.1287i	1.11092	−	0.484775i
$528$	−5.26576			−0.229163
$529$	−16.7103	−	12.1408i	−0.726535	−	0.527859i
$530$	3.08661	−	2.24255i	0.134074	−	0.0974102i
$531$	2.60122	+	8.00574i	0.112883	+	0.347420i
$532$	3.12875			0.135649
$533$	13.3939			0.580155
$534$	0.991032	+	3.05008i	0.0428862	+	0.131990i
$535$	−1.44283	+	4.44057i	−0.0623790	+	0.191983i
$536$	1.12230	−	3.45407i	0.0484758	−	0.149193i
$537$	−0.730238	−	0.530549i	−0.0315121	−	0.0228949i
$538$	5.94591	+	18.2996i	0.256346	+	0.788953i
$539$	31.3240	+	22.7582i	1.34922	+	0.980267i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	3.00708	−	9.25484i	0.129284	−	0.397897i	−0.865373	−	0.501128i	$-0.832918\pi$
$541$	3.00708	−	9.25484i	0.129284	−	0.397897i	0.994657	+	0.103232i	$0.0329184\pi$
$542$	3.44661	−	2.50411i	0.148045	−	0.107561i
$543$	−0.803274	+	0.583613i	−0.0344718	+	0.0250452i
$544$	−1.54433	+	4.75295i	−0.0662125	+	0.203781i
$545$	5.35543	−	3.89095i	0.229401	−	0.166670i
$546$	4.12128	+	2.99429i	0.176375	+	0.128144i
$547$	−1.84811	−	5.68791i	−0.0790197	−	0.243198i	0.903741	−	0.428080i	$-0.140810\pi$
$547$	−1.84811	−	5.68791i	−0.0790197	−	0.243198i	−0.982761	+	0.184882i	$0.940810\pi$
$548$	−12.8558	−	9.34029i	−0.549173	−	0.398997i
$549$	2.25672	−	6.94547i	0.0963144	−	0.296425i
$550$	−1.62721	+	5.00804i	−0.0693845	+	0.213544i
$551$	1.08995	+	3.35453i	0.0464336	+	0.142908i
$552$	−6.60720			−0.281221
$553$	−25.7694			−1.09583
$554$	5.21953	+	16.0641i	0.221756	+	0.682496i
$555$	5.48087	−	3.98208i	0.232650	−	0.169030i
$556$	5.46466	+	3.97031i	0.231753	+	0.168379i
$557$	11.5650			0.490025			0.245013	−	0.969520i	$-0.421208\pi$
$557$	11.5650			0.490025			0.245013	+	0.969520i	$0.421208\pi$
$558$	5.43736	+	1.19795i	0.230182	+	0.0507134i
$559$	7.33939			0.310423
$560$	3.06498	+	2.22684i	0.129519	+	0.0941011i
$561$	−21.2900	+	15.4681i	−0.898865	+	0.653064i
$562$	−6.64513	−	20.4516i	−0.280308	−	0.862700i
$563$	−18.7514			−0.790275			−0.395138	−	0.918622i	$-0.629303\pi$
$563$	−18.7514			−0.790275			−0.395138	+	0.918622i	$0.629303\pi$
$564$	6.74477			0.284006
$565$	1.48844	+	4.58095i	0.0626192	+	0.192722i
$566$	5.78102	−	17.7922i	0.242995	−	0.747860i
$567$	−1.17072	+	3.60310i	−0.0491655	+	0.151316i
$568$	−3.66977	−	2.66624i	−0.153980	−	0.111873i
$569$	11.6125	+	35.7396i	0.486822	+	1.49828i	0.829325	+	0.558767i	$0.188725\pi$
$569$	11.6125	+	35.7396i	0.486822	+	1.49828i	−0.342503	+	0.939517i	$0.611275\pi$
$570$	0.668127	+	0.485423i	0.0279848	+	0.0203321i
$571$	−20.0455	+	14.5639i	−0.838876	+	0.609479i	−0.922057	−	0.387055i	$-0.873492\pi$
$571$	−20.0455	+	14.5639i	−0.838876	+	0.609479i	0.0831802	+	0.996535i	$0.473492\pi$
$572$	−2.18801	+	6.73400i	−0.0914852	+	0.281563i
$573$	−16.8041	+	12.2089i	−0.702003	+	0.510035i
$574$	30.5302	−	22.1815i	1.27431	−	0.925838i
$575$	−2.04174	+	6.28382i	−0.0851463	+	0.262053i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−9.41110	−	6.83757i	−0.391789	−	0.284652i	0.374399	−	0.927268i	$-0.377849\pi$
$577$	−9.41110	−	6.83757i	−0.391789	−	0.284652i	−0.766188	+	0.642616i	$0.777849\pi$
$578$	2.46456	+	7.58514i	0.102512	+	0.315500i
$579$	−21.2307	−	15.4250i	−0.882319	−	0.641042i
$580$	−1.31979	+	4.06191i	−0.0548015	+	0.168662i
$581$	0.549185	−	1.69022i	0.0227840	−	0.0701220i
$582$	−5.38066	−	16.5600i	−0.223035	−	0.686432i
$583$	20.0902			0.832053
$584$	−2.04130			−0.0844697
$585$	0.415516	+	1.27883i	0.0171795	+	0.0528729i
$586$	−19.0830	+	13.8646i	−0.788311	+	0.572741i
$587$	−33.8100	−	24.5644i	−1.39549	−	1.01388i	−0.995238	−	0.0974765i	$-0.968923\pi$
$587$	−33.8100	−	24.5644i	−1.39549	−	1.01388i	−0.400251	−	0.916406i	$-0.631077\pi$
$588$	7.35290			0.303228
$589$	−0.446717	−	4.57639i	−0.0184066	−	0.188567i
$590$	8.41774			0.346553
$591$	4.87251	+	3.54009i	0.200428	+	0.145620i
$592$	5.48087	−	3.98208i	0.225262	−	0.163663i
$593$	−11.4595	−	35.2688i	−0.470586	−	1.44832i	−0.851819	−	0.523836i	$-0.824500\pi$
$593$	−11.4595	−	35.2688i	−0.470586	−	1.44832i	0.381233	−	0.924479i	$-0.375500\pi$
