LMFDB - Embedded newform 124.3.l.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(35,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("124.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.l (of order $10$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.2
Character	$\chi$	$=$	124.35
Dual form			124.3.l.a.39.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99455 - 0.147518i) q^{2} +(-3.91906 - 1.27338i) q^{3} +(3.95648 + 0.588464i) q^{4} -2.43619 q^{5} +(7.62893 + 3.11795i) q^{6} +(-5.14011 - 7.07475i) q^{7} +(-7.80459 - 1.75737i) q^{8} +(6.45639 + 4.69084i) q^{9} +O(q^{10})$	\(q+(-1.99455 - 0.147518i) q^{2} +(-3.91906 - 1.27338i) q^{3} +(3.95648 + 0.588464i) q^{4} -2.43619 q^{5} +(7.62893 + 3.11795i) q^{6} +(-5.14011 - 7.07475i) q^{7} +(-7.80459 - 1.75737i) q^{8} +(6.45639 + 4.69084i) q^{9} +(4.85910 + 0.359381i) q^{10} +(9.96261 + 13.7124i) q^{11} +(-14.7563 - 7.34433i) q^{12} +(-2.97419 + 9.15362i) q^{13} +(9.20856 + 14.8692i) q^{14} +(9.54757 + 3.10219i) q^{15} +(15.3074 + 4.65649i) q^{16} +(15.2711 + 11.0951i) q^{17} +(-12.1856 - 10.3086i) q^{18} +(25.9391 - 8.42811i) q^{19} +(-9.63872 - 1.43361i) q^{20} +(11.1355 + 34.2717i) q^{21} +(-17.8481 - 28.8197i) q^{22} +(-15.8013 + 21.7486i) q^{23} +(28.3489 + 16.8255i) q^{24} -19.0650 q^{25} +(7.28251 - 17.8186i) q^{26} +(2.46926 + 3.39864i) q^{27} +(-16.1735 - 31.0159i) q^{28} +(0.955630 + 2.94113i) q^{29} +(-18.5855 - 7.59592i) q^{30} +(-28.5252 - 12.1372i) q^{31} +(-29.8445 - 11.5457i) q^{32} +(-21.5830 - 66.4257i) q^{33} +(-28.8222 - 24.3825i) q^{34} +(12.5223 + 17.2354i) q^{35} +(22.7842 + 22.3586i) q^{36} +7.76524 q^{37} +(-52.9801 + 12.9838i) q^{38} +(23.3121 - 32.0863i) q^{39} +(19.0135 + 4.28129i) q^{40} +(13.0917 + 40.2922i) q^{41} +(-17.1547 - 69.9993i) q^{42} +(29.5816 - 9.61165i) q^{43} +(31.3476 + 60.1152i) q^{44} +(-15.7290 - 11.4278i) q^{45} +(34.7248 - 41.0478i) q^{46} +(17.0588 + 5.54274i) q^{47} +(-54.0612 - 37.7412i) q^{48} +(-8.48955 + 26.1281i) q^{49} +(38.0261 + 2.81243i) q^{50} +(-45.7200 - 62.9282i) q^{51} +(-17.1539 + 34.4659i) q^{52} +(16.2975 + 11.8408i) q^{53} +(-4.42370 - 7.14302i) q^{54} +(-24.2708 - 33.4059i) q^{55} +(27.6834 + 64.2486i) q^{56} -112.389 q^{57} +(-1.47219 - 6.00720i) q^{58} +(-57.7860 - 18.7758i) q^{59} +(35.9492 + 17.8922i) q^{60} +45.9454 q^{61} +(55.1046 + 28.4163i) q^{62} -69.7888i q^{63} +(57.8233 + 27.4312i) q^{64} +(7.24569 - 22.2999i) q^{65} +(33.2495 + 135.673i) q^{66} +119.158i q^{67} +(53.8906 + 52.8839i) q^{68} +(89.6205 - 65.1131i) q^{69} +(-22.4338 - 36.2242i) q^{70} +(-47.3341 + 65.1498i) q^{71} +(-42.1459 - 47.9564i) q^{72} +(-60.2850 + 43.7996i) q^{73} +(-15.4882 - 1.14551i) q^{74} +(74.7169 + 24.2770i) q^{75} +(107.587 - 18.0814i) q^{76} +(45.8026 - 140.966i) q^{77} +(-51.2305 + 60.5589i) q^{78} +(-50.6431 + 69.7043i) q^{79} +(-37.2918 - 11.3441i) q^{80} +(-27.5445 - 84.7732i) q^{81} +(-20.1683 - 82.2961i) q^{82} +(37.3035 - 12.1206i) q^{83} +(23.8899 + 142.148i) q^{84} +(-37.2032 - 27.0297i) q^{85} +(-60.4200 + 14.8071i) q^{86} -12.7433i q^{87} +(-53.6563 - 124.527i) q^{88} +(-71.6901 + 52.0859i) q^{89} +(29.6865 + 25.1136i) q^{90} +(80.0472 - 26.0089i) q^{91} +(-75.3158 + 76.7494i) q^{92} +(96.3368 + 83.8899i) q^{93} +(-33.2070 - 13.5718i) q^{94} +(-63.1924 + 20.5325i) q^{95} +(102.260 + 83.2519i) q^{96} +(147.412 - 107.101i) q^{97} +(20.7872 - 50.8616i) q^{98} +135.265i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9}+O(q^{10}) $ 120 * q - 3 * q^2 + q^4 - 16 * q^5 - 10 * q^6 + 27 * q^8 + 72 * q^9	$ 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9} - 26 q^{10} - 66 q^{12} - 22 q^{13} - 34 q^{14} - 55 q^{16} - 6 q^{17} + 74 q^{18} - 47 q^{20} - 114 q^{21} - 56 q^{22} + 15 q^{24} + 440 q^{25} - 48 q^{26} - 8 q^{28} - 6 q^{29} - 254 q^{30} - 178 q^{32} - 90 q^{33} + 171 q^{34} - 8 q^{36} - 96 q^{37} - 42 q^{38} + 50 q^{40} - 6 q^{41} + 268 q^{42} + 196 q^{44} - 120 q^{45} - 231 q^{46} - 28 q^{48} + 48 q^{49} - 394 q^{50} - 7 q^{52} + 122 q^{53} - 126 q^{54} - 432 q^{56} - 196 q^{57} - 49 q^{58} - 163 q^{60} + 80 q^{61} + 200 q^{62} + 19 q^{64} - 156 q^{65} + 490 q^{66} + 266 q^{68} - 522 q^{69} + 65 q^{70} + 642 q^{72} + 122 q^{73} + 177 q^{74} + 517 q^{76} - 186 q^{77} + 303 q^{78} - 602 q^{80} - 168 q^{81} + 406 q^{82} + 769 q^{84} - 508 q^{85} - 677 q^{86} - 108 q^{88} - 30 q^{89} + 662 q^{90} + 910 q^{92} - 250 q^{93} + 354 q^{94} - 1230 q^{96} + 530 q^{97} + 76 q^{98}+O(q^{100}) $ 120 * q - 3 * q^2 + q^4 - 16 * q^5 - 10 * q^6 + 27 * q^8 + 72 * q^9 - 26 * q^10 - 66 * q^12 - 22 * q^13 - 34 * q^14 - 55 * q^16 - 6 * q^17 + 74 * q^18 - 47 * q^20 - 114 * q^21 - 56 * q^22 + 15 * q^24 + 440 * q^25 - 48 * q^26 - 8 * q^28 - 6 * q^29 - 254 * q^30 - 178 * q^32 - 90 * q^33 + 171 * q^34 - 8 * q^36 - 96 * q^37 - 42 * q^38 + 50 * q^40 - 6 * q^41 + 268 * q^42 + 196 * q^44 - 120 * q^45 - 231 * q^46 - 28 * q^48 + 48 * q^49 - 394 * q^50 - 7 * q^52 + 122 * q^53 - 126 * q^54 - 432 * q^56 - 196 * q^57 - 49 * q^58 - 163 * q^60 + 80 * q^61 + 200 * q^62 + 19 * q^64 - 156 * q^65 + 490 * q^66 + 266 * q^68 - 522 * q^69 + 65 * q^70 + 642 * q^72 + 122 * q^73 + 177 * q^74 + 517 * q^76 - 186 * q^77 + 303 * q^78 - 602 * q^80 - 168 * q^81 + 406 * q^82 + 769 * q^84 - 508 * q^85 - 677 * q^86 - 108 * q^88 - 30 * q^89 + 662 * q^90 + 910 * q^92 - 250 * q^93 + 354 * q^94 - 1230 * q^96 + 530 * q^97 + 76 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.99455	−	0.147518i	−0.997276	−	0.0737590i
$2$	−1.99455	−	0.147518i	−0.997276	−	0.0737590i
$3$	−3.91906	−	1.27338i	−1.30635	−	0.424460i	−0.428566	−	0.903510i	$-0.640981\pi$
$3$	−3.91906	−	1.27338i	−1.30635	−	0.424460i	−0.877787	+	0.479050i	$0.840981\pi$
$4$	3.95648	+	0.588464i	0.989119	+	0.147116i
$5$	−2.43619			−0.487238			−0.243619	−	0.969871i	$-0.578335\pi$
$5$	−2.43619			−0.487238			−0.243619	+	0.969871i	$0.578335\pi$
$6$	7.62893	+	3.11795i	1.27149	+	0.519659i
$7$	−5.14011	−	7.07475i	−0.734301	−	1.01068i	−0.998926	−	0.0463271i	$-0.985248\pi$
$7$	−5.14011	−	7.07475i	−0.734301	−	1.01068i	0.264625	−	0.964351i	$-0.414752\pi$
$8$	−7.80459	−	1.75737i	−0.975574	−	0.219672i
$9$	6.45639	+	4.69084i	0.717377	+	0.521205i
$10$	4.85910	+	0.359381i	0.485910	+	0.0359381i
$11$	9.96261	+	13.7124i	0.905691	+	1.24658i	0.968617	+	0.248559i	$0.0799570\pi$
$11$	9.96261	+	13.7124i	0.905691	+	1.24658i	−0.0629253	+	0.998018i	$0.520043\pi$
$12$	−14.7563	−	7.34433i	−1.22969	−	0.612027i
$13$	−2.97419	+	9.15362i	−0.228784	+	0.704125i	0.769101	+	0.639127i	$0.220704\pi$
$13$	−2.97419	+	9.15362i	−0.228784	+	0.704125i	−0.997885	+	0.0649980i	$0.979296\pi$
$14$	9.20856	+	14.8692i	0.657754	+	1.06209i
$15$	9.54757	+	3.10219i	0.636505	+	0.206813i
$16$	15.3074	+	4.65649i	0.956714	+	0.291031i
$17$	15.2711	+	11.0951i	0.898298	+	0.652652i	0.938028	−	0.346558i	$-0.112650\pi$
$17$	15.2711	+	11.0951i	0.898298	+	0.652652i	−0.0397299	+	0.999210i	$0.512650\pi$
$18$	−12.1856	−	10.3086i	−0.676979	−	0.572698i
$19$	25.9391	−	8.42811i	1.36521	−	0.443585i	0.467433	−	0.884028i	$-0.345179\pi$
$19$	25.9391	−	8.42811i	1.36521	−	0.443585i	0.897780	+	0.440444i	$0.145179\pi$
$20$	−9.63872	−	1.43361i	−0.481936	−	0.0716805i
$21$	11.1355	+	34.2717i	0.530264	+	1.63198i
$22$	−17.8481	−	28.8197i	−0.811278	−	1.30998i
$23$	−15.8013	+	21.7486i	−0.687013	+	0.945592i	−0.999991	−	0.00416803i	$-0.998673\pi$
$23$	−15.8013	+	21.7486i	−0.687013	+	0.945592i	0.312978	+	0.949760i	$0.398673\pi$
$24$	28.3489	+	16.8255i	1.18120	+	0.701061i
$25$	−19.0650			−0.762600
$26$	7.28251	−	17.8186i	0.280096	−	0.685332i
$27$	2.46926	+	3.39864i	0.0914539	+	0.125876i
$28$	−16.1735	−	31.0159i	−0.577624	−	1.10771i
$29$	0.955630	+	2.94113i	0.0329528	+	0.101418i	0.966180	−	0.257868i	$-0.0830201\pi$
$29$	0.955630	+	2.94113i	0.0329528	+	0.101418i	−0.933227	+	0.359287i	$0.883020\pi$
$30$	−18.5855	−	7.59592i	−0.619517	−	0.253197i
$31$	−28.5252	−	12.1372i	−0.920169	−	0.391522i
$31$	−28.5252	−	12.1372i	−0.920169	−	0.391522i
$32$	−29.8445	−	11.5457i	−0.932642	−	0.360804i
$33$	−21.5830	−	66.4257i	−0.654031	−	2.01290i
$34$	−28.8222	−	24.3825i	−0.847713	−	0.717132i
$35$	12.5223	+	17.2354i	0.357779	+	0.492441i
$36$	22.7842	+	22.3586i	0.632893	+	0.621071i
$37$	7.76524			0.209871			0.104936	−	0.994479i	$-0.466536\pi$
$37$	7.76524			0.209871			0.104936	+	0.994479i	$0.466536\pi$
$38$	−52.9801	+	12.9838i	−1.39421	+	0.341680i
$39$	23.3121	−	32.0863i	0.597746	−	0.822726i
$40$	19.0135	+	4.28129i	0.475336	+	0.107032i
$41$	13.0917	+	40.2922i	0.319310	+	0.982736i	0.973944	+	0.226790i	$0.0728230\pi$
$41$	13.0917	+	40.2922i	0.319310	+	0.982736i	−0.654633	+	0.755946i	$0.727177\pi$
$42$	−17.1547	−	69.9993i	−0.408446	−	1.66665i
$43$	29.5816	−	9.61165i	0.687945	−	0.223527i	0.0558745	−	0.998438i	$-0.482205\pi$
$43$	29.5816	−	9.61165i	0.687945	−	0.223527i	0.632070	+	0.774911i	$0.282205\pi$
$44$	31.3476	+	60.1152i	0.712445	+	1.36626i
$45$	−15.7290	−	11.4278i	−0.349533	−	0.253950i
$46$	34.7248	−	41.0478i	0.754888	−	0.892343i
$47$	17.0588	+	5.54274i	0.362953	+	0.117931i	0.484816	−	0.874616i	$-0.338887\pi$
$47$	17.0588	+	5.54274i	0.362953	+	0.117931i	−0.121863	+	0.992547i	$0.538887\pi$
$48$	−54.0612	−	37.7412i	−1.12628	−	0.786276i
$49$	−8.48955	+	26.1281i	−0.173256	+	0.533228i
$50$	38.0261	+	2.81243i	0.760522	+	0.0562486i
$51$	−45.7200	−	62.9282i	−0.896471	−	1.23389i
$52$	−17.1539	+	34.4659i	−0.329883	+	0.662806i
$53$	16.2975	+	11.8408i	0.307500	+	0.223412i	0.730823	−	0.682567i	$-0.239137\pi$
$53$	16.2975	+	11.8408i	0.307500	+	0.223412i	−0.423323	+	0.905979i	$0.639137\pi$
