LMFDB - Embedded newform 950.2.h.b.191.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.7
Character	$\chi$	$=$	950.191
Dual form			950.2.h.b.761.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.272680 + 0.839224i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.404965 + 2.19909i) q^{5} +(0.272680 - 0.839224i) q^{6} -4.83673 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.79711 - 1.30568i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.272680 + 0.839224i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.404965 + 2.19909i) q^{5} +(0.272680 - 0.839224i) q^{6} -4.83673 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.79711 - 1.30568i) q^{9} +(0.964970 - 2.01713i) q^{10} +(-3.36423 - 2.44426i) q^{11} +(-0.713886 + 0.518669i) q^{12} +(1.69159 - 1.22901i) q^{13} +(3.91299 + 2.84296i) q^{14} +(-1.73510 + 0.939505i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.451195 - 1.38864i) q^{17} -2.22135 q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.96632 + 1.06470i) q^{20} +(-1.31888 - 4.05909i) q^{21} +(1.28502 + 3.95489i) q^{22} +(-3.34168 - 2.42787i) q^{23} +0.882412 q^{24} +(-4.67201 + 1.78111i) q^{25} -2.09092 q^{26} +(3.72745 + 2.70815i) q^{27} +(-1.49463 - 4.60000i) q^{28} +(0.683833 + 2.10462i) q^{29} +(1.95596 + 0.259793i) q^{30} +(2.45331 - 7.55052i) q^{31} +1.00000 q^{32} +(1.13392 - 3.48984i) q^{33} +(-1.18124 + 0.858224i) q^{34} +(-1.95870 - 10.6364i) q^{35} +(1.79711 + 1.30568i) q^{36} +(2.22250 - 1.61474i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(1.49268 + 1.08450i) q^{39} +(2.21660 + 0.294412i) q^{40} +(8.48173 - 6.16234i) q^{41} +(-1.31888 + 4.05909i) q^{42} -9.95970 q^{43} +(1.28502 - 3.95489i) q^{44} +(3.59907 + 3.42326i) q^{45} +(1.27641 + 3.92838i) q^{46} +(0.642918 + 1.97870i) q^{47} +(-0.713886 - 0.518669i) q^{48} +16.3939 q^{49} +(4.82664 + 1.30519i) q^{50} +1.28841 q^{51} +(1.69159 + 1.22901i) q^{52} +(-1.84270 - 5.67123i) q^{53} +(-1.42376 - 4.38188i) q^{54} +(4.01275 - 8.38809i) q^{55} +(-1.49463 + 4.60000i) q^{56} +0.882412 q^{57} +(0.683833 - 2.10462i) q^{58} +(4.19204 - 3.04570i) q^{59} +(-1.42970 - 1.35986i) q^{60} +(-0.825353 - 0.599654i) q^{61} +(-6.42285 + 4.66648i) q^{62} +(-8.69213 + 6.31520i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.38775 + 3.22226i) q^{65} +(-2.96864 + 2.15684i) q^{66} +(-0.0474555 + 0.146053i) q^{67} +1.46010 q^{68} +(1.12632 - 3.46645i) q^{69} +(-4.66730 + 9.75633i) q^{70} +(2.75231 + 8.47075i) q^{71} +(-0.686435 - 2.11263i) q^{72} +(2.07559 + 1.50800i) q^{73} -2.74717 q^{74} +(-2.76871 - 3.43519i) q^{75} +1.00000 q^{76} +(16.2719 + 11.8222i) q^{77} +(-0.570154 - 1.75475i) q^{78} +(-2.24994 - 6.92459i) q^{79} +(-1.62022 - 1.54107i) q^{80} +(0.802962 - 2.47126i) q^{81} -10.4840 q^{82} +(4.66424 - 14.3551i) q^{83} +(3.45287 - 2.50866i) q^{84} +(3.23645 + 0.429871i) q^{85} +(8.05757 + 5.85417i) q^{86} +(-1.57978 + 1.14778i) q^{87} +(-3.36423 + 2.44426i) q^{88} +(-15.0562 - 10.9390i) q^{89} +(-0.899568 - 4.88495i) q^{90} +(-8.18177 + 5.94441i) q^{91} +(1.27641 - 3.92838i) q^{92} +7.00554 q^{93} +(0.642918 - 1.97870i) q^{94} +(2.21660 + 0.294412i) q^{95} +(0.272680 + 0.839224i) q^{96} +(-0.505744 - 1.55652i) q^{97} +(-13.2630 - 9.63610i) q^{98} -9.23730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.272680	+	0.839224i	0.157432	+	0.484526i	0.998399	−	0.0565602i	$-0.0180133\pi$
$3$	0.272680	+	0.839224i	0.157432	+	0.484526i	−0.840967	+	0.541086i	$0.818013\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.404965	+	2.19909i	0.181106	+	0.983464i
$5$	0.404965	+	2.19909i	0.181106	+	0.983464i
$6$	0.272680	−	0.839224i	0.111321	−	0.342612i
$7$	−4.83673			−1.82811			−0.914055	−	0.405590i	$-0.867066\pi$
$7$	−4.83673			−1.82811			−0.914055	+	0.405590i	$0.867066\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	1.79711	−	1.30568i	0.599036	−	0.435225i
$10$	0.964970	−	2.01713i	0.305150	−	0.637874i
$11$	−3.36423	−	2.44426i	−1.01435	−	0.736971i	−0.0492361	−	0.998787i	$-0.515679\pi$
$11$	−3.36423	−	2.44426i	−1.01435	−	0.736971i	−0.965118	+	0.261816i	$0.915679\pi$
$12$	−0.713886	+	0.518669i	−0.206081	+	0.149727i
$13$	1.69159	−	1.22901i	0.469164	−	0.340867i	−0.327952	−	0.944694i	$-0.606358\pi$
$13$	1.69159	−	1.22901i	0.469164	−	0.340867i	0.797115	+	0.603827i	$0.206358\pi$
$14$	3.91299	+	2.84296i	1.04579	+	0.759812i
$15$	−1.73510	+	0.939505i	−0.448002	+	0.242579i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.451195	−	1.38864i	0.109431	−	0.336794i	−0.881314	−	0.472531i	$-0.843340\pi$
$17$	0.451195	−	1.38864i	0.109431	−	0.336794i	0.990745	+	0.135738i	$0.0433404\pi$
$18$	−2.22135			−0.523577
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−1.96632	+	1.06470i	−0.439682	+	0.238074i
$21$	−1.31888	−	4.05909i	−0.287803	−	0.885767i
$22$	1.28502	+	3.95489i	0.273968	+	0.843186i
$23$	−3.34168	−	2.42787i	−0.696788	−	0.506246i	0.182097	−	0.983281i	$-0.441712\pi$
$23$	−3.34168	−	2.42787i	−0.696788	−	0.506246i	−0.878884	+	0.477035i	$0.841712\pi$
$24$	0.882412			0.180122
$25$	−4.67201	+	1.78111i	−0.934401	+	0.356222i
$26$	−2.09092			−0.410064
$27$	3.72745	+	2.70815i	0.717348	+	0.521184i
$28$	−1.49463	−	4.60000i	−0.282459	−	0.869318i
$29$	0.683833	+	2.10462i	0.126985	+	0.390818i	0.994257	−	0.107015i	$-0.0341292\pi$
$29$	0.683833	+	2.10462i	0.126985	+	0.390818i	−0.867273	+	0.497833i	$0.834129\pi$
$30$	1.95596	+	0.259793i	0.357107	+	0.0474315i
$31$	2.45331	−	7.55052i	0.440628	−	1.35611i	−0.446580	−	0.894743i	$-0.647358\pi$
$31$	2.45331	−	7.55052i	0.440628	−	1.35611i	0.887208	−	0.461369i	$-0.152642\pi$
$32$	1.00000			0.176777
$33$	1.13392	−	3.48984i	0.197390	−	0.607504i
$34$	−1.18124	+	0.858224i	−0.202582	+	0.147184i
$35$	−1.95870	−	10.6364i	−0.331081	−	1.79788i
$36$	1.79711	+	1.30568i	0.299518	+	0.217613i
$37$	2.22250	−	1.61474i	0.365377	−	0.265462i	−0.389914	−	0.920851i	$-0.627495\pi$
$37$	2.22250	−	1.61474i	0.365377	−	0.265462i	0.755291	+	0.655389i	$0.227495\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	1.49268	+	1.08450i	0.239020	+	0.173658i
$40$	2.21660	+	0.294412i	0.350475	+	0.0465507i
$41$	8.48173	−	6.16234i	1.32462	−	0.962396i	0.324762	−	0.945796i	$-0.394716\pi$
$41$	8.48173	−	6.16234i	1.32462	−	0.962396i	0.999862	−	0.0165998i	$-0.00528412\pi$
$42$	−1.31888	+	4.05909i	−0.203508	+	0.626332i
$43$	−9.95970			−1.51884			−0.759420	−	0.650601i	$-0.774517\pi$
$43$	−9.95970			−1.51884			−0.759420	+	0.650601i	$0.774517\pi$
$44$	1.28502	−	3.95489i	0.193724	−	0.596222i
$45$	3.59907	+	3.42326i	0.536517	+	0.510309i
$46$	1.27641	+	3.92838i	0.188196	+	0.579208i
$47$	0.642918	+	1.97870i	0.0937793	+	0.288623i	0.986934	−	0.161127i	$-0.0515130\pi$
$47$	0.642918	+	1.97870i	0.0937793	+	0.288623i	−0.893154	+	0.449750i	$0.851513\pi$
$48$	−0.713886	−	0.518669i	−0.103041	−	0.0748634i
$49$	16.3939			2.34199
$50$	4.82664	+	1.30519i	0.682590	+	0.184582i
$51$	1.28841			0.180413
$52$	1.69159	+	1.22901i	0.234582	+	0.170434i
$53$	−1.84270	−	5.67123i	−0.253114	−	0.779004i	−0.994195	−	0.107589i	$-0.965687\pi$
$53$	−1.84270	−	5.67123i	−0.253114	−	0.779004i	0.741082	−	0.671415i	$-0.234313\pi$
$54$	−1.42376	−	4.38188i	−0.193749	−	0.596298i
$55$	4.01275	−	8.38809i	0.541079	−	1.13105i
$56$	−1.49463	+	4.60000i	−0.199728	+	0.614701i
$57$	0.882412			0.116878
$58$	0.683833	−	2.10462i	0.0897916	−	0.276350i
$59$	4.19204	−	3.04570i	0.545757	−	0.396516i	−0.280462	−	0.959865i	$-0.590488\pi$
$59$	4.19204	−	3.04570i	0.545757	−	0.396516i	0.826219	+	0.563349i	$0.190488\pi$
$60$	−1.42970	−	1.35986i	−0.184573	−	0.175557i
$61$	−0.825353	−	0.599654i	−0.105676	−	0.0767778i	0.533692	−	0.845679i	$-0.320804\pi$
$61$	−0.825353	−	0.599654i	−0.105676	−	0.0767778i	−0.639368	+	0.768901i	$0.720804\pi$
$62$	−6.42285	+	4.66648i	−0.815703	+	0.592643i
$63$	−8.69213	+	6.31520i	−1.09510	+	0.795640i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.38775	+	3.22226i	0.420199	+	0.399672i
$66$	−2.96864	+	2.15684i	−0.365414	+	0.265489i
$67$	−0.0474555	+	0.146053i	−0.00579761	+	0.0178432i	−0.953913	−	0.300082i	$-0.902986\pi$
$67$	−0.0474555	+	0.146053i	−0.00579761	+	0.0178432i	0.948116	+	0.317925i	$0.102986\pi$
$68$	1.46010			0.177063
$69$	1.12632	−	3.46645i	0.135593	−	0.417311i
$70$	−4.66730	+	9.75633i	−0.557849	+	1.16610i
$71$	2.75231	+	8.47075i	0.326640	+	1.00529i	0.970695	+	0.240315i	$0.0772506\pi$
$71$	2.75231	+	8.47075i	0.326640	+	1.00529i	−0.644055	+	0.764979i	$0.722749\pi$
$72$	−0.686435	−	2.11263i	−0.0808971	−	0.248976i
$73$	2.07559	+	1.50800i	0.242929	+	0.176498i	0.702587	−	0.711598i	$-0.252028\pi$
$73$	2.07559	+	1.50800i	0.242929	+	0.176498i	−0.459658	+	0.888096i	$0.652028\pi$
$74$	−2.74717			−0.319352
$75$	−2.76871	−	3.43519i	−0.319703	−	0.396661i
$76$	1.00000			0.114708
$77$	16.2719	+	11.8222i	1.85435	+	1.34727i
$78$	−0.570154	−	1.75475i	−0.0645572	−	0.198687i
