LMFDB - Embedded newform 87.3.b.a.59.2

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			59.2
Root			$-3.52466i$ of defining polynomial
Character	$\chi$	$=$	87.59
Dual form			87.3.b.a.59.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.52466i q^{2} +(-0.379125 + 2.97595i) q^{3} -8.42321 q^{4} -8.55504i q^{5} +(10.4892 + 1.33629i) q^{6} -7.79951 q^{7} +15.5903i q^{8} +(-8.71253 - 2.25652i) q^{9} +O(q^{10})$	\(q-3.52466i q^{2} +(-0.379125 + 2.97595i) q^{3} -8.42321 q^{4} -8.55504i q^{5} +(10.4892 + 1.33629i) q^{6} -7.79951 q^{7} +15.5903i q^{8} +(-8.71253 - 2.25652i) q^{9} -30.1536 q^{10} -1.09587i q^{11} +(3.19345 - 25.0670i) q^{12} +14.4321 q^{13} +27.4906i q^{14} +(25.4593 + 3.24343i) q^{15} +21.2576 q^{16} -21.9228i q^{17} +(-7.95344 + 30.7087i) q^{18} +22.6392 q^{19} +72.0608i q^{20} +(2.95699 - 23.2109i) q^{21} -3.86256 q^{22} +0.732029i q^{23} +(-46.3959 - 5.91067i) q^{24} -48.1886 q^{25} -50.8681i q^{26} +(10.0184 - 25.0725i) q^{27} +65.6969 q^{28} -5.38516i q^{29} +(11.4320 - 89.7354i) q^{30} +13.7261 q^{31} -12.5645i q^{32} +(3.26125 + 0.415472i) q^{33} -77.2705 q^{34} +66.7251i q^{35} +(73.3874 + 19.0071i) q^{36} +31.4393 q^{37} -79.7955i q^{38} +(-5.47156 + 42.9491i) q^{39} +133.375 q^{40} -38.8708i q^{41} +(-81.8106 - 10.4224i) q^{42} -30.7276 q^{43} +9.23073i q^{44} +(-19.3046 + 74.5360i) q^{45} +2.58015 q^{46} +9.71303i q^{47} +(-8.05929 + 63.2614i) q^{48} +11.8324 q^{49} +169.848i q^{50} +(65.2412 + 8.31151i) q^{51} -121.564 q^{52} -4.74728i q^{53} +(-88.3720 - 35.3115i) q^{54} -9.37520 q^{55} -121.597i q^{56} +(-8.58311 + 67.3732i) q^{57} -18.9809 q^{58} +48.1028i q^{59} +(-214.449 - 27.3201i) q^{60} +18.5178 q^{61} -48.3797i q^{62} +(67.9535 + 17.5997i) q^{63} +40.7447 q^{64} -123.467i q^{65} +(1.46440 - 11.4948i) q^{66} +63.5000 q^{67} +184.661i q^{68} +(-2.17848 - 0.277531i) q^{69} +235.183 q^{70} +45.5643i q^{71} +(35.1797 - 135.831i) q^{72} -69.2663 q^{73} -110.813i q^{74} +(18.2695 - 143.407i) q^{75} -190.695 q^{76} +8.54724i q^{77} +(151.381 + 19.2854i) q^{78} -97.4352 q^{79} -181.859i q^{80} +(70.8163 + 39.3199i) q^{81} -137.006 q^{82} -121.788i q^{83} +(-24.9074 + 195.510i) q^{84} -187.551 q^{85} +108.304i q^{86} +(16.0260 + 2.04165i) q^{87} +17.0849 q^{88} +78.5721i q^{89} +(262.714 + 68.0420i) q^{90} -112.563 q^{91} -6.16603i q^{92} +(-5.20390 + 40.8481i) q^{93} +34.2351 q^{94} -193.679i q^{95} +(37.3914 + 4.76353i) q^{96} +36.6087 q^{97} -41.7051i q^{98} +(-2.47285 + 9.54779i) 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 $

$2$		−	3.52466i		−	1.76233i	−0.472810	−	0.881164i	$-0.656760\pi$
$2$		−	3.52466i		−	1.76233i	0.472810	−	0.881164i	$-0.343240\pi$
