LMFDB - Embedded newform 507.2.s.a.122.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			122.37
Character	$\chi$	$=$	507.122
Dual form			507.2.s.a.320.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.213424 + 0.684902i) q^{2} +(-0.424347 - 1.67926i) q^{3} +(1.22243 - 0.843781i) q^{4} +(-1.47602 + 3.27958i) q^{5} +(1.05957 - 0.649031i) q^{6} +(-1.08415 + 1.38382i) q^{7} +(1.96823 + 1.54201i) q^{8} +(-2.63986 + 1.42518i) q^{9} +O(q^{10})$	\(q+(0.213424 + 0.684902i) q^{2} +(-0.424347 - 1.67926i) q^{3} +(1.22243 - 0.843781i) q^{4} +(-1.47602 + 3.27958i) q^{5} +(1.05957 - 0.649031i) q^{6} +(-1.08415 + 1.38382i) q^{7} +(1.96823 + 1.54201i) q^{8} +(-2.63986 + 1.42518i) q^{9} +(-2.56120 - 0.310987i) q^{10} +(-1.13328 + 3.63683i) q^{11} +(-1.93566 - 1.69472i) q^{12} +(-3.59206 + 0.311604i) q^{13} +(-1.17916 - 0.447198i) q^{14} +(6.13362 + 1.08695i) q^{15} +(0.417375 - 1.10053i) q^{16} +(-0.229608 - 1.89099i) q^{17} +(-1.53952 - 1.50388i) q^{18} +(-3.45195 + 3.45195i) q^{19} +(0.962919 + 5.25448i) q^{20} +(2.78386 + 1.23336i) q^{21} -2.73274 q^{22} +2.50259 q^{23} +(1.75423 - 3.95952i) q^{24} +(-5.26138 - 5.93887i) q^{25} +(-0.980050 - 2.39370i) q^{26} +(3.51347 + 3.82825i) q^{27} +(-0.157659 + 2.60641i) q^{28} +(-2.62275 + 4.99724i) q^{29} +(0.564610 + 4.43291i) q^{30} +(6.90507 - 0.417680i) q^{31} +(5.83439 + 0.352916i) q^{32} +(6.58811 + 0.359804i) q^{33} +(1.24614 - 0.560841i) q^{34} +(-2.93811 - 5.59811i) q^{35} +(-2.02450 + 3.96964i) q^{36} +(-0.431737 - 7.13746i) q^{37} +(-3.10097 - 1.62752i) q^{38} +(2.04754 + 5.89979i) q^{39} +(-7.96227 + 4.17892i) q^{40} +(2.04321 + 3.37988i) q^{41} +(-0.250589 + 2.16990i) q^{42} +(2.16305 + 2.44157i) q^{43} +(1.68333 + 5.40201i) q^{44} +(-0.777510 - 10.7612i) q^{45} +(0.534113 + 1.71403i) q^{46} +(1.92019 + 10.4781i) q^{47} +(-2.02519 - 0.233878i) q^{48} +(0.935642 + 3.79605i) q^{49} +(2.94464 - 4.87102i) q^{50} +(-3.07804 + 1.18801i) q^{51} +(-4.12811 + 3.41182i) q^{52} +(9.36922 - 1.13763i) q^{53} +(-1.87212 + 3.22342i) q^{54} +(-10.2545 - 9.08472i) q^{55} +(-4.26772 + 1.05190i) q^{56} +(7.26156 + 4.33191i) q^{57} +(-3.98237 - 0.729797i) q^{58} +(-13.7740 - 6.19917i) q^{59} +(8.41505 - 3.84672i) q^{60} +(0.678853 - 5.59086i) q^{61} +(1.75978 + 4.64015i) q^{62} +(0.889820 - 5.19820i) q^{63} +(0.440130 + 1.78568i) q^{64} +(4.28002 - 12.2404i) q^{65} +(1.15963 + 4.58900i) q^{66} +(-1.97296 - 10.7661i) q^{67} +(-1.87626 - 2.11786i) q^{68} +(-1.06197 - 4.20251i) q^{69} +(3.20709 - 3.20709i) q^{70} +(-4.80233 - 7.94402i) q^{71} +(-7.39349 - 1.26560i) q^{72} +(11.9212 + 3.71480i) q^{73} +(4.79631 - 1.81900i) q^{74} +(-7.74029 + 11.3554i) q^{75} +(-1.30707 + 7.13245i) q^{76} +(-3.80407 - 5.51114i) q^{77} +(-3.60378 + 2.66152i) q^{78} +(1.14921 - 1.66492i) q^{79} +(2.99321 + 2.99321i) q^{80} +(4.93772 - 7.52455i) q^{81} +(-1.87882 + 2.12075i) q^{82} +(-4.69865 - 2.84043i) q^{83} +(4.44375 - 0.841270i) q^{84} +(6.54055 + 2.03812i) q^{85} +(-1.21059 + 2.00256i) q^{86} +(9.50464 + 2.28373i) q^{87} +(-7.83859 + 5.41058i) q^{88} +(-8.35630 + 8.35630i) q^{89} +(7.20443 - 2.82922i) q^{90} +(3.46314 - 5.30859i) q^{91} +(3.05924 - 2.11164i) q^{92} +(-3.63154 - 11.4182i) q^{93} +(-6.76666 + 3.55142i) q^{94} +(-6.22579 - 16.4161i) q^{95} +(-1.88317 - 9.94725i) q^{96} +(4.39626 + 9.76809i) q^{97} +(-2.40023 + 1.45099i) q^{98} +(-2.19144 - 11.2159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{47}{52}\right)$

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 $

$2$	0.213424	+	0.684902i	0.150914	+	0.484299i	0.998959	−	0.0456255i	$-0.0145281\pi$
$2$	0.213424	+	0.684902i	0.150914	+	0.484299i	−0.848045	+	0.529924i	$0.822220\pi$
$3$	−0.424347	−	1.67926i	−0.244997	−	0.969524i
$3$	−0.424347	−	1.67926i	−0.244997	−	0.969524i
$4$	1.22243	−	0.843781i	0.611214	−	0.421890i
$5$	−1.47602	+	3.27958i	−0.660095	+	1.46667i	0.211968	+	0.977277i	$0.432013\pi$
$5$	−1.47602	+	3.27958i	−0.660095	+	1.46667i	−0.872063	+	0.489394i	$0.837218\pi$
$6$	1.05957	−	0.649031i	0.432566	−	0.264966i
$7$	−1.08415	+	1.38382i	−0.409771	+	0.523035i	−0.947359	−	0.320173i	$-0.896259\pi$
$7$	−1.08415	+	1.38382i	−0.409771	+	0.523035i	0.537588	+	0.843208i	$0.319336\pi$
$8$	1.96823	+	1.54201i	0.695874	+	0.545182i
$9$	−2.63986	+	1.42518i	−0.879953	+	0.475060i
$10$	−2.56120	−	0.310987i	−0.809924	−	0.0983426i
$11$	−1.13328	+	3.63683i	−0.341698	+	1.09655i	0.610745	+	0.791828i	$0.290870\pi$
$11$	−1.13328	+	3.63683i	−0.341698	+	1.09655i	−0.952442	+	0.304719i	$0.901437\pi$
$12$	−1.93566	−	1.69472i	−0.558778	−	0.489225i
$13$	−3.59206	+	0.311604i	−0.996259	+	0.0864234i
$13$	−3.59206	+	0.311604i	−0.996259	+	0.0864234i
$14$	−1.17916	−	0.447198i	−0.315145	−	0.119519i
$15$	6.13362	+	1.08695i	1.58369	+	0.280648i
$16$	0.417375	−	1.10053i	0.104344	−	0.275132i
$17$	−0.229608	−	1.89099i	−0.0556881	−	0.458633i	−0.993704	−	0.112040i	$-0.964262\pi$
$17$	−0.229608	−	1.89099i	−0.0556881	−	0.458633i	0.938016	−	0.346593i	$-0.112661\pi$
$18$	−1.53952	−	1.50388i	−0.362868	−	0.354467i
$19$	−3.45195	+	3.45195i	−0.791932	+	0.791932i	−0.981808	−	0.189876i	$-0.939191\pi$
$19$	−3.45195	+	3.45195i	−0.791932	+	0.791932i	0.189876	+	0.981808i	$0.439191\pi$
$20$	0.962919	+	5.25448i	0.215315	+	1.17494i
$21$	2.78386	+	1.23336i	0.607487	+	0.269141i
$22$	−2.73274			−0.582623
$23$	2.50259			0.521826			0.260913	−	0.965362i	$-0.415976\pi$
$23$	2.50259			0.521826			0.260913	+	0.965362i	$0.415976\pi$
$24$	1.75423	−	3.95952i	0.358080	−	0.808234i
$25$	−5.26138	−	5.93887i	−1.05228	−	1.18777i
$26$	−0.980050	−	2.39370i	−0.192204	−	0.469444i
$27$	3.51347	+	3.82825i	0.676168	+	0.736748i
$28$	−0.157659	+	2.60641i	−0.0297947	+	0.492565i
$29$	−2.62275	+	4.99724i	−0.487033	+	0.927963i	0.510641	+	0.859794i	$0.329408\pi$
$29$	−2.62275	+	4.99724i	−0.487033	+	0.927963i	−0.997674	+	0.0681694i	$0.978284\pi$
$30$	0.564610	+	4.43291i	0.103083	+	0.809334i
$31$	6.90507	−	0.417680i	1.24019	−	0.0750175i	0.572779	−	0.819710i	$-0.305865\pi$
$31$	6.90507	−	0.417680i	1.24019	−	0.0750175i	0.667408	+	0.744692i	$0.267404\pi$
$32$	5.83439	+	0.352916i	1.03138	+	0.0623873i
$33$	6.58811	+	0.359804i	1.14684	+	0.0626339i
$34$	1.24614	−	0.560841i	0.213711	−	0.0961835i
$35$	−2.93811	−	5.59811i	−0.496632	−	0.946252i
$36$	−2.02450	+	3.96964i	−0.337416	+	0.661607i
$37$	−0.431737	−	7.13746i	−0.0709771	−	1.17339i	−0.843042	−	0.537847i	$-0.819238\pi$
$37$	−0.431737	−	7.13746i	−0.0709771	−	1.17339i	0.772065	−	0.635543i	$-0.219224\pi$
$38$	−3.10097	−	1.62752i	−0.503044	−	0.264018i
$39$	2.04754	+	5.89979i	0.327870	+	0.944723i
$40$	−7.96227	+	4.17892i	−1.25895	+	0.660746i
$41$	2.04321	+	3.37988i	0.319096	+	0.527849i	0.973615	−	0.228196i	$-0.0732827\pi$
$41$	2.04321	+	3.37988i	0.319096	+	0.527849i	−0.654519	+	0.756045i	$0.727129\pi$
$42$	−0.250589	+	2.16990i	−0.0386668	+	0.334822i
$43$	2.16305	+	2.44157i	0.329861	+	0.372337i	0.889920	−	0.456116i	$-0.150760\pi$
$43$	2.16305	+	2.44157i	0.329861	+	0.372337i	−0.560059	+	0.828453i	$0.689221\pi$
$44$	1.68333	+	5.40201i	0.253772	+	0.814383i
$45$	−0.777510	−	10.7612i	−0.115904	−	1.60419i
$46$	0.534113	+	1.71403i	0.0787507	+	0.252720i
$47$	1.92019	+	10.4781i	0.280088	+	1.52839i	0.759329	+	0.650707i	$0.225527\pi$
$47$	1.92019	+	10.4781i	0.280088	+	1.52839i	−0.479241	+	0.877683i	$0.659088\pi$
$48$	−2.02519	−	0.233878i	−0.292311	−	0.0337574i
$49$	0.935642	+	3.79605i	0.133663	+	0.542293i
$50$	2.94464	−	4.87102i	0.416435	−	0.688867i
$51$	−3.07804	+	1.18801i	−0.431012	+	0.166354i
$52$	−4.12811	+	3.41182i	−0.572466	+	0.473135i
$53$	9.36922	−	1.13763i	1.28696	−	0.156265i	0.551696	−	0.834045i	$-0.313981\pi$
$53$	9.36922	−	1.13763i	1.28696	−	0.156265i	0.735265	+	0.677780i	$0.237058\pi$
$54$	−1.87212	+	3.22342i	−0.254763	+	0.438652i
$55$	−10.2545	−	9.08472i	−1.38272	−	1.22498i
$56$	−4.26772	+	1.05190i	−0.570298	+	0.140566i
$57$	7.26156	+	4.33191i	0.961817	+	0.573776i
$58$	−3.98237	−	0.729797i	−0.522911	−	0.0958270i
$59$	−13.7740	−	6.19917i	−1.79322	−	0.807064i	−0.971449	−	0.237249i	$-0.923754\pi$
$59$	−13.7740	−	6.19917i	−1.79322	−	0.807064i	−0.821773	−	0.569815i	$-0.807015\pi$
$60$	8.41505	−	3.84672i	1.08638	−	0.496609i
$61$	0.678853	−	5.59086i	0.0869183	−	0.715836i	−0.882481	−	0.470348i	$-0.844128\pi$
$61$	0.678853	−	5.59086i	0.0869183	−	0.715836i	0.969399	−	0.245489i	$-0.0789484\pi$
$62$	1.75978	+	4.64015i	0.223492	+	0.589300i
$63$	0.889820	−	5.19820i	0.112107	−	0.654912i
$64$	0.440130	+	1.78568i	0.0550163	+	0.223210i
$65$	4.28002	−	12.2404i	0.530871	−	1.51823i
$66$	1.15963	+	4.58900i	0.142741	+	0.564867i
$67$	−1.97296	−	10.7661i	−0.241035	−	1.31528i	−0.851964	−	0.523600i	$-0.824589\pi$
$67$	−1.97296	−	10.7661i	−0.241035	−	1.31528i	0.610930	−	0.791685i	$-0.290796\pi$
$68$	−1.87626	−	2.11786i	−0.227530	−	0.256828i
$69$	−1.06197	−	4.20251i	−0.127846	−	0.505923i
$70$	3.20709	−	3.20709i	0.383320	−	0.383320i
$71$	−4.80233	−	7.94402i	−0.569931	−	0.942781i	−0.999215	−	0.0396118i	$-0.987388\pi$
$71$	−4.80233	−	7.94402i	−0.569931	−	0.942781i	0.429284	−	0.903170i	$-0.358766\pi$
$72$	−7.39349	−	1.26560i	−0.871331	−	0.149153i
$73$	11.9212	+	3.71480i	1.39527	+	0.434785i	0.900734	−	0.434371i	$-0.143029\pi$
$73$	11.9212	+	3.71480i	1.39527	+	0.434785i	0.494539	+	0.869155i	$0.335337\pi$
$74$	4.79631	−	1.81900i	0.557560	−	0.211455i
$75$	−7.74029	+	11.3554i	−0.893771	+	1.31121i
$76$	−1.30707	+	7.13245i	−0.149931	+	0.818148i
