LMFDB - Embedded newform 336.2.u.a.139.16

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			139.16
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.16

$q$-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} +(1.55695 + 3.40234i) 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} +(-1.15626 + 2.37972i) 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} +(4.57827 - 2.65319i) 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} +(4.03302 - 8.30041i) 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} +(3.50675 + 1.30489i) 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} +(-4.35586 - 6.08494i) 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} +(-12.2315 - 4.55142i) 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} +(-0.399733 + 0.822697i) 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} +(1.36124 - 5.11342i) 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} +(-7.91168 - 3.84414i) 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} +(-6.83628 - 7.15997i) 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	$0.534749\pi$
$5$	−2.46638	+	2.46638i	−1.10300	+	1.10300i	−0.994047	+	0.108949i	$0.965251\pi$
$6$	−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	0.953478	−	0.301464i	$-0.0974753\pi$
$13$	2.35087	+	2.35087i	0.652014	+	0.652014i	−0.301464	+	0.953478i	$0.597475\pi$
$14$	1.55695	+	3.40234i	0.416113	+	0.909313i
$15$			3.48798i			0.900593i
$16$	3.70835	−	1.49938i	0.927088	−	0.374844i
$17$			5.19171i			1.25918i	0.776930	+	0.629588i	$0.216776\pi$
$17$			5.19171i			1.25918i	−0.776930	+	0.629588i	$0.783224\pi$
$18$	−1.40769	+	0.135637i	−0.331797	+	0.0319698i
$19$	−1.43102	+	1.43102i	−0.328298	+	0.328298i	−0.851939	−	0.523641i	$-0.824573\pi$
$19$	−1.43102	+	1.43102i	−0.328298	+	0.328298i	0.523641	+	0.851939i	$0.324573\pi$
$20$	3.90017	−	5.78384i	0.872104	−	1.29330i
$21$	−1.15626	+	2.37972i	−0.252317	+	0.519297i
$22$	−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
$28$	4.57827	−	2.65319i	0.865212	−	0.501406i
$29$	−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	$-0.456035\pi$
$31$	1.53315			0.275363			0.137681	+	0.990477i	$0.456035\pi$
$32$	−2.61365	−	5.01685i	−0.462033	−	0.886863i
$33$		−	0.345712i		−	0.0601807i
$34$	7.30834	−	0.704186i	1.25337	−	0.120767i
$35$	4.03302	−	8.30041i	0.681704	−	1.40303i
$36$	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	$-0.767932\pi$
$41$	−9.55090			−1.49160			−0.745800	+	0.666170i	$0.767932\pi$
$42$	3.50675	+	1.30489i	0.541103	+	0.201348i
$43$	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	$-0.675989\pi$
$47$	−7.20043			−1.05029			−0.525145	+	0.851013i	$0.675989\pi$
$48$	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
$56$	−4.35586	−	6.08494i	−0.582077	−	0.813134i
$57$			2.02377i			0.268055i
$58$	7.85844	+	6.47716i	1.03186	+	0.850492i
$59$	3.45643	+	3.45643i	0.449988	+	0.449988i	0.895351	−	0.445362i	$-0.146925\pi$
$59$	3.45643	+	3.45643i	0.449988	+	0.449988i	−0.445362	+	0.895351i	$0.646925\pi$
$60$	−1.33195	−	6.84762i	−0.171955	−	0.884025i
$61$	1.27576	+	1.27576i	0.163344	+	0.163344i	0.784046	−	0.620702i	$-0.213152\pi$
$61$	1.27576	+	1.27576i	0.163344	+	0.163344i	−0.620702	+	0.784046i	$0.713152\pi$
$62$	−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
$70$	−12.2315	−	4.55142i	−1.46194	−	0.543998i
$71$	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	$-0.627921\pi$
