LMFDB - Embedded newform 350.2.m.b.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	350.29
Dual form			350.2.m.b.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.20334 - 1.65626i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.62675 - 1.53418i) q^{5} +(-1.65626 + 1.20334i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.368112 - 1.13293i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.20334 - 1.65626i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.62675 - 1.53418i) q^{5} +(-1.65626 + 1.20334i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.368112 - 1.13293i) q^{9} +(1.07304 + 1.96178i) q^{10} +(1.14482 - 3.52339i) q^{11} +(1.94705 - 0.632635i) q^{12} +(-5.17103 + 1.68017i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-4.49853 + 0.848174i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.616421 - 0.848431i) q^{17} +1.19123i q^{18} +(5.60491 - 4.07221i) q^{19} +(-0.414299 - 2.19735i) q^{20} +(-1.65626 - 1.20334i) q^{21} +(-2.17757 + 2.99717i) q^{22} +(-7.79323 - 2.53217i) q^{23} -2.04725 q^{24} +(0.292607 + 4.99143i) q^{25} +5.43714 q^{26} +(3.52176 + 1.14429i) q^{27} +(0.587785 - 0.809017i) q^{28} +(4.23292 + 3.07540i) q^{29} +(4.54046 + 0.583461i) q^{30} +(-4.20829 + 3.05750i) q^{31} -1.00000i q^{32} +(-4.45804 - 6.13597i) q^{33} +(0.324072 + 0.997390i) q^{34} +(-1.53418 + 1.62675i) q^{35} +(0.368112 - 1.13293i) q^{36} +(1.19843 - 0.389393i) q^{37} +(-6.58897 + 2.14089i) q^{38} +(-3.43972 + 10.5864i) q^{39} +(-0.284997 + 2.21783i) q^{40} +(-1.91282 - 5.88707i) q^{41} +(1.20334 + 1.65626i) q^{42} -2.01832i q^{43} +(2.99717 - 2.17757i) q^{44} +(-1.13929 + 2.40774i) q^{45} +(6.62931 + 4.81648i) q^{46} +(7.56905 - 10.4179i) q^{47} +(1.94705 + 0.632635i) q^{48} -1.00000 q^{49} +(1.26415 - 4.83755i) q^{50} -2.14699 q^{51} +(-5.17103 - 1.68017i) q^{52} +(1.15438 - 1.58887i) q^{53} +(-2.99579 - 2.17657i) q^{54} +(-7.26783 + 3.97531i) q^{55} +(-0.809017 + 0.587785i) q^{56} -14.1835i q^{57} +(-3.07540 - 4.23292i) q^{58} +(-2.55328 - 7.85820i) q^{59} +(-4.13793 - 1.95798i) q^{60} +(-0.236698 + 0.728480i) q^{61} +(4.94714 - 1.60742i) q^{62} +(-1.13293 + 0.368112i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(10.9896 + 5.20006i) q^{65} +(2.34373 + 7.21326i) q^{66} +(8.23650 + 11.3366i) q^{67} -1.04872i q^{68} +(-13.5719 + 9.86054i) q^{69} +(1.96178 - 1.07304i) q^{70} +(12.9126 + 9.38155i) q^{71} +(-0.700190 + 0.963729i) q^{72} +(1.48193 + 0.481508i) q^{73} -1.26010 q^{74} +(8.61922 + 5.52177i) q^{75} +6.92805 q^{76} +(-3.52339 - 1.14482i) q^{77} +(6.54274 - 9.00532i) q^{78} +(4.52283 + 3.28603i) q^{79} +(0.956396 - 2.02121i) q^{80} +(9.02431 - 6.55655i) q^{81} +6.19003i q^{82} +(5.18413 + 7.13534i) q^{83} +(-0.632635 - 1.94705i) q^{84} +(-0.298882 + 2.32588i) q^{85} +(-0.623696 + 1.91954i) q^{86} +(10.1873 - 3.31006i) q^{87} +(-3.52339 + 1.14482i) q^{88} +(1.51164 - 4.65234i) q^{89} +(1.82756 - 1.93784i) q^{90} +(1.68017 + 5.17103i) q^{91} +(-4.81648 - 6.62931i) q^{92} +10.6493i q^{93} +(-10.4179 + 7.56905i) q^{94} +(-15.3653 - 1.97448i) q^{95} +(-1.65626 - 1.20334i) q^{96} +(5.53353 - 7.61626i) q^{97} +(0.951057 + 0.309017i) q^{98} -4.41318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.20334	−	1.65626i	0.694751	−	0.956242i	−0.305241	−	0.952275i	$-0.598737\pi$
$3$	1.20334	−	1.65626i	0.694751	−	0.956242i	0.999992	−	0.00396733i	$-0.00126285\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.62675	−	1.53418i	−0.727503	−	0.686104i
$5$	−1.62675	−	1.53418i	−0.727503	−	0.686104i
$6$	−1.65626	+	1.20334i	−0.676165	+	0.491263i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.368112	−	1.13293i	−0.122704	−	0.377644i
$10$	1.07304	+	1.96178i	0.339325	+	0.620369i
$11$	1.14482	−	3.52339i	0.345176	−	1.06234i	−0.616314	−	0.787501i	$-0.711375\pi$
$11$	1.14482	−	3.52339i	0.345176	−	1.06234i	0.961490	−	0.274841i	$-0.0886253\pi$
$12$	1.94705	−	0.632635i	0.562065	−	0.182626i
$13$	−5.17103	+	1.68017i	−1.43418	+	0.465995i	−0.920079	−	0.391732i	$-0.871876\pi$
$13$	−5.17103	+	1.68017i	−1.43418	+	0.465995i	−0.514105	+	0.857727i	$0.671876\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−4.49853	+	0.848174i	−1.16152	+	0.218998i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.616421	−	0.848431i	−0.149504	−	0.205775i	0.727696	−	0.685900i	$-0.240591\pi$
$17$	−0.616421	−	0.848431i	−0.149504	−	0.205775i	−0.877200	+	0.480125i	$0.840591\pi$
$18$			1.19123i			0.280777i
$19$	5.60491	−	4.07221i	1.28585	−	0.934228i	0.286142	−	0.958187i	$-0.407627\pi$
$19$	5.60491	−	4.07221i	1.28585	−	0.934228i	0.999713	+	0.0239589i	$0.00762709\pi$
$20$	−0.414299	−	2.19735i	−0.0926401	−	0.491343i
$21$	−1.65626	−	1.20334i	−0.361426	−	0.262591i
$22$	−2.17757	+	2.99717i	−0.464260	+	0.639000i
$23$	−7.79323	−	2.53217i	−1.62500	−	0.527995i	−0.651886	−	0.758317i	$-0.726022\pi$
$23$	−7.79323	−	2.53217i	−1.62500	−	0.527995i	−0.973114	+	0.230323i	$0.926022\pi$
$24$	−2.04725			−0.417893
$25$	0.292607	+	4.99143i	0.0585213	+	0.998286i
$26$	5.43714			1.06631
$27$	3.52176	+	1.14429i	0.677763	+	0.220219i
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	4.23292	+	3.07540i	0.786034	+	0.571087i	0.906784	−	0.421596i	$-0.138530\pi$
$29$	4.23292	+	3.07540i	0.786034	+	0.571087i	−0.120750	+	0.992683i	$0.538530\pi$
$30$	4.54046	+	0.583461i	0.828970	+	0.106525i
$31$	−4.20829	+	3.05750i	−0.755831	+	0.549144i	−0.897629	−	0.440752i	$-0.854712\pi$
$31$	−4.20829	+	3.05750i	−0.755831	+	0.549144i	0.141797	+	0.989896i	$0.454712\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.45804	−	6.13597i	−0.776045	−	1.06813i
$34$	0.324072	+	0.997390i	0.0555779	+	0.171051i
$35$	−1.53418	+	1.62675i	−0.259323	+	0.274970i
$36$	0.368112	−	1.13293i	0.0613519	−	0.188822i
$37$	1.19843	−	0.389393i	0.197020	−	0.0640158i	−0.208845	−	0.977949i	$-0.566970\pi$
$37$	1.19843	−	0.389393i	0.197020	−	0.0640158i	0.405865	+	0.913933i	$0.366970\pi$
$38$	−6.58897	+	2.14089i	−1.06887	+	0.347298i
$39$	−3.43972	+	10.5864i	−0.550797	+	1.69518i
$40$	−0.284997	+	2.21783i	−0.0450620	+	0.350670i
$41$	−1.91282	−	5.88707i	−0.298733	−	0.919406i	−0.981942	−	0.189183i	$-0.939416\pi$
$41$	−1.91282	−	5.88707i	−0.298733	−	0.919406i	0.683209	−	0.730223i	$-0.260584\pi$
$42$	1.20334	+	1.65626i	0.185680	+	0.255567i
$43$		−	2.01832i		−	0.307791i	−0.988087	−	0.153896i	$-0.950818\pi$
$43$		−	2.01832i		−	0.307791i	0.988087	−	0.153896i	$-0.0491819\pi$
$44$	2.99717	−	2.17757i	0.451841	−	0.328282i
$45$	−1.13929	+	2.40774i	−0.169836	+	0.358925i
$46$	6.62931	+	4.81648i	0.977439	+	0.710151i
$47$	7.56905	−	10.4179i	1.10406	−	1.51961i	0.274169	−	0.961681i	$-0.411597\pi$
$47$	7.56905	−	10.4179i	1.10406	−	1.51961i	0.829890	−	0.557927i	$-0.188403\pi$
$48$	1.94705	+	0.632635i	0.281033	+	0.0913130i
$49$	−1.00000			−0.142857
$50$	1.26415	−	4.83755i	0.178778	−	0.684133i
$51$	−2.14699			−0.300639
$52$	−5.17103	−	1.68017i	−0.717092	−	0.232997i
$53$	1.15438	−	1.58887i	0.158567	−	0.218248i	−0.722340	−	0.691538i	$-0.756934\pi$
$53$	1.15438	−	1.58887i	0.158567	−	0.218248i	0.880907	+	0.473289i	$0.156934\pi$
$54$	−2.99579	−	2.17657i	−0.407675	−	0.296193i
$55$	−7.26783	+	3.97531i	−0.979994	+	0.536030i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$		−	14.1835i		−	1.87864i
$58$	−3.07540	−	4.23292i	−0.403819	−	0.555810i
$59$	−2.55328	−	7.85820i	−0.332409	−	1.02305i	−0.967984	−	0.251011i	$-0.919237\pi$
$59$	−2.55328	−	7.85820i	−0.332409	−	1.02305i	0.635575	−	0.772039i	$-0.280763\pi$
$60$	−4.13793	−	1.95798i	−0.534205	−	0.252774i
$61$	−0.236698	+	0.728480i	−0.0303060	+	0.0932723i	−0.965065	−	0.262009i	$-0.915615\pi$
$61$	−0.236698	+	0.728480i	−0.0303060	+	0.0932723i	0.934759	+	0.355281i	$0.115615\pi$
$62$	4.94714	−	1.60742i	0.628288	−	0.204143i
$63$	−1.13293	+	0.368112i	−0.142736	+	0.0463777i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	10.9896	+	5.20006i	1.36309	+	0.644988i
$66$	2.34373	+	7.21326i	0.288493	+	0.887891i
$67$	8.23650	+	11.3366i	1.00625	+	1.38498i	0.921412	+	0.388588i	$0.127037\pi$
$67$	8.23650	+	11.3366i	1.00625	+	1.38498i	0.0848372	+	0.996395i	$0.472963\pi$
$68$		−	1.04872i		−	0.127176i
$69$	−13.5719	+	9.86054i	−1.63386	+	1.18707i
$70$	1.96178	−	1.07304i	0.234478	−	0.128253i
$71$	12.9126	+	9.38155i	1.53244	+	1.11338i	0.954861	+	0.297052i	$0.0960034\pi$
$71$	12.9126	+	9.38155i	1.53244	+	1.11338i	0.577581	+	0.816333i	$0.303997\pi$
$72$	−0.700190	+	0.963729i	−0.0825182	+	0.113576i
$73$	1.48193	+	0.481508i	0.173447	+	0.0563563i	0.394453	−	0.918916i	$-0.370934\pi$
$73$	1.48193	+	0.481508i	0.173447	+	0.0563563i	−0.221006	+	0.975272i	$0.570934\pi$
$74$	−1.26010			−0.146484
$75$	8.61922	+	5.52177i	0.995261	+	0.637599i
$76$	6.92805			0.794702
$77$	−3.52339	−	1.14482i	−0.401527	−	0.130464i
$78$	6.54274	−	9.00532i	0.740820	−	1.01965i
$79$	4.52283	+	3.28603i	0.508858	+	0.369707i	0.812390	−	0.583114i	$-0.198166\pi$
$79$	4.52283	+	3.28603i	0.508858	+	0.369707i	−0.303532	+	0.952821i	$0.598166\pi$