$77$	−3.80407	−	5.51114i	−0.433514	−	0.628053i
$78$	−3.60378	+	2.66152i	−0.408048	+	0.301358i
$79$	1.14921	−	1.66492i	0.129297	−	0.187319i	−0.752989	−	0.658033i	$-0.771389\pi$
$79$	1.14921	−	1.66492i	0.129297	−	0.187319i	0.882285	+	0.470715i	$0.156004\pi$
$80$	2.99321	+	2.99321i	0.334651	+	0.334651i
$81$	4.93772	−	7.52455i	0.548635	−	0.836062i
$82$	−1.87882	+	2.12075i	−0.207481	+	0.234197i
$83$	−4.69865	−	2.84043i	−0.515744	−	0.311778i	0.235420	−	0.971894i	$-0.424353\pi$
$83$	−4.69865	−	2.84043i	−0.515744	−	0.311778i	−0.751164	+	0.660116i	$0.770507\pi$
$84$	4.44375	−	0.841270i	0.484853	−	0.0917900i
$85$	6.54055	+	2.03812i	0.709422	+	0.221065i
$86$	−1.21059	+	2.00256i	−0.130541	+	0.215942i
$87$	9.50464	+	2.28373i	1.01900	+	0.244842i
$88$	−7.83859	+	5.41058i	−0.835596	+	0.576770i
$89$	−8.35630	+	8.35630i	−0.885766	+	0.885766i	−0.994113	−	0.108347i	$-0.965444\pi$
$89$	−8.35630	+	8.35630i	−0.885766	+	0.885766i	0.108347	+	0.994113i	$0.465444\pi$
$90$	7.20443	−	2.82922i	0.759414	−	0.298226i
$91$	3.46314	−	5.30859i	0.363036	−	0.556492i
$92$	3.05924	−	2.11164i	0.318947	−	0.220154i
$93$	−3.63154	−	11.4182i	−0.376573	−	1.18401i
$94$	−6.76666	+	3.55142i	−0.697928	+	0.366301i
$95$	−6.22579	−	16.4161i	−0.638753	−	1.68425i
$96$	−1.88317	−	9.94725i	−0.192200	−	1.01524i
$97$	4.39626	+	9.76809i	0.446373	+	0.991799i	0.988461	+	0.151478i	$0.0484031\pi$
$97$	4.39626	+	9.76809i	0.446373	+	0.991799i	−0.542088	+	0.840322i	$0.682366\pi$
$98$	−2.40023	+	1.45099i	−0.242460	+	0.146572i
$99$	−2.19144	−	11.2159i	−0.220248	−	1.12724i
$100$	−11.4428	−	2.82039i	−1.14428	−	0.282039i
$101$	3.52782	−	3.12538i	0.351031	−	0.310987i	−0.469119	−	0.883135i	$-0.655428\pi$
$101$	3.52782	−	3.12538i	0.351031	−	0.310987i	0.820150	+	0.572149i	$0.193890\pi$
$102$	−1.47060	−	1.85461i	−0.145611	−	0.183633i
$103$	−2.38001	+	9.65609i	−0.234510	+	0.951443i	0.729160	+	0.684344i	$0.239911\pi$
$103$	−2.38001	+	9.65609i	−0.234510	+	0.951443i	−0.963669	+	0.267099i	$0.913935\pi$
$104$	−7.55049	−	4.92568i	−0.740386	−	0.483003i
$105$	−8.15392	+	7.30941i	−0.795741	+	0.713325i
$106$	2.77878	+	6.17419i	0.269899	+	0.599691i
$107$	−3.75481	+	1.42401i	−0.362991	+	0.137664i	−0.529356	−	0.848400i	$-0.677566\pi$
$107$	−3.75481	+	1.42401i	−0.362991	+	0.137664i	0.166365	+	0.986064i	$0.446797\pi$
$108$	7.52517	+	1.71516i	0.724110	+	0.165041i
$109$	0.119659	−	1.97820i	0.0114612	−	0.189477i	−0.987939	−	0.154844i	$-0.950512\pi$
$109$	0.119659	−	1.97820i	0.0114612	−	0.189477i	0.999400	−	0.0346324i	$-0.0110260\pi$
$110$	4.03358	−	8.96224i	0.384586	−	0.854516i
$111$	−11.8025	+	3.75376i	−1.12024	+	0.356291i
$112$	1.07043	+	1.77071i	0.101146	+	0.167317i
$113$	−1.61226	−	6.54119i	−0.151669	−	0.615344i	−0.996739	−	0.0806891i	$-0.974288\pi$
$113$	−1.61226	−	6.54119i	−0.151669	−	0.615344i	0.845071	−	0.534655i	$-0.179558\pi$
$114$	−1.41714	+	5.89799i	−0.132728	+	0.552397i
$115$	−3.69387	+	8.20744i	−0.344455	+	0.765348i
$116$	1.01045	+	8.32178i	0.0938177	+	0.772658i
$117$	9.03845	−	5.94193i	0.835605	−	0.549331i
$118$	1.30612	−	10.7569i	0.120238	−	0.990252i
$119$	2.86572	+	1.73239i	0.262700	+	0.158808i
$120$	10.3963	+	11.5974i	0.949046	+	1.05870i
$121$	−2.88940	−	1.99441i	−0.262673	−	0.181310i
$122$	3.97407	−	0.728276i	0.359796	−	0.0659350i
$123$	4.80869	−	4.86534i	0.433585	−	0.438693i
$124$	8.08851	−	6.33695i	0.726370	−	0.569075i
$125$	10.0750	−	3.13949i	0.901133	−	0.280804i
$126$	3.75017	−	0.499982i	0.334091	−	0.0445420i
$127$	17.6592	+	12.1893i	1.56700	+	1.08162i	0.957342	+	0.288958i	$0.0933089\pi$
$127$	17.6592	+	12.1893i	1.56700	+	1.08162i	0.609659	+	0.792664i	$0.291306\pi$
$128$	8.87510	−	5.36518i	0.784455	−	0.474220i
$129$	3.18217	−	4.66840i	0.280174	−	0.411030i
$130$	9.29691	+	0.319001i	0.815393	+	0.0279783i
$131$	−0.411611	+	0.784259i	−0.0359626	+	0.0685210i	−0.902774	−	0.430115i	$-0.858473\pi$
$131$	−0.411611	+	0.784259i	−0.0359626	+	0.0685210i	0.866812	+	0.498636i	$0.166165\pi$
$132$	8.35708	−	5.11909i	0.727391	−	0.445559i
$133$	−1.03443	−	8.51932i	−0.0896967	−	0.738719i
$134$	6.95262	−	3.64902i	0.600615	−	0.315227i
$135$	−17.7410	+	5.87213i	−1.52690	+	0.505392i
$136$	2.46400	−	4.07596i	0.211286	−	0.349510i
$137$	−0.572621	+	9.46655i	−0.0489223	+	0.808782i	0.888130	+	0.459593i	$0.152005\pi$
$137$	−0.572621	+	9.46655i	−0.0489223	+	0.808782i	−0.937052	+	0.349189i	$0.886457\pi$
$138$	2.65166	−	1.62426i	0.225724	−	0.138266i
$139$	−0.160602	+	0.423472i	−0.0136220	+	0.0359184i	−0.941655	−	0.336580i	$-0.890730\pi$
$139$	−0.160602	+	0.423472i	−0.0136220	+	0.0359184i	0.928033	+	0.372499i	$0.121499\pi$
$140$	−8.31520	−	4.36415i	−0.702763	−	0.368838i
$141$	16.7807	−	7.67085i	1.41319	−	0.646002i
$142$	4.41594	−	4.98456i	0.370577	−	0.418295i
$143$	2.93757	−	13.4169i	0.245652	−	1.12197i
$144$	0.466639	+	3.50007i	0.0388866	+	0.291673i
$145$	−12.5176	−	15.9775i	−1.03953	−	1.32686i
$146$			8.95769i			0.741344i
$147$	5.97753	−	3.18203i	0.493019	−	0.262449i
$148$	−6.55021	−	8.36073i	−0.538424	−	0.687248i
$149$	15.0382	−	2.75586i	1.23198	−	0.225769i	0.475459	−	0.879738i	$-0.342282\pi$
$149$	15.0382	−	2.75586i	1.23198	−	0.225769i	0.756521	+	0.653969i	$0.226898\pi$
$150$	−9.42929	−	2.87782i	−0.769898	−	0.234973i
$151$	−2.41830	+	13.1962i	−0.196798	+	1.07389i	0.725734	+	0.687975i	$0.241500\pi$
$151$	−2.41830	+	13.1962i	−0.196798	+	1.07389i	−0.922533	+	0.385919i	$0.873884\pi$
$152$	−12.1172	+	1.47129i	−0.982831	+	0.119337i
$153$	3.30114	+	4.66472i	0.266881	+	0.377120i
$154$	2.96271	−	3.78162i	0.238742	−	0.304732i
$155$	−8.82219	+	23.2622i	−0.708615	+	1.86846i
$156$	7.48111	+	5.48439i	0.598968	+	0.439103i
$157$	−2.40876	−	6.35137i	−0.192240	−	0.506894i	0.803891	−	0.594776i	$-0.202759\pi$
$157$	−2.40876	−	6.35137i	−0.192240	−	0.506894i	−0.996131	+	0.0878819i	$0.971990\pi$
$158$	1.38558	+	0.431764i	0.110231	+	0.0343493i
$159$	−5.88618	−	15.2506i	−0.466804	−	1.20946i
$160$	−9.76908	+	18.6134i	−0.772313	+	1.47152i
$161$	−2.71319	+	3.46314i	−0.213830	+	0.272933i
$162$	6.20741	+	1.77593i	0.487700	+	0.139530i
$163$	−0.309051	−	5.10922i	−0.0242067	−	0.400185i	−0.990018	−	0.140940i	$-0.954988\pi$
$163$	−0.309051	−	5.10922i	−0.0242067	−	0.400185i	0.965811	−	0.259246i	$-0.0834739\pi$
$164$	5.34956	+	2.40764i	0.417730	+	0.188005i
$165$	−10.9042	+	21.0751i	−0.848889	+	1.64070i
$166$	0.942612	−	3.82433i	0.0731609	−	0.296826i
$167$	−4.57053	+	1.42423i	−0.353678	+	0.110211i	−0.469194	−	0.883095i	$-0.655456\pi$
$167$	−4.57053	+	1.42423i	−0.353678	+	0.110211i	0.115516	+	0.993306i	$0.463148\pi$
$168$	3.57741	+	6.72026i	0.276003	+	0.518480i
$169$	12.8058	−	2.23860i	0.985062	−	0.172200i
$170$			4.91462i			0.376934i
$171$	4.19301	−	14.0323i	0.320648	−	1.07308i
$172$	4.70432	+	1.15951i	0.358701	+	0.0884118i
$173$	4.44241	+	6.43595i	0.337750	+	0.489316i	0.954652	−	0.297725i	$-0.0962277\pi$
$173$	4.44241	+	6.43595i	0.337750	+	0.489316i	−0.616901	+	0.787040i	$0.711612\pi$
$174$	0.464384	+	6.99714i	0.0352049	+	0.530452i
$175$	13.9225	−	0.842154i	1.05244	−	0.0636609i
$176$	3.52943	+	2.76513i	0.266041	+	0.208430i
$177$	−4.56510	+	25.7608i	−0.343134	+	1.93630i
$178$	−7.50668	−	3.93981i	−0.562650	−	0.295301i
$179$	−1.45098	+	11.9499i	−0.108452	+	0.893179i	0.832357	+	0.554240i	$0.186991\pi$
$179$	−1.45098	+	11.9499i	−0.108452	+	0.893179i	−0.940808	+	0.338939i	$0.889932\pi$
$180$	−10.0306	−	12.4988i	−0.747633	−	0.931602i
$181$	2.58166	−	0.979094i	0.191893	−	0.0727755i	−0.256786	−	0.966468i	$-0.582664\pi$
$181$	2.58166	−	0.979094i	0.191893	−	0.0727755i	0.448680	+	0.893693i	$0.351894\pi$
$182$	4.37498	+	1.23893i	0.324295	+	0.0918356i
$183$	−9.67661	+	1.23249i	−0.715315	+	0.0911082i
$184$	4.92567	+	3.85902i	0.363125	+	0.284490i
$185$	24.0451	+	9.11910i	1.76783	+	0.670449i
$186$	7.04528	−	4.92416i	0.516585	−	0.361057i
$187$	7.13743	+	1.30798i	0.521940	+	0.0956491i
$188$	11.1885	+	11.1885i	0.816007	+	0.816007i
$189$	−9.10675	+	0.711598i	−0.662419	+	0.0517611i
$190$	9.91466	−	7.76764i	0.719285	−	0.563524i
$191$		−	15.4976i		−	1.12137i	−0.828029	−	0.560685i	$-0.810538\pi$
$191$		−	15.4976i		−	1.12137i	0.828029	−	0.560685i	$-0.189462\pi$
$192$	2.81186	−	1.49684i	0.202928	−	0.108025i
$193$	13.6420	−	10.6878i	0.981974	−	0.769328i	0.00893338	−	0.999960i	$-0.497156\pi$
$193$	13.6420	−	10.6878i	0.981974	−	0.769328i	0.973041	+	0.230632i	$0.0740795\pi$
$194$	−5.75191	+	5.09575i	−0.412963	+	0.365854i
$195$	−22.3710	−	1.99312i	−1.60202	−	0.142730i
$196$	4.34679	+	3.85092i	0.310485	+	0.275065i
$197$	−5.31695	−	0.321616i	−0.378817	−	0.0229142i	−0.130127	−	0.991497i	$-0.541539\pi$
$197$	−5.31695	−	0.321616i	−0.378817	−	0.0229142i	−0.248690	+	0.968583i	$0.580000\pi$
$198$	7.21406	−	3.89465i	0.512681	−	0.276781i
$199$	−24.8988	−	9.44288i	−1.76503	−	0.669388i	−0.999667	−	0.0257914i	$-0.991789\pi$
$199$	−24.8988	−	9.44288i	−1.76503	−	0.669388i	−0.765365	−	0.643597i	$-0.777441\pi$
$200$	−1.19781	−	19.8021i	−0.0846979	−	1.40022i
$201$	−17.2419	+	7.88166i	−1.21615	+	0.555929i
$202$	2.89350	+	1.74918i	0.203586	+	0.123072i
$203$	−4.07181	−	9.04718i	−0.285785	−	0.634988i
$204$	−2.76026	+	4.04944i	−0.193257	+	0.283518i
$205$	−14.1004	+	1.71210i	−0.984815	+	0.119578i
$206$	−7.12142	+	0.430767i	−0.496173	+	0.0300129i
$207$	−6.60649	+	3.56665i	−0.459183	+	0.247899i
$208$	−1.15631	+	4.08322i	−0.0801756	+	0.283120i
$209$	−8.64213	−	16.4662i	−0.597789	−	1.13899i
