LMFDB - Embedded newform 336.2.u.a.139.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.15
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.135637 - 1.40769i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.96321 + 0.381870i) q^{4} +(2.46638 - 2.46638i) q^{5} +(1.09130 + 0.899481i) q^{6} +(-2.50032 - 0.865115i) q^{7} +(0.803838 + 2.71180i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.135637 - 1.40769i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.96321 + 0.381870i) q^{4} +(2.46638 - 2.46638i) q^{5} +(1.09130 + 0.899481i) q^{6} +(-2.50032 - 0.865115i) q^{7} +(0.803838 + 2.71180i) q^{8} -1.00000i q^{9} +(-3.80643 - 3.13737i) q^{10} +(0.244455 - 0.244455i) q^{11} +(1.11817 - 1.65822i) q^{12} +(-2.35087 - 2.35087i) q^{13} +(-0.878683 + 3.63702i) q^{14} +3.48798i q^{15} +(3.70835 - 1.49938i) q^{16} -5.19171i q^{17} +(-1.40769 + 0.135637i) q^{18} +(1.43102 - 1.43102i) q^{19} +(-3.90017 + 5.78384i) q^{20} +(2.37972 - 1.15626i) q^{21} +(-0.377275 - 0.310961i) q^{22} -6.61525 q^{23} +(-2.48593 - 1.34913i) q^{24} -7.16602i q^{25} +(-2.99044 + 3.62817i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.23899 + 0.743604i) q^{28} +(-5.09187 + 5.09187i) q^{29} +(4.91001 - 0.473098i) q^{30} -1.53315 q^{31} +(-2.61365 - 5.01685i) q^{32} +0.345712i q^{33} +(-7.30834 + 0.704186i) q^{34} +(-8.30041 + 4.03302i) q^{35} +(0.381870 + 1.96321i) q^{36} +(-2.40835 - 2.40835i) q^{37} +(-2.20854 - 1.82034i) q^{38} +3.32463 q^{39} +(8.67088 + 4.70574i) q^{40} +9.55090 q^{41} +(-1.95044 - 3.19308i) q^{42} +(6.80405 - 6.80405i) q^{43} +(-0.386566 + 0.573266i) q^{44} +(-2.46638 - 2.46638i) q^{45} +(0.897269 + 9.31224i) q^{46} +7.20043 q^{47} +(-1.56198 + 3.68242i) q^{48} +(5.50315 + 4.32612i) q^{49} +(-10.0876 + 0.971974i) q^{50} +(3.67109 + 3.67109i) q^{51} +(5.51296 + 3.71751i) q^{52} +(5.49720 + 5.49720i) q^{53} +(0.899481 - 1.09130i) q^{54} -1.20584i q^{55} +(0.336168 - 7.47576i) q^{56} +2.02377i q^{57} +(7.85844 + 6.47716i) q^{58} +(-3.45643 - 3.45643i) q^{59} +(-1.33195 - 6.84762i) q^{60} +(-1.27576 - 1.27576i) q^{61} +(0.207952 + 2.15821i) q^{62} +(-0.865115 + 2.50032i) q^{63} +(-6.70769 + 4.35969i) q^{64} -11.5962 q^{65} +(0.486657 - 0.0468912i) q^{66} +(3.83774 + 3.83774i) q^{67} +(1.98256 + 10.1924i) q^{68} +(4.67768 - 4.67768i) q^{69} +(6.80309 + 11.1374i) q^{70} +16.0833 q^{71} +(2.71180 - 0.803838i) q^{72} +6.68392 q^{73} +(-3.06356 + 3.71688i) q^{74} +(5.06714 + 5.06714i) q^{75} +(-2.26292 + 3.35585i) q^{76} +(-0.822697 + 0.399733i) q^{77} +(-0.450941 - 4.68006i) q^{78} -4.09727i q^{79} +(5.44816 - 12.8442i) q^{80} -1.00000 q^{81} +(-1.29545 - 13.4447i) q^{82} +(-9.70907 + 9.70907i) q^{83} +(-4.23034 + 3.17872i) q^{84} +(-12.8047 - 12.8047i) q^{85} +(-10.5009 - 8.65514i) q^{86} -7.20100i q^{87} +(0.859416 + 0.466411i) q^{88} +11.5562 q^{89} +(-3.13737 + 3.80643i) q^{90} +(3.84414 + 7.91168i) q^{91} +(12.9871 - 2.52616i) q^{92} +(1.08410 - 1.08410i) q^{93} +(-0.976641 - 10.1360i) q^{94} -7.05886i q^{95} +(5.39558 + 1.69932i) q^{96} -16.7160i q^{97} +(5.34343 - 8.33353i) q^{98} +(-0.244455 - 0.244455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.135637	−	1.40769i	−0.0959095	−	0.995390i
$2$	−0.135637	−	1.40769i	−0.0959095	−	0.995390i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.96321	+	0.381870i	−0.981603	+	0.190935i
$5$	2.46638	−	2.46638i	1.10300	−	1.10300i	0.108949	−	0.994047i	$-0.465251\pi$
$5$	2.46638	−	2.46638i	1.10300	−	1.10300i	0.994047	−	0.108949i	$-0.0347486\pi$
$6$	1.09130	+	0.899481i	0.445521	+	0.367211i
$7$	−2.50032	−	0.865115i	−0.945030	−	0.326983i
$7$	−2.50032	−	0.865115i	−0.945030	−	0.326983i
$8$	0.803838	+	2.71180i	0.284200	+	0.958765i
$9$		−	1.00000i		−	0.333333i
$10$	−3.80643	−	3.13737i	−1.20370	−	0.992124i
$11$	0.244455	−	0.244455i	0.0737061	−	0.0737061i	−0.669293	−	0.742999i	$-0.733403\pi$
$11$	0.244455	−	0.244455i	0.0737061	−	0.0737061i	0.742999	+	0.669293i	$0.233403\pi$
$12$	1.11817	−	1.65822i	0.322789	−	0.478686i
$13$	−2.35087	−	2.35087i	−0.652014	−	0.652014i	0.301464	−	0.953478i	$-0.402525\pi$
$13$	−2.35087	−	2.35087i	−0.652014	−	0.652014i	−0.953478	+	0.301464i	$0.902525\pi$
$14$	−0.878683	+	3.63702i	−0.234838	+	0.972035i
$15$			3.48798i			0.900593i
$16$	3.70835	−	1.49938i	0.927088	−	0.374844i
$17$		−	5.19171i		−	1.25918i	−0.776930	−	0.629588i	$-0.783224\pi$
$17$		−	5.19171i		−	1.25918i	0.776930	−	0.629588i	$-0.216776\pi$
$18$	−1.40769	+	0.135637i	−0.331797	+	0.0319698i
$19$	1.43102	−	1.43102i	0.328298	−	0.328298i	−0.523641	−	0.851939i	$-0.675427\pi$
$19$	1.43102	−	1.43102i	0.328298	−	0.328298i	0.851939	+	0.523641i	$0.175427\pi$
$20$	−3.90017	+	5.78384i	−0.872104	+	1.29330i
$21$	2.37972	−	1.15626i	0.519297	−	0.252317i
$22$	−0.377275	−	0.310961i	−0.0804354	−	0.0662972i
$23$	−6.61525			−1.37937			−0.689687	−	0.724108i	$-0.742252\pi$
$23$	−6.61525			−1.37937			−0.689687	+	0.724108i	$0.742252\pi$
$24$	−2.48593	−	1.34913i	−0.507438	−	0.275390i
$25$		−	7.16602i		−	1.43320i
$26$	−2.99044	+	3.62817i	−0.586474	+	0.711542i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	5.23899	+	0.743604i	0.990077	+	0.140528i
$29$	−5.09187	+	5.09187i	−0.945537	+	0.945537i	−0.998592	−	0.0530544i	$-0.983104\pi$
$29$	−5.09187	+	5.09187i	−0.945537	+	0.945537i	0.0530544	+	0.998592i	$0.483104\pi$
$30$	4.91001	−	0.473098i	0.896441	−	0.0863755i
$31$	−1.53315			−0.275363			−0.137681	−	0.990477i	$-0.543965\pi$
$31$	−1.53315			−0.275363			−0.137681	+	0.990477i	$0.543965\pi$
$32$	−2.61365	−	5.01685i	−0.462033	−	0.886863i
$33$			0.345712i			0.0601807i
$34$	−7.30834	+	0.704186i	−1.25337	+	0.120767i
$35$	−8.30041	+	4.03302i	−1.40303	+	0.681704i
$36$	0.381870	+	1.96321i	0.0636449	+	0.327201i
$37$	−2.40835	−	2.40835i	−0.395930	−	0.395930i	0.480865	−	0.876795i	$-0.340323\pi$
$37$	−2.40835	−	2.40835i	−0.395930	−	0.395930i	−0.876795	+	0.480865i	$0.840323\pi$
$38$	−2.20854	−	1.82034i	−0.358272	−	0.295298i
$39$	3.32463			0.532367
$40$	8.67088	+	4.70574i	1.37099	+	0.744043i
$41$	9.55090			1.49160			0.745800	−	0.666170i	$-0.232068\pi$
$41$	9.55090			1.49160			0.745800	+	0.666170i	$0.232068\pi$
$42$	−1.95044	−	3.19308i	−0.300959	−	0.492704i
$43$	6.80405	−	6.80405i	1.03761	−	1.03761i	0.0383425	−	0.999265i	$-0.487792\pi$
$43$	6.80405	−	6.80405i	1.03761	−	1.03761i	0.999265	−	0.0383425i	$-0.0122078\pi$
$44$	−0.386566	+	0.573266i	−0.0582770	+	0.0864231i
$45$	−2.46638	−	2.46638i	−0.367666	−	0.367666i
$46$	0.897269	+	9.31224i	0.132295	+	1.37302i
$47$	7.20043			1.05029			0.525145	−	0.851013i	$-0.324011\pi$
$47$	7.20043			1.05029			0.525145	+	0.851013i	$0.324011\pi$
$48$	−1.56198	+	3.68242i	−0.225452	+	0.531512i
$49$	5.50315	+	4.32612i	0.786165	+	0.618017i
$50$	−10.0876	+	0.971974i	−1.42660	+	0.137458i
$51$	3.67109	+	3.67109i	0.514056	+	0.514056i
$52$	5.51296	+	3.71751i	0.764510	+	0.515526i
$53$	5.49720	+	5.49720i	0.755099	+	0.755099i	0.975426	−	0.220327i	$-0.0707126\pi$
$53$	5.49720	+	5.49720i	0.755099	+	0.755099i	−0.220327	+	0.975426i	$0.570713\pi$
$54$	0.899481	−	1.09130i	0.122404	−	0.148507i
$55$		−	1.20584i		−	0.162595i
$56$	0.336168	−	7.47576i	0.0449224	−	0.998990i
$57$			2.02377i			0.268055i
$58$	7.85844	+	6.47716i	1.03186	+	0.850492i
$59$	−3.45643	−	3.45643i	−0.449988	−	0.449988i	0.445362	−	0.895351i	$-0.353075\pi$
$59$	−3.45643	−	3.45643i	−0.449988	−	0.449988i	−0.895351	+	0.445362i	$0.853075\pi$
$60$	−1.33195	−	6.84762i	−0.171955	−	0.884025i
$61$	−1.27576	−	1.27576i	−0.163344	−	0.163344i	0.620702	−	0.784046i	$-0.286848\pi$
$61$	−1.27576	−	1.27576i	−0.163344	−	0.163344i	−0.784046	+	0.620702i	$0.786848\pi$
$62$	0.207952	+	2.15821i	0.0264099	+	0.274093i
$63$	−0.865115	+	2.50032i	−0.108994	+	0.315010i
$64$	−6.70769	+	4.35969i	−0.838461	+	0.544961i
$65$	−11.5962			−1.43834
$66$	0.486657	−	0.0468912i	0.0599033	−	0.00577191i
$67$	3.83774	+	3.83774i	0.468855	+	0.468855i	0.901543	−	0.432689i	$-0.142435\pi$
$67$	3.83774	+	3.83774i	0.468855	+	0.468855i	−0.432689	+	0.901543i	$0.642435\pi$
$68$	1.98256	+	10.1924i	0.240420	+	1.23601i
$69$	4.67768	−	4.67768i	0.563127	−	0.563127i
$70$	6.80309	+	11.1374i	0.813125	+	1.33118i
$71$	16.0833			1.90874			0.954368	−	0.298632i	$-0.0965304\pi$
$71$	16.0833			1.90874			0.954368	+	0.298632i	$0.0965304\pi$
$72$	2.71180	−	0.803838i	0.319588	−	0.0947332i
$73$	6.68392			0.782293			0.391147	−	0.920328i	$-0.372079\pi$
$73$	6.68392			0.782293			0.391147	+	0.920328i	$0.372079\pi$
$74$	−3.06356	+	3.71688i	−0.356131	+	0.432078i
$75$	5.06714	+	5.06714i	0.585103	+	0.585103i
$76$	−2.26292	+	3.35585i	−0.259575	+	0.384942i
$77$	−0.822697	+	0.399733i	−0.0937551	+	0.0455539i
$78$	−0.450941	−	4.68006i	−0.0510591	−	0.529913i
$79$		−	4.09727i		−	0.460979i	−0.973075	−	0.230490i	$-0.925967\pi$