$79$	−2.24994	−	6.92459i	−0.253138	−	0.779077i	−0.994191	−	0.107631i	$-0.965673\pi$
$79$	−2.24994	−	6.92459i	−0.253138	−	0.779077i	0.741053	−	0.671446i	$-0.234327\pi$
$80$	−1.62022	−	1.54107i	−0.181146	−	0.172297i
$81$	0.802962	−	2.47126i	0.0892180	−	0.274585i
$82$	−10.4840			−1.15776
$83$	4.66424	−	14.3551i	0.511967	−	1.57567i	−0.276766	−	0.960937i	$-0.589263\pi$
$83$	4.66424	−	14.3551i	0.511967	−	1.57567i	0.788733	−	0.614736i	$-0.210737\pi$
$84$	3.45287	−	2.50866i	0.376739	−	0.273717i
$85$	3.23645	+	0.429871i	0.351043	+	0.0466260i
$86$	8.05757	+	5.85417i	0.868870	+	0.631271i
$87$	−1.57978	+	1.14778i	−0.169370	+	0.123055i
$88$	−3.36423	+	2.44426i	−0.358628	+	0.260559i
$89$	−15.0562	−	10.9390i	−1.59595	−	1.15953i	−0.894753	−	0.446562i	$-0.852648\pi$
$89$	−15.0562	−	10.9390i	−1.59595	−	1.15953i	−0.701200	−	0.712965i	$-0.747352\pi$
$90$	−0.899568	−	4.88495i	−0.0948228	−	0.514919i
$91$	−8.18177	+	5.94441i	−0.857683	+	0.623143i
$92$	1.27641	−	3.92838i	0.133075	−	0.409562i
$93$	7.00554			0.726441
$94$	0.642918	−	1.97870i	0.0663120	−	0.204087i
$95$	2.21660	+	0.294412i	0.227418	+	0.0302061i
$96$	0.272680	+	0.839224i	0.0278303	+	0.0856529i
$97$	−0.505744	−	1.55652i	−0.0513505	−	0.158041i	0.922093	−	0.386969i	$-0.126478\pi$
$97$	−0.505744	−	1.55652i	−0.0513505	−	0.158041i	−0.973443	+	0.228928i	$0.926478\pi$
$98$	−13.2630	−	9.63610i	−1.33976	−	0.973394i
$99$	−9.23730			−0.928384
$100$	−3.13766	−	3.89295i	−0.313766	−	0.389295i
$101$	−18.5248			−1.84328			−0.921642	−	0.388041i	$-0.873152\pi$
$101$	−18.5248			−1.84328			−0.921642	+	0.388041i	$0.873152\pi$
$102$	−1.04234	−	0.757307i	−0.103207	−	0.0749846i
$103$	1.50070	+	4.61869i	0.147869	+	0.455093i	0.997369	−	0.0724956i	$-0.0230963\pi$
$103$	1.50070	+	4.61869i	0.147869	+	0.455093i	−0.849500	+	0.527588i	$0.823096\pi$
$104$	−0.646131	−	1.98859i	−0.0633584	−	0.194997i
$105$	8.39222	−	4.54413i	0.818997	−	0.443461i
$106$	−1.84270	+	5.67123i	−0.178978	+	0.550839i
$107$	−17.8086			−1.72162			−0.860810	−	0.508927i	$-0.830042\pi$
$107$	−17.8086			−1.72162			−0.860810	+	0.508927i	$0.830042\pi$
$108$	−1.42376	+	4.38188i	−0.137001	+	0.421647i
$109$	4.84527	−	3.52030i	0.464093	−	0.337183i	−0.331042	−	0.943616i	$-0.607400\pi$
$109$	4.84527	−	3.52030i	0.464093	−	0.337183i	0.795135	+	0.606433i	$0.207400\pi$
$110$	−8.17678	+	4.42747i	−0.779625	+	0.422143i
$111$	1.96116	+	1.42487i	0.186145	+	0.135243i
$112$	3.91299	−	2.84296i	0.369743	−	0.268634i
$113$	−12.5836	+	9.14250i	−1.18376	+	0.860054i	−0.992591	−	0.121503i	$-0.961229\pi$
$113$	−12.5836	+	9.14250i	−1.18376	+	0.860054i	−0.191172	+	0.981557i	$0.561229\pi$
$114$	−0.713886	−	0.518669i	−0.0668616	−	0.0485778i
$115$	3.98585	−	8.33186i	0.371682	−	0.776950i
$116$	−1.79030	+	1.30073i	−0.166225	+	0.120769i
$117$	1.43528	−	4.41735i	0.132692	−	0.408384i
$118$	−5.18165			−0.477009
$119$	−2.18231	+	6.71645i	−0.200052	+	0.615696i
$120$	0.357346	+	1.94050i	0.0326210	+	0.177143i
$121$	1.94447	+	5.98447i	0.176770	+	0.544043i
$122$	0.315257	+	0.970261i	0.0285420	+	0.0878433i
$123$	7.48438	+	5.43772i	0.674844	+	0.490303i
$124$	7.93908			0.712951
$125$	−5.80882	−	9.55289i	−0.519557	−	0.854436i
$126$	10.7441			0.957157
$127$	2.89524	+	2.10352i	0.256911	+	0.186657i	0.708784	−	0.705425i	$-0.249244\pi$
$127$	2.89524	+	2.10352i	0.256911	+	0.186657i	−0.451873	+	0.892082i	$0.649244\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.71581	−	8.35842i	−0.239114	−	0.735917i
$130$	−0.846751	−	4.59813i	−0.0742649	−	0.403283i
$131$	5.54182	−	17.0560i	0.484191	−	1.49019i	−0.348958	−	0.937138i	$-0.613464\pi$
$131$	5.54182	−	17.0560i	0.484191	−	1.49019i	0.833149	−	0.553048i	$-0.186536\pi$
$132$	3.66944			0.319384
$133$	−1.49463	+	4.60000i	−0.129601	+	0.398871i
$134$	0.124240	−	0.0902656i	0.0107327	−	0.00779776i
$135$	−4.44599	+	9.29371i	−0.382649	+	0.799875i
$136$	−1.18124	−	0.858224i	−0.101291	−	0.0735921i
$137$	7.40435	−	5.37957i	0.632596	−	0.459608i	−0.224703	−	0.974427i	$-0.572141\pi$
$137$	7.40435	−	5.37957i	0.632596	−	0.459608i	0.857299	+	0.514819i	$0.172141\pi$
$138$	−2.94874	+	2.14238i	−0.251013	+	0.182372i
$139$	9.05843	+	6.58134i	0.768326	+	0.558222i	0.901453	−	0.432877i	$-0.142502\pi$
$139$	9.05843	+	6.58134i	0.768326	+	0.558222i	−0.133127	+	0.991099i	$0.542502\pi$
$140$	9.51055	−	5.14967i	0.803788	−	0.435226i
$141$	−1.48526	+	1.07910i	−0.125081	+	0.0908770i
$142$	2.75231	−	8.47075i	0.230969	−	0.710850i
$143$	−8.69494			−0.727107
$144$	−0.686435	+	2.11263i	−0.0572029	+	0.176052i
$145$	−4.35132	+	2.35611i	−0.361358	+	0.195664i
$146$	−0.792804	−	2.44000i	−0.0656129	−	0.201936i
$147$	4.47030	+	13.7582i	0.368704	+	1.13475i
$148$	2.22250	+	1.61474i	0.182689	+	0.132731i
$149$	−9.64264			−0.789956			−0.394978	−	0.918691i	$-0.629248\pi$
$149$	−9.64264			−0.789956			−0.394978	+	0.918691i	$0.629248\pi$
$150$	0.220785	+	4.40653i	0.0180270	+	0.359792i
$151$	3.39680			0.276428			0.138214	−	0.990402i	$-0.455864\pi$
$151$	3.39680			0.276428			0.138214	+	0.990402i	$0.455864\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−1.00226	−	3.08464i	−0.0810281	−	0.249379i
$154$	−6.21530	−	19.1287i	−0.500843	−	1.54144i
$155$	17.5978	+	2.33736i	1.41349	+	0.187742i
$156$	−0.570154	+	1.75475i	−0.0456488	+	0.140493i
$157$	−15.0226			−1.19894			−0.599468	−	0.800399i	$-0.704621\pi$
$157$	−15.0226			−1.19894			−0.599468	+	0.800399i	$0.704621\pi$
$158$	−2.24994	+	6.92459i	−0.178995	+	0.550891i
$159$	4.25697	−	3.09287i	0.337599	−	0.245280i
$160$	0.404965	+	2.19909i	0.0320153	+	0.173853i
$161$	16.1628	+	11.7429i	1.27381	+	0.925474i
$162$	−2.10218	+	1.52733i	−0.165163	+	0.119998i
$163$	6.03500	−	4.38469i	0.472698	−	0.343435i	−0.325794	−	0.945441i	$-0.605632\pi$
$163$	6.03500	−	4.38469i	0.472698	−	0.343435i	0.798492	+	0.602006i	$0.205632\pi$
$164$	8.48173	+	6.16234i	0.662312	+	0.481198i
$165$	8.13368	+	1.08033i	0.633206	+	0.0841034i
$166$	−12.2111	+	8.87192i	−0.947769	+	0.688594i
$167$	−6.12911	+	18.8635i	−0.474285	+	1.45970i	0.372636	+	0.927978i	$0.378454\pi$
$167$	−6.12911	+	18.8635i	−0.474285	+	1.45970i	−0.846920	+	0.531720i	$0.821546\pi$
$168$	−4.26798			−0.329282
$169$	−2.66621	+	8.20575i	−0.205093	+	0.631212i
$170$	−2.36568	−	2.25011i	−0.181439	−	0.172576i
$171$	−0.686435	−	2.11263i	−0.0524930	−	0.161557i
$172$	−3.07772	−	9.47224i	−0.234674	−	0.722251i
$173$	−13.6407	−	9.91057i	−1.03709	−	0.753487i	−0.0673710	−	0.997728i	$-0.521461\pi$
$173$	−13.6407	−	9.91057i	−1.03709	−	0.753487i	−0.969715	+	0.244241i	$0.921461\pi$
$174$	1.95271			0.148035
$175$	22.5972	−	8.61474i	1.70819	−	0.651213i
$176$	4.15842			0.313453
$177$	3.69911	+	2.68756i	0.278042	+	0.202009i
$178$	5.75095	+	17.6996i	0.431052	+	1.32664i
$179$	−1.20238	−	3.70055i	−0.0898702	−	0.276592i	0.896013	−	0.444029i	$-0.146451\pi$
$179$	−1.20238	−	3.70055i	−0.0898702	−	0.276592i	−0.985883	+	0.167436i	$0.946451\pi$
$180$	−2.14354	+	4.48076i	−0.159770	+	0.333976i
$181$	−2.87113	+	8.83642i	−0.213409	+	0.656806i	0.785854	+	0.618413i	$0.212224\pi$
$181$	−2.87113	+	8.83642i	−0.213409	+	0.656806i	−0.999263	+	0.0383931i	$0.987776\pi$
$182$	10.1132			0.749642
$183$	0.278186	−	0.856169i	0.0205641	−	0.0632899i
$184$	−3.34168	+	2.42787i	−0.246352	+	0.178985i
$185$	4.45100	+	4.23358i	0.327244	+	0.311259i
$186$	−5.66760	−	4.11775i	−0.415569	−	0.301928i
$187$	−4.91211	+	3.56885i	−0.359209	+	0.260980i
$188$	−1.68318	+	1.22290i	−0.122759	+	0.0891894i
$189$	−18.0287	−	13.0986i	−1.31139	−	0.952782i
$190$	−1.62022	−	1.54107i	−0.117543	−	0.111801i
$191$	−14.5459	+	10.5682i	−1.05250	+	0.764688i	−0.972687	−	0.232121i	$-0.925433\pi$
$191$	−14.5459	+	10.5682i	−1.05250	+	0.764688i	−0.0798164	+	0.996810i	$0.525433\pi$
$192$	0.272680	−	0.839224i	0.0196790	−	0.0605657i
$193$	−10.8290			−0.779491			−0.389746	−	0.920923i	$-0.627437\pi$
$193$	−10.8290			−0.779491			−0.389746	+	0.920923i	$0.627437\pi$
$194$	−0.505744	+	1.55652i	−0.0363103	+	0.111752i
$195$	−1.78042	+	3.72173i	−0.127499	+	0.266518i
$196$	5.06600	+	15.5915i	0.361857	+	1.11368i
$197$	0.0165249	+	0.0508585i	0.00117735	+	0.00362352i	0.951643	−	0.307205i	$-0.0993936\pi$
$197$	0.0165249	+	0.0508585i	0.00117735	+	0.00362352i	−0.950466	+	0.310828i	$0.899394\pi$
$198$	7.47313	+	5.42955i	0.531092	+	0.385861i
$199$	22.7215			1.61068			0.805342	−	0.592811i	$-0.201982\pi$
$199$	22.7215			1.61068			0.805342	+	0.592811i	$0.201982\pi$
$200$	0.250206	+	4.99374i	0.0176922	+	0.353110i
$201$	−0.135511			−0.00955822
$202$	14.9869	+	10.8886i	1.05447	+	0.766119i
$203$	−3.30751	−	10.1795i	−0.232142	−	0.714459i
$204$	0.398140	+	1.22535i	0.0278754	+	0.0857915i
$205$	16.9863	+	16.1566i	1.18638	+	1.12842i
$206$	1.50070	−	4.61869i	0.104559	−	0.321799i
$207$	−9.17537			−0.637732
$208$	−0.646131	+	1.98859i	−0.0448011	+	0.137884i
$209$	−3.36423	+	2.44426i	−0.232709	+	0.169073i
$210$	−9.46042	−	1.25655i	−0.652831	−	0.0867100i
$211$	−6.72903	−	4.88893i	−0.463245	−	0.336567i	0.331558	−	0.943435i	$-0.392426\pi$
