LMFDB - Embedded newform 403.2.h.b.222.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.1
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +O(q^{10})$	\(q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +(-1.94115 - 3.36216i) q^{10} +(-1.79571 - 3.11026i) q^{11} +(-6.07388 + 10.5203i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.692707 - 1.19980i) q^{14} -4.48613 q^{15} +5.34528 q^{16} +(-1.01252 + 1.75374i) q^{17} +(6.60787 + 11.4452i) q^{18} +(-0.578215 + 1.00150i) q^{19} +(3.28270 + 5.68580i) q^{20} +(-0.800449 - 1.38642i) q^{21} +(4.47719 + 7.75473i) q^{22} -8.57580 q^{23} +(7.96055 - 13.7881i) q^{24} +(1.28771 - 2.23038i) q^{25} +(1.24664 + 2.15924i) q^{26} +6.62808 q^{27} +(-1.17145 + 2.02901i) q^{28} -4.00739 q^{29} +11.1852 q^{30} +(2.10747 - 5.15350i) q^{31} -2.27502 q^{32} +10.3471 q^{33} +(2.52449 - 4.37255i) q^{34} -0.865224 q^{35} +(-11.1747 - 19.3551i) q^{36} +(4.06515 - 7.04105i) q^{37} +(1.44165 - 2.49701i) q^{38} +2.88107 q^{39} +(-4.30237 - 7.45193i) q^{40} +(-5.94136 - 10.2907i) q^{41} +(1.99574 + 3.45672i) q^{42} +(-1.78415 + 3.09024i) q^{43} +(-7.57145 - 13.1141i) q^{44} +(4.12677 - 7.14778i) q^{45} +21.3818 q^{46} +2.60865 q^{47} +(-7.70006 + 13.3369i) q^{48} +(3.34562 + 5.79478i) q^{49} +(-3.21061 + 5.56094i) q^{50} +(-2.91714 - 5.05264i) q^{51} +(-2.10820 - 3.65152i) q^{52} +(4.10979 + 7.11836i) q^{53} -16.5256 q^{54} +(2.79611 - 4.84301i) q^{55} +(1.53532 - 2.65926i) q^{56} +(-1.66588 - 2.88539i) q^{57} +9.99152 q^{58} +(-2.11371 + 3.66106i) q^{59} -18.9154 q^{60} +0.963652 q^{61} +(-5.25450 + 12.8491i) q^{62} +2.94532 q^{63} -5.01831 q^{64} +(0.778554 - 1.34849i) q^{65} -25.7982 q^{66} +(-2.74115 - 4.74781i) q^{67} +(-4.26920 + 7.39448i) q^{68} +(12.3537 - 21.3973i) q^{69} +2.15724 q^{70} +(-1.95152 - 3.38012i) q^{71} +(14.6457 + 25.3672i) q^{72} +(2.90790 + 5.03663i) q^{73} +(-10.1355 + 17.5553i) q^{74} +(3.70998 + 6.42587i) q^{75} +(-2.43799 + 4.22272i) q^{76} +1.99561 q^{77} -7.18329 q^{78} +(-3.38651 + 5.86560i) q^{79} +(4.16159 + 7.20808i) q^{80} +(-1.59713 + 2.76631i) q^{81} +(14.8134 + 25.6576i) q^{82} +(-0.967334 - 1.67547i) q^{83} +(-3.37502 - 5.84571i) q^{84} -3.15321 q^{85} +(4.44838 - 7.70482i) q^{86} +(5.77279 - 9.99876i) q^{87} +(9.92329 + 17.1876i) q^{88} +7.41559 q^{89} +(-10.2892 + 17.8214i) q^{90} +0.555661 q^{91} -36.1591 q^{92} +(9.82250 + 12.6821i) q^{93} -6.50407 q^{94} -1.80069 q^{95} +(3.27725 - 5.67636i) q^{96} -10.7527 q^{97} +(-8.34154 - 14.4480i) q^{98} +(-9.51827 + 16.4861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.49327			−1.76301			−0.881505	−	0.472175i	$-0.843469\pi$
$2$	−2.49327			−1.76301			−0.881505	+	0.472175i	$0.843469\pi$
$3$	−1.44053	+	2.49508i	−0.831693	+	1.44053i	0.0650016	+	0.997885i	$0.479295\pi$
$3$	−1.44053	+	2.49508i	−0.831693	+	1.44053i	−0.896695	+	0.442650i	$0.854039\pi$
$4$	4.21641			2.10820
$5$	0.778554	+	1.34849i	0.348180	+	0.603065i	0.985926	−	0.167181i	$-0.0534665\pi$
$5$	0.778554	+	1.34849i	0.348180	+	0.603065i	−0.637746	+	0.770246i	$0.720133\pi$
$6$	3.59165	−	6.22091i	1.46628	−	2.53968i
$7$	−0.277831	+	0.481217i	−0.105010	+	0.181883i	−0.913742	−	0.406294i	$-0.866821\pi$
$7$	−0.277831	+	0.481217i	−0.105010	+	0.181883i	0.808732	+	0.588177i	$0.200154\pi$
$8$	−5.52611			−1.95377
$9$	−2.65028	−	4.59042i	−0.883427	−	1.53014i
$10$	−1.94115	−	3.36216i	−0.613844	−	1.06321i
$11$	−1.79571	−	3.11026i	−0.541427	−	0.937779i	−0.998822	−	0.0485156i	$-0.984551\pi$
$11$	−1.79571	−	3.11026i	−0.541427	−	0.937779i	0.457395	−	0.889263i	$-0.348782\pi$
$12$	−6.07388	+	10.5203i	−1.75338	+	3.03694i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	0.692707	−	1.19980i	0.185134	−	0.320661i
$15$	−4.48613			−1.15831
$16$	5.34528			1.33632
$17$	−1.01252	+	1.75374i	−0.245573	+	0.425344i	−0.962292	−	0.272017i	$-0.912309\pi$
$17$	−1.01252	+	1.75374i	−0.245573	+	0.425344i	0.716720	+	0.697361i	$0.245643\pi$
$18$	6.60787	+	11.4452i	1.55749	+	2.69765i
$19$	−0.578215	+	1.00150i	−0.132652	+	0.229759i	−0.924698	−	0.380702i	$-0.875682\pi$
$19$	−0.578215	+	1.00150i	−0.132652	+	0.229759i	0.792046	+	0.610461i	$0.209016\pi$
$20$	3.28270	+	5.68580i	0.734034	+	1.27138i
$21$	−0.800449	−	1.38642i	−0.174672	−	0.302541i
$22$	4.47719	+	7.75473i	0.954541	+	1.65331i
$23$	−8.57580			−1.78818			−0.894089	−	0.447888i	$-0.852176\pi$
$23$	−8.57580			−1.78818			−0.894089	+	0.447888i	$0.852176\pi$
$24$	7.96055	−	13.7881i	1.62494	−	2.81448i
$25$	1.28771	−	2.23038i	0.257542	−	0.446075i
$26$	1.24664	+	2.15924i	0.244485	+	0.423461i
$27$	6.62808			1.27557
$28$	−1.17145	+	2.02901i	−0.221383	+	0.383446i
$29$	−4.00739			−0.744154			−0.372077	−	0.928202i	$-0.621354\pi$
$29$	−4.00739			−0.744154			−0.372077	+	0.928202i	$0.621354\pi$
$30$	11.1852			2.04212
$31$	2.10747	−	5.15350i	0.378513	−	0.925596i
$31$	2.10747	−	5.15350i	0.378513	−	0.925596i
$32$	−2.27502			−0.402171
$33$	10.3471			1.80120
$34$	2.52449	−	4.37255i	0.432947	−	0.749886i
$35$	−0.865224			−0.146250
$36$	−11.1747	−	19.3551i	−1.86244	−	3.22585i
$37$	4.06515	−	7.04105i	0.668307	−	1.15754i	−0.310070	−	0.950714i	$-0.600352\pi$
$37$	4.06515	−	7.04105i	0.668307	−	1.15754i	0.978377	−	0.206829i	$-0.0663142\pi$
$38$	1.44165	−	2.49701i	0.233866	−	0.405068i
$39$	2.88107			0.461340
$40$	−4.30237	−	7.45193i	−0.680265	−	1.17825i
$41$	−5.94136	−	10.2907i	−0.927885	−	1.60714i	−0.786854	−	0.617139i	$-0.788291\pi$
$41$	−5.94136	−	10.2907i	−0.927885	−	1.60714i	−0.141031	−	0.990005i	$-0.545042\pi$
$42$	1.99574	+	3.45672i	0.307949	+	0.533383i
$43$	−1.78415	+	3.09024i	−0.272081	+	0.471258i	−0.969394	−	0.245508i	$-0.921045\pi$
$43$	−1.78415	+	3.09024i	−0.272081	+	0.471258i	0.697314	+	0.716766i	$0.254378\pi$
$44$	−7.57145	−	13.1141i	−1.14144	−	1.97703i
$45$	4.12677	−	7.14778i	0.615183	−	1.06553i
$46$	21.3818			3.15258
$47$	2.60865			0.380510			0.190255	−	0.981735i	$-0.439068\pi$
$47$	2.60865			0.380510			0.190255	+	0.981735i	$0.439068\pi$
$48$	−7.70006	+	13.3369i	−1.11141	+	1.92502i
$49$	3.34562	+	5.79478i	0.477946	+	0.827826i
$50$	−3.21061	+	5.56094i	−0.454048	+	0.786435i
$51$	−2.91714	−	5.05264i	−0.408482	−	0.707512i
$52$	−2.10820	−	3.65152i	−0.292355	−	0.506374i
$53$	4.10979	+	7.11836i	0.564522	+	0.977781i	0.997094	+	0.0761819i	$0.0242730\pi$
$53$	4.10979	+	7.11836i	0.564522	+	0.977781i	−0.432572	+	0.901600i	$0.642394\pi$
$54$	−16.5256			−2.24885
$55$	2.79611	−	4.84301i	0.377028	−	0.653031i
$56$	1.53532	−	2.65926i	0.205166	−	0.355358i
$57$	−1.66588	−	2.88539i	−0.220651	−	0.382179i
$58$	9.99152			1.31195
$59$	−2.11371	+	3.66106i	−0.275182	+	0.476629i	−0.970181	−	0.242382i	$-0.922071\pi$
$59$	−2.11371	+	3.66106i	−0.275182	+	0.476629i	0.694999	+	0.719011i	$0.255405\pi$
$60$	−18.9154			−2.44196
$61$	0.963652			0.123383			0.0616915	−	0.998095i	$-0.480351\pi$
$61$	0.963652			0.123383			0.0616915	+	0.998095i	$0.480351\pi$
$62$	−5.25450	+	12.8491i	−0.667322	+	1.63183i
$63$	2.94532			0.371075
$64$	−5.01831			−0.627289
$65$	0.778554	−	1.34849i	0.0965677	−	0.167260i
$66$	−25.7982			−3.17554
$67$	−2.74115	−	4.74781i	−0.334885	−	0.580038i	0.648578	−	0.761148i	$-0.275364\pi$
$67$	−2.74115	−	4.74781i	−0.334885	−	0.580038i	−0.983463	+	0.181111i	$0.942031\pi$
$68$	−4.26920	+	7.39448i	−0.517717	+	0.896712i
$69$	12.3537	−	21.3973i	1.48722	−	2.57593i
$70$	2.15724			0.257839
$71$	−1.95152	−	3.38012i	−0.231602	−	0.401147i	0.726677	−	0.686979i	$-0.241063\pi$
$71$	−1.95152	−	3.38012i	−0.231602	−	0.401147i	−0.958280	+	0.285832i	$0.907730\pi$
$72$	14.6457	+	25.3672i	1.72602	+	2.98955i
$73$	2.90790	+	5.03663i	0.340344	+	0.589492i	0.984496	−	0.175404i	$-0.0561233\pi$
$73$	2.90790	+	5.03663i	0.340344	+	0.589492i	−0.644153	+	0.764897i	$0.722790\pi$
$74$	−10.1355	+	17.5553i	−1.17823	+	2.04076i
$75$	3.70998	+	6.42587i	0.428391	+	0.741995i
$76$	−2.43799	+	4.22272i	−0.279657	+	0.484380i
$77$	1.99561			0.227421
$78$	−7.18329			−0.813348
$79$	−3.38651	+	5.86560i	−0.381012	+	0.659932i	−0.991207	−	0.132319i	$-0.957758\pi$
$79$	−3.38651	+	5.86560i	−0.381012	+	0.659932i	0.610195	+	0.792251i	$0.291091\pi$
$80$	4.16159	+	7.20808i	0.465280	+	0.805888i
$81$	−1.59713	+	2.76631i	−0.177459	+	0.307368i
