LMFDB - Embedded newform 504.2.y.a.173.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.12
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31489 + 0.520628i) q^{2} +(1.30232 - 1.14191i) q^{3} +(1.45789 - 1.36914i) q^{4} -1.77147i q^{5} +(-1.11790 + 2.17952i) q^{6} +(1.98439 - 1.74991i) q^{7} +(-1.20416 + 2.55930i) q^{8} +(0.392079 - 2.97427i) q^{9} +O(q^{10})$	\(q+(-1.31489 + 0.520628i) q^{2} +(1.30232 - 1.14191i) q^{3} +(1.45789 - 1.36914i) q^{4} -1.77147i q^{5} +(-1.11790 + 2.17952i) q^{6} +(1.98439 - 1.74991i) q^{7} +(-1.20416 + 2.55930i) q^{8} +(0.392079 - 2.97427i) q^{9} +(0.922278 + 2.32930i) q^{10} +1.15601 q^{11} +(0.335208 - 3.44785i) q^{12} +(3.00278 + 5.20096i) q^{13} +(-1.69821 + 3.33408i) q^{14} +(-2.02286 - 2.30703i) q^{15} +(0.250907 - 3.99212i) q^{16} +(-2.28549 - 3.95859i) q^{17} +(1.03294 + 4.11498i) q^{18} +(-0.116580 + 0.201923i) q^{19} +(-2.42540 - 2.58262i) q^{20} +(0.586073 - 4.54494i) q^{21} +(-1.52003 + 0.601850i) q^{22} -0.574823i q^{23} +(1.35428 + 4.70807i) q^{24} +1.86188 q^{25} +(-6.65610 - 5.27539i) q^{26} +(-2.88574 - 4.32117i) q^{27} +(0.497158 - 5.26810i) q^{28} +(-3.92998 + 6.80693i) q^{29} +(3.86095 + 1.98034i) q^{30} +(-2.75720 - 1.59187i) q^{31} +(1.74849 + 5.37985i) q^{32} +(1.50549 - 1.32006i) q^{33} +(5.06613 + 4.01523i) q^{34} +(-3.09992 - 3.51530i) q^{35} +(-3.50058 - 4.87298i) q^{36} +(-4.32149 - 2.49501i) q^{37} +(0.0481641 - 0.326203i) q^{38} +(9.84962 + 3.34442i) q^{39} +(4.53372 + 2.13314i) q^{40} +(-3.82260 - 6.62094i) q^{41} +(1.59560 + 6.28125i) q^{42} +(-1.68826 - 0.974718i) q^{43} +(1.68534 - 1.58274i) q^{44} +(-5.26884 - 0.694557i) q^{45} +(0.299269 + 0.755831i) q^{46} +(6.16558 + 10.6791i) q^{47} +(-4.23189 - 5.48554i) q^{48} +(0.875624 - 6.94502i) q^{49} +(-2.44818 + 0.969348i) q^{50} +(-7.49680 - 2.54552i) q^{51} +(11.4986 + 3.47122i) q^{52} +(-3.05829 - 5.29711i) q^{53} +(6.04416 + 4.17949i) q^{54} -2.04784i q^{55} +(2.08901 + 7.18582i) q^{56} +(0.0787533 + 0.396093i) q^{57} +(1.62364 - 10.9965i) q^{58} +(5.79859 + 3.34782i) q^{59} +(-6.10776 - 0.593812i) q^{60} +(3.50504 + 6.07091i) q^{61} +(4.45419 + 0.657665i) q^{62} +(-4.42667 - 6.58822i) q^{63} +(-5.09998 - 6.16362i) q^{64} +(9.21336 - 5.31934i) q^{65} +(-1.29231 + 2.51954i) q^{66} +(4.17486 + 2.41036i) q^{67} +(-8.75187 - 2.64204i) q^{68} +(-0.656396 - 0.748604i) q^{69} +(5.90623 + 3.00834i) q^{70} -5.51692i q^{71} +(7.13990 + 4.58495i) q^{72} +(11.7060 - 6.75848i) q^{73} +(6.98127 + 1.03079i) q^{74} +(2.42477 - 2.12611i) q^{75} +(0.106500 + 0.453998i) q^{76} +(2.29397 - 2.02291i) q^{77} +(-14.6924 + 0.730428i) q^{78} +(4.44641 + 7.70141i) q^{79} +(-7.07194 - 0.444475i) q^{80} +(-8.69255 - 2.33229i) q^{81} +(8.47336 + 6.71568i) q^{82} +(4.57377 + 2.64067i) q^{83} +(-5.36824 - 7.42846i) q^{84} +(-7.01253 + 4.04869i) q^{85} +(2.72735 + 0.402696i) q^{86} +(2.65481 + 13.3525i) q^{87} +(-1.39202 + 2.95857i) q^{88} +(-2.72029 + 4.71168i) q^{89} +(7.28957 - 1.82983i) q^{90} +(15.0599 + 5.06616i) q^{91} +(-0.787013 - 0.838030i) q^{92} +(-5.40853 + 1.07535i) q^{93} +(-13.6669 - 10.8319i) q^{94} +(0.357702 + 0.206519i) q^{95} +(8.42041 + 5.00966i) q^{96} +(-9.03187 - 5.21455i) q^{97} +(2.46442 + 9.58784i) q^{98} +(0.453246 - 3.43828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.31489	+	0.520628i	−0.929771	+	0.368139i
$2$	−1.31489	+	0.520628i	−0.929771	+	0.368139i
$3$	1.30232	−	1.14191i	0.751895	−	0.659283i
$3$	1.30232	−	1.14191i	0.751895	−	0.659283i
$4$	1.45789	−	1.36914i	0.728947	−	0.684570i
$5$		−	1.77147i		−	0.792227i	−0.918202	−	0.396113i	$-0.870359\pi$
$5$		−	1.77147i		−	0.792227i	0.918202	−	0.396113i	$-0.129641\pi$
$6$	−1.11790	+	2.17952i	−0.456382	+	0.889784i
$7$	1.98439	−	1.74991i	0.750030	−	0.661404i
$7$	1.98439	−	1.74991i	0.750030	−	0.661404i
$8$	−1.20416	+	2.55930i	−0.425736	+	0.904847i
$9$	0.392079	−	2.97427i	0.130693	−	0.991423i
$10$	0.922278	+	2.32930i	0.291650	+	0.736589i
$11$	1.15601			0.348550			0.174275	−	0.984697i	$-0.444242\pi$
$11$	1.15601			0.348550			0.174275	+	0.984697i	$0.444242\pi$
$12$	0.335208	−	3.44785i	0.0967662	−	0.995307i
$13$	3.00278	+	5.20096i	0.832821	+	1.44249i	0.895793	+	0.444472i	$0.146609\pi$
$13$	3.00278	+	5.20096i	0.832821	+	1.44249i	−0.0629721	+	0.998015i	$0.520058\pi$
$14$	−1.69821	+	3.33408i	−0.453867	+	0.891070i
$15$	−2.02286	−	2.30703i	−0.522301	−	0.595672i
$16$	0.250907	−	3.99212i	0.0627267	−	0.998031i
$17$	−2.28549	−	3.95859i	−0.554313	−	0.960099i	−0.997957	−	0.0638952i	$-0.979648\pi$
$17$	−2.28549	−	3.95859i	−0.554313	−	0.960099i	0.443643	−	0.896203i	$-0.353686\pi$
$18$	1.03294	+	4.11498i	0.243467	+	0.969909i
$19$	−0.116580	+	0.201923i	−0.0267454	+	0.0463244i	−0.879088	−	0.476659i	$-0.841848\pi$
$19$	−0.116580	+	0.201923i	−0.0267454	+	0.0463244i	0.852343	+	0.522983i	$0.175181\pi$
$20$	−2.42540	−	2.58262i	−0.542335	−	0.577491i
$21$	0.586073	−	4.54494i	0.127892	−	0.991788i
$22$	−1.52003	+	0.601850i	−0.324071	+	0.128315i
$23$		−	0.574823i		−	0.119859i	−0.998203	−	0.0599294i	$-0.980912\pi$
$23$		−	0.574823i		−	0.119859i	0.998203	−	0.0599294i	$-0.0190876\pi$
$24$	1.35428	+	4.70807i	0.276441	+	0.961031i
$25$	1.86188			0.372377
$26$	−6.65610	−	5.27539i	−1.30537	−	1.03459i
$27$	−2.88574	−	4.32117i	−0.555361	−	0.831610i
$28$	0.497158	−	5.26810i	0.0939540	−	0.995577i
$29$	−3.92998	+	6.80693i	−0.729780	+	1.26402i	0.227197	+	0.973849i	$0.427044\pi$
$29$	−3.92998	+	6.80693i	−0.729780	+	1.26402i	−0.956976	+	0.290166i	$0.906289\pi$
$30$	3.86095	+	1.98034i	0.704911	+	0.361558i
$31$	−2.75720	−	1.59187i	−0.495207	−	0.285908i	0.231525	−	0.972829i	$-0.425629\pi$
$31$	−2.75720	−	1.59187i	−0.495207	−	0.285908i	−0.726732	+	0.686921i	$0.758962\pi$
$32$	1.74849	+	5.37985i	0.309093	+	0.951032i
$33$	1.50549	−	1.32006i	0.262073	−	0.229793i
$34$	5.06613	+	4.01523i	0.868834	+	0.688607i
$35$	−3.09992	−	3.51530i	−0.523982	−	0.594194i
$36$	−3.50058	−	4.87298i	−0.583431	−	0.812163i
$37$	−4.32149	−	2.49501i	−0.710448	−	0.410178i	0.100779	−	0.994909i	$-0.467867\pi$
$37$	−4.32149	−	2.49501i	−0.710448	−	0.410178i	−0.811227	+	0.584731i	$0.801200\pi$
$38$	0.0481641	−	0.326203i	0.00781325	−	0.0529171i
$39$	9.84962	+	3.34442i	1.57720	+	0.535535i
$40$	4.53372	+	2.13314i	0.716844	+	0.337279i
$41$	−3.82260	−	6.62094i	−0.596990	−	1.03402i	−0.993263	−	0.115884i	$-0.963030\pi$
$41$	−3.82260	−	6.62094i	−0.596990	−	1.03402i	0.396273	−	0.918133i	$-0.370303\pi$
$42$	1.59560	+	6.28125i	0.246207	+	0.969217i
$43$	−1.68826	−	0.974718i	−0.257457	−	0.148643i	0.365717	−	0.930726i	$-0.380824\pi$
$43$	−1.68826	−	0.974718i	−0.257457	−	0.148643i	−0.623174	+	0.782083i	$0.714157\pi$
$44$	1.68534	−	1.58274i	0.254074	−	0.238607i
$45$	−5.26884	−	0.694557i	−0.785432	−	0.103538i
$46$	0.299269	+	0.755831i	0.0441248	+	0.111441i
$47$	6.16558	+	10.6791i	0.899342	+	1.55771i	0.828337	+	0.560230i	$0.189287\pi$
$47$	6.16558	+	10.6791i	0.899342	+	1.55771i	0.0710050	+	0.997476i	$0.477379\pi$
$48$	−4.23189	−	5.48554i	−0.610820	−	0.791769i
$49$	0.875624	−	6.94502i	0.125089	−	0.992146i
$50$	−2.44818	+	0.969348i	−0.346225	+	0.137087i
$51$	−7.49680	−	2.54552i	−1.04976	−	0.356445i
$52$	11.4986	+	3.47122i	1.59457	+	0.481372i
$53$	−3.05829	−	5.29711i	−0.420088	−	0.727613i	0.575860	−	0.817548i	$-0.304667\pi$
$53$	−3.05829	−	5.29711i	−0.420088	−	0.727613i	−0.995948	+	0.0899350i	$0.971334\pi$
$54$	6.04416	+	4.17949i	0.822506	+	0.568756i
$55$		−	2.04784i		−	0.276130i
$56$	2.08901	+	7.18582i	0.279155	+	0.960246i
$57$	0.0787533	+	0.396093i	0.0104311	+	0.0524639i
$58$	1.62364	−	10.9965i	0.213194	−	1.44391i
$59$	5.79859	+	3.34782i	0.754913	+	0.435849i	0.827466	−	0.561515i	$-0.189781\pi$
$59$	5.79859	+	3.34782i	0.754913	+	0.435849i	−0.0725535	+	0.997365i	$0.523115\pi$
$60$	−6.10776	−	0.593812i	−0.788509	−	0.0766608i
$61$	3.50504	+	6.07091i	0.448775	+	0.777301i	0.998307	−	0.0581720i	$-0.0185272\pi$
$61$	3.50504	+	6.07091i	0.448775	+	0.777301i	−0.549532	+	0.835473i	$0.685194\pi$
$62$	4.45419	+	0.657665i	0.565683	+	0.0835236i
$63$	−4.42667	−	6.58822i	−0.557708	−	0.830037i
$64$	−5.09998	−	6.16362i	−0.637498	−	0.770452i
$65$	9.21336	−	5.31934i	1.14278	−	0.659783i
$66$	−1.29231	+	2.51954i	−0.159072	+	0.310134i
$67$	4.17486	+	2.41036i	0.510040	+	0.294472i	0.732850	−	0.680390i	$-0.238190\pi$
$67$	4.17486	+	2.41036i	0.510040	+	0.294472i	−0.222810	+	0.974862i	$0.571523\pi$
$68$	−8.75187	−	2.64204i	−1.06132	−	0.320394i
$69$	−0.656396	−	0.748604i	−0.0790208	−	0.0901213i
$70$	5.90623	+	3.00834i	0.705929	+	0.359565i
$71$		−	5.51692i		−	0.654739i	−0.944896	−	0.327369i	$-0.893838\pi$
$71$		−	5.51692i		−	0.654739i	0.944896	−	0.327369i	$-0.106162\pi$
$72$	7.13990	+	4.58495i	0.841446	+	0.540341i
$73$	11.7060	−	6.75848i	1.37009	−	0.791020i	0.379148	−	0.925336i	$-0.376217\pi$
$73$	11.7060	−	6.75848i	1.37009	−	0.791020i	0.990939	+	0.134316i	$0.0428837\pi$
$74$	6.98127	+	1.03079i	0.811557	+	0.119827i
$75$	2.42477	−	2.12611i	0.279988	−	0.245502i
$76$	0.106500	+	0.453998i	0.0122163	+	0.0520771i
$77$	2.29397	−	2.02291i	0.261423	−	0.230532i
$78$	−14.6924	+	0.730428i	−1.66359	+	0.0827047i
