LMFDB - Embedded newform 336.2.s.c.155.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.13
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.244056 - 1.39300i) q^{2} +(0.408017 - 1.68331i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(2.26080 - 2.26080i) q^{5} +(-2.24526 - 0.979187i) q^{6} -1.00000 q^{7} +(-1.40619 + 2.45410i) q^{8} +(-2.66704 - 1.37363i) q^{9} +O(q^{10})$	\(q+(0.244056 - 1.39300i) q^{2} +(0.408017 - 1.68331i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(2.26080 - 2.26080i) q^{5} +(-2.24526 - 0.979187i) q^{6} -1.00000 q^{7} +(-1.40619 + 2.45410i) q^{8} +(-2.66704 - 1.37363i) q^{9} +(-2.59752 - 3.70105i) q^{10} +(1.82069 + 1.82069i) q^{11} +(-1.91197 + 2.88866i) q^{12} +(0.915413 - 0.915413i) q^{13} +(-0.244056 + 1.39300i) q^{14} +(-2.88318 - 4.72806i) q^{15} +(3.07537 + 2.55776i) q^{16} -2.93247i q^{17} +(-2.56438 + 3.37994i) q^{18} +(1.79372 + 1.79372i) q^{19} +(-5.78948 + 2.71507i) q^{20} +(-0.408017 + 1.68331i) q^{21} +(2.98056 - 2.09186i) q^{22} +8.77567i q^{23} +(3.55726 + 3.36837i) q^{24} -5.22244i q^{25} +(-1.05175 - 1.49858i) q^{26} +(-3.40045 + 3.92899i) q^{27} +(1.88087 + 0.679939i) q^{28} +(1.67539 + 1.67539i) q^{29} +(-7.28983 + 2.86234i) q^{30} -8.15507i q^{31} +(4.31351 - 3.65973i) q^{32} +(3.80765 - 2.32191i) q^{33} +(-4.08491 - 0.715687i) q^{34} +(-2.26080 + 2.26080i) q^{35} +(4.08239 + 4.39706i) q^{36} +(-4.29751 - 4.29751i) q^{37} +(2.93642 - 2.06088i) q^{38} +(-1.16742 - 1.91442i) q^{39} +(2.36912 + 8.72736i) q^{40} -4.52681 q^{41} +(2.24526 + 0.979187i) q^{42} +(-3.46653 + 3.46653i) q^{43} +(-2.18653 - 4.66245i) q^{44} +(-9.13517 + 2.92414i) q^{45} +(12.2245 + 2.14176i) q^{46} +8.60844 q^{47} +(5.56029 - 4.13318i) q^{48} +1.00000 q^{49} +(-7.27483 - 1.27457i) q^{50} +(-4.93624 - 1.19649i) q^{51} +(-2.34420 + 1.09935i) q^{52} +(6.48541 - 6.48541i) q^{53} +(4.64316 + 5.69570i) q^{54} +8.23243 q^{55} +(1.40619 - 2.45410i) q^{56} +(3.75125 - 2.28752i) q^{57} +(2.74270 - 1.92492i) q^{58} +(8.08166 + 8.08166i) q^{59} +(2.20809 + 10.8533i) q^{60} +(2.11377 - 2.11377i) q^{61} +(-11.3600 - 1.99030i) q^{62} +(2.66704 + 1.37363i) q^{63} +(-4.04525 - 6.90188i) q^{64} -4.13913i q^{65} +(-2.30513 - 5.87072i) q^{66} +(-2.17584 - 2.17584i) q^{67} +(-1.99390 + 5.51560i) q^{68} +(14.7721 + 3.58062i) q^{69} +(2.59752 + 3.70105i) q^{70} -4.72561i q^{71} +(7.12142 - 4.61361i) q^{72} +8.88001i q^{73} +(-7.03525 + 4.93758i) q^{74} +(-8.79096 - 2.13084i) q^{75} +(-2.15414 - 4.59338i) q^{76} +(-1.82069 - 1.82069i) q^{77} +(-2.95170 + 1.15898i) q^{78} -10.6576i q^{79} +(12.7354 - 1.17021i) q^{80} +(5.22626 + 7.32709i) q^{81} +(-1.10480 + 6.30583i) q^{82} +(-7.45604 + 7.45604i) q^{83} +(1.91197 - 2.88866i) q^{84} +(-6.62972 - 6.62972i) q^{85} +(3.98283 + 5.67489i) q^{86} +(3.50379 - 2.13661i) q^{87} +(-7.02840 + 1.90793i) q^{88} +11.6283 q^{89} +(1.84382 + 13.4389i) q^{90} +(-0.915413 + 0.915413i) q^{91} +(5.96692 - 16.5059i) q^{92} +(-13.7275 - 3.32740i) q^{93} +(2.10095 - 11.9915i) q^{94} +8.11049 q^{95} +(-4.40047 - 8.75419i) q^{96} +9.08157 q^{97} +(0.244056 - 1.39300i) q^{98} +(-2.35490 - 7.35683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * 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 $

$2$	0.244056	−	1.39300i	0.172574	−	0.984997i
$2$	0.244056	−	1.39300i	0.172574	−	0.984997i
$3$	0.408017	−	1.68331i	0.235568	−	0.971858i
$3$	0.408017	−	1.68331i	0.235568	−	0.971858i
$4$	−1.88087	−	0.679939i	−0.940436	−	0.339969i
$5$	2.26080	−	2.26080i	1.01106	−	1.01106i	0.0111224	−	0.999938i	$-0.496460\pi$
$5$	2.26080	−	2.26080i	1.01106	−	1.01106i	0.999938	−	0.0111224i	$-0.00354046\pi$
$6$	−2.24526	−	0.979187i	−0.916624	−	0.399751i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.40619	+	2.45410i	−0.497164	+	0.867657i
$9$	−2.66704	−	1.37363i	−0.889015	−	0.457878i
$10$	−2.59752	−	3.70105i	−0.821409	−	1.17037i
$11$	1.82069	+	1.82069i	0.548959	+	0.548959i	0.926140	−	0.377181i	$-0.123106\pi$
$11$	1.82069	+	1.82069i	0.548959	+	0.548959i	−0.377181	+	0.926140i	$0.623106\pi$
$12$	−1.91197	+	2.88866i	−0.551939	+	0.833884i
$13$	0.915413	−	0.915413i	0.253890	−	0.253890i	−0.568674	−	0.822563i	$-0.692543\pi$
$13$	0.915413	−	0.915413i	0.253890	−	0.253890i	0.822563	+	0.568674i	$0.192543\pi$
$14$	−0.244056	+	1.39300i	−0.0652268	+	0.372294i
$15$	−2.88318	−	4.72806i	−0.744433	−	1.22078i
$16$	3.07537	+	2.55776i	0.768842	+	0.639439i
$17$		−	2.93247i		−	0.711228i	−0.934633	−	0.355614i	$-0.884272\pi$
$17$		−	2.93247i		−	0.711228i	0.934633	−	0.355614i	$-0.115728\pi$
$18$	−2.56438	+	3.37994i	−0.604429	+	0.796659i
$19$	1.79372	+	1.79372i	0.411508	+	0.411508i	0.882264	−	0.470756i	$-0.156019\pi$
$19$	1.79372	+	1.79372i	0.411508	+	0.411508i	−0.470756	+	0.882264i	$0.656019\pi$
$20$	−5.78948	+	2.71507i	−1.29457	+	0.607109i
$21$	−0.408017	+	1.68331i	−0.0890365	+	0.367328i
$22$	2.98056	−	2.09186i	0.635459	−	0.445987i
$23$			8.77567i			1.82985i	0.403619	+	0.914927i	$0.367752\pi$
$23$			8.77567i			1.82985i	−0.403619	+	0.914927i	$0.632248\pi$
$24$	3.55726	+	3.36837i	0.726123	+	0.687565i
$25$		−	5.22244i		−	1.04449i
$26$	−1.05175	−	1.49858i	−0.206266	−	0.293895i
$27$	−3.40045	+	3.92899i	−0.654416	+	0.756134i
$28$	1.88087	+	0.679939i	0.355452	+	0.128496i
$29$	1.67539	+	1.67539i	0.311113	+	0.311113i	0.845340	−	0.534228i	$-0.179398\pi$
$29$	1.67539	+	1.67539i	0.311113	+	0.311113i	−0.534228	+	0.845340i	$0.679398\pi$
$30$	−7.28983	+	2.86234i	−1.33093	+	0.522589i
$31$		−	8.15507i		−	1.46469i	−0.680931	−	0.732347i	$-0.738425\pi$
$31$		−	8.15507i		−	1.46469i	0.680931	−	0.732347i	$-0.261575\pi$
$32$	4.31351	−	3.65973i	0.762528	−	0.646956i
$33$	3.80765	−	2.32191i	0.662827	−	0.404192i
$34$	−4.08491	−	0.715687i	−0.700557	−	0.122739i
$35$	−2.26080	+	2.26080i	−0.382145	+	0.382145i
$36$	4.08239	+	4.39706i	0.680398	+	0.732843i
$37$	−4.29751	−	4.29751i	−0.706506	−	0.706506i	0.259293	−	0.965799i	$-0.416511\pi$
$37$	−4.29751	−	4.29751i	−0.706506	−	0.706506i	−0.965799	+	0.259293i	$0.916511\pi$
$38$	2.93642	−	2.06088i	0.476349	−	0.334318i
$39$	−1.16742	−	1.91442i	−0.186936	−	0.306553i
$40$	2.36912	+	8.72736i	0.374591	+	1.37992i
$41$	−4.52681			−0.706969			−0.353484	−	0.935440i	$-0.615003\pi$
$41$	−4.52681			−0.706969			−0.353484	+	0.935440i	$0.615003\pi$
$42$	2.24526	+	0.979187i	0.346451	+	0.151092i
$43$	−3.46653	+	3.46653i	−0.528641	+	0.528641i	−0.920167	−	0.391526i	$-0.871947\pi$
$43$	−3.46653	+	3.46653i	−0.528641	+	0.528641i	0.391526	+	0.920167i	$0.371947\pi$
$44$	−2.18653	−	4.66245i	−0.329632	−	0.702890i
$45$	−9.13517	+	2.92414i	−1.36179	+	0.435905i
$46$	12.2245	+	2.14176i	1.80240	+	0.315785i
$47$	8.60844			1.25567			0.627835	−	0.778346i	$-0.283941\pi$
$47$	8.60844			1.25567			0.627835	+	0.778346i	$0.283941\pi$
$48$	5.56029	−	4.13318i	0.802559	−	0.596573i
$49$	1.00000			0.142857
$50$	−7.27483	−	1.27457i	−1.02882	−	0.180251i
$51$	−4.93624	−	1.19649i	−0.691212	−	0.167543i
$52$	−2.34420	+	1.09935i	−0.325082	+	0.152452i
$53$	6.48541	−	6.48541i	0.890840	−	0.890840i	−0.103762	−	0.994602i	$-0.533088\pi$
$53$	6.48541	−	6.48541i	0.890840	−	0.890840i	0.994602	+	0.103762i	$0.0330880\pi$
$54$	4.64316	+	5.69570i	0.631855	+	0.775087i
$55$	8.23243			1.11006
$56$	1.40619	−	2.45410i	0.187910	−	0.327943i
$57$	3.75125	−	2.28752i	0.496866	−	0.302989i
$58$	2.74270	−	1.92492i	0.360135	−	0.252755i
$59$	8.08166	+	8.08166i	1.05214	+	1.05214i	0.998564	+	0.0535782i	$0.0170627\pi$
$59$	8.08166	+	8.08166i	1.05214	+	1.05214i	0.0535782	+	0.998564i	$0.482937\pi$
$60$	2.20809	+	10.8533i	0.285064	+	1.40115i
$61$	2.11377	−	2.11377i	0.270641	−	0.270641i	−0.558717	−	0.829358i	$-0.688706\pi$
$61$	2.11377	−	2.11377i	0.270641	−	0.270641i	0.829358	+	0.558717i	$0.188706\pi$
$62$	−11.3600	−	1.99030i	−1.44272	−	0.252768i
$63$	2.66704	+	1.37363i	0.336016	+	0.173062i
$64$	−4.04525	−	6.90188i	−0.505657	−	0.862735i
$65$		−	4.13913i		−	0.513396i
$66$	−2.30513	−	5.87072i	−0.283741	−	0.722636i
$67$	−2.17584	−	2.17584i	−0.265821	−	0.265821i	0.561593	−	0.827414i	$-0.310189\pi$
$67$	−2.17584	−	2.17584i	−0.265821	−	0.265821i	−0.827414	+	0.561593i	$0.810189\pi$
$68$	−1.99390	+	5.51560i	−0.241796	+	0.668864i
$69$	14.7721	+	3.58062i	1.77836	+	0.431056i
$70$	2.59752	+	3.70105i	0.310463	+	0.442360i
$71$		−	4.72561i		−	0.560827i	−0.959879	−	0.280413i	$-0.909528\pi$
$71$		−	4.72561i		−	0.560827i	0.959879	−	0.280413i	$-0.0904715\pi$
$72$	7.12142	−	4.61361i	0.839267	−	0.543720i
$73$			8.88001i			1.03933i	0.854371	+	0.519663i	$0.173942\pi$
$73$			8.88001i			1.03933i	−0.854371	+	0.519663i	$0.826058\pi$
$74$	−7.03525	+	4.93758i	−0.817831	+	0.573982i
$75$	−8.79096	−	2.13084i	−1.01509	−	0.246048i
$76$	−2.15414	−	4.59338i	−0.247097	−	0.526897i
$77$	−1.82069	−	1.82069i	−0.207487	−	0.207487i
$78$	−2.95170	+	1.15898i	−0.334214	+	0.131229i
