LMFDB - Embedded newform 504.2.cs.a.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31153 + 0.529035i) q^{2} +(0.349968 - 1.69633i) q^{3} +(1.44024 - 1.38770i) q^{4} +(-2.84022 - 1.63980i) q^{5} +(0.438422 + 2.40993i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.15479 + 2.58195i) q^{8} +(-2.75505 - 1.18732i) q^{9} +O(q^{10})$	\(q+(-1.31153 + 0.529035i) q^{2} +(0.349968 - 1.69633i) q^{3} +(1.44024 - 1.38770i) q^{4} +(-2.84022 - 1.63980i) q^{5} +(0.438422 + 2.40993i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.15479 + 2.58195i) q^{8} +(-2.75505 - 1.18732i) q^{9} +(4.59255 + 0.648078i) q^{10} +(-1.13497 + 0.655273i) q^{11} +(-1.84995 - 2.92877i) q^{12} +(-1.44124 - 0.832099i) q^{13} +(-1.11393 - 0.871304i) q^{14} +(-3.77562 + 4.24406i) q^{15} +(0.148601 - 3.99724i) q^{16} +0.718794 q^{17} +(4.24147 + 0.0996933i) q^{18} -2.06256i q^{19} +(-6.36614 + 1.57965i) q^{20} +(1.64405 - 0.545082i) q^{21} +(1.14188 - 1.45985i) q^{22} +(-2.21134 + 3.83015i) q^{23} +(3.97569 + 2.86250i) q^{24} +(2.87788 + 4.98464i) q^{25} +(2.33044 + 0.328861i) q^{26} +(-2.97826 + 4.25793i) q^{27} +(1.92190 + 0.553439i) q^{28} +(-3.52068 + 2.03267i) q^{29} +(2.70660 - 7.56366i) q^{30} +(-2.13307 + 3.69458i) q^{31} +(1.91978 + 5.32113i) q^{32} +(0.714355 + 2.15460i) q^{33} +(-0.942723 + 0.380267i) q^{34} -3.27960i q^{35} +(-5.61557 + 2.11314i) q^{36} +11.2721i q^{37} +(1.09117 + 2.70512i) q^{38} +(-1.91590 + 2.15360i) q^{39} +(7.51373 - 5.43967i) q^{40} +(1.31628 - 2.27986i) q^{41} +(-1.86785 + 1.58465i) q^{42} +(4.04806 - 2.33715i) q^{43} +(-0.725308 + 2.51874i) q^{44} +(5.87796 + 7.88996i) q^{45} +(0.873961 - 6.19325i) q^{46} +(-4.19623 - 7.26808i) q^{47} +(-6.72862 - 1.65098i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.41149 - 5.01502i) q^{50} +(0.251555 - 1.21931i) q^{51} +(-3.23043 + 0.801575i) q^{52} -0.336321i q^{53} +(1.65349 - 7.16003i) q^{54} +4.29806 q^{55} +(-2.81343 + 0.290899i) q^{56} +(-3.49878 - 0.721830i) q^{57} +(3.54214 - 4.52847i) q^{58} +(4.54765 + 2.62559i) q^{59} +(0.451648 + 11.3519i) q^{60} +(-10.6978 + 6.17637i) q^{61} +(0.843027 - 5.97404i) q^{62} +(-0.349274 - 2.97960i) q^{63} +(-5.33293 - 5.96321i) q^{64} +(2.72895 + 4.72668i) q^{65} +(-2.07676 - 2.44791i) q^{66} +(-11.4089 - 6.58693i) q^{67} +(1.03524 - 0.997467i) q^{68} +(5.72329 + 5.09158i) q^{69} +(1.73502 + 4.30131i) q^{70} -14.4155 q^{71} +(6.24709 - 5.74229i) q^{72} -1.30967 q^{73} +(-5.96336 - 14.7838i) q^{74} +(9.46274 - 3.13737i) q^{75} +(-2.86221 - 2.97059i) q^{76} +(-1.13497 - 0.655273i) q^{77} +(1.37343 - 3.83810i) q^{78} +(-6.32934 - 10.9627i) q^{79} +(-6.97673 + 11.1093i) q^{80} +(6.18055 + 6.54224i) q^{81} +(-0.520216 + 3.68647i) q^{82} +(12.3260 - 7.11639i) q^{83} +(1.61142 - 3.06649i) q^{84} +(-2.04153 - 1.17868i) q^{85} +(-4.07273 + 5.20682i) q^{86} +(2.21594 + 6.68359i) q^{87} +(-0.381237 - 3.68713i) q^{88} -17.8002 q^{89} +(-11.8832 - 7.23831i) q^{90} -1.66420i q^{91} +(2.13022 + 8.58501i) q^{92} +(5.52071 + 4.91137i) q^{93} +(9.34856 + 7.31238i) q^{94} +(-3.38219 + 5.85812i) q^{95} +(9.69824 - 1.39436i) q^{96} +(2.72164 + 4.71403i) q^{97} +(0.197609 - 1.40034i) q^{98} +(3.90490 - 0.457740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.31153	+	0.529035i	−0.927395	+	0.374084i
$2$	−1.31153	+	0.529035i	−0.927395	+	0.374084i
$3$	0.349968	−	1.69633i	0.202054	−	0.979374i
$3$	0.349968	−	1.69633i	0.202054	−	0.979374i
$4$	1.44024	−	1.38770i	0.720122	−	0.693848i
$5$	−2.84022	−	1.63980i	−1.27018	−	0.733341i	−0.295161	−	0.955448i	$-0.595373\pi$
$5$	−2.84022	−	1.63980i	−1.27018	−	0.733341i	−0.975022	+	0.222107i	$0.928707\pi$
$6$	0.438422	+	2.40993i	0.178985	+	0.983852i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.15479	+	2.58195i	−0.408279	+	0.912857i
$9$	−2.75505	−	1.18732i	−0.918348	−	0.395773i
$10$	4.59255	+	0.648078i	1.45229	+	0.204940i
$11$	−1.13497	+	0.655273i	−0.342205	+	0.197572i	−0.661247	−	0.750168i	$-0.729972\pi$
$11$	−1.13497	+	0.655273i	−0.342205	+	0.197572i	0.319042	+	0.947741i	$0.396639\pi$
$12$	−1.84995	−	2.92877i	−0.534033	−	0.845463i
$13$	−1.44124	−	0.832099i	−0.399727	−	0.230783i	0.286639	−	0.958039i	$-0.407462\pi$
$13$	−1.44124	−	0.832099i	−0.399727	−	0.230783i	−0.686366	+	0.727256i	$0.740795\pi$
$14$	−1.11393	−	0.871304i	−0.297709	−	0.232866i
$15$	−3.77562	+	4.24406i	−0.974861	+	1.09581i
$16$	0.148601	−	3.99724i	0.0371503	−	0.999310i
$17$	0.718794			0.174333			0.0871666	−	0.996194i	$-0.472219\pi$
$17$	0.718794			0.174333			0.0871666	+	0.996194i	$0.472219\pi$
$18$	4.24147	+	0.0996933i	0.999724	+	0.0234979i
$19$		−	2.06256i		−	0.473184i	−0.971609	−	0.236592i	$-0.923969\pi$
$19$		−	2.06256i		−	0.473184i	0.971609	−	0.236592i	$-0.0760305\pi$
$20$	−6.36614	+	1.57965i	−1.42351	+	0.353219i
$21$	1.64405	−	0.545082i	0.358760	−	0.118947i
$22$	1.14188	−	1.45985i	0.243451	−	0.311241i
$23$	−2.21134	+	3.83015i	−0.461096	+	0.798641i	−0.999016	−	0.0443545i	$-0.985877\pi$
$23$	−2.21134	+	3.83015i	−0.461096	+	0.798641i	0.537920	+	0.842996i	$0.319210\pi$
$24$	3.97569	+	2.86250i	0.811534	+	0.584305i
$25$	2.87788	+	4.98464i	0.575577	+	0.996928i
$26$	2.33044	+	0.328861i	0.457037	+	0.0644949i
$27$	−2.97826	+	4.25793i	−0.573166	+	0.819439i
$28$	1.92190	+	0.553439i	0.363205	+	0.104590i
$29$	−3.52068	+	2.03267i	−0.653774	+	0.377457i	−0.789901	−	0.613235i	$-0.789868\pi$
$29$	−3.52068	+	2.03267i	−0.653774	+	0.377457i	0.136127	+	0.990691i	$0.456535\pi$
$30$	2.70660	−	7.56366i	0.494155	−	1.38093i
$31$	−2.13307	+	3.69458i	−0.383111	+	0.663567i	−0.991505	−	0.130068i	$-0.958480\pi$
$31$	−2.13307	+	3.69458i	−0.383111	+	0.663567i	0.608395	+	0.793635i	$0.291814\pi$
$32$	1.91978	+	5.32113i	0.339373	+	0.940652i
$33$	0.714355	+	2.15460i	0.124353	+	0.375067i
$34$	−0.942723	+	0.380267i	−0.161676	+	0.0652153i
$35$		−	3.27960i		−	0.554353i
$36$	−5.61557	+	2.11314i	−0.935929	+	0.352189i
$37$			11.2721i			1.85313i	0.376137	+	0.926564i	$0.377252\pi$
$37$			11.2721i			1.85313i	−0.376137	+	0.926564i	$0.622748\pi$
$38$	1.09117	+	2.70512i	0.177011	+	0.438829i
$39$	−1.91590	+	2.15360i	−0.306789	+	0.344852i
$40$	7.51373	−	5.43967i	1.18802	−	0.860088i
$41$	1.31628	−	2.27986i	0.205568	−	0.356054i	−0.744746	−	0.667349i	$-0.767429\pi$
$41$	1.31628	−	2.27986i	0.205568	−	0.356054i	0.950314	+	0.311294i	$0.100763\pi$
$42$	−1.86785	+	1.58465i	−0.288216	+	0.244517i
$43$	4.04806	−	2.33715i	0.617323	−	0.356412i	−0.158503	−	0.987359i	$-0.550667\pi$
$43$	4.04806	−	2.33715i	0.617323	−	0.356412i	0.775826	+	0.630947i	$0.217333\pi$
$44$	−0.725308	+	2.51874i	−0.109344	+	0.379714i
$45$	5.87796	+	7.88996i	0.876234	+	1.17617i
$46$	0.873961	−	6.19325i	0.128858	−	0.913145i
$47$	−4.19623	−	7.26808i	−0.612082	−	1.06016i	−0.990889	−	0.134682i	$-0.956999\pi$
$47$	−4.19623	−	7.26808i	−0.612082	−	1.06016i	0.378806	−	0.925476i	$-0.376335\pi$
$48$	−6.72862	−	1.65098i	−0.971192	−	0.238299i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−6.41149	−	5.01502i	−0.906722	−	0.709231i
$51$	0.251555	−	1.21931i	0.0352247	−	0.170737i
$52$	−3.23043	+	0.801575i	−0.447981	+	0.111158i
$53$		−	0.336321i		−	0.0461973i	−0.999733	−	0.0230987i	$-0.992647\pi$
$53$		−	0.336321i		−	0.0461973i	0.999733	−	0.0230987i	$-0.00735318\pi$
$54$	1.65349	−	7.16003i	0.225011	−	0.974356i
$55$	4.29806			0.579551
$56$	−2.81343	+	0.290899i	−0.375960	+	0.0388730i
$57$	−3.49878	−	0.721830i	−0.463425	−	0.0956088i
$58$	3.54214	−	4.52847i	0.465106	−	0.594618i
$59$	4.54765	+	2.62559i	0.592054	+	0.341822i	0.765909	−	0.642949i	$-0.222289\pi$
$59$	4.54765	+	2.62559i	0.592054	+	0.341822i	−0.173855	+	0.984771i	$0.555623\pi$
$60$	0.451648	+	11.3519i	0.0583075	+	1.46552i
$61$	−10.6978	+	6.17637i	−1.36971	+	0.790804i	−0.990891	−	0.134666i	$-0.957004\pi$
$61$	−10.6978	+	6.17637i	−1.36971	+	0.790804i	−0.378821	+	0.925470i	$0.623670\pi$
$62$	0.843027	−	5.97404i	0.107065	−	0.758704i
$63$	−0.349274	−	2.97960i	−0.0440044	−	0.375394i
$64$	−5.33293	−	5.96321i	−0.666616	−	0.745401i
$65$	2.72895	+	4.72668i	0.338485	+	0.586273i
$66$	−2.07676	−	2.44791i	−0.255631	−	0.301317i
$67$	−11.4089	−	6.58693i	−1.39382	−	0.804722i	−0.400083	−	0.916479i	$-0.631019\pi$
$67$	−11.4089	−	6.58693i	−1.39382	−	0.804722i	−0.993736	+	0.111757i	$0.964352\pi$
$68$	1.03524	−	0.997467i	0.125541	−	0.120961i
$69$	5.72329	+	5.09158i	0.689003	+	0.612954i
$70$	1.73502	+	4.30131i	0.207375	+	0.514104i
$71$	−14.4155			−1.71081			−0.855403	−	0.517963i	$-0.826690\pi$
$71$	−14.4155			−1.71081			−0.855403	+	0.517963i	$0.826690\pi$
$72$	6.24709	−	5.74229i	0.736227	−	0.676735i
$73$	−1.30967			−0.153285			−0.0766427	−	0.997059i	$-0.524420\pi$
$73$	−1.30967			−0.153285			−0.0766427	+	0.997059i	$0.524420\pi$
$74$	−5.96336	−	14.7838i	−0.693226	−	1.71858i
$75$	9.46274	−	3.13737i	1.09266	−	0.362272i
$76$	−2.86221	−	2.97059i	−0.328318	−	0.340750i
$77$	−1.13497	−	0.655273i	−0.129341	−	0.0746753i
$78$	1.37343	−	3.83810i	0.155511	−	0.434579i
$79$	−6.32934	−	10.9627i	−0.712106	−	1.23340i	−0.964065	−	0.265666i	$-0.914408\pi$