$82$	14.8134	+	25.6576i	1.63587	+	2.83341i
$83$	−0.967334	−	1.67547i	−0.106179	−	0.183907i	0.808040	−	0.589127i	$-0.200528\pi$
$83$	−0.967334	−	1.67547i	−0.106179	−	0.183907i	−0.914219	+	0.405220i	$0.867195\pi$
$84$	−3.37502	−	5.84571i	−0.368245	−	0.637819i
$85$	−3.15321			−0.342014
$86$	4.44838	−	7.70482i	0.479681	−	0.830832i
$87$	5.77279	−	9.99876i	0.618908	−	1.07198i
$88$	9.92329	+	17.1876i	1.05783	+	1.83221i
$89$	7.41559			0.786051			0.393025	−	0.919528i	$-0.371428\pi$
$89$	7.41559			0.786051			0.393025	+	0.919528i	$0.371428\pi$
$90$	−10.2892	+	17.8214i	−1.08457	+	1.87854i
$91$	0.555661			0.0582491
$92$	−36.1591			−3.76985
$93$	9.82250	+	12.6821i	1.01855	+	1.31507i
$94$	−6.50407			−0.670844
$95$	−1.80069			−0.184746
$96$	3.27725	−	5.67636i	0.334483	−	0.579341i
$97$	−10.7527			−1.09177			−0.545886	−	0.837860i	$-0.683807\pi$
$97$	−10.7527			−1.09177			−0.545886	+	0.837860i	$0.683807\pi$
$98$	−8.34154	−	14.4480i	−0.842623	−	1.45947i
$99$	−9.51827	+	16.4861i	−0.956622	+	1.65692i
$100$	5.42950	−	9.40418i	0.542950	−	0.940418i
$101$	10.0007			0.995106			0.497553	−	0.867434i	$-0.334232\pi$
$101$	10.0007			0.995106			0.497553	+	0.867434i	$0.334232\pi$
$102$	7.27324	+	12.5976i	0.720158	+	1.24735i
$103$	−7.68910	−	13.3179i	−0.757630	−	1.31225i	−0.944056	−	0.329785i	$-0.893024\pi$
$103$	−7.68910	−	13.3179i	−0.757630	−	1.31225i	0.186426	−	0.982469i	$-0.440309\pi$
$104$	2.76305	+	4.78575i	0.270940	+	0.469281i
$105$	1.24639	−	2.15880i	0.121635	−	0.210678i
$106$	−10.2468	−	17.7480i	−0.995259	−	1.72384i
$107$	−9.20859	+	15.9497i	−0.890228	+	1.54192i	−0.0506256	+	0.998718i	$0.516122\pi$
$107$	−9.20859	+	15.9497i	−0.890228	+	1.54192i	−0.839602	+	0.543202i	$0.817212\pi$
$108$	27.9467			2.68917
$109$	8.40866			0.805404			0.402702	−	0.915331i	$-0.368071\pi$
$109$	8.40866			0.805404			0.402702	+	0.915331i	$0.368071\pi$
$110$	−6.97147	+	12.0749i	−0.664704	+	1.15130i
$111$	11.7120	+	20.2858i	1.11165	+	1.92544i
$112$	−1.48508	+	2.57224i	−0.140327	+	0.243054i
$113$	−7.42291	−	12.8569i	−0.698289	−	1.20947i	−0.969059	−	0.246828i	$-0.920612\pi$
$113$	−7.42291	−	12.8569i	−0.698289	−	1.20947i	0.270771	−	0.962644i	$-0.412721\pi$
$114$	4.15349	+	7.19405i	0.389010	+	0.673785i
$115$	−6.67672	−	11.5644i	−0.622608	−	1.07839i
$116$	−16.8968			−1.56883
$117$	−2.65028	+	4.59042i	−0.245019	+	0.424385i
$118$	5.27006	−	9.12801i	0.485148	−	0.840302i
$119$	−0.562619	−	0.974484i	−0.0515752	−	0.0893308i
$120$	24.7909			2.26309
$121$	−0.949150	+	1.64398i	−0.0862864	+	0.149452i
$122$	−2.40265			−0.217525
$123$	34.2350			3.08686
$124$	8.88596	−	21.7293i	0.797983	−	1.95135i
$125$	11.7957			1.05504
$126$	−7.34347			−0.654209
$127$	−6.13072	+	10.6187i	−0.544013	+	0.942259i	0.454655	+	0.890668i	$0.349763\pi$
$127$	−6.13072	+	10.6187i	−0.544013	+	0.942259i	−0.998668	+	0.0515911i	$0.983571\pi$
$128$	17.0621			1.50809
$129$	−5.14027	−	8.90320i	−0.452575	−	0.783883i
$130$	−1.94115	+	3.36216i	−0.170250	+	0.294881i
$131$	2.05976	−	3.56761i	0.179962	−	0.311703i	−0.761905	−	0.647689i	$-0.775736\pi$
$131$	2.05976	−	3.56761i	0.179962	−	0.311703i	0.941867	+	0.335985i	$0.109069\pi$
$132$	43.6277			3.79731
$133$	−0.321292	−	0.556493i	−0.0278595	−	0.0482541i
$134$	6.83444	+	11.8376i	0.590405	+	1.02261i
$135$	5.16031	+	8.93792i	0.444129	+	0.769254i
$136$	5.59530	−	9.69135i	0.479793	−	0.831027i
$137$	−8.99664	−	15.5826i	−0.768635	−	1.33131i	−0.938303	−	0.345813i	$-0.887603\pi$
$137$	−8.99664	−	15.5826i	−0.768635	−	1.33131i	0.169668	−	0.985501i	$-0.445730\pi$
$138$	−30.8013	+	53.3493i	−2.62198	+	4.54140i
$139$	−17.2664			−1.46452			−0.732260	−	0.681025i	$-0.761534\pi$
$139$	−17.2664			−1.46452			−0.732260	+	0.681025i	$0.761534\pi$
$140$	−3.64814			−0.308324
$141$	−3.75785	+	6.50878i	−0.316468	+	0.548139i
$142$	4.86566	+	8.42757i	0.408317	+	0.707226i
$143$	−1.79571	+	3.11026i	−0.150165	+	0.260093i
$144$	−14.1665	−	24.5371i	−1.18054	−	2.04476i
$145$	−3.11997	−	5.40395i	−0.259099	−	0.448773i
$146$	−7.25018	−	12.5577i	−0.600029	−	1.03928i
$147$	−19.2779			−1.59002
$148$	17.1404	−	29.6880i	1.40893	−	2.44034i
$149$	−8.48198	+	14.6912i	−0.694871	+	1.20355i	0.275353	+	0.961343i	$0.411205\pi$
$149$	−8.48198	+	14.6912i	−0.694871	+	1.20355i	−0.970224	+	0.242209i	$0.922128\pi$
$150$	−9.24998	−	16.0214i	−0.755258	−	1.30815i
$151$	−22.6970			−1.84705			−0.923527	−	0.383533i	$-0.874707\pi$
$151$	−22.6970			−1.84705			−0.923527	+	0.383533i	$0.874707\pi$
$152$	3.19528	−	5.53439i	0.259171	−	0.448898i
$153$	10.7339			0.867782
$154$	−4.97561			−0.400946
$155$	8.59025	−	1.17036i	0.689985	−	0.0940057i
$156$	12.1478			0.972600
$157$	−6.37607			−0.508866			−0.254433	−	0.967090i	$-0.581889\pi$
$157$	−6.37607			−0.508866			−0.254433	+	0.967090i	$0.581889\pi$
$158$	8.44348	−	14.6245i	0.671727	−	1.16347i
$159$	−23.6812			−1.87804
$160$	−1.77123	−	3.06785i	−0.140028	−	0.242535i
$161$	2.38262	−	4.12682i	0.187777	−	0.325239i
$162$	3.98209	−	6.89717i	0.312862	−	0.541893i
$163$	15.6119			1.22282			0.611410	−	0.791314i	$-0.290603\pi$
$163$	15.6119			1.22282			0.611410	+	0.791314i	$0.290603\pi$
$164$	−25.0512	−	43.3900i	−1.95617	−	3.38819i
$165$	8.05580	+	13.9531i	0.627143	+	1.08624i
$166$	2.41183	+	4.17741i	0.187194	+	0.324230i
$167$	−3.10851	+	5.38410i	−0.240544	+	0.416634i	−0.960869	−	0.277002i	$-0.910659\pi$
$167$	−3.10851	+	5.38410i	−0.240544	+	0.416634i	0.720325	+	0.693636i	$0.243992\pi$
$168$	4.42337	+	7.66150i	0.341270	+	0.591098i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	7.86181			0.602973
$171$	6.12973			0.468752
$172$	−7.52271	+	13.0297i	−0.573602	+	0.993507i
$173$	−11.8858	−	20.5868i	−0.903660	−	1.56518i	−0.822706	−	0.568467i	$-0.807537\pi$
$173$	−11.8858	−	20.5868i	−0.903660	−	1.56518i	−0.0809538	−	0.996718i	$-0.525797\pi$
$174$	−14.3931	+	24.9296i	−1.09114	+	1.88991i
$175$	0.715529	+	1.23933i	0.0540889	+	0.0936848i
$176$	−9.59857	−	16.6252i	−0.723520	−	1.25317i
$177$	−6.08975	−	10.5478i	−0.457734	−	0.792818i
$178$	−18.4891			−1.38582
$179$	2.39926	−	4.15563i	0.179329	−	0.310607i	−0.762322	−	0.647198i	$-0.775941\pi$
$179$	2.39926	−	4.15563i	0.179329	−	0.310607i	0.941651	+	0.336591i	$0.109274\pi$
$180$	17.4002	−	30.1379i	1.29693	−	2.24635i
$181$	−8.59696	−	14.8904i	−0.639007	−	1.10679i	−0.985651	−	0.168796i	$-0.946012\pi$
$181$	−8.59696	−	14.8904i	−0.639007	−	1.10679i	0.346644	−	0.937997i	$-0.387321\pi$
$182$	−1.38541			−0.102694
$183$	−1.38817	+	2.40439i	−0.102617	+	0.177737i
$184$	47.3908			3.49370
$185$	12.6598			0.930764
$186$	−24.4902	−	31.6199i	−1.79571	−	2.31849i
$187$	7.27278			0.531838
$188$	10.9991			0.802194
$189$	−1.84148	+	3.18954i	−0.133948	+	0.232005i
$190$	4.48960			0.325710
$191$	11.5012	+	19.9207i	0.832201	+	1.44141i	0.896289	+	0.443470i	$0.146253\pi$
$191$	11.5012	+	19.9207i	0.832201	+	1.44141i	−0.0640883	+	0.997944i	$0.520414\pi$
$192$	7.22905	−	12.5211i	0.521712	−	0.903631i
$193$	−10.8589	+	18.8082i	−0.781641	+	1.35384i	0.149345	+	0.988785i	$0.452284\pi$
$193$	−10.8589	+	18.8082i	−0.781641	+	1.35384i	−0.930985	+	0.365056i	$0.881050\pi$
$194$	26.8094			1.92480
$195$	2.24307	+	3.88511i	0.160629	+	0.278218i
$196$	14.1065	+	24.4332i	1.00761	+	1.74523i
$197$	−6.99005	−	12.1071i	−0.498021	−	0.862597i	0.501977	−	0.864881i	$-0.332606\pi$
$197$	−6.99005	−	12.1071i	−0.498021	−	0.862597i	−0.999997	+	0.00228395i	$0.999273\pi$
$198$	23.7316	−	41.1044i	1.68653	−	2.92116i
$199$	−6.81031	−	11.7958i	−0.482770	−	0.836182i	0.517034	−	0.855965i	$-0.327036\pi$
$199$	−6.81031	−	11.7958i	−0.482770	−	0.836182i	−0.999804	+	0.0197825i	$0.993703\pi$
$200$	−7.11602	+	12.3253i	−0.503178	+	0.871530i
$201$	15.7949			1.11409
$202$	−24.9344			−1.75438
$203$	1.11338	−	1.92842i	0.0781437	−	0.135349i
$204$	−12.2999	−	21.3040i	−0.861163	−	1.49158i
$205$	9.25134	−	16.0238i	0.646142	−	1.11915i
$206$	19.1710	+	33.2052i	1.33571	+	2.31352i
$207$	22.7283	+	39.3666i	1.57973	+	2.73616i
$208$	−2.67264	−	4.62915i	−0.185314	−	0.320974i
$209$	4.15323			0.287285
$210$	−3.10758	+	5.38248i	−0.214443	+	0.371427i
$211$	0.224037	−	0.388043i	0.0154233	−	0.0267140i	−0.858211	−	0.513298i	$-0.828424\pi$
$211$	0.224037	−	0.388043i	0.0154233	−	0.0267140i	0.873634	+	0.486584i	$0.161757\pi$