$79$		−	10.6576i		−	1.19907i	−0.800349	−	0.599535i	$-0.795352\pi$
$79$		−	10.6576i		−	1.19907i	0.800349	−	0.599535i	$-0.204648\pi$
$80$	12.7354	−	1.17021i	1.42386	−	0.130833i
$81$	5.22626	+	7.32709i	0.580695	+	0.814121i
$82$	−1.10480	+	6.30583i	−0.122004	+	0.696362i
$83$	−7.45604	+	7.45604i	−0.818407	+	0.818407i	−0.985877	−	0.167470i	$-0.946440\pi$
$83$	−7.45604	+	7.45604i	−0.818407	+	0.818407i	0.167470	+	0.985877i	$0.446440\pi$
$84$	1.91197	−	2.88866i	0.208613	−	0.315179i
$85$	−6.62972	−	6.62972i	−0.719094	−	0.719094i
$86$	3.98283	+	5.67489i	0.429480	+	0.611939i
$87$	3.50379	−	2.13661i	0.375646	−	0.229069i
$88$	−7.02840	+	1.90793i	−0.749230	+	0.203386i
$89$	11.6283			1.23260			0.616298	−	0.787513i	$-0.288632\pi$
$89$	11.6283			1.23260			0.616298	+	0.787513i	$0.288632\pi$
$90$	1.84382	+	13.4389i	0.194356	+	1.41658i
$91$	−0.915413	+	0.915413i	−0.0959613	+	0.0959613i
$92$	5.96692	−	16.5059i	0.622094	−	1.72086i
$93$	−13.7275	−	3.32740i	−1.42347	−	0.345036i
$94$	2.10095	−	11.9915i	0.216696	−	1.23683i
$95$	8.11049			0.832119
$96$	−4.40047	−	8.75419i	−0.449121	−	0.893471i
$97$	9.08157			0.922094			0.461047	−	0.887376i	$-0.347474\pi$
$97$	9.08157			0.922094			0.461047	+	0.887376i	$0.347474\pi$
$98$	0.244056	−	1.39300i	0.0246534	−	0.140714i
$99$	−2.35490	−	7.35683i	−0.236676	−	0.739389i
$100$	−3.55094	+	9.82274i	−0.355094	+	0.982274i
$101$	4.72687	−	4.72687i	0.470341	−	0.470341i	−0.431684	−	0.902025i	$-0.642080\pi$
$101$	4.72687	−	4.72687i	0.470341	−	0.470341i	0.902025	+	0.431684i	$0.142080\pi$
$102$	−2.87143	+	6.58415i	−0.284314	+	0.651928i
$103$	−14.7866			−1.45696			−0.728482	−	0.685065i	$-0.759774\pi$
$103$	−14.7866			−1.45696			−0.728482	+	0.685065i	$0.759774\pi$
$104$	0.959273	+	3.53376i	0.0940644	+	0.346514i
$105$	2.88318	+	4.72806i	0.281369	+	0.461412i
$106$	−7.45135	−	10.6170i	−0.723739	−	1.03121i
$107$	−9.12369	−	9.12369i	−0.882020	−	0.882020i	0.111719	−	0.993740i	$-0.464364\pi$
$107$	−9.12369	−	9.12369i	−0.882020	−	0.882020i	−0.993740	+	0.111719i	$0.964364\pi$
$108$	9.06728	−	5.07783i	0.872500	−	0.488615i
$109$	7.45700	−	7.45700i	0.714251	−	0.714251i	−0.253171	−	0.967422i	$-0.581473\pi$
$109$	7.45700	−	7.45700i	0.714251	−	0.714251i	0.967422	+	0.253171i	$0.0814734\pi$
$110$	2.00918	−	11.4677i	0.191568	−	1.09341i
$111$	−8.98748	+	5.48057i	−0.853054	+	0.520193i
$112$	−3.07537	−	2.55776i	−0.290595	−	0.241685i
$113$			18.9798i			1.78547i	0.450580	+	0.892736i	$0.351217\pi$
$113$			18.9798i			1.78547i	−0.450580	+	0.892736i	$0.648783\pi$
$114$	−2.27098	−	5.78376i	−0.212697	−	0.541699i
$115$	19.8400	+	19.8400i	1.85009	+	1.85009i
$116$	−2.01204	−	4.29037i	−0.186813	−	0.398350i
$117$	−3.69889	+	1.18400i	−0.341962	+	0.109461i
$118$	13.2301	−	9.28533i	1.21793	−	0.854784i
$119$			2.93247i			0.268819i
$120$	15.6575	−	0.427054i	1.42932	−	0.0389845i
$121$		−	4.37017i		−	0.397288i
$122$	−2.42860	−	3.46036i	−0.219875	−	0.313286i
$123$	−1.84701	+	7.62001i	−0.166540	+	0.687073i
$124$	−5.54495	+	15.3387i	−0.497951	+	1.37745i
$125$	−0.502881	−	0.502881i	−0.0449791	−	0.0449791i
$126$	2.56438	−	3.37994i	0.228453	−	0.301109i
$127$			20.6001i			1.82796i	0.405757	+	0.913981i	$0.367008\pi$
$127$			20.6001i			1.82796i	−0.405757	+	0.913981i	$0.632992\pi$
$128$	−10.6016	+	3.95057i	−0.937054	+	0.349185i
$129$	4.42083	+	7.24964i	0.389233	+	0.638295i
$130$	−5.76579	−	1.01018i	−0.505693	−	0.0885987i
$131$	−8.07416	+	8.07416i	−0.705443	+	0.705443i	−0.965573	−	0.260131i	$-0.916234\pi$
$131$	−8.07416	+	8.07416i	−0.705443	+	0.705443i	0.260131	+	0.965573i	$0.416234\pi$
$132$	−8.74047	+	1.77824i	−0.760760	+	0.154776i
$133$	−1.79372	−	1.79372i	−0.155535	−	0.155535i
$134$	−3.56196	+	2.49990i	−0.307706	+	0.215959i
$135$	1.19493	+	16.5704i	0.102843	+	1.42615i
$136$	7.19658	+	4.12361i	0.617101	+	0.353596i
$137$	−5.22066			−0.446031			−0.223016	−	0.974815i	$-0.571590\pi$
$137$	−5.22066			−0.446031			−0.223016	+	0.974815i	$0.571590\pi$
$138$	8.59302	−	19.7037i	0.731487	−	1.67729i
$139$	−11.9868	+	11.9868i	−1.01671	+	1.01671i	−0.0168474	+	0.999858i	$0.505363\pi$
$139$	−11.9868	+	11.9868i	−1.01671	+	1.01671i	−0.999858	+	0.0168474i	$0.994637\pi$
$140$	5.78948	−	2.71507i	0.489301	−	0.229465i
$141$	3.51239	−	14.4907i	0.295796	−	1.22033i
$142$	−6.58275	−	1.15332i	−0.552412	−	0.0967840i
$143$	3.33337			0.278750
$144$	−4.68872	−	11.0461i	−0.390726	−	0.920507i
$145$	7.57546			0.629107
$146$	12.3698	+	2.16722i	1.02373	+	0.179361i
$147$	0.408017	−	1.68331i	0.0336526	−	0.138837i
$148$	5.16103	+	11.0051i	0.424234	+	0.904615i
$149$	−11.7493	+	11.7493i	−0.962540	+	0.962540i	−0.999323	−	0.0367834i	$-0.988289\pi$
$149$	−11.7493	+	11.7493i	−0.962540	+	0.962540i	0.0367834	+	0.999323i	$0.488289\pi$
$150$	−5.11374	+	11.7257i	−0.417535	+	0.957401i
$151$	8.14983			0.663223			0.331612	−	0.943416i	$-0.392408\pi$
$151$	8.14983			0.663223			0.331612	+	0.943416i	$0.392408\pi$
$152$	−6.92429	+	1.87966i	−0.561634	+	0.152461i
$153$	−4.02814	+	7.82102i	−0.325656	+	0.632292i
$154$	−2.98056	+	2.09186i	−0.240181	+	0.168567i
$155$	−18.4370	−	18.4370i	−1.48089	−	1.48089i
$156$	0.894071	+	4.39456i	0.0715830	+	0.351846i
$157$	−10.7876	+	10.7876i	−0.860946	+	0.860946i	−0.991448	−	0.130502i	$-0.958341\pi$
$157$	−10.7876	+	10.7876i	−0.860946	+	0.860946i	0.130502	+	0.991448i	$0.458341\pi$
$158$	−14.8459	−	2.60105i	−1.18108	−	0.206928i
$159$	−8.27079	−	13.5631i	−0.655916	−	1.07562i
$160$	1.47805	−	18.0259i	0.116850	−	1.42507i
$161$		−	8.77567i		−	0.691620i
$162$	11.4821	−	5.49193i	0.902119	−	0.431487i
$163$	−2.26578	−	2.26578i	−0.177469	−	0.177469i	0.612782	−	0.790252i	$-0.290050\pi$
$163$	−2.26578	−	2.26578i	−0.177469	−	0.177469i	−0.790252	+	0.612782i	$0.790050\pi$
$164$	8.51435	+	3.07795i	0.664859	+	0.240348i
$165$	3.35897	−	13.8577i	0.261495	−	1.07882i
$166$	8.56654	+	12.2059i	0.664893	+	0.947364i
$167$		−	15.2783i		−	1.18227i	−0.806574	−	0.591133i	$-0.798681\pi$
$167$		−	15.2783i		−	1.18227i	0.806574	−	0.591133i	$-0.201319\pi$
$168$	−3.55726	−	3.36837i	−0.274449	−	0.259875i
$169$			11.3240i			0.871080i
$170$	−10.8532	+	7.61715i	−0.832402	+	0.584208i
$171$	−2.32002	−	7.24785i	−0.177416	−	0.554257i
$172$	8.87713	−	4.16307i	0.676875	−	0.317431i
$173$	12.5993	+	12.5993i	0.957903	+	0.957903i	0.999149	−	0.0412456i	$-0.0131326\pi$
$173$	12.5993	+	12.5993i	0.957903	+	0.957903i	−0.0412456	+	0.999149i	$0.513133\pi$
$174$	−2.12117	−	5.40222i	−0.160805	−	0.409541i
$175$			5.22244i			0.394779i
$176$	0.942405	+	10.2562i	0.0710365	+	0.773088i
$177$	16.9014	−	10.3065i	1.27038	−	0.774681i
$178$	2.83796	−	16.1982i	0.212714	−	1.21410i
$179$	−0.354922	+	0.354922i	−0.0265281	+	0.0265281i	−0.720246	−	0.693718i	$-0.755971\pi$
$179$	−0.354922	+	0.354922i	−0.0265281	+	0.0265281i	0.693718	+	0.720246i	$0.255971\pi$
$180$	19.1703	+	0.711415i	1.42887	+	0.0530258i
$181$	−3.95505	−	3.95505i	−0.293976	−	0.293976i	0.544672	−	0.838649i	$-0.316654\pi$
$181$	−3.95505	−	3.95505i	−0.293976	−	0.293976i	−0.838649	+	0.544672i	$0.816654\pi$
$182$	1.05175	+	1.49858i	0.0779611	+	0.111082i
$183$	−2.69568	−	4.42059i	−0.199270	−	0.326779i
$184$	−21.5364	−	12.3403i	−1.58769	−	0.909737i
$185$	−19.4316			−1.42864
$186$	−7.98534	+	18.3103i	−0.585514	+	1.34257i
$187$	5.33911	−	5.33911i	0.390435	−	0.390435i
$188$	−16.1914	−	5.85321i	−1.18088	−	0.426890i
$189$	3.40045	−	3.92899i	0.247346	−	0.285792i
$190$	1.97942	−	11.2979i	0.143602	−	0.819634i
$191$	11.1317			0.805460			0.402730	−	0.915319i	$-0.368061\pi$
$191$	11.1317			0.805460			0.402730	+	0.915319i	$0.368061\pi$
$192$	−13.2685	+	3.99332i	−0.957572	+	0.288193i
$193$	−24.2243			−1.74370			−0.871852	−	0.489769i	$-0.837081\pi$
$193$	−24.2243			−1.74370			−0.871852	+	0.489769i	$0.837081\pi$
$194$	2.21641	−	12.6506i	0.159129	−	0.908259i
$195$	−6.96743	−	1.68883i	−0.498948	−	0.120940i
$196$	−1.88087	−	0.679939i	−0.134348	−	0.0485671i
$197$	−11.9310	+	11.9310i	−0.850048	+	0.850048i	−0.990139	−	0.140091i	$-0.955261\pi$
$197$	−11.9310	+	11.9310i	−0.850048	+	0.850048i	0.140091	+	0.990139i	$0.455261\pi$
$198$	−10.8228	+	1.48488i	−0.769140	+	0.105526i
$199$	−5.66656			−0.401692			−0.200846	−	0.979623i	$-0.564369\pi$
$199$	−5.66656			−0.401692			−0.200846	+	0.979623i	$0.564369\pi$
$200$	12.8164	+	7.34374i	0.906256	+	0.519281i
$201$	−4.55038	+	2.77482i	−0.320959	+	0.195721i
$202$	−5.43088	−	7.73813i	−0.382116	−	0.544453i
$203$	−1.67539	−	1.67539i	−0.117590	−	0.117590i
$204$	8.47090	+	5.60680i	0.593082	+	0.392554i
$205$	−10.2342	+	10.2342i	−0.714788	+	0.714788i
$206$	−3.60876	+	20.5976i	−0.251434	+	1.43510i
$207$	12.0546	−	23.4051i	0.837850	−	1.62677i
$208$	5.15663	−	0.473825i	0.357548	−	0.0328539i
$209$			6.53162i			0.451802i
$210$	7.28983	−	2.86234i	0.503046	−	0.197520i
$211$	11.8208	+	11.8208i	0.813776	+	0.813776i	0.985198	−	0.171422i	$-0.0548362\pi$
