LMFDB - Embedded newform 585.2.bt.b.376.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.30
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.231678 + 0.133759i) q^{2} +(1.70348 - 0.313309i) q^{3} +(-0.964217 - 1.67007i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.436567 + 0.155269i) q^{6} +(-3.30805 - 1.90990i) q^{7} -1.05093i q^{8} +(2.80367 - 1.06743i) q^{9} +O(q^{10})$	\(q+(0.231678 + 0.133759i) q^{2} +(1.70348 - 0.313309i) q^{3} +(-0.964217 - 1.67007i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.436567 + 0.155269i) q^{6} +(-3.30805 - 1.90990i) q^{7} -1.05093i q^{8} +(2.80367 - 1.06743i) q^{9} -0.267519 q^{10} +(-4.13207 - 2.38565i) q^{11} +(-2.16577 - 2.54283i) q^{12} +(3.37175 + 1.27721i) q^{13} +(-0.510935 - 0.884965i) q^{14} +(-1.31860 + 1.12307i) q^{15} +(-1.78786 + 3.09667i) q^{16} -4.49245 q^{17} +(0.792329 + 0.127717i) q^{18} +0.832616i q^{19} +(1.67007 + 0.964217i) q^{20} +(-6.23357 - 2.21703i) q^{21} +(-0.638207 - 1.10541i) q^{22} +(-2.95117 - 5.11158i) q^{23} +(-0.329266 - 1.79024i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.610322 + 0.746907i) q^{26} +(4.44156 - 2.69676i) q^{27} +7.36623i q^{28} +(1.72114 - 2.98110i) q^{29} +(-0.455713 + 0.0838162i) q^{30} +(4.11935 - 2.37831i) q^{31} +(-2.64868 + 1.52922i) q^{32} +(-7.78634 - 2.76929i) q^{33} +(-1.04080 - 0.600908i) q^{34} +3.81980 q^{35} +(-4.48604 - 3.65310i) q^{36} -1.42971i q^{37} +(-0.111370 + 0.192899i) q^{38} +(6.14387 + 1.11931i) q^{39} +(0.525465 + 0.910132i) q^{40} +(-1.22492 + 0.707206i) q^{41} +(-1.14763 - 1.34744i) q^{42} +(4.57220 - 7.91929i) q^{43} +9.20114i q^{44} +(-1.89434 + 2.32626i) q^{45} -1.57899i q^{46} +(11.2552 + 6.49820i) q^{47} +(-2.07537 + 5.83526i) q^{48} +(3.79544 + 6.57390i) q^{49} +(0.231678 - 0.133759i) q^{50} +(-7.65279 + 1.40753i) q^{51} +(-1.11806 - 6.86258i) q^{52} -8.34571 q^{53} +(1.38973 - 0.0306803i) q^{54} +4.77130 q^{55} +(-2.00717 + 3.47652i) q^{56} +(0.260866 + 1.41834i) q^{57} +(0.797502 - 0.460438i) q^{58} +(0.991497 - 0.572441i) q^{59} +(3.14703 + 1.11927i) q^{60} +(-5.08702 + 8.81097i) q^{61} +1.27248 q^{62} +(-11.3134 - 1.82363i) q^{63} +6.33326 q^{64} +(-3.55863 + 0.579777i) q^{65} +(-1.43351 - 1.68308i) q^{66} +(10.5335 - 6.08150i) q^{67} +(4.33170 + 7.50272i) q^{68} +(-6.62876 - 7.78283i) q^{69} +(0.884965 + 0.510935i) q^{70} -1.12258i q^{71} +(-1.12180 - 2.94647i) q^{72} -6.20857i q^{73} +(0.191238 - 0.331233i) q^{74} +(0.580405 - 1.63191i) q^{75} +(1.39053 - 0.802822i) q^{76} +(9.11272 + 15.7837i) q^{77} +(1.27368 + 1.08112i) q^{78} +(7.21565 - 12.4979i) q^{79} -3.57572i q^{80} +(6.72118 - 5.98546i) q^{81} -0.378382 q^{82} +(7.32055 + 4.22652i) q^{83} +(2.30791 + 12.5482i) q^{84} +(3.89058 - 2.24622i) q^{85} +(2.11856 - 1.22315i) q^{86} +(1.99792 - 5.61750i) q^{87} +(-2.50715 + 4.34252i) q^{88} +5.87702i q^{89} +(-0.750036 + 0.285558i) q^{90} +(-8.71456 - 10.6648i) q^{91} +(-5.69113 + 9.85733i) q^{92} +(6.27207 - 5.34202i) q^{93} +(1.73839 + 3.01098i) q^{94} +(-0.416308 - 0.721066i) q^{95} +(-4.03285 + 3.43484i) q^{96} +(-12.3612 - 7.13676i) q^{97} +2.03070i q^{98} +(-14.1315 - 2.27789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.231678	+	0.133759i	0.163821	+	0.0945822i	0.579669	−	0.814852i	$-0.303182\pi$
$2$	0.231678	+	0.133759i	0.163821	+	0.0945822i	−0.415848	+	0.909434i	$0.636515\pi$
$3$	1.70348	−	0.313309i	0.983503	−	0.180889i
$3$	1.70348	−	0.313309i	0.983503	−	0.180889i
$4$	−0.964217	−	1.67007i	−0.482108	−	0.835036i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	0.436567	+	0.155269i	0.178228	+	0.0633884i
$7$	−3.30805	−	1.90990i	−1.25032	−	0.721875i	−0.279150	−	0.960248i	$-0.590053\pi$
$7$	−3.30805	−	1.90990i	−1.25032	−	0.721875i	−0.971174	+	0.238373i	$0.923386\pi$
$8$		−	1.05093i		−	0.371560i
$9$	2.80367	−	1.06743i	0.934558	−	0.355810i
$10$	−0.267519			−0.0845969
$11$	−4.13207	−	2.38565i	−1.24587	−	0.719301i	−0.275584	−	0.961277i	$-0.588871\pi$
$11$	−4.13207	−	2.38565i	−1.24587	−	0.719301i	−0.970282	+	0.241976i	$0.922205\pi$
$12$	−2.16577	−	2.54283i	−0.625204	−	0.734053i
$13$	3.37175	+	1.27721i	0.935156	+	0.354236i
$13$	3.37175	+	1.27721i	0.935156	+	0.354236i
$14$	−0.510935	−	0.884965i	−0.136553	−	0.236517i
$15$	−1.31860	+	1.12307i	−0.340461	+	0.289976i
$16$	−1.78786	+	3.09667i	−0.446965	+	0.774167i
$17$	−4.49245			−1.08958			−0.544790	−	0.838573i	$-0.683390\pi$
$17$	−4.49245			−1.08958			−0.544790	+	0.838573i	$0.683390\pi$
$18$	0.792329	+	0.127717i	0.186754	+	0.0301033i
$19$			0.832616i			0.191015i	0.995429	+	0.0955076i	$0.0304474\pi$
$19$			0.832616i			0.191015i	−0.995429	+	0.0955076i	$0.969553\pi$
$20$	1.67007	+	0.964217i	0.373440	+	0.215605i
$21$	−6.23357	−	2.21703i	−1.36028	−	0.483796i
$22$	−0.638207	−	1.10541i	−0.136066	−	0.235674i
$23$	−2.95117	−	5.11158i	−0.615361	−	1.06584i	−0.990321	−	0.138796i	$-0.955677\pi$
$23$	−2.95117	−	5.11158i	−0.615361	−	1.06584i	0.374960	−	0.927041i	$-0.377657\pi$
$24$	−0.329266	−	1.79024i	−0.0672112	−	0.365431i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.610322	+	0.746907i	0.119694	+	0.146480i
$27$	4.44156	−	2.69676i	0.854779	−	0.518992i
$28$			7.36623i			1.39209i
$29$	1.72114	−	2.98110i	0.319608	−	0.553577i	−0.660798	−	0.750564i	$-0.729782\pi$
$29$	1.72114	−	2.98110i	0.319608	−	0.553577i	0.980406	+	0.196986i	$0.0631154\pi$
$30$	−0.455713	+	0.0838162i	−0.0832014	+	0.0153027i
$31$	4.11935	−	2.37831i	0.739857	−	0.427157i	−0.0821605	−	0.996619i	$-0.526182\pi$
$31$	4.11935	−	2.37831i	0.739857	−	0.427157i	0.822017	+	0.569463i	$0.192849\pi$
$32$	−2.64868	+	1.52922i	−0.468225	+	0.270330i
$33$	−7.78634	−	2.76929i	−1.35543	−	0.482071i
$34$	−1.04080	−	0.600908i	−0.178496	−	0.103055i
$35$	3.81980			0.645664
$36$	−4.48604	−	3.65310i	−0.747673	−	0.608851i
$37$		−	1.42971i		−	0.235043i	−0.993070	−	0.117522i	$-0.962505\pi$
$37$		−	1.42971i		−	0.235043i	0.993070	−	0.117522i	$-0.0374950\pi$
$38$	−0.111370	+	0.192899i	−0.0180666	+	0.0312923i
$39$	6.14387	+	1.11931i	0.983807	+	0.179232i
$40$	0.525465	+	0.910132i	0.0830833	+	0.143905i
$41$	−1.22492	+	0.707206i	−0.191300	+	0.110447i	−0.592591	−	0.805504i	$-0.701895\pi$
$41$	−1.22492	+	0.707206i	−0.191300	+	0.110447i	0.401291	+	0.915951i	$0.368562\pi$
$42$	−1.14763	−	1.34744i	−0.177084	−	0.207914i
$43$	4.57220	−	7.91929i	0.697255	−	1.20768i	−0.272160	−	0.962252i	$-0.587738\pi$
$43$	4.57220	−	7.91929i	0.697255	−	1.20768i	0.969415	−	0.245429i	$-0.0789287\pi$
$44$			9.20114i			1.38712i
$45$	−1.89434	+	2.32626i	−0.282391	+	0.346778i
$46$		−	1.57899i		−	0.232809i
$47$	11.2552	+	6.49820i	1.64174	+	0.947860i	0.980214	+	0.197940i	$0.0634253\pi$
$47$	11.2552	+	6.49820i	1.64174	+	0.947860i	0.661528	+	0.749920i	$0.269908\pi$
$48$	−2.07537	+	5.83526i	−0.299554	+	0.842247i
$49$	3.79544	+	6.57390i	0.542206	+	0.939128i
$50$	0.231678	−	0.133759i	0.0327642	−	0.0189164i
$51$	−7.65279	+	1.40753i	−1.07160	+	0.197093i
$52$	−1.11806	−	6.86258i	−0.155047	−	0.951669i
$53$	−8.34571			−1.14637			−0.573185	−	0.819426i	$-0.694293\pi$
$53$	−8.34571			−1.14637			−0.573185	+	0.819426i	$0.694293\pi$
$54$	1.38973	−	0.0306803i	0.189118	−	0.00417506i
$55$	4.77130			0.643363
$56$	−2.00717	+	3.47652i	−0.268220	+	0.464570i
$57$	0.260866	+	1.41834i	0.0345526	+	0.187864i
$58$	0.797502	−	0.460438i	0.104717	−	0.0604585i
$59$	0.991497	−	0.572441i	0.129082	−	0.0745255i	−0.434069	−	0.900880i	$-0.642922\pi$
$59$	0.991497	−	0.572441i	0.129082	−	0.0745255i	0.563151	+	0.826354i	$0.309589\pi$
$60$	3.14703	+	1.11927i	0.406280	+	0.144497i
$61$	−5.08702	+	8.81097i	−0.651326	+	1.12813i	0.331476	+	0.943464i	$0.392454\pi$
$61$	−5.08702	+	8.81097i	−0.651326	+	1.12813i	−0.982801	+	0.184666i	$0.940880\pi$
$62$	1.27248			0.161606
$63$	−11.3134	−	1.82363i	−1.42535	−	0.229756i
$64$	6.33326			0.791657
$65$	−3.55863	+	0.579777i	−0.441394	+	0.0719124i
$66$	−1.43351	−	1.68308i	−0.176452	−	0.207173i
$67$	10.5335	−	6.08150i	1.28687	−	0.742974i	0.308774	−	0.951135i	$-0.400081\pi$
$67$	10.5335	−	6.08150i	1.28687	−	0.742974i	0.978094	+	0.208162i	$0.0667480\pi$
$68$	4.33170	+	7.50272i	0.525295	+	0.909838i
$69$	−6.62876	−	7.78283i	−0.798008	−	0.936942i
$70$	0.884965	+	0.510935i	0.105774	+	0.0610684i
$71$		−	1.12258i		−	0.133226i	−0.997779	−	0.0666131i	$-0.978781\pi$
$71$		−	1.12258i		−	0.133226i	0.997779	−	0.0666131i	$-0.0212193\pi$
$72$	−1.12180	−	2.94647i	−0.132205	−	0.347244i
$73$		−	6.20857i		−	0.726658i	−0.931661	−	0.363329i	$-0.881640\pi$
$73$		−	6.20857i		−	0.726658i	0.931661	−	0.363329i	$-0.118360\pi$
$74$	0.191238	−	0.331233i	0.0222309	−	0.0385051i
$75$	0.580405	−	1.63191i	0.0670194	−	0.188437i
$76$	1.39053	−	0.802822i	0.159505	−	0.0920900i
$77$	9.11272	+	15.7837i	1.03849	+	1.79872i
$78$	1.27368	+	1.08112i	0.144216	+	0.122413i
