LMFDB - Embedded newform 151.2.h.a.94.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(9,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("151.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.h (of order $25$, degree $20$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			94.4
Character	$\chi$	$=$	151.94
Dual form			151.2.h.a.98.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.999563 + 0.726225i) q^{2} +(1.53699 - 0.844968i) q^{3} +(-0.146311 + 0.450298i) q^{4} +(-2.06806 + 3.25874i) q^{5} +(-0.922683 + 1.96080i) q^{6} +(-2.24013 + 0.886932i) q^{7} +(-0.944369 - 2.90647i) q^{8} +(0.0408912 - 0.0644343i) q^{9} +O(q^{10})$	\(q+(-0.999563 + 0.726225i) q^{2} +(1.53699 - 0.844968i) q^{3} +(-0.146311 + 0.450298i) q^{4} +(-2.06806 + 3.25874i) q^{5} +(-0.922683 + 1.96080i) q^{6} +(-2.24013 + 0.886932i) q^{7} +(-0.944369 - 2.90647i) q^{8} +(0.0408912 - 0.0644343i) q^{9} +(-0.299423 - 4.75919i) q^{10} +(4.10114 + 2.25462i) q^{11} +(0.155609 + 0.815732i) q^{12} +(0.0152255 + 0.0142977i) q^{13} +(1.59504 - 2.51339i) q^{14} +(-0.425058 + 6.75610i) q^{15} +(2.28861 + 1.66277i) q^{16} +(1.97944 + 0.783717i) q^{17} +(0.00592042 + 0.0941023i) q^{18} +(2.36048 - 7.26482i) q^{19} +(-1.16483 - 1.40803i) q^{20} +(-2.69364 + 3.25605i) q^{21} +(-5.73671 + 0.724715i) q^{22} +(-2.86821 + 8.82744i) q^{23} +(-3.90736 - 3.66926i) q^{24} +(-4.21363 - 8.95441i) q^{25} +(-0.0256023 - 0.00323432i) q^{26} +(-0.321988 + 5.11786i) q^{27} +(-0.0716281 - 1.13850i) q^{28} +(2.72106 - 0.343750i) q^{29} +(-4.48158 - 7.06184i) q^{30} +(8.77554 - 2.25318i) q^{31} +2.61692 q^{32} +8.20850 q^{33} +(-2.54773 + 0.654146i) q^{34} +(1.74245 - 9.13425i) q^{35} +(0.0230318 + 0.0278407i) q^{36} +(-4.67367 - 4.38887i) q^{37} +(2.91644 + 8.97588i) q^{38} +(0.0354827 + 0.00911040i) q^{39} +(11.4244 + 2.93330i) q^{40} +(0.692029 - 1.47064i) q^{41} +(0.327837 - 5.21081i) q^{42} +(3.62674 + 1.43593i) q^{43} +(-1.61529 + 1.51686i) q^{44} +(0.125409 + 0.266508i) q^{45} +(-3.54375 - 10.9065i) q^{46} +(0.363275 - 0.771998i) q^{47} +(4.92257 + 0.621865i) q^{48} +(-0.871227 + 0.818137i) q^{49} +(10.7147 + 5.89046i) q^{50} +(3.70460 - 0.468000i) q^{51} +(-0.00866590 + 0.00476412i) q^{52} +(0.612601 - 3.21137i) q^{53} +(-3.39487 - 5.34946i) q^{54} +(-15.8286 + 8.70186i) q^{55} +(4.69335 + 5.67329i) q^{56} +(-2.51050 - 13.1605i) q^{57} +(-2.47023 + 2.31970i) q^{58} +(-6.39199 - 4.64406i) q^{59} +(-2.98007 - 1.17989i) q^{60} +(3.48013 + 1.91322i) q^{61} +(-7.13539 + 8.62521i) q^{62} +(-0.0344530 + 0.180609i) q^{63} +(-7.19301 + 5.22602i) q^{64} +(-0.0780800 + 0.0200475i) q^{65} +(-8.20491 + 5.96122i) q^{66} +(1.13660 + 1.79100i) q^{67} +(-0.642520 + 0.776673i) q^{68} +(3.05049 + 15.9912i) q^{69} +(4.89183 + 10.3957i) q^{70} +(4.24924 - 1.68239i) q^{71} +(-0.225893 - 0.0579994i) q^{72} +(2.76752 - 1.09574i) q^{73} +(7.85893 + 0.992814i) q^{74} +(-14.0425 - 10.2025i) q^{75} +(2.92597 + 2.12584i) q^{76} +(-11.1868 - 1.41322i) q^{77} +(-0.0420833 + 0.0166620i) q^{78} +(-1.62135 - 0.416293i) q^{79} +(-10.1515 + 4.01928i) q^{80} +(3.92701 + 8.34533i) q^{81} +(0.376286 + 1.97256i) q^{82} +(-9.16582 + 11.0796i) q^{83} +(-1.07208 - 1.68934i) q^{84} +(-6.64754 + 4.82972i) q^{85} +(-4.66796 + 1.19853i) q^{86} +(3.89179 - 2.82755i) q^{87} +(2.68000 - 14.0490i) q^{88} +(6.12990 - 7.40977i) q^{89} +(-0.318899 - 0.175316i) q^{90} +(-0.0467884 - 0.0185248i) q^{91} +(-3.55533 - 2.58310i) q^{92} +(11.5841 - 10.8782i) q^{93} +(0.197528 + 1.03548i) q^{94} +(18.7925 + 22.7163i) q^{95} +(4.02219 - 2.21122i) q^{96} +(3.85266 + 6.07082i) q^{97} +(0.276695 - 1.45049i) q^{98} +(0.312975 - 0.172060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9} - 50 q^{10} - 10 q^{11} + 5 q^{12} - 20 q^{13} + 5 q^{14} - 60 q^{15} - 5 q^{16} - 10 q^{17} + 30 q^{18} - 15 q^{19} - 130 q^{20} - 20 q^{21} + 15 q^{22} + 35 q^{23} - 95 q^{24} + 10 q^{25} + 5 q^{26} + 25 q^{27} + 50 q^{28} + 15 q^{29} + 75 q^{30} + 20 q^{31} + 80 q^{32} - 100 q^{33} - 50 q^{34} + 15 q^{35} + 100 q^{36} + 20 q^{37} + 40 q^{38} - 5 q^{39} + 105 q^{40} - 10 q^{41} - 110 q^{42} - 10 q^{43} + 90 q^{44} + 5 q^{45} + 25 q^{46} - 75 q^{47} - 145 q^{48} - 10 q^{49} + 50 q^{50} - 80 q^{51} + 85 q^{52} - 95 q^{53} + 20 q^{54} + 80 q^{55} - 65 q^{56} + 55 q^{57} - 105 q^{58} - 15 q^{59} - 70 q^{62} + 95 q^{63} + 45 q^{64} - 30 q^{65} - 5 q^{66} - 50 q^{67} + 95 q^{68} + 45 q^{69} + 25 q^{71} - 25 q^{72} + 20 q^{73} - 140 q^{74} + 55 q^{75} + 15 q^{76} - 45 q^{77} + 110 q^{78} - 130 q^{79} + 145 q^{80} - 160 q^{81} - 10 q^{82} - 55 q^{83} + 140 q^{84} + 25 q^{85} - 150 q^{86} + 125 q^{87} - 35 q^{88} + 5 q^{89} + 120 q^{90} - 70 q^{91} + 45 q^{92} - 40 q^{93} + 65 q^{94} + 135 q^{96} - 270 q^{97} + 135 q^{98} + 60 q^{99}+O(q^{100}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9 - 50 * q^10 - 10 * q^11 + 5 * q^12 - 20 * q^13 + 5 * q^14 - 60 * q^15 - 5 * q^16 - 10 * q^17 + 30 * q^18 - 15 * q^19 - 130 * q^20 - 20 * q^21 + 15 * q^22 + 35 * q^23 - 95 * q^24 + 10 * q^25 + 5 * q^26 + 25 * q^27 + 50 * q^28 + 15 * q^29 + 75 * q^30 + 20 * q^31 + 80 * q^32 - 100 * q^33 - 50 * q^34 + 15 * q^35 + 100 * q^36 + 20 * q^37 + 40 * q^38 - 5 * q^39 + 105 * q^40 - 10 * q^41 - 110 * q^42 - 10 * q^43 + 90 * q^44 + 5 * q^45 + 25 * q^46 - 75 * q^47 - 145 * q^48 - 10 * q^49 + 50 * q^50 - 80 * q^51 + 85 * q^52 - 95 * q^53 + 20 * q^54 + 80 * q^55 - 65 * q^56 + 55 * q^57 - 105 * q^58 - 15 * q^59 - 70 * q^62 + 95 * q^63 + 45 * q^64 - 30 * q^65 - 5 * q^66 - 50 * q^67 + 95 * q^68 + 45 * q^69 + 25 * q^71 - 25 * q^72 + 20 * q^73 - 140 * q^74 + 55 * q^75 + 15 * q^76 - 45 * q^77 + 110 * q^78 - 130 * q^79 + 145 * q^80 - 160 * q^81 - 10 * q^82 - 55 * q^83 + 140 * q^84 + 25 * q^85 - 150 * q^86 + 125 * q^87 - 35 * q^88 + 5 * q^89 + 120 * q^90 - 70 * q^91 + 45 * q^92 - 40 * q^93 + 65 * q^94 + 135 * q^96 - 270 * q^97 + 135 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{16}{25}\right)$

Coefficient data

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

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

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

$2$	−0.999563	+	0.726225i	−0.706798	+	0.513519i	−0.882139	−	0.470989i	$-0.843897\pi$
$2$	−0.999563	+	0.726225i	−0.706798	+	0.513519i	0.175341	+	0.984508i	$0.443897\pi$
$3$	1.53699	−	0.844968i	0.887382	−	0.487843i	0.0282529	−	0.999601i	$-0.491006\pi$
$3$	1.53699	−	0.844968i	0.887382	−	0.487843i	0.859130	+	0.511758i	$0.171006\pi$
$4$	−0.146311	+	0.450298i	−0.0731554	+	0.225149i
$5$	−2.06806	+	3.25874i	−0.924865	+	1.45735i	−0.0359118	+	0.999355i	$0.511434\pi$
$5$	−2.06806	+	3.25874i	−0.924865	+	1.45735i	−0.888953	+	0.457999i	$0.848566\pi$
$6$	−0.922683	+	1.96080i	−0.376684	+	0.800493i
$7$	−2.24013	+	0.886932i	−0.846691	+	0.335229i	−0.751097	−	0.660192i	$-0.770475\pi$
$7$	−2.24013	+	0.886932i	−0.846691	+	0.335229i	−0.0955940	+	0.995420i	$0.530475\pi$
$8$	−0.944369	−	2.90647i	−0.333885	−	1.02759i
$9$	0.0408912	−	0.0644343i	0.0136304	−	0.0214781i
$10$	−0.299423	−	4.75919i	−0.0946859	−	1.50499i
$11$	4.10114	+	2.25462i	1.23654	+	0.679794i	0.959674	−	0.281115i	$-0.0907042\pi$
$11$	4.10114	+	2.25462i	1.23654	+	0.679794i	0.276866	+	0.960909i	$0.410704\pi$
$12$	0.155609	+	0.815732i	0.0449205	+	0.235482i
$13$	0.0152255	+	0.0142977i	0.00422280	+	0.00396548i	0.686656	−	0.726983i	$-0.259078\pi$
$13$	0.0152255	+	0.0142977i	0.00422280	+	0.00396548i	−0.682433	+	0.730948i	$0.739078\pi$
$14$	1.59504	−	2.51339i	0.426293	−	0.671731i
$15$	−0.425058	+	6.75610i	−0.109750	+	1.74442i
$16$	2.28861	+	1.66277i	0.572153	+	0.415694i
$17$	1.97944	+	0.783717i	0.480085	+	0.190079i	0.595687	−	0.803216i	$-0.296880\pi$
$17$	1.97944	+	0.783717i	0.480085	+	0.190079i	−0.115602	+	0.993296i	$0.536880\pi$
$18$	0.00592042	+	0.0941023i	0.00139546	+	0.0221801i
$19$	2.36048	−	7.26482i	0.541532	−	1.66666i	−0.187565	−	0.982252i	$-0.560060\pi$
$19$	2.36048	−	7.26482i	0.541532	−	1.66666i	0.729097	−	0.684411i	$-0.239940\pi$
$20$	−1.16483	−	1.40803i	−0.260463	−	0.314846i
$21$	−2.69364	+	3.25605i	−0.587800	+	0.710528i
$22$	−5.73671	+	0.724715i	−1.22307	+	0.154510i
$23$	−2.86821	+	8.82744i	−0.598063	+	1.84065i	−0.0592150	+	0.998245i	$0.518860\pi$
$23$	−2.86821	+	8.82744i	−0.598063	+	1.84065i	−0.538848	+	0.842403i	$0.681140\pi$
$24$	−3.90736	−	3.66926i	−0.797587	−	0.748984i
$25$	−4.21363	−	8.95441i	−0.842726	−	1.79088i
$26$	−0.0256023	−	0.00323432i	−0.00502102	−	0.000634302i
$27$	−0.321988	+	5.11786i	−0.0619667	+	0.984932i
$28$	−0.0716281	−	1.13850i	−0.0135364	−	0.215156i
$29$	2.72106	−	0.343750i	0.505289	−	0.0638328i	0.131443	−	0.991324i	$-0.458039\pi$
$29$	2.72106	−	0.343750i	0.505289	−	0.0638328i	0.373846	+	0.927491i	$0.378039\pi$
$30$	−4.48158	−	7.06184i	−0.818221	−	1.28931i
$31$	8.77554	−	2.25318i	1.57613	−	0.404682i	0.643483	−	0.765461i	$-0.277489\pi$
$31$	8.77554	−	2.25318i	1.57613	−	0.404682i	0.932652	+	0.360778i	$0.117489\pi$
$32$	2.61692			0.462611
$33$	8.20850			1.42892
$34$	−2.54773	+	0.654146i	−0.436932	+	0.112185i
$35$	1.74245	−	9.13425i	0.294528	−	1.54397i
$36$	0.0230318	+	0.0278407i	0.00383863	+	0.00464011i
$37$	−4.67367	−	4.38887i	−0.768347	−	0.721526i	0.197595	−	0.980284i	$-0.436687\pi$
$37$	−4.67367	−	4.38887i	−0.768347	−	0.721526i	−0.965942	+	0.258758i	$0.916687\pi$
$38$	2.91644	+	8.97588i	0.473109	+	1.45608i
$39$	0.0354827	+	0.00911040i	0.00568177	+	0.00145883i
$40$	11.4244	+	2.93330i	1.80636	+	0.463795i
$41$	0.692029	−	1.47064i	0.108077	−	0.229675i	−0.843472	−	0.537174i	$-0.819492\pi$
$41$	0.692029	−	1.47064i	0.108077	−	0.229675i	0.951548	+	0.307499i	$0.0994920\pi$
$42$	0.327837	−	5.21081i	0.0505863	−	0.804046i
$43$	3.62674	+	1.43593i	0.553073	+	0.218977i	0.628002	−	0.778212i	$-0.283873\pi$
$43$	3.62674	+	1.43593i	0.553073	+	0.218977i	−0.0749290	+	0.997189i	$0.523873\pi$
$44$	−1.61529	+	1.51686i	−0.243514	+	0.228675i
$45$	0.125409	+	0.266508i	0.0186949	+	0.0397286i
$46$	−3.54375	−	10.9065i	−0.522498	−	1.60808i
$47$	0.363275	−	0.771998i	0.0529891	−	0.112607i	−0.876579	−	0.481258i	$-0.840180\pi$
