LMFDB - Embedded newform 845.2.e.p.191.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 17 x^{16} - 18 x^{15} + 230 x^{14} - 185 x^{13} + 996 x^{12} - 534 x^{11} + 3020 x^{10} + \cdots + 1 $ x^18 + 17x^16 - 18x^15 + 230x^14 - 185x^13 + 996x^12 - 534x^11 + 3020x^10 - 1485x^9 + 3379x^8 - 1280x^7 + 2595x^6 - 1007x^5 + 541x^4 - 65x^3 + 24*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.9
Root			$-0.493739 - 0.855181i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.p.146.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39471 - 2.41570i) q^{2} +(0.907309 - 1.57151i) q^{3} +(-2.89042 - 5.00635i) q^{4} -1.00000 q^{5} +(-2.53086 - 4.38358i) q^{6} +(0.134800 + 0.233481i) q^{7} -10.5463 q^{8} +(-0.146421 - 0.253609i) q^{9} +O(q^{10})$	\(q+(1.39471 - 2.41570i) q^{2} +(0.907309 - 1.57151i) q^{3} +(-2.89042 - 5.00635i) q^{4} -1.00000 q^{5} +(-2.53086 - 4.38358i) q^{6} +(0.134800 + 0.233481i) q^{7} -10.5463 q^{8} +(-0.146421 - 0.253609i) q^{9} +(-1.39471 + 2.41570i) q^{10} +(0.905401 - 1.56820i) q^{11} -10.4900 q^{12} +0.752028 q^{14} +(-0.907309 + 1.57151i) q^{15} +(-8.92820 + 15.4641i) q^{16} +(0.368683 + 0.638578i) q^{17} -0.816858 q^{18} +(-1.08983 - 1.88763i) q^{19} +(2.89042 + 5.00635i) q^{20} +0.489222 q^{21} +(-2.52554 - 4.37436i) q^{22} +(1.37558 - 2.38258i) q^{23} +(-9.56878 + 16.5736i) q^{24} +1.00000 q^{25} +4.91246 q^{27} +(0.779259 - 1.34972i) q^{28} +(3.60627 - 6.24624i) q^{29} +(2.53086 + 4.38358i) q^{30} -6.19428 q^{31} +(14.3581 + 24.8690i) q^{32} +(-1.64296 - 2.84569i) q^{33} +2.05682 q^{34} +(-0.134800 - 0.233481i) q^{35} +(-0.846436 + 1.46607i) q^{36} +(3.83203 - 6.63727i) q^{37} -6.07995 q^{38} +10.5463 q^{40} +(-4.18948 + 7.25640i) q^{41} +(0.682322 - 1.18182i) q^{42} +(0.584581 + 1.01252i) q^{43} -10.4679 q^{44} +(0.146421 + 0.253609i) q^{45} +(-3.83707 - 6.64600i) q^{46} +0.121132 q^{47} +(16.2013 + 28.0615i) q^{48} +(3.46366 - 5.99923i) q^{49} +(1.39471 - 2.41570i) q^{50} +1.33804 q^{51} +3.85022 q^{53} +(6.85145 - 11.8671i) q^{54} +(-0.905401 + 1.56820i) q^{55} +(-1.42165 - 2.46237i) q^{56} -3.95524 q^{57} +(-10.0594 - 17.4233i) q^{58} +(-5.31538 - 9.20651i) q^{59} +10.4900 q^{60} +(2.12190 + 3.67524i) q^{61} +(-8.63921 + 14.9635i) q^{62} +(0.0394752 - 0.0683730i) q^{63} +44.3888 q^{64} -9.16578 q^{66} +(-4.77547 + 8.27136i) q^{67} +(2.13130 - 3.69151i) q^{68} +(-2.49616 - 4.32347i) q^{69} -0.752028 q^{70} +(4.06048 + 7.03296i) q^{71} +(1.54420 + 2.67464i) q^{72} +0.692889 q^{73} +(-10.6891 - 18.5141i) q^{74} +(0.907309 - 1.57151i) q^{75} +(-6.30010 + 10.9121i) q^{76} +0.488193 q^{77} +6.65811 q^{79} +(8.92820 - 15.4641i) q^{80} +(4.89638 - 8.48079i) q^{81} +(11.6862 + 20.2411i) q^{82} +9.19337 q^{83} +(-1.41406 - 2.44922i) q^{84} +(-0.368683 - 0.638578i) q^{85} +3.26128 q^{86} +(-6.54400 - 11.3345i) q^{87} +(-9.54865 + 16.5388i) q^{88} +(-3.28581 + 5.69120i) q^{89} +0.816858 q^{90} -15.9040 q^{92} +(-5.62013 + 9.73434i) q^{93} +(0.168944 - 0.292620i) q^{94} +(1.08983 + 1.88763i) q^{95} +52.1091 q^{96} +(-8.72012 - 15.1037i) q^{97} +(-9.66158 - 16.7343i) q^{98} -0.530279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 7 q^{3} - 17 q^{4} - 18 q^{5} - 2 q^{6} + 7 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 7 * q^3 - 17 * q^4 - 18 * q^5 - 2 * q^6 + 7 * q^7 - 24 * q^8 - 16 * q^9	\( 18 q + 3 q^{2} - 7 q^{3} - 17 q^{4} - 18 q^{5} - 2 q^{6} + 7 q^{7} - 24 q^{8} - 16 q^{9} - 3 q^{10} - 9 q^{11} + 24 q^{12} - 4 q^{14} + 7 q^{15} - 37 q^{16} + q^{17} + 20 q^{18} - 4 q^{19} + 17 q^{20} + 2 q^{21} - 12 q^{22} - 14 q^{23} - 35 q^{24} + 18 q^{25} + 44 q^{27} + 18 q^{28} - 12 q^{29} + 2 q^{30} + 14 q^{31} + 22 q^{32} - 8 q^{33} + 60 q^{34} - 7 q^{35} - 3 q^{36} - 5 q^{37} - 94 q^{38} + 24 q^{40} - 10 q^{41} + 11 q^{42} - 39 q^{43} + 50 q^{44} + 16 q^{45} + 6 q^{46} - 72 q^{47} + 3 q^{48} - 16 q^{49} + 3 q^{50} + 86 q^{51} - 16 q^{53} - 2 q^{54} + 9 q^{55} + 29 q^{56} + 64 q^{57} + 21 q^{58} - 21 q^{59} - 24 q^{60} + 3 q^{61} + 10 q^{62} + 35 q^{63} + 68 q^{64} - 98 q^{66} + q^{67} + 20 q^{68} + 13 q^{69} + 4 q^{70} - q^{71} - 3 q^{72} + 15 q^{74} - 7 q^{75} - 5 q^{76} - 8 q^{77} + 78 q^{79} + 37 q^{80} - 29 q^{81} + 4 q^{82} - 14 q^{83} + 12 q^{84} - q^{85} + 48 q^{86} - 16 q^{87} - 42 q^{88} - 19 q^{89} - 20 q^{90} - 54 q^{92} + 31 q^{93} - 16 q^{94} + 4 q^{95} + 14 q^{96} - 34 q^{97} + 48 q^{98} + 2 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 7 * q^3 - 17 * q^4 - 18 * q^5 - 2 * q^6 + 7 * q^7 - 24 * q^8 - 16 * q^9 - 3 * q^10 - 9 * q^11 + 24 * q^12 - 4 * q^14 + 7 * q^15 - 37 * q^16 + q^17 + 20 * q^18 - 4 * q^19 + 17 * q^20 + 2 * q^21 - 12 * q^22 - 14 * q^23 - 35 * q^24 + 18 * q^25 + 44 * q^27 + 18 * q^28 - 12 * q^29 + 2 * q^30 + 14 * q^31 + 22 * q^32 - 8 * q^33 + 60 * q^34 - 7 * q^35 - 3 * q^36 - 5 * q^37 - 94 * q^38 + 24 * q^40 - 10 * q^41 + 11 * q^42 - 39 * q^43 + 50 * q^44 + 16 * q^45 + 6 * q^46 - 72 * q^47 + 3 * q^48 - 16 * q^49 + 3 * q^50 + 86 * q^51 - 16 * q^53 - 2 * q^54 + 9 * q^55 + 29 * q^56 + 64 * q^57 + 21 * q^58 - 21 * q^59 - 24 * q^60 + 3 * q^61 + 10 * q^62 + 35 * q^63 + 68 * q^64 - 98 * q^66 + q^67 + 20 * q^68 + 13 * q^69 + 4 * q^70 - q^71 - 3 * q^72 + 15 * q^74 - 7 * q^75 - 5 * q^76 - 8 * q^77 + 78 * q^79 + 37 * q^80 - 29 * q^81 + 4 * q^82 - 14 * q^83 + 12 * q^84 - q^85 + 48 * q^86 - 16 * q^87 - 42 * q^88 - 19 * q^89 - 20 * q^90 - 54 * q^92 + 31 * q^93 - 16 * q^94 + 4 * q^95 + 14 * q^96 - 34 * q^97 + 48 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.39471	−	2.41570i	0.986207	−	1.70816i	0.349763	−	0.936838i	$-0.386262\pi$
$2$	1.39471	−	2.41570i	0.986207	−	1.70816i	0.636444	−	0.771323i	$-0.280405\pi$
$3$	0.907309	−	1.57151i	0.523835	−	0.907309i	−0.475780	−	0.879565i	$-0.657834\pi$
$3$	0.907309	−	1.57151i	0.523835	−	0.907309i	0.999615	−	0.0277450i	$-0.00883264\pi$
$4$	−2.89042	−	5.00635i	−1.44521	−	2.50318i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−2.53086	−	4.38358i	−1.03322	−	1.78959i
$7$	0.134800	+	0.233481i	0.0509497	+	0.0882475i	0.890375	−	0.455227i	$-0.150442\pi$
$7$	0.134800	+	0.233481i	0.0509497	+	0.0882475i	−0.839426	+	0.543474i	$0.817109\pi$
$8$	−10.5463			−3.72869
$9$	−0.146421	−	0.253609i	−0.0488070	−	0.0845362i
$10$	−1.39471	+	2.41570i	−0.441045	+	0.763913i
$11$	0.905401	−	1.56820i	0.272989	−	0.472830i	−0.696637	−	0.717424i	$-0.745321\pi$
$11$	0.905401	−	1.56820i	0.272989	−	0.472830i	0.969626	+	0.244594i	$0.0786545\pi$
$12$	−10.4900			−3.02821
$13$		0			0
$13$		0			0
$14$	0.752028			0.200988
$15$	−0.907309	+	1.57151i	−0.234266	+	0.405761i
$16$	−8.92820	+	15.4641i	−2.23205	+	3.86603i
$17$	0.368683	+	0.638578i	0.0894188	+	0.154878i	0.907266	−	0.420558i	$-0.138166\pi$
$17$	0.368683	+	0.638578i	0.0894188	+	0.154878i	−0.817847	+	0.575436i	$0.804832\pi$
$18$	−0.816858			−0.192535
$19$	−1.08983	−	1.88763i	−0.250023	−	0.433053i	0.713509	−	0.700646i	$-0.247105\pi$
$19$	−1.08983	−	1.88763i	−0.250023	−	0.433053i	−0.963532	+	0.267594i	$0.913772\pi$
$20$	2.89042	+	5.00635i	0.646317	+	1.11945i
$21$	0.489222			0.106757
$22$	−2.52554	−	4.37436i	−0.538447	−	0.932617i
$23$	1.37558	−	2.38258i	0.286829	−	0.496802i	−0.686222	−	0.727392i	$-0.740732\pi$
$23$	1.37558	−	2.38258i	0.286829	−	0.496802i	0.973051	+	0.230590i	$0.0740656\pi$
$24$	−9.56878	+	16.5736i	−1.95322	+	3.38308i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.91246			0.945403
$28$	0.779259	−	1.34972i	0.147266	−	0.255072i
$29$	3.60627	−	6.24624i	0.669667	−	1.15990i	−0.308331	−	0.951279i	$-0.599770\pi$
$29$	3.60627	−	6.24624i	0.669667	−	1.15990i	0.977997	−	0.208618i	$-0.0668964\pi$
$30$	2.53086	+	4.38358i	0.462070	+	0.800329i
$31$	−6.19428			−1.11253			−0.556263	−	0.831007i	$-0.687765\pi$
$31$	−6.19428			−1.11253			−0.556263	+	0.831007i	$0.687765\pi$
$32$	14.3581	+	24.8690i	2.53819	+	4.39627i
$33$	−1.64296	−	2.84569i	−0.286002	−	0.495370i
$34$	2.05682			0.352742
$35$	−0.134800	−	0.233481i	−0.0227854	−	0.0394655i
$36$	−0.846436	+	1.46607i	−0.141073	+	0.244345i
$37$	3.83203	−	6.63727i	0.629982	−	1.09116i	−0.357573	−	0.933885i	$-0.616396\pi$
$37$	3.83203	−	6.63727i	0.629982	−	1.09116i	0.987555	−	0.157275i	$-0.0502711\pi$
$38$	−6.07995			−0.986299
$39$		0			0
$40$	10.5463			1.66752
$41$	−4.18948	+	7.25640i	−0.654287	+	1.13326i	0.327785	+	0.944753i	$0.393698\pi$
$41$	−4.18948	+	7.25640i	−0.654287	+	1.13326i	−0.982072	+	0.188507i	$0.939635\pi$
$42$	0.682322	−	1.18182i	0.105285	−	0.182358i
$43$	0.584581	+	1.01252i	0.0891478	+	0.154408i	0.907151	−	0.420805i	$-0.138252\pi$
$43$	0.584581	+	1.01252i	0.0891478	+	0.154408i	−0.818003	+	0.575213i	$0.804919\pi$
$44$	−10.4679			−1.57810
$45$	0.146421	+	0.253609i	0.0218272	+	0.0378058i
$46$	−3.83707	−	6.64600i	−0.565745	−	0.979899i