$211$	−6.72903	−	4.88893i	−0.463245	−	0.336567i	−0.794803	+	0.606867i	$0.792426\pi$
$212$	4.82424	−	3.50502i	0.331330	−	0.240725i
$213$	−6.35835	+	4.61961i	−0.435667	+	0.316531i
$214$	14.4074	+	10.4676i	0.984872	+	0.715551i
$215$	−4.03333	−	21.9023i	−0.275071	−	1.49372i
$216$	3.72745	−	2.70815i	0.253621	−	0.184266i
$217$	−11.8660	+	36.5198i	−0.805516	+	2.47912i
$218$	−5.98908			−0.405632
$219$	−0.699579	+	2.15308i	−0.0472732	+	0.145492i
$220$	9.21756	+	1.22429i	0.621448	+	0.0825416i
$221$	−0.943415	−	2.90353i	−0.0634609	−	0.195313i
$222$	−0.749098	−	2.30549i	−0.0502762	−	0.154734i
$223$	14.3327	+	10.4133i	0.959789	+	0.697328i	0.953102	−	0.302650i	$-0.0978713\pi$
$223$	14.3327	+	10.4133i	0.959789	+	0.697328i	0.00668741	+	0.999978i	$0.497871\pi$
$224$	−4.83673			−0.323167
$225$	−6.07056	+	9.30098i	−0.404704	+	0.620065i
$226$	15.5541			1.03465
$227$	8.84126	+	6.42355i	0.586815	+	0.426346i	0.841175	−	0.540764i	$-0.181865\pi$
$227$	8.84126	+	6.42355i	0.586815	+	0.426346i	−0.254360	+	0.967110i	$0.581865\pi$
$228$	0.272680	+	0.839224i	0.0180587	+	0.0555789i
$229$	4.86732	+	14.9801i	0.321642	+	0.989911i	0.972934	+	0.231084i	$0.0742273\pi$
$229$	4.86732	+	14.9801i	0.321642	+	0.989911i	−0.651292	+	0.758827i	$0.725773\pi$
$230$	−8.12196	+	4.39779i	−0.535546	+	0.289982i
$231$	−5.48445	+	16.8794i	−0.360851	+	1.11058i
$232$	2.21293			0.145286
$233$	5.50171	−	16.9325i	0.360429	−	1.10929i	−0.592365	−	0.805670i	$-0.701806\pi$
$233$	5.50171	−	16.9325i	0.360429	−	1.10929i	0.952794	−	0.303617i	$-0.0981942\pi$
$234$	−3.75762	+	2.73007i	−0.245643	+	0.178470i
$235$	−4.09098	+	2.21514i	−0.266866	+	0.144500i
$236$	4.19204	+	3.04570i	0.272879	+	0.198258i
$237$	5.19777	−	3.77640i	0.337631	−	0.245303i
$238$	5.71335	−	4.15099i	0.370342	−	0.269069i
$239$	−9.99174	−	7.25942i	−0.646312	−	0.469573i	0.215701	−	0.976459i	$-0.430796\pi$
$239$	−9.99174	−	7.25942i	−0.646312	−	0.469573i	−0.862013	+	0.506886i	$0.830796\pi$
$240$	0.851501	−	1.77994i	0.0549642	−	0.114895i
$241$	22.3689	−	16.2520i	1.44091	−	1.04688i	0.453059	−	0.891481i	$-0.350333\pi$
$241$	22.3689	−	16.2520i	1.44091	−	1.04688i	0.987851	−	0.155402i	$-0.0496673\pi$
$242$	1.94447	−	5.98447i	0.124995	−	0.384696i
$243$	16.1150			1.03378
$244$	0.315257	−	0.970261i	0.0201822	−	0.0621146i
$245$	6.63896	+	36.0517i	0.424148	+	2.30326i
$246$	−2.85878	−	8.79842i	−0.182269	−	0.560967i
$247$	−0.646131	−	1.98859i	−0.0411123	−	0.126531i
$248$	−6.42285	−	4.66648i	−0.407852	−	0.296322i
$249$	13.3190			0.844055
$250$	−0.915611	+	11.1428i	−0.0579083	+	0.704732i
$251$	−16.8768			−1.06525			−0.532627	−	0.846350i	$-0.678795\pi$
$251$	−16.8768			−1.06525			−0.532627	+	0.846350i	$0.678795\pi$
$252$	−8.69213	−	6.31520i	−0.547552	−	0.397820i
$253$	5.30783	+	16.3358i	0.333701	+	1.02703i
$254$	−1.10588	−	3.40356i	−0.0693893	−	0.213558i
$255$	0.521760	+	2.83333i	0.0326739	+	0.177430i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.85158			0.302634			0.151317	−	0.988485i	$-0.451649\pi$
$257$	4.85158			0.302634			0.151317	+	0.988485i	$0.451649\pi$
$258$	−2.71581	+	8.35842i	−0.169079	+	0.520372i
$259$	−10.7496	+	7.81007i	−0.667950	+	0.485294i
$260$	−2.01768	+	4.21768i	−0.125131	+	0.261569i
$261$	3.97687	+	2.88937i	0.246162	+	0.178847i
$262$	−14.5087	+	10.5412i	−0.896349	+	0.651235i
$263$	9.04437	−	6.57112i	0.557700	−	0.405193i	−0.272916	−	0.962038i	$-0.587988\pi$
$263$	9.04437	−	6.57112i	0.557700	−	0.405193i	0.830616	+	0.556845i	$0.187988\pi$
$264$	−2.96864	−	2.15684i	−0.182707	−	0.132744i
$265$	11.7253	−	6.34891i	0.720282	−	0.390010i
$266$	3.91299	−	2.84296i	0.239921	−	0.174313i
$267$	5.07471	−	15.6183i	0.310567	−	0.955827i
$268$	−0.153569			−0.00938072
$269$	−3.41524	+	10.5110i	−0.208231	+	0.640868i	0.791335	+	0.611383i	$0.209387\pi$
$269$	−3.41524	+	10.5110i	−0.208231	+	0.640868i	−0.999565	+	0.0294848i	$0.990613\pi$
$270$	9.05958	−	4.90548i	0.551349	−	0.298538i
$271$	2.10201	+	6.46933i	0.127688	+	0.392984i	0.994381	−	0.105858i	$-0.0337589\pi$
$271$	2.10201	+	6.46933i	0.127688	+	0.392984i	−0.866693	+	0.498842i	$0.833759\pi$
$272$	0.451195	+	1.38864i	0.0273577	+	0.0841984i
$273$	−7.21969	−	5.24541i	−0.436956	−	0.317467i
$274$	−9.15228			−0.552909
$275$	20.0712	+	5.42752i	1.21034	+	0.327292i
$276$	3.64484			0.219393
$277$	7.34414	+	5.33583i	0.441267	+	0.320599i	0.786138	−	0.618051i	$-0.212077\pi$
$277$	7.34414	+	5.33583i	0.441267	+	0.320599i	−0.344871	+	0.938650i	$0.612077\pi$
$278$	−3.46001	−	10.6488i	−0.207518	−	0.638674i
$279$	−5.44966	−	16.7723i	−0.326263	−	1.00413i
$280$	−10.7211	−	1.42399i	−0.640708	−	0.0850998i
$281$	0.0892735	−	0.274756i	0.00532561	−	0.0163906i	−0.948358	−	0.317201i	$-0.897257\pi$
$281$	0.0892735	−	0.274756i	0.00532561	−	0.0163906i	0.953684	+	0.300810i	$0.0972571\pi$
$282$	1.83588			0.109325
$283$	4.01169	−	12.3467i	0.238470	−	0.733936i	−0.758172	−	0.652055i	$-0.773907\pi$
$283$	4.01169	−	12.3467i	0.238470	−	0.733936i	0.996642	−	0.0818813i	$-0.0260928\pi$
$284$	−7.20565	+	5.23521i	−0.427577	+	0.310653i
$285$	0.357346	+	1.94050i	0.0211673	+	0.114946i
$286$	7.03435	+	5.11076i	0.415950	+	0.302205i
$287$	−41.0238	+	29.8055i	−2.42156	+	1.75937i
$288$	1.79711	−	1.30568i	0.105896	−	0.0769377i
$289$	12.0286	+	8.73926i	0.707562	+	0.514074i
$290$	4.90518	+	0.651513i	0.288042	+	0.0382582i
$291$	1.16836	−	0.848865i	0.0684906	−	0.0497613i
$292$	−0.792804	+	2.44000i	−0.0463953	+	0.142790i
$293$	−19.4380			−1.13558			−0.567791	−	0.823173i	$-0.692202\pi$
$293$	−19.4380			−1.13558			−0.567791	+	0.823173i	$0.692202\pi$
$294$	4.47030	−	13.7582i	0.260713	−	0.802392i
$295$	8.39539	+	7.98528i	0.488799	+	0.464921i
$296$	−0.848921	−	2.61271i	−0.0493425	−	0.151861i
$297$	−5.92059	−	18.2217i	−0.343547	−	1.05733i
$298$	7.80106	+	5.66780i	0.451903	+	0.328327i
$299$	−8.63665			−0.499470
$300$	2.41148	−	3.69473i	0.139227	−	0.213316i
$301$	48.1723			2.77661
$302$	−2.74807	−	1.99659i	−0.158134	−	0.114891i
$303$	−5.05134	−	15.5464i	−0.290192	−	0.893119i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	0.984455	−	2.05787i	0.0563697	−	0.117833i
$306$	−1.00226	+	3.08464i	−0.0572955	+	0.176337i
$307$	−21.2455			−1.21255			−0.606274	−	0.795256i	$-0.707336\pi$
$307$	−21.2455			−1.21255			−0.606274	+	0.795256i	$0.707336\pi$
$308$	−6.21530	+	19.1287i	−0.354150	+	1.08996i
$309$	−3.46690	+	2.51885i	−0.197225	+	0.143292i
$310$	−12.8630	−	12.2347i	−0.730571	−	0.694883i
$311$	16.8947	+	12.2747i	0.958010	+	0.696035i	0.952688	−	0.303951i	$-0.0983059\pi$
$311$	16.8947	+	12.2747i	0.958010	+	0.696035i	0.00532218	+	0.999986i	$0.498306\pi$
$312$	1.49268	−	1.08450i	0.0845065	−	0.0613975i
$313$	11.0429	−	8.02315i	0.624183	−	0.453495i	−0.230197	−	0.973144i	$-0.573937\pi$
$313$	11.0429	−	8.02315i	0.624183	−	0.453495i	0.854380	+	0.519649i	$0.173937\pi$
$314$	12.1536	+	8.83008i	0.685865	+	0.498310i
$315$	−17.4077	−	16.5573i	−0.980813	−	0.932901i
$316$	5.89041	−	4.27963i	0.331361	−	0.240748i
$317$	1.36377	−	4.19725i	0.0765970	−	0.235741i	−0.905426	−	0.424505i	$-0.860448\pi$
$317$	1.36377	−	4.19725i	0.0765970	−	0.235741i	0.982022	+	0.188764i	$0.0604481\pi$
$318$	−5.26190			−0.295073
$319$	2.84366	−	8.75189i	0.159215	−	0.490012i
$320$	0.964970	−	2.01713i	0.0539435	−	0.112761i
$321$	−4.85604	−	14.9454i	−0.271038	−	0.834169i
$322$	−6.17363	−	19.0005i	−0.344043	−	1.05886i
$323$	−1.18124	−	0.858224i	−0.0657262	−	0.0477529i
$324$	2.59844			0.144358
$325$	−5.71413	+	8.75488i	−0.316963	+	0.485633i
$326$	−7.45968			−0.413153
$327$	4.27552	+	3.10635i	0.236437	+	0.171782i
$328$	−3.23973	−	9.97087i	−0.178884	−	0.550549i
$329$	−3.10962	−	9.57043i	−0.171439	−	0.527635i
$330$	−5.94529	−	5.65486i	−0.327277	−	0.311290i
$331$	5.48091	−	16.8685i	0.301258	−	0.927176i	−0.679789	−	0.733407i	$-0.737929\pi$
$331$	5.48091	−	16.8685i	0.301258	−	0.927176i	0.981047	−	0.193769i	$-0.0620712\pi$
$332$	15.0938			0.828380
$333$	1.88575	−	5.80374i	0.103338	−	0.318043i
$334$	16.0462	−	11.6583i	0.878010	−	0.637911i
$335$	−0.340401	−	0.0452126i	−0.0185981	−	0.00247023i
$336$	3.45287	+	2.50866i	0.188370	+	0.136859i
$337$	7.39298	−	5.37131i	0.402721	−	0.292594i	−0.367927	−	0.929855i	$-0.619932\pi$
$337$	7.39298	−	5.37131i	0.402721	−	0.292594i	0.770648	+	0.637261i	$0.219932\pi$
$338$	6.98023	−	5.07143i	0.379674	−	0.275850i
$339$	−11.1039	−	8.06745i	−0.603081	−	0.438164i
$340$	0.591288	+	3.21089i	0.0320671	+	0.174135i
$341$	−26.7089	+	19.4052i	−1.44637	+	1.05085i
$342$	−0.686435	+	2.11263i	−0.0371181	+	0.114238i
$343$	−45.4358			−2.45330
$344$	−3.07772	+	9.47224i	−0.165939	+	0.510709i
$345$	8.07915	+	1.07308i	0.434967	+	0.0577730i
$346$	5.21030	+	16.0356i	0.280107	+	0.862081i
$347$	−6.26852	−	19.2925i	−0.336512	−	1.03568i	−0.965973	−	0.258644i	$-0.916724\pi$
$347$	−6.26852	−	19.2925i	−0.336512	−	1.03568i	0.629461	−	0.777032i	$-0.283276\pi$
$348$	−1.57978	−	1.14778i	−0.0846851	−	0.0615273i
