LMFDB - Embedded newform 280.2.bj.f.171.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			171.7
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.f.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.542272 - 1.30612i) q^{2} +(-0.908317 - 0.524417i) q^{3} +(-1.41188 - 1.41654i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.17750 + 0.901991i) q^{6} +(2.14799 - 1.54472i) q^{7} +(-2.61579 + 1.07593i) q^{8} +(-0.949974 - 1.64540i) q^{9} +O(q^{10})$	\(q+(0.542272 - 1.30612i) q^{2} +(-0.908317 - 0.524417i) q^{3} +(-1.41188 - 1.41654i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.17750 + 0.901991i) q^{6} +(2.14799 - 1.54472i) q^{7} +(-2.61579 + 1.07593i) q^{8} +(-0.949974 - 1.64540i) q^{9} +(-1.40227 + 0.183437i) q^{10} +(-1.17590 + 2.03673i) q^{11} +(0.539577 + 2.02708i) q^{12} -1.21209 q^{13} +(-0.852784 - 3.64318i) q^{14} +1.04883i q^{15} +(-0.0131831 + 3.99998i) q^{16} +(-4.23538 - 2.44530i) q^{17} +(-2.66423 + 0.348520i) q^{18} +(-2.21189 + 1.27704i) q^{19} +(-0.520821 + 1.93100i) q^{20} +(-2.76113 + 0.276650i) q^{21} +(2.02254 + 2.64033i) q^{22} +(7.59015 - 4.38218i) q^{23} +(2.94021 + 0.394481i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.657285 + 1.58314i) q^{26} +5.13923i q^{27} +(-5.22086 - 0.861760i) q^{28} -5.21449i q^{29} +(1.36990 + 0.568754i) q^{30} +(1.68841 - 2.92441i) q^{31} +(5.21729 + 2.18630i) q^{32} +(2.13619 - 1.23333i) q^{33} +(-5.49058 + 4.20589i) q^{34} +(-2.41176 - 1.08785i) q^{35} +(-0.989532 + 3.66879i) q^{36} +(6.16385 - 3.55870i) q^{37} +(0.468510 + 3.58149i) q^{38} +(1.10097 + 0.635642i) q^{39} +(2.23968 + 1.72738i) q^{40} -3.18809i q^{41} +(-1.13595 + 3.75638i) q^{42} +11.6101 q^{43} +(4.54535 - 1.20990i) q^{44} +(-0.949974 + 1.64540i) q^{45} +(-1.60770 - 12.2900i) q^{46} +(5.01045 + 8.67836i) q^{47} +(2.10963 - 3.62633i) q^{48} +(2.22771 - 6.63606i) q^{49} +(0.859994 + 1.12268i) q^{50} +(2.56471 + 4.44221i) q^{51} +(1.71133 + 1.71698i) q^{52} +(-7.03102 - 4.05936i) q^{53} +(6.71244 + 2.78686i) q^{54} +2.35181 q^{55} +(-3.95669 + 6.35174i) q^{56} +2.67880 q^{57} +(-6.81073 - 2.82767i) q^{58} +(-9.90904 - 5.72099i) q^{59} +(1.48572 - 1.48083i) q^{60} +(0.560848 + 0.971417i) q^{61} +(-2.90404 - 3.79108i) q^{62} +(-4.58221 - 2.06687i) q^{63} +(5.68475 - 5.62882i) q^{64} +(0.606047 + 1.04970i) q^{65} +(-0.452475 - 3.45891i) q^{66} +(0.386838 - 0.670023i) q^{67} +(2.51599 + 9.45207i) q^{68} -9.19235 q^{69} +(-2.72869 + 2.56012i) q^{70} +2.53216i q^{71} +(4.25527 + 3.28193i) q^{72} +(11.1488 + 6.43675i) q^{73} +(-1.30559 - 9.98048i) q^{74} +(0.908317 - 0.524417i) q^{75} +(4.93190 + 1.33021i) q^{76} +(0.620335 + 6.19130i) q^{77} +(1.42725 - 1.09330i) q^{78} +(-1.34425 + 0.776104i) q^{79} +(3.47067 - 1.98857i) q^{80} +(-0.154821 + 0.268158i) q^{81} +(-4.16402 - 1.72882i) q^{82} -4.47506i q^{83} +(4.29027 + 3.52066i) q^{84} +4.89060i q^{85} +(6.29585 - 15.1642i) q^{86} +(-2.73457 + 4.73641i) q^{87} +(0.884549 - 6.59285i) q^{88} +(-9.58219 + 5.53228i) q^{89} +(1.63394 + 2.13303i) q^{90} +(-2.60356 + 1.87234i) q^{91} +(-16.9239 - 4.56466i) q^{92} +(-3.06722 + 1.77086i) q^{93} +(14.0520 - 1.83820i) q^{94} +(2.21189 + 1.27704i) q^{95} +(-3.59242 - 4.72189i) q^{96} -13.3588i q^{97} +(-7.45945 - 6.50820i) q^{98} +4.46831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.542272	−	1.30612i	0.383445	−	0.923564i
$2$	0.542272	−	1.30612i	0.383445	−	0.923564i
$3$	−0.908317	−	0.524417i	−0.524417	−	0.302772i	0.214323	−	0.976763i	$-0.431245\pi$
$3$	−0.908317	−	0.524417i	−0.524417	−	0.302772i	−0.738740	+	0.673991i	$0.764579\pi$
$4$	−1.41188	−	1.41654i	−0.705941	−	0.708271i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.17750	+	0.901991i	−0.480714	+	0.368236i
$7$	2.14799	−	1.54472i	0.811863	−	0.583848i
$7$	2.14799	−	1.54472i	0.811863	−	0.583848i
$8$	−2.61579	+	1.07593i	−0.924823	+	0.380399i
$9$	−0.949974	−	1.64540i	−0.316658	−	0.548468i
$10$	−1.40227	+	0.183437i	−0.443436	+	0.0580077i
$11$	−1.17590	+	2.03673i	−0.354549	+	0.614096i	−0.987041	−	0.160471i	$-0.948699\pi$
$11$	−1.17590	+	2.03673i	−0.354549	+	0.614096i	0.632492	+	0.774567i	$0.282032\pi$
$12$	0.539577	+	2.02708i	0.155762	+	0.585169i
$13$	−1.21209			−0.336174			−0.168087	−	0.985772i	$-0.553759\pi$
$13$	−1.21209			−0.336174			−0.168087	+	0.985772i	$0.553759\pi$
$14$	−0.852784	−	3.64318i	−0.227916	−	0.973681i
$15$			1.04883i			0.270808i
$16$	−0.0131831	+	3.99998i	−0.00329577	+	0.999995i
$17$	−4.23538	−	2.44530i	−1.02723	−	0.593072i	−0.111041	−	0.993816i	$-0.535418\pi$
$17$	−4.23538	−	2.44530i	−1.02723	−	0.593072i	−0.916190	+	0.400744i	$0.868752\pi$
$18$	−2.66423	+	0.348520i	−0.627966	+	0.0821469i
$19$	−2.21189	+	1.27704i	−0.507442	+	0.292972i	−0.731782	−	0.681539i	$-0.761311\pi$
$19$	−2.21189	+	1.27704i	−0.507442	+	0.292972i	0.224339	+	0.974511i	$0.427978\pi$
$20$	−0.520821	+	1.93100i	−0.116459	+	0.431784i
$21$	−2.76113	+	0.276650i	−0.602528	+	0.0603700i
$22$	2.02254	+	2.64033i	0.431207	+	0.562920i
$23$	7.59015	−	4.38218i	1.58266	−	0.913747i	0.588186	−	0.808726i	$-0.299842\pi$
$23$	7.59015	−	4.38218i	1.58266	−	0.913747i	0.994470	−	0.105021i	$-0.0334909\pi$
$24$	2.94021	+	0.394481i	0.600167	+	0.0805232i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.657285	+	1.58314i	−0.128904	+	0.310478i
$27$			5.13923i			0.989045i
$28$	−5.22086	−	0.861760i	−0.986650	−	0.162857i
$29$		−	5.21449i		−	0.968307i	−0.874983	−	0.484153i	$-0.839128\pi$
$29$		−	5.21449i		−	0.968307i	0.874983	−	0.484153i	$-0.160872\pi$
$30$	1.36990	+	0.568754i	0.250108	+	0.103840i
$31$	1.68841	−	2.92441i	0.303247	−	0.525239i	−0.673623	−	0.739075i	$-0.735263\pi$
$31$	1.68841	−	2.92441i	0.303247	−	0.525239i	0.976869	+	0.213837i	$0.0685961\pi$
$32$	5.21729	+	2.18630i	0.922295	+	0.386486i
$33$	2.13619	−	1.23333i	0.371863	−	0.214695i
$34$	−5.49058	+	4.20589i	−0.941626	+	0.721303i
$35$	−2.41176	−	1.08785i	−0.407661	−	0.183881i
$36$	−0.989532	+	3.66879i	−0.164922	+	0.611465i
$37$	6.16385	−	3.55870i	1.01333	−	0.585046i	0.101165	−	0.994870i	$-0.467743\pi$
$37$	6.16385	−	3.55870i	1.01333	−	0.585046i	0.912165	+	0.409823i	$0.134410\pi$
$38$	0.468510	+	3.58149i	0.0760023	+	0.580994i
$39$	1.10097	+	0.635642i	0.176296	+	0.101784i
$40$	2.23968	+	1.72738i	0.354124	+	0.273123i
$41$		−	3.18809i		−	0.497897i	−0.968517	−	0.248948i	$-0.919915\pi$
$41$		−	3.18809i		−	0.497897i	0.968517	−	0.248948i	$-0.0800849\pi$
$42$	−1.13595	+	3.75638i	−0.175280	+	0.579621i
$43$	11.6101			1.77053			0.885264	−	0.465089i	$-0.153978\pi$
$43$	11.6101			1.77053			0.885264	+	0.465089i	$0.153978\pi$
$44$	4.54535	−	1.20990i	0.685237	−	0.182399i
$45$	−0.949974	+	1.64540i	−0.141614	+	0.245282i
$46$	−1.60770	−	12.2900i	−0.237043	−	1.81205i
$47$	5.01045	+	8.67836i	0.730849	+	1.26587i	0.956521	+	0.291665i	$0.0942092\pi$
$47$	5.01045	+	8.67836i	0.730849	+	1.26587i	−0.225671	+	0.974204i	$0.572457\pi$
$48$	2.10963	−	3.62633i	0.304499	−	0.523416i
$49$	2.22771	−	6.63606i	0.318244	−	0.948009i
$50$	0.859994	+	1.12268i	0.121622	+	0.158771i
$51$	2.56471	+	4.44221i	0.359132	+	0.622034i
$52$	1.71133	+	1.71698i	0.237319	+	0.238103i
$53$	−7.03102	−	4.05936i	−0.965784	−	0.557596i	−0.0678359	−	0.997696i	$-0.521609\pi$
$53$	−7.03102	−	4.05936i	−0.965784	−	0.557596i	−0.897948	+	0.440101i	$0.854943\pi$
$54$	6.71244	+	2.78686i	0.913447	+	0.379244i
$55$	2.35181			0.317118
$56$	−3.95669	+	6.35174i	−0.528735	+	0.848787i
$57$	2.67880			0.354815
$58$	−6.81073	−	2.82767i	−0.894293	−	0.371292i
$59$	−9.90904	−	5.72099i	−1.29005	−	0.744809i	−0.311385	−	0.950284i	$-0.600793\pi$
$59$	−9.90904	−	5.72099i	−1.29005	−	0.744809i	−0.978662	+	0.205475i	$0.934126\pi$
$60$	1.48572	−	1.48083i	0.191805	−	0.191174i
$61$	0.560848	+	0.971417i	0.0718092	+	0.124377i	0.899694	−	0.436521i	$-0.143789\pi$
$61$	0.560848	+	0.971417i	0.0718092	+	0.124377i	−0.827885	+	0.560898i	$0.810456\pi$
$62$	−2.90404	−	3.79108i	−0.368813	−	0.481468i
$63$	−4.58221	−	2.06687i	−0.577304	−	0.260401i
$64$	5.68475	−	5.62882i	0.710594	−	0.703602i
$65$	0.606047	+	1.04970i	0.0751709	+	0.130200i
$66$	−0.452475	−	3.45891i	−0.0556959	−	0.425763i
$67$	0.386838	−	0.670023i	0.0472598	−	0.0818563i	−0.841428	−	0.540369i	$-0.818284\pi$
$67$	0.386838	−	0.670023i	0.0472598	−	0.0818563i	0.888688	+	0.458513i	$0.151618\pi$
$68$	2.51599	+	9.45207i	0.305108	+	1.14623i
$69$	−9.19235			−1.10663
$70$	−2.72869	+	2.56012i	−0.326141	+	0.305993i
$71$			2.53216i			0.300512i	0.988647	+	0.150256i	$0.0480097\pi$
$71$			2.53216i			0.300512i	−0.988647	+	0.150256i	$0.951990\pi$
$72$	4.25527	+	3.28193i	0.501489	+	0.386779i
$73$	11.1488	+	6.43675i	1.30487	+	0.753365i	0.981234	−	0.192819i	$-0.0617629\pi$
$73$	11.1488	+	6.43675i	1.30487	+	0.753365i	0.323631	+	0.946183i	$0.395096\pi$
$74$	−1.30559	−	9.98048i	−0.151772	−	1.16021i
$75$	0.908317	−	0.524417i	0.104883	−	0.0605545i
$76$	4.93190	+	1.33021i	0.565728	+	0.152586i
$77$	0.620335	+	6.19130i	0.0706937	+	0.705565i
$78$	1.42725	−	1.09330i	0.161604	−	0.123792i
