LMFDB - Embedded newform 234.2.z.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.71677 + 0.229570i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.88241 + 0.772339i) q^{5} +(1.59885 - 0.666081i) q^{6} +(2.05205 + 2.05205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.89459 - 0.788239i) q^{9} +(2.58430 - 1.49204i) q^{10} +(-1.47054 - 5.48814i) q^{11} +(-1.37198 + 1.05720i) q^{12} +(-3.00654 - 1.99016i) q^{13} +(-2.51324 - 1.45102i) q^{14} +(4.77112 - 1.98764i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.49277 - 4.31761i) q^{17} +(-2.59195 + 1.51056i) q^{18} +(-1.01552 - 3.78997i) q^{19} +(-2.11007 + 2.11007i) q^{20} +(-3.99399 - 3.05181i) q^{21} +(2.84087 + 4.92053i) q^{22} -1.25580 q^{23} +(1.05161 - 1.37627i) q^{24} +(3.38164 - 1.95239i) q^{25} +(3.41918 + 1.14420i) q^{26} +(-4.78840 + 2.01774i) q^{27} +(2.80315 + 0.751103i) q^{28} +(7.93943 + 4.58383i) q^{29} +(-4.09411 + 3.15477i) q^{30} +(-1.55469 - 5.80218i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.78450 + 9.08428i) q^{33} +(-1.29035 + 4.81566i) q^{34} +(-7.49973 - 4.32997i) q^{35} +(2.11267 - 2.12993i) q^{36} +(-0.714749 + 2.66748i) q^{37} +(1.96184 + 3.39800i) q^{38} +(5.61841 + 2.72643i) q^{39} +(1.49204 - 2.58430i) q^{40} +(-2.81693 - 2.81693i) q^{41} +(4.64776 + 1.91410i) q^{42} -8.85117i q^{43} +(-4.01760 - 4.01760i) q^{44} +(-7.73461 + 4.50763i) q^{45} +(1.21301 - 0.325025i) q^{46} +(-3.91098 - 1.04794i) q^{47} +(-0.659571 + 1.60155i) q^{48} +1.42183i q^{49} +(-2.76110 + 2.76110i) q^{50} +(-3.28832 + 7.98460i) q^{51} +(-3.59882 - 0.220258i) q^{52} +10.8154i q^{53} +(4.10301 - 3.18831i) q^{54} +(8.47741 + 14.6833i) q^{55} -2.90204 q^{56} +(2.61348 + 6.27338i) q^{57} +(-8.85528 - 2.37277i) q^{58} +(-6.40469 - 1.71613i) q^{59} +(3.13809 - 4.10691i) q^{60} -5.53628 q^{61} +(3.00343 + 5.20209i) q^{62} +(7.55736 + 4.32235i) q^{63} -1.00000i q^{64} +(10.2031 + 3.41438i) q^{65} +(-6.00673 - 7.79524i) q^{66} +(-0.350486 + 0.350486i) q^{67} -4.98554i q^{68} +(2.15592 - 0.288294i) q^{69} +(8.36486 + 2.24136i) q^{70} +(0.216213 - 0.0579342i) q^{71} +(-1.48942 + 2.60416i) q^{72} +(4.69747 + 4.69747i) q^{73} -2.76158i q^{74} +(-5.35729 + 4.12813i) q^{75} +(-2.77445 - 2.77445i) q^{76} +(8.24432 - 14.2796i) q^{77} +(-6.13262 - 1.17938i) q^{78} +(-7.68273 - 13.3069i) q^{79} +(-0.772339 + 2.88241i) q^{80} +(7.75736 - 4.56327i) q^{81} +(3.45002 + 1.99187i) q^{82} +(-0.548858 + 2.04837i) q^{83} +(-4.98480 - 0.645949i) q^{84} +(-3.85053 + 14.3704i) q^{85} +(2.29085 + 8.54958i) q^{86} +(-14.6825 - 6.04672i) q^{87} +(4.92053 + 2.84087i) q^{88} +(-9.00272 - 2.41227i) q^{89} +(6.30440 - 6.35591i) q^{90} +(-2.08566 - 10.2535i) q^{91} +(-1.08755 + 0.627900i) q^{92} +(4.00105 + 9.60410i) q^{93} +4.04894 q^{94} +(5.85429 + 10.1399i) q^{95} +(0.222585 - 1.71769i) q^{96} +(1.38610 - 1.38610i) q^{97} +(-0.367996 - 1.37338i) q^{98} +(-8.58260 - 14.7268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.71677	+	0.229570i	−0.991177	+	0.132543i
$3$	−1.71677	+	0.229570i	−0.991177	+	0.132543i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.88241	+	0.772339i	−1.28905	+	0.345400i	−0.837300	−	0.546743i	$-0.815867\pi$
$5$	−2.88241	+	0.772339i	−1.28905	+	0.345400i	−0.451752	+	0.892144i	$0.649201\pi$
$6$	1.59885	−	0.666081i	0.652730	−	0.271926i
$7$	2.05205	+	2.05205i	0.775602	+	0.775602i	0.979080	−	0.203477i	$-0.0652243\pi$
$7$	2.05205	+	2.05205i	0.775602	+	0.775602i	−0.203477	+	0.979080i	$0.565224\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.89459	−	0.788239i	0.964865	−	0.262746i
$10$	2.58430	−	1.49204i	0.817226	−	0.471826i
$11$	−1.47054	−	5.48814i	−0.443386	−	1.65474i	−0.720164	−	0.693804i	$-0.755934\pi$
$11$	−1.47054	−	5.48814i	−0.443386	−	1.65474i	0.276779	−	0.960934i	$-0.410733\pi$
$12$	−1.37198	+	1.05720i	−0.396057	+	0.305187i
$13$	−3.00654	−	1.99016i	−0.833864	−	0.551970i
$13$	−3.00654	−	1.99016i	−0.833864	−	0.551970i
$14$	−2.51324	−	1.45102i	−0.671691	−	0.387801i
$15$	4.77112	−	1.98764i	1.23190	−	0.513207i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.49277	−	4.31761i	0.604586	−	1.04717i	−0.387531	−	0.921857i	$-0.626672\pi$
$17$	2.49277	−	4.31761i	0.604586	−	1.04717i	0.992117	−	0.125317i	$-0.0399947\pi$
$18$	−2.59195	+	1.51056i	−0.610929	+	0.356042i
$19$	−1.01552	−	3.78997i	−0.232976	−	0.869480i	−0.979051	−	0.203617i	$-0.934730\pi$
$19$	−1.01552	−	3.78997i	−0.232976	−	0.869480i	0.746074	−	0.665863i	$-0.231936\pi$
$20$	−2.11007	+	2.11007i	−0.471826	+	0.471826i
$21$	−3.99399	−	3.05181i	−0.871560	−	0.665959i
$22$	2.84087	+	4.92053i	0.605676	+	1.04906i
$23$	−1.25580			−0.261852			−0.130926	−	0.991392i	$-0.541795\pi$
$23$	−1.25580			−0.261852			−0.130926	+	0.991392i	$0.541795\pi$
$24$	1.05161	−	1.37627i	0.214659	−	0.280930i
$25$	3.38164	−	1.95239i	0.676328	−	0.390478i
$26$	3.41918	+	1.14420i	0.670557	+	0.224395i
$27$	−4.78840	+	2.01774i	−0.921527	+	0.388314i
$28$	2.80315	+	0.751103i	0.529746	+	0.141945i
$29$	7.93943	+	4.58383i	1.47431	+	0.851196i	0.999581	−	0.0289336i	$-0.00921112\pi$
$29$	7.93943	+	4.58383i	1.47431	+	0.851196i	0.474733	+	0.880130i	$0.342544\pi$
$30$	−4.09411	+	3.15477i	−0.747479	+	0.575980i
$31$	−1.55469	−	5.80218i	−0.279231	−	1.04210i	−0.952953	−	0.303118i	$-0.901972\pi$
$31$	−1.55469	−	5.80218i	−0.279231	−	1.04210i	0.673722	−	0.738984i	$-0.264694\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	3.78450	+	9.08428i	0.658797	+	1.58137i
$34$	−1.29035	+	4.81566i	−0.221294	+	0.825880i
$35$	−7.49973	−	4.32997i	−1.26769	−	0.731898i
$36$	2.11267	−	2.12993i	0.352112	−	0.354989i
$37$	−0.714749	+	2.66748i	−0.117504	+	0.438531i	−0.999462	−	0.0327970i	$-0.989559\pi$
$37$	−0.714749	+	2.66748i	−0.117504	+	0.438531i	0.881958	+	0.471328i	$0.156225\pi$
$38$	1.96184	+	3.39800i	0.318252	+	0.551228i
$39$	5.61841	+	2.72643i	0.899666	+	0.436578i
$40$	1.49204	−	2.58430i	0.235913	−	0.408613i
$41$	−2.81693	−	2.81693i	−0.439930	−	0.439930i	0.452058	−	0.891989i	$-0.350690\pi$
$41$	−2.81693	−	2.81693i	−0.439930	−	0.439930i	−0.891989	+	0.452058i	$0.850690\pi$
$42$	4.64776	+	1.91410i	0.717165	+	0.295352i
$43$		−	8.85117i		−	1.34979i	−0.737913	−	0.674896i	$-0.764189\pi$
$43$		−	8.85117i		−	1.34979i	0.737913	−	0.674896i	$-0.235811\pi$
$44$	−4.01760	−	4.01760i	−0.605676	−	0.605676i
$45$	−7.73461	+	4.50763i	−1.15301	+	0.671958i
$46$	1.21301	−	0.325025i	0.178848	−	0.0479223i
$47$	−3.91098	−	1.04794i	−0.570475	−	0.152858i	−0.0379606	−	0.999279i	$-0.512086\pi$
$47$	−3.91098	−	1.04794i	−0.570475	−	0.152858i	−0.532514	+	0.846421i	$0.678753\pi$
$48$	−0.659571	+	1.60155i	−0.0952009	+	0.231164i
$49$			1.42183i			0.203118i
$50$	−2.76110	+	2.76110i	−0.390478	+	0.390478i
$51$	−3.28832	+	7.98460i	−0.460457	+	1.11807i
$52$	−3.59882	−	0.220258i	−0.499066	−	0.0305443i
$53$			10.8154i			1.48561i	0.669509	+	0.742804i	$0.266505\pi$
$53$			10.8154i			1.48561i	−0.669509	+	0.742804i	$0.733495\pi$
$54$	4.10301	−	3.18831i	0.558348	−	0.433875i
$55$	8.47741	+	14.6833i	1.14309	+	1.97990i
$56$	−2.90204			−0.387801
$57$	2.61348	+	6.27338i	0.346164	+	0.830929i
$58$	−8.85528	−	2.37277i	−1.16276	−	0.311559i
$59$	−6.40469	−	1.71613i	−0.833820	−	0.223421i	−0.183441	−	0.983031i	$-0.558723\pi$
$59$	−6.40469	−	1.71613i	−0.833820	−	0.223421i	−0.650380	+	0.759609i	$0.725390\pi$
$60$	3.13809	−	4.10691i	0.405126	−	0.530200i
$61$	−5.53628			−0.708848			−0.354424	−	0.935085i	$-0.615323\pi$
$61$	−5.53628			−0.708848			−0.354424	+	0.935085i	$0.615323\pi$
$62$	3.00343	+	5.20209i	0.381436	+	0.660667i
$63$	7.55736	+	4.32235i	0.952138	+	0.544565i
$64$		−	1.00000i		−	0.125000i
$65$	10.2031	+	3.41438i	1.26554	+	0.423502i
$66$	−6.00673	−	7.79524i	−0.739377	−	0.959528i
$67$	−0.350486	+	0.350486i	−0.0428187	+	0.0428187i	−0.728192	−	0.685373i	$-0.759639\pi$
$67$	−0.350486	+	0.350486i	−0.0428187	+	0.0428187i	0.685373	+	0.728192i	$0.259639\pi$
$68$		−	4.98554i		−	0.604586i
$69$	2.15592	−	0.288294i	0.259542	−	0.0347066i
$70$	8.36486	+	2.24136i	0.999792	+	0.267893i
$71$	0.216213	−	0.0579342i	0.0256598	−	0.00687552i	−0.245966	−	0.969278i	$-0.579105\pi$
$71$	0.216213	−	0.0579342i	0.0256598	−	0.00687552i	0.271626	+	0.962403i	$0.412439\pi$
$72$	−1.48942	+	2.60416i	−0.175530	+	0.306903i
$73$	4.69747	+	4.69747i	0.549797	+	0.549797i	0.926382	−	0.376585i	$-0.122902\pi$
$73$	4.69747	+	4.69747i	0.549797	+	0.549797i	−0.376585	+	0.926382i	$0.622902\pi$
$74$		−	2.76158i		−	0.321027i
$75$	−5.35729	+	4.12813i	−0.618606	+	0.476675i
$76$	−2.77445	−	2.77445i	−0.318252	−	0.318252i
$77$	8.24432	−	14.2796i	0.939527	−	1.62731i
$78$	−6.13262	−	1.17938i	−0.694383	−	0.133538i
$79$	−7.68273	−	13.3069i	−0.864375	−	1.49714i	−0.867666	−	0.497147i	$-0.834381\pi$
$79$	−7.68273	−	13.3069i	−0.864375	−	1.49714i	0.00329123	−	0.999995i	$-0.498952\pi$
$80$	−0.772339	+	2.88241i	−0.0863501	+	0.322263i
$81$	7.75736	−	4.56327i	0.861929	−	0.507029i
$82$	3.45002	+	1.99187i	0.380991	+	0.219965i
$83$	−0.548858	+	2.04837i	−0.0602450	+	0.224837i	−0.989484	−	0.144642i	$-0.953797\pi$
$83$	−0.548858	+	2.04837i	−0.0602450	+	0.224837i	0.929239	+	0.369479i	$0.120464\pi$