$79$		−	4.09727i		−	0.460979i	0.973075	−	0.230490i	$-0.0740328\pi$
$80$	5.44816	−	12.8442i	0.609123	−	1.43603i
$81$	−1.00000			−0.111111
$82$	−1.29545	−	13.4447i	−0.143059	−	1.48472i
$83$	−9.70907	+	9.70907i	−1.06571	+	1.06571i	−0.0680257	+	0.997684i	$0.521670\pi$
$83$	−9.70907	+	9.70907i	−1.06571	+	1.06571i	−0.997684	+	0.0680257i	$0.978330\pi$
$84$	−4.23034	+	3.17872i	−0.461567	+	0.346827i
$85$	−12.8047	−	12.8047i	−1.38887	−	1.38887i
$86$	−10.5009	−	8.65514i	−1.13234	−	0.933307i
$87$		−	7.20100i		−	0.772028i
$88$	0.859416	+	0.466411i	0.0916140	+	0.0497196i
$89$	11.5562			1.22495			0.612477	−	0.790489i	$-0.290173\pi$
$89$	11.5562			1.22495			0.612477	+	0.790489i	$0.290173\pi$
$90$	−3.13737	+	3.80643i	−0.330708	+	0.401233i
$91$	3.84414	+	7.91168i	0.402975	+	0.829370i
$92$	12.9871	−	2.52616i	1.35400	−	0.263370i
$93$	1.08410	−	1.08410i	0.112416	−	0.112416i
$94$	−0.976641	−	10.1360i	−0.100733	−	1.04545i
$95$		−	7.05886i		−	0.724224i
$96$	5.39558	+	1.69932i	0.550684	+	0.173436i
$97$		−	16.7160i		−	1.69725i	−0.528995	−	0.848625i	$-0.677431\pi$
$97$		−	16.7160i		−	1.69725i	0.528995	−	0.848625i	$-0.322569\pi$
$98$	5.34343	−	8.33353i	0.539768	−	0.841814i
$99$	−0.244455	−	0.244455i	−0.0245687	−	0.0245687i
$100$	2.73648	+	14.0684i	0.273648	+	1.40684i
$101$	−10.5198	+	10.5198i	−1.04676	+	1.04676i	−0.0479051	+	0.998852i	$0.515255\pi$
$101$	−10.5198	+	10.5198i	−1.04676	+	1.04676i	−0.998852	+	0.0479051i	$0.984745\pi$
$102$	4.66984	−	5.66571i	0.462383	−	0.560989i
$103$		−	5.39742i		−	0.531824i	−0.963997	−	0.265912i	$-0.914327\pi$
$103$		−	5.39742i		−	0.531824i	0.963997	−	0.265912i	$-0.0856730\pi$
$104$	4.48536	−	8.26480i	0.439826	−	0.810430i
$105$	3.01751	−	8.72105i	0.294478	−	0.851088i
$106$	6.99276	−	8.48400i	0.679196	−	0.824039i
$107$	−5.63948	+	5.63948i	−0.545189	+	0.545189i	−0.925045	−	0.379857i	$-0.875973\pi$
$107$	−5.63948	+	5.63948i	−0.545189	+	0.545189i	0.379857	+	0.925045i	$0.375973\pi$
$108$	−1.65822	−	1.11817i	−0.159562	−	0.107596i
$109$	1.70321	−	1.70321i	0.163138	−	0.163138i	−0.620817	−	0.783955i	$-0.713199\pi$
$109$	1.70321	−	1.70321i	0.163138	−	0.163138i	0.783955	+	0.620817i	$0.213199\pi$
$110$	−1.69745	+	0.163556i	−0.161846	+	0.0155944i
$111$	3.40592			0.323275
$112$	−10.5692	+	0.540765i	−0.998694	+	0.0510974i
$113$	5.88021			0.553163			0.276582	−	0.960990i	$-0.410798\pi$
$113$	5.88021			0.553163			0.276582	+	0.960990i	$0.410798\pi$
$114$	2.84885	−	0.274497i	0.266819	−	0.0257090i
$115$	−16.3157	+	16.3157i	−1.52144	+	1.52144i
$116$	8.05196	−	11.9408i	0.747606	−	1.10868i
$117$	−2.35087	+	2.35087i	−0.217338	+	0.217338i
$118$	−4.39677	+	5.33441i	−0.404756	+	0.491072i
$119$	−4.49143	+	12.9809i	−0.411729	+	1.18996i
$120$	−9.45870	+	2.80377i	−0.863457	+	0.255948i
$121$			10.8805i			0.989135i
$122$	−1.62283	+	1.96891i	−0.146925	+	0.178257i
$123$	−6.75350	+	6.75350i	−0.608943	+	0.608943i
$124$	3.00990	−	0.585465i	0.270297	−	0.0525763i
$125$	−5.34221	−	5.34221i	−0.477822	−	0.477822i
$126$	3.63702	+	0.878683i	0.324012	+	0.0782793i
$127$		−	2.54065i		−	0.225446i	−0.993626	−	0.112723i	$-0.964043\pi$
$127$		−	2.54065i		−	0.225446i	0.993626	−	0.112723i	$-0.0359573\pi$
$128$	7.04692	+	8.85104i	0.622866	+	0.782329i
$129$			9.62237i			0.847203i
$130$	1.57288	+	16.3240i	0.137950	+	1.43171i
$131$	1.36457	−	1.36457i	0.119223	−	0.119223i	−0.644978	−	0.764201i	$-0.723134\pi$
$131$	1.36457	−	1.36457i	0.119223	−	0.119223i	0.764201	+	0.644978i	$0.223134\pi$
$132$	−0.132017	−	0.678704i	−0.0114906	−	0.0590736i
$133$	−4.81600	+	2.34000i	−0.417600	+	0.202904i
$134$	4.88183	−	5.92290i	0.421726	−	0.511661i
$135$	3.48798			0.300198
$136$	14.0789	−	4.17330i	1.20725	−	0.357857i
$137$			8.81747i			0.753327i	0.926350	+	0.376664i	$0.122929\pi$
$137$			8.81747i			0.753327i	−0.926350	+	0.376664i	$0.877071\pi$
$138$	−7.21921	−	5.95028i	−0.614540	−	0.506522i
$139$	−0.409417	−	0.409417i	−0.0347263	−	0.0347263i	0.689530	−	0.724257i	$-0.257817\pi$
$139$	−0.409417	−	0.409417i	−0.0347263	−	0.0347263i	−0.724257	+	0.689530i	$0.757817\pi$
$140$	14.7553	−	11.0873i	1.24705	−	0.937049i
$141$	−5.09147	+	5.09147i	−0.428779	+	0.428779i
$142$	−2.18148	−	22.6404i	−0.183066	−	1.89994i
$143$	−1.14936			−0.0961147
$144$	−1.49938	−	3.70835i	−0.124948	−	0.309029i
$145$			25.1169i			2.08585i
$146$	−0.906583	−	9.40891i	−0.0750294	−	0.778687i
$147$	−6.95035	+	0.832287i	−0.573255	+	0.0686459i
$148$	5.64776	+	3.80841i	0.464243	+	0.313049i
$149$	8.59190	+	8.59190i	0.703876	+	0.703876i	0.965240	−	0.261364i	$-0.0841724\pi$
$149$	8.59190	+	8.59190i	0.703876	+	0.703876i	−0.261364	+	0.965240i	$0.584172\pi$
$150$	6.44569	−	7.82027i	0.526289	−	0.638522i
$151$	−15.8215			−1.28753			−0.643767	−	0.765222i	$-0.722629\pi$
$151$	−15.8215			−1.28753			−0.643767	+	0.765222i	$0.722629\pi$
$152$	5.03094	+	2.73033i	0.408063	+	0.221459i
$153$	−5.19171			−0.419725
$154$	0.674290	+	1.10389i	0.0543359	+	0.0889538i
$155$	−3.78134	+	3.78134i	−0.303724	+	0.303724i
$156$	−6.52693	+	1.26958i	−0.522573	+	0.101647i
$157$	−13.3568	−	13.3568i	−1.06599	−	1.06599i	−0.997663	−	0.0683267i	$-0.978234\pi$
$157$	−13.3568	−	13.3568i	−1.06599	−	1.06599i	−0.0683267	−	0.997663i	$-0.521766\pi$
$158$	−5.76771	+	0.555740i	−0.458854	+	0.0442123i
$159$	−7.77422			−0.616535
$160$	−18.8197	−	5.92720i	−1.48783	−	0.468586i
$161$	16.5402	+	5.72295i	1.30355	+	0.451031i
$162$	0.135637	+	1.40769i	0.0106566	+	0.110599i
$163$	11.2072	+	11.2072i	0.877815	+	0.877815i	0.993308	−	0.115493i	$-0.0368449\pi$
$163$	11.2072	+	11.2072i	0.877815	+	0.877815i	−0.115493	+	0.993308i	$0.536845\pi$
$164$	−18.7504	+	3.64720i	−1.46416	+	0.284798i
$165$	0.852656	+	0.852656i	0.0663792	+	0.0663792i
$166$	14.9843	+	12.3505i	1.16301	+	0.958585i
$167$		−	15.6103i		−	1.20796i	−0.796998	−	0.603981i	$-0.793580\pi$
$167$		−	15.6103i		−	1.20796i	0.796998	−	0.603981i	$-0.206420\pi$
$168$	5.04845	+	5.52387i	0.389497	+	0.426176i
$169$		−	1.94683i		−	0.149756i
$170$	−16.2883	+	19.7619i	−1.24926	+	1.51567i
$171$	−1.43102	−	1.43102i	−0.109433	−	0.109433i
$172$	−10.7595	+	15.9560i	−0.820403	+	1.21663i
$173$	−6.62694	−	6.62694i	−0.503837	−	0.503837i	0.408791	−	0.912628i	$-0.365950\pi$
$173$	−6.62694	−	6.62694i	−0.503837	−	0.503837i	−0.912628	+	0.408791i	$0.865950\pi$
$174$	−10.1368	+	0.976718i	−0.768469	+	0.0740448i
$175$	−6.19943	+	17.9173i	−0.468633	+	1.35442i
$176$	0.539996	−	1.27306i	0.0407037	−	0.0959603i
$177$	4.88812			0.367414
$178$	−1.56744	−	16.2676i	−0.117485	−	1.21931i
$179$	−1.58460	−	1.58460i	−0.118439	−	0.118439i	0.645403	−	0.763842i	$-0.276689\pi$
$179$	−1.58460	−	1.58460i	−0.118439	−	0.118439i	−0.763842	+	0.645403i	$0.776689\pi$
$180$	5.78384	+	3.90017i	0.431102	+	0.290701i
$181$	7.37897	−	7.37897i	0.548475	−	0.548475i	−0.377525	−	0.925999i	$-0.623225\pi$
$181$	7.37897	−	7.37897i	0.548475	−	0.548475i	0.925999	+	0.377525i	$0.123225\pi$
$182$	10.6158	−	6.48449i	0.786897	−	0.480662i
$183$	1.80419			0.133370
$184$	−5.31759	−	17.9392i	−0.392018	−	1.32250i
$185$	−11.8798			−0.873419
$186$	−1.67313	−	1.37904i	−0.122680	−	0.101116i
$187$	−1.26914	−	1.26914i	−0.0928088	−	0.0928088i
$188$	−14.1359	+	2.74962i	−1.03097	+	0.200537i
$189$	−1.15626	−	2.37972i	−0.0841056	−	0.173099i
$190$	−9.93672	+	0.957440i	−0.720885	+	0.0694600i
$191$		−	24.9642i		−	1.80635i	−0.429274	−	0.903174i	$-0.641231\pi$
$191$		−	24.9642i		−	1.80635i	0.429274	−	0.903174i	$-0.358769\pi$
$192$	1.66028	−	7.82582i	0.119821	−	0.564780i
$193$	−9.84108			−0.708376			−0.354188	−	0.935174i	$-0.615243\pi$
$193$	−9.84108			−0.708376			−0.354188	+	0.935174i	$0.615243\pi$
$194$	−23.5310	+	2.26730i	−1.68943	+	0.162782i
$195$	8.19979	−	8.19979i	0.587199	−	0.587199i
$196$	−12.4558	−	6.39158i	−0.889702	−	0.456541i
$197$	6.20883	+	6.20883i	0.442360	+	0.442360i	0.892805	−	0.450444i	$-0.148734\pi$
$197$	6.20883	+	6.20883i	0.442360	+	0.442360i	−0.450444	+	0.892805i	$0.648734\pi$
$198$	−0.310961	+	0.377275i	−0.0220991	+	0.0268118i
$199$			10.1707i			0.720981i	0.932763	+	0.360491i	$0.117391\pi$
$199$			10.1707i			0.720981i	−0.932763	+	0.360491i	$0.882609\pi$
$200$	19.4328	−	5.76032i	1.37411	−	0.407316i
$201$	−5.42739			−0.382818
$202$	16.2355	+	13.3818i	1.14233	+	0.941538i
$203$	17.1363	−	8.32623i	1.20274	−	0.584387i
$204$	−8.60899	−	5.80523i	−0.602750	−	0.406448i
$205$	23.5561	−	23.5561i	1.64523	−	1.64523i
$206$	−7.59792	+	0.732088i	−0.529372	+	0.0510070i
$207$			6.61525i			0.459791i
$208$	−12.2427	−	5.19301i	−0.848877	−	0.360070i
$209$		−	0.699641i		−	0.0483952i
$210$	−12.6859	−	3.06483i	−0.875407	−	0.211493i
$211$	−5.69803	−	5.69803i	−0.392269	−	0.392269i	0.483227	−	0.875495i	$-0.339465\pi$
$211$	−5.69803	−	5.69803i	−0.392269	−	0.392269i	−0.875495	+	0.483227i	$0.839465\pi$
