LMFDB - Embedded newform 315.2.be.b.236.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.13
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87276 - 1.08124i) q^{2} +(0.865496 - 1.50031i) q^{3} +(1.33817 - 2.31777i) q^{4} +1.00000 q^{5} +(-0.00132154 - 3.74553i) q^{6} +(-1.75124 + 1.98322i) q^{7} -1.46255i q^{8} +(-1.50183 - 2.59702i) q^{9} +O(q^{10})$	\(q+(1.87276 - 1.08124i) q^{2} +(0.865496 - 1.50031i) q^{3} +(1.33817 - 2.31777i) q^{4} +1.00000 q^{5} +(-0.00132154 - 3.74553i) q^{6} +(-1.75124 + 1.98322i) q^{7} -1.46255i q^{8} +(-1.50183 - 2.59702i) q^{9} +(1.87276 - 1.08124i) q^{10} -1.72665i q^{11} +(-2.31919 - 4.01368i) q^{12} +(-2.89037 + 1.66875i) q^{13} +(-1.13533 + 5.60762i) q^{14} +(0.865496 - 1.50031i) q^{15} +(1.09496 + 1.89652i) q^{16} +(2.47597 + 4.28850i) q^{17} +(-5.62058 - 3.23976i) q^{18} +(2.88684 + 1.66672i) q^{19} +(1.33817 - 2.31777i) q^{20} +(1.45974 + 4.34387i) q^{21} +(-1.86692 - 3.23361i) q^{22} -2.67531i q^{23} +(-2.19428 - 1.26584i) q^{24} +1.00000 q^{25} +(-3.60865 + 6.25037i) q^{26} +(-5.19615 + 0.00550010i) q^{27} +(2.25319 + 6.71285i) q^{28} +(-4.72502 - 2.72799i) q^{29} +(-0.00132154 - 3.74553i) q^{30} +(-6.73911 - 3.89083i) q^{31} +(6.63441 + 3.83038i) q^{32} +(-2.59050 - 1.49441i) q^{33} +(9.27381 + 5.35423i) q^{34} +(-1.75124 + 1.98322i) q^{35} +(-8.02899 + 0.00566577i) q^{36} +(-1.70041 + 2.94520i) q^{37} +7.20850 q^{38} +(0.00203963 + 5.78073i) q^{39} -1.46255i q^{40} +(-0.394491 - 0.683278i) q^{41} +(7.43051 + 6.55671i) q^{42} +(5.82305 - 10.0858i) q^{43} +(-4.00198 - 2.31054i) q^{44} +(-1.50183 - 2.59702i) q^{45} +(-2.89265 - 5.01022i) q^{46} +(5.76865 + 9.99159i) q^{47} +(3.79304 - 0.00133830i) q^{48} +(-0.866300 - 6.94619i) q^{49} +(1.87276 - 1.08124i) q^{50} +(8.57700 - 0.00302624i) q^{51} +8.93228i q^{52} +(5.69516 - 3.28810i) q^{53} +(-9.72522 + 5.62859i) q^{54} -1.72665i q^{55} +(2.90056 + 2.56129i) q^{56} +(4.99914 - 2.88861i) q^{57} -11.7985 q^{58} +(-5.45596 + 9.45000i) q^{59} +(-2.31919 - 4.01368i) q^{60} +(-5.58942 + 3.22705i) q^{61} -16.8277 q^{62} +(7.78052 + 1.56955i) q^{63} +12.1864 q^{64} +(-2.89037 + 1.66875i) q^{65} +(-6.46722 + 0.00228184i) q^{66} +(1.06208 - 1.83958i) q^{67} +13.2530 q^{68} +(-4.01378 - 2.31547i) q^{69} +(-1.13533 + 5.60762i) q^{70} +1.34885i q^{71} +(-3.79828 + 2.19651i) q^{72} +(2.68498 - 1.55018i) q^{73} +7.35423i q^{74} +(0.865496 - 1.50031i) q^{75} +(7.72615 - 4.46069i) q^{76} +(3.42432 + 3.02378i) q^{77} +(6.25419 + 10.8237i) q^{78} +(-6.80923 - 11.7939i) q^{79} +(1.09496 + 1.89652i) q^{80} +(-4.48900 + 7.80057i) q^{81} +(-1.47758 - 0.853079i) q^{82} +(4.95763 - 8.58686i) q^{83} +(12.0215 + 2.42947i) q^{84} +(2.47597 + 4.28850i) q^{85} -25.1845i q^{86} +(-8.18230 + 4.72790i) q^{87} -2.52532 q^{88} +(-5.36098 + 9.28549i) q^{89} +(-5.62058 - 3.23976i) q^{90} +(1.75223 - 8.65462i) q^{91} +(-6.20075 - 3.58001i) q^{92} +(-11.6701 + 6.74323i) q^{93} +(21.6066 + 12.4746i) q^{94} +(2.88684 + 1.66672i) q^{95} +(11.4888 - 6.63847i) q^{96} +(2.88709 + 1.66686i) q^{97} +(-9.13288 - 12.0719i) q^{98} +(-4.48414 + 2.59314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.87276	−	1.08124i	1.32424	−	0.764553i	0.339842	−	0.940483i	$-0.389626\pi$
$2$	1.87276	−	1.08124i	1.32424	−	0.764553i	0.984403	+	0.175929i	$0.0562931\pi$
$3$	0.865496	−	1.50031i	0.499694	−	0.866202i
$3$	0.865496	−	1.50031i	0.499694	−	0.866202i
$4$	1.33817	−	2.31777i	0.669083	−	1.15889i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.00132154	−	3.74553i	−0.000539517	−	1.52911i
$7$	−1.75124	+	1.98322i	−0.661907	+	0.749586i
$7$	−1.75124	+	1.98322i	−0.661907	+	0.749586i
$8$		−	1.46255i		−	0.517091i
$9$	−1.50183	−	2.59702i	−0.500611	−	0.865672i
$10$	1.87276	−	1.08124i	0.592220	−	0.341919i
$11$		−	1.72665i		−	0.520604i	−0.965527	−	0.260302i	$-0.916178\pi$
$11$		−	1.72665i		−	0.520604i	0.965527	−	0.260302i	$-0.0838222\pi$
$12$	−2.31919	−	4.01368i	−0.669492	−	1.15865i
$13$	−2.89037	+	1.66875i	−0.801643	+	0.462829i	−0.844045	−	0.536272i	$-0.819832\pi$
$13$	−2.89037	+	1.66875i	−0.801643	+	0.462829i	0.0424021	+	0.999101i	$0.486499\pi$
$14$	−1.13533	+	5.60762i	−0.303429	+	1.49870i
$15$	0.865496	−	1.50031i	0.223470	−	0.387377i
$16$	1.09496	+	1.89652i	0.273739	+	0.474130i
$17$	2.47597	+	4.28850i	0.600510	+	1.04011i	0.992744	+	0.120248i	$0.0383691\pi$
$17$	2.47597	+	4.28850i	0.600510	+	1.04011i	−0.392234	+	0.919866i	$0.628298\pi$
$18$	−5.62058	−	3.23976i	−1.32478	−	0.763618i
$19$	2.88684	+	1.66672i	0.662287	+	0.382372i	0.793148	−	0.609029i	$-0.208441\pi$
$19$	2.88684	+	1.66672i	0.662287	+	0.382372i	−0.130861	+	0.991401i	$0.541774\pi$
$20$	1.33817	−	2.31777i	0.299223	−	0.518269i
$21$	1.45974	+	4.34387i	0.318541	+	0.947909i
$22$	−1.86692	−	3.23361i	−0.398030	−	0.689408i
$23$		−	2.67531i		−	0.557840i	−0.960314	−	0.278920i	$-0.910024\pi$
$23$		−	2.67531i		−	0.557840i	0.960314	−	0.278920i	$-0.0899765\pi$
$24$	−2.19428	−	1.26584i	−0.447905	−	0.258388i
$25$	1.00000			0.200000
$26$	−3.60865	+	6.25037i	−0.707715	+	1.22580i
$27$	−5.19615	+	0.00550010i	−0.999999	+	0.00105849i
$28$	2.25319	+	6.71285i	0.425813	+	1.26861i
$29$	−4.72502	−	2.72799i	−0.877414	−	0.506575i	−0.00760893	−	0.999971i	$-0.502422\pi$
$29$	−4.72502	−	2.72799i	−0.877414	−	0.506575i	−0.869805	+	0.493396i	$0.835755\pi$
$30$	−0.00132154	−	3.74553i	−0.000241279	−	0.683837i
$31$	−6.73911	−	3.89083i	−1.21038	−	0.698813i	−0.247538	−	0.968878i	$-0.579622\pi$
$31$	−6.73911	−	3.89083i	−1.21038	−	0.698813i	−0.962842	+	0.270065i	$0.912955\pi$
$32$	6.63441	+	3.83038i	1.17281	+	0.677122i
$33$	−2.59050	−	1.49441i	−0.450948	−	0.260143i
$34$	9.27381	+	5.35423i	1.59044	+	0.918244i
$35$	−1.75124	+	1.98322i	−0.296014	+	0.335225i
$36$	−8.02899	+	0.00566577i	−1.33817	+	0.000944294i
$37$	−1.70041	+	2.94520i	−0.279546	+	0.484189i	−0.971272	−	0.237972i	$-0.923517\pi$
$37$	−1.70041	+	2.94520i	−0.279546	+	0.484189i	0.691726	+	0.722160i	$0.256851\pi$
$38$	7.20850			1.16937
$39$	0.00203963	+	5.78073i	0.000326601	+	0.925658i
$40$		−	1.46255i		−	0.231250i
$41$	−0.394491	−	0.683278i	−0.0616091	−	0.106710i	0.833576	−	0.552405i	$-0.186290\pi$
$41$	−0.394491	−	0.683278i	−0.0616091	−	0.106710i	−0.895185	+	0.445695i	$0.852957\pi$
$42$	7.43051	+	6.55671i	1.14655	+	1.01172i
$43$	5.82305	−	10.0858i	0.888006	−	1.53807i	0.0457776	−	0.998952i	$-0.485423\pi$
$43$	5.82305	−	10.0858i	0.888006	−	1.53807i	0.842229	−	0.539120i	$-0.181243\pi$
$44$	−4.00198	−	2.31054i	−0.603321	−	0.348327i
$45$	−1.50183	−	2.59702i	−0.223880	−	0.387140i
$46$	−2.89265	−	5.01022i	−0.426498	−	0.738717i
$47$	5.76865	+	9.99159i	0.841444	+	1.45742i	0.888674	+	0.458539i	$0.151627\pi$
$47$	5.76865	+	9.99159i	0.841444	+	1.45742i	−0.0472307	+	0.998884i	$0.515040\pi$
$48$	3.79304	−	0.00133830i	0.547478	−	0.000193168i
$49$	−0.866300	−	6.94619i	−0.123757	−	0.992313i
$50$	1.87276	−	1.08124i	0.264849	−	0.152911i
$51$	8.57700	−	0.00302624i	1.20102	−	0.000423758i
$52$			8.93228i			1.23868i
$53$	5.69516	−	3.28810i	0.782290	−	0.451656i	−0.0549510	−	0.998489i	$-0.517500\pi$
$53$	5.69516	−	3.28810i	0.782290	−	0.451656i	0.837241	+	0.546833i	$0.184167\pi$
$54$	−9.72522	+	5.62859i	−1.32343	+	0.765954i
$55$		−	1.72665i		−	0.232821i
$56$	2.90056	+	2.56129i	0.387604	+	0.342267i
$57$	4.99914	−	2.88861i	0.662152	−	0.382605i
$58$	−11.7985			−1.54921
$59$	−5.45596	+	9.45000i	−0.710306	+	1.23029i	0.254437	+	0.967089i	$0.418110\pi$
$59$	−5.45596	+	9.45000i	−0.710306	+	1.23029i	−0.964742	+	0.263196i	$0.915223\pi$
$60$	−2.31919	−	4.01368i	−0.299406	−	0.518164i
$61$	−5.58942	+	3.22705i	−0.715651	+	0.413182i	−0.813150	−	0.582054i	$-0.802249\pi$
$61$	−5.58942	+	3.22705i	−0.715651	+	0.413182i	0.0974987	+	0.995236i	$0.468916\pi$
$62$	−16.8277			−2.13712
$63$	7.78052	+	1.56955i	0.980254	+	0.197744i
$64$	12.1864			1.52330
$65$	−2.89037	+	1.66875i	−0.358506	+	0.206983i
$66$	−6.46722	+	0.00228184i	−0.796059	+	0.000280875i
$67$	1.06208	−	1.83958i	0.129754	−	0.224741i	−0.793827	−	0.608143i	$-0.791915\pi$
$67$	1.06208	−	1.83958i	0.129754	−	0.224741i	0.923581	+	0.383403i	$0.125248\pi$
$68$	13.2530			1.60716
$69$	−4.01378	−	2.31547i	−0.483202	−	0.278750i
$70$	−1.13533	+	5.60762i	−0.135698	+	0.670238i
$71$			1.34885i			0.160079i	0.996792	+	0.0800395i	$0.0255047\pi$
$71$			1.34885i			0.160079i	−0.996792	+	0.0800395i	$0.974495\pi$
$72$	−3.79828	+	2.19651i	−0.447632	+	0.258862i
$73$	2.68498	−	1.55018i	0.314254	−	0.181434i	−0.334575	−	0.942369i	$-0.608593\pi$
$73$	2.68498	−	1.55018i	0.314254	−	0.181434i	0.648828	+	0.760935i	$0.275259\pi$
$74$			7.35423i			0.854912i
$75$	0.865496	−	1.50031i	0.0999389	−	0.173240i
$76$	7.72615	−	4.46069i	0.886250	−	0.511677i
$77$	3.42432	+	3.02378i	0.390238	+	0.344592i
$78$	6.25419	+	10.8237i	0.708147	+	1.22555i
$79$	−6.80923	−	11.7939i	−0.766098	−	1.32692i	−0.939664	−	0.342098i	$-0.888862\pi$