$80$	0.956396	−	2.02121i	0.106928	−	0.225979i
$81$	9.02431	−	6.55655i	1.00270	−	0.728505i
$82$			6.19003i			0.683575i
$83$	5.18413	+	7.13534i	0.569032	+	0.783205i	0.992440	−	0.122734i	$-0.0391663\pi$
$83$	5.18413	+	7.13534i	0.569032	+	0.783205i	−0.423408	+	0.905939i	$0.639166\pi$
$84$	−0.632635	−	1.94705i	−0.0690262	−	0.212441i
$85$	−0.298882	+	2.32588i	−0.0324183	+	0.252277i
$86$	−0.623696	+	1.91954i	−0.0672548	+	0.206989i
$87$	10.1873	−	3.31006i	1.09220	−	0.354876i
$88$	−3.52339	+	1.14482i	−0.375595	+	0.122038i
$89$	1.51164	−	4.65234i	0.160233	−	0.493147i	−0.838420	−	0.545024i	$-0.816520\pi$
$89$	1.51164	−	4.65234i	0.160233	−	0.493147i	0.998653	+	0.0518771i	$0.0165204\pi$
$90$	1.82756	−	1.93784i	0.192642	−	0.204266i
$91$	1.68017	+	5.17103i	0.176129	+	0.542071i
$92$	−4.81648	−	6.62931i	−0.502153	−	0.691154i
$93$			10.6493i			1.10428i
$94$	−10.4179	+	7.56905i	−1.07453	+	0.780688i
$95$	−15.3653	−	1.97448i	−1.57644	−	0.202577i
$96$	−1.65626	−	1.20334i	−0.169041	−	0.122816i
$97$	5.53353	−	7.61626i	0.561845	−	0.773314i	−0.429714	−	0.902965i	$-0.641386\pi$
$97$	5.53353	−	7.61626i	0.561845	−	0.773314i	0.991560	+	0.129651i	$0.0413858\pi$
$98$	0.951057	+	0.309017i	0.0960712	+	0.0312154i
$99$	−4.41318			−0.443541
$100$	−2.69717	+	4.21014i	−0.269717	+	0.421014i
$101$	9.21038			0.916467			0.458234	−	0.888832i	$-0.348482\pi$
$101$	9.21038			0.916467			0.458234	+	0.888832i	$0.348482\pi$
$102$	2.04191	+	0.663456i	0.202179	+	0.0656919i
$103$	7.00486	−	9.64136i	0.690209	−	0.949992i	−0.309790	−	0.950805i	$-0.600259\pi$
$103$	7.00486	−	9.64136i	0.690209	−	0.949992i	1.00000		0.000813154i	$0.000258835\pi$
$104$	4.39874	+	3.19587i	0.431332	+	0.313381i
$105$	0.848174	+	4.49853i	0.0827733	+	0.439012i
$106$	−1.58887	+	1.15438i	−0.154325	+	0.112124i
$107$			0.940490i			0.0909206i	0.998966	+	0.0454603i	$0.0144755\pi$
$107$			0.940490i			0.0909206i	−0.998966	+	0.0454603i	$0.985525\pi$
$108$	2.17657	+	2.99579i	0.209440	+	0.288270i
$109$	0.585115	+	1.80080i	0.0560439	+	0.172485i	0.975160	−	0.221501i	$-0.0710957\pi$
$109$	0.585115	+	1.80080i	0.0560439	+	0.172485i	−0.919116	+	0.393986i	$0.871096\pi$
$110$	8.14055	−	1.53486i	0.776171	−	0.146343i
$111$	0.797185	−	2.45348i	0.0756655	−	0.232874i
$112$	0.951057	−	0.309017i	0.0898664	−	0.0291994i
$113$	1.74665	−	0.567520i	0.164311	−	0.0533877i	−0.225707	−	0.974195i	$-0.572469\pi$
$113$	1.74665	−	0.567520i	0.164311	−	0.0533877i	0.390017	+	0.920808i	$0.372469\pi$
$114$	−4.38293	+	13.4893i	−0.410499	+	1.26339i
$115$	8.79280	+	16.0754i	0.819933	+	1.49904i
$116$	1.61683	+	4.97610i	0.150119	+	0.462019i
$117$	3.80703	+	5.23992i	0.351960	+	0.484431i
$118$			8.26260i			0.760634i
$119$	−0.848431	+	0.616421i	−0.0777755	+	0.0565072i
$120$	3.33036	+	3.14084i	0.304019	+	0.286718i
$121$	−2.20448	−	1.60165i	−0.200407	−	0.145604i
$122$	0.450225	−	0.619682i	0.0407615	−	0.0561034i
$123$	−12.0523	−	3.91603i	−1.08672	−	0.353097i
$124$	−5.20173			−0.467130
$125$	7.18174	−	8.56870i	0.642354	−	0.766408i
$126$	1.19123			0.106124
$127$	1.55459	+	0.505117i	0.137948	+	0.0448219i	0.377177	−	0.926141i	$-0.376895\pi$
$127$	1.55459	+	0.505117i	0.137948	+	0.0448219i	−0.239229	+	0.970963i	$0.576895\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−3.34287	−	2.42873i	−0.294323	−	0.213838i
$130$	−8.84484	−	8.34153i	−0.775744	−	0.731600i
$131$	−9.07668	+	6.59459i	−0.793033	+	0.576172i	−0.908862	−	0.417097i	$-0.863048\pi$
$131$	−9.07668	+	6.59459i	−0.793033	+	0.576172i	0.115829	+	0.993269i	$0.463048\pi$
$132$		−	7.58447i		−	0.660143i
$133$	−4.07221	−	5.60491i	−0.353105	−	0.486007i
$134$	−4.33019	−	13.3269i	−0.374071	−	1.15127i
$135$	−3.97347	−	7.26447i	−0.341982	−	0.625226i
$136$	−0.324072	+	0.997390i	−0.0277889	+	0.0855255i
$137$	−18.8727	+	6.13210i	−1.61240	+	0.523901i	−0.970132	−	0.242579i	$-0.922007\pi$
$137$	−18.8727	+	6.13210i	−1.61240	+	0.523901i	−0.642269	+	0.766480i	$0.722007\pi$
$138$	15.9547	−	5.18399i	1.35815	−	0.441291i
$139$	−2.94791	+	9.07272i	−0.250038	+	0.769538i	0.744729	+	0.667367i	$0.232579\pi$
$139$	−2.94791	+	9.07272i	−0.250038	+	0.769538i	−0.994767	+	0.102171i	$0.967421\pi$
$140$	−2.19735	+	0.414299i	−0.185710	+	0.0350147i
$141$	−8.14660	−	25.0726i	−0.686067	−	2.11150i
$142$	−9.38155	−	12.9126i	−0.787282	−	1.08360i
$143$			20.1430i			1.68444i
$144$	0.963729	−	0.700190i	0.0803107	−	0.0583491i
$145$	−2.16769	−	11.4969i	−0.180017	−	0.954769i
$146$	−1.26060	−	0.915883i	−0.104328	−	0.0757990i
$147$	−1.20334	+	1.65626i	−0.0992501	+	0.136606i
$148$	1.19843	+	0.389393i	0.0985102	+	0.0320079i
$149$	7.99240			0.654763			0.327381	−	0.944892i	$-0.393834\pi$
$149$	7.99240			0.654763			0.327381	+	0.944892i	$0.393834\pi$
$150$	−6.49104	−	7.91500i	−0.529991	−	0.646257i
$151$	−4.99617			−0.406583			−0.203291	−	0.979118i	$-0.565164\pi$
$151$	−4.99617			−0.406583			−0.203291	+	0.979118i	$0.565164\pi$
$152$	−6.58897	−	2.14089i	−0.534436	−	0.173649i
$153$	−0.734302	+	1.01068i	−0.0593648	+	0.0817086i
$154$	2.99717	+	2.17757i	0.241519	+	0.175474i
$155$	11.5366	+	1.48248i	0.926640	+	0.119076i
$156$	−9.00532	+	6.54274i	−0.721002	+	0.523839i
$157$		−	15.0745i		−	1.20308i	−0.798843	−	0.601539i	$-0.794554\pi$
$157$		−	15.0745i		−	1.20308i	0.798843	−	0.601539i	$-0.205446\pi$
$158$	−3.28603	−	4.52283i	−0.261423	−	0.359817i
$159$	−1.24247	−	3.82392i	−0.0985340	−	0.303257i
$160$	−1.53418	+	1.62675i	−0.121287	+	0.128606i
$161$	−2.53217	+	7.79323i	−0.199563	+	0.614192i
$162$	−10.6087	+	3.44698i	−0.833499	+	0.270820i
$163$	−1.75204	+	0.569271i	−0.137230	+	0.0445887i	−0.376827	−	0.926284i	$-0.622985\pi$
$163$	−1.75204	+	0.569271i	−0.137230	+	0.0445887i	0.239597	+	0.970872i	$0.422985\pi$
$164$	1.91282	−	5.88707i	0.149367	−	0.459703i
$165$	−2.16155	+	16.8211i	−0.168277	+	1.30952i
$166$	−2.72546	−	8.38809i	−0.211536	−	0.651042i
$167$	5.14404	+	7.08016i	0.398057	+	0.547879i	0.960255	−	0.279124i	$-0.0900440\pi$
$167$	5.14404	+	7.08016i	0.398057	+	0.547879i	−0.562198	+	0.827003i	$0.690044\pi$
$168$			2.04725i			0.157949i
$169$	13.3993	−	9.73517i	1.03072	−	0.748859i
$170$	1.00299	−	2.11968i	0.0769258	−	0.162572i
$171$	−6.67676	−	4.85095i	−0.510585	−	0.370961i
$172$	1.18634	−	1.63286i	0.0904575	−	0.124504i
$173$	−21.9319	−	7.12612i	−1.66745	−	0.541789i	−0.685040	−	0.728505i	$-0.740216\pi$
$173$	−21.9319	−	7.12612i	−1.66745	−	0.541789i	−0.982414	+	0.186716i	$0.940216\pi$
$174$	−10.7116			−0.812043
$175$	4.99143	−	0.292607i	0.377317	−	0.0221190i
$176$	3.70471			0.279253
$177$	−16.0877	−	5.22721i	−1.20923	−	0.392901i
$178$	−2.87531	+	3.95752i	−0.215513	+	0.296629i
$179$	−12.5150	−	9.09267i	−0.935414	−	0.679618i	0.0118987	−	0.999929i	$-0.496212\pi$
$179$	−12.5150	−	9.09267i	−0.935414	−	0.679618i	−0.947312	+	0.320311i	$0.896212\pi$
$180$	−2.33694	+	1.27824i	−0.174185	+	0.0952746i
$181$	7.91006	−	5.74700i	0.587950	−	0.427171i	−0.253631	−	0.967301i	$-0.581625\pi$
$181$	7.91006	−	5.74700i	0.587950	−	0.427171i	0.841581	+	0.540130i	$0.181625\pi$
$182$		−	5.43714i		−	0.403027i
$183$	0.921724	+	1.26864i	0.0681358	+	0.0937809i
$184$	2.53217	+	7.79323i	0.186674	+	0.574524i
$185$	−2.54694	−	1.20516i	−0.187255	−	0.0886049i
$186$	3.29080	−	10.1280i	0.241293	−	0.742624i
$187$	−3.69504	+	1.20059i	−0.270208	+	0.0877960i
$188$	12.2470	−	3.97929i	0.893203	−	0.290219i
$189$	1.14429	−	3.52176i	0.0832348	−	0.256170i
$190$	14.0031	+	6.62596i	1.01589	+	0.480698i
$191$	−1.75638	−	5.40557i	−0.127087	−	0.391134i	0.867189	−	0.497980i	$-0.165925\pi$
$191$	−1.75638	−	5.40557i	−0.127087	−	0.391134i	−0.994276	+	0.106846i	$0.965925\pi$
$192$	1.20334	+	1.65626i	0.0868438	+	0.119530i
$193$			2.69609i			0.194069i	0.995281	+	0.0970344i	$0.0309357\pi$
$193$			2.69609i			0.194069i	−0.995281	+	0.0970344i	$0.969064\pi$
$194$	−7.61626	+	5.53353i	−0.546815	+	0.397285i
$195$	21.8369	−	11.9442i	1.56378	−	0.855343i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−10.2138	+	14.0580i	−0.727700	+	1.00159i	0.271533	+	0.962429i	$0.412469\pi$
$197$	−10.2138	+	14.0580i	−0.727700	+	1.00159i	−0.999233	+	0.0391637i	$0.987531\pi$
$198$	4.19718	+	1.36375i	0.298281	+	0.0969173i
$199$	−20.1465			−1.42815			−0.714073	−	0.700071i	$-0.753152\pi$
$199$	−20.1465			−1.42815			−0.714073	+	0.700071i	$0.753152\pi$
$200$	3.86616	−	3.17061i	0.273379	−	0.224196i
$201$	28.6877			2.02347
$202$	−8.75959	−	2.84616i	−0.616323	−	0.200255i
$203$	3.07540	−	4.23292i	0.215851	−	0.297093i
$204$	−1.73695	−	1.26197i	−0.121611	−	0.0883555i
$205$	−5.92012	+	12.5114i	−0.413479	+	0.873833i
$206$	−9.64136	+	7.00486i	−0.671746	+	0.488052i
$207$			9.76131i			0.678458i
$208$	−3.19587	−	4.39874i	−0.221594	−	0.304998i
$209$	−7.93136	−	24.4102i	−0.548624	−	1.68849i
$210$	0.583461	−	4.54046i	0.0402626	−	0.313321i
$211$	−6.64749	+	20.4589i	−0.457632	+	1.40845i	0.410386	+	0.911912i	$0.365394\pi$
$211$	−6.64749	+	20.4589i	−0.457632	+	1.40845i	−0.868017	+	0.496534i	$0.834606\pi$
