LMFDB - Embedded newform 403.2.k.d.157.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	403.157
Dual form			403.2.k.d.326.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.715177 + 0.519606i) q^{2} +(2.11502 - 1.53665i) q^{3} +(-0.376547 - 1.15889i) q^{4} -3.34815 q^{5} +2.31107 q^{6} +(-0.00198090 - 0.00609658i) q^{7} +(0.879216 - 2.70595i) q^{8} +(1.18497 - 3.64695i) q^{9} +O(q^{10})$	\(q+(0.715177 + 0.519606i) q^{2} +(2.11502 - 1.53665i) q^{3} +(-0.376547 - 1.15889i) q^{4} -3.34815 q^{5} +2.31107 q^{6} +(-0.00198090 - 0.00609658i) q^{7} +(0.879216 - 2.70595i) q^{8} +(1.18497 - 3.64695i) q^{9} +(-2.39452 - 1.73972i) q^{10} +(-0.893105 - 2.74869i) q^{11} +(-2.57722 - 1.87246i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.00175113 - 0.00538942i) q^{14} +(-7.08142 + 5.14495i) q^{15} +(0.0631973 - 0.0459155i) q^{16} +(-0.562356 + 1.73075i) q^{17} +(2.74244 - 1.99250i) q^{18} +(4.90424 + 3.56314i) q^{19} +(1.26074 + 3.88015i) q^{20} +(-0.0135580 - 0.00985045i) q^{21} +(0.789511 - 2.42986i) q^{22} +(2.83562 - 8.72715i) q^{23} +(-2.29855 - 7.07420i) q^{24} +6.21011 q^{25} +0.884007 q^{26} +(-0.674274 - 2.07520i) q^{27} +(-0.00631938 + 0.00459130i) q^{28} +(6.22919 + 4.52577i) q^{29} -7.73781 q^{30} +(0.709268 + 5.52240i) q^{31} -5.62135 q^{32} +(-6.11273 - 4.44116i) q^{33} +(-1.30149 + 0.945591i) q^{34} +(0.00663235 + 0.0204123i) q^{35} -4.67263 q^{36} -7.32028 q^{37} +(1.65597 + 5.09655i) q^{38} +(0.807867 - 2.48636i) q^{39} +(-2.94375 + 9.05993i) q^{40} +(-0.357709 - 0.259891i) q^{41} +(-0.00457800 - 0.0140896i) q^{42} +(5.74406 + 4.17330i) q^{43} +(-2.84915 + 2.07003i) q^{44} +(-3.96745 + 12.2106i) q^{45} +(6.56265 - 4.76804i) q^{46} +(-3.00097 + 2.18033i) q^{47} +(0.0631075 - 0.194225i) q^{48} +(5.66309 - 4.11447i) q^{49} +(4.44133 + 3.22681i) q^{50} +(1.47018 + 4.52474i) q^{51} +(-0.985813 - 0.716235i) q^{52} +(3.34976 - 10.3095i) q^{53} +(0.596063 - 1.83449i) q^{54} +(2.99025 + 9.20304i) q^{55} -0.0182387 q^{56} +15.8479 q^{57} +(2.10335 + 6.47346i) q^{58} +(5.19582 - 3.77498i) q^{59} +(8.62894 + 6.26929i) q^{60} -7.80297 q^{61} +(-2.36222 + 4.31803i) q^{62} -0.0245812 q^{63} +(-4.14665 - 3.01272i) q^{64} +(-2.70871 + 1.96799i) q^{65} +(-2.06403 - 6.35243i) q^{66} +1.91049 q^{67} +2.21751 q^{68} +(-7.41320 - 22.8155i) q^{69} +(-0.00586304 + 0.0180446i) q^{70} +(-1.78369 + 5.48964i) q^{71} +(-8.82663 - 6.41293i) q^{72} +(4.50913 + 13.8777i) q^{73} +(-5.23529 - 3.80366i) q^{74} +(13.1345 - 9.54280i) q^{75} +(2.28262 - 7.02518i) q^{76} +(-0.0149885 + 0.0108898i) q^{77} +(1.86970 - 1.35841i) q^{78} +(-3.77724 + 11.6252i) q^{79} +(-0.211594 + 0.153732i) q^{80} +(4.69188 + 3.40885i) q^{81} +(-0.120784 - 0.371736i) q^{82} +(2.44892 + 1.77925i) q^{83} +(-0.00631040 + 0.0194214i) q^{84} +(1.88285 - 5.79483i) q^{85} +(1.93954 + 5.96930i) q^{86} +20.1294 q^{87} -8.22306 q^{88} +(-2.90992 - 8.95580i) q^{89} +(-9.18211 + 6.67119i) q^{90} +(-0.00518606 - 0.00376789i) q^{91} -11.1816 q^{92} +(9.98615 + 10.5901i) q^{93} -3.27913 q^{94} +(-16.4201 - 11.9299i) q^{95} +(-11.8893 + 8.63808i) q^{96} +(-1.55794 - 4.79484i) q^{97} +6.18801 q^{98} -11.0827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.715177	+	0.519606i	0.505706	+	0.367417i	0.811192	−	0.584779i	$-0.198819\pi$
$2$	0.715177	+	0.519606i	0.505706	+	0.367417i	−0.305486	+	0.952197i	$0.598819\pi$
$3$	2.11502	−	1.53665i	1.22111	−	0.887188i	0.224918	−	0.974378i	$-0.427789\pi$
$3$	2.11502	−	1.53665i	1.22111	−	0.887188i	0.996192	+	0.0871896i	$0.0277886\pi$
$4$	−0.376547	−	1.15889i	−0.188274	−	0.579446i
$5$	−3.34815			−1.49734			−0.748669	−	0.662944i	$-0.769307\pi$
$5$	−3.34815			−1.49734			−0.748669	+	0.662944i	$0.769307\pi$
$6$	2.31107			0.943491
$7$	−0.00198090	−	0.00609658i	−0.000748709	−	0.00230429i	0.950681	−	0.310169i	$-0.100386\pi$
$7$	−0.00198090	−	0.00609658i	−0.000748709	−	0.00230429i	−0.951430	+	0.307865i	$0.900386\pi$
$8$	0.879216	−	2.70595i	0.310850	−	0.956698i
$9$	1.18497	−	3.64695i	0.394989	−	1.21565i
$10$	−2.39452	−	1.73972i	−0.757213	−	0.550148i
$11$	−0.893105	−	2.74869i	−0.269281	−	0.828763i	−0.990676	−	0.136239i	$-0.956499\pi$
$11$	−0.893105	−	2.74869i	−0.269281	−	0.828763i	0.721395	−	0.692524i	$-0.243501\pi$
$12$	−2.57722	−	1.87246i	−0.743981	−	0.540534i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	0.00175113	−	0.00538942i	0.000468009	−	0.00144038i
$15$	−7.08142	+	5.14495i	−1.82841	+	1.32842i
$16$	0.0631973	−	0.0459155i	0.0157993	−	0.0114789i
$17$	−0.562356	+	1.73075i	−0.136391	+	0.419770i	−0.995804	−	0.0915133i	$-0.970830\pi$
$17$	−0.562356	+	1.73075i	−0.136391	+	0.419770i	0.859412	+	0.511283i	$0.170830\pi$
$18$	2.74244	−	1.99250i	0.646400	−	0.469637i
$19$	4.90424	+	3.56314i	1.12511	+	0.817440i	0.984976	−	0.172693i	$-0.0552467\pi$
$19$	4.90424	+	3.56314i	1.12511	+	0.817440i	0.140134	+	0.990133i	$0.455247\pi$
$20$	1.26074	+	3.88015i	0.281909	+	0.867627i
$21$	−0.0135580	−	0.00985045i	−0.00295860	−	0.00214955i
$22$	0.789511	−	2.42986i	0.168324	−	0.518049i
$23$	2.83562	−	8.72715i	0.591268	−	1.81974i	0.0187785	−	0.999824i	$-0.494022\pi$
$23$	2.83562	−	8.72715i	0.591268	−	1.81974i	0.572489	−	0.819912i	$-0.305978\pi$
$24$	−2.29855	−	7.07420i	−0.469189	−	1.44402i
$25$	6.21011			1.24202
$26$	0.884007			0.173368
$27$	−0.674274	−	2.07520i	−0.129764	−	0.399373i
$28$	−0.00631938	+	0.00459130i	−0.00119425	+	0.000867674i
$29$	6.22919	+	4.52577i	1.15673	+	0.840415i	0.989361	−	0.145479i	$-0.0464722\pi$
$29$	6.22919	+	4.52577i	1.15673	+	0.840415i	0.167371	+	0.985894i	$0.446472\pi$
$30$	−7.73781			−1.41273
$31$	0.709268	+	5.52240i	0.127388	+	0.991853i
$31$	0.709268	+	5.52240i	0.127388	+	0.991853i
$32$	−5.62135			−0.993724
$33$	−6.11273	−	4.44116i	−1.06409	−	0.773107i
$34$	−1.30149	+	0.945591i	−0.223205	+	0.162168i
$35$	0.00663235	+	0.0204123i	0.00112107	+	0.00345030i
$36$	−4.67263			−0.778771
$37$	−7.32028			−1.20345			−0.601724	−	0.798704i	$-0.705519\pi$
$37$	−7.32028			−1.20345			−0.601724	+	0.798704i	$0.705519\pi$
$38$	1.65597	+	5.09655i	0.268634	+	0.826769i
$39$	0.807867	−	2.48636i	0.129362	−	0.398136i
$40$	−2.94375	+	9.05993i	−0.465448	+	1.43250i
$41$	−0.357709	−	0.259891i	−0.0558648	−	0.0405882i	0.559502	−	0.828829i	$-0.310992\pi$
$41$	−0.357709	−	0.259891i	−0.0558648	−	0.0405882i	−0.615367	+	0.788241i	$0.710992\pi$
$42$	−0.00457800	−	0.0140896i	−0.000706400	−	0.00217408i
$43$	5.74406	+	4.17330i	0.875961	+	0.636423i	0.932180	−	0.361996i	$-0.117904\pi$
$43$	5.74406	+	4.17330i	0.875961	+	0.636423i	−0.0562189	+	0.998418i	$0.517904\pi$
$44$	−2.84915	+	2.07003i	−0.429525	+	0.312068i
$45$	−3.96745	+	12.2106i	−0.591432	+	1.82024i
$46$	6.56265	−	4.76804i	0.967610	−	0.703010i
$47$	−3.00097	+	2.18033i	−0.437736	+	0.318034i	−0.784735	−	0.619832i	$-0.787201\pi$
$47$	−3.00097	+	2.18033i	−0.437736	+	0.318034i	0.346999	+	0.937866i	$0.387201\pi$
$48$	0.0631075	−	0.194225i	0.00910878	−	0.0280339i
$49$	5.66309	−	4.11447i	0.809012	−	0.587782i
$50$	4.44133	+	3.22681i	0.628099	+	0.456340i
$51$	1.47018	+	4.52474i	0.205866	+	0.633590i
$52$	−0.985813	−	0.716235i	−0.136708	−	0.0993239i
$53$	3.34976	−	10.3095i	0.460124	−	1.41612i	−0.404888	−	0.914366i	$-0.632689\pi$
$53$	3.34976	−	10.3095i	0.460124	−	1.41612i	0.865012	−	0.501751i	$-0.167311\pi$
$54$	0.596063	−	1.83449i	0.0811139	−	0.249643i
$55$	2.99025	+	9.20304i	0.403205	+	1.24094i
$56$	−0.0182387			−0.00243725
$57$	15.8479			2.09911
$58$	2.10335	+	6.47346i	0.276184	+	0.850006i
$59$	5.19582	−	3.77498i	0.676438	−	0.491461i	−0.195736	−	0.980657i	$-0.562710\pi$
$59$	5.19582	−	3.77498i	0.676438	−	0.491461i	0.872174	+	0.489196i	$0.162710\pi$
$60$	8.62894	+	6.26929i	1.11399	+	0.809362i
$61$	−7.80297			−0.999068			−0.499534	−	0.866294i	$-0.666495\pi$
$61$	−7.80297			−0.999068			−0.499534	+	0.866294i	$0.666495\pi$
$62$	−2.36222	+	4.31803i	−0.300003	+	0.548391i
$63$	−0.0245812			−0.00309695
$64$	−4.14665	−	3.01272i	−0.518332	−	0.376590i
$65$	−2.70871	+	1.96799i	−0.335974	+	0.244100i
$66$	−2.06403	−	6.35243i	−0.254064	−	0.781930i
$67$	1.91049			0.233404			0.116702	−	0.993167i	$-0.462768\pi$
$67$	1.91049			0.233404			0.116702	+	0.993167i	$0.462768\pi$
$68$	2.21751			0.268913
$69$	−7.41320	−	22.8155i	−0.892445	−	2.74666i
$70$	−0.00586304	+	0.0180446i	−0.000700767	+	0.00215674i
$71$	−1.78369	+	5.48964i	−0.211685	+	0.651500i	0.787687	+	0.616075i	$0.211278\pi$
$71$	−1.78369	+	5.48964i	−0.211685	+	0.651500i	−0.999372	+	0.0354246i	$0.988722\pi$
$72$	−8.82663	−	6.41293i	−1.04023	−	0.755770i
$73$	4.50913	+	13.8777i	0.527754	+	1.62426i	0.758805	+	0.651318i	$0.225784\pi$
$73$	4.50913	+	13.8777i	0.527754	+	1.62426i	−0.231051	+	0.972942i	$0.574216\pi$
$74$	−5.23529	−	3.80366i	−0.608591	−	0.442167i
$75$	13.1345	−	9.54280i	1.51665	−	1.10191i
$76$	2.28262	−	7.02518i	0.261834	−	0.805843i
$77$	−0.0149885	+	0.0108898i	−0.00170810	+	0.00124100i
$78$	1.86970	−	1.35841i	0.211701	−	0.153810i