$79$	4.44641	+	7.70141i	0.500260	+	0.866476i	1.00000		0.000300263i	$9.55766e-5\pi$
$79$	4.44641	+	7.70141i	0.500260	+	0.866476i	−0.499740	+	0.866175i	$0.666571\pi$
$80$	−7.07194	−	0.444475i	−0.790667	−	0.0496938i
$81$	−8.69255	−	2.33229i	−0.965839	−	0.259144i
$82$	8.47336	+	6.71568i	0.935726	+	0.741623i
$83$	4.57377	+	2.64067i	0.502036	+	0.289851i	0.729554	−	0.683923i	$-0.239728\pi$
$83$	4.57377	+	2.64067i	0.502036	+	0.289851i	−0.227518	+	0.973774i	$0.573061\pi$
$84$	−5.36824	−	7.42846i	−0.585723	−	0.810512i
$85$	−7.01253	+	4.04869i	−0.760616	+	0.439142i
$86$	2.72735	+	0.402696i	0.294098	+	0.0434238i
$87$	2.65481	+	13.3525i	0.284626	+	1.43154i
$88$	−1.39202	+	2.95857i	−0.148390	+	0.315384i
$89$	−2.72029	+	4.71168i	−0.288350	+	0.499437i	−0.973416	−	0.229044i	$-0.926440\pi$
$89$	−2.72029	+	4.71168i	−0.288350	+	0.499437i	0.685066	+	0.728481i	$0.259773\pi$
$90$	7.28957	−	1.82983i	0.768388	−	0.192881i
$91$	15.0599	+	5.06616i	1.57871	+	0.531078i
$92$	−0.787013	−	0.838030i	−0.0820518	−	0.0873707i
$93$	−5.40853	+	1.07535i	−0.560838	+	0.111509i
$94$	−13.6669	−	10.8319i	−1.40963	−	1.11723i
$95$	0.357702	+	0.206519i	0.0366994	+	0.0211884i
$96$	8.42041	+	5.00966i	0.859404	+	0.511297i
$97$	−9.03187	−	5.21455i	−0.917048	−	0.529458i	−0.0343556	−	0.999410i	$-0.510938\pi$
$97$	−9.03187	−	5.21455i	−0.917048	−	0.529458i	−0.882692	+	0.469952i	$0.844271\pi$
$98$	2.46442	+	9.58784i	0.248944	+	0.968518i
$99$	0.453246	−	3.43828i	0.0455530	−	0.345560i
$100$	2.71443	−	2.54918i	0.271443	−	0.254918i
$101$			2.97272i			0.295796i	0.989003	+	0.147898i	$0.0472508\pi$
$101$			2.97272i			0.295796i	−0.989003	+	0.147898i	$0.952749\pi$
$102$	11.1828	−	0.555948i	1.10726	−	0.0550470i
$103$			11.1857i			1.10216i	0.834453	+	0.551079i	$0.185784\pi$
$103$			11.1857i			1.10216i	−0.834453	+	0.551079i	$0.814216\pi$
$104$	−16.9266	+	1.42219i	−1.65979	+	0.139457i
$105$	−8.05125	−	1.03821i	−0.785721	−	0.101319i
$106$	6.77914	+	5.37291i	0.658449	+	0.521863i
$107$	−3.36616	+	5.83037i	−0.325419	+	0.563643i	−0.981597	−	0.190963i	$-0.938839\pi$
$107$	−3.36616	+	5.83037i	−0.325419	+	0.563643i	0.656178	+	0.754606i	$0.272172\pi$
$108$	−10.1234	−	2.34883i	−0.974124	−	0.226016i
$109$	−14.0231	+	8.09624i	−1.34317	+	0.775479i	−0.987271	−	0.159046i	$-0.949158\pi$
$109$	−14.0231	+	8.09624i	−1.34317	+	0.775479i	−0.355898	+	0.934525i	$0.615825\pi$
$110$	1.06616	+	2.69269i	0.101654	+	0.256738i
$111$	−8.47705	+	1.68545i	−0.804606	+	0.159976i
$112$	−6.48796	−	8.36100i	−0.613055	−	0.790040i
$113$	−0.485034	+	0.280035i	−0.0456282	+	0.0263434i	−0.522641	−	0.852553i	$-0.675053\pi$
$113$	−0.485034	+	0.280035i	−0.0456282	+	0.0263434i	0.477012	+	0.878897i	$0.341720\pi$
$114$	−0.309769	−	0.479820i	−0.0290126	−	0.0449392i
$115$	−1.01828			−0.0949554
$116$	3.59015	+	15.3045i	0.333337	+	1.42099i
$117$	16.6464	−	6.89188i	1.53896	−	0.637155i
$118$	−9.36751	−	1.38312i	−0.862349	−	0.127327i
$119$	−11.4625	−	3.85598i	−1.05076	−	0.353477i
$120$	8.34022	−	2.39907i	0.761354	−	0.219004i
$121$	−9.66364			−0.878513
$122$	−7.76945	−	6.15779i	−0.703413	−	0.557500i
$123$	−12.5388	−	4.25752i	−1.13058	−	0.383887i
$124$	−6.19919	+	1.45422i	−0.556704	+	0.130593i
$125$		−	12.1556i		−	1.08723i
$126$	9.25061	+	6.35816i	0.824110	+	0.566430i
$127$	−8.06747			−0.715873			−0.357936	−	0.933746i	$-0.616520\pi$
$127$	−8.06747			−0.715873			−0.357936	+	0.933746i	$0.616520\pi$
$128$	9.91489	+	5.44931i	0.876361	+	0.481656i
$129$	−3.31170	+	0.658449i	−0.291579	+	0.0579732i
$130$	−9.34520	+	11.7911i	−0.819629	+	1.03415i
$131$			11.3010i			0.987377i	0.869639	+	0.493689i	$0.164352\pi$
$131$			11.3010i			0.987377i	−0.869639	+	0.493689i	$0.835648\pi$
$132$	0.387503	−	3.98574i	0.0337278	−	0.346914i
$133$	0.122006	+	0.604700i	0.0105793	+	0.0524342i
$134$	−6.74440	−	0.995816i	−0.582627	−	0.0860254i
$135$	−7.65484	+	5.11201i	−0.658823	+	0.439971i
$136$	12.8833	−	1.08246i	1.10473	−	0.0928204i
$137$		−	0.314105i		−	0.0268358i	−0.999910	−	0.0134179i	$-0.995729\pi$
$137$		−	0.314105i		−	0.0268358i	0.999910	−	0.0134179i	$-0.00427118\pi$
$138$	1.25284	+	0.642596i	0.106648	+	0.0547014i
$139$	10.2258	+	17.7116i	0.867339	+	1.50227i	0.864706	+	0.502278i	$0.167505\pi$
$139$	10.2258	+	17.7116i	0.867339	+	1.50227i	0.00263234	+	0.999997i	$0.499162\pi$
$140$	−9.33229	−	0.880702i	−0.788722	−	0.0744329i
$141$	20.2241	+	6.86707i	1.70318	+	0.578311i
$142$	2.87226	+	7.25417i	0.241035	+	0.608757i
$143$	3.47124	+	6.01236i	0.290279	+	0.502779i
$144$	−11.7753	−	2.31149i	−0.981273	−	0.192624i
$145$	12.0583	+	6.96186i	1.00139	+	0.578151i
$146$	−11.8735	+	14.9812i	−0.982661	+	1.23985i
$147$	−6.79025	−	10.0445i	−0.560050	−	0.828459i
$148$	−9.71629	+	2.27926i	−0.798674	+	0.187354i
$149$	18.3067			1.49975			0.749873	−	0.661582i	$-0.230115\pi$
$149$	18.3067			1.49975			0.749873	+	0.661582i	$0.230115\pi$
$150$	−2.08141	+	4.05801i	−0.169946	+	0.331335i
$151$	4.69017			0.381680			0.190840	−	0.981621i	$-0.438879\pi$
$151$	4.69017			0.381680			0.190840	+	0.981621i	$0.438879\pi$
$152$	−0.376399	−	0.541512i	−0.0305300	−	0.0439225i
$153$	−12.6700	+	5.24559i	−1.02431	+	0.424081i
$154$	−1.96315	+	3.85422i	−0.158195	+	0.310582i
$155$	−2.81995	+	4.88430i	−0.226504	+	0.392317i
$156$	18.9387	−	8.60971i	1.51631	−	0.689328i
$157$	1.88633	−	3.26722i	0.150546	−	0.260753i	−0.780883	−	0.624678i	$-0.785230\pi$
$157$	1.88633	−	3.26722i	0.150546	−	0.260753i	0.931428	+	0.363925i	$0.118564\pi$
$158$	−9.85612	−	7.81161i	−0.784111	−	0.621458i
$159$	−10.0317	−	3.40624i	−0.795565	−	0.270132i
$160$	9.53026	−	3.09741i	0.753433	−	0.244872i
$161$	−1.00589	−	1.14067i	−0.0792751	−	0.0898977i
$162$	12.6440	−	1.45886i	0.993410	−	0.114619i
$163$	−18.9619	−	10.9477i	−1.48521	−	0.857489i	−0.485356	−	0.874317i	$-0.661310\pi$
$163$	−18.9619	−	10.9477i	−1.48521	−	0.857489i	−0.999858	+	0.0168279i	$0.994643\pi$
$164$	−14.6379	−	4.41894i	−1.14303	−	0.345062i
$165$	−2.33845	−	2.66694i	−0.182048	−	0.207621i
$166$	−7.38883	−	1.09097i	−0.573484	−	0.0846754i
$167$	10.9910	+	19.0369i	0.850508	+	1.47312i	0.880750	+	0.473581i	$0.157039\pi$
$167$	10.9910	+	19.0369i	0.850508	+	1.47312i	−0.0302424	+	0.999543i	$0.509628\pi$
$168$	10.9261	+	6.97279i	0.842969	+	0.537962i
$169$	−11.5333	+	19.9763i	−0.887180	+	1.53664i
$170$	7.11288	−	8.97451i	0.545533	−	0.688314i
$171$	0.554865	+	0.425911i	0.0424316	+	0.0325703i
$172$	−3.79583	+	0.890432i	−0.289429	+	0.0678948i
$173$	15.9992	−	9.23713i	1.21639	−	0.702286i	0.252250	−	0.967662i	$-0.418830\pi$
$173$	15.9992	−	9.23713i	1.21639	−	0.702286i	0.964145	+	0.265376i	$0.0854962\pi$
$174$	−10.4425	−	16.1750i	−0.791642	−	1.22622i
$175$	3.69471	−	3.25813i	0.279294	−	0.246292i
$176$	0.290051	−	4.61493i	0.0218634	−	0.347863i
$177$	11.3745	−	2.26154i	0.854963	−	0.169988i
$178$	1.12386	−	7.61162i	0.0842370	−	0.570515i
$179$	9.95192	+	17.2372i	0.743841	+	1.28837i	0.950734	+	0.310007i	$0.100331\pi$
$179$	9.95192	+	17.2372i	0.743841	+	1.28837i	−0.206893	+	0.978364i	$0.566335\pi$
$180$	−8.63235	+	6.20119i	−0.643417	+	0.462209i
$181$	−7.27266			−0.540572			−0.270286	−	0.962780i	$-0.587118\pi$
$181$	−7.27266			−0.540572			−0.270286	+	0.962780i	$0.587118\pi$
$182$	−22.4398	+	1.17915i	−1.66335	+	0.0874041i
$183$	11.4971	+	3.90383i	0.849893	+	0.288579i
$184$	1.47114	+	0.692180i	0.108454	+	0.0510282i
$185$	−4.41985	+	7.65540i	−0.324954	+	0.562836i
$186$	6.55179	−	4.22980i	0.480400	−	0.310144i
$187$	−2.64205	−	4.57616i	−0.193206	−	0.334642i
$188$	23.6099	+	7.12744i	1.72193	+	0.519822i
$189$	−13.2881	−	3.52511i	−0.966567	−	0.256414i
$190$	−0.577859	−	0.0853214i	−0.0419223	−	0.00618987i
$191$	13.8975	−	8.02372i	1.00559	−	0.580576i	0.0956908	−	0.995411i	$-0.469494\pi$
$191$	13.8975	−	8.02372i	1.00559	−	0.580576i	0.909897	+	0.414835i	$0.136161\pi$
$192$	−13.6801	−	2.20328i	−0.987277	−	0.159008i
$193$	12.2407	−	21.2014i	0.881102	−	1.52611i	0.0309842	−	0.999520i	$-0.490136\pi$
$193$	12.2407	−	21.2014i	0.881102	−	1.52611i	0.850117	−	0.526593i	$-0.176531\pi$
$194$	14.5908	+	2.15434i	1.04756	+	0.154673i
$195$	5.92454	−	17.4483i	0.424265	−	1.24950i
$196$	−8.23214	−	11.3240i	−0.588010	−	0.808854i
$197$	5.02613			0.358097			0.179048	−	0.983840i	$-0.442698\pi$
$197$	5.02613			0.358097			0.179048	+	0.983840i	$0.442698\pi$
$198$	1.19409	+	4.75695i	0.0848605	+	0.338062i
$199$	2.10626	−	1.21605i	0.149309	−	0.0862035i	−0.423484	−	0.905903i	$-0.639193\pi$
$199$	2.10626	−	1.21605i	0.149309	−	0.0862035i	0.572793	+	0.819700i	$0.305860\pi$
$200$	−2.24201	+	4.76511i	−0.158534	+	0.336944i
$201$	8.18942	−	1.62826i	0.577637	−	0.114849i
$202$	−1.54768	−	3.90881i	−0.108894	−	0.275023i
$203$	4.11289	+	20.3847i	0.288669	+	1.43073i
$204$	−14.4147	+	6.55307i	−1.00923	+	0.458807i
$205$	−11.7288	+	6.77163i	−0.819176	+	0.472951i
$206$	−5.82357	−	14.7080i	−0.405748	−	1.02475i
$207$	−1.70968	−	0.225376i	−0.118831	−	0.0156647i
$208$	21.5163	−	10.6825i	1.49189	−	0.740698i
$209$	−0.134768	+	0.233425i	−0.00932210	+	0.0161464i
$210$	11.1271	−	2.82656i	0.767840	−	0.195051i
$211$	−4.39055	+	2.53488i	−0.302258	+	0.174509i	−0.643457	−	0.765482i	$-0.722500\pi$
