LMFDB - Embedded newform 294.2.m.b.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	294.235
Dual form			294.2.m.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.189189 - 2.52456i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(2.49030 + 0.893546i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.189189 - 2.52456i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(2.49030 + 0.893546i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.189189 + 2.52456i) q^{10} +(-0.833900 - 2.12474i) q^{11} +(0.955573 - 0.294755i) q^{12} +(-0.709999 + 0.890311i) q^{13} +(-2.32931 - 1.25473i) q^{14} +(-1.57845 - 1.97931i) q^{15} +(0.826239 + 0.563320i) q^{16} +(1.51170 + 1.40265i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.80394 - 4.85657i) q^{19} +(0.563342 - 2.46816i) q^{20} +(2.56093 - 0.664551i) q^{21} +(0.507910 + 2.22530i) q^{22} +(2.58302 - 2.39669i) q^{23} +(-0.988831 + 0.149042i) q^{24} +(-1.39344 + 0.210027i) q^{25} +(0.834763 - 0.774547i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(2.11628 + 1.58788i) q^{28} +(0.266184 - 1.16623i) q^{29} +(1.26582 + 2.19246i) q^{30} +(-3.10019 + 5.36968i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-1.88591 - 1.28579i) q^{33} +(-1.28576 - 1.61229i) q^{34} +(1.78467 - 6.45594i) q^{35} +(0.623490 - 0.781831i) q^{36} +(6.74073 - 2.07924i) q^{37} +(2.04879 + 5.22023i) q^{38} +(-0.0850989 + 1.13557i) q^{39} +(-0.924910 + 2.35663i) q^{40} +(1.04508 + 0.503285i) q^{41} +(-2.63137 + 0.275442i) q^{42} +(3.80358 - 1.83171i) q^{43} +(-0.170573 - 2.27614i) q^{44} +(-2.41916 - 0.746212i) q^{45} +(-2.91138 + 1.98494i) q^{46} +(-6.54164 - 0.985994i) q^{47} +1.00000 q^{48} +(5.40315 + 4.45039i) q^{49} +1.40918 q^{50} +(2.03917 + 0.307355i) q^{51} +(-0.940879 + 0.641481i) q^{52} +(-4.64882 - 1.43397i) q^{53} +(0.0747301 + 0.997204i) q^{54} +(-5.20627 + 2.50721i) q^{55} +(-1.85598 - 1.88556i) q^{56} +(-5.05253 - 2.43317i) q^{57} +(-0.437028 + 1.11353i) q^{58} +(-1.02290 + 13.6497i) q^{59} +(-0.924910 - 2.35663i) q^{60} +(3.45671 - 1.06625i) q^{61} +(3.86587 - 4.84765i) q^{62} +(1.74159 - 1.99170i) q^{63} +(0.623490 + 0.781831i) q^{64} +(2.38196 + 1.62400i) q^{65} +(1.67321 + 1.55251i) q^{66} +(-6.29482 + 10.9029i) q^{67} +(1.03110 + 1.78592i) q^{68} +(0.784086 - 3.43531i) q^{69} +(-2.72694 + 6.11784i) q^{70} +(3.34269 + 14.6453i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(-6.13725 + 0.925042i) q^{73} +(-6.97534 + 1.05136i) q^{74} +(-1.03300 + 0.958483i) q^{75} +(-1.24787 - 5.46728i) q^{76} +(-0.178103 - 6.03637i) q^{77} +(0.253396 - 1.11020i) q^{78} +(7.36630 + 12.7588i) q^{79} +(1.26582 - 2.19246i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(-0.958398 - 0.653425i) q^{82} +(4.61980 + 5.79305i) q^{83} +(2.64304 + 0.119821i) q^{84} +(3.25508 - 4.08174i) q^{85} +(-4.03410 + 1.24435i) q^{86} +(-0.437028 - 1.11353i) q^{87} +(-0.170573 + 2.27614i) q^{88} +(-4.34339 + 11.0668i) q^{89} +(2.28092 + 1.09844i) q^{90} +(-2.56364 + 1.58272i) q^{91} +(3.17470 - 1.52885i) q^{92} +(0.463355 + 6.18304i) q^{93} +(6.32163 + 1.94996i) q^{94} +(-11.7302 + 7.99751i) q^{95} +(-0.988831 - 0.149042i) q^{96} +1.58232 q^{97} +(-4.67951 - 5.20598i) q^{98} -2.28253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	−0.189189	−	2.52456i	−0.0846080	−	1.12902i	−0.864342	−	0.502905i	$-0.832265\pi$
$5$	−0.189189	−	2.52456i	−0.0846080	−	1.12902i	0.779734	−	0.626111i	$-0.215354\pi$
$6$	−0.900969	+	0.433884i	−0.367819	+	0.177132i
$7$	2.49030	+	0.893546i	0.941244	+	0.337729i
$7$	2.49030	+	0.893546i	0.941244	+	0.337729i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	0.365341	−	0.930874i	0.121780	−	0.310291i
$10$	−0.189189	+	2.52456i	−0.0598269	+	0.798335i
$11$	−0.833900	−	2.12474i	−0.251430	−	0.640634i	0.748312	−	0.663347i	$-0.230865\pi$
$11$	−0.833900	−	2.12474i	−0.251430	−	0.640634i	−0.999742	+	0.0227132i	$0.992770\pi$
$12$	0.955573	−	0.294755i	0.275850	−	0.0850885i
$13$	−0.709999	+	0.890311i	−0.196918	+	0.246928i	−0.870481	−	0.492203i	$-0.836192\pi$
$13$	−0.709999	+	0.890311i	−0.196918	+	0.246928i	0.673562	+	0.739130i	$0.264763\pi$
$14$	−2.32931	−	1.25473i	−0.622533	−	0.335339i
$15$	−1.57845	−	1.97931i	−0.407554	−	0.511056i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	1.51170	+	1.40265i	0.366641	+	0.340193i	0.841881	−	0.539663i	$-0.181448\pi$
$17$	1.51170	+	1.40265i	0.366641	+	0.340193i	−0.475240	+	0.879856i	$0.657639\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.80394	−	4.85657i	−0.643268	−	1.11417i	−0.984699	−	0.174266i	$-0.944245\pi$
$19$	−2.80394	−	4.85657i	−0.643268	−	1.11417i	0.341431	−	0.939907i	$-0.389089\pi$
$20$	0.563342	−	2.46816i	0.125967	−	0.551898i
$21$	2.56093	−	0.664551i	0.558841	−	0.145017i
$22$	0.507910	+	2.22530i	0.108287	+	0.474435i
$23$	2.58302	−	2.39669i	0.538597	−	0.499745i	−0.363314	−	0.931667i	$-0.618355\pi$
$23$	2.58302	−	2.39669i	0.538597	−	0.499745i	0.901911	+	0.431922i	$0.142164\pi$
$24$	−0.988831	+	0.149042i	−0.201844	+	0.0304231i
$25$	−1.39344	+	0.210027i	−0.278687	+	0.0420053i
$26$	0.834763	−	0.774547i	0.163710	−	0.151901i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	2.11628	+	1.58788i	0.399940	+	0.300080i
$29$	0.266184	−	1.16623i	0.0494291	−	0.216563i	−0.944182	−	0.329426i	$-0.893145\pi$
$29$	0.266184	−	1.16623i	0.0494291	−	0.216563i	0.993611	+	0.112863i	$0.0360020\pi$
$30$	1.26582	+	2.19246i	0.231106	+	0.400287i
$31$	−3.10019	+	5.36968i	−0.556810	+	0.964424i	0.440950	+	0.897532i	$0.354642\pi$
$31$	−3.10019	+	5.36968i	−0.556810	+	0.964424i	−0.997760	+	0.0668920i	$0.978692\pi$
$32$	−0.733052	−	0.680173i	−0.129586	−	0.120239i
$33$	−1.88591	−	1.28579i	−0.328295	−	0.223828i
$34$	−1.28576	−	1.61229i	−0.220506	−	0.276506i
$35$	1.78467	−	6.45594i	0.301664	−	1.09125i
$36$	0.623490	−	0.781831i	0.103915	−	0.130305i
$37$	6.74073	−	2.07924i	1.10817	−	0.341825i	0.313940	−	0.949443i	$-0.398351\pi$
$37$	6.74073	−	2.07924i	1.10817	−	0.341825i	0.794229	+	0.607618i	$0.207875\pi$
$38$	2.04879	+	5.22023i	0.332357	+	0.846833i
$39$	−0.0850989	+	1.13557i	−0.0136267	+	0.181836i
$40$	−0.924910	+	2.35663i	−0.146241	+	0.372616i
$41$	1.04508	+	0.503285i	0.163214	+	0.0785999i	0.513707	−	0.857965i	$-0.328272\pi$
$41$	1.04508	+	0.503285i	0.163214	+	0.0785999i	−0.350493	+	0.936565i	$0.613986\pi$
$42$	−2.63137	+	0.275442i	−0.406030	+	0.0425016i
$43$	3.80358	−	1.83171i	0.580040	−	0.279333i	−0.120770	−	0.992681i	$-0.538536\pi$
$43$	3.80358	−	1.83171i	0.580040	−	0.279333i	0.700810	+	0.713348i	$0.252822\pi$
$44$	−0.170573	−	2.27614i	−0.0257149	−	0.343141i
$45$	−2.41916	−	0.746212i	−0.360627	−	0.111239i
$46$	−2.91138	+	1.98494i	−0.429259	+	0.292664i
$47$	−6.54164	−	0.985994i	−0.954197	−	0.143822i	−0.346552	−	0.938031i	$-0.612648\pi$
$47$	−6.54164	−	0.985994i	−0.954197	−	0.143822i	−0.607645	+	0.794209i	$0.707886\pi$
$48$	1.00000			0.144338
$49$	5.40315	+	4.45039i	0.771879	+	0.635770i
$50$	1.40918			0.199287
$51$	2.03917	+	0.307355i	0.285541	+	0.0430383i
$52$	−0.940879	+	0.641481i	−0.130477	+	0.0889574i
$53$	−4.64882	−	1.43397i	−0.638564	−	0.196971i	−0.0414669	−	0.999140i	$-0.513203\pi$
$53$	−4.64882	−	1.43397i	−0.638564	−	0.196971i	−0.597097	+	0.802169i	$0.703679\pi$
$54$	0.0747301	+	0.997204i	0.0101695	+	0.135702i
$55$	−5.20627	+	2.50721i	−0.702013	+	0.338072i
$56$	−1.85598	−	1.88556i	−0.248016	−	0.251968i
$57$	−5.05253	−	2.43317i	−0.669223	−	0.322281i
$58$	−0.437028	+	1.11353i	−0.0573846	+	0.146214i
$59$	−1.02290	+	13.6497i	−0.133170	+	1.77703i	0.386132	+	0.922443i	$0.373811\pi$
$59$	−1.02290	+	13.6497i	−0.133170	+	1.77703i	−0.519303	+	0.854590i	$0.673808\pi$
$60$	−0.924910	−	2.35663i	−0.119405	−	0.304240i
$61$	3.45671	−	1.06625i	0.442586	−	0.136520i	−0.0654495	−	0.997856i	$-0.520848\pi$
$61$	3.45671	−	1.06625i	0.442586	−	0.136520i	0.508035	+	0.861336i	$0.330372\pi$
$62$	3.86587	−	4.84765i	0.490966	−	0.615652i
$63$	1.74159	−	1.99170i	0.219419	−	0.250931i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	2.38196	+	1.62400i	0.295446	+	0.201432i
$66$	1.67321	+	1.55251i	0.205958	+	0.191101i
$67$	−6.29482	+	10.9029i	−0.769034	+	1.33201i	0.169053	+	0.985607i	$0.445929\pi$
$67$	−6.29482	+	10.9029i	−0.769034	+	1.33201i	−0.938087	+	0.346400i	$0.887404\pi$
$68$	1.03110	+	1.78592i	0.125039	+	0.216574i
$69$	0.784086	−	3.43531i	0.0943929	−	0.413562i
$70$	−2.72694	+	6.11784i	−0.325932	+	0.731222i
$71$	3.34269	+	14.6453i	0.396704	+	1.73807i	0.640233	+	0.768181i	$0.278838\pi$
$71$	3.34269	+	14.6453i	0.396704	+	1.73807i	−0.243529	+	0.969894i	$0.578305\pi$
$72$	−0.733052	+	0.680173i	−0.0863910	+	0.0801591i
$73$	−6.13725	+	0.925042i	−0.718311	+	0.108268i	−0.498019	−	0.867166i	$-0.665939\pi$
$73$	−6.13725	+	0.925042i	−0.718311	+	0.108268i	−0.220292	+	0.975434i	$0.570701\pi$
$74$	−6.97534	+	1.05136i	−0.810866	+	0.122218i
$75$	−1.03300	+	0.958483i	−0.119280	+	0.110676i
$76$	−1.24787	−	5.46728i	−0.143141	−	0.627140i
$77$	−0.178103	−	6.03637i	−0.0202967	−	0.687908i
$78$	0.253396	−	1.11020i	0.0286914	−	0.125705i
$79$	7.36630	+	12.7588i	0.828774	+	1.43548i	0.899001	+	0.437947i	$0.144294\pi$
$79$	7.36630	+	12.7588i	0.828774	+	1.43548i	−0.0702273	+	0.997531i	$0.522372\pi$
$80$	1.26582	−	2.19246i	0.141523	−	0.245124i
$81$	−0.733052	−	0.680173i	−0.0814502	−	0.0755747i
$82$	−0.958398	−	0.653425i	−0.105837	−	0.0721587i