$212$	17.3285	+	30.0139i	1.19013	+	2.06136i
$213$	11.2449			0.770488
$214$	22.9595	−	39.7670i	1.56948	−	2.71842i
$215$	−5.55623			−0.378932
$216$	−36.6275			−2.49218
$217$	1.89443	+	2.44595i	0.128602	+	0.166042i
$218$	−20.9651			−1.41994
$219$	−16.7557			−1.13225
$220$	11.7896	−	20.4201i	0.794852	−	1.37672i
$221$	2.02504			0.136219
$222$	−29.2012	−	50.5779i	−1.95986	−	3.39457i
$223$	−5.20601	+	9.01707i	−0.348620	+	0.603828i	−0.986005	−	0.166718i	$-0.946683\pi$
$223$	−5.20601	+	9.01707i	−0.348620	+	0.603828i	0.637384	+	0.770546i	$0.280016\pi$
$224$	0.632071	−	1.09478i	0.0422320	−	0.0731480i
$225$	−13.6512			−0.910077
$226$	18.5073	+	32.0556i	1.23109	+	2.13231i
$227$	−7.86656	−	13.6253i	−0.522122	−	0.904342i	−0.999669	−	0.0257356i	$-0.991807\pi$
$227$	−7.86656	−	13.6253i	−0.522122	−	0.904342i	0.477547	−	0.878606i	$-0.341526\pi$
$228$	−7.02402	−	12.1660i	−0.465177	−	0.805710i
$229$	−4.87163	+	8.43790i	−0.321926	+	0.557592i	−0.980885	−	0.194586i	$-0.937664\pi$
$229$	−4.87163	+	8.43790i	−0.321926	+	0.557592i	0.658959	+	0.752179i	$0.270997\pi$
$230$	16.6469	+	28.8333i	1.09766	+	1.90121i
$231$	−2.87475	+	4.97921i	−0.189145	+	0.327608i
$232$	22.1453			1.45391
$233$	13.2879			0.870519			0.435259	−	0.900305i	$-0.356657\pi$
$233$	13.2879			0.870519			0.435259	+	0.900305i	$0.356657\pi$
$234$	6.60787	−	11.4452i	0.431970	−	0.748194i
$235$	2.03097	+	3.51775i	0.132486	+	0.229473i
$236$	−8.91227	+	15.4365i	−0.580140	+	1.00483i
$237$	−9.75676	−	16.8992i	−0.633770	−	1.09772i
$238$	1.40276	+	2.42966i	0.0909276	+	0.157491i
$239$	0.425385	+	0.736788i	0.0275159	+	0.0476589i	0.879455	−	0.475981i	$-0.157907\pi$
$239$	0.425385	+	0.736788i	0.0275159	+	0.0476589i	−0.851940	+	0.523640i	$0.824574\pi$
$240$	−23.9796			−1.54788
$241$	−0.908878	+	1.57422i	−0.0585460	+	0.101405i	−0.893813	−	0.448440i	$-0.851980\pi$
$241$	−0.908878	+	1.57422i	−0.0585460	+	0.101405i	0.835267	+	0.549845i	$0.185313\pi$
$242$	2.36649	−	4.09888i	0.152124	−	0.263486i
$243$	5.34067	+	9.25030i	0.342604	+	0.593407i
$244$	4.06315			0.260117
$245$	−5.20949	+	9.02310i	−0.332822	+	0.576465i
$246$	−85.3571			−5.44217
$247$	1.15643			0.0735819
$248$	−11.6461	+	28.4788i	−0.739529	+	1.80841i
$249$	5.57391			0.353232
$250$	−29.4100			−1.86005
$251$	4.97987	−	8.62539i	0.314327	−	0.544430i	−0.664967	−	0.746872i	$-0.731555\pi$
$251$	4.97987	−	8.62539i	0.314327	−	0.544430i	0.979294	+	0.202442i	$0.0648879\pi$
$252$	12.4187			0.782302
$253$	15.3997	+	26.6730i	0.968168	+	1.67692i
$254$	15.2856	−	26.4754i	0.959101	−	1.66121i
$255$	4.54231	−	7.86751i	0.284450	−	0.492682i
$256$	−32.5037			−2.03148
$257$	−7.29132	−	12.6289i	−0.454820	−	0.787772i	0.543858	−	0.839177i	$-0.316963\pi$
$257$	−7.29132	−	12.6289i	−0.454820	−	0.787772i	−0.998678	+	0.0514059i	$0.983630\pi$
$258$	12.8161	+	22.1981i	0.797895	+	1.38199i
$259$	2.25885	+	3.91244i	0.140358	+	0.243107i
$260$	3.28270	−	5.68580i	0.203584	−	0.352619i
$261$	10.6207	+	18.3956i	0.657406	+	1.13866i
$262$	−5.13554	+	8.89502i	−0.317275	+	0.549536i
$263$	−12.5034			−0.770995			−0.385498	−	0.922709i	$-0.625970\pi$
$263$	−12.5034			−0.770995			−0.385498	+	0.922709i	$0.625970\pi$
$264$	−57.1794			−3.51915
$265$	−6.39938	+	11.0840i	−0.393111	+	0.680888i
$266$	0.801068	+	1.38749i	0.0491166	+	0.0850725i
$267$	−10.6824	+	18.5025i	−0.653753	+	1.13233i
$268$	−11.5578	−	20.0187i	−0.706006	−	1.22284i
$269$	14.5585	+	25.2161i	0.887649	+	1.53745i	0.842648	+	0.538465i	$0.180996\pi$
$269$	14.5585	+	25.2161i	0.887649	+	1.53745i	0.0450010	+	0.998987i	$0.485671\pi$
$270$	−12.8661	−	22.2847i	−0.783004	−	1.35620i
$271$	−5.37556			−0.326542			−0.163271	−	0.986581i	$-0.552204\pi$
$271$	−5.37556			−0.326542			−0.163271	+	0.986581i	$0.552204\pi$
$272$	−5.41221	+	9.37422i	−0.328164	+	0.568396i
$273$	−0.800449	+	1.38642i	−0.0484454	+	0.0839099i
$274$	22.4311	+	38.8518i	1.35511	+	2.34712i
$275$	−9.24940			−0.557760
$276$	52.0884	−	90.2198i	3.13535	−	5.43059i
$277$	2.04699			0.122992			0.0614958	−	0.998107i	$-0.480413\pi$
$277$	2.04699			0.122992			0.0614958	+	0.998107i	$0.480413\pi$
$278$	43.0499			2.58196
$279$	−29.2421	+	3.98404i	−1.75068	+	0.238518i
$280$	4.78132			0.285739
$281$	−21.5339			−1.28461			−0.642304	−	0.766450i	$-0.722021\pi$
$281$	−21.5339			−1.28461			−0.642304	+	0.766450i	$0.722021\pi$
$282$	9.36934	−	16.2282i	0.557936	−	0.966374i
$283$	22.7491			1.35229			0.676146	−	0.736768i	$-0.263649\pi$
$283$	22.7491			1.35229			0.676146	+	0.736768i	$0.263649\pi$
$284$	−8.22839	−	14.2520i	−0.488265	−	0.845700i
$285$	2.59395	−	4.49285i	0.153652	−	0.266134i
$286$	4.47719	−	7.75473i	0.264742	−	0.458547i
$287$	6.60277			0.389749
$288$	6.02945	+	10.4433i	0.355289	+	0.615378i
$289$	6.44960	+	11.1710i	0.379388	+	0.657120i
$290$	7.77894	+	13.4735i	0.456795	+	0.791192i
$291$	15.4896	−	26.8288i	0.908019	−	1.57273i
$292$	12.2609	+	21.2365i	0.717514	+	1.24277i
$293$	12.0567	−	20.8827i	0.704357	−	1.21998i	−0.262566	−	0.964914i	$-0.584569\pi$
$293$	12.0567	−	20.8827i	0.704357	−	1.21998i	0.966923	−	0.255068i	$-0.0820980\pi$
$294$	48.0651			2.80322
$295$	−6.58255			−0.383251
$296$	−22.4645	+	38.9096i	−1.30572	+	2.26158i
$297$	−11.9021	−	20.6150i	−0.690630	−	1.19621i
$298$	21.1479	−	36.6292i	1.22506	−	2.12187i
$299$	4.28790	+	7.42686i	0.247976	+	0.429507i
$300$	15.6428	+	27.0941i	0.903136	+	1.56428i
$301$	−0.991384	−	1.71713i	−0.0571424	−	0.0989736i
$302$	56.5898			3.25637
$303$	−14.4063	+	24.9525i	−0.827623	+	1.43348i
$304$	−3.09072	+	5.35329i	−0.177265	+	0.307032i
$305$	0.750255	+	1.29948i	0.0429595	+	0.0744080i
$306$	−26.7624			−1.52991
$307$	4.21580	−	7.30198i	0.240608	−	0.416746i	−0.720279	−	0.693684i	$-0.755986\pi$
$307$	4.21580	−	7.30198i	0.240608	−	0.416746i	0.960888	+	0.276938i	$0.0893197\pi$
$308$	8.41432			0.479450
$309$	44.3057			2.52046
$310$	−21.4178	+	2.91803i	−1.21645	+	0.165733i
$311$	22.4824			1.27486			0.637431	−	0.770508i	$-0.279997\pi$
$311$	22.4824			1.27486			0.637431	+	0.770508i	$0.279997\pi$
$312$	−15.9211			−0.901355
$313$	−1.77852	+	3.08049i	−0.100528	+	0.174119i	−0.911902	−	0.410407i	$-0.865386\pi$
$313$	−1.77852	+	3.08049i	−0.100528	+	0.174119i	0.811374	+	0.584527i	$0.198720\pi$
$314$	15.8973			0.897136
$315$	2.29309	+	3.97174i	0.129201	+	0.223782i
$316$	−14.2789	+	24.7318i	−0.803250	+	1.39127i
$317$	4.70488	−	8.14908i	0.264252	−	0.457698i	−0.703115	−	0.711076i	$-0.748208\pi$
$317$	4.70488	−	8.14908i	0.264252	−	0.457698i	0.967367	+	0.253378i	$0.0815416\pi$
$318$	59.0436			3.31100
$319$	7.19612	+	12.4640i	0.402905	+	0.697852i
$320$	−3.90702	−	6.76716i	−0.218409	−	0.378296i
$321$	−26.5306	−	45.9523i	−1.48079	−	2.56481i
$322$	−5.94052	+	10.2893i	−0.331052	+	0.573400i
$323$	−1.17091	−	2.02808i	−0.0651512	−	0.112845i
$324$	−6.73416	+	11.6639i	−0.374120	+	0.647995i
$325$	−2.57542			−0.142858
$326$	−38.9248			−2.15584
$327$	−12.1130	+	20.9803i	−0.669849	+	1.16021i
$328$	32.8326	+	56.8678i	1.81288	+	3.14000i
$329$	−0.724762	+	1.25532i	−0.0399574	+	0.0692083i
$330$	−20.0853	−	34.7888i	−1.10566	−	1.91506i
$331$	−14.7420	−	25.5339i	−0.810294	−	1.40347i	−0.912659	−	0.408723i	$-0.865974\pi$
$331$	−14.7420	−	25.5339i	−0.810294	−	1.40347i	0.102365	−	0.994747i	$-0.467359\pi$
$332$	−4.07867	−	7.06447i	−0.223846	−	0.387713i
$333$	−43.0952			−2.36160
$334$	7.75037	−	13.4240i	0.424081	−	0.734530i
$335$	4.26827	−	7.39286i	0.233200	−	0.403915i
$336$	−4.27862	−	7.41079i	−0.233418	−	0.404292i
$337$	−31.5402			−1.71811			−0.859053	−	0.511887i	$-0.828947\pi$
$337$	−31.5402			−1.71811			−0.859053	+	0.511887i	$0.828947\pi$
$338$	1.24664	−	2.15924i	0.0678081	−	0.117447i
$339$	42.7718			2.32305
$340$	−13.2952			−0.721034
$341$	−19.8131	+	2.69940i	−1.07294	+	0.146181i
$342$	−15.2831			−0.826415
$343$	−7.60769			−0.410777
$344$	9.85942	−	17.0770i	0.531584	−	0.920731i
$345$	38.4722			2.07127
$346$	29.6345	+	51.3285i	1.59316	+	2.75944i
$347$	−0.927776	+	1.60696i	−0.0498056	+	0.0862659i	−0.889853	−	0.456247i	$-0.849194\pi$
$347$	−0.927776	+	1.60696i	−0.0498056	+	0.0862659i	0.840048	+	0.542512i	$0.182527\pi$
$348$	24.3404	−	42.1589i	1.30478	−	2.25995i