$73$	−6.68392			−0.782293			−0.391147	+	0.920328i	$0.627921\pi$
$74$	−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
$77$	−0.399733	+	0.822697i	−0.0455539	+	0.0937551i
$78$	−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	$-0.478330\pi$
$83$	9.70907	−	9.70907i	1.06571	−	1.06571i	0.997684	−	0.0680257i	$-0.0216700\pi$
$84$	1.36124	−	5.11342i	0.148523	−	0.557920i
$85$	−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	$-0.709827\pi$
$89$	−11.5562			−1.22495			−0.612477	+	0.790489i	$0.709827\pi$
$90$	3.13737	−	3.80643i	0.330708	−	0.401233i
$91$	−7.91168	−	3.84414i	−0.829370	−	0.402975i
$92$	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	$0.322569\pi$
$97$			16.7160i			1.69725i	−0.528995	+	0.848625i	$0.677431\pi$
$98$	−6.83628	−	7.15997i	−0.690569	−	0.723267i
$99$	−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	$-0.484745\pi$
$101$	10.5198	−	10.5198i	1.04676	−	1.04676i	0.998852	−	0.0479051i	$-0.0152545\pi$
$102$	4.66984	−	5.66571i	0.462383	−	0.560989i
$103$			5.39742i			0.531824i	0.963997	+	0.265912i	$0.0856730\pi$
$103$			5.39742i			0.531824i	−0.963997	+	0.265912i	$0.914327\pi$
$104$	−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
$112$	−7.97491	+	6.95707i	−0.753558	+	0.657381i
$113$	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
$126$	3.40234	−	1.55695i	0.303104	−	0.138704i
$127$		−	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	−0.764201	−	0.644978i	$-0.776866\pi$
$131$	−1.36457	+	1.36457i	−0.119223	+	0.119223i	0.644978	+	0.764201i	$0.276866\pi$
$132$	0.132017	+	0.678704i	0.0114906	+	0.0590736i
$133$	2.34000	−	4.81600i	0.202904	−	0.417600i
$134$	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	0.724257	−	0.689530i	$-0.242183\pi$
$139$	0.409417	+	0.409417i	0.0347263	+	0.0347263i	−0.689530	+	0.724257i	$0.742183\pi$
$140$	−4.74797	+	17.8355i	−0.401276	+	1.50738i
$141$	−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
$147$	0.832287	−	6.95035i	0.0686459	−	0.573255i
$148$	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
$154$	1.21232	+	0.451115i	0.0976919	+	0.0363518i
$155$	−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	$0.0217660\pi$
$157$	13.3568	+	13.3568i	1.06599	+	1.06599i	0.0683267	+	0.997663i	$0.478234\pi$
$158$	−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	$0.206420\pi$
$167$			15.6103i			1.20796i	−0.796998	+	0.603981i	$0.793580\pi$
$168$	−7.38276	−	1.22264i	−0.569592	−	0.0943285i
$169$		−	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	0.912628	−	0.408791i	$-0.134050\pi$
$173$	6.62694	+	6.62694i	0.503837	+	0.503837i	−0.408791	+	0.912628i	$0.634050\pi$
$174$	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	−0.925999	−	0.377525i	$-0.876775\pi$
$181$	−7.37897	+	7.37897i	−0.548475	+	0.548475i	0.377525	+	0.925999i	$0.376775\pi$
$182$	−4.33826	+	11.6586i	−0.321573	+	0.864196i
$183$	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
$189$	2.37972	+	1.15626i	0.173099	+	0.0841056i
$190$	−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
$196$	−9.15180	+	10.5945i	−0.653700	+	0.756754i
$197$	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	$-0.882609\pi$
$199$		−	10.1707i		−	0.720981i	0.932763	−	0.360491i	$-0.117391\pi$
$200$	19.4328	−	5.76032i	1.37411	−	0.407316i
$201$	5.42739			0.382818
$202$	−16.2355	−	13.3818i	−1.14233	−	0.941538i
$203$	8.32623	−	17.1363i	0.584387	−	1.20274i