$83$	4.61980	+	5.79305i	0.507089	+	0.635870i	0.967812	−	0.251674i	$-0.0809812\pi$
$83$	4.61980	+	5.79305i	0.507089	+	0.635870i	−0.460723	+	0.887544i	$0.652410\pi$
$84$	2.64304	+	0.119821i	0.288379	+	0.0130735i
$85$	3.25508	−	4.08174i	0.353063	−	0.442727i
$86$	−4.03410	+	1.24435i	−0.435008	+	0.134182i
$87$	−0.437028	−	1.11353i	−0.0468543	−	0.119383i
$88$	−0.170573	+	2.27614i	−0.0181832	+	0.242638i
$89$	−4.34339	+	11.0668i	−0.460398	+	1.17307i	0.492642	+	0.870232i	$0.336031\pi$
$89$	−4.34339	+	11.0668i	−0.460398	+	1.17307i	−0.953040	+	0.302843i	$0.902064\pi$
$90$	2.28092	+	1.09844i	0.240431	+	0.115785i
$91$	−2.56364	+	1.58272i	−0.268743	+	0.165914i
$92$	3.17470	−	1.52885i	0.330985	−	0.159394i
$93$	0.463355	+	6.18304i	0.0480476	+	0.641151i
$94$	6.32163	+	1.94996i	0.652026	+	0.201123i
$95$	−11.7302	+	7.99751i	−1.20349	+	0.820528i
$96$	−0.988831	−	0.149042i	−0.100922	−	0.0152116i
$97$	1.58232			0.160660			0.0803301	−	0.996768i	$-0.474403\pi$
$97$	1.58232			0.160660			0.0803301	+	0.996768i	$0.474403\pi$
$98$	−4.67951	−	5.20598i	−0.472702	−	0.525883i
$99$	−2.28253			−0.229402
$100$	−1.39344	−	0.210027i	−0.139344	−	0.0210027i
$101$	12.1082	−	8.25526i	1.20481	−	0.821429i	0.216865	−	0.976202i	$-0.430417\pi$
$101$	12.1082	−	8.25526i	1.20481	−	0.821429i	0.987950	+	0.154773i	$0.0494645\pi$
$102$	−1.97058	−	0.607844i	−0.195117	−	0.0601856i
$103$	−0.917862	−	12.2480i	−0.0904396	−	1.20683i	−0.839137	−	0.543920i	$-0.816939\pi$
$103$	−0.917862	−	12.2480i	−0.0904396	−	1.20683i	0.748697	−	0.662912i	$-0.230680\pi$
$104$	1.02598	−	0.494085i	0.100605	−	0.0484490i
$105$	−2.16220	−	6.33949i	−0.211009	−	0.618671i
$106$	4.38317	+	2.11082i	0.425731	+	0.205021i
$107$	−3.43226	+	8.74526i	−0.331809	+	0.845436i	0.663454	+	0.748217i	$0.269090\pi$
$107$	−3.43226	+	8.74526i	−0.331809	+	0.845436i	−0.995263	+	0.0972189i	$0.969005\pi$
$108$	0.0747301	−	0.997204i	0.00719091	−	0.0959560i
$109$	−1.60891	−	4.09944i	−0.154106	−	0.392655i	0.832882	−	0.553451i	$-0.186689\pi$
$109$	−1.60891	−	4.09944i	−0.154106	−	0.392655i	−0.986988	+	0.160795i	$0.948594\pi$
$110$	5.52180	−	1.70325i	0.526483	−	0.162398i
$111$	4.39818	−	5.51514i	0.417456	−	0.523474i
$112$	1.55423	+	2.14112i	0.146861	+	0.202316i
$113$	−0.956349	−	1.19922i	−0.0899657	−	0.112813i	0.734811	−	0.678272i	$-0.237271\pi$
$113$	−0.956349	−	1.19922i	−0.0899657	−	0.112813i	−0.824777	+	0.565458i	$0.808699\pi$
$114$	4.63345	+	3.15903i	0.433962	+	0.295870i
$115$	−6.53926	−	6.06755i	−0.609789	−	0.565802i
$116$	0.598110	−	1.03596i	0.0555331	−	0.0961861i
$117$	0.569375	+	0.986187i	0.0526387	+	0.0911730i
$118$	3.04585	−	13.3447i	0.280393	−	1.22848i
$119$	2.51125	+	4.84380i	0.230206	+	0.444030i
$120$	0.563342	+	2.46816i	0.0514258	+	0.225311i
$121$	4.24443	−	3.93825i	0.385857	−	0.358023i
$122$	−3.57701	+	0.539148i	−0.323848	+	0.0488122i
$123$	1.14700	−	0.172882i	0.103421	−	0.0155882i
$124$	−4.54520	+	4.21733i	−0.408171	+	0.378727i
$125$	−2.02286	−	8.86274i	−0.180930	−	0.792707i
$126$	−2.01898	+	1.70989i	−0.179865	+	0.152329i
$127$	3.68408	−	16.1410i	0.326910	−	1.43228i	−0.498077	−	0.867133i	$-0.665960\pi$
$127$	3.68408	−	16.1410i	0.326910	−	1.43228i	0.824987	−	0.565152i	$-0.191182\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.11083	−	3.65606i	0.185848	−	0.321898i
$130$	−2.11331	−	1.96087i	−0.185350	−	0.171980i
$131$	−12.5616	−	8.56433i	−1.09751	−	0.748269i	−0.127622	−	0.991823i	$-0.540734\pi$
$131$	−12.5616	−	8.56433i	−1.09751	−	0.748269i	−0.969887	+	0.243554i	$0.921687\pi$
$132$	−1.42313	−	1.78455i	−0.123868	−	0.155325i
$133$	−2.64308	−	14.5997i	−0.229184	−	1.26596i
$134$	7.84951	−	9.84297i	0.678094	−	0.850303i
$135$	−2.41916	+	0.746212i	−0.208208	+	0.0642237i
$136$	−0.753407	−	1.91965i	−0.0646041	−	0.164609i
$137$	−0.395290	+	5.27478i	−0.0337719	+	0.450654i	0.954527	+	0.298125i	$0.0963611\pi$
$137$	−0.395290	+	5.27478i	−0.0337719	+	0.450654i	−0.988299	+	0.152530i	$0.951258\pi$
$138$	−1.28733	+	3.28007i	−0.109585	+	0.279218i
$139$	−13.4435	−	6.47405i	−1.14026	−	0.549121i	−0.234168	−	0.972196i	$-0.575236\pi$
$139$	−13.4435	−	6.47405i	−1.14026	−	0.549121i	−0.906095	+	0.423075i	$0.860951\pi$
$140$	3.60830	−	5.64308i	0.304957	−	0.476927i
$141$	−5.96039	+	2.87037i	−0.501955	+	0.241729i
$142$	−1.12259	−	14.9799i	−0.0942055	−	1.25709i
$143$	2.48375	+	0.766135i	0.207702	+	0.0640675i
$144$	0.826239	−	0.563320i	0.0688532	−	0.0469433i
$145$	−2.99457	−	0.451358i	−0.248685	−	0.0374832i
$146$	6.20657			0.513660
$147$	6.97129	+	0.633380i	0.574982	+	0.0522403i
$148$	7.05413			0.579846
$149$	9.60020	+	1.44700i	0.786479	+	0.118543i	0.529989	−	0.848004i	$-0.322196\pi$
$149$	9.60020	+	1.44700i	0.786479	+	0.118543i	0.256490	+	0.966547i	$0.417434\pi$
$150$	1.16432	−	0.793817i	0.0950659	−	0.0648149i
$151$	20.0405	+	6.18167i	1.63087	+	0.503057i	0.969104	−	0.246652i	$-0.0793304\pi$
$151$	20.0405	+	6.18167i	1.63087	+	0.503057i	0.661767	+	0.749709i	$0.269807\pi$
$152$	0.419077	+	5.59220i	0.0339917	+	0.453587i
$153$	1.85798	−	0.894756i	0.150209	−	0.0723367i
$154$	−0.723560	+	5.99549i	−0.0583062	+	0.483130i
$155$	14.1426	+	6.81071i	1.13596	+	0.547050i
$156$	−0.416032	+	1.06003i	−0.0333092	+	0.0848705i
$157$	−1.00682	+	13.4351i	−0.0803533	+	1.07224i	0.800651	+	0.599131i	$0.204487\pi$
$157$	−1.00682	+	13.4351i	−0.0803533	+	1.07224i	−0.881004	+	0.473109i	$0.843132\pi$
$158$	−5.38242	−	13.7142i	−0.428203	−	1.09104i
$159$	−4.64882	+	1.43397i	−0.368675	+	0.113721i
$160$	−1.57845	+	1.97931i	−0.124787	+	0.156478i
$161$	8.57404	−	3.66042i	0.675729	−	0.288482i
$162$	0.623490	+	0.781831i	0.0489860	+	0.0614265i
$163$	−17.3944	−	11.8593i	−1.36243	−	0.928892i	−0.362439	−	0.932007i	$-0.618056\pi$
$163$	−17.3944	−	11.8593i	−1.36243	−	0.928892i	−0.999995	+	0.00311522i	$0.999008\pi$
$164$	0.850305	+	0.788968i	0.0663977	+	0.0616081i
$165$	−2.88926	+	5.00435i	−0.224929	+	0.389588i
$166$	−3.70479	−	6.41689i	−0.287548	−	0.498047i
$167$	−2.17455	+	9.52732i	−0.168272	+	0.737246i	0.818417	+	0.574625i	$0.194852\pi$
$167$	−2.17455	+	9.52732i	−0.168272	+	0.737246i	−0.986689	+	0.162621i	$0.948005\pi$
$168$	−2.59566	−	0.512406i	−0.200259	−	0.0395330i
$169$	2.60422	+	11.4098i	0.200324	+	0.877679i
$170$	−3.82707	+	3.55101i	−0.293523	+	0.272350i
$171$	−5.54525	+	0.835811i	−0.424056	+	0.0639161i
$172$	4.17450	−	0.629205i	0.318303	−	0.0479764i
$173$	16.1339	−	14.9701i	1.22664	−	1.13815i	0.240779	−	0.970580i	$-0.422597\pi$
$173$	16.1339	−	14.9701i	1.22664	−	1.13815i	0.985859	−	0.167574i	$-0.0535933\pi$
$174$	0.266184	+	1.16623i	0.0201793	+	0.0884115i
$175$	−3.65774	−	0.722070i	−0.276499	−	0.0545834i
$176$	0.507910	−	2.22530i	0.0382851	−	0.167738i
$177$	6.84397	+	11.8541i	0.514424	+	0.891008i
$178$	5.94429	−	10.2958i	0.445543	−	0.771704i
$179$	7.98143	+	7.40569i	0.596560	+	0.553527i	0.919599	−	0.392859i	$-0.128514\pi$
$179$	7.98143	+	7.40569i	0.596560	+	0.553527i	−0.323039	+	0.946386i	$0.604704\pi$
$180$	−2.09173	−	1.42612i	−0.155909	−	0.106297i
$181$	1.07176	+	1.34395i	0.0796635	+	0.0998948i	0.820066	−	0.572269i	$-0.193937\pi$
$181$	1.07176	+	1.34395i	0.0796635	+	0.0998948i	−0.740403	+	0.672164i	$0.765365\pi$
$182$	2.77090	−	1.18295i	0.205393	−	0.0876862i
$183$	2.25542	−	2.82821i	0.166726	−	0.209067i
$184$	−3.36710	+	1.03861i	−0.248226	+	0.0765677i
$185$	−6.52443	−	16.6240i	−0.479686	−	1.22222i
$186$	0.463355	−	6.18304i	0.0339748	−	0.453362i
$187$	1.71967	−	4.38165i	0.125755	−	0.320418i
$188$	−5.96039	−	2.87037i	−0.434706	−	0.209343i
$189$	0.317000	−	2.62669i	0.0230584	−	0.191064i
$190$	12.7912	−	6.15989i	0.927968	−	0.446886i
$191$	0.800400	+	10.6806i	0.0579149	+	0.772821i	0.948252	+	0.317519i	$0.102850\pi$
$191$	0.800400	+	10.6806i	0.0579149	+	0.772821i	−0.890337	+	0.455302i	$0.849531\pi$
$192$	0.955573	+	0.294755i	0.0689625	+	0.0212721i
$193$	17.5777	−	11.9843i	1.26527	−	0.862649i	0.270299	−	0.962776i	$-0.412877\pi$
$193$	17.5777	−	11.9843i	1.26527	−	0.862649i	0.994975	+	0.100127i	$0.0319249\pi$
$194$	−1.56465	−	0.235832i	−0.112335	−	0.0169318i
$195$	2.88290			0.206449
$196$	3.85133	+	5.84528i	0.275095	+	0.417520i
$197$	−12.7541			−0.908695			−0.454348	−	0.890825i	$-0.650128\pi$
$197$	−12.7541			−0.908695			−0.454348	+	0.890825i	$0.650128\pi$
$198$	2.25703	+	0.340193i	0.160400	+	0.0241764i
$199$	−19.0478	+	12.9866i	−1.35027	+	0.920596i	−0.999872	−	0.0160066i	$-0.994905\pi$
$199$	−19.0478	+	12.9866i	−1.35027	+	0.920596i	−0.350394	+	0.936602i	$0.613952\pi$
$200$	1.34657	+	0.415362i	0.0952168	+	0.0293705i
$201$	0.940825	+	12.5544i	0.0663607	+	0.885521i
$202$	−13.2034	+	6.35841i	−0.928987	+	0.447376i
$203$	1.70495	−	2.66640i	0.119664	−	0.187145i
$204$	1.85798	+	0.894756i	0.130085	+	0.0626454i
$205$	1.07285	−	2.73358i	0.0749312	−	0.190922i
$206$	−0.917862	+	12.2480i	−0.0639504	+	0.853359i
$207$	−1.28733	−	3.28007i	−0.0894759	−	0.227981i
$208$	−1.08816	+	0.335652i	−0.0754502	+	0.0232733i
$209$	−7.98075	+	10.0075i	−0.552040	+	0.692236i
$210$	1.19320	+	6.59094i	0.0823384	+	0.454818i
$211$	−2.50869	−	3.14580i	−0.172706	−	0.216566i	0.687944	−	0.725764i	$-0.258514\pi$
$211$	−2.50869	−	3.14580i	−0.172706	−	0.216566i	−0.860649	+	0.509198i	$0.829942\pi$
$212$	−4.01961	−	2.74053i	−0.276068	−	0.188220i
$213$	11.0118	+	10.2175i	0.754519	+	0.700091i
$214$	4.69734	−	8.13603i	0.321104	−	0.556168i
