LMFDB - Embedded newform 315.2.bo.b.4.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.627169 - 0.362096i) q^{2} +(-1.09783 - 1.33969i) q^{3} +(-0.737773 - 1.27786i) q^{4} +(0.851637 + 2.06754i) q^{5} +(0.203428 + 1.23773i) q^{6} +(-0.722021 + 2.54533i) q^{7} +2.51696i q^{8} +(-0.589540 + 2.94150i) q^{9} +O(q^{10})$	\(q+(-0.627169 - 0.362096i) q^{2} +(-1.09783 - 1.33969i) q^{3} +(-0.737773 - 1.27786i) q^{4} +(0.851637 + 2.06754i) q^{5} +(0.203428 + 1.23773i) q^{6} +(-0.722021 + 2.54533i) q^{7} +2.51696i q^{8} +(-0.589540 + 2.94150i) q^{9} +(0.214528 - 1.60507i) q^{10} +1.34103 q^{11} +(-0.901987 + 2.39126i) q^{12} +(-1.66641 - 0.962102i) q^{13} +(1.37448 - 1.33491i) q^{14} +(1.83491 - 3.41073i) q^{15} +(-0.564163 + 0.977159i) q^{16} +(4.19747 + 2.42341i) q^{17} +(1.43485 - 1.63135i) q^{18} +(1.70493 + 2.95302i) q^{19} +(2.01371 - 2.61365i) q^{20} +(4.20260 - 1.82705i) q^{21} +(-0.841053 - 0.485582i) q^{22} -6.07484i q^{23} +(3.37195 - 2.76320i) q^{24} +(-3.54943 + 3.52158i) q^{25} +(0.696747 + 1.20680i) q^{26} +(4.58792 - 2.43947i) q^{27} +(3.78526 - 0.955231i) q^{28} +(3.13996 + 5.43857i) q^{29} +(-2.38581 + 1.47469i) q^{30} +(1.82549 + 3.16184i) q^{31} +(5.06716 - 2.92553i) q^{32} +(-1.47222 - 1.79657i) q^{33} +(-1.75501 - 3.03977i) q^{34} +(-5.87746 + 0.674888i) q^{35} +(4.19378 - 1.41681i) q^{36} +(-7.60138 + 4.38866i) q^{37} -2.46939i q^{38} +(0.540515 + 3.28870i) q^{39} +(-5.20392 + 2.14354i) q^{40} +(-2.78942 + 4.83141i) q^{41} +(-3.29731 - 0.375877i) q^{42} +(-0.0106142 + 0.00612811i) q^{43} +(-0.989376 - 1.71365i) q^{44} +(-6.58375 + 1.28620i) q^{45} +(-2.19968 + 3.80995i) q^{46} +(5.20600 + 3.00568i) q^{47} +(1.92844 - 0.316951i) q^{48} +(-5.95737 - 3.67556i) q^{49} +(3.50124 - 0.923392i) q^{50} +(-1.36149 - 8.28379i) q^{51} +2.83925i q^{52} +(2.93139 + 1.69244i) q^{53} +(-3.76072 - 0.131308i) q^{54} +(1.14207 + 2.77263i) q^{55} +(-6.40649 - 1.81730i) q^{56} +(2.08441 - 5.52599i) q^{57} -4.54787i q^{58} +(0.811439 + 1.40545i) q^{59} +(-5.71219 + 0.171590i) q^{60} +(0.207947 - 0.360175i) q^{61} -2.64401i q^{62} +(-7.06143 - 3.62440i) q^{63} -1.98063 q^{64} +(0.570008 - 4.26473i) q^{65} +(0.272803 + 1.65984i) q^{66} +(-11.6289 + 6.71394i) q^{67} -7.15170i q^{68} +(-8.13840 + 6.66914i) q^{69} +(3.93053 + 1.70494i) q^{70} -7.03540 q^{71} +(-7.40366 - 1.48385i) q^{72} +(2.36714 + 1.36667i) q^{73} +6.35647 q^{74} +(8.61450 + 0.889039i) q^{75} +(2.51570 - 4.35732i) q^{76} +(-0.968251 + 3.41336i) q^{77} +(0.851830 - 2.25829i) q^{78} +(7.51571 - 13.0176i) q^{79} +(-2.50078 - 0.334244i) q^{80} +(-8.30489 - 3.46827i) q^{81} +(3.49887 - 2.02007i) q^{82} +(9.97856 - 5.76113i) q^{83} +(-5.43528 - 4.02239i) q^{84} +(-1.43577 + 10.7423i) q^{85} +0.00887586 q^{86} +(3.83886 - 10.1772i) q^{87} +3.37532i q^{88} +(7.29024 + 12.6271i) q^{89} +(4.59485 + 1.57729i) q^{90} +(3.65205 - 3.54690i) q^{91} +(-7.76280 + 4.48185i) q^{92} +(2.23181 - 5.91675i) q^{93} +(-2.17669 - 3.77014i) q^{94} +(-4.65351 + 6.03991i) q^{95} +(-9.48218 - 3.57669i) q^{96} +(6.12763 - 3.53779i) q^{97} +(2.40537 + 4.46234i) q^{98} +(-0.790590 + 3.94465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.627169	−	0.362096i	−0.443475	−	0.256041i	0.261595	−	0.965178i	$-0.415751\pi$
$2$	−0.627169	−	0.362096i	−0.443475	−	0.256041i	−0.705071	+	0.709137i	$0.749085\pi$
$3$	−1.09783	−	1.33969i	−0.633832	−	0.773470i
$3$	−1.09783	−	1.33969i	−0.633832	−	0.773470i
$4$	−0.737773	−	1.27786i	−0.368886	−	0.638930i
$5$	0.851637	+	2.06754i	0.380863	+	0.924631i
$5$	0.851637	+	2.06754i	0.380863	+	0.924631i
$6$	0.203428	+	1.23773i	0.0830492	+	0.505302i
$7$	−0.722021	+	2.54533i	−0.272898	+	0.962043i
$7$	−0.722021	+	2.54533i	−0.272898	+	0.962043i
$8$			2.51696i			0.889881i
$9$	−0.589540	+	2.94150i	−0.196513	+	0.980501i
$10$	0.214528	−	1.60507i	0.0678396	−	0.507568i
$11$	1.34103			0.404336			0.202168	−	0.979351i	$-0.435201\pi$
$11$	1.34103			0.404336			0.202168	+	0.979351i	$0.435201\pi$
$12$	−0.901987	+	2.39126i	−0.260381	+	0.690297i
$13$	−1.66641	−	0.962102i	−0.462179	−	0.266839i	0.250781	−	0.968044i	$-0.419313\pi$
$13$	−1.66641	−	0.962102i	−0.462179	−	0.266839i	−0.712960	+	0.701205i	$0.752646\pi$
$14$	1.37448	−	1.33491i	0.367346	−	0.356769i
$15$	1.83491	−	3.41073i	0.473771	−	0.880648i
$16$	−0.564163	+	0.977159i	−0.141041	+	0.244290i
$17$	4.19747	+	2.42341i	1.01803	+	0.587763i	0.913534	−	0.406762i	$-0.133342\pi$
$17$	4.19747	+	2.42341i	1.01803	+	0.587763i	0.104501	+	0.994525i	$0.466676\pi$
$18$	1.43485	−	1.63135i	0.338197	−	0.384513i
$19$	1.70493	+	2.95302i	0.391137	+	0.677470i	0.992600	−	0.121431i	$-0.0387484\pi$
$19$	1.70493	+	2.95302i	0.391137	+	0.677470i	−0.601463	+	0.798901i	$0.705415\pi$
$20$	2.01371	−	2.61365i	0.450279	−	0.584429i
$21$	4.20260	−	1.82705i	0.917083	−	0.398695i
$22$	−0.841053	−	0.485582i	−0.179313	−	0.103526i
$23$		−	6.07484i		−	1.26669i	−0.773869	−	0.633346i	$-0.781681\pi$
$23$		−	6.07484i		−	1.26669i	0.773869	−	0.633346i	$-0.218319\pi$
$24$	3.37195	−	2.76320i	0.688297	−	0.564035i
$25$	−3.54943	+	3.52158i	−0.709886	+	0.704317i
$26$	0.696747	+	1.20680i	0.136643	+	0.236673i
$27$	4.58792	−	2.43947i	0.882945	−	0.469476i
$28$	3.78526	−	0.955231i	0.715346	−	0.180522i
$29$	3.13996	+	5.43857i	0.583076	+	1.00992i	0.995112	+	0.0987496i	$0.0314843\pi$
$29$	3.13996	+	5.43857i	0.583076	+	1.00992i	−0.412037	+	0.911167i	$0.635182\pi$
$30$	−2.38581	+	1.47469i	−0.435588	+	0.269241i
$31$	1.82549	+	3.16184i	0.327868	+	0.567883i	0.982089	−	0.188420i	$-0.0603367\pi$
$31$	1.82549	+	3.16184i	0.327868	+	0.567883i	−0.654221	+	0.756304i	$0.727003\pi$
$32$	5.06716	−	2.92553i	0.895756	−	0.517165i
$33$	−1.47222	−	1.79657i	−0.256281	−	0.312742i
$34$	−1.75501	−	3.03977i	−0.300982	−	0.521317i
$35$	−5.87746	+	0.674888i	−0.993472	+	0.114077i
$36$	4.19378	−	1.41681i	0.698963	−	0.236135i
$37$	−7.60138	+	4.38866i	−1.24966	+	0.721491i	−0.971042	−	0.238911i	$-0.923210\pi$
$37$	−7.60138	+	4.38866i	−1.24966	+	0.721491i	−0.278618	+	0.960402i	$0.589876\pi$
$38$		−	2.46939i		−	0.400588i
$39$	0.540515	+	3.28870i	0.0865517	+	0.526613i
$40$	−5.20392	+	2.14354i	−0.822812	+	0.338923i
$41$	−2.78942	+	4.83141i	−0.435634	+	0.754540i	−0.997347	−	0.0727922i	$-0.976809\pi$
$41$	−2.78942	+	4.83141i	−0.435634	+	0.754540i	0.561713	+	0.827332i	$0.310142\pi$
$42$	−3.29731	−	0.375877i	−0.508786	−	0.0579991i
$43$	−0.0106142	+	0.00612811i	−0.00161865	+	0.000934528i	−0.500809	−	0.865558i	$-0.666964\pi$
$43$	−0.0106142	+	0.00612811i	−0.00161865	+	0.000934528i	0.499190	+	0.866492i	$0.333631\pi$
$44$	−0.989376	−	1.71365i	−0.149154	−	0.258342i
$45$	−6.58375	+	1.28620i	−0.981447	+	0.191735i
$46$	−2.19968	+	3.80995i	−0.324325	+	0.561747i
$47$	5.20600	+	3.00568i	0.759373	+	0.438424i	0.829071	−	0.559144i	$-0.188870\pi$
$47$	5.20600	+	3.00568i	0.759373	+	0.438424i	−0.0696977	+	0.997568i	$0.522203\pi$
$48$	1.92844	−	0.316951i	0.278347	−	0.0457479i
$49$	−5.95737	−	3.67556i	−0.851053	−	0.525079i
$50$	3.50124	−	0.923392i	0.495151	−	0.130587i
$51$	−1.36149	−	8.28379i	−0.190646	−	1.15996i
$52$			2.83925i			0.393733i
$53$	2.93139	+	1.69244i	0.402657	+	0.232474i	0.687630	−	0.726061i	$-0.258651\pi$
$53$	2.93139	+	1.69244i	0.402657	+	0.232474i	−0.284973	+	0.958536i	$0.591985\pi$
$54$	−3.76072	−	0.131308i	−0.511769	−	0.0178687i
$55$	1.14207	+	2.77263i	0.153997	+	0.373862i
$56$	−6.40649	−	1.81730i	−0.856104	−	0.242847i
$57$	2.08441	−	5.52599i	0.276087	−	0.731935i
$58$		−	4.54787i		−	0.597164i
$59$	0.811439	+	1.40545i	0.105640	+	0.182975i	0.914000	−	0.405715i	$-0.132977\pi$
$59$	0.811439	+	1.40545i	0.105640	+	0.182975i	−0.808359	+	0.588689i	$0.799644\pi$
$60$	−5.71219	+	0.171590i	−0.737440	+	0.0221522i
$61$	0.207947	−	0.360175i	0.0266249	−	0.0461156i	−0.852406	−	0.522881i	$-0.824857\pi$
$61$	0.207947	−	0.360175i	0.0266249	−	0.0461156i	0.879031	+	0.476765i	$0.158191\pi$
$62$		−	2.64401i		−	0.335790i
$63$	−7.06143	−	3.62440i	−0.889656	−	0.456631i
$64$	−1.98063			−0.247579
$65$	0.570008	−	4.26473i	0.0707007	−	0.528974i
$66$	0.272803	+	1.65984i	0.0335798	+	0.204312i
$67$	−11.6289	+	6.71394i	−1.42069	+	0.820238i	−0.996358	−	0.0852662i	$-0.972826\pi$
$67$	−11.6289	+	6.71394i	−1.42069	+	0.820238i	−0.424336	+	0.905505i	$0.639493\pi$
$68$		−	7.15170i		−	0.867271i
$69$	−8.13840	+	6.66914i	−0.979749	+	0.802870i
$70$	3.93053	+	1.70494i	0.469789	+	0.203779i
$71$	−7.03540			−0.834948			−0.417474	−	0.908689i	$-0.637085\pi$
$71$	−7.03540			−0.834948			−0.417474	+	0.908689i	$0.637085\pi$
$72$	−7.40366	−	1.48385i	−0.872529	−	0.174873i
$73$	2.36714	+	1.36667i	0.277053	+	0.159956i	0.632088	−	0.774896i	$-0.282198\pi$
$73$	2.36714	+	1.36667i	0.277053	+	0.159956i	−0.355036	+	0.934853i	$0.615531\pi$
$74$	6.35647			0.738924
$75$	8.61450	+	0.889039i	0.994717	+	0.102657i
$76$	2.51570	−	4.35732i	0.288570	−	0.499819i
$77$	−0.968251	+	3.41336i	−0.110342	+	0.388988i
$78$	0.851830	−	2.25829i	0.0964507	−	0.255701i
$79$	7.51571	−	13.0176i	0.845584	−	1.46459i	−0.0395298	−	0.999218i	$-0.512586\pi$
