LMFDB - Embedded newform 403.2.h.b.118.14

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			118.14
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +O(q^{10})$	\(q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +(0.534831 - 0.926355i) q^{10} +(1.14955 - 1.99108i) q^{11} +(-0.778201 - 1.34788i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(4.31405 + 7.47216i) q^{14} -0.300874 q^{15} -2.48993 q^{16} +(0.938003 + 1.62467i) q^{17} +(2.82336 - 4.89021i) q^{18} +(-2.05191 - 3.55401i) q^{19} +(0.645543 - 1.11811i) q^{20} +(1.21346 - 2.10177i) q^{21} +(2.46131 - 4.26311i) q^{22} -4.23857 q^{23} +(-0.376733 - 0.652520i) q^{24} +(2.37521 + 4.11398i) q^{25} +(-1.07055 + 1.85425i) q^{26} -3.39505 q^{27} +(5.20708 + 9.01893i) q^{28} +6.47268 q^{29} -0.644202 q^{30} +(-4.97197 + 2.50589i) q^{31} -7.83337 q^{32} -1.38463 q^{33} +(2.00836 + 3.47858i) q^{34} +2.01320 q^{35} +(3.40781 - 5.90250i) q^{36} +(-4.34525 - 7.52619i) q^{37} +(-4.39334 - 7.60949i) q^{38} +0.602248 q^{39} +(0.312512 - 0.541287i) q^{40} +(-5.02057 + 8.69589i) q^{41} +(2.59813 - 4.50010i) q^{42} +(-5.16322 - 8.94295i) q^{43} +(2.97081 - 5.14559i) q^{44} +(-0.658777 - 1.14103i) q^{45} -9.07522 q^{46} +5.34751 q^{47} +(0.749779 + 1.29865i) q^{48} +(-4.61944 + 8.00111i) q^{49} +(5.08556 + 8.80845i) q^{50} +(0.564911 - 0.978454i) q^{51} +(-1.29216 + 2.23809i) q^{52} +(-4.26962 + 7.39519i) q^{53} -7.26915 q^{54} +(-0.574298 - 0.994713i) q^{55} +(2.52079 + 4.36613i) q^{56} +(-1.23576 + 2.14039i) q^{57} +13.8587 q^{58} +(5.60232 + 9.70350i) q^{59} -0.777555 q^{60} -8.92279 q^{61} +(-10.6455 + 5.36537i) q^{62} +10.6276 q^{63} -11.7922 q^{64} +(0.249792 + 0.432653i) q^{65} -2.96463 q^{66} +(3.45028 - 5.97606i) q^{67} +(2.42410 + 4.19866i) q^{68} +(1.27634 + 2.21068i) q^{69} +4.31047 q^{70} +(-5.69504 + 9.86409i) q^{71} +(1.64974 - 2.85744i) q^{72} +(5.64714 - 9.78114i) q^{73} +(-9.30362 - 16.1143i) q^{74} +(1.43046 - 2.47764i) q^{75} +(-5.30278 - 9.18468i) q^{76} +9.26480 q^{77} +1.28948 q^{78} +(0.487117 + 0.843712i) q^{79} +(-0.621966 + 1.07728i) q^{80} +(-2.93361 - 5.08117i) q^{81} +(-10.7496 + 18.6188i) q^{82} +(0.735814 - 1.27447i) q^{83} +(3.13596 - 5.43163i) q^{84} +0.937224 q^{85} +(-11.0550 - 19.1478i) q^{86} +(-1.94908 - 3.37591i) q^{87} +(1.43819 - 2.49102i) q^{88} +0.499561 q^{89} +(-1.41051 - 2.44307i) q^{90} -4.02975 q^{91} -10.9538 q^{92} +(2.80416 + 1.83861i) q^{93} +11.4496 q^{94} -2.05020 q^{95} +(2.35882 + 4.08559i) q^{96} +8.56900 q^{97} +(-9.89070 + 17.1312i) q^{98} +(-3.03171 - 5.25107i) 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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.14110			1.51399			0.756994	−	0.653422i	$-0.226667\pi$
$2$	2.14110			1.51399			0.756994	+	0.653422i	$0.226667\pi$
$3$	−0.301124	−	0.521562i	−0.173854	−	0.301124i	0.765910	−	0.642948i	$-0.222289\pi$
$3$	−0.301124	−	0.521562i	−0.173854	−	0.301124i	−0.939764	+	0.341824i	$0.888955\pi$
$4$	2.58432			1.29216
$5$	0.249792	−	0.432653i	0.111711	−	0.193488i	−0.804749	−	0.593615i	$-0.797700\pi$
$5$	0.249792	−	0.432653i	0.111711	−	0.193488i	0.916460	+	0.400126i	$0.131034\pi$
$6$	−0.644738	−	1.11672i	−0.263213	−	0.455898i
$7$	2.01488	+	3.48987i	0.761551	+	1.31905i	0.942051	+	0.335470i	$0.108895\pi$
$7$	2.01488	+	3.48987i	0.761551	+	1.31905i	−0.180499	+	0.983575i	$0.557771\pi$
$8$	1.25109			0.442326
$9$	1.31865	−	2.28397i	0.439549	−	0.761322i
$10$	0.534831	−	0.926355i	0.169128	−	0.292939i
$11$	1.14955	−	1.99108i	0.346603	−	0.600333i	−0.639041	−	0.769173i	$-0.720669\pi$
$11$	1.14955	−	1.99108i	0.346603	−	0.600333i	0.985644	+	0.168839i	$0.0540019\pi$
$12$	−0.778201	−	1.34788i	−0.224647	−	0.389100i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	4.31405	+	7.47216i	1.15298	+	1.99702i
$15$	−0.300874			−0.0776854
$16$	−2.48993			−0.622483
$17$	0.938003	+	1.62467i	0.227499	+	0.394040i	0.957066	−	0.289869i	$-0.0936118\pi$
$17$	0.938003	+	1.62467i	0.227499	+	0.394040i	−0.729567	+	0.683909i	$0.760278\pi$
$18$	2.82336	−	4.89021i	0.665473	−	1.15263i
$19$	−2.05191	−	3.55401i	−0.470739	−	0.815345i	0.528700	−	0.848808i	$-0.322679\pi$
$19$	−2.05191	−	3.55401i	−0.470739	−	0.815345i	−0.999440	+	0.0334638i	$0.989346\pi$
$20$	0.645543	−	1.11811i	0.144348	−	0.250018i
$21$	1.21346	−	2.10177i	0.264798	−	0.458643i
$22$	2.46131	−	4.26311i	0.524752	−	0.908897i
$23$	−4.23857			−0.883804			−0.441902	−	0.897063i	$-0.645696\pi$
$23$	−4.23857			−0.883804			−0.441902	+	0.897063i	$0.645696\pi$
$24$	−0.376733	−	0.652520i	−0.0769002	−	0.133195i
$25$	2.37521	+	4.11398i	0.475042	+	0.822796i
$26$	−1.07055	+	1.85425i	−0.209952	+	0.363648i
$27$	−3.39505			−0.653378
$28$	5.20708	+	9.01893i	0.984046	+	1.70442i
$29$	6.47268			1.20195			0.600973	−	0.799269i	$-0.294780\pi$
$29$	6.47268			1.20195			0.600973	+	0.799269i	$0.294780\pi$
$30$	−0.644202			−0.117615
$31$	−4.97197	+	2.50589i	−0.892993	+	0.450071i
$31$	−4.97197	+	2.50589i	−0.892993	+	0.450071i
$32$	−7.83337			−1.38476
$33$	−1.38463			−0.241033
$34$	2.00836	+	3.47858i	0.344431	+	0.596572i
$35$	2.01320			0.340293
$36$	3.40781	−	5.90250i	0.567968	−	0.983750i
$37$	−4.34525	−	7.52619i	−0.714354	−	1.23730i	−0.963208	−	0.268757i	$-0.913387\pi$
$37$	−4.34525	−	7.52619i	−0.714354	−	1.23730i	0.248854	−	0.968541i	$-0.419946\pi$
$38$	−4.39334	−	7.60949i	−0.712694	−	1.23442i
$39$	0.602248			0.0964369
$40$	0.312512	−	0.541287i	0.0494125	−	0.0855850i
$41$	−5.02057	+	8.69589i	−0.784082	+	1.35807i	0.145464	+	0.989363i	$0.453532\pi$
$41$	−5.02057	+	8.69589i	−0.784082	+	1.35807i	−0.929546	+	0.368706i	$0.879801\pi$
$42$	2.59813	−	4.50010i	0.400900	−	0.694380i
$43$	−5.16322	−	8.94295i	−0.787383	−	1.36379i	−0.927565	−	0.373662i	$-0.878102\pi$
$43$	−5.16322	−	8.94295i	−0.787383	−	1.36379i	0.140182	−	0.990126i	$-0.455231\pi$
$44$	2.97081	−	5.14559i	0.447866	−	0.775726i
$45$	−0.658777	−	1.14103i	−0.0982046	−	0.170095i
$46$	−9.07522			−1.33807
$47$	5.34751			0.780015			0.390007	−	0.920812i	$-0.372472\pi$
$47$	5.34751			0.780015			0.390007	+	0.920812i	$0.372472\pi$
$48$	0.749779	+	1.29865i	0.108221	+	0.187445i
$49$	−4.61944	+	8.00111i	−0.659921	+	1.14302i
$50$	5.08556	+	8.80845i	0.719207	+	1.24570i
$51$	0.564911	−	0.978454i	0.0791033	−	0.137011i
$52$	−1.29216	+	2.23809i	−0.179190	+	0.310367i
$53$	−4.26962	+	7.39519i	−0.586477	+	1.01581i	0.408213	+	0.912887i	$0.366152\pi$
$53$	−4.26962	+	7.39519i	−0.586477	+	1.01581i	−0.994690	+	0.102921i	$0.967181\pi$
$54$	−7.26915			−0.989207
$55$	−0.574298	−	0.994713i	−0.0774383	−	0.134127i
$56$	2.52079	+	4.36613i	0.336854	+	0.583448i
$57$	−1.23576	+	2.14039i	−0.163680	+	0.283502i
$58$	13.8587			1.81973
$59$	5.60232	+	9.70350i	0.729359	+	1.26329i	0.957154	+	0.289578i	$0.0935151\pi$
$59$	5.60232	+	9.70350i	0.729359	+	1.26329i	−0.227795	+	0.973709i	$0.573152\pi$
$60$	−0.777555			−0.100382
$61$	−8.92279			−1.14245			−0.571223	−	0.820795i	$-0.693531\pi$
$61$	−8.92279			−1.14245			−0.571223	+	0.820795i	$0.693531\pi$
$62$	−10.6455	+	5.36537i	−1.35198	+	0.681402i
$63$	10.6276			1.33896
$64$	−11.7922			−1.47402
$65$	0.249792	+	0.432653i	0.0309829	+	0.0536640i
$66$	−2.96463			−0.364921
$67$	3.45028	−	5.97606i	0.421519	−	0.730092i	−0.574569	−	0.818456i	$-0.694830\pi$
$67$	3.45028	−	5.97606i	0.421519	−	0.730092i	0.996088	+	0.0883635i	$0.0281637\pi$
$68$	2.42410	+	4.19866i	0.293965	+	0.509163i
$69$	1.27634	+	2.21068i	0.153653	+	0.266135i
$70$	4.31047			0.515200
$71$	−5.69504	+	9.86409i	−0.675876	+	1.17065i	0.300336	+	0.953834i	$0.402901\pi$
$71$	−5.69504	+	9.86409i	−0.675876	+	1.17065i	−0.976212	+	0.216819i	$0.930432\pi$
$72$	1.64974	−	2.85744i	0.194424	−	0.336753i
$73$	5.64714	−	9.78114i	0.660948	−	1.14480i	−0.319419	−	0.947614i	$-0.603488\pi$
$73$	5.64714	−	9.78114i	0.660948	−	1.14480i	0.980367	−	0.197182i	$-0.0631789\pi$
$74$	−9.30362	−	16.1143i	−1.08152	−	1.87325i
$75$	1.43046	−	2.47764i	0.165176	−	0.286093i
$76$	−5.30278	−	9.18468i	−0.608271	−	1.05356i
$77$	9.26480			1.05582
$78$	1.28948			0.146004
$79$	0.487117	+	0.843712i	0.0548050	+	0.0949250i	0.892126	−	0.451786i	$-0.149213\pi$
$79$	0.487117	+	0.843712i	0.0548050	+	0.0949250i	−0.837321	+	0.546711i	$0.815880\pi$
$80$	−0.621966	+	1.07728i	−0.0695379	+	0.120443i