$212$	−12.8913	−	8.69292i	−0.885381	−	0.597032i
$213$	−11.3726	+	11.3726i	−0.779238	+	0.779238i
$214$	8.70358	+	7.17374i	0.594964	+	0.490387i
$215$		−	33.5627i		−	2.28895i
$216$	−1.34913	+	2.48593i	−0.0917967	+	0.169146i
$217$	3.83337	+	1.32636i	0.260226	+	0.0900389i
$218$	−2.62862	−	2.16658i	−0.178033	−	0.146740i
$219$	−4.72624	+	4.72624i	−0.319370	+	0.319370i
$220$	0.460473	+	2.36731i	0.0310451	+	0.159604i
$221$	−12.2050	+	12.2050i	−0.820999	+	0.820999i
$222$	−0.461967	−	4.79449i	−0.0310052	−	0.321785i
$223$	5.26554			0.352607			0.176303	−	0.984336i	$-0.443586\pi$
$223$	5.26554			0.352607			0.176303	+	0.984336i	$0.443586\pi$
$224$	2.19480	+	14.8048i	0.146646	+	0.989189i
$225$	−7.16602			−0.477734
$226$	−0.797571	−	8.27753i	−0.0530536	−	0.550613i
$227$	11.3768	−	11.3768i	0.755102	−	0.755102i	−0.220325	−	0.975427i	$-0.570712\pi$
$227$	11.3768	−	11.3768i	0.755102	−	0.755102i	0.975427	+	0.220325i	$0.0707117\pi$
$228$	−0.772815	−	3.97307i	−0.0511809	−	0.263123i
$229$	−14.8763	+	14.8763i	−0.983051	+	0.983051i	−0.999859	−	0.0168077i	$-0.994650\pi$
$229$	−14.8763	+	14.8763i	−0.983051	+	0.983051i	0.0168077	+	0.999859i	$0.494650\pi$
$230$	25.1805	+	20.7545i	1.66035	+	1.36851i
$231$	0.299081	−	0.864389i	0.0196781	−	0.0568726i
$232$	−17.9012	−	9.71509i	−1.17527	−	0.637827i
$233$		−	2.12538i		−	0.139238i	−0.997574	−	0.0696190i	$-0.977822\pi$
$233$		−	2.12538i		−	0.139238i	0.997574	−	0.0696190i	$-0.0221783\pi$
$234$	3.62817	+	2.99044i	0.237181	+	0.195491i
$235$	17.7590	−	17.7590i	1.15847	−	1.15847i
$236$	8.10558	+	5.46577i	0.527628	+	0.355791i
$237$	2.89721	+	2.89721i	0.188194	+	0.188194i
$238$	18.8824	+	4.56187i	1.22396	+	0.295702i
$239$			8.94355i			0.578510i	0.957252	+	0.289255i	$0.0934076\pi$
$239$			8.94355i			0.578510i	−0.957252	+	0.289255i	$0.906592\pi$
$240$	5.22980	+	12.9347i	0.337582	+	0.834929i
$241$		−	4.16309i		−	0.268168i	−0.990970	−	0.134084i	$-0.957191\pi$
$241$		−	4.16309i		−	0.268168i	0.990970	−	0.134084i	$-0.0428092\pi$
$242$	15.3164	−	1.47579i	0.984575	−	0.0948675i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	2.99174	+	2.01740i	0.191527	+	0.129151i
$245$	24.2427	−	2.90300i	1.54881	−	0.185466i
$246$	10.4229	+	8.59084i	0.664539	+	0.547732i
$247$	−6.72828			−0.428110
$248$	−1.23241	−	4.15761i	−0.0782580	−	0.264008i
$249$		−	13.7307i		−	0.870148i
$250$	−6.79560	+	8.24480i	−0.429791	+	0.521447i
$251$	−0.848419	−	0.848419i	−0.0535518	−	0.0535518i	0.679824	−	0.733376i	$-0.262056\pi$
$251$	−0.848419	−	0.848419i	−0.0535518	−	0.0535518i	−0.733376	+	0.679824i	$0.762056\pi$
$252$	0.743604	−	5.23899i	0.0468427	−	0.330026i
$253$	−1.61713	+	1.61713i	−0.101668	+	0.101668i
$254$	−3.57646	+	0.344605i	−0.224407	+	0.0216224i
$255$	18.1086			1.13400
$256$	11.5037	−	11.1204i	0.718984	−	0.695027i
$257$			20.1074i			1.25426i	0.778913	+	0.627132i	$0.215772\pi$
$257$			20.1074i			1.25426i	−0.778913	+	0.627132i	$0.784228\pi$
$258$	13.5454	−	1.30515i	0.843297	−	0.0812548i
$259$	3.93813	+	8.10513i	0.244703	+	0.503628i
$260$	22.7658	−	4.42826i	1.41188	−	0.274629i
$261$	5.09187	+	5.09187i	0.315179	+	0.315179i
$262$	−2.10598	−	1.73581i	−0.130108	−	0.107239i
$263$	−6.57887			−0.405671			−0.202835	−	0.979213i	$-0.565016\pi$
$263$	−6.57887			−0.405671			−0.202835	+	0.979213i	$0.565016\pi$
$264$	−0.937501	+	0.277897i	−0.0576992	+	0.0171033i
$265$	27.1163			1.66574
$266$	3.94723	+	6.46206i	0.242020	+	0.396214i
$267$	−8.17146	+	8.17146i	−0.500085	+	0.500085i
$268$	−8.99979	−	6.06876i	−0.549750	−	0.370708i
$269$	18.5658	+	18.5658i	1.13198	+	1.13198i	0.989848	+	0.142129i	$0.0453949\pi$
$269$	18.5658	+	18.5658i	1.13198	+	1.13198i	0.142129	+	0.989848i	$0.454605\pi$
$270$	−0.473098	−	4.91001i	−0.0287918	−	0.298814i
$271$	22.1109			1.34314			0.671569	−	0.740942i	$-0.265621\pi$
$271$	22.1109			1.34314			0.671569	+	0.740942i	$0.265621\pi$
$272$	−7.78433	−	19.2527i	−0.471995	−	1.16737i
$273$	−8.31262	−	2.87619i	−0.503103	−	0.174075i
$274$	12.4123	−	1.19597i	0.749854	−	0.0722513i
$275$	−1.75177	−	1.75177i	−0.105636	−	0.105636i
$276$	−7.39699	+	10.9695i	−0.445247	+	0.660288i
$277$	−14.1965	−	14.1965i	−0.852983	−	0.852983i	0.137516	−	0.990499i	$-0.456088\pi$
$277$	−14.1965	−	14.1965i	−0.852983	−	0.852983i	−0.990499	+	0.137516i	$0.956088\pi$
$278$	−0.520802	+	0.631866i	−0.0312356	+	0.0378968i
$279$			1.53315i			0.0917876i
$280$	−17.6089	−	19.2671i	−1.05233	−	1.15143i
$281$		−	0.533748i		−	0.0318407i	−0.999873	−	0.0159204i	$-0.994932\pi$
$281$		−	0.533748i		−	0.0318407i	0.999873	−	0.0159204i	$-0.00506782\pi$
$282$	7.85782	+	6.47664i	0.467927	+	0.385678i
$283$	−19.5036	−	19.5036i	−1.15937	−	1.15937i	−0.984612	−	0.174754i	$-0.944087\pi$
$283$	−19.5036	−	19.5036i	−1.15937	−	1.15937i	−0.174754	−	0.984612i	$-0.555913\pi$
$284$	−31.5748	+	6.14172i	−1.87362	+	0.364444i
$285$	4.99137	+	4.99137i	0.295663	+	0.295663i
$286$	0.155896	+	1.61795i	0.00921832	+	0.0956716i
$287$	−23.8802	−	8.26262i	−1.40961	−	0.487727i
$288$	−5.01685	+	2.61365i	−0.295621	+	0.154011i
$289$	−9.95388			−0.585522
$290$	35.3570	−	3.40678i	2.07623	−	0.200053i
$291$	11.8200	+	11.8200i	0.692899	+	0.692899i
$292$	−13.1219	+	2.55238i	−0.767901	+	0.149367i
$293$	13.2601	−	13.2601i	0.774661	−	0.774661i	−0.204256	−	0.978917i	$-0.565478\pi$
$293$	13.2601	−	13.2601i	0.774661	−	0.774661i	0.978917	+	0.204256i	$0.0654775\pi$
$294$	2.11433	+	9.67107i	0.123310	+	0.564028i
$295$	−17.0497			−0.992671
$296$	4.59503	−	8.46687i	0.267081	−	0.492127i
$297$	0.345712			0.0200602
$298$	10.9294	−	13.2601i	0.633123	−	0.768139i
$299$	15.5516	+	15.5516i	0.899371	+	0.899371i
$300$	−11.8828	−	8.01285i	−0.686055	−	0.462622i
$301$	−22.8985	+	11.1260i	−1.31985	+	0.641291i
$302$	2.14597	+	22.2718i	0.123487	+	1.28160i
$303$		−	14.8772i		−	0.854674i
$304$	3.16109	−	7.45236i	0.181301	−	0.427422i
$305$	−6.29298			−0.360335
$306$	0.704186	+	7.30834i	0.0402556	+	0.417790i
$307$	8.75073	−	8.75073i	0.499430	−	0.499430i	−0.411830	−	0.911261i	$-0.635110\pi$
$307$	8.75073	−	8.75073i	0.499430	−	0.499430i	0.911261	+	0.411830i	$0.135110\pi$
$308$	1.46248	−	1.09892i	0.0833324	−	0.0626169i
$309$	3.81655	+	3.81655i	0.217116	+	0.217116i
$310$	5.83585	+	4.81008i	0.331454	+	0.273194i
$311$			12.5063i			0.709170i	0.935024	+	0.354585i	$0.115378\pi$
$311$			12.5063i			0.709170i	−0.935024	+	0.354585i	$0.884622\pi$
$312$	2.67246	+	9.01572i	0.151298	+	0.510415i
$313$	−30.6740			−1.73380			−0.866899	−	0.498484i	$-0.833890\pi$
$313$	−30.6740			−1.73380			−0.866899	+	0.498484i	$0.833890\pi$
$314$	−16.9906	+	20.6140i	−0.958837	+	1.16331i
$315$	4.03302	+	8.30041i	0.227235	+	0.467675i
$316$	1.56462	+	8.04379i	0.0880170	+	0.452498i
$317$	−6.56844	+	6.56844i	−0.368920	+	0.368920i	−0.867083	−	0.498163i	$-0.834008\pi$
$317$	−6.56844	+	6.56844i	−0.368920	+	0.368920i	0.498163	+	0.867083i	$0.334008\pi$
$318$	1.05447	+	10.9437i	0.0591316	+	0.613693i
$319$			2.48947i			0.139384i
$320$	−5.79104	+	27.2963i	−0.323729	+	1.52591i
$321$		−	7.97542i		−	0.445145i
$322$	5.81270	−	24.0598i	0.323929	−	1.34080i
$323$	−7.42944	−	7.42944i	−0.413385	−	0.413385i
$324$	1.96321	−	0.381870i	0.109067	−	0.0212150i
$325$	−16.8464	+	16.8464i	−0.934468	+	0.934468i
$326$	14.2562	−	17.2964i	0.789577	−	0.957959i
$327$			2.40871i			0.133202i
$328$	7.67737	+	25.9001i	0.423912	+	1.43009i
$329$	−18.0033	−	6.22920i	−0.992556	−	0.343427i
$330$	1.08463	−	1.31593i	0.0597068	−	0.0724396i
$331$	2.86508	−	2.86508i	0.157479	−	0.157479i	−0.623969	−	0.781449i	$-0.714481\pi$
$331$	2.86508	−	2.86508i	0.157479	−	0.157479i	0.781449	+	0.623969i	$0.214481\pi$
$332$	15.3533	−	22.7685i	0.842622	−	1.24958i
$333$	−2.40835	+	2.40835i	−0.131977	+	0.131977i
$334$	−21.9746	+	2.11733i	−1.20239	+	0.115855i
$335$	18.9306			1.03429
$336$	7.09116	−	7.85592i	0.386855	−	0.428575i
$337$	23.4976			1.28000			0.639999	−	0.768376i	$-0.278935\pi$
$337$	23.4976			1.28000			0.639999	+	0.768376i	$0.278935\pi$
$338$	−2.74055	+	0.264062i	−0.149066	+	0.0143631i
$339$	−4.15793	+	4.15793i	−0.225828	+	0.225828i
$340$	30.0280	+	20.2485i	1.62850	+	1.09813i
$341$	−0.374788	+	0.374788i	−0.0202959	+	0.0202959i
$342$	−1.82034	+	2.20854i	−0.0984327	+	0.119424i
$343$	−10.0170	−	15.5775i	−0.540868	−	0.841107i
$344$	23.9205	+	12.9818i	1.28971	+	0.699934i
$345$		−	23.0739i		−	1.24225i
$346$	−8.42985	+	10.2276i	−0.453191	+	0.549837i
$347$	7.30416	−	7.30416i	0.392108	−	0.392108i	−0.483330	−	0.875438i	$-0.660573\pi$
$347$	7.30416	−	7.30416i	0.392108	−	0.392108i	0.875438	+	0.483330i	$0.160573\pi$
$348$	2.74984	+	14.1370i	0.147407	+	0.757825i
$349$	10.4160	+	10.4160i	0.557555	+	0.557555i	0.928611	−	0.371055i	$-0.121004\pi$