$47$	0.121132			0.0176690			0.00883449	−	0.999961i	$-0.497188\pi$
$47$	0.121132			0.0176690			0.00883449	+	0.999961i	$0.497188\pi$
$48$	16.2013	+	28.0615i	2.33845	+	4.05032i
$49$	3.46366	−	5.99923i	0.494808	−	0.857033i
$50$	1.39471	−	2.41570i	0.197241	−	0.341632i
$51$	1.33804			0.187363
$52$		0			0
$53$	3.85022			0.528868			0.264434	−	0.964404i	$-0.414815\pi$
$53$	3.85022			0.528868			0.264434	+	0.964404i	$0.414815\pi$
$54$	6.85145	−	11.8671i	0.932364	−	1.61490i
$55$	−0.905401	+	1.56820i	−0.122084	+	0.211456i
$56$	−1.42165	−	2.46237i	−0.189976	−	0.329048i
$57$	−3.95524			−0.523884
$58$	−10.0594	−	17.4233i	−1.32086	−	2.28780i
$59$	−5.31538	−	9.20651i	−0.692003	−	1.19859i	−0.971180	−	0.238346i	$-0.923395\pi$
$59$	−5.31538	−	9.20651i	−0.692003	−	1.19859i	0.279177	−	0.960240i	$-0.409938\pi$
$60$	10.4900			1.35426
$61$	2.12190	+	3.67524i	0.271681	+	0.470566i	0.969293	−	0.245911i	$-0.0790869\pi$
$61$	2.12190	+	3.67524i	0.271681	+	0.470566i	−0.697611	+	0.716477i	$0.745754\pi$
$62$	−8.63921	+	14.9635i	−1.09718	+	1.90037i
$63$	0.0394752	−	0.0683730i	0.00497341	−	0.00861419i
$64$	44.3888			5.54860
$65$		0			0
$66$	−9.16578			−1.12823
$67$	−4.77547	+	8.27136i	−0.583417	+	1.01051i	0.411654	+	0.911340i	$0.364951\pi$
$67$	−4.77547	+	8.27136i	−0.583417	+	1.01051i	−0.995071	+	0.0991674i	$0.968382\pi$
$68$	2.13130	−	3.69151i	0.258458	−	0.447662i
$69$	−2.49616	−	4.32347i	−0.300502	−	0.520485i
$70$	−0.752028			−0.0898845
$71$	4.06048	+	7.03296i	0.481891	+	0.834659i	0.999784	−	0.0207860i	$-0.00661687\pi$
$71$	4.06048	+	7.03296i	0.481891	+	0.834659i	−0.517893	+	0.855445i	$0.673284\pi$
$72$	1.54420	+	2.67464i	0.181986	+	0.315209i
$73$	0.692889			0.0810966			0.0405483	−	0.999178i	$-0.487090\pi$
$73$	0.692889			0.0810966			0.0405483	+	0.999178i	$0.487090\pi$
$74$	−10.6891	−	18.5141i	−1.24259	−	2.15222i
$75$	0.907309	−	1.57151i	0.104767	−	0.181462i
$76$	−6.30010	+	10.9121i	−0.722672	+	1.25170i
$77$	0.488193			0.0556348
$78$		0			0
$79$	6.65811			0.749096			0.374548	−	0.927207i	$-0.377798\pi$
$79$	6.65811			0.749096			0.374548	+	0.927207i	$0.377798\pi$
$80$	8.92820	−	15.4641i	0.998204	−	1.72894i
$81$	4.89638	−	8.48079i	0.544043	−	0.942310i
$82$	11.6862	+	20.2411i	1.29053	+	2.23526i
$83$	9.19337			1.00910			0.504552	−	0.863381i	$-0.331658\pi$
$83$	9.19337			1.00910			0.504552	+	0.863381i	$0.331658\pi$
$84$	−1.41406	−	2.44922i	−0.154286	−	0.267232i
$85$	−0.368683	−	0.638578i	−0.0399893	−	0.0692635i
$86$	3.26128			0.351673
$87$	−6.54400	−	11.3345i	−0.701590	−	1.21519i
$88$	−9.54865	+	16.5388i	−1.01789	+	1.76304i
$89$	−3.28581	+	5.69120i	−0.348296	+	0.603266i	−0.985947	−	0.167059i	$-0.946573\pi$
$89$	−3.28581	+	5.69120i	−0.348296	+	0.603266i	0.637651	+	0.770325i	$0.279906\pi$
$90$	0.816858			0.0861044
$91$		0			0
$92$	−15.9040			−1.65811
$93$	−5.62013	+	9.73434i	−0.582780	+	1.00940i
$94$	0.168944	−	0.292620i	0.0174253	−	0.0301815i
$95$	1.08983	+	1.88763i	0.111814	+	0.193667i
$96$	52.1091			5.31836
$97$	−8.72012	−	15.1037i	−0.885394	−	1.53355i	−0.845261	−	0.534354i	$-0.820555\pi$
$97$	−8.72012	−	15.1037i	−0.885394	−	1.53355i	−0.0401336	−	0.999194i	$-0.512778\pi$
$98$	−9.66158	−	16.7343i	−0.975967	−	1.69042i
$99$	−0.530279			−0.0532950
$100$	−2.89042	−	5.00635i	−0.289042	−	0.500635i
$101$	5.90035	−	10.2197i	0.587107	−	1.01690i	−0.407502	−	0.913204i	$-0.633600\pi$
$101$	5.90035	−	10.2197i	0.587107	−	1.01690i	0.994609	−	0.103695i	$-0.0330666\pi$
$102$	1.86617	−	3.23230i	0.184779	−	0.320046i
$103$	−8.03859			−0.792066			−0.396033	−	0.918236i	$-0.629613\pi$
$103$	−8.03859			−0.792066			−0.396033	+	0.918236i	$0.629613\pi$
$104$		0			0
$105$	−0.489222			−0.0477432
$106$	5.36993	−	9.30099i	0.521574	−	0.903392i
$107$	−8.64884	+	14.9802i	−0.836115	+	1.44819i	0.0570036	+	0.998374i	$0.481845\pi$
$107$	−8.64884	+	14.9802i	−0.836115	+	1.44819i	−0.893119	+	0.449820i	$0.851488\pi$
$108$	−14.1991	−	24.5935i	−1.36631	−	2.36651i
$109$	15.1297			1.44916			0.724581	−	0.689189i	$-0.242033\pi$
$109$	15.1297			1.44916			0.724581	+	0.689189i	$0.242033\pi$
$110$	2.52554	+	4.37436i	0.240801	+	0.417079i
$111$	−6.95368	−	12.0441i	−0.660014	−	1.14318i
$112$	−4.81410			−0.454889
$113$	−6.23428	−	10.7981i	−0.586472	−	1.01580i	−0.994690	−	0.102915i	$-0.967183\pi$
$113$	−6.23428	−	10.7981i	−0.586472	−	1.01580i	0.408218	−	0.912884i	$-0.366150\pi$
$114$	−5.51640	+	9.55468i	−0.516658	+	0.894878i
$115$	−1.37558	+	2.38258i	−0.128274	+	0.222177i
$116$	−41.6945			−3.87123
$117$		0			0
$118$	−29.6536			−2.72984
$119$	−0.0993971	+	0.172161i	−0.00911172	+	0.0157820i
$120$	9.56878	−	16.5736i	0.873506	−	1.51296i
$121$	3.86050	+	6.68658i	0.350954	+	0.607871i
$122$	11.8377			1.07174
$123$	7.60232	+	13.1676i	0.685478	+	1.18728i
$124$	17.9041	+	31.0107i	1.60783	+	2.78485i
$125$	−1.00000			−0.0894427
$126$	−0.110113	−	0.190721i	−0.00980962	−	0.0169908i
$127$	−5.94378	+	10.2949i	−0.527425	+	0.913528i	0.472064	+	0.881564i	$0.343509\pi$
$127$	−5.94378	+	10.2949i	−0.527425	+	0.913528i	−0.999489	+	0.0319632i	$0.989824\pi$
$128$	33.1932	−	57.4922i	2.93389	−	5.08164i
$129$	2.12158			0.186795
$130$		0			0
$131$	13.7794			1.20391			0.601955	−	0.798530i	$-0.294389\pi$
$131$	13.7794			1.20391			0.601955	+	0.798530i	$0.294389\pi$
$132$	−9.49767	+	16.4504i	−0.826666	+	1.43183i
$133$	0.293818	−	0.508907i	0.0254772	−	0.0441278i
$134$	13.3208	+	23.0723i	1.15074	+	1.99314i
$135$	−4.91246			−0.422797
$136$	−3.88825	−	6.73465i	−0.333415	−	0.577491i
$137$	7.08021	+	12.2633i	0.604903	+	1.04772i	0.992067	+	0.125712i	$0.0401216\pi$
$137$	7.08021	+	12.2633i	0.604903	+	1.04772i	−0.387163	+	0.922011i	$0.626545\pi$
$138$	−13.9256			−1.18543
$139$	−2.26822	−	3.92868i	−0.192388	−	0.333226i	0.753653	−	0.657273i	$-0.228290\pi$
$139$	−2.26822	−	3.92868i	−0.192388	−	0.333226i	−0.946041	+	0.324046i	$0.894957\pi$
$140$	−0.779259	+	1.34972i	−0.0658594	+	0.114072i
$141$	0.109905	−	0.190360i	0.00925564	−	0.0160312i
$142$	22.6527			1.90098
$143$		0			0
$144$	5.22911			0.435759
$145$	−3.60627	+	6.24624i	−0.299484	+	0.518722i
$146$	0.966378	−	1.67382i	0.0799780	−	0.138526i
$147$	−6.28522	−	10.8863i	−0.518396	−	0.897888i
$148$	−44.3047			−3.64182
$149$	−1.75960	−	3.04772i	−0.144152	−	0.249679i	0.784904	−	0.619617i	$-0.212712\pi$
$149$	−1.75960	−	3.04772i	−0.144152	−	0.249679i	−0.929056	+	0.369938i	$0.879379\pi$
$150$	−2.53086	−	4.38358i	−0.206644	−	0.357918i
$151$	4.49258			0.365601			0.182801	−	0.983150i	$-0.441484\pi$
$151$	4.49258			0.365601			0.182801	+	0.983150i	$0.441484\pi$
$152$	11.4937	+	19.9076i	0.932259	+	1.61472i
$153$	0.107966	−	0.187002i	0.00872852	−	0.0151182i
$154$	0.680887	−	1.17933i	0.0548674	−	0.0950331i
$155$	6.19428			0.497536
$156$		0			0
$157$	10.2430			0.817480			0.408740	−	0.912651i	$-0.365968\pi$
$157$	10.2430			0.817480			0.408740	+	0.912651i	$0.365968\pi$
$158$	9.28612	−	16.0840i	0.738764	−	1.27958i
$159$	3.49334	−	6.05064i	0.277040	−	0.479847i
$160$	−14.3581	−	24.8690i	−1.13511	−	1.96607i
$161$	0.741716			0.0584554
$162$	−13.6581	−	23.6564i	−1.07308	−	1.85863i
$163$	−0.844097	−	1.46202i	−0.0661147	−	0.114514i	0.831073	−	0.556163i	$-0.187727\pi$
$163$	−0.844097	−	1.46202i	−0.0661147	−	0.114514i	−0.897188	+	0.441649i	$0.854394\pi$
$164$	48.4374			3.78233
$165$	1.64296	+	2.84569i	0.127904	+	0.221536i
$166$	12.8221	−	22.2085i	0.995185	−	1.72371i
$167$	−2.14934	+	3.72277i	−0.166321	+	0.288077i	−0.937124	−	0.348997i	$-0.886522\pi$
$167$	−2.14934	+	3.72277i	−0.166321	+	0.288077i	0.770802	+	0.637074i	$0.219856\pi$
$168$	−5.15950			−0.398064
$169$		0			0
$170$	−2.05682			−0.157751
$171$	−0.319147	+	0.552778i	−0.0244058	+	0.0422720i
$172$	3.37937	−	5.85324i	0.257674	−	0.446305i
$173$	5.59562	+	9.69190i	0.425427	+	0.736862i	0.996460	−	0.0840654i	$-0.0267905\pi$
$173$	5.59562	+	9.69190i	0.425427	+	0.736862i	−0.571033	+	0.820927i	$0.693457\pi$
$174$	−36.5079			−2.76765
$175$	0.134800	+	0.233481i	0.0101899	+	0.0176495i
$176$	16.1672	+	28.0024i	1.21865	+	2.11076i
$177$	−19.2908			−1.44998
$178$	9.16550	+	15.8751i	0.686983	+	1.18989i
$179$	−3.84100	+	6.65282i	−0.287090	+	0.497255i	−0.973114	−	0.230324i	$-0.926021\pi$
$179$	−3.84100	+	6.65282i	−0.287090	+	0.497255i	0.686024	+	0.727579i	$0.259355\pi$
$180$	0.846436	−	1.46607i	0.0630896	−	0.109274i
$181$	6.44731			0.479225			0.239612	−	0.970869i	$-0.422980\pi$
$181$	6.44731			0.479225			0.239612	+	0.970869i	$0.422980\pi$
$182$		0			0
$183$	7.70088			0.569266
$184$	−14.5073	+	25.1274i	−1.06950	+	1.85242i
$185$	−3.83203	+	6.63727i	−0.281736	+	0.487982i
$186$	15.6769	+	27.1531i	1.14948	+	1.99096i
$187$	1.33522			0.0976412
$188$	−0.350124	−	0.606432i	−0.0255354	−	0.0442286i
$189$	0.662201	+	1.14697i	0.0481680	+	0.0834295i
