LMFDB - Embedded newform 175.2.t.a.79.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(4,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([3, 20]))

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

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

chi := DirichletCharacter("175.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.t (of order $30$, degree $8$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			79.18
Character	$\chi$	$=$	175.79
Dual form			175.2.t.a.144.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92293 - 1.73141i) q^{2} +(0.0742469 + 0.00780366i) q^{3} +(0.490808 - 4.66973i) q^{4} +(1.31030 + 1.81194i) q^{5} +(0.156283 - 0.113546i) q^{6} +(0.537537 + 2.59057i) q^{7} +(-4.09959 - 5.64260i) q^{8} +(-2.92899 - 0.622576i) q^{9} +O(q^{10})$	\(q+(1.92293 - 1.73141i) q^{2} +(0.0742469 + 0.00780366i) q^{3} +(0.490808 - 4.66973i) q^{4} +(1.31030 + 1.81194i) q^{5} +(0.156283 - 0.113546i) q^{6} +(0.537537 + 2.59057i) q^{7} +(-4.09959 - 5.64260i) q^{8} +(-2.92899 - 0.622576i) q^{9} +(5.65683 + 1.21556i) q^{10} +(-3.69444 + 0.785277i) q^{11} +(0.0728820 - 0.342883i) q^{12} +(-2.66684 + 0.866509i) q^{13} +(5.51899 + 4.05078i) q^{14} +(0.0831458 + 0.144756i) q^{15} +(-8.46720 - 1.79976i) q^{16} +(0.122380 - 0.274870i) q^{17} +(-6.71018 + 3.87412i) q^{18} +(-0.421407 - 4.00942i) q^{19} +(9.10437 - 5.22942i) q^{20} +(0.0196945 + 0.196537i) q^{21} +(-5.74450 + 7.90663i) q^{22} +(5.22426 - 4.70395i) q^{23} +(-0.260349 - 0.450937i) q^{24} +(-1.56624 + 4.74836i) q^{25} +(-3.62786 + 6.28364i) q^{26} +(-0.425616 - 0.138291i) q^{27} +(12.3611 - 1.23868i) q^{28} +(2.21189 + 1.60703i) q^{29} +(0.410516 + 0.134396i) q^{30} +(8.12600 + 3.61793i) q^{31} +(-7.31754 + 4.22478i) q^{32} +(-0.280428 + 0.0294742i) q^{33} +(-0.240586 - 0.740447i) q^{34} +(-3.98962 + 4.36840i) q^{35} +(-4.34484 + 13.3720i) q^{36} +(0.678253 - 3.19093i) q^{37} +(-7.75230 - 6.98020i) q^{38} +(-0.204767 + 0.0435245i) q^{39} +(4.85236 - 14.8217i) q^{40} +(0.700664 + 2.15642i) q^{41} +(0.378157 + 0.343827i) q^{42} -9.05803i q^{43} +(1.85377 + 17.6374i) q^{44} +(-2.70978 - 6.12291i) q^{45} +(1.90141 - 18.0907i) q^{46} +(-2.25775 - 5.07098i) q^{47} +(-0.614619 - 0.199702i) q^{48} +(-6.42211 + 2.78506i) q^{49} +(5.20960 + 11.8426i) q^{50} +(0.0112313 - 0.0194532i) q^{51} +(2.73745 + 12.8787i) q^{52} +(-3.64982 - 0.383611i) q^{53} +(-1.05787 + 0.470993i) q^{54} +(-6.26369 - 5.66514i) q^{55} +(12.4139 - 13.6534i) q^{56} -0.300975i q^{57} +(7.03575 - 0.739487i) q^{58} +(-5.90587 + 6.55913i) q^{59} +(0.716780 - 0.317221i) q^{60} +(9.14775 + 10.1596i) q^{61} +(21.8898 - 7.11244i) q^{62} +(0.0383857 - 7.92241i) q^{63} +(-1.40634 + 4.32826i) q^{64} +(-5.06441 - 3.69676i) q^{65} +(-0.488212 + 0.542215i) q^{66} +(1.39877 - 3.14169i) q^{67} +(-1.22350 - 0.706390i) q^{68} +(0.424593 - 0.308485i) q^{69} +(-0.108243 + 15.3078i) q^{70} +(-2.69801 - 1.96022i) q^{71} +(8.49471 + 19.0794i) q^{72} +(2.72003 + 12.7967i) q^{73} +(-4.22058 - 7.31027i) q^{74} +(-0.153343 + 0.340328i) q^{75} -18.9297 q^{76} +(-4.02021 - 9.14858i) q^{77} +(-0.318393 + 0.438230i) q^{78} +(-7.73783 + 3.44510i) q^{79} +(-7.83351 - 17.7003i) q^{80} +(8.17611 + 3.64024i) q^{81} +(5.08098 + 2.93351i) q^{82} +(-2.74589 - 3.77939i) q^{83} +(0.927439 + 0.00449363i) q^{84} +(0.658402 - 0.138417i) q^{85} +(-15.6832 - 17.4180i) q^{86} +(0.151685 + 0.136578i) q^{87} +(19.5767 + 17.6269i) q^{88} +(-5.15403 - 5.72413i) q^{89} +(-15.8120 - 7.08217i) q^{90} +(-3.67828 - 6.44285i) q^{91} +(-19.4021 - 26.7046i) q^{92} +(0.575097 + 0.332032i) q^{93} +(-13.1215 - 5.84205i) q^{94} +(6.71265 - 6.01709i) q^{95} +(-0.576273 + 0.256573i) q^{96} +(-5.87358 + 8.08430i) q^{97} +(-7.52718 + 16.4748i) q^{98} +11.3099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) $ 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.92293	−	1.73141i	1.35972	−	1.22429i	0.409652	−	0.912242i	$-0.365650\pi$
$2$	1.92293	−	1.73141i	1.35972	−	1.22429i	0.950065	−	0.312052i	$-0.101016\pi$
$3$	0.0742469	+	0.00780366i	0.0428665	+	0.00450545i	0.125937	−	0.992038i	$-0.459806\pi$
$3$	0.0742469	+	0.00780366i	0.0428665	+	0.00450545i	−0.0830710	+	0.996544i	$0.526473\pi$
$4$	0.490808	−	4.66973i	0.245404	−	2.33486i
$5$	1.31030	+	1.81194i	0.585983	+	0.810323i
$5$	1.31030	+	1.81194i	0.585983	+	0.810323i
$6$	0.156283	−	0.113546i	0.0638022	−	0.0463550i
$7$	0.537537	+	2.59057i	0.203170	+	0.979143i
$7$	0.537537	+	2.59057i	0.203170	+	0.979143i
$8$	−4.09959	−	5.64260i	−1.44942	−	1.99496i
$9$	−2.92899	−	0.622576i	−0.976330	−	0.207525i
$10$	5.65683	+	1.21556i	1.78885	+	0.384394i
$11$	−3.69444	+	0.785277i	−1.11391	+	0.236770i	−0.727873	−	0.685712i	$-0.759491\pi$
$11$	−3.69444	+	0.785277i	−1.11391	+	0.236770i	−0.386041	+	0.922482i	$0.626158\pi$
$12$	0.0728820	−	0.342883i	0.0210392	−	0.0989818i
$13$	−2.66684	+	0.866509i	−0.739648	+	0.240326i	−0.654521	−	0.756044i	$-0.727130\pi$
$13$	−2.66684	+	0.866509i	−0.739648	+	0.240326i	−0.0851272	+	0.996370i	$0.527130\pi$
$14$	5.51899	+	4.05078i	1.47501	+	1.08262i
$15$	0.0831458	+	0.144756i	0.0214682	+	0.0373758i
$16$	−8.46720	−	1.79976i	−2.11680	−	0.449940i
$17$	0.122380	−	0.274870i	0.0296815	−	0.0666658i	−0.898096	−	0.439799i	$-0.855050\pi$
$17$	0.122380	−	0.274870i	0.0296815	−	0.0666658i	0.927778	+	0.373133i	$0.121716\pi$
$18$	−6.71018	+	3.87412i	−1.58160	+	0.913140i
$19$	−0.421407	−	4.00942i	−0.0966773	−	0.919823i	−0.930129	−	0.367232i	$-0.880306\pi$
$19$	−0.421407	−	4.00942i	−0.0966773	−	0.919823i	0.833452	−	0.552592i	$-0.186361\pi$
$20$	9.10437	−	5.22942i	2.03580	−	1.16933i
$21$	0.0196945	+	0.196537i	0.00429770	+	0.0428878i
$22$	−5.74450	+	7.90663i	−1.22473	+	1.68570i
$23$	5.22426	−	4.70395i	1.08933	−	0.980841i	0.0894489	−	0.995991i	$-0.471489\pi$
$23$	5.22426	−	4.70395i	1.08933	−	0.980841i	0.999885	+	0.0151506i	$0.00482276\pi$
$24$	−0.260349	−	0.450937i	−0.0531435	−	0.0920472i
$25$	−1.56624	+	4.74836i	−0.313248	+	0.949671i
$26$	−3.62786	+	6.28364i	−0.711482	+	1.23232i
$27$	−0.425616	−	0.138291i	−0.0819098	−	0.0266141i
$28$	12.3611	−	1.23868i	2.33603	−	0.234089i
$29$	2.21189	+	1.60703i	0.410738	+	0.298418i	0.773900	−	0.633307i	$-0.218303\pi$
$29$	2.21189	+	1.60703i	0.410738	+	0.298418i	−0.363163	+	0.931726i	$0.618303\pi$
$30$	0.410516	+	0.134396i	0.0749496	+	0.0245372i
$31$	8.12600	+	3.61793i	1.45947	+	0.649799i	0.974430	−	0.224692i	$-0.0721376\pi$
$31$	8.12600	+	3.61793i	1.45947	+	0.649799i	0.485042	+	0.874491i	$0.338804\pi$
$32$	−7.31754	+	4.22478i	−1.29357	+	0.746843i
$33$	−0.280428	+	0.0294742i	−0.0488163	+	0.00513080i
$34$	−0.240586	−	0.740447i	−0.0412601	−	0.126986i
$35$	−3.98962	+	4.36840i	−0.674369	+	0.738395i
$36$	−4.34484	+	13.3720i	−0.724139	+	2.22867i
$37$	0.678253	−	3.19093i	0.111504	−	0.524585i	−0.886572	−	0.462590i	$-0.846920\pi$
$37$	0.678253	−	3.19093i	0.111504	−	0.524585i	0.998076	−	0.0619955i	$-0.0197464\pi$
$38$	−7.75230	−	6.98020i	−1.25759	−	1.13234i
$39$	−0.204767	+	0.0435245i	−0.0327889	+	0.00696949i
$40$	4.85236	−	14.8217i	0.767225	−	2.34351i
$41$	0.700664	+	2.15642i	0.109425	+	0.336776i	0.990744	−	0.135747i	$-0.0433433\pi$
$41$	0.700664	+	2.15642i	0.109425	+	0.336776i	−0.881318	+	0.472523i	$0.843343\pi$
$42$	0.378157	+	0.343827i	0.0583509	+	0.0530536i
$43$		−	9.05803i		−	1.38134i	−0.723172	−	0.690668i	$-0.757317\pi$
$43$		−	9.05803i		−	1.38134i	0.723172	−	0.690668i	$-0.242683\pi$
$44$	1.85377	+	17.6374i	0.279466	+	2.65894i
$45$	−2.70978	−	6.12291i	−0.403950	−	0.912750i
$46$	1.90141	−	18.0907i	0.280348	−	2.66733i
$47$	−2.25775	−	5.07098i	−0.329326	−	0.739679i	0.670672	−	0.741754i	$-0.266006\pi$
$47$	−2.25775	−	5.07098i	−0.329326	−	0.739679i	−0.999998	+	0.00207553i	$0.999339\pi$
$48$	−0.614619	−	0.199702i	−0.0887126	−	0.0288245i
$49$	−6.42211	+	2.78506i	−0.917444	+	0.397865i
$50$	5.20960	+	11.8426i	0.736749	+	1.67479i
$51$	0.0112313	−	0.0194532i	0.00157270	−	0.00272400i
$52$	2.73745	+	12.8787i	0.379617	+	1.78596i
$53$	−3.64982	−	0.383611i	−0.501341	−	0.0526931i	−0.149517	−	0.988759i	$-0.547772\pi$
$53$	−3.64982	−	0.383611i	−0.501341	−	0.0526931i	−0.351824	+	0.936066i	$0.614439\pi$
$54$	−1.05787	+	0.470993i	−0.143958	+	0.0640941i
$55$	−6.26369	−	5.66514i	−0.844595	−	0.763888i
$56$	12.4139	−	13.6534i	1.65887	−	1.82451i
$57$		−	0.300975i		−	0.0398652i
$58$	7.03575	−	0.739487i	0.923839	−	0.0970994i
$59$	−5.90587	+	6.55913i	−0.768879	+	0.853926i	−0.992688	−	0.120707i	$-0.961484\pi$
$59$	−5.90587	+	6.55913i	−0.768879	+	0.853926i	0.223809	+	0.974633i	$0.428151\pi$
$60$	0.716780	−	0.317221i	0.0925358	−	0.0409531i
$61$	9.14775	+	10.1596i	1.17125	+	1.30080i	0.945126	+	0.326706i	$0.105939\pi$
$61$	9.14775	+	10.1596i	1.17125	+	1.30080i	0.226124	+	0.974099i	$0.427395\pi$
$62$	21.8898	−	7.11244i	2.78001	−	0.903281i
$63$	0.0383857	−	7.92241i	0.00483614	−	0.998130i
$64$	−1.40634	+	4.32826i	−0.175792	+	0.541033i
$65$	−5.06441	−	3.69676i	−0.628163	−	0.458527i
$66$	−0.488212	+	0.542215i	−0.0600948	+	0.0667420i
$67$	1.39877	−	3.14169i	0.170887	−	0.383819i	−0.807717	−	0.589570i	$-0.799297\pi$
$67$	1.39877	−	3.14169i	0.170887	−	0.383819i	0.978604	+	0.205751i	$0.0659638\pi$
$68$	−1.22350	−	0.706390i	−0.148372	−	0.0856624i
$69$	0.424593	−	0.308485i	0.0511150	−	0.0371372i
$70$	−0.108243	+	15.3078i	−0.0129375	+	1.82963i
$71$	−2.69801	−	1.96022i	−0.320195	−	0.232635i	0.416064	−	0.909335i	$-0.363409\pi$
$71$	−2.69801	−	1.96022i	−0.320195	−	0.232635i	−0.736258	+	0.676700i	$0.763409\pi$
$72$	8.49471	+	19.0794i	1.00111	+	2.24853i