$81$	−2.93361	−	5.08117i	−0.325957	−	0.564574i
$82$	−10.7496	+	18.6188i	−1.18709	+	2.05610i
$83$	0.735814	−	1.27447i	0.0807661	−	0.139891i	−0.822813	−	0.568312i	$-0.807597\pi$
$83$	0.735814	−	1.27447i	0.0807661	−	0.139891i	0.903579	+	0.428421i	$0.140930\pi$
$84$	3.13596	−	5.43163i	0.342161	−	0.592640i
$85$	0.937224			0.101656
$86$	−11.0550	−	19.1478i	−1.19209	−	2.06476i
$87$	−1.94908	−	3.37591i	−0.208963	−	0.361935i
$88$	1.43819	−	2.49102i	0.153311	−	0.265543i
$89$	0.499561			0.0529533			0.0264767	−	0.999649i	$-0.491571\pi$
$89$	0.499561			0.0529533			0.0264767	+	0.999649i	$0.491571\pi$
$90$	−1.41051	−	2.44307i	−0.148681	−	0.257522i
$91$	−4.02975			−0.422433
$92$	−10.9538			−1.14202
$93$	2.80416	+	1.83861i	0.290778	+	0.190655i
$94$	11.4496			1.18093
$95$	−2.05020			−0.210346
$96$	2.35882	+	4.08559i	0.240746	+	0.416984i
$97$	8.56900			0.870050			0.435025	−	0.900418i	$-0.356739\pi$
$97$	8.56900			0.870050			0.435025	+	0.900418i	$0.356739\pi$
$98$	−9.89070	+	17.1312i	−0.999112	+	1.73051i
$99$	−3.03171	−	5.25107i	−0.304698	−	0.527752i
$100$	6.13829	+	10.6318i	0.613829	+	1.06318i
$101$	5.68573			0.565751			0.282876	−	0.959157i	$-0.408712\pi$
$101$	5.68573			0.565751			0.282876	+	0.959157i	$0.408712\pi$
$102$	1.20953	−	2.09497i	0.119761	−	0.207433i
$103$	−1.33511	+	2.31248i	−0.131552	+	0.227855i	−0.924275	−	0.381727i	$-0.875329\pi$
$103$	−1.33511	+	2.31248i	−0.131552	+	0.227855i	0.792723	+	0.609582i	$0.208663\pi$
$104$	−0.625544	+	1.08347i	−0.0613396	+	0.106243i
$105$	−0.606224	−	1.05001i	−0.0591614	−	0.102471i
$106$	−9.14169	+	15.8339i	−0.887919	+	1.53792i
$107$	−6.48159	−	11.2264i	−0.626599	−	1.08530i	−0.988229	−	0.152980i	$-0.951113\pi$
$107$	−6.48159	−	11.2264i	−0.626599	−	1.08530i	0.361630	−	0.932322i	$-0.382220\pi$
$108$	−8.77390			−0.844269
$109$	18.2487			1.74791			0.873956	−	0.486006i	$-0.161547\pi$
$109$	18.2487			1.74791			0.873956	+	0.486006i	$0.161547\pi$
$110$	−1.22963	−	2.12978i	−0.117241	−	0.203067i
$111$	−2.61692	+	4.53263i	−0.248387	+	0.430219i
$112$	−5.01690	−	8.68953i	−0.474053	−	0.821084i
$113$	6.60383	−	11.4382i	0.621236	−	1.07601i	−0.368020	−	0.929818i	$-0.619964\pi$
$113$	6.60383	−	11.4382i	0.621236	−	1.07601i	0.989256	−	0.146194i	$-0.0467024\pi$
$114$	−2.64588	+	4.58280i	−0.247810	+	0.429219i
$115$	−1.05876	+	1.83383i	−0.0987302	+	0.171006i
$116$	16.7275			1.55311
$117$	1.31865	+	2.28397i	0.121909	+	0.211153i
$118$	11.9951	+	20.7762i	1.10424	+	1.91260i
$119$	−3.77992	+	6.54701i	−0.346504	+	0.600163i
$120$	−0.376420			−0.0343623
$121$	2.85707	+	4.94859i	0.259733	+	0.449871i
$122$	−19.1046			−1.72965
$123$	6.04726			0.545263
$124$	−12.8492	+	6.47602i	−1.15389	+	0.581564i
$125$	4.87116			0.435690
$126$	22.7549			2.02717
$127$	−3.13031	−	5.42185i	−0.277770	−	0.481111i	0.693060	−	0.720879i	$-0.256262\pi$
$127$	−3.13031	−	5.42185i	−0.277770	−	0.481111i	−0.970830	+	0.239768i	$0.922929\pi$
$128$	−9.58154			−0.846897
$129$	−3.10954	+	5.38588i	−0.273780	+	0.474200i
$130$	0.534831	+	0.926355i	0.0469078	+	0.0812467i
$131$	−5.87697	−	10.1792i	−0.513473	−	0.889361i	−0.999878	−	0.0156278i	$-0.995025\pi$
$131$	−5.87697	−	10.1792i	−0.513473	−	0.889361i	0.486405	−	0.873734i	$-0.338308\pi$
$132$	−3.57833			−0.311453
$133$	8.26867	−	14.3218i	0.716984	−	1.24185i
$134$	7.38741	−	12.7954i	0.638175	−	1.10535i
$135$	−0.848058	+	1.46888i	−0.0729892	+	0.126421i
$136$	1.17352	+	2.03260i	0.100629	+	0.174294i
$137$	9.92619	−	17.1927i	0.848052	−	1.46887i	−0.0348924	−	0.999391i	$-0.511109\pi$
$137$	9.92619	−	17.1927i	0.848052	−	1.46887i	0.882944	−	0.469478i	$-0.155558\pi$
$138$	2.73277	+	4.73329i	0.232629	+	0.402925i
$139$	−0.264089			−0.0223998			−0.0111999	−	0.999937i	$-0.503565\pi$
$139$	−0.264089			−0.0223998			−0.0111999	+	0.999937i	$0.503565\pi$
$140$	5.20276			0.439713
$141$	−1.61027	−	2.78906i	−0.135609	−	0.234881i
$142$	−12.1937	+	21.1200i	−1.02327	+	1.77235i
$143$	1.14955	+	1.99108i	0.0961302	+	0.166502i
$144$	−3.28335	+	5.68692i	−0.273612	+	0.473910i
$145$	1.61683	−	2.80042i	0.134270	−	0.232563i
$146$	12.0911	−	20.9424i	1.00067	−	1.73321i
$147$	5.56411			0.458920
$148$	−11.2295	−	19.4501i	−0.923060	−	1.59879i
$149$	7.58800	+	13.1428i	0.621634	+	1.07670i	0.989182	+	0.146696i	$0.0468640\pi$
$149$	7.58800	+	13.1428i	0.621634	+	1.07670i	−0.367548	+	0.930005i	$0.619803\pi$
$150$	3.06277	−	5.30488i	0.250074	−	0.433141i
$151$	4.28970			0.349091			0.174546	−	0.984649i	$-0.444154\pi$
$151$	4.28970			0.349091			0.174546	+	0.984649i	$0.444154\pi$
$152$	−2.56711	−	4.44637i	−0.208220	−	0.360648i
$153$	4.94758			0.399988
$154$	19.8369			1.59850
$155$	−0.157780	+	2.77709i	−0.0126732	+	0.223061i
$156$	1.55640			0.124612
$157$	21.0273			1.67816			0.839080	−	0.544009i	$-0.183094\pi$
$157$	21.0273			1.67816			0.839080	+	0.544009i	$0.183094\pi$
$158$	1.04297	+	1.80647i	0.0829741	+	0.143715i
$159$	5.14274			0.407846
$160$	−1.95672	+	3.38913i	−0.154692	+	0.267935i
$161$	−8.54020	−	14.7921i	−0.673062	−	1.16578i
$162$	−6.28117	−	10.8793i	−0.493495	−	0.854758i
$163$	−3.33996			−0.261606			−0.130803	−	0.991408i	$-0.541755\pi$
$163$	−3.33996			−0.261606			−0.130803	+	0.991408i	$0.541755\pi$
$164$	−12.9748	+	22.4729i	−1.01316	+	1.75484i
$165$	−0.345870	+	0.599064i	−0.0269259	+	0.0466371i
$166$	1.57545	−	2.72876i	0.122279	−	0.211793i
$167$	0.372394	+	0.645006i	0.0288167	+	0.0499120i	0.880074	−	0.474836i	$-0.157493\pi$
$167$	0.372394	+	0.645006i	0.0288167	+	0.0499120i	−0.851257	+	0.524748i	$0.824159\pi$
$168$	1.51814	−	2.62949i	0.117127	−	0.202870i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.00669			0.153906
$171$	−10.8230			−0.827653
$172$	−13.3434	−	23.1114i	−1.01742	−	1.76223i
$173$	−11.3449	+	19.6499i	−0.862536	+	1.49396i	0.00693745	+	0.999976i	$0.497792\pi$
$173$	−11.3449	+	19.6499i	−0.862536	+	1.49396i	−0.869473	+	0.493980i	$0.835542\pi$
$174$	−4.17318	−	7.22816i	−0.316368	−	0.547965i
$175$	−9.57149	+	16.5783i	−0.723537	+	1.25320i
$176$	−2.86230	+	4.95765i	−0.215754	+	0.373697i
$177$	3.37399	−	5.84391i	0.253604	−	0.439255i
$178$	1.06961			0.0801707
$179$	5.83113	+	10.0998i	0.435839	+	0.754895i	0.997364	−	0.0725647i	$-0.0231184\pi$
$179$	5.83113	+	10.0998i	0.435839	+	0.754895i	−0.561525	+	0.827460i	$0.689785\pi$
$180$	−1.70249	−	2.94880i	−0.126896	−	0.219790i
$181$	1.74861	−	3.02868i	0.129973	−	0.225120i	−0.793693	−	0.608319i	$-0.791844\pi$
$181$	1.74861	−	3.02868i	0.129973	−	0.225120i	0.923666	+	0.383199i	$0.125178\pi$
$182$	−8.62811			−0.639558
$183$	2.68687	+	4.65379i	0.198619	+	0.344018i
$184$	−5.30283			−0.390930
$185$	−4.34164			−0.319204
$186$	6.00399	+	3.93665i	0.440234	+	0.288649i
$187$	4.31313			0.315407
$188$	13.8197			1.00790
$189$	−6.84061	−	11.8483i	−0.497581	−	0.861836i
$190$	−4.38969			−0.318462
$191$	−2.07410	+	3.59245i	−0.150077	+	0.259941i	−0.931255	−	0.364367i	$-0.881285\pi$
$191$	−2.07410	+	3.59245i	−0.150077	+	0.259941i	0.781179	+	0.624307i	$0.214619\pi$
$192$	3.55091	+	6.15036i	0.256265	+	0.443864i
$193$	−9.16800	−	15.8794i	−0.659927	−	1.14303i	−0.980634	−	0.195849i	$-0.937254\pi$
$193$	−9.16800	−	15.8794i	−0.659927	−	1.14303i	0.320707	−	0.947178i	$-0.396079\pi$
$194$	18.3471			1.31725
$195$	0.150437	−	0.260565i	0.0107730	−	0.0186594i
$196$	−11.9381	+	20.6774i	−0.852723	+	1.47696i
$197$	8.98604	−	15.5643i	0.640229	−	1.10891i	−0.345153	−	0.938546i	$-0.612173\pi$
$197$	8.98604	−	15.5643i	0.640229	−	1.10891i	0.985382	−	0.170362i	$-0.0544937\pi$
$198$	−6.49119	−	11.2431i	−0.461309	−	0.799011i
$199$	−10.4843	+	18.1593i	−0.743210	+	1.28728i	0.207816	+	0.978168i	$0.433365\pi$
$199$	−10.4843	+	18.1593i	−0.743210	+	1.28728i	−0.951026	+	0.309110i	$0.899969\pi$
$200$	2.97159	+	5.14695i	0.210123	+	0.363944i
$201$	−4.15585			−0.293131
$202$	12.1737			0.856541
$203$	13.0416	+	22.5888i	0.915344	+	1.58542i
$204$	1.45991	−	2.52864i	0.102214	−	0.177040i
$205$	2.50820	+	4.34433i	0.175180	+	0.303421i
$206$	−2.85860	+	4.95125i	−0.199168	+	0.344970i
$207$	−5.58919	+	9.68076i	−0.388476	+	0.672859i
$208$	1.24497	−	2.15634i	0.0863229	−	0.149516i
$209$	−9.43508			−0.652638
$210$	−1.29799	−	2.24818i	−0.0895696	−	0.155139i
$211$	−1.14184	−	1.97773i	−0.0786076	−	0.136152i	0.824042	−	0.566529i	$-0.191714\pi$