$79$	−6.32934	−	10.9627i	−0.712106	−	1.23340i	0.251959	−	0.967738i	$-0.418925\pi$
$80$	−6.97673	+	11.1093i	−0.780022	+	1.24206i
$81$	6.18055	+	6.54224i	0.686727	+	0.726915i
$82$	−0.520216	+	3.68647i	−0.0574483	+	0.407103i
$83$	12.3260	−	7.11639i	1.35295	−	0.781126i	0.364288	−	0.931287i	$-0.381313\pi$
$83$	12.3260	−	7.11639i	1.35295	−	0.781126i	0.988662	+	0.150161i	$0.0479792\pi$
$84$	1.61142	−	3.06649i	0.175820	−	0.334581i
$85$	−2.04153	−	1.17868i	−0.221435	−	0.127846i
$86$	−4.07273	+	5.20682i	−0.439174	+	0.561465i
$87$	2.21594	+	6.68359i	0.237574	+	0.716556i
$88$	−0.381237	−	3.68713i	−0.0406400	−	0.393049i
$89$	−17.8002			−1.88681			−0.943407	−	0.331637i	$-0.892399\pi$
$89$	−17.8002			−1.88681			−0.943407	+	0.331637i	$0.892399\pi$
$90$	−11.8832	−	7.23831i	−1.25260	−	0.762985i
$91$		−	1.66420i		−	0.174455i
$92$	2.13022	+	8.58501i	0.222091	+	0.895049i
$93$	5.52071	+	4.91137i	0.572471	+	0.509285i
$94$	9.34856	+	7.31238i	0.964231	+	0.754214i
$95$	−3.38219	+	5.85812i	−0.347005	+	0.601031i
$96$	9.69824	−	1.39436i	0.989822	−	0.142311i
$97$	2.72164	+	4.71403i	0.276341	+	0.478637i	0.970473	−	0.241211i	$-0.0775447\pi$
$97$	2.72164	+	4.71403i	0.276341	+	0.478637i	−0.694131	+	0.719848i	$0.744211\pi$
$98$	0.197609	−	1.40034i	0.0199615	−	0.141456i
$99$	3.90490	−	0.457740i	0.392457	−	0.0460046i
$100$	11.0620	+	3.18547i	1.10620	+	0.318547i
$101$	16.6716	−	9.62537i	1.65889	−	0.957760i	0.685659	−	0.727922i	$-0.259514\pi$
$101$	16.6716	−	9.62537i	1.65889	−	0.957760i	0.973229	−	0.229837i	$-0.0738194\pi$
$102$	0.315135	+	1.73225i	0.0312030	+	0.171518i
$103$	9.44092	−	16.3521i	0.930241	−	1.61122i	0.147333	−	0.989087i	$-0.452931\pi$
$103$	9.44092	−	16.3521i	0.930241	−	1.61122i	0.782908	−	0.622138i	$-0.213736\pi$
$104$	3.81276	−	2.76031i	0.373872	−	0.270670i
$105$	−5.56327	−	1.14775i	−0.542919	−	0.112009i
$106$	0.177926	+	0.441097i	0.0172817	+	0.0428431i
$107$			6.68051i			0.645830i	0.946428	+	0.322915i	$0.104663\pi$
$107$			6.68051i			0.645830i	−0.946428	+	0.322915i	$0.895337\pi$
$108$	1.61930	+	10.2654i	0.155817	+	0.987786i
$109$		−	1.63514i		−	0.156618i	−0.996929	−	0.0783088i	$-0.975048\pi$
$109$		−	1.63514i		−	0.156618i	0.996929	−	0.0783088i	$-0.0249520\pi$
$110$	−5.63706	+	2.27383i	−0.537472	+	0.216801i
$111$	19.1212	+	3.94489i	1.81491	+	0.374432i
$112$	3.53601	−	1.86993i	0.334122	−	0.176691i
$113$	7.26767	−	12.5880i	0.683685	−	1.18418i	−0.290163	−	0.956977i	$-0.593710\pi$
$113$	7.26767	−	12.5880i	0.683685	−	1.18418i	0.973848	−	0.227200i	$-0.0729570\pi$
$114$	4.97064	−	0.904272i	0.465543	−	0.0846929i
$115$	12.5614	−	7.25230i	1.17135	−	0.676281i
$116$	−2.24991	+	7.81317i	−0.208899	+	0.725434i
$117$	2.98271	+	4.00368i	0.275751	+	0.370140i
$118$	−7.35343	−	1.03768i	−0.676938	−	0.0955262i
$119$	0.359397	+	0.622494i	0.0329459	+	0.0570639i
$120$	−6.59790	−	14.6494i	−0.602303	−	1.33730i
$121$	−4.64123	+	8.03885i	−0.421930	+	0.730805i
$122$	10.7630	−	13.7600i	0.974436	−	1.24577i
$123$	−3.40673	−	3.03071i	−0.307175	−	0.273270i
$124$	2.05482	+	8.28115i	0.184528	+	0.743669i
$125$		−	2.47861i		−	0.221694i
$126$	2.03440	+	3.72307i	0.181239	+	0.331677i
$127$	−3.40205			−0.301883			−0.150942	−	0.988543i	$-0.548231\pi$
$127$	−3.40205			−0.301883			−0.150942	+	0.988543i	$0.548231\pi$
$128$	10.1491	+	4.99964i	0.897059	+	0.441910i
$129$	−2.54788	−	7.68476i	−0.224328	−	0.676605i
$130$	−6.07969	−	4.75549i	−0.533224	−	0.417084i
$131$	−5.17101	−	2.98548i	−0.451793	−	0.260843i	0.256794	−	0.966466i	$-0.417334\pi$
$131$	−5.17101	−	2.98548i	−0.451793	−	0.260843i	−0.708587	+	0.705623i	$0.750667\pi$
$132$	4.01877	+	2.11184i	0.349789	+	0.183812i
$133$	1.78623	−	1.03128i	0.154886	−	0.0894234i
$134$	18.4479	+	2.60327i	1.59365	+	0.224889i
$135$	15.4410	−	7.20970i	1.32895	−	0.620512i
$136$	−0.830055	+	1.85589i	−0.0711766	+	0.159141i
$137$	4.41844	+	7.65296i	0.377493	+	0.653836i	0.990697	−	0.136088i	$-0.0434530\pi$
$137$	4.41844	+	7.65296i	0.377493	+	0.653836i	−0.613204	+	0.789924i	$0.710120\pi$
$138$	−10.1999	−	3.64996i	−0.868274	−	0.310705i
$139$	−16.6058	−	9.58733i	−1.40848	−	0.813187i	−0.413240	−	0.910622i	$-0.635603\pi$
$139$	−16.6058	−	9.58733i	−1.40848	−	0.813187i	−0.995242	+	0.0974352i	$0.968936\pi$
$140$	−4.55108	−	4.72342i	−0.384637	−	0.399202i
$141$	−13.7976	+	4.57458i	−1.16197	+	0.385249i
$142$	18.9064	−	7.62631i	1.58659	−	0.639986i
$143$	2.18101			0.182385
$144$	−5.15540	+	10.8361i	−0.429617	+	0.903011i
$145$	13.3327			1.10722
$146$	1.71768	−	0.692862i	0.142156	−	0.0573417i
$147$	1.29408	+	1.15124i	0.106734	+	0.0949530i
$148$	15.6423	+	16.2346i	1.28579	+	1.33448i
$149$	0.369359	+	0.213250i	0.0302591	+	0.0174701i	0.515053	−	0.857158i	$-0.327772\pi$
$149$	0.369359	+	0.213250i	0.0302591	+	0.0174701i	−0.484794	+	0.874628i	$0.661105\pi$
$150$	−10.7509	+	9.12089i	−0.877810	+	0.744717i
$151$	−4.59506	−	7.95887i	−0.373940	−	0.647684i	0.616227	−	0.787568i	$-0.288660\pi$
$151$	−4.59506	−	7.95887i	−0.373940	−	0.647684i	−0.990168	+	0.139885i	$0.955327\pi$
$152$	5.32543	+	2.38182i	0.431950	+	0.193191i
$153$	−1.98031	−	0.853438i	−0.160099	−	0.0689963i
$154$	1.83521	+	0.258976i	0.147885	+	0.0208689i
$155$	12.1168	−	6.99561i	0.973241	−	0.561901i
$156$	0.229184	+	5.76039i	0.0183494	+	0.461201i
$157$	−8.93954	−	5.16125i	−0.713453	−	0.411912i	0.0988853	−	0.995099i	$-0.468472\pi$
$157$	−8.93954	−	5.16125i	−0.713453	−	0.411912i	−0.812338	+	0.583187i	$0.801806\pi$
$158$	14.1008	+	11.0296i	1.12180	+	0.877465i
$159$	−0.570511	−	0.117702i	−0.0452445	−	0.00933435i
$160$	3.27298	−	18.2612i	0.258752	−	1.44368i
$161$	−4.42268			−0.348556
$162$	−11.5671	−	5.31064i	−0.908795	−	0.417243i
$163$			11.9320i			0.934583i	0.884103	+	0.467291i	$0.154770\pi$
$163$			11.9320i			0.934583i	−0.884103	+	0.467291i	$0.845230\pi$
$164$	−1.26799	−	5.11014i	−0.0990135	−	0.399035i
$165$	1.50418	−	7.29092i	0.117101	−	0.567597i
$166$	−12.4011	+	15.8543i	−0.962511	+	1.23053i
$167$	0.454487	−	0.787194i	0.0351692	−	0.0609149i	−0.847905	−	0.530148i	$-0.822136\pi$
$167$	0.454487	−	0.787194i	0.0351692	−	0.0609149i	0.883074	+	0.469233i	$0.155470\pi$
$168$	−0.491150	+	4.87430i	−0.0378930	+	0.376060i
$169$	−5.11522	−	8.85982i	−0.393479	−	0.681525i
$170$	3.30110	+	0.465835i	0.253183	+	0.0357279i
$171$	−2.44892	+	5.68245i	−0.187274	+	0.434548i
$172$	2.58694	−	8.98354i	0.197252	−	0.684988i
$173$	−8.90387	+	5.14065i	−0.676949	+	0.390837i	−0.798704	−	0.601724i	$-0.794481\pi$
$173$	−8.90387	+	5.14065i	−0.676949	+	0.390837i	0.121756	+	0.992560i	$0.461148\pi$
$174$	−6.44214	−	7.59345i	−0.488377	−	0.575658i
$175$	−2.87788	+	4.98464i	−0.217548	+	0.376803i
$176$	2.45063	+	4.63410i	0.184723	+	0.349309i
$177$	6.04539	−	6.79543i	0.454399	−	0.510776i
$178$	23.3455	−	9.41692i	1.74982	−	0.705828i
$179$		−	16.3351i		−	1.22094i	−0.792039	−	0.610470i	$-0.790980\pi$
$179$		−	16.3351i		−	1.22094i	0.792039	−	0.610470i	$-0.209020\pi$
$180$	19.4146	+	3.20665i	1.44708	+	0.239010i
$181$		−	7.54305i		−	0.560671i	−0.959902	−	0.280335i	$-0.909554\pi$
$181$		−	7.54305i		−	0.560671i	0.959902	−	0.280335i	$-0.0904456\pi$
$182$	0.880420	+	2.18265i	0.0652610	+	0.161789i
$183$	6.73326	+	20.3085i	0.497737	+	1.50125i
$184$	−7.33563	−	10.1326i	−0.540790	−	0.746983i
$185$	18.4840	−	32.0153i	1.35897	−	2.35381i
$186$	−9.83889	−	3.52077i	−0.721422	−	0.258155i
$187$	−0.815807	+	0.471006i	−0.0596577	+	0.0344434i
$188$	−16.1295	−	4.64471i	−1.17636	−	0.338751i
$189$	−5.17661	−	0.450281i	−0.376543	−	0.0327531i
$190$	1.33670	−	9.47242i	0.0969746	−	0.687202i
$191$	6.67472	+	11.5610i	0.482966	+	0.836522i	0.999809	−	0.0195586i	$-0.00622610\pi$
$191$	6.67472	+	11.5610i	0.482966	+	0.836522i	−0.516843	+	0.856080i	$0.672893\pi$
$192$	−11.9819	+	6.95946i	−0.864719	+	0.502255i
$193$	−5.99068	+	10.3762i	−0.431218	+	0.746892i	−0.996979	−	0.0776776i	$-0.975250\pi$
$193$	−5.99068	+	10.3762i	−0.431218	+	0.746892i	0.565760	+	0.824570i	$0.308583\pi$
$194$	−6.06342	−	4.74276i	−0.435328	−	0.340510i
$195$	8.97304	−	2.97500i	0.642573	−	0.213045i
$196$	0.481658	+	1.94114i	0.0344041	+	0.138653i
$197$			12.3181i			0.877630i	0.898577	+	0.438815i	$0.144602\pi$
$197$			12.3181i			0.877630i	−0.898577	+	0.438815i	$0.855398\pi$
$198$	−4.87925	+	2.66617i	−0.346753	+	0.189477i
$199$	14.0461			0.995698			0.497849	−	0.867264i	$-0.334123\pi$
$199$	14.0461			0.995698			0.497849	+	0.867264i	$0.334123\pi$
$200$	−16.1934	+	1.67435i	−1.14505	+	0.118394i
$201$	−15.1663	+	17.0480i	−1.06975	+	1.20247i
$202$	−16.7732	+	21.4439i	−1.18016	+	1.50879i
$203$	−3.52068	−	2.03267i	−0.247103	−	0.142665i
$204$	−1.32973	−	2.10518i	−0.0930997	−	0.147392i
$205$	−7.47702	+	4.31686i	−0.522218	+	0.301503i
$206$	−3.73122	+	26.4410i	−0.259966	+	1.84223i
$207$	10.6399	−	7.92667i	0.739527	−	0.550942i
$208$	−3.54027	+	5.63732i	−0.245473	+	0.390878i
$209$	1.35154	+	2.34094i	0.0934881	+	0.161926i
$210$	7.90362	−	1.43785i	0.545402	−	0.0992209i
$211$	−23.7198	−	13.6946i	−1.63294	−	0.942776i	−0.983182	−	0.182631i	$-0.941539\pi$