$211$	11.8208	+	11.8208i	0.813776	+	0.813776i	−0.171422	+	0.985198i	$0.554836\pi$
$212$	−16.6079	+	7.78855i	−1.14064	+	0.534920i
$213$	−7.95465	−	1.92813i	−0.545044	−	0.132113i
$214$	−14.9360	+	10.4826i	−1.02100	+	0.716573i
$215$			15.6743i			1.06898i
$216$	−4.86047	−	13.8700i	−0.330713	−	0.943731i
$217$			8.15507i			0.553602i
$218$	−8.56764	−	12.2075i	−0.580274	−	0.826796i
$219$	14.9478	+	3.62319i	1.01008	+	0.244832i
$220$	−15.4842	−	5.59755i	−1.04394	−	0.377387i
$221$	−2.68442	−	2.68442i	−0.180573	−	0.180573i
$222$	5.44096	+	13.8571i	0.365173	+	0.930027i
$223$		−	6.81157i		−	0.456136i	−0.973645	−	0.228068i	$-0.926759\pi$
$223$		−	6.81157i		−	0.456136i	0.973645	−	0.228068i	$-0.0732409\pi$
$224$	−4.31351	+	3.65973i	−0.288208	+	0.244526i
$225$	−7.17372	+	13.9285i	−0.478248	+	0.928565i
$226$	26.4388	+	4.63215i	1.75868	+	0.308126i
$227$	−0.205032	+	0.205032i	−0.0136084	+	0.0136084i	−0.713878	−	0.700270i	$-0.753063\pi$
$227$	−0.205032	+	0.205032i	−0.0136084	+	0.0136084i	0.700270	+	0.713878i	$0.253063\pi$
$228$	−8.61100	+	1.75190i	−0.570277	+	0.116023i
$229$	−13.3965	−	13.3965i	−0.885266	−	0.885266i	0.108798	−	0.994064i	$-0.465300\pi$
$229$	−13.3965	−	13.3965i	−0.885266	−	0.885266i	−0.994064	+	0.108798i	$0.965300\pi$
$230$	32.4792	−	22.7950i	2.14161	−	1.50306i
$231$	−3.80765	+	2.32191i	−0.250525	+	0.152770i
$232$	−6.46751	+	1.75567i	−0.424613	+	0.115265i
$233$	6.01646			0.394151			0.197076	−	0.980388i	$-0.436856\pi$
$233$	6.01646			0.394151			0.197076	+	0.980388i	$0.436856\pi$
$234$	0.746575	+	5.44150i	0.0488052	+	0.355722i
$235$	19.4620	−	19.4620i	1.26956	−	1.26956i
$236$	−9.70553	−	20.6956i	−0.631776	−	1.34717i
$237$	−17.9399	−	4.34846i	−1.16532	−	0.282463i
$238$	4.08491	+	0.715687i	0.264786	+	0.0463911i
$239$	6.89526			0.446017			0.223009	−	0.974816i	$-0.428412\pi$
$239$	6.89526			0.446017			0.223009	+	0.974816i	$0.428412\pi$
$240$	3.22642	−	21.9150i	0.208264	−	1.41461i
$241$	10.9906			0.707966			0.353983	−	0.935252i	$-0.384827\pi$
$241$	10.9906			0.707966			0.353983	+	0.935252i	$0.384827\pi$
$242$	−6.08763	−	1.06657i	−0.391328	−	0.0685616i
$243$	14.4661	−	5.80782i	0.928003	−	0.372572i
$244$	−5.41298	+	2.53850i	−0.346530	+	0.162511i
$245$	2.26080	−	2.26080i	0.144437	−	0.144437i
$246$	10.1639	+	4.43259i	0.648024	+	0.282612i
$247$	3.28399			0.208955
$248$	20.0134	+	11.4676i	1.27085	+	0.728193i
$249$	9.50862	+	15.5930i	0.602584	+	0.988166i
$250$	−0.823243	+	0.577780i	−0.0520664	+	0.0365420i
$251$	11.8940	+	11.8940i	0.750744	+	0.750744i	0.974618	−	0.223874i	$-0.0718706\pi$
$251$	11.8940	+	11.8940i	0.750744	+	0.750744i	−0.223874	+	0.974618i	$0.571871\pi$
$252$	−4.08239	−	4.39706i	−0.257166	−	0.276989i
$253$	−15.9778	+	15.9778i	−1.00451	+	1.00451i
$254$	28.6958	+	5.02758i	1.80054	+	0.315459i
$255$	−13.8649	+	8.45482i	−0.868253	+	0.529461i
$256$	2.91575	+	15.7321i	0.182235	+	0.983255i
$257$		−	14.6730i		−	0.915275i	−0.889139	−	0.457637i	$-0.848696\pi$
$257$		−	14.6730i		−	0.915275i	0.889139	−	0.457637i	$-0.151304\pi$
$258$	11.1776	−	4.38888i	0.695890	−	0.273240i
$259$	4.29751	+	4.29751i	0.267034	+	0.267034i
$260$	−2.81436	+	7.78518i	−0.174539	+	0.482816i
$261$	−2.16697	−	6.76972i	−0.134132	−	0.419035i
$262$	9.27672	+	13.2178i	0.573118	+	0.816600i
$263$		−	20.4151i		−	1.25885i	−0.777061	−	0.629425i	$-0.783290\pi$
$263$		−	20.4151i		−	1.25885i	0.777061	−	0.629425i	$-0.216710\pi$
$264$	0.343920	+	12.6094i	0.0211668	+	0.776056i
$265$		−	29.3245i		−	1.80139i
$266$	−2.93642	+	2.06088i	−0.180043	+	0.126360i
$267$	4.74454	−	19.5740i	0.290361	−	1.19791i
$268$	2.61304	+	5.57191i	0.159617	+	0.340359i
$269$	18.6963	+	18.6963i	1.13993	+	1.13993i	0.988462	+	0.151469i	$0.0484004\pi$
$269$	18.6963	+	18.6963i	1.13993	+	1.13993i	0.151469	+	0.988462i	$0.451600\pi$
$270$	23.3741	+	2.37958i	1.42250	+	0.144817i
$271$			5.42038i			0.329265i	0.986355	+	0.164632i	$0.0526438\pi$
$271$			5.42038i			0.329265i	−0.986355	+	0.164632i	$0.947356\pi$
$272$	7.50054	−	9.01841i	0.454787	−	0.546821i
$273$	1.16742	+	1.91442i	0.0706553	+	0.115866i
$274$	−1.27414	+	7.27236i	−0.0769733	+	0.439339i
$275$	9.50844	−	9.50844i	0.573380	−	0.573380i
$276$	−25.3499	−	16.7788i	−1.52589	−	1.00997i
$277$	−5.12370	−	5.12370i	−0.307854	−	0.307854i	0.536223	−	0.844076i	$-0.319851\pi$
$277$	−5.12370	−	5.12370i	−0.307854	−	0.307854i	−0.844076	+	0.536223i	$0.819851\pi$
$278$	13.7721	+	19.6230i	0.825995	+	1.17691i
$279$	−11.2021	+	21.7499i	−0.670651	+	1.30214i
$280$	−2.36912	−	8.72736i	−0.141582	−	0.521559i
$281$	5.35336			0.319355			0.159677	−	0.987169i	$-0.448955\pi$
$281$	5.35336			0.319355			0.159677	+	0.987169i	$0.448955\pi$
$282$	−19.3282	−	8.42928i	−1.15098	−	0.501956i
$283$	−10.6748	+	10.6748i	−0.634552	+	0.634552i	−0.949206	−	0.314654i	$-0.898111\pi$
$283$	−10.6748	+	10.6748i	−0.634552	+	0.634552i	0.314654	+	0.949206i	$0.398111\pi$
$284$	−3.21313	+	8.88827i	−0.190664	+	0.527422i
$285$	3.30922	−	13.6524i	0.196021	−	0.808701i
$286$	0.813529	−	4.64336i	0.0481050	−	0.274568i
$287$	4.52681			0.267209
$288$	−16.5315	+	3.83549i	−0.974125	+	0.226009i
$289$	8.40064			0.494155
$290$	1.84884	−	10.5526i	0.108568	−	0.619669i
$291$	3.70543	−	15.2871i	0.217216	−	0.896144i
$292$	6.03786	−	16.7022i	0.353339	−	0.977420i
$293$	0.265538	−	0.265538i	0.0155129	−	0.0155129i	−0.699308	−	0.714821i	$-0.746508\pi$
$293$	0.265538	−	0.265538i	0.0155129	−	0.0155129i	0.714821	+	0.699308i	$0.246508\pi$
$294$	−2.24526	−	0.979187i	−0.130946	−	0.0571074i
$295$	36.5420			2.12756
$296$	16.5897	−	4.50342i	0.964254	−	0.261756i
$297$	−13.3446	+	0.962313i	−0.774334	+	0.0558391i
$298$	13.4992	+	19.2342i	0.781989	+	1.11421i
$299$	8.03336	+	8.03336i	0.464581	+	0.464581i
$300$	15.0858	+	9.98516i	0.870981	+	0.576493i
$301$	3.46653	−	3.46653i	0.199808	−	0.199808i
$302$	1.98902	−	11.3527i	0.114455	−	0.653273i
$303$	−6.02813	−	9.88541i	−0.346307	−	0.567902i
$304$	0.928446	+	10.1043i	0.0532500	+	0.579519i
$305$		−	9.55764i		−	0.547269i
$306$	9.91155	+	7.51995i	0.566606	+	0.429887i
$307$	−7.28530	−	7.28530i	−0.415794	−	0.415794i	0.467957	−	0.883751i	$-0.344990\pi$
$307$	−7.28530	−	7.28530i	−0.415794	−	0.415794i	−0.883751	+	0.467957i	$0.844990\pi$
$308$	2.18653	+	4.66245i	0.124589	+	0.265667i
$309$	−6.03317	+	24.8903i	−0.343215	+	1.41596i
$310$	−30.1823	+	21.1830i	−1.71424	+	1.20311i
$311$		−	12.0885i		−	0.685473i	−0.939432	−	0.342737i	$-0.888646\pi$
$311$		−	12.0885i		−	0.685473i	0.939432	−	0.342737i	$-0.111354\pi$
$312$	6.33981	−	0.172917i	0.358921	−	0.00978950i
$313$			0.942109i			0.0532511i	0.999645	+	0.0266256i	$0.00847618\pi$
$313$			0.942109i			0.0532511i	−0.999645	+	0.0266256i	$0.991524\pi$
$314$	12.3943	+	17.6599i	0.699452	+	0.996605i
$315$	9.13517	−	2.92414i	0.514708	−	0.164757i
$316$	−7.24649	+	20.0455i	−0.407647	+	1.12765i
$317$	−3.95890	−	3.95890i	−0.222354	−	0.222354i	0.587135	−	0.809489i	$-0.300256\pi$
$317$	−3.95890	−	3.95890i	−0.222354	−	0.222354i	−0.809489	+	0.587135i	$0.800256\pi$
$318$	−20.9119	+	8.21101i	−1.17268	+	0.460450i
$319$			6.10074i			0.341576i
$320$	−24.7493	−	6.45826i	−1.38353	−	0.361027i
$321$	−19.0806	+	11.6354i	−1.06497	+	0.649422i
$322$	−12.2245	−	2.14176i	−0.681243	−	0.119356i
$323$	5.26003	−	5.26003i	0.292676	−	0.292676i
$324$	−4.84795	−	17.3349i	−0.269331	−	0.963048i
$325$	−4.78068	−	4.78068i	−0.265185	−	0.265185i
$326$	−3.70920	+	2.60324i	−0.205433	+	0.144180i
$327$	−9.50984	−	15.5950i	−0.525895	−	0.862405i
$328$	6.36556	−	11.1093i	0.351479	−	0.613406i
$329$	−8.60844			−0.474599
$330$	−18.4840	−	8.06109i	−1.01751	−	0.443749i
$331$	−16.3244	+	16.3244i	−0.897271	+	0.897271i	−0.995194	−	0.0979228i	$-0.968780\pi$
$331$	−16.3244	+	16.3244i	−0.897271	+	0.897271i	0.0979228	+	0.995194i	$0.468780\pi$
$332$	19.0935	−	8.95422i	1.04789	−	0.491427i
$333$	5.55844	+	17.3649i	0.304601	+	0.951588i
$334$	−21.2825	−	3.72876i	−1.16453	−	0.204028i
$335$	−9.83827			−0.537522
$336$	−5.56029	+	4.13318i	−0.303339	+	0.225483i
$337$	−18.4456			−1.00480			−0.502398	−	0.864636i	$-0.667549\pi$
$337$	−18.4456			−1.00480			−0.502398	+	0.864636i	$0.667549\pi$
$338$	15.7743	+	2.76370i	0.858011	+	0.150326i
$339$	31.9489	+	7.74409i	1.73523	+	0.420601i
$340$	7.96186	+	16.9775i	0.431792	+	0.920732i
$341$	14.8479	−	14.8479i	0.804057	−	0.804057i
$342$	−10.6624	+	1.46289i	−0.576559	+	0.0791040i
$343$	−1.00000			−0.0539949
$344$	−3.63262	−	13.3818i	−0.195858	−	0.721500i
$345$	41.4919	−	25.3018i	2.23385	−	1.36220i
$346$	20.6256	−	14.4758i	1.10884	−	0.778222i
$347$	4.16277	+	4.16277i	0.223469	+	0.223469i	0.809958	−	0.586488i	$-0.199490\pi$
$347$	4.16277	+	4.16277i	0.223469	+	0.223469i	−0.586488	+	0.809958i	$0.699490\pi$
$348$	−8.04295	+	1.63633i	−0.431147	+	0.0877167i
$349$	−1.74656	+	1.74656i	−0.0934910	+	0.0934910i	−0.752305	−	0.658814i	$-0.771058\pi$
$349$	−1.74656	+	1.74656i	−0.0934910	+	0.0934910i	0.658814	+	0.752305i	$0.271058\pi$