$211$	−1.14184	−	1.97773i	−0.0786076	−	0.136152i	−0.902649	+	0.430377i	$0.858381\pi$
$212$	−11.0341	+	19.1115i	−0.757822	+	1.31259i
$213$	6.85965			0.470016
$214$	−13.8778	−	24.0370i	−0.948664	−	1.64313i
$215$	−5.15893			−0.351836
$216$	−4.24751			−0.289006
$217$	−18.7631	−	12.3025i	−1.27372	−	0.835146i
$218$	39.0724			2.64632
$219$	−6.80196			−0.459634
$220$	−1.48417	−	2.57066i	−0.100063	−	0.173314i
$221$	−1.87601			−0.126194
$222$	−5.60309	+	9.70483i	−0.376055	+	0.651346i
$223$	−3.12789	−	5.41767i	−0.209459	−	0.362794i	0.742085	−	0.670306i	$-0.233837\pi$
$223$	−3.12789	−	5.41767i	−0.209459	−	0.362794i	−0.951544	+	0.307512i	$0.900504\pi$
$224$	−15.7833	−	27.3374i	−1.05456	−	1.82656i
$225$	12.5283			0.835217
$226$	14.1395	−	24.4903i	0.940544	−	1.62907i
$227$	−5.67796	+	9.83452i	−0.376859	+	0.652740i	−0.990603	−	0.136765i	$-0.956329\pi$
$227$	−5.67796	+	9.83452i	−0.376859	+	0.652740i	0.613744	+	0.789505i	$0.289663\pi$
$228$	−3.19359	+	5.53146i	−0.211501	+	0.366330i
$229$	5.57406	+	9.65456i	0.368344	+	0.637991i	0.989307	−	0.145849i	$-0.0465914\pi$
$229$	5.57406	+	9.65456i	0.368344	+	0.637991i	−0.620962	+	0.783840i	$0.713258\pi$
$230$	−2.26692	+	3.92642i	−0.149476	+	0.258901i
$231$	−2.78986	−	4.83217i	−0.183559	−	0.317934i
$232$	8.09789			0.531652
$233$	−16.1482			−1.05791			−0.528953	−	0.848651i	$-0.677415\pi$
$233$	−16.1482			−1.05791			−0.528953	+	0.848651i	$0.677415\pi$
$234$	2.82336	+	4.89021i	0.184569	+	0.319683i
$235$	1.33577	−	2.31362i	0.0871359	−	0.150924i
$236$	14.4782	+	25.0769i	0.942449	+	1.63237i
$237$	0.293365	−	0.508124i	0.0190561	−	0.0330062i
$238$	−8.09319	+	14.0178i	−0.524604	+	0.908640i
$239$	2.51377	−	4.35398i	0.162602	−	0.281636i	−0.773199	−	0.634164i	$-0.781345\pi$
$239$	2.51377	−	4.35398i	0.162602	−	0.281636i	0.935801	+	0.352528i	$0.114678\pi$
$240$	0.749156			0.0483578
$241$	14.6060	+	25.2983i	0.940855	+	1.62961i	0.763846	+	0.645399i	$0.223309\pi$
$241$	14.6060	+	25.2983i	0.940855	+	1.62961i	0.177009	+	0.984209i	$0.443358\pi$
$242$	6.11727	+	10.5954i	0.393233	+	0.681100i
$243$	−6.85934	+	11.8807i	−0.440027	+	0.762149i
$244$	−23.0593			−1.47622
$245$	2.30780	+	3.99723i	0.147440	+	0.255374i
$246$	12.9478			0.825522
$247$	4.10381			0.261119
$248$	−6.22037	+	3.13509i	−0.394994	+	0.199078i
$249$	−0.886285			−0.0561661
$250$	10.4297			0.659629
$251$	−1.58991	−	2.75381i	−0.100354	−	0.173819i	0.811476	−	0.584385i	$-0.198664\pi$
$251$	−1.58991	−	2.75381i	−0.100354	−	0.173819i	−0.911831	+	0.410567i	$0.865331\pi$
$252$	27.4652			1.73015
$253$	−4.87246	+	8.43934i	−0.306329	+	0.530577i
$254$	−6.70230	−	11.6087i	−0.420540	−	0.728397i
$255$	−0.282221	−	0.488821i	−0.0176733	−	0.0306111i
$256$	3.06932			0.191833
$257$	2.94786	−	5.10584i	0.183882	−	0.318494i	−0.759317	−	0.650721i	$-0.774467\pi$
$257$	2.94786	−	5.10584i	0.183882	−	0.318494i	0.943199	+	0.332227i	$0.107800\pi$
$258$	−6.65784	+	11.5317i	−0.414499	+	0.717933i
$259$	17.5103	−	30.3287i	1.08803	−	1.88453i
$260$	0.645543	+	1.11811i	0.0400349	+	0.0693425i
$261$	8.53519	−	14.7834i	0.528315	−	0.915068i
$262$	−12.5832	−	21.7947i	−0.777392	−	1.34648i
$263$	14.2010			0.875671			0.437835	−	0.899055i	$-0.355745\pi$
$263$	14.2010			0.875671			0.437835	+	0.899055i	$0.355745\pi$
$264$	−1.73229			−0.106615
$265$	2.13304	+	3.69453i	0.131031	+	0.226953i
$266$	17.7041	−	30.6643i	1.08551	−	1.88015i
$267$	−0.150430	−	0.260552i	−0.00920615	−	0.0159455i
$268$	8.91663	−	15.4441i	0.544670	−	0.943396i
$269$	−3.02456	+	5.23869i	−0.184411	+	0.319409i	−0.943378	−	0.331720i	$-0.892371\pi$
$269$	−3.02456	+	5.23869i	−0.184411	+	0.319409i	0.758967	+	0.651129i	$0.225704\pi$
$270$	−1.81578	+	3.14502i	−0.110505	+	0.191400i
$271$	2.25483			0.136971			0.0684855	−	0.997652i	$-0.478183\pi$
$271$	2.25483			0.136971			0.0684855	+	0.997652i	$0.478183\pi$
$272$	−2.33556	−	4.04531i	−0.141614	−	0.245283i
$273$	1.21346	+	2.10177i	0.0734417	+	0.127205i
$274$	21.2530	−	36.8113i	1.28394	−	2.22385i
$275$	10.9217			0.658602
$276$	3.29846	+	5.71311i	0.198544	+	0.343889i
$277$	5.33059			0.320284			0.160142	−	0.987094i	$-0.448805\pi$
$277$	5.33059			0.320284			0.160142	+	0.987094i	$0.448805\pi$
$278$	−0.565442			−0.0339130
$279$	−0.832916	+	14.6602i	−0.0498654	+	0.877684i
$280$	2.51869			0.150521
$281$	−1.50192			−0.0895970			−0.0447985	−	0.998996i	$-0.514265\pi$
$281$	−1.50192			−0.0895970			−0.0447985	+	0.998996i	$0.514265\pi$
$282$	−3.44774	−	5.97167i	−0.205310	−	0.355608i
$283$	−0.381449			−0.0226748			−0.0113374	−	0.999936i	$-0.503609\pi$
$283$	−0.381449			−0.0226748			−0.0113374	+	0.999936i	$0.503609\pi$
$284$	−14.7178	+	25.4920i	−0.873340	+	1.51267i
$285$	0.617365	+	1.06931i	0.0365696	+	0.0633403i
$286$	2.46131	+	4.26311i	0.145540	+	0.252083i
$287$	−40.4633			−2.38847
$288$	−10.3295	+	17.8912i	−0.608670	+	1.05425i
$289$	6.74030	−	11.6745i	0.396488	−	0.686738i
$290$	3.46179	−	5.99600i	0.203283	−	0.352097i
$291$	−2.58033	−	4.46927i	−0.151262	−	0.261993i
$292$	14.5940	−	25.2776i	0.854050	−	1.47926i
$293$	−2.48423	−	4.30281i	−0.145130	−	0.251373i	0.784291	−	0.620393i	$-0.213027\pi$
$293$	−2.48423	−	4.30281i	−0.145130	−	0.251373i	−0.929421	+	0.369020i	$0.879693\pi$
$294$	11.9133			0.694799
$295$	5.59766			0.325909
$296$	−5.43628	−	9.41592i	−0.315978	−	0.547289i
$297$	−3.90278	+	6.75982i	−0.226463	+	0.392245i
$298$	16.2467	+	28.1401i	0.941146	+	1.63011i
$299$	2.11929	−	3.67071i	0.122562	−	0.212283i
$300$	3.69678	−	6.40301i	0.213434	−	0.369678i
$301$	20.8065	−	36.0379i	1.19927	−	2.07719i
$302$	9.18470			0.528520
$303$	−1.71211	−	2.96546i	−0.0983582	−	0.170361i
$304$	5.10911	+	8.84923i	0.293027	+	0.507538i
$305$	−2.22885	+	3.86047i	−0.127623	+	0.221050i
$306$	10.5933			0.605578
$307$	−11.0598	−	19.1561i	−0.631216	−	1.09330i	−0.987304	−	0.158845i	$-0.949223\pi$
$307$	−11.0598	−	19.1561i	−0.631216	−	1.09330i	0.356088	−	0.934452i	$-0.384110\pi$
$308$	23.9432			1.36429
$309$	1.60813			0.0914835
$310$	−0.337823	+	5.94604i	−0.0191870	+	0.337712i
$311$	−10.7972			−0.612253			−0.306127	−	0.951991i	$-0.599033\pi$
$311$	−10.7972			−0.612253			−0.306127	+	0.951991i	$0.599033\pi$
$312$	0.753465			0.0426566
$313$	15.1342	+	26.2132i	0.855436	+	1.48166i	0.876240	+	0.481875i	$0.160044\pi$
$313$	15.1342	+	26.2132i	0.855436	+	1.48166i	−0.0208035	+	0.999784i	$0.506622\pi$
$314$	45.0215			2.54071
$315$	2.65471	−	4.59809i	0.149576	−	0.259073i
$316$	1.25887	+	2.18042i	0.0708168	+	0.122658i
$317$	4.77770	+	8.27522i	0.268343	+	0.464783i	0.968434	−	0.249270i	$-0.0801908\pi$
$317$	4.77770	+	8.27522i	0.268343	+	0.464783i	−0.700091	+	0.714053i	$0.746857\pi$
$318$	11.0111			0.617473
$319$	7.44067	−	12.8876i	0.416598	−	0.721568i
$320$	−2.94560	+	5.10193i	−0.164664	+	0.285207i
$321$	−3.90353	+	6.76111i	−0.217874	+	0.377368i
$322$	−18.2854	−	31.6713i	−1.01901	−	1.76497i
$323$	3.84939	−	6.66733i	0.214186	−	0.370980i
$324$	−7.58139	−	13.1314i	−0.421189	−	0.729520i
$325$	−4.75042			−0.263506
$326$	−7.15119			−0.396068
$327$	−5.49513	−	9.51785i	−0.303882	−	0.526338i
$328$	−6.28118	+	10.8793i	−0.346820	+	0.600710i
$329$	10.7746	+	18.6621i	0.594021	+	1.02888i
$330$	−0.740543	+	1.28266i	−0.0407656	+	0.0706080i
$331$	−8.03062	+	13.9094i	−0.441403	+	0.764532i	−0.997794	−	0.0663885i	$-0.978852\pi$
$331$	−8.03062	+	13.9094i	−0.441403	+	0.764532i	0.556391	+	0.830921i	$0.312186\pi$
$332$	1.90158	−	3.29363i	0.104363	−	0.180761i
$333$	−22.9194			−1.25598
$334$	0.797334	+	1.38102i	0.0436282	+	0.0755662i
$335$	−1.72371	−	2.98555i	−0.0941763	−	0.163118i
$336$	−3.02142	+	5.23326i	−0.164832	+	0.285497i
$337$	−26.0079			−1.41674			−0.708369	−	0.705842i	$-0.750569\pi$
$337$	−26.0079			−1.41674			−0.708369	+	0.705842i	$0.750569\pi$
$338$	−1.07055	−	1.85425i	−0.0582303	−	0.100858i
$339$	−7.95429			−0.432018
$340$	2.42209			0.131356
$341$	−0.726106	+	12.7802i	−0.0393209	+	0.692089i
$342$	−23.1731			−1.25306
$343$	−9.02217			−0.487151
$344$	−6.45963	−	11.1884i	−0.348280	−	0.603239i
$345$	1.27528			0.0686586
$346$	−24.2906	+	42.0725i	−1.30587	+	2.26183i
$347$	16.6751	+	28.8821i	0.895167	+	1.55047i	0.833598	+	0.552372i	$0.186277\pi$
$347$	16.6751	+	28.8821i	0.895167	+	1.55047i	0.0615693	+	0.998103i	$0.480389\pi$
$348$	−5.03704	−	8.72442i	−0.270014	−	0.467678i