$190$	6.07995			0.441086
$191$	9.26601	+	16.0492i	0.670465	+	1.16128i	0.977772	+	0.209669i	$0.0672386\pi$
$191$	9.26601	+	16.0492i	0.670465	+	1.16128i	−0.307308	+	0.951610i	$0.599428\pi$
$192$	40.2744	−	69.7573i	2.90655	−	5.03430i
$193$	1.98453	−	3.43730i	0.142849	−	0.247422i	−0.785719	−	0.618583i	$-0.787707\pi$
$193$	1.98453	−	3.43730i	0.142849	−	0.247422i	0.928569	+	0.371161i	$0.121040\pi$
$194$	−48.6481			−3.49273
$195$		0			0
$196$	−40.0457			−2.86041
$197$	0.857931	−	1.48598i	0.0611251	−	0.105872i	−0.833843	−	0.552001i	$-0.813864\pi$
$197$	0.857931	−	1.48598i	0.0611251	−	0.105872i	0.894969	+	0.446129i	$0.147198\pi$
$198$	−0.739584	+	1.28100i	−0.0525600	+	0.0910365i
$199$	−10.1256	−	17.5381i	−0.717787	−	1.24324i	−0.961875	−	0.273490i	$-0.911822\pi$
$199$	−10.1256	−	17.5381i	−0.717787	−	1.24324i	0.244088	−	0.969753i	$-0.421512\pi$
$200$	−10.5463			−0.745738
$201$	8.66566	+	15.0094i	0.611229	+	1.05868i
$202$	−16.4585	−	28.5070i	−1.15802	−	2.00575i
$203$	1.94450			0.136477
$204$	−3.86749	−	6.69869i	−0.270779	−	0.469002i
$205$	4.18948	−	7.25640i	0.292606	−	0.506809i
$206$	−11.2115	+	19.4189i	−0.781141	+	1.35298i
$207$	−0.805657			−0.0559970
$208$		0			0
$209$	−3.94692			−0.273014
$210$	−0.682322	+	1.18182i	−0.0470847	+	0.0815531i
$211$	−3.38891	+	5.86976i	−0.233302	+	0.404091i	−0.958778	−	0.284157i	$-0.908286\pi$
$211$	−3.38891	+	5.86976i	−0.233302	+	0.404091i	0.725476	+	0.688248i	$0.241620\pi$
$212$	−11.1287	−	19.2755i	−0.764325	−	1.32385i
$213$	14.7365			1.00973
$214$	24.1252	+	41.7861i	1.64917	+	2.85644i
$215$	−0.584581	−	1.01252i	−0.0398681	−	0.0690536i
$216$	−51.8084			−3.52512
$217$	−0.834990	−	1.44625i	−0.0566828	−	0.0981776i
$218$	21.1015	−	36.5489i	1.42917	−	2.47540i
$219$	0.628665	−	1.08888i	0.0424812	−	0.0735797i
$220$	10.4679			0.705749
$221$		0			0
$222$	−38.7934			−2.60364
$223$	5.10661	−	8.84491i	0.341964	−	0.592299i	−0.642833	−	0.766006i	$-0.722241\pi$
$223$	5.10661	−	8.84491i	0.341964	−	0.592299i	0.984797	+	0.173707i	$0.0555746\pi$
$224$	−3.87096	+	6.70471i	−0.258640	+	0.447977i
$225$	−0.146421	−	0.253609i	−0.00976140	−	0.0169072i
$226$	−34.7800			−2.31353
$227$	−4.54598	−	7.87387i	−0.301727	−	0.522607i	0.674800	−	0.738001i	$-0.264230\pi$
$227$	−4.54598	−	7.87387i	−0.301727	−	0.522607i	−0.976527	+	0.215394i	$0.930897\pi$
$228$	11.4323	+	19.8013i	0.757122	+	1.31137i
$229$	−7.80962			−0.516074			−0.258037	−	0.966135i	$-0.583076\pi$
$229$	−7.80962			−0.516074			−0.258037	+	0.966135i	$0.583076\pi$
$230$	3.83707	+	6.64600i	0.253009	+	0.438224i
$231$	0.442942	−	0.767199i	0.0291435	−	0.0504780i
$232$	−38.0329	+	65.8748i	−2.49698	+	4.32489i
$233$	−3.62746			−0.237643			−0.118821	−	0.992916i	$-0.537912\pi$
$233$	−3.62746			−0.237643			−0.118821	+	0.992916i	$0.537912\pi$
$234$		0			0
$235$	−0.121132			−0.00790181
$236$	−30.7273	+	53.2213i	−2.00018	+	3.46441i
$237$	6.04097	−	10.4633i	0.392403	−	0.679662i
$238$	0.277260	+	0.480228i	0.0179721	+	0.0311286i
$239$	19.0089			1.22959			0.614793	−	0.788688i	$-0.289239\pi$
$239$	19.0089			1.22959			0.614793	+	0.788688i	$0.289239\pi$
$240$	−16.2013	−	28.0615i	−1.04579	−	1.81136i
$241$	5.07291	+	8.78654i	0.326775	+	0.565991i	0.981870	−	0.189556i	$-0.0607047\pi$
$241$	5.07291	+	8.78654i	0.326775	+	0.565991i	−0.655095	+	0.755547i	$0.727371\pi$
$242$	21.5371			1.38446
$243$	−1.51638	−	2.62645i	−0.0972760	−	0.168487i
$244$	12.2664	−	21.2460i	0.785273	−	1.36013i
$245$	−3.46366	+	5.99923i	−0.221285	+	0.383277i
$246$	42.4120			2.70409
$247$		0			0
$248$	65.3269			4.14826
$249$	8.34123	−	14.4474i	0.528604	−	0.915569i
$250$	−1.39471	+	2.41570i	−0.0882091	+	0.152783i
$251$	−0.0643811	−	0.111511i	−0.00406370	−	0.00703853i	0.863986	−	0.503515i	$-0.167960\pi$
$251$	−0.0643811	−	0.111511i	−0.00406370	−	0.00703853i	−0.868050	+	0.496477i	$0.834627\pi$
$252$	−0.456399			−0.0287505
$253$	−2.49091	−	4.31438i	−0.156602	−	0.271243i
$254$	16.5797	+	28.7168i	1.04030	+	1.80186i
$255$	−1.33804			−0.0837912
$256$	−48.2007	−	83.4860i	−3.01254	−	5.21787i
$257$	−3.36934	+	5.83587i	−0.210174	+	0.364032i	−0.951769	−	0.306816i	$-0.900736\pi$
$257$	−3.36934	+	5.83587i	−0.210174	+	0.364032i	0.741595	+	0.670848i	$0.234070\pi$
$258$	2.95899	−	5.12512i	0.184219	−	0.319076i
$259$	2.06624			0.128390
$260$		0			0
$261$	−2.11213			−0.130738
$262$	19.2182	−	33.2869i	1.18730	−	2.05647i
$263$	−8.90337	+	15.4211i	−0.549005	+	0.950905i	0.449338	+	0.893362i	$0.351660\pi$
$263$	−8.90337	+	15.4211i	−0.549005	+	0.950905i	−0.998343	+	0.0575429i	$0.981673\pi$
$264$	17.3272	+	30.0115i	1.06641	+	1.84708i
$265$	−3.85022			−0.236517
$266$	−0.819579	−	1.41955i	−0.0502516	−	0.0870384i
$267$	5.96250	+	10.3274i	0.364899	+	0.632024i
$268$	55.2125			3.37264
$269$	0.102557	+	0.177634i	0.00625302	+	0.0108305i	0.869135	−	0.494575i	$-0.164676\pi$
$269$	0.102557	+	0.177634i	0.00625302	+	0.0108305i	−0.862882	+	0.505405i	$0.831343\pi$
$270$	−6.85145	+	11.8671i	−0.416966	+	0.722206i
$271$	13.2964	−	23.0300i	0.807699	−	1.39898i	−0.106755	−	0.994285i	$-0.534046\pi$
$271$	13.2964	−	23.0300i	0.807699	−	1.39898i	0.914454	−	0.404690i	$-0.132621\pi$
$272$	−13.1667			−0.798349
$273$		0			0
$274$	39.4993			2.38624
$275$	0.905401	−	1.56820i	0.0545977	−	0.0945660i
$276$	−14.4299	+	24.9933i	−0.868577	+	1.50442i
$277$	−12.6075	−	21.8368i	−0.757510	−	1.31205i	−0.944117	−	0.329611i	$-0.893083\pi$
$277$	−12.6075	−	21.8368i	−0.757510	−	1.31205i	0.186607	−	0.982435i	$-0.440251\pi$
$278$	−12.6540			−0.758939
$279$	0.906973	+	1.57092i	0.0542990	+	0.0940487i
$280$	1.42165	+	2.46237i	0.0849597	+	0.147155i
$281$	12.7906			0.763025			0.381513	−	0.924364i	$-0.375403\pi$
$281$	12.7906			0.763025			0.381513	+	0.924364i	$0.375403\pi$
$282$	−0.306570	−	0.530994i	−0.0182560	−	0.0316203i
$283$	−11.2368	+	19.4628i	−0.667961	+	1.15694i	0.310512	+	0.950569i	$0.399500\pi$
$283$	−11.2368	+	19.4628i	−0.667961	+	1.15694i	−0.978473	+	0.206373i	$0.933834\pi$
$284$	23.4730	−	40.6564i	1.39287	−	2.41251i
$285$	3.95524			0.234288
$286$		0			0
$287$	−2.25897			−0.133343
$288$	4.20467	−	7.28270i	0.247762	−	0.429137i
$289$	8.22815	−	14.2516i	0.484009	−	0.838327i
$290$	10.0594	+	17.4233i	0.590707	+	1.02313i
$291$	−31.6474			−1.85520
$292$	−2.00274	−	3.46885i	−0.117201	−	0.202999i
$293$	9.70479	+	16.8092i	0.566960	+	0.982003i	0.996864	+	0.0791289i	$0.0252139\pi$
$293$	9.70479	+	16.8092i	0.566960	+	0.982003i	−0.429905	+	0.902874i	$0.641453\pi$
$294$	−35.0642			−2.04498
$295$	5.31538	+	9.20651i	0.309473	+	0.536024i
$296$	−40.4138	+	69.9988i	−2.34901	+	4.06860i
$297$	4.44775	−	7.70372i	0.258084	−	0.447015i
$298$	−9.81653			−0.568656
$299$		0			0
$300$	−10.4900			−0.605641
$301$	−0.157603	+	0.272977i	−0.00908411	+	0.0157341i
$302$	6.26584	−	10.8527i	0.360558	−	0.624505i
$303$	−10.7069	−	18.5449i	−0.615095	−	1.06538i
$304$	38.9207			2.23226
$305$	−2.12190	−	3.67524i	−0.121500	−	0.210444i
$306$	−0.301162	−	0.521627i	−0.0172163	−	0.0298195i
$307$	−20.9899			−1.19796			−0.598978	−	0.800765i	$-0.704426\pi$
$307$	−20.9899			−1.19796			−0.598978	+	0.800765i	$0.704426\pi$
$308$	−1.41108	−	2.44407i	−0.0804039	−	0.139264i
$309$	−7.29349	+	12.6327i	−0.414912	+	0.718649i
$310$	8.63921	−	14.9635i	0.490674	−	0.849872i
$311$	12.5265			0.710311			0.355155	−	0.934807i	$-0.384428\pi$
$311$	12.5265			0.710311			0.355155	+	0.934807i	$0.384428\pi$
$312$		0			0
$313$	−8.46526			−0.478485			−0.239242	−	0.970960i	$-0.576899\pi$
$313$	−8.46526			−0.478485			−0.239242	+	0.970960i	$0.576899\pi$
$314$	14.2860	−	24.7440i	0.806205	−	1.39639i
$315$	−0.0394752	+	0.0683730i	−0.00222418	+	0.00385238i
$316$	−19.2447	−	33.3329i	−1.08260	−	1.87512i
$317$	15.3660			0.863043			0.431522	−	0.902103i	$-0.357977\pi$
$317$	15.3660			0.863043			0.431522	+	0.902103i	$0.357977\pi$
$318$	−9.74437	−	16.8777i	−0.546437	−	0.946457i
$319$	−6.53023	−	11.3107i	−0.365623	−	0.633277i
$320$	−44.3888			−2.48141
$321$	15.6944	+	27.1834i	0.875974	+	1.51723i
$322$	1.03448	−	1.79177i	0.0576491	−	0.0998512i
$323$	0.803600	−	1.39188i	0.0447135	−	0.0774461i
$324$	−56.6104			−3.14502
$325$		0			0
$326$	−4.70907			−0.260811
$327$	13.7273	−	23.7764i	0.759123	−	1.31484i
$328$	44.1837	−	76.5283i	2.43963	−	4.22557i
$329$	0.0163287	+	0.0282821i	0.000900230	+	0.00155924i
$330$	9.16578			0.504560
$331$	3.44282	+	5.96314i	0.189234	+	0.327764i	0.944995	−	0.327084i	$-0.106066\pi$
$331$	3.44282	+	5.96314i	0.189234	+	0.327764i	−0.755761	+	0.654848i	$0.772733\pi$
$332$	−26.5727	−	46.0253i	−1.45837	−	2.52596i
$333$	−2.24436			−0.122990
$334$	5.99541	+	10.3844i	0.328054	+	0.568207i
$335$	4.77547	−	8.27136i	0.260912	−	0.451913i
$336$	−4.36788	+	7.56538i	−0.238287	+	0.412726i
$337$	−12.4209			−0.676609			−0.338305	−	0.941037i	$-0.609853\pi$
