LMFDB - Embedded newform 525.2.z.a.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	525.169
Dual form			525.2.z.a.379.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.748945 + 0.243347i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.11633 + 0.811064i) q^{4} +(-1.45716 - 1.69608i) q^{5} +(-0.637090 - 0.462873i) q^{6} -1.00000i q^{7} +(1.56445 - 2.15328i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.748945 + 0.243347i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.11633 + 0.811064i) q^{4} +(-1.45716 - 1.69608i) q^{5} +(-0.637090 - 0.462873i) q^{6} -1.00000i q^{7} +(1.56445 - 2.15328i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.50407 + 0.915677i) q^{10} +(0.0975406 + 0.300199i) q^{11} +(-1.31233 - 0.426402i) q^{12} +(4.49580 + 1.46078i) q^{13} +(0.243347 + 0.748945i) q^{14} +(0.515665 - 2.17580i) q^{15} +(0.205111 - 0.631268i) q^{16} +(-0.409871 + 0.564139i) q^{17} -0.787487i q^{18} +(2.61592 + 1.90058i) q^{19} +(3.00230 + 0.711547i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-0.146105 - 0.201096i) q^{22} +(4.33399 - 1.40820i) q^{23} +2.66160 q^{24} +(-0.753391 + 4.94291i) q^{25} -3.72258 q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.811064 + 1.11633i) q^{28} +(4.56029 - 3.31325i) q^{29} +(0.143269 + 1.75504i) q^{30} +(2.31688 + 1.68331i) q^{31} +5.84590i q^{32} +(-0.185533 + 0.255365i) q^{33} +(0.169689 - 0.522249i) q^{34} +(-1.69608 + 1.45716i) q^{35} +(-0.426402 - 1.31233i) q^{36} +(2.93855 + 0.954793i) q^{37} +(-2.42168 - 0.786851i) q^{38} +(1.46078 + 4.49580i) q^{39} +(-5.93178 + 0.484230i) q^{40} +(0.0808975 - 0.248977i) q^{41} +(-0.462873 + 0.637090i) q^{42} +7.09828i q^{43} +(-0.352369 - 0.256011i) q^{44} +(2.06336 - 0.861720i) q^{45} +(-2.90324 + 2.10933i) q^{46} +(-1.27602 - 1.75629i) q^{47} +(0.631268 - 0.205111i) q^{48} -1.00000 q^{49} +(-0.638594 - 3.88530i) q^{50} -0.697314 q^{51} +(-6.20360 + 2.01567i) q^{52} +(2.23421 + 3.07513i) q^{53} +(0.637090 - 0.462873i) q^{54} +(0.367031 - 0.602874i) q^{55} +(-2.15328 - 1.56445i) q^{56} +3.23346i q^{57} +(-2.60914 + 3.59117i) q^{58} +(3.92646 - 12.0844i) q^{59} +(1.18906 + 2.84715i) q^{60} +(-0.333454 - 1.02627i) q^{61} +(-2.14485 - 0.696903i) q^{62} +(0.951057 + 0.309017i) q^{63} +(-1.01236 - 3.11572i) q^{64} +(-4.07349 - 9.75383i) q^{65} +(0.0768120 - 0.236403i) q^{66} +(-5.34532 + 7.35720i) q^{67} -0.962198i q^{68} +(3.68672 + 2.67856i) q^{69} +(0.915677 - 1.50407i) q^{70} +(11.1012 - 8.06549i) q^{71} +(1.56445 + 2.15328i) q^{72} +(7.98591 - 2.59478i) q^{73} -2.43316 q^{74} +(-4.44173 + 2.29587i) q^{75} -4.46173 q^{76} +(0.300199 - 0.0975406i) q^{77} +(-2.18808 - 3.01163i) q^{78} +(4.15082 - 3.01575i) q^{79} +(-1.36956 + 0.571970i) q^{80} +(-0.809017 - 0.587785i) q^{81} +0.206156i q^{82} +(3.16520 - 4.35652i) q^{83} +(-0.426402 + 1.31233i) q^{84} +(1.55407 - 0.126864i) q^{85} +(-1.72734 - 5.31622i) q^{86} +(5.36095 + 1.74188i) q^{87} +(0.799010 + 0.259614i) q^{88} +(0.662740 + 2.03970i) q^{89} +(-1.33564 + 1.14749i) q^{90} +(1.46078 - 4.49580i) q^{91} +(-3.69604 + 5.08717i) q^{92} +2.86382i q^{93} +(1.38306 + 1.00485i) q^{94} +(-0.588269 - 7.20625i) q^{95} +(-4.72943 + 3.43613i) q^{96} +(-8.88646 - 12.2312i) q^{97} +(0.748945 - 0.243347i) q^{98} -0.315648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$1$

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 $

$2$	−0.748945	+	0.243347i	−0.529584	+	0.172072i	−0.561590	−	0.827415i	$-0.689810\pi$
$2$	−0.748945	+	0.243347i	−0.529584	+	0.172072i	0.0320065	+	0.999488i	$0.489810\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	−1.11633	+	0.811064i	−0.558167	+	0.405532i
$5$	−1.45716	−	1.69608i	−0.651660	−	0.758511i
$5$	−1.45716	−	1.69608i	−0.651660	−	0.758511i
$6$	−0.637090	−	0.462873i	−0.260091	−	0.188967i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.56445	−	2.15328i	0.553116	−	0.761299i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	1.50407	+	0.915677i	0.475627	+	0.289563i
$11$	0.0975406	+	0.300199i	0.0294096	+	0.0905135i	0.964684	−	0.263410i	$-0.0848473\pi$
$11$	0.0975406	+	0.300199i	0.0294096	+	0.0905135i	−0.935274	+	0.353924i	$0.884847\pi$
$12$	−1.31233	−	0.426402i	−0.378837	−	0.123092i
$13$	4.49580	+	1.46078i	1.24691	+	0.405146i	0.856813	−	0.515627i	$-0.172441\pi$
$13$	4.49580	+	1.46078i	1.24691	+	0.405146i	0.390099	+	0.920773i	$0.372441\pi$
$14$	0.243347	+	0.748945i	0.0650372	+	0.200164i
$15$	0.515665	−	2.17580i	0.133144	−	0.561788i
$16$	0.205111	−	0.631268i	0.0512778	−	0.157817i
$17$	−0.409871	+	0.564139i	−0.0994082	+	0.136824i	−0.855823	−	0.517268i	$-0.826949\pi$
$17$	−0.409871	+	0.564139i	−0.0994082	+	0.136824i	0.756415	+	0.654092i	$0.226949\pi$
$18$		−	0.787487i		−	0.185612i
$19$	2.61592	+	1.90058i	0.600133	+	0.436022i	0.845926	−	0.533300i	$-0.179048\pi$
$19$	2.61592	+	1.90058i	0.600133	+	0.436022i	−0.245793	+	0.969322i	$0.579048\pi$
$20$	3.00230	+	0.711547i	0.671336	+	0.159107i
$21$	0.809017	−	0.587785i	0.176542	−	0.128265i
$22$	−0.146105	−	0.201096i	−0.0311497	−	0.0428739i
$23$	4.33399	−	1.40820i	0.903700	−	0.293630i	0.179937	−	0.983678i	$-0.442411\pi$
$23$	4.33399	−	1.40820i	0.903700	−	0.293630i	0.723763	+	0.690048i	$0.242411\pi$
$24$	2.66160			0.543297
$25$	−0.753391	+	4.94291i	−0.150678	+	0.988583i
$26$	−3.72258			−0.730059
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	0.811064	+	1.11633i	0.153277	+	0.210967i
$29$	4.56029	−	3.31325i	0.846825	−	0.615255i	−0.0774435	−	0.996997i	$-0.524676\pi$
$29$	4.56029	−	3.31325i	0.846825	−	0.615255i	0.924269	+	0.381742i	$0.124676\pi$
$30$	0.143269	+	1.75504i	0.0261572	+	0.320424i
$31$	2.31688	+	1.68331i	0.416124	+	0.302332i	0.776077	−	0.630639i	$-0.217207\pi$
$31$	2.31688	+	1.68331i	0.416124	+	0.302332i	−0.359952	+	0.932971i	$0.617207\pi$
$32$			5.84590i			1.03342i
$33$	−0.185533	+	0.255365i	−0.0322972	+	0.0444533i
$34$	0.169689	−	0.522249i	0.0291014	−	0.0895650i
$35$	−1.69608	+	1.45716i	−0.286690	+	0.246304i
$36$	−0.426402	−	1.31233i	−0.0710669	−	0.218721i
$37$	2.93855	+	0.954793i	0.483095	+	0.156967i	0.540432	−	0.841388i	$-0.318261\pi$
$37$	2.93855	+	0.954793i	0.483095	+	0.156967i	−0.0573371	+	0.998355i	$0.518261\pi$
$38$	−2.42168	−	0.786851i	−0.392848	−	0.127644i
$39$	1.46078	+	4.49580i	0.233911	+	0.719905i
$40$	−5.93178	+	0.484230i	−0.937897	+	0.0765635i
$41$	0.0808975	−	0.248977i	0.0126341	−	0.0388836i	−0.944541	−	0.328394i	$-0.893493\pi$
$41$	0.0808975	−	0.248977i	0.0126341	−	0.0388836i	0.957175	+	0.289511i	$0.0934925\pi$
$42$	−0.462873	+	0.637090i	−0.0714229	+	0.0983052i
$43$			7.09828i			1.08248i	0.840869	+	0.541238i	$0.182044\pi$
$43$			7.09828i			1.08248i	−0.840869	+	0.541238i	$0.817956\pi$
$44$	−0.352369	−	0.256011i	−0.0531216	−	0.0385951i
$45$	2.06336	−	0.861720i	0.307587	−	0.128458i
$46$	−2.90324	+	2.10933i	−0.428059	+	0.311003i
$47$	−1.27602	−	1.75629i	−0.186127	−	0.256182i	0.705749	−	0.708462i	$-0.250611\pi$
$47$	−1.27602	−	1.75629i	−0.186127	−	0.256182i	−0.891876	+	0.452280i	$0.850611\pi$
$48$	0.631268	−	0.205111i	0.0911156	−	0.0296053i
$49$	−1.00000			−0.142857
$50$	−0.638594	−	3.88530i	−0.0903109	−	0.549465i
$51$	−0.697314			−0.0976434
$52$	−6.20360	+	2.01567i	−0.860285	+	0.279523i
$53$	2.23421	+	3.07513i	0.306892	+	0.422401i	0.934409	−	0.356202i	$-0.115929\pi$
$53$	2.23421	+	3.07513i	0.306892	+	0.422401i	−0.627517	+	0.778603i	$0.715929\pi$
$54$	0.637090	−	0.462873i	0.0866970	−	0.0629891i
$55$	0.367031	−	0.602874i	0.0494904	−	0.0812915i
$56$	−2.15328	−	1.56445i	−0.287744	−	0.209058i
$57$			3.23346i			0.428282i
$58$	−2.60914	+	3.59117i	−0.342597	+	0.471544i
$59$	3.92646	−	12.0844i	0.511181	−	1.57325i	−0.278943	−	0.960308i	$-0.589984\pi$
$59$	3.92646	−	12.0844i	0.511181	−	1.57325i	0.790124	−	0.612947i	$-0.210016\pi$
$60$	1.18906	+	2.84715i	0.153507	+	0.367566i
$61$	−0.333454	−	1.02627i	−0.0426944	−	0.131400i	0.927437	−	0.373979i	$-0.122007\pi$
$61$	−0.333454	−	1.02627i	−0.0426944	−	0.131400i	−0.970132	+	0.242579i	$0.922007\pi$
$62$	−2.14485	−	0.696903i	−0.272396	−	0.0885067i
$63$	0.951057	+	0.309017i	0.119822	+	0.0389325i
$64$	−1.01236	−	3.11572i	−0.126545	−	0.389465i
$65$	−4.07349	−	9.75383i	−0.505255	−	1.20981i
$66$	0.0768120	−	0.236403i	0.00945490	−	0.0290992i
$67$	−5.34532	+	7.35720i	−0.653035	+	0.898825i	−0.999226	−	0.0393386i	$-0.987475\pi$
$67$	−5.34532	+	7.35720i	−0.653035	+	0.898825i	0.346191	+	0.938164i	$0.387475\pi$
$68$		−	0.962198i		−	0.116684i
$69$	3.68672	+	2.67856i	0.443828	+	0.322460i
$70$	0.915677	−	1.50407i	0.109444	−	0.179770i
$71$	11.1012	−	8.06549i	1.31747	−	0.957197i	0.317509	−	0.948255i	$-0.397154\pi$
$71$	11.1012	−	8.06549i	1.31747	−	0.957197i	0.999960	−	0.00894234i	$-0.00284647\pi$
$72$	1.56445	+	2.15328i	0.184372	+	0.253766i
$73$	7.98591	−	2.59478i	0.934680	−	0.303696i	0.198205	−	0.980161i	$-0.436489\pi$
$73$	7.98591	−	2.59478i	0.934680	−	0.303696i	0.736475	+	0.676464i	$0.236489\pi$
$74$	−2.43316			−0.282849
$75$	−4.44173	+	2.29587i	−0.512887	+	0.265104i
$76$	−4.46173			−0.511795