$211$	−23.7198	−	13.6946i	−1.63294	−	0.942776i	−0.649754	−	0.760145i	$-0.725128\pi$
$212$	−0.466712	−	0.484385i	−0.0320539	−	0.0332677i
$213$	−5.04496	+	24.4534i	−0.345675	+	1.67552i
$214$	−3.53423	−	8.76172i	−0.241595	−	0.598939i
$215$	−15.3298			−1.04548
$216$	−7.55451	−	12.6067i	−0.514019	−	0.857779i
$217$	−4.26614			−0.289604
$218$	0.865045	+	2.14454i	0.0585882	+	0.145246i
$219$	−0.458342	+	2.22163i	−0.0309719	+	0.150124i
$220$	6.19026	−	5.96441i	0.417347	−	0.402120i
$221$	−1.03595	−	0.598108i	−0.0696857	−	0.0402331i
$222$	−27.1651	+	4.94195i	−1.82320	+	0.331682i
$223$	3.23477	+	5.60279i	0.216616	+	0.375190i	0.953771	−	0.300533i	$-0.0971646\pi$
$223$	3.23477	+	5.60279i	0.216616	+	0.375190i	−0.737155	+	0.675724i	$0.763831\pi$
$224$	−3.64834	+	4.32315i	−0.243765	+	0.288852i
$225$	−2.01034	−	17.1499i	−0.134023	−	1.14333i
$226$	−2.87231	+	20.3544i	−0.191063	+	1.35396i
$227$	−12.4092	+	7.16445i	−0.823626	+	0.475521i	−0.851665	−	0.524086i	$-0.824407\pi$
$227$	−12.4092	+	7.16445i	−0.823626	+	0.475521i	0.0280390	+	0.999607i	$0.491074\pi$
$228$	−6.04077	+	3.81563i	−0.400060	+	0.252696i
$229$	−0.844229	−	0.487416i	−0.0557882	−	0.0322093i	0.471846	−	0.881681i	$-0.343588\pi$
$229$	−0.844229	−	0.487416i	−0.0557882	−	0.0322093i	−0.527635	+	0.849471i	$0.676921\pi$
$230$	−12.6379	+	16.1570i	−0.833320	+	1.06536i
$231$	−1.50876	+	1.69595i	−0.0992690	+	0.111585i
$232$	−1.18260	−	11.4375i	−0.0776416	−	0.750910i
$233$	−1.72075			−0.112730			−0.0563651	−	0.998410i	$-0.517951\pi$
$233$	−1.72075			−0.112730			−0.0563651	+	0.998410i	$0.517951\pi$
$234$	−6.03001	−	3.67300i	−0.394194	−	0.240112i
$235$			27.5239i			1.79546i
$236$	10.1932	−	2.52927i	0.663524	−	0.164642i
$237$	−20.8114	+	6.90002i	−1.35185	+	0.448204i
$238$	−0.800682	−	0.626288i	−0.0519005	−	0.0405962i
$239$	−2.42402	+	4.19852i	−0.156796	+	0.271579i	−0.933712	−	0.358026i	$-0.883450\pi$
$239$	−2.42402	+	4.19852i	−0.156796	+	0.271579i	0.776915	+	0.629605i	$0.216783\pi$
$240$	16.4034	+	15.7227i	1.05884	+	1.01490i
$241$	6.84873	+	11.8624i	0.441166	+	0.764122i	0.997776	−	0.0666520i	$-0.0212317\pi$
$241$	6.84873	+	11.8624i	0.441166	+	0.764122i	−0.556611	+	0.830774i	$0.687898\pi$
$242$	1.83430	−	12.9986i	0.117913	−	0.835582i
$243$	13.2608	−	8.19465i	0.850678	−	0.525687i
$244$	−6.83650	+	23.7408i	−0.437662	+	1.51985i
$245$	2.84022	−	1.63980i	0.181455	−	0.104763i
$246$	6.07140	+	2.17260i	0.387098	+	0.138520i
$247$	−1.71626	+	2.97264i	−0.109203	+	0.189145i
$248$	−7.07599	−	9.77394i	−0.449326	−	0.620646i
$249$	−7.75804	−	23.3993i	−0.491646	−	1.48287i
$250$	1.31127	+	3.25078i	0.0829322	+	0.205598i
$251$		−	15.8617i		−	1.00118i	−0.865684	−	0.500591i	$-0.833116\pi$
$251$		−	15.8617i		−	1.00118i	0.865684	−	0.500591i	$-0.166884\pi$
$252$	−4.63782	−	3.80666i	−0.292155	−	0.239797i
$253$		−	5.79612i		−	0.364399i
$254$	4.46191	−	1.79981i	0.279965	−	0.112930i
$255$	−2.71389	+	3.05060i	−0.169950	+	0.191036i
$256$	−15.9558	−	1.18799i	−0.997240	−	0.0742494i
$257$	9.20154	−	15.9375i	0.573976	−	0.994156i	−0.422176	−	0.906514i	$-0.638734\pi$
$257$	9.20154	−	15.9375i	0.573976	−	0.994156i	0.996152	−	0.0876418i	$-0.0279331\pi$
$258$	7.40713	+	8.73090i	0.461148	+	0.543562i
$259$	−9.76196	+	5.63607i	−0.606579	+	0.350208i
$260$	10.4895	+	3.02062i	0.650534	+	0.187331i
$261$	12.1131	−	1.41991i	0.749779	−	0.0878905i
$262$	8.36138	+	1.17992i	0.516568	+	0.0728955i
$263$	−7.72662	−	13.3829i	−0.476444	−	0.825225i	0.523192	−	0.852215i	$-0.324741\pi$
$263$	−7.72662	−	13.3829i	−0.476444	−	0.825225i	−0.999636	+	0.0269902i	$0.991408\pi$
$264$	−6.38799	−	0.643674i	−0.393154	−	0.0396154i
$265$	−0.551500	+	0.955225i	−0.0338784	+	0.0586790i
$266$	−1.79712	+	2.29754i	−0.110188	+	0.140871i
$267$	−6.22949	+	30.1949i	−0.381238	+	1.84790i
$268$	−25.5722	+	6.34530i	−1.56207	+	0.387601i
$269$		−	10.6304i		−	0.648148i	−0.946032	−	0.324074i	$-0.894947\pi$
$269$		−	10.6304i		−	0.648148i	0.946032	−	0.324074i	$-0.105053\pi$
$270$	−16.4373	+	17.6246i	−1.00034	+	1.07260i
$271$	−2.07822			−0.126243			−0.0631215	−	0.998006i	$-0.520106\pi$
$271$	−2.07822			−0.126243			−0.0631215	+	0.998006i	$0.520106\pi$
$272$	0.106814	−	2.87319i	0.00647653	−	0.174213i
$273$	−2.82302	−	0.582416i	−0.170857	−	0.0352494i
$274$	−9.84362	−	7.69961i	−0.594675	−	0.465150i
$275$	−6.53260	−	3.77160i	−0.393931	−	0.227436i
$276$	15.3085	−	0.609066i	0.921463	−	0.0366615i
$277$	21.5043	−	12.4155i	1.29207	−	0.745976i	0.313048	−	0.949737i	$-0.398650\pi$
$277$	21.5043	−	12.4155i	1.29207	−	0.745976i	0.979021	+	0.203761i	$0.0653166\pi$
$278$	26.8510	+	3.78909i	1.61042	+	0.227254i
$279$	10.2634	−	7.64611i	0.614451	−	0.457761i
$280$	8.46776	+	3.78724i	0.506045	+	0.226331i
$281$	4.54697	+	7.87559i	0.271250	+	0.469818i	0.969182	−	0.246345i	$-0.0792297\pi$
$281$	4.54697	+	7.87559i	0.271250	+	0.469818i	−0.697932	+	0.716164i	$0.745896\pi$
$282$	15.6759	−	13.2991i	0.933485	−	0.791951i
$283$	1.15776	+	0.668434i	0.0688218	+	0.0397343i	0.534016	−	0.845474i	$-0.320682\pi$
$283$	1.15776	+	0.668434i	0.0688218	+	0.0397343i	−0.465194	+	0.885209i	$0.654016\pi$
$284$	−20.7618	+	20.0043i	−1.23199	+	1.18704i
$285$	8.75363	+	7.78745i	0.518520	+	0.461289i
$286$	−2.86047	+	1.15383i	−0.169143	+	0.0682274i
$287$	2.63255			0.155395
$288$	1.02879	−	16.9394i	0.0606218	−	0.998161i
$289$	−16.4833			−0.969608
$290$	−17.4862	+	7.05345i	−1.02683	+	0.414193i
$291$	8.94902	−	2.96704i	0.524601	−	0.173931i
$292$	−1.88624	+	1.81742i	−0.110384	+	0.106357i
$293$	−3.68914	−	2.12993i	−0.215522	−	0.124432i	0.388353	−	0.921511i	$-0.373044\pi$
$293$	−3.68914	−	2.12993i	−0.215522	−	0.124432i	−0.603875	+	0.797079i	$0.706377\pi$
$294$	−2.30628	−	0.825283i	−0.134505	−	0.0481315i
$295$	−8.61087	−	14.9145i	−0.501344	−	0.868354i
$296$	−29.1041	−	13.0169i	−1.69164	−	0.756594i
$297$	0.590114	−	6.78418i	0.0342419	−	0.393658i
$298$	−0.597243	−	0.0842800i	−0.0345974	−	0.00488221i
$299$	6.37413	−	3.68010i	0.368625	−	0.212826i
$300$	9.27494	−	17.6500i	0.535489	−	1.01902i
$301$	4.04806	+	2.33715i	0.233326	+	0.134711i
$302$	10.2371	+	8.00738i	0.589079	+	0.460773i
$303$	−10.4932	−	31.6491i	−0.602820	−	1.81819i
$304$	−8.24456	−	0.306500i	−0.472858	−	0.0175790i
$305$	40.5120			2.31971
$306$	3.04874	+	0.0716589i	0.174285	+	0.00409647i
$307$			12.6827i			0.723838i	0.932209	+	0.361919i	$0.117878\pi$
$307$			12.6827i			0.723838i	−0.932209	+	0.361919i	$0.882122\pi$
$308$	−2.54395	+	0.631235i	−0.144955	+	0.0359680i
$309$	−24.4346	−	21.7376i	−1.39003	−	1.23661i
$310$	−12.1906	+	15.5852i	−0.692380	+	0.885178i
$311$	1.74365	−	3.02009i	0.0988735	−	0.171254i	−0.812345	−	0.583177i	$-0.801809\pi$
$311$	1.74365	−	3.02009i	0.0988735	−	0.171254i	0.911219	+	0.411923i	$0.135143\pi$
$312$	−3.34803	−	7.43371i	−0.189545	−	0.420851i
$313$	14.3092	+	24.7843i	0.808805	+	1.40089i	0.913692	+	0.406408i	$0.133219\pi$
$313$	14.3092	+	24.7843i	0.808805	+	1.40089i	−0.104887	+	0.994484i	$0.533448\pi$
$314$	14.4550	+	2.03982i	0.815742	+	0.115114i
$315$	−3.89393	+	9.03544i	−0.219398	+	0.509089i
$316$	−24.3287	−	7.00581i	−1.36860	−	0.394108i
$317$	28.2829	−	16.3292i	1.58853	−	0.917137i	0.594978	−	0.803742i	$-0.297161\pi$
$317$	28.2829	−	16.3292i	1.58853	−	0.917137i	0.993550	−	0.113396i	$-0.0361727\pi$
$318$	0.810513	−	0.147451i	0.0454513	−	0.00826862i
$319$	2.66390	−	4.61401i	0.149150	−	0.258335i
$320$	5.36820	+	25.6817i	0.300092	+	1.43565i
$321$	11.3323	+	2.33796i	0.632509	+	0.130492i
$322$	5.80049	−	2.33975i	0.323249	−	0.130389i
$323$		−	1.48256i		−	0.0824917i
$324$	17.9801	+	0.845692i	0.998896	+	0.0469829i
$325$		−	9.57874i		−	0.531333i
$326$	−6.31243	−	15.6492i	−0.349613	−	0.866727i
$327$	−2.77372	−	0.572245i	−0.153387	−	0.0316452i
$328$	4.36646	+	6.03132i	0.241097	+	0.333024i
$329$	4.19623	−	7.26808i	0.231345	−	0.400702i
$330$	1.88437	+	10.3581i	0.103731	+	0.570192i
$331$	−15.3650	+	8.87101i	−0.844539	+	0.487595i	−0.858805	−	0.512303i	$-0.828792\pi$
$331$	−15.3650	+	8.87101i	−0.844539	+	0.487595i	0.0142653	+	0.999898i	$0.495459\pi$
$332$	7.87698	−	27.3540i	0.432306	−	1.50125i
$333$	13.3836	−	31.0553i	0.733418	−	1.70182i
$334$	−0.179621	+	1.27287i	−0.00982844	+	0.0696484i
$335$	21.6025	+	37.4166i	1.18027	+	2.04429i
$336$	−1.93452	−	6.65264i	−0.105536	−	0.362931i
$337$	−11.1322	+	19.2815i	−0.606409	+	1.05033i	0.385418	+	0.922742i	$0.374057\pi$
$337$	−11.1322	+	19.2815i	−0.606409	+	1.05033i	−0.991827	+	0.127589i	$0.959276\pi$
$338$	11.3959	+	8.91383i	0.619858	+	0.484848i
$339$	−18.8099	−	16.7337i	−1.02161	−	0.908851i
$340$	−4.57594	+	1.13544i	−0.248165	+	0.0615778i
$341$		−	5.59097i		−	0.302768i
$342$	0.205624	−	8.74830i	0.0111189	−	0.473054i
$343$	−1.00000			−0.0539949
$344$	1.35975	+	13.1508i	0.0733127	+	0.709043i
$345$	−7.90620	−	23.8462i	−0.425655	−	1.28384i
$346$	8.95814	−	11.4526i	0.481593	−	0.615696i
$347$	−11.0047	−	6.35357i	−0.590764	−	0.341078i	0.174636	−	0.984633i	$-0.444125\pi$
$347$	−11.0047	−	6.35357i	−0.590764	−	0.341078i	−0.765399	+	0.643556i	$0.777459\pi$
$348$	12.4663	+	6.55095i	0.668263	+	0.351168i