$79$	−6.80923	−	11.7939i	−0.766098	−	1.32692i	0.173566	−	0.984822i	$-0.444471\pi$
$80$	1.09496	+	1.89652i	0.122420	+	0.212037i
$81$	−4.48900	+	7.80057i	−0.498777	+	0.866730i
$82$	−1.47758	−	0.853079i	−0.163171	−	0.0942069i
$83$	4.95763	−	8.58686i	0.544170	−	0.942531i	−0.454488	−	0.890753i	$-0.650178\pi$
$83$	4.95763	−	8.58686i	0.544170	−	0.942531i	0.998659	−	0.0517780i	$-0.0164888\pi$
$84$	12.0215	+	2.42947i	1.31165	+	0.265077i
$85$	2.47597	+	4.28850i	0.268556	+	0.465153i
$86$		−	25.1845i		−	2.71571i
$87$	−8.18230	+	4.72790i	−0.877235	+	0.506885i
$88$	−2.52532			−0.269200
$89$	−5.36098	+	9.28549i	−0.568263	+	0.984260i	0.428475	+	0.903554i	$0.359051\pi$
$89$	−5.36098	+	9.28549i	−0.568263	+	0.984260i	−0.996738	+	0.0807066i	$0.974282\pi$
$90$	−5.62058	−	3.23976i	−0.592461	−	0.341501i
$91$	1.75223	−	8.65462i	0.183684	−	0.907250i
$92$	−6.20075	−	3.58001i	−0.646473	−	0.373241i
$93$	−11.6701	+	6.74323i	−1.21013	+	0.699240i
$94$	21.6066	+	12.4746i	2.22855	+	1.28666i
$95$	2.88684	+	1.66672i	0.296184	+	0.171002i
$96$	11.4888	−	6.63847i	1.17257	−	0.677536i
$97$	2.88709	+	1.66686i	0.293139	+	0.169244i	0.639357	−	0.768910i	$-0.279201\pi$
$97$	2.88709	+	1.66686i	0.293139	+	0.169244i	−0.346217	+	0.938154i	$0.612534\pi$
$98$	−9.13288	−	12.0719i	−0.922560	−	1.21945i
$99$	−4.48414	+	2.59314i	−0.450673	+	0.260620i
$100$	1.33817	−	2.31777i	0.133817	−	0.231777i
$101$	−10.8489			−1.07950			−0.539751	−	0.841825i	$-0.681481\pi$
$101$	−10.8489			−1.07950			−0.539751	+	0.841825i	$0.681481\pi$
$102$	16.0594	−	9.27947i	1.59012	−	0.918805i
$103$		−	11.6206i		−	1.14501i	−0.819901	−	0.572505i	$-0.805972\pi$
$103$		−	11.6206i		−	1.14501i	0.819901	−	0.572505i	$-0.194028\pi$
$104$	2.44064	+	4.22732i	0.239325	+	0.414523i
$105$	1.45974	+	4.34387i	0.142456	+	0.423918i
$106$	7.11046	−	12.3157i	0.690629	−	1.19621i
$107$	−3.90865	−	2.25666i	−0.377863	−	0.218159i	0.299025	−	0.954245i	$-0.403339\pi$
$107$	−3.90865	−	2.25666i	−0.377863	−	0.218159i	−0.676888	+	0.736086i	$0.736672\pi$
$108$	−6.94056	+	12.0508i	−0.667856	+	1.15959i
$109$	−3.20833	−	5.55699i	−0.307302	−	0.532263i	0.670469	−	0.741938i	$-0.266093\pi$
$109$	−3.20833	−	5.55699i	−0.307302	−	0.532263i	−0.977771	+	0.209674i	$0.932760\pi$
$110$	−1.86692	−	3.23361i	−0.178004	−	0.308312i
$111$	2.94700	+	5.10020i	0.279717	+	0.484090i
$112$	−5.67875	−	1.14973i	−0.536591	−	0.108639i
$113$	−9.22896	+	5.32834i	−0.868188	+	0.501248i	−0.866746	−	0.498751i	$-0.833792\pi$
$113$	−9.22896	+	5.32834i	−0.868188	+	0.501248i	−0.00144211	+	0.999999i	$0.500459\pi$
$114$	6.23893	−	10.8150i	0.584330	−	1.01291i
$115$		−	2.67531i		−	0.249474i
$116$	−12.6457	+	7.30101i	−1.17412	+	0.677881i
$117$	8.67463	+	5.00014i	0.801970	+	0.462263i
$118$			23.5968i			2.17227i
$119$	−12.8410	−	2.59982i	−1.17714	−	0.238325i
$120$	−2.19428	−	1.26584i	−0.200309	−	0.115554i
$121$	8.01868			0.728971
$122$	−6.97844	+	12.0870i	−0.631798	+	1.09431i
$123$	−1.36656		0.000482164i	−0.123218		4.34753e-5i
$124$	−18.0361	+	10.4131i	−1.61969	+	0.935128i
$125$	1.00000			0.0894427
$126$	16.2681	−	5.47323i	1.44928	−	0.487594i
$127$	9.18737			0.815247			0.407623	−	0.913150i	$-0.366358\pi$
$127$	9.18737			0.815247			0.407623	+	0.913150i	$0.366358\pi$
$128$	9.55350	−	5.51572i	0.844418	−	0.487525i
$129$	−10.0920	−	17.4656i	−0.888549	−	1.53776i
$130$	−3.60865	+	6.25037i	−0.316500	+	0.548193i
$131$	8.96780			0.783521			0.391760	−	0.920067i	$-0.371866\pi$
$131$	8.96780			0.783521			0.391760	+	0.920067i	$0.371866\pi$
$132$	−6.93022	+	4.00442i	−0.603198	+	0.348540i
$133$	−8.36103	+	2.80641i	−0.724993	+	0.243346i
$134$		−	4.59347i		−	0.396816i
$135$	−5.19615	+	0.00550010i	−0.447213	+	0.000473373i
$136$	6.27217	−	3.62124i	0.537834	−	0.310518i
$137$			4.53858i			0.387757i	0.981026	+	0.193878i	$0.0621067\pi$
$137$			4.53858i			0.387757i	−0.981026	+	0.193878i	$0.937893\pi$
$138$	−10.0204	+	0.00353553i	−0.852997	+	0.000300964i
$139$	17.8922	−	10.3300i	1.51759	−	0.876182i	0.517806	−	0.855498i	$-0.326749\pi$
$139$	17.8922	−	10.3300i	1.51759	−	0.876182i	0.999786	−	0.0206846i	$-0.00658457\pi$
$140$	2.25319	+	6.71285i	0.190429	+	0.567340i
$141$	19.9832	−	0.00705070i	1.68289	−	0.000593776i
$142$	1.45843	+	2.52608i	0.122389	+	0.211984i
$143$	2.88135	+	4.99065i	0.240951	+	0.417339i
$144$	3.28085	−	5.69188i	0.273404	−	0.474323i
$145$	−4.72502	−	2.72799i	−0.392391	−	0.226547i
$146$	3.35223	−	5.80623i	0.277432	−	0.480527i
$147$	−11.1712	−	4.71218i	−0.921384	−	0.388654i
$148$	4.55087	+	7.88234i	0.374079	+	0.647925i
$149$			13.5187i			1.10749i	0.832685	+	0.553747i	$0.186802\pi$
$149$			13.5187i			1.10749i	−0.832685	+	0.553747i	$0.813198\pi$
$150$	−0.00132154	−	3.74553i	−0.000107903	−	0.305821i
$151$	−19.7465			−1.60695			−0.803475	−	0.595339i	$-0.797018\pi$
$151$	−19.7465			−1.60695			−0.803475	+	0.595339i	$0.797018\pi$
$152$	2.43767	−	4.22217i	0.197721	−	0.342463i
$153$	7.41882	−	12.8707i	0.599776	−	1.04054i
$154$	9.68238	+	1.96032i	0.780229	+	0.157967i
$155$	−6.73911	−	3.89083i	−0.541299	−	0.312519i
$156$	13.4011	+	7.73085i	1.07295	+	0.618963i
$157$	−4.92641	−	2.84427i	−0.393171	−	0.226997i	0.290362	−	0.956917i	$-0.406224\pi$
$157$	−4.92641	−	2.84427i	−0.393171	−	0.226997i	−0.683533	+	0.729920i	$0.739557\pi$
$158$	−25.5042	−	14.7248i	−2.02900	−	1.17145i
$159$	−0.00401887	−	11.3903i	−0.000318717	−	0.903311i
$160$	6.63441	+	3.83038i	0.524496	+	0.302818i
$161$	5.30572	+	4.68511i	0.418149	+	0.369239i
$162$	0.0274677	+	19.4623i	0.00215807	+	1.52910i
$163$	−7.27331	+	12.5977i	−0.569689	+	0.986731i	0.426907	+	0.904296i	$0.359603\pi$
$163$	−7.27331	+	12.5977i	−0.569689	+	0.986731i	−0.996596	+	0.0824356i	$0.973730\pi$
$164$	−2.11158			−0.164886
$165$	−2.59050	−	1.49441i	−0.201670	−	0.116340i
$166$		−	21.4416i		−	1.66419i
$167$	−7.00178	−	12.1274i	−0.541814	−	0.938450i	−0.998800	−	0.0489756i	$-0.984404\pi$
$167$	−7.00178	−	12.1274i	−0.541814	−	0.938450i	0.456986	−	0.889474i	$-0.348929\pi$
$168$	6.35314	−	2.13495i	0.490155	−	0.164715i
$169$	−0.930521	+	1.61171i	−0.0715785	+	0.123978i
$170$	9.27381	+	5.35423i	0.711268	+	0.410651i
$171$	−0.00705686	−	10.0003i	−0.000539651	−	0.764743i
$172$	−15.5844	−	26.9930i	−1.18830	−	2.05820i
$173$	−0.208244	−	0.360690i	−0.0158325	−	0.0274227i	0.858001	−	0.513649i	$-0.171707\pi$
$173$	−0.208244	−	0.360690i	−0.0158325	−	0.0274227i	−0.873833	+	0.486226i	$0.838373\pi$
$174$	−10.2115	+	17.7013i	−0.774134	+	1.34193i
$175$	−1.75124	+	1.98322i	−0.132381	+	0.149917i
$176$	3.27463	−	1.89061i	0.246834	−	0.142510i
$177$	9.45578	+	16.3646i	0.710740	+	1.23003i
$178$			23.1861i			1.73787i
$179$	18.9614	−	10.9474i	1.41724	−	0.818246i	0.421188	−	0.906973i	$-0.361613\pi$
$179$	18.9614	−	10.9474i	1.41724	−	0.818246i	0.996056	+	0.0887272i	$0.0282799\pi$
$180$	−8.02899	+	0.00566577i	−0.598446	+	0.000422301i
$181$		−	4.86189i		−	0.361382i	−0.983540	−	0.180691i	$-0.942167\pi$
$181$		−	4.86189i		−	0.361382i	0.983540	−	0.180691i	$-0.0578333\pi$
$182$	−6.07621	−	18.1026i	−0.450399	−	1.34186i
$183$	0.00394425	+	11.1788i	0.000291567	+	0.826363i
$184$	−3.91278			−0.288454
$185$	−1.70041	+	2.94520i	−0.125017	+	0.216536i
$186$	−14.5643	+	25.2467i	−1.06791	+	1.85118i
$187$	7.40473	−	4.27513i	0.541488	−	0.312628i
$188$	30.8776			2.25198
$189$	9.08881	−	10.3147i	0.661114	−	0.750286i
$190$	7.20850			0.522960
$191$	−0.931482	+	0.537791i	−0.0673997	+	0.0389132i	−0.533321	−	0.845913i	$-0.679056\pi$
$191$	−0.931482	+	0.537791i	−0.0673997	+	0.0389132i	0.465921	+	0.884826i	$0.345723\pi$
$192$	10.5473	−	18.2834i	0.761187	−	1.31949i
$193$	−4.32095	+	7.48411i	−0.311029	+	0.538718i	−0.978585	−	0.205841i	$-0.934007\pi$
$193$	−4.32095	+	7.48411i	−0.311029	+	0.538718i	0.667556	+	0.744559i	$0.267340\pi$
$194$	7.20911			0.517584
$195$	0.00203963	+	5.78073i	0.000146061	+	0.413967i
$196$	−17.2589	−	7.28727i	−1.23278	−	0.520519i
$197$		−	2.66589i		−	0.189937i	−0.995480	−	0.0949685i	$-0.969725\pi$
$197$		−	2.66589i		−	0.189937i	0.995480	−	0.0949685i	$-0.0302750\pi$
$198$	−5.59393	+	9.70477i	−0.397543	+	0.689688i
$199$	−17.1929	+	9.92633i	−1.21877	+	0.703659i	−0.964655	−	0.263515i	$-0.915118\pi$
$199$	−17.1929	+	9.92633i	−1.21877	+	0.703659i	−0.254117	+	0.967173i	$0.581785\pi$
$200$		−	1.46255i		−	0.103418i
$201$	−1.84071	−	3.18560i	−0.129833	−	0.224695i
$202$	−20.3174	+	11.7302i	−1.42952	+	0.825336i
$203$	13.6848	−	4.59336i	0.960488	−	0.322391i
$204$	11.4704	−	19.8836i	0.803091	−	1.39213i
$205$	−0.394491	−	0.683278i	−0.0275524	−	0.0477222i
$206$	−12.5647	−	21.7626i	−0.875421	−	1.51627i
$207$	−6.94782	+	4.01787i	−0.482907	+	0.279261i
$208$	−6.32965	−	3.65443i	−0.438882	−	0.253389i
$209$	2.87784	−	4.98457i	0.199064	−	0.344790i
$210$	7.43051	+	6.55671i	0.512754	+	0.452456i
$211$	−4.78399	−	8.28611i	−0.329343	−	0.570439i	0.653039	−	0.757325i	$-0.273494\pi$
$211$	−4.78399	−	8.28611i	−0.329343	−	0.570439i	−0.982382	+	0.186886i	$0.940161\pi$