$73$	2.72003	+	12.7967i	0.318356	+	1.49775i	0.788433	+	0.615121i	$0.210893\pi$
$73$	2.72003	+	12.7967i	0.318356	+	1.49775i	−0.470077	+	0.882625i	$0.655774\pi$
$74$	−4.22058	−	7.31027i	−0.490633	−	0.849801i
$75$	−0.153343	+	0.340328i	−0.0177065	+	0.0392977i
$76$	−18.9297			−2.17139
$77$	−4.02021	−	9.14858i	−0.458146	−	1.04258i
$78$	−0.318393	+	0.438230i	−0.0360509	+	0.0496198i
$79$	−7.73783	+	3.44510i	−0.870574	+	0.387605i	−0.792884	−	0.609373i	$-0.791421\pi$
$79$	−7.73783	+	3.44510i	−0.870574	+	0.387605i	−0.0776903	+	0.996978i	$0.524755\pi$
$80$	−7.83351	−	17.7003i	−0.875812	−	1.97895i
$81$	8.17611	+	3.64024i	0.908457	+	0.404471i
$82$	5.08098	+	2.93351i	0.561101	+	0.323952i
$83$	−2.74589	−	3.77939i	−0.301401	−	0.414842i	0.631275	−	0.775559i	$-0.282532\pi$
$83$	−2.74589	−	3.77939i	−0.301401	−	0.414842i	−0.932675	+	0.360717i	$0.882532\pi$
$84$	0.927439	+	0.00449363i	0.101192	+	0.000490295i
$85$	0.658402	−	0.138417i	0.0714137	−	0.0150134i
$86$	−15.6832	−	17.4180i	−1.69116	−	1.87823i
$87$	0.151685	+	0.136578i	0.0162624	+	0.0146427i
$88$	19.5767	+	17.6269i	2.08688	+	1.87904i
$89$	−5.15403	−	5.72413i	−0.546326	−	0.606756i	0.405237	−	0.914212i	$-0.367189\pi$
$89$	−5.15403	−	5.72413i	−0.546326	−	0.606756i	−0.951562	+	0.307456i	$0.900522\pi$
$90$	−15.8120	−	7.08217i	−1.66673	−	0.746527i
$91$	−3.67828	−	6.44285i	−0.385588	−	0.675395i
$92$	−19.4021	−	26.7046i	−2.02280	−	2.78415i
$93$	0.575097	+	0.332032i	0.0596348	+	0.0344302i
$94$	−13.1215	−	5.84205i	−1.35338	−	0.602561i
$95$	6.71265	−	6.01709i	0.688703	−	0.617341i
$96$	−0.576273	+	0.256573i	−0.0588156	+	0.0261864i
$97$	−5.87358	+	8.08430i	−0.596372	+	0.820836i	−0.995370	−	0.0961159i	$-0.969358\pi$
$97$	−5.87358	+	8.08430i	−0.596372	+	0.820836i	0.398998	+	0.916952i	$0.369358\pi$
$98$	−7.52718	+	16.4748i	−0.760360	+	1.66421i
$99$	11.3099			1.13668
$100$	21.4048	+	9.64444i	2.14048	+	0.964444i
$101$	−1.10483	−	1.91362i	−0.109934	−	0.190412i	0.805809	−	0.592175i	$-0.201731\pi$
$101$	−1.10483	−	1.91362i	−0.109934	−	0.190412i	−0.915744	+	0.401763i	$0.868397\pi$
$102$	−0.0120845	−	0.0568533i	−0.00119655	−	0.00562932i
$103$	−1.66704	−	3.74424i	−0.164258	−	0.368930i	0.812599	−	0.582824i	$-0.198052\pi$
$103$	−1.66704	−	3.74424i	−0.164258	−	0.368930i	−0.976857	+	0.213893i	$0.931386\pi$
$104$	15.8223	+	11.4956i	1.55150	+	1.12723i
$105$	−0.330306	+	0.293207i	−0.0322346	+	0.0286140i
$106$	−7.68254	+	5.58169i	−0.746194	+	0.542142i
$107$	8.31490	+	4.80061i	0.803831	+	0.464092i	0.844809	−	0.535068i	$-0.179714\pi$
$107$	8.31490	+	4.80061i	0.803831	+	0.464092i	−0.0409777	+	0.999160i	$0.513047\pi$
$108$	−0.854678	+	1.91964i	−0.0822414	+	0.184717i
$109$	−3.84771	+	4.27331i	−0.368543	+	0.409309i	−0.898681	−	0.438603i	$-0.855474\pi$
$109$	−3.84771	+	4.27331i	−0.368543	+	0.409309i	0.530138	+	0.847912i	$0.322140\pi$
$110$	−21.8533	−	0.0486412i	−2.08363	−	0.00463776i
$111$	0.0752591	−	0.231624i	0.00714328	−	0.0219847i
$112$	0.110966	−	22.9023i	0.0104853	−	2.16407i
$113$	−2.42087	+	0.786587i	−0.227736	+	0.0739959i	−0.420662	−	0.907217i	$-0.638202\pi$
$113$	−2.42087	+	0.786587i	−0.227736	+	0.0739959i	0.192926	+	0.981213i	$0.438202\pi$
$114$	−0.521113	−	0.578754i	−0.0488067	−	0.0542053i
$115$	15.3686	+	3.30247i	1.43313	+	0.307957i
$116$	8.59002	−	9.54018i	0.797563	−	0.885784i
$117$	8.35062	−	0.877685i	0.772015	−	0.0811420i
$118$			22.8383i			2.10243i
$119$	0.777854	+	0.169281i	0.0713058	+	0.0155180i
$120$	0.475936	−	1.06260i	0.0434468	−	0.0970015i
$121$	2.98320	−	1.32821i	0.271200	−	0.120746i
$122$	35.1810	+	3.69767i	3.18514	+	0.334771i
$123$	0.0351941	+	0.165575i	0.00317335	+	0.0149294i
$124$	20.8830	−	36.1705i	1.87535	−	3.24821i
$125$	−10.6560	+	3.38384i	−0.953099	+	0.302660i
$126$	−13.6432	−	15.3007i	−1.21543	−	1.36310i
$127$	12.7417	+	4.14002i	1.13064	+	0.367368i	0.813820	−	0.581118i	$-0.197384\pi$
$127$	12.7417	+	4.14002i	1.13064	+	0.367368i	0.316822	+	0.948485i	$0.397384\pi$
$128$	−2.08377	−	4.68023i	−0.184181	−	0.413678i
$129$	0.0706858	−	0.672531i	0.00622354	−	0.0592130i
$130$	−16.1391	+	1.65998i	−1.41550	+	0.145590i
$131$	−1.74086	−	16.5632i	−0.152100	−	1.44713i	−0.758345	−	0.651854i	$-0.773992\pi$
$131$	−1.74086	−	16.5632i	−0.152100	−	1.44713i	0.606245	−	0.795278i	$-0.292675\pi$
$132$			1.32399i			0.115239i
$133$	10.1602	−	3.24689i	0.880997	−	0.281541i
$134$	−2.74983	−	8.46311i	−0.237549	−	0.731101i
$135$	−0.307109	−	0.952392i	−0.0264317	−	0.0819689i
$136$	−2.05269	+	0.436313i	−0.176017	+	0.0374135i
$137$	−6.52307	−	5.87340i	−0.557303	−	0.501798i	0.341659	−	0.939824i	$-0.389011\pi$
$137$	−6.52307	−	5.87340i	−0.557303	−	0.501798i	−0.898962	+	0.438026i	$0.855678\pi$
$138$	0.282348	−	1.32834i	0.0240350	−	0.113076i
$139$	−3.27911	+	10.0921i	−0.278131	+	0.855998i	0.710243	+	0.703956i	$0.248585\pi$
$139$	−3.27911	+	10.0921i	−0.278131	+	0.855998i	−0.988374	+	0.152042i	$0.951415\pi$
$140$	18.4411	+	20.7745i	1.55856	+	1.75576i
$141$	−0.128058	−	0.394123i	−0.0107845	−	0.0331912i
$142$	−8.58202	+	0.902007i	−0.720187	+	0.0756947i
$143$	9.17202	−	5.29547i	0.767003	−	0.442829i
$144$	23.6799	+	10.5430i	1.97332	+	0.878580i
$145$	−0.0136074	+	6.11350i	−0.00113004	+	0.507698i
$146$	27.3869	+	19.8977i	2.26656	+	1.64675i
$147$	−0.498555	+	0.156666i	−0.0411201	+	0.0129216i
$148$	−14.5679	−	4.73339i	−1.19747	−	0.389082i
$149$	−0.695327	+	1.20434i	−0.0569634	+	0.0986635i	−0.893101	−	0.449856i	$-0.851475\pi$
$149$	−0.695327	+	1.20434i	−0.0569634	+	0.0986635i	0.836138	+	0.548520i	$0.184809\pi$
$150$	0.294382	+	0.919928i	0.0240362	+	0.0751118i
$151$	7.74195	+	13.4095i	0.630031	+	1.09125i	0.987545	+	0.157338i	$0.0502912\pi$
$151$	7.74195	+	13.4095i	0.630031	+	1.09125i	−0.357514	+	0.933908i	$0.616375\pi$
$152$	−20.8959	+	18.8148i	−1.69488	+	1.52608i
$153$	−0.529578	+	0.728901i	−0.0428138	+	0.0589282i
$154$	−23.5706	−	10.6314i	−1.89937	−	0.856705i
$155$	4.09202	+	19.4644i	0.328679	+	1.56342i
$156$	0.102746	+	0.977566i	0.00822629	+	0.0782680i
$157$	1.34793	−	0.778227i	0.107576	−	0.0621093i	−0.445246	−	0.895408i	$-0.646884\pi$
$157$	1.34793	−	0.778227i	0.107576	−	0.0621093i	0.552823	+	0.833299i	$0.313551\pi$
$158$	−8.91440	+	20.0221i	−0.709192	+	1.59287i
$159$	−0.267994	−	0.0569639i	−0.0212533	−	0.00451753i
$160$	−17.2432	−	7.72320i	−1.36319	−	0.610573i
$161$	14.9941	+	11.0053i	1.18170	+	0.867337i
$162$	22.0249	−	7.15631i	1.73044	−	0.562253i
$163$	2.07899	−	9.78086i	0.162839	−	0.766096i	−0.818607	−	0.574354i	$-0.805253\pi$
$163$	2.07899	−	9.78086i	0.162839	−	0.766096i	0.981445	−	0.191742i	$-0.0614136\pi$
$164$	10.4138	−	2.21352i	0.813181	−	0.172847i
$165$	−0.420850	−	0.469499i	−0.0327632	−	0.0365504i
$166$	−11.8238	−	2.51324i	−0.917709	−	0.195065i
$167$	−8.72392	−	12.0074i	−0.675077	−	0.929164i	0.324785	−	0.945788i	$-0.394708\pi$
$167$	−8.72392	−	12.0074i	−0.675077	−	0.929164i	−0.999862	+	0.0166240i	$0.994708\pi$
$168$	1.02824	−	0.916847i	0.0793302	−	0.0707363i
$169$	−4.15602	+	3.01953i	−0.319694	+	0.232271i
$170$	1.02640	−	1.40613i	0.0787216	−	0.107845i
$171$	−1.26187	+	12.0059i	−0.0964977	+	0.918114i
$172$	−42.2985	−	4.44576i	−3.22523	−	0.338986i
$173$	−3.93105	+	3.53953i	−0.298872	+	0.269106i	−0.804899	−	0.593412i	$-0.797780\pi$
$173$	−3.93105	+	3.53953i	−0.298872	+	0.269106i	0.506027	+	0.862518i	$0.331114\pi$
$174$	0.528153			0.0400392
$175$	−13.1429	−	1.50503i	−0.993507	−	0.113770i
$176$	32.6948			2.46447
$177$	−0.489678	+	0.440908i	−0.0368064	+	0.0331407i
$178$	−19.8217	−	2.08334i	−1.48570	−	0.156153i
$179$	0.241725	−	2.29986i	0.0180674	−	0.171900i	−0.981767	−	0.190087i	$-0.939123\pi$
$179$	0.241725	−	2.29986i	0.0180674	−	0.171900i	0.999835	+	0.0181875i	$0.00578960\pi$
$180$	−29.9223	+	9.64877i	−2.23028	+	0.719177i
$181$	−14.4034	+	10.4647i	−1.07060	+	0.777834i	−0.976019	−	0.217684i	$-0.930150\pi$
$181$	−14.4034	+	10.4647i	−1.07060	+	0.777834i	−0.0945769	+	0.995518i	$0.530150\pi$
$182$	−18.2283	−	6.02054i	−1.35117	−	0.446272i
$183$	0.599910	+	0.825706i	0.0443466	+	0.0610379i
$184$	−47.9598	−	10.1942i	−3.53564	−	0.751524i
$185$	6.67048	−	2.95212i	0.490423	−	0.217044i
$186$	1.68076	−	0.357256i	0.123239	−	0.0261953i
$187$	−0.236276	+	1.11159i	−0.0172782	+	0.0812877i
$188$	−24.7882	+	8.05419i	−1.80787	+	0.587412i
$189$	0.129468	−	1.17692i	0.00941742	−	0.0856087i
$190$	2.48987	−	23.1928i	0.180634	−	1.68258i
$191$	12.5797	+	2.67391i	0.910238	+	0.193477i	0.639154	−	0.769079i	$-0.279285\pi$
$191$	12.5797	+	2.67391i	0.910238	+	0.193477i	0.271084	+	0.962556i	$0.412618\pi$
$192$	−0.138192	+	0.310385i	−0.00997318	+	0.0224001i
$193$	23.0217	−	13.2916i	1.65714	−	0.956751i	0.683116	−	0.730310i	$-0.260624\pi$
$193$	23.0217	−	13.2916i	1.65714	−	0.956751i	0.974025	−	0.226441i	$-0.0727090\pi$
$194$	2.70277	+	25.7151i	0.194048	+	1.84624i
$195$	−0.347169	−	0.313994i	−0.0248613	−	0.0224856i
$196$	9.85343	+	31.3564i	0.703817	+	2.23975i
$197$	−1.94609	+	2.67856i	−0.138653	+	0.190840i	−0.872697	−	0.488263i	$-0.837631\pi$
$197$	−1.94609	+	2.67856i	−0.138653	+	0.190840i	0.734044	+	0.679102i	$0.237631\pi$
$198$	21.7481	−	19.5821i	1.54557	−	1.39164i
$199$	7.70711	+	13.3491i	0.546342	+	0.946293i	0.998521	+	0.0543655i	$0.0173136\pi$
$199$	7.70711	+	13.3491i	0.546342	+	0.946293i	−0.452179	+	0.891927i	$0.649353\pi$
$200$	33.2140	−	10.6287i	2.34858	−	0.751559i
$201$	0.128371	−	0.222345i	0.00905461	−	0.0156830i
$202$	−5.43777	−	1.76684i	−0.382600	−	0.124314i
$203$	−2.97416	+	6.59390i	−0.208745	+	0.462801i
$204$	−0.0853290	−	0.0619951i	−0.00597422	−	0.00434053i
$205$	−2.98922	+	4.09511i	−0.208776	+	0.286015i
$206$	−9.68842	−	4.31356i	−0.675024	−	0.300540i