$54$	−4.42370	−	7.14302i	−0.0819204	−	0.132278i
$55$	−24.2708	−	33.4059i	−0.441287	−	0.607379i
$56$	27.6834	+	64.2486i	0.494347	+	1.14730i
$57$	−112.389			−1.97174
$58$	−1.47219	−	6.00720i	−0.0253825	−	0.103572i
$59$	−57.7860	−	18.7758i	−0.979424	−	0.318234i	−0.224809	−	0.974403i	$-0.572176\pi$
$59$	−57.7860	−	18.7758i	−0.979424	−	0.318234i	−0.754614	+	0.656169i	$0.772176\pi$
$60$	35.9492	+	17.8922i	0.599153	+	0.298203i
$61$	45.9454			0.753203			0.376602	−	0.926375i	$-0.377093\pi$
$61$	45.9454			0.753203			0.376602	+	0.926375i	$0.377093\pi$
$62$	55.1046	+	28.4163i	0.888784	+	0.458327i
$63$		−	69.7888i		−	1.10776i
$64$	57.8233	+	27.4312i	0.903489	+	0.428612i
$65$	7.24569	−	22.2999i	0.111472	−	0.343076i
$66$	33.2495	+	135.673i	0.503780	+	2.05566i
$67$			119.158i			1.77848i	0.457437	+	0.889242i	$0.348768\pi$
$67$			119.158i			1.77848i	−0.457437	+	0.889242i	$0.651232\pi$
$68$	53.8906	+	52.8839i	0.792509	+	0.777705i
$69$	89.6205	−	65.1131i	1.29885	−	0.943668i
$70$	−22.4338	−	36.2242i	−0.320483	−	0.517489i
$71$	−47.3341	+	65.1498i	−0.666678	+	0.917603i	−0.999679	−	0.0253231i	$-0.991939\pi$
$71$	−47.3341	+	65.1498i	−0.666678	+	0.917603i	0.333002	+	0.942926i	$0.391939\pi$
$72$	−42.1459	−	47.9564i	−0.585360	−	0.666061i
$73$	−60.2850	+	43.7996i	−0.825821	+	0.599994i	−0.918374	−	0.395713i	$-0.870497\pi$
$73$	−60.2850	+	43.7996i	−0.825821	+	0.599994i	0.0925527	+	0.995708i	$0.470497\pi$
$74$	−15.4882	−	1.14551i	−0.209300	−	0.0154799i
$75$	74.7169	+	24.2770i	0.996225	+	0.323693i
$76$	107.587	−	18.0814i	1.41562	−	0.237913i
$77$	45.8026	−	140.966i	0.594839	−	1.83073i
$78$	−51.2305	+	60.5589i	−0.656801	+	0.776396i
$79$	−50.6431	+	69.7043i	−0.641052	+	0.882332i	−0.998671	−	0.0515351i	$-0.983589\pi$
$79$	−50.6431	+	69.7043i	−0.641052	+	0.882332i	0.357619	+	0.933868i	$0.383589\pi$
$80$	−37.2918	−	11.3441i	−0.466147	−	0.141801i
$81$	−27.5445	−	84.7732i	−0.340056	−	1.04658i
$82$	−20.1683	−	82.2961i	−0.245955	−	1.00361i
$83$	37.3035	−	12.1206i	0.449440	−	0.146032i	−0.0755470	−	0.997142i	$-0.524070\pi$
$83$	37.3035	−	12.1206i	0.449440	−	0.146032i	0.524987	+	0.851110i	$0.324070\pi$
$84$	23.8899	+	142.148i	0.284403	+	1.69224i
$85$	−37.2032	−	27.0297i	−0.437685	−	0.317997i
$86$	−60.4200	+	14.8071i	−0.702558	+	0.172176i
$87$		−	12.7433i		−	0.146475i
$88$	−53.6563	−	124.527i	−0.609731	−	1.41508i
$89$	−71.6901	+	52.0859i	−0.805507	+	0.585235i	−0.912524	−	0.409022i	$-0.865870\pi$
$89$	−71.6901	+	52.0859i	−0.805507	+	0.585235i	0.107018	+	0.994257i	$0.465870\pi$
$90$	29.6865	+	25.1136i	0.329850	+	0.279040i
$91$	80.0472	−	26.0089i	0.879640	−	0.285812i
$92$	−75.3158	+	76.7494i	−0.818650	+	0.834233i
$93$	96.3368	+	83.8899i	1.03588	+	0.902042i
$94$	−33.2070	−	13.5718i	−0.353266	−	0.144380i
$95$	−63.1924	+	20.5325i	−0.665183	+	0.216131i
$96$	102.260	+	83.2519i	1.06521	+	0.867207i
$97$	147.412	−	107.101i	1.51971	−	1.10413i	0.558081	−	0.829787i	$-0.311538\pi$
$97$	147.412	−	107.101i	1.51971	−	1.10413i	0.961631	−	0.274348i	$-0.0884620\pi$
$98$	20.7872	−	50.8616i	0.212114	−	0.518996i
$99$			135.265i			1.36632i
$100$	−75.4302	−	11.2191i	−0.754302	−	0.112191i
$101$	51.6474	+	37.5241i	0.511361	+	0.371525i	0.813340	−	0.581789i	$-0.197647\pi$
$101$	51.6474	+	37.5241i	0.511361	+	0.371525i	−0.301979	+	0.953315i	$0.597647\pi$
$102$	81.9079	+	132.258i	0.803019	+	1.29665i
$103$	32.5686	−	10.5822i	0.316200	−	0.102740i	−0.146617	−	0.989193i	$-0.546839\pi$
$103$	32.5686	−	10.5822i	0.316200	−	0.102740i	0.462817	+	0.886454i	$0.346839\pi$
$104$	39.2987	−	66.2135i	0.377872	−	0.636668i
$105$	−27.1283	−	83.4923i	−0.258365	−	0.795164i
$106$	−30.7595	−	26.0213i	−0.290184	−	0.245484i
$107$	−106.888	+	147.119i	−0.998953	+	1.37494i	−0.0729868	+	0.997333i	$0.523253\pi$
$107$	−106.888	+	147.119i	−0.998953	+	1.37494i	−0.925966	+	0.377607i	$0.876747\pi$
$108$	7.76958	+	14.8997i	0.0719405	+	0.137960i
$109$	−26.2836	+	80.8927i	−0.241134	+	0.742135i	0.755114	+	0.655594i	$0.227582\pi$
$109$	−26.2836	+	80.8927i	−0.241134	+	0.742135i	−0.996248	+	0.0865416i	$0.972418\pi$
$110$	43.4814	+	70.2101i	0.395285	+	0.638274i
$111$	−30.4324	−	9.88810i	−0.274166	−	0.0890820i
$112$	−45.7382	−	132.231i	−0.408377	−	1.18063i
$113$	88.9219	−	64.6055i	0.786919	−	0.571730i	−0.120128	−	0.992758i	$-0.538331\pi$
$113$	88.9219	−	64.6055i	0.786919	−	0.571730i	0.907048	+	0.421028i	$0.138331\pi$
$114$	224.166	+	16.5794i	1.96636	+	0.145433i
$115$	38.4949	−	52.9837i	0.334739	−	0.460728i
$116$	2.05018	+	12.1989i	0.0176740	+	0.105163i
$117$	−62.1407	+	45.1479i	−0.531117	+	0.385879i
$118$	112.487	+	45.9738i	0.953283	+	0.389609i
$119$		−	165.069i		−	1.38713i
$120$	−69.0632	−	40.9900i	−0.575526	−	0.341583i
$121$	−51.3840	+	158.144i	−0.424661	+	1.30697i
$122$	−91.6405	−	6.77777i	−0.751151	−	0.0555555i
$123$		−	174.578i		−	1.41934i
$124$	−105.717	−	64.8066i	−0.852557	−	0.522634i
$125$	107.351			0.858805
$126$	−10.2951	+	139.197i	−0.0817071	+	1.10474i
$127$	12.0049	+	3.90063i	0.0945269	+	0.0307137i	0.355899	−	0.934525i	$-0.384175\pi$
$127$	12.0049	+	3.90063i	0.0945269	+	0.0307137i	−0.261372	+	0.965238i	$0.584175\pi$
$128$	−111.285	−	63.2429i	−0.869414	−	0.494085i
$129$	−128.172			−0.993578
$130$	−17.7416	+	43.4095i	−0.136473	+	0.333920i
$131$	−11.6177	−	15.9904i	−0.0886850	−	0.122064i	0.762369	−	0.647143i	$-0.224036\pi$
$131$	−11.6177	−	15.9904i	−0.0886850	−	0.122064i	−0.851054	+	0.525078i	$0.824036\pi$
$132$	−46.3036	−	275.513i	−0.350785	−	2.08722i
$133$	−192.956	−	140.191i	−1.45080	−	1.05407i
$134$	17.5780	−	237.668i	0.131179	−	1.77364i
$135$	−6.01557	−	8.27973i	−0.0445598	−	0.0613313i
$136$	−99.6863	−	113.430i	−0.732987	−	0.834041i
$137$	−2.87198	+	8.83906i	−0.0209634	+	0.0645187i	−0.960991	−	0.276580i	$-0.910799\pi$
$137$	−2.87198	+	8.83906i	−0.0209634	+	0.0645187i	0.940028	+	0.341099i	$0.110799\pi$
$138$	−188.358	+	116.651i	−1.36491	+	0.845296i
$139$	98.3600	+	31.9591i	0.707626	+	0.229922i	0.640650	−	0.767833i	$-0.278665\pi$
$139$	98.3600	+	31.9591i	0.707626	+	0.229922i	0.0669757	+	0.997755i	$0.478665\pi$
$140$	39.4016	+	75.5604i	0.281440	+	0.539717i
$141$	−59.7964	−	43.4447i	−0.424088	−	0.308118i
$142$	104.021	−	122.962i	0.732543	−	0.865930i
$143$	−155.148	+	50.4108i	−1.08495	+	0.352523i
$144$	76.9878	+	101.869i	0.534637	+	0.707422i
$145$	−2.32809	−	7.16514i	−0.0160558	−	0.0494147i
$146$	126.703	−	78.4674i	0.867827	−	0.537448i
$147$	66.5421	−	91.5874i	0.452668	−	0.623043i
$148$	30.7230	+	4.56957i	0.207588	+	0.0308755i
$149$	−263.240			−1.76671			−0.883356	−	0.468702i	$-0.844722\pi$
$149$	−263.240			−1.76671			−0.883356	+	0.468702i	$0.844722\pi$
$150$	−145.445	−	59.4438i	−0.969636	−	0.396292i
$151$	−75.4278	−	103.817i	−0.499522	−	0.687533i	0.482587	−	0.875848i	$-0.339697\pi$
$151$	−75.4278	−	103.817i	−0.499522	−	0.687533i	−0.982109	+	0.188316i	$0.939697\pi$
$152$	−217.255	+	20.1933i	−1.42931	+	0.132851i
$153$	46.5507	+	143.268i	0.304253	+	0.936395i
$154$	−112.151	+	274.407i	−0.728251	+	1.78186i
$155$	69.4928	+	29.5685i	0.448341	+	0.190764i
$156$	111.115	−	113.230i	0.712278	−	0.725836i
$157$	61.3792	+	188.906i	0.390950	+	1.20322i	0.932071	+	0.362276i	$0.118000\pi$
$157$	61.3792	+	188.906i	0.390950	+	1.20322i	−0.541120	+	0.840945i	$0.682000\pi$
$158$	111.293	−	131.558i	0.704386	−	0.832646i
$159$	−48.7930	−	67.1578i	−0.306874	−	0.422376i
$160$	72.7069	+	28.1276i	0.454418	+	0.175797i
$161$	235.086			1.46016
$162$	42.4334	+	173.148i	0.261934	+	1.06881i
$163$	94.2367	−	129.706i	0.578139	−	0.795741i	−0.415350	−	0.909661i	$-0.636341\pi$
$163$	94.2367	−	129.706i	0.578139	−	0.795741i	0.993490	+	0.113921i	$0.0363410\pi$
$164$	28.0866	+	167.119i	0.171260	+	1.01902i
$165$	52.5803	+	161.826i	0.318669	+	0.980761i
$166$	−76.1918	+	18.6723i	−0.458987	+	0.112484i
$167$	200.958	−	65.2951i	1.20334	−	0.390988i	0.362350	−	0.932042i	$-0.381974\pi$
$167$	200.958	−	65.2951i	1.20334	−	0.390988i	0.840988	+	0.541054i	$0.181974\pi$
$168$	−26.6802	−	287.046i	−0.158811	−	1.70861i
$169$	61.7809	+	44.8864i	0.365567	+	0.265600i
$170$	70.2164	+	59.4003i	0.413037	+	0.349414i
$171$	207.008	+	67.2608i	1.21057	+	0.393338i
$172$	122.695	−	20.6206i	0.713344	−	0.119887i
$173$	0.927266	−	2.85383i	0.00535992	−	0.0164961i	−0.948341	−	0.317253i	$-0.897239\pi$
$173$	0.927266	−	2.85383i	0.00535992	−	0.0164961i	0.953701	+	0.300757i	$0.0972394\pi$
$174$	−1.87987	+	25.4173i	−0.0108039	+	0.146076i
$175$	97.9961	+	134.880i	0.559977	+	0.770743i
$176$	88.6503	+	256.291i	0.503695	+	1.45620i
$177$	202.558	+	147.167i	1.14440	+	0.831452i
$178$	150.673	−	93.3125i	0.846479	−	0.524228i
$179$	−21.1079	−	29.0526i	−0.117921	−	0.162305i	0.745976	−	0.665973i	$-0.231983\pi$
$179$	−21.1079	−	29.0526i	−0.117921	−	0.162305i	−0.863897	+	0.503668i	$0.831983\pi$
$180$	−55.5065	−	54.4697i	−0.308369	−	0.302609i
$181$	−271.318			−1.49899			−0.749496	−	0.662009i	$-0.769704\pi$
$181$	−271.318			−1.49899			−0.749496	+	0.662009i	$0.769704\pi$
$182$	−163.495	+	40.0678i	−0.898325	+	0.220153i
$183$	−180.063	−	58.5059i	−0.983950	−	0.319705i
$184$	161.543	−	141.970i	0.877952	−	0.771578i
$185$	−18.9176			−0.102257
$186$	−179.774	−	181.534i	−0.966525	−	0.975990i
$187$			319.938i			1.71090i
$188$	64.2310	+	31.9682i	0.341654	+	0.170044i
$189$	11.3523	−	34.9387i	0.0600650	−	0.184861i
$190$	129.069	−	31.6310i	0.679313	−	0.166479i
$191$		−	28.6609i		−	0.150057i	−0.997181	−	0.0750285i	$-0.976095\pi$
$191$		−	28.6609i		−	0.150057i	0.997181	−	0.0750285i	$-0.0239048\pi$
$192$	−191.683	−	181.135i	−0.998347	−	0.943414i
$193$	−237.905	+	172.848i	−1.23267	+	0.895586i	−0.997087	−	0.0762683i	$-0.975699\pi$