$350$	7.27483	+	1.27457i	0.388856	+	0.0681286i
$351$	0.483835	+	6.70946i	0.0258252	+	0.358124i
$352$	14.5168	+	1.19032i	0.773748	+	0.0634442i
$353$		−	12.3621i		−	0.657967i	−0.944336	−	0.328983i	$-0.893294\pi$
$353$		−	12.3621i		−	0.657967i	0.944336	−	0.328983i	$-0.106706\pi$
$354$	−10.2320	−	26.0589i	−0.543823	−	1.38501i
$355$	−10.6837	−	10.6837i	−0.567030	−	0.567030i
$356$	−21.8713	−	7.90653i	−1.15918	−	0.419045i
$357$	4.93624	+	1.19649i	0.261254	+	0.0633252i
$358$	0.407784	+	0.581026i	0.0215521	+	0.0307082i
$359$		−	16.2343i		−	0.856814i	−0.903586	−	0.428407i	$-0.859075\pi$
$359$		−	16.2343i		−	0.856814i	0.903586	−	0.428407i	$-0.140925\pi$
$360$	5.66964	−	26.5306i	0.298816	−	1.39828i
$361$		−	12.5651i		−	0.661322i
$362$	−6.47462	+	4.54411i	−0.340299	+	0.238833i
$363$	−7.35634	−	1.78310i	−0.386108	−	0.0935886i
$364$	2.34420	−	1.09935i	0.122869	−	0.0576216i
$365$	20.0759	+	20.0759i	1.05082	+	1.05082i
$366$	−6.81575	+	2.67619i	−0.356265	+	0.139887i
$367$		−	25.8770i		−	1.35077i	−0.737465	−	0.675385i	$-0.763977\pi$
$367$		−	25.8770i		−	1.35077i	0.737465	−	0.675385i	$-0.236023\pi$
$368$	−22.4460	+	26.9884i	−1.17008	+	1.40687i
$369$	12.0732	+	6.21818i	0.628506	+	0.323706i
$370$	−4.74241	+	27.0682i	−0.246546	+	1.40721i
$371$	−6.48541	+	6.48541i	−0.336706	+	0.336706i
$372$	23.5572	+	15.5923i	1.22139	+	0.808422i
$373$	26.0420	+	26.0420i	1.34841	+	1.34841i	0.887394	+	0.461011i	$0.152513\pi$
$373$	26.0420	+	26.0420i	1.34841	+	1.34841i	0.461011	+	0.887394i	$0.347487\pi$
$374$	−6.13432	−	8.74041i	−0.317198	−	0.451956i
$375$	−1.05169	+	0.641320i	−0.0543089	+	0.0331176i
$376$	−12.1051	+	21.1260i	−0.624274	+	1.08949i
$377$	3.06735			0.157977
$378$	−4.64316	−	5.69570i	−0.238819	−	0.292955i
$379$	5.51674	−	5.51674i	0.283376	−	0.283376i	−0.551078	−	0.834454i	$-0.685783\pi$
$379$	5.51674	−	5.51674i	0.283376	−	0.283376i	0.834454	+	0.551078i	$0.185783\pi$
$380$	−15.2548	−	5.51464i	−0.782555	−	0.282895i
$381$	34.6763	+	8.40518i	1.77652	+	0.430610i
$382$	2.71676	−	15.5064i	0.139001	−	0.793375i
$383$	10.8580			0.554818			0.277409	−	0.960752i	$-0.410524\pi$
$383$	10.8580			0.554818			0.277409	+	0.960752i	$0.410524\pi$
$384$	2.32442	+	19.4576i	0.118617	+	0.992940i
$385$	−8.23243			−0.419564
$386$	−5.91210	+	33.7444i	−0.300918	+	1.71754i
$387$	14.0071	−	4.48365i	0.712023	−	0.227917i
$388$	−17.0813	−	6.17491i	−0.867170	−	0.313484i
$389$	−18.0972	+	18.0972i	−0.917566	+	0.917566i	−0.996852	−	0.0792861i	$-0.974736\pi$
$389$	−18.0972	+	18.0972i	−0.917566	+	0.917566i	0.0792861	+	0.996852i	$0.474736\pi$
$390$	−4.05298	+	9.29342i	−0.205231	+	0.470591i
$391$	25.7344			1.30144
$392$	−1.40619	+	2.45410i	−0.0710234	+	0.123951i
$393$	10.2969	+	16.8857i	0.519410	+	0.851770i
$394$	13.7080	+	19.5317i	0.690598	+	0.983991i
$395$	−24.0946	−	24.0946i	−1.21233	−	1.21233i
$396$	−0.572924	+	15.4384i	−0.0287905	+	0.775811i
$397$	12.4866	−	12.4866i	0.626683	−	0.626683i	−0.320549	−	0.947232i	$-0.603867\pi$
$397$	12.4866	−	12.4866i	0.626683	−	0.626683i	0.947232	+	0.320549i	$0.103867\pi$
$398$	−1.38296	+	7.89349i	−0.0693215	+	0.395665i
$399$	−3.75125	+	2.28752i	−0.187798	+	0.114519i
$400$	13.3577	−	16.0609i	0.667886	−	0.803045i
$401$			3.80237i			0.189881i	0.995483	+	0.0949406i	$0.0302661\pi$
$401$			3.80237i			0.189881i	−0.995483	+	0.0949406i	$0.969734\pi$
$402$	2.75477	+	7.01587i	0.137395	+	0.349920i
$403$	−7.46526	−	7.46526i	−0.371871	−	0.371871i
$404$	−12.1046	+	5.67666i	−0.602227	+	0.282424i
$405$	28.3806	+	4.74956i	1.41024	+	0.236008i
$406$	−2.74270	+	1.92492i	−0.136118	+	0.0955324i
$407$		−	15.6489i		−	0.775686i
$408$	9.87762	−	10.4315i	0.489015	−	0.516439i
$409$		−	8.52624i		−	0.421595i	−0.977530	−	0.210798i	$-0.932394\pi$
$409$		−	8.52624i		−	0.421595i	0.977530	−	0.210798i	$-0.0676061\pi$
$410$	11.7585	+	16.7539i	0.580710	+	0.827418i
$411$	−2.13012	+	8.78797i	−0.105071	+	0.433479i
$412$	27.8117	+	10.0540i	1.37018	+	0.495323i
$413$	−8.08166	−	8.08166i	−0.397672	−	0.397672i
$414$	−29.6612	−	22.5041i	−1.45777	−	1.10602i
$415$			33.7133i			1.65492i
$416$	0.598472	−	7.29881i	0.0293425	−	0.357853i
$417$	15.2866	+	25.0682i	0.748589	+	1.22760i
$418$	9.09852	+	1.59408i	0.445023	+	0.0779692i
$419$	−4.56394	+	4.56394i	−0.222963	+	0.222963i	−0.809745	−	0.586782i	$-0.800395\pi$
$419$	−4.56394	+	4.56394i	−0.222963	+	0.222963i	0.586782	+	0.809745i	$0.300395\pi$
$420$	−2.20809	−	10.8533i	−0.107744	−	0.529586i
$421$	−6.35998	−	6.35998i	−0.309966	−	0.309966i	0.534930	−	0.844896i	$-0.320338\pi$
$421$	−6.35998	−	6.35998i	−0.309966	−	0.309966i	−0.844896	+	0.534930i	$0.820338\pi$
$422$	19.3512	−	13.5813i	0.942003	−	0.661130i
$423$	−22.9591	−	11.8249i	−1.11631	−	0.574944i
$424$	6.79615	+	25.0356i	0.330050	+	1.21584i
$425$	−15.3146			−0.742868
$426$	−4.62726	+	10.6102i	−0.224191	+	0.514067i
$427$	−2.11377	+	2.11377i	−0.102293	+	0.102293i
$428$	10.9569	+	23.3641i	0.529624	+	1.12934i
$429$	1.36007	−	5.61108i	0.0656647	−	0.270905i
$430$	21.8342	+	3.82541i	1.05294	+	0.184477i
$431$	−15.4570			−0.744536			−0.372268	−	0.928125i	$-0.621420\pi$
$431$	−15.4570			−0.744536			−0.372268	+	0.928125i	$0.621420\pi$
$432$	−20.5070	+	3.38556i	−0.986645	+	0.162888i
$433$	−6.09769			−0.293036			−0.146518	−	0.989208i	$-0.546807\pi$
$433$	−6.09769			−0.293036			−0.146518	+	0.989208i	$0.546807\pi$
$434$	11.3600	+	1.99030i	0.545296	+	0.0955373i
$435$	3.09091	−	12.7518i	0.148198	−	0.611403i
$436$	−19.0960	+	8.95536i	−0.914531	+	0.428884i
$437$	−15.7411	+	15.7411i	−0.753000	+	0.753000i
$438$	8.69519	−	19.9379i	0.415472	−	0.952671i
$439$	−10.3091			−0.492027			−0.246013	−	0.969266i	$-0.579121\pi$
$439$	−10.3091			−0.492027			−0.246013	+	0.969266i	$0.579121\pi$
$440$	−11.5764	+	20.2033i	−0.551882	+	0.963152i
$441$	−2.66704	−	1.37363i	−0.127002	−	0.0654112i
$442$	−4.39453	+	3.08423i	−0.209026	+	0.146702i
$443$	−9.98250	−	9.98250i	−0.474283	−	0.474283i	0.429015	−	0.903297i	$-0.358861\pi$
$443$	−9.98250	−	9.98250i	−0.474283	−	0.474283i	−0.903297	+	0.429015i	$0.858861\pi$
$444$	20.6308	−	4.19732i	0.979093	−	0.199196i
$445$	26.2892	−	26.2892i	1.24623	−	1.24623i
$446$	−9.48849	−	1.66241i	−0.449293	−	0.0787173i
$447$	14.9838	+	24.5716i	0.708708	+	1.16220i
$448$	4.04525	+	6.90188i	0.191120	+	0.326083i
$449$		−	11.0455i		−	0.521268i	−0.965438	−	0.260634i	$-0.916068\pi$
$449$		−	11.0455i		−	0.521268i	0.965438	−	0.260634i	$-0.0839315\pi$
$450$	17.6515	+	13.3923i	0.832100	+	0.631318i
$451$	−8.24192	−	8.24192i	−0.388097	−	0.388097i
$452$	12.9051	−	35.6987i	0.607006	−	1.67912i
$453$	3.32526	−	13.7187i	0.156235	−	0.644559i
$454$	0.235569	+	0.335648i	0.0110558	+	0.0157527i
$455$			4.13913i			0.194045i
$456$	0.338825	+	12.4226i	0.0158670	+	0.581744i
$457$		−	29.4280i		−	1.37659i	−0.725433	−	0.688293i	$-0.758361\pi$
$457$		−	29.4280i		−	1.37659i	0.725433	−	0.688293i	$-0.241639\pi$
$458$	−21.9308	+	15.3918i	−1.02476	+	0.719210i
$459$	11.5216	+	9.97170i	0.537784	+	0.465439i
$460$	−23.8266	−	50.8066i	−1.11092	−	2.36887i
$461$	−8.61270	−	8.61270i	−0.401134	−	0.401134i	0.477499	−	0.878632i	$-0.341543\pi$
$461$	−8.61270	−	8.61270i	−0.401134	−	0.401134i	−0.878632	+	0.477499i	$0.841543\pi$
$462$	2.30513	+	5.87072i	0.107244	+	0.273131i
$463$		−	4.16285i		−	0.193464i	−0.995310	−	0.0967321i	$-0.969161\pi$
$463$		−	4.16285i		−	0.193464i	0.995310	−	0.0967321i	$-0.0308390\pi$
$464$	0.867198	+	9.43769i	0.0402586	+	0.438134i
$465$	−38.5577	+	23.5125i	−1.78807	+	1.09037i
$466$	1.46835	−	8.38090i	0.0680202	−	0.388238i
$467$	−4.41317	+	4.41317i	−0.204217	+	0.204217i	−0.801804	−	0.597587i	$-0.796126\pi$
$467$	−4.41317	+	4.41317i	−0.204217	+	0.204217i	0.597587	+	0.801804i	$0.296126\pi$
$468$	7.76219	+	0.288057i	0.358807	+	0.0133154i
$469$	2.17584	+	2.17584i	0.100471	+	0.100471i
$470$	−22.3606	−	31.8603i	−1.03142	−	1.46960i
$471$	13.7573	+	22.5604i	0.633905	+	1.03953i
$472$	−31.1976	+	8.46887i	−1.43598	+	0.389811i
$473$	−12.6230			−0.580404
$474$	−10.4357	+	23.9290i	−0.479330	+	1.09909i
$475$	9.36759	−	9.36759i	0.429815	−	0.429815i
$476$	1.99390	−	5.51560i	0.0913902	−	0.252807i
$477$	−26.2055	+	8.38830i	−1.19987	+	0.384074i
$478$	1.68283	−	9.60506i	0.0769709	−	0.439325i
$479$	−19.6658			−0.898553			−0.449277	−	0.893393i	$-0.648318\pi$
$479$	−19.6658			−0.898553			−0.449277	+	0.893393i	$0.648318\pi$
$480$	−29.7401	−	9.84288i	−1.35744	−	0.449264i
$481$	−7.86799			−0.358749
$482$	2.68232	−	15.3098i	0.122176	−	0.697344i
$483$	−14.7721	−	3.58062i	−0.672156	−	0.162924i
$484$	−2.97145	+	8.21974i	−0.135066	+	0.373625i
$485$	20.5316	−	20.5316i	0.932292	−	0.932292i
$486$	−4.55972	−	21.5687i	−0.206833	−	0.978376i
$487$	−0.727896			−0.0329841			−0.0164921	−	0.999864i	$-0.505250\pi$
$487$	−0.727896			−0.0329841			−0.0164921	+	0.999864i	$0.505250\pi$
$488$	2.21505	+	8.15979i	0.100271	+	0.369376i