$79$	7.21565	−	12.4979i	0.811824	−	1.40612i	−0.0997625	−	0.995011i	$-0.531808\pi$
$79$	7.21565	−	12.4979i	0.811824	−	1.40612i	0.911586	−	0.411109i	$-0.134858\pi$
$80$		−	3.57572i		−	0.399778i
$81$	6.72118	−	5.98546i	0.746798	−	0.665051i
$82$	−0.378382			−0.0417853
$83$	7.32055	+	4.22652i	0.803535	+	0.463921i	0.844706	−	0.535231i	$-0.179775\pi$
$83$	7.32055	+	4.22652i	0.803535	+	0.463921i	−0.0411708	+	0.999152i	$0.513109\pi$
$84$	2.30791	+	12.5482i	0.251814	+	1.36912i
$85$	3.89058	−	2.24622i	0.421992	−	0.243637i
$86$	2.11856	−	1.22315i	0.228450	−	0.131896i
$87$	1.99792	−	5.61750i	0.214199	−	0.602259i
$88$	−2.50715	+	4.34252i	−0.267264	+	0.462914i
$89$			5.87702i			0.622963i	0.950252	+	0.311481i	$0.100825\pi$
$89$			5.87702i			0.622963i	−0.950252	+	0.311481i	$0.899175\pi$
$90$	−0.750036	+	0.285558i	−0.0790607	+	0.0301005i
$91$	−8.71456	−	10.6648i	−0.913534	−	1.11797i
$92$	−5.69113	+	9.85733i	−0.593342	+	1.02770i
$93$	6.27207	−	5.34202i	0.650384	−	0.553942i
$94$	1.73839	+	3.01098i	0.179301	+	0.310559i
$95$	−0.416308	−	0.721066i	−0.0427123	−	0.0739799i
$96$	−4.03285	+	3.43484i	−0.411601	+	0.350567i
$97$	−12.3612	−	7.13676i	−1.25509	−	0.724629i	−0.282977	−	0.959127i	$-0.591322\pi$
$97$	−12.3612	−	7.13676i	−1.25509	−	0.724629i	−0.972117	+	0.234498i	$0.924655\pi$
$98$			2.03070i			0.205132i
$99$	−14.1315	−	2.27789i	−1.42027	−	0.228937i
$100$	−1.92843			−0.192843
$101$	4.23325	−	7.33220i	0.421224	−	0.729581i	−0.574836	−	0.818269i	$-0.694934\pi$
$101$	4.23325	−	7.33220i	0.421224	−	0.729581i	0.996059	+	0.0886877i	$0.0282673\pi$
$102$	−1.96125	−	0.697540i	−0.194193	−	0.0690667i
$103$	6.17393	+	10.6936i	0.608336	+	1.05367i	0.991515	+	0.129994i	$0.0414959\pi$
$103$	6.17393	+	10.6936i	0.608336	+	1.05367i	−0.383179	+	0.923674i	$0.625171\pi$
$104$	1.34226	−	3.54348i	0.131620	−	0.347467i
$105$	6.50695	−	1.19678i	0.635013	−	0.116794i
$106$	−1.93352	−	1.11632i	−0.187800	−	0.108426i
$107$	−9.80820			−0.948195			−0.474097	−	0.880472i	$-0.657226\pi$
$107$	−9.80820			−0.948195			−0.474097	+	0.880472i	$0.657226\pi$
$108$	−8.78642	−	4.81747i	−0.845473	−	0.463561i
$109$			14.7105i			1.40901i	0.709701	+	0.704503i	$0.248830\pi$
$109$			14.7105i			1.40901i	−0.709701	+	0.704503i	$0.751170\pi$
$110$	1.10541	+	0.638207i	0.105396	+	0.0608507i
$111$	−0.447942	−	2.43548i	−0.0425168	−	0.231166i
$112$	11.8287	−	6.82928i	1.11770	−	0.645306i
$113$	−7.17072	−	12.4201i	−0.674565	−	1.16838i	−0.976596	−	0.215082i	$-0.930998\pi$
$113$	−7.17072	−	12.4201i	−0.674565	−	1.16838i	0.302031	−	0.953298i	$-0.402335\pi$
$114$	−0.129280	+	0.363492i	−0.0121082	+	0.0340442i
$115$	5.11158	+	2.95117i	0.476657	+	0.275198i
$116$	−6.63821			−0.616343
$117$	10.8166	−	0.0182210i	0.999999	−	0.00168454i
$118$	0.306278			0.0281951
$119$	14.8612	+	8.58013i	1.36233	+	0.786540i
$120$	1.18027	+	1.38576i	0.107744	+	0.126502i
$121$	5.88267	+	10.1891i	0.534788	+	0.926281i
$122$	−2.35710	+	1.36087i	−0.213402	+	0.123208i
$123$	−1.86504	+	1.58849i	−0.168165	+	0.143229i
$124$	−7.94389	−	4.58641i	−0.713382	−	0.411871i
$125$			1.00000i			0.0894427i
$126$	−2.37713	−	1.93577i	−0.211772	−	0.172452i
$127$	−8.48951			−0.753322			−0.376661	−	0.926351i	$-0.622928\pi$
$127$	−8.48951			−0.753322			−0.376661	+	0.926351i	$0.622928\pi$
$128$	6.76464	+	3.90557i	0.597915	+	0.345207i
$129$	5.30746	−	14.9229i	0.467296	−	1.31388i
$130$	−0.902008	−	0.341679i	−0.0791113	−	0.0299672i
$131$	4.78570	+	8.28908i	0.418129	+	0.724220i	0.995751	−	0.0920836i	$-0.0293527\pi$
$131$	4.78570	+	8.28908i	0.418129	+	0.724220i	−0.577622	+	0.816304i	$0.696019\pi$
$132$	2.88280	+	15.6739i	0.250916	+	1.36424i
$133$	1.59021	−	2.75433i	0.137889	−	0.238831i
$134$	3.25383			0.281088
$135$	−2.49812	+	4.55625i	−0.215004	+	0.392139i
$136$			4.72125i			0.404844i
$137$	−10.3403	−	5.96997i	−0.883431	−	0.510049i	−0.0116427	−	0.999932i	$-0.503706\pi$
$137$	−10.3403	−	5.96997i	−0.883431	−	0.510049i	−0.871788	+	0.489883i	$0.837039\pi$
$138$	−0.494711	−	2.68977i	−0.0421126	−	0.228968i
$139$	5.93993	+	10.2883i	0.503819	+	0.872639i	0.999990	+	0.00441494i	$0.00140532\pi$
$139$	5.93993	+	10.2883i	0.503819	+	0.872639i	−0.496172	+	0.868224i	$0.665261\pi$
$140$	−3.68312	−	6.37935i	−0.311280	−	0.539153i
$141$	21.2090	+	7.54318i	1.78612	+	0.635251i
$142$	0.150156	−	0.260078i	0.0126008	−	0.0218253i
$143$	−10.8853	−	13.3214i	−0.910277	−	1.11399i
$144$	−1.70710	+	10.5905i	−0.142259	+	0.882539i
$145$			3.44228i			0.285866i
$146$	0.830454	−	1.43839i	0.0687289	−	0.119042i
$147$	8.52511	+	10.0093i	0.703140	+	0.825557i
$148$	−2.38772	+	1.37855i	−0.196270	+	0.113316i
$149$	11.4392	−	6.60442i	0.937136	−	0.541056i	0.0480744	−	0.998844i	$-0.484692\pi$
$149$	11.4392	−	6.60442i	0.937136	−	0.541056i	0.889061	+	0.457788i	$0.151358\pi$
$150$	0.352751	−	0.300443i	0.0288020	−	0.0245311i
$151$	−1.58329	−	0.914115i	−0.128847	−	0.0743896i	0.434191	−	0.900821i	$-0.357034\pi$
$151$	−1.58329	−	0.914115i	−0.128847	−	0.0743896i	−0.563038	+	0.826431i	$0.690368\pi$
$152$	0.875021			0.0709736
$153$	−12.5954	+	4.79538i	−1.01828	+	0.387684i
$154$			4.87565i			0.392891i
$155$	−2.37831	+	4.11935i	−0.191030	+	0.330874i
$156$	−4.05470	−	11.3400i	−0.324636	−	0.907924i
$157$	2.72779	+	4.72466i	0.217701	+	0.377069i	0.954105	−	0.299473i	$-0.0968109\pi$
$157$	2.72779	+	4.72466i	0.217701	+	0.377069i	−0.736404	+	0.676542i	$0.763478\pi$
$158$	3.34342	−	1.93032i	0.265988	−	0.153568i
$159$	−14.2167	+	2.61479i	−1.12746	+	0.207366i
$160$	1.52922	−	2.64868i	0.120895	−	0.209397i
$161$			22.5458i			1.77685i
$162$	2.35776	−	0.487679i	0.185243	−	0.0383157i
$163$		−	20.0027i		−	1.56673i	−0.621562	−	0.783365i	$-0.713502\pi$
$163$		−	20.0027i		−	1.56673i	0.621562	−	0.783365i	$-0.286498\pi$
$164$	2.36217	+	1.36380i	0.184454	+	0.106495i
$165$	8.12781	−	1.49489i	0.632749	−	0.116377i
$166$	1.13067	+	1.95839i	0.0877574	+	0.152000i
$167$	−15.8612	+	9.15745i	−1.22737	+	0.708625i	−0.966480	−	0.256743i	$-0.917351\pi$
$167$	−15.8612	+	9.15745i	−1.22737	+	0.708625i	−0.260894	+	0.965367i	$0.584017\pi$
$168$	−2.32995	+	6.55105i	−0.179759	+	0.505424i
$169$	9.73745	+	8.61291i	0.749034	+	0.662531i
$170$	1.20182			0.0921750
$171$	0.888760	+	2.33438i	0.0679652	+	0.178515i
$172$	−17.6344			−1.34461
$173$	−8.48559	+	14.6975i	−0.645148	+	1.11743i	0.339120	+	0.940743i	$0.389871\pi$
$173$	−8.48559	+	14.6975i	−0.645148	+	1.11743i	−0.984267	+	0.176685i	$0.943463\pi$
$174$	1.21427	−	1.03421i	0.0920534	−	0.0784033i
$175$	−3.30805	+	1.90990i	−0.250065	+	0.144375i
$176$	14.7751	−	8.53043i	1.11372	−	0.643006i
$177$	1.50964	−	1.28579i	0.113472	−	0.0966456i
$178$	−0.786107	+	1.36158i	−0.0589212	+	0.102054i
$179$	8.16369			0.610183			0.305091	−	0.952323i	$-0.401313\pi$
$179$	8.16369			0.610183			0.305091	+	0.952323i	$0.401313\pi$
$180$	5.71157	+	0.920663i	0.425716	+	0.0686221i
$181$	8.83681			0.656835			0.328417	−	0.944533i	$-0.393485\pi$
$181$	8.83681			0.656835			0.328417	+	0.944533i	$0.393485\pi$
$182$	−0.592456	−	3.63646i	−0.0439157	−	0.269552i
$183$	−5.90506	+	16.6031i	−0.436515	+	1.22734i
$184$	−5.37191	+	3.10147i	−0.396022	+	0.228644i
$185$	0.714856	+	1.23817i	0.0525573	+	0.0910319i
$186$	2.16765	−	0.398681i	0.158940	−	0.0292327i
$187$	18.5631	+	10.7174i	1.35747	+	0.783736i
$188$		−	25.0627i		−	1.82789i
$189$	−19.8434	+	0.438072i	−1.44340	+	0.0318651i
$190$		−	0.222740i		−	0.0161593i
$191$	−3.11255	+	5.39110i	−0.225217	+	0.390086i	−0.956384	−	0.292111i	$-0.905642\pi$
$191$	−3.11255	+	5.39110i	−0.225217	+	0.390086i	0.731168	+	0.682198i	$0.238976\pi$
$192$	10.7886	−	1.98427i	0.778598	−	0.143202i
$193$	3.50344	−	2.02271i	0.252183	−	0.145598i	−0.368580	−	0.929596i	$-0.620156\pi$
$193$	3.50344	−	2.02271i	0.252183	−	0.145598i	0.620764	+	0.783998i	$0.286823\pi$
$194$	−1.90922	−	3.30687i	−0.137074	−	0.237419i
$195$	−5.88040	+	2.10259i	−0.421104	+	0.150570i
$196$	7.31926	−	12.6773i	0.522804	−	0.905523i
$197$		−	0.284920i		−	0.0202997i	−0.999948	−	0.0101498i	$-0.996769\pi$
$197$		−	0.284920i		−	0.0202997i	0.999948	−	0.0101498i	$-0.00323085\pi$
$198$	−2.96927	−	2.41796i	−0.211017	−	0.171837i
$199$	10.3617			0.734520			0.367260	−	0.930118i	$-0.380296\pi$
$199$	10.3617			0.734520			0.367260	+	0.930118i	$0.380296\pi$
$200$	−0.910132	−	0.525465i	−0.0643561	−	0.0371560i
$201$	16.0381	−	13.6599i	1.13124	−	0.963498i
$202$	1.96150	−	1.13247i	0.138011	−	0.0796806i
$203$	−11.3872	+	6.57442i	−0.799227	+	0.461434i
$204$	9.72962	+	11.4236i	0.681210	+	0.799809i
$205$	0.707206	−	1.22492i	0.0493934	−	0.0855519i
$206$			3.30329i			0.230151i
$207$	−13.7304	−	11.1810i	−0.954327	−	0.777135i
$208$	−9.98334	+	8.15772i	−0.692220	+	0.565636i
$209$	1.98633	−	3.44043i	0.137397	−	0.237979i
$210$	1.66760	+	0.593098i	0.115075	+	0.0409277i
$211$	−8.61115	−	14.9149i	−0.592816	−	1.02679i	−0.993851	−	0.110724i	$-0.964683\pi$