$77$	0.300199	−	0.0975406i	0.0342109	−	0.0111158i
$78$	−2.18808	−	3.01163i	−0.247751	−	0.341000i
$79$	4.15082	−	3.01575i	0.467004	−	0.339298i	−0.329269	−	0.944236i	$-0.606802\pi$
$79$	4.15082	−	3.01575i	0.467004	−	0.339298i	0.796272	+	0.604938i	$0.206802\pi$
$80$	−1.36956	+	0.571970i	−0.153122	+	0.0639482i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			0.206156i			0.0227661i
$83$	3.16520	−	4.35652i	0.347426	−	0.478190i	−0.599166	−	0.800625i	$-0.704501\pi$
$83$	3.16520	−	4.35652i	0.347426	−	0.478190i	0.946592	+	0.322434i	$0.104501\pi$
$84$	−0.426402	+	1.31233i	−0.0465242	+	0.143187i
$85$	1.55407	−	0.126864i	0.168563	−	0.0137603i
$86$	−1.72734	−	5.31622i	−0.186264	−	0.573262i
$87$	5.36095	+	1.74188i	0.574754	+	0.186749i
$88$	0.799010	+	0.259614i	0.0851747	+	0.0276749i
$89$	0.662740	+	2.03970i	0.0702503	+	0.216208i	0.980018	−	0.198910i	$-0.0637402\pi$
$89$	0.662740	+	2.03970i	0.0702503	+	0.216208i	−0.909767	+	0.415118i	$0.863740\pi$
$90$	−1.33564	+	1.14749i	−0.140789	+	0.120956i
$91$	1.46078	−	4.49580i	0.153131	−	0.471288i
$92$	−3.69604	+	5.08717i	−0.385339	+	0.530374i
$93$			2.86382i			0.296965i
$94$	1.38306	+	1.00485i	0.142652	+	0.103642i
$95$	−0.588269	−	7.20625i	−0.0603551	−	0.739346i
$96$	−4.72943	+	3.43613i	−0.482695	+	0.350699i
$97$	−8.88646	−	12.2312i	−0.902283	−	1.24189i	−0.969734	−	0.244164i	$-0.921487\pi$
$97$	−8.88646	−	12.2312i	−0.902283	−	1.24189i	0.0674509	−	0.997723i	$-0.478513\pi$
$98$	0.748945	−	0.243347i	0.0756548	−	0.0245817i
$99$	−0.315648			−0.0317238
$100$	−3.16798	−	6.12899i	−0.316798	−	0.612899i
$101$	−14.5648			−1.44925			−0.724625	−	0.689144i	$-0.757987\pi$
$101$	−14.5648			−1.44925			−0.724625	+	0.689144i	$0.757987\pi$
$102$	0.522249	−	0.169689i	0.0517104	−	0.0168017i
$103$	11.3318	+	15.5969i	1.11656	+	1.53681i	0.811386	+	0.584511i	$0.198714\pi$
$103$	11.3318	+	15.5969i	1.11656	+	1.53681i	0.305171	+	0.952297i	$0.401286\pi$
$104$	10.1789	−	7.39541i	0.998124	−	0.725180i
$105$	−2.17580	−	0.515665i	−0.212336	−	0.0503237i
$106$	−2.42162	−	1.75941i	−0.235209	−	0.170889i
$107$			14.2804i			1.38054i	0.723554	+	0.690268i	$0.242507\pi$
$107$			14.2804i			1.38054i	−0.723554	+	0.690268i	$0.757493\pi$
$108$	0.811064	−	1.11633i	0.0780447	−	0.107419i
$109$	2.14107	−	6.58954i	0.205078	−	0.631164i	−0.794633	−	0.607091i	$-0.792336\pi$
$109$	2.14107	−	6.58954i	0.205078	−	0.631164i	0.999710	−	0.0240733i	$-0.00766351\pi$
$110$	−0.128178	+	0.540835i	−0.0122213	+	0.0515666i
$111$	0.954793	+	2.93855i	0.0906249	+	0.278915i
$112$	−0.631268	−	0.205111i	−0.0596492	−	0.0193812i
$113$	−7.60801	−	2.47199i	−0.715701	−	0.232545i	−0.0715427	−	0.997438i	$-0.522792\pi$
$113$	−7.60801	−	2.47199i	−0.715701	−	0.232545i	−0.644158	+	0.764892i	$0.722792\pi$
$114$	−0.786851	−	2.42168i	−0.0736954	−	0.226811i
$115$	−8.70373	−	5.29884i	−0.811627	−	0.494120i
$116$	−2.40355	+	7.39738i	−0.223164	+	0.686829i
$117$	−2.77856	+	3.82436i	−0.256878	+	0.353562i
$118$			10.0060i			0.921130i
$119$	0.564139	+	0.409871i	0.0517145	+	0.0375728i
$120$	−3.87837	−	4.51429i	−0.354045	−	0.412097i
$121$	8.81858	−	6.40707i	0.801689	−	0.582461i
$122$	0.499477	+	0.687471i	0.0452205	+	0.0622407i
$123$	0.248977	−	0.0808975i	0.0224495	−	0.00729428i
$124$	−3.95169			−0.354872
$125$	9.48140	−	5.92479i	0.848042	−	0.529929i
$126$	−0.787487			−0.0701549
$127$	−3.58975	+	1.16638i	−0.318539	+	0.103499i	−0.463922	−	0.885876i	$-0.653558\pi$
$127$	−3.58975	+	1.16638i	−0.318539	+	0.103499i	0.145384	+	0.989375i	$0.453558\pi$
$128$	−5.35586	−	7.37171i	−0.473396	−	0.651574i
$129$	−5.74263	+	4.17226i	−0.505610	+	0.367347i
$130$	5.42439	+	6.31381i	0.475750	+	0.553758i
$131$	5.99753	+	4.35746i	0.524007	+	0.380713i	0.818111	−	0.575060i	$-0.195021\pi$
$131$	5.99753	+	4.35746i	0.524007	+	0.380713i	−0.294104	+	0.955773i	$0.595021\pi$
$132$		−	0.435552i		−	0.0379099i
$133$	1.90058	−	2.61592i	0.164801	−	0.226829i
$134$	2.21300	−	6.81090i	0.191174	−	0.588373i
$135$	1.90996	+	1.16278i	0.164383	+	0.100077i
$136$	0.573526	+	1.76513i	0.0491795	+	0.151359i
$137$	−11.3877	−	3.70009i	−0.972919	−	0.316120i	−0.220925	−	0.975291i	$-0.570908\pi$
$137$	−11.3877	−	3.70009i	−0.972919	−	0.316120i	−0.751994	+	0.659170i	$0.770908\pi$
$138$	−3.41296	−	1.10894i	−0.290531	−	0.0943992i
$139$	−6.00510	−	18.4818i	−0.509346	−	1.56760i	−0.793340	−	0.608779i	$-0.791660\pi$
$139$	−6.00510	−	18.4818i	−0.509346	−	1.56760i	0.283994	−	0.958826i	$-0.408340\pi$
$140$	0.711547	−	3.00230i	0.0601367	−	0.253741i
$141$	0.670845	−	2.06465i	0.0564953	−	0.173875i
$142$	−6.35147	+	8.74205i	−0.533003	+	0.733616i
$143$			1.49212i			0.124777i
$144$	0.536988	+	0.390145i	0.0447490	+	0.0325121i
$145$	−12.2646	−	2.90672i	−1.01852	−	0.241390i
$146$	−5.34957	+	3.88669i	−0.442734	+	0.321665i
$147$	−0.587785	−	0.809017i	−0.0484797	−	0.0667266i
$148$	−4.05480	+	1.31748i	−0.333302	+	0.108297i
$149$	−17.5859			−1.44070			−0.720348	−	0.693613i	$-0.756018\pi$
$149$	−17.5859			−1.44070			−0.720348	+	0.693613i	$0.756018\pi$
$150$	2.76792	−	2.80036i	0.226000	−	0.228648i
$151$	−23.6802			−1.92707			−0.963536	−	0.267580i	$-0.913776\pi$
$151$	−23.6802			−1.92707			−0.963536	+	0.267580i	$0.913776\pi$
$152$	8.18495	−	2.65945i	0.663887	−	0.215710i
$153$	−0.409871	−	0.564139i	−0.0331361	−	0.0456079i
$154$	−0.201096	+	0.146105i	−0.0162048	+	0.0117735i
$155$	−0.521021	−	6.38248i	−0.0418494	−	0.512653i
$156$	−5.27710	−	3.83404i	−0.422506	−	0.306969i
$157$			1.06400i			0.0849162i	0.999098	+	0.0424581i	$0.0135189\pi$
$157$			1.06400i			0.0849162i	−0.999098	+	0.0424581i	$0.986481\pi$
$158$	−2.37486	+	3.26872i	−0.188934	+	0.260045i
$159$	−1.17459	+	3.61503i	−0.0931513	+	0.286690i
$160$	9.91512	−	8.51838i	0.783859	−	0.673437i
$161$	−1.40820	−	4.33399i	−0.110982	−	0.341567i
$162$	0.748945	+	0.243347i	0.0588426	+	0.0191191i
$163$	16.0684	+	5.22094i	1.25857	+	0.408936i	0.860986	−	0.508628i	$-0.169847\pi$
$163$	16.0684	+	5.22094i	1.25857	+	0.408936i	0.397588	+	0.917564i	$0.369847\pi$
$164$	0.111628	+	0.343554i	0.00871665	+	0.0268271i
$165$	0.703471	−	0.0574265i	0.0547651	−	0.00447065i
$166$	−1.31041	+	4.03303i	−0.101708	+	0.313024i
$167$	0.953516	−	1.31240i	0.0737853	−	0.101557i	−0.770529	−	0.637405i	$-0.780008\pi$
$167$	0.953516	−	1.31240i	0.0737853	−	0.101557i	0.844314	+	0.535848i	$0.180008\pi$
$168$		−	2.66160i		−	0.205347i
$169$	7.56117	+	5.49351i	0.581628	+	0.422578i
$170$	−1.13304	+	0.473192i	−0.0869003	+	0.0362922i
$171$	−2.61592	+	1.90058i	−0.200044	+	0.145341i
$172$	−5.75716	−	7.92404i	−0.438979	−	0.604203i
$173$	−10.1767	+	3.30659i	−0.773716	+	0.251396i	−0.669155	−	0.743123i	$-0.733344\pi$
$173$	−10.1767	+	3.30659i	−0.773716	+	0.251396i	−0.104561	+	0.994518i	$0.533344\pi$
$174$	−4.43893			−0.336515
$175$	4.94291	+	0.753391i	0.373649	+	0.0569510i
$176$	0.209513			0.0157926
$177$	12.0844	−	3.92646i	0.908319	−	0.295131i
$178$	−0.992711	−	1.36635i	−0.0744068	−	0.102412i
$179$	−13.9701	+	10.1498i	−1.04417	+	0.758635i	−0.971095	−	0.238692i	$-0.923282\pi$
$179$	−13.9701	+	10.1498i	−1.04417	+	0.758635i	−0.0730758	+	0.997326i	$0.523282\pi$
$180$	−1.60448	+	2.63548i	−0.119591	+	0.196437i
$181$	5.05274	+	3.67103i	0.375567	+	0.272866i	0.759516	−	0.650489i	$-0.225436\pi$
$181$	5.05274	+	3.67103i	0.375567	+	0.272866i	−0.383948	+	0.923355i	$0.625436\pi$
$182$			3.72258i			0.275936i
$183$	0.634267	−	0.872994i	0.0468864	−	0.0645336i
$184$	3.74806	−	11.5354i	0.276311	−	0.850398i
$185$	−2.66252	−	6.37530i	−0.195752	−	0.468722i
$186$	−0.696903	−	2.14485i	−0.0510994	−	0.157268i
$187$	−0.209333	−	0.0680164i	−0.0153079	−	0.00497385i
$188$	2.84893	+	0.925675i	0.207780	+	0.0675118i
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	2.19420	+	5.25393i	0.159184	+	0.381160i
$191$	−2.58168	+	7.94561i	−0.186804	+	0.574924i	−0.999975	−	0.00710144i	$-0.997740\pi$
$191$	−2.58168	+	7.94561i	−0.186804	+	0.574924i	0.813171	+	0.582025i	$0.197740\pi$
$192$	1.92562	−	2.65039i	0.138970	−	0.191275i
$193$			22.1607i			1.59516i	0.603212	+	0.797581i	$0.293887\pi$
$193$			22.1607i			1.59516i	−0.603212	+	0.797581i	$0.706113\pi$
$194$	9.63188	+	6.99797i	0.691529	+	0.502425i
$195$	5.49668	−	9.02868i	0.393625	−	0.646558i
$196$	1.11633	−	0.811064i	0.0797381	−	0.0579331i
$197$	8.50941	+	11.7122i	0.606270	+	0.834459i	0.996264	−	0.0863582i	$-0.0275229\pi$
$197$	8.50941	+	11.7122i	0.606270	+	0.834459i	−0.389994	+	0.920817i	$0.627523\pi$
$198$	0.236403	−	0.0768120i	0.0168004	−	0.00545879i
$199$	7.58339			0.537572			0.268786	−	0.963200i	$-0.413378\pi$
$199$	7.58339			0.537572			0.268786	+	0.963200i	$0.413378\pi$
$200$	9.46483	+	9.35520i	0.669265	+	0.661512i
$201$	−9.09400			−0.641442
$202$	10.9082	−	3.54429i	0.767499	−	0.249376i
$203$	−3.31325	−	4.56029i	−0.232544	−	0.320070i
$204$	0.778435	−	0.565566i	0.0545013	−	0.0395975i
$205$	−0.540165	+	0.225589i	−0.0377268	+	0.0157558i
$206$	−12.2824	−	8.92366i	−0.855753	−	0.621741i
$207$			4.55703i			0.316736i
$208$	1.84428	−	2.53843i	0.127878	−	0.176009i
$209$	−0.315393	+	0.970681i	−0.0218162	+	0.0671434i