$211$	−4.39055	+	2.53488i	−0.302258	+	0.174509i	0.341199	+	0.939991i	$0.389167\pi$
$212$	−11.7111	−	3.53539i	−0.804324	−	0.242812i
$213$	−6.29984	−	7.18481i	−0.431658	−	0.492295i
$214$	1.39070	−	9.41884i	0.0950662	−	0.643858i
$215$	−1.72669	+	2.99071i	−0.117759	+	0.203965i
$216$	14.5341	−	2.18206i	0.988917	−	0.148470i
$217$	−8.25699	+	1.66596i	−0.560521	+	0.113093i
$218$	14.2238	−	17.9465i	0.963355	−	1.21549i
$219$	7.52742	−	22.1689i	0.508656	−	1.49804i
$220$	−2.80378	−	2.98553i	−0.189031	−	0.201284i
$221$	13.7256	−	23.7735i	0.923287	−	1.59918i
$222$	10.2689	−	6.62957i	0.689205	−	0.444948i
$223$	6.92925	+	4.00060i	0.464017	+	0.267900i	0.713732	−	0.700419i	$-0.247004\pi$
$223$	6.92925	+	4.00060i	0.464017	+	0.267900i	−0.249715	+	0.968319i	$0.580337\pi$
$224$	12.8840	+	7.61602i	0.860845	+	0.508867i
$225$	0.730005	−	5.53774i	0.0486670	−	0.369183i
$226$	0.491975	−	0.620738i	0.0327257	−	0.0412909i
$227$		−	16.4831i		−	1.09402i	−0.837125	−	0.547011i	$-0.815766\pi$
$227$		−	16.4831i		−	1.09402i	0.837125	−	0.547011i	$-0.184234\pi$
$228$	0.657122	+	0.469638i	0.0435189	+	0.0311025i
$229$	−24.7719			−1.63697			−0.818487	−	0.574525i	$-0.805187\pi$
$229$	−24.7719			−1.63697			−0.818487	+	0.574525i	$0.805187\pi$
$230$	1.33893	−	0.530146i	0.0882867	−	0.0349568i
$231$	0.677505	−	5.25400i	0.0445766	−	0.345688i
$232$	−12.6886	−	18.2546i	−0.833048	−	1.19848i
$233$	−7.36624	−	4.25290i	−0.482578	−	0.278617i	0.238912	−	0.971041i	$-0.423209\pi$
$233$	−7.36624	−	4.25290i	−0.482578	−	0.278617i	−0.721490	+	0.692425i	$0.756543\pi$
$234$	−18.3001	+	17.7287i	−1.19632	+	1.15896i
$235$	18.9177	−	10.9222i	1.23406	−	0.712483i
$236$	13.0374	−	3.05833i	0.848661	−	0.199080i
$237$	14.5850	+	4.95230i	0.947396	+	0.321686i
$238$	17.0795	−	0.897479i	1.10710	−	0.0581749i
$239$	−0.881002	+	0.508647i	−0.0569873	+	0.0329016i	−0.528223	−	0.849106i	$-0.677141\pi$
$239$	−0.881002	+	0.508647i	−0.0569873	+	0.0329016i	0.471236	+	0.882007i	$0.343808\pi$
$240$	−9.71748	+	7.49667i	−0.627261	+	0.483908i
$241$			27.4800i			1.77014i	0.465455	+	0.885072i	$0.345891\pi$
$241$			27.4800i			1.77014i	−0.465455	+	0.885072i	$0.654109\pi$
$242$	12.7067	−	5.03116i	0.816816	−	0.323415i
$243$	−13.9838	+	6.88872i	−0.897059	+	0.441912i
$244$	13.4219	+	4.05185i	0.859250	+	0.259393i
$245$	−12.3029	−	1.55114i	−0.786004	−	0.0990990i
$246$	18.7037	−	0.929851i	1.19251	−	0.0592851i
$247$	−1.40026			−0.0890965
$248$	7.39418	−	5.13961i	0.469531	−	0.326366i
$249$	8.97192	−	1.78384i	0.568572	−	0.113046i
$250$	6.32856	+	15.9834i	0.400254	+	1.01088i
$251$			4.09789i			0.258657i	0.991602	+	0.129328i	$0.0412821\pi$
$251$			4.09789i			0.258657i	−0.991602	+	0.129328i	$0.958718\pi$
$252$	−15.4738	−	3.54419i	−0.974758	−	0.223263i
$253$		−	0.664500i		−	0.0417768i
$254$	10.6079	−	4.20015i	0.665597	−	0.263541i
$255$	−4.50933	+	13.2804i	−0.282385	+	0.831649i
$256$	−15.8741	−	2.00330i	−0.992131	−	0.125206i
$257$	−4.81483			−0.300341			−0.150170	−	0.988660i	$-0.547982\pi$
$257$	−4.81483			−0.300341			−0.150170	+	0.988660i	$0.547982\pi$
$258$	4.01173	−	2.58995i	0.249759	−	0.161243i
$259$	−12.9416	+	2.61114i	−0.804151	+	0.162248i
$260$	6.14918	−	20.3694i	0.381356	−	1.26326i
$261$	18.7048	+	14.3577i	1.15780	+	0.888718i
$262$	−5.88364	−	14.8597i	−0.363492	−	0.918034i
$263$		−	27.0065i		−	1.66529i	−0.553806	−	0.832646i	$-0.686825\pi$
$263$		−	27.0065i		−	1.66529i	0.553806	−	0.832646i	$-0.313175\pi$
$264$	1.56556	+	5.44257i	0.0963536	+	0.334967i
$265$	−9.38368	+	5.41767i	−0.576435	+	0.332805i
$266$	−0.475249	−	0.731597i	−0.0291394	−	0.0448571i
$267$	1.83763	+	9.24245i	0.112461	+	0.565629i
$268$	9.38662	−	2.20193i	0.573379	−	0.134504i
$269$	−0.898538	+	0.518771i	−0.0547848	+	0.0316300i	−0.527142	−	0.849777i	$-0.676736\pi$
$269$	−0.898538	+	0.518771i	−0.0547848	+	0.0316300i	0.472357	+	0.881407i	$0.343403\pi$
$270$	7.40385	−	10.7071i	0.450584	−	0.651611i
$271$	3.19318	+	1.84359i	0.193972	+	0.111990i	0.593841	−	0.804583i	$-0.297611\pi$
$271$	3.19318	+	1.84359i	0.193972	+	0.111990i	−0.399869	+	0.916572i	$0.630944\pi$
$272$	−16.3766	+	8.13073i	−0.992978	+	0.492998i
$273$	25.3979	−	10.5993i	1.53715	−	0.641500i
$274$	0.163532	+	0.413015i	0.00987932	+	0.0249512i
$275$	2.15235			0.129792
$276$	−1.98190	−	0.192685i	−0.119296	−	0.0115983i
$277$			5.73855i			0.344796i	0.985027	+	0.172398i	$0.0551515\pi$
$277$			5.73855i			0.344796i	−0.985027	+	0.172398i	$0.944849\pi$
$278$	−22.6669	−	17.9650i	−1.35947	−	1.07747i
$279$	−5.81568	+	7.57651i	−0.348176	+	0.453594i
$280$	12.7295	−	3.70062i	0.760733	−	0.221154i
$281$	−6.25748	−	3.61276i	−0.373290	−	0.215519i	0.301605	−	0.953433i	$-0.402478\pi$
$281$	−6.25748	−	3.61276i	−0.373290	−	0.215519i	−0.674895	+	0.737914i	$0.735811\pi$
$282$	−30.1678	+	1.49978i	−1.79647	+	0.0893107i
$283$	−1.88296	+	3.26139i	−0.111930	+	0.193869i	−0.916549	−	0.399923i	$-0.869037\pi$
$283$	−1.88296	+	3.26139i	−0.111930	+	0.193869i	0.804618	+	0.593793i	$0.202370\pi$
$284$	−7.55345	−	8.04309i	−0.448215	−	0.477270i
$285$	0.701669	−	0.139509i	0.0415633	−	0.00826382i
$286$	−7.69451	−	6.09839i	−0.454986	−	0.360606i
$287$	−19.1716	−	6.44933i	−1.13166	−	0.380692i
$288$	16.6867	−	3.09117i	0.983271	−	0.182149i
$289$	−1.94695	+	3.37221i	−0.114526	+	0.198365i
$290$	−19.4799	−	2.87623i	−1.14390	−	0.168898i
$291$	−17.7169	+	3.52257i	−1.03859	+	0.206497i
$292$	7.81283	−	25.8803i	0.457211	−	1.51453i
$293$	0.721433	−	0.416520i	0.0421466	−	0.0243333i	−0.478779	−	0.877936i	$-0.658920\pi$
$293$	0.721433	−	0.416520i	0.0421466	−	0.0243333i	0.520925	+	0.853602i	$0.325587\pi$
$294$	14.1579	+	9.67230i	0.825707	+	0.564100i
$295$	5.93057	−	10.2721i	0.345291	−	0.598062i
$296$	11.5893	−	8.05556i	0.673611	−	0.468220i
$297$	−3.33594	−	4.99531i	−0.193571	−	0.289857i
$298$	−24.0714	+	9.53099i	−1.39442	+	0.552116i
$299$	2.98963	−	1.72606i	0.172895	−	0.0998209i
$300$	0.624118	−	6.41949i	0.0360335	−	0.370629i
$301$	−5.05584	+	1.02008i	−0.291414	+	0.0587967i
$302$	−6.16707	+	2.44183i	−0.354875	+	0.140512i
$303$	3.39458	+	3.87143i	0.195013	+	0.222408i
$304$	0.776852	+	0.516068i	0.0445555	+	0.0295985i
$305$	10.7545	−	6.20909i	0.615799	−	0.355531i
$306$	13.9287	−	13.4937i	0.796251	−	0.771386i
$307$	23.1926			1.32367			0.661835	−	0.749650i	$-0.269778\pi$
$307$	23.1926			1.32367			0.661835	+	0.749650i	$0.269778\pi$
$308$	0.574719	−	6.08996i	0.0327477	−	0.347008i
$309$	12.7730	+	14.5673i	0.726633	+	0.828707i
$310$	1.16504	−	7.89048i	0.0661696	−	0.448149i
$311$	−2.03622	+	3.52684i	−0.115464	+	0.199989i	−0.917965	−	0.396661i	$-0.870169\pi$
$311$	−2.03622	+	3.52684i	−0.115464	+	0.199989i	0.802501	+	0.596650i	$0.203502\pi$
$312$	−20.4199	+	21.1808i	−1.15605	+	1.19913i
$313$	4.29224	−	2.47813i	0.242612	−	0.140072i	−0.373765	−	0.927524i	$-0.621933\pi$
$313$	4.29224	−	2.47813i	0.242612	−	0.140072i	0.616377	+	0.787452i	$0.288600\pi$
$314$	−0.779320	+	5.27813i	−0.0439796	+	0.297862i
$315$	−11.6708	+	7.84172i	−0.657578	+	0.441831i
$316$	17.0267	+	5.14007i	0.957827	+	0.289151i
$317$	8.58311	+	14.8664i	0.482075	+	0.834979i	0.999788	−	0.0205753i	$-0.00654979\pi$
$317$	8.58311	+	14.8664i	0.482075	+	0.834979i	−0.517713	+	0.855554i	$0.673216\pi$
$318$	14.9640	−	0.743931i	0.839139	−	0.0417176i
$319$	−4.54310	+	7.86887i	−0.254365	+	0.440572i
$320$	−10.9187	+	9.03448i	−0.610373	+	0.505043i
$321$	2.27394	+	11.4369i	0.126919	+	0.638344i
$322$	1.91650	+	0.976172i	0.106803	+	0.0543999i
$323$	1.06577			0.0593013
$324$	−15.8660	+	8.50109i	−0.881447	+	0.472283i
$325$	5.59082	+	9.68359i	0.310123	+	0.537149i
$326$	30.6326	+	4.52293i	1.69658	+	0.250502i
$327$	−9.01739	+	26.5570i	−0.498663	+	1.46861i
$328$	21.5480	−	1.81047i	1.18979	−	0.0999667i
$329$	30.9224	+	10.4023i	1.70481	+	0.573497i
$330$	4.46330	+	2.28929i	0.245696	+	0.126021i
$331$	23.1596	−	13.3712i	1.27297	−	0.734948i	0.297421	−	0.954746i	$-0.403873\pi$
$331$	23.1596	−	13.3712i	1.27297	−	0.734948i	0.975545	+	0.219799i	$0.0705401\pi$
$332$	10.2835	−	2.41232i	0.564381	−	0.132393i
$333$	−9.11520	+	11.8750i	−0.499510	+	0.650747i
$334$	−24.3631	−	19.3094i	−1.33309	−	1.05656i
$335$	4.26988	−	7.39565i	0.233289	−	0.404068i
$336$	−17.9969	−	3.48003i	−0.981813	−	0.189851i
$337$	9.98688	+	17.2978i	0.544020	+	0.942270i	0.998668	+	0.0515988i	$0.0164317\pi$
$337$	9.98688	+	17.2978i	0.544020	+	0.942270i	−0.454648	+	0.890671i	$0.650235\pi$
$338$	4.76489	−	32.2713i	0.259176	−	1.75533i
$339$	−0.311895	+	0.918561i	−0.0169398	+	0.0498894i
$340$	−4.68030	+	15.5037i	−0.253825	+	0.840806i
$341$	−3.18734	−	1.84021i	−0.172604	−	0.0996532i
$342$	−0.951331	−	0.271150i	−0.0514421	−	0.0146621i
$343$	−10.4156	−	15.3139i	−0.562389	−	0.826873i
$344$	4.52753	−	3.14704i	0.244108	−	0.169677i
$345$	−1.32613	+	1.16279i	−0.0713965	+	0.0626024i
$346$	−16.2281	+	20.4755i	−0.872429	+	1.10077i
$347$	7.42796	−	12.8656i	0.398754	−	0.690662i	−0.594819	−	0.803860i	$-0.702776\pi$
$347$	7.42796	−	12.8656i	0.398754	−	0.690662i	0.993572	+	0.113198i	$0.0361095\pi$
$348$	22.1519	+	15.8317i	1.18747	+	0.848669i
$349$	−11.4937	+	19.9077i	−0.615244	+	1.06563i	0.375098	+	0.926985i	$0.377609\pi$
$349$	−11.4937	+	19.9077i	−0.615244	+	1.06563i	−0.990342	+	0.138649i	$0.955724\pi$