$349$	−16.1865			−0.866446			−0.433223	−	0.901287i	$-0.642624\pi$
$349$	−16.1865			−0.866446			−0.433223	+	0.901287i	$0.642624\pi$
$350$	−1.78401	−	3.09000i	−0.0953593	−	0.165167i
$351$	−3.31404	−	5.74008i	−0.176890	−	0.306383i
$352$	4.08528	+	7.07591i	0.217746	+	0.377147i
$353$	−16.0898	+	27.8684i	−0.856376	+	1.48329i	0.0189873	+	0.999820i	$0.493956\pi$
$353$	−16.0898	+	27.8684i	−0.856376	+	1.48329i	−0.875363	+	0.483466i	$0.839378\pi$
$354$	15.1834	+	26.2984i	0.806989	+	1.39775i
$355$	3.03872	−	5.26322i	0.161278	−	0.279343i
$356$	31.2671			1.65716
$357$	3.24189			0.171579
$358$	−5.98200	+	10.3611i	−0.316158	+	0.547603i
$359$	−1.92910	−	3.34130i	−0.101814	−	0.176347i	0.810618	−	0.585575i	$-0.199131\pi$
$359$	−1.92910	−	3.34130i	−0.101814	−	0.176347i	−0.912432	+	0.409228i	$0.865798\pi$
$360$	−22.8050	+	39.4994i	−1.20193	+	2.08180i
$361$	8.83133	+	15.2963i	0.464807	+	0.805069i
$362$	21.4346	+	37.1258i	1.12658	+	1.95129i
$363$	−2.73457	−	4.73641i	−0.143528	−	0.248597i
$364$	2.34289			0.122801
$365$	−4.52791	+	7.84257i	−0.237002	+	0.410499i
$366$	3.46110	−	5.99480i	0.180914	−	0.313353i
$367$	0.245949	+	0.425997i	0.0128385	+	0.0222369i	0.872373	−	0.488840i	$-0.162580\pi$
$367$	0.245949	+	0.425997i	0.0128385	+	0.0222369i	−0.859535	+	0.511077i	$0.829247\pi$
$368$	−45.8401			−2.38958
$369$	−31.4926	+	54.5467i	−1.63944	+	2.83959i
$370$	−31.5642			−1.64095
$371$	−4.56730			−0.237122
$372$	41.4157	+	53.4729i	2.14730	+	2.77244i
$373$	0.335471			0.0173700			0.00868501	−	0.999962i	$-0.497235\pi$
$373$	0.335471			0.0173700			0.00868501	+	0.999962i	$0.497235\pi$
$374$	−18.1330			−0.937636
$375$	−16.9922	+	29.4313i	−0.877472	+	1.51983i
$376$	−14.4157			−0.743432
$377$	2.00370	+	3.47050i	0.103196	+	0.178740i
$378$	4.59132	−	7.95239i	0.236152	−	0.409027i
$379$	6.77322	−	11.7316i	0.347917	−	0.602610i	−0.637962	−	0.770068i	$-0.720222\pi$
$379$	6.77322	−	11.7316i	0.347917	−	0.602610i	0.985879	+	0.167458i	$0.0535558\pi$
$380$	−7.59243			−0.389483
$381$	−17.6630	−	30.5933i	−0.904904	−	1.56734i
$382$	−28.6757	−	49.6678i	−1.46718	−	2.54123i
$383$	−3.45793	−	5.98931i	−0.176692	−	0.306039i	0.764054	−	0.645153i	$-0.223206\pi$
$383$	−3.45793	−	5.98931i	−0.176692	−	0.306039i	−0.940745	+	0.339113i	$0.889873\pi$
$384$	−24.5785	+	42.5712i	−1.25427	+	2.17245i
$385$	1.55369	+	2.69107i	0.0791835	+	0.137150i
$386$	27.0742	−	46.8939i	1.37804	−	2.38684i
$387$	18.9140			0.961454
$388$	−45.3378			−2.30168
$389$	4.97047	−	8.60911i	0.252013	−	0.436499i	−0.712067	−	0.702112i	$-0.752241\pi$
$389$	4.97047	−	8.60911i	0.252013	−	0.436499i	0.964080	+	0.265612i	$0.0855741\pi$
$390$	−5.59258	−	9.68663i	−0.283191	−	0.490502i
$391$	8.68319	−	15.0397i	0.439128	−	0.760591i
$392$	−18.4883	−	32.0226i	−0.933798	−	1.61739i
$393$	5.93431	+	10.2785i	0.299346	+	0.518483i
$394$	17.4281	+	30.1864i	0.878015	+	1.52077i
$395$	−10.5463			−0.530642
$396$	−40.1329	+	69.5122i	−2.01675	+	3.49312i
$397$	−6.05106	+	10.4807i	−0.303694	+	0.526013i	−0.976970	−	0.213378i	$-0.931553\pi$
$397$	−6.05106	+	10.4807i	−0.303694	+	0.526013i	0.673276	+	0.739391i	$0.264887\pi$
$398$	16.9800	+	29.4101i	0.851128	+	1.47420i
$399$	1.85133			0.0926823
$400$	6.88316	−	11.9220i	0.344158	−	0.596099i
$401$	12.2445			0.611463			0.305732	−	0.952118i	$-0.401099\pi$
$401$	12.2445			0.611463			0.305732	+	0.952118i	$0.401099\pi$
$402$	−39.3810			−1.96414
$403$	−5.51680	+	0.751626i	−0.274811	+	0.0374411i
$404$	42.1670			2.09789
$405$	−4.97381			−0.247151
$406$	−2.77595	+	4.80809i	−0.137768	+	0.238621i
$407$	−29.1994			−1.44736
$408$	16.1205	+	27.9215i	0.798082	+	1.38232i
$409$	−10.8913	+	18.8643i	−0.538539	+	0.932778i	0.460444	+	0.887689i	$0.347690\pi$
$409$	−10.8913	+	18.8643i	−0.538539	+	0.932778i	−0.998983	+	0.0450887i	$0.985643\pi$
$410$	−23.0661	+	39.9517i	−1.13915	+	1.97307i
$411$	51.8399			2.55707
$412$	−32.4204	−	56.1538i	−1.59724	−	2.76650i
$413$	−1.17451	−	2.03431i	−0.0577938	−	0.100102i
$414$	−56.6678	−	98.1515i	−2.78507	−	4.82389i
$415$	1.50624	−	2.60889i	0.0739386	−	0.128065i
$416$	1.13751	+	1.97023i	0.0557711	+	0.0965983i
$417$	24.8729	−	43.0811i	1.21803	−	2.10969i
$418$	−10.3551			−0.506486
$419$	−13.9437			−0.681193			−0.340596	−	0.940210i	$-0.610629\pi$
$419$	−13.9437			−0.681193			−0.340596	+	0.940210i	$0.610629\pi$
$420$	5.25527	−	9.10239i	0.256431	−	0.444151i
$421$	5.71663	+	9.90150i	0.278612	+	0.482570i	0.971040	−	0.238917i	$-0.0767924\pi$
$421$	5.71663	+	9.90150i	0.278612	+	0.482570i	−0.692428	+	0.721487i	$0.743459\pi$
$422$	−0.558585	+	0.967498i	−0.0271915	+	0.0470970i
$423$	−6.91365	−	11.9748i	−0.336153	−	0.582234i
$424$	−22.7111	−	39.3368i	−1.10295	−	1.91036i
$425$	2.60766	+	4.51661i	0.126490	+	0.219088i
$426$	−28.0366			−1.35838
$427$	−0.267732	+	0.463725i	−0.0129565	+	0.0224412i
$428$	−38.8272	+	67.2506i	−1.87678	+	3.25068i
$429$	−5.17357	−	8.96088i	−0.249782	−	0.432635i
$430$	13.8532			0.668061
$431$	−3.49987	+	6.06195i	−0.168583	+	0.291994i	−0.937922	−	0.346847i	$-0.887252\pi$
$431$	−3.49987	+	6.06195i	−0.168583	+	0.291994i	0.769339	+	0.638841i	$0.220586\pi$
$432$	35.4289			1.70457
$433$	−20.9730			−1.00790			−0.503949	−	0.863733i	$-0.668120\pi$
$433$	−20.9730			−1.00790			−0.503949	+	0.863733i	$0.668120\pi$
$434$	−4.72333	−	6.09842i	−0.226727	−	0.292734i
$435$	17.9777			0.861965
$436$	35.4544			1.69796
$437$	4.95866	−	8.58865i	0.237205	−	0.410851i
$438$	41.7765			1.99616
$439$	−9.22512	−	15.9784i	−0.440291	−	0.762606i	0.557420	−	0.830231i	$-0.311791\pi$
$439$	−9.22512	−	15.9784i	−0.440291	−	0.762606i	−0.997711	+	0.0676243i	$0.978458\pi$
$440$	−15.4516	+	26.7630i	−0.736627	+	1.27588i
$441$	17.7337	−	30.7156i	0.844460	−	1.46265i
$442$	−5.04898			−0.240156
$443$	−4.97714	−	8.62067i	−0.236471	−	0.409580i	0.723228	−	0.690609i	$-0.242658\pi$
$443$	−4.97714	−	8.62067i	−0.236471	−	0.409580i	−0.959699	+	0.281029i	$0.909324\pi$
$444$	49.3825	+	85.5331i	2.34359	+	4.05922i
$445$	5.77343	+	9.99988i	0.273687	+	0.474040i
$446$	12.9800	−	22.4820i	0.614621	−	1.06455i
$447$	−24.4372	−	42.3264i	−1.15584	−	2.00197i
$448$	1.39424	−	2.41489i	0.0658716	−	0.114093i
$449$	19.8008			0.934456			0.467228	−	0.884137i	$-0.345253\pi$
$449$	19.8008			0.934456			0.467228	+	0.884137i	$0.345253\pi$
$450$	34.0360			1.60447
$451$	−21.3379	+	36.9584i	−1.00476	+	1.74030i
$452$	−31.2980	−	54.2098i	−1.47213	−	2.54981i
$453$	32.6958	−	56.6308i	1.53618	−	2.66075i
$454$	19.6135	+	33.9715i	0.920506	+	1.59436i
$455$	0.432612	+	0.749306i	0.0202812	+	0.0351280i
$456$	9.20582	+	15.9450i	0.431102	+	0.746691i
$457$	4.83375			0.226113			0.113057	−	0.993589i	$-0.463936\pi$
$457$	4.83375			0.226113			0.113057	+	0.993589i	$0.463936\pi$
$458$	12.1463	−	21.0380i	0.567559	−	0.983041i
$459$	−6.71107	+	11.6239i	−0.313246	+	0.542558i
$460$	−28.1518	−	48.7603i	−1.31258	−	2.27346i
$461$	14.1690			0.659915			0.329957	−	0.943996i	$-0.392966\pi$
$461$	14.1690			0.659915			0.329957	+	0.943996i	$0.392966\pi$
$462$	7.16753	−	12.4145i	0.333464	−	0.577576i
$463$	−24.4650			−1.13699			−0.568493	−	0.822688i	$-0.692473\pi$
$463$	−24.4650			−1.13699			−0.568493	+	0.822688i	$0.692473\pi$
$464$	−21.4206			−0.994428
$465$	−9.45440	+	23.1193i	−0.438437	+	1.07213i
$466$	−33.1303			−1.53473
$467$	16.9234			0.783122			0.391561	−	0.920152i	$-0.371935\pi$
$467$	16.9234			0.783122			0.391561	+	0.920152i	$0.371935\pi$
$468$	−11.1747	+	19.3551i	−0.516549	+	0.894689i
$469$	3.04630			0.140665
$470$	−5.06377	−	8.77070i	−0.233574	−	0.404562i
$471$	9.18495	−	15.9088i	0.423220	−	0.733039i
$472$	11.6806	−	20.2314i	0.537643	−	0.931226i
$473$	12.8153			0.589247
$474$	24.3263	+	42.1343i	1.11734	+	1.93529i
$475$	1.48914	+	2.57927i	0.0683266	+	0.118345i
$476$	−2.37223	−	4.10882i	−0.108731	−	0.188328i
$477$	21.7842	−	37.7313i	0.997428	−	1.72760i
$478$	−1.06060	−	1.83701i	−0.0485108	−	0.0840231i
$479$	16.3875	−	28.3840i	0.748766	−	1.29690i	−0.199649	−	0.979867i	$-0.563980\pi$
$479$	16.3875	−	28.3840i	0.748766	−	1.29690i	0.948415	−	0.317033i	$-0.102686\pi$
$480$	10.2061			0.465841
$481$	−8.13031			−0.370710
$482$	2.26608	−	3.92497i	0.103217	−	0.178777i
$483$	6.86450	+	11.8897i	0.312345	+	0.540998i
$484$	−4.00200	+	6.93167i	−0.181909	+	0.315076i