$84$	−4.98480	−	0.645949i	−0.543886	−	0.0704788i
$85$	−3.85053	+	14.3704i	−0.417648	+	1.55869i
$86$	2.29085	+	8.54958i	0.247029	+	0.921924i
$87$	−14.6825	−	6.04672i	−1.57413	−	0.648277i
$88$	4.92053	+	2.84087i	0.524531	+	0.302838i
$89$	−9.00272	−	2.41227i	−0.954287	−	0.255700i	−0.252107	−	0.967699i	$-0.581123\pi$
$89$	−9.00272	−	2.41227i	−0.954287	−	0.255700i	−0.702180	+	0.711999i	$0.747790\pi$
$90$	6.30440	−	6.35591i	0.664542	−	0.669971i
$91$	−2.08566	−	10.2535i	−0.218637	−	1.07486i
$92$	−1.08755	+	0.627900i	−0.113385	+	0.0654631i
$93$	4.00105	+	9.60410i	0.414890	+	0.995899i
$94$	4.04894			0.417617
$95$	5.85429	+	10.1399i	0.600637	+	1.04033i
$96$	0.222585	−	1.71769i	0.0227174	−	0.175311i
$97$	1.38610	−	1.38610i	0.140737	−	0.140737i	−0.633228	−	0.773965i	$-0.718271\pi$
$97$	1.38610	−	1.38610i	0.140737	−	0.140737i	0.773965	+	0.633228i	$0.218271\pi$
$98$	−0.367996	−	1.37338i	−0.0371732	−	0.138732i
$99$	−8.58260	−	14.7268i	−0.862583	−	1.48010i
$100$	1.95239	−	3.38164i	0.195239	−	0.338164i
$101$	6.00940	−	10.4086i	0.597958	−	1.03569i	−0.395164	−	0.918610i	$-0.629312\pi$
$101$	6.00940	−	10.4086i	0.597958	−	1.03569i	0.993122	−	0.117083i	$-0.0373543\pi$
$102$	1.10971	−	8.56361i	0.109877	−	0.847924i
$103$	−3.61187	−	2.08532i	−0.355889	−	0.205472i	0.311387	−	0.950283i	$-0.399206\pi$
$103$	−3.61187	−	2.08532i	−0.355889	−	0.205472i	−0.667276	+	0.744811i	$0.732540\pi$
$104$	3.53320	−	0.718689i	0.346459	−	0.0704733i
$105$	13.8693	+	5.71184i	1.35351	+	0.557419i
$106$	−2.79923	−	10.4469i	−0.271885	−	1.01469i
$107$	3.53808	−	2.04271i	0.342039	−	0.197476i	−0.319134	−	0.947710i	$-0.603392\pi$
$107$	3.53808	−	2.04271i	0.342039	−	0.197476i	0.661173	+	0.750233i	$0.270059\pi$
$108$	−3.13800	+	4.14161i	−0.301954	+	0.398527i
$109$	−1.51598	+	1.51598i	−0.145204	+	0.145204i	−0.775972	−	0.630768i	$-0.782740\pi$
$109$	−1.51598	+	1.51598i	−0.145204	+	0.145204i	0.630768	+	0.775972i	$0.282740\pi$
$110$	−11.9889	−	11.9889i	−1.14309	−	1.14309i
$111$	0.614685	−	4.74353i	0.0583433	−	0.450236i
$112$	2.80315	−	0.751103i	0.264873	−	0.0709725i
$113$	9.69146	−	5.59536i	0.911695	−	0.526368i	0.0307192	−	0.999528i	$-0.490220\pi$
$113$	9.69146	−	5.59536i	0.911695	−	0.526368i	0.880976	+	0.473160i	$0.156887\pi$
$114$	−4.14810	−	5.38320i	−0.388505	−	0.504183i
$115$	3.61973	−	0.969903i	0.337541	−	0.0904439i
$116$	9.16766			0.851196
$117$	−10.2714	−	3.39083i	−0.949594	−	0.313482i
$118$	6.63063			0.610399
$119$	13.9752	−	3.74466i	1.28111	−	0.343272i
$120$	−1.96822	+	4.77917i	−0.179673	+	0.436277i
$121$	−18.4309	+	10.6411i	−1.67554	+	0.967373i
$122$	5.34763	−	1.43289i	0.484152	−	0.129728i
$123$	5.48270	+	4.18933i	0.494359	+	0.377740i
$124$	−4.24749	−	4.24749i	−0.381436	−	0.381436i
$125$	2.31099	−	2.31099i	0.206701	−	0.206701i
$126$	−8.41856	−	2.21908i	−0.749985	−	0.197691i
$127$	−5.15260	+	2.97485i	−0.457219	+	0.263976i	−0.710874	−	0.703319i	$-0.751701\pi$
$127$	−5.15260	+	2.97485i	−0.457219	+	0.263976i	0.253655	+	0.967295i	$0.418367\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	2.03197	+	15.1954i	0.178905	+	1.33788i
$130$	−10.7392	−	0.657270i	−0.941889	−	0.0576464i
$131$	1.33669	+	0.771738i	0.116787	+	0.0674270i	0.557256	−	0.830341i	$-0.311854\pi$
$131$	1.33669	+	0.771738i	0.116787	+	0.0674270i	−0.440469	+	0.897768i	$0.645188\pi$
$132$	7.81961	+	5.97497i	0.680610	+	0.520054i
$133$	5.69332	−	9.86112i	0.493674	−	0.855068i
$134$	0.247831	−	0.429256i	0.0214094	−	0.0370821i
$135$	12.2437	−	9.51421i	1.05377	−	0.818853i
$136$	1.29035	+	4.81566i	0.110647	+	0.412940i
$137$	−11.7581	+	11.7581i	−1.00456	+	1.00456i	−0.00457496	+	0.999990i	$0.501456\pi$
$137$	−11.7581	+	11.7581i	−1.00456	+	1.00456i	−0.999990	+	0.00457496i	$0.998544\pi$
$138$	−2.00784	+	0.836464i	−0.170919	+	0.0712045i
$139$	2.85958	+	4.95293i	0.242546	+	0.420102i	0.961439	−	0.275019i	$-0.0886841\pi$
$139$	2.85958	+	4.95293i	0.242546	+	0.420102i	−0.718893	+	0.695121i	$0.755351\pi$
$140$	−8.65994			−0.731898
$141$	6.95483	+	0.901233i	0.585702	+	0.0758975i
$142$	−0.193851	+	0.111920i	−0.0162677	+	0.00939213i
$143$	−6.50102	+	19.4269i	−0.543643	+	1.62456i
$144$	0.764662	−	2.90091i	0.0637219	−	0.241743i
$145$	−26.4249	−	7.08054i	−2.19447	−	0.588007i
$146$	−5.75320	−	3.32161i	−0.476138	−	0.274899i
$147$	−0.326409	−	2.44095i	−0.0269218	−	0.201326i
$148$	0.714749	+	2.66748i	0.0587520	+	0.219266i
$149$	1.48770	−	5.55216i	0.121877	−	0.454851i	−0.877832	−	0.478968i	$-0.841011\pi$
$149$	1.48770	−	5.55216i	0.121877	−	0.454851i	0.999709	+	0.0241173i	$0.00767752\pi$
$150$	4.10630	−	5.37403i	0.335278	−	0.438788i
$151$	−1.77477	+	6.62353i	−0.144429	+	0.539015i	0.855351	+	0.518048i	$0.173341\pi$
$151$	−1.77477	+	6.62353i	−0.144429	+	0.539015i	−0.999780	+	0.0209672i	$0.993325\pi$
$152$	3.39800	+	1.96184i	0.275614	+	0.159126i
$153$	3.81226	−	14.4626i	0.308203	−	1.16923i
$154$	−4.26757	+	15.9268i	−0.343891	+	1.28342i
$155$	8.96250	+	15.5235i	0.719885	+	1.24688i
$156$	6.22890	−	0.448050i	0.498711	−	0.0358727i
$157$	3.63525	−	6.29644i	0.290124	−	0.502510i	−0.683714	−	0.729750i	$-0.739637\pi$
$157$	3.63525	−	6.29644i	0.290124	−	0.502510i	0.973839	+	0.227239i	$0.0729699\pi$
$158$	10.8650	+	10.8650i	0.864375	+	0.864375i
$159$	−2.48289	−	18.5675i	−0.196906	−	1.47250i
$160$		−	2.98409i		−	0.235913i
$161$	−2.57696	−	2.57696i	−0.203093	−	0.203093i
$162$	−6.31197	+	6.41553i	−0.495915	+	0.504051i
$163$	3.48959	−	0.935032i	0.273326	−	0.0732374i	−0.119553	−	0.992828i	$-0.538146\pi$
$163$	3.48959	−	0.935032i	0.273326	−	0.0732374i	0.392878	+	0.919590i	$0.371479\pi$
$164$	−3.84800	−	1.03107i	−0.300478	−	0.0805129i
$165$	−17.9246	−	23.2617i	−1.39543	−	1.81092i
$166$		−	2.12062i		−	0.164592i
$167$	1.46794	−	1.46794i	0.113593	−	0.113593i	−0.648026	−	0.761618i	$-0.724405\pi$
$167$	1.46794	−	1.46794i	0.113593	−	0.113593i	0.761618	+	0.648026i	$0.224405\pi$
$168$	4.98213	−	0.666222i	0.384380	−	0.0514002i
$169$	5.07854	+	11.9670i	0.390657	+	0.920536i
$170$		−	14.8773i		−	1.14104i
$171$	−5.92693	−	10.1700i	−0.453243	−	0.777717i
$172$	−4.42559	−	7.66534i	−0.337448	−	0.584477i
$173$	3.83968			0.291926			0.145963	−	0.989290i	$-0.453372\pi$
$173$	3.83968			0.291926			0.145963	+	0.989290i	$0.453372\pi$
$174$	15.7472	+	2.04058i	1.19379	+	0.154696i
$175$	10.9457	+	2.93289i	0.827417	+	0.221706i
$176$	−5.48814	−	1.47054i	−0.413684	−	0.110846i
$177$	11.3894	+	1.47588i	0.856077	+	0.110934i
$178$	9.32031			0.698587
$179$	6.05203	+	10.4824i	0.452350	+	0.783493i	0.998532	−	0.0541739i	$-0.0172525\pi$
$179$	6.05203	+	10.4824i	0.452350	+	0.783493i	−0.546182	+	0.837667i	$0.683919\pi$
$180$	−4.44456	+	7.77103i	−0.331278	+	0.579219i
$181$			11.5453i			0.858155i	0.903268	+	0.429077i	$0.141161\pi$
$181$			11.5453i			0.858155i	−0.903268	+	0.429077i	$0.858839\pi$
$182$	4.66839	+	9.36429i	0.346044	+	0.694127i
$183$	9.50451	−	1.27097i	0.702594	−	0.0939525i
$184$	0.887984	−	0.887984i	0.0654631	−	0.0654631i
$185$		−	8.24079i		−	0.605875i
$186$	−6.35044	−	8.24130i	−0.465637	−	0.604281i
$187$	−27.3614	−	7.33146i	−2.00086	−	0.536129i
$188$	−3.91098	+	1.04794i	−0.285238	+	0.0764292i
$189$	−13.9665	−	5.68553i	−1.01592	−	0.413561i
$190$	−8.27922	−	8.27922i	−0.600637	−	0.600637i
$191$		−	8.92051i		−	0.645465i	−0.946490	−	0.322733i	$-0.895399\pi$
$191$		−	8.92051i		−	0.645465i	0.946490	−	0.322733i	$-0.104601\pi$
$192$	0.229570	+	1.71677i	0.0165678	+	0.123897i
$193$	3.26824	+	3.26824i	0.235253	+	0.235253i	0.814881	−	0.579628i	$-0.196802\pi$
$193$	3.26824	+	3.26824i	0.235253	+	0.235253i	−0.579628	+	0.814881i	$0.696802\pi$
$194$	−0.980120	+	1.69762i	−0.0703685	+	0.121882i
$195$	−18.3003	−	3.51936i	−1.31051	−	0.252027i
$196$	0.710914	+	1.23134i	0.0507795	+	0.0879527i
$197$	5.12868	−	19.1405i	0.365403	−	1.36370i	−0.501470	−	0.865175i	$-0.667207\pi$
$197$	5.12868	−	19.1405i	0.365403	−	1.36370i	0.866873	−	0.498528i	$-0.166126\pi$
$198$	12.1017	+	12.0037i	0.860032	+	0.853063i
$199$	16.9509	+	9.78661i	1.20162	+	0.693754i	0.960915	−	0.276844i	$-0.0892886\pi$
$199$	16.9509	+	9.78661i	1.20162	+	0.693754i	0.240703	+	0.970599i	$0.422622\pi$
$200$	−1.01063	+	3.77173i	−0.0714625	+	0.266702i
$201$	0.521243	−	0.682165i	0.0367656	−	0.0481162i
$202$	−3.11070	+	11.6093i	−0.218868	+	0.816826i
$203$	6.88586	+	25.6984i	0.483292	+	1.80367i
$204$	1.14453	+	8.55903i	0.0801334	+	0.599252i
$205$	10.2952	+	5.94392i	0.719045	+	0.415141i
$206$	4.02852	+	1.07944i	0.280680	+	0.0752081i
$207$	−3.63503	+	0.989870i	−0.252652	+	0.0688007i
$208$	−3.22680	+	1.60866i	−0.223738	+	0.111540i
$209$	−19.3066	+	11.1466i	−1.33546	+	0.771030i
$210$	−14.8751	−	1.92757i	−1.02648	−	0.133015i
$211$	21.8975			1.50749			0.753743	−	0.657169i	$-0.228246\pi$
$211$	21.8975			1.50749			0.753743	+	0.657169i	$0.228246\pi$
$212$	5.40769	+	9.36640i	0.371402	+	0.643287i
$213$	−0.357888	+	0.149096i	−0.0245221	+	0.0102159i
$214$	−2.88883	+	2.88883i	−0.197476	+	0.197476i
$215$	6.83610	+	25.5127i	0.466218	+	1.73995i
$216$	1.95915	−	4.81266i	0.133303	−	0.327460i
$217$	8.71607	−	15.0967i	0.591685	−	1.02483i