$211$	−8.61115	−	14.9149i	−0.592816	−	1.02679i	0.401035	−	0.916063i	$-0.368650\pi$
$212$	8.04707	+	13.9379i	0.552675	+	0.957261i
$213$	−0.351716	−	1.91230i	−0.0240992	−	0.131029i
$214$	−2.27235	−	1.31194i	−0.155334	−	0.0896824i
$215$			9.14441i			0.623644i
$216$	−2.83411	−	4.66777i	−0.192837	−	0.317602i
$217$	−18.1693			−1.23341
$218$	−1.96766	+	3.40809i	−0.133267	+	0.230825i
$219$	−1.94520	−	10.5762i	−0.131445	−	0.714670i
$220$	−4.60057	−	7.96842i	−0.310170	−	0.537231i
$221$	−15.1474	−	5.73782i	−1.01893	−	0.385968i
$222$	0.221991	−	0.624165i	0.0148990	−	0.0418912i
$223$	−4.17729	−	2.41176i	−0.279732	−	0.161503i	0.353570	−	0.935408i	$-0.384968\pi$
$223$	−4.17729	−	2.41176i	−0.279732	−	0.161503i	−0.633302	+	0.773905i	$0.718301\pi$
$224$	11.6826			0.780577
$225$	0.477415	−	2.96177i	0.0318276	−	0.197451i
$226$		−	3.83661i		−	0.255207i
$227$	−22.5056	−	12.9936i	−1.49375	−	0.862415i	−0.493773	−	0.869591i	$-0.664382\pi$
$227$	−22.5056	−	12.9936i	−1.49375	−	0.862415i	−0.999974	+	0.00717601i	$0.997716\pi$
$228$	2.11720	−	1.80326i	0.140215	−	0.119424i
$229$	17.5404	−	10.1269i	1.15910	−	0.669207i	0.208012	−	0.978126i	$-0.433301\pi$
$229$	17.5404	−	10.1269i	1.15910	−	0.669207i	0.951088	+	0.308919i	$0.0999673\pi$
$230$	0.789494	+	1.36744i	0.0520577	+	0.0901665i
$231$	20.4685	+	24.0321i	1.34673	+	1.58119i
$232$	−3.13293	−	1.80880i	−0.205687	−	0.118754i
$233$	4.52185			0.296237			0.148118	−	0.988970i	$-0.452678\pi$
$233$	4.52185			0.296237			0.148118	+	0.988970i	$0.452678\pi$
$234$	2.50842	+	1.44261i	0.163980	+	0.0943061i
$235$	−12.9964			−0.847792
$236$	−1.91204	−	1.10391i	−0.124463	−	0.0718587i
$237$	8.37600	−	23.5506i	0.544080	−	1.52977i
$238$	2.29535	+	3.97566i	0.148785	+	0.257704i
$239$	4.86344	−	2.80791i	0.314590	−	0.181628i	−0.334389	−	0.942435i	$-0.608530\pi$
$239$	4.86344	−	2.80791i	0.314590	−	0.181628i	0.648978	+	0.760807i	$0.275197\pi$
$240$	−1.12031	−	6.09117i	−0.0723156	−	0.393183i
$241$	12.8454	+	7.41628i	0.827443	+	0.477724i	0.852976	−	0.521950i	$-0.174795\pi$
$241$	12.8454	+	7.41628i	0.827443	+	0.477724i	−0.0255335	+	0.999674i	$0.508128\pi$
$242$			3.14745i			0.202326i
$243$	9.57408	−	12.3019i	0.614178	−	0.789168i
$244$	19.6199			1.25604
$245$	−6.57390	−	3.79544i	−0.419991	−	0.242482i
$246$	−0.644565	+	0.118551i	−0.0410960	+	0.00755851i
$247$	−1.06343	+	2.80738i	−0.0676644	+	0.178629i
$248$	−2.49943	−	4.32915i	−0.158714	−	0.274901i
$249$	13.7946	+	4.90619i	0.874198	+	0.310917i
$250$	−0.133759	+	0.231678i	−0.00845969	+	0.0146526i
$251$	17.6935			1.11681			0.558403	−	0.829570i	$-0.311414\pi$
$251$	17.6935			1.11681			0.558403	+	0.829570i	$0.311414\pi$
$252$	7.86295	+	20.6525i	0.495319	+	1.30099i
$253$			28.1619i			1.77052i
$254$	−1.96683	−	1.13555i	−0.123410	−	0.0712509i
$255$	5.92375	−	5.04535i	0.370959	−	0.315952i
$256$	−5.28844	−	9.15986i	−0.330528	−	0.572491i
$257$	−4.10102	−	7.10317i	−0.255814	−	0.443084i	0.709302	−	0.704905i	$-0.249010\pi$
$257$	−4.10102	−	7.10317i	−0.255814	−	0.443084i	−0.965116	+	0.261821i	$0.915677\pi$
$258$	3.22570	−	2.74738i	0.200823	−	0.171044i
$259$	−2.73061	+	4.72955i	−0.169672	+	0.293880i
$260$	4.39956	+	5.38414i	0.272849	+	0.333910i
$261$	1.64340	−	10.1952i	0.101724	−	0.631070i
$262$			2.56053i			0.158190i
$263$	1.42875	−	2.47467i	0.0881004	−	0.152594i	−0.818608	−	0.574353i	$-0.805254\pi$
$263$	1.42875	−	2.47467i	0.0881004	−	0.152594i	0.906708	+	0.421759i	$0.138587\pi$
$264$	−2.91033	+	8.18290i	−0.179118	+	0.503623i
$265$	7.22759	−	4.17285i	0.443988	−	0.256336i
$266$	0.736836	−	0.425412i	0.0451783	−	0.0260837i
$267$	1.84132	+	10.0114i	0.112687	+	0.612686i
$268$	−20.3131	−	11.7278i	−1.24082	−	0.716388i
$269$	3.93682			0.240032			0.120016	−	0.992772i	$-0.461705\pi$
$269$	3.93682			0.240032			0.120016	+	0.992772i	$0.461705\pi$
$270$	−1.18820	+	0.721435i	−0.0723117	+	0.0439051i
$271$			22.1080i			1.34296i	0.741021	+	0.671482i	$0.234342\pi$
$271$			22.1080i			1.34296i	−0.741021	+	0.671482i	$0.765658\pi$
$272$	8.03188	−	13.9116i	0.487004	−	0.843516i
$273$	−18.1864	−	15.4369i	−1.10069	−	0.934283i
$274$	−1.59708	−	2.76622i	−0.0964831	−	0.167114i
$275$	−4.13207	+	2.38565i	−0.249173	+	0.143860i
$276$	−6.60633	+	18.5748i	−0.397654	+	1.11807i
$277$	4.77717	−	8.27430i	0.287032	−	0.497154i	−0.686068	−	0.727538i	$-0.740665\pi$
$277$	4.77717	−	8.27430i	0.287032	−	0.497154i	0.973100	+	0.230383i	$0.0739980\pi$
$278$			3.17809i			0.190609i
$279$	9.01063	−	11.0651i	0.539452	−	0.662451i
$280$		−	4.01435i		−	0.239903i
$281$	−22.5837	−	13.0387i	−1.34723	−	0.777823i	−0.359373	−	0.933194i	$-0.617009\pi$
$281$	−22.5837	−	13.0387i	−1.34723	−	0.777823i	−0.987856	+	0.155371i	$0.950343\pi$
$282$	3.90468	+	4.58449i	0.232520	+	0.273002i
$283$	−11.6980	−	20.2616i	−0.695376	−	1.20443i	−0.970054	−	0.242890i	$-0.921905\pi$
$283$	−11.6980	−	20.2616i	−0.695376	−	1.20443i	0.274678	−	0.961536i	$-0.411429\pi$
$284$	−1.87480	+	1.08241i	−0.111249	+	0.0642295i
$285$	−0.935088	−	1.09789i	−0.0553898	−	0.0650333i
$286$	−0.740035	−	4.54229i	−0.0437592	−	0.268591i
$287$	5.40277			0.318915
$288$	−5.79371	+	7.11471i	−0.341397	+	0.419238i
$289$	3.18211			0.187183
$290$	−0.460438	+	0.797502i	−0.0270378	+	0.0468309i
$291$	−23.2931	−	8.28443i	−1.36547	−	0.485642i
$292$	−10.3688	+	5.98640i	−0.606786	+	0.350328i
$293$	−8.06287	+	4.65510i	−0.471038	+	0.271954i	−0.716674	−	0.697408i	$-0.754337\pi$
$293$	−8.06287	+	4.65510i	−0.471038	+	0.271954i	0.245636	+	0.969362i	$0.421003\pi$
$294$	0.636239	+	3.45926i	0.0371062	+	0.201748i
$295$	−0.572441	+	0.991497i	−0.0333288	+	0.0577272i
$296$	−1.50253			−0.0873327
$297$	−24.7864	+	0.547195i	−1.43825	+	0.0317515i
$298$	3.53362			0.204697
$299$	−3.42204	−	21.0042i	−0.197902	−	1.21471i
$300$	−3.28504	+	0.604196i	−0.189662	+	0.0348833i
$301$	−30.2501	+	17.4649i	−1.74359	+	1.00666i
$302$	−0.244543	−	0.423561i	−0.0140719	−	0.0243732i
$303$	4.91400	−	13.8166i	0.282302	−	0.793741i
$304$	−2.57833	−	1.48860i	−0.147878	−	0.0853772i
$305$		−	10.1740i		−	0.582563i
$306$	−3.55950	−	0.573764i	−0.203483	−	0.0327999i
$307$		−	23.3836i		−	1.33458i	−0.744800	−	0.667288i	$-0.767455\pi$
$307$		−	23.3836i		−	1.33458i	0.744800	−	0.667288i	$-0.232545\pi$
$308$	17.5733	−	30.4378i	1.00133	−	1.73435i
$309$	13.8676	+	16.2819i	0.788898	+	0.926245i
$310$	−1.10200	+	0.636242i	−0.0625896	+	0.0361361i
$311$	−0.686243	−	1.18861i	−0.0389133	−	0.0673998i	0.845913	−	0.533321i	$-0.179056\pi$
$311$	−0.686243	−	1.18861i	−0.0389133	−	0.0673998i	−0.884826	+	0.465921i	$0.845723\pi$
$312$	1.17631	−	6.45678i	0.0665955	−	0.365543i
$313$	−5.56238	+	9.63433i	−0.314405	+	0.544565i	−0.979311	−	0.202362i	$-0.935138\pi$
$313$	−5.56238	+	9.63433i	−0.314405	+	0.544565i	0.664906	+	0.746927i	$0.268471\pi$
$314$			1.45947i			0.0823626i
$315$	10.7095	−	4.07738i	0.603411	−	0.229734i
$316$	−27.8298			−1.56555
$317$	−0.868084	−	0.501188i	−0.0487564	−	0.0281495i	0.475424	−	0.879757i	$-0.342295\pi$
$317$	−0.868084	−	0.501188i	−0.0487564	−	0.0281495i	−0.524180	+	0.851607i	$0.675628\pi$
$318$	−3.64346	−	1.29583i	−0.204315	−	0.0726667i
$319$	−14.2238	+	8.21209i	−0.796378	+	0.459789i
$320$	−5.48476	+	3.16663i	−0.306608	+	0.177020i
$321$	−16.7081	+	3.07300i	−0.932553	+	0.171518i
$322$	−3.01571	+	5.22336i	−0.168059	+	0.291087i
$323$		−	3.74048i		−	0.208126i
$324$	−16.4768	−	5.45358i	−0.915379	−	0.302977i
$325$	2.79198	−	2.28142i	0.154871	−	0.126550i
$326$	2.67555	−	4.63418i	0.148185	−	0.256664i
$327$	4.60892	+	25.0589i	0.254874	+	1.38576i
$328$	0.743224	+	1.28730i	0.0410377	+	0.0710793i
$329$	−24.8218	−	42.9927i	−1.36847	−	2.37026i
$330$	2.08299	+	0.740837i	0.114665	+	0.0407818i
$331$	−28.8372	−	16.6492i	−1.58504	−	0.915122i	−0.994107	−	0.108399i	$-0.965427\pi$
$331$	−28.8372	−	16.6492i	−1.58504	−	0.915122i	−0.590930	−	0.806723i	$-0.701239\pi$
$332$		−	16.3011i		−	0.894641i
$333$	−1.52612	−	4.00845i	−0.0836309	−	0.219662i
$334$	−4.89958			−0.268093
$335$	−6.08150	+	10.5335i	−0.332268	+	0.575505i
$336$	18.0102	−	15.3396i	0.982536	−	0.836841i
$337$	−14.2103	−	24.6130i	−0.774085	−	1.34075i	−0.935308	−	0.353836i	$-0.884877\pi$
$337$	−14.2103	−	24.6130i	−0.774085	−	1.34075i	0.161223	−	0.986918i	$-0.448456\pi$
$338$	1.10390	+	3.29790i	0.0600440	+	0.179382i
$339$	−16.1065	−	18.9106i	−0.874784	−	1.02708i
$340$	−7.50272	−	4.33170i	−0.406892	−	0.234919i
$341$	−22.6953			−1.22902
$342$	−0.106340	+	0.659706i	−0.00575019	+	0.0356728i
$343$		−	2.25706i		−	0.121870i
$344$	−8.32262	−	4.80507i	−0.448726	−	0.259072i
$345$	9.63208	+	3.42575i	0.518574	+	0.184436i
$346$	−3.93185	+	2.27006i	−0.211378	+	0.122039i
$347$	14.4761	+	25.0733i	0.777115	+	1.34600i	0.933598	+	0.358322i	$0.116651\pi$
$347$	14.4761	+	25.0733i	0.777115	+	1.34600i	−0.156483	+	0.987681i	$0.550016\pi$
$348$	−11.3081	+	2.07981i	−0.606175	+	0.111490i