$215$	−5.34384	−	9.25581i	−0.364447	−	0.631241i
$216$	−0.222521	+	0.974928i	−0.0151406	+	0.0663354i
$217$	−12.5184	+	10.6019i	−0.849808	+	0.719707i
$218$	0.979952	+	4.29345i	0.0663707	+	0.290789i
$219$	−4.54974	+	4.22154i	−0.307443	+	0.285265i
$220$	−5.71398	+	0.861244i	−0.385236	+	0.0580650i
$221$	−2.32210	+	0.350001i	−0.156202	+	0.0235436i
$222$	−5.17104	+	4.79802i	−0.347057	+	0.322022i
$223$	−5.90497	−	25.8714i	−0.395426	−	1.73248i	−0.645057	−	0.764134i	$-0.723166\pi$
$223$	−5.90497	−	25.8714i	−0.395426	−	1.73248i	0.249631	−	0.968341i	$-0.419691\pi$
$224$	−1.21775	−	2.34885i	−0.0813644	−	0.156939i
$225$	−0.313571	+	1.37384i	−0.0209047	+	0.0915896i
$226$	0.766932	+	1.32837i	0.0510156	+	0.0883616i
$227$	1.82799	−	3.16617i	0.121328	−	0.210146i	−0.798964	−	0.601379i	$-0.794618\pi$
$227$	1.82799	−	3.16617i	0.121328	−	0.210146i	0.920292	+	0.391233i	$0.127951\pi$
$228$	−4.11087	−	3.81433i	−0.272249	−	0.252610i
$229$	−1.78349	−	1.21596i	−0.117856	−	0.0803529i	0.502957	−	0.864311i	$-0.332245\pi$
$229$	−1.78349	−	1.21596i	−0.117856	−	0.0803529i	−0.620814	+	0.783958i	$0.713198\pi$
$230$	5.56190	+	6.97440i	0.366741	+	0.459879i
$231$	−3.54756	−	4.88715i	−0.233412	−	0.321551i
$232$	−0.745830	+	0.935242i	−0.0489662	+	0.0614016i
$233$	−6.34035	+	1.95574i	−0.415370	+	0.128125i	−0.495394	−	0.868668i	$-0.664976\pi$
$233$	−6.34035	+	1.95574i	−0.415370	+	0.128125i	0.0800242	+	0.996793i	$0.474500\pi$
$234$	−0.416032	−	1.06003i	−0.0271969	−	0.0692965i
$235$	−1.25159	+	16.7013i	−0.0816446	+	1.08947i
$236$	−5.00076	+	12.7417i	−0.325522	+	0.829416i
$237$	13.2736	+	6.39224i	0.862214	+	0.415220i
$238$	−1.76127	−	5.16398i	−0.114166	−	0.334731i
$239$	−18.0866	+	8.71003i	−1.16992	+	0.563405i	−0.914959	−	0.403546i	$-0.867778\pi$
$239$	−18.0866	+	8.71003i	−1.16992	+	0.563405i	−0.254963	+	0.966951i	$0.582063\pi$
$240$	−0.189189	−	2.52456i	−0.0122121	−	0.162959i
$241$	−22.5616	−	6.95934i	−1.45332	−	0.448290i	−0.535246	−	0.844696i	$-0.679781\pi$
$241$	−22.5616	−	6.95934i	−1.45332	−	0.448290i	−0.918075	+	0.396406i	$0.870257\pi$
$242$	−4.78399	+	3.26167i	−0.307526	+	0.209668i
$243$	−0.988831	−	0.149042i	−0.0634335	−	0.00956107i
$244$	3.61742			0.231581
$245$	10.2130	−	14.4825i	0.652487	−	0.925254i
$246$	−1.15995			−0.0739559
$247$	6.31465	+	0.951780i	0.401791	+	0.0605603i
$248$	5.12299	−	3.49280i	0.325310	−	0.221793i
$249$	7.08040	+	2.18401i	0.448702	+	0.138406i
$250$	0.679346	+	9.06524i	0.0429656	+	0.573336i
$251$	−19.0315	+	9.16509i	−1.20126	+	0.578496i	−0.924034	−	0.382310i	$-0.875129\pi$
$251$	−19.0315	+	9.16509i	−1.20126	+	0.578496i	−0.277224	+	0.960805i	$0.589415\pi$
$252$	2.25128	−	1.38988i	0.141817	−	0.0875539i
$253$	−7.24633	−	3.48965i	−0.455573	−	0.219392i
$254$	−6.04863	+	15.4117i	−0.379525	+	0.967013i
$255$	0.390146	−	5.20614i	0.0244319	−	0.326021i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	−0.137001	+	0.0422591i	−0.00854586	+	0.00263605i	−0.299025	−	0.954245i	$-0.596661\pi$
$257$	−0.137001	+	0.0422591i	−0.00854586	+	0.00263605i	0.290479	+	0.956881i	$0.406185\pi$
$258$	−2.63216	+	3.30062i	−0.163871	+	0.205488i
$259$	18.6443	+	0.845229i	1.15850	+	0.0525200i
$260$	1.79746	+	2.25394i	0.111474	+	0.139784i
$261$	−0.988363	−	0.673854i	−0.0611781	−	0.0417105i
$262$	11.1448	+	10.3409i	0.688529	+	0.638862i
$263$	5.84964	−	10.1319i	0.360704	−	0.624758i	−0.627373	−	0.778719i	$-0.715870\pi$
$263$	5.84964	−	10.1319i	0.360704	−	0.624758i	0.988077	+	0.153961i	$0.0492031\pi$
$264$	1.14126	+	1.97672i	0.0702399	+	0.121659i
$265$	−2.74063	+	12.0075i	−0.168356	+	0.737614i
$266$	0.437577	+	14.8306i	0.0268295	+	0.909323i
$267$	2.64546	+	11.5905i	0.161899	+	0.709328i
$268$	−9.22886	+	8.56313i	−0.563742	+	0.523076i
$269$	19.8852	−	2.99721i	1.21242	−	0.182743i	0.488461	−	0.872586i	$-0.337558\pi$
$269$	19.8852	−	2.99721i	1.21242	−	0.182743i	0.723959	+	0.689842i	$0.242320\pi$
$270$	2.50336	−	0.377321i	0.152350	−	0.0229630i
$271$	12.5259	−	11.6224i	0.760896	−	0.706009i	−0.200949	−	0.979602i	$-0.564403\pi$
$271$	12.5259	−	11.6224i	0.760896	−	0.706009i	0.961846	+	0.273593i	$0.0882121\pi$
$272$	0.458883	+	2.01050i	0.0278239	+	0.121904i
$273$	−1.22660	+	2.75186i	−0.0742373	+	0.166550i
$274$	1.17704	−	5.15695i	0.0711075	−	0.311542i
$275$	1.60824	+	2.78555i	0.0969805	+	0.167975i
$276$	1.76183	−	3.05157i	0.106049	−	0.183683i
$277$	16.5911	+	15.3942i	0.996860	+	0.924951i	0.997180	−	0.0750493i	$-0.0239114\pi$
$277$	16.5911	+	15.3942i	0.996860	+	0.924951i	−0.000320130		1.00000i	$0.500102\pi$
$278$	12.3284	+	8.40539i	0.739410	+	0.504122i
$279$	3.86587	+	4.84765i	0.231444	+	0.290221i
$280$	−4.40906	+	5.04226i	−0.263492	+	0.301333i
$281$	−5.20957	+	6.53260i	−0.310777	+	0.389702i	−0.912550	−	0.408965i	$-0.865890\pi$
$281$	−5.20957	+	6.53260i	−0.310777	+	0.389702i	0.601773	+	0.798667i	$0.294461\pi$
$282$	6.32163	−	1.94996i	0.376447	−	0.116119i
$283$	−0.621965	−	1.58474i	−0.0369720	−	0.0942030i	0.911195	−	0.411975i	$-0.135161\pi$
$283$	−0.621965	−	1.58474i	−0.0369720	−	0.0942030i	−0.948167	+	0.317772i	$0.897066\pi$
$284$	−1.12259	+	14.9799i	−0.0666134	+	0.888894i
$285$	−5.18679	+	13.2157i	−0.307239	+	0.782831i
$286$	−2.34182	−	1.12776i	−0.138475	−	0.0666860i
$287$	2.15285	+	2.18716i	0.127079	+	0.129104i
$288$	−0.900969	+	0.433884i	−0.0530901	+	0.0255668i
$289$	−0.952609	−	12.7117i	−0.0560358	−	0.747746i
$290$	2.89385	+	0.892634i	0.169933	+	0.0524172i
$291$	1.30737	−	0.891352i	0.0766396	−	0.0522520i
$292$	−6.13725	−	0.925042i	−0.359155	−	0.0541340i
$293$	−16.9395			−0.989618			−0.494809	−	0.869002i	$-0.664762\pi$
$293$	−16.9395			−0.989618			−0.494809	+	0.869002i	$0.664762\pi$
$294$	−6.79902	−	1.66532i	−0.396527	−	0.0971236i
$295$	34.6528			2.01757
$296$	−6.97534	−	1.05136i	−0.405433	−	0.0611092i
$297$	−1.88591	+	1.28579i	−0.109432	+	0.0746092i
$298$	−9.27731	−	2.86167i	−0.537420	−	0.165772i
$299$	0.299859	+	4.00134i	0.0173413	+	0.231403i
$300$	−1.26962	+	0.611418i	−0.0733017	+	0.0353002i
$301$	11.1088	−	1.16282i	0.640298	−	0.0670239i
$302$	−18.8953	−	9.09951i	−1.08730	−	0.523618i
$303$	5.35395	−	13.6416i	0.307576	−	0.783691i
$304$	0.419077	−	5.59220i	0.0240357	−	0.320735i
$305$	−3.34579	−	8.52493i	−0.191579	−	0.488136i
$306$	−1.97058	+	0.607844i	−0.112651	+	0.0347482i
$307$	−0.118189	+	0.148204i	−0.00674540	+	0.00845847i	−0.785193	−	0.619251i	$-0.787436\pi$
$307$	−0.118189	+	0.148204i	−0.00674540	+	0.00845847i	0.778447	+	0.627710i	$0.216008\pi$
$308$	1.60906	−	5.82069i	0.0916847	−	0.331664i
$309$	−7.65792	−	9.60273i	−0.435644	−	0.546280i
$310$	−12.9695	−	8.84249i	−0.736621	−	0.502219i
$311$	−19.7208	−	18.2982i	−1.11826	−	1.03760i	−0.998999	−	0.0447347i	$-0.985756\pi$
$311$	−19.7208	−	18.2982i	−1.11826	−	1.03760i	−0.119265	−	0.992862i	$-0.538054\pi$
$312$	0.569375	−	0.986187i	0.0322345	−	0.0558318i
$313$	4.27137	+	7.39823i	0.241432	+	0.418173i	0.961122	−	0.276123i	$-0.0890496\pi$
$313$	4.27137	+	7.39823i	0.241432	+	0.418173i	−0.719690	+	0.694295i	$0.755716\pi$
$314$	2.99798	−	13.1350i	0.169186	−	0.741252i
$315$	−5.35765	−	4.01992i	−0.301870	−	0.226497i
$316$	3.27831	+	14.3632i	0.184419	+	0.807994i
$317$	20.9461	−	19.4351i	1.17645	−	1.09159i	0.182338	−	0.983236i	$-0.441633\pi$
$317$	20.9461	−	19.4351i	1.17645	−	1.09159i	0.994113	−	0.108351i	$-0.0345570\pi$
$318$	4.81062	−	0.725084i	0.269766	−	0.0406607i
$319$	−2.69990	+	0.406945i	−0.151166	+	0.0227845i
$320$	1.85582	−	1.72195i	0.103743	−	0.0962599i
$321$	2.09051	+	9.15914i	0.116681	+	0.511213i
$322$	−9.02383	+	2.34165i	−0.502878	+	0.130495i
$323$	2.57336	−	11.2746i	0.143186	−	0.627337i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	0.802349	−	1.38971i	0.0445063	−	0.0770872i
$326$	15.4326	+	14.3193i	0.854732	+	0.793075i
$327$	−3.63864	−	2.48079i	−0.201217	−	0.137188i
$328$	−0.723219	−	0.906888i	−0.0399331	−	0.0500745i
$329$	−15.4096	−	8.30068i	−0.849559	−	0.457631i
$330$	3.60285	−	4.51783i	0.198330	−	0.248698i
$331$	−15.9234	+	4.91171i	−0.875228	+	0.269972i	−0.699643	−	0.714492i	$-0.746658\pi$
$331$	−15.9234	+	4.91171i	−0.875228	+	0.269972i	−0.175585	+	0.984464i	$0.556182\pi$
$332$	2.70703	+	6.89739i	0.148567	+	0.378544i
$333$	0.527155	−	7.03440i	0.0288879	−	0.385483i
$334$	3.57023	−	9.09681i	0.195355	−	0.497755i
$335$	28.7160	+	13.8289i	1.56892	+	0.755553i
$336$	2.49030	+	0.893546i	0.135857	+	0.0487469i
$337$	−15.1953	+	7.31769i	−0.827743	+	0.398620i	−0.799268	−	0.600974i	$-0.794779\pi$
$337$	−15.1953	+	7.31769i	−0.827743	+	0.398620i	−0.0284750	+	0.999595i	$0.509065\pi$
$338$	−0.874585	−	11.6705i	−0.0475711	−	0.634793i
$339$	−1.46572	−	0.452115i	−0.0796070	−	0.0245555i
$340$	4.31358	−	2.94095i	0.233937	−	0.159495i
$341$	13.9944	+	2.10932i	0.757842	+	0.114226i
$342$	5.60788			0.303239
$343$	9.47882	+	15.9108i	0.511808	+	0.859100i
$344$	−4.22165			−0.227616
$345$	−8.82096	−	1.32955i	−0.474905	−	0.0715803i
$346$	−18.1849	+	12.3982i	−0.977625	+	0.666534i
$347$	−20.4098	−	6.29560i	−1.09566	−	0.337966i	−0.306322	−	0.951928i	$-0.599098\pi$
$347$	−20.4098	−	6.29560i	−1.09566	−	0.337966i	−0.789335	+	0.613962i	$0.789575\pi$
$348$	−0.0893936	−	1.19287i	−0.00479200	−	0.0639448i
$349$	−5.62646	+	2.70956i	−0.301178	+	0.145039i	−0.578369	−	0.815775i	$-0.696311\pi$
$349$	−5.62646	+	2.70956i	−0.301178	+	0.145039i	0.277192	+	0.960815i	$0.410596\pi$
$350$	3.50926	+	1.25916i	0.187578	+	0.0673051i