$79$	−1.34425	+	0.776104i	−0.151240	+	0.0873186i	−0.573710	−	0.819058i	$-0.694496\pi$
$79$	−1.34425	+	0.776104i	−0.151240	+	0.0873186i	0.422470	+	0.906377i	$0.361163\pi$
$80$	3.47067	−	1.98857i	0.388033	−	0.222329i
$81$	−0.154821	+	0.268158i	−0.0172023	+	0.0297953i
$82$	−4.16402	−	1.72882i	−0.459839	−	0.190916i
$83$		−	4.47506i		−	0.491202i	−0.969371	−	0.245601i	$-0.921015\pi$
$83$		−	4.47506i		−	0.491202i	0.969371	−	0.245601i	$-0.0789853\pi$
$84$	4.29027	+	3.52066i	0.468107	+	0.384135i
$85$			4.89060i			0.530460i
$86$	6.29585	−	15.1642i	0.678899	−	1.63520i
$87$	−2.73457	+	4.73641i	−0.293176	+	0.507796i
$88$	0.884549	−	6.59285i	0.0942933	−	0.702800i
$89$	−9.58219	+	5.53228i	−1.01571	+	0.586420i	−0.912858	−	0.408276i	$-0.866130\pi$
$89$	−9.58219	+	5.53228i	−1.01571	+	0.586420i	−0.102851	+	0.994697i	$0.532797\pi$
$90$	1.63394	+	2.13303i	0.172233	+	0.224841i
$91$	−2.60356	+	1.87234i	−0.272928	+	0.196275i
$92$	−16.9239	−	4.56466i	−1.76444	−	0.475898i
$93$	−3.06722	+	1.77086i	−0.318055	+	0.183629i
$94$	14.0520	−	1.83820i	1.44935	−	0.189596i
$95$	2.21189	+	1.27704i	0.226935	+	0.131021i
$96$	−3.59242	−	4.72189i	−0.366650	−	0.481925i
$97$		−	13.3588i		−	1.35638i	−0.734888	−	0.678189i	$-0.762765\pi$
$97$		−	13.3588i		−	1.35638i	0.734888	−	0.678189i	$-0.237235\pi$
$98$	−7.45945	−	6.50820i	−0.753518	−	0.657427i
$99$	4.46831			0.449082
$100$	1.93270	−	0.514454i	0.193270	−	0.0514454i
$101$	−0.799019	+	1.38394i	−0.0795054	+	0.137707i	−0.903037	−	0.429564i	$-0.858667\pi$
$101$	−0.799019	+	1.38394i	−0.0795054	+	0.137707i	0.823531	+	0.567271i	$0.192001\pi$
$102$	7.19282	−	0.940924i	0.712195	−	0.0931654i
$103$	1.77318	+	3.07124i	0.174717	+	0.302618i	0.940063	−	0.341000i	$-0.110766\pi$
$103$	1.77318	+	3.07124i	0.174717	+	0.302618i	−0.765346	+	0.643619i	$0.777432\pi$
$104$	3.17059	−	1.30413i	0.310902	−	0.127880i
$105$	1.62015	+	2.25288i	0.158110	+	0.219859i
$106$	−9.11472	+	6.98205i	−0.885300	+	0.678156i
$107$	4.99959	+	8.65954i	0.483329	+	0.837150i	0.999817	−	0.0191446i	$-0.00609429\pi$
$107$	4.99959	+	8.65954i	0.483329	+	0.837150i	−0.516488	+	0.856294i	$0.672761\pi$
$108$	7.27994	−	7.25598i	0.700512	−	0.698207i
$109$	4.17287	+	2.40921i	0.399689	+	0.230760i	0.686350	−	0.727272i	$-0.259212\pi$
$109$	4.17287	+	2.40921i	0.399689	+	0.230760i	−0.286661	+	0.958032i	$0.592545\pi$
$110$	1.27532	−	3.07174i	0.121597	−	0.292879i
$111$	−7.46497			−0.708543
$112$	6.15051	+	8.61227i	0.581169	+	0.813783i
$113$	8.76609			0.824644			0.412322	−	0.911038i	$-0.364718\pi$
$113$	8.76609			0.824644			0.412322	+	0.911038i	$0.364718\pi$
$114$	1.45264	−	3.49882i	0.136052	−	0.327694i
$115$	−7.59015	−	4.38218i	−0.707785	−	0.408640i
$116$	−7.38655	+	7.36224i	−0.685824	+	0.683567i
$117$	1.15146	+	1.99438i	0.106452	+	0.184381i
$118$	−12.8457	+	9.84003i	−1.18254	+	0.905848i
$119$	−12.8748	+	1.28999i	−1.18024	+	0.118253i
$120$	−1.12847	−	2.74353i	−0.103015	−	0.250449i
$121$	2.73450	+	4.73629i	0.248591	+	0.430571i
$122$	1.57292	−	0.205760i	0.142405	−	0.0186286i
$123$	−1.67189	+	2.89580i	−0.150749	+	0.261105i
$124$	−6.52637	+	1.73721i	−0.586085	+	0.156006i
$125$	1.00000			0.0894427
$126$	−5.18438	+	4.86410i	−0.461861	+	0.433328i
$127$		−	2.51008i		−	0.222734i	−0.993779	−	0.111367i	$-0.964477\pi$
$127$		−	2.51008i		−	0.222734i	0.993779	−	0.111367i	$-0.0355229\pi$
$128$	−4.26921	−	10.4773i	−0.377349	−	0.926071i
$129$	−10.5457	−	6.08855i	−0.928495	−	0.536067i
$130$	1.69968	−	0.222342i	0.149072	−	0.0195007i
$131$	4.72620	−	2.72867i	0.412930	−	0.238405i	−0.279118	−	0.960257i	$-0.590042\pi$
$131$	4.72620	−	2.72867i	0.412930	−	0.238405i	0.692048	+	0.721852i	$0.256709\pi$
$132$	−4.76311	−	1.28469i	−0.414575	−	0.111818i
$133$	−2.77846	+	6.15980i	−0.240923	+	0.534122i
$134$	−0.665356	−	0.868590i	−0.0574780	−	0.0750348i
$135$	4.45070	−	2.56962i	0.383056	−	0.221157i
$136$	13.7099	+	1.83942i	1.17561	+	0.157729i
$137$	−7.53495	+	13.0509i	−0.643754	+	1.11502i	0.340833	+	0.940124i	$0.389291\pi$
$137$	−7.53495	+	13.0509i	−0.643754	+	1.11502i	−0.984588	+	0.174891i	$0.944043\pi$
$138$	−4.98476	+	12.0063i	−0.424331	+	1.02204i
$139$			15.2747i			1.29558i	0.761819	+	0.647789i	$0.224306\pi$
$139$			15.2747i			1.29558i	−0.761819	+	0.647789i	$0.775694\pi$
$140$	1.86412	+	4.95228i	0.157547	+	0.418544i
$141$		−	10.5103i		−	0.885124i
$142$	3.30729	+	1.37312i	0.277542	+	0.115230i
$143$	1.42531	−	2.46870i	0.119190	−	0.206443i
$144$	6.59410	−	3.77818i	0.549508	−	0.314849i
$145$	−4.51588	+	2.60725i	−0.375024	+	0.216520i
$146$	14.4528	−	11.0711i	1.19612	−	0.916253i
$147$	−5.50353	+	4.85940i	−0.453923	+	0.400797i
$148$	−13.7437	−	3.70689i	−1.12972	−	0.304704i
$149$	−3.67599	+	2.12234i	−0.301149	+	0.173869i	−0.642959	−	0.765901i	$-0.722293\pi$
$149$	−3.67599	+	2.12234i	−0.301149	+	0.173869i	0.341810	+	0.939769i	$0.388960\pi$
$150$	−0.192395	−	1.47074i	−0.0157089	−	0.120086i
$151$	1.03731	+	0.598892i	0.0844152	+	0.0487371i	0.541613	−	0.840628i	$-0.317814\pi$
$151$	1.03731	+	0.598892i	0.0844152	+	0.0487371i	−0.457198	+	0.889365i	$0.651147\pi$
$152$	4.41185	−	5.72030i	0.357848	−	0.463977i
$153$			9.29188i			0.751204i
$154$	8.42296	+	2.54714i	0.678741	+	0.205255i
$155$	−3.37681			−0.271232
$156$	−0.654018	−	2.45702i	−0.0523633	−	0.196719i
$157$	−5.51369	+	9.54999i	−0.440040	+	0.762172i	−0.997692	−	0.0679028i	$-0.978369\pi$
$157$	−5.51369	+	9.54999i	−0.440040	+	0.762172i	0.557652	+	0.830075i	$0.311703\pi$
$158$	0.284732	+	2.17661i	0.0226521	+	0.173162i
$159$	4.25759	+	7.37437i	0.337649	+	0.584825i
$160$	−0.715256	−	5.61145i	−0.0565460	−	0.443624i
$161$	9.53434	−	21.1375i	0.751411	−	1.66587i
$162$	0.266290	+	0.347629i	0.0209217	+	0.0273123i
$163$	−6.36400	−	11.0228i	−0.498467	−	0.863370i	0.501532	−	0.865139i	$-0.332770\pi$
$163$	−6.36400	−	11.0228i	−0.498467	−	0.863370i	−0.999998	+	0.00176946i	$0.999437\pi$
$164$	−4.51607	+	4.50121i	−0.352646	+	0.351485i
$165$	−2.13619	−	1.23333i	−0.166302	−	0.0960145i
$166$	−5.84495	−	2.42670i	−0.453656	−	0.188349i
$167$	−15.0560			−1.16507			−0.582535	−	0.812805i	$-0.697939\pi$
$167$	−15.0560			−1.16507			−0.582535	+	0.812805i	$0.697939\pi$
$168$	6.92489	−	3.69444i	0.534267	−	0.285032i
$169$	−11.5308			−0.886987
$170$	6.38769	+	2.65204i	0.489914	+	0.203402i
$171$	4.20247	+	2.42630i	0.321371	+	0.185544i
$172$	−16.3921	−	16.4462i	−1.24989	−	1.25401i
$173$	−6.09623	−	10.5590i	−0.463488	−	0.802784i	0.535644	−	0.844444i	$-0.320069\pi$
$173$	−6.09623	−	10.5590i	−0.463488	−	0.802784i	−0.999132	+	0.0416597i	$0.986735\pi$
$174$	4.70342	+	6.14009i	0.356566	+	0.465479i
$175$	0.263769	+	2.63257i	0.0199391	+	0.199004i
$176$	−8.13136	−	4.73044i	−0.612924	−	0.356571i
$177$	6.00037	+	10.3929i	0.451015	+	0.781181i
$178$	2.02964	+	15.5155i	0.152128	+	1.16293i
$179$	−0.698646	+	1.21009i	−0.0522192	+	0.0904464i	−0.890953	−	0.454095i	$-0.849963\pi$
$179$	−0.698646	+	1.21009i	−0.0522192	+	0.0904464i	0.838734	+	0.544541i	$0.183296\pi$
$180$	3.67203	−	0.977435i	0.273697	−	0.0728537i
$181$	25.6584			1.90717			0.953587	−	0.301118i	$-0.0973599\pi$
$181$	25.6584			1.90717			0.953587	+	0.301118i	$0.0973599\pi$
$182$	1.03365	+	4.41588i	0.0766196	+	0.327326i
$183$		−	1.17647i		−	0.0869674i
$184$	−15.1394	+	19.6293i	−1.11609	+	1.44709i
$185$	−6.16385	−	3.55870i	−0.453175	−	0.261641i
$186$	0.649680	+	4.96643i	0.0476369	+	0.364156i
$187$	9.96081	−	5.75088i	0.728407	−	0.420546i
$188$	5.21910	−	19.3503i	0.380642	−	1.41127i
$189$	7.93865	+	11.0390i	0.577452	+	0.802970i
$190$	2.86740	−	2.19648i	0.208023	−	0.159350i
$191$	−6.13554	+	3.54235i	−0.443952	+	0.256316i	−0.705273	−	0.708936i	$-0.749175\pi$
$191$	−6.13554	+	3.54235i	−0.443952	+	0.256316i	0.261321	+	0.965252i	$0.415842\pi$
$192$	−8.11540	+	2.13157i	−0.585679	+	0.153833i
$193$	−9.51108	+	16.4737i	−0.684622	+	1.18580i	0.288933	+	0.957349i	$0.406699\pi$
$193$	−9.51108	+	16.4737i	−0.684622	+	1.18580i	−0.973555	+	0.228451i	$0.926634\pi$
$194$	−17.4481	−	7.24409i	−1.25270	−	0.520095i
$195$		−	1.27128i		−	0.0910386i
$196$	−12.5455	+	6.21369i	−0.896108	+	0.443835i
$197$		−	25.7446i		−	1.83423i	−0.398626	−	0.917113i	$-0.630513\pi$
$197$		−	25.7446i		−	1.83423i	0.398626	−	0.917113i	$-0.369487\pi$
$198$	2.42304	−	5.83614i	0.172198	−	0.414756i
$199$	3.38261	−	5.85886i	0.239787	−	0.415323i	−0.720866	−	0.693074i	$-0.756256\pi$
$199$	3.38261	−	5.85886i	0.239787	−	0.415323i	0.960653	+	0.277751i	$0.0895891\pi$
$200$	0.376114	−	2.80331i	0.0265953	−	0.198224i
$201$	−0.702743	+	0.405729i	−0.0495676	+	0.0286179i
$202$	1.37430	+	1.79409i	0.0966956	+	0.126231i
$203$	−8.05491	−	11.2007i	−0.565344	−	0.786132i
$204$	2.67151	−	9.90490i	0.187043	−	0.693482i
$205$	−2.76097	+	1.59405i	−0.192835	+	0.111333i
$206$	4.97295	−	0.650533i	0.346482	−	0.0453248i
$207$	−14.4209	−	8.32590i	−1.00232	−	0.578690i
$208$	0.0159791	−	4.84835i	0.00110795	−	0.336172i
$209$		−	6.00669i		−	0.415491i
$210$	3.82109	−	0.894429i	0.263680	−	0.0617215i
$211$	14.7573			1.01593			0.507967	−	0.861377i	$-0.330397\pi$
