LMFDB - Embedded newform 570.2.bc.b.169.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.8
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.b.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.693816 + 2.12570i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.83436 + 1.63642i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.693816 + 2.12570i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.83436 + 1.63642i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.314150 + 2.21389i) q^{10} +(-1.37165 + 2.37577i) q^{11} +(0.866025 - 0.500000i) q^{12} +(3.18236 + 3.79259i) q^{13} +(-3.07546 + 1.11938i) q^{14} +(2.07436 + 0.834883i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.84400 + 0.677801i) q^{17} -1.00000i q^{18} +(4.34562 - 0.339955i) q^{19} +(-0.0750603 + 2.23481i) q^{20} +(-0.568323 + 3.22312i) q^{21} +(-1.76336 + 2.10149i) q^{22} +(1.74075 - 4.78268i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.03724 + 2.94969i) q^{25} +(2.47544 + 4.28759i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-3.22312 + 0.568323i) q^{28} +(-0.848686 - 4.81314i) q^{29} +(1.89787 + 1.18241i) q^{30} +(-5.52708 - 9.57319i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.938263 + 2.57786i) q^{33} +(3.66791 + 1.33501i) q^{34} +(-5.44507 - 4.88964i) q^{35} +(0.173648 - 0.984808i) q^{36} -3.16040i q^{37} +(4.33863 + 0.419819i) q^{38} +4.95088 q^{39} +(-0.461990 + 2.18782i) q^{40} +(-4.47796 - 3.75746i) q^{41} +(-1.11938 + 3.07546i) q^{42} +(2.55437 + 7.01808i) q^{43} +(-2.10149 + 1.76336i) q^{44} +(1.97293 - 1.05240i) q^{45} +(2.54481 - 4.40775i) q^{46} +(-2.58525 + 0.455849i) q^{47} +(0.984808 - 0.173648i) q^{48} +(1.85574 - 3.21424i) q^{49} +(-4.48811 + 2.20382i) q^{50} +(2.99010 - 2.50899i) q^{51} +(1.69330 + 4.65231i) q^{52} +(-3.68305 + 10.1191i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-6.00185 - 1.26738i) q^{55} -3.27284 q^{56} +(2.53289 - 3.54746i) q^{57} -4.88739i q^{58} +(2.23194 - 12.6580i) q^{59} +(1.66371 + 1.49401i) q^{60} +(10.7497 + 3.91256i) q^{61} +(-3.78075 - 10.3875i) q^{62} +(2.10374 + 2.50714i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.85396 + 9.39613i) q^{65} +(0.476369 + 2.70162i) q^{66} +(11.9835 - 2.11301i) q^{67} +(3.38036 + 1.95165i) q^{68} +(-2.54481 - 4.40775i) q^{69} +(-4.51327 - 5.76089i) q^{70} +(-10.7492 + 3.91240i) q^{71} +(0.342020 - 0.939693i) q^{72} +(4.09077 - 4.87518i) q^{73} +(0.548798 - 3.11239i) q^{74} +(-0.335491 + 4.98873i) q^{75} +(4.19982 + 1.16684i) q^{76} -8.97837i q^{77} +(4.87566 + 0.859711i) q^{78} +(-0.515549 - 0.432597i) q^{79} +(-0.834883 + 2.07436i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-3.75746 - 4.47796i) q^{82} +(-6.87753 + 3.97074i) q^{83} +(-1.63642 + 2.83436i) q^{84} +(1.22622 + 8.64148i) q^{85} +(1.29689 + 7.35502i) q^{86} +(-4.23260 - 2.44369i) q^{87} +(-2.37577 + 1.37165i) q^{88} +(4.97213 - 4.17211i) q^{89} +(2.12570 - 0.693816i) q^{90} +(-15.2263 - 5.54190i) q^{91} +(3.27155 - 3.89888i) q^{92} +(-10.8862 - 1.91954i) q^{93} -2.62513 q^{94} +(3.73770 + 9.00164i) q^{95} +1.00000 q^{96} +(10.0260 + 1.76786i) q^{97} +(2.38570 - 2.84316i) q^{98} +(2.57786 + 0.938263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	0.693816	+	2.12570i	0.310284	+	0.950644i
$5$	0.693816	+	2.12570i	0.310284	+	0.950644i
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	−2.83436	+	1.63642i	−1.07129	+	0.618509i	−0.928533	−	0.371249i	$-0.878930\pi$
$7$	−2.83436	+	1.63642i	−1.07129	+	0.618509i	−0.142755	+	0.989758i	$0.545596\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	0.314150	+	2.21389i	0.0993430	+	0.700094i
$11$	−1.37165	+	2.37577i	−0.413568	+	0.716320i	−0.995277	−	0.0970766i	$-0.969051\pi$
$11$	−1.37165	+	2.37577i	−0.413568	+	0.716320i	0.581709	+	0.813397i	$0.302384\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	3.18236	+	3.79259i	0.882629	+	1.05188i	0.998282	+	0.0585867i	$0.0186594\pi$
$13$	3.18236	+	3.79259i	0.882629	+	1.05188i	−0.115653	+	0.993290i	$0.536896\pi$
$14$	−3.07546	+	1.11938i	−0.821952	+	0.299166i
$15$	2.07436	+	0.834883i	0.535598	+	0.215566i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.84400	+	0.677801i	0.932308	+	0.164391i	0.619117	−	0.785299i	$-0.287491\pi$
$17$	3.84400	+	0.677801i	0.932308	+	0.164391i	0.313191	+	0.949690i	$0.398602\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.34562	−	0.339955i	0.996954	−	0.0779909i
$19$	4.34562	−	0.339955i	0.996954	−	0.0779909i
$20$	−0.0750603	+	2.23481i	−0.0167840	+	0.499718i
$21$	−0.568323	+	3.22312i	−0.124018	+	0.703342i
$22$	−1.76336	+	2.10149i	−0.375949	+	0.448039i
$23$	1.74075	−	4.78268i	0.362972	−	0.997259i	−0.615000	−	0.788527i	$-0.710844\pi$
$23$	1.74075	−	4.78268i	0.362972	−	0.997259i	0.977973	−	0.208732i	$-0.0669336\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−4.03724	+	2.94969i	−0.807448	+	0.589939i
$26$	2.47544	+	4.28759i	0.485474	+	0.840865i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	−3.22312	+	0.568323i	−0.609112	+	0.107403i
$29$	−0.848686	−	4.81314i	−0.157597	−	0.893777i	−0.956373	−	0.292148i	$-0.905630\pi$
$29$	−0.848686	−	4.81314i	−0.157597	−	0.893777i	0.798776	−	0.601629i	$-0.205481\pi$
$30$	1.89787	+	1.18241i	0.346502	+	0.215877i
$31$	−5.52708	−	9.57319i	−0.992693	−	1.71940i	−0.600845	−	0.799366i	$-0.705169\pi$
$31$	−5.52708	−	9.57319i	−0.992693	−	1.71940i	−0.391848	−	0.920030i	$-0.628164\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	0.938263	+	2.57786i	0.163331	+	0.448747i
$34$	3.66791	+	1.33501i	0.629041	+	0.228952i
$35$	−5.44507	−	4.88964i	−0.920385	−	0.826501i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$		−	3.16040i		−	0.519567i	−0.965667	−	0.259783i	$-0.916349\pi$
$37$		−	3.16040i		−	0.519567i	0.965667	−	0.259783i	$-0.0836511\pi$
$38$	4.33863	+	0.419819i	0.703819	+	0.0681037i
$39$	4.95088			0.792775
$40$	−0.461990	+	2.18782i	−0.0730471	+	0.345925i
$41$	−4.47796	−	3.75746i	−0.699340	−	0.586816i	0.222245	−	0.974991i	$-0.428661\pi$
$41$	−4.47796	−	3.75746i	−0.699340	−	0.586816i	−0.921586	+	0.388174i	$0.873106\pi$
$42$	−1.11938	+	3.07546i	−0.172724	+	0.474554i
$43$	2.55437	+	7.01808i	0.389538	+	1.07025i	0.967210	+	0.253978i	$0.0817390\pi$
$43$	2.55437	+	7.01808i	0.389538	+	1.07025i	−0.577672	+	0.816269i	$0.696039\pi$
$44$	−2.10149	+	1.76336i	−0.316811	+	0.265836i
$45$	1.97293	−	1.05240i	0.294107	−	0.156882i
$46$	2.54481	−	4.40775i	0.375212	−	0.649887i
$47$	−2.58525	+	0.455849i	−0.377097	+	0.0664924i	−0.358985	−	0.933344i	$-0.616877\pi$
$47$	−2.58525	+	0.455849i	−0.377097	+	0.0664924i	−0.0181129	+	0.999836i	$0.505766\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	1.85574	−	3.21424i	0.265106	−	0.459177i
$50$	−4.48811	+	2.20382i	−0.634715	+	0.311668i
$51$	2.99010	−	2.50899i	0.418698	−	0.351330i
$52$	1.69330	+	4.65231i	0.234819	+	0.645159i
$53$	−3.68305	+	10.1191i	−0.505906	+	1.38997i	0.379519	+	0.925184i	$0.376089\pi$
$53$	−3.68305	+	10.1191i	−0.505906	+	1.38997i	−0.885425	+	0.464782i	$0.846133\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	−6.00185	−	1.26738i	−0.809289	−	0.170893i
$56$	−3.27284			−0.437352
$57$	2.53289	−	3.54746i	0.335490	−	0.469872i
$58$		−	4.88739i		−	0.641745i
$59$	2.23194	−	12.6580i	0.290574	−	1.64793i	−0.394093	−	0.919071i	$-0.628941\pi$
$59$	2.23194	−	12.6580i	0.290574	−	1.64793i	0.684667	−	0.728856i	$-0.259948\pi$
$60$	1.66371	+	1.49401i	0.214785	+	0.192875i
$61$	10.7497	+	3.91256i	1.37636	+	0.500952i	0.921071	−	0.389394i	$-0.127316\pi$
$61$	10.7497	+	3.91256i	1.37636	+	0.500952i	0.455284	+	0.890346i	$0.349538\pi$
$62$	−3.78075	−	10.3875i	−0.480155	−	1.31922i
$63$	2.10374	+	2.50714i	0.265046	+	0.315870i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−5.85396	+	9.39613i	−0.726094	+	1.16545i
$66$	0.476369	+	2.70162i	0.0586369	+	0.332546i
$67$	11.9835	−	2.11301i	1.46401	−	0.258145i	0.615843	−	0.787869i	$-0.288816\pi$
$67$	11.9835	−	2.11301i	1.46401	−	0.258145i	0.848170	+	0.529724i	$0.177704\pi$
$68$	3.38036	+	1.95165i	0.409929	+	0.236673i
$69$	−2.54481	−	4.40775i	−0.306359	−	0.530630i
$70$	−4.51327	−	5.76089i	−0.539439	−	0.688558i
$71$	−10.7492	+	3.91240i	−1.27570	+	0.464316i	−0.889007	−	0.457893i	$-0.848604\pi$
$71$	−10.7492	+	3.91240i	−1.27570	+	0.464316i	−0.386691	+	0.922209i	$0.626382\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	4.09077	−	4.87518i	0.478788	−	0.570597i	−0.471541	−	0.881844i	$-0.656302\pi$
$73$	4.09077	−	4.87518i	0.478788	−	0.570597i	0.950329	+	0.311247i	$0.100747\pi$
$74$	0.548798	−	3.11239i	0.0637964	−	0.361808i
$75$	−0.335491	+	4.98873i	−0.0387392	+	0.576049i
$76$	4.19982	+	1.16684i	0.481752	+	0.133845i
$77$		−	8.97837i		−	1.02318i
$78$	4.87566	+	0.859711i	0.552060	+	0.0973431i
$79$	−0.515549	−	0.432597i	−0.0580038	−	0.0486710i	0.613325	−	0.789831i	$-0.289832\pi$
$79$	−0.515549	−	0.432597i	−0.0580038	−	0.0486710i	−0.671329	+	0.741160i	$0.734276\pi$
$80$	−0.834883	+	2.07436i	−0.0933428	+	0.231921i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−3.75746	−	4.47796i	−0.414942	−	0.494508i
$83$	−6.87753	+	3.97074i	−0.754907	+	0.435846i	−0.827464	−	0.561519i	$-0.810217\pi$
