LMFDB - Embedded newform 315.2.bh.c.169.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.11
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03279 - 0.596282i) q^{2} +(-0.463032 + 1.66901i) q^{3} +(-0.288895 - 0.500381i) q^{4} +(1.52125 - 1.63884i) q^{5} +(1.47342 - 1.44764i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.07418i q^{8} +(-2.57120 - 1.54561i) q^{9} +O(q^{10})$	\(q+(-1.03279 - 0.596282i) q^{2} +(-0.463032 + 1.66901i) q^{3} +(-0.288895 - 0.500381i) q^{4} +(1.52125 - 1.63884i) q^{5} +(1.47342 - 1.44764i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.07418i q^{8} +(-2.57120 - 1.54561i) q^{9} +(-2.54835 + 0.785481i) q^{10} +(2.02111 - 3.50067i) q^{11} +(0.968910 - 0.250477i) q^{12} +(-2.53546 + 1.46385i) q^{13} +(-0.596282 - 1.03279i) q^{14} +(2.03085 + 3.29782i) q^{15} +(1.25529 - 2.17422i) q^{16} -3.25867i q^{17} +(1.73389 + 3.12946i) q^{18} +3.90229 q^{19} +(-1.25953 - 0.287754i) q^{20} +(-1.23550 + 1.21389i) q^{21} +(-4.17478 + 2.41031i) q^{22} +(7.50189 - 4.33122i) q^{23} +(-5.13084 - 1.42345i) q^{24} +(-0.371578 - 4.98617i) q^{25} +3.49147 q^{26} +(3.77020 - 3.57570i) q^{27} -0.577790i q^{28} +(3.27941 - 5.68010i) q^{29} +(-0.131010 - 4.61692i) q^{30} +(1.72072 + 2.98038i) q^{31} +(2.73173 - 1.57717i) q^{32} +(4.90682 + 4.99419i) q^{33} +(-1.94309 + 3.36553i) q^{34} +(2.13686 - 0.658649i) q^{35} +(-0.0305878 + 1.73310i) q^{36} +4.39850i q^{37} +(-4.03025 - 2.32686i) q^{38} +(-1.26918 - 4.90952i) q^{39} +(5.03808 + 4.67661i) q^{40} +(3.10915 + 5.38521i) q^{41} +(1.99984 - 0.516986i) q^{42} +(-5.49353 - 3.17169i) q^{43} -2.33556 q^{44} +(-6.44446 + 1.86251i) q^{45} -10.3305 q^{46} +(-9.71907 - 5.61131i) q^{47} +(3.04757 + 3.10183i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.58940 + 5.37124i) q^{50} +(5.43877 + 1.50887i) q^{51} +(1.46496 + 0.845798i) q^{52} +2.38454i q^{53} +(-6.02595 + 1.44485i) q^{54} +(-2.66241 - 8.63768i) q^{55} +(-1.53709 + 2.66232i) q^{56} +(-1.80689 + 6.51296i) q^{57} +(-6.77389 + 3.91091i) q^{58} +(0.624888 + 1.08234i) q^{59} +(1.06347 - 1.96892i) q^{60} +(2.49109 - 4.31469i) q^{61} -4.10414i q^{62} +(-1.45392 - 2.62414i) q^{63} -8.78290 q^{64} +(-1.45807 + 6.38209i) q^{65} +(-2.08978 - 8.08380i) q^{66} +(-8.47762 + 4.89455i) q^{67} +(-1.63058 + 0.941415i) q^{68} +(3.75524 + 14.5262i) q^{69} +(-2.59967 - 0.593927i) q^{70} -9.24009 q^{71} +(4.75149 - 7.90434i) q^{72} +13.1780i q^{73} +(2.62274 - 4.54273i) q^{74} +(8.49404 + 1.68859i) q^{75} +(-1.12735 - 1.95263i) q^{76} +(3.50067 - 2.02111i) q^{77} +(-1.61666 + 5.82730i) q^{78} +(2.12371 - 3.67837i) q^{79} +(-1.65359 - 5.36476i) q^{80} +(4.22216 + 7.94817i) q^{81} -7.41572i q^{82} +(10.5572 + 6.09519i) q^{83} +(0.964339 + 0.267536i) q^{84} +(-5.34044 - 4.95727i) q^{85} +(3.78245 + 6.55139i) q^{86} +(7.96169 + 8.10344i) q^{87} +(10.7617 + 6.21327i) q^{88} +4.60378 q^{89} +(7.76636 + 1.91913i) q^{90} -2.92770 q^{91} +(-4.33452 - 2.50253i) q^{92} +(-5.77103 + 1.49189i) q^{93} +(6.69185 + 11.5906i) q^{94} +(5.93637 - 6.39521i) q^{95} +(1.36743 + 5.28958i) q^{96} +(1.37170 + 0.791954i) q^{97} -1.19256i q^{98} +(-10.6074 + 5.87707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.03279	−	0.596282i	−0.730294	−	0.421635i	0.0882360	−	0.996100i	$-0.471877\pi$
$2$	−1.03279	−	0.596282i	−0.730294	−	0.421635i	−0.818530	+	0.574464i	$0.805210\pi$
$3$	−0.463032	+	1.66901i	−0.267332	+	0.963605i
$3$	−0.463032	+	1.66901i	−0.267332	+	0.963605i
$4$	−0.288895	−	0.500381i	−0.144448	−	0.250191i
$5$	1.52125	−	1.63884i	0.680325	−	0.732911i
$5$	1.52125	−	1.63884i	0.680325	−	0.732911i
$6$	1.47342	−	1.44764i	0.601520	−	0.590998i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			3.07418i			1.08689i
$9$	−2.57120	−	1.54561i	−0.857067	−	0.515204i
$10$	−2.54835	+	0.785481i	−0.805858	+	0.248391i
$11$	2.02111	−	3.50067i	0.609389	−	1.05549i	−0.381953	−	0.924182i	$-0.624748\pi$
$11$	2.02111	−	3.50067i	0.609389	−	1.05549i	0.991341	−	0.131310i	$-0.0419184\pi$
$12$	0.968910	−	0.250477i	0.279700	−	0.0723064i
$13$	−2.53546	+	1.46385i	−0.703210	+	0.405999i	−0.808542	−	0.588438i	$-0.799743\pi$
$13$	−2.53546	+	1.46385i	−0.703210	+	0.405999i	0.105332	+	0.994437i	$0.466410\pi$
$14$	−0.596282	−	1.03279i	−0.159363	−	0.276025i
$15$	2.03085	+	3.29782i	0.524363	+	0.851495i
$16$	1.25529	−	2.17422i	0.313822	−	0.543556i
$17$		−	3.25867i		−	0.790345i	−0.918607	−	0.395172i	$-0.870685\pi$
$17$		−	3.25867i		−	0.790345i	0.918607	−	0.395172i	$-0.129315\pi$
$18$	1.73389	+	3.12946i	0.408682	+	0.737620i
$19$	3.90229			0.895246			0.447623	−	0.894222i	$-0.352271\pi$
$19$	3.90229			0.895246			0.447623	+	0.894222i	$0.352271\pi$
$20$	−1.25953	−	0.287754i	−0.281639	−	0.0643437i
$21$	−1.23550	+	1.21389i	−0.269609	+	0.264893i
$22$	−4.17478	+	2.41031i	−0.890065	+	0.513879i
$23$	7.50189	−	4.33122i	1.56425	−	0.903121i	0.567433	−	0.823420i	$-0.307937\pi$
$23$	7.50189	−	4.33122i	1.56425	−	0.903121i	0.996819	−	0.0797013i	$-0.0253966\pi$
$24$	−5.13084	−	1.42345i	−1.04733	−	0.290560i
$25$	−0.371578	−	4.98617i	−0.0743156	−	0.997235i
$26$	3.49147			0.684733
$27$	3.77020	−	3.57570i	0.725575	−	0.688143i
$28$		−	0.577790i		−	0.109192i
$29$	3.27941	−	5.68010i	0.608971	−	1.05477i	−0.382439	−	0.923981i	$-0.624916\pi$
$29$	3.27941	−	5.68010i	0.608971	−	1.05477i	0.991410	−	0.130788i	$-0.0417507\pi$
$30$	−0.131010	−	4.61692i	−0.0239190	−	0.842931i
$31$	1.72072	+	2.98038i	0.309051	+	0.535291i	0.978155	−	0.207877i	$-0.0666554\pi$
$31$	1.72072	+	2.98038i	0.309051	+	0.535291i	−0.669104	+	0.743169i	$0.733322\pi$
$32$	2.73173	−	1.57717i	0.482907	−	0.278807i
$33$	4.90682	+	4.99419i	0.854168	+	0.869376i
$34$	−1.94309	+	3.36553i	−0.333237	+	0.577184i
$35$	2.13686	−	0.658649i	0.361196	−	0.111332i
$36$	−0.0305878	+	1.73310i	−0.00509797	+	0.288850i
$37$			4.39850i			0.723108i	0.932351	+	0.361554i	$0.117754\pi$
$37$			4.39850i			0.723108i	−0.932351	+	0.361554i	$0.882246\pi$
$38$	−4.03025	−	2.32686i	−0.653792	−	0.377467i
$39$	−1.26918	−	4.90952i	−0.203232	−	0.786153i
$40$	5.03808	+	4.67661i	0.796591	+	0.739436i
$41$	3.10915	+	5.38521i	0.485568	+	0.841028i	0.999862	−	0.0165856i	$-0.00527959\pi$
$41$	3.10915	+	5.38521i	0.485568	+	0.841028i	−0.514295	+	0.857613i	$0.671946\pi$
$42$	1.99984	−	0.516986i	0.308582	−	0.0797727i
$43$	−5.49353	−	3.17169i	−0.837756	−	0.483678i	0.0187451	−	0.999824i	$-0.494033\pi$
$43$	−5.49353	−	3.17169i	−0.837756	−	0.483678i	−0.856501	+	0.516146i	$0.827366\pi$
$44$	−2.33556			−0.352099
$45$	−6.44446	+	1.86251i	−0.960683	+	0.277647i
$46$	−10.3305			−1.52315
$47$	−9.71907	−	5.61131i	−1.41767	−	0.818493i	−0.421578	−	0.906792i	$-0.638524\pi$
$47$	−9.71907	−	5.61131i	−1.41767	−	0.818493i	−0.996094	+	0.0882989i	$0.971857\pi$
$48$	3.04757	+	3.10183i	0.439878	+	0.447710i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−2.58940	+	5.37124i	−0.366197	+	0.759608i
$51$	5.43877	+	1.50887i	0.761580	+	0.211284i
$52$	1.46496	+	0.845798i	0.203154	+	0.117291i
$53$			2.38454i			0.327542i	0.986498	+	0.163771i	$0.0523659\pi$
$53$			2.38454i			0.327542i	−0.986498	+	0.163771i	$0.947634\pi$
$54$	−6.02595	+	1.44485i	−0.820028	+	0.196619i
$55$	−2.66241	−	8.63768i	−0.358999	−	1.16470i
$56$	−1.53709	+	2.66232i	−0.205402	+	0.355767i
$57$	−1.80689	+	6.51296i	−0.239328	+	0.862663i
$58$	−6.77389	+	3.91091i	−0.889455	+	0.513527i
$59$	0.624888	+	1.08234i	0.0813535	+	0.140908i	0.903832	−	0.427888i	$-0.140742\pi$
$59$	0.624888	+	1.08234i	0.0813535	+	0.140908i	−0.822478	+	0.568797i	$0.807409\pi$
$60$	1.06347	−	1.96892i	0.137293	−	0.254187i
$61$	2.49109	−	4.31469i	0.318951	−	0.552440i	−0.661318	−	0.750105i	$-0.730003\pi$
$61$	2.49109	−	4.31469i	0.318951	−	0.552440i	0.980270	+	0.197666i	$0.0633360\pi$
$62$		−	4.10414i		−	0.521227i
$63$	−1.45392	−	2.62414i	−0.183177	−	0.330611i
$64$	−8.78290			−1.09786
$65$	−1.45807	+	6.38209i	−0.180851	+	0.791601i
$66$	−2.08978	−	8.08380i	−0.257234	−	0.995047i
$67$	−8.47762	+	4.89455i	−1.03571	+	0.597965i	−0.918614	−	0.395156i	$-0.870691\pi$
$67$	−8.47762	+	4.89455i	−1.03571	+	0.597965i	−0.117092	+	0.993121i	$0.537357\pi$
$68$	−1.63058	+	0.941415i	−0.197737	+	0.114163i
$69$	3.75524	+	14.5262i	0.452077	+	1.74875i
$70$	−2.59967	−	0.593927i	−0.310720	−	0.0709878i
$71$	−9.24009			−1.09660			−0.548298	−	0.836283i	$-0.684724\pi$
$71$	−9.24009			−1.09660			−0.548298	+	0.836283i	$0.684724\pi$
$72$	4.75149	−	7.90434i	0.559969	−	0.931535i
$73$			13.1780i			1.54237i	0.636612	+	0.771184i	$0.280335\pi$
$73$			13.1780i			1.54237i	−0.636612	+	0.771184i	$0.719665\pi$
$74$	2.62274	−	4.54273i	0.304888	−	0.528081i
$75$	8.49404	+	1.68859i	0.980807	+	0.194982i
$76$	−1.12735	−	1.95263i	−0.129316	−	0.223982i
$77$	3.50067	−	2.02111i	0.398938	−	0.230327i
$78$	−1.61666	+	5.82730i	−0.183051	+	0.659812i
$79$	2.12371	−	3.67837i	0.238936	−	0.413849i	−0.721473	−	0.692442i	$-0.756535\pi$