$218$	1.07196	−	1.85668i	0.0726021	−	0.125751i
$219$	−9.14287	−	6.98607i	−0.617818	−	0.472075i
$220$	14.6833	+	8.47741i	0.989948	+	0.571547i
$221$	−16.0873	+	8.02004i	−1.08215	+	0.539486i
$222$	0.633977	+	4.74099i	0.0425497	+	0.318195i
$223$	4.34353	+	16.2103i	0.290864	+	1.08552i	0.944447	+	0.328665i	$0.106599\pi$
$223$	4.34353	+	16.2103i	0.290864	+	1.08552i	−0.653582	+	0.756855i	$0.726735\pi$
$224$	−2.51324	+	1.45102i	−0.167923	+	0.0969503i
$225$	8.24953	−	8.31692i	0.549968	−	0.554461i
$226$	−7.91304	+	7.91304i	−0.526368	+	0.526368i
$227$	−12.4280	−	12.4280i	−0.824872	−	0.824872i	0.161930	−	0.986802i	$-0.448228\pi$
$227$	−12.4280	−	12.4280i	−0.824872	−	0.824872i	−0.986802	+	0.161930i	$0.948228\pi$
$228$	5.40003	+	4.12617i	0.357626	+	0.273262i
$229$	−19.7752	+	5.29875i	−1.30678	+	0.350151i	−0.844010	−	0.536327i	$-0.819811\pi$
$229$	−19.7752	+	5.29875i	−1.30678	+	0.350151i	−0.462771	+	0.886478i	$0.653145\pi$
$230$	−3.24536	+	1.87371i	−0.213993	+	0.123549i
$231$	−10.8754	+	26.4074i	−0.715550	+	1.73748i
$232$	−8.85528	+	2.37277i	−0.581378	+	0.155780i
$233$	−18.8411			−1.23432			−0.617160	−	0.786838i	$-0.711717\pi$
$233$	−18.8411			−1.23432			−0.617160	+	0.786838i	$0.711717\pi$
$234$	10.7991	+	0.616848i	0.705956	+	0.0403246i
$235$	12.0824			0.788169
$236$	−6.40469	+	1.71613i	−0.416910	+	0.111711i
$237$	16.2444	+	21.0811i	1.05518	+	1.36937i
$238$	−12.5299	+	7.23412i	−0.812190	+	0.468918i
$239$	0.429286	−	0.115027i	0.0277682	−	0.00744046i	−0.244908	−	0.969546i	$-0.578758\pi$
$239$	0.429286	−	0.115027i	0.0277682	−	0.00744046i	0.272676	+	0.962106i	$0.412091\pi$
$240$	0.664212	−	5.12574i	0.0428747	−	0.330865i
$241$	7.52680	+	7.52680i	0.484844	+	0.484844i	0.906675	−	0.421831i	$-0.138612\pi$
$241$	7.52680	+	7.52680i	0.484844	+	0.484844i	−0.421831	+	0.906675i	$0.638612\pi$
$242$	15.0488	−	15.0488i	0.967373	−	0.967373i
$243$	−12.2700	+	9.61494i	−0.787121	+	0.616798i
$244$	−4.79456	+	2.76814i	−0.306940	+	0.177212i
$245$	−1.09813	−	4.09829i	−0.0701571	−	0.261830i
$246$	−6.38016	−	2.62756i	−0.406784	−	0.167527i
$247$	−4.48945	+	13.4158i	−0.285657	+	0.853624i
$248$	5.20209	+	3.00343i	0.330333	+	0.190718i
$249$	0.472018	−	3.64257i	0.0299129	−	0.230839i
$250$	−1.63411	+	2.83037i	−0.103350	+	0.179008i
$251$	8.43667	−	14.6127i	0.532518	−	0.922348i	−0.466761	−	0.884383i	$-0.654579\pi$
$251$	8.43667	−	14.6127i	0.532518	−	0.922348i	0.999279	−	0.0379648i	$-0.0120875\pi$
$252$	8.70604	−	0.0354171i	0.548429	−	0.00223107i
$253$	1.84671	+	6.89201i	0.116102	+	0.433297i
$254$	4.20708	−	4.20708i	0.263976	−	0.263976i
$255$	3.31146	−	25.5546i	0.207372	−	1.60029i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.94500			−0.308461			−0.154230	−	0.988035i	$-0.549290\pi$
$257$	−4.94500			−0.308461			−0.154230	+	0.988035i	$0.549290\pi$
$258$	−5.89559	−	14.1517i	−0.367044	−	0.881049i
$259$	−6.94051	+	4.00710i	−0.431262	+	0.248989i
$260$	10.5434	−	2.14463i	0.653872	−	0.133004i
$261$	26.5946	+	7.01017i	1.64616	+	0.433918i
$262$	−1.49088	−	0.399481i	−0.0921070	−	0.0246800i
$263$	−25.1144	−	14.4998i	−1.54862	−	0.894096i	−0.998248	−	0.0591757i	$-0.981153\pi$
$263$	−25.1144	−	14.4998i	−1.54862	−	0.894096i	−0.550371	−	0.834920i	$-0.685514\pi$
$264$	−9.09960	−	3.74751i	−0.560042	−	0.230643i
$265$	−8.35314	−	31.1744i	−0.513130	−	1.91503i
$266$	−2.94708	+	10.9987i	−0.180697	+	0.674371i
$267$	16.0094	+	2.07456i	0.979759	+	0.126961i
$268$	−0.128287	+	0.478773i	−0.00783637	+	0.0292457i
$269$	7.67526	+	4.43131i	0.467969	+	0.270182i	0.715389	−	0.698726i	$-0.246250\pi$
$269$	7.67526	+	4.43131i	0.467969	+	0.270182i	−0.247420	+	0.968908i	$0.579583\pi$
$270$	−9.36408	+	12.3589i	−0.569880	+	0.752141i
$271$	2.17051	−	8.10046i	0.131849	−	0.492068i	−0.868142	−	0.496316i	$-0.834686\pi$
$271$	2.17051	−	8.10046i	0.131849	−	0.492068i	0.999991	+	0.00424836i	$0.00135230\pi$
$272$	−2.49277	−	4.31761i	−0.151146	−	0.261793i
$273$	5.93450	+	17.1240i	0.359172	+	1.03639i
$274$	8.31425	−	14.4007i	0.502282	−	0.869978i
$275$	−15.6878	−	15.6878i	−0.946013	−	0.946013i
$276$	1.72293	−	1.32763i	0.103708	−	0.0799139i
$277$		−	28.2050i		−	1.69468i	−0.531054	−	0.847338i	$-0.678204\pi$
$277$		−	28.2050i		−	1.69468i	0.531054	−	0.847338i	$-0.321796\pi$
$278$	−4.04405	−	4.04405i	−0.242546	−	0.242546i
$279$	−9.07370	−	15.5695i	−0.543228	−	0.932121i
$280$	8.36486	−	2.24136i	0.499896	−	0.133947i
$281$	18.1248	+	4.85654i	1.08124	+	0.289717i	0.755103	−	0.655607i	$-0.227587\pi$
$281$	18.1248	+	4.85654i	1.08124	+	0.289717i	0.326135	+	0.945323i	$0.394254\pi$
$282$	−6.95110	+	0.929518i	−0.413932	+	0.0553520i
$283$			16.6230i			0.988137i	0.869423	+	0.494068i	$0.164491\pi$
$283$			16.6230i			0.988137i	−0.869423	+	0.494068i	$0.835509\pi$
$284$	0.158279	−	0.158279i	0.00939213	−	0.00939213i
$285$	−12.3783	−	16.0639i	−0.733227	−	0.951546i
$286$	1.25145	−	20.4476i	0.0739998	−	1.20909i
$287$		−	11.5610i		−	0.682422i
$288$	0.0122042	+	2.99998i	0.000719140	+	0.176775i
$289$	−3.92782	−	6.80318i	−0.231048	−	0.400187i
$290$	27.3571			1.60646
$291$	−2.06140	+	2.69782i	−0.120842	+	0.158149i
$292$	6.41686	+	1.71939i	0.375519	+	0.100620i
$293$	14.0008	+	3.75150i	0.817934	+	0.219165i	0.643443	−	0.765494i	$-0.277505\pi$
$293$	14.0008	+	3.75150i	0.817934	+	0.219165i	0.174491	+	0.984659i	$0.444172\pi$
$294$	0.947051	+	2.27329i	0.0552332	+	0.132581i
$295$	19.7864			1.15201
$296$	−1.38079	−	2.39160i	−0.0802567	−	0.139009i
$297$	18.1152	+	23.3122i	1.05115	+	1.35271i
$298$			5.74802i			0.332974i
$299$	3.77561	+	2.49924i	0.218349	+	0.144535i
$300$	−2.57548	+	6.25371i	−0.148695	+	0.361058i
$301$	18.1631	−	18.1631i	1.04690	−	1.04690i
$302$		−	6.85718i		−	0.394587i
$303$	−7.92725	+	19.2487i	−0.455409	+	1.10581i
$304$	−3.78997	−	1.01552i	−0.217370	−	0.0582441i
$305$	15.9578	−	4.27588i	0.913742	−	0.244836i
$306$	0.0608446	+	14.9565i	0.00347826	+	0.855006i
$307$	−9.29617	−	9.29617i	−0.530561	−	0.530561i	0.390179	−	0.920739i	$-0.372413\pi$
$307$	−9.29617	−	9.29617i	−0.530561	−	0.530561i	−0.920739	+	0.390179i	$0.872413\pi$
$308$		−	16.4886i		−	0.939527i
$309$	6.67948	+	2.75083i	0.379982	+	0.156489i
$310$	−12.6749	−	12.6749i	−0.719885	−	0.719885i
$311$	0.400312	−	0.693361i	0.0226996	−	0.0393169i	−0.854452	−	0.519530i	$-0.826107\pi$
$311$	0.400312	−	0.693361i	0.0226996	−	0.0393169i	0.877152	+	0.480213i	$0.159441\pi$
$312$	−5.90070	+	2.04494i	−0.334061	+	0.115772i
$313$	4.15922	+	7.20399i	0.235093	+	0.407193i	0.959300	−	0.282390i	$-0.0911271\pi$
$313$	4.15922	+	7.20399i	0.235093	+	0.407193i	−0.724207	+	0.689583i	$0.757794\pi$
$314$	−1.88174	+	7.02276i	−0.106193	+	0.396317i
$315$	−25.1217	−	6.62193i	−1.41545	−	0.373103i
$316$	−13.3069	−	7.68273i	−0.748571	−	0.432188i
$317$	−2.48713	+	9.28208i	−0.139691	+	0.521334i	0.860244	+	0.509883i	$0.170311\pi$
$317$	−2.48713	+	9.28208i	−0.139691	+	0.521334i	−0.999934	+	0.0114502i	$0.996355\pi$
$318$	7.20392	+	17.2922i	0.403976	+	0.969700i
$319$	13.4814	−	50.3134i	0.754816	−	2.81701i
$320$	0.772339	+	2.88241i	0.0431751	+	0.161131i
$321$	−5.60512	+	4.31910i	−0.312847	+	0.241069i
$322$	3.15612	+	1.82219i	0.175884	+	0.101547i
$323$	−18.8951	−	5.06292i	−1.05135	−	0.281709i
$324$	4.43644	−	7.83058i	0.246469	−	0.435032i
$325$	−14.0526	−	0.860060i	−0.779498	−	0.0477075i
$326$	−3.12868	+	1.80634i	−0.173281	+	0.100044i
$327$	2.25456	−	2.95061i	0.124677	−	0.163169i
$328$	3.98374			0.219965
$329$	−5.87510	−	10.1760i	−0.323905	−	0.561019i
$330$	23.3344	+	17.8298i	1.28452	+	0.981500i
$331$	10.7608	−	10.7608i	0.591469	−	0.591469i	−0.346559	−	0.938028i	$-0.612650\pi$
$331$	10.7608	−	10.7608i	0.591469	−	0.591469i	0.938028	+	0.346559i	$0.112650\pi$
$332$	0.548858	+	2.04837i	0.0301225	+	0.112419i
$333$	0.0337029	+	8.28467i	0.00184691	+	0.453997i
$334$	−1.03799	+	1.79786i	−0.0567964	+	0.0983743i
$335$	0.739550	−	1.28094i	0.0404059	−	0.0699852i
$336$	−4.63994	+	1.93299i	−0.253129	+	0.105453i
$337$	−17.1685	−	9.91225i	−0.935229	−	0.539955i	−0.0467675	−	0.998906i	$-0.514892\pi$
$337$	−17.1685	−	9.91225i	−0.935229	−	0.539955i	−0.888462	+	0.458951i	$0.848225\pi$
$338$	−8.00278	−	10.2448i	−0.435294	−	0.557243i
$339$	−15.3535	+	11.8308i	−0.833886	+	0.642562i
$340$	3.85053	+	14.3704i	0.208824	+	0.779343i
$341$	−29.5570	+	17.0647i	−1.60060	+	0.924106i
$342$	8.35715	+	8.28943i	0.451903	+	0.448241i
$343$	11.4467	−	11.4467i	0.618063	−	0.618063i
$344$	6.25872	+	6.25872i	0.337448	+	0.337448i
$345$	−5.99157	+	2.49608i	−0.322576	+	0.134385i
$346$	−3.70885	+	0.993784i	−0.199389	+	0.0534261i
$347$	5.37337	−	3.10231i	0.288457	−	0.166541i	−0.348789	−	0.937201i	$-0.613407\pi$
$347$	5.37337	−	3.10231i	0.288457	−	0.166541i	0.637246	+	0.770660i	$0.280074\pi$
$348$	−15.7388	+	2.10462i	−0.843686	+	0.112820i
$349$	−10.4606	+	2.80291i	−0.559943	+	0.150036i	−0.527680	−	0.849443i	$-0.676938\pi$
$349$	−10.4606	+	2.80291i	−0.559943	+	0.150036i	−0.0322631	+	0.999479i	$0.510271\pi$
$350$	−11.3318			−0.605712
$351$	18.4121	+	3.46326i	0.982766	+	0.184855i
$352$	5.68174			0.302838
$353$	7.31376	−	1.95971i	0.389272	−	0.104305i	−0.0588742	−	0.998265i	$-0.518751\pi$