$349$	2.19739	+	1.26867i	0.117624	+	0.0679101i	0.557658	−	0.830071i	$-0.311700\pi$
$349$	2.19739	+	1.26867i	0.117624	+	0.0679101i	−0.440034	+	0.897981i	$0.645034\pi$
$350$	−1.02187			−0.0546212
$351$	18.4202	−	3.41999i	0.983197	−	0.182546i
$352$	14.5927			0.777795
$353$	4.46674	+	2.57887i	0.237741	+	0.137260i	0.614138	−	0.789199i	$-0.289504\pi$
$353$	4.46674	+	2.57887i	0.237741	+	0.137260i	−0.376397	+	0.926458i	$0.622837\pi$
$354$	0.521737	−	0.0959596i	0.0277300	−	0.00510020i
$355$	0.561292	+	0.972187i	0.0297903	+	0.0515983i
$356$	9.81505	−	5.66672i	0.520196	−	0.300336i
$357$	28.0040	+	9.95991i	1.48213	+	0.527134i
$358$	1.89135	+	1.09197i	0.0999609	+	0.0577124i
$359$		−	11.9673i		−	0.631610i	−0.948824	−	0.315805i	$-0.897726\pi$
$359$		−	11.9673i		−	0.631610i	0.948824	−	0.315805i	$-0.102274\pi$
$360$	2.44474	+	1.99082i	0.128849	+	0.104925i
$361$	18.3068			0.963513
$362$	2.04730	+	1.18201i	0.107603	+	0.0621249i
$363$	13.2133	+	15.5138i	0.693520	+	0.814263i
$364$	−9.40826	+	24.8371i	−0.493127	+	1.30182i
$365$	3.10428	+	5.37678i	0.162486	+	0.281433i
$366$	−3.58890	+	3.05672i	−0.187595	+	0.159777i
$367$	−8.68972	+	15.0510i	−0.453600	+	0.785658i	−0.998606	−	0.0527738i	$-0.983194\pi$
$367$	−8.68972	+	15.0510i	−0.453600	+	0.785658i	0.545007	+	0.838432i	$0.316527\pi$
$368$	21.1051			1.10018
$369$	−2.67937	+	3.29029i	−0.139483	+	0.171286i
$370$			0.382475i			0.0198839i
$371$	27.6080	+	15.9395i	1.43333	+	0.827536i
$372$	−14.9692	−	5.32395i	−0.776117	−	0.276034i
$373$	5.21095	+	9.02562i	0.269813	+	0.467329i	0.968813	−	0.247792i	$-0.0797049\pi$
$373$	5.21095	+	9.02562i	0.269813	+	0.467329i	−0.699001	+	0.715121i	$0.746372\pi$
$374$	2.86711	+	4.96599i	0.148255	+	0.256785i
$375$	0.313309	+	1.70348i	0.0161792	+	0.0879672i
$376$	6.82916	−	11.8285i	0.352187	−	0.610006i
$377$	9.61078	−	7.85328i	0.494980	−	0.404465i
$378$	−4.65589	−	2.55276i	−0.239473	−	0.131300i
$379$			21.9098i			1.12543i	0.826651	+	0.562715i	$0.190243\pi$
$379$			21.9098i			1.12543i	−0.826651	+	0.562715i	$0.809757\pi$
$380$	−0.802822	+	1.39053i	−0.0411839	+	0.0713326i
$381$	−14.4617	+	2.65984i	−0.740895	+	0.136268i
$382$	−1.44222	+	0.832667i	−0.0737905	+	0.0426030i
$383$	27.7328	−	16.0115i	1.41708	−	0.818150i	0.421036	−	0.907044i	$-0.361666\pi$
$383$	27.7328	−	16.0115i	1.41708	−	0.818150i	0.996041	+	0.0888937i	$0.0283331\pi$
$384$	12.7471	+	4.53362i	0.650496	+	0.231355i
$385$	−15.7837	−	9.11272i	−0.804411	−	0.464427i
$386$	1.08223			0.0550840
$387$	4.36568	−	27.0836i	0.221920	−	1.37674i
$388$			27.5256i			1.39740i
$389$	4.45126	−	7.70981i	0.225688	−	0.390903i	−0.730838	−	0.682551i	$-0.760870\pi$
$389$	4.45126	−	7.70981i	0.225688	−	0.390903i	0.956526	+	0.291648i	$0.0942037\pi$
$390$	−1.64360	−	0.299435i	−0.0832270	−	0.0151625i
$391$	13.2580	+	22.9635i	0.670485	+	1.16131i
$392$	6.90871	−	3.98874i	0.348942	−	0.201462i
$393$	10.7494	+	12.6209i	0.542235	+	0.636638i
$394$	0.0381107	−	0.0660097i	0.00191999	−	0.00332552i
$395$			14.4313i			0.726117i
$396$	9.82159	+	25.7970i	0.493553	+	1.29635i
$397$			8.79341i			0.441328i	0.975350	+	0.220664i	$0.0708225\pi$
$397$			8.79341i			0.441328i	−0.975350	+	0.220664i	$0.929178\pi$
$398$	2.40058	+	1.38597i	0.120330	+	0.0694726i
$399$	1.84594	−	5.19017i	0.0924124	−	0.259834i
$400$	1.78786	+	3.09667i	0.0893931	+	0.154833i
$401$	−2.80491	+	1.61941i	−0.140070	+	0.0808697i	−0.568398	−	0.822754i	$-0.692436\pi$
$401$	−2.80491	+	1.61941i	−0.140070	+	0.0808697i	0.428327	+	0.903624i	$0.359103\pi$
$402$	5.54283	−	1.01946i	0.276451	−	0.0508459i
$403$	16.9270	−	2.75777i	0.843196	−	0.137374i
$404$	−16.3271			−0.812302
$405$	−2.82798	+	8.54415i	−0.140524	+	0.424562i
$406$	−3.51756			−0.174574
$407$	−3.41080	+	5.90767i	−0.169067	+	0.292833i
$408$	1.47921	+	8.04255i	0.0732319	+	0.398165i
$409$	−16.0582	+	9.27123i	−0.794029	+	0.458433i	−0.841379	−	0.540446i	$-0.818256\pi$
$409$	−16.0582	+	9.27123i	−0.794029	+	0.458433i	0.0473500	+	0.998878i	$0.484922\pi$
$410$	0.327688	−	0.189191i	0.0161834	−	0.00934347i
$411$	−19.4849	−	6.93000i	−0.961120	−	0.341832i
$412$	11.9060	−	20.6218i	0.586568	−	1.01596i
$413$	−4.37322			−0.215192
$414$	−1.68546	−	4.42697i	−0.0828358	−	0.217574i
$415$	−8.45305			−0.414944
$416$	−10.8838	+	1.77321i	−0.533624	+	0.0869387i
$417$	13.3420	+	15.6648i	0.653358	+	0.767108i
$418$	0.920379	−	0.531381i	0.0450172	−	0.0259907i
$419$	1.51665	+	2.62692i	0.0740934	+	0.128334i	0.900692	−	0.434459i	$-0.143060\pi$
$419$	1.51665	+	2.62692i	0.0740934	+	0.128334i	−0.826598	+	0.562792i	$0.809727\pi$
$420$	−8.27282	−	9.71312i	−0.403672	−	0.473952i
$421$	15.2998	+	8.83336i	0.745668	+	0.430512i	0.824127	−	0.566406i	$-0.191666\pi$
$421$	15.2998	+	8.83336i	0.745668	+	0.430512i	−0.0784584	+	0.996917i	$0.525000\pi$
$422$		−	4.60729i		−	0.224279i
$423$	38.4924	+	6.20468i	1.87156	+	0.301682i
$424$			8.77076i			0.425946i
$425$	−2.24622	+	3.89058i	−0.108958	+	0.188721i
$426$	0.174303	−	0.490083i	0.00844501	−	0.0237446i
$427$	33.6562	−	19.4314i	1.62874	−	0.940351i
$428$	9.45723	+	16.3804i	0.457133	+	0.791777i
$429$	−22.7166	−	19.2822i	−1.09677	−	0.930953i
$430$	−1.22315	+	2.11856i	−0.0589856	+	0.102166i
$431$		−	18.4289i		−	0.887690i	−0.896104	−	0.443845i	$-0.853614\pi$
$431$		−	18.4289i		−	0.887690i	0.896104	−	0.443845i	$-0.146386\pi$
$432$	0.410080	+	18.5755i	0.0197300	+	0.893713i
$433$	−4.84859			−0.233008			−0.116504	−	0.993190i	$-0.537169\pi$
$433$	−4.84859			−0.233008			−0.116504	+	0.993190i	$0.537169\pi$
$434$	−4.20943	−	2.43032i	−0.202059	−	0.116659i
$435$	1.07850	+	5.86385i	0.0517101	+	0.281150i
$436$	24.5675	−	14.1841i	1.17657	−	0.679294i
$437$	4.25598	−	2.45719i	0.203591	−	0.117543i
$438$	0.964000	−	2.71045i	0.0460617	−	0.129510i
$439$	−7.77071	+	13.4593i	−0.370876	+	0.642376i	−0.989701	−	0.143153i	$-0.954276\pi$
$439$	−7.77071	+	13.4593i	−0.370876	+	0.642376i	0.618825	+	0.785529i	$0.287609\pi$
$440$		−	5.01431i		−	0.239048i
$441$	17.6584	+	14.3797i	0.840875	+	0.684747i
$442$	−2.74184	−	3.35544i	−0.130416	−	0.159602i
$443$	16.7839	−	29.0706i	0.797427	−	1.38118i	−0.123860	−	0.992300i	$-0.539527\pi$
$443$	16.7839	−	29.0706i	0.797427	−	1.38118i	0.921287	−	0.388884i	$-0.127139\pi$
$444$	−3.63552	+	3.09643i	−0.172534	+	0.146950i
$445$	−2.93851	−	5.08965i	−0.139299	−	0.241272i
$446$	−0.645191	−	1.11750i	−0.0305507	−	0.0529153i
$447$	17.4172	−	14.8345i	0.823805	−	0.701648i
$448$	−20.9507	−	12.0959i	−0.989828	−	0.571477i
$449$			4.17757i			0.197152i	0.995130	+	0.0985760i	$0.0314287\pi$
$449$			4.17757i			0.197152i	−0.995130	+	0.0985760i	$0.968571\pi$
$450$	0.506771	−	0.622318i	0.0238894	−	0.0293364i
$451$	6.74859			0.317779
$452$	−13.8283	+	23.9512i	−0.650427	+	1.12657i
$453$	−2.98351	−	1.06111i	−0.140177	−	0.0498555i
$454$	−3.47603	−	6.02066i	−0.163138	−	0.282564i
$455$	12.8794	+	4.87871i	0.603797	+	0.228717i
$456$	1.49058	−	0.274152i	0.0698028	−	0.0128384i
$457$	−6.76599	−	3.90635i	−0.316500	−	0.182731i	0.333332	−	0.942810i	$-0.391827\pi$
$457$	−6.76599	−	3.90635i	−0.316500	−	0.182731i	−0.649831	+	0.760078i	$0.725160\pi$
$458$	5.41829			0.253180
$459$	−19.9535	+	12.1151i	−0.931349	+	0.565483i
$460$		−	11.3823i		−	0.530701i
$461$	−1.48368	−	0.856604i	−0.0691019	−	0.0398960i	0.465051	−	0.885284i	$-0.346036\pi$
$461$	−1.48368	−	0.856604i	−0.0691019	−	0.0398960i	−0.534153	+	0.845388i	$0.679369\pi$
$462$	1.52759	+	8.30556i	0.0710698	+	0.386410i
$463$	19.1053	−	11.0304i	0.887897	−	0.512627i	0.0146429	−	0.999893i	$-0.495339\pi$
$463$	19.1053	−	11.0304i	0.887897	−	0.512627i	0.873254	+	0.487265i	$0.162006\pi$
$464$	6.15433	+	10.6596i	0.285707	+	0.494860i
$465$	−2.76076	+	7.76236i	−0.128027	+	0.359971i
$466$	1.04761	+	0.604841i	0.0485298	+	0.0280187i
$467$	−23.5518			−1.08985			−0.544923	−	0.838486i	$-0.683441\pi$
$467$	−23.5518			−1.08985			−0.544923	+	0.838486i	$0.683441\pi$
$468$	−10.4600	−	18.0470i	−0.483514	−	0.834223i
$469$	−46.4603			−2.14534
$470$	−3.01098	−	1.73839i	−0.138886	−	0.0801861i
$471$	6.12700	+	7.19372i	0.282317	+	0.331469i
$472$	−0.601596	−	1.04199i	−0.0276907	−	0.0479617i
$473$	−37.7853	+	21.8154i	−1.73737	+	1.00307i
$474$	5.09065	−	4.33579i	0.233821	−	0.199149i
$475$	0.721066	+	0.416308i	0.0330848	+	0.0191015i
$476$		−	33.0924i		−	1.51679i
$477$	−23.3986	+	8.90847i	−1.07135	+	0.407891i
$478$	1.50234			0.0687153
$479$	31.9463	+	18.4442i	1.45966	+	0.842736i	0.998994	−	0.0448367i	$-0.0142767\pi$
$479$	31.9463	+	18.4442i	1.45966	+	0.842736i	0.460667	+	0.887573i	$0.347610\pi$
$480$	1.77513	−	4.99109i	0.0810233	−	0.227811i
$481$	1.82605	−	4.82064i	0.0832607	−	0.219802i
$482$	1.98399	+	3.43638i	0.0903685	+	0.156523i
$483$	7.06380	+	38.4062i	0.321414	+	1.74754i
$484$	11.3443	−	19.6490i	0.515652	−	0.893135i
$485$	14.2735			0.648128
$486$	3.86360	−	1.56946i	0.175257	−	0.0711921i