$212$		−	17.6001i		−	1.20878i
$213$	2.02369	+	1.16742i	0.138661	+	0.0799906i
$214$	−9.75997			−0.667178
$215$	5.82305	−	10.0858i	0.397129	−	0.687847i
$216$	0.00804420	+	7.59965i	0.000547338	+	0.517091i
$217$	19.5182	−	6.55134i	1.32498	−	0.444734i
$218$	−12.0169	−	6.93796i	−0.813887	−	0.469898i
$219$	−0.00189469	−	5.36997i	−0.000128032	−	0.362869i
$220$	−4.00198	−	2.31054i	−0.269813	−	0.155777i
$221$	−14.3129	−	8.26356i	−0.962790	−	0.555867i
$222$	11.0336	+	6.36506i	0.740527	+	0.427195i
$223$	−11.9147	−	6.87897i	−0.797870	−	0.460650i	0.0448561	−	0.998993i	$-0.485717\pi$
$223$	−11.9147	−	6.87897i	−0.797870	−	0.460650i	−0.842726	+	0.538343i	$0.819050\pi$
$224$	−19.2149	+	6.44956i	−1.28385	+	0.430929i
$225$	−1.50183	−	2.59702i	−0.100122	−	0.173134i
$226$	−11.5225	+	19.9575i	−0.766462	+	1.32755i
$227$	28.8798			1.91682			0.958409	−	0.285397i	$-0.0921255\pi$
$227$	28.8798			1.91682			0.958409	+	0.285397i	$0.0921255\pi$
$228$	−0.00545206	−	15.4523i	−0.000361071	−	1.02335i
$229$		−	6.54173i		−	0.432289i	−0.976361	−	0.216145i	$-0.930652\pi$
$229$		−	6.54173i		−	0.432289i	0.976361	−	0.216145i	$-0.0693483\pi$
$230$	−2.89265	−	5.01022i	−0.190736	−	0.330364i
$231$	7.50033	−	2.52046i	0.493486	−	0.165834i
$232$	−3.98984	+	6.91060i	−0.261946	+	0.453703i
$233$	18.1428	+	10.4747i	1.18857	+	0.686222i	0.957982	−	0.286829i	$-0.0926012\pi$
$233$	18.1428	+	10.4747i	1.18857	+	0.686222i	0.230589	+	0.973051i	$0.425935\pi$
$234$	21.6519	−	0.0152790i	1.41543	−	0.000998817i
$235$	5.76865	+	9.99159i	0.376305	+	0.651779i
$236$	14.6020	+	25.2913i	0.950507	+	1.64633i
$237$	−23.5879	+	0.00832254i	−1.53220	+	0.000540607i
$238$	−26.8593	+	9.01541i	−1.74103	+	0.584382i
$239$	25.6748	−	14.8234i	1.66077	−	0.958844i	0.688417	−	0.725316i	$-0.258306\pi$
$239$	25.6748	−	14.8234i	1.66077	−	0.958844i	0.972350	−	0.233528i	$-0.0750272\pi$
$240$	3.79304	−	0.00133830i	0.244840	−	8.63872e-5i
$241$			4.30710i			0.277445i	0.990331	+	0.138722i	$0.0442996\pi$
$241$			4.30710i			0.277445i	−0.990331	+	0.138722i	$0.955700\pi$
$242$	15.0171	−	8.67013i	0.965336	−	0.557337i
$243$	7.81803	+	13.4862i	0.501527	+	0.865142i
$244$			17.2733i			1.10581i
$245$	−0.866300	−	6.94619i	−0.0553459	−	0.443776i
$246$	−2.55872	+	1.47848i	−0.163138	+	0.0942644i
$247$	−11.1254			−0.707891
$248$	−5.69055	+	9.85632i	−0.361350	+	0.625877i
$249$	−8.59211	−	14.8699i	−0.544503	−	0.942339i
$250$	1.87276	−	1.08124i	0.118444	−	0.0683837i
$251$	13.7433			0.867471			0.433735	−	0.901040i	$-0.357195\pi$
$251$	13.7433			0.867471			0.433735	+	0.901040i	$0.357195\pi$
$252$	14.0495	−	15.9332i	0.885034	−	1.00369i
$253$	−4.61932			−0.290414
$254$	17.2058	−	9.93376i	1.07959	−	0.623300i
$255$	8.57700	−	0.00302624i	0.537112	−	0.000189510i
$256$	−0.258793	+	0.448242i	−0.0161746	+	0.0280152i
$257$	2.82020			0.175919			0.0879597	−	0.996124i	$-0.471965\pi$
$257$	2.82020			0.175919			0.0879597	+	0.996124i	$0.471965\pi$
$258$	−37.7844	−	21.7971i	−2.35235	−	1.35703i
$259$	−2.86314	−	8.53006i	−0.177907	−	0.530032i
$260$			8.93228i			0.553956i
$261$	0.0115503	+	16.3679i	0.000714943	+	1.01315i
$262$	16.7946	−	9.69636i	1.03757	−	0.599043i
$263$			18.4774i			1.13937i	0.821864	+	0.569683i	$0.192934\pi$
$263$			18.4774i			1.13937i	−0.821864	+	0.569683i	$0.807066\pi$
$264$	−2.18565	+	3.78875i	−0.134518	+	0.233181i
$265$	5.69516	−	3.28810i	0.349851	−	0.201987i
$266$	−12.6238	+	14.2960i	−0.774017	+	0.876546i
$267$	9.29117	+	16.0797i	0.568610	+	0.984060i
$268$	−2.84249	−	4.92333i	−0.173633	−	0.300740i
$269$	9.72956	+	16.8521i	0.593222	+	1.02749i	0.993795	+	0.111225i	$0.0354776\pi$
$269$	9.72956	+	16.8521i	0.593222	+	1.02749i	−0.400573	+	0.916265i	$0.631189\pi$
$270$	−9.72522	+	5.62859i	−0.591858	+	0.342545i
$271$	16.5777	+	9.57111i	1.00702	+	0.581404i	0.910318	−	0.413910i	$-0.135837\pi$
$271$	16.5777	+	9.57111i	1.00702	+	0.581404i	0.0967028	+	0.995313i	$0.469170\pi$
$272$	−5.42215	+	9.39144i	−0.328766	+	0.569440i
$273$	−11.4680	−	10.1194i	−0.694076	−	0.612455i
$274$	4.90730	+	8.49969i	0.296461	+	0.513485i
$275$		−	1.72665i		−	0.104121i
$276$	−10.7378	+	6.20454i	−0.646341	+	0.373469i
$277$	26.0217			1.56349			0.781745	−	0.623599i	$-0.214330\pi$
$277$	26.0217			1.56349			0.781745	+	0.623599i	$0.214330\pi$
$278$	22.3385	−	38.6915i	1.33978	−	2.32056i
$279$	0.0164737	+	23.3450i	0.000986254	+	1.39763i
$280$	2.90056	+	2.56129i	0.173342	+	0.153066i
$281$	−19.5500	−	11.2872i	−1.16626	−	0.673338i	−0.213460	−	0.976952i	$-0.568473\pi$
$281$	−19.5500	−	11.2872i	−1.16626	−	0.673338i	−0.952795	+	0.303614i	$0.901807\pi$
$282$	37.4162	−	21.6198i	2.22810	−	1.28744i
$283$	9.24160	+	5.33564i	0.549356	+	0.317171i	0.748862	−	0.662726i	$-0.230600\pi$
$283$	9.24160	+	5.33564i	0.549356	+	0.317171i	−0.199506	+	0.979897i	$0.563934\pi$
$284$	3.12633	+	1.80499i	0.185513	+	0.107106i
$285$	4.99914	−	2.88861i	0.296123	−	0.171106i
$286$	10.7922	+	6.23088i	0.638156	+	0.368439i
$287$	2.04594	+	0.414225i	0.120768	+	0.0244509i
$288$	−0.0162177	−	22.9823i	−0.000955640	−	1.35424i
$289$	−3.76082	+	6.51393i	−0.221225	+	0.383172i
$290$	−11.7985			−0.692830
$291$	4.99956	−	2.88885i	0.293079	−	0.169347i
$292$		−	8.29757i		−	0.485578i
$293$	0.0874653	+	0.151494i	0.00510978	+	0.00885040i	0.868569	−	0.495568i	$-0.165040\pi$
$293$	0.0874653	+	0.151494i	0.00510978	+	0.00885040i	−0.863459	+	0.504419i	$0.831707\pi$
$294$	−26.0160	+	3.25393i	−1.51728	+	0.189773i
$295$	−5.45596	+	9.45000i	−0.317658	+	0.550200i
$296$	4.30752	+	2.48695i	0.250370	+	0.144551i
$297$	0.00949674	+	8.97193i	0.000551057	+	0.520604i
$298$	14.6170	+	25.3173i	0.846737	+	1.46659i
$299$	4.46443	+	7.73262i	0.258185	+	0.447189i
$300$	−2.31919	−	4.01368i	−0.133898	−	0.231730i
$301$	9.80479	+	29.2111i	0.565139	+	1.68370i
$302$	−36.9806	+	21.3508i	−2.12799	+	1.22860i
$303$	−9.38964	+	16.2766i	−0.539421	+	0.935066i
$304$			7.29994i			0.418680i
$305$	−5.58942	+	3.22705i	−0.320049	+	0.184780i
$306$	−0.0226697	−	32.1254i	−0.00129594	−	1.83649i
$307$		−	29.6519i		−	1.69232i	−0.532928	−	0.846161i	$-0.678908\pi$
$307$		−	29.6519i		−	1.69232i	0.532928	−	0.846161i	$-0.321092\pi$
$308$	11.5907	−	3.89047i	0.660444	−	0.221680i
$309$	−17.4344	−	10.0576i	−0.991810	−	0.572155i
$310$	−16.8277			−0.955749
$311$	−1.11042	+	1.92330i	−0.0629660	+	0.109060i	−0.895790	−	0.444478i	$-0.853389\pi$
$311$	−1.11042	+	1.92330i	−0.0629660	+	0.109060i	0.832824	+	0.553538i	$0.186723\pi$
$312$	8.45464	−	0.00298306i	0.478650	−	0.000168883i
$313$	−23.6459	+	13.6519i	−1.33654	+	0.771653i	−0.986293	−	0.165003i	$-0.947237\pi$
$313$	−23.6459	+	13.6519i	−1.33654	+	0.771653i	−0.350250	+	0.936656i	$0.613903\pi$
$314$	−12.3014			−0.694205
$315$	7.78052	+	1.56955i	0.438383	+	0.0884339i
$316$	−36.4475			−2.05033
$317$	−13.1016	+	7.56423i	−0.735861	+	0.424849i	−0.820562	−	0.571557i	$-0.806340\pi$
$317$	−13.1016	+	7.56423i	−0.735861	+	0.424849i	0.0847018	+	0.996406i	$0.473006\pi$
$318$	−12.3232	−	21.3270i	−0.691051	−	1.19596i
$319$	−4.71028	+	8.15845i	−0.263725	+	0.456785i
$320$	12.1864			0.681242
$321$	−6.76860	+	3.91104i	−0.377786	+	0.218293i
$322$	15.0021	+	3.03735i	0.836034	+	0.169265i
$323$			16.5070i			0.918472i
$324$	12.0729	+	20.8429i	0.670718	+	1.15794i
$325$	−2.89037	+	1.66875i	−0.160329	+	0.0925658i
$326$			31.4568i			1.74223i
$327$	−11.1140	+	0.00392136i	−0.614604	+	0.000216852i
$328$	−0.999332	+	0.576964i	−0.0551789	+	0.0318575i
$329$	−29.9178	−	6.05722i	−1.64942	−	0.333945i
$330$	−6.46722	+	0.00228184i	−0.356009	+	0.000125611i
$331$	11.3803	+	19.7113i	0.625518	+	1.08343i	0.988440	+	0.151610i	$0.0484457\pi$
$331$	11.3803	+	19.7113i	0.625518	+	1.08343i	−0.362922	+	0.931819i	$0.618221\pi$
$332$	−13.2683	−	22.9813i	−0.728190	−	1.26126i
$333$	10.2025	−	0.00719952i	0.559093	−	0.000394531i
$334$	−26.2254	−	15.1412i	−1.43499	−	0.828491i
$335$	1.06208	−	1.83958i	0.0580278	−	0.100507i
$336$	−6.63988	+	7.52477i	−0.362235	+	0.410510i
$337$	9.02581	+	15.6332i	0.491667	+	0.851592i	0.999954	−	0.00959554i	$-0.00305440\pi$
$337$	9.02581	+	15.6332i	0.491667	+	0.851592i	−0.508287	+	0.861188i	$0.669721\pi$
$338$			4.02447i			0.218902i
$339$	0.00651254	+	18.4579i	0.000353713	+	1.00250i
$340$	13.2530			0.718746
$341$	−6.71810	+	11.6361i	−0.363805	+	0.630129i
$342$	−10.8260	−	18.7206i	−0.585401	−	1.01229i
$343$	15.2929	+	10.4464i	0.825739	+	0.564052i
$344$	−14.7511	−	8.51653i	−0.795324	−	0.459180i
$345$	−4.01378	−	2.31547i	−0.216095	−	0.124661i
$346$	−0.779985	−	0.450325i	−0.0419323	−	0.0242096i
$347$	−6.73424	−	3.88802i	−0.361513	−	0.208720i	0.308231	−	0.951311i	$-0.400263\pi$
$347$	−6.73424	−	3.88802i	−0.361513	−	0.208720i	−0.669744	+	0.742592i	$0.733596\pi$
$348$	0.00892362	+	25.2914i	0.000478356	+	1.35576i
$349$	−23.4206	−	13.5219i	−1.25368	−	0.723810i	−0.281838	−	0.959462i	$-0.590944\pi$