$211$	14.7573			1.01593			0.507967	+	0.861377i	$0.330397\pi$
$212$	4.17671	+	15.6911i	0.286857	+	1.07767i
$213$	1.32791	−	2.30000i	0.0909866	−	0.157593i
$214$	14.0215	−	1.83422i	0.958491	−	0.125384i
$215$	−5.80506	−	10.0547i	−0.395902	−	0.685723i
$216$	−5.52945	−	13.4432i	−0.376232	−	0.914692i
$217$	−0.890699	−	8.88969i	−0.0604646	−	0.603472i
$218$	5.40954	−	4.14381i	0.366380	−	0.280654i
$219$	−6.75108	−	11.6932i	−0.456196	−	0.790154i
$220$	−3.32048	−	3.33144i	−0.223866	−	0.224605i
$221$	5.13368	+	2.96393i	0.345329	+	0.199376i
$222$	−4.04805	+	9.75012i	−0.271687	+	0.654385i
$223$	14.4522			0.967791			0.483896	−	0.875126i	$-0.339221\pi$
$223$	14.4522			0.967791			0.483896	+	0.875126i	$0.339221\pi$
$224$	14.5839	−	3.36309i	0.974427	−	0.224706i
$225$	1.89995			0.126663
$226$	4.75361	−	11.4495i	0.316205	−	0.761611i
$227$	−3.97850	−	2.29699i	−0.264062	−	0.152456i	0.362124	−	0.932130i	$-0.382052\pi$
$227$	−3.97850	−	2.29699i	−0.264062	−	0.152456i	−0.626186	+	0.779673i	$0.715385\pi$
$228$	−3.78214	−	3.79463i	−0.250478	−	0.251305i
$229$	6.54085	+	11.3291i	0.432232	+	0.748647i	0.997065	−	0.0765577i	$-0.0243929\pi$
$229$	6.54085	+	11.3291i	0.432232	+	0.748647i	−0.564833	+	0.825205i	$0.691060\pi$
$230$	−9.83956	+	7.53729i	−0.648801	+	0.496994i
$231$	2.68336	−	5.94898i	0.176552	−	0.391414i
$232$	5.61043	+	13.6400i	0.368342	+	0.895512i
$233$	10.4329	+	18.0703i	0.683483	+	1.18383i	0.973911	+	0.226931i	$0.0728691\pi$
$233$	10.4329	+	18.0703i	0.683483	+	1.18383i	−0.290428	+	0.956897i	$0.593798\pi$
$234$	3.22930	−	0.422439i	0.211106	−	0.0276157i
$235$	5.01045	−	8.67836i	0.326846	−	0.566114i
$236$	5.88637	+	22.1139i	0.383170	+	1.43949i
$237$	1.62801			0.105751
$238$	−5.29680	+	17.5156i	−0.343340	+	1.13537i
$239$		−	2.94959i		−	0.190793i	−0.995439	−	0.0953964i	$-0.969588\pi$
$239$		−	2.94959i		−	0.190793i	0.995439	−	0.0953964i	$-0.0304119\pi$
$240$	−4.19531	−	0.0138269i	−0.270806	−	0.000892521i
$241$	0.798690	+	0.461124i	0.0514481	+	0.0297036i	0.525503	−	0.850791i	$-0.323877\pi$
$241$	0.798690	+	0.461124i	0.0514481	+	0.0297036i	−0.474055	+	0.880495i	$0.657210\pi$
$242$	7.66898	−	1.00321i	0.492981	−	0.0644890i
$243$	13.6334	−	7.87123i	0.874581	−	0.504940i
$244$	0.584203	−	2.16599i	0.0373998	−	0.138663i
$245$	−6.86085	+	1.38878i	−0.438324	+	0.0887260i
$246$	2.87563	+	3.75400i	0.183344	+	0.239346i
$247$	2.68102	−	1.54789i	0.170589	−	0.0984896i
$248$	−1.27007	+	9.46625i	−0.0806494	+	0.601107i
$249$	−2.34680	+	4.06478i	−0.148722	+	0.257595i
$250$	0.542272	−	1.30612i	0.0342963	−	0.0826061i
$251$			9.30464i			0.587304i	0.955912	+	0.293652i	$0.0948706\pi$
$251$			9.30464i			0.587304i	−0.955912	+	0.293652i	$0.905129\pi$
$252$	3.54174	+	9.40907i	0.223108	+	0.592715i
$253$			20.6121i			1.29587i
$254$	−3.27846	−	1.36115i	−0.205709	−	0.0854060i
$255$	2.56471	−	4.44221i	0.160609	−	0.278182i
$256$	−15.9997	−	0.105464i	−0.999978	−	0.00659151i
$257$	26.0684	−	15.0506i	1.62610	−	0.938832i	0.640865	−	0.767654i	$-0.278576\pi$
$257$	26.0684	−	15.0506i	1.62610	−	0.938832i	0.985240	−	0.171178i	$-0.0547575\pi$
$258$	−13.6710	+	10.4722i	−0.851118	+	0.651972i
$259$	7.74269	−	17.1654i	0.481107	−	1.06661i
$260$	0.631284	−	2.34055i	0.0391506	−	0.145155i
$261$	−8.57994	+	4.95363i	−0.531085	+	0.306622i
$262$	−1.00108	−	7.65265i	−0.0618467	−	0.472782i
$263$	15.2475	+	8.80316i	0.940202	+	0.542826i	0.890024	−	0.455914i	$-0.150688\pi$
$263$	15.2475	+	8.80316i	0.940202	+	0.542826i	0.0501785	+	0.998740i	$0.484021\pi$
$264$	−4.26085	+	5.52452i	−0.262237	+	0.340011i
$265$			8.11872i			0.498729i
$266$	6.53873	+	6.96928i	0.400915	+	0.427314i
$267$	11.6049			0.710207
$268$	−1.49528	+	0.398020i	−0.0913390	+	0.0243130i
$269$	4.10363	−	7.10769i	0.250202	−	0.433363i	−0.713379	−	0.700778i	$-0.752836\pi$
$269$	4.10363	−	7.10769i	0.250202	−	0.433363i	0.963581	+	0.267415i	$0.0861695\pi$
$270$	−0.942723	−	7.20657i	−0.0573723	−	0.438578i
$271$	−7.40183	−	12.8204i	−0.449629	−	0.778781i	0.548732	−	0.835998i	$-0.315111\pi$
$271$	−7.40183	−	12.8204i	−0.449629	−	0.778781i	−0.998362	+	0.0572171i	$0.981777\pi$
$272$	9.83698	−	16.9092i	0.596455	−	1.02527i
$273$	3.34675	−	0.335326i	0.202554	−	0.0202948i
$274$	12.9600	+	16.9187i	0.782944	+	1.02209i
$275$	−1.17590	−	2.03673i	−0.0709097	−	0.122819i
$276$	12.9785	+	13.0213i	0.781214	+	0.783793i
$277$	5.53090	+	3.19327i	0.332320	+	0.191865i	0.656870	−	0.754003i	$-0.271880\pi$
$277$	5.53090	+	3.19327i	0.332320	+	0.191865i	−0.324551	+	0.945868i	$0.605213\pi$
$278$	19.9505	+	8.28302i	1.19655	+	0.496783i
$279$	−6.41577			−0.384102
$280$	7.47911	+	0.250721i	0.446963	+	0.0149835i
$281$	−12.2559			−0.731128			−0.365564	−	0.930786i	$-0.619124\pi$
$281$	−12.2559			−0.731128			−0.365564	+	0.930786i	$0.619124\pi$
$282$	−13.7276	−	5.69943i	−0.817468	−	0.339396i
$283$	−14.5951	−	8.42649i	−0.867589	−	0.500903i	−0.00104298	−	0.999999i	$-0.500332\pi$
$283$	−14.5951	−	8.42649i	−0.867589	−	0.500903i	−0.866546	+	0.499096i	$0.833665\pi$
$284$	3.58691	−	3.57510i	0.212844	−	0.212143i
$285$	−1.33940	−	2.31990i	−0.0793391	−	0.137419i
$286$	−2.45151	−	3.20033i	−0.144961	−	0.189239i
$287$	−4.92470	−	6.84799i	−0.290696	−	0.404224i
$288$	−1.35895	−	10.6615i	−0.0800768	−	0.628233i
$289$	3.45898	+	5.99113i	0.203469	+	0.352419i
$290$	0.956528	+	7.31210i	0.0561693	+	0.429382i
$291$	−7.00556	+	12.1340i	−0.410673	+	0.711307i
$292$	−6.62282	−	24.8806i	−0.387571	−	1.45603i
$293$	27.0419			1.57980			0.789902	−	0.613233i	$-0.210131\pi$
$293$	27.0419			1.57980			0.789902	+	0.613233i	$0.210131\pi$
$294$	3.36253	+	9.82337i	0.196107	+	0.572910i
$295$			11.4420i			0.666178i
$296$	−12.2944	+	15.9407i	−0.714600	+	0.926533i
$297$	−10.4672	−	6.04325i	−0.607369	−	0.350665i
$298$	0.778628	+	5.95216i	0.0451047	+	0.344799i
$299$	−9.19997	+	5.31161i	−0.532048	+	0.307178i
$300$	−2.02529	−	0.546255i	−0.116930	−	0.0315380i
$301$	24.9384	−	17.9343i	1.43743	−	1.03372i
$302$	1.34473	−	1.03009i	0.0773804	−	0.0592748i
$303$	1.45153	−	0.838038i	0.0833879	−	0.0481441i
$304$	−5.07895	−	8.86435i	−0.291298	−	0.508405i
$305$	0.560848	−	0.971417i	0.0321141	−	0.0556232i
$306$	12.1363	+	5.03873i	0.693785	+	0.288045i
$307$		−	3.32341i		−	0.189677i	−0.995493	−	0.0948386i	$-0.969766\pi$
$307$		−	3.32341i		−	0.189677i	0.995493	−	0.0948386i	$-0.0302335\pi$
$308$	7.89440	−	9.62012i	0.449825	−	0.548157i
$309$		−	3.71955i		−	0.211598i
$310$	−1.83115	+	4.41051i	−0.104002	+	0.250500i
$311$	−17.2937	+	29.9536i	−0.980637	+	1.69851i	−0.320723	+	0.947173i	$0.603926\pi$
$311$	−17.2937	+	29.9536i	−0.980637	+	1.69851i	−0.659915	+	0.751340i	$0.729408\pi$
$312$	−3.56380	−	0.478148i	−0.201761	−	0.0270698i
$313$	−12.5334	+	7.23619i	−0.708432	+	0.409014i	−0.810480	−	0.585766i	$-0.800794\pi$
$313$	−12.5334	+	7.23619i	−0.708432	+	0.409014i	0.102048	+	0.994779i	$0.467461\pi$
$314$	9.48348	+	12.3802i	0.535184	+	0.698656i
$315$	0.501147	+	5.00174i	0.0282365	+	0.281816i
$316$	2.99731	+	0.808423i	0.168612	+	0.0454773i
$317$	13.1460	−	7.58984i	0.738352	−	0.426288i	−0.0831178	−	0.996540i	$-0.526488\pi$
$317$	13.1460	−	7.58984i	0.738352	−	0.426288i	0.821470	+	0.570252i	$0.193154\pi$
$318$	11.9406	−	1.56200i	0.669593	−	0.0875924i
$319$	10.6205	+	6.13174i	0.594633	+	0.343312i
$320$	−7.71708	−	2.10873i	−0.431398	−	0.117882i
$321$		−	10.4875i		−	0.585354i
$322$	−22.4378	−	23.9152i	−1.25041	−	1.33274i
$323$	12.4909			0.695014
$324$	0.598446	−	0.159297i	0.0332470	−	0.00884981i
$325$	0.606047	−	1.04970i	0.0336174	−	0.0582271i
$326$	−17.8480	+	2.33478i	−0.988512	+	0.129312i
$327$	−2.52686	−	4.37665i	−0.139736	−	0.242029i
$328$	3.43016	+	8.33939i	0.189399	+	0.460466i
$329$	24.1680	+	10.9013i	1.33242	+	0.601007i
$330$	−2.76927	+	2.12131i	−0.152443	+	0.116774i
$331$	8.23079	+	14.2562i	0.452405	+	0.783589i	0.998535	−	0.0541118i	$-0.0172327\pi$
$331$	8.23079	+	14.2562i	0.452405	+	0.783589i	−0.546130	+	0.837701i	$0.683899\pi$
$332$	−6.33912	+	6.31826i	−0.347904	+	0.346759i
$333$	−11.7110	−	6.76134i	−0.641758	−	0.370519i
$334$	−8.16447	+	19.6649i	−0.446740	+	1.07602i
$335$	−0.773676			−0.0422704
$336$	−1.07019	−	11.0481i	−0.0583838	−	0.602723i
$337$	−28.2883			−1.54096			−0.770482	−	0.637462i	$-0.779984\pi$
$337$	−28.2883			−1.54096			−0.770482	+	0.637462i	$0.779984\pi$
$338$	−6.25285	+	15.0606i	−0.340110	+	0.819189i
$339$	−7.96238	−	4.59708i	−0.432457	−	0.249679i
$340$	6.92774	−	6.90494i	0.375709	−	0.374473i
$341$	3.97081	+	6.87764i	0.215031	+	0.372445i
$342$	5.44792	−	4.17321i	0.294590	−	0.225661i
$343$	−5.46574	−	17.6954i	−0.295122	−	0.955459i
$344$	−30.3697	+	12.4917i	−1.63742	+	0.673506i
$345$	4.59617	+	7.96081i	0.247450	+	0.428595i
$346$	−17.0971	+	2.23654i	−0.919144	+	0.120237i
$347$	0.490872	−	0.850215i	0.0263514	−	0.0456420i	−0.852549	−	0.522647i	$-0.824944\pi$
$347$	0.490872	−	0.850215i	0.0263514	−	0.0456420i	0.878900	+	0.477005i	$0.158278\pi$
$348$	10.5702	−	2.81362i	0.566623	−	0.150826i
$349$	25.8547			1.38397			0.691985	−	0.721912i	$-0.256736\pi$
$349$	25.8547			1.38397			0.691985	+	0.721912i	$0.256736\pi$