$489$	−4.73847	+	2.88952i	−0.214281	+	0.130669i
$490$	−2.59752	−	3.70105i	−0.117344	−	0.167196i
$491$	2.15522	+	2.15522i	0.0972636	+	0.0972636i	0.754064	−	0.656801i	$-0.228091\pi$
$491$	2.15522	+	2.15522i	0.0972636	+	0.0972636i	−0.656801	+	0.754064i	$0.728091\pi$
$492$	8.65514	−	13.0764i	0.390204	−	0.589530i
$493$	4.91303	−	4.91303i	0.221272	−	0.221272i
$494$	0.801479	−	4.57458i	0.0360602	−	0.205820i
$495$	−21.9563	−	11.3084i	−0.986861	−	0.508273i
$496$	20.8587	−	25.0798i	0.936583	−	1.12612i
$497$			4.72561i			0.211973i
$498$	24.0416	−	9.43990i	1.07733	−	0.423012i
$499$	−25.4814	−	25.4814i	−1.14070	−	1.14070i	−0.988322	−	0.152381i	$-0.951306\pi$
$499$	−25.4814	−	25.4814i	−1.14070	−	1.14070i	−0.152381	−	0.988322i	$-0.548694\pi$
$500$	0.603927	+	1.28778i	0.0270084	+	0.0575915i
$501$	−25.7180	−	6.23378i	−1.14900	−	0.278505i
$502$	19.4711	−	13.6655i	0.869039	−	0.609921i
$503$			18.0159i			0.803289i	0.915796	+	0.401645i	$0.131561\pi$
$503$			18.0159i			0.803289i	−0.915796	+	0.401645i	$0.868439\pi$
$504$	−7.12142	+	4.61361i	−0.317213	+	0.205507i
$505$		−	21.3730i		−	0.951086i
$506$	18.3575	+	26.1565i	0.816090	+	1.16280i
$507$	19.0618	+	4.62040i	0.846566	+	0.205199i
$508$	14.0068	−	38.7461i	0.621451	−	1.71908i
$509$	−4.60982	−	4.60982i	−0.204327	−	0.204327i	0.597524	−	0.801851i	$-0.296151\pi$
$509$	−4.60982	−	4.60982i	−0.204327	−	0.204327i	−0.801851	+	0.597524i	$0.796151\pi$
$510$	8.39371	+	21.3772i	0.371680	+	0.946598i
$511$		−	8.88001i		−	0.392828i
$512$	22.6263	−	0.222117i	0.999952	−	0.00981626i
$513$	−13.1470	+	0.948059i	−0.580453	+	0.0418578i
$514$	−20.4394	−	3.58103i	−0.901543	−	0.157953i
$515$	−33.4295	+	33.4295i	−1.47308	+	1.47308i
$516$	−3.38572	−	16.6415i	−0.149048	−	0.732603i
$517$	15.6733	+	15.6733i	0.689311	+	0.689311i
$518$	7.03525	−	4.93758i	0.309111	−	0.216945i
$519$	26.3491	−	16.0677i	1.15660	−	0.705294i
$520$	10.1579	+	5.82041i	0.445451	+	0.255242i
$521$	0.205806			0.00901651			0.00450825	−	0.999990i	$-0.498565\pi$
$521$	0.205806			0.00901651			0.00450825	+	0.999990i	$0.498565\pi$
$522$	−9.95906	+	1.36639i	−0.435896	+	0.0598051i
$523$	10.4823	−	10.4823i	0.458361	−	0.458361i	−0.439756	−	0.898117i	$-0.644935\pi$
$523$	10.4823	−	10.4823i	0.458361	−	0.458361i	0.898117	+	0.439756i	$0.144935\pi$
$524$	20.6764	−	9.69654i	0.903253	−	0.423595i
$525$	8.79096	+	2.13084i	0.383669	+	0.0929975i
$526$	−28.4382	−	4.98244i	−1.23996	−	0.217245i
$527$	−23.9145			−1.04173
$528$	17.6488	+	2.59833i	0.768066	+	0.113078i
$529$	−54.0124			−2.34837
$530$	−40.8488	−	7.15682i	−1.77436	−	0.310872i
$531$	−10.4529	−	32.6554i	−0.453617	−	1.41712i
$532$	2.15414	+	4.59338i	0.0933939	+	0.199148i
$533$	−4.14390	+	4.14390i	−0.179492	+	0.179492i
$534$	−26.1085	−	11.3863i	−1.12983	−	0.492732i
$535$	−41.2537			−1.78355
$536$	8.39937	−	2.28009i	0.362798	−	0.0984848i
$537$	0.452629	+	0.742257i	0.0195324	+	0.0320308i
$538$	30.6067	−	21.4809i	1.31955	−	0.926106i
$539$	1.82069	+	1.82069i	0.0784227	+	0.0784227i
$540$	9.01934	−	31.9793i	0.388131	−	1.37617i
$541$	−20.1726	+	20.1726i	−0.867286	+	0.867286i	−0.992171	−	0.124885i	$-0.960144\pi$
$541$	−20.1726	+	20.1726i	−0.867286	+	0.867286i	0.124885	+	0.992171i	$0.460144\pi$
$542$	7.55057	+	1.32288i	0.324325	+	0.0568225i
$543$	−8.27129	+	5.04384i	−0.354955	+	0.216452i
$544$	−10.7320	−	12.6492i	−0.460133	−	0.542331i
$545$		−	33.7176i		−	1.44430i
$546$	2.95170	−	1.15898i	0.126321	−	0.0495997i
$547$	−6.72133	−	6.72133i	−0.287383	−	0.287383i	0.548661	−	0.836045i	$-0.315138\pi$
$547$	−6.72133	−	6.72133i	−0.287383	−	0.287383i	−0.836045	+	0.548661i	$0.815138\pi$
$548$	9.81940	+	3.54973i	0.419464	+	0.151637i
$549$	−8.54109	+	2.73398i	−0.364525	+	0.116683i
$550$	−10.9246	−	15.5658i	−0.465827	−	0.663728i
$551$			6.01038i			0.256051i
$552$	−29.5597	+	31.2174i	−1.25814	+	1.32870i
$553$			10.6576i			0.453205i
$554$	−8.38777	+	5.88682i	−0.356362	+	0.250107i
$555$	−7.92842	+	32.7094i	−0.336543	+	1.38844i
$556$	30.6959	−	14.3953i	1.30180	−	0.610498i
$557$	5.70500	+	5.70500i	0.241729	+	0.241729i	0.817565	−	0.575836i	$-0.195323\pi$
$557$	5.70500	+	5.70500i	0.241729	+	0.241729i	−0.575836	+	0.817565i	$0.695323\pi$
$558$	27.5636	+	20.9127i	1.16686	+	0.885304i
$559$			6.34661i			0.268433i
$560$	−12.7354	+	1.17021i	−0.538167	+	0.0494504i
$561$	−6.80892	−	11.1658i	−0.287473	−	0.471421i
$562$	1.30652	−	7.45721i	0.0551123	−	0.314563i
$563$	−20.8412	+	20.8412i	−0.878353	+	0.878353i	−0.993364	−	0.115011i	$-0.963310\pi$
$563$	−20.8412	+	20.8412i	−0.878353	+	0.878353i	0.115011	+	0.993364i	$0.463310\pi$
$564$	−16.4591	+	24.8669i	−0.693054	+	1.04708i
$565$	42.9096	+	42.9096i	1.80522	+	1.80522i
$566$	12.2647	+	17.4752i	0.515524	+	0.734539i
$567$	−5.22626	−	7.32709i	−0.219482	−	0.307709i
$568$	11.5971	+	6.64511i	0.486605	+	0.278823i
$569$	−7.74936			−0.324870			−0.162435	−	0.986719i	$-0.551935\pi$
$569$	−7.74936			−0.324870			−0.162435	+	0.986719i	$0.551935\pi$
$570$	−18.2102	−	7.94169i	−0.762740	−	0.332641i
$571$	4.96436	−	4.96436i	0.207752	−	0.207752i	−0.595559	−	0.803311i	$-0.703070\pi$
$571$	4.96436	−	4.96436i	0.207752	−	0.207752i	0.803311	+	0.595559i	$0.203070\pi$
$572$	−6.26964	−	2.26649i	−0.262147	−	0.0947665i
$573$	4.54191	−	18.7380i	0.189741	−	0.782792i
$574$	1.10480	−	6.30583i	0.0461133	−	0.263200i
$575$	45.8304			1.91126
$576$	1.30822	+	23.9643i	0.0545091	+	0.998513i
$577$	42.9528			1.78815			0.894073	−	0.447921i	$-0.147835\pi$
$577$	42.9528			1.78815			0.894073	+	0.447921i	$0.147835\pi$
$578$	2.05023	−	11.7021i	0.0852783	−	0.486741i
$579$	−9.88392	+	40.7770i	−0.410762	+	1.69463i
$580$	−14.2485	−	5.15085i	−0.591636	−	0.213877i
$581$	7.45604	−	7.45604i	0.309329	−	0.309329i
$582$	−20.3905	−	8.89255i	−0.845213	−	0.368608i
$583$	23.6159			0.978069
$584$	−21.7925	−	12.4870i	−0.901778	−	0.516715i
$585$	−5.68565	+	11.0392i	−0.235073	+	0.456417i
$586$	−0.305087	−	0.434699i	−0.0126030	−	0.0179573i
$587$	6.19957	+	6.19957i	0.255884	+	0.255884i	0.823378	−	0.567494i	$-0.192087\pi$
$587$	6.19957	+	6.19957i	0.255884	+	0.255884i	−0.567494	+	0.823378i	$0.692087\pi$
$588$	−1.91197	+	2.88866i	−0.0788485	+	0.119126i
$589$	14.6279	−	14.6279i	0.602733	−	0.602733i
$590$	8.91831	−	50.9029i	0.367161	−	2.09564i
$591$	15.2155	+	24.9516i	0.625881	+	1.02637i
$592$	−2.22443	−	24.2084i	−0.0914234	−	0.994959i
$593$		−	14.7953i		−	0.607569i	−0.952741	−	0.303785i	$-0.901750\pi$
$593$		−	14.7953i		−	0.607569i	0.952741	−	0.303785i	$-0.0982504\pi$
$594$	−1.91635	+	18.8239i	−0.0786286	+	0.772353i
$595$	6.62972	+	6.62972i	0.271792	+	0.271792i
$596$	30.0877	−	14.1101i	1.23244	−	0.577973i
$597$	−2.31205	+	9.53856i	−0.0946259	+	0.390387i
$598$	13.1510	−	9.22984i	0.537785	−	0.377436i
$599$		−	21.0039i		−	0.858198i	−0.903257	−	0.429099i	$-0.858831\pi$
$599$		−	21.0039i		−	0.858198i	0.903257	−	0.429099i	$-0.141169\pi$
$600$	17.5911	−	18.5776i	0.718153	−	0.758426i
$601$			39.2853i			1.60248i	0.598343	+	0.801240i	$0.295826\pi$
$601$			39.2853i			1.60248i	−0.598343	+	0.801240i	$0.704174\pi$
$602$	−3.98283	−	5.67489i	−0.162328	−	0.231291i
$603$	2.81425	+	8.79186i	0.114605	+	0.358032i
$604$	−15.3288	−	5.54138i	−0.623720	−	0.225476i
$605$	−9.88009	−	9.88009i	−0.401683	−	0.401683i
$606$	−15.2415	+	5.98456i	−0.619145	+	0.243106i
$607$			13.5867i			0.551466i	0.961234	+	0.275733i	$0.0889205\pi$
$607$			13.5867i			0.551466i	−0.961234	+	0.275733i	$0.911079\pi$
$608$	14.3018	+	1.17269i	0.580014	+	0.0475588i
$609$	−3.50379	+	2.13661i	−0.141981	+	0.0865799i
$610$	−13.3138	−	2.33260i	−0.539058	−	0.0944444i
$611$	7.88028	−	7.88028i	0.318802	−	0.318802i
$612$	12.8942	−	11.9715i	0.521218	−	0.483918i
$613$	7.18766	+	7.18766i	0.290307	+	0.290307i	0.837201	−	0.546895i	$-0.184190\pi$
$613$	7.18766	+	7.18766i	0.290307	+	0.290307i	−0.546895	+	0.837201i	$0.684190\pi$
$614$	−11.9264	+	8.37037i	−0.481311	+	0.337800i
$615$	13.0516	+	21.4031i	0.526291	+	0.863054i
$616$	7.02840	−	1.90793i	0.283182	−	0.0768725i
$617$	−25.4655			−1.02520			−0.512601	−	0.858627i	$-0.671318\pi$
$617$	−25.4655			−1.02520			−0.512601	+	0.858627i	$0.671318\pi$
$618$	33.1997	+	14.4788i	1.33549	+	0.582424i
$619$	24.8928	−	24.8928i	1.00052	−	1.00052i	0.000524244	−	1.00000i	$-0.499833\pi$
$619$	24.8928	−	24.8928i	1.00052	−	1.00052i	1.00000		0.000524244i	$-0.000166872\pi$
$620$	22.1416	+	47.2137i	0.889228	+	1.89615i
$621$	−34.4795	−	29.8412i	−1.38362	−	1.19749i
$622$	−16.8392	−	2.95026i	−0.675189	−	0.118295i
$623$	−11.6283			−0.465878
$624$	1.30640	−	8.87352i	0.0522978	−	0.355225i
$625$	23.8383			0.953534
$626$	1.31235	+	0.229928i	0.0524522	+	0.00918976i
$627$	10.9947	+	2.66501i	0.439087	+	0.106430i
$628$	27.6251	−	12.9552i	1.10236	−	0.516969i
$629$	−12.6023	+	12.6023i	−0.502487	+	0.502487i
$630$	−1.84382	−	13.4389i	−0.0734596	−	0.535419i
$631$	−0.512718			−0.0204110			−0.0102055	−	0.999948i	$-0.503249\pi$