$79$	2.12371	−	3.67837i	0.238936	−	0.413849i	0.960409	+	0.278593i	$0.0898681\pi$
$80$	−1.65359	−	5.36476i	−0.184877	−	0.599798i
$81$	4.22216	+	7.94817i	0.469129	+	0.883130i
$82$		−	7.41572i		−	0.818930i
$83$	10.5572	+	6.09519i	1.15880	+	0.669034i	0.951016	−	0.309140i	$-0.100041\pi$
$83$	10.5572	+	6.09519i	1.15880	+	0.669034i	0.207785	+	0.978175i	$0.433375\pi$
$84$	0.964339	+	0.267536i	0.105218	+	0.0291905i
$85$	−5.34044	−	4.95727i	−0.579252	−	0.537691i
$86$	3.78245	+	6.55139i	0.407872	+	0.706454i
$87$	7.96169	+	8.10344i	0.853582	+	0.868780i
$88$	10.7617	+	6.21327i	1.14720	+	0.662337i
$89$	4.60378			0.487999			0.244000	−	0.969775i	$-0.421540\pi$
$89$	4.60378			0.487999			0.244000	+	0.969775i	$0.421540\pi$
$90$	7.76636	+	1.91913i	0.818646	+	0.202294i
$91$	−2.92770			−0.306906
$92$	−4.33452	−	2.50253i	−0.451905	−	0.260907i
$93$	−5.77103	+	1.49189i	−0.598428	+	0.154702i
$94$	6.69185	+	11.5906i	0.690211	+	1.19548i
$95$	5.93637	−	6.39521i	0.609058	−	0.656135i
$96$	1.36743	+	5.28958i	0.139563	+	0.539865i
$97$	1.37170	+	0.791954i	0.139276	+	0.0804108i	0.568019	−	0.823016i	$-0.307710\pi$
$97$	1.37170	+	0.791954i	0.139276	+	0.0804108i	−0.428743	+	0.903426i	$0.641043\pi$
$98$		−	1.19256i		−	0.120467i
$99$	−10.6074	+	5.87707i	−1.06608	+	0.590668i
$100$	−2.38764	+	1.62641i	−0.238764	+	0.162641i
$101$	−9.61034	+	16.6456i	−0.956264	+	1.65630i	−0.224817	+	0.974401i	$0.572178\pi$
$101$	−9.61034	+	16.6456i	−0.956264	+	1.65630i	−0.731448	+	0.681897i	$0.761155\pi$
$102$	−4.71740	−	4.80139i	−0.467092	−	0.475408i
$103$	13.3744	−	7.72170i	1.31782	−	0.760842i	0.334440	−	0.942417i	$-0.391453\pi$
$103$	13.3744	−	7.72170i	1.31782	−	0.760842i	0.983377	+	0.181575i	$0.0581196\pi$
$104$	−4.50014	−	7.79447i	−0.441275	−	0.764310i
$105$	0.109856	+	3.87143i	0.0107208	+	0.377812i
$106$	1.42186	−	2.46274i	0.138103	−	0.239202i
$107$		−	1.41993i		−	0.137270i	−0.997642	−	0.0686351i	$-0.978136\pi$
$107$		−	1.41993i		−	0.137270i	0.997642	−	0.0686351i	$-0.0218644\pi$
$108$	−2.87840	−	0.853533i	−0.276974	−	0.0821313i
$109$	4.94762			0.473896			0.236948	−	0.971522i	$-0.423853\pi$
$109$	4.94762			0.473896			0.236948	+	0.971522i	$0.423853\pi$
$110$	−2.40079	+	10.5085i	−0.228906	+	1.00194i
$111$	−7.34114	−	2.03665i	−0.696790	−	0.193310i
$112$	2.17422	−	1.25529i	0.205445	−	0.118614i
$113$	−10.7333	+	6.19686i	−1.00970	+	0.582952i	−0.911104	−	0.412176i	$-0.864769\pi$
$113$	−10.7333	+	6.19686i	−1.00970	+	0.582952i	−0.0985975	+	0.995127i	$0.531436\pi$
$114$	5.74970	−	5.64912i	0.538509	−	0.529088i
$115$	4.31411	−	18.8833i	0.402293	−	1.76087i
$116$	−3.78962			−0.351857
$117$	8.78173	+	0.154990i	0.811871	+	0.0143289i
$118$		−	1.49044i		−	0.137206i
$119$	1.62934	−	2.82210i	0.149361	−	0.258701i
$120$	−10.1381	+	6.24320i	−0.925478	+	0.569924i
$121$	−2.66980	−	4.62422i	−0.242709	−	0.420384i
$122$	−5.14555	+	2.97078i	−0.465856	+	0.268962i
$123$	−10.4276	+	2.69568i	−0.940226	+	0.243062i
$124$	0.994216	−	1.72203i	0.0892832	−	0.154643i
$125$	−8.73679	−	6.97628i	−0.781443	−	0.623977i
$126$	−0.0631335	+	3.57714i	−0.00562438	+	0.318677i
$127$			1.19904i			0.106398i	0.998584	+	0.0531989i	$0.0169417\pi$
$127$			1.19904i			0.106398i	−0.998584	+	0.0531989i	$0.983058\pi$
$128$	3.60743	+	2.08275i	0.318855	+	0.184091i
$129$	7.83727	−	7.70017i	0.690033	−	0.677962i
$130$	5.31141	−	5.72195i	0.465841	−	0.501848i
$131$	−6.09913	−	10.5640i	−0.532884	−	0.922981i	−0.999263	−	0.0383963i	$-0.987775\pi$
$131$	−6.09913	−	10.5640i	−0.532884	−	0.922981i	0.466379	−	0.884585i	$-0.345558\pi$
$132$	1.08144	−	3.89808i	0.0941272	−	0.339284i
$133$	3.37948	+	1.95114i	0.293038	+	0.169186i
$134$	11.6741			1.00849
$135$	−0.124565	−	11.6183i	−0.0107209	−	0.999943i
$136$	10.0178			0.859015
$137$	−8.99833	−	5.19519i	−0.768779	−	0.443855i	0.0636599	−	0.997972i	$-0.479723\pi$
$137$	−8.99833	−	5.19519i	−0.768779	−	0.443855i	−0.832439	+	0.554117i	$0.813056\pi$
$138$	4.78336	−	17.2417i	0.407187	−	1.46771i
$139$	2.85630	+	4.94726i	0.242268	+	0.419621i	0.961360	−	0.275294i	$-0.0887752\pi$
$139$	2.85630	+	4.94726i	0.242268	+	0.419621i	−0.719092	+	0.694915i	$0.755442\pi$
$140$	−0.946904	−	0.878965i	−0.0800280	−	0.0742861i
$141$	13.8656	−	13.6230i	1.16769	−	1.14727i
$142$	9.54308	+	5.50970i	0.800837	+	0.462364i
$143$			11.8344i			0.989644i
$144$	−6.58811	+	3.65018i	−0.549009	+	0.304182i
$145$	−4.31996	−	14.0153i	−0.358753	−	1.16391i
$146$	7.85781	−	13.6101i	0.650317	−	1.12638i
$147$	−1.67692	+	0.433508i	−0.138310	+	0.0357552i
$148$	2.20092	−	1.27070i	0.180915	−	0.104451i
$149$	2.66565	+	4.61704i	0.218378	+	0.378242i	0.954312	−	0.298811i	$-0.0965900\pi$
$149$	2.66565	+	4.61704i	0.218378	+	0.378242i	−0.735934	+	0.677053i	$0.763257\pi$
$150$	−7.76569	−	6.80880i	−0.634066	−	0.555937i
$151$	−5.64321	+	9.77432i	−0.459238	+	0.795423i	−0.998921	−	0.0464453i	$-0.985211\pi$
$151$	−5.64321	+	9.77432i	−0.459238	+	0.795423i	0.539683	+	0.841868i	$0.318544\pi$
$152$			11.9963i			0.973031i
$153$	−5.03665	+	8.37871i	−0.407189	+	0.677379i
$154$	−4.82062			−0.388456
$155$	7.50201	+	1.71392i	0.602576	+	0.137666i
$156$	−2.08997	+	2.05341i	−0.167332	+	0.164405i
$157$	−4.10414	+	2.36953i	−0.327546	+	0.189109i	−0.654751	−	0.755845i	$-0.727227\pi$
$157$	−4.10414	+	2.36953i	−0.327546	+	0.189109i	0.327205	+	0.944953i	$0.393893\pi$
$158$	−4.38670	+	2.53266i	−0.348987	+	0.201488i
$159$	−3.97983	−	1.10412i	−0.315621	−	0.0875625i
$160$	1.57094	−	6.87614i	0.124194	−	0.543607i
$161$	8.66243			0.682695
$162$	0.378742	−	10.7264i	0.0297568	−	0.842745i
$163$		−	15.2832i		−	1.19707i	−0.801097	−	0.598535i	$-0.795750\pi$
$163$		−	15.2832i		−	1.19707i	0.801097	−	0.598535i	$-0.204250\pi$
$164$	1.79644	−	3.11152i	0.140278	−	0.242969i
$165$	15.6492	−	0.444062i	1.21829	−	0.0345702i
$166$	−7.26891	−	12.5901i	−0.564177	−	0.977183i
$167$	4.96139	−	2.86446i	0.383924	−	0.221659i	−0.295600	−	0.955312i	$-0.595520\pi$
$167$	4.96139	−	2.86446i	0.383924	−	0.221659i	0.679524	+	0.733653i	$0.262186\pi$
$168$	−3.73172	−	3.79816i	−0.287908	−	0.293035i
$169$	−2.21429	+	3.83527i	−0.170330	+	0.295020i
$170$	2.55963	+	8.30423i	0.196314	+	0.636905i
$171$	−10.0336	−	6.03143i	−0.767286	−	0.461235i
$172$			3.66514i			0.279465i
$173$	−4.68882	−	2.70709i	−0.356484	−	0.205816i	0.311053	−	0.950393i	$-0.399318\pi$
$173$	−4.68882	−	2.70709i	−0.356484	−	0.205816i	−0.667538	+	0.744576i	$0.732652\pi$
$174$	−3.39082	−	13.1166i	−0.257057	−	0.994365i
$175$	2.17129	−	4.50394i	0.164134	−	0.340466i
$176$	−5.07416	−	8.78871i	−0.382479	−	0.662474i
$177$	−2.09578	+	0.541788i	−0.157528	+	0.0407233i
$178$	−4.75474	−	2.74515i	−0.356383	−	0.205758i
$179$	11.7867			0.880981			0.440491	−	0.897757i	$-0.354805\pi$
$179$	11.7867			0.880981			0.440491	+	0.897757i	$0.354805\pi$
$180$	2.79374	+	2.68661i	0.208233	+	0.200248i
$181$	−9.83846			−0.731287			−0.365643	−	0.930755i	$-0.619151\pi$
$181$	−9.83846			−0.731287			−0.365643	+	0.930755i	$0.619151\pi$
$182$	3.02370	+	1.74573i	0.224132	+	0.129402i
$183$	6.04782	+	6.15550i	0.447068	+	0.455028i
$184$	13.3149	+	23.0622i	0.981591	+	1.70016i
$185$	7.20842	+	6.69123i	0.529974	+	0.491949i
$186$	6.84986	+	1.90035i	0.502256	+	0.139340i
$187$	−11.4075	−	6.58615i	−0.834202	−	0.481627i
$188$			6.48432i			0.472917i
$189$	5.05294	−	1.21155i	0.367547	−	0.0881271i
$190$	−9.94438	+	3.06517i	−0.721441	+	0.222371i
$191$	−6.60131	+	11.4338i	−0.477654	+	0.827321i	−0.999672	−	0.0256132i	$-0.991846\pi$
$191$	−6.60131	+	11.4338i	−0.477654	+	0.827321i	0.522018	+	0.852935i	$0.325179\pi$
$192$	4.06677	−	14.6588i	0.293494	−	1.05791i
$193$	−3.63667	+	2.09963i	−0.261773	+	0.151135i	−0.625143	−	0.780510i	$-0.714959\pi$
$193$	−3.63667	+	2.09963i	−0.261773	+	0.151135i	0.363370	+	0.931645i	$0.381626\pi$
$194$	−0.944456	−	1.63585i	−0.0678080	−	0.117447i
$195$	−9.97666	−	5.38865i	−0.714443	−	0.385889i
$196$	0.288895	−	0.500381i	0.0206354	−	0.0357415i
$197$			15.2029i			1.08316i	0.840648	+	0.541581i	$0.182174\pi$
$197$			15.2029i			1.08316i	−0.840648	+	0.541581i	$0.817826\pi$
$198$	14.4596	+	0.255200i	1.02760	+	0.0181363i
$199$	12.6279			0.895166			0.447583	−	0.894242i	$-0.352285\pi$
$199$	12.6279			0.895166			0.447583	+	0.894242i	$0.352285\pi$
$200$	15.3284	−	1.14230i	1.08388	−	0.0807727i
$201$	−4.24366	−	16.4156i	−0.299325	−	1.15787i
$202$	19.8509	−	11.4609i	1.39671	−	0.806389i
$203$	5.68010	−	3.27941i	0.398665	−	0.230169i
$204$	−0.816222	−	3.15736i	−0.0571470	−	0.221060i
$205$	13.5553	+	3.09687i	0.946742	+	0.216295i
$206$	−18.4173			−1.28319
$207$	−25.9833	−	0.458583i	−1.80596	−	0.0318737i
$208$			7.35021i			0.509646i
$209$	7.88696	−	13.6606i	0.545553	−	0.944925i
$210$	2.19500	−	4.06388i	0.151470	−	0.280434i
$211$	−1.77656	−	3.07710i	−0.122304	−	0.211836i	0.798372	−	0.602164i	$-0.205695\pi$
$211$	−1.77656	−	3.07710i	−0.122304	−	0.211836i	−0.920676	+	0.390328i	$0.872362\pi$