$210$	−6.74647	−	4.02463i	−0.465550	−	0.277726i
$211$	−10.4227	+	15.0999i	−0.717531	+	1.03952i	0.279318	+	0.960199i	$0.409892\pi$
$211$	−10.4227	+	15.0999i	−0.717531	+	1.03952i	−0.996849	+	0.0793245i	$0.974724\pi$
$212$	10.4933	−	9.29623i	0.720681	−	0.638468i
$213$	−11.3023	+	11.4354i	−0.774418	+	0.783540i
$214$	−1.77667	−	2.26776i	−0.121451	−	0.155021i
$215$	−11.2000	+	3.49007i	−0.763835	+	0.238021i
$216$	1.01212	+	12.9527i	0.0688658	+	0.881318i
$217$	−6.90816	+	10.0082i	−0.468956	+	0.679401i
$218$	1.38041	−	0.340240i	0.0934930	−	0.0230439i
$219$	1.17941	−	21.5953i	0.0796969	−	1.45927i
$220$	−20.2009	−	2.45284i	−1.36195	−	0.165370i
$221$	1.41401	+	6.72101i	0.0951163	+	0.452104i
$222$	−5.08988	−	7.28239i	−0.341611	−	0.488762i
$223$	18.9746	+	8.53977i	1.27063	+	0.571865i	0.929733	−	0.368235i	$-0.120038\pi$
$223$	18.9746	+	8.53977i	1.27063	+	0.571865i	0.340899	+	0.940100i	$0.389268\pi$
$224$	−6.81375	+	7.69113i	−0.455263	+	0.513885i
$225$	22.3533	+	8.17937i	1.49022	+	0.545291i
$226$	4.13598	−	2.50029i	0.275121	−	0.166317i
$227$	−2.84482	+	15.5237i	−0.188817	+	1.03034i	0.743510	+	0.668725i	$0.233160\pi$
$227$	−2.84482	+	15.5237i	−0.188817	+	1.03034i	−0.932327	+	0.361616i	$0.882225\pi$
$228$	12.5319	−	0.831715i	0.829946	−	0.0550816i
$229$	−17.2972	−	1.04629i	−1.14303	−	0.0691407i	−0.522014	−	0.852937i	$-0.674819\pi$
$229$	−17.2972	−	1.04629i	−1.14303	−	0.0691407i	−0.621018	+	0.783796i	$0.713281\pi$
$230$	−6.40965	−	0.778272i	−0.422640	−	0.0513178i
$231$	−7.64043	+	8.72667i	−0.502703	+	0.574173i
$232$	−12.8680	+	5.79139i	−0.844822	+	0.380224i
$233$	21.3451	−	5.26109i	1.39836	−	0.344665i	0.533128	−	0.846034i	$-0.321016\pi$
$233$	21.3451	−	5.26109i	1.39836	−	0.344665i	0.865234	+	0.501369i	$0.167170\pi$
$234$	5.99866	+	4.92230i	0.392144	+	0.321781i
$235$	−37.1980	−	9.16849i	−2.42653	−	0.598086i
$236$	−22.0685	+	4.04419i	−1.43653	+	0.263255i
$237$	−3.28351	−	1.22333i	−0.213287	−	0.0794638i
$238$	−0.574902	+	2.33247i	−0.0372654	+	0.151191i
$239$	4.59317	+	4.59317i	0.297107	+	0.297107i	0.839880	−	0.542773i	$-0.182625\pi$
$239$	4.59317	+	4.59317i	0.297107	+	0.297107i	−0.542773	+	0.839880i	$0.682625\pi$
$240$	3.75624	−	6.29655i	0.242464	−	0.406441i
$241$	8.39592	−	3.77870i	0.540829	−	0.243407i	−0.121538	−	0.992587i	$-0.538783\pi$
$241$	8.39592	−	3.77870i	0.540829	−	0.243407i	0.662367	+	0.749179i	$0.269552\pi$
$242$	0.749307	−	2.40461i	0.0481673	−	0.154574i
$243$	−14.7310	−	5.09872i	−0.944996	−	0.327083i
$244$	−3.88761	−	7.40723i	−0.248879	−	0.474199i
$245$	−13.8305	−	2.53452i	−0.883595	−	0.161925i
$246$	4.35857	+	2.25510i	0.277892	+	0.143780i
$247$	11.3240	−	13.4753i	0.720527	−	0.857410i
$248$	14.2348	+	9.82558i	0.903912	+	0.623925i
$249$	−2.77598	+	9.09561i	−0.175921	+	0.576411i
$250$	4.30048	+	6.23032i	0.271986	+	0.394040i
$251$	0.367086	+	0.325210i	0.0231703	+	0.0205271i	0.674628	−	0.738158i	$-0.264304\pi$
$251$	0.367086	+	0.325210i	0.0231703	+	0.0205271i	−0.651458	+	0.758685i	$0.725842\pi$
$252$	−3.29840	−	7.10524i	−0.207780	−	0.447588i
$253$	−2.83614	+	9.10151i	−0.178307	+	0.572207i
$254$	−4.57955	+	14.6963i	−0.287347	+	0.922127i
$255$	0.647079	−	11.8482i	0.0405216	−	0.741962i
$256$	8.32198	+	7.37263i	0.520124	+	0.460790i
$257$	4.41532	+	6.39670i	0.275420	+	0.399015i	0.936146	−	0.351613i	$-0.114367\pi$
$257$	4.41532	+	6.39670i	0.275420	+	0.399015i	−0.660725	+	0.750628i	$0.729751\pi$
$258$	3.87655	+	1.18312i	0.241343	+	0.0736580i
$259$	10.3450	+	7.14065i	0.642808	+	0.443699i
$260$	−5.09618	−	18.5744i	−0.316052	−	1.15193i
$261$	−0.198268	−	16.9299i	−0.0122725	−	1.04793i
$262$	−0.624988	−	0.114533i	−0.0386119	−	0.00707589i
$263$	−0.323759	−	0.616872i	−0.0199638	−	0.0380379i	0.875270	−	0.483635i	$-0.160684\pi$
$263$	−0.323759	−	0.616872i	−0.0199638	−	0.0380379i	−0.895234	+	0.445597i	$0.852991\pi$
$264$	12.4121	+	10.8671i	0.763911	+	0.668824i
$265$	−10.0982	+	32.4062i	−0.620327	+	1.99070i
$266$	5.61412	−	2.52671i	0.344224	−	0.154923i
$267$	17.5784	+	10.4865i	1.07578	+	0.641762i
$268$	−11.4960	−	11.4960i	−0.702230	−	0.702230i
$269$	0.630784	−	2.55919i	0.0384595	−	0.156037i	−0.948572	−	0.316560i	$-0.897472\pi$
$269$	0.630784	−	2.55919i	0.0384595	−	0.156037i	0.987032	+	0.160524i	$0.0513183\pi$
$270$	−7.80818	−	10.8976i	−0.475191	−	0.663206i
$271$	−20.7551	+	3.80351i	−1.26078	+	0.231047i	−0.768760	−	0.639537i	$-0.779126\pi$
$271$	−20.7551	+	3.80351i	−1.26078	+	0.231047i	−0.492021	+	0.870584i	$0.663742\pi$
$272$	−2.17692	−	0.536563i	−0.131995	−	0.0325339i
$273$	−10.3841	−	3.56285i	−0.628474	−	0.215633i
$274$	−6.60587	+	1.62820i	−0.399075	+	0.0983631i
$275$	27.5613	−	12.4043i	1.66201	−	0.748010i
$276$	−4.84418	−	4.24120i	−0.291585	−	0.255290i
$277$	19.5772	+	2.37710i	1.17628	+	0.142826i	0.685244	−	0.728313i	$-0.259695\pi$
$277$	19.5772	+	2.37710i	1.17628	+	0.142826i	0.491035	+	0.871140i	$0.336619\pi$
$278$	−0.324313	−	0.0196173i	−0.0194510	−	0.00117657i
$279$	−17.6331	+	10.9436i	−1.05567	+	0.655175i
$280$	2.84945	−	15.5489i	0.170287	−	0.929227i
$281$	−9.99431	+	6.04177i	−0.596211	+	0.360422i	−0.783041	−	0.621970i	$-0.786332\pi$
$281$	−9.99431	+	6.04177i	−0.596211	+	0.360422i	0.186830	+	0.982392i	$0.440179\pi$
$282$	8.83519	+	9.85599i	0.526128	+	0.586916i
$283$	10.0086	−	11.2974i	0.594949	−	0.671558i	−0.371496	−	0.928435i	$-0.621155\pi$
$283$	10.0086	−	11.2974i	0.594949	−	0.671558i	0.966444	+	0.256877i	$0.0826934\pi$
$284$	−12.5735	−	5.65887i	−0.746100	−	0.335792i
$285$	−24.9250	+	17.4209i	−1.47643	+	1.03192i
$286$	9.81618	−	0.851533i	0.580443	−	0.0503522i
$287$	−6.89230	−	0.836877i	−0.406840	−	0.0493993i
$288$	−15.9049	+	7.38341i	−0.937208	+	0.435072i
$289$	12.9829	−	3.19999i	0.763699	−	0.188235i
$290$	8.27148	−	11.9833i	0.485718	−	0.703684i
$291$	14.5377	−	11.5275i	0.852213	−	0.675756i
$292$	17.7073	−	5.51782i	1.03624	−	0.322906i
$293$	−17.2345	−	21.9983i	−1.00685	−	1.28515i	−0.958128	−	0.286339i	$-0.907562\pi$
$293$	−17.2345	−	21.9983i	−1.00685	−	1.28515i	−0.0487236	−	0.998812i	$-0.515515\pi$
$294$	3.45513	+	3.41490i	0.201507	+	0.199161i
$295$	40.6613	−	36.0228i	2.36739	−	2.09733i
$296$	10.1563	−	14.7139i	0.590321	−	0.855227i
$297$	−17.9045	+	8.43942i	−1.03892	+	0.489705i
$298$	5.09701	+	9.71154i	0.295262	+	0.562574i
$299$	−8.98946	+	0.779817i	−0.519874	+	0.0450980i
$300$	0.119521	+	20.4122i	0.00690054	+	1.17850i
$301$	−5.72377	+	0.346224i	−0.329913	+	0.0199560i
$302$	−9.55424	+	1.16010i	−0.549785	+	0.0667560i
$303$	−6.74535	−	4.59790i	−0.387510	−	0.264142i
$304$	2.35821	+	5.23972i	0.135253	+	0.300519i
$305$	17.3337	+	10.4786i	0.992522	+	0.600001i
$306$	−2.49033	+	3.25652i	−0.142363	+	0.186163i
$307$	1.10527	+	18.2723i	0.0630810	+	1.04285i	0.882698	+	0.469941i	$0.155725\pi$
$307$	1.10527	+	18.2723i	0.0630810	+	1.04285i	−0.819617	+	0.572912i	$0.805814\pi$
$308$	−9.30039	−	3.52717i	−0.529939	−	0.200979i
$309$	17.2251	−	0.100859i	0.979901	−	0.00573766i
$310$	−17.8152	−	1.07762i	−1.01183	−	0.0612047i
$311$	10.0906	+	8.93946i	0.572183	+	0.506910i	0.898866	−	0.438224i	$-0.144392\pi$
$311$	10.0906	+	8.93946i	0.572183	+	0.506910i	−0.326682	+	0.945134i	$0.605931\pi$
$312$	−5.06749	+	14.7695i	−0.286890	+	0.836156i
$313$	16.1026	−	14.2657i	0.910174	−	0.806344i	−0.0713958	−	0.997448i	$-0.522745\pi$
$313$	16.1026	−	14.2657i	0.910174	−	0.806344i	0.981570	+	0.191104i	$0.0612069\pi$
$314$	3.83598	−	3.00530i	0.216477	−	0.169599i
$315$	15.7345	+	10.5909i	0.886540	+	0.596728i
$316$		−	3.00493i		−	0.169041i
$317$	−19.0448	+	14.9207i	−1.06966	+	0.838028i	−0.987347	−	0.158578i	$-0.949309\pi$
$317$	−19.0448	+	14.9207i	−1.06966	+	0.838028i	−0.0823178	+	0.996606i	$0.526232\pi$
$318$	9.18894	−	7.28631i	0.515290	−	0.408596i
$319$	−15.2018	−	15.2018i	−0.851137	−	0.851137i
$320$	−6.50591	−	1.19225i	−0.363691	−	0.0666489i
$321$	3.98464	+	5.70105i	0.222401	+	0.318201i
$322$	−2.95097	−	1.11915i	−0.164451	−	0.0623680i
$323$	7.32020	+	5.73501i	0.407307	+	0.319104i
$324$	−0.313071	−	13.3646i	−0.0173928	−	0.742476i
$325$	20.7498	+	19.6933i	1.15099	+	1.09239i
$326$	3.43336	−	1.30210i	0.190156	−	0.0721166i
$327$	−3.37269	+	0.638502i	−0.186510	+	0.0353092i
$328$	−1.19030	+	9.80303i	−0.0657235	+	0.541282i
$329$	−16.5816	−	8.70269i	−0.914173	−	0.479795i
$330$	−16.7616	−	2.97035i	−0.922696	−	0.163512i
$331$	19.8027	+	15.5144i	1.08845	+	0.852750i	0.989813	−	0.142373i	$-0.0454734\pi$
$331$	19.8027	+	15.5144i	1.08845	+	0.852750i	0.0986415	+	0.995123i	$0.468550\pi$
$332$	−8.14046	+	0.492407i	−0.446766	+	0.0270244i
$333$	11.3119	+	18.2266i	0.619888	+	0.998811i
$334$	−1.95092	−	2.82640i	−0.106750	−	0.154653i
$335$	38.2203	+	9.42045i	2.08820	+	0.514694i
$336$	2.51926	−	2.54894i	0.137437	−	0.139056i
$337$			14.5124i			0.790543i	0.918564	+	0.395271i	$0.129349\pi$
$337$			14.5124i			0.790543i	−0.918564	+	0.395271i	$0.870651\pi$
$338$	4.26629	+	8.29295i	0.232055	+	0.451077i
$339$	−10.3002	+	5.48314i	−0.559432	+	0.297803i
$340$	9.71507	−	3.02734i	0.526874	−	0.164181i
$341$	−6.30637	+	25.5859i	−0.341509	+	1.38556i
$342$	10.5056	−	0.123033i	0.568080	−	0.00665285i
$343$	−17.4889	−	7.87110i	−0.944310	−	0.424999i
$344$	0.492440	+	8.14101i	0.0265506	+	0.438934i
$345$	15.3499	+	2.72018i	0.826413	+	0.146450i
$346$	−3.45987	+	4.41620i	−0.186004	+	0.237416i
$347$	−1.86212	+	3.54797i	−0.0999638	+	0.190465i	−0.930302	−	0.366795i	$-0.880455\pi$
$347$	−1.86212	+	3.54797i	−0.0999638	+	0.190465i	0.830338	+	0.557260i	$0.188147\pi$