$204$	−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
$210$	−11.8673	+	5.43062i	−0.818921	+	0.374748i
$211$	−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	$-0.556414\pi$
$223$	−5.26554			−0.352607			−0.176303	+	0.984336i	$0.556414\pi$
$224$	10.8751	+	10.2826i	0.726624	+	0.687036i
$225$	−7.16602			−0.477734
$226$	−0.797571	−	8.27753i	−0.0530536	−	0.550613i
$227$	−11.3768	+	11.3768i	−0.755102	+	0.755102i	−0.975427	−	0.220325i	$-0.929288\pi$
$227$	−11.3768	+	11.3768i	−0.755102	+	0.755102i	0.220325	+	0.975427i	$0.429288\pi$
$228$	−0.772815	−	3.97307i	−0.0511809	−	0.263123i
$229$	14.8763	−	14.8763i	0.983051	−	0.983051i	−0.0168077	−	0.999859i	$-0.505350\pi$
$229$	14.8763	−	14.8763i	0.983051	−	0.983051i	0.999859	+	0.0168077i	$0.00535029\pi$
$230$	−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
$238$	−17.6640	+	8.08324i	−1.14498	+	0.523959i
$239$			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	$0.0428092\pi$
$241$			4.16309i			0.268168i	−0.990970	+	0.134084i	$0.957191\pi$
$242$	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
$245$	−2.90300	+	24.2427i	−0.185466	+	1.54881i
$246$	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	0.733376	−	0.679824i	$-0.237944\pi$
$251$	0.848419	+	0.848419i	0.0535518	+	0.0535518i	−0.679824	+	0.733376i	$0.737944\pi$
$252$	−2.65319	−	4.57827i	−0.167135	−	0.288404i
$253$	−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	$-0.784228\pi$
$257$		−	20.1074i		−	1.25426i	0.778913	−	0.627132i	$-0.215772\pi$
$258$	−13.5454	+	1.30515i	−0.843297	+	0.0812548i
$259$	8.10513	+	3.93813i	0.503628	+	0.244703i
$260$	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
$266$	−7.09684	−	2.64078i	−0.435135	−	0.161917i
$267$	−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	$-0.954605\pi$
$269$	−18.5658	−	18.5658i	−1.13198	−	1.13198i	−0.142129	−	0.989848i	$-0.545395\pi$
$270$	−0.473098	−	4.91001i	−0.0287918	−	0.298814i
$271$	−22.1109			−1.34314			−0.671569	−	0.740942i	$-0.734379\pi$
$271$	−22.1109			−1.34314			−0.671569	+	0.740942i	$0.734379\pi$
$272$	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
$280$	25.7509	+	4.26454i	1.53891	+	0.254855i
$281$		−	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	$0.0559131\pi$
$283$	19.5036	+	19.5036i	1.15937	+	1.15937i	0.174754	+	0.984612i	$0.444087\pi$
$284$	−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	−0.978917	−	0.204256i	$-0.934522\pi$
$293$	−13.2601	+	13.2601i	−0.774661	+	0.774661i	0.204256	+	0.978917i	$0.434522\pi$
$294$	−9.89685	−	0.228885i	−0.577196	−	0.0133488i
$295$	−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
$301$	−11.1260	+	22.8985i	−0.641291	+	1.31985i
$302$	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	−0.911261	−	0.411830i	$-0.864890\pi$
$307$	−8.75073	+	8.75073i	−0.499430	+	0.499430i	0.411830	+	0.911261i	$0.364890\pi$
$308$	0.470596	−	1.76777i	0.0268147	−	0.100728i
$309$	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	$-0.884622\pi$
$311$		−	12.5063i		−	0.709170i	0.935024	−	0.354585i	$-0.115378\pi$
$312$	2.67246	+	9.01572i	0.151298	+	0.510415i
$313$	30.6740			1.73380			0.866899	−	0.498484i	$-0.166110\pi$
$313$	30.6740			1.73380			0.866899	+	0.498484i	$0.166110\pi$
$314$	16.9906	−	20.6140i	0.958837	−	1.16331i
$315$	−8.30041	−	4.03302i	−0.467675	−	0.227235i
$316$	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
$322$	−10.2996	−	22.5073i	−0.573975	−	1.25428i