$594$	−5.26576			−0.216057
$595$	18.9333			0.776190
$596$	−4.96120	−	15.2690i	−0.203219	−	0.625443i
$597$	−1.29530	+	3.98653i	−0.0530132	+	0.163158i
$598$	−2.74540	+	8.44946i	−0.112268	+	0.345524i
$599$	−34.1753	−	24.8298i	−1.39637	−	1.01452i	−0.995133	−	0.0985428i	$-0.968582\pi$
$599$	−34.1753	−	24.8298i	−1.39637	−	1.01452i	−0.401233	−	0.915976i	$-0.631418\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	7.75507	+	5.63439i	0.316336	+	0.229832i	0.734610	−	0.678489i	$-0.237365\pi$
$601$	7.75507	+	5.63439i	0.316336	+	0.229832i	−0.418274	+	0.908321i	$0.637365\pi$
$602$	16.7295	−	12.1547i	0.681842	−	0.495387i
$603$	1.12230	−	3.45407i	0.0457035	−	0.140661i
$604$	−8.02217	+	5.82845i	−0.326417	+	0.237156i
$605$	−13.5335	+	9.83263i	−0.550213	+	0.399753i
$606$	−4.95681	+	15.2555i	−0.201357	+	0.619712i
$607$	27.7332	−	20.1493i	1.12565	−	0.817836i	0.140598	−	0.990067i	$-0.455098\pi$
$607$	27.7332	−	20.1493i	1.12565	−	0.817836i	0.985057	+	0.172231i	$0.0550976\pi$
$608$	0.668127	+	0.485423i	0.0270961	+	0.0196865i
$609$	5.00007	+	15.3886i	0.202613	+	0.623579i
$610$	−5.90817	−	4.29254i	−0.239215	−	0.173800i
$611$	2.80256	−	8.62538i	0.113379	−	0.348946i
$612$	−1.54433	+	4.75295i	−0.0624257	+	0.192127i
$613$	−5.36247	−	16.5040i	−0.216588	−	0.666589i	−0.999037	−	0.0438748i	$-0.986030\pi$
$613$	−5.36247	−	16.5040i	−0.216588	−	0.666589i	0.782449	−	0.622715i	$-0.213970\pi$
$614$	20.7146			0.835973
$615$	9.96099			0.401666
$616$	6.16472	+	18.9731i	0.248384	+	0.764447i
$617$	32.5282	−	23.6332i	1.30954	−	0.951435i	0.309538	−	0.950887i	$-0.399826\pi$
$617$	32.5282	−	23.6332i	1.30954	−	0.951435i	1.00000		0.000547791i	$-0.000174367\pi$
$618$	−13.2793	−	9.64795i	−0.534170	−	0.388098i
$619$	−40.3836			−1.62315			−0.811577	−	0.584245i	$-0.801391\pi$
$619$	−40.3836			−1.62315			−0.811577	+	0.584245i	$0.801391\pi$
$620$	2.81956	−	4.80105i	0.113236	−	0.192815i
$621$	−6.60720			−0.265138
$622$	−12.4064	−	9.01380i	−0.497453	−	0.361421i
$623$	9.82953	−	7.14157i	0.393812	−	0.286121i
$624$	0.415516	+	1.27883i	0.0166339	+	0.0511940i
$625$	1.00000			0.0400000
$626$	8.95798			0.358033
$627$	1.34383	+	4.13589i	0.0536675	+	0.165172i
$628$	6.31796	−	19.4447i	0.252114	−	0.775928i
$629$	10.4624	−	32.1999i	0.417163	−	1.28390i
$630$	3.06498	+	2.22684i	0.122112	+	0.0887193i
$631$	1.40371	+	4.32019i	0.0558810	+	0.171984i	0.975101	−	0.221759i	$-0.0711799\pi$
$631$	1.40371	+	4.32019i	0.0558810	+	0.171984i	−0.919220	+	0.393743i	$0.871180\pi$
$632$	−5.50291	−	3.99809i	−0.218894	−	0.159036i
$633$	2.65844	−	1.93147i	0.105664	−	0.0767691i
$634$	9.80482	−	30.1761i	0.389399	−	1.19845i
$635$	4.84152	−	3.51757i	0.192130	−	0.139591i
$636$	3.08661	−	2.24255i	0.122392	−	0.0889230i
$637$	3.05525	−	9.40308i	0.121053	−	0.372564i
$638$	−18.1946	+	13.2192i	−0.720332	+	0.523352i
$639$	−3.66977	−	2.66624i	−0.145174	−	0.105475i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−5.51114	−	4.00408i	−0.217677	−	0.158152i	0.473603	−	0.880738i	$-0.342953\pi$
$641$	−5.51114	−	4.00408i	−0.217677	−	0.158152i	−0.691280	+	0.722587i	$0.742953\pi$
$642$	−1.44283	+	4.44057i	−0.0569440	+	0.175255i
$643$	−2.64268	+	8.13332i	−0.104217	+	0.320747i	−0.989546	−	0.144218i	$-0.953933\pi$
$643$	−2.64268	+	8.13332i	−0.104217	+	0.320747i	0.885329	+	0.464965i	$0.153933\pi$
$644$	7.73517	+	23.8064i	0.304808	+	0.938103i
$645$	5.45827			0.214919
$646$	4.12723			0.162384
$647$	−10.8394	−	33.3602i	−0.426141	−	1.31153i	−0.901898	−	0.431950i	$-0.857826\pi$
$647$	−10.8394	−	33.3602i	−0.426141	−	1.31153i	0.475757	−	0.879577i	$-0.342174\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	35.8603	+	26.0541i	1.40764	+	1.02271i
$650$	1.34464			0.0527410
$651$	−2.04927	−	20.9938i	−0.0803174	−	0.822813i
$652$	9.66118			0.378361
$653$	−26.4093	−	19.1875i	−1.03348	−	0.750865i	−0.0644752	−	0.997919i	$-0.520537\pi$
$653$	−26.4093	−	19.1875i	−1.03348	−	0.750865i	−0.969002	+	0.247054i	$0.920537\pi$
$654$	5.35543	−	3.89095i	0.209414	−	0.152148i