$79$	−3.77724	+	11.6252i	−0.424973	+	1.30793i	0.478048	+	0.878334i	$0.341345\pi$
$79$	−3.77724	+	11.6252i	−0.424973	+	1.30793i	−0.903020	+	0.429598i	$0.858655\pi$
$80$	−0.211594	+	0.153732i	−0.0236569	+	0.0171878i
$81$	4.69188	+	3.40885i	0.521320	+	0.378761i
$82$	−0.120784	−	0.371736i	−0.0133384	−	0.0410514i
$83$	2.44892	+	1.77925i	0.268804	+	0.195298i	0.714019	−	0.700126i	$-0.246873\pi$
$83$	2.44892	+	1.77925i	0.268804	+	0.195298i	−0.445215	+	0.895424i	$0.646873\pi$
$84$	−0.00631040	+	0.0194214i	−0.000688521	+	0.00211905i
$85$	1.88285	−	5.79483i	0.204224	−	0.628537i
$86$	1.93954	+	5.96930i	0.209146	+	0.643686i
$87$	20.1294			2.15810
$88$	−8.22306			−0.876581
$89$	−2.90992	−	8.95580i	−0.308451	−	0.949313i	−0.978367	−	0.206877i	$-0.933670\pi$
$89$	−2.90992	−	8.95580i	−0.308451	−	0.949313i	0.669916	−	0.742437i	$-0.266330\pi$
$90$	−9.18211	+	6.67119i	−0.967879	+	0.703205i
$91$	−0.00518606	−	0.00376789i	−0.000543647	−	0.000394983i
$92$	−11.1816			−1.16576
$93$	9.98615	+	10.5901i	1.03552	+	1.09814i
$94$	−3.27913			−0.338217
$95$	−16.4201	−	11.9299i	−1.68467	−	1.22398i
$96$	−11.8893	+	8.63808i	−1.21345	+	0.881620i
$97$	−1.55794	−	4.79484i	−0.158185	−	0.486842i	0.840285	−	0.542145i	$-0.182388\pi$
$97$	−1.55794	−	4.79484i	−0.158185	−	0.486842i	−0.998470	+	0.0553027i	$0.982388\pi$
$98$	6.18801			0.625084
$99$	−11.0827			−1.11385
$100$	−2.33840	−	7.19686i	−0.233840	−	0.719686i
$101$	0.225038	−	0.692595i	0.0223921	−	0.0689158i	−0.939236	−	0.343272i	$-0.888465\pi$
$101$	0.225038	−	0.692595i	0.0223921	−	0.0689158i	0.961628	+	0.274356i	$0.0884647\pi$
$102$	−1.29965	+	3.99990i	−0.128684	+	0.396049i
$103$	−1.06810	−	0.776022i	−0.105243	−	0.0764637i	0.533919	−	0.845536i	$-0.320719\pi$
$103$	−1.06810	−	0.776022i	−0.105243	−	0.0764637i	−0.639162	+	0.769072i	$0.720719\pi$
$104$	−0.879216	−	2.70595i	−0.0862143	−	0.265340i
$105$	0.0453942	+	0.0329808i	0.00443002	+	0.00321860i
$106$	7.75254	−	5.63255i	0.752993	−	0.547082i
$107$	−0.159067	+	0.489559i	−0.0153776	+	0.0473274i	−0.958451	−	0.285258i	$-0.907921\pi$
$107$	−0.159067	+	0.489559i	−0.0153776	+	0.0473274i	0.943073	+	0.332585i	$0.107921\pi$
$108$	−2.15104	+	1.56282i	−0.206984	+	0.150383i
$109$	1.76338	−	1.28117i	0.168901	−	0.122714i	−0.500123	−	0.865954i	$-0.666712\pi$
$109$	1.76338	−	1.28117i	0.168901	−	0.122714i	0.669025	+	0.743240i	$0.266712\pi$
$110$	−2.64340	+	8.13555i	−0.252038	+	0.775695i
$111$	−15.4826	+	11.2487i	−1.46954	+	1.06768i
$112$	−0.000405115	0	0.000294333i	−3.82798e−5	0	2.78119e-5i
$113$	−4.48202	−	13.7942i	−0.421633	−	1.29765i	−0.906182	−	0.422888i	$-0.861016\pi$
$113$	−4.48202	−	13.7942i	−0.421633	−	1.29765i	0.484549	−	0.874764i	$-0.338984\pi$
$114$	11.3340	+	8.23467i	1.06153	+	0.771247i
$115$	−9.49409	+	29.2198i	−0.885328	+	2.72476i
$116$	2.89930	−	8.92314i	0.269193	−	0.828492i
$117$	−1.18497	−	3.64695i	−0.109550	−	0.337161i
$118$	5.67743			0.522650
$119$	0.0116657			0.00106939
$120$	7.69588	+	23.6855i	0.702535	+	2.16218i
$121$	2.14150	−	1.55589i	0.194682	−	0.141445i
$122$	−5.58050	−	4.05447i	−0.505235	−	0.367075i
$123$	−1.15593			−0.104226
$124$	6.13280	−	2.90141i	0.550742	−	0.260554i
$125$	−4.05164			−0.362390
$126$	−0.0175799	−	0.0127726i	−0.00156614	−	0.00113787i
$127$	−9.61795	+	6.98785i	−0.853455	+	0.620071i	−0.926096	−	0.377287i	$-0.876857\pi$
$127$	−9.61795	+	6.98785i	−0.853455	+	0.620071i	0.0726415	+	0.997358i	$0.476857\pi$
$128$	2.07403	+	6.38319i	0.183320	+	0.564200i
$129$	18.5618			1.63427
$130$	−2.95979			−0.259591
$131$	4.38073	+	13.4825i	0.382747	+	1.17797i	0.938102	+	0.346360i	$0.112582\pi$
$131$	4.38073	+	13.4825i	0.382747	+	1.17797i	−0.555355	+	0.831613i	$0.687418\pi$
$132$	−2.84510	+	8.75631i	−0.247634	+	0.762139i
$133$	0.0120082	−	0.0369573i	0.00104124	−	0.00320460i
$134$	1.36634	+	0.992703i	0.118034	+	0.0857565i
$135$	2.25757	+	6.94809i	0.194301	+	0.597997i
$136$	4.18890	+	3.04342i	0.359195	+	0.260971i
$137$	−10.4019	+	7.55739i	−0.888691	+	0.645672i	−0.935536	−	0.353230i	$-0.885083\pi$
$137$	−10.4019	+	7.55739i	−0.888691	+	0.645672i	0.0468454	+	0.998902i	$0.485083\pi$
$138$	6.55332	−	20.1691i	0.557856	−	1.71690i
$139$	−9.65030	+	7.01135i	−0.818527	+	0.594695i	−0.916290	−	0.400515i	$-0.868831\pi$
$139$	−9.65030	+	7.01135i	−0.818527	+	0.594695i	0.0977629	+	0.995210i	$0.468831\pi$
$140$	0.0211582	−	0.0153724i	0.00178820	−	0.00129920i
$141$	−2.99670	+	9.22290i	−0.252368	+	0.776708i
$142$	−4.12810	+	2.99924i	−0.346423	+	0.251691i
$143$	−2.33818	−	1.69879i	−0.195528	−	0.142060i
$144$	−0.0925651	−	0.284886i	−0.00771376	−	0.0237405i
$145$	−20.8563	−	15.1530i	−1.73202	−	1.25839i
$146$	−3.98610	+	12.2680i	−0.329892	+	1.01530i
$147$	5.65504	−	17.4044i	0.466420	−	1.43549i
$148$	2.75643	+	8.48342i	0.226577	+	0.697333i
$149$	−0.821389			−0.0672908			−0.0336454	−	0.999434i	$-0.510712\pi$
$149$	−0.821389			−0.0672908			−0.0336454	+	0.999434i	$0.510712\pi$
$150$	14.3520			1.17184
$151$	−3.36961	−	10.3706i	−0.274215	−	0.843947i	−0.989426	−	0.145039i	$-0.953669\pi$
$151$	−3.36961	−	10.3706i	−0.274215	−	0.843947i	0.715211	−	0.698909i	$-0.246331\pi$
$152$	13.9536	−	10.1379i	1.13178	−	0.822289i
$153$	5.64561	+	4.10178i	0.456421	+	0.331609i
$154$	−0.0163778			−0.00131976
$155$	−2.37474	−	18.4898i	−0.190743	−	1.48514i
$156$	−3.18562			−0.255054
$157$	−11.7455	−	8.53364i	−0.937396	−	0.681058i	0.0103962	−	0.999946i	$-0.496691\pi$
$157$	−11.7455	−	8.53364i	−0.937396	−	0.681058i	−0.947793	+	0.318888i	$0.896691\pi$
$158$	−8.74189	+	6.35136i	−0.695468	+	0.505287i
$159$	−8.75731	−	26.9522i	−0.694500	−	2.13745i
$160$	18.8211			1.48794
$161$	−0.0588228			−0.00463589
$162$	1.58426	+	4.87586i	0.124471	+	0.383083i
$163$	2.27365	−	6.99757i	0.178086	−	0.548092i	−0.821675	−	0.569956i	$-0.806960\pi$
$163$	2.27365	−	6.99757i	0.178086	−	0.548092i	0.999761	+	0.0218641i	$0.00696011\pi$
$164$	−0.166492	+	0.512408i	−0.0130008	+	0.0400124i
$165$	20.4664	+	14.8697i	1.59330	+	1.15760i
$166$	0.826904	+	2.54495i	0.0641802	+	0.197526i
$167$	0.356139	+	0.258750i	0.0275589	+	0.0200227i	0.601479	−	0.798888i	$-0.294578\pi$
$167$	0.356139	+	0.258750i	0.0275589	+	0.0200227i	−0.573921	+	0.818911i	$0.694578\pi$
$168$	−0.0385752	+	0.0280266i	−0.00297614	+	0.00216230i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	4.35760	−	3.16598i	0.334213	−	0.242820i
$171$	18.8060	−	13.6633i	1.43813	−	1.04486i
$172$	2.67350	−	8.22819i	0.203853	−	0.627394i
$173$	−14.5766	+	10.5906i	−1.10824	+	0.805185i	−0.982386	−	0.186864i	$-0.940168\pi$
$173$	−14.5766	+	10.5906i	−1.10824	+	0.805185i	−0.125856	+	0.992049i	$0.540168\pi$
$174$	14.3961	+	10.4594i	1.09137	+	0.792924i
$175$	−0.0123016	−	0.0378604i	−0.000929914	−	0.00286198i
$176$	−0.182650	−	0.132703i	−0.0137677	−	0.0100028i
$177$	5.18844	−	15.9684i	0.389987	−	1.20026i
$178$	2.57239	−	7.91699i	0.192809	−	0.593404i
$179$	−4.59524	−	14.1427i	−0.343464	−	1.05707i	−0.962401	−	0.271633i	$-0.912436\pi$
$179$	−4.59524	−	14.1427i	−0.343464	−	1.05707i	0.618937	−	0.785441i	$-0.287564\pi$
$180$	15.6447			1.16608
$181$	1.37418			0.102142			0.0510712	−	0.998695i	$-0.483736\pi$
$181$	1.37418			0.102142			0.0510712	+	0.998695i	$0.483736\pi$
$182$	−0.00175113	−	0.00538942i	−0.000129802	−	0.000399490i
$183$	−16.5035	+	11.9905i	−1.21997	+	0.886361i
$184$	−21.1221	−	15.3461i	−1.55714	−	1.13133i
$185$	24.5094			1.80197
$186$	1.63917	+	12.7627i	0.120190	+	0.935804i
$187$	5.25956			0.384617
$188$	3.65677	+	2.65680i	0.266698	+	0.193767i
$189$	−0.0113160	+	0.00822153i	−0.000823116	+	0.000598029i
$190$	−5.54443	−	17.0640i	−0.402235	−	1.23795i
$191$	−4.59192			−0.332260			−0.166130	−	0.986104i	$-0.553127\pi$
$191$	−4.59192			−0.332260			−0.166130	+	0.986104i	$0.553127\pi$
$192$	−13.3998			−0.967046
$193$	0.606480	+	1.86655i	0.0436554	+	0.134357i	0.970509	−	0.241066i	$-0.0774972\pi$
$193$	0.606480	+	1.86655i	0.0436554	+	0.134357i	−0.926853	+	0.375424i	$0.877497\pi$
$194$	1.37723	−	4.23867i	0.0988792	−	0.304319i
$195$	−2.70486	+	8.32471i	−0.193699	+	0.596145i
$196$	−6.90065	−	5.01362i	−0.492904	−	0.358115i
$197$	7.44067	+	22.9000i	0.530126	+	1.63156i	0.753952	+	0.656930i	$0.228145\pi$
$197$	7.44067	+	22.9000i	0.530126	+	1.63156i	−0.223826	+	0.974629i	$0.571855\pi$
$198$	−7.92606	−	5.75862i	−0.563281	−	0.409247i
$199$	2.60976	−	1.89610i	0.185001	−	0.134411i	−0.491430	−	0.870917i	$-0.663526\pi$
$199$	2.60976	−	1.89610i	0.185001	−	0.134411i	0.676431	+	0.736506i	$0.263526\pi$
$200$	5.46003	−	16.8043i	0.386083	−	1.18824i
$201$	4.04073	−	2.93577i	0.285011	−	0.207073i
$202$	0.520819	−	0.378397i	0.0366447	−	0.0266239i
$203$	0.0152523	−	0.0469419i	0.00107050	−	0.00329467i
$204$	4.69009	−	3.40755i	0.328372	−	0.238576i
$205$	1.19767	+	0.870155i	0.0836486	+	0.0607742i
$206$	−0.360656	−	1.10999i	−0.0251281	−	0.0773364i
$207$	−28.4674	−	20.6828i	−1.97862	−	1.43755i
$208$	0.0241392	−	0.0742929i	0.00167375	−	0.00515128i