$485$	−8.37156	−	14.5000i	−0.380133	−	0.658409i
$486$	−13.3157	−	23.0635i	−0.604014	−	1.04618i
$487$	−13.8452	−	23.9805i	−0.627384	−	1.08666i	−0.988075	−	0.153976i	$-0.950792\pi$
$487$	−13.8452	−	23.9805i	−0.627384	−	1.08666i	0.360691	−	0.932686i	$-0.382541\pi$
$488$	−5.32525			−0.241063
$489$	−22.4895	+	38.9530i	−1.01701	+	1.76151i
$490$	12.9887	−	22.4971i	0.586769	−	1.01631i
$491$	5.29201	+	9.16604i	0.238825	+	0.413657i	0.960377	−	0.278703i	$-0.0899044\pi$
$491$	5.29201	+	9.16604i	0.238825	+	0.413657i	−0.721552	+	0.692360i	$0.756571\pi$
$492$	144.349			6.50774
$493$	4.05757	−	7.02792i	0.182744	−	0.316522i
$494$	−2.88330			−0.129726
$495$	−29.6419			−1.33231
$496$	11.2650	−	27.5469i	0.505815	−	1.23689i
$497$	2.16876			0.0972823
$498$	−13.8973			−0.622752
$499$	−6.54541	+	11.3370i	−0.293013	+	0.507513i	−0.974521	−	0.224298i	$-0.927991\pi$
$499$	−6.54541	+	11.3370i	−0.293013	+	0.507513i	0.681508	+	0.731811i	$0.261325\pi$
$500$	49.7356			2.22425
$501$	−8.95584	−	15.5120i	−0.400117	−	0.693024i
$502$	−12.4162	+	21.5055i	−0.554161	+	0.959835i
$503$	−10.7082	+	18.5471i	−0.477453	+	0.826973i	−0.999666	−	0.0258423i	$-0.991773\pi$
$503$	−10.7082	+	18.5471i	−0.477453	+	0.826973i	0.522213	+	0.852815i	$0.325107\pi$
$504$	−16.2761			−0.724997
$505$	7.78607	+	13.4859i	0.346476	+	0.600114i
$506$	−38.3955	−	66.5030i	−1.70689	−	2.95642i
$507$	−1.44053	−	2.49508i	−0.0639764	−	0.110810i
$508$	−25.8496	+	44.7728i	−1.14689	+	1.98647i
$509$	4.86313	+	8.42319i	0.215555	+	0.373352i	0.953444	−	0.301570i	$-0.0975107\pi$
$509$	4.86313	+	8.42319i	0.215555	+	0.373352i	−0.737889	+	0.674922i	$0.764177\pi$
$510$	−11.3252	+	19.6158i	−0.501489	+	0.868604i
$511$	−3.23161			−0.142958
$512$	46.9166			2.07344
$513$	−3.83245	+	6.63800i	−0.169207	+	0.293075i
$514$	18.1793	+	31.4874i	0.801852	+	1.38885i
$515$	11.9728	−	20.7374i	0.527583	−	0.913800i
$516$	−21.6735	−	37.5395i	−0.954121	−	1.65259i
$517$	−4.68438	−	8.11358i	−0.206019	−	0.356835i
$518$	−5.63192	−	9.75478i	−0.247453	−	0.428600i
$519$	68.4876			3.00627
$520$	−4.30237	+	7.45193i	−0.188672	+	0.326789i
$521$	−12.2327	+	21.1877i	−0.535926	+	0.928250i	0.463192	+	0.886258i	$0.346704\pi$
$521$	−12.2327	+	21.1877i	−0.535926	+	0.928250i	−0.999118	+	0.0419926i	$0.986629\pi$
$522$	−26.4803	−	45.8653i	−1.15901	−	2.00747i
$523$	18.4931			0.808646			0.404323	−	0.914616i	$-0.367507\pi$
$523$	18.4931			0.808646			0.404323	+	0.914616i	$0.367507\pi$
$524$	8.68479	−	15.0425i	0.379397	−	0.657135i
$525$	−4.12298			−0.179942
$526$	31.1745			1.35927
$527$	6.90403	+	8.91398i	0.300744	+	0.388299i
$528$	55.3083			2.40699
$529$	50.5444			2.19758
$530$	15.9554	−	27.6355i	0.693058	−	1.20041i
$531$	22.4077			0.972412
$532$	−1.35470	−	2.34640i	−0.0587335	−	0.101729i
$533$	−5.94136	+	10.2907i	−0.257349	+	0.445742i
$534$	26.6342	−	46.1317i	1.15257	−	1.99632i
$535$	−28.6775			−1.23984
$536$	15.1479	+	26.2369i	0.654290	+	1.13326i
$537$	6.91242	+	11.9727i	0.298293	+	0.516659i
$538$	−36.2984	−	62.8706i	−1.56493	−	2.71054i
$539$	12.0155	−	20.8115i	0.517545	−	0.896415i
$540$	21.7580	+	37.6859i	0.936315	+	1.62174i
$541$	18.8671	−	32.6788i	0.811159	−	1.40497i	−0.100894	−	0.994897i	$-0.532170\pi$
$541$	18.8671	−	32.6788i	0.811159	−	1.40497i	0.912053	−	0.410072i	$-0.134497\pi$
$542$	13.4027			0.575696
$543$	49.5369			2.12583
$544$	2.30351	−	3.98979i	0.0987621	−	0.171061i
$545$	6.54660	+	11.3390i	0.280425	+	0.485711i
$546$	1.99574	−	3.45672i	0.0854097	−	0.147934i
$547$	12.3683	+	21.4225i	0.528830	+	0.915960i	0.999435	+	0.0336164i	$0.0107024\pi$
$547$	12.3683	+	21.4225i	0.528830	+	0.915960i	−0.470605	+	0.882344i	$0.655964\pi$
$548$	−37.9335	−	65.7028i	−1.62044	−	2.80668i
$549$	−2.55395	−	4.42357i	−0.109000	−	0.188793i
$550$	23.0613			0.983336
$551$	2.31714	−	4.01340i	0.0987133	−	0.170976i
$552$	−68.2681	+	118.244i	−2.90569	+	5.03279i
$553$	−1.88175	−	3.25929i	−0.0800201	−	0.138599i
$554$	−5.10370			−0.216836
$555$	−18.2368	+	31.5871i	−0.774110	+	1.34080i
$556$	−72.8023			−3.08751
$557$	−40.6086			−1.72064			−0.860321	−	0.509753i	$-0.829737\pi$
$557$	−40.6086			−1.72064			−0.860321	+	0.509753i	$0.829737\pi$
$558$	72.9086	−	9.93329i	3.08647	−	0.420510i
$559$	3.56830			0.150923
$560$	−4.62486			−0.195436
$561$	−10.4767	+	18.1462i	−0.442326	+	0.766132i
$562$	53.6900			2.26478
$563$	17.2955	+	29.9567i	0.728920	+	1.26253i	0.957340	+	0.288964i	$0.0933107\pi$
$563$	17.2955	+	29.9567i	0.728920	+	1.26253i	−0.228420	+	0.973563i	$0.573356\pi$
$564$	−15.8446	+	27.4437i	−0.667179	+	1.15559i
$565$	11.5583	−	20.0195i	0.486260	−	0.842227i
$566$	−56.7196			−2.38410
$567$	−0.887464	−	1.53713i	−0.0372700	−	0.0645535i
$568$	10.7843	+	18.6789i	0.452499	+	0.783751i
$569$	−14.6619	−	25.3951i	−0.614659	−	1.06462i	−0.990444	−	0.137913i	$-0.955960\pi$
$569$	−14.6619	−	25.3951i	−0.614659	−	1.06462i	0.375786	−	0.926707i	$-0.377373\pi$
$570$	−6.46743	+	11.2019i	−0.270891	+	0.469196i
$571$	10.1038	+	17.5003i	0.422830	+	0.732364i	0.996215	−	0.0869226i	$-0.0277033\pi$
$571$	10.1038	+	17.5003i	0.422830	+	0.732364i	−0.573385	+	0.819286i	$0.694370\pi$
$572$	−7.57145	+	13.1141i	−0.316578	+	0.548329i
$573$	−66.2718			−2.76854
$574$	−16.4625			−0.687132
$575$	−11.0431	+	19.1273i	−0.460531	+	0.797662i
$576$	13.2999	+	23.0362i	0.554164	+	0.959840i
$577$	−2.17047	+	3.75936i	−0.0903578	+	0.156504i	−0.907662	−	0.419702i	$-0.862134\pi$
$577$	−2.17047	+	3.75936i	−0.0903578	+	0.156504i	0.817304	+	0.576207i	$0.195468\pi$
$578$	−16.0806	−	27.8524i	−0.668865	−	1.15851i
$579$	−31.2852	−	54.1876i	−1.30017	−	2.25196i
$580$	−13.1551	−	22.7853i	−0.546235	−	0.946106i
$581$	1.07502			0.0445993
$582$	−38.6199	+	66.8916i	−1.60085	+	2.77275i
$583$	14.7600	−	25.5650i	0.611295	−	1.05879i
$584$	−16.0694	−	27.8329i	−0.664955	−	1.15174i
$585$	−8.25354			−0.341242
$586$	−30.0605	+	52.0664i	−1.24179	+	2.15084i
$587$	34.4381			1.42141			0.710707	−	0.703488i	$-0.248375\pi$
$587$	34.4381			1.42141			0.710707	+	0.703488i	$0.248375\pi$
$588$	−81.2836			−3.35208
$589$	3.94265	+	5.09046i	0.162454	+	0.209749i
$590$	16.4121			0.675676
$591$	40.2777			1.65680
$592$	21.7294	−	37.6364i	0.893072	−	1.54685i
$593$	−45.0974			−1.85193			−0.925964	−	0.377611i	$-0.876746\pi$
$593$	−45.0974			−1.85193			−0.925964	+	0.377611i	$0.876746\pi$
$594$	29.6752	+	51.3989i	1.21759	+	2.10892i
$595$	0.876058	−	1.51738i	0.0359149	−	0.0622064i
$596$	−35.7635	+	61.9442i	−1.46493	+	2.53733i
$597$	39.2419			1.60607
$598$	−10.6909	−	18.5172i	−0.437184	−	0.757225i
$599$	18.0305	+	31.2297i	0.736706	+	1.27601i	0.953971	+	0.299900i	$0.0969532\pi$
$599$	18.0305	+	31.2297i	0.736706	+	1.27601i	−0.217265	+	0.976113i	$0.569713\pi$
$600$	−20.5017	−	35.5101i	−0.836980	−	1.44969i
$601$	7.31944	−	12.6776i	0.298566	−	0.517132i	−0.677242	−	0.735760i	$-0.736825\pi$
$601$	7.31944	−	12.6776i	0.298566	−	0.517132i	0.975808	+	0.218629i	$0.0701583\pi$
$602$	2.47179	+	4.28127i	0.100743	+	0.174491i
$603$	−14.5296	+	25.1661i	−0.591693	+	1.02484i
$604$	−95.6997			−3.89397
$605$	−2.95586			−0.120173
$606$	35.9189	−	62.2134i	1.45911	−	2.52725i
$607$	−17.6227	−	30.5234i	−0.715282	−	1.23890i	−0.962851	−	0.270034i	$-0.912965\pi$
$607$	−17.6227	−	30.5234i	−0.715282	−	1.23890i	0.247569	−	0.968870i	$-0.420368\pi$
$608$	1.31545	−	2.27843i	0.0533486	−	0.0924025i
$609$	3.20771	+	5.55592i	0.129983	+	0.225137i
$610$	−1.87059	−	3.23996i	−0.0757380	−	0.131182i
$611$	−1.30432	−	2.25916i	−0.0527673	−	0.0913957i
$612$	45.2584			1.82946
$613$	−3.88894	+	6.73584i	−0.157073	+	0.272058i	−0.933812	−	0.357765i	$-0.883539\pi$
$613$	−3.88894	+	6.73584i	−0.157073	+	0.272058i	0.776739	+	0.629823i	$0.216872\pi$
$614$	−10.5111	+	18.2058i	−0.424195	+	0.734727i
$615$	26.6538	+	46.1657i	1.07478	+	1.86158i
$616$	−11.0280			−0.444330
$617$	−6.38270	+	11.0552i	−0.256958	+	0.445064i	−0.965425	−	0.260679i	$-0.916054\pi$
$617$	−6.38270	+	11.0552i	−0.256958	+	0.445064i	0.708468	+	0.705743i	$0.249387\pi$
$618$	−110.466			−4.44360
$619$	23.3653			0.939131			0.469565	−	0.882898i	$-0.344411\pi$
$619$	23.3653			0.939131			0.469565	+	0.882898i	$0.344411\pi$
$620$	36.2200	−	4.93472i	1.45463	−	0.198183i
$621$	−56.8411			−2.28095