$323$	−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
$336$	−0.719727	+	10.5585i	−0.0392643	+	0.576014i
$337$	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	0.371055	−	0.928611i	$-0.378996\pi$
$349$	−10.4160	−	10.4160i	−0.557555	−	0.557555i	−0.928611	+	0.371055i	$0.878996\pi$
$350$	24.3812	−	11.1571i	1.30323	−	0.596374i
$351$		−	3.32463i		−	0.177456i
$352$	−1.86532	−	0.587476i	−0.0994218	−	0.0313126i
$353$		−	0.352884i		−	0.0187821i	−0.999956	−	0.00939107i	$-0.997011\pi$
$353$		−	0.352884i		−	0.0187821i	0.999956	−	0.00939107i	$-0.00298931\pi$
$354$	−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
$357$	−12.3548	−	6.00297i	−0.653886	−	0.317711i
$358$	−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
$364$	17.0002	+	4.52561i	0.891054	+	0.237206i
$365$	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	$-0.836262\pi$
$367$	−33.3562			−1.74118			−0.870589	+	0.492010i	$0.836262\pi$
$368$	−24.5317	+	9.91875i	−1.27880	+	0.517050i
$369$			9.55090i			0.497200i
$370$	−1.61133	−	16.7231i	−0.0837692	−	0.869392i
$371$	−18.5004	−	8.98902i	−0.960495	−	0.466687i
$372$	−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
$378$	1.30489	−	3.50675i	0.0671160	−	0.180368i
$379$	−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	$-0.219893\pi$
$383$	30.1669			1.54145			0.770727	+	0.637165i	$0.219893\pi$
$384$	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
$392$	16.1552	+	11.4459i	0.815961	+	0.578107i
$393$			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	0.548411	−	0.836209i	$-0.315233\pi$
$397$	−5.73434	−	5.73434i	−0.287798	−	0.287798i	−0.836209	+	0.548411i	$0.815233\pi$
$398$	−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
$406$	−25.2521	−	9.39647i	−1.25324	−	0.466339i
$407$	−1.17747			−0.0583649
$408$	−7.00430	+	12.9062i	−0.346764	+	0.638954i
$409$	−16.0808			−0.795145			−0.397572	−	0.917571i	$-0.630147\pi$
$409$	−16.0808			−0.795145			−0.397572	+	0.917571i	$0.630147\pi$
$410$	−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
$413$	−11.6324	−	5.65195i	−0.572391	−	0.278114i
$414$	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	−0.527465	−	0.849577i	$-0.676857\pi$
$419$	6.59346	−	6.59346i	0.322112	−	0.322112i	0.849577	+	0.527465i	$0.176857\pi$
$420$	9.25429	+	15.9689i	0.451563	+	0.779204i
$421$	−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
$427$	−4.29347	−	2.08612i	−0.207775	−	0.100954i
$428$	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	$0.164793\pi$
$433$			20.5961i			0.989786i	−0.868954	+	0.494893i	$0.835207\pi$
$434$	2.38705	+	5.21631i	0.114582	+	0.250391i
$435$	−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	$0.259483\pi$
$439$			30.5005i			1.45571i	−0.685731	+	0.727855i	$0.740517\pi$
$440$	−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
$448$	12.9997	−	16.7035i	0.614178	−	0.789167i
$449$	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	$0.0997553\pi$
$461$	27.0443	+	27.0443i	1.25958	+	1.25958i	0.308286	+	0.951294i	$0.400245\pi$
$462$	1.17623	−	0.538257i	0.0547231	−	0.0250420i
$463$		−	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	−0.900631	−	0.434584i	$-0.856895\pi$
$467$	−10.0714	+	10.0714i	−0.466047	+	0.466047i	0.434584	+	0.900631i	$0.356895\pi$
$468$	−3.71751	+	5.51296i	−0.171842	+	0.254837i
$469$	−12.9156	−	6.27547i	−0.596389	−	0.289774i
$470$	−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
