LMFDB - Embedded newform 225.2.u.a.169.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(4,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.u (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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			169.16
Character	$\chi$	$=$	225.169
Dual form			225.2.u.a.4.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0838034 - 0.394264i) q^{2} +(-0.757696 - 1.55753i) q^{3} +(1.67867 + 0.747392i) q^{4} +(-0.252792 - 2.22173i) q^{5} +(-0.677575 + 0.168206i) q^{6} +(4.03987 + 2.33242i) q^{7} +(0.909187 - 1.25139i) q^{8} +(-1.85179 + 2.36027i) q^{9} +O(q^{10})$	\(q+(0.0838034 - 0.394264i) q^{2} +(-0.757696 - 1.55753i) q^{3} +(1.67867 + 0.747392i) q^{4} +(-0.252792 - 2.22173i) q^{5} +(-0.677575 + 0.168206i) q^{6} +(4.03987 + 2.33242i) q^{7} +(0.909187 - 1.25139i) q^{8} +(-1.85179 + 2.36027i) q^{9} +(-0.897134 - 0.0865220i) q^{10} +(-2.61394 - 0.555609i) q^{11} +(-0.107837 - 3.18087i) q^{12} +(-1.01644 - 4.78198i) q^{13} +(1.25815 - 1.39731i) q^{14} +(-3.26887 + 2.07713i) q^{15} +(2.04191 + 2.26778i) q^{16} +(0.388104 - 0.534179i) q^{17} +(0.775381 + 0.927894i) q^{18} +(-3.29002 - 2.39034i) q^{19} +(1.23615 - 3.91849i) q^{20} +(0.571820 - 8.05949i) q^{21} +(-0.438113 + 0.984019i) q^{22} +(3.21237 + 2.89243i) q^{23} +(-2.63796 - 0.467913i) q^{24} +(-4.87219 + 1.12327i) q^{25} -1.97054 q^{26} +(5.07928 + 1.09586i) q^{27} +(5.03838 + 6.93474i) q^{28} +(0.918903 + 8.74277i) q^{29} +(0.544994 + 1.46287i) q^{30} +(-0.115766 + 1.10144i) q^{31} +(3.74436 - 2.16181i) q^{32} +(1.11519 + 4.49226i) q^{33} +(-0.178083 - 0.197781i) q^{34} +(4.16077 - 9.56514i) q^{35} +(-4.87260 + 2.57809i) q^{36} +(-3.15275 - 1.02439i) q^{37} +(-1.21814 + 1.09682i) q^{38} +(-6.67792 + 5.20642i) q^{39} +(-3.01009 - 1.70363i) q^{40} +(-6.87142 + 1.46056i) q^{41} +(-3.12965 - 0.900860i) q^{42} +(1.95550 + 1.12901i) q^{43} +(-3.97268 - 2.88632i) q^{44} +(5.71200 + 3.51753i) q^{45} +(1.40959 - 1.02413i) q^{46} +(1.60516 - 0.168709i) q^{47} +(1.98498 - 4.89863i) q^{48} +(7.38039 + 12.7832i) q^{49} +(0.0345592 + 2.01506i) q^{50} +(-1.12606 - 0.199738i) q^{51} +(1.86774 - 8.78704i) q^{52} +(4.22318 + 5.81270i) q^{53} +(0.857718 - 1.91074i) q^{54} +(-0.573634 + 5.94792i) q^{55} +(6.59177 - 2.93485i) q^{56} +(-1.23019 + 6.93545i) q^{57} +(3.52397 + 0.370384i) q^{58} +(-5.23710 + 1.11318i) q^{59} +(-7.03979 + 1.04368i) q^{60} +(9.75278 + 2.07302i) q^{61} +(0.424558 + 0.137947i) q^{62} +(-12.9862 + 5.21602i) q^{63} +(1.34746 + 4.14704i) q^{64} +(-10.3673 + 3.46711i) q^{65} +(1.86459 - 0.0632126i) q^{66} +(-2.63821 - 0.277287i) q^{67} +(1.05074 - 0.606644i) q^{68} +(2.07104 - 7.19494i) q^{69} +(-3.42250 - 2.44203i) q^{70} +(8.66423 - 6.29493i) q^{71} +(1.26998 + 4.46324i) q^{72} +(-9.14313 + 2.97078i) q^{73} +(-0.668091 + 1.15717i) q^{74} +(5.44117 + 6.73748i) q^{75} +(-3.73634 - 6.47152i) q^{76} +(-9.26406 - 8.34139i) q^{77} +(1.49307 + 3.06918i) q^{78} +(0.356386 + 3.39079i) q^{79} +(4.52221 - 5.10986i) q^{80} +(-2.14172 - 8.74146i) q^{81} +2.83155i q^{82} +(0.555621 + 1.24794i) q^{83} +(6.98349 - 13.1018i) q^{84} +(-1.28491 - 0.727226i) q^{85} +(0.609006 - 0.676369i) q^{86} +(12.9209 - 8.05558i) q^{87} +(-3.07184 + 2.76590i) q^{88} +(1.57433 + 4.84528i) q^{89} +(1.86552 - 1.95725i) q^{90} +(7.04730 - 21.6894i) q^{91} +(3.23073 + 7.25633i) q^{92} +(1.80325 - 0.654250i) q^{93} +(0.0680018 - 0.646994i) q^{94} +(-4.47900 + 7.91380i) q^{95} +(-6.20417 - 4.19396i) q^{96} +(-14.7582 + 1.55114i) q^{97} +(5.65846 - 1.83854i) q^{98} +(6.15186 - 5.14071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.0838034	−	0.394264i	0.0592579	−	0.278787i	−0.938535	−	0.345183i	$-0.887817\pi$
$2$	0.0838034	−	0.394264i	0.0592579	−	0.278787i	0.997793	+	0.0663963i	$0.0211502\pi$
$3$	−0.757696	−	1.55753i	−0.437456	−	0.899240i
$3$	−0.757696	−	1.55753i	−0.437456	−	0.899240i
$4$	1.67867	+	0.747392i	0.839335	+	0.373696i
$5$	−0.252792	−	2.22173i	−0.113052	−	0.993589i
$5$	−0.252792	−	2.22173i	−0.113052	−	0.993589i
$6$	−0.677575	+	0.168206i	−0.276619	+	0.0686698i
$7$	4.03987	+	2.33242i	1.52693	+	0.881573i	0.999488	+	0.0319808i	$0.0101815\pi$
$7$	4.03987	+	2.33242i	1.52693	+	0.881573i	0.527440	+	0.849592i	$0.323152\pi$
$8$	0.909187	−	1.25139i	0.321446	−	0.442433i
$9$	−1.85179	+	2.36027i	−0.617265	+	0.786756i
$10$	−0.897134	−	0.0865220i	−0.283699	−	0.0273607i
$11$	−2.61394	−	0.555609i	−0.788131	−	0.167522i	−0.203773	−	0.979018i	$-0.565320\pi$
$11$	−2.61394	−	0.555609i	−0.788131	−	0.167522i	−0.584358	+	0.811496i	$0.698654\pi$
$12$	−0.107837	−	3.18087i	−0.0311297	−	0.918239i
$13$	−1.01644	−	4.78198i	−0.281910	−	1.32628i	−0.859994	−	0.510305i	$-0.829533\pi$
$13$	−1.01644	−	4.78198i	−0.281910	−	1.32628i	0.578084	−	0.815978i	$-0.303801\pi$
$14$	1.25815	−	1.39731i	0.336253	−	0.373447i
$15$	−3.26887	+	2.07713i	−0.844020	+	0.536312i
$16$	2.04191	+	2.26778i	0.510479	+	0.566944i
$17$	0.388104	−	0.534179i	0.0941289	−	0.129557i	−0.759355	−	0.650677i	$-0.774485\pi$
$17$	0.388104	−	0.534179i	0.0941289	−	0.129557i	0.853484	+	0.521119i	$0.174485\pi$
$18$	0.775381	+	0.927894i	0.182759	+	0.218707i
$19$	−3.29002	−	2.39034i	−0.754782	−	0.548381i	0.142523	−	0.989791i	$-0.454478\pi$
$19$	−3.29002	−	2.39034i	−0.754782	−	0.548381i	−0.897306	+	0.441410i	$0.854478\pi$
$20$	1.23615	−	3.91849i	0.276412	−	0.876201i
$21$	0.571820	−	8.05949i	0.124781	−	1.75872i
$22$	−0.438113	+	0.984019i	−0.0934061	+	0.209794i
$23$	3.21237	+	2.89243i	0.669825	+	0.603113i	0.932239	−	0.361842i	$-0.117852\pi$
$23$	3.21237	+	2.89243i	0.669825	+	0.603113i	−0.262415	+	0.964955i	$0.584519\pi$
$24$	−2.63796	−	0.467913i	−0.538472	−	0.0955124i
$25$	−4.87219	+	1.12327i	−0.974439	+	0.224654i
$26$	−1.97054			−0.386455
$27$	5.07928	+	1.09586i	0.977508	+	0.210898i
$28$	5.03838	+	6.93474i	0.952165	+	1.31054i
$29$	0.918903	+	8.74277i	0.170636	+	1.62349i	0.659898	+	0.751355i	$0.270600\pi$
$29$	0.918903	+	8.74277i	0.170636	+	1.62349i	−0.489262	+	0.872137i	$0.662734\pi$
$30$	0.544994	+	1.46287i	0.0995018	+	0.267082i
$31$	−0.115766	+	1.10144i	−0.0207923	+	0.197825i	−0.999987	−	0.00509760i	$-0.998377\pi$
$31$	−0.115766	+	1.10144i	−0.0207923	+	0.197825i	0.979195	+	0.202923i	$0.0650440\pi$
$32$	3.74436	−	2.16181i	0.661916	−	0.382157i
$33$	1.11519	+	4.49226i	0.194130	+	0.782003i
$34$	−0.178083	−	0.197781i	−0.0305410	−	0.0339192i
$35$	4.16077	−	9.56514i	0.703299	−	1.61680i
$36$	−4.87260	+	2.57809i	−0.812099	+	0.429682i
$37$	−3.15275	−	1.02439i	−0.518308	−	0.168409i	0.0381690	−	0.999271i	$-0.487847\pi$
$37$	−3.15275	−	1.02439i	−0.518308	−	0.168409i	−0.556478	+	0.830863i	$0.687847\pi$
$38$	−1.21814	+	1.09682i	−0.197608	+	0.177927i
$39$	−6.67792	+	5.20642i	−1.06932	+	0.833695i
$40$	−3.01009	−	1.70363i	−0.475937	−	0.269368i
$41$	−6.87142	+	1.46056i	−1.07313	+	0.228102i	−0.710405	−	0.703793i	$-0.751488\pi$
$41$	−6.87142	+	1.46056i	−1.07313	+	0.228102i	−0.362729	+	0.931895i	$0.618155\pi$
$42$	−3.12965	−	0.900860i	−0.482915	−	0.139006i
$43$	1.95550	+	1.12901i	0.298211	+	0.172172i	0.641639	−	0.767007i	$-0.278255\pi$
$43$	1.95550	+	1.12901i	0.298211	+	0.172172i	−0.343428	+	0.939179i	$0.611588\pi$
$44$	−3.97268	−	2.88632i	−0.598904	−	0.435129i
$45$	5.71200	+	3.51753i	0.851495	+	0.524363i
$46$	1.40959	−	1.02413i	0.207832	−	0.150999i
$47$	1.60516	−	0.168709i	0.234136	−	0.0246087i	0.0132664	−	0.999912i	$-0.495777\pi$
$47$	1.60516	−	0.168709i	0.234136	−	0.0246087i	0.220870	+	0.975303i	$0.429110\pi$
$48$	1.98498	−	4.89863i	0.286507	−	0.707056i
$49$	7.38039	+	12.7832i	1.05434	+	1.82617i
$50$	0.0345592	+	2.01506i	0.00488741	+	0.284973i
$51$	−1.12606	−	0.199738i	−0.157680	−	0.0279688i
$52$	1.86774	−	8.78704i	0.259009	−	1.21854i
$53$	4.22318	+	5.81270i	0.580098	+	0.798436i	0.993706	−	0.112019i	$-0.0357316\pi$
$53$	4.22318	+	5.81270i	0.580098	+	0.798436i	−0.413608	+	0.910455i	$0.635732\pi$
$54$	0.857718	−	1.91074i	0.116721	−	0.260019i
$55$	−0.573634	+	5.94792i	−0.0773488	+	0.802017i
$56$	6.59177	−	2.93485i	0.880862	−	0.392185i
$57$	−1.23019	+	6.93545i	−0.162942	+	0.918623i
$58$	3.52397	+	0.370384i	0.462720	+	0.0486338i
$59$	−5.23710	+	1.11318i	−0.681812	+	0.144924i	−0.535782	−	0.844356i	$-0.679983\pi$
$59$	−5.23710	+	1.11318i	−0.681812	+	0.144924i	−0.146030	+	0.989280i	$0.546650\pi$
$60$	−7.03979	+	1.04368i	−0.908833	+	0.134739i
$61$	9.75278	+	2.07302i	1.24872	+	0.265423i	0.784405	−	0.620250i	$-0.212969\pi$
$61$	9.75278	+	2.07302i	1.24872	+	0.265423i	0.464311	+	0.885672i	$0.346302\pi$
$62$	0.424558	+	0.137947i	0.0539189	+	0.0175193i
$63$	−12.9862	+	5.21602i	−1.63610	+	0.657156i
$64$	1.34746	+	4.14704i	0.168432	+	0.518380i
$65$	−10.3673	+	3.46711i	−1.28591	+	0.430041i
$66$	1.86459	−	0.0632126i	0.229516	−	0.00778094i
$67$	−2.63821	−	0.277287i	−0.322309	−	0.0338760i	−0.0580075	−	0.998316i	$-0.518475\pi$
$67$	−2.63821	−	0.277287i	−0.322309	−	0.0338760i	−0.264301	+	0.964440i	$0.585141\pi$
$68$	1.05074	−	0.606644i	0.127421	−	0.0735664i
$69$	2.07104	−	7.19494i	0.249324	−	0.866168i
$70$	−3.42250	−	2.44203i	−0.409067	−	0.291879i
$71$	8.66423	−	6.29493i	1.02826	−	0.747071i	0.0602966	−	0.998181i	$-0.480795\pi$
$71$	8.66423	−	6.29493i	1.02826	−	0.747071i	0.967959	+	0.251109i	$0.0807954\pi$
$72$	1.26998	+	4.46324i	0.149669	+	0.525998i
$73$	−9.14313	+	2.97078i	−1.07012	+	0.347704i	−0.790535	−	0.612416i	$-0.790198\pi$
$73$	−9.14313	+	2.97078i	−1.07012	+	0.347704i	−0.279587	+	0.960120i	$0.590198\pi$
