LMFDB - Embedded newform 272.2.l.c.205.10

Error: no document with id 221828269 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.10
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.551708 + 1.30216i) q^{2} +(1.96031 + 1.96031i) q^{3} +(-1.39124 + 1.43682i) q^{4} +(1.05453 - 1.05453i) q^{5} +(-1.47112 + 3.63416i) q^{6} -1.60770i q^{7} +(-2.63853 - 1.01891i) q^{8} +4.68564i q^{9} +(1.95497 + 0.791377i) q^{10} +(-0.724466 + 0.724466i) q^{11} +(-5.54388 + 0.0893599i) q^{12} +(1.37028 + 1.37028i) q^{13} +(2.09348 - 0.886980i) q^{14} +4.13443 q^{15} +(-0.128916 - 3.99792i) q^{16} +1.00000 q^{17} +(-6.10145 + 2.58510i) q^{18} +(-5.48700 - 5.48700i) q^{19} +(0.0480705 + 2.98229i) q^{20} +(3.15159 - 3.15159i) q^{21} +(-1.34306 - 0.543677i) q^{22} -5.51739i q^{23} +(-3.17496 - 7.16971i) q^{24} +2.77591i q^{25} +(-1.02833 + 2.54031i) q^{26} +(-3.30438 + 3.30438i) q^{27} +(2.30998 + 2.23669i) q^{28} +(-1.28356 - 1.28356i) q^{29} +(2.28100 + 5.38369i) q^{30} +1.34829 q^{31} +(5.13481 - 2.37355i) q^{32} -2.84036 q^{33} +(0.551708 + 1.30216i) q^{34} +(-1.69538 - 1.69538i) q^{35} +(-6.73243 - 6.51884i) q^{36} +(5.94579 - 5.94579i) q^{37} +(4.11773 - 10.1722i) q^{38} +5.37234i q^{39} +(-3.85689 + 1.70795i) q^{40} +6.91756i q^{41} +(5.84263 + 2.36512i) q^{42} +(-5.88071 + 5.88071i) q^{43} +(-0.0330245 - 2.04883i) q^{44} +(4.94117 + 4.94117i) q^{45} +(7.18453 - 3.04399i) q^{46} +5.56036 q^{47} +(7.58446 - 8.08989i) q^{48} +4.41530 q^{49} +(-3.61468 + 1.53149i) q^{50} +(1.96031 + 1.96031i) q^{51} +(-3.87522 + 0.0624635i) q^{52} +(-7.64720 + 7.64720i) q^{53} +(-6.12588 - 2.47978i) q^{54} +1.52795i q^{55} +(-1.63810 + 4.24196i) q^{56} -21.5124i q^{57} +(0.963249 - 2.37955i) q^{58} +(-5.19243 + 5.19243i) q^{59} +(-5.75198 + 5.94044i) q^{60} +(1.72030 + 1.72030i) q^{61} +(0.743864 + 1.75569i) q^{62} +7.53310 q^{63} +(5.92366 + 5.37683i) q^{64} +2.89001 q^{65} +(-1.56705 - 3.69860i) q^{66} +(-1.29869 - 1.29869i) q^{67} +(-1.39124 + 1.43682i) q^{68} +(10.8158 - 10.8158i) q^{69} +(1.27230 - 3.14300i) q^{70} +8.65770i q^{71} +(4.77423 - 12.3632i) q^{72} -14.0841i q^{73} +(11.0227 + 4.46203i) q^{74} +(-5.44165 + 5.44165i) q^{75} +(15.5176 - 0.250122i) q^{76} +(1.16472 + 1.16472i) q^{77} +(-6.99564 + 2.96396i) q^{78} -12.4517 q^{79} +(-4.35189 - 4.08000i) q^{80} +1.10169 q^{81} +(-9.00777 + 3.81647i) q^{82} +(1.07636 + 1.07636i) q^{83} +(0.143664 + 8.91289i) q^{84} +(1.05453 - 1.05453i) q^{85} +(-10.9021 - 4.41319i) q^{86} -5.03235i q^{87} +(2.64969 - 1.17336i) q^{88} -10.0589i q^{89} +(-3.70811 + 9.16027i) q^{90} +(2.20299 - 2.20299i) q^{91} +(7.92751 + 7.67601i) q^{92} +(2.64307 + 2.64307i) q^{93} +(3.06769 + 7.24047i) q^{94} -11.5725 q^{95} +(14.7187 + 5.41292i) q^{96} -13.2842 q^{97} +(2.43595 + 5.74943i) q^{98} +(-3.39459 - 3.39459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.551708	+	1.30216i	0.390116	+	0.920766i
$2$	0.551708	+	1.30216i	0.390116	+	0.920766i
$3$	1.96031	+	1.96031i	1.13179	+	1.13179i	0.989880	+	0.141906i	$0.0453231\pi$
$3$	1.96031	+	1.96031i	1.13179	+	1.13179i	0.141906	+	0.989880i	$0.454677\pi$
$4$	−1.39124	+	1.43682i	−0.695619	+	0.718411i
$5$	1.05453	−	1.05453i	0.471602	−	0.471602i	−0.430831	−	0.902433i	$-0.641779\pi$
$5$	1.05453	−	1.05453i	0.471602	−	0.471602i	0.902433	+	0.430831i	$0.141779\pi$
$6$	−1.47112	+	3.63416i	−0.600582	+	1.48364i
$7$		−	1.60770i		−	0.607653i	−0.952727	−	0.303827i	$-0.901736\pi$
$7$		−	1.60770i		−	0.607653i	0.952727	−	0.303827i	$-0.0982644\pi$
$8$	−2.63853	−	1.01891i	−0.932860	−	0.360238i
$9$			4.68564i			1.56188i
$10$	1.95497	+	0.791377i	0.618215	+	0.250256i
$11$	−0.724466	+	0.724466i	−0.218435	+	0.218435i	−0.807839	−	0.589404i	$-0.799363\pi$
$11$	−0.724466	+	0.724466i	−0.218435	+	0.218435i	0.589404	+	0.807839i	$0.299363\pi$
$12$	−5.54388	+	0.0893599i	−1.60038	+	0.0257960i
$13$	1.37028	+	1.37028i	0.380046	+	0.380046i	0.871119	−	0.491072i	$-0.163395\pi$
$13$	1.37028	+	1.37028i	0.380046	+	0.380046i	−0.491072	+	0.871119i	$0.663395\pi$
$14$	2.09348	−	0.886980i	0.559506	−	0.237055i
$15$	4.13443			1.06751
$16$	−0.128916	−	3.99792i	−0.0322290	−	0.999481i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−6.10145	+	2.58510i	−1.43813	+	0.609315i
$19$	−5.48700	−	5.48700i	−1.25880	−	1.25880i	−0.951665	−	0.307138i	$-0.900629\pi$
$19$	−5.48700	−	5.48700i	−1.25880	−	1.25880i	−0.307138	−	0.951665i	$-0.599371\pi$
$20$	0.0480705	+	2.98229i	0.0107489	+	0.666860i
$21$	3.15159	−	3.15159i	0.687734	−	0.687734i
$22$	−1.34306	−	0.543677i	−0.286342	−	0.115912i
$23$		−	5.51739i		−	1.15046i	−0.817993	−	0.575228i	$-0.804913\pi$
$23$		−	5.51739i		−	1.15046i	0.817993	−	0.575228i	$-0.195087\pi$
$24$	−3.17496	−	7.16971i	−0.648086	−	1.46351i
$25$			2.77591i			0.555183i
$26$	−1.02833	+	2.54031i	−0.201671	+	0.498196i
$27$	−3.30438	+	3.30438i	−0.635928	+	0.635928i
$28$	2.30998	+	2.23669i	0.436545	+	0.422695i
$29$	−1.28356	−	1.28356i	−0.238351	−	0.238351i	0.577816	−	0.816167i	$-0.303905\pi$
$29$	−1.28356	−	1.28356i	−0.238351	−	0.238351i	−0.816167	+	0.577816i	$0.803905\pi$
$30$	2.28100	+	5.38369i	0.416451	+	0.982923i
$31$	1.34829			0.242161			0.121080	−	0.992643i	$-0.461364\pi$
$31$	1.34829			0.242161			0.121080	+	0.992643i	$0.461364\pi$
$32$	5.13481	−	2.37355i	0.907714	−	0.419589i
$33$	−2.84036			−0.494443
$34$	0.551708	+	1.30216i	0.0946171	+	0.223318i
$35$	−1.69538	−	1.69538i	−0.286571	−	0.286571i
$36$	−6.73243	−	6.51884i	−1.12207	−	1.08647i
$37$	5.94579	−	5.94579i	0.977483	−	0.977483i	−0.0222694	−	0.999752i	$-0.507089\pi$
$37$	5.94579	−	5.94579i	0.977483	−	0.977483i	0.999752	+	0.0222694i	$0.00708917\pi$
$38$	4.11773	−	10.1722i	0.667983	−	1.65014i
$39$			5.37234i			0.860262i
$40$	−3.85689	+	1.70795i	−0.609828	+	0.270050i
$41$			6.91756i			1.08034i	0.841555	+	0.540171i	$0.181640\pi$
$41$			6.91756i			1.08034i	−0.841555	+	0.540171i	$0.818360\pi$
$42$	5.84263	+	2.36512i	0.901538	+	0.364946i
$43$	−5.88071	+	5.88071i	−0.896800	+	0.896800i	−0.995152	−	0.0983514i	$-0.968643\pi$
$43$	−5.88071	+	5.88071i	−0.896800	+	0.896800i	0.0983514	+	0.995152i	$0.468643\pi$
$44$	−0.0330245	−	2.04883i	−0.00497863	−	0.308873i
$45$	4.94117	+	4.94117i	0.736586	+	0.736586i
$46$	7.18453	−	3.04399i	1.05930	−	0.448811i
$47$	5.56036			0.811061			0.405531	−	0.914081i	$-0.367087\pi$
$47$	5.56036			0.811061			0.405531	+	0.914081i	$0.367087\pi$
$48$	7.58446	−	8.08989i	1.09472	−	1.16767i
$49$	4.41530			0.630757
$50$	−3.61468	+	1.53149i	−0.511193	+	0.216586i
$51$	1.96031	+	1.96031i	0.274498	+	0.274498i
$52$	−3.87522	+	0.0624635i	−0.537397	+	0.00866212i
$53$	−7.64720	+	7.64720i	−1.05042	+	1.05042i	−0.0517650	+	0.998659i	$0.516485\pi$
$53$	−7.64720	+	7.64720i	−1.05042	+	1.05042i	−0.998659	+	0.0517650i	$0.983515\pi$
$54$	−6.12588	−	2.47978i	−0.833627	−	0.337455i
$55$			1.52795i			0.206029i
$56$	−1.63810	+	4.24196i	−0.218900	+	0.566856i
$57$		−	21.5124i		−	2.84939i
$58$	0.963249	−	2.37955i	0.126481	−	0.312450i
$59$	−5.19243	+	5.19243i	−0.675997	+	0.675997i	−0.959092	−	0.283095i	$-0.908639\pi$
$59$	−5.19243	+	5.19243i	−0.675997	+	0.675997i	0.283095	+	0.959092i	$0.408639\pi$
$60$	−5.75198	+	5.94044i	−0.742577	+	0.766908i
$61$	1.72030	+	1.72030i	0.220262	+	0.220262i	0.808609	−	0.588347i	$-0.200221\pi$
$61$	1.72030	+	1.72030i	0.220262	+	0.220262i	−0.588347	+	0.808609i	$0.700221\pi$
$62$	0.743864	+	1.75569i	0.0944708	+	0.222973i
$63$	7.53310			0.949082
$64$	5.92366	+	5.37683i	0.740457	+	0.672104i
$65$	2.89001			0.358461
$66$	−1.56705	−	3.69860i	−0.192890	−	0.455266i
$67$	−1.29869	−	1.29869i	−0.158661	−	0.158661i	0.623312	−	0.781973i	$-0.285787\pi$
$67$	−1.29869	−	1.29869i	−0.158661	−	0.158661i	−0.781973	+	0.623312i	$0.785787\pi$
$68$	−1.39124	+	1.43682i	−0.168712	+	0.174240i
$69$	10.8158	−	10.8158i	1.30207	−	1.30207i
$70$	1.27230	−	3.14300i	0.152069	−	0.375660i
$71$			8.65770i			1.02748i	0.857946	+	0.513740i	$0.171740\pi$
$71$			8.65770i			1.02748i	−0.857946	+	0.513740i	$0.828260\pi$
$72$	4.77423	−	12.3632i	0.562649	−	1.45702i
$73$		−	14.0841i		−	1.64842i	−0.566286	−	0.824209i	$-0.691620\pi$
$73$		−	14.0841i		−	1.64842i	0.566286	−	0.824209i	$-0.308380\pi$
$74$	11.0227	+	4.46203i	1.28136	+	0.518701i
$75$	−5.44165	+	5.44165i	−0.628348	+	0.628348i
$76$	15.5176	−	0.250122i	1.77999	−	0.0286910i
$77$	1.16472	+	1.16472i	0.132733	+	0.132733i
$78$	−6.99564	+	2.96396i	−0.792100	+	0.335602i
$79$	−12.4517			−1.40093			−0.700463	−	0.713689i	$-0.747023\pi$
$79$	−12.4517			−1.40093			−0.700463	+	0.713689i	$0.747023\pi$