$349$	−11.3647	+	6.56144i	−0.608341	+	0.351226i	−0.772316	−	0.635239i	$-0.780902\pi$
$349$	−11.3647	+	6.56144i	−0.608341	+	0.351226i	0.163975	+	0.986465i	$0.447568\pi$
$350$	1.13739	−	8.06003i	0.0607961	−	0.430827i
$351$	7.83540	−	3.65849i	0.418223	−	0.195276i
$352$	−5.66568	−	4.78132i	−0.301982	−	0.254845i
$353$	11.7142	+	20.2896i	0.623484	+	1.07991i	0.988832	+	0.149035i	$0.0476166\pi$
$353$	11.7142	+	20.2896i	0.623484	+	1.07991i	−0.365348	+	0.930871i	$0.619050\pi$
$354$	−4.33371	+	12.1107i	−0.230334	+	0.643674i
$355$	40.9431	+	23.6385i	2.17304	+	1.25460i
$356$	−25.6366	+	24.7012i	−1.35874	+	1.30916i
$357$	1.18173	−	0.391802i	0.0625438	−	0.0207363i
$358$	8.64183	+	21.4240i	0.456735	+	1.13229i
$359$	−18.8617			−0.995481			−0.497741	−	0.867326i	$-0.665837\pi$
$359$	−18.8617			−0.995481			−0.497741	+	0.867326i	$0.665837\pi$
$360$	−27.1593	+	6.06535i	−1.43142	+	0.319672i
$361$	14.7458			0.776097
$362$	3.99054	+	9.89297i	0.209738	+	0.519963i
$363$	12.0122	+	10.6864i	0.630479	+	0.560890i
$364$	−2.30940	−	2.39685i	−0.121045	−	0.125629i
$365$	3.71975	+	2.14760i	0.194700	+	0.112410i
$366$	−19.5748	−	23.0731i	−1.02319	−	1.20605i
$367$	−5.16206	−	8.94095i	−0.269457	−	0.466714i	0.699264	−	0.714863i	$-0.253511\pi$
$367$	−5.16206	−	8.94095i	−0.269457	−	0.466714i	−0.968722	+	0.248149i	$0.920178\pi$
$368$	14.9814	+	9.40841i	0.780960	+	0.490447i
$369$	−6.33332	+	4.71827i	−0.329700	+	0.245624i
$370$	−7.30523	+	51.7679i	−0.379781	+	2.69128i
$371$	0.291263	−	0.168161i	0.0151216	−	0.00873047i
$372$	14.7667	−	0.587509i	0.765615	−	0.0304609i
$373$	9.93715	+	5.73722i	0.514526	+	0.297062i	0.734692	−	0.678401i	$-0.237327\pi$
$373$	9.93715	+	5.73722i	0.514526	+	0.297062i	−0.220166	+	0.975462i	$0.570660\pi$
$374$	0.820779	−	1.04933i	0.0424415	−	0.0542596i
$375$	−4.20454	−	0.867435i	−0.217121	−	0.0447941i
$376$	23.6116	−	2.44136i	1.21767	−	0.125903i
$377$	6.76552			0.348442
$378$	7.02751	−	2.14805i	0.361456	−	0.110484i
$379$			2.09287i			0.107503i	0.998554	+	0.0537517i	$0.0171180\pi$
$379$			2.09287i			0.107503i	−0.998554	+	0.0537517i	$0.982882\pi$
$380$	3.25812	+	13.1306i	0.167138	+	0.673584i
$381$	−1.19061	+	5.77099i	−0.0609967	+	0.295657i
$382$	−14.8703	−	11.6314i	−0.760830	−	0.595116i
$383$	−2.23434	+	3.86999i	−0.114169	+	0.197747i	−0.917447	−	0.397857i	$-0.869754\pi$
$383$	−2.23434	+	3.86999i	−0.114169	+	0.197747i	0.803278	+	0.595604i	$0.203087\pi$
$384$	12.0329	−	15.4664i	0.614050	−	0.789267i
$385$	2.14903	+	3.72223i	0.109525	+	0.189703i
$386$	2.36762	−	16.7780i	0.120509	−	0.853976i
$387$	−13.9275	+	1.63261i	−0.707976	+	0.0829903i
$388$	10.4615	+	3.01253i	0.531100	+	0.152938i
$389$	−19.9661	+	11.5274i	−1.01232	+	0.584463i	−0.911870	−	0.410479i	$-0.865362\pi$
$389$	−19.9661	+	11.5274i	−1.01232	+	0.584463i	−0.100450	+	0.994942i	$0.532028\pi$
$390$	−10.1946	+	8.64887i	−0.516222	+	0.437953i
$391$	−1.58950	+	2.75309i	−0.0803843	+	0.139230i
$392$	−1.65864	−	2.29105i	−0.0837740	−	0.115716i
$393$	−6.87404	+	7.72690i	−0.346749	+	0.389770i
$394$	−6.51672	−	16.1556i	−0.328308	−	0.813910i
$395$			41.5154i			2.08887i
$396$	4.98880	−	6.07807i	0.250697	−	0.305435i
$397$		−	11.6612i		−	0.585260i	−0.956226	−	0.292630i	$-0.905470\pi$
$397$		−	11.6612i		−	0.585260i	0.956226	−	0.292630i	$-0.0945304\pi$
$398$	−18.4219	+	7.43086i	−0.923405	+	0.372475i
$399$	−1.12427	−	3.39095i	−0.0562837	−	0.169760i
$400$	20.3525	−	10.7629i	1.01762	−	0.538143i
$401$	−11.7460	+	20.3446i	−0.586566	+	1.01596i	0.408112	+	0.912932i	$0.366187\pi$
$401$	−11.7460	+	20.3446i	−0.586566	+	1.01596i	−0.994678	+	0.103030i	$0.967146\pi$
$402$	10.8722	−	30.3826i	0.542254	−	1.51534i
$403$	6.14852	−	3.54985i	0.306280	−	0.176831i
$404$	10.6541	−	36.9980i	0.530062	−	1.84072i
$405$	−6.82613	−	28.7162i	−0.339193	−	1.42692i
$406$	5.69284	+	0.803346i	0.282531	+	0.0398694i
$407$	−7.38633	−	12.7935i	−0.366127	−	0.634150i
$408$	2.85770	+	2.05754i	0.141477	+	0.101864i
$409$	−9.91109	+	17.1665i	−0.490072	+	0.848829i	−0.999935	−	0.0114265i	$-0.996363\pi$
$409$	−9.91109	+	17.1665i	−0.490072	+	0.848829i	0.509863	+	0.860256i	$0.329696\pi$
$410$	7.52260	−	9.61732i	0.371515	−	0.474966i
$411$	14.5282	−	4.81682i	0.716625	−	0.237596i
$412$	−9.09459	−	36.6522i	−0.448058	−	1.80572i
$413$			5.25118i			0.258393i
$414$	−9.76116	+	16.0250i	−0.479735	+	0.787586i
$415$	−46.6778			−2.29132
$416$	1.66084	−	9.26647i	0.0814294	−	0.454326i
$417$	−22.0747	+	24.8135i	−1.08100	+	1.21512i
$418$	−3.01103	−	2.35521i	−0.147274	−	0.115197i
$419$	8.85488	+	5.11237i	0.432589	+	0.249755i	0.700449	−	0.713702i	$-0.252983\pi$
$419$	8.85488	+	5.11237i	0.432589	+	0.249755i	−0.267860	+	0.963458i	$0.586316\pi$
$420$	−9.60519	+	6.06708i	−0.468685	+	0.296043i
$421$	14.4193	−	8.32497i	0.702752	−	0.405734i	−0.105619	−	0.994407i	$-0.533683\pi$
$421$	14.4193	−	8.32497i	0.702752	−	0.405734i	0.808372	+	0.588672i	$0.200349\pi$
$422$	38.3542	+	5.41236i	1.86705	+	0.263469i
$423$	2.93127	+	25.0061i	0.142523	+	1.21584i
$424$	0.868365	+	0.388380i	0.0421715	+	0.0188614i
$425$	2.06860	+	3.58293i	0.100342	+	0.173798i
$426$	−6.32007	−	34.7404i	−0.306208	−	1.68318i
$427$	−10.6978	−	6.17637i	−0.517702	−	0.298896i
$428$	9.27052	+	9.62157i	0.448108	+	0.465076i
$429$	0.763283	−	3.69970i	0.0368516	−	0.178623i
$430$	20.1056	−	8.11001i	0.969577	−	0.391100i
$431$	16.6791			0.803403			0.401701	−	0.915771i	$-0.368419\pi$
$431$	16.6791			0.803403			0.401701	+	0.915771i	$0.368419\pi$
$432$	16.5774	+	12.5375i	0.797580	+	0.603213i
$433$	24.2302			1.16443			0.582214	−	0.813035i	$-0.302187\pi$
$433$	24.2302			1.16443			0.582214	+	0.813035i	$0.302187\pi$
$434$	5.59519	−	2.25694i	0.268577	−	0.108336i
$435$	4.66600	−	22.6165i	0.223718	−	1.08438i
$436$	−2.26907	−	2.35499i	−0.108669	−	0.112784i
$437$	7.89992	+	4.56102i	0.377905	+	0.218183i
$438$	−0.574188	−	3.15622i	−0.0274358	−	0.150810i
$439$	2.48612	+	4.30608i	0.118656	+	0.205518i	0.919235	−	0.393709i	$-0.128808\pi$
$439$	2.48612	+	4.30608i	0.118656	+	0.205518i	−0.800579	+	0.599227i	$0.795475\pi$
$440$	−4.96335	+	11.0974i	−0.236619	+	0.529047i
$441$	2.40577	−	1.79228i	0.114561	−	0.0853466i
$442$	1.67511	+	0.236383i	0.0796767	+	0.0112436i
$443$	−10.6671	+	6.15866i	−0.506809	+	0.292607i	−0.731521	−	0.681819i	$-0.761189\pi$
$443$	−10.6671	+	6.15866i	−0.506809	+	0.292607i	0.224712	+	0.974425i	$0.427856\pi$
$444$	33.0135	−	20.8528i	1.56675	−	0.989632i
$445$	50.5563	+	29.1887i	2.39660	+	1.38368i
$446$	−7.20659	−	5.63694i	−0.341242	−	0.266917i
$447$	0.491004	−	0.551923i	0.0232237	−	0.0261051i
$448$	2.49783	−	7.60006i	0.118011	−	0.359069i
$449$	13.9127			0.656580			0.328290	−	0.944577i	$-0.393528\pi$
$449$	13.9127			0.656580			0.328290	+	0.944577i	$0.393528\pi$
$450$	11.7095	+	21.4291i	0.551992	+	1.01018i
$451$			3.45008i			0.162458i
$452$	−7.00106	−	28.2151i	−0.329302	−	1.32712i
$453$	−15.1090	+	5.00937i	−0.709881	+	0.235361i
$454$	12.4848	−	15.9613i	0.585942	−	0.749101i
$455$	−2.72895	+	4.72668i	−0.127935	+	0.221590i
$456$	5.90408	−	8.20011i	0.276484	−	0.384005i
$457$	−11.8496	−	20.5241i	−0.554300	−	0.960077i	−0.997958	−	0.0638800i	$-0.979653\pi$
$457$	−11.8496	−	20.5241i	−0.554300	−	0.960077i	0.443657	−	0.896197i	$-0.353681\pi$
$458$	1.36509	+	0.192635i	0.0637867	+	0.00900126i
$459$	−2.14075	+	3.06057i	−0.0999218	+	0.142855i
$460$	8.02742	−	27.8764i	0.374280	−	1.29974i
$461$	−4.59750	+	2.65437i	−0.214127	+	0.123626i	−0.603228	−	0.797569i	$-0.706119\pi$
$461$	−4.59750	+	2.65437i	−0.214127	+	0.123626i	0.389101	+	0.921195i	$0.372786\pi$
$462$	1.08157	−	3.02248i	0.0503193	−	0.140619i
$463$	11.0892	−	19.2070i	0.515358	−	0.892627i	−0.484483	−	0.874801i	$-0.660992\pi$
$463$	11.0892	−	19.2070i	0.515358	−	0.892627i	0.999841	−	0.0178260i	$-0.00567448\pi$
$464$	7.60187	+	14.3751i	0.352908	+	0.667345i
$465$	−7.62636	−	23.0022i	−0.353664	−	1.06670i
$466$	2.25682	−	0.910339i	0.104545	−	0.0421706i
$467$			17.8099i			0.824142i	0.911152	+	0.412071i	$0.135194\pi$
$467$			17.8099i			0.824142i	−0.911152	+	0.412071i	$0.864806\pi$
$468$	9.85171	+	1.62718i	0.455396	+	0.0752165i
$469$		−	13.1739i		−	0.608312i
$470$	−14.5611	−	36.0985i	−0.671654	−	1.66510i
$471$	−11.8837	+	13.3581i	−0.547572	+	0.615509i
$472$	−12.0307	+	8.70981i	−0.553758	+	0.400902i
$473$	−3.06294	+	5.30517i	−0.140834	+	0.243932i
$474$	23.6446	−	20.0596i	1.08603	−	0.921368i
$475$	10.2811	−	5.93581i	0.471731	−	0.272354i
$476$	1.38145	+	0.397809i	0.0633187	+	0.0182335i
$477$	−0.399321	+	0.926581i	−0.0182836	+	0.0424252i
$478$	0.958014	−	6.78889i	0.0438186	−	0.310517i
$479$	0.785355	+	1.36028i	0.0358838	+	0.0621526i	0.883410	−	0.468602i	$-0.155242\pi$
$479$	0.785355	+	1.36028i	0.0358838	+	0.0621526i	−0.847526	+	0.530754i	$0.821909\pi$
$480$	−29.8315	−	11.9429i	−1.36162	−	0.545116i
$481$	9.37954	−	16.2458i	0.427670	−	0.740746i
$482$	−15.2580	−	11.9347i	−0.694981	−	0.543609i
$483$	−1.54779	+	7.50230i	−0.0704271	+	0.341367i
$484$	4.47098	+	18.0185i	0.203226	+	0.819024i
$485$		−	17.8518i		−	0.810609i
$486$	−13.0567	+	17.7630i	−0.592263	+	0.805745i