$353$	7.31376	−	1.95971i	0.389272	−	0.104305i	0.448146	+	0.893960i	$0.352084\pi$
$354$	−11.3833	+	1.52220i	−0.605013	+	0.0809038i
$355$	−0.578470	+	0.333980i	−0.0307020	+	0.0177258i
$356$	−9.00272	+	2.41227i	−0.477143	+	0.127850i
$357$	−23.1326	+	9.63701i	−1.22431	+	0.510045i
$358$	−8.55886	−	8.55886i	−0.452350	−	0.452350i
$359$	10.3819	−	10.3819i	0.547937	−	0.547937i	−0.377907	−	0.925844i	$-0.623356\pi$
$359$	10.3819	−	10.3819i	0.547937	−	0.547937i	0.925844	+	0.377907i	$0.123356\pi$
$360$	2.28182	−	8.65658i	0.120262	−	0.456242i
$361$	3.12186	−	1.80240i	0.164308	−	0.0948634i
$362$	−2.98814	−	11.1519i	−0.157053	−	0.586131i
$363$	29.1988	−	22.4995i	1.53254	−	1.18092i
$364$	−6.93298	−	7.83694i	−0.363387	−	0.410767i
$365$	−17.1681	−	9.91199i	−0.898617	−	0.518817i
$366$	−8.85170	+	3.68761i	−0.462686	+	0.192754i
$367$	−6.50385	+	11.2650i	−0.339498	+	0.588028i	−0.984338	−	0.176289i	$-0.943591\pi$
$367$	−6.50385	+	11.2650i	−0.339498	+	0.588028i	0.644840	+	0.764317i	$0.276924\pi$
$368$	−0.627900	+	1.08755i	−0.0327315	+	0.0566927i
$369$	−10.3743	−	5.93346i	−0.540064	−	0.308883i
$370$	2.13287	+	7.96000i	0.110883	+	0.413820i
$371$	−22.1937	+	22.1937i	−1.15224	+	1.15224i
$372$	8.26706	+	6.31687i	0.428627	+	0.327514i
$373$	13.3066	+	23.0477i	0.688991	+	1.19337i	0.972165	+	0.234298i	$0.0752793\pi$
$373$	13.3066	+	23.0477i	0.688991	+	1.19337i	−0.283174	+	0.959069i	$0.591387\pi$
$374$	28.3266			1.46473
$375$	−3.43690	+	4.49797i	−0.177481	+	0.232274i
$376$	3.50649	−	2.02447i	0.180833	−	0.104404i
$377$	−14.7476	−	29.5822i	−0.759542	−	1.52356i
$378$	14.9622	+	1.87700i	0.769570	+	0.0965422i
$379$	34.9351	+	9.36083i	1.79450	+	0.480834i	0.993097	−	0.117296i	$-0.0374227\pi$
$379$	34.9351	+	9.36083i	1.79450	+	0.480834i	0.801399	+	0.598130i	$0.204089\pi$
$380$	10.1399	+	5.85429i	0.520167	+	0.300319i
$381$	8.16289	−	6.29002i	0.418197	−	0.322248i
$382$	2.30880	+	8.61655i	0.118128	+	0.440861i
$383$	0.800991	−	2.98934i	0.0409288	−	0.152748i	−0.942437	−	0.334383i	$-0.891472\pi$
$383$	0.800991	−	2.98934i	0.0409288	−	0.152748i	0.983366	+	0.181635i	$0.0581388\pi$
$384$	−0.666081	−	1.59885i	−0.0339908	−	0.0815912i
$385$	−12.7348	+	47.5270i	−0.649026	+	2.42220i
$386$	−4.00276	−	2.31100i	−0.203735	−	0.117627i
$387$	−6.97684	−	25.6206i	−0.354653	−	1.30237i
$388$	0.507347	−	1.89345i	0.0257567	−	0.0961251i
$389$	5.78149	+	10.0138i	0.293133	+	0.507722i	0.974549	−	0.224175i	$-0.0719687\pi$
$389$	5.78149	+	10.0138i	0.293133	+	0.507722i	−0.681416	+	0.731897i	$0.738635\pi$
$390$	18.5876	−	1.33702i	0.941220	−	0.0677026i
$391$	−3.13042	+	5.42205i	−0.158312	+	0.274205i
$392$	−1.00538	−	1.00538i	−0.0507795	−	0.0507795i
$393$	−2.47195	−	1.01803i	−0.124694	−	0.0513529i
$394$			19.8157i			0.998300i
$395$	32.4222	+	32.4222i	1.63134	+	1.63134i
$396$	−14.7962	−	8.46249i	−0.743535	−	0.425256i
$397$	21.7661	−	5.83222i	1.09241	−	0.292711i	0.332740	−	0.943019i	$-0.392027\pi$
$397$	21.7661	−	5.83222i	1.09241	−	0.292711i	0.759671	+	0.650308i	$0.225360\pi$
$398$	−18.9063	−	5.06592i	−0.947686	−	0.253932i
$399$	−7.51030	+	18.2363i	−0.375985	+	0.912956i
$400$		−	3.90478i		−	0.195239i
$401$	21.0278	−	21.0278i	1.05008	−	1.05008i	0.0514009	−	0.998678i	$-0.483631\pi$
$401$	21.0278	−	21.0278i	1.05008	−	1.05008i	0.998678	−	0.0514009i	$-0.0163686\pi$
$402$	−0.326925	+	0.793829i	−0.0163055	+	0.0395926i
$403$	−6.87302	+	20.5386i	−0.342370	+	1.02310i
$404$		−	12.0188i		−	0.597958i
$405$	−18.8355	+	19.1445i	−0.935943	+	0.951298i
$406$	−13.3025	−	23.0405i	−0.660190	−	1.14348i
$407$	15.6906			0.777753
$408$	−3.32077	−	7.97116i	−0.164403	−	0.394631i
$409$	11.1355	+	2.98375i	0.550616	+	0.147537i	0.523392	−	0.852092i	$-0.324666\pi$
$409$	11.1355	+	2.98375i	0.550616	+	0.147537i	0.0272244	+	0.999629i	$0.491333\pi$
$410$	−11.4828	−	3.07680i	−0.567093	−	0.151952i
$411$	17.4867	−	22.8853i	0.862554	−	1.12885i
$412$	−4.17063			−0.205472
$413$	−9.62117	−	16.6644i	−0.473427	−	0.819999i
$414$	3.25497	−	1.89696i	0.159973	−	0.0932303i
$415$		−	6.32813i		−	0.310636i
$416$	2.70049	−	2.38900i	0.132403	−	0.117130i
$417$	−6.04628	−	7.84657i	−0.296088	−	0.384248i
$418$	15.7637	−	15.7637i	0.771030	−	0.771030i
$419$		−	6.42037i		−	0.313656i	−0.987626	−	0.156828i	$-0.949873\pi$
$419$		−	6.42037i		−	0.313656i	0.987626	−	0.156828i	$-0.0501268\pi$
$420$	14.8671	−	1.98807i	0.725441	−	0.0970077i
$421$	−11.8017	−	3.16224i	−0.575177	−	0.154118i	−0.0405074	−	0.999179i	$-0.512897\pi$
$421$	−11.8017	−	3.16224i	−0.575177	−	0.154118i	−0.534670	+	0.845061i	$0.679564\pi$
$422$	−21.1514	+	5.66749i	−1.02963	+	0.275889i
$423$	−12.1467	+	0.0494142i	−0.590594	+	0.00240260i
$424$	−7.64763	−	7.64763i	−0.371402	−	0.371402i
$425$		−	19.4675i		−	0.944310i
$426$	0.307105	−	0.236644i	0.0148793	−	0.0114654i
$427$	−11.3607	−	11.3607i	−0.549784	−	0.549784i
$428$	2.04271	−	3.53808i	0.0987382	−	0.171020i
$429$	6.70091	−	34.8440i	0.323523	−	1.68228i
$430$	−13.2063	−	22.8740i	−0.636866	−	1.10308i
$431$	−5.37595	+	20.0633i	−0.258951	+	0.966416i	0.706899	+	0.707314i	$0.250093\pi$
$431$	−5.37595	+	20.0633i	−0.258951	+	0.966416i	−0.965850	+	0.259102i	$0.916573\pi$
$432$	−0.646785	+	5.15574i	−0.0311185	+	0.248056i
$433$	−28.1413	−	16.2474i	−1.35239	−	0.780800i	−0.363802	−	0.931476i	$-0.618521\pi$
$433$	−28.1413	−	16.2474i	−1.35239	−	0.780800i	−0.988583	+	0.150676i	$0.951855\pi$
$434$	−4.51177	+	16.8382i	−0.216572	+	0.808257i
$435$	46.9910	+	6.08927i	2.25305	+	0.291958i
$436$	−0.554886	+	2.07086i	−0.0265742	+	0.0991763i
$437$	1.27529	+	4.75945i	0.0610054	+	0.227675i
$438$	10.6395	+	4.38168i	0.508373	+	0.209365i
$439$	26.1122	+	15.0759i	1.24627	+	0.719533i	0.970363	−	0.241652i	$-0.0776893\pi$
$439$	26.1122	+	15.0759i	1.24627	+	0.719533i	0.275904	+	0.961185i	$0.411023\pi$
$440$	−16.3771	−	4.38823i	−0.780748	−	0.209201i
$441$	1.12074	+	4.11561i	0.0533686	+	0.195982i
$442$	13.4634	−	11.9105i	0.640390	−	0.566523i
$443$	−20.7904	+	12.0034i	−0.987783	+	0.570297i	−0.904611	−	0.426238i	$-0.859838\pi$
$443$	−20.7904	+	12.0034i	−0.987783	+	0.570297i	−0.0831722	+	0.996535i	$0.526505\pi$
$444$	−1.83943	−	4.41536i	−0.0872957	−	0.209544i
$445$	27.8126			1.31844
$446$	−8.39106	−	14.5337i	−0.397328	−	0.688192i
$447$	−1.27942	+	9.87332i	−0.0605146	+	0.466992i
$448$	2.05205	−	2.05205i	0.0969503	−	0.0969503i
$449$	3.34047	+	12.4668i	0.157646	+	0.588345i	0.998864	+	0.0476481i	$0.0151726\pi$
$449$	3.34047	+	12.4668i	0.157646	+	0.588345i	−0.841218	+	0.540697i	$0.818161\pi$
$450$	−5.81585	+	10.1687i	−0.274162	+	0.479355i
$451$	−11.3173	+	19.6021i	−0.532911	+	0.923028i
$452$	5.59536	−	9.69146i	0.263184	−	0.455848i
$453$	1.52630	−	11.7785i	0.0717120	−	0.553403i
$454$	15.2211	+	8.78789i	0.714360	+	0.412436i
$455$	13.9309	+	27.9439i	0.653090	+	1.31003i
$456$	−6.28396	−	2.58794i	−0.294273	−	0.121191i
$457$	−0.954127	−	3.56085i	−0.0446322	−	0.166569i	0.940013	−	0.341140i	$-0.110813\pi$
$457$	−0.954127	−	3.56085i	−0.0446322	−	0.166569i	−0.984645	+	0.174570i	$0.944146\pi$
$458$	17.7300	−	10.2364i	0.828466	−	0.478315i
$459$	−3.22458	+	25.7042i	−0.150510	+	1.19977i
$460$	2.64982	−	2.64982i	0.123549	−	0.123549i
$461$	16.2207	+	16.2207i	0.755475	+	0.755475i	0.975495	−	0.220021i	$-0.0706125\pi$
$461$	16.2207	+	16.2207i	0.755475	+	0.755475i	−0.220021	+	0.975495i	$0.570612\pi$
$462$	3.67012	−	28.3224i	0.170749	−	1.31768i
$463$	12.3658	−	3.31340i	0.574686	−	0.153987i	0.0402412	−	0.999190i	$-0.487187\pi$
$463$	12.3658	−	3.31340i	0.574686	−	0.153987i	0.534445	+	0.845203i	$0.320521\pi$
$464$	7.93943	−	4.58383i	0.368579	−	0.212799i
$465$	−18.9503	−	24.5928i	−0.878798	−	1.14046i
$466$	18.1991	−	4.87643i	0.843056	−	0.225896i
$467$	−31.8355			−1.47317			−0.736586	−	0.676344i	$-0.763563\pi$
$467$	−31.8355			−1.47317			−0.736586	+	0.676344i	$0.763563\pi$
$468$	−10.5907	+	2.19917i	−0.489557	+	0.101657i
$469$	−1.43843			−0.0664206
$470$	−11.6707	+	3.12716i	−0.538330	+	0.144245i
$471$	−4.79541	+	11.6441i	−0.220961	+	0.536531i
$472$	5.74229	−	3.31531i	0.264310	−	0.152600i
$473$	−48.5765	+	13.0160i	−2.23355	+	0.598478i
$474$	−21.1470	−	16.1585i	−0.971315	−	0.742182i
$475$	−10.8336	−	10.8336i	−0.497081	−	0.497081i
$476$	10.2306	−	10.2306i	0.468918	−	0.468918i
$477$	8.52511	+	31.3062i	0.390338	+	1.43341i
$478$	−0.384887	+	0.222215i	−0.0176043	+	0.0101639i
$479$	7.83601	+	29.2444i	0.358036	+	1.33621i	0.876620	+	0.481183i	$0.159793\pi$
$479$	7.83601	+	29.2444i	0.358036	+	1.33621i	−0.518584	+	0.855027i	$0.673540\pi$
$480$	0.685058	+	5.12299i	0.0312685	+	0.233831i
$481$	7.45763	−	6.59742i	0.340039	−	0.300816i
$482$	−9.21841	−	5.32225i	−0.419887	−	0.242422i
$483$	5.01565	+	3.83246i	0.228220	+	0.174383i
$484$	−10.6411	+	18.4309i	−0.483687	+	0.837770i
$485$	−2.92476	+	5.06584i	−0.132807	+	0.230028i
$486$	9.36339	−	12.4630i	0.424732	−	0.565334i
$487$	−8.13655	−	30.3660i	−0.368702	−	1.37602i	−0.862332	−	0.506344i	$-0.830997\pi$
$487$	−8.13655	−	30.3660i	−0.368702	−	1.37602i	0.493629	−	0.869672i	$-0.335670\pi$
$488$	3.91474	−	3.91474i	0.177212	−	0.177212i