$350$	−3.16188	+	6.20766i	−0.169009	+	0.331814i
$351$	13.8090	−	27.9841i	0.737071	−	1.49368i
$352$	2.02127	+	6.21915i	0.107734	+	0.331482i
$353$	20.3917			1.08534			0.542669	−	0.839946i	$-0.317414\pi$
$353$	20.3917			1.08534			0.542669	+	0.839946i	$0.317414\pi$
$354$	−13.7789	+	8.89559i	−0.732340	+	0.472795i
$355$	−9.77308			−0.518701
$356$	2.48506	+	10.5936i	0.131708	+	0.561459i
$357$	−19.3310	+	8.06741i	−1.02311	+	0.426973i
$358$	−22.0599	−	17.4839i	−1.16590	−	0.924052i
$359$	−15.4837	−	8.93954i	−0.817201	−	0.471811i	0.0322494	−	0.999480i	$-0.489733\pi$
$359$	−15.4837	−	8.93954i	−0.817201	−	0.471811i	−0.849450	+	0.527669i	$0.823066\pi$
$360$	8.12211	−	12.6481i	0.428073	−	0.666616i
$361$	9.47282	+	16.4074i	0.498569	+	0.863547i
$362$	9.56277	−	3.78635i	0.502608	−	0.199006i
$363$	−12.5852	+	11.0350i	−0.660550	+	0.579188i
$364$	28.8920	−	13.2332i	1.51435	−	0.693609i
$365$	−11.9725	−	20.7369i	−0.626667	−	1.08542i
$366$	−17.1500	+	0.852605i	−0.896443	+	0.0445664i
$367$			0.864377i			0.0451201i	0.999745	+	0.0225601i	$0.00718170\pi$
$367$			0.864377i			0.0451201i	−0.999745	+	0.0225601i	$0.992818\pi$
$368$	−2.29476	−	0.144227i	−0.119623	−	0.00751835i
$369$	−21.1912	+	8.77351i	−1.10317	+	0.456731i
$370$	1.82602	−	12.3671i	0.0949301	−	0.642937i
$371$	−15.3383	−	5.15981i	−0.796325	−	0.267884i
$372$	−6.41275	+	8.97278i	−0.332486	+	0.465217i
$373$		−	26.3922i		−	1.36654i	−0.730168	−	0.683268i	$-0.760558\pi$
$373$		−	26.3922i		−	1.36654i	0.730168	−	0.683268i	$-0.239442\pi$
$374$	5.85649	+	4.64165i	0.302832	+	0.240014i
$375$	−13.8807	−	15.8305i	−0.716794	−	0.817486i
$376$	−34.7553	+	2.92016i	−1.79237	+	0.150596i
$377$	−47.2035			−2.43110
$378$	19.3077	−	2.28300i	0.993082	−	0.117425i
$379$		−	21.4749i		−	1.10309i	−0.834145	−	0.551545i	$-0.814039\pi$
$379$		−	21.4749i		−	1.10309i	0.834145	−	0.551545i	$-0.185961\pi$
$380$	0.804245	−	0.188661i	0.0412569	−	0.00967811i
$381$	−10.5064	+	9.21234i	−0.538261	+	0.471962i
$382$	−14.0964	+	17.7858i	−0.721233	+	0.909999i
$383$	−3.39102			−0.173273			−0.0866364	−	0.996240i	$-0.527612\pi$
$383$	−3.39102			−0.173273			−0.0866364	+	0.996240i	$0.527612\pi$
$384$	19.1350	−	4.22517i	0.976479	−	0.215615i
$385$	−3.58353	−	4.06371i	−0.182634	−	0.207106i
$386$	−5.05711	+	34.2505i	−0.257400	+	1.74330i
$387$	−3.56101	+	4.63918i	−0.181016	+	0.235823i
$388$	−20.3070	+	4.76364i	−1.03093	+	0.241837i
$389$	−24.4946			−1.24193			−0.620963	−	0.783840i	$-0.713258\pi$
$389$	−24.4946			−1.24193			−0.620963	+	0.783840i	$0.713258\pi$
$390$	1.29393	+	26.0272i	0.0655209	+	1.31794i
$391$	−2.27549	+	1.31375i	−0.115076	+	0.0664393i
$392$	16.7200	+	10.6039i	0.844485	+	0.535579i
$393$	12.9048	+	14.7176i	0.650960	+	0.742404i
$394$	−6.60882	+	2.61674i	−0.332948	+	0.131829i
$395$	13.6428	−	7.87669i	0.686445	−	0.396319i
$396$	−4.04671	−	5.63321i	−0.203355	−	0.283079i
$397$	5.50115	−	9.52828i	0.276095	−	0.478211i	−0.694316	−	0.719670i	$-0.744293\pi$
$397$	5.50115	−	9.52828i	0.276095	−	0.478211i	0.970411	+	0.241460i	$0.0776262\pi$
$398$	−2.13640	+	2.69556i	−0.107088	+	0.135116i
$399$	0.849406	+	0.648194i	0.0425235	+	0.0324503i
$400$	0.467159	−	7.43287i	0.0233580	−	0.371643i
$401$			22.2518i			1.11120i	0.831450	+	0.555600i	$0.187511\pi$
$401$			22.2518i			1.11120i	−0.831450	+	0.555600i	$0.812489\pi$
$402$	−9.92050	+	6.40463i	−0.494790	+	0.319434i
$403$		−	19.1201i		−	0.952441i
$404$	4.07007	+	4.33390i	0.202493	+	0.215620i
$405$	−4.13160	+	15.3986i	−0.205301	+	0.765163i
$406$	−16.0209	−	24.6625i	−0.795103	−	1.22398i
$407$	−4.99568	−	2.88426i	−0.247627	−	0.142967i
$408$	15.5421	−	16.1213i	0.769449	−	0.798123i
$409$	−24.0181	−	13.8669i	−1.18762	−	0.685672i	−0.229855	−	0.973225i	$-0.573825\pi$
$409$	−24.0181	−	13.8669i	−1.18762	−	0.685672i	−0.957765	+	0.287553i	$0.907158\pi$
$410$	11.8966	−	15.0103i	0.587533	−	0.741307i
$411$	−0.358680	−	0.409066i	−0.0176924	−	0.0201777i
$412$	15.3148	+	16.3075i	0.754504	+	0.803414i
$413$	17.3651	−	3.50364i	0.854479	−	0.172403i
$414$	2.36538	−	0.593760i	0.116252	−	0.0291817i
$415$	4.67787	−	8.10231i	0.229628	−	0.397727i
$416$	−22.7301	+	25.2483i	−1.11443	+	1.23790i
$417$	33.5423	+	11.3892i	1.64257	+	0.557732i
$418$	0.0556781	−	0.377093i	0.00272331	−	0.0184442i
$419$	−27.7759	+	16.0364i	−1.35694	+	0.783431i	−0.989211	−	0.146500i	$-0.953199\pi$
$419$	−27.7759	+	16.0364i	−1.35694	+	0.783431i	−0.367732	+	0.929932i	$0.619866\pi$
$420$	−13.1593	+	9.50969i	−0.642109	+	0.464025i
$421$	−17.3959	−	10.0435i	−0.847825	−	0.489492i	0.0120912	−	0.999927i	$-0.496151\pi$
$421$	−17.3959	−	10.0435i	−0.847825	−	0.489492i	−0.859916	+	0.510435i	$0.829484\pi$
$422$	4.45338	−	5.61895i	0.216787	−	0.273526i
$423$	34.1799	−	14.1510i	1.66188	−	0.688047i
$424$	17.2395	−	1.44848i	0.837226	−	0.0703442i
$425$	−4.25532	−	7.37043i	−0.206413	−	0.357518i
$426$	12.0242	+	6.16739i	0.582576	+	0.298811i
$427$	17.5789	+	5.91356i	0.850704	+	0.286177i
$428$	3.07509	+	13.1088i	0.148640	+	0.633638i
$429$	11.3862	+	3.86618i	0.549733	+	0.186661i
$430$	0.713364	−	4.83143i	0.0344015	−	0.232992i
$431$	−3.93924	+	2.27432i	−0.189747	+	0.109550i	−0.591864	−	0.806038i	$-0.701608\pi$
$431$	−3.93924	+	2.27432i	−0.189747	+	0.109550i	0.402117	+	0.915588i	$0.368274\pi$
$432$	−17.9747	+	10.4360i	−0.864808	+	0.502103i
$433$			7.16639i			0.344395i	0.985062	+	0.172197i	$0.0550867\pi$
$433$			7.16639i			0.344395i	−0.985062	+	0.172197i	$0.944913\pi$
$434$	9.98972	−	6.48938i	0.479522	−	0.311500i
$435$	23.6536	−	4.70292i	1.13410	−	0.225488i
$436$	−9.35929	+	31.0030i	−0.448229	+	1.48478i
$437$	0.116070	+	0.0670131i	0.00555239	+	0.00320567i
$438$	1.64401	+	33.0688i	0.0785536	+	1.58009i
$439$	−28.9122	+	16.6925i	−1.37991	+	0.796689i	−0.992148	−	0.125072i	$-0.960084\pi$
$439$	−28.9122	+	16.6925i	−1.37991	+	0.796689i	−0.387758	+	0.921761i	$0.626750\pi$
$440$	5.24102	+	2.46593i	0.249856	+	0.117559i
$441$	−20.3130	−	5.32734i	−0.967288	−	0.253683i
$442$	−5.67062	+	38.4056i	−0.269724	+	1.82677i
$443$	5.66303	+	9.80865i	0.269059	+	0.466023i	0.968619	−	0.248550i	$-0.0799541\pi$
$443$	5.66303	+	9.80865i	0.269059	+	0.466023i	−0.699560	+	0.714573i	$0.746621\pi$
$444$	−10.0510	+	14.0635i	−0.477000	+	0.667423i
$445$	8.34662	+	4.81892i	0.395668	+	0.228439i
$446$	−11.1941	−	1.65281i	−0.530054	−	0.0782629i
$447$	23.8412	−	20.9047i	1.12765	−	0.988756i
$448$	−20.9061	−	3.30652i	−0.987723	−	0.156218i
$449$			35.1236i			1.65758i	0.559557	+	0.828792i	$0.310971\pi$
$449$			35.1236i			1.65758i	−0.559557	+	0.828792i	$0.689029\pi$
$450$	1.92322	+	7.66161i	0.0906616	+	0.361172i
$451$	−4.41896	−	7.65386i	−0.208081	−	0.360406i
$452$	−0.323721	+	1.07234i	−0.0152266	+	0.0504387i
$453$	6.10810	−	5.35575i	0.286984	−	0.251635i
$454$	8.58156	+	21.6735i	0.402753	+	1.01719i
$455$	8.97456	−	26.6782i	0.420734	−	1.25069i
$456$	−1.10855	−	0.275408i	−0.0519127	−	0.0128972i
$457$	−12.5450	−	21.7286i	−0.586832	−	1.01642i	−0.994644	−	0.103357i	$-0.967042\pi$
$457$	−12.5450	−	21.7286i	−0.586832	−	1.01642i	0.407813	−	0.913066i	$-0.366292\pi$
$458$	32.5724	−	12.8969i	1.52201	−	0.602635i
$459$	−10.5104	+	21.2994i	−0.490584	+	0.994173i
$460$	−1.48455	+	1.39417i	−0.0692174	+	0.0650036i
$461$	−17.8507	−	10.3061i	−0.831388	−	0.480002i	0.0229397	−	0.999737i	$-0.492697\pi$
$461$	−17.8507	−	10.3061i	−0.831388	−	0.480002i	−0.854328	+	0.519735i	$0.826031\pi$
$462$	1.84453	+	7.26118i	0.0858152	+	0.337820i
$463$	0.0117859	+	0.0204138i	0.000547739	+	0.000948712i	0.866299	−	0.499526i	$-0.166492\pi$
$463$	0.0117859	+	0.0204138i	0.000547739	+	0.000948712i	−0.865751	+	0.500474i	$0.833159\pi$
$464$	26.1880	+	17.3969i	1.21575	+	0.807630i
$465$	1.90495	+	9.58106i	0.0883401	+	0.444311i
$466$	11.9000	+	1.75704i	0.551257	+	0.0813935i
$467$	30.1113	+	17.3848i	1.39339	+	0.804472i	0.993688	−	0.112175i	$-0.0357818\pi$
$467$	30.1113	+	17.3848i	1.39339	+	0.804472i	0.399698	+	0.916647i	$0.369115\pi$
$468$	14.8327	−	32.8389i	0.685642	−	1.51798i
$469$	12.5025	−	2.52254i	0.577310	−	0.116480i
$470$	−19.1884	+	24.2106i	−0.885096	+	1.11675i
$471$	−1.27427	−	6.40900i	−0.0587152	−	0.295311i
$472$	−15.5505	+	10.8090i	−0.715770	+	0.497524i
$473$	−1.95165	−	1.12678i	−0.0897367	−	0.0518095i
$474$	−21.7560	+	1.08159i	−0.999286	+	0.0496792i
$475$	−0.217059	+	0.375958i	−0.00995936	+	0.0172501i
$476$	−21.9905	+	10.0721i	−1.00793	+	0.461656i
$477$	−16.9541	+	7.01928i	−0.776275	+	0.321391i
$478$	0.893609	−	1.12749i	0.0408727	−	0.0515702i
$479$	3.55661			0.162506			0.0812528	−	0.996694i	$-0.474108\pi$
$479$	3.55661			0.162506			0.0812528	+	0.996694i	$0.474108\pi$
$480$	8.87448	−	14.9165i	0.405063	−	0.680843i
$481$		−	29.9679i		−	1.36642i
$482$	−14.3069	−	36.1333i	−0.651660	−	1.64583i
$483$	−2.61254	−	0.336888i	−0.118875	−	0.0153289i
$484$	−14.0886	+	13.2309i	−0.640389	+	0.601404i
$485$	−9.23744	+	15.9997i	−0.419451	+	0.726510i
$486$	14.8007	−	16.3383i	0.671374	−	0.741119i
$487$	−16.6766	−	28.8847i	−0.755688	−	1.30889i	−0.945032	−	0.326978i	$-0.893970\pi$
$487$	−16.6766	−	28.8847i	−0.755688	−	1.30889i	0.189344	−	0.981911i	$-0.439364\pi$