$337$	−12.4209			−0.676609			−0.338305	+	0.941037i	$0.609853\pi$
$338$		0			0
$339$	−22.6257			−1.22886
$340$	−2.13130	+	3.69151i	−0.115586	+	0.200200i
$341$	−5.60830	+	9.71387i	−0.303707	+	0.526035i
$342$	0.890233	+	1.54193i	0.0481383	+	0.0833780i
$343$	3.75481			0.202741
$344$	−6.16518	−	10.6784i	−0.332404	−	0.575741i
$345$	2.49616	+	4.32347i	0.134389	+	0.232768i
$346$	31.2170			1.67824
$347$	−11.7441	−	20.3413i	−0.630455	−	1.09198i	−0.987459	−	0.157877i	$-0.949535\pi$
$347$	−11.7441	−	20.3413i	−0.630455	−	1.09198i	0.357004	−	0.934103i	$-0.383798\pi$
$348$	−37.8298	+	65.5231i	−2.02789	+	3.51241i
$349$	8.76406	−	15.1798i	0.469129	−	0.812556i	−0.530248	−	0.847843i	$-0.677901\pi$
$349$	8.76406	−	15.1798i	0.469129	−	0.812556i	0.999377	+	0.0352867i	$0.0112344\pi$
$350$	0.752028			0.0401976
$351$		0			0
$352$	51.9995			2.77158
$353$	2.00621	−	3.47485i	0.106780	−	0.184948i	−0.807684	−	0.589615i	$-0.799279\pi$
$353$	2.00621	−	3.47485i	0.106780	−	0.184948i	0.914464	+	0.404667i	$0.132613\pi$
$354$	−26.9050	+	46.6008i	−1.42998	+	2.47681i
$355$	−4.06048	−	7.03296i	−0.215508	−	0.373271i
$356$	37.9895			2.01344
$357$	0.180368	+	0.312406i	0.00954608	+	0.0165343i
$358$	10.7142	+	18.5575i	0.566261	+	0.980792i
$359$	5.71225			0.301481			0.150740	−	0.988573i	$-0.451834\pi$
$359$	5.71225			0.301481			0.150740	+	0.988573i	$0.451834\pi$
$360$	−1.54420	−	2.67464i	−0.0813867	−	0.140966i
$361$	7.12456	−	12.3401i	0.374977	−	0.649479i
$362$	8.99211	−	15.5748i	0.472615	−	0.818593i
$363$	14.0107			0.735369
$364$		0			0
$365$	−0.692889			−0.0362675
$366$	10.7405	−	18.6031i	0.561414	−	0.972397i
$367$	−2.21827	+	3.84215i	−0.115793	+	0.200559i	−0.918096	−	0.396357i	$-0.870274\pi$
$367$	−2.21827	+	3.84215i	−0.115793	+	0.200559i	0.802304	+	0.596916i	$0.203607\pi$
$368$	24.5630	+	42.5443i	1.28043	+	2.21777i
$369$	2.45371			0.127735
$370$	10.6891	+	18.5141i	0.555701	+	0.962503i
$371$	0.519010	+	0.898952i	0.0269457	+	0.0466713i
$372$	64.9781			3.36896
$373$	3.74571	+	6.48776i	0.193946	+	0.335924i	0.946554	−	0.322544i	$-0.104538\pi$
$373$	3.74571	+	6.48776i	0.193946	+	0.335924i	−0.752609	+	0.658468i	$0.771205\pi$
$374$	1.86225	−	3.22551i	0.0962945	−	0.166787i
$375$	−0.907309	+	1.57151i	−0.0468533	+	0.0811522i
$376$	−1.27750			−0.0658822
$377$		0			0
$378$	3.69431			0.190015
$379$	5.78381	−	10.0178i	0.297094	−	0.514582i	−0.678376	−	0.734715i	$-0.737316\pi$
$379$	5.78381	−	10.0178i	0.297094	−	0.514582i	0.975470	+	0.220133i	$0.0706491\pi$
$380$	6.30010	−	10.9121i	0.323189	−	0.559779i
$381$	10.7857	+	18.6814i	0.552568	+	0.957076i
$382$	51.6935			2.64487
$383$	13.2833	+	23.0073i	0.678744	+	1.17562i	0.975359	+	0.220622i	$0.0708086\pi$
$383$	13.2833	+	23.0073i	0.678744	+	1.17562i	−0.296616	+	0.954997i	$0.595858\pi$
$384$	−60.2329	−	104.326i	−3.07375	−	5.32389i
$385$	−0.488193			−0.0248806
$386$	−5.53567	−	9.58806i	−0.281758	−	0.488019i
$387$	0.171190	−	0.296510i	0.00870207	−	0.0150724i
$388$	−50.4096	+	87.3120i	−2.55916	+	4.43260i
$389$	32.0328			1.62413			0.812063	−	0.583570i	$-0.198344\pi$
$389$	32.0328			1.62413			0.812063	+	0.583570i	$0.198344\pi$
$390$		0			0
$391$	2.02862			0.102591
$392$	−36.5289	+	63.2698i	−1.84499	+	3.19561i
$393$	12.5022	−	21.6544i	0.630651	−	1.09232i
$394$	−2.39313	−	4.14502i	−0.120564	−	0.208823i
$395$	−6.65811			−0.335006
$396$	1.53273	+	2.65476i	0.0770225	+	0.133407i
$397$	18.9865	+	32.8856i	0.952905	+	1.65048i	0.739090	+	0.673607i	$0.235256\pi$
$397$	18.9865	+	32.8856i	0.952905	+	1.65048i	0.213815	+	0.976874i	$0.431411\pi$
$398$	−56.4892			−2.83155
$399$	−0.533167	−	0.923472i	−0.0266917	−	0.0462314i
$400$	−8.92820	+	15.4641i	−0.446410	+	0.773205i
$401$	−14.5381	+	25.1807i	−0.725997	+	1.25746i	0.232565	+	0.972581i	$0.425288\pi$
$401$	−14.5381	+	25.1807i	−0.725997	+	1.25746i	−0.958562	+	0.284883i	$0.908045\pi$
$402$	48.3443			2.41119
$403$		0			0
$404$	−68.2180			−3.39397
$405$	−4.89638	+	8.48079i	−0.243303	+	0.421414i
$406$	2.71201	−	4.69734i	0.134595	−	0.233125i
$407$	−6.93905	−	12.0188i	−0.343956	−	0.595749i
$408$	−14.1114			−0.698618
$409$	−13.3611	−	23.1421i	−0.660663	−	1.14430i	−0.980442	−	0.196809i	$-0.936942\pi$
$409$	−13.3611	−	23.1421i	−0.660663	−	1.14430i	0.319779	−	0.947492i	$-0.396391\pi$
$410$	−11.6862	−	20.2411i	−0.577141	−	0.999637i
$411$	25.6958			1.26748
$412$	23.2349	+	40.2440i	1.14470	+	1.98268i
$413$	1.43303	−	2.48208i	0.0705148	−	0.122135i
$414$	−1.12366	+	1.94623i	−0.0552247	+	0.0956519i
$415$	−9.19337			−0.451285
$416$		0			0
$417$	−8.23193			−0.403119
$418$	−5.50479	+	9.53458i	−0.269248	+	0.466352i
$419$	−17.6931	+	30.6453i	−0.864363	+	1.49712i	0.00331518	+	0.999995i	$0.498945\pi$
$419$	−17.6931	+	30.6453i	−0.864363	+	1.49712i	−0.867678	+	0.497126i	$0.834389\pi$
$420$	1.41406	+	2.44922i	0.0689989	+	0.119510i
$421$	14.1178			0.688058			0.344029	−	0.938959i	$-0.388208\pi$
$421$	14.1178			0.688058			0.344029	+	0.938959i	$0.388208\pi$
$422$	9.45307	+	16.3732i	0.460168	+	0.797035i
$423$	−0.0177363	−	0.0307202i	−0.000862371	−	0.00149367i
$424$	−40.6057			−1.97198
$425$	0.368683	+	0.638578i	0.0178838	+	0.0309756i
$426$	20.5531	−	35.5989i	0.995799	−	1.72477i
$427$	−0.572066	+	0.990847i	−0.0276842	+	0.0479504i
$428$	99.9951			4.83345
$429$		0			0
$430$	−3.26128			−0.157273
$431$	−7.07413	+	12.2528i	−0.340749	+	0.590195i	−0.984572	−	0.174980i	$-0.944014\pi$
$431$	−7.07413	+	12.2528i	−0.340749	+	0.590195i	0.643823	+	0.765174i	$0.277347\pi$
$432$	−43.8594	+	75.9668i	−2.11019	+	3.65495i
$433$	12.4280	+	21.5260i	0.597253	+	1.03447i	0.993225	+	0.116210i	$0.0370745\pi$
$433$	12.4280	+	21.5260i	0.597253	+	1.03447i	−0.395972	+	0.918263i	$0.629592\pi$
$434$	−4.65827			−0.223604
$435$	6.54400	+	11.3345i	0.313761	+	0.543449i
$436$	−43.7312	−	75.7446i	−2.09434	−	3.62751i
$437$	−5.99658			−0.286855
$438$	−1.75361	−	3.03734i	−0.0837906	−	0.145130i
$439$	−4.88111	+	8.45433i	−0.232963	+	0.403503i	−0.958679	−	0.284491i	$-0.908175\pi$
$439$	−4.88111	+	8.45433i	−0.232963	+	0.403503i	0.725716	+	0.687995i	$0.241509\pi$
$440$	9.54865	−	16.5388i	0.455214	−	0.788454i
$441$	−2.02861			−0.0966005
$442$		0			0
$443$	−32.5970			−1.54873			−0.774365	−	0.632740i	$-0.781930\pi$
$443$	−32.5970			−1.54873			−0.774365	+	0.632740i	$0.781930\pi$
$444$	−40.1981	+	69.6251i	−1.90772	+	3.30426i
$445$	3.28581	−	5.69120i	0.155763	−	0.269789i
$446$	−14.2445	−	24.6721i	−0.674495	−	1.16826i
$447$	−6.38602			−0.302048
$448$	5.98363	+	10.3639i	0.282700	+	0.489650i
$449$	6.09290	+	10.5532i	0.287542	+	0.498037i	0.973222	−	0.229866i	$-0.0738287\pi$
$449$	6.09290	+	10.5532i	0.287542	+	0.498037i	−0.685681	+	0.727902i	$0.740495\pi$
$450$	−0.816858			−0.0385071
$451$	7.58632	+	13.1399i	0.357226	+	0.618734i
$452$	−36.0394	+	62.4220i	−1.69515	+	2.93609i
$453$	4.07616	−	7.06012i	0.191515	−	0.331713i
$454$	−25.3613			−1.19026
$455$		0			0
$456$	41.7132			1.95340
$457$	15.0734	−	26.1079i	0.705105	−	1.22128i	−0.261548	−	0.965190i	$-0.584233\pi$
$457$	15.0734	−	26.1079i	0.705105	−	1.22128i	0.966654	−	0.256088i	$-0.0824336\pi$
$458$	−10.8921	+	18.8657i	−0.508956	+	0.881538i
$459$	1.81114	+	3.13699i	0.0845368	+	0.146422i
$460$	15.9040			0.741530
$461$	15.9191	+	27.5727i	0.741427	+	1.28419i	0.951846	+	0.306578i	$0.0991839\pi$
$461$	15.9191	+	27.5727i	0.741427	+	1.28419i	−0.210419	+	0.977611i	$0.567483\pi$
$462$	−1.23555	−	2.14004i	−0.0574830	−	0.0995635i
$463$	15.5796			0.724045			0.362023	−	0.932169i	$-0.382086\pi$
$463$	15.5796			0.724045			0.362023	+	0.932169i	$0.382086\pi$
$464$	64.3950	+	111.535i	2.98946	+	5.17790i
$465$	5.62013	−	9.73434i	0.260627	−	0.451419i
$466$	−5.05925	+	8.76288i	−0.234365	+	0.405932i
$467$	−29.7598			−1.37712			−0.688560	−	0.725179i	$-0.741757\pi$
$467$	−29.7598			−1.37712			−0.688560	+	0.725179i	$0.741757\pi$
$468$		0			0
$469$	−2.57494			−0.118900
$470$	−0.168944	+	0.292620i	−0.00779282	+	0.0134976i
$471$	9.29356	−	16.0969i	0.428225	−	0.741707i
$472$	56.0577	+	97.0948i	2.58027	+	4.46915i
$473$	2.11712			0.0973453
$474$	−16.8508	−	29.1864i	−0.773982	−	1.34058i
$475$	−1.08983	−	1.88763i	−0.0500046	−	0.0866106i
$476$	1.14920			0.0526734
$477$	−0.563753	−	0.976449i	−0.0258125	−	0.0447085i
$478$	26.5119	−	45.9200i	1.21263	−	2.10033i
$479$	−7.55192	+	13.0803i	−0.345056	+	0.597654i	−0.985364	−	0.170464i	$-0.945473\pi$
$479$	−7.55192	+	13.0803i	−0.345056	+	0.597654i	0.640308	+	0.768118i	$0.278807\pi$
$480$	−52.1091			−2.37844
$481$		0			0
$482$	28.3009			1.28907
$483$	0.672966	−	1.16561i	0.0306210	−	0.0530371i
$484$	22.3169	−	38.6540i	1.01441	−	1.75700i
$485$	8.72012	+	15.1037i	0.395960	+	0.685824i
$486$	−8.45964			−0.383737
$487$	3.49536	+	6.05414i	0.158390	+	0.274339i	0.934288	−	0.356519i	$-0.116036\pi$
