LMFDB - Embedded newform 87.3.b.a.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,3,Mod(59,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("87.59");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	87.b (of order $2$, degree $1$, 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:	$2.37057829993$
Analytic rank:	$0$
Dimension:	$18$
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} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 $ x^18 + 54x^16 + 1187x^14 + 13673x^12 + 88449x^10 + 318861x^8 + 593533x^6 + 482583x^4 + 152462x^2 + 15341
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.12
Root			$0.949055i$ of defining polynomial
Character	$\chi$	$=$	87.59
Dual form			87.3.b.a.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.949055i q^{2} +(-2.83105 - 0.992548i) q^{3} +3.09929 q^{4} +4.66941i q^{5} +(0.941983 - 2.68682i) q^{6} +2.70818 q^{7} +6.73762i q^{8} +(7.02970 + 5.61991i) q^{9} +O(q^{10})$	\(q+0.949055i q^{2} +(-2.83105 - 0.992548i) q^{3} +3.09929 q^{4} +4.66941i q^{5} +(0.941983 - 2.68682i) q^{6} +2.70818 q^{7} +6.73762i q^{8} +(7.02970 + 5.61991i) q^{9} -4.43152 q^{10} +13.8330i q^{11} +(-8.77426 - 3.07620i) q^{12} +6.42457 q^{13} +2.57021i q^{14} +(4.63461 - 13.2193i) q^{15} +6.00280 q^{16} -8.06761i q^{17} +(-5.33360 + 6.67157i) q^{18} -18.9043 q^{19} +14.4719i q^{20} +(-7.66700 - 2.68800i) q^{21} -13.1283 q^{22} -45.5759i q^{23} +(6.68741 - 19.0745i) q^{24} +3.19665 q^{25} +6.09727i q^{26} +(-14.3234 - 22.8876i) q^{27} +8.39346 q^{28} -5.38516i q^{29} +(12.5459 + 4.39850i) q^{30} +0.734353 q^{31} +32.6475i q^{32} +(13.7299 - 39.1619i) q^{33} +7.65661 q^{34} +12.6456i q^{35} +(21.7871 + 17.4178i) q^{36} +45.0418 q^{37} -17.9412i q^{38} +(-18.1883 - 6.37670i) q^{39} -31.4607 q^{40} +22.1078i q^{41} +(2.55106 - 7.27641i) q^{42} -54.1714 q^{43} +42.8725i q^{44} +(-26.2416 + 32.8245i) q^{45} +43.2540 q^{46} -52.7654i q^{47} +(-16.9942 - 5.95807i) q^{48} -41.6657 q^{49} +3.03380i q^{50} +(-8.00749 + 22.8398i) q^{51} +19.9116 q^{52} +10.8047i q^{53} +(21.7216 - 13.5937i) q^{54} -64.5918 q^{55} +18.2467i q^{56} +(53.5191 + 18.7635i) q^{57} +5.11082 q^{58} -0.612120i q^{59} +(14.3640 - 40.9706i) q^{60} +24.1156 q^{61} +0.696942i q^{62} +(19.0377 + 15.2197i) q^{63} -6.97304 q^{64} +29.9989i q^{65} +(37.1668 + 13.0304i) q^{66} +106.201 q^{67} -25.0039i q^{68} +(-45.2363 + 129.028i) q^{69} -12.0014 q^{70} -25.3182i q^{71} +(-37.8648 + 47.3634i) q^{72} -18.3423 q^{73} +42.7471i q^{74} +(-9.04988 - 3.17283i) q^{75} -58.5901 q^{76} +37.4623i q^{77} +(6.05184 - 17.2617i) q^{78} +141.252 q^{79} +28.0295i q^{80} +(17.8333 + 79.0125i) q^{81} -20.9816 q^{82} -155.906i q^{83} +(-23.7623 - 8.33091i) q^{84} +37.6709 q^{85} -51.4116i q^{86} +(-5.34504 + 15.2457i) q^{87} -93.2015 q^{88} -63.6274i q^{89} +(-31.1523 - 24.9048i) q^{90} +17.3989 q^{91} -141.253i q^{92} +(-2.07899 - 0.728881i) q^{93} +50.0772 q^{94} -88.2720i q^{95} +(32.4042 - 92.4267i) q^{96} +12.1334 q^{97} -39.5431i q^{98} +(-77.7401 + 97.2417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.949055i			0.474528i	0.971445	+	0.237264i	$0.0762506\pi$
$2$			0.949055i			0.474528i	−0.971445	+	0.237264i	$0.923749\pi$
$3$	−2.83105	−	0.992548i	−0.943684	−	0.330849i
$3$	−2.83105	−	0.992548i	−0.943684	−	0.330849i
$4$	3.09929			0.774824
$5$			4.66941i			0.933881i	0.884289	+	0.466941i	$0.154644\pi$
$5$			4.66941i			0.933881i	−0.884289	+	0.466941i	$0.845356\pi$
$6$	0.941983	−	2.68682i	0.156997	−	0.447804i
$7$	2.70818			0.386883			0.193442	−	0.981112i	$-0.438035\pi$
$7$	2.70818			0.386883			0.193442	+	0.981112i	$0.438035\pi$
$8$			6.73762i			0.842203i
$9$	7.02970	+	5.61991i	0.781077	+	0.624434i
$10$	−4.43152			−0.443152
$11$			13.8330i			1.25754i	0.777589	+	0.628772i	$0.216442\pi$
$11$			13.8330i			1.25754i	−0.777589	+	0.628772i	$0.783558\pi$
$12$	−8.77426	−	3.07620i	−0.731188	−	0.256350i
$13$	6.42457			0.494198			0.247099	−	0.968990i	$-0.420523\pi$
$13$	6.42457			0.494198			0.247099	+	0.968990i	$0.420523\pi$
$14$			2.57021i			0.183587i
$15$	4.63461	−	13.2193i	0.308974	−	0.881288i
$16$	6.00280			0.375175
$17$		−	8.06761i		−	0.474565i	−0.971441	−	0.237283i	$-0.923743\pi$
$17$		−	8.06761i		−	0.474565i	0.971441	−	0.237283i	$-0.0762568\pi$
$18$	−5.33360	+	6.67157i	−0.296311	+	0.370643i
$19$	−18.9043			−0.994964			−0.497482	−	0.867474i	$-0.665742\pi$
$19$	−18.9043			−0.994964			−0.497482	+	0.867474i	$0.665742\pi$
$20$			14.4719i			0.723593i
$21$	−7.66700	−	2.68800i	−0.365095	−	0.128000i
$22$	−13.1283			−0.596740
$23$		−	45.5759i		−	1.98156i	−0.135481	−	0.990780i	$-0.543258\pi$
$23$		−	45.5759i		−	1.98156i	0.135481	−	0.990780i	$-0.456742\pi$
$24$	6.68741	−	19.0745i	0.278642	−	0.794773i
$25$	3.19665			0.127866
$26$			6.09727i			0.234511i
$27$	−14.3234	−	22.8876i	−0.530496	−	0.847687i
$28$	8.39346			0.299766
$29$		−	5.38516i		−	0.185695i
$29$		−	5.38516i		−	0.185695i
$30$	12.5459	+	4.39850i	0.418196	+	0.146617i
$31$	0.734353			0.0236888			0.0118444	−	0.999930i	$-0.496230\pi$
$31$	0.734353			0.0236888			0.0118444	+	0.999930i	$0.496230\pi$
$32$			32.6475i			1.02023i
$33$	13.7299	−	39.1619i	0.416058	−	1.18672i
$34$	7.65661			0.225194
$35$			12.6456i			0.361303i
$36$	21.7871	+	17.4178i	0.605197	+	0.483826i
$37$	45.0418			1.21735			0.608673	−	0.793421i	$-0.291702\pi$
$37$	45.0418			1.21735			0.608673	+	0.793421i	$0.291702\pi$
$38$		−	17.9412i		−	0.472138i
$39$	−18.1883	−	6.37670i	−0.466366	−	0.163505i
$40$	−31.4607			−0.786517
$41$			22.1078i			0.539216i	0.962970	+	0.269608i	$0.0868940\pi$
$41$			22.1078i			0.539216i	−0.962970	+	0.269608i	$0.913106\pi$
$42$	2.55106	−	7.27641i	0.0607396	−	0.173248i
$43$	−54.1714			−1.25980			−0.629900	−	0.776677i	$-0.716904\pi$
$43$	−54.1714			−1.25980			−0.629900	+	0.776677i	$0.716904\pi$
$44$			42.8725i			0.974375i
$45$	−26.2416	+	32.8245i	−0.583147	+	0.729433i
$46$	43.2540			0.940305
$47$		−	52.7654i		−	1.12267i	−0.827590	−	0.561334i	$-0.810288\pi$
$47$		−	52.7654i		−	1.12267i	0.827590	−	0.561334i	$-0.189712\pi$
$48$	−16.9942	−	5.95807i	−0.354047	−	0.124127i
$49$	−41.6657			−0.850321
$50$			3.03380i			0.0606760i
$51$	−8.00749	+	22.8398i	−0.157010	+	0.447839i
$52$	19.9116			0.382916
$53$			10.8047i			0.203863i	0.994791	+	0.101931i	$0.0325022\pi$
$53$			10.8047i			0.203863i	−0.994791	+	0.101931i	$0.967498\pi$
$54$	21.7216	−	13.5937i	0.402251	−	0.251735i
$55$	−64.5918			−1.17440
$56$			18.2467i			0.325834i
$57$	53.5191	+	18.7635i	0.938932	+	0.329183i
$58$	5.11082			0.0881175
$59$		−	0.612120i		−	0.0103749i	−0.999987	−	0.00518746i	$-0.998349\pi$
$59$		−	0.612120i		−	0.0103749i	0.999987	−	0.00518746i	$-0.00165123\pi$
$60$	14.3640	−	40.9706i	0.239400	−	0.682843i
$61$	24.1156			0.395337			0.197669	−	0.980269i	$-0.436663\pi$
$61$	24.1156			0.395337			0.197669	+	0.980269i	$0.436663\pi$
$62$			0.696942i			0.0112410i
$63$	19.0377	+	15.2197i	0.302186	+	0.241583i
$64$	−6.97304			−0.108954
$65$			29.9989i			0.461522i
$66$	37.1668	+	13.0304i	0.563133	+	0.197431i
$67$	106.201			1.58508			0.792541	−	0.609818i	$-0.208758\pi$
$67$	106.201			1.58508			0.792541	+	0.609818i	$0.208758\pi$
$68$		−	25.0039i		−	0.367704i
$69$	−45.2363	+	129.028i	−0.655598	+	1.86997i
$70$	−12.0014			−0.171448