$488$	−19.7579	+	1.66007i	−0.894398	+	0.0751479i
$489$	−37.1958	+	7.39546i	−1.68205	+	0.334434i
$490$	16.9846	−	4.36565i	0.767286	−	0.197220i
$491$	−20.1913	−	34.9724i	−0.911223	−	1.57828i	−0.812339	−	0.583185i	$-0.801806\pi$
$491$	−20.1913	−	34.9724i	−0.911223	−	1.57828i	−0.0988831	−	0.995099i	$-0.531527\pi$
$492$	−24.1093	+	10.9603i	−1.08693	+	0.494130i
$493$	35.9278			1.61811
$494$	1.84119	−	0.729015i	0.0828393	−	0.0327999i
$495$	−6.09082	−	0.802914i	−0.273762	−	0.0360883i
$496$	−7.04674	+	10.6077i	−0.316408	+	0.476298i
$497$	−9.65413	−	10.9477i	−0.433047	−	0.491073i
$498$	−10.8684	+	7.01659i	−0.487025	+	0.314421i
$499$		−	16.3495i		−	0.731906i	−0.930633	−	0.365953i	$-0.880743\pi$
$499$		−	16.3495i		−	0.731906i	0.930633	−	0.365953i	$-0.119257\pi$
$500$	−16.6428	−	17.7216i	−0.744288	−	0.792535i
$501$	36.0523	+	12.2415i	1.61070	+	0.546909i
$502$	−2.13348	−	5.38829i	−0.0952217	−	0.240491i
$503$	−4.53610			−0.202255			−0.101127	−	0.994873i	$-0.532245\pi$
$503$	−4.53610			−0.202255			−0.101127	+	0.994873i	$0.532245\pi$
$504$	22.1916	−	3.39586i	0.988493	−	0.151264i
$505$	5.26609			0.234338
$506$	0.345957	+	0.873747i	0.0153797	+	0.0388428i
$507$	7.79108	+	39.1856i	0.346014	+	1.74030i
$508$	−11.7615	+	11.0455i	−0.521833	+	0.490065i
$509$			19.0020i			0.842247i	0.907003	+	0.421124i	$0.138364\pi$
$509$			19.0020i			0.842247i	−0.907003	+	0.421124i	$0.861636\pi$
$510$	−0.984846	−	19.8100i	−0.0436097	−	0.877200i
$511$	11.4026	−	33.8960i	0.504422	−	1.49947i
$512$	21.9157	−	5.63036i	0.968547	−	0.248829i
$513$	1.20897	−	0.0789336i	0.0533771	−	0.00348500i
$514$	6.33099	−	2.50673i	0.279248	−	0.110567i
$515$	19.8151			0.873158
$516$	−3.92660	+	5.49413i	−0.172859	+	0.241866i
$517$	7.12746	+	12.3451i	0.313465	+	0.542938i
$518$	15.6574	−	10.1711i	0.687946	−	0.446893i
$519$	10.2881	−	30.2993i	0.451596	−	1.32999i
$520$	2.51936	+	29.9851i	0.110481	+	1.31493i
$521$	1.33039	+	2.30430i	0.0582854	+	0.100953i	0.893696	−	0.448673i	$-0.148103\pi$
$521$	1.33039	+	2.30430i	0.0582854	+	0.100953i	−0.835410	+	0.549627i	$0.814770\pi$
$522$	−32.0698	−	9.14060i	−1.40366	−	0.400073i
$523$	−9.94919	+	17.2325i	−0.435047	+	0.753524i	−0.997300	−	0.0734416i	$-0.976602\pi$
$523$	−9.94919	+	17.2325i	−0.435047	+	0.753524i	0.562252	+	0.826966i	$0.309935\pi$
$524$	15.4727	+	16.4757i	0.675929	+	0.719745i
$525$	1.09120	−	8.46216i	0.0476238	−	0.369319i
$526$	14.0603	+	35.5107i	0.613059	+	1.54834i
$527$			14.5528i			0.633930i
$528$	−4.89210	−	6.34133i	−0.212901	−	0.275971i
$529$	22.6696			0.985634
$530$	9.51796	−	12.0091i	0.413434	−	0.521641i
$531$	12.2308	−	15.9340i	0.530772	−	0.691475i
$532$	1.00579	+	0.714545i	0.0436066	+	0.0309795i
$533$	22.9568	−	39.7624i	0.994371	−	1.72230i
$534$	−7.22817	−	11.1961i	−0.312793	−	0.484504i
$535$	10.3283	+	5.96307i	0.446533	+	0.257806i
$536$	−11.1960	+	7.78224i	−0.483595	+	0.336141i
$537$	32.6440	+	11.0842i	1.40869	+	0.478318i
$538$	0.911395	−	1.14993i	0.0392930	−	0.0495771i
$539$	1.01223	−	8.02850i	0.0435998	−	0.345812i
$540$	−4.16088	+	17.9333i	−0.179056	+	0.771727i
$541$	−16.6597	−	9.61848i	−0.716256	−	0.413531i	0.0971168	−	0.995273i	$-0.469038\pi$
$541$	−16.6597	−	9.61848i	−0.716256	−	0.413531i	−0.813373	+	0.581742i	$0.802371\pi$
$542$	−5.15852	−	0.761660i	−0.221577	−	0.0327161i
$543$	−9.47133	+	8.30473i	−0.406454	+	0.356390i
$544$	17.3004	−	19.2172i	0.741750	−	0.823929i
$545$	14.3423	+	24.8415i	0.614355	+	1.06409i
$546$	−27.8773	+	27.1598i	−1.19304	+	1.16233i
$547$	5.71687	+	3.30064i	0.244436	+	0.141125i	0.617214	−	0.786795i	$-0.288261\pi$
$547$	5.71687	+	3.30064i	0.244436	+	0.141125i	−0.372778	+	0.927921i	$0.621595\pi$
$548$	−0.430054	−	0.457932i	−0.0183710	−	0.0195619i
$549$	19.4308	−	8.04467i	0.829286	−	0.343338i
$550$	−2.83012	+	1.12058i	−0.120677	+	0.0477815i
$551$	−0.916319	−	1.58711i	−0.0390365	−	0.0676132i
$552$	2.70631	−	0.778471i	0.115188	−	0.0331339i
$553$	22.3002	+	7.50179i	0.948301	+	0.319009i
$554$	−2.98765	−	7.54558i	−0.126933	−	0.320581i
$555$	2.98573	+	15.0169i	0.126737	+	0.637430i
$556$	39.1577	+	11.8210i	1.66066	+	0.501324i
$557$	−20.8273	−	36.0740i	−0.882481	−	1.52850i	−0.848573	−	0.529078i	$-0.822538\pi$
$557$	−20.8273	−	36.0740i	−0.882481	−	1.52850i	−0.0339080	−	0.999425i	$-0.510795\pi$
$558$	3.70247	−	12.9901i	0.156738	−	0.549915i
$559$		−	11.7074i		−	0.495172i
$560$	−14.8113	+	11.4932i	−0.625891	+	0.485678i
$561$	−8.66636	−	2.94265i	−0.365894	−	0.124239i
$562$	10.1088	+	1.49258i	0.426415	+	0.0629606i
$563$	−16.0045	−	9.24021i	−0.674510	−	0.389429i	0.123273	−	0.992373i	$-0.460661\pi$
$563$	−16.0045	−	9.24021i	−0.674510	−	0.389429i	−0.797783	+	0.602944i	$0.793994\pi$
$564$	38.8866	−	17.6782i	1.63742	−	0.744388i
$565$	0.496074	+	0.859225i	0.0208700	+	0.0361479i
$566$	0.777928	−	5.26870i	0.0326988	−	0.221460i
$567$	−21.3307	+	10.5830i	−0.895807	+	0.444444i
$568$	14.1194	+	6.64328i	0.592438	+	0.278746i
$569$	−9.74549	+	5.62656i	−0.408552	+	0.235878i	−0.690167	−	0.723650i	$-0.742463\pi$
$569$	−9.74549	+	5.62656i	−0.408552	+	0.235878i	0.281615	+	0.959527i	$0.409130\pi$
$570$	−0.849988	+	0.548748i	−0.0356021	+	0.0229845i
$571$	−5.87464	−	3.39172i	−0.245846	−	0.141939i	0.372015	−	0.928227i	$-0.378667\pi$
$571$	−5.87464	−	3.39172i	−0.245846	−	0.141939i	−0.617861	+	0.786288i	$0.712000\pi$
$572$	13.2925	+	4.01277i	0.555786	+	0.167782i
$573$	8.93662	−	26.3192i	0.373333	−	1.09950i
$574$	28.5663	−	1.50108i	1.19233	−	0.0626538i
$575$		−	1.07025i		−	0.0446326i
$576$	−20.3318	+	12.7521i	−0.847160	+	0.531337i
$577$	14.8903	−	8.59693i	0.619892	−	0.357895i	−0.156935	−	0.987609i	$-0.550161\pi$
$577$	14.8903	−	8.59693i	0.619892	−	0.357895i	0.776827	+	0.629714i	$0.216828\pi$
$578$	0.804362	−	5.44773i	0.0334571	−	0.226596i
$579$	−8.26889	−	41.5888i	−0.343644	−	1.72837i
$580$	27.1115	−	6.35985i	1.12574	−	0.264079i
$581$	13.6971	−	2.76357i	0.568251	−	0.114652i
$582$	21.4620	−	13.8557i	0.889627	−	0.574339i
$583$	−3.53540	−	6.12350i	−0.146422	−	0.253609i
$584$	3.20098	+	38.0975i	0.132457	+	1.57649i
$585$	−12.2088	−	29.4886i	−0.504771	−	1.21920i
$586$	−0.731757	+	0.923278i	−0.0302286	+	0.0381402i
$587$	−31.6666	−	18.2827i	−1.30702	−	0.754609i	−0.325423	−	0.945569i	$-0.605507\pi$
$587$	−31.6666	−	18.2827i	−1.30702	−	0.754609i	−0.981598	+	0.190960i	$0.938840\pi$
$588$	−23.6518	−	5.34704i	−0.975385	−	0.220508i
$589$	0.642871	−	0.371162i	0.0264890	−	0.0152935i
$590$	−2.45016	+	16.5943i	−0.100871	+	0.683176i
$591$	6.54563	−	5.73939i	0.269251	−	0.236087i
$592$	−11.0447	+	16.6259i	−0.453934	+	0.683320i
$593$	21.8275	−	37.8064i	0.896349	−	1.55252i	0.0642238	−	0.997936i	$-0.479543\pi$
$593$	21.8275	−	37.8064i	0.896349	−	1.55252i	0.832126	−	0.554587i	$-0.187124\pi$
$594$	6.98710	+	4.83152i	0.286684	+	0.198240i
$595$	−6.83077	+	20.3055i	−0.280034	+	0.832444i
$596$	26.6893	−	25.0645i	1.09323	−	1.02668i
$597$	1.35441	−	3.98885i	0.0554322	−	0.163253i
$598$	−3.03241	+	3.82608i	−0.124005	+	0.156460i
$599$	9.39761	+	5.42571i	0.383976	+	0.221689i	0.679547	−	0.733632i	$-0.262176\pi$
$599$	9.39761	+	5.42571i	0.383976	+	0.221689i	−0.295571	+	0.955321i	$0.595510\pi$
$600$	2.52151	+	8.76588i	0.102940	+	0.357866i
$601$	−2.08978	−	1.20654i	−0.0852440	−	0.0492157i	0.456772	−	0.889584i	$-0.349005\pi$
$601$	−2.08978	−	1.20654i	−0.0852440	−	0.0492157i	−0.542016	+	0.840368i	$0.682339\pi$
$602$	6.11681	−	3.97351i	0.249303	−	0.161948i
$603$	8.80592	−	11.4721i	0.358605	−	0.467180i
$604$	6.83776	−	6.42150i	0.278225	−	0.261287i
$605$			17.1189i			0.695982i
$606$	−6.47908	−	3.32321i	−0.263195	−	0.134996i
$607$			16.4878i			0.669220i	0.942357	+	0.334610i	$0.108605\pi$
$607$			16.4878i			0.669220i	−0.942357	+	0.334610i	$0.891395\pi$
$608$	−1.29016	−	0.274124i	−0.0523228	−	0.0111172i
$609$	28.6339	+	21.8509i	1.16030	+	0.885444i
$610$	−10.9084	+	13.7634i	−0.441666	+	0.557262i
$611$	−37.0277	+	64.1339i	−1.49798	+	2.59458i
$612$	−11.2896	+	24.9945i	−0.456353	+	1.01034i
$613$	−21.2743	+	12.2827i	−0.859259	+	0.496094i	−0.863764	−	0.503896i	$-0.831899\pi$
$613$	−21.2743	+	12.2827i	−0.859259	+	0.496094i	0.00450495	+	0.999990i	$0.498566\pi$
$614$	−30.4958	+	12.0747i	−1.23071	+	0.487295i
$615$	−7.54207	+	22.2121i	−0.304126	+	0.895678i
$616$	2.41491	+	8.30687i	0.0972995	+	0.334693i
$617$	−3.33271	+	1.92414i	−0.134170	+	0.0774630i	−0.565583	−	0.824692i	$-0.691349\pi$
$617$	−3.33271	+	1.92414i	−0.134170	+	0.0774630i	0.431413	+	0.902155i	$0.358015\pi$
$618$	−24.3794	−	12.5045i	−0.980682	−	0.503005i
$619$	−8.93439			−0.359103			−0.179552	−	0.983749i	$-0.557465\pi$
$619$	−8.93439			−0.359103			−0.179552	+	0.983749i	$0.557465\pi$
$620$	2.57611	+	10.9817i	0.103459	+	0.441036i
$621$	−2.48391	+	1.65879i	−0.0996758	+	0.0665649i
$622$	0.841246	−	5.69754i	0.0337309	−	0.228450i
$623$	2.84690	+	14.1101i	0.114059	+	0.565309i
$624$	15.8227	−	38.4817i	0.633413	−	1.54050i
$625$	−12.2240			−0.488959
$626$	−4.35366	+	5.49313i	−0.174007	+	0.219550i
$627$	0.0910395	+	0.457887i	0.00363577	+	0.0182863i
$628$	−1.72322	−	7.34592i	−0.0687638	−	0.293134i
$629$			22.8093i			0.909467i
$630$	11.2633	−	16.3872i	0.448741	−	0.652882i