$212$	1.19318	−	0.688883i	0.0819480	−	0.0473127i
$213$	4.27846	−	15.4218i	0.293155	−	1.05669i
$214$	−0.846681	+	1.46649i	−0.0578779	+	0.100248i
$215$	−13.5549	+	4.17806i	−0.924439	+	0.284941i
$216$	10.9923	+	11.5903i	0.747934	+	0.788618i
$217$			3.44144i			0.233620i
$218$	−5.10986	−	2.95018i	−0.346083	−	0.199811i
$219$	−21.9942	−	6.10184i	−1.48623	−	0.412324i
$220$	−3.55298	+	3.82760i	−0.239542	+	0.258057i
$221$	4.77021	+	8.26224i	0.320879	+	0.555779i
$222$	6.36745	+	6.48082i	0.427355	+	0.434964i
$223$	8.89357	+	5.13470i	0.595557	+	0.343845i	0.767292	−	0.641298i	$-0.221604\pi$
$223$	8.89357	+	5.13470i	0.595557	+	0.343845i	−0.171735	+	0.985143i	$0.554937\pi$
$224$	3.15434			0.210758
$225$	−6.75129	+	13.3948i	−0.450086	+	0.892985i
$226$	14.7803			0.983172
$227$	7.88525	+	4.55255i	0.523362	+	0.302163i	0.738309	−	0.674462i	$-0.235625\pi$
$227$	7.88525	+	4.55255i	0.523362	+	0.302163i	−0.214947	+	0.976626i	$0.568958\pi$
$228$	3.78096	−	0.977432i	0.250400	−	0.0647320i
$229$	14.6780	+	25.4231i	0.969951	+	1.68000i	0.695681	+	0.718351i	$0.255103\pi$
$229$	14.6780	+	25.4231i	0.969951	+	1.68000i	0.274270	+	0.961653i	$0.411564\pi$
$230$	−15.7153	+	16.9300i	−1.03624	+	1.11633i
$231$	1.75234	+	6.77850i	0.115295	+	0.445993i
$232$	17.4617	+	10.0815i	1.14641	+	0.661883i
$233$		−	16.2244i		−	1.06290i	−0.847091	−	0.531448i	$-0.821648\pi$
$233$		−	16.2244i		−	1.06290i	0.847091	−	0.531448i	$-0.178352\pi$
$234$	−8.97727	−	5.39646i	−0.586863	−	0.352778i
$235$	−23.9812	+	7.39176i	−1.56436	+	0.482185i
$236$	0.361054	−	0.625364i	0.0235026	−	0.0407077i
$237$	5.15590	+	5.24770i	0.334912	+	0.340875i
$238$	−3.36553	+	1.94309i	−0.218155	+	0.125952i
$239$	−8.20101	−	14.2046i	−0.530479	−	0.918817i	−0.999368	−	0.0355593i	$-0.988679\pi$
$239$	−8.20101	−	14.2046i	−0.530479	−	0.918817i	0.468889	−	0.883257i	$-0.344655\pi$
$240$	9.71951	−	0.275801i	0.627392	−	0.0178029i
$241$	−0.695013	+	1.20380i	−0.0447697	+	0.0775434i	−0.887542	−	0.460727i	$-0.847589\pi$
$241$	−0.695013	+	1.20380i	−0.0447697	+	0.0775434i	0.842772	+	0.538270i	$0.180922\pi$
$242$			6.36781i			0.409338i
$243$	−15.2206	+	3.36658i	−0.976401	+	0.215966i
$244$	−2.87865			−0.184287
$245$	2.17990	+	0.498025i	0.139269	+	0.0318176i
$246$	12.3769	+	3.43372i	0.789124	+	0.218926i
$247$	−9.89410	+	5.71236i	−0.629546	+	0.363469i
$248$	−9.16222	+	5.28981i	−0.581801	+	0.335903i
$249$	−15.0613	+	14.7978i	−0.954469	+	0.937772i
$250$	4.86345	+	12.4146i	0.307592	+	0.785170i
$251$	13.0190			0.821752			0.410876	−	0.911691i	$-0.365223\pi$
$251$	13.0190			0.821752			0.410876	+	0.911691i	$0.365223\pi$
$252$	−0.893040	+	1.48562i	−0.0562562	+	0.0935850i
$253$		−	35.0155i		−	2.20141i
$254$	0.714967	−	1.23836i	0.0448610	−	0.0777016i
$255$	10.7465	−	6.61788i	0.672974	−	0.414428i
$256$	6.29909	+	10.9103i	0.393693	+	0.681896i
$257$	−5.25151	+	3.03196i	−0.327580	+	0.189128i	−0.654766	−	0.755831i	$-0.727233\pi$
$257$	−5.25151	+	3.03196i	−0.327580	+	0.189128i	0.327186	+	0.944960i	$0.393900\pi$
$258$	−12.6857	+	3.27944i	−0.789780	+	0.204169i
$259$	−2.19925	+	3.80921i	−0.136655	+	0.236693i
$260$	3.61471	−	1.11417i	0.224175	−	0.0690977i
$261$	−17.2113	+	9.53599i	−1.06535	+	0.590263i
$262$			14.5472i			0.898730i
$263$	23.6992	+	13.6827i	1.46135	+	0.843713i	0.999074	−	0.0430209i	$-0.0136982\pi$
$263$	23.6992	+	13.6827i	1.46135	+	0.843713i	0.462280	+	0.886734i	$0.347032\pi$
$264$	−15.3530	+	15.0845i	−0.944914	+	0.928384i
$265$	3.90788	+	3.62750i	0.240059	+	0.222835i
$266$	−2.32686	−	4.03025i	−0.142669	−	0.247110i
$267$	−2.13170	+	7.68376i	−0.130458	+	0.470238i
$268$	4.89828	+	2.82803i	0.299210	+	0.172749i
$269$	−18.6269			−1.13570			−0.567850	−	0.823132i	$-0.692225\pi$
$269$	−18.6269			−1.13570			−0.567850	+	0.823132i	$0.692225\pi$
$270$	−6.79912	+	12.0735i	−0.413782	+	0.734772i
$271$	16.8341			1.02260			0.511300	−	0.859402i	$-0.329164\pi$
$271$	16.8341			1.02260			0.511300	+	0.859402i	$0.329164\pi$
$272$	−7.08509	−	4.09058i	−0.429597	−	0.248028i
$273$	1.35562	−	4.88636i	0.0820458	−	0.295736i
$274$	6.19559	+	10.7311i	0.374290	+	0.648288i
$275$	−18.2060	−	8.77685i	−1.09786	−	0.529264i
$276$	6.18378	−	6.07561i	0.372220	−	0.365709i
$277$	−15.3556	−	8.86557i	−0.922629	−	0.532680i	−0.0381563	−	0.999272i	$-0.512148\pi$
$277$	−15.3556	−	8.86557i	−0.922629	−	0.532680i	−0.884473	+	0.466592i	$0.845482\pi$
$278$		−	6.81265i		−	0.408595i
$279$	0.182187	−	10.3227i	0.0109073	−	0.618005i
$280$	2.02480	+	6.56910i	0.121005	+	0.392579i
$281$	14.6728	−	25.4141i	0.875307	−	1.51608i	0.0188725	−	0.999822i	$-0.493992\pi$
$281$	14.6728	−	25.4141i	0.875307	−	1.51608i	0.856435	−	0.516255i	$-0.172674\pi$
$282$	−22.4434	+	5.80194i	−1.33649	+	0.345500i
$283$	15.0805	−	8.70671i	0.896440	−	0.517560i	0.0203967	−	0.999792i	$-0.493507\pi$
$283$	15.0805	−	8.70671i	0.896440	−	0.517560i	0.876044	+	0.482232i	$0.160174\pi$
$284$	2.66942	+	4.62356i	0.158401	+	0.274358i
$285$	7.92496	+	12.8691i	0.469434	+	0.762297i
$286$	7.05665	−	12.2225i	0.417269	−	0.722730i
$287$			6.21830i			0.367055i
$288$	−9.46153	−	0.166988i	−0.557526	−	0.00983988i
$289$	6.38104			0.375355
$290$	−3.89546	+	17.0508i	−0.228749	+	1.00126i
$291$	−1.95692	+	1.92269i	−0.114717	+	0.112710i
$292$	6.59402	−	3.80706i	0.385886	−	0.222791i
$293$	5.29842	−	3.05904i	0.309537	−	0.178711i	−0.337182	−	0.941439i	$-0.609474\pi$
$293$	5.29842	−	3.05904i	0.309537	−	0.178711i	0.646719	+	0.762728i	$0.276141\pi$
$294$	1.99040	+	0.552196i	0.116083	+	0.0322047i
$295$	2.72439	+	0.622420i	0.158620	+	0.0362387i
$296$	−13.5218			−0.785937
$297$	−4.89735	−	20.4251i	−0.284173	−	1.18518i
$298$		−	6.35791i		−	0.368304i
$299$	−12.6805	+	21.9633i	−0.733332	+	1.27017i
$300$	−1.60895	−	4.73808i	−0.0928926	−	0.273553i
$301$	−3.17169	−	5.49353i	−0.182813	−	0.316642i
$302$	11.6565	−	6.72989i	0.670756	−	0.387261i
$303$	−23.3318	−	23.7472i	−1.34038	−	1.36424i
$304$	4.89850	−	8.48445i	0.280948	−	0.486616i
$305$	−3.28150	−	10.6462i	−0.187898	−	0.609601i
$306$	10.1979	−	5.65019i	0.582974	−	0.323000i
$307$		−	5.40835i		−	0.308671i	−0.988019	−	0.154335i	$-0.950676\pi$
$307$		−	5.40835i		−	0.308671i	0.988019	−	0.154335i	$-0.0493236\pi$
$308$	−2.02265	−	1.16778i	−0.115251	−	0.0665404i
$309$	6.69484	+	25.8974i	0.380856	+	1.47325i
$310$	−6.72602	−	6.24344i	−0.382012	−	0.354603i
$311$	9.87784	+	17.1089i	0.560121	+	0.970158i	0.997485	+	0.0708733i	$0.0225786\pi$
$311$	9.87784	+	17.1089i	0.560121	+	0.970158i	−0.437365	+	0.899284i	$0.644088\pi$
$312$	15.0928	−	3.90169i	0.854460	−	0.220890i
$313$	−11.4466	−	6.60869i	−0.647000	−	0.373545i	0.140306	−	0.990108i	$-0.455191\pi$
$313$	−11.4466	−	6.60869i	−0.647000	−	0.373545i	−0.787306	+	0.616563i	$0.788525\pi$
$314$	5.65163			0.318940
$315$	−6.51232	−	1.60924i	−0.366928	−	0.0906707i
$316$	−2.45412			−0.138055
$317$	−16.6240	−	9.59784i	−0.933694	−	0.539069i	−0.0457161	−	0.998954i	$-0.514557\pi$
$317$	−16.6240	−	9.59784i	−0.933694	−	0.539069i	−0.887978	+	0.459886i	$0.847890\pi$
$318$	3.45197	+	3.51343i	0.193577	+	0.197023i
$319$	−13.2561	−	22.9603i	−0.742200	−	1.28553i
$320$	−13.3610	+	14.3938i	−0.746904	+	0.804635i
$321$	2.36989	+	0.657475i	0.132274	+	0.0366967i
$322$	−8.94648	−	5.16525i	−0.498568	−	0.287848i
$323$		−	12.7163i		−	0.707553i
$324$	2.75735	−	4.40888i	0.153186	−	0.244938i
$325$	8.24113	+	12.0983i	0.457136	+	0.671094i
$326$	−9.11308	+	15.7843i	−0.504727	+	0.874212i
$327$	−2.29091	+	8.25764i	−0.126688	+	0.456648i
$328$	−16.5551	+	9.55809i	−0.914102	+	0.527757i
$329$	−5.61131	−	9.71907i	−0.309361	−	0.535830i
$330$	−16.4271	−	8.87270i	−0.904283	−	0.488426i
$331$	−17.2640	+	29.9021i	−0.948915	+	1.64357i	−0.201199	+	0.979550i	$0.564484\pi$
$331$	−17.2640	+	29.9021i	−0.948915	+	1.64357i	−0.747716	+	0.664019i	$0.768849\pi$
$332$		−	7.04348i		−	0.386561i
$333$	6.79837	−	11.3094i	0.372549	−	0.619752i
$334$	−6.83210			−0.373836
$335$	−4.87522	+	21.3393i	−0.266362	+	1.16589i
$336$	1.08836	+	4.21005i	0.0593747	+	0.229677i
$337$	8.37265	−	4.83395i	0.456087	−	0.263322i	−0.254310	−	0.967123i	$-0.581848\pi$
$337$	8.37265	−	4.83395i	0.456087	−	0.263322i	0.710398	+	0.703800i	$0.248515\pi$
$338$	4.57380	−	2.64069i	0.248782	−	0.143634i
$339$	−5.37278	−	20.7833i	−0.291809	−	1.12879i
$340$	−0.937697	+	4.10439i	−0.0508537	+	0.222592i
$341$	13.9111			0.753328
$342$	6.76615	+	12.2120i	0.365871	+	0.660352i
$343$			1.00000i			0.0539949i
$344$	9.75035	−	16.8881i	0.525704	−	0.910546i
$345$	29.5188	+	15.9439i	1.58924	+	0.858388i
$346$	3.22838	+	5.59172i	0.173559	+	0.300613i
$347$	−0.805161	+	0.464860i	−0.0432233	+	0.0249550i	−0.521456	−	0.853278i	$-0.674611\pi$
$347$	−0.805161	+	0.464860i	−0.0432233	+	0.0249550i	0.478233	+	0.878233i	$0.341278\pi$
$348$	1.75472	−	6.32492i	0.0940627	−	0.339051i
$349$	−15.8412	+	27.4378i	−0.847961	+	1.46871i	0.0350631	+	0.999385i	$0.488837\pi$
$349$	−15.8412	+	27.4378i	−0.847961	+	1.46871i	−0.883024	+	0.469327i	$0.844497\pi$