$350$	3.58148	+	1.08306i	0.191438	+	0.0578918i
$351$		−	6.22923i		−	0.332492i
$352$	−10.5879	+	8.05532i	−0.564338	+	0.429350i
$353$	11.4688	+	6.62150i	0.610421	+	0.352427i	0.773130	−	0.634247i	$-0.218690\pi$
$353$	11.4688	+	6.62150i	0.610421	+	0.352427i	−0.162709	+	0.986674i	$0.552023\pi$
$354$	16.8282	−	2.20137i	0.894410	−	0.117002i
$355$	2.19291	−	1.26608i	0.116388	−	0.0671965i
$356$	21.3656	+	5.76265i	1.13238	+	0.305420i
$357$	12.3709	+	5.58007i	0.654739	+	0.295329i
$358$	1.20166	+	1.56871i	0.0635098	+	0.0829090i
$359$	4.64380	−	2.68110i	0.245090	−	0.141503i	−0.372424	−	0.928063i	$-0.621473\pi$
$359$	4.64380	−	2.68110i	0.245090	−	0.141503i	0.617514	+	0.786560i	$0.288140\pi$
$360$	0.714597	−	5.32614i	0.0376626	−	0.280712i
$361$	−6.23836	+	10.8052i	−0.328335	+	0.568693i
$362$	13.9138	−	33.5129i	0.731295	−	1.76140i
$363$		−	5.73606i		−	0.301065i
$364$	6.32817	+	1.04453i	0.331686	+	0.0547485i
$365$		−	12.8735i		−	0.673830i
$366$	−1.53661	−	0.637969i	−0.0803199	−	0.0333472i
$367$	10.6905	−	18.5165i	0.558041	−	0.966556i	−0.439619	−	0.898185i	$-0.644886\pi$
$367$	10.6905	−	18.5165i	0.558041	−	0.966556i	0.997660	−	0.0683713i	$-0.0217803\pi$
$368$	17.4285	+	30.4182i	0.908526	+	1.58566i
$369$	−5.24570	+	3.02861i	−0.273080	+	0.157663i
$370$	−7.99056	+	6.12092i	−0.415409	+	0.318211i
$371$	−21.3731	+	2.14147i	−1.10964	+	0.111179i
$372$	6.83904	+	1.84460i	0.354588	+	0.0956380i
$373$	−7.38217	+	4.26210i	−0.382234	+	0.220683i	−0.678790	−	0.734333i	$-0.737495\pi$
$373$	−7.38217	+	4.26210i	−0.382234	+	0.220683i	0.296556	+	0.955016i	$0.404162\pi$
$374$	−2.10984	−	16.1285i	−0.109097	−	0.833986i
$375$	−0.908317	−	0.524417i	−0.0469053	−	0.0270808i
$376$	−22.4436	−	17.3099i	−1.15744	−	0.892690i
$377$			6.32045i			0.325520i
$378$	18.7231	−	4.38266i	0.963015	−	0.225419i
$379$	−4.45055			−0.228609			−0.114305	−	0.993446i	$-0.536464\pi$
$379$	−4.45055			−0.228609			−0.114305	+	0.993446i	$0.536464\pi$
$380$	−1.31395	−	4.93626i	−0.0674043	−	0.253225i
$381$	−1.31633	+	2.27995i	−0.0674376	+	0.116805i
$382$	1.29959	+	9.93465i	0.0664931	+	0.508301i
$383$	−5.77418	−	10.0012i	−0.295047	−	0.511036i	0.679949	−	0.733259i	$-0.262002\pi$
$383$	−5.77418	−	10.0012i	−0.295047	−	0.511036i	−0.974996	+	0.222223i	$0.928669\pi$
$384$	−1.61668	+	11.7556i	−0.0825008	+	0.599898i
$385$	5.05166	−	3.63288i	0.257456	−	0.185149i
$386$	16.3589	+	21.3558i	0.832648	+	1.08698i
$387$	−11.0293	−	19.1033i	−0.560652	−	0.971077i
$388$	−18.9233	+	18.8610i	−0.960683	+	0.957522i
$389$	−8.52646	−	4.92276i	−0.432309	−	0.249594i	0.268021	−	0.963413i	$-0.413630\pi$
$389$	−8.52646	−	4.92276i	−0.432309	−	0.249594i	−0.700330	+	0.713819i	$0.746964\pi$
$390$	−1.66045	−	0.689383i	−0.0840800	−	0.0349083i
$391$	−42.8629			−2.16767
$392$	1.31272	+	19.7554i	0.0663023	+	0.997800i
$393$	−5.72385			−0.288730
$394$	−33.6254	−	13.9606i	−1.69403	−	0.703324i
$395$	1.34425	+	0.776104i	0.0676367	+	0.0390500i
$396$	−6.30873	−	6.32956i	−0.317026	−	0.318072i
$397$	−13.9206	−	24.1113i	−0.698657	−	1.21011i	−0.968932	−	0.247327i	$-0.920448\pi$
$397$	−13.9206	−	24.1113i	−0.698657	−	1.21011i	0.270275	−	0.962783i	$-0.412885\pi$
$398$	−5.81805	−	7.59518i	−0.291633	−	0.380712i
$399$	5.75402	−	4.13798i	0.288061	−	0.207158i
$400$	−3.45749	−	2.01141i	−0.172875	−	0.100570i
$401$	−18.2301	−	31.5755i	−0.910370	−	1.57681i	−0.813543	−	0.581505i	$-0.802464\pi$
$401$	−18.2301	−	31.5755i	−0.910370	−	1.57681i	−0.0968267	−	0.995301i	$-0.530869\pi$
$402$	0.148851	+	1.13788i	0.00742401	+	0.0567523i
$403$	−2.04651	+	3.54465i	−0.101944	+	0.176572i
$404$	3.08853	−	0.822117i	0.153660	−	0.0409019i
$405$	0.309642			0.0153862
$406$	−18.9973	+	4.44684i	−0.942822	+	0.220693i
$407$			16.7388i			0.829709i
$408$	−11.4883	−	8.86046i	−0.568754	−	0.438658i
$409$	3.55633	+	2.05325i	0.175849	+	0.101527i	0.585341	−	0.810787i	$-0.300961\pi$
$409$	3.55633	+	2.05325i	0.175849	+	0.101527i	−0.409492	+	0.912314i	$0.634294\pi$
$410$	0.584813	+	4.47056i	0.0288819	+	0.220785i
$411$	13.6882	−	7.90291i	0.675191	−	0.389822i
$412$	1.84702	−	6.84801i	0.0909961	−	0.337377i
$413$	−30.1218	+	3.01804i	−1.48220	+	0.148508i
$414$	−18.6946	+	14.3205i	−0.918792	+	0.703812i
$415$	−3.87552	+	2.23753i	−0.190242	+	0.109836i
$416$	−6.32384	−	2.65000i	−0.310052	−	0.129927i
$417$	8.01029	−	13.8742i	0.392265	−	0.679424i
$418$	−7.84543	−	3.25726i	−0.383733	−	0.159318i
$419$			39.8516i			1.94688i	0.228943	+	0.973440i	$0.426473\pi$
$419$			39.8516i			1.94688i	−0.228943	+	0.973440i	$0.573527\pi$
$420$	0.903844	−	5.47581i	0.0441031	−	0.267192i
$421$		−	10.2595i		−	0.500020i	−0.968243	−	0.250010i	$-0.919566\pi$
$421$		−	10.2595i		−	0.500020i	0.968243	−	0.250010i	$-0.0804339\pi$
$422$	8.00247	−	19.2747i	0.389554	−	0.938279i
$423$	9.51959	−	16.4884i	0.462859	−	0.801694i
$424$	22.7593	+	3.05357i	1.10529	+	0.148294i
$425$	4.23538	−	2.44530i	0.205446	−	0.118614i
$426$	−2.28398	−	2.98163i	−0.110659	−	0.144460i
$427$	2.70526	+	1.22024i	0.130917	+	0.0590517i
$428$	5.20778	−	19.3084i	0.251728	−	0.933306i
$429$	−2.58926	+	1.49491i	−0.125011	+	0.0721749i
$430$	−16.2805	+	2.12972i	−0.785115	+	0.102704i
$431$	13.6969	+	7.90789i	0.659755	+	0.380909i	0.792183	−	0.610283i	$-0.208944\pi$
$431$	13.6969	+	7.90789i	0.659755	+	0.380909i	−0.132429	+	0.991193i	$0.542278\pi$
$432$	−20.5568	−	0.0677510i	−0.989040	−	0.00325967i
$433$		−	32.7619i		−	1.57443i	−0.616676	−	0.787217i	$-0.711521\pi$
$433$		−	32.7619i		−	1.57443i	0.616676	−	0.787217i	$-0.288479\pi$
$434$	−12.0940	−	3.65728i	−0.580530	−	0.175555i
$435$	5.46913			0.262225
$436$	−2.47885	−	9.31256i	−0.118716	−	0.445991i
$437$	−11.1924	+	19.3858i	−0.535404	+	0.927347i
$438$	−18.9336	+	2.47679i	−0.904684	+	0.118346i
$439$	−0.202051	−	0.349962i	−0.00964336	−	0.0167028i	0.861163	−	0.508328i	$-0.169736\pi$
$439$	−0.202051	−	0.349962i	−0.00964336	−	0.0167028i	−0.870807	+	0.491625i	$0.836403\pi$
$440$	−6.15185	+	2.53038i	−0.293278	+	0.120631i
$441$	−13.0353	+	2.63861i	−0.620727	+	0.125648i
$442$	6.65509	−	5.09793i	0.316551	−	0.242484i
$443$	−16.1659	−	28.0002i	−0.768066	−	1.33033i	−0.938610	−	0.344979i	$-0.887886\pi$
$443$	−16.1659	−	28.0002i	−0.768066	−	1.33033i	0.170544	−	0.985350i	$-0.445447\pi$
$444$	10.5396	+	10.5744i	0.500189	+	0.501841i
$445$	9.58219	+	5.53228i	0.454239	+	0.262255i
$446$	7.83703	−	18.8763i	0.371094	−	0.893817i
$447$	4.45196			0.210570
$448$	3.51585	−	20.8720i	0.166108	−	0.986108i
$449$	4.91848			0.232117			0.116059	−	0.993242i	$-0.462974\pi$
$449$	4.91848			0.232117			0.116059	+	0.993242i	$0.462974\pi$
$450$	1.03029	−	2.48155i	0.0485683	−	0.116982i
$451$	6.49328	+	3.74889i	0.305756	+	0.176529i
$452$	−12.3767	−	12.4175i	−0.582150	−	0.584071i
$453$	−0.628138	−	1.08797i	−0.0295125	−	0.0511172i
$454$	−5.15757	+	3.95079i	−0.242057	+	0.185420i
$455$	2.92328	+	1.31858i	0.137045	+	0.0618160i
$456$	−7.00718	+	2.88220i	−0.328141	+	0.134971i
$457$	10.7472	+	18.6147i	0.502733	+	0.870759i	0.999995	+	0.00315885i	$0.00100550\pi$
$457$	10.7472	+	18.6147i	0.502733	+	0.870759i	−0.497262	+	0.867601i	$0.665661\pi$
$458$	18.3440	−	2.39966i	0.857160	−	0.112129i
$459$	12.5670	−	21.7666i	0.586575	−	1.01598i
$460$	4.50885	+	16.9389i	0.210226	+	0.789779i
$461$	−27.8967			−1.29928			−0.649639	−	0.760243i	$-0.725080\pi$
$461$	−27.8967			−1.29928			−0.649639	+	0.760243i	$0.725080\pi$
$462$	−6.31495	−	6.73075i	−0.293798	−	0.313143i
$463$			38.9342i			1.80942i	0.426024	+	0.904712i	$0.359914\pi$
$463$			38.9342i			1.80942i	−0.426024	+	0.904712i	$0.640086\pi$
$464$	20.8578	+	0.0687431i	0.968301	+	0.00319132i
$465$	3.06722	+	1.77086i	0.142239	+	0.0821216i
$466$	29.2595	−	3.82756i	1.35542	−	0.177308i
$467$	−21.6588	+	12.5047i	−1.00225	+	0.578650i	−0.908914	−	0.416984i	$-0.863087\pi$
$467$	−21.6588	+	12.5047i	−1.00225	+	0.578650i	−0.0933379	+	0.995634i	$0.529754\pi$
$468$	1.19941	−	4.44692i	0.0554425	−	0.205559i
$469$	−0.204072	−	2.03676i	−0.00942316	−	0.0940486i
$470$	−8.61792	−	11.2503i	−0.397515	−	0.518936i
$471$	10.0164	−	5.78295i	0.461529	−	0.266464i
$472$	32.0754	+	4.30349i	1.47639	+	0.198084i
$473$	−13.6524	+	23.6467i	−0.627738	+	1.08727i
$474$	0.882825	−	2.12637i	0.0405495	−	0.0976674i
$475$		−	2.55407i		−	0.117189i
$476$	20.0051	+	16.4164i	0.916931	+	0.752447i
$477$			15.4251i			0.706268i
$478$	−3.85250	−	1.59948i	−0.176209	−	0.0731585i
$479$	−4.29962	+	7.44716i	−0.196455	+	0.340269i	−0.947376	−	0.320122i	$-0.896276\pi$
$479$	−4.29962	+	7.44716i	−0.196455	+	0.340269i	0.750922	+	0.660391i	$0.229609\pi$
$480$	−2.29306	+	5.47207i	−0.104663	+	0.249765i
$481$	−7.47116	+	4.31348i	−0.340655	+	0.196678i
$482$	1.03539	−	0.793127i	0.0471607	−	0.0361260i
$483$	−19.7451	+	14.1996i	−0.898431	+	0.646103i
$484$	2.84836	−	10.5606i	0.129471	−	0.480027i
$485$	−11.5690	+	6.67938i	−0.525323	+	0.303295i
$486$	−2.88774	−	22.0751i	−0.130991	−	1.00135i
$487$	12.9204	+	7.45959i	0.585478	+	0.338026i	0.763308	−	0.646035i	$-0.223574\pi$