$71$		−	25.3182i		−	0.356594i	−0.983977	−	0.178297i	$-0.942941\pi$
$71$		−	25.3182i		−	0.356594i	0.983977	−	0.178297i	$-0.0570588\pi$
$72$	−37.8648	+	47.3634i	−0.525900	+	0.657825i
$73$	−18.3423			−0.251264			−0.125632	−	0.992077i	$-0.540096\pi$
$73$	−18.3423			−0.251264			−0.125632	+	0.992077i	$0.540096\pi$
$74$			42.7471i			0.577664i
$75$	−9.04988	−	3.17283i	−0.120665	−	0.0423044i
$76$	−58.5901			−0.770922
$77$			37.4623i			0.486523i
$78$	6.05184	−	17.2617i	0.0775877	−	0.221304i
$79$	141.252			1.78801			0.894003	−	0.448061i	$-0.147885\pi$
$79$	141.252			1.78801			0.894003	+	0.448061i	$0.147885\pi$
$80$			28.0295i			0.350369i
$81$	17.8333	+	79.0125i	0.220164	+	0.975463i
$82$	−20.9816			−0.255873
$83$		−	155.906i		−	1.87839i	−0.343390	−	0.939193i	$-0.611575\pi$
$83$		−	155.906i		−	1.87839i	0.343390	−	0.939193i	$-0.388425\pi$
$84$	−23.7623	−	8.33091i	−0.282885	−	0.0991775i
$85$	37.6709			0.443188
$86$		−	51.4116i		−	0.597809i
$87$	−5.34504	+	15.2457i	−0.0614372	+	0.175238i
$88$	−93.2015			−1.05911
$89$		−	63.6274i		−	0.714914i	−0.933930	−	0.357457i	$-0.883644\pi$
$89$		−	63.6274i		−	0.714914i	0.933930	−	0.357457i	$-0.116356\pi$
$90$	−31.1523	−	24.9048i	−0.346136	−	0.276719i
$91$	17.3989			0.191197
$92$		−	141.253i		−	1.53536i
$93$	−2.07899	−	0.728881i	−0.0223547	−	0.00783743i
$94$	50.0772			0.532737
$95$		−	88.2720i		−	0.929178i
$96$	32.4042	−	92.4267i	0.337544	−	0.962778i
$97$	12.1334			0.125086			0.0625431	−	0.998042i	$-0.480079\pi$
$97$	12.1334			0.125086			0.0625431	+	0.998042i	$0.480079\pi$
$98$		−	39.5431i		−	0.403501i
$99$	−77.7401	+	97.2417i	−0.785254	+	0.982240i
$100$	9.90737			0.0990737
$101$		−	43.8464i		−	0.434123i	−0.976158	−	0.217061i	$-0.930353\pi$
$101$		−	43.8464i		−	0.434123i	0.976158	−	0.217061i	$-0.0696472\pi$
$102$	−21.6762	−	7.59955i	−0.212512	−	0.0745054i
$103$	−145.324			−1.41091			−0.705454	−	0.708756i	$-0.749257\pi$
$103$	−145.324			−1.41091			−0.705454	+	0.708756i	$0.749257\pi$
$104$			43.2863i			0.416215i
$105$	12.5514	−	35.8003i	0.119537	−	0.340956i
$106$	−10.2543			−0.0967385
$107$			66.5513i			0.621975i	0.950414	+	0.310988i	$0.100660\pi$
$107$			66.5513i			0.621975i	−0.950414	+	0.310988i	$0.899340\pi$
$108$	−44.3924	−	70.9353i	−0.411041	−	0.656808i
$109$	−80.5353			−0.738856			−0.369428	−	0.929259i	$-0.620446\pi$
$109$	−80.5353			−0.738856			−0.369428	+	0.929259i	$0.620446\pi$
$110$		−	61.3012i		−	0.557284i
$111$	−127.516	−	44.7061i	−1.14879	−	0.402758i
$112$	16.2567			0.145149
$113$			90.4762i			0.800675i	0.916368	+	0.400337i	$0.131107\pi$
$113$			90.4762i			0.800675i	−0.916368	+	0.400337i	$0.868893\pi$
$114$	−17.8076	+	50.7926i	−0.156207	+	0.445549i
$115$	212.812			1.85054
$116$		−	16.6902i		−	0.143881i
$117$	45.1628	+	36.1055i	0.386007	+	0.308594i
$118$	0.580936			0.00492318
$119$		−	21.8486i		−	0.183601i
$120$	89.0668	+	31.2262i	0.742223	+	0.260219i
$121$	−70.3516			−0.581418
$122$			22.8870i			0.187598i
$123$	21.9431	−	62.5884i	0.178399	−	0.508849i
$124$	2.27598			0.0183547
$125$			131.662i			1.05329i
$126$	−14.4444	+	18.0678i	−0.114638	+	0.143395i
$127$	−173.633			−1.36719			−0.683596	−	0.729861i	$-0.739585\pi$
$127$	−173.633			−1.36719			−0.683596	+	0.729861i	$0.739585\pi$
$128$			123.972i			0.968532i
$129$	153.362	+	53.7677i	1.18885	+	0.416804i
$130$	−28.4706			−0.219005
$131$			8.21316i			0.0626959i	0.999509	+	0.0313480i	$0.00998000\pi$
$131$			8.21316i			0.0626959i	−0.999509	+	0.0313480i	$0.990020\pi$
$132$	42.5530	−	121.374i	0.322371	−	0.919502i
$133$	−51.1964			−0.384935
$134$			100.790i			0.752165i
$135$	106.871	−	66.8817i	0.791639	−	0.495420i
$136$	54.3565			0.399680
$137$		−	168.338i		−	1.22874i	−0.789017	−	0.614371i	$-0.789410\pi$
$137$		−	168.338i		−	1.22874i	0.789017	−	0.614371i	$-0.210590\pi$
$138$	−122.454	−	42.9317i	−0.887350	−	0.311099i
$139$	165.153			1.18815			0.594075	−	0.804410i	$-0.297518\pi$
$139$	165.153			1.18815			0.594075	+	0.804410i	$0.297518\pi$
$140$			39.1925i			0.279946i
$141$	−52.3722	+	149.381i	−0.371434	+	1.05944i
$142$	24.0283			0.169214
$143$			88.8711i			0.621476i
$144$	42.1979	+	33.7352i	0.293041	+	0.234272i
$145$	25.1455			0.173417
$146$		−	17.4078i		−	0.119232i
$147$	117.958	+	41.3553i	0.802434	+	0.281328i
$148$	139.598			0.943228
$149$			38.0573i			0.255418i	0.991812	+	0.127709i	$0.0407623\pi$
$149$			38.0573i			0.255418i	−0.991812	+	0.127709i	$0.959238\pi$
$150$	3.01119	−	8.58884i	0.0200746	−	0.0572589i
$151$	9.99308			0.0661793			0.0330897	−	0.999452i	$-0.489465\pi$
$151$	9.99308			0.0661793			0.0330897	+	0.999452i	$0.489465\pi$
$152$		−	127.370i		−	0.837962i
$153$	45.3392	−	56.7128i	0.296335	−	0.370672i
$154$	−35.5538			−0.230869
$155$			3.42899i			0.0221225i
$156$	−56.3709	−	19.7633i	−0.361352	−	0.126688i
$157$	−86.1231			−0.548555			−0.274277	−	0.961651i	$-0.588439\pi$
$157$	−86.1231			−0.548555			−0.274277	+	0.961651i	$0.588439\pi$
$158$			134.056i			0.848458i
$159$	10.7242	−	30.5887i	0.0674479	−	0.192382i
$160$	−152.444			−0.952777
$161$		−	123.428i		−	0.766632i
$162$	−74.9872	+	16.9247i	−0.462884	+	0.104474i
$163$	−186.345			−1.14322			−0.571611	−	0.820525i	$-0.693681\pi$
$163$	−186.345			−1.14322			−0.571611	+	0.820525i	$0.693681\pi$
$164$			68.5187i			0.417797i
$165$	182.863	+	64.1105i	1.10826	+	0.388549i
$166$	147.963			0.891346
$167$			285.991i			1.71252i	0.516546	+	0.856260i	$0.327218\pi$
$167$			285.991i			1.71252i	−0.516546	+	0.856260i	$0.672782\pi$
$168$	18.1107	−	51.6574i	0.107802	−	0.307484i
$169$	−127.725			−0.755768
$170$			35.7518i			0.210305i
$171$	−132.892	−	106.241i	−0.777144	−	0.621290i
$172$	−167.893			−0.976122
$173$		−	191.064i		−	1.10441i	−0.833707	−	0.552207i	$-0.813786\pi$
$173$		−	191.064i		−	1.10441i	0.833707	−	0.552207i	$-0.186214\pi$
$174$	−14.4690	−	5.07273i	−0.0831551	−	0.0291536i
$175$	8.65712			0.0494692
$176$			83.0367i			0.471800i
$177$	−0.607559	+	1.73294i	−0.00343254	+	0.00979064i
$178$	60.3859			0.339247
$179$			335.224i			1.87276i	0.350985	+	0.936381i	$0.385847\pi$
$179$			335.224i			1.87276i	−0.350985	+	0.936381i	$0.614153\pi$
$180$	−81.3305	+	101.733i	−0.451836	+	0.565182i
$181$	209.048			1.15496			0.577480	−	0.816405i	$-0.304036\pi$
$181$	209.048			1.15496			0.577480	+	0.816405i	$0.304036\pi$
$182$			16.5125i			0.0907282i
$183$	−68.2724	−	23.9359i	−0.373073	−	0.130797i
$184$	307.073			1.66888
$185$			210.318i			1.13686i
$186$	0.691748	−	1.97308i	0.00371908	−	0.0106079i
$187$	111.599			0.596787
$188$		−	163.535i		−	0.869869i
$189$	−38.7904	−	61.9837i	−0.205240	−	0.327956i
$190$	83.7749			0.440921
$191$		−	202.381i		−	1.05959i	−0.848127	−	0.529794i	$-0.822269\pi$
$191$		−	202.381i		−	1.05959i	0.848127	−	0.529794i	$-0.177731\pi$
$192$	19.7410	+	6.92107i	0.102818	+	0.0360473i
$193$	324.176			1.67967			0.839834	−	0.542844i	$-0.182652\pi$
$193$	324.176			1.67967			0.839834	+	0.542844i	$0.182652\pi$
$194$			11.5152i			0.0593568i
$195$	29.7754	−	84.9285i	0.152694	−	0.435531i
$196$	−129.134			−0.658849
$197$			272.338i			1.38243i	0.722650	+	0.691214i	$0.242924\pi$
$197$			272.338i			1.38243i	−0.722650	+	0.691214i	$0.757076\pi$
$198$	−92.2877	−	73.7797i	−0.466100	−	0.372625i
$199$	−336.191			−1.68940			−0.844701	−	0.535238i	$-0.820222\pi$
$199$	−336.191			−1.68940			−0.844701	+	0.535238i	$0.820222\pi$
