LMFDB - Embedded newform 349.2.e.a.123.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.5
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +O(q^{10})$	\(q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +5.76535i q^{10} +0.545693i q^{11} +(-3.06454 - 5.30794i) q^{12} +(0.131290 - 0.0758002i) q^{13} +(-3.55887 + 6.16414i) q^{14} +(-3.19734 - 5.53795i) q^{15} +(1.24924 + 2.16374i) q^{16} -2.30327 q^{17} +(4.88720 + 2.82163i) q^{18} +(-2.50657 + 4.34151i) q^{19} +(-3.47679 - 6.02197i) q^{20} -7.89469i q^{21} +(-0.584020 - 1.01155i) q^{22} +(-2.56604 - 4.44452i) q^{23} +(2.55966 + 1.47782i) q^{24} +(-1.12745 - 1.95280i) q^{25} +(-0.162248 + 0.281022i) q^{26} +0.863107 q^{27} -8.58470i q^{28} +(-2.81549 + 4.87657i) q^{29} +(11.8538 + 6.84382i) q^{30} +2.33848 q^{31} +(-6.78774 - 3.91890i) q^{32} +(1.12197 + 0.647770i) q^{33} +(4.26959 - 2.46505i) q^{34} -8.95671i q^{35} -6.80632 q^{36} -3.26599 q^{37} -10.7305i q^{38} -0.359918i q^{39} +(2.90400 + 1.67662i) q^{40} +10.0059 q^{41} +(8.44919 + 14.6344i) q^{42} +(6.94329 + 4.00871i) q^{43} +(1.22003 + 0.704386i) q^{44} -7.10126 q^{45} +(9.51336 + 5.49254i) q^{46} +3.68216i q^{47} +5.93169 q^{48} +(2.02885 - 3.51407i) q^{49} +(4.17992 + 2.41328i) q^{50} +(-2.73413 + 4.73565i) q^{51} -0.391375i q^{52} -7.63103i q^{53} +(-1.59994 + 0.923728i) q^{54} +(1.27290 + 0.734910i) q^{55} +(2.06991 + 3.58519i) q^{56} +(5.95091 + 10.3073i) q^{57} -12.0529i q^{58} +(-2.78764 - 1.60944i) q^{59} -16.5086 q^{60} -8.03093i q^{61} +(-4.33486 + 2.50273i) q^{62} +(-7.59247 - 4.38351i) q^{63} +11.7796 q^{64} -0.408335i q^{65} -2.77307 q^{66} +8.84653 q^{67} +(-2.97309 + 5.14954i) q^{68} -12.1842 q^{69} +(9.58579 + 16.6031i) q^{70} +(-13.5642 + 7.83131i) q^{71} +(2.84250 - 1.64112i) q^{72} +(-7.17140 + 12.4212i) q^{73} +(6.05418 - 3.49538i) q^{74} -5.35342 q^{75} +(6.47102 + 11.2081i) q^{76} +(0.907299 + 1.57149i) q^{77} +(0.385197 + 0.667181i) q^{78} -0.708893i q^{79} +6.72963 q^{80} +(4.97924 - 8.62429i) q^{81} +(-18.5480 + 10.7087i) q^{82} +(-3.54508 - 6.14026i) q^{83} +(-17.6506 - 10.1906i) q^{84} +(-3.10193 + 5.37269i) q^{85} -17.1611 q^{86} +(6.68431 + 11.5776i) q^{87} -0.679356 q^{88} +(-12.3681 - 7.14073i) q^{89} +(13.1636 - 7.60003i) q^{90} +(0.252059 - 0.436580i) q^{91} -13.2491 q^{92} +(2.77592 - 4.80804i) q^{93} +(-3.94078 - 6.82563i) q^{94} +(6.75143 + 11.6938i) q^{95} +(-16.1149 + 9.30395i) q^{96} +(2.04436 - 1.18031i) q^{97} +8.68540i q^{98} +(1.24594 - 0.719346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.85370	+	1.07024i	−1.31077	+	0.756771i	−0.982223	−	0.187718i	$-0.939891\pi$
$2$	−1.85370	+	1.07024i	−1.31077	+	0.756771i	−0.328543	+	0.944489i	$0.606558\pi$
$3$	1.18706	−	2.05605i	0.685350	−	1.18706i	−0.287977	−	0.957637i	$-0.592983\pi$
$3$	1.18706	−	2.05605i	0.685350	−	1.18706i	0.973327	−	0.229423i	$-0.0736840\pi$
$4$	1.29081	−	2.23575i	0.645405	−	1.11787i
$5$	1.34675	−	2.33263i	0.602283	−	1.04319i	−0.390191	−	0.920734i	$-0.627591\pi$
$5$	1.34675	−	2.33263i	0.602283	−	1.04319i	0.992475	−	0.122451i	$-0.0390756\pi$
$6$			5.08174i			2.07461i
$7$	2.87980	−	1.66266i	1.08846	−	0.628425i	0.155297	−	0.987868i	$-0.450367\pi$
$7$	2.87980	−	1.66266i	1.08846	−	0.628425i	0.933167	+	0.359443i	$0.117033\pi$
$8$			1.24494i			0.440154i
$9$	−1.31823	−	2.28323i	−0.439409	−	0.761078i
$10$			5.76535i			1.82316i
$11$			0.545693i			0.164533i	0.996610	+	0.0822663i	$0.0262158\pi$
$11$			0.545693i			0.164533i	−0.996610	+	0.0822663i	$0.973784\pi$
$12$	−3.06454	−	5.30794i	−0.884657	−	1.53227i
$13$	0.131290	−	0.0758002i	0.0364133	−	0.0210232i	−0.481683	−	0.876346i	$-0.659974\pi$
$13$	0.131290	−	0.0758002i	0.0364133	−	0.0210232i	0.518096	+	0.855322i	$0.326641\pi$
$14$	−3.55887	+	6.16414i	−0.951148	+	1.64744i
$15$	−3.19734	−	5.53795i	−0.825549	−	1.42989i
$16$	1.24924	+	2.16374i	0.312309	+	0.540936i
$17$	−2.30327			−0.558626			−0.279313	−	0.960200i	$-0.590107\pi$
$17$	−2.30327			−0.558626			−0.279313	+	0.960200i	$0.590107\pi$
$18$	4.88720	+	2.82163i	1.15192	+	0.665064i
$19$	−2.50657	+	4.34151i	−0.575047	+	0.996011i	0.420989	+	0.907066i	$0.361683\pi$
$19$	−2.50657	+	4.34151i	−0.575047	+	0.996011i	−0.996037	+	0.0889452i	$0.971650\pi$
$20$	−3.47679	−	6.02197i	−0.777434	−	1.34655i
$21$		−	7.89469i		−	1.72276i
$22$	−0.584020	−	1.01155i	−0.124513	−	0.215664i
$23$	−2.56604	−	4.44452i	−0.535057	−	0.926746i	−0.999161	−	0.0409649i	$-0.986957\pi$
$23$	−2.56604	−	4.44452i	−0.535057	−	0.926746i	0.464104	−	0.885781i	$-0.346377\pi$
$24$	2.55966	+	1.47782i	0.522489	+	0.301659i
$25$	−1.12745	−	1.95280i	−0.225490	−	0.390561i
$26$	−0.162248	+	0.281022i	−0.0318195	+	0.0551130i
$27$	0.863107			0.166105
$28$		−	8.58470i		−	1.62235i
$29$	−2.81549	+	4.87657i	−0.522823	+	0.905556i	0.476824	+	0.878999i	$0.341788\pi$
$29$	−2.81549	+	4.87657i	−0.522823	+	0.905556i	−0.999647	+	0.0265573i	$0.991546\pi$
$30$	11.8538	+	6.84382i	2.16420	+	1.24950i
$31$	2.33848			0.420004			0.210002	−	0.977701i	$-0.432653\pi$
$31$	2.33848			0.420004			0.210002	+	0.977701i	$0.432653\pi$
$32$	−6.78774	−	3.91890i	−1.19991	−	0.692771i
$33$	1.12197	+	0.647770i	0.195310	+	0.112762i
$34$	4.26959	−	2.46505i	0.732228	−	0.422752i
$35$		−	8.95671i		−	1.51396i
$36$	−6.80632			−1.13439
$37$	−3.26599			−0.536925			−0.268463	−	0.963290i	$-0.586516\pi$
$37$	−3.26599			−0.536925			−0.268463	+	0.963290i	$0.586516\pi$
$38$		−	10.7305i		−	1.74072i
$39$		−	0.359918i		−	0.0576330i
$40$	2.90400	+	1.67662i	0.459162	+	0.265097i
$41$	10.0059			1.56266			0.781330	−	0.624118i	$-0.214541\pi$
$41$	10.0059			1.56266			0.781330	+	0.624118i	$0.214541\pi$
$42$	8.44919	+	14.6344i	1.30374	+	2.25814i
$43$	6.94329	+	4.00871i	1.05884	+	0.611322i	0.925112	−	0.379695i	$-0.123971\pi$
$43$	6.94329	+	4.00871i	1.05884	+	0.611322i	0.133730	+	0.991018i	$0.457305\pi$
$44$	1.22003	+	0.704386i	0.183927	+	0.106190i
$45$	−7.10126			−1.05859
$46$	9.51336	+	5.49254i	1.40267	+	0.809831i
$47$			3.68216i			0.537098i	0.963266	+	0.268549i	$0.0865442\pi$
$47$			3.68216i			0.537098i	−0.963266	+	0.268549i	$0.913456\pi$
$48$	5.93169			0.856165
$49$	2.02885	−	3.51407i	0.289836	−	0.502010i
$50$	4.17992	+	2.41328i	0.591130	+	0.341289i
$51$	−2.73413	+	4.73565i	−0.382854	+	0.663123i
$52$		−	0.391375i		−	0.0542739i
$53$		−	7.63103i		−	1.04820i	−0.851656	−	0.524101i	$-0.824401\pi$
$53$		−	7.63103i		−	1.04820i	0.851656	−	0.524101i	$-0.175599\pi$
$54$	−1.59994	+	0.923728i	−0.217725	+	0.125703i
$55$	1.27290	+	0.734910i	0.171638	+	0.0990952i
$56$	2.06991	+	3.58519i	0.276604	+	0.479092i
$57$	5.95091	+	10.3073i	0.788217	+	1.36523i
$58$		−	12.0529i		−	1.58263i
$59$	−2.78764	−	1.60944i	−0.362919	−	0.209532i	0.307441	−	0.951567i	$-0.400527\pi$
$59$	−2.78764	−	1.60944i	−0.362919	−	0.209532i	−0.670361	+	0.742035i	$0.733861\pi$
$60$	−16.5086			−2.13126
$61$		−	8.03093i		−	1.02826i	−0.857714	−	0.514128i	$-0.828116\pi$
$61$		−	8.03093i		−	1.02826i	0.857714	−	0.514128i	$-0.171884\pi$
$62$	−4.33486	+	2.50273i	−0.550527	+	0.317847i
$63$	−7.59247	−	4.38351i	−0.956561	−	0.552271i
$64$	11.7796			1.47246
$65$		−	0.408335i		−	0.0506477i
$66$	−2.77307			−0.341341
$67$	8.84653			1.08078			0.540388	−	0.841416i	$-0.318278\pi$
$67$	8.84653			1.08078			0.540388	+	0.841416i	$0.318278\pi$
$68$	−2.97309	+	5.14954i	−0.360540	+	0.624474i
$69$	−12.1842			−1.46680
$70$	9.58579	+	16.6031i	1.14572	+	1.98445i
$71$	−13.5642	+	7.83131i	−1.60978	+	0.929405i	−0.620358	+	0.784319i	$0.713013\pi$
$71$	−13.5642	+	7.83131i	−1.60978	+	0.929405i	−0.989419	+	0.145087i	$0.953654\pi$
$72$	2.84250	−	1.64112i	0.334991	−	0.193407i
$73$	−7.17140	+	12.4212i	−0.839349	+	1.45379i	0.0510915	+	0.998694i	$0.483730\pi$
$73$	−7.17140	+	12.4212i	−0.839349	+	1.45379i	−0.890440	+	0.455100i	$0.849603\pi$
$74$	6.05418	−	3.49538i	0.703784	−	0.406330i
$75$	−5.35342			−0.618159
$76$	6.47102	+	11.2081i	0.742277	+	1.28566i
$77$	0.907299	+	1.57149i	0.103396	+	0.179088i
$78$	0.385197	+	0.667181i	0.0436150	+	0.0755434i
$79$		−	0.708893i		−	0.0797567i	−0.999205	−	0.0398783i	$-0.987303\pi$
$79$		−	0.708893i		−	0.0797567i	0.999205	−	0.0398783i	$-0.0126970\pi$
$80$	6.72963			0.752395
$81$	4.97924	−	8.62429i	0.553249	−	0.958255i
$82$	−18.5480	+	10.7087i	−2.04828	+	1.18258i