$631$	−0.512718			−0.0204110			−0.0102055	+	0.999948i	$0.503249\pi$
$632$	26.1548	+	14.9866i	1.04038	+	0.596133i
$633$	24.7211	−	15.0749i	0.982574	−	0.599174i
$634$	−6.48092	+	4.54853i	−0.257390	+	0.180645i
$635$	46.5727	+	46.5727i	1.84818	+	1.84818i
$636$	6.33422	+	31.1341i	0.251168	+	1.23455i
$637$	0.915413	−	0.915413i	0.0362700	−	0.0362700i
$638$	8.49831	+	1.48893i	0.336451	+	0.0589471i
$639$	−6.49126	+	12.6034i	−0.256790	+	0.498583i
$640$	−15.0365	+	32.8995i	−0.594371	+	1.30047i
$641$		−	24.2180i		−	0.956553i	−0.878209	−	0.478277i	$-0.841262\pi$
$641$		−	24.2180i		−	0.956553i	0.878209	−	0.478277i	$-0.158738\pi$
$642$	11.5513	+	29.4189i	0.455892	+	1.16107i
$643$	−1.22963	−	1.22963i	−0.0484917	−	0.0484917i	0.682445	−	0.730937i	$-0.260917\pi$
$643$	−1.22963	−	1.22963i	−0.0484917	−	0.0484917i	−0.730937	+	0.682445i	$0.760917\pi$
$644$	−5.96692	+	16.5059i	−0.235130	+	0.650424i
$645$	26.3846	+	6.39536i	1.03889	+	0.251817i
$646$	−6.04345	−	8.61094i	−0.237776	−	0.338793i
$647$		−	32.1398i		−	1.26355i	−0.775153	−	0.631773i	$-0.782327\pi$
$647$		−	32.1398i		−	1.26355i	0.775153	−	0.631773i	$-0.217673\pi$
$648$	−25.3306	+	2.52249i	−0.995078	+	0.0990929i
$649$			29.4284i			1.15517i
$650$	−7.82623	+	5.49271i	−0.306970	+	0.215442i
$651$	13.7275	+	3.32740i	0.538023	+	0.130411i
$652$	2.72105	+	5.80223i	0.106565	+	0.227233i
$653$	−4.20090	−	4.20090i	−0.164394	−	0.164394i	0.620116	−	0.784510i	$-0.287085\pi$
$653$	−4.20090	−	4.20090i	−0.164394	−	0.164394i	−0.784510	+	0.620116i	$0.787085\pi$
$654$	−24.0447	+	9.44110i	−0.940222	+	0.369176i
$655$			36.5081i			1.42649i
$656$	−13.9216	−	11.5785i	−0.543547	−	0.452064i
$657$	12.1979	−	23.6834i	0.475885	−	0.923976i
$658$	−2.10095	+	11.9915i	−0.0819034	+	0.467478i
$659$	19.3636	−	19.3636i	0.754299	−	0.754299i	−0.220979	−	0.975279i	$-0.570925\pi$
$659$	19.3636	−	19.3636i	0.754299	−	0.754299i	0.975279	+	0.220979i	$0.0709253\pi$
$660$	−15.7402	+	23.7807i	−0.612686	+	0.925663i
$661$	−4.66027	−	4.66027i	−0.181264	−	0.181264i	0.610643	−	0.791906i	$-0.290911\pi$
$661$	−4.66027	−	4.66027i	−0.181264	−	0.181264i	−0.791906	+	0.610643i	$0.790911\pi$
$662$	18.7558	+	26.7239i	0.728963	+	1.03865i
$663$	−5.61398	+	3.42341i	−0.218029	+	0.132954i
$664$	−7.81329	−	28.7825i	−0.303214	−	1.11698i
$665$	−8.11049			−0.314511
$666$	25.5457	−	3.50488i	0.989877	−	0.135811i
$667$	−14.7027	+	14.7027i	−0.569291	+	0.569291i
$668$	−10.3883	+	28.7365i	−0.401935	+	1.11185i
$669$	−11.4660	−	2.77923i	−0.443300	−	0.107451i
$670$	−2.40109	+	13.7047i	−0.0927623	+	0.529457i
$671$	7.69706			0.297142
$672$	4.40047	+	8.75419i	0.169752	+	0.337700i
$673$	−38.8503			−1.49757			−0.748784	−	0.662814i	$-0.769362\pi$
$673$	−38.8503			−1.49757			−0.748784	+	0.662814i	$0.769362\pi$
$674$	−4.50177	+	25.6946i	−0.173402	+	0.989721i
$675$	20.5189	+	17.7586i	0.789773	+	0.683529i
$676$	7.69966	−	21.2991i	0.296141	−	0.819195i
$677$	−3.77109	+	3.77109i	−0.144935	+	0.144935i	−0.775851	−	0.630916i	$-0.782679\pi$
$677$	−3.77109	+	3.77109i	−0.144935	+	0.144935i	0.630916	+	0.775851i	$0.282679\pi$
$678$	18.5848	−	42.6147i	0.713745	−	1.63661i
$679$	−9.08157			−0.348519
$680$	25.5927	−	6.94737i	0.981434	−	0.266420i
$681$	0.261475	+	0.428788i	0.0100197	+	0.0164312i
$682$	−17.0593	−	24.3067i	−0.653234	−	0.930752i
$683$	−26.2664	−	26.2664i	−1.00506	−	1.00506i	−0.999987	−	0.00507032i	$-0.998386\pi$
$683$	−26.2664	−	26.2664i	−1.00506	−	1.00506i	−0.00507032	−	0.999987i	$-0.501614\pi$
$684$	−0.564438	+	15.2098i	−0.0215818	+	0.581560i
$685$	−11.8029	+	11.8029i	−0.450964	+	0.450964i
$686$	−0.244056	+	1.39300i	−0.00931812	+	0.0531848i
$687$	−28.0164	+	17.0844i	−1.06889	+	0.651812i
$688$	−19.5274	+	1.79431i	−0.744475	+	0.0684073i
$689$		−	11.8737i		−	0.452350i
$690$	−25.1189	−	63.9732i	−0.956262	−	2.43542i
$691$	16.9641	+	16.9641i	0.645344	+	0.645344i	0.951864	−	0.306520i	$-0.0991648\pi$
$691$	16.9641	+	16.9641i	0.645344	+	0.645344i	−0.306520	+	0.951864i	$0.599165\pi$
$692$	−15.1309	−	32.2643i	−0.575189	−	1.22651i
$693$	2.35490	+	7.35683i	0.0894553	+	0.279463i
$694$	6.81467	−	4.78277i	0.258681	−	0.181551i
$695$			54.1994i			2.05590i
$696$	0.316474	+	11.6031i	0.0119959	+	0.439816i
$697$			13.2747i			0.502816i
$698$	2.00669	+	2.85920i	0.0759542	+	0.108222i
$699$	2.45481	−	10.1275i	0.0928496	−	0.383059i
$700$	3.55094	−	9.82274i	0.134213	−	0.371265i
$701$	3.53373	+	3.53373i	0.133467	+	0.133467i	0.770684	−	0.637217i	$-0.219915\pi$
$701$	3.53373	+	3.53373i	0.133467	+	0.133467i	−0.637217	+	0.770684i	$0.719915\pi$
$702$	9.46433	+	0.963507i	0.357208	+	0.0363652i
$703$		−	15.4171i		−	0.581466i
$704$	5.20103	−	19.9313i	0.196021	−	0.751191i
$705$	−24.8197	−	40.7013i	−0.934762	−	1.53290i
$706$	−17.2203	−	3.01704i	−0.648095	−	0.113548i
$707$	−4.72687	+	4.72687i	−0.177772	+	0.177772i
$708$	−38.7971	+	7.89325i	−1.45808	+	0.296646i
$709$	36.9985	+	36.9985i	1.38951	+	1.38951i	0.826346	+	0.563162i	$0.190415\pi$
$709$	36.9985	+	36.9985i	1.38951	+	1.38951i	0.563162	+	0.826346i	$0.309585\pi$
$710$	−17.4897	+	12.2749i	−0.656377	+	0.460668i
$711$	−14.6396	+	28.4242i	−0.549027	+	1.06599i
$712$	−16.3516	+	28.5370i	−0.612802	+	1.06947i
$713$	71.5662			2.68018
$714$	2.87143	−	6.58415i	0.107461	−	0.246406i
$715$	7.53607	−	7.53607i	0.281833	−	0.281833i
$716$	0.908889	−	0.426238i	0.0339668	−	0.0159293i
$717$	2.81338	−	11.6068i	0.105068	−	0.433465i
$718$	−22.6143	−	3.96209i	−0.843959	−	0.147864i
$719$	−1.47388			−0.0549663			−0.0274831	−	0.999622i	$-0.508749\pi$
$719$	−1.47388			−0.0549663			−0.0274831	+	0.999622i	$0.508749\pi$
$720$	−35.5732	−	14.3727i	−1.32574	−	0.535640i
$721$	14.7866			0.550681
$722$	−17.5032	−	3.06660i	−0.651400	−	0.114127i
$723$	4.48434	−	18.5005i	0.166774	−	0.688042i
$724$	4.74975	+	10.1281i	0.176523	+	0.376409i
$725$	8.74963	−	8.74963i	0.324953	−	0.324953i
$726$	−4.27922	+	9.81218i	−0.158817	+	0.364164i
$727$	−31.5533			−1.17025			−0.585124	−	0.810944i	$-0.698954\pi$
$727$	−31.5533			−1.17025			−0.585124	+	0.810944i	$0.698954\pi$
$728$	−0.959273	−	3.53376i	−0.0355530	−	0.130970i
$729$	−3.87392	−	26.7206i	−0.143479	−	0.989653i
$730$	32.8653	−	23.0660i	1.21640	−	0.853711i
$731$	10.1655	+	10.1655i	0.375984	+	0.375984i
$732$	2.06450	+	10.1475i	0.0763060	+	0.375061i
$733$	4.14193	−	4.14193i	0.152986	−	0.152986i	−0.626464	−	0.779450i	$-0.715499\pi$
$733$	4.14193	−	4.14193i	0.152986	−	0.152986i	0.779450	+	0.626464i	$0.215499\pi$
$734$	−36.0466	−	6.31546i	−1.33050	−	0.233108i
$735$	−2.88318	−	4.72806i	−0.106348	−	0.174397i
$736$	32.1166	+	37.8539i	1.18383	+	1.39531i
$737$		−	7.92305i		−	0.291849i
$738$	11.6084	−	15.3003i	0.427313	−	0.563213i
$739$	24.0249	+	24.0249i	0.883769	+	0.883769i	0.993915	−	0.110147i	$-0.0351321\pi$
$739$	24.0249	+	24.0249i	0.883769	+	0.883769i	−0.110147	+	0.993915i	$0.535132\pi$
$740$	36.5484	+	13.2123i	1.34355	+	0.485694i
$741$	1.33992	−	5.52796i	0.0492233	−	0.203075i
$742$	7.45135	+	10.6170i	0.273548	+	0.389761i
$743$			14.1448i			0.518923i	0.965753	+	0.259461i	$0.0835450\pi$
$743$			14.1448i			0.518923i	−0.965753	+	0.259461i	$0.916455\pi$
$744$	27.4693	−	29.0097i	1.00707	−	1.06355i
$745$			53.1256i			1.94637i
$746$	42.6322	−	29.9207i	1.56087	−	1.09548i
$747$	30.1275	−	9.64373i	1.10231	−	0.352845i
$748$	−13.6725	+	6.41192i	−0.499915	+	0.234443i
$749$	9.12369	+	9.12369i	0.333372	+	0.333372i
$750$	0.636684	+	1.62151i	0.0232484	+	0.0592093i
$751$			2.98228i			0.108825i	0.998519	+	0.0544125i	$0.0173286\pi$
$751$			2.98228i			0.108825i	−0.998519	+	0.0544125i	$0.982671\pi$
$752$	26.4741	+	22.0183i	0.965411	+	0.802925i
$753$	24.8742	−	15.1683i	0.906467	−	0.552764i
$754$	0.748607	−	4.27281i	0.0272626	−	0.155606i
$755$	18.4251	−	18.4251i	0.670559	−	0.670559i
$756$	−9.06728	+	5.07783i	−0.329774	+	0.184679i
$757$	−11.2382	−	11.2382i	−0.408459	−	0.408459i	0.472742	−	0.881201i	$-0.343264\pi$
$757$	−11.2382	−	11.2382i	−0.408459	−	0.408459i	−0.881201	+	0.472742i	$0.843264\pi$
$758$	−6.33840	−	9.03119i	−0.230221	−	0.328028i
$759$	20.3763	+	33.4147i	0.739613	+	1.21288i
$760$	−11.4049	+	19.9040i	−0.413699	+	0.721994i
$761$	−46.7489			−1.69465			−0.847324	−	0.531077i	$-0.821788\pi$
$761$	−46.7489			−1.69465			−0.847324	+	0.531077i	$0.821788\pi$
$762$	20.1713	−	46.2526i	0.730731	−	1.67555i
$763$	−7.45700	+	7.45700i	−0.269961	+	0.269961i
$764$	−20.9373	−	7.56886i	−0.757484	−	0.273832i
$765$	8.57495	+	26.7886i	0.310028	+	0.968543i
$766$	2.64997	−	15.1252i	0.0957472	−	0.546494i
$767$	14.7961			0.534256
$768$	27.6716	+	1.51084i	0.998513	+	0.0545178i
$769$	45.7155			1.64854			0.824272	−	0.566194i	$-0.191585\pi$
$769$	45.7155			1.64854			0.824272	+	0.566194i	$0.191585\pi$
$770$	−2.00918	+	11.4677i	−0.0724058	+	0.413269i
$771$	−24.6991	−	5.98682i	−0.889517	−	0.215610i
$772$	45.5629	+	16.4711i	1.63984	+	0.592806i