$83$	−6.87753	+	3.97074i	−0.754907	+	0.435846i	0.0725573	+	0.997364i	$0.476884\pi$
$84$	−1.63642	+	2.83436i	−0.178548	+	0.309254i
$85$	1.22622	+	8.64148i	0.133003	+	0.937301i
$86$	1.29689	+	7.35502i	0.139847	+	0.793112i
$87$	−4.23260	−	2.44369i	−0.453783	−	0.261991i
$88$	−2.37577	+	1.37165i	−0.253257	+	0.146218i
$89$	4.97213	−	4.17211i	0.527044	−	0.442243i	−0.340035	−	0.940413i	$-0.610439\pi$
$89$	4.97213	−	4.17211i	0.527044	−	0.442243i	0.867079	+	0.498170i	$0.165994\pi$
$90$	2.12570	−	0.693816i	0.224069	−	0.0731346i
$91$	−15.2263	−	5.54190i	−1.59614	−	0.580949i
$92$	3.27155	−	3.89888i	0.341083	−	0.406486i
$93$	−10.8862	−	1.91954i	−1.12885	−	0.199047i
$94$	−2.62513			−0.270762
$95$	3.73770	+	9.00164i	0.383480	+	0.923549i
$96$	1.00000			0.102062
$97$	10.0260	+	1.76786i	1.01799	+	0.179499i	0.657650	−	0.753323i	$-0.271550\pi$
$97$	10.0260	+	1.76786i	1.01799	+	0.179499i	0.360337	+	0.932822i	$0.382662\pi$
$98$	2.38570	−	2.84316i	0.240992	−	0.287203i
$99$	2.57786	+	0.938263i	0.259084	+	0.0942990i
$100$	−4.80262	+	1.39099i	−0.480262	+	0.139099i
$101$	−0.891722	+	0.748244i	−0.0887297	+	0.0744530i	−0.686074	−	0.727532i	$-0.740667\pi$
$101$	−0.891722	+	0.748244i	−0.0887297	+	0.0744530i	0.597344	+	0.801985i	$0.296223\pi$
$102$	3.38036	−	1.95165i	0.334705	−	0.193242i
$103$	−11.9285	−	6.88693i	−1.17535	−	0.678590i	−0.220417	−	0.975406i	$-0.570742\pi$
$103$	−11.9285	−	6.88693i	−1.17535	−	0.678590i	−0.954935	+	0.296816i	$0.904075\pi$
$104$	0.859711	+	4.87566i	0.0843016	+	0.478098i
$105$	−7.24571	+	1.02816i	−0.707109	+	0.100339i
$106$	−5.38426	+	9.32582i	−0.522966	+	0.905803i
$107$	−6.21349	+	3.58736i	−0.600681	+	0.346803i	−0.769309	−	0.638876i	$-0.779400\pi$
$107$	−6.21349	+	3.58736i	−0.600681	+	0.346803i	0.168628	+	0.985680i	$0.446066\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	1.67732	−	0.610495i	0.160658	−	0.0584748i	−0.260439	−	0.965490i	$-0.583867\pi$
$109$	1.67732	−	0.610495i	0.160658	−	0.0584748i	0.421097	+	0.907015i	$0.361645\pi$
$110$	−5.69059	−	2.29033i	−0.542576	−	0.218375i
$111$	−2.42101	−	2.03147i	−0.229792	−	0.192818i
$112$	−3.22312	−	0.568323i	−0.304556	−	0.0537015i
$113$		−	12.5610i		−	1.18164i	−0.806804	−	0.590820i	$-0.798804\pi$
$113$		−	12.5610i		−	1.18164i	0.806804	−	0.590820i	$-0.201196\pi$
$114$	3.11042	−	3.05373i	0.291318	−	0.286008i
$115$	11.3743	+	0.382029i	1.06066	+	0.0356244i
$116$	0.848686	−	4.81314i	0.0787985	−	0.446889i
$117$	3.18236	−	3.79259i	0.294210	−	0.350625i
$118$	4.39606	−	12.0781i	0.404691	−	1.11188i
$119$	−12.0045	+	4.36927i	−1.10045	+	0.400530i
$120$	1.37901	+	1.76021i	0.125886	+	0.160684i
$121$	1.73716	+	3.00885i	0.157924	+	0.273532i
$122$	9.90696	+	5.71978i	0.896934	+	0.517845i
$123$	−5.75676	+	1.01507i	−0.519069	+	0.0915260i
$124$	−1.91954	−	10.8862i	−0.172379	−	0.977612i
$125$	−9.07128	−	6.53544i	−0.811360	−	0.584547i
$126$	1.63642	+	2.83436i	0.145784	+	0.252505i
$127$	−9.13248	−	10.8837i	−0.810376	−	0.965769i	0.189494	−	0.981882i	$-0.439315\pi$
$127$	−9.13248	−	10.8837i	−0.810376	−	0.965769i	−0.999870	+	0.0161131i	$0.994871\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	7.01808	+	2.55437i	0.617907	+	0.224900i
$130$	−7.39665	+	8.23685i	−0.648729	+	0.722419i
$131$	−2.09510	+	11.8819i	−0.183050	+	1.03813i	0.745386	+	0.666633i	$0.232265\pi$
$131$	−2.09510	+	11.8819i	−0.183050	+	1.03813i	−0.928436	+	0.371494i	$0.878846\pi$
$132$			2.74330i			0.238773i
$133$	−11.7608	+	8.07482i	−1.01979	+	0.700176i
$134$	12.1683			1.05118
$135$	0.461990	−	2.18782i	0.0397618	−	0.188298i
$136$	2.99010	+	2.50899i	0.256399	+	0.215145i
$137$	3.77902	−	10.3828i	0.322863	−	0.887060i	−0.667003	−	0.745055i	$-0.732423\pi$
$137$	3.77902	−	10.3828i	0.322863	−	0.887060i	0.989866	−	0.142004i	$-0.0453547\pi$
$138$	−1.74075	−	4.78268i	−0.148183	−	0.407129i
$139$	9.16083	−	7.68685i	0.777012	−	0.651990i	−0.165482	−	0.986213i	$-0.552918\pi$
$139$	9.16083	−	7.68685i	0.777012	−	0.651990i	0.942494	+	0.334222i	$0.108474\pi$
$140$	−3.44434	−	6.45709i	−0.291100	−	0.545723i
$141$	−1.31257	+	2.27343i	−0.110538	+	0.191457i
$142$	−11.2653	+	1.98638i	−0.945363	+	0.166693i
$143$	−13.3754	+	2.35844i	−1.11851	+	0.197223i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	9.64248	−	5.14348i	0.800764	−	0.427143i
$146$	4.87518	−	4.09077i	0.403473	−	0.338554i
$147$	−1.26940	−	3.48765i	−0.104699	−	0.287657i
$148$	1.08092	−	2.96980i	0.0888511	−	0.244116i
$149$	−9.21996	−	7.73646i	−0.755328	−	0.633796i	0.181578	−	0.983377i	$-0.441880\pi$
$149$	−9.21996	−	7.73646i	−0.755328	−	0.633796i	−0.936906	+	0.349581i	$0.886324\pi$
$150$	−1.19668	+	4.85468i	−0.0977084	+	0.396383i
$151$	11.5780			0.942203			0.471102	−	0.882079i	$-0.343857\pi$
$151$	11.5780			0.942203			0.471102	+	0.882079i	$0.343857\pi$
$152$	3.93340	+	1.87840i	0.319041	+	0.152359i
$153$		−	3.90330i		−	0.315563i
$154$	1.55908	−	8.84197i	0.125634	−	0.712506i
$155$	16.5150	−	18.3910i	1.32652	−	1.47720i
$156$	4.65231	+	1.69330i	0.372483	+	0.135573i
$157$	4.92665	+	13.5359i	0.393190	+	1.08028i	0.965536	+	0.260268i	$0.0838109\pi$
$157$	4.92665	+	13.5359i	0.393190	+	1.08028i	−0.572347	+	0.820012i	$0.693967\pi$
$158$	−0.432597	−	0.515549i	−0.0344156	−	0.0410149i
$159$	5.38426	+	9.32582i	0.427000	+	0.739585i
$160$	−1.18241	+	1.89787i	−0.0934776	+	0.150040i
$161$	2.89255	+	16.4045i	0.227965	+	1.29285i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	13.4031	+	7.73828i	1.04981	+	0.606109i	0.922596	−	0.385767i	$-0.126063\pi$
$163$	13.4031	+	7.73828i	1.04981	+	0.606109i	0.127214	+	0.991875i	$0.459396\pi$
$164$	−2.92278	−	5.06241i	−0.228231	−	0.395308i
$165$	−4.82878	+	3.78303i	−0.375920	+	0.294508i
$166$	−7.46256	+	2.71615i	−0.579207	+	0.210814i
$167$	−0.781238	+	2.14643i	−0.0604540	+	0.166096i	−0.966243	−	0.257634i	$-0.917057\pi$
$167$	−0.781238	+	2.14643i	−0.0604540	+	0.166096i	0.905789	+	0.423730i	$0.139279\pi$
$168$	−2.10374	+	2.50714i	−0.162307	+	0.193430i
$169$	−1.99890	+	11.3363i	−0.153762	+	0.872025i
$170$	−0.292983	+	8.72313i	−0.0224708	+	0.669034i
$171$	−1.08940	−	4.22057i	−0.0833084	−	0.322755i
$172$			7.46848i			0.569466i
$173$	−8.64097	−	1.52364i	−0.656961	−	0.115840i	−0.164777	−	0.986331i	$-0.552690\pi$
$173$	−8.64097	−	1.52364i	−0.656961	−	0.115840i	−0.492184	+	0.870491i	$0.663801\pi$
$174$	−3.74396	−	3.14155i	−0.283829	−	0.238160i
$175$	6.61606	−	14.9671i	0.500127	−	1.13141i
$176$	−2.57786	+	0.938263i	−0.194313	+	0.0707242i
$177$	−8.26190	−	9.84615i	−0.621002	−	0.740082i
$178$	5.62107	−	3.24533i	0.421317	−	0.243247i
$179$	9.58236	−	16.5971i	0.716219	−	1.24053i	−0.246269	−	0.969202i	$-0.579205\pi$
$179$	9.58236	−	16.5971i	0.716219	−	1.24053i	0.962488	−	0.271326i	$-0.0874621\pi$
$180$	2.21389	−	0.314150i	0.165014	−	0.0234154i
$181$	2.81419	+	15.9601i	0.209177	+	1.18630i	0.890730	+	0.454533i	$0.150194\pi$
$181$	2.81419	+	15.9601i	0.209177	+	1.18630i	−0.681553	+	0.731769i	$0.738695\pi$
$182$	−14.0326	−	8.10172i	−1.04016	−	0.600539i
$183$	9.90696	−	5.71978i	0.732343	−	0.422819i
$184$	3.89888	−	3.27155i	0.287429	−	0.241182i
$185$	6.71808	−	2.19273i	0.493923	−	0.161213i
$186$	−10.3875	−	3.78075i	−0.761650	−	0.277218i
$187$	−6.88292	+	8.20274i	−0.503329	+	0.599844i
$188$	−2.58525	−	0.455849i	−0.188549	−	0.0332462i
$189$	3.27284			0.238064
$190$	2.11780	+	9.51393i	0.153641	+	0.690213i
$191$	12.7051			0.919307			0.459653	−	0.888098i	$-0.347974\pi$
$191$	12.7051			0.919307			0.459653	+	0.888098i	$0.347974\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	8.03106	−	9.57104i	0.578088	−	0.688939i	−0.395182	−	0.918603i	$-0.629318\pi$
$193$	8.03106	−	9.57104i	0.578088	−	0.688939i	0.973270	+	0.229664i	$0.0737628\pi$
$194$	9.56671	+	3.48200i	0.686850	+	0.249993i
$195$	3.43500	+	10.5241i	0.245985	+	0.753647i
$196$	2.84316	−	2.38570i	0.203083	−	0.170407i
$197$	−16.1974	+	9.35155i	−1.15401	+	0.666270i	−0.949862	−	0.312669i	$-0.898777\pi$
$197$	−16.1974	+	9.35155i	−1.15401	+	0.666270i	−0.204151	+	0.978939i	$0.565444\pi$
$198$	2.37577	+	1.37165i	0.168838	+	0.0974788i
$199$	−2.85494	−	16.1912i	−0.202381	−	1.14776i	−0.901507	−	0.432764i	$-0.857538\pi$
$199$	−2.85494	−	16.1912i	−0.202381	−	1.14776i	0.699126	−	0.714999i	$-0.253573\pi$
$200$	−4.97120	+	0.535890i	−0.351517	+	0.0378932i
$201$	6.08417	−	10.5381i	0.429144	−	0.743299i
$202$	−1.00811	+	0.582030i	−0.0709301	+	0.0409515i
$203$	10.2818	+	12.2534i	0.721641	+	0.860018i
$204$	3.66791	−	1.33501i	0.256805	−	0.0934693i
$205$	4.88036	−	12.1258i	0.340859	−	0.846903i
$206$	−10.5514	−	8.85367i	−0.735151	−	0.616865i
$207$	−5.01230	−	0.883804i	−0.348379	−	0.0614286i
$208$			4.95088i			0.343282i
$209$	−5.15301	+	10.7905i	−0.356441	+	0.746393i
$210$	−7.31417	−	0.245661i	−0.504726	−	0.0169522i
$211$	2.07846	−	11.7875i	0.143087	−	0.811487i	−0.825796	−	0.563969i	$-0.809274\pi$
$211$	2.07846	−	11.7875i	0.143087	−	0.811487i	0.968883	−	0.247518i	$-0.0796150\pi$
$212$	−6.92187	+	8.24917i	−0.475396	+	0.566555i
$213$	−3.91240	+	10.7492i	−0.268073	+	0.736525i
$214$	−6.74203	+	2.45390i	−0.460876	+	0.167745i
$215$	−13.1461	+	10.2991i	−0.896556	+	0.702392i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	31.3315	+	18.0893i	2.12692	+	1.22798i