$349$	−18.4329			−0.986691			−0.493346	−	0.869833i	$-0.664226\pi$
$349$	−18.4329			−0.986691			−0.493346	+	0.869833i	$0.664226\pi$
$350$	−23.3451	−	6.31284i	−1.24785	−	0.337436i
$351$	9.63368			0.514208
$352$	−3.36423	−	2.44426i	−0.179314	−	0.130279i
$353$	−9.99819	−	30.7713i	−0.532150	−	1.63779i	−0.749727	−	0.661747i	$-0.769815\pi$
$353$	−9.99819	−	30.7713i	−0.532150	−	1.63779i	0.217577	−	0.976043i	$-0.430185\pi$
$354$	−1.41293	−	4.34856i	−0.0750965	−	0.231123i
$355$	−17.5134	+	9.48295i	−0.929513	+	0.503303i
$356$	5.75095	−	17.6996i	0.304800	−	0.938077i
$357$	−6.23167			−0.329815
$358$	−1.20238	+	3.70055i	−0.0635479	+	0.195580i
$359$	24.4727	−	17.7804i	1.29162	−	0.938416i	0.291781	−	0.956485i	$-0.405752\pi$
$359$	24.4727	−	17.7804i	1.29162	−	0.938416i	0.999837	+	0.0180695i	$0.00575200\pi$
$360$	4.36788	−	2.36507i	0.230208	−	0.124650i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	7.51671	−	5.46121i	0.395069	−	0.287035i
$363$	−4.49209	+	3.26369i	−0.235774	+	0.171300i
$364$	−8.18177	−	5.94441i	−0.428841	−	0.311572i
$365$	−2.47570	+	5.17509i	−0.129584	+	0.270877i
$366$	−0.728301	+	0.529142i	−0.0380689	+	0.0276587i
$367$	−8.77047	+	26.9927i	−0.457815	+	1.40901i	0.409984	+	0.912093i	$0.365534\pi$
$367$	−8.77047	+	26.9927i	−0.457815	+	1.40901i	−0.867799	+	0.496916i	$0.834466\pi$
$368$	4.13054			0.215319
$369$	7.19658	−	22.1488i	0.374639	−	1.15302i
$370$	−1.11251	−	6.04127i	−0.0578364	−	0.314071i
$371$	8.91261	+	27.4302i	0.462720	+	1.42411i
$372$	2.16483	+	6.66267i	0.112241	+	0.345443i
$373$	12.0694	+	8.76895i	0.624931	+	0.454039i	0.854640	−	0.519220i	$-0.173778\pi$
$373$	12.0694	+	8.76895i	0.624931	+	0.454039i	−0.229710	+	0.973259i	$0.573778\pi$
$374$	6.07170			0.313960
$375$	6.43306	−	7.47978i	0.332202	−	0.386254i
$376$	2.08053			0.107295
$377$	3.74337	+	2.71972i	0.192794	+	0.140073i
$378$	6.88633	+	21.1940i	0.354195	+	1.09010i
$379$	9.69831	+	29.8483i	0.498169	+	1.53321i	0.811960	+	0.583713i	$0.198401\pi$
$379$	9.69831	+	29.8483i	0.498169	+	1.53321i	−0.313791	+	0.949492i	$0.601599\pi$
$380$	0.404965	+	2.19909i	0.0207743	+	0.112811i
$381$	−0.975845	+	3.00334i	−0.0499941	+	0.153866i
$382$	17.9797			0.919922
$383$	3.61976	−	11.1405i	0.184961	−	0.569251i	−0.814987	−	0.579480i	$-0.803256\pi$
$383$	3.61976	−	11.1405i	0.184961	−	0.569251i	0.999948	+	0.0102284i	$0.00325586\pi$
$384$	−0.713886	+	0.518669i	−0.0364304	+	0.0264682i
$385$	−19.4086	+	40.5709i	−0.989153	+	2.06768i
$386$	8.76088	+	6.36515i	0.445917	+	0.323978i
$387$	−17.8987	+	13.0041i	−0.909841	+	0.661038i
$388$	1.32406	−	0.961982i	0.0672187	−	0.0488373i
$389$	−10.6251	−	7.71958i	−0.538714	−	0.391398i	0.284893	−	0.958559i	$-0.408042\pi$
$389$	−10.6251	−	7.71958i	−0.538714	−	0.391398i	−0.823607	+	0.567161i	$0.808042\pi$
$390$	3.62797	−	1.96443i	0.183709	−	0.0994729i
$391$	−4.87917	+	3.54493i	−0.246750	+	0.179275i
$392$	5.06600	−	15.5915i	0.255872	−	0.787492i
$393$	15.8249			0.798261
$394$	0.0165249	−	0.0508585i	0.000832513	−	0.00256221i
$395$	14.3167	−	7.75203i	0.720350	−	0.390047i
$396$	−2.85448	−	8.78520i	−0.143443	−	0.441473i
$397$	11.8308	+	36.4114i	0.593771	+	1.82744i	0.560753	+	0.827983i	$0.310512\pi$
$397$	11.8308	+	36.4114i	0.593771	+	1.82744i	0.0330178	+	0.999455i	$0.489488\pi$
$398$	−18.3821	−	13.3554i	−0.921410	−	0.669443i
$399$	−4.26798			−0.213666
$400$	2.73282	−	4.18708i	0.136641	−	0.209354i
$401$	−5.54879			−0.277093			−0.138547	−	0.990356i	$-0.544243\pi$
$401$	−5.54879			−0.277093			−0.138547	+	0.990356i	$0.544243\pi$
$402$	0.109631	+	0.0796515i	0.00546789	+	0.00397265i
$403$	−5.12969	−	15.7876i	−0.255528	−	0.786434i
$404$	−5.72447	−	17.6181i	−0.284803	−	0.876534i
$405$	5.75971	+	0.765013i	0.286202	+	0.0380138i
$406$	−3.30751	+	10.1795i	−0.164149	+	0.505199i
$407$	−11.4239			−0.566260
$408$	0.398140	−	1.22535i	0.0197109	−	0.0606638i
$409$	14.9704	−	10.8766i	0.740238	−	0.537815i	−0.152548	−	0.988296i	$-0.548748\pi$
$409$	14.9704	−	10.8766i	0.740238	−	0.537815i	0.892786	+	0.450482i	$0.148748\pi$
$410$	−4.24565	−	23.0553i	−0.209678	−	1.13862i
$411$	6.53368	+	4.74700i	0.322283	+	0.234152i
$412$	−3.92889	+	2.85451i	−0.193563	+	0.140631i
$413$	−20.2757	+	14.7312i	−0.997704	+	0.724875i
$414$	7.42303	+	5.39315i	0.364822	+	0.265059i
$415$	33.4570	+	4.44380i	1.64234	+	0.218138i
$416$	1.69159	−	1.22901i	0.0829372	−	0.0602574i
$417$	−3.05316	+	9.39665i	−0.149514	+	0.460156i
$418$	4.15842			0.203395
$419$	−12.3521	+	38.0157i	−0.603437	+	1.85719i	−0.0962407	+	0.995358i	$0.530682\pi$
$419$	−12.3521	+	38.0157i	−0.603437	+	1.85719i	−0.507196	+	0.861830i	$0.669318\pi$
$420$	6.91506	+	6.57726i	0.337420	+	0.320938i
$421$	−5.69603	−	17.5306i	−0.277608	−	0.854388i	−0.988518	−	0.151105i	$-0.951717\pi$
$421$	−5.69603	−	17.5306i	−0.277608	−	0.854388i	0.710910	−	0.703283i	$-0.248283\pi$
$422$	2.57026	+	7.91045i	0.125118	+	0.385075i
$423$	3.73894	+	2.71650i	0.181793	+	0.132081i
$424$	−5.96309			−0.289593
$425$	0.365325	+	7.29134i	0.0177209	+	0.353682i
$426$	7.85936			0.380787
$427$	3.99201	+	2.90036i	0.193187	+	0.140358i
$428$	−5.50315	−	16.9370i	−0.266005	−	0.818678i
$429$	−2.37094	−	7.29700i	−0.114470	−	0.352302i
$430$	−9.61082	+	20.0901i	−0.463475	+	0.968829i
$431$	−2.45313	+	7.54997i	−0.118163	+	0.363669i	−0.992594	−	0.121482i	$-0.961235\pi$
$431$	−2.45313	+	7.54997i	−0.118163	+	0.363669i	0.874430	+	0.485151i	$0.161235\pi$
$432$	−4.60738			−0.221673
$433$	−5.38789	+	16.5822i	−0.258926	+	0.796891i	0.734105	+	0.679036i	$0.237602\pi$
$433$	−5.38789	+	16.5822i	−0.258926	+	0.796891i	−0.993031	+	0.117855i	$0.962398\pi$
$434$	31.0656	−	22.5705i	1.49120	−	1.08342i
$435$	−3.16382	−	3.00927i	−0.151694	−	0.144283i
$436$	4.84527	+	3.52030i	0.232046	+	0.168592i
$437$	−3.34168	+	2.42787i	−0.159854	+	0.116141i
$438$	1.83152	−	1.33068i	0.0875135	−	0.0635823i
$439$	−26.7465	−	19.4325i	−1.27654	−	0.927461i	−0.277097	−	0.960842i	$-0.589372\pi$
$439$	−26.7465	−	19.4325i	−1.27654	−	0.927461i	−0.999443	+	0.0333813i	$0.989372\pi$
$440$	−6.73754	−	6.40841i	−0.321200	−	0.305509i
$441$	29.4617	−	21.4052i	1.40294	−	1.01929i
$442$	−0.943415	+	2.90353i	−0.0448737	+	0.138107i
$443$	3.75350			0.178334			0.0891672	−	0.996017i	$-0.471579\pi$
$443$	3.75350			0.178334			0.0891672	+	0.996017i	$0.471579\pi$
$444$	−0.749098	+	2.30549i	−0.0355506	+	0.109414i
$445$	17.9585	−	37.5398i	0.851317	−	1.77956i
$446$	−5.47461	−	16.8491i	−0.259230	−	0.797828i
$447$	−2.62936	−	8.09233i	−0.124364	−	0.382754i
$448$	3.91299	+	2.84296i	0.184872	+	0.134317i
$449$	−27.0227			−1.27528			−0.637640	−	0.770334i	$-0.720089\pi$
$449$	−27.0227			−1.27528			−0.637640	+	0.770334i	$0.720089\pi$
$450$	10.3782	−	3.95647i	0.489231	−	0.186510i
$451$	−43.5968			−2.05290
$452$	−12.5836	−	9.14250i	−0.591881	−	0.430027i
$453$	0.926240	+	2.85067i	0.0435186	+	0.133936i
$454$	−3.37706	−	10.3935i	−0.158493	−	0.487792i
$455$	−16.3856	−	15.5852i	−0.768170	−	0.730645i
$456$	0.272680	−	0.839224i	0.0127694	−	0.0393002i
$457$	15.4561			0.723007			0.361503	−	0.932371i	$-0.382264\pi$
$457$	15.4561			0.723007			0.361503	+	0.932371i	$0.382264\pi$
$458$	4.86732	−	14.9801i	0.227435	−	0.699973i
$459$	5.44244	−	3.95416i	0.254031	−	0.184565i
$460$	9.15576	+	1.21608i	0.426890	+	0.0567001i
$461$	2.97668	+	2.16268i	0.138638	+	0.100726i	0.654943	−	0.755679i	$-0.272693\pi$
$461$	2.97668	+	2.16268i	0.138638	+	0.100726i	−0.516305	+	0.856405i	$0.672693\pi$
$462$	14.3585	−	10.4321i	0.668017	−	0.485343i
$463$	14.0561	−	10.2124i	0.653244	−	0.474609i	−0.211131	−	0.977458i	$-0.567715\pi$
$463$	14.0561	−	10.2124i	0.653244	−	0.474609i	0.864375	+	0.502849i	$0.167715\pi$
$464$	−1.79030	−	1.30073i	−0.0831124	−	0.0603847i
$465$	2.83700	+	15.4058i	0.131563	+	0.714428i
$466$	−14.4037	+	10.4649i	−0.667237	+	0.484776i
$467$	0.0517602	−	0.159301i	0.00239518	−	0.00737159i	−0.949852	−	0.312700i	$-0.898766\pi$
$467$	0.0517602	−	0.159301i	0.00239518	−	0.00737159i	0.952247	+	0.305329i	$0.0987664\pi$
$468$	4.64467			0.214700
$469$	0.229529	−	0.706418i	0.0105987	−	0.0326193i
$470$	4.61170	+	0.612533i	0.212722	+	0.0282540i
$471$	−4.09637	−	12.6073i	−0.188751	−	0.580915i
$472$	−1.60122	−	4.92804i	−0.0737020	−	0.226831i
$473$	33.5067	+	24.3441i	1.54064	+	1.11934i
$474$	−6.42479			−0.295101
$475$	0.250206	+	4.99374i	0.0114802	+	0.229128i
$476$	−7.06209			−0.323691
$477$	−10.7163	−	7.78586i	−0.490667	−	0.356490i
$478$	3.81650	+	11.7460i	0.174563	+	0.537249i
$479$	0.331484	+	1.02020i	0.0151459	+	0.0466142i	0.958344	−	0.285617i	$-0.0921985\pi$
$479$	0.331484	+	1.02020i	0.0151459	+	0.0466142i	−0.943198	+	0.332231i	$0.892199\pi$
$480$	−1.73510	+	0.939505i	−0.0791963	+	0.0428823i
$481$	1.77503	−	5.46298i	0.0809344	−	0.249090i
$482$	−27.6495			−1.25940
$483$	−5.44769	+	16.7663i	−0.247878	+	0.762891i
$484$	−5.09070	+	3.69861i	−0.231395	+	0.168119i
$485$	3.21812	−	1.74251i	0.146127	−	0.0791235i
$486$	−13.0373	−	9.47218i	−0.591386	−	0.429667i