$631$	2.64653			0.105357			0.0526783	−	0.998612i	$-0.483224\pi$
$631$	2.64653			0.105357			0.0526783	+	0.998612i	$0.483224\pi$
$632$	−25.0644	+	2.10592i	−0.997007	+	0.0837692i
$633$	−2.82329	+	8.31485i	−0.112216	+	0.330486i
$634$	−19.0257	−	15.0791i	−0.755608	−	0.598868i
$635$			14.2913i			0.567133i
$636$	−19.2888	+	8.76886i	−0.764849	+	0.347708i
$637$	38.7501	−	16.3003i	1.53533	−	0.645840i
$638$	1.87694	−	12.7120i	0.0743086	−	0.503273i
$639$	−16.4088	−	2.16307i	−0.649123	−	0.0855697i
$640$	9.65331	−	17.5640i	0.381580	−	0.694276i
$641$		−	22.4844i		−	0.888080i	−0.896007	−	0.444040i	$-0.853545\pi$
$641$		−	22.4844i		−	0.888080i	0.896007	−	0.444040i	$-0.146455\pi$
$642$	−8.94434	−	13.8544i	−0.353005	−	0.546790i
$643$	−11.3907	−	19.7293i	−0.449207	−	0.778050i	0.549127	−	0.835739i	$-0.314960\pi$
$643$	−11.3907	−	19.7293i	−0.449207	−	0.778050i	−0.998335	+	0.0576890i	$0.981627\pi$
$644$	−3.02822	−	0.285778i	−0.119329	−	0.0112612i
$645$	1.16642	+	5.86659i	0.0459279	+	0.230997i
$646$	−1.40138	+	0.554872i	−0.0551366	+	0.0218311i
$647$	15.7026	+	27.1978i	0.617334	+	1.06925i	0.989970	+	0.141277i	$0.0451207\pi$
$647$	15.7026	+	27.1978i	0.617334	+	1.06925i	−0.372636	+	0.927978i	$0.621546\pi$
$648$	16.4363	−	19.4383i	0.645678	−	0.763610i
$649$	6.70323	+	3.87011i	0.263125	+	0.151915i
$650$	−12.3929	−	9.82216i	−0.486089	−	0.385257i
$651$	−8.85087	+	11.5984i	−0.346893	+	0.454576i
$652$	−42.6334	+	10.0010i	−1.66965	+	0.391670i
$653$	−34.3344			−1.34361			−0.671805	−	0.740728i	$-0.734481\pi$
$653$	−34.3344			−1.34361			−0.671805	+	0.740728i	$0.734481\pi$
$654$	−1.96942	−	39.6144i	−0.0770103	−	1.54905i
$655$	20.0195			0.782227
$656$	−27.3907	+	13.5990i	−1.06943	+	0.530954i
$657$	−15.5118	−	37.4667i	−0.605175	−	1.46172i
$658$	−46.0754	+	2.42113i	−1.79621	+	0.0943855i
$659$	−15.4024	+	26.6777i	−0.599991	+	1.03921i	0.392831	+	0.919611i	$0.371496\pi$
$659$	−15.4024	+	26.6777i	−0.599991	+	1.03921i	−0.992822	+	0.119604i	$0.961838\pi$
$660$	−7.06063	−	0.686452i	−0.274835	−	0.0267201i
$661$	18.9501	−	32.8225i	0.737073	−	1.27665i	−0.216734	−	0.976231i	$-0.569541\pi$
$661$	18.9501	−	32.8225i	0.737073	−	1.27665i	0.953808	−	0.300418i	$-0.0971261\pi$
$662$	−23.4910	+	29.6392i	−0.913004	+	1.15196i
$663$	−9.27205	−	46.6342i	−0.360096	−	1.81112i
$664$	−12.2658	+	8.52583i	−0.476006	+	0.330866i
$665$	1.07121	−	0.216131i	0.0415398	−	0.00838120i
$666$	5.80306	−	20.3600i	0.224864	−	0.788935i
$667$	3.91278	+	2.25904i	0.151503	+	0.0874705i
$668$	42.0879	+	12.7056i	1.62843	+	0.491596i
$669$	13.5924	−	2.70252i	0.525514	−	0.104485i
$670$	−1.76406	+	11.9475i	−0.0681516	+	0.461573i
$671$	4.05186	+	7.01803i	0.156420	+	0.270928i
$672$	25.4759	−	4.79383i	0.982752	−	0.184926i
$673$	−10.7780	+	18.6680i	−0.415460	+	0.719598i	−0.995477	−	0.0950064i	$-0.969713\pi$
$673$	−10.7780	+	18.6680i	−0.415460	+	0.719598i	0.580016	+	0.814605i	$0.303046\pi$
$674$	−22.1374	−	17.5453i	−0.852700	−	0.675820i
$675$	−5.37291	−	8.04552i	−0.206803	−	0.309672i
$676$	10.5360	+	44.9141i	0.405232	+	1.72747i
$677$	8.74808	−	5.05071i	0.336216	−	0.194114i	−0.322381	−	0.946610i	$-0.604483\pi$
$677$	8.74808	−	5.05071i	0.336216	−	0.194114i	0.658597	+	0.752495i	$0.271150\pi$
$678$	−0.0681187	−	1.37019i	−0.00261608	−	0.0526219i
$679$	−27.0478	+	5.45725i	−1.03800	+	0.209430i
$680$	−1.91755	−	22.8224i	−0.0735348	−	0.875200i
$681$	−18.8222	−	21.4663i	−0.721270	−	0.822590i
$682$	5.14909	+	0.760267i	0.197169	+	0.0291121i
$683$	−14.0077	−	24.2620i	−0.535990	−	0.928362i	−0.999115	−	0.0420685i	$-0.986605\pi$
$683$	−14.0077	−	24.2620i	−0.535990	−	0.928362i	0.463125	−	0.886293i	$-0.346728\pi$
$684$	1.39207	−	0.138755i	0.0532270	−	0.00530544i
$685$	−0.556429			−0.0212600
$686$	21.6682	+	14.7135i	0.827297	+	0.561765i
$687$	−32.2610	+	28.2873i	−1.23083	+	1.07923i
$688$	−4.31479	+	6.49518i	−0.164500	+	0.247627i
$689$	18.3667	−	31.8121i	0.699716	−	1.21194i
$690$	1.13834	−	2.21936i	0.0433359	−	0.0844897i
$691$	6.71914	+	11.6379i	0.255608	+	0.442726i	0.965060	−	0.262027i	$-0.0843910\pi$
$691$	6.71914	+	11.6379i	0.255608	+	0.442726i	−0.709452	+	0.704753i	$0.751058\pi$
$692$	10.6782	−	35.3719i	0.405923	−	1.34464i
$693$	−5.11727	−	7.61604i	−0.194389	−	0.289309i
$694$	−3.06879	+	20.7841i	−0.116490	+	0.788954i
$695$	31.3755	−	18.1147i	1.19014	−	0.687129i
$696$	−37.3698	−	9.28414i	−1.41650	−	0.351915i
$697$	−17.4730	+	30.2642i	−0.661839	+	1.14634i
$698$	4.74852	−	32.1604i	0.179734	−	1.21729i
$699$	−14.4496	+	2.87295i	−0.546535	+	0.108665i
$700$	0.925650	−	9.80858i	0.0349863	−	0.370730i
$701$	−20.6925			−0.781543			−0.390772	−	0.920488i	$-0.627792\pi$
$701$	−20.6925			−0.781543			−0.390772	+	0.920488i	$0.627792\pi$
$702$	−3.58809	+	43.9855i	−0.135424	+	1.66013i
$703$	1.00760	−	0.581740i	0.0380024	−	0.0219407i
$704$	−5.89562	−	7.12520i	−0.222200	−	0.268541i
$705$	12.1648	−	35.8265i	0.458154	−	1.34930i
$706$	−26.8129	+	10.6165i	−1.00912	+	0.399556i
$707$	5.20199	+	5.89903i	0.195641	+	0.221856i
$708$	13.4865	−	18.8704i	0.506854	−	0.709195i
$709$	9.99410	−	5.77010i	0.375336	−	0.216700i	−0.300451	−	0.953797i	$-0.597137\pi$
$709$	9.99410	−	5.77010i	0.375336	−	0.216700i	0.675787	+	0.737097i	$0.263804\pi$
$710$	12.8506	−	5.08814i	0.482273	−	0.190954i
$711$	24.6494	−	10.2053i	0.924424	−	0.382727i
$712$	−8.78291	−	12.6357i	−0.329153	−	0.473541i
$713$	−0.915042	+	1.58490i	−0.0342686	+	0.0593550i
$714$	21.2181	−	20.6721i	0.794069	−	0.773633i
$715$	10.6507	−	6.14920i	0.398315	−	0.229967i
$716$	38.1090	+	11.5045i	1.42420	+	0.429942i
$717$	−0.566518	+	1.66845i	−0.0211570	+	0.0623093i
$718$	25.0137	+	3.69329i	0.933502	+	0.137832i
$719$	7.10318	−	12.3031i	0.264904	−	0.458827i	−0.702635	−	0.711551i	$-0.747993\pi$
$719$	7.10318	−	12.3031i	0.264904	−	0.458827i	0.967538	+	0.252724i	$0.0813264\pi$
$720$	−4.09474	+	20.8596i	−0.152602	+	0.777390i
$721$	19.5739	+	22.1968i	0.728971	+	0.826651i
$722$	−20.9979	−	16.6422i	−0.781461	−	0.619358i
$723$	31.3797	+	35.7878i	1.16702	+	1.33096i
$724$	−10.6028	+	9.95729i	−0.394048	+	0.370060i
$725$	−7.31717	+	12.6737i	−0.271753	+	0.470690i
$726$	10.8030	−	21.0621i	0.400938	−	0.781687i
$727$	6.41206	+	3.70201i	0.237810	+	0.137300i	0.614170	−	0.789174i	$-0.289491\pi$
$727$	6.41206	+	3.70201i	0.237810	+	0.137300i	−0.376360	+	0.926474i	$0.622824\pi$
$728$	−31.1004	+	32.4423i	−1.15266	+	1.20239i
$729$	−10.3450	+	24.9395i	−0.383149	+	0.923686i
$730$	26.5387	+	21.0336i	0.982242	+	0.778490i
$731$			8.91084i			0.329579i
$732$	22.1065	−	10.0498i	0.817079	−	0.371452i
$733$	−47.8936			−1.76899			−0.884495	−	0.466550i	$-0.845497\pi$
$733$	−47.8936			−1.76899			−0.884495	+	0.466550i	$0.845497\pi$
$734$	−0.450019	−	1.13656i	−0.0166105	−	0.0419514i
$735$	−17.7936	+	12.0287i	−0.656327	+	0.443687i
$736$	3.09246	−	1.00507i	0.113990	−	0.0370475i
$737$	4.82617	+	2.78639i	0.177774	+	0.102638i
$738$	23.2965	−	22.5690i	0.857555	−	0.830775i
$739$	−1.22048	+	0.704644i	−0.0448960	+	0.0259207i	−0.522280	−	0.852774i	$-0.674918\pi$
$739$	−1.22048	+	0.704644i	−0.0448960	+	0.0259207i	0.477384	+	0.878695i	$0.341585\pi$
$740$	4.03765	+	17.2122i	0.148427	+	0.632731i
$741$	−1.82359	+	1.59897i	−0.0669912	+	0.0587397i
$742$	22.8546	−	1.20094i	0.839018	−	0.0440880i
$743$	19.3135	−	11.1507i	0.708545	−	0.409079i	−0.101977	−	0.994787i	$-0.532517\pi$
$743$	19.3135	−	11.1507i	0.708545	−	0.409079i	0.810522	+	0.585708i	$0.199183\pi$
$744$	3.76061	−	15.1369i	0.137871	−	0.554946i
$745$		−	32.4299i		−	1.18814i
$746$	13.7405	+	34.7029i	0.503076	+	1.27056i
$747$	9.64733	−	12.5683i	0.352977	−	0.459849i
$748$	−10.1172	−	3.05422i	−0.369923	−	0.111673i
$749$	3.52283	+	17.4602i	0.128722	+	0.637983i
$750$	26.4934	+	13.5888i	0.967403	+	0.496194i
$751$	−18.0849			−0.659928			−0.329964	−	0.943994i	$-0.607037\pi$
$751$	−18.0849			−0.659928			−0.329964	+	0.943994i	$0.607037\pi$
$752$	44.1792	−	21.9343i	1.61105	−	0.799861i
$753$	4.67943	+	5.33677i	0.170528	+	0.194483i
$754$	62.0676	−	24.5754i	2.26037	−	0.894984i
$755$		−	8.30850i		−	0.302377i
$756$	−24.1990	+	13.0540i	−0.880109	+	0.474771i
$757$		−	1.80008i		−	0.0654250i	−0.999465	−	0.0327125i	$-0.989585\pi$
$757$		−	1.80008i		−	0.0654250i	0.999465	−	0.0327125i	$-0.0104146\pi$
$758$	11.1804	+	28.2372i	0.406091	+	1.02562i
$759$	−0.758800	−	0.865392i	−0.0275427	−	0.0314117i
$760$	−0.959275	+	0.666781i	−0.0347965	+	0.0241867i
$761$	0.442910			0.0160555			0.00802774	−	0.999968i	$-0.497445\pi$
$761$	0.442910			0.0160555			0.00802774	+	0.999968i	$0.497445\pi$
$762$	9.01866	−	17.5832i	0.326711	−	0.636972i
$763$	−13.6596	+	40.6053i	−0.494512	+	1.47001i
$764$	9.27546	−	30.7254i	0.335574	−	1.11160i
$765$	9.29242	+	22.4446i	0.335968	+	0.811485i
$766$	4.45883	−	1.76546i	0.161104	−	0.0637885i
$767$			40.2110i			1.45194i
$768$	−22.9608	+	15.5179i	−0.828525	+	0.559952i
$769$	35.5038	−	20.4981i	1.28030	−	0.739181i	0.303397	−	0.952864i	$-0.401879\pi$
$769$	35.5038	−	20.4981i	1.28030	−	0.739181i	0.976903	+	0.213683i	$0.0685460\pi$
$770$	6.82765	+	3.47767i	0.246051	+	0.125326i
$771$	−6.27045	+	5.49811i	−0.225825	+	0.198009i
$772$	−11.1822	−	47.6686i	−0.402456	−	1.71563i