$350$	−4.92811	+	3.35693i	−0.263419	+	0.179435i
$351$	−4.32490	+	14.5850i	−0.230846	+	0.778492i
$352$		−	12.7505i		−	0.679606i
$353$	−7.15773	−	4.13252i	−0.380967	−	0.219952i	0.297272	−	0.954793i	$-0.403923\pi$
$353$	−7.15773	−	4.13252i	−0.380967	−	0.219952i	−0.678239	+	0.734841i	$0.737257\pi$
$354$	2.48756	+	0.690121i	0.132212	+	0.0366795i
$355$	−14.0565	+	15.1430i	−0.746042	+	0.803707i
$356$	−1.33001	−	2.30364i	−0.0704903	−	0.122093i
$357$	3.95567	+	4.02610i	0.209356	+	0.213084i
$358$	−12.1732	−	7.02821i	−0.643375	−	0.371453i
$359$	16.7567			0.884386			0.442193	−	0.896920i	$-0.354201\pi$
$359$	16.7567			0.884386			0.442193	+	0.896920i	$0.354201\pi$
$360$	−5.72570	−	19.8114i	−0.301771	−	1.04415i
$361$	−3.77216			−0.198535
$362$	10.1611	+	5.86650i	0.534054	+	0.308336i
$363$	8.95409	−	2.31476i	0.469968	−	0.121493i
$364$	0.845798	+	1.46496i	0.0443318	+	0.0767850i
$365$	21.5966	+	20.0471i	1.13042	+	1.04931i
$366$	−2.57572	−	9.96355i	−0.134635	−	0.520803i
$367$	3.47459	+	2.00605i	0.181372	+	0.104715i	0.587937	−	0.808907i	$-0.299940\pi$
$367$	3.47459	+	2.00605i	0.181372	+	0.104715i	−0.406565	+	0.913622i	$0.633274\pi$
$368$		−	21.7477i		−	1.13368i
$369$	0.329192	−	18.6520i	0.0171371	−	0.970984i
$370$	−3.45493	−	11.2089i	−0.179613	−	0.582722i
$371$	−1.19227	+	2.06508i	−0.0618997	+	0.107213i
$372$	2.41374	+	2.45672i	0.125147	+	0.127375i
$373$	−5.76983	+	3.33121i	−0.298750	+	0.172484i	−0.641881	−	0.766804i	$-0.721846\pi$
$373$	−5.76983	+	3.33121i	−0.298750	+	0.172484i	0.343131	+	0.939288i	$0.388513\pi$
$374$	7.85441	+	13.6042i	0.406142	+	0.703458i
$375$	15.6889	−	11.3516i	0.810172	−	0.586193i
$376$	17.2502	−	29.8782i	0.889610	−	1.54085i
$377$			19.2022i			0.988966i
$378$	−5.94105	−	1.76170i	−0.305575	−	0.0906121i
$379$	−16.9848			−0.872450			−0.436225	−	0.899838i	$-0.643685\pi$
$379$	−16.9848			−0.872450			−0.436225	+	0.899838i	$0.643685\pi$
$380$	−4.91503	−	1.12290i	−0.252136	−	0.0576035i
$381$	−2.00122	−	0.555195i	−0.102525	−	0.0284435i
$382$	13.6356	−	7.87249i	0.697656	−	0.402792i
$383$	7.54893	−	4.35838i	0.385732	−	0.222703i	−0.294577	−	0.955628i	$-0.595179\pi$
$383$	7.54893	−	4.35838i	0.385732	−	0.222703i	0.680309	+	0.732925i	$0.261845\pi$
$384$	−5.14650	+	5.05647i	−0.262631	+	0.258037i
$385$	2.01313	−	8.81166i	0.102599	−	0.449084i
$386$	5.00789			0.254895
$387$	9.22277	+	16.6459i	0.468820	+	0.846160i
$388$		−	0.915167i		−	0.0464606i
$389$	10.0602	−	17.4248i	0.510074	−	0.883474i	−0.489858	−	0.871802i	$-0.662951\pi$
$389$	10.0602	−	17.4248i	0.510074	−	0.883474i	0.999932	−	0.0116719i	$-0.00371538\pi$
$390$	7.09065	+	11.5143i	0.359049	+	0.583047i
$391$	−14.1140	−	24.4462i	−0.713777	−	1.23630i
$392$	−2.66232	+	1.53709i	−0.134467	+	0.0776348i
$393$	20.4555	−	5.28805i	1.03185	−	0.266747i
$394$	9.06522	−	15.7014i	0.456699	−	0.791026i
$395$	−2.79756	−	9.07615i	−0.140760	−	0.456671i
$396$	6.00519	+	3.60987i	0.301772	+	0.181403i
$397$			29.2717i			1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$397$			29.2717i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$398$	−13.0420	−	7.52978i	−0.653734	−	0.377434i
$399$	−4.82129	+	4.73695i	−0.241366	+	0.237144i
$400$	−11.3075	−	5.45119i	−0.565375	−	0.272560i
$401$	−2.19436	−	3.80075i	−0.109581	−	0.189800i	0.806019	−	0.591889i	$-0.201618\pi$
$401$	−2.19436	−	3.80075i	−0.109581	−	0.189800i	−0.915601	+	0.402089i	$0.868284\pi$
$402$	−5.40551	+	19.4843i	−0.269602	+	0.971788i
$403$	−8.72564	−	5.03775i	−0.434655	−	0.250948i
$404$	11.1055			0.552520
$405$	19.4487	+	5.17174i	0.966415	+	0.256986i
$406$	−7.82181			−0.388190
$407$	15.3977	+	8.88986i	0.763235	+	0.440654i
$408$	−4.63854	+	16.7198i	−0.229642	+	0.827751i
$409$	1.93960	+	3.35948i	0.0959069	+	0.166116i	0.909987	−	0.414637i	$-0.136092\pi$
$409$	1.93960	+	3.35948i	0.0959069	+	0.166116i	−0.814080	+	0.580753i	$0.802758\pi$
$410$	−12.1532	−	11.2812i	−0.600202	−	0.557138i
$411$	12.8373	−	12.6128i	0.633220	−	0.622142i
$412$	−7.72759	−	4.46152i	−0.380711	−	0.219804i
$413$			1.24978i			0.0614974i
$414$	26.5618	+	15.9670i	1.30544	+	0.784734i
$415$	26.0492	−	8.02918i	1.27870	−	0.394137i
$416$	−4.61747	+	7.99770i	−0.226390	+	0.392119i
$417$	−9.57959	+	2.47646i	−0.469115	+	0.121273i
$418$	−16.2912	+	9.40571i	−0.796827	+	0.460048i
$419$	−11.4391	−	19.8131i	−0.558835	−	0.967931i	−0.997594	−	0.0693264i	$-0.977915\pi$
$419$	−11.4391	−	19.8131i	−0.558835	−	0.967931i	0.438759	−	0.898605i	$-0.355418\pi$
$420$	1.90545	−	1.17341i	0.0929765	−	0.0572563i
$421$	−9.08277	+	15.7318i	−0.442667	+	0.766722i	−0.997886	−	0.0649822i	$-0.979301\pi$
$421$	−9.08277	+	15.7318i	−0.442667	+	0.766722i	0.555219	+	0.831704i	$0.312634\pi$
$422$			4.23733i			0.206270i
$423$	16.3168	+	29.4497i	0.793349	+	1.43189i
$424$	−7.33052			−0.356002
$425$	−16.2483	+	1.21085i	−0.788159	+	0.0587350i
$426$	−13.6145	+	13.3763i	−0.659625	+	0.648086i
$427$	4.31469	−	2.49109i	0.208803	−	0.120552i
$428$	−0.710508	+	0.410212i	−0.0343437	+	0.0198283i
$429$	−19.7518	−	5.47972i	−0.953625	−	0.264563i
$430$	16.4907	+	3.76750i	0.795253	+	0.181685i
$431$	−11.0896			−0.534165			−0.267083	−	0.963674i	$-0.586060\pi$
$431$	−11.0896			−0.534165			−0.267083	+	0.963674i	$0.586060\pi$
$432$	−3.04168	−	12.6858i	−0.146343	−	0.610345i
$433$			19.4639i			0.935376i	0.883894	+	0.467688i	$0.154913\pi$
$433$			19.4639i			0.935376i	−0.883894	+	0.467688i	$0.845087\pi$
$434$	2.05207	−	3.55429i	0.0985026	−	0.170611i
$435$	25.3920	−	0.720524i	1.21745	−	0.0345465i
$436$	−1.42934	−	2.47570i	−0.0684531	−	0.118564i
$437$	29.2745	−	16.9016i	1.40039	−	0.808516i
$438$	19.0770	+	19.4167i	0.911536	+	0.927766i
$439$	1.31143	−	2.27146i	0.0625911	−	0.108411i	−0.833032	−	0.553225i	$-0.813397\pi$
$439$	1.31143	−	2.27146i	0.0625911	−	0.108411i	0.895623	+	0.444814i	$0.146730\pi$
$440$	26.5538	−	8.18472i	1.26590	−	0.390191i
$441$	0.0529393	−	2.99953i	0.00252092	−	0.142835i
$442$		−	11.3776i		−	0.541175i
$443$	−10.2895	−	5.94064i	−0.488868	−	0.282248i	0.235236	−	0.971938i	$-0.424414\pi$
$443$	−10.2895	−	5.94064i	−0.488868	−	0.282248i	−0.724105	+	0.689690i	$0.757747\pi$
$444$	1.10172	+	4.26175i	0.0522854	+	0.202253i
$445$	7.00351	−	7.54484i	0.331998	−	0.357660i
$446$	−6.12346	−	10.6062i	−0.289954	−	0.502216i
$447$	−8.94017	+	2.31116i	−0.422856	+	0.109314i
$448$	−7.60622	−	4.39145i	−0.359360	−	0.207477i
$449$	−20.2366			−0.955022			−0.477511	−	0.878626i	$-0.658461\pi$
$449$	−20.2366			−0.955022			−0.477511	+	0.878626i	$0.658461\pi$
$450$	14.9597	−	9.80833i	0.705209	−	0.462369i
$451$	25.1358			1.18360
$452$	6.20158	+	3.58049i	0.291698	+	0.168412i
$453$	−13.7005	−	13.9444i	−0.643704	−	0.655165i
$454$	−5.42921	−	9.40367i	−0.254805	−	0.441336i
$455$	−4.45377	+	4.79802i	−0.208796	+	0.224935i
$456$	−20.0220	−	5.55469i	−0.937617	−	0.260122i
$457$	25.7674	+	14.8768i	1.20535	+	0.695908i	0.961740	−	0.273965i	$-0.0883353\pi$
$457$	25.7674	+	14.8768i	1.20535	+	0.695908i	0.243609	+	0.969873i	$0.421669\pi$
$458$		−	35.0090i		−	1.63586i
$459$	−11.6520	−	12.2858i	−0.543870	−	0.573454i
$460$	−10.6951	+	3.29658i	−0.498664	+	0.153704i
$461$	−6.40055	+	11.0861i	−0.298103	+	0.516330i	−0.975702	−	0.219102i	$-0.929687\pi$
$461$	−6.40055	+	11.0861i	−0.298103	+	0.516330i	0.677599	+	0.735432i	$0.263021\pi$
$462$	2.23210	−	8.04566i	0.103847	−	0.374318i
$463$	21.6269	−	12.4863i	1.00509	−	0.580287i	0.0953374	−	0.995445i	$-0.469607\pi$
$463$	21.6269	−	12.4863i	1.00509	−	0.580287i	0.909749	+	0.415158i	$0.136274\pi$
$464$	−8.23321	−	14.2603i	−0.382217	−	0.662020i
$465$	−6.33423	+	11.7273i	−0.293743	+	0.543842i
$466$	−9.67433	+	16.7564i	−0.448155	+	0.776227i
$467$			1.50301i			0.0695509i	0.999395	+	0.0347754i	$0.0110716\pi$
$467$			1.50301i			0.0695509i	−0.999395	+	0.0347754i	$0.988928\pi$
$468$	−2.45944	−	4.43899i	−0.113688	−	0.205192i
$469$	−9.78911			−0.452019
$470$	29.1751	+	6.66541i	1.34575	+	0.307453i
$471$	−2.05442	−	7.94703i	−0.0946626	−	0.366180i
$472$	−3.32730	+	1.92102i	−0.153151	+	0.0884220i
$473$	−22.2061	+	12.8207i	−1.02104	+	0.589496i
$474$	−2.19586	−	8.49415i	−0.100859	−	0.390149i
$475$	−1.45000	−	19.4575i	−0.0665308	−	0.892770i
$476$	−1.88283			−0.0862994
$477$	3.68558	−	6.13115i	0.168751	−	0.280726i
$478$			19.5605i			0.894674i
$479$	6.43125	−	11.1393i	0.293852	−	0.508966i	−0.680866	−	0.732408i	$-0.738396\pi$
$479$	6.43125	−	11.1393i	0.293852	−	0.508966i	0.974717	+	0.223443i	$0.0717295\pi$
$480$	10.7490	+	5.80579i	0.490621	+	0.264997i
$481$	−6.43873	−	11.1522i	−0.293581	−	0.508497i
$482$	1.43561	−	0.828848i	0.0653901	−	0.0377530i
$483$	−4.01099	+	14.4577i	−0.182506	+	0.657848i
$484$	−1.54258	+	2.67183i	−0.0701174	+	0.121447i
$485$	3.38459	−	1.04324i	0.153687	−	0.0473710i
$486$	17.7271	+	5.59879i	0.804118	+	0.253966i
$487$		−	15.1180i		−	0.685063i	−0.939506	−	0.342532i	$-0.888716\pi$