$487$	12.9204	+	7.45959i	0.585478	+	0.338026i	−0.177829	+	0.984061i	$0.556907\pi$
$488$	−2.51224	−	1.93759i	−0.113724	−	0.0877108i
$489$			13.3496i			0.603688i
$490$	−1.90654	+	9.71417i	−0.0861287	+	0.438841i
$491$	3.92024			0.176918			0.0884589	−	0.996080i	$-0.471806\pi$
$491$	3.92024			0.176918			0.0884589	+	0.996080i	$0.471806\pi$
$492$	6.46253	−	1.72022i	0.291353	−	0.0775536i
$493$	−12.7510	+	22.0854i	−0.574276	+	0.994675i
$494$	−0.567878	−	4.34110i	−0.0255500	−	0.195315i
$495$	−2.23416	−	3.86967i	−0.100418	−	0.173929i
$496$	11.6753	+	6.79214i	0.524236	+	0.304976i
$497$	3.91146	+	5.43904i	0.175453	+	0.243974i
$498$	4.03647	+	5.26941i	0.180878	+	0.236128i
$499$	5.70995	+	9.88993i	0.255613	+	0.442734i	0.965062	−	0.262023i	$-0.0843895\pi$
$499$	5.70995	+	9.88993i	0.255613	+	0.442734i	−0.709449	+	0.704757i	$0.751056\pi$
$500$	−1.41188	−	1.41654i	−0.0631412	−	0.0633497i
$501$	13.6756	+	7.89564i	0.610983	+	0.352751i
$502$	12.1529	+	5.04565i	0.542412	+	0.225198i
$503$	22.9658			1.02399			0.511997	−	0.858987i	$-0.328906\pi$
$503$	22.9658			1.02399			0.511997	+	0.858987i	$0.328906\pi$
$504$	14.2099	+	0.476357i	0.632960	+	0.0212186i
$505$	1.59804			0.0711118
$506$	26.9218	+	11.1774i	1.19682	+	0.496894i
$507$	10.4736	+	6.04696i	0.465151	+	0.268555i
$508$	−3.55564	+	3.54394i	−0.157756	+	0.157237i
$509$	−12.4956	−	21.6429i	−0.553856	−	0.959306i	−0.997992	−	0.0633469i	$-0.979823\pi$
$509$	−12.4956	−	21.6429i	−0.553856	−	0.959306i	0.444136	−	0.895959i	$-0.353511\pi$
$510$	−4.41128	−	5.75870i	−0.195335	−	0.255000i
$511$	33.8904	−	3.39563i	1.49922	−	0.150214i
$512$	−8.81392	+	20.8402i	−0.389524	+	0.921016i
$513$	−6.56298	−	11.3674i	−0.289763	−	0.501883i
$514$	−5.52167	−	42.2100i	−0.243550	−	1.86180i
$515$	1.77318	−	3.07124i	0.0781357	−	0.135335i
$516$	6.26455	+	23.5347i	0.275782	+	1.03606i
$517$	−23.5673			−1.03649
$518$	−18.2214	−	19.4212i	−0.800603	−	0.853318i
$519$			12.7879i			0.561325i
$520$	−2.71470	−	2.09374i	−0.119048	−	0.0918168i
$521$	14.0875	+	8.13341i	0.617184	+	0.356331i	0.775772	−	0.631014i	$-0.217361\pi$
$521$	14.0875	+	8.13341i	0.617184	+	0.356331i	−0.158588	+	0.987345i	$0.550694\pi$
$522$	1.81735	+	13.8926i	0.0795434	+	0.608063i
$523$	−16.4913	+	9.52126i	−0.721114	+	0.416336i	−0.815163	−	0.579232i	$-0.803353\pi$
$523$	−16.4913	+	9.52126i	−0.721114	+	0.416336i	0.0940483	+	0.995568i	$0.470019\pi$
$524$	−10.5381	−	2.84230i	−0.460359	−	0.124166i
$525$	1.14098	−	2.52953i	0.0497964	−	0.110398i
$526$	19.7663	−	15.1413i	0.861850	−	0.660193i
$527$	−14.3021	+	8.25732i	−0.623009	+	0.359694i
$528$	4.90513	+	8.56097i	0.213468	+	0.372568i
$529$	26.9069	−	46.6042i	1.16987	−	2.02627i
$530$	10.6040	+	4.40256i	0.460608	+	0.191235i
$531$			21.7392i			0.943399i
$532$	12.6485	−	4.76110i	0.548380	−	0.206420i
$533$			3.86427i			0.167380i
$534$	6.29301	−	15.1573i	0.272325	−	0.655922i
$535$	4.99959	−	8.65954i	0.216151	−	0.374385i
$536$	−0.290990	+	2.16885i	−0.0125689	+	0.0936801i
$537$	1.26918	−	0.732763i	0.0547693	−	0.0316211i
$538$	−7.05819	−	9.21412i	−0.304300	−	0.397249i
$539$	10.8963	+	12.3406i	0.469336	+	0.531548i
$540$	−9.92383	−	2.67662i	−0.427054	−	0.115183i
$541$	−33.7035	+	19.4587i	−1.44902	+	0.836595i	−0.998423	−	0.0561307i	$-0.982124\pi$
$541$	−33.7035	+	19.4587i	−1.44902	+	0.836595i	−0.450601	+	0.892725i	$0.648790\pi$
$542$	−20.7587	+	2.71553i	−0.891662	+	0.116642i
$543$	−23.3060	−	13.4557i	−1.00015	−	0.577439i
$544$	−16.7511	−	22.0176i	−0.718196	−	0.943998i
$545$		−	4.81842i		−	0.206398i
$546$	1.37687	−	4.55308i	0.0589248	−	0.194854i
$547$	−1.29047			−0.0551764			−0.0275882	−	0.999619i	$-0.508783\pi$
$547$	−1.29047			−0.0551764			−0.0275882	+	0.999619i	$0.508783\pi$
$548$	29.1256	−	7.75277i	1.24419	−	0.331182i
$549$	1.06558	−	1.84564i	0.0454779	−	0.0787701i
$550$	−3.29786	+	0.431408i	−0.140621	+	0.0183953i
$551$	6.65909	+	11.5339i	0.283687	+	0.491360i
$552$	24.0453	−	9.89032i	1.02344	−	0.420960i
$553$	−1.68858	+	3.74355i	−0.0718056	+	0.159192i
$554$	7.17003	−	5.49238i	0.304625	−	0.233349i
$555$	3.73248	+	6.46485i	0.158435	+	0.274418i
$556$	21.6372	−	21.5660i	0.917621	−	0.914602i
$557$	−5.64503	−	3.25916i	−0.239188	−	0.138095i	0.375616	−	0.926776i	$-0.377431\pi$
$557$	−5.64503	−	3.25916i	−0.239188	−	0.138095i	−0.614803	+	0.788680i	$0.710765\pi$
$558$	−3.47909	+	8.37974i	−0.147282	+	0.354743i
$559$	−14.0726			−0.595206
$560$	4.38319	−	9.63264i	0.185224	−	0.407053i
$561$	−12.0634			−0.509319
$562$	−6.64605	+	16.0077i	−0.280347	+	0.675243i
$563$	24.9474	+	14.4034i	1.05141	+	0.607030i	0.923043	−	0.384697i	$-0.125694\pi$
$563$	24.9474	+	14.4034i	1.05141	+	0.607030i	0.128364	+	0.991727i	$0.459027\pi$
$564$	−14.8882	+	14.8392i	−0.626908	+	0.624845i
$565$	−4.38304	−	7.59165i	−0.184396	−	0.319383i
$566$	−18.9205	+	14.4935i	−0.795288	+	0.609206i
$567$	0.0816740	+	0.815154i	0.00342999	+	0.0342333i
$568$	−2.72442	−	6.62360i	−0.114314	−	0.277920i
$569$	5.68292	+	9.84310i	0.238240	+	0.412644i	0.960209	−	0.279281i	$-0.0900961\pi$
$569$	5.68292	+	9.84310i	0.238240	+	0.412644i	−0.721969	+	0.691925i	$0.756763\pi$
$570$	−3.75638	+	0.491389i	−0.157338	+	0.0205820i
$571$	−1.36107	+	2.35745i	−0.0569592	+	0.0986562i	−0.893099	−	0.449860i	$-0.851474\pi$
$571$	−1.36107	+	2.35745i	−0.0569592	+	0.0986562i	0.836140	+	0.548516i	$0.184807\pi$
$572$	−5.50939	+	1.46651i	−0.230359	+	0.0613178i
$573$	7.43068			0.310421
$574$	−11.6148	+	2.71876i	−0.484792	+	0.113479i
$575$			8.76435i			0.365499i
$576$	−14.6620	−	4.00647i	−0.610918	−	0.166936i
$577$	−8.29404	−	4.78857i	−0.345285	−	0.199351i	0.317321	−	0.948318i	$-0.397217\pi$
$577$	−8.29404	−	4.78857i	−0.345285	−	0.199351i	−0.662607	+	0.748967i	$0.730550\pi$
$578$	9.70082	−	1.26901i	0.403501	−	0.0527837i
$579$	17.2781	−	9.97554i	0.718055	−	0.414569i
$580$	10.0692	+	2.71582i	0.418099	+	0.112768i
$581$	−6.91270	−	9.61238i	−0.286787	−	0.398789i
$582$	12.0495	+	15.7300i	0.499467	+	0.652030i
$583$	16.5356	−	9.54684i	0.684835	−	0.395390i
$584$	−36.0884	−	4.84191i	−1.49335	−	0.200360i
$585$	1.15146	−	1.99438i	0.0476069	−	0.0824576i
$586$	14.6641	−	35.3199i	0.605767	−	1.45905i
$587$			37.9535i			1.56651i	0.621703	+	0.783253i	$0.286441\pi$
$587$			37.9535i			1.56651i	−0.621703	+	0.783253i	$0.713559\pi$
$588$	14.6539	+	0.935081i	0.604315	+	0.0385621i
$589$			8.62461i			0.355371i
$590$	14.9446	+	6.20467i	0.615258	+	0.255442i
$591$	−13.5009	+	23.3843i	−0.555353	+	0.961900i
$592$	14.1535	+	24.7022i	0.581703	+	1.01525i
$593$	22.1702	−	12.7999i	0.910419	−	0.525631i	0.0298534	−	0.999554i	$-0.490496\pi$
$593$	22.1702	−	12.7999i	0.910419	−	0.525631i	0.880566	+	0.473923i	$0.157163\pi$
$594$	−13.5693	+	10.3943i	−0.556754	+	0.426484i
$595$	7.55459	+	10.5049i	0.309708	+	0.430661i
$596$	8.19645	+	2.21071i	0.335740	+	0.0905544i
$597$	−6.14497	+	3.54780i	−0.251497	+	0.145202i
$598$	1.94869	+	14.8966i	0.0796877	+	0.609166i
$599$	28.0612	+	16.2011i	1.14655	+	0.661960i	0.948044	−	0.318140i	$-0.103058\pi$
$599$	28.0612	+	16.2011i	1.14655	+	0.661960i	0.198504	+	0.980100i	$0.436392\pi$
$600$	−1.81173	+	2.34905i	−0.0739637	+	0.0958996i
$601$		−	22.3390i		−	0.911226i	−0.890178	−	0.455613i	$-0.849420\pi$
$601$		−	22.3390i		−	0.911226i	0.890178	−	0.455613i	$-0.150580\pi$
$602$	−9.90093	−	42.2978i	−0.403532	−	1.72393i
$603$	−1.46994			−0.0598607
$604$	−0.616205	−	2.31496i	−0.0250730	−	0.0941944i
$605$	2.73450	−	4.73629i	0.111173	−	0.192557i
$606$	−0.307454	−	2.35031i	−0.0124895	−	0.0954747i
$607$	14.9462	+	25.8877i	0.606649	+	1.05075i	0.991789	+	0.127889i	$0.0408201\pi$
$607$	14.9462	+	25.8877i	0.606649	+	1.05075i	−0.385139	+	0.922858i	$0.625847\pi$
$608$	−14.3320	+	1.82681i	−0.581241	+	0.0740871i
$609$	1.44259	+	14.3979i	0.0584566	+	0.583432i
$610$	−0.964652	−	1.25931i	−0.0390576	−	0.0509878i
$611$	−6.07314	−	10.5190i	−0.245693	−	0.425552i
$612$	13.1623	−	13.1190i	0.532056	−	0.530305i
$613$	−7.53192	−	4.34856i	−0.304211	−	0.175637i	0.340122	−	0.940381i	$-0.389532\pi$
$613$	−7.53192	−	4.34856i	−0.304211	−	0.175637i	−0.644333	+	0.764745i	$0.722865\pi$
$614$	−4.34076	−	1.80220i	−0.175179	−	0.0727307i
$615$	3.34378			0.134834
$616$	−8.28407	−	15.5277i	−0.333775	−	0.625630i
$617$	14.2056			0.571897			0.285948	−	0.958245i	$-0.407691\pi$
$617$	14.2056			0.571897			0.285948	+	0.958245i	$0.407691\pi$
$618$	−4.85816	−	2.01701i	−0.195424	−	0.0811359i
$619$	16.3642	+	9.44785i	0.657731	+	0.379741i	0.791412	−	0.611283i	$-0.209346\pi$
$619$	16.3642	+	9.44785i	0.657731	+	0.379741i	−0.133681	+	0.991024i	$0.542680\pi$
$620$	4.76766	+	4.78340i	0.191474	+	0.192106i
$621$	22.5210	+	39.0075i	0.903737	+	1.56532i
$622$	29.7450	+	38.8306i	1.19267	+	1.55697i
$623$	−12.0366	+	26.6850i	−0.482237	+	1.06911i
$624$	−2.55707	+	4.39546i	−0.102365	+	0.175959i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.65476	+	20.2941i	0.106106	+	0.811117i
$627$	−3.15001	+	5.45597i	−0.125799	+	0.217891i
$628$	21.3126	−	5.67308i	0.850467	−	0.226381i
$629$	−34.8083			−1.38790
$630$	6.80462	+	2.05775i	0.271103	+	0.0819828i