$349$	−23.4206	−	13.5219i	−1.25368	−	0.723810i	−0.971838	+	0.235652i	$0.924277\pi$
$350$	−1.13533	+	5.60762i	−0.0606859	+	0.299740i
$351$	15.0096	−	8.68699i	0.801153	−	0.463677i
$352$	6.61372	−	11.4553i	0.352513	−	0.610570i
$353$	6.01892			0.320355			0.160177	−	0.987088i	$-0.448793\pi$
$353$	6.01892			0.320355			0.160177	+	0.987088i	$0.448793\pi$
$354$	35.4025	+	20.4230i	1.88162	+	1.08547i
$355$			1.34885i			0.0715895i
$356$	14.3478	+	24.8511i	0.760430	+	1.31710i
$357$	−15.0144	+	17.0153i	−0.794646	+	0.900548i
$358$	23.6735	−	41.0038i	1.25119	−	2.16712i
$359$	−6.21974	−	3.59097i	−0.328265	−	0.189524i	0.326805	−	0.945092i	$-0.394028\pi$
$359$	−6.21974	−	3.59097i	−0.328265	−	0.189524i	−0.655071	+	0.755568i	$0.727361\pi$
$360$	−3.79828	+	2.19651i	−0.200187	+	0.115766i
$361$	−3.94409	−	6.83137i	−0.207584	−	0.359546i
$362$	−5.25688	−	9.10518i	−0.276295	−	0.478558i
$363$	6.94014	−	12.0305i	0.364263	−	0.631436i
$364$	−17.7146	−	15.6426i	−0.928500	−	0.819894i
$365$	2.68498	−	1.55018i	0.140538	−	0.0811399i
$366$	12.0944	+	20.9311i	0.632184	+	1.09408i
$367$			21.9618i			1.14640i	0.819416	+	0.573199i	$0.194298\pi$
$367$			21.9618i			1.14640i	−0.819416	+	0.573199i	$0.805702\pi$
$368$	5.07378	−	2.92935i	0.264489	−	0.152703i
$369$	−1.18203	+	2.05067i	−0.0615338	+	0.106754i
$370$			7.35423i			0.382328i
$371$	−3.45259	+	17.0530i	−0.179249	+	0.885348i
$372$	0.0127274	+	36.0722i	0.000659886	+	1.87026i
$373$	36.8807			1.90961			0.954806	−	0.297229i	$-0.0960625\pi$
$373$	36.8807			1.90961			0.954806	+	0.297229i	$0.0960625\pi$
$374$	9.24488	−	16.0126i	0.478042	−	0.827992i
$375$	0.865496	−	1.50031i	0.0446940	−	0.0774754i
$376$	14.6132	−	8.43696i	0.753621	−	0.435103i
$377$	18.2094			0.937831
$378$	5.86850	−	29.1443i	0.301843	−	1.49902i
$379$	7.89653			0.405618			0.202809	−	0.979218i	$-0.434993\pi$
$379$	7.89653			0.405618			0.202809	+	0.979218i	$0.434993\pi$
$380$	7.72615	−	4.46069i	0.396343	−	0.228829i
$381$	7.95163	−	13.7839i	0.407374	−	0.706168i
$382$	−1.16296	+	2.01431i	−0.0595024	+	0.103061i
$383$	22.1516			1.13189			0.565946	−	0.824443i	$-0.308511\pi$
$383$	22.1516			1.13189			0.565946	+	0.824443i	$0.308511\pi$
$384$	−0.00674155	−	19.1070i	−0.000344028	−	0.975050i
$385$	3.42432	+	3.02378i	0.174520	+	0.154106i
$386$			18.6880i			0.951193i
$387$	−34.9383	+	0.0246547i	−1.77601	+	0.00125327i
$388$	7.72680	−	4.46107i	0.392269	−	0.226477i
$389$			13.4670i			0.682805i	0.939917	+	0.341402i	$0.110902\pi$
$389$			13.4670i			0.682805i	−0.939917	+	0.341402i	$0.889098\pi$
$390$	6.25419	+	10.8237i	0.316693	+	0.548082i
$391$	11.4731	−	6.62397i	0.580217	−	0.334989i
$392$	−10.1592	+	1.26701i	−0.513116	+	0.0639937i
$393$	7.76160	−	13.4544i	0.391521	−	0.678687i
$394$	−2.88247	−	4.99259i	−0.145217	−	0.251523i
$395$	−6.80923	−	11.7939i	−0.342609	−	0.593417i
$396$	0.00978279	+	13.8633i	0.000491604	+	0.696655i
$397$	2.97013	+	1.71481i	0.149067	+	0.0860637i	0.572678	−	0.819780i	$-0.305904\pi$
$397$	2.97013	+	1.71481i	0.149067	+	0.0860637i	−0.423611	+	0.905844i	$0.639238\pi$
$398$	−21.4655	+	37.1794i	−1.07597	+	1.86363i
$399$	−3.02597	+	14.9730i	−0.151488	+	0.749589i
$400$	1.09496	+	1.89652i	0.0547478	+	0.0948260i
$401$		−	10.6402i		−	0.531346i	−0.964063	−	0.265673i	$-0.914406\pi$
$401$		−	10.6402i		−	0.531346i	0.964063	−	0.265673i	$-0.0855941\pi$
$402$	−6.89161	−	3.97563i	−0.343722	−	0.198287i
$403$	25.9713			1.29372
$404$	−14.5176	+	25.1452i	−0.722276	+	1.25102i
$405$	−4.48900	+	7.80057i	−0.223060	+	0.387614i
$406$	20.6620	−	23.3989i	1.02544	−	1.16127i
$407$	5.08533	+	2.93602i	0.252071	+	0.145533i
$408$	−0.00442604	−	12.5443i	−0.000219121	−	0.621037i
$409$	−7.51434	−	4.33841i	−0.371560	−	0.214520i	0.302580	−	0.953124i	$-0.402152\pi$
$409$	−7.51434	−	4.33841i	−0.371560	−	0.214520i	−0.674140	+	0.738604i	$0.735485\pi$
$410$	−1.47758	−	0.853079i	−0.0729723	−	0.0421306i
$411$	6.80925	+	3.92812i	0.335876	+	0.193760i
$412$	−26.9339	−	15.5503i	−1.32694	−	0.766107i
$413$	−9.18670	−	27.3696i	−0.452048	−	1.34677i
$414$	−8.66735	+	15.0368i	−0.425977	+	0.739018i
$415$	4.95763	−	8.58686i	0.243360	−	0.421513i
$416$	−25.5678			−1.25357
$417$	−0.0126258	−	35.7843i	−0.000618290	−	1.75236i
$418$		−	12.4466i		−	0.608781i
$419$	−9.02520	−	15.6321i	−0.440910	−	0.763678i	0.556848	−	0.830615i	$-0.312011\pi$
$419$	−9.02520	−	15.6321i	−0.440910	−	0.763678i	−0.997757	+	0.0669367i	$0.978677\pi$
$420$	12.0215	+	2.42947i	0.586587	+	0.118546i
$421$	−14.6491	+	25.3730i	−0.713953	+	1.23660i	0.249409	+	0.968398i	$0.419764\pi$
$421$	−14.6491	+	25.3730i	−0.713953	+	1.23660i	−0.963362	+	0.268204i	$0.913570\pi$
$422$	−17.9186	−	10.3453i	−0.872262	−	0.503601i
$423$	17.2848	−	29.9870i	0.840415	−	1.45802i
$424$	−4.80903	−	8.32948i	−0.233547	−	0.404515i
$425$	2.47597	+	4.28850i	0.120102	+	0.208023i
$426$	5.05216	−	0.00178256i	0.244778	−	8.63654e-5i
$427$	3.38848	−	16.7364i	0.163980	−	0.809930i
$428$	−10.4608	+	6.03957i	−0.505644	+	0.291934i
$429$	9.98130	−	0.00352172i	0.481902	−	0.000170030i
$430$		−	25.1845i		−	1.21450i
$431$	28.5071	−	16.4586i	1.37314	−	0.792783i	0.381818	−	0.924238i	$-0.375298\pi$
$431$	28.5071	−	16.4586i	1.37314	−	0.792783i	0.991322	+	0.131455i	$0.0419649\pi$
$432$	−5.69999	−	9.84858i	−0.274241	−	0.473840i
$433$		−	7.13725i		−	0.342994i	−0.985185	−	0.171497i	$-0.945140\pi$
$433$		−	7.13725i		−	0.342994i	0.985185	−	0.171497i	$-0.0548604\pi$
$434$	29.4694	−	33.3730i	1.41458	−	1.60195i
$435$	−8.18230	+	4.72790i	−0.392311	+	0.226686i
$436$	−17.1731			−0.822443
$437$	4.45899	−	7.72319i	0.213302	−	0.369450i
$438$	−5.80978	−	10.0546i	−0.277602	−	0.480429i
$439$	19.6537	−	11.3471i	0.938020	−	0.541566i	0.0486809	−	0.998814i	$-0.484498\pi$
$439$	19.6537	−	11.3471i	0.938020	−	0.541566i	0.889339	+	0.457248i	$0.151165\pi$
$440$	−2.52532			−0.120390
$441$	−16.7383	+	12.6818i	−0.797063	+	0.603896i
$442$	−35.7396			−1.69996
$443$	2.04657	−	1.18159i	0.0972356	−	0.0561390i	−0.450594	−	0.892729i	$-0.648788\pi$
$443$	2.04657	−	1.18159i	0.0972356	−	0.0561390i	0.547829	+	0.836590i	$0.315454\pi$
$444$	15.7647	−	0.00556228i	0.748159	−	0.000263974i
$445$	−5.36098	+	9.28549i	−0.254135	+	0.440175i
$446$	−29.7513			−1.40877
$447$	20.2821	+	11.7004i	0.959313	+	0.553408i
$448$	−21.3414	+	24.1683i	−1.00829	+	1.14185i
$449$		−	2.75417i		−	0.129978i	−0.997886	−	0.0649888i	$-0.979299\pi$
$449$		−	2.75417i		−	0.129978i	0.997886	−	0.0649888i	$-0.0207012\pi$
$450$	−5.62058	−	3.23976i	−0.264957	−	0.152724i
$451$	−1.17978	+	0.681147i	−0.0555537	+	0.0320740i
$452$			28.5208i			1.34151i
$453$	−17.0905	+	29.6258i	−0.802984	+	1.39194i
$454$	54.0850	−	31.2260i	2.53834	−	1.46551i
$455$	1.75223	−	8.65462i	0.0821459	−	0.405735i
$456$	−4.22475	−	7.31152i	−0.197842	−	0.342393i
$457$	−4.45984	−	7.72468i	−0.208623	−	0.361345i	0.742658	−	0.669671i	$-0.233565\pi$
$457$	−4.45984	−	7.72468i	−0.208623	−	0.361345i	−0.951281	+	0.308326i	$0.900231\pi$
$458$	−7.07319	−	12.2511i	−0.330508	−	0.572457i
$459$	−12.8891	−	22.2701i	−0.601611	−	1.03948i
$460$	−6.20075	−	3.58001i	−0.289111	−	0.166919i
$461$	−4.13030	+	7.15390i	−0.192367	+	0.333190i	−0.946034	−	0.324066i	$-0.894950\pi$
$461$	−4.13030	+	7.15390i	−0.192367	+	0.333190i	0.753667	+	0.657257i	$0.228283\pi$
$462$	11.3211	−	12.8299i	0.526707	−	0.596901i
$463$	1.50983	+	2.61509i	0.0701675	+	0.121534i	0.898975	−	0.438001i	$-0.144313\pi$
$463$	1.50983	+	2.61509i	0.0701675	+	0.121534i	−0.828807	+	0.559534i	$0.810980\pi$
$464$		−	11.9481i		−	0.554678i
$465$	−11.6701	+	6.74323i	−0.541188	+	0.312710i
$466$	45.3028			2.09861
$467$	−14.6749	+	25.4177i	−0.679074	+	1.17619i	0.296186	+	0.955130i	$0.404285\pi$
$467$	−14.6749	+	25.4177i	−0.679074	+	1.17619i	−0.975260	+	0.221061i	$0.929048\pi$
$468$	23.1973	−	13.4148i	1.07229	−	0.620099i
$469$	1.78833	+	5.32790i	0.0825772	+	0.246019i
$470$	21.6066	+	12.4746i	0.996640	+	0.575410i
$471$	−8.53106	+	4.92942i	−0.393090	+	0.227136i
$472$	13.8211	+	7.97964i	0.636170	+	0.367293i
$473$	−17.4147	−	10.0544i	−0.800727	−	0.462300i
$474$	−44.1655	+	25.5198i	−2.02859	+	1.17216i
$475$	2.88684	+	1.66672i	0.132457	+	0.0764743i
$476$	−23.2092	+	26.2836i	−1.06379	+	1.20471i
$477$	−17.0924	−	9.85225i	−0.782609	−	0.451103i
$478$	32.0553	−	55.5214i	1.46617	−	2.53949i
$479$	0.796214			0.0363800			0.0181900	−	0.999835i	$-0.494210\pi$
$479$	0.796214			0.0363800			0.0181900	+	0.999835i	$0.494210\pi$
$480$	11.4888	−	6.63847i	0.524389	−	0.303003i
$481$		−	11.3503i		−	0.517529i
$482$	4.65702	+	8.06619i	0.212121	+	0.367405i
$483$	11.6212	−	3.90525i	0.528782	−	0.177695i
$484$	10.7303	−	18.5855i	0.487742	−	0.844794i
$485$	2.88709	+	1.66686i	0.131096	+	0.0756882i
$486$	29.2232	+	16.8034i	1.32559	+	0.762216i
$487$	−4.82550	−	8.35802i	−0.218664	−	0.378738i	0.735736	−	0.677269i	$-0.236837\pi$
$487$	−4.82550	−	8.35802i	−0.218664	−	0.378738i	−0.954400	+	0.298531i	$0.903503\pi$