$3$	−0.379125	+	2.97595i	−0.126375	+	0.991983i
$3$	−0.379125	+	2.97595i	−0.126375	+	0.991983i
$4$	−8.42321			−2.10580
$5$		−	8.55504i		−	1.71101i	−0.517797	−	0.855504i	$-0.673248\pi$
$5$		−	8.55504i		−	1.71101i	0.517797	−	0.855504i	$-0.326752\pi$
$6$	10.4892	+	1.33629i	1.74820	+	0.222715i
$7$	−7.79951			−1.11422			−0.557108	−	0.830440i	$-0.688089\pi$
$7$	−7.79951			−1.11422			−0.557108	+	0.830440i	$0.688089\pi$
$8$			15.5903i			1.94879i
$9$	−8.71253	−	2.25652i	−0.968059	−	0.250724i
$10$	−30.1536			−3.01536
$11$		−	1.09587i		−	0.0996245i	−0.998759	−	0.0498122i	$-0.984138\pi$
$11$		−	1.09587i		−	0.0996245i	0.998759	−	0.0498122i	$-0.0158623\pi$
$12$	3.19345	−	25.0670i	0.266121	−	2.08892i
$13$	14.4321			1.11016			0.555079	−	0.831797i	$-0.312688\pi$
$13$	14.4321			1.11016			0.555079	+	0.831797i	$0.312688\pi$
$14$			27.4906i			1.96361i
$15$	25.4593	+	3.24343i	1.69729	+	0.216229i
$16$	21.2576			1.32860
$17$		−	21.9228i		−	1.28958i	−0.764360	−	0.644790i	$-0.776945\pi$
$17$		−	21.9228i		−	1.28958i	0.764360	−	0.644790i	$-0.223055\pi$
$18$	−7.95344	+	30.7087i	−0.441858	+	1.70604i
$19$	22.6392			1.19154			0.595769	−	0.803156i	$-0.296847\pi$
$19$	22.6392			1.19154			0.595769	+	0.803156i	$0.296847\pi$
$20$			72.0608i			3.60304i
$21$	2.95699	−	23.2109i	0.140809	−	1.10528i
$22$	−3.86256			−0.175571
$23$			0.732029i			0.0318274i	0.999873	+	0.0159137i	$0.00506569\pi$
$23$			0.732029i			0.0318274i	−0.999873	+	0.0159137i	$0.994934\pi$
$24$	−46.3959	−	5.91067i	−1.93316	−	0.246278i
$25$	−48.1886			−1.92755
$26$		−	50.8681i		−	1.95646i
$27$	10.0184	−	25.0725i	0.371052	−	0.928612i
$28$	65.6969			2.34632
$29$		−	5.38516i		−	0.185695i
$29$		−	5.38516i		−	0.185695i
$30$	11.4320	−	89.7354i	0.381066	−	2.99118i
$31$	13.7261			0.442777			0.221388	−	0.975186i	$-0.428941\pi$
$31$	13.7261			0.442777			0.221388	+	0.975186i	$0.428941\pi$
$32$		−	12.5645i		−	0.392641i
$33$	3.26125	+	0.415472i	0.0988257	+	0.0125901i
$34$	−77.2705			−2.27266
$35$			66.7251i			1.90643i
$36$	73.3874	+	19.0071i	2.03854	+	0.527975i
$37$	31.4393			0.849710			0.424855	−	0.905261i	$-0.360325\pi$
$37$	31.4393			0.849710			0.424855	+	0.905261i	$0.360325\pi$
$38$		−	79.7955i		−	2.09988i
$39$	−5.47156	+	42.9491i	−0.140296	+	1.10126i
$40$	133.375			3.33439
$41$		−	38.8708i		−	0.948069i	−0.880506	−	0.474035i	$-0.842797\pi$
$41$		−	38.8708i		−	0.948069i	0.880506	−	0.474035i	$-0.157203\pi$
$42$	−81.8106	−	10.4224i	−1.94787	−	0.248152i
$43$	−30.7276			−0.714595			−0.357298	−	0.933991i	$-0.616302\pi$
$43$	−30.7276			−0.714595			−0.357298	+	0.933991i	$0.616302\pi$
$44$			9.23073i			0.209789i
$45$	−19.3046	+	74.5360i	−0.428990	+	1.65636i
$46$	2.58015			0.0560903
$47$			9.71303i			0.206660i	0.994647	+	0.103330i	$0.0329498\pi$