$218$	1.75785	−	0.309957i	0.119057	−	0.0209929i
$219$	−1.10511	−	6.26742i	−0.0746767	−	0.423513i
$220$	−5.20642	−	3.24370i	−0.351017	−	0.218690i
$221$	9.66239	+	16.7358i	0.649963	+	1.12577i
$222$	−2.03147	−	2.42101i	−0.136343	−	0.162487i
$223$	0.451639	+	1.24087i	0.0302440	+	0.0830946i	0.953896	−	0.300138i	$-0.0970329\pi$
$223$	0.451639	+	1.24087i	0.0302440	+	0.0830946i	−0.923652	+	0.383233i	$0.874811\pi$
$224$	−3.07546	−	1.11938i	−0.205488	−	0.0747915i
$225$	3.60594	+	3.46370i	0.240396	+	0.230913i
$226$	2.18120	−	12.3702i	0.145091	−	0.822852i
$227$		−	10.5757i		−	0.701933i	−0.936388	−	0.350966i	$-0.885853\pi$
$227$		−	10.5757i		−	0.701933i	0.936388	−	0.350966i	$-0.114147\pi$
$228$	3.59344	−	2.46722i	0.237981	−	0.163396i
$229$	0.382704			0.0252898			0.0126449	−	0.999920i	$-0.495975\pi$
$229$	0.382704			0.0252898			0.0126449	+	0.999920i	$0.495975\pi$
$230$	11.1352	+	2.35136i	0.734233	+	0.155044i
$231$	−6.87783	−	5.77119i	−0.452528	−	0.379716i
$232$	1.67158	−	4.59264i	0.109745	−	0.301522i
$233$	−1.05220	−	2.89088i	−0.0689316	−	0.189388i	0.900443	−	0.434973i	$-0.143242\pi$
$233$	−1.05220	−	2.89088i	−0.0689316	−	0.189388i	−0.969375	+	0.245585i	$0.921020\pi$
$234$	3.79259	−	3.18236i	0.247930	−	0.208038i
$235$	−2.76269	−	5.17920i	−0.180218	−	0.337854i
$236$	6.42662	−	11.1312i	0.418337	−	0.724581i
$237$	−0.662777	+	0.116866i	−0.0430520	+	0.00759123i
$238$	−12.5808	+	2.21834i	−0.815493	+	0.143793i
$239$	3.33035	−	5.76833i	0.215422	−	0.373122i	−0.737981	−	0.674822i	$-0.764221\pi$
$239$	3.33035	−	5.76833i	0.215422	−	0.373122i	0.953403	+	0.301699i	$0.0975539\pi$
$240$	1.05240	+	1.97293i	0.0679321	+	0.127352i
$241$	−12.6122	+	10.5829i	−0.812425	+	0.681705i	−0.951185	−	0.308621i	$-0.900133\pi$
$241$	−12.6122	+	10.5829i	−0.812425	+	0.681705i	0.138760	+	0.990326i	$0.455688\pi$
$242$	1.18829	+	3.26479i	0.0763860	+	0.209869i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	8.76322	+	7.35321i	0.561008	+	0.470741i
$245$	8.12007	+	1.71467i	0.518772	+	0.109546i
$246$	−5.84557			−0.372700
$247$	15.1187	+	15.3993i	0.961977	+	0.979835i
$248$		−	11.0542i		−	0.701940i
$249$	−1.37902	+	7.82084i	−0.0873921	+	0.495625i
$250$	−7.79860	−	8.01136i	−0.493227	−	0.506683i
$251$	−12.1120	−	4.40840i	−0.764501	−	0.278255i	−0.0698063	−	0.997561i	$-0.522238\pi$
$251$	−12.1120	−	4.40840i	−0.764501	−	0.278255i	−0.694694	+	0.719305i	$0.744460\pi$
$252$	1.11938	+	3.07546i	0.0705141	+	0.193736i
$253$	8.97483	+	10.6958i	0.564243	+	0.672438i
$254$	−7.10381	−	12.3042i	−0.445732	−	0.772031i
$255$	7.40796	+	4.61530i	0.463905	+	0.289021i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−16.4468	+	2.90001i	−1.02592	+	0.180898i	−0.661193	−	0.750216i	$-0.729950\pi$
$257$	−16.4468	+	2.90001i	−1.02592	+	0.180898i	−0.364729	+	0.931114i	$0.618838\pi$
$258$	6.46789	+	3.73424i	0.402673	+	0.232484i
$259$	5.17174	+	8.95772i	0.321356	+	0.556606i
$260$	−8.71459	+	6.82730i	−0.540456	+	0.423411i
$261$	−4.59264	+	1.67158i	−0.284277	+	0.103469i
$262$	−4.12654	+	11.3376i	−0.254939	+	0.700438i
$263$	−7.61999	+	9.08116i	−0.469869	+	0.559968i	−0.947979	−	0.318332i	$-0.896877\pi$
$263$	−7.61999	+	9.08116i	−0.469869	+	0.559968i	0.478110	+	0.878300i	$0.341322\pi$
$264$	−0.476369	+	2.70162i	−0.0293185	+	0.166273i
$265$	−24.0656	−	0.808289i	−1.47834	−	0.0496528i
$266$	−12.9843	+	5.90991i	−0.796116	+	0.362360i
$267$		−	6.49065i		−	0.397221i
$268$	11.9835	+	2.11301i	0.732007	+	0.129073i
$269$	4.63589	+	3.88997i	0.282655	+	0.237176i	0.773081	−	0.634307i	$-0.218714\pi$
$269$	4.63589	+	3.88997i	0.282655	+	0.237176i	−0.490426	+	0.871483i	$0.663159\pi$
$270$	0.834883	−	2.07436i	0.0508094	−	0.126242i
$271$	−12.4771	+	4.54128i	−0.757927	+	0.275863i	−0.691937	−	0.721957i	$-0.743243\pi$
$271$	−12.4771	+	4.54128i	−0.757927	+	0.275863i	−0.0659896	+	0.997820i	$0.521020\pi$
$272$	2.50899	+	2.99010i	0.152130	+	0.181302i
$273$	−14.0326	+	8.10172i	−0.849291	+	0.490338i
$274$	5.52455	−	9.56881i	0.333751	−	0.578073i
$275$	−1.47011	−	13.6375i	−0.0886507	−	0.822371i
$276$	−0.883804	−	5.01230i	−0.0531988	−	0.301705i
$277$	4.12227	+	2.37999i	0.247683	+	0.143000i	0.618703	−	0.785625i	$-0.287658\pi$
$277$	4.12227	+	2.37999i	0.247683	+	0.143000i	−0.371020	+	0.928625i	$0.620992\pi$
$278$	10.3565	−	5.97931i	0.621140	−	0.358615i
$279$	−8.46798	+	7.10548i	−0.506965	+	0.425394i
$280$	−2.27075	−	6.95709i	−0.135703	−	0.415766i
$281$	10.2681	+	3.73728i	0.612543	+	0.222947i	0.629615	−	0.776907i	$-0.283212\pi$
$281$	10.2681	+	3.73728i	0.612543	+	0.222947i	−0.0170727	+	0.999854i	$0.505435\pi$
$282$	−1.68740	+	2.01097i	−0.100483	+	0.119751i
$283$	−16.5801	−	2.92352i	−0.985583	−	0.173785i	−0.342447	−	0.939537i	$-0.611256\pi$
$283$	−16.5801	−	2.92352i	−0.985583	−	0.173785i	−0.643136	+	0.765752i	$0.722367\pi$
$284$	−11.4391			−0.678785
$285$	9.29821	+	2.92290i	0.550778	+	0.173138i
$286$	−13.5817			−0.803105
$287$	18.8410	+	3.32217i	1.11215	+	0.196101i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	−1.65783	−	0.603400i	−0.0975194	−	0.0354941i
$290$	10.3891	−	3.39095i	0.610071	−	0.199123i
$291$	7.79886	−	6.54402i	0.457177	−	0.383617i
$292$	5.51147	−	3.18205i	0.322535	−	0.186215i
$293$	12.1629	+	7.02225i	0.710564	+	0.410244i	0.811270	−	0.584672i	$-0.198777\pi$
$293$	12.1629	+	7.02225i	0.710564	+	0.410244i	−0.100706	+	0.994916i	$0.532110\pi$
$294$	−0.644492	−	3.65510i	−0.0375876	−	0.213170i
$295$	28.4556	−	4.03785i	1.65675	−	0.235093i
$296$	1.58020	−	2.73699i	0.0918473	−	0.159084i
$297$	2.37577	−	1.37165i	0.137856	−	0.0795911i
$298$	−7.73646	−	9.21996i	−0.448161	−	0.534098i
$299$	23.6785	−	8.61827i	1.36936	−	0.498407i
$300$	−2.02151	+	4.57313i	−0.116712	+	0.264030i
$301$	−18.7245	−	15.7117i	−1.07926	−	0.905610i
$302$	11.4021	+	2.01050i	0.656117	+	0.115691i
$303$			1.16406i			0.0668735i
$304$	3.54746	+	2.53289i	0.203461	+	0.145271i
$305$	−0.858658	+	25.5652i	−0.0491666	+	1.46386i
$306$	0.677801	−	3.84400i	0.0387473	−	0.219747i
$307$	−8.79814	+	10.4852i	−0.502136	+	0.598423i	−0.956261	−	0.292515i	$-0.905508\pi$
$307$	−8.79814	+	10.4852i	−0.502136	+	0.598423i	0.454124	+	0.890938i	$0.349952\pi$
$308$	3.07078	−	8.43691i	0.174974	−	0.480738i
$309$	−12.9432	+	4.71094i	−0.736313	+	0.267996i
$310$	19.4577	−	15.2438i	1.10512	−	0.865788i
$311$	13.6733	+	23.6829i	0.775344	+	1.34294i	0.934601	+	0.355698i	$0.115757\pi$
$311$	13.6733	+	23.6829i	0.775344	+	1.34294i	−0.159257	+	0.987237i	$0.550910\pi$
$312$	4.28759	+	2.47544i	0.242737	+	0.140144i
$313$	−24.0529	+	4.24118i	−1.35955	+	0.239726i	−0.805421	−	0.592704i	$-0.798061\pi$
$313$	−24.0529	+	4.24118i	−1.35955	+	0.239726i	−0.554131	+	0.832429i	$0.686949\pi$
$314$	2.50133	+	14.1857i	0.141158	+	0.800547i
$315$	−3.86983	+	6.21143i	−0.218040	+	0.349974i
$316$	−0.336501	−	0.582837i	−0.0189297	−	0.0327871i
$317$	−14.8008	−	17.6389i	−0.831296	−	0.990700i	−0.999987	−	0.00503066i	$-0.998399\pi$
$317$	−14.8008	−	17.6389i	−0.831296	−	0.990700i	0.168692	−	0.985669i	$-0.446046\pi$
$318$	3.68305	+	10.1191i	0.206535	+	0.567451i
$319$	12.5990	+	4.58565i	0.705408	+	0.256747i
$320$	−1.49401	+	1.66371i	−0.0835175	+	0.0930045i
$321$	−1.24588	+	7.06572i	−0.0695381	+	0.394370i
$322$			16.6575i			0.928288i
$323$	16.9350	+	1.63868i	0.942289	+	0.0911787i
$324$	−1.00000			−0.0555556
$325$	−24.0350	−	5.92461i	−1.33322	−	0.328638i
$326$	11.8557	+	9.94814i	0.656628	+	0.550976i
$327$	0.610495	−	1.67732i	0.0337605	−	0.0927561i
$328$	−1.99930	−	5.49304i	−0.110393	−	0.303302i
$329$	6.58157	−	5.52260i	0.362854	−	0.304471i
$330$	−5.41233	+	2.88705i	−0.297939	+	0.158927i
$331$	−13.5514	+	23.4718i	−0.744854	+	1.29013i	0.205409	+	0.978676i	$0.434148\pi$
$331$	−13.5514	+	23.4718i	−0.744854	+	1.29013i	−0.950263	+	0.311449i	$0.899186\pi$
$332$	−7.82084	+	1.37902i	−0.429224	+	0.0756838i
$333$	−3.11239	+	0.548798i	−0.170558	+	0.0300739i
$334$	−1.14209	+	1.97816i	−0.0624926	+	0.108240i
$335$	12.8059	+	24.0073i	0.699664	+	1.31166i
$336$	−2.50714	+	2.10374i	−0.136776	+	0.114768i
$337$	7.03763	+	19.3357i	0.383364	+	1.05328i	0.969930	+	0.243383i	$0.0782572\pi$
$337$	7.03763	+	19.3357i	0.383364	+	1.05328i	−0.586566	+	0.809901i	$0.699521\pi$
$338$	−3.93707	+	10.8170i	−0.214148	+	0.588367i
$339$	−9.62229	−	8.07406i	−0.522611	−	0.438523i
$340$	−1.80329	+	8.53973i	−0.0977970	+	0.463132i
$341$	30.3249			1.64218
$342$	−0.339955	−	4.34562i	−0.0183826	−	0.234984i
$343$		−	10.7628i		−	0.581136i
$344$	−1.29689	+	7.35502i	−0.0699235	+	0.396556i
$345$	7.60393	−	8.46768i	0.409382	−	0.455885i
$346$	−8.24512	−	3.00098i	−0.443260	−	0.161334i
$347$	6.22446	+	17.1016i	0.334147	+	0.918060i	0.987021	+	0.160594i	$0.0513409\pi$
$347$	6.22446	+	17.1016i	0.334147	+	0.918060i	−0.652874	+	0.757466i	$0.726437\pi$
$348$	−3.14155	−	3.74396i	−0.168405	−	0.200697i
$349$	8.51625	+	14.7506i	0.455864	+	0.789580i	0.998737	−	0.0502346i	$-0.0159969\pi$
$349$	8.51625	+	14.7506i	0.455864	+	0.789580i	−0.542873	+	0.839815i	$0.682664\pi$
$350$	9.11456	−	13.5909i	0.487194	−	0.726463i
$351$	−0.859711	−	4.87566i	−0.0458880	−	0.260244i
$352$	−2.70162	+	0.476369i	−0.143997	+	0.0253905i