$773$	−39.9041	+	23.0386i	−1.43525	+	0.828642i	−0.997514	−	0.0704616i	$-0.977553\pi$
$773$	−39.9041	+	23.0386i	−1.43525	+	0.828642i	−0.437736	+	0.899104i	$0.644219\pi$
$774$	2.26706	−	7.95399i	0.0814878	−	0.285900i
$775$	−5.13358	−	2.96387i	−0.184404	−	0.106466i
$776$	24.2214	−	16.8361i	0.869499	−	0.604379i
$777$	−13.8724	+	18.1787i	−0.497670	+	0.652156i
$778$	32.2078	−	12.7526i	1.15471	−	0.457202i
$779$	1.78256			0.0638669
$780$	−15.2519	−	33.5493i	−0.546104	−	1.20126i
$781$		−	6.37761i		−	0.228209i
$782$	2.30805	−	2.91213i	0.0825356	−	0.104137i
$783$	40.7548	−	2.66089i	1.45646	−	0.0950924i
$784$	−27.5057	−	5.23815i	−0.982345	−	0.187077i
$785$	−5.78780	−	3.34159i	−0.206575	−	0.119266i
$786$	−24.6308	−	12.6335i	−0.878552	−	0.450621i
$787$	12.8870	−	22.3209i	0.459372	−	0.795656i	−0.539556	−	0.841950i	$-0.681408\pi$
$787$	12.8870	−	22.3209i	0.459372	−	0.795656i	0.998928	+	0.0462940i	$0.0147411\pi$
$788$	7.32756	−	6.88147i	0.261033	−	0.245142i
$789$	−30.8390	−	35.1711i	−1.09790	−	1.25212i
$790$	−13.8381	+	17.4599i	−0.492336	+	0.621194i
$791$	−0.472462	+	1.40447i	−0.0167988	+	0.0499370i
$792$	8.25379	+	5.30024i	0.293286	+	0.188336i
$793$	−21.0497	+	36.4592i	−0.747498	+	1.29470i
$794$	−2.27275	+	15.3927i	−0.0806569	+	0.546268i
$795$	−6.03406	+	17.7709i	−0.214006	+	0.630268i
$796$	1.40576	−	4.65664i	0.0498259	−	0.165050i
$797$	−2.62645	+	1.51638i	−0.0930335	+	0.0537129i	−0.545795	−	0.837919i	$-0.683772\pi$
$797$	−2.62645	+	1.51638i	−0.0930335	+	0.0537129i	0.452761	+	0.891632i	$0.350439\pi$
$798$	−1.45435	−	0.410082i	−0.0514833	−	0.0145167i
$799$	28.1828	−	48.8140i	0.997034	−	1.72691i
$800$	3.25549	+	10.0167i	0.115099	+	0.354142i
$801$	12.9472	+	9.93823i	0.457468	+	0.351150i
$802$	−11.5849	−	29.2587i	−0.409077	−	1.03316i
$803$	13.5323	−	7.81286i	0.477543	−	0.275710i
$804$	9.70998	−	13.5863i	0.342445	−	0.479152i
$805$	−2.02067	+	1.78190i	−0.0712193	+	0.0628039i
$806$	9.95446	+	25.1409i	0.350631	+	0.885551i
$807$	−0.577794	+	1.70166i	−0.0203393	+	0.0599011i
$808$	−7.60806	−	3.57963i	−0.267651	−	0.125931i
$809$	−12.8313	+	7.40818i	−0.451126	+	0.260458i	−0.708306	−	0.705906i	$-0.750540\pi$
$809$	−12.8313	+	7.40818i	−0.451126	+	0.260458i	0.257180	+	0.966364i	$0.417207\pi$
$810$	−2.58433	−	22.3986i	−0.0908042	−	0.787006i
$811$	13.1986			0.463466			0.231733	−	0.972779i	$-0.425560\pi$
$811$	13.1986			0.463466			0.231733	+	0.972779i	$0.425560\pi$
$812$	33.9057	+	24.0877i	1.18986	+	0.845311i
$813$	6.26376	−	1.24539i	0.219680	−	0.0436778i
$814$	8.07041	+	1.19160i	0.282868	+	0.0417657i
$815$	−19.3935	+	33.5906i	−0.679326	+	1.17663i
$816$	−12.0430	+	29.2895i	−0.421591	+	1.02534i
$817$	0.393637	−	0.227266i	0.0137716	−	0.00795104i
$818$	38.8008	+	5.72896i	1.35664	+	0.200309i
$819$	20.9728	−	42.8059i	0.732848	−	1.49576i
$820$	−7.82804	+	25.9307i	−0.273367	+	0.905540i
$821$	−2.43413	−	4.21603i	−0.0849517	−	0.147141i	0.820419	−	0.571763i	$-0.193740\pi$
$821$	−2.43413	−	4.21603i	−0.0849517	−	0.147141i	−0.905371	+	0.424622i	$0.860407\pi$
$822$	0.684597	+	0.351139i	0.0238781	+	0.0122474i
$823$	−6.06588	+	10.5064i	−0.211443	+	0.366230i	−0.952166	−	0.305580i	$-0.901150\pi$
$823$	−6.06588	+	10.5064i	−0.211443	+	0.366230i	0.740723	+	0.671810i	$0.234483\pi$
$824$	−28.6274	−	13.4694i	−0.997284	−	0.469228i
$825$	2.80306	−	2.45780i	0.0975899	−	0.0855695i
$826$	−21.0091	+	13.6476i	−0.731002	+	0.474862i
$827$	−24.3006			−0.845016			−0.422508	−	0.906359i	$-0.638850\pi$
$827$	−24.3006			−0.845016			−0.422508	+	0.906359i	$0.638850\pi$
$828$	−2.80110	+	2.01221i	−0.0973449	+	0.0699293i
$829$	−6.03085	−	10.4457i	−0.209460	−	0.362795i	0.742085	−	0.670306i	$-0.233837\pi$
$829$	−6.03085	−	10.4457i	−0.209460	−	0.362795i	−0.951545	+	0.307511i	$0.900504\pi$
$830$	−1.93262	+	13.0891i	−0.0670821	+	0.454329i
$831$	6.55291	+	7.47343i	0.227318	+	0.259250i
$832$	16.7426	−	45.0328i	0.580446	−	1.56123i
$833$	−29.4937	+	12.4065i	−1.02190	+	0.429861i
$834$	−50.0340	+	2.48743i	−1.73254	+	0.0861326i
$835$	33.7234	−	19.4702i	1.16705	−	0.673795i
$836$	0.123114	+	0.524825i	0.00425800	+	0.0181515i
$837$	1.07781	+	16.5080i	0.0372547	+	0.570601i
$838$	28.1734	−	35.5471i	0.973234	−	1.22796i
$839$	0.261066	−	0.452179i	0.00901299	−	0.0156110i	−0.861484	−	0.507785i	$-0.830464\pi$
$839$	0.261066	−	0.452179i	0.00901299	−	0.0156110i	0.870497	+	0.492174i	$0.163798\pi$
$840$	12.3521	−	19.3553i	0.426188	−	0.667823i
$841$	−16.3895	−	28.3875i	−0.565157	−	0.978880i
$842$	28.1027	+	4.14939i	0.968484	+	0.142998i
$843$	−12.2747	+	2.44052i	−0.422763	+	0.0840559i
$844$	−2.93034	+	9.70687i	−0.100866	+	0.334124i
$845$	35.3875	+	20.4310i	1.21737	+	0.702848i
$846$	−37.5755	+	36.4021i	−1.29187	+	1.25153i
$847$	−19.1765	+	16.9105i	−0.658911	+	0.581052i
$848$	−21.9140	+	10.8800i	−0.752531	+	0.373620i
$849$	1.27199	+	6.39755i	0.0436547	+	0.219563i
$850$	9.43255	+	7.47590i	0.323534	+	0.256421i
$851$	−1.43419	+	2.48409i	−0.0491634	+	0.0851535i
$852$	−19.0215	−	1.84932i	−0.651666	−	0.0633566i
$853$	10.5786	−	18.3227i	0.362204	−	0.627357i	−0.626119	−	0.779728i	$-0.715358\pi$
$853$	10.5786	−	18.3227i	0.362204	−	0.627357i	0.988323	+	0.152371i	$0.0486909\pi$
$854$	−26.1932	+	1.37638i	−0.896313	+	0.0470987i
$855$	0.754491	−	0.982929i	0.0258030	−	0.0336155i
$856$	−10.8682	−	15.6357i	−0.371468	−	0.534418i
$857$	2.13882			0.0730608			0.0365304	−	0.999333i	$-0.488369\pi$
$857$	2.13882			0.0730608			0.0365304	+	0.999333i	$0.488369\pi$
$858$	−16.9845	+	0.844381i	−0.579843	+	0.0288267i
$859$	26.0884			0.890124			0.445062	−	0.895500i	$-0.353182\pi$
$859$	26.0884			0.890124			0.445062	+	0.895500i	$0.353182\pi$
$860$	1.57738	+	6.72421i	0.0537881	+	0.229294i
$861$	−32.3321	+	13.4932i	−1.10188	+	0.459845i
$862$	3.99561	−	5.04137i	0.136091	−	0.171710i
$863$	−0.940467	−	0.542979i	−0.0320139	−	0.0184832i	0.483908	−	0.875119i	$-0.339217\pi$
$863$	−0.940467	−	0.542979i	−0.0320139	−	0.0184832i	−0.515922	+	0.856636i	$0.672550\pi$
$864$	18.2015	−	23.0804i	0.619229	−	0.785210i
$865$	−16.3633	−	28.3421i	−0.556370	−	0.963660i
$866$	−3.73102	−	9.42305i	−0.126785	−	0.320208i
$867$	1.31521	+	6.61494i	0.0446670	+	0.224655i
$868$	−9.75688	+	13.7338i	−0.331170	+	0.466155i
$869$	5.14009	+	8.90289i	0.174366	+	0.302010i
$870$	−28.6535	+	18.4986i	−0.971445	+	0.627160i
$871$			28.9511i			0.980969i
$872$	−3.83457	−	45.6384i	−0.129855	−	1.54551i
$873$	−19.0507	+	24.8187i	−0.644768	+	0.839986i
$874$	−0.187509	−	0.0276858i	−0.00634258	−	0.000936487i
$875$	−21.2713	−	24.1216i	−0.719101	−	0.815458i
$876$	−19.3782	−	42.6261i	−0.654730	−	1.44020i
$877$		−	28.0268i		−	0.946398i	−0.880956	−	0.473199i	$-0.843099\pi$
$877$		−	28.0268i		−	0.946398i	0.880956	−	0.473199i	$-0.156901\pi$
$878$	29.3260	−	37.0014i	0.989703	−	1.24874i
$879$	0.463909	−	1.36626i	0.0156473	−	0.0460826i
$880$	−8.17522	−	0.513817i	−0.275587	−	0.0173208i
$881$	1.98225			0.0667838			0.0333919	−	0.999442i	$-0.489369\pi$
$881$	1.98225			0.0667838			0.0333919	+	0.999442i	$0.489369\pi$
$882$	29.4831	−	3.57065i	0.992746	−	0.120230i
$883$			51.4877i			1.73270i	0.499437	+	0.866350i	$0.333540\pi$
$883$			51.4877i			1.73270i	−0.499437	+	0.866350i	$0.666460\pi$
$884$	−12.5388	−	53.4516i	−0.421724	−	1.79777i
$885$	−4.00626	−	20.1497i	−0.134669	−	0.677325i
$886$	−12.5529	−	9.94901i	−0.421724	−	0.334244i
$887$	−20.4281			−0.685909			−0.342954	−	0.939352i	$-0.611428\pi$
$887$	−20.4281			−0.685909			−0.342954	+	0.939352i	$0.611428\pi$
$888$	5.89419	−	23.7248i	0.197796	−	0.796153i
$889$	−16.0090	+	14.1174i	−0.536926	+	0.473481i
$890$	−13.4838	−	1.99089i	−0.451977	−	0.0667348i
$891$	−10.0487	−	2.69615i	−0.336643	−	0.0903245i
$892$	15.5795	−	3.65466i	0.521640	−	0.122367i
$893$	−2.87514			−0.0962130
$894$	−20.4652	+	39.8998i	−0.684457	+	1.33445i
$895$	30.5353	−	17.6296i	1.02068	−	0.589291i
$896$	29.2108	−	6.53660i	0.975865	−	0.218372i
$897$	1.92245	−	5.66178i	0.0641886	−	0.189041i
$898$	−18.2863	−	46.1838i	−0.610222	−	1.54117i
$899$	21.6715	−	12.5120i	0.722784	−	0.417300i
$900$	−6.51768	−	9.07292i	−0.217256	−	0.302431i
$901$	−13.9794	+	24.2130i	−0.465720	+	0.806651i
$902$	9.79528	+	7.76338i	0.326147	+	0.258492i
$903$	−5.41948	+	7.10180i	−0.180349	+	0.236333i
$904$	−0.132631	−	1.57855i	−0.00441124	−	0.0525019i
$905$			12.8833i			0.428256i
$906$	−5.24315	+	10.2223i	−0.174192	+	0.339613i
$907$		−	46.4808i		−	1.54337i	−0.636005	−	0.771685i	$-0.719414\pi$
$907$		−	46.4808i		−	1.54337i	0.636005	−	0.771685i	$-0.280586\pi$
$908$	−22.5677	−	24.0306i	−0.748935	−	0.797484i
$909$	8.84166	+	1.16554i	0.293259	+	0.0386585i
$910$	2.08882	+	39.7514i	0.0692439	+	1.31775i
$911$	−29.7753	−	17.1908i	−0.986501	−	0.569557i	−0.0822746	−	0.996610i	$-0.526218\pi$
$911$	−29.7753	−	17.1908i	−0.986501	−	0.569557i	−0.904227	+	0.427053i	$0.859552\pi$
$912$	1.60101	−	0.215010i	0.0530149	−	0.00711970i
$913$	5.28732	+	3.05263i	0.174985	+	0.101027i
$914$	27.8079	+	22.0396i	0.919804	+	0.729004i
$915$	6.91553	−	20.3669i	0.228620	−	0.673308i
$916$	−36.1148	+	33.9162i	−1.19327	+	1.12062i
$917$	19.7758	+	22.4257i	0.653055	+	0.740562i
$918$	2.73099	−	33.4785i	0.0901360	−	1.10496i