$348$	13.5457	−	5.22813i	0.726126	−	0.280257i
$349$	23.8807	+	7.44154i	1.27831	+	0.398337i	0.860151	−	0.510039i	$-0.170369\pi$
$349$	23.8807	+	7.44154i	1.27831	+	0.398337i	0.418156	+	0.908375i	$0.362677\pi$
$350$	3.54818	+	9.35578i	0.189658	+	0.500088i
$351$	−13.8135	−	12.6565i	−0.737310	−	0.675554i
$352$	−7.89551	+	20.8188i	−0.420832	+	1.10964i
$353$	11.1157	−	14.1882i	0.591630	−	0.755159i	−0.394903	−	0.918723i	$-0.629222\pi$
$353$	11.1157	−	14.1882i	0.591630	−	0.755159i	0.986533	+	0.163563i	$0.0522988\pi$
$354$	−18.6179	+	2.37132i	−0.989531	+	0.126034i
$355$	33.1413	−	4.02409i	1.75896	−	0.213576i
$356$	−3.16409	+	17.2659i	−0.167696	+	0.915089i
$357$	1.69308	−	5.54743i	0.0896072	−	0.293601i
$358$	−8.49419	+	1.55662i	−0.448932	+	0.0822698i
$359$	4.64169	+	5.92467i	0.244979	+	0.312692i	0.893990	−	0.448086i	$-0.147894\pi$
$359$	4.64169	+	5.92467i	0.244979	+	0.312692i	−0.649012	+	0.760779i	$0.724817\pi$
$360$	15.0636	−	22.3794i	0.793919	−	1.17950i
$361$		−	4.83191i		−	0.254311i
$362$	1.22157	+	1.55922i	0.0642043	+	0.0819508i
$363$	−2.12304	+	5.69840i	−0.111430	+	0.299088i
$364$	−0.245847	−	9.41150i	−0.0128859	−	0.493297i
$365$	−29.7789	+	33.6134i	−1.55870	+	1.75941i
$366$	−2.90935	−	6.36448i	−0.152074	−	0.332677i
$367$	−11.6077	−	6.09218i	−0.605916	−	0.318009i	0.133717	−	0.991020i	$-0.457309\pi$
$367$	−11.6077	−	6.09218i	−0.605916	−	0.318009i	−0.739633	+	0.673010i	$0.765001\pi$
$368$	1.04452	−	2.75417i	0.0544493	−	0.143571i
$369$	−10.2107	−	6.01048i	−0.531550	−	0.312893i
$370$	−1.11389	+	18.4147i	−0.0579082	+	0.957337i
$371$	−8.58340	+	14.1987i	−0.445628	+	0.737158i
$372$	−14.0737	−	10.8937i	−0.729690	−	0.564812i
$373$	0.0938037	−	0.0492320i	0.00485697	−	0.00254914i	−0.462293	−	0.886727i	$-0.652973\pi$
$373$	0.0938037	−	0.0492320i	0.00485697	−	0.00254914i	0.467150	+	0.884178i	$0.345281\pi$
$374$	0.627459	+	5.16759i	0.0324451	+	0.267210i
$375$	−9.54731	−	15.5863i	−0.493021	−	0.804874i
$376$	−12.3780	+	23.5843i	−0.638345	+	1.21627i
$377$	7.86393	−	18.7676i	0.405013	−	0.966582i
$378$	−2.43097	−	6.08536i	−0.125036	−	0.312997i
$379$	1.96825	−	1.18985i	0.101102	−	0.0611185i	−0.465883	−	0.884846i	$-0.654263\pi$
$379$	1.96825	−	1.18985i	0.101102	−	0.0611185i	0.566986	+	0.823728i	$0.308109\pi$
$380$	−21.4621	−	14.8142i	−1.10098	−	0.759955i
$381$	12.9754	−	34.8269i	0.664749	−	1.78424i
$382$	10.6144	−	3.30757i	0.543078	−	0.169230i
$383$	17.1961	−	13.4723i	0.878681	−	0.688403i	−0.0723895	−	0.997376i	$-0.523062\pi$
$383$	17.1961	−	13.4723i	0.878681	−	0.688403i	0.951071	+	0.308974i	$0.0999855\pi$
$384$	−12.7757	−	12.6269i	−0.651956	−	0.644366i
$385$	23.6891	−	4.34119i	1.20731	−	0.221247i
$386$	10.2317	+	7.06240i	0.520778	+	0.359467i
$387$	−9.18982	−	3.36268i	−0.467145	−	0.170935i
$388$	13.6162	+	8.23130i	0.691260	+	0.417881i
$389$	−0.161804	+	1.33258i	−0.00820380	+	0.0675644i	−0.996236	−	0.0866847i	$-0.972373\pi$
$389$	−0.161804	+	1.33258i	−0.00820380	+	0.0675644i	0.988032	+	0.154249i	$0.0492958\pi$
$390$	−3.40942	−	15.7473i	−0.172643	−	0.797397i
$391$	−0.574615	−	4.73238i	−0.0290595	−	0.239327i
$392$	−4.01198	+	8.91425i	−0.202636	+	0.450238i
$393$	1.49164	+	0.358406i	0.0752435	+	0.0180792i
$394$	−0.914490	−	3.71023i	−0.0460713	−	0.186919i
$395$	3.76398	+	6.22639i	0.189387	+	0.313284i
$396$	−12.1426	−	11.8615i	−0.610189	−	0.596062i
$397$	10.9839	−	24.4052i	0.551265	−	1.22486i	−0.400008	−	0.916512i	$-0.630993\pi$
$397$	10.9839	−	24.4052i	0.551265	−	1.22486i	0.951273	−	0.308350i	$-0.0997767\pi$
$398$	1.15344	−	19.0686i	0.0578166	−	0.955822i
$399$	−13.8672	+	5.35223i	−0.694230	+	0.267947i
$400$	−8.73186	+	3.31156i	−0.436593	+	0.165578i
$401$	0.505820	+	1.12389i	0.0252594	+	0.0561242i	0.924098	−	0.382156i	$-0.124818\pi$
$401$	0.505820	+	1.12389i	0.0252594	+	0.0561242i	−0.898838	+	0.438281i	$0.855588\pi$
$402$	−9.07799	−	10.1268i	−0.452769	−	0.505081i
$403$	−24.6733	+	3.65198i	−1.22906	+	0.181918i
$404$	1.67537	−	6.79725i	0.0833529	−	0.338176i
$405$	17.3892	+	27.3000i	0.864076	+	1.35655i
$406$	5.32741	−	4.71967i	0.264395	−	0.234233i
$407$	26.4470	+	6.51860i	1.31093	+	0.323115i
$408$	−7.89020	−	2.40809i	−0.390623	−	0.119218i
$409$	−17.7332	+	10.7201i	−0.876851	+	0.530075i	−0.882716	−	0.469908i	$-0.844287\pi$
$409$	−17.7332	+	10.7201i	−0.876851	+	0.530075i	0.00586416	+	0.999983i	$0.498133\pi$
$410$	−4.18198	−	9.29199i	−0.206533	−	0.458898i
$411$	16.1398	−	3.05552i	0.796119	−	0.150718i
$412$	5.23823	+	13.8121i	0.258069	+	0.680472i
$413$	23.5117	−	12.3399i	1.15693	−	0.607206i
$414$	−3.85278	−	3.76359i	−0.189354	−	0.184970i
$415$	16.2507	−	11.2171i	0.797716	−	0.550623i
$416$	−21.0675	+	0.550325i	−1.03292	+	0.0269819i
$417$	0.779271	+	0.0899938i	0.0381611	+	0.00440702i
$418$	9.43329	−	9.43329i	0.461397	−	0.461397i
$419$	−10.1122	+	6.97994i	−0.494013	+	0.340992i	−0.788882	−	0.614545i	$-0.789339\pi$
$419$	−10.1122	+	6.97994i	−0.494013	+	0.340992i	0.294869	+	0.955538i	$0.404724\pi$
$420$	−3.80004	+	15.8153i	−0.185423	+	0.771710i
$421$	−7.13381	+	11.8008i	−0.347681	+	0.575134i	−0.979859	−	0.199688i	$-0.936007\pi$
$421$	−7.13381	+	11.8008i	−0.347681	+	0.575134i	0.632179	+	0.774823i	$0.282161\pi$
$422$	−12.5664	−	3.91586i	−0.611725	−	0.190621i
$423$	−20.0022	−	24.9241i	−0.972542	−	1.21185i
$424$	20.1950	+	12.2083i	0.980755	+	0.592887i
$425$	−10.0223	+	11.3128i	−0.486153	+	0.548753i
$426$	−10.2443	−	5.30035i	−0.496338	−	0.256803i
$427$	7.00076	+	7.00076i	0.338791	+	0.338791i
$428$	−3.38843	+	4.90899i	−0.163786	+	0.237285i
$429$	−23.7770	+	0.760443i	−1.14796	+	0.0367145i
$430$	−4.78071	−	6.92605i	−0.230546	−	0.334004i
$431$	4.58958	−	25.0445i	0.221072	−	1.20635i	−0.666437	−	0.745561i	$-0.732182\pi$
$431$	4.58958	−	25.0445i	0.221072	−	1.20635i	0.887509	−	0.460790i	$-0.152434\pi$
$432$	5.67953	−	2.26886i	0.273257	−	0.109160i
$433$	19.0332	−	7.21832i	0.914675	−	0.346890i	0.148046	−	0.988981i	$-0.452702\pi$
$433$	19.0332	−	7.21832i	0.914675	−	0.346890i	0.766629	+	0.642090i	$0.221932\pi$
$434$	−8.32900	−	2.59542i	−0.399805	−	0.124584i
$435$	−21.5187	+	27.8004i	−1.03174	+	1.33292i
$436$	−1.52289	−	2.51917i	−0.0729331	−	0.120646i
$437$	−8.63882	+	8.63882i	−0.413251	+	0.413251i
$438$	15.0423	−	3.80117i	0.718751	−	0.181627i
$439$	7.71552	+	8.70903i	0.368242	+	0.415659i	0.903200	−	0.429219i	$-0.141211\pi$
$439$	7.71552	+	8.70903i	0.368242	+	0.415659i	−0.534958	+	0.844878i	$0.679673\pi$
$440$	−6.17454	−	33.6934i	−0.294359	−	1.60627i
$441$	−7.88002	−	8.68757i	−0.375239	−	0.413694i
$442$	−4.30145	+	2.40288i	−0.204599	+	0.114293i
$443$	9.11880	+	36.9964i	0.433247	+	1.75775i	0.629302	+	0.777161i	$0.283341\pi$
$443$	9.11880	+	36.9964i	0.433247	+	1.75775i	−0.196054	+	0.980593i	$0.562813\pi$
$444$	−11.2603	+	14.5474i	−0.534391	+	0.690389i
$445$	−15.0711	−	39.7392i	−0.714438	−	1.88382i
$446$	−1.79927	+	14.8183i	−0.0851979	+	0.701667i
$447$	−11.0092	−	24.0837i	−0.520719	−	1.13912i
$448$	−2.94823	−	1.32689i	−0.139291	−	0.0626896i
$449$	27.3784	+	5.01727i	1.29207	+	0.236780i	0.781958	−	0.623331i	$-0.214221\pi$
$449$	27.3784	+	5.01727i	1.29207	+	0.236780i	0.510107	+	0.860111i	$0.329606\pi$
$450$	−0.831338	+	17.0555i	−0.0391897	+	0.804002i
$451$	−14.6076	+	3.60045i	−0.687846	+	0.169539i
$452$	−7.49020	−	6.63574i	−0.352309	−	0.312119i
$453$	23.1862	−	1.53881i	1.08938	−	0.0722997i
$454$	−11.2393	+	1.36470i	−0.527488	+	0.0640486i
$455$	12.2983	+	19.1932i	0.576552	+	0.899792i
$456$	7.61256	+	19.7236i	0.356491	+	0.923641i
$457$	2.08394	−	3.44726i	0.0974827	−	0.161256i	−0.803233	−	0.595665i	$-0.796889\pi$
$457$	2.08394	−	3.44726i	0.0974827	−	0.161256i	0.900716	+	0.434409i	$0.143043\pi$
$458$	−2.97503	−	12.0702i	−0.139014	−	0.564003i
$459$	6.43247	−	7.52294i	0.300242	−	0.351141i
$460$	2.40979	+	13.1498i	0.112357	+	0.613113i
$461$	1.91208	+	6.13607i	0.0890543	+	0.285785i	0.988494	−	0.151259i	$-0.0483329\pi$
$461$	1.91208	+	6.13607i	0.0890543	+	0.285785i	−0.899440	+	0.437045i	$0.856025\pi$
$462$	−7.60756	−	3.37046i	−0.353936	−	0.156808i
$463$	−12.5150	−	40.1620i	−0.581621	−	1.86649i	−0.492180	−	0.870494i	$-0.663800\pi$
$463$	−12.5150	−	40.1620i	−0.581621	−	1.86649i	−0.0894410	−	0.995992i	$-0.528508\pi$
$464$	4.40493	+	4.97213i	0.204494	+	0.230825i
$465$	42.8071	+	4.94355i	1.98513	+	0.229252i
$466$	8.15888	+	13.4964i	0.377953	+	0.625210i
$467$	18.7923	−	9.86294i	0.869602	−	0.456402i	0.0299656	−	0.999551i	$-0.490460\pi$
$467$	18.7923	−	9.86294i	0.869602	−	0.456402i	0.839637	+	0.543148i	$0.182768\pi$
$468$	6.03516	−	14.8900i	0.278975	−	0.688292i
$469$	17.0373	+	8.94186i	0.786709	+	0.412897i
$470$	−1.65944	−	27.4337i	−0.0765441	−	1.26542i
$471$	−9.64348	+	6.74012i	−0.444348	+	0.310568i
$472$	−17.5512	−	33.4410i	−0.807859	−	1.53925i
$473$	−11.3309	+	5.09964i	−0.520997	+	0.234482i
$474$	0.137080	−	2.50997i	0.00629629	−	0.115287i
$475$	38.6627	+	2.33866i	1.77397	+	0.107305i
$476$	4.96489	−	0.300320i	0.227565	−	0.0137652i
$477$	−23.1121	+	16.3560i	−1.05823	+	0.748890i
$478$	−2.16558	+	4.12616i	−0.0990511	+	0.188726i
$479$	0.0360300	−	0.595647i	0.00164625	−	0.0272158i	−0.997260	−	0.0739808i	$-0.976430\pi$
$479$	0.0360300	−	0.595647i	0.00164625	−	0.0272158i	0.998906	+	0.0467650i	$0.0148912\pi$
$480$	35.4023	+	8.50632i	1.61589	+	0.388259i
$481$	3.77488	+	25.5036i	0.172120	+	1.16287i
$482$	4.37993	+	4.94392i	0.199500	+	0.225189i
$483$	6.96686	+	3.08660i	0.317003	+	0.140445i
$484$	−5.21493			−0.237042