$47$	0.363275	−	0.771998i	0.0529891	−	0.112607i	0.929568	+	0.368650i	$0.120180\pi$
$48$	4.92257	+	0.621865i	0.710512	+	0.0897585i
$49$	−0.871227	+	0.818137i	−0.124461	+	0.116877i
$50$	10.7147	+	5.89046i	1.51529	+	0.833037i
$51$	3.70460	−	0.468000i	0.518748	−	0.0655331i
$52$	−0.00866590	+	0.00476412i	−0.00120174	+	0.000660665i
$53$	0.612601	−	3.21137i	0.0841473	−	0.441115i	−0.915132	−	0.403154i	$-0.867914\pi$
$53$	0.612601	−	3.21137i	0.0841473	−	0.441115i	0.999279	−	0.0379610i	$-0.0120863\pi$
$54$	−3.39487	−	5.34946i	−0.461983	−	0.727969i
$55$	−15.8286	+	8.70186i	−2.13433	+	1.17336i
$56$	4.69335	+	5.67329i	0.627176	+	0.758125i
$57$	−2.51050	−	13.1605i	−0.332524	−	1.74315i
$58$	−2.47023	+	2.31970i	−0.324358	+	0.304592i
$59$	−6.39199	−	4.64406i	−0.832167	−	0.604605i	0.0880047	−	0.996120i	$-0.471951\pi$
$59$	−6.39199	−	4.64406i	−0.832167	−	0.604605i	−0.920172	+	0.391515i	$0.871951\pi$
$60$	−2.98007	−	1.17989i	−0.384725	−	0.152324i
$61$	3.48013	+	1.91322i	0.445586	+	0.244963i	0.688716	−	0.725031i	$-0.258174\pi$
$61$	3.48013	+	1.91322i	0.445586	+	0.244963i	−0.243131	+	0.969993i	$0.578174\pi$
$62$	−7.13539	+	8.62521i	−0.906196	+	1.09540i
$63$	−0.0344530	+	0.180609i	−0.00434067	+	0.0227546i
$64$	−7.19301	+	5.22602i	−0.899126	+	0.653253i
$65$	−0.0780800	+	0.0200475i	−0.00968463	+	0.00248659i
$66$	−8.20491	+	5.96122i	−1.00995	+	0.733775i
$67$	1.13660	+	1.79100i	0.138858	+	0.218805i	0.906639	−	0.421907i	$-0.138639\pi$
$67$	1.13660	+	1.79100i	0.138858	+	0.218805i	−0.767781	+	0.640712i	$0.778639\pi$
$68$	−0.642520	+	0.776673i	−0.0779170	+	0.0941855i
$69$	3.05049	+	15.9912i	0.367236	+	1.92512i
$70$	4.89183	+	10.3957i	0.584685	+	1.24252i
$71$	4.24924	−	1.68239i	0.504292	−	0.199663i	−0.102184	−	0.994766i	$-0.532583\pi$
$71$	4.24924	−	1.68239i	0.504292	−	0.199663i	0.606475	+	0.795102i	$0.292583\pi$
$72$	−0.225893	−	0.0579994i	−0.0266217	−	0.00683529i
$73$	2.76752	−	1.09574i	0.323914	−	0.128246i	−0.200540	−	0.979686i	$-0.564270\pi$
$73$	2.76752	−	1.09574i	0.323914	−	0.128246i	0.524454	+	0.851439i	$0.324270\pi$
$74$	7.85893	+	0.992814i	0.913583	+	0.115412i
$75$	−14.0425	−	10.2025i	−1.62149	−	1.17808i
$76$	2.92597	+	2.12584i	0.335632	+	0.243851i
$77$	−11.1868	−	1.41322i	−1.27485	−	0.161051i
$78$	−0.0420833	+	0.0166620i	−0.00476500	+	0.00188660i
$79$	−1.62135	−	0.416293i	−0.182417	−	0.0468366i	0.156377	−	0.987698i	$-0.450019\pi$
$79$	−1.62135	−	0.416293i	−0.182417	−	0.0468366i	−0.338793	+	0.940861i	$0.610019\pi$
$80$	−10.1515	+	4.01928i	−1.13498	+	0.449369i
$81$	3.92701	+	8.34533i	0.436335	+	0.927259i
$82$	0.376286	+	1.97256i	0.0415539	+	0.217833i
$83$	−9.16582	+	11.0796i	−1.00608	+	1.21614i	−0.0298156	+	0.999555i	$0.509492\pi$
$83$	−9.16582	+	11.0796i	−1.00608	+	1.21614i	−0.976264	+	0.216585i	$0.930508\pi$
$84$	−1.07208	−	1.68934i	−0.116974	−	0.184322i
$85$	−6.64754	+	4.82972i	−0.721027	+	0.523856i
$86$	−4.66796	+	1.19853i	−0.503359	+	0.129241i
$87$	3.89179	−	2.82755i	0.417244	−	0.303146i
$88$	2.68000	−	14.0490i	0.285688	−	1.49763i
$89$	6.12990	−	7.40977i	0.649768	−	0.785434i	−0.338037	−	0.941133i	$-0.609763\pi$
$89$	6.12990	−	7.40977i	0.649768	−	0.785434i	0.987805	+	0.155698i	$0.0497628\pi$
$90$	−0.318899	−	0.175316i	−0.0336149	−	0.0184799i
$91$	−0.0467884	−	0.0185248i	−0.00490475	−	0.00194193i
$92$	−3.55533	−	2.58310i	−0.370669	−	0.269307i
$93$	11.5841	−	10.8782i	1.20121	−	1.12801i
$94$	0.197528	+	1.03548i	0.0203735	+	0.106802i
$95$	18.7925	+	22.7163i	1.92807	+	2.33064i
$96$	4.02219	−	2.21122i	0.410513	−	0.225681i
$97$	3.85266	+	6.07082i	0.391178	+	0.616398i	0.981657	−	0.190655i	$-0.0610612\pi$
$97$	3.85266	+	6.07082i	0.391178	+	0.616398i	−0.590479	+	0.807053i	$0.701061\pi$
$98$	0.276695	−	1.45049i	0.0279504	−	0.146521i
$99$	0.312975	−	0.172060i	0.0314552	−	0.0172926i
$100$	4.64866	−	0.587262i	0.464866	−	0.0587262i
$101$	4.55847	+	2.50604i	0.453585	+	0.249360i	0.692133	−	0.721770i	$-0.256671\pi$
$101$	4.55847	+	2.50604i	0.453585	+	0.249360i	−0.238548	+	0.971131i	$0.576671\pi$
$102$	−3.36311	+	3.15817i	−0.332997	+	0.312705i
$103$	−3.02325	−	0.381925i	−0.297890	−	0.0376322i	−0.0250322	−	0.999687i	$-0.507969\pi$
$103$	−3.02325	−	0.381925i	−0.297890	−	0.0376322i	−0.272858	+	0.962054i	$0.587969\pi$
$104$	0.0271774	−	0.0577549i	0.00266496	−	0.00566333i
$105$	−5.04002	−	15.5116i	−0.491855	−	1.51377i
$106$	1.71984	+	3.65485i	0.167046	+	0.354990i
$107$	1.96972	−	1.84969i	0.190420	−	0.178817i	−0.583473	−	0.812133i	$-0.698307\pi$
$107$	1.96972	−	1.84969i	0.190420	−	0.178817i	0.773893	+	0.633316i	$0.218307\pi$
$108$	−2.25745	−	0.893788i	−0.217223	−	0.0860048i
$109$	−0.330990	+	5.26093i	−0.0317031	+	0.503906i	0.949849	+	0.312710i	$0.101237\pi$
$109$	−0.330990	+	5.26093i	−0.0317031	+	0.503906i	−0.981552	+	0.191196i	$0.938763\pi$
$110$	9.50220	−	20.1932i	0.905999	−	1.92535i
$111$	−10.8918	−	2.79655i	−1.03381	−	0.265437i
$112$	−6.60157	−	1.69499i	−0.623790	−	0.160162i
$113$	−0.435803	−	1.34126i	−0.0409969	−	0.126175i	0.928463	−	0.371424i	$-0.121130\pi$
$113$	−0.435803	−	1.34126i	−0.0409969	−	0.126175i	−0.969460	+	0.245249i	$0.921130\pi$
$114$	12.0669	+	11.3316i	1.13017	+	1.06130i
$115$	−22.8347	−	27.6024i	−2.12935	−	2.57394i
$116$	−0.243331	+	1.27558i	−0.0225927	+	0.118435i
$117$	0.00154385		0.000396395i	0.000142729		3.66467e-5i
$118$	9.76183			0.898649
$119$	−5.12932			−0.470204
$120$	20.0378	−	5.14484i	1.82919	−	0.469657i
$121$	5.84193	+	9.20542i	0.531085	+	0.836856i
$122$	−4.86804	+	0.614977i	−0.440732	+	0.0556774i
$123$	−0.178998	−	2.84510i	−0.0161397	−	0.256534i
$124$	−0.269355	+	4.28128i	−0.0241888	+	0.384470i
$125$	18.7485	+	2.36848i	1.67692	+	0.211844i
$126$	−0.0967249	−	0.205551i	−0.00861694	−	0.0183119i
$127$	−2.04253	−	1.91807i	−0.181246	−	0.170201i	0.588614	−	0.808414i	$-0.299674\pi$
$127$	−2.04253	−	1.91807i	−0.181246	−	0.170201i	−0.769860	+	0.638213i	$0.779674\pi$
$128$	1.77724	−	5.46980i	0.157088	−	0.483466i
$129$	6.78758	−	0.857471i	0.597613	−	0.0754961i
$130$	0.0634868	−	0.0767424i	0.00556816	−	0.00673075i
$131$	1.39422	+	1.68532i	0.121814	+	0.147247i	0.827895	−	0.560884i	$-0.189539\pi$
$131$	1.39422	+	1.68532i	0.121814	+	0.147247i	−0.706081	+	0.708131i	$0.749539\pi$
$132$	−1.20099	+	3.69627i	−0.104533	+	0.321719i
$133$	1.15560	+	18.3677i	0.100203	+	1.59269i
$134$	−2.43677	−	0.964786i	−0.210505	−	0.0833448i
$135$	−16.0119	−	11.6333i	−1.37808	−	1.00124i
$136$	0.408524	−	6.49331i	0.0350307	−	0.556796i
$137$	5.12794	−	8.08034i	0.438109	−	0.690350i	−0.551493	−	0.834179i	$-0.685942\pi$
$137$	5.12794	−	8.08034i	0.438109	−	0.690350i	0.989602	+	0.143830i	$0.0459417\pi$
$138$	−14.6624	−	13.7689i	−1.24815	−	1.17209i
$139$	0.685142	+	3.59164i	0.0581130	+	0.304639i	0.999462	−	0.0327954i	$-0.0104410\pi$
$139$	0.685142	+	3.59164i	0.0581130	+	0.304639i	−0.941349	+	0.337434i	$0.890441\pi$
$140$	3.85820	+	2.12106i	0.326077	+	0.179262i
$141$	−0.0939637	−	1.49351i	−0.00791317	−	0.125776i
$142$	−3.02558	+	4.76756i	−0.253901	+	0.400085i
$143$	0.0302061	+	0.0929648i	0.00252596	+	0.00777411i
$144$	0.200724	−	0.0794722i	0.0167270	−	0.00662268i
$145$	−4.50713	+	9.57814i	−0.374297	+	0.795421i
$146$	−1.97056	+	3.10510i	−0.163084	+	0.256980i
$147$	−0.647769	+	1.99363i	−0.0534271	+	0.164432i
$148$	2.66011	−	1.46241i	0.218660	−	0.120209i
$149$	4.71897	−	3.42853i	0.386593	−	0.280877i	−0.377465	−	0.926024i	$-0.623204\pi$
$149$	4.71897	−	3.42853i	0.386593	−	0.280877i	0.764058	+	0.645147i	$0.223204\pi$
$150$	21.4457			1.75103
$151$	−1.82945	−	12.1513i	−0.148879	−	0.988855i
$151$	−1.82945	−	12.1513i	−0.148879	−	0.988855i
$152$	−23.3441			−1.89346
$153$	0.131440	−	0.0954968i	0.0106263	−	0.00772046i
$154$	12.2082	−	6.71153i	0.983767	−	0.540830i
$155$	−10.8058	+	33.2569i	−0.867945	+	2.67126i
$156$	−0.00929389	+	0.0146448i	−0.000744107	+	0.00117252i
$157$	7.28846	−	15.4888i	0.581682	−	1.23614i	−0.369994	−	0.929034i	$-0.620640\pi$
$157$	7.28846	−	15.4888i	0.581682	−	1.23614i	0.951676	−	0.307104i	$-0.0993599\pi$
$158$	1.92297	−	0.761356i	0.152983	−	0.0605703i
$159$	−1.77194	−	5.45347i	−0.140524	−	0.432489i
$160$	−5.41196	+	8.52788i	−0.427853	+	0.674188i
$161$	−1.40416	−	22.3186i	−0.110664	−	1.75895i
$162$	−9.98588	−	5.48978i	−0.784565	−	0.431318i
$163$	0.298168	+	1.56305i	0.0233543	+	0.122427i	0.992055	−	0.125803i	$-0.0401508\pi$
$163$	0.298168	+	1.56305i	0.0233543	+	0.122427i	−0.968701	+	0.248231i	$0.920151\pi$
$164$	0.560974	+	0.526789i	0.0438047	+	0.0411353i
$165$	−16.9757	+	26.7494i	−1.32155	+	2.08244i
$166$	1.11555	−	17.7312i	0.0865835	−	1.37621i
$167$	−13.2457	−	9.62359i	−1.02499	−	0.744695i	−0.0576865	−	0.998335i	$-0.518372\pi$
$167$	−13.2457	−	9.62359i	−1.02499	−	0.744695i	−0.967299	+	0.253639i	$0.918372\pi$
$168$	12.0074	+	4.75406i	0.926391	+	0.366784i
$169$	−0.816249	−	12.9739i	−0.0627884	−	0.997993i
$170$	3.13717	−	9.65521i	0.240610	−	0.740521i
$171$	−0.371580	−	0.449163i	−0.0284154	−	0.0343484i
$172$	−1.17723	+	1.42302i	−0.0897627	+	0.108505i
$173$	−3.23730	+	0.408966i	−0.246127	+	0.0310931i	−0.247429	−	0.968906i	$-0.579586\pi$
$173$	−3.23730	+	0.408966i	−0.246127	+	0.0310931i	0.00130160	+	0.999999i	$0.499586\pi$
$174$	−1.83665	+	5.65263i	−0.139236	+	0.428525i
$175$	17.3810	+	16.3219i	1.31388	+	1.23382i
$176$	5.63700	+	11.9792i	0.424905	+	0.902968i
$177$	−13.7485	−	1.73684i	−1.03340	−	0.130549i
$178$	−0.746056	+	11.8582i	−0.0559193	+	0.888811i
$179$	0.0626563	+	0.995894i	0.00468315	+	0.0744366i	0.999674	−	0.0255286i	$-0.00812687\pi$
$179$	0.0626563	+	0.995894i	0.00468315	+	0.0744366i	−0.994991	+	0.0999651i	$0.968127\pi$
$180$	−0.138357	+	0.0174785i	−0.0103125	+	0.00130277i
$181$	8.54227	+	13.4605i	0.634942	+	1.00051i	0.997644	+	0.0686034i	$0.0218543\pi$
$181$	8.54227	+	13.4605i	0.634942	+	1.00051i	−0.362702	+	0.931905i	$0.618146\pi$
$182$	0.0602211	−	0.0154622i	0.00446389	−	0.00114613i
$183$	6.96555			0.514908
$184$	28.3653			2.09112
$185$	23.9676	−	6.15384i	1.76214	−	0.452439i
$186$	−3.67901	+	19.2861i	−0.269758	+	1.41412i
$187$	6.35099	+	7.67702i	0.464430	+	0.561399i
$188$	0.294478	+	0.276534i	0.0214770	+	0.0201683i