$80$	−4.35189	−	4.08000i	−0.486557	−	0.456158i
$81$	1.10169			0.122410
$82$	−9.00777	+	3.81647i	−0.994742	+	0.421459i
$83$	1.07636	+	1.07636i	0.118146	+	0.118146i	0.763708	−	0.645562i	$-0.223377\pi$
$83$	1.07636	+	1.07636i	0.118146	+	0.118146i	−0.645562	+	0.763708i	$0.723377\pi$
$84$	0.143664	+	8.91289i	0.0156750	+	0.972476i
$85$	1.05453	−	1.05453i	0.114380	−	0.114380i
$86$	−10.9021	−	4.41319i	−1.17560	−	0.475887i
$87$		−	5.03235i		−	0.539525i
$88$	2.64969	−	1.17336i	0.282458	−	0.125081i
$89$		−	10.0589i		−	1.06624i	−0.846039	−	0.533121i	$-0.821019\pi$
$89$		−	10.0589i		−	1.06624i	0.846039	−	0.533121i	$-0.178981\pi$
$90$	−3.70811	+	9.16027i	−0.390869	+	0.965577i
$91$	2.20299	−	2.20299i	0.230936	−	0.230936i
$92$	7.92751	+	7.67601i	0.826500	+	0.800279i
$93$	2.64307	+	2.64307i	0.274074	+	0.274074i
$94$	3.06769	+	7.24047i	0.316408	+	0.746797i
$95$	−11.5725			−1.18731
$96$	14.7187	+	5.41292i	1.50222	+	0.552454i
$97$	−13.2842			−1.34881			−0.674404	−	0.738363i	$-0.735599\pi$
$97$	−13.2842			−1.34881			−0.674404	+	0.738363i	$0.735599\pi$
$98$	2.43595	+	5.74943i	0.246069	+	0.580780i
$99$	−3.39459	−	3.39459i	−0.341169	−	0.341169i
$100$	−3.98849	−	3.86195i	−0.398849	−	0.386195i
$101$	0.716729	−	0.716729i	0.0713172	−	0.0713172i	−0.670549	−	0.741866i	$-0.733941\pi$
$101$	0.716729	−	0.716729i	0.0713172	−	0.0713172i	0.741866	+	0.670549i	$0.233941\pi$
$102$	−1.47112	+	3.63416i	−0.145662	+	0.359835i
$103$		−	17.8298i		−	1.75682i	−0.477905	−	0.878411i	$-0.658604\pi$
$103$		−	17.8298i		−	1.75682i	0.477905	−	0.878411i	$-0.341396\pi$
$104$	−2.21933	−	5.01170i	−0.217623	−	0.491437i
$105$		−	6.64693i		−	0.648674i
$106$	−14.1769	−	5.73886i	−1.37698	−	0.557407i
$107$	0.386461	−	0.386461i	0.0373606	−	0.0373606i	−0.688180	−	0.725540i	$-0.741590\pi$
$107$	0.386461	−	0.386461i	0.0373606	−	0.0373606i	0.725540	+	0.688180i	$0.241590\pi$
$108$	−0.150629	−	9.34499i	−0.0144943	−	0.899222i
$109$	0.258287	+	0.258287i	0.0247394	+	0.0247394i	0.719368	−	0.694629i	$-0.244431\pi$
$109$	0.258287	+	0.258287i	0.0247394	+	0.0247394i	−0.694629	+	0.719368i	$0.744431\pi$
$110$	−1.98963	+	0.842981i	−0.189704	+	0.0803751i
$111$	23.3112			2.21260
$112$	−6.42746	+	0.207258i	−0.607338	+	0.0195840i
$113$	10.6745			1.00417			0.502085	−	0.864818i	$-0.332566\pi$
$113$	10.6745			1.00417			0.502085	+	0.864818i	$0.332566\pi$
$114$	28.0126	−	11.8686i	2.62362	−	1.11159i
$115$	−5.81828	−	5.81828i	−0.542558	−	0.542558i
$116$	3.62998	−	0.0585105i	0.337035	−	0.00543256i
$117$	−6.42062	+	6.42062i	−0.593587	+	0.593587i
$118$	−9.62608	−	3.89667i	−0.886153	−	0.358718i
$119$		−	1.60770i		−	0.147378i
$120$	−10.9088	−	4.21260i	−0.995834	−	0.384556i
$121$			9.95030i			0.904573i
$122$	−1.29100	+	3.18921i	−0.116882	+	0.288737i
$123$	−13.5606	+	13.5606i	−1.22272	+	1.22272i
$124$	−1.87580	+	1.93726i	−0.168451	+	0.173971i
$125$	8.19997	+	8.19997i	0.733428	+	0.733428i
$126$	4.15607	+	9.80930i	0.370252	+	0.873882i
$127$	−15.3191			−1.35935			−0.679677	−	0.733511i	$-0.737880\pi$
$127$	−15.3191			−1.35935			−0.679677	+	0.733511i	$0.737880\pi$
$128$	−3.73336	+	10.6800i	−0.329986	+	0.943986i
$129$	−23.0561			−2.02997
$130$	1.59444	+	3.76325i	0.139842	+	0.330059i
$131$	5.04411	+	5.04411i	0.440706	+	0.440706i	0.892249	−	0.451543i	$-0.149126\pi$
$131$	5.04411	+	5.04411i	0.440706	+	0.440706i	−0.451543	+	0.892249i	$0.649126\pi$
$132$	3.95161	−	4.08109i	0.343944	−	0.355213i
$133$	−8.82144	+	8.82144i	−0.764916	+	0.764916i
$134$	0.974607	−	2.40760i	0.0841932	−	0.207985i
$135$			6.96917i			0.599810i
$136$	−2.63853	−	1.01891i	−0.226252	−	0.0873706i
$137$			15.6615i			1.33805i	0.743240	+	0.669025i	$0.233288\pi$
$137$			15.6615i			1.33805i	−0.743240	+	0.669025i	$0.766712\pi$
$138$	20.0511	+	8.11674i	1.70686	+	0.690943i
$139$	−7.00332	+	7.00332i	−0.594014	+	0.594014i	−0.938713	−	0.344699i	$-0.887981\pi$
$139$	−7.00332	+	7.00332i	−0.594014	+	0.594014i	0.344699	+	0.938713i	$0.387981\pi$
$140$	4.79462	−	0.0772829i	0.405220	−	0.00653160i
$141$	10.9000	+	10.9000i	0.917948	+	0.917948i
$142$	−11.2737	+	4.77652i	−0.946068	+	0.400836i
$143$	−1.98544			−0.166031
$144$	18.7328	−	0.604053i	1.56107	−	0.0503378i
$145$	−2.70712			−0.224814
$146$	18.3397	−	7.77030i	1.51781	−	0.643074i
$147$	8.65536	+	8.65536i	0.713882	+	0.713882i
$148$	0.271036	+	16.8151i	0.0222791	+	1.38219i
$149$	−4.30738	+	4.30738i	−0.352875	+	0.352875i	−0.861178	−	0.508303i	$-0.830273\pi$
$149$	−4.30738	+	4.30738i	−0.352875	+	0.352875i	0.508303	+	0.861178i	$0.330273\pi$
$150$	−10.0881	−	4.08370i	−0.823690	−	0.333433i
$151$		−	23.9641i		−	1.95017i	−0.221837	−	0.975084i	$-0.571205\pi$
$151$		−	23.9641i		−	1.95017i	0.221837	−	0.975084i	$-0.428795\pi$
$152$	8.88685	+	20.0683i	0.720819	+	1.62776i
$153$			4.68564i			0.378812i
$154$	−0.874069	+	2.15924i	−0.0704345	+	0.173997i
$155$	1.42182	−	1.42182i	0.114203	−	0.114203i
$156$	−7.71909	−	7.47420i	−0.618022	−	0.598415i
$157$	−7.80772	−	7.80772i	−0.623124	−	0.623124i	0.323205	−	0.946329i	$-0.395240\pi$
$157$	−7.80772	−	7.80772i	−0.623124	−	0.623124i	−0.946329	+	0.323205i	$0.895240\pi$
$158$	−6.86970	−	16.2141i	−0.546524	−	1.28992i
$159$	−29.9818			−2.37771
$160$	2.91184	−	7.91783i	0.230201	−	0.625959i
$161$	−8.87031			−0.699079
$162$	0.607812	+	1.43458i	0.0477542	+	0.112711i
$163$	13.4225	+	13.4225i	1.05133	+	1.05133i	0.998609	+	0.0527235i	$0.0167902\pi$
$163$	13.4225	+	13.4225i	1.05133	+	1.05133i	0.0527235	+	0.998609i	$0.483210\pi$
$164$	−9.93931	−	9.62397i	−0.776130	−	0.751506i
$165$	−2.99526	+	2.99526i	−0.233180	+	0.233180i
$166$	−0.807760	+	1.99544i	−0.0626943	+	0.154876i
$167$			14.9633i			1.15789i	0.815366	+	0.578946i	$0.196536\pi$
$167$			14.9633i			1.15789i	−0.815366	+	0.578946i	$0.803464\pi$
$168$	−11.5267	+	5.10438i	−0.889308	+	0.393812i
$169$		−	9.24468i		−	0.711130i
$170$	1.95497	+	0.791377i	0.149939	+	0.0606959i
$171$	25.7101	−	25.7101i	1.96610	−	1.96610i
$172$	−0.268070	−	16.6310i	−0.0204401	−	1.26810i
$173$	−1.20838	−	1.20838i	−0.0918714	−	0.0918714i	0.659677	−	0.751549i	$-0.270693\pi$
$173$	−1.20838	−	1.20838i	−0.0918714	−	0.0918714i	−0.751549	+	0.659677i	$0.770693\pi$
$174$	6.55292	−	2.77639i	0.496776	−	0.210477i
$175$	4.46284			0.337359
$176$	2.98975	+	2.80296i	0.225361	+	0.211281i
$177$	−20.3576			−1.53017
$178$	13.0983	−	5.54958i	0.981760	−	0.415959i
$179$	−10.4732	−	10.4732i	−0.782803	−	0.782803i	0.197500	−	0.980303i	$-0.436718\pi$
$179$	−10.4732	−	10.4732i	−0.782803	−	0.782803i	−0.980303	+	0.197500i	$0.936718\pi$
$180$	−13.9739	+	0.225241i	−1.04155	+	0.0167885i
$181$	−7.87464	+	7.87464i	−0.585317	+	0.585317i	−0.936360	−	0.351042i	$-0.885827\pi$
$181$	−7.87464	+	7.87464i	−0.585317	+	0.585317i	0.351042	+	0.936360i	$0.385827\pi$
$182$	4.08406	+	1.65324i	0.302730	+	0.122546i
$183$			6.74465i			0.498579i
$184$	−5.62171	+	14.5578i	−0.414438	+	1.07321i
$185$		−	12.5401i		−	0.921966i
$186$	−1.98350	+	4.89991i	−0.145437	+	0.359279i
$187$	−0.724466	+	0.724466i	−0.0529782	+	0.0529782i
$188$	−7.73578	+	7.98924i	−0.564189	+	0.582675i
$189$	5.31245	+	5.31245i	0.386424	+	0.386424i
$190$	−6.38461	−	15.0692i	−0.463188	−	1.09323i
$191$	13.3673			0.967227			0.483614	−	0.875282i	$-0.339324\pi$
$191$	13.3673			0.967227			0.483614	+	0.875282i	$0.339324\pi$
$192$	1.07195	+	22.1525i	0.0773612	+	1.59872i
$193$	4.82232			0.347118			0.173559	−	0.984823i	$-0.444473\pi$
$193$	4.82232			0.347118			0.173559	+	0.984823i	$0.444473\pi$
$194$	−7.32900	−	17.2982i	−0.526191	−	1.24194i
$195$	5.66532	+	5.66532i	0.405702	+	0.405702i
$196$	−6.14273	+	6.34400i	−0.438767	+	0.453143i
$197$	−14.6378	+	14.6378i	−1.04290	+	1.04290i	−0.0438628	+	0.999038i	$0.513966\pi$
$197$	−14.6378	+	14.6378i	−1.04290	+	1.04290i	−0.999038	+	0.0438628i	$0.986034\pi$
$198$	2.54747	−	6.29311i	0.181041	−	0.447232i
$199$		−	23.7624i		−	1.68447i	−0.539108	−	0.842237i	$-0.681238\pi$
$199$		−	23.7624i		−	1.68447i	0.539108	−	0.842237i	$-0.318762\pi$
$200$	2.82840	−	7.32432i	0.199998	−	0.517908i
$201$		−	5.09169i		−	0.359140i
$202$	1.32872	+	0.537870i	0.0934884	+	0.0378444i
$203$	−2.06358	+	2.06358i	−0.144835	+	0.144835i
$204$	−5.54388	+	0.0893599i	−0.388149	+	0.00625645i
$205$	7.29481	+	7.29481i	0.509492	+	0.509492i
$206$	23.2172	−	9.83684i	1.61762	−	0.685365i
$207$	25.8525			1.79687
$208$	5.30161	−	5.65491i	0.367600	−	0.392097i
$209$	7.95028			0.549933
$210$	8.65536	−	3.66716i	0.597276	−	0.253058i
$211$	−0.627868	−	0.627868i	−0.0432242	−	0.0432242i	0.685164	−	0.728389i	$-0.259730\pi$