$622$	−56.0548			−2.24759
$623$	−2.06028	+	3.56850i	−0.0825433	+	0.142969i
$624$	15.4001			0.616498
$625$	2.74507	+	4.75461i	0.109803	+	0.190184i
$626$	4.43433	−	7.68049i	0.177232	−	0.306974i
$627$	−5.98287	+	10.3626i	−0.238933	+	0.413844i
$628$	−26.8841			−1.07279
$629$	8.23211	+	14.2584i	0.328236	+	0.568521i
$630$	−5.71729	−	9.90263i	−0.227782	−	0.394530i
$631$	−0.321643	−	0.557102i	−0.0128044	−	0.0221779i	0.859552	−	0.511048i	$-0.170743\pi$
$631$	−0.321643	−	0.557102i	−0.0128044	−	0.0221779i	−0.872357	+	0.488870i	$0.837409\pi$
$632$	18.7142	−	32.4139i	0.744411	−	1.28936i
$633$	0.645466	+	1.11798i	0.0256550	+	0.0444357i
$634$	−11.7305	+	20.3179i	−0.465879	+	0.806926i
$635$	−19.0924			−0.757658
$636$	−99.8494			−3.95929
$637$	3.34562	−	5.79478i	0.132558	−	0.229598i
$638$	−17.9419	−	31.0762i	−0.710326	−	1.23032i
$639$	−10.3441	+	17.9166i	−0.409207	+	0.708768i
$640$	13.2837	+	23.0081i	0.525086	+	0.909475i
$641$	3.54201	+	6.13494i	0.139901	+	0.242315i	0.927459	−	0.373925i	$-0.121988\pi$
$641$	3.54201	+	6.13494i	0.139901	+	0.242315i	−0.787558	+	0.616240i	$0.788655\pi$
$642$	66.1480	+	114.572i	2.61065	+	4.52178i
$643$	6.02780			0.237713			0.118857	−	0.992911i	$-0.462077\pi$
$643$	6.02780			0.237713			0.118857	+	0.992911i	$0.462077\pi$
$644$	10.0461	−	17.4004i	0.395872	−	0.685670i
$645$	8.00395	−	13.8632i	0.315155	−	0.545865i
$646$	2.91940	+	5.05655i	0.114862	+	0.198947i
$647$	5.72271			0.224983			0.112491	−	0.993653i	$-0.464117\pi$
$647$	5.72271			0.224983			0.112491	+	0.993653i	$0.464117\pi$
$648$	8.82593	−	15.2870i	0.346715	−	0.600528i
$649$	15.1825			0.595964
$650$	6.42122			0.251861
$651$	−8.83183	+	1.20328i	−0.346147	+	0.0471601i
$652$	65.8262			2.57795
$653$	−4.52278			−0.176990			−0.0884950	−	0.996077i	$-0.528206\pi$
$653$	−4.52278			−0.176990			−0.0884950	+	0.996077i	$0.528206\pi$
$654$	30.2009	−	52.3096i	1.18095	−	2.04547i
$655$	6.41454			0.250637
$656$	−31.7583	−	55.0069i	−1.23995	−	2.14766i
$657$	15.4135	−	26.6969i	0.601337	−	1.04155i
$658$	1.80703	−	3.12987i	0.0704453	−	0.122015i
$659$	1.75700			0.0684431			0.0342215	−	0.999414i	$-0.489105\pi$
$659$	1.75700			0.0684431			0.0342215	+	0.999414i	$0.489105\pi$
$660$	33.9665	+	58.8318i	1.32215	+	2.29002i
$661$	−0.604777	−	1.04750i	−0.0235231	−	0.0407432i	0.854024	−	0.520233i	$-0.174155\pi$
$661$	−0.604777	−	1.04750i	−0.0235231	−	0.0407432i	−0.877547	+	0.479490i	$0.840822\pi$
$662$	36.7558	+	63.6630i	1.42856	+	2.47433i
$663$	−2.91714	+	5.05264i	−0.113293	+	0.196228i
$664$	5.34559	+	9.25884i	0.207449	+	0.359313i
$665$	0.500286	−	0.866520i	0.0194002	−	0.0336022i
$666$	107.448			4.16353
$667$	34.3666			1.33068
$668$	−13.1068	+	22.7016i	−0.507116	+	0.878350i
$669$	−14.9989	−	25.9788i	−0.579890	−	1.00440i
$670$	−10.6420	+	18.4324i	−0.411134	+	0.712106i
$671$	−1.73044	−	2.99721i	−0.0668029	−	0.115706i
$672$	1.82104	+	3.15413i	0.0702481	+	0.121673i
$673$	−2.24304	−	3.88507i	−0.0864630	−	0.149758i	0.819551	−	0.573007i	$-0.194223\pi$
$673$	−2.24304	−	3.88507i	−0.0864630	−	0.149758i	−0.906014	+	0.423248i	$0.860890\pi$
$674$	78.6384			3.02904
$675$	8.53503	−	14.7831i	0.328513	−	0.569002i
$676$	−2.10820	+	3.65152i	−0.0810848	+	0.140443i
$677$	1.28839	+	2.23156i	0.0495170	+	0.0857659i	0.889722	−	0.456504i	$-0.150898\pi$
$677$	1.28839	+	2.23156i	0.0495170	+	0.0857659i	−0.840205	+	0.542270i	$0.817565\pi$
$678$	−106.642			−4.09556
$679$	2.98743	−	5.17438i	0.114647	−	0.198574i
$680$	17.4250			0.668217
$681$	45.3282			1.73698
$682$	49.3996	−	6.73035i	1.89161	−	0.257718i
$683$	11.5867			0.443353			0.221676	−	0.975120i	$-0.428847\pi$
$683$	11.5867			0.443353			0.221676	+	0.975120i	$0.428847\pi$
$684$	25.8454			0.988225
$685$	14.0087	−	24.2638i	0.535246	−	0.927074i
$686$	18.9680			0.724203
$687$	−14.0355	−	24.3102i	−0.535487	−	0.927491i
$688$	−9.53679	+	16.5182i	−0.363587	+	0.629751i
$689$	4.10979	−	7.11836i	0.156570	−	0.271188i
$690$	−95.9217			−3.65168
$691$	2.76942	+	4.79677i	0.105354	+	0.182478i	0.913883	−	0.405978i	$-0.133069\pi$
$691$	2.76942	+	4.79677i	0.105354	+	0.182478i	−0.808529	+	0.588456i	$0.799736\pi$
$692$	−50.1153	−	86.8023i	−1.90510	−	3.29973i
$693$	−5.28893	−	9.16070i	−0.200910	−	0.347986i
$694$	2.31320	−	4.00658i	0.0878078	−	0.152088i
$695$	−13.4428	−	23.2837i	−0.509916	−	0.883201i
$696$	−31.9011	+	55.2543i	−1.20921	+	2.09441i
$697$	24.0630			0.911453
$698$	40.3575			1.52755
$699$	−19.1417	+	33.1543i	−0.724004	+	1.25401i
$700$	3.01696	+	5.22553i	0.114031	+	0.197507i
$701$	−18.8164	+	32.5910i	−0.710686	+	1.23094i	0.253914	+	0.967227i	$0.418282\pi$
$701$	−18.8164	+	32.5910i	−0.710686	+	1.23094i	−0.964600	+	0.263718i	$0.915051\pi$
$702$	8.26280	+	14.3116i	0.311859	+	0.540156i
$703$	4.70107	+	8.14249i	0.177304	+	0.307100i
$704$	9.01143	+	15.6083i	0.339631	+	0.588258i
$705$	−11.7027			−0.440751
$706$	40.1163	−	69.4836i	1.50980	−	2.61505i
$707$	−2.77850	+	4.81250i	−0.104496	+	0.180993i
$708$	−25.6769	−	44.4737i	−0.964996	−	1.67142i
$709$	−35.3759			−1.32857			−0.664285	−	0.747479i	$-0.731264\pi$
$709$	−35.3759			−1.32857			−0.664285	+	0.747479i	$0.731264\pi$
$710$	−7.57636	+	13.1226i	−0.284336	+	0.492484i
$711$	35.9008			1.34638
$712$	−40.9793			−1.53577
$713$	−18.0733	+	44.1954i	−0.676849	+	1.65513i
$714$	−8.08291			−0.302495
$715$	−5.59223			−0.209137
$716$	10.1162	−	17.5218i	0.378062	−	0.654822i
$717$	−2.45113			−0.0915390
$718$	4.80977	+	8.33076i	0.179499	+	0.310901i
$719$	−4.18401	+	7.24691i	−0.156037	+	0.270264i	−0.933436	−	0.358744i	$-0.883205\pi$
$719$	−4.18401	+	7.24691i	−0.156037	+	0.270264i	0.777399	+	0.629008i	$0.216539\pi$
$720$	22.0587	−	38.2069i	0.822081	−	1.42389i
$721$	8.54507			0.318235
$722$	−22.0189	−	38.1379i	−0.819460	−	1.41935i
$723$	−2.61854	−	4.53545i	−0.0973846	−	0.168675i
$724$	−36.2483	−	62.7839i	−1.34716	−	2.33335i
$725$	−5.16035	+	8.93799i	−0.191651	+	0.331949i
$726$	6.81802	+	11.8092i	0.253040	+	0.438279i
$727$	−11.8589	+	20.5402i	−0.439822	+	0.761794i	−0.997675	−	0.0681454i	$-0.978292\pi$
$727$	−11.8589	+	20.5402i	−0.439822	+	0.761794i	0.557853	+	0.829940i	$0.311625\pi$
$728$	−3.07064			−0.113806
$729$	−40.3564			−1.49468
$730$	11.2893	−	19.5537i	0.417836	−	0.723713i
$731$	−3.61299	−	6.25787i	−0.133631	−	0.231456i
$732$	−5.85311	+	10.1379i	−0.216337	+	0.374707i
$733$	−4.24009	−	7.34406i	−0.156611	−	0.271259i	0.777033	−	0.629460i	$-0.216724\pi$
$733$	−4.24009	−	7.34406i	−0.156611	−	0.271259i	−0.933645	+	0.358201i	$0.883390\pi$
$734$	−0.613219	−	1.06213i	−0.0226343	−	0.0392038i
$735$	−15.0089	−	25.9962i	−0.553612	−	0.958884i
$736$	19.5101			0.719153
$737$	−9.84463	+	17.0514i	−0.362631	+	0.628096i
$738$	78.5196	−	136.000i	2.89034	−	5.00622i
$739$	22.3917	+	38.7835i	0.823691	+	1.42667i	0.902916	+	0.429817i	$0.141422\pi$
$739$	22.3917	+	38.7835i	0.823691	+	1.42667i	−0.0792252	+	0.996857i	$0.525245\pi$
$740$	53.3787			1.96224
$741$	−1.66588	+	2.88539i	−0.0611976	+	0.105997i
$742$	11.3875			0.418049
$743$	12.0562			0.442298			0.221149	−	0.975240i	$-0.429019\pi$
$743$	12.0562			0.442298			0.221149	+	0.975240i	$0.429019\pi$
$744$	−54.2802	−	70.0827i	−1.99001	−	2.56936i
$745$	−26.4147			−0.967760
$746$	−0.836420			−0.0306235
$747$	−5.12741	+	8.88094i	−0.187602	+	0.324937i
$748$	30.6650			1.12122
$749$	−5.11685	−	8.86265i	−0.186966	−	0.323834i
$750$	42.3661	−	73.3803i	1.54699	−	2.67947i
$751$	−1.25096	+	2.16672i	−0.0456481	+	0.0790649i	−0.887947	−	0.459946i	$-0.847869\pi$
$751$	−1.25096	+	2.16672i	−0.0456481	+	0.0790649i	0.842299	+	0.539011i	$0.181202\pi$
$752$	13.9440			0.508484
$753$	14.3474	+	24.8504i	0.522847	+	0.905597i
$754$	−4.99576	−	8.65291i	−0.181935	−	0.315121i
$755$	−17.6708	−	30.6068i	−0.643107	−	1.11389i
$756$	−7.76444	+	13.4484i	−0.282390	+	0.489114i
$757$	20.0902	+	34.7972i	0.730190	+	1.26473i	0.956802	+	0.290741i	$0.0939017\pi$
$757$	20.0902	+	34.7972i	0.730190	+	1.26473i	−0.226612	+	0.973985i	$0.572765\pi$
$758$	−16.8875	+	29.2500i	−0.613381	+	1.06241i
$759$	−88.7350			−3.22088
$760$	9.95079			0.360953
$761$	−11.8050	+	20.4468i	−0.427930	+	0.741196i	−0.996689	−	0.0813081i	$-0.974090\pi$
$761$	−11.8050	+	20.4468i	−0.427930	+	0.741196i	0.568759	+	0.822504i	$0.307424\pi$