$200$			21.5378i			0.107689i
$201$	−300.659	−	105.409i	−1.49582	−	0.524424i
$202$	41.6126			0.206003
$203$		−	14.5840i		−	0.0718424i
$204$	−24.8176	+	70.7873i	−0.121655	+	0.346997i
$205$	−103.230			−0.503563
$206$		−	137.920i		−	0.669515i
$207$	256.132	−	320.385i	1.23735	−	1.54775i
$208$	38.5655			0.185411
$209$		−	261.503i		−	1.25121i
$210$	33.9765	+	11.9119i	0.161793	+	0.0567235i
$211$	−262.151			−1.24242			−0.621212	−	0.783643i	$-0.713359\pi$
$211$	−262.151			−1.24242			−0.621212	+	0.783643i	$0.713359\pi$
$212$			33.4870i			0.157958i
$213$	−25.1295	+	71.6770i	−0.117979	+	0.336512i
$214$	−63.1609			−0.295144
$215$		−	252.948i		−	1.17650i
$216$	154.208	−	96.5056i	0.713925	−	0.446785i
$217$	1.98876			0.00916480
$218$		−	76.4324i		−	0.350607i
$219$	51.9279	+	18.2056i	0.237114	+	0.0831305i
$220$	−200.189			−0.909951
$221$		−	51.8310i		−	0.234529i
$222$	42.4286	−	121.019i	0.191120	−	0.545132i
$223$	−37.9013			−0.169961			−0.0849805	−	0.996383i	$-0.527083\pi$
$223$	−37.9013			−0.169961			−0.0849805	+	0.996383i	$0.527083\pi$
$224$			88.4153i			0.394711i
$225$	22.4715	+	17.9649i	0.0998733	+	0.0798440i
$226$	−85.8669			−0.379942
$227$			325.184i			1.43253i	0.697829	+	0.716265i	$0.254150\pi$
$227$			325.184i			1.43253i	−0.697829	+	0.716265i	$0.745850\pi$
$228$	165.871	+	58.1535i	0.727506	+	0.255059i
$229$	−184.820			−0.807076			−0.403538	−	0.914963i	$-0.632220\pi$
$229$	−184.820			−0.807076			−0.403538	+	0.914963i	$0.632220\pi$
$230$			201.971i			0.878133i
$231$	37.1831	−	106.058i	0.160966	−	0.459124i
$232$	36.2832			0.156393
$233$		−	243.534i		−	1.04521i	−0.852574	−	0.522606i	$-0.824960\pi$
$233$		−	243.534i		−	1.04521i	0.852574	−	0.522606i	$-0.175040\pi$
$234$	−34.2661	+	42.8620i	−0.146436	+	0.183171i
$235$	246.383			1.04844
$236$		−	1.89714i		−	0.00803873i
$237$	−399.893	−	140.200i	−1.68731	−	0.591561i
$238$	20.7355			0.0871239
$239$			82.0366i			0.343250i	0.985162	+	0.171625i	$0.0549017\pi$
$239$			82.0366i			0.343250i	−0.985162	+	0.171625i	$0.945098\pi$
$240$	27.8207	−	79.3530i	0.115919	−	0.330638i
$241$	42.4682			0.176217			0.0881084	−	0.996111i	$-0.471918\pi$
$241$	42.4682			0.176217			0.0881084	+	0.996111i	$0.471918\pi$
$242$		−	66.7676i		−	0.275899i
$243$	27.9369	−	241.389i	0.114967	−	0.993369i
$244$	74.7413			0.306317
$245$		−	194.554i		−	0.794099i
$246$	59.3998	+	20.8252i	0.241463	+	0.0846553i
$247$	−121.452			−0.491709
$248$			4.94779i			0.0199508i
$249$	−154.744	+	441.378i	−0.621463	+	1.77260i
$250$	−124.954			−0.499816
$251$		−	431.753i		−	1.72013i	−0.510185	−	0.860065i	$-0.670423\pi$
$251$		−	431.753i		−	1.72013i	0.510185	−	0.860065i	$-0.329577\pi$
$252$	59.0034	+	47.1705i	0.234141	+	0.187184i
$253$	630.451			2.49190
$254$		−	164.788i		−	0.648770i
$255$	−106.648	−	37.3902i	−0.418229	−	0.146628i
$256$	−145.549			−0.568549
$257$			111.923i			0.435499i	0.976005	+	0.217749i	$0.0698715\pi$
$257$			111.923i			0.435499i	−0.976005	+	0.217749i	$0.930128\pi$
$258$	−51.0285	+	145.549i	−0.197785	+	0.564143i
$259$	121.981			0.470971
$260$			92.9755i			0.357598i
$261$	30.2641	−	37.8561i	0.115955	−	0.145042i
$262$	−7.79474			−0.0297509
$263$		−	109.884i		−	0.417810i	−0.977936	−	0.208905i	$-0.933010\pi$
$263$		−	109.884i		−	0.417810i	0.977936	−	0.208905i	$-0.0669899\pi$
$264$	263.858	+	92.5069i	0.999462	+	0.350405i
$265$	−50.4516			−0.190384
$266$		−	48.5882i		−	0.182662i
$267$	−63.1532	+	180.132i	−0.236529	+	0.674653i
$268$	329.147			1.22816
$269$			452.187i			1.68099i	0.541817	+	0.840496i	$0.317737\pi$
$269$			452.187i			1.68099i	−0.541817	+	0.840496i	$0.682263\pi$
$270$	63.4745	+	101.427i	0.235091	+	0.375655i
$271$	167.060			0.616457			0.308229	−	0.951312i	$-0.400264\pi$
$271$	167.060			0.616457			0.308229	+	0.951312i	$0.400264\pi$
$272$		−	48.4283i		−	0.178045i
$273$	−49.2572	−	17.2693i	−0.180429	−	0.0632574i
$274$	159.762			0.583072
$275$			44.2193i			0.160797i
$276$	−140.200	+	399.895i	−0.507973	+	1.44889i
$277$	−57.7609			−0.208523			−0.104262	−	0.994550i	$-0.533248\pi$
$277$	−57.7609			−0.208523			−0.104262	+	0.994550i	$0.533248\pi$
$278$			156.739i			0.563810i
$279$	5.16228	+	4.12700i	0.0185028	+	0.0147921i
$280$	−85.2013			−0.304290
$281$		−	205.841i		−	0.732530i	−0.930511	−	0.366265i	$-0.880636\pi$
$281$		−	205.841i		−	0.732530i	0.930511	−	0.366265i	$-0.119364\pi$
$282$	−141.771	−	49.7041i	−0.502735	−	0.176256i
$283$	−348.975			−1.23313			−0.616564	−	0.787305i	$-0.711476\pi$
$283$	−348.975			−1.23313			−0.616564	+	0.787305i	$0.711476\pi$
$284$		−	78.4685i		−	0.276297i
$285$	−87.6142	+	249.902i	−0.307418	+	0.876850i
$286$	−84.3435			−0.294907
$287$			59.8721i			0.208613i
$288$	−183.476	+	229.502i	−0.637069	+	0.796881i
$289$	223.914			0.774788
$290$			23.8645i			0.0822913i
$291$	−34.3501	−	12.0429i	−0.118042	−	0.0413847i
$292$	−56.8481			−0.194685
$293$		−	77.4168i		−	0.264221i	−0.991235	−	0.132111i	$-0.957825\pi$
$293$		−	77.4168i		−	0.264221i	0.991235	−	0.132111i	$-0.0421754\pi$
$294$	−39.2484	+	111.948i	−0.133498	+	0.380777i
$295$	2.85824			0.00968894
$296$			303.474i			1.02525i
$297$	316.603	−	198.135i	1.06600	−	0.667123i
$298$	−36.1184			−0.121203
$299$		−	292.806i		−	0.979283i
$300$	−28.0483	−	9.83354i	−0.0934942	−	0.0327785i
$301$	−146.706			−0.487395
$302$			9.48398i			0.0314039i
$303$	−43.5197	+	124.131i	−0.143629	+	0.409674i
$304$	−113.479			−0.373286
$305$			112.605i			0.369198i
$306$	53.8236	+	43.0294i	0.175894	+	0.140619i
$307$	−107.603			−0.350498			−0.175249	−	0.984524i	$-0.556073\pi$
$307$	−107.603			−0.350498			−0.175249	+	0.984524i	$0.556073\pi$
$308$			116.107i			0.376970i
$309$	411.418	+	144.241i	1.33145	+	0.466798i
$310$	−3.25430			−0.0104978
$311$			219.086i			0.704458i	0.935914	+	0.352229i	$0.114576\pi$
$311$			219.086i			0.704458i	−0.935914	+	0.352229i	$0.885424\pi$
$312$	42.9638	−	122.546i	0.137704	−	0.392775i
$313$	−372.719			−1.19080			−0.595398	−	0.803431i	$-0.703005\pi$
$313$	−372.719			−1.19080			−0.595398	+	0.803431i	$0.703005\pi$
$314$		−	81.7356i		−	0.260304i
$315$	−71.0671	+	88.8948i	−0.225610	+	0.282206i
$316$	437.783			1.38539
$317$		−	379.417i		−	1.19690i	−0.801160	−	0.598450i	$-0.795784\pi$
$317$		−	379.417i		−	1.19690i	0.801160	−	0.598450i	$-0.204216\pi$
$318$	29.0304	+	10.1779i	0.0912905	+	0.0320059i
$319$	74.4929			0.233520
$320$		−	32.5599i		−	0.101750i
$321$	66.0554	−	188.410i	0.205780	−	0.586948i
$322$	117.140			0.363788
$323$			152.513i			0.472176i
$324$	55.2705	+	244.883i	0.170588	+	0.755812i
$325$	20.5371			0.0631912
$326$		−	176.852i		−	0.542490i
$327$	228.000	+	79.9352i	0.697246	+	0.244450i
$328$	−148.954			−0.454129
$329$		−	142.898i		−	0.434341i
$330$	−60.8444	+	173.547i	−0.184377	+	0.525900i
$331$	−32.9150			−0.0994412			−0.0497206	−	0.998763i	$-0.515833\pi$
$331$	−32.9150			−0.0994412			−0.0497206	+	0.998763i	$0.515833\pi$
$332$		−	483.199i		−	1.45542i
$333$	316.630	+	253.131i	0.950841	+	0.760152i
$334$	−271.421			−0.812638
$335$			495.893i			1.48028i
$336$	−46.0235	−	16.1356i	−0.136975	−	0.0480225i
$337$	−69.7498			−0.206973			−0.103486	−	0.994631i	$-0.533000\pi$
$337$	−69.7498			−0.206973			−0.103486	+	0.994631i	$0.533000\pi$
$338$		−	121.218i		−	0.358633i
$339$	89.8020	−	256.143i	0.264903	−	0.755583i
$340$	116.753			0.343392