$631$		−	3.99376i		−	0.158989i	−0.996835	−	0.0794945i	$-0.974669\pi$
$631$		−	3.99376i		−	0.158989i	0.996835	−	0.0794945i	$-0.0253306\pi$
$632$	2.68125	−	3.47645i	0.106654	−	0.138286i
$633$	−13.4043	−	7.73897i	−0.532773	−	0.307596i
$634$	−2.78451	−	21.2859i	−0.110587	−	0.845373i
$635$	−2.17379	+	1.25504i	−0.0862644	+	0.0498048i
$636$	4.43489	−	16.4428i	0.175855	−	0.651999i
$637$	−2.70019	+	8.04353i	−0.106985	+	0.318696i
$638$	13.7680	−	10.5465i	0.545079	−	0.417541i
$639$	4.16642	−	2.40548i	0.164821	−	0.0951594i
$640$	−6.93900	+	8.93590i	−0.274288	+	0.353222i
$641$	9.65359	−	16.7205i	0.381294	−	0.660420i	−0.609954	−	0.792437i	$-0.708812\pi$
$641$	9.65359	−	16.7205i	0.381294	−	0.660420i	0.991247	+	0.132017i	$0.0421453\pi$
$642$	−13.6979	−	5.68707i	−0.540612	−	0.224451i
$643$		−	21.3394i		−	0.841544i	−0.907166	−	0.420772i	$-0.861759\pi$
$643$		−	21.3394i		−	0.841544i	0.907166	−	0.420772i	$-0.138241\pi$
$644$	−43.4035	+	16.3378i	−1.71034	+	0.643801i
$645$			12.1771i			0.479473i
$646$	6.77349	−	16.3146i	0.266499	−	0.641890i
$647$	11.9178	−	20.6422i	0.468535	−	0.811527i	−0.530818	−	0.847486i	$-0.678115\pi$
$647$	11.9178	−	20.6422i	0.468535	−	0.811527i	0.999353	+	0.0359589i	$0.0114485\pi$
$648$	0.116461	−	0.868022i	0.00457501	−	0.0340991i
$649$	23.3042	−	13.4547i	0.914769	−	0.528142i
$650$	−1.04239	−	1.36079i	−0.0408860	−	0.0533747i
$651$	−3.85287	+	8.54176i	−0.151006	+	0.334778i
$652$	−6.62901	+	24.5777i	−0.259612	+	0.962537i
$653$	−3.56712	+	2.05948i	−0.139592	+	0.0805936i	−0.568170	−	0.822911i	$-0.692348\pi$
$653$	−3.56712	+	2.05948i	−0.139592	+	0.0805936i	0.428577	+	0.903505i	$0.359015\pi$
$654$	−7.08666	+	0.927037i	−0.277110	+	0.0362500i
$655$	−4.72620	−	2.72867i	−0.184668	−	0.106618i
$656$	12.7523	+	0.0420289i	0.497894	+	0.00164095i
$657$		−	24.4590i		−	0.954235i
$658$	27.3440	−	25.6547i	1.06598	−	1.00013i
$659$	39.8908			1.55393			0.776963	−	0.629546i	$-0.216759\pi$
$659$	39.8908			1.55393			0.776963	+	0.629546i	$0.216759\pi$
$660$	1.26898	+	4.76731i	0.0493950	+	0.185567i
$661$	20.1318	−	34.8692i	0.783035	−	1.35626i	−0.147132	−	0.989117i	$-0.547004\pi$
$661$	20.1318	−	34.8692i	0.783035	−	1.35626i	0.930166	−	0.367139i	$-0.119663\pi$
$662$	23.0835	−	3.01966i	0.897167	−	0.117362i
$663$	−3.10867	−	5.38438i	−0.120731	−	0.209112i
$664$	4.81485	+	11.7058i	0.186853	+	0.454275i
$665$	6.72377	−	0.673685i	0.260737	−	0.0261244i
$666$	−15.1816	+	11.6294i	−0.588277	+	0.450631i
$667$	−22.8508	−	39.5788i	−0.884787	−	1.53250i
$668$	21.2573	+	21.3275i	0.822471	+	0.825186i
$669$	−13.1272	−	7.57898i	−0.507526	−	0.293020i
$670$	−0.419543	+	1.01051i	−0.0162084	+	0.0390394i
$671$	−2.63802			−0.101839
$672$	−15.0104	−	4.59328i	−0.579041	−	0.177190i
$673$	−23.6181			−0.910412			−0.455206	−	0.890386i	$-0.650434\pi$
$673$	−23.6181			−0.910412			−0.455206	+	0.890386i	$0.650434\pi$
$674$	−15.3400	+	36.9479i	−0.590874	+	1.42318i
$675$	−4.45070	−	2.56962i	−0.171308	−	0.0989045i
$676$	16.2802	+	16.3339i	0.626160	+	0.628227i
$677$	12.2908	+	21.2883i	0.472374	+	0.818175i	0.999500	−	0.0316116i	$-0.0100639\pi$
$677$	12.2908	+	21.2883i	0.472374	+	0.818175i	−0.527127	+	0.849787i	$0.676731\pi$
$678$	−10.3221	+	7.90693i	−0.396418	+	0.303664i
$679$	−20.6355	−	28.6945i	−0.791918	−	1.10119i
$680$	−5.26194	−	12.7928i	−0.201786	−	0.490581i
$681$	2.40916	+	4.17279i	0.0923192	+	0.159902i
$682$	11.1363	−	1.45678i	0.426430	−	0.0557831i
$683$	−10.5724	+	18.3120i	−0.404543	+	0.700688i	−0.994268	−	0.106915i	$-0.965903\pi$
$683$	−10.5724	+	18.3120i	−0.404543	+	0.700688i	0.589726	+	0.807604i	$0.299236\pi$
$684$	−2.49644	−	9.37863i	−0.0954537	−	0.358601i
$685$	15.0699			0.575791
$686$	−26.0761	−	2.45680i	−0.995591	−	0.0938012i
$687$		−	13.7205i		−	0.523471i
$688$	−0.153057	+	46.4403i	−0.00583526	+	1.77052i
$689$	8.52225	+	4.92032i	0.324672	+	0.187449i
$690$	12.8901	−	1.68621i	0.490719	−	0.0641930i
$691$	−1.87978	+	1.08529i	−0.0715102	+	0.0412864i	−0.535329	−	0.844644i	$-0.679812\pi$
$691$	−1.87978	+	1.08529i	−0.0715102	+	0.0412864i	0.463819	+	0.885930i	$0.346479\pi$
$692$	−6.35008	+	23.5436i	−0.241394	+	0.894993i
$693$	9.59789	−	6.90228i	0.364594	−	0.262196i
$694$	−0.844294	−	1.10218i	−0.0320490	−	0.0418384i
$695$	13.2282	−	7.63733i	0.501776	−	0.289700i
$696$	2.05702	−	15.3317i	0.0779711	−	0.581146i
$697$	−7.79584	+	13.5028i	−0.295289	+	0.511455i
$698$	14.0203	−	33.7692i	0.530676	−	1.27818i
$699$		−	21.8848i		−	0.827759i
$700$	3.35674	−	4.09052i	0.126873	−	0.154607i
$701$		−	45.6142i		−	1.72283i	−0.507906	−	0.861413i	$-0.669580\pi$
$701$		−	45.6142i		−	1.72283i	0.507906	−	0.861413i	$-0.330420\pi$
$702$	−8.13610	−	3.37794i	−0.307077	−	0.127492i
$703$	−9.08916	+	15.7429i	−0.342804	+	0.593754i
$704$	4.77964	+	18.1972i	0.180140	+	0.685834i
$705$	−9.10216	+	5.25513i	−0.342807	+	0.197920i
$706$	14.8677	−	11.3889i	0.559552	−	0.428627i
$707$	0.421513	+	4.20695i	0.0158526	+	0.158219i
$708$	6.25023	−	23.1734i	0.234898	−	0.870908i
$709$	−22.2197	+	12.8285i	−0.834477	+	0.481785i	−0.855383	−	0.517996i	$-0.826678\pi$
$709$	−22.2197	+	12.8285i	−0.834477	+	0.481785i	0.0209062	+	0.999781i	$0.493345\pi$
$710$	−0.464490	−	3.55076i	−0.0174320	−	0.133258i
$711$	2.55401	+	1.47456i	0.0957828	+	0.0553002i
$712$	19.1127	−	24.7811i	0.716278	−	0.928709i
$713$		−	29.5956i		−	1.10836i
$714$	13.9966	−	13.1320i	0.523811	−	0.491451i
$715$	−2.85061			−0.106607
$716$	2.70055	−	0.718842i	0.100924	−	0.0268644i
$717$	−1.54681	+	2.67916i	−0.0577668	+	0.100055i
$718$	−0.983624	−	7.51923i	−0.0367085	−	0.280615i
$719$	−11.6722	−	20.2169i	−0.435301	−	0.753964i	0.562019	−	0.827124i	$-0.310025\pi$
$719$	−11.6722	−	20.2169i	−0.435301	−	0.753964i	−0.997320	+	0.0731603i	$0.976692\pi$
$720$	−6.56905	−	3.82157i	−0.244814	−	0.142421i
$721$	8.55297	+	3.85793i	0.318529	+	0.143677i
$722$	10.7299	+	14.0074i	0.399326	+	0.521300i
$723$	−0.483642	−	0.837693i	−0.0179868	−	0.0311541i
$724$	−36.2266	−	36.3462i	−1.34635	−	1.35080i
$725$	4.51588	+	2.60725i	0.167716	+	0.0968307i
$726$	−7.49197	−	3.11051i	−0.278053	−	0.115442i
$727$	−17.2636			−0.640273			−0.320136	−	0.947371i	$-0.603729\pi$
$727$	−17.2636			−0.640273			−0.320136	+	0.947371i	$0.603729\pi$
$728$	4.79588	−	7.69891i	0.177747	−	0.285340i
$729$	−15.5823			−0.577122
$730$	−16.8143	−	6.98094i	−0.622325	−	0.258376i
$731$	−49.1733	−	28.3902i	−1.81874	−	1.05005i
$732$	−1.66652	+	1.66104i	−0.0615965	+	0.0613938i
$733$	−13.4244	−	23.2518i	−0.495843	−	0.858825i	0.504146	−	0.863619i	$-0.331807\pi$
$733$	−13.4244	−	23.2518i	−0.495843	−	0.858825i	−0.999989	+	0.00479386i	$0.998474\pi$
$734$	−18.3876	−	24.0041i	−0.678698	−	0.886007i
$735$	6.96013	+	2.33649i	0.256728	+	0.0861829i
$736$	49.1807	−	6.26876i	1.81283	−	0.231069i
$737$	0.909769	+	1.57577i	0.0335118	+	0.0580441i
$738$	1.11111	+	8.49382i	0.0409007	+	0.312662i
$739$	−6.14064	+	10.6359i	−0.225887	+	0.391248i	−0.956585	−	0.291453i	$-0.905861\pi$
$739$	−6.14064	+	10.6359i	−0.225887	+	0.391248i	0.730698	+	0.682701i	$0.239195\pi$
$740$	3.66157	+	13.7558i	0.134602	+	0.505673i
$741$	−3.24695			−0.119280
$742$	−8.79304	+	29.0770i	−0.322802	+	1.06745i
$743$			24.4507i			0.897009i	0.893781	+	0.448505i	$0.148043\pi$
$743$			24.4507i			0.897009i	−0.893781	+	0.448505i	$0.851957\pi$
$744$	6.11788	−	7.93231i	0.224292	−	0.290812i
$745$	3.67599	+	2.12234i	0.134678	+	0.0777564i
$746$	1.56365	+	11.9532i	0.0572493	+	0.437637i
$747$	−7.36328	+	4.25119i	−0.269408	+	0.155543i
$748$	−22.2098	−	5.99036i	−0.812072	−	0.219029i
$749$	24.1156	+	10.8777i	0.881165	+	0.397461i
$750$	−1.17750	+	0.901991i	−0.0429964	+	0.0329360i
$751$	31.9771	−	18.4620i	1.16686	−	0.673687i	0.213921	−	0.976851i	$-0.431376\pi$
$751$	31.9771	−	18.4620i	1.16686	−	0.673687i	0.952938	+	0.303164i	$0.0980430\pi$
$752$	−34.7793	+	19.9273i	−1.26827	+	0.726674i
$753$	4.87951	−	8.45156i	0.177819	−	0.307992i
$754$	8.25525	+	3.42741i	0.300638	+	0.124819i
$755$		−	1.19778i		−	0.0435918i
$756$	4.42879	−	26.8312i	0.161073	−	0.975841i
$757$		−	14.6178i		−	0.531293i	−0.964071	−	0.265646i	$-0.914415\pi$
$757$		−	14.6178i		−	0.531293i	0.964071	−	0.265646i	$-0.0855854\pi$
$758$	−2.41341	+	5.81294i	−0.0876590	+	0.211135i
$759$	10.8093	−	18.7223i	0.392354	−	0.679577i
$760$	−7.15985	−	0.960622i	−0.259715	−	0.0348454i
$761$	−15.3433	+	8.85843i	−0.556193	+	0.321118i	−0.751616	−	0.659601i	$-0.770725\pi$
$761$	−15.3433	+	8.85843i	−0.556193	+	0.321118i	0.195423	+	0.980719i	$0.437392\pi$
$762$	2.26407	+	2.95563i	0.0820186	+	0.107071i
$763$	12.6848	−	1.27095i	0.459221	−	0.0460115i
$764$	13.6805	+	3.68986i	0.494945	+	0.133495i
$765$	8.04700	−	4.64594i	0.290940	−	0.167974i
$766$	−16.1939	+	2.11839i	−0.585108	+	0.0765406i
$767$	12.0107	+	6.93437i	0.433681	+	0.250386i
$768$	14.4774	+	8.48628i	0.522410	+	0.306222i
$769$		−	3.82227i		−	0.137834i	−0.997622	−	0.0689172i	$-0.978046\pi$
$769$		−	3.82227i		−	0.137834i	0.997622	−	0.0689172i	$-0.0219544\pi$
$770$	−2.00559	−	8.56807i	−0.0722763	−	0.308772i
$771$	−31.5712			−1.13701