$488$	4.71974	+	8.17483i	0.213653	+	0.370057i
$489$	12.6054	+	21.8155i	0.570038	+	0.986530i
$490$	−9.13288	−	12.0719i	−0.412582	−	0.545353i
$491$	11.0595	−	6.38522i	0.499110	−	0.288161i	−0.229236	−	0.973371i	$-0.573623\pi$
$491$	11.0595	−	6.38522i	0.499110	−	0.288161i	0.728346	+	0.685210i	$0.240289\pi$
$492$	−1.82756	+	3.16801i	−0.0823928	+	0.142825i
$493$		−	27.0176i		−	1.21681i
$494$	−20.8352	+	12.0292i	−0.937421	+	0.541220i
$495$	−4.48414	+	2.59314i	−0.201547	+	0.116553i
$496$		−	17.0412i		−	0.765170i
$497$	−2.67506	−	2.36216i	−0.119993	−	0.105958i
$498$	−32.1689	−	18.5576i	−1.44152	−	0.831586i
$499$	−33.6786			−1.50766			−0.753831	−	0.657068i	$-0.771796\pi$
$499$	−33.6786			−1.50766			−0.753831	+	0.657068i	$0.771796\pi$
$500$	1.33817	−	2.31777i	0.0598446	−	0.103654i
$501$	−24.2549	+	0.00855789i	−1.08363	+	0.000382338i
$502$	25.7380	−	14.8598i	1.14874	−	0.663227i
$503$	−9.90713			−0.441737			−0.220869	−	0.975304i	$-0.570889\pi$
$503$	−9.90713			−0.441737			−0.220869	+	0.975304i	$0.570889\pi$
$504$	2.29555	−	11.3794i	0.102252	−	0.506881i
$505$	−10.8489			−0.482768
$506$	−8.65090	+	4.99460i	−0.384579	+	0.222037i
$507$	1.61269	+	2.79099i	0.0716223	+	0.123952i
$508$	12.2942	−	21.2942i	0.545468	−	0.944778i
$509$	35.6778			1.58139			0.790695	−	0.612210i	$-0.209719\pi$
$509$	35.6778			1.58139			0.790695	+	0.612210i	$0.209719\pi$
$510$	16.0594	−	9.27947i	0.711123	−	0.410902i
$511$	−1.62772	+	8.03964i	−0.0720062	+	0.355653i
$512$			23.1821i			1.02452i
$513$	−15.0096	−	8.64465i	−0.662692	−	0.381670i
$514$	5.28158	−	3.04932i	0.232960	−	0.134500i
$515$		−	11.6206i		−	0.512064i
$516$	−53.9860	+	0.0190480i	−2.37660	+	0.000838539i
$517$	17.2520	−	9.96043i	0.758741	−	0.438059i
$518$	−14.5850	−	12.8790i	−0.640830	−	0.565873i
$519$	−0.721380		0.000254526i	−0.0316650		1.11724e-5i
$520$	2.44064	+	4.22732i	0.107029	+	0.185380i
$521$	−9.14291	−	15.8360i	−0.400558	−	0.693787i	0.593235	−	0.805029i	$-0.297850\pi$
$521$	−9.14291	−	15.8360i	−0.400558	−	0.693787i	−0.993793	+	0.111242i	$0.964517\pi$
$522$	17.7193	+	30.6408i	0.775554	+	1.34111i
$523$	−17.6652	−	10.1990i	−0.772446	−	0.445972i	0.0613005	−	0.998119i	$-0.480475\pi$
$523$	−17.6652	−	10.1990i	−0.772446	−	0.445972i	−0.833746	+	0.552147i	$0.813809\pi$
$524$	12.0004	−	20.7853i	0.524240	−	0.908011i
$525$	1.45974	+	4.34387i	0.0637082	+	0.189582i
$526$	19.9786	+	34.6039i	0.871106	+	1.50880i
$527$		−	38.5342i		−	1.67858i
$528$	−0.00231078	−	6.54925i	−0.000100564	−	0.285020i
$529$	15.8427			0.688814
$530$	7.11046	−	12.3157i	0.308859	−	0.534959i
$531$	32.7358	−	0.0231004i	1.42061	−	0.00100247i
$532$	−4.68383	+	23.1344i	−0.203070	+	1.00300i
$533$	2.28045	+	1.31662i	0.0987771	+	0.0570290i
$534$	34.7862	+	20.0674i	1.50534	+	0.868403i
$535$	−3.90865	−	2.25666i	−0.168986	−	0.0975639i
$536$	−2.69049	−	1.55336i	−0.116211	−	0.0670947i
$537$	−0.0133804	−	37.9229i	−0.000577406	−	1.63649i
$538$	36.4424	+	21.0400i	1.57114	+	0.907099i
$539$	−11.9936	+	1.49580i	−0.516602	+	0.0644285i
$540$	−6.94056	+	12.0508i	−0.298674	+	0.518586i
$541$	−3.98849	+	6.90827i	−0.171479	+	0.297010i	−0.938937	−	0.344089i	$-0.888188\pi$
$541$	−3.98849	+	6.90827i	−0.171479	+	0.297010i	0.767458	+	0.641099i	$0.221521\pi$
$542$	41.3947			1.77806
$543$	−7.29432	−	4.20795i	−0.313029	−	0.180580i
$544$			37.9356i			1.62647i
$545$	−3.20833	−	5.55699i	−0.137430	−	0.238035i
$546$	−32.4184	−	6.55160i	−1.38738	−	0.280382i
$547$	−8.04726	+	13.9383i	−0.344076	+	0.595957i	−0.985185	−	0.171492i	$-0.945141\pi$
$547$	−8.04726	+	13.9383i	−0.344076	+	0.595957i	0.641109	+	0.767449i	$0.278474\pi$
$548$	10.5194	+	6.07337i	0.449366	+	0.259442i
$549$	16.7751	+	9.66932i	0.715943	+	0.412676i
$550$	−1.86692	−	3.23361i	−0.0796059	−	0.137882i
$551$	−9.09359	−	15.7506i	−0.387400	−	0.670996i
$552$	−3.38650	+	5.87037i	−0.144139	+	0.249860i
$553$	35.3145	+	7.14985i	1.50173	+	0.304043i
$554$	48.7324	−	28.1357i	2.07044	−	1.19537i
$555$	2.94700	+	5.10020i	0.125093	+	0.216492i
$556$		−	55.2932i		−	2.34495i
$557$	4.36517	−	2.52023i	0.184958	−	0.106786i	−0.404662	−	0.914466i	$-0.632611\pi$
$557$	4.36517	−	2.52023i	0.184958	−	0.106786i	0.589620	+	0.807681i	$0.299277\pi$
$558$	25.2724	+	43.7018i	1.06987	+	1.85005i
$559$			38.8689i			1.64398i
$560$	−5.67875	−	1.14973i	−0.239971	−	0.0485850i
$561$	−0.00522525	−	14.8095i	−0.000220610	−	0.625256i
$562$	−48.8168			−2.05921
$563$	−12.7290	+	22.0473i	−0.536465	+	0.929185i	0.462626	+	0.886554i	$0.346907\pi$
$563$	−12.7290	+	22.0473i	−0.536465	+	0.929185i	−0.999091	+	0.0426311i	$0.986426\pi$
$564$	26.7245	−	46.3259i	1.12530	−	1.95067i
$565$	−9.22896	+	5.32834i	−0.388265	+	0.224165i
$566$	23.0765			0.969976
$567$	−7.60891	−	22.5633i	−0.319544	−	0.947571i
$568$	1.97277			0.0827755
$569$	−13.5116	+	7.80094i	−0.566437	+	0.327032i	−0.755725	−	0.654889i	$-0.772715\pi$
$569$	−13.5116	+	7.80094i	−0.566437	+	0.327032i	0.189288	+	0.981922i	$0.439382\pi$
$570$	6.23893	−	10.8150i	0.261320	−	0.452989i
$571$	6.01702	−	10.4218i	0.251804	−	0.436138i	−0.712218	−	0.701958i	$-0.752309\pi$
$571$	6.01702	−	10.4218i	0.251804	−	0.436138i	0.964023	+	0.265820i	$0.0856427\pi$
$572$	15.4229			0.644864
$573$	0.000657313		1.86296i	2.74596e−5		0.0778264i
$574$	4.27944	−	1.43641i	0.178620	−	0.0599545i
$575$		−	2.67531i		−	0.111568i
$576$	−18.3020	−	31.6484i	−0.762583	−	1.31868i
$577$	−2.90129	+	1.67506i	−0.120782	+	0.0697337i	−0.559174	−	0.829050i	$-0.688882\pi$
$577$	−2.90129	+	1.67506i	−0.120782	+	0.0697337i	0.438392	+	0.898784i	$0.355548\pi$
$578$			16.2654i			0.676552i
$579$	7.48868	+	12.9602i	0.311219	+	0.538608i
$580$	−12.6457	+	7.30101i	−0.525085	+	0.303158i
$581$	8.34761	+	24.8697i	0.346317	+	1.03177i
$582$	6.23946	−	10.8159i	0.258634	−	0.448332i
$583$	−5.67740	−	9.83354i	−0.235134	−	0.407264i
$584$	−2.26722	−	3.92694i	−0.0938181	−	0.162498i
$585$	8.67463	+	5.00014i	0.358652	+	0.206730i
$586$	0.327604	+	0.189142i	0.0135332	+	0.00781340i
$587$	−21.0363	+	36.4359i	−0.868260	+	1.50387i	−0.00448747	+	0.999990i	$0.501428\pi$
$587$	−21.0363	+	36.4359i	−0.868260	+	1.50387i	−0.863773	+	0.503881i	$0.831905\pi$
$588$	−25.8707	+	19.5866i	−1.06689	+	0.807736i
$589$	−12.9698	−	22.4644i	−0.534413	−	0.925630i
$590$			23.5968i			0.971467i
$591$	−3.99965	−	2.30732i	−0.164524	−	0.0949105i
$592$	−7.44752			−0.306091
$593$	−13.5045	+	23.3905i	−0.554564	+	0.960534i	0.443373	+	0.896337i	$0.353782\pi$
$593$	−13.5045	+	23.3905i	−0.554564	+	0.960534i	−0.997937	+	0.0641964i	$0.979552\pi$
$594$	9.71860	+	16.7920i	0.398759	+	0.688986i
$595$	−12.8410	−	2.59982i	−0.526431	−	0.106582i
$596$	31.3332	+	18.0902i	1.28346	+	0.741005i
$597$	0.0121324	+	34.3858i	0.000496546	+	1.40732i
$598$	16.7217	+	9.65425i	0.683799	+	0.394792i
$599$	19.3762	+	11.1869i	0.791690	+	0.457082i	0.840557	−	0.541723i	$-0.182228\pi$
$599$	19.3762	+	11.1869i	0.791690	+	0.457082i	−0.0488672	+	0.998805i	$0.515561\pi$
$600$	−2.19428	−	1.26584i	−0.0895811	−	0.0516775i
$601$	−33.0130	−	19.0601i	−1.34663	−	0.777476i	−0.358858	−	0.933392i	$-0.616834\pi$
$601$	−33.0130	−	19.0601i	−1.34663	−	0.777476i	−0.987770	+	0.155916i	$0.950167\pi$
$602$	49.9463	+	44.1041i	2.03566	+	1.79755i
$603$	−6.37250	+	0.00449684i	−0.259508	+	0.000183125i
$604$	−26.4241	+	45.7679i	−1.07518	+	1.86227i
$605$	8.01868			0.326006
$606$	0.0143372	+	40.6347i	0.000582409	+	1.65067i
$607$		−	3.05245i		−	0.123895i	−0.998079	−	0.0619476i	$-0.980269\pi$
$607$		−	3.05245i		−	0.123895i	0.998079	−	0.0619476i	$-0.0197312\pi$
$608$	12.7683	+	22.1154i	0.517824	+	0.896898i
$609$	4.95273	−	24.5070i	0.200695	−	0.993073i
$610$	−6.97844	+	12.0870i	−0.282549	+	0.489389i
$611$	−33.3470	−	19.2529i	−1.34908	−	0.778889i
$612$	−19.9038	−	34.4183i	−0.804564	−	1.39128i
$613$	19.9401	+	34.5372i	0.805372	+	1.39495i	0.916040	+	0.401088i	$0.131368\pi$
$613$	19.9401	+	34.5372i	0.805372	+	1.39495i	−0.110668	+	0.993857i	$0.535299\pi$
$614$	−32.0608	−	55.5310i	−1.29387	−	2.24105i
$615$	−1.36656		0.000482164i	−0.0551049		1.94427e-5i
$616$	4.42245	−	5.00826i	0.178185	−	0.201788i
$617$	9.69826	−	5.59929i	0.390437	−	0.225419i	−0.291912	−	0.956445i	$-0.594292\pi$
$617$	9.69826	−	5.59929i	0.390437	−	0.225419i	0.682350	+	0.731026i	$0.260958\pi$
$618$	−43.5253	+	0.0153571i	−1.75084	+	0.000617753i
$619$		−	39.5580i		−	1.58997i	−0.606628	−	0.794986i	$-0.707478\pi$
$619$		−	39.5580i		−	1.58997i	0.606628	−	0.794986i	$-0.292522\pi$
$620$	−18.0361	+	10.4131i	−0.724347	+	0.418202i
$621$	0.0147145	+	13.9013i	0.000590471	+	0.557840i
$622$			4.80252i			0.192563i
$623$	−9.02677	−	26.8931i	−0.361650	−	1.07745i
$624$	−10.9610	+	6.33352i	−0.438793	+	0.253544i
$625$	1.00000			0.0400000
$626$	−29.5221	+	51.1337i	−1.17994	+	2.04372i
$627$	−4.98761	−	8.63176i	−0.199186	−	0.344719i
$628$	−13.1847	+	7.61220i	−0.526127	+	0.303760i
$629$	−16.8407			−0.671482
$630$	16.2681	−	5.47323i	0.648138	−	0.218059i