$489$	−5.77616	+	2.40634i	−0.261207	+	0.108818i
$490$	2.12143	+	3.67442i	0.0958364	+	0.165993i
$491$	−13.5858			−0.613118			−0.306559	−	0.951852i	$-0.599178\pi$
$491$	−13.5858			−0.613118			−0.306559	+	0.951852i	$0.599178\pi$
$492$	6.84283	+	0.886719i	0.308498	+	0.0399764i
$493$	39.5824	−	22.8529i	1.78270	−	1.02924i
$494$	0.864220	−	14.1206i	0.0388831	−	0.635315i
$495$	36.1126	+	35.8200i	1.62314	+	1.60999i
$496$	−5.80218	−	1.55469i	−0.260526	−	0.0698076i
$497$	0.562564	+	0.324797i	0.0252345	+	0.0145691i
$498$	0.486833	+	3.64062i	0.0218155	+	0.163140i
$499$	6.78578	+	25.3249i	0.303773	+	1.13370i	0.933996	+	0.357283i	$0.116297\pi$
$499$	6.78578	+	25.3249i	0.303773	+	1.13370i	−0.630223	+	0.776414i	$0.717037\pi$
$500$	0.845880	−	3.15687i	0.0378289	−	0.141179i
$501$	−2.18312	+	2.85712i	−0.0975347	+	0.127647i
$502$	−4.36714	+	16.2984i	−0.194915	+	0.727433i
$503$	5.09635	+	2.94238i	0.227235	+	0.131194i	0.609296	−	0.792943i	$-0.291452\pi$
$503$	5.09635	+	2.94238i	0.227235	+	0.131194i	−0.382061	+	0.924137i	$0.624785\pi$
$504$	−8.40023	+	2.28750i	−0.374176	+	0.101893i
$505$	−9.28259	+	34.6431i	−0.413070	+	1.54160i
$506$	−3.56757	−	6.17920i	−0.158598	−	0.274699i
$507$	−11.4660	−	19.3786i	−0.509221	−	0.860636i
$508$	−2.97485	+	5.15260i	−0.131988	+	0.228610i
$509$	−2.84585	−	2.84585i	−0.126140	−	0.126140i	0.641218	−	0.767359i	$-0.278429\pi$
$509$	−2.84585	−	2.84585i	−0.126140	−	0.126140i	−0.767359	+	0.641218i	$0.778429\pi$
$510$	3.41539	+	25.5409i	0.151236	+	1.13097i
$511$			19.2789i			0.852848i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	12.5099	+	16.0988i	0.552325	+	0.710781i
$514$	4.77650	−	1.27986i	0.210683	−	0.0564522i
$515$	12.0215	+	3.22114i	0.529729	+	0.141940i
$516$	9.35745	+	12.1436i	0.411939	+	0.534594i
$517$			23.0051i			1.01176i
$518$	5.66690	−	5.66690i	0.248989	−	0.248989i
$519$	−6.59185	+	0.881478i	−0.289350	+	0.0386926i
$520$	−9.62904	+	4.80038i	−0.422262	+	0.210511i
$521$		−	18.6800i		−	0.818387i	−0.912448	−	0.409193i	$-0.865810\pi$
$521$		−	18.6800i		−	0.818387i	0.912448	−	0.409193i	$-0.134190\pi$
$522$	−27.5028	+	0.111884i	−1.20376	+	0.00489703i
$523$	0.860091	+	1.48972i	0.0376092	+	0.0651410i	0.884217	−	0.467076i	$-0.154692\pi$
$523$	0.860091	+	1.48972i	0.0376092	+	0.0651410i	−0.846608	+	0.532217i	$0.821359\pi$
$524$	1.54348			0.0674270
$525$	−19.4646	−	2.52229i	−0.849503	−	0.110082i
$526$	28.0115	+	7.50565i	1.22136	+	0.327262i
$527$	−28.9270	−	7.75097i	−1.26008	−	0.337638i
$528$	9.75947	+	1.26467i	0.424726	+	0.0550376i
$529$	−21.4230			−0.931433
$530$	16.1370	+	27.9502i	0.700948	+	1.21408i
$531$	−19.8917	+	0.0809216i	−0.863227	+	0.00351170i
$532$		−	11.3866i		−	0.493674i
$533$	2.86307	+	14.0753i	0.124013	+	0.609671i
$534$	−16.0008	+	2.13967i	−0.692423	+	0.0925924i
$535$	−8.62052	+	8.62052i	−0.372698	+	0.372698i
$536$		−	0.495662i		−	0.0214094i
$537$	−12.7964	−	16.6065i	−0.552205	−	0.716625i
$538$	−8.56064	−	2.29382i	−0.369075	−	0.0988934i
$539$	7.80319	−	2.09086i	0.336107	−	0.0900596i
$540$	5.84628	−	14.3614i	0.251584	−	0.618017i
$541$	−9.88421	−	9.88421i	−0.424955	−	0.424955i	0.461950	−	0.886906i	$-0.347150\pi$
$541$	−9.88421	−	9.88421i	−0.424955	−	0.424955i	−0.886906	+	0.461950i	$0.847150\pi$
$542$			8.38621i			0.360219i
$543$	−2.65046	−	19.8206i	−0.113742	−	0.850584i
$544$	3.52531	+	3.52531i	0.151146	+	0.151146i
$545$	3.19881	−	5.54051i	0.137022	−	0.237329i
$546$	−10.1643	−	15.0046i	−0.434993	−	0.642137i
$547$	−10.7646	−	18.6448i	−0.460259	−	0.797193i	0.538714	−	0.842489i	$-0.318910\pi$
$547$	−10.7646	−	18.6448i	−0.460259	−	0.797193i	−0.998974	+	0.0452960i	$0.985577\pi$
$548$	−4.30377	+	16.0619i	−0.183848	+	0.686130i
$549$	−16.0253	+	4.36391i	−0.683942	+	0.186247i
$550$	19.2136	+	11.0930i	0.819271	+	0.473006i
$551$	9.30995	−	34.7452i	0.396617	−	1.48020i
$552$	−1.32061	+	1.72832i	−0.0562089	+	0.0735622i
$553$	11.5410	−	43.0718i	0.490775	−	1.83160i
$554$	7.30000	+	27.2440i	0.310147	+	1.15749i
$555$	1.89184	+	14.1475i	0.0803043	+	0.600530i
$556$	4.95293	+	2.85958i	0.210051	+	0.121273i
$557$	34.9723	+	9.37080i	1.48182	+	0.397054i	0.906968	−	0.421200i	$-0.138391\pi$
$557$	34.9723	+	9.37080i	1.48182	+	0.397054i	0.574857	+	0.818254i	$0.305058\pi$
$558$	12.7942	+	12.6905i	0.541622	+	0.537233i
$559$	−17.6152	+	26.6114i	−0.745045	+	1.12554i
$560$	−7.49973	+	4.32997i	−0.316921	+	0.182975i
$561$	48.6563	+	6.30506i	2.05427	+	0.266200i
$562$	−18.7642			−0.791521
$563$	11.5895	+	20.0735i	0.488437	+	0.845998i	0.999912	−	0.0133006i	$-0.00423384\pi$
$563$	11.5895	+	20.0735i	0.488437	+	0.845998i	−0.511474	+	0.859298i	$0.670901\pi$
$564$	6.47367	−	2.69692i	0.272591	−	0.113561i
$565$	−23.6132	+	23.6132i	−0.993415	+	0.993415i
$566$	−4.30236	−	16.0566i	−0.180842	−	0.674910i
$567$	25.2825	+	6.55444i	1.06177	+	0.275261i
$568$	−0.111920	+	0.193851i	−0.00469607	+	0.00813383i
$569$	12.5307	−	21.7038i	0.525313	−	0.909869i	−0.474252	−	0.880389i	$-0.657282\pi$
$569$	12.5307	−	21.7038i	0.525313	−	0.909869i	0.999565	−	0.0294797i	$-0.00938505\pi$
$570$	16.1142	+	12.3128i	0.674948	+	0.515728i
$571$	−31.4540	−	18.1600i	−1.31631	−	0.759970i	−0.333175	−	0.942865i	$-0.608120\pi$
$571$	−31.4540	−	18.1600i	−1.31631	−	0.759970i	−0.983132	+	0.182895i	$0.941453\pi$
$572$	4.08341	+	20.0747i	0.170736	+	0.839366i
$573$	2.04788	+	15.3145i	0.0855516	+	0.639770i
$574$	2.99220	+	11.1670i	0.124892	+	0.466103i
$575$	−4.24666	+	2.45181i	−0.177098	+	0.102248i
$576$	−0.788239	−	2.89459i	−0.0328433	−	0.120608i
$577$	19.8647	−	19.8647i	0.826979	−	0.826979i	−0.160119	−	0.987098i	$-0.551188\pi$
$577$	19.8647	−	19.8647i	0.826979	−	0.826979i	0.987098	+	0.160119i	$0.0511877\pi$
$578$	5.55478	+	5.55478i	0.231048	+	0.231048i
$579$	−6.36111	−	4.86053i	−0.264359	−	0.201997i
$580$	−26.4249	+	7.08054i	−1.09724	+	0.294003i
$581$	−5.32963	+	3.07707i	−0.221111	+	0.127658i
$582$	1.29292	−	3.13942i	0.0535931	−	0.130133i
$583$	59.3564	−	15.9045i	2.45829	−	0.658697i
$584$	−6.64323			−0.274899
$585$	32.2253	+	1.84073i	1.33235	+	0.0761048i
$586$	−14.4947			−0.598769
$587$	−0.387214	+	0.103754i	−0.0159820	+	0.00428238i	−0.266801	−	0.963752i	$-0.585967\pi$
$587$	−0.387214	+	0.103754i	−0.0159820	+	0.00428238i	0.250819	+	0.968034i	$0.419300\pi$
$588$	−1.50315	−	1.95072i	−0.0619890	−	0.0804463i
$589$	−20.4113	+	11.7845i	−0.841033	+	0.485571i
$590$	−19.1122	+	5.12109i	−0.786836	+	0.210832i
$591$	−4.41067	+	34.0372i	−0.181431	+	1.40010i
$592$	1.95273	+	1.95273i	0.0802567	+	0.0802567i
$593$	1.03657	−	1.03657i	0.0425668	−	0.0425668i	−0.685503	−	0.728070i	$-0.740418\pi$
$593$	1.03657	−	1.03657i	0.0425668	−	0.0425668i	0.728070	+	0.685503i	$0.240418\pi$
$594$	−23.5316	−	17.8293i	−0.965512	−	0.731546i
$595$	−37.3902	+	21.5872i	−1.53285	+	0.884991i
$596$	−1.48770	−	5.55216i	−0.0609385	−	0.227426i
$597$	−31.3475	−	12.9099i	−1.28297	−	0.528368i
$598$	−4.29381	−	1.43688i	−0.175587	−	0.0587584i
$599$	14.5596	+	8.40599i	0.594889	+	0.343459i	0.767028	−	0.641613i	$-0.221735\pi$
$599$	14.5596	+	8.40599i	0.594889	+	0.343459i	−0.172139	+	0.985073i	$0.555068\pi$
$600$	0.869144	−	6.70720i	0.0354827	−	0.273820i
$601$	−6.62486	+	11.4746i	−0.270234	+	0.468058i	−0.968922	−	0.247368i	$-0.920434\pi$
$601$	−6.62486	+	11.4746i	−0.270234	+	0.468058i	0.698688	+	0.715427i	$0.253768\pi$
$602$	−12.8432	+	22.2451i	−0.523451	+	0.906643i
$603$	−0.738249	+	1.29078i	−0.0300638	+	0.0525647i
$604$	1.77477	+	6.62353i	0.0722144	+	0.269508i
$605$	44.9069	−	44.9069i	1.82573	−	1.82573i
$606$	2.67520	−	20.6446i	0.108673	−	0.838628i
$607$	17.3676	+	30.0815i	0.704929	+	1.22097i	0.966717	+	0.255847i	$0.0823544\pi$
$607$	17.3676	+	30.0815i	0.704929	+	1.22097i	−0.261789	+	0.965125i	$0.584312\pi$
$608$	3.92367			0.159126
$609$	−17.7210	−	42.5374i	−0.718092	−	1.72370i
$610$	−14.3074	+	8.26037i	−0.579289	+	0.334453i
$611$	9.67294	+	10.9341i	0.391325	+	0.442348i
$612$	−3.92980	−	14.4311i	−0.158853	−	0.583344i
$613$	−28.3704	−	7.60182i	−1.14587	−	0.307035i	−0.364560	−	0.931180i	$-0.618781\pi$
$613$	−28.3704	−	7.60182i	−1.14587	−	0.307035i	−0.781308	+	0.624145i	$0.785447\pi$
$614$	11.3854	+	6.57339i	0.459479	+	0.265280i
$615$	−19.0390	−	7.84087i	−0.767725	−	0.316174i
$616$	4.26757	+	15.9268i	0.171945	+	0.641709i
$617$	11.1051	−	41.4449i	0.447076	−	1.66851i	−0.263321	−	0.964708i	$-0.584818\pi$
$617$	11.1051	−	41.4449i	0.447076	−	1.66851i	0.710397	−	0.703801i	$-0.248515\pi$
$618$	−7.16385	−	0.928319i	−0.288172	−	0.0373425i
$619$	5.52275	−	20.6112i	0.221978	−	0.828433i	−0.761615	−	0.648030i	$-0.775593\pi$
$619$	5.52275	−	20.6112i	0.221978	−	0.828433i	0.983593	−	0.180403i	$-0.0577403\pi$
$620$	15.5235	+	8.96250i	0.623439	+	0.359943i
$621$	6.01327	−	2.53387i	0.241304	−	0.101681i
$622$	−0.207217	+	0.773343i	−0.00830863	+	0.0310082i
$623$	−13.5239	−	23.4242i	−0.541825	−	0.938469i
$624$	5.17036	−	3.50247i	0.206980	−	0.140211i
$625$	−14.6383	+	25.3543i	−0.585532	+	1.01417i
$626$	−5.88203	−	5.88203i	−0.235093	−	0.235093i
$627$	30.5860	−	23.5684i	1.22149	−	0.941233i
$628$		−	7.27050i		−	0.290124i
$629$	9.73542	+	9.73542i	0.388177	+	0.388177i