$349$	10.4160	+	10.4160i	0.557555	+	0.557555i	−0.371055	+	0.928611i	$0.621004\pi$
$350$	26.0629	+	6.29666i	1.39312	+	0.336571i
$351$		−	3.32463i		−	0.177456i
$352$	−1.86532	−	0.587476i	−0.0994218	−	0.0313126i
$353$			0.352884i			0.0187821i	0.999956	+	0.00939107i	$0.00298931\pi$
$353$			0.352884i			0.0187821i	−0.999956	+	0.00939107i	$0.997011\pi$
$354$	−0.663008	−	6.88098i	−0.0352385	−	0.365720i
$355$	39.6675	−	39.6675i	2.10533	−	2.10533i
$356$	−22.6872	+	4.41296i	−1.20242	+	0.233886i
$357$	−6.00297	−	12.3548i	−0.317711	−	0.653886i
$358$	−2.01571	+	2.44557i	−0.106533	+	0.129252i
$359$	2.93757			0.155039			0.0775194	−	0.996991i	$-0.475300\pi$
$359$	2.93757			0.155039			0.0775194	+	0.996991i	$0.475300\pi$
$360$	4.70574	−	8.67088i	0.248014	−	0.456995i
$361$			14.9044i			0.784440i
$362$	−11.3882	−	9.38647i	−0.598550	−	0.493342i
$363$	−7.69366	−	7.69366i	−0.403813	−	0.403813i
$364$	−10.5681	−	14.0643i	−0.553917	−	0.737170i
$365$	16.4850	−	16.4850i	0.862867	−	0.862867i
$366$	−0.244714	−	2.53975i	−0.0127914	−	0.132755i
$367$	33.3562			1.74118			0.870589	−	0.492010i	$-0.163738\pi$
$367$	33.3562			1.74118			0.870589	+	0.492010i	$0.163738\pi$
$368$	−24.5317	+	9.91875i	−1.27880	+	0.517050i
$369$		−	9.55090i		−	0.497200i
$370$	1.61133	+	16.7231i	0.0837692	+	0.869392i
$371$	−8.98902	−	18.5004i	−0.466687	−	0.960495i
$372$	−1.71433	+	2.54231i	−0.0888840	+	0.131812i
$373$	19.0617	+	19.0617i	0.986977	+	0.986977i	0.999916	−	0.0129389i	$-0.00411870\pi$
$373$	19.0617	+	19.0617i	0.986977	+	0.986977i	−0.0129389	+	0.999916i	$0.504119\pi$
$374$	−1.61442	+	1.95871i	−0.0834797	+	0.101282i
$375$	7.55502			0.390140
$376$	5.78798	+	19.5261i	0.298492	+	1.00698i
$377$	23.9407			1.23301
$378$	−3.19308	+	1.95044i	−0.164235	+	0.100320i
$379$	−8.93678	+	8.93678i	−0.459051	+	0.459051i	−0.898344	−	0.439293i	$-0.855229\pi$
$379$	−8.93678	+	8.93678i	−0.459051	+	0.459051i	0.439293	+	0.898344i	$0.355229\pi$
$380$	2.69557	+	13.8580i	0.138280	+	0.710900i
$381$	1.79651	+	1.79651i	0.0920381	+	0.0920381i
$382$	−35.1420	+	3.38606i	−1.79802	+	0.173246i
$383$	−30.1669			−1.54145			−0.770727	−	0.637165i	$-0.780107\pi$
$383$	−30.1669			−1.54145			−0.770727	+	0.637165i	$0.780107\pi$
$384$	−11.2416	−	1.27571i	−0.573668	−	0.0651006i
$385$	−1.04319	+	3.01497i	−0.0531658	+	0.153657i
$386$	1.33481	+	13.8532i	0.0679400	+	0.705111i
$387$	−6.80405	−	6.80405i	−0.345869	−	0.345869i
$388$	6.38332	+	32.8169i	0.324064	+	1.66602i
$389$	9.88128	+	9.88128i	0.501001	+	0.501001i	0.911749	−	0.410748i	$-0.134732\pi$
$389$	9.88128	+	9.88128i	0.501001	+	0.501001i	−0.410748	+	0.911749i	$0.634732\pi$
$390$	−12.6550	−	10.4306i	−0.640810	−	0.528174i
$391$			34.3445i			1.73687i
$392$	−7.30792	+	18.4009i	−0.369106	+	0.929387i
$393$			1.92979i			0.0973451i
$394$	7.89798	−	9.58227i	0.397895	−	0.482748i
$395$	−10.1054	−	10.1054i	−0.508459	−	0.508459i
$396$	0.573266	+	0.386566i	0.0288077	+	0.0194257i
$397$	5.73434	+	5.73434i	0.287798	+	0.287798i	0.836209	−	0.548411i	$-0.184767\pi$
$397$	5.73434	+	5.73434i	0.287798	+	0.287798i	−0.548411	+	0.836209i	$0.684767\pi$
$398$	14.3172	−	1.37952i	0.717657	−	0.0691490i
$399$	1.75079	−	5.06006i	0.0876492	−	0.253320i
$400$	−10.7446	−	26.5741i	−0.537228	−	1.32871i
$401$	10.0283			0.500789			0.250394	−	0.968144i	$-0.419440\pi$
$401$	10.0283			0.500789			0.250394	+	0.968144i	$0.419440\pi$
$402$	0.736152	+	7.64010i	0.0367159	+	0.381053i
$403$	3.60425	+	3.60425i	0.179540	+	0.179540i
$404$	16.6353	−	24.6697i	0.827637	−	1.22736i
$405$	−2.46638	+	2.46638i	−0.122555	+	0.122555i
$406$	−14.0451	−	22.9934i	−0.697047	−	1.14114i
$407$	−1.17747			−0.0583649
$408$	−7.00430	+	12.9062i	−0.346764	+	0.638954i
$409$	16.0808			0.795145			0.397572	−	0.917571i	$-0.369853\pi$
$409$	16.0808			0.795145			0.397572	+	0.917571i	$0.369853\pi$
$410$	−36.3548	−	29.9647i	−1.79544	−	1.47985i
$411$	−6.23489	−	6.23489i	−0.307545	−	0.307545i
$412$	2.06111	+	10.5962i	0.101544	+	0.522040i
$413$	5.65195	+	11.6324i	0.278114	+	0.572391i
$414$	9.31224	−	0.897269i	0.457672	−	0.0440984i
$415$			47.8924i			2.35095i
$416$	−5.64961	+	17.9383i	−0.276995	+	0.879498i
$417$	0.579003			0.0283539
$418$	−0.984880	+	0.0948969i	−0.0481721	+	0.00464156i
$419$	−6.59346	+	6.59346i	−0.322112	+	0.322112i	−0.849577	−	0.527465i	$-0.823143\pi$
$419$	−6.59346	+	6.59346i	−0.322112	+	0.322112i	0.527465	+	0.849577i	$0.323143\pi$
$420$	−2.59368	+	18.2735i	−0.126559	+	0.891656i
$421$	−4.63581	−	4.63581i	−0.225936	−	0.225936i	0.585057	−	0.810992i	$-0.301072\pi$
$421$	−4.63581	−	4.63581i	−0.225936	−	0.225936i	−0.810992	+	0.585057i	$0.801072\pi$
$422$	−7.24822	+	8.79395i	−0.352838	+	0.428083i
$423$		−	7.20043i		−	0.350097i
$424$	−10.4884	+	19.3262i	−0.509363	+	0.938561i
$425$	−37.2039			−1.80465
$426$	17.5517	+	14.4666i	0.850383	+	0.700910i
$427$	2.08612	+	4.29347i	0.100954	+	0.207775i
$428$	8.91791	−	13.2250i	0.431063	−	0.639254i
$429$	0.812724	−	0.812724i	0.0392387	−	0.0392387i
$430$	−47.2460	+	4.55232i	−2.27840	+	0.219533i
$431$		−	9.22678i		−	0.444438i	−0.974997	−	0.222219i	$-0.928670\pi$
$431$		−	9.22678i		−	0.444438i	0.974997	−	0.222219i	$-0.0713301\pi$
$432$	3.68242	+	1.56198i	0.177171	+	0.0751508i
$433$		−	20.5961i		−	0.989786i	−0.868954	−	0.494893i	$-0.835207\pi$
$433$		−	20.5961i		−	0.989786i	0.868954	−	0.494893i	$-0.164793\pi$
$434$	1.34716	−	5.57611i	0.0646656	−	0.267662i
$435$	−17.7604	−	17.7604i	−0.851544	−	0.851544i
$436$	−2.69335	+	3.99416i	−0.128988	+	0.191286i
$437$	−9.46655	+	9.46655i	−0.452846	+	0.452846i
$438$	7.29415	+	6.01205i	0.348528	+	0.287267i
$439$		−	30.5005i		−	1.45571i	−0.685731	−	0.727855i	$-0.740517\pi$
$439$		−	30.5005i		−	1.45571i	0.685731	−	0.727855i	$-0.259483\pi$
$440$	3.26999	−	0.969298i	0.155890	−	0.0462095i
$441$	4.32612	−	5.50315i	0.206006	−	0.262055i
$442$	18.8364	+	15.5255i	0.895956	+	0.738473i
$443$	−16.6469	+	16.6469i	−0.790916	+	0.790916i	−0.981643	−	0.190727i	$-0.938916\pi$
$443$	−16.6469	+	16.6469i	−0.790916	+	0.790916i	0.190727	+	0.981643i	$0.438916\pi$
$444$	−6.68652	+	1.30062i	−0.317328	+	0.0617245i
$445$	28.5019	−	28.5019i	1.35112	−	1.35112i
$446$	−0.714200	−	7.41228i	−0.0338184	−	0.350981i
$447$	−12.1508			−0.574712
$448$	20.5430	−	5.09768i	0.970564	−	0.240843i
$449$	10.8337			0.511272			0.255636	−	0.966773i	$-0.417715\pi$
$449$	10.8337			0.511272			0.255636	+	0.966773i	$0.417715\pi$
$450$	0.971974	+	10.0876i	0.0458193	+	0.475532i
$451$	2.33477	−	2.33477i	0.109940	−	0.109940i
$452$	−11.5441	+	2.24547i	−0.542987	+	0.105618i
$453$	11.1875	−	11.1875i	0.525633	−	0.525633i
$454$	−17.5581	−	14.4719i	−0.824043	−	0.679200i
$455$	28.9943	+	10.0321i	1.35927	+	0.470312i
$456$	−5.48805	+	1.62678i	−0.257001	+	0.0761810i
$457$			35.1980i			1.64650i	0.567683	+	0.823248i	$0.307840\pi$
$457$			35.1980i			1.64650i	−0.567683	+	0.823248i	$0.692160\pi$
$458$	22.9590	+	18.9235i	1.07280	+	0.884235i
$459$	3.67109	−	3.67109i	0.171352	−	0.171352i
$460$	25.8006	−	38.2615i	1.20296	−	1.78395i
$461$	−27.0443	−	27.0443i	−1.25958	−	1.25958i	−0.951294	−	0.308286i	$-0.900245\pi$
$461$	−27.0443	−	27.0443i	−1.25958	−	1.25958i	−0.308286	−	0.951294i	$-0.599755\pi$
$462$	−1.25736	−	0.303771i	−0.0584978	−	0.0141327i
$463$		−	18.6030i		−	0.864556i	−0.901740	−	0.432278i	$-0.857710\pi$
$463$		−	18.6030i		−	0.864556i	0.901740	−	0.432278i	$-0.142290\pi$
$464$	−11.2478	+	26.5171i	−0.522167	+	1.23103i
$465$		−	5.34762i		−	0.247990i
$466$	−2.99188	+	0.288279i	−0.138596	+	0.0133542i
$467$	10.0714	−	10.0714i	0.466047	−	0.466047i	−0.434584	−	0.900631i	$-0.643105\pi$
$467$	10.0714	−	10.0714i	0.466047	−	0.466047i	0.900631	+	0.434584i	$0.143105\pi$
$468$	3.71751	−	5.51296i	0.171842	−	0.254837i
$469$	−6.27547	−	12.9156i	−0.289774	−	0.596389i
$470$	−27.4079	−	22.5904i	−1.26423	−	1.04202i
$471$	18.8894			0.870377
$472$	6.59472	−	12.1515i	0.303547	−	0.559320i
$473$		−	3.32657i		−	0.152956i
$474$	3.68542	−	4.47135i	0.169277	−	0.205376i
$475$	−10.2547	−	10.2547i	−0.470518	−	0.470518i
$476$	3.86058	−	27.1993i	0.176949	−	1.24668i
$477$	5.49720	−	5.49720i	0.251700	−	0.251700i
$478$	12.5898	−	1.21307i	0.575843	−	0.0554847i
$479$	8.19876			0.374611			0.187305	−	0.982302i	$-0.440025\pi$
$479$	8.19876			0.374611			0.187305	+	0.982302i	$0.440025\pi$
$480$	17.4987	−	9.11637i	0.798702	−	0.416103i
$481$			11.3234i			0.516303i
$482$	−5.86036	+	0.564667i	−0.266932	+	0.0257199i
$483$	−15.7424	+	7.64895i	−0.716305	+	0.348039i
$484$	−4.15493	−	21.3606i	−0.188860	−	0.970937i
$485$	−41.2279	−	41.2279i	−1.87206	−	1.87206i
$486$	−1.09130	−	0.899481i	−0.0495024	−	0.0408013i
$487$	18.4865			0.837705			0.418852	−	0.908054i	$-0.362432\pi$
$487$	18.4865			0.837705			0.418852	+	0.908054i	$0.362432\pi$
$488$	2.43409	−	4.48509i	0.110186	−	0.203031i
