LMFDB - Embedded newform 117.2.l.b.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(4,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.93463i q^{2} +(0.820210 + 1.52553i) q^{3} -1.74278 q^{4} +(-2.26677 - 1.30872i) q^{5} +(-2.95134 + 1.58680i) q^{6} +(2.01692 + 1.16447i) q^{7} +0.497616i q^{8} +(-1.65451 + 2.50252i) q^{9} +(2.53189 - 4.38536i) q^{10} -5.38716i q^{11} +(-1.42945 - 2.65868i) q^{12} +(3.56568 - 0.534742i) q^{13} +(-2.25282 + 3.90199i) q^{14} +(0.137271 - 4.53147i) q^{15} -4.44827 q^{16} +(0.835786 + 1.44762i) q^{17} +(-4.84144 - 3.20086i) q^{18} +(1.90355 - 1.09901i) q^{19} +(3.95050 + 2.28082i) q^{20} +(-0.122141 + 4.03200i) q^{21} +10.4221 q^{22} +(2.10438 + 3.64489i) q^{23} +(-0.759130 + 0.408149i) q^{24} +(0.925505 + 1.60302i) q^{25} +(1.03453 + 6.89826i) q^{26} +(-5.17472 - 0.471426i) q^{27} +(-3.51506 - 2.02942i) q^{28} +5.72509 q^{29} +(8.76670 + 0.265569i) q^{30} +(-7.55059 - 4.35934i) q^{31} -7.61052i q^{32} +(8.21830 - 4.41860i) q^{33} +(-2.80061 + 1.61693i) q^{34} +(-3.04794 - 5.27918i) q^{35} +(2.88346 - 4.36135i) q^{36} +(-1.22479 - 0.707130i) q^{37} +(2.12618 + 3.68265i) q^{38} +(3.74037 + 5.00096i) q^{39} +(0.651240 - 1.12798i) q^{40} +(-1.31938 + 0.761744i) q^{41} +(-7.80041 - 0.236297i) q^{42} +(-0.938835 + 1.62611i) q^{43} +9.38866i q^{44} +(7.02550 - 3.50734i) q^{45} +(-7.05150 + 4.07119i) q^{46} +(4.47809 - 2.58543i) q^{47} +(-3.64852 - 6.78599i) q^{48} +(-0.788015 - 1.36488i) q^{49} +(-3.10125 + 1.79051i) q^{50} +(-1.52288 + 2.46238i) q^{51} +(-6.21421 + 0.931939i) q^{52} -9.81151 q^{53} +(0.912035 - 10.0112i) q^{54} +(-7.05029 + 12.2115i) q^{55} +(-0.579459 + 1.00365i) q^{56} +(3.23789 + 2.00250i) q^{57} +11.0759i q^{58} -7.61266i q^{59} +(-0.239234 + 7.89737i) q^{60} +(0.467085 - 0.809015i) q^{61} +(8.43369 - 14.6076i) q^{62} +(-6.25113 + 3.12075i) q^{63} +5.82698 q^{64} +(-8.78241 - 3.45434i) q^{65} +(8.54835 + 15.8993i) q^{66} +(-1.79128 + 1.03420i) q^{67} +(-1.45659 - 2.52290i) q^{68} +(-3.83437 + 6.19987i) q^{69} +(10.2133 - 5.89662i) q^{70} +(-10.9702 + 6.33363i) q^{71} +(-1.24529 - 0.823311i) q^{72} -12.6627i q^{73} +(1.36803 - 2.36950i) q^{74} +(-1.68636 + 2.72670i) q^{75} +(-3.31747 + 1.91534i) q^{76} +(6.27319 - 10.8655i) q^{77} +(-9.67500 + 7.23622i) q^{78} +(3.46731 + 6.00556i) q^{79} +(10.0832 + 5.82155i) q^{80} +(-3.52518 - 8.28089i) q^{81} +(-1.47369 - 2.55251i) q^{82} +(-7.95495 + 4.59279i) q^{83} +(0.212865 - 7.02690i) q^{84} -4.37524i q^{85} +(-3.14592 - 1.81630i) q^{86} +(4.69577 + 8.73382i) q^{87} +2.68073 q^{88} +(8.62292 + 4.97845i) q^{89} +(6.78540 + 13.5917i) q^{90} +(7.81439 + 3.07359i) q^{91} +(-3.66748 - 6.35226i) q^{92} +(0.457249 - 15.0943i) q^{93} +(5.00184 + 8.66343i) q^{94} -5.75321 q^{95} +(11.6101 - 6.24222i) q^{96} +(2.03695 + 1.17603i) q^{97} +(2.64054 - 1.52452i) q^{98} +(13.4815 + 8.91312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.93463i			1.36799i	0.729487	+	0.683994i	$0.239759\pi$
$2$			1.93463i			1.36799i	−0.729487	+	0.683994i	$0.760241\pi$
$3$	0.820210	+	1.52553i	0.473548	+	0.880768i
$3$	0.820210	+	1.52553i	0.473548	+	0.880768i
$4$	−1.74278			−0.871392
$5$	−2.26677	−	1.30872i	−1.01373	−	0.585278i	−0.101449	−	0.994841i	$-0.532348\pi$
$5$	−2.26677	−	1.30872i	−1.01373	−	0.585278i	−0.912282	+	0.409563i	$0.865681\pi$
$6$	−2.95134	+	1.58680i	−1.20488	+	0.647809i
$7$	2.01692	+	1.16447i	0.762325	+	0.440129i	0.830130	−	0.557570i	$-0.188266\pi$
$7$	2.01692	+	1.16447i	0.762325	+	0.440129i	−0.0678048	+	0.997699i	$0.521600\pi$
$8$			0.497616i			0.175934i
$9$	−1.65451	+	2.50252i	−0.551504	+	0.834172i
$10$	2.53189	−	4.38536i	0.800654	−	1.38677i
$11$		−	5.38716i		−	1.62429i	−0.583456	−	0.812145i	$-0.698300\pi$
$11$		−	5.38716i		−	1.62429i	0.583456	−	0.812145i	$-0.301700\pi$
$12$	−1.42945	−	2.65868i	−0.412646	−	0.767494i
$13$	3.56568	−	0.534742i	0.988941	−	0.148311i
$13$	3.56568	−	0.534742i	0.988941	−	0.148311i
$14$	−2.25282	+	3.90199i	−0.602091	+	1.04285i
$15$	0.137271	−	4.53147i	0.0354433	−	1.17002i
$16$	−4.44827			−1.11207
$17$	0.835786	+	1.44762i	0.202708	+	0.351100i	0.949400	−	0.314069i	$-0.101692\pi$
$17$	0.835786	+	1.44762i	0.202708	+	0.351100i	−0.746692	+	0.665170i	$0.768359\pi$
$18$	−4.84144	−	3.20086i	−1.14114	−	0.754451i
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	−0.265495	−	0.964112i	$-0.585535\pi$
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	0.702198	+	0.711982i	$0.252202\pi$
$20$	3.95050	+	2.28082i	0.883358	+	0.510007i
$21$	−0.122141	+	4.03200i	−0.0266533	+	0.879854i
$22$	10.4221			2.22201
$23$	2.10438	+	3.64489i	0.438793	+	0.760012i	0.997597	−	0.0692882i	$-0.0220728\pi$
$23$	2.10438	+	3.64489i	0.438793	+	0.760012i	−0.558804	+	0.829300i	$0.688739\pi$
$24$	−0.759130	+	0.408149i	−0.154957	+	0.0833131i
$25$	0.925505	+	1.60302i	0.185101	+	0.320604i
$26$	1.03453	+	6.89826i	0.202887	+	1.35286i
$27$	−5.17472	−	0.471426i	−0.995876	−	0.0907261i
$28$	−3.51506	−	2.02942i	−0.664284	−	0.383525i
$29$	5.72509			1.06312			0.531561	−	0.847020i	$-0.321606\pi$
$29$	5.72509			1.06312			0.531561	+	0.847020i	$0.321606\pi$
$30$	8.76670	+	0.265569i	1.60057	+	0.0484860i
$31$	−7.55059	−	4.35934i	−1.35613	−	0.782960i	−0.367027	−	0.930210i	$-0.619624\pi$
$31$	−7.55059	−	4.35934i	−1.35613	−	0.782960i	−0.989099	+	0.147251i	$0.952958\pi$
$32$		−	7.61052i		−	1.34536i
$33$	8.21830	−	4.41860i	1.43062	−	0.769180i
$34$	−2.80061	+	1.61693i	−0.480301	+	0.277302i
$35$	−3.04794	−	5.27918i	−0.515195	−	0.892344i
$36$	2.88346	−	4.36135i	0.480576	−	0.726891i
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	0.395933	−	0.918279i	$-0.370421\pi$
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	−0.597287	+	0.802028i	$0.703755\pi$
$38$	2.12618	+	3.68265i	0.344912	+	0.597405i
$39$	3.74037	+	5.00096i	0.598938	+	0.800795i
$40$	0.651240	−	1.12798i	0.102970	−	0.178350i
$41$	−1.31938	+	0.761744i	−0.206052	+	0.118964i	−0.599475	−	0.800393i	$-0.704624\pi$
$41$	−1.31938	+	0.761744i	−0.206052	+	0.118964i	0.393423	+	0.919358i	$0.371291\pi$
$42$	−7.80041	−	0.236297i	−1.20363	−	0.0364615i
$43$	−0.938835	+	1.62611i	−0.143171	+	0.247979i	−0.928689	−	0.370859i	$-0.879063\pi$
$43$	−0.938835	+	1.62611i	−0.143171	+	0.247979i	0.785518	+	0.618839i	$0.212397\pi$
$44$			9.38866i			1.41539i
$45$	7.02550	−	3.50734i	1.04730	−	0.522843i
$46$	−7.05150	+	4.07119i	−1.03969	+	0.600264i
$47$	4.47809	−	2.58543i	0.653196	−	0.377123i	−0.136483	−	0.990642i	$-0.543580\pi$
$47$	4.47809	−	2.58543i	0.653196	−	0.377123i	0.789680	+	0.613519i	$0.210247\pi$
$48$	−3.64852	−	6.78599i	−0.526618	−	0.979473i
$49$	−0.788015	−	1.36488i	−0.112574	−	0.194983i
$50$	−3.10125	+	1.79051i	−0.438583	+	0.253216i
$51$	−1.52288	+	2.46238i	−0.213246	+	0.344802i
$52$	−6.21421	+	0.931939i	−0.861756	+	0.129237i
$53$	−9.81151			−1.34771			−0.673857	−	0.738862i	$-0.735364\pi$
$53$	−9.81151			−1.34771			−0.673857	+	0.738862i	$0.735364\pi$
$54$	0.912035	−	10.0112i	0.124112	−	1.36235i
$55$	−7.05029	+	12.2115i	−0.950661	+	1.64659i
$56$	−0.579459	+	1.00365i	−0.0774335	+	0.134119i
$57$	3.23789	+	2.00250i	0.428869	+	0.265238i
$58$			11.0759i			1.45434i
$59$		−	7.61266i		−	0.991084i	−0.868584	−	0.495542i	$-0.834969\pi$
$59$		−	7.61266i		−	0.991084i	0.868584	−	0.495542i	$-0.165031\pi$
$60$	−0.239234	+	7.89737i	−0.0308850	+	1.01955i
$61$	0.467085	−	0.809015i	0.0598041	−	0.103584i	−0.834573	−	0.550897i	$-0.814286\pi$
$61$	0.467085	−	0.809015i	0.0598041	−	0.103584i	0.894377	+	0.447313i	$0.147619\pi$
$62$	8.43369	−	14.6076i	1.07108	−	1.85516i
$63$	−6.25113	+	3.12075i	−0.787568	+	0.393178i
$64$	5.82698			0.728372
$65$	−8.78241	−	3.45434i	−1.08932	−	0.428458i
$66$	8.54835	+	15.8993i	1.05223	+	1.95707i
$67$	−1.79128	+	1.03420i	−0.218840	+	0.126347i	−0.605413	−	0.795912i	$-0.706992\pi$
$67$	−1.79128	+	1.03420i	−0.218840	+	0.126347i	0.386573	+	0.922259i	$0.373659\pi$
$68$	−1.45659	−	2.52290i	−0.176638	−	0.305946i
$69$	−3.83437	+	6.19987i	−0.461604	+	0.746377i
$70$	10.2133	−	5.89662i	1.22072	−	0.704781i
$71$	−10.9702	+	6.33363i	−1.30192	+	0.751664i	−0.980733	−	0.195352i	$-0.937415\pi$
$71$	−10.9702	+	6.33363i	−1.30192	+	0.751664i	−0.321187	+	0.947016i	$0.604082\pi$
$72$	−1.24529	−	0.823311i	−0.146759	−	0.0970281i
$73$		−	12.6627i		−	1.48206i	−0.671473	−	0.741029i	$-0.734338\pi$
$73$		−	12.6627i		−	1.48206i	0.671473	−	0.741029i	$-0.265662\pi$
$74$	1.36803	−	2.36950i	0.159031	−	0.275449i
$75$	−1.68636	+	2.72670i	−0.194724	+	0.314853i
$76$	−3.31747	+	1.91534i	−0.380540	+	0.219705i
$77$	6.27319	−	10.8655i	0.714896	−	1.23824i
$78$	−9.67500	+	7.23622i	−1.09548	+	0.819341i
$79$	3.46731	+	6.00556i	0.390103	+	0.675678i	0.992463	−	0.122547i	$-0.0391061\pi$
$79$	3.46731	+	6.00556i	0.390103	+	0.675678i	−0.602360	+	0.798225i	$0.705773\pi$