$189$	−3.81789	−	11.7503i	−0.277711	−	0.854706i
$190$	−35.2815	−	9.05874i	−2.55959	−	0.657190i
$191$	−25.8043	−	6.62543i	−1.86714	−	0.479399i	−0.867305	−	0.497777i	$-0.834150\pi$
$191$	−25.8043	−	6.62543i	−1.86714	−	0.479399i	−0.999831	+	0.0183775i	$0.994150\pi$
$192$	−6.63976	+	14.1102i	−0.479184	+	1.01832i
$193$	0.921770	−	14.6511i	0.0663505	−	1.05461i	−0.814177	−	0.580616i	$-0.802812\pi$
$193$	0.921770	−	14.6511i	0.0663505	−	1.05461i	0.880528	−	0.473994i	$-0.157188\pi$
$194$	−8.25975	−	3.27027i	−0.593015	−	0.234791i
$195$	−0.103069	+	0.0967880i	−0.00738090	+	0.00693113i
$196$	−0.240936	−	0.512014i	−0.0172097	−	0.0365724i
$197$	−8.53168	−	26.2578i	−0.607857	−	1.87079i	−0.475813	−	0.879547i	$-0.657846\pi$
$197$	−8.53168	−	26.2578i	−0.607857	−	1.87079i	−0.132044	−	0.991244i	$-0.542154\pi$
$198$	−0.187885	+	0.399275i	−0.0133524	+	0.0283752i
$199$	23.6394	+	2.98636i	1.67576	+	0.211697i	0.904993	−	0.425426i	$-0.139876\pi$
$199$	23.6394	+	2.98636i	1.67576	+	0.211697i	0.770762	+	0.637123i	$0.219876\pi$
$200$	−22.0465	+	20.7030i	−1.55892	+	1.46393i
$201$	3.26028	+	1.79236i	0.229963	+	0.126423i
$202$	−6.37643	+	0.805530i	−0.448644	+	0.0566769i
$203$	−5.79066	+	3.18344i	−0.406425	+	0.223434i
$204$	−0.331284	+	1.73665i	−0.0231945	+	0.121590i
$205$	3.36127	+	5.29651i	0.234761	+	0.369924i
$206$	3.29929	−	1.81380i	0.229873	−	0.126374i
$207$	0.451505	+	0.545776i	0.0313818	+	0.0379340i
$208$	0.0110715	+	0.0580386i	0.000767668	+	0.00402425i
$209$	26.0601	−	24.4720i	1.80261	−	1.69277i
$210$	16.3027	+	11.8446i	1.12499	+	0.817356i
$211$	−1.79101	−	0.709110i	−0.123298	−	0.0488172i	0.305665	−	0.952139i	$-0.401121\pi$
$211$	−1.79101	−	0.709110i	−0.123298	−	0.0488172i	−0.428963	+	0.903322i	$0.641121\pi$
$212$	1.35644	+	0.745711i	0.0931609	+	0.0512156i
$213$	5.10947	−	6.17629i	0.350095	−	0.423192i
$214$	−0.625569	+	3.27935i	−0.0427630	+	0.224172i
$215$	−12.1796	+	8.84903i	−0.830645	+	0.603499i
$216$	15.1790	−	3.89730i	1.03280	−	0.265177i
$217$	−17.6600	+	12.8307i	−1.19884	+	0.871007i
$218$	−3.48978	−	5.49901i	−0.236357	−	0.372440i
$219$	3.32779	−	4.02261i	0.224871	−	0.271823i
$220$	−1.60253	−	8.40078i	−0.108043	−	0.566380i
$221$	0.0189327	+	0.0402341i	0.00127355	+	0.00270644i
$222$	12.9180	−	5.11460i	0.867000	−	0.343270i
$223$	0.477192	+	0.122522i	0.0319552	+	0.00820469i	0.264634	−	0.964349i	$-0.414749\pi$
$223$	0.477192	+	0.122522i	0.0319552	+	0.00820469i	−0.232678	+	0.972554i	$0.574749\pi$
$224$	−5.86226	+	2.32103i	−0.391689	+	0.155081i
$225$	−0.749271	−	0.0946550i	−0.0499514	−	0.00631033i
$226$	1.40967	+	1.02419i	0.0937699	+	0.0681278i
$227$	13.0845	+	9.50642i	0.868446	+	0.630963i	0.930170	−	0.367130i	$-0.119660\pi$
$227$	13.0845	+	9.50642i	0.868446	+	0.630963i	−0.0617232	+	0.998093i	$0.519660\pi$
$228$	6.29346	+	0.795049i	0.416794	+	0.0526534i
$229$	1.53856	−	0.609158i	0.101671	−	0.0402543i	−0.316739	−	0.948513i	$-0.602588\pi$
$229$	1.53856	−	0.609158i	0.101671	−	0.0402543i	0.418409	+	0.908259i	$0.362588\pi$
$230$	42.8703	+	11.0072i	2.82678	+	0.725795i
$231$	−18.3881	+	7.28038i	−1.20985	+	0.479014i
$232$	−3.56879	−	7.58406i	−0.234302	−	0.497918i
$233$	−0.0805415	−	0.422213i	−0.00527645	−	0.0276601i	0.979552	−	0.201193i	$-0.0644818\pi$
$233$	−0.0805415	−	0.422213i	−0.00527645	−	0.0276601i	−0.984828	+	0.173533i	$0.944482\pi$
$234$	−0.00125531	+	0.00151741i	−8.20621e−5	+	9.91960e-5i
$235$	1.76447	+	2.78036i	0.115101	+	0.181370i
$236$	3.02643	−	2.19883i	0.197004	−	0.143132i
$237$	−2.84376	+	0.730154i	−0.184722	+	0.0474286i
$238$	5.12708	−	3.72504i	0.332339	−	0.241458i
$239$	−3.77852	+	19.8077i	−0.244412	+	1.28125i	0.622432	+	0.782674i	$0.286145\pi$
$239$	−3.77852	+	19.8077i	−0.244412	+	1.28125i	−0.866844	+	0.498579i	$0.833855\pi$
$240$	−12.2067	+	14.7553i	−0.787937	+	0.952453i
$241$	1.65069	+	0.907474i	0.106330	+	0.0584556i	0.534031	−	0.845465i	$-0.320676\pi$
$241$	1.65069	+	0.907474i	0.106330	+	0.0584556i	−0.427701	+	0.903920i	$0.640676\pi$
$242$	−12.5246	−	4.95883i	−0.805111	−	0.318766i
$243$	0.641462	+	0.466049i	0.0411498	+	0.0298971i
$244$	−1.37070	+	1.28717i	−0.0877501	+	0.0824028i
$245$	−0.864346	−	4.53106i	−0.0552210	−	0.289479i
$246$	2.24510	+	2.71386i	0.143142	+	0.173030i
$247$	0.139810	−	0.0768612i	0.00889590	−	0.00489056i
$248$	−14.8361	−	23.3780i	−0.942096	−	1.48451i
$249$	−4.72590	+	24.7740i	−0.299492	+	1.56999i
$250$	−20.4603	+	11.2482i	−1.29403	+	0.711397i
$251$	23.3866	−	2.95442i	1.47615	−	0.186481i	0.654323	−	0.756216i	$-0.272954\pi$
$251$	23.3866	−	2.95442i	1.47615	−	0.186481i	0.821829	+	0.569734i	$0.192954\pi$
$252$	−0.0762871	−	0.0419392i	−0.00480564	−	0.00264192i
$253$	−31.6654	+	29.7358i	−1.99079	+	1.86948i
$254$	3.43459	+	0.433889i	0.215505	+	0.0272246i
$255$	−6.13625	+	13.0402i	−0.384267	+	0.816609i
$256$	−3.29913	−	10.1537i	−0.206196	−	0.634605i
$257$	0.501805	+	1.06639i	0.0313017	+	0.0665196i	0.919866	−	0.392232i	$-0.128297\pi$
$257$	0.501805	+	1.06639i	0.0313017	+	0.0665196i	−0.888565	+	0.458751i	$0.848297\pi$
$258$	−6.16190	+	5.78641i	−0.383623	+	0.360246i
$259$	14.3623	+	5.68643i	0.892429	+	0.353338i
$260$	0.00239657	−	0.0380924i	0.000148629	−	0.00236239i
$261$	0.0891183	−	0.189386i	0.00551628	−	0.0117227i
$262$	−2.61754	−	0.672069i	−0.161712	−	0.0415206i
$263$	−17.5476	−	4.50547i	−1.08203	−	0.277819i	−0.334738	−	0.942311i	$-0.608648\pi$
$263$	−17.5476	−	4.50547i	−1.08203	−	0.277819i	−0.747295	+	0.664492i	$0.768648\pi$
$264$	−7.75185	−	23.8577i	−0.477093	−	1.46834i
$265$	9.19812	+	8.63761i	0.565036	+	0.530604i
$266$	−14.4942	−	17.5205i	−0.888697	−	1.07425i
$267$	3.16058	−	16.5683i	0.193424	−	1.01397i
$268$	−0.972780	+	0.249767i	−0.0594220	+	0.0152570i
$269$	−23.0298			−1.40415			−0.702077	−	0.712101i	$-0.747744\pi$
$269$	−23.0298			−1.40415			−0.702077	+	0.712101i	$0.747744\pi$
$270$	24.4533			1.48818
$271$	−14.6213	+	3.75411i	−0.888180	+	0.228046i	−0.665100	−	0.746754i	$-0.731611\pi$
$271$	−14.6213	+	3.75411i	−0.888180	+	0.228046i	−0.223080	+	0.974800i	$0.571611\pi$
$272$	3.22703	+	5.08499i	0.195668	+	0.308323i
$273$	−0.0875662	+	0.0110622i	−0.00529975	+	0.000669514i
$274$	0.742446	+	11.8008i	0.0448528	+	0.712915i
$275$	2.90813	−	46.2234i	0.175367	−	2.78738i
$276$	−7.64715	−	0.966060i	−0.460304	−	0.0581500i
$277$	6.58759	+	13.9993i	0.395810	+	0.841139i	0.999050	+	0.0435791i	$0.0138761\pi$
$277$	6.58759	+	13.9993i	0.395810	+	0.841139i	−0.603240	+	0.797560i	$0.706124\pi$
$278$	−3.29318	−	3.09250i	−0.197512	−	0.185476i
$279$	0.213661	−	0.657581i	0.0127915	−	0.0393683i
$280$	−28.1939	+	3.56172i	−1.68491	+	0.212854i
$281$	1.44188	−	1.74293i	0.0860151	−	0.103974i	−0.725750	−	0.687959i	$-0.758507\pi$
$281$	1.44188	−	1.74293i	0.0860151	−	0.103974i	0.811765	+	0.583984i	$0.198507\pi$
$282$	1.17855	+	1.42462i	0.0701814	+	0.0848348i
$283$	−1.18158	+	3.63653i	−0.0702377	+	0.216169i	−0.980014	−	0.198930i	$-0.936253\pi$
$283$	−1.18158	+	3.63653i	−0.0702377	+	0.216169i	0.909776	+	0.415100i	$0.136253\pi$
$284$	0.135869	+	2.15958i	0.00806234	+	0.128147i
$285$	48.0785	+	19.0356i	2.84792	+	1.12757i
$286$	−0.0977062	−	0.0709877i	−0.00577749	−	0.00419759i
$287$	−0.245884	+	3.90821i	−0.0145140	+	0.230694i
$288$	0.107009	−	0.168620i	0.00630558	−	0.00993600i
$289$	−9.08849	−	8.53466i	−0.534617	−	0.502039i
$290$	−2.45072	−	12.8471i	−0.143911	−	0.754410i
$291$	11.0511	+	6.07542i	0.647830	+	0.356147i
$292$	0.0884912	+	1.40653i	0.00517855	+	0.0823108i
$293$	15.3152	−	24.1328i	0.894722	−	1.40986i	−0.0173612	−	0.999849i	$-0.505527\pi$
$293$	15.3152	−	24.1328i	0.894722	−	1.40986i	0.912083	−	0.410006i	$-0.134473\pi$
$294$	−0.800337	−	2.46318i	−0.0466766	−	0.143656i
$295$	28.3528	−	11.2257i	1.65076	−	0.653584i
$296$	−8.34244	+	17.7286i	−0.484895	+	1.03045i
$297$	−12.8593	+	20.2631i	−0.746175	+	1.17578i
$298$	−2.22702	+	6.85407i	−0.129008	+	0.397046i
$299$	−0.169882	+	0.0933936i	−0.00982455	+	0.00540109i
$300$	6.64873	−	4.83058i	0.383864	−	0.278894i
$301$	−9.39796			−0.541689
$302$	10.6532	+	10.8174i	0.613023	+	0.622469i
$303$	9.12386			0.524152
$304$	17.4820	−	12.7014i	1.00266	−	0.728475i
$305$	−13.4318	+	7.38420i	−0.769104	+	0.422818i
$306$	−0.0620304	+	0.190910i	−0.00354604	+	0.0109136i
$307$	3.02782	−	4.77108i	0.172807	−	0.272300i	−0.746875	−	0.664964i	$-0.768447\pi$
$307$	3.02782	−	4.77108i	0.172807	−	0.272300i	0.919682	+	0.392665i	$0.128447\pi$
$308$	2.27312	−	4.83062i	0.129523	−	0.275250i
$309$	−4.96943	+	1.96754i	−0.282701	+	0.111929i
$310$	−13.3509	−	41.0899i	−0.758281	−	2.33375i
$311$	10.7715	−	16.9731i	0.610795	−	0.962458i	−0.388366	−	0.921505i	$-0.626961\pi$
$311$	10.7715	−	16.9731i	0.610795	−	0.962458i	0.999161	−	0.0409533i	$-0.0130395\pi$
$312$	−0.00702963	−	0.111733i	−0.000397975	−	0.00632563i
$313$	−4.51209	−	2.48054i	−0.255038	−	0.140208i	0.349107	−	0.937083i	$-0.386485\pi$
$313$	−4.51209	−	2.48054i	−0.255038	−	0.140208i	−0.604145	+	0.796875i	$0.706485\pi$
$314$	3.96305	+	20.7751i	0.223648	+	1.17240i
$315$	−0.517308	−	0.485784i	−0.0291470	−	0.0273708i
$316$	0.424677	−	0.669184i	0.0238900	−	0.0376446i
$317$	−0.362997	+	5.76968i	−0.0203880	+	0.324057i	0.974592	+	0.223986i	$0.0719071\pi$
$317$	−0.362997	+	5.76968i	−0.0203880	+	0.324057i	−0.994980	+	0.100071i	$0.968093\pi$
$318$	5.73162	+	4.16426i	0.321413	+	0.233520i
$319$	11.9345	+	4.72520i	0.668203	+	0.264560i
$320$	−2.15469	−	34.2479i	−0.120451	−	1.91451i
$321$	1.46452	−	4.50732i	0.0817414	−	0.251574i
$322$	17.6118	+	21.2891i	0.981470	+	1.18639i
$323$	10.3660	−	12.5303i	0.576779	−	0.697207i
$324$	−4.33245	+	0.547316i	−0.240692	+	0.0304064i
$325$	0.0638731	−	0.196581i	0.00354304	−	0.0109044i
$326$	−1.43316	−	1.34583i	−0.0793755	−	0.0745386i
$327$	3.93659	+	8.36569i	0.217694	+	0.462623i
$328$	−4.92789	−	0.622537i	−0.272097	−	0.0343739i
$329$	−0.129074	+	2.05158i	−0.00711610	+	0.113107i
$330$	−2.45781	−	39.0658i	−0.135298	−	2.15050i
$331$	−2.01501	+	0.254554i	−0.110755	+	0.0139916i	−0.180515	−	0.983572i	$-0.557776\pi$
$331$	−2.01501	+	0.254554i	−0.110755	+	0.0139916i	0.0697605	+	0.997564i	$0.477776\pi$
$332$	−3.64805	−	5.74841i	−0.200213	−	0.315485i