$211$	−0.627868	−	0.627868i	−0.0432242	−	0.0432242i	−0.728389	+	0.685164i	$0.759730\pi$
$212$	−0.348594	−	21.6267i	−0.0239416	−	1.48533i
$213$	−16.9718	+	16.9718i	−1.16289	+	1.16289i
$214$	0.716447	+	0.290020i	0.0489753	+	0.0198254i
$215$			12.4028i			0.845866i
$216$	12.0856	−	5.35184i	0.822318	−	0.364147i
$217$		−	2.16765i		−	0.147150i
$218$	−0.193832	+	0.478830i	−0.0131280	+	0.0324305i
$219$	27.6092	−	27.6092i	1.86566	−	1.86566i
$220$	−2.19539	−	2.12574i	−0.148013	−	0.143317i
$221$	1.37028	+	1.37028i	0.0921748	+	0.0921748i
$222$	12.8610	+	30.3549i	0.863172	+	2.03729i
$223$	6.74698			0.451811			0.225906	−	0.974149i	$-0.427466\pi$
$223$	6.74698			0.451811			0.225906	+	0.974149i	$0.427466\pi$
$224$	−3.81596	−	8.25523i	−0.254965	−	0.551576i
$225$	−13.0069			−0.867129
$226$	5.88919	+	13.8999i	0.391743	+	0.924606i
$227$	4.32687	+	4.32687i	0.287184	+	0.287184i	0.835966	−	0.548781i	$-0.184908\pi$
$227$	4.32687	+	4.32687i	0.287184	+	0.287184i	−0.548781	+	0.835966i	$0.684908\pi$
$228$	30.9096	+	29.9289i	2.04704	+	1.98209i
$229$	10.2496	−	10.2496i	0.677310	−	0.677310i	−0.282081	−	0.959391i	$-0.591025\pi$
$229$	10.2496	−	10.2496i	0.677310	−	0.677310i	0.959391	+	0.282081i	$0.0910246\pi$
$230$	4.36634	−	10.7863i	0.287908	−	0.711229i
$231$			4.56644i			0.300450i
$232$	2.07888	+	4.69453i	0.136485	+	0.308211i
$233$			6.26605i			0.410503i	0.978709	+	0.205251i	$0.0658012\pi$
$233$			6.26605i			0.410503i	−0.978709	+	0.205251i	$0.934199\pi$
$234$	−11.9030	−	4.81837i	−0.778122	−	0.314987i
$235$	5.86359	−	5.86359i	0.382498	−	0.382498i
$236$	−0.236695	−	14.6845i	−0.0154075	−	0.955880i
$237$	−24.4092	−	24.4092i	−1.58555	−	1.58555i
$238$	2.09348	−	0.886980i	0.135700	−	0.0574944i
$239$	18.2979			1.18359			0.591797	−	0.806087i	$-0.298419\pi$
$239$	18.2979			1.18359			0.591797	+	0.806087i	$0.298419\pi$
$240$	−0.532994	−	16.5291i	−0.0344046	−	1.06695i
$241$	23.1376			1.49043			0.745213	−	0.666827i	$-0.232348\pi$
$241$	23.1376			1.49043			0.745213	+	0.666827i	$0.232348\pi$
$242$	−12.9569	+	5.48965i	−0.832899	+	0.352888i
$243$	12.0728	+	12.0728i	0.774471	+	0.774471i
$244$	−4.86511	+	0.0784192i	−0.311457	+	0.00502027i
$245$	4.65609	−	4.65609i	0.297467	−	0.297467i
$246$	−25.1395	−	10.1766i	−1.60284	−	0.648834i
$247$		−	15.0374i		−	0.956807i
$248$	−3.55751	−	1.37379i	−0.225902	−	0.0872355i
$249$			4.22002i			0.267433i
$250$	−6.15368	+	15.2017i	−0.389193	+	0.961437i
$251$	−12.9086	+	12.9086i	−0.814787	+	0.814787i	−0.985347	−	0.170561i	$-0.945442\pi$
$251$	−12.9086	+	12.9086i	−0.814787	+	0.814787i	0.170561	+	0.985347i	$0.445442\pi$
$252$	−10.4803	+	10.8237i	−0.660199	+	0.681831i
$253$	3.99716	+	3.99716i	0.251300	+	0.251300i
$254$	−8.45169	−	19.9480i	−0.530306	−	1.25165i
$255$	4.13443			0.258908
$256$	−15.9668	+	1.03079i	−0.997923	+	0.0644245i
$257$	10.0549			0.627210			0.313605	−	0.949554i	$-0.398463\pi$
$257$	10.0549			0.627210			0.313605	+	0.949554i	$0.398463\pi$
$258$	−12.7202	−	30.0227i	−0.791925	−	1.86913i
$259$	−9.55905	−	9.55905i	−0.593971	−	0.593971i
$260$	−4.02069	+	4.15243i	−0.249352	+	0.257523i
$261$	6.01430	−	6.01430i	0.372276	−	0.372276i
$262$	−3.78536	+	9.35112i	−0.233861	+	0.577714i
$263$		−	10.4858i		−	0.646584i	−0.946299	−	0.323292i	$-0.895210\pi$
$263$		−	10.4858i		−	0.646584i	0.946299	−	0.323292i	$-0.104790\pi$
$264$	7.49436	+	2.89406i	0.461246	+	0.178117i
$265$			16.1285i			0.990765i
$266$	−16.3538	−	6.62007i	−1.00271	−	0.405902i
$267$	19.7186	−	19.7186i	1.20676	−	1.20676i
$268$	3.67278	−	0.0592004i	0.224351	−	0.00361624i
$269$	9.98749	+	9.98749i	0.608948	+	0.608948i	0.942671	−	0.333723i	$-0.108305\pi$
$269$	9.98749	+	9.98749i	0.608948	+	0.608948i	−0.333723	+	0.942671i	$0.608305\pi$
$270$	−9.07497	+	3.84494i	−0.552285	+	0.233996i
$271$	−19.4844			−1.18359			−0.591797	−	0.806087i	$-0.701581\pi$
$271$	−19.4844			−1.18359			−0.591797	+	0.806087i	$0.701581\pi$
$272$	−0.128916	−	3.99792i	−0.00781667	−	0.242410i
$273$	8.63711			0.522741
$274$	−20.3937	+	8.64056i	−1.23203	+	0.521995i
$275$	−2.01105	−	2.01105i	−0.121271	−	0.121271i
$276$	0.493034	+	30.5878i	0.0296772	+	1.84117i
$277$	−2.73538	+	2.73538i	−0.164353	+	0.164353i	−0.784492	−	0.620139i	$-0.787076\pi$
$277$	−2.73538	+	2.73538i	−0.164353	+	0.164353i	0.620139	+	0.784492i	$0.287076\pi$
$278$	−12.9832	−	5.25566i	−0.778682	−	0.315213i
$279$			6.31762i			0.378226i
$280$	2.74586	+	6.20072i	0.164097	+	0.370564i
$281$		−	2.29100i		−	0.136670i	−0.997662	−	0.0683349i	$-0.978231\pi$
$281$		−	2.29100i		−	0.136670i	0.997662	−	0.0683349i	$-0.0217686\pi$
$282$	−8.17995	+	20.2072i	−0.487109	+	1.20332i
$283$	−11.4138	+	11.4138i	−0.678480	+	0.678480i	−0.959656	−	0.281176i	$-0.909276\pi$
$283$	−11.4138	+	11.4138i	−0.678480	+	0.678480i	0.281176	+	0.959656i	$0.409276\pi$
$284$	−12.4396	−	12.0449i	−0.738153	−	0.714734i
$285$	−22.6856	−	22.6856i	−1.34378	−	1.34378i
$286$	−1.09538	−	2.58536i	−0.0647712	−	0.152875i
$287$	11.1214			0.656473
$288$	11.1216	+	24.0599i	0.655347	+	1.41774i
$289$	1.00000			0.0588235
$290$	−1.49354	−	3.52510i	−0.0877035	−	0.207001i
$291$	−26.0412	−	26.0412i	−1.52656	−	1.52656i
$292$	20.2363	+	19.5943i	1.18424	+	1.14667i
$293$	18.6185	−	18.6185i	1.08770	−	1.08770i	0.0919402	−	0.995765i	$-0.470693\pi$
$293$	18.6185	−	18.6185i	1.08770	−	1.08770i	0.995765	−	0.0919402i	$-0.0293069\pi$
$294$	−6.49543	+	16.0459i	−0.378821	+	0.935816i
$295$			10.9512i			0.637604i
$296$	−21.7464	+	9.62993i	−1.26398	+	0.559728i
$297$		−	4.78782i		−	0.277818i
$298$	−7.98532	−	3.23248i	−0.462577	−	0.187253i
$299$	7.56035	−	7.56035i	0.437227	−	0.437227i
$300$	−0.248055	−	15.3893i	−0.0143215	−	0.888503i
$301$	9.45442	+	9.45442i	0.544944	+	0.544944i
$302$	31.2050	−	13.2212i	1.79565	−	0.760792i
$303$	2.81002			0.161432
$304$	−21.2292	+	22.6439i	−1.21758	+	1.29872i
$305$	3.62823			0.207752
$306$	−6.10145	+	2.58510i	−0.348797	+	0.147781i
$307$	12.1838	+	12.1838i	0.695365	+	0.695365i	0.963407	−	0.268042i	$-0.0863766\pi$
$307$	12.1838	+	12.1838i	0.695365	+	0.695365i	−0.268042	+	0.963407i	$0.586377\pi$
$308$	−3.29391	+	0.0530934i	−0.187688	+	0.00302528i
$309$	34.9520	−	34.9520i	1.98835	−	1.98835i
$310$	2.63587	+	1.06701i	0.149707	+	0.0606020i
$311$			15.8776i			0.900335i	0.892944	+	0.450168i	$0.148636\pi$
$311$			15.8776i			0.900335i	−0.892944	+	0.450168i	$0.851364\pi$
$312$	5.47391	−	14.1751i	0.309899	−	0.802505i
$313$			23.0261i			1.30151i	0.759286	+	0.650757i	$0.225548\pi$
$313$			23.0261i			1.30151i	−0.759286	+	0.650757i	$0.774452\pi$
$314$	5.85931	−	14.4745i	0.330660	−	0.816841i
$315$	7.94392	−	7.94392i	0.447589	−	0.447589i
$316$	17.3233	−	17.8909i	0.974510	−	1.00644i
$317$	−22.4225	−	22.4225i	−1.25937	−	1.25937i	−0.951393	−	0.307980i	$-0.900347\pi$
$317$	−22.4225	−	22.4225i	−1.25937	−	1.25937i	−0.307980	−	0.951393i	$-0.599653\pi$
$318$	−16.5412	−	39.0411i	−0.927584	−	2.18932i
$319$	1.85979			0.104128
$320$	11.9168	−	0.576646i	0.666167	−	0.0322355i
$321$	1.51517			0.0845684
$322$	−4.89382	−	11.5506i	−0.272722	−	0.643688i
$323$	−5.48700	−	5.48700i	−0.305305	−	0.305305i
$324$	−1.53272	+	1.58294i	−0.0851509	+	0.0879409i
$325$	−3.80377	+	3.80377i	−0.210995	+	0.210995i
$326$	−10.0730	+	24.8836i	−0.557889	+	1.37817i
$327$			1.01265i			0.0559995i
$328$	7.04836	−	18.2522i	0.389180	−	1.00781i
$329$		−	8.93938i		−	0.492844i
$330$	−5.55280	−	2.24779i	−0.305672	−	0.123737i
$331$	19.7761	−	19.7761i	1.08699	−	1.08699i	0.0911571	−	0.995837i	$-0.470943\pi$
$331$	19.7761	−	19.7761i	1.08699	−	1.08699i	0.995837	−	0.0911571i	$-0.0290565\pi$
$332$	−3.04402	+	0.0490656i	−0.167062	+	0.00269282i
$333$	27.8599	+	27.8599i	1.52671	+	1.52671i
$334$	−19.4845	+	8.25534i	−1.06615	+	0.451712i
$335$	−2.73903			−0.149649
$336$	−13.0061	−	12.1935i	−0.709541	−	0.665212i
$337$	5.02378			0.273663			0.136831	−	0.990594i	$-0.456308\pi$
$337$	5.02378			0.273663			0.136831	+	0.990594i	$0.456308\pi$
$338$	12.0381	−	5.10036i	0.654784	−	0.277423i
$339$	20.9253	+	20.9253i	1.13651	+	1.13651i
$340$	0.0480705	+	2.98229i	0.00260699	+	0.161737i
$341$	−0.976793	+	0.976793i	−0.0528963	+	0.0528963i
$342$	47.6631	+	19.2942i	2.57732	+	1.04331i
$343$		−	18.3524i		−	0.990935i
$344$	21.5083	−	9.52452i	1.15965	−	0.513528i
$345$		−	22.8113i		−	1.22812i
$346$	0.906831	−	2.24018i	0.0487515	−	0.120433i
$347$	−13.9269	+	13.9269i	−0.747638	+	0.747638i	−0.974035	−	0.226397i	$-0.927305\pi$
$347$	−13.9269	+	13.9269i	−0.747638	+	0.747638i	0.226397	+	0.974035i	$0.427305\pi$
$348$	7.23059	+	7.00120i	0.387601	+	0.375304i
$349$	−6.52029	−	6.52029i	−0.349023	−	0.349023i	0.510722	−	0.859746i	$-0.329378\pi$