$210$	1.75504	−	0.143269i	0.121109	−	0.00988650i
$211$	−2.28351	−	7.02792i	−0.157203	−	0.483822i	0.841174	−	0.540764i	$-0.181865\pi$
$211$	−2.28351	−	7.02792i	−0.157203	−	0.483822i	−0.998377	+	0.0569425i	$0.981865\pi$
$212$	−4.98825	−	1.62078i	−0.342594	−	0.111316i
$213$	13.0502	+	4.24028i	0.894187	+	0.290539i
$214$	−3.47508	−	10.6952i	−0.237552	−	0.731110i
$215$	12.0393	−	10.3433i	0.821071	−	0.705407i
$216$	−0.822479	+	2.53133i	−0.0559626	+	0.172235i
$217$	1.68331	−	2.31688i	0.114271	−	0.157280i
$218$			5.45623i			0.369542i
$219$	6.79322	+	4.93557i	0.459043	+	0.333515i
$220$	0.0792407	+	0.970694i	0.00534241	+	0.0654442i
$221$	−2.66678	+	1.93753i	−0.179387	+	0.130332i
$222$	−1.43017	−	1.96846i	−0.0959870	−	0.132115i
$223$	−11.3540	+	3.68913i	−0.760319	+	0.247043i	−0.663416	−	0.748251i	$-0.730894\pi$
$223$	−11.3540	+	3.68913i	−0.760319	+	0.247043i	−0.0969035	+	0.995294i	$0.530894\pi$
$224$	5.84590			0.390595
$225$	−4.46818	−	2.24396i	−0.297879	−	0.149597i
$226$	6.29953			0.419038
$227$	19.8883	−	6.46210i	1.32003	−	0.428905i	0.437526	−	0.899206i	$-0.355855\pi$
$227$	19.8883	−	6.46210i	1.32003	−	0.428905i	0.882506	+	0.470301i	$0.155855\pi$
$228$	−2.62254	−	3.60961i	−0.173682	−	0.239053i
$229$	9.62567	−	6.99346i	0.636082	−	0.462141i	−0.222420	−	0.974951i	$-0.571396\pi$
$229$	9.62567	−	6.99346i	0.636082	−	0.462141i	0.858502	+	0.512810i	$0.171396\pi$
$230$	7.80807	+	1.85052i	0.514849	+	0.122019i
$231$	0.255365	+	0.185533i	0.0168018	+	0.0122072i
$232$		−	15.0030i		−	0.984995i
$233$	−10.1581	+	13.9815i	−0.665481	+	0.915955i	−0.999647	−	0.0265586i	$-0.991545\pi$
$233$	−10.1581	+	13.9815i	−0.665481	+	0.915955i	0.334167	+	0.942514i	$0.391545\pi$
$234$	1.15034	−	3.54039i	0.0752002	−	0.231442i
$235$	−1.11946	+	4.72343i	−0.0730252	+	0.308123i
$236$	5.41798	+	16.6748i	0.352680	+	1.08544i
$237$	4.87958	+	1.58547i	0.316963	+	0.102988i
$238$	−0.522249	−	0.169689i	−0.0338524	−	0.0109993i
$239$	5.26761	+	16.2120i	0.340733	+	1.04867i	0.963829	+	0.266523i	$0.0858748\pi$
$239$	5.26761	+	16.2120i	0.340733	+	1.04867i	−0.623096	+	0.782146i	$0.714125\pi$
$240$	−1.26774	−	0.771803i	−0.0818324	−	0.0498197i
$241$	0.604319	−	1.85990i	0.0389276	−	0.119807i	−0.929704	−	0.368307i	$-0.879938\pi$
$241$	0.604319	−	1.85990i	0.0389276	−	0.119807i	0.968632	+	0.248500i	$0.0799376\pi$
$242$	−5.04549	+	6.94452i	−0.324336	+	0.446411i
$243$		−	1.00000i		−	0.0641500i
$244$	1.20461	+	0.875202i	0.0771174	+	0.0560291i
$245$	1.45716	+	1.69608i	0.0930943	+	0.108359i
$246$	−0.166784	+	0.121175i	−0.0106337	+	0.00772586i
$247$	8.98435	+	12.3659i	0.571660	+	0.786823i
$248$	7.24929	−	2.35544i	0.460330	−	0.149570i
$249$	5.38496			0.341258
$250$	−5.65926	+	6.74460i	−0.357923	+	0.426566i
$251$	3.95090			0.249379			0.124689	−	0.992196i	$-0.460207\pi$
$251$	3.95090			0.249379			0.124689	+	0.992196i	$0.460207\pi$
$252$	−1.31233	+	0.426402i	−0.0826690	+	0.0268608i
$253$	0.845481	+	1.16370i	0.0531549	+	0.0731615i
$254$	2.40469	−	1.74711i	0.150883	−	0.109623i
$255$	1.01609	+	1.18270i	0.0636303	+	0.0740636i
$256$	11.1059	+	8.06891i	0.694119	+	0.504307i
$257$			6.41652i			0.400252i	0.979770	+	0.200126i	$0.0641351\pi$
$257$			6.41652i			0.400252i	−0.979770	+	0.200126i	$0.935865\pi$
$258$	3.28560	−	4.52224i	0.204553	−	0.281543i
$259$	0.954793	−	2.93855i	0.0593279	−	0.182593i
$260$	12.4584	+	7.58467i	0.772635	+	0.470381i
$261$	1.74188	+	5.36095i	0.107820	+	0.331834i
$262$	−5.55220	−	1.80402i	−0.343016	−	0.111453i
$263$	−4.98734	−	1.62049i	−0.307533	−	0.0999234i	0.151185	−	0.988505i	$-0.451691\pi$
$263$	−4.98734	−	1.62049i	−0.307533	−	0.0999234i	−0.458718	+	0.888582i	$0.651691\pi$
$264$	0.259614	+	0.799010i	0.0159781	+	0.0491757i
$265$	1.96007	−	8.27034i	0.120406	−	0.508043i
$266$	−0.786851	+	2.42168i	−0.0482449	+	0.148483i
$267$	−1.26061	+	1.73507i	−0.0771478	+	0.106185i
$268$		−	12.5485i		−	0.766521i
$269$	−6.86600	−	4.98844i	−0.418627	−	0.304150i	0.358458	−	0.933546i	$-0.383303\pi$
$269$	−6.86600	−	4.98844i	−0.418627	−	0.304150i	−0.777085	+	0.629395i	$0.783303\pi$
$270$	−1.71341	−	0.406079i	−0.104275	−	0.0247132i
$271$	9.68814	−	7.03884i	0.588512	−	0.427579i	−0.253270	−	0.967396i	$-0.581506\pi$
$271$	9.68814	−	7.03884i	0.588512	−	0.427579i	0.841783	+	0.539816i	$0.181506\pi$
$272$	0.272053	+	0.374449i	0.0164957	+	0.0227043i
$273$	4.49580	−	1.46078i	0.272098	−	0.0884101i
$274$	9.42918			0.569637
$275$	−1.55734	+	0.255968i	−0.0939114	+	0.0154354i
$276$	−6.28808			−0.378498
$277$	4.68906	−	1.52357i	0.281738	−	0.0915424i	−0.164739	−	0.986337i	$-0.552678\pi$
$277$	4.68906	−	1.52357i	0.281738	−	0.0915424i	0.446478	+	0.894795i	$0.352678\pi$
$278$	8.99497	+	12.3805i	0.539482	+	0.742534i
$279$	−2.31688	+	1.68331i	−0.138708	+	0.100777i
$280$	0.484230	+	5.93178i	0.0289383	+	0.354492i
$281$	4.05285	+	2.94457i	0.241773	+	0.175658i	0.702073	−	0.712105i	$-0.252258\pi$
$281$	4.05285	+	2.94457i	0.241773	+	0.175658i	−0.460300	+	0.887763i	$0.652258\pi$
$282$			1.70955i			0.101802i
$283$	16.9375	−	23.3125i	1.00683	−	1.38578i	0.0857929	−	0.996313i	$-0.472658\pi$
$283$	16.9375	−	23.3125i	1.00683	−	1.38578i	0.921039	−	0.389472i	$-0.127342\pi$
$284$	−5.85101	+	18.0076i	−0.347194	+	1.06855i
$285$	5.48421	−	4.71165i	0.324856	−	0.279094i
$286$	−0.363103	−	1.11752i	−0.0214707	−	0.0660801i
$287$	−0.248977	−	0.0808975i	−0.0146966	−	0.00477523i
$288$	−5.55978	−	1.80648i	−0.327613	−	0.106448i
$289$	5.10303	+	15.7055i	0.300178	+	0.923854i
$290$	9.89285	−	0.807584i	0.580928	−	0.0474230i
$291$	4.67189	−	14.3786i	0.273871	−	0.842888i
$292$	−6.81041	+	9.37373i	−0.398549	+	0.548556i
$293$			12.2073i			0.713156i	0.934265	+	0.356578i	$0.116057\pi$
$293$			12.2073i			0.713156i	−0.934265	+	0.356578i	$0.883943\pi$
$294$	0.637090	+	0.462873i	0.0371559	+	0.0269953i
$295$	−26.2176	+	10.9493i	−1.52645	+	0.637490i
$296$	6.65314	−	4.83379i	0.386706	−	0.280958i
$297$	−0.185533	−	0.255365i	−0.0107657	−	0.0148178i
$298$	13.1709	−	4.27948i	0.762970	−	0.247904i
$299$	21.5419			1.24580
$300$	3.09636	−	6.16548i	0.178769	−	0.355964i
$301$	7.09828			0.409138
$302$	17.7352	−	5.76251i	1.02055	−	0.331595i
$303$	−8.56096	−	11.7832i	−0.491814	−	0.676925i
$304$	1.73633	−	1.26152i	0.0995852	−	0.0723529i
$305$	−1.25474	+	2.06099i	−0.0718460	+	0.118012i
$306$	0.444252	+	0.322768i	0.0253962	+	0.0184514i
$307$		−	18.0833i		−	1.03207i	−0.856567	−	0.516035i	$-0.827407\pi$
$307$		−	18.0833i		−	1.03207i	0.856567	−	0.516035i	$-0.172593\pi$
$308$	−0.256011	+	0.352369i	−0.0145876	+	0.0200781i
$309$	−5.95749	+	18.3353i	−0.338910	+	1.04306i
$310$	1.94337	+	4.65333i	0.110376	+	0.264291i
$311$	3.02527	+	9.31081i	0.171547	+	0.527968i	0.999459	−	0.0328905i	$-0.0104713\pi$
$311$	3.02527	+	9.31081i	0.171547	+	0.527968i	−0.827912	+	0.560858i	$0.810471\pi$
$312$	11.9660	+	3.88800i	0.677443	+	0.220115i
$313$	−23.6689	−	7.69050i	−1.33785	−	0.434693i	−0.449259	−	0.893401i	$-0.648312\pi$
$313$	−23.6689	−	7.69050i	−1.33785	−	0.434693i	−0.888587	+	0.458709i	$0.848312\pi$
$314$	−0.258920	−	0.796875i	−0.0146117	−	0.0449703i
$315$	−0.861720	−	2.06336i	−0.0485524	−	0.116257i
$316$	−2.18774	+	6.73316i	−0.123070	+	0.378770i
$317$	−15.9618	+	21.9696i	−0.896506	+	1.23393i	0.0750630	+	0.997179i	$0.476084\pi$
$317$	−15.9618	+	21.9696i	−0.896506	+	1.23393i	−0.971569	+	0.236756i	$0.923916\pi$
$318$		−	2.99329i		−	0.167855i
$319$	1.43945	+	1.04582i	0.0805936	+	0.0585547i
$320$	−3.80935	+	6.25713i	−0.212949	+	0.349784i
$321$	−11.5531	+	8.39380i	−0.644829	+	0.468496i
$322$	2.10933	+	2.90324i	0.117548	+	0.161791i
$323$	−2.14438	+	0.696751i	−0.119316	+	0.0387682i
$324$	1.37986			0.0766591
$325$	−10.6076	+	21.1218i	−0.588403	+	1.17163i
$326$	−13.3048			−0.736887
$327$	6.58954	−	2.14107i	0.364403	−	0.118402i
$328$	−0.409557	−	0.563706i	−0.0226140	−	0.0311255i
$329$	−1.75629	+	1.27602i	−0.0968276	+	0.0703494i
$330$	−0.512886	+	0.214197i	−0.0282334	+	0.0117911i
$331$	17.1043	+	12.4270i	0.940139	+	0.683051i	0.948454	−	0.316914i	$-0.102647\pi$
$331$	17.1043	+	12.4270i	0.940139	+	0.683051i	−0.00831501	+	0.999965i	$0.502647\pi$
$332$			7.43051i			0.407802i
$333$	−1.81612	+	2.49968i	−0.0995229	+	0.136982i
$334$	−0.394762	+	1.21495i	−0.0216004	+	0.0664792i
$335$	20.2674	−	1.65449i	1.10733	−	0.0903944i
$336$	−0.205111	−	0.631268i	−0.0111897	−	0.0344385i
$337$	−13.6689	−	4.44129i	−0.744592	−	0.241933i	−0.0879397	−	0.996126i	$-0.528028\pi$
$337$	−13.6689	−	4.44129i	−0.744592	−	0.241933i	−0.656653	+	0.754193i	$0.728028\pi$
$338$	−6.99973	−	2.27435i	−0.380735	−	0.123708i
$339$	−2.47199	−	7.60801i	−0.134260	−	0.413210i
$340$	−1.63197	+	1.40207i	−0.0885059	+	0.0760381i
$341$	−0.279339	+	0.859718i	−0.0151271	+	0.0465563i
$342$	1.49668	−	2.06000i	0.0809312	−	0.111392i
$343$			1.00000i			0.0539949i
$344$	15.2846	+	11.1049i	0.824089	+	0.598735i
$345$	−0.829070	−	10.1560i	−0.0446356	−	0.546783i
$346$	6.81710	−	4.95291i	0.366489	−	0.266270i
$347$	−13.4597	−	18.5257i	−0.722554	−	0.994510i	−0.999435	−	0.0336059i	$-0.989301\pi$
$347$	−13.4597	−	18.5257i	−0.722554	−	0.994510i	0.276881	−	0.960904i	$-0.410699\pi$