$341$			10.1583i			0.0297897i
$342$	100.828	−	126.121i	0.294819	−	0.368776i
$343$	−245.539			−0.715858
$344$		−	364.986i		−	1.06101i
$345$	−602.482	−	211.226i	−1.74633	−	0.612251i
$346$	181.330			0.524075
$347$			218.421i			0.629454i	0.949182	+	0.314727i	$0.101913\pi$
$347$			218.421i			0.629454i	−0.949182	+	0.314727i	$0.898087\pi$
$348$	−16.5658	+	47.2508i	−0.0476030	+	0.135778i
$349$	398.726			1.14248			0.571241	−	0.820782i	$-0.306462\pi$
$349$	398.726			1.14248			0.571241	+	0.820782i	$0.306462\pi$
$350$			8.21608i			0.0234745i
$351$	−92.0217	−	147.043i	−0.262170	−	0.418925i
$352$	−451.612			−1.28299
$353$		−	133.004i		−	0.376782i	−0.982094	−	0.188391i	$-0.939673\pi$
$353$		−	133.004i		−	0.376782i	0.982094	−	0.188391i	$-0.0603273\pi$
$354$	−1.64466	−	0.576607i	−0.00464593	−	0.00162883i
$355$	118.221			0.333016
$356$		−	197.200i		−	0.553933i
$357$	−21.6858	+	61.8544i	−0.0607444	+	0.173262i
$358$	−318.146			−0.888677
$359$			99.0249i			0.275835i	0.990444	+	0.137918i	$0.0440409\pi$
$359$			99.0249i			0.275835i	−0.990444	+	0.137918i	$0.955959\pi$
$360$	−221.159	−	176.806i	−0.614331	−	0.491128i
$361$	−3.62652			−0.0100458
$362$			198.398i			0.548061i
$363$	199.169	+	69.8274i	0.548675	+	0.192362i
$364$	53.9244			0.148144
$365$		−	85.6474i		−	0.234651i
$366$	22.7165	−	64.7943i	0.0620668	−	0.177034i
$367$	380.440			1.03662			0.518310	−	0.855193i	$-0.326561\pi$
$367$	380.440			1.03662			0.518310	+	0.855193i	$0.326561\pi$
$368$		−	273.583i		−	0.743432i
$369$	−124.244	+	155.411i	−0.336705	+	0.421169i
$370$	−199.604			−0.539469
$371$			29.2612i			0.0788711i
$372$	−6.44341	−	2.25902i	−0.0173210	−	0.00607263i
$373$	−141.610			−0.379651			−0.189826	−	0.981818i	$-0.560792\pi$
$373$	−141.610			−0.379651			−0.189826	+	0.981818i	$0.560792\pi$
$374$			105.914i			0.283192i
$375$	130.680	−	372.741i	0.348481	−	0.993975i
$376$	355.513			0.945514
$377$		−	34.5974i		−	0.0917703i
$378$	58.8259	−	36.8142i	0.155624	−	0.0973921i
$379$	428.220			1.12987			0.564934	−	0.825136i	$-0.308901\pi$
$379$	428.220			1.12987			0.564934	+	0.825136i	$0.308901\pi$
$380$		−	273.581i		−	0.719949i
$381$	491.565	+	172.339i	1.29020	+	0.452335i
$382$	192.071			0.502803
$383$		−	236.854i		−	0.618419i	−0.950994	−	0.309209i	$-0.899936\pi$
$383$		−	236.854i		−	0.618419i	0.950994	−	0.309209i	$-0.100064\pi$
$384$	123.048	−	350.971i	0.320438	−	0.913988i
$385$	−174.927			−0.454355
$386$			307.661i			0.797048i
$387$	−380.808	−	304.438i	−0.984001	−	0.786662i
$388$	37.6048			0.0969197
$389$			150.510i			0.386916i	0.981109	+	0.193458i	$0.0619703\pi$
$389$			150.510i			0.386916i	−0.981109	+	0.193458i	$0.938030\pi$
$390$	80.6018	+	28.2585i	0.206671	+	0.0724577i
$391$	−367.688			−0.940380
$392$		−	280.728i		−	0.716143i
$393$	8.15196	−	23.2519i	0.0207429	−	0.0591651i
$394$	−258.464			−0.656000
$395$			659.565i			1.66979i
$396$	−240.940	+	301.381i	−0.608433	+	0.761062i
$397$	−421.169			−1.06088			−0.530439	−	0.847723i	$-0.677973\pi$
$397$	−421.169			−1.06088			−0.530439	+	0.847723i	$0.677973\pi$
$398$		−	319.064i		−	0.801668i
$399$	144.940	+	50.8149i	0.363257	+	0.127356i
$400$	19.1889			0.0479722
$401$		−	399.836i		−	0.997096i	−0.866862	−	0.498548i	$-0.833867\pi$
$401$		−	399.836i		−	0.997096i	0.866862	−	0.498548i	$-0.166133\pi$
$402$	100.039	−	285.342i	0.248853	−	0.709806i
$403$	4.71791			0.0117070
$404$		−	135.893i		−	0.336369i
$405$	−368.941	+	83.2707i	−0.910966	+	0.205607i
$406$	13.8410			0.0340912
$407$			623.063i			1.53087i
$408$	−153.886	−	53.9515i	−0.377172	−	0.132234i
$409$	−486.637			−1.18982			−0.594911	−	0.803791i	$-0.702813\pi$
$409$	−486.637			−1.18982			−0.594911	+	0.803791i	$0.702813\pi$
$410$		−	97.9714i		−	0.238955i
$411$	−167.083	+	476.572i	−0.406529	+	1.15954i
$412$	−450.400			−1.09320
$413$		−	1.65773i		−	0.00401388i
$414$	304.063	+	243.084i	0.734451	+	0.587159i
$415$	727.988			1.75419
$416$			209.746i			0.504197i
$417$	−467.556	−	163.922i	−1.12124	−	0.393099i
$418$	248.181			0.593735
$419$		−	508.231i		−	1.21296i	−0.795098	−	0.606480i	$-0.792581\pi$
$419$		−	508.231i		−	1.21296i	0.795098	−	0.606480i	$-0.207419\pi$
$420$	38.9004	−	110.956i	0.0926200	−	0.264181i
$421$	502.174			1.19281			0.596406	−	0.802683i	$-0.296595\pi$
$421$	502.174			1.19281			0.596406	+	0.802683i	$0.296595\pi$
$422$		−	248.796i		−	0.589564i
$423$	296.537	−	370.925i	0.701032	−	0.876890i
$424$	−72.7981			−0.171694
$425$		−	25.7893i		−	0.0606808i
$426$	−68.0254	−	23.8493i	−0.159684	−	0.0559842i
$427$	65.3094			0.152949
$428$			206.262i			0.481921i
$429$	88.2088	−	251.598i	0.205615	−	0.586477i
$430$	240.062			0.558283
$431$			675.282i			1.56678i	0.621531	+	0.783390i	$0.286511\pi$
$431$			675.282i			1.56678i	−0.621531	+	0.783390i	$0.713489\pi$
$432$	−85.9805	−	137.390i	−0.199029	−	0.318031i
$433$	−103.034			−0.237953			−0.118977	−	0.992897i	$-0.537961\pi$
$433$	−103.034			−0.237953			−0.118977	+	0.992897i	$0.537961\pi$
$434$			1.88745i			0.00434895i
$435$	−71.1882	−	24.9581i	−0.163651	−	0.0573750i
$436$	−249.603			−0.572483
$437$			861.581i			1.97158i
$438$	−17.2781	+	49.2824i	−0.0394477	+	0.112517i
$439$	15.7852			0.0359572			0.0179786	−	0.999838i	$-0.494277\pi$
$439$	15.7852			0.0359572			0.0179786	+	0.999838i	$0.494277\pi$
$440$		−	435.195i		−	0.989080i
$441$	−292.898	−	234.158i	−0.664167	−	0.530970i
$442$	49.1904			0.111291
$443$		−	130.391i		−	0.294336i	−0.989112	−	0.147168i	$-0.952984\pi$
$443$		−	130.391i		−	0.294336i	0.989112	−	0.147168i	$-0.0470157\pi$
$444$	−395.208	−	138.558i	−0.890109	−	0.312066i
$445$	297.102			0.667645
$446$		−	35.9704i		−	0.0806511i
$447$	37.7737	−	107.742i	0.0845049	−	0.241034i
$448$	−18.8843			−0.0421524
$449$		−	218.937i		−	0.487609i	−0.969824	−	0.243805i	$-0.921604\pi$
$449$		−	218.937i		−	0.487609i	0.969824	−	0.243805i	$-0.0783956\pi$
$450$	−17.0497	+	21.3267i	−0.0378882	+	0.0473926i
$451$	−305.817			−0.678088
$452$			280.412i			0.620382i
$453$	−28.2909	−	9.91861i	−0.0624523	−	0.0218954i
$454$	−308.618			−0.679774
$455$			81.2426i			0.178555i
$456$	−126.421	+	360.591i	−0.277239	+	0.790771i
$457$	−273.649			−0.598795			−0.299398	−	0.954128i	$-0.596786\pi$
$457$	−273.649			−0.598795			−0.299398	+	0.954128i	$0.596786\pi$
$458$		−	175.405i		−	0.382980i
$459$	−184.648	+	115.556i	−0.402283	+	0.251755i
$460$	659.568			1.43384
$461$			472.126i			1.02414i	0.858945	+	0.512068i	$0.171120\pi$
$461$			472.126i			1.02414i	−0.858945	+	0.512068i	$0.828880\pi$
$462$	100.654	+	35.2888i	0.217867	+	0.0763827i
$463$	225.800			0.487688			0.243844	−	0.969814i	$-0.421592\pi$
$463$	225.800			0.487688			0.243844	+	0.969814i	$0.421592\pi$
$464$		−	32.3261i		−	0.0696683i
$465$	3.40344	−	9.70765i	0.00731923	−	0.0208767i
$466$	231.128			0.495982
$467$			727.136i			1.55704i	0.627622	+	0.778519i	$0.284029\pi$
$467$			727.136i			1.55704i	−0.627622	+	0.778519i	$0.715971\pi$
$468$	139.973	+	111.902i	0.299087	+	0.239106i
$469$	287.610			0.613242
$470$			233.831i			0.497513i
$471$	243.819	+	85.4813i	0.517662	+	0.181489i
$472$	4.12423			0.00873778
$473$		−	749.352i		−	1.58425i
$474$	133.057	−	379.520i	0.280712	−	0.800676i
$475$	−60.4305			−0.127222
$476$		−	67.7151i		−	0.142259i
$477$	−60.7216	+	75.9539i	−0.127299	+	0.159233i
$478$	−77.8573			−0.162881