$83$	−3.54508	−	6.14026i	−0.389123	−	0.673981i	0.603209	−	0.797584i	$-0.293889\pi$
$83$	−3.54508	−	6.14026i	−0.389123	−	0.673981i	−0.992332	+	0.123602i	$0.960555\pi$
$84$	−17.6506	−	10.1906i	−1.92583	−	1.11188i
$85$	−3.10193	+	5.37269i	−0.336451	+	0.582750i
$86$	−17.1611			−1.85052
$87$	6.68431	+	11.5776i	0.716633	+	1.24125i
$88$	−0.679356			−0.0724196
$89$	−12.3681	−	7.14073i	−1.31102	−	0.756915i	−0.328752	−	0.944416i	$-0.606628\pi$
$89$	−12.3681	−	7.14073i	−1.31102	−	0.756915i	−0.982264	+	0.187501i	$0.939961\pi$
$90$	13.1636	−	7.60003i	1.38757	−	0.801113i
$91$	0.252059	−	0.436580i	0.0264230	−	0.0457660i
$92$	−13.2491			−1.38131
$93$	2.77592	−	4.80804i	0.287850	−	0.498570i
$94$	−3.94078	−	6.82563i	−0.406461	−	0.704010i
$95$	6.75143	+	11.6938i	0.692683	+	1.19976i
$96$	−16.1149	+	9.30395i	−1.64472	+	0.949580i
$97$	2.04436	−	1.18031i	0.207573	−	0.119843i	−0.392610	−	0.919705i	$-0.628428\pi$
$97$	2.04436	−	1.18031i	0.207573	−	0.119843i	0.600183	+	0.799863i	$0.295094\pi$
$98$			8.68540i			0.877358i
$99$	1.24594	−	0.719346i	0.125222	−	0.0722970i
$100$	−5.82131			−0.582131
$101$			19.9091i			1.98103i	0.137402	+	0.990515i	$0.456125\pi$
$101$			19.9091i			1.98103i	−0.137402	+	0.990515i	$0.543875\pi$
$102$		−	11.7046i		−	1.15893i
$103$		−	1.32750i		−	0.130802i	−0.997859	−	0.0654012i	$-0.979167\pi$
$103$		−	1.32750i		−	0.130802i	0.997859	−	0.0654012i	$-0.0208327\pi$
$104$	0.0943670	+	0.163448i	0.00925344	+	0.0160274i
$105$	−18.4154	−	10.6322i	−1.79716	−	1.03759i
$106$	8.16700	+	14.1457i	0.793249	+	1.37395i
$107$	−3.90280	+	2.25329i	−0.377298	+	0.217833i	−0.676642	−	0.736312i	$-0.736566\pi$
$107$	−3.90280	+	2.25329i	−0.377298	+	0.217833i	0.299344	+	0.954145i	$0.403232\pi$
$108$	1.11411	−	1.92969i	0.107205	−	0.185685i
$109$	4.43872	−	7.68809i	0.425152	−	0.736386i	−0.571282	−	0.820754i	$-0.693554\pi$
$109$	4.43872	−	7.68809i	0.425152	−	0.736386i	0.996435	+	0.0843680i	$0.0268871\pi$
$110$	−3.14611			−0.299970
$111$	−3.87693	+	6.71504i	−0.367982	+	0.637363i
$112$	7.19512	+	4.15411i	0.679875	+	0.392526i
$113$	10.9736	−	6.33560i	1.03231	−	0.596003i	0.114662	−	0.993405i	$-0.463421\pi$
$113$	10.9736	−	6.33560i	1.03231	−	0.596003i	0.917645	+	0.397402i	$0.130088\pi$
$114$	−22.0624	−	12.7377i	−2.06634	−	1.19300i
$115$	−13.8232			−1.28902
$116$	7.26852	+	12.5894i	0.674865	+	1.16890i
$117$	−0.346139	−	0.199844i	−0.0320006	−	0.0184756i
$118$	6.88993			0.634270
$119$	−6.63298	+	3.82955i	−0.608044	+	0.351055i
$120$	6.89444	−	3.98050i	0.629373	−	0.363369i
$121$	10.7022			0.972929
$122$	8.59500	+	14.8870i	0.778154	+	1.34780i
$123$	11.8776	−	20.5726i	1.07097	−	1.85497i
$124$	3.01854	−	5.22826i	0.271073	−	0.469512i
$125$	7.39390			0.661330
$126$	18.7656			1.67177
$127$			15.6113i			1.38528i	0.721284	+	0.692640i	$0.243552\pi$
$127$			15.6113i			1.38528i	−0.721284	+	0.692640i	$0.756448\pi$
$128$	−8.26050	+	4.76920i	−0.730132	+	0.421542i
$129$	16.4842	−	9.51716i	1.45135	−	0.837939i
$130$	0.437015	+	0.756931i	0.0383287	+	0.0663873i
$131$			16.0664i			1.40373i	0.712310	+	0.701865i	$0.247649\pi$
$131$			16.0664i			1.40373i	−0.712310	+	0.701865i	$0.752351\pi$
$132$	2.89650	−	1.67230i	0.252108	−	0.145555i
$133$			16.6703i			1.44550i
$134$	−16.3988	+	9.46787i	−1.41664	+	0.817900i
$135$	1.16239	−	2.01331i	0.100042	−	0.173278i
$136$		−	2.86744i		−	0.245881i
$137$	3.90723	+	2.25584i	0.333818	+	0.192730i	0.657535	−	0.753424i	$-0.271599\pi$
$137$	3.90723	+	2.25584i	0.333818	+	0.192730i	−0.323717	+	0.946154i	$0.604933\pi$
$138$	22.5859	−	13.0400i	1.92264	−	1.11004i
$139$	−3.43043			−0.290966			−0.145483	−	0.989361i	$-0.546474\pi$
$139$	−3.43043			−0.290966			−0.145483	+	0.989361i	$0.546474\pi$
$140$	−20.0249	−	11.5614i	−1.69242	−	0.977117i
$141$	7.57071	+	4.37095i	0.637568	+	0.368100i
$142$	16.7627	−	29.0338i	1.40669	−	2.43647i
$143$	0.0413636	+	0.0716439i	0.00345900	+	0.00599117i
$144$	3.29356	−	5.70461i	0.274463	−	0.475384i
$145$	7.58350	+	13.1350i	0.629775	+	1.09080i
$146$		−	30.7004i		−	2.54078i
$147$	−4.81674	−	8.34284i	−0.397278	−	0.688106i
$148$	−4.21577	+	7.30193i	−0.346534	+	0.600215i
$149$	14.6945	−	8.48388i	1.20382	−	0.695026i	0.242418	−	0.970172i	$-0.422059\pi$
$149$	14.6945	−	8.48388i	1.20382	−	0.695026i	0.961403	+	0.275145i	$0.0887260\pi$
$150$	9.92364	−	5.72942i	0.810262	−	0.467805i
$151$	6.54280	−	11.3325i	0.532445	−	0.922222i	−0.466837	−	0.884343i	$-0.654607\pi$
$151$	6.54280	−	11.3325i	0.532445	−	0.922222i	0.999282	−	0.0378788i	$-0.0120601\pi$
$152$	−5.40493	−	3.12054i	−0.438398	−	0.253109i
$153$	3.03624	+	5.25891i	0.245465	+	0.425158i
$154$	−3.36373	−	1.94205i	−0.271057	−	0.156495i
$155$	3.14935	−	5.45483i	0.252961	−	0.438142i
$156$	−0.804686	−	0.464586i	−0.0644265	−	0.0371966i
$157$	11.9336	−	20.6695i	0.952402	−	1.64961i	0.212197	−	0.977227i	$-0.431938\pi$
$157$	11.9336	−	20.6695i	0.952402	−	1.64961i	0.740205	−	0.672382i	$-0.234729\pi$
$158$	0.758683	+	1.31408i	0.0603576	+	0.104542i
$159$	−15.6898	−	9.05849i	−1.24428	−	0.718385i
$160$	−18.2827	+	10.5555i	−1.44538	+	0.834488i
$161$	−14.7794	−	8.53289i	−1.16478	−	0.672486i
$162$			21.3158i			1.67473i
$163$			11.8530i			0.928402i	0.885730	+	0.464201i	$0.153658\pi$
$163$			11.8530i			0.928402i	−0.885730	+	0.464201i	$0.846342\pi$
$164$	12.9157	−	22.3707i	1.00855	−	1.74686i
$165$	3.02202	−	1.74476i	0.235264	−	0.135830i
$166$	13.1431	+	7.58815i	1.02010	+	0.588955i
$167$		−	4.69956i		−	0.363663i	−0.983330	−	0.181832i	$-0.941797\pi$
$167$		−	4.69956i		−	0.363663i	0.983330	−	0.181832i	$-0.0582026\pi$
$168$	9.82844			0.758281
$169$	−6.48851	+	11.2384i	−0.499116	+	0.864494i
$170$		−	13.2792i		−	1.01847i
$171$	13.2169			1.01072
$172$	17.9249	−	10.3490i	1.36676	−	0.789101i
$173$	3.72588	−	2.15114i	0.283273	−	0.163548i	−0.351631	−	0.936139i	$-0.614373\pi$
$173$	3.72588	−	2.15114i	0.283273	−	0.163548i	0.634904	+	0.772591i	$0.281040\pi$
$174$	−24.7815	−	14.3076i	−1.87868	−	1.08465i
$175$	−6.49368	−	3.74913i	−0.490876	−	0.283408i
$176$	−1.18074	+	0.681700i	−0.0890016	+	0.0513851i
$177$	−6.61819	+	3.82101i	−0.497453	+	0.287205i
$178$	30.5690			2.29125
$179$			0.731822i			0.0546990i	0.999626	+	0.0273495i	$0.00870669\pi$
$179$			0.731822i			0.0546990i	−0.999626	+	0.0273495i	$0.991293\pi$
$180$	−9.16639	+	15.8766i	−0.683222	+	1.18338i
$181$	−21.5060			−1.59853			−0.799266	−	0.600978i	$-0.794778\pi$
$181$	−21.5060			−1.59853			−0.799266	+	0.600978i	$0.794778\pi$
$182$			1.07905i			0.0799847i
$183$	−16.5120	−	9.53321i	−1.22060	−	0.704715i
$184$	5.53317	−	3.19458i	0.407911	−	0.235507i
$185$	−4.39846	+	7.61836i	−0.323381	+	0.560113i
$186$			11.8836i			0.871346i
$187$		−	1.25688i		−	0.0919122i
$188$	8.23239	+	4.75297i	0.600409	+	0.346646i
$189$	2.48558	−	1.43505i	0.180799	−	0.104385i
$190$	−25.0303	−	14.4513i	−1.81589	−	1.04840i
$191$	−0.550318	−	0.953179i	−0.0398196	−	0.0689696i	0.845429	−	0.534088i	$-0.179345\pi$
$191$	−0.550318	−	0.953179i	−0.0398196	−	0.0689696i	−0.885248	+	0.465119i	$0.846012\pi$
$192$	13.9832	−	24.2195i	1.00915	−	1.74789i
$193$	6.78851	+	3.91935i	0.488648	+	0.282121i	0.724013	−	0.689786i	$-0.242295\pi$
$193$	6.78851	+	3.91935i	0.488648	+	0.282121i	−0.235366	+	0.971907i	$0.575629\pi$
$194$	−2.52643	+	4.37590i	−0.181387	+	0.314171i
$195$	−0.839556	−	0.484718i	−0.0601219	−	0.0347114i
$196$	−5.23772	−	9.07200i	−0.374123	−	0.648000i
$197$	16.4978	+	9.52503i	1.17542	+	0.678630i	0.954951	−	0.296763i	$-0.0959073\pi$
$197$	16.4978	+	9.52503i	1.17542	+	0.678630i	0.220471	+	0.975394i	$0.429241\pi$
$198$	−1.53974	+	2.66691i	−0.109425	+	0.189529i
$199$	−15.7666	+	9.10283i	−1.11766	+	0.645283i	−0.940803	−	0.338954i	$-0.889927\pi$
$199$	−15.7666	+	9.10283i	−1.11766	+	0.645283i	−0.176859	+	0.984236i	$0.556594\pi$
$200$	2.43113	−	1.40361i	0.171907	−	0.0992504i
$201$	10.5014	−	18.1889i	0.740709	−	1.28295i
$202$	−21.3075	−	36.9056i	−1.49919	−	2.59667i
$203$			18.7248i			1.31422i
$204$	7.05848	+	12.2256i	0.494192	+	0.855966i
$205$	13.4754	−	23.3401i	0.941164	−	1.63014i
$206$	1.42074	+	2.46079i	0.0989874	+	0.171451i
$207$	−6.76525	+	11.7178i	−0.470217	+	0.814440i
$208$	0.328025	+	0.189385i	0.0227444	+	0.0131315i
$209$	−2.36913	−	1.36782i	−0.163876	−	0.0946140i
$210$	45.5157			3.14088
$211$	−9.64710	+	5.56975i	−0.664134	+	0.383438i	−0.793850	−	0.608113i	$-0.791927\pi$