$333$	−0.473906	+	0.121678i	−0.0259699	+	0.00666793i
$334$	20.2288			1.10687
$335$	−8.18696			−0.447301
$336$	−11.5788	+	2.97292i	−0.631674	+	0.162186i
$337$	1.75477	−	9.19881i	0.0955882	−	0.501091i	−0.902003	−	0.431729i	$-0.857904\pi$
$337$	1.75477	−	9.19881i	0.0955882	−	0.501091i	0.997592	−	0.0693619i	$-0.0220963\pi$
$338$	10.2379	+	12.3755i	0.556867	+	0.673136i
$339$	−1.80315	−	1.69327i	−0.0979337	−	0.0919658i
$340$	−1.20221	−	3.70001i	−0.0651988	−	0.200661i
$341$	41.0698	+	10.5449i	2.22405	+	0.571040i
$342$	0.697611	+	0.179116i	0.0377225	+	0.00968549i
$343$	8.40692	−	17.8656i	0.453931	−	0.964653i
$344$	0.748499	−	11.8971i	0.0403564	−	0.641446i
$345$	−58.4199	−	23.1301i	−3.14522	−	1.24528i
$346$	2.93888	−	2.75980i	0.157995	−	0.148368i
$347$	8.92109	+	18.9583i	0.478909	+	1.01773i	0.987630	+	0.156802i	$0.0501186\pi$
$347$	8.92109	+	18.9583i	0.478909	+	1.01773i	−0.508721	+	0.860932i	$0.669881\pi$
$348$	0.703831	+	2.16617i	0.0377293	+	0.116119i
$349$	2.79052	−	5.93016i	0.149373	−	0.317434i	−0.816111	−	0.577895i	$-0.803874\pi$
$349$	2.79052	−	5.93016i	0.149373	−	0.317434i	0.965485	+	0.260460i	$0.0838744\pi$
$350$	−29.2268	−	3.69220i	−1.56224	−	0.197357i
$351$	−0.0780762	+	0.0733184i	−0.00416740	+	0.00391345i
$352$	10.7324	+	5.90017i	0.572037	+	0.314480i
$353$	−33.6836	+	4.25523i	−1.79280	+	0.226483i	−0.950109	−	0.311917i	$-0.899029\pi$
$353$	−33.6836	+	4.25523i	−1.79280	+	0.226483i	−0.842689	+	0.538400i	$0.819029\pi$
$354$	15.0038	−	8.24844i	0.797446	−	0.438399i
$355$	−3.30520	+	17.3265i	−0.175422	+	0.919593i
$356$	2.43974	+	3.84441i	0.129306	+	0.203753i
$357$	−7.88372	+	4.33411i	−0.417251	+	0.229386i
$358$	−0.785872	−	0.949956i	−0.0415346	−	0.0502067i
$359$	0.256980	+	1.34713i	0.0135629	+	0.0710991i	0.988425	−	0.151709i	$-0.0484777\pi$
$359$	0.256980	+	1.34713i	0.0135629	+	0.0710991i	−0.974862	+	0.222808i	$0.928478\pi$
$360$	0.656164	−	0.616179i	0.0345829	−	0.0324755i
$361$	−31.8343	−	23.1290i	−1.67549	−	1.21732i
$362$	−18.3139	−	7.25097i	−0.962555	−	0.381103i
$363$	16.7573	+	9.21240i	0.879529	+	0.483525i
$364$	0.0151873	−	0.0183583i	0.000796033	−	0.000962238i
$365$	−2.15267	+	11.2847i	−0.112676	+	0.590667i
$366$	−6.96250	+	5.05855i	−0.363936	+	0.264415i
$367$	26.1724	−	6.71994i	1.36619	−	0.350778i	0.506785	−	0.862073i	$-0.330834\pi$
$367$	26.1724	−	6.71994i	1.36619	−	0.350778i	0.859406	+	0.511295i	$0.170834\pi$
$368$	−21.2423	+	15.4334i	−1.10733	+	0.804522i
$369$	−0.0664615	−	0.104727i	−0.00345985	−	0.00545185i
$370$	−19.4881	+	23.5570i	−1.01314	+	1.22467i
$371$	1.47596	+	7.73723i	0.0766278	+	0.401697i
$372$	3.20355	+	6.80788i	0.166096	+	0.352972i
$373$	24.1637	−	9.56708i	1.25115	−	0.495365i	0.353234	−	0.935535i	$-0.385082\pi$
$373$	24.1637	−	9.56708i	1.25115	−	0.495365i	0.897914	+	0.440170i	$0.145082\pi$
$374$	−11.9235	−	3.06142i	−0.616547	−	0.158302i
$375$	30.8176	−	12.2015i	1.59141	−	0.630085i
$376$	−2.58685	−	0.326796i	−0.133407	−	0.0168532i
$377$	0.0463445	+	0.0336713i	0.00238686	+	0.00173416i
$378$	12.3496	+	8.97248i	0.635193	+	0.461495i
$379$	22.3877	+	2.82822i	1.14998	+	0.145276i	0.677126	−	0.735867i	$-0.263225\pi$
$379$	22.3877	+	2.82822i	1.14998	+	0.145276i	0.472850	+	0.881143i	$0.343225\pi$
$380$	−12.9786	+	5.13861i	−0.665791	+	0.263605i
$381$	−4.76006	−	1.22218i	−0.243865	−	0.0626140i
$382$	30.6046	−	12.1172i	1.56587	−	0.619971i
$383$	9.51370	+	20.2177i	0.486128	+	1.03307i	0.985965	+	0.166954i	$0.0533932\pi$
$383$	9.51370	+	20.2177i	0.486128	+	1.03307i	−0.499837	+	0.866119i	$0.666607\pi$
$384$	−1.89019	−	9.90875i	−0.0964586	−	0.505654i
$385$	27.7403	−	33.5323i	1.41378	−	1.70896i
$386$	9.71864	+	15.3141i	0.494666	+	0.779468i
$387$	0.240825	−	0.174970i	0.0122418	−	0.00889420i
$388$	−3.29736	+	0.846619i	−0.167398	+	0.0429806i
$389$	−11.1442	+	8.09677i	−0.565036	+	0.410523i	−0.833299	−	0.552823i	$-0.813550\pi$
$389$	−11.1442	+	8.09677i	−0.565036	+	0.410523i	0.268263	+	0.963346i	$0.413550\pi$
$390$	0.0327338	−	0.171597i	0.00165754	−	0.00868914i
$391$	−12.5957	+	15.2255i	−0.636990	+	0.769989i
$392$	3.20065	+	1.75957i	0.161657	+	0.0888718i
$393$	3.56695	+	1.41226i	0.179929	+	0.0712389i
$394$	27.5970	+	20.0504i	1.39032	+	1.01012i
$395$	4.70965	−	4.42265i	0.236968	−	0.222528i
$396$	0.0316865	+	0.166106i	0.00159231	+	0.00834716i
$397$	−7.11211	−	8.59706i	−0.356946	−	0.431474i	0.561221	−	0.827666i	$-0.310332\pi$
$397$	−7.11211	−	8.59706i	−0.356946	−	0.431474i	−0.918168	+	0.396192i	$0.870332\pi$
$398$	−25.7979	+	14.1825i	−1.29313	+	0.710905i
$399$	17.2963	+	27.2546i	0.865899	+	1.36444i
$400$	5.24581	−	27.4995i	0.262291	−	1.37498i
$401$	−15.3878	+	8.45954i	−0.768432	+	0.422449i	−0.817195	−	0.576361i	$-0.804472\pi$
$401$	−15.3878	+	8.45954i	−0.768432	+	0.422449i	0.0487629	+	0.998810i	$0.484472\pi$
$402$	−4.56051	+	0.576127i	−0.227458	+	0.0287346i
$403$	0.165828	+	0.0911646i	0.00826047	+	0.00454123i
$404$	−1.79542	+	1.68601i	−0.0893255	+	0.0838822i
$405$	−35.3166	−	4.46152i	−1.75489	−	0.221695i
$406$	3.47624	−	7.38738i	0.172523	−	0.366629i
$407$	−9.27214	−	28.5367i	−0.459603	−	1.41451i
$408$	−4.85874	−	10.3253i	−0.240543	−	0.511181i
$409$	−9.01689	+	8.46742i	−0.445856	+	0.418687i	−0.874680	−	0.484701i	$-0.838928\pi$
$409$	−9.01689	+	8.46742i	−0.445856	+	0.418687i	0.428823	+	0.903388i	$0.358928\pi$
$410$	−7.20626	−	2.85316i	−0.355892	−	0.140907i
$411$	1.05397	−	16.7524i	0.0519885	−	0.826333i
$412$	0.614315	−	1.30548i	0.0302651	−	0.0643166i
$413$	18.4379	+	4.73405i	0.907269	+	0.232947i
$414$	−0.847663	−	0.217643i	−0.0416604	−	0.0106966i
$415$	−17.1500	−	52.7823i	−0.841860	−	2.59098i
$416$	0.0398441	+	0.0374161i	0.00195352	+	0.00183447i
$417$	4.08788	+	4.94139i	0.200184	+	0.241981i
$418$	−8.27647	+	43.3868i	−0.404816	+	2.12212i
$419$	−31.7881	+	8.16181i	−1.55295	+	0.398730i	−0.925137	−	0.379632i	$-0.876050\pi$
$419$	−31.7881	+	8.16181i	−1.55295	+	0.398730i	−0.627815	+	0.778363i	$0.716050\pi$
$420$	7.72224			0.376807
$421$	1.04216			0.0507915			0.0253958	−	0.999677i	$-0.491915\pi$
$421$	1.04216			0.0507915			0.0253958	+	0.999677i	$0.491915\pi$
$422$	2.30520	−	0.591874i	0.112215	−	0.0288120i
$423$	−0.0348884	−	0.0549753i	−0.00169633	−	0.00267299i
$424$	−9.91226	+	1.25221i	−0.481382	+	0.0608127i
$425$	−1.32291	−	21.0270i	−0.0641705	−	1.01996i
$426$	−0.621862	+	9.88422i	−0.0301293	+	0.478892i
$427$	−9.49286	−	1.19923i	−0.459392	−	0.0580347i
$428$	0.544722	+	1.15759i	0.0263301	+	0.0559544i
$429$	0.124979	+	0.117363i	0.00603403	+	0.00566634i
$430$	5.74793	−	17.6903i	0.277190	−	0.853103i
$431$	−7.28424	+	0.920213i	−0.350869	+	0.0443251i	−0.298793	−	0.954318i	$-0.596584\pi$
$431$	−7.28424	+	0.920213i	−0.350869	+	0.0443251i	−0.0520765	+	0.998643i	$0.516584\pi$
$432$	−9.24675	+	11.1774i	−0.444885	+	0.537773i
$433$	10.3151	+	12.4688i	0.495712	+	0.599213i	0.957734	−	0.287655i	$-0.0928758\pi$
$433$	10.3151	+	12.4688i	0.495712	+	0.599213i	−0.462022	+	0.886869i	$0.652876\pi$
$434$	8.33427	−	25.6502i	0.400058	−	1.23125i
$435$	1.16580	+	18.5299i	0.0558959	+	0.888441i
$436$	−2.32056	−	0.918775i	−0.111135	−	0.0440014i
$437$	57.3594	+	41.6740i	2.74387	+	1.99354i
$438$	−0.405018	+	6.43757i	−0.0193525	+	0.307599i
$439$	−10.5967	+	16.6977i	−0.505753	+	0.796939i	−0.997263	−	0.0739329i	$-0.976445\pi$
$439$	−10.5967	+	16.6977i	−0.505753	+	0.796939i	0.491511	+	0.870872i	$0.336445\pi$
$440$	40.2398	+	37.7876i	1.91836	+	1.80146i
$441$	0.0170905	+	0.0895915i	0.000813833	+	0.00426626i
$442$	−0.0481434	−	0.0264671i	−0.00228995	−	0.00125891i
$443$	−0.175434	−	2.78844i	−0.00833510	−	0.132483i	−0.999994	−	0.00358927i	$-0.998857\pi$
$443$	−0.175434	−	2.78844i	−0.00833510	−	0.132483i	0.991658	−	0.128893i	$-0.0411425\pi$
$444$	2.85288	−	4.49541i	0.135392	−	0.213343i
$445$	11.4695	+	35.2996i	0.543708	+	1.67336i
$446$	−0.565962	+	0.224080i	−0.0267991	+	0.0106105i
$447$	4.35602	−	9.25701i	0.206033	−	0.437842i
$448$	11.4782	−	18.0867i	0.542293	−	0.854516i
$449$	−8.27304	+	25.4618i	−0.390429	+	1.20162i	0.542036	+	0.840355i	$0.317654\pi$
$449$	−8.27304	+	25.4618i	−0.390429	+	1.20162i	−0.932465	+	0.361261i	$0.882346\pi$
$450$	0.817685	−	0.449526i	0.0385460	−	0.0211909i
$451$	6.15384	−	4.47102i	0.289773	−	0.210532i
$452$	0.667731			0.0314074
$453$	−13.0793	−	17.1306i	−0.614518	−	0.804864i
$454$	−19.9825			−0.937827
$455$	0.157129	−	0.114161i	0.00736631	−	0.00535194i
$456$	−35.8797	+	19.7250i	−1.68022	+	0.923710i
$457$	−0.406456	+	1.25094i	−0.0190132	+	0.0585167i	−0.960113	−	0.279612i	$-0.909794\pi$
$457$	−0.406456	+	1.25094i	−0.0190132	+	0.0585167i	0.941100	+	0.338129i	$0.109794\pi$
$458$	−1.09550	+	1.72623i	−0.0511893	+	0.0806615i
$459$	−4.64831	+	9.87816i	−0.216964	+	0.461073i
$460$	15.7703	−	6.24390i	0.735294	−	0.291123i
$461$	−7.09303	−	21.8301i	−0.330355	−	1.01673i	−0.968965	−	0.247198i	$-0.920490\pi$
$461$	−7.09303	−	21.8301i	−0.330355	−	1.01673i	0.638610	−	0.769531i	$-0.279510\pi$
$462$	13.0929	−	20.6311i	0.609137	−	0.959847i
$463$	−1.21492	−	19.3105i	−0.0564620	−	0.897437i	−0.919695	−	0.392632i	$-0.871564\pi$
$463$	−1.21492	−	19.3105i	−0.0564620	−	0.897437i	0.863234	−	0.504805i	$-0.168436\pi$
$464$	6.79904	+	3.73780i	0.315638	+	0.173523i
$465$	11.4926	+	60.2462i	0.532956	+	2.79385i
$466$	0.387128	+	0.363537i	0.0179334	+	0.0168405i
$467$	−8.88509	+	14.0007i	−0.411153	+	0.647873i	−0.985291	−	0.170885i	$-0.945337\pi$
$467$	−8.88509	+	14.0007i	−0.411153	+	0.647873i	0.574138	+	0.818759i	$0.305337\pi$
$468$	−4.73868e−5	0	0.000753192i	−2.19046e−6	0	3.48163e-5i
$469$	−4.13463	−	3.00399i	−0.190920	−	0.138711i
$470$	−3.78286	−	1.49774i	−0.174490	−	0.0690856i
$471$	−1.88521	−	29.9646i	−0.0868661	−	1.38070i
$472$	−7.46140	+	22.9638i	−0.343439	+	1.05700i
$473$	11.6363	+	14.0659i	0.535037	+	0.646749i
$474$	2.31226	−	2.79504i	0.106206	−	0.128381i
$475$	−74.9984	+	9.47450i	−3.44116	+	0.434720i
$476$	0.750475	−	2.30972i	0.0343980	−	0.105866i
$477$	−0.181872	−	0.170789i	−0.00832735	−	0.00781990i
$478$	−10.6080	−	22.5431i	−0.485197	−	1.03110i
$479$	31.2401	+	3.94655i	1.42740	+	0.180322i	0.800759	−	0.598987i	$-0.204430\pi$
$479$	31.2401	+	3.94655i	1.42740	+	0.180322i	0.626640	+	0.779309i	$0.284430\pi$