$485$	−38.5242			−1.74929
$486$	0.348166	−	11.1775i	0.0157931	−	0.507021i
$487$	−3.53068	−	19.2663i	−0.159990	−	0.873040i	−0.961448	−	0.274988i	$-0.911326\pi$
$487$	−3.53068	−	19.2663i	−0.159990	−	0.873040i	0.801457	−	0.598052i	$-0.204058\pi$
$488$	9.95729	−	9.95729i	0.450745	−	0.450745i
$489$	−8.44859	+	2.68706i	−0.382058	+	0.121513i
$490$	−1.21585	−	10.0134i	−0.0549265	−	0.452360i
$491$	6.56022	−	17.2979i	0.296059	−	0.780642i	−0.701621	−	0.712551i	$-0.747540\pi$
$491$	6.56022	−	17.2979i	0.296059	−	0.780642i	0.997679	−	0.0680914i	$-0.0216909\pi$
$492$	1.77300	−	10.0050i	0.0799330	−	0.451060i
$493$	10.0519	+	3.81219i	0.452716	+	0.171693i
$494$	11.6460	+	4.87986i	0.523980	+	0.219555i
$495$	40.0179	+	9.36783i	1.79867	+	0.421053i
$496$	2.42234	−	7.77355i	0.108766	−	0.349043i
$497$	16.1995	+	1.96698i	0.726649	+	0.0882311i
$498$	−6.82206	+	0.0399455i	−0.305704	+	0.00179000i
$499$	2.54388	+	1.99300i	0.113880	+	0.0892190i	0.672043	−	0.740512i	$-0.265417\pi$
$499$	2.54388	+	1.99300i	0.113880	+	0.0892190i	−0.558164	+	0.829731i	$0.688494\pi$
$500$	9.66688	−	12.3389i	0.432316	−	0.551811i
$501$	4.33115	+	7.07076i	0.193502	+	0.315898i
$502$	−0.144392	+	0.320825i	−0.00644452	+	0.0143191i
$503$	3.97677	−	2.74497i	0.177315	−	0.122392i	−0.476101	−	0.879391i	$-0.657950\pi$
$503$	3.97677	−	2.74497i	0.177315	−	0.122392i	0.653417	+	0.756999i	$0.273335\pi$
$504$	9.76704	−	8.85914i	0.435059	−	0.394617i
$505$	5.04278	+	16.1829i	0.224401	+	0.720128i
$506$	−6.83894			−0.304028
$507$	−9.19330	−	20.5544i	−0.408289	−	0.912853i
$508$	31.8722			1.41410
$509$	−1.92741	−	6.18528i	−0.0854310	−	0.274158i	0.902113	−	0.431499i	$-0.142015\pi$
$509$	−1.92741	−	6.18528i	−0.0854310	−	0.274158i	−0.987544	+	0.157342i	$0.949708\pi$
$510$	8.25294	−	2.08550i	0.365446	−	0.0923476i
$511$	−18.0650	+	12.4694i	−0.799151	+	0.551614i
$512$	5.23916	−	11.6409i	0.231540	−	0.514462i
$513$	−25.3433	−	1.08661i	−1.11893	−	0.0479749i
$514$	−3.43877	+	4.38927i	−0.151678	+	0.193602i
$515$	−28.1549	−	22.0580i	−1.24066	−	0.971991i
$516$	−0.0491371	−	8.39183i	−0.00216314	−	0.369430i
$517$	−40.2833	−	4.89128i	−1.77166	−	0.215118i
$518$	−2.68277	+	8.60931i	−0.117874	+	0.378271i
$519$	8.92253	−	10.1911i	0.391656	−	0.447338i
$520$	27.2988	−	17.4920i	1.19713	−	0.767076i
$521$	−17.7030	−	6.71388i	−0.775585	−	0.294140i	−0.0651238	−	0.997877i	$-0.520744\pi$
$521$	−17.7030	−	6.71388i	−0.775585	−	0.294140i	−0.710461	+	0.703737i	$0.751513\pi$
$522$	11.5530	−	3.74904i	0.505661	−	0.164091i
$523$	−7.16728	+	18.8986i	−0.313403	+	0.826376i	0.682066	+	0.731291i	$0.261082\pi$
$523$	−7.16728	+	18.8986i	−0.313403	+	0.826376i	−0.995469	+	0.0950855i	$0.969688\pi$
$524$	0.158578	+	1.30601i	0.00692752	+	0.0570532i
$525$	−7.32215	−	23.0221i	−0.319565	−	1.00477i
$526$	0.353398	−	0.353398i	0.0154089	−	0.0154089i
$527$	−2.37529	−	12.9615i	−0.103469	−	0.564612i
$528$	3.14569	−	7.10023i	0.136899	−	0.308998i
$529$	−16.7370			−0.727697
$530$	−24.3503			−1.05771
$531$	45.1964	−	3.26549i	1.96136	−	0.141710i
$532$	−8.45295	−	9.54141i	−0.366482	−	0.413673i
$533$	−8.39253	−	11.5041i	−0.363521	−	0.498297i
$534$	−3.43055	+	14.2775i	−0.148454	+	0.617850i
$535$	0.872011	−	14.4161i	0.0377003	−	0.623260i
$536$	12.7181	−	24.2324i	0.549340	−	1.04668i
$537$	20.6828	−	2.63432i	0.892529	−	0.113679i
$538$	1.88742	−	0.114168i	0.0813723	−	0.00492212i
$539$	−14.8659	−	0.899224i	−0.640321	−	0.0387323i
$540$	−16.7323	+	22.1478i	−0.720043	+	0.953088i
$541$	−20.5905	+	9.26704i	−0.885256	+	0.398421i	−0.801451	−	0.598061i	$-0.795938\pi$
$541$	−20.5905	+	9.26704i	−0.885256	+	0.398421i	−0.0838051	+	0.996482i	$0.526707\pi$
$542$	−7.03466	−	13.4034i	−0.302164	−	0.575726i
$543$	−2.73968	−	3.91981i	−0.117571	−	0.168215i
$544$	−0.672262	−	11.1138i	−0.0288230	−	0.476501i
$545$	6.31102	+	3.31228i	0.270335	+	0.141883i
$546$	0.223984	−	7.87248i	0.00958565	−	0.336911i
$547$	11.8572	−	6.22316i	0.506979	−	0.266083i	−0.191783	−	0.981437i	$-0.561427\pi$
$547$	11.8572	−	6.22316i	0.506979	−	0.266083i	0.698762	+	0.715354i	$0.253735\pi$
$548$	7.28770	+	12.0553i	0.311315	+	0.514978i
$549$	6.17591	+	15.7266i	0.263581	+	0.671194i
$550$	14.3780	+	16.2294i	0.613080	+	0.692024i
$551$	−8.19660	−	26.3038i	−0.349187	−	1.12058i
$552$	4.39012	−	9.90907i	0.186856	−	0.421758i
$553$	1.05803	+	3.39534i	0.0449920	+	0.144384i
$554$	2.55016	+	13.9158i	0.108346	+	0.591225i
$555$	5.10993	−	44.2477i	0.216904	−	1.87821i
$556$	0.160993	+	0.653176i	0.00682764	+	0.0277008i
$557$	11.1998	−	18.5268i	0.474552	−	0.785004i	−0.523187	−	0.852218i	$-0.675257\pi$
$557$	11.1998	−	18.5268i	0.474552	−	0.785004i	0.997739	+	0.0672136i	$0.0214109\pi$
$558$	−11.2586	−	9.74134i	−0.476615	−	0.412384i
$559$	−8.53060	−	8.09627i	−0.360806	−	0.342436i
$560$	−7.38717	+	0.896964i	−0.312165	+	0.0379037i
$561$	−0.832295	−	12.5407i	−0.0351395	−	0.529467i
$562$	−6.27104	−	5.55566i	−0.264528	−	0.234351i
$563$	2.56486	−	0.632182i	0.108096	−	0.0266433i	−0.184897	−	0.982758i	$-0.559195\pi$
$563$	2.56486	−	0.632182i	0.108096	−	0.0266433i	0.292993	+	0.956115i	$0.405349\pi$
$564$	14.0407	−	23.5363i	0.591219	−	0.991057i
$565$	23.8321	+	4.36739i	1.00262	+	0.183737i
$566$	9.87365	+	4.44377i	0.415020	+	0.186786i
$567$	5.05938	+	14.9907i	0.212474	+	0.629550i
$568$	2.79767	−	23.0409i	0.117388	−	0.966773i
$569$	14.4861	+	38.1968i	0.607290	+	1.60129i	0.786575	+	0.617495i	$0.211852\pi$
$569$	14.4861	+	38.1968i	0.607290	+	1.60129i	−0.179285	+	0.983797i	$0.557378\pi$
$570$	−17.2512	−	13.3532i	−0.722572	−	0.559303i
$571$	−2.76737	−	11.2277i	−0.115811	−	0.469863i	−0.999996	−	0.00272703i	$-0.999132\pi$
$571$	−2.76737	−	11.2277i	−0.115811	−	0.469863i	0.884185	−	0.467136i	$-0.154714\pi$
$572$	−7.72992	−	18.8798i	−0.323204	−	0.789404i
$573$	−26.0247	+	6.57638i	−1.08720	+	0.274732i
$574$	−0.897804	−	4.89916i	−0.0374736	−	0.204487i
$575$	−13.1671	−	14.8626i	−0.549105	−	0.619812i
$576$	−3.70680	−	4.08668i	−0.154450	−	0.170278i
$577$	−16.3235	+	16.3235i	−0.679557	+	0.679557i	−0.959900	−	0.280343i	$-0.909552\pi$
$577$	−16.3235	+	16.3235i	−0.679557	+	0.679557i	0.280343	+	0.959900i	$0.409552\pi$
$578$	4.96254	+	8.20904i	0.206414	+	0.341451i
$579$	−23.7367	−	18.3732i	−0.986462	−	0.763565i
$580$	−28.7834	−	8.96926i	−1.19516	−	0.372428i
$581$	9.02470	−	3.42262i	0.374408	−	0.141994i
$582$	10.9979	+	7.49662i	0.455878	+	0.310745i
$583$	−6.48061	+	35.3635i	−0.268399	+	1.46461i
$584$	17.7354	+	25.6942i	0.733897	+	1.06323i
$585$	6.14610	+	38.4127i	0.254110	+	1.58817i
$586$	11.3884	−	16.4989i	0.470449	−	0.681564i
$587$	3.06007	+	3.06007i	0.126303	+	0.126303i	0.767432	−	0.641130i	$-0.221534\pi$
$587$	3.06007	+	3.06007i	0.126303	+	0.126303i	−0.641130	+	0.767432i	$0.721534\pi$
$588$	4.62216	−	8.93353i	0.190615	−	0.368412i
$589$	−22.3941	+	25.2778i	−0.922734	+	1.04155i
$590$	33.3502	+	20.1609i	1.37300	+	0.830010i
$591$	1.71615	+	9.06505i	0.0705931	+	0.372886i
$592$	−8.03517	−	2.50386i	−0.330243	−	0.102908i
$593$	0.833884	−	1.37941i	0.0342435	−	0.0566457i	−0.838191	−	0.545377i	$-0.816386\pi$
$593$	0.833884	−	1.37941i	0.0342435	−	0.0566457i	0.872434	+	0.488732i	$0.162540\pi$
$594$	−9.60141	−	10.4616i	−0.393951	−	0.429246i
$595$	−9.91135	+	6.84131i	−0.406326	+	0.280466i
$596$	16.0578	−	16.0578i	0.657753	−	0.657753i
$597$	−5.29136	+	45.8188i	−0.216561	+	1.87524i
$598$	−2.45266	−	5.99047i	−0.100297	−	0.244968i
$599$	−14.1892	+	9.79413i	−0.579757	+	0.400177i	−0.821538	−	0.570154i	$-0.806884\pi$
$599$	−14.1892	+	9.79413i	−0.579757	+	0.400177i	0.241781	+	0.970331i	$0.422268\pi$
$600$	−32.7447	+	10.4144i	−1.33680	+	0.425166i
$601$	−8.37346	+	4.39473i	−0.341561	+	0.179265i	−0.626778	−	0.779198i	$-0.715627\pi$
$601$	−8.37346	+	4.39473i	−0.341561	+	0.179265i	0.285217	+	0.958463i	$0.407934\pi$
$602$	−1.45872	−	3.84633i	−0.0594530	−	0.156765i
$603$	20.5519	+	25.6091i	0.836939	+	1.04288i
$604$	8.17853	+	18.1720i	0.332780	+	0.739406i
$605$	10.8056	−	6.53223i	0.439312	−	0.265573i
$606$	1.70949	−	5.60120i	0.0694433	−	0.227533i
$607$	−28.2147	−	6.95431i	−1.14520	−	0.282267i	−0.379330	−	0.925261i	$-0.623846\pi$
$607$	−28.2147	−	6.95431i	−1.14520	−	0.282267i	−0.765871	+	0.642995i	$0.777692\pi$
$608$	−21.3583	+	18.9218i	−0.866192	+	0.767379i
$609$	−13.4648	+	10.6768i	−0.545620	+	0.432645i
$610$	−3.47737	+	14.1082i	−0.140794	+	0.571225i
$611$	−10.1624	−	37.0397i	−0.411129	−	1.49847i
$612$	7.97140	+	2.91684i	0.322225	+	0.117906i
$613$	−10.5960	−	23.5433i	−0.427967	−	0.950904i	−0.992127	−	0.125238i	$-0.960030\pi$
$613$	−10.5960	−	23.5433i	−0.427967	−	0.950904i	0.564159	−	0.825666i	$-0.309200\pi$
$614$	−12.2788	+	4.65674i	−0.495532	+	0.187931i
$615$	8.85853	+	22.9518i	0.357210	+	0.925505i
$616$	1.01096	−	16.7131i	0.0407326	−	0.673390i
$617$	5.86099	−	13.0226i	0.235954	−	0.524269i	−0.755434	−	0.655225i	$-0.772574\pi$
$617$	5.86099	−	13.0226i	0.235954	−	0.524269i	0.991388	+	0.130956i	$0.0418046\pi$
$618$	3.74532	+	11.7760i	0.150659	+	0.473699i
$619$	5.03276	+	8.32520i	0.202284	+	0.334618i	0.940409	−	0.340046i	$-0.110443\pi$
$619$	5.03276	+	8.32520i	0.202284	+	0.334618i	−0.738125	+	0.674664i	$0.764289\pi$
$620$	8.84371	+	35.8803i	0.355172	+	1.44099i
$621$	8.79278	+	9.58055i	0.352842	+	0.384454i
$622$	−3.96908	+	8.81894i	−0.159146	+	0.353607i
$623$	−2.50410	−	20.6231i	−0.100325	−	0.826248i
$624$	7.34748	+	0.209047i	0.294135	+	0.00836859i
$625$	0.207197	−	1.70642i	0.00828786	−	0.0682567i