$193$	−237.905	+	172.848i	−1.23267	+	0.895586i	−0.235581	+	0.971855i	$0.575699\pi$
$194$	−309.820	+	191.873i	−1.59701	+	0.989035i
$195$	−56.7926	+	78.1683i	−0.291244	+	0.400863i
$196$	−48.9642	+	98.3796i	−0.249817	+	0.501937i
$197$	−77.7521	+	56.4902i	−0.394681	+	0.286752i	−0.767371	−	0.641204i	$-0.778435\pi$
$197$	−77.7521	+	56.4902i	−0.394681	+	0.286752i	0.372690	+	0.927956i	$0.378435\pi$
$198$	19.9541	−	269.794i	0.100778	−	1.36259i
$199$	5.42406	+	1.76238i	0.0272566	+	0.00885620i	0.322614	−	0.946531i	$-0.395439\pi$
$199$	5.42406	+	1.76238i	0.0272566	+	0.00885620i	−0.295357	+	0.955387i	$0.595439\pi$
$200$	148.794	+	33.5043i	0.743972	+	0.167522i
$201$	151.734	−	466.989i	0.754896	−	2.32333i
$202$	−97.4780	−	82.4626i	−0.482565	−	0.408231i
$203$	15.8957	−	21.8785i	0.0783039	−	0.107776i
$204$	−143.859	−	275.879i	−0.705192	−	1.35235i
$205$	−31.8939	−	98.1593i	−0.155580	−	0.478826i
$206$	−66.5208	+	16.3022i	−0.322916	+	0.0791371i
$207$	−204.039	+	66.2962i	−0.985694	+	0.320271i
$208$	−88.1510	+	126.269i	−0.423803	+	0.607063i
$209$	373.990	+	271.719i	1.78942	+	1.30009i
$210$	41.7922	+	170.532i	0.199010	+	0.812055i
$211$			126.346i			0.598797i	0.954128	+	0.299398i	$0.0967859\pi$
$211$			126.346i			0.598797i	−0.954128	+	0.299398i	$0.903214\pi$
$212$	57.5127	+	56.4384i	0.271287	+	0.266219i
$213$	268.466	−	195.052i	1.26040	−	0.915736i
$214$	234.896	−	277.668i	1.09765	−	1.29751i
$215$	−72.0664	+	23.4158i	−0.335193	+	0.108911i
$216$	−13.2989	−	30.8644i	−0.0615688	−	0.142891i
$217$	60.7551	+	264.195i	0.279977	+	1.21749i
$218$	64.3572	−	157.467i	0.295217	−	0.722328i
$219$	292.034	−	94.8876i	1.33349	−	0.433277i
$220$	−76.3686	−	146.452i	−0.347130	−	0.665691i
$221$	−146.979	+	106.787i	−0.665065	+	0.483198i
$222$	59.2404	+	24.2117i	0.266849	+	0.109062i
$223$		−	324.244i		−	1.45401i	−0.686633	−	0.727004i	$-0.740912\pi$
$223$		−	324.244i		−	1.45401i	0.686633	−	0.727004i	$-0.259088\pi$
$224$	71.7209	+	270.489i	0.320182	+	1.20754i
$225$	−123.091	−	89.4308i	−0.547071	−	0.397470i
$226$	−186.890	+	115.742i	−0.826946	+	0.512131i
$227$	−67.6355	+	21.9761i	−0.297954	+	0.0968110i	−0.454179	−	0.890910i	$-0.650067\pi$
$227$	−67.6355	+	21.9761i	−0.297954	+	0.0968110i	0.156225	+	0.987721i	$0.450067\pi$
$228$	−444.664	−	66.1369i	−1.95028	−	0.290074i
$229$	65.8718	+	202.733i	0.287650	+	0.885295i	0.985592	+	0.169141i	$0.0540992\pi$
$229$	65.8718	+	202.733i	0.287650	+	0.885295i	−0.697942	+	0.716154i	$0.745901\pi$
$230$	−84.5962	+	100.000i	−0.367810	+	0.434783i
$231$	−359.006	+	494.130i	−1.55414	+	2.13909i
$232$	−2.28964	−	24.6337i	−0.00986914	−	0.106180i
$233$	49.5729	−	152.570i	0.212759	−	0.654805i	−0.786546	−	0.617532i	$-0.788133\pi$
$233$	49.5729	−	152.570i	0.212759	−	0.654805i	0.999305	−	0.0372736i	$-0.0118673\pi$
$234$	130.603	−	80.8829i	0.558133	−	0.345654i
$235$	−41.5584	−	13.5032i	−0.176844	−	0.0574602i
$236$	−217.580	−	108.291i	−0.921949	−	0.458860i
$237$	287.233	−	208.687i	1.21196	−	0.880537i
$238$	−24.3506	+	329.239i	−0.102314	+	1.38336i
$239$	158.260	−	217.826i	0.662174	−	0.911404i	−0.337377	−	0.941370i	$-0.609540\pi$
$239$	158.260	−	217.826i	0.662174	−	0.911404i	0.999551	+	0.0299652i	$0.00953965\pi$
$240$	131.703	+	91.9448i	0.548764	+	0.383103i
$241$	297.280	−	215.986i	1.23353	−	0.896209i	0.236376	−	0.971662i	$-0.424040\pi$
$241$	297.280	−	215.986i	1.23353	−	0.896209i	0.997149	+	0.0754526i	$0.0240402\pi$
$242$	125.817	−	307.846i	0.519905	−	1.27209i
$243$			329.498i			1.35596i
$244$	181.782	+	27.0372i	0.745008	+	0.110808i
$245$	20.6821	−	63.6531i	0.0844169	−	0.259808i
$246$	−25.7534	+	348.205i	−0.104689	+	1.41547i
$247$			262.503i			1.06277i
$248$	201.298	+	144.855i	0.811686	+	0.584094i
$249$	−161.629			−0.649112
$250$	−214.116	−	15.8361i	−0.856465	−	0.0633446i
$251$	307.892	+	100.040i	1.22666	+	0.398566i	0.849503	−	0.527584i	$-0.176902\pi$
$251$	307.892	+	100.040i	1.22666	+	0.398566i	0.377156	+	0.926150i	$0.376902\pi$
$252$	41.0682	−	276.118i	0.162969	−	1.09570i
$253$	−455.647			−1.80098
$254$	−23.3690	−	9.55096i	−0.0920040	−	0.0376022i
$255$	111.383	+	153.305i	0.436794	+	0.601196i
$256$	212.634	+	142.558i	0.830602	+	0.556866i
$257$	−53.2142	−	38.6624i	−0.207059	−	0.150437i	0.479423	−	0.877584i	$-0.340846\pi$
$257$	−53.2142	−	38.6624i	−0.207059	−	0.150437i	−0.686482	+	0.727147i	$0.740846\pi$
$258$	255.645	+	18.9076i	0.990871	+	0.0732853i
$259$	−39.9142	−	54.9371i	−0.154109	−	0.212112i
$260$	41.7901	−	83.9654i	0.160731	−	0.322944i
$261$	−7.62644	+	23.4718i	−0.0292201	+	0.0899302i
$262$	20.8133	+	33.6076i	0.0794401	+	0.128273i
$263$	−463.756	−	150.683i	−1.76333	−	0.572940i	−0.765793	−	0.643087i	$-0.777653\pi$
$263$	−463.756	−	150.683i	−1.76333	−	0.572940i	−0.997537	+	0.0701469i	$0.977653\pi$
$264$	51.7118	+	556.355i	0.195878	+	2.10741i
$265$	−39.7038	−	28.8465i	−0.149825	−	0.108855i
$266$	364.181	+	308.083i	1.36910	+	1.15821i
$267$	347.283	−	112.839i	1.30069	−	0.422618i
$268$	−70.1205	+	471.448i	−0.261644	+	1.75913i
$269$	−73.4797	−	226.147i	−0.273159	−	0.840697i	−0.989701	−	0.143152i	$-0.954276\pi$
$269$	−73.4797	−	226.147i	−0.273159	−	0.840697i	0.716542	−	0.697544i	$-0.245724\pi$
$270$	10.7770	+	17.4018i	0.0399147	+	0.0644509i
$271$	246.927	−	339.866i	0.911171	−	1.25412i	−0.0555936	−	0.998453i	$-0.517705\pi$
$271$	246.927	−	339.866i	0.911171	−	1.25412i	0.966765	−	0.255666i	$-0.0822949\pi$
$272$	182.097	+	240.947i	0.669473	+	0.885834i
$273$	−346.829			−1.27044
$274$	7.03224	−	17.2063i	0.0256651	−	0.0627967i
$275$	−189.937	−	261.426i	−0.690680	−	0.950639i
$276$	392.898	−	204.880i	1.42354	−	0.742319i
$277$	131.118	+	403.539i	0.473349	+	1.45682i	0.848171	+	0.529723i	$0.177704\pi$
$277$	131.118	+	403.539i	0.473349	+	1.45682i	−0.374822	+	0.927097i	$0.622296\pi$
$278$	−191.470	−	78.2539i	−0.688739	−	0.281489i
$279$	−127.236	−	212.170i	−0.456044	−	0.760465i
$280$	−67.4421	−	156.522i	−0.240865	−	0.559006i
$281$	−67.2792	−	207.064i	−0.239428	−	0.736883i	−0.996503	−	0.0835555i	$-0.973372\pi$
$281$	−67.2792	−	207.064i	−0.239428	−	0.736883i	0.757075	−	0.653328i	$-0.226628\pi$
$282$	112.858	+	95.4737i	0.400207	+	0.338559i
$283$	−175.522	−	241.585i	−0.620219	−	0.853658i	0.377150	−	0.926152i	$-0.376904\pi$
$283$	−175.522	−	241.585i	−0.620219	−	0.853658i	−0.997369	+	0.0724944i	$0.976904\pi$
$284$	−225.615	+	229.909i	−0.794418	+	0.809540i
$285$	273.801			0.960704
$286$	316.888	−	77.6597i	1.10800	−	0.271538i
$287$	217.764	−	299.727i	0.758760	−	1.04434i
$288$	−138.529	−	214.540i	−0.481002	−	0.744930i
$289$	20.7989	+	64.0124i	0.0719685	+	0.221496i
$290$	3.58652	+	14.6347i	0.0123673	+	0.0504644i
$291$	−714.097	+	232.024i	−2.45394	+	0.797334i
$292$	−264.291	+	137.816i	−0.905105	+	0.471974i
$293$	−458.597	−	333.190i	−1.56518	−	1.13717i	−0.931599	−	0.363487i	$-0.881586\pi$
$293$	−458.597	−	333.190i	−1.56518	−	1.13717i	−0.633577	−	0.773680i	$-0.718414\pi$
$294$	−146.233	+	172.860i	−0.497390	+	0.587958i
$295$	140.778	+	45.7414i	0.477212	+	0.155056i
$296$	−60.6045	−	13.6464i	−0.204745	−	0.0461028i
$297$	−22.0031	+	67.7186i	−0.0740846	+	0.228009i
$298$	525.046	+	38.8326i	1.76190	+	0.130311i
$299$	−152.083	−	209.324i	−0.508637	−	0.700079i
$300$	281.329	+	140.020i	0.937765	+	0.466732i
$301$	−220.053	−	159.878i	−0.731072	−	0.531155i
$302$	135.130	+	218.196i	0.447449	+	0.722504i
$303$	−154.627	−	212.826i	−0.510320	−	0.702396i
$304$	436.305	−	8.22760i	1.43522	−	0.0270645i
$305$	−111.932			−0.366989
$306$	−71.7132	−	292.623i	−0.234357	−	0.956285i
$307$	186.391	+	60.5620i	0.607135	+	0.197270i	0.596420	−	0.802672i	$-0.296589\pi$
$307$	186.391	+	60.5620i	0.607135	+	0.197270i	0.0107151	+	0.999943i	$0.496589\pi$
$308$	264.170	−	530.775i	0.857696	−	1.72330i
$309$	−141.113			−0.456677
$310$	−134.245	−	69.2273i	−0.433049	−	0.223314i
$311$			321.185i			1.03275i	0.856363	+	0.516375i	$0.172719\pi$
$311$			321.185i			1.03275i	−0.856363	+	0.516375i	$0.827281\pi$
$312$	−238.329	+	209.453i	−0.763875	+	0.671322i
$313$	−106.649	+	328.233i	−0.340733	+	1.04867i	0.623095	+	0.782146i	$0.285875\pi$
$313$	−106.649	+	328.233i	−0.340733	+	1.04867i	−0.963829	+	0.266523i	$0.914125\pi$
$314$	−94.5570	−	385.837i	−0.301137	−	1.22878i
$315$			170.019i			0.539741i
$316$	−241.387	+	245.982i	−0.763882	+	0.778423i
$317$	201.123	−	146.125i	0.634459	−	0.460961i	−0.223483	−	0.974708i	$-0.571743\pi$
$317$	201.123	−	146.125i	0.634459	−	0.460961i	0.857942	+	0.513746i	$0.171743\pi$
$318$	87.4132	+	141.148i	0.274884	+	0.443860i
$319$	−30.8092	+	42.4052i	−0.0965806	+	0.132932i
$320$	−140.868	−	66.8275i	−0.440214	−	0.208836i
$321$	606.238	−	440.458i	1.88859	−	1.37214i
$322$	−468.892	−	34.6795i	−1.45619	−	0.107700i
$323$	489.628	+	159.090i	1.51588	+	0.492538i
$324$	−59.0931	−	351.612i	−0.182386	−	1.08522i
$325$	56.7029	−	174.514i	0.174471	−	0.536965i
$326$	−207.094	+	244.803i	−0.635258	+	0.750930i
$327$	206.014	−	283.554i	0.630013	−	0.867139i
$328$	−31.3671	−	337.471i	−0.0956314	−	1.02888i
$329$	−48.4705	−	149.177i	−0.147327	−	0.453425i
$330$	−81.0020	−	330.526i	−0.245461	−	1.00159i
$331$	−109.963	+	35.7292i	−0.332215	+	0.107943i	−0.470375	−	0.882467i	$-0.655881\pi$
$331$	−109.963	+	35.7292i	−0.332215	+	0.107943i	0.138160	+	0.990410i	$0.455881\pi$
$332$	154.723	−	26.0032i	0.466033	−	0.0783230i
$333$	50.1354	+	36.4255i	0.150557	+	0.109386i
$334$	−410.452	+	100.590i	−1.22890	+	0.301166i
$335$		−	290.292i		−	0.866545i
$336$	10.8706	+	576.464i	0.0323531	+	1.71567i
$337$	−59.2529	+	43.0497i	−0.175825	+	0.127744i	−0.672217	−	0.740354i	$-0.734658\pi$