$630$	25.9796	−	0.105688i	1.03505	−	0.00421070i
$631$	−20.2052	+	5.41397i	−0.804357	+	0.215527i	−0.637496	−	0.770454i	$-0.720030\pi$
$631$	−20.2052	+	5.41397i	−0.804357	+	0.215527i	−0.166861	+	0.985980i	$0.553363\pi$
$632$	14.8419	+	3.97688i	0.590379	+	0.158192i
$633$	−37.5930	+	5.02702i	−1.49419	+	0.199806i
$634$		−	9.60952i		−	0.381643i
$635$	12.5543	−	12.5543i	0.498202	−	0.498202i
$636$	−11.4340	−	14.8385i	−0.453388	−	0.588385i
$637$	2.82966	−	4.27478i	0.112115	−	0.169373i
$638$			52.0883i			2.06220i
$639$	0.580184	−	0.338124i	0.0229517	−	0.0133760i
$640$	−1.49204	−	2.58430i	−0.0589782	−	0.102153i
$641$	−36.0558			−1.42412			−0.712059	−	0.702119i	$-0.752237\pi$
$641$	−36.0558			−1.42412			−0.712059	+	0.702119i	$0.752237\pi$
$642$	4.29627	−	5.62264i	0.169560	−	0.221908i
$643$	18.2413	+	4.88775i	0.719368	+	0.192754i	0.599890	−	0.800083i	$-0.295211\pi$
$643$	18.2413	+	4.88775i	0.719368	+	0.192754i	0.119478	+	0.992837i	$0.461878\pi$
$644$	−3.52020	−	0.943235i	−0.138715	−	0.0371687i
$645$	−17.5930	−	42.2300i	−0.692723	−	1.66281i
$646$	19.5616			0.769642
$647$	−6.94544	−	12.0299i	−0.273054	−	0.472943i	0.696589	−	0.717471i	$-0.254700\pi$
$647$	−6.94544	−	12.0299i	−0.273054	−	0.472943i	−0.969642	+	0.244528i	$0.921367\pi$
$648$	−2.25856	+	8.71200i	−0.0887248	+	0.342240i
$649$			37.6735i			1.47882i
$650$	13.7964	−	2.80633i	0.541138	−	0.110073i
$651$	−11.4977	+	27.9185i	−0.450632	+	1.09421i
$652$	2.55456	−	2.55456i	0.100044	−	0.100044i
$653$			29.3441i			1.14832i	0.818742	+	0.574162i	$0.194672\pi$
$653$			29.3441i			1.14832i	−0.818742	+	0.574162i	$0.805328\pi$
$654$	−1.41406	+	3.43359i	−0.0552943	+	0.134264i
$655$	−4.44893	−	1.19209i	−0.173834	−	0.0465787i
$656$	−3.84800	+	1.03107i	−0.150239	+	0.0402564i
$657$	17.3000	+	9.89454i	0.674937	+	0.386023i
$658$	8.30864	+	8.30864i	0.323905	+	0.323905i
$659$		−	13.4647i		−	0.524511i	−0.964998	−	0.262255i	$-0.915534\pi$
$659$		−	13.4647i		−	0.524511i	0.964998	−	0.262255i	$-0.0844663\pi$
$660$	−27.1540	−	11.1829i	−1.05697	−	0.435294i
$661$	5.70063	+	5.70063i	0.221729	+	0.221729i	0.809226	−	0.587497i	$-0.199887\pi$
$661$	5.70063	+	5.70063i	0.221729	+	0.221729i	−0.587497	+	0.809226i	$0.699887\pi$
$662$	−7.60906	+	13.1793i	−0.295735	+	0.512227i
$663$	25.7771	−	17.4617i	1.00110	−	0.678158i
$664$	−1.06031	−	1.83651i	−0.0411481	−	0.0712706i
$665$	−8.79435	+	32.8209i	−0.341030	+	1.27274i
$666$	−2.17678	−	7.99365i	−0.0843487	−	0.309748i
$667$	−9.97033	−	5.75637i	−0.386053	−	0.222888i
$668$	0.537304	−	2.00525i	0.0207889	−	0.0775853i
$669$	−11.1782	−	26.8322i	−0.432176	−	1.03739i
$670$	−0.382819	+	1.42870i	−0.0147896	+	0.0551955i
$671$	8.14134	+	30.3839i	0.314293	+	1.17296i
$672$	3.98154	−	3.06803i	0.153591	−	0.118352i
$673$	−27.6766	−	15.9791i	−1.06685	−	0.615948i	−0.139533	−	0.990217i	$-0.544560\pi$
$673$	−27.6766	−	15.9791i	−1.06685	−	0.615948i	−0.927320	+	0.374269i	$0.877894\pi$
$674$	19.1490	+	5.13096i	0.737592	+	0.197637i
$675$	−12.2532	+	16.1721i	−0.471627	+	0.622464i
$676$	10.3816	+	7.82443i	0.399294	+	0.300940i
$677$	−29.3729	+	16.9584i	−1.12889	+	0.651765i	−0.943656	−	0.330929i	$-0.892638\pi$
$677$	−29.3729	+	16.9584i	−1.12889	+	0.651765i	−0.185235	+	0.982694i	$0.559305\pi$
$678$	11.7683	−	15.4015i	0.451958	−	0.591490i
$679$	5.68869			0.218312
$680$	−7.43865	−	12.8841i	−0.285259	−	0.494083i
$681$	24.1890	+	18.4828i	0.926926	+	0.708264i
$682$	24.1332	−	24.1332i	0.924106	−	0.924106i
$683$	−6.75901	−	25.2250i	−0.258626	−	0.965207i	−0.966037	−	0.258404i	$-0.916804\pi$
$683$	−6.75901	−	25.2250i	−0.258626	−	0.965207i	0.707411	−	0.706803i	$-0.249863\pi$
$684$	−10.2179	−	5.84399i	−0.390689	−	0.223450i
$685$	24.8105	−	42.9730i	0.947959	−	1.64191i
$686$	−8.09404	+	14.0193i	−0.309032	+	0.535259i
$687$	32.7330	−	13.6365i	1.24884	−	0.520266i
$688$	−7.66534	−	4.42559i	−0.292238	−	0.168724i
$689$	21.5243	−	32.5169i	0.820012	−	1.23879i
$690$	5.14138	−	3.96176i	0.195729	−	0.150822i
$691$	−6.00262	−	22.4021i	−0.228350	−	0.852216i	−0.981034	−	0.193834i	$-0.937908\pi$
$691$	−6.00262	−	22.4021i	−0.228350	−	0.852216i	0.752684	−	0.658382i	$-0.228759\pi$
$692$	3.32526	−	1.91984i	0.126408	−	0.0729815i
$693$	12.6082	−	47.8321i	0.478947	−	1.81699i
$694$	−4.38734	+	4.38734i	−0.166541	+	0.166541i
$695$	−12.0678	−	12.0678i	−0.457758	−	0.457758i
$696$	14.6578	−	6.10640i	0.555601	−	0.231463i
$697$	−19.1844	+	5.14043i	−0.726659	+	0.194708i
$698$	9.37872	−	5.41481i	0.354990	−	0.204954i
$699$	32.3458	−	4.32535i	1.22343	−	0.163600i
$700$	10.9457	−	2.93289i	0.413709	−	0.110853i
$701$	15.7744			0.595790			0.297895	−	0.954599i	$-0.403716\pi$
$701$	15.7744			0.595790			0.297895	+	0.954599i	$0.403716\pi$
$702$	−18.6811	+	1.42016i	−0.705072	+	0.0536004i
$703$	10.8355			0.408670
$704$	−5.48814	+	1.47054i	−0.206842	+	0.0554232i
$705$	−20.7427	+	2.77376i	−0.781215	+	0.104466i
$706$	−6.55733	+	3.78588i	−0.246789	+	0.142483i
$707$	33.6906	−	9.02736i	1.26706	−	0.339509i
$708$	10.6014	−	4.41653i	0.398425	−	0.165983i
$709$	−12.8515	−	12.8515i	−0.482649	−	0.482649i	0.423328	−	0.905977i	$-0.360862\pi$
$709$	−12.8515	−	12.8515i	−0.482649	−	0.482649i	−0.905977	+	0.423328i	$0.860862\pi$
$710$	0.472319	−	0.472319i	0.0177258	−	0.0177258i
$711$	−32.7274	−	32.4622i	−1.22737	−	1.21743i
$712$	8.07162	−	4.66015i	0.302497	−	0.174647i
$713$	1.95238	+	7.28638i	0.0731172	+	0.272877i
$714$	19.8501	−	15.2958i	0.742873	−	0.572431i
$715$	3.73444	−	61.0173i	0.139660	−	2.28192i
$716$	10.4824	+	6.05203i	0.391746	+	0.226175i
$717$	−0.710578	+	0.296026i	−0.0265370	+	0.0110553i
$718$	−7.34113	+	12.7152i	−0.273968	+	0.474527i
$719$	12.7722	−	22.1221i	0.476322	−	0.825014i	−0.523310	−	0.852143i	$-0.675303\pi$
$719$	12.7722	−	22.1221i	0.476322	−	0.825014i	0.999632	+	0.0271283i	$0.00863626\pi$
$720$	0.0364184	+	8.95219i	0.00135724	+	0.333628i
$721$	−3.13257	−	11.6909i	−0.116663	−	0.435393i
$722$	−2.54898	+	2.54898i	−0.0948634	+	0.0948634i
$723$	−14.6497	−	11.1938i	−0.544829	−	0.416304i
$724$	5.77265	+	9.99852i	0.214539	+	0.371592i
$725$	35.7977			1.32949
$726$	−22.3806	+	29.2901i	−0.830620	+	1.08706i
$727$	−17.9550	+	10.3663i	−0.665913	+	0.384465i	−0.794526	−	0.607230i	$-0.792281\pi$
$727$	−17.9550	+	10.3663i	−0.665913	+	0.384465i	0.128613	+	0.991695i	$0.458947\pi$
$728$	8.72509	+	5.77551i	0.323373	+	0.214055i
$729$	18.8575	−	19.3235i	0.698425	−	0.715684i
$730$	19.1485	+	5.13082i	0.708717	+	0.189900i
$731$	−38.2159	−	22.0639i	−1.41347	−	0.816065i
$732$	7.59567	−	5.85295i	0.280744	−	0.216331i
$733$	−6.16718	−	23.0162i	−0.227790	−	0.850124i	−0.981267	−	0.192650i	$-0.938292\pi$
$733$	−6.16718	−	23.0162i	−0.227790	−	0.850124i	0.753477	−	0.657474i	$-0.228375\pi$
$734$	3.36664	−	12.5645i	0.124265	−	0.463763i
$735$	2.82609	+	6.78371i	0.104242	+	0.250221i
$736$	0.325025	−	1.21301i	0.0119806	−	0.0447121i
$737$	2.43892	+	1.40811i	0.0898389	+	0.0518685i
$738$	11.5565	+	3.04622i	0.425400	+	0.112133i
$739$	−4.57798	+	17.0853i	−0.168404	+	0.628492i	0.829178	+	0.558985i	$0.188809\pi$
$739$	−4.57798	+	17.0853i	−0.168404	+	0.628492i	−0.997581	+	0.0695066i	$0.977858\pi$
$740$	−4.12040	−	7.13674i	−0.151469	−	0.262352i
$741$	4.62748	−	24.0624i	0.169995	−	0.883954i
$742$	15.6933	−	27.1817i	0.576121	−	0.997870i
$743$	−6.71743	−	6.71743i	−0.246439	−	0.246439i	0.573069	−	0.819507i	$-0.305753\pi$
$743$	−6.71743	−	6.71743i	−0.246439	−	0.246439i	−0.819507	+	0.573069i	$0.805753\pi$
$744$	−9.62029	−	3.96195i	−0.352697	−	0.145252i
$745$			17.1526i			0.628423i
$746$	−18.8184	−	18.8184i	−0.688991	−	0.688991i
$747$	0.0258805	+	6.36182i	0.000946920	+	0.232767i
$748$	−27.3614	+	7.33146i	−1.00043	+	0.268065i
$749$	11.4521	+	3.06857i	0.418449	+	0.112123i
$750$	2.15563	−	5.23424i	0.0787124	−	0.191127i
$751$		−	37.3401i		−	1.36256i	−0.732023	−	0.681280i	$-0.761424\pi$
$751$		−	37.3401i		−	1.36256i	0.732023	−	0.681280i	$-0.238576\pi$
$752$	−2.86304	+	2.86304i	−0.104404	+	0.104404i
$753$	−11.1292	+	27.0235i	−0.405569	+	0.984792i
$754$	21.9016	+	24.7572i	0.797608	+	0.901605i
$755$		−	20.4624i		−	0.744705i
$756$	−14.9381	+	2.05945i	−0.543295	+	0.0749016i
$757$	−10.0183	−	17.3521i	−0.364120	−	0.630675i	0.624514	−	0.781013i	$-0.285297\pi$
$757$	−10.0183	−	17.3521i	−0.364120	−	0.630675i	−0.988635	+	0.150339i	$0.951964\pi$
$758$	−36.1675			−1.31366
$759$	−4.75257	−	11.4080i	−0.172507	−	0.414086i
$760$	−11.3096	−	3.03040i	−0.410243	−	0.109924i
$761$	41.3538	+	11.0807i	1.49908	+	0.401676i	0.912790	−	0.408429i	$-0.133923\pi$
$761$	41.3538	+	11.0807i	1.49908	+	0.401676i	0.586285	+	0.810105i	$0.300590\pi$
$762$	−6.25676	+	8.18841i	−0.226659	+	0.296635i
$763$	−6.22172			−0.225241
$764$	−4.46025	−	7.72539i	−0.161366	−	0.279495i
$765$	0.181566	+	44.6315i	0.00656452	+	1.61366i
$766$			3.09479i			0.111819i
$767$	15.8406	+	17.9060i	0.571970	+	0.646547i
$768$	1.05720	+	1.37198i	0.0381484	+	0.0495071i
$769$	−26.8480	+	26.8480i	−0.968165	+	0.968165i	−0.999509	−	0.0313439i	$-0.990021\pi$
$769$	−26.8480	+	26.8480i	−0.968165	+	0.968165i	0.0313439	+	0.999509i	$0.490021\pi$
$770$		−	49.2035i		−	1.77317i