$487$		−	15.1180i		−	0.685063i	0.939506	−	0.342532i	$-0.111284\pi$
$488$	13.2641	+	7.65806i	0.600440	+	0.346664i
$489$	25.5078	+	7.07660i	1.15350	+	0.320015i
$490$	−1.95442	−	1.81419i	−0.0882917	−	0.0819568i
$491$	11.7851	+	20.4124i	0.531853	+	0.921197i	0.999309	+	0.0371799i	$0.0118375\pi$
$491$	11.7851	+	20.4124i	0.531853	+	0.921197i	−0.467456	+	0.884017i	$0.654829\pi$
$492$	4.36136	+	4.43901i	0.196625	+	0.200126i
$493$	−18.5096	−	10.6865i	−0.833631	−	0.481297i
$494$	13.6247			0.613005
$495$	−6.50493	+	26.3243i	−0.292375	+	1.18319i
$496$	8.64001			0.387948
$497$	−8.00215	−	4.62004i	−0.358945	−	0.207237i
$498$	24.3788	−	6.30226i	1.09244	−	0.282411i
$499$	−17.0342	−	29.5041i	−0.762554	−	1.32078i	−0.941530	−	0.336929i	$-0.890612\pi$
$499$	−17.0342	−	29.5041i	−0.762554	−	1.32078i	0.178976	−	0.983854i	$-0.442722\pi$
$500$	−0.966779	+	6.38714i	−0.0432357	+	0.285642i
$501$	2.48353	+	9.60696i	0.110956	+	0.429207i
$502$	−13.4459	−	7.76300i	−0.600120	−	0.346479i
$503$			5.01986i			0.223825i	0.993718	+	0.111912i	$0.0356976\pi$
$503$			5.01986i			0.223825i	−0.993718	+	0.111912i	$0.964302\pi$
$504$	8.06708	−	4.46961i	0.359337	−	0.199092i
$505$	12.6597	+	41.0719i	0.563348	+	1.82768i
$506$	−20.8791	+	36.1637i	−0.928190	+	1.60767i
$507$	−5.37582	−	5.47153i	−0.238748	−	0.242999i
$508$	0.599978	−	0.346397i	0.0266197	−	0.0153689i
$509$	1.83554	+	3.17925i	0.0813590	+	0.140918i	0.903834	−	0.427883i	$-0.140741\pi$
$509$	1.83554	+	3.17925i	0.0813590	+	0.140918i	−0.822475	+	0.568801i	$0.807407\pi$
$510$	−15.0451	+	0.426919i	−0.666206	+	0.0189043i
$511$	−6.58900	+	11.4125i	−0.291480	+	0.504859i
$512$		−	23.3551i		−	1.03216i
$513$	14.7124	−	13.9534i	0.649568	−	0.616058i
$514$	7.23161			0.318973
$515$	7.69120	−	33.6651i	0.338915	−	1.48346i
$516$	−6.11717	−	1.69708i	−0.269293	−	0.0747098i
$517$	−39.2867	+	22.6822i	−1.72783	+	0.997561i
$518$	4.54273	−	2.62274i	0.199596	−	0.115237i
$519$	6.68924	−	6.57223i	0.293625	−	0.288489i
$520$	−19.6197	−	4.48236i	−0.860381	−	0.196565i
$521$	10.7339			0.470261			0.235131	−	0.971964i	$-0.424448\pi$
$521$	10.7339			0.470261			0.235131	+	0.971964i	$0.424448\pi$
$522$	23.4618	+	0.414081i	1.02689	+	0.0181238i
$523$			36.6402i			1.60216i	0.598555	+	0.801081i	$0.295742\pi$
$523$			36.6402i			1.60216i	−0.598555	+	0.801081i	$0.704258\pi$
$524$	−3.52402	+	6.10378i	−0.153947	+	0.266645i
$525$	6.51176	+	5.70938i	0.284196	+	0.249178i
$526$	−16.3175	−	28.2628i	−0.711478	−	1.23232i
$527$	9.71208	−	5.60727i	0.423065	−	0.244257i
$528$	17.0180	−	4.39938i	0.740612	−	0.191459i
$529$	26.0189	−	45.0660i	1.13126	−	1.95939i
$530$	−1.87301	−	6.07665i	−0.0813585	−	0.263953i
$531$	0.0661622	−	3.74874i	0.00287120	−	0.162682i
$532$		−	2.25470i		−	0.0977538i
$533$	−15.7663	−	9.10265i	−0.682912	−	0.394280i
$534$	6.78329	−	6.66462i	0.293541	−	0.288406i
$535$	−2.32704	−	2.16008i	−0.100607	−	0.0933884i
$536$	−15.0467	−	26.0617i	−0.649920	−	1.12570i
$537$	−5.45763	+	19.6722i	−0.235514	+	0.848917i
$538$	19.2377	+	11.1069i	0.829395	+	0.478851i
$539$	4.04223			0.174111
$540$	−5.77758	+	3.41880i	−0.248628	+	0.147122i
$541$	1.34533			0.0578401			0.0289201	−	0.999582i	$-0.490793\pi$
$541$	1.34533			0.0578401			0.0289201	+	0.999582i	$0.490793\pi$
$542$	−17.3861	−	10.0379i	−0.746798	−	0.431164i
$543$	4.55552	−	16.4205i	0.195496	−	0.704671i
$544$	−5.13948	−	8.90184i	−0.220353	−	0.381663i
$545$	7.52658	−	8.10835i	0.322403	−	0.347323i
$546$	−4.31372	+	4.23826i	−0.184610	+	0.181381i
$547$	−29.1966	−	16.8567i	−1.24836	−	0.720739i	−0.277575	−	0.960704i	$-0.589531\pi$
$547$	−29.1966	−	16.8567i	−1.24836	−	0.720739i	−0.970781	+	0.239965i	$0.922864\pi$
$548$			6.00346i			0.256455i
$549$	−13.0739	+	7.24369i	−0.557982	+	0.309153i
$550$	13.5695	+	19.9205i	0.578604	+	0.849415i
$551$	12.7972	−	22.1654i	0.545179	−	0.944277i
$552$	−44.6563	+	11.5443i	−1.90070	+	0.491357i
$553$	3.67837	−	2.12371i	0.156420	−	0.0903093i
$554$	10.5728	+	18.3126i	0.449193	+	0.778026i
$555$	−14.5055	+	8.93269i	−0.615723	+	0.379171i
$556$	1.65034	−	2.85848i	0.0699901	−	0.121226i
$557$			13.8322i			0.586090i	0.956099	+	0.293045i	$0.0946686\pi$
$557$			13.8322i			0.586090i	−0.956099	+	0.293045i	$0.905331\pi$
$558$	−6.34342	+	10.5526i	−0.268538	+	0.446726i
$559$	18.5715			0.785491
$560$	1.25033	−	5.47281i	0.0528361	−	0.231269i
$561$	16.2744	−	15.9897i	0.687107	−	0.675087i
$562$	−30.3079	+	17.4983i	−1.27846	+	0.738121i
$563$	−10.6277	+	6.13592i	−0.447906	+	0.258598i	−0.706945	−	0.707268i	$-0.749927\pi$
$563$	−10.6277	+	6.13592i	−0.447906	+	0.258598i	0.259040	+	0.965867i	$0.416594\pi$
$564$	−10.8224	−	3.00245i	−0.455705	−	0.126426i
$565$	−6.17238	+	27.0171i	−0.259674	+	1.13662i
$566$	−20.7666			−0.872886
$567$	−0.317586	+	8.99439i	−0.0133374	+	0.377729i
$568$		−	28.4057i		−	1.19188i
$569$	−5.61071	+	9.71803i	−0.235213	+	0.407401i	−0.959335	−	0.282271i	$-0.908912\pi$
$569$	−5.61071	+	9.71803i	−0.235213	+	0.407401i	0.724122	+	0.689672i	$0.242245\pi$
$570$	−0.511239	−	18.0166i	−0.0214134	−	0.754631i
$571$	−10.0493	−	17.4060i	−0.420551	−	0.728416i	0.575442	−	0.817843i	$-0.304830\pi$
$571$	−10.0493	−	17.4060i	−0.420551	−	0.728416i	−0.995993	+	0.0894262i	$0.971497\pi$
$572$	5.92172	−	3.41891i	0.247600	−	0.142952i
$573$	−16.0265	−	16.3119i	−0.669518	−	0.681439i
$574$	3.70786	−	6.42221i	0.154763	−	0.268058i
$575$	−24.3837	−	35.7963i	−1.01687	−	1.49281i
$576$	22.5826	+	13.5750i	0.940943	+	0.565624i
$577$		−	13.8945i		−	0.578435i	−0.957263	−	0.289218i	$-0.906605\pi$
$577$		−	13.8945i		−	0.578435i	0.957263	−	0.289218i	$-0.0933951\pi$
$578$	−6.59028	−	3.80490i	−0.274120	−	0.158263i
$579$	−1.82041	−	7.04183i	−0.0756538	−	0.292649i
$580$	−5.76497	+	6.21057i	−0.239377	+	0.257880i
$581$	6.09519	+	10.5572i	0.252871	+	0.437986i
$582$	3.16756	−	0.818859i	0.131300	−	0.0339428i
$583$	8.34751	+	4.81943i	0.345718	+	0.199601i
$584$	−40.5116			−1.67638
$585$	13.6132	−	14.1560i	0.562838	−	0.585280i
$586$	−7.29621			−0.301404
$587$	−6.48110	−	3.74186i	−0.267504	−	0.154443i	0.360249	−	0.932856i	$-0.382692\pi$
$587$	−6.48110	−	3.74186i	−0.267504	−	0.154443i	−0.627753	+	0.778413i	$0.716025\pi$
$588$	0.701374	+	0.713862i	0.0289242	+	0.0294392i
$589$	6.71475	+	11.6303i	0.276676	+	0.479218i
$590$	−2.44259	−	2.26733i	−0.100560	−	0.0933446i
$591$	−25.3738	−	7.03944i	−1.04374	−	0.289564i
$592$	9.56332	+	5.52138i	0.393050	+	0.226927i
$593$		−	26.8374i		−	1.10208i	−0.834479	−	0.551040i	$-0.814231\pi$
$593$		−	26.8374i		−	1.10208i	0.834479	−	0.551040i	$-0.185769\pi$
$594$	−7.12119	+	24.0151i	−0.292186	+	0.985350i
$595$	−2.14632	−	6.96334i	−0.0879906	−	0.285469i
$596$	1.54019	−	2.66768i	0.0630884	−	0.109272i
$597$	−5.84712	+	21.0761i	−0.239307	+	0.862586i
$598$	26.1926	−	15.1223i	1.07110	−	0.618397i
$599$	23.0585	+	39.9385i	0.942144	+	1.63184i	0.761370	+	0.648317i	$0.224527\pi$
$599$	23.0585	+	39.9385i	0.942144	+	1.63184i	0.180774	+	0.983525i	$0.442140\pi$
$600$	−5.19104	+	26.1122i	−0.211923	+	1.06603i
$601$	−3.70152	+	6.41122i	−0.150988	+	0.261519i	−0.931591	−	0.363508i	$-0.881579\pi$
$601$	−3.70152	+	6.41122i	−0.150988	+	0.261519i	0.780603	+	0.625027i	$0.214912\pi$
$602$			7.56489i			0.308322i
$603$	29.3628	+	0.518228i	1.19574	+	0.0211039i
$604$	6.52118			0.265343
$605$	−11.6398	−	2.65925i	−0.473225	−	0.108114i
$606$	9.93683	+	38.4383i	0.403656	+	1.56145i
$607$	29.0245	−	16.7573i	1.17807	−	0.680157i	0.222500	−	0.974933i	$-0.428578\pi$
$607$	29.0245	−	16.7573i	1.17807	−	0.680157i	0.955567	+	0.294775i	$0.0952448\pi$
$608$	10.6600	−	6.15456i	0.432321	−	0.249600i
$609$	2.84330	+	10.9986i	0.115216	+	0.445687i
$610$	−2.95905	+	12.9520i	−0.119808	+	0.524413i
$611$	32.8564			1.32923
$612$	5.64761	+	0.0996757i	0.228291	+	0.00402915i
$613$		−	2.95377i		−	0.119302i	−0.998219	−	0.0596508i	$-0.981001\pi$
$613$		−	2.95377i		−	0.119302i	0.998219	−	0.0596508i	$-0.0189987\pi$
$614$	−3.22490	+	5.58569i	−0.130146	+	0.225420i
$615$	−11.4452	+	21.1900i	−0.461517	+	0.854462i
$616$	6.21327	+	10.7617i	0.250340	+	0.433601i
$617$	32.6188	−	18.8325i	1.31318	−	0.758166i	0.330560	−	0.943785i	$-0.392762\pi$
$617$	32.6188	−	18.8325i	1.31318	−	0.758166i	0.982622	+	0.185619i	$0.0594289\pi$
$618$	8.52778	−	30.7386i	0.343038	−	1.23649i
$619$	−17.9983	+	31.1739i	−0.723411	+	1.25298i	0.236214	+	0.971701i	$0.424093\pi$
$619$	−17.9983	+	31.1739i	−0.723411	+	1.25298i	−0.959625	+	0.281283i	$0.909240\pi$
$620$	−1.30968	−	4.24901i	−0.0525979	−	0.170644i
$621$	12.7965	−	43.1540i	0.513505	−	1.73171i
$622$		−	23.5599i		−	0.944666i
$623$	3.98699	+	2.30189i	0.159735	+	0.0922232i
$624$	−12.2676	−	3.40339i	−0.491097	−	0.136245i
$625$	−24.7239	+	3.70551i	−0.988954	+	0.148220i
$626$	7.88129	+	13.6508i	0.315000	+	0.545596i
$627$	19.1478	+	19.4887i	0.764690	+	0.778306i
$628$	2.37133	+	1.36909i	0.0946265	+	0.0546326i
$629$	14.3333			0.571505
$630$	5.76630	+	5.54519i	0.229735	+	0.220926i