$487$	−2.34194	+	1.70152i	−0.106123	+	0.0771031i	−0.639581	−	0.768723i	$-0.720892\pi$
$487$	−2.34194	+	1.70152i	−0.106123	+	0.0771031i	0.533458	+	0.845827i	$0.320892\pi$
$488$	−0.825353	+	0.599654i	−0.0373620	+	0.0271451i
$489$	5.32536	+	3.86910i	0.240821	+	0.174967i
$490$	15.8196	−	33.0687i	0.714659	−	1.49389i
$491$	−10.1276	+	7.35813i	−0.457052	+	0.332068i	−0.792374	−	0.610036i	$-0.791155\pi$
$491$	−10.1276	+	7.35813i	−0.457052	+	0.332068i	0.335322	+	0.942104i	$0.391155\pi$
$492$	−2.85878	+	8.79842i	−0.128884	+	0.396663i
$493$	3.23109			0.145521
$494$	−0.646131	+	1.98859i	−0.0290708	+	0.0894708i
$495$	−3.74078	−	20.3137i	−0.168136	−	0.913032i
$496$	2.45331	+	7.55052i	0.110157	+	0.339028i
$497$	−13.3122	−	40.9707i	−0.597133	−	1.83779i
$498$	−10.7753	−	7.82869i	−0.482851	−	0.350812i
$499$	12.5083			0.559949			0.279974	−	0.960007i	$-0.409674\pi$
$499$	12.5083			0.559949			0.279974	+	0.960007i	$0.409674\pi$
$500$	7.29031	−	8.47652i	0.326033	−	0.379081i
$501$	−17.5019			−0.781929
$502$	13.6536	+	9.91993i	0.609390	+	0.442748i
$503$	1.33362	+	4.10446i	0.0594632	+	0.183009i	0.976376	−	0.216079i	$-0.0693269\pi$
$503$	1.33362	+	4.10446i	0.0594632	+	0.183009i	−0.916913	+	0.399088i	$0.869327\pi$
$504$	3.32010	+	10.2182i	0.147889	+	0.455155i
$505$	−7.50188	−	40.7377i	−0.333829	−	1.81280i
$506$	5.30783	−	16.3358i	0.235962	−	0.726216i
$507$	−7.61348			−0.338127
$508$	−1.10588	+	3.40356i	−0.0490657	+	0.151009i
$509$	17.1931	−	12.4915i	0.762071	−	0.553677i	−0.137474	−	0.990505i	$-0.543898\pi$
$509$	17.1931	−	12.4915i	0.762071	−	0.553677i	0.899545	+	0.436829i	$0.143898\pi$
$510$	1.24327	−	2.59889i	0.0550531	−	0.115081i
$511$	−10.0390	−	7.29379i	−0.444101	−	0.322658i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	3.72745	−	2.70815i	0.164571	−	0.119568i
$514$	−3.92501	−	2.85169i	−0.173125	−	0.125783i
$515$	−9.54919	+	5.17059i	−0.420787	+	0.227843i
$516$	7.11009	−	5.16579i	0.313004	−	0.227411i
$517$	2.67352	−	8.22826i	0.117581	−	0.361879i
$518$	13.2873			0.583810
$519$	4.59763	−	14.1500i	0.201813	−	0.621118i
$520$	4.11142	−	2.22621i	0.180298	−	0.0976257i
$521$	−2.33397	−	7.18322i	−0.102253	−	0.314703i	0.886823	−	0.462109i	$-0.152907\pi$
$521$	−2.33397	−	7.18322i	−0.102253	−	0.314703i	−0.989076	+	0.147407i	$0.952907\pi$
$522$	−1.51903	−	4.67510i	−0.0664862	−	0.204623i
$523$	−33.1128	−	24.0578i	−1.44792	−	1.05198i	−0.986312	−	0.164891i	$-0.947273\pi$
$523$	−33.1128	−	24.0578i	−1.44792	−	1.05198i	−0.461608	−	0.887084i	$-0.652727\pi$
$524$	17.9337			0.783437
$525$	13.3915	+	16.6150i	0.584453	+	0.725140i
$526$	−11.1795			−0.487448
$527$	−9.37799	−	6.81351i	−0.408512	−	0.296801i
$528$	1.13392	+	3.48984i	0.0493475	+	0.151876i
$529$	−1.83514	−	5.64798i	−0.0797887	−	0.245564i
$530$	−13.2178	−	1.75561i	−0.574144	−	0.0762587i
$531$	3.55686	−	10.9469i	0.154355	−	0.475055i
$532$	−4.83673			−0.209699
$533$	6.77404	−	20.8483i	0.293416	−	0.903042i
$534$	−13.2858	+	9.65267i	−0.574931	+	0.417712i
$535$	−7.21184	−	39.1627i	−0.311795	−	1.69315i
$536$	0.124240	+	0.0902656i	0.00536635	+	0.00389888i
$537$	2.77772	−	2.01813i	0.119868	−	0.0870889i
$538$	8.94121	−	6.49617i	0.385483	−	0.280070i
$539$	−55.1529	−	40.0710i	−2.37561	−	1.72598i
$540$	−10.2127	−	1.35647i	−0.439486	−	0.0583732i
$541$	23.8972	−	17.3623i	1.02742	−	0.746465i	0.0596301	−	0.998221i	$-0.481008\pi$
$541$	23.8972	−	17.3623i	1.02742	−	0.746465i	0.967791	+	0.251756i	$0.0810079\pi$
$542$	2.10201	−	6.46933i	0.0902892	−	0.277881i
$543$	−8.19863			−0.351837
$544$	0.451195	−	1.38864i	0.0193448	−	0.0595373i
$545$	9.70362	+	9.22960i	0.415657	+	0.395353i
$546$	2.75768	+	8.48726i	0.118018	+	0.363221i
$547$	−12.7919	−	39.3694i	−0.546942	−	1.68332i	−0.716326	−	0.697766i	$-0.754178\pi$
$547$	−12.7919	−	39.3694i	−0.546942	−	1.68332i	0.169384	−	0.985550i	$-0.445822\pi$
$548$	7.40435	+	5.37957i	0.316298	+	0.229804i
$549$	−2.26620			−0.0967192
$550$	−13.0477	−	16.1885i	−0.556357	−	0.690281i
$551$	2.21293			0.0942739
$552$	−2.94874	−	2.14238i	−0.125507	−	0.0911858i
$553$	10.8823	+	33.4924i	0.462764	+	1.42424i
$554$	−2.80521	−	8.63355i	−0.119182	−	0.366804i
$555$	−2.33922	+	4.88980i	−0.0992941	+	0.207560i
$556$	−3.46001	+	10.6488i	−0.146737	+	0.451611i
$557$	22.9401			0.972003			0.486001	−	0.873958i	$-0.338455\pi$
$557$	22.9401			0.972003			0.486001	+	0.873958i	$0.338455\pi$
$558$	−5.44966	+	16.7723i	−0.230703	+	0.710030i
$559$	−16.8478	+	12.2406i	−0.712584	+	0.517723i
$560$	7.83655	+	7.45373i	0.331154	+	0.314978i
$561$	−4.33450	−	3.14920i	−0.183003	−	0.132959i
$562$	−0.233721	+	0.169808i	−0.00985893	+	0.00716293i
$563$	36.8821	−	26.7964i	1.55439	−	1.12933i	0.613971	−	0.789329i	$-0.289571\pi$
$563$	36.8821	−	26.7964i	1.55439	−	1.12933i	0.940424	−	0.340005i	$-0.110429\pi$
$564$	−1.48526	−	1.07910i	−0.0625407	−	0.0454385i
$565$	−25.2011	−	23.9700i	−1.06022	−	1.00843i
$566$	−10.5027	+	7.63069i	−0.441463	+	0.320742i
$567$	−3.88371	+	11.9528i	−0.163100	+	0.501972i
$568$	8.90668			0.373716
$569$	−12.6005	+	38.7802i	−0.528239	+	1.62575i	0.229582	+	0.973289i	$0.426264\pi$
$569$	−12.6005	+	38.7802i	−0.528239	+	1.62575i	−0.757821	+	0.652463i	$0.773736\pi$
$570$	0.851501	−	1.77994i	0.0356655	−	0.0745536i
$571$	−3.61550	−	11.1274i	−0.151304	−	0.465666i	0.846464	−	0.532447i	$-0.178727\pi$
$571$	−3.61550	−	11.1274i	−0.151304	−	0.465666i	−0.997768	+	0.0667804i	$0.978727\pi$
$572$	−2.68688	−	8.26938i	−0.112344	−	0.345760i
$573$	−12.8355	−	9.32551i	−0.536209	−	0.389579i
$574$	50.7082			2.11652
$575$	19.9366	+	5.39114i	0.831415	+	0.224826i
$576$	−2.22135			−0.0925562
$577$	12.4354	+	9.03484i	0.517692	+	0.376125i	0.815734	−	0.578428i	$-0.196333\pi$
$577$	12.4354	+	9.03484i	0.517692	+	0.376125i	−0.298042	+	0.954553i	$0.596333\pi$
$578$	−4.59450	−	14.1404i	−0.191106	−	0.588164i
$579$	−2.95286	−	9.08798i	−0.122717	−	0.377684i
$580$	−3.58542	−	3.41028i	−0.148877	−	0.141604i
$581$	−22.5597	+	69.4315i	−0.935933	+	2.88051i
$582$	−1.44417			−0.0598630
$583$	−7.66270	+	23.5834i	−0.317357	+	0.976723i
$584$	2.07559	−	1.50800i	0.0858884	−	0.0624016i
$585$	10.2954	+	1.36745i	0.425662	+	0.0565371i
$586$	15.7257	+	11.4254i	0.649623	+	0.471979i
$587$	15.0928	−	10.9655i	0.622945	−	0.452596i	−0.231004	−	0.972953i	$-0.574201\pi$
$587$	15.0928	−	10.9655i	0.622945	−	0.452596i	0.853949	+	0.520357i	$0.174201\pi$
$588$	−11.7034	+	8.50301i	−0.482640	+	0.350658i
$589$	−6.42285	−	4.66648i	−0.264649	−	0.192279i
$590$	−2.09838	−	11.3949i	−0.0863891	−	0.469121i
$591$	−0.0381756	+	0.0277362i	−0.00157033	+	0.00114091i
$592$	−0.848921	+	2.61271i	−0.0348904	+	0.107382i
$593$	22.4100			0.920267			0.460133	−	0.887850i	$-0.347802\pi$
$593$	22.4100			0.920267			0.460133	+	0.887850i	$0.347802\pi$
$594$	−5.92059	+	18.2217i	−0.242925	+	0.747645i
$595$	−15.6538	−	2.07917i	−0.641745	−	0.0852375i
$596$	−2.97974	−	9.17070i	−0.122055	−	0.375646i
$597$	6.19570	+	19.0684i	0.253573	+	0.780418i
$598$	6.98719	+	5.07649i	0.285728	+	0.207593i
$599$	12.2339			0.499864			0.249932	−	0.968263i	$-0.419592\pi$
$599$	12.2339			0.499864			0.249932	+	0.968263i	$0.419592\pi$
$600$	−4.12263	+	1.57167i	−0.168306	+	0.0641632i
$601$	−12.5001			−0.509891			−0.254946	−	0.966955i	$-0.582058\pi$
$601$	−12.5001			−0.509891			−0.254946	+	0.966955i	$0.582058\pi$
$602$	−38.9722	−	28.3150i	−1.58839	−	1.15403i
$603$	0.105415	+	0.324434i	0.00429284	+	0.0132120i
$604$	1.04967	+	3.23055i	0.0427104	+	0.131449i
$605$	−12.3730	+	6.69957i	−0.503032	+	0.272376i
$606$	−5.05134	+	15.5464i	−0.205197	+	0.631531i
$607$	−0.126120			−0.00511905			−0.00255952	−	0.999997i	$-0.500815\pi$
$607$	−0.126120			−0.00511905			−0.00255952	+	0.999997i	$0.500815\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	7.64096	−	5.55148i	0.309627	−	0.224957i
$610$	−2.00602	+	1.08620i	−0.0812215	+	0.0439789i
$611$	3.51941	+	2.55700i	0.142380	+	0.103445i
$612$	2.62396	−	1.90642i	0.106067	−	0.0770623i
$613$	−7.77581	+	5.64946i	−0.314062	+	0.228179i	−0.733637	−	0.679541i	$-0.762179\pi$
$613$	−7.77581	+	5.64946i	−0.314062	+	0.228179i	0.419576	+	0.907720i	$0.362179\pi$
$614$	17.1880	+	12.4878i	0.693651	+	0.503967i
$615$	−8.92714	+	18.6609i	−0.359977	+	0.752481i
$616$	16.2719	−	11.8222i	0.655612	−	0.476330i
$617$	−1.15769	+	3.56299i	−0.0466067	+	0.143441i	−0.971652	−	0.236417i	$-0.924027\pi$
$617$	−1.15769	+	3.56299i	−0.0466067	+	0.143441i	0.925045	+	0.379857i	$0.124027\pi$
$618$	4.28532			0.172381
$619$	−9.38391	+	28.8807i	−0.377171	+	1.16081i	0.564831	+	0.825207i	$0.308941\pi$
$619$	−9.38391	+	28.8807i	−0.377171	+	1.16081i	−0.942002	+	0.335607i	$0.891059\pi$
$620$	3.21505	+	17.4588i	0.129119	+	0.701161i
$621$	−5.88089	−	18.0995i	−0.235992	−	0.726309i
$622$	−6.45320	−	19.8609i	−0.258750	−	0.796349i
$623$	72.8226	+	52.9087i	2.91758	+	2.11974i
$624$	−1.84506			−0.0738614
$625$	18.6553	−	16.6427i	0.746212	−	0.665708i
$626$	−13.6498			−0.545556
$627$	−2.96864	−	2.15684i	−0.118556	−	0.0861360i