$771$	8.48943	−	1.13523i	0.305739	−	0.0408842i
$772$	4.46450	+	1.19626i	0.160681	+	0.0430543i
$773$	−27.0383	+	7.24488i	−0.972499	+	0.260580i	−0.709882	−	0.704320i	$-0.751252\pi$
$773$	−27.0383	+	7.24488i	−0.972499	+	0.260580i	−0.262616	+	0.964900i	$0.584585\pi$
$774$	13.3702	+	22.9418i	0.480582	+	0.824627i
$775$	−16.5855	−	16.5855i	−0.595770	−	0.595770i
$776$			1.96024i			0.0703685i
$777$	10.9953	−	8.47261i	0.394456	−	0.303953i
$778$	−8.17627	−	8.17627i	−0.293133	−	0.293133i
$779$	−7.81544	+	13.5367i	−0.280017	+	0.485004i
$780$	−17.6082	+	6.10229i	−0.630475	+	0.218497i
$781$	−0.635902	−	1.10141i	−0.0227544	−	0.0394117i
$782$	1.62043	−	6.04751i	0.0579463	−	0.216259i
$783$	−47.2661	−	5.92951i	−1.68915	−	0.211903i
$784$	1.23134	+	0.710914i	0.0439764	+	0.0253898i
$785$	−5.61529	+	20.9565i	−0.200418	+	0.747971i
$786$	2.65121	+	0.343554i	0.0945656	+	0.0122542i
$787$	−13.8350	+	51.6330i	−0.493165	+	1.84052i	0.0469068	+	0.998899i	$0.485064\pi$
$787$	−13.8350	+	51.6330i	−0.493165	+	1.84052i	−0.540072	+	0.841619i	$0.681603\pi$
$788$	−5.12868	−	19.1405i	−0.182702	−	0.681852i
$789$	46.4443	+	19.1273i	1.65346	+	0.680949i
$790$	−39.7089	−	22.9260i	−1.41278	−	0.815669i
$791$	31.3693	+	8.40539i	1.11537	+	0.298861i
$792$	16.4822	+	4.34462i	0.585671	+	0.154379i
$793$	16.6450	+	11.0181i	0.591082	+	0.391263i
$794$	−19.5150	+	11.2670i	−0.692561	+	0.399850i
$795$	21.4971	+	51.6016i	0.762425	+	1.83012i
$796$	19.5732			0.693754
$797$	23.2743	+	40.3123i	0.824418	+	1.42793i	0.902363	+	0.430977i	$0.141831\pi$
$797$	23.2743	+	40.3123i	0.824418	+	1.42793i	−0.0779448	+	0.996958i	$0.524836\pi$
$798$	2.53449	−	19.5587i	0.0897200	−	0.692371i
$799$	−14.2738	+	14.2738i	−0.504970	+	0.504970i
$800$	1.01063	+	3.77173i	0.0357312	+	0.133351i
$801$	−27.9607	+	0.113747i	−0.987942	+	0.00401905i
$802$	−14.8689	+	25.7537i	−0.525040	+	0.909395i
$803$	18.8726	−	32.6882i	0.665998	−	1.15354i
$804$	0.110327	−	0.851394i	0.00389093	−	0.0300264i
$805$	9.41815	+	5.43757i	0.331946	+	0.191649i
$806$	1.32306	−	21.6176i	0.0466028	−	0.761447i
$807$	−14.1939	−	5.84553i	−0.499650	−	0.205772i
$808$	3.11070	+	11.6093i	0.109434	+	0.408413i
$809$	−0.728475	+	0.420585i	−0.0256118	+	0.0147870i	−0.512751	−	0.858537i	$-0.671374\pi$
$809$	−0.728475	+	0.420585i	−0.0256118	+	0.0147870i	0.487139	+	0.873324i	$0.338040\pi$
$810$	13.2387	−	23.3671i	0.465161	−	0.821038i
$811$	20.9572	−	20.9572i	0.735908	−	0.735908i	−0.235875	−	0.971783i	$-0.575796\pi$
$811$	20.9572	−	20.9572i	0.735908	−	0.735908i	0.971783	+	0.235875i	$0.0757956\pi$
$812$	18.8125	+	18.8125i	0.660190	+	0.660190i
$813$	−1.86664	+	14.4049i	−0.0654660	+	0.505202i
$814$	−15.1559	+	4.06102i	−0.531215	+	0.142339i
$815$	−9.33625	+	5.39029i	−0.327035	+	0.188814i
$816$	5.27071	+	6.84007i	0.184512	+	0.239450i
$817$	−33.5457	+	8.98855i	−1.17362	+	0.314469i
$818$	−11.5283			−0.403079
$819$	−14.1193	−	28.0357i	−0.493370	−	0.979645i
$820$	11.8878			0.415141
$821$	25.3292	−	6.78695i	0.883997	−	0.236866i	0.211866	−	0.977299i	$-0.432046\pi$
$821$	25.3292	−	6.78695i	0.883997	−	0.236866i	0.672131	+	0.740433i	$0.265379\pi$
$822$	−10.9677	+	26.6314i	−0.382542	+	0.928877i
$823$	33.2104	−	19.1740i	1.15764	−	0.668365i	0.206904	−	0.978361i	$-0.433661\pi$
$823$	33.2104	−	19.1740i	1.15764	−	0.668365i	0.950738	+	0.309996i	$0.100328\pi$
$824$	4.02852	−	1.07944i	0.140340	−	0.0376040i
$825$	30.5339	+	23.3310i	1.06305	+	0.812279i
$826$	13.6064	+	13.6064i	0.473427	+	0.473427i
$827$	−18.4973	+	18.4973i	−0.643213	+	0.643213i	−0.951344	−	0.308131i	$-0.900296\pi$
$827$	−18.4973	+	18.4973i	−0.643213	+	0.643213i	0.308131	+	0.951344i	$0.400296\pi$
$828$	−2.65309	+	2.67477i	−0.0922014	+	0.0929546i
$829$	−10.3588	+	5.98064i	−0.359775	+	0.207716i	−0.668982	−	0.743278i	$-0.733270\pi$
$829$	−10.3588	+	5.98064i	−0.359775	+	0.207716i	0.309207	+	0.950995i	$0.399936\pi$
$830$	1.63784	+	6.11250i	0.0568503	+	0.212168i
$831$	6.47504	+	48.4215i	0.224617	+	1.67972i
$832$	−1.99016	+	3.00654i	−0.0689963	+	0.104233i
$833$	6.13889	+	3.54429i	0.212700	+	0.122802i
$834$	7.87110	+	6.01431i	0.272554	+	0.208259i
$835$	−3.09746	+	5.36496i	−0.107192	+	0.185662i
$836$	−11.1466	+	19.3066i	−0.385515	+	0.667731i
$837$	19.1518	+	24.6462i	0.661981	+	0.851897i
$838$	1.66171	+	6.20160i	0.0574030	+	0.214231i
$839$	21.8717	−	21.8717i	0.755094	−	0.755094i	−0.220331	−	0.975425i	$-0.570714\pi$
$839$	21.8717	−	21.8717i	0.755094	−	0.755094i	0.975425	+	0.220331i	$0.0707137\pi$
$840$	−13.8460	+	5.76822i	−0.477732	+	0.199022i
$841$	27.5230	+	47.6713i	0.949069	+	1.64384i
$842$	12.2180			0.421059
$843$	−32.2311	−	4.17663i	−1.11010	−	0.143851i
$844$	18.9638	−	10.9487i	0.652760	−	0.376871i
$845$	−23.8810	−	30.5713i	−0.821531	−	1.05169i
$846$	11.7201	−	3.19154i	0.402944	−	0.109727i
$847$	−59.6573	−	15.9851i	−2.04985	−	0.549255i
$848$	9.36640	+	5.40769i	0.321644	+	0.185701i
$849$	−3.81616	−	28.5379i	−0.130970	−	0.979419i
$850$	5.03855	+	18.8041i	0.172821	+	0.644976i
$851$	0.897582	−	3.34982i	0.0307687	−	0.114830i
$852$	−0.235392	+	0.308065i	−0.00806441	+	0.0105541i
$853$	11.1571	−	41.6390i	0.382013	−	1.42569i	−0.460808	−	0.887500i	$-0.652440\pi$
$853$	11.1571	−	41.6390i	0.382013	−	1.42569i	0.842822	−	0.538193i	$-0.180893\pi$
$854$	13.9140	+	8.03325i	0.476127	+	0.274892i
$855$	24.9385	+	24.7364i	0.852878	+	0.845967i
$856$	−1.05739	+	3.94622i	−0.0361407	+	0.134879i
$857$	17.2317	+	29.8461i	0.588623	+	1.01952i	0.994413	+	0.105559i	$0.0336630\pi$
$857$	17.2317	+	29.8461i	0.588623	+	1.01952i	−0.405790	+	0.913966i	$0.633004\pi$
$858$	2.54570	+	35.3910i	0.0869089	+	1.20823i
$859$	−17.1669	+	29.7340i	−0.585728	+	1.01451i	0.409057	+	0.912509i	$0.365858\pi$
$859$	−17.1669	+	29.7340i	−0.585728	+	1.01451i	−0.994784	+	0.102001i	$0.967476\pi$
$860$	18.6766	+	18.6766i	0.636866	+	0.636866i
$861$	2.65406	+	19.8475i	0.0904500	+	0.676401i
$862$		−	20.7711i		−	0.707466i
$863$	−7.63976	−	7.63976i	−0.260060	−	0.260060i	0.565018	−	0.825078i	$-0.308869\pi$
$863$	−7.63976	−	7.63976i	−0.260060	−	0.260060i	−0.825078	+	0.565018i	$0.808869\pi$
$864$	−0.709657	−	5.14746i	−0.0241430	−	0.175120i
$865$	−11.0675	+	2.96554i	−0.376308	+	0.100831i
$866$	31.3876	+	8.41027i	1.06659	+	0.285793i
$867$	8.30497	+	10.7778i	0.282052	+	0.366033i
$868$		−	17.4321i		−	0.591685i
$869$	−61.7323	+	61.7323i	−2.09412	+	2.09412i
$870$	−46.9659	+	6.28038i	−1.59229	+	0.212925i
$871$	1.75127	−	0.356227i	0.0593396	−	0.0120703i
$872$		−	2.14391i		−	0.0726021i
$873$	2.91962	−	5.10477i	0.0988141	−	0.172770i
$874$	−2.46367	−	4.26721i	−0.0833350	−	0.144340i
$875$	9.48452			0.320635
$876$	−11.4110	−	1.47868i	−0.385542	−	0.0499600i
$877$	27.2995	+	7.31487i	0.921838	+	0.247006i	0.688371	−	0.725359i	$-0.258326\pi$
$877$	27.2995	+	7.31487i	0.921838	+	0.247006i	0.233467	+	0.972365i	$0.424993\pi$
$878$	−29.1244	−	7.80385i	−0.982900	−	0.263367i
$879$	−24.8973	−	3.22629i	−0.839767	−	0.108820i
$880$	16.9548			0.571547
$881$	0.136731	+	0.236826i	0.00460660	+	0.00797886i	0.868320	−	0.496005i	$-0.165200\pi$
$881$	0.136731	+	0.236826i	0.00460660	+	0.00797886i	−0.863713	+	0.503984i	$0.831867\pi$
$882$	−2.14775	−	3.68531i	−0.0723185	−	0.124091i
$883$		−	48.9984i		−	1.64893i	−0.565915	−	0.824464i	$-0.691477\pi$
$883$		−	48.9984i		−	1.64893i	0.565915	−	0.824464i	$-0.308523\pi$
$884$	−9.92202	+	14.9892i	−0.333714	+	0.504142i
$885$	−33.9686	+	4.54237i	−1.14184	+	0.152690i
$886$	16.9753	−	16.9753i	0.570297	−	0.570297i
$887$			36.7411i			1.23364i	0.787103	+	0.616822i	$0.211580\pi$
$887$			36.7411i			1.23364i	−0.787103	+	0.616822i	$0.788420\pi$
$888$	2.91954	+	3.78883i	0.0979732	+	0.127145i
$889$	−16.6779	−	4.46884i	−0.559360	−	0.149880i
$890$	−26.8649	+	7.19843i	−0.900514	+	0.241292i
$891$	−36.4514	−	35.8630i	−1.22117	−	1.20146i
$892$	11.8667	+	11.8667i	0.397328	+	0.397328i
$893$			15.8867i			0.531629i
$894$	−1.31958	−	9.86803i	−0.0441332	−	0.330036i
$895$	−25.5404	−	25.5404i	−0.853721	−	0.853721i
$896$	−1.45102	+	2.51324i	−0.0484751	+	0.0839614i
$897$	−7.05560	−	3.42385i	−0.235580	−	0.114319i
$898$	−6.45329	−	11.1774i	−0.215349	−	0.372996i
$899$	14.2529	−	53.1924i	0.475360	−	1.77407i
$900$	2.98584	−	11.3274i	0.0995280	−	0.377581i
$901$	46.6966	+	26.9603i	1.55569	+	0.898178i
$902$	5.85826	−	21.8633i	0.195059	−	0.727969i
$903$	−27.0121	+	35.3515i	−0.898906	+	1.17642i
$904$	−2.89637	+	10.8094i	−0.0963320	+	0.359516i
$905$	−8.91688	−	33.2782i	−0.296407	−	1.10621i
$906$	1.57421	+	11.7722i	0.0522995	+	0.391105i
$907$	12.2765	+	7.08785i	0.407635	+	0.235348i	0.689773	−	0.724026i	$-0.257710\pi$
$907$	12.2765	+	7.08785i	0.407635	+	0.235348i	−0.282138	+	0.959374i	$0.591044\pi$
$908$	−16.9769	−	4.54895i	−0.563398	−	0.150962i
$909$	9.19033	−	34.8655i	0.304824	−	1.15642i
$910$	−20.6886	−	23.3861i	−0.685821	−	0.775242i
$911$	11.4857	−	6.63129i	0.380539	−	0.219705i	−0.297514	−	0.954718i	$-0.596157\pi$
$911$	11.4857	−	6.63129i	0.380539	−	0.219705i	0.678053	+	0.735013i	$0.262824\pi$
$912$	6.73965	+	0.873349i	0.223172	+	0.0289195i
$913$	12.0488			0.398758
$914$	1.84323	+	3.19257i	0.0609687	+	0.105601i