$476$	13.7746	+	23.7691i	0.631358	+	1.08945i
$477$	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	$-0.559975\pi$
$479$	−8.19876			−0.374611			−0.187305	+	0.982302i	$0.559975\pi$
$480$	17.4987	−	9.11637i	0.798702	−	0.416103i
$481$		−	11.3234i		−	0.516303i
$482$	5.86036	−	0.564667i	0.266932	−	0.0257199i
$483$	7.64895	−	15.7424i	0.348039	−	0.716305i
$484$	−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
$490$	34.5200	+	0.798345i	1.55946	+	0.0360656i
$491$	−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	$0.0329751\pi$
$503$			4.63846i			0.206819i	−0.994639	+	0.103409i	$0.967025\pi$
$504$	−6.08494	+	4.35586i	−0.271045	+	0.194026i
$505$			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	0.535815	−	0.844335i	$-0.320004\pi$
$509$	−6.96054	−	6.96054i	−0.308520	−	0.308520i	−0.844335	+	0.535815i	$0.820004\pi$
$510$	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
$518$	4.44433	−	11.9437i	0.195273	−	0.524776i
$519$	9.37191			0.411381
$520$	−9.32151	−	31.4467i	−0.408775	−	1.37903i
$521$	11.4231			0.500457			0.250229	−	0.968187i	$-0.419494\pi$
$521$	11.4231			0.500457			0.250229	+	0.968187i	$0.419494\pi$
$522$	6.47716	−	7.85844i	0.283497	−	0.343955i
$523$	6.27518	+	6.27518i	0.274394	+	0.274394i	0.830866	−	0.556472i	$-0.187845\pi$
$523$	6.27518	+	6.27518i	0.274394	+	0.274394i	−0.556472	+	0.830866i	$0.687845\pi$
$524$	2.15784	−	3.20002i	0.0942658	−	0.139793i
$525$	17.0531	+	8.28579i	0.744258	+	0.361621i
$526$	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
$532$	−2.75482	+	10.3484i	−0.119437	+	0.448659i
$533$	−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
$539$	0.287732	−	2.40282i	0.0123935	−	0.103497i
$540$	−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
$546$	5.17629	+	11.3115i	0.221525	+	0.484088i
$547$	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
$560$	2.51040	−	36.8279i	0.106084	−	1.55626i
$561$	1.79484			0.0757781
$562$	−0.751354	+	0.0723957i	−0.0316939	+	0.00305383i
$563$	−0.450781	+	0.450781i	−0.0189981	+	0.0189981i	−0.716542	−	0.697544i	$-0.754276\pi$
$563$	−0.450781	+	0.450781i	−0.0189981	+	0.0189981i	0.697544	+	0.716542i	$0.254276\pi$
$564$	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
$574$	−14.8703	−	32.4954i	−0.620674	−	1.35633i
$575$			47.4050i			1.97692i
$576$	4.35969	+	6.70769i	0.181654	+	0.279487i
$577$			44.9253i			1.87026i	0.354300	+	0.935132i	$0.384719\pi$
$577$			44.9253i			1.87026i	−0.354300	+	0.935132i	$0.615281\pi$
$578$	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
$581$	−15.8763	+	32.6752i	−0.658659	+	1.35560i
$582$	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	0.0612514	−	0.998122i	$-0.480491\pi$
$587$	−22.6986	−	22.6986i	−0.936871	−	0.936871i	−0.998122	+	0.0612514i	$0.980491\pi$
$588$	1.02018	+	13.9628i	0.0420713	+	0.575815i
$589$	−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	$-0.881948\pi$
$593$		−	17.6514i		−	0.724855i	0.932012	−	0.362427i	$-0.118052\pi$
$594$	0.0468912	+	0.486657i	0.00192397	+	0.0199678i
$595$	43.0934	+	20.9383i	1.76666	+	0.858385i
$596$	−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	$-0.165687\pi$
$601$	42.5370			1.73512			0.867560	+	0.497333i	$0.165687\pi$
$602$	33.7432	+	12.5561i	1.37527	+	0.511748i
$603$	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	$-0.295001\pi$
$607$	29.5855			1.20084			0.600419	+	0.799686i	$0.295001\pi$
$608$	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