$655$	−5.15122	−	15.8538i	−0.201275	−	0.619460i
$656$	9.96099			0.388911
$657$	−2.04130			−0.0796388
$658$	−7.89622	−	24.3021i	−0.307827	−	0.947393i
$659$	−8.25007	+	25.3911i	−0.321377	+	0.989097i	0.651672	+	0.758500i	$0.274068\pi$
$659$	−8.25007	+	25.3911i	−0.321377	+	0.989097i	−0.973050	+	0.230596i	$0.925932\pi$
$660$	−1.62721	+	5.00804i	−0.0633391	+	0.194938i
$661$	14.6635	+	10.6536i	0.570343	+	0.414379i	0.835230	−	0.549901i	$-0.185335\pi$
$661$	14.6635	+	10.6536i	0.570343	+	0.414379i	−0.264887	+	0.964280i	$0.585335\pi$
$662$	0.745779	+	2.29527i	0.0289855	+	0.0892083i
$663$	5.43650	+	3.94985i	0.211136	+	0.153400i
$664$	0.379511	−	0.275731i	0.0147279	−	0.0107004i
$665$	0.966838	−	2.97562i	0.0374924	−	0.115390i
$666$	5.48087	−	3.98208i	0.212379	−	0.154303i
$667$	−22.8296	+	16.5867i	−0.883967	+	0.642240i
$668$	−1.46238	+	4.50074i	−0.0565812	+	0.174139i
$669$	−16.9544	+	12.3181i	−0.655496	+	0.476246i
$670$	−2.93821	−	2.13474i	−0.113513	−	0.0824720i
$671$	−11.8834	−	36.5732i	−0.458752	−	1.41189i
$672$	3.06498	+	2.22684i	0.118234	+	0.0859021i
$673$	14.5236	−	44.6990i	0.559843	−	1.72302i	−0.122953	−	0.992412i	$-0.539237\pi$
$673$	14.5236	−	44.6990i	0.559843	−	1.72302i	0.682797	−	0.730608i	$-0.260763\pi$
$674$	9.46082	−	29.1174i	0.364417	−	1.12156i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−11.1920			−0.430460
$677$	−6.31126			−0.242561			−0.121281	−	0.992618i	$-0.538700\pi$
$677$	−6.31126			−0.242561			−0.121281	+	0.992618i	$0.538700\pi$
$678$	1.48844	+	4.58095i	0.0571633	+	0.175930i
$679$	−53.3679	+	38.7741i	−2.04807	+	1.48801i
$680$	4.04310	+	2.93749i	0.155046	+	0.112647i
$681$	20.2071			0.774340
$682$	26.8715	−	11.7260i	1.02896	−	0.449012i
$683$	−15.5095			−0.593455			−0.296727	−	0.954962i	$-0.595895\pi$
$683$	−15.5095			−0.593455			−0.296727	+	0.954962i	$0.595895\pi$
$684$	0.668127	+	0.485423i	0.0255465	+	0.0185606i
$685$	−12.8558	+	9.34029i	−0.491195	+	0.356874i
$686$	−0.413145	−	1.27153i	−0.0157740	−	0.0485473i
$687$	5.13151			0.195779
$688$	5.45827			0.208094
$689$	−1.58530	−	4.87905i	−0.0603951	−	0.185877i
$690$	−2.04174	+	6.28382i	−0.0777276	+	0.239221i
$691$	3.33819	−	10.2739i	0.126991	−	0.390837i	−0.867268	−	0.497842i	$-0.834126\pi$
$691$	3.33819	−	10.2739i	0.126991	−	0.390837i	0.994259	+	0.107005i	$0.0341260\pi$
$692$	9.45979	+	6.87294i	0.359607	+	0.261270i
$693$	6.16472	+	18.9731i	0.234178	+	0.720727i
$694$	4.84316	+	3.51876i	0.183844	+	0.133570i
$695$	5.46466	−	3.97031i	0.207286	−	0.150602i
$696$	−1.31979	+	4.06191i	−0.0500267	+	0.153966i
$697$	40.2733	−	29.2603i	1.52546	−	1.10831i
$698$	−17.7500	+	12.8961i	−0.671847	+	0.488126i
$699$	−7.57182	+	23.3037i	−0.286393	+	0.881426i
$700$	3.06498	−	2.22684i	0.115845	−	0.0841665i
$701$	37.4065	+	27.1774i	1.41282	+	1.02648i	0.992904	+	0.118916i	$0.0379420\pi$
$701$	37.4065	+	27.1774i	1.41282	+	1.02648i	0.419920	+	0.907561i	$0.362058\pi$
$702$	0.415516	+	1.27883i	0.0156826	+	0.0482662i
$703$	−4.52638	−	3.28861i	−0.170716	−	0.124032i
$704$	−1.62721	+	5.00804i	−0.0613278	+	0.188748i
$705$	2.08425	−	6.41465i	0.0784973	−	0.241590i
$706$	−8.35381	−	25.7104i	−0.314400	−	0.967623i
$707$	60.7700			2.28549
$708$	8.41774			0.316358
$709$	−12.5491	−	38.6222i	−0.471292	−	1.45049i	−0.850893	−	0.525339i	$-0.823939\pi$
$709$	−12.5491	−	38.6222i	−0.471292	−	1.45049i	0.379601	−	0.925150i	$-0.376061\pi$
$710$	−3.66977	+	2.66624i	−0.137724	+	0.100062i
$711$	−5.50291	−	3.99809i	−0.206375	−	0.149940i
$712$	3.20705			0.120189
$713$	33.7169	−	14.7132i	1.26271	−	0.551012i
$714$	18.9333			0.708562
$715$	5.72828	+	4.16184i	0.214225	+	0.155644i
$716$	−0.730238	+	0.530549i	−0.0272903	+	0.0198276i
$717$	4.73751	+	14.5805i	0.176925	+	0.544520i
$718$	−1.10662			−0.0412988
$719$	30.6326			1.14240			0.571202	−	0.820809i	$-0.306477\pi$
$719$	30.6326			1.14240			0.571202	+	0.820809i	$0.306477\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	−19.2162	+	59.1415i	−0.715650	+	2.20255i
$722$	−5.66056	+	17.4214i	−0.210664	+	0.648358i