$79$	7.51571	−	13.0176i	0.845584	−	1.46459i	0.885113	−	0.465375i	$-0.154081\pi$
$80$	−2.50078	−	0.334244i	−0.279595	−	0.0373696i
$81$	−8.30489	−	3.46827i	−0.922765	−	0.385363i
$82$	3.49887	−	2.02007i	0.386386	−	0.223080i
$83$	9.97856	−	5.76113i	1.09529	−	0.632366i	0.160310	−	0.987067i	$-0.448751\pi$
$83$	9.97856	−	5.76113i	1.09529	−	0.632366i	0.934980	+	0.354701i	$0.115417\pi$
$84$	−5.43528	−	4.02239i	−0.593038	−	0.438879i
$85$	−1.43577	+	10.7423i	−0.155732	+	1.16516i
$86$	0.00887586			0.000957109
$87$	3.83886	−	10.1772i	0.411569	−	1.09111i
$88$			3.37532i			0.359811i
$89$	7.29024	+	12.6271i	0.772764	+	1.33847i	0.936042	+	0.351887i	$0.114460\pi$
$89$	7.29024	+	12.6271i	0.772764	+	1.33847i	−0.163278	+	0.986580i	$0.552207\pi$
$90$	4.59485	+	1.57729i	0.484339	+	0.166261i
$91$	3.65205	−	3.54690i	0.382838	−	0.371816i
$92$	−7.76280	+	4.48185i	−0.809327	+	0.467265i
$93$	2.23181	−	5.91675i	0.231428	−	0.613539i
$94$	−2.17669	−	3.77014i	−0.224509	−	0.388861i
$95$	−4.65351	+	6.03991i	−0.477440	+	0.619681i
$96$	−9.48218	−	3.57669i	−0.967771	−	0.365045i
$97$	6.12763	−	3.53779i	0.622167	−	0.359208i	−0.155545	−	0.987829i	$-0.549713\pi$
$97$	6.12763	−	3.53779i	0.622167	−	0.359208i	0.777712	+	0.628620i	$0.216380\pi$
$98$	2.40537	+	4.46234i	0.242980	+	0.450764i
$99$	−0.790590	+	3.94465i	−0.0794573	+	0.396452i
$100$	7.11876	+	1.93755i	0.711876	+	0.193755i
$101$	−7.13924			−0.710381			−0.355191	−	0.934794i	$-0.615584\pi$
$101$	−7.13924			−0.710381			−0.355191	+	0.934794i	$0.615584\pi$
$102$	−2.14565	+	5.68833i	−0.212451	+	0.563228i
$103$		−	9.44220i		−	0.930367i	−0.885214	−	0.465184i	$-0.845988\pi$
$103$		−	9.44220i		−	0.930367i	0.885214	−	0.465184i	$-0.154012\pi$
$104$	2.42158	−	4.19429i	0.237455	−	0.411284i
$105$	7.35659	+	7.13306i	0.717930	+	0.696116i
$106$	−1.22565	−	2.12289i	−0.119046	−	0.206193i
$107$	−7.56343	+	4.36675i	−0.731184	+	0.422149i	−0.818855	−	0.574000i	$-0.805391\pi$
$107$	−7.56343	+	4.36675i	−0.731184	+	0.422149i	0.0876711	+	0.996149i	$0.472058\pi$
$108$	−6.50214	−	4.06294i	−0.625669	−	0.390957i
$109$	−5.98507	+	10.3664i	−0.573266	+	0.992925i	0.422962	+	0.906147i	$0.360990\pi$
$109$	−5.98507	+	10.3664i	−0.573266	+	0.992925i	−0.996228	+	0.0867777i	$0.972343\pi$
$110$	0.287688	−	2.15245i	0.0274300	−	0.205228i
$111$	14.2245	+	5.36549i	1.35013	+	0.509270i
$112$	−2.07985	−	2.14151i	−0.196527	−	0.202353i
$113$	1.88860	+	1.09038i	0.177664	+	0.102574i	0.586195	−	0.810170i	$-0.300625\pi$
$113$	1.88860	+	1.09038i	0.177664	+	0.102574i	−0.408531	+	0.912745i	$0.633959\pi$
$114$	−3.30822	+	2.71097i	−0.309843	+	0.253906i
$115$	12.5600	−	5.17356i	1.17122	−	0.482437i
$116$	4.63315	−	8.02486i	0.430177	−	0.745089i
$117$	3.81244	−	4.33455i	0.352460	−	0.400730i
$118$		−	1.17528i		−	0.108193i
$119$	−9.19902	+	8.93417i	−0.843273	+	0.818994i
$120$	8.58469	+	4.61840i	0.783672	+	0.421600i
$121$	−9.20164			−0.836512
$122$	−0.260836	+	0.150594i	−0.0236150	+	0.0136341i
$123$	9.53490	−	1.56711i	0.859733	−	0.141302i
$124$	2.69359	−	4.66544i	0.241892	−	0.418969i
$125$	−10.3038	−	4.33947i	−0.921603	−	0.388134i
$126$	3.11633	+	4.83002i	0.277625	+	0.430293i
$127$		−	10.7378i		−	0.952828i	−0.879221	−	0.476414i	$-0.841936\pi$
$127$		−	10.7378i		−	0.952828i	0.879221	−	0.476414i	$-0.158064\pi$
$128$	−8.89213	−	5.13387i	−0.785960	−	0.453774i
$129$	0.0198624	+	0.00749212i	0.00174878	+	0.000659644i
$130$	−1.90173	+	2.46831i	−0.166793	+	0.216485i
$131$	−2.03400			−0.177711			−0.0888555	−	0.996045i	$-0.528321\pi$
$131$	−2.03400			−0.177711			−0.0888555	+	0.996045i	$0.528321\pi$
$132$	−1.20959	+	3.20675i	−0.105282	+	0.279112i
$133$	−8.74740	+	2.20746i	−0.758496	+	0.191411i
$134$	9.72437			0.840057
$135$	8.95094	+	7.40815i	0.770374	+	0.637592i
$136$	−6.09963	+	10.5649i	−0.523039	+	0.905930i
$137$			10.0734i			0.860625i	0.902680	+	0.430313i	$0.141597\pi$
$137$			10.0734i			0.860625i	−0.902680	+	0.430313i	$0.858403\pi$
$138$	7.51902	−	1.23579i	0.640062	−	0.105198i
$139$	8.78396	−	15.2143i	0.745046	−	1.29046i	−0.205128	−	0.978735i	$-0.565761\pi$
$139$	8.78396	−	15.2143i	0.745046	−	1.29046i	0.950173	−	0.311722i	$-0.100906\pi$
$140$	5.19864	+	7.01266i	0.439365	+	0.592678i
$141$	−1.68861	−	10.2742i	−0.142207	−	0.865240i
$142$	4.41238	+	2.54749i	0.370279	+	0.213781i
$143$	−2.23471	−	1.29021i	−0.186875	−	0.107893i
$144$	−2.54172	−	2.23556i	−0.211810	−	0.186297i
$145$	−8.57035	+	11.1237i	−0.711729	+	0.923771i
$146$	−0.989730	−	1.71426i	−0.0819107	−	0.141873i
$147$	1.61608	+	12.0162i	0.133292	+	0.991077i
$148$	11.2162	+	6.47567i	0.921965	+	0.532297i
$149$	−1.46781			−0.120248			−0.0601240	−	0.998191i	$-0.519150\pi$
$149$	−1.46781			−0.120248			−0.0601240	+	0.998191i	$0.519150\pi$
$150$	−5.08083	−	3.67685i	−0.414848	−	0.300214i
$151$	12.6827			1.03211			0.516053	−	0.856557i	$-0.327401\pi$
$151$	12.6827			1.03211			0.516053	+	0.856557i	$0.327401\pi$
$152$	−7.43265	+	4.29124i	−0.602867	+	0.348066i
$153$	−9.60303	+	10.9182i	−0.776359	+	0.882681i
$154$	1.84322	−	1.79015i	0.148531	−	0.144255i
$155$	−4.98257	+	6.46701i	−0.400210	+	0.519443i
$156$	3.80372	−	3.11701i	0.304541	−	0.249561i
$157$	14.9324	−	8.62124i	1.19174	−	0.688050i	0.233037	−	0.972468i	$-0.425134\pi$
$157$	14.9324	−	8.62124i	1.19174	−	0.688050i	0.958700	+	0.284418i	$0.0918004\pi$
$158$	−9.42724	+	5.44282i	−0.749991	+	0.433008i
$159$	−0.950823	−	5.78516i	−0.0754052	−	0.458793i
$160$	10.3640	+	7.98506i	0.819347	+	0.631275i
$161$	15.4625	+	4.38616i	1.21861	+	0.345678i
$162$	3.95272	+	5.18236i	0.310555	+	0.407164i
$163$	−17.7373	+	10.2406i	−1.38929	+	0.802108i	−0.993235	−	0.116119i	$-0.962955\pi$
$163$	−17.7373	+	10.2406i	−1.38929	+	0.802108i	−0.396056	+	0.918226i	$0.629621\pi$
$164$	8.23182			0.642797
$165$	2.46067	−	4.57390i	0.191563	−	0.356078i
$166$	−8.34433			−0.647645
$167$	11.4618	+	6.61747i	0.886940	+	0.512075i	0.872941	−	0.487827i	$-0.162210\pi$
$167$	11.4618	+	6.61747i	0.886940	+	0.512075i	0.0140000	+	0.999902i	$0.495544\pi$
$168$	4.59862	+	10.5778i	0.354791	+	0.816095i
$169$	−4.64872	−	8.05182i	−0.357594	−	0.619371i
$170$	4.79021	−	6.21734i	0.367392	−	0.476848i
$171$	−9.69145	+	3.27413i	−0.741123	+	0.250379i
$172$	0.0156617	+	0.00904231i	0.00119420	+	0.000689470i
$173$	1.05186	+	0.607291i	0.0799713	+	0.0461715i	0.539452	−	0.842016i	$-0.318631\pi$
$173$	1.05186	+	0.607291i	0.0799713	+	0.0461715i	−0.459481	+	0.888188i	$0.651965\pi$
$174$	−6.09273	+	4.99279i	−0.461889	+	0.378502i
$175$	−6.40082	−	11.5771i	−0.483856	−	0.875148i
$176$	−0.756560	+	1.31040i	−0.0570278	+	0.0987751i
$177$	0.992051	−	2.63003i	0.0745671	−	0.197685i
$178$		−	10.5591i		−	0.791436i
$179$	9.81486	−	16.9998i	0.733597	−	1.27063i	−0.221739	−	0.975106i	$-0.571173\pi$
$179$	9.81486	−	16.9998i	0.733597	−	1.27063i	0.955336	−	0.295521i	$-0.0954932\pi$
$180$	6.50089	+	7.46418i	0.484547	+	0.556347i
$181$	23.9837			1.78270			0.891349	−	0.453318i	$-0.149760\pi$
$181$	23.9837			1.78270			0.891349	+	0.453318i	$0.149760\pi$
$182$	−3.57477	+	0.902113i	−0.264979	+	0.0668691i
$183$	−0.710813	+	0.116826i	−0.0525448	+	0.00863603i
$184$	15.2902			1.12720
$185$	−15.5473	−	11.9786i	−1.14306	−	0.880685i
$186$	−3.54216	+	2.90267i	−0.259723	+	0.212834i
$187$	5.62893	+	3.24986i	0.411628	+	0.237654i
$188$		−	8.87005i		−	0.646915i
$189$	2.89668	+	13.4391i	0.210702	+	0.977550i
$190$	5.10556	−	2.10302i	0.370396	−	0.152569i
$191$	10.8875	−	18.8577i	0.787790	−	1.36449i	−0.139528	−	0.990218i	$-0.544558\pi$
$191$	10.8875	−	18.8577i	0.787790	−	1.36449i	0.927318	−	0.374274i	$-0.122108\pi$
$192$	2.17440	+	2.65344i	0.156924	+	0.191495i
$193$	7.54163	−	4.35416i	0.542858	−	0.313419i	−0.203378	−	0.979100i	$-0.565192\pi$
$193$	7.54163	−	4.35416i	0.542858	−	0.313419i	0.746237	+	0.665681i	$0.231859\pi$
$194$	−5.12408			−0.367888
$195$	−6.33918	+	3.91831i	−0.453958	+	0.280596i
$196$	−0.301658	+	10.3244i	−0.0215470	+	0.737458i
$197$		−	24.4554i		−	1.74238i	−0.490949	−	0.871188i	$-0.663350\pi$
$197$		−	24.4554i		−	1.74238i	0.490949	−	0.871188i	$-0.336650\pi$
$198$	1.92417	−	2.18769i	0.136745	−	0.155472i
$199$	−2.12468	+	3.68005i	−0.150614	+	0.260872i	−0.931454	−	0.363860i	$-0.881459\pi$
$199$	−2.12468	+	3.68005i	−0.150614	+	0.260872i	0.780839	+	0.624732i	$0.214792\pi$
$200$	−8.86369	−	8.93379i	−0.626758	−	0.631714i
$201$	21.7611	+	8.20834i	1.53491	+	0.578972i
$202$	4.47751	+	2.58509i	0.315037	+	0.181886i
$203$	−16.1100	+	4.06546i	−1.13070	+	0.285340i
$204$	−9.58106	+	7.85135i	−0.670808	+	0.549704i
$205$	−12.3647	−	1.65262i	−0.863588	−	0.115424i
$206$	−3.41898	+	5.92185i	−0.238212	+	0.412595i
$207$	17.8692	+	3.58136i	1.24199	+	0.248922i
$208$	1.88025	−	1.08556i	0.130372	−	0.0752704i
$209$	2.28636	+	3.96009i	0.158151	+	0.273925i
$210$	−2.03097	−	7.13743i	−0.140150	−	0.492529i
$211$	−9.23723	+	15.9994i	−0.635917	+	1.10144i	0.350403	+	0.936599i	$0.386045\pi$
$211$	−9.23723	+	15.9994i	−0.635917	+	1.10144i	−0.986320	+	0.164842i	$0.947289\pi$
$212$		−	4.99454i		−	0.343026i
$213$	7.72367	+	9.42525i	0.529217	+	0.645808i
$214$	6.32473			0.432349
$215$	−0.0217096	−	0.0167263i	−0.00148058	−	0.00114073i