$337$	−59.2529	+	43.0497i	−0.175825	+	0.127744i	0.496392	+	0.868098i	$0.334658\pi$
$338$	−116.604	−	98.6421i	−0.344981	−	0.291841i
$339$	−430.758	+	139.962i	−1.27067	+	0.412866i
$340$	−131.288	−	128.835i	−0.386140	−	0.378927i
$341$	−117.756	−	512.066i	−0.345326	−	1.50166i
$342$	−402.965	−	164.693i	−1.17826	−	0.481557i
$343$	−179.039	+	58.1734i	−0.521980	+	0.169602i
$344$	−247.764	+	23.0290i	−0.720244	+	0.0669448i
$345$	−218.332	+	158.628i	−0.632848	+	0.459791i
$346$	−2.27047	+	5.55533i	−0.00656206	+	0.0160559i
$347$			621.939i			1.79233i	0.443718	+	0.896166i	$0.353659\pi$
$347$			621.939i			1.79233i	−0.443718	+	0.896166i	$0.646341\pi$
$348$	7.49900	−	50.4187i	0.0215489	−	0.144881i
$349$	62.2816	+	45.2503i	0.178457	+	0.129657i	0.673428	−	0.739253i	$-0.264821\pi$
$349$	62.2816	+	45.2503i	0.178457	+	0.129657i	−0.494971	+	0.868910i	$0.664821\pi$
$350$	−175.561	−	283.481i	−0.501603	−	0.809947i
$351$	−38.4539	+	12.4944i	−0.109555	+	0.0355967i
$352$	−139.010	−	524.264i	−0.394915	−	1.48939i
$353$	−109.591	−	337.286i	−0.310456	−	0.955486i	−0.977585	−	0.210543i	$-0.932477\pi$
$353$	−109.591	−	337.286i	−0.310456	−	0.955486i	0.667128	−	0.744943i	$-0.267523\pi$
$354$	−382.303	−	323.413i	−1.07995	−	0.913597i
$355$	115.315	−	158.717i	0.324830	−	0.447091i
$356$	−314.291	+	163.890i	−0.882840	+	0.460364i
$357$	−210.195	+	646.915i	−0.588783	+	1.81209i
$358$	37.8151	+	61.0606i	0.105629	+	0.170560i
$359$	−19.6936	−	6.39884i	−0.0548568	−	0.0178241i	0.281460	−	0.959573i	$-0.409181\pi$
$359$	−19.6936	−	6.39884i	−0.0548568	−	0.0178241i	−0.336317	+	0.941749i	$0.609181\pi$
$360$	102.675	+	116.831i	0.285209	+	0.324530i
$361$	309.746	−	225.044i	0.858023	−	0.623390i
$362$	541.157	+	40.0242i	1.49491	+	0.110564i
$363$	402.754	−	554.343i	1.10952	−	1.52712i
$364$	332.010	−	55.7988i	0.912116	−	0.153293i
$365$	146.865	−	106.704i	0.402371	−	0.292340i
$366$	350.514	+	143.256i	0.957688	+	0.391409i
$367$			509.186i			1.38743i	0.720251	+	0.693713i	$0.244026\pi$
$367$			509.186i			1.38743i	−0.720251	+	0.693713i	$0.755974\pi$
$368$	−343.149	+	259.337i	−0.932471	+	0.704719i
$369$	−104.479	+	321.553i	−0.283141	+	0.871418i
$370$	37.7321	+	2.79068i	0.101979	+	0.00754239i
$371$		−	176.164i		−	0.474835i
$372$	331.788	+	388.599i	0.891904	+	1.04462i
$373$	340.299			0.912329			0.456165	−	0.889895i	$-0.349223\pi$
$373$	340.299			0.912329			0.456165	+	0.889895i	$0.349223\pi$
$374$	47.1966	−	638.134i	0.126194	−	1.70624i
$375$	−420.714	−	136.698i	−1.12190	−	0.364528i
$376$	−123.396	−	73.2375i	−0.328181	−	0.194781i
$377$	−29.7642			−0.0789501
$378$	−27.7968	+	68.0125i	−0.0735366	+	0.179927i
$379$	103.796	+	142.863i	0.273868	+	0.376947i	0.923691	−	0.383139i	$-0.125157\pi$
$379$	103.796	+	142.863i	0.273868	+	0.376947i	−0.649823	+	0.760086i	$0.725157\pi$
$380$	−262.102	+	44.0497i	−0.689742	+	0.115920i
$381$	−42.0810	−	30.5736i	−0.110449	−	0.0802458i
$382$	−4.22799	+	57.1656i	−0.0110680	+	0.149648i
$383$	179.221	+	246.676i	0.467939	+	0.644063i	0.976131	−	0.217181i	$-0.0696862\pi$
$383$	179.221	+	246.676i	0.467939	+	0.644063i	−0.508192	+	0.861244i	$0.669686\pi$
$384$	355.600	+	389.561i	0.926042	+	1.01448i
$385$	−111.584	+	343.419i	−0.289828	+	0.891998i
$386$	500.012	−	309.659i	1.29537	−	0.802226i
$387$	236.077	+	76.7062i	0.610019	+	0.198207i
$388$	646.257	−	336.996i	1.66561	−	0.868547i
$389$	109.630	+	79.6505i	0.281824	+	0.204757i	0.719713	−	0.694272i	$-0.244274\pi$
$389$	109.630	+	79.6505i	0.281824	+	0.204757i	−0.437889	+	0.899029i	$0.644274\pi$
$390$	124.807	−	147.533i	0.320018	−	0.378289i
$391$	−482.606	+	156.808i	−1.23429	+	0.401044i
$392$	112.174	−	189.000i	0.286159	−	0.482143i
$393$	25.1687	+	77.4613i	0.0640425	+	0.197103i
$394$	163.414	−	101.203i	0.414756	−	0.256860i
$395$	123.376	−	169.813i	0.312345	−	0.429906i
$396$	−79.5988	+	535.174i	−0.201007	+	1.35145i
$397$	467.058			1.17647			0.588234	−	0.808691i	$-0.299823\pi$
$397$	467.058			1.17647			0.588234	+	0.808691i	$0.299823\pi$
$398$	−10.5586	−	4.31531i	−0.0265291	−	0.0108425i
$399$	577.691	+	795.123i	1.44785	+	1.99279i
$400$	−291.836	−	88.7760i	−0.729589	−	0.221940i
$401$	177.044	+	544.885i	0.441506	+	1.35881i	0.886271	+	0.463168i	$0.153287\pi$
$401$	177.044	+	544.885i	0.441506	+	1.35881i	−0.444765	+	0.895647i	$0.646713\pi$
$402$	−371.531	+	909.051i	−0.924206	+	2.26132i
$403$	195.939	−	225.011i	0.486201	−	0.558339i
$404$	182.260	+	178.856i	0.451139	+	0.442712i
$405$	67.1036	+	206.524i	0.165688	+	0.509935i
$406$	−34.9323	+	41.2930i	−0.0860401	+	0.101707i
$407$	77.3620	+	106.480i	0.190079	+	0.261621i
$408$	246.238	+	571.476i	0.603523	+	1.40068i
$409$	−66.6548			−0.162970			−0.0814851	−	0.996675i	$-0.525966\pi$
$409$	−66.6548			−0.162970			−0.0814851	+	0.996675i	$0.525966\pi$
$410$	49.1338	+	200.489i	0.119838	+	0.488997i
$411$	22.5110	−	30.9837i	0.0547712	−	0.0753861i
$412$	135.084	−	22.7027i	0.327874	−	0.0551036i
$413$	164.192	+	505.331i	0.397559	+	1.22356i
$414$	416.746	−	102.132i	1.00663	−	0.246695i
$415$	−90.8783	+	29.5282i	−0.218984	+	0.0711522i
$416$	194.449	−	238.846i	0.467425	−	0.574150i
$417$	−344.783	−	250.499i	−0.826817	−	0.600718i
$418$	−705.859	−	597.129i	−1.68866	−	1.42854i
$419$	89.2628	+	29.0032i	0.213038	+	0.0692201i	0.413592	−	0.910463i	$-0.364274\pi$
$419$	89.2628	+	29.0032i	0.213038	+	0.0692201i	−0.200554	+	0.979683i	$0.564274\pi$
$420$	−58.2002	−	346.299i	−0.138572	−	0.824522i
$421$	43.7496	−	134.647i	0.103918	−	0.319827i	−0.885557	−	0.464531i	$-0.846223\pi$
$421$	43.7496	−	134.647i	0.103918	−	0.319827i	0.989475	+	0.144704i	$0.0462229\pi$
$422$	18.6383	−	252.004i	0.0441666	−	0.597165i
$423$	84.1381	+	115.806i	0.198908	+	0.273773i
$424$	−106.386	−	121.054i	−0.250912	−	0.285504i
$425$	−291.143	−	211.528i	−0.685042	−	0.497712i
$426$	−564.243	+	349.437i	−1.32451	+	0.820276i
$427$	−236.164	−	325.052i	−0.553078	−	0.761246i
$428$	−509.474	+	519.172i	−1.19036	+	1.21302i
$429$	672.228			1.56697
$430$	147.194	−	36.0729i	0.342313	−	0.0838906i
$431$	−347.862	−	113.027i	−0.807104	−	0.262244i	−0.123733	−	0.992316i	$-0.539487\pi$
$431$	−347.862	−	113.027i	−0.807104	−	0.262244i	−0.683371	+	0.730072i	$0.739487\pi$
$432$	21.9722	+	63.5225i	0.0508616	+	0.147043i
$433$	−511.761			−1.18190			−0.590949	−	0.806709i	$-0.701246\pi$
$433$	−511.761			−1.18190			−0.590949	+	0.806709i	$0.701246\pi$
$434$	−82.2056	−	535.914i	−0.189414	−	1.23482i
$435$			31.0452i			0.0713682i
$436$	−151.593	+	304.583i	−0.347691	+	0.698585i
$437$	−226.571	+	697.314i	−0.518469	+	1.59568i
$438$	−596.475	+	146.178i	−1.36181	+	0.333740i
$439$		−	312.597i		−	0.712066i	−0.934473	−	0.356033i	$-0.884129\pi$
$439$		−	312.597i		−	0.712066i	0.934473	−	0.356033i	$-0.115871\pi$
$440$	130.717	+	303.372i	0.297084	+	0.689482i
$441$	−177.375	+	128.870i	−0.402211	+	0.292223i
$442$	308.911	−	191.310i	0.698893	−	0.432827i
$443$	462.965	−	637.217i	1.04507	−	1.43841i	0.152060	−	0.988371i	$-0.451409\pi$
$443$	462.965	−	637.217i	1.04507	−	1.43841i	0.893008	−	0.450041i	$-0.148591\pi$
$444$	−114.586	−	57.0305i	−0.258078	−	0.128447i
$445$	174.651	−	126.891i	0.392473	−	0.285149i
$446$	−47.8318	+	646.721i	−0.107246	+	1.45005i
$447$	1031.65	+	335.205i	2.30795	+	0.749899i
$448$	−103.149	−	550.084i	−0.230243	−	1.22787i
$449$	−51.8897	+	159.700i	−0.115567	+	0.355679i	−0.992065	−	0.125727i	$-0.959874\pi$
$449$	−51.8897	+	159.700i	−0.115567	+	0.355679i	0.876498	+	0.481406i	$0.159874\pi$
$450$	232.319	+	196.533i	0.516264	+	0.436739i
$451$	−422.073	+	580.933i	−0.935860	+	1.28810i
$452$	389.835	−	203.283i	0.862468	−	0.449741i
$453$	163.407	+	502.915i	0.360722	+	1.11019i
$454$	138.144	−	33.8550i	0.304283	−	0.0745705i
$455$	−195.010	+	63.3626i	−0.428594	+	0.139259i
$456$	877.149	+	197.509i	1.92357	+	0.433135i
$457$	−205.883	−	149.583i	−0.450509	−	0.327314i	0.339288	−	0.940683i	$-0.389814\pi$
$457$	−205.883	−	149.583i	−0.450509	−	0.327314i	−0.789797	+	0.613369i	$0.789814\pi$
$458$	−101.478	−	414.078i	−0.221568	−	0.904100i
$459$			79.2975i			0.172761i
$460$	183.483	−	186.976i	0.398877	−	0.406470i
$461$	165.322	−	120.114i	0.358616	−	0.260550i	−0.393858	−	0.919171i	$-0.628860\pi$
$461$	165.322	−	120.114i	0.358616	−	0.260550i	0.752475	+	0.658621i	$0.228860\pi$
$462$	788.950	−	932.608i	1.70768	−	2.01863i
$463$	−70.0810	+	22.7707i	−0.151363	+	0.0491808i	−0.383718	−	0.923450i	$-0.625357\pi$
$463$	−70.0810	+	22.7707i	−0.151363	+	0.0491808i	0.232356	+	0.972631i	$0.425357\pi$
$464$	0.932896	+	49.4709i	0.00201055	+	0.106618i
$465$	−234.695	−	204.371i	−0.504720	−	0.439509i
$466$	−121.382	+	296.995i	−0.260477	+	0.637329i
$467$	−281.448	+	91.4479i	−0.602672	+	0.195820i	−0.594432	−	0.804146i	$-0.702623\pi$
$467$	−281.448	+	91.4479i	−0.602672	+	0.195820i	−0.00824001	+	0.999966i	$0.502623\pi$
$468$	−272.426	+	142.059i	−0.582107	+	0.303545i
$469$	843.016	−	612.487i	1.79748	−	1.30594i
$470$	80.8985	+	33.0634i	0.172124	+	0.0703476i
$471$		−	818.492i		−	1.73778i
$472$	418.000	+	248.089i	0.885593	+	0.525613i
$473$	426.509	+	309.877i	0.901709	+	0.655130i
$474$	−603.687	+	373.866i	−1.27360	+	0.788746i
$475$	−494.528	+	160.682i	−1.04111	+	0.338277i
$476$	97.1372	−	653.091i	0.204070	−	1.37204i
$477$	49.6795	+	152.898i	0.104150	+	0.320541i
$478$	−347.790	+	411.119i	−0.727595	+	0.860081i
$479$	−20.0702	+	27.6243i	−0.0419002	+	0.0576707i	−0.829453	−	0.558576i	$-0.811348\pi$
$479$	−20.0702	+	27.6243i	−0.0419002	+	0.0576707i	0.787553	+	0.616247i	$0.211348\pi$
$480$	−249.126	−	202.817i	−0.519012	−	0.422536i
$481$	−23.0953	+	71.0801i	−0.0480152	+	0.147776i
$482$	−624.802	+	386.942i	−1.29627	+	0.802784i