$211$	−9.64710	+	5.56975i	−0.664134	+	0.383438i	0.129717	+	0.991551i	$0.458593\pi$
$212$	−17.0611	−	9.85021i	−1.17176	−	0.676515i
$213$			37.1850i			2.54787i
$214$	4.82309	−	8.35384i	0.329700	−	0.571057i
$215$	18.7017	−	10.7974i	1.27545	−	0.736379i
$216$			1.07452i			0.0731117i
$217$	6.73438	−	3.88809i	0.457159	−	0.263941i
$218$			19.0019i			1.28697i
$219$	17.0258	+	29.4895i	1.15049	+	1.99272i
$220$	3.28615	−	1.89726i	0.221552	−	0.127913i
$221$	−0.302397	+	0.174589i	−0.0203414	+	0.0117441i
$222$		−	16.5969i		−	1.11391i
$223$	−4.73226			−0.316896			−0.158448	−	0.987367i	$-0.550649\pi$
$223$	−4.73226			−0.316896			−0.158448	+	0.987367i	$0.550649\pi$
$224$	−26.0631			−1.74142
$225$	−2.97247	+	5.14847i	−0.198165	+	0.343232i
$226$	−13.5612	+	23.4886i	−0.902075	+	1.56244i
$227$	9.56248	+	16.5627i	0.634684	+	1.09930i	0.986582	+	0.163266i	$0.0522030\pi$
$227$	9.56248	+	16.5627i	0.634684	+	1.09930i	−0.351898	+	0.936038i	$0.614464\pi$
$228$	30.7260			2.03488
$229$	11.3029	−	6.52576i	0.746919	−	0.431234i	−0.0776603	−	0.996980i	$-0.524745\pi$
$229$	11.3029	−	6.52576i	0.746919	−	0.431234i	0.824580	+	0.565746i	$0.191412\pi$
$230$	25.6242	−	14.7941i	1.68961	−	0.975496i
$231$	4.30808			0.283451
$232$	−6.07105	−	3.50512i	−0.398584	−	0.230122i
$233$	4.97511	+	8.61714i	0.325930	+	0.564528i	0.981700	−	0.190433i	$-0.0609892\pi$
$233$	4.97511	+	8.61714i	0.325930	+	0.564528i	−0.655770	+	0.754961i	$0.727656\pi$
$234$	0.855520			0.0559271
$235$	8.58913	+	4.95894i	0.560293	+	0.323485i
$236$	−7.19662	+	4.15497i	−0.468460	+	0.270466i
$237$	−1.45752	−	0.841499i	−0.0946760	−	0.0546612i
$238$	8.19705	−	14.1977i	0.531336	−	0.920301i
$239$	−13.4507			−0.870051			−0.435026	−	0.900418i	$-0.643261\pi$
$239$	−13.4507			−0.870051			−0.435026	+	0.900418i	$0.643261\pi$
$240$	7.98848	−	13.8364i	0.515654	−	0.893139i
$241$	10.0761	−	17.4523i	0.649058	−	1.12420i	−0.334290	−	0.942470i	$-0.608497\pi$
$241$	10.0761	−	17.4523i	0.649058	−	1.12420i	0.983348	−	0.181731i	$-0.0581700\pi$
$242$	−19.8387	+	11.4539i	−1.27528	+	0.736285i
$243$	−10.5267	−	18.2327i	−0.675285	−	1.16963i
$244$	−17.9552	−	10.3664i	−1.14946	−	0.663642i
$245$	−5.46470	−	9.46513i	−0.349127	−	0.604705i
$246$			50.8474i			3.24191i
$247$			0.759995i			0.0483573i
$248$			2.91128i			0.184866i
$249$	−16.8329			−1.06674
$250$	−13.7061	+	7.91321i	−0.866849	+	0.500476i
$251$			15.4563i			0.975593i	0.872957	+	0.487796i	$0.162199\pi$
$251$			15.4563i			0.975593i	−0.872957	+	0.487796i	$0.837801\pi$
$252$	−19.6009	+	11.3166i	−1.23474	+	0.712877i
$253$	2.42534	−	1.40027i	0.152480	−	0.0880343i
$254$	−16.7078	−	28.9387i	−1.04834	−	1.81578i
$255$	7.36435	+	12.7554i	0.461173	+	0.798776i
$256$	−1.57131	+	2.72159i	−0.0982068	+	0.170099i
$257$	−19.5280			−1.21812			−0.609061	−	0.793123i	$-0.708454\pi$
$257$	−19.5280			−1.21812			−0.609061	+	0.793123i	$0.708454\pi$
$258$	−20.3712	+	35.2840i	−1.26826	+	2.19668i
$259$	−9.40541	+	5.43022i	−0.584424	+	0.337417i
$260$	−0.912934	−	0.527083i	−0.0566178	−	0.0326883i
$261$	14.8458			0.918932
$262$	−17.1949	−	29.7824i	−1.06230	−	1.83996i
$263$	14.8779			0.917410			0.458705	−	0.888589i	$-0.348313\pi$
$263$	14.8779			0.917410			0.458705	+	0.888589i	$0.348313\pi$
$264$	−0.806437	+	1.39679i	−0.0496328	+	0.0859665i
$265$	−17.8004	−	10.2771i	−1.09347	−	0.631315i
$266$	−17.8411	−	30.9017i	−1.09391	−	1.89471i
$267$	−29.3634	+	16.9530i	−1.79701	+	1.03750i
$268$	11.4192	−	19.7786i	0.697538	−	1.20817i
$269$	−5.42046			−0.330491			−0.165246	−	0.986252i	$-0.552842\pi$
$269$	−5.42046			−0.330491			−0.165246	+	0.986252i	$0.552842\pi$
$270$			4.97611i			0.302836i
$271$	−14.1788	−	24.5584i	−0.861302	−	1.49182i	−0.870673	−	0.491863i	$-0.836316\pi$
$271$	−14.1788	−	24.5584i	−0.861302	−	1.49182i	0.00937068	−	0.999956i	$-0.497017\pi$
$272$	−2.87734	−	4.98369i	−0.174464	−	0.302181i
$273$	−0.598420	−	1.03649i	−0.0362180	−	0.0627314i
$274$	−9.65714			−0.583409
$275$	1.06563	−	0.615242i	0.0642600	−	0.0371005i
$276$	−15.7275	+	27.2408i	−0.946683	+	1.63970i
$277$	−16.5475	+	9.55371i	−0.994244	+	0.574027i	−0.906540	−	0.422120i	$-0.861286\pi$
$277$	−16.5475	+	9.55371i	−0.994244	+	0.574027i	−0.0877038	+	0.996147i	$0.527953\pi$
$278$	6.35900	−	3.67137i	0.381388	−	0.220194i
$279$	−3.08265	−	5.33931i	−0.184553	−	0.319656i
$280$	11.1506			0.666375
$281$	11.4041	−	19.7525i	0.680314	−	1.17834i	−0.294571	−	0.955630i	$-0.595177\pi$
$281$	11.4041	−	19.7525i	0.680314	−	1.17834i	0.974885	−	0.222709i	$-0.0714899\pi$
$282$	−18.7118			−1.11427
$283$	−7.38519			−0.439004			−0.219502	−	0.975612i	$-0.570443\pi$
$283$	−7.38519			−0.439004			−0.219502	+	0.975612i	$0.570443\pi$
$284$			40.4349i			2.39937i
$285$	32.0574			1.89892
$286$	−0.153352	−	0.0885377i	−0.00906788	−	0.00523534i
$287$	28.8151	−	16.6364i	1.70090	−	0.982015i
$288$			20.6640i			1.21764i
$289$	−11.6949			−0.687937
$290$	−28.1151	−	16.2323i	−1.65098	−	0.953191i
$291$		−	5.60441i		−	0.328536i
$292$	18.5138	+	32.0669i	1.08344	+	1.87657i
$293$	14.5160	+	25.1424i	0.848033	+	1.46884i	0.882961	+	0.469446i	$0.155546\pi$
$293$	14.5160	+	25.1424i	0.848033	+	1.46884i	−0.0349283	+	0.999390i	$0.511120\pi$
$294$	17.8576	+	10.3101i	1.04148	+	0.601297i
$295$	−7.50848	+	4.33502i	−0.437161	+	0.252395i
$296$		−	4.06597i		−	0.236330i
$297$			0.470991i			0.0273297i
$298$	−18.1595	+	31.4532i	−1.05195	+	1.82203i
$299$	−0.673791	−	0.389013i	−0.0389663	−	0.0224972i
$300$	−6.91024	+	11.9689i	−0.398963	+	0.691024i
$301$	26.6604			1.53668
$302$			28.0093i			1.61176i
$303$	40.9341	+	23.6333i	2.35160	+	1.35770i
$304$	−12.5252			−0.718371
$305$	−18.7332	−	10.8156i	−1.07266	−	0.619301i
$306$	−11.2566	−	6.49898i	−0.643495	−	0.371522i
$307$	−10.4670	−	18.1294i	−0.597385	−	1.03470i	−0.993206	−	0.116374i	$-0.962873\pi$
$307$	−10.4670	−	18.1294i	−0.597385	−	1.03470i	0.395820	−	0.918328i	$-0.370460\pi$
$308$	4.68461			0.266930
$309$	−2.72940	−	1.57582i	−0.155270	−	0.0896454i
$310$			13.4822i			0.765736i
$311$		−	16.5490i		−	0.938407i	−0.883090	−	0.469203i	$-0.844541\pi$
$311$		−	16.5490i		−	0.938407i	0.883090	−	0.469203i	$-0.155459\pi$
$312$	0.448077			0.0253674
$313$	−3.00317			−0.169749			−0.0848747	−	0.996392i	$-0.527049\pi$
$313$	−3.00317			−0.169749			−0.0848747	+	0.996392i	$0.527049\pi$
$314$			51.0869i			2.88300i
$315$	−20.4503	+	11.8070i	−1.15224	+	0.665247i
$316$	−1.58491	−	0.915046i	−0.0891580	−	0.0514754i
$317$	−15.2838	−	8.82411i	−0.858424	−	0.495611i	0.00506015	−	0.999987i	$-0.498389\pi$
$317$	−15.2838	−	8.82411i	−0.858424	−	0.495611i	−0.863484	+	0.504376i	$0.831723\pi$
$318$	38.7789			2.17461
$319$	−2.66111	−	1.53639i	−0.148993	−	0.0860214i
$320$	15.8642	−	27.4776i	0.886836	−	1.53604i
$321$			10.6991i			0.597168i
$322$	36.5288			2.03567
$323$	5.77332	−	9.99969i	0.321236	−	0.556398i
$324$	−12.8545	−	22.2647i	−0.714139	−	1.23693i
$325$	−0.296046	−	0.170922i	−0.0164217	−	0.00948106i
$326$	−12.6856	−	21.9720i	−0.702588	−	1.21692i
$327$	−10.5381	−	18.2525i	−0.582756	−	1.00936i
$328$			12.4568i			0.687811i
$329$	6.12217	+	10.6039i	0.337526	+	0.584612i
$330$	−3.73462	+	6.46855i	−0.205584	+	0.356082i
$331$	−7.02727	−	4.05720i	−0.386254	−	0.223004i	0.294282	−	0.955719i	$-0.404920\pi$
$331$	−7.02727	−	4.05720i	−0.386254	−	0.223004i	−0.680536	+	0.732715i	$0.738253\pi$
$332$	−18.3041			−1.00457
$333$	4.30531	+	7.45702i	0.235930	+	0.408642i
$334$	5.02964	+	8.71160i	0.275210	+	0.476677i
$335$	11.9140	−	20.6357i	0.650933	−	1.12745i
$336$	17.0821	−	9.86235i	0.931905	−	0.538035i
$337$	−2.20795	−	3.82428i	−0.120275	−	0.208322i	0.799601	−	0.600531i	$-0.205044\pi$
$337$	−2.20795	−	3.82428i	−0.120275	−	0.208322i	−0.919876	+	0.392210i	$0.871711\pi$
$338$		−	27.7769i		−	1.51087i
$339$		−	30.0829i		−	1.63388i
$340$	8.00800	+	13.8703i	0.434295	+	0.752220i
$341$			1.27609i			0.0691044i
$342$	−24.5002	+	14.1452i	−1.32482	+	0.764886i
$343$			9.78406i			0.528290i
$344$	−4.99061	+	8.64400i	−0.269076	+	0.466053i
$345$	−16.4090	+	28.4213i	−0.883432	+	1.53015i
$346$	−4.60445	+	7.97513i	−0.247537	+	0.428746i
$347$	−1.18322	+	0.683131i	−0.0635185	+	0.0366724i	−0.531423	−	0.847107i	$-0.678342\pi$
$347$	−1.18322	+	0.683131i	−0.0635185	+	0.0366724i	0.467904	+	0.883779i	$0.345009\pi$
$348$	34.5127			1.85008