$74$	−0.668091	+	1.15717i	−0.0776640	+	0.134518i
$75$	5.44117	+	6.73748i	0.628292	+	0.777978i
$76$	−3.73634	−	6.47152i	−0.428587	−	0.742335i
$77$	−9.26406	−	8.34139i	−1.05574	−	0.950590i
$78$	1.49307	+	3.06918i	0.169057	+	0.347516i
$79$	0.356386	+	3.39079i	0.0400966	+	0.381494i	0.996106	+	0.0881589i	$0.0280983\pi$
$79$	0.356386	+	3.39079i	0.0400966	+	0.381494i	−0.956010	+	0.293335i	$0.905235\pi$
$80$	4.52221	−	5.10986i	0.505599	−	0.571300i
$81$	−2.14172	−	8.74146i	−0.237969	−	0.971273i
$82$			2.83155i			0.312693i
$83$	0.555621	+	1.24794i	0.0609873	+	0.136980i	0.941468	−	0.337102i	$-0.109447\pi$
$83$	0.555621	+	1.24794i	0.0609873	+	0.136980i	−0.880481	+	0.474082i	$0.842780\pi$
$84$	6.98349	−	13.1018i	0.761962	−	1.42953i
$85$	−1.28491	−	0.727226i	−0.139368	−	0.0788788i
$86$	0.609006	−	0.676369i	0.0656708	−	0.0729348i
$87$	12.9209	−	8.05558i	1.38526	−	0.863649i
$88$	−3.07184	+	2.76590i	−0.327459	+	0.294846i
$89$	1.57433	+	4.84528i	0.166878	+	0.513599i	0.999170	−	0.0407393i	$-0.0129713\pi$
$89$	1.57433	+	4.84528i	0.166878	+	0.513599i	−0.832291	+	0.554338i	$0.812971\pi$
$90$	1.86552	−	1.95725i	0.196643	−	0.206313i
$91$	7.04730	−	21.6894i	0.738758	−	2.27366i
$92$	3.23073	+	7.25633i	0.336826	+	0.756525i
$93$	1.80325	−	0.654250i	0.186988	−	0.0678426i
$94$	0.0680018	−	0.646994i	0.00701385	−	0.0667324i
$95$	−4.47900	+	7.91380i	−0.459536	+	0.811939i
$96$	−6.20417	−	4.19396i	−0.633210	−	0.428044i
$97$	−14.7582	+	1.55114i	−1.49846	+	0.157495i	−0.817971	−	0.575260i	$-0.804901\pi$
$97$	−14.7582	+	1.55114i	−1.49846	+	0.157495i	−0.680493	+	0.732755i	$0.738234\pi$
$98$	5.65846	−	1.83854i	0.571591	−	0.185721i
$99$	6.15186	−	5.14071i	0.618285	−	0.516661i
$100$	−9.01833	−	1.75584i	−0.901833	−	0.175584i
$101$	−5.14470	+	8.91088i	−0.511916	+	0.886665i	0.487988	+	0.872850i	$0.337731\pi$
$101$	−5.14470	+	8.91088i	−0.511916	+	0.886665i	−0.999905	+	0.0138151i	$0.995602\pi$
$102$	−0.173117	+	0.427227i	−0.0171412	+	0.0423018i
$103$	5.07859	−	11.4067i	0.500408	−	1.12393i	−0.470045	−	0.882643i	$-0.655762\pi$
$103$	5.07859	−	11.4067i	0.500408	−	1.12393i	0.970453	−	0.241292i	$-0.0775712\pi$
$104$	−6.90825	−	3.07575i	−0.677410	−	0.301602i
$105$	−18.0506	+	0.766942i	−1.76156	+	0.0748459i
$106$	2.64566	−	1.17792i	0.256969	−	0.114410i
$107$		−	17.3230i		−	1.67468i	−0.546685	−	0.837338i	$-0.684111\pi$
$107$		−	17.3230i		−	1.67468i	0.546685	−	0.837338i	$-0.315889\pi$
$108$	7.70740	+	5.63580i	0.741645	+	0.542305i
$109$	−0.109625	+	0.337390i	−0.0105001	+	0.0323161i	−0.956169	−	0.292814i	$-0.905408\pi$
$109$	−0.109625	+	0.337390i	−0.0105001	+	0.0323161i	0.945669	+	0.325130i	$0.105408\pi$
$110$	2.29698	+	0.724619i	0.219008	+	0.0690897i
$111$	0.793307	+	5.68667i	0.0752974	+	0.539755i
$112$	2.95967	+	13.9241i	0.279662	+	1.31571i
$113$	−2.22369	−	10.4616i	−0.209187	−	0.984147i	−0.949955	−	0.312386i	$-0.898872\pi$
$113$	−2.22369	−	10.4616i	−0.209187	−	0.984147i	0.740768	−	0.671761i	$-0.234462\pi$
$114$	2.63130	+	1.06623i	0.246444	+	0.0998619i
$115$	5.61414	−	7.86820i	0.523521	−	0.733714i
$116$	−4.99175	+	15.3630i	−0.463472	+	1.42642i
$117$	13.1690	+	6.45617i	1.21747	+	0.596873i
$118$			2.15809i			0.198668i
$119$	2.81382	−	1.25279i	0.257942	−	0.114843i
$120$	−0.372723	+	5.97913i	−0.0340248	+	0.545818i
$121$	−3.52504	−	1.56945i	−0.320458	−	0.142677i
$122$	1.63463	−	3.67144i	0.147993	−	0.332397i
$123$	7.48132	+	9.59577i	0.674567	+	0.865221i
$124$	−1.01754	+	1.76244i	−0.0913782	+	0.158272i
$125$	3.72726	+	10.5408i	0.333376	+	0.942794i
$126$	0.968203	+	5.55709i	0.0862544	+	0.495065i
$127$	3.59630	−	1.16851i	0.319120	−	0.103688i	−0.145077	−	0.989420i	$-0.546343\pi$
$127$	3.59630	−	1.16851i	0.319120	−	0.103688i	0.464197	+	0.885732i	$0.346343\pi$
$128$	10.3478	−	1.08760i	0.914626	−	0.0961311i
$129$	0.276790	−	3.90120i	0.0243700	−	0.343481i
$130$	0.498137	+	4.37802i	0.0436895	+	0.383978i
$131$	−0.558586	+	5.31459i	−0.0488039	+	0.464338i	0.942641	+	0.333809i	$0.108334\pi$
$131$	−0.558586	+	5.31459i	−0.0488039	+	0.464338i	−0.991445	+	0.130529i	$0.958333\pi$
$132$	−1.48544	+	8.37451i	−0.129291	+	0.728908i
$133$	−7.71598	−	17.3304i	−0.669061	−	1.50273i
$134$	−0.330416	+	1.01691i	−0.0285436	+	0.0878480i
$135$	1.15070	−	11.5618i	0.0990368	−	0.995084i
$136$	−0.315607	−	0.971337i	−0.0270630	−	0.0832915i
$137$	−6.59272	+	5.93611i	−0.563254	+	0.507156i	−0.900847	−	0.434136i	$-0.857054\pi$
$137$	−6.59272	+	5.93611i	−0.563254	+	0.507156i	0.337594	+	0.941292i	$0.390387\pi$
$138$	−2.66314	−	1.41950i	−0.226702	−	0.120836i
$139$	6.28758	−	6.98307i	0.533306	−	0.592296i	−0.414934	−	0.909852i	$-0.636195\pi$
$139$	6.28758	−	6.98307i	0.533306	−	0.592296i	0.948240	+	0.317555i	$0.102862\pi$
$140$	14.1335	−	12.9470i	1.19450	−	1.09422i
$141$	−1.47899	−	2.37225i	−0.124553	−	0.199780i
$142$	−1.75577	−	3.94353i	−0.147341	−	0.330934i
$143$			13.0645i			1.09251i
$144$	−9.13376	+	0.620010i	−0.761147	+	0.0516675i
$145$	19.1918	−	4.25166i	1.59379	−	0.353081i
$146$	0.405047	+	3.85377i	0.0335220	+	0.318940i
$147$	14.3181	−	21.1810i	1.18094	−	1.74698i
$148$	−4.52680	−	4.07595i	−0.372101	−	0.335041i
$149$	−9.05535	−	15.6843i	−0.741843	−	1.28491i	−0.951655	−	0.307168i	$-0.900619\pi$
$149$	−9.05535	−	15.6843i	−0.741843	−	1.28491i	0.209812	−	0.977742i	$-0.432715\pi$
$150$	3.11234	−	1.58063i	0.254121	−	0.129058i
$151$	−0.803549	+	1.39179i	−0.0653919	+	0.113262i	−0.896868	−	0.442299i	$-0.854163\pi$
$151$	−0.803549	+	1.39179i	−0.0653919	+	0.113262i	0.831476	+	0.555561i	$0.187496\pi$
$152$	−5.98249	+	1.94383i	−0.485244	+	0.157665i
$153$	0.542116	+	1.90522i	0.0438275	+	0.154028i
$154$	−4.06507	+	2.95345i	−0.327573	+	0.237995i
$155$	2.47638	−	0.0212339i	0.198908	−	0.00170555i
$156$	−15.1013	+	3.74884i	−1.20907	+	0.300148i
$157$	−5.96877	+	3.44607i	−0.476359	+	0.275026i	−0.718898	−	0.695116i	$-0.755353\pi$
$157$	−5.96877	+	3.44607i	−0.476359	+	0.275026i	0.242539	+	0.970142i	$0.422020\pi$
$158$	1.36673	+	0.143649i	0.108731	+	0.0114281i
$159$	5.85357	−	10.9820i	0.464219	−	0.870928i
$160$	−5.74950	−	7.77248i	−0.454538	−	0.614469i
$161$	6.23119	+	19.1776i	0.491087	+	1.51141i
$162$	−3.62592	+	0.111839i	−0.284879	+	0.00878691i
$163$	−9.77187	−	3.17507i	−0.765392	−	0.248691i	−0.0998006	−	0.995007i	$-0.531820\pi$
$163$	−9.77187	−	3.17507i	−0.765392	−	0.248691i	−0.665591	+	0.746317i	$0.731820\pi$
$164$	−12.6265	−	2.68384i	−0.985960	−	0.209572i
$165$	9.69870	−	3.61326i	0.755043	−	0.281292i
$166$	0.538583	−	0.114479i	0.0418021	−	0.00888531i
$167$	0.701282	+	0.0737077i	0.0542668	+	0.00570367i	0.131623	−	0.991300i	$-0.457981\pi$
$167$	0.701282	+	0.0737077i	0.0542668	+	0.00570367i	−0.0773561	+	0.997004i	$0.524648\pi$
$168$	−9.56567	−	8.04316i	−0.738007	−	0.620543i
$169$	−9.95808	+	4.43362i	−0.766006	+	0.341048i
$170$	−0.394399	+	0.445650i	−0.0302490	+	0.0341798i
$171$	11.7343	−	3.33891i	0.897343	−	0.255333i
$172$	2.43883	+	3.35676i	0.185959	+	0.255951i
$173$	0.0793070	−	0.373110i	0.00602960	−	0.0283670i	−0.975030	−	0.222073i	$-0.928718\pi$
$173$	0.0793070	−	0.373110i	0.00602960	−	0.0283670i	0.981060	+	0.193706i	$0.0620509\pi$
$174$	−2.09321	−	5.76932i	−0.158686	−	0.437371i
$175$	−22.3030	−	6.82614i	−1.68595	−	0.516007i
$176$	−4.07744	−	7.06233i	−0.307348	−	0.532343i
$177$	5.70194	+	7.31348i	0.428584	+	0.549715i
$178$	2.04226	−	0.214650i	0.153073	−	0.0160887i
$179$	−10.4612	+	7.60049i	−0.781905	+	0.568087i	−0.905550	−	0.424240i	$-0.860541\pi$
$179$	−10.4612	+	7.60049i	−0.781905	+	0.568087i	0.123645	+	0.992326i	$0.460541\pi$
$180$	6.95959	+	10.1739i	0.518737	+	0.758316i
$181$	−6.07632	−	4.41471i	−0.451649	−	0.328143i	0.338597	−	0.940931i	$-0.390048\pi$
$181$	−6.07632	−	4.41471i	−0.451649	−	0.328143i	−0.790247	+	0.612789i	$0.790048\pi$
$182$	−7.96075	−	4.59614i	−0.590090	−	0.340688i
$183$	−4.16086	−	16.7610i	−0.307579	−	1.23901i
$184$	6.54020	−	1.39016i	0.482150	−	0.102484i
$185$	−1.47893	+	7.26352i	−0.108733	+	0.534025i
$186$	−0.106829	−	0.765784i	−0.00783308	−	0.0561500i
$187$	−1.31127	+	1.18067i	−0.0958897	+	0.0863395i
$188$	2.82062	+	0.916476i	0.205715	+	0.0668409i
$189$	17.9637	+	16.2742i	1.30666	+	1.18377i
$190$	2.74477	+	2.42911i	0.199127	+	0.176226i
$191$	0.751271	+	0.834371i	0.0543601	+	0.0603730i	0.769712	−	0.638392i	$-0.220400\pi$
$191$	0.751271	+	0.834371i	0.0543601	+	0.0603730i	−0.715351	+	0.698765i	$0.753733\pi$
$192$	5.43818	−	5.24090i	0.392467	−	0.378229i
$193$	−2.46433	+	1.42278i	−0.177386	+	0.102414i	−0.586064	−	0.810265i	$-0.699323\pi$
$193$	−2.46433	+	1.42278i	−0.177386	+	0.102414i	0.408678	+	0.912679i	$0.365990\pi$
$194$	−0.625223	+	5.94860i	−0.0448884	+	0.427085i
$195$	13.2554	+	13.5204i	0.949239	+	0.968217i
$196$	2.83517	+	26.9748i	0.202512	+	1.92677i
$197$	−0.907927	−	1.24965i	−0.0646872	−	0.0890342i	0.775448	−	0.631412i	$-0.217524\pi$
$197$	−0.907927	−	1.24965i	−0.0646872	−	0.0890342i	−0.840135	+	0.542378i	$0.817524\pi$
$198$	−1.51125	−	2.85626i	−0.107400	−	0.202986i
$199$	12.0990			0.857678			0.428839	−	0.903381i	$-0.358923\pi$
$199$	12.0990			0.857678			0.428839	+	0.903381i	$0.358923\pi$
$200$	−3.02409	+	7.11827i	−0.213835	+	0.503338i
$201$	1.56708	+	4.31919i	0.110533	+	0.304652i
$202$	3.08209	+	2.77513i	0.216855	+	0.195257i
$203$	−16.6796	+	37.4630i	−1.17068	+	2.62939i
$204$	−1.74101	−	1.17690i	−0.121895	−	0.0823998i
$205$	4.98202	+	14.8972i	0.347959	+	1.04047i
$206$	−4.07164	−	2.95822i	−0.283685	−	0.206109i
$207$	−12.7755	+	2.22586i	−0.887962	+	0.154708i
$208$	8.76897	−	12.0695i	0.608019	−	0.836866i