$487$	3.49536	+	6.05414i	0.158390	+	0.274339i	−0.775898	+	0.630858i	$0.782703\pi$
$488$	−22.3783	−	38.7603i	−1.01302	−	1.75460i
$489$	−3.06343			−0.138533
$490$	9.66158	+	16.7343i	0.436466	+	0.755981i
$491$	9.23041	−	15.9875i	0.416563	−	0.721508i	−0.579029	−	0.815307i	$-0.696568\pi$
$491$	9.23041	−	15.9875i	0.416563	−	0.721508i	0.995591	+	0.0937997i	$0.0299013\pi$
$492$	43.9478	−	76.1197i	1.98132	−	3.43174i
$493$	5.31827			0.239523
$494$		0			0
$495$	0.530279			0.0238343
$496$	55.3038	−	95.7889i	2.48321	−	4.30105i
$497$	−1.09471	+	1.89609i	−0.0491044	+	0.0850513i
$498$	−23.2672	−	40.2999i	−1.04263	−	1.80588i
$499$	9.65233			0.432097			0.216049	−	0.976383i	$-0.430683\pi$
$499$	9.65233			0.432097			0.216049	+	0.976383i	$0.430683\pi$
$500$	2.89042	+	5.00635i	0.129263	+	0.223891i
$501$	3.90024	+	6.75541i	0.174250	+	0.301810i
$502$	−0.359171			−0.0160306
$503$	−3.42677	−	5.93533i	−0.152792	−	0.264643i	0.779461	−	0.626451i	$-0.215493\pi$
$503$	−3.42677	−	5.93533i	−0.152792	−	0.264643i	−0.932253	+	0.361807i	$0.882160\pi$
$504$	−0.416318	+	0.721084i	−0.0185443	+	0.0321197i
$505$	−5.90035	+	10.2197i	−0.262562	+	0.454771i
$506$	−13.8963			−0.617768
$507$		0			0
$508$	68.7201			3.04896
$509$	−16.9217	+	29.3092i	−0.750039	+	1.29911i	0.197764	+	0.980250i	$0.436632\pi$
$509$	−16.9217	+	29.3092i	−0.750039	+	1.29911i	−0.947803	+	0.318856i	$0.896701\pi$
$510$	−1.86617	+	3.23230i	−0.0826355	+	0.143129i
$511$	0.0934017	+	0.161776i	0.00413185	+	0.00715657i
$512$	−136.131			−6.01618
$513$	−5.35372	−	9.27292i	−0.236373	−	0.409410i
$514$	9.39850	+	16.2787i	0.414550	+	0.718021i
$515$	8.03859			0.354223
$516$	−6.13226	−	10.6214i	−0.269958	−	0.467581i
$517$	0.109673	−	0.189960i	0.00482343	−	0.00835443i
$518$	2.88179	−	4.99141i	0.126619	−	0.219310i
$519$	20.3078			0.891416
$520$		0			0
$521$	−36.7411			−1.60966			−0.804828	−	0.593508i	$-0.797742\pi$
$521$	−36.7411			−1.60966			−0.804828	+	0.593508i	$0.797742\pi$
$522$	−2.94581	+	5.10229i	−0.128935	+	0.223321i
$523$	−16.1115	+	27.9059i	−0.704505	+	1.22024i	0.262365	+	0.964969i	$0.415498\pi$
$523$	−16.1115	+	27.9059i	−0.704505	+	1.22024i	−0.966870	+	0.255270i	$0.917836\pi$
$524$	−39.8282	−	68.9844i	−1.73990	−	3.01360i
$525$	0.489222			0.0213514
$526$	24.8352	+	43.0158i	1.08287	+	1.87558i
$527$	−2.28372	−	3.95553i	−0.0994806	−	0.172305i
$528$	58.6746			2.55349
$529$	7.71555	+	13.3637i	0.335459	+	0.581031i
$530$	−5.36993	+	9.30099i	−0.233255	+	0.404009i
$531$	−1.55657	+	2.69605i	−0.0675492	+	0.116999i
$532$	−3.39702			−0.147280
$533$		0			0
$534$	33.2638			1.43946
$535$	8.64884	−	14.9802i	0.373922	−	0.647652i
$536$	50.3637	−	87.2325i	2.17538	−	3.76787i
$537$	6.96996	+	12.0723i	0.300776	+	0.520959i
$538$	0.572149			0.0246671
$539$	−6.27200	−	10.8634i	−0.270154	−	0.467921i
$540$	14.1991	+	24.5935i	0.611031	+	1.05834i
$541$	−9.68462			−0.416375			−0.208187	−	0.978089i	$-0.566756\pi$
$541$	−9.68462			−0.416375			−0.208187	+	0.978089i	$0.566756\pi$
$542$	−37.0892	−	64.2404i	−1.59312	−	2.75936i
$543$	5.84971	−	10.1320i	0.251035	−	0.434805i
$544$	−10.5872	+	18.3376i	−0.453923	+	0.786217i
$545$	−15.1297			−0.648085
$546$		0			0
$547$	−5.81447			−0.248609			−0.124304	−	0.992244i	$-0.539670\pi$
$547$	−5.81447			−0.248609			−0.124304	+	0.992244i	$0.539670\pi$
$548$	40.9296	−	70.8921i	1.74842	−	3.02836i
$549$	0.621382	−	1.07626i	0.0265199	−	0.0459339i
$550$	−2.52554	−	4.37436i	−0.107689	−	0.186523i
$551$	−15.7208			−0.669729
$552$	26.3253	+	45.5967i	1.12048	+	1.94073i
$553$	0.897515	+	1.55454i	0.0381662	+	0.0661059i
$554$	−70.3350			−2.98825
$555$	6.95368	+	12.0441i	0.295167	+	0.511244i
$556$	−13.1122	+	22.7111i	−0.556083	+	0.963164i
$557$	−15.4947	+	26.8376i	−0.656531	+	1.13715i	0.324976	+	0.945722i	$0.394644\pi$
$557$	−15.4947	+	26.8376i	−0.656531	+	1.13715i	−0.981508	+	0.191423i	$0.938690\pi$
$558$	5.05985			0.214200
$559$		0			0
$560$	4.81410			0.203433
$561$	1.21146	−	2.09831i	0.0511479	−	0.0885908i
$562$	17.8392	−	30.8984i	0.752501	−	1.30337i
$563$	7.01670	+	12.1533i	0.295719	+	0.512199i	0.975152	−	0.221538i	$-0.0711076\pi$
$563$	7.01670	+	12.1533i	0.295719	+	0.512199i	−0.679433	+	0.733737i	$0.737774\pi$
$564$	−1.27068			−0.0535054
$565$	6.23428	+	10.7981i	0.262278	+	0.454279i
$566$	31.3442	+	54.2898i	1.31750	+	2.28197i
$567$	2.64014			0.110875
$568$	−42.8232	−	74.1719i	−1.79682	−	3.11219i
$569$	−9.48586	+	16.4300i	−0.397668	+	0.688781i	−0.993438	−	0.114374i	$-0.963514\pi$
$569$	−9.48586	+	16.4300i	−0.397668	+	0.688781i	0.595770	+	0.803155i	$0.296847\pi$
$570$	5.51640	−	9.55468i	0.231057	−	0.400202i
$571$	18.6462			0.780318			0.390159	−	0.920748i	$-0.372420\pi$
$571$	18.6462			0.780318			0.390159	+	0.920748i	$0.372420\pi$
$572$		0			0
$573$	33.6285			1.40485
$574$	−3.15061	+	5.45701i	−0.131504	+	0.227771i
$575$	1.37558	−	2.38258i	0.0573657	−	0.0993604i
$576$	−6.49946	−	11.2574i	−0.270811	−	0.469058i
$577$	−10.6262			−0.442374			−0.221187	−	0.975231i	$-0.570993\pi$
$577$	−10.6262			−0.442374			−0.221187	+	0.975231i	$0.570993\pi$
$578$	−22.9517	−	39.7535i	−0.954666	−	1.65353i
$579$	−3.60116	−	6.23739i	−0.149659	−	0.259217i
$580$	41.6945			1.73127
$581$	1.23927	+	2.14648i	0.0514136	+	0.0890509i
$582$	−44.1389	+	76.4508i	−1.82962	+	3.16899i
$583$	3.48599	−	6.03791i	0.144375	−	0.250065i
$584$	−7.30744			−0.302384
$585$		0			0
$586$	54.1414			2.23656
$587$	−7.14682	+	12.3787i	−0.294981	+	0.510922i	−0.974980	−	0.222291i	$-0.928647\pi$
$587$	−7.14682	+	12.3787i	−0.294981	+	0.510922i	0.680000	+	0.733213i	$0.261980\pi$
$588$	−36.3338	+	62.9320i	−1.49838	+	2.59527i
$589$	6.75068	+	11.6925i	0.278157	+	0.481782i
$590$	29.6536			1.22082
$591$	−1.55682	−	2.69649i	−0.0640390	−	0.110919i
$592$	68.4263	+	118.518i	2.81230	+	4.87105i
$593$	−0.474392			−0.0194809			−0.00974047	−	0.999953i	$-0.503101\pi$
$593$	−0.474392			−0.0194809			−0.00974047	+	0.999953i	$0.503101\pi$
$594$	−12.4066	−	21.4889i	−0.509049	−	0.881699i
$595$	0.0993971	−	0.172161i	0.00407489	−	0.00705791i
$596$	−10.1720	+	17.6184i	−0.416660	+	0.721677i
$597$	−36.7483			−1.50401
$598$		0			0
$599$	−32.2915			−1.31940			−0.659698	−	0.751531i	$-0.729316\pi$
$599$	−32.2915			−1.31940			−0.659698	+	0.751531i	$0.729316\pi$
$600$	−9.56878	+	16.5736i	−0.390644	+	0.676615i
$601$	−9.85973	+	17.0776i	−0.402187	+	0.696608i	−0.993990	−	0.109475i	$-0.965083\pi$
$601$	−9.85973	+	17.0776i	−0.402187	+	0.696608i	0.591803	+	0.806083i	$0.298416\pi$
$602$	0.439621	+	0.761446i	0.0179176	+	0.0310342i
$603$	2.79692			0.113899
$604$	−12.9854	−	22.4914i	−0.528370	−	0.915164i
$605$	−3.86050	−	6.68658i	−0.156952	−	0.271848i
$606$	−59.7319			−2.42644
$607$	−12.0383	−	20.8509i	−0.488618	−	0.846311i	0.511297	−	0.859404i	$-0.329165\pi$
$607$	−12.0383	−	20.8509i	−0.488618	−	0.846311i	−0.999914	+	0.0130936i	$0.995832\pi$
$608$	31.2957	−	54.2058i	1.26921	−	2.19834i
$609$	1.76427	−	3.05580i	0.0714917	−	0.123827i
$610$	−11.8377			−0.479295
$611$		0			0
$612$	−1.24827			−0.0504582
$613$	−6.79744	+	11.7735i	−0.274546	+	0.475528i	−0.970021	−	0.243023i	$-0.921861\pi$
$613$	−6.79744	+	11.7735i	−0.274546	+	0.475528i	0.695474	+	0.718551i	$0.255194\pi$
$614$	−29.2748	+	50.7054i	−1.18143	+	2.04630i
$615$	−7.60232	−	13.1676i	−0.306555	−	0.530969i
$616$	−5.14864			−0.207445
$617$	1.20695	+	2.09050i	0.0485899	+	0.0841602i	0.889297	−	0.457329i	$-0.151194\pi$
$617$	1.20695	+	2.09050i	0.0485899	+	0.0841602i	−0.840708	+	0.541489i	$0.817861\pi$
$618$	20.3446	+	35.2378i	0.818379	+	1.41747i
$619$	11.6882			0.469790			0.234895	−	0.972021i	$-0.424525\pi$
$619$	11.6882			0.469790			0.234895	+	0.972021i	$0.424525\pi$
$620$	−17.9041	−	31.0107i	−0.719044	−	1.24542i
$621$	6.75749	−	11.7043i	0.271169	−	0.469678i
$622$	17.4708	−	30.2602i	0.700514	−	1.21333i
$623$	−1.77172			−0.0709823
$624$		0			0
$625$	1.00000			0.0400000
$626$	−11.8066	+	20.4496i	−0.471885	+	0.817329i
$627$	−3.58107	+	6.20260i	−0.143014	+	0.247708i
$628$	−29.6065	−	51.2800i	−1.18143	−	2.04630i
$629$	5.65122			0.225329
$630$	0.110113	+	0.190721i	0.00438700	+	0.00759850i
$631$	−19.3714	−	33.5522i	−0.771162	−	1.33569i	−0.936927	−	0.349526i	$-0.886343\pi$
$631$	−19.3714	−	33.5522i	−0.771162	−	1.33569i	0.165765	−	0.986165i	$-0.446991\pi$
$632$	−70.2186			−2.79315
$633$	6.14958	+	10.6514i	0.244424	+	0.423354i
$634$	21.4311	−	37.1198i	0.851139	−	1.47422i
$635$	5.94378	−	10.2949i	0.235872	−	0.408542i
$636$	−40.3889			−1.60152
$637$		0			0
$638$	−36.4311			−1.44232
$639$	1.18908	−	2.05955i	0.0470393	−	0.0814745i
$640$	−33.1932	+	57.4922i	−1.31207	+	2.27258i
$641$	18.5540	+	32.1364i	0.732838	+	1.26931i	0.955666	+	0.294454i	$0.0951379\pi$
$641$	18.5540	+	32.1364i	0.732838	+	1.26931i	−0.222828	+	0.974858i	$0.571529\pi$