$209$	5.41398	−	16.6625i	0.374493	−	1.15257i
$210$	0.0153278	+	0.0471742i	0.00105772	+	0.00325533i
$211$	12.3274			0.848650			0.424325	−	0.905510i	$-0.360511\pi$
$211$	12.3274			0.848650			0.424325	+	0.905510i	$0.360511\pi$
$212$	−13.2089			−0.907193
$213$	4.66313	+	14.3516i	0.319512	+	0.983358i
$214$	−0.368139	+	0.267469i	−0.0251655	+	0.0182838i
$215$	−19.2320	−	13.9728i	−1.31161	−	0.952940i
$216$	−6.20823			−0.422416
$217$	0.0322628	−	0.0152634i	0.00219014	−	0.00103615i
$218$	1.92684			0.130502
$219$	30.8621	+	22.4227i	2.08547	+	1.51518i
$220$	9.53937	−	6.93076i	0.643144	−	0.467272i
$221$	0.562356	+	1.73075i	0.0378282	+	0.116423i
$222$	−16.9177			−1.13544
$223$	21.6061			1.44685			0.723426	−	0.690402i	$-0.242566\pi$
$223$	21.6061			1.44685			0.723426	+	0.690402i	$0.242566\pi$
$224$	0.0111353	+	0.0342710i	0.000744011	+	0.00228983i
$225$	7.35878	−	22.6480i	0.490585	−	1.50987i
$226$	3.96213	−	12.1942i	0.263557	−	0.811146i
$227$	−3.70404	−	2.69115i	−0.245846	−	0.178618i	0.458038	−	0.888933i	$-0.348552\pi$
$227$	−3.70404	−	2.69115i	−0.245846	−	0.178618i	−0.703884	+	0.710315i	$0.748552\pi$
$228$	−5.96748	−	18.3660i	−0.395206	−	1.21632i
$229$	−9.33587	−	6.78290i	−0.616931	−	0.448227i	0.234917	−	0.972015i	$-0.424518\pi$
$229$	−9.33587	−	6.78290i	−0.616931	−	0.448227i	−0.851848	+	0.523789i	$0.824518\pi$
$230$	−21.9727	+	15.9641i	−1.44884	+	1.05264i
$231$	−0.0149672	+	0.0460643i	−0.000984768	+	0.00303081i
$232$	17.7233	−	12.8768i	1.16359	−	0.845400i
$233$	13.9261	−	10.1179i	0.912332	−	0.662848i	−0.0292718	−	0.999571i	$-0.509319\pi$
$233$	13.9261	−	10.1179i	0.912332	−	0.662848i	0.941604	+	0.336724i	$0.109319\pi$
$234$	1.04752	−	3.22393i	0.0684785	−	0.210755i
$235$	10.0477	−	7.30007i	0.655439	−	0.476204i
$236$	−6.33127	−	4.59994i	−0.412131	−	0.299430i
$237$	9.87489	+	30.3918i	0.641443	+	1.97416i
$238$	0.00834300	+	0.00606155i	0.000540797	+	0.000392912i
$239$	0.359562	−	1.10662i	0.0232582	−	0.0715812i	−0.938754	−	0.344589i	$-0.888018\pi$
$239$	0.359562	−	1.10662i	0.0232582	−	0.0715812i	0.962012	+	0.273007i	$0.0880184\pi$
$240$	−0.211293	+	0.650294i	−0.0136389	+	0.0419763i
$241$	4.87744	+	15.0112i	0.314184	+	0.966958i	0.976089	+	0.217371i	$0.0697480\pi$
$241$	4.87744	+	15.0112i	0.314184	+	0.966958i	−0.661905	+	0.749587i	$0.730252\pi$
$242$	2.34000			0.150421
$243$	21.7076			1.39255
$244$	2.93819	+	9.04280i	0.188098	+	0.578906i
$245$	−18.9609	+	13.7759i	−1.21137	+	0.880108i
$246$	−0.826692	−	0.600627i	−0.0527080	−	0.0382946i
$247$	6.06197			0.385714
$248$	15.5669	+	2.93614i	0.988502	+	0.186445i
$249$	7.91362			0.501505
$250$	−2.89764	−	2.10526i	−0.183263	−	0.133148i
$251$	−9.32285	+	6.77345i	−0.588453	+	0.427536i	−0.841762	−	0.539849i	$-0.818481\pi$
$251$	−9.32285	+	6.77345i	−0.588453	+	0.427536i	0.253309	+	0.967386i	$0.418481\pi$
$252$	0.00925600	+	0.0284870i	0.000583073	+	0.00179451i
$253$	−26.5208			−1.66735
$254$	−10.5095			−0.659422
$255$	−4.92237	−	15.1495i	−0.308251	−	0.948698i
$256$	−5.00122	+	15.3922i	−0.312576	+	0.962010i
$257$	0.791903	−	2.43723i	0.0493975	−	0.152030i	−0.923315	−	0.384043i	$-0.874531\pi$
$257$	0.791903	−	2.43723i	0.0493975	−	0.152030i	0.972713	+	0.232013i	$0.0745313\pi$
$258$	13.2749	+	9.64480i	0.826461	+	0.600459i
$259$	0.0145007	+	0.0446287i	0.000901032	+	0.00277309i
$260$	3.30065	+	2.39806i	0.204698	+	0.148722i
$261$	23.8867	−	17.3547i	1.47855	−	1.07423i
$262$	−3.87260	+	11.9186i	−0.239250	+	0.736336i
$263$	−12.1792	+	8.84871i	−0.751002	+	0.545635i	−0.896137	−	0.443777i	$-0.853638\pi$
$263$	−12.1792	+	8.84871i	−0.751002	+	0.545635i	0.145135	+	0.989412i	$0.453638\pi$
$264$	−17.3920	+	12.6360i	−1.07040	+	0.777693i
$265$	−11.2155	+	34.5177i	−0.688962	+	2.12041i
$266$	0.0277912	−	0.0201915i	0.00170399	−	0.00123802i
$267$	−19.9165	−	14.4702i	−1.21887	−	0.885562i
$268$	−0.719390	−	2.21405i	−0.0439437	−	0.135245i
$269$	18.6854	+	13.5757i	1.13927	+	0.827726i	0.987017	−	0.160616i	$-0.0513481\pi$
$269$	18.6854	+	13.5757i	1.13927	+	0.827726i	0.152250	+	0.988342i	$0.451348\pi$
$270$	−1.99571	+	6.14216i	−0.121455	+	0.373800i
$271$	9.26352	−	28.5102i	0.562719	−	1.73187i	−0.111916	−	0.993718i	$-0.535699\pi$
$271$	9.26352	−	28.5102i	0.562719	−	1.73187i	0.674635	−	0.738152i	$-0.264301\pi$
$272$	0.0439291	+	0.135200i	0.00266359	+	0.00819770i
$273$	−0.0167586			−0.00101428
$274$	−11.3660			−0.686647
$275$	−5.54628	−	17.0697i	−0.334454	−	1.02934i
$276$	−23.6493	+	17.1822i	−1.42352	+	1.03425i
$277$	8.00518	+	5.81610i	0.480985	+	0.349456i	0.801707	−	0.597718i	$-0.203926\pi$
$277$	8.00518	+	5.81610i	0.480985	+	0.349456i	−0.320722	+	0.947173i	$0.603926\pi$
$278$	−10.5448			−0.632435
$279$	20.9804	+	3.95720i	1.25606	+	0.236911i
$280$	0.0610658			0.00364938
$281$	−8.63259	−	6.27194i	−0.514977	−	0.374153i	0.299731	−	0.954024i	$-0.403103\pi$
$281$	−8.63259	−	6.27194i	−0.514977	−	0.374153i	−0.814708	+	0.579871i	$0.803103\pi$
$282$	−6.93545	+	5.03890i	−0.413000	+	0.300062i
$283$	4.76702	+	14.6714i	0.283370	+	0.872123i	0.986882	+	0.161440i	$0.0516140\pi$
$283$	4.76702	+	14.6714i	0.283370	+	0.872123i	−0.703512	+	0.710683i	$0.748386\pi$
$284$	7.03354			0.417364
$285$	−53.0612			−3.14307
$286$	−0.789511	−	2.42986i	−0.0466848	−	0.143681i
$287$	−0.000875861		0.00269562i	−5.17004e−5		0.000159118i
$288$	−6.66112	+	20.5008i	−0.392510	+	1.20802i
$289$	11.0740	+	8.04575i	0.651413	+	0.473279i
$290$	−7.04234	−	21.6741i	−0.413541	−	1.27275i
$291$	−10.6631	−	7.74719i	−0.625081	−	0.454148i
$292$	14.3848	−	10.4512i	0.841809	−	0.611610i
$293$	−7.34622	+	22.6093i	−0.429171	+	1.32085i	0.469773	+	0.882787i	$0.344336\pi$
$293$	−7.34622	+	22.6093i	−0.429171	+	1.32085i	−0.898944	+	0.438064i	$0.855664\pi$
$294$	13.0878	−	9.50884i	0.763296	−	0.554567i
$295$	−17.3964	+	12.6392i	−1.01286	+	0.735884i
$296$	−6.43611	+	19.8083i	−0.374091	+	1.15134i
$297$	−5.10190	+	3.70675i	−0.296042	+	0.215087i
$298$	−0.587438	−	0.426799i	−0.0340294	−	0.0247238i
$299$	−2.83562	−	8.72715i	−0.163988	−	0.504704i
$300$	−16.0049	−	11.6282i	−0.924041	−	0.671355i
$301$	0.0140645	−	0.0432860i	0.000810663	−	0.00249496i
$302$	2.97876	−	9.16768i	0.171408	−	0.527541i
$303$	−0.588319	−	1.81066i	−0.0337981	−	0.104020i
$304$	0.473538			0.0271593
$305$	26.1255			1.49594
$306$	1.90630	+	5.86699i	0.108976	+	0.335393i
$307$	8.72291	−	6.33757i	0.497843	−	0.361704i	−0.310350	−	0.950622i	$-0.600446\pi$
$307$	8.72291	−	6.33757i	0.497843	−	0.361704i	0.808192	+	0.588919i	$0.200446\pi$
$308$	0.0182639	+	0.0132695i	0.00104068	+	0.000756102i
$309$	−3.45154			−0.196351
$310$	7.90908	−	14.4574i	0.449206	−	0.821127i
$311$	−0.653158			−0.0370372			−0.0185186	−	0.999829i	$-0.505895\pi$
$311$	−0.653158			−0.0370372			−0.0185186	+	0.999829i	$0.505895\pi$
$312$	−6.01768	−	4.37210i	−0.340684	−	0.247521i
$313$	22.8587	−	16.6078i	1.29205	−	0.938730i	0.292206	−	0.956355i	$-0.405611\pi$
$313$	22.8587	−	16.6078i	1.29205	−	0.938730i	0.999845	+	0.0176259i	$0.00561080\pi$
$314$	−3.96601	−	12.2061i	−0.223815	−	0.688831i
$315$	0.0823017			0.00463718
$316$	14.8946			0.837887
$317$	1.44729	+	4.45431i	0.0812882	+	0.250179i	0.983438	−	0.181243i	$-0.0580120\pi$
$317$	1.44729	+	4.45431i	0.0812882	+	0.250179i	−0.902150	+	0.431422i	$0.858012\pi$
$318$	7.74152	−	23.8260i	0.434123	−	1.33609i
$319$	6.87665	−	21.1641i	0.385018	−	1.18496i
$320$	13.8836	+	10.0870i	0.776118	+	0.563883i
$321$	0.415852	+	1.27986i	0.0232106	+	0.0714348i
$322$	−0.0420687	−	0.0305647i	−0.00234440	−	0.00170330i
$323$	−8.92485	+	6.48428i	−0.496592	+	0.360795i
$324$	2.18378	−	6.72097i	0.121321	−	0.373387i
$325$	5.02409	−	3.65021i	0.278686	−	0.202477i
$326$	5.26204	−	3.82310i	0.291438	−	0.211742i
$327$	1.76088	−	5.41942i	0.0973767	−	0.299695i
$328$	−1.01776	+	0.739443i	−0.0561962	+	0.0408289i
$329$	0.0192372	+	0.0139766i	0.00106058	+	0.000770556i
$330$	6.91068	+	21.2689i	0.380420	+	1.17081i
$331$	−16.4772	−	11.9714i	−0.905667	−	0.658006i	0.0342480	−	0.999413i	$-0.489096\pi$
$331$	−16.4772	−	11.9714i	−0.905667	−	0.658006i	−0.939915	+	0.341407i	$0.889096\pi$
$332$	1.13982	−	3.50801i	0.0625558	−	0.192527i
$333$	−8.67430	+	26.6967i	−0.475348	+	1.46297i
$334$	0.120254	+	0.370104i	0.00658002	+	0.0202512i
$335$	−6.39661			−0.349484
$336$	−0.00130912			−7.14182e−5
$337$	8.97750	+	27.6299i	0.489036	+	1.50510i	0.826049	+	0.563598i	$0.190583\pi$
$337$	8.97750	+	27.6299i	0.489036	+	1.50510i	−0.337014	+	0.941500i	$0.609417\pi$
$338$	0.715177	−	0.519606i	0.0389005	−	0.0282629i
$339$	−30.6766	−	22.2878i	−1.66612	−	1.21051i
$340$	−7.42457			−0.402654
$341$	14.5460	−	6.88165i	0.787707	−	0.372662i
$342$	20.5491			1.11117
$343$	−0.0726046	−	0.0527503i	−0.00392028	−	0.00284825i
$344$	16.3430	−	11.8739i	0.881157	−	0.640198i
$345$	24.8205	+	76.3897i	1.33629	+	4.11268i
$346$	−15.9278			−0.856283
$347$	−30.6033			−1.64287			−0.821434	−	0.570303i	$-0.806826\pi$
$347$	−30.6033			−1.64287			−0.821434	+	0.570303i	$0.806826\pi$