$209$	7.27181	+	8.07616i	0.503001	+	0.558640i
$210$	−1.21032	+	7.18097i	−0.0835202	+	0.495534i
$211$	4.42451	−	4.91392i	0.304596	−	0.338288i	−0.571342	−	0.820712i	$-0.693577\pi$
$211$	4.42451	−	4.91392i	0.304596	−	0.338288i	0.875938	+	0.482424i	$0.160244\pi$
$212$	2.74495	+	12.9140i	0.188524	+	0.886936i
$213$	−16.3694	−	8.72515i	−1.12161	−	0.597837i
$214$	−6.82983	−	1.45172i	−0.466877	−	0.0992379i
$215$	2.01402	−	4.63001i	0.137355	−	0.315764i
$216$	5.98936	−	5.35982i	0.407525	−	0.364689i
$217$	−3.03671	+	4.17968i	−0.206146	+	0.283735i
$218$	0.123834	+	0.0714954i	0.00838708	+	0.00484228i
$219$	11.5548	+	11.9897i	0.780801	+	0.810192i
$220$	−5.40837	+	9.55587i	−0.364632	+	0.644256i
$221$	−2.94892	−	1.31294i	−0.198366	−	0.0883180i
$222$	2.30853	+	0.163790i	0.154938	+	0.0109929i
$223$	4.23664	−	19.9318i	0.283706	−	1.33473i	−0.573266	−	0.819370i	$-0.694324\pi$
$223$	4.23664	−	19.9318i	0.283706	−	1.33473i	0.856972	−	0.515363i	$-0.172343\pi$
$224$	20.1690			1.34760
$225$	6.37108	−	13.5797i	0.424738	−	0.905316i
$226$	−4.31100			−0.286763
$227$	−1.64917	+	7.75874i	−0.109459	+	0.514965i	0.888920	+	0.458062i	$0.151456\pi$
$227$	−1.64917	+	7.75874i	−0.109459	+	0.514965i	−0.998380	+	0.0569037i	$0.981877\pi$
$228$	−7.24858	+	10.7229i	−0.480049	+	0.710141i
$229$	−0.587109	−	0.261398i	−0.0387972	−	0.0172736i	0.387246	−	0.921976i	$-0.373426\pi$
$229$	−0.587109	−	0.261398i	−0.0387972	−	0.0172736i	−0.426044	+	0.904703i	$0.640093\pi$
$230$	−2.63166	−	2.87284i	−0.173527	−	0.189429i
$231$	−5.97263	+	20.7493i	−0.392970	+	1.36520i
$232$	11.7761	+	6.79892i	0.773137	+	0.446371i
$233$	14.5616	−	20.0423i	0.953960	−	1.31301i	0.00421421	−	0.999991i	$-0.498659\pi$
$233$	14.5616	−	20.0423i	0.953960	−	1.31301i	0.949746	−	0.313022i	$-0.101341\pi$
$234$	3.64904	−	4.65101i	0.238545	−	0.304046i
$235$	−0.780597	−	3.52358i	−0.0509205	−	0.229853i
$236$	−9.62334	−	2.04550i	−0.626426	−	0.133151i
$237$	5.01122	−	3.12427i	0.325514	−	0.202943i
$238$	−0.258124	−	1.21438i	−0.0167317	−	0.0787163i
$239$	−3.21980	+	3.57595i	−0.208271	+	0.231309i	−0.838226	−	0.545323i	$-0.816407\pi$
$239$	−3.21980	+	3.57595i	−0.208271	+	0.231309i	0.629954	+	0.776632i	$0.283074\pi$
$240$	−11.3852	−	3.17176i	−0.734913	−	0.204736i
$241$	6.35852	+	7.06185i	0.409588	+	0.454894i	0.912277	−	0.409574i	$-0.134323\pi$
$241$	6.35852	+	7.06185i	0.409588	+	0.454894i	−0.502689	+	0.864467i	$0.667656\pi$
$242$	−0.914187	+	1.25827i	−0.0587662	+	0.0808847i
$243$	−11.9923	+	9.95915i	−0.769306	+	0.638880i
$244$	14.8223	+	10.7691i	0.948903	+	0.689419i
$245$	26.5352	−	19.6287i	1.69527	−	1.25403i
$246$	4.41022	−	2.14546i	0.281186	−	0.136789i
$247$	−8.08644	+	18.1624i	−0.514528	+	1.15565i
$248$	1.27308	+	1.14629i	0.0808408	+	0.0727894i
$249$	1.52272	−	1.81096i	0.0964984	−	0.114765i
$250$	4.46820	−	0.586173i	0.282594	−	0.0370728i
$251$	7.03498			0.444044			0.222022	−	0.975042i	$-0.428734\pi$
$251$	7.03498			0.444044			0.222022	+	0.975042i	$0.428734\pi$
$252$	−25.6979	−	0.949779i	−1.61881	−	0.0598304i
$253$	−6.78986	−	9.34544i	−0.426875	−	0.587543i
$254$	−0.159319	−	1.51581i	−0.00999653	−	0.0951106i
$255$	−0.159104	+	2.55230i	−0.00996347	+	0.159831i
$256$	−0.473203	+	4.50223i	−0.0295752	+	0.281389i
$257$	−7.02533	+	4.05608i	−0.438228	+	0.253011i	−0.702846	−	0.711342i	$-0.748088\pi$
$257$	−7.02533	+	4.05608i	−0.438228	+	0.253011i	0.264618	+	0.964353i	$0.414754\pi$
$258$	−1.51491	−	0.436062i	−0.0943139	−	0.0271480i
$259$	−10.3474	−	11.4919i	−0.642956	−	0.714075i
$260$	−19.9946	−	1.92834i	−1.24001	−	0.119590i
$261$	−22.3369	−	14.0210i	−1.38262	−	0.867876i
$262$	2.04854	+	0.665611i	0.126559	+	0.0411216i
$263$	−4.47543	+	4.02970i	−0.275967	+	0.248482i	−0.795479	−	0.605982i	$-0.792781\pi$
$263$	−4.47543	+	4.02970i	−0.275967	+	0.248482i	0.519512	+	0.854463i	$0.326114\pi$
$264$	6.63549	+	2.68877i	0.408386	+	0.165483i
$265$	11.8467	−	10.8522i	0.727736	−	0.666644i
$266$	−7.47937	+	1.58979i	−0.458590	+	0.0974762i
$267$	6.35381	−	6.12331i	0.388847	−	0.374741i
$268$	−4.22145	−	2.43725i	−0.257866	−	0.148879i
$269$	−24.6282	−	17.8934i	−1.50161	−	1.09098i	−0.969736	−	0.244157i	$-0.921489\pi$
$269$	−24.6282	−	17.8934i	−1.50161	−	1.09098i	−0.531872	−	0.846825i	$-0.678511\pi$
$270$	−4.46198	−	1.42260i	−0.271547	−	0.0865768i
$271$	−6.18082	+	4.49063i	−0.375458	+	0.272786i	−0.759471	−	0.650542i	$-0.774542\pi$
$271$	−6.18082	+	4.49063i	−0.375458	+	0.272786i	0.384012	+	0.923328i	$0.374542\pi$
$272$	2.00387	−	0.210615i	0.121503	−	0.0127704i
$273$	−39.1215	+	5.45756i	−2.36774	+	0.330307i
$274$	1.78790	+	3.09674i	0.108011	+	0.187081i
$275$	13.3597	−	0.229125i	0.805620	−	0.0138167i
$276$	8.85404	−	10.5300i	0.532950	−	0.633834i
$277$	−4.66689	+	21.9560i	−0.280406	+	1.31921i	0.582083	+	0.813130i	$0.302238\pi$
$277$	−4.66689	+	21.9560i	−0.280406	+	1.31921i	−0.862488	+	0.506077i	$0.831095\pi$
$278$	−2.22625	−	3.06417i	−0.133522	−	0.183777i
$279$	−2.38533	−	2.31289i	−0.142806	−	0.138469i
$280$	−8.18679	−	13.9032i	−0.489254	−	0.830878i
$281$	25.6939	−	11.4397i	1.53277	−	0.682434i	0.545013	−	0.838427i	$-0.316525\pi$
$281$	25.6939	−	11.4397i	1.53277	−	0.682434i	0.987758	+	0.155994i	$0.0498579\pi$
$282$	−1.05924	+	0.384310i	−0.0630767	+	0.0228853i
$283$	18.9623	+	1.99302i	1.12719	+	0.118473i	0.649719	−	0.760175i	$-0.274887\pi$
$283$	18.9623	+	1.99302i	1.12719	+	0.118473i	0.477472	+	0.878647i	$0.341553\pi$
$284$	19.2492	−	4.09154i	1.14223	−	0.242788i
$285$	15.7197	+	0.979925i	0.931155	+	0.0580457i
$286$	5.15087	+	1.09485i	0.304578	+	0.0647400i
$287$	−31.1663	−	10.1265i	−1.83969	−	0.597751i
$288$	−1.83134	+	12.8409i	−0.107913	+	0.756658i
$289$	5.11857	+	15.7533i	0.301092	+	0.926666i
$290$	−0.0679359	−	7.92294i	−0.00398934	−	0.465251i
$291$	13.5981	+	21.8110i	0.797138	+	1.27858i
$292$	−17.5686	−	1.84654i	−1.02813	−	0.108060i
$293$	23.3812	−	13.4992i	1.36595	−	0.788629i	0.375538	−	0.926807i	$-0.377458\pi$
$293$	23.3812	−	13.4992i	1.36595	−	0.788629i	0.990407	+	0.138178i	$0.0441246\pi$
$294$	−7.15098	−	7.42016i	−0.417054	−	0.432752i
$295$	3.79708	+	11.3540i	0.221075	+	0.661057i
$296$	−4.14835	+	3.01395i	−0.241118	+	0.175182i
$297$	−12.6680	−	5.68660i	−0.735075	−	0.329970i
$298$	−6.94263	+	2.25580i	−0.402176	+	0.130675i
$299$	10.5663	−	18.3015i	0.611068	−	1.05840i
$300$	4.09838	+	15.3767i	0.236620	+	0.887774i
$301$	5.26666	+	9.12211i	0.303565	+	0.525790i
$302$	0.481391	+	0.433447i	0.0277010	+	0.0249421i
$303$	17.7771	+	1.26128i	1.02127	+	0.0724587i
$304$	−1.29719	−	12.3419i	−0.0743987	−	0.707856i
$305$	2.14027	−	22.1921i	0.122551	−	1.27072i
$306$	0.796589	−	0.0540734i	0.0455380	−	0.00309117i
$307$		−	28.7446i		−	1.64054i	−0.571975	−	0.820271i	$-0.693823\pi$
$307$		−	28.7446i		−	1.64054i	0.571975	−	0.820271i	$-0.306177\pi$
$308$	−9.31700	−	20.9263i	−0.530885	−	1.19239i
$309$	−21.6143	+	0.732758i	−1.22959	+	0.0416851i
$310$	0.199157	−	0.978126i	0.0113114	−	0.0555538i
$311$	13.9302	−	15.4710i	0.789909	−	0.877282i	−0.204928	−	0.978777i	$-0.565696\pi$
$311$	13.9302	−	15.4710i	0.789909	−	0.877282i	0.994836	+	0.101495i	$0.0323625\pi$
$312$	0.443781	+	13.0903i	0.0251242	+	0.741092i
$313$	18.6907	−	16.8292i	1.05646	−	0.951240i	0.0575690	−	0.998342i	$-0.481665\pi$
$313$	18.6907	−	16.8292i	1.05646	−	0.951240i	0.998890	+	0.0471015i	$0.0149984\pi$
$314$	0.858458	+	2.64206i	0.0484456	+	0.149100i
$315$	14.8714	+	27.5332i	0.837908	+	1.55132i
$316$	−1.93599	+	5.95838i	−0.108908	+	0.335185i
$317$	−9.73795	−	21.8718i	−0.546938	−	1.22844i	−0.949707	−	0.313140i	$-0.898619\pi$
$317$	−9.73795	−	21.8718i	−0.546938	−	1.22844i	0.402769	−	0.915302i	$-0.368048\pi$
$318$	−3.83925	−	3.22818i	−0.215294	−	0.181027i
$319$	2.45561	−	23.3636i	0.137488	−	1.30811i
$320$	8.87299	−	4.04202i	0.496015	−	0.225956i
$321$	−26.9811	+	13.1256i	−1.50594	+	0.732597i
$322$	8.08325	−	0.849583i	0.450462	−	0.0473454i
$323$	−2.55374	+	0.829759i	−0.142094	+	0.0461690i
$324$	2.93805	−	16.2747i	0.163225	−	0.904151i
$325$	10.3238	+	22.1570i	0.572659	+	1.22905i
$326$	−2.07073	+	3.58661i	−0.114687	+	0.198644i
$327$	0.608556	−	0.0848954i	0.0336532	−	0.00469472i
$328$	−4.41967	+	9.92674i	−0.244035	+	0.548113i
$329$	6.87814	+	3.06234i	0.379204	+	0.168832i
$330$	−0.611796	−	4.12665i	−0.0336782	−	0.227165i
$331$	8.72890	−	3.88636i	0.479784	−	0.213614i	−0.152571	−	0.988293i	$-0.548755\pi$
$331$	8.72890	−	3.88636i	0.479784	−	0.213614i	0.632355	+	0.774679i	$0.282089\pi$
$332$			2.51015i			0.137763i
$333$	8.25607	−	5.54437i	0.452430	−	0.303829i
$334$	0.0878301	−	0.270313i	0.00480585	−	0.0147909i
$335$	0.0508601	+	5.93150i	0.00277879	+	0.324072i
$336$	19.4447	−	15.1600i	1.06080	−	0.827047i
$337$	−2.89851	−	13.6364i	−0.157892	−	0.742824i	−0.983836	−	0.179072i	$-0.942691\pi$
$337$	−2.89851	−	13.6364i	−0.157892	−	0.742824i	0.825944	−	0.563752i	$-0.190643\pi$
$338$	0.913497	+	4.29766i	0.0496877	+	0.233762i
$339$	−14.6094	+	11.3902i	−0.793474	+	0.618630i
$340$	−1.61342	−	2.18111i	−0.0874999	−	0.118287i
$341$	0.914579	−	2.81478i	0.0495272	−	0.152429i
$342$	−0.333039	−	4.90621i	−0.0180087	−	0.265298i
$343$			36.2028i			1.95477i
$344$	3.19075	−	1.42061i	0.172034	−	0.0765943i
$345$	−16.5088	−	2.78248i	−0.888802	−	0.149804i
$346$	−0.140458	−	0.0625357i	−0.00755105	−	0.00336194i
$347$	1.60634	−	3.60790i	0.0862329	−	0.193682i	−0.865282	−	0.501286i	$-0.832860\pi$
$347$	1.60634	−	3.60790i	0.0862329	−	0.193682i	0.951515	+	0.307604i	$0.0995271\pi$
$348$	27.7106	−	3.86570i	1.48544	−	0.207223i