$762$	44.0387	+	76.2773i	1.59536	+	2.76324i
$763$	−2.33618	+	4.04639i	−0.0845755	+	0.146489i
$764$	48.4939	+	83.9940i	1.75445	+	3.03880i
$765$	8.35689	+	14.4746i	0.302144	+	0.523329i
$766$	8.62156	+	14.9330i	0.311509	+	0.539550i
$767$	4.22743			0.152643
$768$	46.8228	−	81.0994i	1.68957	−	2.92642i
$769$	11.6952	−	20.2567i	0.421740	−	0.730476i	−0.574370	−	0.818596i	$-0.694753\pi$
$769$	11.6952	−	20.2567i	0.421740	−	0.730476i	0.996110	+	0.0881205i	$0.0280861\pi$
$770$	−3.87378	−	6.70958i	−0.139601	−	0.241796i
$771$	42.0136			1.51308
$772$	−45.7856	+	79.3029i	−1.64786	+	2.85417i
$773$	−22.2171			−0.799092			−0.399546	−	0.916713i	$-0.630832\pi$
$773$	−22.2171			−0.799092			−0.399546	+	0.916713i	$0.630832\pi$
$774$	−47.1578			−1.69505
$775$	−8.78043	−	11.3367i	−0.315403	−	0.407225i
$776$	59.4206			2.13308
$777$	−13.0158			−0.466939
$778$	−12.3927	+	21.4649i	−0.444301	+	0.769552i
$779$	13.7415			0.492342
$780$	9.45769	+	16.3812i	0.338640	+	0.586541i
$781$	−7.00871	+	12.1394i	−0.250791	+	0.434384i
$782$	−21.6496	+	37.4981i	−0.774186	+	1.34093i
$783$	−26.5613			−0.949224
$784$	17.8833	+	30.9747i	0.638688	+	1.10624i
$785$	−4.96411	−	8.59810i	−0.177177	−	0.306879i
$786$	−14.7959	−	25.6272i	−0.527751	−	0.914091i
$787$	−11.2308	+	19.4524i	−0.400336	+	0.693402i	−0.993766	−	0.111483i	$-0.964440\pi$
$787$	−11.2308	+	19.4524i	−0.400336	+	0.693402i	0.593430	+	0.804885i	$0.297773\pi$
$788$	−29.4729	−	51.0486i	−1.04993	−	1.81853i
$789$	18.0116	−	31.1971i	0.641231	−	1.11065i
$790$	26.2948			0.935527
$791$	8.24924			0.293309
$792$	52.5990	−	91.1041i	1.86902	−	3.23725i
$793$	−0.481826	−	0.834547i	−0.0171101	−	0.0296356i
$794$	15.0869	−	26.1313i	0.535415	−	0.927366i
$795$	−18.4370	−	31.9339i	−0.653895	−	1.13258i
$796$	−28.7150	−	49.7359i	−1.01778	−	1.76284i
$797$	−15.3817	−	26.6418i	−0.544847	−	0.943702i	−0.998617	−	0.0525832i	$-0.983255\pi$
$797$	−15.3817	−	26.6418i	−0.544847	−	0.943702i	0.453770	−	0.891119i	$-0.350079\pi$
$798$	−4.61586			−0.163400
$799$	−2.64131	+	4.57489i	−0.0934429	+	0.161848i
$800$	−2.92956	+	5.07415i	−0.103576	+	0.179398i
$801$	−19.6534	−	34.0407i	−0.694418	−	1.20277i
$802$	−30.5290			−1.07802
$803$	10.4435	−	18.0886i	0.368542	−	0.638334i
$804$	66.5977			2.34872
$805$	7.41999			0.261520
$806$	13.7549	−	1.87401i	0.484495	−	0.0660091i
$807$	−83.8882			−2.95300
$808$	−55.2649			−1.94421
$809$	−0.738841	+	1.27971i	−0.0259763	+	0.0449922i	−0.878721	−	0.477335i	$-0.841603\pi$
$809$	−0.738841	+	1.27971i	−0.0259763	+	0.0449922i	0.852745	+	0.522327i	$0.174936\pi$
$810$	12.4011			0.435729
$811$	−16.8949	−	29.2629i	−0.593262	−	1.02756i	−0.993790	−	0.111275i	$-0.964507\pi$
$811$	−16.8949	−	29.2629i	−0.593262	−	1.02756i	0.400528	−	0.916285i	$-0.368827\pi$
$812$	4.69445	−	8.13102i	0.164743	−	0.285343i
$813$	7.74368	−	13.4124i	0.271583	−	0.470395i
$814$	72.8020			2.55171
$815$	12.1547	+	21.0526i	0.425761	+	0.737440i
$816$	−15.5930	−	27.0078i	−0.545863	−	0.945462i
$817$	−2.06325	−	3.57365i	−0.0721839	−	0.125026i
$818$	27.1549	−	47.0337i	0.949450	−	1.64450i
$819$	−1.47266	−	2.55072i	−0.0514588	−	0.0891293i
$820$	39.0074	−	67.5629i	1.36220	−	2.35940i
$821$	11.6775			0.407549			0.203775	−	0.979018i	$-0.434679\pi$
$821$	11.6775			0.407549			0.203775	+	0.979018i	$0.434679\pi$
$822$	−129.251			−4.50815
$823$	19.0058	−	32.9191i	0.662501	−	1.14749i	−0.317455	−	0.948273i	$-0.602828\pi$
$823$	19.0058	−	32.9191i	0.662501	−	1.14749i	0.979956	−	0.199213i	$-0.0638385\pi$
$824$	42.4908	+	73.5963i	1.48024	+	2.56385i
$825$	13.3241	−	23.0780i	0.463885	−	0.803473i
$826$	2.92837	+	5.07208i	0.101891	+	0.176480i
$827$	−1.28280	−	2.22187i	−0.0446073	−	0.0772621i	0.842860	−	0.538133i	$-0.180870\pi$
$827$	−1.28280	−	2.22187i	−0.0446073	−	0.0772621i	−0.887467	+	0.460871i	$0.847537\pi$
$828$	95.8317	+	165.985i	3.33038	+	5.76839i
$829$	14.8437			0.515544			0.257772	−	0.966206i	$-0.417012\pi$
$829$	14.8437			0.515544			0.257772	+	0.966206i	$0.417012\pi$
$830$	−3.75547	+	6.50467i	−0.130354	+	0.225780i
$831$	−2.94876	+	5.10740i	−0.102291	+	0.177174i
$832$	2.50916	+	4.34598i	0.0869893	+	0.150670i
$833$	−13.5501			−0.469481
$834$	−62.0149	+	107.413i	−2.14740	+	3.71941i
$835$	−9.68058			−0.335010
$836$	17.5117			0.605655
$837$	13.9685	−	34.1578i	0.482821	−	1.18067i
$838$	34.7654			1.20095
$839$	−35.6059			−1.22925			−0.614625	−	0.788819i	$-0.710693\pi$
$839$	−35.6059			−1.22925			−0.614625	+	0.788819i	$0.710693\pi$
$840$	−6.88766	+	11.9298i	−0.237647	+	0.411616i
$841$	−12.9408			−0.446234
$842$	−14.2531	−	24.6871i	−0.491195	−	0.850775i
$843$	31.0204	−	53.7289i	1.06840	−	1.85052i
$844$	0.944631	−	1.63615i	0.0325155	−	0.0563186i
$845$	−1.55711			−0.0535661
$846$	17.2376	+	29.8564i	0.592641	+	1.02648i
$847$	−0.527406	−	0.913493i	−0.0181219	−	0.0313880i
$848$	21.9680	+	38.0496i	0.754383	+	1.30663i
$849$	−32.7708	+	56.7607i	−1.12469	+	1.94802i
$850$	−6.50162	−	11.2611i	−0.223004	−	0.386254i
$851$	−34.8620	+	60.3827i	−1.19505	+	2.06989i
$852$	47.4131			1.62435
$853$	9.24029			0.316382			0.158191	−	0.987409i	$-0.449434\pi$
$853$	9.24029			0.316382			0.158191	+	0.987409i	$0.449434\pi$
$854$	0.667529	−	1.15619i	0.0228424	−	0.0395641i
$855$	4.77232	+	8.26591i	0.163210	+	0.282688i
$856$	50.8877	−	88.1400i	1.73930	−	3.01256i
$857$	14.7293	+	25.5118i	0.503142	+	0.871468i	0.999993	+	0.00363222i	$0.00115617\pi$
$857$	14.7293	+	25.5118i	0.503142	+	0.871468i	−0.496851	+	0.867836i	$0.665510\pi$
$858$	12.8991	+	22.3419i	0.440368	+	0.762740i
$859$	−8.56749	−	14.8393i	−0.292319	−	0.506311i	0.682039	−	0.731316i	$-0.261094\pi$
$859$	−8.56749	−	14.8393i	−0.292319	−	0.506311i	−0.974358	+	0.225005i	$0.927760\pi$
$860$	−23.4273			−0.798866
$861$	−9.51152	+	16.4744i	−0.324152	+	0.561447i
$862$	8.72612	−	15.1141i	0.297213	−	0.514788i
$863$	5.61540	+	9.72616i	0.191151	+	0.331082i	0.945632	−	0.325239i	$-0.105445\pi$
$863$	5.61540	+	9.72616i	0.191151	+	0.331082i	−0.754481	+	0.656322i	$0.772111\pi$
$864$	−15.0790			−0.512999
$865$	18.5075	−	32.0558i	0.629272	−	1.08993i
$866$	52.2914			1.77693
$867$	−37.1635			−1.26214
$868$	7.98769	+	10.3131i	0.271120	+	0.350050i
$869$	24.3247			0.825160
$870$	−44.8233			−1.51965
$871$	−2.74115	+	4.74781i	−0.0928804	+	0.160874i
$872$	−46.4672			−1.57358
$873$	28.4977	+	49.3594i	0.964500	+	1.67056i
$874$	−12.3633	+	21.4138i	−0.418195	+	0.724334i
$875$	−3.27722	+	5.67630i	−0.110790	+	0.191894i
$876$	−70.6489			−2.38700
$877$	8.77933	+	15.2062i	0.296457	+	0.513478i	0.975323	−	0.220784i	$-0.0708616\pi$
$877$	8.77933	+	15.2062i	0.296457	+	0.513478i	−0.678866	+	0.734262i	$0.737528\pi$
$878$	23.0007	+	39.8385i	0.776237	+	1.34448i
$879$	34.7361	+	60.1646i	1.17162	+	2.02930i
$880$	14.9460	−	25.8872i	0.503830	−	0.872659i
$881$	0.690510	+	1.19600i	0.0232639	+	0.0402942i	0.877423	−	0.479718i	$-0.159261\pi$
$881$	0.690510	+	1.19600i	0.0232639	+	0.0402942i	−0.854159	+	0.520012i	$0.825928\pi$
$882$	−44.2149	+	76.5824i	−1.48879	+	2.57866i
$883$	−44.9334			−1.51213			−0.756064	−	0.654498i	$-0.772880\pi$
$883$	−44.9334			−1.51213			−0.756064	+	0.654498i	$0.772880\pi$
$884$	8.53841			0.287178
$885$	9.48240	−	16.4240i	0.318747	−	0.552087i
$886$	12.4094	+	21.4937i	0.416901	+	0.722094i
$887$	19.7520	−	34.2114i	0.663206	−	1.14871i	−0.316562	−	0.948572i	$-0.602529\pi$
$887$	19.7520	−	34.2114i	0.663206	−	1.14871i	0.979768	−	0.200135i	$-0.0641380\pi$
$888$	−64.7218	−	112.101i	−2.17192	−	3.76188i
$889$	−3.40660	−	5.90041i	−0.114254	−	0.197893i
$890$	−14.3947	−	24.9324i	−0.482513	−	0.835737i
$891$	11.4719			0.384325
$892$	−21.9507	+	38.0196i	−0.734962	+	1.27299i
$893$	−1.50836	+	2.61256i	−0.0504753	+	0.0874258i
$894$	60.9285	+	105.531i	2.03775	+	3.52950i
$895$	7.47180			0.249755
$896$	−4.74036	+	8.21055i	−0.158364	+	0.274295i
$897$	−24.7075			−0.824959
$898$	−49.3687			−1.64746
$899$	−8.44547	+	20.6521i	−0.281672	+	0.688786i
$900$	−57.5588			−1.91863
$901$	−16.6450			−0.554525
$902$	53.2013	−	92.1473i	1.77141	−	3.06817i
$903$	5.71249			0.190100
$904$	41.0198	+	71.0484i	1.36430	+	2.36303i
$905$	13.3864	−	23.1859i	0.444979	−	0.770726i
$906$	−81.5195	+	141.196i	−2.70830	+	4.69092i