$351$	1.02598	+	0.494085i	0.0547627	+	0.0263723i
$352$	−0.833900	+	2.12474i	−0.0444470	+	0.113249i
$353$	2.00030	−	26.6921i	0.106465	−	1.42068i	−0.646650	−	0.762787i	$-0.723830\pi$
$353$	2.00030	−	26.6921i	0.106465	−	1.42068i	0.753115	−	0.657889i	$-0.228551\pi$
$354$	−5.00076	−	12.7417i	−0.265788	−	0.677216i
$355$	36.3404	−	11.2095i	1.92875	−	0.594940i
$356$	−7.41241	+	9.29487i	−0.392857	+	0.492627i
$357$	4.80350	+	2.58750i	0.254228	+	0.136945i
$358$	−6.78853	−	8.51254i	−0.358785	−	0.449902i
$359$	14.2411	+	9.70940i	0.751615	+	0.512443i	0.877485	−	0.479604i	$-0.159220\pi$
$359$	14.2411	+	9.70940i	0.751615	+	0.512443i	−0.125870	+	0.992047i	$0.540172\pi$
$360$	1.85582	+	1.72195i	0.0978103	+	0.0907547i
$361$	−6.22416	+	10.7806i	−0.327588	+	0.567398i
$362$	−0.859487	−	1.48867i	−0.0451736	−	0.0782430i
$363$	1.28841	−	5.64491i	0.0676242	−	0.296281i
$364$	−2.91626	+	0.756758i	−0.152854	+	0.0396649i
$365$	3.49642	+	15.3188i	0.183011	+	0.801824i
$366$	−2.65176	+	2.46047i	−0.138609	+	0.128611i
$367$	−0.471242	+	0.0710283i	−0.0245986	+	0.00370765i	−0.161330	−	0.986901i	$-0.551578\pi$
$367$	−0.471242	+	0.0710283i	−0.0245986	+	0.00370765i	0.136731	+	0.990608i	$0.456340\pi$
$368$	3.48429	−	0.525173i	0.181631	−	0.0273765i
$369$	0.850305	−	0.788968i	0.0442651	−	0.0410720i
$370$	3.97388	+	17.4107i	0.206592	+	0.905140i
$371$	−10.2956	−	7.72494i	−0.534522	−	0.401059i
$372$	−1.37971	+	6.04492i	−0.0715348	+	0.313415i
$373$	−12.5952	−	21.8155i	−0.652153	−	1.12956i	−0.982599	−	0.185737i	$-0.940533\pi$
$373$	−12.5952	−	21.8155i	−0.652153	−	1.12956i	0.330447	−	0.943825i	$-0.392801\pi$
$374$	−2.35351	+	4.07640i	−0.121697	+	0.210786i
$375$	−6.66392	−	6.18322i	−0.344124	−	0.319300i
$376$	5.46601	+	3.72666i	0.281888	+	0.192188i
$377$	0.849314	+	1.06501i	0.0437419	+	0.0548506i
$378$	−0.704947	+	2.55011i	−0.0362586	+	0.131163i
$379$	−17.2233	+	21.5973i	−0.884700	+	1.10938i	0.108631	+	0.994082i	$0.465353\pi$
$379$	−17.2233	+	21.5973i	−0.884700	+	1.10938i	−0.993331	+	0.115297i	$0.963218\pi$
$380$	−13.5664	+	4.18467i	−0.695940	+	0.214669i
$381$	−6.04863	−	15.4117i	−0.309881	−	0.789563i
$382$	0.800400	−	10.6806i	0.0409520	−	0.546467i
$383$	−12.7821	+	32.5681i	−0.653132	+	1.66415i	0.0907754	+	0.995871i	$0.471065\pi$
$383$	−12.7821	+	32.5681i	−0.653132	+	1.66415i	−0.743908	+	0.668282i	$0.767030\pi$
$384$	−0.900969	−	0.433884i	−0.0459774	−	0.0221415i
$385$	−15.2055	+	1.59165i	−0.774942	+	0.0811178i
$386$	−19.1676	+	9.23062i	−0.975605	+	0.469826i
$387$	−0.315485	−	4.20985i	−0.0160370	−	0.213999i
$388$	1.51202	+	0.466397i	0.0767612	+	0.0236777i
$389$	19.0914	−	13.0163i	0.967971	−	0.659951i	0.0274270	−	0.999624i	$-0.491269\pi$
$389$	19.0914	−	13.0163i	0.967971	−	0.659951i	0.940544	+	0.339672i	$0.110316\pi$
$390$	−2.85070	−	0.429674i	−0.144351	−	0.0217574i
$391$	7.26648			0.367482
$392$	−2.93712	−	6.35400i	−0.148347	−	0.320926i
$393$	−15.2033			−0.766906
$394$	12.6117	+	1.90091i	0.635368	+	0.0957663i
$395$	30.8167	−	21.0105i	1.55056	−	1.05715i
$396$	−2.18112	−	0.672786i	−0.109605	−	0.0338088i
$397$	1.71328	+	22.8621i	0.0859868	+	1.14741i	0.858638	+	0.512583i	$0.171311\pi$
$397$	1.71328	+	22.8621i	0.0859868	+	1.14741i	−0.772651	+	0.634831i	$0.781070\pi$
$398$	20.7706	−	10.0026i	1.04114	−	0.501386i
$399$	−10.4081	−	10.5740i	−0.521059	−	0.529361i
$400$	−1.26962	−	0.611418i	−0.0634811	−	0.0305709i
$401$	4.99613	−	12.7299i	0.249495	−	0.635702i	−0.750179	−	0.661234i	$-0.770033\pi$
$401$	4.99613	−	12.7299i	0.249495	−	0.635702i	0.999674	+	0.0255324i	$0.00812811\pi$
$402$	0.940825	−	12.5544i	0.0469241	−	0.626158i
$403$	−2.57956	−	6.57260i	−0.128497	−	0.327405i
$404$	14.0036	−	4.31953i	0.696704	−	0.214905i
$405$	−1.57845	+	1.97931i	−0.0784337	+	0.0983528i
$406$	−2.08332	+	2.38251i	−0.103393	+	0.118242i
$407$	−10.0389	−	12.5884i	−0.497612	−	0.623986i
$408$	−1.70387	−	1.16168i	−0.0843542	−	0.0575117i
$409$	6.64136	+	6.16228i	0.328394	+	0.304705i	0.827087	−	0.562073i	$-0.189996\pi$
$409$	6.64136	+	6.16228i	0.328394	+	0.304705i	−0.498693	+	0.866778i	$0.666187\pi$
$410$	−1.46829	+	2.54315i	−0.0725136	+	0.125597i
$411$	2.64478	+	4.58090i	0.130458	+	0.225959i
$412$	2.73308	−	11.9744i	0.134649	−	0.589937i
$413$	−14.7439	+	33.0777i	−0.725501	+	1.62765i
$414$	0.784086	+	3.43531i	0.0385357	+	0.168836i
$415$	13.7509	−	12.7589i	0.675003	−	0.626311i
$416$	1.12603	−	0.169722i	0.0552082	−	0.00832130i
$417$	−14.7545	+	2.22388i	−0.722531	+	0.108904i
$418$	9.38316	−	8.70630i	0.458945	−	0.425839i
$419$	−0.520209	−	2.27919i	−0.0254139	−	0.111346i	0.960630	−	0.277831i	$-0.0896154\pi$
$419$	−0.520209	−	2.27919i	−0.0254139	−	0.111346i	−0.986044	+	0.166485i	$0.946758\pi$
$420$	−0.197541	−	6.69516i	−0.00963899	−	0.326690i
$421$	−2.25511	+	9.88028i	−0.109907	+	0.481535i	0.889777	+	0.456396i	$0.150860\pi$
$421$	−2.25511	+	9.88028i	−0.109907	+	0.481535i	−0.999684	+	0.0251392i	$0.991997\pi$
$422$	2.01182	+	3.48457i	0.0979337	+	0.169626i
$423$	−3.30777	+	5.72922i	−0.160829	+	0.278564i
$424$	3.56626	+	3.30901i	0.173193	+	0.160700i
$425$	−2.40105	−	1.63701i	−0.116468	−	0.0794066i
$426$	−9.36601	−	11.7446i	−0.453784	−	0.569028i
$427$	9.56097	+	0.433441i	0.462688	+	0.0209757i
$428$	−5.85749	+	7.34506i	−0.283132	+	0.355037i
$429$	2.48375	−	0.766135i	0.119917	−	0.0369894i
$430$	3.90465	+	9.94889i	0.188299	+	0.479778i
$431$	2.44382	−	32.6105i	0.117715	−	1.57079i	−0.555607	−	0.831445i	$-0.687514\pi$
$431$	2.44382	−	32.6105i	0.117715	−	1.57079i	0.673322	−	0.739349i	$-0.264867\pi$
$432$	0.365341	−	0.930874i	0.0175775	−	0.0447867i
$433$	6.02466	+	2.90132i	0.289526	+	0.139429i	0.573010	−	0.819549i	$-0.305776\pi$
$433$	6.02466	+	2.90132i	0.289526	+	0.139429i	−0.283483	+	0.958977i	$0.591490\pi$
$434$	13.9588	−	8.61775i	0.670042	−	0.413665i
$435$	−2.72848	+	1.31397i	−0.130821	+	0.0630000i
$436$	−0.329101	−	4.39155i	−0.0157611	−	0.210317i
$437$	−18.8823	−	5.82442i	−0.903264	−	0.278620i
$438$	5.12811	−	3.49629i	0.245031	−	0.167059i
$439$	10.2117	+	1.53917i	0.487380	+	0.0734607i	0.388135	−	0.921602i	$-0.373119\pi$
$439$	10.2117	+	1.53917i	0.487380	+	0.0734607i	0.0992444	+	0.995063i	$0.468357\pi$
$440$	5.77852			0.275480
$441$	6.11674	−	3.40374i	0.291273	−	0.162083i
$442$	2.34833			0.111699
$443$	20.3189	+	3.06258i	0.965380	+	0.145508i	0.612769	−	0.790262i	$-0.290056\pi$
$443$	20.3189	+	3.06258i	0.965380	+	0.145508i	0.352611	+	0.935770i	$0.385294\pi$
$444$	5.82839	−	3.97373i	0.276603	−	0.188585i
$445$	28.7604	+	8.87141i	1.36337	+	0.420545i
$446$	1.98309	+	26.4625i	0.0939021	+	1.25304i
$447$	8.74718	−	4.21242i	0.413728	−	0.199241i
$448$	0.854072	+	2.50411i	0.0403511	+	0.118308i
$449$	−18.4176	−	8.86944i	−0.869179	−	0.418575i	−0.0545185	−	0.998513i	$-0.517362\pi$
$449$	−18.4176	−	8.86944i	−0.869179	−	0.418575i	−0.814660	+	0.579938i	$0.803077\pi$
$450$	0.514830	−	1.31176i	0.0242693	−	0.0618372i
$451$	0.197857	−	2.64022i	0.00931672	−	0.124323i
$452$	−0.560384	−	1.42783i	−0.0263582	−	0.0671597i
$453$	20.0405	−	6.18167i	0.941584	−	0.290440i
$454$	−2.27947	+	2.85836i	−0.106981	+	0.134149i
$455$	4.48068	+	6.17262i	0.210058	+	0.289377i
$456$	3.49646	+	4.38442i	0.163737	+	0.205319i
$457$	−29.7773	−	20.3018i	−1.39292	−	0.949678i	−0.999541	−	0.0303021i	$-0.990353\pi$
$457$	−29.7773	−	20.3018i	−1.39292	−	0.949678i	−0.393381	−	0.919376i	$-0.628695\pi$
$458$	1.58234	+	1.46819i	0.0739378	+	0.0686042i
$459$	1.03110	−	1.78592i	0.0481277	−	0.0833595i
$460$	−4.46030	−	7.72546i	−0.207962	−	0.360202i
$461$	−1.70480	+	7.46923i	−0.0794006	+	0.347877i	−0.998986	−	0.0450124i	$-0.985667\pi$
$461$	−1.70480	+	7.46923i	−0.0794006	+	0.347877i	0.919586	+	0.392889i	$0.128524\pi$
$462$	2.77955	+	5.36130i	0.129316	+	0.249430i
$463$	−4.26515	−	18.6868i	−0.198218	−	0.868450i	−0.971997	−	0.234994i	$-0.924493\pi$
$463$	−4.26515	−	18.6868i	−0.198218	−	0.868450i	0.773779	−	0.633456i	$-0.218364\pi$
$464$	0.876891	−	0.813636i	0.0407086	−	0.0377721i
$465$	15.5218	−	2.33953i	0.719805	−	0.108493i
$466$	6.56102	−	0.988915i	0.303933	−	0.0458106i
$467$	10.1725	−	9.43872i	0.470728	−	0.436772i	−0.408796	−	0.912626i	$-0.634051\pi$
$467$	10.1725	−	9.43872i	0.470728	−	0.436772i	0.879524	+	0.475854i	$0.157861\pi$
$468$	0.253396	+	1.11020i	0.0117132	+	0.0513190i
$469$	−25.4182	+	21.5269i	−1.17371	+	0.994018i
$470$	3.72681	−	16.3282i	0.171905	−	0.753164i
$471$	6.73640	+	11.6678i	0.310397	+	0.537623i
$472$	6.84397	−	11.8541i	0.315019	−	0.545629i
$473$	−7.06371	−	6.55417i	−0.324790	−	0.301361i
$474$	−12.1726	−	8.29917i	−0.559108	−	0.381193i
$475$	4.92712	+	6.17841i	0.226072	+	0.283485i
$476$	0.971946	+	5.36880i	0.0445490	+	0.246079i
$477$	−3.03325	+	3.80357i	−0.138883	+	0.174154i
$478$	19.1827	−	5.91708i	0.877397	−	0.270641i
$479$	1.14237	+	2.91070i	0.0521961	+	0.132993i	0.954594	−	0.297911i	$-0.0962899\pi$
$479$	1.14237	+	2.91070i	0.0521961	+	0.132993i	−0.902398	+	0.430904i	$0.858195\pi$
$480$	−0.189189	+	2.52456i	−0.00863527	+	0.115230i
$481$	−2.93474	+	7.47760i	−0.133813	+	0.340949i
$482$	21.2724	+	10.2442i	0.968930	+	0.466612i
$483$	5.02221	−	7.85431i	0.228518	−	0.357384i
$484$	5.21668	−	2.51222i	0.237122	−	0.114192i
$485$	−0.299358	−	3.99465i	−0.0135931	−	0.181388i
$486$	0.955573	+	0.294755i	0.0433457	+	0.0133704i
$487$	−3.87262	+	2.64031i	−0.175485	+	0.119644i	−0.647877	−	0.761745i	$-0.724343\pi$