$353$	0.214876	+	0.124059i	0.0114367	+	0.00660298i	0.505707	−	0.862705i	$-0.331232\pi$
$353$	0.214876	+	0.124059i	0.0114367	+	0.00660298i	−0.494271	+	0.869308i	$0.664565\pi$
$354$	−6.42662	−	11.1312i	−0.341571	−	0.591618i
$355$	−15.7746	−	20.1352i	−0.837228	−	1.06867i
$356$	6.09922	−	2.21993i	0.323258	−	0.117656i
$357$	−4.36927	+	12.0045i	−0.231246	+	0.635344i
$358$	12.3188	−	14.6810i	0.651071	−	0.775916i
$359$	2.21568	−	12.5657i	0.116939	−	0.663193i	−0.868833	−	0.495105i	$-0.835130\pi$
$359$	2.21568	−	12.5657i	0.116939	−	0.663193i	0.985772	−	0.168088i	$-0.0537593\pi$
$360$	2.23481	+	0.0750603i	0.117785	+	0.00395603i
$361$	18.7689	−	2.95463i	0.987835	−	0.155507i
$362$			16.2063i			0.851783i
$363$	3.42154	+	0.603309i	0.179584	+	0.0316655i
$364$	−12.4126	−	10.4154i	−0.650595	−	0.545914i
$365$	13.2014	+	5.31328i	0.690995	+	0.278110i
$366$	10.7497	−	3.91256i	0.561895	−	0.204513i
$367$	−0.732345	−	0.872774i	−0.0382281	−	0.0455585i	0.746592	−	0.665283i	$-0.231689\pi$
$367$	−0.732345	−	0.872774i	−0.0382281	−	0.0455585i	−0.784820	+	0.619724i	$0.787244\pi$
$368$	4.40775	−	2.54481i	0.229770	−	0.132658i
$369$	−2.92278	+	5.06241i	−0.152154	+	0.263538i
$370$	6.99678	−	0.992840i	0.363745	−	0.0516153i
$371$	−6.12000	−	34.7082i	−0.317734	−	1.80196i
$372$	−9.57319	−	5.52708i	−0.496347	−	0.286566i
$373$	6.15301	−	3.55244i	0.318591	−	0.183939i	−0.332173	−	0.943218i	$-0.607782\pi$
$373$	6.15301	−	3.55244i	0.318591	−	0.183939i	0.650764	+	0.759280i	$0.274449\pi$
$374$	−8.20274	+	6.88292i	−0.424154	+	0.355907i
$375$	−10.8373	+	2.74811i	−0.559638	+	0.141912i
$376$	−2.46682	−	0.897848i	−0.127216	−	0.0463030i
$377$	15.5534	−	18.5359i	0.801043	−	0.954646i
$378$	3.22312	+	0.568323i	0.165779	+	0.0292314i
$379$	−16.7214			−0.858920			−0.429460	−	0.903086i	$-0.641296\pi$
$379$	−16.7214			−0.858920			−0.429460	+	0.903086i	$0.641296\pi$
$380$	0.433549	+	9.73715i	0.0222406	+	0.499505i
$381$	−14.2076			−0.727878
$382$	12.5121	+	2.20621i	0.640172	+	0.112880i
$383$	−10.5431	+	12.5647i	−0.538726	+	0.642028i	−0.964902	−	0.262612i	$-0.915416\pi$
$383$	−10.5431	+	12.5647i	−0.538726	+	0.642028i	0.426176	+	0.904640i	$0.359861\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	19.0854	−	6.22934i	0.972681	−	0.317476i
$386$	9.57104	−	8.03106i	0.487153	−	0.408770i
$387$	6.46789	−	3.73424i	0.328782	−	0.189822i
$388$	8.81673	+	5.09034i	0.447602	+	0.258423i
$389$	0.863026	+	4.89447i	0.0437572	+	0.248159i	0.998838	−	0.0481848i	$-0.0153436\pi$
$389$	0.863026	+	4.89447i	0.0437572	+	0.248159i	−0.955081	+	0.296344i	$0.904233\pi$
$390$	1.55532	+	10.9607i	0.0787567	+	0.555017i
$391$	9.93318	−	17.2048i	0.502342	−	0.870082i
$392$	3.21424	−	1.85574i	0.162344	−	0.0937291i
$393$	7.75536	+	9.24248i	0.391206	+	0.466222i
$394$	−17.5752	+	6.39683i	−0.885424	+	0.322268i
$395$	0.561878	−	1.39605i	0.0282711	−	0.0702428i
$396$	2.10149	+	1.76336i	0.105604	+	0.0886120i
$397$	1.91789	+	0.338176i	0.0962562	+	0.0169726i	0.221569	−	0.975145i	$-0.428882\pi$
$397$	1.91789	+	0.338176i	0.0962562	+	0.0169726i	−0.125313	+	0.992117i	$0.539993\pi$
$398$		−	16.4410i		−	0.824111i
$399$	−1.37400	+	14.1997i	−0.0687861	+	0.710872i
$400$	−4.98873	−	0.335491i	−0.249437	−	0.0167745i
$401$	4.89599	−	27.7666i	0.244494	−	1.38660i	−0.577170	−	0.816624i	$-0.695843\pi$
$401$	4.89599	−	27.7666i	0.244494	−	1.38660i	0.821664	−	0.569972i	$-0.193046\pi$
$402$	7.82165	−	9.32148i	0.390109	−	0.464913i
$403$	18.7180	−	51.4274i	0.932411	−	2.56178i
$404$	−1.09386	+	0.398132i	−0.0544215	+	0.0198078i
$405$	−1.37901	−	1.76021i	−0.0685234	−	0.0874655i
$406$	7.99782	+	13.8526i	0.396925	+	0.687494i
$407$	7.50837	+	4.33496i	0.372176	+	0.214876i
$408$	3.84400	−	0.677801i	0.190307	−	0.0335562i
$409$	−3.25309	−	18.4492i	−0.160855	−	0.912254i	−0.953236	−	0.302227i	$-0.902270\pi$
$409$	−3.25309	−	18.4492i	−0.160855	−	0.912254i	0.792381	−	0.610027i	$-0.208841\pi$
$410$	6.91184	−	11.0941i	0.341352	−	0.547900i
$411$	−5.52455	−	9.56881i	−0.272506	−	0.471995i
$412$	−8.85367	−	10.5514i	−0.436189	−	0.519830i
$413$	14.3876	+	39.5297i	0.707968	+	1.94513i
$414$	−4.78268	−	1.74075i	−0.235056	−	0.0855534i
$415$	−13.2124	−	11.8646i	−0.648569	−	0.582412i
$416$	−0.859711	+	4.87566i	−0.0421508	+	0.239049i
$417$		−	11.9586i		−	0.585616i
$418$	−6.94847	+	9.73173i	−0.339861	+	0.475995i
$419$	−11.5186			−0.562721			−0.281361	−	0.959602i	$-0.590786\pi$
$419$	−11.5186			−0.562721			−0.281361	+	0.959602i	$0.590786\pi$
$420$	−7.16039	−	1.51202i	−0.349391	−	0.0737790i
$421$	−1.17418	−	0.985252i	−0.0572259	−	0.0480182i	0.613726	−	0.789519i	$-0.289670\pi$
$421$	−1.17418	−	0.985252i	−0.0572259	−	0.0480182i	−0.670952	+	0.741501i	$0.734114\pi$
$422$	4.09376	−	11.2475i	0.199281	−	0.547521i
$423$	0.897848	+	2.46682i	0.0436549	+	0.119941i
$424$	−8.24917	+	6.92187i	−0.400615	+	0.336156i
$425$	−17.5185	+	8.60219i	−0.849771	+	0.417267i
$426$	−5.71954	+	9.90654i	−0.277113	+	0.479973i
$427$	−36.8711	+	6.50137i	−1.78432	+	0.314623i
$428$	−7.06572	+	1.24588i	−0.341535	+	0.0602218i
$429$	−6.79087	+	11.7621i	−0.327866	+	0.567881i
$430$	−14.7348	+	7.85983i	−0.710575	+	0.379035i
$431$	15.1467	−	12.7096i	0.729591	−	0.612199i	−0.200429	−	0.979708i	$-0.564234\pi$
$431$	15.1467	−	12.7096i	0.729591	−	0.612199i	0.930020	+	0.367509i	$0.119789\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	−11.7615	+	32.3144i	−0.565222	+	1.55293i	0.246655	+	0.969103i	$0.420669\pi$
$433$	−11.7615	+	32.3144i	−0.565222	+	1.55293i	−0.811876	+	0.583830i	$0.801554\pi$
$434$	27.7144	+	23.2551i	1.33033	+	1.11628i
$435$	2.25793	−	10.6927i	0.108259	−	0.512677i
$436$	1.78497			0.0854845
$437$	5.93877	−	21.3755i	0.284090	−	1.02253i
$438$		−	6.36410i		−	0.304089i
$439$	−6.24813	+	35.4349i	−0.298207	+	1.69121i	0.355668	+	0.934612i	$0.384253\pi$
$439$	−6.24813	+	35.4349i	−0.298207	+	1.69121i	−0.653875	+	0.756603i	$0.726858\pi$
$440$	−4.56406	−	4.09850i	−0.217583	−	0.195388i
$441$	−3.48765	−	1.26940i	−0.166079	−	0.0604477i
$442$	6.60947	+	18.1594i	0.314380	+	0.863753i
$443$	−8.21900	−	9.79502i	−0.390496	−	0.465376i	0.534601	−	0.845104i	$-0.320462\pi$
$443$	−8.21900	−	9.79502i	−0.390496	−	0.465376i	−0.925098	+	0.379729i	$0.876017\pi$
$444$	−1.58020	−	2.73699i	−0.0749930	−	0.129892i
$445$	12.3184	+	7.67460i	0.583949	+	0.363811i
$446$	0.229303	+	1.30044i	0.0108578	+	0.0615777i
$447$	−11.8529	+	2.08999i	−0.560625	+	0.0988534i
$448$	−2.83436	−	1.63642i	−0.133911	−	0.0773136i
$449$	9.93480	+	17.2076i	0.468852	+	0.812076i	0.999366	−	0.0356001i	$-0.0113343\pi$
$449$	9.93480	+	17.2076i	0.468852	+	0.812076i	−0.530514	+	0.847676i	$0.678001\pi$
$450$	2.94969	+	4.03724i	0.139050	+	0.190317i
$451$	15.0690	−	5.48468i	0.709573	−	0.258263i
$452$	4.29612	−	11.8035i	0.202072	−	0.555189i
$453$	7.44219	−	8.86925i	0.349664	−	0.416714i
$454$	1.83645	−	10.4150i	0.0861888	−	0.488801i
$455$	1.21624	−	36.2116i	0.0570180	−	1.69762i
$456$	3.96728	−	1.80574i	0.185785	−	0.0845617i
$457$			17.6625i			0.826215i	0.910682	+	0.413107i	$0.135557\pi$
$457$			17.6625i			0.826215i	−0.910682	+	0.413107i	$0.864443\pi$
$458$	0.376890	+	0.0664559i	0.0176109	+	0.00310528i
$459$	−2.99010	−	2.50899i	−0.139566	−	0.117110i
$460$	10.5577	+	4.24924i	0.492256	+	0.198122i
$461$	−11.6136	+	4.22699i	−0.540897	+	0.196870i	−0.597997	−	0.801498i	$-0.704037\pi$
$461$	−11.6136	+	4.22699i	−0.540897	+	0.196870i	0.0571003	+	0.998368i	$0.481815\pi$
$462$	−5.77119	−	6.87783i	−0.268500	−	0.319986i
$463$	−16.5546	+	9.55783i	−0.769359	+	0.444190i	−0.832646	−	0.553805i	$-0.813175\pi$
$463$	−16.5546	+	9.55783i	−0.769359	+	0.444190i	0.0632866	+	0.997995i	$0.479842\pi$
$464$	2.44369	−	4.23260i	0.113446	−	0.196494i
$465$	−3.47267	−	24.4727i	−0.161041	−	1.13489i
$466$	−0.534214	−	3.02968i	−0.0247470	−	0.140347i
$467$	5.32115	+	3.07217i	0.246233	+	0.142163i	0.618038	−	0.786148i	$-0.287928\pi$
$467$	5.32115	+	3.07217i	0.246233	+	0.142163i	−0.371805	+	0.928311i	$0.621261\pi$
$468$	4.28759	−	2.47544i	0.198194	−	0.114427i
$469$	−30.5077	+	25.5990i	−1.40872	+	1.18205i
$470$	−1.82136	−	5.58025i	−0.0840129	−	0.257398i
$471$	13.5359	+	4.92665i	0.623700	+	0.227008i
$472$	8.26190	−	9.84615i	0.380285	−	0.453206i
$473$	−20.1770	−	3.55775i	−0.927739	−	0.163585i
$474$	−0.673002			−0.0309120
$475$	−16.5416	+	14.1907i	−0.758979	+	0.651116i
$476$	−12.7749			−0.585536
$477$	10.6049	+	1.86993i	0.485566	+	0.0856184i
$478$	4.28141	−	5.10238i	0.195827	−	0.233378i
$479$	−9.06320	−	3.29874i	−0.414108	−	0.150723i	0.126560	−	0.991959i	$-0.459606\pi$
$479$	−9.06320	−	3.29874i	−0.414108	−	0.150723i	−0.540668	+	0.841236i	$0.681829\pi$
$480$	0.693816	+	2.12570i	0.0316682	+	0.0970247i
$481$	11.9861	−	10.0575i	0.546520	−	0.458584i
$482$	−14.2583	+	8.23204i	−0.649449	+	0.374959i
$483$	14.4258	+	8.32877i	0.656399	+	0.378972i
$484$	0.603309	+	3.42154i	0.0274232	+	0.155524i
$485$	3.19827	+	22.5389i	0.145226	+	1.02344i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−27.0128	+	15.5958i	−1.22407	+	0.706715i	−0.965782	−	0.259354i	$-0.916491\pi$
$487$	−27.0128	+	15.5958i	−1.22407	+	0.706715i	−0.258284	+	0.966069i	$0.583157\pi$