$483$	−921.318	−	299.354i	−1.90749	−	0.619781i
$484$	−296.361	+	595.454i	−0.612317	+	1.23028i
$485$	−359.123	+	260.918i	−0.740460	+	0.537976i
$486$	48.6068	−	657.200i	0.100014	−	1.35226i
$487$	393.290	−	541.317i	0.807577	−	1.11153i	−0.184116	−	0.982904i	$-0.558942\pi$
$487$	393.290	−	541.317i	0.807577	−	1.11153i	0.991693	−	0.128629i	$-0.0410577\pi$
$488$	−358.585	−	80.7432i	−0.734805	−	0.165457i
$489$	−534.484	+	388.325i	−1.09301	+	0.794122i
$490$	−50.6416	+	123.908i	−0.103350	+	0.252874i
$491$			104.460i			0.212749i	0.994326	+	0.106374i	$0.0339242\pi$
$491$			104.460i			0.212749i	−0.994326	+	0.106374i	$0.966076\pi$
$492$	102.733	−	690.715i	0.208807	−	1.40389i
$493$	−18.0386	+	55.5170i	−0.0365894	+	0.112610i
$494$	38.7239	−	523.576i	0.0783885	−	1.05987i
$495$		−	329.532i		−	0.665721i
$496$	−380.131	−	318.617i	−0.766393	−	0.642372i
$497$	704.221			1.41694
$498$	322.377	+	23.8432i	0.647344	+	0.0478778i
$499$	−144.920	−	47.0873i	−0.290420	−	0.0943633i	0.160184	−	0.987087i	$-0.448791\pi$
$499$	−144.920	−	47.0873i	−0.290420	−	0.0943633i	−0.450604	+	0.892724i	$0.648791\pi$
$500$	424.730	+	63.1720i	0.849460	+	0.126344i
$501$	−870.710			−1.73794
$502$	−599.348	−	244.955i	−1.19392	−	0.487957i
$503$	538.535	+	741.230i	1.07065	+	1.47362i	0.869420	+	0.494074i	$0.164493\pi$
$503$	538.535	+	741.230i	1.07065	+	1.47362i	0.201227	+	0.979545i	$0.435507\pi$
$504$	−122.645	+	544.673i	−0.243343	+	1.08070i
$505$	−125.823	−	91.4157i	−0.249154	−	0.181021i
$506$	908.811	+	67.2161i	1.79607	+	0.132838i
$507$	−184.966	−	254.583i	−0.364824	−	0.502137i
$508$	45.2018	+	22.4972i	0.0889799	+	0.0442859i
$509$	80.4434	−	247.579i	0.158042	−	0.486404i	−0.840414	−	0.541944i	$-0.817688\pi$
$509$	80.4434	−	247.579i	0.158042	−	0.486404i	0.998456	+	0.0555409i	$0.0176883\pi$
$510$	−199.543	−	322.206i	−0.391261	−	0.631776i
$511$	619.742	+	201.366i	1.21280	+	0.394063i
$512$	−403.080	−	315.706i	−0.787266	−	0.616614i
$513$	92.6943	+	67.3463i	0.180691	+	0.131279i
$514$	100.435	+	84.9642i	0.195399	+	0.165300i
$515$	−79.3432	+	25.7802i	−0.154064	+	0.0500586i
$516$	−507.108	−	75.4244i	−0.982767	−	0.146171i
$517$	93.9461	+	289.136i	0.181714	+	0.559258i
$518$	71.5066	+	115.463i	0.138044	+	0.222902i
$519$	−7.26803	+	10.0036i	−0.0140039	+	0.0192747i
$520$	−95.7390	+	161.309i	−0.184113	+	0.310209i
$521$	−444.099			−0.852397			−0.426198	−	0.904630i	$-0.640147\pi$
$521$	−444.099			−0.852397			−0.426198	+	0.904630i	$0.640147\pi$
$522$	18.6738	−	45.6906i	0.0357736	−	0.0875300i
$523$	219.381	+	301.952i	0.419467	+	0.577346i	0.965495	−	0.260420i	$-0.0838611\pi$
$523$	219.381	+	301.952i	0.419467	+	0.577346i	−0.546029	+	0.837766i	$0.683861\pi$
$524$	−36.5555	−	70.1025i	−0.0697624	−	0.133783i
$525$	−212.299	−	653.389i	−0.404379	−	1.24455i
$526$	902.756	+	368.958i	1.71627	+	0.701441i
$527$	−300.948	−	501.838i	−0.571058	−	0.952254i
$528$	−21.0696	−	1117.31i	−0.0399045	−	2.11611i
$529$	−59.8515	−	184.204i	−0.113141	−	0.348212i
$530$	74.9358	+	63.3928i	0.141388	+	0.119609i
$531$	−285.015	−	392.289i	−0.536751	−	0.738774i
$532$	−680.930	−	668.210i	−1.27994	−	1.25603i
$533$	−407.757			−0.765022
$534$	−709.320	+	173.833i	−1.32831	+	0.325530i
$535$	260.399	−	358.409i	0.486727	−	0.669923i
$536$	209.406	−	929.983i	0.390683	−	1.73504i
$537$	45.7283	+	140.737i	0.0851550	+	0.262080i
$538$	113.198	+	461.902i	0.210406	+	0.858555i
$539$	−442.856	+	143.893i	−0.821626	+	0.266962i
$540$	−18.9282	−	36.2985i	−0.0350521	−	0.0672194i
$541$	119.947	+	87.1463i	0.221713	+	0.161084i	0.693097	−	0.720844i	$-0.256246\pi$
$541$	119.947	+	87.1463i	0.221713	+	0.161084i	−0.471385	+	0.881928i	$0.656246\pi$
$542$	−542.646	+	641.455i	−1.00119	+	1.18350i
$543$	1063.31	+	345.490i	1.95821	+	0.636262i
$544$	−327.657	−	507.443i	−0.602311	−	0.932800i
$545$	64.0319	−	197.070i	0.117490	−	0.361596i
$546$	691.769	+	51.1635i	1.26698	+	0.0937061i
$547$	−264.432	−	363.959i	−0.483422	−	0.665373i	0.495736	−	0.868473i	$-0.334898\pi$
$547$	−264.432	−	363.959i	−0.483422	−	0.665373i	−0.979158	+	0.203100i	$0.934898\pi$
$548$	−16.5644	+	33.2815i	−0.0302270	+	0.0607326i
$549$	296.641	+	215.523i	0.540330	+	0.392573i
$550$	340.274	+	549.447i	0.618680	+	0.998994i
$551$	49.5763	+	68.2359i	0.0899751	+	0.123840i
$552$	−813.880	+	350.684i	−1.47442	+	0.635298i
$553$	753.451			1.36248
$554$	−201.992	−	824.222i	−0.364606	−	1.48776i
$555$	74.1392	+	24.0893i	0.133584	+	0.0434041i
$556$	370.352	+	184.327i	0.666101	+	0.331523i
$557$	−173.719			−0.311884			−0.155942	−	0.987766i	$-0.549841\pi$
$557$	−173.719			−0.311884			−0.155942	+	0.987766i	$0.549841\pi$
$558$	222.481	+	441.953i	0.398711	+	0.792031i
$559$			299.366i			0.535538i
$560$	111.427	+	322.140i	0.198977	+	0.575249i
$561$	407.403	−	1253.86i	0.726209	−	2.23504i
$562$	103.646	+	422.925i	0.184424	+	0.752536i
$563$			545.326i			0.968608i	0.874900	+	0.484304i	$0.160927\pi$
$563$			545.326i			0.968608i	−0.874900	+	0.484304i	$0.839073\pi$
$564$	−211.018	−	207.076i	−0.374145	−	0.367156i
$565$	−216.630	+	157.391i	−0.383417	+	0.278568i
$566$	314.449	+	507.747i	0.555564	+	0.897079i
$567$	−458.168	+	630.614i	−0.808056	+	1.11219i
$568$	483.916	−	425.284i	0.851965	−	0.748739i
$569$	−275.930	+	200.475i	−0.484939	+	0.352329i	−0.803235	−	0.595663i	$-0.796890\pi$
$569$	−275.930	+	200.475i	−0.484939	+	0.352329i	0.318296	+	0.947992i	$0.396890\pi$
$570$	−546.109	−	40.3905i	−0.958087	−	0.0708605i
$571$	−188.248	−	61.1654i	−0.329681	−	0.107120i	0.139500	−	0.990222i	$-0.455451\pi$
$571$	−188.248	−	61.1654i	−0.329681	−	0.107120i	−0.469180	+	0.883102i	$0.655451\pi$
$572$	−643.506	+	108.150i	−1.12501	+	0.189073i
$573$	−36.4962	+	112.324i	−0.0636932	+	0.196027i
$574$	−478.557	+	565.696i	−0.833723	+	0.985534i
$575$	301.252	−	414.637i	0.523916	−	0.721108i
$576$	244.654	+	448.346i	0.424747	+	0.778379i
$577$	−53.2960	−	164.028i	−0.0923674	−	0.284278i	0.894191	−	0.447685i	$-0.147751\pi$
$577$	−53.2960	−	164.028i	−0.0923674	−	0.284278i	−0.986559	+	0.163408i	$0.947751\pi$
$578$	−32.0415	−	130.744i	−0.0554351	−	0.226201i
$579$	1152.47	−	374.459i	1.99044	−	0.646734i
$580$	−4.99462	−	29.7187i	−0.00861142	−	0.0512391i
$581$	−277.494	−	201.611i	−0.477615	−	0.347008i
$582$	1458.53	−	357.442i	2.50607	−	0.614162i
$583$			341.442i			0.585664i
$584$	547.472	−	235.895i	0.937452	−	0.403929i
$585$	151.387	−	109.989i	0.258780	−	0.188015i
$586$	865.543	+	732.216i	1.47704	+	1.24952i
$587$	224.623	−	72.9844i	0.382663	−	0.124335i	−0.111368	−	0.993779i	$-0.535523\pi$
$587$	224.623	−	72.9844i	0.382663	−	0.124335i	0.494030	+	0.869445i	$0.335523\pi$
$588$	317.168	−	323.206i	0.539402	−	0.549670i
$589$	−842.211	−	74.4137i	−1.42990	−	0.126339i
$590$	−274.041	−	112.001i	−0.464475	−	0.189832i
$591$	376.649	−	122.381i	0.637307	−	0.207074i
$592$	118.866	+	36.1588i	0.200787	+	0.0610790i
$593$	−5.59472	+	4.06481i	−0.00943461	+	0.00685465i	−0.592493	−	0.805576i	$-0.701856\pi$
$593$	−5.59472	+	4.06481i	−0.00943461	+	0.00685465i	0.583058	+	0.812431i	$0.301856\pi$
$594$	53.8761	−	131.822i	0.0907005	−	0.221923i
$595$			402.139i			0.675864i
$596$	−1041.50	−	154.907i	−1.74749	−	0.259912i
$597$	−19.0130	−	13.8138i	−0.0318476	−	0.0231387i
$598$	272.458	+	439.942i	0.455615	+	0.735689i
$599$	−767.133	+	249.256i	−1.28069	+	0.416121i	−0.868823	−	0.495123i	$-0.835123\pi$
$599$	−767.133	+	249.256i	−1.28069	+	0.416121i	−0.411866	+	0.911244i	$0.635123\pi$
$600$	−540.471	−	320.777i	−0.900784	−	0.534629i
$601$	−70.5005	−	216.978i	−0.117305	−	0.361029i	0.875116	−	0.483914i	$-0.160785\pi$
$601$	−70.5005	−	216.978i	−0.117305	−	0.361029i	−0.992421	+	0.122885i	$0.960785\pi$
$602$	415.322	+	351.346i	0.689903	+	0.583631i
$603$	−558.953	+	769.333i	−0.926954	+	1.27584i
$604$	−237.335	−	455.138i	−0.392939	−	0.753539i
$605$	125.181	−	385.268i	0.206911	−	0.636806i
$606$	277.016	+	447.303i	0.457122	+	0.738123i
$607$	−732.795	−	238.099i	−1.20724	−	0.392256i	−0.364820	−	0.931078i	$-0.618870\pi$
$607$	−732.795	−	238.099i	−1.20724	−	0.392256i	−0.842420	+	0.538822i	$0.818870\pi$
$608$	−871.448	−	47.9525i	−1.43330	−	0.0788692i
$609$	−90.1559	+	65.5021i	−0.148039	+	0.107557i
$610$	223.253	+	16.5119i	0.365989	+	0.0270687i
$611$	−101.472	+	139.665i	−0.166076	+	0.228584i
$612$	99.8685	+	594.231i	0.163184	+	0.970966i
$613$	473.820	−	344.250i	0.772953	−	0.561583i	−0.129903	−	0.991527i	$-0.541467\pi$
$613$	473.820	−	344.250i	0.772953	−	0.561583i	0.902856	+	0.429944i	$0.141467\pi$
$614$	−362.832	−	148.290i	−0.590931	−	0.241515i
$615$			425.305i			0.691554i
$616$	−605.200	+	1019.69i	−0.982468	+	1.65534i
$617$	75.9769	−	233.833i	0.123139	−	0.378983i	−0.870418	−	0.492313i	$-0.836152\pi$
$617$	75.9769	−	233.833i	0.123139	−	0.378983i	0.993557	+	0.113330i	$0.0361516\pi$
$618$	281.458	+	20.8167i	0.455434	+	0.0336841i
$619$		−	435.046i		−	0.702820i	−0.936222	−	0.351410i	$-0.885702\pi$
$619$		−	435.046i		−	0.702820i	0.936222	−	0.351410i	$-0.114298\pi$
$620$	257.547	+	157.881i	0.415398	+	0.254647i
$621$	−112.933			−0.181857
$622$	47.3806	−	640.621i	0.0761746	−	1.02994i
$623$	736.990	+	239.462i	1.18297	+	0.384370i
$624$	506.258	−	382.606i	0.811310	−	0.613151i
$625$	215.098			0.344158
$626$	261.138	−	638.946i	0.417154	−	1.02068i
$627$	−1119.69	−	1541.12i	−1.78578	−	2.45792i
$628$	131.681	+	783.521i	0.209683	+	1.24764i
$629$	118.584	+	86.1560i	0.188527	+	0.136973i
$630$	25.0808	−	339.111i	0.0398108	−	0.538271i
$631$	685.897	+	944.057i	1.08700	+	1.49613i	0.851573	+	0.524236i	$0.175649\pi$
$631$	685.897	+	944.057i	1.08700	+	1.49613i	0.235428	+	0.971892i	$0.424351\pi$
$632$	517.745	−	455.014i	0.819217	−	0.719959i