$349$	−6.52029	−	6.52029i	−0.349023	−	0.349023i	−0.859746	+	0.510722i	$0.829378\pi$
$350$	2.46218	+	5.81132i	0.131609	+	0.310628i
$351$	−9.05583			−0.483364
$352$	−2.00043	+	5.43955i	−0.106624	+	0.289929i
$353$	−0.872178			−0.0464213			−0.0232107	−	0.999731i	$-0.507389\pi$
$353$	−0.872178			−0.0464213			−0.0232107	+	0.999731i	$0.507389\pi$
$354$	−11.2314	−	26.5088i	−0.596944	−	1.40893i
$355$	9.12984	+	9.12984i	0.484562	+	0.484562i
$356$	14.4529	+	13.9943i	0.766001	+	0.741699i
$357$	3.15159	−	3.15159i	0.166800	−	0.166800i
$358$	7.85962	−	19.4159i	0.415394	−	1.02616i
$359$			14.4136i			0.760722i	0.924838	+	0.380361i	$0.124200\pi$
$359$			14.4136i			0.760722i	−0.924838	+	0.380361i	$0.875800\pi$
$360$	−8.00282	−	18.0720i	−0.421786	−	0.952479i
$361$			41.2143i			2.16917i
$362$	−14.5985	−	5.90954i	−0.767282	−	0.310598i
$363$	−19.5057	+	19.5057i	−1.02378	+	1.02378i
$364$	0.100422	+	6.23020i	0.00526357	+	0.326551i
$365$	−14.8522	−	14.8522i	−0.777398	−	0.777398i
$366$	−8.78261	+	3.72108i	−0.459074	+	0.194504i
$367$	13.9046			0.725812			0.362906	−	0.931826i	$-0.381785\pi$
$367$	13.9046			0.725812			0.362906	+	0.931826i	$0.381785\pi$
$368$	−22.0581	+	0.711280i	−1.14986	+	0.0370780i
$369$	−32.4132			−1.68736
$370$	16.3292	−	6.91846i	0.848915	−	0.359674i
$371$	12.2944	+	12.2944i	0.638294	+	0.638294i
$372$	−7.47477	+	0.120483i	−0.387549	+	0.00624677i
$373$	−3.82213	+	3.82213i	−0.197902	+	0.197902i	−0.799100	−	0.601198i	$-0.794690\pi$
$373$	−3.82213	+	3.82213i	−0.197902	+	0.197902i	0.601198	+	0.799100i	$0.294690\pi$
$374$	−1.34306	−	0.543677i	−0.0694482	−	0.0281129i
$375$			32.1490i			1.66017i
$376$	−14.6712	−	5.66549i	−0.756607	−	0.292175i
$377$		−	3.51766i		−	0.181169i
$378$	−3.98674	+	9.84858i	−0.205056	+	0.506556i
$379$	−11.1715	+	11.1715i	−0.573843	+	0.573843i	−0.933200	−	0.359357i	$-0.882996\pi$
$379$	−11.1715	+	11.1715i	−0.573843	+	0.573843i	0.359357	+	0.933200i	$0.382996\pi$
$380$	16.1000	−	16.6276i	0.825914	−	0.852976i
$381$	−30.0303	−	30.0303i	−1.53850	−	1.53850i
$382$	7.37487	+	17.4064i	0.377331	+	0.890590i
$383$	4.06550			0.207737			0.103869	−	0.994591i	$-0.466878\pi$
$383$	4.06550			0.207737			0.103869	+	0.994591i	$0.466878\pi$
$384$	−28.2546	+	13.6175i	−1.44186	+	0.694917i
$385$	2.45648			0.125194
$386$	2.66051	+	6.27943i	0.135417	+	0.319615i
$387$	−27.5549	−	27.5549i	−1.40069	−	1.40069i
$388$	18.4815	−	19.0870i	0.938256	−	0.968998i
$389$	−17.8061	+	17.8061i	−0.902804	+	0.902804i	−0.995678	−	0.0928740i	$-0.970395\pi$
$389$	−17.8061	+	17.8061i	−0.902804	+	0.902804i	0.0928740	+	0.995678i	$0.470395\pi$
$390$	−4.25155	+	10.5027i	−0.215285	+	0.531827i
$391$		−	5.51739i		−	0.279027i
$392$	−11.6499	−	4.49878i	−0.588409	−	0.227223i
$393$			19.7761i			0.997571i
$394$	−27.1365	−	10.9850i	−1.36712	−	0.553415i
$395$	−13.1308	+	13.1308i	−0.660680	+	0.660680i
$396$	9.60010	−	0.154741i	0.482423	−	0.00777602i
$397$	16.6170	+	16.6170i	0.833984	+	0.833984i	0.988059	−	0.154075i	$-0.0492397\pi$
$397$	16.6170	+	16.6170i	0.833984	+	0.833984i	−0.154075	+	0.988059i	$0.549240\pi$
$398$	30.9425	−	13.1099i	1.55101	−	0.657140i
$399$	−34.5856			−1.73144
$400$	11.0979	−	0.357859i	0.554894	−	0.0178930i
$401$	38.8482			1.93999			0.969994	−	0.243128i	$-0.0781736\pi$
$401$	38.8482			1.93999			0.969994	+	0.243128i	$0.0781736\pi$
$402$	6.63019	−	2.80912i	0.330684	−	0.140106i
$403$	1.84753	+	1.84753i	0.0920323	+	0.0920323i
$404$	0.0326718	+	2.02695i	0.00162548	+	0.100845i
$405$	1.16177	−	1.16177i	0.0577290	−	0.0577290i
$406$	−3.82560	−	1.54862i	−0.189861	−	0.0768565i
$407$			8.61505i			0.427032i
$408$	−3.17496	−	7.16971i	−0.157184	−	0.354954i
$409$			16.3370i			0.807812i	0.914801	+	0.403906i	$0.132348\pi$
$409$			16.3370i			0.807812i	−0.914801	+	0.403906i	$0.867652\pi$
$410$	−5.47440	+	13.5236i	−0.270362	+	0.667883i
$411$	−30.7014	+	30.7014i	−1.51439	+	1.51439i
$412$	25.6183	+	24.8055i	1.26212	+	1.22208i
$413$	8.34787	+	8.34787i	0.410772	+	0.410772i
$414$	14.2630	+	33.6641i	0.700990	+	1.65450i
$415$	2.27013			0.111436
$416$	10.2885	+	3.78368i	0.504437	+	0.185510i
$417$	−27.4574			−1.34459
$418$	4.38623	+	10.3525i	0.214538	+	0.506359i
$419$	−9.28636	−	9.28636i	−0.453668	−	0.453668i	0.442902	−	0.896570i	$-0.353949\pi$
$419$	−9.28636	−	9.28636i	−0.453668	−	0.453668i	−0.896570	+	0.442902i	$0.853949\pi$
$420$	9.55045	+	9.24745i	0.466014	+	0.451230i
$421$	17.7027	−	17.7027i	0.862775	−	0.862775i	−0.128884	−	0.991660i	$-0.541140\pi$
$421$	17.7027	−	17.7027i	0.862775	−	0.862775i	0.991660	+	0.128884i	$0.0411396\pi$
$422$	0.471185	−	1.16398i	0.0229369	−	0.0566619i
$423$			26.0538i			1.26678i
$424$	27.9692	−	12.3856i	1.35830	−	0.601496i
$425$			2.77591i			0.134652i
$426$	−31.4634	−	12.7365i	−1.52441	−	0.617086i
$427$	2.76573	−	2.76573i	0.133843	−	0.133843i
$428$	0.0176166	+	1.09293i	0.000851533	+	0.0528290i
$429$	−3.89208	−	3.89208i	−0.187911	−	0.187911i
$430$	−16.1505	+	6.84274i	−0.778844	+	0.329986i
$431$	−8.02649			−0.386622			−0.193311	−	0.981138i	$-0.561923\pi$
$431$	−8.02649			−0.386622			−0.193311	+	0.981138i	$0.561923\pi$
$432$	13.6366	+	12.7847i	0.656093	+	0.615103i
$433$	0.547906			0.0263307			0.0131653	−	0.999913i	$-0.495809\pi$
$433$	0.547906			0.0263307			0.0131653	+	0.999913i	$0.495809\pi$
$434$	2.82263	−	1.19591i	0.135490	−	0.0574055i
$435$	−5.30679	−	5.30679i	−0.254441	−	0.254441i
$436$	−0.730452	+	0.0117739i	−0.0349823	+	0.000563868i
$437$	−30.2739	+	30.2739i	−1.44820	+	1.44820i
$438$	51.1838	+	20.7194i	2.44566	+	0.990010i
$439$			10.8097i			0.515919i	0.966156	+	0.257960i	$0.0830502\pi$
$439$			10.8097i			0.515919i	−0.966156	+	0.257960i	$0.916950\pi$
$440$	1.55684	−	4.03154i	0.0742194	−	0.192196i
$441$			20.6885i			0.985167i
$442$	−1.02833	+	2.54031i	−0.0489125	+	0.120830i
$443$	−0.406832	+	0.406832i	−0.0193292	+	0.0193292i	−0.716705	−	0.697376i	$-0.754351\pi$
$443$	−0.406832	+	0.406832i	−0.0193292	+	0.0193292i	0.697376	+	0.716705i	$0.254351\pi$
$444$	−32.4314	+	33.4941i	−1.53913	+	1.58956i
$445$	−10.6075	−	10.6075i	−0.502843	−	0.502843i
$446$	3.72236	+	8.78565i	0.176259	+	0.416013i
$447$	−16.8876			−0.798757
$448$	8.64433	−	9.52346i	0.408406	−	0.449941i
$449$	16.3972			0.773830			0.386915	−	0.922115i	$-0.373541\pi$
$449$	16.3972			0.773830			0.386915	+	0.922115i	$0.373541\pi$
$450$	−7.17602	−	16.9371i	−0.338281	−	0.798422i
$451$	−5.01154	−	5.01154i	−0.235984	−	0.235984i
$452$	−14.8507	+	15.3373i	−0.698520	+	0.721407i
$453$	46.9770	−	46.9770i	2.20717	−	2.20717i
$454$	−3.24711	+	8.02144i	−0.152394	+	0.376465i
$455$		−	4.64627i		−	0.217820i
$456$	−21.9192	+	56.7612i	−1.02646	+	2.65809i
$457$		−	13.0164i		−	0.608881i	−0.952531	−	0.304440i	$-0.901531\pi$
$457$		−	13.0164i		−	0.608881i	0.952531	−	0.304440i	$-0.0984694\pi$
$458$	19.0013	+	7.69180i	0.887873	+	0.359414i
$459$	−3.30438	+	3.30438i	−0.154235	+	0.154235i
$460$	16.4545	−	0.265224i	0.767193	−	0.0123661i
$461$	−16.4089	−	16.4089i	−0.764237	−	0.764237i	0.212848	−	0.977085i	$-0.431726\pi$
$461$	−16.4089	−	16.4089i	−0.764237	−	0.764237i	−0.977085	+	0.212848i	$0.931726\pi$
$462$	−5.94624	+	2.51934i	−0.276644	+	0.117210i
$463$	33.3526			1.55003			0.775014	−	0.631945i	$-0.217743\pi$
$463$	33.3526			1.55003			0.775014	+	0.631945i	$0.217743\pi$
$464$	−4.96610	+	5.29704i	−0.230545	+	0.245909i
$465$	5.57443			0.258508
$466$	−8.15940	+	3.45703i	−0.377977	+	0.160144i
$467$	17.7121	+	17.7121i	0.819619	+	0.819619i	0.986053	−	0.166434i	$-0.0532253\pi$
$467$	17.7121	+	17.7121i	0.819619	+	0.819619i	−0.166434	+	0.986053i	$0.553225\pi$
$468$	−0.292681	−	18.1579i	−0.0135292	−	0.839350i
$469$	−2.08791	+	2.08791i	−0.0964107	+	0.0964107i
$470$	10.8703	+	4.40034i	0.501410	+	0.202973i
$471$		−	30.6111i		−	1.41049i
$472$	18.9910	−	8.40977i	0.874131	−	0.387091i
$473$		−	8.52075i		−	0.391785i
$474$	18.3179	−	45.2514i	0.841371	−	2.07847i
$475$	15.2314	−	15.2314i	0.698866	−	0.698866i
$476$	2.30998	+	2.23669i	0.105878	+	0.102519i
$477$	−35.8321	−	35.8321i	−1.64064	−	1.64064i
$478$	10.0951	+	23.8268i	0.461739	+	1.08981i
$479$	18.3863			0.840091			0.420045	−	0.907503i	$-0.362014\pi$
$479$	18.3863			0.840091			0.420045	+	0.907503i	$0.362014\pi$
$480$	21.2295	−	9.81329i	0.968990	−	0.447914i
$481$	16.2948			0.742977
$482$	12.7652	+	30.1289i	0.581439	+	1.37233i
$483$	−17.3886	−	17.3886i	−0.791208	−	0.791208i
$484$	−14.2968	−	13.8432i	−0.649855	−	0.629238i
$485$	−14.0087	+	14.0087i	−0.636100	+	0.636100i
$486$	−9.06006	+	22.3814i	−0.410972	+	1.01524i