$349$	−9.65976	+	16.7312i	−0.517075	+	0.895600i	0.482728	+	0.875770i	$0.339646\pi$
$349$	−9.65976	+	16.7312i	−0.517075	+	0.895600i	−0.999803	+	0.0198299i	$0.993688\pi$
$350$	−4.56036	+	8.22121i	−0.243762	+	0.439442i
$351$	0.0775817	−	25.4029i	0.00414100	−	1.35591i
$352$	−10.9886	+	3.57043i	−0.585697	+	0.190304i
$353$	2.81630	−	0.296005i	0.149896	−	0.0157547i	−0.0292830	−	0.999571i	$-0.509322\pi$
$353$	2.81630	−	0.296005i	0.149896	−	0.0157547i	0.179179	+	0.983816i	$0.442656\pi$
$354$	3.36128	−	1.63517i	0.178650	−	0.0869085i
$355$	−16.1759	−	17.6583i	−0.858528	−	0.937205i
$356$	−0.978549	+	9.31027i	−0.0518630	+	0.493444i
$357$	−4.08328	−	3.43337i	−0.216110	−	0.181713i
$358$	2.11992	+	4.76141i	0.112041	+	0.251648i
$359$	−2.23700	+	6.88478i	−0.118064	+	0.363365i	−0.992574	−	0.121644i	$-0.961183\pi$
$359$	−2.23700	+	6.88478i	−0.118064	+	0.363365i	0.874509	+	0.485008i	$0.161183\pi$
$360$	9.59508	−	3.94984i	0.505705	−	0.208175i
$361$	−0.760815	−	2.34155i	−0.0400429	−	0.123239i
$362$	−2.24978	+	2.02571i	−0.118246	+	0.106469i
$363$	0.226446	+	6.67952i	0.0118853	+	0.350584i
$364$	28.0405	−	31.1422i	1.46972	−	1.63229i
$365$	8.91159	+	19.5626i	0.466454	+	1.02395i
$366$	−6.95693	+	0.235851i	−0.363645	+	0.0123281i
$367$	−0.288982	−	0.649064i	−0.0150847	−	0.0338808i	0.905846	−	0.423607i	$-0.139236\pi$
$367$	−0.288982	−	0.649064i	−0.0150847	−	0.0338808i	−0.920931	+	0.389726i	$0.872570\pi$
$368$			13.1910i			0.687629i
$369$	9.27712	−	18.9230i	0.482948	−	0.985094i
$370$	2.73980	+	1.19180i	0.142436	+	0.0619586i
$371$	3.50342	+	33.3328i	0.181889	+	1.73055i
$372$	3.51604	+	0.249462i	0.182298	+	0.0129340i
$373$	15.0619	+	13.5618i	0.779876	+	0.702203i	0.959555	−	0.281522i	$-0.0908392\pi$
$373$	15.0619	+	13.5618i	0.779876	+	0.702203i	−0.179679	+	0.983725i	$0.557506\pi$
$374$	0.355608	+	0.615932i	0.0183881	+	0.0318491i
$375$	13.5934	−	13.7920i	0.701960	−	0.712216i
$376$	1.24827	−	2.16207i	0.0643746	−	0.111500i
$377$	40.8738	−	13.2807i	2.10511	−	0.683990i
$378$	7.92173	−	5.71859i	0.407450	−	0.294133i
$379$	−14.6035	+	10.6101i	−0.750134	+	0.545004i	−0.895868	−	0.444320i	$-0.853445\pi$
$379$	−14.6035	+	10.6101i	−0.750134	+	0.545004i	0.145735	+	0.989324i	$0.453445\pi$
$380$	−13.4335	+	9.93709i	−0.689123	+	0.509762i
$381$	−4.54488	−	4.71596i	−0.232841	−	0.241606i
$382$	0.391922	−	0.226276i	0.0200524	−	0.0115773i
$383$	−4.01300	−	0.421783i	−0.205055	−	0.0215521i	0.00144425	−	0.999999i	$-0.499540\pi$
$383$	−4.01300	−	0.421783i	−0.205055	−	0.0215521i	−0.206499	+	0.978447i	$0.566207\pi$
$384$	−9.53446	−	15.2929i	−0.486553	−	0.780415i
$385$	−16.1905	+	22.6909i	−0.825143	+	1.15644i
$386$	0.354432	+	1.09083i	0.0180401	+	0.0555217i
$387$	−6.28595	+	2.52481i	−0.319533	+	0.128344i
$388$	−25.9334	−	8.42627i	−1.31657	−	0.427779i
$389$	−17.9629	−	3.81814i	−0.910756	−	0.193587i	−0.271372	−	0.962475i	$-0.587477\pi$
$389$	−17.9629	−	3.81814i	−0.910756	−	0.193587i	−0.639384	+	0.768887i	$0.720811\pi$
$390$	6.44146	−	4.09307i	0.326176	−	0.207261i
$391$	2.79180	−	0.593416i	0.141188	−	0.0300104i
$392$	22.7069	+	2.38659i	1.14687	+	0.120541i
$393$	8.70087	−	3.15683i	0.438901	−	0.159241i
$394$	−0.568781	+	0.253238i	−0.0286548	+	0.0127579i
$395$	7.44334	−	1.64896i	0.374515	−	0.0829681i
$396$	14.1691	−	4.03171i	0.712022	−	0.202601i
$397$	−1.68812	−	2.32349i	−0.0847241	−	0.116613i	0.764551	−	0.644563i	$-0.222961\pi$
$397$	−1.68812	−	2.32349i	−0.0847241	−	0.116613i	−0.849275	+	0.527950i	$0.822961\pi$
$398$	1.01394	−	4.77021i	0.0508242	−	0.239109i
$399$	−21.1462	+	25.1490i	−1.05863	+	1.25903i
$400$	−12.4959	−	8.75542i	−0.624796	−	0.437771i
$401$	12.3674	+	21.4210i	0.617601	+	1.06972i	0.989922	+	0.141612i	$0.0452285\pi$
$401$	12.3674	+	21.4210i	0.617601	+	1.06972i	−0.372322	+	0.928104i	$0.621438\pi$
$402$	1.83423	−	0.255880i	0.0914830	−	0.0127621i
$403$	5.38475	−	0.565960i	0.268234	−	0.0281925i
$404$	−15.2962	+	11.1133i	−0.761013	+	0.552908i
$405$	−18.8798	+	6.96810i	−0.938143	+	0.346247i
$406$	13.3725	+	9.71569i	0.663666	+	0.482181i
$407$	7.67192	+	4.42938i	0.380283	+	0.219556i
$408$	−1.27375	+	1.22754i	−0.0630601	+	0.0607725i
$409$	−24.5223	+	5.21237i	−1.21255	+	0.257735i	−0.769432	−	0.638729i	$-0.779461\pi$
$409$	−24.5223	+	5.21237i	−1.21255	+	0.257735i	−0.443117	+	0.896464i	$0.646127\pi$
$410$	6.29095	−	0.715793i	0.310688	−	0.0353505i
$411$	14.2409	+	5.77058i	0.702454	+	0.284642i
$412$	17.0505	−	15.3524i	0.840020	−	0.756357i
$413$	−23.7536	−	7.71802i	−1.16884	−	0.379779i
$414$	−0.193056	+	5.22347i	−0.00948821	+	0.256720i
$415$	2.63214	−	1.54991i	0.129207	−	0.0760822i
$416$	−14.1436	−	15.7081i	−0.693449	−	0.770153i
$417$	−15.6404	−	4.50205i	−0.765914	−	0.220466i
$418$	3.79354	−	2.19020i	0.185548	−	0.107126i
$419$	1.42492	−	13.5572i	0.0696117	−	0.662311i	−0.902963	−	0.429719i	$-0.858613\pi$
$419$	1.42492	−	13.5572i	0.0696117	−	0.662311i	0.972574	−	0.232592i	$-0.0747206\pi$
$420$	−30.8742	−	12.2034i	−1.50651	−	0.595466i
$421$	−2.67578	−	25.4584i	−0.130410	−	1.24077i	−0.842507	−	0.538685i	$-0.818921\pi$
$421$	−2.67578	−	25.4584i	−0.130410	−	1.24077i	0.712097	−	0.702081i	$-0.247745\pi$
$422$	−1.56659	−	2.15623i	−0.0762605	−	0.104964i
$423$	−2.57422	+	4.10102i	−0.125163	+	0.199398i
$424$	11.1136			0.539725
$425$	−1.29089	+	3.03857i	−0.0626172	+	0.147392i
$426$	−4.81182	+	5.72267i	−0.233134	+	0.277264i
$427$	34.5649	+	31.1223i	1.67271	+	1.50612i
$428$	12.9471	−	29.0796i	0.625820	−	1.40561i
$429$	20.3484	−	9.89894i	0.982429	−	0.477925i
$430$	−1.65666	−	1.18207i	−0.0798914	−	0.0570043i
$431$	−19.3152	−	14.0333i	−0.930380	−	0.675961i	0.0157056	−	0.999877i	$-0.495001\pi$
$431$	−19.3152	−	14.0333i	−0.930380	−	0.675961i	−0.946086	+	0.323916i	$0.895001\pi$
$432$	7.88630	+	13.7563i	0.379430	+	0.661851i
$433$	−10.1886	+	14.0235i	−0.489635	+	0.673924i	−0.980321	−	0.197412i	$-0.936746\pi$
$433$	−10.1886	+	14.0235i	−0.489635	+	0.673924i	0.490686	+	0.871337i	$0.336746\pi$
$434$	1.39341	+	1.54754i	0.0668858	+	0.0742842i
$435$	−21.1636	−	26.6703i	−1.01472	−	1.27875i
$436$	−0.436186	+	0.484433i	−0.0208895	+	0.0232002i
$437$	−3.65487	−	17.1948i	−0.174836	−	0.822538i
$438$	5.69545	−	3.55086i	0.272139	−	0.169667i
$439$	21.4720	+	4.56401i	1.02480	+	0.217828i	0.689503	−	0.724283i	$-0.257829\pi$
$439$	21.4720	+	4.56401i	1.02480	+	0.217828i	0.335300	+	0.942112i	$0.391162\pi$
$440$	6.92162	+	6.12561i	0.329975	+	0.292027i
$441$	−43.8387	−	6.25218i	−2.08756	−	0.297723i
$442$	−0.764775	+	1.05262i	−0.0363766	+	0.0500681i
$443$	−31.3345	−	18.0910i	−1.48875	−	0.859527i	−0.488828	−	0.872380i	$-0.662575\pi$
$443$	−31.3345	−	18.0910i	−1.48875	−	0.859527i	−0.999917	+	0.0128529i	$0.995909\pi$
$444$	−2.91847	+	10.1390i	−0.138505	+	0.481174i
$445$	10.3670	−	4.72259i	0.491441	−	0.223872i
$446$	−7.50335	−	3.34071i	−0.355294	−	0.158187i
$447$	−17.5676	+	25.9879i	−0.830918	+	1.22919i
$448$	−4.22910	+	19.8964i	−0.199806	+	0.940015i
$449$	34.7150			1.63830			0.819151	−	0.573578i	$-0.194445\pi$
$449$	34.7150			1.63830			0.819151	+	0.573578i	$0.194445\pi$
$450$	−4.82008	−	3.64991i	−0.227221	−	0.172059i
$451$	18.7729			0.883983
$452$	4.08610	−	19.2236i	0.192194	−	0.904201i
$453$	2.77659	+	0.196999i	0.130456	+	0.00925582i
$454$	2.92078	+	1.30042i	0.137079	+	0.0610316i
$455$	−49.9695	−	10.1743i	−2.34260	−	0.476980i
$456$	7.56048	+	7.84507i	0.354052	+	0.367379i
$457$	−10.3841	−	5.99527i	−0.485748	−	0.280447i	0.237061	−	0.971495i	$-0.423816\pi$
$457$	−10.3841	−	5.99527i	−0.485748	−	0.280447i	−0.722809	+	0.691048i	$0.757149\pi$
$458$	−0.152261	+	0.209570i	−0.00711470	+	0.00979255i
$459$	2.55667	−	2.28794i	0.119335	−	0.106792i
$460$	15.3049	−	9.01215i	0.713596	−	0.420194i
$461$	−28.1330	−	5.97985i	−1.31028	−	0.278509i	−0.500755	−	0.865589i	$-0.666944\pi$
$461$	−28.1330	−	5.97985i	−1.31028	−	0.278509i	−0.809529	+	0.587080i	$0.800278\pi$
$462$	7.68017	+	4.09365i	0.357314	+	0.190454i
$463$	4.87838	+	22.9510i	0.226717	+	1.06662i	0.933330	+	0.359020i	$0.116889\pi$
$463$	4.87838	+	22.9510i	0.226717	+	1.06662i	−0.706612	+	0.707601i	$0.749778\pi$
$464$	−17.9503	+	19.9359i	−0.833323	+	0.925499i
$465$	−1.90941	−	3.84094i	−0.0885470	−	0.178119i
$466$	−6.68164	−	7.42071i	−0.309521	−	0.343758i
$467$	−21.1565	+	29.1194i	−0.979005	+	1.34748i	−0.0416409	+	0.999133i	$0.513259\pi$
$467$	−21.1565	+	29.1194i	−0.979005	+	1.34748i	−0.937364	+	0.348352i	$0.886741\pi$
$468$	17.2811	+	20.6802i	0.798819	+	0.955941i
$469$	−10.0113	−	7.27363i	−0.462279	−	0.335865i
$470$	−1.45464	+	0.0124729i	−0.0670975	+	0.000575333i
$471$	9.88986	+	6.68545i	0.455701	+	0.308050i
$472$	−3.36848	+	7.56574i	−0.155047	+	0.348241i
$473$	−4.48427	−	4.03765i	−0.206187	−	0.185652i
$474$	−0.811829	−	2.23757i	−0.0372886	−	0.102775i
$475$	18.7146	+	7.95061i	0.858685	+	0.364799i
$476$	5.65980			0.259417
$477$	−21.5400	−	0.796106i	−0.986248	−	0.0364512i
$478$	1.14004	+	1.56913i	0.0521441	+	0.0717702i
$479$	1.66485	+	15.8400i	0.0760690	+	0.723748i	0.964383	+	0.264511i	$0.0852105\pi$
$479$	1.66485	+	15.8400i	0.0760690	+	0.723748i	−0.888314	+	0.459237i	$0.848123\pi$
$480$	−7.74949	+	14.8442i	−0.353714	+	0.677542i
$481$	−1.69403	+	16.1176i	−0.0772410	+	0.734899i
$482$	3.31710	−	1.91513i	0.151090	−	0.0872316i
$483$	25.1484	−	24.2361i	1.14429	−	1.10278i
$484$	−4.74438	−	5.26917i	−0.215654	−	0.239508i
$485$	7.17697	+	32.3966i	0.325889	+	1.47105i
$486$	2.92154	+	5.56274i	0.132524	+	0.252331i
$487$	−17.7128	−	5.75525i	−0.802645	−	0.260795i	−0.121166	−	0.992632i	$-0.538663\pi$