$631$	−31.1354			−1.23948			−0.619740	−	0.784807i	$-0.712762\pi$
$631$	−31.1354			−1.23948			−0.619740	+	0.784807i	$0.712762\pi$
$632$	−17.2493	+	9.95887i	−0.686139	+	0.396143i
$633$	−16.5722	+	0.00584720i	−0.658686	+	0.000232405i
$634$	−16.3575	+	28.3320i	−0.649640	+	1.12521i
$635$	9.18737			0.364590
$636$	−26.4055	−	15.2328i	−1.04705	−	0.604021i
$637$	14.0954	+	18.6314i	0.558480	+	0.738202i
$638$			20.3718i			0.806528i
$639$	3.50299	−	2.02575i	0.138576	−	0.0801373i
$640$	9.55350	−	5.51572i	0.377635	−	0.218028i
$641$		−	42.9406i		−	1.69605i	−0.529955	−	0.848026i	$-0.677791\pi$
$641$		−	42.9406i		−	1.69605i	0.529955	−	0.848026i	$-0.322209\pi$
$642$	−8.44722	+	14.6429i	−0.333385	+	0.577911i
$643$	−25.1028	+	14.4931i	−0.989959	+	0.571553i	−0.905262	−	0.424854i	$-0.860326\pi$
$643$	−25.1028	+	14.4931i	−0.989959	+	0.571553i	−0.0846970	+	0.996407i	$0.526992\pi$
$644$	17.9589	−	6.02798i	0.707682	−	0.237536i
$645$	−10.0920	−	17.4656i	−0.397371	−	0.687707i
$646$	17.8480	+	30.9137i	0.702221	+	1.21628i
$647$	−14.4462	−	25.0215i	−0.567937	−	0.983696i	−0.996770	−	0.0803122i	$-0.974408\pi$
$647$	−14.4462	−	25.0215i	−0.567937	−	0.983696i	0.428833	−	0.903384i	$-0.358925\pi$
$648$	11.4088	+	6.56540i	0.448179	+	0.257913i
$649$	16.3168	+	9.42053i	0.640492	+	0.369788i
$650$	−3.60865	+	6.25037i	−0.141543	+	0.245160i
$651$	7.06390	−	34.9534i	0.276856	−	1.36993i
$652$	19.4658	+	33.7157i	0.762339	+	1.32041i
$653$			44.1588i			1.72807i	0.503435	+	0.864033i	$0.332069\pi$
$653$			44.1588i			1.72807i	−0.503435	+	0.864033i	$0.667931\pi$
$654$	−20.8096	+	12.0242i	−0.813721	+	0.470185i
$655$	8.96780			0.350401
$656$	0.863900	−	1.49632i	0.0337296	−	0.0584215i
$657$	−8.05823	−	4.64484i	−0.314381	−	0.181213i
$658$	−62.5783	+	21.0046i	−2.43956	+	0.818845i
$659$	−11.1900	−	6.46056i	−0.435901	−	0.251668i	0.265956	−	0.963985i	$-0.414312\pi$
$659$	−11.1900	−	6.46056i	−0.435901	−	0.251668i	−0.701858	+	0.712317i	$0.747646\pi$
$660$	−6.93022	+	4.00442i	−0.269758	+	0.155872i
$661$	16.7305	+	9.65938i	0.650743	+	0.375706i	0.788741	−	0.614726i	$-0.210733\pi$
$661$	16.7305	+	9.65938i	0.650743	+	0.375706i	−0.137998	+	0.990432i	$0.544067\pi$
$662$	42.6253	+	24.6097i	1.65668	+	0.956484i
$663$	−24.7856	+	14.3216i	−0.962594	+	0.556207i
$664$	−12.5588	−	7.25080i	−0.487374	−	0.281386i
$665$	−8.36103	+	2.80641i	−0.324227	+	0.108828i
$666$	19.0991	−	11.0448i	0.740074	−	0.427978i
$667$	−7.29821	+	12.6409i	−0.282588	+	0.489457i
$668$	−37.4782			−1.45007
$669$	−20.6327	+	11.9220i	−0.797707	+	0.460932i
$670$		−	4.59347i		−	0.177461i
$671$	5.57199	+	9.65096i	0.215104	+	0.372571i
$672$	−6.95415	+	34.4103i	−0.268262	+	1.32741i
$673$	13.1315	−	22.7444i	0.506180	−	0.876730i	−0.493794	−	0.869579i	$-0.664390\pi$
$673$	13.1315	−	22.7444i	0.506180	−	0.876730i	0.999974	−	0.00715136i	$-0.00227637\pi$
$674$	33.8064	+	19.5181i	1.30217	+	0.751811i
$675$	−5.19615	+	0.00550010i	−0.200000	+	0.000211699i
$676$	2.49038	+	4.31347i	0.0957839	+	0.165903i
$677$	−3.26374	−	5.65296i	−0.125436	−	0.217261i	0.796468	−	0.604681i	$-0.206700\pi$
$677$	−3.26374	−	5.65296i	−0.125436	−	0.217261i	−0.921903	+	0.387420i	$0.873366\pi$
$678$	19.9697	+	34.5603i	0.766930	+	1.32728i
$679$	−8.36173	+	2.80664i	−0.320894	+	0.107709i
$680$	6.27217	−	3.62124i	0.240527	−	0.138868i
$681$	24.9953	−	43.3285i	0.957824	−	1.66035i
$682$			29.0555i			1.11259i
$683$	−4.15228	+	2.39732i	−0.158883	+	0.0917309i	−0.577333	−	0.816509i	$-0.695907\pi$
$683$	−4.15228	+	2.39732i	−0.158883	+	0.0917309i	0.418451	+	0.908240i	$0.362573\pi$
$684$	−23.1879	−	13.3657i	−0.886611	−	0.511051i
$685$			4.53858i			0.173410i
$686$	39.9351	+	3.02833i	1.52473	+	0.115622i
$687$	−9.81459	−	5.66184i	−0.374450	−	0.216013i
$688$	25.5039			0.972328
$689$	−10.9741	+	19.0076i	−0.418079	+	0.724133i
$690$	−10.0204	+	0.00353553i	−0.381472	+	0.000134595i
$691$	9.76593	−	5.63836i	0.371513	−	0.214493i	−0.302606	−	0.953116i	$-0.597857\pi$
$691$	9.76593	−	5.63836i	0.371513	−	0.214493i	0.674119	+	0.738622i	$0.264523\pi$
$692$	−1.11466			−0.0423731
$693$	2.71005	−	13.4342i	0.102946	−	0.510324i
$694$	−16.8155			−0.638309
$695$	17.8922	−	10.3300i	0.678688	−	0.391841i
$696$	6.91482	+	11.9671i	0.262106	+	0.453611i
$697$	1.95349	−	3.38355i	0.0739938	−	0.128161i
$698$	−58.4817			−2.21356
$699$	31.4178	−	18.1538i	1.18833	−	0.686641i
$700$	2.25319	+	6.71285i	0.0851626	+	0.253722i
$701$		−	25.1208i		−	0.948799i	−0.880310	−	0.474399i	$-0.842665\pi$
$701$		−	25.1208i		−	0.948799i	0.880310	−	0.474399i	$-0.157335\pi$
$702$	18.7167	−	32.4977i	0.706417	−	1.22655i
$703$	−9.81766	+	5.66823i	−0.370280	+	0.213781i
$704$		−	21.0417i		−	0.793039i
$705$	19.9832	−	0.00705070i	0.752610	−	0.000265545i
$706$	11.2720	−	6.50790i	0.424228	−	0.244928i
$707$	18.9990	−	21.5156i	0.714530	−	0.809179i
$708$	50.5827	−	0.0178472i	1.90101	−	0.000670738i
$709$	−10.5485	−	18.2706i	−0.396159	−	0.686168i	0.597089	−	0.802175i	$-0.296324\pi$
$709$	−10.5485	−	18.2706i	−0.396159	−	0.686168i	−0.993248	+	0.116007i	$0.962990\pi$
$710$	1.45843	+	2.52608i	0.0547340	+	0.0948021i
$711$	−20.4027	+	35.3962i	−0.765161	+	1.32746i
$712$	13.5805	+	7.84073i	0.508952	+	0.293844i
$713$	−10.4092	+	18.0292i	−0.389826	+	0.675199i
$714$	−9.72075	+	48.0999i	−0.363790	+	1.80010i
$715$	2.88135	+	4.99065i	0.107756	+	0.186640i
$716$		−	58.5977i		−	2.18990i
$717$	−0.0181178	−	51.3497i	−0.000676621	−	1.91769i
$718$	−15.5308			−0.579605
$719$	−18.8427	+	32.6366i	−0.702716	+	1.21714i	0.264794	+	0.964305i	$0.414696\pi$
$719$	−18.8427	+	32.6366i	−0.702716	+	1.21714i	−0.967510	+	0.252835i	$0.918637\pi$
$720$	3.28085	−	5.69188i	0.122270	−	0.212124i
$721$	23.0461	+	20.3505i	0.858283	+	0.757891i
$722$	−14.7727	−	8.52903i	−0.549784	−	0.317418i
$723$	6.46197	+	3.72778i	0.240323	+	0.138638i
$724$	−11.2688	−	6.50602i	−0.418800	−	0.241794i
$725$	−4.72502	−	2.72799i	−0.175483	−	0.101315i
$726$	−0.0105970	−	30.0342i	−0.000393292	−	1.11467i
$727$	−13.1307	−	7.58102i	−0.486991	−	0.281165i	0.236334	−	0.971672i	$-0.424054\pi$
$727$	−13.1307	−	7.58102i	−0.486991	−	0.281165i	−0.723325	+	0.690507i	$0.757387\pi$
$728$	−12.6579	−	2.56273i	−0.469131	−	0.0949813i
$729$	26.9999	−	0.0571587i	0.999998	−	0.00211699i
$730$	3.35223	−	5.80623i	0.124072	−	0.214898i
$731$	57.6707			2.13303
$732$	25.9152	+	14.9500i	0.957855	+	0.552567i
$733$			9.72729i			0.359286i	0.983732	+	0.179643i	$0.0574942\pi$
$733$			9.72729i			0.359286i	−0.983732	+	0.179643i	$0.942506\pi$
$734$	23.7460	+	41.1293i	0.876482	+	1.51811i
$735$	−11.1712	−	4.71218i	−0.412055	−	0.173812i
$736$	10.2474	−	17.7491i	0.377726	−	0.654240i
$737$	−3.17631	−	1.83385i	−0.117001	−	0.0675506i
$738$	0.00361192	+	5.11847i	0.000132957	+	0.188414i
$739$	1.17078	+	2.02785i	0.0430678	+	0.0745956i	0.886756	−	0.462238i	$-0.152954\pi$
$739$	1.17078	+	2.02785i	0.0430678	+	0.0745956i	−0.843688	+	0.536834i	$0.819620\pi$
$740$	4.55087	+	7.88234i	0.167293	+	0.289761i
$741$	−9.62897	+	16.6915i	−0.353729	+	0.613176i
$742$	11.9725	+	35.6693i	0.439525	+	1.30946i
$743$	−22.8122	+	13.1707i	−0.836900	+	0.483185i	−0.856209	−	0.516629i	$-0.827187\pi$
$743$	−22.8122	+	13.1707i	−0.836900	+	0.483185i	0.0193092	+	0.999814i	$0.493853\pi$
$744$	9.86234	+	17.0682i	0.361571	+	0.625750i
$745$			13.5187i			0.495286i
$746$	69.0690	−	39.8770i	2.52879	−	1.46000i
$747$	−29.7458	+	0.0209905i	−1.08834	+	0.000768002i
$748$		−	22.8833i		−	0.836697i
$749$	11.3204	−	3.79974i	0.413640	−	0.138840i
$750$	−0.00132154	−	3.74553i	−4.82559e−5	−	0.136767i
$751$	−46.6505			−1.70230			−0.851151	−	0.524921i	$-0.824095\pi$
$751$	−46.6505			−1.70230			−0.851151	+	0.524921i	$0.824095\pi$
$752$	−12.6328	+	21.8807i	−0.460672	+	0.797907i
$753$	11.8948	−	20.6192i	0.433470	−	0.751405i
$754$	34.1019	−	19.6887i	1.24192	−	0.717021i
$755$	−19.7465			−0.718650
$756$	−11.7448	−	34.8686i	−0.427156	−	1.26816i
$757$	4.42659			0.160887			0.0804435	−	0.996759i	$-0.474366\pi$
$757$	4.42659			0.160887			0.0804435	+	0.996759i	$0.474366\pi$
$758$	14.7883	−	8.53806i	0.537137	−	0.310116i
$759$	−3.99800	+	6.93039i	−0.145118	+	0.251557i
$760$	2.43767	−	4.22217i	0.0884235	−	0.153154i
$761$	−45.3737			−1.64480			−0.822398	−	0.568913i	$-0.807364\pi$
$761$	−45.3737			−1.64480			−0.822398	+	0.568913i	$0.807364\pi$
$762$	−0.0121415	−	34.4116i	−0.000439840	−	1.24660i
$763$	16.6393	+	3.36882i	0.602382	+	0.121960i
$764$			2.87862i			0.104145i
$765$	7.41882	−	12.8707i	0.268228	−	0.465342i
$766$	41.4846	−	23.9512i	1.49890	−	0.865391i
$767$		−	36.4186i		−	1.31500i
$768$	0.448516	+	0.776221i	0.0161844	+	0.0280094i
$769$	−9.23372	+	5.33109i	−0.332976	+	0.192244i	−0.657162	−	0.753750i	$-0.728243\pi$
$769$	−9.23372	+	5.33109i	−0.332976	+	0.192244i	0.324185	+	0.945994i	$0.394910\pi$
$770$	9.68238	+	1.96032i	0.348929	+	0.0706449i
$771$	2.44087	−	4.23117i	0.0879060	−	0.152382i
$772$	11.5643	+	20.0300i	0.416208	+	0.720894i