$479$			436.959i			0.912231i	0.889921	+	0.456115i	$0.150760\pi$
$479$			436.959i			0.912231i	−0.889921	+	0.456115i	$0.849240\pi$
$480$	431.578	+	151.308i	0.899120	+	0.315226i
$481$	289.374			0.601610
$482$			40.3047i			0.0836197i
$483$	−122.508	+	349.430i	−0.253640	+	0.723458i
$484$	−218.040			−0.450497
$485$			56.6555i			0.116816i
$486$	229.091	+	26.5136i	0.471381	+	0.0545548i
$487$	−43.1395			−0.0885821			−0.0442910	−	0.999019i	$-0.514103\pi$
$487$	−43.1395			−0.0885821			−0.0442910	+	0.999019i	$0.514103\pi$
$488$			162.482i			0.332954i
$489$	527.553	+	184.957i	1.07884	+	0.378234i
$490$	184.643			0.376822
$491$			585.317i			1.19209i	0.802950	+	0.596046i	$0.203263\pi$
$491$			585.317i			1.19209i	−0.802950	+	0.596046i	$0.796737\pi$
$492$	68.0081	−	193.980i	0.138228	−	0.394268i
$493$	−43.4454			−0.0881246
$494$		−	115.265i		−	0.233330i
$495$	−454.061	−	363.000i	−0.917295	−	0.733334i
$496$	4.40818			0.00888746
$497$		−	68.5662i		−	0.137960i
$498$	−418.892	−	146.861i	−0.841148	−	0.294901i
$499$	304.266			0.609752			0.304876	−	0.952392i	$-0.401385\pi$
$499$	304.266			0.609752			0.304876	+	0.952392i	$0.401385\pi$
$500$			408.058i			0.816116i
$501$	283.860	−	809.654i	0.566586	−	1.61608i
$502$	409.757			0.816249
$503$			929.099i			1.84711i	0.383460	+	0.923557i	$0.374732\pi$
$503$			929.099i			1.84711i	−0.383460	+	0.923557i	$0.625268\pi$
$504$	−102.545	+	128.269i	−0.203462	+	0.254502i
$505$	204.737			0.405419
$506$			598.332i			1.18248i
$507$	361.596	+	126.773i	0.713206	+	0.250046i
$508$	−538.141			−1.05933
$509$		−	309.936i		−	0.608911i	−0.952527	−	0.304455i	$-0.901526\pi$
$509$		−	309.936i		−	0.608911i	0.952527	−	0.304455i	$-0.0984745\pi$
$510$	35.4854	−	101.215i	0.0695792	−	0.198461i
$511$	−49.6742			−0.0972098
$512$			357.755i			0.698740i
$513$	270.774	+	432.674i	0.527825	+	0.843419i
$514$	−106.221			−0.206656
$515$		−	678.575i		−	1.31762i
$516$	475.314	+	166.642i	0.921150	+	0.322949i
$517$	729.903			1.41180
$518$			115.767i			0.223489i
$519$	−189.640	+	540.911i	−0.365395	+	1.04222i
$520$	−202.121			−0.388695
$521$		−	523.170i		−	1.00416i	−0.864820	−	0.502082i	$-0.832567\pi$
$521$		−	523.170i		−	1.00416i	0.864820	−	0.502082i	$-0.167433\pi$
$522$	35.9275	+	28.7223i	0.0688266	+	0.0550236i
$523$	458.129			0.875964			0.437982	−	0.898984i	$-0.355693\pi$
$523$	458.129			0.875964			0.437982	+	0.898984i	$0.355693\pi$
$524$			25.4550i			0.0485783i
$525$	−24.5087	−	8.59261i	−0.0466833	−	0.0163669i
$526$	104.286			0.198262
$527$		−	5.92447i		−	0.0112419i
$528$	82.4180	−	235.081i	0.156095	−	0.445230i
$529$	−1548.16			−2.92658
$530$		−	47.8814i		−	0.0903422i
$531$	3.44006	−	4.30302i	0.00647846	−	0.00810361i
$532$	−158.673			−0.298257
$533$			142.033i			0.266479i
$534$	−170.956	−	59.9359i	−0.320141	−	0.112240i
$535$	−310.755			−0.580851
$536$			715.539i			1.33496i
$537$	332.726	−	949.037i	0.619602	−	1.76730i
$538$	−429.150			−0.797677
$539$		−	576.362i		−	1.06932i
$540$	331.226	−	207.286i	0.613381	−	0.383863i
$541$	−589.955			−1.09049			−0.545245	−	0.838277i	$-0.683563\pi$
$541$	−589.955			−1.09049			−0.545245	+	0.838277i	$0.683563\pi$
$542$			158.549i			0.292526i
$543$	−591.825	−	207.490i	−1.08992	−	0.382118i
$544$	263.387			0.484168
$545$		−	376.052i		−	0.690004i
$546$	16.3895	−	46.7478i	0.0300174	−	0.0856187i
$547$	−673.623			−1.23149			−0.615743	−	0.787947i	$-0.711144\pi$
$547$	−673.623			−1.23149			−0.615743	+	0.787947i	$0.711144\pi$
$548$		−	521.728i		−	0.952058i
$549$	169.525	+	135.527i	0.308789	+	0.246862i
$550$	−41.9665			−0.0763027
$551$			101.803i			0.184760i
$552$	−869.339	−	304.785i	−1.57489	−	0.552146i
$553$	382.538			0.691750
$554$		−	54.8183i		−	0.0989500i
$555$	208.751	−	595.422i	0.376128	−	1.07283i
$556$	511.857			0.920606
$557$		−	242.707i		−	0.435740i	−0.975978	−	0.217870i	$-0.930089\pi$
$557$		−	242.707i		−	0.435740i	0.975978	−	0.217870i	$-0.0699109\pi$
$558$	−3.91675	+	4.89929i	−0.00701926	+	0.00878008i
$559$	−348.028			−0.622590
$560$			75.9091i			0.135552i
$561$	−315.943	−	110.768i	−0.563178	−	0.197447i
$562$	195.354			0.347606
$563$		−	264.932i		−	0.470571i	−0.971926	−	0.235286i	$-0.924397\pi$
$563$		−	264.932i		−	0.470571i	0.971926	−	0.235286i	$-0.0756025\pi$
$564$	−162.317	+	462.977i	−0.287796	+	0.820881i
$565$	−422.470			−0.747735
$566$		−	331.197i		−	0.585153i
$567$	48.2957	+	213.980i	0.0851776	+	0.377390i
$568$	170.584			0.300324
$569$		−	1091.42i		−	1.91813i	−0.283187	−	0.959065i	$-0.591392\pi$
$569$		−	1091.42i		−	1.91813i	0.283187	−	0.959065i	$-0.408608\pi$
$570$	−237.171	−	83.1507i	−0.416090	−	0.145878i
$571$	−401.706			−0.703513			−0.351757	−	0.936091i	$-0.614416\pi$
$571$	−401.706			−0.703513			−0.351757	+	0.936091i	$0.614416\pi$
$572$			275.438i			0.481534i
$573$	−200.873	+	572.951i	−0.350564	+	0.999915i
$574$	−56.8219			−0.0989928
$575$		−	145.690i		−	0.253374i
$576$	−49.0183	−	39.1878i	−0.0851012	−	0.0680344i
$577$	445.201			0.771579			0.385790	−	0.922587i	$-0.373929\pi$
$577$	445.201			0.771579			0.385790	+	0.922587i	$0.373929\pi$
$578$			212.506i			0.367658i
$579$	−917.758	−	321.760i	−1.58507	−	0.555717i
$580$	77.9334			0.134368
$581$		−	422.222i		−	0.726716i
$582$	11.4294	−	32.6002i	0.0196382	−	0.0560140i
$583$	−149.462			−0.256366
$584$		−	123.583i		−	0.211615i
$585$	−168.591	+	210.883i	−0.288190	+	0.360484i
$586$	73.4728			0.125380
$587$			396.043i			0.674689i	0.941381	+	0.337345i	$0.109529\pi$
$587$			396.043i			0.674689i	−0.941381	+	0.337345i	$0.890471\pi$
$588$	365.586	+	128.172i	0.621745	+	0.217980i
$589$	−13.8824			−0.0235695
$590$			2.71262i			0.00459767i
$591$	270.309	−	771.004i	0.457376	−	1.30458i
$592$	270.377			0.456718
$593$			212.616i			0.358544i	0.983800	+	0.179272i	$0.0573741\pi$
$593$			212.616i			0.358544i	−0.983800	+	0.179272i	$0.942626\pi$
$594$	188.041	+	300.474i	0.316568	+	0.505849i
$595$	102.020			0.171462
$596$			117.951i			0.197904i
$597$	951.774	+	333.686i	1.59426	+	0.558938i
$598$	277.889			0.464697
$599$			55.1819i			0.0921234i	0.998939	+	0.0460617i	$0.0146671\pi$
$599$			55.1819i			0.0921234i	−0.998939	+	0.0460617i	$0.985333\pi$
$600$	21.3773	−	60.9747i	0.0356289	−	0.101624i
$601$	300.501			0.500002			0.250001	−	0.968246i	$-0.419569\pi$
$601$	300.501			0.500002			0.250001	+	0.968246i	$0.419569\pi$
$602$		−	139.232i		−	0.231282i
$603$	746.557	+	596.837i	1.23807	+	0.989780i
$604$	30.9715			0.0512773
$605$		−	328.500i		−	0.542976i
$606$	−117.808	−	41.3026i	−0.194402	−	0.0681560i
$607$	560.525			0.923435			0.461717	−	0.887027i	$-0.347233\pi$
$607$	560.525			0.923435			0.461717	+	0.887027i	$0.347233\pi$
$608$		−	617.178i		−	1.01510i
$609$	−14.4753	+	41.2881i	−0.0237690	+	0.0677965i
$610$	−106.869			−0.175195
$611$		−	338.995i		−	0.554820i
$612$	140.520	−	175.770i	0.229607	−	0.287206i
$613$	−979.730			−1.59825			−0.799127	−	0.601162i	$-0.794705\pi$
$613$	−979.730			−1.59825			−0.799127	+	0.601162i	$0.794705\pi$
$614$		−	102.121i		−	0.166321i
$615$	292.251	+	102.461i	0.475204	+	0.166604i
$616$	−252.407			−0.409751
$617$		−	155.269i		−	0.251652i	−0.992052	−	0.125826i	$-0.959842\pi$
$617$		−	155.269i		−	0.251652i	0.992052	−	0.125826i	$-0.0401581\pi$
$618$	−136.892	+	390.459i	−0.221509	+	0.631810i
$619$	1038.72			1.67805			0.839027	−	0.544089i	$-0.183125\pi$