$907$	11.1664			0.370775			0.185387	−	0.982666i	$-0.440646\pi$
$907$	11.1664			0.370775			0.185387	+	0.982666i	$0.440646\pi$
$908$	−33.1686	−	57.4498i	−1.10074	−	1.90654i
$909$	−26.5046	−	45.9074i	−0.879103	−	1.52265i
$910$	−1.07862	−	1.86822i	−0.0357559	−	0.0619310i
$911$	28.1968	−	48.8383i	0.934202	−	1.61809i	0.158152	−	0.987415i	$-0.449446\pi$
$911$	28.1968	−	48.8383i	0.934202	−	1.61809i	0.776050	−	0.630671i	$-0.217220\pi$
$912$	−8.90458	−	15.4232i	−0.294860	−	0.510713i
$913$	−3.47410	+	6.01732i	−0.114976	+	0.199144i
$914$	−12.0518			−0.398640
$915$	−4.32307			−0.142916
$916$	−20.5408	+	35.5776i	−0.678686	+	1.17552i
$917$	1.14453	+	1.98238i	0.0377957	+	0.0654640i
$918$	16.7325	−	28.9816i	0.552256	−	0.956535i
$919$	7.09189	+	12.2835i	0.233940	+	0.405196i	0.958964	−	0.283528i	$-0.0915048\pi$
$919$	7.09189	+	12.2835i	0.233940	+	0.405196i	−0.725024	+	0.688723i	$0.758171\pi$
$920$	36.8963	+	63.9063i	1.21644	+	2.10693i
$921$	12.1460	+	21.0375i	0.400225	+	0.693210i
$922$	−35.3271			−1.16344
$923$	−1.95152	+	3.38012i	−0.0642349	+	0.111258i
$924$	−12.1211	+	20.9944i	−0.398755	+	0.690665i
$925$	−10.4695	−	18.1336i	−0.344234	−	0.596231i
$926$	60.9979			2.00452
$927$	−40.7566	+	70.5924i	−1.33862	+	2.31856i
$928$	9.11691			0.299277
$929$	17.6484			0.579025			0.289513	−	0.957174i	$-0.406507\pi$
$929$	17.6484			0.579025			0.289513	+	0.957174i	$0.406507\pi$
$930$	23.5724	−	57.6427i	0.772970	−	1.89018i
$931$	−7.73795			−0.253601
$932$	56.0272			1.83523
$933$	−32.3867	+	56.0954i	−1.06029	+	1.83648i
$934$	−42.1946			−1.38065
$935$	5.66225	+	9.80731i	0.185175	+	0.320733i
$936$	14.6457	−	25.3672i	0.478711	−	0.829152i
$937$	13.7458	−	23.8085i	0.449057	−	0.777790i	−0.549268	−	0.835646i	$-0.685093\pi$
$937$	13.7458	−	23.8085i	0.449057	−	0.777790i	0.998325	+	0.0578565i	$0.0184266\pi$
$938$	−7.59526			−0.247994
$939$	−5.12404	−	8.87509i	−0.167217	−	0.289628i
$940$	8.56341	+	14.8323i	0.279308	+	0.483775i
$941$	14.1649	+	24.5344i	0.461764	+	0.799799i	0.999049	−	0.0436021i	$-0.0138834\pi$
$941$	14.1649	+	24.5344i	0.461764	+	0.799799i	−0.537285	+	0.843401i	$0.680550\pi$
$942$	−22.9006	+	39.6650i	−0.746141	+	1.29235i
$943$	50.9520	+	88.2514i	1.65922	+	2.87386i
$944$	−11.2984	+	19.5694i	−0.367731	+	0.636929i
$945$	−5.73477			−0.186552
$946$	−31.9520			−1.03885
$947$	−1.79436	+	3.10792i	−0.0583088	+	0.100994i	−0.893706	−	0.448652i	$-0.851904\pi$
$947$	−1.79436	+	3.10792i	−0.0583088	+	0.100994i	0.835398	+	0.549646i	$0.185237\pi$
$948$	−41.1385	−	71.2539i	−1.33612	−	2.31422i
$949$	2.90790	−	5.03663i	0.0943943	−	0.163496i
$950$	−3.71284	−	6.43083i	−0.120461	−	0.208644i
$951$	13.5551	+	23.4781i	0.439553	+	0.761329i
$952$	3.10909	+	5.38511i	0.100766	+	0.174532i
$953$	51.8924			1.68096			0.840480	−	0.541843i	$-0.182273\pi$
$953$	51.8924			1.68096			0.840480	+	0.541843i	$0.182273\pi$
$954$	−54.3139	+	94.0744i	−1.75848	+	3.04577i
$955$	−17.9087	+	31.0187i	−0.579511	+	1.00374i
$956$	1.79360	+	3.10660i	0.0580091	+	0.100475i
$957$	−41.4650			−1.34037
$958$	−40.8586	+	70.7692i	−1.32008	+	2.28645i
$959$	9.99817			0.322858
$960$	22.5128			0.726598
$961$	−22.1171	−	21.7217i	−0.713456	−	0.700700i
$962$	20.2711			0.653566
$963$	97.6214			3.14580
$964$	−3.83220	+	6.63757i	−0.123427	+	0.213782i
$965$	−33.8169			−1.08861
$966$	−17.1151	−	29.6441i	−0.550668	−	0.953785i
$967$	17.8004	−	30.8313i	0.572423	−	0.991466i	−0.423893	−	0.905712i	$-0.639337\pi$
$967$	17.8004	−	30.8313i	0.572423	−	0.991466i	0.996316	−	0.0857541i	$-0.0273300\pi$
$968$	5.24511	−	9.08479i	0.168584	−	0.291996i
$969$	6.74695			0.216743
$970$	20.8726	+	36.1524i	0.670178	+	1.16078i
$971$	−7.32028	−	12.6791i	−0.234919	−	0.406892i	0.724330	−	0.689453i	$-0.242149\pi$
$971$	−7.32028	−	12.6791i	−0.234919	−	0.406892i	−0.959249	+	0.282562i	$0.908816\pi$
$972$	22.5184	+	39.0031i	0.722279	+	1.25102i
$973$	4.79714	−	8.30890i	0.153789	−	0.266371i
$974$	34.5198	+	59.7900i	1.10608	+	1.91579i
$975$	3.70998	−	6.42587i	0.118814	−	0.205792i
$976$	5.15099			0.164879
$977$	58.8915			1.88411			0.942053	−	0.335464i	$-0.108893\pi$
$977$	58.8915			1.88411			0.942053	+	0.335464i	$0.108893\pi$
$978$	56.0725	−	97.1204i	1.79300	−	3.10557i
$979$	−13.3162	−	23.0644i	−0.425589	−	0.737142i
$980$	−21.9653	+	38.0451i	−0.701657	+	1.21531i
$981$	−22.2853	−	38.5993i	−0.711516	−	1.23238i
$982$	−13.1944	−	22.8534i	−0.421051	−	0.729282i
$983$	−14.9552	−	25.9032i	−0.476997	−	0.826183i	0.522656	−	0.852544i	$-0.324941\pi$
$983$	−14.9552	−	25.9032i	−0.476997	−	0.826183i	−0.999652	+	0.0263611i	$0.991608\pi$
$984$	−189.186			−6.03103
$985$	10.8843	−	18.8521i	0.346802	−	0.600678i
$986$	−10.1166	+	17.5225i	−0.322179	+	0.558031i
$987$	−2.08809	−	3.61668i	−0.0664646	−	0.115120i
$988$	4.87598			0.155126
$989$	15.3005	−	26.5013i	0.486529	−	0.842693i
$990$	73.9054			2.34887
$991$	−44.7705			−1.42218			−0.711092	−	0.703099i	$-0.751799\pi$
$991$	−44.7705			−1.42218			−0.711092	+	0.703099i	$0.751799\pi$
$992$	−4.79454	+	11.7243i	−0.152227	+	0.372248i
$993$	84.9455			2.69566
$994$	−5.40732			−0.171510
$995$	10.6044	−	18.3673i	0.336181	−	0.582283i
$996$	23.5019			0.744686
$997$	−6.76114	−	11.7106i	−0.214128	−	0.370880i	0.738875	−	0.673843i	$-0.235357\pi$
$997$	−6.76114	−	11.7106i	−0.214128	−	0.370880i	−0.953002	+	0.302963i	$0.902024\pi$
$998$	16.3195	−	28.2662i	0.516584	−	0.894751i
$999$	26.9442	−	46.6686i	0.852475	−	1.47653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.1	yes	34
31.25	even	3	inner	403.2.h.b.118.1	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.1	✓	34	31.25	even	3	inner
403.2.h.b.222.1	yes	34	1.1	even	1	trivial

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +O(q^{10})\)	\(q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +(-1.94115 - 3.36216i) q^{10} +(-1.79571 - 3.11026i) q^{11} +(-6.07388 + 10.5203i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.692707 - 1.19980i) q^{14} -4.48613 q^{15} +5.34528 q^{16} +(-1.01252 + 1.75374i) q^{17} +(6.60787 + 11.4452i) q^{18} +(-0.578215 + 1.00150i) q^{19} +(3.28270 + 5.68580i) q^{20} +(-0.800449 - 1.38642i) q^{21} +(4.47719 + 7.75473i) q^{22} -8.57580 q^{23} +(7.96055 - 13.7881i) q^{24} +(1.28771 - 2.23038i) q^{25} +(1.24664 + 2.15924i) q^{26} +6.62808 q^{27} +(-1.17145 + 2.02901i) q^{28} -4.00739 q^{29} +11.1852 q^{30} +(2.10747 - 5.15350i) q^{31} -2.27502 q^{32} +10.3471 q^{33} +(2.52449 - 4.37255i) q^{34} -0.865224 q^{35} +(-11.1747 - 19.3551i) q^{36} +(4.06515 - 7.04105i) q^{37} +(1.44165 - 2.49701i) q^{38} +2.88107 q^{39} +(-4.30237 - 7.45193i) q^{40} +(-5.94136 - 10.2907i) q^{41} +(1.99574 + 3.45672i) q^{42} +(-1.78415 + 3.09024i) q^{43} +(-7.57145 - 13.1141i) q^{44} +(4.12677 - 7.14778i) q^{45} +21.3818 q^{46} +2.60865 q^{47} +(-7.70006 + 13.3369i) q^{48} +(3.34562 + 5.79478i) q^{49} +(-3.21061 + 5.56094i) q^{50} +(-2.91714 - 5.05264i) q^{51} +(-2.10820 - 3.65152i) q^{52} +(4.10979 + 7.11836i) q^{53} -16.5256 q^{54} +(2.79611 - 4.84301i) q^{55} +(1.53532 - 2.65926i) q^{56} +(-1.66588 - 2.88539i) q^{57} +9.99152 q^{58} +(-2.11371 + 3.66106i) q^{59} -18.9154 q^{60} +0.963652 q^{61} +(-5.25450 + 12.8491i) q^{62} +2.94532 q^{63} -5.01831 q^{64} +(0.778554 - 1.34849i) q^{65} -25.7982 q^{66} +(-2.74115 - 4.74781i) q^{67} +(-4.26920 + 7.39448i) q^{68} +(12.3537 - 21.3973i) q^{69} +2.15724 q^{70} +(-1.95152 - 3.38012i) q^{71} +(14.6457 + 25.3672i) q^{72} +(2.90790 + 5.03663i) q^{73} +(-10.1355 + 17.5553i) q^{74} +(3.70998 + 6.42587i) q^{75} +(-2.43799 + 4.22272i) q^{76} +1.99561 q^{77} -7.18329 q^{78} +(-3.38651 + 5.86560i) q^{79} +(4.16159 + 7.20808i) q^{80} +(-1.59713 + 2.76631i) q^{81} +(14.8134 + 25.6576i) q^{82} +(-0.967334 - 1.67547i) q^{83} +(-3.37502 - 5.84571i) q^{84} -3.15321 q^{85} +(4.44838 - 7.70482i) q^{86} +(5.77279 - 9.99876i) q^{87} +(9.92329 + 17.1876i) q^{88} +7.41559 q^{89} +(-10.2892 + 17.8214i) q^{90} +0.555661 q^{91} -36.1591 q^{92} +(9.82250 + 12.6821i) q^{93} -6.50407 q^{94} -1.80069 q^{95} +(3.27725 - 5.67636i) q^{96} -10.7527 q^{97} +(-8.34154 - 14.4480i) q^{98} +(-9.51827 + 16.4861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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