$80$	10.0832	+	5.82155i	1.12734	+	0.650869i
$81$	−3.52518	−	8.28089i	−0.391687	−	0.920099i
$82$	−1.47369	−	2.55251i	−0.162742	−	0.281877i
$83$	−7.95495	+	4.59279i	−0.873169	+	0.504124i	−0.868400	−	0.495864i	$-0.834851\pi$
$83$	−7.95495	+	4.59279i	−0.873169	+	0.504124i	−0.00476882	+	0.999989i	$0.501518\pi$
$84$	0.212865	−	7.02690i	0.0232255	−	0.766698i
$85$		−	4.37524i		−	0.474562i
$86$	−3.14592	−	1.81630i	−0.339233	−	0.195856i
$87$	4.69577	+	8.73382i	0.503440	+	0.936363i
$88$	2.68073			0.285767
$89$	8.62292	+	4.97845i	0.914028	+	0.527714i	0.881725	−	0.471764i	$-0.156383\pi$
$89$	8.62292	+	4.97845i	0.914028	+	0.527714i	0.0323029	+	0.999478i	$0.489716\pi$
$90$	6.78540	+	13.5917i	0.715244	+	1.43269i
$91$	7.81439	+	3.07359i	0.819170	+	0.322200i
$92$	−3.66748	−	6.35226i	−0.382361	−	0.662268i
$93$	0.457249	−	15.0943i	0.0474145	−	1.56520i
$94$	5.00184	+	8.66343i	0.515900	+	0.893565i
$95$	−5.75321			−0.590266
$96$	11.6101	−	6.24222i	1.18495	−	0.637094i
$97$	2.03695	+	1.17603i	0.206821	+	0.119408i	0.599833	−	0.800125i	$-0.295234\pi$
$97$	2.03695	+	1.17603i	0.206821	+	0.119408i	−0.393012	+	0.919533i	$0.628567\pi$
$98$	2.64054	−	1.52452i	0.266735	−	0.153999i
$99$	13.4815	+	8.91312i	1.35494	+	0.895802i
$100$	−1.61296	−	2.79372i	−0.161296	−	0.279372i
$101$	12.2572			1.21964			0.609820	−	0.792540i	$-0.291242\pi$
$101$	12.2572			1.21964			0.609820	+	0.792540i	$0.291242\pi$
$102$	−4.76378	−	2.94621i	−0.471685	−	0.291718i
$103$	−5.10150	+	8.83607i	−0.502666	+	0.870643i	0.497329	+	0.867562i	$0.334314\pi$
$103$	−5.10150	+	8.83607i	−0.502666	+	0.870643i	−0.999995	+	0.00308139i	$0.999019\pi$
$104$	0.266096	+	1.77434i	0.0260928	+	0.173988i
$105$	5.55363	−	8.97977i	0.541978	−	0.876336i
$106$		−	18.9816i		−	1.84366i
$107$	2.96835	−	5.14133i	0.286961	−	0.497032i	−0.686122	−	0.727487i	$-0.740688\pi$
$107$	2.96835	−	5.14133i	0.286961	−	0.497032i	0.973083	+	0.230455i	$0.0740215\pi$
$108$	9.01843	+	0.821595i	0.867799	+	0.0790580i
$109$			12.1858i			1.16719i	0.812046	+	0.583594i	$0.198354\pi$
$109$			12.1858i			1.16719i	−0.812046	+	0.583594i	$0.801646\pi$
$110$	−23.6246	−	13.6397i	−2.25252	−	1.30049i
$111$	0.0741707	−	2.44845i	0.00703997	−	0.232396i
$112$	−8.97182	−	5.17988i	−0.847757	−	0.489453i
$113$	−0.874510			−0.0822670			−0.0411335	−	0.999154i	$-0.513097\pi$
$113$	−0.874510			−0.0822670			−0.0411335	+	0.999154i	$0.513097\pi$
$114$	−3.87410	+	6.26411i	−0.362843	+	0.586687i
$115$		−	11.0162i		−	1.02726i
$116$	−9.97759			−0.926396
$117$	−4.56126	+	9.80790i	−0.421688	+	0.906741i
$118$	14.7277			1.35579
$119$			3.89299i			0.356870i
$120$	2.25493	+	0.0683084i	0.205846	+	0.00623567i
$121$	−18.0215			−1.63832
$122$	1.56514	+	0.903635i	0.141701	+	0.0818113i
$123$	−2.24423	−	1.38797i	−0.202356	−	0.125149i
$124$	13.1591	+	7.59738i	1.18172	+	0.682265i
$125$			8.24230i			0.737214i
$126$	−6.03749	−	12.0936i	−0.537863	−	1.07738i
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	0.195808	+	0.980642i	$0.437267\pi$
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	−0.947165	+	0.320746i	$0.896066\pi$
$128$		−	3.94800i		−	0.348957i
$129$	−3.25073	−	0.0984740i	−0.286211	−	0.00867016i
$130$	6.68286	−	16.9907i	0.586126	−	1.49018i
$131$	6.88997	−	11.9338i	0.601980	−	1.04266i	−0.390541	−	0.920585i	$-0.627712\pi$
$131$	6.88997	−	11.9338i	0.601980	−	1.04266i	0.992521	−	0.122074i	$-0.0389546\pi$
$132$	−14.3227	+	7.70067i	−1.24663	+	0.670257i
$133$	5.11907			0.443880
$134$	−2.00078	−	3.46546i	−0.172841	−	0.299370i
$135$	11.1130	+	7.84089i	0.956451	+	0.674836i
$136$	−0.720360	+	0.415900i	−0.0617704	+	0.0356631i
$137$	5.88782	+	3.39934i	0.503031	+	0.290425i	0.729964	−	0.683485i	$-0.239537\pi$
$137$	5.88782	+	3.39934i	0.503031	+	0.290425i	−0.226933	+	0.973910i	$0.572870\pi$
$138$	−11.9944	−	7.41808i	−1.02104	−	0.631469i
$139$	9.37249			0.794965			0.397482	−	0.917610i	$-0.369884\pi$
$139$	9.37249			0.794965			0.397482	+	0.917610i	$0.369884\pi$
$140$	5.31190	+	9.20048i	0.448937	+	0.777582i
$141$	7.61713	+	4.71089i	0.641478	+	0.396728i
$142$	−12.2532	−	21.2232i	−1.02827	−	1.78101i
$143$	−2.88074	−	19.2089i	−0.240899	−	1.60633i
$144$	7.35972	−	11.1319i	0.613310	−	0.927656i
$145$	−12.9775	−	7.49254i	−1.07772	−	0.622222i
$146$	24.4976			2.02744
$147$	1.43584	−	2.32163i	0.118426	−	0.191485i
$148$	2.13454	+	1.23238i	0.175458	+	0.101301i
$149$			15.1119i			1.23802i	0.785384	+	0.619009i	$0.212466\pi$
$149$			15.1119i			1.23802i	−0.785384	+	0.619009i	$0.787534\pi$
$150$	−5.27516	−	3.26247i	−0.430715	−	0.266380i
$151$	−16.8896	+	9.75122i	−1.37446	+	0.793543i	−0.991486	−	0.130217i	$-0.958433\pi$
$151$	−16.8896	+	9.75122i	−1.37446	+	0.793543i	−0.382972	+	0.923760i	$0.625099\pi$
$152$	0.546886	+	0.947234i	0.0443583	+	0.0768308i
$153$	−5.00552	−	0.303542i	−0.404672	−	0.0245399i
$154$	21.0207	+	12.1363i	1.69389	+	0.977970i
$155$	11.4103	+	19.7632i	0.916498	+	1.58742i
$156$	−6.51866	−	8.71560i	−0.521910	−	0.697807i
$157$	−1.95414	+	3.38466i	−0.155957	+	0.270125i	−0.933407	−	0.358819i	$-0.883179\pi$
$157$	−1.95414	+	3.38466i	−0.155957	+	0.270125i	0.777450	+	0.628945i	$0.216513\pi$
$158$	−11.6185	+	6.70796i	−0.924320	+	0.533656i
$159$	−8.04750	−	14.9678i	−0.638208	−	1.18702i
$160$	−9.96005	+	17.2513i	−0.787411	+	1.36384i
$161$			9.80194i			0.772501i
$162$	16.0204	−	6.81991i	1.25868	−	0.535823i
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	−0.723541	−	0.690281i	$-0.757487\pi$
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	0.236030	+	0.971746i	$0.424154\pi$
$164$	2.29939	−	1.32756i	0.179552	−	0.103665i
$165$	−24.4117	−	0.739503i	−1.90045	−	0.0575702i
$166$	−8.88534	−	15.3899i	−0.689636	−	1.19448i
$167$	−5.19037	+	2.99666i	−0.401643	+	0.231889i	−0.687193	−	0.726475i	$-0.741157\pi$
$167$	−5.19037	+	2.99666i	−0.401643	+	0.231889i	0.285550	+	0.958364i	$0.407824\pi$
$168$	−2.00638	−	0.0607793i	−0.154796	−	0.00468922i
$169$	12.4281	−	3.81343i	0.956008	−	0.293341i
$170$	8.46447			0.649195
$171$	−0.399141	+	6.58198i	−0.0305231	+	0.503337i
$172$	1.63619	−	2.83396i	0.124758	−	0.216087i
$173$	1.09116	−	1.88994i	0.0829591	−	0.143689i	−0.821561	−	0.570121i	$-0.806896\pi$
$173$	1.09116	−	1.88994i	0.0829591	−	0.143689i	0.904520	+	0.426432i	$0.140230\pi$
$174$	−16.8967	+	9.08457i	−1.28093	+	0.688699i
$175$			4.31089i			0.325873i
$176$			23.9635i			1.80632i
$177$	11.6134	−	6.24398i	0.872915	−	0.469326i
$178$	−9.63144	+	16.6821i	−0.721907	+	1.25038i
$179$	−1.46465	+	2.53684i	−0.109473	+	0.189612i	−0.915557	−	0.402189i	$-0.868250\pi$
$179$	−1.46465	+	2.53684i	−0.109473	+	0.189612i	0.806084	+	0.591801i	$0.201583\pi$
$180$	−12.2439	+	6.11254i	−0.912609	+	0.455602i
$181$	23.2244			1.72625			0.863127	−	0.504986i	$-0.168502\pi$
$181$	23.2244			1.72625			0.863127	+	0.504986i	$0.168502\pi$
$182$	−5.94626	+	15.1179i	−0.440766	+	1.12062i
$183$	1.61729	+	0.0489924i	0.119553	+	0.00362162i
$184$	−1.81375	+	1.04717i	−0.133712	+	0.0771985i
$185$	1.85087	+	3.20581i	0.136079	+	0.235696i
$186$	29.2018	+	0.884607i	2.14118	+	0.0648625i
$187$	7.79858	−	4.50251i	0.570289	−	0.329256i
$188$	−7.80434	+	4.50584i	−0.569190	+	0.328622i
$189$	−9.88805	−	6.97664i	−0.719250	−	0.507476i
$190$		−	11.1303i		−	0.807478i
$191$	−4.81042	+	8.33189i	−0.348070	+	0.602874i	−0.985906	−	0.167297i	$-0.946496\pi$
$191$	−4.81042	+	8.33189i	−0.348070	+	0.602874i	0.637837	+	0.770171i	$0.279829\pi$
$192$	4.77934	+	8.88925i	0.344919	+	0.641527i
$193$	17.4030	−	10.0476i	1.25270	−	0.723245i	0.281052	−	0.959692i	$-0.409317\pi$
$193$	17.4030	−	10.0476i	1.25270	−	0.723245i	0.971644	+	0.236448i	$0.0759832\pi$
$194$	−2.27519	+	3.94074i	−0.163349	+	0.282929i
$195$	−1.93370	−	16.2311i	−0.138475	−	1.16234i
$196$	1.37334	+	2.37870i	0.0980958	+	0.169907i
$197$	10.3727	+	5.98869i	0.739025	+	0.426676i	0.821715	−	0.569899i	$-0.193018\pi$
$197$	10.3727	+	5.98869i	0.739025	+	0.426676i	−0.0826895	+	0.996575i	$0.526351\pi$
$198$	−17.2436	+	26.0816i	−1.22545	+	1.85354i
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	−0.988054	−	0.154108i	$-0.950750\pi$
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	0.360566	−	0.932734i	$-0.382584\pi$
$200$	−0.797688	+	0.460546i	−0.0564051	+	0.0325655i
$201$	−3.04693	−	1.88440i	−0.214914	−	0.132915i
$202$			23.7132i			1.66845i
$203$	11.5471	+	6.66670i	0.810444	+	0.467910i
$204$	2.65405	−	4.29139i	0.185821	−	0.300457i
$205$	3.98764			0.278509
$206$	−17.0945	−	9.86951i	−1.19103	−	0.687642i
$207$	−12.6031	−	0.764272i	−0.875977	−	0.0531205i
$208$	−15.8611	+	2.37867i	−1.09977	+	0.164931i
$209$	−5.92055	−	10.2547i	−0.409533	−	0.709333i
$210$	17.3725	+	10.7442i	1.19882	+	0.741420i
$211$	−11.0954	−	19.2178i	−0.763840	−	1.32301i	−0.940857	−	0.338803i	$-0.889978\pi$