$487$	−3.87262	+	2.64031i	−0.175485	+	0.119644i	0.472392	+	0.881389i	$0.343391\pi$
$488$	−3.57701	−	0.539148i	−0.161924	−	0.0244061i
$489$	−21.0525			−0.952027
$490$	−12.2575	+	12.7986i	−0.553736	+	0.578181i
$491$	20.8358			0.940305			0.470153	−	0.882585i	$-0.344199\pi$
$491$	20.8358			0.940305			0.470153	+	0.882585i	$0.344199\pi$
$492$	1.14700	+	0.172882i	0.0517106	+	0.00779412i
$493$	2.03820	−	1.38962i	0.0917960	−	0.0625855i
$494$	−6.10226	−	1.88230i	−0.274554	−	0.0846886i
$495$	0.431829	+	5.76236i	0.0194093	+	0.258999i
$496$	−5.58635	+	2.69024i	−0.250834	+	0.120795i
$497$	−4.76194	+	39.4579i	−0.213602	+	1.76993i
$498$	−6.67581	−	3.21490i	−0.299150	−	0.144063i
$499$	−3.97116	+	10.1183i	−0.177773	+	0.452959i	−0.991789	−	0.127884i	$-0.959182\pi$
$499$	−3.97116	+	10.1183i	−0.177773	+	0.452959i	0.814016	+	0.580843i	$0.197277\pi$
$500$	0.679346	−	9.06524i	0.0303813	−	0.405410i
$501$	3.57023	+	9.09681i	0.159506	+	0.406415i
$502$	20.1849	−	6.22623i	0.900898	−	0.277890i
$503$	10.9770	−	13.7647i	0.489440	−	0.613738i	−0.474371	−	0.880325i	$-0.657324\pi$
$503$	10.9770	−	13.7647i	0.489440	−	0.613738i	0.963811	+	0.266587i	$0.0858959\pi$
$504$	−2.43328	+	1.03882i	−0.108387	+	0.0462725i
$505$	−23.1316	−	29.0061i	−1.02934	−	1.29076i
$506$	6.64529	+	4.53068i	0.295419	+	0.201413i
$507$	8.57909	+	7.96023i	0.381011	+	0.353526i
$508$	8.27806	−	14.3380i	0.367280	−	0.636147i
$509$	−10.6218	−	18.3976i	−0.470804	−	0.815457i	0.528638	−	0.848847i	$-0.322703\pi$
$509$	−10.6218	−	18.3976i	−0.470804	−	0.815457i	−0.999442	+	0.0333902i	$0.989370\pi$
$510$	−1.16172	+	5.08985i	−0.0514420	+	0.225382i
$511$	−16.1101	−	3.18029i	−0.712671	−	0.140688i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	−4.11087	+	3.81433i	−0.181499	+	0.168407i
$514$	0.141769	−	0.0213682i	0.00625315	−	0.000942511i
$515$	−30.7471	+	4.63439i	−1.35488	+	0.204215i
$516$	3.09469	−	2.87145i	0.136236	−	0.126409i
$517$	3.36009	+	14.7215i	0.147777	+	0.647452i
$518$	−18.3101	−	3.61458i	−0.804499	−	0.158815i
$519$	4.89751	−	21.4574i	0.214977	−	0.941876i
$520$	−1.44145	−	2.49666i	−0.0632118	−	0.109486i
$521$	−12.2754	+	21.2616i	−0.537795	+	0.931488i	0.461228	+	0.887282i	$0.347409\pi$
$521$	−12.2754	+	21.2616i	−0.537795	+	0.931488i	−0.999022	+	0.0442061i	$0.985924\pi$
$522$	0.876891	+	0.813636i	0.0383805	+	0.0356119i
$523$	−20.0262	−	13.6536i	−0.875684	−	0.597031i	0.0398798	−	0.999204i	$-0.487303\pi$
$523$	−20.0262	−	13.6536i	−0.875684	−	0.597031i	−0.915564	+	0.402173i	$0.868255\pi$
$524$	−9.47911	−	11.8864i	−0.414097	−	0.519261i
$525$	−3.42892	+	1.46387i	−0.149650	+	0.0638887i
$526$	−7.29438	+	9.14686i	−0.318050	+	0.398822i
$527$	−12.2184	+	3.76886i	−0.532240	+	0.164174i
$528$	−0.833900	−	2.12474i	−0.0362908	−	0.0924676i
$529$	−0.790935	+	10.5543i	−0.0343885	+	0.458882i
$530$	4.49964	−	11.4649i	0.195452	−	0.498004i
$531$	12.3324	+	5.93897i	0.535181	+	0.257729i
$532$	1.77770	−	14.7302i	0.0770730	−	0.638634i
$533$	−1.19009	+	0.573115i	−0.0515484	+	0.0248244i
$534$	−0.888435	−	11.8553i	−0.0384463	−	0.513031i
$535$	22.7272	+	7.01043i	0.982585	+	0.303087i
$536$	10.4020	−	7.09199i	0.449300	−	0.306328i
$537$	10.7663	+	1.62276i	0.464602	+	0.0700275i
$538$	−20.1098			−0.866995
$539$	4.95024	−	15.1915i	0.213222	−	0.654344i
$540$	−2.53163			−0.108944
$541$	2.18659	+	0.329576i	0.0940090	+	0.0141696i	0.195878	−	0.980628i	$-0.437244\pi$
$541$	2.18659	+	0.329576i	0.0940090	+	0.0141696i	−0.101869	+	0.994798i	$0.532482\pi$
$542$	−14.1183	+	9.62566i	−0.606431	+	0.413458i
$543$	1.64260	+	0.506676i	0.0704909	+	0.0217436i
$544$	−0.154108	−	2.05643i	−0.00660735	−	0.0881689i
$545$	−10.0449	+	4.83736i	−0.430276	+	0.207210i
$546$	1.62304	−	2.53830i	0.0694599	−	0.108629i
$547$	16.4135	+	7.90430i	0.701789	+	0.337964i	0.750519	−	0.660848i	$-0.229803\pi$
$547$	16.4135	+	7.90430i	0.701789	+	0.337964i	−0.0487308	+	0.998812i	$0.515518\pi$
$548$	−1.93250	+	4.92392i	−0.0825521	+	0.210339i
$549$	0.270330	−	3.60730i	0.0115374	−	0.153956i
$550$	−1.17511	−	2.99414i	−0.0501069	−	0.127670i
$551$	−6.41022	+	1.97729i	−0.273085	+	0.0842355i
$552$	−2.19696	+	2.75490i	−0.0935088	+	0.117256i
$553$	6.94369	+	38.3553i	0.295276	+	1.63103i
$554$	−14.1114	−	17.6951i	−0.599534	−	0.751792i
$555$	−14.7554	−	10.0600i	−0.626330	−	0.427025i
$556$	−10.9380	−	10.1490i	−0.463874	−	0.430412i
$557$	13.4544	−	23.3037i	0.570082	−	0.987410i	−0.426475	−	0.904499i	$-0.640245\pi$
$557$	13.4544	−	23.3037i	0.570082	−	0.987410i	0.996557	−	0.0829111i	$-0.0264218\pi$
$558$	−3.10019	−	5.36968i	−0.131241	−	0.227317i
$559$	−1.06975	+	4.68688i	−0.0452456	+	0.198234i
$560$	5.11132	−	4.32881i	0.215993	−	0.182926i
$561$	−1.04741	−	4.58901i	−0.0442218	−	0.193748i
$562$	6.12502	−	5.68319i	0.258368	−	0.239731i
$563$	20.0418	−	3.02081i	0.844660	−	0.127312i	0.287565	−	0.957761i	$-0.407154\pi$
$563$	20.0418	−	3.02081i	0.844660	−	0.127312i	0.557095	+	0.830449i	$0.311916\pi$
$564$	−6.54164	+	0.985994i	−0.275453	+	0.0415178i
$565$	−2.84658	+	2.64124i	−0.119756	+	0.111118i
$566$	0.378825	+	1.65974i	0.0159232	+	0.0697640i
$567$	−1.21775	−	2.34885i	−0.0511407	−	0.0986423i
$568$	3.34269	−	14.6453i	0.140256	−	0.614502i
$569$	−16.7594	−	29.0282i	−0.702591	−	1.21692i	−0.967554	−	0.252665i	$-0.918693\pi$
$569$	−16.7594	−	29.0282i	−0.702591	−	1.21692i	0.264962	−	0.964259i	$-0.414640\pi$
$570$	7.09855	−	12.2951i	0.297326	−	0.514983i
$571$	3.06021	+	2.83946i	0.128066	+	0.118828i	0.741606	−	0.670836i	$-0.234065\pi$
$571$	3.06021	+	2.83946i	0.128066	+	0.118828i	−0.613540	+	0.789664i	$0.710255\pi$
$572$	2.14758	+	1.46420i	0.0897949	+	0.0612211i
$573$	6.67792	+	8.37384i	0.278974	+	0.349822i
$574$	−1.80283	−	2.48359i	−0.0752487	−	0.103663i
$575$	−3.09590	+	3.88214i	−0.129108	+	0.161896i
$576$	0.955573	−	0.294755i	0.0398155	−	0.0122815i
$577$	11.0081	+	28.0482i	0.458273	+	1.16766i	0.954166	+	0.299277i	$0.0967454\pi$
$577$	11.0081	+	28.0482i	0.458273	+	1.16766i	−0.495894	+	0.868383i	$0.665159\pi$
$578$	−0.952609	+	12.7117i	−0.0396233	+	0.528736i
$579$	7.77242	−	19.8038i	0.323011	−	0.823018i
$580$	−2.72848	−	1.31397i	−0.113294	−	0.0545596i
$581$	6.32832	+	18.5544i	0.262543	+	0.769767i
$582$	−1.42562	+	0.686542i	−0.0590938	+	0.0284581i
$583$	0.829831	+	11.0733i	0.0343681	+	0.458610i
$584$	5.93083	+	1.82942i	0.245420	+	0.0757019i
$585$	2.38196	−	1.62400i	0.0984821	−	0.0671439i
$586$	16.7503	+	2.52471i	0.691950	+	0.104295i
$587$	14.1449			0.583823			0.291912	−	0.956445i	$-0.405709\pi$
$587$	14.1449			0.583823			0.291912	+	0.956445i	$0.405709\pi$
$588$	6.47488	+	2.66006i	0.267020	+	0.109699i
$589$	34.7710			1.43271
$590$	−34.2658	−	5.16474i	−1.41070	−	0.212629i
$591$	−10.5380	+	7.18466i	−0.433474	+	0.295538i
$592$	6.74073	+	2.07924i	0.277042	+	0.0854562i
$593$	0.867650	+	11.5780i	0.0356301	+	0.475451i	0.986268	+	0.165150i	$0.0528108\pi$
$593$	0.867650	+	11.5780i	0.0356301	+	0.475451i	−0.950638	+	0.310301i	$0.899570\pi$
$594$	2.05648	−	0.990351i	0.0843786	−	0.0406346i
$595$	11.7533	−	7.25618i	0.481840	−	0.297474i
$596$	8.74718	+	4.21242i	0.358299	+	0.172548i
$597$	−8.42246	+	21.4601i	−0.344708	+	0.878302i
$598$	0.299859	−	4.00134i	0.0122621	−	0.163627i
$599$	−1.88543	−	4.80399i	−0.0770364	−	0.196286i	0.887167	−	0.461448i	$-0.152670\pi$
$599$	−1.88543	−	4.80399i	−0.0770364	−	0.196286i	−0.964204	+	0.265162i	$0.914575\pi$
$600$	1.34657	−	0.415362i	0.0549735	−	0.0169571i
$601$	−14.4592	+	18.1312i	−0.589802	+	0.739588i	−0.983750	−	0.179544i	$-0.942538\pi$
$601$	−14.4592	+	18.1312i	−0.589802	+	0.739588i	0.393948	+	0.919133i	$0.371109\pi$
$602$	−11.1580	−	0.505841i	−0.454766	−	0.0206165i
$603$	7.84951	+	9.84297i	0.319657	+	0.400837i
$604$	17.3281	+	11.8141i	0.705069	+	0.480708i
$605$	−10.7453	−	9.97022i	−0.436860	−	0.405347i
$606$	−7.32733	+	12.6913i	−0.297652	+	0.515549i
$607$	−8.49966	−	14.7218i	−0.344991	−	0.597541i	0.640361	−	0.768074i	$-0.278785\pi$
$607$	−8.49966	−	14.7218i	−0.344991	−	0.597541i	−0.985352	+	0.170532i	$0.945451\pi$
$608$	−1.24787	+	5.46728i	−0.0506078	+	0.221727i
$609$	−0.0933396	−	3.16352i	−0.00378231	−	0.128192i
$610$	2.03784	+	8.92837i	0.0825098	+	0.361499i
$611$	5.52240	−	5.12404i	0.223413	−	0.207297i
$612$	2.03917	−	0.307355i	0.0824285	−	0.0124241i
$613$	3.63552	−	0.547966i	0.146837	−	0.0221321i	−0.0752123	−	0.997168i	$-0.523963\pi$
$613$	3.63552	−	0.547966i	0.146837	−	0.0221321i	0.222049	+	0.975035i	$0.428725\pi$
$614$	0.138958	−	0.128934i	0.00560787	−	0.00520335i
$615$	−0.653450	−	2.86295i	−0.0263496	−	0.115445i
$616$	−2.45862	+	5.51586i	−0.0990605	+	0.222240i
$617$	6.25119	−	27.3883i	0.251664	−	1.10261i	−0.678250	−	0.734831i	$-0.737261\pi$
$617$	6.25119	−	27.3883i	0.251664	−	1.10261i	0.929913	−	0.367779i	$-0.119882\pi$
$618$	6.14118	+	10.6368i	0.247034	+	0.427876i
$619$	6.73168	−	11.6596i	0.270569	−	0.468639i	−0.698439	−	0.715670i	$-0.746122\pi$
$619$	6.73168	−	11.6596i	0.270569	−	0.468639i	0.969008	+	0.247031i	$0.0794548\pi$
$620$	11.5068	+	10.6767i	0.462123	+	0.428788i
$621$	−2.91138	−	1.98494i	−0.116830	−	0.0796530i
$622$	16.7733	+	21.0331i	0.672549	+	0.843350i
$623$	−20.7050	+	23.6785i	−0.829528	+	0.948660i
$624$	−0.709999	+	0.890311i	−0.0284227	+	0.0356410i
$625$	−28.7246	+	8.86037i	−1.14898	+	0.354415i
$626$	−3.12101	−	7.95221i	−0.124741	−	0.317834i