$348$	−7.39738	+	2.40355i	−0.396541	+	0.128844i
$349$	−35.2305			−1.88584			−0.942922	−	0.333014i	$-0.891934\pi$
$349$	−35.2305			−1.88584			−0.942922	+	0.333014i	$0.891934\pi$
$350$	−3.88530	+	0.638594i	−0.207678	+	0.0341343i
$351$	−4.72717			−0.252318
$352$	−1.75493	+	0.570212i	−0.0935382	+	0.0303924i
$353$	−5.21401	−	7.17647i	−0.277514	−	0.381965i	0.647395	−	0.762155i	$-0.275859\pi$
$353$	−5.21401	−	7.17647i	−0.277514	−	0.381965i	−0.924908	+	0.380190i	$0.875859\pi$
$354$	−8.09505	+	5.88140i	−0.430247	+	0.312593i
$355$	−29.8559	−	7.07586i	−1.58459	−	0.375548i
$356$	−2.39417	−	1.73946i	−0.126891	−	0.0921915i
$357$			0.697314i			0.0369058i
$358$	7.99287	−	11.0012i	0.422436	−	0.581434i
$359$	−2.30070	+	7.08084i	−0.121427	+	0.373713i	−0.993233	−	0.116138i	$-0.962949\pi$
$359$	−2.30070	+	7.08084i	−0.121427	+	0.373713i	0.871807	+	0.489850i	$0.162949\pi$
$360$	1.37249	−	5.79110i	0.0723367	−	0.305218i
$361$	−2.64048	−	8.12656i	−0.138973	−	0.427714i
$362$	−4.67756	−	1.51983i	−0.245847	−	0.0798805i
$363$	10.3669	+	3.36840i	0.544119	+	0.176795i
$364$	2.01567	+	6.20360i	0.105650	+	0.325157i
$365$	−16.0377	−	9.76377i	−0.839451	−	0.511059i
$366$	−0.262591	+	0.808171i	−0.0137258	+	0.0422438i
$367$	6.48227	−	8.92209i	0.338372	−	0.465729i	−0.605593	−	0.795774i	$-0.707064\pi$
$367$	6.48227	−	8.92209i	0.338372	−	0.465729i	0.943965	+	0.330045i	$0.107064\pi$
$368$		−	3.02475i		−	0.157676i
$369$	0.211792	+	0.153876i	0.0110255	+	0.00801047i
$370$	3.54549	+	4.12683i	0.184321	+	0.214544i
$371$	3.07513	−	2.23421i	0.159653	−	0.115994i
$372$	−2.32274	−	3.19698i	−0.120429	−	0.165756i
$373$	−17.6010	+	5.71892i	−0.911346	+	0.296114i	−0.726912	−	0.686731i	$-0.759045\pi$
$373$	−17.6010	+	5.71892i	−0.911346	+	0.296114i	−0.184434	+	0.982845i	$0.559045\pi$
$374$	0.173330			0.00896270
$375$	10.3663	+	4.18811i	0.535312	+	0.216273i
$376$	−5.77806			−0.297981
$377$	25.3421	−	8.23415i	1.30518	−	0.424080i
$378$	−0.462873	−	0.637090i	−0.0238076	−	0.0327684i
$379$	16.7471	−	12.1675i	0.860242	−	0.625003i	−0.0677085	−	0.997705i	$-0.521569\pi$
$379$	16.7471	−	12.1675i	0.860242	−	0.625003i	0.927951	+	0.372702i	$0.121569\pi$
$380$	6.50144	+	7.56746i	0.333517	+	0.388203i
$381$	−3.05362	−	2.21859i	−0.156442	−	0.113662i
$382$		−	6.57906i		−	0.336614i
$383$	20.4621	−	28.1637i	1.04557	−	1.43910i	0.152975	−	0.988230i	$-0.451114\pi$
$383$	20.4621	−	28.1637i	1.04557	−	1.43910i	0.892591	−	0.450868i	$-0.148886\pi$
$384$	2.81574	−	8.66597i	0.143690	−	0.442233i
$385$	−0.602874	−	0.367031i	−0.0307253	−	0.0187056i
$386$	−5.39274	−	16.5971i	−0.274483	−	0.844772i
$387$	−6.75086	−	2.19349i	−0.343166	−	0.111501i
$388$	19.8405	+	6.44657i	1.00725	+	0.327275i
$389$	7.42647	+	22.8563i	0.376537	+	1.15886i	0.942436	+	0.334387i	$0.108529\pi$
$389$	7.42647	+	22.8563i	0.376537	+	1.15886i	−0.565899	+	0.824475i	$0.691471\pi$
$390$	−1.91960	+	8.09958i	−0.0972029	+	0.410138i
$391$	−0.981957	+	3.02215i	−0.0496597	+	0.152837i
$392$	−1.56445	+	2.15328i	−0.0790166	+	0.108757i
$393$			7.41336i			0.373955i
$394$	−9.22320	−	6.70105i	−0.464658	−	0.337594i
$395$	−11.1634	−	2.64572i	−0.561689	−	0.133121i
$396$	0.352369	−	0.256011i	0.0177072	−	0.0128650i
$397$	−5.08697	−	7.00161i	−0.255308	−	0.351401i	0.662054	−	0.749456i	$-0.269685\pi$
$397$	−5.08697	−	7.00161i	−0.255308	−	0.351401i	−0.917361	+	0.398056i	$0.869685\pi$
$398$	−5.67954	+	1.84539i	−0.284689	+	0.0925012i
$399$	3.23346			0.161875
$400$	2.96577	+	1.48944i	0.148289	+	0.0744720i
$401$	−7.35004			−0.367043			−0.183522	−	0.983016i	$-0.558750\pi$
$401$	−7.35004			−0.367043			−0.183522	+	0.983016i	$0.558750\pi$
$402$	6.81090	−	2.21300i	0.339697	−	0.110374i
$403$	7.95731	+	10.9523i	0.396382	+	0.545573i
$404$	16.2592	−	11.8130i	0.808923	−	0.587717i
$405$	0.181932	+	2.22865i	0.00904027	+	0.110743i
$406$	3.59117	+	2.60914i	0.178227	+	0.129489i
$407$			0.975281i			0.0483429i
$408$	−1.09091	+	1.50151i	−0.0540082	+	0.0743359i
$409$	0.847569	−	2.60855i	0.0419096	−	0.128984i	−0.927913	−	0.372798i	$-0.878398\pi$
$409$	0.847569	−	2.60855i	0.0419096	−	0.128984i	0.969822	+	0.243813i	$0.0783985\pi$
$410$	0.349658	−	0.300401i	0.0172684	−	0.0148358i
$411$	−3.70009	−	11.3877i	−0.182512	−	0.561715i
$412$	−25.3002	−	8.22052i	−1.24645	−	0.404996i
$413$	−12.0844	−	3.92646i	−0.594634	−	0.193208i
$414$	−1.10894	−	3.41296i	−0.0545014	−	0.167738i
$415$	−12.0012	+	0.979696i	−0.589116	+	0.0480914i
$416$	−8.53954	+	26.2820i	−0.418685	+	1.28858i
$417$	11.4224	−	15.7215i	0.559356	−	0.769887i
$418$		−	0.803736i		−	0.0393120i
$419$	−31.6930	−	23.0263i	−1.54830	−	1.12491i	−0.944847	−	0.327511i	$-0.893790\pi$
$419$	−31.6930	−	23.0263i	−1.54830	−	1.12491i	−0.603456	−	0.797397i	$-0.706210\pi$
$420$	2.84715	−	1.18906i	0.138927	−	0.0580200i
$421$	26.9469	−	19.5780i	1.31331	−	0.954175i	0.313320	−	0.949648i	$-0.398559\pi$
$421$	26.9469	−	19.5780i	1.31331	−	0.954175i	0.999990	−	0.00452778i	$-0.00144124\pi$
$422$	3.42044	+	4.70783i	0.166505	+	0.229174i
$423$	2.06465	−	0.670845i	0.100387	−	0.0326176i
$424$	10.1169			0.491321
$425$	−2.47970	−	2.45097i	−0.120283	−	0.118890i
$426$	−10.8058			−0.523541
$427$	−1.02627	+	0.333454i	−0.0496645	+	0.0161370i
$428$	−11.5823	−	15.9417i	−0.559852	−	0.770570i
$429$	−1.20715	+	0.877047i	−0.0582818	+	0.0423442i
$430$	−6.49973	+	10.6763i	−0.313445	+	0.514856i
$431$	1.44172	+	1.04747i	0.0694450	+	0.0504548i	0.621966	−	0.783044i	$-0.286334\pi$
$431$	1.44172	+	1.04747i	0.0694450	+	0.0504548i	−0.552521	+	0.833499i	$0.686334\pi$
$432$			0.663754i			0.0319349i
$433$	−18.4265	+	25.3619i	−0.885521	+	1.21882i	0.0893395	+	0.996001i	$0.471524\pi$
$433$	−18.4265	+	25.3619i	−0.885521	+	1.21882i	−0.974861	+	0.222814i	$0.928476\pi$
$434$	−0.696903	+	2.14485i	−0.0334524	+	0.102956i
$435$	−4.85737	−	11.6308i	−0.232893	−	0.557654i
$436$	2.95439	+	9.09268i	0.141490	+	0.435460i
$437$	14.0138	+	4.55335i	0.670370	+	0.217816i
$438$	−6.28880	−	2.04336i	−0.300491	−	0.0976353i
$439$	−5.33070	−	16.4062i	−0.254420	−	0.783026i	−0.993943	−	0.109894i	$-0.964949\pi$
$439$	−5.33070	−	16.4062i	−0.254420	−	0.783026i	0.739523	−	0.673132i	$-0.235051\pi$
$440$	−0.723955	−	1.73348i	−0.0345132	−	0.0826406i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	1.52578	−	2.10005i	0.0725738	−	0.0998893i
$443$		−	32.0399i		−	1.52226i	−0.648597	−	0.761132i	$-0.724644\pi$
$443$		−	32.0399i		−	1.52226i	0.648597	−	0.761132i	$-0.275356\pi$
$444$	−3.44922	−	2.50600i	−0.163693	−	0.118930i
$445$	2.49379	−	4.09623i	0.118217	−	0.194180i
$446$	7.60577	−	5.52591i	0.360144	−	0.261660i
$447$	−10.3368	−	14.2273i	−0.488912	−	0.672929i
$448$	−3.11572	+	1.01236i	−0.147204	+	0.0478294i
$449$	−15.8045			−0.745861			−0.372930	−	0.927859i	$-0.621647\pi$
$449$	−15.8045			−0.745861			−0.372930	+	0.927859i	$0.621647\pi$
$450$	3.89248	+	0.593286i	0.183493	+	0.0279678i
$451$	0.0826334			0.00389106
$452$	10.4980	−	3.41101i	0.493785	−	0.160441i
$453$	−13.9189	−	19.1577i	−0.653967	−	0.900108i
$454$	−13.3227	+	9.67951i	−0.625265	+	0.454282i
$455$	−9.75383	+	4.07349i	−0.457267	+	0.190968i
$456$	6.96253	+	5.05857i	0.326050	+	0.236889i
$457$			39.3142i			1.83904i	0.393045	+	0.919519i	$0.371422\pi$
$457$			39.3142i			1.83904i	−0.393045	+	0.919519i	$0.628578\pi$
$458$	−5.50726	+	7.58009i	−0.257337	+	0.354194i
$459$	0.215482	−	0.663185i	0.0100578	−	0.0309548i
$460$	14.0140	−	1.14400i	0.653405	−	0.0533394i
$461$	−0.399063	−	1.22819i	−0.0185862	−	0.0572024i	0.941333	−	0.337478i	$-0.109574\pi$
$461$	−0.399063	−	1.22819i	−0.0185862	−	0.0572024i	−0.959919	+	0.280276i	$0.909574\pi$
$462$	−0.236403	−	0.0768120i	−0.0109985	−	0.00357362i
$463$	−7.43571	−	2.41601i	−0.345567	−	0.112282i	0.131091	−	0.991370i	$-0.458152\pi$
$463$	−7.43571	−	2.41601i	−0.345567	−	0.112282i	−0.476658	+	0.879089i	$0.658152\pi$
$464$	−1.15618	−	3.55835i	−0.0536742	−	0.165192i
$465$	4.85728	−	4.17304i	0.225251	−	0.193520i
$466$	4.20553	−	12.9433i	0.194817	−	0.599586i
$467$	12.1144	−	16.6741i	0.560590	−	0.771585i	−0.430812	−	0.902442i	$-0.641773\pi$
$467$	12.1144	−	16.6741i	0.560590	−	0.771585i	0.991401	+	0.130856i	$0.0417727\pi$
$468$		−	6.52285i		−	0.301519i
$469$	7.35720	+	5.34532i	0.339724	+	0.246824i
$470$	−0.311023	−	3.81001i	−0.0143464	−	0.175742i
$471$	−0.860792	+	0.625402i	−0.0396632	+	0.0288170i
$472$	−19.8783	−	27.3602i	−0.914974	−	1.25935i
$473$	−2.13090	+	0.692370i	−0.0979787	+	0.0318352i
$474$	−4.04036			−0.185580
$475$	−11.3652	+	11.4984i	−0.521471	+	0.527582i
$476$	−0.962198			−0.0441023
$477$	−3.61503	+	1.17459i	−0.165521	+	0.0537810i
$478$	−7.89029	−	10.8601i	−0.360893	−	0.496727i
$479$	−23.2440	+	16.8877i	−1.06204	+	0.771620i	−0.974465	−	0.224538i	$-0.927913\pi$
$479$	−23.2440	+	16.8877i	−1.06204	+	0.771620i	−0.0875784	+	0.996158i	$0.527913\pi$
$480$	12.7195	+	3.01452i	0.580562	+	0.137593i
$481$	11.8164	+	8.58512i	0.538782	+	0.391448i
$482$			1.54002i			0.0701461i
$483$	2.67856	−	3.68672i	0.121879	−	0.167751i
$484$	−4.64793	+	14.3049i	−0.211270	+	0.650221i