$628$	−4.64225	−	14.2874i	−0.185246	−	0.570128i
$629$	−1.23951	−	3.81481i	−0.0494224	−	0.152107i
$630$	4.35096	+	23.6272i	0.173347	+	0.941329i
$631$	−8.02971	+	24.7129i	−0.319658	+	0.983805i	0.654137	+	0.756376i	$0.273032\pi$
$631$	−8.02971	+	24.7129i	−0.319658	+	0.983805i	−0.973795	+	0.227429i	$0.926968\pi$
$632$	−7.28095			−0.289620
$633$	2.26803	−	6.98027i	0.0901460	−	0.277441i
$634$	−3.57040	+	2.59405i	−0.141799	+	0.103023i
$635$	−3.45335	+	7.21875i	−0.137042	+	0.286467i
$636$	4.25697	+	3.09287i	0.168800	+	0.122640i
$637$	27.7318	−	20.1484i	1.09878	−	0.798307i
$638$	−7.44480	+	5.40897i	−0.294743	+	0.214143i
$639$	16.0063	+	11.6292i	0.633198	+	0.460046i
$640$	−1.96632	+	1.06470i	−0.0777256	+	0.0420860i
$641$	2.68602	−	1.95151i	0.106091	−	0.0770799i	−0.533475	−	0.845816i	$-0.679114\pi$
$641$	2.68602	−	1.95151i	0.106091	−	0.0770799i	0.639566	+	0.768736i	$0.279114\pi$
$642$	−4.85604	+	14.9454i	−0.191653	+	0.589847i
$643$	33.3548			1.31539			0.657693	−	0.753286i	$-0.271532\pi$
$643$	33.3548			1.31539			0.657693	+	0.753286i	$0.271532\pi$
$644$	−6.17363	+	19.0005i	−0.243275	+	0.748724i
$645$	17.2811	−	9.35719i	0.680443	−	0.368439i
$646$	0.451195	+	1.38864i	0.0177520	+	0.0546351i
$647$	−3.79392	−	11.6765i	−0.149154	−	0.459050i	0.848368	−	0.529408i	$-0.177586\pi$
$647$	−3.79392	−	11.6765i	−0.149154	−	0.459050i	−0.997522	+	0.0703581i	$0.977586\pi$
$648$	−2.10218	−	1.52733i	−0.0825815	−	0.0599990i
$649$	−21.5475			−0.845812
$650$	9.76881	−	3.72416i	0.383164	−	0.146074i
$651$	−33.8839			−1.32801
$652$	6.03500	+	4.38469i	0.236349	+	0.171718i
$653$	−3.57324	−	10.9973i	−0.139832	−	0.430358i	0.856479	−	0.516183i	$-0.172647\pi$
$653$	−3.57324	−	10.9973i	−0.139832	−	0.430358i	−0.996310	+	0.0858249i	$0.972647\pi$
$654$	−1.63311	−	5.02618i	−0.0638595	−	0.196539i
$655$	39.7519	+	5.27990i	1.55323	+	0.206303i
$656$	−3.23973	+	9.97087i	−0.126490	+	0.389297i
$657$	5.69902			0.222340
$658$	−3.10962	+	9.57043i	−0.121226	+	0.373094i
$659$	−40.4608	+	29.3965i	−1.57613	+	1.14512i	−0.655158	+	0.755492i	$0.727398\pi$
$659$	−40.4608	+	29.3965i	−1.57613	+	1.14512i	−0.920971	+	0.389632i	$0.872602\pi$
$660$	1.48599	+	8.06943i	0.0578422	+	0.314102i
$661$	−20.9732	−	15.2379i	−0.815762	−	0.592686i	0.0997334	−	0.995014i	$-0.468201\pi$
$661$	−20.9732	−	15.2379i	−0.815762	−	0.592686i	−0.915495	+	0.402328i	$0.868201\pi$
$662$	−14.3492	+	10.4253i	−0.557697	+	0.405191i
$663$	2.17946	−	1.58347i	0.0846433	−	0.0614969i
$664$	−12.2111	−	8.87192i	−0.473884	−	0.344297i
$665$	−10.7211	−	1.42399i	−0.415746	−	0.0552200i
$666$	−4.93696	+	3.58691i	−0.191303	+	0.138990i
$667$	2.82460	−	8.69322i	0.109369	−	0.336603i
$668$	−19.8342			−0.767409
$669$	−4.83086	+	14.8679i	−0.186772	+	0.574824i
$670$	0.248815	+	0.236661i	0.00961257	+	0.00914300i
$671$	1.31097	+	4.03475i	0.0506094	+	0.155760i
$672$	−1.31888	−	4.05909i	−0.0508769	−	0.156583i
$673$	5.90731	+	4.29191i	0.227710	+	0.165441i	0.695790	−	0.718245i	$-0.255054\pi$
$673$	5.90731	+	4.29191i	0.227710	+	0.165441i	−0.468080	+	0.883686i	$0.655054\pi$
$674$	−9.13822			−0.351991
$675$	−22.2382	−	6.01350i	−0.855948	−	0.231460i
$676$	−8.62804			−0.331848
$677$	26.4734	+	19.2341i	1.01746	+	0.739225i	0.965760	−	0.259437i	$-0.0835372\pi$
$677$	26.4734	+	19.2341i	1.01746	+	0.739225i	0.0516965	+	0.998663i	$0.483537\pi$
$678$	4.24131	+	13.0534i	0.162887	+	0.501313i
$679$	2.44615	+	7.52846i	0.0938745	+	0.288916i
$680$	1.40895	−	2.94521i	0.0540308	−	0.112944i
$681$	−2.97996	+	9.17137i	−0.114192	+	0.351448i
$682$	33.0140			1.26417
$683$	−3.11191	+	9.57748i	−0.119074	+	0.366472i	−0.992775	−	0.119991i	$-0.961713\pi$
$683$	−3.11191	+	9.57748i	−0.119074	+	0.366472i	0.873701	+	0.486463i	$0.161713\pi$
$684$	1.79711	−	1.30568i	0.0687142	−	0.0499238i
$685$	14.8287	+	14.1043i	0.566574	+	0.538898i
$686$	36.7583	+	26.7065i	1.40344	+	1.01966i
$687$	−11.2444	+	8.16954i	−0.429001	+	0.311687i
$688$	8.05757	−	5.85417i	0.307192	−	0.223188i
$689$	−10.0871	−	7.32872i	−0.384289	−	0.279202i
$690$	−5.90543	−	5.61695i	−0.224816	−	0.213834i
$691$	3.15305	−	2.29083i	0.119948	−	0.0871472i	−0.526194	−	0.850365i	$-0.676381\pi$
$691$	3.15305	−	2.29083i	0.119948	−	0.0871472i	0.646142	+	0.763217i	$0.276381\pi$
$692$	5.21030	−	16.0356i	0.198066	−	0.609584i
$693$	44.6783			1.69719
$694$	−6.26852	+	19.2925i	−0.237950	+	0.732334i
$695$	−10.8046	+	22.5855i	−0.409842	+	0.856718i
$696$	0.603422	+	1.85714i	0.0228726	+	0.0703948i
$697$	−4.73033	−	14.5585i	−0.179174	−	0.551441i
$698$	14.9125	+	10.8346i	0.564448	+	0.410096i
$699$	15.7104			0.594221
$700$	15.1760	+	18.8291i	0.573600	+	0.711674i
$701$	−9.55713			−0.360968			−0.180484	−	0.983578i	$-0.557766\pi$
$701$	−9.55713			−0.360968			−0.180484	+	0.983578i	$0.557766\pi$
$702$	−7.79381	−	5.66254i	−0.294159	−	0.213719i
$703$	−0.848921	−	2.61271i	−0.0320177	−	0.0985402i
$704$	1.28502	+	3.95489i	0.0484311	+	0.149056i
$705$	−2.97453	−	2.82922i	−0.112027	−	0.106555i
$706$	−9.99819	+	30.7713i	−0.376287	+	1.15809i
$707$	89.5993			3.36973
$708$	−1.41293	+	4.34856i	−0.0531013	+	0.163429i
$709$	0.820525	−	0.596146i	0.0308154	−	0.0223887i	−0.572271	−	0.820065i	$-0.693937\pi$
$709$	0.820525	−	0.596146i	0.0308154	−	0.0223887i	0.603086	+	0.797676i	$0.293937\pi$
$710$	19.7426	+	2.62224i	0.740925	+	0.0984108i
$711$	−13.0847	−	9.50656i	−0.490713	−	0.356524i
$712$	−15.0562	+	10.9390i	−0.564254	+	0.409955i
$713$	−26.5298	+	19.2751i	−0.993551	+	0.721857i
$714$	5.04153	+	3.66289i	0.188675	+	0.137080i
$715$	−3.52114	−	19.1210i	−0.131683	−	0.715084i
$716$	3.14788	−	2.28707i	0.117642	−	0.0854717i
$717$	3.36773	−	10.3648i	0.125770	−	0.387081i
$718$	−30.2499			−1.12892
$719$	−5.14219	+	15.8260i	−0.191771	+	0.590212i	0.808228	+	0.588870i	$0.200427\pi$
$719$	−5.14219	+	15.8260i	−0.191771	+	0.590212i	−0.999999	+	0.00134173i	$0.999573\pi$
$720$	−4.92385	−	0.653993i	−0.183501	−	0.0243729i
$721$	−7.25849	−	22.3393i	−0.270320	−	0.831960i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	19.7386	+	14.3409i	0.734087	+	0.533346i
$724$	−9.29116			−0.345303
$725$	−6.94343	−	8.61482i	−0.257872	−	0.319946i
$726$	5.55253			0.206074
$727$	−7.79508	−	5.66345i	−0.289103	−	0.210046i	0.433775	−	0.901021i	$-0.357181\pi$
$727$	−7.79508	−	5.66345i	−0.289103	−	0.210046i	−0.722878	+	0.690975i	$0.757181\pi$
$728$	3.12516	+	9.61825i	0.115826	+	0.356476i
$729$	1.98537	+	6.11033i	0.0735320	+	0.226308i
$730$	5.04472	−	2.73156i	0.186714	−	0.101100i
$731$	−4.49377	+	13.8304i	−0.166208	+	0.511536i
$732$	0.900230			0.0332735
$733$	8.78869	−	27.0488i	0.324618	−	0.999071i	−0.646995	−	0.762494i	$-0.723975\pi$
$733$	8.78869	−	27.0488i	0.324618	−	0.999071i	0.971613	−	0.236577i	$-0.0760254\pi$
$734$	22.9614	−	16.6824i	0.847520	−	0.615759i
$735$	−28.4451	+	15.4022i	−1.04922	+	0.568117i
$736$	−3.34168	−	2.42787i	−0.123176	−	0.0894925i
$737$	0.516642	−	0.375362i	0.0190307	−	0.0138266i
$738$	−18.8409	+	13.6887i	−0.693543	+	0.503888i
$739$	−2.08385	−	1.51401i	−0.0766557	−	0.0556936i	0.548797	−	0.835955i	$-0.315086\pi$
$739$	−2.08385	−	1.51401i	−0.0766557	−	0.0556936i	−0.625453	+	0.780262i	$0.715086\pi$
$740$	−2.65093	+	5.54140i	−0.0974502	+	0.203706i
$741$	1.49268	−	1.08450i	0.0548350	−	0.0398400i
$742$	8.91261	−	27.4302i	0.327192	−	1.00699i
$743$	15.9725			0.585974			0.292987	−	0.956116i	$-0.405351\pi$
$743$	15.9725			0.585974			0.292987	+	0.956116i	$0.405351\pi$
$744$	2.16483	−	6.66267i	0.0793666	−	0.244265i
$745$	−3.90493	−	21.2050i	−0.143066	−	0.776893i
$746$	−4.61011	−	14.1885i	−0.168788	−	0.519476i
$747$	−10.3609	−	31.8876i	−0.379086	−	1.16671i
$748$	−4.91211	−	3.56885i	−0.179604	−	0.130490i
$749$	86.1352			3.14731
$750$	−9.60096	+	2.27002i	−0.350577	+	0.0828892i
$751$	23.7583			0.866952			0.433476	−	0.901165i	$-0.357287\pi$
$751$	23.7583			0.866952			0.433476	+	0.901165i	$0.357287\pi$
$752$	−1.68318	−	1.22290i	−0.0613793	−	0.0445947i
$753$	−4.60197	−	14.1634i	−0.167705	−	0.516143i
$754$	−1.42984	−	4.40060i	−0.0520718	−	0.160260i
$755$	1.37558	+	7.46987i	0.0500626	+	0.271856i
$756$	6.88633	−	21.1940i	0.250453	−	0.770817i
$757$	11.3740			0.413394			0.206697	−	0.978405i	$-0.433729\pi$
$757$	11.3740			0.413394			0.206697	+	0.978405i	$0.433729\pi$
$758$	9.69831	−	29.8483i	0.352258	−	1.08414i
$759$	−12.2621	+	8.90892i	−0.445085	+	0.323373i
$760$	0.964970	−	2.01713i	0.0350031	−	0.0731692i
$761$	−4.16975	−	3.02950i	−0.151153	−	0.109819i	0.509638	−	0.860389i	$-0.329779\pi$
$761$	−4.16975	−	3.02950i	−0.151153	−	0.109819i	−0.660791	+	0.750570i	$0.729779\pi$
$762$	2.55480	−	1.85617i	0.0925505	−	0.0672419i
$763$	−23.4352	+	17.0267i	−0.848413	+	0.616408i
$764$	−14.5459	−	10.5682i	−0.526252	−	0.382344i
$765$	6.37753	−	3.45324i	0.230580	−	0.124852i
$766$	−9.47665	+	6.88519i	−0.342405	+	0.248772i
$767$	3.34802	−	10.3042i	0.120890	−	0.372061i
$768$	0.882412			0.0318413