$633$	160.887	−	495.158i	0.254165	−	0.782240i
$634$	−422.707	+	261.784i	−0.666731	+	0.412909i
$635$	−29.2462	−	9.50268i	−0.0460571	−	0.0149648i
$636$	−153.528	−	294.421i	−0.241397	−	0.462926i
$637$	−213.918	−	155.420i	−0.335820	−	0.243988i
$638$	67.7061	−	80.0345i	0.106122	−	0.125446i
$639$	−611.215	+	198.596i	−0.956518	+	0.310792i
$640$	271.111	+	154.072i	0.423611	+	0.240737i
$641$	322.731	+	993.263i	0.503480	+	1.54955i	0.803311	+	0.595560i	$0.203070\pi$
$641$	322.731	+	993.263i	0.503480	+	1.54955i	−0.299830	+	0.953993i	$0.596930\pi$
$642$	−1274.15	+	789.085i	−1.98466	+	1.22910i
$643$	12.3398	−	16.9842i	0.0191909	−	0.0264140i	−0.799314	−	0.600914i	$-0.794803\pi$
$643$	12.3398	−	16.9842i	0.0191909	−	0.0264140i	0.818505	+	0.574500i	$0.194803\pi$
$644$	930.114	+	138.340i	1.44428	+	0.214814i
$645$	312.250			0.484108
$646$	−953.120	−	389.542i	−1.47542	−	0.603006i
$647$	−315.946	−	434.863i	−0.488325	−	0.672122i	0.491753	−	0.870735i	$-0.336356\pi$
$647$	−315.946	−	434.863i	−0.488325	−	0.672122i	−0.980078	+	0.198613i	$0.936356\pi$
$648$	65.9952	+	710.026i	0.101844	+	1.09572i
$649$	−318.239	−	979.438i	−0.490352	−	1.50915i
$650$	−138.841	+	339.712i	−0.213601	+	0.522634i
$651$	98.3182	−	1112.76i	0.151026	−	1.70931i
$652$	449.173	−	457.723i	0.688915	−	0.702029i
$653$	−194.157	−	597.554i	−0.297331	−	0.915090i	−0.982429	−	0.186639i	$-0.940241\pi$
$653$	−194.157	−	597.554i	−0.297331	−	0.915090i	0.685098	−	0.728451i	$-0.259759\pi$
$654$	−452.736	+	535.173i	−0.692257	+	0.818308i
$655$	28.3030	+	38.9557i	0.0432107	+	0.0594744i
$656$	12.7803	+	677.731i	0.0194821	+	1.03313i
$657$	−594.680			−0.905145
$658$	74.6707	+	304.691i	0.113481	+	0.463057i
$659$	−142.125	+	195.618i	−0.215668	+	0.296841i	−0.903120	−	0.429388i	$-0.858729\pi$
$659$	−142.125	+	195.618i	−0.215668	+	0.296841i	0.687452	+	0.726230i	$0.258729\pi$
$660$	112.804	+	671.201i	0.170915	+	1.01697i
$661$	−219.228	−	674.714i	−0.331661	−	1.02075i	−0.968343	−	0.249622i	$-0.919694\pi$
$661$	−219.228	−	674.714i	−0.331661	−	1.02075i	0.636682	−	0.771126i	$-0.280306\pi$
$662$	224.598	−	55.0421i	0.339271	−	0.0831452i
$663$	712.001	−	231.343i	1.07391	−	0.348934i
$664$	−312.439	+	29.0404i	−0.470541	+	0.0437356i
$665$	470.078	+	341.531i	0.706884	+	0.513581i
$666$	−94.6243	−	80.0484i	−0.142078	−	0.120193i
$667$	−79.0657	−	25.6900i	−0.118539	−	0.0385157i
$668$	833.508	−	140.082i	1.24777	−	0.209704i
$669$	−412.886	+	1270.73i	−0.617168	+	1.89945i
$670$	−42.8233	+	579.003i	−0.0639154	+	0.864184i
$671$	457.736	+	630.019i	0.682170	+	0.938926i
$672$	63.3567	−	1151.39i	0.0942808	−	1.71338i
$673$	446.199	+	324.182i	0.663000	+	0.481697i	0.867675	−	0.497133i	$-0.165614\pi$
$673$	446.199	+	324.182i	0.663000	+	0.481697i	−0.204675	+	0.978830i	$0.565614\pi$
$674$	124.534	−	77.1241i	0.184768	−	0.114427i
$675$	−47.0763	−	64.7950i	−0.0697427	−	0.0959926i
$676$	218.021	+	213.948i	0.322516	+	0.316491i
$677$	−297.902			−0.440032			−0.220016	−	0.975496i	$-0.570611\pi$
$677$	−297.902			−0.440032			−0.220016	+	0.975496i	$0.570611\pi$
$678$	879.815	−	215.616i	1.29766	−	0.318018i
$679$	−1515.43	−	492.392i	−2.23185	−	0.725172i
$680$	242.854	+	276.336i	0.357139	+	0.406376i
$681$	293.051			0.430325
$682$	159.332	+	1038.71i	0.233624	+	1.52304i
$683$			745.826i			1.09199i	0.837790	+	0.545993i	$0.183847\pi$
$683$			745.826i			1.09199i	−0.837790	+	0.545993i	$0.816153\pi$
$684$	779.440	+	387.932i	1.13953	+	0.567153i
$685$	6.99669	−	21.5336i	0.0102142	−	0.0314359i
$686$	365.685	−	89.6183i	0.533068	−	0.130639i
$687$		−	878.401i		−	1.27860i
$688$	497.575	−	9.38299i	0.723220	−	0.0136381i
$689$	−156.858	+	113.964i	−0.227661	+	0.165405i
$690$	458.876	−	284.183i	0.665037	−	0.411860i
$691$	19.0192	−	26.1777i	0.0275242	−	0.0378838i	−0.795033	−	0.606566i	$-0.792547\pi$
$691$	19.0192	−	26.1777i	0.0275242	−	0.0378838i	0.822557	+	0.568682i	$0.192547\pi$
$692$	5.34809	−	10.7455i	0.00772845	−	0.0155281i
$693$	956.968	−	695.278i	1.38091	−	1.00329i
$694$	91.7472	−	1240.49i	0.132201	−	1.78745i
$695$	−239.623	−	77.8584i	−0.344782	−	0.112026i
$696$	−22.3948	+	99.4565i	−0.0321765	+	0.142897i
$697$	−247.120	+	760.559i	−0.354549	+	1.09119i
$698$	−117.549	−	99.4417i	−0.168408	−	0.142467i
$699$	−388.558	+	534.805i	−0.555877	+	0.765100i
$700$	308.347	+	591.317i	0.440496	+	0.844738i
$701$	124.810	+	384.125i	0.178045	+	0.547967i	0.999759	−	0.0219330i	$-0.00698206\pi$
$701$	124.810	+	384.125i	0.178045	+	0.547967i	−0.821714	+	0.569900i	$0.806982\pi$
$702$	78.5415	−	19.2482i	0.111882	−	0.0274190i
$703$	201.423	−	65.4463i	0.286519	−	0.0930957i
$704$	199.925	+	1066.18i	0.283984	+	1.51446i
$705$	145.675	+	105.839i	0.206632	+	0.150127i
$706$	168.829	+	688.902i	0.239135	+	0.975782i
$707$		−	558.270i		−	0.789633i
$708$	714.814	+	701.461i	1.00962	+	0.990765i
$709$	731.081	−	531.161i	1.03114	−	0.749170i	0.0626066	−	0.998038i	$-0.480059\pi$
$709$	731.081	−	531.161i	1.03114	−	0.749170i	0.968537	+	0.248868i	$0.0800587\pi$
$710$	−253.415	+	299.559i	−0.356923	+	0.421914i
$711$	−653.943	+	212.479i	−0.919751	+	0.298845i
$712$	651.046	−	280.523i	0.914391	−	0.393993i
$713$	714.703	−	428.601i	1.00239	−	0.601123i
$714$	514.677	−	1259.30i	0.720837	−	1.76372i
$715$	377.971	−	122.810i	0.528630	−	0.171762i
$716$	−66.4166	−	127.367i	−0.0927606	−	0.177887i
$717$	−897.604	+	652.147i	−1.25189	+	0.909550i
$718$	38.3360	+	15.6680i	0.0533927	+	0.0218217i
$719$		−	120.591i		−	0.167721i	−0.996478	−	0.0838603i	$-0.973275\pi$
$719$		−	120.591i		−	0.167721i	0.996478	−	0.0838603i	$-0.0267250\pi$
$720$	−187.557	−	248.172i	−0.260495	−	0.344683i
$721$	−242.272	−	176.021i	−0.336022	−	0.244134i
$722$	−651.003	+	403.169i	−0.901666	+	0.558405i
$723$	−1440.09	+	467.914i	−1.99183	+	0.647183i
$724$	−1073.46	−	159.661i	−1.48268	−	0.220526i
$725$	−18.2191	−	56.0726i	−0.0251298	−	0.0773415i
$726$	−885.089	+	1046.25i	−1.21913	+	1.44112i
$727$	−164.756	+	226.767i	−0.226624	+	0.311921i	−0.907154	−	0.420799i	$-0.861750\pi$
$727$	−164.756	+	226.767i	−0.226624	+	0.311921i	0.680530	+	0.732720i	$0.261750\pi$
$728$	−670.443	+	62.3160i	−0.920939	+	0.0855990i
$729$	171.675	−	528.362i	0.235494	−	0.724776i
$730$	−308.672	+	191.161i	−0.422838	+	0.261865i
$731$	558.385	+	181.430i	0.763865	+	0.248195i
$732$	−677.986	−	337.438i	−0.926210	−	0.460981i
$733$	−771.389	+	560.447i	−1.05237	+	0.764593i	−0.972662	−	0.232225i	$-0.925399\pi$
$733$	−771.389	+	560.447i	−1.05237	+	0.764593i	−0.0797101	+	0.996818i	$0.525399\pi$
$734$	75.1140	−	1015.60i	0.102335	−	1.38365i
$735$	−162.109	+	223.124i	−0.220557	+	0.303570i
$736$	722.686	−	466.640i	0.981911	−	0.634021i
$737$	−1633.94	+	1187.13i	−2.21702	+	1.61076i
$738$	255.824	−	625.942i	0.346644	−	0.848160i
$739$		−	669.227i		−	0.905585i	−0.891616	−	0.452792i	$-0.850428\pi$
$739$		−	669.227i		−	0.905585i	0.891616	−	0.452792i	$-0.149572\pi$
$740$	−74.8470	−	11.1323i	−0.101145	−	0.0150437i
$741$	334.266	−	1028.77i	0.451102	−	1.38835i
$742$	−25.9873	+	351.368i	−0.0350233	+	0.473541i
$743$		−	205.920i		−	0.277147i	−0.990352	−	0.138574i	$-0.955748\pi$
$743$		−	205.920i		−	0.277147i	0.990352	−	0.138574i	$-0.0442518\pi$
$744$	−604.444	−	824.026i	−0.812424	−	1.10756i
$745$	641.303			0.860809
$746$	−678.744	−	50.2002i	−0.909844	−	0.0672925i
$747$	297.702	+	96.7292i	0.398530	+	0.129490i
$748$	−188.272	+	1265.83i	−0.251701	+	1.69228i
$749$	1590.24			2.12315
$750$	818.970	+	334.714i	1.09196	+	0.446286i
$751$	632.461	+	870.508i	0.842158	+	1.15913i	0.985536	+	0.169464i	$0.0542035\pi$
$751$	632.461	+	870.508i	0.842158	+	1.15913i	−0.143378	+	0.989668i	$0.545797\pi$
$752$	235.316	+	164.279i	0.312921	+	0.218456i
$753$	−1079.26	−	784.126i	−1.43328	−	1.04134i
$754$	59.3662	+	4.39075i	0.0787351	+	0.00582328i
$755$	183.756	+	252.919i	0.243386	+	0.334992i
$756$	65.4753	−	131.554i	0.0866075	−	0.174013i
$757$	370.380	−	1139.91i	0.489273	−	1.50583i	−0.336422	−	0.941711i	$-0.609217\pi$
$757$	370.380	−	1139.91i	0.489273	−	1.50583i	0.825695	−	0.564117i	$-0.190783\pi$
$758$	−185.951	−	300.259i	−0.245319	−	0.396120i
$759$	1785.71	+	580.212i	2.35271	+	0.764442i
$760$	529.274	−	49.1947i	0.696413	−	0.0647299i
$761$	846.820	+	615.250i	1.11277	+	0.808476i	0.983098	−	0.183080i	$-0.0586069\pi$
$761$	846.820	+	615.250i	1.11277	+	0.808476i	0.129674	+	0.991557i	$0.458607\pi$
$762$	79.4226	+	67.1884i	0.104229	+	0.0881738i
$763$	707.396	−	229.847i	0.927125	−	0.301241i
$764$	16.8659	−	113.396i	0.0220758	−	0.148424i
$765$	−113.406	−	349.029i	−0.148244	−	0.456247i
$766$	−321.076	−	518.446i	−0.419159	−	0.676823i
$767$	343.733	−	473.108i	0.448153	−	0.616830i
$768$	−651.796	−	829.457i	−0.848693	−	1.08002i
$769$	353.464			0.459642			0.229821	−	0.973233i	$-0.426186\pi$
$769$	353.464			0.459642			0.229821	+	0.973233i	$0.426186\pi$
$770$	273.220	−	668.507i	0.354831	−	0.868191i
$771$	159.318	+	219.282i	0.206638	+	0.284413i
$772$	−1042.98	+	543.871i	−1.35101	+	0.704496i
$773$	227.355	+	699.725i	0.294120	+	0.905207i	0.983516	+	0.180823i	$0.0578760\pi$
$773$	227.355	+	699.725i	0.294120	+	0.905207i	−0.689396	+	0.724385i	$0.742124\pi$
$774$	−459.553	−	187.820i	−0.593738	−	0.242662i
$775$	543.833	+	231.395i	0.701720	+	0.298575i
$776$	−1338.71	+	576.822i	−1.72514	+	0.743327i
$777$	86.4702	+	266.128i	0.111287	+	0.342507i
$778$	−206.912	−	175.039i	−0.265954	−	0.224986i
$779$	679.174	+	934.802i	0.871853	+	1.20000i
$780$	−270.698	+	275.851i	−0.347049	+	0.353655i
$781$	−1364.93			−1.74767
$782$	985.714	−	241.569i	1.26050	−	0.308912i
$783$	−7.63614	+	10.5102i	−0.00975241	+	0.0134230i
$784$	−251.619	+	360.423i	−0.320942	+	0.459723i