$47$			9.71303i			0.206660i	−0.994647	+	0.103330i	$0.967050\pi$
$48$	−8.05929	+	63.2614i	−0.167902	+	1.31795i
$49$	11.8324			0.241477
$50$			169.848i			3.39697i
$51$	65.2412	+	8.31151i	1.27924	+	0.162971i
$52$	−121.564			−2.33777
$53$		−	4.74728i		−	0.0895713i	−0.998997	−	0.0447856i	$-0.985740\pi$
$53$		−	4.74728i		−	0.0895713i	0.998997	−	0.0447856i	$-0.0142605\pi$
$54$	−88.3720	−	35.3115i	−1.63652	−	0.653916i
$55$	−9.37520			−0.170458
$56$		−	121.597i		−	2.17137i
$57$	−8.58311	+	67.3732i	−0.150581	+	1.18199i
$58$	−18.9809			−0.327256
$59$			48.1028i			0.815302i	0.913138	+	0.407651i	$0.133652\pi$
$59$			48.1028i			0.815302i	−0.913138	+	0.407651i	$0.866348\pi$
$60$	−214.449	−	27.3201i	−3.57415	−	0.455335i
$61$	18.5178			0.303571			0.151785	−	0.988413i	$-0.451498\pi$
$61$	18.5178			0.303571			0.151785	+	0.988413i	$0.451498\pi$
$62$		−	48.3797i		−	0.780318i
$63$	67.9535	+	17.5997i	1.07863	+	0.279361i
$64$	40.7447			0.636635
$65$		−	123.467i		−	1.89949i
$66$	1.46440	−	11.4948i	0.0221878	−	0.174163i
$67$	63.5000			0.947762			0.473881	−	0.880589i	$-0.342853\pi$
$67$	63.5000			0.947762			0.473881	+	0.880589i	$0.342853\pi$
$68$			184.661i			2.71560i
$69$	−2.17848	−	0.277531i	−0.0315722	−	0.00402219i
$70$	235.183			3.35976
$71$			45.5643i			0.641751i	0.947121	+	0.320875i	$0.103977\pi$
$71$			45.5643i			0.641751i	−0.947121	+	0.320875i	$0.896023\pi$
$72$	35.1797	−	135.831i	0.488607	−	1.88654i
$73$	−69.2663			−0.948853			−0.474426	−	0.880295i	$-0.657344\pi$
$73$	−69.2663			−0.948853			−0.474426	+	0.880295i	$0.657344\pi$
$74$		−	110.813i		−	1.49747i
$75$	18.2695	−	143.407i	0.243594	−	1.91209i
$76$	−190.695			−2.50914
$77$			8.54724i			0.111003i
$78$	151.381	+	19.2854i	1.94078	+	0.247248i
$79$	−97.4352			−1.23336			−0.616678	−	0.787215i	$-0.711522\pi$
$79$	−97.4352			−1.23336			−0.616678	+	0.787215i	$0.711522\pi$
$80$		−	181.859i		−	2.27324i
$81$	70.8163	+	39.3199i	0.874275	+	0.485431i
$82$	−137.006			−1.67081
$83$		−	121.788i		−	1.46733i	−0.679513	−	0.733664i	$-0.737809\pi$
$83$		−	121.788i		−	1.46733i	0.679513	−	0.733664i	$-0.262191\pi$
$84$	−24.9074	+	195.510i	−0.296516	+	2.32751i
$85$	−187.551			−2.20648
$86$			108.304i			1.25935i
$87$	16.0260	+	2.04165i	0.184207	+	0.0234673i
$88$	17.0849			0.194147
$89$			78.5721i			0.882833i	0.897302	+	0.441416i	$0.145524\pi$
$89$			78.5721i			0.882833i	−0.897302	+	0.441416i	$0.854476\pi$
$90$	262.714	+	68.0420i	2.91904	+	0.756022i
$91$	−112.563			−1.23696
$92$		−	6.16603i		−	0.0670221i
$93$	−5.20390	+	40.8481i	−0.0559560	+	0.439227i
$94$	34.2351			0.364203
$95$		−	193.679i		−	2.03873i
$96$	37.3914	+	4.76353i	0.389493	+	0.0496201i