$480$	−1.11234	+	17.6802i	−0.0507713	+	0.806987i
$481$	−0.00840828	−	0.133646i	−0.000383385	−	0.00609372i
$482$	−2.30900	+	0.291694i	−0.105172	+	0.0132863i
$483$	−21.0167	−	33.1170i	−0.956291	−	1.50687i
$484$	−4.99992	+	1.28376i	−0.227269	+	0.0583528i
$485$	−27.7507			−1.26010
$486$	−0.979638			−0.0444373
$487$	−29.9485	+	7.68948i	−1.35710	+	0.348443i	−0.856013	−	0.516955i	$-0.827066\pi$
$487$	−29.9485	+	7.68948i	−1.35710	+	0.348443i	−0.501085	+	0.865398i	$0.667066\pi$
$488$	2.27418	−	11.9217i	0.102947	−	0.539669i
$489$	1.77901	+	2.15045i	0.0804495	+	0.0972468i
$490$	4.15454	+	3.90137i	0.187683	+	0.176246i
$491$	−2.85450	−	8.78526i	−0.128822	−	0.396473i	0.865756	−	0.500466i	$-0.166838\pi$
$491$	−2.85450	−	8.78526i	−0.128822	−	0.396473i	−0.994578	+	0.103993i	$0.966838\pi$
$492$	1.30733	+	0.335666i	0.0589391	+	0.0151330i
$493$	5.65559	+	1.45211i	0.254715	+	0.0653997i
$494$	−0.0839304	+	0.178361i	−0.00377621	+	0.00802485i
$495$	−0.0865540	+	1.37574i	−0.00389031	+	0.0618347i
$496$	23.8304	+	9.43510i	1.07001	+	0.423649i
$497$	−8.02669	+	7.53757i	−0.360046	+	0.338106i
$498$	−13.2677	−	28.1953i	−0.594539	−	1.26346i
$499$	9.42353	+	29.0026i	0.421855	+	1.29834i	0.905974	+	0.423334i	$0.139140\pi$
$499$	9.42353	+	29.0026i	0.421855	+	1.29834i	−0.484119	+	0.875002i	$0.660860\pi$
$500$	−3.80963	+	8.09587i	−0.170372	+	0.362059i
$501$	−28.4902	−	3.59915i	−1.27285	−	0.160798i
$502$	−21.2308	+	19.9371i	−0.947579	+	0.889836i
$503$	8.87517	+	4.87917i	0.395724	+	0.217551i	0.667175	−	0.744901i	$-0.267503\pi$
$503$	8.87517	+	4.87917i	0.395724	+	0.217551i	−0.271451	+	0.962452i	$0.587503\pi$
$504$	0.557471	−	0.0704250i	0.0248317	−	0.00313698i
$505$	−17.5937	+	9.67224i	−0.782911	+	0.430409i
$506$	10.0567	−	52.7191i	0.447075	−	2.34365i
$507$	−12.2171	−	19.2511i	−0.542581	−	0.854971i
$508$	1.16255	−	0.639115i	0.0515797	−	0.0283562i
$509$	6.35064	+	7.67661i	0.281487	+	0.340260i	0.892240	−	0.451562i	$-0.149133\pi$
$509$	6.35064	+	7.67661i	0.281487	+	0.340260i	−0.610752	+	0.791822i	$0.709133\pi$
$510$	−3.33655	−	17.4908i	−0.147745	−	0.774505i
$511$	−5.22777	+	4.90920i	−0.231263	+	0.217170i
$512$	19.9773	+	14.5144i	0.882881	+	0.641451i
$513$	36.4202	+	14.4198i	1.60799	+	0.636650i
$514$	−1.27603	−	0.701501i	−0.0562831	−	0.0309419i
$515$	7.49686	−	9.06215i	0.330351	−	0.399326i
$516$	−0.606979	+	3.18189i	−0.0267208	+	0.140075i
$517$	3.23040	−	2.34702i	0.142073	−	0.103222i
$518$	−18.4856	+	4.74630i	−0.812212	+	0.208541i
$519$	−4.63014	+	3.36399i	−0.203241	+	0.147663i
$520$	0.132004	+	0.208005i	0.00578875	+	0.00912161i
$521$	−0.197106	+	0.238261i	−0.00863538	+	0.0104384i	−0.774813	−	0.632190i	$-0.782156\pi$
$521$	−0.197106	+	0.238261i	−0.00863538	+	0.0104384i	0.766178	+	0.642629i	$0.222156\pi$
$522$	0.0484575	+	0.254023i	0.00212093	+	0.0111183i
$523$	−5.62243	−	11.9483i	−0.245852	−	0.522462i	0.743371	−	0.668879i	$-0.233226\pi$
$523$	−5.62243	−	11.9483i	−0.245852	−	0.522462i	−0.989223	+	0.146418i	$0.953226\pi$
$524$	−0.962888	+	0.381234i	−0.0420640	+	0.0166543i
$525$	40.5060	+	10.4002i	1.76783	+	0.453901i
$526$	20.8119	−	8.24003i	0.907444	−	0.359283i
$527$	19.1365	+	2.41751i	0.833601	+	0.105308i
$528$	18.7861	+	13.6489i	0.817559	+	0.593991i
$529$	−51.0897	−	37.1188i	−2.22129	−	1.61386i
$530$	−15.4670	−	1.95393i	−0.671841	−	0.0848733i
$531$	−0.560613	+	0.221962i	−0.0243285	+	0.00963234i
$532$	−8.44004	−	2.16703i	−0.365922	−	0.0939528i
$533$	0.0315633	−	0.0124968i	0.00136716	−	0.000541296i
$534$	8.87314	+	18.8564i	0.383978	+	0.815995i
$535$	1.95417	+	10.2441i	0.0844860	+	0.442891i
$536$	4.13211	−	4.99486i	0.178480	−	0.215745i
$537$	0.937801	+	1.47774i	0.0404691	+	0.0637691i
$538$	23.0198	−	16.7248i	0.992453	−	0.721059i
$539$	−5.41761	+	1.39101i	−0.233353	+	0.0599149i
$540$	7.58117	−	5.50804i	0.326242	−	0.237028i
$541$	−6.61536	+	34.6789i	−0.284417	+	1.49096i	0.497436	+	0.867501i	$0.334275\pi$
$541$	−6.61536	+	34.6789i	−0.284417	+	1.49096i	−0.781853	+	0.623463i	$0.785725\pi$
$542$	11.8886	−	14.3708i	0.510658	−	0.617279i
$543$	24.5031	+	13.4707i	1.05153	+	0.578082i
$544$	5.18005	+	2.05093i	0.222093	+	0.0879328i
$545$	−16.4595	−	11.9585i	−0.705048	−	0.512248i
$546$	0.0794943	−	0.0746501i	0.00340204	−	0.00319473i
$547$	5.99709	+	31.4379i	0.256417	+	1.34419i	0.844574	+	0.535439i	$0.179854\pi$
$547$	5.99709	+	31.4379i	0.256417	+	1.34419i	−0.588157	+	0.808747i	$0.700146\pi$
$548$	2.88829	+	3.49134i	0.123382	+	0.149143i
$549$	0.265584	−	0.146006i	0.0113348	−	0.00623138i
$550$	30.6617	+	48.3152i	1.30742	+	2.06017i
$551$	3.92574	−	20.5794i	0.167242	−	0.876714i
$552$	43.5973	−	23.9678i	1.85562	−	1.02014i
$553$	4.00127	−	0.505478i	0.170151	−	0.0214951i
$554$	−16.7514	−	9.20915i	−0.711698	−	0.391259i
$555$	31.6382	−	29.7103i	1.34297	−	1.26113i
$556$	−1.71755	−	0.216977i	−0.0728404	−	0.00920188i
$557$	10.7521	−	22.8495i	0.455583	−	0.968163i	−0.536654	−	0.843802i	$-0.680312\pi$
$557$	10.7521	−	22.8495i	0.455583	−	0.968163i	0.992237	−	0.124361i	$-0.0396881\pi$
$558$	0.263984	+	0.812459i	0.0111753	+	0.0343941i
$559$	0.0346886	+	0.0737170i	0.00146717	+	0.00311790i
$560$	19.1760	−	18.0075i	0.810334	−	0.760954i
$561$	16.2483	+	6.43314i	0.686002	+	0.271607i
$562$	−0.175487	+	2.78929i	−0.00740249	+	0.117659i
$563$	−10.6533	+	22.6394i	−0.448983	+	0.954138i	0.544350	+	0.838858i	$0.316776\pi$
$563$	−10.6533	+	22.6394i	−0.448983	+	0.954138i	−0.993333	+	0.115280i	$0.963224\pi$
$564$	0.686273	+	0.176205i	0.0288973	+	0.00741956i
$565$	5.27210	+	1.35364i	0.221799	+	0.0569483i
$566$	−1.45988	−	4.49303i	−0.0613631	−	0.188856i
$567$	−16.1988	−	15.2117i	−0.680285	−	0.638830i
$568$	−8.90267	−	10.7615i	−0.373548	−	0.451541i
$569$	8.05257	−	42.2131i	0.337581	−	1.76966i	−0.257779	−	0.966204i	$-0.582991\pi$
$569$	8.05257	−	42.2131i	0.337581	−	1.76966i	0.595360	−	0.803459i	$-0.297009\pi$
$570$	−61.8816	+	15.8885i	−2.59194	+	0.665496i
$571$	5.10456			0.213619			0.106810	−	0.994279i	$-0.465936\pi$
$571$	5.10456			0.213619			0.106810	+	0.994279i	$0.465936\pi$
$572$	−0.0462814			−0.00193512
$573$	−45.2593	+	11.6206i	−1.89074	+	0.485458i
$574$	−2.59246	−	4.08507i	−0.108207	−	0.170507i
$575$	91.1301	−	11.5124i	3.80039	−	0.480101i
$576$	0.0426042	+	0.677175i	0.00177518	+	0.0282156i
$577$	1.43379	−	22.7895i	0.0596895	−	0.948737i	−0.848239	−	0.529613i	$-0.822337\pi$
$577$	1.43379	−	22.7895i	0.0596895	−	0.948737i	0.907929	−	0.419124i	$-0.137663\pi$
$578$	15.2826	+	1.93064i	0.635672	+	0.0803041i
$579$	−10.9630	−	23.2975i	−0.455606	−	0.968211i
$580$	−3.65358	−	3.43094i	−0.151707	−	0.142462i
$581$	10.7058	−	32.9492i	0.444153	−	1.36696i
$582$	−15.4584	+	1.95285i	−0.640773	+	0.0809484i
$583$	9.75278	−	11.7891i	0.403919	−	0.488254i
$584$	−5.79829	−	7.00893i	−0.239935	−	0.290031i
$585$	−0.00190104	+	0.00585079i	−7.85982e−5	+	0.000241900i
$586$	2.21740	+	35.2445i	0.0915999	+	1.45594i
$587$	−2.64963	−	1.04906i	−0.109362	−	0.0432994i	0.312807	−	0.949817i	$-0.398731\pi$
$587$	−2.64963	−	1.04906i	−0.109362	−	0.0432994i	−0.422168	+	0.906517i	$0.638731\pi$
$588$	−0.802952	−	0.583378i	−0.0331132	−	0.0240581i
$589$	4.34560	−	69.0713i	0.179057	−	2.84603i
$590$	−20.1881	+	31.8113i	−0.831129	+	1.30965i
$591$	−35.3001	−	33.1490i	−1.45205	−	1.36357i
$592$	−3.39852	−	17.8157i	−0.139678	−	0.732220i
$593$	35.6249	+	19.5849i	1.46294	+	0.804257i	0.996760	−	0.0804340i	$-0.0256306\pi$
$593$	35.6249	+	19.5849i	1.46294	+	0.804257i	0.466178	+	0.884691i	$0.345631\pi$
$594$	−1.86183	−	29.5930i	−0.0763920	−	1.21422i
$595$	10.6077	−	16.7151i	0.434875	−	0.685254i
$596$	0.853427	+	2.62658i	0.0349577	+	0.107589i
$597$	38.8570	−	15.3846i	1.59031	−	0.629649i
$598$	0.101983	−	0.216726i	0.00417041	−	0.00886257i
$599$	−24.5543	+	38.6914i	−1.00326	+	1.58089i	−0.204833	+	0.978797i	$0.565665\pi$
$599$	−24.5543	+	38.6914i	−1.00326	+	1.58089i	−0.798428	+	0.602090i	$0.794335\pi$
$600$	−16.3919	+	50.4490i	−0.669196	+	2.05957i
$601$	14.9849	−	8.23804i	0.611248	−	0.336037i	−0.145880	−	0.989302i	$-0.546602\pi$
$601$	14.9849	−	8.23804i	0.611248	−	0.336037i	0.757129	+	0.653266i	$0.226602\pi$
$602$	9.39385	−	6.82503i	0.382865	−	0.278168i
$603$	0.161879			0.00659221
$604$	5.73936	+	0.954060i	0.233531	+	0.0388201i
$605$	−42.0795			−1.71078
$606$	−9.11987	+	6.62597i	−0.370469	+	0.269162i
$607$	30.5446	−	16.7920i	1.23977	−	0.681568i	0.279365	−	0.960185i	$-0.409876\pi$
$607$	30.5446	−	16.7920i	1.23977	−	0.681568i	0.960402	+	0.278617i	$0.0898761\pi$
$608$	6.17720	−	19.0115i	0.250519	−	0.771017i
$609$	−6.21029	+	9.78585i	−0.251654	+	0.396543i
$610$	8.06335	−	17.1355i	0.326476	−	0.693796i
$611$	0.0165689	−	0.00656008i	0.000670305	−	0.000265392i
$612$	0.0237709	+	0.0731594i	0.000960883	+	0.00295729i
$613$	−17.9733	+	28.3214i	−0.725935	+	1.14389i	0.258135	+	0.966109i	$0.416892\pi$
$613$	−17.9733	+	28.3214i	−0.725935	+	1.14389i	−0.984070	+	0.177782i	$0.943108\pi$
$614$	0.438381	+	6.96787i	0.0176916	+	0.281200i
$615$	9.64162	+	5.30053i	0.388788	+	0.213738i
$616$	6.45698	+	33.8487i	0.260159	+	1.36380i
$617$	−19.0928	−	17.9293i	−0.768647	−	0.721807i	0.197358	−	0.980331i	$-0.436764\pi$
$617$	−19.0928	−	17.9293i	−0.768647	−	0.721807i	−0.966005	+	0.258524i	$0.916764\pi$
$618$	3.53838	−	5.57560i	0.142335	−	0.224283i
$619$	−1.79052	+	28.4595i	−0.0719670	+	1.14388i	0.781904	+	0.623399i	$0.214249\pi$
$619$	−1.79052	+	28.4595i	−0.0719670	+	1.14388i	−0.853871	+	0.520484i	$0.825751\pi$
$620$	−13.3945	−	9.73169i	−0.537937	−	0.390834i
$621$	−44.2540	−	17.5214i	−1.77585	−	0.703110i
$622$	1.55954	+	24.7882i	0.0625320	+	0.993918i
$623$	−7.15983	+	22.0357i	−0.286853	+	0.882841i
$624$	0.0660575	+	0.0798498i	0.00264442	+	0.00319655i
$625$	−14.9507	+	18.0723i	−0.598027	+	0.722890i
$626$	6.31154	−	0.797333i	0.252260	−	0.0318678i
$627$	19.3760	−	59.6332i	0.773803	−	2.38152i
$628$	5.90818	+	5.54815i	0.235762	+	0.221395i
$629$	−5.81163	−	12.3503i	−0.231725	−	0.492441i
$630$	0.869870	+	0.109890i	0.0346564	+	0.00437813i
$631$	2.61491	−	41.5628i	0.104098	−	1.65459i	−0.506198	−	0.862417i	$-0.668950\pi$