$487$			26.5286i			1.20213i	0.799202	+	0.601063i	$0.205256\pi$
$487$			26.5286i			1.20213i	−0.799202	+	0.601063i	$0.794744\pi$
$488$	−2.78623	−	6.29189i	−0.126127	−	0.284820i
$489$			52.6246i			2.37977i
$490$	8.63177	+	3.49417i	0.389944	+	0.157850i
$491$	18.7029	−	18.7029i	0.844052	−	0.844052i	−0.145331	−	0.989383i	$-0.546425\pi$
$491$	18.7029	−	18.7029i	0.844052	−	0.844052i	0.989383	+	0.145331i	$0.0464247\pi$
$492$	−0.618153	−	38.3501i	−0.0278685	−	1.72896i
$493$	−1.28356	−	1.28356i	−0.0578086	−	0.0578086i
$494$	19.5811	−	8.29625i	0.880995	−	0.373266i
$495$	−7.15942			−0.321792
$496$	−0.173816	−	5.39037i	−0.00780459	−	0.242035i
$497$	13.9190			0.624351
$498$	−5.49514	+	2.32822i	−0.246243	+	0.104330i
$499$	−16.1932	−	16.1932i	−0.724908	−	0.724908i	0.244693	−	0.969601i	$-0.421313\pi$
$499$	−16.1932	−	16.1932i	−0.724908	−	0.724908i	−0.969601	+	0.244693i	$0.921313\pi$
$500$	−23.1900	+	0.373792i	−1.03709	+	0.0167165i
$501$	−29.3326	+	29.3326i	−1.31049	+	1.31049i
$502$	−23.9309	−	9.68732i	−1.06809	−	0.432366i
$503$		−	18.0801i		−	0.806150i	−0.915167	−	0.403075i	$-0.867941\pi$
$503$		−	18.0801i		−	0.806150i	0.915167	−	0.403075i	$-0.132059\pi$
$504$	−19.8763	−	7.67553i	−0.885361	−	0.341896i
$505$		−	1.51163i		−	0.0672667i
$506$	−2.99968	+	7.41021i	−0.133352	+	0.329424i
$507$	18.1225	−	18.1225i	0.804847	−	0.804847i
$508$	21.3126	−	22.0109i	0.945593	−	0.976575i
$509$	19.5862	+	19.5862i	0.868141	+	0.868141i	0.992267	−	0.124125i	$-0.0396125\pi$
$509$	19.5862	+	19.5862i	0.868141	+	0.868141i	−0.124125	+	0.992267i	$0.539612\pi$
$510$	2.28100	+	5.38369i	0.101004	+	0.238394i
$511$	−22.6430			−1.00167
$512$	−10.1512	−	20.2226i	−0.448626	−	0.893720i
$513$	36.2622			1.60102
$514$	5.54738	+	13.0931i	0.244685	+	0.577513i
$515$	−18.8021	−	18.8021i	−0.828521	−	0.828521i
$516$	32.0765	−	33.1275i	1.41209	−	1.45835i
$517$	−4.02829	+	4.02829i	−0.177164	+	0.177164i
$518$	7.17361	−	17.7212i	0.315190	−	0.778625i
$519$		−	4.73760i		−	0.207958i
$520$	−7.62537	−	2.94465i	−0.334394	−	0.129131i
$521$		−	13.8684i		−	0.607586i	−0.952738	−	0.303793i	$-0.901747\pi$
$521$		−	13.8684i		−	0.607586i	0.952738	−	0.303793i	$-0.0982531\pi$
$522$	11.1497	+	4.51344i	0.488009	+	0.197548i
$523$	2.87639	−	2.87639i	0.125776	−	0.125776i	−0.641417	−	0.767193i	$-0.721653\pi$
$523$	2.87639	−	2.87639i	0.125776	−	0.125776i	0.767193	+	0.641417i	$0.221653\pi$
$524$	−14.2651	+	0.229934i	−0.623172	+	0.0100447i
$525$	8.74855	+	8.74855i	0.381818	+	0.381818i
$526$	13.6542	−	5.78511i	0.595352	−	0.252243i
$527$	1.34829			0.0587326
$528$	0.366167	+	11.3555i	0.0159354	+	0.494186i
$529$	−7.44163			−0.323549
$530$	−21.0019	+	8.89821i	−0.912262	+	0.386513i
$531$	−24.3299	−	24.3299i	−1.05583	−	1.05583i
$532$	−0.402122	−	24.9476i	−0.0174342	−	1.08161i
$533$	−9.47898	+	9.47898i	−0.410580	+	0.410580i
$534$	36.5557	+	14.7979i	1.58192	+	0.640366i
$535$		−	0.815072i		−	0.0352387i
$536$	2.10339	+	4.74989i	0.0908526	+	0.205164i
$537$		−	41.0614i		−	1.77193i
$538$	−7.49513	+	18.5155i	−0.323138	+	0.798259i
$539$	−3.19874	+	3.19874i	−0.137779	+	0.137779i
$540$	−10.0135	−	9.69577i	−0.430910	−	0.417239i
$541$	−1.40656	−	1.40656i	−0.0604729	−	0.0604729i	0.676224	−	0.736696i	$-0.263615\pi$
$541$	−1.40656	−	1.40656i	−0.0604729	−	0.0604729i	−0.736696	+	0.676224i	$0.763615\pi$
$542$	−10.7497	−	25.3718i	−0.461739	−	1.08981i
$543$	−30.8735			−1.32491
$544$	5.13481	−	2.37355i	0.220153	−	0.101765i
$545$	0.544746			0.0233343
$546$	4.76516	+	11.2469i	0.203930	+	0.481322i
$547$	−5.30002	−	5.30002i	−0.226613	−	0.226613i	0.584663	−	0.811276i	$-0.301227\pi$
$547$	−5.30002	−	5.30002i	−0.226613	−	0.226613i	−0.811276	+	0.584663i	$0.801227\pi$
$548$	−22.5028	−	21.7888i	−0.961270	−	0.930773i
$549$	−8.06071	+	8.06071i	−0.344023	+	0.344023i
$550$	1.50920	−	3.72823i	0.0643525	−	0.158972i
$551$			14.0858i			0.600074i
$552$	−39.5581	+	17.5175i	−1.68371	+	0.745594i
$553$			20.0186i			0.851277i
$554$	−5.07102	−	2.05277i	−0.215447	−	0.0872137i
$555$	24.5825	−	24.5825i	1.04347	−	1.04347i
$556$	−0.319244	−	19.8058i	−0.0135389	−	0.839954i
$557$	−29.8547	−	29.8547i	−1.26498	−	1.26498i	−0.948646	−	0.316339i	$-0.897546\pi$
$557$	−29.8547	−	29.8547i	−1.26498	−	1.26498i	−0.316339	−	0.948646i	$-0.602454\pi$
$558$	−8.22654	+	3.48548i	−0.348257	+	0.147552i
$559$	−16.1164			−0.681651
$560$	−6.55942	+	6.99654i	−0.277186	+	0.295658i
$561$	−2.84036			−0.119920
$562$	2.98325	−	1.26396i	0.125841	−	0.0533171i
$563$	17.8004	+	17.8004i	0.750195	+	0.750195i	0.974516	−	0.224320i	$-0.0720161\pi$
$563$	17.8004	+	17.8004i	0.750195	+	0.750195i	−0.224320	+	0.974516i	$0.572016\pi$
$564$	−30.8259	+	0.496873i	−1.29801	+	0.0209221i
$565$	11.2566	−	11.2566i	0.473569	−	0.473569i
$566$	−21.1597	−	8.56551i	−0.889408	−	0.360035i
$567$		−	1.77119i		−	0.0743831i
$568$	8.82139	−	22.8436i	0.370137	−	0.958495i
$569$		−	34.6136i		−	1.45108i	−0.688181	−	0.725539i	$-0.741591\pi$
$569$		−	34.6136i		−	1.45108i	0.688181	−	0.725539i	$-0.258409\pi$
$570$	17.0245	−	42.0561i	0.713076	−	1.76154i
$571$	13.8067	−	13.8067i	0.577792	−	0.577792i	−0.356503	−	0.934294i	$-0.616031\pi$
$571$	13.8067	−	13.8067i	0.577792	−	0.577792i	0.934294	+	0.356503i	$0.116031\pi$
$572$	2.76222	−	2.85272i	0.115494	−	0.119278i
$573$	26.2042	+	26.2042i	1.09469	+	1.09469i
$574$	6.13574	+	14.4818i	0.256101	+	0.604458i
$575$	15.3158			0.638713
$576$	−25.1939	+	27.7561i	−1.04975	+	1.15651i
$577$	−19.5711			−0.814754			−0.407377	−	0.913260i	$-0.633557\pi$
$577$	−19.5711			−0.814754			−0.407377	+	0.913260i	$0.633557\pi$
$578$	0.551708	+	1.30216i	0.0229480	+	0.0541627i
$579$	9.45325	+	9.45325i	0.392864	+	0.392864i
$580$	3.76624	−	3.88964i	0.156385	−	0.161509i
$581$	1.73047	−	1.73047i	0.0717920	−	0.0717920i
$582$	19.5427	−	48.2769i	0.810069	−	2.00114i
$583$		−	11.0803i		−	0.458898i
$584$	−14.3504	+	37.1613i	−0.593823	+	1.53774i
$585$			13.5415i			0.559874i
$586$	34.5162	+	13.9723i	1.42585	+	0.577190i
$587$	−10.5006	+	10.5006i	−0.433406	+	0.433406i	−0.889785	−	0.456379i	$-0.849146\pi$
$587$	−10.5006	+	10.5006i	−0.433406	+	0.433406i	0.456379	+	0.889785i	$0.349146\pi$
$588$	−24.4779	+	0.394551i	−1.00945	+	0.0162710i
$589$	−7.39808	−	7.39808i	−0.304833	−	0.304833i
$590$	−14.2602	+	6.04186i	−0.587084	+	0.248739i
$591$	−57.3893			−2.36068
$592$	−24.5373	−	23.0043i	−1.00848	−	0.945472i
$593$	−0.986056			−0.0404925			−0.0202462	−	0.999795i	$-0.506445\pi$
$593$	−0.986056			−0.0404925			−0.0202462	+	0.999795i	$0.506445\pi$
$594$	6.23451	−	2.64148i	0.255805	−	0.108381i
$595$	−1.69538	−	1.69538i	−0.0695036	−	0.0695036i
$596$	−0.196350	−	12.1815i	−0.00804282	−	0.498975i
$597$	46.5818	−	46.5818i	1.90646	−	1.90646i
$598$	14.0159	+	5.67368i	0.573152	+	0.232014i
$599$		−	12.1146i		−	0.494987i	−0.968890	−	0.247494i	$-0.920393\pi$
$599$		−	12.1146i		−	0.494987i	0.968890	−	0.247494i	$-0.0796069\pi$
$600$	19.9025	−	8.81341i	0.812516	−	0.359806i
$601$		−	24.2797i		−	0.990388i	−0.868782	−	0.495194i	$-0.835097\pi$
$601$		−	24.2797i		−	0.990388i	0.868782	−	0.495194i	$-0.164903\pi$
$602$	−7.09509	+	17.5272i	−0.289174	+	0.714357i
$603$	6.08521	−	6.08521i	0.247809	−	0.247809i
$604$	34.4321	+	33.3397i	1.40102	+	1.35657i
$605$	10.4929	+	10.4929i	0.426598	+	0.426598i
$606$	1.55031	+	3.65910i	0.0629771	+	0.148641i
$607$	−0.141271			−0.00573400			−0.00286700	−	0.999996i	$-0.500913\pi$
$607$	−0.141271			−0.00573400			−0.00286700	+	0.999996i	$0.500913\pi$
$608$	−41.1983	−	15.1510i	−1.67081	−	0.614454i
$609$	−8.09051			−0.327844
$610$	2.00172	+	4.72454i	0.0810475	+	0.191291i
$611$	7.61923	+	7.61923i	0.308241	+	0.308241i
$612$	−6.73243	−	6.51884i	−0.272142	−	0.263508i
$613$	−7.07751	+	7.07751i	−0.285858	+	0.285858i	−0.835440	−	0.549582i	$-0.814787\pi$
$613$	−7.07751	+	7.07751i	−0.285858	+	0.285858i	0.549582	+	0.835440i	$0.314787\pi$
$614$	−9.14334	+	22.5871i	−0.368995	+	0.911542i
$615$			28.6002i			1.15327i
$616$	−1.88641	−	4.25990i	−0.0760056	−	0.171636i
$617$		−	22.9643i		−	0.924508i	−0.886748	−	0.462254i	$-0.847041\pi$
$617$		−	22.9643i		−	0.924508i	0.886748	−	0.462254i	$-0.152959\pi$
$618$	64.7963	+	26.2298i	2.60649	+	1.05512i
$619$	17.9971	−	17.9971i	0.723365	−	0.723365i	−0.245924	−	0.969289i	$-0.579091\pi$
$619$	17.9971	−	17.9971i	0.723365	−	0.723365i	0.969289	+	0.245924i	$0.0790915\pi$
$620$	0.0648131	+	4.02100i	0.00260296	+	0.161487i
$621$	18.2316	+	18.2316i	0.731608	+	0.731608i
$622$	−20.6751	+	8.75978i	−0.828998	+	0.351235i
$623$	−16.1717			−0.647906
$624$	21.4782	−	0.692580i	0.859816	−	0.0277254i