$348$	−7.57969	−	23.3279i	−0.406314	−	1.25051i
$349$	−4.25703	+	13.1018i	−0.227874	+	0.701323i	0.770113	+	0.637907i	$0.220200\pi$
$349$	−4.25703	+	13.1018i	−0.227874	+	0.701323i	−0.997987	+	0.0634164i	$0.979800\pi$
$350$	0.0108747	−	0.0334689i	0.000581277	−	0.00178899i
$351$	−1.76527	−	1.28255i	−0.0942233	−	0.0684572i
$352$	5.02046	+	15.4514i	0.267591	+	0.823562i
$353$	−28.6864	−	20.8419i	−1.52683	−	1.10930i	−0.957971	−	0.286866i	$-0.907387\pi$
$353$	−28.6864	−	20.8419i	−1.52683	−	1.10930i	−0.568855	−	0.822438i	$-0.692613\pi$
$354$	12.0079	−	8.72426i	0.638213	−	0.463689i
$355$	5.97207	−	18.3801i	0.316964	−	0.975516i
$356$	−9.28310	+	6.74456i	−0.492003	+	0.357461i
$357$	0.0246731	−	0.0179261i	0.00130584	−	0.000948749i
$358$	4.06222	−	12.5022i	0.214695	−	0.660764i
$359$	−11.8104	+	8.58079i	−0.623331	+	0.452877i	−0.854083	−	0.520136i	$-0.825881\pi$
$359$	−11.8104	+	8.58079i	−0.623331	+	0.452877i	0.230752	+	0.973013i	$0.425881\pi$
$360$	29.5529	+	21.4714i	1.55757	+	1.13164i
$361$	5.48428	+	16.8789i	0.288647	+	0.888363i
$362$	0.982784	+	0.714035i	0.0516540	+	0.0375288i
$363$	2.13846	−	6.58149i	0.112240	−	0.345439i
$364$	−0.00241379	+	0.00742888i	−0.000126517	+	0.000389379i
$365$	−15.0973	−	46.4646i	−0.790226	−	2.43207i
$366$	−18.0332			−0.942611
$367$	−0.120365			−0.00628302			−0.00314151	−	0.999995i	$-0.501000\pi$
$367$	−0.120365			−0.00628302			−0.00314151	+	0.999995i	$0.501000\pi$
$368$	−0.221508	−	0.681731i	−0.0115469	−	0.0355377i
$369$	−1.37169	+	0.996588i	−0.0714071	+	0.0518803i
$370$	17.5286	+	12.7352i	0.911266	+	0.662074i
$371$	−0.0694881			−0.00360764
$372$	8.51255	−	15.5606i	0.441355	−	0.806777i
$373$	−27.0000			−1.39801			−0.699004	−	0.715118i	$-0.746373\pi$
$373$	−27.0000			−1.39801			−0.699004	+	0.715118i	$0.746373\pi$
$374$	3.76151	+	2.73290i	0.194503	+	0.141315i
$375$	−8.56932	+	6.22598i	−0.442518	+	0.321508i
$376$	3.26136	+	10.0374i	0.168192	+	0.517642i
$377$	7.69971			0.396555
$378$	−0.0123649			−0.000635981
$379$	9.09416	+	27.9889i	0.467135	+	1.43770i	0.856277	+	0.516517i	$0.172772\pi$
$379$	9.09416	+	27.9889i	0.467135	+	1.43770i	−0.389141	+	0.921178i	$0.627228\pi$
$380$	−7.64255	+	23.5213i	−0.392055	+	1.20662i
$381$	−9.60428	+	29.5589i	−0.492042	+	1.51435i
$382$	−3.28404	−	2.38599i	−0.168026	−	0.122078i
$383$	−5.74719	−	17.6880i	−0.293667	−	0.903815i	−0.983666	−	0.180005i	$-0.942389\pi$
$383$	−5.74719	−	17.6880i	−0.293667	−	0.903815i	0.689998	−	0.723811i	$-0.257611\pi$
$384$	14.1954	+	10.3135i	0.724405	+	0.526311i
$385$	0.0501837	−	0.0364606i	0.00255760	−	0.00185820i
$386$	−0.536132	+	1.65004i	−0.0272884	+	0.0839851i
$387$	22.0264	−	16.0031i	1.11966	−	0.813483i
$388$	−4.97007	+	3.61097i	−0.252317	+	0.183319i
$389$	−7.44900	+	22.9257i	−0.377679	+	1.16238i	0.563974	+	0.825793i	$0.309272\pi$
$389$	−7.44900	+	22.9257i	−0.377679	+	1.16238i	−0.941653	+	0.336585i	$0.890728\pi$
$390$	−6.26002	+	4.54817i	−0.316989	+	0.230306i
$391$	13.5099	+	9.81553i	0.683226	+	0.496393i
$392$	−6.15448	−	18.9415i	−0.310848	−	0.956692i
$393$	29.9833	+	21.7842i	1.51246	+	1.09887i
$394$	−6.57760	+	20.2438i	−0.331375	+	1.01987i
$395$	12.6468	−	38.9228i	0.636328	−	1.95842i
$396$	4.17315	+	12.8436i	0.209708	+	0.645416i
$397$	30.3952			1.52549			0.762746	−	0.646698i	$-0.223851\pi$
$397$	30.3952			1.52549			0.762746	+	0.646698i	$0.223851\pi$
$398$	2.85167			0.142941
$399$	−0.0313931	−	0.0966180i	−0.00157162	−	0.00483695i
$400$	0.392462	−	0.285141i	0.0196231	−	0.0142570i
$401$	−13.7081	−	9.95951i	−0.684549	−	0.497354i	0.190314	−	0.981723i	$-0.439049\pi$
$401$	−13.7081	−	9.95951i	−0.684549	−	0.497354i	−0.874864	+	0.484369i	$0.839049\pi$
$402$	4.41528			0.220214
$403$	3.81980	+	4.05082i	0.190278	+	0.201786i
$404$	−0.887381			−0.0441489
$405$	−15.7091	−	11.4133i	−0.780592	−	0.567133i
$406$	0.0352994	−	0.0256465i	0.00175188	−	0.00127282i
$407$	6.53778	+	20.1212i	0.324066	+	0.997372i
$408$	13.5363			0.670147
$409$	27.0153			1.33582			0.667910	−	0.744242i	$-0.267189\pi$
$409$	27.0153			1.33582			0.667910	+	0.744242i	$0.267189\pi$
$410$	0.404404	+	1.24463i	0.0199721	+	0.0614678i
$411$	−10.3871	+	31.9681i	−0.512357	+	1.57687i
$412$	−0.497135	+	1.53003i	−0.0244921	+	0.0753790i
$413$	−0.0333069	−	0.0241989i	−0.00163892	−	0.00119075i
$414$	−9.61231	−	29.5837i	−0.472419	−	1.45396i
$415$	−8.19936	−	5.95718i	−0.402491	−	0.292427i
$416$	−4.54777	+	3.30415i	−0.222973	+	0.161999i
$417$	−9.63658	+	29.6583i	−0.471905	+	1.45238i
$418$	12.5299	−	9.10350i	0.612857	−	0.445267i
$419$	−18.0894	+	13.1427i	−0.883725	+	0.642064i	−0.934234	−	0.356660i	$-0.883915\pi$
$419$	−18.0894	+	13.1427i	−0.883725	+	0.642064i	0.0505095	+	0.998724i	$0.483915\pi$
$420$	0.0211282	−	0.0650258i	0.00103095	−	0.00317293i
$421$	−10.0705	+	7.31662i	−0.490804	+	0.356590i	−0.805494	−	0.592605i	$-0.798100\pi$
$421$	−10.0705	+	7.31662i	−0.490804	+	0.356590i	0.314689	+	0.949195i	$0.398100\pi$
$422$	8.81623	+	6.40537i	0.429168	+	0.311808i
$423$	4.39552	+	13.5280i	0.213717	+	0.657754i
$424$	−24.9518	−	18.1285i	−1.21177	−	0.880400i
$425$	−3.49230	+	10.7482i	−0.169401	+	0.521364i
$426$	−4.12224	+	12.6869i	−0.199723	+	0.614684i
$427$	0.0154569	+	0.0475714i	0.000748011	+	0.00230214i
$428$	0.627242			0.0303189
$429$	−7.55575			−0.364795
$430$	−6.49388	−	19.9861i	−0.313163	−	0.963816i
$431$	10.6986	−	7.77302i	0.515335	−	0.374413i	−0.299508	−	0.954094i	$-0.596823\pi$
$431$	10.6986	−	7.77302i	0.515335	−	0.374413i	0.814844	+	0.579681i	$0.196823\pi$
$432$	−0.137896	−	0.100188i	−0.00663454	−	0.00482027i
$433$	−1.95364			−0.0938862			−0.0469431	−	0.998898i	$-0.514948\pi$
$433$	−1.95364			−0.0938862			−0.0469431	+	0.998898i	$0.514948\pi$
$434$	0.0310046	+	0.00584789i	0.00148827	+	0.000280708i
$435$	−67.3964			−3.23141
$436$	−2.14874	−	1.56115i	−0.102906	−	0.0747655i
$437$	45.0026	−	32.6963i	2.15277	−	1.56408i
$438$	10.4209	+	32.0723i	0.497931	+	1.53247i
$439$	3.36124			0.160423			0.0802117	−	0.996778i	$-0.474440\pi$
$439$	3.36124			0.160423			0.0802117	+	0.996778i	$0.474440\pi$
$440$	27.5321			1.31254
$441$	−8.29472	−	25.5285i	−0.394987	−	1.21564i
$442$	−0.497127	+	1.53000i	−0.0236459	+	0.0727746i
$443$	−5.46384	+	16.8160i	−0.259595	+	0.798951i	0.733294	+	0.679911i	$0.237982\pi$
$443$	−5.46384	+	16.8160i	−0.259595	+	0.798951i	−0.992889	+	0.119040i	$0.962018\pi$
$444$	18.8660	+	13.7070i	0.895341	+	0.650503i
$445$	9.74284	+	29.9854i	0.461855	+	1.42144i
$446$	15.4522	+	11.2267i	0.731682	+	0.531598i
$447$	−1.73726	+	1.26219i	−0.0821695	+	0.0596996i
$448$	−0.0101532	+	0.0312483i	−0.000479693	+	0.00147634i
$449$	−18.5117	+	13.4496i	−0.873623	+	0.634724i	−0.931557	−	0.363596i	$-0.881549\pi$
$449$	−18.5117	+	13.4496i	−0.873623	+	0.634724i	0.0579335	+	0.998320i	$0.481549\pi$
$450$	17.0309	−	12.3737i	0.802843	−	0.583300i
$451$	−0.394889	+	1.21534i	−0.0185946	+	0.0572283i
$452$	−14.2983	+	10.3884i	−0.672538	+	0.488627i
$453$	−23.0628	−	16.7561i	−1.08359	−	0.787272i
$454$	−1.25071	−	3.84929i	−0.0586987	−	0.180656i
$455$	0.0173637	+	0.0126155i	0.000814023	+	0.000591423i
$456$	13.9337	−	42.8836i	0.652507	−	2.00821i
$457$	−3.54221	+	10.9018i	−0.165698	+	0.509965i	−0.999087	−	0.0427212i	$-0.986397\pi$
$457$	−3.54221	+	10.9018i	−0.165698	+	0.509965i	0.833389	+	0.552686i	$0.186397\pi$
$458$	−3.15235	−	9.70195i	−0.147300	−	0.453342i
$459$	3.97085			0.185343
$460$	37.4376			1.74554
$461$	7.23098	+	22.2547i	0.336780	+	1.03650i	0.965838	+	0.259145i	$0.0834407\pi$
$461$	7.23098	+	22.2547i	0.336780	+	1.03650i	−0.629058	+	0.777358i	$0.716559\pi$
$462$	−0.0346395	+	0.0251670i	−0.00161157	+	0.00117088i
$463$	−25.7055	−	18.6761i	−1.19463	−	0.867953i	−0.200889	−	0.979614i	$-0.564383\pi$
$463$	−25.7055	−	18.6761i	−1.19463	−	0.867953i	−0.993746	+	0.111661i	$0.964383\pi$
$464$	0.601471			0.0279226
$465$	−33.4351	−	35.4573i	−1.55052	−	1.64429i
$466$	15.2170			0.704913
$467$	22.9893	+	16.7027i	1.06382	+	0.772909i	0.974791	−	0.223120i	$-0.0716241\pi$
$467$	22.9893	+	16.7027i	1.06382	+	0.772909i	0.0890274	+	0.996029i	$0.471624\pi$
$468$	−3.78023	+	2.74650i	−0.174741	+	0.126957i
$469$	−0.00378449	−	0.0116475i	−0.000174751	−	0.000537830i
$470$	10.9790			0.506425
$471$	−37.9554			−1.74889
$472$	−5.64667	−	17.3787i	−0.259909	−	0.799917i
$473$	6.34109	−	19.5159i	0.291564	−	0.897340i
$474$	−8.72947	+	26.8666i	−0.400958	+	1.23402i
$475$	30.4559	+	22.1275i	1.39741	+	1.01528i
$476$	−0.00439267	−	0.0135192i	−0.000201338	−	0.000619653i
$477$	−33.6289	−	24.4328i	−1.53976	−	1.11870i
$478$	0.832157	−	0.604597i	0.0380620	−	0.0276536i
$479$	−10.4712	+	32.2270i	−0.478440	+	1.47249i	0.362821	+	0.931859i	$0.381814\pi$
$479$	−10.4712	+	32.2270i	−0.478440	+	1.47249i	−0.841261	+	0.540629i	$0.818186\pi$
$480$	39.8072	−	28.9216i	1.81694	−	1.32008i
$481$	−5.92223	+	4.30275i	−0.270031	+	0.196189i
$482$	−4.31169	+	13.2700i	−0.196392	+	0.604433i
$483$	−0.124412	+	0.0903904i	−0.00566093	+	0.00411290i