$216$	6.14006	+	11.5476i	0.417778	+	0.785716i
$217$	−9.36596	+	2.36355i	−0.635803	+	0.160448i
$218$	7.50730	−	4.33434i	0.508458	−	0.293559i
$219$	−0.767803	−	4.67160i	−0.0518833	−	0.315678i
$220$	2.70045	−	3.50498i	0.182064	−	0.236306i
$221$	−4.66313	−	8.07678i	−0.313676	−	0.543303i
$222$	−6.97832	−	8.51570i	−0.468354	−	0.571536i
$223$	12.3398	−	7.12437i	0.826333	−	0.477083i	−0.0262627	−	0.999655i	$-0.508361\pi$
$223$	12.3398	−	7.12437i	0.826333	−	0.477083i	0.852595	+	0.522572i	$0.175027\pi$
$224$	3.78782	+	15.0099i	0.253085	+	1.00289i
$225$	−8.26622	−	12.5168i	−0.551081	−	0.834452i
$226$	−0.789646	−	1.36771i	−0.0525265	−	0.0909785i
$227$			12.5572i			0.833449i	0.909033	+	0.416725i	$0.136822\pi$
$227$			12.5572i			0.833449i	−0.909033	+	0.416725i	$0.863178\pi$
$228$	−8.59927	+	1.41334i	−0.569500	+	0.0936005i
$229$	−14.7005			−0.971436			−0.485718	−	0.874115i	$-0.661442\pi$
$229$	−14.7005			−0.971436			−0.485718	+	0.874115i	$0.661442\pi$
$230$	−9.75055	−	1.30322i	−0.642932	−	0.0859319i
$231$	5.63582	−	2.45013i	0.370810	−	0.161207i
$232$	−13.6887	+	7.90316i	−0.898706	+	0.518868i
$233$	−0.268631	+	0.155094i	−0.0175986	+	0.0101606i	−0.508774	−	0.860900i	$-0.669901\pi$
$233$	−0.268631	+	0.155094i	−0.0175986	+	0.0101606i	0.491175	+	0.871061i	$0.336568\pi$
$234$	−3.96057	+	1.33803i	−0.258910	+	0.0874695i
$235$	−1.78075	+	13.3234i	−0.116163	+	0.869120i
$236$	1.19732	−	2.07381i	0.0779386	−	0.134994i
$237$	−25.6905	+	4.22238i	−1.66878	+	0.274273i
$238$	9.00437	−	2.27230i	0.583666	−	0.147292i
$239$	9.63449	−	16.6874i	0.623203	−	1.07942i	−0.365682	−	0.930740i	$-0.619164\pi$
$239$	9.63449	−	16.6874i	0.623203	−	1.07942i	0.988885	−	0.148680i	$-0.0475024\pi$
$240$	2.29764	+	3.71721i	0.148312	+	0.239945i
$241$	−3.36431			−0.216714			−0.108357	−	0.994112i	$-0.534559\pi$
$241$	−3.36431			−0.216714			−0.108357	+	0.994112i	$0.534559\pi$
$242$	5.77098	+	3.33188i	0.370973	+	0.214181i
$243$	4.47095	+	14.9335i	0.286812	+	0.957987i
$244$	−0.613670			−0.0392862
$245$	2.52584	−	15.4473i	0.161370	−	0.986894i
$246$	−6.54744	−	2.46971i	−0.417449	−	0.157463i
$247$		−	6.56126i		−	0.417483i
$248$	−7.95824	+	4.59469i	−0.505349	+	0.291763i
$249$	−18.6729	−	7.04345i	−1.18335	−	0.446360i
$250$	4.89094	+	6.45256i	0.309330	+	0.408096i
$251$	−26.2232			−1.65519			−0.827597	−	0.561323i	$-0.810293\pi$
$251$	−26.2232			−1.65519			−0.827597	+	0.561323i	$0.810293\pi$
$252$	0.578257	+	11.6975i	0.0364268	+	0.736873i
$253$		−	8.14655i		−	0.512169i
$254$	−3.88813	+	6.73443i	−0.243963	+	0.422556i
$255$	15.9676	−	9.86971i	0.999928	−	0.618065i
$256$	5.69854	+	9.87017i	0.356159	+	0.616886i
$257$			2.64479i			0.164978i	0.996592	+	0.0824889i	$0.0262869\pi$
$257$			2.64479i			0.164978i	−0.996592	+	0.0824889i	$0.973713\pi$
$258$	−0.00974419	−	0.0118909i	−0.000606647	−	0.000740296i
$259$	−5.68222	−	22.5167i	−0.353076	−	1.39912i
$260$	−5.87026	+	2.41801i	−0.364058	+	0.149959i
$261$	−17.8487	+	6.02995i	−1.10481	+	0.373245i
$262$	1.27566	+	0.736502i	0.0788105	+	0.0455012i
$263$			10.8661i			0.670034i	0.942212	+	0.335017i	$0.108742\pi$
$263$			10.8661i			0.670034i	−0.942212	+	0.335017i	$0.891258\pi$
$264$	4.52189	−	3.70553i	0.278303	−	0.228060i
$265$	−1.00270	+	7.50210i	−0.0615955	+	0.460850i
$266$	6.28541	+	1.78295i	0.385383	+	0.109320i
$267$	8.91292	−	23.6290i	0.545462	−	1.44607i
$268$	17.1590	+	9.90673i	1.04815	+	0.605150i
$269$	11.7399	−	20.3341i	0.715794	−	1.23979i	−0.246859	−	0.969051i	$-0.579398\pi$
$269$	11.7399	−	20.3341i	0.715794	−	1.23979i	0.962653	−	0.270740i	$-0.0872682\pi$
$270$	−2.93128	−	7.88726i	−0.178392	−	0.480004i
$271$	−14.2471	−	24.6767i	−0.865449	−	1.49900i	−0.866601	−	0.499002i	$-0.833700\pi$
$271$	−14.2471	−	24.6767i	−0.865449	−	1.49900i	0.00115175	−	0.999999i	$-0.499633\pi$
$272$	−4.73611	+	2.73439i	−0.287169	+	0.165797i
$273$	−8.76107	−	0.998718i	−0.530244	−	0.0604452i
$274$	3.64752	−	6.31770i	0.220355	−	0.381666i
$275$	−4.75989	+	4.72255i	−0.287032	+	0.284780i
$276$	14.5265	+	5.47943i	0.874394	+	0.329823i
$277$		−	31.7952i		−	1.91039i	−0.295979	−	0.955195i	$-0.595646\pi$
$277$		−	31.7952i		−	1.91039i	0.295979	−	0.955195i	$-0.404354\pi$
$278$	−11.0181	+	6.36128i	−0.660819	+	0.381524i
$279$	−10.3768	+	3.50565i	−0.621241	+	0.209878i
$280$	−1.69867	−	14.7933i	−0.101515	−	0.884072i
$281$	4.84577	+	8.39313i	0.289075	+	0.500692i	0.973589	−	0.228307i	$-0.0733191\pi$
$281$	4.84577	+	8.39313i	0.289075	+	0.500692i	−0.684515	+	0.728999i	$0.739986\pi$
$282$	−2.66119	+	7.05507i	−0.158471	+	0.420123i
$283$	−21.4962	+	12.4108i	−1.27782	+	0.737747i	−0.976446	−	0.215760i	$-0.930777\pi$
$283$	−21.4962	+	12.4108i	−1.27782	+	0.737747i	−0.301369	+	0.953507i	$0.597444\pi$
$284$	5.19052	+	8.99025i	0.308001	+	0.533473i
$285$	13.2004	−	0.396530i	0.781922	−	0.0234884i
$286$	0.934359	+	1.61836i	0.0552498	+	0.0956954i
$287$	−10.2835	−	10.5884i	−0.607016	−	0.625011i
$288$	5.61815	+	16.6298i	0.331053	+	0.979919i
$289$	3.24581	+	5.62191i	0.190930	+	0.330700i
$290$	9.40289	−	3.87313i	0.552157	−	0.227438i
$291$	−11.4666	−	4.32524i	−0.672187	−	0.253550i
$292$		−	4.03316i		−	0.236023i
$293$	3.39503	+	1.96012i	0.198339	+	0.114511i	0.595881	−	0.803073i	$-0.296803\pi$
$293$	3.39503	+	1.96012i	0.198339	+	0.114511i	−0.397541	+	0.917584i	$0.630136\pi$
$294$	3.33746	−	8.12134i	0.194644	−	0.473646i
$295$	−2.21478	+	2.87462i	−0.128949	+	0.167367i
$296$	−11.0461	−	19.1324i	−0.642041	−	1.11205i
$297$	6.15254	−	3.27140i	0.357006	−	0.189826i
$298$	0.920566	+	0.531489i	0.0533270	+	0.0307883i
$299$	−5.84462	+	10.1232i	−0.338003	+	0.585438i
$300$	−5.21948	−	11.6640i	−0.301347	−	0.673423i
$301$	−0.00793437	−	0.0314412i	−0.000457330	−	0.00181224i
$302$	−7.95421	−	4.59237i	−0.457714	−	0.264261i
$303$	7.83767	+	9.56437i	0.450262	+	0.549459i
$304$	−3.84743			−0.220665
$305$	0.921770	+	0.123200i	0.0527804	+	0.00705443i
$306$	9.97615	−	3.37031i	0.570298	−	0.192668i
$307$			10.3291i			0.589514i	0.955572	+	0.294757i	$0.0952388\pi$
$307$			10.3291i			0.589514i	−0.955572	+	0.294757i	$0.904761\pi$
$308$	5.07615	−	1.28099i	0.289240	−	0.0729914i
$309$	−12.6496	+	10.3659i	−0.719612	+	0.589697i
$310$	5.46659	−	2.25174i	0.310482	−	0.127890i
$311$	10.5510	+	18.2748i	0.598291	+	1.03627i	0.993073	+	0.117496i	$0.0374867\pi$
$311$	10.5510	+	18.2748i	0.598291	+	1.03627i	−0.394782	+	0.918775i	$0.629180\pi$
$312$	−8.27753	+	1.36046i	−0.468623	+	0.0770207i
$313$	2.12515	+	1.22696i	0.120121	+	0.0693516i	0.558856	−	0.829264i	$-0.311240\pi$
$313$	2.12515	+	1.22696i	0.120121	+	0.0693516i	−0.438736	+	0.898616i	$0.644574\pi$
$314$	−12.4869			−0.704675
$315$	1.47981	−	17.6864i	0.0833778	−	0.996518i
$316$	−22.1795			−1.24770
$317$	11.9978	+	6.92695i	0.673865	+	0.389056i	0.797540	−	0.603267i	$-0.206135\pi$
$317$	11.9978	+	6.92695i	0.673865	+	0.389056i	−0.123675	+	0.992323i	$0.539468\pi$
$318$	−1.49846	+	3.97256i	−0.0840293	+	0.222770i
$319$	4.21078	+	7.29329i	0.235758	+	0.408346i
$320$	−1.68678	−	4.09504i	−0.0942939	−	0.228920i
$321$	14.1534	+	5.33870i	0.789968	+	0.297977i
$322$	−8.10936	−	8.34976i	−0.451917	−	0.465314i
$323$			16.5269i			0.919584i
$324$	1.69516	+	13.1713i	0.0941756	+	0.731737i
$325$	9.30293	−	2.45349i	0.516033	−	0.136095i
$326$	14.8324			0.821489
$327$	20.4584	−	3.36245i	1.13135	−	0.185944i
$328$	−12.1605	−	7.02086i	−0.671450	−	0.387662i
$329$	−11.4093	+	11.0808i	−0.629014	+	0.610904i
$330$	−3.19945	+	1.97761i	−0.176124	+	0.108864i
$331$	−5.16113	+	8.93935i	−0.283682	+	0.491351i	−0.972289	−	0.233784i	$-0.924889\pi$
$331$	−5.16113	+	8.93935i	−0.283682	+	0.491351i	0.688607	+	0.725135i	$0.258223\pi$
$332$	−14.7238	−	8.50080i	−0.808075	−	0.466542i
$333$	−8.42794	−	24.9468i	−0.461848	−	1.36708i
$334$	−4.79232	−	8.30054i	−0.262224	−	0.454186i
$335$	−23.7849	−	18.3253i	−1.29951	−	1.00122i
$336$	−0.585634	+	5.13737i	−0.0319490	+	0.280266i
$337$	6.53450	+	3.77269i	0.355957	+	0.205512i	0.667306	−	0.744784i	$-0.267447\pi$
$337$	6.53450	+	3.77269i	0.355957	+	0.205512i	−0.311349	+	0.950296i	$0.600781\pi$
$338$			6.73313i			0.366234i
$339$	−0.612584	−	3.72719i	−0.0332710	−	0.202433i
$340$	14.7864	−	6.09065i	0.801906	−	0.330312i
$341$	2.44804	+	4.24012i	0.132569	+	0.229616i
$342$	7.26372	+	1.45580i	0.392777	+	0.0787209i
$343$	13.6568	−	12.5096i	0.737400	−	0.675457i
$344$	−0.0154242	−	0.0267156i	−0.000831619	−	0.00144041i
$345$	−20.7197	−	11.1468i	−1.11551	−	0.600122i
$346$	−0.439795	−	0.761748i	−0.0236435	−	0.0409518i
$347$	27.1935	−	15.7002i	1.45982	−	0.842829i	0.460821	−	0.887493i	$-0.347555\pi$
$347$	27.1935	−	15.7002i	1.45982	−	0.842829i	0.999002	+	0.0446637i	$0.0142216\pi$
$348$	−15.8372	+	2.60294i	−0.848965	+	0.139532i
$349$	−11.7843	−	20.4109i	−0.630797	−	1.09257i	−0.987389	−	0.158312i	$-0.949395\pi$
$349$	−11.7843	−	20.4109i	−0.630797	−	1.09257i	0.356592	−	0.934260i	$-0.383938\pi$
$350$	−0.177635	+	9.57852i	−0.00949501	+	0.511993i
$351$	−9.99237	−	0.348889i	−0.533353	−	0.0186223i
$352$	6.79521	−	3.92322i	0.362186	−	0.209108i
$353$			2.89995i			0.154349i	0.997018	+	0.0771745i	$0.0245899\pi$