$488$	7.35321	+	8.76322i	0.332864	+	0.396692i
$489$	14.5432	−	5.29329i	0.657666	−	0.239371i
$490$	7.69895	+	3.09865i	0.347803	+	0.139983i
$491$	22.0689	+	18.5180i	0.995956	+	0.835706i	0.986419	−	0.164248i	$-0.0525198\pi$
$491$	22.0689	+	18.5180i	0.995956	+	0.835706i	0.00953683	+	0.999955i	$0.496964\pi$
$492$	−5.75676	−	1.01507i	−0.259535	−	0.0457630i
$493$		−	19.0770i		−	0.859183i
$494$	12.2149	+	17.7907i	0.549575	+	0.800441i
$495$	−0.205913	+	6.13074i	−0.00925509	+	0.275556i
$496$	1.91954	−	10.8862i	0.0861897	−	0.488806i
$497$	24.0649	−	28.6794i	1.07946	−	1.28645i
$498$	−2.71615	+	7.46256i	−0.121714	+	0.334405i
$499$	26.6514	−	9.70033i	1.19308	−	0.434246i	0.332277	−	0.943182i	$-0.392183\pi$
$499$	26.6514	−	9.70033i	1.19308	−	0.434246i	0.860805	+	0.508935i	$0.169961\pi$
$500$	−6.28896	−	9.24386i	−0.281251	−	0.413398i
$501$	1.14209	+	1.97816i	0.0510250	+	0.0883778i
$502$	−11.1624	−	6.44464i	−0.498204	−	0.287638i
$503$	−2.48362	+	0.437929i	−0.110739	+	0.0195263i	−0.228743	−	0.973487i	$-0.573462\pi$
$503$	−2.48362	+	0.437929i	−0.110739	+	0.0195263i	0.118004	+	0.993013i	$0.462350\pi$
$504$	0.568323	+	3.22312i	0.0253151	+	0.143569i
$505$	−2.20924	−	1.37639i	−0.0983097	−	0.0612488i
$506$	6.98118	+	12.0918i	0.310351	+	0.537544i
$507$	7.39926	+	8.81810i	0.328613	+	0.391626i
$508$	−4.85929	−	13.3508i	−0.215596	−	0.592345i
$509$	−20.4740	−	7.45194i	−0.907495	−	0.330301i	−0.154243	−	0.988033i	$-0.549294\pi$
$509$	−20.4740	−	7.45194i	−0.907495	−	0.330301i	−0.753252	+	0.657732i	$0.771516\pi$
$510$	6.49398	+	5.83156i	0.287558	+	0.258226i
$511$	−3.61686	+	20.5123i	−0.160001	+	0.907409i
$512$			1.00000i			0.0441942i
$513$	−3.93340	−	1.87840i	−0.173664	−	0.0829335i
$514$	−16.7005			−0.736628
$515$	6.36339	−	30.1348i	0.280405	−	1.32790i
$516$	5.72119	+	4.80065i	0.251861	+	0.211337i
$517$	2.46306	−	6.76721i	0.108325	−	0.297622i
$518$	3.53768	+	9.71970i	0.155437	+	0.427059i
$519$	−6.72148	+	5.63999i	−0.295040	+	0.247568i
$520$	−9.76774	+	5.21030i	−0.428344	+	0.228487i
$521$	−14.6262	+	25.3333i	−0.640784	+	1.10987i	0.344474	+	0.938796i	$0.388057\pi$
$521$	−14.6262	+	25.3333i	−0.640784	+	1.10987i	−0.985258	+	0.171075i	$0.945276\pi$
$522$	−4.81314	+	0.848686i	−0.210665	+	0.0371460i
$523$	−18.5958	+	3.27893i	−0.813135	+	0.143378i	−0.564727	−	0.825278i	$-0.691019\pi$
$523$	−18.5958	+	3.27893i	−0.813135	+	0.143378i	−0.248408	+	0.968655i	$0.579907\pi$
$524$	−6.03260	+	10.4488i	−0.263535	+	0.456457i
$525$	−7.21276	−	14.6889i	−0.314791	−	0.641075i
$526$	−9.08116	+	7.61999i	−0.395957	+	0.332248i
$527$	−14.7574	−	40.5456i	−0.642843	−	1.76620i
$528$	−0.938263	+	2.57786i	−0.0408327	+	0.112187i
$529$	−2.22482	−	1.86684i	−0.0967312	−	0.0811671i
$530$	−23.5596	−	4.97495i	−1.02336	−	0.216098i
$531$	−12.8532			−0.557783
$532$	−13.8133	+	3.56543i	−0.598880	+	0.154581i
$533$		−	28.9407i		−	1.25356i
$534$	1.12709	−	6.39204i	0.0487739	−	0.276611i
$535$	−11.9367	−	10.7191i	−0.516068	−	0.463426i
$536$	11.4345	+	4.16181i	0.493895	+	0.179763i
$537$	−6.55472	−	18.0089i	−0.282857	−	0.777143i
$538$	3.88997	+	4.63589i	0.167709	+	0.199867i
$539$	5.09085	+	8.81761i	0.219278	+	0.379801i
$540$	1.18241	−	1.89787i	0.0508827	−	0.0816713i
$541$	−5.50983	−	31.2478i	−0.236886	−	1.34345i	−0.838605	−	0.544740i	$-0.816628\pi$
$541$	−5.50983	−	31.2478i	−0.236886	−	1.34345i	0.601719	−	0.798708i	$-0.294483\pi$
$542$	−13.0761	+	2.30567i	−0.561666	+	0.0990368i
$543$	14.0350	+	8.10313i	0.602301	+	0.347739i
$544$	1.95165	+	3.38036i	0.0836764	+	0.144932i
$545$	2.46149	+	3.14192i	0.105438	+	0.134585i
$546$	−15.2263	+	5.54190i	−0.651623	+	0.237172i
$547$	−2.04223	+	5.61097i	−0.0873193	+	0.239908i	−0.975665	−	0.219268i	$-0.929633\pi$
$547$	−2.04223	+	5.61097i	−0.0873193	+	0.239908i	0.888345	+	0.459176i	$0.151855\pi$
$548$	7.10223	−	8.46411i	0.303392	−	0.361569i
$549$	1.98646	−	11.2658i	0.0847801	−	0.480812i
$550$	0.920351	−	13.6856i	0.0392439	−	0.583555i
$551$	−5.32432	−	20.6276i	−0.226823	−	0.878764i
$552$		−	5.08963i		−	0.216629i
$553$	2.16916	+	0.382482i	0.0922423	+	0.0162648i
$554$	3.64636	+	3.05966i	0.154919	+	0.129993i
$555$	2.63856	−	6.55581i	0.112001	−	0.278279i
$556$	11.2374	−	4.09009i	0.476573	−	0.173458i
$557$	5.95048	+	7.09151i	0.252130	+	0.300477i	0.877232	−	0.480066i	$-0.159387\pi$
$557$	5.95048	+	7.09151i	0.252130	+	0.300477i	−0.625102	+	0.780543i	$0.714943\pi$
$558$	−9.57319	+	5.52708i	−0.405265	+	0.233980i
$559$	−18.4878	+	32.0218i	−0.781950	+	1.35438i
$560$	−1.02816	−	7.24571i	−0.0434478	−	0.306187i
$561$	1.85941	+	10.5452i	0.0785044	+	0.445221i
$562$	9.46312	+	5.46354i	0.399178	+	0.230465i
$563$	20.8830	−	12.0568i	0.880113	−	0.508134i	0.00941748	−	0.999956i	$-0.497002\pi$
$563$	20.8830	−	12.0568i	0.880113	−	0.508134i	0.870696	+	0.491822i	$0.163669\pi$
$564$	−2.01097	+	1.68740i	−0.0846770	+	0.0710524i
$565$	26.7010	−	8.71502i	1.12332	−	0.366644i
$566$	−15.8205	−	5.75820i	−0.664986	−	0.242035i
$567$	2.10374	−	2.50714i	0.0883488	−	0.105290i
$568$	−11.2653	−	1.98638i	−0.472682	−	0.0833465i
$569$	−16.6759			−0.699090			−0.349545	−	0.936919i	$-0.613664\pi$
$569$	−16.6759			−0.699090			−0.349545	+	0.936919i	$0.613664\pi$
$570$	8.64939	+	4.49311i	0.362283	+	0.188196i
$571$	4.21830			0.176531			0.0882653	−	0.996097i	$-0.471868\pi$
$571$	4.21830			0.176531			0.0882653	+	0.996097i	$0.471868\pi$
$572$	−13.3754	−	2.35844i	−0.559253	−	0.0986115i
$573$	8.16666	−	9.73265i	0.341167	−	0.406587i
$574$	17.9778	+	6.54339i	0.750380	+	0.273116i
$575$	7.07961	+	24.4435i	0.295240	+	1.01937i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	17.1928	−	9.92624i	0.715744	−	0.413235i	−0.0974405	−	0.995241i	$-0.531066\pi$
$577$	17.1928	−	9.92624i	0.715744	−	0.413235i	0.813184	+	0.582007i	$0.197732\pi$
$578$	−1.52786	−	0.882112i	−0.0635507	−	0.0366910i
$579$	−2.16958	−	12.3043i	−0.0901647	−	0.511349i
$580$	10.8201	−	1.53537i	0.449282	−	0.0637529i
$581$	12.9956	−	22.5091i	0.539149	−	0.933833i
$582$	8.81673	−	5.09034i	0.365465	−	0.211001i
$583$	−18.9888	−	22.6299i	−0.786434	−	0.937236i
$584$	5.98030	−	2.17665i	0.247467	−	0.0900705i
$585$	10.2699	+	4.13341i	0.424608	+	0.170895i
$586$	10.7587	+	9.02763i	0.444438	+	0.372928i
$587$	−44.3155	−	7.81402i	−1.82910	−	0.322519i	−0.850135	−	0.526564i	$-0.823480\pi$
$587$	−44.3155	−	7.81402i	−1.82910	−	0.322519i	−0.978961	+	0.204045i	$0.934591\pi$
$588$		−	3.71148i		−	0.153059i
$589$	−27.2731	−	39.7225i	−1.12377	−	1.63674i
$590$	28.7245	+	0.964768i	1.18257	+	0.0397189i
$591$	−3.24776	+	18.4189i	−0.133595	+	0.757654i
$592$	2.03147	−	2.42101i	0.0834927	−	0.0995028i
$593$	7.37628	−	20.2662i	0.302908	−	0.832232i	−0.691084	−	0.722775i	$-0.742866\pi$
$593$	7.37628	−	20.2662i	0.302908	−	0.832232i	0.993991	−	0.109457i	$-0.0349113\pi$
$594$	2.57786	−	0.938263i	0.105771	−	0.0384974i
$595$	−17.6167	−	22.4865i	−0.722213	−	0.921856i
$596$	−6.01790	−	10.4233i	−0.246503	−	0.426955i
$597$	−14.2383	−	8.22048i	−0.582734	−	0.336442i
$598$	24.8153	−	4.37561i	1.01477	−	0.178932i
$599$	0.988877	+	5.60820i	0.0404044	+	0.229145i	0.998323	−	0.0578966i	$-0.0184394\pi$
$599$	0.988877	+	5.60820i	0.0404044	+	0.229145i	−0.957918	+	0.287041i	$0.907328\pi$
$600$	−2.78491	+	4.15262i	−0.113693	+	0.169530i
$601$	−2.84030	−	4.91954i	−0.115858	−	0.200672i	0.802264	−	0.596969i	$-0.203628\pi$
$601$	−2.84030	−	4.91954i	−0.115858	−	0.200672i	−0.918122	+	0.396297i	$0.870295\pi$
$602$	−15.7117	−	18.7245i	−0.640363	−	0.763155i
$603$	−4.16181	−	11.4345i	−0.169482	−	0.465648i
$604$	10.8797	+	3.95990i	0.442691	+	0.161126i
$605$	−5.19066	+	5.78028i	−0.211030	+	0.235002i
$606$	−0.202137	+	1.14638i	−0.00821125	+	0.0465683i
$607$			4.75759i			0.193104i	0.995328	+	0.0965522i	$0.0307815\pi$
$607$			4.75759i			0.193104i	−0.995328	+	0.0965522i	$0.969219\pi$
$608$	3.05373	+	3.11042i	0.123845	+	0.126144i
$609$	15.9956			0.648176
$610$	−5.28497	+	25.0277i	−0.213982	+	1.01334i
$611$	−9.95606	−	8.35412i	−0.402779	−	0.337972i
$612$	1.33501	−	3.66791i	0.0539645	−	0.148266i
$613$	−12.7682	−	35.0804i	−0.515704	−	1.41688i	−0.875211	−	0.483742i	$-0.839277\pi$
$613$	−12.7682	−	35.0804i	−0.515704	−	1.41688i	0.359507	−	0.933142i	$-0.382945\pi$
$614$	−10.4852	+	8.79814i	−0.423149	+	0.355064i
$615$	−6.15187	−	11.5329i	−0.248067	−	0.465051i
$616$	4.48919	−	7.77550i	0.180874	−	0.313284i
$617$	−21.3383	+	3.76251i	−0.859047	+	0.151473i	−0.585785	−	0.810467i	$-0.699214\pi$
$617$	−21.3383	+	3.76251i	−0.859047	+	0.151473i	−0.273262	+	0.961940i	$0.588103\pi$
$618$	−13.5646	+	2.39181i	−0.545649	+	0.0962126i
$619$	15.7762	−	27.3252i	0.634099	−	1.09829i	−0.352606	−	0.935772i	$-0.614705\pi$
$619$	15.7762	−	27.3252i	0.634099	−	1.09829i	0.986705	−	0.162520i	$-0.0519621\pi$
$620$	21.8091	−	11.6334i	0.875875	−	0.467209i
$621$	−3.89888	+	3.27155i	−0.156457	+	0.131283i
$622$	9.35312	+	25.6975i	0.375026	+	1.03038i
$623$	−7.26549	+	19.9618i	−0.291086	+	0.799751i
$624$	3.79259	+	3.18236i	0.151825	+	0.127397i
$625$	7.59861	−	23.8172i	0.303944	−	0.952690i
$626$	−24.4240			−0.976179
$627$	4.95369	+	10.8834i	0.197831	+	0.434642i
$628$			14.4046i			0.574805i
$629$	2.14212	−	12.1486i	0.0854121	−	0.484396i