$484$	−2.60949	−	1.89590i	−0.118613	−	0.0861774i
$485$	5.21621	+	16.0538i	0.236856	+	0.728968i
$486$	15.5248	+	11.2794i	0.704219	+	0.511645i
$487$	12.8994	−	39.7003i	0.584529	−	1.79899i	−0.0166269	−	0.999862i	$-0.505293\pi$
$487$	12.8994	−	39.7003i	0.584529	−	1.79899i	0.601155	−	0.799132i	$-0.294707\pi$
$488$	−6.86050	+	21.1144i	−0.310560	+	0.955806i
$489$	−5.94403	−	18.2938i	−0.268798	−	0.827276i
$490$	−20.7184			−0.935962
$491$	28.6070			1.29102			0.645509	−	0.763753i	$-0.276645\pi$
$491$	28.6070			1.29102			0.645509	+	0.763753i	$0.276645\pi$
$492$	0.435261	+	1.33960i	0.0196231	+	0.0603936i
$493$	−11.3360	+	8.23611i	−0.510549	+	0.370936i
$494$	4.33538	+	3.14984i	0.195058	+	0.141718i
$495$	37.1064			1.66781
$496$	0.298388	+	0.316434i	0.0133980	+	0.0142083i
$497$	0.0370013			0.00165974
$498$	5.65963	+	4.11196i	0.253614	+	0.184262i
$499$	−9.12185	+	6.62741i	−0.408350	+	0.296684i	−0.772934	−	0.634487i	$-0.781211\pi$
$499$	−9.12185	+	6.62741i	−0.408350	+	0.296684i	0.364583	+	0.931171i	$0.381211\pi$
$500$	1.52563	+	4.69542i	0.0682284	+	0.209986i
$501$	1.15085			0.0514163
$502$	−10.1870			−0.454669
$503$	−12.6243	−	38.8535i	−0.562888	−	1.73239i	−0.674145	−	0.738599i	$-0.735488\pi$
$503$	−12.6243	−	38.8535i	−0.562888	−	1.73239i	0.111257	−	0.993792i	$-0.464512\pi$
$504$	−0.0216122	+	0.0665156i	−0.000962686	+	0.00296284i
$505$	−0.753461	+	2.31891i	−0.0335286	+	0.103190i
$506$	−18.9670	−	13.7804i	−0.843187	−	0.612612i
$507$	−0.807867	−	2.48636i	−0.0358786	−	0.110423i
$508$	11.7198	+	8.51492i	0.519981	+	0.377788i
$509$	22.0918	−	16.0507i	0.979204	−	0.711433i	0.0216733	−	0.999765i	$-0.493101\pi$
$509$	22.0918	−	16.0507i	0.979204	−	0.711433i	0.957531	+	0.288332i	$0.0931006\pi$
$510$	4.35141	−	13.3923i	0.192684	−	0.593019i
$511$	0.0756743	−	0.0549806i	0.00334763	−	0.00243220i
$512$	−0.714872	+	0.519385i	−0.0315932	+	0.0229538i
$513$	4.08743	−	12.5798i	0.180465	−	0.555413i
$514$	1.83275	−	1.33157i	0.0808390	−	0.0587330i
$515$	3.57617	+	2.59824i	0.157585	+	0.114492i
$516$	−6.98937	−	21.5111i	−0.307690	−	0.946972i
$517$	8.67324	+	6.30148i	0.381449	+	0.277139i
$518$	−0.0128188	+	0.0394521i	−0.000563224	+	0.00173342i
$519$	−14.5559	+	44.7985i	−0.638934	+	1.96644i
$520$	2.94375	+	9.05993i	0.129092	+	0.397304i
$521$	−4.04717			−0.177310			−0.0886548	−	0.996062i	$-0.528257\pi$
$521$	−4.04717			−0.177310			−0.0886548	+	0.996062i	$0.528257\pi$
$522$	26.1008			1.14240
$523$	3.02951	+	9.32389i	0.132471	+	0.407705i	0.995188	−	0.0979824i	$-0.0312389\pi$
$523$	3.02951	+	9.32389i	0.132471	+	0.407705i	−0.862717	+	0.505688i	$0.831239\pi$
$524$	13.9752	−	10.1536i	0.610511	−	0.443562i
$525$	−0.0841966	−	0.0611724i	−0.00367464	−	0.00266978i
$526$	−13.3081			−0.580262
$527$	−9.95679	−	1.87799i	−0.433724	−	0.0818065i
$528$	−0.590226			−0.0256863
$529$	−49.5149	−	35.9747i	−2.15282	−	1.56412i
$530$	−25.9567	+	18.8586i	−1.12749	+	0.819166i
$531$	−7.61032	−	23.4222i	−0.330260	−	1.01643i
$532$	−0.0473512			−0.00205293
$533$	−0.442153			−0.0191518
$534$	−6.72503	−	20.6975i	−0.291020	−	0.895668i
$535$	0.532581	−	1.63912i	0.0230255	−	0.0708652i
$536$	1.67974	−	5.16969i	0.0725535	−	0.223297i
$537$	−31.4515	−	22.8508i	−1.35723	−	0.986086i
$538$	6.30931	+	19.4181i	0.272014	+	0.837172i
$539$	−16.3672	−	11.8914i	−0.704983	−	0.512200i
$540$	7.20201	−	5.23257i	0.309925	−	0.225174i
$541$	−1.58155	+	4.86751i	−0.0679962	+	0.209271i	−0.979281	−	0.202506i	$-0.935092\pi$
$541$	−1.58155	+	4.86751i	−0.0679962	+	0.209271i	0.911285	+	0.411776i	$0.135092\pi$
$542$	21.4391	−	15.5764i	0.920889	−	0.669065i
$543$	2.90643	−	2.11165i	0.124727	−	0.0906194i
$544$	3.16120	−	9.72918i	0.135535	−	0.417135i
$545$	−5.90407	+	4.28956i	−0.252903	+	0.183745i
$546$	−0.0119854	−	0.00870787i	−0.000512926	−	0.000372662i
$547$	−7.52176	−	23.1496i	−0.321607	−	0.989805i	−0.972949	−	0.231021i	$-0.925793\pi$
$547$	−7.52176	−	23.1496i	−0.321607	−	0.989805i	0.651342	−	0.758785i	$-0.274207\pi$
$548$	12.6750	+	9.20893i	0.541449	+	0.393386i
$549$	−9.24626	+	28.4571i	−0.394621	+	1.21452i
$550$	4.90295	−	15.0897i	0.209063	−	0.643429i
$551$	14.4235	+	44.3910i	0.614462	+	1.89112i
$552$	−68.2554			−2.90514
$553$	0.0783560			0.00333204
$554$	2.70303	+	8.31908i	0.114841	+	0.353444i
$555$	51.8380	−	37.6625i	2.20040	−	1.59868i
$556$	11.7592	+	8.54355i	0.498701	+	0.362327i
$557$	−2.28902			−0.0969889			−0.0484944	−	0.998823i	$-0.515442\pi$
$557$	−2.28902			−0.0969889			−0.0484944	+	0.998823i	$0.515442\pi$
$558$	12.9485	+	13.7316i	0.548154	+	0.581307i
$559$	7.10005			0.300300
$560$	0.00135639		0.000985472i	5.73178e−5		4.16438e-5i
$561$	11.1241	−	8.08213i	0.469660	−	0.341228i
$562$	−2.91489	−	8.97110i	−0.122957	−	0.378423i
$563$	−10.3537			−0.436358			−0.218179	−	0.975909i	$-0.570012\pi$
$563$	−10.3537			−0.436358			−0.218179	+	0.975909i	$0.570012\pi$
$564$	11.8168			0.497575
$565$	15.0065	+	46.1852i	0.631327	+	1.94302i
$566$	−4.21408	+	12.9696i	−0.177131	+	0.545153i
$567$	0.0114882	−	0.0353570i	0.000482458	−	0.00148485i
$568$	13.2864	+	9.65316i	0.557486	+	0.405037i
$569$	2.25000	+	6.92478i	0.0943248	+	0.290302i	0.987077	−	0.160246i	$-0.0512287\pi$
$569$	2.25000	+	6.92478i	0.0943248	+	0.290302i	−0.892752	+	0.450548i	$0.851229\pi$
$570$	−37.9481	−	27.5709i	−1.58947	−	1.15482i
$571$	7.50141	−	5.45009i	0.313924	−	0.228079i	−0.419654	−	0.907684i	$-0.637849\pi$
$571$	7.50141	−	5.45009i	0.313924	−	0.228079i	0.733579	+	0.679605i	$0.237849\pi$
$572$	−1.08828	+	3.34937i	−0.0455031	+	0.140044i
$573$	−9.71203	+	7.05620i	−0.405726	+	0.294777i
$574$	−0.00202706	+	0.00147274i	−8.46077e−5	+	6.14711e-5i
$575$	17.6095	−	54.1966i	0.734368	−	2.26015i
$576$	−15.9009	+	11.5527i	−0.662538	+	0.481362i
$577$	−22.2064	−	16.1339i	−0.924466	−	0.671664i	0.0201656	−	0.999797i	$-0.493581\pi$
$577$	−22.2064	−	16.1339i	−0.924466	−	0.671664i	−0.944632	+	0.328133i	$0.893581\pi$
$578$	3.73926	+	11.5083i	0.155533	+	0.478680i
$579$	4.15097	+	3.01585i	0.172508	+	0.125335i
$580$	−9.70730	+	29.8760i	−0.403074	+	1.24053i
$581$	0.00599625	−	0.0184546i	0.000248766	−	0.000765624i
$582$	−3.60051	−	11.0812i	−0.149246	−	0.459331i
$583$	−31.3293			−1.29753
$584$	41.5168			1.71798
$585$	3.96745	+	12.2106i	0.164034	+	0.504844i
$586$	−17.0018	+	12.3525i	−0.702338	+	0.510278i
$587$	−0.486055	−	0.353140i	−0.0200617	−	0.0145756i	0.577709	−	0.816243i	$-0.303947\pi$
$587$	−0.486055	−	0.353140i	−0.0200617	−	0.0145756i	−0.597771	+	0.801667i	$0.703947\pi$
$588$	−22.2992			−0.919605
$589$	−16.1987	+	29.6104i	−0.667454	+	1.22008i
$590$	−19.0089			−0.782584
$591$	50.9266	+	37.0004i	2.09484	+	1.52199i
$592$	−0.462622	+	0.336114i	−0.0190136	+	0.0138142i
$593$	−1.71026	−	5.26362i	−0.0702318	−	0.216151i	0.909780	−	0.415091i	$-0.136250\pi$
$593$	−1.71026	−	5.26362i	−0.0702318	−	0.216151i	−0.980012	+	0.198940i	$0.936250\pi$
$594$	−5.57481			−0.228737
$595$	−0.0390584			−0.00160124
$596$	0.309292	+	0.951902i	0.0126691	+	0.0389914i
$597$	2.60605	−	8.02061i	0.106659	−	0.328262i
$598$	2.50671	−	7.71486i	0.102507	−	0.315484i
$599$	−5.78814	−	4.20533i	−0.236497	−	0.171825i	0.463224	−	0.886241i	$-0.346692\pi$
$599$	−5.78814	−	4.20533i	−0.236497	−	0.171825i	−0.699721	+	0.714416i	$0.746692\pi$
$600$	−14.2742	−	43.9316i	−0.582743	−	1.79350i
$601$	−22.6726	−	16.4726i	−0.924834	−	0.671931i	0.0198884	−	0.999802i	$-0.493669\pi$
$601$	−22.6726	−	16.4726i	−0.924834	−	0.671931i	−0.944723	+	0.327871i	$0.893669\pi$
$602$	0.0325503	−	0.0236491i	0.00132665	−	0.000963867i
$603$	2.26387	−	6.96747i	0.0921919	−	0.283737i
$604$	−10.7496	+	7.81004i	−0.437395	+	0.317786i
$605$	−7.17007	+	5.20936i	−0.291505	+	0.211791i
$606$	0.520078	−	1.60064i	0.0211267	−	0.0650214i
$607$	6.83370	−	4.96497i	0.277371	−	0.201522i	−0.440399	−	0.897802i	$-0.645163\pi$
$607$	6.83370	−	4.96497i	0.277371	−	0.201522i	0.717770	+	0.696280i	$0.245163\pi$
$608$	−27.5685	−	20.0297i	−1.11805	−	0.812310i
$609$	−0.0398744	−	0.122721i	−0.00161579	−	0.00497290i
$610$	18.6844	+	13.5750i	0.756508	+	0.549635i
$611$	−1.14627	+	3.52785i	−0.0463730	+	0.142721i
$612$	2.62768	−	8.08717i	0.106218	−	0.326904i
$613$	2.34712	+	7.22368i	0.0947991	+	0.291762i	0.987201	−	0.159479i	$-0.0509815\pi$
$613$	2.34712	+	7.22368i	0.0947991	+	0.291762i	−0.892402	+	0.451241i	$0.850982\pi$
$614$	9.53146			0.384658
$615$	3.87022			0.156062
$616$	0.0162891	+	0.0501326i	0.000656305	+	0.00201990i
$617$	24.0020	−	17.4385i	0.966286	−	0.702048i	0.0116836	−	0.999932i	$-0.496281\pi$
$617$	24.0020	−	17.4385i	0.966286	−	0.702048i	0.954602	+	0.297884i	$0.0962809\pi$
$618$	−2.46846	−	1.79344i	−0.0992961	−	0.0721428i
$619$	1.59733			0.0642020			0.0321010	−	0.999485i	$-0.489780\pi$
$619$	1.59733			0.0642020			0.0321010	+	0.999485i	$0.489780\pi$
$620$	−20.5335	+	9.71436i	−0.824647	+	0.390138i
$621$	−20.0226			−0.803479
$622$	−0.467123	−	0.339385i	−0.0187299	−	0.0136081i