$625$	3.41474			0.136590
$626$	−29.9837	+	12.7037i	−1.19839	+	0.507742i
$627$	15.5850	+	15.5850i	0.622406	+	0.622406i
$628$	22.0807	−	0.355911i	0.881115	−	0.0142024i
$629$	5.94579	−	5.94579i	0.237074	−	0.237074i
$630$	14.7270	+	5.96153i	0.586736	+	0.237513i
$631$		−	37.4712i		−	1.49171i	−0.666111	−	0.745853i	$-0.732042\pi$
$631$		−	37.4712i		−	1.49171i	0.666111	−	0.745853i	$-0.267958\pi$
$632$	32.8542	+	12.6871i	1.30687	+	0.504667i
$633$		−	2.46163i		−	0.0978412i
$634$	16.8270	−	41.5683i	0.668286	−	1.65089i
$635$	−16.1546	+	16.1546i	−0.641075	+	0.641075i
$636$	41.7118	−	43.0785i	1.65398	−	1.70817i
$637$	6.05018	+	6.05018i	0.239717	+	0.239717i
$638$	1.02606	+	2.42174i	0.0406221	+	0.0958777i
$639$	−40.5669			−1.60480
$640$	7.32545	+	15.1994i	0.289564	+	0.600808i
$641$	−8.80447			−0.347756			−0.173878	−	0.984767i	$-0.555630\pi$
$641$	−8.80447			−0.347756			−0.173878	+	0.984767i	$0.555630\pi$
$642$	0.835929	+	1.97299i	0.0329915	+	0.0778676i
$643$	17.3055	+	17.3055i	0.682463	+	0.682463i	0.960555	−	0.278091i	$-0.0897018\pi$
$643$	17.3055	+	17.3055i	0.682463	+	0.682463i	−0.278091	+	0.960555i	$0.589702\pi$
$644$	12.3407	−	12.7451i	0.486292	−	0.502226i
$645$	−24.3134	+	24.3134i	−0.957340	+	0.957340i
$646$	4.11773	−	10.1722i	0.162010	−	0.400218i
$647$			31.7670i			1.24889i	0.781069	+	0.624445i	$0.214675\pi$
$647$			31.7670i			1.24889i	−0.781069	+	0.624445i	$0.785325\pi$
$648$	−2.90685	−	1.12252i	−0.114192	−	0.0440969i
$649$		−	7.52348i		−	0.295323i
$650$	−7.05168	−	2.85454i	−0.276590	−	0.111964i
$651$	4.24927	−	4.24927i	0.166542	−	0.166542i
$652$	−37.9597	+	0.611860i	−1.48662	+	0.0239623i
$653$	−26.2777	−	26.2777i	−1.02833	−	1.02833i	−0.999587	−	0.0287392i	$-0.990851\pi$
$653$	−26.2777	−	26.2777i	−1.02833	−	1.02833i	−0.0287392	−	0.999587i	$-0.509149\pi$
$654$	−1.31863	+	0.558685i	−0.0515624	+	0.0218463i
$655$	10.6384			0.415676
$656$	27.6559	−	0.891784i	1.07978	−	0.0348183i
$657$	65.9930			2.57463
$658$	11.6405	−	4.93193i	0.453794	−	0.192266i
$659$	0.0375684	+	0.0375684i	0.00146346	+	0.00146346i	0.707838	−	0.706375i	$-0.249671\pi$
$659$	0.0375684	+	0.0375684i	0.00146346	+	0.00146346i	−0.706375	+	0.707838i	$0.749671\pi$
$660$	−0.136537	−	8.47076i	−0.00531471	−	0.329724i
$661$	1.32128	−	1.32128i	0.0513920	−	0.0513920i	−0.680944	−	0.732336i	$-0.738430\pi$
$661$	1.32128	−	1.32128i	0.0513920	−	0.0513920i	0.732336	+	0.680944i	$0.238430\pi$
$662$	36.6623	+	14.8410i	1.42492	+	0.576813i
$663$			5.37234i			0.208644i
$664$	−1.74330	−	3.93673i	−0.0676532	−	0.152775i
$665$			18.6050i			0.721472i
$666$	−20.9075	+	51.6485i	−0.810148	+	2.00134i
$667$	−7.08190	+	7.08190i	−0.274212	+	0.274212i
$668$	−21.4995	−	20.8174i	−0.831842	−	0.805451i
$669$	13.2262	+	13.2262i	0.511354	+	0.511354i
$670$	−1.51115	−	3.56666i	−0.0583807	−	0.137792i
$671$	−2.49260			−0.0962257
$672$	8.70235	−	23.6633i	0.335700	−	0.912831i
$673$	23.8648			0.919922			0.459961	−	0.887939i	$-0.347863\pi$
$673$	23.8648			0.919922			0.459961	+	0.887939i	$0.347863\pi$
$674$	2.77166	+	6.54176i	0.106760	+	0.251979i
$675$	−9.17267	−	9.17267i	−0.353056	−	0.353056i
$676$	13.2830	+	12.8616i	0.510883	+	0.494675i
$677$	−4.29055	+	4.29055i	−0.164899	+	0.164899i	−0.784733	−	0.619834i	$-0.787200\pi$
$677$	−4.29055	+	4.29055i	−0.164899	+	0.164899i	0.619834	+	0.784733i	$0.287200\pi$
$678$	−15.7034	+	38.7927i	−0.603087	+	1.48983i
$679$			21.3570i			0.819607i
$680$	−3.85689	+	1.70795i	−0.147905	+	0.0654967i
$681$			16.9640i			0.650063i
$682$	−1.81084	−	0.733036i	−0.0693408	−	0.0280694i
$683$	7.19132	−	7.19132i	0.275168	−	0.275168i	−0.556008	−	0.831177i	$-0.687668\pi$
$683$	7.19132	−	7.19132i	0.275168	−	0.275168i	0.831177	+	0.556008i	$0.187668\pi$
$684$	1.17198	+	72.7097i	0.0448119	+	2.78012i
$685$	16.5156	+	16.5156i	0.631028	+	0.631028i
$686$	23.8977	−	10.1251i	0.912419	−	0.386580i
$687$	40.1846			1.53314
$688$	24.2687	+	22.7525i	0.925237	+	0.867431i
$689$	−20.9576			−0.798420
$690$	29.7039	−	12.5852i	1.13081	−	0.479109i
$691$	10.9845	+	10.9845i	0.417871	+	0.417871i	0.884469	−	0.466598i	$-0.154521\pi$
$691$	10.9845	+	10.9845i	0.417871	+	0.417871i	−0.466598	+	0.884469i	$0.654521\pi$
$692$	3.41737	−	0.0550835i	0.129909	−	0.00209396i
$693$	−5.45748	+	5.45748i	−0.207312	+	0.207312i
$694$	−25.8187	−	10.4515i	−0.980065	−	0.396734i
$695$			14.7705i			0.560277i
$696$	−5.12750	+	13.2780i	−0.194357	+	0.503301i
$697$			6.91756i			0.262021i
$698$	4.89316	−	12.0878i	0.185209	−	0.457528i
$699$	−12.2834	+	12.2834i	−0.464601	+	0.464601i
$700$	−6.20886	+	6.41230i	−0.234673	+	0.242362i
$701$	−5.15162	−	5.15162i	−0.194574	−	0.194574i	0.603095	−	0.797669i	$-0.293934\pi$
$701$	−5.15162	−	5.15162i	−0.194574	−	0.194574i	−0.797669	+	0.603095i	$0.793934\pi$
$702$	−4.99617	−	11.7921i	−0.188568	−	0.445065i
$703$	−65.2491			−2.46092
$704$	−8.18682	+	0.396156i	−0.308552	+	0.0149307i
$705$	22.9889			0.865813
$706$	−0.481187	−	1.13571i	−0.0181097	−	0.0427432i
$707$	−1.15228	−	1.15228i	−0.0433361	−	0.0433361i
$708$	28.3222	−	29.2502i	1.06441	−	1.09929i
$709$	10.4973	−	10.4973i	0.394234	−	0.394234i	−0.481959	−	0.876194i	$-0.660075\pi$
$709$	10.4973	−	10.4973i	0.394234	−	0.394234i	0.876194	+	0.481959i	$0.160075\pi$
$710$	−6.85151	+	16.9255i	−0.257132	+	0.635203i
$711$		−	58.3442i		−	2.18808i
$712$	−10.2491	+	26.5407i	−0.384101	+	0.994656i
$713$		−	7.43906i		−	0.278595i
$714$	5.84263	+	2.36512i	0.218655	+	0.0885123i
$715$	−2.09371	+	2.09371i	−0.0783004	+	0.0783004i
$716$	29.6188	−	0.477416i	1.10691	−	0.0178419i
$717$	35.8696	+	35.8696i	1.33958	+	1.33958i
$718$	−18.7688	+	7.95211i	−0.700447	+	0.296770i
$719$	−50.8662			−1.89699			−0.948494	−	0.316795i	$-0.897393\pi$
$719$	−50.8662			−1.89699			−0.948494	+	0.316795i	$0.897393\pi$
$720$	19.1174	−	20.3914i	0.712464	−	0.759943i
$721$	−28.6650			−1.06754
$722$	−53.6675	+	22.7382i	−1.99730	+	0.846229i
$723$	45.3570	+	45.3570i	1.68684	+	1.68684i
$724$	−0.358962	−	22.2700i	−0.0133407	−	0.827656i
$725$	3.56305	−	3.56305i	0.132328	−	0.132328i
$726$	−36.1609	−	14.6381i	−1.34206	−	0.543270i
$727$			8.05077i			0.298587i	0.988793	+	0.149293i	$0.0476998\pi$
$727$			8.05077i			0.298587i	−0.988793	+	0.149293i	$0.952300\pi$
$728$	−8.05730	+	3.56801i	−0.298624	+	0.132239i
$729$			44.0278i			1.63066i
$730$	11.1458	−	27.5339i	0.412526	−	1.01908i
$731$	−5.88071	+	5.88071i	−0.217506	+	0.217506i
$732$	−9.69087	−	9.38341i	−0.358185	−	0.346821i
$733$	−1.03075	−	1.03075i	−0.0380715	−	0.0380715i	0.687815	−	0.725886i	$-0.258570\pi$
$733$	−1.03075	−	1.03075i	−0.0380715	−	0.0380715i	−0.725886	+	0.687815i	$0.758570\pi$
$734$	7.67125	+	18.1059i	0.283151	+	0.668303i
$735$	18.2548			0.673337
$736$	−13.0958	−	28.3308i	−0.482718	−	1.04429i
$737$	1.88172			0.0693140
$738$	−17.8826	−	42.2072i	−0.658268	−	1.55367i
$739$	−11.4242	−	11.4242i	−0.420247	−	0.420247i	0.465042	−	0.885289i	$-0.346039\pi$
$739$	−11.4242	−	11.4242i	−0.420247	−	0.420247i	−0.885289	+	0.465042i	$0.846039\pi$
$740$	18.0179	+	17.4462i	0.662351	+	0.641337i
$741$	29.4780	−	29.4780i	1.08290	−	1.08290i
$742$	−9.22636	+	22.7922i	−0.338710	+	0.836728i
$743$			4.82892i			0.177156i	0.996069	+	0.0885780i	$0.0282322\pi$
$743$			4.82892i			0.177156i	−0.996069	+	0.0885780i	$0.971768\pi$
$744$	−4.28078	−	9.66687i	−0.156941	−	0.354405i
$745$			9.08457i			0.332833i
$746$	−7.08572	−	2.86832i	−0.259427	−	0.105017i
$747$	−5.04346	+	5.04346i	−0.184530	+	0.184530i
$748$	−0.0330245	−	2.04883i	−0.00120749	−	0.0749128i
$749$	−0.621313	−	0.621313i	−0.0227023	−	0.0227023i
$750$	−41.8631	+	17.7368i	−1.52862	+	0.647658i
$751$	3.20091			0.116803			0.0584014	−	0.998293i	$-0.481400\pi$
$751$	3.20091			0.116803			0.0584014	+	0.998293i	$0.481400\pi$
$752$	−0.716818	−	22.2299i	−0.0261397	−	0.810640i
$753$	−50.6099			−1.84433
$754$	4.58056	−	1.94072i	0.166814	−	0.0706769i
$755$	−25.2709	−	25.2709i	−0.919703	−	0.919703i
$756$	−15.0239	+	0.242166i	−0.546415	+	0.00880749i
$757$	−10.3375	+	10.3375i	−0.375722	+	0.375722i	−0.869556	−	0.493834i	$-0.835595\pi$
$757$	−10.3375	+	10.3375i	−0.375722	+	0.375722i	0.493834	+	0.869556i	$0.335595\pi$
$758$	−20.7105	−	8.38369i	−0.752240	−	0.304509i
$759$			15.6714i			0.568835i
$760$	30.5342	+	11.7913i	1.10759	+	0.427714i
$761$		−	18.0845i		−	0.655561i	−0.944754	−	0.327781i	$-0.893699\pi$
$761$		−	18.0845i		−	0.655561i	0.944754	−	0.327781i	$-0.106301\pi$
$762$	22.5363	−	55.6722i	0.816404	−	2.01679i
$763$	0.415248	−	0.415248i	0.0150330	−	0.0150330i
$764$	−18.5972	+	19.2065i	−0.672821	+	0.694867i