$349$	−6.99731			−0.374558			−0.187279	−	0.982307i	$-0.559967\pi$
$349$	−6.99731			−0.374558			−0.187279	+	0.982307i	$0.559967\pi$
$350$	−20.4935	+	35.4959i	−1.09543	+	1.89733i
$351$	1.69753	−	2.94020i	0.0906072	−	0.156936i
$352$	−9.00486	+	15.5969i	−0.479961	+	0.831316i
$353$	−9.26765	−	16.0520i	−0.493267	−	0.854364i	0.506703	−	0.862121i	$-0.330864\pi$
$353$	−9.26765	−	16.0520i	−0.493267	−	0.854364i	−0.999970	+	0.00775705i	$0.997531\pi$
$354$	7.22405	−	12.5124i	0.383954	−	0.665027i
$355$	2.84515	+	4.92795i	0.151005	+	0.261548i
$356$	1.29102			0.0684242
$357$	4.55290			0.240965
$358$	12.4850	+	21.6247i	0.659855	+	1.14290i
$359$	−9.57736	+	16.5885i	−0.505474	+	0.875506i	0.494506	+	0.869174i	$0.335349\pi$
$359$	−9.57736	+	16.5885i	−0.505474	+	0.875506i	−0.999980	+	0.00633219i	$0.997984\pi$
$360$	−0.824187	−	1.42753i	−0.0434385	−	0.0752377i
$361$	1.07937	−	1.86952i	0.0568087	−	0.0983956i
$362$	3.74395	−	6.48471i	0.196778	−	0.340829i
$363$	1.72066	−	2.98028i	0.0903114	−	0.156424i
$364$	−10.4142			−0.545850
$365$	−2.82123	−	4.88651i	−0.147670	−	0.255771i
$366$	5.75286	+	9.96425i	0.300707	+	0.520839i
$367$	−4.92909	+	8.53744i	−0.257296	+	0.445650i	−0.965517	−	0.260341i	$-0.916165\pi$
$367$	−4.92909	+	8.53744i	−0.257296	+	0.445650i	0.708220	+	0.705992i	$0.249498\pi$
$368$	10.5538			0.550153
$369$	13.2407	+	22.9336i	0.689285	+	1.19388i
$370$	−9.29589			−0.483270
$371$	−34.4110			−1.78653
$372$	7.24684	+	4.75155i	0.375731	+	0.246357i
$373$	6.33943			0.328243			0.164122	−	0.986440i	$-0.447521\pi$
$373$	6.33943			0.328243			0.164122	+	0.986440i	$0.447521\pi$
$374$	9.23485			0.477522
$375$	−1.46682	−	2.54061i	−0.0757465	−	0.131197i
$376$	6.69021			0.345021
$377$	−3.23634	+	5.60550i	−0.166680	+	0.288698i
$378$	−14.6464	−	25.3684i	−0.753332	−	1.30481i
$379$	−10.1840	−	17.6392i	−0.523118	−	0.906067i	−0.999638	−	0.0269031i	$-0.991435\pi$
$379$	−10.1840	−	17.6392i	−0.523118	−	0.906067i	0.476520	−	0.879163i	$-0.341898\pi$
$380$	−5.29838			−0.271801
$381$	−1.88522	+	3.26530i	−0.0965828	+	0.167286i
$382$	−4.44087	+	7.69180i	−0.227214	+	0.393547i
$383$	−1.66590	+	2.88542i	−0.0851233	+	0.147438i	−0.905444	−	0.424466i	$-0.860462\pi$
$383$	−1.66590	+	2.88542i	−0.0851233	+	0.147438i	0.820320	+	0.571904i	$0.193795\pi$
$384$	2.88523	+	4.99737i	0.147236	+	0.255021i
$385$	2.31428	−	4.00845i	0.117947	−	0.204289i
$386$	−19.6296	−	33.9995i	−0.999122	−	1.73053i
$387$	−27.2339			−1.38438
$388$	22.1450			1.12424
$389$	−15.0700	−	26.1021i	−0.764081	−	1.32343i	−0.940731	−	0.339153i	$-0.889859\pi$
$389$	−15.0700	−	26.1021i	−0.764081	−	1.32343i	0.176650	−	0.984274i	$-0.443474\pi$
$390$	0.322101	−	0.557896i	0.0163102	−	0.0282501i
$391$	−3.97580	−	6.88628i	−0.201065	−	0.348254i
$392$	−5.77933	+	10.0101i	−0.291900	+	0.505586i
$393$	−3.53939	+	6.13041i	−0.178539	+	0.309238i
$394$	19.2400	−	33.3247i	0.969298	−	1.67887i
$395$	0.486713			0.0244892
$396$	−7.83490	−	13.5704i	−0.393718	−	0.681940i
$397$	−13.7673	−	23.8456i	−0.690959	−	1.19678i	−0.971524	−	0.236941i	$-0.923855\pi$
$397$	−13.7673	−	23.8456i	−0.690959	−	1.19678i	0.280565	−	0.959835i	$-0.409478\pi$
$398$	−22.4479	+	38.8809i	−1.12521	+	1.94892i
$399$	−9.95958			−0.498603
$400$	−5.91411	−	10.2435i	−0.295705	−	0.512177i
$401$	30.2799			1.51211			0.756053	−	0.654511i	$-0.227125\pi$
$401$	30.2799			1.51211			0.756053	+	0.654511i	$0.227125\pi$
$402$	−8.89811			−0.443797
$403$	0.315822	−	5.55880i	0.0157322	−	0.276904i
$404$	14.6937			0.731041
$405$	−2.93118			−0.145651
$406$	27.9235	+	48.3649i	1.38582	+	2.40031i
$407$	−19.9803			−0.990388
$408$	0.706753	−	1.22413i	0.0349895	−	0.0606035i
$409$	−12.0981	−	20.9546i	−0.598214	−	1.03614i	−0.993085	−	0.117401i	$-0.962544\pi$
$409$	−12.0981	−	20.9546i	−0.598214	−	1.03614i	0.394870	−	0.918737i	$-0.370790\pi$
$410$	5.37032	+	9.30166i	0.265221	+	0.459376i
$411$	−11.9561			−0.589749
$412$	−3.45035	+	5.97618i	−0.169986	+	0.294425i
$413$	−22.5759	+	39.1027i	−1.11089	+	1.92412i
$414$	−11.9670	+	20.7275i	−0.588147	+	1.01870i
$415$	−0.367602	−	0.636704i	−0.0180448	−	0.0312546i
$416$	3.91669	−	6.78390i	0.192031	−	0.332608i
$417$	0.0795236	+	0.137739i	0.00389429	+	0.00674511i
$418$	−20.2015			−0.988086
$419$	0.857869			0.0419096			0.0209548	−	0.999780i	$-0.493329\pi$
$419$	0.857869			0.0419096			0.0209548	+	0.999780i	$0.493329\pi$
$420$	−1.56668	−	2.71356i	−0.0764460	−	0.132408i
$421$	11.5427	−	19.9925i	0.562554	−	0.974373i	−0.434718	−	0.900567i	$-0.643152\pi$
$421$	11.5427	−	19.9925i	0.562554	−	0.974373i	0.997273	−	0.0738063i	$-0.0235147\pi$
$422$	−2.44480	−	4.23452i	−0.119011	−	0.206133i
$423$	7.05149	−	12.2135i	0.342855	−	0.593843i
$424$	−5.34166	+	9.25203i	−0.259414	+	0.449318i
$425$	−4.45590	+	7.71785i	−0.216143	+	0.374371i
$426$	14.6872			0.711598
$427$	−17.9783	−	31.1394i	−0.870032	−	1.50694i
$428$	−16.7505	−	29.0127i	−0.809666	−	1.40238i
$429$	0.692315	−	1.19912i	0.0334253	−	0.0578943i
$430$	−11.0458			−0.532675
$431$	2.96685	+	5.13873i	0.142908	+	0.247524i	0.928590	−	0.371106i	$-0.121021\pi$
$431$	2.96685	+	5.13873i	0.142908	+	0.247524i	−0.785683	+	0.618630i	$0.787688\pi$
$432$	8.45345			0.406717
$433$	−26.2879			−1.26331			−0.631657	−	0.775248i	$-0.717625\pi$
$433$	−26.2879			−1.26331			−0.631657	+	0.775248i	$0.717625\pi$
$434$	−40.1738	−	26.3408i	−1.92840	−	1.26440i
$435$	−1.94746			−0.0933736
$436$	47.1605			2.25858
$437$	8.69716	+	15.0639i	0.416041	+	0.720605i
$438$	−14.5637			−0.695880
$439$	−4.86495	+	8.42634i	−0.232191	+	0.402167i	−0.958453	−	0.285251i	$-0.907923\pi$
$439$	−4.86495	+	8.42634i	−0.232191	+	0.402167i	0.726261	+	0.687419i	$0.241256\pi$
$440$	−0.718497	−	1.24447i	−0.0342530	−	0.0593279i
$441$	12.1828	+	21.1013i	0.580136	+	1.00482i
$442$	−4.01672			−0.191056
$443$	−13.4526	+	23.3006i	−0.639154	+	1.10705i	0.346465	+	0.938063i	$0.387382\pi$
$443$	−13.4526	+	23.3006i	−0.639154	+	1.10705i	−0.985619	+	0.168984i	$0.945951\pi$
$444$	−6.76295	+	11.7138i	−0.320955	+	0.555911i
$445$	0.124786	−	0.216137i	0.00591545	−	0.0102459i
$446$	−6.69714	−	11.5998i	−0.317119	−	0.549266i
$447$	4.56986	−	7.91523i	0.216147	−	0.374378i
$448$	−23.7598	−	41.1532i	−1.12254	−	1.94430i
$449$	0.801101			0.0378063			0.0189032	−	0.999821i	$-0.493983\pi$
$449$	0.801101			0.0378063			0.0189032	+	0.999821i	$0.493983\pi$
$450$	26.8243			1.26451
$451$	11.5428	+	19.9927i	0.543529	+	0.941421i
$452$	17.0664	−	29.5599i	0.802736	−	1.39038i
$453$	−1.29173	−	2.23735i	−0.0606909	−	0.105120i
$454$	−12.1571	+	21.0567i	−0.570561	+	0.988240i
$455$	−1.00660	+	1.74348i	−0.0471902	+	0.0817358i
$456$	−1.54604	+	2.67782i	−0.0723999	+	0.125400i
$457$	9.22192			0.431383			0.215692	−	0.976462i	$-0.430799\pi$
$457$	9.22192			0.431383			0.215692	+	0.976462i	$0.430799\pi$
$458$	11.9346	+	20.6714i	0.557669	+	0.965911i
$459$	−3.18457	−	5.51584i	−0.148643	−	0.257457i
$460$	−2.73618	+	4.73921i	−0.127575	+	0.220967i
$461$	−13.5273			−0.630030			−0.315015	−	0.949087i	$-0.602009\pi$
$461$	−13.5273			−0.630030			−0.315015	+	0.949087i	$0.602009\pi$
$462$	−5.97337	−	10.3462i	−0.277906	−	0.481348i
$463$	−15.2980			−0.710960			−0.355480	−	0.934684i	$-0.615683\pi$
$463$	−15.2980			−0.710960			−0.355480	+	0.934684i	$0.615683\pi$
$464$	−16.1165			−0.748191
$465$	1.49594	−	0.753957i	0.0693725	−	0.0349639i
$466$	−34.5750			−1.60166
$467$	12.3764			0.572710			0.286355	−	0.958124i	$-0.407556\pi$
$467$	12.3764			0.572710			0.286355	+	0.958124i	$0.407556\pi$
$468$	3.40781	+	5.90250i	0.157526	+	0.272843i
$469$	27.8076			1.28403
$470$	2.86002	−	4.95369i	0.131923	−	0.228497i
$471$	−6.33182	−	10.9670i	−0.291755	−	0.505334i
$472$	7.00899	+	12.1399i	0.322615	+	0.558785i
$473$	−23.7415			−1.09164
$474$	0.628126	−	1.08795i	0.0288508	−	0.0499710i
$475$	9.74740	−	16.8830i	0.447242	−	0.774645i
$476$	−9.76851	+	16.9196i	−0.447739	+	0.775507i
$477$	11.2602	+	19.5033i	0.515571	+	0.892996i
$478$	5.38224	−	9.32232i	0.246178	−	0.426393i
$479$	−0.474937	−	0.822614i	−0.0217004	−	0.0375862i	0.854971	−	0.518675i	$-0.173575\pi$
$479$	−0.474937	−	0.822614i	−0.0217004	−	0.0375862i	−0.876672	+	0.481089i	$0.840241\pi$
$480$	2.35686			0.107575
$481$	8.69049			0.396252
$482$	31.2729	+	54.1663i	1.42444	+	2.46721i
$483$	−5.14332	+	8.90849i	−0.234029	+	0.405350i