$349$	18.6790	+	0.308348i	0.999864	+	0.0165055i
$349$	18.6790	+	0.308348i	0.999864	+	0.0165055i
$350$	16.0498			0.857899
$351$	0.113317	−	0.0654237i	0.00604842	−	0.00349206i
$352$	2.13852	−	3.70402i	0.113983	−	0.197425i
$353$	8.51907	−	14.7555i	0.453424	−	0.785354i	−0.545172	−	0.838324i	$-0.683536\pi$
$353$	8.51907	−	14.7555i	0.453424	−	0.785354i	0.998596	+	0.0529706i	$0.0168690\pi$
$354$	8.17877	−	14.1660i	0.434697	−	0.752917i
$355$			42.1871i			2.23906i
$356$	−31.9297	+	18.4346i	−1.69227	+	0.977034i
$357$			18.1836i			0.962381i
$358$	−0.783222	−	1.35658i	−0.0413946	−	0.0716975i
$359$		−	13.6052i		−	0.718055i	−0.933327	−	0.359027i	$-0.883108\pi$
$359$		−	13.6052i		−	0.718055i	0.933327	−	0.359027i	$-0.116892\pi$
$360$		−	8.84067i		−	0.465944i
$361$	−3.06581	−	5.31014i	−0.161358	−	0.279481i
$362$	39.8658	−	23.0165i	2.09530	−	1.20972i
$363$	12.7042	−	22.0043i	0.666797	−	1.15493i
$364$	−0.650722	−	1.12708i	−0.0341071	−	0.0590752i
$365$	19.3161	+	33.4565i	1.01105	+	1.75119i
$366$	40.8111			2.13323
$367$	−17.1081	−	9.87738i	−0.893037	−	0.515595i	−0.0181021	−	0.999836i	$-0.505762\pi$
$367$	−17.1081	−	9.87738i	−0.893037	−	0.515595i	−0.874935	+	0.484241i	$0.839096\pi$
$368$	6.41120	−	11.1045i	0.334207	−	0.578863i
$369$	−13.1900	−	22.8458i	−0.686647	−	1.18931i
$370$		−	18.8296i		−	0.978902i
$371$	−12.6878	−	21.9759i	−0.658716	−	1.14093i
$372$	−7.16638	−	12.4125i	−0.371559	−	0.643560i
$373$	−20.1239	−	11.6185i	−1.04198	−	0.601585i	−0.121584	−	0.992581i	$-0.538797\pi$
$373$	−20.1239	−	11.6185i	−1.04198	−	0.601585i	−0.920392	+	0.390996i	$0.872131\pi$
$374$	1.34516	+	2.32988i	0.0695565	+	0.120475i
$375$	8.77700	−	15.2022i	0.453243	−	0.785039i
$376$	−4.58408			−0.236406
$377$			0.853658i			0.0439656i
$378$	−3.07168	+	5.32031i	−0.157990	+	0.273647i
$379$	0.807071	+	0.465963i	0.0414564	+	0.0239349i	0.520585	−	0.853810i	$-0.325714\pi$
$379$	0.807071	+	0.465963i	0.0414564	+	0.0239349i	−0.479129	+	0.877745i	$0.659047\pi$
$380$	34.8593			1.78824
$381$	32.0976	+	18.5316i	1.64441	+	0.949401i
$382$	2.04025	+	1.17794i	0.104388	+	0.0602687i
$383$	−12.8462	+	7.41678i	−0.656412	+	0.378980i	−0.790908	−	0.611934i	$-0.790392\pi$
$383$	−12.8462	+	7.41678i	−0.656412	+	0.378980i	0.134497	+	0.990914i	$0.457058\pi$
$384$			22.6453i			1.15561i
$385$	4.88761			0.249096
$386$	−16.7785			−0.854004
$387$		−	21.1375i		−	1.07448i
$388$		−	6.09424i		−	0.309388i
$389$	10.4362	+	6.02533i	0.529135	+	0.305496i	0.740664	−	0.671875i	$-0.234511\pi$
$389$	10.4362	+	6.02533i	0.529135	+	0.305496i	−0.211529	+	0.977372i	$0.567844\pi$
$390$	2.07505			0.105074
$391$	5.91030	+	10.2369i	0.298897	+	0.517704i
$392$	4.37482	+	2.52580i	0.220962	+	0.127572i
$393$	33.0333	+	19.0718i	1.66631	+	0.962046i
$394$	−40.7761			−2.05427
$395$	−1.65359	−	0.954699i	−0.0832010	−	0.0480361i
$396$		−	3.71416i		−	0.186644i
$397$	33.0092			1.65669			0.828343	−	0.560222i	$-0.189284\pi$
$397$	33.0092			1.65669			0.828343	+	0.560222i	$0.189284\pi$
$398$	19.4844	−	33.7479i	0.976663	−	1.69163i
$399$	34.2749	+	19.7886i	1.71589	+	0.990670i
$400$	2.81691	−	4.87903i	0.140846	−	0.243952i
$401$			23.7136i			1.18420i	0.805865	+	0.592099i	$0.201701\pi$
$401$			23.7136i			1.18420i	−0.805865	+	0.592099i	$0.798299\pi$
$402$			44.9558i			2.24219i
$403$	0.307019	−	0.177258i	0.0152937	−	0.00882983i
$404$	44.5118	+	25.6989i	2.21454	+	1.27857i
$405$	−13.4115	−	23.2295i	−0.666425	−	1.15428i
$406$	−20.0399	−	34.7101i	−0.994564	−	1.72263i
$407$		−	1.78223i		−	0.0883417i
$408$	−5.89561	−	3.40383i	−0.291876	−	0.168515i
$409$	−15.5294			−0.767881			−0.383941	−	0.923358i	$-0.625433\pi$
$409$	−15.5294			−0.767881			−0.383941	+	0.923358i	$0.625433\pi$
$410$			57.6875i			2.84898i
$411$	9.27625	−	5.35564i	0.457564	−	0.264174i
$412$	−2.96795	−	1.71355i	−0.146221	−	0.0844205i
$413$	−10.7038			−0.526699
$414$		−	28.9617i		−	1.42339i
$415$	−19.0973			−0.937450
$416$	−1.18821			−0.0582570
$417$	−4.07213	+	7.05314i	−0.199413	+	0.345394i
$418$	5.85555			0.286404
$419$	18.6327	+	32.2728i	0.910267	+	1.57663i	0.813687	+	0.581304i	$0.197457\pi$
$419$	18.6327	+	32.2728i	0.910267	+	1.57663i	0.0965806	+	0.995325i	$0.469209\pi$
$420$	−47.5417	+	27.4482i	−2.31980	+	1.33933i
$421$	5.92803	−	3.42255i	0.288914	−	0.166805i	−0.348538	−	0.937295i	$-0.613322\pi$
$421$	5.92803	−	3.42255i	0.288914	−	0.166805i	0.637452	+	0.770490i	$0.279988\pi$
$422$	11.9219	−	20.6493i	0.580349	−	1.00519i
$423$	8.40724	−	4.85392i	0.408774	−	0.236006i
$424$	9.50019			0.461370
$425$	2.59683	+	4.49784i	0.125965	+	0.218177i
$426$	−39.7967	−	68.9299i	−1.92816	−	3.33966i
$427$	−13.3527	−	23.1275i	−0.646182	−	1.11922i
$428$			11.6343i			0.562363i
$429$	0.196405			0.00948250
$430$	−23.1116	+	40.0305i	−1.11454	+	1.93044i
$431$	−13.9570	+	8.05807i	−0.672285	+	0.388144i	−0.796942	−	0.604056i	$-0.793550\pi$
$431$	−13.9570	+	8.05807i	−0.672285	+	0.388144i	0.124657	+	0.992200i	$0.460217\pi$
$432$	1.07823	+	1.86754i	0.0518762	+	0.0898522i
$433$	−11.3754	−	6.56757i	−0.546665	−	0.315617i	0.201111	−	0.979568i	$-0.435545\pi$
$433$	−11.3754	−	6.56757i	−0.546665	−	0.315617i	−0.747776	+	0.663951i	$0.768878\pi$
$434$	−8.32236	+	14.4147i	−0.399486	+	0.691930i
$435$	36.0083			1.72646
$436$	−11.4591	−	19.8477i	−0.548791	−	0.950534i
$437$	25.7279			1.23073
$438$	−63.1214	−	36.4432i	−3.01606	−	1.74132i
$439$	−28.7553	+	16.6019i	−1.37242	+	0.792364i	−0.991232	−	0.132135i	$-0.957817\pi$
$439$	−28.7553	+	16.6019i	−1.37242	+	0.792364i	−0.381184	+	0.924499i	$0.624483\pi$
$440$	−0.914921	+	1.58469i	−0.0436171	+	0.0755471i
$441$	−10.6979			−0.509426
$442$	0.373702	−	0.647271i	0.0177752	−	0.0307876i
$443$	2.61699	+	4.53275i	0.124337	+	0.215358i	0.921474	−	0.388441i	$-0.126986\pi$
$443$	2.61699	+	4.53275i	0.124337	+	0.215358i	−0.797137	+	0.603799i	$0.793653\pi$
$444$	10.0088	+	17.3357i	0.474995	+	0.822715i
$445$	−33.3134	+	19.2335i	−1.57921	+	0.911755i
$446$	8.77221	−	5.06464i	0.415376	−	0.239818i
$447$		−	40.2835i		−	1.90534i
$448$	33.9231	−	19.5855i	1.60272	−	0.925328i
$449$	−6.81397			−0.321571			−0.160786	−	0.986989i	$-0.551403\pi$
$449$	−6.81397			−0.321571			−0.160786	+	0.986989i	$0.551403\pi$
$450$		−	12.7250i		−	0.599862i
$451$			5.46015i			0.257109i
$452$		−	32.7122i		−	1.53865i
$453$	−15.5334	−	26.9046i	−0.729822	−	1.26409i
$454$	−35.4520	−	20.4682i	−1.66384	−	0.960621i
$455$	−0.678920	−	1.17592i	−0.0318283	−	0.0551282i
$456$	−12.8320	+	7.40854i	−0.600912	+	0.346937i
$457$	12.8648	−	22.2825i	0.601791	−	1.04233i	−0.390759	−	0.920493i	$-0.627787\pi$
$457$	12.8648	−	22.2825i	0.601791	−	1.04233i	0.992550	−	0.121840i	$-0.0388794\pi$
$458$	−13.9682	+	24.1936i	−0.652691	+	1.13049i
$459$	−1.98797			−0.0927906
$460$	−17.8432	+	30.9053i	−0.831942	+	1.44097i
$461$	21.7770	+	12.5729i	1.01425	+	0.585580i	0.912435	−	0.409223i	$-0.134200\pi$
$461$	21.7770	+	12.5729i	1.01425	+	0.585580i	0.101820	+	0.994803i	$0.467533\pi$
$462$	−7.98590	+	4.61066i	−0.371538	+	0.214507i
$463$	6.54872	+	3.78090i	0.304345	+	0.175714i	0.644393	−	0.764694i	$-0.277110\pi$
$463$	6.54872	+	3.78090i	0.304345	+	0.175714i	−0.340048	+	0.940408i	$0.610443\pi$
$464$	−14.0689			−0.653130
$465$	−7.47693	−	12.9504i	−0.346734	−	0.600561i
$466$	−18.4447	−	10.6491i	−0.854436	−	0.493309i
$467$	0.873460			0.0404189			0.0202095	−	0.999796i	$-0.493567\pi$
$467$	0.873460			0.0404189			0.0202095	+	0.999796i	$0.493567\pi$
$468$	−0.893601	+	0.515921i	−0.0413067	+	0.0238484i
$469$	25.4763	−	14.7087i	1.17639	−	0.679186i
$470$	−21.2289			−0.979218
$471$	−28.3317	−	49.0720i	−1.30546	−	2.26112i
$472$	2.00366	−	3.47045i	0.0922261	−	0.159740i
$473$	−2.18752	+	3.78890i	−0.100582	+	0.174214i
$474$	3.60241			0.165464
$475$	11.3042			0.518670
$476$			19.7729i			0.906290i
$477$	−17.4234	+	10.0594i	−0.797764	+	0.460589i
$478$	24.9335	−	14.3954i	1.14043	−	0.658430i
$479$	−15.7140	−	27.2174i	−0.717990	−	1.24359i	−0.961795	−	0.273770i	$-0.911729\pi$
$479$	−15.7140	−	27.2174i	−0.717990	−	1.24359i	0.243806	−	0.969824i	$-0.421604\pi$
$480$			50.1202i			2.28767i
$481$	−0.428791	+	0.247563i	−0.0195512	+	0.0112879i
$482$			43.1352i			1.96475i
$483$	−35.0881	+	20.2581i	−1.59656	+	0.921777i
$484$	13.8145	−	23.9275i	0.627933	−	1.08761i
$485$		−	6.35832i		−	0.288717i
$486$	39.0266	+	22.5320i	1.77028	+	1.02207i