$616$	−2.55231	−	0.422681i	−0.102835	−	0.0170303i
$617$		−	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	0.162333	−	0.986736i	$-0.448098\pi$
$619$	−20.5109	−	20.5109i	−0.824404	−	0.824404i	−0.986736	+	0.162333i	$0.948098\pi$
$620$	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
$630$	−4.55142	+	12.2315i	−0.181333	+	0.487313i
$631$	−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
$637$	23.1073	+	2.76705i	0.915546	+	0.109634i
$638$	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	−0.466689	−	0.884422i	$-0.654553\pi$
$643$	10.5926	−	10.5926i	0.417733	−	0.417733i	0.884422	+	0.466689i	$0.154553\pi$
$644$	−30.2864	+	17.5515i	−1.19345	+	0.691627i
$645$	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	$-0.707786\pi$
$647$		−	40.4129i		−	1.58880i	0.607397	−	0.794398i	$-0.292214\pi$
$648$	−0.803838	−	2.71180i	−0.0315777	−	0.106529i
$649$	1.68988			0.0663337
$650$	−25.9995	−	21.4295i	−1.01978	−	0.840536i
$651$	−1.77273	+	3.64848i	−0.0694787	+	0.142995i
$652$	−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
$658$	−11.2107	−	24.4983i	−0.437039	−	0.955042i
$659$	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	−0.518239	−	0.855236i	$-0.673412\pi$
$661$	8.66416	−	8.66416i	0.336997	−	0.336997i	0.855236	+	0.518239i	$0.173412\pi$
$662$	−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
$672$	14.9608	−	0.418963i	0.577124	−	0.0161619i
$673$	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	−0.672277	−	0.740300i	$-0.734684\pi$
$677$	1.76989	−	1.76989i	0.0680223	−	0.0680223i	0.740300	+	0.672277i	$0.234684\pi$
$678$	−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
$686$	23.2871	+	11.9880i	0.889104	+	0.457705i
$687$		−	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	−0.480466	−	0.877013i	$-0.659533\pi$
$691$	10.4240	−	10.4240i	0.396547	−	0.396547i	0.877013	+	0.480466i	$0.159533\pi$
$692$	−15.5407	−	10.4794i	−0.590768	−	0.398368i
$693$	0.822697	+	0.399733i	0.0312517	+	0.0151846i
$694$	−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
$700$	−19.0128	−	32.8080i	−0.718617	−	1.24002i
$701$	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
$707$	−17.2019	+	35.4036i	−0.646946	+	1.33149i
$708$	−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
$714$	−6.77459	+	18.2060i	−0.253533	+	0.681343i
$715$	−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	$-0.615435\pi$
$719$	−19.0248			−0.709506			−0.354753	+	0.934960i	$0.615435\pi$
$720$	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	$-0.727126\pi$
$727$		−	40.7707i		−	1.51210i	0.654513	−	0.756050i	$-0.272874\pi$
$728$	4.06482	−	24.5450i	0.150652	−	0.909696i
$729$			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	0.817456	−	0.575992i	$-0.195384\pi$
$733$	6.53739	+	6.53739i	0.241464	+	0.241464i	−0.575992	+	0.817456i	$0.695384\pi$
$734$	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
$742$	−10.1445	+	27.2622i	−0.372415	+	1.00083i
$743$	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
$749$	9.22167	−	18.9793i	0.336953	−	0.693487i
$750$	−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
$756$	−5.11342	−	1.36124i	−0.185973	−	0.0495077i
$757$	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	$-0.366068\pi$
$761$	22.5355			0.816910			0.408455	+	0.912778i	$0.366068\pi$
$762$	−2.28527	+	2.77261i	−0.0827864	+	0.100441i
$763$	−2.78509	+	5.73204i	−0.100827	+	0.207514i