$487$	30.4242			1.37865			0.689325	−	0.724452i	$-0.257907\pi$
$487$	30.4242			1.37865			0.689325	+	0.724452i	$0.257907\pi$
$488$	−3.59340	−	34.7536i	−0.162666	−	1.57322i
$489$	20.2405	+	4.17580i	0.915307	+	0.188836i
$490$	−2.85753	+	3.65323i	−0.129090	+	0.165036i
$491$	35.4791	+	20.4839i	1.60115	+	0.924425i	0.991257	+	0.131942i	$0.0421212\pi$
$491$	35.4791	+	20.4839i	1.60115	+	0.924425i	0.609894	+	0.792483i	$0.291212\pi$
$492$	−9.11223	+	0.362541i	−0.410811	+	0.0163446i
$493$	−2.53064	+	1.46107i	−0.113974	+	0.0658032i
$494$	0.678295	−	4.80668i	0.0305180	−	0.216263i
$495$	−11.8414	−	5.10317i	−0.532230	−	0.229371i
$496$	14.4512	+	9.07541i	0.648876	+	0.407498i
$497$	−7.20775	−	12.4842i	−0.323312	−	0.559993i
$498$	22.5540	+	26.5848i	1.01067	+	1.19129i
$499$	17.2554	+	9.96243i	0.772460	+	0.445980i	0.833751	−	0.552140i	$-0.186189\pi$
$499$	17.2554	+	9.96243i	0.772460	+	0.445980i	−0.0612916	+	0.998120i	$0.519522\pi$
$500$	−3.43956	−	3.56981i	−0.153822	−	0.159647i
$501$	−1.17628	−	1.04645i	−0.0525524	−	0.0467520i
$502$	8.39141	+	20.8032i	0.374527	+	0.928491i
$503$	−9.90427			−0.441610			−0.220805	−	0.975318i	$-0.570868\pi$
$503$	−9.90427			−0.441610			−0.220805	+	0.975318i	$0.570868\pi$
$504$	8.09651	+	2.53900i	0.360647	+	0.113096i
$505$	−63.1347			−2.80946
$506$	3.06635	+	7.60181i	0.136316	+	0.337942i
$507$	−16.8193	+	5.57643i	−0.746972	+	0.247658i
$508$	−4.89978	+	4.72101i	−0.217393	+	0.209461i
$509$	−32.9028	−	18.9965i	−1.45839	−	0.842004i	−0.459461	−	0.888198i	$-0.651957\pi$
$509$	−32.9028	−	18.9965i	−1.45839	−	0.842004i	−0.998932	+	0.0461944i	$0.985291\pi$
$510$	1.94549	−	5.43671i	0.0861475	−	0.240742i
$511$	−0.654835	−	1.13421i	−0.0289682	−	0.0501744i
$512$	21.5551	−	6.88311i	0.952610	−	0.304193i
$513$	8.78225	+	6.14284i	0.387746	+	0.271213i
$514$	−3.63661	+	25.7705i	−0.160404	+	1.13669i
$515$	−53.6285	+	30.9624i	−2.36315	+	1.36437i
$516$	−14.3337	−	7.53224i	−0.631004	−	0.331588i
$517$	9.52515	+	5.49935i	0.418916	+	0.241861i
$518$	9.82146	−	12.5563i	0.431530	−	0.551693i
$519$	5.60416	+	16.9029i	0.245995	+	0.741956i
$520$	−15.3554	+	1.58770i	−0.673379	+	0.0696252i
$521$	−25.8800			−1.13382			−0.566912	−	0.823778i	$-0.691862\pi$
$521$	−25.8800			−1.13382			−0.566912	+	0.823778i	$0.691862\pi$
$522$	−15.1355	+	8.27050i	−0.662463	+	0.361990i
$523$		−	9.65268i		−	0.422082i	−0.977477	−	0.211041i	$-0.932315\pi$
$523$		−	9.65268i		−	0.422082i	0.977477	−	0.211041i	$-0.0676854\pi$
$524$	−11.5905	+	2.87596i	−0.506331	+	0.125637i
$525$	7.44841	+	6.62629i	0.325075	+	0.289195i
$526$	17.2137	+	13.4645i	0.750555	+	0.587079i
$527$	−1.53324	+	2.65564i	−0.0667888	+	0.115682i
$528$	8.71859	−	2.53527i	0.379428	−	0.110334i
$529$	1.71997	+	2.97907i	0.0747813	+	0.129525i
$530$	0.217963	−	1.54457i	0.00946769	−	0.0670920i
$531$	−9.41157	−	12.6331i	−0.408428	−	0.548231i
$532$	1.14150	−	3.96404i	0.0494904	−	0.171863i
$533$	−3.79414	+	2.19055i	−0.164342	+	0.0948831i
$534$	−7.80398	−	42.8972i	−0.337711	−	1.85635i
$535$	10.9547	−	18.9741i	0.473613	−	0.820322i
$536$	30.1820	−	21.8507i	1.30366	−	0.943806i
$537$	−27.7096	−	5.71675i	−1.19576	−	0.246696i
$538$	5.62387	+	13.9422i	0.242462	+	0.601089i
$539$		−	1.31055i		−	0.0564492i
$540$	12.2340	−	31.8112i	0.526467	−	1.36894i
$541$		−	33.7387i		−	1.45054i	−0.688465	−	0.725270i	$-0.741715\pi$
$541$		−	33.7387i		−	1.45054i	0.688465	−	0.725270i	$-0.258285\pi$
$542$	2.72566	−	1.09945i	0.117077	−	0.0472256i
$543$	−12.7955	−	2.63982i	−0.549106	−	0.113286i
$544$	1.37993	+	3.82480i	0.0591640	+	0.163987i
$545$	−2.68129	+	4.64414i	−0.114854	+	0.198933i
$546$	4.01061	−	0.729621i	0.171638	−	0.0312249i
$547$	15.4632	−	8.92768i	0.661159	−	0.381720i	−0.131560	−	0.991308i	$-0.541998\pi$
$547$	15.4632	−	8.92768i	0.661159	−	0.381720i	0.792718	+	0.609588i	$0.208665\pi$
$548$	16.9836	+	4.89068i	0.725504	+	0.208919i
$549$	36.8062	−	4.31449i	1.57085	−	0.184138i
$550$	10.5630	+	1.49060i	0.450409	+	0.0635596i
$551$	4.19250	+	7.26162i	0.178607	+	0.309356i
$552$	−19.7554	+	8.89754i	−0.840845	+	0.378705i
$553$	6.32934	−	10.9627i	0.269151	−	0.466183i
$554$	−21.6354	+	27.6599i	−0.919200	+	1.17516i
$555$	−47.8396	−	42.5593i	−2.03068	−	1.80654i
$556$	−37.2206	+	9.23563i	−1.57851	+	0.391678i
$557$		−	4.50669i		−	0.190955i	−0.995432	−	0.0954773i	$-0.969562\pi$
$557$		−	4.50669i		−	0.190955i	0.995432	−	0.0954773i	$-0.0304377\pi$
$558$	−9.41567	+	15.4578i	−0.398597	+	0.654381i
$559$	−7.77896			−0.329015
$560$	−13.1093	−	0.487353i	−0.553971	−	0.0205944i
$561$	0.513474	+	1.54871i	0.0216789	+	0.0653866i
$562$	−10.1300	−	7.92359i	−0.427307	−	0.334237i
$563$	−13.2519	−	7.65097i	−0.558499	−	0.322450i	0.194044	−	0.980993i	$-0.437840\pi$
$563$	−13.2519	−	7.65097i	−0.558499	−	0.322450i	−0.752543	+	0.658543i	$0.771173\pi$
$564$	−13.5237	+	25.7353i	−0.569452	+	1.08365i
$565$	−41.2835	+	23.8350i	−1.73681	+	1.00275i
$566$	−1.87207	−	0.264177i	−0.0786890	−	0.0111042i
$567$	−2.57547	+	8.62363i	−0.108160	+	0.362158i
$568$	16.6469	−	37.2201i	0.698486	−	1.56172i
$569$	−11.8572	−	20.5373i	−0.497080	−	0.860967i	0.502915	−	0.864336i	$-0.332261\pi$
$569$	−11.8572	−	20.5373i	−0.497080	−	0.860967i	−0.999994	+	0.00336902i	$0.998928\pi$
$570$	−15.6005	−	5.58253i	−0.653434	−	0.233826i
$571$	−13.3485	−	7.70678i	−0.558619	−	0.322519i	0.193972	−	0.981007i	$-0.437863\pi$
$571$	−13.3485	−	7.70678i	−0.558619	−	0.322519i	−0.752591	+	0.658488i	$0.771196\pi$
$572$	3.14118	−	3.02658i	0.131339	−	0.126547i
$573$	21.9471	−	7.27655i	0.916853	−	0.303982i
$574$	−3.45268	+	1.39271i	−0.144112	+	0.0581308i
$575$	−25.4559			−1.06158
$576$	7.61223	+	22.7608i	0.317176	+	0.948367i
$577$	−6.72286			−0.279876			−0.139938	−	0.990160i	$-0.544690\pi$
$577$	−6.72286			−0.279876			−0.139938	+	0.990160i	$0.544690\pi$
$578$	21.6185	−	8.72027i	0.899209	−	0.362715i
$579$	15.5048	+	13.7935i	0.644358	+	0.573237i
$580$	19.2023	−	18.5017i	0.797331	−	0.768240i
$581$	12.3260	+	7.11639i	0.511367	+	0.295238i
$582$	−10.1673	+	8.62572i	−0.421447	+	0.357548i
$583$	0.220382	+	0.381713i	0.00912730	+	0.0158090i
$584$	1.51239	−	3.38150i	0.0625832	−	0.139928i
$585$	−1.90630	−	16.2624i	−0.0788160	−	0.672366i
$586$	5.96524	+	0.841785i	0.246422	+	0.0347738i
$587$	17.8707	−	10.3177i	0.737603	−	0.425855i	−0.0835942	−	0.996500i	$-0.526640\pi$
$587$	17.8707	−	10.3177i	0.737603	−	0.425855i	0.821197	+	0.570645i	$0.193307\pi$
$588$	3.46136	−	0.137714i	0.142744	−	0.00567925i
$589$	7.62031	+	4.39959i	0.313989	+	0.181282i
$590$	19.1837	+	15.0054i	0.789782	+	0.617762i
$591$	20.8956	+	4.31095i	0.859529	+	0.177329i
$592$	45.0574	+	1.67505i	1.85185	+	0.0688443i
$593$	−16.3836			−0.672795			−0.336398	−	0.941720i	$-0.609209\pi$
$593$	−16.3836			−0.672795			−0.336398	+	0.941720i	$0.609209\pi$
$594$	2.81512	+	9.20987i	0.115506	+	0.377886i
$595$		−	2.35736i		−	0.0966421i
$596$	0.827892	−	0.205427i	0.0339118	−	0.00841461i
$597$	4.91567	−	23.8267i	0.201185	−	0.975161i
$598$	−6.41298	+	8.19872i	−0.262246	+	0.335271i
$599$	−8.41971	+	14.5834i	−0.344020	+	0.595860i	−0.985175	−	0.171551i	$-0.945122\pi$
$599$	−8.41971	+	14.5834i	−0.344020	+	0.595860i	0.641155	+	0.767411i	$0.278455\pi$
$600$	−2.82694	+	28.0553i	−0.115409	+	1.14535i
$601$	−4.10222	−	7.10525i	−0.167333	−	0.289829i	0.770148	−	0.637865i	$-0.220182\pi$
$601$	−4.10222	−	7.10525i	−0.167333	−	0.289829i	−0.937481	+	0.348036i	$0.886849\pi$
$602$	−6.54560	−	0.923683i	−0.266779	−	0.0376465i
$603$	23.6112	+	31.6933i	0.961524	+	1.29065i
$604$	−17.6625	−	5.08617i	−0.718676	−	0.206953i
$605$	26.3642	−	15.2214i	1.07186	−	0.618837i
$606$	30.5057	+	35.9576i	1.23921	+	1.46068i
$607$	−18.3566	+	31.7945i	−0.745070	+	1.29050i	0.205093	+	0.978743i	$0.434250\pi$
$607$	−18.3566	+	31.7945i	−0.745070	+	1.29050i	−0.950162	+	0.311756i	$0.899083\pi$
$608$	10.9752	−	3.95968i	0.445102	−	0.160586i
$609$	−4.68019	+	5.26085i	−0.189651	+	0.213181i
$610$	−53.1329	+	21.4323i	−2.15129	+	0.867769i
$611$			13.9667i			0.565032i
$612$	−4.03644	+	1.51891i	−0.163163	+	0.0613983i
$613$			34.7228i			1.40244i	0.712944	+	0.701221i	$0.247361\pi$
$613$			34.7228i			1.40244i	−0.712944	+	0.701221i	$0.752639\pi$
$614$	−6.70958	−	16.6338i	−0.270777	−	0.671284i
$615$	4.70609	+	14.1942i	0.189768	+	0.572367i
$616$	3.00253	−	2.17372i	0.120975	−	0.0875818i
$617$	−16.4710	+	28.5286i	−0.663098	+	1.14852i	0.316699	+	0.948526i	$0.397425\pi$
$617$	−16.4710	+	28.5286i	−0.663098	+	1.14852i	−0.979797	+	0.199993i	$0.935908\pi$
$618$	43.5467	+	15.5829i	1.75171	+	0.626834i
$619$	20.4163	−	11.7874i	0.820602	−	0.473775i	−0.0300220	−	0.999549i	$-0.509558\pi$
$619$	20.4163	−	11.7874i	0.820602	−	0.473775i	0.850624	+	0.525774i	$0.176224\pi$
$620$	7.74329	−	26.8897i	0.310978	−	1.07992i
$621$	−9.72258	−	20.8229i	−0.390154	−	0.835594i
$622$	−0.689123	+	4.88341i	−0.0276313	+	0.195807i
$623$	−8.90008	−	15.4154i	−0.356574	−	0.617605i
$624$	8.32376	+	7.97833i	0.333217	+	0.319389i
$625$	10.3250	−	17.8834i	0.413000	−	0.715336i
$626$	−31.8788	−	24.9354i	−1.27413	−	0.996618i
$627$	4.44399	−	1.47340i	0.177476	−	0.0588420i