$487$	2.09840	−	1.21151i	0.0950876	−	0.0548988i	−0.451702	−	0.892169i	$-0.649183\pi$
$487$	2.09840	−	1.21151i	0.0950876	−	0.0548988i	0.546790	+	0.837270i	$0.315850\pi$
$488$	9.99805			0.452591
$489$	24.3704	+	14.0703i	1.10207	+	0.636280i
$490$	20.2598	+	11.6970i	0.915247	+	0.528418i
$491$	−9.13356	+	15.8198i	−0.412192	+	0.713937i	−0.995129	−	0.0985799i	$-0.968570\pi$
$491$	−9.13356	+	15.8198i	−0.412192	+	0.713937i	0.582937	+	0.812517i	$0.301903\pi$
$492$	−30.6635	−	53.1108i	−1.38242	−	2.39442i
$493$	6.48484	−	11.2321i	0.292062	−	0.505867i
$494$	−0.813374	−	1.40881i	−0.0365954	−	0.0633851i
$495$		−	3.87511i		−	0.174173i
$496$	2.92132	+	5.05988i	0.131171	+	0.227195i
$497$	−26.0415	+	45.1053i	−1.16812	+	2.02325i
$498$	31.2032	−	18.0152i	1.39825	−	0.807280i
$499$	−23.5856	+	13.6171i	−1.05583	+	0.609586i	−0.924277	−	0.381722i	$-0.875331\pi$
$499$	−23.5856	+	13.6171i	−1.05583	+	0.609586i	−0.131557	+	0.991309i	$0.541998\pi$
$500$	9.54412	−	16.5309i	0.426826	−	0.739284i
$501$	−9.66253	−	5.57867i	−0.431690	−	0.249236i
$502$	−16.5419	−	28.6514i	−0.738301	−	1.27877i
$503$	1.15067	+	0.664340i	0.0513059	+	0.0296215i	0.525434	−	0.850835i	$-0.323903\pi$
$503$	1.15067	+	0.664340i	0.0513059	+	0.0296215i	−0.474128	+	0.880456i	$0.657236\pi$
$504$	5.45722	−	9.45219i	0.243084	−	0.421034i
$505$	46.4407	+	26.8125i	2.06658	+	1.19314i
$506$	−2.99724	+	5.19137i	−0.133244	+	0.230785i
$507$	15.4045	+	26.6814i	0.684138	+	1.18496i
$508$	34.9030	+	20.1512i	1.54857	+	0.894067i
$509$	27.5488	−	15.9053i	1.22108	−	0.704991i	0.255932	−	0.966695i	$-0.417618\pi$
$509$	27.5488	−	15.9053i	1.22108	−	0.704991i	0.965148	+	0.261703i	$0.0842843\pi$
$510$	−27.3026	−	15.7632i	−1.20898	−	0.698005i
$511$			47.6943i			2.10987i
$512$		−	25.8035i		−	1.14036i
$513$	−2.16344	+	3.74719i	−0.0955182	+	0.165442i
$514$	36.1991	−	20.8996i	1.59667	−	0.921840i
$515$	−3.09657	−	1.78780i	−0.136451	−	0.0787801i
$516$		−	49.1394i		−	2.16324i
$517$	−2.00933			−0.0883702
$518$	11.6232	−	20.1320i	0.510695	−	0.884550i
$519$		−	10.2141i		−	0.448350i
$520$	0.508353			0.0222928
$521$	−11.2082	+	6.47108i	−0.491042	+	0.283503i	−0.725007	−	0.688742i	$-0.758163\pi$
$521$	−11.2082	+	6.47108i	−0.491042	+	0.283503i	0.233965	+	0.972245i	$0.424830\pi$
$522$	−27.5197	+	15.8885i	−1.20450	+	0.695421i
$523$	−15.8896	−	9.17388i	−0.694805	−	0.401146i	0.110605	−	0.993864i	$-0.464721\pi$
$523$	−15.8896	−	9.17388i	−0.694805	−	0.401146i	−0.805410	+	0.592719i	$0.798055\pi$
$524$	35.9205	+	20.7387i	1.56919	+	0.905974i
$525$	−15.4168	+	8.90089i	−0.672844	+	0.388467i
$526$	−27.5792	+	15.9229i	−1.20251	+	0.694269i
$527$	−5.38617			−0.234625
$528$			3.23688i			0.140867i
$529$	−1.66915	+	2.89106i	−0.0725719	+	0.125698i
$530$	43.9955			1.91104
$531$			8.48644i			0.368280i
$532$	37.2705	+	21.5182i	1.61588	+	0.932930i
$533$	1.31367	−	0.758450i	0.0569016	−	0.0328521i
$534$	36.2873	−	62.8515i	1.57031	−	2.71985i
$535$			12.1384i			0.524790i
$536$			11.0134i			0.475707i
$537$	1.50466	+	0.868717i	0.0649310	+	0.0374879i
$538$	10.0479	−	5.80117i	0.433197	−	0.250106i
$539$	1.91760	+	1.10713i	0.0825971	+	0.0476874i
$540$	−3.00084	−	5.19761i	−0.129136	−	0.223669i
$541$	8.86271	−	15.3507i	0.381038	−	0.659977i	−0.610173	−	0.792268i	$-0.708900\pi$
$541$	8.86271	−	15.3507i	0.381038	−	0.659977i	0.991211	+	0.132291i	$0.0422335\pi$
$542$	52.5667	+	30.3494i	2.25793	+	1.30362i
$543$	−25.5290	+	44.2175i	−1.09555	+	1.89755i
$544$	15.6340	+	9.02630i	0.670303	+	0.387000i
$545$	−11.9557	−	20.7078i	−0.512124	−	0.887026i
$546$	2.21859	+	1.28090i	0.0949467	+	0.0548175i
$547$	−16.8807	+	29.2383i	−0.721768	+	1.25014i	0.238523	+	0.971137i	$0.423337\pi$
$547$	−16.8807	+	29.2383i	−0.721768	+	1.25014i	−0.960291	+	0.279002i	$0.909996\pi$
$548$	10.0870	−	5.82373i	0.430895	−	0.248777i
$549$	−18.3365	+	10.5866i	−0.782583	+	0.451825i
$550$	−1.31691	+	2.28095i	−0.0561532	+	0.0972602i
$551$	−14.1144	−	24.4469i	−0.601296	−	1.04147i
$552$		−	15.1686i		−	0.645620i
$553$	−1.17865	−	2.04147i	−0.0501211	−	0.0868123i
$554$	20.4495	−	35.4195i	0.868814	−	1.50483i
$555$	10.4425	+	18.0869i	0.443258	+	0.767746i
$556$	−4.42804	+	7.66959i	−0.187791	+	0.325263i
$557$	−10.7250	−	6.19206i	−0.454432	−	0.262366i	0.255268	−	0.966870i	$-0.417836\pi$
$557$	−10.7250	−	6.19206i	−0.454432	−	0.262366i	−0.709700	+	0.704504i	$0.751169\pi$
$558$	11.4286	+	6.59833i	0.483813	+	0.279329i
$559$	1.21544			0.0514078
$560$	19.3800	−	11.1891i	0.818955	−	0.472824i
$561$	−2.58421	−	1.49199i	−0.109105	−	0.0629920i
$562$			48.8205i			2.05937i
$563$	−8.98229	+	15.5578i	−0.378558	+	0.655682i	−0.990853	−	0.134948i	$-0.956913\pi$
$563$	−8.98229	+	15.5578i	−0.378558	+	0.655682i	0.612295	+	0.790630i	$0.290247\pi$
$564$	19.5447	−	11.2841i	0.822980	−	0.475148i
$565$		−	34.1298i		−	1.43585i
$566$	13.6900	−	7.90390i	0.575432	−	0.332226i
$567$		−	33.1150i		−	1.39070i
$568$	−9.74953	−	16.8867i	−0.409081	−	0.708550i
$569$	−31.5138	+	18.1945i	−1.32113	+	0.762754i	−0.983909	−	0.178672i	$-0.942820\pi$
$569$	−31.5138	+	18.1945i	−1.32113	+	0.762754i	−0.337220	+	0.941426i	$0.609487\pi$
$570$	−59.4250	+	34.3090i	−2.48904	+	1.43705i
$571$			14.0268i			0.587003i	0.955959	+	0.293502i	$0.0948206\pi$
$571$			14.0268i			0.587003i	−0.955959	+	0.293502i	$0.905179\pi$
$572$	0.213570			0.00892983
$573$	−2.61304			−0.109161
$574$	−35.6097	+	61.6778i	−1.48632	+	2.57438i
$575$	−5.78618	+	10.0220i	−0.241300	+	0.417945i
$576$	−15.5282	−	26.8957i	−0.647010	−	1.12065i
$577$	−24.5499			−1.02203			−0.511013	−	0.859573i	$-0.670730\pi$
$577$	−24.5499			−1.02203			−0.511013	+	0.859573i	$0.670730\pi$
$578$	21.6789	−	12.5163i	0.901724	−	0.520611i
$579$	16.1167	−	9.30501i	0.669789	−	0.386703i
$580$	39.1554			1.62584
$581$	−20.4183	−	11.7885i	−0.847093	−	0.489070i
$582$	5.99804	+	10.3889i	0.248627	+	0.430634i
$583$	4.16420			0.172463
$584$	−15.4637	−	8.92798i	−0.639893	−	0.369442i
$585$	−0.932324	+	0.538278i	−0.0385469	+	0.0222550i
$586$	−53.8167	−	31.0711i	−2.22315	−	1.28353i
$587$	20.9862	−	36.3491i	0.866192	−	1.50029i	0.000333499	−	1.00000i	$-0.499894\pi$
$587$	20.9862	−	36.3491i	0.866192	−	1.50029i	0.865859	−	0.500289i	$-0.166773\pi$
$588$	−24.8700			−1.02562
$589$	−5.86158	+	10.1526i	−0.241522	+	0.418329i
$590$	9.27899	−	16.0717i	0.382010	−	0.661661i
$591$	39.1679	−	22.6136i	1.61115	−	0.930198i
$592$	−4.08000	−	7.06676i	−0.167687	−	0.290442i
$593$	−24.1573	−	13.9472i	−0.992021	−	0.572744i	−0.0861435	−	0.996283i	$-0.527454\pi$
$593$	−24.1573	−	13.9472i	−0.992021	−	0.572744i	−0.905878	+	0.423539i	$0.860788\pi$
$594$	−0.504072	−	0.873078i	−0.0206823	−	0.0358228i
$595$			20.6297i			0.845737i
$596$		−	43.8043i		−	1.79429i
$597$			43.2225i			1.76898i
$598$	1.66534			0.0681010
$599$	−16.1054	+	9.29847i	−0.658050	+	0.379925i	−0.791533	−	0.611126i	$-0.790717\pi$
$599$	−16.1054	+	9.29847i	−0.658050	+	0.379925i	0.133484	+	0.991051i	$0.457384\pi$
$600$		−	6.66470i		−	0.272085i
$601$	6.42472	−	3.70931i	0.262070	−	0.151306i	−0.363209	−	0.931708i	$-0.618319\pi$
$601$	6.42472	−	3.70931i	0.262070	−	0.151306i	0.625278	+	0.780402i	$0.284985\pi$
$602$	−49.4205	+	28.5329i	−2.01423	+	1.16292i
$603$	−11.6617	−	20.1987i	−0.474902	−	0.822555i
$604$	−16.8910	−	29.2561i	−0.687286	−	1.19041i
$605$	14.4132	−	24.9644i	0.585979	−	1.01495i
$606$	−101.173			−4.10987
$607$	7.81867	−	13.5423i	0.317350	−	0.549666i	−0.662584	−	0.748987i	$-0.730540\pi$
$607$	7.81867	−	13.5423i	0.317350	−	0.549666i	0.979934	+	0.199321i	$0.0638737\pi$
$608$	34.0279	−	19.6460i	1.38001	−	0.796751i
$609$	38.4990	+	22.2274i	1.56006	+	0.900700i
$610$	46.3011			1.87468
$611$	0.279109	+	0.483430i	0.0112915	+	0.0195575i
$612$	15.6768			0.633698
$613$	−14.9829	+	25.9512i	−0.605154	+	1.04816i	0.386873	+	0.922133i	$0.373555\pi$
$613$	−14.9829	+	25.9512i	−0.605154	+	1.04816i	−0.992027	+	0.126025i	$0.959778\pi$
$614$	38.8056	+	22.4044i	1.56606	+	0.904168i
$615$	−31.9923	−	55.4123i	−1.29005	−	2.23444i
$616$	−1.95641	+	1.12954i	−0.0788262	+	0.0455103i
$617$	−1.30545	+	2.26111i	−0.0525555	+	0.0910288i	−0.891106	−	0.453795i	$-0.850070\pi$
$617$	−1.30545	+	2.26111i	−0.0525555	+	0.0910288i	0.838551	+	0.544823i	$0.183403\pi$
$618$	6.74600			0.271364
$619$			3.08230i			0.123888i	0.998080	+	0.0619440i	$0.0197300\pi$