$773$	7.19154	+	12.4561i	0.258662	+	0.448015i	0.965884	−	0.258976i	$-0.0833852\pi$
$773$	7.19154	+	12.4561i	0.258662	+	0.448015i	−0.707222	+	0.706992i	$0.750052\pi$
$774$	−65.4045	+	37.8229i	−2.35092	+	1.35952i
$775$	−6.73911	−	3.89083i	−0.242076	−	0.139763i
$776$	2.43787	−	4.22252i	0.0875146	−	0.151580i
$777$	−15.2757	−	3.08714i	−0.548014	−	0.110751i
$778$	14.5611	+	25.2205i	0.522040	+	0.904200i
$779$		−	2.63002i		−	0.0942303i
$780$	13.4011	+	7.73085i	0.479838	+	0.276809i
$781$	2.32899			0.0833379
$782$	14.3242	−	24.8103i	0.512233	−	0.887214i
$783$	24.5669	+	14.1491i	0.877949	+	0.505646i
$784$	12.2250	−	9.24873i	0.436608	−	0.330312i
$785$	−4.92641	−	2.84427i	−0.175831	−	0.101516i
$786$	−0.0118513	−	33.5892i	−0.000422723	−	1.19809i
$787$	−18.5423	−	10.7054i	−0.660961	−	0.381606i	0.131682	−	0.991292i	$-0.457962\pi$
$787$	−18.5423	−	10.7054i	−0.660961	−	0.381606i	−0.792643	+	0.609686i	$0.791295\pi$
$788$	−6.17893	−	3.56741i	−0.220115	−	0.127084i
$789$	27.7218	+	15.9921i	0.986922	+	0.569335i
$790$	−25.5042	−	14.7248i	−0.907398	−	0.523886i
$791$	5.59489	−	27.6343i	0.198931	−	0.982561i
$792$	3.79261	+	6.55830i	0.134764	+	0.233039i
$793$	10.7703	−	18.6547i	0.382465	−	0.662448i
$794$	7.41648			0.263201
$795$	−0.00401887	−	11.3903i	−0.000142534	−	0.403973i
$796$			53.1323i			1.88322i
$797$	−8.94216	−	15.4883i	−0.316748	−	0.548623i	0.663060	−	0.748566i	$-0.269257\pi$
$797$	−8.94216	−	15.4883i	−0.316748	−	0.548623i	−0.979807	+	0.199944i	$0.935924\pi$
$798$	10.5225	+	31.3128i	0.372493	+	1.10846i
$799$	−28.5659	+	49.4777i	−1.01059	+	1.75039i
$800$	6.63441	+	3.83038i	0.234562	+	0.135424i
$801$	32.1659	−	0.0226983i	1.13653	−	0.000802005i
$802$	−11.5046	−	19.9266i	−0.406242	−	0.703632i
$803$	−2.67661	−	4.63602i	−0.0944555	−	0.163602i
$804$	−9.84666	+	0.00347421i	−0.347265	+	0.000122526i
$805$	5.30572	+	4.68511i	0.187002	+	0.165129i
$806$	48.6382	−	28.0813i	1.71321	−	0.989121i
$807$	33.7042	−	0.0118919i	1.18644	−	0.000418615i
$808$			15.8670i			0.558201i
$809$	28.6232	−	16.5256i	1.00634	−	0.581010i	0.0962218	−	0.995360i	$-0.469324\pi$
$809$	28.6232	−	16.5256i	1.00634	−	0.581010i	0.910118	+	0.414349i	$0.135991\pi$
$810$	0.0274677	+	19.4623i	0.000965117	+	0.683836i
$811$			35.2859i			1.23905i	0.784975	+	0.619527i	$0.212676\pi$
$811$			35.2859i			1.23905i	−0.784975	+	0.619527i	$0.787324\pi$
$812$	7.66623	−	37.8650i	0.269032	−	1.32880i
$813$	28.7075	−	16.5878i	1.00682	−	0.581759i
$814$	12.6982			0.445071
$815$	−7.27331	+	12.5977i	−0.254773	+	0.441280i
$816$	9.39718	+	16.2631i	0.328967	+	0.569324i
$817$	33.6204	−	19.4108i	1.17623	−	0.679097i
$818$	−18.7635			−0.656049
$819$	−25.1077	+	8.44721i	−0.877336	+	0.295170i
$820$	−2.11158			−0.0737394
$821$	4.35529	−	2.51453i	0.152001	−	0.0877576i	−0.422071	−	0.906563i	$-0.638697\pi$
$821$	4.35529	−	2.51453i	0.152001	−	0.0877576i	0.574071	+	0.818805i	$0.305363\pi$
$822$	16.9994	−	0.00599792i	0.592922	−	0.000209201i
$823$	1.34511	−	2.32979i	0.0468875	−	0.0812115i	−0.841629	−	0.540056i	$-0.818403\pi$
$823$	1.34511	−	2.32979i	0.0468875	−	0.0812115i	0.888517	+	0.458844i	$0.151736\pi$
$824$	−16.9957			−0.592075
$825$	−2.59050	−	1.49441i	−0.0901897	−	0.0520286i
$826$	−46.7977	−	41.3238i	−1.62830	−	1.43784i
$827$			18.8965i			0.657097i	0.944487	+	0.328548i	$0.106559\pi$
$827$			18.8965i			0.657097i	−0.944487	+	0.328548i	$0.893441\pi$
$828$	0.0151577	+	21.4800i	0.000526765	+	0.746482i
$829$	−15.3012	+	8.83413i	−0.531432	+	0.306822i	−0.741599	−	0.670843i	$-0.765932\pi$
$829$	−15.3012	+	8.83413i	−0.531432	+	0.306822i	0.210168	+	0.977665i	$0.432599\pi$
$830$		−	21.4416i		−	0.744248i
$831$	22.5216	−	39.0404i	0.781267	−	1.35430i
$832$	−35.2233	+	20.3362i	−1.22115	+	0.705029i
$833$	27.6438	−	20.9137i	0.957801	−	0.724615i
$834$	−38.7151	−	67.0019i	−1.34059	−	2.32009i
$835$	−7.00178	−	12.1274i	−0.242307	−	0.419687i
$836$	−7.70205	−	13.3403i	−0.266381	−	0.461386i
$837$	35.0388	+	20.1803i	1.21112	+	0.697532i
$838$	−33.8041	−	19.5168i	−1.16774	−	0.674198i
$839$	6.02682	−	10.4388i	0.208069	−	0.360386i	−0.743037	−	0.669250i	$-0.766616\pi$
$839$	6.02682	−	10.4388i	0.208069	−	0.360386i	0.951106	+	0.308864i	$0.0999489\pi$
$840$	6.35314	−	2.13495i	0.219204	−	0.0736627i
$841$	0.383861	+	0.664866i	0.0132366	+	0.0229264i
$842$			63.3568i			2.18342i
$843$	−33.8547	+	19.5620i	−1.16602	+	0.673749i
$844$	−25.6071			−0.881431
$845$	−0.930521	+	1.61171i	−0.0320109	+	0.0554445i
$846$	−0.0528172	−	74.8476i	−0.00181589	−	2.57331i
$847$	−14.0427	+	15.9028i	−0.482511	+	0.546426i
$848$	12.4719	+	7.20066i	0.428287	+	0.247272i
$849$	16.0037	−	9.24725i	0.549244	−	0.317365i
$850$	9.27381	+	5.35423i	0.318089	+	0.183649i
$851$	7.87933	+	4.54913i	0.270100	+	0.155942i
$852$	5.41385	−	3.12824i	0.185476	−	0.107172i
$853$	−10.5988	−	6.11923i	−0.362896	−	0.209518i	0.307454	−	0.951563i	$-0.400523\pi$
$853$	−10.5988	−	6.11923i	−0.362896	−	0.209518i	−0.670351	+	0.742045i	$0.733856\pi$
$854$	−11.7502	−	35.0071i	−0.402085	−	1.19792i
$855$	−0.00705686	−	10.0003i	−0.000241339	−	0.342004i
$856$	−3.30049	+	5.71661i	−0.112808	+	0.195390i
$857$	0.591040			0.0201896			0.0100948	−	0.999949i	$-0.496787\pi$
$857$	0.591040			0.0201896			0.0100948	+	0.999949i	$0.496787\pi$
$858$	18.6888	−	10.7988i	0.638026	−	0.368665i
$859$		−	12.3165i		−	0.420235i	−0.977676	−	0.210117i	$-0.932615\pi$
$859$		−	12.3165i		−	0.420235i	0.977676	−	0.210117i	$-0.0673846\pi$
$860$	−15.5844	−	26.9930i	−0.531424	−	0.920453i
$861$	2.39221	−	2.71102i	0.0815264	−	0.0923914i
$862$	35.5914	−	61.6462i	1.21225	−	2.09968i
$863$	7.47167	+	4.31377i	0.254339	+	0.146843i	0.621749	−	0.783216i	$-0.286422\pi$
$863$	7.47167	+	4.31377i	0.254339	+	0.146843i	−0.367411	+	0.930059i	$0.619756\pi$
$864$	−34.4945	−	19.8667i	−1.17353	−	0.675880i
$865$	−0.208244	−	0.360690i	−0.00708052	−	0.0122638i
$866$	−7.71708	−	13.3664i	−0.262237	−	0.454208i
$867$	6.51791	+	11.2802i	0.221360	+	0.383094i
$868$	10.9341	−	54.0054i	0.371126	−	1.83306i
$869$	−20.3640	+	11.7571i	−0.690801	+	0.398834i
$870$	−10.2115	+	17.7013i	−0.346203	+	0.600130i
$871$			7.08942i			0.240216i
$872$	−8.12740	+	4.69236i	−0.275229	+	0.158903i
$873$	−0.00705745	−	10.0012i	−0.000238859	−	0.338488i
$874$		−	19.2850i		−	0.652324i
$875$	−1.75124	+	1.98322i	−0.0592028	+	0.0670450i
$876$	−12.4489	−	7.18151i	−0.420609	−	0.242641i
$877$	19.4720			0.657521			0.328761	−	0.944413i	$-0.393369\pi$
$877$	19.4720			0.657521			0.328761	+	0.944413i	$0.393369\pi$
$878$	24.5378	−	42.5008i	0.828112	−	1.43433i
$879$	0.302989		0.000106904i	0.0102196		3.60578e-6i
$880$	3.27463	−	1.89061i	0.110388	−	0.0637323i
$881$	−35.4636			−1.19480			−0.597400	−	0.801944i	$-0.703799\pi$
$881$	−35.4636			−1.19480			−0.597400	+	0.801944i	$0.703799\pi$
$882$	−17.6349	+	41.8482i	−0.593797	+	1.40910i
$883$	−45.6972			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$883$	−45.6972			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$884$	−38.3061	+	22.1160i	−1.28837	+	0.743842i
$885$	9.45578	+	16.3646i	0.317852	+	0.550088i
$886$	2.55517	−	4.42568i	0.0858425	−	0.148684i
$887$	−5.43400			−0.182456			−0.0912280	−	0.995830i	$-0.529079\pi$
$887$	−5.43400			−0.182456			−0.0912280	+	0.995830i	$0.529079\pi$
$888$	7.45933	−	4.31016i	0.250319	−	0.144639i
$889$	−16.0893	+	18.2205i	−0.539618	+	0.611097i
$890$			23.1861i			0.777198i
$891$	13.4689	+	7.75092i	0.451224	+	0.259666i
$892$	−31.8878	+	18.4104i	−1.06768	+	0.616426i
$893$			38.4589i			1.28698i
$894$	50.6346	−	0.0178655i	1.69347	−	0.000597512i
$895$	18.9614	−	10.9474i	0.633811	−	0.365931i
$896$	−5.79163	+	28.6060i	−0.193485	+	0.955660i
$897$	15.4652	−	0.00545663i	0.516369	−	0.000182191i
$898$	−2.97793	−	5.15792i	−0.0993747	−	0.172122i
$899$	21.2283	+	36.7685i	0.708003	+	1.22630i
$900$	−8.02899	+	0.00566577i	−0.267633	+	0.000188859i
$901$	28.2020	+	16.2825i	0.939546	+	0.542447i
$902$	−1.47297	+	2.55126i	−0.0490445	+	0.0849476i
$903$	52.3115	+	10.5719i	1.74082	+	0.351810i
$904$	7.79299	+	13.4979i	0.259191	+	0.448932i
$905$		−	4.86189i		−	0.161615i
$906$	0.0260958	+	73.9612i	0.000866977	+	2.45720i
$907$	−54.0819			−1.79576			−0.897880	−	0.440241i	$-0.854893\pi$
$907$	−54.0819			−1.79576			−0.897880	+	0.440241i	$0.854893\pi$
$908$	38.6459	−	66.9367i	1.28251	−	2.22137i
$909$	16.2932	+	28.1747i	0.540410	+	0.934494i
$910$	−6.07621	−	18.1026i	−0.201424	−	0.600097i
$911$	25.6198	+	14.7916i	0.848822	+	0.490068i	0.860253	−	0.509867i	$-0.170305\pi$
$911$	25.6198	+	14.7916i	0.848822	+	0.490068i	−0.0114310	+	0.999935i	$0.503639\pi$
$912$	10.9521	+	6.31807i	0.362662	+	0.209212i
$913$	−14.8265	−	8.56008i	−0.490686	−	0.283297i
$914$	−16.7045	−	9.64433i	−0.552535	−	0.319006i
$915$	0.00394425	+	11.1788i	0.000130393	+	0.369561i
$916$	−15.1622	−	8.75391i	−0.500974	−	0.289237i
$917$	−15.7048	+	17.7851i	−0.518618	+	0.587316i