$207$	−18.2304	+	10.5253i	−1.26710	+	0.731560i
$208$	24.1402	−	2.53723i	1.67382	−	0.175926i
$209$	4.70536	+	14.4816i	0.325477	+	1.00171i
$210$	−0.127494	+	1.13571i	−0.00879790	+	0.0783716i
$211$	3.86469	−	11.8943i	0.266056	−	0.818836i	−0.725392	−	0.688336i	$-0.758342\pi$
$211$	3.86469	−	11.8943i	0.266056	−	0.818836i	0.991448	−	0.130500i	$-0.0416584\pi$
$212$	−3.58272	+	16.8554i	−0.246062	+	1.15763i
$213$	−0.185022	−	0.166594i	−0.0126775	−	0.0114149i
$214$	24.3008	−	5.16529i	1.66117	−	0.353092i
$215$	16.4126	−	11.8687i	1.11933	−	0.809440i
$216$	0.964529	+	2.96852i	0.0656279	+	0.201982i
$217$	−5.00447	+	22.9957i	−0.339725	+	1.56105i
$218$			14.8792i			1.00775i
$219$	0.102092	+	0.971345i	0.00689877	+	0.0656374i
$220$	−29.5290	+	26.4692i	−1.99084	+	1.78455i
$221$	−0.0881907	+	0.839078i	−0.00593235	+	0.0564425i
$222$	−0.256318	−	0.575701i	−0.0172030	−	0.0386385i
$223$	7.39692	+	2.40341i	0.495334	+	0.160944i	0.546022	−	0.837771i	$-0.316141\pi$
$223$	7.39692	+	2.40341i	0.495334	+	0.160944i	−0.0506879	+	0.998715i	$0.516141\pi$
$224$	−14.8780	−	16.6856i	−0.994081	−	1.11485i
$225$	7.54371	−	12.9328i	0.502914	−	0.862186i
$226$	−3.29325	+	5.70407i	−0.219064	+	0.379429i
$227$	−1.43417	−	6.74725i	−0.0951894	−	0.447831i	−0.999768	−	0.0215248i	$-0.993148\pi$
$227$	−1.43417	−	6.74725i	−0.0951894	−	0.447831i	0.904579	−	0.426306i	$-0.140185\pi$
$228$	−1.40547	−	0.147721i	−0.0930797	−	0.00978308i
$229$	16.7763	−	7.46928i	1.10861	−	0.493584i	0.230996	−	0.972955i	$-0.425802\pi$
$229$	16.7763	−	7.46928i	1.10861	−	0.493584i	0.877613	+	0.479371i	$0.159135\pi$
$230$	35.2707	−	20.2590i	2.32568	−	1.33584i
$231$	−0.227096	−	0.710626i	−0.0149418	−	0.0467558i
$232$		−	19.0690i		−	1.25194i
$233$	−8.90777	+	0.936244i	−0.583567	+	0.0613354i	−0.391712	−	0.920088i	$-0.628117\pi$
$233$	−8.90777	+	0.936244i	−0.583567	+	0.0613354i	−0.191855	+	0.981423i	$0.561450\pi$
$234$	14.5380	−	16.1461i	0.950380	−	1.05550i
$235$	6.22998	−	10.7354i	0.406399	−	0.700300i
$236$	27.7307	+	30.7981i	1.80512	+	2.00478i
$237$	−0.601394	+	0.195405i	−0.0390648	+	0.0126929i
$238$	1.78886	−	1.02127i	0.115954	−	0.0661992i
$239$	5.12153	−	15.7624i	0.331284	−	1.01959i	−0.637240	−	0.770666i	$-0.719924\pi$
$239$	5.12153	−	15.7624i	0.331284	−	1.01959i	0.968524	−	0.248922i	$-0.0800761\pi$
$240$	−0.443487	−	1.37532i	−0.0286269	−	0.0887765i
$241$	−3.92748	+	4.36190i	−0.252991	+	0.280975i	−0.856240	−	0.516578i	$-0.827206\pi$
$241$	−3.92748	+	4.36190i	−0.252991	+	0.280975i	0.603249	+	0.797553i	$0.293872\pi$
$242$	3.43681	−	7.71920i	0.220927	−	0.496209i
$243$	1.74133	+	1.00536i	0.111707	+	0.0644938i
$244$	51.9324	−	37.7311i	3.32463	−	2.41549i
$245$	−13.4612	−	7.98721i	−0.860006	−	0.510284i
$246$	0.354355	+	0.257454i	0.0225929	+	0.0164147i
$247$	4.59802	+	10.3273i	0.292565	+	0.657112i
$248$	−12.8987	−	60.6837i	−0.819070	−	3.85342i
$249$	−0.174381	−	0.302036i	−0.0110509	−	0.0191408i
$250$	−14.6319	+	24.9568i	−0.925400	+	1.57840i
$251$	−3.59519			−0.226927			−0.113463	−	0.993542i	$-0.536194\pi$
$251$	−3.59519			−0.226927			−0.113463	+	0.993542i	$0.536194\pi$
$252$	−36.9767	−	4.06764i	−2.32931	−	0.256237i
$253$	−15.6068	+	21.4809i	−0.981192	+	1.35049i
$254$	31.6694	−	14.1001i	1.98712	−	0.884722i
$255$	0.0499645	−	0.00513906i	0.00312890	−	0.000321821i
$256$	−20.4255	−	9.09400i	−1.27659	−	0.568375i
$257$	−3.78375	−	2.18455i	−0.236024	−	0.136268i	0.377324	−	0.926081i	$-0.376844\pi$
$257$	−3.78375	−	2.18455i	−0.236024	−	0.136268i	−0.613348	+	0.789813i	$0.710178\pi$
$258$	−1.02850	−	1.41562i	−0.0640319	−	0.0881324i
$259$	8.63091	+	0.0418185i	0.536299	+	0.00259847i
$260$	−19.7485	+	21.8350i	−1.22475	+	1.35415i
$261$	−5.47811	−	6.08405i	−0.339086	−	0.376593i
$262$	−32.0253	−	28.8357i	−1.97853	−	1.78147i
$263$	5.86181	+	5.27800i	0.361455	+	0.325455i	0.829769	−	0.558107i	$-0.188472\pi$
$263$	5.86181	+	5.27800i	0.361455	+	0.325455i	−0.468315	+	0.883562i	$0.655139\pi$
$264$	1.31595	+	1.46151i	0.0809913	+	0.0899499i
$265$	−4.08727	−	7.11589i	−0.251079	−	0.437126i
$266$	13.9155	−	23.8350i	0.853217	−	1.46142i
$267$	−0.338001	−	0.465219i	−0.0206854	−	0.0284709i
$268$	−13.9843	−	8.07386i	−0.854229	−	0.493189i
$269$	−16.2693	−	7.24356i	−0.991957	−	0.441648i	−0.154407	−	0.988007i	$-0.549347\pi$
$269$	−16.2693	−	7.24356i	−0.991957	−	0.441648i	−0.837551	+	0.546360i	$0.816013\pi$
$270$	−2.23953	−	1.29965i	−0.136294	−	0.0790942i
$271$	−9.73896	+	4.33606i	−0.591600	+	0.263397i	−0.680625	−	0.732632i	$-0.738292\pi$
$271$	−9.73896	+	4.33606i	−0.591600	+	0.263397i	0.0890251	+	0.996029i	$0.471625\pi$
$272$	−1.53092	+	2.10713i	−0.0928255	+	0.127763i
$273$	−0.222823	−	0.507066i	−0.0134859	−	0.0306890i
$274$	−22.7127			−1.37212
$275$	2.05759	−	18.7724i	0.124078	−	1.13202i
$276$	−1.23215	−	2.13414i	−0.0741666	−	0.128460i
$277$	0.569159	+	2.67768i	0.0341974	+	0.160886i	0.991933	−	0.126764i	$-0.0404592\pi$
$277$	0.569159	+	2.67768i	0.0341974	+	0.160886i	−0.957735	+	0.287651i	$0.907126\pi$
$278$	11.1680	+	25.0838i	0.669815	+	1.50443i
$279$	−21.5485	−	15.6559i	−1.29008	−	0.937296i
$280$	41.0049	+	4.60316i	2.45051	+	0.275092i
$281$	11.9857	−	8.70811i	0.715006	−	0.519483i	−0.169779	−	0.985482i	$-0.554305\pi$
$281$	11.9857	−	8.70811i	0.715006	−	0.519483i	0.884785	+	0.466000i	$0.154305\pi$
$282$	−0.928638	−	0.536150i	−0.0552996	−	0.0319272i
$283$	−2.66639	+	5.98882i	−0.158501	+	0.355998i	−0.975287	−	0.220942i	$-0.929087\pi$
$283$	−2.66639	+	5.98882i	−0.158501	+	0.355998i	0.816786	+	0.576940i	$0.195754\pi$
$284$	−10.4779	+	11.6369i	−0.621748	+	0.690521i
$285$	0.545349	−	0.394367i	0.0323037	−	0.0233603i
$286$	8.46850	−	26.0634i	0.500753	−	1.54116i
$287$	−5.20973	+	2.97428i	−0.307521	+	0.175566i
$288$	24.0633	−	7.81862i	1.41794	−	0.460717i
$289$	11.3146	+	12.5662i	0.665567	+	0.739187i
$290$	10.5588	+	11.7794i	0.620036	+	0.691709i
$291$	−0.499183	+	0.554398i	−0.0292626	+	0.0324994i
$292$	61.0924	−	6.42107i	3.57516	−	0.375764i
$293$		−	31.4682i		−	1.83839i	−0.393798	−	0.919197i	$-0.628839\pi$
$293$		−	31.4682i		−	1.83839i	0.393798	−	0.919197i	$-0.371161\pi$
$294$	−0.687433	+	1.16446i	−0.0400919	+	0.0679128i
$295$	−19.6232	−	2.10665i	−1.14251	−	0.122654i
$296$	−20.7857	+	9.25438i	−1.20814	+	0.537900i
$297$	1.68101	+	0.176681i	0.0975420	+	0.0102521i
$298$	0.748149	+	3.51976i	0.0433391	+	0.203894i
$299$	−9.85626	+	17.0715i	−0.570002	+	0.987273i
$300$	1.51398	+	0.883106i	0.0874097	+	0.0509861i
$301$	23.4655	−	4.86903i	1.35253	−	0.280646i
$302$	38.1045	+	12.3809i	2.19267	+	0.712442i
$303$	−0.0670968	−	0.150702i	−0.00385461	−	0.00865760i
$304$	−3.64785	+	34.7070i	−0.209219	+	1.99058i
$305$	−6.42230	+	29.8873i	−0.367740	+	1.71134i
$306$	0.243689	+	2.31854i	0.0139308	+	0.132542i
$307$		−	19.5635i		−	1.11655i	−0.829657	−	0.558274i	$-0.811464\pi$
$307$		−	19.5635i		−	1.11655i	0.829657	−	0.558274i	$-0.188536\pi$
$308$	−44.6946	+	14.2831i	−2.54671	+	0.813855i
$309$	−0.0945539	−	0.291007i	−0.00537898	−	0.0165548i
$310$	41.5695	+	30.3436i	2.36099	+	1.72340i
$311$	−32.3352	+	6.87305i	−1.83356	+	0.389735i	−0.989264	−	0.146142i	$-0.953314\pi$
$311$	−32.3352	+	6.87305i	−1.83356	+	0.389735i	−0.844296	+	0.535877i	$0.819981\pi$
$312$	1.08505	+	0.976983i	0.0614288	+	0.0553108i
$313$	−1.58255	+	7.44532i	−0.0894511	+	0.420834i	0.910522	+	0.413461i	$0.135680\pi$
$313$	−1.58255	+	7.44532i	−0.0894511	+	0.420834i	−0.999973	+	0.00737299i	$0.997653\pi$
$314$	1.24454	−	3.83030i	0.0702334	−	0.216156i
$315$	14.4052	−	10.3112i	0.811642	−	0.580969i
$316$	12.2899	+	37.8245i	0.691362	+	2.12779i
$317$	−22.2781	+	2.34152i	−1.25126	+	0.131513i	−0.706886	−	0.707328i	$-0.749900\pi$
$317$	−22.2781	+	2.34152i	−1.25126	+	0.131513i	−0.544377	+	0.838841i	$0.683234\pi$
$318$	−0.613962	+	0.354471i	−0.0344293	+	0.0198778i
$319$	−9.43365	−	4.20013i	−0.528183	−	0.235162i
$320$	−9.68526	+	3.12312i	−0.541423	+	0.174588i
$321$	0.579893	+	0.421317i	0.0323665	+	0.0235156i
$322$	47.8874	−	4.79870i	2.66866	−	0.267421i
$323$	−1.15364	−	0.374841i	−0.0641903	−	0.0208567i
$324$	21.0118	−	36.3936i	1.16732	−	2.02187i
$325$	0.0624130	−	14.0203i	0.00346205	−	0.777704i
$326$	−12.9370	−	22.4075i	−0.716513	−	1.24104i
$327$	−0.319028	+	0.287254i	−0.0176423	+	0.0158852i
$328$	9.29539	−	12.7940i	0.513252	−	0.706431i
$329$	11.9231	−	8.57469i	0.657343	−	0.472738i
$330$	−1.62216	−	0.174148i	−0.0892971	−	0.00958651i
$331$	−0.973552	−	9.26272i	−0.0535112	−	0.509125i	−0.988146	−	0.153516i	$-0.950940\pi$
$331$	−0.973552	−	9.26272i	−0.0535112	−	0.509125i	0.934635	−	0.355609i	$-0.115726\pi$
$332$	−18.9965	+	10.9676i	−1.04257	+	0.601926i
$333$	−3.97319	+	8.92394i	−0.217730	+	0.489029i
$334$	−37.5653	−	7.98476i	−2.05548	−	0.436907i
$335$	7.52536	−	1.58207i	0.411154	−	0.0864375i
$336$	0.186961	−	1.69956i	0.0101996	−	0.0927186i
$337$	13.7643	−	4.47228i	0.749788	−	0.243621i	0.0908979	−	0.995860i	$-0.471026\pi$
$337$	13.7643	−	4.47228i	0.749788	−	0.243621i	0.658890	+	0.752239i	$0.271026\pi$
$338$	−2.76369	+	13.0021i	−0.150325	+	0.707223i
$339$	−0.185880	+	0.0395100i	−0.0100956	+	0.00214589i
$340$	−0.323219	−	3.14250i	−0.0175290	−	0.170426i
$341$	−32.8620	−	6.98504i	−1.77958	−	0.378261i
$342$	18.3607	+	25.2713i	0.992833	+	1.36652i
$343$	−10.6670	−	15.1398i	−0.575964	−	0.817475i
$344$	−51.1108	+	37.1342i	−2.75571	+	2.00214i
$345$	1.11530	+	0.365129i	0.0600457	+	0.0196579i
$346$	−1.43074	+	13.6125i	−0.0769168	+	0.731815i
$347$	3.25103	+	0.341697i	0.174524	+	0.0183433i	0.191387	−	0.981515i	$-0.438701\pi$
$347$	3.25103	+	0.341697i	0.174524	+	0.0183433i	−0.0168631	+	0.999858i	$0.505368\pi$