$489$	−15.8494			−0.716733
$490$	−7.37473	−	33.7325i	−0.333156	−	1.52388i
$491$	−7.92543	+	7.92543i	−0.357670	+	0.357670i	−0.862953	−	0.505284i	$-0.831388\pi$
$491$	−7.92543	+	7.92543i	−0.357670	+	0.357670i	0.505284	+	0.862953i	$0.331388\pi$
$492$	10.6796	−	15.8375i	0.481472	−	0.714008i
$493$	26.4355	+	26.4355i	1.19060	+	1.19060i
$494$	0.912601	+	9.47136i	0.0410598	+	0.426137i
$495$	−1.20584			−0.0541984
$496$	−5.68548	+	2.29878i	−0.255285	+	0.103218i
$497$	−40.2133	−	13.9139i	−1.80381	−	0.624124i
$498$	−19.3286	+	1.86239i	−0.866137	+	0.0834555i
$499$	−2.98057	−	2.98057i	−0.133429	−	0.133429i	0.637238	−	0.770667i	$-0.280077\pi$
$499$	−2.98057	−	2.98057i	−0.133429	−	0.133429i	−0.770667	+	0.637238i	$0.780077\pi$
$500$	12.5279	+	8.44783i	0.560264	+	0.377798i
$501$	11.0382	+	11.0382i	0.493149	+	0.493149i
$502$	−1.07924	+	1.30939i	−0.0481688	+	0.0584410i
$503$		−	4.63846i		−	0.206819i	−0.994639	−	0.103409i	$-0.967025\pi$
$503$		−	4.63846i		−	0.206819i	0.994639	−	0.103409i	$-0.0329751\pi$
$504$	−7.47576	−	0.336168i	−0.332997	−	0.0149741i
$505$			51.8914i			2.30914i
$506$	2.49577	+	2.05709i	0.110950	+	0.0914486i
$507$	1.37662	+	1.37662i	0.0611378	+	0.0611378i
$508$	0.970197	+	4.98782i	0.0430455	+	0.221299i
$509$	6.96054	+	6.96054i	0.308520	+	0.308520i	0.844335	−	0.535815i	$-0.179996\pi$
$509$	6.96054	+	6.96054i	0.308520	+	0.308520i	−0.535815	+	0.844335i	$0.679996\pi$
$510$	−2.45619	−	25.4914i	−0.108762	−	1.12878i
$511$	−16.7119	−	5.78236i	−0.739291	−	0.255796i
$512$	−17.2145	−	14.6854i	−0.760780	−	0.649009i
$513$	2.02377			0.0893515
$514$	28.3051	−	2.72730i	1.24848	−	0.120296i
$515$	−13.3121	−	13.3121i	−0.586600	−	0.586600i
$516$	−3.67449	−	18.8907i	−0.161760	−	0.831616i
$517$	1.76018	−	1.76018i	0.0774127	−	0.0774127i
$518$	10.8754	−	6.64303i	0.477837	−	0.291878i
$519$	9.37191			0.411381
$520$	−9.32151	−	31.4467i	−0.408775	−	1.37903i
$521$	−11.4231			−0.500457			−0.250229	−	0.968187i	$-0.580506\pi$
$521$	−11.4231			−0.500457			−0.250229	+	0.968187i	$0.580506\pi$
$522$	6.47716	−	7.85844i	0.283497	−	0.343955i
$523$	−6.27518	−	6.27518i	−0.274394	−	0.274394i	0.556472	−	0.830866i	$-0.312155\pi$
$523$	−6.27518	−	6.27518i	−0.274394	−	0.274394i	−0.830866	+	0.556472i	$0.812155\pi$
$524$	−2.15784	+	3.20002i	−0.0942658	+	0.139793i
$525$	−8.28579	−	17.0531i	−0.361621	−	0.744258i
$526$	0.892335	+	9.26104i	0.0389077	+	0.403800i
$527$			7.95970i			0.346730i
$528$	0.518353	+	1.28202i	0.0225584	+	0.0557928i
$529$	20.7615			0.902673
$530$	−3.67796	−	38.1715i	−0.159761	−	1.65806i
$531$	−3.45643	+	3.45643i	−0.149996	+	0.149996i
$532$	8.56121	−	6.43299i	0.371176	−	0.278906i
$533$	−22.4529	−	22.4529i	−0.972543	−	0.972543i
$534$	12.6113	+	10.3946i	0.545743	+	0.449817i
$535$			27.8181i			1.20268i
$536$	−7.32225	+	13.4921i	−0.316273	+	0.582770i
$537$	2.24097			0.0967049
$538$	23.6168	−	28.6532i	1.01819	−	1.23533i
$539$	2.40282	−	0.287732i	0.103497	−	0.0123935i
$540$	−6.84762	+	1.33195i	−0.294675	+	0.0573182i
$541$	−28.9885	+	28.9885i	−1.24631	+	1.24631i	−0.288978	+	0.957336i	$0.593315\pi$
$541$	−28.9885	+	28.9885i	−1.24631	+	1.24631i	−0.957336	+	0.288978i	$0.906685\pi$
$542$	−2.99904	−	31.1253i	−0.128820	−	1.33695i
$543$			10.4354i			0.447828i
$544$	−26.0461	+	13.5693i	−1.11672	+	0.581780i
$545$		−	8.40153i		−	0.359882i
$546$	−2.92130	+	12.0917i	−0.125020	+	0.517479i
$547$	1.24129	+	1.24129i	0.0530738	+	0.0530738i	0.733146	−	0.680072i	$-0.238051\pi$
$547$	1.24129	+	1.24129i	0.0530738	+	0.0530738i	−0.680072	+	0.733146i	$0.738051\pi$
$548$	−3.36712	−	17.3105i	−0.143836	−	0.739468i
$549$	−1.27576	+	1.27576i	−0.0544479	+	0.0544479i
$550$	−2.22835	+	2.70356i	−0.0950173	+	0.115280i
$551$			14.5731i			0.620837i
$552$	16.4450	+	8.92483i	0.699947	+	0.379866i
$553$	−3.54461	+	10.2445i	−0.150732	+	0.435639i
$554$	−18.0587	+	21.9098i	−0.767242	+	0.930860i
$555$	8.40027	−	8.40027i	0.356572	−	0.356572i
$556$	0.960114	+	0.647426i	0.0407179	+	0.0274570i
$557$	−18.6847	+	18.6847i	−0.791695	+	0.791695i	−0.981770	−	0.190075i	$-0.939127\pi$
$557$	−18.6847	+	18.6847i	−0.791695	+	0.791695i	0.190075	+	0.981770i	$0.439127\pi$
$558$	2.15821	−	0.207952i	0.0913644	−	0.00880330i
$559$	−31.9908			−1.35307
$560$	−24.7338	+	27.4013i	−1.04520	+	1.15792i
$561$	1.79484			0.0757781
$562$	−0.751354	+	0.0723957i	−0.0316939	+	0.00305383i
$563$	0.450781	−	0.450781i	0.0189981	−	0.0189981i	−0.697544	−	0.716542i	$-0.745724\pi$
$563$	0.450781	−	0.450781i	0.0189981	−	0.0189981i	0.716542	+	0.697544i	$0.245724\pi$
$564$	8.05132	−	11.9399i	0.339022	−	0.502760i
$565$	14.5028	−	14.5028i	0.610137	−	0.610137i
$566$	−24.8097	+	30.1004i	−1.04283	+	1.26522i
$567$	2.50032	+	0.865115i	0.105003	+	0.0363314i
$568$	12.9284	+	43.6146i	0.542462	+	1.83003i
$569$		−	19.8762i		−	0.833254i	−0.909077	−	0.416627i	$-0.863212\pi$
$569$		−	19.8762i		−	0.833254i	0.909077	−	0.416627i	$-0.136788\pi$
$570$	6.34931	−	7.70333i	0.265943	−	0.322657i
$571$	0.229081	−	0.229081i	0.00958675	−	0.00958675i	−0.702297	−	0.711884i	$-0.747842\pi$
$571$	0.229081	−	0.229081i	0.00958675	−	0.00958675i	0.711884	+	0.702297i	$0.247842\pi$
$572$	2.25644	−	0.438907i	0.0943465	−	0.0183516i
$573$	17.6524	+	17.6524i	0.737439	+	0.737439i
$574$	−8.39221	+	34.7368i	−0.350284	+	1.44989i
$575$			47.4050i			1.97692i
$576$	4.35969	+	6.70769i	0.181654	+	0.279487i
$577$		−	44.9253i		−	1.87026i	−0.354300	−	0.935132i	$-0.615281\pi$
$577$		−	44.9253i		−	1.87026i	0.354300	−	0.935132i	$-0.384719\pi$
$578$	1.35011	+	14.0120i	0.0561572	+	0.582823i
$579$	6.95869	−	6.95869i	0.289193	−	0.289193i
$580$	−9.59140	−	49.3097i	−0.398261	−	2.04747i
$581$	32.6752	−	15.8763i	1.35560	−	0.658659i
$582$	15.0357	−	18.2421i	0.623249	−	0.756161i
$583$	2.68764			0.111311
$584$	5.37279	+	18.1254i	0.222327	+	0.750035i
$585$			11.5962i			0.479446i
$586$	−20.4647	−	16.8676i	−0.845388	−	0.696793i
$587$	22.6986	+	22.6986i	0.936871	+	0.936871i	0.998122	−	0.0612514i	$-0.0195092\pi$
$587$	22.6986	+	22.6986i	0.936871	+	0.936871i	−0.0612514	+	0.998122i	$0.519509\pi$
$588$	13.3271	−	4.28808i	0.549602	−	0.176837i
$589$	−2.19397	+	2.19397i	−0.0904011	+	0.0904011i
$590$	2.31256	+	24.0007i	0.0952066	+	0.988095i
$591$	−8.78060			−0.361186
$592$	−12.5420	−	5.31998i	−0.515474	−	0.218650i
$593$			17.6514i			0.724855i	0.932012	+	0.362427i	$0.118052\pi$
$593$			17.6514i			0.724855i	−0.932012	+	0.362427i	$0.881948\pi$
$594$	−0.0468912	−	0.486657i	−0.00192397	−	0.0199678i
$595$	20.9383	+	43.0934i	0.858385	+	1.76666i
$596$	−20.1486	−	13.5867i	−0.825321	−	0.556532i
$597$	−7.19176	−	7.19176i	−0.294339	−	0.294339i
$598$	19.7825	−	24.0012i	0.808966	−	0.981483i
$599$	13.0847			0.534627			0.267314	−	0.963610i	$-0.413864\pi$
$599$	13.0847			0.534627			0.267314	+	0.963610i	$0.413864\pi$
$600$	−9.66789	+	17.8142i	−0.394690	+	0.727262i
$601$	−42.5370			−1.73512			−0.867560	−	0.497333i	$-0.834313\pi$
$601$	−42.5370			−1.73512			−0.867560	+	0.497333i	$0.834313\pi$
$602$	18.7679	+	30.7251i	0.764920	+	1.25226i
$603$	3.83774	−	3.83774i	0.156285	−	0.156285i
$604$	31.0608	−	6.04174i	1.26385	−	0.245835i
$605$	26.8354	+	26.8354i	1.09101	+	1.09101i
$606$	−20.9426	+	2.01789i	−0.850734	+	0.0819713i
$607$	−29.5855			−1.20084			−0.600419	−	0.799686i	$-0.704999\pi$
$607$	−29.5855			−1.20084			−0.600419	+	0.799686i	$0.704999\pi$
$608$	−10.9194	−	3.43903i	−0.442840	−	0.139471i
$609$	−6.22969	+	18.0048i	−0.252440	+	0.729590i
$610$	0.853559	+	8.85860i	0.0345596	+	0.358674i
$611$	−16.9273	−	16.9273i	−0.684804	−	0.684804i
$612$	10.1924	−	1.98256i	0.412003	−	0.0801401i
$613$	−20.2489	−	20.2489i	−0.817847	−	0.817847i	0.167949	−	0.985796i	$-0.446286\pi$
$613$	−20.2489	−	20.2489i	−0.817847	−	0.817847i	−0.985796	+	0.167949i	$0.946286\pi$
$614$	−13.5053	−	11.1314i	−0.545028	−	0.449228i
$615$			33.3133i			1.34332i
$616$	−1.74531	−	1.90967i	−0.0703206	−	0.0769427i
$617$		−	32.9416i		−	1.32618i	−0.748541	−	0.663089i	$-0.769245\pi$
$617$		−	32.9416i		−	1.32618i	0.748541	−	0.663089i	$-0.230755\pi$
$618$	4.85488	−	5.89021i	0.195292	−	0.236939i
$619$	20.5109	+	20.5109i	0.824404	+	0.824404i	0.986736	−	0.162333i	$-0.0519017\pi$
$619$	20.5109	+	20.5109i	0.824404	+	0.824404i	−0.162333	+	0.986736i	$0.551902\pi$
$620$	5.97956	−	8.86752i	0.240145	−	0.356128i
$621$	−4.67768	−	4.67768i	−0.187709	−	0.187709i
$622$	17.6051	−	1.69632i	0.705901	−	0.0680161i
$623$	−28.8941	−	9.99743i	−1.15762	−	0.400539i
$624$	12.3289	−	4.98487i	0.493551	−	0.199555i
$625$	9.47829			0.379132
$626$	4.16052	+	43.1796i	0.166288	+	1.72581i
$627$	0.494721	+	0.494721i	0.0197572	+	0.0197572i
$628$	31.3227	+	21.1216i	1.24991	+	0.842844i
$629$	−12.5034	+	12.5034i	−0.498545	+	0.498545i
$630$	11.1374	−	6.80309i	0.443725	−	0.271042i