$97$	36.6087			0.377409			0.188705	−	0.982034i	$-0.439571\pi$
$97$	36.6087			0.377409			0.188705	+	0.982034i	$0.439571\pi$
$98$		−	41.7051i		−	0.425562i
$99$	−2.47285	+	9.54779i	−0.0249782	+	0.0964423i
$100$	405.903			4.05903
$101$			166.039i			1.64395i	0.569524	+	0.821975i	$0.307128\pi$
$101$			166.039i			1.64395i	−0.569524	+	0.821975i	$0.692872\pi$
$102$	29.2952	−	229.953i	0.287208	−	2.25444i
$103$	5.50897			0.0534852			0.0267426	−	0.999642i	$-0.491487\pi$
$103$	5.50897			0.0534852			0.0267426	+	0.999642i	$0.491487\pi$
$104$			225.000i			2.16346i
$105$	−198.570	−	25.2972i	−1.89115	−	0.240926i
$106$	−16.7325			−0.157854
$107$		−	154.725i		−	1.44603i	−0.690833	−	0.723014i	$-0.742756\pi$
$107$		−	154.725i		−	1.44603i	0.690833	−	0.723014i	$-0.257244\pi$
$108$	−84.3871	+	211.191i	−0.781362	+	1.95547i
$109$	81.2908			0.745787			0.372893	−	0.927874i	$-0.378366\pi$
$109$	81.2908			0.745787			0.372893	+	0.927874i	$0.378366\pi$
$110$			33.0444i			0.300403i
$111$	−11.9194	+	93.5617i	−0.107382	+	0.842898i
$112$	−165.799			−1.48035
$113$		−	97.5663i		−	0.863419i	−0.902013	−	0.431709i	$-0.857911\pi$
$113$		−	97.5663i		−	0.863419i	0.902013	−	0.431709i	$-0.142089\pi$
$114$	237.467	+	30.2525i	2.08305	+	0.265373i
$115$	6.26254			0.0544568
$116$			45.3604i			0.391038i
$117$	−125.740	−	32.5662i	−1.07470	−	0.278343i
$118$	169.546			1.43683
$119$			170.987i			1.43687i
$120$	−50.5660	+	396.918i	−0.421384	+	3.30765i
$121$	119.799			0.990075
$122$		−	65.2689i		−	0.534991i
$123$	115.678	+	14.7369i	0.940468	+	0.119812i
$124$	−115.618			−0.932399
$125$			198.380i			1.58704i
$126$	62.0330	−	239.513i	0.492325	−	1.90089i
$127$	234.726			1.84824			0.924119	−	0.382106i	$-0.124801\pi$
$127$	234.726			1.84824			0.924119	+	0.382106i	$0.124801\pi$
$128$		−	193.869i		−	1.51460i
$129$	11.6496	−	91.4437i	0.0903071	−	0.708866i
$130$	−435.178			−3.34752
$131$			27.3000i			0.208397i	0.994557	+	0.104198i	$0.0332277\pi$
$131$			27.3000i			0.208397i	−0.994557	+	0.104198i	$0.966772\pi$
$132$	−27.4702	−	3.49961i	−0.208107	−	0.0265122i
$133$	−176.575			−1.32763
$134$		−	223.816i		−	1.67027i
$135$	−214.496	−	85.7079i	−1.58886	−	0.634873i
$136$	341.783			2.51311
$137$		−	239.849i		−	1.75072i	−0.483470	−	0.875361i	$-0.660624\pi$
$137$		−	239.849i		−	1.75072i	0.483470	−	0.875361i	$-0.339376\pi$
$138$	−0.978201	+	7.67840i	−0.00708841	+	0.0556405i
$139$	213.889			1.53877			0.769387	−	0.638783i	$-0.220562\pi$
$139$	213.889			1.53877			0.769387	+	0.638783i	$0.220562\pi$
$140$		−	562.039i		−	4.01457i
$141$	−28.9055	−	3.68246i	−0.205003	−	0.0261167i
$142$	160.599			1.13098
$143$		−	15.8157i		−	0.110599i
$144$	−185.207	−	47.9680i	−1.28616	−	0.333111i
$145$	−46.0703			−0.317726