$353$			2.89995i			0.154349i	−0.997018	+	0.0771745i	$0.975410\pi$
$354$	−1.57451	+	1.29025i	−0.0836841	+	0.0685762i
$355$	−5.99160	−	14.5460i	−0.318001	−	0.772019i
$356$	10.7571	−	18.6318i	0.570124	−	0.987485i
$357$	22.0680	+	2.51564i	1.16796	+	0.133142i
$358$	−12.3111	+	7.10784i	−0.650664	+	0.375661i
$359$	11.3585	+	19.6735i	0.599480	+	1.03833i	0.992898	+	0.118970i	$0.0379592\pi$
$359$	11.3585	+	19.6735i	0.599480	+	1.03833i	−0.393418	+	0.919360i	$0.628707\pi$
$360$	−3.23731	−	16.5710i	−0.170621	−	0.873371i
$361$	3.68644	−	6.38510i	0.194023	−	0.336058i
$362$	−15.0419	−	8.68442i	−0.790583	−	0.456443i
$363$	10.1018	+	12.3273i	0.530209	+	0.647018i
$364$	−7.22682	−	2.05000i	−0.378788	−	0.107449i
$365$	−0.809697	+	6.05805i	−0.0423815	+	0.317093i
$366$	0.488102	+	0.184113i	0.0255135	+	0.00962374i
$367$			14.7368i			0.769255i	0.923072	+	0.384628i	$0.125670\pi$
$367$			14.7368i			0.769255i	−0.923072	+	0.384628i	$0.874330\pi$
$368$	5.93608	+	3.42720i	0.309440	+	0.178655i
$369$	−12.5671	−	11.0534i	−0.654219	−	0.575416i
$370$	5.41340	+	13.1422i	0.281429	+	0.683232i
$371$	−6.42433	+	6.23937i	−0.333535	+	0.323932i
$372$	−9.20735	+	1.51328i	−0.477379	+	0.0784598i
$373$			34.0853i			1.76487i	0.470434	+	0.882435i	$0.344097\pi$
$373$			34.0853i			1.76487i	−0.470434	+	0.882435i	$0.655903\pi$
$374$	−2.35353	−	4.07643i	−0.121698	−	0.210787i
$375$	5.49830	+	18.5679i	0.283931	+	0.958845i
$376$	−7.56520	+	13.1033i	−0.390145	+	0.675751i
$377$		−	12.0838i		−	0.622350i
$378$	3.04954	−	9.47746i	0.156851	−	0.487468i
$379$	28.8334			1.48107			0.740537	−	0.672016i	$-0.234571\pi$
$379$	28.8334			1.48107			0.740537	+	0.672016i	$0.234571\pi$
$380$	11.1514	+	1.49045i	0.572054	+	0.0764586i
$381$	−14.3854	+	11.7883i	−0.736985	+	0.603933i
$382$	−13.6566	+	7.88463i	−0.698731	+	0.403413i
$383$			2.93710i			0.150079i	0.997181	+	0.0750395i	$0.0239083\pi$
$383$			2.93710i			0.150079i	−0.997181	+	0.0750395i	$0.976092\pi$
$384$	2.88424	+	17.5488i	0.147186	+	0.895534i
$385$	−7.88185	+	0.905045i	−0.401696	+	0.0461254i
$386$	−6.30650			−0.320992
$387$	−0.0117684	−	0.0348345i	−0.000598220	−	0.00177074i
$388$	−9.04160	−	5.22017i	−0.459018	−	0.265014i
$389$	−5.73116			−0.290581			−0.145291	−	0.989389i	$-0.546412\pi$
$389$	−5.73116			−0.290581			−0.145291	+	0.989389i	$0.546412\pi$
$390$	5.39454	−	0.162049i	0.273163	−	0.00820565i
$391$	14.7218	−	25.4989i	0.744514	−	1.28954i
$392$	9.25124	−	14.9945i	0.467258	−	0.757336i
$393$	2.23298	+	2.72492i	0.112639	+	0.137454i
$394$	−8.85521	+	15.3377i	−0.446119	+	0.772701i
$395$	33.3150	+	4.45276i	1.67626	+	0.224043i
$396$	5.62398	−	1.89999i	0.282616	−	0.0954780i
$397$	7.80579	−	4.50667i	0.391761	−	0.226184i	−0.291162	−	0.956674i	$-0.594042\pi$
$397$	7.80579	−	4.50667i	0.391761	−	0.226184i	0.682923	+	0.730490i	$0.260708\pi$
$398$	2.66507	−	1.53868i	0.133588	−	0.0771269i
$399$	12.5605	+	9.29539i	0.628810	+	0.465352i
$400$	−1.43869	−	5.45510i	−0.0719344	−	0.272755i
$401$	−1.90628			−0.0951951			−0.0475975	−	0.998867i	$-0.515156\pi$
$401$	−1.90628			−0.0951951			−0.0475975	+	0.998867i	$0.515156\pi$
$402$	−10.6757	−	13.0276i	−0.532456	−	0.649760i
$403$		−	7.02523i		−	0.349952i
$404$	5.26714	+	9.12295i	0.262050	+	0.453884i
$405$	0.0980271	−	20.1244i	0.00487101	−	0.999988i
$406$	11.5758	+	3.28365i	0.574498	+	0.162965i
$407$	−10.1937	+	5.88533i	−0.505282	+	0.291725i
$408$	20.8500	−	3.42681i	1.03223	−	0.169652i
$409$	11.1422	+	19.2989i	0.550948	+	0.954270i	0.998206	+	0.0598652i	$0.0190671\pi$
$409$	11.1422	+	19.2989i	0.550948	+	0.954270i	−0.447258	+	0.894405i	$0.647600\pi$
$410$	7.15635	+	5.51368i	0.353427	+	0.272301i
$411$	13.4952	−	11.0588i	0.665668	−	0.545492i
$412$	−12.0658	+	6.96620i	−0.594440	+	0.343200i
$413$	−4.16322	+	1.05061i	−0.204858	+	0.0516972i
$414$	−9.91019	−	8.71647i	−0.487059	−	0.428391i
$415$	20.4095	+	15.7247i	1.00186	+	0.771894i
$416$	−11.2586			−0.551999
$417$	−30.0257	+	4.93489i	−1.47036	+	0.241663i
$418$		−	3.31153i		−	0.161972i
$419$	−2.67074	+	4.62585i	−0.130474	+	0.225988i	−0.923859	−	0.382732i	$-0.874983\pi$
$419$	−2.67074	+	4.62585i	−0.130474	+	0.225988i	0.793385	+	0.608720i	$0.208317\pi$
$420$	3.68756	−	14.6633i	0.179935	−	0.715494i
$421$	1.58894	+	2.75212i	0.0774401	+	0.134130i	0.902145	−	0.431433i	$-0.141992\pi$
$421$	1.58894	+	2.75212i	0.0774401	+	0.134130i	−0.824705	+	0.565564i	$0.808659\pi$
$422$	11.5866	−	6.68953i	0.564027	−	0.325641i
$423$	−11.9104	+	13.5415i	−0.579102	+	0.658410i
$424$	−4.25980	+	7.37820i	−0.206874	+	0.358317i
$425$	−23.4328	+	6.18000i	−1.13666	+	0.299774i
$426$	−1.43120	−	8.70794i	−0.0693417	−	0.421901i
$427$	0.766620	+	0.789346i	0.0370994	+	0.0381992i
$428$	11.1602	+	6.44333i	0.539448	+	0.311450i
$429$	0.724848	+	4.41024i	0.0349960	+	0.212929i
$430$	0.00755901	+	0.0183512i	0.000364528	+	0.000884973i
$431$	−1.23311	+	2.13581i	−0.0593969	+	0.102878i	−0.894195	−	0.447678i	$-0.852251\pi$
$431$	−1.23311	+	2.13581i	−0.0593969	+	0.102878i	0.834798	+	0.550556i	$0.185584\pi$
$432$	−0.204583	+	5.85938i	−0.00984302	+	0.281910i
$433$			24.1289i			1.15956i	0.814773	+	0.579780i	$0.196862\pi$
$433$			24.1289i			1.15956i	−0.814773	+	0.579780i	$0.803138\pi$
$434$	6.72987	+	1.90903i	0.323044	+	0.0916364i
$435$	24.3111	−	0.730288i	1.16563	−	0.0350146i
$436$	17.6625			0.845879
$437$	17.9391	−	10.3572i	0.858145	−	0.495450i
$438$	−1.21003	+	3.20790i	−0.0578173	+	0.153279i
$439$	−2.74817	+	4.75996i	−0.131163	+	0.227181i	−0.924125	−	0.382090i	$-0.875204\pi$
$439$	−2.74817	+	4.75996i	−0.131163	+	0.227181i	0.792962	+	0.609271i	$0.208538\pi$
$440$	−6.97861	+	2.87455i	−0.332692	+	0.137039i
$441$	14.3238	−	15.3567i	0.682084	−	0.731274i
$442$			6.75401i			0.321255i
$443$	−3.91662	−	2.26126i	−0.186084	−	0.107436i	0.404064	−	0.914731i	$-0.367597\pi$
$443$	−3.91662	−	2.26126i	−0.186084	−	0.107436i	−0.590148	+	0.807295i	$0.700931\pi$
$444$	−3.63807	−	22.1354i	−0.172655	−	1.05050i
$445$	−19.8983	+	25.8265i	−0.943271	+	1.22430i
$446$	−10.3188			−0.488611
$447$	1.61141	+	1.96641i	0.0762170	+	0.0930082i
$448$	1.43006	−	5.04136i	0.0675639	−	0.238182i
$449$	25.2735			1.19273			0.596366	−	0.802713i	$-0.296611\pi$
$449$	25.2735			1.19273			0.596366	+	0.802713i	$0.296611\pi$
$450$	0.652040	+	10.8433i	0.0307374	+	0.511158i
$451$	−3.74069	+	6.47907i	−0.176142	+	0.305087i
$452$		−	3.21782i		−	0.151353i
$453$	−13.9235	−	16.9909i	−0.654182	−	0.798304i
$454$	4.54691	−	7.87547i	0.213397	−	0.369614i
$455$	10.4436	+	4.53008i	0.489602	+	0.212373i
$456$	13.9087	+	5.24639i	0.651335	+	0.245685i
$457$	4.34598	+	2.50915i	0.203296	+	0.117373i	0.598192	−	0.801353i	$-0.295886\pi$
$457$	4.34598	+	2.50915i	0.203296	+	0.117373i	−0.394896	+	0.918726i	$0.629219\pi$
$458$	9.21970	+	5.32299i	0.430808	+	0.248727i
$459$	25.1695	+	0.878805i	1.17481	+	0.0410191i
$460$	−15.8775	−	12.2330i	−0.740291	−	0.570365i
$461$	−3.76847	−	6.52717i	−0.175515	−	0.304001i	0.764824	−	0.644239i	$-0.222826\pi$
$461$	−3.76847	−	6.52717i	−0.175515	−	0.304001i	−0.940339	+	0.340238i	$0.889492\pi$
$462$	−4.42179	−	0.504063i	−0.205720	−	0.0234511i
$463$	−9.35557	−	5.40144i	−0.434790	−	0.251026i	0.266595	−	0.963809i	$-0.414101\pi$
$463$	−9.35557	−	5.40144i	−0.434790	−	0.251026i	−0.701385	+	0.712782i	$0.747435\pi$
$464$	−7.08579			−0.328950
$465$	14.1338	−	0.424570i	0.655440	−	0.0196890i
$466$	0.224636			0.0104061
$467$	−7.84275	+	4.52802i	−0.362919	+	0.209532i	−0.670361	−	0.742035i	$-0.733861\pi$
$467$	−7.84275	+	4.52802i	−0.362919	+	0.209532i	0.307441	+	0.951567i	$0.400527\pi$
$468$	−8.35167	−	1.67385i	−0.386056	−	0.0773738i
$469$	−8.69288	−	34.4469i	−0.401400	−	1.59061i
$470$	5.94117	−	7.71119i	0.274046	−	0.355691i
$471$	−27.9430	−	10.5402i	−1.28755	−	0.485665i
$472$	−3.53748	+	2.04236i	−0.162826	+	0.0940074i
$473$	−0.0142340	+	0.00821799i	−0.000654479	+	0.000377863i
$474$	17.6412	+	6.65429i	0.810287	+	0.305642i
$475$	−16.4508	−	4.47750i	−0.754816	−	0.205442i
$476$	18.2034	+	5.16367i	0.834352	+	0.236677i
$477$	−6.70648	+	7.62493i	−0.307069	+	0.349122i
$478$	−12.0849	+	6.97722i	−0.552751	+	0.319131i
$479$	17.2862			0.789829			0.394914	−	0.918718i	$-0.370774\pi$
$479$	17.2862			0.789829			0.394914	+	0.918718i	$0.370774\pi$
$480$	−0.680416	−	22.6508i	−0.0310566	−	1.03386i
$481$	16.8894			0.770088
$482$	2.10999	+	1.21820i	0.0961074	+	0.0554876i
$483$	−11.0990	−	25.5302i	−0.505024	−	1.16166i
$484$	6.78872	+	11.7584i	0.308578	+	0.534473i
$485$	12.5330	+	9.65621i	0.569096	+	0.438466i
$486$	2.60334	−	10.9848i	0.118090	−	0.498279i
$487$	7.97561	+	4.60472i	0.361410	+	0.208660i	0.669699	−	0.742633i	$-0.266423\pi$
$487$	7.97561	+	4.60472i	0.361410	+	0.208660i	−0.308289	+	0.951293i	$0.599756\pi$
$488$	0.906547	+	0.523395i	0.0410374	+	0.0236930i
$489$	33.1918	+	12.5200i	1.50098	+	0.566174i
$490$	−7.17755	+	8.77349i	−0.324248	+	0.396346i
$491$	3.63296	−	6.29247i	0.163953	−	0.283975i	−0.772330	−	0.635222i	$-0.780909\pi$
$491$	3.63296	−	6.29247i	0.163953	−	0.283975i	0.936283	+	0.351246i	$0.114242\pi$
$492$	−9.03714	−	11.0281i	−0.407426	−	0.497185i