$631$	−1.92496			−0.0766314			−0.0383157	−	0.999266i	$-0.512199\pi$
$631$	−1.92496			−0.0766314			−0.0383157	+	0.999266i	$0.512199\pi$
$632$	11.1110	−	3.29354i	0.441971	−	0.131010i
$633$	8.05823			0.320286
$634$	10.1373	+	8.35544i	0.402603	+	0.331837i
$635$	−6.26620	−	6.26620i	−0.248666	−	0.248666i
$636$	15.2624	−	2.96874i	0.605193	−	0.117718i
$637$	−2.76705	−	23.1073i	−0.109634	−	0.915546i
$638$	3.50441	−	0.337663i	0.138741	−	0.0133682i
$639$		−	16.0833i		−	0.636246i
$640$	39.2103	+	4.44964i	1.54992	+	0.175887i
$641$	0.665171			0.0262727			0.0131363	−	0.999914i	$-0.495818\pi$
$641$	0.665171			0.0262727			0.0131363	+	0.999914i	$0.495818\pi$
$642$	−11.2270	+	1.08176i	−0.443093	+	0.0426936i
$643$	−10.5926	+	10.5926i	−0.417733	+	0.417733i	−0.884422	−	0.466689i	$-0.845447\pi$
$643$	−10.5926	+	10.5926i	−0.417733	+	0.417733i	0.466689	+	0.884422i	$0.345447\pi$
$644$	−34.6572	−	4.91912i	−1.36569	−	0.193841i
$645$	23.7324	+	23.7324i	0.934462	+	0.934462i
$646$	−9.45068	+	11.4661i	−0.371832	+	0.451127i
$647$			40.4129i			1.58880i	0.607397	+	0.794398i	$0.292214\pi$
$647$			40.4129i			1.58880i	−0.607397	+	0.794398i	$0.707786\pi$
$648$	−0.803838	−	2.71180i	−0.0315777	−	0.106529i
$649$	−1.68988			−0.0663337
$650$	25.9995	+	21.4295i	1.01978	+	0.840536i
$651$	−3.64848	+	1.77273i	−0.142995	+	0.0694787i
$652$	−26.2817	−	17.7223i	−1.02927	−	0.694060i
$653$	6.72324	−	6.72324i	0.263101	−	0.263101i	−0.563212	−	0.826313i	$-0.690435\pi$
$653$	6.72324	−	6.72324i	0.263101	−	0.263101i	0.826313	+	0.563212i	$0.190435\pi$
$654$	3.39072	−	0.326709i	0.132588	−	0.0127753i
$655$		−	6.73108i		−	0.263005i
$656$	35.4181	−	14.3204i	1.38284	−	0.559117i
$657$		−	6.68392i		−	0.260764i
$658$	−6.32689	+	26.1881i	−0.246648	+	1.02092i
$659$	33.6058	+	33.6058i	1.30910	+	1.30910i	0.922067	+	0.387029i	$0.126499\pi$
$659$	33.6058	+	33.6058i	1.30910	+	1.30910i	0.387029	+	0.922067i	$0.373501\pi$
$660$	−1.99954	−	1.34834i	−0.0778321	−	0.0524839i
$661$	−8.66416	+	8.66416i	−0.336997	+	0.336997i	−0.855236	−	0.518239i	$-0.826588\pi$
$661$	−8.66416	+	8.66416i	−0.336997	+	0.336997i	0.518239	+	0.855236i	$0.326588\pi$
$662$	−4.42177	−	3.64455i	−0.171857	−	0.141650i
$663$		−	17.2605i		−	0.670343i
$664$	−34.1336	−	18.5245i	−1.32464	−	0.718891i
$665$	−6.10673	+	17.6494i	−0.236809	+	0.684414i
$666$	3.71688	+	3.06356i	0.144026	+	0.118710i
$667$	33.6840	−	33.6840i	1.30425	−	1.30425i
$668$	5.96111	+	30.6463i	0.230642	+	1.18574i
$669$	−3.72330	+	3.72330i	−0.143951	+	0.143951i
$670$	−2.56768	−	26.6485i	−0.0991983	−	1.02952i
$671$	−0.623731			−0.0240789
$672$	−12.0205	−	8.91664i	−0.463703	−	0.343967i
$673$	5.60669			0.216122			0.108061	−	0.994144i	$-0.465536\pi$
$673$	5.60669			0.216122			0.108061	+	0.994144i	$0.465536\pi$
$674$	−3.18714	−	33.0775i	−0.122764	−	1.27410i
$675$	5.06714	−	5.06714i	0.195034	−	0.195034i
$676$	0.743437	+	3.82203i	0.0285937	+	0.147001i
$677$	−1.76989	+	1.76989i	−0.0680223	+	0.0680223i	−0.740300	−	0.672277i	$-0.765316\pi$
$677$	−1.76989	+	1.76989i	−0.0680223	+	0.0680223i	0.672277	+	0.740300i	$0.265316\pi$
$678$	6.41707	+	5.28913i	0.246446	+	0.203128i
$679$	−14.4612	+	41.7952i	−0.554971	+	1.60395i
$680$	24.4309	−	45.0167i	0.936881	−	1.72631i
$681$			16.0892i			0.616538i
$682$	0.578422	+	0.476752i	0.0221489	+	0.0182558i
$683$	−28.4450	+	28.4450i	−1.08842	+	1.08842i	−0.0927272	+	0.995692i	$0.529558\pi$
$683$	−28.4450	+	28.4450i	−1.08842	+	1.08842i	−0.995692	+	0.0927272i	$0.970442\pi$
$684$	3.35585	+	2.26292i	0.128314	+	0.0865250i
$685$	21.7472	+	21.7472i	0.830917	+	0.830917i
$686$	−20.5697	+	16.2138i	−0.785355	+	0.619045i
$687$		−	21.0382i		−	0.802658i
$688$	15.0300	−	35.4336i	0.573012	−	1.35089i
$689$		−	25.8464i		−	0.984669i
$690$	−32.4809	+	3.12966i	−1.23653	+	0.119144i
$691$	−10.4240	+	10.4240i	−0.396547	+	0.396547i	−0.877013	−	0.480466i	$-0.840467\pi$
$691$	−10.4240	+	10.4240i	−0.396547	+	0.396547i	0.480466	+	0.877013i	$0.340467\pi$
$692$	15.5407	+	10.4794i	0.590768	+	0.398368i
$693$	0.399733	+	0.822697i	0.0151846	+	0.0312517i
$694$	−11.2727	−	9.29132i	−0.427907	−	0.352694i
$695$	−2.01955			−0.0766060
$696$	19.5276	−	5.78843i	0.740193	−	0.219410i
$697$		−	49.5855i		−	1.87818i
$698$	13.2497	−	16.0753i	0.501510	−	0.608460i
$699$	1.50287	+	1.50287i	0.0568437	+	0.0568437i
$700$	5.32868	−	37.5427i	0.201405	−	1.41898i
$701$	37.1588	−	37.1588i	1.40347	−	1.40347i	0.614732	−	0.788736i	$-0.289264\pi$
$701$	37.1588	−	37.1588i	1.40347	−	1.40347i	0.788736	−	0.614732i	$-0.210736\pi$
$702$	−4.68006	+	0.450941i	−0.176638	+	0.0170197i
$703$	−6.89278			−0.259966
$704$	−0.573981	+	2.70548i	−0.0216327	+	0.101967i
$705$			25.1150i			0.945884i
$706$	0.496753	−	0.0478640i	0.0186956	−	0.00180139i
$707$	35.4036	−	17.2019i	1.33149	−	0.646946i
$708$	−9.59639	+	1.86663i	−0.360655	+	0.0701521i
$709$	−2.24522	−	2.24522i	−0.0843210	−	0.0843210i	0.663688	−	0.748009i	$-0.268990\pi$
$709$	−2.24522	−	2.24522i	−0.0843210	−	0.0843210i	−0.748009	+	0.663688i	$0.768990\pi$
$710$	−61.2200	−	50.4593i	−2.29755	−	1.89370i
$711$	−4.09727			−0.153660
$712$	9.28930	+	31.3380i	0.348131	+	1.17444i
$713$	10.1422			0.379828
$714$	−16.5776	+	10.1261i	−0.620400	+	0.378960i
$715$	−2.83477	+	2.83477i	−0.106014	+	0.106014i
$716$	3.71601	+	2.50579i	0.138874	+	0.0936457i
$717$	−6.32405	−	6.32405i	−0.236176	−	0.236176i
$718$	−0.398441	−	4.13519i	−0.0148697	−	0.154324i
$719$	19.0248			0.709506			0.354753	−	0.934960i	$-0.384565\pi$
$719$	19.0248			0.709506			0.354753	+	0.934960i	$0.384565\pi$
$720$	−12.8442	−	5.44816i	−0.478676	−	0.203041i
$721$	−4.66939	+	13.4953i	−0.173897	+	0.502590i
$722$	20.9808	−	2.02158i	0.780824	−	0.0752353i
$723$	2.94375	+	2.94375i	0.109479	+	0.109479i
$724$	−11.6686	+	17.3042i	−0.433661	+	0.643107i
$725$	36.4884	+	36.4884i	1.35515	+	1.35515i
$726$	−9.78678	+	11.8739i	−0.363222	+	0.440681i
$727$			40.7707i			1.51210i	0.654513	+	0.756050i	$0.272874\pi$
$727$			40.7707i			1.51210i	−0.654513	+	0.756050i	$0.727126\pi$
$728$	−18.3648	+	16.7842i	−0.680645	+	0.622065i
$729$			1.00000i			0.0370370i
$730$	−25.4419	−	20.9699i	−0.941646	−	0.776132i
$731$	−35.3246	−	35.3246i	−1.30653	−	1.30653i
$732$	−3.54200	+	0.688966i	−0.130916	+	0.0254649i
$733$	−6.53739	−	6.53739i	−0.241464	−	0.241464i	0.575992	−	0.817456i	$-0.304616\pi$
$733$	−6.53739	−	6.53739i	−0.241464	−	0.241464i	−0.817456	+	0.575992i	$0.804616\pi$
$734$	−4.52432	−	46.9553i	−0.166996	−	1.73315i
$735$	−15.0894	+	19.1949i	−0.556582	+	0.708014i
$736$	17.2899	+	33.1877i	0.637316	+	1.22332i
$737$	1.87631			0.0691149
$738$	−13.4447	+	1.29545i	−0.494908	+	0.0476862i
$739$	−25.7167	−	25.7167i	−0.946003	−	0.946003i	0.0526125	−	0.998615i	$-0.483245\pi$
$739$	−25.7167	−	25.7167i	−0.946003	−	0.946003i	−0.998615	+	0.0526125i	$0.983245\pi$
$740$	23.3224	−	4.53653i	0.857350	−	0.166766i
$741$	4.75761	−	4.75761i	0.174775	−	0.174775i
$742$	−24.8237	+	15.1631i	−0.911308	+	0.556656i
$743$	9.46009			0.347057			0.173529	−	0.984829i	$-0.444483\pi$
$743$	9.46009			0.347057			0.173529	+	0.984829i	$0.444483\pi$
$744$	3.81131	+	2.06843i	0.139730	+	0.0758322i
$745$	42.3817			1.55275
$746$	24.2476	−	29.4185i	0.887767	−	1.07709i
$747$	9.70907	+	9.70907i	0.355236	+	0.355236i
$748$	2.97623	+	2.00694i	0.108822	+	0.0733810i
$749$	18.9793	−	9.22167i	0.693487	−	0.336953i
$750$	−1.02474	−	10.6352i	−0.0374181	−	0.388341i
$751$			26.5634i			0.969313i	0.874705	+	0.484656i	$0.161055\pi$
$751$			26.5634i			0.969313i	−0.874705	+	0.484656i	$0.838945\pi$
$752$	26.7017	−	10.7962i	0.973711	−	0.393695i
$753$	1.19985			0.0437248
$754$	−3.24723	−	33.7011i	−0.118257	−	1.22732i
$755$	−39.0217	+	39.0217i	−1.42015	+	1.42015i
$756$	3.17872	+	4.23034i	0.115609	+	0.153856i
$757$	7.83618	+	7.83618i	0.284811	+	0.284811i	0.835024	−	0.550213i	$-0.185454\pi$
$757$	7.83618	+	7.83618i	0.284811	+	0.284811i	−0.550213	+	0.835024i	$0.685454\pi$
$758$	13.7924	+	11.3681i	0.500963	+	0.412908i
$759$		−	2.28697i		−	0.0830118i
$760$	19.1422	−	5.67418i	0.694361	−	0.205824i
$761$	−22.5355			−0.816910			−0.408455	−	0.912778i	$-0.633932\pi$
$761$	−22.5355			−0.816910			−0.408455	+	0.912778i	$0.633932\pi$
$762$	2.28527	−	2.77261i	0.0827864	−	0.100441i
$763$	−5.73204	+	2.78509i	−0.207514	+	0.100827i
$764$	9.53308	+	49.0099i	0.344895	+	1.77312i
$765$	−12.8047	+	12.8047i	−0.462955	+	0.462955i
$766$	4.09173	+	42.4657i	0.147840	+	1.53435i
$767$			16.2512i			0.586797i
$768$	−0.271038	+	15.9977i	−0.00978023	+	0.577267i
$769$		−	5.25162i		−	0.189378i	−0.995507	−	0.0946892i	$-0.969814\pi$
$769$		−	5.25162i		−	0.189378i	0.995507	−	0.0946892i	$-0.0301857\pi$
$770$	4.38565	+	1.05955i	0.158048	+	0.0381835i
$771$	−14.2181	−	14.2181i	−0.512052	−	0.512052i
$772$	19.3201	−	3.75801i	0.695344	−	0.135254i