$484$	7.38357	+	12.7887i	0.335617	+	0.581306i
$485$	2.14047	−	3.70741i	0.0971938	−	0.168345i
$486$	−14.6866	+	25.4379i	−0.666196	+	1.15388i
$487$	7.40653	−	12.8285i	0.335622	−	0.581314i	−0.647982	−	0.761656i	$-0.724387\pi$
$487$	7.40653	−	12.8285i	0.335622	−	0.581314i	0.983604	+	0.180341i	$0.0577202\pi$
$488$	−11.1632			−0.505334
$489$	1.00574	+	1.74200i	0.0454812	+	0.0787758i
$490$	4.94125	+	8.55849i	0.223223	+	0.386633i
$491$	−4.74094	+	8.21155i	−0.213956	+	0.370582i	−0.952949	−	0.303131i	$-0.901968\pi$
$491$	−4.74094	+	8.21155i	−0.213956	+	0.370582i	0.738993	+	0.673713i	$0.235301\pi$
$492$	15.6281			0.704567
$493$	6.07139	+	10.5160i	0.273442	+	0.473615i
$494$	8.78668			0.395331
$495$	−3.02919			−0.136152
$496$	12.3799	−	6.23950i	0.555873	−	0.280162i
$497$	−45.8991			−2.05886
$498$	−1.89763			−0.0850347
$499$	−18.4128	−	31.8919i	−0.824269	−	1.42768i	−0.902477	−	0.430739i	$-0.858253\pi$
$499$	−18.4128	−	31.8919i	−0.824269	−	1.42768i	0.0782078	−	0.996937i	$-0.475080\pi$
$500$	12.5886			0.562981
$501$	0.224274	−	0.388454i	0.0100198	−	0.0173548i
$502$	−3.40416	−	5.89618i	−0.151935	−	0.263160i
$503$	3.63550	+	6.29686i	0.162099	+	0.280763i	0.935621	−	0.353006i	$-0.114840\pi$
$503$	3.63550	+	6.29686i	0.162099	+	0.280763i	−0.773522	+	0.633769i	$0.781507\pi$
$504$	13.2961			0.592256
$505$	1.42025	−	2.45995i	0.0632004	−	0.109466i
$506$	−10.4324	+	18.0695i	−0.463778	+	0.803287i
$507$	−0.301124	+	0.521562i	−0.0133734	+	0.0231634i
$508$	−8.08971	−	14.0118i	−0.358923	−	0.621673i
$509$	−16.1632	+	27.9956i	−0.716423	+	1.24088i	0.245985	+	0.969274i	$0.420889\pi$
$509$	−16.1632	+	27.9956i	−0.716423	+	1.24088i	−0.962408	+	0.271608i	$0.912445\pi$
$510$	−0.604264	−	1.04662i	−0.0267572	−	0.0463449i
$511$	45.5131			2.01338
$512$	25.7348			1.13733
$513$	6.96633	+	12.0660i	0.307571	+	0.532728i
$514$	6.31167	−	10.9321i	0.278396	−	0.482195i
$515$	0.667000	+	1.15528i	0.0293915	+	0.0509076i
$516$	−8.03604	+	13.9188i	−0.353767	+	0.612742i
$517$	6.14724	−	10.6473i	0.270355	−	0.468269i
$518$	37.4913	−	64.9368i	1.64727	−	2.85316i
$519$	13.6649			0.599822
$520$	0.312512	+	0.541287i	0.0137046	+	0.0237370i
$521$	4.48863	+	7.77454i	0.196650	+	0.340609i	0.947440	−	0.319933i	$-0.103660\pi$
$521$	4.48863	+	7.77454i	0.196650	+	0.340609i	−0.750790	+	0.660541i	$0.770327\pi$
$522$	18.2747	−	31.6527i	0.799862	−	1.38540i
$523$	15.6380			0.683804			0.341902	−	0.939736i	$-0.388929\pi$
$523$	15.6380			0.683804			0.341902	+	0.939736i	$0.388929\pi$
$524$	−15.1880	−	26.3063i	−0.663489	−	1.14920i
$525$	11.5288			0.503159
$526$	30.4058			1.32576
$527$	−8.73497	−	5.72728i	−0.380501	−	0.249484i
$528$	3.44763			0.150039
$529$	−5.03448			−0.218891
$530$	4.56705	+	7.91036i	0.198380	+	0.343604i
$531$	29.5499			1.28236
$532$	21.3689	−	37.0120i	0.926458	−	1.60467i
$533$	−5.02057	−	8.69589i	−0.217465	−	0.376661i
$534$	−0.322086	−	0.557869i	−0.0139380	−	0.0241413i
$535$	−6.47621			−0.279991
$536$	4.31660	−	7.47658i	0.186449	−	0.322939i
$537$	3.51179	−	6.08259i	0.151545	−	0.262483i
$538$	−6.47590	+	11.2166i	−0.279196	+	0.483581i
$539$	10.6206	+	18.3954i	0.457460	+	0.792345i
$540$	−2.19165	+	3.79606i	−0.0943138	+	0.163356i
$541$	1.68124	+	2.91199i	0.0722820	+	0.125196i	0.899901	−	0.436094i	$-0.143639\pi$
$541$	1.68124	+	2.91199i	0.0722820	+	0.125196i	−0.827619	+	0.561290i	$0.810305\pi$
$542$	4.82782			0.207372
$543$	−2.10619			−0.0903854
$544$	−7.34773	−	12.7266i	−0.315031	−	0.545650i
$545$	4.55839	−	7.89537i	0.195260	−	0.338201i
$546$	2.59813	+	4.50010i	0.111190	+	0.192586i
$547$	2.70281	−	4.68140i	0.115564	−	0.200162i	−0.802441	−	0.596731i	$-0.796466\pi$
$547$	2.70281	−	4.68140i	0.115564	−	0.200162i	0.918005	+	0.396569i	$0.129799\pi$
$548$	25.6525	−	44.4313i	1.09582	−	1.89801i
$549$	−11.7660	+	20.3794i	−0.502162	+	0.869770i
$550$	23.3844			0.997116
$551$	−13.2813	−	23.0039i	−0.565804	−	0.980000i
$552$	1.59681	+	2.76576i	0.0679647	+	0.117718i
$553$	−1.96296	+	3.39995i	−0.0834736	+	0.144580i
$554$	11.4133			0.484906
$555$	1.30737	+	2.26444i	0.0554949	+	0.0961199i
$556$	−0.682491			−0.0289441
$557$	−4.53565			−0.192182			−0.0960908	−	0.995373i	$-0.530634\pi$
$557$	−4.53565			−0.192182			−0.0960908	+	0.995373i	$0.530634\pi$
$558$	−1.78336	+	31.3890i	−0.0754956	+	1.32880i
$559$	10.3264			0.436761
$560$	−5.01274			−0.211827
$561$	−1.29879	−	2.24956i	−0.0548348	−	0.0949767i
$562$	−3.21576			−0.135649
$563$	4.39876	−	7.61887i	0.185386	−	0.321097i	−0.758321	−	0.651882i	$-0.773980\pi$
$563$	4.39876	−	7.61887i	0.185386	−	0.321097i	0.943706	+	0.330784i	$0.107313\pi$
$564$	−4.16144	−	7.20782i	−0.175228	−	0.303504i
$565$	−3.29917	−	5.71433i	−0.138797	−	0.240404i
$566$	−0.816722			−0.0343294
$567$	11.8217	−	20.4758i	0.496466	−	0.859904i
$568$	−7.12499	+	12.3408i	−0.298958	+	0.517810i
$569$	−20.7601	+	35.9575i	−0.870308	+	1.50742i	−0.00862879	+	0.999963i	$0.502747\pi$
$569$	−20.7601	+	35.9575i	−0.870308	+	1.50742i	−0.861679	+	0.507454i	$0.830587\pi$
$570$	1.32184	+	2.28950i	0.0553659	+	0.0958965i
$571$	−22.4133	+	38.8210i	−0.937969	+	1.62461i	−0.168716	+	0.985665i	$0.553962\pi$
$571$	−22.4133	+	38.8210i	−0.937969	+	1.62461i	−0.769253	+	0.638945i	$0.779371\pi$
$572$	2.97081	+	5.14559i	0.124216	+	0.215148i
$573$	2.49825			0.104366
$574$	−86.6361			−3.61612
$575$	−10.0675	−	17.4374i	−0.419844	−	0.727190i
$576$	−15.5498	+	26.9330i	−0.647907	+	1.12221i
$577$	3.17562	+	5.50034i	0.132203	+	0.228982i	0.924525	−	0.381120i	$-0.124462\pi$
$577$	3.17562	+	5.50034i	0.132203	+	0.228982i	−0.792323	+	0.610102i	$0.791128\pi$
$578$	14.4317	−	24.9964i	0.600279	−	1.03971i
$579$	−5.52141	+	9.56337i	−0.229462	+	0.397440i
$580$	4.17839	−	7.23719i	0.173498	−	0.300508i
$581$	5.93029			0.246030
$582$	−5.52476	−	9.56916i	−0.229009	−	0.396655i
$583$	9.81628	+	17.0023i	0.406549	+	0.704163i
$584$	7.06507	−	12.2371i	0.292355	−	0.506373i
$585$	1.31755			0.0544741
$586$	−5.31898	−	9.21275i	−0.219725	−	0.380575i
$587$	26.7946			1.10593			0.552967	−	0.833203i	$-0.313496\pi$
$587$	26.7946			1.10593			0.552967	+	0.833203i	$0.313496\pi$
$588$	14.3794			0.592998
$589$	19.1080	+	12.5286i	0.787330	+	0.516231i
$590$	11.9852			0.493422
$591$	−10.8237			−0.445226
$592$	10.8194	+	18.7397i	0.444673	+	0.770197i
$593$	25.2464			1.03675			0.518374	−	0.855154i	$-0.326538\pi$
$593$	25.2464			1.03675			0.518374	+	0.855154i	$0.326538\pi$
$594$	−8.35626	+	14.4735i	−0.342862	+	0.593854i
$595$	1.88839	+	3.27079i	0.0774164	+	0.134089i
$596$	19.6098	+	33.9652i	0.803250	+	1.39127i
$597$	12.6283			0.516841
$598$	4.53761	−	7.85937i	0.185557	−	0.321394i
$599$	21.0874	−	36.5244i	0.861608	−	1.49235i	−0.00876879	−	0.999962i	$-0.502791\pi$
$599$	21.0874	−	36.5244i	0.861608	−	1.49235i	0.870377	−	0.492387i	$-0.163875\pi$
$600$	1.78964	−	3.09974i	0.0730616	−	0.126546i
$601$	−0.947188	−	1.64058i	−0.0386366	−	0.0669206i	0.846060	−	0.533087i	$-0.178968\pi$
$601$	−0.947188	−	1.64058i	−0.0386366	−	0.0669206i	−0.884697	+	0.466166i	$0.845635\pi$
$602$	44.5488	−	77.1608i	1.81567	−	3.14484i
$603$	−9.09942	−	15.7607i	−0.370557	−	0.641824i
$604$	11.0860			0.451082
$605$	2.85469			0.116060
$606$	−3.66581	−	6.34936i	−0.148913	−	0.257925i
$607$	−6.13743	+	10.6303i	−0.249111	+	0.431472i	−0.963279	−	0.268502i	$-0.913472\pi$
$607$	−6.13743	+	10.6303i	−0.249111	+	0.431472i	0.714169	+	0.699974i	$0.246805\pi$
$608$	16.0733	+	27.8399i	0.651860	+	1.12906i
$609$	7.85431	−	13.6041i	0.318273	−	0.551264i
$610$	−4.77219	+	8.26567i	−0.193220	+	0.334667i
$611$	−2.67376	+	4.63108i	−0.108169	+	0.187354i
$612$	12.7861			0.516849
$613$	−0.883703	−	1.53062i	−0.0356924	−	0.0618211i	0.847627	−	0.530592i	$-0.178030\pi$
$613$	−0.883703	−	1.53062i	−0.0356924	−	0.0618211i	−0.883320	+	0.468771i	$0.844697\pi$
$614$	−23.6801	−	41.0152i	−0.955653	−	1.65524i
$615$	1.51056	−	2.61637i	0.0609117	−	0.105502i
$616$	11.5911			0.467018
$617$	4.23109	+	7.32846i	0.170337	+	0.295033i	0.938538	−	0.345177i	$-0.112181\pi$
$617$	4.23109	+	7.32846i	0.170337	+	0.295033i	−0.768201	+	0.640209i	$0.778848\pi$
$618$	3.44318			0.138505
$619$	−30.7408			−1.23558			−0.617788	−	0.786345i	$-0.711971\pi$
$619$	−30.7408			−1.23558			−0.617788	+	0.786345i	$0.711971\pi$
$620$	−0.407753	+	7.17689i	−0.0163758	+	0.288231i