$765$	4.94117	+	4.94117i	0.178648	+	0.178648i
$766$	2.24297	+	5.29393i	0.0810417	+	0.191277i
$767$	−14.2301			−0.513821
$768$	−33.3205	−	29.2792i	−1.20235	−	1.05652i
$769$	−32.2184			−1.16183			−0.580913	−	0.813966i	$-0.697304\pi$
$769$	−32.2184			−1.16183			−0.580913	+	0.813966i	$0.697304\pi$
$770$	1.35526	+	3.19873i	0.0488402	+	0.115274i
$771$	19.7108	+	19.7108i	0.709867	+	0.709867i
$772$	−6.70900	+	6.92882i	−0.241462	+	0.249374i
$773$	−27.3466	+	27.3466i	−0.983589	+	0.983589i	−0.999867	−	0.0162783i	$-0.994818\pi$
$773$	−27.3466	+	27.3466i	−0.983589	+	0.983589i	0.0162783	+	0.999867i	$0.494818\pi$
$774$	20.6786	−	51.0831i	0.743278	−	1.83615i
$775$			3.74275i			0.134443i
$776$	35.0508	+	13.5354i	1.25825	+	0.485892i
$777$		−	37.4774i		−	1.34450i
$778$	−33.0101	−	13.3626i	−1.18347	−	0.479072i
$779$	37.9566	−	37.9566i	1.35994	−	1.35994i
$780$	−16.0219	+	0.258251i	−0.573674	+	0.00924687i
$781$	−6.27221	−	6.27221i	−0.224437	−	0.224437i
$782$	7.18453	−	3.04399i	0.256918	−	0.108853i
$783$	8.48274			0.303148
$784$	−0.569202	−	17.6520i	−0.0203287	−	0.630430i
$785$	−16.4670			−0.587733
$786$	−25.7516	+	10.9106i	−0.918529	+	0.389168i
$787$	38.0877	+	38.0877i	1.35768	+	1.35768i	0.876769	+	0.480912i	$0.159694\pi$
$787$	38.0877	+	38.0877i	1.35768	+	1.35768i	0.480912	+	0.876769i	$0.340306\pi$
$788$	−0.667258	−	41.3966i	−0.0237701	−	1.47469i
$789$	20.5555	−	20.5555i	0.731795	−	0.731795i
$790$	−24.3427	−	9.85399i	−0.866073	−	0.350589i
$791$		−	17.1614i		−	0.610188i
$792$	5.49794	+	12.4155i	0.195361	+	0.441165i
$793$			4.71458i			0.167420i
$794$	−12.4703	+	30.8057i	−0.442553	+	1.09326i
$795$	−31.6168	+	31.6168i	−1.12133	+	1.12133i
$796$	34.1424	+	33.0592i	1.21014	+	1.17175i
$797$	11.5851	+	11.5851i	0.410365	+	0.410365i	0.881866	−	0.471501i	$-0.156288\pi$
$797$	11.5851	+	11.5851i	0.410365	+	0.410365i	−0.471501	+	0.881866i	$0.656288\pi$
$798$	−19.0811	−	45.0359i	−0.675464	−	1.59425i
$799$	5.56036			0.196711
$800$	6.58878	+	14.2538i	0.232948	+	0.503947i
$801$	47.1325			1.66534
$802$	21.4329	+	50.5866i	0.756821	+	1.78627i
$803$	10.2034	+	10.2034i	0.360072	+	0.360072i
$804$	7.31585	+	7.08375i	0.258010	+	0.249824i
$805$	−9.35405	+	9.35405i	−0.329687	+	0.329687i
$806$	−1.38649	+	3.42508i	−0.0488369	+	0.120643i
$807$			39.1572i			1.37840i
$808$	−2.62139	+	1.16083i	−0.0922201	+	0.0408378i
$809$		−	42.8571i		−	1.50677i	−0.657577	−	0.753387i	$-0.728419\pi$
$809$		−	42.8571i		−	1.50677i	0.657577	−	0.753387i	$-0.271581\pi$
$810$	2.15377	+	0.871855i	0.0756759	+	0.0306339i
$811$	−21.5592	+	21.5592i	−0.757047	+	0.757047i	−0.975784	−	0.218737i	$-0.929806\pi$
$811$	−21.5592	+	21.5592i	−0.757047	+	0.757047i	0.218737	+	0.975784i	$0.429806\pi$
$812$	−0.0940673	−	5.83592i	−0.00330112	−	0.204801i
$813$	−38.1955	−	38.1955i	−1.33958	−	1.33958i
$814$	−11.2182	+	4.75299i	−0.393197	+	0.166592i
$815$	28.3090			0.991622
$816$	7.58446	−	8.08989i	0.265509	−	0.283203i
$817$	64.5349			2.25779
$818$	−21.2733	+	9.01323i	−0.743805	+	0.315140i
$819$	10.3224	+	10.3224i	0.360695	+	0.360695i
$820$	−20.6302	+	0.332531i	−0.720436	+	0.0116125i
$821$	15.3863	−	15.3863i	0.536986	−	0.536986i	−0.385656	−	0.922643i	$-0.626025\pi$
$821$	15.3863	−	15.3863i	0.536986	−	0.536986i	0.922643	+	0.385656i	$0.126025\pi$
$822$	−56.9163	−	23.0399i	−1.98518	−	0.803609i
$823$			34.7750i			1.21218i	0.795396	+	0.606090i	$0.207263\pi$
$823$			34.7750i			1.21218i	−0.795396	+	0.606090i	$0.792737\pi$
$824$	−18.1669	+	47.0444i	−0.632875	+	1.63887i
$825$		−	7.88459i		−	0.274506i
$826$	−6.26468	+	15.4758i	−0.217976	+	0.538474i
$827$	26.4305	−	26.4305i	0.919080	−	0.919080i	−0.0778829	−	0.996963i	$-0.524816\pi$
$827$	26.4305	−	26.4305i	0.919080	−	0.919080i	0.996963	+	0.0778829i	$0.0248160\pi$
$828$	−35.9670	+	37.1455i	−1.24994	+	1.29089i
$829$	26.4893	+	26.4893i	0.920010	+	0.920010i	0.997030	−	0.0770194i	$-0.0245403\pi$
$829$	26.4893	+	26.4893i	0.920010	+	0.920010i	−0.0770194	+	0.997030i	$0.524540\pi$
$830$	1.25245	+	2.95607i	0.0434730	+	0.102607i
$831$	−10.7244			−0.372024
$832$	0.749302	+	15.4848i	0.0259774	+	0.536839i
$833$	4.41530			0.152981
$834$	−15.1485	−	35.7539i	−0.524548	−	1.23806i
$835$	15.7793	+	15.7793i	0.546064	+	0.546064i
$836$	−11.0607	+	11.4231i	−0.382543	+	0.395078i
$837$	−4.45527	+	4.45527i	−0.153997	+	0.153997i
$838$	6.96897	−	17.2157i	0.240739	−	0.594706i
$839$			27.1949i			0.938872i	0.882966	+	0.469436i	$0.155543\pi$
$839$			27.1949i			0.938872i	−0.882966	+	0.469436i	$0.844457\pi$
$840$	−6.77260	+	17.5381i	−0.233677	+	0.605122i
$841$		−	25.7050i		−	0.886378i
$842$	32.8184	+	13.2850i	1.13100	+	0.457831i
$843$	4.49108	−	4.49108i	0.154681	−	0.154681i
$844$	1.77565	−	0.0286211i	0.0611204	−	0.000985179i
$845$	−9.74884	−	9.74884i	−0.335370	−	0.335370i
$846$	−33.9262	+	14.3741i	−1.16641	+	0.494192i
$847$	15.9971			0.549667
$848$	31.5588	+	29.5871i	1.08373	+	1.01602i
$849$	−44.7492			−1.53579
$850$	−3.61468	+	1.53149i	−0.123983	+	0.0525298i
$851$	−32.8053	−	32.8053i	−1.12455	−	1.12455i
$852$	−0.773651	−	47.9972i	−0.0265049	−	1.64436i
$853$	1.36829	−	1.36829i	0.0468494	−	0.0468494i	−0.683294	−	0.730143i	$-0.739453\pi$
$853$	1.36829	−	1.36829i	0.0468494	−	0.0468494i	0.730143	+	0.683294i	$0.239453\pi$
$854$	5.12729	+	2.07555i	0.175452	+	0.0710237i
$855$		−	54.2244i		−	1.85443i
$856$	−1.41345	+	0.625920i	−0.0483109	+	0.0213935i
$857$		−	27.4342i		−	0.937133i	−0.883428	−	0.468566i	$-0.844771\pi$
$857$		−	27.4342i		−	0.937133i	0.883428	−	0.468566i	$-0.155229\pi$
$858$	2.92081	−	7.21539i	0.0997150	−	0.246329i
$859$	3.37645	−	3.37645i	0.115203	−	0.115203i	−0.647155	−	0.762358i	$-0.724041\pi$
$859$	3.37645	−	3.37645i	0.115203	−	0.115203i	0.762358	+	0.647155i	$0.224041\pi$
$860$	−17.8207	−	17.2553i	−0.607680	−	0.588400i
$861$	21.8013	+	21.8013i	0.742988	+	0.742988i
$862$	−4.42827	−	10.4518i	−0.150828	−	0.355989i
$863$	−0.905468			−0.0308225			−0.0154112	−	0.999881i	$-0.504906\pi$
$863$	−0.905468			−0.0308225			−0.0154112	+	0.999881i	$0.504906\pi$
$864$	−9.12424	+	24.8105i	−0.310413	+	0.844070i
$865$	−2.54856			−0.0866535
$866$	0.302284	+	0.713461i	0.0102720	+	0.0242444i
$867$	1.96031	+	1.96031i	0.0665757	+	0.0665757i
$868$	3.11453	+	3.01572i	0.105714	+	0.102360i
$869$	9.02083	−	9.02083i	0.306011	−	0.306011i
$870$	3.98249	−	9.83808i	0.135019	−	0.333542i
$871$		−	3.55914i		−	0.120597i
$872$	−0.418327	−	0.944669i	−0.0141663	−	0.0319905i
$873$		−	62.2450i		−	2.10668i
$874$	−56.1238	−	22.7191i	−1.89842	−	0.768486i
$875$	13.1831	−	13.1831i	0.445670	−	0.445670i
$876$	1.25855	+	78.0805i	0.0425226	+	2.63809i
$877$	−16.4845	−	16.4845i	−0.556643	−	0.556643i	0.371707	−	0.928350i	$-0.378773\pi$
$877$	−16.4845	−	16.4845i	−0.556643	−	0.556643i	−0.928350	+	0.371707i	$0.878773\pi$
$878$	−14.0760	+	5.96380i	−0.475041	+	0.201268i
$879$	72.9961			2.46210
$880$	6.10862	−	0.196977i	0.205922	−	0.00664009i
$881$	−21.5569			−0.726269			−0.363135	−	0.931737i	$-0.618293\pi$
$881$	−21.5569			−0.726269			−0.363135	+	0.931737i	$0.618293\pi$
$882$	−26.9397	+	11.4140i	−0.907108	+	0.384330i
$883$	−27.4338	−	27.4338i	−0.923221	−	0.923221i	0.0740348	−	0.997256i	$-0.476412\pi$
$883$	−27.4338	−	27.4338i	−0.923221	−	0.923221i	−0.997256	+	0.0740348i	$0.976412\pi$
$884$	−3.87522	+	0.0624635i	−0.130338	+	0.00210087i
$885$	−21.4678	+	21.4678i	−0.721631	+	0.721631i
$886$	−0.754212	−	0.305308i	−0.0253383	−	0.0102570i
$887$		−	0.424757i		−	0.0142620i	−0.999975	−	0.00713098i	$-0.997730\pi$
$887$		−	0.424757i		−	0.0142620i	0.999975	−	0.00713098i	$-0.00226988\pi$
$888$	−61.5073	−	23.7520i	−2.06405	−	0.797064i
$889$			24.6286i			0.826016i
$890$	7.96040	−	19.6648i	0.266833	−	0.659167i
$891$	−0.798139	+	0.798139i	−0.0267387	+	0.0267387i
$892$	−9.38666	+	9.69422i	−0.314289	+	0.324586i
$893$	−30.5097	−	30.5097i	−1.02097	−	1.02097i
$894$	−9.31703	−	21.9904i	−0.311608	−	0.735468i
$895$	−22.0887			−0.738343
$896$	17.1702	+	6.00213i	0.573616	+	0.200517i
$897$	29.6413			0.989694
$898$	9.04644	+	21.3517i	0.301883	+	0.712516i
$899$	−1.73061	−	1.73061i	−0.0577192	−	0.0577192i
$900$	18.0957	−	18.6886i	0.603191	−	0.622955i
$901$	−7.64720	+	7.64720i	−0.254765	+	0.254765i
$902$	3.76092	−	9.29073i	0.125225	−	0.309347i
$903$			37.0672i			1.23352i
$904$	−28.1649	−	10.8763i	−0.936751	−	0.361741i
$905$			16.6082i			0.552074i
$906$	87.0891	+	35.2540i	2.89334	+	1.17124i
$907$	−11.9394	+	11.9394i	−0.396443	+	0.396443i	−0.876976	−	0.480534i	$-0.840443\pi$
$907$	−11.9394	+	11.9394i	−0.396443	+	0.396443i	0.480534	+	0.876976i	$0.340443\pi$