$627$	−0.956555	+	12.7643i	−0.0382011	+	0.509759i
$628$	−4.92217	+	12.5415i	−0.196416	+	0.500460i
$629$	13.1064	+	6.31172i	0.522587	+	0.251665i
$630$	4.69867	+	4.77354i	0.187200	+	0.190182i
$631$	−26.9262	+	12.9670i	−1.07192	+	0.516208i	−0.884724	−	0.466116i	$-0.845653\pi$
$631$	−26.9262	+	12.9670i	−1.07192	+	0.516208i	−0.187192	+	0.982323i	$0.559939\pi$
$632$	−1.10097	−	14.6914i	−0.0437942	−	0.584393i
$633$	−3.84487	−	1.18599i	−0.152820	−	0.0471387i
$634$	−23.6088	+	16.0962i	−0.937626	+	0.639263i
$635$	−41.4459	−	6.24696i	−1.64473	−	0.247903i
$636$	−4.86495			−0.192908
$637$	−7.79846	+	1.65071i	−0.308986	+	0.0654036i
$638$	2.73040			0.108098
$639$	14.8541	+	2.23890i	0.587620	+	0.0885695i
$640$	−2.09173	+	1.42612i	−0.0826831	+	0.0563724i
$641$	33.7596	+	10.4135i	1.33342	+	0.411307i	0.877869	−	0.478900i	$-0.158965\pi$
$641$	33.7596	+	10.4135i	1.33342	+	0.411307i	0.455555	+	0.890207i	$0.349441\pi$
$642$	−0.702065	−	9.36841i	−0.0277083	−	0.369742i
$643$	6.00811	−	2.89336i	0.236937	−	0.114103i	−0.311648	−	0.950198i	$-0.600881\pi$
$643$	6.00811	−	2.89336i	0.236937	−	0.114103i	0.548585	+	0.836095i	$0.315167\pi$
$644$	9.27204	−	0.970561i	0.365370	−	0.0382455i
$645$	−9.62927	−	4.63721i	−0.379152	−	0.182590i
$646$	−4.22502	+	10.7652i	−0.166231	+	0.423550i
$647$	−2.28178	+	30.4482i	−0.0897060	+	1.19704i	0.752760	+	0.658295i	$0.228722\pi$
$647$	−2.28178	+	30.4482i	−0.0897060	+	1.19704i	−0.842466	+	0.538749i	$0.818897\pi$
$648$	0.365341	+	0.930874i	0.0143520	+	0.0365682i
$649$	29.8550	−	9.20905i	1.17191	−	0.361487i
$650$	−1.00051	+	1.25460i	−0.0392434	+	0.0492096i
$651$	−4.37094	+	15.8116i	−0.171311	+	0.619707i
$652$	−13.1260	−	16.4595i	−0.514055	−	0.644604i
$653$	−6.40260	−	4.36522i	−0.250553	−	0.170824i	0.431531	−	0.902098i	$-0.357974\pi$
$653$	−6.40260	−	4.36522i	−0.250553	−	0.170824i	−0.682084	+	0.731274i	$0.738926\pi$
$654$	3.22826	+	2.99539i	0.126235	+	0.117129i
$655$	−19.2446	+	33.3327i	−0.751950	+	1.30242i
$656$	0.579976	+	1.00455i	0.0226443	+	0.0392210i
$657$	−1.38109	+	6.05096i	−0.0538815	+	0.236070i
$658$	14.0003	+	10.5046i	0.545790	+	0.409514i
$659$	4.39490	+	19.2553i	0.171201	+	0.750081i	0.985506	+	0.169643i	$0.0542614\pi$
$659$	4.39490	+	19.2553i	0.171201	+	0.750081i	−0.814305	+	0.580438i	$0.802881\pi$
$660$	−4.23596	+	3.93039i	−0.164884	+	0.152990i
$661$	29.2223	−	4.40455i	1.13662	−	0.171317i	0.446339	−	0.894864i	$-0.352727\pi$
$661$	29.2223	−	4.40455i	1.13662	−	0.171317i	0.690276	+	0.723547i	$0.257489\pi$
$662$	16.4776	−	2.48360i	0.640419	−	0.0965277i
$663$	−1.72145	+	1.59727i	−0.0668555	+	0.0620329i
$664$	−1.64879	−	7.22381i	−0.0639854	−	0.280338i
$665$	−36.3578	+	9.43471i	−1.40990	+	0.365862i
$666$	−1.56969	+	6.87726i	−0.0608243	+	0.266489i
$667$	−2.10753	−	3.65035i	−0.0816038	−	0.141342i
$668$	−4.88617	+	8.46309i	−0.189051	+	0.327447i
$669$	−19.4528	−	18.0495i	−0.752088	−	0.697836i
$670$	−26.3342	−	17.9543i	−1.01738	−	0.693637i
$671$	−5.14806	−	6.45546i	−0.198739	−	0.249210i
$672$	−2.32931	−	1.25473i	−0.0898549	−	0.0484021i
$673$	−13.9747	+	17.5237i	−0.538683	+	0.675488i	−0.974458	−	0.224568i	$-0.927903\pi$
$673$	−13.9747	+	17.5237i	−0.538683	+	0.675488i	0.435775	+	0.900056i	$0.356474\pi$
$674$	16.1163	−	4.97121i	0.620776	−	0.191484i
$675$	0.514830	+	1.31176i	0.0198158	+	0.0504898i
$676$	−0.874585	+	11.6705i	−0.0336379	+	0.448866i
$677$	−10.5533	+	26.8895i	−0.405598	+	1.03345i	0.571490	+	0.820609i	$0.306366\pi$
$677$	−10.5533	+	26.8895i	−0.405598	+	1.03345i	−0.977088	+	0.212837i	$0.931730\pi$
$678$	1.38196	+	0.665519i	0.0530740	+	0.0255591i
$679$	3.94044	+	1.41387i	0.151220	+	0.0542595i
$680$	−4.70372	+	2.26519i	−0.180380	+	0.0868662i
$681$	−0.273212	−	3.64576i	−0.0104695	−	0.139706i
$682$	−13.5238	−	4.17153i	−0.517852	−	0.159736i
$683$	19.4009	−	13.2273i	0.742354	−	0.506128i	−0.132100	−	0.991236i	$-0.542172\pi$
$683$	19.4009	−	13.2273i	0.742354	−	0.506128i	0.874454	+	0.485108i	$0.161220\pi$
$684$	−5.54525	−	0.835811i	−0.212028	−	0.0319580i
$685$	13.3913			0.511653
$686$	−7.00157	−	17.1458i	−0.267321	−	0.654629i
$687$	−2.15856			−0.0823542
$688$	4.17450	+	0.629205i	0.159151	+	0.0239882i
$689$	4.57733	−	3.12077i	0.174383	−	0.118892i
$690$	8.52428	+	2.62939i	0.324514	+	0.100099i
$691$	1.87522	+	25.0230i	0.0713366	+	0.951920i	0.911954	+	0.410292i	$0.134573\pi$
$691$	1.87522	+	25.0230i	0.0713366	+	0.951920i	−0.840618	+	0.541629i	$0.817808\pi$
$692$	19.8296	−	9.54945i	0.753810	−	0.363016i
$693$	−5.68416	−	2.03954i	−0.215924	−	0.0774758i
$694$	19.2436	+	9.26721i	0.730476	+	0.351779i
$695$	−13.8007	+	35.1637i	−0.523491	+	1.33383i
$696$	−0.0893936	+	1.19287i	−0.00338845	+	0.0452158i
$697$	0.873916	+	2.22670i	0.0331019	+	0.0843424i
$698$	5.96746	−	1.84072i	0.225872	−	0.0696722i
$699$	−4.13694	+	5.18755i	−0.156473	+	0.196211i
$700$	−3.28240	−	1.76813i	−0.124063	−	0.0668289i
$701$	−4.02765	−	5.05051i	−0.152122	−	0.190755i	0.699931	−	0.714211i	$-0.253214\pi$
$701$	−4.02765	−	5.05051i	−0.152122	−	0.190755i	−0.852053	+	0.523455i	$0.824643\pi$
$702$	−0.940879	−	0.641481i	−0.0355112	−	0.0242111i
$703$	−28.9986	−	26.9067i	−1.09370	−	1.01481i
$704$	1.14126	−	1.97672i	0.0430130	−	0.0745006i
$705$	8.37406	+	14.5043i	0.315385	+	0.546263i
$706$	−5.95620	+	26.0958i	−0.224165	+	0.982130i
$707$	37.5296	−	9.73877i	1.41144	−	0.366264i
$708$	3.04585	+	13.3447i	0.114470	+	0.501526i
$709$	0.867595	−	0.805011i	0.0325832	−	0.0302328i	−0.663713	−	0.747987i	$-0.731020\pi$
$709$	0.867595	−	0.805011i	0.0325832	−	0.0302328i	0.696296	+	0.717754i	$0.254830\pi$
$710$	−37.6052	+	5.66807i	−1.41130	+	0.212719i
$711$	14.5681	−	2.19578i	0.546345	−	0.0823482i
$712$	8.71495	−	8.08629i	0.326606	−	0.303046i
$713$	4.86163	+	21.3002i	0.182069	+	0.797698i
$714$	−4.36420	−	3.27452i	−0.163326	−	0.122546i
$715$	1.46425	−	6.41531i	0.0547599	−	0.239919i
$716$	5.44398	+	9.42924i	0.203451	+	0.352387i
$717$	−10.0373	+	17.3851i	−0.374849	+	0.649258i
$718$	−12.6349	−	11.7235i	−0.471531	−	0.437516i
$719$	−14.3721	−	9.79875i	−0.535990	−	0.365432i	0.264869	−	0.964284i	$-0.414671\pi$
$719$	−14.3721	−	9.79875i	−0.535990	−	0.365432i	−0.800859	+	0.598852i	$0.795624\pi$
$720$	−1.57845	−	1.97931i	−0.0588253	−	0.0737646i
$721$	8.65841	−	31.3213i	0.322456	−	1.16647i
$722$	7.76140	−	9.73249i	0.288850	−	0.362206i
$723$	−22.5616	+	6.95934i	−0.839075	+	0.258820i
$724$	0.628011	+	1.60015i	0.0233399	+	0.0594690i
$725$	−0.125971	+	1.68097i	−0.00467845	+	0.0624296i
$726$	−2.11535	+	5.38983i	−0.0785081	+	0.200035i
$727$	−14.7863	−	7.12070i	−0.548393	−	0.264092i	0.139106	−	0.990278i	$-0.455577\pi$
$727$	−14.7863	−	7.12070i	−0.548393	−	0.264092i	−0.687499	+	0.726185i	$0.741291\pi$
$728$	2.99648	−	0.313659i	0.111057	−	0.0116250i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−1.17422	−	15.6688i	−0.0434597	−	0.579930i
$731$	8.31912	+	2.56611i	0.307694	+	0.0949110i
$732$	2.98885	−	2.03776i	0.110471	−	0.0753179i
$733$	0.865597	+	0.130468i	0.0319716	+	0.00481894i	0.165009	−	0.986292i	$-0.447235\pi$
$733$	0.865597	+	0.130468i	0.0319716	+	0.00481894i	−0.133037	+	0.991111i	$0.542473\pi$
$734$	0.476565			0.0175903
$735$	0.280111	−	17.7192i	0.0103321	−	0.653584i
$736$	−3.52365			−0.129883
$737$	28.4152	+	4.28290i	1.04669	+	0.157763i
$738$	−0.958398	+	0.653425i	−0.0352791	+	0.0240529i
$739$	−14.1681	−	4.37027i	−0.521181	−	0.160763i	0.0229929	−	0.999736i	$-0.492680\pi$
$739$	−14.1681	−	4.37027i	−0.521181	−	0.160763i	−0.544173	+	0.838973i	$0.683157\pi$
$740$	−1.33457	−	17.8085i	−0.0490596	−	0.654655i
$741$	5.75356	−	2.77077i	0.211362	−	0.101787i
$742$	9.02928	+	9.17314i	0.331475	+	0.336757i
$743$	14.3609	+	6.91585i	0.526851	+	0.253718i	0.678349	−	0.734740i	$-0.262696\pi$
$743$	14.3609	+	6.91585i	0.526851	+	0.253718i	−0.151499	+	0.988457i	$0.548410\pi$
$744$	2.26525	−	5.77177i	0.0830482	−	0.211603i
$745$	1.83677	−	24.5100i	0.0672941	−	0.897977i
$746$	9.20306	+	23.4490i	0.336948	+	0.858530i
$747$	7.08040	−	2.18401i	0.259058	−	0.0799089i
$748$	2.93478	−	3.68010i	0.107306	−	0.134558i
$749$	−16.3616	+	18.7114i	−0.597841	+	0.683700i
$750$	5.66793	+	7.10736i	0.206964	+	0.259524i
$751$	−17.3988	−	11.8623i	−0.634892	−	0.432862i	0.202637	−	0.979254i	$-0.435049\pi$
$751$	−17.3988	−	11.8623i	−0.634892	−	0.432862i	−0.837530	+	0.546391i	$0.816001\pi$
$752$	−4.84953	−	4.49971i	−0.176844	−	0.164087i
$753$	−10.5617	+	18.2934i	−0.384890	+	0.666648i
$754$	−0.681097	−	1.17970i	−0.0248041	−	0.0429620i
$755$	11.8145	−	51.7628i	0.429975	−	1.88384i
$756$	1.07715	−	2.41656i	0.0391755	−	0.0878894i
$757$	−8.18912	−	35.8789i	−0.297638	−	1.30404i	−0.873633	−	0.486586i	$-0.838242\pi$
$757$	−8.18912	−	35.8789i	−0.297638	−	1.30404i	0.575994	−	0.817454i	$-0.304615\pi$
$758$	20.2498	−	18.7891i	0.735507	−	0.682450i
$759$	−7.95299	+	1.19872i	−0.288675	+	0.0435108i
$760$	14.0385	−	2.11597i	0.509231	−	0.0767543i
$761$	−7.85470	+	7.28810i	−0.284733	+	0.264193i	−0.809589	−	0.586998i	$-0.800310\pi$
$761$	−7.85470	+	7.28810i	−0.284733	+	0.264193i	0.524856	+	0.851191i	$0.324119\pi$
$762$	3.68408	+	16.1410i	0.133460	+	0.584728i
$763$	−0.343629	−	11.6465i	−0.0124402	−	0.421630i
$764$	−2.38332	+	10.4420i	−0.0862255	+	0.377779i
$765$	−2.61037	−	4.52129i	−0.0943781	−	0.163468i
$766$	17.4933	−	30.2993i	0.632059	−	1.09476i
$767$	−11.4262	−	10.6019i	−0.412575	−	0.382814i