$485$	−7.79610	+	32.8949i	−0.354003	+	1.49368i
$486$	0.243347	+	0.748945i	0.0110384	+	0.0339728i
$487$	14.6188	+	4.74994i	0.662442	+	0.215240i	0.620892	−	0.783896i	$-0.286771\pi$
$487$	14.6188	+	4.74994i	0.662442	+	0.215240i	0.0415496	+	0.999136i	$0.486771\pi$
$488$	−2.73151	−	0.887521i	−0.123650	−	0.0401762i
$489$	5.22094	+	16.0684i	0.236099	+	0.726638i
$490$	−1.50407	−	0.915677i	−0.0679468	−	0.0413661i
$491$	−3.53834	+	10.8899i	−0.159683	+	0.491454i	−0.998605	−	0.0527973i	$-0.983186\pi$
$491$	−3.53834	+	10.8899i	−0.159683	+	0.491454i	0.838922	+	0.544251i	$0.183186\pi$
$492$	−0.212328	+	0.292245i	−0.00957249	+	0.0131754i
$493$			3.93064i			0.177027i
$494$	−9.73798	−	7.07506i	−0.438132	−	0.318322i
$495$	0.459949	+	0.535365i	0.0206732	+	0.0240629i
$496$	1.53784	−	1.11731i	0.0690511	−	0.0501685i
$497$	−8.06549	−	11.1012i	−0.361787	−	0.497957i
$498$	−4.03303	+	1.31041i	−0.180725	+	0.0587210i
$499$	4.20172			0.188095			0.0940475	−	0.995568i	$-0.470019\pi$
$499$	4.20172			0.188095			0.0940475	+	0.995568i	$0.470019\pi$
$500$	−5.77903	+	14.3041i	−0.258446	+	0.639697i
$501$	1.62222			0.0724754
$502$	−2.95901	+	0.961440i	−0.132067	+	0.0429112i
$503$	16.9425	+	23.3194i	0.755429	+	1.03976i	0.997581	+	0.0695202i	$0.0221468\pi$
$503$	16.9425	+	23.3194i	0.755429	+	1.03976i	−0.242152	+	0.970238i	$0.577853\pi$
$504$	2.15328	−	1.56445i	0.0959147	−	0.0696861i
$505$	21.2232	+	24.7031i	0.944418	+	1.09927i
$506$	−0.916402	−	0.665805i	−0.0407391	−	0.0295987i
$507$			9.34612i			0.415076i
$508$	3.06135	−	4.21358i	0.135825	−	0.186948i
$509$	−7.62655	+	23.4721i	−0.338041	+	1.04038i	0.627164	+	0.778887i	$0.284216\pi$
$509$	−7.62655	+	23.4721i	−0.338041	+	1.04038i	−0.965205	+	0.261495i	$0.915784\pi$
$510$	−1.04881	−	0.638514i	−0.0464419	−	0.0282739i
$511$	−2.59478	−	7.98591i	−0.114786	−	0.353276i
$512$	7.05069	+	2.29091i	0.311599	+	0.101245i
$513$	−3.07520	−	0.999193i	−0.135773	−	0.0441154i
$514$	−1.56144	−	4.80562i	−0.0688722	−	0.211967i
$515$	9.94141	−	41.9468i	0.438071	−	1.84840i
$516$	3.02672	−	9.31527i	0.133244	−	0.410082i
$517$	0.402774	−	0.554371i	0.0177140	−	0.0243812i
$518$			2.43316i			0.106907i
$519$	−8.65678	−	6.28952i	−0.379990	−	0.276079i
$520$	−27.3755	−	6.48800i	−1.20049	−	0.284518i
$521$	−3.94895	+	2.86908i	−0.173007	+	0.125697i	−0.670919	−	0.741531i	$-0.734100\pi$
$521$	−3.94895	+	2.86908i	−0.173007	+	0.125697i	0.497912	+	0.867227i	$0.334100\pi$
$522$	−2.60914	−	3.59117i	−0.114199	−	0.157181i
$523$	−9.64961	+	3.13535i	−0.421948	+	0.137099i	−0.512292	−	0.858811i	$-0.671203\pi$
$523$	−9.64961	+	3.13535i	−0.421948	+	0.137099i	0.0903438	+	0.995911i	$0.471203\pi$
$524$	−10.2294			−0.446875
$525$	2.29587	+	4.44173i	0.100200	+	0.193853i
$526$	4.12958			0.180058
$527$	−1.89924	+	0.617102i	−0.0827324	+	0.0268814i
$528$	0.123148	+	0.169499i	0.00535935	+	0.00737651i
$529$	−1.80691	+	1.31280i	−0.0785614	+	0.0570782i
$530$	0.544575	+	6.67101i	0.0236548	+	0.289770i
$531$	10.2796	+	7.46857i	0.446097	+	0.324108i
$532$			4.46173i			0.193440i
$533$	0.727398	−	1.00118i	0.0315071	−	0.0433658i
$534$	0.521899	−	1.60624i	0.0225848	−	0.0695088i
$535$	24.2207	−	20.8087i	1.04715	−	0.899640i
$536$	7.47963	+	23.0199i	0.323071	+	0.994310i
$537$	−16.4228	−	5.33609i	−0.708696	−	0.230269i
$538$	6.35617	+	2.06525i	0.274034	+	0.0890390i
$539$	−0.0975406	−	0.300199i	−0.00420137	−	0.0129305i
$540$	−3.07524	+	0.251041i	−0.132337	+	0.0108031i
$541$	9.08156	−	27.9502i	0.390447	−	1.20167i	−0.542004	−	0.840376i	$-0.682334\pi$
$541$	9.08156	−	27.9502i	0.390447	−	1.20167i	0.932451	−	0.361296i	$-0.117666\pi$
$542$	−5.54300	+	7.62928i	−0.238092	+	0.327706i
$543$			6.24553i			0.268021i
$544$	−3.29790	−	2.39606i	−0.141396	−	0.102730i
$545$	−14.2963	+	5.97056i	−0.612386	+	0.255751i
$546$	−3.01163	+	2.18808i	−0.128886	+	0.0936412i
$547$	−20.4019	−	28.0807i	−0.872320	−	1.20065i	−0.978489	−	0.206298i	$-0.933858\pi$
$547$	−20.4019	−	28.0807i	−0.872320	−	1.20065i	0.106169	−	0.994348i	$-0.466142\pi$
$548$	15.7135	−	5.10563i	0.671248	−	0.218102i
$549$	1.07908			0.0460540
$550$	1.10408	−	0.570681i	0.0470780	−	0.0243339i
$551$	18.2264			0.776473
$552$	11.5354	−	3.74806i	0.490977	−	0.159528i
$553$	−3.01575	−	4.15082i	−0.128243	−	0.176511i
$554$	−3.14109	+	2.28214i	−0.133452	+	0.0969587i
$555$	3.59274	−	5.90133i	0.152503	−	0.250498i
$556$	21.6936	+	15.7613i	0.920014	+	0.668429i
$557$		−	33.6417i		−	1.42545i	−0.701445	−	0.712723i	$-0.747462\pi$
$557$		−	33.6417i		−	1.42545i	0.701445	−	0.712723i	$-0.252538\pi$
$558$	1.32559	−	1.82451i	0.0561166	−	0.0772379i
$559$	−10.3690	+	31.9125i	−0.438561	+	1.34975i
$560$	0.571970	+	1.36956i	0.0241701	+	0.0578745i
$561$	−0.0680164	−	0.209333i	−0.00287165	−	0.00883804i
$562$	−3.75191	−	1.21907i	−0.158265	−	0.0514234i
$563$	10.0530	+	3.26641i	0.423683	+	0.137663i	0.513095	−	0.858332i	$-0.328499\pi$
$563$	10.0530	+	3.26641i	0.423683	+	0.137663i	−0.0894123	+	0.995995i	$0.528499\pi$
$564$	0.925675	+	2.84893i	0.0389779	+	0.119962i
$565$	6.89335	+	16.5059i	0.290006	+	0.694408i
$566$	−7.01224	+	21.5815i	−0.294747	+	0.907137i
$567$	−0.587785	+	0.809017i	−0.0246847	+	0.0339755i
$568$		−	36.5220i		−	1.53243i
$569$	−11.4743	−	8.33653i	−0.481026	−	0.349486i	0.320697	−	0.947182i	$-0.396083\pi$
$569$	−11.4743	−	8.33653i	−0.481026	−	0.349486i	−0.801723	+	0.597696i	$0.796083\pi$
$570$	−2.96080	+	4.86333i	−0.124014	+	0.203702i
$571$	7.22694	−	5.25068i	0.302438	−	0.219734i	−0.426207	−	0.904626i	$-0.640150\pi$
$571$	7.22694	−	5.25068i	0.302438	−	0.219734i	0.728645	+	0.684892i	$0.240150\pi$
$572$	−1.21021	−	1.66571i	−0.0506013	−	0.0696467i
$573$	−7.94561	+	2.58168i	−0.331932	+	0.107851i
$574$	0.206156			0.00860478
$575$	3.69542	+	22.4835i	0.154110	+	0.937626i
$576$	3.27606			0.136502
$577$	6.40443	−	2.08092i	0.266620	−	0.0866300i	−0.172656	−	0.984982i	$-0.555235\pi$
$577$	6.40443	−	2.08092i	0.266620	−	0.0866300i	0.439276	+	0.898352i	$0.355235\pi$
$578$	−7.64377	−	10.5208i	−0.317939	−	0.437606i
$579$	−17.9284	+	13.0257i	−0.745078	+	0.541331i
$580$	16.0489	−	6.70251i	0.666395	−	0.278307i
$581$	−4.35652	−	3.16520i	−0.180739	−	0.131315i
$582$			11.9057i			0.493505i
$583$	−0.705224	+	0.970658i	−0.0292074	+	0.0402005i
$584$	6.90626	−	21.2553i	0.285783	−	0.879550i
$585$	10.5352	−	0.860023i	0.435578	−	0.0355576i
$586$	−2.97060	−	9.14257i	−0.122714	−	0.377676i
$587$	13.4345	+	4.36512i	0.554500	+	0.180168i	0.572845	−	0.819664i	$-0.305840\pi$
$587$	13.4345	+	4.36512i	0.554500	+	0.180168i	−0.0183451	+	0.999832i	$0.505840\pi$
$588$	1.31233	+	0.426402i	0.0541195	+	0.0175845i
$589$	2.86151	+	8.80683i	0.117907	+	0.362879i
$590$	16.9711	−	14.5804i	0.698687	−	0.600264i
$591$	−4.47366	+	13.7685i	−0.184022	+	0.566361i
$592$	1.20546	−	1.65917i	0.0495441	−	0.0681916i
$593$		−	38.1558i		−	1.56687i	−0.621472	−	0.783436i	$-0.713465\pi$
$593$		−	38.1558i		−	1.56687i	0.621472	−	0.783436i	$-0.286535\pi$
$594$	0.201096	+	0.146105i	0.00825108	+	0.00599476i
$595$	−0.126864	−	1.55407i	−0.00520090	−	0.0637107i
$596$	19.6318	−	14.2633i	0.804149	−	0.584248i
$597$	4.45740	+	6.13509i	0.182429	+	0.251093i
$598$	−16.1337	+	5.24214i	−0.659754	+	0.214367i
$599$	−41.1616			−1.68182			−0.840910	−	0.541176i	$-0.817979\pi$
$599$	−41.1616			−1.68182			−0.840910	+	0.541176i	$0.817979\pi$
$600$	−2.00523	+	13.1561i	−0.0818630	+	0.537094i
$601$	25.2545			1.03015			0.515076	−	0.857144i	$-0.327764\pi$
$601$	25.2545			1.03015			0.515076	+	0.857144i	$0.327764\pi$
$602$	−5.31622	+	1.72734i	−0.216673	+	0.0704013i
$603$	−5.34532	−	7.35720i	−0.217678	−	0.299608i
$604$	26.4351	−	19.2062i	1.07563	−	0.781489i
$605$	−23.7170	−	5.62093i	−0.964232	−	0.228523i
$606$	9.27908	+	6.74165i	0.376937	+	0.273861i
$607$			40.6370i			1.64941i	0.565566	+	0.824703i	$0.308658\pi$
$607$			40.6370i			1.64941i	−0.565566	+	0.824703i	$0.691342\pi$
$608$	−11.1106	+	15.2924i	−0.450593	+	0.620189i
$609$	1.74188	−	5.36095i	0.0705844	−	0.217237i
$610$	0.438192	−	1.84891i	0.0177419	−	0.0748601i
$611$	−3.17120	−	9.75994i	−0.128293	−	0.394845i
$612$	0.915105	+	0.297336i	0.0369909	+	0.0120191i
$613$	15.2240	+	4.94657i	0.614890	+	0.199790i	0.599870	−	0.800097i	$-0.295219\pi$
$613$	15.2240	+	4.94657i	0.614890	+	0.199790i	0.0150201	+	0.999887i	$0.495219\pi$
$614$	4.40052	+	13.5434i	0.177591	+	0.546568i
$615$	−0.500007	−	0.304405i	−0.0201622	−	0.0122748i
$616$	0.259614	−	0.799010i	0.0104601	−	0.0321930i
$617$	−22.6277	+	31.1443i	−0.910957	+	1.25382i	0.0558824	+	0.998437i	$0.482203\pi$
$617$	−22.6277	+	31.1443i	−0.910957	+	1.25382i	−0.966839	+	0.255387i	$0.917797\pi$
$618$		−	15.1818i		−	0.610703i
$619$	−29.5489	−	21.4686i	−1.18767	−	0.862894i	−0.194656	−	0.980872i	$-0.562359\pi$
$619$	−29.5489	−	21.4686i	−1.18767	−	0.862894i	−0.993016	+	0.117978i	$0.962359\pi$
$620$	5.75823	+	6.70239i	0.231256	+	0.269175i
$621$	−3.68672	+	2.67856i	−0.147943	+	0.107487i
$622$	−4.53151	−	6.23709i	−0.181697	−	0.250085i
$623$	2.03970	−	0.662740i	0.0817190	−	0.0265521i
$624$	3.13768			0.125608
$625$	−23.8648	−	7.44790i	−0.954592	−	0.297916i
$626$	19.5982			0.783300