$723$	9.70122	+	7.04835i	0.360792	+	0.262131i
$724$	0.306823	+	0.944305i	0.0114030	+	0.0350948i
$725$	3.45527	+	2.51040i	0.128325	+	0.0932339i
$726$	−13.5335	+	9.83263i	−0.502274	+	0.364923i
$727$	2.91016	−	8.95655i	0.107932	−	0.332180i	−0.882476	−	0.470358i	$-0.844125\pi$
$727$	2.91016	−	8.95655i	0.107932	−	0.332180i	0.990407	+	0.138178i	$0.0441247\pi$
$728$	4.12128	−	2.99429i	0.152745	−	0.110976i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−0.630797	+	1.94139i	−0.0233469	+	0.0718542i
$731$	22.0683	−	16.0336i	0.816226	−	0.593023i
$732$	−5.90817	−	4.29254i	−0.218372	−	0.158657i
$733$	1.07655	+	3.31327i	0.0397631	+	0.122378i	0.968968	−	0.247188i	$-0.0795064\pi$
$733$	1.07655	+	3.31327i	0.0397631	+	0.122378i	−0.929205	+	0.369566i	$0.879506\pi$
$734$	−1.27780	−	0.928378i	−0.0471646	−	0.0342671i
$735$	2.27217	−	6.99302i	0.0838103	−	0.257942i
$736$	−2.04174	+	6.28382i	−0.0752594	+	0.231625i
$737$	−5.90975	−	18.1883i	−0.217688	−	0.669976i
$738$	9.96099			0.366669
$739$	−1.56186			−0.0574541			−0.0287270	−	0.999587i	$-0.509145\pi$
$739$	−1.56186			−0.0574541			−0.0287270	+	0.999587i	$0.509145\pi$
$740$	−2.09351	−	6.44315i	−0.0769588	−	0.236855i
$741$	0.898389	−	0.652718i	0.0330031	−	0.0239782i
$742$	−11.6937	−	8.49596i	−0.429289	−	0.311896i
$743$	−47.6516			−1.74817			−0.874084	−	0.485774i	$-0.838538\pi$
$743$	−47.6516			−1.74817			−0.874084	+	0.485774i	$0.838538\pi$
$744$	2.81956	−	4.80105i	0.103370	−	0.176015i
$745$	−16.0548			−0.588202
$746$	25.1330	+	18.2602i	0.920183	+	0.668552i
$747$	0.379511	−	0.275731i	0.0138856	−	0.0100885i
$748$	8.13206	+	25.0279i	0.297338	+	0.915111i
$749$	17.6890			0.646341
$750$	1.00000			0.0365148
$751$	2.18989	+	6.73978i	0.0799102	+	0.245938i	0.983028	−	0.183454i	$-0.0587278\pi$
$751$	2.18989	+	6.73978i	0.0799102	+	0.245938i	−0.903118	+	0.429392i	$0.858728\pi$
$752$	2.08425	−	6.41465i	0.0760047	−	0.233918i
$753$	2.46751	−	7.59422i	0.0899211	−	0.276749i
$754$	4.64608	+	3.37558i	0.169200	+	0.122931i
$755$	3.06420	+	9.43063i	0.111518	+	0.343216i
$756$	3.06498	+	2.22684i	0.111472	+	0.0809893i
$757$	28.1371	−	20.4428i	1.02266	−	0.743007i	0.0558344	−	0.998440i	$-0.482218\pi$
$757$	28.1371	−	20.4428i	1.02266	−	0.743007i	0.966827	+	0.255433i	$0.0822181\pi$
$758$	−3.22507	+	9.92576i	−0.117140	+	0.360520i
$759$	−28.1473	+	20.4502i	−1.02168	+	0.742295i
$760$	0.668127	−	0.485423i	0.0242355	−	0.0176081i
$761$	−14.1548	+	43.5640i	−0.513111	+	1.57919i	0.273582	+	0.961849i	$0.411792\pi$
$761$	−14.1548	+	43.5640i	−0.513111	+	1.57919i	−0.786693	+	0.617345i	$0.788208\pi$
$762$	4.84152	−	3.51757i	0.175390	−	0.127428i
$763$	−20.2892	−	14.7409i	−0.734517	−	0.533658i
$764$	6.41861	+	19.7545i	0.232217	+	0.714691i
$765$	4.04310	+	2.93749i	0.146179	+	0.106205i
$766$	−7.18366	+	22.1090i	−0.259556	+	0.798831i
$767$	3.49770	−	10.7648i	0.126295	−	0.388695i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	25.5495			0.921340			0.460670	−	0.887571i	$-0.347609\pi$
$769$	25.5495			0.921340			0.460670	+	0.887571i	$0.347609\pi$
$770$	19.9495			0.718929
$771$	6.34512	+	19.5283i	0.228514	+	0.703293i
$772$	−21.2307	+	15.4250i	−0.764111	+	0.555159i
$773$	38.9216	+	28.2782i	1.39991	+	1.01710i	0.994694	+	0.102878i	$0.0328052\pi$
$773$	38.9216	+	28.2782i	1.39991	+	1.01710i	0.405220	+	0.914219i	$0.367195\pi$
$774$	5.45827			0.196193
$775$	−3.69478	−	4.16517i	−0.132720	−	0.149617i
$776$	−17.4122			−0.625060
$777$	−20.7644	−	15.0862i	−0.744919	−	0.541215i
$778$	−26.0745	+	18.9443i	−0.934817	+	0.679184i
$779$	−2.54206	−	7.82367i	−0.0910789	−	0.280312i
$780$	1.34464			0.0481457
$781$	−23.8859			−0.854706
$782$	10.2037	+	31.4037i	0.364883	+	1.12299i
$783$	−1.31979	+	4.06191i	−0.0471656	+	0.145161i
$784$	2.27217	−	6.99302i	0.0811490	−	0.249751i
$785$	−16.5406	−	12.0175i	−0.590361	−	0.428922i
$786$	−5.15122	−	15.8538i	−0.183738	−	0.565487i
$787$	25.7742	+	18.7261i	0.918751	+	0.667512i	0.943213	−	0.332189i	$-0.107787\pi$