$773$	−14.0908	+	14.0908i	−0.506812	+	0.506812i	−0.913546	−	0.406735i	$-0.866667\pi$
$773$	−14.0908	+	14.0908i	−0.506812	+	0.506812i	0.406735	+	0.913546i	$0.366667\pi$
$774$	−2.82717	−	20.6061i	−0.101620	−	0.740673i
$775$	−42.5893			−1.52985
$776$	−12.7704	+	22.2871i	−0.458431	+	0.800061i
$777$	8.98748	−	5.48057i	0.322424	−	0.196614i
$778$	20.7926	+	29.6261i	0.745451	+	1.06215i
$779$	−8.11984	−	8.11984i	−0.290923	−	0.290923i
$780$	11.9565	+	7.91391i	0.428113	+	0.283363i
$781$	8.60387	−	8.60387i	0.307871	−	0.307871i
$782$	6.28064	−	35.8479i	0.224595	−	1.28192i
$783$	−12.2797	+	0.885517i	−0.438840	+	0.0316458i
$784$	3.07537	+	2.55776i	0.109835	+	0.0913485i
$785$			48.7773i			1.74094i
$786$	26.0347	−	10.2225i	0.928627	−	0.364624i
$787$	−14.7212	−	14.7212i	−0.524752	−	0.524752i	0.394251	−	0.919003i	$-0.371004\pi$
$787$	−14.7212	−	14.7212i	−0.524752	−	0.524752i	−0.919003	+	0.394251i	$0.871004\pi$
$788$	30.5530	−	14.3283i	1.08841	−	0.510426i
$789$	−34.3649	−	8.32971i	−1.22342	−	0.296546i
$790$	−39.4441	+	27.6832i	−1.40336	+	0.984925i
$791$		−	18.9798i		−	0.674845i
$792$	21.3659	+	4.56593i	0.759203	+	0.162243i
$793$		−	3.86995i		−	0.137426i
$794$	−14.3463	−	20.4412i	−0.509131	−	0.725430i
$795$	−49.3621	−	11.9649i	−1.75069	−	0.424350i
$796$	10.6581	+	3.85291i	0.377766	+	0.136563i
$797$	5.16925	+	5.16925i	0.183104	+	0.183104i	0.792707	−	0.609603i	$-0.208671\pi$
$797$	5.16925	+	5.16925i	0.183104	+	0.183104i	−0.609603	+	0.792707i	$0.708671\pi$
$798$	2.27098	+	5.78376i	0.0803919	+	0.204743i
$799$		−	25.2440i		−	0.893067i
$800$	−19.1127	−	22.5270i	−0.675737	−	0.796450i
$801$	−31.0132	−	15.9730i	−1.09580	−	0.564379i
$802$	5.29668	+	0.927992i	0.187032	+	0.0327685i
$803$	−16.1677	+	16.1677i	−0.570547	+	0.570547i
$804$	10.4454	−	2.12511i	0.368381	−	0.0749469i
$805$	−19.8400	−	19.8400i	−0.699270	−	0.699270i
$806$	−12.2210	+	8.57712i	−0.430467	+	0.302116i
$807$	39.0999	−	23.8432i	1.37638	−	0.839319i
$808$	4.95335	+	18.2471i	0.174258	+	0.641931i
$809$	40.7474			1.43260			0.716302	−	0.697790i	$-0.245833\pi$
$809$	40.7474			1.43260			0.716302	+	0.697790i	$0.245833\pi$
$810$	13.5426	−	38.3749i	0.475838	−	1.34836i
$811$	−3.79131	+	3.79131i	−0.133131	+	0.133131i	−0.770532	−	0.637401i	$-0.780009\pi$
$811$	−3.79131	+	3.79131i	−0.133131	+	0.133131i	0.637401	+	0.770532i	$0.280009\pi$
$812$	2.01204	+	4.29037i	0.0706086	+	0.150562i
$813$	9.12417	+	2.21161i	0.319999	+	0.0775644i
$814$	−21.7988	−	3.81921i	−0.764048	−	0.133863i
$815$	−10.2449			−0.358865
$816$	−12.1204	−	16.3054i	−0.424299	−	0.570802i
$817$	−12.4360			−0.435080
$818$	−11.8770	−	2.08088i	−0.415270	−	0.0727564i
$819$	3.69889	−	1.18400i	0.129250	−	0.0413725i
$820$	26.2079	−	12.2906i	0.915219	−	0.429207i
$821$	−3.18885	+	3.18885i	−0.111291	+	0.111291i	−0.760560	−	0.649268i	$-0.775075\pi$
$821$	−3.18885	+	3.18885i	−0.111291	+	0.111291i	0.649268	+	0.760560i	$0.275075\pi$
$822$	11.7217	+	5.11200i	0.408843	+	0.178302i
$823$	−48.4703			−1.68957			−0.844784	−	0.535107i	$-0.820271\pi$
$823$	−48.4703			−1.68957			−0.844784	+	0.535107i	$0.820271\pi$
$824$	20.7927	−	36.2878i	0.724350	−	1.26414i
$825$	−12.1260	−	19.8852i	−0.422174	−	0.692314i
$826$	−13.2301	+	9.28533i	−0.460334	+	0.323078i
$827$	13.1317	+	13.1317i	0.456633	+	0.456633i	0.897548	−	0.440916i	$-0.145346\pi$
$827$	13.1317	+	13.1317i	0.456633	+	0.456633i	−0.440916	+	0.897548i	$0.645346\pi$
$828$	−38.5871	+	35.8257i	−1.34100	+	1.24503i
$829$	22.4142	−	22.4142i	0.778479	−	0.778479i	−0.201093	−	0.979572i	$-0.564449\pi$
$829$	22.4142	−	22.4142i	0.778479	−	0.778479i	0.979572	+	0.201093i	$0.0644494\pi$
$830$	46.9624	+	8.22793i	1.63009	+	0.285596i
$831$	−10.7153	+	6.53421i	−0.371710	+	0.226669i
$832$	−10.0211	−	2.61499i	−0.347421	−	0.0906584i
$833$		−	2.93247i		−	0.101604i
$834$	38.6507	−	15.1761i	1.33837	−	0.525507i
$835$	−34.5411	−	34.5411i	−1.19534	−	1.19534i
$836$	4.44110	−	12.2852i	0.153599	−	0.424891i
$837$	32.0412	+	27.7309i	1.10751	+	0.958520i
$838$	5.24369	+	7.47141i	0.181140	+	0.258096i
$839$			44.4390i			1.53420i	0.641525	+	0.767102i	$0.278302\pi$
$839$			44.4390i			1.53420i	−0.641525	+	0.767102i	$0.721698\pi$
$840$	−15.6575	+	0.427054i	−0.540234	+	0.0147348i
$841$		−	23.3861i		−	0.806418i
$842$	−10.4116	+	7.30723i	−0.358808	+	0.251824i
$843$	2.18426	−	9.01135i	0.0752299	−	0.310367i
$844$	−14.1960	−	30.2708i	−0.488645	−	1.04196i
$845$	25.6014	+	25.6014i	0.880715	+	0.880715i
$846$	−22.0753	+	29.0960i	−0.758964	+	1.00034i
$847$			4.37017i			0.150161i
$848$	36.5331	−	3.35691i	1.25455	−	0.115277i
$849$	13.6135	+	22.3245i	0.467214	+	0.766175i
$850$	−3.73763	+	21.3332i	−0.128200	+	0.731722i
$851$	37.7135	−	37.7135i	1.29280	−	1.29280i
$852$	13.6507	+	9.03524i	0.467665	+	0.309542i
$853$	−28.2563	−	28.2563i	−0.967478	−	0.967478i	0.0320095	−	0.999488i	$-0.489809\pi$
$853$	−28.2563	−	28.2563i	−0.967478	−	0.967478i	−0.999488	+	0.0320095i	$0.989809\pi$
$854$	2.42860	+	3.46036i	0.0831049	+	0.118411i
$855$	−21.6310	−	11.1409i	−0.739766	−	0.381009i
$856$	35.2201	−	9.56083i	1.20380	−	0.326783i
$857$	−14.0907			−0.481328			−0.240664	−	0.970609i	$-0.577365\pi$
$857$	−14.0907			−0.481328			−0.240664	+	0.970609i	$0.577365\pi$
$858$	−7.48427	−	3.26399i	−0.255509	−	0.111431i
$859$	−11.8054	+	11.8054i	−0.402796	+	0.402796i	−0.879217	−	0.476421i	$-0.841934\pi$
$859$	−11.8054	+	11.8054i	−0.402796	+	0.402796i	0.476421	+	0.879217i	$0.341934\pi$
$860$	10.6575	−	29.4813i	0.363419	−	1.00530i
$861$	1.84701	−	7.62001i	0.0629461	−	0.259689i
$862$	−3.77237	+	21.5315i	−0.128488	+	0.733366i
$863$	−10.6934			−0.364009			−0.182004	−	0.983298i	$-0.558259\pi$
$863$	−10.6934			−0.364009			−0.182004	+	0.983298i	$0.558259\pi$
$864$	−0.288795	+	29.3925i	−0.00982500	+	0.999952i
$865$	56.9688			1.93700
$866$	−1.48818	+	8.49406i	−0.0505704	+	0.288640i
$867$	3.42760	−	14.1409i	0.116407	−	0.480249i
$868$	5.54495	−	15.3387i	0.188208	−	0.520628i
$869$	19.4041	−	19.4041i	0.658239	−	0.658239i
$870$	−17.0089	−	7.41779i	−0.576655	−	0.251487i
$871$	−3.98358			−0.134978
$872$	7.81429	+	28.7862i	0.264625	+	0.974824i
$873$	−24.2210	−	12.4748i	−0.819755	−	0.422206i
$874$	18.0856	+	25.7690i	0.611754	+	0.871650i
$875$	0.502881	+	0.502881i	0.0170005	+	0.0170005i
$876$	−25.6513	−	16.9783i	−0.866678	−	0.573645i
$877$	0.535576	−	0.535576i	0.0180851	−	0.0180851i	−0.698006	−	0.716092i	$-0.745929\pi$
$877$	0.535576	−	0.535576i	0.0180851	−	0.0180851i	0.716092	+	0.698006i	$0.245929\pi$
$878$	−2.51600	+	14.3605i	−0.0849110	+	0.484645i
$879$	−0.338638	−	0.555326i	−0.0114220	−	0.0187307i
$880$	25.3177	+	21.0566i	0.853461	+	0.709817i
$881$		−	53.6084i		−	1.80611i	−0.429522	−	0.903057i	$-0.641318\pi$
$881$		−	53.6084i		−	1.80611i	0.429522	−	0.903057i	$-0.358682\pi$
$882$	−2.56438	+	3.37994i	−0.0863470	+	0.113808i
$883$	−8.11686	−	8.11686i	−0.273154	−	0.273154i	0.557215	−	0.830369i	$-0.311870\pi$
$883$	−8.11686	−	8.11686i	−0.273154	−	0.273154i	−0.830369	+	0.557215i	$0.811870\pi$
$884$	3.22381	+	6.87429i	0.108428	+	0.231207i
$885$	14.9097	−	61.5114i	0.501186	−	2.06768i
$886$	−16.3419	+	11.4693i	−0.549016	+	0.385318i
$887$			19.7832i			0.664254i	0.943235	+	0.332127i	$0.107766\pi$
$887$			19.7832i			0.664254i	−0.943235	+	0.332127i	$0.892234\pi$
$888$	−0.811779	−	29.7630i	−0.0272415	−	0.998779i
$889$		−	20.6001i		−	0.690905i
$890$	−30.2047	−	43.0369i	−1.01247	−	1.44260i
$891$	−3.82496	+	22.8558i	−0.128141	+	0.765697i
$892$	−4.63145	+	12.8117i	−0.155072	+	0.428967i
$893$	15.4411	+	15.4411i	0.516718	+	0.516718i
$894$	37.8850	−	14.8755i	1.26706	−	0.497510i
$895$			1.60482i			0.0536431i
$896$	10.6016	−	3.95057i	0.354173	−	0.131979i
$897$	16.8004	−	10.2449i	0.560948	−	0.342066i
$898$	−15.3863	−	2.69572i	−0.513447	−	0.0899572i
$899$	13.6629	−	13.6629i	0.455685	−	0.455685i
$900$	22.9634	−	21.3200i	0.765445	−	0.710666i
$901$	−19.0183	−	19.0183i	−0.633590	−	0.633590i
$902$	−13.4924	+	9.46946i	−0.449249	+	0.315299i
$903$	−4.42083	−	7.24964i	−0.147116	−	0.241253i
$904$	−46.5785	−	26.6893i	−1.54918	−	0.887672i
$905$	−17.8832			−0.594456
$906$	−18.2985	−	7.98020i	−0.607926	−	0.265125i
$907$	24.7075	−	24.7075i	0.820398	−	0.820398i	−0.165767	−	0.986165i	$-0.553010\pi$
$907$	24.7075	−	24.7075i	0.820398	−	0.820398i	0.986165	+	0.165767i	$0.0530100\pi$
$908$	0.525048	−	0.246230i	0.0174243	−	0.00817142i
$909$	−19.0998	+	6.11378i	−0.633499	+	0.202781i
$910$	5.76579	+	1.01018i	0.191134	+	0.0334872i
$911$	−39.4269			−1.30627			−0.653135	−	0.757241i	$-0.726547\pi$
$911$	−39.4269			−1.30627			−0.653135	+	0.757241i	$0.726547\pi$
$912$	17.3874	+	2.55984i	0.575754	+	0.0847649i
$913$	−27.1503			−0.898544
$914$	−40.9931	−	7.18210i	−1.35593	−	0.237563i
$915$	−16.0884	−	3.89968i	−0.531868	−	0.128919i
$916$	16.0883	+	34.3059i	0.531573	+	1.13350i
$917$	8.07416	−	8.07416i	0.266632	−	0.266632i
$918$	16.7025	−	13.6159i	0.551263	−	0.449392i