$487$		−	20.6923i		−	0.937657i	−0.883289	−	0.468829i	$-0.844676\pi$
$487$		−	20.6923i		−	0.937657i	0.883289	−	0.468829i	$-0.155324\pi$
$488$	9.25972	+	5.34610i	0.419168	+	0.242007i
$489$	−6.26702	−	34.0741i	−0.283405	−	1.54088i
$490$	−1.01535	−	1.75864i	−0.0458689	−	0.0794473i
$491$	−4.33370	−	7.50620i	−0.195577	−	0.338750i	0.751512	−	0.659719i	$-0.229325\pi$
$491$	−4.33370	−	7.50620i	−0.195577	−	0.338750i	−0.947090	+	0.320969i	$0.895991\pi$
$492$	4.45120	+	1.58311i	0.200675	+	0.0713722i
$493$	−7.73214	+	13.3925i	−0.348238	+	0.603166i
$494$	−0.621886	+	0.508164i	−0.0279800	+	0.0228634i
$495$	13.3772	−	5.09304i	0.601260	−	0.228915i
$496$			17.0083i			0.763697i
$497$	−2.14403	+	3.71356i	−0.0961727	+	0.166576i
$498$	2.53966	+	2.98182i	0.113805	+	0.133618i
$499$	1.92096	−	1.10907i	0.0859941	−	0.0496487i	−0.456386	−	0.889782i	$-0.650856\pi$
$499$	1.92096	−	1.10907i	0.0859941	−	0.0496487i	0.542380	+	0.840133i	$0.317523\pi$
$500$	1.67007	−	0.964217i	0.0746879	−	0.0431211i
$501$	−24.1500	+	20.5690i	−1.07894	+	0.918954i
$502$	4.09921	+	2.36668i	0.182957	+	0.105630i
$503$	8.41584			0.375244			0.187622	−	0.982241i	$-0.439922\pi$
$503$	8.41584			0.375244			0.187622	+	0.982241i	$0.439922\pi$
$504$	−1.91651	+	11.8896i	−0.0853680	+	0.529603i
$505$			8.46650i			0.376754i
$506$	−3.76691	+	6.52449i	−0.167460	+	0.290049i
$507$	19.2860	+	11.6211i	0.856523	+	0.516110i
$508$	8.18573	+	14.1781i	0.363183	+	0.629051i
$509$	8.71784	−	5.03325i	0.386412	−	0.223095i	−0.294193	−	0.955746i	$-0.595051\pi$
$509$	8.71784	−	5.03325i	0.386412	−	0.223095i	0.680604	+	0.732651i	$0.261717\pi$
$510$	2.04727	−	0.376540i	0.0906545	−	0.0166735i
$511$	−11.8577	+	20.5382i	−0.524556	+	0.908557i
$512$		−	18.4518i		−	0.815462i
$513$	2.24537	+	3.69811i	0.0991354	+	0.163276i
$514$		−	2.19420i		−	0.0967820i
$515$	−10.6936	−	6.17393i	−0.471215	−	0.272056i
$516$	−30.0398	+	5.52502i	−1.32243	+	0.243225i
$517$	−31.0049	−	53.7021i	−1.36359	−	2.36181i
$518$	−1.26525	+	0.730490i	−0.0555917	+	0.0320959i
$519$	−9.85016	+	27.6954i	−0.432374	+	1.21569i
$520$	0.609305	+	3.73987i	0.0267198	+	0.164004i
$521$	13.2577			0.580832			0.290416	−	0.956900i	$-0.406206\pi$
$521$	13.2577			0.580832			0.290416	+	0.956900i	$0.406206\pi$
$522$	1.74445	−	2.14220i	0.0763525	−	0.0937614i
$523$	27.9447			1.22193			0.610967	−	0.791656i	$-0.290781\pi$
$523$	27.9447			1.22193			0.610967	+	0.791656i	$0.290781\pi$
$524$	9.22891	−	15.9849i	0.403167	−	0.698306i
$525$	−5.03679	+	4.28992i	−0.219824	+	0.187227i
$526$	0.662020	−	0.382217i	0.0288654	−	0.0166655i
$527$	−18.5060	+	10.6844i	−0.806133	+	0.465421i
$528$	22.4965	−	19.1606i	0.979033	−	0.833858i
$529$	−5.91880	+	10.2517i	−0.257339	+	0.445724i
$530$	2.23263			0.0969794
$531$	2.16879	−	2.66329i	0.0941176	−	0.115577i
$532$	−6.13324			−0.265910
$533$	−5.03337	+	0.820043i	−0.218019	+	0.0355200i
$534$	−0.912521	+	2.56571i	−0.0394886	+	0.111029i
$535$	8.49415	−	4.90410i	0.367234	−	0.212023i
$536$	−6.39124	−	11.0699i	−0.276059	−	0.478149i
$537$	13.9067	−	2.55776i	0.600117	−	0.110376i
$538$	0.912076	+	0.526588i	0.0393224	+	0.0227028i
$539$		−	36.2184i		−	1.56004i
$540$	10.0180	−	0.221162i	0.431106	−	0.00951728i
$541$			37.7179i			1.62162i	0.585310	+	0.810810i	$0.300973\pi$
$541$			37.7179i			1.62162i	−0.585310	+	0.810810i	$0.699027\pi$
$542$	−2.95715	+	5.12194i	−0.127021	+	0.220006i
$543$	15.0533	−	2.76866i	0.645999	−	0.118814i
$544$	11.8991	−	6.86993i	0.510168	−	0.294546i
$545$	−7.35523	−	12.7396i	−0.315063	−	0.545706i
$546$	−2.14857	−	6.00900i	−0.0919503	−	0.257161i
$547$	7.56197	−	13.0977i	0.323326	−	0.560018i	−0.657846	−	0.753153i	$-0.728532\pi$
$547$	7.56197	−	13.0977i	0.323326	−	0.560018i	0.981172	+	0.193135i	$0.0618655\pi$
$548$			23.0254i			0.983596i
$549$	−4.85723	+	30.1331i	−0.207302	+	1.28605i
$550$	−1.27641			−0.0544265
$551$	2.48212	+	1.43305i	0.105742	+	0.0610500i
$552$	−8.17921	+	6.96636i	−0.348130	+	0.296508i
$553$	−47.7394	+	27.5623i	−2.03008	+	1.17207i
$554$	2.21353	−	1.27798i	0.0940439	−	0.0542963i
$555$	1.60567	+	1.88522i	0.0681570	+	0.0800231i
$556$	11.4548	−	19.8402i	0.485790	−	0.841414i
$557$			29.0794i			1.23213i	0.787694	+	0.616066i	$0.211275\pi$
$557$			29.0794i			1.23213i	−0.787694	+	0.616066i	$0.788725\pi$
$558$	3.56763	−	1.35829i	0.151030	−	0.0575010i
$559$	25.5310	−	20.8622i	1.07985	−	0.882378i
$560$	−6.82928	+	11.8287i	−0.288590	+	0.499852i
$561$	34.9797	+	12.4409i	1.47685	+	0.525255i
$562$	−3.48810	−	6.04156i	−0.147136	−	0.254848i
$563$	7.70300	+	13.3420i	0.324643	+	0.562298i	0.981440	−	0.191770i	$-0.0614226\pi$
$563$	7.70300	+	13.3420i	0.324643	+	0.562298i	−0.656797	+	0.754067i	$0.728089\pi$
$564$	−7.85238	−	42.6938i	−0.330645	−	1.79773i
$565$	12.4201	+	7.17072i	0.522516	+	0.301674i
$566$		−	6.25889i		−	0.263081i
$567$	−33.6656	+	6.96338i	−1.41382	+	0.292435i
$568$	−1.17976			−0.0495016
$569$	−3.04754	+	5.27850i	−0.127760	+	0.221286i	−0.922808	−	0.385260i	$-0.874112\pi$
$569$	−3.04754	+	5.27850i	−0.127760	+	0.221286i	0.795049	+	0.606546i	$0.207445\pi$
$570$	−0.0697867	−	0.379434i	−0.00292304	−	0.0158927i
$571$	7.94152	+	13.7551i	0.332342	+	0.575634i	0.982971	−	0.183762i	$-0.0588277\pi$
$571$	7.94152	+	13.7551i	0.332342	+	0.575634i	−0.650628	+	0.759396i	$0.725494\pi$
$572$	−11.7518	+	31.0240i	−0.491369	+	1.29718i
$573$	−3.61308	+	10.1588i	−0.150939	+	0.424391i
$574$	1.25170	+	0.722672i	0.0522451	+	0.0301637i
$575$	−5.90234			−0.246145
$576$	17.7564	−	6.76032i	0.739850	−	0.281680i
$577$			11.4920i			0.478418i	0.970968	+	0.239209i	$0.0768882\pi$
$577$			11.4920i			0.478418i	−0.970968	+	0.239209i	$0.923112\pi$
$578$	0.737224	+	0.425637i	0.0306645	+	0.0177042i
$579$	5.33430	−	4.54331i	0.221686	−	0.188813i
$580$	5.74886	−	3.31911i	0.238709	−	0.137818i
$581$	−16.1445	−	27.9631i	−0.669786	−	1.16010i
$582$	−4.28839	−	5.03500i	−0.177759	−	0.208707i
$583$	34.4851	+	19.9100i	1.42822	+	0.824586i
$584$	−6.52477			−0.269997
$585$	−9.35837	+	5.42410i	−0.386921	+	0.224259i
$586$	−2.49066			−0.102888
$587$	10.1519	+	5.86119i	0.419013	+	0.241917i	0.694655	−	0.719343i	$-0.255557\pi$
$587$	10.1519	+	5.86119i	0.419013	+	0.241917i	−0.275642	+	0.961260i	$0.588890\pi$
$588$	8.49627	−	23.8887i	0.350380	−	0.985155i
$589$	1.98022	+	3.42983i	0.0815934	+	0.141324i
$590$	−0.265244	+	0.153139i	−0.0109199	+	0.00630462i
$591$	−0.0892681	−	0.485355i	−0.00367200	−	0.0199648i
$592$	4.42734	+	2.55613i	0.181963	+	0.105056i
$593$			45.8759i			1.88390i	0.335758	+	0.941948i	$0.391008\pi$
$593$			45.8759i			1.88390i	−0.335758	+	0.941948i	$0.608992\pi$
$594$	−5.81566	−	3.18864i	−0.238619	−	0.130831i
$595$	−17.1603			−0.703502
$596$	−22.0597	−	12.7362i	−0.903602	−	0.521695i
$597$	17.6509	−	3.24641i	0.722403	−	0.132867i
$598$	2.01671	−	5.32396i	0.0824692	−	0.217713i
$599$	4.04403	+	7.00446i	0.165234	+	0.286194i	0.936738	−	0.350030i	$-0.113829\pi$
$599$	4.04403	+	7.00446i	0.165234	+	0.286194i	−0.771504	+	0.636224i	$0.780495\pi$
$600$	−1.71502	−	0.609965i	−0.0700155	−	0.0249017i
$601$	−0.350315	+	0.606763i	−0.0142896	+	0.0247504i	−0.873082	−	0.487574i	$-0.837882\pi$
$601$	−0.350315	+	0.606763i	−0.0142896	+	0.0247504i	0.858792	+	0.512324i	$0.171215\pi$
$602$	−9.34439			−0.380849
$603$	23.0408	−	28.2943i	0.938296	−	1.15223i
$604$			3.52562i			0.143455i
$605$	−10.1891	−	5.88267i	−0.414245	−	0.239165i
$606$	2.98656	−	2.54370i	0.121321	−	0.103331i
$607$	9.23783	+	16.0004i	0.374952	+	0.649436i	0.990320	−	0.138804i	$-0.0443258\pi$
$607$	9.23783	+	16.0004i	0.374952	+	0.649436i	−0.615368	+	0.788240i	$0.710993\pi$
$608$	−1.27325	−	2.20533i	−0.0516371	−	0.0894381i
$609$	−17.3381	+	14.7671i	−0.702574	+	0.598393i
$610$	1.36087	−	2.35710i	0.0551001	−	0.0954363i
$611$	29.6502	+	36.2857i	1.19952	+	1.46796i
$612$	20.1533	+	16.4114i	0.814649	+	0.663391i
$613$			14.1482i			0.571442i	0.958313	+	0.285721i	$0.0922331\pi$
$613$			14.1482i			0.571442i	−0.958313	+	0.285721i	$0.907767\pi$
$614$	3.12778	−	5.41748i	0.126227	−	0.218632i
$615$	0.820932	−	2.30819i	0.0331032	−	0.0930753i
$616$	16.5876	−	9.57683i	0.668332	−	0.385862i
$617$	21.1972	−	12.2382i	0.853365	−	0.492691i	−0.00841953	−	0.999965i	$-0.502680\pi$
$617$	21.1972	−	12.2382i	0.853365	−	0.492691i	0.861785	+	0.507274i	$0.169347\pi$
$618$	1.03495	+	5.62708i	0.0416318	+	0.226354i
$619$	−21.2194	−	12.2510i	−0.852879	−	0.492410i	0.00874197	−	0.999962i	$-0.497217\pi$
$619$	−21.2194	−	12.2510i	−0.852879	−	0.492410i	−0.861621	+	0.507552i	$0.830551\pi$
$620$	9.17281			0.368389
$621$	−26.8925	−	14.7448i	−1.07916	−	0.591687i
$622$		−	0.367166i		−	0.0147220i
$623$	11.2245	−	19.4414i	0.449701	−	0.778905i
$624$	−14.4505	+	17.0244i	−0.578483	+	0.681520i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.57737	+	1.48804i	−0.103012	+	0.0594742i
$627$	2.30575	−	6.48303i	0.0920830	−	0.258907i