$626$	13.2073	+	7.98407i	0.527869	+	0.319108i
$627$	−23.9839	+	21.4998i	−0.957823	+	0.858619i
$628$	−8.30369	−	5.73163i	−0.331353	−	0.228717i
$629$	−13.3977	+	2.45523i	−0.534203	+	0.0978962i
$630$	−3.89558	+	13.0369i	−0.155204	+	0.519404i
$631$	−3.12226	+	2.44613i	−0.124295	+	0.0973790i	−0.676941	−	0.736037i	$-0.736695\pi$
$631$	−3.12226	+	2.44613i	−0.124295	+	0.0973790i	0.552646	+	0.833416i	$0.313618\pi$
$632$	4.82924	−	1.50485i	0.192097	−	0.0598598i
$633$	29.7797	+	11.0949i	1.18364	+	0.440984i
$634$	−14.2838	−	9.85941i	−0.567283	−	0.391567i
$635$	−66.0409	+	39.9231i	−2.62075	+	1.58430i
$636$	−20.0636	−	13.6762i	−0.795575	−	0.542295i
$637$	−4.54375	−	13.3441i	−0.180030	−	0.528712i
$638$	7.16731	−	13.6562i	0.283756	−	0.540653i
$639$	23.9991	+	14.1269i	0.949391	+	0.558852i
$640$	4.49573	+	37.0257i	0.177709	+	1.46357i
$641$	−3.54090	+	1.85841i	−0.139857	+	0.0734028i	−0.533200	−	0.845989i	$-0.679011\pi$
$641$	−3.54090	+	1.85841i	−0.139857	+	0.0734028i	0.393343	+	0.919392i	$0.371318\pi$
$642$	−3.05424	+	3.94582i	−0.120541	+	0.155729i
$643$	−18.6244	+	30.8085i	−0.734474	+	1.21497i	0.235527	+	0.971868i	$0.424318\pi$
$643$	−18.6244	+	30.8085i	−0.734474	+	1.21497i	−0.970001	+	0.243100i	$0.921836\pi$
$644$	−0.394555	+	6.52277i	−0.0155476	+	0.257033i
$645$	10.6134	+	17.3268i	0.417904	+	0.682242i
$646$	−2.36561	+	6.23760i	−0.0930737	+	0.245415i
$647$	−26.7019	−	14.0143i	−1.04976	−	0.550957i	−0.150609	−	0.988593i	$-0.548124\pi$
$647$	−26.7019	−	14.0143i	−1.04976	−	0.550957i	−0.899152	+	0.437636i	$0.855816\pi$
$648$	21.3215	−	7.19604i	0.837587	−	0.282687i
$649$	38.1552	−	43.0683i	1.49772	−	1.69058i
$650$	−9.05948	+	18.4146i	−0.355342	+	0.722279i
$651$	19.7379	+	7.35368i	0.773588	+	0.288214i
$652$	−4.68886	−	5.98488i	−0.183630	−	0.234386i
$653$		−	34.7470i		−	1.35976i	−0.733325	−	0.679878i	$-0.762033\pi$
$653$		−	34.7470i		−	1.35976i	0.733325	−	0.679878i	$-0.237967\pi$
$654$	−1.15712	−	2.17369i	−0.0452471	−	0.0849980i
$655$	−1.96449	−	2.50749i	−0.0767590	−	0.0979757i
$656$	4.57244	−	0.837931i	0.178524	−	0.0327157i
$657$	−36.7646	+	7.18334i	−1.43432	+	0.280249i
$658$	2.42158	−	13.2141i	0.0944030	−	0.515140i
$659$	1.72786	−	0.209800i	0.0673077	−	0.00817263i	−0.0868136	−	0.996225i	$-0.527668\pi$
$659$	1.72786	−	0.209800i	0.0673077	−	0.00817263i	0.154121	+	0.988052i	$0.450745\pi$
$660$	4.45323	+	34.9636i	0.173342	+	1.36095i
$661$	25.3018	−	32.2954i	0.984128	−	1.25615i	0.0175305	−	0.999846i	$-0.494420\pi$
$661$	25.3018	−	32.2954i	0.984128	−	1.25615i	0.966597	−	0.256300i	$-0.0825035\pi$
$662$	−6.39948	+	16.8740i	−0.248723	+	0.655828i
$663$	10.6863	−	5.22653i	0.415022	−	0.202981i
$664$	−4.86804	−	12.8360i	−0.188917	−	0.498132i
$665$	29.4666	+	9.18216i	1.14267	+	0.356069i
$666$	−10.0692	+	11.6375i	−0.390173	+	0.450945i
$667$	−6.56368	+	12.5060i	−0.254147	+	0.484236i
$668$	−4.38540	+	5.59754i	−0.169676	+	0.216575i
$669$	6.28873	−	35.4872i	0.243136	−	1.37201i
$670$	1.70504	+	28.1877i	0.0658714	+	1.08898i
$671$	19.5637	+	8.80491i	0.755248	+	0.339910i
$672$	15.8068	+	8.17838i	0.609762	+	0.315488i
$673$	−10.4001	+	42.1949i	−0.400894	+	1.62649i	0.329985	+	0.943986i	$0.392956\pi$
$673$	−10.4001	+	42.1949i	−0.400894	+	1.62649i	−0.730879	+	0.682507i	$0.760890\pi$
$674$	−9.93959	+	3.09730i	−0.382859	+	0.119304i
$675$	4.24979	−	41.0079i	0.163574	−	1.57840i
$676$	13.7653	−	13.5418i	0.529434	−	0.520839i
$677$			19.5322i			0.750683i	0.926887	+	0.375341i	$0.122474\pi$
$677$			19.5322i			0.750683i	−0.926887	+	0.375341i	$0.877526\pi$
$678$	−5.95373	−	5.88441i	−0.228652	−	0.225990i
$679$	−18.2835	−	4.50648i	−0.701656	−	0.172943i
$680$	9.73050	+	14.0971i	0.373148	+	0.540598i
$681$	27.2755	−	1.81021i	1.04520	−	0.0693675i
$682$	−18.8698	+	1.14141i	−0.722561	+	0.0437069i
$683$	−31.8875	−	24.9823i	−1.22014	−	0.955921i	−0.220333	−	0.975425i	$-0.570714\pi$
$683$	−31.8875	−	24.9823i	−1.22014	−	0.955921i	−0.999810	+	0.0195040i	$0.993791\pi$
$684$	−6.71455	−	20.6915i	−0.256737	−	0.791158i
$685$	−30.2011	−	15.8507i	−1.15392	−	0.605626i
$686$	1.65839	−	13.6580i	0.0633174	−	0.521466i
$687$	5.58302	+	29.4906i	0.213005	+	1.12514i
$688$	3.58982	−	1.36144i	0.136861	−	0.0519044i
$689$	−33.3003	+	7.00592i	−1.26864	+	0.266904i
$690$	1.41299	+	11.0938i	0.0537915	+	0.422332i
$691$	6.79479	+	5.32338i	0.258486	+	0.202511i	0.737593	−	0.675246i	$-0.235962\pi$
$691$	6.79479	+	5.32338i	0.258486	+	0.202511i	−0.479107	+	0.877757i	$0.659039\pi$
$692$	10.8611	+	4.11905i	0.412875	+	0.156583i
$693$	17.8966	+	9.12716i	0.679835	+	0.346712i
$694$	−2.82743	−	0.518146i	−0.107328	−	0.0196686i
$695$	−1.15176	−	1.15176i	−0.0436886	−	0.0436886i
$696$	15.1858	+	19.1511i	0.575615	+	0.725922i
$697$	5.92219	−	4.63974i	0.224319	−	0.175743i
$698$			17.9442i			0.679197i
$699$	−17.8925	−	33.6115i	−0.676755	−	1.27130i
$700$	16.3086	−	12.7770i	0.616408	−	0.482924i
$701$	18.5593	−	16.4421i	0.700975	−	0.621010i	−0.235446	−	0.971887i	$-0.575655\pi$
$701$	18.5593	−	16.4421i	0.700975	−	0.621010i	0.936421	+	0.350877i	$0.114117\pi$
$702$	5.72033	−	12.1621i	0.215900	−	0.459029i
$703$	26.1285	+	23.1478i	0.985454	+	0.873036i
$704$	−6.99301	−	0.422999i	−0.263559	−	0.0159424i
$705$	0.388537	+	66.3559i	0.0146332	+	2.49911i
$706$	12.0898	+	4.58508i	0.455008	+	0.172562i
$707$	0.500258	+	8.27025i	0.0188141	+	0.311035i
$708$	16.1560	+	35.3426i	0.607178	+	1.32826i
$709$	−30.0929	−	18.1918i	−1.13016	−	0.683207i	−0.176564	−	0.984289i	$-0.556498\pi$
$709$	−30.0929	−	18.1918i	−1.13016	−	0.683207i	−0.953598	+	0.301082i	$0.902652\pi$
$710$	9.82926	+	21.8397i	0.368885	+	0.819630i
$711$	−0.660946	+	6.03300i	−0.0247874	+	0.226255i
$712$	−29.3326	+	3.56162i	−1.09929	+	0.133477i
$713$	17.2806	−	1.04528i	0.647162	−	0.0391461i
$714$	4.16079	−	0.0243629i	0.155714	−	0.000911758i
$715$	39.6657	+	29.4375i	1.48341	+	1.10090i
$716$	8.30939	+	15.8322i	0.310536	+	0.591678i
$717$	5.76405	−	9.66224i	0.215262	−	0.360843i
$718$	−3.06717	+	4.44356i	−0.114466	+	0.165832i
$719$	12.0483	−	10.6739i	0.449326	−	0.398068i	−0.407885	−	0.913033i	$-0.633734\pi$
$719$	12.0483	−	10.6739i	0.449326	−	0.398068i	0.857211	+	0.514965i	$0.172195\pi$
$720$	−12.1675	−	3.63579i	−0.453457	−	0.135498i
$721$	−10.7820	−	13.7622i	−0.401542	−	0.512531i
$722$	3.30939	−	1.03125i	0.123163	−	0.0383790i
$723$	−9.90822	−	12.4955i	−0.368491	−	0.464713i
$724$	2.32975	−	3.37522i	0.0865844	−	0.125439i
$725$	43.4772	−	10.7162i	1.61470	−	0.397989i
$726$	−4.35595	−	0.237896i	−0.161664	−	0.00882916i
$727$	−5.37828	−	0.653041i	−0.199469	−	0.0242200i	0.0201922	−	0.999796i	$-0.493572\pi$
$727$	−5.37828	−	0.653041i	−0.199469	−	0.0242200i	−0.219661	+	0.975576i	$0.570495\pi$
$728$	15.0021	−	5.10832i	0.556016	−	0.189327i
$729$	−2.31104	+	26.9009i	−0.0855939	+	0.996330i
$730$	−29.3774	−	13.2217i	−1.08731	−	0.489357i
$731$	4.12034	−	4.65090i	0.152396	−	0.172020i
$732$	−10.7890	+	9.67156i	−0.398773	+	0.357471i
$733$	26.4907	−	16.0142i	0.978456	−	0.591498i	0.0647626	−	0.997901i	$-0.479371\pi$
$733$	26.4907	−	16.0142i	0.978456	−	0.591498i	0.913694	+	0.406403i	$0.133217\pi$
$734$	1.69519	−	9.25033i	0.0625705	−	0.341436i
$735$	1.61277	+	24.3005i	0.0594879	+	0.896338i
$736$	14.6011	+	0.883204i	0.538204	+	0.0325553i
$737$	41.3903	+	5.02569i	1.52463	+	0.185124i
$738$	1.93737	−	8.27613i	0.0713155	−	0.304649i
$739$	−27.1833	+	12.2342i	−0.999955	+	0.450043i	−0.843203	−	0.537595i	$-0.819333\pi$
$739$	−27.1833	+	12.2342i	−0.999955	+	0.450043i	−0.156752	+	0.987638i	$0.550102\pi$
$740$	37.0879	−	9.14134i	1.36338	−	0.336042i
$741$	−27.4338	−	13.2978i	−1.00781	−	0.488506i
$742$	−11.5566	−	2.84844i	−0.424256	−	0.104570i
$743$	−35.0018	+	6.41432i	−1.28409	+	0.235318i	−0.778604	−	0.627516i	$-0.784072\pi$
$743$	−35.0018	+	6.41432i	−1.28409	+	0.235318i	−0.505487	+	0.862834i	$0.668687\pi$
$744$	10.4593	−	28.0735i	0.383455	−	1.02922i
$745$	−13.1586	+	53.3867i	−0.482095	+	1.95594i
$746$	0.0537390	+	0.0537390i	0.00196753	+	0.00196753i
$747$	16.4519	+	0.801919i	0.601944	+	0.0293407i
$748$	9.82864	−	4.42351i	0.359371	−	0.161740i
$749$	2.10022	−	6.73983i	0.0767402	−	0.246268i
$750$	8.63746	−	9.86546i	0.315396	−	0.360236i
$751$	−1.38648	−	2.64172i	−0.0505934	−	0.0963976i	0.858847	−	0.512233i	$-0.171182\pi$
$751$	−1.38648	−	2.64172i	−0.0505934	−	0.0963976i	−0.909440	+	0.415835i	$0.863489\pi$
$752$	12.3329	+	2.26009i	0.449734	+	0.0824169i
$753$	0.390342	−	0.754436i	0.0142248	−	0.0274932i
$754$	14.5323	+	1.38055i	0.529236	+	0.0502767i
$755$	−39.7086	−	27.4089i	−1.44514	−	0.997511i
$756$	−10.5319	+	8.55398i	−0.383042	+	0.311105i
$757$	−4.39066	−	6.36097i	−0.159581	−	0.231193i	0.735034	−	0.678030i	$-0.237166\pi$
$757$	−4.39066	−	6.36097i	−0.159581	−	0.231193i	−0.894616	+	0.446836i	$0.852551\pi$
$758$	1.23500	+	1.09412i	0.0448573	+	0.0397401i
$759$	16.4874	+	0.900443i	0.598453	+	0.0326840i
$760$	13.0599	−	41.9108i	0.473733	−	1.52026i
$761$	−2.43234	+	7.80566i	−0.0881723	+	0.282955i	−0.988266	−	0.152741i	$-0.951190\pi$
$761$	−2.43234	+	7.80566i	−0.0881723	+	0.282955i	0.900094	+	0.435696i	$0.143498\pi$
$762$	26.6223	+	1.45395i	0.964424	+	0.0526712i
$763$	2.60774	+	2.31025i	0.0944064	+	0.0836368i
$764$	−13.0766	−	18.9447i	−0.473095	−	0.685397i
$765$	−20.1708	+	3.94112i	−0.729278	+	0.142492i
$766$	12.8973	+	8.90234i	0.465997	+	0.321655i
$767$	51.4087	+	17.9758i	1.85626	+	0.649068i
$768$	8.84920	−	17.1034i	0.319318	−	0.617165i