$146$			244.140i			1.67219i
$147$	−4.48595	+	35.2125i	−0.0305167	+	0.239541i
$148$	−264.820			−1.78932
$149$			99.0838i			0.664992i	0.943105	+	0.332496i	$0.107891\pi$
$149$			99.0838i			0.664992i	−0.943105	+	0.332496i	$0.892109\pi$
$150$	−505.460	−	64.3939i	−3.36973	−	0.429292i
$151$	−152.599			−1.01059			−0.505293	−	0.862948i	$-0.668616\pi$
$151$	−152.599			−1.01059			−0.505293	+	0.862948i	$0.668616\pi$
$152$			352.952i			2.32205i
$153$	−49.4692	+	191.003i	−0.323328	+	1.24839i
$154$	30.1261			0.195624
$155$		−	117.427i		−	0.757594i
$156$	46.0881	−	361.769i	0.295437	−	2.31903i
$157$	0.582361			0.00370931			0.00185465	−	0.999998i	$-0.499410\pi$
$157$	0.582361			0.00370931			0.00185465	+	0.999998i	$0.499410\pi$
$158$			343.426i			2.17358i
$159$	14.1277	+	1.79981i	0.0888532	+	0.0113196i
$160$	−107.490			−0.671812
$161$		−	5.70947i		−	0.0354625i
$162$	138.589	−	249.603i	0.855489	−	1.54076i
$163$	12.0213			0.0737502			0.0368751	−	0.999320i	$-0.488260\pi$
$163$	12.0213			0.0737502			0.0368751	+	0.999320i	$0.488260\pi$
$164$			327.417i			1.99645i
$165$	3.55438	−	27.9001i	0.0215417	−	0.169092i
$166$	−429.261			−2.58591
$167$		−	9.47494i		−	0.0567362i	−0.999598	−	0.0283681i	$-0.990969\pi$
$167$		−	9.47494i		−	0.0567362i	0.999598	−	0.0283681i	$-0.00903105\pi$
$168$	361.865	+	46.1004i	2.15396	+	0.274407i
$169$	39.2844			0.232452
$170$			661.052i			3.88854i
$171$	−197.245	−	51.0858i	−1.15348	−	0.298747i
$172$	258.825			1.50480
$173$		−	44.1437i		−	0.255166i	−0.991828	−	0.127583i	$-0.959278\pi$
$173$		−	44.1437i		−	0.255166i	0.991828	−	0.127583i	$-0.0407219\pi$
$174$	7.19613	−	56.4860i	0.0413571	−	0.324632i
$175$	375.848			2.14770
$176$		−	23.2955i		−	0.132361i
$177$	−143.151	−	18.2370i	−0.808765	−	0.103034i
$178$	276.940			1.55584
$179$		−	107.358i		−	0.599765i	−0.953976	−	0.299882i	$-0.903053\pi$
$179$		−	107.358i		−	0.599765i	0.953976	−	0.299882i	$-0.0969475\pi$
$180$	162.606	−	627.832i	0.903369	−	3.48796i
$181$	25.0608			0.138457			0.0692287	−	0.997601i	$-0.477946\pi$
$181$	25.0608			0.138457			0.0692287	+	0.997601i	$0.477946\pi$
$182$			396.746i			2.17992i
$183$	−7.02057	+	55.1080i	−0.0383638	+	0.301137i
$184$	−11.4125			−0.0620247
$185$		−	268.964i		−	1.45386i
$186$	143.975	+	18.3420i	0.774062	+	0.0986128i
$187$	−24.0246			−0.128474
$188$		−	81.8148i		−	0.435185i
$189$	−78.1387	+	195.553i	−0.413432	+	1.03467i
$190$	−682.653			−3.59291
$191$			201.504i			1.05500i	0.849556	+	0.527498i	$0.176870\pi$
$191$			201.504i			1.05500i	−0.849556	+	0.527498i	$0.823130\pi$
$192$	−15.4473	+	121.254i	−0.0804549	+	0.631531i
$193$	311.099			1.61191			0.805956	−	0.591975i	$-0.201652\pi$
$193$	311.099			1.61191			0.805956	+	0.591975i	$0.201652\pi$