$787$	25.7742	+	18.7261i	0.918751	+	0.667512i	−0.0244615	+	0.999701i	$0.507787\pi$
$788$	4.87251	−	3.54009i	0.173576	−	0.126110i
$789$	1.52913	−	4.70617i	0.0544384	−	0.167544i
$790$	−5.50291	+	3.99809i	−0.195785	+	0.142246i
$791$	14.7631	−	10.7260i	0.524915	−	0.381373i
$792$	−1.62721	+	5.00804i	−0.0578204	+	0.177953i
$793$	−7.94434	+	5.77190i	−0.282112	+	0.204966i
$794$	−19.5268	−	14.1871i	−0.692982	−	0.503481i
$795$	−1.17898	−	3.62853i	−0.0418141	−	0.128691i
$796$	3.39114	+	2.46381i	0.120196	+	0.0873274i
$797$	3.26114	−	10.0368i	0.115516	−	0.355520i	−0.876539	−	0.481331i	$-0.840153\pi$
$797$	3.26114	−	10.0368i	0.115516	−	0.355520i	0.992054	+	0.125811i	$0.0401533\pi$
$798$	0.966838	−	2.97562i	0.0342257	−	0.105336i
$799$	−10.4161	−	32.0575i	−0.368496	−	1.13411i
$800$	1.00000			0.0353553
$801$	3.20705			0.113315
$802$	−12.1351	−	37.3481i	−0.428507	−	1.31881i
$803$	−8.69614	+	6.31812i	−0.306880	+	0.222961i
$804$	−2.93821	−	2.13474i	−0.103623	−	0.0752863i
$805$	25.0315			0.882245
$806$	−4.96814	−	5.60064i	−0.174995	−	0.197274i
$807$	19.2414			0.677328
$808$	12.9771	+	9.42841i	0.456532	+	0.331690i
$809$	−23.5134	+	17.0835i	−0.826688	+	0.600624i	−0.918620	−	0.395141i	$-0.870696\pi$
$809$	−23.5134	+	17.0835i	−0.826688	+	0.600624i	0.0919324	+	0.995765i	$0.470696\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	46.9718			1.64940			0.824701	−	0.565569i	$-0.191343\pi$
$811$	46.9718			1.64940			0.824701	+	0.565569i	$0.191343\pi$
$812$	16.1806			0.567827
$813$	−1.31649	−	4.05173i	−0.0461713	−	0.142100i
$814$	11.0239	−	33.9281i	0.386388	−	1.18918i
$815$	2.98547	−	9.18833i	0.104576	−	0.321853i
$816$	4.04310	+	2.93749i	0.141537	+	0.102833i
$817$	−1.39296	−	4.28709i	−0.0487335	−	0.149986i
$818$	−3.66205	−	2.66063i	−0.128040	−	0.0930268i
$819$	4.12128	−	2.99429i	0.144009	−	0.104629i
$820$	3.07811	−	9.47346i	0.107492	−	0.330828i
$821$	−22.0501	+	16.0203i	−0.769552	+	0.559112i	−0.901825	−	0.432101i	$-0.857772\pi$
$821$	−22.0501	+	16.0203i	−0.769552	+	0.559112i	0.132273	+	0.991213i	$0.457772\pi$
$822$	−12.8558	+	9.34029i	−0.448398	+	0.325780i
$823$	1.71347	−	5.27353i	0.0597280	−	0.183824i	−0.916741	−	0.399482i	$-0.869190\pi$
$823$	1.71347	−	5.27353i	0.0597280	−	0.183824i	0.976469	+	0.215659i	$0.0691898\pi$
$824$	−13.2793	+	9.64795i	−0.462605	+	0.336102i
$825$	4.26009	+	3.09514i	0.148317	+	0.107759i
$826$	−9.85479	−	30.3299i	−0.342892	−	1.05531i
$827$	36.1959	+	26.2978i	1.25865	+	0.914465i	0.998691	−	0.0511537i	$-0.0162898\pi$
$827$	36.1959	+	26.2978i	1.25865	+	0.914465i	0.259962	+	0.965619i	$0.416290\pi$
$828$	−2.04174	+	6.28382i	−0.0709553	+	0.218378i
$829$	0.122146	−	0.375927i	0.00424231	−	0.0130565i	−0.948913	−	0.315538i	$-0.897815\pi$
$829$	0.122146	−	0.375927i	0.00424231	−	0.0130565i	0.953155	+	0.302481i	$0.0978150\pi$
$830$	−0.144960	−	0.446142i	−0.00503164	−	0.0154858i
$831$	16.8907			0.585934
$832$	1.34464			0.0466169
$833$	−11.3553	−	34.9480i	−0.393437	−	1.21088i
$834$	5.46466	−	3.97031i	0.189226	−	0.137481i
$835$	3.82856	+	2.78161i	0.132493	+	0.0962616i
$836$	4.34874			0.150404
$837$	2.81956	−	4.80105i	0.0974582	−	0.165949i
$838$	−5.57898			−0.192723
$839$	−32.8788	−	23.8878i	−1.13510	−	0.824699i	−0.148672	−	0.988887i	$-0.547500\pi$
$839$	−32.8788	−	23.8878i	−1.13510	−	0.824699i	−0.986429	+	0.164187i	$0.947500\pi$
$840$	3.06498	−	2.22684i	0.105752	−	0.0768332i
$841$	−3.32472	−	10.2324i	−0.114646	−	0.352843i
$842$	14.6822			0.505983
$843$	−21.5041			−0.740641
$844$	−1.01544	−	3.12519i	−0.0349527	−	0.107573i
$845$	−3.45850	+	10.6442i	−0.118976	+	0.366171i
$846$	2.08425	−	6.41465i	0.0716579	−	0.220540i
$847$	51.2718	+	37.2511i	1.76172	+	1.27996i
$848$	−1.17898	−	3.62853i	−0.0404863	−	0.124604i
$849$	−15.1349	−	10.9962i	−0.519429	−	0.377387i
$850$	4.04310	−	2.93749i	0.138677	−	0.100755i
$851$	13.8322	−	42.5712i	0.474162	−	1.45932i
$852$	−3.66977	+	2.66624i	−0.125724	+	0.0913439i
$853$	1.67671	−	1.21820i	0.0574093	−	0.0417103i	−0.558711	−	0.829363i	$-0.688704\pi$