$631$	6.29101			0.250441			0.125221	−	0.992129i	$-0.460036\pi$
$631$	6.29101			0.250441			0.125221	+	0.992129i	$0.460036\pi$
$632$	11.3080	+	6.52867i	0.449807	+	0.259696i
$633$	5.95832	−	1.54031i	0.236822	−	0.0612218i
$634$	11.4460	+	19.8251i	0.454580	+	0.787357i
$635$	1.96504	+	1.82405i	0.0779800	+	0.0723851i
$636$	0.597273	+	2.31041i	0.0236834	+	0.0916137i
$637$	−2.53546	−	1.46385i	−0.100459	−	0.0579998i
$638$			31.6175i			1.25175i
$639$	23.7581	+	14.2816i	0.939857	+	0.564971i
$640$	8.90112	−	2.74361i	0.351848	−	0.108451i
$641$	18.9637	−	32.8460i	0.749020	−	1.29734i	−0.199273	−	0.979944i	$-0.563858\pi$
$641$	18.9637	−	32.8460i	0.749020	−	1.29734i	0.948293	−	0.317397i	$-0.102809\pi$
$642$	−2.05556	−	2.09216i	−0.0811264	−	0.0825708i
$643$	−10.2039	+	5.89122i	−0.402402	+	0.232327i	−0.687520	−	0.726165i	$-0.741301\pi$
$643$	−10.2039	+	5.89122i	−0.402402	+	0.232327i	0.285118	+	0.958493i	$0.407967\pi$
$644$	−2.50253	−	4.33452i	−0.0986137	−	0.170804i
$645$	−0.696857	−	24.5579i	−0.0274387	−	0.966968i
$646$	−7.58249	+	13.1333i	−0.298329	+	0.516721i
$647$			34.7373i			1.36566i	0.730575	+	0.682832i	$0.239252\pi$
$647$			34.7373i			1.36566i	−0.730575	+	0.682832i	$0.760748\pi$
$648$	−24.4341	+	12.9797i	−0.959862	+	0.509890i
$649$	5.05188			0.198303
$650$	−1.29735	−	17.4091i	−0.0508864	−	0.682840i
$651$	−5.74381	−	1.59350i	−0.225118	−	0.0624542i
$652$	−7.64741	+	4.41523i	−0.299496	+	0.172914i
$653$	−36.5637	+	21.1100i	−1.43085	+	0.826100i	−0.997185	−	0.0749764i	$-0.976112\pi$
$653$	−36.5637	+	21.1100i	−1.43085	+	0.826100i	−0.433661	+	0.901076i	$0.642779\pi$
$654$	7.28991	−	7.16239i	0.285058	−	0.280071i
$655$	−26.5910	−	6.07504i	−1.03900	−	0.237371i
$656$	15.6115			0.609528
$657$	20.3681	−	33.8833i	0.794635	−	1.32191i
$658$			13.3837i			0.521751i
$659$	−5.03664	+	8.72372i	−0.196200	+	0.339828i	−0.947293	−	0.320368i	$-0.896193\pi$
$659$	−5.03664	+	8.72372i	−0.196200	+	0.339828i	0.751093	+	0.660196i	$0.229527\pi$
$660$	−4.74317	−	7.70226i	−0.184628	−	0.299810i
$661$	8.24919	+	14.2880i	0.320856	+	0.555740i	0.980665	−	0.195694i	$-0.0626960\pi$
$661$	8.24919	+	14.2880i	0.320856	+	0.555740i	−0.659809	+	0.751434i	$0.729363\pi$
$662$	35.6602	−	20.5884i	1.38597	−	0.800192i
$663$	−15.9985	+	4.13585i	−0.621332	+	0.160623i
$664$	−18.7377	+	32.4547i	−0.727165	+	1.25949i
$665$	8.33865	−	2.57024i	0.323359	−	0.0996695i
$666$	−13.7649	+	7.62652i	−0.533379	+	0.295522i
$667$		−	56.8153i		−	2.19990i
$668$	−2.86664	−	1.65506i	−0.110914	−	0.0640361i
$669$	−12.6879	+	12.4659i	−0.490542	+	0.481961i
$670$	17.7593	−	19.1320i	0.686103	−	0.739135i
$671$	−10.0695	−	17.4410i	−0.388731	−	0.673301i
$672$	−1.46056	+	5.26462i	−0.0563423	+	0.203087i
$673$	39.0265	+	22.5320i	1.50436	+	0.868544i	0.999987	+	0.00505962i	$0.00161053\pi$
$673$	39.0265	+	22.5320i	1.50436	+	0.868544i	0.504375	+	0.863485i	$0.331723\pi$
$674$	−11.5296			−0.444104
$675$	−19.2300	−	17.4702i	−0.740162	−	0.672429i
$676$	2.55879			0.0984151
$677$	−30.0957	−	17.3758i	−1.15667	−	0.667805i	−0.206168	−	0.978517i	$-0.566099\pi$
$677$	−30.0957	−	17.3758i	−1.15667	−	0.667805i	−0.950504	+	0.310712i	$0.899433\pi$
$678$	−6.84376	+	24.6685i	−0.262833	+	0.947389i
$679$	0.791954	+	1.37170i	0.0303924	+	0.0526412i
$680$	15.2395	−	16.4175i	0.584410	−	0.629581i
$681$	−11.2494	+	11.0526i	−0.431077	+	0.423536i
$682$	−14.3672	−	8.29493i	−0.550150	−	0.317629i
$683$			13.7295i			0.525344i	0.964885	+	0.262672i	$0.0846038\pi$
$683$			13.7295i			0.525344i	−0.964885	+	0.262672i	$0.915396\pi$
$684$	−0.119362	+	6.76306i	−0.00456393	+	0.258592i
$685$	−22.2028	+	6.84360i	−0.848325	+	0.261481i
$686$	0.596282	−	1.03279i	0.0227662	−	0.0394321i
$687$	−49.2278	+	12.7261i	−1.87816	+	0.485530i
$688$	−13.7919	+	7.96278i	−0.525813	+	0.303578i
$689$	−3.49061	−	6.04592i	−0.132982	−	0.230331i
$690$	−20.9797	−	34.0682i	−0.798684	−	1.29695i
$691$	−19.4006	+	33.6028i	−0.738033	+	1.27831i	0.215346	+	0.976538i	$0.430912\pi$
$691$	−19.4006	+	33.6028i	−0.738033	+	1.27831i	−0.953380	+	0.301774i	$0.902421\pi$
$692$			3.12826i			0.118919i
$693$	−12.1248	−	0.213993i	−0.460583	−	0.00812890i
$694$	1.10875			0.0420876
$695$	12.4529	+	2.84502i	0.472366	+	0.107918i
$696$	−24.9115	+	24.4757i	−0.944266	+	0.927748i
$697$	17.5486	−	10.1317i	0.664702	−	0.383766i
$698$	32.7213	−	18.8917i	1.23852	−	0.715061i
$699$	27.0787	+	7.51243i	1.02421	+	0.284146i
$700$	−2.88096	+	0.214694i	−0.108890	+	0.00811468i
$701$	11.4854			0.433798			0.216899	−	0.976194i	$-0.430406\pi$
$701$	11.4854			0.433798			0.216899	+	0.976194i	$0.430406\pi$
$702$	13.1635	−	12.4844i	0.496825	−	0.471195i
$703$			17.1642i			0.647360i
$704$	−17.7512	+	30.7461i	−0.669025	+	1.15879i
$705$	−1.23287	−	43.4475i	−0.0464325	−	1.63633i
$706$	4.92829	+	8.53605i	0.185479	+	0.321258i
$707$	−16.6456	+	9.61034i	−0.626022	+	0.361434i
$708$	0.876560	+	0.892167i	0.0329432	+	0.0335297i
$709$	1.31096	−	2.27065i	0.0492341	−	0.0852759i	−0.840358	−	0.542032i	$-0.817655\pi$
$709$	1.31096	−	2.27065i	0.0492341	−	0.0852759i	0.889592	+	0.456756i	$0.150989\pi$
$710$	23.5469	−	7.25791i	0.883701	−	0.272385i
$711$	−11.1458	+	6.17541i	−0.418001	+	0.231596i
$712$			14.1528i			0.530400i
$713$	25.8173	+	14.9056i	0.966866	+	0.558220i
$714$	−1.68469	−	6.51682i	−0.0630480	−	0.243886i
$715$	19.3947	+	18.0031i	0.725320	+	0.673280i
$716$	−3.40513	−	5.89785i	−0.127256	−	0.220413i
$717$	27.5049	−	7.11041i	1.02719	−	0.265543i
$718$	−17.3062	−	9.99174i	−0.645862	−	0.372888i
$719$	−36.5399			−1.36271			−0.681353	−	0.731955i	$-0.738608\pi$
$719$	−36.5399			−1.36271			−0.681353	+	0.731955i	$0.738608\pi$
$720$	−4.04013	+	16.3497i	−0.150567	+	0.609317i
$721$	15.4434			0.575142
$722$	3.89585	+	2.24927i	0.144989	+	0.0837092i
$723$	−1.68734	−	1.71738i	−0.0627528	−	0.0638701i
$724$	2.84228	+	4.92298i	0.105633	+	0.182961i
$725$	−29.5405	−	14.2411i	−1.09711	−	0.528901i
$726$	−10.6280	−	2.94850i	−0.394440	−	0.109429i
$727$	9.44506	+	5.45311i	0.350298	+	0.202245i	0.664817	−	0.747007i	$-0.268510\pi$
$727$	9.44506	+	5.45311i	0.350298	+	0.202245i	−0.314519	+	0.949251i	$0.601843\pi$
$728$		−	9.00027i		−	0.333572i
$729$	1.42877	−	26.9622i	0.0529173	−	0.998599i
$730$	−10.3511	−	33.5821i	−0.383110	−	1.24293i
$731$	−10.3355	+	17.9016i	−0.382273	+	0.662116i
$732$	1.33291	−	4.80451i	0.0492658	−	0.177580i
$733$	−30.8217	+	17.7949i	−1.13843	+	0.657271i	−0.946041	−	0.324048i	$-0.894956\pi$
$733$	−30.8217	+	17.7949i	−1.13843	+	0.657271i	−0.192386	+	0.981319i	$0.561623\pi$
$734$	−2.39235	−	4.14367i	−0.0883031	−	0.152946i
$735$	−1.84057	+	3.40768i	−0.0678906	+	0.125694i
$736$	13.6621	−	23.6635i	0.503592	−	0.872247i
$737$			39.5698i			1.45757i
$738$	−11.4618	+	19.0673i	−0.421916	+	0.701878i
$739$	44.8355			1.64930			0.824651	−	0.565642i	$-0.191372\pi$
$739$	44.8355			1.64930			0.824651	+	0.565642i	$0.191372\pi$
$740$	1.26568	−	5.54002i	0.0465275	−	0.203655i
$741$	−4.95271	−	19.1584i	−0.181942	−	0.703800i
$742$	2.46274	−	1.42186i	0.0904099	−	0.0521982i
$743$	−40.8171	+	23.5658i	−1.49743	+	0.864544i	−0.999996	−	0.00295558i	$-0.999059\pi$
$743$	−40.8171	+	23.5658i	−1.49743	+	0.864544i	−0.497438	+	0.867499i	$0.665726\pi$
$744$	−4.58635	−	17.7412i	−0.168144	−	0.650424i
$745$	11.6217	+	2.65512i	0.425786	+	0.0972760i
$746$	7.94537			0.290901
$747$	−17.7238	−	31.9893i	−0.648481	−	1.17043i
$748$			7.61083i			0.278279i
$749$	0.709967	−	1.22970i	0.0259416	−	0.0449322i
$750$	−22.9721	+	2.36879i	−0.838823	+	0.0864958i
$751$	8.89808	+	15.4119i	0.324695	+	0.562389i	0.981451	−	0.191715i	$-0.0614048\pi$
$751$	8.89808	+	15.4119i	0.324695	+	0.562389i	−0.656755	+	0.754104i	$0.728072\pi$
$752$	−24.4005	+	14.0876i	−0.889794	+	0.513723i
$753$	−6.02822	+	21.7289i	−0.219680	+	0.791844i
$754$	11.4500	−	19.8319i	0.416983	−	0.722235i
$755$	7.43378	+	24.1175i	0.270543	+	0.877726i
$756$	−2.06600	−	2.17838i	−0.0751398	−	0.0792270i
$757$			54.7392i			1.98953i	0.102192	+	0.994765i	$0.467414\pi$
$757$			54.7392i			1.98953i	−0.102192	+	0.994765i	$0.532586\pi$
$758$	17.5417	+	10.1277i	0.637145	+	0.367856i
$759$	58.4413	+	16.2133i	2.12129	+	0.588506i
$760$	19.6600	+	18.2495i	0.713145	+	0.661978i
$761$	−16.4392	−	28.4735i	−0.595921	−	1.03217i	−0.993416	−	0.114561i	$-0.963454\pi$
$761$	−16.4392	−	28.4735i	−0.595921	−	1.03217i	0.397495	−	0.917604i	$-0.369880\pi$
$762$	1.73578	+	1.76669i	0.0628808	+	0.0640004i
$763$	4.28476	+	2.47381i	0.155119	+	0.0895579i
$764$	7.62835			0.275984
$765$	6.06933	+	21.0004i	0.219437	+	0.759271i
$766$	−10.3953			−0.375597
$767$	−3.16876	−	1.82948i	−0.114417	−	0.0660588i
$768$	−21.1262	+	5.46141i	−0.762325	+	0.197072i
$769$	−10.5703	−	18.3083i	−0.381175	−	0.660215i	0.610055	−	0.792359i	$-0.291147\pi$
$769$	−10.5703	−	18.3083i	−0.381175	−	0.660215i	−0.991231	+	0.132144i	$0.957814\pi$
$770$	−7.33338	+	7.90021i	−0.264277	+	0.284704i
$771$	−2.62876	−	10.1687i	−0.0946724	−	0.366218i