$628$	5.26035	−	9.11120i	0.209911	−	0.363576i
$629$			6.42291i			0.256098i
$630$	3.02654	+	0.487855i	0.120580	+	0.0194366i
$631$			9.58282i			0.381486i	0.981640	+	0.190743i	$0.0610897\pi$
$631$			9.58282i			0.381486i	−0.981640	+	0.190743i	$0.938910\pi$
$632$	−13.1344	−	7.58314i	−0.522458	−	0.301641i
$633$	−19.3419	−	22.7093i	−0.768771	−	0.902614i
$634$	−0.134077	−	0.232229i	−0.00532489	−	0.00922298i
$635$	7.35213	−	4.24475i	0.291760	−	0.168448i
$636$	18.0749	+	21.2217i	0.716716	+	0.841497i
$637$	4.40102	+	27.0132i	0.174375	+	1.07030i
$638$	−4.39378			−0.173951
$639$	−1.19828	−	3.14736i	−0.0474033	−	0.124508i
$640$	−7.81113			−0.308762
$641$	10.9001	−	18.8796i	0.430529	−	0.745698i	−0.566390	−	0.824137i	$-0.691660\pi$
$641$	10.9001	−	18.8796i	0.430529	−	0.745698i	0.996919	+	0.0784393i	$0.0249937\pi$
$642$	−4.28194	−	1.52291i	−0.168994	−	0.0601046i
$643$	−10.1778	+	5.87618i	−0.401375	+	0.231734i	−0.687077	−	0.726585i	$-0.741107\pi$
$643$	−10.1778	+	5.87618i	−0.401375	+	0.231734i	0.285702	+	0.958318i	$0.407773\pi$
$644$	37.6531	−	21.7390i	1.48374	−	0.856637i
$645$	2.86503	+	15.5773i	0.112810	+	0.613356i
$646$	0.500325	−	0.866589i	0.0196850	−	0.0340955i
$647$	−14.5742			−0.572970			−0.286485	−	0.958085i	$-0.592487\pi$
$647$	−14.5742			−0.572970			−0.286485	+	0.958085i	$0.592487\pi$
$648$	−6.29030	−	7.06349i	−0.247106	−	0.277480i
$649$	−5.46258			−0.214425
$650$	0.952001	−	0.155101i	0.0373406	−	0.00608357i
$651$	−30.9510	+	5.69262i	−1.21307	+	0.223111i
$652$	−33.4059	+	19.2869i	−1.30828	+	0.755334i
$653$	11.0634	+	19.1624i	0.432944	+	0.749881i	0.997125	−	0.0757697i	$-0.0241414\pi$
$653$	11.0634	+	19.1624i	0.432944	+	0.749881i	−0.564181	+	0.825651i	$0.690808\pi$
$654$	−2.28408	+	6.42209i	−0.0893147	+	0.251124i
$655$	−8.28908	−	4.78570i	−0.323881	−	0.186993i
$656$		−	5.05754i		−	0.197464i
$657$	−6.62722	−	17.4068i	−0.258552	−	0.679104i
$658$		−	13.2806i		−	0.517733i
$659$	−16.5680	+	28.6966i	−0.645397	+	1.11786i	0.338813	+	0.940854i	$0.389975\pi$
$659$	−16.5680	+	28.6966i	−0.645397	+	1.11786i	−0.984210	+	0.177006i	$0.943359\pi$
$660$	−10.3336	−	12.1326i	−0.402233	−	0.472262i
$661$	12.5256	−	7.23168i	0.487191	−	0.281280i	−0.236218	−	0.971700i	$-0.575908\pi$
$661$	12.5256	−	7.23168i	0.487191	−	0.281280i	0.723408	+	0.690421i	$0.242574\pi$
$662$	−4.45397	−	7.71451i	−0.173109	−	0.299833i
$663$	−27.6010	−	5.02842i	−1.07194	−	0.195288i
$664$	4.44178	−	7.69339i	0.172375	−	0.298561i
$665$			3.18043i			0.123332i
$666$	0.182599	−	1.13280i	0.00707558	−	0.0438952i
$667$	−20.3175			−0.786698
$668$	30.5872	+	17.6595i	1.18345	+	0.683268i
$669$	−7.87155	−	2.79959i	−0.304332	−	0.108239i
$670$	−2.81790	+	1.62692i	−0.108865	+	0.0628533i
$671$	42.0398	−	24.2717i	1.62293	−	0.936999i
$672$	19.9011	−	3.66027i	0.767701	−	0.141198i
$673$	−5.87759	+	10.1803i	−0.226565	+	0.392421i	−0.956788	−	0.290787i	$-0.906083\pi$
$673$	−5.87759	+	10.1803i	−0.226565	+	0.392421i	0.730223	+	0.683209i	$0.239416\pi$
$674$		−	7.60305i		−	0.292859i
$675$	−0.114685	−	5.19489i	−0.00441421	−	0.199951i
$676$	4.99517	−	24.5669i	0.192122	−	0.944883i
$677$	5.78307	−	10.0166i	0.222262	−	0.384968i	−0.733233	−	0.679978i	$-0.761989\pi$
$677$	5.78307	−	10.0166i	0.222262	−	0.384968i	0.955494	+	0.295009i	$0.0953228\pi$
$678$	−1.20204	−	6.53557i	−0.0461643	−	0.250997i
$679$	27.2610	+	47.2175i	1.04618	+	1.81204i
$680$	−2.36063	−	4.08872i	−0.0905259	−	0.156795i
$681$	−42.4087	−	15.0831i	−1.62511	−	0.577986i
$682$	−5.25799	−	3.03570i	−0.201339	−	0.116243i
$683$			8.58495i			0.328494i	0.986419	+	0.164247i	$0.0525194\pi$
$683$			8.58495i			0.328494i	−0.986419	+	0.164247i	$0.947481\pi$
$684$	3.04163	−	3.73515i	0.116300	−	0.142817i
$685$	11.9399			0.456202
$686$	0.301903	−	0.522911i	0.0115267	−	0.0199648i
$687$	26.7068	−	22.7466i	1.01893	−	0.867836i
$688$	16.3489	+	28.3172i	0.623298	+	1.07958i
$689$	−28.1397	−	10.6593i	−1.07204	−	0.406085i
$690$	1.77332	+	2.08205i	0.0675090	+	0.0792624i
$691$	11.7004	+	6.75524i	0.445105	+	0.256981i	0.705761	−	0.708450i	$-0.250605\pi$
$691$	11.7004	+	6.75524i	0.445105	+	0.256981i	−0.260656	+	0.965432i	$0.583939\pi$
$692$	32.7278			1.24412
$693$	42.3971	+	34.5251i	1.61053	+	1.31150i
$694$			7.74524i			0.294005i
$695$	−10.2883	−	5.93993i	−0.390256	−	0.225315i
$696$	−5.90360	−	2.09967i	−0.223775	−	0.0795879i
$697$	5.50288	−	3.17709i	0.208436	−	0.120341i
$698$	0.339392	+	0.587844i	0.0128462	+	0.0222502i
$699$	7.70288	−	1.41674i	0.291350	−	0.0535860i
$700$	6.37935	+	3.68312i	0.241117	+	0.139209i
$701$	31.6071			1.19378			0.596892	−	0.802321i	$-0.296402\pi$
$701$	31.6071			1.19378			0.596892	+	0.802321i	$0.296402\pi$
$702$	4.72501	+	1.67154i	0.178334	+	0.0630881i
$703$	1.19040			0.0448968
$704$	−26.1695	−	15.1090i	−0.986299	−	0.569440i
$705$	−22.1391	+	4.07190i	−0.833807	+	0.153356i
$706$	0.689897	+	1.19494i	0.0259646	+	0.0449721i
$707$	−28.0076	+	16.1702i	−1.05333	+	0.608142i
$708$	−3.60298	−	1.28144i	−0.135408	−	0.0481593i
$709$	21.4899	+	12.4072i	0.807069	+	0.465962i	0.845937	−	0.533283i	$-0.179042\pi$
$709$	21.4899	+	12.4072i	0.807069	+	0.465962i	−0.0388678	+	0.999244i	$0.512375\pi$
$710$			0.300313i			0.0112705i
$711$	6.88971	−	42.7422i	0.258384	−	1.60296i
$712$	6.17634			0.231468
$713$	−24.3138	−	14.0376i	−0.910559	−	0.525711i
$714$	5.15569	+	6.05329i	0.192947	+	0.226539i
$715$	16.0877	+	6.09398i	0.601644	+	0.227902i
$716$	−7.87157	−	13.6340i	−0.294174	−	0.509525i
$717$	7.40502	−	6.30697i	0.276545	−	0.235538i
$718$	1.60074	−	2.77256i	0.0597390	−	0.103471i
$719$	−52.7117			−1.96582			−0.982908	−	0.184097i	$-0.941064\pi$
$719$	−52.7117			−1.96582			−0.982908	+	0.184097i	$0.941064\pi$
$720$	−3.81684	−	10.0252i	−0.142245	−	0.373616i
$721$		−	47.1664i		−	1.75657i
$722$	4.24127	+	2.44870i	0.157844	+	0.0911312i
$723$	24.2054	+	8.60889i	0.900208	+	0.320168i
$724$	−8.52060	−	14.7581i	−0.316666	−	0.548481i
$725$	−1.72114	−	2.98110i	−0.0639216	−	0.110715i
$726$	0.986126	+	5.36162i	0.0365986	+	0.198988i
$727$	−23.5424	+	40.7766i	−0.873140	+	1.51232i	−0.0144080	+	0.999896i	$0.504586\pi$
$727$	−23.5424	+	40.7766i	−0.873140	+	1.51232i	−0.858732	+	0.512426i	$0.828747\pi$
$728$	−11.2080	+	9.15840i	−0.415395	+	0.339433i
$729$	12.4549	−	23.9557i	0.461294	−	0.887247i
$730$			1.66091i			0.0614730i
$731$	−20.5404	+	35.5770i	−0.759714	+	1.31586i
$732$	33.4222	−	6.14711i	1.23532	−	0.227204i
$733$	26.6295	−	15.3746i	0.983585	−	0.567873i	0.0802342	−	0.996776i	$-0.474433\pi$
$733$	26.6295	−	15.3746i	0.983585	−	0.567873i	0.903350	+	0.428903i	$0.141100\pi$
$734$	−4.02644	+	2.32466i	−0.148619	+	0.0858049i
$735$	−12.3876	−	4.40579i	−0.456925	−	0.162510i
$736$	15.6334	+	9.02596i	0.576255	+	0.332701i
$737$	−58.0334			−2.13769
$738$	−1.06086	+	0.403897i	−0.0390508	+	0.0148676i
$739$		−	26.2948i		−	0.967271i	−0.875269	−	0.483636i	$-0.839316\pi$
$739$		−	26.2948i		−	0.967271i	0.875269	−	0.483636i	$-0.160684\pi$
$740$	1.37855	−	2.38772i	0.0506766	−	0.0877745i
$741$	−0.931951	+	5.11548i	−0.0342361	+	0.187922i
$742$	4.26411	+	7.38566i	0.156540	+	0.271136i
$743$	40.9295	−	23.6307i	1.50156	−	0.866926i	0.501561	−	0.865122i	$-0.332759\pi$
$743$	40.9295	−	23.6307i	1.50156	−	0.866926i	0.999998	−	0.00180359i	$-0.000574101\pi$
$744$	−5.61409	−	6.59151i	−0.205823	−	0.241657i
$745$	−6.60442	+	11.4392i	−0.241967	+	0.419100i
$746$			2.78805i			0.102078i
$747$	25.0360	+	4.03561i	0.916018	+	0.147655i
$748$		−	41.3357i		−	1.51138i
$749$	32.4460	+	18.7327i	1.18555	+	0.684478i
$750$	−0.155269	+	0.436567i	−0.00566963	+	0.0159412i
$751$	4.66988	+	8.08847i	0.170406	+	0.295153i	0.938562	−	0.345111i	$-0.112159\pi$
$751$	4.66988	+	8.08847i	0.170406	+	0.295153i	−0.768156	+	0.640263i	$0.778825\pi$
$752$	−40.2456	+	23.2358i	−1.46760	+	0.847322i
$753$	30.1406	−	5.54355i	1.09838	−	0.202018i
$754$	3.27706	−	0.533902i	0.119343	−	0.0194436i
$755$	1.82823			0.0665361
$756$	19.8650	+	32.7176i	0.722483	+	1.18993i
$757$	6.34739			0.230700			0.115350	−	0.993325i	$-0.463201\pi$
$757$	6.34739			0.230700			0.115350	+	0.993325i	$0.463201\pi$
$758$	−2.93064	+	5.07602i	−0.106446	+	0.184369i
$759$	8.82337	+	47.9731i	0.320268	+	1.74131i
$760$	−0.757791	+	0.437511i	−0.0274880	+	0.0158702i
$761$	−3.37436	+	1.94819i	−0.122321	+	0.0706218i	−0.559912	−	0.828552i	$-0.689165\pi$
$761$	−3.37436	+	1.94819i	−0.122321	+	0.0706218i	0.437591	+	0.899174i	$0.355832\pi$
$762$	−3.70624	−	1.31816i	−0.134263	−	0.0477519i
$763$	28.0955	−	48.6628i	1.01713	−	1.76171i
$764$	12.0047			0.434315
$765$	8.51022	−	10.4506i	0.307688	−	0.377842i
$766$	8.56676			0.309530
$767$	4.07421	−	0.663776i	0.147111	−	0.0239676i
$768$	−11.8786	−	13.9467i	−0.428633	−	0.503258i
$769$	−16.9967	+	9.81305i	−0.612916	+	0.353867i	−0.774106	−	0.633056i	$-0.781800\pi$
$769$	−16.9967	+	9.81305i	−0.612916	+	0.353867i	0.161190	+	0.986923i	$0.448467\pi$