$619$			3.08230i			0.123888i	−0.998080	+	0.0619440i	$0.980270\pi$
$620$	−8.13041	−	14.0823i	−0.326525	−	0.565558i
$621$	−2.21477	−	3.83609i	−0.0888756	−	0.153937i
$622$	17.7113	+	30.6769i	0.710159	+	1.23003i
$623$	−47.4903			−1.90266
$624$	0.778770	−	0.449623i	0.0311758	−	0.0179993i
$625$	15.5950	−	27.0113i	0.623799	−	1.08045i
$626$	5.56699	−	3.21410i	0.222502	−	0.128461i
$627$	−5.62460	+	3.24737i	−0.224625	+	0.129687i
$628$	−30.8079	−	53.3609i	−1.22937	−	2.12933i
$629$	7.52247			0.299940
$630$	25.2725	−	43.7732i	1.00688	−	1.74397i
$631$	11.6553			0.463991			0.231995	−	0.972717i	$-0.425475\pi$
$631$	11.6553			0.463991			0.231995	+	0.972717i	$0.425475\pi$
$632$	0.882531			0.0351052
$633$			26.4465i			1.05116i
$634$	37.7755			1.50026
$635$	36.4155	+	21.0245i	1.44510	+	0.834331i
$636$	−40.5050	+	23.3856i	−1.60613	+	0.927299i
$637$		−	0.615150i		−	0.0243731i
$638$	6.57720			0.260394
$639$	35.7614	+	20.6469i	1.41470	+	0.816778i
$640$			25.6916i			1.01555i
$641$	−5.25790	−	9.10696i	−0.207675	−	0.359703i	0.743307	−	0.668951i	$-0.233256\pi$
$641$	−5.25790	−	9.10696i	−0.207675	−	0.359703i	−0.950982	+	0.309247i	$0.899923\pi$
$642$	−11.4506	−	19.8330i	−0.451920	−	0.782748i
$643$	−28.5085	−	16.4594i	−1.12427	−	0.649095i	−0.181779	−	0.983339i	$-0.558186\pi$
$643$	−28.5085	−	16.4594i	−1.12427	−	0.649095i	−0.942486	+	0.334245i	$0.891519\pi$
$644$	−38.1548	+	22.0287i	−1.50351	+	0.868052i
$645$		−	51.2688i		−	2.01871i
$646$			24.7153i			0.972409i
$647$	−13.9890	+	24.2297i	−0.549965	+	0.952568i	0.448311	+	0.893878i	$0.352026\pi$
$647$	−13.9890	+	24.2297i	−0.549965	+	0.952568i	−0.998276	+	0.0586902i	$0.981308\pi$
$648$	10.7368	+	6.19887i	0.421779	+	0.243515i
$649$	0.878261	−	1.52119i	0.0344748	−	0.0597120i
$650$	0.731709			0.0287000
$651$		−	18.4616i		−	0.723568i
$652$	26.5004	+	15.3000i	1.03784	+	0.599195i
$653$	−13.4927			−0.528009			−0.264005	−	0.964521i	$-0.585043\pi$
$653$	−13.4927			−0.528009			−0.264005	+	0.964521i	$0.585043\pi$
$654$	39.0689	+	22.5564i	1.52771	+	0.882026i
$655$	37.4771	+	21.6374i	1.46435	+	0.845443i
$656$	12.4998	+	21.6502i	0.488034	+	0.845299i
$657$	37.8141			1.47527
$658$	−22.6974	−	13.1043i	−0.884835	−	0.510860i
$659$			8.01200i			0.312103i	0.987749	+	0.156052i	$0.0498766\pi$
$659$			8.01200i			0.312103i	−0.987749	+	0.156052i	$0.950123\pi$
$660$		−	9.00864i		−	0.350661i
$661$	26.2209			1.01987			0.509936	−	0.860212i	$-0.329669\pi$
$661$	26.2209			1.01987			0.509936	+	0.860212i	$0.329669\pi$
$662$	17.3686			0.675051
$663$			0.828990i			0.0321953i
$664$	7.64428	−	4.41342i	0.296655	−	0.171274i
$665$	38.8856	+	22.4506i	1.50792	+	0.870598i
$666$	−15.9615	−	9.21540i	−0.618497	−	0.357090i
$667$	28.8986			1.11896
$668$	−10.5070	−	6.06624i	−0.406530	−	0.234710i
$669$	−5.61749	+	9.72977i	−0.217185	+	0.376175i
$670$			51.0033i			1.97043i
$671$	4.38242			0.169182
$672$	−30.9385	+	53.5871i	−1.19348	+	2.06717i
$673$	11.7245	+	20.3074i	0.451947	+	0.782795i	0.998507	−	0.0546252i	$-0.0173964\pi$
$673$	11.7245	+	20.3074i	0.451947	+	0.782795i	−0.546560	+	0.837420i	$0.684063\pi$
$674$	8.18576	+	4.72605i	0.315304	+	0.182041i
$675$	−0.973112	−	1.68548i	−0.0374551	−	0.0648741i
$676$	16.7509	+	29.0134i	0.644264	+	1.11590i
$677$		−	32.5105i		−	1.24948i	−0.780832	−	0.624741i	$-0.785205\pi$
$677$		−	32.5105i		−	1.24948i	0.780832	−	0.624741i	$-0.214795\pi$
$678$	32.1959	+	55.7649i	1.23647	+	2.14164i
$679$	3.92491	−	6.79814i	0.150624	−	0.260889i
$680$	−6.68870	−	3.86172i	−0.256500	−	0.148090i
$681$	45.4050			1.73992
$682$	−1.36572	−	2.36550i	−0.0522962	−	0.0905796i
$683$	−11.9471	−	20.6930i	−0.457144	−	0.791797i	0.541664	−	0.840595i	$-0.317794\pi$
$683$	−11.9471	−	20.6930i	−0.457144	−	0.791797i	−0.998809	+	0.0487975i	$0.984461\pi$
$684$	17.0605	−	29.5497i	0.652326	−	1.12986i
$685$	10.5241	−	6.07610i	0.402105	−	0.232156i
$686$	−10.4713	−	18.1367i	−0.399794	−	0.692464i
$687$		−	30.9859i		−	1.18218i
$688$			20.0313i			0.763687i
$689$	−0.578434	−	1.00188i	−0.0220366	−	0.0381684i
$690$		−	70.2461i		−	2.67422i
$691$	3.87792	−	2.23892i	0.147523	−	0.0851726i	−0.424421	−	0.905465i	$-0.639523\pi$
$691$	3.87792	−	2.23892i	0.147523	−	0.0851726i	0.571945	+	0.820292i	$0.306189\pi$
$692$		−	11.1068i		−	0.422218i
$693$	2.39205	−	4.14315i	0.0908665	−	0.157385i
$694$	1.46222	−	2.53264i	0.0555052	−	0.0961379i
$695$	−4.61992	+	8.00194i	−0.175244	+	0.303531i
$696$	−14.4134	+	8.32158i	−0.546339	+	0.315429i
$697$	−23.0464			−0.872943
$698$	−34.9553	+	19.4193i	−1.32308	+	0.735033i
$699$	23.6230			0.893505
$700$	−16.7642	+	9.67883i	−0.633628	+	0.365825i
$701$	18.0656	−	31.2906i	0.682329	−	1.18183i	−0.291940	−	0.956437i	$-0.594301\pi$
$701$	18.0656	−	31.2906i	0.682329	−	1.18183i	0.974268	−	0.225391i	$-0.0723661\pi$
$702$	−0.140038	+	0.242552i	−0.00528538	+	0.00915455i
$703$	8.18644	−	14.1793i	0.308757	−	0.534783i
$704$			6.42807i			0.242267i
$705$	20.3916	−	11.7731i	0.767994	−	0.443401i
$706$			36.4696i			1.37255i
$707$	33.1020	+	57.3344i	1.24493	+	2.15628i
$708$			19.7288i			0.741454i
$709$		−	28.9871i		−	1.08863i	−0.838879	−	0.544317i	$-0.816789\pi$
$709$		−	28.9871i		−	1.08863i	0.838879	−	0.544317i	$-0.183211\pi$
$710$	−45.1502	−	78.2024i	−1.69446	−	2.93489i
$711$	−1.61857	+	0.934481i	−0.0607011	+	0.0350458i
$712$	8.88980	−	15.3976i	0.333159	−	0.577049i
$713$	−6.00065	−	10.3934i	−0.224726	−	0.389237i
$714$	−19.4608	−	33.7071i	−0.728302	−	1.26146i
$715$	0.222825			0.00833319
$716$	1.63617	+	0.944644i	0.0611466	+	0.0353030i
$717$	−15.9668	+	27.6552i	−0.596289	+	1.03280i
$718$	14.5608	+	25.2200i	0.543403	+	0.941202i
$719$			10.8238i			0.403659i	0.979421	+	0.201830i	$0.0646887\pi$
$719$			10.8238i			0.403659i	−0.979421	+	0.201830i	$0.935311\pi$
$720$	−8.87117	−	15.3653i	−0.330609	−	0.572632i
$721$	−2.20717	−	3.82294i	−0.0821995	−	0.142374i
$722$	11.3662	+	6.56228i	0.423006	+	0.244223i
$723$	−23.9219	−	41.4339i	−0.889663	−	1.54094i
$724$	−27.7602	+	48.0821i	−1.03170	+	1.78696i
$725$	12.6973			0.471566
$726$			54.3859i			2.01845i
$727$	26.1171	−	45.2361i	0.968628	−	1.67771i	0.269093	−	0.963114i	$-0.413276\pi$
$727$	26.1171	−	45.2361i	0.968628	−	1.67771i	0.699535	−	0.714599i	$-0.253391\pi$
$728$	0.543517	+	0.313800i	0.0201441	+	0.0116302i
$729$	−20.1077			−0.744729
$730$	−71.6127	−	41.3456i	−2.65050	−	1.53027i
$731$	−15.9923	−	9.23316i	−0.591496	−	0.341501i
$732$	−42.6277	+	24.6111i	−1.57557	+	0.909653i
$733$			30.0239i			1.10896i	0.832198	+	0.554478i	$0.187082\pi$
$733$			30.0239i			1.10896i	−0.832198	+	0.554478i	$0.812918\pi$
$734$	42.2845			1.56075
$735$	−25.9477			−0.957095
$736$			40.2243i			1.48269i
$737$			4.82749i			0.177823i
$738$	48.9009	+	28.2329i	1.80007	+	1.03927i
$739$	24.5199			0.901979			0.450990	−	0.892529i	$-0.351071\pi$
$739$	24.5199			0.901979			0.450990	+	0.892529i	$0.351071\pi$
$740$	11.3552	+	19.6677i	0.417424	+	0.722999i
$741$	1.56259	+	0.902160i	0.0574031	+	0.0331417i
$742$	47.0387	+	27.1578i	1.72685	+	0.996995i
$743$	−6.60204			−0.242205			−0.121103	−	0.992640i	$-0.538643\pi$
$743$	−6.60204			−0.242205			−0.121103	+	0.992640i	$0.538643\pi$
$744$	5.98573	+	3.45586i	0.219448	+	0.126698i
$745$		−	45.7025i		−	1.67441i
$746$	49.7383			1.82105
$747$	−9.34644	+	16.1885i	−0.341968	+	0.592307i
$748$	−2.81007	−	1.62239i	−0.102746	−	0.0593206i
$749$	−7.49288	+	12.9780i	−0.273784	+	0.474207i
$750$			37.5739i			1.37200i
$751$		−	14.3601i		−	0.524008i	−0.965067	−	0.262004i	$-0.915617\pi$
$751$		−	14.3601i		−	0.524008i	0.965067	−	0.262004i	$-0.0843833\pi$
$752$	−7.96725	+	4.59990i	−0.290536	+	0.167741i
$753$	31.7789	+	18.3476i	1.15809	+	0.668622i
$754$	−0.913616	−	1.58243i	−0.0332719	−	0.0576287i
$755$	−17.6230	−	30.5239i	−0.641366	−	1.11088i
$756$		−	7.40951i		−	0.269481i
$757$	5.78032	+	3.33727i	0.210089	+	0.121295i	0.601353	−	0.798983i	$-0.294629\pi$
$757$	5.78032	+	3.33727i	0.210089	+	0.121295i	−0.391264	+	0.920279i	$0.627962\pi$
$758$	−1.99476			−0.0724529
$759$		−	6.64883i		−	0.241337i
$760$	−14.5581	+	8.40515i	−0.528079	+	0.304887i
$761$	−33.3744	−	19.2687i	−1.20982	−	0.698490i	−0.247100	−	0.968990i	$-0.579477\pi$
$761$	−33.3744	−	19.2687i	−1.20982	−	0.698490i	−0.962720	+	0.270501i	$0.912811\pi$
$762$	−79.3326			−2.87392
$763$		−	29.5203i		−	1.06871i
$764$	−2.84142			−0.102799