$628$	−20.0373	+	4.97191i	−0.799577	+	0.198401i
$629$			8.10234i			0.323062i
$630$	0.326954	−	13.9103i	0.0130262	−	0.554200i
$631$	26.1234			1.03996			0.519979	−	0.854179i	$-0.325940\pi$
$631$	26.1234			1.03996			0.519979	+	0.854179i	$0.325940\pi$
$632$	35.6143	−	3.68240i	1.41666	−	0.146478i
$633$	−31.5317	+	35.4438i	−1.25327	+	1.40876i
$634$	−28.4553	+	36.3789i	−1.13011	+	1.44479i
$635$	9.66256	+	5.57868i	0.383447	+	0.221383i
$636$	−0.985009	+	0.622176i	−0.0390581	+	0.0246709i
$637$	1.44124	−	0.832099i	0.0571039	−	0.0329690i
$638$	−1.05282	+	7.46073i	−0.0416816	+	0.295373i
$639$	39.7154	+	17.1158i	1.57112	+	0.677091i
$640$	−20.6271	−	30.8425i	−0.815359	−	1.21916i
$641$	−8.23572	−	14.2647i	−0.325291	−	0.563421i	0.656280	−	0.754517i	$-0.272129\pi$
$641$	−8.23572	−	14.2647i	−0.325291	−	0.563421i	−0.981571	+	0.191096i	$0.938796\pi$
$642$	−16.0996	+	2.92888i	−0.635401	+	0.115594i
$643$	−1.56119	−	0.901351i	−0.0615672	−	0.0355458i	0.468900	−	0.883251i	$-0.344650\pi$
$643$	−1.56119	−	0.901351i	−0.0615672	−	0.0355458i	−0.530468	+	0.847705i	$0.677984\pi$
$644$	−6.36973	+	6.13733i	−0.251002	+	0.241845i
$645$	−5.36494	+	26.0044i	−0.211244	+	1.02392i
$646$	0.784325	+	1.94442i	0.0308589	+	0.0765023i
$647$	−30.6107			−1.20343			−0.601716	−	0.798710i	$-0.705516\pi$
$647$	−30.6107			−1.20343			−0.601716	+	0.798710i	$0.705516\pi$
$648$	−24.0289	+	8.40297i	−0.943946	+	0.330100i
$649$	−6.88191			−0.270138
$650$	5.06749	+	12.5628i	0.198763	+	0.492755i
$651$	−1.49301	+	7.23676i	−0.0585157	+	0.283631i
$652$	16.5579	+	17.1849i	0.648458	+	0.673013i
$653$	3.77460	+	2.17926i	0.147711	+	0.0852812i	0.572034	−	0.820230i	$-0.306154\pi$
$653$	3.77460	+	2.17926i	0.147711	+	0.0852812i	−0.424323	+	0.905511i	$0.639488\pi$
$654$	3.94057	−	0.716879i	0.154089	−	0.0280322i
$655$	9.79119	+	16.9588i	0.382573	+	0.662637i
$656$	−8.91754	−	5.60026i	−0.348171	−	0.218654i
$657$	3.60820	+	1.55500i	0.140769	+	0.0606662i
$658$	−1.65842	+	11.7523i	−0.0646521	+	0.458152i
$659$	17.3545	−	10.0196i	0.676034	−	0.390309i	−0.122325	−	0.992490i	$-0.539035\pi$
$659$	17.3545	−	10.0196i	0.676034	−	0.390309i	0.798359	+	0.602182i	$0.205702\pi$
$660$	−7.95119	−	12.5880i	−0.309500	−	0.489989i
$661$	−39.8575	−	23.0117i	−1.55028	−	0.895053i	−0.998119	−	0.0613138i	$-0.980471\pi$
$661$	−39.8575	−	23.0117i	−1.55028	−	0.895053i	−0.552159	−	0.833739i	$-0.686196\pi$
$662$	15.4587	−	19.7633i	0.600820	−	0.768122i
$663$	−1.37714	+	1.54800i	−0.0534835	+	0.0601192i
$664$	4.14030	+	40.0429i	0.160675	+	1.55397i
$665$	−6.76438			−0.262311
$666$	−1.12376	+	47.8104i	−0.0435447	+	1.85262i
$667$		−	17.9796i		−	0.696175i
$668$	−0.437814	−	1.76444i	−0.0169395	−	0.0682682i
$669$	10.6362	−	3.52643i	0.411220	−	0.136340i
$670$	−48.1271	−	37.6447i	−1.85931	−	1.45434i
$671$	8.09442	−	14.0199i	0.312482	−	0.541234i
$672$	6.05667	+	7.70174i	0.233641	+	0.297101i
$673$	12.8478	+	22.2531i	0.495247	+	0.857792i	0.999985	−	0.00548012i	$-0.00174439\pi$
$673$	12.8478	+	22.2531i	0.495247	+	0.857792i	−0.504738	+	0.863272i	$0.668411\pi$
$674$	4.39964	−	31.1777i	0.169468	−	1.20092i
$675$	−29.7953	−	2.59171i	−1.14682	−	0.0997550i
$676$	−19.6619	−	5.66193i	−0.756227	−	0.217767i
$677$	−40.8730	+	23.5980i	−1.57088	+	0.906945i	−0.574813	+	0.818285i	$0.694925\pi$
$677$	−40.8730	+	23.5980i	−1.57088	+	0.906945i	−0.996062	+	0.0886607i	$0.971741\pi$
$678$	33.5225	+	11.9958i	1.28742	+	0.460695i
$679$	−2.72164	+	4.71403i	−0.104447	+	0.180908i
$680$	5.40082	−	3.91000i	0.207112	−	0.149942i
$681$	7.81042	+	23.5573i	0.299296	+	0.902720i
$682$	2.95782	+	7.33275i	0.113261	+	0.280785i
$683$			19.0349i			0.728352i	0.931330	+	0.364176i	$0.118649\pi$
$683$			19.0349i			0.728352i	−0.931330	+	0.364176i	$0.881351\pi$
$684$	4.35848	+	11.5825i	0.166650	+	0.442867i
$685$		−	28.9814i		−	1.10732i
$686$	1.31153	−	0.529035i	0.0500746	−	0.0201987i
$687$	−1.12227	+	1.26151i	−0.0428172	+	0.0481295i
$688$	−8.74059	−	16.5284i	−0.333232	−	0.630138i
$689$	−0.279853	+	0.484719i	−0.0106615	+	0.0184663i
$690$	22.9847	+	27.0925i	0.875014	+	1.03139i
$691$	30.5702	−	17.6497i	1.16295	−	0.671427i	0.210938	−	0.977499i	$-0.432348\pi$
$691$	30.5702	−	17.6497i	1.16295	−	0.671427i	0.952008	+	0.306072i	$0.0990149\pi$
$692$	−5.69008	+	19.7597i	−0.216304	+	0.751149i
$693$	2.34886	+	3.15287i	0.0892260	+	0.119768i
$694$	17.7943	+	2.51105i	0.675463	+	0.0953180i
$695$	31.4426	+	54.4602i	1.19269	+	2.06579i
$696$	−19.8156	−	1.99669i	−0.751110	−	0.0756842i
$697$	0.946132	−	1.63875i	0.0358373	−	0.0620720i
$698$	11.4340	−	14.6179i	0.432784	−	0.553296i
$699$	−0.602208	+	2.91896i	−0.0227776	+	0.110405i
$700$	2.77231	+	11.1727i	0.104784	+	0.422289i
$701$			9.28360i			0.350637i	0.984512	+	0.175318i	$0.0560955\pi$
$701$			9.28360i			0.350637i	−0.984512	+	0.175318i	$0.943905\pi$
$702$	−8.34092	+	8.94343i	−0.314808	+	0.337548i
$703$	23.2495			0.876871
$704$	9.96022	+	3.27352i	0.375390	+	0.123375i
$705$	46.6895	+	9.63247i	1.75843	+	0.362780i
$706$	−26.0975	−	20.4133i	−0.982192	−	0.768263i
$707$	16.6716	+	9.62537i	0.627001	+	0.361999i
$708$	−0.723163	−	18.1762i	−0.0271781	−	0.683104i
$709$	−15.0244	+	8.67435i	−0.564254	+	0.325772i	−0.754851	−	0.655896i	$-0.772291\pi$
$709$	−15.0244	+	8.67435i	−0.564254	+	0.325772i	0.190597	+	0.981668i	$0.438958\pi$
$710$	−66.2040	−	9.34238i	−2.48459	−	0.350613i
$711$	4.42135	+	37.7178i	0.165814	+	1.41453i
$712$	20.5554	−	45.9591i	0.770347	−	1.72239i
$713$	−9.43387	−	16.3399i	−0.353301	−	0.611936i
$714$	−1.34260	+	1.13904i	−0.0502456	+	0.0426274i
$715$	−6.19453	−	3.57642i	−0.231662	−	0.133750i
$716$	−22.6681	−	23.5265i	−0.847147	−	0.879226i
$717$	6.27373	+	5.58127i	0.234297	+	0.208436i
$718$	24.7377	−	9.97849i	0.923204	−	0.372394i
$719$	34.9316			1.30273			0.651364	−	0.758766i	$-0.274197\pi$
$719$	34.9316			1.30273			0.651364	+	0.758766i	$0.274197\pi$
$720$	32.4115	−	22.3231i	1.20791	−	0.831934i
$721$	18.8818			0.703196
$722$	−19.3397	+	7.80107i	−0.719748	+	0.290326i
$723$	22.5193	−	7.46625i	0.837500	−	0.277673i
$724$	−10.4675	−	10.8638i	−0.389020	−	0.403751i
$725$	−20.2642	−	11.6996i	−0.752594	−	0.434510i
$726$	−21.4079	−	7.66066i	−0.794523	−	0.284314i
$727$	−19.3347	−	33.4887i	−0.717084	−	1.24203i	−0.962150	−	0.272519i	$-0.912143\pi$
$727$	−19.3347	−	33.4887i	−0.717084	−	1.24203i	0.245067	−	0.969506i	$-0.421190\pi$
$728$	4.29688	+	1.92180i	0.159253	+	0.0712265i
$729$	−9.25996	−	25.3624i	−0.342962	−	0.939349i
$730$	−6.01473	−	0.848769i	−0.222615	−	0.0314143i
$731$	2.90972	−	1.67993i	0.107620	−	0.0621344i
$732$	37.8795	+	19.9054i	1.40007	+	0.735726i
$733$	27.8847	+	16.0992i	1.02994	+	0.594639i	0.916969	−	0.398959i	$-0.130628\pi$
$733$	27.8847	+	16.0992i	1.02994	+	0.594639i	0.112976	+	0.993598i	$0.463962\pi$
$734$	11.5003	+	8.99545i	0.424484	+	0.332028i
$735$	−1.78765	−	5.39181i	−0.0659385	−	0.198880i
$736$	−24.6260	−	4.41375i	−0.907727	−	0.162693i
$737$	17.2649			0.635963
$738$	5.81024	−	9.53873i	0.213878	−	0.351125i
$739$			43.4773i			1.59934i	0.600440	+	0.799669i	$0.294992\pi$
$739$			43.4773i			1.59934i	−0.600440	+	0.799669i	$0.705008\pi$
$740$	−17.8060	−	71.7601i	−0.654561	−	2.63795i
$741$	4.44194	+	3.95166i	0.163179	+	0.145168i
$742$	−0.293038	+	0.374637i	−0.0107578	+	0.0137534i
$743$	16.0268	−	27.7592i	0.587966	−	1.01839i	−0.406532	−	0.913637i	$-0.633262\pi$
$743$	16.0268	−	27.7592i	0.587966	−	1.01839i	0.994498	−	0.104751i	$-0.0334046\pi$
$744$	−19.0562	+	8.58262i	−0.698633	+	0.314654i
$745$	−0.699373	−	1.21135i	−0.0256230	−	0.0443804i
$746$	−16.0681	−	2.26745i	−0.588295	−	0.0830173i
$747$	−42.4080	+	4.97114i	−1.55163	+	0.181885i
$748$	−0.521347	+	1.81045i	−0.0190623	+	0.0661968i
$749$	−5.78550	+	3.34026i	−0.211397	+	0.122050i
$750$	5.97330	−	1.08668i	0.218114	−	0.0396799i
$751$	12.0299	−	20.8364i	0.438978	−	0.760332i	−0.558633	−	0.829415i	$-0.688674\pi$
$751$	12.0299	−	20.8364i	0.438978	−	0.760332i	0.997611	+	0.0690829i	$0.0220073\pi$
$752$	−29.6758	+	15.6933i	−1.08217	+	0.572275i
$753$	−26.9066	−	5.55109i	−0.980533	−	0.202293i
$754$	−8.87321	+	3.57920i	−0.323143	+	0.130347i
$755$			30.1399i			1.09690i
$756$	−8.08042	+	6.53504i	−0.293882	+	0.237677i
$757$		−	2.27296i		−	0.0826120i	−0.999147	−	0.0413060i	$-0.986848\pi$
$757$		−	2.27296i		−	0.0826120i	0.999147	−	0.0413060i	$-0.0131518\pi$
$758$	−1.10720	−	2.74487i	−0.0402154	−	0.0996981i
$759$	−9.83211	−	2.02846i	−0.356883	−	0.0736283i
$760$	−11.2197	−	15.4975i	−0.406980	−	0.562155i
$761$	19.7750	−	34.2513i	0.716842	−	1.24161i	−0.245403	−	0.969421i	$-0.578920\pi$
$761$	19.7750	−	34.2513i	0.716842	−	1.24161i	0.962245	−	0.272186i	$-0.0877465\pi$
$762$	−1.49153	−	8.19872i	−0.0540325	−	0.297008i
$763$	1.41607	−	0.817568i	0.0512651	−	0.0295979i
$764$	25.6563	+	7.38811i	0.928213	+	0.267292i
$765$	4.22504	+	5.67126i	0.152757	+	0.205045i
$766$	0.883051	−	6.25767i	0.0319059	−	0.226099i
$767$	−4.36950	−	7.56819i	−0.157773	−	0.273272i
$768$	−7.59925	+	26.6505i	−0.274214	+	0.961669i
$769$	18.3746	−	31.8257i	0.662605	−	1.14767i	−0.317324	−	0.948317i	$-0.602784\pi$