$769$	−14.0651	+	43.2880i	−0.507202	+	1.56101i	0.289836	+	0.957076i	$0.406399\pi$
$769$	−14.0651	+	43.2880i	−0.507202	+	1.56101i	−0.797037	+	0.603930i	$0.793601\pi$
$770$	39.5488	−	21.4145i	1.42524	−	0.771724i
$771$	1.32293	+	4.07156i	0.0476442	+	0.146634i
$772$	−3.34636	−	10.2990i	−0.120438	−	0.370670i
$773$	11.5620	+	8.40027i	0.415856	+	0.302137i	0.775968	−	0.630772i	$-0.217262\pi$
$773$	11.5620	+	8.40027i	0.415856	+	0.302137i	−0.360113	+	0.932909i	$0.617262\pi$
$774$	22.1240			0.795230
$775$	1.98640	+	39.6457i	0.0713537	+	1.42411i
$776$	−1.63662			−0.0587513
$777$	−9.48561	−	6.89170i	−0.340294	−	0.247238i
$778$	4.05843	+	12.4905i	0.145502	+	0.447808i
$779$	−3.23973	−	9.97087i	−0.116075	−	0.357244i
$780$	−4.08975	−	0.543207i	−0.146437	−	0.0194499i
$781$	11.4453	−	35.2249i	0.409544	−	1.26045i
$782$	6.03099			0.215668
$783$	−3.15068	+	9.69679i	−0.112596	+	0.346535i
$784$	−13.2630	+	9.63610i	−0.473677	+	0.344147i
$785$	−6.08363	−	33.0361i	−0.217134	−	1.17911i
$786$	−12.8026	−	9.30165i	−0.456654	−	0.331779i
$787$	−16.6936	+	12.1286i	−0.595063	+	0.432338i	−0.844123	−	0.536150i	$-0.819878\pi$
$787$	−16.6936	+	12.1286i	−0.595063	+	0.432338i	0.249060	+	0.968488i	$0.419878\pi$
$788$	−0.0432628	+	0.0314323i	−0.00154117	+	0.00111973i
$789$	7.98086	+	5.79844i	0.284126	+	0.206430i
$790$	−16.1390	−	2.14360i	−0.574198	−	0.0762659i
$791$	60.8633	−	44.2198i	2.16405	−	1.57227i
$792$	−2.85448	+	8.78520i	−0.101430	+	0.312168i
$793$	−2.13314			−0.0757502
$794$	11.8308	−	36.4114i	0.419859	−	1.29219i
$795$	8.52542	+	8.10896i	0.302365	+	0.287595i
$796$	7.02133	+	21.6094i	0.248864	+	0.765925i
$797$	6.65172	+	20.4719i	0.235616	+	0.725151i	0.997039	+	0.0768962i	$0.0245010\pi$
$797$	6.65172	+	20.4719i	0.235616	+	0.725151i	−0.761423	+	0.648255i	$0.775499\pi$
$798$	3.45287	+	2.50866i	0.122230	+	0.0888055i
$799$	3.03777			0.107469
$800$	−4.67201	+	1.78111i	−0.165180	+	0.0629717i
$801$	−41.3403			−1.46069
$802$	4.48906	+	3.26149i	0.158514	+	0.115167i
$803$	−3.29681	−	10.1465i	−0.116342	−	0.358064i
$804$	−0.0418753	−	0.128879i	−0.00147683	−	0.00454520i
$805$	−19.2785	+	40.2989i	−0.679476	+	1.42035i
$806$	−5.12969	+	15.7876i	−0.180686	+	0.556093i
$807$	−9.75236			−0.343299
$808$	−5.72447	+	17.6181i	−0.201386	+	0.619803i
$809$	−16.0558	+	11.6652i	−0.564492	+	0.410128i	−0.833100	−	0.553122i	$-0.813436\pi$
$809$	−16.0558	+	11.6652i	−0.564492	+	0.410128i	0.268608	+	0.963250i	$0.413436\pi$
$810$	−4.21004	−	4.00438i	−0.147926	−	0.140700i
$811$	19.5312	+	14.1902i	0.685833	+	0.498287i	0.875288	−	0.483603i	$-0.160672\pi$
$811$	19.5312	+	14.1902i	0.685833	+	0.498287i	−0.189455	+	0.981889i	$0.560672\pi$
$812$	8.65918	−	6.29126i	0.303877	−	0.220780i
$813$	−4.85604	+	3.52812i	−0.170309	+	0.123736i
$814$	9.24210	+	6.71478i	0.323936	+	0.235353i
$815$	12.0863	+	11.4959i	0.423364	+	0.402683i
$816$	−1.04234	+	0.757307i	−0.0364893	+	0.0265110i
$817$	−3.07772	+	9.47224i	−0.107676	+	0.331392i
$818$	−18.5044			−0.646992
$819$	−6.94207	+	21.3655i	−0.242576	+	0.746571i
$820$	−10.1167	+	21.1476i	−0.353292	+	0.738507i
$821$	14.5104	+	44.6585i	0.506418	+	1.55859i	0.798374	+	0.602161i	$0.205694\pi$
$821$	14.5104	+	44.6585i	0.506418	+	1.55859i	−0.291957	+	0.956431i	$0.594306\pi$
$822$	−2.49564	−	7.68081i	−0.0870456	−	0.267899i
$823$	−32.9750	−	23.9577i	−1.14943	−	0.835113i	−0.161029	−	0.986950i	$-0.551481\pi$
$823$	−32.9750	−	23.9577i	−1.14943	−	0.835113i	−0.988406	+	0.151836i	$0.951481\pi$
$824$	4.85638			0.169180
$825$	0.918114	+	18.3242i	0.0319646	+	0.637967i
$826$	25.0622			0.872026
$827$	35.4681	+	25.7691i	1.23335	+	0.896079i	0.997136	−	0.0756234i	$-0.0240947\pi$
$827$	35.4681	+	25.7691i	1.23335	+	0.896079i	0.236210	+	0.971702i	$0.424095\pi$
$828$	−2.83535	−	8.72630i	−0.0985351	−	0.303260i
$829$	9.25292	+	28.4776i	0.321367	+	0.989067i	0.973054	+	0.230578i	$0.0740617\pi$
$829$	9.25292	+	28.4776i	0.321367	+	0.989067i	−0.651687	+	0.758488i	$0.725938\pi$
$830$	−24.4552	−	23.2606i	−0.848854	−	0.807388i
$831$	−2.47535	+	7.61835i	−0.0858690	+	0.264278i
$832$	−2.09092			−0.0724898
$833$	7.39686	−	22.7652i	0.256286	−	0.788767i
$834$	7.99327	−	5.80745i	0.276784	−	0.201095i
$835$	−43.9645	−	5.83944i	−1.52146	−	0.202082i
$836$	−3.36423	−	2.44426i	−0.116354	−	0.0845364i
$837$	29.5925	−	21.5002i	1.02287	−	0.743157i
$838$	32.3381	−	23.4950i	1.11710	−	0.811621i
$839$	−11.0092	−	7.99862i	−0.380078	−	0.276143i	0.381299	−	0.924452i	$-0.375477\pi$
$839$	−11.0092	−	7.99862i	−0.380078	−	0.276143i	−0.761378	+	0.648308i	$0.775477\pi$
$840$	−1.72838	−	9.38569i	−0.0596349	−	0.323837i
$841$	19.4997	−	14.1674i	0.672403	−	0.488530i
$842$	−5.69603	+	17.5306i	−0.196298	+	0.604144i
$843$	0.254925			0.00878007
$844$	2.57026	−	7.91045i	0.0884720	−	0.272289i
$845$	−19.1249	−	2.54020i	−0.657917	−	0.0873855i
$846$	−1.42815	−	4.39538i	−0.0491007	−	0.151116i
$847$	−9.40488	−	28.9453i	−0.323156	−	0.994571i
$848$	4.82424	+	3.50502i	0.165665	+	0.120363i
$849$	11.4556			0.393154
$850$	3.99019	−	6.11355i	0.136862	−	0.209693i
$851$	−11.3473			−0.388980
$852$	−6.35835	−	4.61961i	−0.217834	−	0.158265i
$853$	14.2551	+	43.8728i	0.488086	+	1.50218i	0.827460	+	0.561524i	$0.189785\pi$
$853$	14.2551	+	43.8728i	0.488086	+	1.50218i	−0.339374	+	0.940652i	$0.610215\pi$
$854$	−1.52481	−	4.69288i	−0.0521779	−	0.160587i
$855$	4.36788	−	2.36507i	0.149378	−	0.0808838i
$856$	−5.50315	+	16.9370i	−0.188094	+	0.578893i
$857$	−8.79924			−0.300576			−0.150288	−	0.988642i	$-0.548020\pi$
$857$	−8.79924			−0.300576			−0.150288	+	0.988642i	$0.548020\pi$
$858$	−2.37094	+	7.29700i	−0.0809425	+	0.249115i
$859$	−34.0146	+	24.7130i	−1.16056	+	0.843197i	−0.989849	−	0.142123i	$-0.954607\pi$
$859$	−34.0146	+	24.7130i	−1.16056	+	0.843197i	−0.170713	+	0.985321i	$0.554607\pi$
$860$	19.5840	−	10.6041i	0.667807	−	0.361597i
$861$	−36.1999	−	26.3008i	−1.23369	−	0.896328i
$862$	6.42238	−	4.66614i	0.218747	−	0.158929i
$863$	22.1042	−	16.0596i	0.752435	−	0.546676i	−0.144146	−	0.989556i	$-0.546043\pi$
$863$	22.1042	−	16.0596i	0.752435	−	0.546676i	0.896581	+	0.442881i	$0.146043\pi$
$864$	3.72745	+	2.70815i	0.126810	+	0.0921331i
$865$	16.2702	−	34.0106i	0.553205	−	1.15640i
$866$	14.1057	−	10.2484i	0.479331	−	0.348254i
$867$	−4.05424	+	12.4777i	−0.137689	+	0.423764i
$868$	−38.3992			−1.30335
$869$	−9.35618	+	28.7954i	−0.317387	+	0.976815i
$870$	0.790780	+	4.29420i	0.0268100	+	0.145587i
$871$	0.0992257	+	0.305385i	0.00336214	+	0.0103476i
$872$	−1.85073	−	5.69596i	−0.0626736	−	0.192889i
$873$	−2.94119	−	2.13690i	−0.0995442	−	0.0723231i
$874$	4.13054			0.139718
$875$	28.0957	+	46.2047i	0.949807	+	1.56200i
$876$	−2.26389			−0.0764896
$877$	7.00741	+	5.09118i	0.236623	+	0.171917i	0.699778	−	0.714361i	$-0.253282\pi$
$877$	7.00741	+	5.09118i	0.236623	+	0.171917i	−0.463154	+	0.886278i	$0.653282\pi$
$878$	10.2162	+	31.4424i	0.344782	+	1.06113i
$879$	−5.30037	−	16.3129i	−0.178777	−	0.550219i
$880$	1.68401	+	9.14474i	0.0567681	+	0.308269i
$881$	−2.60306	+	8.01139i	−0.0876993	+	0.269911i	−0.985282	−	0.170935i	$-0.945321\pi$
$881$	−2.60306	+	8.01139i	−0.0876993	+	0.269911i	0.897583	+	0.440845i	$0.145321\pi$
$882$	−36.4166			−1.22621
$883$	6.71426	−	20.6644i	0.225953	−	0.695412i	−0.772241	−	0.635330i	$-0.780864\pi$
$883$	6.71426	−	20.6644i	0.225953	−	0.695412i	0.998193	−	0.0600813i	$-0.0191360\pi$
$884$	2.46989	−	1.79448i	0.0830714	−	0.0603549i
$885$	−4.41218	+	9.22304i	−0.148314	+	0.310029i
$886$	−3.03665	−	2.20625i	−0.102018	−	0.0741206i
$887$	32.2481	−	23.4296i	1.08279	−	0.786690i	0.104619	−	0.994512i	$-0.466638\pi$
$887$	32.2481	−	23.4296i	1.08279	−	0.786690i	0.978167	+	0.207822i	$0.0666376\pi$
$888$	1.96116	−	1.42487i	0.0658123	−	0.0478155i
$889$	−14.0035	−	10.1741i	−0.469662	−	0.341229i
$890$	−36.5941	+	19.8146i	−1.22664	+	0.664186i
$891$	−8.74176	+	6.35126i	−0.292860	+	0.212775i
$892$	−5.47461	+	16.8491i	−0.183303	+	0.564150i
$893$	2.08053			0.0696222
$894$	−2.62936	+	8.09233i	−0.0879389	+	0.270648i
$895$	7.65093	−	4.14274i	0.255742	−	0.138477i
$896$	−1.49463	−	4.60000i	−0.0499321	−	0.153675i
$897$	−2.35504	−	7.24808i	−0.0786326	−	0.242006i
$898$	21.8618	+	15.8836i	0.729539	+	0.530041i
$899$	17.5686			0.585946
$900$	−10.7217	−	2.89928i	−0.357389	−	0.0966427i
$901$	−8.70669			−0.290062
$902$	35.2706	+	25.6256i	1.17438	+	0.853239i
$903$	13.1356	+	40.4274i	0.437127	+	1.34534i
$904$	4.80650	+	14.7929i	0.159862	+	0.492004i
$905$	−20.5948	−	2.73543i	−0.684594	−	0.0909288i
$906$	0.926240	−	2.85067i	0.0307723	−	0.0947073i
$907$	20.3291			0.675016			0.337508	−	0.941323i	$-0.390416\pi$
$907$	20.3291			0.675016			0.337508	+	0.941323i	$0.390416\pi$
$908$	−3.37706	+	10.3935i	−0.112072	+	0.344921i
$909$	−33.2911	+	24.1874i	−1.10419	+	0.802244i
$910$	4.09550	+	22.2399i	0.135765	+	0.737246i
$911$	15.9129	+	11.5614i	0.527218	+	0.383046i	0.819316	−	0.573342i	$-0.194353\pi$
$911$	15.9129	+	11.5614i	0.527218	+	0.383046i	−0.292098	+	0.956388i	$0.594353\pi$