$773$	−10.2035	+	10.2035i	−0.366995	+	0.366995i	−0.866380	−	0.499385i	$-0.833559\pi$
$773$	−10.2035	+	10.2035i	−0.366995	+	0.366995i	0.499385	+	0.866380i	$0.333559\pi$
$774$	−8.65514	+	10.5009i	−0.311102	+	0.377447i
$775$			10.9866i			0.394651i
$776$	45.3303	−	13.4369i	1.62726	−	0.482358i
$777$	−8.51587	−	2.94651i	−0.305505	−	0.105705i
$778$	12.5696	−	15.2501i	0.450641	−	0.546742i
$779$	13.6675	−	13.6675i	0.489690	−	0.489690i
$780$	−12.9666	+	19.2291i	−0.464279	+	0.688513i
$781$	3.93165	−	3.93165i	0.140685	−	0.140685i
$782$	48.3465	−	4.65836i	1.72887	−	0.166583i
$783$	−7.20100			−0.257343
$784$	26.8941	+	7.79147i	0.960504	+	0.278267i
$785$	−65.8858			−2.35157
$786$	2.71656	−	0.261750i	0.0968964	−	0.00933633i
$787$	9.39612	−	9.39612i	0.334936	−	0.334936i	−0.519522	−	0.854457i	$-0.673890\pi$
$787$	9.39612	−	9.39612i	0.334936	−	0.334936i	0.854457	+	0.519522i	$0.173890\pi$
$788$	−14.5602	−	9.81824i	−0.518684	−	0.349760i
$789$	4.65196	−	4.65196i	0.165614	−	0.165614i
$790$	−12.8547	+	15.5960i	−0.457349	+	0.554881i
$791$	−14.7024	−	5.08706i	−0.522756	−	0.180875i
$792$	0.466411	−	0.859416i	0.0165732	−	0.0305380i
$793$			5.99827i			0.213005i
$794$	7.29441	−	8.84998i	0.258869	−	0.314074i
$795$	−19.1741	+	19.1741i	−0.680036	+	0.680036i
$796$	−3.88388	−	19.9672i	−0.137660	−	0.707717i
$797$	15.0117	+	15.0117i	0.531741	+	0.531741i	0.921090	−	0.389349i	$-0.127300\pi$
$797$	15.0117	+	15.0117i	0.531741	+	0.531741i	−0.389349	+	0.921090i	$0.627300\pi$
$798$	−7.36048	−	1.77825i	−0.260558	−	0.0629494i
$799$		−	37.3825i		−	1.32250i
$800$	−35.9509	+	18.7295i	−1.27105	+	0.662187i
$801$		−	11.5562i		−	0.408318i
$802$	−1.36020	−	14.1168i	−0.0480304	−	0.498480i
$803$	1.63392	−	1.63392i	0.0576597	−	0.0576597i
$804$	10.6551	−	2.07255i	0.375775	−	0.0730933i
$805$	54.9093	−	26.6794i	1.93530	−	0.940325i
$806$	4.58481	−	5.56254i	0.161493	−	0.195932i
$807$	−26.2560			−0.924256
$808$	−36.9837	−	20.0713i	−1.30108	−	0.706106i
$809$			9.85392i			0.346445i	0.984883	+	0.173223i	$0.0554180\pi$
$809$			9.85392i			0.346445i	−0.984883	+	0.173223i	$0.944582\pi$
$810$	3.80643	+	3.13737i	0.133744	+	0.110236i
$811$	−5.99202	−	5.99202i	−0.210408	−	0.210408i	0.594033	−	0.804441i	$-0.297535\pi$
$811$	−5.99202	−	5.99202i	−0.210408	−	0.210408i	−0.804441	+	0.594033i	$0.797535\pi$
$812$	−30.4626	+	22.8900i	−1.06903	+	0.803280i
$813$	−15.6347	+	15.6347i	−0.548334	+	0.548334i
$814$	0.159708	+	1.65751i	0.00559775	+	0.0580958i
$815$	55.2823			1.93645
$816$	19.1181	+	8.10935i	0.669266	+	0.283884i
$817$		−	19.4734i		−	0.681290i
$818$	−2.18114	−	22.6369i	−0.0762619	−	0.791479i
$819$	7.91168	−	3.84414i	0.276457	−	0.134325i
$820$	−37.2501	+	55.2408i	−1.30083	+	1.92909i
$821$	7.92158	+	7.92158i	0.276465	+	0.276465i	0.831696	−	0.555231i	$-0.187370\pi$
$821$	7.92158	+	7.92158i	0.276465	+	0.276465i	−0.555231	+	0.831696i	$0.687370\pi$
$822$	−7.93114	+	9.62250i	−0.276630	+	0.335623i
$823$	−31.5025			−1.09811			−0.549055	−	0.835786i	$-0.685012\pi$
$823$	−31.5025			−1.09811			−0.549055	+	0.835786i	$0.685012\pi$
$824$	14.6367	−	4.33865i	0.509894	−	0.151144i
$825$	2.47738			0.0862512
$826$	15.6082	−	9.53399i	0.543079	−	0.331730i
$827$	2.82748	−	2.82748i	0.0983211	−	0.0983211i	−0.656235	−	0.754556i	$-0.727852\pi$
$827$	2.82748	−	2.82748i	0.0983211	−	0.0983211i	0.754556	+	0.656235i	$0.227852\pi$
$828$	−2.52616	−	12.9871i	−0.0877902	−	0.451332i
$829$	−5.54898	−	5.54898i	−0.192724	−	0.192724i	0.604148	−	0.796872i	$-0.293514\pi$
$829$	−5.54898	−	5.54898i	−0.192724	−	0.192724i	−0.796872	+	0.604148i	$0.793514\pi$
$830$	67.4179	−	6.49597i	2.34011	−	0.225478i
$831$	20.0768			0.696458
$832$	26.0180	+	5.51983i	0.902010	+	0.191366i
$833$	22.4600	−	28.5708i	0.778192	−	0.989919i
$834$	−0.0785340	−	0.815060i	−0.00271941	−	0.0282232i
$835$	−38.5009	−	38.5009i	−1.33238	−	1.33238i
$836$	0.267172	+	1.37354i	0.00924032	+	0.0475048i
$837$	−1.08410	−	1.08410i	−0.0374721	−	0.0374721i
$838$	10.1759	+	8.38726i	0.351520	+	0.289733i
$839$			25.5143i			0.880850i	0.897789	+	0.440425i	$0.145172\pi$
$839$			25.5143i			0.880850i	−0.897789	+	0.440425i	$0.854828\pi$
$840$	26.0753	+	1.17255i	0.899684	+	0.0404568i
$841$		−	22.8544i		−	0.788081i
$842$	−5.89702	+	7.15459i	−0.203225	+	0.246563i
$843$	0.377417	+	0.377417i	0.0129989	+	0.0129989i
$844$	13.3623	+	9.01050i	0.459950	+	0.310154i
$845$	−4.80162	−	4.80162i	−0.165181	−	0.165181i
$846$	−10.1360	+	0.976641i	−0.348483	+	0.0335776i
$847$	9.41287	−	27.2046i	0.323430	−	0.934762i
$848$	28.6279	+	12.1432i	0.983087	+	0.416998i
$849$	27.5822			0.946619
$850$	5.04621	+	52.3717i	0.173084	+	1.79633i
$851$	15.9318	+	15.9318i	0.546135	+	0.546135i
$852$	17.9839	−	26.6696i	0.616119	−	0.913686i
$853$	9.34018	−	9.34018i	0.319802	−	0.319802i	−0.528889	−	0.848691i	$-0.677391\pi$
$853$	9.34018	−	9.34018i	0.319802	−	0.319802i	0.848691	+	0.528889i	$0.177391\pi$
$854$	5.76093	−	3.51896i	0.197135	−	0.120416i
$855$	−7.05886			−0.241408
$856$	−19.8263	−	10.7599i	−0.677650	−	0.367765i
$857$	14.6466			0.500317			0.250159	−	0.968205i	$-0.419517\pi$
$857$	14.6466			0.500317			0.250159	+	0.968205i	$0.419517\pi$
$858$	−1.25430	−	1.03383i	−0.0428211	−	0.0352944i
$859$	35.4037	+	35.4037i	1.20796	+	1.20796i	0.971687	+	0.236272i	$0.0759257\pi$
$859$	35.4037	+	35.4037i	1.20796	+	1.20796i	0.236272	+	0.971687i	$0.424074\pi$
$860$	12.8166	+	65.8904i	0.437041	+	2.24684i
$861$	22.7284	−	11.0433i	0.774583	−	0.376356i
$862$	−12.9885	+	1.25149i	−0.442390	+	0.0426259i
$863$			31.2983i			1.06541i	0.846302	+	0.532703i	$0.178824\pi$
$863$			31.2983i			1.06541i	−0.846302	+	0.532703i	$0.821176\pi$
$864$	1.69932	−	5.39558i	0.0578120	−	0.183561i
$865$	−32.6890			−1.11146
$866$	−28.9930	+	2.79359i	−0.985223	+	0.0949299i
$867$	7.03845	−	7.03845i	0.239038	−	0.239038i
$868$	−8.03219	−	1.14006i	−0.272630	−	0.0386962i
$869$	−1.00160	−	1.00160i	−0.0339770	−	0.0339770i
$870$	−22.5922	+	27.4101i	−0.765947	+	0.929290i
$871$		−	18.0440i		−	0.611399i
$872$	5.98788	+	3.24966i	0.202775	+	0.110047i
$873$	−16.7160			−0.565750
$874$	14.6100	+	12.0420i	0.494191	+	0.407326i
$875$	8.73558	+	17.9788i	0.295317	+	0.607795i
$876$	7.47378	−	11.0834i	0.252516	−	0.374473i
$877$	14.5201	−	14.5201i	0.490310	−	0.490310i	−0.418094	−	0.908404i	$-0.637302\pi$
$877$	14.5201	−	14.5201i	0.490310	−	0.490310i	0.908404	+	0.418094i	$0.137302\pi$
$878$	−42.9354	+	4.13698i	−1.44900	+	0.139616i
$879$			18.7526i			0.632508i
$880$	−1.80800	−	4.47167i	−0.0609478	−	0.150740i
$881$		−	10.6714i		−	0.359529i	−0.983710	−	0.179764i	$-0.942466\pi$
$881$		−	10.6714i		−	0.359529i	0.983710	−	0.179764i	$-0.0575335\pi$
$882$	−8.33353	−	5.34343i	−0.280605	−	0.179923i
$883$	35.8490	+	35.8490i	1.20641	+	1.20641i	0.972180	+	0.234235i	$0.0752585\pi$
$883$	35.8490	+	35.8490i	1.20641	+	1.20641i	0.234235	+	0.972180i	$0.424742\pi$
$884$	19.3003	−	28.6217i	0.649138	−	0.962653i
$885$	12.0560	−	12.0560i	0.405256	−	0.405256i
$886$	25.6916	+	21.1758i	0.863127	+	0.711414i
$887$		−	4.16513i		−	0.139852i	−0.997552	−	0.0699258i	$-0.977724\pi$
$887$		−	4.16513i		−	0.139852i	0.997552	−	0.0699258i	$-0.0222762\pi$
$888$	2.73781	+	9.23616i	0.0918748	+	0.309945i
$889$	−2.19795	+	6.35243i	−0.0737170	+	0.213054i
$890$	−43.9879	−	36.2561i	−1.47448	−	1.21531i
$891$	−0.244455	+	0.244455i	−0.00818956	+	0.00818956i
$892$	−10.3373	+	2.01075i	−0.346120	+	0.0673249i
$893$	10.3040	−	10.3040i	0.344809	−	0.344809i
$894$	1.64809	+	17.1046i	0.0551204	+	0.572063i
$895$	−7.81645			−0.261275
$896$	−9.96235	−	28.2268i	−0.332819	−	0.942991i
$897$	−21.9932			−0.734333
$898$	−1.46944	−	15.2505i	−0.0490359	−	0.508915i
$899$	7.80663	−	7.80663i	0.260366	−	0.260366i
$900$	14.0684	−	2.73648i	0.468945	−	0.0912161i
$901$	28.5399	−	28.5399i	0.950801	−	0.950801i
$902$	−3.60332	−	2.96996i	−0.119977	−	0.0988888i
$903$	8.32446	−	24.0590i	0.277021	−	0.800632i
$904$	4.72673	+	15.9459i	0.157209	+	0.530354i
$905$		−	36.3986i		−	1.20993i
$906$	−17.2660	−	14.2311i	−0.573624	−	0.472797i
$907$	7.88170	−	7.88170i	0.261708	−	0.261708i	−0.564040	−	0.825747i	$-0.690754\pi$
$907$	7.88170	−	7.88170i	0.261708	−	0.261708i	0.825747	+	0.564040i	$0.190754\pi$
$908$	−17.9905	+	26.6794i	−0.597035	+	0.885385i
$909$	10.5198	+	10.5198i	0.348919	+	0.348919i
$910$	10.1894	−	42.1758i	0.337776	−	1.39811i
$911$		−	22.4309i		−	0.743169i	−0.928399	−	0.371585i	$-0.878815\pi$
$911$		−	22.4309i		−	0.743169i	0.928399	−	0.371585i	$-0.121185\pi$
$912$	3.03439	+	7.50484i	0.100479	+	0.248510i
$913$			4.74687i			0.157098i
$914$	49.5481	−	4.77414i	1.63890	−	0.157915i
$915$	4.44981	−	4.44981i	0.147106	−	0.147106i
$916$	23.5244	−	34.8860i	0.777267	−	1.15266i
$917$	−4.59236	+	2.23134i	−0.151653	+	0.0736855i