$212$	1.86783	−	0.606895i	0.128283	−	0.0416818i
$213$	31.0766	−	10.0974i	2.12933	−	0.691862i
$214$	0.290627	−	0.894459i	0.0198669	−	0.0611440i
$215$	−3.09646	+	3.28330i	−0.211177	+	0.223919i
$216$	−1.14429	−	3.52176i	−0.0778590	−	0.239625i
$217$	3.05750	+	4.20829i	0.207557	+	0.285677i
$218$		−	1.89347i		−	0.128242i
$219$	2.58077	−	1.87504i	0.174393	−	0.126704i
$220$	−8.21642	−	1.05583i	−0.553951	−	0.0711842i
$221$	4.61304	+	3.35157i	0.310306	+	0.225451i
$222$	−1.51634	+	2.08706i	−0.101770	+	0.140074i
$223$	−4.24919	−	1.38064i	−0.284547	−	0.0924548i	0.163266	−	0.986582i	$-0.447797\pi$
$223$	−4.24919	−	1.38064i	−0.284547	−	0.0924548i	−0.447813	+	0.894127i	$0.647797\pi$
$224$	−1.00000			−0.0668153
$225$	5.54723	−	2.16891i	0.369816	−	0.144594i
$226$	−1.83653			−0.122164
$227$	26.5494	+	8.62641i	1.76214	+	0.572555i	0.997419	−	0.0718033i	$-0.0228754\pi$
$227$	26.5494	+	8.62641i	1.76214	+	0.572555i	0.764724	+	0.644358i	$0.222875\pi$
$228$	8.33683	−	11.4747i	0.552120	−	0.759928i
$229$	13.3984	+	9.73452i	0.885393	+	0.643275i	0.934673	−	0.355510i	$-0.115693\pi$
$229$	13.3984	+	9.73452i	0.885393	+	0.643275i	−0.0492801	+	0.998785i	$0.515693\pi$
$230$	−3.39489	−	18.0057i	−0.223852	−	1.18726i
$231$	−6.13597	+	4.45804i	−0.403717	+	0.293317i
$232$		−	5.23218i		−	0.343509i
$233$	−8.97637	−	12.3549i	−0.588061	−	0.809397i	0.406489	−	0.913656i	$-0.366753\pi$
$233$	−8.97637	−	12.3549i	−0.588061	−	0.809397i	−0.994550	+	0.104259i	$0.966753\pi$
$234$	−2.00147	−	6.15990i	−0.130840	−	0.402685i
$235$	−28.2958	+	5.33503i	−1.84582	+	0.348019i
$236$	2.55328	−	7.85820i	0.166205	−	0.511525i
$237$	10.8850	−	3.53677i	0.707060	−	0.229738i
$238$	0.997390	−	0.324072i	0.0646512	−	0.0210065i
$239$	−2.53920	+	7.81485i	−0.164247	+	0.505501i	−0.998980	−	0.0451544i	$-0.985622\pi$
$239$	−2.53920	+	7.81485i	−0.164247	+	0.505501i	0.834733	+	0.550655i	$0.185622\pi$
$240$	−2.19678	−	4.01626i	−0.141802	−	0.259248i
$241$	−1.30607	−	4.01968i	−0.0841315	−	0.258930i	0.900138	−	0.435605i	$-0.143466\pi$
$241$	−1.30607	−	4.01968i	−0.0841315	−	0.258930i	−0.984269	+	0.176675i	$0.943466\pi$
$242$	1.60165	+	2.20448i	0.102958	+	0.141709i
$243$		−	11.7274i		−	0.752313i
$244$	−0.619682	+	0.450225i	−0.0396711	+	0.0288227i
$245$	1.62675	+	1.53418i	0.103929	+	0.0980149i
$246$	10.2523	+	7.44873i	0.653663	+	0.474914i
$247$	−22.1411	+	30.4747i	−1.40881	+	1.93906i
$248$	4.94714	+	1.60742i	0.314144	+	0.102072i
$249$	18.0563			1.14427
$250$	−9.47811	+	5.93004i	−0.599448	+	0.375049i
$251$	−14.9206			−0.941778			−0.470889	−	0.882193i	$-0.656067\pi$
$251$	−14.9206			−0.941778			−0.470889	+	0.882193i	$0.656067\pi$
$252$	−1.13293	−	0.368112i	−0.0713679	−	0.0231888i
$253$	−17.8437	+	24.5597i	−1.12182	+	1.54405i
$254$	−1.32241	−	0.960790i	−0.0829756	−	0.0602853i
$255$	3.49261	+	3.29386i	0.218716	+	0.206269i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			5.15022i			0.321262i	0.987015	+	0.160631i	$0.0513529\pi$
$257$			5.15022i			0.321262i	−0.987015	+	0.160631i	$0.948647\pi$
$258$	2.42873	+	3.34287i	0.151206	+	0.208118i
$259$	−0.389393	−	1.19843i	−0.0241957	−	0.0744667i
$260$	5.83427	+	10.6665i	0.361826	+	0.661506i
$261$	1.92603	−	5.92770i	0.119218	−	0.366915i
$262$	10.6703	−	3.46698i	0.659212	−	0.214191i
$263$	2.59767	−	0.844033i	0.160179	−	0.0520453i	−0.227830	−	0.973701i	$-0.573163\pi$
$263$	2.59767	−	0.844033i	0.160179	−	0.0520453i	0.388009	+	0.921656i	$0.373163\pi$
$264$	−2.34373	+	7.21326i	−0.144247	+	0.443945i
$265$	−4.31550	+	0.813665i	−0.265099	+	0.0499830i
$266$	2.14089	+	6.58897i	0.131266	+	0.403996i
$267$	−5.88647	−	8.10203i	−0.360246	−	0.495836i
$268$			14.0128i			0.855966i
$269$	2.90991	−	2.11417i	0.177420	−	0.128903i	−0.495531	−	0.868590i	$-0.665026\pi$
$269$	2.90991	−	2.11417i	0.177420	−	0.128903i	0.672951	+	0.739687i	$0.265026\pi$
$270$	1.53415	+	8.13679i	0.0933653	+	0.495189i
$271$	−11.4232	−	8.29944i	−0.693910	−	0.504155i	0.184033	−	0.982920i	$-0.441085\pi$
$271$	−11.4232	−	8.29944i	−0.693910	−	0.504155i	−0.877943	+	0.478765i	$0.841085\pi$
$272$	0.616421	−	0.848431i	0.0373760	−	0.0514437i
$273$	10.5864	+	3.43972i	0.640717	+	0.208182i
$274$	19.8439			1.19881
$275$	17.9217	+	4.68332i	1.08072	+	0.282415i
$276$	−16.7758			−1.00978
$277$	20.0641	+	6.51922i	1.20553	+	0.391702i	0.841794	−	0.539798i	$-0.181500\pi$
$277$	20.0641	+	6.51922i	1.20553	+	0.391702i	0.363740	+	0.931500i	$0.381500\pi$
$278$	5.60725	−	7.71772i	0.336300	−	0.462878i
$279$	5.01306	+	3.64220i	0.300124	+	0.218053i
$280$	2.21783	+	0.284997i	0.132541	+	0.0170318i
$281$	−15.8770	+	11.5353i	−0.947143	+	0.688140i	−0.950129	−	0.311856i	$-0.899049\pi$
$281$	−15.8770	+	11.5353i	−0.947143	+	0.688140i	0.00298618	+	0.999996i	$0.499049\pi$
$282$			26.3629i			1.56989i
$283$	−3.76104	−	5.17663i	−0.223571	−	0.307719i	0.682466	−	0.730917i	$-0.260907\pi$
$283$	−3.76104	−	5.17663i	−0.223571	−	0.307719i	−0.906037	+	0.423198i	$0.860907\pi$
$284$	4.93217	+	15.1797i	0.292671	+	0.900747i
$285$	−21.7599	+	23.0729i	−1.28895	+	1.36672i
$286$	6.22454	−	19.1572i	0.368065	−	1.13279i
$287$	−5.88707	+	1.91282i	−0.347503	+	0.112910i
$288$	−1.13293	+	0.368112i	−0.0667586	+	0.0216912i
$289$	4.91343	−	15.1220i	0.289025	−	0.889528i
$290$	−1.49116	+	11.6041i	−0.0875637	+	0.681416i
$291$	−5.95576	−	18.3299i	−0.349133	−	1.07452i
$292$	0.915883	+	1.26060i	0.0535980	+	0.0737713i
$293$			26.5777i			1.55269i	0.630309	+	0.776344i	$0.282928\pi$
$293$			26.5777i			1.55269i	−0.630309	+	0.776344i	$0.717072\pi$
$294$	1.65626	−	1.20334i	0.0965951	−	0.0701804i
$295$	−7.90232	+	16.7005i	−0.460091	+	0.972340i
$296$	−1.01944	−	0.740670i	−0.0592540	−	0.0430505i
$297$	8.06355	−	11.0985i	0.467895	−	0.644002i
$298$	−7.60122	−	2.46979i	−0.440327	−	0.143071i
$299$	44.5534			2.57659
$300$	3.72747	+	9.53346i	0.215206	+	0.550414i
$301$	−2.01832			−0.116334
$302$	4.75164	+	1.54390i	0.273426	+	0.0888415i
$303$	11.0833	−	15.2548i	0.636716	−	0.876365i
$304$	5.60491	+	4.07221i	0.321464	+	0.233557i
$305$	1.50266	−	0.821916i	0.0860423	−	0.0470628i
$306$	1.01068	−	0.734302i	0.0577767	−	0.0419772i
$307$			7.25901i			0.414293i	0.978310	+	0.207147i	$0.0664177\pi$
$307$			7.25901i			0.414293i	−0.978310	+	0.207147i	$0.933582\pi$
$308$	−2.17757	−	2.99717i	−0.124079	−	0.170780i
$309$	−7.53935	−	23.2037i	−0.428899	−	1.32001i
$310$	−10.5138	−	4.97492i	−0.597145	−	0.282556i
$311$	2.15817	−	6.64215i	0.122378	−	0.376642i	−0.871036	−	0.491219i	$-0.836551\pi$
$311$	2.15817	−	6.64215i	0.122378	−	0.376642i	0.993414	+	0.114577i	$0.0365514\pi$
$312$	10.5864	−	3.43972i	0.599336	−	0.194736i
$313$	−6.15492	+	1.99985i	−0.347897	+	0.113038i	−0.477753	−	0.878494i	$-0.658548\pi$
$313$	−6.15492	+	1.99985i	−0.347897	+	0.113038i	0.129856	+	0.991533i	$0.458548\pi$
$314$	−4.65829	+	14.3367i	−0.262882	+	0.809069i
$315$	2.40774	+	1.13929i	0.135661	+	0.0641918i
$316$	1.72757	+	5.31691i	0.0971833	+	0.299100i
$317$	−3.84707	−	5.29504i	−0.216073	−	0.297399i	0.687197	−	0.726471i	$-0.258841\pi$
$317$	−3.84707	−	5.29504i	−0.216073	−	0.297399i	−0.903270	+	0.429072i	$0.858841\pi$
$318$			4.02071i			0.225470i
$319$	15.6818	−	11.3935i	0.878009	−	0.637911i
$320$	1.96178	−	1.07304i	0.109667	−	0.0599848i
$321$	1.55770	+	1.13173i	0.0869421	+	0.0631671i
$322$	4.81648	−	6.62931i	0.268412	−	0.369437i
$323$	−6.90997	−	2.24519i	−0.384481	−	0.124926i
$324$	11.1547			0.619704
$325$	−9.89952	−	25.3192i	−0.549126	−	1.40446i
$326$	1.84220			0.102030
$327$	3.68669	+	1.19788i	0.203874	+	0.0662428i
$328$	−3.63841	+	5.00784i	−0.200898	+	0.276512i
$329$	−10.4179	−	7.56905i	−0.574358	−	0.417295i
$330$	7.25376	−	15.3298i	0.399306	−	0.843880i
$331$	21.8398	−	15.8675i	1.20042	−	0.872159i	0.206097	−	0.978531i	$-0.433924\pi$
$331$	21.8398	−	15.8675i	1.20042	−	0.872159i	0.994326	+	0.106373i	$0.0339237\pi$
$332$			8.81976i			0.484047i
$333$	−0.882311	−	1.21440i	−0.0483503	−	0.0665485i
$334$	−2.70438	−	8.32322i	−0.147977	−	0.455427i
$335$	3.99360	−	31.0780i	0.218194	−	1.69797i
$336$	0.632635	−	1.94705i	0.0345131	−	0.106220i
$337$	18.2729	−	5.93724i	0.995390	−	0.323422i	0.234368	−	0.972148i	$-0.424698\pi$
$337$	18.2729	−	5.93724i	0.995390	−	0.323422i	0.761022	+	0.648726i	$0.224698\pi$
$338$	−15.7518	+	5.11808i	−0.856787	+	0.278387i
$339$	1.16185	−	3.57582i	0.0631033	−	0.194212i
$340$	−1.60892	+	1.70600i	−0.0872559	+	0.0925208i
$341$	5.95504	+	18.3277i	0.322484	+	0.992503i
$342$	4.85095	+	6.67676i	0.262309	+	0.361038i
$343$			1.00000i			0.0539949i
$344$	−1.63286	+	1.18634i	−0.0880377	+	0.0639631i
$345$	37.2058	+	4.78104i	2.00309	+	0.257403i
$346$	18.6564	+	13.5547i	1.00298	+	0.728704i
$347$	−15.2226	+	20.9522i	−0.817194	+	1.12477i	0.172980	+	0.984925i	$0.444660\pi$
$347$	−15.2226	+	20.9522i	−0.817194	+	1.12477i	−0.990173	+	0.139845i	$0.955340\pi$
$348$	10.1873	+	3.31006i	0.546098	+	0.177438i
$349$	−7.59474			−0.406537			−0.203269	−	0.979123i	$-0.565156\pi$
$349$	−7.59474			−0.406537			−0.203269	+	0.979123i	$0.565156\pi$