$769$	18.3746	−	31.8257i	0.662605	−	1.14767i	0.979929	−	0.199348i	$-0.0638825\pi$
$770$	−4.78772	−	3.74492i	−0.172538	−	0.134958i
$771$	−23.8150	−	21.1864i	−0.857676	−	0.763011i
$772$	5.77092	+	23.2574i	0.207700	+	0.837053i
$773$			0.684612i			0.0246238i	0.999924	+	0.0123119i	$0.00391910\pi$
$773$			0.684612i			0.0246238i	−0.999924	+	0.0123119i	$0.996081\pi$
$774$	17.4027	−	9.50938i	0.625528	−	0.341808i
$775$	−24.5549			−0.882038
$776$	−15.3143	+	1.58345i	−0.549751	+	0.0568425i
$777$	6.14424	+	18.5319i	0.220423	+	0.664829i
$778$	20.0878	−	25.6814i	0.720181	−	0.920721i
$779$	−4.70235	−	2.71490i	−0.168479	−	0.0972715i
$780$	8.79496	−	16.7366i	0.314910	−	0.599266i
$781$	16.3611	−	9.44609i	0.585447	−	0.338008i
$782$	0.628197	−	4.45167i	0.0224643	−	0.159191i
$783$	1.83054	−	21.0446i	0.0654182	−	0.752073i
$784$	3.38741	+	2.12731i	0.120979	+	0.0759754i
$785$	16.9268	+	29.3181i	0.604144	+	1.04641i
$786$	4.92774	−	13.7707i	0.175767	−	0.491184i
$787$	−32.9098	−	19.0005i	−1.17311	−	0.677295i	−0.218699	−	0.975792i	$-0.570181\pi$
$787$	−32.9098	−	19.0005i	−1.17311	−	0.677295i	−0.954410	+	0.298497i	$0.903515\pi$
$788$	17.0938	+	17.7411i	0.608942	+	0.632001i
$789$	−25.4058	+	8.42328i	−0.904471	+	0.299877i
$790$	−21.9631	−	54.4488i	−0.781412	−	1.93720i
$791$	14.5353			0.516817
$792$	−3.32747	+	10.6109i	−0.118237	+	0.377040i
$793$	20.5574			0.730015
$794$	6.16920	+	15.2941i	0.218937	+	0.542767i
$795$	1.42737	+	1.26982i	0.0506235	+	0.0450359i
$796$	20.2297	−	19.4916i	0.717024	−	0.690863i
$797$	39.6117	+	22.8698i	1.40312	+	0.810091i	0.994711	−	0.102709i	$-0.0327512\pi$
$797$	39.6117	+	22.8698i	1.40312	+	0.810091i	0.408407	+	0.912800i	$0.366085\pi$
$798$	3.26844	+	3.85257i	0.115702	+	0.136379i
$799$	−3.01622	−	5.22425i	−0.106706	−	0.184821i
$800$	−20.9990	+	24.8830i	−0.742427	+	0.879748i
$801$	49.0403	+	21.1345i	1.73275	+	0.746750i
$802$	4.64222	−	32.8967i	0.163923	−	1.16162i
$803$	1.48643	−	0.858192i	0.0524550	−	0.0302849i
$804$	1.81423	+	45.5995i	0.0639830	+	1.60817i
$805$	12.5614	+	7.25230i	0.442730	+	0.255610i
$806$	−6.18600	+	7.90853i	−0.217892	+	0.278566i
$807$	−18.0327	−	3.72031i	−0.634780	−	0.130961i
$808$	5.60002	+	54.1606i	0.197008	+	1.90536i
$809$	−41.8615			−1.47177			−0.735886	−	0.677106i	$-0.763234\pi$
$809$	−41.8615			−1.47177			−0.735886	+	0.677106i	$0.763234\pi$
$810$	24.1446	+	34.0510i	0.848355	+	1.19643i
$811$		−	28.5347i		−	1.00199i	−0.865450	−	0.500995i	$-0.832968\pi$
$811$		−	28.5347i		−	1.00199i	0.865450	−	0.500995i	$-0.167032\pi$
$812$	−7.89136	+	1.95810i	−0.276932	+	0.0687158i
$813$	−0.727311	+	3.52534i	−0.0255079	+	0.123639i
$814$	16.4556	+	12.8715i	0.576770	+	0.451145i
$815$	19.5660	−	33.8893i	0.685368	−	1.18709i
$816$	−4.83649	−	1.18671i	−0.169311	−	0.0415433i
$817$	−4.82051	−	8.34938i	−0.168648	−	0.292108i
$818$	3.91704	−	27.7578i	0.136956	−	0.970528i
$819$	−1.97593	+	4.58494i	−0.0690447	+	0.160211i
$820$	−4.77824	+	16.5932i	−0.166863	+	0.579458i
$821$	−34.7280	+	20.0502i	−1.21202	+	0.699758i	−0.963198	−	0.268792i	$-0.913376\pi$
$821$	−34.7280	+	20.0502i	−1.21202	+	0.699758i	−0.248819	+	0.968550i	$0.580042\pi$
$822$	−16.5060	+	14.0034i	−0.575713	+	0.488424i
$823$	6.88296	−	11.9216i	0.239925	−	0.415562i	−0.720768	−	0.693177i	$-0.756210\pi$
$823$	6.88296	−	11.9216i	0.239925	−	0.415562i	0.960693	+	0.277615i	$0.0895438\pi$
$824$	31.3182	+	43.2592i	1.09102	+	1.50701i
$825$	−8.68406	+	9.76148i	−0.302340	+	0.339851i
$826$	−2.77806	−	6.88710i	−0.0966610	−	0.239633i
$827$		−	3.05446i		−	0.106214i	−0.998589	−	0.0531069i	$-0.983088\pi$
$827$		−	3.05446i		−	0.106214i	0.998589	−	0.0531069i	$-0.0169124\pi$
$828$	4.32430	−	26.1813i	0.150280	−	0.909865i
$829$			8.78105i			0.304979i	0.988305	+	0.152489i	$0.0487290\pi$
$829$			8.78105i			0.304979i	−0.988305	+	0.152489i	$0.951271\pi$
$830$	61.2196	−	24.6942i	2.12496	−	0.857149i
$831$	−13.5350	−	40.8234i	−0.469522	−	1.41615i
$832$	2.72404	+	13.0319i	0.0944390	+	0.451801i
$833$	−0.359397	+	0.622494i	−0.0124524	+	0.0215681i
$834$	15.8245	−	44.2221i	0.547959	−	1.53129i
$835$	−2.58168	+	1.49053i	−0.0893428	+	0.0515821i
$836$	5.19506	+	1.49599i	0.179675	+	0.0517400i
$837$	−9.37846	−	20.0859i	−0.324167	−	0.694270i
$838$	−14.3181	−	2.02050i	−0.494610	−	0.0697970i
$839$	2.80464	+	4.85777i	0.0968268	+	0.167709i	0.910370	−	0.413796i	$-0.135797\pi$
$839$	2.80464	+	4.85777i	0.0968268	+	0.167709i	−0.813543	+	0.581505i	$0.802464\pi$
$840$	9.38784	−	13.0387i	0.323911	−	0.449877i
$841$	−6.23654	+	10.8020i	−0.215053	+	0.372483i
$842$	−14.5072	+	18.5468i	−0.499950	+	0.639165i
$843$	14.9509	−	4.95695i	0.514935	−	0.170726i
$844$	−53.1662	+	13.1922i	−1.83005	+	0.454096i
$845$			33.5518i			1.15422i
$846$	−17.0736	−	31.2457i	−0.587002	−	1.07425i
$847$	−9.28247			−0.318949
$848$	−1.34436	−	0.0499778i	−0.0461654	−	0.00171624i
$849$	1.53906	−	1.73001i	0.0528205	−	0.0593739i
$850$	−4.60854	−	3.60477i	−0.158072	−	0.123643i
$851$	−43.1740	−	24.9265i	−1.47998	−	0.854470i
$852$	26.6679	+	42.2197i	0.913627	+	1.44642i
$853$	6.06616	−	3.50230i	0.207701	−	0.119916i	−0.392541	−	0.919734i	$-0.628404\pi$
$853$	6.06616	−	3.50230i	0.207701	−	0.119916i	0.600243	+	0.799818i	$0.295071\pi$
$854$	17.2980	+	2.44101i	0.591927	+	0.0835298i
$855$	16.2735	−	12.1237i	0.556543	−	0.414620i
$856$	−17.2488	−	7.71458i	−0.589550	−	0.263679i
$857$	−4.81627	−	8.34203i	−0.164521	−	0.284958i	0.771964	−	0.635666i	$-0.219274\pi$
$857$	−4.81627	−	8.34203i	−0.164521	−	0.284958i	−0.936485	+	0.350708i	$0.885941\pi$
$858$	0.956201	+	5.25609i	0.0326442	+	0.179440i
$859$	4.08749	+	2.35991i	0.139463	+	0.0805192i	0.568108	−	0.822954i	$-0.307676\pi$
$859$	4.08749	+	2.35991i	0.139463	+	0.0805192i	−0.428645	+	0.903473i	$0.641009\pi$
$860$	−22.0787	+	21.2731i	−0.752876	+	0.725407i
$861$	0.921309	−	4.46567i	0.0313981	−	0.152190i
$862$	−21.8752	+	8.82382i	−0.745071	+	0.300540i
$863$	−20.1351			−0.685406			−0.342703	−	0.939444i	$-0.611342\pi$
$863$	−20.1351			−0.685406			−0.342703	+	0.939444i	$0.611342\pi$
$864$	−28.3746	−	7.67338i	−0.965324	−	0.261054i
$865$	33.7186			1.14647
$866$	−31.7787	+	12.8186i	−1.07988	+	0.435595i
$867$	−5.76864	+	27.9611i	−0.195913	+	0.949609i
$868$	−6.14428	+	5.92010i	−0.208550	+	0.200941i
$869$	14.3672	+	8.29489i	0.487373	+	0.281385i
$870$	5.84533	+	32.1308i	0.198175	+	1.08934i
$871$	10.9620	+	18.9867i	0.371432	+	0.643339i
$872$	4.22184	+	1.88824i	0.142970	+	0.0639437i
$873$	−1.90120	−	16.2188i	−0.0643459	−	0.548924i
$874$	−12.7740	−	1.80260i	−0.432086	−	0.0609738i
$875$	2.14654	−	1.23931i	0.0725663	−	0.0418962i
$876$	2.42282	+	3.83573i	0.0818595	+	0.129597i
$877$	32.4638	+	18.7430i	1.09623	+	0.632906i	0.935227	−	0.354049i	$-0.115195\pi$
$877$	32.4638	+	18.7430i	1.09623	+	0.632906i	0.160998	+	0.986955i	$0.448529\pi$
$878$	−5.53870	−	4.33233i	−0.186922	−	0.146209i
$879$	−4.90413	+	5.51258i	−0.165412	+	0.185935i
$880$	0.638698	−	17.1804i	0.0215305	−	0.579151i
$881$	19.6839			0.663168			0.331584	−	0.943426i	$-0.392417\pi$
$881$	19.6839			0.663168			0.331584	+	0.943426i	$0.392417\pi$
$882$	−2.20707	+	3.62337i	−0.0743160	+	0.122005i
$883$			22.6769i			0.763138i	0.924340	+	0.381569i	$0.124616\pi$
$883$			22.6769i			0.763138i	−0.924340	+	0.381569i	$0.875384\pi$
$884$	−2.32202	+	0.576167i	−0.0780978	+	0.0193786i
$885$	−28.3133	+	9.38727i	−0.951742	+	0.315550i
$886$	10.7321	−	13.7206i	0.360553	−	0.460951i
$887$	18.4752	−	31.9999i	0.620336	−	1.07445i	−0.369088	−	0.929395i	$-0.620330\pi$
$887$	18.4752	−	31.9999i	0.620336	−	1.07445i	0.989423	−	0.145058i	$-0.0463369\pi$
$888$	−32.2665	+	44.8145i	−1.08279	+	1.50388i
$889$	−1.70103	−	2.94626i	−0.0570506	−	0.0988145i
$890$	−81.7482	−	11.5359i	−2.74021	−	0.386684i
$891$	−11.3017	−	3.37527i	−0.378620	−	0.113076i
$892$	12.4338	+	3.58050i	0.416315	+	0.119884i
$893$	−14.9909	+	8.65498i	−0.501650	+	0.289628i
$894$	−0.351982	+	0.983624i	−0.0117721	+	0.0328973i
$895$	−26.7862	+	46.3951i	−0.895365	+	1.55082i
$896$	0.744714	+	11.2892i	0.0248791	+	0.377145i
$897$	−4.01192	−	12.1005i	−0.133954	−	0.404025i
$898$	−18.2469	+	7.36030i	−0.608908	+	0.245616i
$899$		−	17.3433i		−	0.578430i
$900$	−26.6942	−	21.9103i	−0.889806	−	0.730342i
$901$		−	0.241746i		−	0.00805372i
$902$	−1.82522	−	4.52490i	−0.0607730	−	0.150663i
$903$	5.38126	−	6.04890i	0.179077	−	0.201295i
$904$	24.1089	+	33.3012i	0.801850	+	1.10758i
$905$	−12.3691	+	21.4239i	−0.411162	+	0.712154i
$906$	17.1658	−	14.5631i	0.570295	−	0.483827i
$907$	14.5779	−	8.41654i	0.484050	−	0.279467i	−0.238053	−	0.971252i	$-0.576509\pi$
$907$	14.5779	−	8.41654i	0.484050	−	0.279467i	0.722103	+	0.691786i	$0.243176\pi$
$908$	−7.93017	+	27.5387i	−0.263172	+	0.913904i
$909$	−57.3595	+	6.72378i	−1.90249	+	0.223014i
$910$	1.07853	−	7.64292i	0.0357529	−	0.253360i
$911$	−13.5423	−	23.4560i	−0.448678	−	0.777132i	0.549623	−	0.835413i	$-0.314772\pi$
$911$	−13.5423	−	23.4560i	−0.448678	−	0.777132i	−0.998300	+	0.0582806i	$0.981438\pi$
$912$	−3.40525	+	13.8782i	−0.112759	+	0.459553i