$772$	2.10123	+	1.21315i	0.0756249	+	0.0436621i
$773$			28.7144i			1.03278i	0.856352	+	0.516392i	$0.172725\pi$
$773$			28.7144i			1.03278i	−0.856352	+	0.516392i	$0.827275\pi$
$774$	0.400480	−	22.6911i	0.0143950	−	0.815616i
$775$	14.2213	−	9.68726i	0.510844	−	0.347977i
$776$	−2.43461	+	4.21687i	−0.0873974	+	0.151377i
$777$	−5.33929	−	5.43436i	−0.191546	−	0.194957i
$778$	−20.7802	+	11.9975i	−0.745008	+	0.430130i
$779$	12.1328	+	21.0146i	0.434703	+	0.752927i
$780$	0.185831	+	6.54889i	0.00665383	+	0.234488i
$781$	−18.6753	+	32.3465i	−0.668253	+	1.15745i
$782$			33.6638i			1.20381i
$783$	−7.94632	−	33.1413i	−0.283978	−	1.18437i
$784$	2.51058			0.0896635
$785$	−2.36017	+	10.3307i	−0.0842380	+	0.368717i
$786$	−24.2795	−	6.73583i	−0.866020	−	0.240259i
$787$	17.0525	−	9.84527i	0.607856	−	0.350946i	−0.164270	−	0.986415i	$-0.552527\pi$
$787$	17.0525	−	9.84527i	0.607856	−	0.350946i	0.772126	+	0.635469i	$0.219193\pi$
$788$	7.60725	−	4.39205i	0.270997	−	0.156460i
$789$	−33.8101	+	33.2187i	−1.20367	+	1.18262i
$790$	−2.52266	+	11.0419i	−0.0897521	+	0.392853i
$791$	−12.3937			−0.440670
$792$	−18.0672	−	32.6090i	−0.641989	−	1.15871i
$793$			14.5863i			0.517975i
$794$	17.4542	−	30.2316i	0.619427	−	1.07288i
$795$	−7.86381	+	4.84265i	−0.278901	+	0.171751i
$796$	−3.64813	−	6.31875i	−0.129305	−	0.223962i
$797$	6.19641	−	3.57750i	0.219488	−	0.126721i	−0.386225	−	0.922405i	$-0.626221\pi$
$797$	6.19641	−	3.57750i	0.219488	−	0.126721i	0.605713	+	0.795683i	$0.292888\pi$
$798$	7.80394	−	2.01743i	0.276257	−	0.0714162i
$799$	−18.2854	+	31.6713i	−0.646892	+	1.12045i
$800$	−8.87909	−	13.0349i	−0.313923	−	0.460852i
$801$	−11.8372	−	7.11566i	−0.418248	−	0.251419i
$802$			5.23384i			0.184813i
$803$	46.1318	+	26.6342i	1.62796	+	0.939902i
$804$	−6.98807	+	6.86583i	−0.246450	+	0.242139i
$805$	13.1778	−	14.1963i	0.464455	−	0.500355i
$806$	6.00784	+	10.4059i	0.211617	+	0.366532i
$807$	8.62485	−	31.0885i	0.303609	−	1.09437i
$808$	−51.1716	−	29.5439i	−1.80021	−	1.03935i
$809$	8.45266			0.297180			0.148590	−	0.988899i	$-0.452527\pi$
$809$	8.45266			0.297180			0.148590	+	0.988899i	$0.452527\pi$
$810$	−17.0027	−	16.9383i	−0.597412	−	0.595150i
$811$	32.5014			1.14128			0.570640	−	0.821201i	$-0.306695\pi$
$811$	32.5014			1.14128			0.570640	+	0.821201i	$0.306695\pi$
$812$	−3.28191	−	1.89481i	−0.115172	−	0.0664948i
$813$	−7.79474	+	28.0963i	−0.273373	+	0.985382i
$814$	−10.6017	−	18.3627i	−0.371590	−	0.643613i
$815$	−25.0466	−	23.2496i	−0.877345	−	0.814397i
$816$	10.1079	−	9.93103i	0.353846	−	0.347656i
$817$	−21.4373	−	12.3768i	−0.749997	−	0.433011i
$818$		−	4.62619i		−	0.161751i
$819$	7.52770	+	4.52509i	0.263039	+	0.158119i
$820$	−2.36644	−	7.67748i	−0.0826397	−	0.268109i
$821$	18.6761	−	32.3479i	0.651799	−	1.12895i	−0.330887	−	0.943670i	$-0.607348\pi$
$821$	18.6761	−	32.3479i	0.651799	−	1.12895i	0.982686	−	0.185278i	$-0.0593186\pi$
$822$	−20.7791	+	5.37168i	−0.724753	+	0.187359i
$823$	32.7571	−	18.9123i	1.14184	−	0.659243i	0.194956	−	0.980812i	$-0.437544\pi$
$823$	32.7571	−	18.9123i	1.14184	−	0.659243i	0.946886	+	0.321569i	$0.104210\pi$
$824$	23.7379	+	41.1153i	0.826949	+	1.43232i
$825$	23.0786	−	26.3220i	0.803494	−	0.916414i
$826$	0.745219	−	1.29076i	0.0259295	−	0.0449112i
$827$		−	9.34608i		−	0.324995i	−0.986709	−	0.162498i	$-0.948045\pi$
$827$		−	9.34608i		−	0.324995i	0.986709	−	0.162498i	$-0.0519549\pi$
$828$	7.27697	+	13.1340i	0.252892	+	0.456438i
$829$	−22.4253			−0.778862			−0.389431	−	0.921056i	$-0.627328\pi$
$829$	−22.4253			−0.778862			−0.389431	+	0.921056i	$0.627328\pi$
$830$	−31.6910	−	7.24020i	−1.10001	−	0.251311i
$831$	21.9069	−	21.5237i	0.759941	−	0.746647i
$832$	22.2687	−	12.8568i	0.772029	−	0.445731i
$833$	2.82210	−	1.62934i	0.0977798	−	0.0564532i
$834$	11.3704	+	3.15448i	0.393724	+	0.109231i
$835$	2.85314	−	12.4885i	0.0987371	−	0.432182i
$836$	−9.11402			−0.315215
$837$	17.1444	+	5.08383i	0.592597	+	0.175723i
$838$			27.2837i			0.942499i
$839$	−22.9325	+	39.7203i	−0.791718	+	1.37130i	0.133184	+	0.991091i	$0.457480\pi$
$839$	−22.9325	+	39.7203i	−0.791718	+	1.37130i	−0.924902	+	0.380205i	$0.875853\pi$
$840$	−11.9015	+	0.337716i	−0.410639	+	0.0116523i
$841$	−7.00904	−	12.1400i	−0.241691	−	0.418621i
$842$	18.7612	−	10.8318i	0.646554	−	0.373288i
$843$	35.6224	+	36.2567i	1.22690	+	1.24875i
$844$	−1.02648	+	1.77792i	−0.0353330	+	0.0611985i
$845$	2.91688	+	9.46327i	0.100344	+	0.325547i
$846$	0.708523	−	40.1448i	0.0243595	−	1.38021i
$847$		−	5.33959i		−	0.183471i
$848$	5.18453	+	2.99329i	0.178038	+	0.102790i
$849$	7.54886	+	29.2010i	0.259076	+	1.00217i
$850$	17.5031	+	8.43803i	0.600352	+	0.289422i
$851$	19.0508	+	32.9970i	0.653054	+	1.13112i
$852$	−8.95281	+	2.31443i	−0.306718	+	0.0792910i
$853$	16.9551	+	9.78905i	0.580533	+	0.335171i	0.761345	−	0.648347i	$-0.224539\pi$
$853$	16.9551	+	9.78905i	0.580533	+	0.335171i	−0.180812	+	0.983518i	$0.557873\pi$
$854$	−5.94157			−0.203316
$855$	−25.1481	+	7.26806i	−0.860048	+	0.248563i
$856$	4.36513			0.149197
$857$	−21.1551	−	12.2139i	−0.722646	−	0.417220i	0.0930797	−	0.995659i	$-0.470329\pi$
$857$	−21.1551	−	12.2139i	−0.722646	−	0.417220i	−0.815726	+	0.578439i	$0.803662\pi$
$858$	17.1320	+	17.4370i	0.584877	+	0.595291i
$859$	−20.8624	−	36.1348i	−0.711817	−	1.23290i	−0.964174	−	0.265270i	$-0.914539\pi$
$859$	−20.8624	−	36.1348i	−0.711817	−	1.23290i	0.252357	−	0.967634i	$-0.418794\pi$
$860$	6.00658	+	5.57561i	0.204823	+	0.190127i
$861$	−10.3784	−	2.87927i	−0.353696	−	0.0981254i
$862$	11.4532	+	6.61251i	0.390098	+	0.225223i
$863$			14.4518i			0.491946i	0.969277	+	0.245973i	$0.0791075\pi$
$863$			14.4518i			0.491946i	−0.969277	+	0.245973i	$0.920892\pi$
$864$	4.65970	−	15.7141i	0.158526	−	0.534604i
$865$	−11.5694	+	3.56604i	−0.393370	+	0.121249i
$866$	11.6060	−	20.1021i	0.394387	−	0.683099i
$867$	−2.95463	+	10.6500i	−0.100344	+	0.361694i
$868$	1.72203	−	0.994216i	0.0584496	−	0.0337459i
$869$	−8.58452	−	14.8688i	−0.291210	−	0.504390i
$870$	−26.6542	−	14.3966i	−0.903663	−	0.488091i
$871$	14.3298	−	24.8199i	0.485546	−	0.840990i
$872$			15.2099i			0.515071i
$873$	−2.30288	−	4.15640i	−0.0779405	−	0.140673i
$874$	−40.3126			−1.36359
$875$	−4.07815	−	10.4100i	−0.137867	−	0.351923i
$876$	3.30078	+	12.7683i	0.111523	+	0.431401i
$877$	12.3359	−	7.12212i	0.416553	−	0.240497i	−0.277049	−	0.960856i	$-0.589356\pi$
$877$	12.3359	−	7.12212i	0.416553	−	0.240497i	0.693601	+	0.720359i	$0.256023\pi$
$878$	−2.70886	+	1.56396i	−0.0914197	+	0.0527812i
$879$	2.65224	+	10.2596i	0.0894578	+	0.346046i
$880$	−22.1223	−	5.05412i	−0.745744	−	0.170374i
$881$	6.84632			0.230658			0.115329	−	0.993327i	$-0.463208\pi$
$881$	6.84632			0.230658			0.115329	+	0.993327i	$0.463208\pi$
$882$	−1.84324	+	3.06632i	−0.0620652	+	0.103248i
$883$		−	34.7167i		−	1.16831i	−0.811642	−	0.584155i	$-0.801426\pi$
$883$		−	34.7167i		−	1.16831i	0.811642	−	0.584155i	$-0.198574\pi$
$884$	2.75618	−	4.77384i	0.0927004	−	0.160562i
$885$	−2.30031	+	4.25884i	−0.0773239	+	0.143159i
$886$	7.08460	+	12.2709i	0.238012	+	0.412248i
$887$	23.0060	−	13.2825i	0.772466	−	0.445984i	−0.0612873	−	0.998120i	$-0.519521\pi$
$887$	23.0060	−	13.2825i	0.772466	−	0.445984i	0.833754	+	0.552136i	$0.186187\pi$
$888$	6.26102	−	22.5680i	0.210106	−	0.757332i
$889$	−0.599521	+	1.03840i	−0.0201073	+	0.0348268i
$890$	−11.7320	+	3.61618i	−0.393258	+	0.121215i
$891$	36.3574	+	1.28376i	1.21802	+	0.0430074i
$892$		−	5.93356i		−	0.198670i
$893$	−37.9266	−	21.8969i	−1.26917	−	0.732753i
$894$	10.6114	+	2.94392i	0.354899	+	0.0984594i
$895$	17.9306	−	19.3165i	0.599354	−	0.645680i
$896$	2.08275	+	3.60743i	0.0695799	+	0.120516i
$897$	−30.7855	−	31.3336i	−1.02790	−	1.04620i
$898$	20.9001	+	12.0667i	0.697446	+	0.402671i
$899$	22.5718			0.752811
$900$	8.65291	−	0.491466i	0.288430	−	0.0163822i
$901$	7.77045			0.258871
$902$	−25.9600	−	14.9880i	−0.864374	−	0.499046i
$903$	10.6374	−	2.74991i	0.353989	−	0.0915112i
$904$	−19.0503	−	32.9960i	−0.633603	−	1.09743i
$905$	−14.9668	+	16.1236i	−0.497513	+	0.535968i
$906$	5.83492	+	22.5710i	0.193852	+	0.749871i
$907$	44.7576	+	25.8408i	1.48615	+	0.858029i	0.999876	−	0.0157765i	$-0.00502202\pi$
$907$	44.7576	+	25.8408i	1.48615	+	0.858029i	0.486275	+	0.873806i	$0.338355\pi$
$908$		−	5.26084i		−	0.174587i
$909$	50.4378	−	27.9453i	1.67292	−	0.926888i
$910$	7.46079	−	2.29965i	0.247323	−	0.0762327i
$911$	12.5192	−	21.6839i	0.414779	−	0.718419i	−0.580626	−	0.814170i	$-0.697192\pi$
$911$	12.5192	−	21.6839i	0.414779	−	0.718419i	0.995405	+	0.0957518i	$0.0305255\pi$
$912$	11.8925	+	12.1042i	0.393799	+	0.400811i
$913$	42.6745	−	24.6381i	1.41232	−	0.815404i
$914$	−17.7416	−	30.7293i	−0.586839	−	1.01643i
$915$	19.2881	−	0.547321i	0.637646	−	0.0180939i
$916$	8.48081	−	14.6892i	0.280214	−	0.485345i
$917$		−	12.1983i		−	0.402822i
$918$	4.70829	+	19.6366i	0.155397	+	0.648105i