$768$	0.826239	+	0.563320i	0.0298143	+	0.0203271i
$769$	11.6518	+	14.6109i	0.420175	+	0.526883i	0.946198	−	0.323588i	$-0.104889\pi$
$769$	11.6518	+	14.6109i	0.420175	+	0.526883i	−0.526023	+	0.850470i	$0.676318\pi$
$770$	15.2728	+	0.692386i	0.550395	+	0.0249518i
$771$	−0.0893898	+	0.112091i	−0.00321930	+	0.00403687i
$772$	20.3293	−	6.27074i	0.731666	−	0.225689i
$773$	7.45575	+	18.9969i	0.268165	+	0.683272i	0.999998	+	0.00178913i	$0.000569498\pi$
$773$	7.45575	+	18.9969i	0.268165	+	0.683272i	−0.731834	+	0.681483i	$0.761335\pi$
$774$	−0.315485	+	4.20985i	−0.0113399	+	0.151320i
$775$	3.19214	−	8.13343i	0.114665	−	0.292162i
$776$	−1.42562	−	0.686542i	−0.0511768	−	0.0246454i
$777$	15.8808	−	9.80435i	0.569720	−	0.351729i
$778$	−20.8181	+	10.0255i	−0.746365	+	0.359431i
$779$	−0.486110	−	6.48669i	−0.0174167	−	0.232410i
$780$	2.75482	+	0.849750i	0.0986384	+	0.0304259i
$781$	28.3300	−	19.3151i	1.01373	−	0.691147i
$782$	−7.18532	−	1.08301i	−0.256946	−	0.0387284i
$783$	−1.19622			−0.0427494
$784$	1.95730	+	6.72079i	0.0699036	+	0.240028i
$785$	34.1082			1.21737
$786$	15.0335	+	2.26594i	0.536228	+	0.0808233i
$787$	−25.5679	+	17.4319i	−0.911399	+	0.621381i	−0.925594	−	0.378518i	$-0.876434\pi$
$787$	−25.5679	+	17.4319i	−0.911399	+	0.621381i	0.0141952	+	0.999899i	$0.495481\pi$
$788$	−12.1875	−	3.75935i	−0.434162	−	0.133921i
$789$	−0.874288	−	11.6666i	−0.0311255	−	0.415341i
$790$	−33.6039	+	16.1828i	−1.19557	+	0.575758i
$791$	−1.31003	−	3.84096i	−0.0465793	−	0.136569i
$792$	2.05648	+	0.990351i	0.0730740	+	0.0351906i
$793$	−1.50496	+	3.83458i	−0.0534428	+	0.136170i
$794$	1.71328	−	22.8621i	0.0608019	−	0.811345i
$795$	4.49964	+	11.4649i	0.159586	+	0.406618i
$796$	−22.0295	+	6.79519i	−0.780814	+	0.240849i
$797$	5.95895	−	7.47229i	0.211077	−	0.264682i	−0.665011	−	0.746834i	$-0.731573\pi$
$797$	5.95895	−	7.47229i	0.211077	−	0.264682i	0.876088	+	0.482152i	$0.160145\pi$
$798$	8.71592	+	12.0071i	0.308540	+	0.425048i
$799$	−8.50600	−	10.6662i	−0.300921	−	0.377343i
$800$	1.16432	+	0.793817i	0.0411648	+	0.0280657i
$801$	8.71495	+	8.08629i	0.307927	+	0.285715i
$802$	−6.83762	+	11.8431i	−0.241445	+	0.418195i
$803$	7.08333	+	12.2687i	0.249965	+	0.432953i
$804$	−2.80146	+	12.2740i	−0.0987998	+	0.432870i
$805$	−10.8631	−	20.9531i	−0.382873	−	0.738500i
$806$	1.57115	+	6.88365i	0.0553414	+	0.242466i
$807$	14.7415	−	13.6781i	0.518926	−	0.481493i
$808$	−14.4910	+	2.18416i	−0.509791	+	0.0768386i
$809$	14.6913	−	2.21435i	0.516517	−	0.0778524i	0.114389	−	0.993436i	$-0.463509\pi$
$809$	14.6913	−	2.21435i	0.516517	−	0.0778524i	0.402128	+	0.915584i	$0.368271\pi$
$810$	1.85582	−	1.72195i	0.0652069	−	0.0605031i
$811$	−10.4355	−	45.7207i	−0.366438	−	1.60547i	−0.736482	−	0.676457i	$-0.763515\pi$
$811$	−10.4355	−	45.7207i	−0.366438	−	1.60547i	0.370044	−	0.929014i	$-0.379343\pi$
$812$	2.41514	−	2.04540i	0.0847550	−	0.0717794i
$813$	3.80230	−	16.6590i	0.133352	−	0.584255i
$814$	8.05061	+	13.9441i	0.282174	+	0.488739i
$815$	−26.6486	+	46.1568i	−0.933461	+	1.61680i
$816$	1.51170	+	1.40265i	0.0529201	+	0.0491027i
$817$	−19.5608	−	13.3363i	−0.684346	−	0.466579i
$818$	−5.64874	−	7.08329i	−0.197503	−	0.247662i
$819$	0.536710	+	2.96466i	0.0187541	+	0.103594i
$820$	1.83093	−	2.29591i	0.0639387	−	0.0801766i
$821$	−34.5006	+	10.6420i	−1.20408	+	0.371410i	−0.830938	−	0.556364i	$-0.812196\pi$
$821$	−34.5006	+	10.6420i	−1.20408	+	0.371410i	−0.373142	+	0.927774i	$0.621720\pi$
$822$	−1.93250	−	4.92392i	−0.0674035	−	0.171741i
$823$	3.27331	−	43.6793i	0.114100	−	1.52256i	−0.587050	−	0.809551i	$-0.699711\pi$
$823$	3.27331	−	43.6793i	0.114100	−	1.52256i	0.701150	−	0.713014i	$-0.252670\pi$
$824$	−4.48725	+	11.4333i	−0.156321	+	0.398299i
$825$	2.89795	+	1.39558i	0.100894	+	0.0485878i
$826$	19.5092	−	30.5108i	0.678812	−	1.06161i
$827$	−37.0768	+	17.8552i	−1.28929	+	0.620887i	−0.947760	−	0.318985i	$-0.896658\pi$
$827$	−37.0768	+	17.8552i	−1.28929	+	0.620887i	−0.341526	+	0.939872i	$0.610944\pi$
$828$	−0.263323	−	3.51380i	−0.00915110	−	0.122113i
$829$	28.4308	+	8.76974i	0.987442	+	0.304586i	0.746085	−	0.665851i	$-0.231931\pi$
$829$	28.4308	+	8.76974i	0.987442	+	0.304586i	0.241357	+	0.970436i	$0.422407\pi$
$830$	−15.4989	+	10.5670i	−0.537974	+	0.366785i
$831$	22.3801	+	3.37325i	0.776356	+	0.117017i
$832$	−1.13875			−0.0394791
$833$	1.92559	+	14.3064i	0.0667179	+	0.495687i
$834$	14.9212			0.516677
$835$	24.4637	+	3.68730i	0.846600	+	0.127604i
$836$	−10.5760	+	7.21057i	−0.365777	+	0.249383i
$837$	5.92491	+	1.82759i	0.204795	+	0.0631709i
$838$	0.174704	+	2.33126i	0.00603505	+	0.0805321i
$839$	5.22787	−	2.51761i	0.180486	−	0.0869175i	−0.341459	−	0.939897i	$-0.610921\pi$
$839$	5.22787	−	2.51761i	0.180486	−	0.0869175i	0.521945	+	0.852979i	$0.325207\pi$
$840$	−0.802528	+	6.64983i	−0.0276898	+	0.229441i
$841$	24.8389	+	11.9618i	0.856513	+	0.412475i
$842$	3.70250	−	9.43382i	0.127597	−	0.325111i
$843$	−0.624408	+	8.33214i	−0.0215057	+	0.286974i
$844$	−1.47000	−	3.74549i	−0.0505994	−	0.128925i
$845$	28.3120	−	8.73311i	0.973964	−	0.300428i
$846$	4.12472	−	5.17223i	0.141811	−	0.177825i
$847$	14.0889	−	6.01483i	0.484100	−	0.206672i
$848$	−3.03325	−	3.80357i	−0.104162	−	0.130615i
$849$	−1.40661	−	0.959009i	−0.0482746	−	0.0329131i
$850$	2.13025	+	1.97658i	0.0730670	+	0.0677963i
$851$	12.4281	−	21.5262i	0.426031	−	0.737907i
$852$	7.51095	+	13.0094i	0.257321	+	0.445693i
$853$	7.08511	−	31.0419i	0.242590	−	1.06285i	−0.696060	−	0.717983i	$-0.745065\pi$
$853$	7.08511	−	31.0419i	0.242590	−	1.06285i	0.938650	−	0.344871i	$-0.112077\pi$
$854$	−9.38958	−	1.85359i	−0.321305	−	0.0634285i
$855$	3.15915	+	13.8412i	0.108041	+	0.473358i
$856$	6.88679	−	6.39000i	0.235386	−	0.218406i
$857$	8.96912	−	1.35188i	0.306379	−	0.0461792i	0.00594676	−	0.999982i	$-0.498107\pi$
$857$	8.96912	−	1.35188i	0.306379	−	0.0461792i	0.300433	+	0.953803i	$0.402869\pi$
$858$	−2.57019	+	0.387395i	−0.0877450	+	0.0132254i
$859$	−21.5802	+	20.0235i	−0.736306	+	0.683192i	−0.956326	−	0.292304i	$-0.905578\pi$
$859$	−21.5802	+	20.0235i	−0.736306	+	0.683192i	0.220020	+	0.975495i	$0.429388\pi$
$860$	−2.37823	−	10.4197i	−0.0810971	−	0.355310i
$861$	3.01084	+	0.594367i	0.102609	+	0.0202560i
$862$	−7.27687	+	31.8821i	−0.247851	+	1.08591i
$863$	24.7419	+	42.8542i	0.842225	+	1.45878i	0.888010	+	0.459824i	$0.152088\pi$
$863$	24.7419	+	42.8542i	0.842225	+	1.45878i	−0.0457854	+	0.998951i	$0.514579\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−40.8452	−	37.8988i	−1.38878	−	1.28860i
$866$	−5.52495	−	3.76684i	−0.187745	−	0.128003i
$867$	−7.94783	−	9.96626i	−0.269922	−	0.338472i
$868$	−15.0873	+	6.44105i	−0.512095	+	0.218624i
$869$	20.9664	−	26.2911i	0.711237	−	0.891863i
$870$	2.89385	−	0.892634i	0.0981106	−	0.0302631i
$871$	−5.23769	−	13.3454i	−0.177472	−	0.452192i
$872$	−0.329101	+	4.39155i	−0.0111448	+	0.148717i
$873$	0.578086	−	1.47294i	0.0195652	−	0.0498514i
$874$	17.8033	+	8.57364i	0.602207	+	0.290008i
$875$	2.88174	−	23.8784i	0.0974205	−	0.807236i
$876$	−5.59193	+	2.69293i	−0.188934	+	0.0909857i
$877$	1.19528	+	15.9499i	0.0403617	+	0.538589i	0.980335	+	0.197341i	$0.0632307\pi$
$877$	1.19528	+	15.9499i	0.0403617	+	0.538589i	−0.939973	+	0.341248i	$0.889150\pi$
$878$	−9.86828	−	3.04396i	−0.333038	−	0.102729i
$879$	−13.9961	+	9.54238i	−0.472077	+	0.321857i
$880$	−5.71398	−	0.861244i	−0.192618	−	0.0290325i
$881$	−43.2484			−1.45708			−0.728538	−	0.685005i	$-0.759800\pi$
$881$	−43.2484			−1.45708			−0.728538	+	0.685005i	$0.759800\pi$
$882$	−6.55573	+	2.45407i	−0.220743	+	0.0826329i
$883$	43.8038			1.47412			0.737058	−	0.675830i	$-0.236215\pi$
$883$	43.8038			1.47412			0.737058	+	0.675830i	$0.236215\pi$
$884$	−2.32210	−	0.350001i	−0.0781008	−	0.0117718i
$885$	28.6315	−	19.5206i	0.962438	−	0.656179i
$886$	−19.6355	−	6.05675i	−0.659668	−	0.203480i
$887$	1.37608	+	18.3624i	0.0462041	+	0.616551i	0.971459	+	0.237206i	$0.0762316\pi$
$887$	1.37608	+	18.3624i	0.0462041	+	0.616551i	−0.925255	+	0.379345i	$0.876149\pi$
$888$	−6.35555	+	3.06067i	−0.213278	+	0.102709i
$889$	23.5972	−	36.9040i	0.791425	−	1.23772i
$890$	−27.1169	−	13.0588i	−0.908962	−	0.437733i
$891$	−0.833900	+	2.12474i	−0.0279367	+	0.0711816i
$892$	1.98309	−	26.4625i	0.0663988	−	0.886030i
$893$	13.5538	+	34.5346i	0.453562	+	1.15566i
$894$	−9.27731	+	2.86167i	−0.310280	+	0.0957086i
$895$	17.1861	−	21.5506i	0.574467	−	0.720359i
$896$	−0.471315	−	2.60343i	−0.0157455	−	0.0869746i
$897$	2.50179	+	3.13714i	0.0835323	+	0.104746i
$898$	16.8899	+	11.5154i	0.563625	+	0.384273i
$899$	5.43705	+	5.04485i	0.181336	+	0.168255i
$900$	−0.704588	+	1.22038i	−0.0234863	+	0.0406794i
$901$	−5.01626	−	8.68841i	−0.167116	−	0.289453i
$902$	−0.589151	+	2.58124i	−0.0196166	+	0.0859459i
$903$	8.52344	−	7.21855i	0.283642	−	0.240218i
$904$	0.341317	+	1.49541i	0.0113520	+	0.0497365i
$905$	3.19010	−	2.95998i	0.106043	−	0.0983932i
$906$	−20.7380	+	3.12575i	−0.688973	+	0.103846i
$907$	−49.7215	+	7.49432i	−1.65098	+	0.248845i	−0.907541	−	0.419963i	$-0.862043\pi$
$907$	−49.7215	+	7.49432i	−1.65098	+	0.248845i	−0.743435	+	0.668808i	$0.766805\pi$
$908$	2.68002	−	2.48670i	0.0889396	−	0.0825239i
$909$	−3.26097	−	14.2872i	−0.108159	−	0.473877i
$910$	−3.51065	−	6.77149i	−0.116377	−	0.224473i
$911$	7.32450	−	32.0907i	0.242672	−	1.06321i	−0.695903	−	0.718136i	$-0.744996\pi$