$619$	1038.72			1.67805			0.839027	+	0.544089i	$0.183125\pi$
$620$			10.6275i			0.0171411i
$621$	−1043.12	+	652.801i	−1.67974	+	1.05121i
$622$	−207.925			−0.334285
$623$		−	172.315i		−	0.276588i
$624$	−109.181	−	38.2781i	−0.174969	−	0.0613431i
$625$	−534.865			−0.855784
$626$		−	353.731i		−	0.565065i
$627$	−259.555	+	740.329i	−0.413963	+	1.18075i
$628$	−266.921			−0.425033
$629$		−	363.380i		−	0.577710i
$630$	−84.3660	−	67.4466i	−0.133914	−	0.107058i
$631$	400.409			0.634562			0.317281	−	0.948332i	$-0.397230\pi$
$631$	400.409			0.634562			0.317281	+	0.948332i	$0.397230\pi$
$632$			951.706i			1.50586i
$633$	742.164	+	260.198i	1.17245	+	0.411055i
$634$	360.088			0.567962
$635$		−	810.765i		−	1.27679i
$636$	33.2375	−	94.8035i	0.0522602	−	0.149062i
$637$	−267.685			−0.420227
$638$			70.6979i			0.110812i
$639$	142.286	−	177.979i	0.222670	−	0.278527i
$640$	−578.876			−0.904494
$641$		−	305.576i		−	0.476717i	−0.971177	−	0.238358i	$-0.923391\pi$
$641$		−	305.576i		−	0.476717i	0.971177	−	0.238358i	$-0.0766093\pi$
$642$	178.812	+	62.6902i	0.278523	+	0.0976483i
$643$	1185.24			1.84330			0.921648	−	0.388026i	$-0.126843\pi$
$643$	1185.24			1.84330			0.921648	+	0.388026i	$0.126843\pi$
$644$		−	382.539i		−	0.594005i
$645$	−251.063	+	716.109i	−0.389245	+	1.11025i
$646$	−144.743			−0.224060
$647$			19.5144i			0.0301614i	0.999886	+	0.0150807i	$0.00480052\pi$
$647$			19.5144i			0.0301614i	−0.999886	+	0.0150807i	$0.995199\pi$
$648$	−532.356	+	120.154i	−0.821538	+	0.185422i
$649$	8.46745			0.0130469
$650$			19.4909i			0.0299859i
$651$	−5.63029	−	1.97394i	−0.00864868	−	0.00303217i
$652$	−577.539			−0.885795
$653$		−	287.643i		−	0.440494i	−0.975444	−	0.220247i	$-0.929314\pi$
$653$		−	287.643i		−	0.440494i	0.975444	−	0.220247i	$-0.0706864\pi$
$654$	−75.8629	+	216.384i	−0.115998	+	0.330863i
$655$	−38.3506			−0.0585505
$656$			132.709i			0.202300i
$657$	−128.940	−	103.082i	−0.196256	−	0.156898i
$658$	135.618			0.206107
$659$		−	195.498i		−	0.296659i	−0.988938	−	0.148330i	$-0.952610\pi$
$659$		−	195.498i		−	0.296659i	0.988938	−	0.148330i	$-0.0473896\pi$
$660$	566.746	+	198.697i	0.858705	+	0.301057i
$661$	−724.026			−1.09535			−0.547674	−	0.836692i	$-0.684487\pi$
$661$	−724.026			−1.09535			−0.547674	+	0.836692i	$0.684487\pi$
$662$		−	31.2382i		−	0.0471876i
$663$	−51.4447	+	146.736i	−0.0775938	+	0.221321i
$664$	1050.44			1.58198
$665$		−	239.057i		−	0.359484i
$666$	−240.235	+	300.499i	−0.360713	+	0.451200i
$667$	−245.434			−0.367966
$668$			886.370i			1.32690i
$669$	107.300	+	37.6189i	0.160389	+	0.0562315i
$670$	−470.630			−0.702433
$671$			333.591i			0.497154i
$672$	87.7565	−	250.308i	0.130590	−	0.372483i
$673$	819.856			1.21821			0.609105	−	0.793089i	$-0.291529\pi$
$673$	819.856			1.21821			0.609105	+	0.793089i	$0.291529\pi$
$674$		−	66.1964i		−	0.0982142i
$675$	−45.7869	−	73.1636i	−0.0678325	−	0.108390i
$676$	−395.857			−0.585587
$677$			478.457i			0.706731i	0.935485	+	0.353365i	$0.114963\pi$
$677$			478.457i			0.706731i	−0.935485	+	0.353365i	$0.885037\pi$
$678$	243.094	+	85.2271i	0.358545	+	0.125704i
$679$	32.8593			0.0483937
$680$			253.813i			0.373254i
$681$	322.761	−	920.613i	0.473951	−	1.35185i
$682$	−9.64079			−0.0141361
$683$		−	391.554i		−	0.573286i	−0.958037	−	0.286643i	$-0.907461\pi$
$683$		−	391.554i		−	0.573286i	0.958037	−	0.286643i	$-0.0925394\pi$
$684$	−411.870	−	329.271i	−0.602150	−	0.481390i
$685$	786.037			1.14750
$686$		−	233.030i		−	0.339695i
$687$	523.236	+	183.443i	0.761625	+	0.267021i
$688$	−325.180			−0.472645
$689$			69.4157i			0.100749i
$690$	200.466	−	571.789i	0.290530	−	0.828679i
$691$	2.76994			0.00400859			0.00200430	−	0.999998i	$-0.499362\pi$
$691$	2.76994			0.00400859			0.00200430	+	0.999998i	$0.499362\pi$
$692$		−	592.163i		−	0.855726i
$693$	−210.535	+	263.348i	−0.303802	+	0.380012i
$694$	−207.293			−0.298693
$695$			771.165i			1.10959i
$696$	−102.720	−	36.0128i	−0.147586	−	0.0517426i
$697$	178.357			0.255893
$698$			378.413i			0.542139i
$699$	−241.720	+	689.458i	−0.345808	+	0.986349i
$700$	26.8310			0.0383299
$701$		−	549.171i		−	0.783411i	−0.920091	−	0.391705i	$-0.871885\pi$
$701$		−	549.171i		−	0.783411i	0.920091	−	0.391705i	$-0.128115\pi$
$702$	139.552	−	87.3337i	0.198792	−	0.124407i
$703$	−851.485			−1.21122
$704$		−	96.4579i		−	0.137014i
$705$	−697.523	−	244.547i	−0.989394	−	0.346875i
$706$	126.228			0.178794
$707$		−	118.744i		−	0.167955i
$708$	−1.88300	+	5.37090i	−0.00265961	+	0.00758602i
$709$	−113.955			−0.160727			−0.0803634	−	0.996766i	$-0.525608\pi$
$709$	−113.955			−0.160727			−0.0803634	+	0.996766i	$0.525608\pi$
$710$			112.198i			0.158025i
$711$	992.962	+	793.826i	1.39657	+	1.11649i
$712$	428.697			0.602103
$713$		−	33.4688i		−	0.0469408i
$714$	−58.7032	−	20.5810i	−0.0822174	−	0.0288249i
$715$	−414.975			−0.580385
$716$			1038.96i			1.45106i
$717$	81.4253	−	232.250i	0.113564	−	0.323919i
$718$	−93.9801			−0.130891
$719$		−	750.475i		−	1.04378i	−0.853014	−	0.521888i	$-0.825228\pi$
$719$		−	750.475i		−	1.04378i	0.853014	−	0.521888i	$-0.174772\pi$
$720$	−157.523	+	197.039i	−0.218782	+	0.273665i
$721$	−393.563			−0.545857
$722$		−	3.44177i		−	0.00476700i
$723$	−120.230	−	42.1518i	−0.166293	−	0.0583012i
$724$	647.901			0.894891
$725$		−	17.2145i		−	0.0237441i
$726$	−66.2700	+	189.022i	−0.0912810	+	0.260361i
$727$	222.043			0.305424			0.152712	−	0.988271i	$-0.451199\pi$
$727$	222.043			0.305424			0.152712	+	0.988271i	$0.451199\pi$
$728$			117.227i			0.161027i
$729$	−318.681	+	655.655i	−0.437148	+	0.899390i
$730$	81.2841			0.111348
$731$			437.033i			0.597857i
$732$	−211.596	−	74.1843i	−0.289066	−	0.101345i
$733$	−865.403			−1.18063			−0.590316	−	0.807173i	$-0.700997\pi$
$733$	−865.403			−1.18063			−0.590316	+	0.807173i	$0.700997\pi$
$734$			361.058i			0.491905i
$735$	−193.104	+	550.793i	−0.262727	+	0.749378i
$736$	1487.94			2.02165
$737$			1469.07i			1.99331i
$738$	−147.494	−	117.914i	−0.199856	−	0.159776i
$739$	−394.545			−0.533891			−0.266946	−	0.963712i	$-0.586014\pi$
$739$	−394.545			−0.533891			−0.266946	+	0.963712i	$0.586014\pi$
$740$			651.839i			0.880863i
$741$	343.837	+	120.547i	0.464018	+	0.162682i
$742$	−27.7705			−0.0374265
$743$		−	357.323i		−	0.480919i	−0.970659	−	0.240459i	$-0.922702\pi$
$743$		−	357.323i		−	0.480919i	0.970659	−	0.240459i	$-0.0772981\pi$
$744$	4.91092	−	14.0075i	0.00660070	−	0.0188272i
$745$	−177.705			−0.238530
$746$		−	134.396i		−	0.180155i
$747$	876.178	−	1095.97i	1.17293	−	1.46716i
$748$	345.879			0.462405
$749$			180.233i			0.240632i
$750$	353.751	+	124.023i	0.471669	+	0.165364i
$751$	475.360			0.632970			0.316485	−	0.948598i	$-0.397497\pi$
$751$	475.360			0.632970			0.316485	+	0.948598i	$0.397497\pi$
$752$		−	316.740i		−	0.421197i
$753$	−428.535	+	1222.31i	−0.569104	+	1.62326i
$754$	32.8348			0.0435475
$755$			46.6617i			0.0618036i
$756$	−120.223	−	192.106i	−0.159025	−	0.254108i
$757$	−143.413			−0.189449			−0.0947243	−	0.995504i	$-0.530197\pi$
$757$	−143.413			−0.189449			−0.0947243	+	0.995504i	$0.530197\pi$
$758$			406.405i			0.536154i
$759$	−1784.84	−	625.753i	−2.35157	−	0.824444i
$760$	594.743			0.782557
$761$		−	67.5801i		−	0.0888044i	−0.999014	−	0.0444022i	$-0.985862\pi$
$761$		−	67.5801i		−	0.0888044i	0.999014	−	0.0444022i	$-0.0141383\pi$