$919$	32.0840			1.05836			0.529178	−	0.848511i	$-0.322501\pi$
$919$	32.0840			1.05836			0.529178	+	0.848511i	$0.322501\pi$
$920$	58.0505	+	13.2623i	1.91387	+	0.437247i
$921$	9.02660	+	2.50424i	0.297437	+	0.0825175i
$922$	13.2209	−	7.63307i	0.435406	−	0.251382i
$923$	23.4279	−	13.5261i	0.771138	−	0.445217i
$924$	2.88559	−	2.83511i	0.0949290	−	0.0932684i
$925$	21.9317	−	1.63438i	0.721109	−	0.0537382i
$926$	−29.7814			−0.978678
$927$	−46.3230	−	0.817563i	−1.52145	−	0.0268523i
$928$		−	20.6887i		−	0.679140i
$929$	−5.41000	+	9.37039i	−0.177496	+	0.307433i	−0.941022	−	0.338344i	$-0.890133\pi$
$929$	−5.41000	+	9.37039i	−0.177496	+	0.307433i	0.763526	+	0.645777i	$0.223466\pi$
$930$	13.5347	−	8.33490i	0.443822	−	0.273312i
$931$	1.95114	+	3.37948i	0.0639461	+	0.110758i
$932$	−8.11839	+	4.68715i	−0.265927	+	0.153533i
$933$	−33.1287	+	8.56425i	−1.08459	+	0.280381i
$934$	0.896217	−	1.55229i	0.0293251	−	0.0507926i
$935$	−28.1474	+	8.67592i	−0.920518	+	0.283733i
$936$	−0.476468	+	26.9966i	−0.0155738	+	0.882412i
$937$			12.4877i			0.407956i	0.978975	+	0.203978i	$0.0653871\pi$
$937$			12.4877i			0.407956i	−0.978975	+	0.203978i	$0.934613\pi$
$938$	10.1101	+	5.83707i	0.330107	+	0.190587i
$939$	16.3301	−	16.0445i	0.532914	−	0.523591i
$940$	10.6267	+	9.86429i	0.346606	+	0.321738i
$941$	−10.6230	−	18.3995i	−0.346299	−	0.599807i	0.639290	−	0.768966i	$-0.279228\pi$
$941$	−10.6230	−	18.3995i	−0.346299	−	0.599807i	−0.985589	+	0.169159i	$0.945895\pi$
$942$	−2.61689	+	9.43263i	−0.0852628	+	0.307332i
$943$	46.6490	+	26.9328i	1.51910	+	0.877053i
$944$	3.13766			0.102122
$945$	5.70126	−	10.1240i	0.185462	−	0.329334i
$946$	30.5790			0.994209
$947$	−33.7201	−	19.4683i	−1.09576	−	0.632636i	−0.160654	−	0.987011i	$-0.551360\pi$
$947$	−33.7201	−	19.4683i	−1.09576	−	0.632636i	−0.935103	+	0.354375i	$0.884694\pi$
$948$	1.13634	−	4.09595i	0.0369065	−	0.133030i
$949$	−19.2906	−	33.4123i	−0.626200	−	1.08461i
$950$	−10.1046	+	20.9601i	−0.327836	+	0.680036i
$951$	23.7163	−	23.3015i	0.769055	−	0.755602i
$952$	8.67563	+	5.00888i	0.281179	+	0.162339i
$953$			9.56336i			0.309788i	0.987931	+	0.154894i	$0.0495036\pi$
$953$			9.56336i			0.309788i	−0.987931	+	0.154894i	$0.950496\pi$
$954$	−7.46233	+	4.13454i	−0.241602	+	0.133861i
$955$	8.69589	+	28.2122i	0.281392	+	0.912925i
$956$	−4.73846	+	8.20726i	−0.153253	+	0.265442i
$957$	44.4590	−	11.4933i	1.43715	−	0.371525i
$958$	−13.2843	+	7.66969i	−0.429196	+	0.247796i
$959$	−5.19519	−	8.99833i	−0.167761	−	0.290571i
$960$	−17.8368	−	28.9645i	−0.575679	−	0.934824i
$961$	9.57824	−	16.5900i	0.308975	−	0.535161i
$962$			15.3572i			0.495136i
$963$	−2.19467	+	3.65094i	−0.0707222	+	0.117650i
$964$	0.803143			0.0258675
$965$	−2.09134	+	9.15397i	−0.0673225	+	0.294677i
$966$	12.7634	−	12.5401i	0.410655	−	0.403471i
$967$	3.17303	−	1.83195i	0.102038	−	0.0589116i	−0.448113	−	0.893977i	$-0.647904\pi$
$967$	3.17303	−	1.83195i	0.102038	−	0.0589116i	0.550151	+	0.835066i	$0.314570\pi$
$968$	14.2157	−	8.20744i	0.456910	−	0.263797i
$969$	21.2236	+	5.88805i	0.681801	+	0.189151i
$970$	−4.11764	−	0.940726i	−0.132210	−	0.0302049i
$971$	−42.0771			−1.35032			−0.675159	−	0.737672i	$-0.735925\pi$
$971$	−42.0771			−1.35032			−0.675159	+	0.737672i	$0.735925\pi$
$972$	6.08172	+	6.64350i	0.195071	+	0.213090i
$973$			5.71260i			0.183138i
$974$	−9.01461	+	15.6138i	−0.288847	+	0.500297i
$975$	−24.0081	+	8.15263i	−0.768876	+	0.261093i
$976$	−6.25407	−	10.8324i	−0.200188	−	0.346736i
$977$	−11.5743	+	6.68243i	−0.370295	+	0.213790i	−0.673587	−	0.739108i	$-0.735247\pi$
$977$	−11.5743	+	6.68243i	−0.370295	+	0.213790i	0.303292	+	0.952898i	$0.401914\pi$
$978$	−22.1246	−	22.5185i	−0.707465	−	0.720062i
$979$	9.30475	−	16.1163i	0.297381	−	0.515079i
$980$	−0.380561	−	1.23466i	−0.0121566	−	0.0394397i
$981$	−12.7213	−	7.64711i	−0.406161	−	0.244153i
$982$		−	28.1089i		−	0.896992i
$983$	18.7616	+	10.8320i	0.598401	+	0.345487i	0.768412	−	0.639955i	$-0.221047\pi$
$983$	18.7616	+	10.8320i	0.598401	+	0.345487i	−0.170011	+	0.985442i	$0.554380\pi$
$984$	−8.28702	−	32.0564i	−0.264181	−	1.02192i
$985$	24.9151	+	23.1275i	0.793861	+	0.736903i
$986$	12.7444	+	22.0739i	0.405863	+	0.702976i
$987$	18.8195	−	4.86510i	0.599030	−	0.154858i
$988$	5.71671	+	3.30055i	0.181873	+	0.105004i
$989$	−54.9491			−1.74728
$990$	22.4149	−	23.3087i	0.712393	−	0.740799i
$991$	−34.3470			−1.09107			−0.545534	−	0.838089i	$-0.683673\pi$
$991$	−34.3470			−1.09107			−0.545534	+	0.838089i	$0.683673\pi$
$992$	9.40111	+	5.42773i	0.298486	+	0.172331i
$993$	−41.9132	−	42.6595i	−1.33008	−	1.35376i
$994$	5.50970	+	9.54308i	0.174757	+	0.302688i
$995$	19.2102	−	20.6950i	0.609004	−	0.656077i
$996$	11.7557	+	3.26136i	0.372492	+	0.103340i
$997$	2.76981	+	1.59915i	0.0877208	+	0.0506456i	0.543219	−	0.839591i	$-0.317205\pi$
$997$	2.76981	+	1.59915i	0.0877208	+	0.0506456i	−0.455498	+	0.890237i	$0.650539\pi$
$998$			40.6287i			1.28608i
$999$	15.7277	+	16.5832i	0.497602	+	0.524669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.11	✓	64
3.2	odd	2		945.2.bh.c.694.22		64
5.4	even	2	inner	315.2.bh.c.169.22	yes	64
9.4	even	3	inner	315.2.bh.c.274.22	yes	64
9.5	odd	6		945.2.bh.c.64.11		64
15.14	odd	2		945.2.bh.c.694.11		64
45.4	even	6	inner	315.2.bh.c.274.11	yes	64
45.14	odd	6		945.2.bh.c.64.22		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.11	✓	64	1.1	even	1	trivial
315.2.bh.c.169.22	yes	64	5.4	even	2	inner
315.2.bh.c.274.11	yes	64	45.4	even	6	inner
315.2.bh.c.274.22	yes	64	9.4	even	3	inner
945.2.bh.c.64.11		64	9.5	odd	6
945.2.bh.c.64.22		64	45.14	odd	6
945.2.bh.c.694.11		64	15.14	odd	2
945.2.bh.c.694.22		64	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.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03279 - 0.596282i) q^{2} +(-0.463032 + 1.66901i) q^{3} +(-0.288895 - 0.500381i) q^{4} +(1.52125 - 1.63884i) q^{5} +(1.47342 - 1.44764i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.07418i q^{8} +(-2.57120 - 1.54561i) q^{9} +O(q^{10})\)	\(q+(-1.03279 - 0.596282i) q^{2} +(-0.463032 + 1.66901i) q^{3} +(-0.288895 - 0.500381i) q^{4} +(1.52125 - 1.63884i) q^{5} +(1.47342 - 1.44764i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.07418i q^{8} +(-2.57120 - 1.54561i) q^{9} +(-2.54835 + 0.785481i) q^{10} +(2.02111 - 3.50067i) q^{11} +(0.968910 - 0.250477i) q^{12} +(-2.53546 + 1.46385i) q^{13} +(-0.596282 - 1.03279i) q^{14} +(2.03085 + 3.29782i) q^{15} +(1.25529 - 2.17422i) q^{16} -3.25867i q^{17} +(1.73389 + 3.12946i) q^{18} +3.90229 q^{19} +(-1.25953 - 0.287754i) q^{20} +(-1.23550 + 1.21389i) q^{21} +(-4.17478 + 2.41031i) q^{22} +(7.50189 - 4.33122i) q^{23} +(-5.13084 - 1.42345i) q^{24} +(-0.371578 - 4.98617i) q^{25} +3.49147 q^{26} +(3.77020 - 3.57570i) q^{27} -0.577790i q^{28} +(3.27941 - 5.68010i) q^{29} +(-0.131010 - 4.61692i) q^{30} +(1.72072 + 2.98038i) q^{31} +(2.73173 - 1.57717i) q^{32} +(4.90682 + 4.99419i) q^{33} +(-1.94309 + 3.36553i) q^{34} +(2.13686 - 0.658649i) q^{35} +(-0.0305878 + 1.73310i) q^{36} +4.39850i q^{37} +(-4.03025 - 2.32686i) q^{38} +(-1.26918 - 4.90952i) q^{39} +(5.03808 + 4.67661i) q^{40} +(3.10915 + 5.38521i) q^{41} +(1.99984 - 0.516986i) q^{42} +(-5.49353 - 3.17169i) q^{43} -2.33556 q^{44} +(-6.44446 + 1.86251i) q^{45} -10.3305 q^{46} +(-9.71907 - 5.61131i) q^{47} +(3.04757 + 3.10183i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.58940 + 5.37124i) q^{50} +(5.43877 + 1.50887i) q^{51} +(1.46496 + 0.845798i) q^{52} +2.38454i q^{53} +(-6.02595 + 1.44485i) q^{54} +(-2.66241 - 8.63768i) q^{55} +(-1.53709 + 2.66232i) q^{56} +(-1.80689 + 6.51296i) q^{57} +(-6.77389 + 3.91091i) q^{58} +(0.624888 + 1.08234i) q^{59} +(1.06347 - 1.96892i) q^{60} +(2.49109 - 4.31469i) q^{61} -4.10414i q^{62} +(-1.45392 - 2.62414i) q^{63} -8.78290 q^{64} +(-1.45807 + 6.38209i) q^{65} +(-2.08978 - 8.08380i) q^{66} +(-8.47762 + 4.89455i) q^{67} +(-1.63058 + 0.941415i) q^{68} +(3.75524 + 14.5262i) q^{69} +(-2.59967 - 0.593927i) q^{70} -9.24009 q^{71} +(4.75149 - 7.90434i) q^{72} +13.1780i q^{73} +(2.62274 - 4.54273i) q^{74} +(8.49404 + 1.68859i) q^{75} +(-1.12735 - 1.95263i) q^{76} +(3.50067 - 2.02111i) q^{77} +(-1.61666 + 5.82730i) q^{78} +(2.12371 - 3.67837i) q^{79} +(-1.65359 - 5.36476i) q^{80} +(4.22216 + 7.94817i) q^{81} -7.41572i q^{82} +(10.5572 + 6.09519i) q^{83} +(0.964339 + 0.267536i) q^{84} +(-5.34044 - 4.95727i) q^{85} +(3.78245 + 6.55139i) q^{86} +(7.96169 + 8.10344i) q^{87} +(10.7617 + 6.21327i) q^{88} +4.60378 q^{89} +(7.76636 + 1.91913i) q^{90} -2.92770 q^{91} +(-4.33452 - 2.50253i) q^{92} +(-5.77103 + 1.49189i) q^{93} +(6.69185 + 11.5906i) q^{94} +(5.93637 - 6.39521i) q^{95} +(1.36743 + 5.28958i) q^{96} +(1.37170 + 0.791954i) q^{97} -1.19256i q^{98} +(-10.6074 + 5.87707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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