$765$	16.3562			0.591358
$766$	15.8754	−	27.4970i	0.573602	−	0.993507i
$767$	−0.487984			−0.0176201
$768$	3.73048	+	6.46137i	0.134612	+	0.233155i
$769$	16.0096	−	9.24312i	0.577319	−	0.333316i	−0.182748	−	0.983160i	$-0.558499\pi$
$769$	16.0096	−	9.24312i	0.577319	−	0.333316i	0.760067	+	0.649844i	$0.225166\pi$
$770$	−9.06018	+	5.23090i	−0.326506	+	0.188508i
$771$	−23.1809	+	40.1505i	−0.834840	+	1.44599i
$772$	17.5254	−	10.1183i	0.630751	−	0.364164i
$773$	26.3100			0.946304			0.473152	−	0.880981i	$-0.343116\pi$
$773$	26.3100			0.946304			0.473152	+	0.880981i	$0.343116\pi$
$774$	22.6222	+	39.1827i	0.813137	+	1.40839i
$775$	−2.63653	−	4.56660i	−0.0947069	−	0.164037i
$776$	1.46942	+	2.54511i	0.0527491	+	0.0913642i
$777$			25.7840i			0.924996i
$778$	−25.7941			−0.924764
$779$	−25.0805	+	43.4408i	−0.898603	+	1.55643i
$780$	−2.16742	+	1.25136i	−0.0776060	+	0.0448058i
$781$	−4.27349	−	7.40190i	−0.152917	−	0.264861i
$782$	−21.9119	−	12.6508i	−0.783567	−	0.452393i
$783$	−2.43007	+	4.20900i	−0.0868435	+	0.150417i
$784$	10.1381			0.362074
$785$	−32.1430	−	55.6732i	−1.14723	−	1.98706i
$786$	−81.6454			−2.91219
$787$	−15.0490	−	8.68856i	−0.536440	−	0.309714i	0.207195	−	0.978300i	$-0.433567\pi$
$787$	−15.0490	−	8.68856i	−0.536440	−	0.309714i	−0.743635	+	0.668586i	$0.766900\pi$
$788$	42.5911	−	24.5900i	1.51725	−	0.875983i
$789$	17.6610	−	30.5897i	0.628747	−	1.08902i
$790$	4.08701			0.145409
$791$	21.0678	−	36.4906i	0.749086	−	1.29746i
$792$	0.895545	+	1.55113i	0.0318218	+	0.0551170i
$793$	−0.608747	−	1.05438i	−0.0216172	−	0.0374421i
$794$	−61.1893	+	35.3277i	−2.17153	+	1.25373i
$795$	−42.2603	+	24.3990i	−1.49882	+	0.865343i
$796$			47.0001i			1.66587i
$797$	−29.6758	+	17.1333i	−1.05117	+	0.606894i	−0.922977	−	0.384855i	$-0.874251\pi$
$797$	−29.6758	+	17.1333i	−1.05117	+	0.606894i	−0.128194	+	0.991749i	$0.540918\pi$
$798$	−84.7140			−2.99884
$799$		−	8.48103i		−	0.300037i
$800$			17.6735i			0.624852i
$801$			37.6524i			1.33038i
$802$	−25.3791	−	43.9579i	−0.896168	−	1.55221i
$803$	−6.77817	−	3.91338i	−0.239197	−	0.138100i
$804$	−27.1105	−	46.9568i	−0.956115	−	1.65604i
$805$	−39.8082	+	22.9833i	−1.40306	+	0.810055i
$806$	−0.379415	+	0.657166i	−0.0133643	+	0.0231477i
$807$	−6.43441	+	11.1447i	−0.226502	+	0.392313i
$808$	−24.7857			−0.871958
$809$	−23.9368	+	41.4598i	−0.841574	+	1.45765i	0.0469894	+	0.998895i	$0.485037\pi$
$809$	−23.9368	+	41.4598i	−0.841574	+	1.45765i	−0.888563	+	0.458754i	$0.848296\pi$
$810$	49.7220	+	28.7070i	1.74705	+	1.00866i
$811$	0.0745088	−	0.0430177i	0.00261636	−	0.00151056i	−0.498691	−	0.866780i	$-0.666186\pi$
$811$	0.0745088	−	0.0430177i	0.00261636	−	0.00151056i	0.501308	+	0.865269i	$0.332853\pi$
$812$	41.8638	+	24.1701i	1.46913	+	0.848204i
$813$	−67.3245			−2.36117
$814$	1.90740	+	3.30372i	0.0668545	+	0.115795i
$815$	27.6488	+	15.9630i	0.968495	+	0.559161i
$816$	−13.6623			−0.478276
$817$	−34.8077	+	20.0962i	−1.21777	+	0.703078i
$818$	28.7870	−	16.6202i	1.00651	−	0.581110i
$819$	−1.32909			−0.0464420
$820$	−34.7884	−	60.2553i	−1.21486	−	2.10421i
$821$	−27.0443	+	46.8422i	−0.943854	+	1.63480i	−0.185823	+	0.982583i	$0.559495\pi$
$821$	−27.0443	+	46.8422i	−0.943854	+	1.63480i	−0.758030	+	0.652219i	$0.773838\pi$
$822$	−11.4636	+	19.8556i	−0.399839	+	0.692542i
$823$	41.2950			1.43945			0.719726	−	0.694258i	$-0.244267\pi$
$823$	41.2950			1.43945			0.719726	+	0.694258i	$0.244267\pi$
$824$	1.65266			0.0575731
$825$		−	2.92132i		−	0.101707i
$826$	19.8417	−	11.4556i	0.690380	−	0.398591i
$827$	−25.8779	+	14.9406i	−0.899864	+	0.519537i	−0.877156	−	0.480205i	$-0.840562\pi$
$827$	−25.8779	+	14.9406i	−0.899864	+	0.519537i	−0.0227079	+	0.999742i	$0.507229\pi$
$828$	17.4653	+	30.2508i	0.606961	+	1.05129i
$829$			50.3440i			1.74852i	0.485460	+	0.874259i	$0.338652\pi$
$829$			50.3440i			1.74852i	−0.485460	+	0.874259i	$0.661348\pi$
$830$	35.4007	−	20.4386i	1.22878	−	0.709435i
$831$			45.3634i			1.57364i
$832$	1.54655	−	0.892900i	0.0536169	−	0.0309557i
$833$	−4.67300	+	8.09387i	−0.161910	+	0.280436i
$834$		−	17.4326i		−	0.603640i
$835$	−10.9624	−	6.32912i	−0.379368	−	0.219028i
$836$	−6.11620	+	3.53119i	−0.211533	+	0.122129i
$837$	2.01836			0.0697648
$838$	−69.0790	−	39.8828i	−2.38629	−	1.37773i
$839$	13.8815	+	8.01450i	0.479243	+	0.276691i	0.720101	−	0.693869i	$-0.244095\pi$
$839$	13.8815	+	8.01450i	0.479243	+	0.276691i	−0.240858	+	0.970560i	$0.577429\pi$
$840$	13.2364	−	22.9262i	0.456700	−	0.791028i
$841$	−1.35394	−	2.34509i	−0.0466876	−	0.0808653i
$842$	−7.32587	+	12.6888i	−0.252466	+	0.437284i
$843$	−27.0748	−	46.8949i	−0.932506	−	1.61515i
$844$			28.7580i			0.989891i
$845$	17.4768	+	30.2706i	0.601219	+	1.04134i
$846$	−10.3897	+	17.9955i	−0.357205	+	0.618697i
$847$	30.8203	−	17.7941i	1.05900	−	0.611413i
$848$	16.5116	−	9.53297i	0.567010	−	0.327363i
$849$	−8.76667	+	15.1843i	−0.300871	+	0.521125i
$850$	−9.62751	−	5.55844i	−0.330221	−	0.190653i
$851$	8.38067	+	14.5157i	0.287286	+	0.497593i
$852$	83.1362	+	47.9987i	2.84820	+	1.64441i
$853$	15.0859	−	26.1296i	0.516533	−	0.894661i	−0.483283	−	0.875464i	$-0.660556\pi$
$853$	15.0859	−	26.1296i	0.516533	−	0.894661i	0.999816	−	0.0191967i	$-0.00611088\pi$
$854$	49.5038	+	28.5810i	1.69399	+	0.978023i
$855$	17.7998	−	30.8302i	0.608741	−	1.05437i
$856$	−2.80521	−	4.85877i	−0.0958802	−	0.166069i
$857$	−39.4640	−	22.7846i	−1.34807	−	0.778306i	−0.360090	−	0.932917i	$-0.617254\pi$
$857$	−39.4640	−	22.7846i	−1.34807	−	0.778306i	−0.987975	+	0.154611i	$0.950587\pi$
$858$	−0.364076	+	0.210199i	−0.0124293	+	0.00717608i
$859$	3.23021	+	1.86496i	0.110213	+	0.0636317i	0.554093	−	0.832454i	$-0.313065\pi$
$859$	3.23021	+	1.86496i	0.110213	+	0.0636317i	−0.443880	+	0.896086i	$0.646398\pi$
$860$		−	55.7497i		−	1.90105i
$861$		−	78.9936i		−	2.69209i
$862$	17.2481	−	29.8745i	0.587472	−	1.01753i
$863$	−20.7093	+	11.9565i	−0.704954	+	0.407006i	−0.809190	−	0.587547i	$-0.800094\pi$
$863$	−20.7093	+	11.9565i	−0.704954	+	0.407006i	0.104236	+	0.994553i	$0.466760\pi$
$864$	−5.85854	−	3.38243i	−0.199312	−	0.115073i
$865$		−	11.5881i		−	0.394008i
$866$	28.1154			0.955400
$867$	−13.8826	+	24.0454i	−0.471477	+	0.816623i
$868$		−	20.0752i		−	0.681396i
$869$	0.386838			0.0131226
$870$	−66.7487	+	38.5374i	−2.26299	+	1.30654i
$871$	1.16146	−	0.670569i	0.0393545	−	0.0227214i
$872$	9.57124	+	5.52596i	0.324123	+	0.187132i
$873$	−5.38986	−	3.11184i	−0.182419	−	0.105320i
$874$	−47.6919	+	27.5349i	−1.61320	+	0.931382i
$875$	21.2930	−	12.2935i	0.719834	−	0.415596i
$876$	87.9081			2.97014
$877$		−	42.8379i		−	1.44653i	−0.690569	−	0.723266i	$-0.742640\pi$
$877$		−	42.8379i		−	1.44653i	0.690569	−	0.723266i	$-0.257360\pi$
$878$	35.5359	−	61.5499i	1.19928	−	2.07721i
$879$	68.9254			2.32480
$880$			3.67231i			0.123794i
$881$	16.5289	+	9.54299i	0.556874	+	0.321512i	0.751890	−	0.659289i	$-0.229142\pi$
$881$	16.5289	+	9.54299i	0.556874	+	0.321512i	−0.195016	+	0.980800i	$0.562476\pi$
$882$	19.8308	−	11.4493i	0.667738	−	0.385519i
$883$	−1.70459	+	2.95244i	−0.0573642	+	0.0993577i	−0.893281	−	0.449498i	$-0.851603\pi$
$883$	−1.70459	+	2.95244i	−0.0573642	+	0.0993577i	0.835917	+	0.548855i	$0.184936\pi$
$884$			0.901444i			0.0303188i
$885$			20.5837i			0.691915i
$886$	−9.70223	−	5.60159i	−0.325953	−	0.188189i
$887$	44.7439	−	25.8329i	1.50235	−	0.867385i	0.502358	−	0.864659i	$-0.332466\pi$
$887$	44.7439	−	25.8329i	1.50235	−	0.867385i	0.999996	−	0.00272547i	$-0.000867546\pi$
$888$	−8.35984	−	4.82655i	−0.280538	−	0.161969i
$889$	25.9562	+	44.9575i	0.870544	+	1.50783i
$890$	41.1688	−	71.3064i	1.37998	−	2.39020i
$891$	4.70621	+	2.71713i	0.157664	+	0.0910274i
$892$	−6.10846	+	10.5802i	−0.204526	+	0.354250i
$893$	−15.9861	−	9.22960i	−0.534956	−	0.308857i
$894$	43.1129	+	74.6737i	1.44191	+	2.49746i
$895$	1.70707	+	0.985579i	0.0570611	+	0.0329443i
$896$	−15.8591	+	27.4687i	−0.529815	+	0.917666i
$897$	−1.59966	+	0.923565i	−0.0534111	+	0.0308369i
$898$	12.6311	−	7.29256i	0.421505	−	0.243356i
$899$	−6.58397	+	11.4038i	−0.219588	+	0.380337i
$900$	7.67380	+	13.2914i	0.255793	+	0.443047i
$901$			17.5763i			0.585553i
$902$	−5.84365	−	10.1215i	−0.194572	−	0.337009i
$903$	31.6475	−	54.8151i	1.05316	−	1.82413i
$904$	7.88746	+	13.6615i	0.262333	+	0.454374i