$762$	−163.560	+	466.522i	−0.214645	+	0.612234i
$763$	−218.104			−0.285851
$764$		−	627.239i		−	0.820993i
$765$	264.815	+	211.707i	0.346164	+	0.276742i
$766$	224.788			0.293457
$767$		−	3.93261i		−	0.00512726i
$768$	412.055	+	144.464i	0.536530	+	0.188104i
$769$	436.330			0.567399			0.283700	−	0.958913i	$-0.408438\pi$
$769$	436.330			0.567399			0.283700	+	0.958913i	$0.408438\pi$
$770$		−	166.015i		−	0.215604i
$771$	111.089	−	316.860i	0.144084	−	0.410973i
$772$	1004.72			1.30145
$773$			1009.69i			1.30620i	0.757274	+	0.653098i	$0.226531\pi$
$773$			1009.69i			1.30620i	−0.757274	+	0.653098i	$0.773469\pi$
$774$	288.929	−	361.408i	0.373293	−	0.466935i
$775$	2.34747			0.00302900
$776$			81.7499i			0.105348i
$777$	−345.336	−	121.072i	−0.444447	−	0.155820i
$778$	−142.842			−0.183602
$779$		−	417.934i		−	0.536500i
$780$	92.2827	−	263.218i	0.118311	−	0.337460i
$781$	350.226			0.448433
$782$		−	348.957i		−	0.446236i
$783$	−123.253	+	77.1338i	−0.157412	+	0.0985107i
$784$	−250.111			−0.319020
$785$		−	402.144i		−	0.512285i
$786$	22.0673	+	7.73666i	0.0280755	+	0.00984308i
$787$	−601.017			−0.763681			−0.381841	−	0.924228i	$-0.624710\pi$
$787$	−601.017			−0.763681			−0.381841	+	0.924228i	$0.624710\pi$
$788$			844.057i			1.07114i
$789$	−109.065	+	311.087i	−0.138232	+	0.394280i
$790$	−625.964			−0.792359
$791$			245.026i			0.309768i
$792$	−655.178	−	523.784i	−0.827245	−	0.661343i
$793$	154.932			0.195375
$794$		−	399.713i		−	0.503416i
$795$	142.831	+	50.0757i	0.179662	+	0.0629883i
$796$	−1041.96			−1.30899
$797$		−	1058.83i		−	1.32852i	−0.747503	−	0.664258i	$-0.768748\pi$
$797$		−	1058.83i		−	1.32852i	0.747503	−	0.664258i	$-0.231252\pi$
$798$	−48.2261	+	137.556i	−0.0604337	+	0.172375i
$799$	−425.690			−0.532779
$800$			104.363i			0.130453i
$801$	357.580	−	447.281i	0.446417	−	0.558403i
$802$	379.466			0.473150
$803$		−	253.728i		−	0.315975i
$804$	−931.831	−	326.694i	−1.15899	−	0.406336i
$805$	576.335			0.715943
$806$			4.47755i			0.00555528i
$807$	448.817	−	1280.16i	0.556155	−	1.58633i
$808$	295.420			0.365619
$809$		−	587.804i		−	0.726581i	−0.931676	−	0.363290i	$-0.881653\pi$
$809$		−	587.804i		−	0.726581i	0.931676	−	0.363290i	$-0.118347\pi$
$810$	−79.0285	−	350.146i	−0.0975660	−	0.432279i
$811$	−1241.37			−1.53067			−0.765336	−	0.643631i	$-0.777427\pi$
$811$	−1241.37			−1.53067			−0.765336	+	0.643631i	$0.777427\pi$
$812$		−	45.2001i		−	0.0556652i
$813$	−472.955	−	165.815i	−0.581740	−	0.203954i
$814$	−591.321			−0.726438
$815$		−	870.121i		−	1.06763i
$816$	−48.0674	+	137.103i	−0.0589061	+	0.168018i
$817$	1024.07			1.25346
$818$		−	461.846i		−	0.564604i
$819$	122.309	+	97.7803i	0.149340	+	0.119390i
$820$	−319.942			−0.390173
$821$			1271.68i			1.54894i	0.632613	+	0.774468i	$0.281982\pi$
$821$			1271.68i			1.54894i	−0.632613	+	0.774468i	$0.718018\pi$
$822$	−452.293	−	158.571i	−0.550235	−	0.192909i
$823$	1278.94			1.55400			0.777000	−	0.629501i	$-0.216741\pi$
$823$	1278.94			1.55400			0.777000	+	0.629501i	$0.216741\pi$
$824$		−	979.135i		−	1.18827i
$825$	43.8897	−	125.187i	0.0531997	−	0.151742i
$826$	1.57328			0.00190470
$827$		−	564.985i		−	0.683175i	−0.939850	−	0.341587i	$-0.889036\pi$
$827$		−	564.985i		−	0.683175i	0.939850	−	0.341587i	$-0.110964\pi$
$828$	793.829	−	992.966i	0.958731	−	1.19923i
$829$	477.364			0.575831			0.287916	−	0.957656i	$-0.407038\pi$
$829$	477.364			0.575831			0.287916	+	0.957656i	$0.407038\pi$
$830$			690.901i			0.832411i
$831$	163.524	+	57.3305i	0.196780	+	0.0689898i
$832$	−44.7988			−0.0538447
$833$			336.143i			0.403533i
$834$	155.571	−	443.736i	0.186536	−	0.532058i
$835$	−1335.41			−1.59929
$836$		−	810.476i		−	0.969469i
$837$	−10.5184	−	16.8076i	−0.0125668	−	0.0200807i
$838$	482.339			0.575583
$839$		−	650.601i		−	0.775448i	−0.921776	−	0.387724i	$-0.873261\pi$
$839$		−	650.601i		−	0.775448i	0.921776	−	0.387724i	$-0.126739\pi$
$840$	241.209	+	84.5664i	0.287154	+	0.100674i
$841$	−29.0000			−0.0344828
$842$			476.590i			0.566022i
$843$	−204.307	+	582.746i	−0.242357	+	0.691277i
$844$	−812.484			−0.962659
$845$		−	596.399i		−	0.705798i
$846$	352.028	+	281.430i	0.416109	+	0.332659i
$847$	−190.525			−0.224941
$848$			64.8586i			0.0764843i
$849$	987.967	+	346.375i	1.16368	+	0.407980i
$850$	24.4755			0.0287947
$851$		−	2052.82i		−	2.41224i
$852$	−77.8837	+	222.148i	−0.0914128	+	0.260737i
$853$	1143.95			1.34109			0.670547	−	0.741867i	$-0.266059\pi$
$853$	1143.95			1.34109			0.670547	+	0.741867i	$0.266059\pi$
$854$			61.9822i			0.0725787i
$855$	496.080	−	620.525i	0.580211	−	0.725760i
$856$	−448.398			−0.523829
$857$			882.999i			1.03034i	0.857089	+	0.515169i	$0.172271\pi$
$857$			882.999i			1.03034i	−0.857089	+	0.515169i	$0.827729\pi$
$858$	238.781	+	83.7150i	0.278299	+	0.0975700i
$859$	−1370.92			−1.59595			−0.797974	−	0.602692i	$-0.794095\pi$
$859$	−1370.92			−1.59595			−0.797974	+	0.602692i	$0.794095\pi$
$860$		−	783.961i		−	0.911582i
$861$	59.4259	−	169.501i	0.0690196	−	0.196865i
$862$	−640.880			−0.743480
$863$			720.415i			0.834780i	0.908727	+	0.417390i	$0.137055\pi$
$863$			720.415i			0.834780i	−0.908727	+	0.417390i	$0.862945\pi$
$864$	747.221	−	467.623i	0.864839	−	0.541230i
$865$	892.154			1.03139
$866$		−	97.7847i		−	0.112915i
$867$	−633.911	−	222.245i	−0.731154	−	0.256338i
$868$	6.16376			0.00710111
$869$			1953.94i			2.24850i
$870$	23.6866	−	67.5616i	0.0272260	−	0.0776570i
$871$	682.293			0.783345
$872$		−	542.616i		−	0.622266i
$873$	85.2938	+	68.1883i	0.0977019	+	0.0781081i
$874$	−817.688			−0.935570
$875$			356.564i			0.407501i
$876$	160.940	+	56.4244i	0.183721	+	0.0644115i
$877$	−978.182			−1.11537			−0.557686	−	0.830052i	$-0.688311\pi$
$877$	−978.182			−1.11537			−0.557686	+	0.830052i	$0.688311\pi$
$878$			14.9810i			0.0170627i
$879$	−76.8399	+	219.171i	−0.0874174	+	0.249341i
$880$	−387.732			−0.440605
$881$			685.916i			0.778565i	0.921118	+	0.389283i	$0.127277\pi$
$881$			685.916i			0.778565i	−0.921118	+	0.389283i	$0.872723\pi$
$882$	222.229	−	277.976i	0.251960	−	0.315165i
$883$	−644.054			−0.729393			−0.364696	−	0.931127i	$-0.618827\pi$
$883$	−644.054			−0.729393			−0.364696	+	0.931127i	$0.618827\pi$
$884$		−	160.639i		−	0.181719i
$885$	−8.09182	−	2.83694i	−0.00914329	−	0.00320558i
$886$	123.748			0.139670
$887$			1680.35i			1.89442i	0.320608	+	0.947212i	$0.396113\pi$
$887$			1680.35i			1.89442i	−0.320608	+	0.947212i	$0.603887\pi$
$888$	301.213	−	859.152i	0.339204	−	0.967513i
$889$	−470.231			−0.528944
$890$			281.966i			0.316816i
$891$	−1092.98	+	246.687i	−1.22669	+	0.276866i
$892$	−117.467			−0.131690
$893$			997.494i			1.11701i
$894$	102.253	+	35.8493i	0.114377	+	0.0400999i
$895$	−1565.30			−1.74894
$896$			335.739i			0.374709i
$897$	−290.624	+	828.947i	−0.323995	+	0.924133i
$898$	207.783			0.231384
$899$		−	3.95461i		−	0.00439890i
$900$	69.6458	+	55.6785i	0.0773842	+	0.0618650i
$901$	87.1683			0.0967462
$902$		−	290.238i		−	0.321771i
$903$	415.332	+	145.613i	0.459947	+	0.161254i
$904$	−609.595			−0.674330
$905$			976.130i			1.07860i
$906$	9.41331	−	26.8496i	0.0103900	−	0.0296354i
$907$	46.1140			0.0508424			0.0254212	−	0.999677i	$-0.491907\pi$
$907$	46.1140			0.0508424			0.0254212	+	0.999677i	$0.491907\pi$
$908$			1007.84i			1.10996i