$350$	−4.83755	−	1.26415i	−0.258578	−	0.0675717i
$351$	−20.1337			−1.07466
$352$	−3.52339	−	1.14482i	−0.187797	−	0.0610190i
$353$	−5.40534	+	7.43981i	−0.287697	+	0.395981i	−0.928264	−	0.371921i	$-0.878699\pi$
$353$	−5.40534	+	7.43981i	−0.287697	+	0.395981i	0.640567	+	0.767902i	$0.278699\pi$
$354$	13.6850	+	9.94275i	0.727351	+	0.528451i
$355$	−6.61256	−	35.0716i	−0.350958	−	1.86141i
$356$	3.95752	−	2.87531i	0.209748	−	0.152391i
$357$			2.14699i			0.113631i
$358$	9.09267	+	12.5150i	0.480562	+	0.661437i
$359$	1.51355	+	4.65822i	0.0798820	+	0.245851i	0.983020	−	0.183499i	$-0.0587425\pi$
$359$	1.51355	+	4.65822i	0.0798820	+	0.245851i	−0.903138	+	0.429351i	$0.858742\pi$
$360$	2.61756	−	0.493527i	0.137958	−	0.0260112i
$361$	8.96084	−	27.5786i	0.471623	−	1.45151i
$362$	−9.29883	+	3.02137i	−0.488736	+	0.158800i
$363$	−5.30548	+	1.72386i	−0.278466	+	0.0904790i
$364$	−1.68017	+	5.17103i	−0.0880647	+	0.271035i
$365$	−1.67201	−	3.05683i	−0.0875168	−	0.160002i
$366$	−0.484579	−	1.49138i	−0.0253294	−	0.0779557i
$367$	7.59134	+	10.4486i	0.396265	+	0.545411i	0.959802	−	0.280679i	$-0.0905598\pi$
$367$	7.59134	+	10.4486i	0.396265	+	0.545411i	−0.563537	+	0.826091i	$0.690560\pi$
$368$		−	8.19428i		−	0.427157i
$369$	−5.96551	+	4.33420i	−0.310552	+	0.225629i
$370$	2.04987	+	1.93322i	0.106568	+	0.100503i
$371$	−1.58887	−	1.15438i	−0.0824902	−	0.0599326i
$372$	−6.25947	+	8.61543i	−0.324539	+	0.446689i
$373$	2.76168	+	0.897324i	0.142994	+	0.0464617i	0.379640	−	0.925134i	$-0.376048\pi$
$373$	2.76168	+	0.897324i	0.142994	+	0.0464617i	−0.236645	+	0.971596i	$0.576048\pi$
$374$	3.88520			0.200899
$375$	−5.54990	−	22.2059i	−0.286596	−	1.14671i
$376$	−12.8772			−0.664093
$377$	−27.0557	−	8.79094i	−1.39344	−	0.452756i
$378$	−2.17657	+	2.99579i	−0.111951	+	0.154087i
$379$	15.4142	+	11.1991i	0.791776	+	0.575259i	0.908490	−	0.417907i	$-0.137236\pi$
$379$	15.4142	+	11.1991i	0.791776	+	0.575259i	−0.116714	+	0.993166i	$0.537236\pi$
$380$	−11.2702	−	10.6289i	−0.578148	−	0.545249i
$381$	2.70731	−	1.96698i	0.138700	−	0.100771i
$382$			5.68376i			0.290806i
$383$	−2.63616	−	3.62836i	−0.134702	−	0.185401i	0.736338	−	0.676614i	$-0.236553\pi$
$383$	−2.63616	−	3.62836i	−0.134702	−	0.185401i	−0.871039	+	0.491213i	$0.836553\pi$
$384$	−0.632635	−	1.94705i	−0.0322840	−	0.0993600i
$385$	3.97531	+	7.26783i	0.202600	+	0.370403i
$386$	0.833137	−	2.56413i	0.0424056	−	0.130511i
$387$	−2.28662	+	0.742967i	−0.116235	+	0.0377672i
$388$	8.95345	−	2.90915i	0.454542	−	0.147690i
$389$	−4.38681	+	13.5012i	−0.222420	+	0.684539i	0.776123	+	0.630581i	$0.217183\pi$
$389$	−4.38681	+	13.5012i	−0.222420	+	0.684539i	−0.998543	+	0.0539573i	$0.982817\pi$
$390$	−24.4591	+	4.61164i	−1.23854	+	0.233519i
$391$	2.65554	+	8.17290i	0.134296	+	0.413321i
$392$	0.587785	+	0.809017i	0.0296876	+	0.0408615i
$393$			22.9689i			1.15863i
$394$	14.0580	−	10.2138i	0.708233	−	0.514561i
$395$	−2.31615	−	12.2844i	−0.116538	−	0.618093i
$396$	−3.57034	−	2.59400i	−0.179416	−	0.130353i
$397$	−2.36395	+	3.25370i	−0.118643	+	0.163299i	−0.864208	−	0.503135i	$-0.832180\pi$
$397$	−2.36395	+	3.25370i	−0.118643	+	0.163299i	0.745565	+	0.666433i	$0.232180\pi$
$398$	19.1604	+	6.22560i	0.960426	+	0.312061i
$399$	−14.1835			−0.710061
$400$	−4.65671	+	1.82072i	−0.232836	+	0.0910361i
$401$	1.16128			0.0579914			0.0289957	−	0.999580i	$-0.490769\pi$
$401$	1.16128			0.0579914			0.0289957	+	0.999580i	$0.490769\pi$
$402$	−27.2836	−	8.86497i	−1.36078	−	0.442145i
$403$	16.6241	−	22.8811i	0.828104	−	1.13979i
$404$	7.45135	+	5.41373i	0.370719	+	0.269343i
$405$	−24.7392	−	3.17905i	−1.22930	−	0.157968i
$406$	−4.23292	+	3.07540i	−0.210076	+	0.152629i
$407$		−	4.66831i		−	0.231400i
$408$	1.26197	+	1.73695i	0.0624768	+	0.0859919i
$409$	−0.202092	−	0.621975i	−0.00999280	−	0.0307547i	0.945936	−	0.324354i	$-0.105147\pi$
$409$	−0.202092	−	0.621975i	−0.00999280	−	0.0307547i	−0.955929	+	0.293599i	$0.905147\pi$
$410$	9.49660	−	10.0696i	0.469004	−	0.497303i
$411$	−12.5539	+	38.6371i	−0.619240	+	1.90583i
$412$	11.3341	−	3.68267i	0.558391	−	0.181432i
$413$	−7.85820	+	2.55328i	−0.386677	+	0.125639i
$414$	3.01641	−	9.28356i	0.148248	−	0.456262i
$415$	2.51361	−	19.5607i	0.123388	−	0.960199i
$416$	1.68017	+	5.17103i	0.0823770	+	0.253530i
$417$	11.4794	+	15.8001i	0.562151	+	0.773734i
$418$			25.6664i			1.25539i
$419$	26.3707	−	19.1594i	1.28829	−	0.936000i	0.288524	−	0.957473i	$-0.406836\pi$
$419$	26.3707	−	19.1594i	1.28829	−	0.936000i	0.999769	+	0.0214732i	$0.00683564\pi$
$420$	−1.95798	+	4.13793i	−0.0955397	+	0.201910i
$421$	−22.1215	−	16.0722i	−1.07813	−	0.783311i	−0.100778	−	0.994909i	$-0.532133\pi$
$421$	−22.1215	−	16.0722i	−1.07813	−	0.783311i	−0.977357	+	0.211598i	$0.932133\pi$
$422$	12.6443	−	17.4033i	0.615513	−	0.847182i
$423$	−14.5890	−	4.74026i	−0.709343	−	0.230479i
$424$	−1.96396			−0.0953781
$425$	4.05452	−	3.32508i	0.196673	−	0.161290i
$426$	−32.6758			−1.58315
$427$	0.728480	+	0.236698i	0.0352536	+	0.0114546i
$428$	−0.552806	+	0.760872i	−0.0267209	+	0.0367782i
$429$	33.3621	+	24.2390i	1.61074	+	1.17027i
$430$	3.95950	−	2.16574i	0.190944	−	0.104441i
$431$	14.1594	−	10.2874i	0.682035	−	0.495528i	−0.191997	−	0.981396i	$-0.561496\pi$
$431$	14.1594	−	10.2874i	0.682035	−	0.495528i	0.874032	+	0.485868i	$0.161496\pi$
$432$			3.70300i			0.178161i
$433$	18.7372	+	25.7896i	0.900455	+	1.23937i	0.970323	+	0.241813i	$0.0777421\pi$
$433$	18.7372	+	25.7896i	0.900455	+	1.23937i	−0.0698683	+	0.997556i	$0.522258\pi$
$434$	−1.60742	−	4.94714i	−0.0771588	−	0.237470i
$435$	−21.6504	−	10.2445i	−1.03806	−	0.491187i
$436$	−0.585115	+	1.80080i	−0.0280219	+	0.0862426i
$437$	−53.9919	+	17.5430i	−2.58278	+	0.839197i
$438$	−3.03388	+	0.985768i	−0.144964	+	0.0471018i
$439$	−2.67562	+	8.23470i	−0.127700	+	0.393021i	−0.994383	−	0.105838i	$-0.966247\pi$
$439$	−2.67562	+	8.23470i	−0.127700	+	0.393021i	0.866683	+	0.498859i	$0.166247\pi$
$440$	7.48801	+	3.54317i	0.356977	+	0.168914i
$441$	0.368112	+	1.13293i	0.0175291	+	0.0539491i
$442$	−3.35157	−	4.61304i	−0.159418	−	0.219420i
$443$			9.67961i			0.459892i	0.973203	+	0.229946i	$0.0738550\pi$
$443$			9.67961i			0.459892i	−0.973203	+	0.229946i	$0.926145\pi$
$444$	2.08706	−	1.51634i	0.0990474	−	0.0719621i
$445$	−9.59656	+	5.24906i	−0.454921	+	0.248829i
$446$	3.61457	+	2.62614i	0.171155	+	0.124351i
$447$	9.61760	−	13.2375i	0.454897	−	0.626112i
$448$	0.951057	+	0.309017i	0.0449332	+	0.0145997i
$449$	−26.0284			−1.22835			−0.614177	−	0.789168i	$-0.710512\pi$
$449$	−26.0284			−1.22835			−0.614177	+	0.789168i	$0.710512\pi$
$450$	−5.94596	+	0.348563i	−0.280295	+	0.0164314i
$451$	−22.9323			−1.07984
$452$	1.74665	+	0.567520i	0.0821553	+	0.0266939i
$453$	−6.01211	+	8.27496i	−0.282474	+	0.388791i
$454$	−22.5842	−	16.4084i	−1.05993	−	0.770085i
$455$	5.20006	−	10.9896i	0.243782	−	0.515201i
$456$	−11.4747	+	8.33683i	−0.537350	+	0.390408i
$457$		−	1.06105i		−	0.0496338i	−0.999692	−	0.0248169i	$-0.992100\pi$
$457$		−	1.06105i		−	0.0496338i	0.999692	−	0.0248169i	$-0.00790027\pi$
$458$	−9.73452	−	13.3984i	−0.454864	−	0.626067i
$459$	−1.20004	−	3.69333i	−0.0560129	−	0.172390i
$460$	−2.33535	+	18.1735i	−0.108886	+	0.847346i
$461$	−13.2451	+	40.7643i	−0.616886	+	1.89858i	−0.250508	+	0.968114i	$0.580598\pi$
$461$	−13.2451	+	40.7643i	−0.616886	+	1.89858i	−0.366378	+	0.930466i	$0.619402\pi$
$462$	7.21326	−	2.34373i	0.335591	−	0.109040i
$463$	31.4835	−	10.2296i	1.46316	−	0.475410i	0.534127	−	0.845404i	$-0.320640\pi$
$463$	31.4835	−	10.2296i	1.46316	−	0.475410i	0.929034	+	0.369994i	$0.120640\pi$
$464$	−1.61683	+	4.97610i	−0.0750595	+	0.231010i
$465$	16.3378	−	17.3236i	0.757649	−	0.803364i
$466$	4.71915	+	14.5241i	0.218611	+	0.672814i
$467$	18.9278	+	26.0519i	0.875873	+	1.20554i	0.977547	+	0.210718i	$0.0675803\pi$
$467$	18.9278	+	26.0519i	0.875873	+	1.20554i	−0.101673	+	0.994818i	$0.532420\pi$
$468$			6.47690i			0.299395i
$469$	11.3366	−	8.23650i	0.523474	−	0.380326i
$470$	28.5596	+	3.66998i	1.31735	+	0.169283i
$471$	−24.9673	−	18.1398i	−1.15043	−	0.835840i
$472$	−4.85664	+	6.68459i	−0.223545	+	0.307683i
$473$	−7.11133	−	2.31061i	−0.326979	−	0.106242i
$474$	−11.4452			−0.525696
$475$	21.9662	+	26.7850i	1.00788	+	1.22898i
$476$	−1.04872			−0.0480679
$477$	−2.22503	−	0.722955i	−0.101877	−	0.0331018i
$478$	4.82984	−	6.64771i	0.220912	−	0.304059i
$479$	−18.3459	−	13.3290i	−0.838244	−	0.609020i	0.0836358	−	0.996496i	$-0.473347\pi$
$479$	−18.3459	−	13.3290i	−0.838244	−	0.609020i	−0.921879	+	0.387477i	$0.873347\pi$
$480$	0.848174	+	4.49853i	0.0387137	+	0.205329i
$481$	−5.54286	+	4.02712i	−0.252733	+	0.183621i
$482$			4.22654i			0.192513i
$483$	9.86054	+	13.5719i	0.448670	+	0.617541i
$484$	−0.842035	−	2.59152i	−0.0382743	−	0.117796i
$485$	−20.6863	+	3.90030i	−0.939318	+	0.177103i
$486$	−3.62397	+	11.1534i	−0.164386	+	0.505929i
$487$	31.6556	−	10.2855i	1.43445	−	0.466082i	0.514289	−	0.857617i	$-0.328056\pi$