$785$	−149.531	−	460.210i	−0.190486	−	0.586255i
$786$	−38.7734	−	158.214i	−0.0493300	−	0.201289i
$787$	16.2567	−	5.28213i	0.0206566	−	0.00671173i	−0.298670	−	0.954356i	$-0.596543\pi$
$787$	16.2567	−	5.28213i	0.0206566	−	0.00671173i	0.319327	+	0.947645i	$0.396543\pi$
$788$	−340.867	+	177.748i	−0.432572	+	0.225568i
$789$	1625.61	+	1181.07i	2.06034	+	1.49693i
$790$	−271.131	+	320.500i	−0.343203	+	0.405696i
$791$	−914.136	−	297.021i	−1.15567	−	0.375500i
$792$	237.712	−	1055.69i	0.300141	−	1.33294i
$793$	−136.650	+	420.567i	−0.172321	+	0.530349i
$794$	−931.571	−	68.8994i	−1.17326	−	0.0867751i
$795$	118.869	+	163.609i	0.149521	+	0.205798i
$796$	20.4231	+	10.1647i	0.0256571	+	0.0127697i
$797$	139.860	+	101.614i	0.175483	+	0.127496i	0.672060	−	0.740497i	$-0.265410\pi$
$797$	139.860	+	101.614i	0.175483	+	0.127496i	−0.496576	+	0.867993i	$0.665410\pi$
$798$	−1034.94	−	1671.13i	−1.29692	−	2.09415i
$799$	199.009	+	273.912i	0.249073	+	0.342819i
$800$	568.986	+	220.119i	0.711232	+	0.275149i
$801$	−707.186			−0.882879
$802$	−272.743	−	1112.92i	−0.340078	−	1.38768i
$803$	−1201.19	−	390.290i	−1.49588	−	0.486040i
$804$	875.139	−	1758.34i	1.08848	−	2.18699i
$805$	−572.715			−0.711447
$806$	−424.003	+	419.891i	−0.526059	+	0.520957i
$807$			979.853i			1.21419i
$808$	−337.143	−	383.624i	−0.417257	−	0.474782i
$809$	−115.288	+	354.819i	−0.142506	+	0.438590i	−0.996682	−	0.0813950i	$-0.974062\pi$
$809$	−115.288	+	354.819i	−0.142506	+	0.438590i	0.854175	+	0.519985i	$0.174062\pi$
$810$	−103.376	−	421.821i	−0.127624	−	0.520767i
$811$		−	924.100i		−	1.13946i	−0.821833	−	0.569728i	$-0.807048\pi$
$811$		−	924.100i		−	1.13946i	0.821833	−	0.569728i	$-0.192952\pi$
$812$	75.7657	−	77.2079i	0.0933075	−	0.0950836i
$813$	−1400.50	+	1017.52i	−1.72264	+	1.25157i
$814$	−138.595	−	223.792i	−0.170264	−	0.274928i
$815$	−229.578	+	315.988i	−0.281691	+	0.387715i
$816$	−406.831	−	1176.16i	−0.498567	−	1.44138i
$817$	686.311	−	498.634i	0.840038	−	0.610324i
$818$	132.947	+	9.83278i	0.162526	+	0.0120205i
$819$	638.820	+	207.565i	0.780000	+	0.253437i
$820$	−68.4242	−	407.134i	−0.0834441	−	0.496504i
$821$	239.782	−	737.975i	0.292062	−	0.898873i	−0.692131	−	0.721772i	$-0.743328\pi$
$821$	239.782	−	737.975i	0.292062	−	0.898873i	0.984193	−	0.177101i	$-0.0566720\pi$
$822$	−49.4699	+	58.4778i	−0.0601824	+	0.0711409i
$823$	238.930	−	328.859i	0.290316	−	0.399585i	−0.638801	−	0.769372i	$-0.720569\pi$
$823$	238.930	−	328.859i	0.290316	−	0.399585i	0.929117	+	0.369787i	$0.120569\pi$
$824$	−272.781	+	25.3543i	−0.331045	+	0.0307698i
$825$	411.480	+	1266.41i	0.498764	+	1.53504i
$826$	−252.944	−	1032.13i	−0.306228	−	1.24955i
$827$	−593.043	+	192.691i	−0.717102	+	0.233001i	−0.644766	−	0.764380i	$-0.723045\pi$
$827$	−593.043	+	192.691i	−0.717102	+	0.233001i	−0.0723357	+	0.997380i	$0.523045\pi$
$828$	−846.287	+	142.230i	−1.02209	+	0.171775i
$829$	−588.769	−	427.766i	−0.710216	−	0.516002i	0.173027	−	0.984917i	$-0.444645\pi$
$829$	−588.769	−	427.766i	−0.710216	−	0.516002i	−0.883243	+	0.468915i	$0.844645\pi$
$830$	185.617	−	45.4893i	0.223636	−	0.0548063i
$831$		−	1748.46i		−	2.10404i
$832$	−423.072	+	447.707i	−0.508500	+	0.538109i
$833$	−419.539	+	304.813i	−0.503648	+	0.365922i
$834$	650.734	+	550.495i	0.780256	+	0.660067i
$835$	−489.570	+	159.071i	−0.586312	+	0.190504i
$836$	1319.78	+	1295.13i	1.57869	+	1.54920i
$837$	−29.1861	−	126.917i	−0.0348699	−	0.151633i
$838$	−173.761	−	71.0163i	−0.207352	−	0.0847450i
$839$	816.065	−	265.156i	0.972664	−	0.316038i	0.220773	−	0.975325i	$-0.429142\pi$
$839$	816.065	−	265.156i	0.972664	−	0.316038i	0.751891	+	0.659288i	$0.229142\pi$
$840$	64.9980	+	699.297i	0.0773785	+	0.832497i
$841$	672.646	−	488.706i	0.799817	−	0.581101i
$842$	−107.124	+	262.107i	−0.127225	+	0.311291i
$843$			897.169i			1.06426i
$844$	−74.3502	+	499.885i	−0.0880926	+	0.592281i
$845$	−150.510	−	109.352i	−0.178118	−	0.129410i
$846$	−150.734	−	243.393i	−0.178173	−	0.287699i
$847$	1382.95	−	449.346i	1.63276	−	0.530515i
$848$	194.336	+	257.142i	0.229170	+	0.303233i
$849$	380.251	+	1170.29i	0.447881	+	1.37844i
$850$	549.495	+	464.852i	0.646465	+	0.546884i
$851$	−122.701	+	168.883i	−0.144184	+	0.198453i
$852$	1176.96	−	613.735i	1.38141	−	0.720347i
$853$	−103.241	+	317.744i	−0.121033	+	0.372501i	−0.993157	−	0.116783i	$-0.962742\pi$
$853$	−103.241	+	317.744i	−0.121033	+	0.372501i	0.872124	+	0.489284i	$0.162742\pi$
$854$	423.091	+	683.172i	0.495422	+	0.799967i
$855$	−504.309	−	163.860i	−0.589835	−	0.191649i
$856$	1092.76	−	960.358i	1.27659	−	1.12191i
$857$	−832.142	+	604.587i	−0.970994	+	0.705469i	−0.955678	−	0.294414i	$-0.904875\pi$
$857$	−832.142	+	604.587i	−0.970994	+	0.705469i	−0.0153162	+	0.999883i	$0.504875\pi$
$858$	−1340.79	−	99.1657i	−1.56270	−	0.115578i
$859$	278.527	−	383.359i	0.324245	−	0.446285i	−0.615512	−	0.788127i	$-0.711051\pi$
$859$	278.527	−	383.359i	0.324245	−	0.446285i	0.939757	+	0.341842i	$0.111051\pi$
$860$	−298.908	+	50.2355i	−0.347568	+	0.0584134i
$861$	−1235.10	+	897.351i	−1.43449	+	1.04222i
$862$	677.155	+	276.754i	0.785562	+	0.321061i
$863$		−	1284.66i		−	1.48860i	−0.667847	−	0.744299i	$-0.732784\pi$
$863$		−	1284.66i		−	1.48860i	0.667847	−	0.744299i	$-0.267216\pi$
$864$	−34.4540	−	129.940i	−0.0398773	−	0.150394i
$865$	−2.25900	+	6.95247i	−0.00261156	+	0.00803754i
$866$	1020.73	+	75.4940i	1.17868	+	0.0871755i
$867$		−	277.353i		−	0.319900i
$868$	84.9065	+	1081.03i	0.0978185	+	1.24543i
$869$	−1460.35			−1.68049
$870$	4.57972	−	61.9212i	0.00526404	−	0.0711738i
$871$	−1090.73	−	354.400i	−1.25228	−	0.406889i
$872$	347.292	−	585.144i	0.398271	−	0.671037i
$873$	1454.14			1.66569
$874$	554.774	−	1357.41i	0.634753	−	1.55310i
$875$	−551.793	−	759.479i	−0.630621	−	0.867975i
$876$	1211.26	−	203.569i	1.38272	−	0.232385i
$877$	664.752	+	482.970i	0.757983	+	0.550707i	0.898291	−	0.439401i	$-0.144809\pi$
$877$	664.752	+	482.970i	0.757983	+	0.550707i	−0.140308	+	0.990108i	$0.544809\pi$
$878$	−46.1136	+	623.491i	−0.0525212	+	0.710126i
$879$	1372.99	+	1889.76i	1.56199	+	2.14990i
$880$	−215.969	−	624.374i	−0.245419	−	0.709516i
$881$	258.836	−	796.614i	0.293798	−	0.904216i	−0.689825	−	0.723976i	$-0.742313\pi$
$881$	258.836	−	796.614i	0.293798	−	0.904216i	0.983623	−	0.180240i	$-0.0576874\pi$
$882$	372.794	−	230.873i	0.422669	−	0.261760i
$883$	76.0130	+	24.6981i	0.0860849	+	0.0279707i	0.351743	−	0.936097i	$-0.385589\pi$
$883$	76.0130	+	24.6981i	0.0860849	+	0.0279707i	−0.265658	+	0.964067i	$0.585589\pi$
$884$	−644.361	+	336.007i	−0.728915	+	0.380099i
$885$	−493.470	−	358.527i	−0.557593	−	0.405115i
$886$	−1017.41	+	1202.67i	−1.14832	+	1.35741i
$887$	−354.371	+	115.142i	−0.399517	+	0.129811i	−0.501882	−	0.864936i	$-0.667359\pi$
$887$	−354.371	+	115.142i	−0.399517	+	0.129811i	0.102365	+	0.994747i	$0.467359\pi$
$888$	220.136	+	130.654i	0.247901	+	0.147133i
$889$	−34.1105	−	104.981i	−0.0383696	−	0.118089i
$890$	−367.068	+	227.327i	−0.412436	+	0.255423i
$891$	888.026	−	1222.26i	0.996662	−	1.37179i
$892$	190.806	−	1282.86i	0.213908	−	1.43819i
$893$	489.204			0.547821
$894$	−2008.24	−	820.771i	−2.24635	−	0.918088i
$895$	51.4228	+	70.7775i	0.0574557	+	0.0790810i
$896$	124.589	+	1112.39i	0.139050	+	1.24150i
$897$	329.472	+	1014.01i	0.367305	+	1.13045i
$898$	127.055	−	310.875i	0.141487	−	0.346186i
$899$	8.43747	−	95.4950i	0.00938540	−	0.106224i
$900$	−434.380	−	426.266i	−0.482644	−	0.473629i
$901$	117.505	+	361.644i	0.130417	+	0.401381i
$902$	927.544	−	1096.44i	1.02832	−	1.21556i
$903$	658.815	+	906.781i	0.729585	+	1.00419i
$904$	−807.535	+	347.951i	−0.893291	+	0.384901i
$905$	660.981			0.730365
$906$	−251.735	−	1027.20i	−0.277853	−	1.13377i
$907$	118.705	−	163.384i	0.130877	−	0.180136i	−0.738549	−	0.674199i	$-0.764489\pi$
$907$	118.705	−	163.384i	0.130877	−	0.180136i	0.869426	+	0.494063i	$0.164489\pi$
$908$	−280.530	+	47.1469i	−0.308954	+	0.0519238i
$909$	157.437	+	484.540i	0.173198	+	0.533047i
$910$	398.305	−	97.6126i	0.437698	−	0.107267i
$911$	−490.998	+	159.535i	−0.538966	+	0.175121i	−0.565835	−	0.824518i	$-0.691446\pi$
$911$	−490.998	+	159.535i	−0.538966	+	0.175121i	0.0268695	+	0.999639i	$0.491446\pi$
$912$	−1720.38	−	523.338i	−1.88639	−	0.573836i
$913$	537.842	+	390.765i	0.589094	+	0.428002i
$914$	388.578	+	328.722i	0.425140	+	0.359652i
$915$	438.667	+	142.531i	0.479417	+	0.155772i
$916$	141.319	+	840.870i	0.154279	+	0.917980i
$917$	−53.4120	+	164.385i	−0.0582464	+	0.179264i
$918$	11.6978	−	158.163i	0.0127427	−	0.172291i
$919$	−706.969	−	973.059i	−0.769280	−	1.05882i	−0.996385	−	0.0849533i	$-0.972926\pi$
$919$	−706.969	−	973.059i	−0.769280	−	1.05882i	0.227105	−	0.973870i	$-0.427074\pi$
$920$	−393.549	+	345.866i	−0.427771	+	0.375942i
$921$	−653.358	−	474.692i	−0.709400	−	0.515409i
$922$	−347.463	+	215.185i	−0.376857	+	0.233389i
$923$	−455.576	−	627.047i	−0.493582	−	0.679357i
$924$	−1711.18	+	1743.75i	−1.85192	+	1.88718i
$925$	−148.044			−0.160048
$926$	143.139	−	35.0791i	0.154578	−	0.0378824i
$927$	259.915	+	84.4514i	0.280383	+	0.0911018i
$928$	5.43714	−	98.8100i	0.00585899	−	0.106476i
$929$	−0.992160			−0.00106799			−0.000533994	−	1.00000i	$-0.500170\pi$
$929$	−0.992160			−0.00106799			−0.000533994		1.00000i	$0.500170\pi$
$930$	437.962	+	442.251i	0.470927	+	0.475539i
$931$			749.290i			0.804823i
$932$	285.916	−	574.466i	0.306777	−	0.616380i
$933$	408.991	−	1258.74i	0.438361	−	1.34914i
$934$	574.852	−	140.879i	0.615473	−	0.150834i
$935$		−	779.430i		−	0.833615i
$936$	564.325	−	243.156i	0.602911	−	0.259782i
$937$	1488.91	−	1081.76i	1.58902	−	1.15449i	0.683704	−	0.729759i	$-0.260368\pi$