$642$	87.5562			3.45557
$643$	−19.2794	−	33.3930i	−0.760307	−	1.31689i	−0.942692	−	0.333663i	$-0.891715\pi$
$643$	−19.2794	−	33.3930i	−0.760307	−	1.31689i	0.182385	−	0.983227i	$-0.441618\pi$
$644$	−2.14387	−	3.71329i	−0.0844803	−	0.146324i
$645$	−2.12158			−0.0835373
$646$	−2.24157	−	3.88252i	−0.0881936	−	0.152756i
$647$	20.5829	−	35.6507i	0.809198	−	1.40157i	−0.104222	−	0.994554i	$-0.533235\pi$
$647$	20.5829	−	35.6507i	0.809198	−	1.40157i	0.913420	−	0.407018i	$-0.133432\pi$
$648$	−51.6389	+	89.4412i	−2.02857	+	3.51358i
$649$	−19.2502			−0.755636
$650$		0			0
$651$	−3.03038			−0.118770
$652$	−4.87959	+	8.45169i	−0.191099	+	0.330994i
$653$	3.66706	−	6.35153i	0.143503	−	0.248555i	−0.785310	−	0.619102i	$-0.787497\pi$
$653$	3.66706	−	6.35153i	0.143503	−	0.248555i	0.928813	+	0.370548i	$0.120830\pi$
$654$	−38.2912	−	66.3223i	−1.49730	−	2.59341i
$655$	−13.7794			−0.538405
$656$	−74.8091	−	129.573i	−2.92081	−	5.05898i
$657$	−0.101454	−	0.175723i	−0.00395808	−	0.00685560i
$658$	0.0910950			0.00355125
$659$	−15.7740	−	27.3214i	−0.614468	−	1.06429i	−0.990478	−	0.137674i	$-0.956037\pi$
$659$	−15.7740	−	27.3214i	−0.614468	−	1.06429i	0.376010	−	0.926616i	$-0.377296\pi$
$660$	9.49767	−	16.4504i	0.369696	−	0.640333i
$661$	−2.80911	+	4.86551i	−0.109262	+	0.189247i	−0.915471	−	0.402383i	$-0.868182\pi$
$661$	−2.80911	+	4.86551i	−0.109262	+	0.189247i	0.806210	+	0.591630i	$0.201515\pi$
$662$	19.2069			0.746497
$663$		0			0
$664$	−96.9563			−3.76263
$665$	−0.293818	+	0.508907i	−0.0113938	+	0.0197346i
$666$	−3.13023	+	5.42171i	−0.121294	+	0.210087i
$667$	−9.92143	−	17.1844i	−0.384159	−	0.665383i
$668$	24.8500			0.961476
$669$	−9.26656	−	16.0501i	−0.358266	−	0.620534i
$670$	−13.3208	−	23.0723i	−0.514627	−	0.891359i
$671$	7.68468			0.296664
$672$	7.02432	+	12.1665i	0.270969	+	0.469332i
$673$	−25.3634	+	43.9306i	−0.977686	+	1.69340i	−0.306916	+	0.951737i	$0.599297\pi$
$673$	−25.3634	+	43.9306i	−0.977686	+	1.69340i	−0.670770	+	0.741666i	$0.734036\pi$
$674$	−17.3235	+	30.0052i	−0.667277	+	1.15576i
$675$	4.91246			0.189081
$676$		0			0
$677$	33.0566			1.27047			0.635234	−	0.772320i	$-0.280904\pi$
$677$	33.0566			1.27047			0.635234	+	0.772320i	$0.280904\pi$
$678$	−31.5562	+	54.6570i	−1.21191	+	2.09909i
$679$	2.35095	−	4.07197i	0.0902212	−	0.156268i
$680$	3.88825	+	6.73465i	0.149108	+	0.258262i
$681$	−16.4984			−0.632222
$682$	15.6439	+	27.0960i	0.599035	+	1.03756i
$683$	−7.95182	−	13.7730i	−0.304268	−	0.527007i	0.672830	−	0.739797i	$-0.265078\pi$
$683$	−7.95182	−	13.7730i	−0.304268	−	0.527007i	−0.977098	+	0.212790i	$0.931745\pi$
$684$	3.68987			0.141086
$685$	−7.08021	−	12.2633i	−0.270521	−	0.468556i
$686$	5.23687	−	9.07052i	0.199944	−	0.346314i
$687$	−7.08574	+	12.2729i	−0.270338	+	0.468239i
$688$	−20.8770			−0.795929
$689$		0			0
$690$	13.9256			0.530140
$691$	−9.69578	+	16.7936i	−0.368845	+	0.638858i	−0.989385	−	0.145317i	$-0.953580\pi$
$691$	−9.69578	+	16.7936i	−0.368845	+	0.638858i	0.620541	+	0.784174i	$0.286913\pi$
$692$	32.3474	−	56.0273i	1.22966	−	2.12984i
$693$	−0.0714817	−	0.123810i	−0.00271537	−	0.00470315i
$694$	−65.5182			−2.48704
$695$	2.26822	+	3.92868i	0.0860387	+	0.149023i
$696$	69.0151	+	119.538i	2.61601	+	4.53107i
$697$	−6.17836			−0.234022
$698$	−24.4466	−	42.3428i	−0.925318	−	1.60270i
$699$	−3.29123	+	5.70058i	−0.124486	+	0.215616i
$700$	0.779259	−	1.34972i	0.0294532	−	0.0510144i
$701$	14.2486			0.538162			0.269081	−	0.963118i	$-0.413280\pi$
$701$	14.2486			0.538162			0.269081	+	0.963118i	$0.413280\pi$
$702$		0			0
$703$	−16.7050			−0.630040
$704$	40.1897	−	69.6106i	1.51471	−	2.62355i
$705$	−0.109905	+	0.190360i	−0.00413925	+	0.00716939i
$706$	−5.59614	−	9.69281i	−0.210614	−	0.364794i
$707$	3.18148			0.119652
$708$	55.7584	+	96.5764i	2.09553	+	3.62956i
$709$	−8.64889	−	14.9803i	−0.324816	−	0.562598i	0.656659	−	0.754187i	$-0.271969\pi$
$709$	−8.64889	−	14.9803i	−0.324816	−	0.562598i	−0.981475	+	0.191590i	$0.938636\pi$
$710$	−22.6527			−0.850143
$711$	−0.974888	−	1.68856i	−0.0365611	−	0.0633258i
$712$	34.6533	−	60.0212i	1.29869	−	2.24939i
$713$	−8.52074	+	14.7584i	−0.319104	+	0.552705i
$714$	1.00624			0.0376577
$715$		0			0
$716$	44.4084			1.65962
$717$	17.2470	−	29.8727i	0.644101	−	1.11562i
$718$	7.96691	−	13.7991i	0.297323	−	0.514978i
$719$	12.6637	+	21.9342i	0.472278	+	0.818009i	0.999497	−	0.0317202i	$-0.0100986\pi$
$719$	12.6637	+	21.9342i	0.472278	+	0.818009i	−0.527219	+	0.849730i	$0.676765\pi$
$720$	−5.22911			−0.194877
$721$	−1.08360	−	1.87686i	−0.0403555	−	0.0698978i
$722$	−19.8734	−	34.4217i	−0.739610	−	1.28104i
$723$	18.4108			0.684705
$724$	−18.6354	−	32.2775i	−0.692580	−	1.19958i
$725$	3.60627	−	6.24624i	0.133933	−	0.231979i
$726$	19.5408	−	33.8456i	0.725227	−	1.25613i
$727$	−43.3262			−1.60688			−0.803439	−	0.595387i	$-0.796999\pi$
$727$	−43.3262			−1.60688			−0.803439	+	0.595387i	$0.796999\pi$
$728$		0			0
$729$	23.8750			0.884259
$730$	−0.966378	+	1.67382i	−0.0357673	+	0.0619507i
$731$	−0.431050	+	0.746601i	−0.0159430	+	0.0276140i
$732$	−22.2588	−	38.5533i	−0.822708	−	1.42497i
$733$	−39.9598			−1.47595			−0.737975	−	0.674828i	$-0.764218\pi$
$733$	−39.9598			−1.47595			−0.737975	+	0.674828i	$0.764218\pi$
$734$	6.18767	+	10.7174i	0.228391	+	0.395585i
$735$	6.28522	+	10.8863i	0.231834	+	0.401548i
$736$	79.0032			2.91210
$737$	8.64743	+	14.9778i	0.318532	+	0.551714i
$738$	3.42221	−	5.92745i	0.125973	−	0.218192i
$739$	5.54513	−	9.60444i	0.203981	−	0.353305i	−0.745827	−	0.666140i	$-0.767945\pi$
$739$	5.54513	−	9.60444i	0.203981	−	0.353305i	0.949808	+	0.312835i	$0.101279\pi$
$740$	44.3047			1.62867
$741$		0			0
$742$	2.89547			0.106296
$743$	9.93424	−	17.2066i	0.364452	−	0.631249i	−0.624236	−	0.781236i	$-0.714590\pi$
$743$	9.93424	−	17.2066i	0.364452	−	0.631249i	0.988688	+	0.149986i	$0.0479230\pi$
$744$	59.2717	−	102.662i	2.17301	−	3.76376i
$745$	1.75960	+	3.04772i	0.0644669	+	0.111660i
$746$	20.8967			0.765082
$747$	−1.34610	−	2.33152i	−0.0492513	−	0.0853058i
$748$	−3.85935	−	6.68460i	−0.141112	−	0.244413i
$749$	−4.66347			−0.170399
$750$	2.53086	+	4.38358i	0.0924140	+	0.160066i
$751$	−3.75199	+	6.49863i	−0.136912	+	0.237138i	−0.926326	−	0.376722i	$-0.877051\pi$
$751$	−3.75199	+	6.49863i	−0.136912	+	0.237138i	0.789414	+	0.613861i	$0.210384\pi$
$752$	−1.08150	+	1.87321i	−0.0394381	+	0.0683088i
$753$	−0.233654			−0.00851483
$754$		0			0
$755$	−4.49258			−0.163502
$756$	3.82808	−	6.63042i	0.139226	−	0.241146i
$757$	16.6884	−	28.9052i	0.606551	−	1.05058i	−0.385253	−	0.922811i	$-0.625886\pi$
$757$	16.6884	−	28.9052i	0.606551	−	1.05058i	0.991804	−	0.127767i	$-0.0407809\pi$
$758$	−16.1334	−	27.9439i	−0.585993	−	1.01497i
$759$	−9.04009			−0.328135
$760$	−11.4937	−	19.9076i	−0.416919	−	0.722124i
$761$	−6.84601	−	11.8576i	−0.248168	−	0.429839i	0.714850	−	0.699278i	$-0.246495\pi$
$761$	−6.84601	−	11.8576i	−0.248168	−	0.429839i	−0.963017	+	0.269439i	$0.913162\pi$
$762$	60.1716			2.17979
$763$	2.03949	+	3.53250i	0.0738344	+	0.127885i
$764$	53.5653	−	92.7778i	1.93792	−	3.35658i
$765$	−0.107966	+	0.187002i	−0.00390351	+	0.00676109i
$766$	74.1051			2.67753
$767$		0			0
$768$	−174.932			−6.31230
$769$	14.0137	−	24.2724i	0.505346	−	0.875285i	−0.494635	−	0.869101i	$-0.664698\pi$
$769$	14.0137	−	24.2724i	0.505346	−	0.875285i	0.999981	−	0.00618377i	$-0.00196837\pi$
$770$	−0.680887	+	1.17933i	−0.0245375	+	0.0425001i
$771$	6.11407	+	10.5899i	0.220193	+	0.381385i
$772$	−22.9445			−0.825789
$773$	−6.73801	−	11.6706i	−0.242349	−	0.419761i	0.719034	−	0.694975i	$-0.244585\pi$
$773$	−6.73801	−	11.6706i	−0.242349	−	0.419761i	−0.961383	+	0.275214i	$0.911251\pi$
$774$	−0.477520	−	0.827089i	−0.0171641	−	0.0297291i
$775$	−6.19428			−0.222505
$776$	91.9653	+	159.289i	3.30136	+	5.71812i
$777$	1.87471	−	3.24710i	0.0672550	−	0.116489i
$778$	44.6764	−	77.3817i	1.60173	−	2.77427i
$779$	18.2632			0.654348
$780$		0			0
$781$	14.7055			0.526203
$782$	2.82932	−	4.90053i	0.101176	−	0.175243i
$783$	17.7156	−	30.6844i	0.633105	−	1.09657i
$784$	61.8485	+	107.125i	2.20887	+	3.82588i
$785$	−10.2430			−0.365588
$786$	−34.8737	−	60.4031i	−1.24390	−	2.15451i
$787$	−8.50715	−	14.7348i	−0.303247	−	0.525240i	0.673622	−	0.739076i	$-0.264737\pi$
$787$	−8.50715	−	14.7348i	−0.303247	−	0.525240i	−0.976870	+	0.213836i	$0.931404\pi$
$788$	−9.91912			−0.353354
$789$	16.1562	+	27.9834i	0.575177	+	0.996235i
$790$	−9.28612	+	16.0840i	−0.330385	+	0.572244i
$791$	1.68077	−	2.91117i	0.0597612	−	0.103509i
$792$	5.59249			0.198721
$793$		0			0
$794$	105.923			3.75905
$795$	−3.49334	+	6.05064i	−0.123896	+	0.214594i
$796$	−58.5346	+	101.385i	−2.07471	+	3.59349i
$797$	−12.2474	−	21.2131i	−0.433825	−	0.751407i	0.563374	−	0.826202i	$-0.309503\pi$