$487$	31.6556	−	10.2855i	1.43445	−	0.466082i	0.920163	+	0.391535i	$0.128056\pi$
$488$	0.728480	−	0.236698i	0.0329767	−	0.0107148i
$489$	−1.16544	+	3.58685i	−0.0527030	+	0.162203i
$490$	−1.07304	−	1.96178i	−0.0484751	−	0.0886242i
$491$	−1.33230	−	4.10039i	−0.0601257	−	0.185048i	0.916482	−	0.400075i	$-0.131016\pi$
$491$	−1.33230	−	4.10039i	−0.0601257	−	0.185048i	−0.976608	+	0.215027i	$0.931016\pi$
$492$	−7.44873	−	10.2523i	−0.335815	−	0.462209i
$493$		−	5.48708i		−	0.247126i
$494$	30.4747	−	22.1411i	1.37112	−	0.996177i
$495$	7.17912	+	6.77059i	0.322677	+	0.304315i
$496$	−4.20829	−	3.05750i	−0.188958	−	0.137286i
$497$	9.38155	−	12.9126i	0.420820	−	0.579209i
$498$	−17.1725	−	5.57969i	−0.769519	−	0.250032i
$499$	0.685540			0.0306890			0.0153445	−	0.999882i	$-0.495116\pi$
$499$	0.685540			0.0306890			0.0153445	+	0.999882i	$0.495116\pi$
$500$	10.8467	−	2.71091i	0.485079	−	0.121235i
$501$	17.9166			0.800456
$502$	14.1903	+	4.61071i	0.633344	+	0.205786i
$503$	−23.9292	+	32.9357i	−1.06695	+	1.46853i	−0.193826	+	0.981036i	$0.562090\pi$
$503$	−23.9292	+	32.9357i	−1.06695	+	1.46853i	−0.873125	+	0.487496i	$0.837910\pi$
$504$	0.963729	+	0.700190i	0.0429279	+	0.0311889i
$505$	−14.9830	−	14.1303i	−0.666733	−	0.628792i
$506$	24.5597	−	17.8437i	1.09181	−	0.793248i
$507$		−	33.9075i		−	1.50589i
$508$	0.960790	+	1.32241i	0.0426282	+	0.0586726i
$509$	−6.23231	−	19.1811i	−0.276242	−	0.850186i	−0.988888	−	0.148662i	$-0.952503\pi$
$509$	−6.23231	−	19.1811i	−0.276242	−	0.850186i	0.712646	−	0.701524i	$-0.247497\pi$
$510$	−2.30381	−	4.21192i	−0.102014	−	0.186507i
$511$	0.481508	−	1.48193i	0.0213007	−	0.0655567i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	24.3989	−	7.92769i	1.07724	−	0.350016i
$514$	1.59150	−	4.89815i	0.0701982	−	0.216048i
$515$	−26.1867	+	4.93736i	−1.15392	+	0.217566i
$516$	−1.27686	−	3.92977i	−0.0562107	−	0.172999i
$517$	−28.0412	−	38.5953i	−1.23325	−	1.69742i
$518$			1.26010i			0.0553657i
$519$	−38.1944	+	27.7498i	−1.67655	+	1.21808i
$520$	−2.25260	−	11.9473i	−0.0987831	−	0.523924i
$521$	20.9994	+	15.2569i	0.919998	+	0.668418i	0.943524	−	0.331305i	$-0.107489\pi$
$521$	20.9994	+	15.2569i	0.919998	+	0.668418i	−0.0235253	+	0.999723i	$0.507489\pi$
$522$	−3.66352	+	5.04240i	−0.160348	+	0.220700i
$523$	−18.2038	−	5.91478i	−0.795998	−	0.258635i	−0.117342	−	0.993092i	$-0.537437\pi$
$523$	−18.2038	−	5.91478i	−0.795998	−	0.258635i	−0.678656	+	0.734456i	$0.737437\pi$
$524$	−11.2194			−0.490121
$525$	5.52177	−	8.61922i	0.240990	−	0.376173i
$526$	−2.73135			−0.119092
$527$	5.18816	+	1.68574i	0.226000	+	0.0734318i
$528$	4.45804	−	6.13597i	0.194011	−	0.267034i
$529$	35.7151	+	25.9485i	1.55283	+	1.12820i
$530$	4.35572	+	0.559722i	0.189200	+	0.0243128i
$531$	−7.96291	+	5.78539i	−0.345561	+	0.251065i
$532$		−	6.92805i		−	0.300369i
$533$	19.7825	+	27.2283i	0.856876	+	1.17939i
$534$	3.09470	+	9.52451i	0.133921	+	0.412166i
$535$	1.44288	−	1.52994i	0.0623810	−	0.0661450i
$536$	4.33019	−	13.3269i	0.187036	−	0.575636i
$537$	−30.1196	+	9.78647i	−1.29976	+	0.422317i
$538$	−3.42080	+	1.11149i	−0.147481	+	0.0479195i
$539$	−1.14482	+	3.52339i	−0.0493108	+	0.151763i
$540$	1.05534	−	8.21262i	0.0454148	−	0.353415i
$541$	−7.96729	−	24.5208i	−0.342541	−	1.05423i	−0.962887	−	0.269904i	$-0.913008\pi$
$541$	−7.96729	−	24.5208i	−0.342541	−	1.05423i	0.620347	−	0.784328i	$-0.286992\pi$
$542$	8.29944	+	11.4232i	0.356492	+	0.490669i
$543$		−	20.0167i		−	0.859000i
$544$	−0.848431	+	0.616421i	−0.0363762	+	0.0264288i
$545$	1.81091	−	3.82711i	0.0775708	−	0.163935i
$546$	−9.00532	−	6.54274i	−0.385392	−	0.280004i
$547$	20.0776	−	27.6344i	0.858455	−	1.18156i	−0.123481	−	0.992347i	$-0.539406\pi$
$547$	20.0776	−	27.6344i	0.858455	−	1.18156i	0.981936	−	0.189215i	$-0.0605943\pi$
$548$	−18.8727	−	6.13210i	−0.806200	−	0.261950i
$549$	0.912449			0.0389424
$550$	−15.5974	−	9.99222i	−0.665074	−	0.426070i
$551$	36.2488			1.54425
$552$	15.9547	+	5.18399i	0.679077	+	0.220645i
$553$	3.28603	−	4.52283i	0.139736	−	0.192330i
$554$	−17.0675	−	12.4003i	−0.725130	−	0.526838i
$555$	−5.06089	+	2.76817i	−0.214823	+	0.117502i
$556$	−7.71772	+	5.60725i	−0.327304	+	0.237800i
$557$		−	6.76593i		−	0.286682i	−0.989673	−	0.143341i	$-0.954215\pi$
$557$		−	6.76593i		−	0.286682i	0.989673	−	0.143341i	$-0.0457845\pi$
$558$	−3.64220	−	5.01306i	−0.154187	−	0.212220i
$559$	3.39112	+	10.4368i	0.143429	+	0.441429i
$560$	−2.02121	−	0.956396i	−0.0854119	−	0.0404151i
$561$	−2.45791	+	7.56468i	−0.103773	+	0.319381i
$562$	18.6646	−	6.06448i	0.787317	−	0.255815i
$563$	31.9353	−	10.3764i	1.34591	−	0.437313i	0.454596	−	0.890698i	$-0.349784\pi$
$563$	31.9353	−	10.3764i	1.34591	−	0.437313i	0.891315	+	0.453385i	$0.149784\pi$
$564$	8.14660	−	25.0726i	0.343034	−	1.05575i
$565$	−3.71202	−	1.75645i	−0.156166	−	0.0738945i
$566$	1.97730	+	6.08550i	0.0831120	+	0.255792i
$567$	−6.55655	−	9.02431i	−0.275349	−	0.378985i
$568$		−	15.9608i		−	0.669702i
$569$	−0.536702	+	0.389937i	−0.0224997	+	0.0163470i	−0.598978	−	0.800765i	$-0.704426\pi$
$569$	−0.536702	+	0.389937i	−0.0224997	+	0.0163470i	0.576479	+	0.817112i	$0.304426\pi$
$570$	27.8248	−	15.2194i	1.16545	−	0.637472i
$571$	−14.1560	−	10.2850i	−0.592411	−	0.430412i	0.250766	−	0.968048i	$-0.419317\pi$
$571$	−14.1560	−	10.2850i	−0.592411	−	0.430412i	−0.843177	+	0.537636i	$0.819317\pi$
$572$	−11.8398	+	16.2960i	−0.495046	+	0.681372i
$573$	−11.0666	−	3.59574i	−0.462312	−	0.150214i
$574$	6.19003			0.258367
$575$	10.3588	−	39.6403i	0.431992	−	1.65311i
$576$	1.19123			0.0496347
$577$	9.49872	+	3.08632i	0.395437	+	0.128485i	0.499984	−	0.866035i	$-0.333339\pi$
$577$	9.49872	+	3.08632i	0.395437	+	0.128485i	−0.104547	+	0.994520i	$0.533339\pi$
$578$	−9.34590	+	12.8635i	−0.388738	+	0.535052i
$579$	4.46543	+	3.24432i	0.185577	+	0.134829i
$580$	5.00404	−	10.5754i	0.207781	−	0.439118i
$581$	7.13534	−	5.18413i	0.296024	−	0.215074i
$582$			19.2732i			0.798902i
$583$	−4.27666	−	5.88631i	−0.177121	−	0.243786i
$584$	−0.481508	−	1.48193i	−0.0199250	−	0.0613227i
$585$	1.84590	−	14.3647i	0.0763185	−	0.593906i
$586$	8.21298	−	25.2769i	0.339275	−	1.04418i
$587$	1.67070	−	0.542844i	0.0689573	−	0.0224056i	−0.274335	−	0.961634i	$-0.588458\pi$
$587$	1.67070	−	0.542844i	0.0689573	−	0.0224056i	0.343293	+	0.939229i	$0.388458\pi$
$588$	−1.94705	+	0.632635i	−0.0802950	+	0.0260894i
$589$	−11.1363	+	34.2741i	−0.458864	+	1.41224i
$590$	12.6763	−	13.4412i	0.521875	−	0.553364i
$591$	10.9931	+	33.8333i	0.452196	+	1.39171i
$592$	0.740670	+	1.01944i	0.0304413	+	0.0418989i
$593$			4.63989i			0.190537i	0.995452	+	0.0952687i	$0.0303710\pi$
$593$			4.63989i			0.190537i	−0.995452	+	0.0952687i	$0.969629\pi$
$594$	−11.0985	+	8.06355i	−0.455378	+	0.330852i
$595$	2.32588	+	0.298882i	0.0953518	+	0.0122530i
$596$	6.46599	+	4.69781i	0.264857	+	0.192430i
$597$	−24.2431	+	33.3678i	−0.992205	+	1.36565i
$598$	−42.3728	−	13.7678i	−1.73275	−	0.563006i
$599$	−6.81358			−0.278395			−0.139198	−	0.990265i	$-0.544452\pi$
$599$	−6.81358			−0.278395			−0.139198	+	0.990265i	$0.544452\pi$
$600$	−0.599039	−	10.2187i	−0.0244557	−	0.417177i
$601$	−41.8748			−1.70811			−0.854055	−	0.520183i	$-0.825864\pi$
$601$	−41.8748			−1.70811			−0.854055	+	0.520183i	$0.825864\pi$
$602$	1.91954	+	0.623696i	0.0782345	+	0.0254199i
$603$	9.81160	−	13.5045i	0.399559	−	0.549946i
$604$	−4.04199	−	2.93668i	−0.164466	−	0.119492i
$605$	1.12892	+	5.98753i	0.0458970	+	0.243428i
$606$	−15.2548	+	11.0833i	−0.619683	+	0.450226i
$607$			19.7475i			0.801525i	0.916182	+	0.400762i	$0.131255\pi$
$607$			19.7475i			0.801525i	−0.916182	+	0.400762i	$0.868745\pi$
$608$	−4.07221	−	5.60491i	−0.165150	−	0.227309i
$609$	−3.31006	−	10.1873i	−0.134130	−	0.412811i
$610$	−1.68310	+	0.317340i	−0.0681469	+	0.0128487i
$611$	−21.6359	+	66.5885i	−0.875296	+	2.69388i
$612$	−1.18813	+	0.386045i	−0.0480271	+	0.0156050i
$613$	27.7019	−	9.00090i	1.11887	−	0.363543i	0.309534	−	0.950888i	$-0.399827\pi$
$613$	27.7019	−	9.00090i	1.11887	−	0.363543i	0.809337	+	0.587345i	$0.199827\pi$
$614$	2.24316	−	6.90372i	0.0905264	−	0.278612i
$615$	13.5982	+	24.8607i	0.548331	+	1.00248i
$616$	1.14482	+	3.52339i	0.0461261	+	0.141961i
$617$	−15.1666	−	20.8750i	−0.610583	−	0.840396i	0.386042	−	0.922481i	$-0.373842\pi$
$617$	−15.1666	−	20.8750i	−0.610583	−	0.840396i	−0.996625	+	0.0820854i	$0.973842\pi$
$618$			24.3979i			0.981426i
$619$	3.89174	−	2.82751i	0.156422	−	0.113647i	−0.506821	−	0.862051i	$-0.669179\pi$
$619$	3.89174	−	2.82751i	0.156422	−	0.113647i	0.663243	+	0.748404i	$0.269179\pi$
$620$	8.46190	+	7.98038i	0.339838	+	0.320500i
$621$	−24.5483	−	17.8354i	−0.985091	−	0.715710i
$622$	−4.10508	+	5.65015i	−0.164599	+	0.226550i
$623$	−4.65234	−	1.51164i	−0.186392	−	0.0605625i
$624$	−11.1312			−0.445604
$625$	−24.8288	+	2.92105i	−0.993151	+	0.116842i
$626$	6.47167			0.258660
$627$	−49.9738	−	16.2375i	−1.99576	−	0.648463i
$628$	8.86059	−	12.1956i	0.353576	−	0.486656i