$621$	14.3902			0.577458
$622$	−23.1179			−0.926944
$623$	1.00655	+	1.74340i	0.0403267	+	0.0698479i
$624$	−1.49956			−0.0600303
$625$	−10.6593	+	18.4624i	−0.426370	+	0.738495i
$626$	32.4039	+	56.1252i	1.29512	+	2.24321i
$627$	2.84113	+	4.92098i	0.113464	+	0.196525i
$628$	54.3412			2.16845
$629$	8.15171	−	14.1192i	0.325030	−	0.562968i
$630$	5.68400	−	9.84497i	0.226456	−	0.392233i
$631$	22.2951	−	38.6162i	0.887554	−	1.53729i	0.0447958	−	0.998996i	$-0.485736\pi$
$631$	22.2951	−	38.6162i	0.887554	−	1.53729i	0.842758	−	0.538292i	$-0.180930\pi$
$632$	0.609426	+	1.05556i	0.0242417	+	0.0419878i
$633$	−0.687672	+	1.19108i	−0.0273325	+	0.0473413i
$634$	10.2296	+	17.7181i	0.406267	+	0.703676i
$635$	−3.12771			−0.124119
$636$	13.2905			0.527002
$637$	−4.61944	−	8.00111i	−0.183029	−	0.317016i
$638$	15.9312	−	27.5937i	0.630724	−	1.09245i
$639$	15.0195	+	26.0145i	0.594162	+	1.02912i
$640$	−2.39340	+	4.14548i	−0.0946073	+	0.163865i
$641$	−5.40987	+	9.37017i	−0.213677	+	0.370099i	−0.952862	−	0.303403i	$-0.901877\pi$
$641$	−5.40987	+	9.37017i	−0.213677	+	0.370099i	0.739186	+	0.673502i	$0.235211\pi$
$642$	−8.35785	+	14.4762i	−0.329858	+	0.571331i
$643$	6.31086			0.248876			0.124438	−	0.992227i	$-0.460287\pi$
$643$	6.31086			0.248876			0.124438	+	0.992227i	$0.460287\pi$
$644$	−22.0706	−	38.2274i	−0.869704	−	1.50637i
$645$	1.55348	+	2.69070i	0.0611681	+	0.105946i
$646$	8.24193	−	14.2754i	0.324274	−	0.561660i
$647$	4.44275			0.174663			0.0873313	−	0.996179i	$-0.472166\pi$
$647$	4.44275			0.174663			0.0873313	+	0.996179i	$0.472166\pi$
$648$	−3.67021	−	6.35698i	−0.144179	−	0.249726i
$649$	25.7606			1.01119
$650$	−10.1711			−0.398944
$651$	−0.766471	+	13.4907i	−0.0300404	+	0.528743i
$652$	−8.63151			−0.338036
$653$	24.0053			0.939402			0.469701	−	0.882826i	$-0.344362\pi$
$653$	24.0053			0.939402			0.469701	+	0.882826i	$0.344362\pi$
$654$	−11.7656	−	20.3787i	−0.460073	−	0.796870i
$655$	−5.87209			−0.229441
$656$	12.5009	−	21.6522i	0.488078	−	0.845375i
$657$	−14.8932	−	25.7958i	−0.581039	−	1.00639i
$658$	23.0695	+	39.9575i	0.899341	+	1.55770i
$659$	−23.7302			−0.924396			−0.462198	−	0.886777i	$-0.652939\pi$
$659$	−23.7302			−0.924396			−0.462198	+	0.886777i	$0.652939\pi$
$660$	−0.893838	+	1.54817i	−0.0347926	+	0.0602626i
$661$	22.0903	−	38.2615i	0.859212	−	1.48820i	−0.0134704	−	0.999909i	$-0.504288\pi$
$661$	22.0903	−	38.2615i	0.859212	−	1.48820i	0.872682	−	0.488289i	$-0.162379\pi$
$662$	−17.1944	+	29.7815i	−0.668279	+	1.15749i
$663$	0.564911	+	0.978454i	0.0219393	+	0.0380000i
$664$	0.920568	−	1.59447i	0.0357250	−	0.0618774i
$665$	−4.13090	−	7.15493i	−0.160189	−	0.277456i
$666$	−49.0728			−1.90153
$667$	−27.4349			−1.06228
$668$	0.962386	+	1.66690i	0.0372358	+	0.0644943i
$669$	−1.88377	+	3.26278i	−0.0728307	+	0.126147i
$670$	−3.69064	−	6.39237i	−0.142582	−	0.246959i
$671$	−10.2572	+	17.7660i	−0.395975	+	0.685848i
$672$	−9.50545	+	16.4639i	−0.366681	+	0.635110i
$673$	2.60837	−	4.51783i	0.100545	−	0.174149i	−0.811364	−	0.584541i	$-0.801275\pi$
$673$	2.60837	−	4.51783i	0.100545	−	0.174149i	0.911909	+	0.410392i	$0.134608\pi$
$674$	−55.6855			−2.14492
$675$	−8.06395	−	13.9672i	−0.310382	−	0.537597i
$676$	−1.29216	−	2.23809i	−0.0496984	−	0.0860802i
$677$	20.5401	−	35.5765i	0.789420	−	1.36731i	−0.136903	−	0.990584i	$-0.543715\pi$
$677$	20.5401	−	35.5765i	0.789420	−	1.36731i	0.926323	−	0.376731i	$-0.122952\pi$
$678$	−17.0309			−0.654069
$679$	17.2655	+	29.9047i	0.662588	+	1.14764i
$680$	1.17255			0.0449652
$681$	6.83908			0.262074
$682$	−1.55467	+	27.3638i	−0.0595313	+	1.04781i
$683$	44.0834			1.68680			0.843402	−	0.537283i	$-0.180549\pi$
$683$	44.0834			1.68680			0.843402	+	0.537283i	$0.180549\pi$
$684$	−27.9700			−1.06946
$685$	−4.95898	−	8.58920i	−0.189473	−	0.328176i
$686$	−19.3174			−0.737541
$687$	3.35697	−	5.81444i	0.128076	−	0.221835i
$688$	12.8561	+	22.2673i	0.490133	+	0.848935i
$689$	−4.26962	−	7.39519i	−0.162659	−	0.281734i
$690$	2.73050			0.103948
$691$	14.8787	−	25.7706i	0.566012	−	0.980361i	−0.430943	−	0.902379i	$-0.641819\pi$
$691$	14.8787	−	25.7706i	0.566012	−	0.980361i	0.996955	−	0.0779819i	$-0.0248476\pi$
$692$	−29.3188	+	50.7817i	−1.11453	+	1.93043i
$693$	12.2170	−	21.1605i	0.464086	−	0.803821i
$694$	35.7031	+	61.8396i	1.35527	+	2.34740i
$695$	−0.0659675	+	0.114259i	−0.00250229	+	0.00433409i
$696$	−2.43847	−	4.22355i	−0.0924299	−	0.160093i
$697$	−18.8372			−0.713512
$698$	−14.9820			−0.567076
$699$	4.86262	+	8.42230i	0.183921	+	0.318561i
$700$	−24.7358	+	42.8437i	−0.934925	+	1.61934i
$701$	−1.43690	−	2.48878i	−0.0542709	−	0.0940000i	0.837614	−	0.546263i	$-0.183950\pi$
$701$	−1.43690	−	2.48878i	−0.0542709	−	0.0940000i	−0.891885	+	0.452263i	$0.850617\pi$
$702$	3.63458	−	6.29527i	0.137178	−	0.237600i
$703$	−17.8321	+	30.8861i	−0.672549	+	1.16489i
$704$	−13.5557	+	23.4792i	−0.510900	+	0.884906i
$705$	−1.60893			−0.0605957
$706$	−19.8430	−	34.3691i	−0.746801	−	1.29350i
$707$	11.4560	+	19.8424i	0.430849	+	0.746252i
$708$	8.71945	−	15.1025i	0.327697	−	0.567588i
$709$	4.29375			0.161255			0.0806276	−	0.996744i	$-0.474308\pi$
$709$	4.29375			0.161255			0.0806276	+	0.996744i	$0.474308\pi$
$710$	6.09176	+	10.5512i	0.228620	+	0.395981i
$711$	2.56935			0.0963580
$712$	0.624994			0.0234226
$713$	21.0741	−	10.6214i	0.789230	−	0.397775i
$714$	9.74822			0.364818
$715$	1.14860			0.0429551
$716$	15.0695	+	26.1011i	0.563173	+	0.975445i
$717$	−3.02783			−0.113076
$718$	−20.5061	+	35.5176i	−0.765281	+	1.32551i
$719$	−14.4946	−	25.1053i	−0.540556	−	0.936271i	−0.998872	−	0.0474817i	$-0.984880\pi$
$719$	−14.4946	−	25.1053i	−0.540556	−	0.936271i	0.458316	−	0.888789i	$-0.348453\pi$
$720$	1.64031	+	2.84110i	0.0611307	+	0.105882i
$721$	−10.7603			−0.400735
$722$	2.31103	−	4.00283i	0.0860077	−	0.148970i
$723$	8.79643	−	15.2359i	0.327143	−	0.566628i
$724$	4.51896	−	7.82707i	0.167946	−	0.290891i
$725$	15.3740	+	26.6285i	0.570974	+	0.988957i
$726$	3.68412	−	6.38108i	0.136730	−	0.236824i
$727$	−10.4545	−	18.1078i	−0.387737	−	0.671580i	0.604408	−	0.796675i	$-0.293410\pi$
$727$	−10.4545	−	18.1078i	−0.387737	−	0.671580i	−0.992145	+	0.125095i	$0.960076\pi$
$728$	−5.04157			−0.186853
$729$	−9.33962			−0.345912
$730$	−6.04053	−	10.4625i	−0.223570	−	0.387235i
$731$	9.68622	−	16.7770i	0.358258	−	0.620521i
$732$	6.94373	+	12.0269i	0.256647	+	0.444526i
$733$	2.19582	−	3.80327i	0.0811044	−	0.140477i	−0.822620	−	0.568591i	$-0.807489\pi$
$733$	2.19582	−	3.80327i	0.0811044	−	0.140477i	0.903725	+	0.428114i	$0.140822\pi$
$734$	−10.5537	+	18.2795i	−0.389544	+	0.674709i
$735$	1.38987	−	2.40733i	0.0512662	−	0.0887956i
$736$	33.2023			1.22385
$737$	−7.93255	−	13.7396i	−0.292199	−	0.506104i
$738$	28.3498	+	49.1033i	1.04357	+	1.80752i
$739$	2.89447	−	5.01337i	0.106475	−	0.184420i	−0.807865	−	0.589368i	$-0.799377\pi$
$739$	2.89447	−	5.01337i	0.106475	−	0.184420i	0.914340	+	0.404948i	$0.132710\pi$
$740$	−11.2202			−0.412462
$741$	−1.23576	−	2.14039i	−0.0453967	−	0.0786293i
$742$	−73.6774			−2.70478
$743$	36.3130			1.33220			0.666098	−	0.745865i	$-0.267963\pi$
$743$	36.3130			1.33220			0.666098	+	0.745865i	$0.267963\pi$
$744$	3.50825	+	2.30026i	0.128619	+	0.0843317i
$745$	7.58170			0.277772
$746$	13.5734			0.496956
$747$	−1.94056	−	3.36115i	−0.0710014	−	0.122978i
$748$	11.1465			0.407556
$749$	26.1192	−	45.2398i	0.954375	−	1.65303i
$750$	−3.14062	−	5.43971i	−0.114679	−	0.198630i
$751$	1.31849	+	2.28369i	0.0481124	+	0.0833331i	0.889079	−	0.457754i	$-0.151346\pi$
$751$	1.31849	+	2.28369i	0.0481124	+	0.0833331i	−0.840966	+	0.541088i	$0.818013\pi$
$752$	−13.3149			−0.485546
$753$	−0.957521	+	1.65848i	−0.0348940	+	0.0604382i
$754$	−6.92933	+	12.0020i	−0.252351	+	0.437086i
$755$	1.07154	−	1.85595i	0.0389972	−	0.0675451i
$756$	−17.6783	−	30.6197i	−0.642954	−	1.11363i
$757$	−5.28490	+	9.15371i	−0.192083	+	0.332697i	−0.945940	−	0.324341i	$-0.894858\pi$
$757$	−5.28490	+	9.15371i	−0.192083	+	0.332697i	0.753857	+	0.657038i	$0.228191\pi$
$758$	−21.8050	−	37.7674i	−0.791994	−	1.37177i
$759$	5.86886			0.213026
$760$	−2.56498			−0.0930417
$761$	−6.74433	−	11.6815i	−0.244482	−	0.423455i	0.717504	−	0.696554i	$-0.245284\pi$
$761$	−6.74433	−	11.6815i	−0.244482	−	0.423455i	−0.961986	+	0.273100i	$0.911951\pi$