$211$	−11.0954	−	19.2178i	−0.763840	−	1.32301i	0.177017	−	0.984208i	$-0.443355\pi$
$212$	17.0993			1.17439
$213$	−18.6600	−	11.5405i	−1.27856	−	0.790740i
$214$	9.94657	+	5.74265i	0.679933	+	0.392560i
$215$	4.25625	−	2.45735i	0.290274	−	0.167590i
$216$	0.234589	−	2.57502i	0.0159618	−	0.175208i
$217$	−10.1526	−	17.5849i	−0.689206	−	1.19374i
$218$	−23.5750			−1.59670
$219$	19.3174	−	10.3861i	1.30535	−	0.701826i
$220$	12.2871	−	21.2820i	0.828399	−	1.43483i
$221$	3.75425	+	4.71483i	0.252538	+	0.317154i
$222$	4.73684	+	0.143493i	0.317916	+	0.00963059i
$223$			4.33152i			0.290060i	0.989427	+	0.145030i	$0.0463279\pi$
$223$			4.33152i			0.290060i	−0.989427	+	0.145030i	$0.953672\pi$
$224$	8.86223	−	15.3498i	0.592132	−	1.02560i
$225$	−5.54285	−	0.336126i	−0.369523	−	0.0224084i
$226$		−	1.69185i		−	0.112540i
$227$	−2.56338	−	1.47997i	−0.170137	−	0.0982289i	0.412513	−	0.910952i	$-0.364651\pi$
$227$	−2.56338	−	1.47997i	−0.170137	−	0.0982289i	−0.582651	+	0.812723i	$0.697984\pi$
$228$	−5.64294	−	3.48993i	−0.373713	−	0.231126i
$229$	9.82313	+	5.67139i	0.649131	+	0.374776i	0.788123	−	0.615518i	$-0.211053\pi$
$229$	9.82313	+	5.67139i	0.649131	+	0.374776i	−0.138992	+	0.990293i	$0.544386\pi$
$230$	21.3122			1.40528
$231$	21.7210	+	0.657993i	1.42914	+	0.0432927i
$232$			2.84889i			0.187039i
$233$	2.31530			0.151680			0.0758401	−	0.997120i	$-0.475836\pi$
$233$	2.31530			0.151680			0.0758401	+	0.997120i	$0.475836\pi$
$234$	−18.9746	−	8.82433i	−1.24041	−	0.576865i
$235$	−13.5344			−0.882887
$236$			13.2672i			0.863623i
$237$	−6.31777	+	10.2153i	−0.410383	+	0.663556i
$238$	−7.53149			−0.488194
$239$	−17.6746	−	10.2044i	−1.14327	−	0.660069i	−0.196034	−	0.980597i	$-0.562806\pi$
$239$	−17.6746	−	10.2044i	−1.14327	−	0.660069i	−0.947239	+	0.320528i	$0.896140\pi$
$240$	−0.610620	+	20.1572i	−0.0394154	+	1.30114i
$241$	−7.56925	−	4.37011i	−0.487578	−	0.281503i	0.235991	−	0.971755i	$-0.424166\pi$
$241$	−7.56925	−	4.37011i	−0.487578	−	0.281503i	−0.723569	+	0.690252i	$0.757500\pi$
$242$		−	34.8649i		−	2.24120i
$243$	9.74139	−	12.1699i	0.624911	−	0.780696i
$244$	−0.814028	+	1.40994i	−0.0521128	+	0.0902621i
$245$			4.12517i			0.263547i
$246$	2.68520	−	4.34176i	0.171202	−	0.276820i
$247$	6.19974	−	4.93663i	0.394480	−	0.314110i
$248$	2.16927	−	3.75729i	0.137749	−	0.238588i
$249$	−13.5312	−	8.36849i	−0.857504	−	0.530332i
$250$	−15.9458			−1.00850
$251$	−9.27060	−	16.0571i	−0.585155	−	1.01352i	−0.994856	−	0.101298i	$-0.967700\pi$
$251$	−9.27060	−	16.0571i	−0.585155	−	1.01352i	0.409701	−	0.912220i	$-0.365633\pi$
$252$	10.8944	−	5.43880i	0.686281	−	0.342612i
$253$	19.6356	−	11.3366i	1.23448	−	0.712727i
$254$	−28.3731	−	16.3812i	−1.78028	−	1.02785i
$255$	6.67459	−	3.58862i	0.417979	−	0.224728i
$256$	19.2919			1.20574
$257$	−7.18835	−	12.4506i	−0.448397	−	0.776647i	0.549885	−	0.835241i	$-0.314672\pi$
$257$	−7.18835	−	12.4506i	−0.448397	−	0.776647i	−0.998282	+	0.0585939i	$0.981338\pi$
$258$	0.190511	−	6.28895i	0.0118607	−	0.391533i
$259$	−1.64687	−	2.85245i	−0.102331	−	0.177243i
$260$	15.3058	+	6.02017i	0.949228	+	0.373355i
$261$	−9.47222	+	14.3271i	−0.586316	+	0.886827i
$262$	23.0874	+	13.3295i	1.42635	+	0.823501i
$263$	5.60712			0.345750			0.172875	−	0.984944i	$-0.444694\pi$
$263$	5.60712			0.345750			0.172875	+	0.984944i	$0.444694\pi$
$264$	2.19877	+	4.08955i	0.135325	+	0.251695i
$265$	22.2405	+	12.8405i	1.36622	+	0.788788i
$266$			9.90350i			0.607222i
$267$	−0.522187	+	17.2379i	−0.0319574	+	1.05494i
$268$	3.12181	−	1.80238i	0.190695	−	0.110098i
$269$	−1.16337	−	2.01502i	−0.0709319	−	0.122858i	0.828378	−	0.560169i	$-0.189264\pi$
$269$	−1.16337	−	2.01502i	−0.0709319	−	0.122858i	−0.899310	+	0.437312i	$0.855931\pi$
$270$	−15.1692	+	21.4994i	−0.923168	+	1.30841i
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	0.547766	−	0.836631i	$-0.315478\pi$
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	−0.450661	+	0.892695i	$0.648812\pi$
$272$	−3.71780	−	6.43942i	−0.225425	−	0.390447i
$273$	1.72056	+	14.4421i	0.104133	+	0.874076i
$274$	−6.57645	+	11.3907i	−0.397298	+	0.688140i
$275$	8.63573	−	4.98584i	0.520754	−	0.300658i
$276$	6.68249	−	10.8050i	0.402238	−	0.650387i
$277$	0.267853	−	0.463934i	0.0160937	−	0.0278751i	−0.857866	−	0.513873i	$-0.828210\pi$
$277$	0.267853	−	0.463934i	0.0160937	−	0.0278751i	0.873960	+	0.485998i	$0.161544\pi$
$278$			18.1323i			1.08750i
$279$	23.4019	−	11.6829i	1.40103	−	0.699437i
$280$	2.62700	−	1.51670i	0.156993	−	0.0906402i
$281$	−18.0707	+	10.4331i	−1.07801	+	0.622387i	−0.930358	−	0.366653i	$-0.880504\pi$
$281$	−18.0707	+	10.4331i	−1.07801	+	0.622387i	−0.147648	+	0.989040i	$0.547170\pi$
$282$	−9.11381	+	14.7363i	−0.542720	+	0.877534i
$283$	4.36529	+	7.56090i	0.259489	+	0.449449i	0.966105	−	0.258149i	$-0.0831124\pi$
$283$	4.36529	+	7.56090i	0.259489	+	0.449449i	−0.706616	+	0.707597i	$0.749779\pi$
$284$	19.1187	−	11.0382i	1.13448	−	0.654994i
$285$	−4.71884	−	8.77671i	−0.279520	−	0.519888i
$286$	37.1620	−	5.57316i	2.19744	−	0.329548i
$287$	−3.54811			−0.209439
$288$	19.0454	+	12.5917i	1.12226	+	0.741972i
$289$	7.10292	−	12.3026i	0.417819	−	0.723684i
$290$	14.4953	−	25.1066i	0.851192	−	1.47431i
$291$	−0.123354	+	4.07203i	−0.00723112	+	0.238707i
$292$			22.0684i			1.29145i
$293$		−	3.04751i		−	0.178038i	−0.996030	−	0.0890188i	$-0.971627\pi$
$293$		−	3.04751i		−	0.178038i	0.996030	−	0.0890188i	$-0.0283731\pi$
$294$	4.49150	+	2.77781i	0.261949	+	0.162005i
$295$	−9.96286	+	17.2562i	−0.580060	+	1.00469i
$296$	0.351879	−	0.609473i	0.0204526	−	0.0354249i
$297$	−2.53965	+	27.8771i	−0.147365	+	1.61759i
$298$	−29.2360			−1.69359
$299$	9.45260	+	11.8712i	0.546658	+	0.686529i
$300$	2.93896	−	4.75206i	0.169681	−	0.274360i
$301$	−3.78711	+	2.18649i	−0.218286	+	0.126027i
$302$	−18.8650	−	32.6751i	−1.08556	−	1.88024i
$303$	10.0535	+	18.6988i	0.577559	+	1.07422i
$304$	−8.46748	+	4.88870i	−0.485644	+	0.280386i
$305$	−2.11755	+	1.22257i	−0.121251	+	0.0700040i
$306$	0.587241	−	9.68382i	0.0335704	−	0.553587i
$307$			22.0214i			1.25683i	0.777880	+	0.628413i	$0.216295\pi$
$307$			22.0214i			1.25683i	−0.777880	+	0.628413i	$0.783705\pi$
$308$	−10.9328	+	18.9362i	−0.622955	+	1.07899i
$309$	−17.6640	−	0.535095i	−1.00487	−	0.0304405i
$310$	−38.2345	+	22.0747i	−2.17157	+	1.25376i
$311$	3.39883	−	5.88694i	0.192730	−	0.333818i	−0.753424	−	0.657535i	$-0.771599\pi$
$311$	3.39883	−	5.88694i	0.192730	−	0.333818i	0.946154	+	0.323717i	$0.104933\pi$
$312$	−2.48856	+	1.86127i	−0.140887	+	0.105373i
$313$	3.05617	+	5.29344i	0.172745	+	0.299203i	0.939379	−	0.342882i	$-0.111403\pi$
$313$	3.05617	+	5.29344i	0.172745	+	0.299203i	−0.766634	+	0.642085i	$0.778070\pi$
$314$	−6.54806	−	3.78052i	−0.369528	−	0.213347i
$315$	18.2541	+	1.10696i	1.02850	+	0.0623699i
$316$	−6.04278	−	10.4664i	−0.339933	−	0.588781i
$317$	15.0342	−	8.67999i	0.844404	−	0.487517i	−0.0143546	−	0.999897i	$-0.504569\pi$
$317$	15.0342	−	8.67999i	0.844404	−	0.487517i	0.858759	+	0.512380i	$0.171236\pi$
$318$	28.9571	−	15.5689i	1.62383	−	0.873061i
$319$		−	30.8420i		−	1.72682i
$320$	−13.2084	−	7.62589i	−0.738374	−	0.426300i
$321$	10.2780	+	0.311349i	0.573660	+	0.0173778i
$322$	−18.9631			−1.05677
$323$	3.18191	+	1.83708i	0.177046	+	0.102218i
$324$	6.14363	+	14.4318i	0.341313	+	0.801767i
$325$	4.15725	+	5.22095i	0.230603	+	0.289606i
$326$	−6.95209	−	12.0414i	−0.385041	−	0.666910i
$327$	−18.5898	+	9.99490i	−1.02802	+	0.552719i
$328$	−0.379056	−	0.656544i	−0.0209298	−	0.0362516i
$329$	12.0426			0.663931
$330$	1.43066	−	47.2276i	0.0787554	−	2.59979i
$331$	−16.5137	−	9.53421i	−0.907677	−	0.524048i	−0.0279940	−	0.999608i	$-0.508912\pi$
$331$	−16.5137	−	9.53421i	−0.907677	−	0.524048i	−0.879683	+	0.475561i	$0.842245\pi$
$332$	13.8638	−	8.00425i	0.760873	−	0.439290i
$333$	3.79603	−	1.89509i	0.208021	−	0.103850i
$334$	−5.79743	−	10.0414i	−0.317221	−	0.549443i
$335$	5.41390			0.295793
$336$	0.543316	−	17.9354i	0.0296403	−	0.978457i
$337$	−12.0678	+	20.9020i	−0.657372	+	1.13860i	0.323921	+	0.946084i	$0.394999\pi$
$337$	−12.0678	+	20.9020i	−0.657372	+	1.13860i	−0.981293	+	0.192518i	$0.938335\pi$
$338$	7.37757	+	24.0438i	0.401287	+	1.30781i
$339$	−0.717281	−	1.33409i	−0.0389574	−	0.0724581i
$340$			7.62511i			0.413530i
$341$	−23.4844	+	40.6762i	−1.27175	+	2.20274i
$342$	−12.7337	−	0.772190i	−0.688559	−	0.0417552i
$343$		−	19.9731i		−	1.07844i
$344$	−0.809178	−	0.467179i	−0.0436279	−	0.0251886i
$345$	16.8056	−	9.03557i	0.904781	−	0.486459i
$346$	3.65633	+	2.11098i	0.196565	+	0.113487i
$347$	1.02919			0.0552500			0.0276250	−	0.999618i	$-0.491206\pi$
$347$	1.02919			0.0552500			0.0276250	+	0.999618i	$0.491206\pi$
$348$	−8.18372	−	15.2212i	−0.438693	−	0.815940i