$493$			30.4376i			1.37084i
$494$	−2.37581	+	4.11502i	−0.106893	+	0.185143i
$495$	−8.82900	+	1.72483i	−0.396834	+	0.0775253i
$496$	−4.11949			−0.184971
$497$	5.07970	−	17.9074i	0.227856	−	0.803256i
$498$	9.16065	+	11.1788i	0.410498	+	0.500934i
$499$	−3.83511			−0.171683			−0.0858416	−	0.996309i	$-0.527358\pi$
$499$	−3.83511			−0.171683			−0.0858416	+	0.996309i	$0.527358\pi$
$500$	2.05665	+	16.3684i	0.0919760	+	0.732017i
$501$	−3.71774	−	22.6201i	−0.166096	−	1.01059i
$502$	16.4464	+	9.49532i	0.734038	+	0.423797i
$503$			6.48313i			0.289069i	0.989500	+	0.144534i	$0.0461684\pi$
$503$			6.48313i			0.289069i	−0.989500	+	0.144534i	$0.953832\pi$
$504$	9.12247	−	17.7734i	0.406347	−	0.791688i
$505$	−6.08004	−	14.7607i	−0.270558	−	0.656841i
$506$	−2.94983	+	5.10926i	−0.131136	+	0.227134i
$507$	−5.68344	+	15.0674i	−0.252410	+	0.669165i
$508$	−13.7214	+	7.92208i	−0.608791	+	0.351485i
$509$	23.4396			1.03894			0.519471	−	0.854488i	$-0.326129\pi$
$509$	23.4396			1.03894			0.519471	+	0.854488i	$0.326129\pi$
$510$	−13.5881	+	0.408179i	−0.601693	+	0.0180745i
$511$	−5.18774	+	5.03838i	−0.229492	+	0.222885i
$512$			12.2818i			0.542784i
$513$	15.0259	+	9.38910i	0.663409	+	0.414539i
$514$	0.957670	−	1.65873i	0.0422410	−	0.0731636i
$515$	19.5221	−	8.04132i	0.860247	−	0.354343i
$516$	−0.00508003	−	0.0309088i	−0.000223636	−	0.00136068i
$517$	6.98140	+	4.03071i	0.307042	+	0.177271i
$518$	−4.58950	+	16.1793i	−0.201651	+	0.710877i
$519$	−0.341180	−	2.07587i	−0.0149761	−	0.0911205i
$520$	10.7342	+	1.43469i	0.470724	+	0.0629152i
$521$	−15.2613	+	26.4333i	−0.668609	+	1.15806i	0.309685	+	0.950839i	$0.399777\pi$
$521$	−15.2613	+	26.4333i	−0.668609	+	1.15806i	−0.978293	+	0.207225i	$0.933557\pi$
$522$	13.3776	+	2.68115i	0.585520	+	0.117351i
$523$	−0.683476	+	0.394605i	−0.0298863	+	0.0172549i	−0.514869	−	0.857269i	$-0.672159\pi$
$523$	−0.683476	+	0.394605i	−0.0298863	+	0.0172549i	0.484982	+	0.874524i	$0.338826\pi$
$524$	1.50063	+	2.59916i	0.0655552	+	0.113545i
$525$	−8.48274	+	21.2848i	−0.370217	+	0.928945i
$526$	3.93458	−	6.81490i	0.171556	−	0.297144i
$527$			17.6956i			0.770833i
$528$	2.58610	−	0.425040i	0.112546	−	0.0184975i
$529$	−13.9037			−0.604508
$530$	3.34535	−	4.34201i	0.145313	−	0.188605i
$531$	−4.61252	+	1.55828i	−0.200167	+	0.0676236i
$532$	9.27441	+	9.54935i	0.402097	+	0.414017i
$533$	9.29662	−	5.36741i	0.402681	−	0.232488i
$534$	−14.1459	+	11.5921i	−0.612153	+	0.501638i
$535$	−15.4697	−	11.9188i	−0.668814	−	0.515294i
$536$	−16.8987	−	29.2695i	−0.729914	−	1.26425i
$537$	−33.5495	+	5.51405i	−1.44777	+	0.237949i
$538$	−14.7258	+	8.50194i	−0.634874	+	0.366545i
$539$	−7.98902	−	4.92903i	−0.344111	−	0.212308i
$540$	2.86283	−	16.9036i	0.123196	−	0.727414i
$541$	−13.2859	−	23.0118i	−0.571204	−	0.989354i	−0.996443	−	0.0842726i	$-0.973143\pi$
$541$	−13.2859	−	23.0118i	−0.571204	−	0.989354i	0.425239	−	0.905081i	$-0.360190\pi$
$542$			20.6353i			0.886360i
$543$	−26.3301	−	32.1308i	−1.12993	−	1.37886i
$544$	28.3590			1.21588
$545$	−26.5301	−	3.54592i	−1.13643	−	0.151890i
$546$	5.13304	+	3.79871i	0.219674	+	0.162570i
$547$	−13.1269	+	7.57882i	−0.561266	+	0.324047i	−0.753654	−	0.657272i	$-0.771710\pi$
$547$	−13.1269	+	7.57882i	−0.561266	+	0.324047i	0.192387	+	0.981319i	$0.438377\pi$
$548$	12.8723	−	7.43185i	0.549879	−	0.317473i
$549$	0.936862	+	0.824014i	0.0399843	+	0.0351681i
$550$	4.69527	−	1.23830i	0.200207	−	0.0528012i
$551$	−10.7068	+	18.5447i	−0.456125	+	0.790032i
$552$	−16.7860	−	20.4841i	−0.714459	−	0.871860i
$553$	27.7075	+	28.5289i	1.17824	+	1.21317i
$554$	−11.5129	+	19.9410i	−0.489137	+	0.847211i
$555$	1.02071	+	33.9791i	0.0433267	+	1.44233i
$556$	−25.9223			−1.09935
$557$	−15.8165	−	9.13168i	−0.670168	−	0.386922i	0.125972	−	0.992034i	$-0.459795\pi$
$557$	−15.8165	−	9.13168i	−0.670168	−	0.386922i	−0.796140	+	0.605112i	$0.793128\pi$
$558$	7.77737	+	1.55875i	0.329242	+	0.0659871i
$559$	0.0235835			0.000997475
$560$	2.65637	−	6.12396i	0.112252	−	0.258784i
$561$	−1.82580	−	11.1088i	−0.0770851	−	0.469015i
$562$		−	7.01854i		−	0.296059i
$563$	22.4670	−	12.9713i	0.946870	−	0.546675i	0.0547625	−	0.998499i	$-0.482560\pi$
$563$	22.4670	−	12.9713i	0.946870	−	0.546675i	0.892107	+	0.451824i	$0.149226\pi$
$564$	−11.8831	+	9.73780i	−0.500370	+	0.410036i
$565$	−0.646008	+	4.83336i	−0.0271778	+	0.203341i
$566$	17.9757			0.755573
$567$	14.8242	−	18.6345i	0.622556	−	0.782575i
$568$		−	17.7078i		−	0.743004i
$569$	3.83307	−	6.63907i	0.160691	−	0.278324i	−0.774426	−	0.632664i	$-0.781961\pi$
$569$	3.83307	−	6.63907i	0.160691	−	0.278324i	0.935117	+	0.354340i	$0.115295\pi$
$570$	−8.42244	−	4.53111i	−0.352777	−	0.189787i
$571$	−3.64084	−	6.30612i	−0.152364	−	0.263903i	0.779732	−	0.626114i	$-0.215355\pi$
$571$	−3.64084	−	6.30612i	−0.152364	−	0.263903i	−0.932096	+	0.362211i	$0.882022\pi$
$572$			3.80752i			0.159200i
$573$	−37.2160	+	6.11666i	−1.55472	+	0.255527i
$574$	2.61549	+	10.3643i	0.109168	+	0.432598i
$575$	21.3931	+	21.5622i	0.892152	+	0.899207i
$576$	1.16766	−	5.82604i	0.0486526	−	0.242752i
$577$	0.185836	+	0.107293i	0.00773646	+	0.00446665i	0.503863	−	0.863783i	$-0.331912\pi$
$577$	0.185836	+	0.107293i	0.00773646	+	0.00446665i	−0.496127	+	0.868250i	$0.665245\pi$
$578$		−	4.70118i		−	0.195543i
$579$	−14.1126	−	5.32332i	−0.586502	−	0.221229i
$580$	20.5375	+	2.74496i	0.852772	+	0.113978i
$581$	7.45922	+	29.5583i	0.309461	+	1.22629i
$582$	5.62537	+	6.86468i	0.233179	+	0.284550i
$583$	3.93108	+	2.26961i	0.162809	+	0.0939977i
$584$	−3.43985	+	5.95800i	−0.142342	+	0.246544i
$585$	12.2087	+	4.19090i	0.504766	+	0.173273i
$586$	−1.41950	−	2.45865i	−0.0586391	−	0.101566i
$587$	−20.6019	+	11.8945i	−0.850330	+	0.490938i	−0.860762	−	0.509007i	$-0.830013\pi$
$587$	−20.6019	+	11.8945i	−0.850330	+	0.490938i	0.0104322	+	0.999946i	$0.496679\pi$
$588$	14.1627	−	10.9303i	0.584059	−	0.450759i
$589$	−6.22466	+	10.7814i	−0.256482	+	0.444241i
$590$	2.42993	−	1.00091i	0.100039	−	0.0412067i
$591$	−32.7627	+	26.8479i	−1.34768	+	1.10437i
$592$		−	9.90368i		−	0.407039i
$593$	28.8062	−	16.6312i	1.18293	−	0.682963i	0.226237	−	0.974072i	$-0.427358\pi$
$593$	28.8062	−	16.6312i	1.18293	−	0.682963i	0.956690	+	0.291109i	$0.0940242\pi$
$594$	−5.04324	−	0.176087i	−0.206927	−	0.00722496i
$595$	−26.3060	−	11.4107i	−1.07844	−	0.467791i
$596$	1.08291	+	1.87566i	0.0443578	+	0.0768300i
$597$	7.26266	−	1.19366i	0.297241	−	0.0488532i
$598$	7.33112	−	4.23263i	0.299792	−	0.173085i
$599$	6.79242	+	11.7648i	0.277531	+	0.480698i	0.970771	−	0.240010i	$-0.0771506\pi$
$599$	6.79242	+	11.7648i	0.277531	+	0.480698i	−0.693240	+	0.720707i	$0.743817\pi$
$600$	−2.23768	+	21.6824i	−0.0913528	+	0.885179i
$601$	7.84506	+	13.5880i	0.320007	+	0.554268i	0.980489	−	0.196574i	$-0.0629815\pi$
$601$	7.84506	+	13.5880i	0.320007	+	0.554268i	−0.660482	+	0.750842i	$0.729648\pi$
$602$	−0.00640856	+	0.0225920i	−0.000261193	+	0.000920780i
$603$	−12.8934	−	38.1645i	−0.525060	−	1.55418i
$604$	−9.35697	−	16.2068i	−0.380730	−	0.659443i
$605$	−7.83645	−	19.0247i	−0.318597	−	0.773466i
$606$	−1.45232	−	8.83647i	−0.0589966	−	0.358957i
$607$		−	21.8816i		−	0.888145i	−0.895991	−	0.444073i	$-0.853533\pi$
$607$		−	21.8816i		−	0.888145i	0.895991	−	0.444073i	$-0.146467\pi$
$608$	17.2783	+	9.97562i	0.700727	+	0.404565i
$609$	23.1326	+	17.1193i	0.937378	+	0.693709i
$610$	−0.533495	−	0.411037i	−0.0216006	−	0.0166424i
$611$	−5.78355	−	10.0174i	−0.233977	−	0.405261i
$612$	21.0367	+	4.21621i	0.850360	+	0.170430i
$613$	32.6732	+	18.8639i	1.31966	+	0.761906i	0.983674	−	0.179961i	$-0.0575972\pi$
$613$	32.6732	+	18.8639i	1.31966	+	0.761906i	0.335986	+	0.941867i	$0.390931\pi$
$614$	3.74014	−	6.47811i	0.150940	−	0.261435i
$615$	11.3603	+	18.3792i	0.458093	+	0.741119i
$616$	−8.59130	−	2.43705i	−0.346153	−	0.0981917i
$617$	26.2962	+	15.1821i	1.05865	+	0.611210i	0.925057	−	0.379827i	$-0.124017\pi$
$617$	26.2962	+	15.1821i	1.05865	+	0.611210i	0.133589	+	0.991037i	$0.457350\pi$
$618$	11.6869	−	1.92081i	0.470116	−	0.0772662i
$619$	−16.1400			−0.648723			−0.324361	−	0.945933i	$-0.605149\pi$
$619$	−16.1400			−0.648723			−0.324361	+	0.945933i	$0.605149\pi$
$620$	11.9399	+	1.59585i	0.479519	+	0.0640908i
$621$	−14.8194	−	27.8709i	−0.594682	−	1.11842i
$622$		−	15.2819i		−	0.612747i
$623$	−37.4037	+	9.43904i	−1.49855	+	0.378167i
$624$	−3.51852	−	1.32719i	−0.140853	−	0.0531302i
$625$	0.196911	−	24.9992i	0.00787643	−	0.999969i
$626$	−0.888552	−	1.53902i	−0.0355137	−	0.0615115i
$627$	2.79526	−	7.41052i	0.111632	−	0.295948i
$628$	−22.0335	−	12.7210i	−0.879231	−	0.507624i
$629$	−42.5420			−1.69626
$630$	−7.33228	+	10.5566i	−0.292125	+	0.420583i
$631$	6.81190			0.271178			0.135589	−	0.990765i	$-0.456707\pi$
$631$	6.81190			0.271178			0.135589	+	0.990765i	$0.456707\pi$
$632$	32.7648	+	18.9168i	1.30331	+	0.752469i
$633$	31.5751	−	5.18954i	1.25500	−	0.206266i
$634$	−5.01644	−	8.68873i	−0.199228	−	0.345074i
$635$	22.2009	−	9.14473i	0.881015	−	0.362898i
$636$	−6.69113	+	5.48315i	−0.265321	+	0.217421i
$637$	6.39116	+	11.8566i	0.253227	+	0.469775i