$905$	−28.9632	+	50.1657i	−0.962769	+	1.66756i
$906$	57.5886	+	33.2488i	1.91325	+	1.10462i
$907$	20.9133	+	12.0743i	0.694414	+	0.400920i	0.805263	−	0.592917i	$-0.202024\pi$
$907$	20.9133	+	12.0743i	0.694414	+	0.400920i	−0.110850	+	0.993837i	$0.535357\pi$
$908$	49.3734			1.63851
$909$	45.4572	−	26.2447i	1.50772	−	0.870482i
$910$	2.51703	+	1.45321i	0.0834389	+	0.0481734i
$911$		−	10.1151i		−	0.335128i	−0.985861	−	0.167564i	$-0.946410\pi$
$911$		−	10.1151i		−	0.335128i	0.985861	−	0.167564i	$-0.0535901\pi$
$912$	−14.8682	+	25.7525i	−0.492335	+	0.852750i
$913$	3.35070	−	1.93453i	0.110892	−	0.0640235i
$914$			55.0736i			1.82167i
$915$	−44.4749	+	25.6776i	−1.47030	+	0.848876i
$916$		−	33.6941i		−	1.11328i
$917$	26.7129	+	46.2681i	0.882139	+	1.52791i
$918$	3.68511	−	2.12760i	0.121627	−	0.0702212i
$919$	0.663283	−	0.382946i	0.0218797	−	0.0126322i	−0.489020	−	0.872272i	$-0.662646\pi$
$919$	0.663283	−	0.382946i	0.0218797	−	0.0126322i	0.510900	+	0.859640i	$0.329312\pi$
$920$		−	17.2091i		−	0.567369i
$921$	−49.7000			−1.63767
$922$	−53.8240			−1.77260
$923$	−1.18723	+	2.05634i	−0.0390782	+	0.0676853i
$924$	5.56091	−	9.63178i	0.182941	−	0.316862i
$925$	3.68225	+	6.37784i	0.121072	+	0.209702i
$926$	−16.1858			−0.531900
$927$	−3.03099	+	1.74994i	−0.0995508	+	0.0574757i
$928$	38.2216	−	22.0672i	1.25468	−	0.724393i
$929$	−34.2812			−1.12473			−0.562365	−	0.826889i	$-0.690109\pi$
$929$	−34.2812			−1.12473			−0.562365	+	0.826889i	$0.690109\pi$
$930$	27.7200	+	16.0042i	0.908975	+	0.524797i
$931$	10.1709	+	17.6166i	0.333339	+	0.577359i
$932$	25.6877			0.841428
$933$	−34.0255	−	19.6446i	−1.11395	−	0.643137i
$934$	−1.61914	+	0.934808i	−0.0529797	+	0.0305879i
$935$	−2.93184	−	1.69270i	−0.0958814	−	0.0553572i
$936$	0.248794	−	0.430924i	0.00813209	−	0.0140852i
$937$	−37.5813			−1.22773			−0.613864	−	0.789412i	$-0.710385\pi$
$937$	−37.5813			−1.22773			−0.613864	+	0.789412i	$0.710385\pi$
$938$	−31.4836	+	54.5313i	−1.02798	+	1.78051i
$939$	−3.56495	+	6.17467i	−0.116338	+	0.201503i
$940$	22.1739	−	12.8021i	0.723232	−	0.417558i
$941$	−14.8815	−	25.7756i	−0.485124	−	0.840260i	0.514730	−	0.857353i	$-0.327892\pi$
$941$	−14.8815	−	25.7756i	−0.485124	−	0.840260i	−0.999854	+	0.0170927i	$0.994559\pi$
$942$	105.037	+	60.6433i	3.42230	+	1.97586i
$943$	−25.6756	−	44.4714i	−0.836112	−	1.44819i
$944$		−	8.04231i		−	0.261755i
$945$		−	7.73059i		−	0.251476i
$946$		−	9.36467i		−	0.304472i
$947$	37.6096			1.22215			0.611073	−	0.791574i	$-0.290738\pi$
$947$	37.6096			1.22215			0.611073	+	0.791574i	$0.290738\pi$
$948$	−3.76276	+	2.17243i	−0.122209	+	0.0705573i
$949$			2.17437i			0.0705832i
$950$	−20.9546	+	12.0981i	−0.679856	+	0.392515i
$951$	−36.2856	+	20.9495i	−1.17664	+	0.679334i
$952$	−4.76757	−	8.25768i	−0.154518	−	0.267633i
$953$	−4.27583	−	7.40595i	−0.138508	−	0.239902i	0.788424	−	0.615132i	$-0.210897\pi$
$953$	−4.27583	−	7.40595i	−0.138508	−	0.239902i	−0.926932	+	0.375230i	$0.877564\pi$
$954$	21.5319	−	37.2943i	0.697121	−	1.20745i
$955$	−2.96456			−0.0959308
$956$	−17.3623	+	30.0723i	−0.561536	+	0.972608i
$957$	−6.31779	+	3.64758i	−0.204225	+	0.117909i
$958$	58.2581	+	33.6353i	1.88223	+	1.08671i
$959$	15.0028			0.484465
$960$	−37.6635	−	65.2352i	−1.21559	−	2.10546i
$961$	−25.5315			−0.823597
$962$	0.529901	−	0.917816i	0.0170847	−	0.0295916i
$963$	10.2896	+	5.94068i	0.331576	+	0.191436i
$964$	−26.0126	−	45.0552i	−0.837811	−	1.45113i
$965$	18.2848	−	10.5567i	0.588609	−	0.339833i
$966$	43.3620	−	75.1051i	1.39515	−	2.41647i
$967$	25.3267			0.814453			0.407227	−	0.913327i	$-0.366496\pi$
$967$	25.3267			0.814453			0.407227	+	0.913327i	$0.366496\pi$
$968$			13.3237i			0.428238i
$969$	−13.7066	−	23.7405i	−0.440318	−	0.762654i
$970$	6.80491	+	11.7864i	0.218492	+	0.378440i
$971$	−8.10254	−	14.0340i	−0.260023	−	0.450373i	0.706225	−	0.707988i	$-0.250397\pi$
$971$	−8.10254	−	14.0340i	−0.260023	−	0.450373i	−0.966248	+	0.257615i	$0.917063\pi$
$972$	−54.3517			−1.74333
$973$	−9.87898	+	5.70363i	−0.316705	+	0.182850i
$974$	−2.59321	+	4.49157i	−0.0830917	+	0.143919i
$975$	−0.702849	+	0.405790i	−0.0225092	+	0.0129957i
$976$	17.3769	−	10.0325i	0.556220	−	0.321134i
$977$	−18.9474	−	32.8179i	−0.606182	−	1.04994i	−0.991864	−	0.127306i	$-0.959367\pi$
$977$	−18.9474	−	32.8179i	−0.606182	−	1.04994i	0.385682	−	0.922632i	$-0.373966\pi$
$978$	−60.2341			−1.92607
$979$	3.89664	−	6.74918i	0.124537	−	0.215705i
$980$	−28.2155			−0.901313
$981$	−23.4050			−0.747263
$982$		−	39.1003i		−	1.24774i
$983$	−43.1019			−1.37474			−0.687368	−	0.726309i	$-0.741234\pi$
$983$	−43.1019			−1.37474			−0.687368	+	0.726309i	$0.741234\pi$
$984$	25.6118	+	14.7870i	0.816473	+	0.471391i
$985$	44.4368	−	25.6556i	1.41587	−	0.817455i
$986$			27.7612i			0.884098i
$987$	29.0695			0.925294
$988$	1.69916	+	0.981009i	0.0540574	+	0.0312101i
$989$		−	41.1461i		−	1.30837i
$990$	4.14728	+	7.18330i	0.131809	+	0.228300i
$991$	−8.25139	−	14.2918i	−0.262114	−	0.453995i	0.704689	−	0.709516i	$-0.251086\pi$
$991$	−8.25139	−	14.2918i	−0.262114	−	0.453995i	−0.966804	+	0.255521i	$0.917753\pi$
$992$	−15.8730	−	9.16429i	−0.503969	−	0.290966i
$993$	−16.6836	+	9.63228i	−0.529438	+	0.305671i
$994$		−	111.482i		−	3.53601i
$995$			49.0368i			1.55457i
$996$	−21.7281	+	37.6342i	−0.688481	+	1.19248i
$997$	−47.9931	−	27.7089i	−1.51996	−	0.877548i	−0.999723	−	0.0235248i	$-0.992511\pi$
$997$	−47.9931	−	27.7089i	−1.51996	−	0.877548i	−0.520235	−	0.854023i	$-0.674156\pi$
$998$	29.1471	−	50.4842i	0.922635	−	1.59805i
$999$	−2.81890			−0.0891860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.5	✓	58
349.227	even	6	inner	349.2.e.a.227.5	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.5	✓	58	1.1	even	1	trivial
349.2.e.a.227.5	yes	58	349.227	even	6	inner

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +O(q^{10})\)	\(q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +5.76535i q^{10} +0.545693i q^{11} +(-3.06454 - 5.30794i) q^{12} +(0.131290 - 0.0758002i) q^{13} +(-3.55887 + 6.16414i) q^{14} +(-3.19734 - 5.53795i) q^{15} +(1.24924 + 2.16374i) q^{16} -2.30327 q^{17} +(4.88720 + 2.82163i) q^{18} +(-2.50657 + 4.34151i) q^{19} +(-3.47679 - 6.02197i) q^{20} -7.89469i q^{21} +(-0.584020 - 1.01155i) q^{22} +(-2.56604 - 4.44452i) q^{23} +(2.55966 + 1.47782i) q^{24} +(-1.12745 - 1.95280i) q^{25} +(-0.162248 + 0.281022i) q^{26} +0.863107 q^{27} -8.58470i q^{28} +(-2.81549 + 4.87657i) q^{29} +(11.8538 + 6.84382i) q^{30} +2.33848 q^{31} +(-6.78774 - 3.91890i) q^{32} +(1.12197 + 0.647770i) q^{33} +(4.26959 - 2.46505i) q^{34} -8.95671i q^{35} -6.80632 q^{36} -3.26599 q^{37} -10.7305i q^{38} -0.359918i q^{39} +(2.90400 + 1.67662i) q^{40} +10.0059 q^{41} +(8.44919 + 14.6344i) q^{42} +(6.94329 + 4.00871i) q^{43} +(1.22003 + 0.704386i) q^{44} -7.10126 q^{45} +(9.51336 + 5.49254i) q^{46} +3.68216i q^{47} +5.93169 q^{48} +(2.02885 - 3.51407i) q^{49} +(4.17992 + 2.41328i) q^{50} +(-2.73413 + 4.73565i) q^{51} -0.391375i q^{52} -7.63103i q^{53} +(-1.59994 + 0.923728i) q^{54} +(1.27290 + 0.734910i) q^{55} +(2.06991 + 3.58519i) q^{56} +(5.95091 + 10.3073i) q^{57} -12.0529i q^{58} +(-2.78764 - 1.60944i) q^{59} -16.5086 q^{60} -8.03093i q^{61} +(-4.33486 + 2.50273i) q^{62} +(-7.59247 - 4.38351i) q^{63} +11.7796 q^{64} -0.408335i q^{65} -2.77307 q^{66} +8.84653 q^{67} +(-2.97309 + 5.14954i) q^{68} -12.1842 q^{69} +(9.58579 + 16.6031i) q^{70} +(-13.5642 + 7.83131i) q^{71} +(2.84250 - 1.64112i) q^{72} +(-7.17140 + 12.4212i) q^{73} +(6.05418 - 3.49538i) q^{74} -5.35342 q^{75} +(6.47102 + 11.2081i) q^{76} +(0.907299 + 1.57149i) q^{77} +(0.385197 + 0.667181i) q^{78} -0.708893i q^{79} +6.72963 q^{80} +(4.97924 - 8.62429i) q^{81} +(-18.5480 + 10.7087i) q^{82} +(-3.54508 - 6.14026i) q^{83} +(-17.6506 - 10.1906i) q^{84} +(-3.10193 + 5.37269i) q^{85} -17.1611 q^{86} +(6.68431 + 11.5776i) q^{87} -0.679356 q^{88} +(-12.3681 - 7.14073i) q^{89} +(13.1636 - 7.60003i) q^{90} +(0.252059 - 0.436580i) q^{91} -13.2491 q^{92} +(2.77592 - 4.80804i) q^{93} +(-3.94078 - 6.82563i) q^{94} +(6.75143 + 11.6938i) q^{95} +(-16.1149 + 9.30395i) q^{96} +(2.04436 - 1.18031i) q^{97} +8.68540i q^{98} +(1.24594 - 0.719346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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