$487$	−17.7128	−	5.75525i	−0.802645	−	0.260795i	−0.681480	+	0.731837i	$0.738663\pi$
$488$	11.4613	−	10.3198i	0.518827	−	0.467154i
$489$	2.45884	+	17.6257i	0.111192	+	0.797062i
$490$	−5.51517	−	12.1068i	−0.249150	−	0.546930i
$491$	38.5010	−	8.18364i	1.73752	−	0.369322i	0.773224	−	0.634133i	$-0.218643\pi$
$491$	38.5010	−	8.18364i	1.73752	−	0.369322i	0.964300	+	0.264810i	$0.0853094\pi$
$492$	5.38686	+	21.6996i	0.242858	+	0.978293i
$493$	5.02683	+	2.90224i	0.226397	+	0.130710i
$494$	6.48312	+	4.71027i	0.291690	+	0.211925i
$495$	−12.9764	−	12.3683i	−0.583247	−	0.555912i
$496$	−2.73421	+	1.98652i	−0.122770	+	0.0891975i
$497$	49.6849	−	5.22209i	2.22867	−	0.234243i
$498$	−0.586387	−	0.752118i	−0.0262766	−	0.0337032i
$499$	12.0416	+	20.8566i	0.539054	+	0.933669i	0.998955	+	0.0456988i	$0.0145515\pi$
$499$	12.0416	+	20.8566i	0.539054	+	0.933669i	−0.459901	+	0.887970i	$0.652115\pi$
$500$	−1.62124	+	20.4802i	−0.0725040	+	0.915901i
$501$	−0.416557	−	1.14812i	−0.0186104	−	0.0512940i
$502$	0.589555	−	2.77364i	0.0263131	−	0.123794i
$503$	−5.34452	−	7.35611i	−0.238301	−	0.327993i	0.673070	−	0.739578i	$-0.264975\pi$
$503$	−5.34452	−	7.35611i	−0.238301	−	0.327993i	−0.911371	+	0.411586i	$0.864975\pi$
$504$	−5.27958	+	20.9931i	−0.235171	+	0.935106i
$505$	21.0981	+	9.17755i	0.938854	+	0.408395i
$506$	−4.25358	+	1.89382i	−0.189095	+	0.0841905i
$507$	14.4507	+	12.1507i	0.641778	+	0.539630i
$508$	6.91033	+	0.726304i	0.306596	+	0.0322245i
$509$	1.98502	−	0.421929i	0.0879845	−	0.0187017i	−0.163709	−	0.986509i	$-0.552346\pi$
$509$	1.98502	−	0.421929i	0.0879845	−	0.0187017i	0.251694	+	0.967807i	$0.419012\pi$
$510$	0.992948	+	0.276621i	0.0439685	+	0.0122490i
$511$	−43.8662	−	9.32405i	−1.94053	−	0.412472i
$512$	21.5265	+	6.99440i	0.951347	+	0.309112i
$513$	−14.0915	−	15.7466i	−0.622153	−	0.695229i
$514$	1.01042	+	3.10975i	0.0445676	+	0.137165i
$515$	−26.6264	−	8.39974i	−1.17330	−	0.370137i
$516$	3.38036	−	6.34195i	0.148812	−	0.279189i
$517$	−4.28952	−	0.450846i	−0.188653	−	0.0198282i
$518$	−5.39801	+	3.11654i	−0.237175	+	0.136933i
$519$	−0.641220	+	0.159181i	−0.0281464	+	0.00698727i
$520$	−5.08715	+	16.1258i	−0.223086	+	0.707164i
$521$	−1.22226	+	0.888024i	−0.0535482	+	0.0389050i	−0.614237	−	0.789121i	$-0.710536\pi$
$521$	−1.22226	+	0.888024i	−0.0535482	+	0.0389050i	0.560689	+	0.828026i	$0.310536\pi$
$522$	−7.39987	+	7.63163i	−0.323883	+	0.334027i
$523$	0.0869563	−	0.0282538i	0.00380233	−	0.00123545i	−0.307115	−	0.951672i	$-0.599364\pi$
$523$	0.0869563	−	0.0282538i	0.00380233	−	0.00123545i	0.310918	+	0.950437i	$0.399364\pi$
$524$	−4.90976	+	8.50396i	−0.214484	+	0.371497i
$525$	6.26698	+	39.9097i	0.273513	+	1.74180i
$526$	1.21371	+	2.10220i	0.0529202	+	0.0916604i
$527$	0.543439	+	0.489314i	0.0236726	+	0.0213149i
$528$	−7.91032	+	11.7018i	−0.344253	+	0.509256i
$529$	−0.450994	−	4.29092i	−0.0196085	−	0.186562i
$530$	−3.28583	−	5.58017i	−0.142727	−	0.242387i
$531$	7.07063	−	14.4223i	0.306839	−	0.625876i
$532$		−	34.8589i		−	1.51132i
$533$	13.9688	+	31.3744i	0.605055	+	1.35898i
$534$	−1.88173	−	3.01823i	−0.0814305	−	0.130612i
$535$	−38.4870	+	4.37911i	−1.66394	+	0.189325i
$536$	−2.74562	+	3.04932i	−0.118593	+	0.131711i
$537$	19.7644	+	10.5347i	0.852895	+	0.454607i
$538$	−9.11866	+	8.21048i	−0.393133	+	0.353979i
$539$	−12.1894	−	37.5151i	−0.525034	−	1.61589i
$540$	10.5729	−	18.5485i	0.454984	−	0.798199i
$541$	1.62629	−	5.00522i	0.0699198	−	0.215191i	−0.909991	−	0.414629i	$-0.863911\pi$
$541$	1.62629	−	5.00522i	0.0699198	−	0.215191i	0.979911	+	0.199438i	$0.0639115\pi$
$542$	1.25252	+	2.81321i	0.0538003	+	0.120838i
$543$	−2.27203	+	12.8091i	−0.0975021	+	0.549689i
$544$	0.298408	−	2.83916i	0.0127941	−	0.121728i
$545$	0.777302	+	0.158267i	0.0332960	+	0.00677942i
$546$	−1.12680	+	15.8816i	−0.0482224	+	0.679668i
$547$	33.8483	−	3.55760i	1.44725	−	0.152112i	0.651918	−	0.758289i	$-0.273964\pi$
$547$	33.8483	−	3.55760i	1.44725	−	0.152112i	0.795330	+	0.606177i	$0.207298\pi$
$548$	−15.5036	+	5.03742i	−0.662281	+	0.215188i
$549$	−22.9530	+	19.1804i	−0.979611	+	0.818598i
$550$	1.02925	−	5.28645i	0.0438875	−	0.225415i
$551$	17.8750	−	30.9604i	0.761500	−	1.31896i
$552$	−7.12070	−	9.13323i	−0.303077	−	0.388736i
$553$	−6.46900	+	14.5296i	−0.275090	+	0.617862i
$554$	8.26535	+	3.67997i	0.351161	+	0.156347i
$555$	12.4337	−	3.20006i	0.527782	−	0.135835i
$556$	15.7739	−	7.02298i	0.668961	−	0.297841i
$557$			40.7325i			1.72589i	0.505297	+	0.862946i	$0.331383\pi$
$557$			40.7325i			1.72589i	−0.505297	+	0.862946i	$0.668617\pi$
$558$	−1.11179	+	0.746620i	−0.0470657	+	0.0316070i
$559$	3.41125	−	10.4987i	0.144280	−	0.444049i
$560$	30.1875	−	10.0955i	1.27566	−	0.426613i
$561$	2.83248	+	1.14775i	0.119587	+	0.0484581i
$562$	−2.35701	−	11.0889i	−0.0994246	−	0.467756i
$563$	2.65425	+	12.4873i	0.111863	+	0.526276i	0.998020	+	0.0628910i	$0.0200321\pi$
$563$	2.65425	+	12.4873i	0.111863	+	0.526276i	−0.886157	+	0.463385i	$0.846635\pi$
$564$	−0.709736	−	5.08761i	−0.0298853	−	0.214227i
$565$	−22.6808	+	7.58505i	−0.954189	+	0.319106i
$566$	2.37488	−	7.30912i	0.0998236	−	0.307225i
$567$	11.7365	−	40.3098i	0.492886	−	1.69285i
$568$		−	16.5656i		−	0.695077i
$569$	−14.6555	+	6.52506i	−0.614392	+	0.273545i	−0.690247	−	0.723574i	$-0.742498\pi$
$569$	−14.6555	+	6.52506i	−0.614392	+	0.273545i	0.0758549	+	0.997119i	$0.475831\pi$
$570$	1.70371	−	6.11559i	0.0713607	−	0.256154i
$571$	−42.0032	−	18.7010i	−1.75778	−	0.782614i	−0.989857	−	0.142070i	$-0.954624\pi$
$571$	−42.0032	−	18.7010i	−1.75778	−	0.782614i	−0.767922	−	0.640543i	$-0.778709\pi$
$572$	−9.76433	+	21.9310i	−0.408267	+	0.916983i
$573$	0.730322	−	1.80233i	0.0305097	−	0.0752933i
$574$	−6.60437	+	11.4391i	−0.275661	+	0.477459i
$575$	−18.9003	−	10.4841i	−0.788195	−	0.437217i
$576$	−12.2833	−	4.49911i	−0.511806	−	0.187463i
$577$	−21.5727	+	7.00940i	−0.898084	+	0.291805i	−0.721446	−	0.692471i	$-0.756522\pi$
$577$	−21.5727	+	7.00940i	−0.898084	+	0.291805i	−0.176638	+	0.984276i	$0.556522\pi$
$578$	6.63992	−	0.697884i	0.276184	−	0.0290281i
$579$	4.08323	+	2.76022i	0.169693	+	0.114711i
$580$	35.3944	+	7.20668i	1.46967	+	0.299241i
$581$	−0.666096	+	6.33748i	−0.0276343	+	0.262923i
$582$	9.73885	−	3.53343i	0.403688	−	0.146465i
$583$	−7.80952	−	17.5405i	−0.323437	−	0.726452i
$584$	−4.59521	+	14.1426i	−0.190151	+	0.585226i
$585$	11.0149	−	30.8900i	0.455409	−	1.27715i
$586$	−3.36280	−	10.3496i	−0.138916	−	0.427540i
$587$	−11.4257	+	10.2877i	−0.471589	+	0.424621i	−0.870350	−	0.492434i	$-0.836107\pi$
$587$	−11.4257	+	10.2877i	−0.471589	+	0.424621i	0.398761	+	0.917055i	$0.369440\pi$
$588$	39.8659	−	24.8546i	1.64404	−	1.02499i
$589$	3.01370	−	3.34705i	0.124177	−	0.137913i
$590$	4.79469	−	0.545547i	0.197394	−	0.0224598i
$591$	−1.25844	+	2.36098i	−0.0517653	+	0.0971178i
$592$	−4.11455	−	9.24144i	−0.169107	−	0.379821i
$593$			32.8164i			1.34761i	0.738909	+	0.673805i	$0.235341\pi$
$593$			32.8164i			1.34761i	−0.738909	+	0.673805i	$0.764659\pi$
$594$	−3.30365	+	4.51800i	−0.135550	+	0.185376i
$595$	−3.49468	−	5.93486i	−0.143268	−	0.243306i
$596$	−3.47860	−	33.0967i	−0.142489	−	1.35569i
$597$	−9.16739	−	18.8446i	−0.375196	−	0.771258i
$598$	−6.33011	−	5.69965i	−0.258857	−	0.233076i
$599$	6.66854	+	11.5503i	0.272469	+	0.471931i	0.969494	−	0.245117i	$-0.0788264\pi$
$599$	6.66854	+	11.5503i	0.272469	+	0.471931i	−0.697024	+	0.717048i	$0.745493\pi$
$600$	13.3783	−	0.683384i	0.546165	−	0.0278990i
$601$	−3.22848	+	5.59189i	−0.131692	+	0.228098i	−0.924329	−	0.381596i	$-0.875374\pi$
$601$	−3.22848	+	5.59189i	−0.131692	+	0.228098i	0.792637	+	0.609694i	$0.208708\pi$
$602$	4.03788	−	1.31199i	0.164572	−	0.0534726i
$603$	5.53990	−	5.71341i	0.225602	−	0.232668i
$604$	−2.38910	+	1.73579i	−0.0972112	+	0.0706281i
$605$	−2.59579	+	8.22844i	−0.105534	+	0.334534i
$606$	1.98706	−	6.90316i	0.0807186	−	0.280422i
$607$	31.8170	−	18.3695i	1.29141	−	0.745596i	0.312506	−	0.949916i	$-0.398832\pi$
$607$	31.8170	−	18.3695i	1.29141	−	0.745596i	0.978904	+	0.204320i	$0.0654982\pi$
$608$	−17.4865	−	1.83790i	−0.709170	−	0.0745368i
$609$	70.9877	−	2.40659i	2.87657	−	0.0975201i
$610$	−8.57019	−	2.70360i	−0.346997	−	0.109466i
$611$	−2.43831	−	7.50435i	−0.0986435	−	0.303593i
$612$	−0.513909	+	3.60340i	−0.0207735	+	0.145659i
$613$	27.5726	+	8.95887i	1.11365	+	0.361846i	0.807339	−	0.590087i	$-0.200907\pi$
$613$	27.5726	+	8.95887i	1.11365	+	0.361846i	0.306307	+	0.951933i	$0.400907\pi$
$614$	−11.3330	−	2.40890i	−0.457361	−	0.0972151i
$615$	19.4280	−	19.0472i	0.783413	−	0.768058i
$616$	−18.8611	+	4.00905i	−0.759935	+	0.161529i
$617$	11.2936	+	1.18701i	0.454664	+	0.0477871i	0.329093	−	0.944298i	$-0.393257\pi$
$617$	11.2936	+	1.18701i	0.454664	+	0.0477871i	0.125571	+	0.992085i	$0.459924\pi$
$618$	−1.52245	+	8.58314i	−0.0612419	+	0.345264i
$619$	−23.5361	+	10.4789i	−0.945994	+	0.421184i	−0.820971	−	0.570970i	$-0.806567\pi$
$619$	−23.5361	+	10.4789i	−0.945994	+	0.421184i	−0.125023	+	0.992154i	$0.539901\pi$
$620$	4.17289	+	1.81518i	0.167587	+	0.0728994i
$621$	13.1468	+	18.2118i	0.527564	+	0.730812i
$622$	−4.93228	−	6.78870i	−0.197766	−	0.272202i
$623$	−4.94116	+	23.2463i	−0.197963	+	0.931345i
$624$	−25.4427	−	4.51295i	−1.01852	−	0.180663i
$625$	22.4765	−	10.9456i	0.899061	−	0.437824i
$626$	−5.06879	−	8.77940i	−0.202589	−	0.350895i
$627$	7.06903	−	17.4453i	0.282310	−	0.696699i
$628$	−12.5952	+	1.32380i	−0.502601	+	0.0528255i
$629$	−1.77080	+	1.28656i	−0.0706064	+	0.0512986i