$629$	−1.06911	−	0.776754i	−0.0426282	−	0.0309712i
$630$	−1.93784	−	1.82756i	−0.0772052	−	0.0728118i
$631$	5.37738	−	3.90690i	0.214070	−	0.155531i	−0.475583	−	0.879671i	$-0.657763\pi$
$631$	5.37738	−	3.90690i	0.214070	−	0.155531i	0.689653	+	0.724140i	$0.257763\pi$
$632$		−	5.59053i		−	0.222379i
$633$	25.8860	+	35.6290i	1.02888	+	1.41613i
$634$	2.02253	+	6.22470i	0.0803248	+	0.247214i
$635$	−1.75399	−	3.20671i	−0.0696048	−	0.127255i
$636$	1.24247	−	3.82392i	0.0492670	−	0.151628i
$637$	5.17103	−	1.68017i	0.204883	−	0.0665707i
$638$	−18.4350	+	5.98990i	−0.729849	+	0.237142i
$639$	5.87537	−	18.0825i	0.232426	−	0.715334i
$640$	−2.19735	+	0.414299i	−0.0868580	+	0.0163766i
$641$	6.94305	+	21.3685i	0.274234	+	0.844005i	0.989421	+	0.145072i	$0.0463415\pi$
$641$	6.94305	+	21.3685i	0.274234	+	0.844005i	−0.715187	+	0.698933i	$0.753659\pi$
$642$	−1.13173	−	1.55770i	−0.0446659	−	0.0614774i
$643$		−	36.8627i		−	1.45372i	−0.686783	−	0.726862i	$-0.740978\pi$
$643$		−	36.8627i		−	1.45372i	0.686783	−	0.726862i	$-0.259022\pi$
$644$	−6.62931	+	4.81648i	−0.261232	+	0.189796i
$645$	1.71189	+	9.07948i	0.0674055	+	0.357504i
$646$	5.87797	+	4.27060i	0.231266	+	0.168024i
$647$	23.8340	−	32.8047i	0.937011	−	1.28969i	−0.0200498	−	0.999799i	$-0.506382\pi$
$647$	23.8340	−	32.8047i	0.937011	−	1.28969i	0.957061	−	0.289886i	$-0.0936175\pi$
$648$	−10.6087	−	3.44698i	−0.416750	−	0.135410i
$649$	−30.6106			−1.20157
$650$	1.59094	+	27.1391i	0.0624019	+	1.06448i
$651$	10.6493			0.417377
$652$	−1.75204	−	0.569271i	−0.0686150	−	0.0222944i
$653$	0.260330	−	0.358314i	0.0101875	−	0.0140219i	−0.803893	−	0.594774i	$-0.797241\pi$
$653$	0.260330	−	0.358314i	0.0101875	−	0.0140219i	0.814080	+	0.580752i	$0.197241\pi$
$654$	−3.13608	−	2.27850i	−0.122631	−	0.0890963i
$655$	24.8827	+	3.19749i	0.972248	+	0.124936i
$656$	5.00784	−	3.63841i	0.195523	−	0.142056i
$657$		−	1.85617i		−	0.0724162i
$658$	7.56905	+	10.4179i	0.295072	+	0.406132i
$659$	11.5111	+	35.4277i	0.448411	+	1.38007i	0.878700	+	0.477375i	$0.158412\pi$
$659$	11.5111	+	35.4277i	0.448411	+	1.38007i	−0.430289	+	0.902691i	$0.641588\pi$
$660$	−11.6359	+	12.3380i	−0.452927	+	0.480256i
$661$	0.0373244	−	0.114873i	0.00145175	−	0.00446803i	−0.950328	−	0.311250i	$-0.899252\pi$
$661$	0.0373244	−	0.114873i	0.00145175	−	0.00446803i	0.951780	+	0.306782i	$0.0992523\pi$
$662$	−25.6742	+	8.34206i	−0.997857	+	0.324223i
$663$	11.1021	−	3.60730i	0.431171	−	0.140096i
$664$	2.72546	−	8.38809i	0.105768	−	0.325521i
$665$	−1.97448	+	15.3653i	−0.0765669	+	0.595839i
$666$	0.463858	+	1.42761i	0.0179741	+	0.0553187i
$667$	−25.2007	−	34.6858i	−0.975774	−	1.34304i
$668$			8.75156i			0.338608i
$669$	−7.39994	+	5.37637i	−0.286098	+	0.207862i
$670$	−13.4018	+	28.3228i	−0.517755	+	1.09421i
$671$	2.29574	+	1.66795i	0.0886262	+	0.0643907i
$672$	−1.20334	+	1.65626i	−0.0464200	+	0.0638916i
$673$	8.97331	+	2.91560i	0.345896	+	0.112388i	0.476812	−	0.879005i	$-0.341792\pi$
$673$	8.97331	+	2.91560i	0.345896	+	0.112388i	−0.130917	+	0.991393i	$0.541792\pi$
$674$	−19.2133			−0.740069
$675$	−4.68115	+	17.9134i	−0.180178	+	0.689489i
$676$	16.5625			0.637018
$677$	0.392572	+	0.127554i	0.0150878	+	0.00490231i	0.316551	−	0.948575i	$-0.397475\pi$
$677$	0.392572	+	0.127554i	0.0150878	+	0.00490231i	−0.301463	+	0.953478i	$0.597475\pi$
$678$	−2.20998	+	3.04177i	−0.0848737	+	0.116819i
$679$	−7.61626	−	5.53353i	−0.292285	−	0.212358i
$680$	2.05736	−	1.12532i	0.0788960	−	0.0431540i
$681$	46.2356	−	33.5921i	1.77175	−	1.28725i
$682$		−	19.2709i		−	0.737922i
$683$	−14.9643	−	20.5966i	−0.572592	−	0.788106i	0.420267	−	0.907401i	$-0.361937\pi$
$683$	−14.9643	−	20.5966i	−0.572592	−	0.788106i	−0.992859	+	0.119295i	$0.961937\pi$
$684$	−2.55030	−	7.84900i	−0.0975130	−	0.300114i
$685$	40.1087	+	18.9786i	1.53248	+	0.725136i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	32.2458	−	10.4773i	1.23025	−	0.399734i
$688$	1.91954	−	0.623696i	0.0731817	−	0.0237782i
$689$	−3.29977	+	10.1557i	−0.125711	+	0.386900i
$690$	−33.9074	−	16.0443i	−1.29083	−	0.610795i
$691$	−0.298861	−	0.919799i	−0.0113692	−	0.0349908i	0.945211	−	0.326460i	$-0.105856\pi$
$691$	−0.298861	−	0.919799i	−0.0113692	−	0.0349908i	−0.956580	+	0.291469i	$0.905856\pi$
$692$	−13.5547	−	18.6564i	−0.515272	−	0.709211i
$693$			4.41318i			0.167643i
$694$	20.9522	−	15.2226i	0.795333	−	0.577843i
$695$	18.7146	−	10.2364i	0.709887	−	0.388289i
$696$	−8.66585	−	6.29611i	−0.328478	−	0.238653i
$697$	−3.81567	+	5.25181i	−0.144529	+	0.198927i
$698$	7.22303	+	2.34690i	0.273396	+	0.0888316i
$699$	−31.2646			−1.18254
$700$	4.21014	+	2.69717i	0.159128	+	0.101943i
$701$	19.9764			0.754500			0.377250	−	0.926111i	$-0.376870\pi$
$701$	19.9764			0.754500			0.377250	+	0.926111i	$0.376870\pi$
$702$	19.1483	+	6.22166i	0.722706	+	0.234821i
$703$	5.13140	−	7.06276i	0.193534	−	0.266377i
$704$	2.99717	+	2.17757i	0.112960	+	0.0820704i
$705$	−25.2134	+	53.2851i	−0.949592	+	2.00683i
$706$	7.43981	−	5.40534i	0.280001	−	0.203432i
$707$		−	9.21038i		−	0.346392i
$708$	−9.94275	−	13.6850i	−0.373671	−	0.514315i
$709$	−1.41372	−	4.35097i	−0.0530933	−	0.163404i	0.920994	−	0.389577i	$-0.127379\pi$
$709$	−1.41372	−	4.35097i	−0.0530933	−	0.163404i	−0.974087	+	0.226172i	$0.927379\pi$
$710$	−4.54879	+	35.3985i	−0.170713	+	1.32848i
$711$	2.05794	−	6.33368i	0.0771787	−	0.237532i
$712$	−4.65234	+	1.51164i	−0.174354	+	0.0566510i
$713$	40.5383	−	13.1717i	1.51817	−	0.493284i
$714$	0.663456	−	2.04191i	0.0248292	−	0.0764165i
$715$	30.9029	−	32.7676i	1.15570	−	1.22544i
$716$	−4.78030	−	14.7122i	−0.178648	−	0.549822i
$717$	9.88790	+	13.6095i	0.369270	+	0.508257i
$718$		−	4.89794i		−	0.182790i
$719$	−2.52700	+	1.83597i	−0.0942412	+	0.0684702i	−0.633908	−	0.773408i	$-0.718550\pi$
$719$	−2.52700	+	1.83597i	−0.0942412	+	0.0684702i	0.539667	+	0.841879i	$0.318550\pi$
$720$	−2.64196	−	0.339498i	−0.0984599	−	0.0126524i
$721$	−9.64136	−	7.00486i	−0.359063	−	0.260875i
$722$	−17.0445	+	23.4598i	−0.634332	+	0.873083i
$723$	−8.22928	−	2.67386i	−0.306050	−	0.0994418i
$724$	9.77737			0.363373
$725$	−14.1121	+	22.0282i	−0.524108	+	0.818107i
$726$	5.57852			0.207038
$727$	0.362410	+	0.117754i	0.0134410	+	0.00436726i	0.315730	−	0.948849i	$-0.397751\pi$
$727$	0.362410	+	0.117754i	0.0134410	+	0.00436726i	−0.302289	+	0.953216i	$0.597751\pi$
$728$	3.19587	−	4.39874i	0.118447	−	0.163028i
$729$	7.64931	+	5.55755i	0.283308	+	0.205835i
$730$	0.645558	+	3.42390i	0.0238932	+	0.126724i
$731$	−1.71241	+	1.24414i	−0.0633356	+	0.0460160i
$732$			1.56813i			0.0579598i
$733$	−8.32327	−	11.4560i	−0.307427	−	0.423137i	0.627150	−	0.778899i	$-0.284221\pi$
$733$	−8.32327	−	11.4560i	−0.307427	−	0.423137i	−0.934577	+	0.355762i	$0.884221\pi$
$734$	−3.99100	−	12.2830i	−0.147311	−	0.453375i
$735$	4.49853	−	0.848174i	0.165931	−	0.0312854i
$736$	−2.53217	+	7.79323i	−0.0933371	+	0.287262i
$737$	49.3725	−	16.0421i	1.81866	−	0.590918i
$738$	7.01288	−	2.27862i	0.258148	−	0.0838772i
$739$	−7.61202	+	23.4274i	−0.280013	+	0.861790i	0.707837	+	0.706376i	$0.249671\pi$
$739$	−7.61202	+	23.4274i	−0.280013	+	0.861790i	−0.987849	+	0.155414i	$0.950329\pi$
$740$	−1.35214	−	2.47204i	−0.0497057	−	0.0908742i
$741$	23.8306	+	73.3430i	0.875439	+	2.69432i
$742$	1.15438	+	1.58887i	0.0423788	+	0.0583294i
$743$			11.7675i			0.431709i	0.976426	+	0.215854i	$0.0692537\pi$
$743$			11.7675i			0.431709i	−0.976426	+	0.215854i	$0.930746\pi$
$744$	8.61543	−	6.25947i	0.315857	−	0.229483i
$745$	−13.0016	−	12.2618i	−0.476342	−	0.449236i
$746$	−2.34922	−	1.70681i	−0.0860112	−	0.0624908i
$747$	6.17551	−	8.49985i	0.225950	−	0.310993i
$748$	−3.69504	−	1.20059i	−0.135104	−	0.0438980i
$749$	0.940490			0.0343648
$750$	−1.58374	+	22.8341i	−0.0578298	+	0.833783i
$751$	15.2594			0.556823			0.278411	−	0.960462i	$-0.410192\pi$
$751$	15.2594			0.556823			0.278411	+	0.960462i	$0.410192\pi$
$752$	12.2470	+	3.97929i	0.446602	+	0.145110i
$753$	−17.9546	+	24.7123i	−0.654301	+	0.900568i
$754$	23.0150	+	16.7214i	0.838156	+	0.608956i
$755$	8.12750	+	7.66501i	0.295790	+	0.278958i
$756$	2.99579	−	2.17657i	0.108956	−	0.0791610i
$757$			54.1781i			1.96914i	0.174996	+	0.984569i	$0.444009\pi$
$757$			54.1781i			1.96914i	−0.174996	+	0.984569i	$0.555991\pi$
$758$	−11.1991	−	15.4142i	−0.406769	−	0.559870i
$759$	19.2052	+	59.1075i	0.697104	+	2.14547i
$760$	7.43408	+	13.5913i	0.269663	+	0.493009i
$761$	2.01401	−	6.19848i	0.0730077	−	0.224695i	−0.907894	−	0.419201i	$-0.862310\pi$
$761$	2.01401	−	6.19848i	0.0730077	−	0.224695i	0.980901	+	0.194506i	$0.0623104\pi$
$762$	−3.18264	+	1.03410i	−0.115295	+	0.0374615i
$763$	1.80080	−	0.585115i	0.0651933	−	0.0211826i
$764$	1.75638	−	5.40557i	0.0635435	−	0.195567i
$765$	2.74508	−	0.517571i	0.0992487	−	0.0187128i
$766$	1.38591	+	4.26540i	0.0500750	+	0.154115i
$767$	26.4062	+	36.3450i	0.953472	+	1.31234i
$768$			2.04725i			0.0738738i
$769$	24.8801	−	18.0765i	0.897200	−	0.651854i	−0.0405453	−	0.999178i	$-0.512910\pi$