$631$	2.61491	−	41.5628i	0.104098	−	1.65459i	0.610296	−	0.792173i	$-0.291050\pi$
$632$	0.321214	+	5.10555i	0.0127772	+	0.203088i
$633$	−3.35194	+	0.423448i	−0.133228	+	0.0168306i
$634$	−3.82725	−	6.03077i	−0.151999	−	0.239513i
$635$	10.4746	−	2.68941i	0.415670	−	0.106726i
$636$	2.71494			0.107655
$637$	−0.0249624			−0.000989046
$638$	−15.3608	+	3.94399i	−0.608141	+	0.156144i
$639$	0.0653528	−	0.342591i	0.00258532	−	0.0135527i
$640$	14.1492	+	17.1034i	0.559296	+	0.676073i
$641$	−4.55957	−	4.28172i	−0.180092	−	0.169118i	0.589258	−	0.807945i	$-0.299420\pi$
$641$	−4.55957	−	4.28172i	−0.180092	−	0.169118i	−0.769351	+	0.638827i	$0.779420\pi$
$642$	1.80945	+	5.56892i	0.0714133	+	0.219788i
$643$	−8.00046	−	2.05417i	−0.315507	−	0.0810085i	0.0876157	−	0.996154i	$-0.472075\pi$
$643$	−8.00046	−	2.05417i	−0.315507	−	0.0810085i	−0.403123	+	0.915146i	$0.632075\pi$
$644$	10.2554	+	2.63315i	0.404121	+	0.103761i
$645$	−11.2429	+	23.8923i	−0.442687	+	0.940758i
$646$	−1.26162	+	20.0529i	−0.0496378	+	0.788971i
$647$	30.5125	+	12.0808i	1.19957	+	0.474944i	0.881073	−	0.472980i	$-0.156822\pi$
$647$	30.5125	+	12.0808i	1.19957	+	0.474944i	0.318498	+	0.947924i	$0.396822\pi$
$648$	20.5469	−	19.2948i	0.807158	−	0.757972i
$649$	−15.7439	−	33.4574i	−0.618001	−	1.31332i
$650$	0.0789169	+	0.242881i	0.00309538	+	0.00952659i
$651$	−16.3017	+	34.6428i	−0.638913	+	1.35776i
$652$	−0.747463	−	0.0944266i	−0.0292729	−	0.00369803i
$653$	−16.0819	+	15.1019i	−0.629334	+	0.590984i	−0.932153	−	0.362064i	$-0.882072\pi$
$653$	−16.0819	+	15.1019i	−0.629334	+	0.590984i	0.302819	+	0.953048i	$0.402072\pi$
$654$	−10.0102	−	5.50318i	−0.391431	−	0.215191i
$655$	−8.37537	+	1.05806i	−0.327253	+	0.0413416i
$656$	4.02913	−	2.21503i	0.157311	−	0.0864824i
$657$	0.0425642	−	0.223129i	0.00166059	−	0.00870510i
$658$	−1.36089	−	2.14442i	−0.0530530	−	0.0835982i
$659$	0.839176	−	0.461341i	0.0326896	−	0.0179713i	−0.465325	−	0.885140i	$-0.654063\pi$
$659$	0.839176	−	0.461341i	0.0326896	−	0.0179713i	0.498015	+	0.867169i	$0.334063\pi$
$660$	−9.56147	−	11.5578i	−0.372180	−	0.449888i
$661$	6.37161	+	33.4012i	0.247827	+	1.29915i	0.860756	+	0.509017i	$0.169991\pi$
$661$	6.37161	+	33.4012i	0.247827	+	1.29915i	−0.612929	+	0.790138i	$0.710009\pi$
$662$	1.82926	−	1.71779i	0.0710962	−	0.0667638i
$663$	0.0630959	+	0.0458419i	0.00245044	+	0.00178035i
$664$	40.8583	+	16.1770i	1.58561	+	0.627788i
$665$	−62.2456	−	34.2198i	−2.41378	−	1.32699i
$666$	0.385333	−	0.465787i	0.0149313	−	0.0180489i
$667$	−4.77014	+	25.0060i	−0.184701	+	0.968235i
$668$	6.27148	−	4.55649i	0.242651	−	0.176296i
$669$	0.836968	−	0.214897i	0.0323591	−	0.00830839i
$670$	8.18338	−	5.94557i	0.316152	−	0.229698i
$671$	9.95893	+	15.6928i	0.384460	+	0.605812i
$672$	−7.04904	+	8.52083i	−0.271923	+	0.328698i
$673$	−6.00076	−	31.4571i	−0.231312	−	1.21258i	−0.888508	−	0.458861i	$-0.848258\pi$
$673$	−6.00076	−	31.4571i	−0.231312	−	1.21258i	0.657196	−	0.753720i	$-0.271742\pi$
$674$	4.92640	+	10.4691i	0.189758	+	0.403256i
$675$	47.1842	−	18.6815i	1.81612	−	0.719052i
$676$	5.96156	+	1.53067i	0.229291	+	0.0588718i
$677$	−8.24246	+	3.26342i	−0.316784	+	0.125423i	−0.521135	−	0.853474i	$-0.674491\pi$
$677$	−8.24246	+	3.26342i	−0.316784	+	0.125423i	0.204352	+	0.978898i	$0.434491\pi$
$678$	3.03206	+	0.383038i	0.116445	+	0.0147105i
$679$	−14.0149	−	10.1824i	−0.537841	−	0.390765i
$680$	20.3152	+	14.7598i	0.779051	+	0.566013i
$681$	28.1433	+	3.55533i	1.07845	+	0.136241i
$682$	−48.7098	+	19.2856i	−1.86520	+	0.738483i
$683$	8.66277	+	2.22422i	0.331472	+	0.0851074i	0.410758	−	0.911744i	$-0.365264\pi$
$683$	8.66277	+	2.22422i	0.331472	+	0.0851074i	−0.0792863	+	0.996852i	$0.525264\pi$
$684$	0.256623	−	0.101604i	0.00981224	−	0.00388494i
$685$	15.7268	+	33.4213i	0.600892	+	1.27696i
$686$	4.57121	+	23.9631i	0.174530	+	0.914916i
$687$	1.85003	−	2.23630i	0.0705831	−	0.0853203i
$688$	5.91258	+	9.31674i	0.225415	+	0.355197i
$689$	0.0552425	−	0.0401360i	0.00210457	−	0.00152906i
$690$	75.1921	−	19.3060i	2.86251	−	0.734968i
$691$	−13.6334	+	9.90521i	−0.518637	+	0.376812i	−0.816090	−	0.577924i	$-0.803863\pi$
$691$	−13.6334	+	9.90521i	−0.518637	+	0.376812i	0.297453	+	0.954736i	$0.403863\pi$
$692$	0.289495	−	1.51759i	0.0110050	−	0.0576900i
$693$	−0.548502	+	0.663025i	−0.0208359	+	0.0251862i
$694$	−22.6852	−	12.4713i	−0.861117	−	0.473403i
$695$	−13.1211	−	5.19502i	−0.497713	−	0.197059i
$696$	−11.8935	−	8.64112i	−0.450821	−	0.327541i
$697$	2.52239	−	2.36869i	0.0955425	−	0.0897204i
$698$	1.51733	+	7.95412i	0.0574318	+	0.301068i
$699$	−0.480548	−	0.580883i	−0.0181760	−	0.0219710i
$700$	−9.89275	+	5.43859i	−0.373911	+	0.205559i
$701$	−0.881560	−	1.38912i	−0.0332960	−	0.0524662i	0.827272	−	0.561801i	$-0.189891\pi$
$701$	−0.881560	−	1.38912i	−0.0332960	−	0.0524662i	−0.860568	+	0.509335i	$0.829891\pi$
$702$	0.0247964	−	0.129987i	0.000935880	−	0.00490605i
$703$	−42.9164	+	23.5935i	−1.61862	+	0.889846i
$704$	−41.2822	+	5.21516i	−1.55588	+	0.196554i
$705$	5.06129	+	2.78247i	0.190619	+	0.104794i
$706$	30.5786	−	28.7153i	1.15084	−	1.08071i
$707$	−12.4343	−	1.57081i	−0.467639	−	0.0590766i
$708$	2.79365	−	5.93682i	0.104992	−	0.223119i
$709$	−1.05166	−	3.23668i	−0.0394960	−	0.121556i	0.929365	−	0.369163i	$-0.120356\pi$
$709$	−1.05166	−	3.23668i	−0.0394960	−	0.121556i	−0.968860	+	0.247607i	$0.920356\pi$
$710$	−9.27915	−	19.7192i	−0.348240	−	0.740048i
$711$	−0.0931226	+	0.0874480i	−0.00349237	+	0.00327956i
$712$	−27.3252	−	10.8188i	−1.02405	−	0.405452i
$713$	−5.28031	+	83.9282i	−0.197749	+	3.14313i
$714$	4.73273	−	10.0576i	0.177118	−	0.376395i
$715$	−0.365416	−	0.0938230i	−0.0136658	−	0.00350878i
$716$	−0.457616	−	0.117496i	−0.0171019	−	0.00439103i
$717$	10.9293	+	33.6370i	0.408163	+	1.25620i
$718$	−1.23519	−	1.15992i	−0.0460969	−	0.0432879i
$719$	12.3594	+	14.9399i	0.460926	+	0.557164i	0.948852	−	0.315721i	$-0.102246\pi$
$719$	12.3594	+	14.9399i	0.460926	+	0.557164i	−0.487926	+	0.872885i	$0.662246\pi$
$720$	−0.156130	+	0.818461i	−0.00581861	+	0.0305022i
$721$	7.11123	−	1.82585i	0.264836	−	0.0679984i
$722$	48.6173			1.80935
$723$	3.30388			0.122873
$724$	−7.31105	+	1.87716i	−0.271713	+	0.0697641i
$725$	−14.5436	−	22.9171i	−0.540137	−	0.851119i
$726$	−23.4402	+	2.96119i	−0.869949	+	0.109900i
$727$	−0.0933122	−	1.48315i	−0.00346076	−	0.0550072i	0.995917	−	0.0902703i	$-0.0287731\pi$
$727$	−0.0933122	−	1.48315i	−0.00346076	−	0.0550072i	−0.999378	+	0.0352631i	$0.988773\pi$
$728$	−0.00965635	+	0.153483i	−0.000357888	+	0.00568847i
$729$	−26.0715	−	3.29359i	−0.965610	−	0.121985i
$730$	−6.04349	−	12.8431i	−0.223680	−	0.475343i
$731$	6.05356	+	5.68468i	0.223899	+	0.210255i
$732$	−1.01913	+	3.13657i	−0.0376683	+	0.115931i
$733$	−37.6855	+	4.76079i	−1.39195	+	0.175844i	−0.785294	−	0.619123i	$-0.787488\pi$
$733$	−37.6855	+	4.76079i	−1.39195	+	0.175844i	−0.606653	+	0.794967i	$0.707488\pi$
$734$	−21.2808	+	25.7241i	−0.785489	+	0.949493i
$735$	−5.15709	−	6.23386i	−0.190222	−	0.229939i
$736$	−7.50588	+	23.1007i	−0.276671	+	0.851504i
$737$	0.623342	+	9.90773i	0.0229611	+	0.364956i
$738$	0.142487	+	0.0564148i	0.00524503	+	0.00207666i
$739$	−17.9629	−	13.0508i	−0.660775	−	0.480081i	0.206149	−	0.978521i	$-0.433907\pi$
$739$	−17.9629	−	13.0508i	−0.660775	−	0.480081i	−0.866925	+	0.498439i	$0.833907\pi$
$740$	−0.735658	+	11.6930i	−0.0270433	+	0.429841i
$741$	0.149942	−	0.236270i	0.00550824	−	0.00867960i
$742$	−7.09428	−	6.66197i	−0.260439	−	0.244569i
$743$	−3.06659	−	16.0756i	−0.112502	−	0.589757i	−0.993233	−	0.116140i	$-0.962948\pi$
$743$	−3.06659	−	16.0756i	−0.112502	−	0.589757i	0.880731	−	0.473617i	$-0.157052\pi$
$744$	−42.5567	−	23.3957i	−1.56020	−	0.857730i
$745$	1.41359	+	22.4683i	0.0517898	+	0.823176i
$746$	−17.2053	+	27.1112i	−0.629930	+	0.992610i
$747$	0.339102	+	1.04365i	0.0124071	+	0.0381852i
$748$	−4.38617	+	1.73661i	−0.160374	+	0.0634966i
$749$	−2.77190	+	5.89058i	−0.101283	+	0.215237i
$750$	−21.9430	+	34.5767i	−0.801246	+	1.26256i
$751$	0.497300	−	1.53053i	0.0181468	−	0.0558500i	−0.941573	−	0.336809i	$-0.890652\pi$
$751$	0.497300	−	1.53053i	0.0181468	−	0.0558500i	0.959720	+	0.280959i	$0.0906524\pi$
$752$	2.11505	−	1.16276i	0.0771281	−	0.0424015i
$753$	33.4487	−	24.3019i	1.21894	−	0.885610i
$754$	−0.0707771			−0.00257755
$755$	43.3812	+	19.1678i	1.57880	+	0.697588i
$756$	5.84972			0.212752
$757$	23.0882	−	16.7745i	0.839153	−	0.609681i	−0.0829806	−	0.996551i	$-0.526444\pi$
$757$	23.0882	−	16.7745i	0.839153	−	0.609681i	0.922134	+	0.386871i	$0.126444\pi$
$758$	−24.4318	+	13.4315i	−0.887403	+	0.487854i
$759$	−23.5437	+	72.4600i	−0.854582	+	2.63013i
$760$	48.2771	−	76.0725i	1.75119	−	2.75944i
$761$	7.09842	−	15.0849i	0.257317	−	0.546827i	−0.733871	−	0.679289i	$-0.762288\pi$
$761$	7.09842	−	15.0849i	0.257317	−	0.546827i	0.991188	+	0.132462i	$0.0422882\pi$
$762$	5.64556	−	2.23523i	0.204517	−	0.0809740i
$763$	−3.92463	−	12.0788i	−0.142081	−	0.437281i
$764$	6.75887	−	10.6503i	0.244527	−	0.385313i
$765$	0.0393734	+	0.625822i	0.00142355	+	0.0226266i
$766$	−24.1921	−	13.2997i	−0.874096	−	0.480539i
$767$	−0.0309221	−	0.162099i	−0.00111653	−	0.00585307i
$768$	−13.6503	−	12.8185i	−0.492562	−	0.462547i
$769$	15.8096	−	24.9119i	0.570108	−	0.898347i	−0.429881	−	0.902885i	$-0.641445\pi$
$769$	15.8096	−	24.9119i	0.570108	−	0.898347i	0.999990	+	0.00453836i	$0.00144461\pi$
$770$	−3.37621	+	53.6633i	−0.121670	+	1.93389i
$771$	1.67234	+	1.21502i	0.0602277	+	0.0437580i
$772$	6.46251	+	2.55869i	0.232591	+	0.0920892i
$773$	2.66790	+	42.4051i	0.0959577	+	1.52520i	0.691792	+	0.722097i	$0.256822\pi$
$773$	2.66790	+	42.4051i	0.0959577	+	1.52520i	−0.595834	+	0.803107i	$0.703178\pi$
$774$	−0.113652	+	0.349786i	−0.00408515	+	0.0125728i
$775$	−57.1528	−	69.0858i	−2.05299	−	2.48164i
$776$	14.0063	−	16.9307i	0.502797	−	0.607777i
$777$	26.8796	−	3.39568i	0.964299	−	0.121819i
$778$	5.25930	−	16.1865i	0.188555	−	0.580313i
$779$	−9.05038	−	8.49888i	−0.324264	−	0.304504i
$780$	−0.0285034	−	0.0605728i	−0.00102058	−	0.00216885i
$781$	21.2199	+	2.68069i	0.759306	+	0.0959227i
$782$	1.53299	−	24.3662i	0.0548196	−	0.871333i
$783$	0.883114	+	14.0367i	0.0315599	+	0.501631i