$769$	11.3515	+	2.08023i	0.409344	+	0.0750151i	0.380982	−	0.924583i	$-0.375586\pi$
$769$	11.3515	+	2.08023i	0.409344	+	0.0750151i	0.0283626	+	0.999598i	$0.490971\pi$
$770$	8.02910	+	15.2982i	0.289349	+	0.551308i
$771$	8.86812	−	10.1289i	0.319378	−	0.364784i
$772$	7.65819	−	24.5760i	0.275624	−	0.884509i
$773$	−24.2282	+	10.9042i	−0.871429	+	0.392198i	−0.796247	−	0.604972i	$-0.793184\pi$
$773$	−24.2282	+	10.9042i	−0.871429	+	0.392198i	−0.0751817	+	0.997170i	$0.523954\pi$
$774$	0.341778	−	7.01180i	0.0122849	−	0.252034i
$775$	−38.8107	−	38.8107i	−1.39412	−	1.39412i
$776$	−6.40963	+	26.0049i	−0.230092	+	0.933521i
$777$	7.60117	−	20.4021i	0.272690	−	0.731923i
$778$	−0.947217	+	0.173584i	−0.0339594	+	0.00622329i
$779$	−18.7203	−	4.61413i	−0.670723	−	0.165318i
$780$	−29.0287	+	16.4398i	−1.03939	+	0.588639i
$781$	34.3335	−	8.46244i	1.22855	−	0.302810i
$782$	3.11858	−	1.40356i	0.111520	−	0.0501911i
$783$	−28.3456	+	7.51709i	−1.01299	+	0.268639i
$784$	4.56817	+	0.554676i	0.163149	+	0.0198099i
$785$	24.3852	+	1.47503i	0.870344	+	0.0526461i
$786$	0.0728798	+	1.09812i	0.00259954	+	0.0391687i
$787$	−2.22893	+	12.1629i	−0.0794529	+	0.433560i	0.919708	+	0.392603i	$0.128425\pi$
$787$	−2.22893	+	12.1629i	−0.0794529	+	0.433560i	−0.999161	+	0.0409572i	$0.986959\pi$
$788$	−6.77096	+	4.09319i	−0.241206	+	0.145814i
$789$	−0.898504	+	0.805445i	−0.0319876	+	0.0286746i
$790$	−3.46114	+	3.90682i	−0.123142	+	0.138998i
$791$	10.7998	+	4.86058i	0.383996	+	0.172822i
$792$	12.9817	−	25.4546i	0.461285	−	0.904489i
$793$	−0.696349	+	20.2942i	−0.0247281	+	0.720670i
$794$	19.0594	+	2.31423i	0.676392	+	0.0821289i
$795$	58.7038	+	3.20606i	2.08201	+	0.113707i
$796$	−38.4047	+	9.46592i	−1.36122	+	0.335511i
$797$	−7.30423	+	10.5820i	−0.258729	+	0.374834i	−0.930724	−	0.365722i	$-0.880822\pi$
$797$	−7.30423	+	10.5820i	−0.258729	+	0.374834i	0.671995	+	0.740556i	$0.265438\pi$
$798$	−6.62535	−	8.35539i	−0.234535	−	0.295778i
$799$	19.3731	−	6.03691i	0.685372	−	0.213571i
$800$	−28.6010	−	36.5065i	−1.01120	−	1.29070i
$801$	10.1502	−	33.9687i	0.358641	−	1.20023i
$802$	−0.661797	+	0.586301i	−0.0233689	+	0.0207030i
$803$	−27.0202	+	39.1456i	−0.953524	+	1.38142i
$804$	−14.4265	+	24.1831i	−0.508785	+	0.852872i
$805$	−7.35290	−	14.0098i	−0.259156	−	0.493780i
$806$	−7.76711	−	16.1193i	−0.273585	−	0.567780i
$807$	−4.56523	+	0.0267310i	−0.160704	+	0.000940976i
$808$	11.7629	−	0.711525i	0.413818	−	0.0250314i
$809$	7.96634	−	0.967289i	0.280082	−	0.0340081i	0.0207095	−	0.999786i	$-0.493407\pi$
$809$	7.96634	−	0.967289i	0.280082	−	0.0340081i	0.259372	+	0.965777i	$0.416484\pi$
$810$	−14.9865	+	17.7364i	−0.526573	+	0.623192i
$811$	2.59667	+	5.76957i	0.0911815	+	0.202597i	0.951847	−	0.306574i	$-0.0991828\pi$
$811$	2.59667	+	5.76957i	0.0911815	+	0.202597i	−0.860665	+	0.509171i	$0.829952\pi$
$812$	−12.6113	−	7.62381i	−0.442571	−	0.267543i
$813$	15.1944	+	33.2393i	0.532892	+	1.16575i
$814$	1.17982	+	19.5048i	0.0413528	+	0.683644i
$815$	17.2122	+	6.52774i	0.602919	+	0.228657i
$816$	0.0227382	+	3.88331i	0.000795995	+	0.135943i
$817$	−15.8949	−	0.961465i	−0.556093	−	0.0336374i
$818$	−11.1269	−	9.85758i	−0.389043	−	0.344662i
$819$	−1.57651	+	18.9495i	−0.0550876	+	0.662150i
$820$	−15.7921	+	13.9906i	−0.551484	+	0.488572i
$821$	0.943148	−	0.738909i	0.0329161	−	0.0257881i	−0.600126	−	0.799905i	$-0.704883\pi$
$821$	0.943148	−	0.738909i	0.0329161	−	0.0257881i	0.633042	+	0.774117i	$0.281806\pi$
$822$	5.53736	+	10.4021i	0.193137	+	0.362814i
$823$			39.1442i			1.36448i	0.731127	+	0.682241i	$0.238995\pi$
$823$			39.1442i			1.36448i	−0.731127	+	0.682241i	$0.761005\pi$
$824$	−19.5742	+	15.3354i	−0.681899	+	0.534233i
$825$	−32.5257	−	41.0190i	−1.13240	−	1.42810i
$826$	13.4696	+	13.4696i	0.468666	+	0.468666i
$827$	45.5525	+	8.34780i	1.58401	+	0.290281i	0.898900	−	0.438154i	$-0.144368\pi$
$827$	45.5525	+	8.34780i	1.58401	+	0.290281i	0.685114	+	0.728436i	$0.259752\pi$
$828$	−5.06649	+	9.93440i	−0.176073	+	0.345244i
$829$	−17.3209	−	6.56894i	−0.601578	−	0.228149i	0.0349662	−	0.999388i	$-0.488868\pi$
$829$	−17.3209	−	6.56894i	−0.601578	−	0.228149i	−0.636545	+	0.771240i	$0.719637\pi$
$830$	11.1509	+	8.73615i	0.387052	+	0.303236i
$831$	−4.31573	−	33.8840i	−0.149711	−	1.17542i
$832$	−2.13740	−	6.27712i	−0.0741010	−	0.217620i
$833$	6.96346	−	2.64089i	0.241270	−	0.0915015i
$834$	0.104678	+	0.552931i	0.00362471	+	0.0191464i
$835$	2.07529	−	17.0916i	0.0718185	−	0.591479i
$836$	−24.4582	−	12.8367i	−0.845906	−	0.443966i
$837$	25.8597	+	24.9668i	0.893844	+	0.862980i
$838$	−6.93876	−	5.43617i	−0.239695	−	0.187789i
$839$	19.2172	−	1.16242i	0.663450	−	0.0401313i	0.274778	−	0.961508i	$-0.411396\pi$
$839$	19.2172	−	1.16242i	0.663450	−	0.0401313i	0.388672	+	0.921376i	$0.372934\pi$
$840$	−27.3199	+	1.81316i	−0.942627	+	0.0625600i
$841$	−1.61966	−	2.34648i	−0.0558504	−	0.0809133i
$842$	−9.60489	−	2.36739i	−0.331006	−	0.0815858i
$843$	14.3868	+	14.2193i	0.495507	+	0.489738i
$844$			27.2531i			0.938090i
$845$	−11.5599	+	45.3018i	−0.397674	+	1.55843i
$846$	12.8016	−	19.0190i	0.440129	−	0.653886i
$847$	5.89246	−	1.83617i	0.202467	−	0.0630914i
$848$	2.65849	−	10.7859i	0.0912928	−	0.370389i
$849$	−23.2184	−	12.0131i	−0.796852	−	0.412287i
$850$	−9.88717	−	4.44985i	−0.339127	−	0.152629i
$851$	−1.08046	−	17.8621i	−0.0370377	−	0.612306i
$852$	−4.16722	+	23.5156i	−0.142767	+	0.805630i
$853$	31.3258	−	39.9845i	1.07258	−	1.36904i	0.147586	−	0.989049i	$-0.452850\pi$
$853$	31.3258	−	39.9845i	1.07258	−	1.36904i	0.924989	−	0.379993i	$-0.124074\pi$
$854$	−3.30070	+	6.28896i	−0.112948	+	0.215204i
$855$	39.8311	+	34.4632i	1.36219	+	1.17862i
$856$	−9.58616	−	2.98717i	−0.327648	−	0.102099i
$857$	−13.9075	−	36.6710i	−0.475071	−	1.25266i	−0.931774	−	0.363039i	$-0.881739\pi$
$857$	−13.9075	−	36.6710i	−0.475071	−	1.25266i	0.456703	−	0.889619i	$-0.349030\pi$
$858$	−5.59541	−	16.1226i	−0.191024	−	0.550417i
$859$	−2.84710	+	7.50719i	−0.0971418	+	0.256142i	−0.974775	−	0.223192i	$-0.928352\pi$
$859$	−2.84710	+	7.50719i	−0.0971418	+	0.256142i	0.877633	+	0.479334i	$0.159122\pi$
$860$	−10.7464	+	13.7167i	−0.366448	+	0.467736i
$861$	1.51939	+	11.9291i	0.0517806	+	0.406544i
$862$	18.1325	−	2.20169i	0.617597	−	0.0749898i
$863$	−1.42278	+	7.76387i	−0.0484321	+	0.264285i	−0.998919	−	0.0464784i	$-0.985200\pi$
$863$	−1.42278	+	7.76387i	−0.0484321	+	0.264285i	0.950487	+	0.310764i	$0.100585\pi$
$864$	19.1479	+	23.5755i	0.651425	+	0.802054i
$865$	−27.6643	+	5.06966i	−0.940613	+	0.172374i
$866$	9.00597	+	11.4953i	0.306035	+	0.390625i
$867$	−10.8829	−	20.4438i	−0.369602	−	0.694308i
$868$			18.0633i			0.613107i
$869$	4.75267	+	6.06633i	0.161223	+	0.205786i
$870$	−23.6331	−	8.80492i	−0.801237	−	0.298515i
$871$	10.4417	+	38.0576i	0.353804	+	1.28953i
$872$	3.28591	−	3.70902i	0.111275	−	0.125603i
$873$	−25.5268	−	19.5209i	−0.863951	−	0.660683i
$874$	−7.76047	−	4.07301i	−0.262502	−	0.137772i
$875$	−6.57833	+	17.3456i	−0.222388	+	0.586389i
$876$	−16.7799	−	27.3938i	−0.566941	−	0.925550i
$877$	2.86854	−	47.4227i	0.0968639	−	1.60135i	−0.547616	−	0.836729i	$-0.684465\pi$
$877$	2.86854	−	47.4227i	0.0968639	−	1.60135i	0.644480	−	0.764621i	$-0.277074\pi$
$878$	−4.31815	+	7.14309i	−0.145730	+	0.241068i
$879$	−29.6275	+	38.2762i	−0.999310	+	1.29102i
$880$	−14.2780	+	7.49366i	−0.481310	+	0.252611i
$881$	−5.80228	−	47.7861i	−0.195484	−	1.60995i	−0.678675	−	0.734439i	$-0.737445\pi$
$881$	−5.80228	−	47.7861i	−0.195484	−	1.60995i	0.483191	−	0.875515i	$-0.339478\pi$
$882$	4.26835	−	7.25117i	0.143723	−	0.244160i
$883$	−13.7933	+	26.2808i	−0.464180	+	0.884421i	0.535036	+	0.844829i	$0.320298\pi$
$883$	−13.7933	+	26.2808i	−0.464180	+	0.884421i	−0.999216	+	0.0395916i	$0.987394\pi$
$884$	7.39957	+	7.02283i	0.248875	+	0.236203i
$885$	−77.7463	−	52.9950i	−2.61341	−	1.78141i
$886$	−23.3927	+	14.1414i	−0.785895	+	0.475090i
$887$	−5.02478	−	3.46835i	−0.168715	−	0.116456i	0.480715	−	0.876877i	$-0.340377\pi$
$887$	−5.02478	−	3.46835i	−0.168715	−	0.116456i	−0.649430	+	0.760421i	$0.724993\pi$
$888$	−29.0183	−	10.8113i	−0.973790	−	0.362802i
$889$	−36.0130	+	11.2221i	−1.20784	+	0.376378i
$890$	24.0009	−	18.8035i	0.804512	−	0.630295i
$891$	21.7697	+	26.4851i	0.729313	+	0.887285i
$892$	30.4007	−	5.57114i	1.01789	−	0.186536i
$893$	−42.7983	−	29.5415i	−1.43219	−	0.988570i
$894$	14.1453	−	12.6803i	0.473091	−	0.424092i
$895$	−37.0490	−	22.3969i	−1.23841	−	0.748646i
$896$	−2.19752	+	18.0982i	−0.0734140	+	0.604619i
$897$	5.12417	+	14.7648i	0.171091	+	0.492981i
$898$	2.40686	+	19.8223i	0.0803180	+	0.661479i
$899$	−16.0230	+	35.6017i	−0.534398	+	1.18738i
$900$	34.2268	−	8.86257i	1.14089	−	0.295419i
$901$	−4.30249	−	17.4559i	−0.143337	−	0.581540i
$902$	−5.58357	−	9.23635i	−0.185913	−	0.307537i
$903$	3.01027	+	9.46481i	0.100175	+	0.314969i
$904$	6.91328	−	15.3607i	0.229932	−	0.510888i
$905$	−0.599560	+	9.91190i	−0.0199300	+	0.329483i
$906$	6.00242	+	15.5518i	0.199417	+	0.516675i
$907$	7.32420	−	2.77770i	0.243196	−	0.0922321i	−0.229995	−	0.973192i	$-0.573871\pi$
$907$	7.32420	−	2.77770i	0.243196	−	0.0922321i	0.473191	+	0.880960i	$0.343102\pi$
$908$	9.62098	+	21.3769i	0.319283	+	0.709419i
$909$	−4.85872	+	13.2783i	−0.161154	+	0.440415i
$910$	−10.5207	+	12.5194i	−0.348758	+	0.415014i
$911$	6.73183	−	27.3121i	0.223035	−	0.904890i	−0.747564	−	0.664190i	$-0.768777\pi$
$911$	6.73183	−	27.3121i	0.223035	−	0.904890i	0.970599	−	0.240700i	$-0.0773771\pi$