$194$		−	129.033i		−	0.665119i
$195$	367.431	+	46.8094i	1.88426	+	0.240048i
$196$	−99.6665			−0.508503
$197$			162.605i			0.825406i	0.910866	+	0.412703i	$0.135415\pi$
$197$			162.605i			0.825406i	−0.910866	+	0.412703i	$0.864585\pi$
$198$	33.6527	+	8.71593i	0.169963	+	0.0440199i
$199$	80.0381			0.402202			0.201101	−	0.979571i	$-0.435548\pi$
$199$	80.0381			0.402202			0.201101	+	0.979571i	$0.435548\pi$
$200$		−	751.274i		−	3.75637i
$201$	−24.0745	+	188.973i	−0.119774	+	0.940163i
$202$	585.230			2.89718
$203$			42.0017i			0.206905i
$204$	−549.540	−	70.0096i	−2.69383	−	0.343184i
$205$	−332.541			−1.62215
$206$		−	19.4172i		−	0.0942585i
$207$	1.65183	−	6.37782i	0.00797988	−	0.0308107i
$208$	306.791			1.47495
$209$		−	24.8096i		−	0.118706i
$210$	−89.1639	+	699.892i	−0.424590	+	3.33282i
$211$	−224.505			−1.06401			−0.532004	−	0.846742i	$-0.678561\pi$
$211$	−224.505			−1.06401			−0.532004	+	0.846742i	$0.678561\pi$
$212$			39.9873i			0.188619i
$213$	−135.597	−	17.2746i	−0.636605	−	0.0811013i
$214$	−545.353			−2.54838
$215$			262.876i			1.22268i
$216$	390.888	+	156.190i	1.80967	+	0.723101i
$217$	−107.057			−0.493349
$218$		−	286.522i		−	1.31432i
$219$	26.2606	−	206.133i	0.119911	−	0.941245i
$220$	78.9692			0.358951
$221$		−	316.392i		−	1.43164i
$222$	329.773	+	42.0119i	1.48546	+	0.189243i
$223$	58.2663			0.261284			0.130642	−	0.991430i	$-0.458296\pi$
$223$	58.2663			0.261284			0.130642	+	0.991430i	$0.458296\pi$
$224$			97.9971i			0.437487i
$225$	419.845	+	108.738i	1.86598	+	0.483282i
$226$	−343.888			−1.52163
$227$			295.346i			1.30108i	0.759471	+	0.650541i	$0.225458\pi$
$227$			295.346i			1.30108i	−0.759471	+	0.650541i	$0.774542\pi$
$228$	72.2973	−	567.498i	0.317093	−	2.48903i
$229$	−247.829			−1.08222			−0.541112	−	0.840951i	$-0.681996\pi$
$229$	−247.829			−1.08222			−0.541112	+	0.840951i	$0.681996\pi$
$230$		−	22.0733i		−	0.0959708i
$231$	−25.4361	−	3.24048i	−0.110113	−	0.0140280i
$232$	83.9562			0.361880
$233$			11.8297i			0.0507713i	0.999678	+	0.0253857i	$0.00808138\pi$
$233$			11.8297i			0.0507713i	−0.999678	+	0.0253857i	$0.991919\pi$
$234$	−114.785	+	443.189i	−0.490532	+	1.89397i
$235$	83.0953			0.353597
$236$		−	405.180i		−	1.71686i
$237$	36.9402	−	289.962i	0.155866	−	1.22347i
$238$	602.672			2.53224
$239$			181.449i			0.759203i	0.925150	+	0.379601i	$0.123939\pi$
$239$			181.449i			0.759203i	−0.925150	+	0.379601i	$0.876061\pi$
$240$	541.204	+	68.9475i	2.25502	+	0.287281i
$241$	335.388			1.39165			0.695826	−	0.718211i	$-0.255039\pi$
$241$	335.388			1.39165			0.695826	+	0.718211i	$0.255039\pi$
$242$		−	422.251i		−	1.74484i
$243$	−143.862	+	195.838i	−0.592026	+	0.805919i
$244$	−155.979			−0.639259
$245$		−	101.226i		−	0.413169i