$769$	24.8801	−	18.0765i	0.897200	−	0.651854i	0.937745	+	0.347324i	$0.112910\pi$
$770$	−1.53486	−	8.14055i	−0.0553125	−	0.293365i
$771$	8.53010	+	6.19748i	0.307204	+	0.223197i
$772$	−1.58472	+	2.18118i	−0.0570354	+	0.0785025i
$773$	15.3013	+	4.97171i	0.550351	+	0.178820i	0.570975	−	0.820967i	$-0.306565\pi$
$773$	15.3013	+	4.97171i	0.550351	+	0.178820i	−0.0206241	+	0.999787i	$0.506565\pi$
$774$	2.40429			0.0864205
$775$	−16.4927	−	20.1108i	−0.592435	−	0.722399i
$776$	−9.41421			−0.337950
$777$	−2.45348	−	0.797185i	−0.0880182	−	0.0285989i
$778$	8.34421	−	11.4848i	0.299154	−	0.411751i
$779$	−34.6946	−	25.2071i	−1.24306	−	0.903138i
$780$	24.6871	+	3.17236i	0.883939	+	0.113589i
$781$	47.8374	−	34.7559i	1.71176	−	1.24366i
$782$		−	8.59350i		−	0.307303i
$783$	11.3882	+	15.6745i	0.406981	+	0.560161i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−23.1270	+	24.5224i	−0.825438	+	0.875243i
$786$	7.09778	−	21.8447i	0.253169	−	0.779175i
$787$	−19.5581	+	6.35483i	−0.697173	+	0.226525i	−0.636098	−	0.771608i	$-0.719453\pi$
$787$	−19.5581	+	6.35483i	−0.697173	+	0.226525i	−0.0610744	+	0.998133i	$0.519453\pi$
$788$	−16.5262	+	5.36969i	−0.588722	+	0.191287i
$789$	1.72795	−	5.31807i	0.0615165	−	0.189328i
$790$	−1.59329	+	12.3989i	−0.0566865	+	0.441131i
$791$	−0.567520	−	1.74665i	−0.0201787	−	0.0621036i
$792$	2.59400	+	3.57034i	0.0921738	+	0.126866i
$793$		−	4.16468i		−	0.147892i
$794$	3.25370	−	2.36395i	0.115470	−	0.0838936i
$795$	−3.84539	+	8.12671i	−0.136382	+	0.288225i
$796$	−16.2988	−	11.8418i	−0.577697	−	0.419722i
$797$	−23.6497	+	32.5510i	−0.837715	+	1.15302i	0.148722	+	0.988879i	$0.452484\pi$
$797$	−23.6497	+	32.5510i	−0.837715	+	1.15302i	−0.986437	+	0.164137i	$0.947516\pi$
$798$	13.4893	+	4.38293i	0.477515	+	0.155154i
$799$	−13.5046			−0.477758
$800$	4.99143	−	0.292607i	0.176474	−	0.0103452i
$801$	−5.82723			−0.205895
$802$	−1.10444	−	0.358854i	−0.0389991	−	0.0126716i
$803$	3.39308	−	4.67018i	0.119739	−	0.164807i
$804$	23.2088	+	16.8622i	0.818511	+	0.594683i
$805$	16.0754	−	8.79280i	0.566583	−	0.309906i
$806$	−22.8811	+	16.6241i	−0.805951	+	0.585558i
$807$		−	7.36364i		−	0.259212i
$808$	−5.41373	−	7.45135i	−0.190454	−	0.262138i
$809$	−11.8040	−	36.3290i	−0.415007	−	1.27726i	−0.912245	−	0.409645i	$-0.865653\pi$
$809$	−11.8040	−	36.3290i	−0.415007	−	1.27726i	0.497238	−	0.867614i	$-0.334347\pi$
$810$	22.5460	+	10.6683i	0.792184	+	0.374845i
$811$	0.673162	−	2.07178i	0.0236379	−	0.0727501i	−0.938542	−	0.345166i	$-0.887823\pi$
$811$	0.673162	−	2.07178i	0.0236379	−	0.0727501i	0.962180	+	0.272416i	$0.0878226\pi$
$812$	4.97610	−	1.61683i	0.174627	−	0.0567397i
$813$	−27.4921	+	8.93272i	−0.964189	+	0.313284i
$814$	−1.44259	+	4.43983i	−0.0505627	+	0.155616i
$815$	3.72348	+	1.76187i	0.130428	+	0.0617157i
$816$	−0.663456	−	2.04191i	−0.0232256	−	0.0714811i
$817$	−8.21902	−	11.3125i	−0.287547	−	0.395775i
$818$			0.653983i			0.0228660i
$819$	5.23992	−	3.80703i	0.183098	−	0.133028i
$820$	−12.1435	+	6.64216i	−0.424069	+	0.231954i
$821$	41.9688	+	30.4921i	1.46472	+	1.06418i	0.982101	+	0.188354i	$0.0603152\pi$
$821$	41.9688	+	30.4921i	1.46472	+	1.06418i	0.482621	+	0.875829i	$0.339685\pi$
$822$	23.8790	−	32.8666i	0.832876	−	1.14636i
$823$	−45.8612	−	14.9012i	−1.59862	−	0.519424i	−0.631856	−	0.775086i	$-0.717707\pi$
$823$	−45.8612	−	14.9012i	−1.59862	−	0.519424i	−0.966766	+	0.255662i	$0.917707\pi$
$824$	−11.9174			−0.415162
$825$	29.3228	−	24.0474i	1.02089	−	0.837224i
$826$	8.26260			0.287493
$827$	25.3019	+	8.22107i	0.879832	+	0.285875i	0.713887	−	0.700260i	$-0.246933\pi$
$827$	25.3019	+	8.22107i	0.879832	+	0.285875i	0.165944	+	0.986135i	$0.446933\pi$
$828$	−5.73755	+	7.89707i	−0.199394	+	0.274442i
$829$	−38.2145	−	27.7644i	−1.32724	−	0.964299i	−0.999811	−	0.0194241i	$-0.993817\pi$
$829$	−38.2145	−	27.7644i	−1.32724	−	0.964299i	−0.327432	−	0.944875i	$-0.606183\pi$
$830$	−8.43518	+	17.8266i	−0.292790	+	0.618771i
$831$	34.9415	−	25.3865i	1.21211	−	0.880648i
$832$		−	5.43714i		−	0.188499i
$833$	0.616421	+	0.848431i	0.0213577	+	0.0293964i
$834$	−6.03510	−	18.5741i	−0.208978	−	0.643169i
$835$	2.49417	−	19.4095i	0.0863143	−	0.671693i
$836$	7.93136	−	24.4102i	0.274312	−	0.844245i
$837$	−18.3193	+	5.95229i	−0.633206	+	0.205741i
$838$	−31.0006	+	10.0727i	−1.07090	+	0.347956i
$839$	9.50325	−	29.2480i	0.328089	−	1.00975i	−0.641939	−	0.766756i	$-0.721870\pi$
$839$	9.50325	−	29.2480i	0.328089	−	1.00975i	0.970027	−	0.242997i	$-0.0781304\pi$
$840$	3.14084	−	3.33036i	0.108369	−	0.114908i
$841$	−0.501938	−	1.54481i	−0.0173082	−	0.0532691i
$842$	16.0722	+	22.1215i	0.553884	+	0.762356i
$843$			40.1774i			1.38378i
$844$	−17.4033	+	12.6443i	−0.599048	+	0.435234i
$845$	−36.7328	−	4.72026i	−1.26365	−	0.162382i
$846$	12.4102	+	9.01651i	0.426670	+	0.309994i
$847$	−1.60165	+	2.20448i	−0.0550332	+	0.0757467i
$848$	1.86783	+	0.606895i	0.0641416	+	0.0208409i
$849$	−13.0997			−0.449580
$850$	−4.88358	+	1.90943i	−0.167505	+	0.0654927i
$851$	−10.3256			−0.353958
$852$	31.0766	+	10.0974i	1.06467	+	0.345931i
$853$	29.3190	−	40.3541i	1.00386	−	1.38170i	0.0809367	−	0.996719i	$-0.474209\pi$
$853$	29.3190	−	40.3541i	1.00386	−	1.38170i	0.922926	−	0.384979i	$-0.125791\pi$
$854$	−0.619682	−	0.450225i	−0.0212051	−	0.0154064i
$855$	3.41918	+	18.1346i	0.116934	+	0.620190i
$856$	0.760872	−	0.552806i	0.0260061	−	0.0188945i
$857$			13.7442i			0.469493i	0.972057	+	0.234746i	$0.0754260\pi$
$857$			13.7442i			0.469493i	−0.972057	+	0.234746i	$0.924574\pi$
$858$	−24.2390	−	33.3621i	−0.827505	−	1.13896i
$859$	11.5691	+	35.6060i	0.394733	+	1.21486i	0.929169	+	0.369654i	$0.120524\pi$
$859$	11.5691	+	35.6060i	0.394733	+	1.21486i	−0.534437	+	0.845208i	$0.679476\pi$
$860$	−4.43496	+	0.836189i	−0.151231	+	0.0285138i
$861$	−3.91603	+	12.0523i	−0.133458	+	0.410741i
$862$	−16.6454	+	5.40842i	−0.566945	+	0.184211i
$863$	−16.3379	+	5.30850i	−0.556148	+	0.180704i	−0.573587	−	0.819144i	$-0.694449\pi$
$863$	−16.3379	+	5.30850i	−0.556148	+	0.180704i	0.0174390	+	0.999848i	$0.494449\pi$
$864$	1.14429	−	3.52176i	0.0389295	−	0.119813i
$865$	24.7450	+	45.2398i	0.841354	+	1.53820i
$866$	−9.85075	−	30.3175i	−0.334742	−	1.03023i
$867$	−19.1334	−	26.3349i	−0.649804	−	0.894379i
$868$			5.20173i			0.176558i
$869$	16.7558	−	12.1738i	0.568401	−	0.412968i
$870$	17.4250	+	16.4335i	0.590764	+	0.557146i
$871$	−61.6385	−	44.7830i	−2.08854	−	1.51741i
$872$	1.11296	−	1.53185i	0.0376894	−	0.0518750i
$873$	−10.6656	−	3.46548i	−0.360977	−	0.117289i
$874$	56.7704			1.92029
$875$	−8.56870	−	7.18174i	−0.289675	−	0.242787i
$876$	3.19001			0.107781
$877$	34.6870	+	11.2705i	1.17130	+	0.380578i	0.829127	−	0.559060i	$-0.188838\pi$
$877$	34.6870	+	11.2705i	1.17130	+	0.380578i	0.342171	+	0.939638i	$0.388838\pi$
$878$	5.08932	−	7.00485i	0.171756	−	0.236402i
$879$	44.0197	+	31.9822i	1.48475	+	1.07873i
$880$	−6.02662	−	5.68368i	−0.203157	−	0.191597i
$881$	10.3434	−	7.51489i	0.348476	−	0.253183i	−0.399753	−	0.916623i	$-0.630904\pi$
$881$	10.3434	−	7.51489i	0.348476	−	0.253183i	0.748230	+	0.663440i	$0.230904\pi$
$882$		−	1.19123i		−	0.0401109i
$883$	13.2759	+	18.2727i	0.446768	+	0.614924i	0.971699	−	0.236221i	$-0.0759089\pi$
$883$	13.2759	+	18.2727i	0.446768	+	0.614924i	−0.524931	+	0.851145i	$0.675909\pi$
$884$	1.76202	+	5.42295i	0.0592632	+	0.182394i
$885$	18.1512	+	33.1847i	0.610144	+	1.11549i
$886$	2.99117	−	9.20586i	0.100490	−	0.309277i
$887$	−30.5932	+	9.94032i	−1.02722	+	0.333763i	−0.773690	−	0.633565i	$-0.781591\pi$
$887$	−30.5932	+	9.94032i	−1.02722	+	0.333763i	−0.253528	+	0.967328i	$0.581591\pi$
$888$	−2.45348	+	0.797185i	−0.0823335	+	0.0267518i
$889$	0.505117	−	1.55459i	0.0169411	−	0.0521393i
$890$	10.7489	−	2.02665i	0.360305	−	0.0679336i
$891$	−12.7701	−	39.3022i	−0.427813	−	1.31667i
$892$	−2.62614	−	3.61457i	−0.0879297	−	0.121025i
$893$		−	89.2142i		−	2.98544i
$894$	−13.2375	+	9.61760i	−0.442728	+	0.321661i
$895$	6.40895	+	33.9916i	0.214227	+	1.13622i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	53.6131	−	73.7921i	1.79009	−	2.46385i
$898$	24.7544	+	8.04320i	0.826066	+	0.268405i
$899$	−27.2164			−0.907718
$900$	5.76266	+	1.50590i	0.192089	+	0.0501967i
$901$	−2.05964			−0.0686164
$902$	21.8099	+	7.08646i	0.726190	+	0.235953i
$903$	−2.42873	+	3.34287i	−0.0808232	+	0.111244i
$904$	−1.48579	−	1.07949i	−0.0494165	−	0.0359032i
$905$	−21.6846	−	2.78652i	−0.720819	−	0.0926272i
$906$	8.27496	−	6.01211i	0.274917	−	0.199739i
$907$			30.7234i			1.02015i	0.860129	+	0.510077i	$0.170383\pi$
$907$			30.7234i			1.02015i	−0.860129	+	0.510077i	$0.829617\pi$
$908$	16.4084	+	22.5842i	0.544532	+	0.749484i
$909$	−3.39045	−	10.4347i	−0.112454	−	0.346098i
$910$	−8.34153	+	8.84484i	−0.276519	+	0.293204i
$911$	17.9479	−	55.2381i	0.594642	−	1.83012i	0.0381411	−	0.999272i	$-0.487856\pi$
$911$	17.9479	−	55.2381i	0.594642	−	1.83012i	0.556501	−	0.830847i	$-0.312144\pi$