$909$	246.413	−	308.227i	0.271081	−	0.339083i
$910$	−77.1037			−0.0847294
$911$		−	1367.36i		−	1.50094i	−0.660903	−	0.750471i	$-0.729827\pi$
$911$		−	1367.36i		−	1.50094i	0.660903	−	0.750471i	$-0.270173\pi$
$912$	321.265	+	112.633i	0.352264	+	0.123501i
$913$	2156.65			2.36215
$914$		−	259.708i		−	0.284145i
$915$	111.766	−	318.792i	0.122149	−	0.348406i
$916$	−572.813			−0.625342
$917$			22.2427i			0.0242560i
$918$	−109.669	−	175.241i	−0.119465	−	0.190894i
$919$	1162.56			1.26503			0.632514	−	0.774549i	$-0.282023\pi$
$919$	1162.56			1.26503			0.632514	+	0.774549i	$0.282023\pi$
$920$			1433.85i			1.55853i
$921$	304.629	+	106.801i	0.330759	+	0.115962i
$922$	−448.074			−0.485980
$923$		−	162.658i		−	0.176228i
$924$	115.241	−	328.704i	0.124720	−	0.355740i
$925$	143.983			0.155657
$926$			214.296i			0.231421i
$927$	−1021.58	−	816.705i	−1.10203	−	0.881019i
$928$	175.812			0.189453
$929$		−	1146.89i		−	1.23455i	−0.786749	−	0.617273i	$-0.788238\pi$
$929$		−	1146.89i		−	1.23455i	0.786749	−	0.617273i	$-0.211762\pi$
$930$	9.21310	+	3.23005i	0.00990655	+	0.00347317i
$931$	787.663			0.846039
$932$		−	754.785i		−	0.809855i
$933$	217.454	−	620.245i	0.233070	−	0.664785i
$934$	−690.092			−0.738857
$935$			521.102i			0.557328i
$936$	−243.265	+	304.290i	−0.259899	+	0.325096i
$937$	965.585			1.03051			0.515254	−	0.857038i	$-0.327698\pi$
$937$	965.585			1.03051			0.515254	+	0.857038i	$0.327698\pi$
$938$			272.958i			0.291000i
$939$	1055.19	+	369.942i	1.12373	+	0.393974i
$940$	763.613			0.812355
$941$			787.513i			0.836890i	0.908242	+	0.418445i	$0.137425\pi$
$941$			787.513i			0.836890i	−0.908242	+	0.418445i	$0.862575\pi$
$942$	−81.1265	+	231.398i	−0.0861215	+	0.245645i
$943$	1007.58			1.06849
$944$		−	3.67444i		−	0.00389241i
$945$	289.427	−	181.128i	0.306272	−	0.191670i
$946$	711.176			0.751772
$947$		−	177.474i		−	0.187407i	−0.995600	−	0.0937033i	$-0.970129\pi$
$947$		−	177.474i		−	0.187407i	0.995600	−	0.0937033i	$-0.0298705\pi$
$948$	−1239.39	−	434.521i	−1.30737	−	0.458355i
$949$	−117.841			−0.124174
$950$		−	57.3519i		−	0.0603704i
$951$	−376.590	+	1074.15i	−0.395994	+	1.12949i
$952$	147.207			0.154630
$953$		−	216.064i		−	0.226719i	−0.993554	−	0.113360i	$-0.963839\pi$
$953$		−	216.064i		−	0.226719i	0.993554	−	0.113360i	$-0.0361612\pi$
$954$	−72.0845	−	57.6281i	−0.0755602	−	0.0604068i
$955$	945.000			0.989529
$956$			254.256i			0.265958i
$957$	−210.893	−	73.9378i	−0.220369	−	0.0772600i
$958$	−414.698			−0.432879
$959$		−	455.889i		−	0.475380i
$960$	−32.3173	+	92.1788i	−0.0336639	+	0.0960196i
$961$	−960.461			−0.999439
$962$			274.632i			0.285480i
$963$	−374.012	+	467.836i	−0.388383	+	0.485811i
$964$	131.622			0.136537
$965$			1513.71i			1.56861i
$966$	−331.629	−	116.267i	−0.343301	−	0.120359i
$967$	95.6676			0.0989324			0.0494662	−	0.998776i	$-0.484248\pi$
$967$	95.6676			0.0989324			0.0494662	+	0.998776i	$0.484248\pi$
$968$		−	474.003i		−	0.489672i
$969$	151.376	−	431.771i	0.156219	−	0.445584i
$970$	−53.7692			−0.0554322
$971$			1116.58i			1.14992i	0.818180	+	0.574962i	$0.194983\pi$
$971$			1116.58i			1.14992i	−0.818180	+	0.574962i	$0.805017\pi$
$972$	86.5846	−	748.135i	0.0890788	−	0.769686i
$973$	447.264			0.459675
$974$		−	40.9417i		−	0.0420346i
$975$	−58.1416	−	20.3841i	−0.0596325	−	0.0209068i
$976$	144.761			0.148321
$977$		−	501.812i		−	0.513625i	−0.966461	−	0.256812i	$-0.917328\pi$
$977$		−	501.812i		−	0.513625i	0.966461	−	0.256812i	$-0.0826723\pi$
$978$	−175.534	+	500.676i	−0.179483	+	0.511939i
$979$	880.157			0.899037
$980$		−	602.981i		−	0.615287i
$981$	−566.139	−	452.601i	−0.577104	−	0.461367i
$982$	−555.498			−0.565681
$983$			1252.51i			1.27418i	0.770791	+	0.637088i	$0.219861\pi$
$983$			1252.51i			1.27418i	−0.770791	+	0.637088i	$0.780139\pi$
$984$	421.697	+	147.844i	0.428554	+	0.150248i
$985$	−1271.66			−1.29102
$986$		−	41.2321i		−	0.0418175i
$987$	−141.833	+	404.552i	−0.143702	+	0.409881i
$988$	−376.416			−0.380988
$989$			2468.91i			2.49637i
$990$	344.507	−	430.929i	0.347987	−	0.435282i
$991$	−438.469			−0.442451			−0.221226	−	0.975223i	$-0.571006\pi$
$991$	−438.469			−0.442451			−0.221226	+	0.975223i	$0.571006\pi$
$992$			23.9748i			0.0241681i
$993$	93.1841	+	32.6698i	0.0938410	+	0.0329001i
$994$	65.0731			0.0654659
$995$		−	1569.81i		−	1.57770i
$996$	−479.598	+	1367.96i	−0.481524	+	1.37345i
$997$	−107.167			−0.107489			−0.0537447	−	0.998555i	$-0.517116\pi$
$997$	−107.167			−0.107489			−0.0537447	+	0.998555i	$0.517116\pi$
$998$			288.766i			0.289344i
$999$	−645.151	−	1030.90i	−0.645797	−	1.03193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.3.b.a.59.12	yes	18
3.2	odd	2	inner	87.3.b.a.59.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.3.b.a.59.7	✓	18	3.2	odd	2	inner
87.3.b.a.59.12	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	87.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.949055i q^{2} +(-2.83105 - 0.992548i) q^{3} +3.09929 q^{4} +4.66941i q^{5} +(0.941983 - 2.68682i) q^{6} +2.70818 q^{7} +6.73762i q^{8} +(7.02970 + 5.61991i) q^{9} +O(q^{10})\)	\(q+0.949055i q^{2} +(-2.83105 - 0.992548i) q^{3} +3.09929 q^{4} +4.66941i q^{5} +(0.941983 - 2.68682i) q^{6} +2.70818 q^{7} +6.73762i q^{8} +(7.02970 + 5.61991i) q^{9} -4.43152 q^{10} +13.8330i q^{11} +(-8.77426 - 3.07620i) q^{12} +6.42457 q^{13} +2.57021i q^{14} +(4.63461 - 13.2193i) q^{15} +6.00280 q^{16} -8.06761i q^{17} +(-5.33360 + 6.67157i) q^{18} -18.9043 q^{19} +14.4719i q^{20} +(-7.66700 - 2.68800i) q^{21} -13.1283 q^{22} -45.5759i q^{23} +(6.68741 - 19.0745i) q^{24} +3.19665 q^{25} +6.09727i q^{26} +(-14.3234 - 22.8876i) q^{27} +8.39346 q^{28} -5.38516i q^{29} +(12.5459 + 4.39850i) q^{30} +0.734353 q^{31} +32.6475i q^{32} +(13.7299 - 39.1619i) q^{33} +7.65661 q^{34} +12.6456i q^{35} +(21.7871 + 17.4178i) q^{36} +45.0418 q^{37} -17.9412i q^{38} +(-18.1883 - 6.37670i) q^{39} -31.4607 q^{40} +22.1078i q^{41} +(2.55106 - 7.27641i) q^{42} -54.1714 q^{43} +42.8725i q^{44} +(-26.2416 + 32.8245i) q^{45} +43.2540 q^{46} -52.7654i q^{47} +(-16.9942 - 5.95807i) q^{48} -41.6657 q^{49} +3.03380i q^{50} +(-8.00749 + 22.8398i) q^{51} +19.9116 q^{52} +10.8047i q^{53} +(21.7216 - 13.5937i) q^{54} -64.5918 q^{55} +18.2467i q^{56} +(53.5191 + 18.7635i) q^{57} +5.11082 q^{58} -0.612120i q^{59} +(14.3640 - 40.9706i) q^{60} +24.1156 q^{61} +0.696942i q^{62} +(19.0377 + 15.2197i) q^{63} -6.97304 q^{64} +29.9989i q^{65} +(37.1668 + 13.0304i) q^{66} +106.201 q^{67} -25.0039i q^{68} +(-45.2363 + 129.028i) q^{69} -12.0014 q^{70} -25.3182i q^{71} +(-37.8648 + 47.3634i) q^{72} -18.3423 q^{73} +42.7471i q^{74} +(-9.04988 - 3.17283i) q^{75} -58.5901 q^{76} +37.4623i q^{77} +(6.05184 - 17.2617i) q^{78} +141.252 q^{79} +28.0295i q^{80} +(17.8333 + 79.0125i) q^{81} -20.9816 q^{82} -155.906i q^{83} +(-23.7623 - 8.33091i) q^{84} +37.6709 q^{85} -51.4116i q^{86} +(-5.34504 + 15.2457i) q^{87} -93.2015 q^{88} -63.6274i q^{89} +(-31.1523 - 24.9048i) q^{90} +17.3989 q^{91} -141.253i q^{92} +(-2.07899 - 0.728881i) q^{93} +50.0772 q^{94} -88.2720i q^{95} +(32.4042 - 92.4267i) q^{96} +12.1334 q^{97} -39.5431i q^{98} +(-77.7401 + 97.2417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

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