$349$		−	28.3410i		−	1.51706i	−0.651637	−	0.758531i	$-0.725918\pi$
$349$		−	28.3410i		−	1.51706i	0.651637	−	0.758531i	$-0.274082\pi$
$350$	−8.33997			−0.445790
$351$	−18.7035	+	1.08618i	−0.998318	+	0.0579762i
$352$	−40.9991			−2.18526
$353$		−	7.71417i		−	0.410584i	−0.978701	−	0.205292i	$-0.934186\pi$
$353$		−	7.71417i		−	0.410584i	0.978701	−	0.205292i	$-0.0658144\pi$
$354$	12.0798	+	22.4676i	0.642033	+	1.19414i
$355$	33.1559			1.75973
$356$	−15.0279	−	8.67636i	−0.796477	−	0.459846i
$357$	−5.93890	+	3.19307i	−0.314320	+	0.168995i
$358$	−4.90784	−	2.83354i	−0.259388	−	0.149757i
$359$			6.01669i			0.317549i	0.987315	+	0.158774i	$0.0507543\pi$
$359$			6.01669i			0.317549i	−0.987315	+	0.158774i	$0.949246\pi$
$360$	1.74531	+	3.49600i	0.0919858	+	0.184255i
$361$	−7.08434	+	12.2704i	−0.372860	+	0.645813i
$362$			44.9305i			2.36150i
$363$	−14.7814	−	27.4924i	−0.775822	−	1.44298i
$364$	−13.6188	−	5.35661i	−0.713819	−	0.280763i
$365$	−16.5720	+	28.7035i	−0.867416	+	1.50241i
$366$	−0.0947820	+	3.12885i	−0.00495433	+	0.163548i
$367$	24.3910			1.27320			0.636600	−	0.771194i	$-0.280340\pi$
$367$	24.3910			1.27320			0.636600	+	0.771194i	$0.280340\pi$
$368$	−9.36084	−	16.2134i	−0.487967	−	0.845184i
$369$	0.276651	−	4.56208i	0.0144019	−	0.237492i
$370$	−6.20204	+	3.58075i	−0.322429	+	0.186154i
$371$	−19.7891	−	11.4252i	−1.02740	−	0.593168i
$372$	−0.796887	+	26.3060i	−0.0413167	+	1.36390i
$373$	5.37633			0.278376			0.139188	−	0.990266i	$-0.455551\pi$
$373$	5.37633			0.278376			0.139188	+	0.990266i	$0.455551\pi$
$374$	8.71068	+	15.0873i	0.450419	+	0.780148i
$375$	−12.5739	+	6.76042i	−0.649315	+	0.349107i
$376$	1.28655	+	2.22837i	0.0663487	+	0.114919i
$377$	20.4138	−	3.06144i	1.05136	−	0.157672i
$378$	13.4972	−	19.1297i	0.694222	−	0.983926i
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.912296	−	0.409532i	$-0.134308\pi$
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.101482	+	0.994837i	$0.467641\pi$
$380$	10.0266			0.514354
$381$	−29.3184	−	0.888139i	−1.50202	−	0.0455007i
$382$	−16.1191	−	9.30637i	−0.824725	−	0.476155i
$383$		−	24.8883i		−	1.27173i	−0.771799	−	0.635866i	$-0.780643\pi$
$383$		−	24.8883i		−	1.27173i	0.771799	−	0.635866i	$-0.219357\pi$
$384$	6.02282	−	3.23819i	0.307351	−	0.165248i
$385$	−28.4398	+	16.4197i	−1.44943	+	0.836826i
$386$	19.4384	+	33.6684i	0.989390	+	1.71367i
$387$	−2.51605	−	5.03987i	−0.127898	−	0.256191i
$388$	−3.54996	−	2.04957i	−0.180222	−	0.104051i
$389$	−7.53659	−	13.0537i	−0.382120	−	0.661851i	0.609245	−	0.792982i	$-0.291473\pi$
$389$	−7.53659	−	13.0537i	−0.382120	−	0.661851i	−0.991365	+	0.131131i	$0.958139\pi$
$390$	31.4012	−	3.74099i	1.59006	−	0.189432i
$391$	−3.51762	+	6.09269i	−0.177894	+	0.308121i
$392$	0.679187	−	0.392129i	0.0343041	−	0.0198055i
$393$	23.8566	+	0.722687i	1.20341	+	0.0364547i
$394$	−11.5859	+	20.0673i	−0.583688	+	1.01098i
$395$		−	18.1510i		−	0.913275i
$396$	−23.4953	−	15.5336i	−1.18068	−	0.780595i
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	−0.557461	−	0.830203i	$-0.688224\pi$
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	0.440246	+	0.897877i	$0.354891\pi$
$398$	29.6613	−	17.1250i	1.48679	−	0.858397i
$399$	4.19871	+	7.80932i	0.210199	+	0.390955i
$400$	−4.11690	−	7.13067i	−0.205845	−	0.356534i
$401$	1.05376	−	0.608391i	0.0526225	−	0.0303816i	−0.473458	−	0.880816i	$-0.656994\pi$
$401$	1.05376	−	0.608391i	0.0526225	−	0.0303816i	0.526080	+	0.850435i	$0.323661\pi$
$402$	3.64561	−	5.89467i	0.181827	−	0.293999i
$403$	−29.2541	−	11.5064i	−1.45725	−	0.573173i
$404$	−21.3617			−1.06279
$405$	−2.84659	+	23.3844i	−0.141448	+	1.16198i
$406$	−12.8976	+	22.3393i	−0.640096	+	1.10868i
$407$	−3.80942	+	6.59812i	−0.188826	+	0.327056i
$408$	−1.22532	−	0.757809i	−0.0606622	−	0.0375171i
$409$			34.4077i			1.70135i	0.525693	+	0.850675i	$0.323806\pi$
$409$			34.4077i			1.70135i	−0.525693	+	0.850675i	$0.676194\pi$
$410$			7.71460i			0.380997i
$411$	−0.356555	+	11.7703i	−0.0175876	+	0.580584i
$412$	8.89082	−	15.3994i	0.438019	−	0.758672i
$413$	8.86472	−	15.3542i	0.436205	−	0.755528i
$414$	1.47858	−	24.3823i	0.0726683	−	1.19833i
$415$	24.0427			1.18021
$416$	−4.06966	−	27.1366i	−0.199531	−	1.33048i
$417$	7.68741	+	14.2981i	0.376454	+	0.700179i
$418$	19.8390	−	11.4541i	0.970359	−	0.560237i
$419$	10.8961	+	18.8726i	0.532310	+	0.921988i	0.999288	+	0.0377193i	$0.0120093\pi$
$419$	10.8961	+	18.8726i	0.532310	+	0.921988i	−0.466978	+	0.884269i	$0.654657\pi$
$420$	−9.67877	+	15.6498i	−0.472276	+	0.763632i
$421$	22.4288	−	12.9493i	1.09311	−	0.631109i	0.158710	−	0.987325i	$-0.449267\pi$
$421$	22.4288	−	12.9493i	1.09311	−	0.631109i	0.934404	+	0.356216i	$0.115933\pi$
$422$	37.1794	−	21.4655i	1.80986	−	1.04492i
$423$	−0.938979	+	15.4841i	−0.0456547	+	0.752863i
$424$		−	4.88236i		−	0.237108i
$425$	−1.54705	+	2.67956i	−0.0750428	+	0.129978i
$426$	22.3265	−	36.1002i	1.08172	−	1.74906i
$427$	1.88415	−	1.08781i	0.0911803	−	0.0526430i
$428$	−5.17320	+	8.96024i	−0.250056	+	0.433110i
$429$	26.9410	−	20.1500i	1.30072	−	0.972850i
$430$	4.75405	+	8.23426i	0.229261	+	0.397091i
$431$	24.4387	+	14.1097i	1.17717	+	0.679639i	0.955358	−	0.295450i	$-0.0954697\pi$
$431$	24.4387	+	14.1097i	1.17717	+	0.679639i	0.221812	+	0.975090i	$0.428803\pi$
$432$	23.0186	+	2.09703i	1.10748	+	0.100894i
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	0.984099	+	0.177622i	$0.0568403\pi$
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	−0.338225	+	0.941065i	$0.609826\pi$
$434$	34.0202	−	19.6416i	1.63302	−	0.942826i
$435$	0.785890	−	25.9430i	0.0376806	−	1.24387i
$436$		−	21.2372i		−	1.01708i
$437$	8.01155	+	4.62547i	0.383245	+	0.221266i
$438$	20.0932	+	37.3720i	0.960090	+	1.78570i
$439$	1.69589			0.0809402			0.0404701	−	0.999181i	$-0.487114\pi$
$439$	1.69589			0.0809402			0.0404701	+	0.999181i	$0.487114\pi$
$440$	−6.07662	−	3.50834i	−0.289691	−	0.167253i
$441$	4.71942	+	0.286193i	0.224734	+	0.0136282i
$442$	−9.12144	+	7.26307i	−0.433863	+	0.345469i
$443$	1.72899	+	2.99471i	0.0821470	+	0.142283i	0.904172	−	0.427169i	$-0.140489\pi$
$443$	1.72899	+	2.99471i	0.0821470	+	0.142283i	−0.822025	+	0.569452i	$0.807156\pi$
$444$	−0.129264	+	4.26712i	−0.00613457	+	0.202508i
$445$	−13.0308	−	22.5700i	−0.617719	−	1.06992i
$446$	−8.37988			−0.396799
$447$	−23.0538	+	12.3950i	−1.09041	+	0.586261i
$448$	11.7526	+	6.78534i	0.555256	+	0.320577i
$449$	−24.3114	+	14.0362i	−1.14732	+	0.662408i	−0.948234	−	0.317574i	$-0.897132\pi$
$449$	−24.3114	+	14.0362i	−1.14732	+	0.662408i	−0.199090	+	0.979981i	$0.563799\pi$
$450$	0.650280	−	10.7233i	0.0306545	−	0.505503i
$451$	4.10363	+	7.10770i	0.193233	+	0.334689i
$452$	1.52408			0.0716868
$453$	−28.7289	−	17.7676i	−1.34980	−	0.834797i
$454$	2.86319	−	4.95918i	0.134376	−	0.232746i
$455$	−13.6910	−	17.1940i	−0.641842	−	0.806067i
$456$	−0.996477	+	1.61122i	−0.0466643	+	0.0754525i
$457$		−	9.85430i		−	0.460965i	−0.973076	−	0.230482i	$-0.925970\pi$
$457$		−	9.85430i		−	0.460965i	0.973076	−	0.230482i	$-0.0740304\pi$
$458$	−10.9720	+	19.0041i	−0.512689	+	0.888004i
$459$	−3.64251	−	7.88506i	−0.170018	−	0.368043i
$460$			19.1988i			0.895150i
$461$	3.58315	+	2.06873i	0.166884	+	0.0963506i	0.581116	−	0.813821i	$-0.302616\pi$
$461$	3.58315	+	2.06873i	0.166884	+	0.0963506i	−0.414232	+	0.910171i	$0.635950\pi$
$462$	−1.27297	+	42.0221i	−0.0592240	+	1.95504i
$463$	−1.95999	−	1.13160i	−0.0910883	−	0.0525898i	0.453764	−	0.891122i	$-0.350081\pi$
$463$	−1.95999	−	1.13160i	−0.0910883	−	0.0525898i	−0.544852	+	0.838532i	$0.683414\pi$
$464$	−25.4667			−1.18226
$465$	−20.7907	+	33.6168i	−0.964144	+	1.55894i
$466$			4.47924i			0.207497i
$467$	−11.5713			−0.535454			−0.267727	−	0.963495i	$-0.586273\pi$
$467$	−11.5713			−0.535454			−0.267727	+	0.963495i	$0.586273\pi$
$468$	7.94929	−	17.0931i	0.367456	−	0.790127i
$469$	−4.81716			−0.222436
$470$		−	26.1840i		−	1.20778i
$471$	−6.76622	−	0.204969i	−0.311771	−	0.00944445i
$472$	3.78818			0.174365
$473$	8.76011	+	5.05765i	0.402790	+	0.232551i
$474$	−19.7628	−	12.2225i	−0.907737	−	0.561399i
$475$	3.52348	+	2.03428i	0.161668	+	0.0933393i
$476$		−	6.78465i		−	0.310974i
$477$	16.2333	−	24.5535i	0.743270	−	1.12423i
$478$	19.7417	−	34.1937i	0.902967	−	1.56398i
$479$			28.9364i			1.32214i	0.750325	+	0.661069i	$0.229897\pi$
$479$			28.9364i			1.32214i	−0.750325	+	0.661069i	$0.770103\pi$
$480$	−34.4868	−	1.04471i	−1.57410	−	0.0476841i
$481$	−4.74532	−	1.86645i	−0.216368	−	0.0851030i
$482$	8.45453	−	14.6437i	0.385093	−	0.667001i
$483$	−14.9532	+	8.03965i	−0.680394	+	0.365817i
$484$	31.4076			1.42762
$485$	−3.07820	−	5.33160i	−0.139774	−	0.242095i
$486$	23.5441	+	18.8460i	1.06798	+	0.854871i
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	−0.415061	−	0.909794i	$-0.636240\pi$