$797$	−12.2474	−	21.2131i	−0.433825	−	0.751407i	−0.997199	+	0.0747953i	$0.976170\pi$
$798$	−2.97445			−0.105294
$799$	0.0446595	+	0.0773525i	0.00157994	+	0.00273653i
$800$	14.3581	+	24.8690i	0.507637	+	0.879253i
$801$	1.92445			0.0679971
$802$	40.5528	+	70.2394i	1.43197	+	2.48024i
$803$	0.627342	−	1.08659i	0.0221384	−	0.0383449i
$804$	50.0948	−	86.7667i	1.76671	−	3.06003i
$805$	−0.741716			−0.0261420
$806$		0			0
$807$	0.372204			0.0131022
$808$	−62.2270	+	107.780i	−2.18914	+	3.79170i
$809$	5.82854	−	10.0953i	0.204920	−	0.354933i	−0.745187	−	0.666856i	$-0.767640\pi$
$809$	5.82854	−	10.0953i	0.204920	−	0.354933i	0.950107	+	0.311923i	$0.100973\pi$
$810$	13.6581	+	23.6564i	0.479895	+	0.831203i
$811$	−40.2610			−1.41376			−0.706878	−	0.707335i	$-0.749897\pi$
$811$	−40.2610			−1.41376			−0.706878	+	0.707335i	$0.749897\pi$
$812$	−5.62043	−	9.73486i	−0.197238	−	0.341627i
$813$	−24.1279	−	41.7908i	−0.846202	−	1.46567i
$814$	−38.7118			−1.35685
$815$	0.844097	+	1.46202i	0.0295674	+	0.0512123i
$816$	−11.9463	+	20.6916i	−0.418203	+	0.724350i
$817$	1.27418	−	2.20695i	0.0445780	−	0.0772114i
$818$	−74.5392			−2.60620
$819$		0			0
$820$	−48.4374			−1.69151
$821$	−9.18355	+	15.9064i	−0.320508	+	0.555136i	−0.980593	−	0.196055i	$-0.937187\pi$
$821$	−9.18355	+	15.9064i	−0.320508	+	0.555136i	0.660085	+	0.751191i	$0.270520\pi$
$822$	35.8381	−	62.0734i	1.25000	−	2.16506i
$823$	−10.4039	−	18.0200i	−0.362656	−	0.628138i	0.625741	−	0.780031i	$-0.284797\pi$
$823$	−10.4039	−	18.0200i	−0.362656	−	0.628138i	−0.988397	+	0.151892i	$0.951463\pi$
$824$	84.7776			2.95337
$825$	−1.64296	−	2.84569i	−0.0572004	−	0.0990741i
$826$	−3.99731	−	6.92355i	−0.139084	−	0.240901i
$827$	25.7766			0.896341			0.448171	−	0.893948i	$-0.352076\pi$
$827$	25.7766			0.896341			0.448171	+	0.893948i	$0.352076\pi$
$828$	2.32869	+	4.03340i	0.0809274	+	0.140170i
$829$	−23.3144	+	40.3817i	−0.809743	+	1.40252i	0.103299	+	0.994650i	$0.467060\pi$
$829$	−23.3144	+	40.3817i	−0.809743	+	1.40252i	−0.913042	+	0.407866i	$0.866273\pi$
$830$	−12.8221	+	22.2085i	−0.445060	+	0.770867i
$831$	−45.7555			−1.58724
$832$		0			0
$833$	5.10797			0.176981
$834$	−11.4811	+	19.8859i	−0.397559	+	0.688592i
$835$	2.14934	−	3.72277i	0.0743811	−	0.128832i
$836$	11.4082	+	19.7597i	0.394562	+	0.683402i
$837$	−30.4291			−1.05178
$838$	49.3533	+	85.4825i	1.70488	+	2.95294i
$839$	−4.42021	−	7.65602i	−0.152602	−	0.264315i	0.779581	−	0.626301i	$-0.215432\pi$
$839$	−4.42021	−	7.65602i	−0.152602	−	0.264315i	−0.932183	+	0.361986i	$0.882099\pi$
$840$	5.15950			0.178020
$841$	−11.5103	−	19.9364i	−0.396907	−	0.687463i
$842$	19.6902	−	34.1043i	0.678567	−	1.17531i
$843$	11.6051	−	20.1006i	0.399700	−	0.692300i
$844$	39.1814			1.34868
$845$		0			0
$846$	−0.0989481			−0.00340190
$847$	−1.04079	+	1.80271i	−0.0357621	+	0.0619417i
$848$	−34.3755	+	59.5402i	−1.18046	+	2.04462i
$849$	20.3906	+	35.3176i	0.699804	+	1.21210i
$850$	2.05682			0.0705483
$851$	−10.5425	−	18.2602i	−0.361394	−	0.625953i
$852$	−42.5945	−	73.7759i	−1.45927	−	2.52752i
$853$	−26.7505			−0.915920			−0.457960	−	0.888973i	$-0.651420\pi$
$853$	−26.7505			−0.915920			−0.457960	+	0.888973i	$0.651420\pi$
$854$	1.59573	+	2.76388i	0.0546047	+	0.0945781i
$855$	0.319147	−	0.552778i	0.0109146	−	0.0189046i
$856$	91.2135	−	157.986i	3.11761	−	5.39987i
$857$	−14.3257			−0.489356			−0.244678	−	0.969604i	$-0.578682\pi$
$857$	−14.3257			−0.489356			−0.244678	+	0.969604i	$0.578682\pi$
$858$		0			0
$859$	14.9290			0.509370			0.254685	−	0.967024i	$-0.418028\pi$
$859$	14.9290			0.509370			0.254685	+	0.967024i	$0.418028\pi$
$860$	−3.37937	+	5.85324i	−0.115235	+	0.199594i
$861$	−2.04959	+	3.54999i	−0.0698498	+	0.120983i
$862$	19.7327	+	34.1780i	0.672098	+	1.16411i
$863$	−12.0275			−0.409422			−0.204711	−	0.978822i	$-0.565625\pi$
$863$	−12.0275			−0.409422			−0.204711	+	0.978822i	$0.565625\pi$
$864$	70.5338	+	122.168i	2.39961	+	4.15624i
$865$	−5.59562	−	9.69190i	−0.190257	−	0.329535i
$866$	69.3339			2.35606
$867$	−14.9309	−	25.8612i	−0.507082	−	0.878291i
$868$	−4.82694	+	8.36051i	−0.163837	+	0.283774i
$869$	6.02826	−	10.4413i	0.204495	−	0.354195i
$870$	36.5079			1.23773
$871$		0			0
$872$	−159.563			−5.40348
$873$	−2.55362	+	4.42300i	−0.0864269	+	0.149696i
$874$	−8.36347	+	14.4860i	−0.282899	+	0.489995i
$875$	−0.134800	−	0.233481i	−0.00455708	−	0.00789310i
$876$	−7.26842			−0.245577
$877$	−7.55779	−	13.0905i	−0.255208	−	0.442034i	0.709744	−	0.704460i	$-0.248811\pi$
$877$	−7.55779	−	13.0905i	−0.255208	−	0.442034i	−0.964952	+	0.262426i	$0.915477\pi$
$878$	13.6154	+	23.5826i	0.459499	+	0.795876i
$879$	35.2210			1.18797
$880$	−16.1672	−	28.0024i	−0.544996	−	0.943961i
$881$	−8.85277	+	15.3334i	−0.298257	+	0.516597i	−0.975737	−	0.218944i	$-0.929739\pi$
$881$	−8.85277	+	15.3334i	−0.298257	+	0.516597i	0.677480	+	0.735541i	$0.263072\pi$
$882$	−2.82932	+	4.90052i	−0.0952681	+	0.165009i
$883$	39.3891			1.32555			0.662775	−	0.748818i	$-0.269379\pi$
$883$	39.3891			1.32555			0.662775	+	0.748818i	$0.269379\pi$
$884$		0			0
$885$	19.2908			0.648452
$886$	−45.4633	+	78.7447i	−1.52737	+	2.64548i
$887$	−5.02068	+	8.69607i	−0.168578	+	0.291985i	−0.937920	−	0.346851i	$-0.887251\pi$
$887$	−5.02068	+	8.69607i	−0.168578	+	0.291985i	0.769342	+	0.638837i	$0.220584\pi$
$888$	73.3357	+	127.021i	2.46099	+	4.26255i
$889$	−3.20489			−0.107489
$890$	−9.16550	−	15.8751i	−0.307228	−	0.532135i
$891$	−8.86638	−	15.3570i	−0.297035	−	0.514480i
$892$	−59.0410			−1.97684
$893$	−0.132013	−	0.228654i	−0.00441766	−	0.00765160i
$894$	−8.90663	+	15.4267i	−0.297882	+	0.515947i
$895$	3.84100	−	6.65282i	0.128391	−	0.222379i
$896$	17.8978			0.597923
$897$		0			0
$898$	33.9913			1.13430
$899$	−22.3382	+	38.6909i	−0.745021	+	1.29041i
$900$	−0.846436	+	1.46607i	−0.0282145	+	0.0488690i
$901$	1.41951	+	2.45866i	0.0472907	+	0.0819099i
$902$	42.3228			1.40920
$903$	0.285990	+	0.495349i	0.00951715	+	0.0164842i
$904$	65.7488	+	113.880i	2.18677	+	3.78760i
$905$	−6.44731			−0.214316
$906$	−11.3701	−	19.6936i	−0.377746	−	0.654276i
$907$	−1.95616	+	3.38817i	−0.0649534	+	0.112503i	−0.896673	−	0.442693i	$-0.854023\pi$
$907$	−1.95616	+	3.38817i	−0.0649534	+	0.112503i	0.831720	+	0.555195i	$0.187357\pi$
$908$	−26.2796	+	45.5176i	−0.872119	+	1.51055i
$909$	−3.45574			−0.114620
$910$		0			0
$911$	15.8817			0.526183			0.263092	−	0.964771i	$-0.415258\pi$
$911$	15.8817			0.526183			0.263092	+	0.964771i	$0.415258\pi$
$912$	35.3132	−	61.1642i	1.16934	−	2.02535i
$913$	8.32369	−	14.4170i	0.275474	−	0.477135i
$914$	−42.0461	−	72.8259i	−1.39076	−	2.40887i
$915$	−7.70088			−0.254583
$916$	22.5731	+	39.0977i	0.745835	+	1.29182i
$917$	1.85746	+	3.21722i	0.0613389	+	0.106242i
$918$	10.1040			0.333483
$919$	−12.7946	−	22.1610i	−0.422056	−	0.731023i	0.574084	−	0.818796i	$-0.305358\pi$
$919$	−12.7946	−	22.1610i	−0.422056	−	0.731023i	−0.996140	+	0.0877733i	$0.972025\pi$
$920$	14.5073	−	25.1274i	0.478293	−	0.828427i
$921$	−19.0443	+	32.9857i	−0.627532	+	1.08692i
$922$	88.8100			2.92480
$923$		0			0
$924$	−5.12115			−0.168474
$925$	3.83203	−	6.63727i	0.125996	−	0.218232i
$926$	21.7290	−	37.6357i	0.714059	−	1.23679i
$927$	1.17702	+	2.03866i	0.0386584	+	0.0669583i
$928$	207.117			6.79895
$929$	10.1360	+	17.5561i	0.332552	+	0.575997i	0.983012	−	0.183544i	$-0.0587569\pi$
$929$	10.1360	+	17.5561i	0.332552	+	0.575997i	−0.650459	+	0.759541i	$0.725424\pi$
$930$	−15.6769	−	27.1531i	−0.514065	−	0.890386i
$931$	−15.0991			−0.494854
$932$	10.4849	+	18.1604i	0.343444	+	0.594862i
$933$	11.3654	−	19.6854i	0.372086	−	0.644472i
$934$	−41.5063	+	71.8909i	−1.35813	+	2.35234i
$935$	−1.33522			−0.0436665
$936$		0			0
$937$	8.15562			0.266433			0.133216	−	0.991087i	$-0.457470\pi$
$937$	8.15562			0.266433			0.133216	+	0.991087i	$0.457470\pi$
$938$	−3.59129	+	6.22030i	−0.117260	+	0.203100i
$939$	−7.68061	+	13.3032i	−0.250647	+	0.434134i
$940$	0.350124	+	0.606432i	0.0114198	+	0.0197796i
$941$	48.8847			1.59359			0.796797	−	0.604247i	$-0.206526\pi$
$941$	48.8847			1.59359			0.796797	+	0.604247i	$0.206526\pi$
$942$	−25.9236	−	44.9010i	−0.844637	−	1.46295i
$943$	11.5260	+	19.9635i	0.375337	+	0.650103i
$944$	189.827			6.17835
$945$	−0.662201	−	1.14697i	−0.0215414	−	0.0373108i
$946$	2.95276	−	5.11434i	0.0960026	−	0.166281i
$947$	−14.3099	+	24.7855i	−0.465010	+	0.805420i	−0.999202	−	0.0399427i	$-0.987282\pi$
$947$	−14.3099	+	24.7855i	−0.465010	+	0.805420i	0.534192	+	0.845363i	$0.320616\pi$
$948$	−69.8437			−2.26842
$949$		0			0
$950$	−6.07995			−0.197260
$951$	13.9418	−	24.1478i	0.452093	−	0.783047i
$952$	1.04827	−	1.81566i	0.0339748	−	0.0588460i
$953$	21.1215	+	36.5836i	0.684194	+	1.18506i	0.973689	+	0.227879i	$0.0731792\pi$