$348$	0.712231	−	0.641295i	0.0381796	−	0.0343770i
$349$	20.1244			1.07724			0.538618	−	0.842550i	$-0.318947\pi$
$349$	20.1244			1.07724			0.538618	+	0.842550i	$0.318947\pi$
$350$	−27.8786	+	19.8617i	−1.49018	+	1.06165i
$351$	1.25488			0.0669805
$352$	23.7166	−	21.3545i	1.26410	−	1.13820i
$353$	31.4386	+	3.30433i	1.67331	+	0.175872i	0.893166	−	0.449728i	$-0.148479\pi$
$353$	31.4386	+	3.30433i	1.67331	+	0.175872i	0.780144	+	0.625600i	$0.215146\pi$
$354$	−0.178222	+	1.69567i	−0.00947240	+	0.0901238i
$355$	0.0165980	−	7.45709i	0.000880931	−	0.395781i
$356$	−29.2598	+	21.2585i	−1.55076	+	1.12670i
$357$	0.0564323	+	0.0186387i	0.00298671	+	0.000986466i
$358$	−3.51719	−	4.84100i	−0.185889	−	0.255855i
$359$	−10.1064	−	2.14818i	−0.533396	−	0.113377i	−0.0666637	−	0.997776i	$-0.521235\pi$
$359$	−10.1064	−	2.14818i	−0.533396	−	0.113377i	−0.466732	+	0.884399i	$0.654569\pi$
$360$	−23.4401	+	40.3916i	−1.23540	+	2.12883i
$361$	2.68696	−	0.571131i	0.141419	−	0.0300596i
$362$	−9.57803	+	45.0611i	−0.503410	+	2.36836i
$363$	0.231858	−	0.0753353i	0.0121694	−	0.00395408i
$364$	−31.8917	+	14.0144i	−1.67158	+	0.734552i
$365$	−19.6229	+	21.6961i	−1.02711	+	1.13562i
$366$	2.58322	+	0.549081i	0.135027	+	0.0287009i
$367$	6.95238	−	15.6153i	0.362911	−	0.815112i	−0.636141	−	0.771573i	$-0.719470\pi$
$367$	6.95238	−	15.6153i	0.362911	−	0.815112i	0.999052	−	0.0435386i	$-0.0138631\pi$
$368$	−52.7009	+	30.4269i	−2.74722	+	1.58611i
$369$	−0.709701	−	6.75236i	−0.0369456	−	0.351514i
$370$	7.71553	−	17.2261i	0.401111	−	0.895541i
$371$	−0.968142	−	9.66132i	−0.0502634	−	0.501591i
$372$	1.83276	−	2.52258i	0.0950244	−	0.130790i
$373$	−19.2705	+	17.3512i	−0.997787	+	0.898411i	−0.994827	−	0.101584i	$-0.967609\pi$
$373$	−19.2705	+	17.3512i	−0.997787	+	0.898411i	−0.00295977	+	0.999996i	$0.500942\pi$
$374$	1.47028	+	2.54661i	0.0760266	+	0.131682i
$375$	−0.817579	+	0.168084i	−0.0422196	+	0.00867981i
$376$	−19.3577	+	33.5285i	−0.998297	+	1.72910i
$377$	−7.29126	−	2.36908i	−0.375519	−	0.122014i
$378$	−1.78879	−	2.48731i	−0.0920052	−	0.127933i
$379$	6.09850	+	4.43082i	0.313259	+	0.227596i	0.733293	−	0.679912i	$-0.237982\pi$
$379$	6.09850	+	4.43082i	0.313259	+	0.227596i	−0.420035	+	0.907508i	$0.637982\pi$
$380$	−24.8036	−	34.2995i	−1.27240	−	1.75953i
$381$	0.913723	+	0.406816i	0.0468114	+	0.0208418i
$382$	28.8196	−	16.6390i	1.47454	−	0.851325i
$383$	16.7836	−	1.76402i	0.857600	−	0.0901374i	0.334487	−	0.942401i	$-0.391437\pi$
$383$	16.7836	−	1.76402i	0.857600	−	0.0901374i	0.523113	+	0.852263i	$0.324770\pi$
$384$	−0.118191	−	0.363754i	−0.00603139	−	0.0185627i
$385$	11.3090	−	19.2717i	0.576359	−	0.982179i
$386$	21.2559	−	65.4190i	1.08190	−	3.32974i
$387$	−5.63931	+	26.5309i	−0.286662	+	1.34864i
$388$	34.8687	+	31.3959i	1.77019	+	1.59388i
$389$	10.3597	−	2.20203i	0.525259	−	0.111647i	0.0623520	−	0.998054i	$-0.480140\pi$
$389$	10.3597	−	2.20203i	0.525259	−	0.111647i	0.462907	+	0.886407i	$0.346807\pi$
$390$	−1.21124	−	0.00269597i	−0.0613333	−	0.000136516i
$391$	−0.653629	−	2.01166i	−0.0330554	−	0.101734i
$392$	42.0429	+	24.8198i	2.12349	+	1.25359i
$393$		−	1.24335i		−	0.0627187i
$394$	0.895507	+	8.52018i	0.0451150	+	0.429240i
$395$	−16.3812	−	9.50636i	−0.824227	−	0.478317i
$396$	5.55098	−	52.8140i	0.278947	−	2.65400i
$397$	−14.4920	−	32.5495i	−0.727331	−	1.63361i	−0.772802	−	0.634647i	$-0.781145\pi$
$397$	−14.4920	−	32.5495i	−0.727331	−	1.63361i	0.0454708	−	0.998966i	$-0.485521\pi$
$398$	37.9330	+	12.3252i	1.90141	+	0.617806i
$399$	0.779698	−	0.161785i	0.0390337	−	0.00809940i
$400$	21.8076	−	37.3864i	1.09038	−	1.86932i
$401$	2.81098	−	4.86877i	0.140374	−	0.243135i	−0.787264	−	0.616617i	$-0.788503\pi$
$401$	2.81098	−	4.86877i	0.140374	−	0.243135i	0.927637	+	0.373482i	$0.121836\pi$
$402$	−0.138123	−	0.649818i	−0.00688896	−	0.0324100i
$403$	−24.8057	−	2.60718i	−1.23566	−	0.129873i
$404$	−9.47834	+	4.22003i	−0.471565	+	0.209954i
$405$	4.11726	+	19.5844i	0.204588	+	0.973157i
$406$	5.69767	+	17.8291i	0.282771	+	0.884843i
$407$			12.3213i			0.610744i
$408$	−0.155811	+	0.0163764i	−0.00771378	+	0.000810751i
$409$	7.33995	−	8.15184i	0.362937	−	0.403083i	−0.533825	−	0.845595i	$-0.679246\pi$
$409$	7.33995	−	8.15184i	0.362937	−	0.403083i	0.896762	+	0.442512i	$0.145913\pi$
$410$	1.34227	+	13.0502i	0.0662900	+	0.644503i
$411$	−0.438483	−	0.486985i	−0.0216288	−	0.0240212i
$412$	−18.3028	+	5.94693i	−0.901712	+	0.292984i
$413$	−20.1665	−	11.7738i	−0.992330	−	0.579350i
$414$	−16.8321	+	51.8038i	−0.827251	+	2.54602i
$415$	3.25009	−	9.92752i	0.159541	−	0.487323i
$416$	15.8539	−	17.6075i	0.777301	−	0.863280i
$417$	−0.322219	+	0.723716i	−0.0157791	+	0.0354405i
$418$	34.1217	+	19.7002i	1.66895	+	0.963568i
$419$	−10.3403	+	7.51266i	−0.505156	+	0.367018i	−0.810983	−	0.585070i	$-0.801067\pi$
$419$	−10.3403	+	7.51266i	−0.505156	+	0.367018i	0.305827	+	0.952087i	$0.401067\pi$
$420$	1.20708	+	1.68635i	0.0588994	+	0.0822854i
$421$	−31.8380	−	23.1317i	−1.55169	−	1.12737i	−0.942432	−	0.334399i	$-0.891467\pi$
$421$	−31.8380	−	23.1317i	−1.55169	−	1.12737i	−0.609260	−	0.792971i	$-0.708533\pi$
$422$	−13.1624	−	29.5632i	−0.640736	−	1.43912i
$423$	3.45585	+	16.2585i	0.168029	+	0.790515i
$424$	12.7982	+	22.1671i	0.621535	+	1.07653i
$425$	1.11351	+	1.01162i	0.0540129	+	0.0490706i
$426$	−0.644228			−0.0312129
$427$	−21.4019	+	29.1591i	−1.03571	+	1.41111i
$428$	26.4986	−	36.4721i	1.28086	−	1.76295i
$429$	0.722318	−	0.321597i	0.0348738	−	0.0155268i
$430$	11.0106	−	51.2397i	0.530978	−	2.47100i
$431$	−11.8437	−	5.27316i	−0.570491	−	0.253999i	0.101156	−	0.994871i	$-0.467746\pi$
$431$	−11.8437	−	5.27316i	−0.570491	−	0.253999i	−0.671647	+	0.740872i	$0.734413\pi$
$432$	3.35489	+	1.93694i	0.161412	+	0.0931913i
$433$	18.1008	+	24.9136i	0.869868	+	1.19727i	0.979126	+	0.203257i	$0.0651525\pi$
$433$	18.1008	+	24.9136i	0.869868	+	1.19727i	−0.109258	+	0.994013i	$0.534847\pi$
$434$	30.1919	+	52.8840i	1.44926	+	2.53851i
$435$	−0.0487180	+	0.453802i	−0.00233585	+	0.0217581i
$436$	18.0667	+	20.0651i	0.865239	+	0.960945i
$437$	−21.0616	−	18.9640i	−1.00751	−	0.907170i
$438$	1.87812	+	1.69106i	0.0897399	+	0.0808022i
$439$	6.55033	+	7.27487i	0.312630	+	0.347211i	0.878897	−	0.477011i	$-0.158280\pi$
$439$	6.55033	+	7.27487i	0.312630	+	0.347211i	−0.566267	+	0.824222i	$0.691613\pi$
$440$	−6.28760	+	58.5682i	−0.299750	+	2.79213i
$441$	20.5442	−	4.15915i	0.978295	−	0.198055i
$442$	1.28321	+	1.76618i	0.0610359	+	0.0840087i
$443$	23.8217	+	13.7534i	1.13180	+	0.653446i	0.944387	−	0.328835i	$-0.106656\pi$
$443$	23.8217	+	13.7534i	1.13180	+	0.653446i	0.187414	+	0.982281i	$0.439989\pi$
$444$	−1.04468	−	0.465122i	−0.0495784	−	0.0220737i
$445$	3.61845	−	16.8391i	0.171531	−	0.798250i
$446$	18.3850	−	8.18555i	0.870557	−	0.387597i
$447$	−0.0610241	+	0.0839925i	−0.00288634	+	0.00397271i
$448$	−11.9686	−	1.31661i	−0.565464	−	0.0622042i
$449$	21.4940			1.01436			0.507182	−	0.861839i	$-0.330687\pi$
$449$	21.4940			1.01436			0.507182	+	0.861839i	$0.330687\pi$
$450$	−7.88599	−	37.9301i	−0.371749	−	1.78804i
$451$	−4.28195	−	7.41655i	−0.201629	−	0.349232i
$452$	2.48497	+	11.6909i	0.116883	+	0.549891i
$453$	0.470173	+	1.05603i	0.0220907	+	0.0496164i
$454$	−14.4401	−	10.4913i	−0.677708	−	0.492383i
$455$	6.85441	−	15.1069i	0.321340	−	0.708221i
$456$	−1.69828	+	1.23387i	−0.0795294	+	0.0577815i
$457$	−17.1453	−	9.89884i	−0.802023	−	0.463048i	0.0421551	−	0.999111i	$-0.486578\pi$
$457$	−17.1453	−	9.89884i	−0.802023	−	0.463048i	−0.844178	+	0.536063i	$0.819911\pi$
$458$	19.3272	−	43.4096i	0.903101	−	2.02840i
$459$	−0.0900990	+	0.100065i	−0.00420546	+	0.00467064i
$460$	22.9647	−	70.1463i	1.07073	−	3.27059i
$461$	−1.92363	+	5.92031i	−0.0895922	+	0.275736i	−0.985807	−	0.167885i	$-0.946306\pi$
$461$	−1.92363	+	5.92031i	−0.0895922	+	0.275736i	0.896214	+	0.443621i	$0.146306\pi$
$462$	−1.66708	−	0.973287i	−0.0775594	−	0.0452814i
$463$	−10.4735	+	3.40304i	−0.486744	+	0.158153i	−0.542100	−	0.840314i	$-0.682371\pi$
$463$	−10.4735	+	3.40304i	−0.486744	+	0.158153i	0.0553559	+	0.998467i	$0.482371\pi$
$464$	−15.8362	−	17.5879i	−0.735179	−	0.816499i
$465$	0.151926	+	1.47710i	0.00704541	+	0.0684989i
$466$	−15.5080	+	17.2234i	−0.718393	+	0.797857i
$467$	11.1849	−	1.17558i	0.517573	−	0.0543992i	0.157859	−	0.987462i	$-0.449541\pi$
$467$	11.1849	−	1.17558i	0.517573	−	0.0543992i	0.359714	+	0.933063i	$0.382874\pi$
$468$		−	39.4259i		−	1.82246i
$469$	8.89067	+	1.93484i	0.410533	+	0.0893426i
$470$	−6.60759	−	31.4301i	−0.304785	−	1.44976i
$471$	0.106153	−	0.0472622i	0.00489125	−	0.00217772i
$472$	61.2222	+	6.43471i	2.81798	+	0.296182i
$473$	7.11306	+	33.4643i	0.327059	+	1.53869i
$474$	−0.818112	+	1.41701i	−0.0375772	+	0.0650855i
$475$	19.6982	+	4.27871i	0.903814	+	0.196321i
$476$	1.17228	−	3.54928i	0.0537311	−	0.162681i
$477$	10.4515	+	3.39589i	0.478540	+	0.155487i
$478$	−17.4430	−	39.1775i	−0.797823	−	1.79194i
$479$	−3.10987	+	29.5884i	−0.142093	+	1.35193i	0.658437	+	0.752636i	$0.271218\pi$
$479$	−3.10987	+	29.5884i	−0.142093	+	1.35193i	−0.800530	+	0.599293i	$0.795449\pi$
$480$	−1.21998	−	0.707984i	−0.0556844	−	0.0323149i
$481$	0.956176	+	9.09741i	0.0435979	+	0.414806i
$482$			15.1877i			0.691782i
$483$	1.02739	+	0.934117i	0.0467477	+	0.0425038i
$484$	−4.73819	−	14.5826i	−0.215372	−	0.662847i
$485$	−22.3444	−	0.0497342i	−1.01461	−	0.00225831i
$486$	5.08915	−	1.08173i	0.230849	−	0.0490684i
$487$	26.0637	+	23.4679i	1.18106	+	1.06343i	0.996750	+	0.0805626i	$0.0256717\pi$
$487$	26.0637	+	23.4679i	1.18106	+	1.06343i	0.184310	+	0.982868i	$0.440995\pi$