$764$	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	$0.0301857\pi$
$769$			5.25162i			0.189378i	−0.995507	+	0.0946892i	$0.969814\pi$
$770$	−4.10267	+	1.87743i	−0.147850	+	0.0676579i
$771$	−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	−0.499385	−	0.866380i	$-0.666441\pi$
$773$	10.2035	−	10.2035i	0.366995	−	0.366995i	0.866380	+	0.499385i	$0.166441\pi$
$774$	−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
$784$	13.9211	−	24.2941i	0.497183	−	0.867645i
$785$	−65.8858			−2.35157
$786$	2.71656	−	0.261750i	0.0968964	−	0.00933633i
$787$	−9.39612	+	9.39612i	−0.334936	+	0.334936i	−0.854457	−	0.519522i	$-0.826110\pi$
$787$	−9.39612	+	9.39612i	−0.334936	+	0.334936i	0.519522	+	0.854457i	$0.326110\pi$
$788$	−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	0.389349	−	0.921090i	$-0.372700\pi$
$797$	−15.0117	−	15.0117i	−0.531741	−	0.531741i	−0.921090	+	0.389349i	$0.872700\pi$
$798$	−6.88554	+	3.15091i	−0.243745	+	0.111541i
$799$		−	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
$805$	−26.6794	+	54.9093i	−0.940325	+	1.93530i
$806$	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	0.804441	−	0.594033i	$-0.202465\pi$
$811$	5.99202	+	5.99202i	0.210408	+	0.210408i	−0.594033	+	0.804441i	$0.702465\pi$
$812$	−9.80226	+	36.8217i	−0.343992	+	1.29219i
$813$	−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
$819$	−3.84414	+	7.91168i	−0.134325	+	0.276457i
$820$	−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
$826$	−6.37844	+	17.1414i	−0.221934	+	0.596426i
$827$	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	0.796872	−	0.604148i	$-0.206486\pi$
$829$	5.54898	+	5.54898i	0.192724	+	0.192724i	−0.604148	+	0.796872i	$0.706486\pi$
$830$	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	$-0.854828\pi$
$839$		−	25.5143i		−	0.880850i	0.897789	−	0.440425i	$-0.145172\pi$
$840$	21.2241	−	15.1932i	0.732303	−	0.524214i
$841$		−	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	−0.848691	−	0.528889i	$-0.822609\pi$
$853$	−9.34018	+	9.34018i	−0.319802	+	0.319802i	0.528889	+	0.848691i	$0.322609\pi$
$854$	−2.35426	+	6.32684i	−0.0805612	+	0.216500i
$855$	−7.05886			−0.241408
$856$	−19.8263	−	10.7599i	−0.677650	−	0.367765i
$857$	−14.6466			−0.500317			−0.250159	−	0.968205i	$-0.580483\pi$
$857$	−14.6466			−0.500317			−0.250159	+	0.968205i	$0.580483\pi$
$858$	−1.25430	−	1.03383i	−0.0428211	−	0.0352944i
$859$	−35.4037	−	35.4037i	−1.20796	−	1.20796i	−0.971687	−	0.236272i	$-0.924074\pi$
$859$	−35.4037	−	35.4037i	−1.20796	−	1.20796i	−0.236272	−	0.971687i	$-0.575926\pi$
$860$	−12.8166	−	65.8904i	−0.437041	−	2.24684i
$861$	11.0433	−	22.7284i	0.376356	−	0.774583i
$862$	−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
$868$	7.01920	−	4.06776i	0.238247	−	0.138069i
$869$	−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
$875$	−17.9788	−	8.73558i	−0.607795	−	0.295317i
$876$	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	$0.0575335\pi$
$881$			10.6714i			0.359529i	−0.983710	+	0.179764i	$0.942466\pi$
$882$	−7.15997	+	6.83628i	−0.241089	+	0.230190i
$883$	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	$0.0222762\pi$
$887$			4.16513i			0.139852i	−0.997552	+	0.0699258i	$0.977724\pi$
$888$	−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
$896$	−25.2767	−	16.0340i	−0.844435	−	0.535658i
$897$	−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
$910$	−18.0548	−	39.4544i	−0.598511	−	1.30790i