$762$	−4.03645	+	6.99134i	−0.146225	+	0.253270i
$763$	36.7689	+	63.6856i	1.33112	+	2.30557i
$764$	−5.36014	+	9.28404i	−0.193923	+	0.335885i
$765$	1.23587	−	2.14059i	0.0446829	−	0.0773931i
$766$	−3.56685	+	6.17797i	−0.128876	+	0.223219i
$767$	−11.2046			−0.404576
$768$	−0.924247	−	1.60084i	−0.0333509	−	0.0577655i
$769$	−16.5924	−	28.7389i	−0.598337	−	1.03635i	−0.993067	−	0.117553i	$-0.962495\pi$
$769$	−16.5924	−	28.7389i	−0.598337	−	1.03635i	0.394730	−	0.918797i	$-0.370838\pi$
$770$	4.95511	−	8.58249i	0.178570	−	0.309292i
$771$	−3.55068			−0.127875
$772$	−23.6930	−	41.0375i	−0.852731	−	1.47697i
$773$	−20.2954			−0.729974			−0.364987	−	0.931013i	$-0.618927\pi$
$773$	−20.2954			−0.729974			−0.364987	+	0.931013i	$0.618927\pi$
$774$	−58.3105			−2.09593
$775$	−22.1186	−	14.5026i	−0.794525	−	0.520948i
$776$	10.7206			0.384846
$777$	−21.0911			−0.756637
$778$	−32.2665	−	55.8872i	−1.15681	−	2.00365i
$779$	41.2070			1.47639
$780$	0.388777	−	0.673382i	0.0139205	−	0.0241109i
$781$	13.0935	+	22.6785i	0.468521	+	0.811502i
$782$	−8.51258	−	14.7442i	−0.304409	−	0.527253i
$783$	−21.9751			−0.785325
$784$	11.5021	−	19.9222i	0.410789	−	0.711508i
$785$	5.25245	−	9.09752i	0.187468	−	0.324704i
$786$	−7.57820	+	13.1258i	−0.270306	+	0.468183i
$787$	26.0612	+	45.1393i	0.928980	+	1.60904i	0.785031	+	0.619456i	$0.212647\pi$
$787$	26.0612	+	45.1393i	0.928980	+	1.60904i	0.143949	+	0.989585i	$0.454020\pi$
$788$	23.2228	−	40.2231i	0.827278	−	1.43289i
$789$	−4.27626	−	7.40670i	−0.152239	−	0.263686i
$790$	1.04210			0.0370763
$791$	53.2236			1.89241
$792$	−3.79293	−	6.56955i	−0.134776	−	0.233439i
$793$	4.46140	−	7.72736i	0.158429	−	0.274407i
$794$	−29.4771	−	51.0558i	−1.04610	−	1.81190i
$795$	1.28462	−	2.22502i	0.0455607	−	0.0789134i
$796$	−27.0947	+	46.9294i	−0.960347	+	1.66337i
$797$	−2.14801	+	3.72046i	−0.0760863	+	0.131785i	−0.901558	−	0.432658i	$-0.857576\pi$
$797$	−2.14801	+	3.72046i	−0.0760863	+	0.131785i	0.825472	+	0.564443i	$0.190909\pi$
$798$	−21.3245			−0.754879
$799$	5.01598	+	8.68794i	0.177453	+	0.307357i
$800$	−18.6059	−	32.2263i	−0.657818	−	1.13937i
$801$	0.658745	−	1.14098i	0.0232756	−	0.0403145i
$802$	64.8324			2.28931
$803$	−12.9833	−	22.4878i	−0.458172	−	0.793578i
$804$	−10.7401			−0.378772
$805$	−8.53311			−0.300753
$806$	0.676207	−	11.9020i	0.0238184	−	0.419229i
$807$	3.64307			0.128242
$808$	7.11335			0.250247
$809$	19.3896	+	33.5838i	0.681702	+	1.18074i	0.974461	+	0.224556i	$0.0720933\pi$
$809$	19.3896	+	33.5838i	0.681702	+	1.18074i	−0.292759	+	0.956186i	$0.594573\pi$
$810$	−6.27595			−0.220514
$811$	−16.6833	+	28.8963i	−0.585829	+	1.01469i	0.408942	+	0.912560i	$0.365898\pi$
$811$	−16.6833	+	28.8963i	−0.585829	+	1.01469i	−0.994771	+	0.102126i	$0.967436\pi$
$812$	33.7038	+	58.3766i	1.18277	+	2.04862i
$813$	−0.678983	−	1.17603i	−0.0238130	−	0.0412453i
$814$	−42.7799			−1.49944
$815$	−0.834296	+	1.44504i	−0.0292241	+	0.0506176i
$816$	−1.40659	+	2.43628i	−0.0492405	+	0.0852870i
$817$	−21.1889	+	36.7002i	−0.741304	+	1.28398i
$818$	−25.9033	−	44.8659i	−0.905689	−	1.56870i
$819$	−5.31382	+	9.20381i	−0.185680	+	0.321607i
$820$	6.48199	+	11.2271i	0.226361	+	0.392069i
$821$	12.1054			0.422481			0.211241	−	0.977434i	$-0.432250\pi$
$821$	12.1054			0.422481			0.211241	+	0.977434i	$0.432250\pi$
$822$	−25.5992			−0.892873
$823$	−19.7689	−	34.2407i	−0.689099	−	1.19355i	−0.972130	−	0.234444i	$-0.924673\pi$
$823$	−19.7689	−	34.2407i	−0.689099	−	1.19355i	0.283031	−	0.959111i	$-0.408660\pi$
$824$	−1.67034	+	2.89311i	−0.0581890	+	0.100786i
$825$	−3.28878	−	5.69634i	−0.114501	−	0.198321i
$826$	−48.3374	+	83.7228i	−1.68187	+	2.91309i
$827$	10.2657	−	17.7808i	0.356975	−	0.618299i	−0.630479	−	0.776206i	$-0.717141\pi$
$827$	10.2657	−	17.7808i	0.356975	−	0.618299i	0.987454	+	0.157908i	$0.0504748\pi$
$828$	−14.4443	+	25.0182i	−0.501972	+	0.869442i
$829$	5.47892			0.190291			0.0951454	−	0.995463i	$-0.469668\pi$
$829$	5.47892			0.190291			0.0951454	+	0.995463i	$0.469668\pi$
$830$	−0.787072	−	1.36325i	−0.0273197	−	0.0473191i
$831$	−1.60517	−	2.78023i	−0.0556827	−	0.0964453i
$832$	5.89610	−	10.2123i	0.204410	−	0.354049i
$833$	−17.3322			−0.600525
$834$	0.170268	+	0.294913i	0.00589591	+	0.0102120i
$835$	0.372085			0.0128765
$836$	−24.3833			−0.843312
$837$	16.8801	−	8.50763i	0.583462	−	0.294067i
$838$	1.83678			0.0634507
$839$	2.95070			0.101869			0.0509347	−	0.998702i	$-0.483780\pi$
$839$	2.95070			0.101869			0.0509347	+	0.998702i	$0.483780\pi$
$840$	−0.758439	−	1.31365i	−0.0261686	−	0.0453254i
$841$	12.8956			0.444675
$842$	24.7140	−	42.8059i	0.851701	−	1.47519i
$843$	0.452264	+	0.783344i	0.0155768	+	0.0269798i
$844$	−2.95088	−	5.11108i	−0.101574	−	0.175931i
$845$	−0.499585			−0.0171862
$846$	15.0980	−	26.1504i	0.519079	−	0.899070i
$847$	−11.5133	+	19.9416i	−0.395601	+	0.685200i
$848$	10.6311	−	18.4135i	0.365072	−	0.632323i
$849$	0.114864	+	0.198950i	0.00394211	+	0.00682793i
$850$	−9.54054	+	16.5247i	−0.327238	+	0.566793i
$851$	18.4177	+	31.9003i	0.631349	+	1.09353i
$852$	17.7275			0.607335
$853$	−22.7885			−0.780264			−0.390132	−	0.920759i	$-0.627571\pi$
$853$	−22.7885			−0.780264			−0.390132	+	0.920759i	$0.627571\pi$
$854$	−38.4934	−	66.6725i	−1.31722	−	2.28149i
$855$	−2.70350	+	4.68259i	−0.0924576	+	0.160141i
$856$	−8.10904	−	14.0453i	−0.277161	−	0.480057i
$857$	−21.9347	+	37.9920i	−0.749275	+	1.29778i	0.198895	+	0.980021i	$0.436265\pi$
$857$	−21.9347	+	37.9920i	−0.749275	+	1.29778i	−0.948170	+	0.317762i	$0.897069\pi$
$858$	1.48232	−	2.56745i	0.0506055	−	0.0876512i
$859$	13.7858	−	23.8777i	0.470365	−	0.814697i	−0.529060	−	0.848584i	$-0.677455\pi$
$859$	13.7858	−	23.8777i	0.470365	−	0.814697i	0.999426	+	0.0338875i	$0.0107888\pi$
$860$	−13.3323			−0.454628
$861$	12.1845	+	21.1041i	0.415246	+	0.719227i
$862$	6.35232	+	11.0025i	0.216361	+	0.374748i
$863$	−4.49592	+	7.78715i	−0.153043	+	0.265078i	−0.932345	−	0.361571i	$-0.882241\pi$
$863$	−4.49592	+	7.78715i	−0.153043	+	0.265078i	0.779302	+	0.626649i	$0.215574\pi$
$864$	26.5947			0.904771
$865$	5.66773	+	9.81680i	0.192709	+	0.333781i
$866$	−56.2850			−1.91264
$867$	−8.11867			−0.275724
$868$	−48.4899	−	31.7935i	−1.64585	−	1.07914i
$869$	2.23986			0.0759822
$870$	−4.16971			−0.141367
$871$	3.45028	+	5.97606i	0.116908	+	0.202491i
$872$	22.8308			0.773147
$873$	11.2995	−	19.5713i	0.382430	−	0.662389i
$874$	18.6215	+	32.2534i	0.629882	+	1.09099i
$875$	9.81478	+	16.9997i	0.331800	+	0.574695i
$876$	−17.5784			−0.593921
$877$	−18.7550	+	32.4846i	−0.633311	+	1.09693i	0.353560	+	0.935412i	$0.384971\pi$
$877$	−18.7550	+	32.4846i	−0.633311	+	1.09693i	−0.986870	+	0.161514i	$0.948362\pi$
$878$	−10.4164	+	18.0417i	−0.351535	+	0.608876i
$879$	−1.49612	+	2.59136i	−0.0504629	+	0.0874043i
$880$	1.42996	+	2.47677i	0.0482040	+	0.0834919i
$881$	−22.8937	+	39.6531i	−0.771310	+	1.33595i	0.165535	+	0.986204i	$0.447065\pi$
$881$	−22.8937	+	39.6531i	−0.771310	+	1.33595i	−0.936845	+	0.349744i	$0.886269\pi$
$882$	26.0847	+	45.1801i	0.878318	+	1.52129i
$883$	−1.64321			−0.0552983			−0.0276492	−	0.999618i	$-0.508802\pi$
$883$	−1.64321			−0.0552983			−0.0276492	+	0.999618i	$0.508802\pi$
$884$	−4.84820			−0.163063
$885$	−1.68559	−	2.91953i	−0.0566605	−	0.0981389i
$886$	−28.8035	+	49.8890i	−0.967671	+	1.67606i
$887$	−11.4605	−	19.8502i	−0.384806	−	0.666503i	0.606936	−	0.794750i	$-0.292398\pi$
$887$	−11.4605	−	19.8502i	−0.384806	−	0.666503i	−0.991742	+	0.128247i	$0.959065\pi$
$888$	−3.27399	+	5.67072i	−0.109868	+	0.190297i
$889$	12.6144	−	21.8487i	0.423072	−	0.732782i
$890$	0.267181	−	0.462770i	0.00895592	−	0.0155121i
$891$	−13.4893			−0.451910
$892$	−8.08348	−	14.0010i	−0.270655	−	0.468788i
$893$	−10.9726	−	19.0051i	−0.367184	−	0.635981i
$894$	9.78454	−	16.9473i	0.327244	−	0.566803i
$895$	5.82629			0.194751
$896$	−19.3056	−	33.4383i	−0.644955	−	1.11710i
$897$	−2.55267			−0.0852313
$898$	1.71524			0.0572383
$899$	−32.1820	+	16.2198i	−1.07333	+	0.540961i
$900$	32.3770			1.07923
$901$	−16.0196			−0.533692
$902$	24.7143	+	42.8065i	0.822897	+	1.42530i
$903$	−25.0613			−0.833989
$904$	8.26197	−	14.3101i	0.274789	−	0.475948i
$905$	−0.873578	−	1.51308i	−0.0290387	−	0.0502966i
$906$	−2.76573	−	4.79039i	−0.0918853	−	0.159150i