$623$	−0.0488355	+	0.0354811i	−0.00195655	+	0.00142152i
$624$	−0.0631075	−	0.194225i	−0.00252632	−	0.00777521i
$625$	−17.4851			−0.699402
$626$	24.9775			0.998303
$627$	−14.1538	−	43.5610i	−0.565250	−	1.73966i
$628$	−5.46682	+	16.8251i	−0.218150	+	0.671396i
$629$	4.11661	−	12.6696i	0.164140	−	0.505171i
$630$	0.0588603	+	0.0427645i	0.00234505	+	0.00170378i
$631$	−11.9469	−	36.7689i	−0.475600	−	1.46375i	−0.845147	−	0.534534i	$-0.820487\pi$
$631$	−11.9469	−	36.7689i	−0.475600	−	1.46375i	0.369547	−	0.929212i	$-0.379513\pi$
$632$	28.1361	+	20.4420i	1.11919	+	0.813141i
$633$	26.0726	−	18.9429i	1.03629	−	0.752912i
$634$	−1.27942	+	3.93764i	−0.0508122	+	0.156384i
$635$	32.2023	−	23.3964i	1.27791	−	0.928457i
$636$	−27.9372	+	20.2976i	−1.10778	+	0.804851i
$637$	2.16311	−	6.65736i	0.0857054	−	0.263774i
$638$	15.9150	−	11.5630i	0.630082	−	0.457782i
$639$	17.9068	+	13.0101i	0.708384	+	0.514671i
$640$	−6.94415	−	21.3719i	−0.274492	−	0.844798i
$641$	19.9728	+	14.5111i	0.788876	+	0.573152i	0.907630	−	0.419772i	$-0.137890\pi$
$641$	19.9728	+	14.5111i	0.788876	+	0.573152i	−0.118753	+	0.992924i	$0.537890\pi$
$642$	−0.367616	+	1.13140i	−0.0145086	+	0.0446530i
$643$	6.07305	−	18.6909i	0.239498	−	0.737099i	−0.756995	−	0.653421i	$-0.773333\pi$
$643$	6.07305	−	18.6909i	0.239498	−	0.737099i	0.996493	−	0.0836779i	$-0.0266667\pi$
$644$	0.0221496	+	0.0681693i	0.000872815	+	0.00268625i
$645$	−62.1475			−2.44706
$646$	−9.75212			−0.383692
$647$	5.03816	+	15.5059i	0.198070	+	0.609598i	0.999927	+	0.0120815i	$0.00384575\pi$
$647$	5.03816	+	15.5059i	0.198070	+	0.609598i	−0.801857	+	0.597516i	$0.796154\pi$
$648$	13.3493	−	9.69887i	0.524412	−	0.381008i
$649$	−15.0167	−	10.9103i	−0.589457	−	0.428265i
$650$	5.48978			0.215327
$651$	0.0447819	−	0.0818593i	0.00175514	−	0.00320832i
$652$	−8.96557			−0.351119
$653$	35.8871	+	26.0735i	1.40437	+	1.02033i	0.994111	+	0.108366i	$0.0345617\pi$
$653$	35.8871	+	26.0735i	1.40437	+	1.02033i	0.410259	+	0.911969i	$0.365438\pi$
$654$	4.07530	−	2.96088i	0.159357	−	0.115780i
$655$	−14.6674	−	45.1415i	−0.573101	−	1.76382i
$656$	−0.0345393			−0.00134853
$657$	55.9545			2.18299
$658$	0.00649563	+	0.0199915i	0.000253226	+	0.000779350i
$659$	−3.88433	+	11.9547i	−0.151312	+	0.465690i	−0.997769	−	0.0667673i	$-0.978731\pi$
$659$	−3.88433	+	11.9547i	−0.151312	+	0.465690i	0.846457	+	0.532458i	$0.178731\pi$
$660$	9.52581	−	29.3174i	0.370792	−	1.14118i
$661$	25.3443	+	18.4137i	0.985777	+	0.716209i	0.958992	−	0.283432i	$-0.0914731\pi$
$661$	25.3443	+	18.4137i	0.985777	+	0.716209i	0.0267849	+	0.999641i	$0.491473\pi$
$662$	−5.56369	−	17.1233i	−0.216239	−	0.665515i
$663$	3.84897	+	2.79644i	0.149482	+	0.108605i
$664$	6.96768	−	5.06232i	0.270399	−	0.196456i
$665$	−0.0402051	+	0.123739i	−0.00155909	+	0.00479838i
$666$	−20.0754	+	14.5857i	−0.777908	+	0.565183i
$667$	57.1607	−	41.5297i	2.21327	−	1.60804i
$668$	0.165761	−	0.510159i	0.00641347	−	0.0197386i
$669$	45.6974	−	33.2011i	1.76676	−	1.28363i
$670$	−4.57471	−	3.32372i	−0.176736	−	0.128406i
$671$	6.96887	+	21.4480i	0.269030	+	0.827990i
$672$	0.0762142	+	0.0553729i	0.00294003	+	0.00213606i
$673$	7.79446	−	23.9889i	0.300455	−	0.924704i	−0.680880	−	0.732395i	$-0.738402\pi$
$673$	7.79446	−	23.9889i	0.300455	−	0.924704i	0.981334	−	0.192309i	$-0.0615976\pi$
$674$	−7.93618	+	24.4250i	−0.305690	+	0.940817i
$675$	−4.18732	−	12.8872i	−0.161170	−	0.496030i
$676$	−1.21853			−0.0468666
$677$	−9.25425			−0.355670			−0.177835	−	0.984060i	$-0.556909\pi$
$677$	−9.25425			−0.355670			−0.177835	+	0.984060i	$0.556909\pi$
$678$	−10.3583	−	31.8795i	−0.397807	−	1.22432i
$679$	−0.0261460	+	0.0189962i	−0.00100339	+	0.000729007i
$680$	−14.0251	−	10.1898i	−0.537837	−	0.390762i
$681$	−11.9695			−0.458672
$682$	13.9787	+	2.63657i	0.535271	+	0.100960i
$683$	−33.5007			−1.28187			−0.640935	−	0.767596i	$-0.721453\pi$
$683$	−33.5007			−1.28187			−0.640935	+	0.767596i	$0.721453\pi$
$684$	−22.9157	−	16.6492i	−0.876203	−	0.636598i
$685$	34.8270	−	25.3033i	1.33067	−	0.966789i
$686$	−0.0245157	−	0.0754516i	−0.000936015	−	0.00288076i
$687$	−30.1686			−1.15100
$688$	0.554628			0.0211450
$689$	−3.34976	−	10.3095i	−0.127616	−	0.392760i
$690$	−21.9415	+	67.5290i	−0.835299	+	2.57079i
$691$	−8.48100	+	26.1018i	−0.322633	+	0.992961i	0.649865	+	0.760049i	$0.274825\pi$
$691$	−8.48100	+	26.1018i	−0.322633	+	0.992961i	−0.972498	+	0.232912i	$0.925175\pi$
$692$	17.7621	+	12.9049i	0.675214	+	0.490572i
$693$	0.0219536	+	0.0675663i	0.000833950	+	0.00256663i
$694$	−21.8867	−	15.9016i	−0.830809	−	0.603618i
$695$	32.3106	−	23.4751i	1.22561	−	0.890460i
$696$	17.6981	−	54.4693i	0.670846	−	2.06465i
$697$	0.650968	−	0.472956i	0.0246572	−	0.0179145i
$698$	−9.85231	+	7.15812i	−0.372915	+	0.270939i
$699$	13.9063	−	42.7993i	0.525986	−	1.61882i
$700$	−0.0392441	+	0.0285125i	−0.00148329	+	0.00107767i
$701$	17.3909	+	12.6352i	0.656845	+	0.477226i	0.865596	−	0.500743i	$-0.166940\pi$
$701$	17.3909	+	12.6352i	0.656845	+	0.477226i	−0.208751	+	0.977969i	$0.566940\pi$
$702$	−0.596063	−	1.83449i	−0.0224970	−	0.0692385i
$703$	−35.9004	−	26.0832i	−1.35401	−	0.983746i
$704$	−4.57765	+	14.0886i	−0.172527	+	0.530983i
$705$	10.0334	−	30.8797i	0.377880	−	1.16300i
$706$	−9.68628	−	29.8113i	−0.364548	−	1.12196i
$707$	−0.00466824			−0.000175567
$708$	−20.4593			−0.768908
$709$	−5.44664	−	16.7630i	−0.204553	−	0.629548i	−0.999731	−	0.0231734i	$-0.992623\pi$
$709$	−5.44664	−	16.7630i	−0.204553	−	0.629548i	0.795179	−	0.606375i	$-0.207377\pi$
$710$	13.8215	−	10.0419i	0.518712	−	0.376866i
$711$	37.9205	+	27.5509i	1.42213	+	1.03324i
$712$	−26.7924			−1.00409
$713$	50.2060	+	9.46956i	1.88023	+	0.354638i
$714$	0.0269602			0.00100896
$715$	7.82858	+	5.68779i	0.292772	+	0.212711i
$716$	−14.6595	+	10.6508i	−0.547853	+	0.398038i
$717$	−0.940009	−	2.89305i	−0.0351053	−	0.108043i
$718$	−12.9052			−0.481617
$719$	−31.2934			−1.16705			−0.583524	−	0.812096i	$-0.698327\pi$
$719$	−31.2934			−1.16705			−0.583524	+	0.812096i	$0.698327\pi$
$720$	0.309922	+	0.953841i	0.0115501	+	0.0355476i
$721$	−0.00261528	+	0.00804900i	−9.73980e−5	+	0.000299760i
$722$	−4.84814	+	14.9211i	−0.180429	+	0.555304i
$723$	33.3830	+	24.2542i	1.24153	+	0.902022i
$724$	−0.517445	−	1.59253i	−0.0192307	−	0.0591860i
$725$	38.6840	+	28.1056i	1.43669	+	1.04381i
$726$	4.94916	−	3.59578i	0.183681	−	0.133452i
$727$	−1.84610	+	5.68172i	−0.0684681	+	0.210723i	−0.979436	−	0.201753i	$-0.935336\pi$
$727$	−1.84610	+	5.68172i	−0.0684681	+	0.210723i	0.910968	+	0.412476i	$0.135336\pi$
$728$	−0.0147554	+	0.0107204i	−0.000546872	+	0.000397325i
$729$	31.8366	−	23.1306i	1.17913	−	0.856690i
$730$	13.3461	−	41.0750i	0.493960	−	1.52025i
$731$	−10.4532	+	7.59468i	−0.386625	+	0.280899i
$732$	20.1100	+	14.6108i	0.743287	+	0.540030i
$733$	10.1404	+	31.2091i	0.374546	+	1.15273i	0.943785	+	0.330561i	$0.107238\pi$
$733$	10.1404	+	31.2091i	0.374546	+	1.15273i	−0.569239	+	0.822172i	$0.692762\pi$
$734$	−0.0860825	−	0.0625426i	−0.00317736	−	0.00230849i
$735$	−18.9339	+	58.2726i	−0.698388	+	2.14942i
$736$	−15.9400	+	49.0584i	−0.587557	+	1.80832i
$737$	−1.70627	−	5.25136i	−0.0628512	−	0.193436i
$738$	−1.49883			−0.0551727
$739$	−47.4783			−1.74652			−0.873258	−	0.487258i	$-0.837997\pi$
$739$	−47.4783			−1.74652			−0.873258	+	0.487258i	$0.837997\pi$
$740$	−9.22895	−	28.4038i	−0.339263	−	1.04414i
$741$	12.8212	−	9.31516i	0.470999	−	0.342201i
$742$	−0.0496963	−	0.0361065i	−0.00182441	−	0.00132551i
$743$	24.4392			0.896587			0.448293	−	0.893887i	$-0.352032\pi$
$743$	24.4392			0.896587			0.448293	+	0.893887i	$0.352032\pi$
$744$	37.4363	−	17.7110i	1.37248	−	0.649317i
$745$	2.75013			0.100757
$746$	−19.3098	−	14.0294i	−0.706981	−	0.513652i
$747$	9.39072	−	6.82276i	0.343589	−	0.249632i
$748$	−1.98047	−	6.09527i	−0.0724132	−	0.222865i
$749$	0.00329973			0.000120569
$750$	−9.36363			−0.341912
$751$	8.25690	+	25.4121i	0.301299	+	0.927302i	0.981033	+	0.193843i	$0.0620953\pi$
$751$	8.25690	+	25.4121i	0.301299	+	0.927302i	−0.679734	+	0.733459i	$0.737905\pi$
$752$	−0.0895420	+	0.275582i	−0.00326526	+	0.0100494i
$753$	−9.30960	+	28.6520i	−0.339261	+	1.04414i
$754$	5.50665	+	4.00082i	0.200540	+	0.145701i
$755$	11.2820	+	34.7223i	0.410593	+	1.26367i
$756$	0.0137889	+	0.0100182i	0.000501496	+	0.000364358i
$757$	−11.5485	+	8.39049i	−0.419738	+	0.304957i	−0.777532	−	0.628843i	$-0.783529\pi$
$757$	−11.5485	+	8.39049i	−0.419738	+	0.304957i	0.357795	+	0.933800i	$0.383529\pi$
$758$	−8.03930	+	24.7424i	−0.292000	+	0.898685i
$759$	−56.0921	+	40.7533i	−2.03601	+	1.47925i
$760$	−46.7186	+	33.9431i	−1.69466	+	1.23124i
$761$	9.65727	−	29.7220i	0.350076	−	1.07742i	−0.608734	−	0.793374i	$-0.708322\pi$
$761$	9.65727	−	29.7220i	0.350076	−	1.07742i	0.958810	−	0.284048i	$-0.0916777\pi$
$762$	−22.2278	+	16.1494i	−0.805227	+	0.585032i
$763$	−0.0113039	−	0.00821273i	−0.000409227	−	0.000297321i
$764$	1.72908	+	5.32155i	0.0625557	+	0.192527i