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	0.580374	+	0.814350i	$0.302906\pi$
$488$	0.402578	+	0.232429i	0.0182239	+	0.0105216i
$489$	−10.5871	−	6.54770i	−0.478765	−	0.296097i
$490$	−7.98067			−0.360530
$491$	−6.93597	−	12.0135i	−0.313016	−	0.542159i	0.665998	−	0.745954i	$-0.268006\pi$
$491$	−6.93597	−	12.0135i	−0.313016	−	0.542159i	−0.979014	+	0.203794i	$0.934673\pi$
$492$	3.91122	+	2.41893i	0.176331	+	0.109054i
$493$	4.78495	+	8.28777i	0.215503	+	0.373262i
$494$	9.55054	+	11.9942i	0.429699	+	0.539644i
$495$	−18.8946	−	37.8475i	−0.849249	−	1.70112i
$496$	33.5871	+	19.3915i	1.50810	+	0.870704i
$497$	−29.5013			−1.32332
$498$	16.1899	−	26.1778i	0.725488	−	1.17306i
$499$	−9.03377	−	5.21565i	−0.404407	−	0.233484i	0.283977	−	0.958831i	$-0.408346\pi$
$499$	−9.03377	−	5.21565i	−0.404407	−	0.233484i	−0.688384	+	0.725347i	$0.741679\pi$
$500$		−	14.3646i		−	0.642403i
$501$	−8.82870	−	5.46020i	−0.394437	−	0.243944i
$502$	31.0646	−	17.9352i	1.38648	−	0.800485i
$503$	−13.8296	−	23.9535i	−0.616630	−	1.06803i	−0.990096	−	0.140390i	$-0.955164\pi$
$503$	−13.8296	−	23.9535i	−0.616630	−	1.06803i	0.373466	−	0.927644i	$-0.378169\pi$
$504$	−1.55294	−	3.11066i	−0.0691732	−	0.138560i
$505$	−27.7844	−	16.0413i	−1.23639	−	0.713829i
$506$	21.9321	+	37.9876i	0.975002	+	1.68875i
$507$	16.0112	+	15.8317i	0.711081	+	0.703110i
$508$	14.7568	−	25.5595i	0.654727	−	1.13402i
$509$	−22.6496	+	13.0768i	−1.00393	+	0.579618i	−0.909408	−	0.415905i	$-0.863465\pi$
$509$	−22.6496	+	13.0768i	−1.00393	+	0.579618i	−0.0945197	+	0.995523i	$0.530132\pi$
$510$	6.94264	+	12.9128i	0.307425	+	0.571790i
$511$	14.7454	−	25.5397i	0.652296	−	1.12981i
$512$			29.4266i			1.30048i
$513$	−10.3684	+	4.78970i	−0.457777	+	0.211471i
$514$	24.0873	−	13.9068i	1.06244	−	0.613402i
$515$	23.1279	−	13.3529i	1.01914	−	0.588399i
$516$	5.66532	+	0.171619i	0.249402	+	0.00755511i
$517$	−13.9281	−	24.1242i	−0.612557	−	1.06098i
$518$	5.51844	−	3.18607i	0.242466	−	0.139988i
$519$	3.77814	+	0.114451i	0.165842	+	0.00502384i
$520$	1.71893	−	4.37026i	0.0753803	−	0.191649i
$521$	9.78810			0.428825			0.214412	−	0.976743i	$-0.431216\pi$
$521$	9.78810			0.428825			0.214412	+	0.976743i	$0.431216\pi$
$522$	−27.7177	−	18.3252i	−1.21317	−	0.802073i
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	−0.206425	−	0.978462i	$-0.566183\pi$
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	0.950586	−	0.310462i	$-0.100484\pi$
$524$	−12.0077	+	20.7980i	−0.524561	+	0.908566i
$525$	−6.57642	+	3.53584i	−0.287018	+	0.154317i
$526$			10.8477i			0.472982i
$527$		−	14.5739i		−	0.634848i
$528$	−36.5572	+	19.6551i	−1.59095	+	0.855380i
$529$	2.64319	−	4.57815i	0.114921	−	0.199050i
$530$	−24.8417	+	43.0270i	−1.07905	+	1.86897i
$531$	19.0508	+	12.5952i	0.826735	+	0.546587i
$532$	−8.92144			−0.386793
$533$	−4.29714	+	3.42166i	−0.186130	+	0.148208i
$534$	−33.3490	−	1.01024i	−1.44315	−	0.0437173i
$535$	−13.4572	+	7.76949i	−0.581803	+	0.335904i
$536$	−0.514632	−	0.891369i	−0.0222287	−	0.0385013i
$537$	−5.07136	−	0.153626i	−0.218845	−	0.00662946i
$538$	3.89831	−	2.25069i	0.168068	−	0.0970340i
$539$	−7.35284	+	4.24516i	−0.316709	+	0.182852i
$540$	−19.3675	−	13.6650i	−0.833444	−	0.588047i
$541$		−	21.1460i		−	0.909138i	−0.890711	−	0.454569i	$-0.849793\pi$
$541$		−	21.1460i		−	0.909138i	0.890711	−	0.454569i	$-0.150207\pi$
$542$	−1.78552	+	3.09261i	−0.0766946	+	0.132839i
$543$	19.0489	+	35.4296i	0.817465	+	1.52043i
$544$	11.0172	−	6.36076i	0.472357	−	0.272715i
$545$	15.9478	−	27.6224i	0.683129	−	1.18321i
$546$	−27.9401	+	3.32864i	−1.19573	+	0.142453i
$547$	0.443127	+	0.767519i	0.0189468	+	0.0328168i	0.875343	−	0.483502i	$-0.160635\pi$
$547$	0.443127	+	0.767519i	0.0189468	+	0.0328168i	−0.856397	+	0.516319i	$0.827302\pi$
$548$	−10.2612	−	5.92431i	−0.438337	−	0.253074i
$549$	1.25178	+	2.50741i	0.0534245	+	0.107014i
$550$	9.64575	+	16.7069i	0.411296	+	0.712386i
$551$	10.8980	−	6.29194i	0.464269	−	0.268046i
$552$	−3.08515	−	1.90804i	−0.131313	−	0.0812117i
$553$			16.1503i			0.686782i
$554$	0.897540	+	0.518195i	0.0381328	+	0.0220160i
$555$	−3.37247	+	5.45301i	−0.143153	+	0.231467i
$556$	−16.3342			−0.692726
$557$	8.55128	+	4.93708i	0.362329	+	0.209191i	0.670102	−	0.742269i	$-0.266250\pi$
$557$	8.55128	+	4.93708i	0.362329	+	0.209191i	−0.307773	+	0.951460i	$0.599584\pi$
$558$	22.6021	+	45.2739i	0.956822	+	1.91660i
$559$	−2.47803	+	6.30021i	−0.104810	+	0.266471i
$560$	13.5580	+	23.4832i	0.572932	+	0.992347i
$561$	13.2652	+	8.20400i	0.560058	+	0.346373i
$562$	−20.1842	−	34.9600i	−0.851418	−	1.47470i
$563$	5.29479			0.223149			0.111574	−	0.993756i	$-0.464411\pi$
$563$	5.29479			0.223149			0.111574	+	0.993756i	$0.464411\pi$
$564$	−13.2750	−	8.21006i	−0.558979	−	0.345706i
$565$	1.98231	+	1.14449i	0.0833966	+	0.0481491i
$566$	−14.6275	+	8.44521i	−0.614841	+	0.354978i
$567$	2.53284	−	20.8069i	0.106369	−	0.873807i
$568$	−3.15172	−	5.45893i	−0.132243	−	0.229052i
$569$	−3.83481			−0.160764			−0.0803818	−	0.996764i	$-0.525614\pi$
$569$	−3.83481			−0.160764			−0.0803818	+	0.996764i	$0.525614\pi$
$570$	16.9797	−	9.12919i	0.711200	−	0.382380i
$571$	−20.0761	+	34.7728i	−0.840159	+	1.45520i	0.0496009	+	0.998769i	$0.484205\pi$
$571$	−20.0761	+	34.7728i	−0.840159	+	1.45520i	−0.889760	+	0.456429i	$0.849128\pi$
$572$	5.02051	+	33.4769i	0.209918	+	1.39974i
$573$	−16.6561	−	0.504563i	−0.695820	−	0.0210784i
$574$		−	6.86428i		−	0.286509i
$575$	−3.89522	+	6.74672i	−0.162442	+	0.281358i
$576$	−9.64080	+	14.5821i	−0.401700	+	0.607588i
$577$			31.4632i			1.30983i	0.755702	+	0.654915i	$0.227296\pi$
$577$			31.4632i			1.30983i	−0.755702	+	0.654915i	$0.772704\pi$
$578$	23.8010	+	13.7415i	0.989991	+	0.571572i
$579$	29.6021	+	18.3077i	1.23022	+	0.760844i
$580$	22.6169	+	13.0579i	0.939117	+	0.542199i
$581$	−21.3927			−0.887518
$582$	−7.87786	−	0.238644i	−0.326548	−	0.00989209i
$583$			52.8562i			2.18908i
$584$	6.30116			0.260744
$585$	23.1751	−	16.2629i	0.958174	−	0.672387i
$586$	5.89580			0.243553
$587$		−	34.6673i		−	1.43087i	−0.698679	−	0.715436i	$-0.746228\pi$
$587$		−	34.6673i		−	1.43087i	0.698679	−	0.715436i	$-0.253772\pi$
$588$	−2.50236	+	4.04611i	−0.103195	+	0.166859i
$589$	−19.1639			−0.789633
$590$	−33.3843	−	19.2744i	−1.37441	−	0.793515i
$591$	−0.628152	+	20.7359i	−0.0258387	+	0.852962i
$592$	5.44818	+	3.14551i	0.223919	+	0.129280i
$593$			8.17407i			0.335669i	0.985815	+	0.167835i	$0.0536774\pi$
$593$			8.17407i			0.335669i	−0.985815	+	0.167835i	$0.946323\pi$
$594$	−53.9317	−	4.91328i	−2.21285	−	0.201594i
$595$	5.09484	−	8.82453i	0.208868	−	0.361770i
$596$		−	26.3369i		−	1.07880i
$597$	16.1288	−	26.0790i	0.660109	−	1.06734i
$598$	−22.9663	+	18.2873i	−0.939164	+	0.747822i
$599$	−20.5243	+	35.5492i	−0.838601	+	1.45250i	0.0524634	+	0.998623i	$0.483293\pi$
$599$	−20.5243	+	35.5492i	−0.838601	+	1.45250i	−0.891064	+	0.453877i	$0.850041\pi$
$600$	−1.35685	−	0.839157i	−0.0553932	−	0.0342585i
$601$	−16.0851			−0.656127			−0.328063	−	0.944656i	$-0.606396\pi$
$601$	−16.0851			−0.656127			−0.328063	+	0.944656i	$0.606396\pi$
$602$	−4.23005	−	7.32666i	−0.172404	−	0.298612i
$603$	0.375601	−	6.19379i	0.0152957	−	0.252231i
$604$	29.4350	−	16.9943i	1.19769	−	0.691488i
$605$	40.8506	+	23.5851i	1.66081	+	0.958871i
$606$	−36.1753	+	19.4498i	−1.46952	+	0.790094i
$607$	12.3021			0.499328			0.249664	−	0.968333i	$-0.419680\pi$
$607$	12.3021			0.499328			0.249664	+	0.968333i	$0.419680\pi$
$608$	−8.36405	−	14.4870i	−0.339207	−	0.587524i
$609$	−0.699267	+	23.0835i	−0.0283357	+	0.935392i
$610$	−2.36521	−	4.09667i	−0.0957647	−	0.165869i
$611$	14.5849	−	11.6134i	0.590041	−	0.469828i
$612$	8.72354	+	0.529009i	0.352628	+	0.0213839i
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	0.709101	−	0.705107i	$-0.249101\pi$
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	−0.256091	+	0.966653i	$0.582435\pi$
$614$	−42.6032			−1.71932
$615$	3.27070	+	6.08329i	0.131887	+	0.245302i
$616$	5.40684	+	3.12164i	0.217848	+	0.125774i
$617$			39.4798i			1.58940i	0.607004	+	0.794699i	$0.292371\pi$
$617$			39.4798i			1.58940i	−0.607004	+	0.794699i	$0.707629\pi$
$618$	1.03521	−	34.1733i	0.0416422	−	1.37465i
$619$	0.671784	−	0.387855i	0.0270013	−	0.0155892i	−0.486439	−	0.873715i	$-0.661704\pi$
$619$	0.671784	−	0.387855i	0.0270013	−	0.0155892i	0.513440	+	0.858126i	$0.328371\pi$
$620$	−19.8857	−	34.4431i	−0.798630	−	1.38327i
$621$	−9.17127	−	19.8533i	−0.368030	−	0.796687i
$622$	11.3890	+	6.57547i	0.456659	+	0.263652i
$623$	11.5945	+	20.0823i	0.464524	+	0.804580i
$624$	−16.6382	−	22.2456i	−0.666060	−	0.890538i
$625$	15.4144	−	26.6985i	0.616576	−	1.06794i
$626$	−10.2408	+	5.91255i	−0.409306	+	0.236313i
$627$	10.7878	−	17.4430i	0.430823	−	0.696607i
$628$	3.40564	−	5.89874i	0.135900	−	0.235385i