$630$	12.1016	−	3.55588i	0.482140	−	0.141669i
$631$	−13.7657	−	10.0014i	−0.548004	−	0.398148i	0.279045	−	0.960278i	$-0.409982\pi$
$631$	−13.7657	−	10.0014i	−0.548004	−	0.398148i	−0.827049	+	0.562130i	$0.809982\pi$
$632$	4.56722	+	2.63688i	0.181674	+	0.104890i
$633$	−11.0060	−	3.16805i	−0.437450	−	0.125919i
$634$	−9.43933	+	2.00639i	−0.374884	+	0.0796840i
$635$	−3.50522	−	7.69462i	−0.139101	−	0.305352i
$636$	18.0341	−	14.0602i	0.715097	−	0.557524i
$637$	53.6273	−	48.2862i	2.12479	−	1.91317i
$638$	−9.00564	−	2.92611i	−0.356537	−	0.115846i
$639$	−1.18665	+	32.1068i	−0.0469431	+	1.27013i
$640$	−5.03220	−	22.7151i	−0.198915	−	0.897895i
$641$	15.9546	+	17.7193i	0.630167	+	0.699872i	0.970682	−	0.240367i	$-0.0772679\pi$
$641$	15.9546	+	17.7193i	0.630167	+	0.699872i	−0.340515	+	0.940239i	$0.610601\pi$
$642$	2.91383	+	11.7376i	0.115000	+	0.463247i
$643$	8.90132	−	5.13918i	0.351034	−	0.202670i	−0.314107	−	0.949388i	$-0.601705\pi$
$643$	8.90132	−	5.13918i	0.351034	−	0.202670i	0.665141	+	0.746718i	$0.268372\pi$
$644$	−3.87310	+	36.8501i	−0.152621	+	1.45210i
$645$	−8.73739	+	0.371238i	−0.344034	+	0.0146175i
$646$	0.113132	+	1.07638i	0.00445113	+	0.0423497i
$647$	−3.54997	−	4.88611i	−0.139564	−	0.192093i	0.733514	−	0.679675i	$-0.237879\pi$
$647$	−3.54997	−	4.88611i	−0.139564	−	0.192093i	−0.873077	+	0.487582i	$0.837879\pi$
$648$	−12.8862	−	5.26750i	−0.506217	−	0.206927i
$649$	14.3079			0.561635
$650$	9.60086	−	2.21345i	0.376577	−	0.0868188i
$651$	8.81088	+	1.56285i	0.345326	+	0.0612527i
$652$	−14.0307	−	12.6333i	−0.549485	−	0.494759i
$653$	0.376469	−	0.845563i	0.0147324	−	0.0330894i	−0.906029	−	0.423215i	$-0.860902\pi$
$653$	0.376469	−	0.845563i	0.0147324	−	0.0330894i	0.920762	+	0.390125i	$0.127568\pi$
$654$	0.0175279	−	0.247046i	0.000685395	−	0.00966028i
$655$	11.9488	−	0.102456i	0.466878	−	0.00400329i
$656$	−17.3431	−	12.6005i	−0.677133	−	0.491966i
$657$	9.91935	−	27.0815i	0.386991	−	1.05655i
$658$	1.78378	−	2.45517i	0.0695391	−	0.0957123i
$659$	29.1983	+	32.4280i	1.13740	+	1.26321i	0.960284	+	0.279025i	$0.0900113\pi$
$659$	29.1983	+	32.4280i	1.13740	+	1.26321i	0.177120	+	0.984189i	$0.443322\pi$
$660$	18.9814	+	1.18325i	0.738852	+	0.0460581i
$661$	−27.2373	+	30.2501i	−1.05941	+	1.17659i	−0.0756439	+	0.997135i	$0.524101\pi$
$661$	−27.2373	+	30.2501i	−1.05941	+	1.17659i	−0.983766	+	0.179459i	$0.942565\pi$
$662$	−0.800739	−	3.76718i	−0.0311216	−	0.146416i
$663$	0.189436	+	5.58783i	0.00735709	+	0.217013i
$664$	2.06683	+	0.439318i	0.0802085	+	0.0170488i
$665$	−36.5529	+	21.5238i	−1.41746	+	0.834658i
$666$	−1.49406	−	3.71971i	−0.0578935	−	0.144136i
$667$	−22.3360	+	30.7429i	−0.864853	+	1.19037i
$668$	1.12213	+	0.647863i	0.0434166	+	0.0250666i
$669$	−34.2545	+	8.50357i	−1.32435	+	0.328767i
$670$	2.34284	+	0.477027i	0.0905117	+	0.0184292i
$671$	−24.3414	−	10.8375i	−0.939688	−	0.418376i
$672$	−15.2820	−	31.4138i	−0.589515	−	1.21181i
$673$	0.159691	−	0.751285i	0.00615562	−	0.0289599i	−0.974963	−	0.222369i	$-0.928621\pi$
$673$	0.159691	−	0.751285i	0.00615562	−	0.0289599i	0.981118	+	0.193409i	$0.0619544\pi$
$674$	−5.61926			−0.216446
$675$	−25.9782	+	0.366179i	−0.999901	+	0.0140942i
$676$	−20.0300			−0.770384
$677$	5.68282	−	26.7356i	0.218409	−	1.02753i	−0.723152	−	0.690689i	$-0.757307\pi$
$677$	5.68282	−	26.7356i	0.218409	−	1.02753i	0.941561	−	0.336843i	$-0.109359\pi$
$678$	3.26642	+	6.71450i	0.125446	+	0.257869i
$679$	−63.2390	−	28.1558i	−2.42689	−	1.08052i
$680$	−2.07827	+	0.946739i	−0.0796980	+	0.0363058i
$681$	13.3340	−	3.31013i	0.510961	−	0.126845i
$682$	−1.03312	−	0.596474i	−0.0395603	−	0.0228402i
$683$	−1.63289	+	2.24748i	−0.0624809	+	0.0859975i	−0.839114	−	0.543956i	$-0.816926\pi$
$683$	−1.63289	+	2.24748i	−0.0624809	+	0.0859975i	0.776633	+	0.629953i	$0.216926\pi$
$684$	22.1934	+	3.16518i	0.848588	+	0.121024i
$685$	14.8550	+	13.1467i	0.567582	+	0.502308i
$686$	14.2735	+	3.03392i	0.544963	+	0.115836i
$687$	0.0377154	+	1.11250i	0.00143893	+	0.0424445i
$688$	1.43263	+	6.73998i	0.0546184	+	0.256959i
$689$	23.5036	−	26.1034i	0.895417	−	0.994461i
$690$	−2.48052	+	6.27563i	−0.0944319	+	0.238909i
$691$	22.6931	+	25.2032i	0.863285	+	0.958775i	0.999491	−	0.0319058i	$-0.0101577\pi$
$691$	22.6931	+	25.2032i	0.863285	+	0.958775i	−0.136206	+	0.990681i	$0.543491\pi$
$692$	0.411990	−	0.567055i	0.0156615	−	0.0215562i
$693$	36.8430	−	6.41910i	1.39955	−	0.243842i
$694$	−1.28785	−	0.935677i	−0.0488861	−	0.0355178i
$695$	−17.1040	−	12.2041i	−0.648790	−	0.462927i
$696$	1.66683	−	23.4931i	0.0631811	−	0.890503i
$697$	−1.88662	+	4.23741i	−0.0714608	+	0.160503i
$698$	5.78698	+	5.21062i	0.219041	+	0.197225i
$699$	−42.2497	−	7.49411i	−1.59803	−	0.283453i
$700$	−32.3376	−	28.1279i	−1.22224	−	1.06313i
$701$	−2.42588			−0.0916243			−0.0458121	−	0.998950i	$-0.514588\pi$
$701$	−2.42588			−0.0916243			−0.0458121	+	0.998950i	$0.514588\pi$
$702$	−10.0089	−	2.15944i	−0.377763	−	0.0815026i
$703$	7.92396	+	10.9064i	0.298858	+	0.411343i
$704$	−1.21803	−	11.5888i	−0.0459062	−	0.436768i
$705$	−4.89663	+	3.88561i	−0.184418	+	0.146340i
$706$	0.119311	−	1.13517i	0.00449034	−	0.0427227i
$707$	−41.5679	+	23.9992i	−1.56332	+	0.902583i
$708$	4.10563	+	16.5385i	0.154299	+	0.621555i
$709$	−19.3533	−	21.4940i	−0.726827	−	0.807223i	0.260575	−	0.965454i	$-0.416088\pi$
$709$	−19.3533	−	21.4940i	−0.726827	−	0.807223i	−0.987402	+	0.158230i	$0.949421\pi$
$710$	−8.31763	+	4.89775i	−0.312155	+	0.183809i
$711$	−8.66312	−	5.43788i	−0.324892	−	0.203936i
$712$	7.49470	+	2.43517i	0.280876	+	0.0912620i
$713$	−3.55773	+	3.20340i	−0.133238	+	0.119968i
$714$	−1.69585	+	1.32216i	−0.0634655	+	0.0494807i
$715$	29.0259	−	3.30261i	1.08551	−	0.123510i
$716$	−23.2414	+	4.94011i	−0.868572	+	0.184621i
$717$	8.00927	+	2.30545i	0.299112	+	0.0860986i
$718$	2.52695	+	1.45894i	0.0943050	+	0.0544470i
$719$	41.6638	+	30.2705i	1.55380	+	1.12890i	0.940873	+	0.338761i	$0.110008\pi$
$719$	41.6638	+	30.2705i	1.55380	+	1.12890i	0.612926	+	0.790140i	$0.289992\pi$
$720$	3.68644	+	20.1360i	0.137385	+	0.750426i
$721$	47.1221	−	34.2362i	1.75492	−	1.27502i
$722$	−0.986947	+	0.103732i	−0.0367304	+	0.00386052i
$723$	6.18121	−	15.2543i	0.229882	−	0.567314i
$724$	−6.90062	−	11.9522i	−0.256460	−	0.444201i
$725$	−14.2976	−	41.5643i	−0.530999	−	1.54366i
$726$	2.65247	+	0.470487i	0.0984424	+	0.0174614i
$727$	1.69425	−	7.97084i	0.0628364	−	0.295622i	−0.935497	−	0.353335i	$-0.885048\pi$
$727$	1.69425	−	7.97084i	0.0628364	−	0.295622i	0.998333	+	0.0577131i	$0.0183809\pi$
$728$	−20.7345	−	28.5386i	−0.768472	−	1.05771i
$729$	24.5982	+	11.1323i	0.911044	+	0.412309i
$730$	8.45965	−	1.87411i	0.313106	−	0.0693638i
$731$	1.36203	−	0.606415i	0.0503765	−	0.0224291i
$732$	5.54230	−	31.2459i	0.204849	−	1.15488i
$733$	2.66219	+	0.279808i	0.0983304	+	0.0103349i	0.153566	−	0.988138i	$-0.450924\pi$
$733$	2.66219	+	0.279808i	0.0983304	+	0.0103349i	−0.0552355	+	0.998473i	$0.517591\pi$
$734$	−0.280120	+	0.0595413i	−0.0103394	+	0.00219771i
$735$	−50.6779	−	26.4567i	−1.86928	−	0.975869i
$736$	18.2811	+	3.88578i	0.673852	+	0.143232i
$737$	6.74206	+	2.19063i	0.248347	+	0.0806928i
$738$	−6.68322	−	5.24345i	−0.246013	−	0.193014i
$739$	−13.1689	−	40.5297i	−0.484426	−	1.49091i	−0.832811	−	0.553557i	$-0.813270\pi$
$739$	−13.1689	−	40.5297i	−0.484426	−	1.49091i	0.348385	−	0.937351i	$-0.386730\pi$
$740$	−7.91133	+	11.0877i	−0.290826	+	0.407592i
$741$	34.4156	−	1.16674i	1.26429	−	0.0428613i
$742$	13.4355	+	1.41213i	0.493234	+	0.0518410i
$743$	18.4359	−	10.6440i	0.676347	−	0.390489i	−0.122130	−	0.992514i	$-0.538973\pi$
$743$	18.4359	−	10.6440i	0.676347	−	0.390489i	0.798477	+	0.602025i	$0.205639\pi$
$744$	0.820768	−	2.85140i	0.0300908	−	0.104537i
$745$	−32.5573	+	24.0834i	−1.19281	+	0.882349i
$746$	6.60917	−	4.80184i	0.241979	−	0.175808i
$747$	−3.97438	−	0.999523i	−0.145415	−	0.0365706i
$748$	−3.08362	+	1.00193i	−0.112748	+	0.0366342i
$749$	40.4045	−	69.9827i	1.47635	−	2.55711i
$750$	−4.29852	−	6.51521i	−0.156960	−	0.237902i
$751$	−7.90783	−	13.6968i	−0.288561	−	0.499802i	0.684906	−	0.728632i	$-0.259843\pi$
$751$	−7.90783	−	13.6968i	−0.288561	−	0.499802i	−0.973466	+	0.228830i	$0.926510\pi$
$752$	3.66019	+	3.29565i	0.133473	+	0.120180i
$753$	−5.33038	−	10.9572i	−0.194250	−	0.399302i
$754$	−1.81074	−	17.2280i	−0.0659432	−	0.627407i
$755$	3.29531	+	1.43344i	0.119929	+	0.0521681i
$756$	17.9919	+	40.7448i	0.654358	+	1.48188i
$757$			50.3254i			1.82911i	0.404464	+	0.914554i	$0.367458\pi$
$757$			50.3254i			1.82911i	−0.404464	+	0.914554i	$0.632542\pi$
$758$	2.95935	+	6.64681i	0.107489	+	0.241423i
$759$	−9.41115	+	17.6564i	−0.341603	+	0.640887i
$760$	5.83099	+	12.8001i	0.211512	+	0.464309i
$761$	9.32321	−	10.3545i	0.337966	−	0.375350i	−0.550073	−	0.835116i	$-0.685400\pi$
$761$	9.32321	−	10.3545i	0.337966	−	0.375350i	0.888040	+	0.459767i	$0.152067\pi$
$762$	−2.24021	+	1.39667i	−0.0811542	+	0.0505960i
$763$	−1.22980	+	1.10732i	−0.0445219	+	0.0400877i
$764$	0.637534	+	1.96213i	0.0230652	+	0.0709873i
$765$	4.09584	−	1.68606i	0.148085	−	0.0609597i
$766$	−0.502596	+	1.54683i	−0.0181595	+	0.0558893i
$767$	10.6464	+	23.9122i	0.384419	+	0.863420i
$768$	7.37090	−	2.67429i	0.265974	−	0.0965002i
$769$	0.290989	−	2.76858i	0.0104933	−	0.0998374i	−0.988022	−	0.154315i	$-0.950683\pi$
$769$	0.290989	−	2.76858i	0.0104933	−	0.0998374i	0.998515	+	0.0544780i	$0.0173495\pi$
$770$	7.58938	+	8.28489i	0.273502	+	0.298567i
$771$	11.6405	+	7.86888i	0.419223	+	0.283391i