$630$	−4.88964	+	5.44507i	−0.194808	+	0.216937i
$631$	−19.8894	−	7.23916i	−0.791786	−	0.288186i	−0.0857075	−	0.996320i	$-0.527315\pi$
$631$	−19.8894	−	7.23916i	−0.791786	−	0.288186i	−0.706078	+	0.708134i	$0.749537\pi$
$632$	−0.230180	−	0.632415i	−0.00915608	−	0.0251561i
$633$	−7.69376	−	9.16907i	−0.305800	−	0.364438i
$634$	−11.5130	−	19.9411i	−0.457239	−	0.791961i
$635$	16.7992	−	26.9642i	0.666656	−	1.07004i
$636$	1.86993	+	10.6049i	0.0741477	+	0.420513i
$637$	18.0959	−	3.19080i	0.716988	−	0.126424i
$638$	11.6113	+	6.70378i	0.459695	+	0.265405i
$639$	5.71954	+	9.90654i	0.226262	+	0.391897i
$640$	−1.76021	+	1.37901i	−0.0695784	+	0.0545100i
$641$	−39.6445	+	14.4294i	−1.56586	+	0.569927i	−0.972070	−	0.234692i	$-0.924592\pi$
$641$	−39.6445	+	14.4294i	−1.56586	+	0.569927i	−0.593792	+	0.804619i	$0.702370\pi$
$642$	−2.45390	+	6.74203i	−0.0968477	+	0.266087i
$643$	−7.26162	+	8.65406i	−0.286370	+	0.341283i	−0.889982	−	0.455996i	$-0.849283\pi$
$643$	−7.26162	+	8.65406i	−0.286370	+	0.341283i	0.603612	+	0.797278i	$0.293728\pi$
$644$	−2.89255	+	16.4045i	−0.113982	+	0.646427i
$645$	−0.560587	+	16.6906i	−0.0220731	+	0.657192i
$646$	16.3932	+	4.55452i	0.644981	+	0.179195i
$647$			36.6128i			1.43940i	0.694286	+	0.719699i	$0.255720\pi$
$647$			36.6128i			1.43940i	−0.694286	+	0.719699i	$0.744280\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	27.0109	+	22.6648i	1.06027	+	0.889673i
$650$	−22.6410	−	10.0082i	−0.888054	−	0.392555i
$651$	33.9967	−	12.3738i	1.33244	−	0.484967i
$652$	9.94814	+	11.8557i	0.389599	+	0.464306i
$653$	10.5184	−	6.07281i	0.411617	−	0.237647i	−0.279867	−	0.960039i	$-0.590290\pi$
$653$	10.5184	−	6.07281i	0.411617	−	0.237647i	0.691484	+	0.722391i	$0.256957\pi$
$654$	0.892484	−	1.54583i	0.0348989	−	0.0604467i
$655$	−26.7110	+	3.79029i	−1.04369	+	0.148099i
$656$	−1.01507	−	5.75676i	−0.0396319	−	0.224764i
$657$	−5.51147	−	3.18205i	−0.215023	−	0.124144i
$658$	7.44057	−	4.29582i	0.290064	−	0.167468i
$659$	−1.76538	+	1.48133i	−0.0687693	+	0.0577043i	−0.676524	−	0.736420i	$-0.736515\pi$
$659$	−1.76538	+	1.48133i	−0.0687693	+	0.0577043i	0.607755	+	0.794124i	$0.292070\pi$
$660$	−5.83144	+	1.90334i	−0.226988	+	0.0740875i
$661$	−9.77959	−	3.55948i	−0.380382	−	0.138448i	0.144751	−	0.989468i	$-0.453762\pi$
$661$	−9.77959	−	3.55948i	−0.380382	−	0.138448i	−0.525133	+	0.851020i	$0.675984\pi$
$662$	−17.4214	+	20.7620i	−0.677102	+	0.806938i
$663$	19.0312	+	3.35571i	0.739110	+	0.130325i
$664$	−7.94149			−0.308189
$665$	−25.3245	−	19.3975i	−0.982041	−	0.752202i
$666$	−3.16040			−0.122463
$667$	−24.4971	−	4.31949i	−0.948530	−	0.167251i
$668$	−1.46825	+	1.74979i	−0.0568082	+	0.0677014i
$669$	1.24087	+	0.451639i	0.0479747	+	0.0174614i
$670$	8.44258	+	25.8663i	0.326165	+	0.999301i
$671$	−24.0401	+	20.1720i	−0.928058	+	0.778733i
$672$	−2.83436	+	1.63642i	−0.109338	+	0.0631263i
$673$	33.9462	+	19.5989i	1.30853	+	0.755481i	0.981851	−	0.189654i	$-0.0607367\pi$
$673$	33.9462	+	19.5989i	1.30853	+	0.755481i	0.326680	+	0.945135i	$0.394070\pi$
$674$	3.57310	+	20.2641i	0.137631	+	0.780542i
$675$	4.97120	−	0.535890i	0.191342	−	0.0206264i
$676$	−5.75561	+	9.96900i	−0.221369	+	0.383423i
$677$	26.1391	−	15.0914i	1.00461	−	0.580011i	0.0949999	−	0.995477i	$-0.469715\pi$
$677$	26.1391	−	15.0914i	1.00461	−	0.580011i	0.909609	+	0.415466i	$0.136382\pi$
$678$	−8.07406	−	9.62229i	−0.310082	−	0.369542i
$679$	−31.3103	+	11.3960i	−1.20158	+	0.437339i
$680$	−3.25880	+	8.09686i	−0.124969	+	0.310500i
$681$	−8.10144	−	6.79792i	−0.310448	−	0.260497i
$682$	29.8642	+	5.26586i	1.14356	+	0.201640i
$683$			20.2022i			0.773015i	0.922286	+	0.386507i	$0.126319\pi$
$683$			20.2022i			0.773015i	−0.922286	+	0.386507i	$0.873681\pi$
$684$	0.419819	−	4.33863i	0.0160522	−	0.165892i
$685$	24.6926	+	0.829350i	0.943457	+	0.0316878i
$686$	1.86894	−	10.5993i	0.0713564	−	0.404682i
$687$	0.245998	−	0.293169i	0.00938540	−	0.0111851i
$688$	−2.55437	+	7.01808i	−0.0973845	+	0.267562i
$689$	−50.0985	+	18.2344i	−1.90860	+	0.694673i
$690$	8.95881	−	7.01863i	0.341056	−	0.267195i
$691$	−5.43024	−	9.40545i	−0.206576	−	0.357800i	0.744058	−	0.668115i	$-0.232899\pi$
$691$	−5.43024	−	9.40545i	−0.206576	−	0.357800i	−0.950634	+	0.310315i	$0.899565\pi$
$692$	−7.59874	−	4.38714i	−0.288861	−	0.166774i
$693$	−8.84197	+	1.55908i	−0.335879	+	0.0592245i
$694$	3.16024	+	17.9226i	0.119961	+	0.680333i
$695$	22.6959	+	14.1400i	0.860905	+	0.536360i
$696$	−2.44369	−	4.23260i	−0.0926280	−	0.160436i
$697$	−14.6665	−	17.4788i	−0.555533	−	0.662059i
$698$	5.82546	+	16.0053i	0.220497	+	0.605810i
$699$	−2.89088	−	1.05220i	−0.109343	−	0.0397977i
$700$	11.3361	−	11.8017i	0.428465	−	0.446061i
$701$	3.65292	−	20.7167i	0.137969	−	0.782460i	−0.834778	−	0.550587i	$-0.814404\pi$
$701$	3.65292	−	20.7167i	0.137969	−	0.782460i	0.972746	−	0.231872i	$-0.0744851\pi$
$702$		−	4.95088i		−	0.186859i
$703$	−1.07439	−	13.7339i	−0.0405215	−	0.517984i
$704$	−2.74330			−0.103392
$705$	−5.74332	−	1.21279i	−0.216306	−	0.0456761i
$706$	0.190069	+	0.159487i	0.00715334	+	0.00600237i
$707$	1.30302	−	3.58003i	0.0490052	−	0.134641i
$708$	−4.39606	−	12.0781i	−0.165214	−	0.453922i
$709$	−33.6647	+	28.2480i	−1.26430	+	1.06088i	−0.269095	+	0.963114i	$0.586724\pi$
$709$	−33.6647	+	28.2480i	−1.26430	+	1.06088i	−0.995210	+	0.0977636i	$0.968831\pi$
$710$	−12.0385	−	22.5685i	−0.451797	−	0.846982i
$711$	−0.336501	+	0.582837i	−0.0126198	+	0.0218581i
$712$	6.39204	−	1.12709i	0.239552	−	0.0422395i
$713$	−55.4068	+	9.76972i	−2.07500	+	0.365879i
$714$	−6.38744	+	11.0634i	−0.239044	+	0.414036i
$715$	−14.2934	−	26.7958i	−0.534543	−	1.00211i
$716$	14.6810	−	12.3188i	0.548655	−	0.460377i
$717$	−2.27809	−	6.25900i	−0.0850768	−	0.233747i
$718$	4.36403	−	11.9901i	0.162864	−	0.447465i
$719$	5.91506	+	4.96332i	0.220594	+	0.185101i	0.746387	−	0.665512i	$-0.231787\pi$
$719$	5.91506	+	4.96332i	0.220594	+	0.185101i	−0.525793	+	0.850613i	$0.676231\pi$
$720$	2.18782	+	0.461990i	0.0815353	+	0.0172174i
$721$	45.0797			1.67885
$722$	18.9968	+	0.349438i	0.706987	+	0.0130047i
$723$			16.4641i			0.612306i
$724$	−2.81419	+	15.9601i	−0.104589	+	0.593151i
$725$	17.6236	+	16.9284i	0.654525	+	0.628706i
$726$	3.26479	+	1.18829i	0.121168	+	0.0441015i
$727$	0.224451	+	0.616674i	0.00832442	+	0.0228712i	0.943785	−	0.330559i	$-0.107237\pi$
$727$	0.224451	+	0.616674i	0.00832442	+	0.0228712i	−0.935461	+	0.353430i	$0.885015\pi$
$728$	−10.4154	−	12.4126i	−0.386019	−	0.460040i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	12.0782	+	7.52497i	0.447036	+	0.278511i
$731$	5.06215	+	28.7089i	0.187230	+	1.06184i
$732$	11.2658	−	1.98646i	0.416395	−	0.0734217i
$733$	−8.87886	−	5.12621i	−0.327948	−	0.189341i	0.326982	−	0.945031i	$-0.393968\pi$
$733$	−8.87886	−	5.12621i	−0.327948	−	0.189341i	−0.654930	+	0.755690i	$0.727302\pi$
$734$	−0.569663	−	0.986685i	−0.0210266	−	0.0364192i
$735$	6.53299	−	5.11816i	0.240973	−	0.188786i
$736$	4.78268	−	1.74075i	0.176292	−	0.0641651i
$737$	−11.4171	+	31.3682i	−0.420554	+	1.15546i
$738$	−3.75746	+	4.47796i	−0.138314	+	0.164836i
$739$	−6.45825	+	36.6266i	−0.237571	+	1.34733i	0.599561	+	0.800329i	$0.295342\pi$
$739$	−6.45825	+	36.6266i	−0.237571	+	1.34733i	−0.837132	+	0.547001i	$0.815769\pi$
$740$	7.06289	+	0.237221i	0.259637	+	0.00872041i
$741$	21.5147	−	1.68307i	0.790360	−	0.0618293i
$742$		−	35.2437i		−	1.29384i
$743$	37.1904	+	6.55766i	1.36438	+	0.240577i	0.807428	−	0.589966i	$-0.200859\pi$
$743$	37.1904	+	6.55766i	1.36438	+	0.240577i	0.556954	+	0.830543i	$0.311970\pi$
$744$	−8.46798	−	7.10548i	−0.310451	−	0.260500i
$745$	10.0485	−	24.9666i	0.368148	−	0.914705i
$746$	6.67641	−	2.43001i	0.244441	−	0.0889691i
$747$	5.10469	+	6.08353i	0.186771	+	0.222585i
$748$	−9.27333	+	5.35396i	−0.339067	+	0.195760i
$749$	11.7409	−	20.3358i	0.429002	−	0.743053i
$750$	−11.1499	+	0.824472i	−0.407137	+	0.0301054i
$751$	−1.66352	−	9.43428i	−0.0607026	−	0.344262i	−0.999999	−	0.00115579i	$-0.999632\pi$
$751$	−1.66352	−	9.43428i	−0.0607026	−	0.344262i	0.939297	−	0.343106i	$-0.111479\pi$
$752$	−2.27343	−	1.31257i	−0.0829035	−	0.0478643i
$753$	−11.1624	+	6.44464i	−0.406782	+	0.234856i
$754$	18.5359	−	15.5534i	0.675037	−	0.566423i
$755$	8.03299	+	24.6114i	0.292350	+	0.895700i
$756$	3.07546	+	1.11938i	0.111854	+	0.0407114i
$757$	27.2812	−	32.5125i	0.991552	−	1.18169i	0.00820183	−	0.999966i	$-0.497389\pi$
$757$	27.2812	−	32.5125i	0.991552	−	1.18169i	0.983350	−	0.181720i	$-0.0581663\pi$
$758$	−16.4674	−	2.90364i	−0.598121	−	0.105465i
$759$	13.9624			0.506801
$760$	−1.26388	+	9.66450i	−0.0458456	+	0.350568i
$761$	−15.2573			−0.553076			−0.276538	−	0.961003i	$-0.589187\pi$
$761$	−15.2573			−0.553076			−0.276538	+	0.961003i	$0.589187\pi$
$762$	−13.9918	−	2.46713i	−0.506868	−	0.0893745i
$763$	−3.75511	+	4.47517i	−0.135944	+	0.162012i
$764$	11.9389	+	4.34539i	0.431933	+	0.157211i
$765$	8.29727	−	2.70817i	0.299988	−	0.0979142i
$766$	−12.5647	+	10.5431i	−0.453983	+	0.380937i
$767$	55.1094	−	31.8174i	1.98988	−	1.14886i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−3.49627	−	19.8283i	−0.126079	−	0.715028i	−0.980661	−	0.195712i	$-0.937298\pi$