$765$	−18.9024	−	13.7334i	−0.683416	−	0.496531i
$766$	5.08055	−	15.6363i	0.183568	−	0.564964i
$767$	1.98463	−	6.10805i	0.0716607	−	0.220549i
$768$	13.0747	+	40.2399i	0.471794	+	1.45203i
$769$	−18.8352			−0.679214			−0.339607	−	0.940567i	$-0.610294\pi$
$769$	−18.8352			−0.679214			−0.339607	+	0.940567i	$0.610294\pi$
$770$	0.0548354			0.00197613
$771$	−2.07028	−	6.37167i	−0.0745594	−	0.229470i
$772$	1.93477	−	1.40569i	0.0696337	−	0.0505919i
$773$	−15.3018	−	11.1174i	−0.550368	−	0.399866i	0.277553	−	0.960710i	$-0.410477\pi$
$773$	−15.3018	−	11.1174i	−0.550368	−	0.399866i	−0.827921	+	0.560845i	$0.810477\pi$
$774$	24.0681			0.865108
$775$	4.40463	+	34.2948i	0.158219	+	1.23190i
$776$	−14.3444			−0.514933
$777$	0.0992483	+	0.0721081i	0.00356051	+	0.00258686i
$778$	−17.2397	+	12.5254i	−0.618072	+	0.449056i
$779$	−0.828265	−	2.54914i	−0.0296757	−	0.0913323i
$780$	10.6660			0.381902
$781$	16.6824			0.596942
$782$	4.56177	+	14.0397i	0.163128	+	0.502058i
$783$	5.19172	−	15.9785i	0.185537	−	0.571023i
$784$	0.168973	−	0.520047i	0.00603477	−	0.0185731i
$785$	39.3258	+	28.5719i	1.40360	+	1.01977i
$786$	10.1242	+	31.1591i	0.361118	+	1.11141i
$787$	−19.9834	−	14.5188i	−0.712331	−	0.517539i	0.171594	−	0.985168i	$-0.445108\pi$
$787$	−19.9834	−	14.5188i	−0.712331	−	0.517539i	−0.883925	+	0.467629i	$0.845108\pi$
$788$	23.7369	−	17.2459i	0.845592	−	0.614359i
$789$	−12.1619	+	37.4305i	−0.432975	+	1.33256i
$790$	29.2692	−	21.2653i	1.04135	−	0.756586i
$791$	−0.0752192	+	0.0546500i	−0.00267449	+	0.00194313i
$792$	−9.74406	+	29.9891i	−0.346240	+	1.06562i
$793$	−6.31273	+	4.58647i	−0.224172	+	0.162870i
$794$	21.7380	+	15.7935i	0.771451	+	0.560492i
$795$	29.3208	+	90.2401i	1.03990	+	3.20049i
$796$	−3.18008	−	2.31046i	−0.112715	−	0.0818922i
$797$	14.6093	−	44.9627i	0.517487	−	1.59266i	−0.261223	−	0.965278i	$-0.584126\pi$
$797$	14.6093	−	44.9627i	0.517487	−	1.59266i	0.778710	−	0.627383i	$-0.215874\pi$
$798$	0.0277517	−	0.0854109i	0.000982399	−	0.00302351i
$799$	−2.08600	−	6.42006i	−0.0737975	−	0.227125i
$800$	−34.9092			−1.23423
$801$	−36.1096			−1.27587
$802$	−4.62868	−	14.2456i	−0.163444	−	0.503030i
$803$	34.1184	−	24.7885i	1.20401	−	0.874766i
$804$	−4.92376	−	3.57732i	−0.173648	−	0.126162i
$805$	0.196948			0.00694149
$806$	0.626998	+	4.88184i	0.0220851	+	0.171956i
$807$	60.3812			2.12552
$808$	−1.67627	−	1.21788i	−0.0589710	−	0.0428450i
$809$	−13.3087	+	9.66931i	−0.467908	+	0.339955i	−0.796625	−	0.604473i	$-0.793384\pi$
$809$	−13.3087	+	9.66931i	−0.467908	+	0.339955i	0.328718	+	0.944428i	$0.393384\pi$
$810$	−5.30435	−	16.3251i	−0.186376	−	0.573606i
$811$	6.25567			0.219666			0.109833	−	0.993950i	$-0.464968\pi$
$811$	6.25567			0.219666			0.109833	+	0.993950i	$0.464968\pi$
$812$	−0.0601438			−0.00211063
$813$	−24.2177	−	74.5345i	−0.849353	−	2.61404i
$814$	−5.77944	+	17.7873i	−0.202569	+	0.623444i
$815$	−7.61252	+	23.4289i	−0.266655	+	0.820680i
$816$	0.300667	+	0.218447i	0.0105254	+	0.00764718i
$817$	13.3002	+	40.9338i	0.465315	+	1.43209i
$818$	19.3207	+	14.0373i	0.675533	+	0.490803i
$819$	−0.0198866	+	0.0144485i	−0.000694896	+	0.000504871i
$820$	0.557439	−	1.71562i	0.0194666	−	0.0599120i
$821$	−18.2192	+	13.2370i	−0.635853	+	0.461975i	−0.858423	−	0.512942i	$-0.828555\pi$
$821$	−18.2192	+	13.2370i	−0.635853	+	0.461975i	0.222570	+	0.974917i	$0.428555\pi$
$822$	−24.0394	+	17.4657i	−0.838472	+	0.609185i
$823$	−3.08713	+	9.50122i	−0.107611	+	0.331192i	−0.990334	−	0.138701i	$-0.955707\pi$
$823$	−3.08713	+	9.50122i	−0.107611	+	0.331192i	0.882724	+	0.469893i	$0.155707\pi$
$824$	−3.03897	+	2.20794i	−0.105868	+	0.0769173i
$825$	−37.9608	−	27.5801i	−1.32162	−	0.960216i
$826$	−0.0112464	−	0.0346129i	−0.000391313	−	0.00120434i
$827$	−20.5285	−	14.9148i	−0.713846	−	0.518639i	0.170566	−	0.985346i	$-0.445440\pi$
$827$	−20.5285	−	14.9148i	−0.713846	−	0.518639i	−0.884412	+	0.466707i	$0.845440\pi$
$828$	−13.2498	+	40.7787i	−0.460462	+	1.41716i
$829$	2.25620	−	6.94387i	0.0783611	−	0.241171i	−0.904200	−	0.427108i	$-0.859532\pi$
$829$	2.25620	−	6.94387i	0.0783611	−	0.241171i	0.982562	+	0.185938i	$0.0595323\pi$
$830$	−2.76860	−	8.52088i	−0.0960995	−	0.295764i
$831$	25.8685			0.897368
$832$	−5.12555			−0.177696
$833$	3.93647	+	12.1152i	0.136391	+	0.419767i
$834$	−22.3025	+	16.2037i	−0.772273	+	0.561089i
$835$	−1.19241	−	0.866335i	−0.0412650	−	0.0299808i
$836$	−21.3487			−0.738360
$837$	10.9819	−	5.19549i	0.379589	−	0.179582i
$838$	−19.7661			−0.682810
$839$	12.1691	+	8.84140i	0.420126	+	0.305239i	0.777688	−	0.628650i	$-0.216392\pi$
$839$	12.1691	+	8.84140i	0.420126	+	0.305239i	−0.357563	+	0.933889i	$0.616392\pi$
$840$	0.129156	−	0.0938371i	0.00445630	−	0.00323769i
$841$	9.35873	+	28.8032i	0.322715	+	0.993215i
$842$	−11.0039			−0.379220
$843$	−27.8960			−0.960788
$844$	−4.64183	−	14.2861i	−0.159778	−	0.491747i
$845$	−1.03464	+	3.18428i	−0.0355925	+	0.109543i
$846$	−3.88567	+	11.9589i	−0.133592	+	0.411154i
$847$	−0.0137277	−	0.00997376i	−0.000471690	−	0.000342703i
$848$	−0.261670	−	0.805337i	−0.00898578	−	0.0276554i
$849$	32.6272	+	23.7051i	1.11976	+	0.813556i
$850$	−8.08243	+	5.87223i	−0.277225	+	0.201416i
$851$	−20.7576	+	63.8852i	−0.711560	+	2.18996i
$852$	14.8761	−	10.8081i	0.509647	−	0.370280i
$853$	12.4578	−	9.05114i	0.426548	−	0.309905i	−0.353719	−	0.935352i	$-0.615083\pi$
$853$	12.4578	−	9.05114i	0.426548	−	0.309905i	0.780267	+	0.625447i	$0.215083\pi$
$854$	−0.0136640	+	0.0420535i	−0.000467572	+	0.00143904i
$855$	−62.9652	+	45.7469i	−2.15336	+	1.56451i
$856$	1.18487	+	0.860856i	0.0404979	+	0.0294235i
$857$	4.25236	+	13.0874i	0.145258	+	0.447057i	0.997044	−	0.0768320i	$-0.0244805\pi$
$857$	4.25236	+	13.0874i	0.145258	+	0.447057i	−0.851786	+	0.523889i	$0.824481\pi$
$858$	−5.40370	−	3.92602i	−0.184479	−	0.134032i
$859$	−15.6436	+	48.1461i	−0.533753	+	1.64272i	0.212576	+	0.977145i	$0.431815\pi$
$859$	−15.6436	+	48.1461i	−0.533753	+	1.64272i	−0.746329	+	0.665578i	$0.768185\pi$
$860$	−8.95129	+	27.5492i	−0.305236	+	0.939421i
$861$	0.00228977	+	0.00704720i	7.80353e−5	+	0.000240168i
$862$	11.6903			0.398174
$863$	−30.1360			−1.02584			−0.512920	−	0.858436i	$-0.671436\pi$
$863$	−30.1360			−1.02584			−0.512920	+	0.858436i	$0.671436\pi$
$864$	3.79033	+	11.6654i	0.128950	+	0.396867i
$865$	48.8048	−	35.4588i	1.65941	−	1.20563i
$866$	−1.39720	−	1.01513i	−0.0474788	−	0.0344954i
$867$	35.7854			1.21533
$868$	−0.0298371	−	0.0316417i	−0.00101274	−	0.00107399i
$869$	35.3275			1.19840
$870$	−48.2003	−	35.0196i	−1.63414	−	1.18728i
$871$	1.54562	−	1.12296i	0.0523713	−	0.0380500i
$872$	−1.91639	−	5.89805i	−0.0648973	−	0.199733i
$873$	−19.3327			−0.654312
$874$	49.1740			1.66334
$875$	0.00802589	+	0.0247012i	0.000271325	+	0.000835052i
$876$	14.3644	−	44.2091i	0.485328	−	1.49369i
$877$	11.2301	−	34.5625i	0.379212	−	1.16709i	−0.561381	−	0.827558i	$-0.689730\pi$
$877$	11.2301	−	34.5625i	0.379212	−	1.16709i	0.940593	−	0.339537i	$-0.110270\pi$
$878$	2.40388	+	1.74652i	0.0811271	+	0.0589423i
$879$	19.2053	+	59.1079i	0.647779	+	1.99366i
$880$	0.611538	+	0.444308i	0.0206149	+	0.0149776i
$881$	−9.56685	+	6.95073i	−0.322316	+	0.234176i	−0.737163	−	0.675715i	$-0.763835\pi$
$881$	−9.56685	+	6.95073i	−0.322316	+	0.234176i	0.414847	+	0.909891i	$0.363835\pi$
$882$	7.33259	−	22.5674i	0.246901	−	0.759884i
$883$	12.9798	−	9.43039i	0.436806	−	0.317358i	−0.347559	−	0.937658i	$-0.612989\pi$
$883$	12.9798	−	9.43039i	0.436806	−	0.317358i	0.784364	+	0.620300i	$0.212989\pi$
$884$	1.79401	−	1.30342i	0.0603389	−	0.0438388i
$885$	−17.3717	+	53.4645i	−0.583942	+	1.79719i
$886$	−12.6453	+	9.18735i	−0.424827	+	0.308655i
$887$	−43.4067	−	31.5368i	−1.45745	−	1.05890i	−0.984017	−	0.178074i	$-0.943013\pi$
$887$	−43.4067	−	31.5368i	−1.45745	−	1.05890i	−0.473437	−	0.880828i	$-0.656987\pi$
$888$	16.8260	+	51.7852i	0.564644	+	1.73780i
$889$	0.0616542	+	0.0447944i	0.00206781	+	0.00150235i
$890$	−8.61274	+	26.5073i	−0.288700	+	0.888526i
$891$	5.17954	−	15.9410i	0.173521	−	0.534044i
$892$	−8.13571	−	25.0391i	−0.272404	−	0.838373i
$893$	−22.4863			−0.752475
$894$	−1.89829			−0.0634883
$895$	15.3855	+	47.3519i	0.514282	+	1.58280i
$896$	0.0348072	−	0.0252889i	0.00116283	−	0.000844844i
$897$	−19.4080	−	14.1008i	−0.648015	−	0.470810i
$898$	−20.2276			−0.675005
$899$	−20.5750	+	37.6101i	−0.686214	+	1.25437i
$900$	−29.0175			−0.967251
$901$	15.9594	+	11.5952i	0.531686	+	0.386292i
$902$	−0.913916	+	0.663999i	−0.0304301	+	0.0221087i
$903$	−0.0367689	−	0.113163i	−0.00122359	−	0.00376584i
$904$	−41.2672			−1.37253
$905$	−4.60098			−0.152942
$906$	−7.78741	−	23.9672i	−0.258719	−	0.796256i
$907$	−8.71514	+	26.8224i	−0.289382	+	0.890625i	0.695670	+	0.718362i	$0.255108\pi$
$907$	−8.71514	+	26.8224i	−0.289382	+	0.890625i	−0.985051	+	0.172263i	$0.944892\pi$
$908$	−1.72400	+	5.30593i	−0.0572130	+	0.176084i
$909$	−2.25920	−	1.64141i	−0.0749330	−	0.0544420i