$913$	−9.32636	+	16.1537i	−0.308657	+	0.534610i
$914$	26.3991	+	20.6492i	0.873205	+	0.683015i
$915$	14.1779	−	68.7217i	0.468707	−	2.27187i
$916$	−1.89228	+	0.469535i	−0.0625227	+	0.0155139i
$917$		−	5.97097i		−	0.197179i
$918$	1.18852	−	5.14658i	0.0392269	−	0.169863i
$919$	7.97073			0.262930			0.131465	−	0.991321i	$-0.458032\pi$
$919$	7.97073			0.262930			0.131465	+	0.991321i	$0.458032\pi$
$920$	4.21937	+	40.8077i	0.139109	+	1.34539i
$921$	21.5140	+	4.43853i	0.708909	+	0.146254i
$922$	4.62553	−	5.91354i	0.152334	−	0.194752i
$923$	20.7762	+	11.9951i	0.683856	+	0.394824i
$924$	0.180481	+	4.53628i	0.00593739	+	0.149233i
$925$	−56.1876	+	32.4399i	−1.84744	+	1.06662i
$926$	−4.38265	+	31.0573i	−0.144023	+	1.02060i
$927$	−45.4254	+	33.8415i	−1.49196	+	1.11150i
$928$	−17.5750	−	14.8317i	−0.576929	−	0.486875i
$929$	12.9039	+	22.3503i	0.423365	+	0.733289i	0.996266	−	0.0863350i	$-0.0275155\pi$
$929$	12.9039	+	22.3503i	0.423365	+	0.733289i	−0.572901	+	0.819624i	$0.694182\pi$
$930$	22.1712	+	26.1336i	0.727023	+	0.856953i
$931$	1.78623	+	1.03128i	0.0585414	+	0.0337989i
$932$	−2.47830	+	2.38788i	−0.0811795	+	0.0782176i
$933$	−4.51284	−	4.01474i	−0.147744	−	0.131437i
$934$	−9.42204	−	23.3582i	−0.308299	−	0.764305i
$935$	3.08942			0.101035
$936$	−13.7817	+	3.07780i	−0.450469	+	0.100601i
$937$	−34.3160			−1.12105			−0.560527	−	0.828136i	$-0.689401\pi$
$937$	−34.3160			−1.12105			−0.560527	+	0.828136i	$0.689401\pi$
$938$	6.96944	+	17.2780i	0.227560	+	0.564146i
$939$	47.0500	−	15.5994i	1.53542	−	0.509067i
$940$	38.1948	+	39.6411i	1.24578	+	1.29295i
$941$	−22.2014	−	12.8180i	−0.723744	−	0.417854i	0.0923852	−	0.995723i	$-0.470551\pi$
$941$	−22.2014	−	12.8180i	−0.723744	−	0.417854i	−0.816129	+	0.577870i	$0.803884\pi$
$942$	8.51898	−	23.8065i	0.277563	−	0.775658i
$943$	5.82147	+	10.0831i	0.189573	+	0.328350i
$944$	11.1709	−	17.7879i	0.363581	−	0.578946i
$945$	13.9643	+	9.76749i	0.454259	+	0.317736i
$946$	1.21053	−	8.57831i	0.0393577	−	0.278905i
$947$	−28.6691	+	16.5521i	−0.931620	+	0.537871i	−0.887324	−	0.461147i	$-0.847438\pi$
$947$	−28.6691	+	16.5521i	−0.931620	+	0.537871i	−0.0442968	+	0.999018i	$0.514105\pi$
$948$	−20.3984	+	38.8177i	−0.662510	+	1.26074i
$949$	1.88755	+	1.08978i	0.0612724	+	0.0353756i
$950$	−10.3438	+	13.2241i	−0.335597	+	0.429047i
$951$	−17.8015	−	53.6918i	−0.577252	−	1.74108i
$952$	−2.02227	+	0.209096i	−0.0655423	+	0.00677685i
$953$	48.0637			1.55694			0.778468	−	0.627684i	$-0.215997\pi$
$953$	48.0637			1.55694			0.778468	+	0.627684i	$0.215997\pi$
$954$	0.0335290	−	1.42650i	0.00108554	−	0.0461845i
$955$		−	43.7808i		−	1.41671i
$956$	2.33509	+	9.41068i	0.0755223	+	0.304363i
$957$	−6.89459	−	6.13360i	−0.222871	−	0.198271i
$958$	−1.74965	−	1.36857i	−0.0565287	−	0.0442164i
$959$	−4.41844	+	7.65296i	−0.142679	+	0.247127i
$960$	45.4433	−	0.118441i	1.46668	−	0.00382267i
$961$	6.40003	+	11.0852i	0.206453	+	0.357587i
$962$	−3.70696	+	26.2691i	−0.119517	+	0.846949i
$963$	7.93190	−	18.4051i	0.255602	−	0.593097i
$964$	26.3252	+	7.58072i	0.847877	+	0.244159i
$965$	34.0296	−	19.6470i	1.09545	−	0.632460i
$966$	−1.93900	−	10.6584i	−0.0623862	−	0.342927i
$967$	16.9977	−	29.4409i	0.546609	−	0.946755i	−0.451894	−	0.892071i	$-0.649252\pi$
$967$	16.9977	−	29.4409i	0.546609	−	0.946755i	0.998504	−	0.0546837i	$-0.0174151\pi$
$968$	−15.3963	−	21.2666i	−0.494855	−	0.683535i
$969$	−2.51490	−	0.518847i	−0.0807902	−	0.0166678i
$970$	9.44424	+	23.4133i	0.303236	+	0.751754i
$971$		−	46.7937i		−	1.50168i	−0.660483	−	0.750841i	$-0.729648\pi$
$971$		−	46.7937i		−	1.50168i	0.660483	−	0.750841i	$-0.270352\pi$
$972$	7.72703	−	30.2042i	0.247845	−	0.968800i
$973$		−	19.1747i		−	0.614712i
$974$	−39.9023	+	16.0955i	−1.27855	+	0.515732i
$975$	−16.2487	−	3.35225i	−0.520374	−	0.107358i
$976$	23.0987	+	43.6794i	0.739372	+	1.39815i
$977$	5.31576	−	9.20716i	0.170066	−	0.294563i	−0.768377	−	0.639998i	$-0.778935\pi$
$977$	5.31576	−	9.20716i	0.170066	−	0.294563i	0.938443	+	0.345435i	$0.112269\pi$
$978$	−28.7552	+	5.23123i	−0.919491	+	0.167276i
$979$	20.2026	−	11.6640i	0.645677	−	0.372782i
$980$	1.81506	−	6.30307i	0.0579799	−	0.201344i
$981$	−1.94143	+	4.50487i	−0.0619850	+	0.143830i
$982$	−57.3688	−	8.09560i	−1.83071	−	0.258341i
$983$	−29.2874	−	50.7272i	−0.934123	−	1.61795i	−0.776191	−	0.630498i	$-0.782851\pi$
$983$	−29.2874	−	50.7272i	−0.934123	−	1.61795i	−0.157931	−	0.987450i	$-0.550482\pi$
$984$	11.7592	−	5.29617i	0.374870	−	0.168836i
$985$	20.1993	−	34.9861i	0.643602	−	1.11475i
$986$	2.54607	−	3.25504i	0.0810833	−	0.103662i
$987$	−10.8605	−	9.66176i	−0.345693	−	0.307537i
$988$	1.65330	+	6.66297i	0.0525984	+	0.211977i
$989$			20.6729i			0.657360i
$990$	18.2301	+	0.428488i	0.579391	+	0.0136182i
$991$	27.7912			0.882816			0.441408	−	0.897307i	$-0.354479\pi$
$991$	27.7912			0.882816			0.441408	+	0.897307i	$0.354479\pi$
$992$	−23.7544	−	4.25753i	−0.754203	−	0.135177i
$993$	9.67086	+	29.1687i	0.306896	+	0.925641i
$994$	16.0578	+	12.5603i	0.509322	+	0.398388i
$995$	−39.8938	−	23.0327i	−1.26472	−	0.730186i
$996$	−43.6446	−	22.9350i	−1.38293	−	0.726722i
$997$	49.3804	−	28.5098i	1.56389	−	0.902914i	0.567036	−	0.823693i	$-0.308090\pi$
$997$	49.3804	−	28.5098i	1.56389	−	0.902914i	0.996857	−	0.0792215i	$-0.0252435\pi$
$998$	−27.9016	−	3.93733i	−0.883209	−	0.124634i
$999$	−47.9960	−	33.5713i	−1.51853	−	1.06215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.4	✓	72
8.5	even	2	inner	504.2.cs.a.85.28	yes	72
9.7	even	3	inner	504.2.cs.a.421.28	yes	72
72.61	even	6	inner	504.2.cs.a.421.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.4	✓	72	1.1	even	1	trivial
504.2.cs.a.85.28	yes	72	8.5	even	2	inner
504.2.cs.a.421.4	yes	72	72.61	even	6	inner
504.2.cs.a.421.28	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31153 + 0.529035i) q^{2} +(0.349968 - 1.69633i) q^{3} +(1.44024 - 1.38770i) q^{4} +(-2.84022 - 1.63980i) q^{5} +(0.438422 + 2.40993i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.15479 + 2.58195i) q^{8} +(-2.75505 - 1.18732i) q^{9} +O(q^{10})\)	\(q+(-1.31153 + 0.529035i) q^{2} +(0.349968 - 1.69633i) q^{3} +(1.44024 - 1.38770i) q^{4} +(-2.84022 - 1.63980i) q^{5} +(0.438422 + 2.40993i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.15479 + 2.58195i) q^{8} +(-2.75505 - 1.18732i) q^{9} +(4.59255 + 0.648078i) q^{10} +(-1.13497 + 0.655273i) q^{11} +(-1.84995 - 2.92877i) q^{12} +(-1.44124 - 0.832099i) q^{13} +(-1.11393 - 0.871304i) q^{14} +(-3.77562 + 4.24406i) q^{15} +(0.148601 - 3.99724i) q^{16} +0.718794 q^{17} +(4.24147 + 0.0996933i) q^{18} -2.06256i q^{19} +(-6.36614 + 1.57965i) q^{20} +(1.64405 - 0.545082i) q^{21} +(1.14188 - 1.45985i) q^{22} +(-2.21134 + 3.83015i) q^{23} +(3.97569 + 2.86250i) q^{24} +(2.87788 + 4.98464i) q^{25} +(2.33044 + 0.328861i) q^{26} +(-2.97826 + 4.25793i) q^{27} +(1.92190 + 0.553439i) q^{28} +(-3.52068 + 2.03267i) q^{29} +(2.70660 - 7.56366i) q^{30} +(-2.13307 + 3.69458i) q^{31} +(1.91978 + 5.32113i) q^{32} +(0.714355 + 2.15460i) q^{33} +(-0.942723 + 0.380267i) q^{34} -3.27960i q^{35} +(-5.61557 + 2.11314i) q^{36} +11.2721i q^{37} +(1.09117 + 2.70512i) q^{38} +(-1.91590 + 2.15360i) q^{39} +(7.51373 - 5.43967i) q^{40} +(1.31628 - 2.27986i) q^{41} +(-1.86785 + 1.58465i) q^{42} +(4.04806 - 2.33715i) q^{43} +(-0.725308 + 2.51874i) q^{44} +(5.87796 + 7.88996i) q^{45} +(0.873961 - 6.19325i) q^{46} +(-4.19623 - 7.26808i) q^{47} +(-6.72862 - 1.65098i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.41149 - 5.01502i) q^{50} +(0.251555 - 1.21931i) q^{51} +(-3.23043 + 0.801575i) q^{52} -0.336321i q^{53} +(1.65349 - 7.16003i) q^{54} +4.29806 q^{55} +(-2.81343 + 0.290899i) q^{56} +(-3.49878 - 0.721830i) q^{57} +(3.54214 - 4.52847i) q^{58} +(4.54765 + 2.62559i) q^{59} +(0.451648 + 11.3519i) q^{60} +(-10.6978 + 6.17637i) q^{61} +(0.843027 - 5.97404i) q^{62} +(-0.349274 - 2.97960i) q^{63} +(-5.33293 - 5.96321i) q^{64} +(2.72895 + 4.72668i) q^{65} +(-2.07676 - 2.44791i) q^{66} +(-11.4089 - 6.58693i) q^{67} +(1.03524 - 0.997467i) q^{68} +(5.72329 + 5.09158i) q^{69} +(1.73502 + 4.30131i) q^{70} -14.4155 q^{71} +(6.24709 - 5.74229i) q^{72} -1.30967 q^{73} +(-5.96336 - 14.7838i) q^{74} +(9.46274 - 3.13737i) q^{75} +(-2.86221 - 2.97059i) q^{76} +(-1.13497 - 0.655273i) q^{77} +(1.37343 - 3.83810i) q^{78} +(-6.32934 - 10.9627i) q^{79} +(-6.97673 + 11.1093i) q^{80} +(6.18055 + 6.54224i) q^{81} +(-0.520216 + 3.68647i) q^{82} +(12.3260 - 7.11639i) q^{83} +(1.61142 - 3.06649i) q^{84} +(-2.04153 - 1.17868i) q^{85} +(-4.07273 + 5.20682i) q^{86} +(2.21594 + 6.68359i) q^{87} +(-0.381237 - 3.68713i) q^{88} -17.8002 q^{89} +(-11.8832 - 7.23831i) q^{90} -1.66420i q^{91} +(2.13022 + 8.58501i) q^{92} +(5.52071 + 4.91137i) q^{93} +(9.34856 + 7.31238i) q^{94} +(-3.38219 + 5.85812i) q^{95} +(9.69824 - 1.39436i) q^{96} +(2.72164 + 4.71403i) q^{97} +(0.197609 - 1.40034i) q^{98} +(3.90490 - 0.457740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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