$918$	−5.66571	−	4.66984i	−0.186996	−	0.154128i
$919$	38.3187			1.26402			0.632009	−	0.774961i	$-0.282230\pi$
$919$	38.3187			1.26402			0.632009	+	0.774961i	$0.282230\pi$
$920$	−57.3600	−	31.1297i	−1.89110	−	1.02631i
$921$			12.3754i			0.407783i
$922$	−34.4019	+	41.7383i	−1.13297	+	1.37458i
$923$	−37.8097	−	37.8097i	−1.24452	−	1.24452i
$924$	−0.257073	+	1.81118i	−0.00845708	+	0.0595836i
$925$	−17.2583	+	17.2583i	−0.567448	+	0.567448i
$926$	−26.1874	+	2.52325i	−0.860571	+	0.0829192i
$927$	−5.39742			−0.177275
$928$	38.8536	+	12.2368i	1.27543	+	0.401693i
$929$			28.5117i			0.935438i	0.883877	+	0.467719i	$0.154924\pi$
$929$			28.5117i			0.935438i	−0.883877	+	0.467719i	$0.845076\pi$
$930$	−7.52781	+	0.725332i	−0.246847	+	0.0237846i
$931$	14.0659	−	1.68436i	0.460991	−	0.0552025i
$932$	0.811616	+	4.17255i	0.0265854	+	0.136676i
$933$	−8.84332	−	8.84332i	−0.289517	−	0.289517i
$934$	−15.5434	−	12.8113i	−0.508597	−	0.419200i
$935$	−6.26036			−0.204736
$936$	−8.26480	−	4.48536i	−0.270143	−	0.146609i
$937$	−16.8510			−0.550499			−0.275250	−	0.961373i	$-0.588760\pi$
$937$	−16.8510			−0.550499			−0.275250	+	0.961373i	$0.588760\pi$
$938$	−17.3301	+	10.5858i	−0.565848	+	0.345638i
$939$	21.6898	−	21.6898i	0.707820	−	0.707820i
$940$	−28.0829	+	41.6461i	−0.915962	+	1.35835i
$941$	−28.9571	−	28.9571i	−0.943975	−	0.943975i	0.0545372	−	0.998512i	$-0.482632\pi$
$941$	−28.9571	−	28.9571i	−0.943975	−	0.943975i	−0.998512	+	0.0545372i	$0.982632\pi$
$942$	−2.56209	−	26.5905i	−0.0834774	−	0.866365i
$943$	−63.1815			−2.05747
$944$	−18.0001	−	7.63516i	−0.585854	−	0.248503i
$945$	−8.72105	−	3.01751i	−0.283696	−	0.0981595i
$946$	−4.68279	+	0.451205i	−0.152251	+	0.0146699i
$947$	42.0974	+	42.0974i	1.36798	+	1.36798i	0.863315	+	0.504666i	$0.168384\pi$
$947$	42.0974	+	42.0974i	1.36798	+	1.36798i	0.504666	+	0.863315i	$0.331616\pi$
$948$	−6.79417	−	4.58146i	−0.220665	−	0.148799i
$949$	−15.7130	−	15.7130i	−0.510066	−	0.510066i
$950$	−13.0446	+	15.8264i	−0.423222	+	0.513476i
$951$		−	9.28918i		−	0.301222i
$952$	−38.8120	−	1.74529i	−1.25790	−	0.0565651i
$953$		−	20.9090i		−	0.677308i	−0.940911	−	0.338654i	$-0.890028\pi$
$953$		−	20.9090i		−	0.677308i	0.940911	−	0.338654i	$-0.109972\pi$
$954$	−8.48400	−	6.99276i	−0.274680	−	0.226399i
$955$	−61.5712	−	61.5712i	−1.99240	−	1.99240i
$956$	−3.41527	−	17.5580i	−0.110458	−	0.567867i
$957$	−1.76032	−	1.76032i	−0.0569031	−	0.0569031i
$958$	−1.11205	−	11.5413i	−0.0359288	−	0.372884i
$959$	7.62812	−	22.0465i	0.246325	−	0.711917i
$960$	−15.2065	−	23.3963i	−0.490788	−	0.755112i
$961$	−28.6494			−0.924175
$962$	15.9399	−	1.53587i	0.513923	−	0.0495184i
$963$	5.63948	+	5.63948i	0.181730	+	0.181730i
$964$	1.58976	+	8.17300i	0.0512026	+	0.263235i
$965$	−24.2718	+	24.2718i	−0.781337	+	0.781337i
$966$	12.9026	+	21.1230i	0.415135	+	0.679623i
$967$	−19.1350			−0.615340			−0.307670	−	0.951493i	$-0.599549\pi$
$967$	−19.1350			−0.615340			−0.307670	+	0.951493i	$0.599549\pi$
$968$	−29.5057	+	8.74615i	−0.948348	+	0.281112i
$969$	10.5068			0.337528
$970$	−52.4442	+	63.6282i	−1.68388	+	2.04298i
$971$	13.3830	+	13.3830i	0.429480	+	0.429480i	0.888451	−	0.458971i	$-0.151782\pi$
$971$	13.3830	+	13.3830i	0.429480	+	0.429480i	−0.458971	+	0.888451i	$0.651782\pi$
$972$	−1.11817	+	1.65822i	−0.0358654	+	0.0531874i
$973$	0.669479	+	1.37787i	0.0214625	+	0.0441723i
$974$	−2.50745	−	26.0234i	−0.0803439	−	0.833843i
$975$		−	23.8244i		−	0.762990i
$976$	−6.64379	−	2.81811i	−0.212662	−	0.0902055i
$977$	36.3850			1.16406			0.582029	−	0.813168i	$-0.302259\pi$
$977$	36.3850			1.16406			0.582029	+	0.813168i	$0.302259\pi$
$978$	2.14975	+	22.3111i	0.0687415	+	0.713429i
$979$	2.82497	−	2.82497i	0.0902865	−	0.0902865i
$980$	−46.4848	+	14.9567i	−1.48490	+	0.477775i
$981$	−1.70321	−	1.70321i	−0.0543794	−	0.0543794i
$982$	12.2316	+	10.0816i	0.390325	+	0.321717i
$983$		−	13.6512i		−	0.435406i	−0.976015	−	0.217703i	$-0.930144\pi$
$983$		−	13.6512i		−	0.435406i	0.976015	−	0.217703i	$-0.0698563\pi$
$984$	−23.7429	−	12.8854i	−0.756894	−	0.410772i
$985$	30.6266			0.975844
$986$	33.6275	−	40.7988i	1.07092	−	1.29930i
$987$	17.1350	−	8.32557i	0.545413	−	0.265006i
$988$	13.2090	−	2.56932i	0.420234	−	0.0817411i
$989$	−45.0104	+	45.0104i	−1.43125	+	1.43125i
$990$	0.163556	+	1.69745i	0.00519814	+	0.0539485i
$991$		−	14.6044i		−	0.463926i	−0.972725	−	0.231963i	$-0.925485\pi$
$991$		−	14.6044i		−	0.463926i	0.972725	−	0.231963i	$-0.0745148\pi$
$992$	4.00713	+	7.69161i	0.127227	+	0.244209i
$993$			4.05184i			0.128581i
$994$	−14.1321	+	58.4953i	−0.448244	+	1.85536i
$995$	25.0847	+	25.0847i	0.795240	+	0.795240i
$996$	5.24334	+	26.9562i	0.166142	+	0.854140i
$997$	−33.5387	+	33.5387i	−1.06218	+	1.06218i	−0.0642464	+	0.997934i	$0.520464\pi$
$997$	−33.5387	+	33.5387i	−1.06218	+	1.06218i	−0.997934	+	0.0642464i	$0.979536\pi$
$998$	−3.79146	+	4.60001i	−0.120017	+	0.145611i
$999$		−	3.40592i		−	0.107758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.15	✓	64
4.3	odd	2		1344.2.u.a.1231.18		64
7.6	odd	2	inner	336.2.u.a.139.16	yes	64
16.3	odd	4	inner	336.2.u.a.307.16	yes	64
16.13	even	4		1344.2.u.a.559.15		64
28.27	even	2		1344.2.u.a.1231.15		64
112.13	odd	4		1344.2.u.a.559.18		64
112.83	even	4	inner	336.2.u.a.307.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.15	✓	64	1.1	even	1	trivial
336.2.u.a.139.16	yes	64	7.6	odd	2	inner
336.2.u.a.307.15	yes	64	112.83	even	4	inner
336.2.u.a.307.16	yes	64	16.3	odd	4	inner
1344.2.u.a.559.15		64	16.13	even	4
1344.2.u.a.559.18		64	112.13	odd	4
1344.2.u.a.1231.15		64	28.27	even	2
1344.2.u.a.1231.18		64	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.135637 - 1.40769i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.96321 + 0.381870i) q^{4} +(2.46638 - 2.46638i) q^{5} +(1.09130 + 0.899481i) q^{6} +(-2.50032 - 0.865115i) q^{7} +(0.803838 + 2.71180i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.135637 - 1.40769i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.96321 + 0.381870i) q^{4} +(2.46638 - 2.46638i) q^{5} +(1.09130 + 0.899481i) q^{6} +(-2.50032 - 0.865115i) q^{7} +(0.803838 + 2.71180i) q^{8} -1.00000i q^{9} +(-3.80643 - 3.13737i) q^{10} +(0.244455 - 0.244455i) q^{11} +(1.11817 - 1.65822i) q^{12} +(-2.35087 - 2.35087i) q^{13} +(-0.878683 + 3.63702i) q^{14} +3.48798i q^{15} +(3.70835 - 1.49938i) q^{16} -5.19171i q^{17} +(-1.40769 + 0.135637i) q^{18} +(1.43102 - 1.43102i) q^{19} +(-3.90017 + 5.78384i) q^{20} +(2.37972 - 1.15626i) q^{21} +(-0.377275 - 0.310961i) q^{22} -6.61525 q^{23} +(-2.48593 - 1.34913i) q^{24} -7.16602i q^{25} +(-2.99044 + 3.62817i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.23899 + 0.743604i) q^{28} +(-5.09187 + 5.09187i) q^{29} +(4.91001 - 0.473098i) q^{30} -1.53315 q^{31} +(-2.61365 - 5.01685i) q^{32} +0.345712i q^{33} +(-7.30834 + 0.704186i) q^{34} +(-8.30041 + 4.03302i) q^{35} +(0.381870 + 1.96321i) q^{36} +(-2.40835 - 2.40835i) q^{37} +(-2.20854 - 1.82034i) q^{38} +3.32463 q^{39} +(8.67088 + 4.70574i) q^{40} +9.55090 q^{41} +(-1.95044 - 3.19308i) q^{42} +(6.80405 - 6.80405i) q^{43} +(-0.386566 + 0.573266i) q^{44} +(-2.46638 - 2.46638i) q^{45} +(0.897269 + 9.31224i) q^{46} +7.20043 q^{47} +(-1.56198 + 3.68242i) q^{48} +(5.50315 + 4.32612i) q^{49} +(-10.0876 + 0.971974i) q^{50} +(3.67109 + 3.67109i) q^{51} +(5.51296 + 3.71751i) q^{52} +(5.49720 + 5.49720i) q^{53} +(0.899481 - 1.09130i) q^{54} -1.20584i q^{55} +(0.336168 - 7.47576i) q^{56} +2.02377i q^{57} +(7.85844 + 6.47716i) q^{58} +(-3.45643 - 3.45643i) q^{59} +(-1.33195 - 6.84762i) q^{60} +(-1.27576 - 1.27576i) q^{61} +(0.207952 + 2.15821i) q^{62} +(-0.865115 + 2.50032i) q^{63} +(-6.70769 + 4.35969i) q^{64} -11.5962 q^{65} +(0.486657 - 0.0468912i) q^{66} +(3.83774 + 3.83774i) q^{67} +(1.98256 + 10.1924i) q^{68} +(4.67768 - 4.67768i) q^{69} +(6.80309 + 11.1374i) q^{70} +16.0833 q^{71} +(2.71180 - 0.803838i) q^{72} +6.68392 q^{73} +(-3.06356 + 3.71688i) q^{74} +(5.06714 + 5.06714i) q^{75} +(-2.26292 + 3.35585i) q^{76} +(-0.822697 + 0.399733i) q^{77} +(-0.450941 - 4.68006i) q^{78} -4.09727i q^{79} +(5.44816 - 12.8442i) q^{80} -1.00000 q^{81} +(-1.29545 - 13.4447i) q^{82} +(-9.70907 + 9.70907i) q^{83} +(-4.23034 + 3.17872i) q^{84} +(-12.8047 - 12.8047i) q^{85} +(-10.5009 - 8.65514i) q^{86} -7.20100i q^{87} +(0.859416 + 0.466411i) q^{88} +11.5562 q^{89} +(-3.13737 + 3.80643i) q^{90} +(3.84414 + 7.91168i) q^{91} +(12.9871 - 2.52616i) q^{92} +(1.08410 - 1.08410i) q^{93} +(-0.976641 - 10.1360i) q^{94} -7.05886i q^{95} +(5.39558 + 1.69932i) q^{96} -16.7160i q^{97} +(5.34343 - 8.33353i) q^{98} +(-0.244455 - 0.244455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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