$772$	−5.20016	+	0.546559i	−0.187158	+	0.0196711i
$773$	11.4468	−	3.71930i	0.411713	−	0.133774i	−0.0958346	−	0.995397i	$-0.530552\pi$
$773$	11.4468	−	3.71930i	0.411713	−	0.133774i	0.507548	+	0.861623i	$0.330552\pi$
$774$	0.468659	+	2.68991i	0.0168456	+	0.0966869i
$775$	−0.673184	−	5.49648i	−0.0241815	−	0.197440i
$776$	−11.4768	+	19.8785i	−0.411995	+	0.713596i
$777$	−10.0589	+	24.8238i	−0.360860	+	0.890548i
$778$	−3.01071	+	6.76216i	−0.107939	+	0.242435i
$779$	26.0983	+	11.6197i	0.935070	+	0.416320i
$780$	12.1464	+	32.6033i	0.434911	+	1.16738i
$781$	−26.1453	+	11.6406i	−0.935552	+	0.416534i
$782$		−	1.15044i		−	0.0411396i
$783$	−4.91348	+	45.4140i	−0.175593	+	1.62296i
$784$	−13.9193	+	42.8393i	−0.497119	+	1.52997i
$785$	9.16510	+	12.3899i	0.327116	+	0.442213i
$786$	−0.515462	−	3.69499i	−0.0183859	−	0.131796i
$787$	3.38963	+	15.9470i	0.120827	+	0.568447i	0.996357	+	0.0852829i	$0.0271794\pi$
$787$	3.38963	+	15.9470i	0.120827	+	0.568447i	−0.875530	+	0.483165i	$0.839487\pi$
$788$	−0.590128	−	2.77634i	−0.0210225	−	0.0989029i
$789$	9.66739	+	3.91733i	0.344168	+	0.139461i
$790$	−0.0263482	−	3.07283i	−0.000937427	−	0.109326i
$791$	15.4175	−	47.4502i	0.548184	−	1.68714i
$792$	−0.839841	−	12.3722i	−0.0298425	−	0.439628i
$793$		−	48.7447i		−	1.73097i
$794$	−1.05754	+	0.470847i	−0.0375306	+	0.0167097i
$795$	−25.8788	−	10.2289i	−0.917825	−	0.362782i
$796$	20.3103	+	9.04272i	0.719879	+	0.320511i
$797$	−10.5447	+	23.6838i	−0.373512	+	0.838922i	0.624797	+	0.780787i	$0.285182\pi$
$797$	−10.5447	+	23.6838i	−0.373512	+	0.838922i	−0.998309	+	0.0581344i	$0.981485\pi$
$798$	8.14323	+	10.4448i	0.288267	+	0.369741i
$799$	0.532847	−	0.922918i	0.0188508	−	0.0326505i
$800$	−15.8150	+	14.7387i	−0.559143	+	0.521091i
$801$	−14.3515	−	5.25663i	−0.507085	−	0.185734i
$802$	9.48198	−	3.08088i	0.334820	−	0.108790i
$803$	25.5502	−	2.68543i	0.901645	−	0.0947667i
$804$	−0.597520	+	8.42172i	−0.0210729	+	0.297011i
$805$	41.0324	−	18.6920i	1.44620	−	0.658806i
$806$	0.228123	−	2.17044i	0.00803528	−	0.0764506i
$807$	−9.20886	+	51.9169i	−0.324167	+	1.82756i
$808$	6.47348	+	14.5397i	0.227736	+	0.511504i
$809$	15.8564	−	48.8010i	0.557482	−	1.71575i	−0.131817	−	0.991274i	$-0.542081\pi$
$809$	15.8564	−	48.8010i	0.557482	−	1.71575i	0.689298	−	0.724478i	$-0.257919\pi$
$810$	1.16508	+	8.02756i	0.0409367	+	0.282060i
$811$	6.90998	+	21.2667i	0.242642	+	0.746776i	0.996015	+	0.0891825i	$0.0284254\pi$
$811$	6.90998	+	21.2667i	0.242642	+	0.746776i	−0.753373	+	0.657593i	$0.771575\pi$
$812$	−55.9991	+	50.4218i	−1.96518	+	1.76946i
$813$	11.6775	+	6.22428i	0.409547	+	0.218295i
$814$	2.38928	−	2.65356i	0.0837442	−	0.0930074i
$815$	−4.58391	+	22.5131i	−0.160568	+	0.788600i
$816$	−1.84636	−	2.96151i	−0.0646357	−	0.103673i
$817$	−3.73492	−	8.38878i	−0.130668	−	0.293486i
$818$			10.1051i			0.353315i
$819$	38.1425	+	56.7977i	1.33281	+	1.98467i
$820$	−2.77090	+	28.7311i	−0.0967641	+	1.00333i
$821$	−4.32432	−	41.1432i	−0.150920	−	1.43591i	−0.763658	−	0.645621i	$-0.776599\pi$
$821$	−4.32432	−	41.1432i	−0.150920	−	1.43591i	0.612738	−	0.790286i	$-0.290068\pi$
$822$	3.46857	−	5.13109i	0.120980	−	0.178967i
$823$	15.4384	+	13.9008i	0.538148	+	0.484551i	0.892803	−	0.450446i	$-0.148735\pi$
$823$	15.4384	+	13.9008i	0.538148	+	0.484551i	−0.354655	+	0.934997i	$0.615402\pi$
$824$	−9.65682	−	16.7261i	−0.336411	−	0.582682i
$825$	−10.4795	−	20.6345i	−0.364848	−	0.718402i
$826$	−5.03357	+	8.71840i	−0.175140	+	0.303352i
$827$	35.1321	−	11.4151i	1.22166	−	0.396942i	0.373975	−	0.927439i	$-0.377995\pi$
$827$	35.1321	−	11.4151i	1.22166	−	0.396942i	0.847687	+	0.530497i	$0.177995\pi$
$828$	−23.1095	−	5.81185i	−0.803111	−	0.201976i
$829$	0.494171	−	0.359036i	0.0171633	−	0.0124698i	−0.579171	−	0.815206i	$-0.696623\pi$
$829$	0.494171	−	0.359036i	0.0171633	−	0.0124698i	0.596334	+	0.802737i	$0.296623\pi$
$830$	−0.390492	−	1.16765i	−0.0135542	−	0.0405296i
$831$	37.7331	−	9.36714i	1.30895	−	0.324942i
$832$	18.4615	−	10.6587i	0.640036	−	0.369525i
$833$	9.69287	+	1.01876i	0.335838	+	0.0352980i
$834$	−3.08572	+	5.78916i	−0.106850	+	0.200462i
$835$	−0.0135195	−	1.57669i	−0.000467861	−	0.0545637i
$836$	6.17091	+	18.9921i	0.213425	+	0.656855i
$837$	−1.79504	+	5.46768i	−0.0620455	+	0.188991i
$838$	−5.22569	−	1.69793i	−0.180518	−	0.0586540i
$839$	−22.8854	−	4.86445i	−0.790092	−	0.167939i	−0.204845	−	0.978794i	$-0.565669\pi$
$839$	−22.8854	−	4.86445i	−0.790092	−	0.167939i	−0.585247	+	0.810855i	$0.699002\pi$
$840$	−15.4516	+	23.2856i	−0.533132	+	0.803429i
$841$	−47.2254	+	10.0381i	−1.62846	+	0.346141i
$842$	−10.2616	−	1.07853i	−0.353637	−	0.0371687i
$843$	−37.2858	−	31.3512i	−1.28419	−	1.07979i
$844$	11.0999	−	4.94201i	0.382075	−	0.170111i
$845$	12.3676	+	21.0034i	0.425460	+	0.722539i
$846$	1.40115	+	1.35860i	0.0481727	+	0.0467097i
$847$	−10.5801	−	14.5623i	−0.363537	−	0.500365i
$848$	−4.55854	+	21.4463i	−0.156541	+	0.736468i
$849$	−11.2635	−	31.0444i	−0.386561	−	1.06544i
$850$	1.08982	+	0.763593i	0.0373804	+	0.0261910i
$851$	−7.16481	−	12.4098i	−0.245606	−	0.425403i
$852$	−20.9577	−	26.8810i	−0.717999	−	0.920928i
$853$	−0.475111	+	0.0499362i	−0.0162675	+	0.00170978i	−0.112659	−	0.993634i	$-0.535937\pi$
$853$	−0.475111	+	0.0499362i	−0.0162675	+	0.00170978i	0.0963912	+	0.995344i	$0.469270\pi$
$854$	15.1671	−	11.0195i	0.519006	−	0.377080i
$855$	−10.3845	−	25.2264i	−0.355142	−	0.862724i
$856$	−21.6778	−	15.7498i	−0.740932	−	0.538319i
$857$	−40.5723	−	23.4244i	−1.38592	−	0.800163i	−0.393070	−	0.919509i	$-0.628587\pi$
$857$	−40.5723	−	23.4244i	−1.38592	−	0.800163i	−0.992853	+	0.119346i	$0.961920\pi$
$858$	−2.19753	−	8.85220i	−0.0750225	−	0.302209i
$859$	−12.8436	+	2.73000i	−0.438219	+	0.0931463i	−0.421738	−	0.906718i	$-0.638580\pi$
$859$	−12.8436	+	2.73000i	−0.438219	+	0.0931463i	−0.0164811	+	0.999864i	$0.505246\pi$
$860$	6.84131	−	6.26699i	0.233287	−	0.213703i
$861$	7.84219	+	56.2153i	0.267261	+	1.91581i
$862$	−7.15151	+	6.43925i	−0.243581	+	0.219322i
$863$	4.35551	+	1.41519i	0.148263	+	0.0481737i	0.382209	−	0.924076i	$-0.375164\pi$
$863$	4.35551	+	1.41519i	0.148263	+	0.0481737i	−0.233945	+	0.972250i	$0.575164\pi$
$864$	21.3877	−	6.87714i	0.727624	−	0.233965i
$865$	−0.848999	−	0.0818797i	−0.0288668	−	0.00278399i
$866$	4.67510	+	5.19223i	0.158866	+	0.176439i
$867$	20.6579	−	19.9085i	0.701581	−	0.676130i
$868$	−8.22150	+	4.74669i	−0.279056	+	0.161113i
$869$	0.952383	−	9.06132i	0.0323074	−	0.307384i
$870$	−12.2887	+	6.10899i	−0.416627	+	0.207114i
$871$	1.35561	+	12.8977i	0.0459329	+	0.437023i
$872$	0.322537	+	0.443934i	0.0109225	+	0.0150335i
$873$	23.6679	−	37.7056i	0.801039	−	1.27614i
$874$	−7.08558			−0.239673
$875$	−9.52784	+	51.2769i	−0.322100	+	1.73347i
$876$	10.4356	+	28.7628i	0.352588	+	0.971804i
$877$	8.75825	+	7.88596i	0.295745	+	0.266290i	0.803623	−	0.595139i	$-0.202903\pi$
$877$	8.75825	+	7.88596i	0.295745	+	0.266290i	−0.507878	+	0.861429i	$0.669570\pi$
$878$	3.59885	−	8.08315i	0.121455	−	0.272793i
$879$	−38.7412	−	26.1887i	−1.30671	−	0.883322i
$880$	−14.6599	+	10.8443i	−0.494184	+	0.365560i
$881$	12.4003	+	9.00931i	0.417775	+	0.303532i	0.776742	−	0.629819i	$-0.216871\pi$
$881$	12.4003	+	9.00931i	0.417775	+	0.303532i	−0.358967	+	0.933350i	$0.616871\pi$
$882$	−6.13884	+	16.7601i	−0.206706	+	0.564341i
$883$	−22.0819	+	30.3931i	−0.743115	+	1.02281i	0.255319	+	0.966857i	$0.417820\pi$
$883$	−22.0819	+	30.3931i	−0.743115	+	1.02281i	−0.998433	+	0.0559529i	$0.982180\pi$
$884$	−3.96897	−	4.40799i	−0.133491	−	0.148257i
$885$	14.8072	−	14.5170i	0.497739	−	0.487983i
$886$	−9.75855	+	10.8380i	−0.327845	+	0.364109i
$887$	−0.290810	−	1.36815i	−0.00976444	−	0.0459381i	0.972996	−	0.230823i	$-0.0741420\pi$
$887$	−0.290810	−	1.36815i	−0.00976444	−	0.0459381i	−0.982760	+	0.184885i	$0.940809\pi$
$888$	7.83750	+	4.17751i	0.263009	+	0.140188i
$889$	17.2540	+	3.66746i	0.578682	+	0.123003i
$890$	−0.993159	−	4.48308i	−0.0332908	−	0.150273i
$891$	0.741484	+	24.0396i	0.0248406	+	0.805356i
$892$	22.0088	−	30.2925i	0.736909	−	1.01427i
$893$	−5.68427	−	3.28182i	−0.190217	−	0.109822i
$894$	8.77387	+	9.10414i	0.293442	+	0.304488i
$895$	19.5307	+	21.3206i	0.652841	+	0.712669i
$896$	44.3406	+	19.7417i	1.48132	+	0.659524i
$897$	−36.5111	−	2.59046i	−1.21907	−	0.0864929i
$898$	2.90923	−	13.6869i	0.0970824	−	0.456737i
$899$	−9.73605			−0.324716
$900$	20.8443	−	18.0342i	0.694811	−	0.601140i
$901$	4.74405			0.158047
$902$	1.57324	−	7.40149i	0.0523830	−	0.246443i
$903$	10.2174	−	15.1148i	0.340015	−	0.502988i
$904$	−15.1133	−	6.72888i	−0.502661	−	0.223799i
$905$	−8.27225	+	14.6160i	−0.274979	+	0.485851i
$906$	0.310358	−	1.07820i	0.0103109	−	0.0358209i
$907$	32.2735	+	18.6331i	1.07163	+	0.618703i	0.928625	−	0.371020i	$-0.120992\pi$
$907$	32.2735	+	18.6331i	1.07163	+	0.618703i	0.143000	+	0.989723i	$0.454325\pi$
$908$	−8.56723	+	11.7918i	−0.284314	+	0.391324i
$909$	−11.5051	−	28.6440i	−0.381601	−	0.950060i
$910$	−8.19898	+	18.8485i	−0.271794	+	0.624822i
$911$	−15.5725	−	3.31004i	−0.515941	−	0.109667i	−0.0574199	−	0.998350i	$-0.518287\pi$
$911$	−15.5725	−	3.31004i	−0.515941	−	0.109667i	−0.458521	+	0.888683i	$0.651621\pi$
$912$	−18.2400	+	11.3718i	−0.603986	+	0.376558i
$913$	−0.758988	−	3.57076i	−0.0251188	−	0.118175i
$914$	−3.23394	+	3.59166i	−0.106969	+	0.118801i
$915$	−36.1865	+	13.4813i	−1.19629	+	0.445679i
$916$	−0.790195	−	0.877601i	−0.0261088	−	0.0289967i
$917$	−14.6525	+	20.1674i	−0.483868	+	0.665987i