$772$	36.7641	−	9.78602i	1.32317	−	0.352207i
$773$	22.2173	−	38.4815i	0.799101	−	1.38408i	−0.121102	−	0.992640i	$-0.538643\pi$
$773$	22.2173	−	38.4815i	0.799101	−	1.38408i	0.920202	−	0.391443i	$-0.128024\pi$
$774$	−30.9321	+	4.04636i	−1.11183	+	0.145443i
$775$	1.68841	+	2.92441i	0.0606493	+	0.105048i
$776$	14.3731	+	34.9438i	0.515964	+	1.25441i
$777$	−16.0347	+	11.5313i	−0.575240	+	0.413681i
$778$	−11.0534	+	8.46708i	−0.396282	+	0.303560i
$779$	4.07131	+	7.05171i	0.145870	+	0.252654i
$780$	−1.80083	+	1.79490i	−0.0644800	+	0.0642678i
$781$	−5.15731	−	2.97758i	−0.184543	−	0.106546i
$782$	−23.2434	+	55.9840i	−0.831182	+	2.00198i
$783$	26.7985			0.957699
$784$	26.5147	+	8.99826i	0.946955	+	0.321366i
$785$	11.0274			0.393584
$786$	−3.10388	+	7.47601i	−0.110712	+	0.266661i
$787$	46.4327	+	26.8079i	1.65515	+	0.955600i	0.974907	+	0.222611i	$0.0714580\pi$
$787$	46.4327	+	26.8079i	1.65515	+	0.955600i	0.680240	+	0.732989i	$0.261875\pi$
$788$	−36.4683	+	36.3483i	−1.29913	+	1.29486i
$789$	−9.23305	−	15.9921i	−0.328705	−	0.569334i
$790$	1.74263	−	1.33489i	0.0620001	−	0.0474933i
$791$	18.8294	−	13.5411i	0.669498	−	0.481466i
$792$	−11.6882	+	4.80759i	−0.415322	+	0.170830i
$793$	−0.679800	−	1.17745i	−0.0241404	−	0.0418124i
$794$	−39.0409	+	5.10711i	−1.38551	+	0.181245i
$795$	4.25759	−	7.37437i	0.151001	−	0.261542i
$796$	−13.0752	+	3.48040i	−0.463437	+	0.123359i
$797$	30.6896			1.08708			0.543541	−	0.839383i	$-0.317083\pi$
$797$	30.6896			1.08708			0.543541	+	0.839383i	$0.317083\pi$
$798$	−2.28443	−	9.75933i	−0.0808681	−	0.345477i
$799$		−	49.0082i		−	1.73379i
$800$	−4.50203	+	3.42516i	−0.159171	+	0.121098i
$801$	18.2057	+	10.5110i	0.643265	+	0.371389i
$802$	−51.1270	+	6.68815i	−1.80536	+	0.236167i
$803$	−26.2198	+	15.1380i	−0.925277	+	0.534209i
$804$	1.56692	+	0.422624i	0.0552610	+	0.0149048i
$805$	−23.0728	+	2.31176i	−0.813208	+	0.0814790i
$806$	3.51997	+	4.59514i	0.123986	+	0.161857i
$807$	−7.45478	+	4.30402i	−0.262421	+	0.151509i
$808$	0.601045	−	4.47979i	0.0211447	−	0.157599i
$809$	−4.24657	+	7.35528i	−0.149302	+	0.258598i	−0.930970	−	0.365097i	$-0.881036\pi$
$809$	−4.24657	+	7.35528i	−0.149302	+	0.258598i	0.781668	+	0.623695i	$0.214369\pi$
$810$	0.167910	−	0.404429i	0.00589977	−	0.0142102i
$811$		−	21.1581i		−	0.742961i	−0.928441	−	0.371480i	$-0.878850\pi$
$811$		−	21.1581i		−	0.742961i	0.928441	−	0.371480i	$-0.121150\pi$
$812$	−4.49364	+	27.2241i	−0.157696	+	0.955379i
$813$			15.5266i			0.544541i
$814$	21.8628	+	9.07697i	0.766290	+	0.318148i
$815$	−6.36400	+	11.0228i	−0.222921	+	0.386111i
$816$	−17.8026	+	10.2002i	−0.623215	+	0.357080i
$817$	−25.6803	+	14.8265i	−0.898441	+	0.518715i
$818$	4.61029	−	3.53157i	0.161195	−	0.123478i
$819$	5.55407	+	2.50524i	0.194075	+	0.0875400i
$820$	6.15620	+	1.66043i	0.214984	+	0.0579846i
$821$	−15.7431	+	9.08930i	−0.549439	+	0.317219i	−0.748896	−	0.662688i	$-0.769416\pi$
$821$	−15.7431	+	9.08930i	−0.549439	+	0.317219i	0.199457	+	0.979907i	$0.436082\pi$
$822$	−2.89937	−	22.1640i	−0.101127	−	0.773057i
$823$	−29.4225	−	16.9871i	−1.02561	−	0.592133i	−0.109883	−	0.993945i	$-0.535048\pi$
$823$	−29.4225	−	16.9871i	−1.02561	−	0.592133i	−0.915723	+	0.401811i	$0.868381\pi$
$824$	−7.94272	−	6.12591i	−0.276698	−	0.213406i
$825$			2.46666i			0.0858780i
$826$	−12.3923	+	40.9792i	−0.431184	+	1.42585i
$827$	−29.9169			−1.04031			−0.520157	−	0.854071i	$-0.674126\pi$
$827$	−29.9169			−1.04031			−0.520157	+	0.854071i	$0.674126\pi$
$828$	8.56659	+	32.1830i	0.297709	+	1.11844i
$829$	7.84211	−	13.5829i	0.272368	−	0.471755i	−0.697100	−	0.716974i	$-0.745527\pi$
$829$	7.84211	−	13.5829i	0.272368	−	0.471755i	0.969468	+	0.245219i	$0.0788600\pi$
$830$	0.820890	+	6.27523i	0.0284935	+	0.217816i
$831$	−3.34921	−	5.80099i	−0.116183	−	0.201234i
$832$	−6.89045	+	6.82266i	−0.238883	+	0.236533i
$833$	−25.6623	+	22.6589i	−0.889148	+	0.785083i
$834$	−13.7776	−	17.9860i	−0.477079	−	0.622803i
$835$	7.52802	+	13.0389i	0.260518	+	0.451230i
$836$	−8.50872	+	8.48073i	−0.294280	+	0.293312i
$837$	15.0292	+	8.67711i	0.519485	+	0.299925i
$838$	52.0509	+	21.6104i	1.79807	+	0.746520i
$839$	10.8159			0.373405			0.186702	−	0.982417i	$-0.440220\pi$
$839$	10.8159			0.373405			0.186702	+	0.982417i	$0.440220\pi$
$840$	−6.66192	−	4.14991i	−0.229858	−	0.143185i
$841$	1.80909			0.0623823
$842$	−13.4002	−	5.56347i	−0.461800	−	0.191730i
$843$	11.1323	+	6.42722i	0.383416	+	0.221365i
$844$	−20.8355	−	20.9043i	−0.717189	−	0.719556i
$845$	5.76541	+	9.98599i	0.198336	+	0.343529i
$846$	−16.3736	−	21.3749i	−0.562936	−	0.734885i
$847$	13.1899	+	5.94947i	0.453210	+	0.204426i
$848$	16.3300	−	28.0704i	0.560776	−	0.963941i
$849$	8.83799	+	15.3078i	0.303319	+	0.525364i
$850$	−0.897115	−	6.85792i	−0.0307708	−	0.235225i
$851$	31.1897	−	54.0221i	1.06917	−	1.85185i
$852$	−5.13289	+	1.36629i	−0.175850	+	0.0468084i
$853$	37.5530			1.28579			0.642894	−	0.765955i	$-0.277733\pi$
$853$	37.5530			1.28579			0.642894	+	0.765955i	$0.277733\pi$
$854$	3.06077	−	2.87168i	0.104737	−	0.0982669i
$855$		−	4.85260i		−	0.165955i
$856$	−22.3950	−	17.2724i	−0.765444	−	0.590358i
$857$	4.42892	+	2.55704i	0.151289	+	0.0873467i	0.573733	−	0.819042i	$-0.305495\pi$
$857$	4.42892	+	2.55704i	0.151289	+	0.0873467i	−0.422444	+	0.906389i	$0.638828\pi$
$858$	0.548442	+	4.19252i	0.0187235	+	0.143130i
$859$	−29.0706	+	16.7839i	−0.991876	+	0.572660i	−0.905835	−	0.423631i	$-0.860755\pi$
$859$	−29.0706	+	16.7839i	−0.991876	+	0.572660i	−0.0860417	+	0.996292i	$0.527422\pi$
$860$	−6.04680	+	22.4191i	−0.206194	+	0.764485i
$861$	0.881986	+	8.80274i	0.0300580	+	0.299997i
$862$	17.7561	−	13.6015i	0.604773	−	0.463268i
$863$	−12.8472	+	7.41734i	−0.437324	+	0.252489i	−0.702462	−	0.711721i	$-0.747916\pi$
$863$	−12.8472	+	7.41734i	−0.437324	+	0.252489i	0.265138	+	0.964210i	$0.414582\pi$
$864$	−11.2359	+	26.8129i	−0.382253	+	0.912192i
$865$	−6.09623	+	10.5590i	−0.207278	+	0.359016i
$866$	−42.7908	−	17.7659i	−1.45409	−	0.603708i
$867$		−	7.25579i		−	0.246419i
$868$	−11.3351	+	13.8129i	−0.384737	+	0.468841i
$869$		−	3.65050i		−	0.123835i
$870$	2.96576	−	7.14333i	0.100549	−	0.242181i
$871$	−0.468884	+	0.812130i	−0.0158875	+	0.0275180i
$872$	−13.5075	−	1.81228i	−0.457422	−	0.0613714i
$873$	−21.9805	+	12.6905i	−0.743929	+	0.429507i
$874$	19.2508	+	25.1309i	0.651167	+	0.850066i
$875$	2.14799	−	1.54472i	0.0726153	−	0.0522209i
$876$	−7.03221	+	26.0726i	−0.237596	+	0.880912i
$877$	19.7181	−	11.3843i	0.665833	−	0.384419i	−0.128663	−	0.991688i	$-0.541069\pi$
$877$	19.7181	−	11.3843i	0.665833	−	0.384419i	0.794496	+	0.607270i	$0.207735\pi$
$878$	−0.566658	+	0.0741271i	−0.0191238	+	0.00250167i
$879$	−24.5626	−	14.1812i	−0.828476	−	0.478321i
$880$	−0.0310041	+	9.40719i	−0.00104515	+	0.317116i
$881$			46.0172i			1.55036i	0.631742	+	0.775179i	$0.282340\pi$
$881$			46.0172i			1.55036i	−0.631742	+	0.775179i	$0.717660\pi$
$882$	−3.62233	+	18.4564i	−0.121970	+	0.621460i
$883$	−48.2392			−1.62338			−0.811689	−	0.584090i	$-0.801452\pi$
$883$	−48.2392			−1.62338			−0.811689	+	0.584090i	$0.801452\pi$
$884$	−3.04961	−	11.4568i	−0.102570	−	0.385334i
$885$	6.00037	−	10.3929i	0.201700	−	0.349355i
$886$	−45.3378	+	5.93084i	−1.52315	+	0.199251i
$887$	26.5340	+	45.9583i	0.890926	+	1.54313i	0.838767	+	0.544490i	$0.183277\pi$
$887$	26.5340	+	45.9583i	0.890926	+	1.54313i	0.0521586	+	0.998639i	$0.483390\pi$
$888$	19.5268	−	8.03178i	0.655277	−	0.269529i
$889$	−3.87736	−	5.39162i	−0.130043	−	0.180829i
$890$	12.4220	−	9.51545i	0.416385	−	0.318959i
$891$	−0.364110	−	0.630656i	−0.0121981	−	0.0211278i
$892$	−20.4048	−	20.4722i	−0.683203	−	0.685459i
$893$	−22.1651	−	12.7970i	−0.741728	−	0.428237i
$894$	2.41417	−	5.81477i	0.0807420	−	0.194475i
$895$	1.39729			0.0467063
$896$	−25.3547	−	15.9104i	−0.847040	−	0.531529i
$897$	11.1420			0.372020
$898$	2.66716	−	6.42411i	0.0890042	−	0.214375i
$899$	−15.2493	−	8.80418i	−0.508592	−	0.293636i
$900$	−2.68250	−	2.69136i	−0.0894167	−	0.0897118i
$901$	19.8527	+	34.3859i	0.661389	+	1.14556i
$902$	8.41762	−	6.44805i	0.280276	−	0.214697i
$903$	−32.0571	+	3.21194i	−1.06679	+	0.106887i
$904$	−22.9303	+	9.43169i	−0.762649	+	0.313693i
$905$	−12.8292	−	22.2208i	−0.426457	−	0.738645i
$906$	−1.76163	+	0.230447i	−0.0585264	+	0.00765609i
$907$	19.4872	−	33.7529i	0.647063	−	1.12075i	−0.336758	−	0.941591i	$-0.609330\pi$
$907$	19.4872	−	33.7529i	0.647063	−	1.12075i	0.983821	−	0.179155i	$-0.0573364\pi$
$908$	2.36339	+	8.87879i	0.0784318	+	0.294653i
$909$	3.03619			0.100704
$910$	3.30743	−	3.10311i	0.109640	−	0.102867i
$911$		−	23.8599i		−	0.790512i	−0.918571	−	0.395256i	$-0.870656\pi$
$911$		−	23.8599i		−	0.790512i	0.918571	−	0.395256i	$-0.129344\pi$
$912$	−0.0353148	+	10.7151i	−0.00116939	+	0.354813i
$913$	9.11448	+	5.26225i	0.301645	+	0.174155i
$914$	30.1409	−	3.94286i	0.996972	−	0.130418i
$915$	−1.01886	+	0.588237i	−0.0336823	+	0.0194465i
$916$	6.81322	−	25.2607i	0.225115	−	0.834638i
$917$	5.93680	−	13.1618i	0.196050	−	0.434641i
$918$	−21.6150	−	28.2173i	−0.713402	−	0.931311i