$915$	−26.4143	+	11.0041i	−0.873229	+	0.363786i
$916$	−14.4764	+	14.4764i	−0.478315	+	0.478315i
$917$	1.15931	+	4.32660i	0.0382837	+	0.142877i
$918$	−3.53803	−	25.6629i	−0.116772	−	0.847002i
$919$	−17.5758	+	30.4422i	−0.579773	+	1.00420i	0.415732	+	0.909487i	$0.363525\pi$
$919$	−17.5758	+	30.4422i	−0.579773	+	1.00420i	−0.995505	+	0.0947089i	$0.969808\pi$
$920$	−1.87371	+	3.24536i	−0.0617743	+	0.106996i
$921$	18.0935	+	13.8253i	0.596201	+	0.455558i
$922$	−19.8663	−	11.4698i	−0.654260	−	0.377737i
$923$	−0.765351	−	0.256117i	−0.0251918	−	0.00843020i
$924$	3.78530	+	28.3072i	0.124527	+	0.931238i
$925$	2.79094	+	10.4159i	0.0917655	+	0.342474i
$926$	−11.0868	+	6.40099i	−0.364336	+	0.210350i
$927$	−12.0986	−	3.18913i	−0.397371	−	0.104745i
$928$	−6.48252	+	6.48252i	−0.212799	+	0.212799i
$929$	−26.0390	−	26.0390i	−0.854313	−	0.854313i	0.136348	−	0.990661i	$-0.456463\pi$
$929$	−26.0390	−	26.0390i	−0.854313	−	0.854313i	−0.990661	+	0.136348i	$0.956463\pi$
$930$	24.6696	+	18.8501i	0.808949	+	0.618119i
$931$	5.38869	−	1.44389i	0.176607	−	0.0473217i
$932$	−16.3168	+	9.42054i	−0.534476	+	0.308580i
$933$	−0.528068	+	1.28224i	−0.0172882	+	0.0419787i
$934$	30.7507	−	8.23964i	1.00620	−	0.269609i
$935$	84.5290			2.76439
$936$	9.66068	−	4.86532i	0.315769	−	0.159028i
$937$	50.7974			1.65948			0.829740	−	0.558150i	$-0.188489\pi$
$937$	50.7974			1.65948			0.829740	+	0.558150i	$0.188489\pi$
$938$	1.38942	−	0.372293i	0.0453661	−	0.0121558i
$939$	−8.79425	−	11.4128i	−0.286990	−	0.372441i
$940$	10.4637	−	6.04120i	0.341287	−	0.197042i
$941$	13.5290	−	3.62508i	0.441032	−	0.118174i	−0.0314679	−	0.999505i	$-0.510018\pi$
$941$	13.5290	−	3.62508i	0.441032	−	0.118174i	0.472500	+	0.881330i	$0.343352\pi$
$942$	1.61830	−	12.4885i	0.0527271	−	0.406896i
$943$	3.53750	+	3.53750i	0.115197	+	0.115197i
$944$	−4.68856	+	4.68856i	−0.152600	+	0.152600i
$945$	44.6484	+	5.60112i	1.45241	+	0.182204i
$946$	43.5525	−	25.1450i	1.41601	−	0.817536i
$947$	−1.59734	−	5.96134i	−0.0519065	−	0.193718i	0.935104	−	0.354373i	$-0.115306\pi$
$947$	−1.59734	−	5.96134i	−0.0519065	−	0.193718i	−0.987011	+	0.160656i	$0.948639\pi$
$948$	24.6086	+	10.1346i	0.799250	+	0.329157i
$949$	−4.77442	−	23.4718i	−0.154984	−	0.761928i
$950$	13.2684	+	7.66054i	0.430485	+	0.248541i
$951$	2.13893	−	16.5062i	0.0693596	−	0.535249i
$952$	−7.23412	+	12.5299i	−0.234459	+	0.406095i
$953$	9.04214	−	15.6614i	0.292904	−	0.507324i	−0.681591	−	0.731733i	$-0.738712\pi$
$953$	9.04214	−	15.6614i	0.292904	−	0.507324i	0.974495	+	0.224409i	$0.0720452\pi$
$954$	−16.3373	−	28.0330i	−0.528938	−	0.907601i
$955$	6.88965	+	25.7125i	0.222944	+	0.832038i
$956$	0.314259	−	0.314259i	0.0101639	−	0.0101639i
$957$	−11.5941	+	89.4715i	−0.374783	+	2.89220i
$958$	−15.1380	−	26.2198i	−0.489087	−	0.847123i
$959$	−48.2565			−1.55829
$960$	−1.98764	−	4.77112i	−0.0641509	−	0.153987i
$961$	−4.40146	+	2.54119i	−0.141983	+	0.0819737i
$962$	−5.49598	+	8.30279i	−0.177197	+	0.267693i
$963$	8.63116	−	8.70167i	0.278135	−	0.280408i
$964$	10.2818	+	2.75500i	0.331154	+	0.0887326i
$965$	−11.9446	−	6.89622i	−0.384510	−	0.221997i
$966$	−5.83666	−	2.40373i	−0.187791	−	0.0773386i
$967$	−3.03347	−	11.3211i	−0.0975499	−	0.364061i	0.899844	−	0.436212i	$-0.143680\pi$
$967$	−3.03347	−	11.3211i	−0.0975499	−	0.364061i	−0.997394	+	0.0721510i	$0.977014\pi$
$968$	5.50824	−	20.5570i	0.177042	−	0.660728i
$969$	33.6008	+	4.35412i	1.07941	+	0.139874i
$970$	1.51397	−	5.65021i	0.0486106	−	0.181417i
$971$	−28.3125	−	16.3463i	−0.908593	−	0.524576i	−0.0286145	−	0.999591i	$-0.509110\pi$
$971$	−28.3125	−	16.3463i	−0.908593	−	0.524576i	−0.879978	+	0.475014i	$0.842443\pi$
$972$	−5.81867	+	14.4618i	−0.186634	+	0.463862i
$973$	−4.29567	+	16.0317i	−0.137713	+	0.513952i
$974$	15.7186	+	27.2254i	0.503657	+	0.872359i
$975$	24.3225	−	1.74954i	0.778944	−	0.0560300i
$976$	−2.76814	+	4.79456i	−0.0886060	+	0.153470i
$977$	−34.0229	−	34.0229i	−1.08849	−	1.08849i	−0.995684	−	0.0928035i	$-0.970417\pi$
$977$	−34.0229	−	34.0229i	−1.08849	−	1.08849i	−0.0928035	−	0.995684i	$-0.529583\pi$
$978$	4.95654	−	3.81933i	0.158493	−	0.122129i
$979$			52.9556i			1.69247i
$980$	−3.00015	−	3.00015i	−0.0958364	−	0.0958364i
$981$	−3.19319	+	5.58309i	−0.101951	+	0.178254i
$982$	13.1229	−	3.51626i	0.418767	−	0.112208i
$983$	−5.80457	−	1.55533i	−0.185137	−	0.0496073i	0.165059	−	0.986284i	$-0.447218\pi$
$983$	−5.80457	−	1.55533i	−0.185137	−	0.0496073i	−0.350196	+	0.936676i	$0.613885\pi$
$984$	−6.83916	+	0.914549i	−0.218025	+	0.0291548i
$985$			59.1318i			1.88409i
$986$	−32.3189	+	32.3189i	−1.02924	+	1.02924i
$987$	12.4223	+	16.1210i	0.395406	+	0.513138i
$988$	2.81990	+	13.8631i	0.0897130	+	0.441044i
$989$			11.1153i			0.353446i
$990$	−44.1530	−	25.2528i	−1.40327	−	0.802587i
$991$	−2.33804	−	4.04960i	−0.0742703	−	0.128640i	0.826498	−	0.562939i	$-0.190329\pi$
$991$	−2.33804	−	4.04960i	−0.0742703	−	0.128640i	−0.900769	+	0.434299i	$0.856996\pi$
$992$	6.00686			0.190718
$993$	−16.0035	+	20.9442i	−0.507856	+	0.664646i
$994$	−0.627459	−	0.168127i	−0.0199018	−	0.00533267i
$995$	−56.4180	−	15.1172i	−1.78857	−	0.479246i
$996$	−1.41251	−	3.39057i	−0.0447570	−	0.107434i
$997$	41.5388			1.31555			0.657774	−	0.753216i	$-0.271498\pi$
$997$	41.5388			1.31555			0.657774	+	0.753216i	$0.271498\pi$
$998$	−13.1091	−	22.7057i	−0.414962	−	0.718735i
$999$	−1.95977	−	14.2151i	−0.0620045	−	0.449747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.41.1	yes	56
3.2	odd	2		702.2.bc.a.665.14		56
9.2	odd	6		234.2.y.a.119.6	yes	56
9.7	even	3		702.2.bb.a.197.14		56
13.7	odd	12		234.2.y.a.59.6	✓	56
39.20	even	12		702.2.bb.a.449.14		56
117.7	odd	12		702.2.bc.a.683.14		56
117.20	even	12	inner	234.2.z.a.137.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.6	✓	56	13.7	odd	12
234.2.y.a.119.6	yes	56	9.2	odd	6
234.2.z.a.41.1	yes	56	1.1	even	1	trivial
234.2.z.a.137.1	yes	56	117.20	even	12	inner
702.2.bb.a.197.14		56	9.7	even	3
702.2.bb.a.449.14		56	39.20	even	12
702.2.bc.a.665.14		56	3.2	odd	2
702.2.bc.a.683.14		56	117.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.71677 + 0.229570i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.88241 + 0.772339i) q^{5} +(1.59885 - 0.666081i) q^{6} +(2.05205 + 2.05205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.89459 - 0.788239i) q^{9} +(2.58430 - 1.49204i) q^{10} +(-1.47054 - 5.48814i) q^{11} +(-1.37198 + 1.05720i) q^{12} +(-3.00654 - 1.99016i) q^{13} +(-2.51324 - 1.45102i) q^{14} +(4.77112 - 1.98764i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.49277 - 4.31761i) q^{17} +(-2.59195 + 1.51056i) q^{18} +(-1.01552 - 3.78997i) q^{19} +(-2.11007 + 2.11007i) q^{20} +(-3.99399 - 3.05181i) q^{21} +(2.84087 + 4.92053i) q^{22} -1.25580 q^{23} +(1.05161 - 1.37627i) q^{24} +(3.38164 - 1.95239i) q^{25} +(3.41918 + 1.14420i) q^{26} +(-4.78840 + 2.01774i) q^{27} +(2.80315 + 0.751103i) q^{28} +(7.93943 + 4.58383i) q^{29} +(-4.09411 + 3.15477i) q^{30} +(-1.55469 - 5.80218i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.78450 + 9.08428i) q^{33} +(-1.29035 + 4.81566i) q^{34} +(-7.49973 - 4.32997i) q^{35} +(2.11267 - 2.12993i) q^{36} +(-0.714749 + 2.66748i) q^{37} +(1.96184 + 3.39800i) q^{38} +(5.61841 + 2.72643i) q^{39} +(1.49204 - 2.58430i) q^{40} +(-2.81693 - 2.81693i) q^{41} +(4.64776 + 1.91410i) q^{42} -8.85117i q^{43} +(-4.01760 - 4.01760i) q^{44} +(-7.73461 + 4.50763i) q^{45} +(1.21301 - 0.325025i) q^{46} +(-3.91098 - 1.04794i) q^{47} +(-0.659571 + 1.60155i) q^{48} +1.42183i q^{49} +(-2.76110 + 2.76110i) q^{50} +(-3.28832 + 7.98460i) q^{51} +(-3.59882 - 0.220258i) q^{52} +10.8154i q^{53} +(4.10301 - 3.18831i) q^{54} +(8.47741 + 14.6833i) q^{55} -2.90204 q^{56} +(2.61348 + 6.27338i) q^{57} +(-8.85528 - 2.37277i) q^{58} +(-6.40469 - 1.71613i) q^{59} +(3.13809 - 4.10691i) q^{60} -5.53628 q^{61} +(3.00343 + 5.20209i) q^{62} +(7.55736 + 4.32235i) q^{63} -1.00000i q^{64} +(10.2031 + 3.41438i) q^{65} +(-6.00673 - 7.79524i) q^{66} +(-0.350486 + 0.350486i) q^{67} -4.98554i q^{68} +(2.15592 - 0.288294i) q^{69} +(8.36486 + 2.24136i) q^{70} +(0.216213 - 0.0579342i) q^{71} +(-1.48942 + 2.60416i) q^{72} +(4.69747 + 4.69747i) q^{73} -2.76158i q^{74} +(-5.35729 + 4.12813i) q^{75} +(-2.77445 - 2.77445i) q^{76} +(8.24432 - 14.2796i) q^{77} +(-6.13262 - 1.17938i) q^{78} +(-7.68273 - 13.3069i) q^{79} +(-0.772339 + 2.88241i) q^{80} +(7.75736 - 4.56327i) q^{81} +(3.45002 + 1.99187i) q^{82} +(-0.548858 + 2.04837i) q^{83} +(-4.98480 - 0.645949i) q^{84} +(-3.85053 + 14.3704i) q^{85} +(2.29085 + 8.54958i) q^{86} +(-14.6825 - 6.04672i) q^{87} +(4.92053 + 2.84087i) q^{88} +(-9.00272 - 2.41227i) q^{89} +(6.30440 - 6.35591i) q^{90} +(-2.08566 - 10.2535i) q^{91} +(-1.08755 + 0.627900i) q^{92} +(4.00105 + 9.60410i) q^{93} +4.04894 q^{94} +(5.85429 + 10.1399i) q^{95} +(0.222585 - 1.71769i) q^{96} +(1.38610 - 1.38610i) q^{97} +(-0.367996 - 1.37338i) q^{98} +(-8.58260 - 14.7268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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