$907$	−25.5807			−0.849392			−0.424696	−	0.905336i	$-0.639619\pi$
$907$	−25.5807			−0.849392			−0.424696	+	0.905336i	$0.639619\pi$
$908$	−14.6737	+	25.4155i	−0.486963	+	0.843444i
$909$	7.49748	−	12.9860i	0.248676	−	0.430719i
$910$	−2.15524	+	3.73298i	−0.0714454	+	0.123747i
$911$	14.2410	+	24.6662i	0.471827	+	0.817228i	0.999480	−	0.0322316i	$-0.0102614\pi$
$911$	14.2410	+	24.6662i	0.471827	+	0.817228i	−0.527654	+	0.849460i	$0.676928\pi$
$912$	3.07695	−	5.32943i	0.101888	−	0.176475i
$913$	−1.69171	−	2.93013i	−0.0559875	−	0.0969731i
$914$	19.7451			0.653109
$915$	2.68464			0.0887514
$916$	14.4052	+	24.9505i	0.475960	+	0.824386i
$917$	23.6827	−	41.0197i	0.782072	−	1.35459i
$918$	−6.81849	−	11.8100i	−0.225044	−	0.389787i
$919$	−23.6529	+	40.9680i	−0.780237	+	1.35141i	0.151566	+	0.988447i	$0.451568\pi$
$919$	−23.6529	+	40.9680i	−0.780237	+	1.35141i	−0.931803	+	0.362964i	$0.881765\pi$
$920$	−1.32461	+	2.29429i	−0.0436710	+	0.0756403i
$921$	−6.66074	+	11.5367i	−0.219479	+	0.380149i
$922$	−28.9634			−0.953857
$923$	−5.69504	−	9.86409i	−0.187454	−	0.324681i
$924$	−7.20988	−	12.4879i	−0.237188	−	0.410821i
$925$	20.6417	−	35.7525i	0.678696	−	1.17554i
$926$	−32.7547			−1.07639
$927$	3.52108	+	6.09869i	0.115647	+	0.200307i
$928$	−50.7029			−1.66440
$929$	−16.2540			−0.533276			−0.266638	−	0.963797i	$-0.585913\pi$
$929$	−16.2540			−0.533276			−0.266638	+	0.963797i	$0.585913\pi$
$930$	3.20296	−	1.61430i	0.105029	−	0.0529350i
$931$	37.9147			1.24260
$932$	−41.7322			−1.36698
$933$	3.25130	+	5.63141i	0.106443	+	0.184364i
$934$	26.4991			0.867076
$935$	1.07739	−	1.86609i	0.0352343	−	0.0610276i
$936$	1.64974	+	2.85744i	0.0539236	+	0.0933984i
$937$	−2.45700	−	4.25566i	−0.0802668	−	0.139026i	0.823098	−	0.567900i	$-0.192244\pi$
$937$	−2.45700	−	4.25566i	−0.0802668	−	0.139026i	−0.903365	+	0.428874i	$0.858911\pi$
$938$	59.5388			1.94401
$939$	9.11455	−	15.7869i	0.297442	−	0.515185i
$940$	3.45205	−	5.97913i	0.112593	−	0.195018i
$941$	−20.5081	+	35.5211i	−0.668546	+	1.15796i	0.309764	+	0.950813i	$0.399750\pi$
$941$	−20.5081	+	35.5211i	−0.668546	+	1.15796i	−0.978311	+	0.207143i	$0.933584\pi$
$942$	−13.5571	−	23.4815i	−0.441713	−	0.765070i
$943$	21.2801	−	36.8582i	0.692975	−	1.20027i
$944$	−13.9494	−	24.1610i	−0.454014	−	0.786375i
$945$	−6.83493			−0.222340
$946$	−50.8330			−1.65272
$947$	−4.69423	−	8.13064i	−0.152542	−	0.264210i	0.779619	−	0.626254i	$-0.215413\pi$
$947$	−4.69423	−	8.13064i	−0.152542	−	0.264210i	−0.932161	+	0.362043i	$0.882079\pi$
$948$	0.758150	−	1.31315i	0.0246236	−	0.0426493i
$949$	5.64714	+	9.78114i	0.183314	+	0.317509i
$950$	20.8702	−	36.1482i	0.677118	−	1.17280i
$951$	2.87736	−	4.98374i	0.0933049	−	0.161609i
$952$	−4.72901	+	8.19088i	−0.153268	+	0.265468i
$953$	13.3826			0.433505			0.216752	−	0.976227i	$-0.430454\pi$
$953$	13.3826			0.433505			0.216752	+	0.976227i	$0.430454\pi$
$954$	24.1093	+	41.7586i	0.780569	+	1.35198i
$955$	1.03619	+	1.79473i	0.0335303	+	0.0580762i
$956$	6.49639	−	11.2521i	0.210108	−	0.363918i
$957$	−8.96226			−0.289709
$958$	−1.01689	−	1.76130i	−0.0328542	−	0.0569051i
$959$	80.0002			2.58334
$960$	3.54797			0.114510
$961$	18.4410	−	24.9184i	0.594872	−	0.803821i
$962$	18.6072			0.599921
$963$	−34.1878			−1.10169
$964$	37.7465	+	65.3789i	1.21573	+	2.10571i
$965$	−9.16039			−0.294883
$966$	−11.0124	+	19.0740i	−0.354317	+	0.613696i
$967$	11.9974	+	20.7801i	0.385810	+	0.668242i	0.991881	−	0.127168i	$-0.0405888\pi$
$967$	11.9974	+	20.7801i	0.385810	+	0.668242i	−0.606072	+	0.795410i	$0.707256\pi$
$968$	3.57444	+	6.19111i	0.114887	+	0.198990i
$969$	−4.63657			−0.148948
$970$	4.58297	−	7.93794i	0.147150	−	0.254872i
$971$	22.8155	−	39.5176i	0.732185	−	1.26818i	−0.223763	−	0.974644i	$-0.571834\pi$
$971$	22.8155	−	39.5176i	0.732185	−	1.26818i	0.955947	−	0.293538i	$-0.0948326\pi$
$972$	−17.7267	+	30.7036i	−0.568585	+	0.984818i
$973$	−0.532107	−	0.921636i	−0.0170586	−	0.0295463i
$974$	15.8581	−	27.4671i	0.508128	−	0.880103i
$975$	1.43046	+	2.47764i	0.0458115	+	0.0793479i
$976$	22.2171			0.711154
$977$	26.0679			0.833986			0.416993	−	0.908910i	$-0.363084\pi$
$977$	26.0679			0.833986			0.416993	+	0.908910i	$0.363084\pi$
$978$	2.15340	+	3.72979i	0.0688580	+	0.119266i
$979$	0.574270	−	0.994665i	0.0183538	−	0.0317896i
$980$	5.96410	+	10.3301i	0.190516	+	0.329984i
$981$	24.0637	−	41.6795i	0.768294	−	1.33072i
$982$	−10.1508	+	17.5818i	−0.323926	+	0.561057i
$983$	16.3534	−	28.3249i	0.521592	−	0.903423i	−0.478093	−	0.878309i	$-0.658672\pi$
$983$	16.3534	−	28.3249i	0.521592	−	0.903423i	0.999685	−	0.0251139i	$-0.00799484\pi$
$984$	7.56565			0.241184
$985$	−4.48929	−	7.77567i	−0.143041	−	0.247754i
$986$	12.9995	+	22.5157i	0.413987	+	0.717047i
$987$	6.48897	−	11.2392i	0.206546	−	0.357748i
$988$	10.6056			0.337408
$989$	21.8847	+	37.9054i	0.695892	+	1.20532i
$990$	−6.48580			−0.206132
$991$	−30.6192			−0.972652			−0.486326	−	0.873777i	$-0.661663\pi$
$991$	−30.6192			−0.972652			−0.486326	+	0.873777i	$0.661663\pi$
$992$	38.9473	−	19.6296i	1.23658	−	0.623240i
$993$	9.67285			0.306959
$994$	−98.2748			−3.11709
$995$	5.23778	+	9.07211i	0.166049	+	0.287605i
$996$	−2.29044			−0.0725755
$997$	0.322107	−	0.557906i	0.0102012	−	0.0176690i	−0.860880	−	0.508809i	$-0.830086\pi$
$997$	0.322107	−	0.557906i	0.0102012	−	0.0176690i	0.871081	+	0.491139i	$0.163419\pi$
$998$	−39.4236	−	68.2837i	−1.24793	−	2.16148i
$999$	14.7523	+	25.5518i	0.466743	+	0.808423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.14	✓	34
31.5	even	3	inner	403.2.h.b.222.14	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.14	✓	34	1.1	even	1	trivial
403.2.h.b.222.14	yes	34	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +O(q^{10})\)	\(q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +(0.534831 - 0.926355i) q^{10} +(1.14955 - 1.99108i) q^{11} +(-0.778201 - 1.34788i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(4.31405 + 7.47216i) q^{14} -0.300874 q^{15} -2.48993 q^{16} +(0.938003 + 1.62467i) q^{17} +(2.82336 - 4.89021i) q^{18} +(-2.05191 - 3.55401i) q^{19} +(0.645543 - 1.11811i) q^{20} +(1.21346 - 2.10177i) q^{21} +(2.46131 - 4.26311i) q^{22} -4.23857 q^{23} +(-0.376733 - 0.652520i) q^{24} +(2.37521 + 4.11398i) q^{25} +(-1.07055 + 1.85425i) q^{26} -3.39505 q^{27} +(5.20708 + 9.01893i) q^{28} +6.47268 q^{29} -0.644202 q^{30} +(-4.97197 + 2.50589i) q^{31} -7.83337 q^{32} -1.38463 q^{33} +(2.00836 + 3.47858i) q^{34} +2.01320 q^{35} +(3.40781 - 5.90250i) q^{36} +(-4.34525 - 7.52619i) q^{37} +(-4.39334 - 7.60949i) q^{38} +0.602248 q^{39} +(0.312512 - 0.541287i) q^{40} +(-5.02057 + 8.69589i) q^{41} +(2.59813 - 4.50010i) q^{42} +(-5.16322 - 8.94295i) q^{43} +(2.97081 - 5.14559i) q^{44} +(-0.658777 - 1.14103i) q^{45} -9.07522 q^{46} +5.34751 q^{47} +(0.749779 + 1.29865i) q^{48} +(-4.61944 + 8.00111i) q^{49} +(5.08556 + 8.80845i) q^{50} +(0.564911 - 0.978454i) q^{51} +(-1.29216 + 2.23809i) q^{52} +(-4.26962 + 7.39519i) q^{53} -7.26915 q^{54} +(-0.574298 - 0.994713i) q^{55} +(2.52079 + 4.36613i) q^{56} +(-1.23576 + 2.14039i) q^{57} +13.8587 q^{58} +(5.60232 + 9.70350i) q^{59} -0.777555 q^{60} -8.92279 q^{61} +(-10.6455 + 5.36537i) q^{62} +10.6276 q^{63} -11.7922 q^{64} +(0.249792 + 0.432653i) q^{65} -2.96463 q^{66} +(3.45028 - 5.97606i) q^{67} +(2.42410 + 4.19866i) q^{68} +(1.27634 + 2.21068i) q^{69} +4.31047 q^{70} +(-5.69504 + 9.86409i) q^{71} +(1.64974 - 2.85744i) q^{72} +(5.64714 - 9.78114i) q^{73} +(-9.30362 - 16.1143i) q^{74} +(1.43046 - 2.47764i) q^{75} +(-5.30278 - 9.18468i) q^{76} +9.26480 q^{77} +1.28948 q^{78} +(0.487117 + 0.843712i) q^{79} +(-0.621966 + 1.07728i) q^{80} +(-2.93361 - 5.08117i) q^{81} +(-10.7496 + 18.6188i) q^{82} +(0.735814 - 1.27447i) q^{83} +(3.13596 - 5.43163i) q^{84} +0.937224 q^{85} +(-11.0550 - 19.1478i) q^{86} +(-1.94908 - 3.37591i) q^{87} +(1.43819 - 2.49102i) q^{88} +0.499561 q^{89} +(-1.41051 - 2.44307i) q^{90} -4.02975 q^{91} -10.9538 q^{92} +(2.80416 + 1.83861i) q^{93} +11.4496 q^{94} -2.05020 q^{95} +(2.35882 + 4.08559i) q^{96} +8.56900 q^{97} +(-9.89070 + 17.1312i) q^{98} +(-3.03171 - 5.25107i) 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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