$911$		−	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
$917$	2.23134	−	4.59236i	0.0736855	−	0.151653i
$918$	−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
$924$	−0.917241	−	1.58276i	−0.0301750	−	0.0520691i
$925$	−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	$-0.845076\pi$
$929$		−	28.5117i		−	0.935438i	0.883877	−	0.467719i	$-0.154924\pi$
$930$	7.52781	−	0.725332i	0.246847	−	0.0237846i
$931$	−1.68436	+	14.0659i	−0.0552025	+	0.460991i
$932$	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	$-0.411240\pi$
$937$	16.8510			0.550499			0.275250	+	0.961373i	$0.411240\pi$
$938$	−7.08211	+	19.0325i	−0.231239	+	0.621432i
$939$	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	0.998512	−	0.0545372i	$-0.0173683\pi$
$941$	28.9571	+	28.9571i	0.943975	+	0.943975i	−0.0545372	+	0.998512i	$0.517368\pi$
$942$	−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
$952$	31.5912	−	22.6144i	1.02388	−	0.732937i
$953$		−	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
$966$	−23.1980	−	8.63214i	−0.746383	−	0.277734i
$967$	−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	0.458971	−	0.888451i	$-0.348218\pi$
$971$	−13.3830	−	13.3830i	−0.429480	−	0.429480i	−0.888451	+	0.458971i	$0.848218\pi$
$972$	1.11817	−	1.65822i	0.0358654	−	0.0531874i
$973$	−1.37787	−	0.669479i	−0.0441723	−	0.0214625i
$974$	−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
$980$	−3.55835	−	48.7019i	−0.113667	−	1.55573i
$981$	−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	$0.0698563\pi$
$983$			13.6512i			0.435406i	−0.976015	+	0.217703i	$0.930144\pi$
$984$	−23.7429	−	12.8854i	−0.756894	−	0.410772i
$985$	−30.6266			−0.975844
$986$	−33.6275	+	40.7988i	−1.07092	+	1.29930i
$987$	8.32557	−	17.1350i	0.265006	−	0.545413i
$988$	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
$994$	25.0409	+	54.7208i	0.794250	+	1.73564i
$995$	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	$-0.479536\pi$
$997$	33.5387	−	33.5387i	1.06218	−	1.06218i	0.997934	−	0.0642464i	$-0.0204643\pi$
$998$	−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.139.16	yes	64
4.3	odd	2		1344.2.u.a.1231.15		64
7.6	odd	2	inner	336.2.u.a.139.15	✓	64
16.3	odd	4	inner	336.2.u.a.307.15	yes	64
16.13	even	4		1344.2.u.a.559.18		64
28.27	even	2		1344.2.u.a.1231.18		64
112.13	odd	4		1344.2.u.a.559.15		64
112.83	even	4	inner	336.2.u.a.307.16	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
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} +(1.55695 + 3.40234i) 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} +(-1.15626 + 2.37972i) 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} +(4.57827 - 2.65319i) 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} +(4.03302 - 8.30041i) 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} +(3.50675 + 1.30489i) 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} +(-4.35586 - 6.08494i) 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} +(-12.2315 - 4.55142i) 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} +(-0.399733 + 0.822697i) 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} +(1.36124 - 5.11342i) 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} +(-7.91168 - 3.84414i) 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} +(-6.83628 - 7.15997i) 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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