$912$	7.79819	−	6.18352i	0.258224	−	0.204757i
$913$	15.6551	−	13.8692i	0.518108	−	0.459003i
$914$	2.80580	+	0.691567i	0.0928076	+	0.0228750i
$915$	10.2408	−	33.5543i	0.338550	−	1.10927i
$916$	−22.0274	+	13.3160i	−0.727807	+	0.439974i
$917$	−0.639023	−	1.41985i	−0.0211024	−	0.0468876i
$918$	6.52531	+	2.80003i	0.215367	+	0.0924148i
$919$	−10.9122	−	28.7732i	−0.359961	−	0.949140i	−0.985610	−	0.169035i	$-0.945935\pi$
$919$	−10.9122	−	28.7732i	−0.359961	−	0.949140i	0.625648	−	0.780105i	$-0.284834\pi$
$920$	−19.9263	+	10.4581i	−0.656951	+	0.344795i
$921$	30.2149	−	9.60981i	0.995616	−	0.316654i
$922$	−3.79452	+	2.61917i	−0.124966	+	0.0862577i
$923$	19.7256	+	27.0390i	0.649277	+	0.889999i
$924$	−1.97647	+	17.1146i	−0.0650210	+	0.563028i
$925$	−40.1169	+	40.1169i	−1.31904	+	1.31904i
$926$	24.8360	−	17.1431i	0.816162	−	0.563356i
$927$	−7.47877	−	28.8827i	−0.245635	−	0.948631i
$928$	−17.0658	+	28.2302i	−0.560211	+	0.926702i
$929$	−57.4511	−	17.9025i	−1.88491	−	0.587361i	−0.989991	−	0.141132i	$-0.954926\pi$
$929$	−57.4511	−	17.9025i	−1.88491	−	0.587361i	−0.894918	−	0.446230i	$-0.852766\pi$
$930$	5.75020	+	30.3737i	0.188557	+	0.995993i
$931$	−16.3336	−	9.87398i	−0.535311	−	0.323607i
$932$	21.6536	−	24.4419i	0.709287	−	0.800620i
$933$	10.7298	−	20.7382i	0.351279	−	0.678937i
$934$	10.7659	+	10.7659i	0.352270	+	0.352270i
$935$	−14.8246	+	21.4771i	−0.484816	+	0.702377i
$936$	26.9522	+	2.24229i	0.880961	+	0.0732915i
$937$	−16.3583	−	23.6991i	−0.534402	−	0.774215i	0.459057	−	0.888407i	$-0.348188\pi$
$937$	−16.3583	−	23.6991i	−0.534402	−	0.774215i	−0.993459	+	0.114192i	$0.963572\pi$
$938$	−2.48813	+	13.5773i	−0.0812402	+	0.443314i
$939$	−30.7889	−	20.9870i	−1.00476	−	0.684884i
$940$	−53.2081	+	20.1792i	−1.73546	+	0.658171i
$941$	−26.6308	−	8.29850i	−0.868140	−	0.270523i	−0.169094	−	0.985600i	$-0.554084\pi$
$941$	−26.6308	−	8.29850i	−0.868140	−	0.270523i	−0.699046	+	0.715077i	$0.746392\pi$
$942$	−6.67447	−	5.16633i	−0.217466	−	0.168328i
$943$	5.11332	+	8.45847i	0.166513	+	0.275446i
$944$	−12.5713	+	12.5713i	−0.409161	+	0.409161i
$945$	11.1080	−	30.9166i	0.361343	−	1.00572i
$946$	−5.91105	−	6.67219i	−0.192185	−	0.216932i
$947$	−9.66763	−	52.7545i	−0.314156	−	1.71429i	−0.639581	−	0.768724i	$-0.720892\pi$
$947$	−9.66763	−	52.7545i	−0.314156	−	1.71429i	0.325425	−	0.945568i	$-0.394493\pi$
$948$	−5.04608	+	1.27513i	−0.163889	+	0.0414144i
$949$	−43.9793	−	9.62910i	−1.42763	−	0.312574i
$950$	6.64979	+	26.9793i	0.215748	+	0.875323i
$951$	33.1374	+	25.6498i	1.07455	+	0.831751i
$952$	2.96903	+	7.82870i	0.0962269	+	0.253729i
$953$	−2.12206	+	17.4768i	−0.0687404	+	0.566128i	0.917126	+	0.398596i	$0.130503\pi$
$953$	−2.12206	+	17.4768i	−0.0687404	+	0.566128i	−0.985867	+	0.167531i	$0.946420\pi$
$954$	−16.1349	−	12.3387i	−0.522388	−	0.399482i
$955$	50.8257	+	22.8748i	1.64468	+	0.740211i
$956$	9.49044	+	1.73919i	0.306943	+	0.0562493i
$957$	−19.0770	+	31.9787i	−0.616672	+	1.03372i
$958$	0.415649	−	0.102448i	0.0134290	−	0.00330996i
$959$	−12.4792	−	11.0556i	−0.402974	−	0.357004i
$960$	0.758654	+	11.4311i	0.0244855	+	0.368936i
$961$	16.7315	−	2.03158i	0.539727	−	0.0655347i
$962$	−16.6618	+	8.02851i	−0.537199	+	0.258850i
$963$	7.88270	−	9.11048i	0.254016	−	0.293581i
$964$	7.07501	−	11.7035i	0.227871	−	0.376944i
$965$	14.9157	+	60.5155i	0.480154	+	1.94806i
$966$	−0.627123	+	5.43036i	−0.0201774	+	0.174719i
$967$	−0.296817	−	1.61968i	−0.00954500	−	0.0520854i	0.978503	−	0.206235i	$-0.0661210\pi$
$967$	−0.296817	−	1.61968i	−0.00954500	−	0.0520854i	−0.988048	+	0.154149i	$0.950736\pi$
$968$	−2.61161	−	8.38094i	−0.0839402	−	0.269374i
$969$	6.52430	−	14.7262i	0.209591	−	0.473073i
$970$	−8.22198	−	26.3853i	−0.263992	−	0.847179i
$971$	0.331273	+	0.373930i	0.0106311	+	0.0120000i	0.753802	−	0.657101i	$-0.228218\pi$
$971$	0.331273	+	0.373930i	0.0106311	+	0.0120000i	−0.743171	+	0.669101i	$0.766679\pi$
$972$	−22.3098	+	6.19694i	−0.715587	+	0.198767i
$973$	−0.411891	−	0.681352i	−0.0132046	−	0.0218431i
$974$	12.4420	−	6.53006i	0.398667	−	0.209237i
$975$	24.2652	−	43.2012i	0.777108	−	1.38354i
$976$	−5.86956	−	3.08058i	−0.187880	−	0.0986071i
$977$	0.0973281	+	1.60902i	0.00311380	+	0.0514773i	0.999401	−	0.0346198i	$-0.0110220\pi$
$977$	0.0973281	+	1.60902i	0.00311380	+	0.0514773i	−0.996287	+	0.0860971i	$0.972560\pi$
$978$	−3.64350	−	5.21297i	−0.116506	−	0.166692i
$979$	−20.9204	−	39.8605i	−0.668620	−	1.27395i
$980$	−19.0453	+	8.57160i	−0.608380	+	0.273810i
$981$	2.50340	+	5.39269i	0.0799275	+	0.172175i
$982$	13.2474	+	0.801323i	0.422743	+	0.0255712i
$983$	48.8639	−	2.95572i	1.55852	−	0.0942729i	0.741526	−	0.670924i	$-0.234102\pi$
$983$	48.8639	−	2.95572i	1.55852	−	0.0942729i	0.816990	+	0.576651i	$0.195641\pi$
$984$	16.9670	−	2.16105i	0.540888	−	0.0688917i
$985$	8.90268	−	16.9626i	0.283663	−	0.540475i
$986$	−0.465655	+	7.69820i	−0.0148295	+	0.245160i
$987$	−7.57778	+	31.5379i	−0.241203	+	1.00386i
$988$	2.47257	−	26.0275i	0.0786631	−	0.828044i
$989$	5.41322	+	6.11026i	0.172130	+	0.194295i
$990$	2.12473	+	29.4076i	0.0675285	+	0.934636i
$991$	−30.4249			−0.966478			−0.483239	−	0.875488i	$-0.660540\pi$
$991$	−30.4249			−0.966478			−0.483239	+	0.875488i	$0.660540\pi$
$992$	40.4343			1.28379
$993$	17.6496	−	39.8375i	0.560093	−	1.26420i
$994$	2.11018	+	11.5149i	0.0669309	+	0.365230i
$995$	67.7198	−	67.7198i	2.14686	−	2.14686i
$996$	4.28126	+	13.4610i	0.135657	+	0.426529i
$997$	−0.441271	−	3.63419i	−0.0139752	−	0.115096i	0.984052	−	0.177882i	$-0.0569245\pi$
$997$	−0.441271	−	3.63419i	−0.0139752	−	0.115096i	−0.998027	+	0.0627860i	$0.980001\pi$
$998$	−0.822086	+	2.16766i	−0.0260227	+	0.0686161i
$999$	25.8071	−	26.7300i	0.816500	−	0.845701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.122.37	yes	1392
3.2	odd	2	inner	507.2.s.a.122.22	✓	1392
169.151	odd	52	inner	507.2.s.a.320.22	yes	1392
507.320	even	52	inner	507.2.s.a.320.37	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.122.22	✓	1392	3.2	odd	2	inner
507.2.s.a.122.37	yes	1392	1.1	even	1	trivial
507.2.s.a.320.22	yes	1392	169.151	odd	52	inner
507.2.s.a.320.37	yes	1392	507.320	even	52	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.213424 + 0.684902i) q^{2} +(-0.424347 - 1.67926i) q^{3} +(1.22243 - 0.843781i) q^{4} +(-1.47602 + 3.27958i) q^{5} +(1.05957 - 0.649031i) q^{6} +(-1.08415 + 1.38382i) q^{7} +(1.96823 + 1.54201i) q^{8} +(-2.63986 + 1.42518i) q^{9} +O(q^{10})\)	\(q+(0.213424 + 0.684902i) q^{2} +(-0.424347 - 1.67926i) q^{3} +(1.22243 - 0.843781i) q^{4} +(-1.47602 + 3.27958i) q^{5} +(1.05957 - 0.649031i) q^{6} +(-1.08415 + 1.38382i) q^{7} +(1.96823 + 1.54201i) q^{8} +(-2.63986 + 1.42518i) q^{9} +(-2.56120 - 0.310987i) q^{10} +(-1.13328 + 3.63683i) q^{11} +(-1.93566 - 1.69472i) q^{12} +(-3.59206 + 0.311604i) q^{13} +(-1.17916 - 0.447198i) q^{14} +(6.13362 + 1.08695i) q^{15} +(0.417375 - 1.10053i) q^{16} +(-0.229608 - 1.89099i) q^{17} +(-1.53952 - 1.50388i) q^{18} +(-3.45195 + 3.45195i) q^{19} +(0.962919 + 5.25448i) q^{20} +(2.78386 + 1.23336i) q^{21} -2.73274 q^{22} +2.50259 q^{23} +(1.75423 - 3.95952i) q^{24} +(-5.26138 - 5.93887i) q^{25} +(-0.980050 - 2.39370i) q^{26} +(3.51347 + 3.82825i) q^{27} +(-0.157659 + 2.60641i) q^{28} +(-2.62275 + 4.99724i) q^{29} +(0.564610 + 4.43291i) q^{30} +(6.90507 - 0.417680i) q^{31} +(5.83439 + 0.352916i) q^{32} +(6.58811 + 0.359804i) q^{33} +(1.24614 - 0.560841i) q^{34} +(-2.93811 - 5.59811i) q^{35} +(-2.02450 + 3.96964i) q^{36} +(-0.431737 - 7.13746i) q^{37} +(-3.10097 - 1.62752i) q^{38} +(2.04754 + 5.89979i) q^{39} +(-7.96227 + 4.17892i) q^{40} +(2.04321 + 3.37988i) q^{41} +(-0.250589 + 2.16990i) q^{42} +(2.16305 + 2.44157i) q^{43} +(1.68333 + 5.40201i) q^{44} +(-0.777510 - 10.7612i) q^{45} +(0.534113 + 1.71403i) q^{46} +(1.92019 + 10.4781i) q^{47} +(-2.02519 - 0.233878i) q^{48} +(0.935642 + 3.79605i) q^{49} +(2.94464 - 4.87102i) q^{50} +(-3.07804 + 1.18801i) q^{51} +(-4.12811 + 3.41182i) q^{52} +(9.36922 - 1.13763i) q^{53} +(-1.87212 + 3.22342i) q^{54} +(-10.2545 - 9.08472i) q^{55} +(-4.26772 + 1.05190i) q^{56} +(7.26156 + 4.33191i) q^{57} +(-3.98237 - 0.729797i) q^{58} +(-13.7740 - 6.19917i) q^{59} +(8.41505 - 3.84672i) q^{60} +(0.678853 - 5.59086i) q^{61} +(1.75978 + 4.64015i) q^{62} +(0.889820 - 5.19820i) q^{63} +(0.440130 + 1.78568i) q^{64} +(4.28002 - 12.2404i) q^{65} +(1.15963 + 4.58900i) q^{66} +(-1.97296 - 10.7661i) q^{67} +(-1.87626 - 2.11786i) q^{68} +(-1.06197 - 4.20251i) q^{69} +(3.20709 - 3.20709i) q^{70} +(-4.80233 - 7.94402i) q^{71} +(-7.39349 - 1.26560i) q^{72} +(11.9212 + 3.71480i) q^{73} +(4.79631 - 1.81900i) q^{74} +(-7.74029 + 11.3554i) q^{75} +(-1.30707 + 7.13245i) q^{76} +(-3.80407 - 5.51114i) q^{77} +(-3.60378 + 2.66152i) q^{78} +(1.14921 - 1.66492i) q^{79} +(2.99321 + 2.99321i) q^{80} +(4.93772 - 7.52455i) q^{81} +(-1.87882 + 2.12075i) q^{82} +(-4.69865 - 2.84043i) q^{83} +(4.44375 - 0.841270i) q^{84} +(6.54055 + 2.03812i) q^{85} +(-1.21059 + 2.00256i) q^{86} +(9.50464 + 2.28373i) q^{87} +(-7.83859 + 5.41058i) q^{88} +(-8.35630 + 8.35630i) q^{89} +(7.20443 - 2.82922i) q^{90} +(3.46314 - 5.30859i) q^{91} +(3.05924 - 2.11164i) q^{92} +(-3.63154 - 11.4182i) q^{93} +(-6.76666 + 3.55142i) q^{94} +(-6.22579 - 16.4161i) q^{95} +(-1.88317 - 9.94725i) q^{96} +(4.39626 + 9.76809i) q^{97} +(-2.40023 + 1.45099i) q^{98} +(-2.19144 - 11.2159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more