$769$	−3.49627	−	19.8283i	−0.126079	−	0.715028i	0.854583	−	0.519315i	$-0.173813\pi$
$770$	19.8771	−	2.82056i	0.716322	−	0.101646i
$771$	−8.35025	+	14.4631i	−0.300727	+	0.520874i
$772$	10.8202	−	6.24706i	0.389428	−	0.224836i
$773$	13.7631	+	16.4023i	0.495025	+	0.589948i	0.954488	−	0.298249i	$-0.0964025\pi$
$773$	13.7631	+	16.4023i	0.495025	+	0.589948i	−0.459463	+	0.888197i	$0.651958\pi$
$774$	7.01808	−	2.55437i	0.252260	−	0.0918150i
$775$	50.5521	+	22.3461i	1.81589	+	0.802694i
$776$	7.79886	+	6.54402i	0.279963	+	0.234917i
$777$	10.1863	+	1.79613i	0.365433	+	0.0644357i
$778$			4.96997i			0.178182i
$779$	−20.7369	−	14.8062i	−0.742977	−	0.530487i
$780$	−0.371615	+	11.0643i	−0.0133059	+	0.396164i
$781$	5.44922	−	30.9041i	0.194988	−	1.10583i
$782$	12.7698	−	15.2185i	0.456649	−	0.544213i
$783$	−1.67158	+	4.59264i	−0.0597376	+	0.164128i
$784$	3.48765	−	1.26940i	0.124559	−	0.0453358i
$785$	−25.3551	+	19.8640i	−0.904961	+	0.708977i
$786$	6.03260	+	10.4488i	0.215176	+	0.372695i
$787$	13.0478	+	7.53315i	0.465104	+	0.268528i	0.714188	−	0.699954i	$-0.246796\pi$
$787$	13.0478	+	7.53315i	0.465104	+	0.268528i	−0.249084	+	0.968482i	$0.580129\pi$
$788$	−18.4189	+	3.24776i	−0.656148	+	0.115697i
$789$	2.05853	+	11.6745i	0.0732856	+	0.415624i
$790$	0.795763	−	1.27727i	0.0283120	−	0.0454432i
$791$	20.5551	+	35.6024i	0.730854	+	1.26588i
$792$	1.76336	+	2.10149i	0.0626582	+	0.0746731i
$793$	19.3706	+	53.2204i	0.687871	+	1.88991i
$794$	1.83003	+	0.666076i	0.0649453	+	0.0236382i
$795$	−16.0882	+	17.9157i	−0.570591	+	0.635406i
$796$	2.85494	−	16.1912i	0.101191	−	0.573881i
$797$			39.5543i			1.40109i	0.713611	+	0.700543i	$0.247059\pi$
$797$			39.5543i			1.40109i	−0.713611	+	0.700543i	$0.752941\pi$
$798$	−3.81887	+	13.7453i	−0.135187	+	0.486580i
$799$	−10.2467			−0.362502
$800$	−4.85468	−	1.19668i	−0.171639	−	0.0423090i
$801$	−4.97213	−	4.17211i	−0.175681	−	0.147414i
$802$	9.64322	−	26.4945i	0.340514	−	0.935555i
$803$	5.97120	+	16.4057i	0.210719	+	0.578946i
$804$	9.32148	−	7.82165i	0.328743	−	0.275848i
$805$	−32.8642	+	17.5304i	−1.15831	+	0.617865i
$806$	27.3639	−	47.3957i	0.963853	−	1.66944i
$807$	5.95979	−	1.05087i	0.209794	−	0.0369924i
$808$	−1.14638	+	0.202137i	−0.0403294	+	0.00711115i
$809$	25.7339	−	44.5725i	0.904757	−	1.56709i	0.0835145	−	0.996507i	$-0.473386\pi$
$809$	25.7339	−	44.5725i	0.904757	−	1.56709i	0.821243	−	0.570579i	$-0.193281\pi$
$810$	−1.05240	−	1.97293i	−0.0369776	−	0.0693217i
$811$	36.1678	−	30.3484i	1.27002	−	1.06568i	0.275485	−	0.961305i	$-0.411162\pi$
$811$	36.1678	−	30.3484i	1.27002	−	1.06568i	0.994538	−	0.104371i	$-0.0332828\pi$
$812$	5.47083	+	15.0310i	0.191989	+	0.527484i
$813$	−4.54128	+	12.4771i	−0.159270	+	0.437589i
$814$	6.64154	+	5.57291i	0.232786	+	0.195331i
$815$	−7.15002	+	33.8599i	−0.250454	+	1.18606i
$816$	3.90330			0.136643
$817$	13.4862	+	29.6295i	0.471821	+	1.03661i
$818$		−	18.7338i		−	0.655012i
$819$	−2.81370	+	15.9573i	−0.0983186	+	0.557592i
$820$	8.73331	−	9.72535i	0.304981	−	0.339624i
$821$	−24.7616	−	9.01248i	−0.864185	−	0.314538i	−0.128375	−	0.991726i	$-0.540976\pi$
$821$	−24.7616	−	9.01248i	−0.864185	−	0.314538i	−0.735810	+	0.677188i	$0.763198\pi$
$822$	−3.77902	−	10.3828i	−0.131808	−	0.362141i
$823$	24.7101	+	29.4483i	0.861339	+	1.02650i	0.999349	+	0.0360729i	$0.0114849\pi$
$823$	24.7101	+	29.4483i	0.861339	+	1.02650i	−0.138010	+	0.990431i	$0.544071\pi$
$824$	−6.88693	−	11.9285i	−0.239918	−	0.415550i
$825$	−11.3919	−	7.63983i	−0.396614	−	0.265985i
$826$	7.30479	+	41.4275i	0.254166	+	1.44145i
$827$	6.88811	−	1.21456i	0.239523	−	0.0422344i	−0.0525979	−	0.998616i	$-0.516750\pi$
$827$	6.88811	−	1.21456i	0.239523	−	0.0422344i	0.292121	+	0.956381i	$0.405639\pi$
$828$	−4.40775	−	2.54481i	−0.153180	−	0.0884384i
$829$	−4.13718	−	7.16580i	−0.143690	−	0.248879i	0.785193	−	0.619251i	$-0.212564\pi$
$829$	−4.13718	−	7.16580i	−0.143690	−	0.248879i	−0.928884	+	0.370372i	$0.879230\pi$
$830$	−10.9514	−	13.9787i	−0.380127	−	0.485207i
$831$	4.47292	−	1.62801i	0.155164	−	0.0564751i
$832$	−1.69330	+	4.65231i	−0.0587046	+	0.161290i
$833$	9.31209	−	11.0977i	0.322645	−	0.384513i
$834$	2.07659	−	11.7769i	0.0719065	−	0.407802i
$835$	−5.10472	−	0.171452i	−0.176656	−	0.00593334i
$836$	−8.53281	+	8.37730i	−0.295113	+	0.289735i
$837$			11.0542i			0.382088i
$838$	−11.3436	−	2.00019i	−0.391859	−	0.0690953i
$839$	6.65036	+	5.58031i	0.229596	+	0.192654i	0.750327	−	0.661067i	$-0.229896\pi$
$839$	6.65036	+	5.58031i	0.229596	+	0.192654i	−0.520731	+	0.853721i	$0.674341\pi$
$840$	−6.78905	−	2.73244i	−0.234244	−	0.0942781i
$841$	4.80507	−	1.74890i	0.165692	−	0.0603070i
$842$	−0.985252	−	1.17418i	−0.0339540	−	0.0404648i
$843$	9.46312	−	5.46354i	0.325927	−	0.188174i
$844$	5.98468	−	10.3658i	0.206001	−	0.356805i
$845$	−25.4846	+	3.61625i	−0.876695	+	0.124403i
$846$	0.455849	+	2.58525i	0.0156724	+	0.0888827i
$847$	−9.84748	−	5.68545i	−0.338364	−	0.195354i
$848$	−9.32582	+	5.38426i	−0.320250	+	0.184896i
$849$	−12.8970	+	10.8219i	−0.442624	+	0.371406i
$850$	−18.7461	+	5.42945i	−0.642985	+	0.186229i
$851$	−15.1152	−	5.50148i	−0.518142	−	0.188588i
$852$	−7.35290	+	8.76285i	−0.251906	+	0.300210i
$853$	−34.2208	−	6.03405i	−1.17170	−	0.206602i	−0.446269	−	0.894899i	$-0.647248\pi$
$853$	−34.2208	−	6.03405i	−1.17170	−	0.206602i	−0.725429	+	0.688297i	$0.758359\pi$
$854$	−37.4399			−1.28117
$855$	8.21584	−	5.24404i	0.280976	−	0.179342i
$856$	−7.17472			−0.245227
$857$	26.3952	+	4.65418i	0.901642	+	0.158984i	0.605206	−	0.796069i	$-0.293091\pi$
$857$	26.3952	+	4.65418i	0.901642	+	0.158984i	0.296436	+	0.955053i	$0.404202\pi$
$858$	−8.73017	+	10.4042i	−0.298043	+	0.355194i
$859$	−4.80627	−	1.74934i	−0.163988	−	0.0596867i	0.258722	−	0.965952i	$-0.416699\pi$
$859$	−4.80627	−	1.74934i	−0.163988	−	0.0596867i	−0.422710	+	0.906265i	$0.638921\pi$
$860$	−15.8758	+	5.18175i	−0.541360	+	0.176696i
$861$	14.6557	−	12.2976i	0.499464	−	0.419100i
$862$	17.1236	−	9.88631i	0.583232	−	0.336729i
$863$	15.5775	+	8.99368i	0.530265	+	0.306149i	0.741124	−	0.671368i	$-0.234293\pi$
$863$	15.5775	+	8.99368i	0.530265	+	0.306149i	−0.210859	+	0.977516i	$0.567626\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	−2.75644	−	19.4253i	−0.0937218	−	0.660479i
$866$	−17.1942	+	29.7812i	−0.584281	+	1.01200i
$867$	−1.52786	+	0.882112i	−0.0518890	+	0.0299581i
$868$	23.2551	+	27.7144i	0.789330	+	0.940686i
$869$	1.73490	−	0.631453i	0.0588525	−	0.0214206i
$870$	4.08040	−	10.1382i	0.138338	−	0.343717i
$871$	46.1495	+	38.7241i	1.56372	+	1.31211i
$872$	1.75785	+	0.309957i	0.0595284	+	0.0104965i
$873$		−	10.1807i		−	0.344564i
$874$	9.56036	−	20.0195i	0.323384	−	0.677170i
$875$	36.4060	+	3.67937i	1.23075	+	0.124385i
$876$	1.10511	−	6.26742i	0.0373384	−	0.211756i
$877$	4.72569	−	5.63186i	0.159575	−	0.190174i	−0.680332	−	0.732904i	$-0.738165\pi$
$877$	4.72569	−	5.63186i	0.159575	−	0.190174i	0.839908	+	0.542729i	$0.182609\pi$
$878$	−12.3064	+	33.8116i	−0.415321	+	1.14109i
$879$	13.1975	−	4.80350i	0.445141	−	0.162018i
$880$	−3.78303	−	4.82878i	−0.127526	−	0.162778i
$881$	−22.9080	−	39.6778i	−0.771790	−	1.33678i	−0.936581	−	0.350450i	$-0.886029\pi$
$881$	−22.9080	−	39.6778i	−0.771790	−	1.33678i	0.164792	−	0.986328i	$-0.447305\pi$
$882$	−3.21424	−	1.85574i	−0.108229	−	0.0624861i
$883$	53.5152	−	9.43618i	1.80093	−	0.317553i	0.830153	−	0.557535i	$-0.188253\pi$
$883$	53.5152	−	9.43618i	1.80093	−	0.317553i	0.970777	+	0.239983i	$0.0771418\pi$
$884$	3.35571	+	19.0312i	0.112865	+	0.640088i
$885$	15.1978	−	24.3938i	0.510867	−	0.819988i
$886$	−6.39325	−	11.0734i	−0.214785	−	0.372019i
$887$	−30.4930	−	36.3401i	−1.02385	−	1.22018i	−0.975191	−	0.221367i	$-0.928948\pi$
$887$	−30.4930	−	36.3401i	−1.02385	−	1.22018i	−0.0486638	−	0.998815i	$-0.515496\pi$
$888$	−1.08092	−	2.96980i	−0.0362733	−	0.0996601i
$889$	43.6950	+	15.9037i	1.46548	+	0.533392i
$890$	10.7986	+	9.69707i	0.361970	+	0.325047i
$891$	0.476369	−	2.70162i	0.0159589	−	0.0905077i
$892$			1.32050i			0.0442137i
$893$	−11.0795	+	2.85982i	−0.370763	+	0.0957001i
$894$	−12.0358			−0.402537
$895$	41.9290	+	8.85391i	1.40153	+	0.295954i
$896$	−2.50714	−	2.10374i	−0.0837577	−	0.0702811i
$897$	8.61827	−	23.6785i	0.287756	−	0.790602i
$898$	6.79581	+	18.6713i	0.226779	+	0.623070i
$899$	−41.3863	+	34.7272i	−1.38031	+	1.15822i
$900$	2.20382	+	4.48811i	0.0734607	+	0.149604i
$901$	−21.0164	+	36.4015i	−0.700158	+	1.21271i
$902$	15.7925	−	2.78464i	0.525833	−	0.0927185i
$903$	−24.0718	+	4.24451i	−0.801059	+	0.141248i
$904$	6.28050	−	10.8781i	0.208886	−	0.361802i
$905$	−31.9738	+	17.0555i	−1.06285	+	0.566943i
$906$	8.86925	−	7.44219i	0.294661	−	0.247250i
$907$	−2.87801	−	7.90727i	−0.0955628	−	0.262557i	0.882696	−	0.469944i	$-0.155726\pi$
$907$	−2.87801	−	7.90727i	−0.0955628	−	0.262557i	−0.978259	+	0.207388i	$0.933504\pi$
$908$	3.61710	−	9.93789i	0.120038	−	0.329800i
$909$	0.891722	+	0.748244i	0.0295766	+	0.0248177i
$910$	7.48583	−	35.4502i	0.248153	−	1.17516i
$911$	17.1421			0.567942			0.283971	−	0.958833i	$-0.408348\pi$
$911$	17.1421			0.567942			0.283971	+	0.958833i	$0.408348\pi$
$912$	4.22057	−	1.08940i	0.139757	−	0.0360736i