$627$	−0.970681	+	0.315393i	−0.0387652	+	0.0125956i
$628$	−0.862970	−	1.18778i	−0.0344363	−	0.0473974i
$629$	−1.74306	+	1.26641i	−0.0695004	+	0.0504950i
$630$	1.14749	+	1.33564i	0.0457172	+	0.0532133i
$631$	14.6067	+	10.6124i	0.581485	+	0.422474i	0.839259	−	0.543731i	$-0.182989\pi$
$631$	14.6067	+	10.6124i	0.581485	+	0.422474i	−0.257774	+	0.966205i	$0.582989\pi$
$632$		−	13.6559i		−	0.543201i
$633$	4.34349	−	5.97830i	0.172638	−	0.237616i
$634$	6.60830	−	20.3383i	0.262449	−	0.807736i
$635$	7.20910	+	4.38891i	0.286084	+	0.174169i
$636$	−1.62078	−	4.98825i	−0.0642681	−	0.197797i
$637$	−4.49580	−	1.46078i	−0.178130	−	0.0578780i
$638$	−1.33256	−	0.432976i	−0.0527567	−	0.0171417i
$639$	4.24028	+	13.0502i	0.167743	+	0.516259i
$640$	−4.69870	+	19.8257i	−0.185733	+	0.783681i
$641$	1.85163	−	5.69872i	0.0731349	−	0.225086i	−0.907807	−	0.419389i	$-0.862244\pi$
$641$	1.85163	−	5.69872i	0.0731349	−	0.225086i	0.980942	+	0.194303i	$0.0622444\pi$
$642$	6.61000	−	9.09789i	0.260876	−	0.359065i
$643$			40.6987i			1.60500i	0.596653	+	0.802500i	$0.296497\pi$
$643$			40.6987i			1.60500i	−0.596653	+	0.802500i	$0.703503\pi$
$644$	5.08717	+	3.69604i	0.200462	+	0.145645i
$645$	15.4444	+	3.66033i	0.608123	+	0.144125i
$646$	1.43647	−	1.04366i	0.0565171	−	0.0410621i
$647$	3.08807	+	4.25037i	0.121405	+	0.167099i	0.865394	−	0.501093i	$-0.167068\pi$
$647$	3.08807	+	4.25037i	0.121405	+	0.167099i	−0.743989	+	0.668192i	$0.767068\pi$
$648$	−2.53133	+	0.822479i	−0.0994401	+	0.0323100i
$649$	4.01072			0.157434
$650$	2.80456	−	18.4004i	0.110004	−	0.721723i
$651$	2.86382			0.112242
$652$	−22.1722	+	7.20419i	−0.868331	+	0.282138i
$653$	−13.6858	−	18.8369i	−0.535568	−	0.737147i	0.452398	−	0.891816i	$-0.350569\pi$
$653$	−13.6858	−	18.8369i	−0.535568	−	0.737147i	−0.987966	+	0.154670i	$0.950569\pi$
$654$	−4.41418	+	3.20709i	−0.172608	+	0.125407i
$655$	−1.34873	−	16.5218i	−0.0526991	−	0.645561i
$656$	−0.140578	−	0.102136i	−0.00548865	−	0.00398774i
$657$			8.39689i			0.327594i
$658$	1.00485	−	1.38306i	0.0391732	−	0.0539172i
$659$	3.94887	−	12.1534i	0.153826	−	0.473428i	−0.844214	−	0.536006i	$-0.819932\pi$
$659$	3.94887	−	12.1534i	0.153826	−	0.473428i	0.998040	+	0.0625781i	$0.0199323\pi$
$660$	−0.738731	+	0.634667i	−0.0287551	+	0.0247044i
$661$	−10.5867	−	32.5824i	−0.411773	−	1.26731i	−0.915106	−	0.403214i	$-0.867893\pi$
$661$	−10.5867	−	32.5824i	−0.411773	−	1.26731i	0.503333	−	0.864093i	$-0.332107\pi$
$662$	−15.8343	−	5.14487i	−0.615417	−	0.199961i
$663$	−3.13499	−	1.01862i	−0.121753	−	0.0395599i
$664$	−4.42902	−	13.6311i	−0.171879	−	0.528990i
$665$	−7.20625	+	0.588269i	−0.279447	+	0.0228121i
$666$	0.751887	−	2.31407i	0.0291350	−	0.0896684i
$667$	15.0986	−	20.7814i	0.584619	−	0.804659i
$668$			2.23844i			0.0866079i
$669$	−9.65828	−	7.01715i	−0.373411	−	0.271299i
$670$	−14.7765	+	6.17113i	−0.570867	+	0.238411i
$671$	0.275559	−	0.200205i	0.0106378	−	0.00772884i
$672$	3.43613	+	4.72943i	0.132552	+	0.182442i
$673$	−36.7415	+	11.9380i	−1.41628	+	0.460178i	−0.914419	−	0.404769i	$-0.867352\pi$
$673$	−36.7415	+	11.9380i	−1.41628	+	0.460178i	−0.501863	+	0.864947i	$0.667352\pi$
$674$	11.3180			0.435954
$675$	−0.810927	−	4.93380i	−0.0312126	−	0.189902i
$676$	−12.8964			−0.496015
$677$	26.2092	−	8.51589i	1.00730	−	0.327292i	0.241522	−	0.970395i	$-0.422353\pi$
$677$	26.2092	−	8.51589i	1.00730	−	0.327292i	0.765780	+	0.643103i	$0.222353\pi$
$678$	3.70277	+	5.09642i	0.142204	+	0.195727i
$679$	−12.2312	+	8.88646i	−0.469389	+	0.341031i
$680$	2.15809	−	3.54482i	0.0827590	−	0.135938i
$681$	16.9180	+	12.2916i	0.648299	+	0.471017i
$682$		−	0.711857i		−	0.0272584i
$683$	−13.3251	+	18.3404i	−0.509870	+	0.701776i	−0.983897	−	0.178734i	$-0.942800\pi$
$683$	−13.3251	+	18.3404i	−0.509870	+	0.701776i	0.474028	+	0.880510i	$0.342800\pi$
$684$	1.37875	−	4.24336i	0.0527178	−	0.162249i
$685$	10.3180	+	24.7061i	0.394231	+	0.943973i
$686$	−0.243347	−	0.748945i	−0.00929103	−	0.0285948i
$687$	11.3157	+	3.67668i	0.431719	+	0.140274i
$688$	4.48091	+	1.45594i	0.170833	+	0.0555071i
$689$	5.55250	+	17.0888i	0.211533	+	0.651033i
$690$	3.09237	+	7.40457i	0.117725	+	0.281887i
$691$	6.51104	−	20.0389i	0.247692	−	0.762317i	−0.747490	−	0.664273i	$-0.768741\pi$
$691$	6.51104	−	20.0389i	0.247692	−	0.762317i	0.995182	−	0.0980442i	$-0.0312587\pi$
$692$	8.67868	−	11.9452i	0.329914	−	0.454087i
$693$			0.315648i			0.0119905i
$694$	14.5887	+	10.5993i	0.553780	+	0.402345i
$695$	−22.5963	+	37.1160i	−0.857125	+	1.40789i
$696$	12.1377	−	8.81854i	0.460077	−	0.334266i
$697$	0.107300	+	0.147686i	0.00406427	+	0.00559399i
$698$	26.3857	−	8.57322i	0.998712	−	0.324501i
$699$	−17.2820			−0.653666
$700$	−6.12899	+	3.16798i	−0.231654	+	0.119739i
$701$	17.8742			0.675098			0.337549	−	0.941308i	$-0.390402\pi$
$701$	17.8742			0.675098			0.337549	+	0.941308i	$0.390402\pi$
$702$	3.54039	−	1.15034i	0.133623	−	0.0434168i
$703$	5.87235	+	8.08260i	0.221480	+	0.304841i
$704$	0.836590	−	0.607818i	0.0315302	−	0.0229080i
$705$	−4.47934	+	1.87071i	−0.168702	+	0.0704549i
$706$	5.65138	+	4.10596i	0.212692	+	0.154530i
$707$			14.5648i			0.547765i
$708$	−10.3056	+	14.1845i	−0.387309	+	0.533084i
$709$	−0.474276	+	1.45967i	−0.0178118	+	0.0548191i	−0.959567	−	0.281479i	$-0.909175\pi$
$709$	−0.474276	+	1.45967i	−0.0178118	+	0.0548191i	0.941756	+	0.336298i	$0.109175\pi$
$710$	24.0823	−	1.96591i	0.903793	−	0.0737794i
$711$	1.58547	+	4.87958i	0.0594599	+	0.182999i
$712$	5.42887	+	1.76395i	0.203456	+	0.0661067i
$713$	12.4118	+	4.03284i	0.464826	+	0.151031i
$714$	−0.169689	−	0.522249i	−0.00635045	−	0.0195447i
$715$	2.53076	−	2.17425i	0.0946451	−	0.0813125i
$716$	7.36308	−	22.6612i	0.275171	−	0.846890i
$717$	−10.0196	+	13.7908i	−0.374188	+	0.515026i
$718$		−	5.86303i		−	0.218806i
$719$	−9.22180	−	6.70003i	−0.343915	−	0.249869i	0.402397	−	0.915465i	$-0.368177\pi$
$719$	−9.22180	−	6.70003i	−0.343915	−	0.249869i	−0.746312	+	0.665596i	$0.768177\pi$
$720$	−0.120758	−	1.47928i	−0.00450039	−	0.0551295i
$721$	15.5969	−	11.3318i	0.580859	−	0.422019i
$722$	3.95514	+	5.44379i	0.147195	+	0.202597i
$723$	1.85990	−	0.604319i	0.0691705	−	0.0224748i
$724$	−8.61799			−0.320285
$725$	12.9414	+	25.0373i	0.480632	+	0.929863i
$726$	−8.58390			−0.318578
$727$	39.4559	−	12.8200i	1.46334	−	0.475468i	0.534251	−	0.845326i	$-0.320594\pi$
$727$	39.4559	−	12.8200i	1.46334	−	0.475468i	0.929088	+	0.369858i	$0.120594\pi$
$728$	−7.39541	−	10.1789i	−0.274092	−	0.377256i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	14.3873	+	3.40980i	0.532499	+	0.126202i
$731$	−4.00441	−	2.90938i	−0.148109	−	0.107607i
$732$			1.48898i			0.0550344i
$733$	6.82223	−	9.39000i	0.251985	−	0.346828i	−0.664220	−	0.747537i	$-0.731236\pi$
$733$	6.82223	−	9.39000i	0.251985	−	0.346828i	0.916205	+	0.400709i	$0.131236\pi$
$734$	−2.68370	+	8.25959i	−0.0990573	+	0.304867i
$735$	−0.515665	+	2.17580i	−0.0190206	+	0.0802555i
$736$	8.23219	+	25.3361i	0.303443	+	0.933900i
$737$	−2.73001	−	0.887035i	−0.100561	−	0.0326743i
$738$	−0.196066	−	0.0637057i	−0.00721729	−	0.00234504i
$739$	−16.0427	−	49.3743i	−0.590140	−	1.81626i	−0.577567	−	0.816343i	$-0.695998\pi$
$739$	−16.0427	−	49.3743i	−0.590140	−	1.81626i	−0.0125724	−	0.999921i	$-0.504002\pi$
$740$	8.14304	+	4.95749i	0.299344	+	0.182241i
$741$	−4.72335	+	14.5370i	−0.173517	+	0.534029i
$742$	−1.75941	+	2.42162i	−0.0645900	+	0.0889005i
$743$		−	0.896913i		−	0.0329045i	−0.999865	−	0.0164523i	$-0.994763\pi$
$743$		−	0.896913i		−	0.0329045i	0.999865	−	0.0164523i	$-0.00523716\pi$
$744$	6.16661	+	4.48031i	0.226079	+	0.164256i
$745$	25.6255	+	29.8272i	0.938844	+	1.09278i
$746$	11.7905	−	8.56630i	0.431681	−	0.313635i
$747$	3.16520	+	4.35652i	0.115809	+	0.159397i
$748$	0.288851	−	0.0938534i	0.0105614	−	0.00343162i
$749$	14.2804			0.521794
$750$	−8.78293	−	0.614062i	−0.320707	−	0.0224224i
$751$	−16.0817			−0.586829			−0.293415	−	0.955985i	$-0.594792\pi$
$751$	−16.0817			−0.586829			−0.293415	+	0.955985i	$0.594792\pi$
$752$	−1.37042	+	0.445276i	−0.0499740	+	0.0162375i
$753$	2.32228	+	3.19635i	0.0846287	+	0.116481i
$754$	−16.9761	+	12.3338i	−0.618232	+	0.449172i
$755$	34.5058	+	40.1637i	1.25580	+	1.46170i
$756$	−1.11633	−	0.811064i	−0.0406007	−	0.0294981i
$757$			31.6228i			1.14935i	0.818382	+	0.574674i	$0.194871\pi$
$757$			31.6228i			1.14935i	−0.818382	+	0.574674i	$0.805129\pi$
$758$	−9.58175	+	13.1881i	−0.348025	+	0.479015i
$759$	−0.444496	+	1.36802i	−0.0161342	+	0.0496559i
$760$	−16.4374	−	10.0071i	−0.596247	−	0.362996i
$761$	−4.98954	−	15.3562i	−0.180871	−	0.556662i	0.818982	−	0.573819i	$-0.194539\pi$
$761$	−4.98954	−	15.3562i	−0.180871	−	0.556662i	−0.999853	+	0.0171565i	$0.994539\pi$
$762$	2.82688	+	0.918509i	0.102407	+	0.0332741i
$763$	−6.58954	−	2.14107i	−0.238558	−	0.0775120i
$764$	−3.56237	−	10.9639i	−0.128882	−	0.396658i
$765$	−0.359580	+	1.51721i	−0.0130006	+	0.0548549i
$766$	−8.47145	+	26.0724i	−0.306086	+	0.942036i
$767$	35.3052	−	48.5934i	1.27480	−	1.75461i
$768$			13.7276i			0.495354i