$246$	51.9426	−	407.724i	0.211149	−	1.65741i
$247$	326.731			1.32280
$248$			213.993i			0.862876i
$249$	362.435	+	46.1730i	1.45556	+	0.185434i
$250$	699.220			2.79688
$251$		−	92.3594i		−	0.367966i	−0.982929	−	0.183983i	$-0.941101\pi$
$251$		−	92.3594i		−	0.367966i	0.982929	−	0.183983i	$-0.0588991\pi$
$252$	−572.386	−	148.246i	−2.27137	−	0.588278i
$253$	0.802208			0.00317078
$254$		−	827.329i		−	3.25720i
$255$	71.1053	−	558.141i	0.278844	−	2.18879i
$256$	−520.343			−2.03259
$257$			380.757i			1.48155i	0.671755	+	0.740773i	$0.265541\pi$
$257$			380.757i			1.48155i	−0.671755	+	0.740773i	$0.734459\pi$
$258$	−322.308	−	41.0609i	−1.24925	−	0.159151i
$259$	−245.211			−0.946761
$260$			1039.99i			3.99995i
$261$	−12.1517	+	46.9184i	−0.0465583	+	0.179764i
$262$	96.2230			0.367264
$263$		−	65.2022i		−	0.247917i	−0.992287	−	0.123959i	$-0.960441\pi$
$263$		−	65.2022i		−	0.247917i	0.992287	−	0.123959i	$-0.0395590\pi$
$264$	−6.47733	+	50.8438i	−0.0245353	+	0.192590i
$265$	−40.6131			−0.153257
$266$			622.366i			2.33972i
$267$	−233.826	−	29.7887i	−0.875754	−	0.111568i
$268$	−534.874			−1.99580
$269$		−	184.826i		−	0.687086i	−0.939137	−	0.343543i	$-0.888373\pi$
$269$		−	184.826i		−	0.687086i	0.939137	−	0.343543i	$-0.111627\pi$
$270$	−302.091	+	756.026i	−1.11885	+	2.80010i
$271$	221.177			0.816150			0.408075	−	0.912948i	$-0.366200\pi$
$271$	221.177			0.816150			0.408075	+	0.912948i	$0.366200\pi$
$272$		−	466.027i		−	1.71333i
$273$	42.6755	−	334.982i	0.156321	−	1.22704i
$274$	−845.385			−3.08535
$275$			52.8084i			0.192031i
$276$	18.3498	+	2.33770i	0.0664847	+	0.00846993i
$277$	73.2320			0.264376			0.132188	−	0.991225i	$-0.457800\pi$
$277$	73.2320			0.264376			0.132188	+	0.991225i	$0.457800\pi$
$278$		−	753.887i		−	2.71182i
$279$	−119.589	−	30.9731i	−0.428634	−	0.111015i
$280$	−1040.26			−3.71523
$281$			436.091i			1.55192i	0.630779	+	0.775962i	$0.282735\pi$
$281$			436.091i			1.55192i	−0.630779	+	0.775962i	$0.717265\pi$
$282$	−12.9794	+	101.882i	−0.0460262	+	0.361283i
$283$	−153.965			−0.544044			−0.272022	−	0.962291i	$-0.587692\pi$
$283$	−153.965			−0.544044			−0.272022	+	0.962291i	$0.587692\pi$
$284$		−	383.797i		−	1.35140i
$285$	576.380	+	73.4288i	2.02239	+	0.257645i
$286$	−55.7447			−0.194912
$287$			303.174i			1.05635i
$288$	−28.3520	+	109.469i	−0.0984446	+	0.380100i
$289$	−191.611			−0.663015
$290$			162.382i			0.559938i
$291$	−13.8793	+	108.946i	−0.0476952	+	0.374384i
$292$	583.444			1.99810
$293$		−	417.041i		−	1.42335i	−0.702510	−	0.711674i	$-0.747937\pi$
$293$		−	417.041i		−	1.42335i	0.702510	−	0.711674i	$-0.252063\pi$
$294$	124.112	+	15.8115i	0.422150	+	0.0537804i
$295$	411.521			1.39499
$296$			490.147i			1.65590i