$913$		−	21.7859i		−	0.721007i
$914$	−3.06705	+	17.3941i	−0.101449	+	0.575346i
$915$	19.0322	+	17.0908i	0.629184	+	0.565004i
$916$	0.359625	+	0.130893i	0.0118823	+	0.00432481i
$917$	−13.5055	−	37.1061i	−0.445991	−	1.22535i
$918$	−2.50899	−	2.99010i	−0.0828092	−	0.0986881i
$919$	13.3991	+	23.2079i	0.441996	+	0.765559i	0.997838	−	0.0657290i	$-0.0209373\pi$
$919$	13.3991	+	23.2079i	0.441996	+	0.765559i	−0.555842	+	0.831288i	$0.687604\pi$
$920$	9.65945	+	6.01801i	0.318463	+	0.198408i
$921$	2.37681	+	13.4795i	0.0783184	+	0.444166i
$922$	−12.1711	+	2.14610i	−0.400835	+	0.0706780i
$923$	−49.0461	−	28.3168i	−1.61437	−	0.932058i
$924$	−4.48919	−	7.77550i	−0.147683	−	0.255795i
$925$	9.32221	+	12.7593i	0.306512	+	0.419523i
$926$	−17.9628	+	6.53794i	−0.590296	+	0.214850i
$927$	−4.71094	+	12.9432i	−0.154728	+	0.425111i
$928$	3.14155	−	3.74396i	0.103126	−	0.122901i
$929$	−2.10388	+	11.9317i	−0.0690259	+	0.391465i	0.930648	+	0.365917i	$0.119244\pi$
$929$	−2.10388	+	11.9317i	−0.0690259	+	0.391465i	−0.999674	+	0.0255489i	$0.991867\pi$
$930$	0.829730	−	24.7039i	0.0272079	−	0.810074i
$931$	6.97166	−	14.5987i	0.228487	−	0.478454i
$932$		−	3.07641i		−	0.100771i
$933$	26.9312	+	4.74870i	0.881689	+	0.155466i
$934$	4.70683	+	3.94950i	0.154012	+	0.129232i
$935$	−22.2121	−	8.93986i	−0.726413	−	0.292365i
$936$	4.65231	−	1.69330i	0.152065	−	0.0553473i
$937$	15.5176	+	18.4931i	0.506937	+	0.604144i	0.957441	−	0.288631i	$-0.0932000\pi$
$937$	15.5176	+	18.4931i	0.506937	+	0.604144i	−0.450503	+	0.892775i	$0.648756\pi$
$938$	−34.4895	+	19.9125i	−1.12612	+	0.650166i
$939$	−12.2120	+	21.1518i	−0.398523	+	0.690263i
$940$	−0.824686	−	5.81175i	−0.0268983	−	0.189558i
$941$	−3.29111	−	18.6648i	−0.107287	−	0.608455i	−0.990282	−	0.139073i	$-0.955588\pi$
$941$	−3.29111	−	18.6648i	−0.107287	−	0.608455i	0.882995	−	0.469382i	$-0.155523\pi$
$942$	12.4747	+	7.20228i	0.406448	+	0.234663i
$943$	−25.7658	+	14.8759i	−0.839049	+	0.484425i
$944$	9.84615	−	8.26190i	0.320465	−	0.268902i
$945$	2.27075	+	6.95709i	0.0738674	+	0.226314i
$946$	−19.2527	−	7.00740i	−0.625958	−	0.227830i
$947$	−20.3544	+	24.2574i	−0.661428	+	0.788259i	−0.987590	−	0.157055i	$-0.949800\pi$
$947$	−20.3544	+	24.2574i	−0.661428	+	0.788259i	0.326162	+	0.945314i	$0.394245\pi$
$948$	−0.662777	−	0.116866i	−0.0215260	−	0.00379562i
$949$	31.5079			1.02279
$950$	−18.7544	+	11.1027i	−0.608475	+	0.360220i
$951$	−23.0260			−0.746668
$952$	−12.5808	−	2.21834i	−0.407746	−	0.0718967i
$953$	27.4496	−	32.7132i	0.889180	−	1.05968i	−0.108666	−	0.994078i	$-0.534658\pi$
$953$	27.4496	−	32.7132i	0.889180	−	1.05968i	0.997846	−	0.0656051i	$-0.0208977\pi$
$954$	10.1191	+	3.68305i	0.327618	+	0.119243i
$955$	8.81498	+	27.0072i	0.285246	+	0.873933i
$956$	5.10238	−	4.28141i	0.165023	−	0.138471i
$957$	11.6113	−	6.70378i	0.375339	−	0.216702i
$958$	−8.35269	−	4.82243i	−0.269863	−	0.155806i
$959$	6.27946	+	35.6126i	0.202774	+	1.14999i
$960$	0.314150	+	2.21389i	0.0101392	+	0.0714530i
$961$	−45.5973	+	78.9768i	−1.47088	+	2.54764i
$962$	13.5505	−	7.82338i	0.436885	−	0.252236i
$963$	4.61182	+	5.49616i	0.148614	+	0.177111i
$964$	−15.4712	+	5.63105i	−0.498293	+	0.181364i
$965$	25.9173	+	10.4311i	0.834307	+	0.335790i
$966$	12.7604	+	10.7073i	0.410559	+	0.344500i
$967$	−25.7318	−	4.53720i	−0.827478	−	0.145907i	−0.256159	−	0.966635i	$-0.582457\pi$
$967$	−25.7318	−	4.53720i	−0.827478	−	0.145907i	−0.571319	+	0.820728i	$0.693568\pi$
$968$			3.47432i			0.111669i
$969$	12.1409	−	11.9196i	0.390022	−	0.382914i
$970$	−0.764166	+	22.7519i	−0.0245359	+	0.730519i
$971$	−1.67510	+	9.49998i	−0.0537566	+	0.304869i	−0.999817	−	0.0191210i	$-0.993913\pi$
$971$	−1.67510	+	9.49998i	−0.0537566	+	0.304869i	0.946061	+	0.323990i	$0.105024\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	−13.3862	+	36.7783i	−0.429142	+	1.17906i
$974$	−29.3106	+	10.6682i	−0.939172	+	0.341831i
$975$	−19.9879	+	14.6036i	−0.640125	+	0.467689i
$976$	5.71978	+	9.90696i	0.183086	+	0.317114i
$977$	20.4298	+	11.7952i	0.653608	+	0.377361i	0.789837	−	0.613317i	$-0.210165\pi$
$977$	20.4298	+	11.7952i	0.653608	+	0.377361i	−0.136229	+	0.990677i	$0.543498\pi$
$978$	15.2414	−	2.68748i	0.487367	−	0.0859360i
$979$	3.09194	+	17.5353i	0.0988189	+	0.560430i
$980$	7.04391	+	4.38849i	0.225010	+	0.140185i
$981$	−0.892484	−	1.54583i	−0.0284948	−	0.0493545i
$982$	18.5180	+	22.0689i	0.590934	+	0.704247i
$983$	1.29156	+	3.54852i	0.0411943	+	0.113180i	0.958584	−	0.284809i	$-0.0919302\pi$
$983$	1.29156	+	3.54852i	0.0411943	+	0.113180i	−0.917390	+	0.397990i	$0.869708\pi$
$984$	−5.49304	−	1.99930i	−0.175112	−	0.0637354i
$985$	−31.1166	−	27.9425i	−0.991457	−	0.890323i
$986$	3.31268	−	18.7871i	0.105497	−	0.598304i
$987$		−	8.59164i		−	0.273475i
$988$	8.94002	+	19.6415i	0.284420	+	0.624880i
$989$	38.0118			1.20870
$990$	−1.26738	+	6.00185i	−0.0402799	+	0.190751i
$991$	−11.5863	−	9.72209i	−0.368052	−	0.308832i	0.439938	−	0.898028i	$-0.355000\pi$
$991$	−11.5863	−	9.72209i	−0.368052	−	0.308832i	−0.807990	+	0.589196i	$0.799445\pi$
$992$	3.78075	−	10.3875i	0.120039	−	0.329804i
$993$	9.26973	+	25.4684i	0.294166	+	0.808214i
$994$	28.6794	−	24.0649i	0.909656	−	0.763292i
$995$	32.4369	−	17.3025i	1.02832	−	0.548525i
$996$	−3.97074	+	6.87753i	−0.125818	+	0.217923i
$997$	33.0316	−	5.82437i	1.04612	−	0.184460i	0.375931	−	0.926648i	$-0.377323\pi$
$997$	33.0316	−	5.82437i	1.04612	−	0.184460i	0.670191	+	0.742188i	$0.266212\pi$
$998$	27.9310	−	4.92499i	0.884140	−	0.155898i
$999$	−1.58020	+	2.73699i	−0.0499953	+	0.0865944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.169.8	yes	60
5.4	even	2	inner	570.2.bc.b.169.2	✓	60
19.9	even	9	inner	570.2.bc.b.199.2	yes	60
95.9	even	18	inner	570.2.bc.b.199.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.169.2	✓	60	5.4	even	2	inner
570.2.bc.b.169.8	yes	60	1.1	even	1	trivial
570.2.bc.b.199.2	yes	60	19.9	even	9	inner
570.2.bc.b.199.8	yes	60	95.9	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.693816 + 2.12570i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.83436 + 1.63642i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.693816 + 2.12570i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.83436 + 1.63642i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.314150 + 2.21389i) q^{10} +(-1.37165 + 2.37577i) q^{11} +(0.866025 - 0.500000i) q^{12} +(3.18236 + 3.79259i) q^{13} +(-3.07546 + 1.11938i) q^{14} +(2.07436 + 0.834883i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.84400 + 0.677801i) q^{17} -1.00000i q^{18} +(4.34562 - 0.339955i) q^{19} +(-0.0750603 + 2.23481i) q^{20} +(-0.568323 + 3.22312i) q^{21} +(-1.76336 + 2.10149i) q^{22} +(1.74075 - 4.78268i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.03724 + 2.94969i) q^{25} +(2.47544 + 4.28759i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-3.22312 + 0.568323i) q^{28} +(-0.848686 - 4.81314i) q^{29} +(1.89787 + 1.18241i) q^{30} +(-5.52708 - 9.57319i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.938263 + 2.57786i) q^{33} +(3.66791 + 1.33501i) q^{34} +(-5.44507 - 4.88964i) q^{35} +(0.173648 - 0.984808i) q^{36} -3.16040i q^{37} +(4.33863 + 0.419819i) q^{38} +4.95088 q^{39} +(-0.461990 + 2.18782i) q^{40} +(-4.47796 - 3.75746i) q^{41} +(-1.11938 + 3.07546i) q^{42} +(2.55437 + 7.01808i) q^{43} +(-2.10149 + 1.76336i) q^{44} +(1.97293 - 1.05240i) q^{45} +(2.54481 - 4.40775i) q^{46} +(-2.58525 + 0.455849i) q^{47} +(0.984808 - 0.173648i) q^{48} +(1.85574 - 3.21424i) q^{49} +(-4.48811 + 2.20382i) q^{50} +(2.99010 - 2.50899i) q^{51} +(1.69330 + 4.65231i) q^{52} +(-3.68305 + 10.1191i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-6.00185 - 1.26738i) q^{55} -3.27284 q^{56} +(2.53289 - 3.54746i) q^{57} -4.88739i q^{58} +(2.23194 - 12.6580i) q^{59} +(1.66371 + 1.49401i) q^{60} +(10.7497 + 3.91256i) q^{61} +(-3.78075 - 10.3875i) q^{62} +(2.10374 + 2.50714i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.85396 + 9.39613i) q^{65} +(0.476369 + 2.70162i) q^{66} +(11.9835 - 2.11301i) q^{67} +(3.38036 + 1.95165i) q^{68} +(-2.54481 - 4.40775i) q^{69} +(-4.51327 - 5.76089i) q^{70} +(-10.7492 + 3.91240i) q^{71} +(0.342020 - 0.939693i) q^{72} +(4.09077 - 4.87518i) q^{73} +(0.548798 - 3.11239i) q^{74} +(-0.335491 + 4.98873i) q^{75} +(4.19982 + 1.16684i) q^{76} -8.97837i q^{77} +(4.87566 + 0.859711i) q^{78} +(-0.515549 - 0.432597i) q^{79} +(-0.834883 + 2.07436i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-3.75746 - 4.47796i) q^{82} +(-6.87753 + 3.97074i) q^{83} +(-1.63642 + 2.83436i) q^{84} +(1.22622 + 8.64148i) q^{85} +(1.29689 + 7.35502i) q^{86} +(-4.23260 - 2.44369i) q^{87} +(-2.37577 + 1.37165i) q^{88} +(4.97213 - 4.17211i) q^{89} +(2.12570 - 0.693816i) q^{90} +(-15.2263 - 5.54190i) q^{91} +(3.27155 - 3.89888i) q^{92} +(-10.8862 - 1.91954i) q^{93} -2.62513 q^{94} +(3.73770 + 9.00164i) q^{95} +1.00000 q^{96} +(10.0260 + 1.76786i) q^{97} +(2.38570 - 2.84316i) q^{98} +(2.57786 + 0.938263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

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Database

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