$912$	13.4893	−	4.38293i	0.446674	−	0.145133i
$913$	31.0754	−	10.0970i	1.02845	−	0.334163i
$914$	−0.327882	+	1.00912i	−0.0108454	+	0.0333786i
$915$	0.446913	−	3.47785i	0.0147745	−	0.114974i
$916$	5.11774	+	15.7508i	0.169095	+	0.520421i
$917$	6.59459	+	9.07668i	0.217773	+	0.299738i
$918$			3.88340i			0.128171i
$919$	−43.3033	+	31.4617i	−1.42844	+	1.03783i	−0.438141	+	0.898906i	$0.644363\pi$
$919$	−43.3033	+	31.4617i	−1.42844	+	1.03783i	−0.990304	+	0.138919i	$0.955637\pi$
$920$	7.83698	−	16.5624i	0.258378	−	0.546046i
$921$	12.0228	+	8.73508i	0.396165	+	0.287831i
$922$	25.1937	−	34.6761i	0.829710	−	1.14200i
$923$	−82.5339	−	26.8169i	−2.71664	−	0.882689i
$924$	−7.58447			−0.249511
$925$	2.29430	+	5.86793i	0.0754360	+	0.192936i
$926$	−33.1037			−1.08785
$927$	−13.5016	−	4.38693i	−0.443450	−	0.144086i
$928$	3.07540	−	4.23292i	0.100955	−	0.138952i
$929$	6.16111	+	4.47631i	0.202140	+	0.146863i	0.684250	−	0.729247i	$-0.260130\pi$
$929$	6.16111	+	4.47631i	0.202140	+	0.146863i	−0.482111	+	0.876110i	$0.660130\pi$
$930$	−20.8915	+	11.4271i	−0.685059	+	0.374709i
$931$	−5.60491	+	4.07221i	−0.183694	+	0.133461i
$932$		−	15.2715i		−	0.500235i
$933$	−8.40412	−	11.5673i	−0.275139	−	0.378696i
$934$	−9.95093	−	30.6258i	−0.325604	−	1.00211i
$935$	7.85282	+	3.71579i	0.256815	+	0.121519i
$936$	2.00147	−	6.15990i	0.0654202	−	0.201343i
$937$	−34.5775	+	11.2349i	−1.12960	+	0.367028i	−0.813423	−	0.581673i	$-0.802398\pi$
$937$	−34.5775	+	11.2349i	−1.12960	+	0.367028i	−0.316174	+	0.948701i	$0.602398\pi$
$938$	−13.3269	+	4.33019i	−0.435140	+	0.141386i
$939$	−4.09420	+	12.6007i	−0.133609	+	0.411207i
$940$	−26.0277	−	12.3157i	−0.848929	−	0.401695i
$941$	−3.67094	−	11.2980i	−0.119669	−	0.368304i	0.873223	−	0.487321i	$-0.162026\pi$
$941$	−3.67094	−	11.2980i	−0.119669	−	0.368304i	−0.992892	+	0.119017i	$0.962026\pi$
$942$	18.1398	+	24.9673i	0.591028	+	0.813480i
$943$			50.7229i			1.65176i
$944$	6.68459	−	4.85664i	0.217565	−	0.158070i
$945$	−7.26447	+	3.97347i	−0.236313	+	0.129257i
$946$	6.04926	+	4.39504i	0.196678	+	0.142895i
$947$	−26.0099	+	35.7995i	−0.845207	+	1.16333i	0.139691	+	0.990195i	$0.455389\pi$
$947$	−26.0099	+	35.7995i	−0.845207	+	1.16333i	−0.984898	+	0.173133i	$0.944611\pi$
$948$	10.8850	+	3.53677i	0.353530	+	0.114869i
$949$	−8.47211			−0.275016
$950$	−12.6141	−	32.2619i	−0.409254	−	1.04672i
$951$	−13.3993			−0.434503
$952$	0.997390	+	0.324072i	0.0323256	+	0.0105032i
$953$	8.00006	−	11.0111i	0.259148	−	0.356686i	−0.659541	−	0.751668i	$-0.729249\pi$
$953$	8.00006	−	11.0111i	0.259148	−	0.356686i	0.918689	+	0.394983i	$0.129249\pi$
$954$	1.89272	+	1.37514i	0.0612791	+	0.0445218i
$955$	−5.43592	+	11.4881i	−0.175902	+	0.371746i
$956$	−6.64771	+	4.82984i	−0.215002	+	0.156208i
$957$		−	39.6833i		−	1.28278i
$958$	13.3290	+	18.3459i	0.430642	+	0.592728i
$959$	6.13210	+	18.8727i	0.198016	+	0.609430i
$960$	0.583461	−	4.54046i	0.0188311	−	0.146543i
$961$	−1.21813	+	3.74903i	−0.0392946	+	0.120936i
$962$	6.51602	−	2.11718i	0.210085	−	0.0682607i
$963$	1.06551	−	0.346205i	0.0343356	−	0.0111563i
$964$	1.30607	−	4.01968i	0.0420657	−	0.129465i
$965$	4.13628	−	4.38585i	0.133151	−	0.141186i
$966$	−5.18399	−	15.9547i	−0.166792	−	0.513334i
$967$	3.08919	+	4.25190i	0.0993416	+	0.136732i	0.855794	−	0.517317i	$-0.173069\pi$
$967$	3.08919	+	4.25190i	0.0993416	+	0.136732i	−0.756452	+	0.654049i	$0.773069\pi$
$968$			2.72488i			0.0875810i
$969$	−12.0337	+	8.74298i	−0.386578	+	0.280865i
$970$	20.8791	+	2.68302i	0.670388	+	0.0861467i
$971$	21.6692	+	15.7436i	0.695398	+	0.505236i	0.878430	−	0.477871i	$-0.158591\pi$
$971$	21.6692	+	15.7436i	0.695398	+	0.505236i	−0.183032	+	0.983107i	$0.558591\pi$
$972$	6.89319	−	9.48766i	0.221099	−	0.304317i
$973$	9.07272	+	2.94791i	0.290858	+	0.0945055i
$974$	−33.2847			−1.06651
$975$	−53.8477	−	14.0715i	−1.72451	−	0.450649i
$976$	−0.765969			−0.0245181
$977$	−28.1638	−	9.15099i	−0.901041	−	0.292766i	−0.178375	−	0.983963i	$-0.557084\pi$
$977$	−28.1638	−	9.15099i	−0.901041	−	0.292766i	−0.722667	+	0.691197i	$0.757084\pi$
$978$	2.21680	−	3.05116i	0.0708854	−	0.0975654i
$979$	−14.6615	−	10.6522i	−0.468582	−	0.340445i
$980$	0.414299	+	2.19735i	0.0132343	+	0.0701918i
$981$	1.82479	−	1.32579i	0.0582612	−	0.0423292i
$982$			4.31141i			0.137582i
$983$	−13.5137	−	18.6000i	−0.431020	−	0.593248i	0.537167	−	0.843476i	$-0.319494\pi$
$983$	−13.5137	−	18.6000i	−0.431020	−	0.593248i	−0.968187	+	0.250228i	$0.919494\pi$
$984$	3.91603	+	12.0523i	0.124839	+	0.384213i
$985$	38.1827	−	7.19914i	1.21660	−	0.229384i
$986$	−1.69560	+	5.21853i	−0.0539990	+	0.166192i
$987$	−25.0726	+	8.14660i	−0.798071	+	0.259309i
$988$	−35.8251	+	11.6403i	−1.13975	+	0.370327i
$989$	−5.11074	+	15.7292i	−0.162512	+	0.500161i
$990$	−4.73552	−	8.65769i	−0.150505	−	0.275159i
$991$	−0.933090	−	2.87176i	−0.0296406	−	0.0912244i	0.935142	−	0.354274i	$-0.115272\pi$
$991$	−0.933090	−	2.87176i	−0.0296406	−	0.0912244i	−0.964782	+	0.263049i	$0.915272\pi$
$992$	3.05750	+	4.20829i	0.0970758	+	0.133613i
$993$		−	55.2665i		−	1.75383i
$994$	−12.9126	+	9.38155i	−0.409563	+	0.297565i
$995$	32.7732	+	30.9082i	1.03898	+	0.979857i
$996$	14.6078	+	10.6132i	0.462866	+	0.336292i
$997$	19.2868	−	26.5460i	0.610819	−	0.840721i	−0.385825	−	0.922572i	$-0.626083\pi$
$997$	19.2868	−	26.5460i	0.610819	−	0.840721i	0.996645	+	0.0818511i	$0.0260832\pi$
$998$	−0.651987	−	0.211844i	−0.0206383	−	0.00670579i
$999$	4.66616			0.147631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.29.4	✓	40
25.12	odd	20		8750.2.a.bf.1.16		20
25.13	odd	20		8750.2.a.be.1.5		20
25.19	even	10	inner	350.2.m.b.169.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.4	✓	40	1.1	even	1	trivial
350.2.m.b.169.4	yes	40	25.19	even	10	inner
8750.2.a.be.1.5		20	25.13	odd	20
8750.2.a.bf.1.16		20	25.12	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.20334 - 1.65626i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.62675 - 1.53418i) q^{5} +(-1.65626 + 1.20334i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.368112 - 1.13293i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.20334 - 1.65626i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.62675 - 1.53418i) q^{5} +(-1.65626 + 1.20334i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.368112 - 1.13293i) q^{9} +(1.07304 + 1.96178i) q^{10} +(1.14482 - 3.52339i) q^{11} +(1.94705 - 0.632635i) q^{12} +(-5.17103 + 1.68017i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-4.49853 + 0.848174i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.616421 - 0.848431i) q^{17} +1.19123i q^{18} +(5.60491 - 4.07221i) q^{19} +(-0.414299 - 2.19735i) q^{20} +(-1.65626 - 1.20334i) q^{21} +(-2.17757 + 2.99717i) q^{22} +(-7.79323 - 2.53217i) q^{23} -2.04725 q^{24} +(0.292607 + 4.99143i) q^{25} +5.43714 q^{26} +(3.52176 + 1.14429i) q^{27} +(0.587785 - 0.809017i) q^{28} +(4.23292 + 3.07540i) q^{29} +(4.54046 + 0.583461i) q^{30} +(-4.20829 + 3.05750i) q^{31} -1.00000i q^{32} +(-4.45804 - 6.13597i) q^{33} +(0.324072 + 0.997390i) q^{34} +(-1.53418 + 1.62675i) q^{35} +(0.368112 - 1.13293i) q^{36} +(1.19843 - 0.389393i) q^{37} +(-6.58897 + 2.14089i) q^{38} +(-3.43972 + 10.5864i) q^{39} +(-0.284997 + 2.21783i) q^{40} +(-1.91282 - 5.88707i) q^{41} +(1.20334 + 1.65626i) q^{42} -2.01832i q^{43} +(2.99717 - 2.17757i) q^{44} +(-1.13929 + 2.40774i) q^{45} +(6.62931 + 4.81648i) q^{46} +(7.56905 - 10.4179i) q^{47} +(1.94705 + 0.632635i) q^{48} -1.00000 q^{49} +(1.26415 - 4.83755i) q^{50} -2.14699 q^{51} +(-5.17103 - 1.68017i) q^{52} +(1.15438 - 1.58887i) q^{53} +(-2.99579 - 2.17657i) q^{54} +(-7.26783 + 3.97531i) q^{55} +(-0.809017 + 0.587785i) q^{56} -14.1835i q^{57} +(-3.07540 - 4.23292i) q^{58} +(-2.55328 - 7.85820i) q^{59} +(-4.13793 - 1.95798i) q^{60} +(-0.236698 + 0.728480i) q^{61} +(4.94714 - 1.60742i) q^{62} +(-1.13293 + 0.368112i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(10.9896 + 5.20006i) q^{65} +(2.34373 + 7.21326i) q^{66} +(8.23650 + 11.3366i) q^{67} -1.04872i q^{68} +(-13.5719 + 9.86054i) q^{69} +(1.96178 - 1.07304i) q^{70} +(12.9126 + 9.38155i) q^{71} +(-0.700190 + 0.963729i) q^{72} +(1.48193 + 0.481508i) q^{73} -1.26010 q^{74} +(8.61922 + 5.52177i) q^{75} +6.92805 q^{76} +(-3.52339 - 1.14482i) q^{77} +(6.54274 - 9.00532i) q^{78} +(4.52283 + 3.28603i) q^{79} +(0.956396 - 2.02121i) q^{80} +(9.02431 - 6.55655i) q^{81} +6.19003i q^{82} +(5.18413 + 7.13534i) q^{83} +(-0.632635 - 1.94705i) q^{84} +(-0.298882 + 2.32588i) q^{85} +(-0.623696 + 1.91954i) q^{86} +(10.1873 - 3.31006i) q^{87} +(-3.52339 + 1.14482i) q^{88} +(1.51164 - 4.65234i) q^{89} +(1.82756 - 1.93784i) q^{90} +(1.68017 + 5.17103i) q^{91} +(-4.81648 - 6.62931i) q^{92} +10.6493i q^{93} +(-10.4179 + 7.56905i) q^{94} +(-15.3653 - 1.97448i) q^{95} +(-1.65626 - 1.20334i) q^{96} +(5.53353 - 7.61626i) q^{97} +(0.951057 + 0.309017i) q^{98} -4.41318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more