$918$	−48.2175	−	27.7704i	−1.59142	−	0.916560i
$919$	26.3746	−	45.6822i	0.870019	−	1.50692i	0.00804249	−	0.999968i	$-0.497440\pi$
$919$	26.3746	−	45.6822i	0.870019	−	1.50692i	0.861976	−	0.506949i	$-0.169227\pi$
$920$	−3.91278			−0.129001
$921$	−44.4869	−	25.6636i	−1.46589	−	0.845644i
$922$			17.8634i			0.588300i
$923$	−2.25090	−	3.89867i	−0.0740892	−	0.128326i
$924$	4.19485	−	20.7568i	0.138000	−	0.682850i
$925$	−1.70041	+	2.94520i	−0.0559093	+	0.0968377i
$926$	5.65510	+	3.26497i	0.185838	+	0.107294i
$927$	−30.1789	+	17.4522i	−0.991204	+	0.573205i
$928$	−20.8985	−	36.1972i	−0.686026	−	1.18823i
$929$	−5.00434	−	8.66777i	−0.164187	−	0.284380i	0.772179	−	0.635405i	$-0.219167\pi$
$929$	−5.00434	−	8.66777i	−0.164187	−	0.284380i	−0.936366	+	0.351024i	$0.885833\pi$
$930$	−14.5643	+	25.2467i	−0.477582	+	0.827871i
$931$	9.07647	−	21.4964i	0.297469	−	0.704517i
$932$	48.5560	−	28.0338i	1.59051	−	0.918279i
$933$	1.92447	+	3.33057i	0.0630045	+	0.109038i
$934$			63.4685i			2.07675i
$935$	7.40473	−	4.27513i	0.242161	−	0.139812i
$936$	7.31298	−	12.6871i	0.239032	−	0.414692i
$937$		−	11.9255i		−	0.389590i	−0.980844	−	0.194795i	$-0.937596\pi$
$937$		−	11.9255i		−	0.389590i	0.980844	−	0.194795i	$-0.0624042\pi$
$938$	9.10986	+	8.04429i	0.297447	+	0.262655i
$939$	0.0166860	+	47.2917i	0.000544527	+	1.54331i
$940$	30.8776			1.00712
$941$	−12.5261	+	21.6959i	−0.408339	+	0.707265i	−0.994704	−	0.102783i	$-0.967225\pi$
$941$	−12.5261	+	21.6959i	−0.408339	+	0.707265i	0.586364	+	0.810047i	$0.300559\pi$
$942$	−10.6468	+	18.4558i	−0.346891	+	0.601322i
$943$	−1.82798	+	1.05538i	−0.0595272	+	0.0343680i
$944$	−23.8962			−0.777754
$945$	9.08881	−	10.3147i	0.295659	−	0.335538i
$946$	−43.4848			−1.41381
$947$	8.37805	−	4.83707i	0.272250	−	0.157184i	−0.357660	−	0.933852i	$-0.616425\pi$
$947$	8.37805	−	4.83707i	0.272250	−	0.157184i	0.629910	+	0.776668i	$0.283092\pi$
$948$	−31.5452	+	54.6824i	−1.02454	+	1.77600i
$949$	−5.17372	+	8.96115i	−0.167946	+	0.290891i
$950$	7.20850			0.233875
$951$	0.00924534	+	26.2032i	0.000299801	+	0.849698i
$952$	−3.80238	+	18.7807i	−0.123236	+	0.608687i
$953$		−	26.6999i		−	0.864895i	−0.901659	−	0.432447i	$-0.857650\pi$
$953$		−	26.6999i		−	0.864895i	0.901659	−	0.432447i	$-0.142350\pi$
$954$	−42.6628	+	0.0301056i	−1.38126	+	0.000974703i
$955$	−0.931482	+	0.537791i	−0.0301421	+	0.0174025i
$956$		−	79.3445i		−	2.56618i
$957$	8.16343	+	14.1280i	0.263886	+	0.456692i
$958$	1.49112	−	0.860900i	0.0481760	−	0.0278144i
$959$	−9.00099	−	7.94815i	−0.290657	−	0.256659i
$960$	10.5473	−	18.2834i	0.340413	−	0.590093i
$961$	14.7771	+	25.5947i	0.476680	+	0.825635i
$962$	−12.2724	−	21.2564i	−0.395678	−	0.685335i
$963$	0.00955465	+	13.5400i	0.000307894	+	0.436319i
$964$	9.98288	+	5.76362i	0.321527	+	0.185634i
$965$	−4.32095	+	7.48411i	−0.139096	+	0.240922i
$966$	17.5412	−	19.8789i	0.564379	−	0.639593i
$967$	−1.97863	−	3.42710i	−0.0636286	−	0.110208i	0.832456	−	0.554091i	$-0.186934\pi$
$967$	−1.97863	−	3.42710i	−0.0636286	−	0.110208i	−0.896085	+	0.443883i	$0.853601\pi$
$968$		−	11.7278i		−	0.376945i
$969$	24.7655	+	14.2867i	0.795582	+	0.458955i
$970$	7.20911			0.231471
$971$	−15.7464	+	27.2736i	−0.505327	+	0.875251i	0.494654	+	0.869090i	$0.335295\pi$
$971$	−15.7464	+	27.2736i	−0.505327	+	0.875251i	−0.999981	+	0.00616165i	$0.998039\pi$
$972$	41.7198	−	0.0736004i	1.33816	−	0.00236073i
$973$	−10.8468	+	53.5744i	−0.347732	+	1.71752i
$974$	−18.0741	−	10.4351i	−0.579130	−	0.334361i
$975$	0.00203963	+	5.78073i	6.53203e−5	+	0.185132i
$976$	−12.2403	−	7.06696i	−0.391804	−	0.226208i
$977$	12.1168	+	6.99563i	0.387650	+	0.223810i	0.681142	−	0.732152i	$-0.261484\pi$
$977$	12.1168	+	6.99563i	0.387650	+	0.223810i	−0.293491	+	0.955962i	$0.594817\pi$
$978$	47.1948	+	27.2257i	1.50912	+	0.870583i
$979$	16.0328	+	9.25654i	0.512410	+	0.295840i
$980$	−17.2589	−	7.28727i	−0.551316	−	0.232783i
$981$	−9.61322	+	16.6778i	−0.306927	+	0.532480i
$982$	13.8079	−	23.9161i	0.440629	−	0.763192i
$983$	−2.02425			−0.0645635			−0.0322818	−	0.999479i	$-0.510277\pi$
$983$	−2.02425			−0.0645635			−0.0322818	+	0.999479i	$0.510277\pi$
$984$	0.000705192		1.99866i	2.24807e−5		0.0637150i
$985$		−	2.66589i		−	0.0849424i
$986$	−29.2126	−	50.5977i	−0.930319	−	1.61136i
$987$	−34.9814	+	39.6433i	−1.11347	+	1.26186i
$988$	−14.8876	+	25.7861i	−0.473638	+	0.820364i
$989$	−26.9827	−	15.5784i	−0.857999	−	0.495366i
$990$	−5.59393	+	9.70477i	−0.177787	+	0.308438i
$991$	−12.3884	−	21.4573i	−0.393529	−	0.681612i	0.599383	−	0.800462i	$-0.295413\pi$
$991$	−12.3884	−	21.4573i	−0.393529	−	0.681612i	−0.992912	+	0.118850i	$0.962079\pi$
$992$	−29.8067	−	51.6267i	−0.946364	−	1.63915i
$993$	39.4225	−	0.0139095i	1.25104	−	0.000441405i
$994$	−7.56383	−	1.53139i	−0.239910	−	0.0485727i
$995$	−17.1929	+	9.92633i	−0.545052	+	0.314686i
$996$	−45.9626	+	0.0162171i	−1.45638	+	0.000513857i
$997$		−	12.2634i		−	0.388387i	−0.980963	−	0.194193i	$-0.937791\pi$
$997$		−	12.2634i		−	0.388387i	0.980963	−	0.194193i	$-0.0622089\pi$
$998$	−63.0721	+	36.4147i	−1.99651	+	1.15269i
$999$	8.81941	−	15.3131i	0.279034	−	0.484484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.13	yes	30
3.2	odd	2		945.2.be.b.656.3		30
7.3	odd	6		315.2.t.b.101.13	✓	30
9.4	even	3		945.2.t.b.341.13		30
9.5	odd	6		315.2.t.b.131.3	yes	30
21.17	even	6		945.2.t.b.521.3		30
63.31	odd	6		945.2.be.b.206.3		30
63.59	even	6	inner	315.2.be.b.311.13	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.13	✓	30	7.3	odd	6
315.2.t.b.131.3	yes	30	9.5	odd	6
315.2.be.b.236.13	yes	30	1.1	even	1	trivial
315.2.be.b.311.13	yes	30	63.59	even	6	inner
945.2.t.b.341.13		30	9.4	even	3
945.2.t.b.521.3		30	21.17	even	6
945.2.be.b.206.3		30	63.31	odd	6
945.2.be.b.656.3		30	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87276 - 1.08124i) q^{2} +(0.865496 - 1.50031i) q^{3} +(1.33817 - 2.31777i) q^{4} +1.00000 q^{5} +(-0.00132154 - 3.74553i) q^{6} +(-1.75124 + 1.98322i) q^{7} -1.46255i q^{8} +(-1.50183 - 2.59702i) q^{9} +O(q^{10})\)	\(q+(1.87276 - 1.08124i) q^{2} +(0.865496 - 1.50031i) q^{3} +(1.33817 - 2.31777i) q^{4} +1.00000 q^{5} +(-0.00132154 - 3.74553i) q^{6} +(-1.75124 + 1.98322i) q^{7} -1.46255i q^{8} +(-1.50183 - 2.59702i) q^{9} +(1.87276 - 1.08124i) q^{10} -1.72665i q^{11} +(-2.31919 - 4.01368i) q^{12} +(-2.89037 + 1.66875i) q^{13} +(-1.13533 + 5.60762i) q^{14} +(0.865496 - 1.50031i) q^{15} +(1.09496 + 1.89652i) q^{16} +(2.47597 + 4.28850i) q^{17} +(-5.62058 - 3.23976i) q^{18} +(2.88684 + 1.66672i) q^{19} +(1.33817 - 2.31777i) q^{20} +(1.45974 + 4.34387i) q^{21} +(-1.86692 - 3.23361i) q^{22} -2.67531i q^{23} +(-2.19428 - 1.26584i) q^{24} +1.00000 q^{25} +(-3.60865 + 6.25037i) q^{26} +(-5.19615 + 0.00550010i) q^{27} +(2.25319 + 6.71285i) q^{28} +(-4.72502 - 2.72799i) q^{29} +(-0.00132154 - 3.74553i) q^{30} +(-6.73911 - 3.89083i) q^{31} +(6.63441 + 3.83038i) q^{32} +(-2.59050 - 1.49441i) q^{33} +(9.27381 + 5.35423i) q^{34} +(-1.75124 + 1.98322i) q^{35} +(-8.02899 + 0.00566577i) q^{36} +(-1.70041 + 2.94520i) q^{37} +7.20850 q^{38} +(0.00203963 + 5.78073i) q^{39} -1.46255i q^{40} +(-0.394491 - 0.683278i) q^{41} +(7.43051 + 6.55671i) q^{42} +(5.82305 - 10.0858i) q^{43} +(-4.00198 - 2.31054i) q^{44} +(-1.50183 - 2.59702i) q^{45} +(-2.89265 - 5.01022i) q^{46} +(5.76865 + 9.99159i) q^{47} +(3.79304 - 0.00133830i) q^{48} +(-0.866300 - 6.94619i) q^{49} +(1.87276 - 1.08124i) q^{50} +(8.57700 - 0.00302624i) q^{51} +8.93228i q^{52} +(5.69516 - 3.28810i) q^{53} +(-9.72522 + 5.62859i) q^{54} -1.72665i q^{55} +(2.90056 + 2.56129i) q^{56} +(4.99914 - 2.88861i) q^{57} -11.7985 q^{58} +(-5.45596 + 9.45000i) q^{59} +(-2.31919 - 4.01368i) q^{60} +(-5.58942 + 3.22705i) q^{61} -16.8277 q^{62} +(7.78052 + 1.56955i) q^{63} +12.1864 q^{64} +(-2.89037 + 1.66875i) q^{65} +(-6.46722 + 0.00228184i) q^{66} +(1.06208 - 1.83958i) q^{67} +13.2530 q^{68} +(-4.01378 - 2.31547i) q^{69} +(-1.13533 + 5.60762i) q^{70} +1.34885i q^{71} +(-3.79828 + 2.19651i) q^{72} +(2.68498 - 1.55018i) q^{73} +7.35423i q^{74} +(0.865496 - 1.50031i) q^{75} +(7.72615 - 4.46069i) q^{76} +(3.42432 + 3.02378i) q^{77} +(6.25419 + 10.8237i) q^{78} +(-6.80923 - 11.7939i) q^{79} +(1.09496 + 1.89652i) q^{80} +(-4.48900 + 7.80057i) q^{81} +(-1.47758 - 0.853079i) q^{82} +(4.95763 - 8.58686i) q^{83} +(12.0215 + 2.42947i) q^{84} +(2.47597 + 4.28850i) q^{85} -25.1845i q^{86} +(-8.18230 + 4.72790i) q^{87} -2.52532 q^{88} +(-5.36098 + 9.28549i) q^{89} +(-5.62058 - 3.23976i) q^{90} +(1.75223 - 8.65462i) q^{91} +(-6.20075 - 3.58001i) q^{92} +(-11.6701 + 6.74323i) q^{93} +(21.6066 + 12.4746i) q^{94} +(2.88684 + 1.66672i) q^{95} +(11.4888 - 6.63847i) q^{96} +(2.88709 + 1.66686i) q^{97} +(-9.13288 - 12.0719i) q^{98} +(-4.48414 + 2.59314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

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