$769$	−9.95000	−	7.22910i	−0.358806	−	0.260688i	0.393748	−	0.919219i	$-0.371178\pi$
$769$	−9.95000	−	7.22910i	−0.358806	−	0.260688i	−0.752554	+	0.658531i	$0.771178\pi$
$770$	0.540835	+	0.128178i	0.0194903	+	0.00461922i
$771$	−5.19108	+	3.77154i	−0.186952	+	0.135829i
$772$	−17.9737	−	24.7387i	−0.646889	−	0.890367i
$773$	−16.8637	+	5.47935i	−0.606545	+	0.197078i	−0.596157	−	0.802868i	$-0.703307\pi$
$773$	−16.8637	+	5.47935i	−0.606545	+	0.197078i	−0.0103875	+	0.999946i	$0.503307\pi$
$774$	5.58980			0.200921
$775$	−10.0660	+	10.1840i	−0.361581	+	0.365819i
$776$	−40.2395			−1.44451
$777$	2.93855	−	0.954793i	0.105420	−	0.0342530i
$778$	−11.1240	−	15.3109i	−0.398816	−	0.548923i
$779$	0.684821	−	0.497552i	0.0245363	−	0.0178266i
$780$	1.18672	+	14.5372i	0.0424912	+	0.520515i
$781$	3.50407	+	2.54586i	0.125386	+	0.0910979i
$782$		−	2.50238i		−	0.0894850i
$783$	−3.31325	+	4.56029i	−0.118406	+	0.162972i
$784$	−0.205111	+	0.631268i	−0.00732540	+	0.0225453i
$785$	1.80463	−	1.55041i	0.0644099	−	0.0553365i
$786$	−1.80402	−	5.55220i	−0.0643472	−	0.198040i
$787$	20.8395	+	6.77116i	0.742848	+	0.241366i	0.655901	−	0.754847i	$-0.272289\pi$
$787$	20.8395	+	6.77116i	0.742848	+	0.241366i	0.0869470	+	0.996213i	$0.472289\pi$
$788$	−18.9987	−	6.17304i	−0.676800	−	0.219906i
$789$	−1.62049	−	4.98734i	−0.0576908	−	0.177554i
$790$	9.00456	−	0.735070i	0.320368	−	0.0261526i
$791$	−2.47199	+	7.60801i	−0.0878939	+	0.270510i
$792$	−0.493815	+	0.679678i	−0.0175470	+	0.0241513i
$793$		−	5.10099i		−	0.181141i
$794$	5.51368	+	4.00592i	0.195673	+	0.142165i
$795$	7.84295	−	3.27545i	0.278161	−	0.116168i
$796$	−8.46559	+	6.15061i	−0.300055	+	0.218003i
$797$	−30.3173	−	41.7282i	−1.07389	−	1.47809i	−0.866071	−	0.499921i	$-0.833362\pi$
$797$	−30.3173	−	41.7282i	−1.07389	−	1.47809i	−0.207822	−	0.978167i	$-0.566638\pi$
$798$	−2.42168	+	0.786851i	−0.0857265	+	0.0278542i
$799$	1.51380			0.0535543
$800$	−28.8958	−	4.40425i	−1.02162	−	0.155714i
$801$	−2.14467			−0.0757782
$802$	5.50477	−	1.78861i	0.194380	−	0.0631580i
$803$	1.55790	+	2.14427i	0.0549772	+	0.0756696i
$804$	10.1519	−	7.37582i	0.358031	−	0.260125i
$805$	−5.29884	+	8.70373i	−0.186760	+	0.306766i
$806$	−8.62479	−	6.26628i	−0.303795	−	0.220720i
$807$		−	8.48684i		−	0.298751i
$808$	−22.7858	+	31.3620i	−0.801603	+	1.10331i
$809$	5.41475	−	16.6649i	0.190372	−	0.585906i	−0.809627	−	0.586945i	$-0.800331\pi$
$809$	5.41475	−	16.6649i	0.190372	−	0.585906i	0.999999	+	0.00103877i	$0.000330652\pi$
$810$	−0.678593	−	1.62487i	−0.0238433	−	0.0570920i
$811$	6.60664	+	20.3331i	0.231990	+	0.713993i	0.997506	+	0.0705761i	$0.0224838\pi$
$811$	6.60664	+	20.3331i	0.231990	+	0.713993i	−0.765516	+	0.643417i	$0.777516\pi$
$812$	7.39738	+	2.40355i	0.259597	+	0.0843482i
$813$	11.3891	+	3.70054i	0.399433	+	0.129784i
$814$	−0.237332	−	0.730432i	−0.00831847	−	0.0256016i
$815$	−14.5590	−	34.8611i	−0.509981	−	1.22113i
$816$	−0.143027	+	0.440192i	−0.00500694	+	0.0154098i
$817$	−13.4908	+	18.5685i	−0.471984	+	0.649630i
$818$			2.15991i			0.0755196i
$819$	3.82436	+	2.77856i	0.133634	+	0.0970907i
$820$	0.420037	−	0.689942i	0.0146683	−	0.0240938i
$821$	29.6417	−	21.5360i	1.03450	−	0.751610i	0.0652977	−	0.997866i	$-0.479200\pi$
$821$	29.6417	−	21.5360i	1.03450	−	0.751610i	0.969205	+	0.246256i	$0.0792003\pi$
$822$	5.54233	+	7.62837i	0.193311	+	0.266070i
$823$	22.5940	−	7.34123i	0.787577	−	0.255899i	0.112505	−	0.993651i	$-0.464113\pi$
$823$	22.5940	−	7.34123i	0.787577	−	0.255899i	0.675072	+	0.737752i	$0.264113\pi$
$824$	51.3125			1.78756
$825$	−1.12247	−	1.10946i	−0.0390793	−	0.0386266i
$826$	10.0060			0.348154
$827$	−12.2157	+	3.96911i	−0.424780	+	0.138020i	−0.513603	−	0.858028i	$-0.671690\pi$
$827$	−12.2157	+	3.96911i	−0.424780	+	0.138020i	0.0888226	+	0.996047i	$0.471690\pi$
$828$	−3.69604	−	5.08717i	−0.128446	−	0.176791i
$829$	−22.1187	+	16.0702i	−0.768214	+	0.558140i	−0.901419	−	0.432949i	$-0.857473\pi$
$829$	−22.1187	+	16.0702i	−0.768214	+	0.558140i	0.133205	+	0.991089i	$0.457473\pi$
$830$	8.74984	−	3.65419i	0.303711	−	0.126839i
$831$	3.98875	+	2.89800i	0.138368	+	0.100530i
$832$		−	15.4865i		−	0.536897i
$833$	0.409871	−	0.564139i	0.0142012	−	0.0195462i
$834$	−4.72894	+	14.5542i	−0.163750	+	0.503970i
$835$	−3.61536	+	0.295133i	−0.125115	+	0.0102135i
$836$	−0.435200	−	1.33941i	−0.0150517	−	0.0463244i
$837$	−2.72366	−	0.884970i	−0.0941434	−	0.0305891i
$838$	29.3397	+	9.53303i	1.01352	+	0.329313i
$839$	4.23208	+	13.0250i	0.146108	+	0.449673i	0.997152	−	0.0754210i	$-0.0240301\pi$
$839$	4.23208	+	13.0250i	0.146108	+	0.449673i	−0.851044	+	0.525094i	$0.824030\pi$
$840$	−4.51429	+	3.87837i	−0.155758	+	0.133816i
$841$	0.857181	−	2.63813i	0.0295580	−	0.0909700i
$842$	−15.4175	+	21.2203i	−0.531321	+	0.731300i
$843$			5.00960i			0.172540i
$844$	8.24925	+	5.99343i	0.283951	+	0.206302i
$845$	−1.70036	−	20.8293i	−0.0584941	−	0.716549i
$846$	−1.38306	+	1.00485i	−0.0475505	+	0.0345475i
$847$	−6.40707	−	8.81858i	−0.220150	−	0.303010i
$848$	2.39949	−	0.779641i	0.0823988	−	0.0267730i
$849$	28.8158			0.988957
$850$	2.45359	+	1.23222i	0.0841575	+	0.0422647i
$851$	14.0802			0.482663
$852$	−18.0076	+	5.85101i	−0.616929	+	0.200452i
$853$	8.24342	+	11.3461i	0.282249	+	0.388483i	0.926477	−	0.376351i	$-0.122821\pi$
$853$	8.24342	+	11.3461i	0.282249	+	0.388483i	−0.644228	+	0.764834i	$0.722821\pi$
$854$	0.687471	−	0.499477i	0.0235248	−	0.0170918i
$855$	7.03534	+	1.66738i	0.240604	+	0.0570231i
$856$	30.7496	+	22.3409i	1.05100	+	0.763597i
$857$		−	18.6420i		−	0.636799i	−0.947957	−	0.318400i	$-0.896855\pi$
$857$		−	18.6420i		−	0.636799i	0.947957	−	0.318400i	$-0.103145\pi$
$858$	0.690663	−	0.950616i	0.0235789	−	0.0324535i
$859$	12.8128	−	39.4338i	0.437168	−	1.34547i	−0.453680	−	0.891164i	$-0.649889\pi$
$859$	12.8128	−	39.4338i	0.437168	−	1.34547i	0.890848	−	0.454301i	$-0.150111\pi$
$860$	−5.05076	+	21.3112i	−0.172229	+	0.726705i
$861$	−0.0808975	−	0.248977i	−0.00275698	−	0.00848511i
$862$	−1.33466	−	0.433658i	−0.0454588	−	0.0147705i
$863$	22.1767	+	7.20564i	0.754903	+	0.245283i	0.661090	−	0.750307i	$-0.270094\pi$
$863$	22.1767	+	7.20564i	0.754903	+	0.245283i	0.0938134	+	0.995590i	$0.470094\pi$
$864$	−1.80648	−	5.55978i	−0.0614577	−	0.189147i
$865$	20.4372	+	12.4422i	0.694887	+	0.423048i
$866$	7.62869	−	23.4787i	0.259233	−	0.797839i
$867$	−9.70654	+	13.3599i	−0.329651	+	0.453726i
$868$			3.95169i			0.134129i
$869$	1.31020	+	0.951915i	0.0444455	+	0.0322915i
$870$	6.46822	+	7.52880i	0.219293	+	0.255250i
$871$	−34.7787	+	25.2682i	−1.17843	+	0.856181i
$872$	−10.8395	−	14.9193i	−0.367073	−	0.505232i
$873$	14.3786	−	4.67189i	0.486642	−	0.158119i
$874$	−11.6036			−0.392497
$875$	−5.92479	−	9.48140i	−0.200294	−	0.320530i
$876$	−11.5866			−0.391474
$877$	50.8951	−	16.5368i	1.71860	−	0.558409i	0.726877	−	0.686768i	$-0.240971\pi$
$877$	50.8951	−	16.5368i	1.71860	−	0.558409i	0.991728	+	0.128359i	$0.0409710\pi$
$878$	7.98480	+	10.9901i	0.269474	+	0.370899i
$879$	−9.87589	+	7.17525i	−0.333105	+	0.242015i
$880$	−0.305293	−	0.355351i	−0.0102914	−	0.0119789i
$881$	−46.8095	−	34.0091i	−1.57705	−	1.14580i	−0.919977	−	0.391973i	$-0.871793\pi$
$881$	−46.8095	−	34.0091i	−1.57705	−	1.14580i	−0.657077	−	0.753823i	$-0.728207\pi$
$882$			0.787487i			0.0265161i
$883$	16.3342	−	22.4822i	0.549691	−	0.756585i	−0.440279	−	0.897861i	$-0.645120\pi$
$883$	16.3342	−	22.4822i	0.549691	−	0.756585i	0.989970	+	0.141276i	$0.0451205\pi$
$884$	1.40556	−	4.32585i	0.0472739	−	0.145494i
$885$	−24.2685	−	14.7747i	−0.815775	−	0.496645i
$886$	7.79682	+	23.9961i	0.261939	+	0.806166i
$887$	38.6830	+	12.5689i	1.29885	+	0.422021i	0.875181	−	0.483796i	$-0.160742\pi$
$887$	38.6830	+	12.5689i	1.29885	+	0.422021i	0.423668	+	0.905818i	$0.360742\pi$
$888$	7.82124	+	2.54127i	0.262464	+	0.0852796i
$889$	1.16638	+	3.58975i	0.0391191	+	0.120396i
$890$	−0.870906	+	3.67470i	−0.0291928	+	0.123176i
$891$	0.0975406	−	0.300199i	0.00326773	−	0.0100571i
$892$	9.68271	−	13.3271i	0.324201	−	0.446225i
$893$		−	7.01950i		−	0.234899i
$894$	11.2038	+	8.14006i	0.374712	+	0.272244i
$895$	37.5715	+	8.90447i	1.25588	+	0.297643i
$896$	−7.37171	+	5.35586i	−0.246272	+	0.178927i
$897$	12.6620	+	17.4277i	0.422771	+	0.581895i
$898$	11.8367	−	3.84598i	0.394996	−	0.128342i
$899$	16.1429			0.538396
$900$	6.80798	−	1.11897i	0.226933	−	0.0372990i
$901$	−2.65053			−0.0883021
$902$	−0.0618879	+	0.0201086i	−0.00206064	+	0.000669543i
$903$	4.17226	+	5.74263i	0.138844	+	0.191103i
$904$	−17.2252	+	12.5149i	−0.572902	+	0.416238i
$905$	−1.13626	−	13.9191i	−0.0377706	−	0.462688i
$906$	15.0865	+	10.9610i	0.501214	+	0.364153i
$907$			5.88495i			0.195407i	0.995216	+	0.0977034i	$0.0311496\pi$
$907$			5.88495i			0.195407i	−0.995216	+	0.0977034i	$0.968850\pi$
$908$	−16.9608	+	23.3445i	−0.562864	+	0.774716i
$909$	4.50076	−	13.8519i	0.149281	−	0.459439i
$910$	6.31381	−	5.42439i	0.209301	−	0.179817i
$911$	−8.38578	−	25.8088i	−0.277833	−	0.855083i	−0.988456	−	0.151509i	$-0.951587\pi$
$911$	−8.38578	−	25.8088i	−0.277833	−	0.855083i	0.710623	−	0.703573i	$-0.248413\pi$