$638$		−	6.09883i		−	0.241455i
$639$	4.14764	−	20.6946i	0.164078	−	0.818667i
$640$	3.04162	−	22.7570i	0.120230	−	0.899550i
$641$	23.7403			0.937687			0.468843	−	0.883281i	$-0.344671\pi$
$641$	23.7403			0.937687			0.468843	+	0.883281i	$0.344671\pi$
$642$	−6.94347	−	8.47318i	−0.274037	−	0.334410i
$643$	−38.2529	−	22.0853i	−1.50855	−	0.870959i	−0.999950	−	0.00995298i	$-0.996832\pi$
$643$	−38.2529	−	22.0853i	−1.50855	−	0.870959i	−0.508595	−	0.861006i	$-0.669835\pi$
$644$	−5.80288	−	22.9948i	−0.228665	−	0.906124i
$645$	0.00142527	+	0.0474468i	5.61199e−5	+	0.00186821i
$646$	5.98434	−	10.3652i	0.235451	−	0.407813i
$647$	−28.3391	−	16.3616i	−1.11412	−	0.643240i	−0.174229	−	0.984705i	$-0.555743\pi$
$647$	−28.3391	−	16.3616i	−1.11412	−	0.643240i	−0.939894	+	0.341466i	$0.889077\pi$
$648$	8.72950	−	20.9031i	0.342927	−	0.821151i
$649$	1.08816	+	1.88476i	0.0427142	+	0.0739832i
$650$	−6.72290	−	1.82980i	−0.263694	−	0.0717708i
$651$	13.4487	+	9.95270i	0.527094	+	0.390077i
$652$	26.1722	+	15.1105i	1.02498	+	0.591773i
$653$		−	33.5624i		−	1.31340i	−0.754153	−	0.656698i	$-0.771952\pi$
$653$		−	33.5624i		−	1.31340i	0.754153	−	0.656698i	$-0.228048\pi$
$654$	−14.0484	−	5.29908i	−0.549336	−	0.207211i
$655$	−1.73223	−	4.20536i	−0.0676836	−	0.164317i
$656$	−3.14737	−	5.45141i	−0.122884	−	0.212842i
$657$	−5.41558	+	6.15724i	−0.211282	+	0.240217i
$658$	11.1679	−	2.81827i	0.435369	−	0.109868i
$659$	−23.4862	−	40.6792i	−0.914891	−	1.58464i	−0.807061	−	0.590467i	$-0.798943\pi$
$659$	−23.4862	−	40.6792i	−0.914891	−	1.58464i	−0.107829	−	0.994169i	$-0.534390\pi$
$660$	−7.66022	+	0.230108i	−0.298174	+	0.00895694i
$661$	22.1634	+	38.3881i	0.862056	+	1.49312i	0.869941	+	0.493156i	$0.164157\pi$
$661$	22.1634	+	38.3881i	0.862056	+	1.49312i	−0.00788532	+	0.999969i	$0.502510\pi$
$662$	6.47380	−	3.73765i	0.251612	−	0.145268i
$663$	−5.70106	+	15.1141i	−0.221411	+	0.586982i
$664$	14.5005	+	25.1157i	0.562730	+	0.974677i
$665$	−12.0136	−	16.2056i	−0.465868	−	0.628427i
$666$	−3.74739	+	18.6976i	−0.145208	+	0.724516i
$667$	33.0384	−	19.0748i	1.27925	−	0.738577i
$668$		−	19.5288i		−	0.755590i
$669$	−23.0914	−	8.71013i	−0.892766	−	0.336753i
$670$	8.28163	+	20.1055i	0.319947	+	0.776743i
$671$	0.278863	−	0.483005i	0.0107654	−	0.0186462i
$672$	15.9502	−	21.5528i	0.615292	−	0.831417i
$673$	1.19031	−	0.687224i	0.0458830	−	0.0264905i	−0.476883	−	0.878967i	$-0.658233\pi$
$673$	1.19031	−	0.687224i	0.0458830	−	0.0264905i	0.522766	+	0.852476i	$0.324900\pi$
$674$	−2.73216	−	4.73223i	−0.105239	−	0.182279i
$675$	−7.69370	+	24.8155i	−0.296131	+	0.955147i
$676$	−6.85940	+	11.8808i	−0.263823	+	0.456955i
$677$	8.96039	+	5.17328i	0.344376	+	0.198825i	0.662205	−	0.749322i	$-0.269621\pi$
$677$	8.96039	+	5.17328i	0.344376	+	0.198825i	−0.317830	+	0.948148i	$0.602954\pi$
$678$	−0.965407	+	2.55939i	−0.0370762	+	0.0982928i
$679$	4.58056	+	18.1512i	0.175786	+	0.696579i
$680$	−27.0379	−	3.61379i	−1.03686	−	0.138582i
$681$	16.8227	−	13.7856i	0.644649	−	0.528267i
$682$		−	3.54570i		−	0.135772i
$683$	3.61004	+	2.08426i	0.138135	+	0.0797520i	0.567475	−	0.823391i	$-0.307920\pi$
$683$	3.61004	+	2.08426i	0.138135	+	0.0797520i	−0.429340	+	0.903143i	$0.641254\pi$
$684$	11.3340	+	9.96875i	0.433365	+	0.381165i
$685$	−20.8271	+	8.57884i	−0.795761	+	0.327781i
$686$	−13.0948	+	2.90056i	−0.499963	+	0.110744i
$687$	16.1386	+	19.6941i	0.615728	+	0.751377i
$688$		−	0.0138290i		−	0.000527226i
$689$	−3.25660	−	5.64059i	−0.124066	−	0.214889i
$690$	8.95853	+	14.4934i	0.341045	+	0.551755i
$691$	−2.26033	+	3.91500i	−0.0859869	+	0.148934i	−0.905811	−	0.423681i	$-0.860738\pi$
$691$	−2.26033	+	3.91500i	−0.0859869	+	0.148934i	0.819824	+	0.572615i	$0.194071\pi$
$692$		−	1.79217i		−	0.0681281i
$693$	−9.46959	−	4.86043i	−0.359720	−	0.184632i
$694$	−22.7399			−0.863194
$695$	38.9368	+	5.20415i	1.47696	+	0.197405i
$696$	25.6156	+	9.66226i	0.970958	+	0.366247i
$697$	−23.4170	+	13.5198i	−0.886981	+	0.512098i
$698$			17.0681i			0.646038i
$699$	0.502690	+	0.189616i	0.0190135	+	0.00717192i
$700$	−10.0716	+	16.7206i	−0.380670	+	0.631980i
$701$	−17.8754			−0.675146			−0.337573	−	0.941299i	$-0.609606\pi$
$701$	−17.8754			−0.675146			−0.337573	+	0.941299i	$0.609606\pi$
$702$	6.14057	+	3.83701i	0.231761	+	0.144819i
$703$	−25.9196	−	14.9647i	−0.977577	−	0.564404i
$704$	−2.65609			−0.100105
$705$	19.8041	−	12.2411i	0.745866	−	0.461027i
$706$	1.05006	−	1.81876i	0.0395196	−	0.0684500i
$707$	5.15468	−	18.1717i	0.193862	−	0.683417i
$708$	−4.09271	+	0.672660i	−0.153814	+	0.0252801i
$709$	−7.59920	+	13.1622i	−0.285394	+	0.494317i	−0.972705	−	0.232047i	$-0.925458\pi$
$709$	−7.59920	+	13.1622i	−0.285394	+	0.494317i	0.687311	+	0.726364i	$0.258791\pi$
$710$	−1.50929	+	11.2923i	−0.0566425	+	0.423793i
$711$	33.8605	+	29.7819i	1.26987	+	1.11691i
$712$	−31.7819	+	18.3493i	−1.19108	+	0.687668i
$713$	19.2077	−	11.0896i	0.719333	−	0.415307i
$714$	−12.9294	−	9.56846i	−0.483872	−	0.358091i
$715$	0.764397	−	5.71913i	0.0285868	−	0.213883i
$716$	−28.9645			−1.08246
$717$	−32.9330	+	5.41272i	−1.22991	+	0.202142i
$718$		−	16.4515i		−	0.613965i
$719$	−17.9155	−	31.0305i	−0.668135	−	1.15724i	−0.978425	−	0.206602i	$-0.933760\pi$
$719$	−17.9155	−	31.0305i	−0.668135	−	1.15724i	0.310290	−	0.950642i	$-0.399574\pi$
$720$	2.45749	−	7.15899i	0.0915851	−	0.266800i
$721$	24.0335	+	6.81746i	0.895053	+	0.253895i
$722$	−4.62404	+	2.66969i	−0.172089	+	0.0993557i
$723$	3.69344	+	4.50713i	0.137360	+	0.167622i
$724$	−17.6946	−	30.6479i	−0.657613	−	1.13902i
$725$	−30.2974	−	8.24620i	−1.12522	−	0.306256i
$726$	−1.87187	−	11.3892i	−0.0694717	−	0.422691i
$727$	24.9585	−	14.4098i	0.925659	−	0.534430i	0.0402231	−	0.999191i	$-0.487193\pi$
$727$	24.9585	−	14.4098i	0.925659	−	0.534430i	0.885436	+	0.464761i	$0.153860\pi$
$728$	8.92741	+	9.19206i	0.330872	+	0.340681i
$729$	15.0980	−	22.3842i	0.559184	−	0.829043i
$730$	2.70141	−	3.50624i	0.0999838	−	0.129772i
$731$	−0.0594037			−0.00219712
$732$	0.673706	+	0.822128i	0.0249009	+	0.0303867i
$733$		−	32.7988i		−	1.21145i	−0.795673	−	0.605726i	$-0.792883\pi$
$733$		−	32.7988i		−	1.21145i	0.795673	−	0.605726i	$-0.207117\pi$
$734$	5.33614	−	9.24247i	0.196961	−	0.341146i
$735$	−23.4676	+	13.5747i	−0.865615	+	0.500711i
$736$	−17.7721	−	30.7822i	−0.655088	−	1.13465i
$737$	−15.5947	+	9.00360i	−0.574438	+	0.331652i
$738$	3.87933	+	11.4829i	0.142800	+	0.422690i
$739$	−10.6796	+	18.4976i	−0.392856	+	0.680447i	−0.992825	−	0.119577i	$-0.961846\pi$
$739$	−10.6796	+	18.4976i	−0.392856	+	0.680447i	0.599969	+	0.800023i	$0.295180\pi$
$740$	−3.83658	+	28.7048i	−0.141035	+	1.05521i
$741$	−8.79005	+	7.20314i	−0.322911	+	0.264614i
$742$	6.28839	−	1.58691i	0.230854	−	0.0582573i
$743$	−32.5421	−	18.7882i	−1.19386	−	0.689273i	−0.234677	−	0.972073i	$-0.575403\pi$
$743$	−32.5421	−	18.7882i	−1.19386	−	0.689273i	−0.959179	+	0.282801i	$0.908736\pi$
$744$	14.8923	+	5.61738i	0.545976	+	0.205943i
$745$	−1.25004	−	3.03476i	−0.0457980	−	0.111185i
$746$	12.3422	−	21.3772i	0.451878	−	0.782676i
$747$	11.0636	+	32.7484i	0.404796	+	1.19820i
$748$		−	9.59064i		−	0.350669i
$749$	−5.65385	−	22.4043i	−0.206587	−	0.818634i
$750$	3.27502	−	13.6362i	0.119587	−	0.497922i
$751$	10.1997			0.372194			0.186097	−	0.982531i	$-0.440416\pi$
$751$	10.1997			0.372194			0.186097	+	0.982531i	$0.440416\pi$
$752$	−5.87406	+	3.39139i	−0.214205	+	0.123671i
$753$	28.7886	+	35.1310i	1.04912	+	1.28024i
$754$	−4.37551	+	7.57861i	−0.159347	+	0.275997i
$755$	10.8011	+	26.2220i	0.393091	+	0.954318i
$756$	15.0362	−	13.6165i	0.546861	−	0.495229i
$757$			4.08190i			0.148359i	0.997245	+	0.0741797i	$0.0236338\pi$
$757$			4.08190i			0.148359i	−0.997245	+	0.0741797i	$0.976366\pi$
$758$	−18.0834	−	10.4405i	−0.656820	−	0.379215i
$759$	−10.9138	+	8.94352i	−0.396148	+	0.324629i
$760$	−15.2022	−	11.7127i	−0.551442	−	0.424865i
$761$	12.1975			0.442158			0.221079	−	0.975256i	$-0.429042\pi$
$761$	12.1975			0.442158			0.221079	+	0.975256i	$0.429042\pi$
$762$	13.2906	−	2.18438i	0.481466	−	0.0791316i
$763$	−22.0646	−	22.7187i	−0.798793	−	0.822473i
$764$	−32.1299			−1.16242
$765$	−30.7520	−	10.5563i	−1.11184	−	0.381665i
$766$	1.06351	−	1.84206i	0.0384263	−	0.0665564i
$767$		−	3.12275i		−	0.112756i
$768$	6.96694	−	18.4700i	0.251398	−	0.666480i
$769$	−11.1259	+	19.2707i	−0.401212	+	0.694919i	−0.993872	−	0.110533i	$-0.964744\pi$
$769$	−11.1259	+	19.2707i	−0.401212	+	0.694919i	0.592661	+	0.805452i	$0.298078\pi$
$770$	5.27097	+	2.28637i	0.189952	+	0.0823951i
$771$	3.54321	−	2.90353i	0.127605	−	0.104568i
$772$	−11.1280	−	6.42476i	−0.400506	−	0.231232i
$773$	−0.432518	−	0.249715i	−0.0155566	−	0.00898161i	0.492202	−	0.870481i	$-0.336192\pi$
$773$	−0.432518	−	0.249715i	−0.0155566	−	0.00898161i	−0.507758	+	0.861500i	$0.669526\pi$
$774$	−0.00523267	+	0.0261084i	−0.000188085	+	0.000938446i
$775$	−17.6141	−	4.79412i	−0.632718	−	0.172210i
$776$	8.90449	+	15.4230i	0.319653	+	0.553655i
$777$	−23.9273	+	32.3319i	−0.858387	+	1.15990i
$778$	3.59440	+	2.07523i	0.128866	+	0.0744006i