$853$	1.67671	−	1.21820i	0.0574093	−	0.0417103i	0.616120	+	0.787652i	$0.288704\pi$
$854$	−8.54963	+	26.3131i	−0.292562	+	0.900414i
$855$	0.668127	−	0.485423i	0.0228495	−	0.0166011i
$856$	3.77738	+	2.74443i	0.129108	+	0.0938025i
$857$	12.2504	+	37.7027i	0.418464	+	1.28790i	0.909116	+	0.416544i	$0.136759\pi$
$857$	12.2504	+	37.7027i	0.418464	+	1.28790i	−0.490652	+	0.871356i	$0.663241\pi$
$858$	5.72828	+	4.16184i	0.195560	+	0.142083i
$859$	10.3730	−	31.9248i	0.353922	−	1.08926i	−0.602710	−	0.797961i	$-0.705912\pi$
$859$	10.3730	−	31.9248i	0.353922	−	1.08926i	0.956632	−	0.291300i	$-0.0940877\pi$
$860$	1.68670	−	5.19112i	0.0575159	−	0.177016i
$861$	−11.6615	−	35.8904i	−0.397423	−	1.22314i
$862$	−6.47653			−0.220591
$863$	53.2834			1.81379			0.906894	−	0.421359i	$-0.138447\pi$
$863$	53.2834			1.81379			0.906894	+	0.421359i	$0.138447\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	9.45979	−	6.87294i	0.321642	−	0.233687i
$866$	4.68480	+	3.40371i	0.159196	+	0.115663i
$867$	7.97549			0.270862
$868$	−20.5996	−	4.53847i	−0.699195	−	0.154046i
$869$	−35.8175			−1.21503
$870$	3.45527	+	2.51040i	0.117145	+	0.0851105i
$871$	−3.95083	+	2.87044i	−0.133869	+	0.0972613i
$872$	−2.04559	−	6.29568i	−0.0692725	−	0.213199i
$873$	−17.4122			−0.589313
$874$	5.45656			0.184571
$875$	−1.17072	−	3.60310i	−0.0395775	−	0.121807i
$876$	−0.630797	+	1.94139i	−0.0213127	+	0.0655936i
$877$	9.24825	−	28.4632i	0.312291	−	0.961134i	−0.664564	−	0.747232i	$-0.731383\pi$
$877$	9.24825	−	28.4632i	0.312291	−	0.961134i	0.976855	−	0.213902i	$-0.0686174\pi$
$878$	22.2598	+	16.1727i	0.751233	+	0.545803i
$879$	7.28905	+	22.4334i	0.245854	+	0.756660i
$880$	4.26009	+	3.09514i	0.143608	+	0.104337i
$881$	42.7814	−	31.0825i	1.44134	−	1.04720i	0.453581	−	0.891215i	$-0.350146\pi$
$881$	42.7814	−	31.0825i	1.44134	−	1.04720i	0.987760	−	0.155980i	$-0.0498537\pi$
$882$	2.27217	−	6.99302i	0.0765080	−	0.235467i
$883$	−30.6483	+	22.2673i	−1.03140	+	0.749354i	−0.968588	−	0.248671i	$-0.920006\pi$
$883$	−30.6483	+	22.2673i	−1.03140	+	0.749354i	−0.0628095	+	0.998026i	$0.520006\pi$
$884$	5.43650	−	3.94985i	0.182849	−	0.132848i
$885$	2.60122	−	8.00574i	0.0874392	−	0.269110i
$886$	−9.71333	+	7.05715i	−0.326326	+	0.237090i
$887$	13.8509	+	10.0632i	0.465067	+	0.337891i	0.795516	−	0.605933i	$-0.207200\pi$
$887$	13.8509	+	10.0632i	0.465067	+	0.337891i	−0.330449	+	0.943824i	$0.607200\pi$
$888$	−2.09351	−	6.44315i	−0.0702535	−	0.216218i
$889$	−18.3422	−	13.3264i	−0.615178	−	0.446953i
$890$	0.991032	−	3.05008i	0.0332195	−	0.102239i
$891$	−1.62721	+	5.00804i	−0.0545136	+	0.167776i
$892$	6.47602	+	19.9311i	0.216833	+	0.667343i
$893$	−5.57017			−0.186399
$894$	−16.0548			−0.536953
$895$	0.278926	+	0.858447i	0.00932347	+	0.0286947i
$896$	3.06498	−	2.22684i	0.102394	−	0.0743934i
$897$	7.18754	+	5.22205i	0.239985	+	0.174359i
$898$	16.5000			0.550610
$899$	−2.31023	−	23.6671i	−0.0770503	−	0.789343i
$900$	1.00000			0.0333333
$901$	−15.4255	−	11.2073i	−0.513897	−	0.373368i
$902$	42.4347	−	30.8306i	1.41292	−	1.02655i
$903$	−6.39009	−	19.6667i	−0.212649	−	0.654466i
$904$	4.81670			0.160201
$905$	0.992901			0.0330052
$906$	3.06420	+	9.43063i	0.101801	+	0.313312i
$907$	−13.7904	+	42.4426i	−0.457904	+	1.40928i	0.409788	+	0.912181i	$0.365603\pi$
$907$	−13.7904	+	42.4426i	−0.457904	+	1.40928i	−0.867692	+	0.497102i	$0.834397\pi$
$908$	6.24435	−	19.2181i	0.207226	−	0.637776i
$909$	12.9771	+	9.42841i	0.430423	+	0.312721i
$910$	−1.57419	−	4.84486i	−0.0521839	−	0.160606i
$911$	−3.15123	−	2.28950i	−0.104405	−	0.0758546i	0.534358	−	0.845258i	$-0.320553\pi$
$911$	−3.15123	−	2.28950i	−0.104405	−	0.0758546i	−0.638763	+	0.769404i	$0.720553\pi$
$912$	0.668127	−	0.485423i	0.0221239	−	0.0160740i
$913$	0.763326	−	2.34928i	0.0252624	−	0.0777497i
$914$	−27.5579	+	20.0220i	−0.911533	+	0.662268i
$915$	−5.90817	+	4.29254i	−0.195318	+	0.141907i
$916$	1.58572	−	4.88036i	0.0523938	−	0.161251i
$917$	−51.0923	+	37.1207i	−1.68722	+	1.22583i
$918$	4.04310	+	2.93749i	0.133442	+	0.0969515i