$912$	2.04118	+	0.663218i	0.0675901	+	0.0219613i
$913$	1.61656	+	0.525252i	0.0535003	+	0.0173833i
$914$	−9.56698	−	29.4441i	−0.316447	−	0.973925i
$915$	−2.40490	+	0.196319i	−0.0795034	+	0.00649011i
$916$	−5.07332	+	15.6141i	−0.167627	+	0.515903i
$917$	4.35746	−	5.99753i	0.143896	−	0.198056i
$918$			0.549125i			0.0181238i
$919$	25.9473	+	18.8518i	0.855922	+	0.621864i	0.926773	−	0.375623i	$-0.122571\pi$
$919$	25.9473	+	18.8518i	0.855922	+	0.621864i	−0.0708503	+	0.997487i	$0.522571\pi$
$920$	−25.0264	+	10.4518i	−0.825097	+	0.344585i
$921$	14.6297	−	10.6291i	0.482066	−	0.350241i
$922$	0.597752	+	0.822735i	0.0196859	+	0.0270953i
$923$	61.6907	−	20.0445i	2.03057	−	0.659773i
$924$	−0.435552			−0.0143286
$925$	−6.93333	+	13.8057i	−0.227967	+	0.453927i
$926$	6.15687			0.202327
$927$	−18.3353	+	5.95749i	−0.602209	+	0.195670i
$928$	19.3689	+	26.6590i	0.635815	+	0.875125i
$929$	−29.7818	+	21.6377i	−0.977108	+	0.709910i	−0.957060	−	0.289889i	$-0.906382\pi$
$929$	−29.7818	+	21.6377i	−0.977108	+	0.709910i	−0.0200475	+	0.999799i	$0.506382\pi$
$930$	−2.62234	+	4.30738i	−0.0859899	+	0.141245i
$931$	−2.61592	−	1.90058i	−0.0857333	−	0.0622889i
$932$		−	23.8469i		−	0.781130i
$933$	−5.75440	+	7.92025i	−0.188391	+	0.259297i
$934$	−5.01546	+	15.4360i	−0.164111	+	0.505081i
$935$	0.189669	+	0.454156i	0.00620285	+	0.0148525i
$936$	3.88800	+	11.9660i	0.127083	+	0.391122i
$937$	−24.1007	−	7.83078i	−0.787334	−	0.255820i	−0.112366	−	0.993667i	$-0.535843\pi$
$937$	−24.1007	−	7.83078i	−0.787334	−	0.255820i	−0.674969	+	0.737847i	$0.735843\pi$
$938$	−6.81090	−	2.21300i	−0.222384	−	0.0722569i
$939$	−7.69050	−	23.6689i	−0.250970	−	0.772406i
$940$	−2.58132	−	6.18088i	−0.0841934	−	0.201598i
$941$	−16.7042	+	51.4101i	−0.544540	+	1.67592i	0.177542	+	0.984113i	$0.443185\pi$
$941$	−16.7042	+	51.4101i	−0.544540	+	1.67592i	−0.722082	+	0.691808i	$0.756815\pi$
$942$	0.492496	−	0.677863i	0.0160464	−	0.0220860i
$943$		−	1.19298i		−	0.0388489i
$944$	−6.82313	−	4.95729i	−0.222074	−	0.161346i
$945$	1.16278	−	1.90996i	0.0378254	−	0.0621309i
$946$	1.42744	−	1.03709i	0.0464100	−	0.0337188i
$947$	1.99078	+	2.74007i	0.0646917	+	0.0890404i	0.840137	−	0.542374i	$-0.182475\pi$
$947$	1.99078	+	2.74007i	0.0646917	+	0.0890404i	−0.775445	+	0.631415i	$0.782475\pi$
$948$	−6.73316	+	2.18774i	−0.218683	+	0.0710544i
$949$	39.6935			1.28851
$950$	5.71381	−	11.3773i	0.185380	−	0.369130i
$951$	−27.1559			−0.880590
$952$	1.76513	−	0.573526i	0.0572082	−	0.0185881i
$953$	18.4530	+	25.3984i	0.597752	+	0.822735i	0.995500	−	0.0947598i	$-0.0302083\pi$
$953$	18.4530	+	25.3984i	0.597752	+	0.822735i	−0.397748	+	0.917495i	$0.630208\pi$
$954$	2.42162	−	1.75941i	0.0784029	−	0.0569630i
$955$	17.2383	−	7.19924i	0.557819	−	0.232962i
$956$	−19.0294	−	13.8257i	−0.615454	−	0.447154i
$957$			1.77926i			0.0575152i
$958$	13.2989	−	18.3043i	0.429667	−	0.591386i
$959$	−3.70009	+	11.3877i	−0.119482	+	0.367729i
$960$	−7.30120	+	0.596020i	−0.235645	+	0.0192365i
$961$	−7.04513	−	21.6827i	−0.227262	−	0.699441i
$962$	−10.9390	−	3.55429i	−0.352687	−	0.114595i
$963$	−13.5814	−	4.41288i	−0.437656	−	0.142203i
$964$	0.833878	+	2.56641i	0.0268574	+	0.0826585i
$965$	37.5864	−	32.2916i	1.20995	−	1.03950i
$966$	−1.10894	+	3.41296i	−0.0356795	+	0.109810i
$967$	−10.8156	+	14.8864i	−0.347806	+	0.478714i	−0.946701	−	0.322113i	$-0.895607\pi$
$967$	−10.8156	+	14.8864i	−0.347806	+	0.478714i	0.598895	+	0.800828i	$0.295607\pi$
$968$		−	29.0124i		−	0.932494i
$969$	−1.82412	−	1.32530i	−0.0585991	−	0.0425747i
$970$	−2.16602	−	26.5336i	−0.0695467	−	0.851942i
$971$	22.6577	−	16.4618i	0.727121	−	0.528284i	−0.161531	−	0.986868i	$-0.551643\pi$
$971$	22.6577	−	16.4618i	0.727121	−	0.528284i	0.888651	+	0.458584i	$0.151643\pi$
$972$	0.811064	+	1.11633i	0.0260149	+	0.0358064i
$973$	−18.4818	+	6.00510i	−0.592499	+	0.192515i
$974$	−12.1046			−0.387855
$975$	−23.3229	+	3.83339i	−0.746931	+	0.122767i
$976$	−0.716244			−0.0229264
$977$	−2.69519	+	0.875721i	−0.0862269	+	0.0280168i	−0.351813	−	0.936070i	$-0.614435\pi$
$977$	−2.69519	+	0.875721i	−0.0862269	+	0.0280168i	0.265586	+	0.964087i	$0.414435\pi$
$978$	−7.82039	−	10.7638i	−0.250069	−	0.344190i
$979$	−0.547673	+	0.397908i	−0.0175037	+	0.0127172i
$980$	−3.00230	−	0.711547i	−0.0959051	−	0.0227295i
$981$	5.60540	+	4.07256i	0.178967	+	0.130027i
$982$		−	9.01697i		−	0.287743i
$983$	0.227078	−	0.312546i	0.00724267	−	0.00996868i	−0.805380	−	0.592758i	$-0.798039\pi$
$983$	0.227078	−	0.312546i	0.00724267	−	0.00996868i	0.812623	+	0.582790i	$0.198039\pi$
$984$	0.215317	−	0.662676i	0.00686404	−	0.0211254i
$985$	7.46531	−	31.4992i	0.237865	−	1.00365i
$986$	−0.956509	−	2.94383i	−0.0304615	−	0.0937507i
$987$	−2.06465	−	0.670845i	−0.0657185	−	0.0213532i
$988$	−20.0591	−	6.51758i	−0.638164	−	0.207352i
$989$	9.99579	+	30.7639i	0.317848	+	0.978235i
$990$	−0.474755	−	0.289032i	−0.0150887	−	0.00918603i
$991$	−11.3928	+	35.0633i	−0.361903	+	1.11382i	0.589994	+	0.807407i	$0.299130\pi$
$991$	−11.3928	+	35.0633i	−0.361903	+	1.11382i	−0.951898	+	0.306416i	$0.900870\pi$
$992$	−9.84048	+	13.5443i	−0.312435	+	0.430031i
$993$			21.1421i			0.670925i
$994$	8.74205	+	6.35147i	0.277281	+	0.201456i
$995$	−11.0502	−	12.8621i	−0.350314	−	0.407754i
$996$	−6.01141	+	4.36754i	−0.190479	+	0.138391i
$997$	−12.0534	−	16.5901i	−0.381734	−	0.525412i	0.574309	−	0.818639i	$-0.305271\pi$
$997$	−12.0534	−	16.5901i	−0.381734	−	0.525412i	−0.956043	+	0.293227i	$0.905271\pi$
$998$	−3.14686	+	1.02248i	−0.0996121	+	0.0323659i
$999$	−3.08977			−0.0977561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.169.6	✓	56
25.4	even	10	inner	525.2.z.a.379.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.169.6	✓	56	1.1	even	1	trivial
525.2.z.a.379.6	yes	56	25.4	even	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748945 + 0.243347i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.11633 + 0.811064i) q^{4} +(-1.45716 - 1.69608i) q^{5} +(-0.637090 - 0.462873i) q^{6} -1.00000i q^{7} +(1.56445 - 2.15328i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.748945 + 0.243347i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.11633 + 0.811064i) q^{4} +(-1.45716 - 1.69608i) q^{5} +(-0.637090 - 0.462873i) q^{6} -1.00000i q^{7} +(1.56445 - 2.15328i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.50407 + 0.915677i) q^{10} +(0.0975406 + 0.300199i) q^{11} +(-1.31233 - 0.426402i) q^{12} +(4.49580 + 1.46078i) q^{13} +(0.243347 + 0.748945i) q^{14} +(0.515665 - 2.17580i) q^{15} +(0.205111 - 0.631268i) q^{16} +(-0.409871 + 0.564139i) q^{17} -0.787487i q^{18} +(2.61592 + 1.90058i) q^{19} +(3.00230 + 0.711547i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-0.146105 - 0.201096i) q^{22} +(4.33399 - 1.40820i) q^{23} +2.66160 q^{24} +(-0.753391 + 4.94291i) q^{25} -3.72258 q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.811064 + 1.11633i) q^{28} +(4.56029 - 3.31325i) q^{29} +(0.143269 + 1.75504i) q^{30} +(2.31688 + 1.68331i) q^{31} +5.84590i q^{32} +(-0.185533 + 0.255365i) q^{33} +(0.169689 - 0.522249i) q^{34} +(-1.69608 + 1.45716i) q^{35} +(-0.426402 - 1.31233i) q^{36} +(2.93855 + 0.954793i) q^{37} +(-2.42168 - 0.786851i) q^{38} +(1.46078 + 4.49580i) q^{39} +(-5.93178 + 0.484230i) q^{40} +(0.0808975 - 0.248977i) q^{41} +(-0.462873 + 0.637090i) q^{42} +7.09828i q^{43} +(-0.352369 - 0.256011i) q^{44} +(2.06336 - 0.861720i) q^{45} +(-2.90324 + 2.10933i) q^{46} +(-1.27602 - 1.75629i) q^{47} +(0.631268 - 0.205111i) q^{48} -1.00000 q^{49} +(-0.638594 - 3.88530i) q^{50} -0.697314 q^{51} +(-6.20360 + 2.01567i) q^{52} +(2.23421 + 3.07513i) q^{53} +(0.637090 - 0.462873i) q^{54} +(0.367031 - 0.602874i) q^{55} +(-2.15328 - 1.56445i) q^{56} +3.23346i q^{57} +(-2.60914 + 3.59117i) q^{58} +(3.92646 - 12.0844i) q^{59} +(1.18906 + 2.84715i) q^{60} +(-0.333454 - 1.02627i) q^{61} +(-2.14485 - 0.696903i) q^{62} +(0.951057 + 0.309017i) q^{63} +(-1.01236 - 3.11572i) q^{64} +(-4.07349 - 9.75383i) q^{65} +(0.0768120 - 0.236403i) q^{66} +(-5.34532 + 7.35720i) q^{67} -0.962198i q^{68} +(3.68672 + 2.67856i) q^{69} +(0.915677 - 1.50407i) q^{70} +(11.1012 - 8.06549i) q^{71} +(1.56445 + 2.15328i) q^{72} +(7.98591 - 2.59478i) q^{73} -2.43316 q^{74} +(-4.44173 + 2.29587i) q^{75} -4.46173 q^{76} +(0.300199 - 0.0975406i) q^{77} +(-2.18808 - 3.01163i) q^{78} +(4.15082 - 3.01575i) q^{79} +(-1.36956 + 0.571970i) q^{80} +(-0.809017 - 0.587785i) q^{81} +0.206156i q^{82} +(3.16520 - 4.35652i) q^{83} +(-0.426402 + 1.31233i) q^{84} +(1.55407 - 0.126864i) q^{85} +(-1.72734 - 5.31622i) q^{86} +(5.36095 + 1.74188i) q^{87} +(0.799010 + 0.259614i) q^{88} +(0.662740 + 2.03970i) q^{89} +(-1.33564 + 1.14749i) q^{90} +(1.46078 - 4.49580i) q^{91} +(-3.69604 + 5.08717i) q^{92} +2.86382i q^{93} +(1.38306 + 1.00485i) q^{94} +(-0.588269 - 7.20625i) q^{95} +(-4.72943 + 3.43613i) q^{96} +(-8.88646 - 12.2312i) q^{97} +(0.748945 - 0.243347i) q^{98} -0.315648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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