$629$		−	2.36404i		−	0.0942604i
$630$	−2.14155	+	35.3149i	−0.0853212	+	1.40698i
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	−0.603801	−	0.797135i	$-0.706348\pi$
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	0.388438	+	0.921475i	$0.373015\pi$
$632$	−2.98846	+	1.72539i	−0.118875	+	0.0686323i
$633$	20.2169	−	32.6891i	0.803550	−	1.29928i
$634$	16.7926	+	29.0856i	0.666918	+	1.15514i
$635$	38.3872	−	22.1628i	1.52335	−	0.879506i
$636$	14.0251	+	26.0857i	0.556130	+	1.03436i
$637$	−3.53967	−	4.44534i	−0.140247	−	0.176131i
$638$	59.6677			2.36227
$639$	2.30026	−	37.9321i	0.0909969	−	1.50057i
$640$	−5.16684	+	8.94922i	−0.204237	+	0.353749i
$641$	13.1720	−	22.8145i	0.520262	−	0.901120i	−0.479461	−	0.877563i	$-0.659168\pi$
$641$	13.1720	−	22.8145i	0.520262	−	0.901120i	0.999723	−	0.0235565i	$-0.00749896\pi$
$642$	−0.602345	+	19.8840i	−0.0237727	+	0.784760i
$643$		−	22.5012i		−	0.887361i	−0.896185	−	0.443681i	$-0.853672\pi$
$643$		−	22.5012i		−	0.887361i	0.896185	−	0.443681i	$-0.146328\pi$
$644$		−	17.0827i		−	0.673152i
$645$	7.23978	+	4.47752i	0.285066	+	0.176302i
$646$	−3.55406	+	6.15582i	−0.139833	+	0.242197i
$647$	−2.07443	+	3.59302i	−0.0815542	+	0.141256i	−0.903918	−	0.427706i	$-0.859322\pi$
$647$	−2.07443	+	3.59302i	−0.0815542	+	0.141256i	0.822363	+	0.568962i	$0.192655\pi$
$648$	4.12070	−	1.75419i	0.161876	−	0.0689109i
$649$	−41.0106			−1.60981
$650$	−10.1006	+	8.04274i	−0.396178	+	0.315462i
$651$	18.4991	−	29.9115i	0.725035	−	1.17232i
$652$	10.8473	−	6.26270i	0.424814	−	0.245266i
$653$	2.22555	+	3.85477i	0.0870927	+	0.150849i	0.906281	−	0.422676i	$-0.138909\pi$
$653$	2.22555	+	3.85477i	0.0870927	+	0.150849i	−0.819188	+	0.573525i	$0.805576\pi$
$654$	−19.3364	−	35.9644i	−0.756114	−	1.40632i
$655$	−31.2360	+	18.0341i	−1.22049	+	0.704651i
$656$	5.86895	−	3.38844i	0.229144	−	0.132296i
$657$	31.6886	+	20.9506i	1.23629	+	0.817361i
$658$			23.2980i			0.908249i
$659$	−6.70705	+	11.6169i	−0.261269	+	0.452532i	−0.966580	−	0.256367i	$-0.917474\pi$
$659$	−6.70705	+	11.6169i	−0.261269	+	0.452532i	0.705310	+	0.708899i	$0.250808\pi$
$660$	42.5444	+	1.28879i	1.65604	+	0.0501662i
$661$	−4.79886	+	2.77062i	−0.186654	+	0.107765i	−0.590415	−	0.807100i	$-0.701036\pi$
$661$	−4.79886	+	2.77062i	−0.186654	+	0.107765i	0.403761	+	0.914864i	$0.367703\pi$
$662$	18.4451	−	31.9479i	0.716891	−	1.24169i
$663$	−4.11336	+	9.59438i	−0.159750	+	0.372615i
$664$	−2.28544	−	3.95851i	−0.0886924	−	0.153620i
$665$	−11.6038	−	6.69944i	−0.449975	−	0.259793i
$666$	3.66630	+	7.34390i	0.142066	+	0.284570i
$667$	12.0477	+	20.8673i	0.466490	+	0.807985i
$668$	9.04570	−	5.22254i	0.349989	−	0.202066i
$669$	−6.60789	+	3.55276i	−0.255476	+	0.137357i
$670$			10.4739i			0.404641i
$671$	−4.35829	−	2.51626i	−0.168250	−	0.0971392i
$672$	30.6856	+	0.929556i	1.18372	+	0.0358584i
$673$	13.8135			0.532473			0.266236	−	0.963908i	$-0.414220\pi$
$673$	13.8135			0.532473			0.266236	+	0.963908i	$0.414220\pi$
$674$	−40.4375	−	23.3466i	−1.55759	−	0.899278i
$675$	−4.03352	−	8.73150i	−0.155250	−	0.336075i
$676$	−21.6595	+	6.64599i	−0.833058	+	0.255615i
$677$	4.70621	+	8.15139i	0.180874	+	0.313284i	0.942179	−	0.335111i	$-0.108774\pi$
$677$	4.70621	+	8.15139i	0.180874	+	0.313284i	−0.761304	+	0.648395i	$0.775441\pi$
$678$	2.58098	−	1.38767i	0.0991218	−	0.0532932i
$679$	2.73891	+	4.74394i	0.105110	+	0.182056i
$680$	2.17719			0.0834914
$681$	0.155233	−	5.12440i	0.00594855	−	0.196368i
$682$	−78.6934	−	45.4336i	−3.01332	−	1.73974i
$683$	−16.9642	+	9.79429i	−0.649117	+	0.374768i	−0.788118	−	0.615524i	$-0.788944\pi$
$683$	−16.9642	+	9.79429i	−0.649117	+	0.374768i	0.139001	+	0.990292i	$0.455611\pi$
$684$	0.695617	−	11.4710i	0.0265976	−	0.438604i
$685$	−8.89757	−	15.4110i	−0.339959	−	0.588826i
$686$	38.6405			1.47530
$687$	−0.594870	+	19.6373i	−0.0226957	+	0.749208i
$688$	4.17619	−	7.23337i	0.159216	−	0.275770i
$689$	−34.9847	+	5.24662i	−1.33281	+	0.199880i
$690$	17.4805	+	32.5125i	0.665470	+	1.23773i
$691$		−	1.40342i		−	0.0533886i	−0.999644	−	0.0266943i	$-0.991502\pi$
$691$		−	1.40342i		−	0.0533886i	0.999644	−	0.0266943i	$-0.00849807\pi$
$692$	−1.90165	+	3.29375i	−0.0722899	+	0.125210i
$693$	16.8120	+	33.6758i	0.638635	+	1.27924i
$694$			1.99110i			0.0755813i
$695$	−21.2453	−	12.2660i	−0.805881	−	0.465275i
$696$	−4.34608	+	2.33669i	−0.164738	+	0.0885720i
$697$	−2.20544	−	1.27331i	−0.0835369	−	0.0482300i
$698$	54.8294			2.07532
$699$	1.89903	+	3.53206i	0.0718279	+	0.133595i
$700$		−	7.51296i		−	0.283963i
$701$	19.4308			0.733892			0.366946	−	0.930242i	$-0.380403\pi$
$701$	19.4308			0.733892			0.366946	+	0.930242i	$0.380403\pi$
$702$	−2.10136	−	36.1843i	−0.0793108	−	1.36569i
$703$	−3.10858			−0.117242
$704$		−	31.3909i		−	1.18309i
$705$	−11.1011	−	20.6472i	−0.418090	−	0.777619i
$706$	14.9241			0.561674
$707$	24.7219	+	14.2732i	0.929763	+	0.536799i
$708$	−20.2396	+	10.8819i	−0.760652	+	0.408967i
$709$	−3.16828	−	1.82921i	−0.118987	−	0.0686972i	0.439325	−	0.898328i	$-0.355218\pi$
$709$	−3.16828	−	1.82921i	−0.118987	−	0.0686972i	−0.558312	+	0.829631i	$0.688551\pi$
$710$			64.1442i			2.40729i
$711$	−20.7657	−	1.25926i	−0.778775	−	0.0472261i
$712$	−2.47735	+	4.29090i	−0.0928427	+	0.160808i
$713$		−	36.6947i		−	1.37423i
$714$	−6.17740	−	11.4896i	−0.231184	−	0.429986i
$715$	−18.6091	+	47.3122i	−0.695940	+	1.76938i
$716$	2.55256	−	4.42117i	0.0953937	−	0.165227i
$717$	1.07034	−	35.3329i	0.0399725	−	1.31953i
$718$	−11.6401			−0.434403
$719$	3.56798	+	6.17992i	0.133063	+	0.230472i	0.924856	−	0.380318i	$-0.124185\pi$
$719$	3.56798	+	6.17992i	0.133063	+	0.230472i	−0.791793	+	0.610790i	$0.790852\pi$
$720$	−31.2513	+	15.6016i	−1.16467	+	0.581437i
$721$	−20.5787	+	11.8811i	−0.766390	+	0.442476i
$722$	−23.7387	−	13.7056i	−0.883464	−	0.510068i
$723$	0.458379	−	15.1316i	0.0170473	−	0.562748i
$724$	−40.4751			−1.50425
$725$	5.29859	+	9.17743i	0.196785	+	0.340841i
$726$	53.1876	−	28.5965i	1.97398	−	1.06132i
$727$	−18.8741	−	32.6908i	−0.700000	−	1.21244i	−0.968466	−	0.249146i	$-0.919850\pi$
$727$	−18.8741	−	32.6908i	−0.700000	−	1.21244i	0.268466	−	0.963289i	$-0.413483\pi$
$728$	−1.52947	+	3.88856i	−0.0566859	+	0.144120i
$729$	26.5555	+	4.87900i	0.983538	+	0.180704i
$730$	−55.5305	−	32.0606i	−2.05528	−	1.18662i
$731$	−3.13866			−0.116088
$732$	−2.81858	−	0.0853832i	−0.104178	−	0.00315585i
$733$	25.7477	+	14.8654i	0.951012	+	0.549067i	0.893395	−	0.449272i	$-0.148316\pi$
$733$	25.7477	+	14.8654i	0.951012	+	0.549067i	0.0576170	+	0.998339i	$0.481650\pi$
$734$			47.1875i			1.74172i
$735$	−6.29309	+	3.38350i	−0.232124	+	0.124802i
$736$	27.7395	−	16.0154i	1.02249	−	0.590335i
$737$	5.57138	+	9.64991i	0.205224	+	0.355459i
$738$	8.82593	+	0.535218i	0.324887	+	0.0197016i
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.245023	−	0.969517i	$-0.578795\pi$
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.962138	+	0.272563i	$0.912129\pi$
$740$	−3.22567	−	5.58703i	−0.118578	−	0.205383i
$741$	12.6161	+	5.40885i	0.463463	+	0.198699i
$742$	22.1035	−	38.2845i	0.811447	−	1.40547i
$743$	4.18486	−	2.41613i	0.153528	−	0.0886393i	−0.421268	−	0.906936i	$-0.638415\pi$
$743$	4.18486	−	2.41613i	0.153528	−	0.0886393i	0.574796	+	0.818297i	$0.305081\pi$
$744$	7.51114	+	0.227534i	0.275372	+	0.00834181i
$745$	19.7773	−	34.2553i	0.724585	−	1.25502i
$746$			10.4012i			0.380815i
$747$	1.66802	−	27.5062i	0.0610296	−	1.00640i
$748$	−13.5912	+	7.84691i	−0.496945	+	0.286911i
$749$	11.9739	−	6.91312i	0.437516	−	0.252600i
$750$	−13.0789	−	24.3259i	−0.477574	−	0.888255i
$751$	17.1031	+	29.6234i	0.624100	+	1.08097i	0.988714	+	0.149815i	$0.0478677\pi$
$751$	17.1031	+	29.6234i	0.624100	+	1.08097i	−0.364614	+	0.931159i	$0.618799\pi$
$752$	−19.9197	+	11.5007i	−0.726398	+	0.419386i
$753$	16.8919	−	27.3128i	0.615575	−	0.995335i
$754$	5.92275	+	39.4931i	0.215694	+	1.43825i
$755$	51.0466			1.85777
$756$	17.2328	+	12.1588i	0.626749	+	0.442211i
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	−0.628579	−	0.777746i	$-0.716363\pi$
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	0.987837	+	0.155492i	$0.0496964\pi$
$758$	−22.0445	+	38.1821i	−0.800690	+	1.38684i
$759$	33.3997	+	20.6564i	1.21233	+	0.749779i
$760$		−	2.86289i		−	0.103848i
$761$		−	17.7648i		−	0.643972i	−0.946744	−	0.321986i	$-0.895650\pi$
$761$		−	17.7648i		−	0.643972i	0.946744	−	0.321986i	$-0.104350\pi$
$762$	1.71822	−	56.7201i	0.0622445	−	2.05475i
$763$	−14.1900	+	24.5778i	−0.513712	+	0.889776i
$764$	8.38352	−	14.5207i	0.303305	−	0.525340i
$765$	10.9491	+	7.23889i	0.395866	+	0.261723i
$766$	48.1496			1.73971
$767$	−4.07081	−	27.1443i	−0.146988	−	0.980124i
$768$	15.8234	+	29.4304i	0.570977	+	1.06198i