$779$	−19.0230			−0.681570
$780$	9.68393	+	5.20977i	0.346740	+	0.186540i
$781$	−9.43468			−0.337599
$782$	−18.4661	+	10.6614i	−0.660347	+	0.381252i
$783$	27.6731	+	17.2919i	0.988956	+	0.617961i
$784$	6.95253	−	3.74769i	0.248305	−	0.133846i
$785$	30.5417	+	23.5312i	1.09008	+	0.839864i
$786$	−0.413772	−	2.51754i	−0.0147588	−	0.0897977i
$787$	−1.10504	+	0.637995i	−0.0393904	+	0.0227420i	−0.519566	−	0.854430i	$-0.673906\pi$
$787$	−1.10504	+	0.637995i	−0.0393904	+	0.0227420i	0.480175	+	0.877172i	$0.340573\pi$
$788$	−31.2506	+	18.0425i	−1.11326	+	0.642739i
$789$	14.5572	−	11.9292i	0.518252	−	0.424689i
$790$	−19.2818	−	14.8559i	−0.686016	−	0.528548i
$791$	−4.13898	+	4.01982i	−0.147165	+	0.142928i
$792$	−9.92853	−	1.98989i	−0.352795	−	0.0707076i
$793$	−0.693050	+	0.400132i	−0.0246109	+	0.0142091i
$794$	−6.52740			−0.231649
$795$	11.1513	−	6.89272i	0.395495	−	0.244460i
$796$	6.27012			0.222239
$797$	−36.9863	−	21.3541i	−1.31012	−	0.756400i	−0.328006	−	0.944676i	$-0.606377\pi$
$797$	−36.9863	−	21.3541i	−1.31012	−	0.756400i	−0.982116	+	0.188276i	$0.939710\pi$
$798$	−4.51170	−	10.3779i	−0.159713	−	0.367373i
$799$	14.5680	+	25.2325i	0.515379	+	0.892662i
$800$	−7.68305	+	28.2284i	−0.271637	+	0.998024i
$801$	−41.4405	+	14.0001i	−1.46423	+	0.494670i
$802$	1.19556	+	0.690257i	0.0422167	+	0.0243738i
$803$	3.17440	+	1.83274i	0.112022	+	0.0646761i
$804$	−5.56567	−	33.8636i	−0.196286	−	1.19428i
$805$	4.09984	+	35.7046i	0.144500	+	1.25842i
$806$	−2.54381	+	4.40600i	−0.0896018	+	0.155195i
$807$	−40.1298	+	6.59555i	−1.41263	+	0.232174i
$808$		−	17.9692i		−	0.632155i
$809$	8.77185	−	15.1933i	0.308402	−	0.534168i	−0.669611	−	0.742712i	$-0.733539\pi$
$809$	8.77185	−	15.1933i	0.308402	−	0.534168i	0.978013	+	0.208544i	$0.0668725\pi$
$810$	−7.34844	+	12.5859i	−0.258198	+	0.442223i
$811$	−4.42279			−0.155305			−0.0776527	−	0.996980i	$-0.524743\pi$
$811$	−4.42279			−0.155305			−0.0776527	+	0.996980i	$0.524743\pi$
$812$	17.0806	+	17.5870i	0.599413	+	0.617183i
$813$	−17.4182	+	46.1775i	−0.610884	+	1.61951i
$814$	8.52422			0.298774
$815$	−36.2786	−	27.9512i	−1.27078	−	0.979089i
$816$	8.86268	+	3.34302i	0.310256	+	0.117029i
$817$	−0.0361929	−	0.0208960i	−0.00126623	−	0.000731058i
$818$		−	16.1382i		−	0.564260i
$819$	8.28019	+	12.8335i	0.289333	+	0.448440i
$820$	7.01052	+	17.0196i	0.244818	+	0.594351i
$821$	−1.78226	+	3.08697i	−0.0622014	+	0.107736i	−0.895449	−	0.445164i	$-0.853145\pi$
$821$	−1.78226	+	3.08697i	−0.0622014	+	0.107736i	0.833248	+	0.552900i	$0.186479\pi$
$822$	−12.4681	+	2.04920i	−0.434875	+	0.0714742i
$823$	41.0730	−	23.7135i	1.43172	−	0.826602i	0.434465	−	0.900689i	$-0.356938\pi$
$823$	41.0730	−	23.7135i	1.43172	−	0.826602i	0.997252	+	0.0740871i	$0.0236043\pi$
$824$	23.7657			0.827916
$825$	11.5523	+	1.19223i	0.402200	+	0.0415080i
$826$	2.99146	+	0.848574i	0.104086	+	0.0295257i
$827$		−	5.96691i		−	0.207490i	−0.994604	−	0.103745i	$-0.966917\pi$
$827$		−	5.96691i		−	0.207490i	0.994604	−	0.103745i	$-0.0330825\pi$
$828$	−8.60691	−	25.4765i	−0.299111	−	0.885370i
$829$	5.85915	−	10.1483i	0.203497	−	0.352466i	−0.746156	−	0.665771i	$-0.768103\pi$
$829$	5.85915	−	10.1483i	0.203497	−	0.352466i	0.949653	+	0.313305i	$0.101436\pi$
$830$	−7.10633	−	17.2522i	−0.246664	−	0.598833i
$831$	−42.5957	+	34.9057i	−1.47763	+	1.21087i
$832$	3.30055	+	1.90557i	0.114426	+	0.0660638i
$833$	−16.0985	−	29.8652i	−0.557780	−	1.03477i
$834$	20.6181	+	7.77718i	0.713946	+	0.269302i
$835$	−3.92059	+	29.3334i	−0.135678	+	1.01512i
$836$	3.37363	−	5.84330i	0.116679	−	0.202095i
$837$	16.0884	+	10.0530i	0.556097	+	0.347484i
$838$	3.35001	−	1.93413i	0.115724	−	0.0668133i
$839$	15.3970	+	26.6684i	0.531563	+	0.920694i	0.999321	+	0.0368378i	$0.0117285\pi$
$839$	15.3970	+	26.6684i	0.531563	+	0.920694i	−0.467758	+	0.883856i	$0.654938\pi$
$840$	−17.9537	+	18.5163i	−0.619460	+	0.638872i
$841$	−5.21869	+	9.03903i	−0.179955	+	0.311691i
$842$		−	2.30139i		−	0.0793112i
$843$	5.92435	−	15.7061i	0.204046	−	0.540945i
$844$	27.2599			0.938325
$845$	12.6884	−	16.4686i	0.436495	−	0.566538i
$846$	12.3731	−	4.18010i	0.425397	−	0.143715i
$847$	6.64377	−	23.4212i	0.228283	−	0.804761i
$848$	−3.30756	+	1.90962i	−0.113582	+	0.0655767i
$849$	40.2258	+	15.1733i	1.38055	+	0.520745i
$850$	16.9341	+	4.60903i	0.580835	+	0.158089i
$851$	26.6604	+	46.1772i	0.913907	+	1.58293i
$852$	6.34584	−	16.8235i	0.217405	−	0.576362i
$853$	32.3974	−	18.7047i	1.10927	−	0.640436i	0.170628	−	0.985336i	$-0.445420\pi$
$853$	32.3974	−	18.7047i	1.10927	−	0.640436i	0.938640	+	0.344900i	$0.112087\pi$
$854$	−0.194981	−	0.772644i	−0.00667212	−	0.0264393i
$855$	−15.0230	−	17.2491i	−0.513775	−	0.589906i
$856$	−10.9909	−	19.0369i	−0.375663	−	0.650667i
$857$			7.58418i			0.259071i	0.991575	+	0.129535i	$0.0413485\pi$
$857$			7.58418i			0.259071i	−0.991575	+	0.129535i	$0.958651\pi$
$858$	1.14233	−	3.02843i	0.0389985	−	0.103389i
$859$	−14.6842			−0.501017			−0.250509	−	0.968114i	$-0.580598\pi$
$859$	−14.6842			−0.501017			−0.250509	+	0.968114i	$0.580598\pi$
$860$	−0.00535721	+	0.0400820i	−0.000182679	+	0.00136679i
$861$	−2.89558	+	25.4009i	−0.0986810	+	0.865661i
$862$	1.54674	−	0.893010i	0.0526821	−	0.0304160i
$863$	−31.8559	+	18.3920i	−1.08439	+	0.626072i	−0.932077	−	0.362261i	$-0.882005\pi$
$863$	−31.8559	+	18.3920i	−1.08439	+	0.626072i	−0.152311	+	0.988333i	$0.548672\pi$
$864$	16.1110	−	25.7833i	0.548107	−	0.877164i
$865$	−0.359796	+	2.69195i	−0.0122334	+	0.0915290i
$866$	8.73698	−	15.1329i	0.296895	−	0.514236i
$867$	3.96827	−	10.5203i	0.134769	−	0.357287i
$868$	9.93024	+	10.2246i	0.337054	+	0.347046i
$869$	10.0788	−	17.4570i	0.341900	−	0.592188i
$870$	−15.5116	−	8.34492i	−0.525892	−	0.282919i
$871$	25.8380			0.875487
$872$	−26.0920	−	15.0642i	−0.883585	−	0.510138i
$873$	6.79394	+	20.1101i	0.229940	+	0.680625i
$874$	−15.0012			−0.507422
$875$	18.4850	−	23.0934i	0.624906	−	0.780700i
$876$	−5.40319	+	4.42773i	−0.182557	+	0.149599i
$877$		−	4.22976i		−	0.142829i	−0.997447	−	0.0714144i	$-0.977249\pi$
$877$		−	4.22976i		−	0.142829i	0.997447	−	0.0714144i	$-0.0227513\pi$
$878$	3.44713	−	1.99020i	0.116335	−	0.0671660i
$879$	−1.10121	−	6.70016i	−0.0371428	−	0.225991i
$880$	−3.35362	−	0.448232i	−0.113050	−	0.0151099i
$881$	53.7413			1.81059			0.905295	−	0.424783i	$-0.139649\pi$
$881$	53.7413			1.81059			0.905295	+	0.424783i	$0.139649\pi$
$882$	−14.5440	+	4.44469i	−0.489723	+	0.149661i
$883$		−	35.5705i		−	1.19704i	−0.801106	−	0.598522i	$-0.795755\pi$
$883$		−	35.5705i		−	1.19704i	0.801106	−	0.598522i	$-0.204245\pi$
$884$	−6.88066	+	11.9177i	−0.231422	+	0.400834i
$885$	6.28255	−	0.188724i	0.211186	−	0.00634388i
$886$	1.63759	+	2.83638i	0.0550158	+	0.0952902i
$887$			2.10427i			0.0706546i	0.999376	+	0.0353273i	$0.0112474\pi$
$887$			2.10427i			0.0706546i	−0.999376	+	0.0353273i	$0.988753\pi$
$888$	−13.5048	+	35.8025i	−0.453190	+	1.20145i
$889$	27.3313	+	7.75293i	0.916662	+	0.260025i
$890$	21.8313	−	8.99250i	0.731787	−	0.301429i
$891$	−11.1371	−	4.65105i	−0.373107	−	0.155816i
$892$	−18.2079	−	10.5123i	−0.609646	−	0.351979i
$893$			20.4979i			0.685936i
$894$	−0.298594	−	1.81676i	−0.00998649	−	0.0607615i
$895$	43.5065	+	5.81492i	1.45426	+	0.194371i
$896$	19.4877	−	18.9266i	0.651038	−	0.632293i
$897$	19.9783	−	3.28355i	0.667056	−	0.109634i
$898$	−15.8508	−	9.15145i	−0.528947	−	0.305388i
$899$	−11.4639	+	19.8561i	−0.382343	+	0.662238i
$900$	−9.89609	+	19.7976i	−0.329870	+	0.659920i
$901$	8.20293	+	14.2079i	0.273279	+	0.473334i
$902$	4.69209	−	2.70898i	0.156230	−	0.0901992i
$903$	−0.0334109	+	0.0451467i	−0.00111185	+	0.00150239i
$904$	−2.74445	+	4.75353i	−0.0912791	+	0.158100i
$905$	20.4254	+	49.5873i	0.678964	+	1.64834i
$906$	2.58002	+	15.6978i	0.0857155	+	0.521525i
$907$		−	10.8295i		−	0.359588i	−0.983704	−	0.179794i	$-0.942457\pi$
$907$		−	10.8295i		−	0.359588i	0.983704	−	0.179794i	$-0.0575431\pi$
$908$	16.0463	−	9.26435i	0.532516	−	0.307448i
$909$	4.20887	−	21.0001i	0.139599	−	0.696530i
$910$	−4.90956	−	6.62270i	−0.162750	−	0.219540i
$911$	11.5702	+	20.0402i	0.383339	+	0.663963i	0.991537	−	0.129822i	$-0.0414407\pi$
$911$	11.5702	+	20.0402i	0.383339	+	0.663963i	−0.608198	+	0.793785i	$0.708107\pi$
$912$	4.22382	+	5.15436i	0.139865	+	0.170678i
$913$	13.3816	−	7.72584i	0.442865	−	0.255688i
$914$	−1.81711	−	3.14733i	−0.0601046	−	0.104104i
$915$	−0.846897	−	1.37014i	−0.0279975	−	0.0452954i
$916$	10.8456	+	18.7852i	0.358350	+	0.620680i
$917$	1.46859	−	5.17718i	0.0484970	−	0.170966i
$918$	−15.4673	−	9.66492i	−0.510497	−	0.318990i
$919$	10.1541	+	17.5875i	0.334954	+	0.580158i	0.983476	−	0.181038i	$-0.0579458\pi$
$919$	10.1541	+	17.5875i	0.334954	+	0.580158i	−0.648522	+	0.761196i	$0.724612\pi$
$920$	13.0217	+	31.6130i	0.429311	+	1.04225i
$921$	13.8378	−	11.3396i	0.455972	−	0.373653i
$922$			5.45819i			0.179756i
$923$	11.7239	+	6.76877i	0.385895	+	0.222797i
$924$	−7.28888	−	5.39415i	−0.239787	−	0.177454i
$925$	11.5255	−	42.3461i	0.378958	−	1.39233i
$926$	3.91168	+	6.77523i	0.128546	+	0.222648i
$927$	27.7743	+	5.56655i	0.912226	+	0.182829i