$919$	−27.9981	+	48.4942i	−0.923574	+	1.59968i	−0.129735	+	0.991549i	$0.541413\pi$
$919$	−27.9981	+	48.4942i	−0.923574	+	1.59968i	−0.793839	+	0.608128i	$0.791921\pi$
$920$	1.22618	−	2.60609i	0.0404259	−	0.0859201i
$921$	30.2042	−	26.4838i	0.995261	−	0.872672i
$922$	28.8374	+	4.25786i	0.949708	+	0.140225i
$923$	28.6933	−	16.5661i	0.944452	−	0.545280i
$924$	−6.20573	−	8.58737i	−0.204154	−	0.282504i
$925$	−8.04611	−	4.64542i	−0.264554	−	0.152741i
$926$	−0.0261253	−	0.0207060i	−0.000858530	−	0.000680440i
$927$	33.2692	+	4.38566i	1.09270	+	0.144044i
$928$	−43.4918	−	9.24084i	−1.42769	−	0.303345i
$929$	13.9222	+	24.1139i	0.456772	+	0.791152i	0.998788	−	0.0492159i	$-0.0156723\pi$
$929$	13.9222	+	24.1139i	0.456772	+	0.791152i	−0.542016	+	0.840368i	$0.682339\pi$
$930$	−7.49298	−	11.6063i	−0.245704	−	0.380586i
$931$	1.30028	+	0.986463i	0.0426150	+	0.0323300i
$932$	−16.5620	+	3.88514i	−0.542506	+	0.127262i
$933$	1.37552	+	6.91826i	0.0450326	+	0.226494i
$934$	−48.6442	−	7.18236i	−1.59169	−	0.235014i
$935$	−8.10655	+	4.68032i	−0.265112	+	0.153063i
$936$	−2.40661	+	50.9020i	−0.0786624	+	1.66378i
$937$		−	6.03849i		−	0.197269i	−0.995124	−	0.0986344i	$-0.968553\pi$
$937$		−	6.03849i		−	0.197269i	0.995124	−	0.0986344i	$-0.0314474\pi$
$938$	−15.1261	+	9.82601i	−0.493885	+	0.320830i
$939$	2.76008	−	8.12867i	0.0900716	−	0.265269i
$940$	12.6261	−	41.8244i	0.411817	−	1.36416i
$941$	−10.4564	−	6.03702i	−0.340870	−	0.196801i	0.319787	−	0.947490i	$-0.396389\pi$
$941$	−10.4564	−	6.03702i	−0.340870	−	0.196801i	−0.660657	+	0.750688i	$0.729722\pi$
$942$	5.01223	+	7.76373i	0.163307	+	0.252956i
$943$	−3.80586	+	2.19732i	−0.123936	+	0.0715545i
$944$	14.8198	−	22.3087i	0.482344	−	0.726087i
$945$	−6.24464	+	23.5395i	−0.203138	+	0.765740i
$946$	3.15284	+	0.465520i	0.102508	+	0.0151353i
$947$	2.71098	+	4.69555i	0.0880949	+	0.152585i	0.906706	−	0.421764i	$-0.138589\pi$
$947$	2.71098	+	4.69555i	0.0880949	+	0.152585i	−0.818611	+	0.574348i	$0.805255\pi$
$948$	28.0437	−	12.7490i	0.910818	−	0.414067i
$949$	70.3012	+	40.5884i	2.28207	+	1.31756i
$950$	0.0896760	−	0.607352i	0.00290947	−	0.0197051i
$951$	28.1540	+	9.55965i	0.912957	+	0.309993i
$952$	23.6713	−	24.6927i	0.767191	−	0.800294i
$953$			41.6456i			1.34903i	0.738260	+	0.674517i	$0.235648\pi$
$953$			41.6456i			1.34903i	−0.738260	+	0.674517i	$0.764352\pi$
$954$	18.6384	−	18.0564i	0.603441	−	0.584597i
$955$	−14.2138	−	24.6190i	−0.459948	−	0.796653i
$956$	−0.587998	+	1.94777i	−0.0190172	+	0.0629954i
$957$	3.06898	+	15.4356i	0.0992062	+	0.498962i
$958$	−4.67657	+	1.85167i	−0.151093	+	0.0598247i
$959$	−0.549656	−	0.623308i	−0.0177493	−	0.0201277i
$960$	−3.90305	+	24.2340i	−0.125970	+	0.782147i
$961$	−10.4319	−	18.0686i	−0.336513	−	0.582858i
$962$	15.6021	+	39.4046i	0.503032	+	1.27045i
$963$	16.0213	+	12.2978i	0.516279	+	0.396292i
$964$	37.6240	+	40.0629i	1.21179	+	1.29034i
$965$	−37.5578	−	21.6840i	−1.20903	−	0.698032i
$966$	3.61060	−	0.917187i	0.116169	−	0.0295100i
$967$	18.5038	+	32.0494i	0.595041	+	1.03064i	0.993541	+	0.113473i	$0.0361974\pi$
$967$	18.5038	+	32.0494i	0.595041	+	1.03064i	−0.398500	+	0.917168i	$0.630469\pi$
$968$	11.6366	−	24.7321i	0.374015	−	0.794920i
$969$	1.38798	−	1.21702i	0.0445884	−	0.0390963i
$970$	3.81636	−	25.8472i	0.122536	−	0.829904i
$971$	−31.4872	−	18.1791i	−1.01047	−	0.583396i	−0.0991419	−	0.995073i	$-0.531610\pi$
$971$	−31.4872	−	18.1791i	−1.01047	−	0.583396i	−0.911330	+	0.411677i	$0.864943\pi$
$972$	−10.9552	+	29.1888i	−0.351388	+	0.936230i
$973$	51.2856	+	17.2525i	1.64414	+	0.553089i
$974$	36.9661	+	29.2980i	1.18447	+	0.938768i
$975$	18.3388	+	6.22692i	0.587313	+	0.199421i
$976$	25.1153	−	12.4693i	0.803920	−	0.399134i
$977$	−26.1542	−	15.1001i	−0.836746	−	0.483096i	0.0194106	−	0.999812i	$-0.493821\pi$
$977$	−26.1542	−	15.1001i	−0.836746	−	0.483096i	−0.856157	+	0.516716i	$0.827154\pi$
$978$	45.0583	−	29.0894i	1.44081	−	0.930177i
$979$	−3.14468	+	5.44675i	−0.100504	+	0.174079i
$980$	−20.0601	+	14.5830i	−0.640795	+	0.465837i
$981$	18.5822	+	44.8828i	0.593285	+	1.43300i
$982$	44.7571	+	35.4729i	1.42826	+	1.13198i
$983$	−21.4096			−0.682860			−0.341430	−	0.939907i	$-0.610911\pi$
$983$	−21.4096			−0.682860			−0.341430	+	0.939907i	$0.610911\pi$
$984$	25.9950	−	26.9637i	0.828689	−	0.859571i
$985$		−	8.90365i		−	0.283694i
$986$	−47.2412	+	18.7050i	−1.50447	+	0.595689i
$987$	52.1494	−	21.7635i	1.65993	−	0.692739i
$988$	−2.04143	+	1.91715i	−0.0649466	+	0.0609928i
$989$	−0.560290	+	0.970451i	−0.0178162	+	0.0308585i
$990$	8.42680	−	2.11530i	0.267821	−	0.0672288i
$991$	−11.0746	−	19.1818i	−0.351797	−	0.609330i	0.634768	−	0.772703i	$-0.281096\pi$
$991$	−11.0746	−	19.1818i	−0.351797	−	0.609330i	−0.986564	+	0.163373i	$0.947763\pi$
$992$	3.74307	−	17.6167i	0.118843	−	0.559330i
$993$	14.8925	−	43.8598i	0.472599	−	1.39185i
$994$	18.3939	+	9.36892i	0.583418	+	0.297164i
$995$	−2.15420	−	3.73119i	−0.0682928	−	0.118287i
$996$	10.6378	−	14.8845i	0.337071	−	0.471633i
$997$	11.3913			0.360765			0.180383	−	0.983596i	$-0.442266\pi$
$997$	11.3913			0.360765			0.180383	+	0.983596i	$0.442266\pi$
$998$	8.51202	+	21.4979i	0.269443	+	0.680504i
$999$	1.68931	+	25.8738i	0.0534473	+	0.818612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.12	✓	184
7.3	odd	6		504.2.ca.a.101.51	yes	184
8.5	even	2	inner	504.2.y.a.173.22	yes	184
9.5	odd	6		504.2.ca.a.5.42	yes	184
56.45	odd	6		504.2.ca.a.101.42	yes	184
63.59	even	6	inner	504.2.y.a.437.22	yes	184
72.5	odd	6		504.2.ca.a.5.51	yes	184
504.437	even	6	inner	504.2.y.a.437.12	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.12	✓	184	1.1	even	1	trivial
504.2.y.a.173.22	yes	184	8.5	even	2	inner
504.2.y.a.437.12	yes	184	504.437	even	6	inner
504.2.y.a.437.22	yes	184	63.59	even	6	inner
504.2.ca.a.5.42	yes	184	9.5	odd	6
504.2.ca.a.5.51	yes	184	72.5	odd	6
504.2.ca.a.101.42	yes	184	56.45	odd	6
504.2.ca.a.101.51	yes	184	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31489 + 0.520628i) q^{2} +(1.30232 - 1.14191i) q^{3} +(1.45789 - 1.36914i) q^{4} -1.77147i q^{5} +(-1.11790 + 2.17952i) q^{6} +(1.98439 - 1.74991i) q^{7} +(-1.20416 + 2.55930i) q^{8} +(0.392079 - 2.97427i) q^{9} +O(q^{10})\)	\(q+(-1.31489 + 0.520628i) q^{2} +(1.30232 - 1.14191i) q^{3} +(1.45789 - 1.36914i) q^{4} -1.77147i q^{5} +(-1.11790 + 2.17952i) q^{6} +(1.98439 - 1.74991i) q^{7} +(-1.20416 + 2.55930i) q^{8} +(0.392079 - 2.97427i) q^{9} +(0.922278 + 2.32930i) q^{10} +1.15601 q^{11} +(0.335208 - 3.44785i) q^{12} +(3.00278 + 5.20096i) q^{13} +(-1.69821 + 3.33408i) q^{14} +(-2.02286 - 2.30703i) q^{15} +(0.250907 - 3.99212i) q^{16} +(-2.28549 - 3.95859i) q^{17} +(1.03294 + 4.11498i) q^{18} +(-0.116580 + 0.201923i) q^{19} +(-2.42540 - 2.58262i) q^{20} +(0.586073 - 4.54494i) q^{21} +(-1.52003 + 0.601850i) q^{22} -0.574823i q^{23} +(1.35428 + 4.70807i) q^{24} +1.86188 q^{25} +(-6.65610 - 5.27539i) q^{26} +(-2.88574 - 4.32117i) q^{27} +(0.497158 - 5.26810i) q^{28} +(-3.92998 + 6.80693i) q^{29} +(3.86095 + 1.98034i) q^{30} +(-2.75720 - 1.59187i) q^{31} +(1.74849 + 5.37985i) q^{32} +(1.50549 - 1.32006i) q^{33} +(5.06613 + 4.01523i) q^{34} +(-3.09992 - 3.51530i) q^{35} +(-3.50058 - 4.87298i) q^{36} +(-4.32149 - 2.49501i) q^{37} +(0.0481641 - 0.326203i) q^{38} +(9.84962 + 3.34442i) q^{39} +(4.53372 + 2.13314i) q^{40} +(-3.82260 - 6.62094i) q^{41} +(1.59560 + 6.28125i) q^{42} +(-1.68826 - 0.974718i) q^{43} +(1.68534 - 1.58274i) q^{44} +(-5.26884 - 0.694557i) q^{45} +(0.299269 + 0.755831i) q^{46} +(6.16558 + 10.6791i) q^{47} +(-4.23189 - 5.48554i) q^{48} +(0.875624 - 6.94502i) q^{49} +(-2.44818 + 0.969348i) q^{50} +(-7.49680 - 2.54552i) q^{51} +(11.4986 + 3.47122i) q^{52} +(-3.05829 - 5.29711i) q^{53} +(6.04416 + 4.17949i) q^{54} -2.04784i q^{55} +(2.08901 + 7.18582i) q^{56} +(0.0787533 + 0.396093i) q^{57} +(1.62364 - 10.9965i) q^{58} +(5.79859 + 3.34782i) q^{59} +(-6.10776 - 0.593812i) q^{60} +(3.50504 + 6.07091i) q^{61} +(4.45419 + 0.657665i) q^{62} +(-4.42667 - 6.58822i) q^{63} +(-5.09998 - 6.16362i) q^{64} +(9.21336 - 5.31934i) q^{65} +(-1.29231 + 2.51954i) q^{66} +(4.17486 + 2.41036i) q^{67} +(-8.75187 - 2.64204i) q^{68} +(-0.656396 - 0.748604i) q^{69} +(5.90623 + 3.00834i) q^{70} -5.51692i q^{71} +(7.13990 + 4.58495i) q^{72} +(11.7060 - 6.75848i) q^{73} +(6.98127 + 1.03079i) q^{74} +(2.42477 - 2.12611i) q^{75} +(0.106500 + 0.453998i) q^{76} +(2.29397 - 2.02291i) q^{77} +(-14.6924 + 0.730428i) q^{78} +(4.44641 + 7.70141i) q^{79} +(-7.07194 - 0.444475i) q^{80} +(-8.69255 - 2.33229i) q^{81} +(8.47336 + 6.71568i) q^{82} +(4.57377 + 2.64067i) q^{83} +(-5.36824 - 7.42846i) q^{84} +(-7.01253 + 4.04869i) q^{85} +(2.72735 + 0.402696i) q^{86} +(2.65481 + 13.3525i) q^{87} +(-1.39202 + 2.95857i) q^{88} +(-2.72029 + 4.71168i) q^{89} +(7.28957 - 1.82983i) q^{90} +(15.0599 + 5.06616i) q^{91} +(-0.787013 - 0.838030i) q^{92} +(-5.40853 + 1.07535i) q^{93} +(-13.6669 - 10.8319i) q^{94} +(0.357702 + 0.206519i) q^{95} +(8.42041 + 5.00966i) q^{96} +(-9.03187 - 5.21455i) q^{97} +(2.46442 + 9.58784i) q^{98} +(0.453246 - 3.43828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more