$919$	18.2454	+	56.1535i	0.601860	+	1.85233i	0.517085	+	0.855934i	$0.327017\pi$
$919$	18.2454	+	56.1535i	0.601860	+	1.85233i	0.0847751	+	0.996400i	$0.472983\pi$
$920$	5.34534	+	3.88361i	0.176231	+	0.128039i
$921$	6.40116	−	19.7008i	0.210926	−	0.649162i
$922$	−8.42830	+	25.9396i	−0.277571	+	0.854276i
$923$	1.88481	+	5.80086i	0.0620394	+	0.190938i
$924$	19.9495			0.656289
$925$	−6.77473			−0.222752
$926$	−10.3732	−	31.9255i	−0.340886	−	1.04914i
$927$	−13.2793	+	9.64795i	−0.436148	+	0.316880i
$928$	3.45527	+	2.51040i	0.113425	+	0.0824079i
$929$	−8.65042			−0.283811			−0.141906	−	0.989880i	$-0.545323\pi$
$929$	−8.65042			−0.283811			−0.141906	+	0.989880i	$0.545323\pi$
$930$	−3.69478	−	4.16517i	−0.121157	−	0.136581i
$931$	−6.07240			−0.199015
$932$	19.8233	+	14.4025i	0.649333	+	0.471768i
$933$	−12.4064	+	9.01380i	−0.406169	+	0.295099i
$934$	11.8478	+	36.4639i	0.387673	+	1.19314i
$935$	26.3159			0.860622
$936$	1.34464			0.0439508
$937$	−11.5572	−	35.5695i	−0.377558	−	1.16200i	−0.941737	−	0.336351i	$-0.890807\pi$
$937$	−11.5572	−	35.5695i	−0.377558	−	1.16200i	0.564179	−	0.825653i	$-0.309193\pi$
$938$	−4.25185	+	13.0858i	−0.138828	+	0.427268i
$939$	2.76817	−	8.51954i	0.0903357	−	0.278025i
$940$	−5.45663	−	3.96447i	−0.177976	−	0.129307i
$941$	16.8956	+	51.9992i	0.550780	+	1.69513i	0.706835	+	0.707378i	$0.250122\pi$
$941$	16.8956	+	51.9992i	0.550780	+	1.69513i	−0.156055	+	0.987748i	$0.549878\pi$
$942$	−16.5406	−	12.0175i	−0.538923	−	0.391551i
$943$	53.2448	−	38.6846i	1.73389	−	1.25975i
$944$	2.60122	−	8.00574i	0.0846626	−	0.260565i
$945$	3.06498	−	2.22684i	0.0997038	−	0.0724390i
$946$	23.2527	−	16.8941i	0.756011	−	0.549274i
$947$	2.36308	−	7.27280i	0.0767896	−	0.236334i	−0.905292	−	0.424790i	$-0.860348\pi$
$947$	2.36308	−	7.27280i	0.0767896	−	0.236334i	0.982082	+	0.188455i	$0.0603481\pi$
$948$	−5.50291	+	3.99809i	−0.178726	+	0.129852i
$949$	2.22060	+	1.61336i	0.0720837	+	0.0523719i
$950$	−0.255202	−	0.785431i	−0.00827984	−	0.0254827i
$951$	−25.6693	−	18.6499i	−0.832386	−	0.604764i
$952$	5.85072	−	18.0067i	0.189623	−	0.583599i
$953$	2.86117	−	8.80578i	0.0926824	−	0.285247i	−0.893960	−	0.448146i	$-0.852084\pi$
$953$	2.86117	−	8.80578i	0.0926824	−	0.285247i	0.986643	+	0.162899i	$0.0520845\pi$
$954$	−1.17898	−	3.62853i	−0.0381709	−	0.117478i
$955$	20.7711			0.672136
$956$	15.3309			0.495836
$957$	6.94973	+	21.3891i	0.224653	+	0.691410i
$958$	8.87634	−	6.44904i	0.286782	−	0.208359i
$959$	48.7045	+	35.3859i	1.57275	+	1.14267i
$960$	1.00000			0.0322749
$961$	−3.69721	+	30.7787i	−0.119265	+	0.992862i
$962$	−9.10955			−0.293704
$963$	3.77738	+	2.74443i	0.121724	+	0.0884379i
$964$	9.70122	−	7.04835i	0.312455	−	0.227012i
$965$	8.10942	+	24.9582i	0.261051	+	0.803434i
$966$	25.0315			0.805376
$967$	4.32819			0.139185			0.0695927	−	0.997575i	$-0.477830\pi$
$967$	4.32819			0.139185			0.0695927	+	0.997575i	$0.477830\pi$
$968$	5.16932	+	15.9095i	0.166148	+	0.511352i
$969$	1.27538	−	3.92523i	0.0409712	−	0.126096i
$970$	−5.38066	+	16.5600i	−0.172762	+	0.531708i
$971$	−41.3441	−	30.0383i	−1.32680	−	0.963974i	−0.999821	−	0.0189412i	$-0.993970\pi$
$971$	−41.3441	−	30.0383i	−1.32680	−	0.963974i	−0.326976	−	0.945033i	$-0.606030\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−20.7030	−	15.0416i	−0.663707	−	0.482212i
$974$	−11.6234	+	8.44492i	−0.372439	+	0.270593i
$975$	0.415516	−	1.27883i	0.0133072	−	0.0409552i
$976$	−5.90817	+	4.29254i	−0.189116	+	0.137401i
$977$	−0.686416	+	0.498711i	−0.0219604	+	0.0159552i	−0.598711	−	0.800965i	$-0.704320\pi$
$977$	−0.686416	+	0.498711i	−0.0219604	+	0.0159552i	0.576751	+	0.816920i	$0.304320\pi$
$978$	2.98547	−	9.18833i	0.0954647	−	0.293810i
$979$	13.6623	−	9.92626i	0.436650	−	0.317244i
$980$	−5.94862	−	4.32193i	−0.190022	−	0.138059i
$981$	−2.04559	−	6.29568i	−0.0653107	−	0.201006i
$982$	19.5645	+	14.2144i	0.624328	+	0.453601i
$983$	−6.70062	+	20.6224i	−0.213717	+	0.657752i	0.785526	+	0.618829i	$0.212393\pi$