$918$	−0.687793	−	1.19974i	−0.0227006	−	0.0395973i
$919$	15.8659	+	11.5272i	0.523367	+	0.380248i	0.817871	−	0.575402i	$-0.195154\pi$
$919$	15.8659	+	11.5272i	0.523367	+	0.380248i	−0.294504	+	0.955650i	$0.595154\pi$
$920$	−4.74188	−	14.1791i	−0.156335	−	0.467473i
$921$	−44.7706	+	21.7797i	−1.47524	+	0.717665i
$922$	−4.71528	+	10.5907i	−0.155289	+	0.348786i
$923$	−38.9089	−	35.0338i	−1.28070	−	1.15315i
$924$	−25.5339	+	30.3673i	−0.840004	+	0.999011i
$925$	16.5115	+	1.44963i	0.542893	+	0.0476636i
$926$	9.45756			0.310795
$927$	17.5183	+	33.1097i	0.575378	+	1.08746i
$928$	22.3409	+	30.7496i	0.733376	+	1.00941i
$929$	−1.40368	−	13.3551i	−0.0460532	−	0.438167i	−0.993117	−	0.117123i	$-0.962633\pi$
$929$	−1.40368	−	13.3551i	−0.0460532	−	0.438167i	0.947064	−	0.321044i	$-0.104034\pi$
$930$	−1.67436	+	0.430929i	−0.0549045	+	0.0141307i
$931$	6.27458	−	59.6986i	0.205641	−	1.95654i
$932$	39.4235	−	22.7612i	1.29136	−	0.745567i
$933$	−34.6514	−	9.97433i	−1.13444	−	0.326545i
$934$	9.70774	+	10.7815i	0.317647	+	0.352783i
$935$	2.95462	+	2.61483i	0.0966265	+	0.0855141i
$936$	20.0523	−	10.6097i	0.655428	−	0.346788i
$937$	−40.7258	−	13.2326i	−1.33045	−	0.432290i	−0.444381	−	0.895838i	$-0.646576\pi$
$937$	−40.7258	−	13.2326i	−1.33045	−	0.432290i	−0.886072	+	0.463548i	$0.846576\pi$
$938$	−3.70671	+	3.33754i	−0.121028	+	0.108974i
$939$	−40.3737	−	16.3599i	−1.31755	−	0.533884i
$940$	1.32313	−	6.49835i	0.0431559	−	0.211953i
$941$	25.1651	−	5.34901i	0.820359	−	0.174373i	0.221431	−	0.975176i	$-0.428927\pi$
$941$	25.1651	−	5.34901i	0.820359	−	0.174373i	0.598927	+	0.800803i	$0.295594\pi$
$942$	3.46464	−	3.33895i	0.112884	−	0.108789i
$943$	−26.2981	−	15.1832i	−0.856383	−	0.494433i
$944$	−13.2181	−	9.60355i	−0.430214	−	0.312569i
$945$	31.6158	−	44.0244i	1.02846	−	1.43211i
$946$	−1.96770	+	1.42962i	−0.0639754	+	0.0464808i
$947$	39.8091	−	4.18410i	1.29362	−	0.135965i	0.567410	−	0.823436i	$-0.307946\pi$
$947$	39.8091	−	4.18410i	1.29362	−	0.135965i	0.726212	+	0.687471i	$0.241279\pi$
$948$	10.7472	−	1.49927i	0.349054	−	0.0486940i
$949$	23.4997	+	40.7026i	0.762832	+	1.32126i
$950$	4.70299	−	6.71221i	0.152585	−	0.217773i
$951$	−26.6875	+	31.7393i	−0.865403	+	1.02922i
$952$	0.990558	−	4.66021i	0.0321042	−	0.151038i
$953$	−3.27273	−	4.50452i	−0.106014	−	0.145916i	0.752714	−	0.658348i	$-0.228745\pi$
$953$	−3.27273	−	4.50452i	−0.106014	−	0.145916i	−0.858728	+	0.512432i	$0.828745\pi$
$954$	−2.11900	+	8.42572i	−0.0686051	+	0.272793i
$955$	1.66383	−	1.88005i	0.0538404	−	0.0608369i
$956$	−8.07762	+	3.59639i	−0.261249	+	0.116315i
$957$	−38.2501	+	13.8778i	−1.23645	+	0.448606i
$958$	6.38466	+	0.671055i	0.206279	+	0.0216808i
$959$	−40.4793	+	8.60413i	−1.30714	+	0.277842i
$960$	−13.0186	−	10.7573i	−0.420174	−	0.347191i
$961$	29.1228	+	6.19024i	0.939445	+	0.199685i
$962$	6.21262	+	2.01860i	0.200303	+	0.0650824i
$963$	40.8869	+	32.0786i	1.31756	+	1.03372i
$964$	5.39588	+	16.6068i	0.173790	+	0.534870i
$965$	3.78400	+	5.11541i	0.121811	+	0.164671i
$966$	−7.44789	−	11.9462i	−0.239632	−	0.384362i
$967$	−14.7128	−	1.54638i	−0.473132	−	0.0497281i	−0.135038	−	0.990840i	$-0.543116\pi$
$967$	−14.7128	−	1.54638i	−0.473132	−	0.0497281i	−0.338094	+	0.941112i	$0.609782\pi$
$968$	−5.16891	+	2.98427i	−0.166135	+	0.0959182i
$969$	3.22733	+	3.34881i	0.103677	+	0.107579i
$970$	13.3743	−	0.114679i	0.429421	−	0.00368211i
$971$	−12.3168	+	8.94868i	−0.395265	+	0.287177i	−0.767610	−	0.640918i	$-0.778554\pi$
$971$	−12.3168	+	8.94868i	−0.395265	+	0.287177i	0.372345	+	0.928095i	$0.378554\pi$
$972$	−27.5745	+	7.75519i	−0.884453	+	0.248748i
$973$	41.6885	−	13.5454i	1.33647	−	0.434246i
$974$	−3.75348	+	6.50122i	−0.120269	+	0.208313i
$975$	26.6879	−	32.8678i	0.854696	−	1.05261i
$976$	15.2132	+	26.3500i	0.486963	+	0.843444i
$977$	−33.4117	−	30.0840i	−1.06894	−	0.962474i	−0.0695515	−	0.997578i	$-0.522157\pi$
$977$	−33.4117	−	30.0840i	−1.06894	−	0.962474i	−0.999384	+	0.0351048i	$0.988823\pi$
$978$	7.15524	+	0.507663i	0.228799	+	0.0162333i
$979$	−1.42311	−	13.5400i	−0.0454828	−	0.432740i
$980$	59.2142	−	13.1180i	1.89153	−	0.419039i
$981$	−0.593328	−	0.883519i	−0.0189435	−	0.0282086i
$982$		−	15.8654i		−	0.506284i
$983$	3.12080	+	7.00943i	0.0995380	+	0.223566i	0.956450	−	0.291897i	$-0.0942865\pi$
$983$	3.12080	+	7.00943i	0.0995380	+	0.223566i	−0.856912	+	0.515463i	$0.827620\pi$
$984$	18.8100	−	0.637687i	0.599640	−	0.0203287i
$985$	−2.54688	+	2.33307i	−0.0811504	+	0.0743379i
$986$	1.56552	−	1.73868i	0.0498562	−	0.0553709i
$987$	−0.441846	−	13.0332i	−0.0140641	−	0.414852i
$988$	−27.1489	+	24.4450i	−0.863722	+	0.777699i
$989$	3.01621	+	9.28294i	0.0959099	+	0.295180i
$990$	−5.96382	+	4.07964i	−0.189543	+	0.129659i
$991$	−14.3742	+	44.2393i	−0.456612	+	1.40531i	0.412620	+	0.910903i	$0.364614\pi$
$991$	−14.3742	+	44.2393i	−0.456612	+	1.40531i	−0.869232	+	0.494404i	$0.835386\pi$
$992$	1.94764	+	4.37447i	0.0618376	+	0.138890i
$993$	−12.6670	−	10.6508i	−0.401974	−	0.337994i
$994$	2.10488	−	20.0266i	0.0667627	−	0.635204i
$995$	−3.05854	−	26.8808i	−0.0969621	−	0.852179i
$996$	3.90964	−	1.90193i	0.123882	−	0.0602651i
$997$	−31.0900	+	3.26769i	−0.984630	+	0.103489i	−0.583137	−	0.812374i	$-0.698175\pi$
$997$	−31.0900	+	3.26769i	−0.984630	+	0.103489i	−0.401492	+	0.915862i	$0.631508\pi$
$998$	9.23212	−	2.99970i	0.292238	−	0.0949538i
$999$	−14.8911	−	8.65813i	−0.471134	−	0.273931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.u.a.169.16	yes	224
3.2	odd	2		675.2.y.a.19.13		224
9.4	even	3	inner	225.2.u.a.94.16	yes	224
9.5	odd	6		675.2.y.a.469.13		224
25.4	even	10	inner	225.2.u.a.79.16	yes	224
75.29	odd	10		675.2.y.a.154.13		224
225.4	even	30	inner	225.2.u.a.4.16	✓	224
225.104	odd	30		675.2.y.a.604.13		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.16	✓	224	225.4	even	30	inner
225.2.u.a.79.16	yes	224	25.4	even	10	inner
225.2.u.a.94.16	yes	224	9.4	even	3	inner
225.2.u.a.169.16	yes	224	1.1	even	1	trivial
675.2.y.a.19.13		224	3.2	odd	2
675.2.y.a.154.13		224	75.29	odd	10
675.2.y.a.469.13		224	9.5	odd	6
675.2.y.a.604.13		224	225.104	odd	30

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0838034 - 0.394264i) q^{2} +(-0.757696 - 1.55753i) q^{3} +(1.67867 + 0.747392i) q^{4} +(-0.252792 - 2.22173i) q^{5} +(-0.677575 + 0.168206i) q^{6} +(4.03987 + 2.33242i) q^{7} +(0.909187 - 1.25139i) q^{8} +(-1.85179 + 2.36027i) q^{9} +O(q^{10})\)	\(q+(0.0838034 - 0.394264i) q^{2} +(-0.757696 - 1.55753i) q^{3} +(1.67867 + 0.747392i) q^{4} +(-0.252792 - 2.22173i) q^{5} +(-0.677575 + 0.168206i) q^{6} +(4.03987 + 2.33242i) q^{7} +(0.909187 - 1.25139i) q^{8} +(-1.85179 + 2.36027i) q^{9} +(-0.897134 - 0.0865220i) q^{10} +(-2.61394 - 0.555609i) q^{11} +(-0.107837 - 3.18087i) q^{12} +(-1.01644 - 4.78198i) q^{13} +(1.25815 - 1.39731i) q^{14} +(-3.26887 + 2.07713i) q^{15} +(2.04191 + 2.26778i) q^{16} +(0.388104 - 0.534179i) q^{17} +(0.775381 + 0.927894i) q^{18} +(-3.29002 - 2.39034i) q^{19} +(1.23615 - 3.91849i) q^{20} +(0.571820 - 8.05949i) q^{21} +(-0.438113 + 0.984019i) q^{22} +(3.21237 + 2.89243i) q^{23} +(-2.63796 - 0.467913i) q^{24} +(-4.87219 + 1.12327i) q^{25} -1.97054 q^{26} +(5.07928 + 1.09586i) q^{27} +(5.03838 + 6.93474i) q^{28} +(0.918903 + 8.74277i) q^{29} +(0.544994 + 1.46287i) q^{30} +(-0.115766 + 1.10144i) q^{31} +(3.74436 - 2.16181i) q^{32} +(1.11519 + 4.49226i) q^{33} +(-0.178083 - 0.197781i) q^{34} +(4.16077 - 9.56514i) q^{35} +(-4.87260 + 2.57809i) q^{36} +(-3.15275 - 1.02439i) q^{37} +(-1.21814 + 1.09682i) q^{38} +(-6.67792 + 5.20642i) q^{39} +(-3.01009 - 1.70363i) q^{40} +(-6.87142 + 1.46056i) q^{41} +(-3.12965 - 0.900860i) q^{42} +(1.95550 + 1.12901i) q^{43} +(-3.97268 - 2.88632i) q^{44} +(5.71200 + 3.51753i) q^{45} +(1.40959 - 1.02413i) q^{46} +(1.60516 - 0.168709i) q^{47} +(1.98498 - 4.89863i) q^{48} +(7.38039 + 12.7832i) q^{49} +(0.0345592 + 2.01506i) q^{50} +(-1.12606 - 0.199738i) q^{51} +(1.86774 - 8.78704i) q^{52} +(4.22318 + 5.81270i) q^{53} +(0.857718 - 1.91074i) q^{54} +(-0.573634 + 5.94792i) q^{55} +(6.59177 - 2.93485i) q^{56} +(-1.23019 + 6.93545i) q^{57} +(3.52397 + 0.370384i) q^{58} +(-5.23710 + 1.11318i) q^{59} +(-7.03979 + 1.04368i) q^{60} +(9.75278 + 2.07302i) q^{61} +(0.424558 + 0.137947i) q^{62} +(-12.9862 + 5.21602i) q^{63} +(1.34746 + 4.14704i) q^{64} +(-10.3673 + 3.46711i) q^{65} +(1.86459 - 0.0632126i) q^{66} +(-2.63821 - 0.277287i) q^{67} +(1.05074 - 0.606644i) q^{68} +(2.07104 - 7.19494i) q^{69} +(-3.42250 - 2.44203i) q^{70} +(8.66423 - 6.29493i) q^{71} +(1.26998 + 4.46324i) q^{72} +(-9.14313 + 2.97078i) q^{73} +(-0.668091 + 1.15717i) q^{74} +(5.44117 + 6.73748i) q^{75} +(-3.73634 - 6.47152i) q^{76} +(-9.26406 - 8.34139i) q^{77} +(1.49307 + 3.06918i) q^{78} +(0.356386 + 3.39079i) q^{79} +(4.52221 - 5.10986i) q^{80} +(-2.14172 - 8.74146i) q^{81} +2.83155i q^{82} +(0.555621 + 1.24794i) q^{83} +(6.98349 - 13.1018i) q^{84} +(-1.28491 - 0.727226i) q^{85} +(0.609006 - 0.676369i) q^{86} +(12.9209 - 8.05558i) q^{87} +(-3.07184 + 2.76590i) q^{88} +(1.57433 + 4.84528i) q^{89} +(1.86552 - 1.95725i) q^{90} +(7.04730 - 21.6894i) q^{91} +(3.23073 + 7.25633i) q^{92} +(1.80325 - 0.654250i) q^{93} +(0.0680018 - 0.646994i) q^{94} +(-4.47900 + 7.91380i) q^{95} +(-6.20417 - 4.19396i) q^{96} +(-14.7582 + 1.55114i) q^{97} +(5.65846 - 1.83854i) q^{98} +(6.15186 - 5.14071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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