$488$	19.8246	−	93.2673i	0.897417	−	4.22201i
$489$	0.230685	−	0.709975i	0.0104319	−	0.0321062i
$490$	−39.7141	+	7.94811i	−1.79410	+	0.359059i
$491$	0.608859	+	1.87387i	0.0274774	+	0.0845667i	0.963855	−	0.266428i	$-0.0858435\pi$
$491$	0.608859	+	1.87387i	0.0274774	+	0.0845667i	−0.936377	+	0.350995i	$0.885843\pi$
$492$	0.790466	−	0.0830813i	0.0356369	−	0.00374559i
$493$	0.712417	−	0.411314i	0.0320856	−	0.0185246i
$494$	26.7225	+	11.8976i	1.20230	+	0.535300i
$495$	14.8193	+	20.4928i	0.666078	+	0.921082i
$496$	−62.2930	−	45.2585i	−2.79704	−	2.03217i
$497$	3.62780	−	8.04307i	0.162729	−	0.360781i
$498$	−0.858272	−	0.278869i	−0.0384601	−	0.0124964i
$499$	−8.83166	+	15.2969i	−0.395359	+	0.684783i	−0.993147	−	0.116872i	$-0.962713\pi$
$499$	−8.83166	+	15.2969i	−0.395359	+	0.684783i	0.597788	+	0.801655i	$0.296047\pi$
$500$	10.5716	+	51.4213i	0.472775	+	2.29963i
$501$	−0.554022	−	0.959594i	−0.0247519	−	0.0428715i
$502$	−6.91330	+	6.22477i	−0.308556	+	0.277825i
$503$	−2.37581	+	3.27003i	−0.105932	+	0.145803i	−0.858692	−	0.512492i	$-0.828722\pi$
$503$	−2.37581	+	3.27003i	−0.105932	+	0.145803i	0.752760	+	0.658296i	$0.228722\pi$
$504$	−44.8604	+	32.2620i	−1.99824	+	1.43707i
$505$	2.01970	−	4.50929i	0.0898756	−	0.200661i
$506$	7.18158	+	68.3282i	0.319260	+	3.03756i
$507$	−0.332135	+	0.191758i	−0.0147506	+	0.00851629i
$508$	25.5865	−	57.4682i	1.13522	−	2.54974i
$509$	13.4406	+	2.85689i	0.595744	+	0.126629i	0.495909	−	0.868375i	$-0.334835\pi$
$509$	13.4406	+	2.85689i	0.595744	+	0.126629i	0.0998355	+	0.995004i	$0.468168\pi$
$510$	0.0871803	−	0.0963912i	0.00386041	−	0.00426828i
$511$	−31.6888	+	13.9252i	−1.40183	+	0.616013i
$512$	−45.2774	+	14.7115i	−2.00100	+	0.650163i
$513$	−0.375109	+	1.76475i	−0.0165615	+	0.0779156i
$514$	−11.0582	+	2.35050i	−0.487758	+	0.103676i
$515$	4.60000	−	7.92664i	0.202700	−	0.349289i
$516$	−3.10584	−	0.660167i	−0.136727	−	0.0290622i
$517$	12.3232	+	16.9615i	0.541975	+	0.745965i
$518$	16.6690	−	14.8633i	0.732396	−	0.653054i
$519$	−0.319489	+	0.232123i	−0.0140240	+	0.0101891i
$520$	−0.0973380	+	43.7317i	−0.00426856	+	1.91776i
$521$	1.57768	−	15.0106i	0.0691194	−	0.657628i	−0.904032	−	0.427464i	$-0.859407\pi$
$521$	1.57768	−	15.0106i	0.0691194	−	0.657628i	0.973152	−	0.230164i	$-0.0739262\pi$
$522$	−21.0680	−	2.21434i	−0.922122	−	0.0969190i
$523$	−15.9981	+	14.4047i	−0.699547	+	0.629875i	−0.940155	−	0.340747i	$-0.889320\pi$
$523$	−15.9981	+	14.4047i	−0.699547	+	0.629875i	0.240608	+	0.970622i	$0.422653\pi$
$524$	−78.2000			−3.41618
$525$	−0.964072	−	0.214306i	−0.0420756	−	0.00935310i
$526$	20.4102			0.889929
$527$	1.98892	−	1.79083i	0.0866387	−	0.0780099i
$528$	2.42749	+	0.255140i	0.105643	+	0.0111035i
$529$	2.76165	−	26.2753i	0.120072	−	1.14240i
$530$	−20.1801	−	6.60660i	−0.876567	−	0.286972i
$531$	21.3818	−	15.5348i	0.927891	−	0.674152i
$532$	−10.1754	−	49.0388i	−0.441161	−	2.12610i
$533$	−3.73712	−	5.14370i	−0.161872	−	0.222798i
$534$	−1.45544	−	0.309363i	−0.0629830	−	0.0133875i
$535$	2.19659	+	21.3563i	0.0949668	+	0.923314i
$536$	−23.4617	+	4.98694i	−1.01339	+	0.215403i
$537$	0.0358947	−	0.168871i	0.00154897	−	0.00728733i
$538$	−43.8263	+	14.2400i	−1.88949	+	0.613932i
$539$	21.5390	−	15.3323i	0.927752	−	0.660411i
$540$	−4.59815	+	0.966674i	−0.197873	+	0.0415990i
$541$	36.9236	+	7.84835i	1.58747	+	0.337427i	0.915238	−	0.402915i	$-0.132003\pi$
$541$	36.9236	+	7.84835i	1.58747	+	0.337427i	0.672231	+	0.740342i	$0.265336\pi$
$542$	−11.2198	+	25.2001i	−0.481932	+	1.08244i
$543$	−1.15107	+	0.664571i	−0.0493972	+	0.0285195i
$544$	0.265746	+	2.52840i	0.0113938	+	0.108404i
$545$	−12.7846	−	1.37249i	−0.547633	−	0.0587912i
$546$	−1.30641	−	0.589254i	−0.0559093	−	0.0252177i
$547$	−2.11101	+	2.90556i	−0.0902603	+	0.124233i	−0.851759	−	0.523934i	$-0.824464\pi$
$547$	−2.11101	+	2.90556i	−0.0902603	+	0.124233i	0.761499	+	0.648166i	$0.224464\pi$
$548$	−30.6287	+	27.5782i	−1.30840	+	1.17808i
$549$	−20.4686	−	35.4526i	−0.873577	−	1.51308i
$550$	−28.5462	−	39.6606i	−1.21722	−	1.69113i
$551$	5.51116	−	9.54560i	0.234783	−	0.406656i
$552$	−3.48132	−	1.13115i	−0.148175	−	0.0481449i
$553$	−13.0842	−	18.1935i	−0.556395	−	0.773667i
$554$	5.73063	+	4.16354i	0.243471	+	0.176892i
$555$	0.518300	−	0.167131i	0.0220006	−	0.00709433i
$556$	45.5178	+	20.2658i	1.93039	+	0.859463i
$557$	12.2763	−	7.08773i	0.520164	−	0.300317i	−0.216838	−	0.976208i	$-0.569574\pi$
$557$	12.2763	−	7.08773i	0.520164	−	0.300317i	0.737002	+	0.675891i	$0.236241\pi$
$558$	−68.5432	+	7.20418i	−2.90167	+	0.304977i
$559$	7.84886	+	24.1563i	0.331971	+	1.02170i
$560$	41.6430	−	29.8078i	1.75974	−	1.25961i
$561$	−0.0262173	+	0.0806885i	−0.00110689	+	0.00340667i
$562$	7.97029	−	37.4973i	0.336207	−	1.58173i
$563$	−11.8505	−	10.6703i	−0.499441	−	0.449699i	0.380501	−	0.924781i	$-0.375752\pi$
$563$	−11.8505	−	10.6703i	−0.499441	−	0.449699i	−0.879941	+	0.475082i	$0.842418\pi$
$564$	−1.90330	+	0.404559i	−0.0801435	+	0.0170350i
$565$	−4.59730	−	3.35580i	−0.193410	−	0.141179i
$566$	5.24183	+	16.1327i	0.220331	+	0.678108i
$567$	−5.03533	+	23.1376i	−0.211464	+	0.971686i
$568$			23.2599i			0.975962i
$569$	3.69782	+	35.1824i	0.155021	+	1.47492i	0.744761	+	0.667331i	$0.232563\pi$
$569$	3.69782	+	35.1824i	0.155021	+	1.47492i	−0.589740	+	0.807593i	$0.700770\pi$
$570$	0.365854	−	1.70256i	0.0153239	−	0.0713126i
$571$	−2.07135	+	19.7076i	−0.0866833	+	0.824737i	0.861659	+	0.507488i	$0.169426\pi$
$571$	−2.07135	+	19.7076i	−0.0866833	+	0.824737i	−0.948342	+	0.317249i	$0.897241\pi$
$572$	−20.2267	−	45.4299i	−0.845721	−	1.89952i
$573$	0.913140	+	0.296697i	0.0381470	+	0.0123947i
$574$	−4.86824	+	14.7395i	−0.203196	+	0.615216i
$575$	14.1536	+	32.1742i	0.590245	+	1.34176i
$576$	6.81382	−	11.8019i	0.283909	−	0.491745i
$577$	−4.16033	−	19.5728i	−0.173197	−	0.814827i	−0.975860	−	0.218395i	$-0.929918\pi$
$577$	−4.16033	−	19.5728i	−0.173197	−	0.814827i	0.802663	−	0.596432i	$-0.203416\pi$
$578$	43.5145	+	4.57356i	1.80997	+	0.190235i
$579$	1.81302	−	0.807207i	0.0753464	−	0.0335464i
$580$	28.5417	+	3.06410i	1.18513	+	0.127230i
$581$	8.31477	−	9.14499i	0.344955	−	0.379398i
$582$			1.93036i			0.0800160i
$583$	13.7853	−	1.44889i	0.570927	−	0.0600069i
$584$	61.0559	−	67.8094i	2.52651	−	2.80597i
$585$	12.5321	+	13.9808i	0.518139	+	0.578034i
$586$	−54.4845	−	60.5112i	−2.25074	−	2.49970i
$587$	−14.6973	+	4.77544i	−0.606623	+	0.197104i	−0.596192	−	0.802842i	$-0.703320\pi$
$587$	−14.6973	+	4.77544i	−0.606623	+	0.197104i	−0.0104308	+	0.999946i	$0.503320\pi$
$588$	0.486892	+	2.40501i	0.0200791	+	0.0991810i
$589$	11.0814	−	34.1051i	0.456602	−	1.40528i
$590$	−41.3815	+	29.9249i	−1.70365	+	1.23199i
$591$	−0.165394	+	0.183688i	−0.00680339	+	0.00755593i
$592$	−11.4858	+	25.7975i	−0.472064	+	1.06027i
$593$	3.16592	+	1.82785i	0.130009	+	0.0750607i	0.563594	−	0.826052i	$-0.309418\pi$
$593$	3.16592	+	1.82785i	0.130009	+	0.0750607i	−0.433585	+	0.901113i	$0.642752\pi$
$594$	3.53837	−	2.57077i	0.145181	−	0.105480i
$595$	0.712494	+	1.63123i	0.0292094	+	0.0668740i
$596$	5.28268	+	3.83809i	0.216387	+	0.157214i
$597$	0.468057	+	1.05127i	0.0191563	+	0.0430258i
$598$	10.6050	+	49.8926i	0.433671	+	2.04026i
$599$	3.07128	+	5.31962i	0.125489	+	0.217354i	0.921924	−	0.387371i	$-0.126617\pi$
$599$	3.07128	+	5.31962i	0.125489	+	0.217354i	−0.796435	+	0.604724i	$0.793283\pi$
$600$	2.54898	−	0.529954i	0.104062	−	0.0216353i
$601$	33.2947			1.35812			0.679060	−	0.734083i	$-0.262388\pi$
$601$	33.2947			1.35812			0.679060	+	0.734083i	$0.262388\pi$
$602$	36.6921	−	49.9912i	1.49546	−	2.03749i
$603$	−6.05293	+	8.33115i	−0.246495	+	0.339271i
$604$	66.4183	−	29.5714i	2.70252	−	1.20324i
$605$	6.31551	+	3.66503i	0.256762	+	0.149005i
$606$	−0.389950	−	0.173617i	−0.0158406	−	0.00705270i
$607$	35.6231	+	20.5670i	1.44590	+	0.834788i	0.998233	−	0.0594149i	$-0.0189235\pi$
$607$	35.6231	+	20.5670i	1.44590	+	0.834788i	0.447662	+	0.894203i	$0.352257\pi$
$608$	20.0226	+	27.5587i	0.812023	+	1.11765i
$609$	−0.272278	+	0.466367i	−0.0110333	+	0.0188981i
$610$	39.3976	+	68.5908i	1.59516	+	2.77716i
$611$	10.4151	+	11.5671i	0.421350	+	0.467956i
$612$	3.14385	+	2.83074i	0.127083	+	0.114426i
$613$	−17.2617	−	15.5425i	−0.697194	−	0.627756i	0.242348	−	0.970189i	$-0.422082\pi$
$613$	−17.2617	−	15.5425i	−0.697194	−	0.627756i	−0.939542	+	0.342433i	$0.888749\pi$
$614$	−33.8725	−	37.6192i	−1.36698	−	1.51819i
$615$	−0.253897	+	0.280723i	−0.0102381	+	0.0113198i
$616$	−35.1406	+	60.1899i	−1.41585	+	2.42512i
$617$	1.58759	+	2.18514i	0.0639141	+	0.0879702i	0.839777	−	0.542931i	$-0.182685\pi$
$617$	1.58759	+	2.18514i	0.0639141	+	0.0879702i	−0.775863	+	0.630901i	$0.782685\pi$
$618$	−0.685674	−	0.395874i	−0.0275818	−	0.0159244i
$619$	−43.8477	−	19.5222i	−1.76239	−	0.784665i	−0.988477	−	0.151370i	$-0.951631\pi$
$619$	−43.8477	−	19.5222i	−1.76239	−	0.784665i	−0.773910	−	0.633295i	$-0.781702\pi$
$620$	92.9017	−	9.55535i	3.73102	−	0.383752i
$621$	−2.87404	+	1.27961i	−0.115331	+	0.0513488i
$622$	−50.2782	+	69.2020i	−2.01597	+	2.77475i
$623$	12.0583	−	16.4288i	0.483104	−	0.658206i
$624$	1.81213			0.0725434
$625$	−20.0938	−	14.8741i	−0.803752	−	0.594965i
$626$	9.84779	+	17.0569i	0.393597	+	0.681730i
$627$	0.236349	+	1.11193i	0.00943887	+	0.0444064i
$628$	−2.97253	−	6.67642i	−0.118617	−	0.266418i
$629$	−0.794086	−	0.576938i	−0.0316623	−	0.0230040i
$630$	9.84732	−	44.7691i	0.392327	−	1.78364i
$631$	−18.3629	+	13.3414i	−0.731016	+	0.531114i	−0.889885	−	0.456186i	$-0.849215\pi$
$631$	−18.3629	+	13.3414i	−0.731016	+	0.531114i	0.158869	+	0.987300i	$0.449215\pi$