$784$	−3.35428	+	0.423744i	−0.119796	+	0.0151337i
$785$	35.4009	+	55.7829i	1.26351	+	1.99098i
$786$	−4.59101	+	1.17877i	−0.163756	+	0.0420454i
$787$	20.6118			0.734730			0.367365	−	0.930077i	$-0.380260\pi$
$787$	20.6118			0.734730			0.367365	+	0.930077i	$0.380260\pi$
$788$	13.0721			0.465675
$789$	−30.7775	+	7.90233i	−1.09571	+	0.281330i
$790$	−1.49575	+	7.84098i	−0.0532163	+	0.278970i
$791$	2.16587	+	2.61808i	0.0770093	+	0.0930883i
$792$	−0.795650	−	0.747165i	−0.0282722	−	0.0265494i
$793$	0.0256322	+	0.0788878i	0.000910227	+	0.00280139i
$794$	13.3524	+	3.42831i	0.473859	+	0.121666i
$795$	21.4359	+	5.50382i	0.760255	+	0.195200i
$796$	−4.80346	+	10.2079i	−0.170254	+	0.361808i
$797$	0.257172	−	4.08764i	0.00910951	−	0.144791i	−0.990843	−	0.135021i	$-0.956890\pi$
$797$	0.257172	−	4.08764i	0.00910951	−	0.144791i	0.999952	−	0.00977064i	$-0.00311014\pi$
$798$	−37.0817	−	14.6817i	−1.31268	−	0.519727i
$799$	1.32411	−	1.24342i	0.0468436	−	0.0439891i
$800$	−11.0267	−	23.4330i	−0.389854	−	0.828482i
$801$	−0.226784	−	0.697970i	−0.00801303	−	0.0246616i
$802$	9.23759	−	19.6309i	0.326191	−	0.693190i
$803$	13.8205	+	1.74593i	0.487713	+	0.0616125i
$804$	−1.28411	+	1.20586i	−0.0452870	+	0.0425274i
$805$	75.6343	+	41.5803i	2.66576	+	1.46551i
$806$	−0.231961	+	0.0293035i	−0.00817048	+	0.00103217i
$807$	−35.3967	+	19.4595i	−1.24602	+	0.685006i
$808$	2.97885	−	15.6157i	0.104796	−	0.549358i
$809$	−25.2967	−	39.8612i	−0.889384	−	1.40144i	−0.915731	−	0.401792i	$-0.868387\pi$
$809$	−25.2967	−	39.8612i	−0.889384	−	1.40144i	0.0263470	−	0.999653i	$-0.491613\pi$
$810$	38.5412	−	21.1882i	1.35420	−	0.744478i
$811$	26.4254	+	31.9428i	0.927922	+	1.12167i	0.992315	+	0.123741i	$0.0394890\pi$
$811$	26.4254	+	31.9428i	0.927922	+	1.12167i	−0.0643925	+	0.997925i	$0.520511\pi$
$812$	−0.586263	−	3.07330i	−0.0205738	−	0.107852i
$813$	−19.3007	+	18.1246i	−0.676905	+	0.635656i
$814$	29.9922	+	21.7906i	1.05122	+	0.763760i
$815$	−5.71020	−	2.26083i	−0.200020	−	0.0791934i
$816$	9.25658	+	5.08885i	0.324045	+	0.178145i
$817$	18.9926	−	22.9581i	0.664467	−	0.803203i
$818$	2.86369	−	15.0120i	0.100127	−	0.524882i
$819$	−0.00310687	+	0.00225727i	−0.000108563	+	7.88754e-5i
$820$	−2.87680	+	0.738636i	−0.100462	+	0.0257943i
$821$	34.5548	−	25.1055i	1.20597	−	0.876189i	0.211112	−	0.977462i	$-0.432291\pi$
$821$	34.5548	−	25.1055i	1.20597	−	0.876189i	0.994859	+	0.101273i	$0.0322914\pi$
$822$	11.1125	+	17.5105i	0.387592	+	0.610747i
$823$	20.4840	−	24.7609i	0.714027	−	0.863110i	−0.281306	−	0.959618i	$-0.590767\pi$
$823$	20.4840	−	24.7609i	0.714027	−	0.863110i	0.995332	+	0.0965083i	$0.0307674\pi$
$824$	1.74501	+	9.14767i	0.0607903	+	0.318674i
$825$	−34.5876	−	73.5023i	−1.20418	−	2.55902i
$826$	−21.8678	+	8.65808i	−0.760878	+	0.301253i
$827$	−36.0581	−	9.25814i	−1.25386	−	0.321937i	−0.437363	−	0.899285i	$-0.644088\pi$
$827$	−36.0581	−	9.25814i	−1.25386	−	0.321937i	−0.816498	+	0.577348i	$0.804088\pi$
$828$	−0.311822	+	0.123459i	−0.0108366	+	0.00429050i
$829$	−29.9792	−	3.78725i	−1.04122	−	0.131537i	−0.413919	−	0.910314i	$-0.635840\pi$
$829$	−29.9792	−	3.78725i	−1.04122	−	0.131537i	−0.627300	+	0.778777i	$0.715840\pi$
$830$	55.4743	+	40.3044i	1.92554	+	1.39899i
$831$	21.9541	+	15.9506i	0.761578	+	0.553319i
$832$	−0.184238	−	0.0232746i	−0.00638729	−	0.000806903i
$833$	−2.36573	+	0.936659i	−0.0819677	+	0.0324533i
$834$	−7.67465	−	1.97052i	−0.265752	−	0.0682334i
$835$	58.7538	−	23.2623i	2.03326	−	0.805024i
$836$	7.20684	+	15.3153i	0.249254	+	0.529691i
$837$	8.70582	+	45.6375i	0.300917	+	1.57746i
$838$	25.8469	−	31.2436i	0.892868	−	1.07929i
$839$	−7.91620	−	12.4739i	−0.273298	−	0.430648i	0.679761	−	0.733434i	$-0.262083\pi$
$839$	−7.91620	−	12.4739i	−0.273298	−	0.430648i	−0.953059	+	0.302785i	$0.902083\pi$
$840$	−40.3243	+	29.2973i	−1.39132	+	1.01085i
$841$	−20.8029	+	5.34127i	−0.717341	+	0.184182i
$842$	−1.04170	+	0.756839i	−0.0358993	+	0.0260824i
$843$	0.743431	−	3.89720i	0.0256051	−	0.134227i
$844$	0.581355	−	0.702737i	0.0200111	−	0.0241892i
$845$	43.9667	+	24.1709i	1.51250	+	0.831504i
$846$	0.0747975	+	0.0296144i	0.00257159	+	0.00101817i
$847$	−21.2513	−	15.4400i	−0.730203	−	0.530524i
$848$	6.74179	−	6.33096i	0.231514	−	0.217406i
$849$	1.25667	+	6.58771i	0.0431289	+	0.226090i
$850$	16.5927	+	20.0571i	0.569125	+	0.687953i
$851$	52.1475	−	28.6684i	1.78759	−	0.982739i
$852$	2.03360	+	3.20444i	0.0696701	+	0.109782i
$853$	4.27760	−	22.4239i	0.146462	−	0.767781i	−0.830935	−	0.556370i	$-0.812194\pi$
$853$	4.27760	−	22.4239i	0.146462	−	0.767781i	0.977397	−	0.211412i	$-0.0678061\pi$
$854$	10.3596	−	5.69525i	0.354499	−	0.194887i
$855$	2.23216	−	0.281987i	0.0763381	−	0.00964375i
$856$	−7.23623	−	3.97815i	−0.247329	−	0.135970i
$857$	27.2367	−	25.5770i	0.930389	−	0.873693i	−0.0618444	−	0.998086i	$-0.519698\pi$
$857$	27.2367	−	25.5770i	0.930389	−	0.873693i	0.992233	+	0.124393i	$0.0396982\pi$
$858$	−0.210156	−	0.0265489i	−0.00717461	−	0.000906364i
$859$	−16.9564	+	36.0343i	−0.578546	+	1.22947i	0.374663	+	0.927161i	$0.377758\pi$
$859$	−16.9564	+	36.0343i	−0.578546	+	1.22947i	−0.953209	+	0.302312i	$0.902242\pi$
$860$	−2.20269	−	6.77918i	−0.0751110	−	0.231168i
$861$	2.92439	+	6.21464i	0.0996629	+	0.211795i
$862$	6.61277	−	6.20981i	0.225232	−	0.211507i
$863$	15.6492	+	6.19594i	0.532704	+	0.210912i	0.619048	−	0.785353i	$-0.287519\pi$
$863$	15.6492	+	6.19594i	0.532704	+	0.210912i	−0.0863445	+	0.996265i	$0.527519\pi$
$864$	−0.842619	+	13.3930i	−0.0286665	+	0.455641i
$865$	5.36222	−	11.3953i	0.182321	−	0.387452i
$866$	−19.3658	−	4.97228i	−0.658075	−	0.168965i
$867$	−21.1804	−	5.43821i	−0.719325	−	0.184691i
$868$	−3.19381	−	9.82953i	−0.108405	−	0.333636i
$869$	−5.71081	−	5.36281i	−0.193726	−	0.181921i
$870$	−14.6222	−	17.6752i	−0.495738	−	0.599244i
$871$	−0.00830183	+	0.0435197i	−0.000281297	+	0.00147461i
$872$	15.6033	−	4.00625i	0.528395	−	0.135669i
$873$	0.548708			0.0185710
$874$	−87.5990			−2.96308
$875$	−44.0998	+	11.3229i	−1.49085	+	0.382784i
$876$	1.32448	+	2.08705i	0.0447501	+	0.0705148i
$877$	−34.5161	+	4.36040i	−1.16553	+	0.147240i	−0.684195	−	0.729299i	$-0.739846\pi$
$877$	−34.5161	+	4.36040i	−1.16553	+	0.147240i	−0.481331	+	0.876539i	$0.659846\pi$
$878$	−1.53424	−	24.3860i	−0.0517780	−	0.822988i
$879$	3.14780	−	50.0328i	0.106173	−	1.68756i
$880$	−50.6948	−	6.40425i	−1.70892	−	0.215887i
$881$	−9.42843	−	20.0364i	−0.317652	−	0.675044i	0.680692	−	0.732569i	$-0.261679\pi$
$881$	−9.42843	−	20.0364i	−0.317652	−	0.675044i	−0.998344	+	0.0575251i	$0.981679\pi$
$882$	−0.0821466	−	0.0771408i	−0.00276602	−	0.00259746i
$883$	−14.8662	+	45.7534i	−0.500287	+	1.53972i	0.308266	+	0.951300i	$0.400251\pi$
$883$	−14.8662	+	45.7534i	−0.500287	+	1.53972i	−0.808553	+	0.588424i	$0.799749\pi$
$884$	−0.0208874	+	0.00263869i	−0.000702519	+	8.87487e-5i
$885$	34.0927	−	41.2110i	1.14601	−	1.38529i
$886$	2.20039	+	2.65981i	0.0739235	+	0.0893582i
$887$	−4.44436	+	13.6783i	−0.149227	+	0.459273i	−0.997530	−	0.0702374i	$-0.977624\pi$
$887$	−4.44436	+	13.6783i	−0.149227	+	0.459273i	0.848303	+	0.529510i	$0.177624\pi$
$888$	2.15783	+	34.2978i	0.0724122	+	1.15096i
$889$	6.27674	+	2.48514i	0.210515	+	0.0833489i
$890$	−37.1000	−	26.9547i	−1.24359	−	0.903524i
$891$	−2.71032	+	43.0793i	−0.0907991	+	1.44321i
$892$	−0.124990	+	0.196953i	−0.00418497	+	0.00659446i
$893$	−4.75092	−	4.46141i	−0.158983	−	0.149295i
$894$	2.36856	+	12.4164i	0.0792164	+	0.415267i
$895$	−3.37494	−	1.85539i	−0.112812	−	0.0620188i
$896$	0.870070	+	13.8294i	0.0290670	+	0.462007i
$897$	−0.182193	+	0.287090i	−0.00608325	+	0.00958567i
$898$	−10.2216	−	31.4588i	−0.341098	−	1.04979i
$899$	23.1043	−	9.14763i	0.770571	−	0.305091i
$900$	0.152249	−	0.323547i	0.00507498	−	0.0107849i
$901$	3.72941	−	5.87661i	0.124245	−	0.195778i
$902$	−2.90418	+	8.93814i	−0.0966985	+	0.297607i
$903$	−14.4446	+	7.94098i	−0.480686	+	0.264259i
$904$	−3.48678	+	2.53330i	−0.115969	+	0.0842561i
$905$	−61.5301			−2.04533
$906$	25.5142	+	7.62456i	0.847652	+	0.253309i
$907$	−37.3984			−1.24179			−0.620897	−	0.783892i	$-0.713232\pi$
$907$	−37.3984			−1.24179			−0.620897	+	0.783892i	$0.713232\pi$
$908$	−6.19512	+	4.50102i	−0.205592	+	0.149372i
$909$	0.347876	−	0.191247i	0.0115383	−	0.00634325i
$910$	−0.0741537	+	0.228222i	−0.00245817	+	0.00756548i
$911$	9.82466	−	15.4812i	0.325506	−	0.512915i	−0.641684	−	0.766969i	$-0.721764\pi$
$911$	9.82466	−	15.4812i	0.325506	−	0.512915i	0.967190	+	0.254054i	$0.0817641\pi$
$912$	16.1374	−	34.2937i	0.534362	−	1.13558i
$913$	−62.5705	+	24.7734i	−2.07078	+	0.819881i
$914$	−0.502188	−	1.54558i	−0.0166109	−	0.0511231i
$915$	−14.4052	+	22.6989i	−0.476220	+	0.750403i
$916$	0.0491953	+	0.781937i	0.00162546	+	0.0258359i
$917$	−4.61801	−	2.53877i	−0.152500	−	0.0838377i
$918$	−2.52749	−	13.2496i	−0.0834195	−	0.437301i
$919$	19.1891	+	18.0197i	0.632989	+	0.594416i	0.933156	−	0.359470i	$-0.117043\pi$
$919$	19.1891	+	18.0197i	0.632989	+	0.594416i	−0.300168	+	0.953886i	$0.597043\pi$
$920$	−58.6612	+	92.4353i	−1.93400	+	3.04750i
$921$	0.622321	−	9.89151i	0.0205062	−	0.325936i
$922$	22.9435	+	16.6694i	0.755603	+	0.548978i
$923$	0.0887513	+	0.0351391i	0.00292128	+	0.00115662i
$924$	−0.587959	−	9.34534i	−0.0193424	−	0.307439i
$925$	−19.6066	+	60.3431i	−0.644663	+	1.98407i
$926$	15.2382	+	18.4198i	0.500758	+	0.605312i
$927$	−0.148234	+	0.179184i	−0.00486863	+	0.00588516i
$928$	7.12081	−	0.899568i	0.233752	−	0.0295298i
$929$	−5.70979	+	17.5729i	−0.187332	+	0.576549i	−0.999981	−	0.00620487i	$-0.998025\pi$
$929$	−5.70979	+	17.5729i	−0.187332	+	0.576549i	0.812649	+	0.582754i	$0.198025\pi$
$930$	−55.2399	−	51.8737i	−1.81139	−	1.70101i
$931$	3.88710	+	8.26050i	0.127394	+	0.270727i
$932$	0.201906	+	0.0255066i	0.00661365	+	0.000835498i
$933$	2.21391	−	35.1891i	0.0724802	−	1.15204i
$934$	−1.28642	−	20.4471i	−0.0420931	−	0.669050i
$935$	−38.1517	+	4.81967i	−1.24769	+	0.157620i
$936$	−0.00261008	−	0.00411282i	−8.53130e−5	−	0.000134432i
$937$	35.5150	−	9.11871i	1.16023	−	0.297895i	0.380961	−	0.924591i	$-0.375593\pi$