$911$	7.32450	−	32.0907i	0.242672	−	1.06321i	0.938574	−	0.345077i	$-0.112147\pi$
$912$	−2.80394	−	4.85657i	−0.0928477	−	0.160817i
$913$	8.45629	−	14.6467i	0.279862	−	0.484736i
$914$	26.4188	+	24.5131i	0.873858	+	0.810822i
$915$	−7.56668	−	5.15887i	−0.250147	−	0.170547i
$916$	−1.34584	−	1.68763i	−0.0444678	−	0.0557609i
$917$	−23.6294	−	32.5521i	−0.780312	−	1.07496i
$918$	−1.28576	+	1.61229i	−0.0424365	+	0.0532136i
$919$	9.74984	−	3.00743i	0.321618	−	0.0992059i	−0.129743	−	0.991548i	$-0.541415\pi$
$919$	9.74984	−	3.00743i	0.321618	−	0.0992059i	0.451360	+	0.892342i	$0.350939\pi$
$920$	3.25906	+	8.30395i	0.107448	+	0.273773i
$921$	−0.0141659	+	0.189030i	−0.000466781	+	0.00622876i
$922$	2.79899	−	7.13172i	0.0921799	−	0.234871i
$923$	−15.4122	−	7.42210i	−0.507297	−	0.244301i
$924$	−1.94944	−	5.71569i	−0.0641319	−	0.188032i
$925$	−8.95608	+	4.31302i	−0.294474	+	0.141811i
$926$	1.43238	+	19.1138i	0.0470710	+	0.628118i
$927$	−11.7367	−	3.62029i	−0.385483	−	0.118906i
$928$	−0.988363	+	0.673854i	−0.0324446	+	0.0221203i
$929$	17.4591	+	2.63154i	0.572815	+	0.0863379i	0.429061	−	0.903276i	$-0.358845\pi$
$929$	17.4591	+	2.63154i	0.572815	+	0.0863379i	0.143754	+	0.989613i	$0.454083\pi$
$930$	−15.6971			−0.514728
$931$	6.46350	−	38.7194i	0.211833	−	1.26898i
$932$	−6.63513			−0.217341
$933$	−26.6018	−	4.00958i	−0.870905	−	0.131268i
$934$	−11.4657	+	7.81716i	−0.375168	+	0.255785i
$935$	−11.3871	−	3.51244i	−0.372397	−	0.114869i
$936$	−0.0850989	−	1.13557i	−0.00278154	−	0.0371171i
$937$	26.5972	−	12.8085i	0.868893	−	0.418437i	0.0543377	−	0.998523i	$-0.482695\pi$
$937$	26.5972	−	12.8085i	0.868893	−	0.418437i	0.814555	+	0.580086i	$0.196981\pi$
$938$	28.3428	−	17.4980i	0.925424	−	0.571331i
$939$	7.69674	+	3.70655i	0.251174	+	0.120959i
$940$	−6.11877	+	15.5904i	−0.199572	+	0.508502i
$941$	2.34863	−	31.3403i	0.0765631	−	1.02166i	−0.818145	−	0.575012i	$-0.804997\pi$
$941$	2.34863	−	31.3403i	0.0765631	−	1.02166i	0.894708	−	0.446652i	$-0.147384\pi$
$942$	−4.92217	−	12.5415i	−0.160373	−	0.408623i
$943$	3.90568	−	1.20474i	0.127187	−	0.0392318i
$944$	−8.53429	+	10.7017i	−0.277767	+	0.348309i
$945$	−6.69120	−	0.303342i	−0.217665	−	0.00986771i
$946$	6.00797	+	7.53375i	0.195336	+	0.244943i
$947$	7.02035	+	4.78639i	0.228131	+	0.155537i	0.671991	−	0.740559i	$-0.265439\pi$
$947$	7.02035	+	4.78639i	0.228131	+	0.155537i	−0.443861	+	0.896096i	$0.646392\pi$
$948$	10.7998	+	10.0207i	0.350760	+	0.325458i
$949$	3.53387	−	6.12084i	0.114714	−	0.198691i
$950$	−3.95124	−	6.84375i	−0.128195	−	0.222041i
$951$	6.35828	−	27.8574i	0.206181	−	0.903339i
$952$	−0.160911	−	5.45370i	−0.00521516	−	0.176755i
$953$	7.20489	+	31.5667i	0.233389	+	1.02255i	0.946806	+	0.321805i	$0.104290\pi$
$953$	7.20489	+	31.5667i	0.233389	+	1.02255i	−0.713417	+	0.700740i	$0.752853\pi$
$954$	3.56626	−	3.30901i	0.115462	−	0.107133i
$955$	26.8123	−	4.04131i	0.867627	−	0.130774i
$956$	−19.8504	+	2.99196i	−0.642006	+	0.0967669i
$957$	−2.00153	+	1.85714i	−0.0647001	+	0.0600329i
$958$	−0.695789	−	3.04845i	−0.0224799	−	0.0984910i
$959$	−5.69764	+	12.7825i	−0.183986	+	0.412770i
$960$	0.563342	−	2.46816i	0.0181818	−	0.0796596i
$961$	−3.72234	−	6.44727i	−0.120075	−	0.207977i
$962$	4.01644	−	6.95668i	0.129495	−	0.224292i
$963$	6.88679	+	6.39000i	0.221924	+	0.205915i
$964$	−19.5080	−	13.3003i	−0.628309	−	0.428374i
$965$	−33.5806	−	42.1087i	−1.08100	−	1.35553i
$966$	−6.13674	+	7.01806i	−0.197446	+	0.225802i
$967$	19.3779	−	24.2991i	0.623152	−	0.781407i	−0.365633	−	0.930759i	$-0.619147\pi$
$967$	19.3779	−	24.2991i	0.623152	−	0.781407i	0.988784	+	0.149352i	$0.0477187\pi$
$968$	−5.53284	+	1.70666i	−0.177832	+	0.0548540i
$969$	−4.22502	−	10.7652i	−0.135727	−	0.345827i
$970$	−0.299358	+	3.99465i	−0.00961180	+	0.128261i
$971$	−0.467802	+	1.19194i	−0.0150125	+	0.0382512i	−0.938183	−	0.346138i	$-0.887493\pi$
$971$	−0.467802	+	1.19194i	−0.0150125	+	0.0382512i	0.923171	+	0.384390i	$0.125588\pi$
$972$	−0.900969	−	0.433884i	−0.0288986	−	0.0139168i
$973$	−27.6934	−	28.1347i	−0.887811	−	0.901956i
$974$	4.22288	−	2.03363i	0.135310	−	0.0651618i
$975$	−0.119919	−	1.60021i	−0.00384049	−	0.0512478i
$976$	3.45671	+	1.06625i	0.110646	+	0.0341299i
$977$	−28.3961	+	19.3602i	−0.908473	+	0.619386i	−0.924789	−	0.380480i	$-0.875759\pi$
$977$	−28.3961	+	19.3602i	−0.908473	+	0.619386i	0.0163159	+	0.999867i	$0.494806\pi$
$978$	20.8174	+	3.13771i	0.665666	+	0.100333i
$979$	27.1360			0.867270
$980$	14.0281	−	10.8288i	0.448111	−	0.345912i
$981$	−4.40387			−0.140605
$982$	−20.6031	−	3.10541i	−0.657470	−	0.0990977i
$983$	25.9263	−	17.6762i	0.826920	−	0.563785i	−0.0742552	−	0.997239i	$-0.523658\pi$
$983$	25.9263	−	17.6762i	0.826920	−	0.563785i	0.901175	+	0.433455i	$0.142706\pi$
$984$	−1.10842	−	0.341902i	−0.0353351	−	0.0108994i
$985$	2.41295	+	32.1985i	0.0768829	+	1.02593i
$986$	−2.22255	+	1.07032i	−0.0707804	+	0.0340860i
$987$	−17.4079	+	1.82220i	−0.554101	+	0.0580011i
$988$	5.75356	+	2.77077i	0.183045	+	0.0881500i
$989$	5.43468	−	13.8473i	0.172813	−	0.440320i
$990$	0.431829	−	5.76236i	0.0137244	−	0.183140i
$991$	−3.61802	−	9.21856i	−0.114930	−	0.292837i	0.861821	−	0.507212i	$-0.169324\pi$
$991$	−3.61802	−	9.21856i	−0.114930	−	0.292837i	−0.976751	+	0.214375i	$0.931229\pi$
$992$	5.92491	−	1.82759i	0.188116	−	0.0580261i
$993$	−10.3896	+	13.0282i	−0.329706	+	0.413438i
$994$	10.5897	−	38.3075i	0.335883	−	1.21504i
$995$	36.3890	+	45.6304i	1.15361	+	1.44658i
$996$	6.12209	+	4.17397i	0.193986	+	0.132257i
$997$	−14.0207	−	13.0093i	−0.444039	−	0.412008i	0.426207	−	0.904626i	$-0.359850\pi$
$997$	−14.0207	−	13.0093i	−0.444039	−	0.412008i	−0.870246	+	0.492618i	$0.836040\pi$
$998$	5.43486	−	9.41346i	0.172038	−	0.297978i
$999$	−3.52706	−	6.10905i	−0.111591	−	0.193282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.235.1	✓	24
3.2	odd	2		882.2.z.a.235.2		24
49.44	even	21	inner	294.2.m.b.289.1	yes	24
147.44	odd	42		882.2.z.a.289.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.235.1	✓	24	1.1	even	1	trivial
294.2.m.b.289.1	yes	24	49.44	even	21	inner
882.2.z.a.235.2		24	3.2	odd	2
882.2.z.a.289.2		24	147.44	odd	42

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.189189 - 2.52456i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(2.49030 + 0.893546i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.189189 - 2.52456i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(2.49030 + 0.893546i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.189189 + 2.52456i) q^{10} +(-0.833900 - 2.12474i) q^{11} +(0.955573 - 0.294755i) q^{12} +(-0.709999 + 0.890311i) q^{13} +(-2.32931 - 1.25473i) q^{14} +(-1.57845 - 1.97931i) q^{15} +(0.826239 + 0.563320i) q^{16} +(1.51170 + 1.40265i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.80394 - 4.85657i) q^{19} +(0.563342 - 2.46816i) q^{20} +(2.56093 - 0.664551i) q^{21} +(0.507910 + 2.22530i) q^{22} +(2.58302 - 2.39669i) q^{23} +(-0.988831 + 0.149042i) q^{24} +(-1.39344 + 0.210027i) q^{25} +(0.834763 - 0.774547i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(2.11628 + 1.58788i) q^{28} +(0.266184 - 1.16623i) q^{29} +(1.26582 + 2.19246i) q^{30} +(-3.10019 + 5.36968i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-1.88591 - 1.28579i) q^{33} +(-1.28576 - 1.61229i) q^{34} +(1.78467 - 6.45594i) q^{35} +(0.623490 - 0.781831i) q^{36} +(6.74073 - 2.07924i) q^{37} +(2.04879 + 5.22023i) q^{38} +(-0.0850989 + 1.13557i) q^{39} +(-0.924910 + 2.35663i) q^{40} +(1.04508 + 0.503285i) q^{41} +(-2.63137 + 0.275442i) q^{42} +(3.80358 - 1.83171i) q^{43} +(-0.170573 - 2.27614i) q^{44} +(-2.41916 - 0.746212i) q^{45} +(-2.91138 + 1.98494i) q^{46} +(-6.54164 - 0.985994i) q^{47} +1.00000 q^{48} +(5.40315 + 4.45039i) q^{49} +1.40918 q^{50} +(2.03917 + 0.307355i) q^{51} +(-0.940879 + 0.641481i) q^{52} +(-4.64882 - 1.43397i) q^{53} +(0.0747301 + 0.997204i) q^{54} +(-5.20627 + 2.50721i) q^{55} +(-1.85598 - 1.88556i) q^{56} +(-5.05253 - 2.43317i) q^{57} +(-0.437028 + 1.11353i) q^{58} +(-1.02290 + 13.6497i) q^{59} +(-0.924910 - 2.35663i) q^{60} +(3.45671 - 1.06625i) q^{61} +(3.86587 - 4.84765i) q^{62} +(1.74159 - 1.99170i) q^{63} +(0.623490 + 0.781831i) q^{64} +(2.38196 + 1.62400i) q^{65} +(1.67321 + 1.55251i) q^{66} +(-6.29482 + 10.9029i) q^{67} +(1.03110 + 1.78592i) q^{68} +(0.784086 - 3.43531i) q^{69} +(-2.72694 + 6.11784i) q^{70} +(3.34269 + 14.6453i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(-6.13725 + 0.925042i) q^{73} +(-6.97534 + 1.05136i) q^{74} +(-1.03300 + 0.958483i) q^{75} +(-1.24787 - 5.46728i) q^{76} +(-0.178103 - 6.03637i) q^{77} +(0.253396 - 1.11020i) q^{78} +(7.36630 + 12.7588i) q^{79} +(1.26582 - 2.19246i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(-0.958398 - 0.653425i) q^{82} +(4.61980 + 5.79305i) q^{83} +(2.64304 + 0.119821i) q^{84} +(3.25508 - 4.08174i) q^{85} +(-4.03410 + 1.24435i) q^{86} +(-0.437028 - 1.11353i) q^{87} +(-0.170573 + 2.27614i) q^{88} +(-4.34339 + 11.0668i) q^{89} +(2.28092 + 1.09844i) q^{90} +(-2.56364 + 1.58272i) q^{91} +(3.17470 - 1.52885i) q^{92} +(0.463355 + 6.18304i) q^{93} +(6.32163 + 1.94996i) q^{94} +(-11.7302 + 7.99751i) q^{95} +(-0.988831 - 0.149042i) q^{96} +1.58232 q^{97} +(-4.67951 - 5.20598i) q^{98} -2.28253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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