$928$	31.8213	+	18.3721i	1.04459	+	0.603093i
$929$	11.9907	−	20.7685i	0.393402	−	0.681393i	−0.599494	−	0.800380i	$-0.704631\pi$
$929$	11.9907	−	20.7685i	0.393402	−	0.681393i	0.992896	+	0.118987i	$0.0379646\pi$
$930$	−9.01802	−	4.85152i	−0.295712	−	0.159088i
$931$	0.697105	−	23.8588i	0.0228467	−	0.781941i
$932$	0.396378	+	0.228849i	0.0129838	+	0.00749619i
$933$	12.8994	−	34.1977i	0.422309	−	1.11958i
$934$	6.55831			0.214594
$935$	−1.92542	+	14.4057i	−0.0629678	+	0.471118i
$936$	10.9099	+	9.59577i	0.356602	+	0.313648i
$937$			53.8560i			1.75940i	0.475532	+	0.879699i	$0.342256\pi$
$937$			53.8560i			1.75940i	−0.475532	+	0.879699i	$0.657744\pi$
$938$	−7.02119	+	24.7517i	−0.229250	+	0.808171i
$939$	−0.689312	−	4.19403i	−0.0224948	−	0.136867i
$940$	18.3392	−	7.55406i	0.598158	−	0.246386i
$941$	−18.3793	−	31.8339i	−0.599149	−	1.03776i	−0.992947	−	0.118559i	$-0.962172\pi$
$941$	−18.3793	−	31.8339i	−0.599149	−	1.03776i	0.393798	−	0.919197i	$-0.371161\pi$
$942$	13.7085	+	16.7285i	0.446646	+	0.545045i
$943$	29.3501	+	16.9453i	0.955769	+	0.551814i
$944$	−1.83114			−0.0595984
$945$	−25.3189	+	17.4342i	−0.823625	+	0.567135i
$946$	0.0119028			0.000386994
$947$	−15.7682	−	9.10379i	−0.512398	−	0.295833i	0.221421	−	0.975178i	$-0.428931\pi$
$947$	−15.7682	−	9.10379i	−0.512398	−	0.295833i	−0.733819	+	0.679345i	$0.762264\pi$
$948$	24.3494	+	29.7137i	0.790831	+	0.965057i
$949$	−2.62975	−	4.55486i	−0.0853652	−	0.147857i
$950$	8.69617	+	8.76493i	0.282141	+	0.284372i
$951$	−3.89161	−	23.6780i	−0.126194	−	0.767811i
$952$	−22.4870	−	23.1536i	−0.728807	−	0.750412i
$953$		−	7.13363i		−	0.231081i	−0.993303	−	0.115540i	$-0.963140\pi$
$953$		−	7.13363i		−	0.231081i	0.993303	−	0.115540i	$-0.0368600\pi$
$954$	6.96705	−	2.35373i	0.225567	−	0.0762048i
$955$	48.2611	+	6.45040i	1.56169	+	0.208730i
$956$	−28.4323			−0.919565
$957$	5.14802	−	13.6479i	0.166412	−	0.441175i
$958$	−10.8414	−	6.25928i	−0.350270	−	0.202228i
$959$	−25.6400	−	7.27317i	−0.827958	−	0.234863i
$960$	−3.63428	+	6.75542i	−0.117296	+	0.218030i
$961$	8.83518	−	15.3030i	0.285006	−	0.493644i
$962$	−10.5925	−	6.11557i	−0.341515	−	0.197174i
$963$	−8.38586	−	24.8222i	−0.270231	−	0.799885i
$964$	2.48209	+	4.29911i	0.0799429	+	0.138465i
$965$	15.4251	+	11.8844i	0.496552	+	0.382574i
$966$	−2.28339	+	20.0306i	−0.0734670	+	0.644475i
$967$	11.3726	+	6.56600i	0.365720	+	0.211148i	0.671587	−	0.740926i	$-0.265613\pi$
$967$	11.3726	+	6.56600i	0.365720	+	0.211148i	−0.305867	+	0.952074i	$0.598946\pi$
$968$		−	23.1602i		−	0.744396i
$969$	22.1410	−	18.1438i	0.711271	−	0.582862i
$970$	−4.36386	−	10.5942i	−0.140115	−	0.340160i
$971$	5.38612	+	9.32903i	0.172849	+	0.299383i	0.939415	−	0.342783i	$-0.111369\pi$
$971$	5.38612	+	9.32903i	0.172849	+	0.299383i	−0.766566	+	0.642166i	$0.778036\pi$
$972$	15.7844	−	16.7308i	0.506286	−	0.536641i
$973$	32.3831	+	33.3431i	1.03815	+	1.06893i
$974$	−3.33470	−	5.77588i	−0.106851	−	0.185071i
$975$	−13.4999	−	9.76953i	−0.432344	−	0.312875i
$976$	0.234632	+	0.406394i	0.00751039	+	0.0130084i
$977$	−13.6934	+	7.90591i	−0.438092	+	0.252933i	−0.702788	−	0.711399i	$-0.748062\pi$
$977$	−13.6934	+	7.90591i	−0.438092	+	0.252933i	0.264696	+	0.964332i	$0.414728\pi$
$978$	−16.2834	−	19.8708i	−0.520686	−	0.635397i
$979$	9.77644	+	16.9333i	0.312456	+	0.541190i
$980$	−21.6030	+	8.16896i	−0.690083	+	0.260948i
$981$	−26.9645	−	23.7165i	−0.860910	−	0.757210i
$982$	−4.55696	+	2.63096i	−0.145418	+	0.0839574i
$983$		−	41.6510i		−	1.32846i	−0.747528	−	0.664231i	$-0.768759\pi$
$983$		−	41.6510i		−	1.32846i	0.747528	−	0.664231i	$-0.231241\pi$
$984$	3.94437	+	23.9990i	0.125742	+	0.765060i
$985$	50.5625	−	20.8271i	1.61106	−	0.663608i
$986$	11.0213	−	19.0895i	0.350991	−	0.607934i
$987$	27.3703	+	3.12008i	0.871206	+	0.0993131i
$988$	−8.38437	+	4.84072i	−0.266742	+	0.154004i
$989$	0.0372273	+	0.0644796i	0.00118376	+	0.00205033i
$990$	6.16183	+	2.11519i	0.195836	+	0.0672251i
$991$	19.5283	−	33.8239i	0.620335	−	1.07445i	−0.369088	−	0.929395i	$-0.620330\pi$
$991$	19.5283	−	33.8239i	0.620335	−	1.07445i	0.989423	−	0.145058i	$-0.0463369\pi$
$992$	18.5001	+	10.6810i	0.587378	+	0.339123i
$993$	17.6420	−	2.89956i	0.559852	−	0.0920147i
$994$	−9.67002	+	9.39161i	−0.306715	+	0.297884i
$995$	−9.41810	−	1.25879i	−0.298574	−	0.0399063i
$996$	4.77581	+	29.0578i	0.151327	+	0.920731i
$997$			4.68826i			0.148479i	0.997240	+	0.0742393i	$0.0236529\pi$
$997$			4.68826i			0.148479i	−0.997240	+	0.0742393i	$0.976347\pi$
$998$	2.40526	+	1.38868i	0.0761373	+	0.0439579i
$999$	−24.1685	+	38.6781i	−0.764658	+	1.22372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.17	yes	84
3.2	odd	2		945.2.bo.b.739.26		84
5.4	even	2	inner	315.2.bo.b.4.26	yes	84
7.2	even	3		315.2.r.b.184.26	yes	84
9.2	odd	6		945.2.r.b.424.17		84
9.7	even	3		315.2.r.b.214.26	yes	84
15.14	odd	2		945.2.bo.b.739.17		84
21.2	odd	6		945.2.r.b.604.17		84
35.9	even	6		315.2.r.b.184.17	✓	84
45.29	odd	6		945.2.r.b.424.26		84
45.34	even	6		315.2.r.b.214.17	yes	84
63.2	odd	6		945.2.bo.b.289.17		84
63.16	even	3	inner	315.2.bo.b.79.26	yes	84
105.44	odd	6		945.2.r.b.604.26		84
315.79	even	6	inner	315.2.bo.b.79.17	yes	84
315.254	odd	6		945.2.bo.b.289.26		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.17	✓	84	35.9	even	6
315.2.r.b.184.26	yes	84	7.2	even	3
315.2.r.b.214.17	yes	84	45.34	even	6
315.2.r.b.214.26	yes	84	9.7	even	3
315.2.bo.b.4.17	yes	84	1.1	even	1	trivial
315.2.bo.b.4.26	yes	84	5.4	even	2	inner
315.2.bo.b.79.17	yes	84	315.79	even	6	inner
315.2.bo.b.79.26	yes	84	63.16	even	3	inner
945.2.r.b.424.17		84	9.2	odd	6
945.2.r.b.424.26		84	45.29	odd	6
945.2.r.b.604.17		84	21.2	odd	6
945.2.r.b.604.26		84	105.44	odd	6
945.2.bo.b.289.17		84	63.2	odd	6
945.2.bo.b.289.26		84	315.254	odd	6
945.2.bo.b.739.17		84	15.14	odd	2
945.2.bo.b.739.26		84	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.627169 - 0.362096i) q^{2} +(-1.09783 - 1.33969i) q^{3} +(-0.737773 - 1.27786i) q^{4} +(0.851637 + 2.06754i) q^{5} +(0.203428 + 1.23773i) q^{6} +(-0.722021 + 2.54533i) q^{7} +2.51696i q^{8} +(-0.589540 + 2.94150i) q^{9} +O(q^{10})\)	\(q+(-0.627169 - 0.362096i) q^{2} +(-1.09783 - 1.33969i) q^{3} +(-0.737773 - 1.27786i) q^{4} +(0.851637 + 2.06754i) q^{5} +(0.203428 + 1.23773i) q^{6} +(-0.722021 + 2.54533i) q^{7} +2.51696i q^{8} +(-0.589540 + 2.94150i) q^{9} +(0.214528 - 1.60507i) q^{10} +1.34103 q^{11} +(-0.901987 + 2.39126i) q^{12} +(-1.66641 - 0.962102i) q^{13} +(1.37448 - 1.33491i) q^{14} +(1.83491 - 3.41073i) q^{15} +(-0.564163 + 0.977159i) q^{16} +(4.19747 + 2.42341i) q^{17} +(1.43485 - 1.63135i) q^{18} +(1.70493 + 2.95302i) q^{19} +(2.01371 - 2.61365i) q^{20} +(4.20260 - 1.82705i) q^{21} +(-0.841053 - 0.485582i) q^{22} -6.07484i q^{23} +(3.37195 - 2.76320i) q^{24} +(-3.54943 + 3.52158i) q^{25} +(0.696747 + 1.20680i) q^{26} +(4.58792 - 2.43947i) q^{27} +(3.78526 - 0.955231i) q^{28} +(3.13996 + 5.43857i) q^{29} +(-2.38581 + 1.47469i) q^{30} +(1.82549 + 3.16184i) q^{31} +(5.06716 - 2.92553i) q^{32} +(-1.47222 - 1.79657i) q^{33} +(-1.75501 - 3.03977i) q^{34} +(-5.87746 + 0.674888i) q^{35} +(4.19378 - 1.41681i) q^{36} +(-7.60138 + 4.38866i) q^{37} -2.46939i q^{38} +(0.540515 + 3.28870i) q^{39} +(-5.20392 + 2.14354i) q^{40} +(-2.78942 + 4.83141i) q^{41} +(-3.29731 - 0.375877i) q^{42} +(-0.0106142 + 0.00612811i) q^{43} +(-0.989376 - 1.71365i) q^{44} +(-6.58375 + 1.28620i) q^{45} +(-2.19968 + 3.80995i) q^{46} +(5.20600 + 3.00568i) q^{47} +(1.92844 - 0.316951i) q^{48} +(-5.95737 - 3.67556i) q^{49} +(3.50124 - 0.923392i) q^{50} +(-1.36149 - 8.28379i) q^{51} +2.83925i q^{52} +(2.93139 + 1.69244i) q^{53} +(-3.76072 - 0.131308i) q^{54} +(1.14207 + 2.77263i) q^{55} +(-6.40649 - 1.81730i) q^{56} +(2.08441 - 5.52599i) q^{57} -4.54787i q^{58} +(0.811439 + 1.40545i) q^{59} +(-5.71219 + 0.171590i) q^{60} +(0.207947 - 0.360175i) q^{61} -2.64401i q^{62} +(-7.06143 - 3.62440i) q^{63} -1.98063 q^{64} +(0.570008 - 4.26473i) q^{65} +(0.272803 + 1.65984i) q^{66} +(-11.6289 + 6.71394i) q^{67} -7.15170i q^{68} +(-8.13840 + 6.66914i) q^{69} +(3.93053 + 1.70494i) q^{70} -7.03540 q^{71} +(-7.40366 - 1.48385i) q^{72} +(2.36714 + 1.36667i) q^{73} +6.35647 q^{74} +(8.61450 + 0.889039i) q^{75} +(2.51570 - 4.35732i) q^{76} +(-0.968251 + 3.41336i) q^{77} +(0.851830 - 2.25829i) q^{78} +(7.51571 - 13.0176i) q^{79} +(-2.50078 - 0.334244i) q^{80} +(-8.30489 - 3.46827i) q^{81} +(3.49887 - 2.02007i) q^{82} +(9.97856 - 5.76113i) q^{83} +(-5.43528 - 4.02239i) q^{84} +(-1.43577 + 10.7423i) q^{85} +0.00887586 q^{86} +(3.83886 - 10.1772i) q^{87} +3.37532i q^{88} +(7.29024 + 12.6271i) q^{89} +(4.59485 + 1.57729i) q^{90} +(3.65205 - 3.54690i) q^{91} +(-7.76280 + 4.48185i) q^{92} +(2.23181 - 5.91675i) q^{93} +(-2.17669 - 3.77014i) q^{94} +(-4.65351 + 6.03991i) q^{95} +(-9.48218 - 3.57669i) q^{96} +(6.12763 - 3.53779i) q^{97} +(2.40537 + 4.46234i) q^{98} +(-0.790590 + 3.94465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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