$953$	21.1215	+	36.5836i	0.684194	+	1.18506i	−0.289495	+	0.957179i	$0.593487\pi$
$954$	−3.14508			−0.101826
$955$	−9.26601	−	16.0492i	−0.299841	−	0.519340i
$956$	−54.9438	−	95.1655i	−1.77701	−	3.07787i
$957$	−23.6998			−0.766105
$958$	21.0654	+	36.4864i	0.680593	+	1.17882i
$959$	−1.90883	+	3.30619i	−0.0616393	+	0.106762i
$960$	−40.2744	+	69.7573i	−1.29985	+	2.25141i
$961$	7.36907			0.237712
$962$		0			0
$963$	5.06549			0.163233
$964$	29.3257	−	50.7936i	0.944517	−	1.63595i
$965$	−1.98453	+	3.43730i	−0.0638842	+	0.110651i
$966$	−1.87718	−	3.25137i	−0.0603973	−	0.104611i
$967$	9.15979			0.294559			0.147280	−	0.989095i	$-0.452948\pi$
$967$	9.15979			0.294559			0.147280	+	0.989095i	$0.452948\pi$
$968$	−40.7141	−	70.5189i	−1.30860	−	2.26656i
$969$	−1.45823	−	2.52573i	−0.0468450	−	0.0811380i
$970$	48.6481			1.56200
$971$	−15.7858	−	27.3417i	−0.506589	−	0.877438i	−0.999971	−	0.00762547i	$-0.997573\pi$
$971$	−15.7858	−	27.3417i	−0.506589	−	0.877438i	0.493382	−	0.869813i	$-0.335761\pi$
$972$	−8.76596	+	15.1831i	−0.281168	+	0.486998i
$973$	0.611515	−	1.05917i	0.0196043	−	0.0339556i
$974$	19.5000			0.624820
$975$		0			0
$976$	−75.7790			−2.42563
$977$	−4.23202	+	7.33008i	−0.135394	+	0.234510i	−0.925748	−	0.378141i	$-0.876563\pi$
$977$	−4.23202	+	7.33008i	−0.135394	+	0.234510i	0.790354	+	0.612651i	$0.209897\pi$
$978$	−4.27259	+	7.40034i	−0.136622	+	0.236637i
$979$	5.94996	+	10.3056i	0.190161	+	0.329369i
$980$	40.0457			1.27921
$981$	−2.21531	−	3.83702i	−0.0707293	−	0.122507i
$982$	−25.7474	−	44.5959i	−0.821634	−	1.42311i
$983$	5.80225			0.185063			0.0925315	−	0.995710i	$-0.470504\pi$
$983$	5.80225			0.185063			0.0925315	+	0.995710i	$0.470504\pi$
$984$	−80.1765	−	138.870i	−2.55593	−	4.42701i
$985$	−0.857931	+	1.48598i	−0.0273360	+	0.0473473i
$986$	7.41744	−	12.8474i	0.236219	−	0.409144i
$987$	0.0592607			0.00188629
$988$		0			0
$989$	3.21656			0.102281
$990$	0.739584	−	1.28100i	0.0235055	−	0.0407128i
$991$	23.5370	−	40.7673i	0.747677	−	1.29501i	−0.201257	−	0.979539i	$-0.564503\pi$
$991$	23.5370	−	40.7673i	0.747677	−	1.29501i	0.948934	−	0.315476i	$-0.102164\pi$
$992$	−88.9383	−	154.046i	−2.82379	−	4.89096i
$993$	12.4948			0.396511
$994$	3.05360	+	5.28899i	0.0968542	+	0.167756i
$995$	10.1256	+	17.5381i	0.321004	+	0.555995i
$996$	−96.4386			−3.05578
$997$	−3.23041	−	5.59524i	−0.102308	−	0.177203i	0.810327	−	0.585978i	$-0.199289\pi$
$997$	−3.23041	−	5.59524i	−0.102308	−	0.177203i	−0.912635	+	0.408775i	$0.865956\pi$
$998$	13.4622	−	23.3172i	0.426138	−	0.738092i
$999$	18.8247	−	32.6053i	0.595587	−	1.03159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.p.191.9		18
13.2	odd	12		845.2.m.j.361.18		36
13.3	even	3	inner	845.2.e.p.146.9		18
13.4	even	6		845.2.a.o.1.9	yes	9
13.5	odd	4		845.2.m.j.316.1		36
13.6	odd	12		845.2.c.h.506.18		18
13.7	odd	12		845.2.c.h.506.1		18
13.8	odd	4		845.2.m.j.316.18		36
13.9	even	3		845.2.a.n.1.1	✓	9
13.10	even	6		845.2.e.o.146.1		18
13.11	odd	12		845.2.m.j.361.1		36
13.12	even	2		845.2.e.o.191.1		18
39.17	odd	6		7605.2.a.cp.1.1		9
39.35	odd	6		7605.2.a.cs.1.9		9
65.4	even	6		4225.2.a.bs.1.1		9
65.9	even	6		4225.2.a.bt.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.1	✓	9	13.9	even	3
845.2.a.o.1.9	yes	9	13.4	even	6
845.2.c.h.506.1		18	13.7	odd	12
845.2.c.h.506.18		18	13.6	odd	12
845.2.e.o.146.1		18	13.10	even	6
845.2.e.o.191.1		18	13.12	even	2
845.2.e.p.146.9		18	13.3	even	3	inner
845.2.e.p.191.9		18	1.1	even	1	trivial
845.2.m.j.316.1		36	13.5	odd	4
845.2.m.j.316.18		36	13.8	odd	4
845.2.m.j.361.1		36	13.11	odd	12
845.2.m.j.361.18		36	13.2	odd	12
4225.2.a.bs.1.1		9	65.4	even	6
4225.2.a.bt.1.9		9	65.9	even	6
7605.2.a.cp.1.1		9	39.17	odd	6
7605.2.a.cs.1.9		9	39.35	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39471 - 2.41570i) q^{2} +(0.907309 - 1.57151i) q^{3} +(-2.89042 - 5.00635i) q^{4} -1.00000 q^{5} +(-2.53086 - 4.38358i) q^{6} +(0.134800 + 0.233481i) q^{7} -10.5463 q^{8} +(-0.146421 - 0.253609i) q^{9} +O(q^{10})\)	\(q+(1.39471 - 2.41570i) q^{2} +(0.907309 - 1.57151i) q^{3} +(-2.89042 - 5.00635i) q^{4} -1.00000 q^{5} +(-2.53086 - 4.38358i) q^{6} +(0.134800 + 0.233481i) q^{7} -10.5463 q^{8} +(-0.146421 - 0.253609i) q^{9} +(-1.39471 + 2.41570i) q^{10} +(0.905401 - 1.56820i) q^{11} -10.4900 q^{12} +0.752028 q^{14} +(-0.907309 + 1.57151i) q^{15} +(-8.92820 + 15.4641i) q^{16} +(0.368683 + 0.638578i) q^{17} -0.816858 q^{18} +(-1.08983 - 1.88763i) q^{19} +(2.89042 + 5.00635i) q^{20} +0.489222 q^{21} +(-2.52554 - 4.37436i) q^{22} +(1.37558 - 2.38258i) q^{23} +(-9.56878 + 16.5736i) q^{24} +1.00000 q^{25} +4.91246 q^{27} +(0.779259 - 1.34972i) q^{28} +(3.60627 - 6.24624i) q^{29} +(2.53086 + 4.38358i) q^{30} -6.19428 q^{31} +(14.3581 + 24.8690i) q^{32} +(-1.64296 - 2.84569i) q^{33} +2.05682 q^{34} +(-0.134800 - 0.233481i) q^{35} +(-0.846436 + 1.46607i) q^{36} +(3.83203 - 6.63727i) q^{37} -6.07995 q^{38} +10.5463 q^{40} +(-4.18948 + 7.25640i) q^{41} +(0.682322 - 1.18182i) q^{42} +(0.584581 + 1.01252i) q^{43} -10.4679 q^{44} +(0.146421 + 0.253609i) q^{45} +(-3.83707 - 6.64600i) q^{46} +0.121132 q^{47} +(16.2013 + 28.0615i) q^{48} +(3.46366 - 5.99923i) q^{49} +(1.39471 - 2.41570i) q^{50} +1.33804 q^{51} +3.85022 q^{53} +(6.85145 - 11.8671i) q^{54} +(-0.905401 + 1.56820i) q^{55} +(-1.42165 - 2.46237i) q^{56} -3.95524 q^{57} +(-10.0594 - 17.4233i) q^{58} +(-5.31538 - 9.20651i) q^{59} +10.4900 q^{60} +(2.12190 + 3.67524i) q^{61} +(-8.63921 + 14.9635i) q^{62} +(0.0394752 - 0.0683730i) q^{63} +44.3888 q^{64} -9.16578 q^{66} +(-4.77547 + 8.27136i) q^{67} +(2.13130 - 3.69151i) q^{68} +(-2.49616 - 4.32347i) q^{69} -0.752028 q^{70} +(4.06048 + 7.03296i) q^{71} +(1.54420 + 2.67464i) q^{72} +0.692889 q^{73} +(-10.6891 - 18.5141i) q^{74} +(0.907309 - 1.57151i) q^{75} +(-6.30010 + 10.9121i) q^{76} +0.488193 q^{77} +6.65811 q^{79} +(8.92820 - 15.4641i) q^{80} +(4.89638 - 8.48079i) q^{81} +(11.6862 + 20.2411i) q^{82} +9.19337 q^{83} +(-1.41406 - 2.44922i) q^{84} +(-0.368683 - 0.638578i) q^{85} +3.26128 q^{86} +(-6.54400 - 11.3345i) q^{87} +(-9.54865 + 16.5388i) q^{88} +(-3.28581 + 5.69120i) q^{89} +0.816858 q^{90} -15.9040 q^{92} +(-5.62013 + 9.73434i) q^{93} +(0.168944 - 0.292620i) q^{94} +(1.08983 + 1.88763i) q^{95} +52.1091 q^{96} +(-8.72012 - 15.1037i) q^{97} +(-9.66158 - 16.7343i) q^{98} -0.530279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 7 q^{3} - 17 q^{4} - 18 q^{5} - 2 q^{6} + 7 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 7 * q^3 - 17 * q^4 - 18 * q^5 - 2 * q^6 + 7 * q^7 - 24 * q^8 - 16 * q^9	\( 18 q + 3 q^{2} - 7 q^{3} - 17 q^{4} - 18 q^{5} - 2 q^{6} + 7 q^{7} - 24 q^{8} - 16 q^{9} - 3 q^{10} - 9 q^{11} + 24 q^{12} - 4 q^{14} + 7 q^{15} - 37 q^{16} + q^{17} + 20 q^{18} - 4 q^{19} + 17 q^{20} + 2 q^{21} - 12 q^{22} - 14 q^{23} - 35 q^{24} + 18 q^{25} + 44 q^{27} + 18 q^{28} - 12 q^{29} + 2 q^{30} + 14 q^{31} + 22 q^{32} - 8 q^{33} + 60 q^{34} - 7 q^{35} - 3 q^{36} - 5 q^{37} - 94 q^{38} + 24 q^{40} - 10 q^{41} + 11 q^{42} - 39 q^{43} + 50 q^{44} + 16 q^{45} + 6 q^{46} - 72 q^{47} + 3 q^{48} - 16 q^{49} + 3 q^{50} + 86 q^{51} - 16 q^{53} - 2 q^{54} + 9 q^{55} + 29 q^{56} + 64 q^{57} + 21 q^{58} - 21 q^{59} - 24 q^{60} + 3 q^{61} + 10 q^{62} + 35 q^{63} + 68 q^{64} - 98 q^{66} + q^{67} + 20 q^{68} + 13 q^{69} + 4 q^{70} - q^{71} - 3 q^{72} + 15 q^{74} - 7 q^{75} - 5 q^{76} - 8 q^{77} + 78 q^{79} + 37 q^{80} - 29 q^{81} + 4 q^{82} - 14 q^{83} + 12 q^{84} - q^{85} + 48 q^{86} - 16 q^{87} - 42 q^{88} - 19 q^{89} - 20 q^{90} - 54 q^{92} + 31 q^{93} - 16 q^{94} + 4 q^{95} + 14 q^{96} - 34 q^{97} + 48 q^{98} + 2 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 7 * q^3 - 17 * q^4 - 18 * q^5 - 2 * q^6 + 7 * q^7 - 24 * q^8 - 16 * q^9 - 3 * q^10 - 9 * q^11 + 24 * q^12 - 4 * q^14 + 7 * q^15 - 37 * q^16 + q^17 + 20 * q^18 - 4 * q^19 + 17 * q^20 + 2 * q^21 - 12 * q^22 - 14 * q^23 - 35 * q^24 + 18 * q^25 + 44 * q^27 + 18 * q^28 - 12 * q^29 + 2 * q^30 + 14 * q^31 + 22 * q^32 - 8 * q^33 + 60 * q^34 - 7 * q^35 - 3 * q^36 - 5 * q^37 - 94 * q^38 + 24 * q^40 - 10 * q^41 + 11 * q^42 - 39 * q^43 + 50 * q^44 + 16 * q^45 + 6 * q^46 - 72 * q^47 + 3 * q^48 - 16 * q^49 + 3 * q^50 + 86 * q^51 - 16 * q^53 - 2 * q^54 + 9 * q^55 + 29 * q^56 + 64 * q^57 + 21 * q^58 - 21 * q^59 - 24 * q^60 + 3 * q^61 + 10 * q^62 + 35 * q^63 + 68 * q^64 - 98 * q^66 + q^67 + 20 * q^68 + 13 * q^69 + 4 * q^70 - q^71 - 3 * q^72 + 15 * q^74 - 7 * q^75 - 5 * q^76 - 8 * q^77 + 78 * q^79 + 37 * q^80 - 29 * q^81 + 4 * q^82 - 14 * q^83 + 12 * q^84 - q^85 + 48 * q^86 - 16 * q^87 - 42 * q^88 - 19 * q^89 - 20 * q^90 - 54 * q^92 + 31 * q^93 - 16 * q^94 + 4 * q^95 + 14 * q^96 - 34 * q^97 + 48 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more