$770$	−2.43782	−	4.22244i	−0.0878531	−	0.152166i
$771$	−9.21148	−	10.8152i	−0.331743	−	0.389500i
$772$	−6.75615	−	3.90067i	−0.243159	−	0.140388i
$773$		−	41.6088i		−	1.49656i	−0.663381	−	0.748282i	$-0.730879\pi$
$773$		−	41.6088i		−	1.49656i	0.663381	−	0.748282i	$-0.269121\pi$
$774$	4.63412	−	5.69074i	0.166570	−	0.204549i
$775$		−	4.75661i		−	0.170863i
$776$	−7.50024	+	12.9908i	−0.269243	+	0.466343i
$777$	−3.16972	+	8.91222i	−0.113713	+	0.319724i
$778$	2.06252	−	1.19080i	0.0739450	−	0.0426921i
$779$	−0.588831	−	1.01988i	−0.0210970	−	0.0365412i
$780$	9.18146	+	7.79334i	0.328749	+	0.279047i
$781$	−2.67810	+	4.63860i	−0.0958298	+	0.165982i
$782$			7.09352i			0.253664i
$783$	−0.394777	−	17.8823i	−0.0141082	−	0.639060i
$784$	−27.1429			−0.969389
$785$	−4.72466	−	2.72779i	−0.168630	−	0.0973588i
$786$	0.802239	+	4.36181i	0.0286149	+	0.155581i
$787$	−34.9256	+	20.1643i	−1.24496	+	0.718779i	−0.970100	−	0.242705i	$-0.921965\pi$
$787$	−34.9256	+	20.1643i	−1.24496	+	0.718779i	−0.274862	+	0.961484i	$0.588632\pi$
$788$	−0.475837	+	0.274725i	−0.0169510	+	0.00978666i
$789$	1.65851	−	4.66318i	0.0590444	−	0.166014i
$790$	−1.93032	+	3.34342i	−0.0686778	+	0.118953i
$791$			54.7815i			1.94780i
$792$	−2.39390	+	14.8512i	−0.0850637	+	0.527715i
$793$	−28.4057	+	23.2112i	−1.00871	+	0.824254i
$794$	−1.17620	+	2.03724i	−0.0417418	+	0.0722990i
$795$	11.0047	−	9.37284i	0.390295	−	0.332420i
$796$	−9.99091	−	17.3048i	−0.354119	−	0.613351i
$797$	10.3330	+	17.8972i	0.366013	+	0.633953i	0.988938	−	0.148329i	$-0.0473893\pi$
$797$	10.3330	+	17.8972i	0.366013	+	0.633953i	−0.622925	+	0.782281i	$0.714056\pi$
$798$	1.12190	−	0.955538i	0.0397147	−	0.0338257i
$799$	−50.5635	−	29.1929i	−1.78881	−	1.03277i
$800$			3.05843i			0.108132i
$801$	6.27331	+	16.4772i	0.221657	+	0.582195i
$802$	−0.866448			−0.0305953
$803$	−14.8115	+	25.6542i	−0.522686	+	0.905318i
$804$	−38.2773	−	13.6137i	−1.34994	−	0.480119i
$805$	−11.2729	−	19.5252i	−0.397317	−	0.688173i
$806$	4.29050	+	1.62524i	0.151127	+	0.0572465i
$807$	6.70629	−	1.23344i	0.236073	−	0.0434193i
$808$	−7.70563	−	4.44885i	−0.271083	−	0.156510i
$809$	−14.7271			−0.517779			−0.258889	−	0.965907i	$-0.583357\pi$
$809$	−14.7271			−0.517779			−0.258889	+	0.965907i	$0.583357\pi$
$810$	−1.79804	+	1.60122i	−0.0631768	+	0.0562613i
$811$			7.46751i			0.262220i	0.991368	+	0.131110i	$0.0418541\pi$
$811$			7.46751i			0.262220i	−0.991368	+	0.131110i	$0.958146\pi$
$812$	21.9595	+	12.6783i	0.770628	+	0.444922i
$813$	6.92664	+	37.6605i	0.242928	+	1.32081i
$814$	−1.58041	+	0.912453i	−0.0553935	+	0.0319815i
$815$	10.0013	+	17.3228i	0.350331	+	0.606792i
$816$	9.32349	−	26.2146i	0.326387	−	0.917695i
$817$	6.59373	+	3.80689i	0.230685	+	0.133186i
$818$	−4.96046			−0.173438
$819$	−35.8167	−	20.5984i	−1.25154	−	0.719767i
$820$	−2.72760			−0.0952519
$821$	−0.298560	−	0.172373i	−0.0104198	−	0.00601588i	0.494781	−	0.869018i	$-0.335248\pi$
$821$	−0.298560	−	0.172373i	−0.0104198	−	0.00601588i	−0.505201	+	0.863002i	$0.668582\pi$
$822$	−3.58727	−	4.21182i	−0.125121	−	0.146904i
$823$	−5.31913	−	9.21300i	−0.185413	−	0.321145i	0.758302	−	0.651903i	$-0.226029\pi$
$823$	−5.31913	−	9.21300i	−0.185413	−	0.321145i	−0.943716	+	0.330758i	$0.892696\pi$
$824$	11.2382	−	6.48837i	0.391501	−	0.226033i
$825$	−6.29144	+	5.35852i	−0.219040	+	0.186560i
$826$	−1.01318	−	0.584960i	−0.0352530	−	0.0203534i
$827$		−	17.3648i		−	0.603833i	−0.953334	−	0.301917i	$-0.902374\pi$
$827$		−	17.3648i		−	0.603833i	0.953334	−	0.301917i	$-0.0976265\pi$
$828$	−5.43406	+	33.7116i	−0.188847	+	1.17156i
$829$	37.0181			1.28569			0.642847	−	0.765995i	$-0.277753\pi$
$829$	37.0181			1.28569			0.642847	+	0.765995i	$0.277753\pi$
$830$	−1.95839	−	1.13067i	−0.0679766	−	0.0392463i
$831$	5.54538	−	15.5918i	0.192367	−	0.540874i
$832$	21.3542	+	8.08893i	0.740323	+	0.280433i
$833$	−17.0508	−	29.5329i	−0.590776	−	1.02325i
$834$	0.995725	+	5.41380i	0.0344791	+	0.187465i
$835$	9.15745	−	15.8612i	0.316907	−	0.548898i
$836$	−7.66102			−0.264962
$837$	11.8826	−	21.6723i	0.410723	−	0.749104i
$838$			0.811468i			0.0280317i
$839$	−1.16269	−	0.671279i	−0.0401405	−	0.0231751i	0.479795	−	0.877380i	$-0.340711\pi$
$839$	−1.16269	−	0.671279i	−0.0401405	−	0.0231751i	−0.519936	+	0.854205i	$0.674044\pi$
$840$	−1.25773	−	6.83835i	−0.0433959	−	0.235945i
$841$	8.57534	+	14.8529i	0.295701	+	0.512170i
$842$	2.36309	+	4.09299i	0.0814375	+	0.141054i
$843$	−42.5559	−	15.1354i	−1.46570	−	0.521292i
$844$	−16.6060	+	28.7625i	−0.571603	+	0.990045i
$845$	−12.7393	−	2.59027i	−0.438246	−	0.0891081i
$846$	8.08791	+	6.58620i	0.278068	+	0.226438i
$847$		−	44.9413i		−	1.54420i
$848$	14.9210	−	25.8439i	0.512388	−	0.887482i
$849$	−26.2755	−	30.8501i	−0.901772	−	1.05877i
$850$	−1.04080	+	0.600908i	−0.0356992	+	0.0206110i
$851$	−7.30808	+	4.21932i	−0.250518	+	0.144637i
$852$	−2.85455	+	2.43126i	−0.0977951	+	0.0832937i
$853$	−32.8590	−	18.9712i	−1.12507	−	0.649560i	−0.182381	−	0.983228i	$-0.558380\pi$
$853$	−32.8590	−	18.9712i	−1.12507	−	0.649560i	−0.942691	+	0.333668i	$0.891714\pi$
$854$	10.3965			0.355762
$855$	−1.93688	−	1.57726i	−0.0662399	−	0.0539410i
$856$			10.3077i			0.352311i
$857$	12.1748	−	21.0874i	0.415883	−	0.720331i	−0.579638	−	0.814874i	$-0.696806\pi$
$857$	12.1748	−	21.0874i	0.415883	−	0.720331i	0.995521	+	0.0945436i	$0.0301392\pi$
$858$	−2.68377	−	7.50583i	−0.0916226	−	0.256245i
$859$	−19.7298	−	34.1730i	−0.673173	−	1.16597i	−0.976999	−	0.213242i	$-0.931598\pi$
$859$	−19.7298	−	34.1730i	−0.673173	−	1.16597i	0.303827	−	0.952727i	$-0.401736\pi$
$860$	15.2718	−	8.81719i	0.520765	−	0.300664i
$861$	9.20350	−	1.69274i	0.313654	−	0.0576884i
$862$	2.46504	−	4.26958i	0.0839597	−	0.145422i
$863$			2.74234i			0.0933503i	0.998910	+	0.0466752i	$0.0148626\pi$
$863$			2.74234i			0.0933503i	−0.998910	+	0.0466752i	$0.985137\pi$
$864$	−7.64035	+	13.9350i	−0.259930	+	0.474078i
$865$		−	16.9712i		−	0.577037i
$866$	−1.12331	−	0.648544i	−0.0381717	−	0.0220384i
$867$	5.42065	−	0.996983i	0.184095	−	0.0338593i
$868$	17.5192	+	30.3441i	0.594639	+	1.02995i
$869$	−59.6311	+	34.4281i	−2.02285	+	1.16789i
$870$	−0.534481	+	1.50279i	−0.0181206	+	0.0509492i
$871$	43.2837	−	7.05183i	1.46661	−	0.238942i
$872$	15.4597			0.523530
$873$	−42.2749	−	6.81439i	−1.43079	−	0.230632i
$874$	1.31469			0.0444700
$875$	1.90990	−	3.30805i	0.0645664	−	0.111832i
$876$	−15.7874	+	13.4463i	−0.533405	+	0.454310i
$877$	24.0108	−	13.8627i	0.810789	−	0.468109i	−0.0364411	−	0.999336i	$-0.511602\pi$
$877$	24.0108	−	13.8627i	0.810789	−	0.468109i	0.847230	+	0.531227i	$0.178269\pi$
$878$	−3.60061	+	2.07881i	−0.121515	+	0.0701565i
$879$	−12.2764	+	10.4560i	−0.414074	+	0.352673i
$880$	−8.53043	+	14.7751i	−0.287561	+	0.498070i
$881$	55.0259			1.85387			0.926934	−	0.375224i	$-0.122434\pi$
$881$	55.0259			1.85387			0.926934	+	0.375224i	$0.122434\pi$
$882$	2.16764	+	5.69344i	0.0729882	+	0.191708i
$883$	12.5397			0.421994			0.210997	−	0.977487i	$-0.432329\pi$
$883$	12.5397			0.421994			0.210997	+	0.977487i	$0.432329\pi$
$884$	5.02283	+	30.8298i	0.168936	+	1.03692i
$885$	−0.664495	+	1.86834i	−0.0223368	+	0.0628037i
$886$	7.77693	−	4.49001i	0.261271	−	0.150845i
$887$	−4.05100	−	7.01653i	−0.136019	−	0.235592i	0.789967	−	0.613149i	$-0.210098\pi$
$887$	−4.05100	−	7.01653i	−0.136019	−	0.235592i	−0.925986	+	0.377557i	$0.876764\pi$
$888$	−2.55952	+	0.470756i	−0.0858920	+	0.0157975i
$889$	28.0837	+	16.2141i	0.941896	+	0.543804i
$890$		−	1.57221i		−	0.0527007i
$891$	−42.0516	+	8.69794i	−1.40878	+	0.291392i
$892$			9.30183i			0.311448i
$893$	−5.41051	+	9.37127i	−0.181056	+	0.313598i
$894$	6.01944	−	1.10712i	0.201320	−	0.0370275i
$895$	−7.06996	+	4.08185i	−0.236323	+	0.136441i
$896$	−14.9185	−	25.8396i	−0.498392	−	0.863240i
$897$	−12.4102	−	34.7081i	−0.414364	−	1.15887i
$898$	−0.558790	+	0.967853i	−0.0186471	+	0.0322977i
$899$		−	16.3736i		−	0.546091i
$900$	−5.40670	+	2.05847i	−0.180223	+	0.0686157i
$901$	37.4927			1.24906
$902$	1.56350	+	0.902687i	0.0520589	+	0.0300562i
$903$	−46.0585	+	39.2287i	−1.53273	+	1.30545i
$904$	−13.0526	+	7.53593i	−0.434123	+	0.250641i
$905$	−7.65290	+	4.41841i	−0.254391	+	0.146873i
$906$	−0.549279	−	0.644909i	−0.0182486	−	0.0214257i
$907$	13.0546	−	22.6112i	0.433470	−	0.750792i	−0.563699	−	0.825980i	$-0.690622\pi$
$907$	13.0546	−	22.6112i	0.433470	−	0.750792i	0.997169	+	0.0751879i	$0.0239557\pi$
$908$			50.1146i			1.66311i
$909$	4.04203	−	25.0758i	0.134066	−	0.831712i
$910$	2.33131	+	2.85304i	0.0772822	+	0.0945772i
$911$	−6.34012	+	10.9814i	−0.210057	+	0.363830i	−0.951732	−	0.306929i	$-0.900698\pi$
$911$	−6.34012	+	10.9814i	−0.210057	+	0.363830i	0.741675	+	0.670760i	$0.234032\pi$
$912$	−4.85853	−	1.72798i	−0.160882	−	0.0572193i
$913$	−20.1660	−	34.9286i	−0.667398	−	1.15597i