$632$	51.1613	+	29.5380i	2.03509	+	1.17496i
$633$	0.379760	−	0.852955i	0.0150941	−	0.0339019i
$634$	−38.7851	+	43.0752i	−1.54035	+	1.71073i
$635$	9.19393	+	28.5118i	0.364850	+	1.13146i
$636$	−0.397540	+	1.22350i	−0.0157635	+	0.0485150i
$637$	14.7135	−	12.9921i	0.582968	−	0.514766i
$638$	−25.4124	+	8.25699i	−1.00609	+	0.326898i
$639$	6.68205	+	7.42117i	0.264338	+	0.293577i
$640$	5.74992	−	9.90816i	0.227286	−	0.391654i
$641$	−22.4890	+	24.9766i	−0.888262	+	0.986515i	−0.999974	−	0.00722548i	$-0.997700\pi$
$641$	−22.4890	+	24.9766i	−0.888262	+	0.986515i	0.111712	+	0.993741i	$0.464367\pi$
$642$	1.84457	−	0.193872i	0.0727993	−	0.00765151i
$643$			2.04600i			0.0806863i	0.999186	+	0.0403432i	$0.0128451\pi$
$643$			2.04600i			0.0806863i	−0.999186	+	0.0403432i	$0.987155\pi$
$644$	58.7509	−	64.6171i	2.31511	−	2.54627i
$645$	1.31120	−	0.753137i	0.0516286	−	0.0296547i
$646$	−2.86737	+	1.27664i	−0.112815	+	0.0502286i
$647$	15.5173	+	1.63093i	0.610047	+	0.0641186i	0.404514	−	0.914532i	$-0.367441\pi$
$647$	15.5173	+	1.63093i	0.610047	+	0.0641186i	0.205533	+	0.978650i	$0.434107\pi$
$648$	−12.9783	−	61.0580i	−0.509835	−	2.39858i
$649$	16.6681	−	28.8700i	0.654281	−	1.13325i
$650$	−24.1549	−	27.0680i	−0.947432	−	1.06170i
$651$	−0.551017	+	1.66831i	−0.0215961	+	0.0653862i
$652$	−44.6536	−	14.5088i	−1.74877	−	0.568210i
$653$	14.4964	+	32.5595i	0.567290	+	1.27415i	0.938396	+	0.345563i	$0.112312\pi$
$653$	14.4964	+	32.5595i	0.567290	+	1.27415i	−0.371106	+	0.928590i	$0.621021\pi$
$654$	−0.116113	+	1.10474i	−0.00454036	+	0.0431987i
$655$	27.7304	−	24.8570i	1.08352	−	0.971245i
$656$	−2.05162	−	19.5199i	−0.0801024	−	0.762123i
$657$		−	39.1750i		−	1.52836i
$658$	8.08097	−	37.1324i	0.315029	−	1.44757i
$659$	−4.30237	−	13.2413i	−0.167596	−	0.515809i	0.831622	−	0.555342i	$-0.187413\pi$
$659$	−4.30237	−	13.2413i	−0.167596	−	0.515809i	−0.999218	+	0.0395337i	$0.987413\pi$
$660$	−2.39899	+	1.73482i	−0.0933806	+	0.0675279i
$661$	−7.45664	+	1.58496i	−0.290030	+	0.0616477i	−0.350629	−	0.936514i	$-0.614032\pi$
$661$	−7.45664	+	1.58496i	−0.290030	+	0.0616477i	0.0605992	+	0.998162i	$0.480699\pi$
$662$	−17.9097	−	16.1259i	−0.696079	−	0.626753i
$663$	−0.0130958	+	0.0616107i	−0.000508597	+	0.00239276i
$664$	−10.0686	+	30.9879i	−0.390737	+	1.20256i
$665$	19.1960	+	14.1552i	0.744389	+	0.548914i
$666$	7.81086	+	24.0393i	0.302665	+	0.931506i
$667$	19.1149	−	2.00906i	0.740131	−	0.0777910i
$668$	−60.3533	+	34.8450i	−2.33514	+	1.34819i
$669$	0.530443	+	0.236168i	0.0205081	+	0.00913080i
$670$	11.7315	−	16.0717i	0.453228	−	0.620905i
$671$	−41.7739	−	30.3505i	−1.61266	−	1.17167i
$672$	−0.974440	−	1.35496i	−0.0375898	−	0.0522687i
$673$	−15.9860	−	5.19416i	−0.616214	−	0.200220i	−0.0157555	−	0.999876i	$-0.505015\pi$
$673$	−15.9860	−	5.19416i	−0.616214	−	0.200220i	−0.600459	+	0.799656i	$0.705015\pi$
$674$	18.7244	−	32.4315i	0.721235	−	1.24922i
$675$	1.32327	−	1.80438i	0.0509327	−	0.0694506i
$676$	12.0606	+	20.8895i	0.463868	+	0.803443i
$677$	−8.73203	+	7.86236i	−0.335599	+	0.302175i	−0.819650	−	0.572865i	$-0.805832\pi$
$677$	−8.73203	+	7.86236i	−0.335599	+	0.302175i	0.484050	+	0.875040i	$0.339165\pi$
$678$	−0.289026	+	0.397810i	−0.0111000	+	0.0152778i
$679$	−24.1002	−	10.8703i	−0.924881	−	0.417165i
$680$	−3.48021	−	3.14765i	−0.133460	−	0.120707i
$681$	−0.0538296	−	0.512155i	−0.00206276	−	0.0196258i
$682$	−75.2854	+	43.4661i	−2.88283	+	1.66440i
$683$	1.62936	−	3.65961i	0.0623458	−	0.140031i	−0.879686	−	0.475556i	$-0.842247\pi$
$683$	1.62936	−	3.65961i	0.0623458	−	0.140031i	0.942031	+	0.335525i	$0.108914\pi$
$684$	55.4450	+	11.7852i	2.11999	+	0.450618i
$685$	2.09507	−	19.5153i	0.0800484	−	0.745641i
$686$	−46.7252	−	10.6439i	−1.78398	−	0.406385i
$687$	1.30388	−	0.423655i	0.0497459	−	0.0161634i
$688$	−16.3023	+	76.6961i	−0.621518	+	2.92401i
$689$	10.0659	−	2.13957i	0.383480	−	0.0815111i
$690$	2.77683	−	1.22893i	0.105712	−	0.0467845i
$691$	−16.6506	−	3.53919i	−0.633419	−	0.134637i	−0.119998	−	0.992774i	$-0.538289\pi$
$691$	−16.6506	−	3.53919i	−0.633419	−	0.134637i	−0.513421	+	0.858137i	$0.671622\pi$
$692$	14.5993	+	20.0942i	0.554981	+	0.763865i
$693$	6.07947	+	29.2990i	0.230940	+	1.11298i
$694$	6.84312	−	4.97182i	0.259761	−	0.188728i
$695$	−22.5828	+	7.28207i	−0.856615	+	0.276225i
$696$	0.148808	−	1.41581i	0.00564055	−	0.0536662i
$697$	0.678483	+	0.0713115i	0.0256994	+	0.00270111i
$698$	38.6978	−	34.8437i	1.46473	−	1.31885i
$699$	−0.668680			−0.0252918
$700$	−13.4787	+	60.6349i	−0.509448	+	2.29179i
$701$	−42.3252			−1.59860			−0.799300	−	0.600932i	$-0.794796\pi$
$701$	−42.3252			−1.59860			−0.799300	+	0.600932i	$0.794796\pi$
$702$	2.41305	−	2.17272i	0.0910746	−	0.0820039i
$703$	−13.0796	−	1.37472i	−0.493306	−	0.0518485i
$704$	1.79674	−	17.0949i	0.0677172	−	0.644286i
$705$	0.546332	−	0.748453i	0.0205761	−	0.0281884i
$706$	66.1755	−	48.0793i	2.49055	−	1.80949i
$707$	4.36348	−	3.89078i	0.164105	−	0.146328i
$708$	1.81858	+	2.50306i	0.0683465	+	0.0940709i
$709$	−10.6075	−	2.25469i	−0.398373	−	0.0846768i	0.00436876	−	0.999990i	$-0.498609\pi$
$709$	−10.6075	−	2.25469i	−0.398373	−	0.0846768i	−0.402742	+	0.915314i	$0.631943\pi$
$710$	−12.8794	−	14.3682i	−0.483355	−	0.539229i
$711$	24.8089	−	5.27329i	0.930406	−	0.197764i
$712$	−11.1696	+	52.5487i	−0.418597	+	1.96934i
$713$	59.4709	−	19.3233i	2.22720	−	0.723662i
$714$	0.140787	−	0.0618666i	0.00526881	−	0.00231530i
$715$	21.6131	+	9.68049i	0.808286	+	0.362030i
$716$	−10.6211	−	2.25758i	−0.396929	−	0.0843698i
$717$	0.503262	−	1.13035i	0.0187947	−	0.0422135i
$718$	−23.1533	+	13.3676i	−0.864074	+	0.498873i
$719$	−0.880176	−	8.37431i	−0.0328250	−	0.312309i	−0.998599	−	0.0529226i	$-0.983146\pi$
$719$	−0.880176	−	8.37431i	−0.0328250	−	0.312309i	0.965774	−	0.259386i	$-0.0835203\pi$
$720$	11.9245	+	56.7209i	0.444400	+	2.11386i
$721$	8.80361	−	6.33125i	0.327863	−	0.235788i
$722$	4.17797	−	5.75049i	0.155488	−	0.214011i
$723$	−0.325642	+	0.293209i	−0.0121107	+	0.0109046i
$724$	41.7979	+	72.3961i	1.55341	+	2.69058i
$725$	−11.0951	+	7.98585i	−0.412062	+	0.296587i
$726$	0.315411	−	0.546307i	0.0117060	−	0.0202754i
$727$	−10.6486	−	3.45993i	−0.394934	−	0.128322i	0.104816	−	0.994492i	$-0.466575\pi$
$727$	−10.6486	−	3.45993i	−0.394934	−	0.128322i	−0.499750	+	0.866170i	$0.666575\pi$
$728$	−21.2750	+	47.1681i	−0.788505	+	1.74817i
$729$	−21.6003	−	15.6936i	−0.800013	−	0.581243i
$730$	−0.168483	+	75.6953i	−0.00623583	+	2.80161i
$731$	−2.48978	−	1.10852i	−0.0920879	−	0.0410002i
$732$	4.15026	−	2.39616i	0.153398	−	0.0885644i
$733$	−21.2313	+	2.23150i	−0.784196	+	0.0824223i	−0.488160	−	0.872754i	$-0.662332\pi$
$733$	−21.2313	+	2.23150i	−0.784196	+	0.0824223i	−0.296036	+	0.955177i	$0.595665\pi$
$734$	−13.6676	−	42.0646i	−0.504480	−	1.55263i
$735$	−0.937125	−	0.698072i	−0.0345664	−	0.0257488i
$736$	−18.3556	+	56.4927i	−0.676596	+	2.08235i
$737$	−2.70058	+	12.7052i	−0.0994770	+	0.468002i
$738$	−13.0558	−	11.7555i	−0.480592	−	0.432727i
$739$	5.79857	−	1.23252i	0.213304	−	0.0453391i	−0.100020	−	0.994985i	$-0.531891\pi$
$739$	5.79857	−	1.23252i	0.213304	−	0.0453391i	0.313324	+	0.949646i	$0.398557\pi$
$740$	−10.5117	−	32.5983i	−0.386416	−	1.19834i
$741$	0.260798	+	0.802653i	0.00958064	+	0.0294862i
$742$	−18.5894	−	16.9018i	−0.682439	−	0.620484i
$743$		−	31.5615i		−	1.15788i	−0.815371	−	0.578939i	$-0.803467\pi$
$743$		−	31.5615i		−	1.15788i	0.815371	−	0.578939i	$-0.196533\pi$
$744$	−0.484135	−	4.60624i	−0.0177493	−	0.168873i
$745$	−3.09328	+	0.318157i	−0.113329	+	0.0116564i
$746$	−7.01364	+	66.7303i	−0.256787	+	2.44317i
$747$	5.68973	+	12.7793i	0.208176	+	0.467572i
$748$	5.07487	+	1.64893i	0.185556	+	0.0602907i
$749$	−7.96674	+	24.1208i	−0.291099	+	0.881356i
$750$	−1.28112	+	1.73878i	−0.0467800	+	0.0634913i
$751$	17.6528	−	30.5755i	0.644160	−	1.11572i	−0.340335	−	0.940304i	$-0.610540\pi$
$751$	17.6528	−	30.5755i	0.644160	−	1.11572i	0.984495	−	0.175413i	$-0.0561262\pi$
$752$	9.99025	+	47.0004i	0.364307	+	1.71393i
$753$	−0.266932	−	0.0280557i	−0.00972754	−	0.00102241i
$754$	−18.1224	+	8.06863i	−0.659980	+	0.293842i
$755$	−14.1528	+	31.5983i	−0.515074	+	1.14998i
$756$	−5.43238	−	1.18223i	−0.197574	−	0.0429971i
$757$			9.26089i			0.336593i	0.985736	+	0.168296i	$0.0538266\pi$
$757$			9.26089i			0.336593i	−0.985736	+	0.168296i	$0.946173\pi$
$758$	19.3986	−	2.03887i	0.704587	−	0.0740551i
$759$	−1.32639	+	1.47310i	−0.0481448	+	0.0534702i
$760$	−61.4711	−	13.2092i	−2.22979	−	0.479147i
$761$	33.8335	+	37.5759i	1.22646	+	1.36213i	0.910583	+	0.413327i	$0.135633\pi$
$761$	33.8335	+	37.5759i	1.22646	+	1.36213i	0.315881	+	0.948799i	$0.397700\pi$
$762$	2.46139	−	0.799754i	0.0891668	−	0.0289720i
$763$	−13.1386	−	7.67069i	−0.475649	−	0.277698i
$764$	18.6607	−	57.4316i	0.675119	−	2.07780i
$765$	−2.01463	−	0.00448417i	−0.0728391	−	0.000162125i
$766$	29.2194	−	32.4514i	1.05574	−	1.17252i
$767$	10.0665	−	22.6096i	0.363479	−	0.816387i
$768$	−1.44556	−	0.834595i	−0.0521622	−	0.0301158i
$769$	14.4845	−	10.5236i	0.522325	−	0.379492i	−0.295154	−	0.955450i	$-0.595371\pi$
$769$	14.4845	−	10.5236i	0.522325	−	0.379492i	0.817479	+	0.575958i	$0.195371\pi$
$770$	−11.6210	−	56.6387i	−0.418791	−	2.04112i
$771$	−0.263884	−	0.191723i	−0.00950356	−	0.00690474i
$772$	−50.7689	−	114.029i	−1.82721	−	4.10399i
$773$	1.99734	+	9.39675i	0.0718394	+	0.337978i	0.999359	−	0.0357966i	$-0.0113968\pi$
$773$	1.99734	+	9.39675i	0.0718394	+	0.337978i	−0.927520	+	0.373774i	$0.878063\pi$
$774$	35.0919	+	60.7810i	1.26135	+	2.18473i
$775$	−29.9065	+	32.9186i	−1.07427	+	1.18247i
$776$	69.6957			2.50193