$919$	−7.10328			−0.234315			−0.117158	−	0.993113i	$-0.537378\pi$
$919$	−7.10328			−0.234315			−0.117158	+	0.993113i	$0.537378\pi$
$920$	−76.5884	+	20.7906i	−2.52505	+	0.685447i
$921$	−15.2359	+	9.29087i	−0.502041	+	0.306145i
$922$	−14.0994	+	9.89547i	−0.464340	+	0.325890i
$923$	−4.32588	−	4.32588i	−0.142388	−	0.142388i
$924$	8.74047	−	1.77824i	0.287540	−	0.0584999i
$925$	−22.4435	+	22.4435i	−0.737937	+	0.737937i
$926$	−5.79884	−	1.01597i	−0.190562	−	0.0333869i
$927$	39.4365	+	20.3113i	1.29526	+	0.667112i
$928$	13.3583	+	1.09533i	0.438508	+	0.0359559i
$929$			17.0263i			0.558615i	0.960202	+	0.279308i	$0.0901049\pi$
$929$			17.0263i			0.558615i	−0.960202	+	0.279308i	$0.909895\pi$
$930$	23.3426	+	59.4491i	0.765433	+	1.94941i
$931$	1.79372	+	1.79372i	0.0587869	+	0.0587869i
$932$	−11.3162	−	4.09082i	−0.370674	−	0.133999i
$933$	−20.3486	−	4.93229i	−0.666182	−	0.161476i
$934$	5.07046	+	7.22458i	0.165910	+	0.236396i
$935$		−	24.1413i		−	0.789506i
$936$	2.29567	−	10.7424i	0.0750364	−	0.351126i
$937$		−	52.6704i		−	1.72067i	−0.509731	−	0.860334i	$-0.670255\pi$
$937$		−	52.6704i		−	1.72067i	0.509731	−	0.860334i	$-0.329745\pi$
$938$	3.56196	−	2.49990i	0.116302	−	0.0816248i
$939$	1.58586	+	0.384396i	0.0517525	+	0.0125443i
$940$	−49.8384	+	23.3725i	−1.62555	+	0.762328i
$941$	11.0340	+	11.0340i	0.359698	+	0.359698i	0.863701	−	0.504004i	$-0.168140\pi$
$941$	11.0340	+	11.0340i	0.359698	+	0.359698i	−0.504004	+	0.863701i	$0.668140\pi$
$942$	34.7841	−	13.6579i	1.13333	−	0.444999i
$943$		−	39.7258i		−	1.29365i
$944$	4.18313	+	45.5250i	0.136149	+	1.48171i
$945$	−1.19493	−	16.5704i	−0.0388711	−	0.539035i
$946$	−3.08071	+	17.5837i	−0.100163	+	0.571696i
$947$	−1.96456	+	1.96456i	−0.0638396	+	0.0638396i	−0.738306	−	0.674466i	$-0.764374\pi$
$947$	−1.96456	+	1.96456i	−0.0638396	+	0.0638396i	0.674466	+	0.738306i	$0.264374\pi$
$948$	30.7861	+	20.3770i	0.999885	+	0.661813i
$949$	8.12887	+	8.12887i	0.263874	+	0.263874i
$950$	−10.7628	−	15.3352i	−0.349191	−	0.497541i
$951$	−8.27934	+	5.04874i	−0.268476	+	0.163717i
$952$	−7.19658	−	4.12361i	−0.233242	−	0.133647i
$953$	32.9580			1.06761			0.533807	−	0.845606i	$-0.320761\pi$
$953$	32.9580			1.06761			0.533807	+	0.845606i	$0.320761\pi$
$954$	5.28925	+	38.5513i	0.171246	+	1.24815i
$955$	25.1665	−	25.1665i	0.814368	−	0.814368i
$956$	−12.9691	−	4.68835i	−0.419451	−	0.151632i
$957$	10.2694	+	2.48920i	0.331963	+	0.0804645i
$958$	−4.79956	+	27.3944i	−0.155067	+	0.885072i
$959$	5.22066			0.168584
$960$	−20.9693	+	39.0256i	−0.676783	+	1.25954i
$961$	−35.5052			−1.14533
$962$	−1.92023	+	10.9601i	−0.0619108	+	0.353367i
$963$	11.8007	+	36.8659i	0.380271	+	1.18799i
$964$	−20.6719	−	7.47293i	−0.665797	−	0.240687i
$965$	−54.7663	+	54.7663i	−1.76299	+	1.76299i
$966$	−8.59302	+	19.7037i	−0.276476	+	0.633955i
$967$	−3.67868			−0.118298			−0.0591492	−	0.998249i	$-0.518839\pi$
$967$	−3.67868			−0.118298			−0.0591492	+	0.998249i	$0.518839\pi$
$968$	10.7249	+	6.14530i	0.344710	+	0.197517i
$969$	−6.70806	−	11.0004i	−0.215494	−	0.353384i
$970$	−23.5896	−	33.6113i	−0.757415	−	1.07919i
$971$	−19.8765	−	19.8765i	−0.637866	−	0.637866i	0.312162	−	0.950029i	$-0.398947\pi$
$971$	−19.8765	−	19.8765i	−0.637866	−	0.637866i	−0.950029	+	0.312162i	$0.898947\pi$
$972$	−31.1579	+	1.08768i	−0.999391	+	0.0348874i
$973$	11.9868	−	11.9868i	0.384279	−	0.384279i
$974$	−0.177648	+	1.01396i	−0.00569220	+	0.0324893i
$975$	−9.99795	+	6.09676i	−0.320191	+	0.195253i
$976$	11.9072	−	1.09411i	0.381139	−	0.0350215i
$977$			33.2269i			1.06302i	0.847051	+	0.531511i	$0.178376\pi$
$977$			33.2269i			1.06302i	−0.847051	+	0.531511i	$0.821624\pi$
$978$	2.86864	+	7.30588i	0.0917290	+	0.233616i
$979$	21.1715	+	21.1715i	0.676645	+	0.676645i
$980$	−5.78948	+	2.71507i	−0.184938	+	0.0867298i
$981$	−30.1313	+	9.64496i	−0.962020	+	0.307940i
$982$	3.52820	−	2.47621i	0.112589	−	0.0790191i
$983$		−	17.2861i		−	0.551341i	−0.961252	−	0.275671i	$-0.911100\pi$
$983$		−	17.2861i		−	0.551341i	0.961252	−	0.275671i	$-0.0888999\pi$
$984$	−16.1030	−	15.2480i	−0.513346	−	0.486087i
$985$			53.9472i			1.71890i
$986$	−5.64478	−	8.04289i	−0.179766	−	0.256138i
$987$	−3.51239	+	14.4907i	−0.111801	+	0.461242i
$988$	−6.17677	−	2.23291i	−0.196509	−	0.0710384i
$989$	−30.4211	−	30.4211i	−0.967336	−	0.967336i
$990$	−21.1111	+	27.8251i	−0.670953	+	0.884340i
$991$			36.1152i			1.14724i	0.819123	+	0.573618i	$0.194461\pi$
$991$			36.1152i			1.14724i	−0.819123	+	0.573618i	$0.805539\pi$
$992$	−29.8454	−	35.1770i	−0.947592	−	1.11687i
$993$	20.8184	+	34.1396i	0.660651	+	1.08339i
$994$	6.58275	+	1.15332i	0.208792	+	0.0365809i
$995$	−12.8110	+	12.8110i	−0.406135	+	0.406135i
$996$	−7.28222	−	35.7937i	−0.230746	−	1.13417i
$997$	0.871700	+	0.871700i	0.0276070	+	0.0276070i	0.720776	−	0.693169i	$-0.243786\pi$
$997$	0.871700	+	0.871700i	0.0276070	+	0.0276070i	−0.693169	+	0.720776i	$0.743786\pi$
$998$	−41.7143	+	29.2765i	−1.32044	+	0.926733i
$999$	31.4983	−	2.27142i	0.996563	−	0.0718645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.13	yes	40
3.2	odd	2	inner	336.2.s.c.155.8	✓	40
4.3	odd	2		1344.2.s.c.911.10		40
12.11	even	2		1344.2.s.c.911.19		40
16.3	odd	4	inner	336.2.s.c.323.8	yes	40
16.13	even	4		1344.2.s.c.239.19		40
48.29	odd	4		1344.2.s.c.239.10		40
48.35	even	4	inner	336.2.s.c.323.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.8	✓	40	3.2	odd	2	inner
336.2.s.c.155.13	yes	40	1.1	even	1	trivial
336.2.s.c.323.8	yes	40	16.3	odd	4	inner
336.2.s.c.323.13	yes	40	48.35	even	4	inner
1344.2.s.c.239.10		40	48.29	odd	4
1344.2.s.c.239.19		40	16.13	even	4
1344.2.s.c.911.10		40	4.3	odd	2
1344.2.s.c.911.19		40	12.11	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.244056 - 1.39300i) q^{2} +(0.408017 - 1.68331i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(2.26080 - 2.26080i) q^{5} +(-2.24526 - 0.979187i) q^{6} -1.00000 q^{7} +(-1.40619 + 2.45410i) q^{8} +(-2.66704 - 1.37363i) q^{9} +O(q^{10})\)	\(q+(0.244056 - 1.39300i) q^{2} +(0.408017 - 1.68331i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(2.26080 - 2.26080i) q^{5} +(-2.24526 - 0.979187i) q^{6} -1.00000 q^{7} +(-1.40619 + 2.45410i) q^{8} +(-2.66704 - 1.37363i) q^{9} +(-2.59752 - 3.70105i) q^{10} +(1.82069 + 1.82069i) q^{11} +(-1.91197 + 2.88866i) q^{12} +(0.915413 - 0.915413i) q^{13} +(-0.244056 + 1.39300i) q^{14} +(-2.88318 - 4.72806i) q^{15} +(3.07537 + 2.55776i) q^{16} -2.93247i q^{17} +(-2.56438 + 3.37994i) q^{18} +(1.79372 + 1.79372i) q^{19} +(-5.78948 + 2.71507i) q^{20} +(-0.408017 + 1.68331i) q^{21} +(2.98056 - 2.09186i) q^{22} +8.77567i q^{23} +(3.55726 + 3.36837i) q^{24} -5.22244i q^{25} +(-1.05175 - 1.49858i) q^{26} +(-3.40045 + 3.92899i) q^{27} +(1.88087 + 0.679939i) q^{28} +(1.67539 + 1.67539i) q^{29} +(-7.28983 + 2.86234i) q^{30} -8.15507i q^{31} +(4.31351 - 3.65973i) q^{32} +(3.80765 - 2.32191i) q^{33} +(-4.08491 - 0.715687i) q^{34} +(-2.26080 + 2.26080i) q^{35} +(4.08239 + 4.39706i) q^{36} +(-4.29751 - 4.29751i) q^{37} +(2.93642 - 2.06088i) q^{38} +(-1.16742 - 1.91442i) q^{39} +(2.36912 + 8.72736i) q^{40} -4.52681 q^{41} +(2.24526 + 0.979187i) q^{42} +(-3.46653 + 3.46653i) q^{43} +(-2.18653 - 4.66245i) q^{44} +(-9.13517 + 2.92414i) q^{45} +(12.2245 + 2.14176i) q^{46} +8.60844 q^{47} +(5.56029 - 4.13318i) q^{48} +1.00000 q^{49} +(-7.27483 - 1.27457i) q^{50} +(-4.93624 - 1.19649i) q^{51} +(-2.34420 + 1.09935i) q^{52} +(6.48541 - 6.48541i) q^{53} +(4.64316 + 5.69570i) q^{54} +8.23243 q^{55} +(1.40619 - 2.45410i) q^{56} +(3.75125 - 2.28752i) q^{57} +(2.74270 - 1.92492i) q^{58} +(8.08166 + 8.08166i) q^{59} +(2.20809 + 10.8533i) q^{60} +(2.11377 - 2.11377i) q^{61} +(-11.3600 - 1.99030i) q^{62} +(2.66704 + 1.37363i) q^{63} +(-4.04525 - 6.90188i) q^{64} -4.13913i q^{65} +(-2.30513 - 5.87072i) q^{66} +(-2.17584 - 2.17584i) q^{67} +(-1.99390 + 5.51560i) q^{68} +(14.7721 + 3.58062i) q^{69} +(2.59752 + 3.70105i) q^{70} -4.72561i q^{71} +(7.12142 - 4.61361i) q^{72} +8.88001i q^{73} +(-7.03525 + 4.93758i) q^{74} +(-8.79096 - 2.13084i) q^{75} +(-2.15414 - 4.59338i) q^{76} +(-1.82069 - 1.82069i) q^{77} +(-2.95170 + 1.15898i) q^{78} -10.6576i q^{79} +(12.7354 - 1.17021i) q^{80} +(5.22626 + 7.32709i) q^{81} +(-1.10480 + 6.30583i) q^{82} +(-7.45604 + 7.45604i) q^{83} +(1.91197 - 2.88866i) q^{84} +(-6.62972 - 6.62972i) q^{85} +(3.98283 + 5.67489i) q^{86} +(3.50379 - 2.13661i) q^{87} +(-7.02840 + 1.90793i) q^{88} +11.6283 q^{89} +(1.84382 + 13.4389i) q^{90} +(-0.915413 + 0.915413i) q^{91} +(5.96692 - 16.5059i) q^{92} +(-13.7275 - 3.32740i) q^{93} +(2.10095 - 11.9915i) q^{94} +8.11049 q^{95} +(-4.40047 - 8.75419i) q^{96} +9.08157 q^{97} +(0.244056 - 1.39300i) q^{98} +(-2.35490 - 7.35683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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