$919$	−23.6619	+	13.6612i	−0.780535	+	0.450642i	−0.836620	−	0.547784i	$-0.815472\pi$
$919$	−23.6619	+	13.6612i	−0.780535	+	0.450642i	0.0560847	+	0.998426i	$0.482138\pi$
$920$	24.5692	+	3.29640i	0.810022	+	0.108679i
$921$	−1.74285	+	3.01871i	−0.0574290	+	0.0994699i
$922$	−15.1276	+	36.4363i	−0.498201	+	1.19997i
$923$		−	3.06921i		−	0.101024i
$924$	−12.2156	+	4.59815i	−0.401863	+	0.151268i
$925$			7.11740i			0.234019i
$926$	50.8525	+	21.1129i	1.67112	+	0.693814i
$927$	3.36895	−	5.83520i	0.110651	−	0.191653i
$928$	11.4004	−	27.2055i	0.374237	−	0.893064i
$929$	14.1805	−	8.18709i	0.465246	−	0.268610i	−0.249002	−	0.968503i	$-0.580102\pi$
$929$	14.1805	−	8.18709i	0.465246	−	0.268610i	0.714247	+	0.699893i	$0.246769\pi$
$930$	3.97621	−	3.04585i	0.130385	−	0.0998775i
$931$	3.54704	+	17.5231i	0.116250	+	0.574296i
$932$	10.8674	−	40.2919i	0.355972	−	1.31980i
$933$	31.4164	−	18.1382i	1.02853	−	0.593820i
$934$	4.58765	+	35.0699i	0.150113	+	1.14752i
$935$	−9.96081	−	5.75088i	−0.325753	−	0.188074i
$936$	−5.15779	−	3.97800i	−0.168588	−	0.130025i
$937$			9.65373i			0.315374i	0.987489	+	0.157687i	$0.0504036\pi$
$937$			9.65373i			0.315374i	−0.987489	+	0.157687i	$0.949596\pi$
$938$	−2.77090	−	0.837935i	−0.0904732	−	0.0273595i
$939$	15.1791			0.495352
$940$	−19.3674	+	5.15529i	−0.631696	+	0.168147i
$941$	−14.1753	+	24.5524i	−0.462103	+	0.800385i	−0.999066	−	0.0432207i	$-0.986238\pi$
$941$	−14.1753	+	24.5524i	−0.462103	+	0.800385i	0.536963	+	0.843606i	$0.319571\pi$
$942$	−2.12161	−	16.2185i	−0.0691257	−	0.528426i
$943$	−13.9708	−	24.1981i	−0.454951	−	0.787999i
$944$	23.0145	−	39.5605i	0.749057	−	1.28759i
$945$	5.59074	−	12.3946i	0.181867	−	0.403196i
$946$	23.4820	+	30.6546i	0.763465	+	0.996666i
$947$	−1.38549	−	2.39973i	−0.0450223	−	0.0779808i	0.842636	−	0.538483i	$-0.181003\pi$
$947$	−1.38549	−	2.39973i	−0.0450223	−	0.0779808i	−0.887658	+	0.460503i	$0.847669\pi$
$948$	−2.29856	−	2.30614i	−0.0746536	−	0.0749001i
$949$	−13.5134	−	7.80194i	−0.438662	−	0.253262i
$950$	−3.33591	−	1.38500i	−0.108231	−	0.0449354i
$951$	−15.9210			−0.516272
$952$	32.2900	−	17.2268i	1.04652	−	0.558323i
$953$	−10.6334			−0.344451			−0.172225	−	0.985058i	$-0.555096\pi$
$953$	−10.6334			−0.344451			−0.172225	+	0.985058i	$0.555096\pi$
$954$	20.1470	+	8.36463i	0.652284	+	0.270815i
$955$	6.13554	+	3.54235i	0.198541	+	0.114628i
$956$	−4.17821	+	4.16447i	−0.135133	+	0.134688i
$957$	−6.43118	−	11.1391i	−0.207891	−	0.360077i
$958$	7.39529	+	9.65419i	0.238931	+	0.311913i
$959$	3.97497	+	39.6726i	0.128359	+	1.28109i
$960$	5.90370	+	5.96236i	0.190541	+	0.192434i
$961$	9.79857	+	16.9716i	0.316083	+	0.547472i
$962$	1.58250	+	12.0973i	0.0510218	+	0.390032i
$963$	9.49896	−	16.4527i	0.306100	−	0.530180i
$964$	−0.474454	−	1.78243i	−0.0152811	−	0.0574082i
$965$	19.0222			0.612345
$966$	7.83909	+	33.4894i	0.252219	+	1.07750i
$967$		−	7.65003i		−	0.246008i	−0.992406	−	0.123004i	$-0.960747\pi$
$967$		−	7.65003i		−	0.246008i	0.992406	−	0.123004i	$-0.0392528\pi$
$968$	−12.2488	−	9.44702i	−0.393691	−	0.303639i
$969$	−11.3457	−	6.55046i	−0.364477	−	0.210431i
$970$	2.45049	+	18.7325i	0.0786804	+	0.601466i
$971$	26.8992	−	15.5302i	0.863235	−	0.498389i	−0.00185907	−	0.999998i	$-0.500592\pi$
$971$	26.8992	−	15.5302i	0.863235	−	0.498389i	0.865094	+	0.501609i	$0.167258\pi$
$972$	−30.3986	−	8.19900i	−0.975036	−	0.262983i
$973$	23.5950	+	32.8098i	0.756421	+	1.05183i
$974$	16.7495	−	12.8304i	0.536687	−	0.411112i
$975$	−1.10097	+	0.635642i	−0.0352591	+	0.0203569i
$976$	−3.89304	+	2.23057i	−0.124613	+	0.0713989i
$977$	2.12922	−	3.68791i	0.0681197	−	0.117987i	−0.829954	−	0.557832i	$-0.811633\pi$
$977$	2.12922	−	3.68791i	0.0681197	−	0.117987i	0.898074	+	0.439845i	$0.144967\pi$
$978$	17.4361	+	7.23910i	0.557544	+	0.231481i
$979$		−	26.0217i		−	0.831658i
$980$	11.6540	+	7.75789i	0.372273	+	0.247817i
$981$		−	9.15474i		−	0.292288i
$982$	2.12584	−	5.12029i	0.0678382	−	0.163395i
$983$	3.78011	−	6.54734i	0.120567	−	0.208828i	−0.799425	−	0.600767i	$-0.794862\pi$
$983$	3.78011	−	6.54734i	0.120567	−	0.208828i	0.919991	+	0.391939i	$0.128195\pi$
$984$	1.25764	−	9.37365i	0.0400922	−	0.298821i
$985$	−22.2955	+	12.8723i	−0.710393	+	0.410146i
$986$	21.9315	+	28.6306i	0.698443	+	0.911783i
$987$	−16.2354	−	22.5759i	−0.516778	−	0.718599i
$988$	−5.97792	−	1.61234i	−0.190183	−	0.0512955i
$989$	88.1226	−	50.8776i	2.80214	−	1.61781i
$990$	−6.26577	+	0.819652i	−0.199139	+	0.0260503i
$991$	−36.3263	−	20.9730i	−1.15394	−	0.666229i	−0.204097	−	0.978951i	$-0.565426\pi$
$991$	−36.3263	−	20.9730i	−1.15394	−	0.666229i	−0.949845	+	0.312722i	$0.898759\pi$
$992$	15.2025	−	11.5661i	0.482680	−	0.367224i
$993$		−	17.2655i		−	0.547903i
$994$	9.22510	−	2.15938i	0.292602	−	0.0684915i
$995$	−6.76522			−0.214472
$996$	9.07133	−	2.41464i	0.287436	−	0.0765108i
$997$	−7.07310	+	12.2510i	−0.224007	+	0.387992i	−0.956021	−	0.293298i	$-0.905247\pi$
$997$	−7.07310	+	12.2510i	−0.224007	+	0.387992i	0.732014	+	0.681290i	$0.238581\pi$
$998$	16.0137	−	2.09483i	0.506906	−	0.0663106i
$999$	18.2890	+	31.6774i	0.578637	+	1.00223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.f.171.7	yes	24
4.3	odd	2		1120.2.bz.e.591.10		24
7.5	odd	6		280.2.bj.e.131.1	✓	24
8.3	odd	2		280.2.bj.e.171.1	yes	24
8.5	even	2		1120.2.bz.f.591.10		24
28.19	even	6		1120.2.bz.f.271.10		24
56.5	odd	6		1120.2.bz.e.271.10		24
56.19	even	6	inner	280.2.bj.f.131.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.1	✓	24	7.5	odd	6
280.2.bj.e.171.1	yes	24	8.3	odd	2
280.2.bj.f.131.7	yes	24	56.19	even	6	inner
280.2.bj.f.171.7	yes	24	1.1	even	1	trivial
1120.2.bz.e.271.10		24	56.5	odd	6
1120.2.bz.e.591.10		24	4.3	odd	2
1120.2.bz.f.271.10		24	28.19	even	6
1120.2.bz.f.591.10		24	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.542272 - 1.30612i) q^{2} +(-0.908317 - 0.524417i) q^{3} +(-1.41188 - 1.41654i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.17750 + 0.901991i) q^{6} +(2.14799 - 1.54472i) q^{7} +(-2.61579 + 1.07593i) q^{8} +(-0.949974 - 1.64540i) q^{9} +O(q^{10})\)	\(q+(0.542272 - 1.30612i) q^{2} +(-0.908317 - 0.524417i) q^{3} +(-1.41188 - 1.41654i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.17750 + 0.901991i) q^{6} +(2.14799 - 1.54472i) q^{7} +(-2.61579 + 1.07593i) q^{8} +(-0.949974 - 1.64540i) q^{9} +(-1.40227 + 0.183437i) q^{10} +(-1.17590 + 2.03673i) q^{11} +(0.539577 + 2.02708i) q^{12} -1.21209 q^{13} +(-0.852784 - 3.64318i) q^{14} +1.04883i q^{15} +(-0.0131831 + 3.99998i) q^{16} +(-4.23538 - 2.44530i) q^{17} +(-2.66423 + 0.348520i) q^{18} +(-2.21189 + 1.27704i) q^{19} +(-0.520821 + 1.93100i) q^{20} +(-2.76113 + 0.276650i) q^{21} +(2.02254 + 2.64033i) q^{22} +(7.59015 - 4.38218i) q^{23} +(2.94021 + 0.394481i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.657285 + 1.58314i) q^{26} +5.13923i q^{27} +(-5.22086 - 0.861760i) q^{28} -5.21449i q^{29} +(1.36990 + 0.568754i) q^{30} +(1.68841 - 2.92441i) q^{31} +(5.21729 + 2.18630i) q^{32} +(2.13619 - 1.23333i) q^{33} +(-5.49058 + 4.20589i) q^{34} +(-2.41176 - 1.08785i) q^{35} +(-0.989532 + 3.66879i) q^{36} +(6.16385 - 3.55870i) q^{37} +(0.468510 + 3.58149i) q^{38} +(1.10097 + 0.635642i) q^{39} +(2.23968 + 1.72738i) q^{40} -3.18809i q^{41} +(-1.13595 + 3.75638i) q^{42} +11.6101 q^{43} +(4.54535 - 1.20990i) q^{44} +(-0.949974 + 1.64540i) q^{45} +(-1.60770 - 12.2900i) q^{46} +(5.01045 + 8.67836i) q^{47} +(2.10963 - 3.62633i) q^{48} +(2.22771 - 6.63606i) q^{49} +(0.859994 + 1.12268i) q^{50} +(2.56471 + 4.44221i) q^{51} +(1.71133 + 1.71698i) q^{52} +(-7.03102 - 4.05936i) q^{53} +(6.71244 + 2.78686i) q^{54} +2.35181 q^{55} +(-3.95669 + 6.35174i) q^{56} +2.67880 q^{57} +(-6.81073 - 2.82767i) q^{58} +(-9.90904 - 5.72099i) q^{59} +(1.48572 - 1.48083i) q^{60} +(0.560848 + 0.971417i) q^{61} +(-2.90404 - 3.79108i) q^{62} +(-4.58221 - 2.06687i) q^{63} +(5.68475 - 5.62882i) q^{64} +(0.606047 + 1.04970i) q^{65} +(-0.452475 - 3.45891i) q^{66} +(0.386838 - 0.670023i) q^{67} +(2.51599 + 9.45207i) q^{68} -9.19235 q^{69} +(-2.72869 + 2.56012i) q^{70} +2.53216i q^{71} +(4.25527 + 3.28193i) q^{72} +(11.1488 + 6.43675i) q^{73} +(-1.30559 - 9.98048i) q^{74} +(0.908317 - 0.524417i) q^{75} +(4.93190 + 1.33021i) q^{76} +(0.620335 + 6.19130i) q^{77} +(1.42725 - 1.09330i) q^{78} +(-1.34425 + 0.776104i) q^{79} +(3.47067 - 1.98857i) q^{80} +(-0.154821 + 0.268158i) q^{81} +(-4.16402 - 1.72882i) q^{82} -4.47506i q^{83} +(4.29027 + 3.52066i) q^{84} +4.89060i q^{85} +(6.29585 - 15.1642i) q^{86} +(-2.73457 + 4.73641i) q^{87} +(0.884549 - 6.59285i) q^{88} +(-9.58219 + 5.53228i) q^{89} +(1.63394 + 2.13303i) q^{90} +(-2.60356 + 1.87234i) q^{91} +(-16.9239 - 4.56466i) q^{92} +(-3.06722 + 1.77086i) q^{93} +(14.0520 - 1.83820i) q^{94} +(2.21189 + 1.27704i) q^{95} +(-3.59242 - 4.72189i) q^{96} -13.3588i q^{97} +(-7.45945 - 6.50820i) q^{98} +4.46831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

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