$983$	−6.70062	+	20.6224i	−0.213717	+	0.657752i	−0.999242	+	0.0389228i	$0.987607\pi$
$984$	3.07811	−	9.47346i	0.0981267	−	0.302003i
$985$	−1.86113	−	5.72798i	−0.0593006	−	0.182509i
$986$	21.3443			0.679739
$987$	−25.5527			−0.813351
$988$	−0.343154	−	1.05612i	−0.0109172	−	0.0335996i
$989$	29.1763	−	21.1978i	0.927752	−	0.674051i
$990$	4.26009	+	3.09514i	0.135395	+	0.0983700i
$991$	−27.2001			−0.864041			−0.432020	−	0.901864i	$-0.642199\pi$
$991$	−27.2001			−0.864041			−0.432020	+	0.901864i	$0.642199\pi$
$992$	−3.69478	−	4.16517i	−0.117309	−	0.132244i
$993$	2.41339			0.0765867
$994$	13.9030	+	10.1011i	0.440976	+	0.320388i
$995$	3.39114	−	2.46381i	0.107506	−	0.0781080i
$996$	−0.144960	−	0.446142i	−0.00459324	−	0.0141365i
$997$	0.429809			0.0136122			0.00680610	−	0.999977i	$-0.497834\pi$
$997$	0.429809			0.0136122			0.00680610	+	0.999977i	$0.497834\pi$
$998$	−8.84069			−0.279847
$999$	−2.09351	−	6.44315i	−0.0662356	−	0.203852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.901.1	yes	16
31.16	even	5	inner	930.2.n.g.481.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.481.1	✓	16	31.16	even	5	inner
930.2.n.g.901.1	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.17072 - 3.60310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.17072 - 3.60310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-1.62721 - 5.00804i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-1.08783 + 0.790358i) q^{13} +(-1.17072 + 3.60310i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.54433 + 4.75295i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(0.668127 + 0.485423i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.06498 + 2.22684i) q^{21} +(-1.62721 + 5.00804i) q^{22} +(-2.04174 + 6.28382i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +1.34464 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.06498 - 2.22684i) q^{28} +(3.45527 + 2.51040i) q^{29} +1.00000 q^{30} +(-3.69478 - 4.16517i) q^{31} +1.00000 q^{32} +(4.26009 + 3.09514i) q^{33} +(4.04310 - 2.93749i) q^{34} +(-1.17072 - 3.60310i) q^{35} +1.00000 q^{36} -6.77473 q^{37} +(-0.255202 - 0.785431i) q^{38} +(0.415516 - 1.27883i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-8.05861 - 5.85492i) q^{41} +(-1.17072 - 3.60310i) q^{42} +(-4.41583 - 3.20829i) q^{43} +(4.26009 - 3.09514i) q^{44} +(0.309017 - 0.951057i) q^{45} +(5.34534 - 3.88361i) q^{46} +(-5.45663 + 3.96447i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-5.94862 + 4.32193i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.54433 - 4.75295i) q^{51} +(-1.08783 - 0.790358i) q^{52} +(-1.17898 + 3.62853i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-1.62721 - 5.00804i) q^{55} -3.78852 q^{56} -0.825851 q^{57} +(-1.31979 - 4.06191i) q^{58} +(-6.81009 + 4.94782i) q^{59} +(-0.809017 - 0.587785i) q^{60} +7.30290 q^{61} +(0.540917 + 5.54143i) q^{62} -3.78852 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.08783 + 0.790358i) q^{65} +(-1.62721 - 5.00804i) q^{66} +3.63183 q^{67} -4.99755 q^{68} +(-2.04174 - 6.28382i) q^{69} +(-1.17072 + 3.60310i) q^{70} +(1.40173 - 4.31407i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.630797 - 1.94139i) q^{73} +(5.48087 + 3.98208i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-0.255202 + 0.785431i) q^{76} +(-16.1395 + 11.7260i) q^{77} +(-1.08783 + 0.790358i) q^{78} +(2.10192 - 6.46905i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.07811 + 9.47346i) q^{82} +(0.379511 + 0.275731i) q^{83} +(-1.17072 + 3.60310i) q^{84} +(-1.54433 + 4.75295i) q^{85} +(1.68670 + 5.19112i) q^{86} -4.27094 q^{87} -5.26576 q^{88} +(0.991032 + 3.05008i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(4.12128 + 2.99429i) q^{91} -6.60720 q^{92} +(5.43736 + 1.19795i) q^{93} +6.74477 q^{94} +(0.668127 + 0.485423i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-5.38066 - 16.5600i) q^{97} +7.35290 q^{98} -5.26576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

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