$914$	−1.04502	−	1.81003i	−0.0345662	−	0.0598705i
$915$	−3.18762	−	17.3312i	−0.105379	−	0.572953i
$916$	−33.8254	−	19.5291i	−1.11762	−	0.645261i
$917$		−	36.5609i		−	1.20735i
$918$	−6.24329	+	0.137830i	−0.206059	+	0.00454906i
$919$	30.5912			1.00911			0.504555	−	0.863380i	$-0.331657\pi$
$919$	30.5912			1.00911			0.504555	+	0.863380i	$0.331657\pi$
$920$	3.10147	−	5.37191i	0.102253	−	0.177107i
$921$	−7.32632	−	39.8335i	−0.241410	−	1.31256i
$922$	−0.229158	−	0.396913i	−0.00754691	−	0.0130716i
$923$	1.43378	−	3.78508i	0.0471935	−	0.124587i
$924$	20.3992	−	57.3560i	0.671086	−	1.88687i
$925$	−1.23817	−	0.714856i	−0.0407107	−	0.0235043i
$926$	5.90170			0.193942
$927$	28.7243	+	23.3910i	0.943431	+	0.768262i
$928$			10.5280i			0.345598i
$929$	24.1037	+	13.9163i	0.790817	+	0.456579i	0.840250	−	0.542199i	$-0.182408\pi$
$929$	24.1037	+	13.9163i	0.790817	+	0.456579i	−0.0494328	+	0.998777i	$0.515741\pi$
$930$	−1.67790	+	1.42909i	−0.0550205	+	0.0468618i
$931$	−5.47353	+	3.16014i	−0.179388	+	0.103570i
$932$	−4.36005	−	7.55182i	−0.142818	−	0.247368i
$933$	−1.54140	−	1.80976i	−0.0504632	−	0.0592489i
$934$	−5.45643	−	3.15027i	−0.178540	−	0.103080i
$935$	−21.4348			−0.700994
$936$	−0.0191490	−	11.3675i	−0.000625906	−	0.371559i
$937$	20.7487			0.677832			0.338916	−	0.940817i	$-0.389940\pi$
$937$	20.7487			0.677832			0.338916	+	0.940817i	$0.389940\pi$
$938$	−10.7638	−	6.21450i	−0.351452	−	0.202911i
$939$	−6.45687	+	18.1546i	−0.210712	+	0.592454i
$940$	12.5314	+	21.7049i	0.408728	+	0.707937i
$941$	−13.9038	+	8.02735i	−0.453250	+	0.261684i	−0.709202	−	0.705006i	$-0.750944\pi$
$941$	−13.9038	+	8.02735i	−0.453250	+	0.261684i	0.255952	+	0.966690i	$0.417611\pi$
$942$	0.457265	+	2.48617i	0.0148985	+	0.0810039i
$943$	7.22987	+	4.17417i	0.235437	+	0.135930i
$944$			4.09378i			0.133241i
$945$	16.9659	−	10.3011i	0.551900	−	0.335095i
$946$	−11.6721			−0.379491
$947$	45.7470	+	26.4120i	1.48658	+	0.858276i	0.999883	−	0.0152957i	$-0.00486896\pi$
$947$	45.7470	+	26.4120i	1.48658	+	0.858276i	0.486695	+	0.873572i	$0.338202\pi$
$948$	−47.4074	+	8.71934i	−1.53972	+	0.283191i
$949$	7.92967	−	20.9338i	0.257408	−	0.679538i
$950$	0.111370	+	0.192899i	0.00361333	+	0.00625847i
$951$	−1.63579	−	0.581785i	−0.0530441	−	0.0188657i
$952$	9.01712	−	15.6181i	0.292247	−	0.506186i
$953$	5.17555			0.167653			0.0838263	−	0.996480i	$-0.473286\pi$
$953$	5.17555			0.167653			0.0838263	+	0.996480i	$0.473286\pi$
$954$	−6.61255	−	1.06589i	−0.214089	−	0.0345095i
$955$		−	6.22511i		−	0.201440i
$956$	−9.37882	−	5.41486i	−0.303333	−	0.175129i
$957$	−21.6569	+	18.4456i	−0.700069	+	0.596260i
$958$	4.93417	+	8.54623i	0.159416	+	0.276116i
$959$	22.8041	+	39.4979i	0.736383	+	1.27545i
$960$	−8.35104	+	7.11271i	−0.269529	+	0.229562i
$961$	−4.18731	+	7.25264i	−0.135075	+	0.233956i
$962$	1.06786	−	0.872585i	0.0344293	−	0.0281333i
$963$	−27.4990	+	10.4696i	−0.886143	+	0.337378i
$964$		−	28.6036i		−	0.921260i
$965$	−2.02271	+	3.50344i	−0.0651134	+	0.112780i
$966$	−3.50067	+	9.84273i	−0.112632	+	0.316685i
$967$	−9.25809	+	5.34516i	−0.297720	+	0.171889i	−0.641418	−	0.767191i	$-0.721654\pi$
$967$	−9.25809	+	5.34516i	−0.297720	+	0.171889i	0.343698	+	0.939080i	$0.388320\pi$
$968$	10.7080	−	6.18228i	0.344169	−	0.198706i
$969$	−1.17193	−	6.37183i	−0.0376478	−	0.204693i
$970$	3.30687	+	1.90922i	0.106177	+	0.0613013i
$971$	27.0694			0.868698			0.434349	−	0.900745i	$-0.356978\pi$
$971$	27.0694			0.868698			0.434349	+	0.900745i	$0.356978\pi$
$972$	−29.7766	−	4.12771i	−0.955084	−	0.132396i
$973$		−	45.3787i		−	1.45478i
$974$	2.76779	−	4.79395i	0.0886857	−	0.153608i
$975$	4.04128	−	4.76110i	0.129425	−	0.152477i
$976$	−18.1898	−	31.5056i	−0.582240	−	1.00847i
$977$	2.13248	−	1.23119i	0.0682240	−	0.0393891i	−0.465500	−	0.885048i	$-0.654125\pi$
$977$	2.13248	−	1.23119i	0.0682240	−	0.0393891i	0.533724	+	0.845659i	$0.320792\pi$
$978$	3.10580	−	8.73250i	0.0993126	−	0.279235i
$979$	14.0205	−	24.2843i	0.448098	−	0.776128i
$980$			14.6385i			0.467610i
$981$	15.7024	+	41.2433i	0.501339	+	1.31680i
$982$		−	2.31870i		−	0.0739925i
$983$	−32.3054	−	18.6515i	−1.03038	−	0.594892i	−0.113289	−	0.993562i	$-0.536138\pi$
$983$	−32.3054	−	18.6515i	−1.03038	−	0.594892i	−0.917094	+	0.398670i	$0.869472\pi$
$984$	1.66939	+	1.96003i	0.0532182	+	0.0624835i
$985$	0.142460	+	0.246748i	0.00453915	+	0.00786204i
$986$	−3.58274	+	2.06849i	−0.114098	+	0.0658743i
$987$	−55.7535	−	65.4602i	−1.77465	−	2.08362i
$988$	5.71390	−	0.930915i	0.181783	−	0.0296163i
$989$	−53.9734			−1.71625
$990$	3.78044	+	0.609379i	0.120150	+	0.0193673i
$991$	30.3791			0.965024			0.482512	−	0.875889i	$-0.339724\pi$
$991$	30.3791			0.965024			0.482512	+	0.875889i	$0.339724\pi$
$992$	−7.27390	+	12.5988i	−0.230946	+	0.400011i
$993$	−54.3399	−	19.3265i	−1.72443	−	0.613309i
$994$	−0.993448	+	0.573567i	−0.0315102	+	0.0181924i
$995$	−8.97348	+	5.18084i	−0.284479	+	0.164244i
$996$	−5.10730	−	27.7686i	−0.161831	−	0.879883i
$997$	−0.712739	+	1.23450i	−0.0225727	+	0.0390970i	−0.877091	−	0.480324i	$-0.840519\pi$
$997$	−0.712739	+	1.23450i	−0.0225727	+	0.0390970i	0.854518	+	0.519421i	$0.173852\pi$
$998$	0.593393			0.0187835
$999$	−3.85560	−	6.35016i	−0.121986	−	0.200910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.30	yes	108
9.4	even	3	inner	585.2.bt.b.571.25	yes	108
13.12	even	2	inner	585.2.bt.b.376.25	✓	108
117.103	even	6	inner	585.2.bt.b.571.30	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.25	✓	108	13.12	even	2	inner
585.2.bt.b.376.30	yes	108	1.1	even	1	trivial
585.2.bt.b.571.25	yes	108	9.4	even	3	inner
585.2.bt.b.571.30	yes	108	117.103	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.231678 + 0.133759i) q^{2} +(1.70348 - 0.313309i) q^{3} +(-0.964217 - 1.67007i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.436567 + 0.155269i) q^{6} +(-3.30805 - 1.90990i) q^{7} -1.05093i q^{8} +(2.80367 - 1.06743i) q^{9} +O(q^{10})\)	\(q+(0.231678 + 0.133759i) q^{2} +(1.70348 - 0.313309i) q^{3} +(-0.964217 - 1.67007i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.436567 + 0.155269i) q^{6} +(-3.30805 - 1.90990i) q^{7} -1.05093i q^{8} +(2.80367 - 1.06743i) q^{9} -0.267519 q^{10} +(-4.13207 - 2.38565i) q^{11} +(-2.16577 - 2.54283i) q^{12} +(3.37175 + 1.27721i) q^{13} +(-0.510935 - 0.884965i) q^{14} +(-1.31860 + 1.12307i) q^{15} +(-1.78786 + 3.09667i) q^{16} -4.49245 q^{17} +(0.792329 + 0.127717i) q^{18} +0.832616i q^{19} +(1.67007 + 0.964217i) q^{20} +(-6.23357 - 2.21703i) q^{21} +(-0.638207 - 1.10541i) q^{22} +(-2.95117 - 5.11158i) q^{23} +(-0.329266 - 1.79024i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.610322 + 0.746907i) q^{26} +(4.44156 - 2.69676i) q^{27} +7.36623i q^{28} +(1.72114 - 2.98110i) q^{29} +(-0.455713 + 0.0838162i) q^{30} +(4.11935 - 2.37831i) q^{31} +(-2.64868 + 1.52922i) q^{32} +(-7.78634 - 2.76929i) q^{33} +(-1.04080 - 0.600908i) q^{34} +3.81980 q^{35} +(-4.48604 - 3.65310i) q^{36} -1.42971i q^{37} +(-0.111370 + 0.192899i) q^{38} +(6.14387 + 1.11931i) q^{39} +(0.525465 + 0.910132i) q^{40} +(-1.22492 + 0.707206i) q^{41} +(-1.14763 - 1.34744i) q^{42} +(4.57220 - 7.91929i) q^{43} +9.20114i q^{44} +(-1.89434 + 2.32626i) q^{45} -1.57899i q^{46} +(11.2552 + 6.49820i) q^{47} +(-2.07537 + 5.83526i) q^{48} +(3.79544 + 6.57390i) q^{49} +(0.231678 - 0.133759i) q^{50} +(-7.65279 + 1.40753i) q^{51} +(-1.11806 - 6.86258i) q^{52} -8.34571 q^{53} +(1.38973 - 0.0306803i) q^{54} +4.77130 q^{55} +(-2.00717 + 3.47652i) q^{56} +(0.260866 + 1.41834i) q^{57} +(0.797502 - 0.460438i) q^{58} +(0.991497 - 0.572441i) q^{59} +(3.14703 + 1.11927i) q^{60} +(-5.08702 + 8.81097i) q^{61} +1.27248 q^{62} +(-11.3134 - 1.82363i) q^{63} +6.33326 q^{64} +(-3.55863 + 0.579777i) q^{65} +(-1.43351 - 1.68308i) q^{66} +(10.5335 - 6.08150i) q^{67} +(4.33170 + 7.50272i) q^{68} +(-6.62876 - 7.78283i) q^{69} +(0.884965 + 0.510935i) q^{70} -1.12258i q^{71} +(-1.12180 - 2.94647i) q^{72} -6.20857i q^{73} +(0.191238 - 0.331233i) q^{74} +(0.580405 - 1.63191i) q^{75} +(1.39053 - 0.802822i) q^{76} +(9.11272 + 15.7837i) q^{77} +(1.27368 + 1.08112i) q^{78} +(7.21565 - 12.4979i) q^{79} -3.57572i q^{80} +(6.72118 - 5.98546i) q^{81} -0.378382 q^{82} +(7.32055 + 4.22652i) q^{83} +(2.30791 + 12.5482i) q^{84} +(3.89058 - 2.24622i) q^{85} +(2.11856 - 1.22315i) q^{86} +(1.99792 - 5.61750i) q^{87} +(-2.50715 + 4.34252i) q^{88} +5.87702i q^{89} +(-0.750036 + 0.285558i) q^{90} +(-8.71456 - 10.6648i) q^{91} +(-5.69113 + 9.85733i) q^{92} +(6.27207 - 5.34202i) q^{93} +(1.73839 + 3.01098i) q^{94} +(-0.416308 - 0.721066i) q^{95} +(-4.03285 + 3.43484i) q^{96} +(-12.3612 - 7.13676i) q^{97} +2.03070i q^{98} +(-14.1315 - 2.27789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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