$937$	1488.91	−	1081.76i	1.58902	−	1.15449i	0.905319	−	0.424733i	$-0.139632\pi$
$938$	−1771.79	+	1097.28i	−1.88890	+	1.16981i
$939$	835.932	−	1150.56i	0.890236	−	1.22530i
$940$	−156.479	−	77.8806i	−0.166467	−	0.0828517i
$941$	−901.273	+	654.813i	−0.957782	+	0.695869i	−0.952635	−	0.304117i	$-0.901638\pi$
$941$	−901.273	+	654.813i	−0.957782	+	0.695869i	−0.00514740	+	0.999987i	$0.501638\pi$
$942$	−120.742	+	1632.53i	−0.128177	+	1.73304i
$943$	−1083.17	−	351.942i	−1.14864	−	0.373215i
$944$	−797.125	−	556.489i	−0.844412	−	0.589501i
$945$	−27.6563	+	85.1173i	−0.0292659	+	0.0900713i
$946$	−804.981	−	680.983i	−0.850931	−	0.719855i
$947$	−701.144	+	965.042i	−0.740384	+	1.01905i	0.258212	+	0.966088i	$0.416867\pi$
$947$	−701.144	+	965.042i	−0.740384	+	1.01905i	−0.998596	+	0.0529632i	$0.983133\pi$
$948$	1259.24	−	656.640i	1.32831	−	0.692658i
$949$	−221.626	−	682.094i	−0.233536	−	0.718750i
$950$	1010.06	−	247.537i	1.06323	−	0.260565i
$951$	−974.288	+	316.565i	−1.02449	+	0.332876i
$952$	−290.088	+	1288.30i	−0.304714	+	1.35325i
$953$	−1312.06	−	953.267i	−1.37677	−	1.00028i	−0.997174	−	0.0751273i	$-0.976064\pi$
$953$	−1312.06	−	953.267i	−1.37677	−	1.00028i	−0.379594	−	0.925153i	$-0.623936\pi$
$954$	−76.5332	−	312.291i	−0.0802235	−	0.327350i
$955$			69.8233i			0.0731134i
$956$	754.333	−	768.692i	0.789051	−	0.804071i
$957$	174.741	−	126.957i	0.182593	−	0.132661i
$958$	44.1061	−	52.1373i	0.0460398	−	0.0544231i
$959$	77.2964	−	25.1151i	0.0806011	−	0.0261889i
$960$	466.975	+	441.280i	0.486432	+	0.459667i
$961$	666.377	+	692.432i	0.693420	+	0.720533i
$962$	56.5504	−	138.366i	0.0587842	−	0.143832i
$963$	−1380.22	+	448.461i	−1.43325	+	0.465691i
$964$	1303.28	−	679.606i	1.35195	−	0.704986i
$965$	579.582	−	421.091i	0.600603	−	0.436363i
$966$	1793.46	+	732.989i	1.85658	+	0.758788i
$967$			886.406i			0.916656i	0.888783	+	0.458328i	$0.151551\pi$
$967$			886.406i			0.916656i	−0.888783	+	0.458328i	$0.848449\pi$
$968$	678.949	−	1143.95i	0.701393	−	1.18176i
$969$	−1716.30	−	1246.96i	−1.77121	−	1.28686i
$970$	754.780	−	467.438i	0.778124	−	0.481895i
$971$	429.313	−	139.492i	0.442135	−	0.143658i	−0.0794854	−	0.996836i	$-0.525328\pi$
$971$	429.313	−	139.492i	0.442135	−	0.143658i	0.521620	+	0.853178i	$0.325328\pi$
$972$	−193.898	+	1303.65i	−0.199483	+	1.34120i
$973$	−279.478	−	860.145i	−0.287233	−	0.884014i
$974$	−864.291	+	1021.67i	−0.887362	+	1.04894i
$975$	−444.445	+	611.725i	−0.455841	+	0.627411i
$976$	703.305	+	213.944i	0.720600	+	0.219205i
$977$	−24.8604	+	76.5123i	−0.0254456	+	0.0783135i	−0.962973	−	0.269598i	$-0.913109\pi$
$977$	−24.8604	+	76.5123i	−0.0254456	+	0.0783135i	0.937527	+	0.347912i	$0.113109\pi$
$978$	1123.34	−	695.689i	1.14861	−	0.711339i
$979$	−1428.44	−	464.129i	−1.45908	−	0.474084i
$980$	119.286	−	239.671i	0.121720	−	0.244562i
$981$	−549.152	+	398.983i	−0.559788	+	0.406710i
$982$	15.4097	−	208.350i	0.0156921	−	0.212169i
$983$	571.144	−	786.113i	0.581022	−	0.799708i	−0.412785	−	0.910828i	$-0.635444\pi$
$983$	571.144	−	786.113i	0.581022	−	0.799708i	0.993807	+	0.111121i	$0.0354440\pi$
$984$	−306.799	+	1362.51i	−0.311788	+	1.38467i
$985$	189.419	−	137.621i	0.192303	−	0.139716i
$986$	44.1686	−	108.070i	0.0447957	−	0.109605i
$987$			646.355i			0.654868i
$988$	−154.474	+	1038.59i	−0.156350	+	1.05120i
$989$	−258.388	+	795.236i	−0.261262	+	0.804081i
$990$	−48.6118	+	657.268i	−0.0491029	+	0.663907i
$991$			230.662i			0.232757i	0.993205	+	0.116378i	$0.0371285\pi$
$991$			230.662i			0.232757i	−0.993205	+	0.116378i	$0.962871\pi$
$992$	711.189	+	691.574i	0.716924	+	0.697151i
$993$	476.449			0.479807
$994$	−1404.61	−	103.885i	−1.41308	−	0.104512i
$995$	−13.2140	−	4.29350i	−0.0132804	−	0.00431508i
$996$	−639.481	−	95.1128i	−0.642049	−	0.0954948i
$997$	774.160			0.776490			0.388245	−	0.921556i	$-0.373081\pi$
$997$	774.160			0.776490			0.388245	+	0.921556i	$0.373081\pi$
$998$	282.104	+	115.296i	0.282669	+	0.115527i
$999$	19.1744	+	26.3913i	0.0191936	+	0.0264177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.l.a.35.2	✓	120
4.3	odd	2	inner	124.3.l.a.35.23	yes	120
31.8	even	5	inner	124.3.l.a.39.23	yes	120
124.39	odd	10	inner	124.3.l.a.39.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.l.a.35.2	✓	120	1.1	even	1	trivial
124.3.l.a.35.23	yes	120	4.3	odd	2	inner
124.3.l.a.39.2	yes	120	124.39	odd	10	inner
124.3.l.a.39.23	yes	120	31.8	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99455 - 0.147518i) q^{2} +(-3.91906 - 1.27338i) q^{3} +(3.95648 + 0.588464i) q^{4} -2.43619 q^{5} +(7.62893 + 3.11795i) q^{6} +(-5.14011 - 7.07475i) q^{7} +(-7.80459 - 1.75737i) q^{8} +(6.45639 + 4.69084i) q^{9} +O(q^{10})\)	\(q+(-1.99455 - 0.147518i) q^{2} +(-3.91906 - 1.27338i) q^{3} +(3.95648 + 0.588464i) q^{4} -2.43619 q^{5} +(7.62893 + 3.11795i) q^{6} +(-5.14011 - 7.07475i) q^{7} +(-7.80459 - 1.75737i) q^{8} +(6.45639 + 4.69084i) q^{9} +(4.85910 + 0.359381i) q^{10} +(9.96261 + 13.7124i) q^{11} +(-14.7563 - 7.34433i) q^{12} +(-2.97419 + 9.15362i) q^{13} +(9.20856 + 14.8692i) q^{14} +(9.54757 + 3.10219i) q^{15} +(15.3074 + 4.65649i) q^{16} +(15.2711 + 11.0951i) q^{17} +(-12.1856 - 10.3086i) q^{18} +(25.9391 - 8.42811i) q^{19} +(-9.63872 - 1.43361i) q^{20} +(11.1355 + 34.2717i) q^{21} +(-17.8481 - 28.8197i) q^{22} +(-15.8013 + 21.7486i) q^{23} +(28.3489 + 16.8255i) q^{24} -19.0650 q^{25} +(7.28251 - 17.8186i) q^{26} +(2.46926 + 3.39864i) q^{27} +(-16.1735 - 31.0159i) q^{28} +(0.955630 + 2.94113i) q^{29} +(-18.5855 - 7.59592i) q^{30} +(-28.5252 - 12.1372i) q^{31} +(-29.8445 - 11.5457i) q^{32} +(-21.5830 - 66.4257i) q^{33} +(-28.8222 - 24.3825i) q^{34} +(12.5223 + 17.2354i) q^{35} +(22.7842 + 22.3586i) q^{36} +7.76524 q^{37} +(-52.9801 + 12.9838i) q^{38} +(23.3121 - 32.0863i) q^{39} +(19.0135 + 4.28129i) q^{40} +(13.0917 + 40.2922i) q^{41} +(-17.1547 - 69.9993i) q^{42} +(29.5816 - 9.61165i) q^{43} +(31.3476 + 60.1152i) q^{44} +(-15.7290 - 11.4278i) q^{45} +(34.7248 - 41.0478i) q^{46} +(17.0588 + 5.54274i) q^{47} +(-54.0612 - 37.7412i) q^{48} +(-8.48955 + 26.1281i) q^{49} +(38.0261 + 2.81243i) q^{50} +(-45.7200 - 62.9282i) q^{51} +(-17.1539 + 34.4659i) q^{52} +(16.2975 + 11.8408i) q^{53} +(-4.42370 - 7.14302i) q^{54} +(-24.2708 - 33.4059i) q^{55} +(27.6834 + 64.2486i) q^{56} -112.389 q^{57} +(-1.47219 - 6.00720i) q^{58} +(-57.7860 - 18.7758i) q^{59} +(35.9492 + 17.8922i) q^{60} +45.9454 q^{61} +(55.1046 + 28.4163i) q^{62} -69.7888i q^{63} +(57.8233 + 27.4312i) q^{64} +(7.24569 - 22.2999i) q^{65} +(33.2495 + 135.673i) q^{66} +119.158i q^{67} +(53.8906 + 52.8839i) q^{68} +(89.6205 - 65.1131i) q^{69} +(-22.4338 - 36.2242i) q^{70} +(-47.3341 + 65.1498i) q^{71} +(-42.1459 - 47.9564i) q^{72} +(-60.2850 + 43.7996i) q^{73} +(-15.4882 - 1.14551i) q^{74} +(74.7169 + 24.2770i) q^{75} +(107.587 - 18.0814i) q^{76} +(45.8026 - 140.966i) q^{77} +(-51.2305 + 60.5589i) q^{78} +(-50.6431 + 69.7043i) q^{79} +(-37.2918 - 11.3441i) q^{80} +(-27.5445 - 84.7732i) q^{81} +(-20.1683 - 82.2961i) q^{82} +(37.3035 - 12.1206i) q^{83} +(23.8899 + 142.148i) q^{84} +(-37.2032 - 27.0297i) q^{85} +(-60.4200 + 14.8071i) q^{86} -12.7433i q^{87} +(-53.6563 - 124.527i) q^{88} +(-71.6901 + 52.0859i) q^{89} +(29.6865 + 25.1136i) q^{90} +(80.0472 - 26.0089i) q^{91} +(-75.3158 + 76.7494i) q^{92} +(96.3368 + 83.8899i) q^{93} +(-33.2070 - 13.5718i) q^{94} +(-63.1924 + 20.5325i) q^{95} +(102.260 + 83.2519i) q^{96} +(147.412 - 107.101i) q^{97} +(20.7872 - 50.8616i) q^{98} +135.265i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9}+O(q^{10}) \) 120 * q - 3 * q^2 + q^4 - 16 * q^5 - 10 * q^6 + 27 * q^8 + 72 * q^9	\( 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9} - 26 q^{10} - 66 q^{12} - 22 q^{13} - 34 q^{14} - 55 q^{16} - 6 q^{17} + 74 q^{18} - 47 q^{20} - 114 q^{21} - 56 q^{22} + 15 q^{24} + 440 q^{25} - 48 q^{26} - 8 q^{28} - 6 q^{29} - 254 q^{30} - 178 q^{32} - 90 q^{33} + 171 q^{34} - 8 q^{36} - 96 q^{37} - 42 q^{38} + 50 q^{40} - 6 q^{41} + 268 q^{42} + 196 q^{44} - 120 q^{45} - 231 q^{46} - 28 q^{48} + 48 q^{49} - 394 q^{50} - 7 q^{52} + 122 q^{53} - 126 q^{54} - 432 q^{56} - 196 q^{57} - 49 q^{58} - 163 q^{60} + 80 q^{61} + 200 q^{62} + 19 q^{64} - 156 q^{65} + 490 q^{66} + 266 q^{68} - 522 q^{69} + 65 q^{70} + 642 q^{72} + 122 q^{73} + 177 q^{74} + 517 q^{76} - 186 q^{77} + 303 q^{78} - 602 q^{80} - 168 q^{81} + 406 q^{82} + 769 q^{84} - 508 q^{85} - 677 q^{86} - 108 q^{88} - 30 q^{89} + 662 q^{90} + 910 q^{92} - 250 q^{93} + 354 q^{94} - 1230 q^{96} + 530 q^{97} + 76 q^{98}+O(q^{100}) \) 120 * q - 3 * q^2 + q^4 - 16 * q^5 - 10 * q^6 + 27 * q^8 + 72 * q^9 - 26 * q^10 - 66 * q^12 - 22 * q^13 - 34 * q^14 - 55 * q^16 - 6 * q^17 + 74 * q^18 - 47 * q^20 - 114 * q^21 - 56 * q^22 + 15 * q^24 + 440 * q^25 - 48 * q^26 - 8 * q^28 - 6 * q^29 - 254 * q^30 - 178 * q^32 - 90 * q^33 + 171 * q^34 - 8 * q^36 - 96 * q^37 - 42 * q^38 + 50 * q^40 - 6 * q^41 + 268 * q^42 + 196 * q^44 - 120 * q^45 - 231 * q^46 - 28 * q^48 + 48 * q^49 - 394 * q^50 - 7 * q^52 + 122 * q^53 - 126 * q^54 - 432 * q^56 - 196 * q^57 - 49 * q^58 - 163 * q^60 + 80 * q^61 + 200 * q^62 + 19 * q^64 - 156 * q^65 + 490 * q^66 + 266 * q^68 - 522 * q^69 + 65 * q^70 + 642 * q^72 + 122 * q^73 + 177 * q^74 + 517 * q^76 - 186 * q^77 + 303 * q^78 - 602 * q^80 - 168 * q^81 + 406 * q^82 + 769 * q^84 - 508 * q^85 - 677 * q^86 - 108 * q^88 - 30 * q^89 + 662 * q^90 + 910 * q^92 - 250 * q^93 + 354 * q^94 - 1230 * q^96 + 530 * q^97 + 76 * q^98

Introduction

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