$777$	0.640492	+	0.0704576i	0.0229775	+	0.00252765i
$778$	16.1084	−	22.1713i	0.577514	−	0.794880i
$779$	8.35073	−	3.71798i	0.299196	−	0.133211i
$780$	−1.63666	+	1.46707i	−0.0586019	+	0.0525297i
$781$	11.5069	+	5.12321i	0.411750	+	0.183323i
$782$	−4.73990	−	2.73659i	−0.169499	−	0.0978601i
$783$	−0.719178	−	0.989863i	−0.0257013	−	0.0353748i
$784$	59.3897	−	12.0234i	2.12106	−	0.429407i
$785$	3.17629	+	1.42265i	0.113367	+	0.0507767i
$786$	−2.15275	−	2.39087i	−0.0767862	−	0.0852797i
$787$	0.565642	+	0.509306i	0.0201629	+	0.0181548i	0.679151	−	0.733999i	$-0.262348\pi$
$787$	0.565642	+	0.509306i	0.0201629	+	0.0181548i	−0.658988	+	0.752154i	$0.729015\pi$
$788$	11.5530	+	10.4024i	0.411559	+	0.370569i
$789$	0.394033	+	0.437618i	0.0140280	+	0.0155796i
$790$	−47.9593	+	10.0825i	−1.70632	+	0.358721i
$791$	−3.33901	−	5.84860i	−0.118722	−	0.207952i
$792$	−46.3658	−	63.8170i	−1.64754	−	2.26764i
$793$	−33.1990	−	19.1674i	−1.17893	−	0.680656i
$794$	−84.2237	−	37.4988i	−2.98899	−	1.33078i
$795$	−0.247937	−	0.560229i	−0.00879343	−	0.0198693i
$796$	66.1194	−	29.4383i	2.34354	−	1.04341i
$797$	10.7176	−	14.7515i	0.379636	−	0.522524i	−0.575852	−	0.817554i	$-0.695330\pi$
$797$	10.7176	−	14.7515i	0.379636	−	0.522524i	0.955488	+	0.295030i	$0.0953296\pi$
$798$	1.21919	−	1.66108i	0.0431587	−	0.0588016i
$799$	−1.67017			−0.0590862
$800$	−8.59977	−	41.3633i	−0.304048	−	1.46241i
$801$	11.5324	+	19.9747i	0.407477	+	0.705771i
$802$	−3.02453	−	14.2293i	−0.106800	−	0.502453i
$803$	−20.0980	−	45.1408i	−0.709242	−	1.59298i
$804$	−0.975287	−	0.708588i	−0.0343957	−	0.0249900i
$805$	−0.294077	+	41.5886i	−0.0103648	+	1.46581i
$806$	−52.2137	+	37.9355i	−1.83915	+	1.33622i
$807$	−1.15142	−	0.664772i	−0.0405319	−	0.0234011i
$808$	−6.26844	+	14.0791i	−0.220523	+	0.495303i
$809$	−18.3654	+	20.3968i	−0.645692	+	0.717114i	−0.973769	−	0.227537i	$-0.926933\pi$
$809$	−18.3654	+	20.3968i	−0.645692	+	0.717114i	0.328077	+	0.944651i	$0.393599\pi$
$810$	41.8259	+	30.5308i	1.46961	+	1.07274i
$811$	−8.93291	+	27.4927i	−0.313677	+	0.965399i	0.662619	+	0.748957i	$0.269445\pi$
$811$	−8.93291	+	27.4927i	−0.313677	+	0.965399i	−0.976296	+	0.216442i	$0.930555\pi$
$812$	29.3320	+	17.1248i	1.02935	+	0.600964i
$813$	−0.756925	+	0.245940i	−0.0265465	+	0.00862548i
$814$	21.3333	+	23.6930i	0.747731	+	0.830439i
$815$	20.4464	−	9.04885i	0.716206	−	0.316967i
$816$	−0.130109	+	0.144501i	−0.00455473	+	0.00505854i
$817$	−36.3174	+	3.81711i	−1.27059	+	0.133544i
$818$		−	28.3839i		−	0.992420i
$819$	6.76247	+	21.1611i	0.236300	+	0.739428i
$820$	17.6559	+	15.9688i	0.616572	+	0.557654i
$821$	21.0073	−	9.35303i	0.733158	−	0.326423i	−0.00597520	−	0.999982i	$-0.501902\pi$
$821$	21.0073	−	9.35303i	0.733158	−	0.326423i	0.739133	+	0.673559i	$0.235235\pi$
$822$	−1.68635	−	0.177242i	−0.0588181	−	0.00618203i
$823$	−8.93181	−	42.0209i	−0.311343	−	1.46476i	−0.804051	−	0.594560i	$-0.797326\pi$
$823$	−8.93181	−	42.0209i	−0.311343	−	1.46476i	0.492708	−	0.870195i	$-0.336007\pi$
$824$	−14.2930	+	24.7563i	−0.497921	+	0.862425i
$825$	0.299264	−	1.37774i	0.0104190	−	0.0479667i
$826$	−59.1641	+	12.2764i	−2.05858	+	0.427151i
$827$	32.8898	+	10.6865i	1.14369	+	0.371608i	0.818763	−	0.574131i	$-0.194660\pi$
$827$	32.8898	+	10.6865i	1.14369	+	0.371608i	0.324927	+	0.945739i	$0.394660\pi$
$828$	40.2028	+	90.2969i	1.39714	+	3.13803i
$829$	3.60595	−	34.3083i	0.125240	−	1.19158i	−0.733690	−	0.679484i	$-0.762204\pi$
$829$	3.60595	−	34.3083i	0.125240	−	1.19158i	0.858930	−	0.512093i	$-0.171130\pi$
$830$	−10.9389	−	24.7172i	−0.379696	−	0.857946i
$831$	0.0213625	+	0.203251i	0.000741059	+	0.00705070i
$832$		−	12.7614i		−	0.442421i
$833$	−0.0204092	+	2.10608i	−0.000707138	+	0.0729714i
$834$	0.633447	+	1.94955i	0.0219345	+	0.0675074i
$835$	10.3258	−	31.5405i	0.357339	−	1.09151i
$836$	69.9347	−	14.8651i	2.41874	−	0.514119i
$837$	−2.95823	−	2.66360i	−0.102251	−	0.0920675i
$838$	−6.87613	+	32.3496i	−0.237532	+	1.11750i
$839$	0.970542	−	2.98702i	0.0335068	−	0.103123i	−0.932904	−	0.360124i	$-0.882734\pi$
$839$	0.970542	−	2.98702i	0.0335068	−	0.103123i	0.966411	+	0.257001i	$0.0827343\pi$
$840$	3.00857	+	0.661759i	0.103805	+	0.0228329i
$841$	−6.65159	−	20.4715i	−0.229365	−	0.705913i
$842$	−101.273	+	10.6442i	−3.49009	+	0.366824i
$843$	0.957856	−	0.553018i	0.0329903	−	0.0190470i
$844$	−53.6463	−	23.8849i	−1.84658	−	0.822151i
$845$	−10.9168	−	3.57398i	−0.375550	−	0.122949i
$846$	34.7955	+	25.2804i	1.19629	+	0.869159i
$847$	5.04440	+	7.01423i	0.173327	+	0.241012i
$848$	30.2133	+	9.81691i	1.03753	+	0.337114i
$849$	−0.244706	+	0.423844i	−0.00839830	+	0.0145463i
$850$	3.89272	+	0.0173289i	0.133519	+	0.000594377i
$851$	−11.4666	−	19.8607i	−0.393070	−	0.680817i
$852$	−0.868761	+	0.782236i	−0.0297633	+	0.0267990i
$853$	−3.81712	+	5.25381i	−0.130696	+	0.179887i	−0.869349	−	0.494198i	$-0.835462\pi$
$853$	−3.81712	+	5.25381i	−0.130696	+	0.179887i	0.738654	+	0.674085i	$0.235462\pi$
$854$	9.33201	+	93.1264i	0.319335	+	3.18672i
$855$	−23.4074	+	13.4449i	−0.800516	+	0.459805i
$856$	−6.99975	−	66.5981i	−0.239246	−	2.27628i
$857$	29.0894	−	16.7947i	0.993674	−	0.573698i	0.0873032	−	0.996182i	$-0.472175\pi$
$857$	29.0894	−	16.7947i	0.993674	−	0.573698i	0.906370	+	0.422484i	$0.138842\pi$
$858$	0.832150	−	1.86904i	0.0284091	−	0.0638080i
$859$	−52.0090	−	11.0549i	−1.77453	−	0.377187i	−0.799743	−	0.600343i	$-0.795031\pi$
$859$	−52.0090	−	11.0549i	−1.77453	−	0.377187i	−0.974783	+	0.223156i	$0.928364\pi$
$860$	−47.3683	−	82.4676i	−1.61524	−	2.81212i
$861$	−0.410016	+	0.180176i	−0.0139733	+	0.00614037i
$862$	−31.9046	+	10.3664i	−1.08668	+	0.353082i
$863$	4.23483	−	19.9233i	0.144155	−	0.678197i	−0.845411	−	0.534117i	$-0.820644\pi$
$863$	4.23483	−	19.9233i	0.144155	−	0.678197i	0.989566	−	0.144080i	$-0.0460224\pi$
$864$	3.69871	−	0.786185i	0.125833	−	0.0267466i
$865$	−11.5643	−	2.48497i	−0.393196	−	0.0844916i
$866$	77.9422	+	16.5671i	2.64858	+	0.562974i
$867$	0.742015	+	1.02130i	0.0252001	+	0.0346850i
$868$	104.928	+	34.6560i	3.56148	+	1.17630i
$869$	25.8816	−	18.8041i	0.877972	−	0.637884i
$870$	0.692038	+	0.956981i	0.0234623	+	0.0324447i
$871$	−1.00800	+	9.59044i	−0.0341546	+	0.324960i
$872$	39.8866	+	4.19225i	1.35073	+	0.141967i
$873$	22.2368	−	20.0221i	0.752601	−	0.677645i
$874$	−73.3345			−2.48058
$875$	−14.4940	−	25.7861i	−0.489988	−	0.871729i
$876$	4.58603			0.154947
$877$	36.1231	−	32.5254i	1.21979	−	1.09830i	0.227577	−	0.973760i	$-0.426920\pi$
$877$	36.1231	−	32.5254i	1.21979	−	1.09830i	0.992214	−	0.124544i	$-0.0397469\pi$
$878$	25.1916	+	2.64775i	0.850176	+	0.0893571i
$879$	0.245568	−	2.33642i	0.00828279	−	0.0788055i
$880$	42.8400	+	59.2410i	1.44414	+	1.99701i
$881$	−21.5813	+	15.6797i	−0.727092	+	0.528263i	−0.888642	−	0.458602i	$-0.848351\pi$
$881$	−21.5813	+	15.6797i	−0.727092	+	0.528263i	0.161550	+	0.986864i	$0.448351\pi$
$882$	32.3038	−	43.5683i	1.08773	−	1.46702i
$883$	12.0556	+	16.5931i	0.405702	+	0.558401i	0.962164	−	0.272472i	$-0.0878413\pi$
$883$	12.0556	+	16.5931i	0.405702	+	0.558401i	−0.556461	+	0.830873i	$0.687841\pi$
$884$	3.87498	+	0.823653i	0.130330	+	0.0277025i
$885$	−1.44052	−	0.309545i	−0.0484226	−	0.0104052i
$886$	69.6203	−	14.7982i	2.33894	−	0.497157i
$887$	2.39082	−	11.2479i	0.0802757	−	0.377668i	−0.919609	−	0.392834i	$-0.871495\pi$
$887$	2.39082	−	11.2479i	0.0802757	−	0.377668i	0.999885	+	0.0151667i	$0.00482791\pi$
$888$	−1.61549	+	0.524905i	−0.0542123	+	0.0176147i
$889$	−3.87589	+	35.2336i	−0.129993	+	1.18170i
$890$	−22.1974	−	38.6454i	−0.744059	−	1.29540i
$891$	−33.0647	−	7.02812i	−1.10771	−	0.235451i
$892$	14.8537	−	33.3620i	0.497339	−	1.11704i
$893$	−19.3803	+	11.1892i	−0.648536	+	0.374432i
$894$	0.0280807	+	0.267170i	0.000939158	+	0.00893549i
$895$	4.48394	−	2.57551i	0.149881	−	0.0860899i
$896$	11.0044	−	7.91395i	0.367630	−	0.264387i
$897$	−0.865017	+	1.19059i	−0.0288821	+	0.0397528i
$898$	41.3314	−	37.2150i	1.37925	−	1.24188i
$899$	12.1597	+	21.0612i	0.405548	+	0.702430i
$900$	−56.6901	−	41.5746i	−1.88967	−	1.38582i
$901$	−0.552109	+	0.956280i	−0.0183934	+	0.0318583i
$902$	−21.0750	−	6.84768i	−0.701720	−	0.228003i
$903$	1.78023	−	0.178394i	0.0592425	−	0.00593657i
$904$	14.3629	+	10.4353i	0.477705	+	0.347073i
$905$	−37.8341	−	12.3862i	−1.25765	−	0.411732i
$906$	2.73253	+	1.21660i	0.0907822	+	0.0404188i
$907$	−21.9203	+	12.6557i	−0.727851	+	0.420225i	−0.817635	−	0.575736i	$-0.804715\pi$
$907$	−21.9203	+	12.6557i	−0.727851	+	0.420225i	0.0897847	+	0.995961i	$0.471382\pi$
$908$	−32.2118	+	3.38559i	−1.06898	+	0.112355i
$909$	2.04466	+	6.29281i	0.0678170	+	0.208719i
$910$	−12.9757	−	40.9173i	−0.430140	−	1.35639i
$911$	−1.82038	+	5.60255i	−0.0603118	+	0.185621i	−0.976673	−	0.214732i	$-0.931112\pi$
$911$	−1.82038	+	5.60255i	−0.0603118	+	0.185621i	0.916361	+	0.400352i	$0.131112\pi$
$912$	−0.541683	+	2.54842i	−0.0179369	+	0.0843866i
$913$	13.1124	+	11.8064i	0.433957	+	0.390736i
$914$	−50.1082	+	10.6508i	−1.65743	+	0.352298i
$915$	−0.710066	+	2.16892i	−0.0234741	+	0.0717023i
$916$	−26.6456	−	82.0067i	−0.880395	−	2.70958i
$917$	41.9723	−	13.4131i	1.38605	−	0.442941i
$918$			0.348417i			0.0114995i
$919$	1.49944	+	14.2662i	0.0494620	+	0.470599i	0.991017	+	0.133739i	$0.0426983\pi$
$919$	1.49944	+	14.2662i	0.0494620	+	0.470599i	−0.941555	+	0.336860i	$0.890635\pi$
$920$	−44.3704	−	100.258i	−1.46285	−	3.30540i
$921$	0.152667	−	1.45253i	0.00503055	−	0.0478625i
$922$	6.55151	+	14.7149i	0.215763	+	0.484611i
$923$	8.89370	+	2.88974i	0.292740	+	0.0951169i
$924$	−3.42989	+	0.711695i	−0.112835	+	0.0234130i