$912$	−0.713886	+	0.518669i	−0.0236391	+	0.0171748i
$913$	−50.7791	+	36.8932i	−1.68054	+	1.22099i
$914$	−12.5043	−	9.08488i	−0.413604	−	0.300501i
$915$	1.99545	+	0.265039i	0.0659676	+	0.00876191i
$916$	−12.7428	+	9.25820i	−0.421034	+	0.305899i
$917$	−26.8043	+	82.4950i	−0.885155	+	2.72423i
$918$	−6.72723			−0.222032
$919$	15.8994	−	48.9334i	0.524474	−	1.61416i	−0.240880	−	0.970555i	$-0.577436\pi$
$919$	15.8994	−	48.9334i	0.524474	−	1.61416i	0.765354	−	0.643610i	$-0.222564\pi$
$920$	−6.69237	−	6.36545i	−0.220641	−	0.209863i
$921$	−5.79324	−	17.8298i	−0.190894	−	0.587511i
$922$	−1.13699	−	3.49930i	−0.0374448	−	0.115243i
$923$	15.0665	+	10.9464i	0.495919	+	0.360306i
$924$	−17.7481			−0.583869
$925$	−7.50752	+	11.5026i	−0.246846	+	0.378204i
$926$	−17.3743			−0.570956
$927$	8.72744	+	6.34085i	0.286647	+	0.208261i
$928$	0.683833	+	2.10462i	0.0224479	+	0.0690875i
$929$	−14.3186	−	44.0680i	−0.469777	−	1.44582i	−0.852874	−	0.522116i	$-0.825143\pi$
$929$	−14.3186	−	44.0680i	−0.469777	−	1.44582i	0.383098	−	0.923708i	$-0.374857\pi$
$930$	6.76014	−	14.1311i	0.221674	−	0.463378i
$931$	5.06600	−	15.5915i	0.166031	−	0.510992i
$932$	17.8039			0.583186
$933$	−5.69438	+	17.5255i	−0.186426	+	0.573759i
$934$	−0.135510	+	0.0984537i	−0.00443402	+	0.00322150i
$935$	−9.83747	−	9.35691i	−0.321720	−	0.306004i
$936$	−3.75762	−	2.73007i	−0.122822	−	0.0892351i
$937$	24.4902	−	17.7932i	0.800059	−	0.581277i	−0.110872	−	0.993835i	$-0.535364\pi$
$937$	24.4902	−	17.7932i	0.800059	−	0.581277i	0.910931	+	0.412558i	$0.135364\pi$
$938$	−0.600915	+	0.436590i	−0.0196206	+	0.0142552i
$939$	9.74440	+	7.07972i	0.317996	+	0.231038i
$940$	−3.37091	−	3.20624i	−0.109947	−	0.104576i
$941$	30.9927	−	22.5175i	1.01033	−	0.734049i	0.0460536	−	0.998939i	$-0.485336\pi$
$941$	30.9927	−	22.5175i	1.01033	−	0.734049i	0.964279	+	0.264890i	$0.0853355\pi$
$942$	−4.09637	+	12.6073i	−0.133467	+	0.410769i
$943$	−43.3046			−1.41019
$944$	−1.60122	+	4.92804i	−0.0521152	+	0.160394i
$945$	21.5040	−	44.9511i	0.699526	−	1.46226i
$946$	−12.7984	−	39.3895i	−0.416113	−	1.28066i
$947$	0.619057	+	1.90526i	0.0201166	+	0.0619127i	0.960611	−	0.277897i	$-0.0896374\pi$
$947$	0.619057	+	1.90526i	0.0201166	+	0.0619127i	−0.940494	+	0.339810i	$0.889637\pi$
$948$	5.19777	+	3.77640i	0.168816	+	0.122652i
$949$	5.36440			0.174136
$950$	2.73282	−	4.18708i	0.0886645	−	0.135847i
$951$	3.89431			0.126282
$952$	5.71335	+	4.15099i	0.185171	+	0.134534i
$953$	−7.98474	−	24.5745i	−0.258651	−	0.796046i	−0.993088	−	0.117370i	$-0.962554\pi$
$953$	−7.98474	−	24.5745i	−0.258651	−	0.796046i	0.734437	−	0.678677i	$-0.237446\pi$
$954$	4.09327	+	12.5978i	0.132525	+	0.407869i
$955$	−29.1310	−	27.7080i	−0.942658	−	0.896609i
$956$	3.81650	−	11.7460i	0.123435	−	0.379893i
$957$	8.12020			0.262489
$958$	0.331484	−	1.02020i	0.0107097	−	0.0329612i
$959$	−35.8128	+	26.0195i	−1.15646	+	0.840214i
$960$	1.95596	+	0.259793i	0.0631282	+	0.00838478i
$961$	−25.9120	−	18.8262i	−0.835872	−	0.607297i
$962$	−4.64709	+	3.37631i	−0.149828	+	0.108856i
$963$	−32.0039	+	23.2522i	−1.03131	+	0.749292i
$964$	22.3689	+	16.2520i	0.720455	+	0.523441i
$965$	−4.38538	−	23.8140i	−0.141170	−	0.766601i
$966$	14.2622	−	10.3621i	0.458880	−	0.333396i
$967$	−9.19007	+	28.2841i	−0.295533	+	0.909556i	0.687509	+	0.726175i	$0.258704\pi$
$967$	−9.19007	+	28.2841i	−0.295533	+	0.909556i	−0.983042	+	0.183380i	$0.941296\pi$
$968$	6.29245			0.202247
$969$	0.398140	−	1.22535i	0.0127901	−	0.0393639i
$970$	−3.62774	−	0.481842i	−0.116480	−	0.0154710i
$971$	−8.13495	−	25.0368i	−0.261063	−	0.803470i	−0.992574	−	0.121640i	$-0.961185\pi$
$971$	−8.13495	−	25.0368i	−0.261063	−	0.803470i	0.731511	−	0.681829i	$-0.238815\pi$
$972$	4.97982	+	15.3263i	0.159728	+	0.491592i
$973$	−43.8132	−	31.8321i	−1.40459	−	1.02049i
$974$	2.89480			0.0927552
$975$	−8.90543	−	2.40815i	−0.285202	−	0.0771225i
$976$	1.02019			0.0326556
$977$	−18.2203	−	13.2378i	−0.582920	−	0.423516i	0.256856	−	0.966450i	$-0.417313\pi$
$977$	−18.2203	−	13.2378i	−0.582920	−	0.423516i	−0.839776	+	0.542934i	$0.817313\pi$
$978$	−2.03411	−	6.26034i	−0.0650435	−	0.200183i
$979$	23.9149	+	73.6024i	0.764322	+	2.35234i
$980$	−32.2357	+	17.4546i	−1.02973	+	0.557567i
$981$	4.11112	−	12.6527i	0.131258	−	0.403970i
$982$	12.5184			0.399478
$983$	8.20213	−	25.2436i	0.261607	−	0.805145i	−0.730848	−	0.682540i	$-0.760875\pi$
$983$	8.20213	−	25.2436i	0.261607	−	0.805145i	0.992456	−	0.122605i	$-0.0391247\pi$
$984$	7.48438	−	5.43772i	0.238593	−	0.173348i
$985$	−0.105150	+	0.0569357i	−0.00335037	+	0.00181412i
$986$	−2.61401	−	1.89919i	−0.0832470	−	0.0604825i
$987$	7.18380	−	5.21933i	0.228663	−	0.166133i
$988$	1.69159	−	1.22901i	0.0538167	−	0.0391002i
$989$	33.2821	+	24.1809i	1.05831	+	0.768907i
$990$	−8.91372	+	18.6329i	−0.283297	+	0.592192i
$991$	−19.0806	+	13.8629i	−0.606117	+	0.440370i	−0.848045	−	0.529925i	$-0.822220\pi$
$991$	−19.0806	+	13.8629i	−0.606117	+	0.440370i	0.241928	+	0.970294i	$0.422220\pi$
$992$	2.45331	−	7.55052i	0.0778927	−	0.239729i
$993$	15.6510			0.496669
$994$	−13.3122	+	40.9707i	−0.422237	+	1.29951i
$995$	9.20140	+	49.9666i	0.291704	+	1.58405i
$996$	4.11578	+	12.6671i	0.130414	+	0.401372i
$997$	−0.741128	−	2.28096i	−0.0234718	−	0.0722386i	0.938635	−	0.344913i	$-0.112092\pi$
$997$	−0.741128	−	2.28096i	−0.0234718	−	0.0722386i	−0.962106	+	0.272675i	$0.912092\pi$
$998$	−10.1194	−	7.35220i	−0.320325	−	0.232730i
$999$	12.6572			0.400457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.b.191.7	✓	40
25.11	even	5	inner	950.2.h.b.761.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.b.191.7	✓	40	1.1	even	1	trivial
950.2.h.b.761.7	yes	40	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.272680 + 0.839224i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.404965 + 2.19909i) q^{5} +(0.272680 - 0.839224i) q^{6} -4.83673 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.79711 - 1.30568i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.272680 + 0.839224i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.404965 + 2.19909i) q^{5} +(0.272680 - 0.839224i) q^{6} -4.83673 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.79711 - 1.30568i) q^{9} +(0.964970 - 2.01713i) q^{10} +(-3.36423 - 2.44426i) q^{11} +(-0.713886 + 0.518669i) q^{12} +(1.69159 - 1.22901i) q^{13} +(3.91299 + 2.84296i) q^{14} +(-1.73510 + 0.939505i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.451195 - 1.38864i) q^{17} -2.22135 q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.96632 + 1.06470i) q^{20} +(-1.31888 - 4.05909i) q^{21} +(1.28502 + 3.95489i) q^{22} +(-3.34168 - 2.42787i) q^{23} +0.882412 q^{24} +(-4.67201 + 1.78111i) q^{25} -2.09092 q^{26} +(3.72745 + 2.70815i) q^{27} +(-1.49463 - 4.60000i) q^{28} +(0.683833 + 2.10462i) q^{29} +(1.95596 + 0.259793i) q^{30} +(2.45331 - 7.55052i) q^{31} +1.00000 q^{32} +(1.13392 - 3.48984i) q^{33} +(-1.18124 + 0.858224i) q^{34} +(-1.95870 - 10.6364i) q^{35} +(1.79711 + 1.30568i) q^{36} +(2.22250 - 1.61474i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(1.49268 + 1.08450i) q^{39} +(2.21660 + 0.294412i) q^{40} +(8.48173 - 6.16234i) q^{41} +(-1.31888 + 4.05909i) q^{42} -9.95970 q^{43} +(1.28502 - 3.95489i) q^{44} +(3.59907 + 3.42326i) q^{45} +(1.27641 + 3.92838i) q^{46} +(0.642918 + 1.97870i) q^{47} +(-0.713886 - 0.518669i) q^{48} +16.3939 q^{49} +(4.82664 + 1.30519i) q^{50} +1.28841 q^{51} +(1.69159 + 1.22901i) q^{52} +(-1.84270 - 5.67123i) q^{53} +(-1.42376 - 4.38188i) q^{54} +(4.01275 - 8.38809i) q^{55} +(-1.49463 + 4.60000i) q^{56} +0.882412 q^{57} +(0.683833 - 2.10462i) q^{58} +(4.19204 - 3.04570i) q^{59} +(-1.42970 - 1.35986i) q^{60} +(-0.825353 - 0.599654i) q^{61} +(-6.42285 + 4.66648i) q^{62} +(-8.69213 + 6.31520i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.38775 + 3.22226i) q^{65} +(-2.96864 + 2.15684i) q^{66} +(-0.0474555 + 0.146053i) q^{67} +1.46010 q^{68} +(1.12632 - 3.46645i) q^{69} +(-4.66730 + 9.75633i) q^{70} +(2.75231 + 8.47075i) q^{71} +(-0.686435 - 2.11263i) q^{72} +(2.07559 + 1.50800i) q^{73} -2.74717 q^{74} +(-2.76871 - 3.43519i) q^{75} +1.00000 q^{76} +(16.2719 + 11.8222i) q^{77} +(-0.570154 - 1.75475i) q^{78} +(-2.24994 - 6.92459i) q^{79} +(-1.62022 - 1.54107i) q^{80} +(0.802962 - 2.47126i) q^{81} -10.4840 q^{82} +(4.66424 - 14.3551i) q^{83} +(3.45287 - 2.50866i) q^{84} +(3.23645 + 0.429871i) q^{85} +(8.05757 + 5.85417i) q^{86} +(-1.57978 + 1.14778i) q^{87} +(-3.36423 + 2.44426i) q^{88} +(-15.0562 - 10.9390i) q^{89} +(-0.899568 - 4.88495i) q^{90} +(-8.18177 + 5.94441i) q^{91} +(1.27641 - 3.92838i) q^{92} +7.00554 q^{93} +(0.642918 - 1.97870i) q^{94} +(2.21660 + 0.294412i) q^{95} +(0.272680 + 0.839224i) q^{96} +(-0.505744 - 1.55652i) q^{97} +(-13.2630 - 9.63610i) q^{98} -9.23730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

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