$769$	−14.0558	+	8.11511i	−0.506865	+	0.292638i	−0.731544	−	0.681794i	$-0.761200\pi$
$769$	−14.0558	+	8.11511i	−0.506865	+	0.292638i	0.224679	+	0.974433i	$0.427867\pi$
$770$	−31.7660	−	55.0204i	−1.14477	−	1.98280i
$771$	13.0979	−	21.1782i	0.471708	−	0.762714i
$772$	−30.3297	+	17.5109i	−1.09159	+	0.630230i
$773$	14.3635	−	8.29274i	0.516617	−	0.298269i	−0.218932	−	0.975740i	$-0.570257\pi$
$773$	14.3635	−	8.29274i	0.516617	−	0.298269i	0.735550	+	0.677471i	$0.236924\pi$
$774$	9.75027	−	4.86763i	0.350466	−	0.174963i
$775$		−	16.1383i		−	0.579706i
$776$	−0.585213	+	1.01362i	−0.0210079	+	0.0363868i
$777$	3.00074	−	4.85196i	0.107651	−	0.174063i
$778$	25.2541	−	14.5805i	0.905405	−	0.522736i
$779$	−1.67433	+	2.90003i	−0.0599891	+	0.103904i
$780$	3.37002	+	28.2874i	0.120666	+	1.01285i
$781$	34.1203	+	59.0981i	1.22092	+	2.11470i
$782$	−11.7871	−	6.80528i	−0.421506	−	0.243356i
$783$	−29.6257	−	2.69896i	−1.05874	−	0.0964529i
$784$	3.50530	+	6.07137i	0.125189	+	0.216834i
$785$	8.85916	−	5.11484i	0.316197	−	0.182556i
$786$	−1.39813	+	46.1537i	−0.0498697	+	1.64625i
$787$		−	10.2478i		−	0.365295i	−0.983178	−	0.182648i	$-0.941533\pi$
$787$		−	10.2478i		−	0.365295i	0.983178	−	0.182648i	$-0.0584668\pi$
$788$	−18.0774	−	10.4370i	−0.643981	−	0.371803i
$789$	4.59901	+	8.55386i	0.163729	+	0.304525i
$790$	35.1154			1.24935
$791$	−1.76382	−	1.01834i	−0.0627142	−	0.0362080i
$792$	−4.43531	+	6.70858i	−0.157602	+	0.238379i
$793$	1.23286	−	3.13445i	0.0437801	−	0.111308i
$794$	−2.60865	−	4.51831i	−0.0925774	−	0.160349i
$795$	−1.34684	+	44.4605i	−0.0477675	+	1.57685i
$796$	15.4268	+	26.7200i	0.546789	+	0.947066i
$797$	−20.3566			−0.721067			−0.360534	−	0.932746i	$-0.617405\pi$
$797$	−20.3566			−0.721067			−0.360534	+	0.932746i	$0.617405\pi$
$798$	−15.1081	+	8.12295i	−0.534822	+	0.287549i
$799$	7.48545	+	4.32172i	0.264816	+	0.152892i
$800$	12.1998	−	7.04357i	0.431329	−	0.249028i
$801$	−26.7254	+	13.3421i	−0.944294	+	0.471420i
$802$	1.17701	+	2.03864i	0.0415617	+	0.0719870i
$803$	−68.2160			−2.40729
$804$	5.31014	+	3.28411i	0.187274	+	0.115821i
$805$	12.8280	−	22.2188i	0.452128	−	0.783109i
$806$	22.2605	−	56.5958i	0.784094	−	1.99350i
$807$	2.11977	−	3.42750i	0.0746194	−	0.120654i
$808$			6.09939i			0.214576i
$809$	18.8460	−	32.6423i	0.662591	−	1.14764i	−0.317342	−	0.948311i	$-0.602790\pi$
$809$	18.8460	−	32.6423i	0.662591	−	1.14764i	0.979932	−	0.199330i	$-0.0638765\pi$
$810$	−45.2400	−	5.50710i	−1.58957	−	0.193500i
$811$		−	28.8949i		−	1.01464i	−0.861758	−	0.507319i	$-0.830637\pi$
$811$		−	28.8949i		−	1.01464i	0.861758	−	0.507319i	$-0.169363\pi$
$812$	−20.1240	−	11.6186i	−0.706215	−	0.407734i
$813$	−0.0968054	+	3.19565i	−0.00339511	+	0.112076i
$814$	−12.7649	−	7.36982i	−0.447409	−	0.258312i
$815$	18.8116			0.658941
$816$	6.77418	−	10.9533i	0.237144	−	0.383443i
$817$			4.12716i			0.144391i
$818$	−66.5660			−2.32743
$819$	−20.6207	+	14.4703i	−0.720546	+	0.505634i
$820$	−6.94960			−0.242691
$821$			5.18436i			0.180935i	0.995899	+	0.0904677i	$0.0288362\pi$
$821$			5.18436i			0.180935i	−0.995899	+	0.0904677i	$0.971164\pi$
$822$	−22.7711	−	0.689802i	−0.794232	−	0.0240596i
$823$	17.6885			0.616582			0.308291	−	0.951292i	$-0.400243\pi$
$823$	17.6885			0.616582			0.308291	+	0.951292i	$0.400243\pi$
$824$	−4.39696	−	2.53859i	−0.153176	−	0.0884359i
$825$	14.6892	+	9.08467i	0.511412	+	0.316288i
$826$	29.7046	+	17.1499i	1.03355	+	0.596723i
$827$		−	15.0588i		−	0.523644i	−0.965116	−	0.261822i	$-0.915677\pi$
$827$		−	15.0588i		−	0.523644i	0.965116	−	0.261822i	$-0.0843234\pi$
$828$	21.9645	+	1.33196i	0.763319	+	0.0462888i
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	−0.772335	−	0.635215i	$-0.780911\pi$
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	0.936280	+	0.351255i	$0.114245\pi$
$830$			46.5137i			1.61452i
$831$	0.927443	+	0.0280950i	0.0321726	+	0.000974603i
$832$	20.7771	−	3.11593i	0.720317	−	0.108025i
$833$	1.31722	−	2.28150i	0.0456391	−	0.0790492i
$834$	−27.6614	+	14.8723i	−0.957837	+	0.514985i
$835$	15.6872			0.542877
$836$	10.3183	+	17.8717i	0.356864	+	0.618107i
$837$	37.0171	+	26.1179i	1.27950	+	0.902767i
$838$	−36.5115	+	21.0799i	−1.26127	+	0.728194i
$839$	25.9632	+	14.9899i	0.896350	+	0.517508i	0.876014	−	0.482285i	$-0.160193\pi$
$839$	25.9632	+	14.9899i	0.896350	+	0.517508i	0.0203361	+	0.999793i	$0.493526\pi$
$840$	4.46847	+	2.76357i	0.154177	+	0.0953523i
$841$	3.77661			0.130228
$842$	25.0520	+	43.3914i	0.863350	+	1.49537i
$843$	−30.7378	−	19.0101i	−1.05867	−	0.654743i
$844$	19.3369	+	33.4926i	0.665605	+	1.15286i
$845$	−33.1624	−	7.62075i	−1.14082	−	0.262162i
$846$	−29.9560	−	1.81658i	−1.02991	−	0.0624552i
$847$	−36.3479	−	20.9855i	−1.24893	−	0.721070i
$848$	43.6443			1.49875
$849$	−7.95396	+	12.8609i	−0.272979	+	0.441386i
$850$	−5.18396	−	2.99296i	−0.177808	−	0.102658i
$851$		−	5.95228i		−	0.204041i
$852$	32.5204	+	20.1126i	1.11413	+	0.689045i
$853$	−45.8672	+	26.4814i	−1.57046	+	0.906706i	−0.574349	+	0.818610i	$0.694745\pi$
$853$	−45.8672	+	26.4814i	−1.57046	+	0.906706i	−0.996112	+	0.0880960i	$0.971922\pi$
$854$	2.10451	+	3.64513i	0.0720150	+	0.124734i
$855$	9.51875	−	14.3975i	0.325534	−	0.492384i
$856$	2.55841	+	1.47710i	0.0874446	+	0.0504862i
$857$	−15.1376	−	26.2190i	−0.517089	−	0.895624i	−0.999803	−	0.0198464i	$-0.993682\pi$
$857$	−15.1376	−	26.2190i	−0.517089	−	0.895624i	0.482714	−	0.875778i	$-0.339651\pi$
$858$	38.9827	+	52.1208i	1.33085	+	1.77937i
$859$	−24.2634	+	42.0254i	−0.827856	+	1.43389i	0.0718602	+	0.997415i	$0.477106\pi$
$859$	−24.2634	+	42.0254i	−0.827856	+	1.43389i	−0.899717	+	0.436475i	$0.856227\pi$
$860$	−7.41773	+	4.28263i	−0.252942	+	0.146036i
$861$	−2.91020	−	5.41277i	−0.0991793	−	0.184467i
$862$	−27.2970	+	47.2797i	−0.929739	+	1.61035i
$863$			21.2534i			0.723473i	0.932280	+	0.361737i	$0.117816\pi$
$863$			21.2534i			0.723473i	−0.932280	+	0.361737i	$0.882184\pi$
$864$	−3.58780	+	39.3823i	−0.122059	+	1.33981i
$865$	−4.94680	+	2.85604i	−0.168196	+	0.0971082i
$866$	−45.0350	+	26.0010i	−1.53035	+	0.883548i
$867$	24.5940	+	0.745023i	0.835255	+	0.0253023i
$868$	17.6939	+	30.6467i	0.600569	+	1.04022i
$869$	32.3529	−	18.6790i	1.09750	−	0.633640i
$870$	50.1901	+	1.52041i	1.70160	+	0.0515466i
$871$	−5.83409	+	4.64548i	−0.197681	+	0.157406i
$872$	−6.06384			−0.205348
$873$	−6.31320	+	3.15174i	−0.213669	+	0.106670i
$874$	−8.94857	+	15.4994i	−0.302690	+	0.524274i
$875$	−9.59792	+	16.6241i	−0.324469	+	0.561997i
$876$	−33.6661	+	18.1007i	−1.13747	+	0.611566i
$877$		−	43.3602i		−	1.46417i	−0.681213	−	0.732085i	$-0.738547\pi$
$877$		−	43.3602i		−	1.46417i	0.681213	−	0.732085i	$-0.261453\pi$
$878$			3.28091i			0.110725i
$879$	4.64908	−	2.49960i	0.156810	−	0.0843094i
$880$	31.3616	−	54.3199i	1.05720	−	1.83112i
$881$	25.4246	−	44.0368i	0.856578	−	1.48364i	−0.0185957	−	0.999827i	$-0.505920\pi$
$881$	25.4246	−	44.0368i	0.856578	−	1.48364i	0.875174	−	0.483809i	$-0.160747\pi$
$882$	−0.553676	+	9.13032i	−0.0186433	+	0.307434i
$883$	29.1681			0.981586			0.490793	−	0.871276i	$-0.336707\pi$
$883$	29.1681			0.981586			0.490793	+	0.871276i	$0.336707\pi$
$884$	−6.54284	−	8.21693i	−0.220060	−	0.276365i
$885$	−34.4965	−	1.04500i	−1.15959	−	0.0351273i
$886$	−5.79364	+	3.34496i	−0.194641	+	0.112376i
$887$	22.0569	+	38.2037i	0.740598	+	1.28275i	0.952223	+	0.305403i	$0.0987912\pi$
$887$	22.0569	+	38.2037i	0.740598	+	1.28275i	−0.211625	+	0.977351i	$0.567875\pi$
$888$	1.21839	+	0.0369085i	0.0408864	+	0.00123857i
$889$	−34.1560	+	19.7200i	−1.14556	+	0.661387i
$890$	43.6646	−	25.2097i	1.46364	−	0.845033i
$891$	−44.6105	+	18.9907i	−1.49451	+	0.636213i
$892$		−	7.54891i		−	0.252756i
$893$	5.68283	−	9.84295i	0.190169	−	0.329382i
$894$	−23.9796	−	44.6005i	−0.801999	−	1.49166i
$895$	6.64004	−	3.83363i	0.221952	−	0.128144i
$896$	4.59734	−	7.96282i	0.153586	−	0.266019i
$897$	−10.3568	+	24.1571i	−0.345804	+	0.806584i
$898$	−27.1548	−	47.0334i	−0.906166	−	1.56953i
$899$	−43.2278	−	24.9576i	−1.44173	−	0.832382i
$900$	9.65999	+	0.585796i	0.322000	+	0.0195265i
$901$	−8.20032	−	14.2034i	−0.273192	−	0.473183i
$902$	−13.7508	+	7.93901i	−0.457850	+	0.264340i
$903$	−6.44180	−	3.98399i	−0.214370	−	0.132579i
$904$		−	0.435170i		−	0.0144735i
$905$	−52.6444	−	30.3942i	−1.74996	−	1.01034i
$906$	34.3738	−	55.5796i	1.14199	−	1.84651i
$907$	21.2054			0.704113			0.352057	−	0.935979i	$-0.385482\pi$
$907$	21.2054			0.704113			0.352057	+	0.935979i	$0.385482\pi$
$908$	4.46742	+	2.57926i	0.148256	+	0.0855959i
$909$	−20.2797	+	30.6739i	−0.672637	+	1.01739i
$910$	33.2640	−	26.4869i	1.10269	−	0.878032i
$911$	−18.2141	−	31.5478i	−0.603460	−	1.04522i	−0.992293	−	0.123915i	$-0.960455\pi$
$911$	−18.2141	−	31.5478i	−0.603460	−	1.04522i	0.388833	−	0.921308i	$-0.372878\pi$