$925$	14.0894	+	8.21834i	0.463255	+	0.270217i
$926$	−14.2477	+	24.6777i	−0.468209	+	0.810961i
$927$	2.55168	+	12.0047i	0.0838080	+	0.394286i
$928$	−22.9749	−	2.41476i	−0.754190	−	0.0792685i
$929$	−16.6590	+	7.41709i	−0.546566	+	0.243347i	−0.661394	−	0.750039i	$-0.730035\pi$
$929$	−16.6590	+	7.41709i	−0.546566	+	0.243347i	0.114828	+	0.993385i	$0.463368\pi$
$930$	2.84962	+	2.57731i	0.0934426	+	0.0845135i
$931$	13.8728	+	24.5753i	0.454662	+	0.805422i
$932$			42.0564i			1.37760i
$933$	−2.45442	+	0.257970i	−0.0803542	+	0.00844556i
$934$	19.4723	−	21.6262i	0.637152	−	0.707630i
$935$	−2.32373	+	1.02840i	−0.0759941	+	0.0336323i
$936$	−39.1865	−	43.5210i	−1.28085	−	1.42253i
$937$	34.5518	−	11.2266i	1.12876	−	0.366756i	0.315655	−	0.948874i	$-0.397776\pi$
$937$	34.5518	−	11.2266i	1.12876	−	0.366756i	0.813104	+	0.582118i	$0.197776\pi$
$938$	20.4461	−	11.6729i	0.667590	−	0.381133i
$939$	−0.175600	+	0.540442i	−0.00573050	+	0.0176367i
$940$	−47.0737	−	34.3614i	−1.53537	−	1.12074i
$941$	29.0169	−	32.2266i	0.945925	−	1.05056i	−0.0527249	−	0.998609i	$-0.516791\pi$
$941$	29.0169	−	32.2266i	0.945925	−	1.05056i	0.998650	−	0.0519470i	$-0.0165427\pi$
$942$	0.122294	−	0.274676i	0.00398454	−	0.00894942i
$943$	13.8041	+	7.96983i	0.449525	+	0.259533i
$944$	61.8110	−	44.9084i	2.01178	−	1.46164i
$945$	2.30216	−	1.30753i	0.0748892	−	0.0425341i
$946$	71.6185	+	52.0339i	2.32852	+	1.69177i
$947$	11.1950	+	25.1444i	0.363789	+	0.817083i	0.998999	+	0.0447431i	$0.0142469\pi$
$947$	11.1950	+	25.1444i	0.363789	+	0.817083i	−0.635210	+	0.772340i	$0.719086\pi$
$948$	0.617319	+	2.90426i	0.0200496	+	0.0943258i
$949$	−18.3424	−	31.7699i	−0.595419	−	1.03130i
$950$	45.2864	−	25.8780i	1.46929	−	0.839594i
$951$	−1.67235			−0.0542297
$952$	−2.23370	−	5.08310i	−0.0723945	−	0.164744i
$953$	−19.5661	+	26.9305i	−0.633809	+	0.872363i	−0.998266	−	0.0588568i	$-0.981254\pi$
$953$	−19.5661	+	26.9305i	−0.633809	+	0.872363i	0.364457	+	0.931220i	$0.381254\pi$
$954$	25.9771	−	11.5658i	0.841040	−	0.374455i
$955$	11.6383	+	26.2973i	0.376605	+	0.850961i
$956$	−71.0926	−	31.6525i	−2.29930	−	1.02371i
$957$	−0.667643	−	0.385464i	−0.0215818	−	0.0124603i
$958$	45.2497	+	62.2809i	1.46195	+	2.01220i
$959$	11.7091	−	20.0556i	0.378105	−	0.647630i
$960$	−0.743472	+	0.156301i	−0.0239955	+	0.00504460i
$961$	32.1994	+	35.7610i	1.03869	+	1.15358i
$962$	17.5900	+	15.8381i	0.567125	+	0.510642i
$963$	−21.3655	−	19.2376i	−0.688494	−	0.619923i
$964$	18.4413	+	20.4811i	0.593953	+	0.659652i
$965$	54.2489	+	24.2980i	1.74633	+	0.782180i
$966$	3.59294	+	0.0174085i	0.115601	+	0.000560109i
$967$	−10.1761	−	14.0062i	−0.327242	−	0.450410i	0.613419	−	0.789758i	$-0.289794\pi$
$967$	−10.1761	−	14.0062i	−0.327242	−	0.450410i	−0.940661	+	0.339348i	$0.889794\pi$
$968$	−19.7244	−	11.3879i	−0.633967	−	0.366021i
$969$	−0.0827291	−	0.0368334i	−0.00265764	−	0.00118326i
$970$	−43.0528	+	38.5917i	−1.38234	+	1.23911i
$971$	−20.1372	+	8.96566i	−0.646233	+	0.287722i	−0.703562	−	0.710634i	$-0.748408\pi$
$971$	−20.1372	+	8.96566i	−0.646233	+	0.287722i	0.0573289	+	0.998355i	$0.481742\pi$
$972$	5.54941	−	7.63811i	0.177998	−	0.244993i
$973$	−27.9069	−	3.06991i	−0.894653	−	0.0984167i
$974$	90.7513			2.90786
$975$	0.114043	−	1.04047i	0.00365231	−	0.0333218i
$976$	−59.1710	−	102.487i	−1.89402	−	3.28054i
$977$	−4.20243	−	19.7709i	−0.134448	−	0.632526i	−0.992832	−	0.119519i	$-0.961865\pi$
$977$	−4.20243	−	19.7709i	−0.134448	−	0.632526i	0.858384	−	0.513007i	$-0.171469\pi$
$978$	−0.785669	−	1.76464i	−0.0251229	−	0.0564270i
$979$	23.5363	+	17.1001i	0.752222	+	0.546521i
$980$	−43.9050	+	58.9401i	−1.40249	+	1.88277i
$981$	13.9304	−	10.1210i	0.444762	−	0.323139i
$982$	4.41524	+	2.54914i	0.140896	+	0.0813464i
$983$	−23.8098	+	53.4776i	−0.759413	+	1.70567i	−0.0522357	+	0.998635i	$0.516635\pi$
$983$	−23.8098	+	53.4776i	−0.759413	+	1.70567i	−0.707178	+	0.707036i	$0.750032\pi$
$984$	0.789994	−	0.877377i	0.0251841	−	0.0279698i
$985$	−7.40335	−	0.0164784i	−0.235890	−	0.000525045i
$986$	0.657772	−	2.02442i	0.0209477	−	0.0644705i
$987$	0.952168	−	0.543601i	0.0303079	−	0.0173030i
$988$	50.4825	−	16.4028i	1.60606	−	0.521842i
$989$	−42.6085	−	47.3215i	−1.35487	−	1.50474i
$990$	63.9779	+	13.7478i	2.03335	+	0.436935i
$991$	8.48545	−	9.42405i	0.269549	−	0.299365i	−0.593140	−	0.805099i	$-0.702112\pi$
$991$	8.48545	−	9.42405i	0.269549	−	0.299365i	0.862689	+	0.505735i	$0.168779\pi$
$992$	−74.7472	+	7.85625i	−2.37323	+	0.249436i
$993$		−	0.695326i		−	0.0220655i
$994$	−6.94987	−	21.7475i	−0.220436	−	0.689788i
$995$	−14.0891	+	31.4561i	−0.446656	+	0.997226i
$996$	−1.49602	+	0.666069i	−0.0474031	+	0.0211052i
$997$	0.735041	+	0.0772559i	0.0232790	+	0.00244672i	0.116161	−	0.993230i	$-0.462941\pi$
$997$	0.735041	+	0.0772559i	0.0232790	+	0.00244672i	−0.0928818	+	0.995677i	$0.529608\pi$
$998$	9.50257	+	44.7061i	0.300799	+	1.41515i
$999$	−0.729952	+	1.26431i	−0.0230947	+	0.0400011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.t.a.79.18	yes	144
5.2	odd	4		875.2.q.b.226.35		288
5.3	odd	4		875.2.q.b.226.2		288
5.4	even	2		875.2.u.a.149.1		144
7.4	even	3	inner	175.2.t.a.4.18	✓	144
25.6	even	5		875.2.u.a.849.1		144
25.8	odd	20		875.2.q.b.401.35		288
25.17	odd	20		875.2.q.b.401.2		288
25.19	even	10	inner	175.2.t.a.44.18	yes	144
35.4	even	6		875.2.u.a.774.1		144
35.18	odd	12		875.2.q.b.851.35		288
35.32	odd	12		875.2.q.b.851.2		288
175.67	odd	60		875.2.q.b.151.35		288
175.81	even	15		875.2.u.a.599.1		144
175.144	even	30	inner	175.2.t.a.144.18	yes	144
175.158	odd	60		875.2.q.b.151.2		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.4.18	✓	144	7.4	even	3	inner
175.2.t.a.44.18	yes	144	25.19	even	10	inner
175.2.t.a.79.18	yes	144	1.1	even	1	trivial
175.2.t.a.144.18	yes	144	175.144	even	30	inner
875.2.q.b.151.2		288	175.158	odd	60
875.2.q.b.151.35		288	175.67	odd	60
875.2.q.b.226.2		288	5.3	odd	4
875.2.q.b.226.35		288	5.2	odd	4
875.2.q.b.401.2		288	25.17	odd	20
875.2.q.b.401.35		288	25.8	odd	20
875.2.q.b.851.2		288	35.32	odd	12
875.2.q.b.851.35		288	35.18	odd	12
875.2.u.a.149.1		144	5.4	even	2
875.2.u.a.599.1		144	175.81	even	15
875.2.u.a.774.1		144	35.4	even	6
875.2.u.a.849.1		144	25.6	even	5

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92293 - 1.73141i) q^{2} +(0.0742469 + 0.00780366i) q^{3} +(0.490808 - 4.66973i) q^{4} +(1.31030 + 1.81194i) q^{5} +(0.156283 - 0.113546i) q^{6} +(0.537537 + 2.59057i) q^{7} +(-4.09959 - 5.64260i) q^{8} +(-2.92899 - 0.622576i) q^{9} +O(q^{10})\)	\(q+(1.92293 - 1.73141i) q^{2} +(0.0742469 + 0.00780366i) q^{3} +(0.490808 - 4.66973i) q^{4} +(1.31030 + 1.81194i) q^{5} +(0.156283 - 0.113546i) q^{6} +(0.537537 + 2.59057i) q^{7} +(-4.09959 - 5.64260i) q^{8} +(-2.92899 - 0.622576i) q^{9} +(5.65683 + 1.21556i) q^{10} +(-3.69444 + 0.785277i) q^{11} +(0.0728820 - 0.342883i) q^{12} +(-2.66684 + 0.866509i) q^{13} +(5.51899 + 4.05078i) q^{14} +(0.0831458 + 0.144756i) q^{15} +(-8.46720 - 1.79976i) q^{16} +(0.122380 - 0.274870i) q^{17} +(-6.71018 + 3.87412i) q^{18} +(-0.421407 - 4.00942i) q^{19} +(9.10437 - 5.22942i) q^{20} +(0.0196945 + 0.196537i) q^{21} +(-5.74450 + 7.90663i) q^{22} +(5.22426 - 4.70395i) q^{23} +(-0.260349 - 0.450937i) q^{24} +(-1.56624 + 4.74836i) q^{25} +(-3.62786 + 6.28364i) q^{26} +(-0.425616 - 0.138291i) q^{27} +(12.3611 - 1.23868i) q^{28} +(2.21189 + 1.60703i) q^{29} +(0.410516 + 0.134396i) q^{30} +(8.12600 + 3.61793i) q^{31} +(-7.31754 + 4.22478i) q^{32} +(-0.280428 + 0.0294742i) q^{33} +(-0.240586 - 0.740447i) q^{34} +(-3.98962 + 4.36840i) q^{35} +(-4.34484 + 13.3720i) q^{36} +(0.678253 - 3.19093i) q^{37} +(-7.75230 - 6.98020i) q^{38} +(-0.204767 + 0.0435245i) q^{39} +(4.85236 - 14.8217i) q^{40} +(0.700664 + 2.15642i) q^{41} +(0.378157 + 0.343827i) q^{42} -9.05803i q^{43} +(1.85377 + 17.6374i) q^{44} +(-2.70978 - 6.12291i) q^{45} +(1.90141 - 18.0907i) q^{46} +(-2.25775 - 5.07098i) q^{47} +(-0.614619 - 0.199702i) q^{48} +(-6.42211 + 2.78506i) q^{49} +(5.20960 + 11.8426i) q^{50} +(0.0112313 - 0.0194532i) q^{51} +(2.73745 + 12.8787i) q^{52} +(-3.64982 - 0.383611i) q^{53} +(-1.05787 + 0.470993i) q^{54} +(-6.26369 - 5.66514i) q^{55} +(12.4139 - 13.6534i) q^{56} -0.300975i q^{57} +(7.03575 - 0.739487i) q^{58} +(-5.90587 + 6.55913i) q^{59} +(0.716780 - 0.317221i) q^{60} +(9.14775 + 10.1596i) q^{61} +(21.8898 - 7.11244i) q^{62} +(0.0383857 - 7.92241i) q^{63} +(-1.40634 + 4.32826i) q^{64} +(-5.06441 - 3.69676i) q^{65} +(-0.488212 + 0.542215i) q^{66} +(1.39877 - 3.14169i) q^{67} +(-1.22350 - 0.706390i) q^{68} +(0.424593 - 0.308485i) q^{69} +(-0.108243 + 15.3078i) q^{70} +(-2.69801 - 1.96022i) q^{71} +(8.49471 + 19.0794i) q^{72} +(2.72003 + 12.7967i) q^{73} +(-4.22058 - 7.31027i) q^{74} +(-0.153343 + 0.340328i) q^{75} -18.9297 q^{76} +(-4.02021 - 9.14858i) q^{77} +(-0.318393 + 0.438230i) q^{78} +(-7.73783 + 3.44510i) q^{79} +(-7.83351 - 17.7003i) q^{80} +(8.17611 + 3.64024i) q^{81} +(5.08098 + 2.93351i) q^{82} +(-2.74589 - 3.77939i) q^{83} +(0.927439 + 0.00449363i) q^{84} +(0.658402 - 0.138417i) q^{85} +(-15.6832 - 17.4180i) q^{86} +(0.151685 + 0.136578i) q^{87} +(19.5767 + 17.6269i) q^{88} +(-5.15403 - 5.72413i) q^{89} +(-15.8120 - 7.08217i) q^{90} +(-3.67828 - 6.44285i) q^{91} +(-19.4021 - 26.7046i) q^{92} +(0.575097 + 0.332032i) q^{93} +(-13.1215 - 5.84205i) q^{94} +(6.71265 - 6.01709i) q^{95} +(-0.576273 + 0.256573i) q^{96} +(-5.87358 + 8.08430i) q^{97} +(-7.52718 + 16.4748i) q^{98} +11.3099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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