$910$	0.00586304	+	0.0180446i	0.000194358	+	0.000598172i
$911$	40.0177	+	29.0745i	1.32584	+	0.963283i	0.999840	+	0.0179147i	$0.00570273\pi$
$911$	40.0177	+	29.0745i	1.32584	+	0.963283i	0.326005	+	0.945368i	$0.394297\pi$
$912$	1.00154	−	0.727664i	0.0331644	−	0.0240954i
$913$	2.70346	−	8.32039i	0.0894715	−	0.275365i
$914$	−8.19796	+	5.95616i	−0.271164	+	0.197012i
$915$	55.2561	−	40.1459i	1.82671	−	1.32718i
$916$	−4.34526	+	13.3733i	−0.143572	+	0.441868i
$917$	0.0735194	−	0.0534150i	0.00242783	−	0.00176392i
$918$	2.83986	+	2.06328i	0.0937293	+	0.0680983i
$919$	−14.9896	−	46.1332i	−0.494461	−	1.52179i	−0.817795	−	0.575510i	$-0.804804\pi$
$919$	−14.9896	−	46.1332i	−0.494461	−	1.52179i	0.323334	−	0.946285i	$-0.395196\pi$
$920$	70.7200	+	51.3811i	2.33157	+	1.69398i
$921$	8.71051	−	26.8082i	0.287021	−	0.883360i
$922$	−6.39223	+	19.6733i	−0.210517	+	0.647905i
$923$	1.78369	+	5.48964i	0.0587109	+	0.180694i
$924$	0.0590194			0.00194160
$925$	−45.4598			−1.49471
$926$	−8.67973	−	26.7135i	−0.285234	−	0.877858i
$927$	−4.09578	+	2.97576i	−0.134523	+	0.0977368i
$928$	−35.0165	−	25.4410i	−1.14947	−	0.835141i
$929$	28.3718			0.930848			0.465424	−	0.885088i	$-0.345902\pi$
$929$	28.3718			0.930848			0.465424	+	0.885088i	$0.345902\pi$
$930$	−5.48818	−	42.7313i	−0.179965	−	1.40122i
$931$	42.4336			1.39070
$932$	−16.9694	−	12.3290i	−0.555853	−	0.403851i
$933$	−1.38144	+	1.00368i	−0.0452265	+	0.0328589i
$934$	7.76258	+	23.8908i	0.254000	+	0.781730i
$935$	−17.6098			−0.575902
$936$	−10.9103			−0.356615
$937$	8.04339	+	24.7550i	0.262766	+	0.808711i	0.992200	+	0.124659i	$0.0397838\pi$
$937$	8.04339	+	24.7550i	0.262766	+	0.808711i	−0.729433	+	0.684052i	$0.760216\pi$
$938$	0.00334551	−	0.0102964i	0.000109235	−	0.000336190i
$939$	22.8262	−	70.2519i	0.744906	−	2.29258i
$940$	−12.2434	−	8.89537i	−0.399337	−	0.290135i
$941$	−11.6342	−	35.8062i	−0.379262	−	1.16725i	−0.940558	−	0.339634i	$-0.889697\pi$
$941$	−11.6342	−	35.8062i	−0.379262	−	1.16725i	0.561295	−	0.827616i	$-0.310303\pi$
$942$	−27.1448	−	19.7218i	−0.884425	−	0.642572i
$943$	−3.28244	+	2.38483i	−0.106891	+	0.0776608i
$944$	0.155031	−	0.477137i	0.00504584	−	0.0155295i
$945$	0.0378876	−	0.0275269i	0.00123248	−	0.000895451i
$946$	14.6756	−	10.6624i	0.477144	−	0.346665i
$947$	14.4603	−	44.5041i	0.469896	−	1.44619i	−0.382824	−	0.923821i	$-0.625048\pi$
$947$	14.4603	−	44.5041i	0.469896	−	1.44619i	0.852720	−	0.522369i	$-0.174952\pi$
$948$	31.5025	−	22.8879i	1.02315	−	0.743364i
$949$	11.8051	+	8.57688i	0.383209	+	0.278417i
$950$	10.2838	+	31.6501i	0.333649	+	1.02687i
$951$	9.90581	+	7.19699i	0.321218	+	0.233378i
$952$	0.0102566	−	0.0315667i	0.000332419	−	0.00102308i
$953$	9.63196	−	29.6441i	0.312010	−	0.960267i	−0.664958	−	0.746881i	$-0.731551\pi$
$953$	9.63196	−	29.6441i	0.312010	−	0.960267i	0.976968	−	0.213387i	$-0.0684494\pi$
$954$	−11.3551	−	34.9475i	−0.367636	−	1.13147i
$955$	15.3745			0.497506
$956$	−1.41784			−0.0458564
$957$	−17.9777	−	55.3297i	−0.581137	−	1.78856i
$958$	−24.2341	+	17.6071i	−0.782968	+	0.568859i
$959$	0.0666793	+	0.0484453i	0.00215319	+	0.00156438i
$960$	44.8645			1.44800
$961$	−29.9939	+	7.83373i	−0.967544	+	0.252701i
$962$	−6.47118			−0.208639
$963$	1.59691	+	1.16022i	0.0514597	+	0.0373876i
$964$	15.5598	−	11.3049i	0.501148	−	0.364105i
$965$	−2.03059	−	6.24950i	−0.0653668	−	0.201178i
$966$	−0.135944			−0.00437392
$967$	−1.38122			−0.0444171			−0.0222085	−	0.999753i	$-0.507070\pi$
$967$	−1.38122			−0.0444171			−0.0222085	+	0.999753i	$0.507070\pi$
$968$	−2.32732	−	7.16276i	−0.0748029	−	0.230220i
$969$	−8.91217	+	27.4288i	−0.286300	+	0.881141i
$970$	−4.61117	+	14.1917i	−0.148056	+	0.455668i
$971$	−2.81495	−	2.04518i	−0.0903362	−	0.0656331i	0.541700	−	0.840572i	$-0.317781\pi$
$971$	−2.81495	−	2.04518i	−0.0903362	−	0.0656331i	−0.632037	+	0.774939i	$0.717781\pi$
$972$	−8.17395	−	25.1568i	−0.262180	−	0.806906i
$973$	0.0618615	+	0.0449450i	0.00198319	+	0.00144087i
$974$	29.8539	−	21.6901i	0.956581	−	0.694997i
$975$	5.01695	−	15.4406i	0.160671	−	0.494494i
$976$	−0.493126	+	0.358277i	−0.0157846	+	0.0114682i
$977$	27.9379	−	20.2981i	0.893813	−	0.649393i	−0.0430564	−	0.999073i	$-0.513710\pi$
$977$	27.9379	−	20.2981i	0.893813	−	0.649393i	0.936869	+	0.349679i	$0.113710\pi$
$978$	5.25456	−	16.1719i	0.168022	−	0.517120i
$979$	−22.0179	+	15.9969i	−0.703696	+	0.511265i
$980$	23.1044	+	16.7863i	0.738044	+	0.536220i
$981$	−2.58283	−	7.94913i	−0.0824633	−	0.253796i
$982$	20.4591	+	14.8644i	0.652876	+	0.474342i
$983$	11.5654	−	35.5947i	0.368879	−	1.13529i	−0.578637	−	0.815585i	$-0.696415\pi$
$983$	11.5654	−	35.5947i	0.368879	−	1.13529i	0.947516	−	0.319708i	$-0.103585\pi$
$984$	−1.01631	+	3.12788i	−0.0323988	+	0.0997132i
$985$	−24.9125	−	76.6727i	−0.793777	−	2.44300i
$986$	−12.3868			−0.394476
$987$	0.0621643			0.00197871
$988$	−2.28262	−	7.02518i	−0.0726198	−	0.223501i
$989$	52.7090	−	38.2953i	1.67605	−	1.21772i
$990$	26.5377	+	19.2807i	0.843422	+	0.612782i
$991$	−17.9906			−0.571490			−0.285745	−	0.958306i	$-0.592241\pi$
$991$	−17.9906			−0.571490			−0.285745	+	0.958306i	$0.592241\pi$
$992$	−3.98705	−	31.0434i	−0.126589	−	0.985628i
$993$	−53.2455			−1.68969
$994$	0.0264625	+	0.0192261i	0.000839339	+	0.000609815i
$995$	−8.73788	+	6.34844i	−0.277009	+	0.201259i
$996$	−2.97985	−	9.17103i	−0.0944201	−	0.290595i
$997$	15.7403			0.498501			0.249250	−	0.968439i	$-0.419816\pi$
$997$	15.7403			0.498501			0.249250	+	0.968439i	$0.419816\pi$
$998$	−9.96738			−0.315512
$999$	4.93588	+	15.1911i	0.156164	+	0.480624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.157.7	✓	48
31.16	even	5	inner	403.2.k.d.326.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.157.7	✓	48	1.1	even	1	trivial
403.2.k.d.326.7	yes	48	31.16	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.715177 + 0.519606i) q^{2} +(2.11502 - 1.53665i) q^{3} +(-0.376547 - 1.15889i) q^{4} -3.34815 q^{5} +2.31107 q^{6} +(-0.00198090 - 0.00609658i) q^{7} +(0.879216 - 2.70595i) q^{8} +(1.18497 - 3.64695i) q^{9} +O(q^{10})\)	\(q+(0.715177 + 0.519606i) q^{2} +(2.11502 - 1.53665i) q^{3} +(-0.376547 - 1.15889i) q^{4} -3.34815 q^{5} +2.31107 q^{6} +(-0.00198090 - 0.00609658i) q^{7} +(0.879216 - 2.70595i) q^{8} +(1.18497 - 3.64695i) q^{9} +(-2.39452 - 1.73972i) q^{10} +(-0.893105 - 2.74869i) q^{11} +(-2.57722 - 1.87246i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.00175113 - 0.00538942i) q^{14} +(-7.08142 + 5.14495i) q^{15} +(0.0631973 - 0.0459155i) q^{16} +(-0.562356 + 1.73075i) q^{17} +(2.74244 - 1.99250i) q^{18} +(4.90424 + 3.56314i) q^{19} +(1.26074 + 3.88015i) q^{20} +(-0.0135580 - 0.00985045i) q^{21} +(0.789511 - 2.42986i) q^{22} +(2.83562 - 8.72715i) q^{23} +(-2.29855 - 7.07420i) q^{24} +6.21011 q^{25} +0.884007 q^{26} +(-0.674274 - 2.07520i) q^{27} +(-0.00631938 + 0.00459130i) q^{28} +(6.22919 + 4.52577i) q^{29} -7.73781 q^{30} +(0.709268 + 5.52240i) q^{31} -5.62135 q^{32} +(-6.11273 - 4.44116i) q^{33} +(-1.30149 + 0.945591i) q^{34} +(0.00663235 + 0.0204123i) q^{35} -4.67263 q^{36} -7.32028 q^{37} +(1.65597 + 5.09655i) q^{38} +(0.807867 - 2.48636i) q^{39} +(-2.94375 + 9.05993i) q^{40} +(-0.357709 - 0.259891i) q^{41} +(-0.00457800 - 0.0140896i) q^{42} +(5.74406 + 4.17330i) q^{43} +(-2.84915 + 2.07003i) q^{44} +(-3.96745 + 12.2106i) q^{45} +(6.56265 - 4.76804i) q^{46} +(-3.00097 + 2.18033i) q^{47} +(0.0631075 - 0.194225i) q^{48} +(5.66309 - 4.11447i) q^{49} +(4.44133 + 3.22681i) q^{50} +(1.47018 + 4.52474i) q^{51} +(-0.985813 - 0.716235i) q^{52} +(3.34976 - 10.3095i) q^{53} +(0.596063 - 1.83449i) q^{54} +(2.99025 + 9.20304i) q^{55} -0.0182387 q^{56} +15.8479 q^{57} +(2.10335 + 6.47346i) q^{58} +(5.19582 - 3.77498i) q^{59} +(8.62894 + 6.26929i) q^{60} -7.80297 q^{61} +(-2.36222 + 4.31803i) q^{62} -0.0245812 q^{63} +(-4.14665 - 3.01272i) q^{64} +(-2.70871 + 1.96799i) q^{65} +(-2.06403 - 6.35243i) q^{66} +1.91049 q^{67} +2.21751 q^{68} +(-7.41320 - 22.8155i) q^{69} +(-0.00586304 + 0.0180446i) q^{70} +(-1.78369 + 5.48964i) q^{71} +(-8.82663 - 6.41293i) q^{72} +(4.50913 + 13.8777i) q^{73} +(-5.23529 - 3.80366i) q^{74} +(13.1345 - 9.54280i) q^{75} +(2.28262 - 7.02518i) q^{76} +(-0.0149885 + 0.0108898i) q^{77} +(1.86970 - 1.35841i) q^{78} +(-3.77724 + 11.6252i) q^{79} +(-0.211594 + 0.153732i) q^{80} +(4.69188 + 3.40885i) q^{81} +(-0.120784 - 0.371736i) q^{82} +(2.44892 + 1.77925i) q^{83} +(-0.00631040 + 0.0194214i) q^{84} +(1.88285 - 5.79483i) q^{85} +(1.93954 + 5.96930i) q^{86} +20.1294 q^{87} -8.22306 q^{88} +(-2.90992 - 8.95580i) q^{89} +(-9.18211 + 6.67119i) q^{90} +(-0.00518606 - 0.00376789i) q^{91} -11.1816 q^{92} +(9.98615 + 10.5901i) q^{93} -3.27913 q^{94} +(-16.4201 - 11.9299i) q^{95} +(-11.8893 + 8.63808i) q^{96} +(-1.55794 - 4.79484i) q^{97} +6.18801 q^{98} -11.0827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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