$912$	−14.4030	−	8.90768i	−0.476931	−	0.294963i
$913$	24.7421	+	42.8546i	0.818844	+	1.41828i
$914$	19.0644			0.630594
$915$	−3.60191	−	2.22763i	−0.119075	−	0.0736433i
$916$	−17.1196	−	9.88401i	−0.565648	−	0.326577i
$917$	27.7931	−	16.0463i	0.917809	−	0.529897i
$918$	15.2547	−	7.04691i	0.503479	−	0.232583i
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	0.920318	−	0.391170i	$-0.127930\pi$
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	−0.798922	+	0.601434i	$0.794596\pi$
$920$	5.48182			0.180730
$921$	−33.5944	+	18.0621i	−1.10697	+	0.595168i
$922$	−4.00223	+	6.93207i	−0.131806	+	0.228296i
$923$	−35.7292	+	28.4499i	−1.17604	+	0.936440i
$924$	−37.8550	−	1.14674i	−1.24534	−	0.0377250i
$925$		−	2.61781i		−	0.0860731i
$926$	2.18922	−	3.79184i	0.0719423	−	0.124608i
$927$	−13.6719	−	27.3860i	−0.449044	−	0.899473i
$928$		−	43.5709i		−	1.43028i
$929$	2.05280	+	1.18519i	0.0673502	+	0.0388847i	0.533297	−	0.845928i	$-0.320953\pi$
$929$	2.05280	+	1.18519i	0.0673502	+	0.0388847i	−0.465947	+	0.884813i	$0.654286\pi$
$930$	−65.0361	−	40.2222i	−2.13262	−	1.31894i
$931$	−3.00004	−	1.73208i	−0.0983225	−	0.0567665i
$932$	−4.03506			−0.132173
$933$	11.7685	+	0.356502i	0.385283	+	0.0116714i
$934$		−	22.3861i		−	0.732495i
$935$	−23.5701			−0.770826
$936$	−4.88057	−	2.26975i	−0.159526	−	0.0741892i
$937$	36.8188			1.20282			0.601409	−	0.798941i	$-0.294606\pi$
$937$	36.8188			1.20282			0.601409	+	0.798941i	$0.294606\pi$
$938$		−	9.31942i		−	0.304290i
$939$	−5.56863	+	9.00402i	−0.181725	+	0.293835i
$940$	23.5876			0.769341
$941$	−42.7909	−	24.7053i	−1.39494	−	0.805371i	−0.401086	−	0.916040i	$-0.631367\pi$
$941$	−42.7909	−	24.7053i	−1.39494	−	0.805371i	−0.993857	+	0.110669i	$0.964701\pi$
$942$	0.396538	−	13.0901i	0.0129199	−	0.426499i
$943$	−5.55294	−	3.20599i	−0.180829	−	0.104401i
$944$			33.8632i			1.10215i
$945$	13.2835	+	28.7552i	0.432112	+	0.935406i
$946$	−9.78467	+	16.9476i	−0.318127	+	0.551012i
$947$			27.1891i			0.883525i	0.897132	+	0.441763i	$0.145647\pi$
$947$			27.1891i			0.883525i	−0.897132	+	0.441763i	$0.854353\pi$
$948$	11.0105	−	17.8031i	0.357605	−	0.578218i
$949$	−6.77128	−	45.1511i	−0.219805	−	1.46567i
$950$	−3.93558	+	6.81662i	−0.127687	+	0.221160i
$951$	25.5728	+	15.8158i	0.829256	+	0.512861i
$952$	−1.93721			−0.0627855
$953$	27.1090	+	46.9542i	0.878147	+	1.52100i	0.853372	+	0.521303i	$0.174554\pi$
$953$	27.1090	+	46.9542i	0.878147	+	1.52100i	0.0247753	+	0.999693i	$0.492113\pi$
$954$	47.5018	+	31.4053i	1.53793	+	1.01678i
$955$	21.8082	−	12.5910i	0.705698	−	0.407435i
$956$	30.8030	+	17.7841i	0.996239	+	0.575179i
$957$	47.0505	−	25.2969i	1.52093	−	0.817732i
$958$	−55.9811			−1.80867
$959$	7.91686	+	13.7124i	0.255649	+	0.442797i
$960$	0.799877	−	26.4047i	0.0258159	−	0.852209i
$961$	22.5076	+	38.9843i	0.726052	+	1.25756i
$962$	3.61090	−	9.18043i	0.116420	−	0.295989i
$963$	7.95510	+	15.9347i	0.256350	+	0.513490i
$964$	13.1916	+	7.61615i	0.424872	+	0.245300i
$965$	−52.5982			−1.69320
$966$	−15.5537	−	28.9289i	−0.500433	−	0.930772i
$967$	−19.6716	−	11.3574i	−0.632595	−	0.365229i	0.149161	−	0.988813i	$-0.452343\pi$
$967$	−19.6716	−	11.3574i	−0.632595	−	0.365229i	−0.781756	+	0.623584i	$0.785676\pi$
$968$		−	8.96777i		−	0.288235i
$969$	−0.192690	+	6.36091i	−0.00619011	+	0.204342i
$970$	10.3147	−	5.95517i	0.331184	−	0.191209i
$971$	−23.0225	−	39.8762i	−0.738828	−	1.27969i	−0.953023	−	0.302897i	$-0.902046\pi$
$971$	−23.0225	−	39.8762i	−0.738828	−	1.27969i	0.214195	−	0.976791i	$-0.431287\pi$
$972$	−16.9772	+	21.2094i	−0.544542	+	0.680293i
$973$	18.9036	+	10.9140i	0.606022	+	0.349887i
$974$	4.07483	+	7.05781i	0.130566	+	0.226147i
$975$	−4.55492	+	10.6243i	−0.145874	+	0.340250i
$976$	−2.07772	+	3.59872i	−0.0665062	+	0.115192i
$977$	27.6584	−	15.9686i	0.884871	−	0.510881i	0.0126097	−	0.999920i	$-0.495986\pi$
$977$	27.6584	−	15.9686i	0.884871	−	0.510881i	0.872261	+	0.489040i	$0.162653\pi$
$978$	12.6674	−	20.4821i	0.405057	−	0.654945i
$979$	26.8197	−	46.4530i	0.857161	−	1.48465i
$980$		−	7.18928i		−	0.229653i
$981$	−30.4951	−	20.1615i	−0.973635	−	0.643708i
$982$	23.2416	−	13.4185i	0.741668	−	0.428202i
$983$	−2.20776	+	1.27465i	−0.0704167	+	0.0406551i	−0.534795	−	0.844982i	$-0.679611\pi$
$983$	−2.20776	+	1.27465i	−0.0704167	+	0.0406551i	0.464378	+	0.885637i	$0.346278\pi$
$984$	0.690675	−	1.11677i	0.0220179	−	0.0356012i
$985$	−15.6751	−	27.1500i	−0.499449	−	0.865071i
$986$	−16.0338	+	9.25709i	−0.510619	+	0.294806i
$987$	9.87747	+	18.3714i	0.314403	+	0.584769i
$988$	−10.8048	+	8.60348i	−0.343747	+	0.273713i
$989$	−7.90265			−0.251290
$990$	73.2208	−	36.5540i	2.32711	−	1.16176i
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	0.175949	+	0.984399i	$0.443701\pi$
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	−0.940489	+	0.339824i	$0.889633\pi$
$992$	−33.1768	+	57.4639i	−1.05336	+	1.82448i
$993$	1.00004	−	33.0123i	0.0317353	−	1.04761i
$994$		−	57.0741i		−	1.81028i
$995$			46.3382i			1.46902i
$996$	23.5819	+	14.5845i	0.747222	+	0.462127i
$997$	−11.9132	+	20.6343i	−0.377295	+	0.653494i	−0.990668	−	0.136299i	$-0.956479\pi$
$997$	−11.9132	+	20.6343i	−0.377295	+	0.653494i	0.613373	+	0.789794i	$0.289812\pi$
$998$	10.0903	−	17.4770i	0.319404	−	0.553224i
$999$	6.00457	+	4.23660i	0.189976	+	0.134040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.9	✓	22
3.2	odd	2		351.2.l.b.199.3		22
9.2	odd	6		351.2.r.b.316.3		22
9.7	even	3		117.2.r.b.43.9	yes	22
13.10	even	6		117.2.r.b.49.9	yes	22
39.23	odd	6		351.2.r.b.10.3		22
117.88	even	6	inner	117.2.l.b.88.3	yes	22
117.101	odd	6		351.2.l.b.127.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.9	✓	22	1.1	even	1	trivial
117.2.l.b.88.3	yes	22	117.88	even	6	inner
117.2.r.b.43.9	yes	22	9.7	even	3
117.2.r.b.49.9	yes	22	13.10	even	6
351.2.l.b.127.9		22	117.101	odd	6
351.2.l.b.199.3		22	3.2	odd	2
351.2.r.b.10.3		22	39.23	odd	6
351.2.r.b.316.3		22	9.2	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.93463i q^{2} +(0.820210 + 1.52553i) q^{3} -1.74278 q^{4} +(-2.26677 - 1.30872i) q^{5} +(-2.95134 + 1.58680i) q^{6} +(2.01692 + 1.16447i) q^{7} +0.497616i q^{8} +(-1.65451 + 2.50252i) q^{9} +(2.53189 - 4.38536i) q^{10} -5.38716i q^{11} +(-1.42945 - 2.65868i) q^{12} +(3.56568 - 0.534742i) q^{13} +(-2.25282 + 3.90199i) q^{14} +(0.137271 - 4.53147i) q^{15} -4.44827 q^{16} +(0.835786 + 1.44762i) q^{17} +(-4.84144 - 3.20086i) q^{18} +(1.90355 - 1.09901i) q^{19} +(3.95050 + 2.28082i) q^{20} +(-0.122141 + 4.03200i) q^{21} +10.4221 q^{22} +(2.10438 + 3.64489i) q^{23} +(-0.759130 + 0.408149i) q^{24} +(0.925505 + 1.60302i) q^{25} +(1.03453 + 6.89826i) q^{26} +(-5.17472 - 0.471426i) q^{27} +(-3.51506 - 2.02942i) q^{28} +5.72509 q^{29} +(8.76670 + 0.265569i) q^{30} +(-7.55059 - 4.35934i) q^{31} -7.61052i q^{32} +(8.21830 - 4.41860i) q^{33} +(-2.80061 + 1.61693i) q^{34} +(-3.04794 - 5.27918i) q^{35} +(2.88346 - 4.36135i) q^{36} +(-1.22479 - 0.707130i) q^{37} +(2.12618 + 3.68265i) q^{38} +(3.74037 + 5.00096i) q^{39} +(0.651240 - 1.12798i) q^{40} +(-1.31938 + 0.761744i) q^{41} +(-7.80041 - 0.236297i) q^{42} +(-0.938835 + 1.62611i) q^{43} +9.38866i q^{44} +(7.02550 - 3.50734i) q^{45} +(-7.05150 + 4.07119i) q^{46} +(4.47809 - 2.58543i) q^{47} +(-3.64852 - 6.78599i) q^{48} +(-0.788015 - 1.36488i) q^{49} +(-3.10125 + 1.79051i) q^{50} +(-1.52288 + 2.46238i) q^{51} +(-6.21421 + 0.931939i) q^{52} -9.81151 q^{53} +(0.912035 - 10.0112i) q^{54} +(-7.05029 + 12.2115i) q^{55} +(-0.579459 + 1.00365i) q^{56} +(3.23789 + 2.00250i) q^{57} +11.0759i q^{58} -7.61266i q^{59} +(-0.239234 + 7.89737i) q^{60} +(0.467085 - 0.809015i) q^{61} +(8.43369 - 14.6076i) q^{62} +(-6.25113 + 3.12075i) q^{63} +5.82698 q^{64} +(-8.78241 - 3.45434i) q^{65} +(8.54835 + 15.8993i) q^{66} +(-1.79128 + 1.03420i) q^{67} +(-1.45659 - 2.52290i) q^{68} +(-3.83437 + 6.19987i) q^{69} +(10.2133 - 5.89662i) q^{70} +(-10.9702 + 6.33363i) q^{71} +(-1.24529 - 0.823311i) q^{72} -12.6627i q^{73} +(1.36803 - 2.36950i) q^{74} +(-1.68636 + 2.72670i) q^{75} +(-3.31747 + 1.91534i) q^{76} +(6.27319 - 10.8655i) q^{77} +(-9.67500 + 7.23622i) q^{78} +(3.46731 + 6.00556i) q^{79} +(10.0832 + 5.82155i) q^{80} +(-3.52518 - 8.28089i) q^{81} +(-1.47369 - 2.55251i) q^{82} +(-7.95495 + 4.59279i) q^{83} +(0.212865 - 7.02690i) q^{84} -4.37524i q^{85} +(-3.14592 - 1.81630i) q^{86} +(4.69577 + 8.73382i) q^{87} +2.68073 q^{88} +(8.62292 + 4.97845i) q^{89} +(6.78540 + 13.5917i) q^{90} +(7.81439 + 3.07359i) q^{91} +(-3.66748 - 6.35226i) q^{92} +(0.457249 - 15.0943i) q^{93} +(5.00184 + 8.66343i) q^{94} -5.75321 q^{95} +(11.6101 - 6.24222i) q^{96} +(2.03695 + 1.17603i) q^{97} +(2.64054 - 1.52452i) q^{98} +(13.4815 + 8.91312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more