$937$	35.5150	−	9.11871i	1.16023	−	0.297895i	0.779264	+	0.626696i	$0.215593\pi$
$938$	6.31440			0.206172
$939$	−9.03101			−0.294716
$940$	−1.51015	+	0.387741i	−0.0492557	+	0.0126467i
$941$	8.03514	−	42.1217i	0.261938	−	1.37313i	−0.571540	−	0.820574i	$-0.693654\pi$
$941$	8.03514	−	42.1217i	0.261938	−	1.37313i	0.833478	−	0.552553i	$-0.186346\pi$
$942$	23.6454	+	28.5824i	0.770410	+	0.931266i
$943$	10.9971	+	10.3269i	0.358114	+	0.336291i
$944$	−6.90678	−	21.2569i	−0.224797	−	0.691853i
$945$	46.1867	+	11.8587i	1.50245	+	0.385765i
$946$	−21.8462	−	5.60915i	−0.710281	−	0.182369i
$947$	−20.9624	+	44.5474i	−0.681187	+	1.44760i	0.202388	+	0.979305i	$0.435130\pi$
$947$	−20.9624	+	44.5474i	−0.681187	+	1.44760i	−0.883575	+	0.468290i	$0.844870\pi$
$948$	0.0872859	−	1.38737i	0.00283491	−	0.0450597i
$949$	0.0578035	+	0.0228860i	0.00187638	+	0.000742912i
$950$	68.0850	−	63.9360i	2.20897	−	2.07436i
$951$	4.31727	+	9.17467i	0.139997	+	0.297509i
$952$	4.84397	+	14.9082i	0.156994	+	0.483178i
$953$	14.7802	−	31.4096i	0.478778	−	1.01746i	−0.508881	−	0.860837i	$-0.669941\pi$
$953$	14.7802	−	31.4096i	0.478778	−	1.01746i	0.987659	−	0.156618i	$-0.0500593\pi$
$954$	0.305824	+	0.0386346i	0.00990142	+	0.00125084i
$955$	74.9555	−	70.3879i	2.42550	−	2.27770i
$956$	−8.36653	−	4.59954i	−0.270593	−	0.148760i
$957$	22.3358	−	2.82167i	0.722015	−	0.0912117i
$958$	−34.0926	+	18.7425i	−1.10148	+	0.605544i
$959$	−4.32056	+	22.6492i	−0.139518	+	0.731380i
$960$	−32.2501	−	50.8181i	−1.04087	−	1.64015i
$961$	44.7679	−	24.6113i	1.44412	−	0.793914i
$962$	0.105462	+	0.127481i	0.00340022	+	0.00411016i
$963$	−0.0386393	−	0.202554i	−0.00124513	−	0.00652721i
$964$	−0.650148	+	0.610529i	−0.0209398	+	0.0196638i
$965$	45.8379	+	33.3032i	1.47558	+	1.07207i
$966$	45.0578	+	17.8397i	1.44971	+	0.573982i
$967$	21.7270	+	11.9445i	0.698693	+	0.384109i	0.791162	−	0.611606i	$-0.209476\pi$
$967$	21.7270	+	11.9445i	0.698693	+	0.384109i	−0.0924700	+	0.995715i	$0.529476\pi$
$968$	21.2383	−	25.6727i	0.682625	−	0.825152i
$969$	5.34471	−	28.0180i	0.171697	−	0.900066i
$970$	27.7386	−	20.1533i	0.890633	−	0.647083i
$971$	1.50644	−	0.386789i	0.0483441	−	0.0124127i	−0.224440	−	0.974488i	$-0.572055\pi$
$971$	1.50644	−	0.386789i	0.0483441	−	0.0124127i	0.272784	+	0.962075i	$0.412055\pi$
$972$	−0.303714	+	0.220661i	−0.00974163	+	0.00707770i
$973$	−4.72035	−	7.43808i	−0.151327	−	0.238454i
$974$	24.3511	−	29.4355i	0.780261	−	0.943174i
$975$	−0.0679324	−	0.356114i	−0.00217558	−	0.0114048i
$976$	4.78343	+	10.1653i	0.153114	+	0.325383i
$977$	−14.6237	+	5.78995i	−0.467855	+	0.185237i	−0.590210	−	0.807249i	$-0.700955\pi$
$977$	−14.6237	+	5.78995i	−0.467855	+	0.185237i	0.122355	+	0.992486i	$0.460955\pi$
$978$	−3.33994	−	0.857551i	−0.106800	−	0.0274215i
$979$	41.8458	−	16.5679i	1.33740	−	0.529513i
$980$	2.16679	+	0.273729i	0.0692156	+	0.00874396i
$981$	0.325450	+	0.236453i	0.0103908	+	0.00754937i
$982$	9.23333	+	6.70841i	0.294647	+	0.214074i
$983$	−35.7579	−	4.51728i	−1.14050	−	0.144079i	−0.467689	−	0.883893i	$-0.654913\pi$
$983$	−35.7579	−	4.51728i	−1.14050	−	0.144079i	−0.672811	+	0.739814i	$0.734913\pi$
$984$	−8.10015	+	3.20708i	−0.258223	+	0.102238i
$985$	103.211	+	26.5002i	3.28859	+	0.844366i
$986$	−6.70768	+	2.65576i	−0.213616	+	0.0845765i
$987$	1.53513	+	3.26232i	0.0488638	+	0.103841i
$988$	0.0141548	+	0.0742018i	0.000450323	+	0.00236067i
$989$	−23.0778	+	27.8963i	−0.733832	+	0.887051i
$990$	−0.912577	−	1.43799i	−0.0290036	−	0.0457024i
$991$	−20.7130	+	15.0489i	−0.657971	+	0.478044i	−0.865977	−	0.500084i	$-0.833303\pi$
$991$	−20.7130	+	15.0489i	−0.657971	+	0.478044i	0.208006	+	0.978128i	$0.433303\pi$
$992$	22.9649	−	5.89639i	0.729137	−	0.187211i
$993$	−2.88196	+	2.09386i	−0.0914561	+	0.0664467i
$994$	2.54922	−	13.3635i	0.0808562	−	0.423863i
$995$	−58.6196	+	70.8589i	−1.85837	+	2.24638i
$996$	−10.4643	−	5.75277i	−0.331573	−	0.182284i
$997$	−19.3140	−	7.64694i	−0.611679	−	0.242181i	0.0417993	−	0.999126i	$-0.486691\pi$
$997$	−19.3140	−	7.64694i	−0.611679	−	0.242181i	−0.653478	+	0.756945i	$0.726691\pi$
$998$	−30.4818	−	22.1464i	−0.964886	−	0.701031i
$999$	23.9665	−	22.5060i	0.758266	−	0.712059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.h.a.94.4	✓	220
151.98	even	25	inner	151.2.h.a.98.4	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.h.a.94.4	✓	220	1.1	even	1	trivial
151.2.h.a.98.4	yes	220	151.98	even	25	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.h (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.999563 + 0.726225i) q^{2} +(1.53699 - 0.844968i) q^{3} +(-0.146311 + 0.450298i) q^{4} +(-2.06806 + 3.25874i) q^{5} +(-0.922683 + 1.96080i) q^{6} +(-2.24013 + 0.886932i) q^{7} +(-0.944369 - 2.90647i) q^{8} +(0.0408912 - 0.0644343i) q^{9} +O(q^{10})\)	\(q+(-0.999563 + 0.726225i) q^{2} +(1.53699 - 0.844968i) q^{3} +(-0.146311 + 0.450298i) q^{4} +(-2.06806 + 3.25874i) q^{5} +(-0.922683 + 1.96080i) q^{6} +(-2.24013 + 0.886932i) q^{7} +(-0.944369 - 2.90647i) q^{8} +(0.0408912 - 0.0644343i) q^{9} +(-0.299423 - 4.75919i) q^{10} +(4.10114 + 2.25462i) q^{11} +(0.155609 + 0.815732i) q^{12} +(0.0152255 + 0.0142977i) q^{13} +(1.59504 - 2.51339i) q^{14} +(-0.425058 + 6.75610i) q^{15} +(2.28861 + 1.66277i) q^{16} +(1.97944 + 0.783717i) q^{17} +(0.00592042 + 0.0941023i) q^{18} +(2.36048 - 7.26482i) q^{19} +(-1.16483 - 1.40803i) q^{20} +(-2.69364 + 3.25605i) q^{21} +(-5.73671 + 0.724715i) q^{22} +(-2.86821 + 8.82744i) q^{23} +(-3.90736 - 3.66926i) q^{24} +(-4.21363 - 8.95441i) q^{25} +(-0.0256023 - 0.00323432i) q^{26} +(-0.321988 + 5.11786i) q^{27} +(-0.0716281 - 1.13850i) q^{28} +(2.72106 - 0.343750i) q^{29} +(-4.48158 - 7.06184i) q^{30} +(8.77554 - 2.25318i) q^{31} +2.61692 q^{32} +8.20850 q^{33} +(-2.54773 + 0.654146i) q^{34} +(1.74245 - 9.13425i) q^{35} +(0.0230318 + 0.0278407i) q^{36} +(-4.67367 - 4.38887i) q^{37} +(2.91644 + 8.97588i) q^{38} +(0.0354827 + 0.00911040i) q^{39} +(11.4244 + 2.93330i) q^{40} +(0.692029 - 1.47064i) q^{41} +(0.327837 - 5.21081i) q^{42} +(3.62674 + 1.43593i) q^{43} +(-1.61529 + 1.51686i) q^{44} +(0.125409 + 0.266508i) q^{45} +(-3.54375 - 10.9065i) q^{46} +(0.363275 - 0.771998i) q^{47} +(4.92257 + 0.621865i) q^{48} +(-0.871227 + 0.818137i) q^{49} +(10.7147 + 5.89046i) q^{50} +(3.70460 - 0.468000i) q^{51} +(-0.00866590 + 0.00476412i) q^{52} +(0.612601 - 3.21137i) q^{53} +(-3.39487 - 5.34946i) q^{54} +(-15.8286 + 8.70186i) q^{55} +(4.69335 + 5.67329i) q^{56} +(-2.51050 - 13.1605i) q^{57} +(-2.47023 + 2.31970i) q^{58} +(-6.39199 - 4.64406i) q^{59} +(-2.98007 - 1.17989i) q^{60} +(3.48013 + 1.91322i) q^{61} +(-7.13539 + 8.62521i) q^{62} +(-0.0344530 + 0.180609i) q^{63} +(-7.19301 + 5.22602i) q^{64} +(-0.0780800 + 0.0200475i) q^{65} +(-8.20491 + 5.96122i) q^{66} +(1.13660 + 1.79100i) q^{67} +(-0.642520 + 0.776673i) q^{68} +(3.05049 + 15.9912i) q^{69} +(4.89183 + 10.3957i) q^{70} +(4.24924 - 1.68239i) q^{71} +(-0.225893 - 0.0579994i) q^{72} +(2.76752 - 1.09574i) q^{73} +(7.85893 + 0.992814i) q^{74} +(-14.0425 - 10.2025i) q^{75} +(2.92597 + 2.12584i) q^{76} +(-11.1868 - 1.41322i) q^{77} +(-0.0420833 + 0.0166620i) q^{78} +(-1.62135 - 0.416293i) q^{79} +(-10.1515 + 4.01928i) q^{80} +(3.92701 + 8.34533i) q^{81} +(0.376286 + 1.97256i) q^{82} +(-9.16582 + 11.0796i) q^{83} +(-1.07208 - 1.68934i) q^{84} +(-6.64754 + 4.82972i) q^{85} +(-4.66796 + 1.19853i) q^{86} +(3.89179 - 2.82755i) q^{87} +(2.68000 - 14.0490i) q^{88} +(6.12990 - 7.40977i) q^{89} +(-0.318899 - 0.175316i) q^{90} +(-0.0467884 - 0.0185248i) q^{91} +(-3.55533 - 2.58310i) q^{92} +(11.5841 - 10.8782i) q^{93} +(0.197528 + 1.03548i) q^{94} +(18.7925 + 22.7163i) q^{95} +(4.02219 - 2.21122i) q^{96} +(3.85266 + 6.07082i) q^{97} +(0.276695 - 1.45049i) q^{98} +(0.312975 - 0.172060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9} - 50 q^{10} - 10 q^{11} + 5 q^{12} - 20 q^{13} + 5 q^{14} - 60 q^{15} - 5 q^{16} - 10 q^{17} + 30 q^{18} - 15 q^{19} - 130 q^{20} - 20 q^{21} + 15 q^{22} + 35 q^{23} - 95 q^{24} + 10 q^{25} + 5 q^{26} + 25 q^{27} + 50 q^{28} + 15 q^{29} + 75 q^{30} + 20 q^{31} + 80 q^{32} - 100 q^{33} - 50 q^{34} + 15 q^{35} + 100 q^{36} + 20 q^{37} + 40 q^{38} - 5 q^{39} + 105 q^{40} - 10 q^{41} - 110 q^{42} - 10 q^{43} + 90 q^{44} + 5 q^{45} + 25 q^{46} - 75 q^{47} - 145 q^{48} - 10 q^{49} + 50 q^{50} - 80 q^{51} + 85 q^{52} - 95 q^{53} + 20 q^{54} + 80 q^{55} - 65 q^{56} + 55 q^{57} - 105 q^{58} - 15 q^{59} - 70 q^{62} + 95 q^{63} + 45 q^{64} - 30 q^{65} - 5 q^{66} - 50 q^{67} + 95 q^{68} + 45 q^{69} + 25 q^{71} - 25 q^{72} + 20 q^{73} - 140 q^{74} + 55 q^{75} + 15 q^{76} - 45 q^{77} + 110 q^{78} - 130 q^{79} + 145 q^{80} - 160 q^{81} - 10 q^{82} - 55 q^{83} + 140 q^{84} + 25 q^{85} - 150 q^{86} + 125 q^{87} - 35 q^{88} + 5 q^{89} + 120 q^{90} - 70 q^{91} + 45 q^{92} - 40 q^{93} + 65 q^{94} + 135 q^{96} - 270 q^{97} + 135 q^{98} + 60 q^{99}+O(q^{100}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9 - 50 * q^10 - 10 * q^11 + 5 * q^12 - 20 * q^13 + 5 * q^14 - 60 * q^15 - 5 * q^16 - 10 * q^17 + 30 * q^18 - 15 * q^19 - 130 * q^20 - 20 * q^21 + 15 * q^22 + 35 * q^23 - 95 * q^24 + 10 * q^25 + 5 * q^26 + 25 * q^27 + 50 * q^28 + 15 * q^29 + 75 * q^30 + 20 * q^31 + 80 * q^32 - 100 * q^33 - 50 * q^34 + 15 * q^35 + 100 * q^36 + 20 * q^37 + 40 * q^38 - 5 * q^39 + 105 * q^40 - 10 * q^41 - 110 * q^42 - 10 * q^43 + 90 * q^44 + 5 * q^45 + 25 * q^46 - 75 * q^47 - 145 * q^48 - 10 * q^49 + 50 * q^50 - 80 * q^51 + 85 * q^52 - 95 * q^53 + 20 * q^54 + 80 * q^55 - 65 * q^56 + 55 * q^57 - 105 * q^58 - 15 * q^59 - 70 * q^62 + 95 * q^63 + 45 * q^64 - 30 * q^65 - 5 * q^66 - 50 * q^67 + 95 * q^68 + 45 * q^69 + 25 * q^71 - 25 * q^72 + 20 * q^73 - 140 * q^74 + 55 * q^75 + 15 * q^76 - 45 * q^77 + 110 * q^78 - 130 * q^79 + 145 * q^80 - 160 * q^81 - 10 * q^82 - 55 * q^83 + 140 * q^84 + 25 * q^85 - 150 * q^86 + 125 * q^87 - 35 * q^88 + 5 * q^89 + 120 * q^90 - 70 * q^91 + 45 * q^92 - 40 * q^93 + 65 * q^94 + 135 * q^96 - 270 * q^97 + 135 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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