$908$	−12.2366	+	0.197238i	−0.406087	+	0.00654559i
$909$	3.35833	+	3.35833i	0.111389	+	0.111389i
$910$	6.05018	−	2.56338i	0.200561	−	0.0849752i
$911$	47.3601			1.56911			0.784554	−	0.620060i	$-0.212892\pi$
$911$	47.3601			1.56911			0.784554	+	0.620060i	$0.212892\pi$
$912$	−86.0051	+	2.77330i	−2.84791	+	0.0918330i
$913$	−1.55958			−0.0516145
$914$	16.9494	−	7.18124i	0.560637	−	0.237534i
$915$	7.11247	+	7.11247i	0.235131	+	0.235131i
$916$	0.467222	+	28.9864i	0.0154374	+	0.957736i
$917$	8.10942	−	8.10942i	0.267797	−	0.267797i
$918$	−6.12588	−	2.47978i	−0.202184	−	0.0818449i
$919$		−	32.1577i		−	1.06078i	−0.847753	−	0.530392i	$-0.822045\pi$
$919$		−	32.1577i		−	1.06078i	0.847753	−	0.530392i	$-0.177955\pi$
$920$	9.42341	+	21.2800i	0.310681	+	0.701580i
$921$			47.7680i			1.57401i
$922$	12.3141	−	30.4199i	0.405542	−	1.00182i
$923$	−11.8634	+	11.8634i	−0.390490	+	0.390490i
$924$	−6.56117	−	6.35301i	−0.215847	−	0.208999i
$925$	16.5050	+	16.5050i	0.542681	+	0.542681i
$926$	18.4009	+	43.4304i	0.604691	+	1.42721i
$927$	83.5440			2.74395
$928$	−9.63743	−	3.54423i	−0.316364	−	0.116345i
$929$	−27.9562			−0.917214			−0.458607	−	0.888639i	$-0.651651\pi$
$929$	−27.9562			−0.917214			−0.458607	+	0.888639i	$0.651651\pi$
$930$	3.07545	+	7.25879i	0.100848	+	0.238025i
$931$	−24.2267	−	24.2267i	−0.793999	−	0.793999i
$932$	−9.00320	−	8.71757i	−0.294910	−	0.285553i
$933$	−31.1250	+	31.1250i	−1.01899	+	1.01899i
$934$	−13.2921	+	32.8359i	−0.434930	+	1.07442i
$935$			1.52795i			0.0499693i
$936$	23.4830	−	10.3990i	0.767566	−	0.339901i
$937$		−	41.5355i		−	1.35691i	−0.734643	−	0.678454i	$-0.762650\pi$
$937$		−	41.5355i		−	1.35691i	0.734643	−	0.678454i	$-0.237350\pi$
$938$	−3.87071	−	1.56688i	−0.126383	−	0.0511603i
$939$	−45.1384	+	45.1384i	−1.47304	+	1.47304i
$940$	0.267289	+	16.5826i	0.00871801	+	0.540864i
$941$	22.5117	+	22.5117i	0.733861	+	0.733861i	0.971382	−	0.237521i	$-0.0763350\pi$
$941$	22.5117	+	22.5117i	0.733861	+	0.733861i	−0.237521	+	0.971382i	$0.576335\pi$
$942$	39.8605	−	16.8884i	1.29873	−	0.550253i
$943$	38.1669			1.24289
$944$	21.4283	+	20.0896i	0.697433	+	0.653859i
$945$	11.2043			0.364477
$946$	11.0954	−	4.70096i	0.360742	−	0.152842i
$947$	−10.1370	−	10.1370i	−0.329407	−	0.329407i	0.522954	−	0.852361i	$-0.324830\pi$
$947$	−10.1370	−	10.1370i	−0.329407	−	0.329407i	−0.852361	+	0.522954i	$0.824830\pi$
$948$	69.0307	−	1.11268i	2.24201	−	0.0361383i
$949$	19.2991	−	19.2991i	0.626475	−	0.626475i
$950$	28.2370	+	11.4305i	0.916130	+	0.370853i
$951$		−	87.9102i		−	2.85068i
$952$	−1.63810	+	4.24196i	−0.0530910	+	0.137483i
$953$			45.8289i			1.48454i	0.670100	+	0.742271i	$0.266251\pi$
$953$			45.8289i			1.48454i	−0.670100	+	0.742271i	$0.733749\pi$
$954$	26.8902	−	66.4278i	0.870603	−	2.15068i
$955$	14.0963	−	14.0963i	0.456147	−	0.456147i
$956$	−25.4568	+	26.2909i	−0.823331	+	0.850308i
$957$	3.64577	+	3.64577i	0.117851	+	0.117851i
$958$	10.1439	+	23.9419i	0.327733	+	0.773527i
$959$	25.1790			0.813071
$960$	24.4910	+	22.2301i	0.790442	+	0.717475i
$961$	−29.1821			−0.941358
$962$	8.98994	+	21.2184i	0.289847	+	0.684108i
$963$	1.81082	+	1.81082i	0.0583527	+	0.0583527i
$964$	−32.1899	+	33.2447i	−1.03677	+	1.07074i
$965$	5.08531	−	5.08531i	0.163702	−	0.163702i
$966$	13.0493	−	32.2361i	0.419854	−	1.03718i
$967$		−	6.78233i		−	0.218105i	−0.994036	−	0.109052i	$-0.965218\pi$
$967$		−	6.78233i		−	0.218105i	0.994036	−	0.109052i	$-0.0347816\pi$
$968$	10.1384	−	26.2541i	0.325862	−	0.843840i
$969$		−	21.5124i		−	0.691079i
$970$	−25.9702	−	10.5128i	−0.833853	−	0.337546i
$971$	−43.3608	+	43.3608i	−1.39151	+	1.39151i	−0.569574	+	0.821940i	$0.692892\pi$
$971$	−43.3608	+	43.3608i	−1.39151	+	1.39151i	−0.821940	+	0.569574i	$0.807108\pi$
$972$	−34.1426	+	0.550333i	−1.09512	+	0.0176520i
$973$	11.2592	+	11.2592i	0.360955	+	0.360955i
$974$	−34.5445	+	14.6360i	−1.10688	+	0.468968i
$975$	−14.9131			−0.477603
$976$	6.65586	−	7.09940i	0.213049	−	0.227246i
$977$	−20.6037			−0.659172			−0.329586	−	0.944126i	$-0.606909\pi$
$977$	−20.6037			−0.659172			−0.329586	+	0.944126i	$0.606909\pi$
$978$	−68.5256	+	29.0334i	−2.19121	+	0.928386i
$979$	7.28734	+	7.28734i	0.232904	+	0.232904i
$980$	0.212246	+	13.1677i	0.00677994	+	0.420627i
$981$	−1.21024	+	1.21024i	−0.0386400	+	0.0386400i
$982$	34.6728	+	14.0357i	1.10645	+	0.447896i
$983$		−	23.5152i		−	0.750017i	−0.927021	−	0.375009i	$-0.877640\pi$
$983$		−	23.5152i		−	0.750017i	0.927021	−	0.375009i	$-0.122360\pi$
$984$	49.5969	−	21.9630i	1.58109	−	0.700154i
$985$			30.8721i			0.983668i
$986$	0.963249	−	2.37955i	0.0306761	−	0.0757802i
$987$	17.5240	−	17.5240i	0.557794	−	0.557794i
$988$	21.6061	+	20.9206i	0.687381	+	0.665573i
$989$	32.4462	+	32.4462i	1.03173	+	1.03173i
$990$	−3.94991	−	9.32270i	−0.125536	−	0.296295i
$991$	37.6217			1.19509			0.597546	−	0.801835i	$-0.296143\pi$
$991$	37.6217			1.19509			0.597546	+	0.801835i	$0.296143\pi$
$992$	6.92323	−	3.20025i	0.219813	−	0.101608i
$993$	77.5347			2.46049
$994$	7.67920	+	18.1247i	0.243570	+	0.574881i
$995$	−25.0583	−	25.0583i	−0.794402	−	0.794402i
$996$	−6.06342	−	5.87105i	−0.192127	−	0.186031i
$997$	−32.7812	+	32.7812i	−1.03819	+	1.03819i	−0.0389496	+	0.999241i	$0.512401\pi$
$997$	−32.7812	+	32.7812i	−1.03819	+	1.03819i	−0.999241	+	0.0389496i	$0.987599\pi$
$998$	12.1522	−	30.0201i	0.384672	−	0.950269i
$999$			39.2943i			1.24322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.10	yes	32
4.3	odd	2		1088.2.l.c.273.2		32
16.5	even	4	inner	272.2.l.c.69.10	✓	32
16.11	odd	4		1088.2.l.c.817.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.10	✓	32	16.5	even	4	inner
272.2.l.c.205.10	yes	32	1.1	even	1	trivial
1088.2.l.c.273.2		32	4.3	odd	2
1088.2.l.c.817.2		32	16.11	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.551708 + 1.30216i) q^{2} +(1.96031 + 1.96031i) q^{3} +(-1.39124 + 1.43682i) q^{4} +(1.05453 - 1.05453i) q^{5} +(-1.47112 + 3.63416i) q^{6} -1.60770i q^{7} +(-2.63853 - 1.01891i) q^{8} +4.68564i q^{9} +(1.95497 + 0.791377i) q^{10} +(-0.724466 + 0.724466i) q^{11} +(-5.54388 + 0.0893599i) q^{12} +(1.37028 + 1.37028i) q^{13} +(2.09348 - 0.886980i) q^{14} +4.13443 q^{15} +(-0.128916 - 3.99792i) q^{16} +1.00000 q^{17} +(-6.10145 + 2.58510i) q^{18} +(-5.48700 - 5.48700i) q^{19} +(0.0480705 + 2.98229i) q^{20} +(3.15159 - 3.15159i) q^{21} +(-1.34306 - 0.543677i) q^{22} -5.51739i q^{23} +(-3.17496 - 7.16971i) q^{24} +2.77591i q^{25} +(-1.02833 + 2.54031i) q^{26} +(-3.30438 + 3.30438i) q^{27} +(2.30998 + 2.23669i) q^{28} +(-1.28356 - 1.28356i) q^{29} +(2.28100 + 5.38369i) q^{30} +1.34829 q^{31} +(5.13481 - 2.37355i) q^{32} -2.84036 q^{33} +(0.551708 + 1.30216i) q^{34} +(-1.69538 - 1.69538i) q^{35} +(-6.73243 - 6.51884i) q^{36} +(5.94579 - 5.94579i) q^{37} +(4.11773 - 10.1722i) q^{38} +5.37234i q^{39} +(-3.85689 + 1.70795i) q^{40} +6.91756i q^{41} +(5.84263 + 2.36512i) q^{42} +(-5.88071 + 5.88071i) q^{43} +(-0.0330245 - 2.04883i) q^{44} +(4.94117 + 4.94117i) q^{45} +(7.18453 - 3.04399i) q^{46} +5.56036 q^{47} +(7.58446 - 8.08989i) q^{48} +4.41530 q^{49} +(-3.61468 + 1.53149i) q^{50} +(1.96031 + 1.96031i) q^{51} +(-3.87522 + 0.0624635i) q^{52} +(-7.64720 + 7.64720i) q^{53} +(-6.12588 - 2.47978i) q^{54} +1.52795i q^{55} +(-1.63810 + 4.24196i) q^{56} -21.5124i q^{57} +(0.963249 - 2.37955i) q^{58} +(-5.19243 + 5.19243i) q^{59} +(-5.75198 + 5.94044i) q^{60} +(1.72030 + 1.72030i) q^{61} +(0.743864 + 1.75569i) q^{62} +7.53310 q^{63} +(5.92366 + 5.37683i) q^{64} +2.89001 q^{65} +(-1.56705 - 3.69860i) q^{66} +(-1.29869 - 1.29869i) q^{67} +(-1.39124 + 1.43682i) q^{68} +(10.8158 - 10.8158i) q^{69} +(1.27230 - 3.14300i) q^{70} +8.65770i q^{71} +(4.77423 - 12.3632i) q^{72} -14.0841i q^{73} +(11.0227 + 4.46203i) q^{74} +(-5.44165 + 5.44165i) q^{75} +(15.5176 - 0.250122i) q^{76} +(1.16472 + 1.16472i) q^{77} +(-6.99564 + 2.96396i) q^{78} -12.4517 q^{79} +(-4.35189 - 4.08000i) q^{80} +1.10169 q^{81} +(-9.00777 + 3.81647i) q^{82} +(1.07636 + 1.07636i) q^{83} +(0.143664 + 8.91289i) q^{84} +(1.05453 - 1.05453i) q^{85} +(-10.9021 - 4.41319i) q^{86} -5.03235i q^{87} +(2.64969 - 1.17336i) q^{88} -10.0589i q^{89} +(-3.70811 + 9.16027i) q^{90} +(2.20299 - 2.20299i) q^{91} +(7.92751 + 7.67601i) q^{92} +(2.64307 + 2.64307i) q^{93} +(3.06769 + 7.24047i) q^{94} -11.5725 q^{95} +(14.7187 + 5.41292i) q^{96} -13.2842 q^{97} +(2.43595 + 5.74943i) q^{98} +(-3.39459 - 3.39459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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