$297$	−27.4762	−	10.9789i	−0.0925125	−	0.0369659i
$298$	349.236			1.17193
$299$			10.5647i			0.0353334i
$300$	−153.888	+	1207.95i	−0.512960	+	4.02648i
$301$	239.660			0.796214
$302$			537.858i			1.78099i
$303$	−494.123	−	62.9496i	−1.63077	−	0.207754i
$304$	481.255			1.58308
$305$		−	158.421i		−	0.519412i
$306$	673.221	+	174.362i	2.20007	+	0.569811i
$307$	−604.777			−1.96996			−0.984979	−	0.172675i	$-0.944759\pi$
$307$	−604.777			−1.96996			−0.984979	+	0.172675i	$0.944759\pi$
$308$		−	71.9952i		−	0.233751i
$309$	−2.08859	+	16.3944i	−0.00675920	+	0.0530564i
$310$	−413.890			−1.33513
$311$			567.551i			1.82492i	0.409164	+	0.912461i	$0.365820\pi$
$311$			567.551i			1.82492i	−0.409164	+	0.912461i	$0.634180\pi$
$312$	−669.588	−	85.3032i	−2.14612	−	0.273408i
$313$	41.4749			0.132508			0.0662539	−	0.997803i	$-0.478895\pi$
$313$	41.4749			0.132508			0.0662539	+	0.997803i	$0.478895\pi$
$314$		−	2.05262i		−	0.00653702i
$315$	150.566	−	581.344i	0.477988	−	1.84554i
$316$	820.717			2.59720
$317$		−	220.909i		−	0.696875i	−0.937332	−	0.348437i	$-0.886712\pi$
$317$		−	220.909i		−	0.696875i	0.937332	−	0.348437i	$-0.113288\pi$
$318$	6.34373	−	49.7951i	0.0199488	−	0.156588i
$319$	−5.90144			−0.0184998
$320$		−	348.572i		−	1.08929i
$321$	460.454	+	58.6602i	1.43443	+	0.182742i
$322$	−20.1239			−0.0624966
$323$		−	496.316i		−	1.53658i
$324$	−596.500	−	331.200i	−1.84105	−	1.02222i
$325$	−695.461			−2.13988
$326$		−	42.3709i		−	0.129972i
$327$	−30.8194	+	241.917i	−0.0942490	+	0.739808i
$328$	606.007			1.84758
$329$		−	75.7569i		−	0.230264i
$330$	−98.3383	−	12.5280i	−0.297995	−	0.0379635i
$331$	−547.419			−1.65383			−0.826917	−	0.562324i	$-0.809907\pi$
$331$	−547.419			−1.65383			−0.826917	+	0.562324i	$0.809907\pi$
$332$			1025.85i			3.08990i
$333$	−273.916	−	70.9432i	−0.822569	−	0.213043i
$334$	−33.3959			−0.0999878
$335$		−	543.245i		−	1.62163i
$336$	62.8585	−	493.408i	0.187079	−	1.46848i
$337$	−293.970			−0.872315			−0.436157	−	0.899870i	$-0.643661\pi$
$337$	−293.970			−0.872315			−0.436157	+	0.899870i	$0.643661\pi$
$338$		−	138.464i		−	0.409657i
$339$	290.352	+	36.9899i	0.856497	+	0.109115i
$340$	1579.78			4.64641
$341$		−	15.0420i		−	0.0441114i
$342$	−180.060	+	695.221i	−0.526491	+	2.03281i
$343$	289.889			0.845158
$344$		−	479.052i		−	1.39259i
$345$	−2.37429	+	18.6370i	−0.00688199	+	0.0540202i
$346$	−155.592			−0.449687
$347$		−	37.7244i		−	0.108716i	−0.998522	−	0.0543579i	$-0.982689\pi$
$347$		−	37.7244i		−	0.108716i	0.998522	−	0.0543579i	$-0.0173112\pi$
$348$	−134.990	−	17.1973i	−0.387902	−	0.0494174i
$349$	−56.7192			−0.162519			−0.0812596	−	0.996693i	$-0.525894\pi$
$349$	−56.7192			−0.162519			−0.0812596	+	0.996693i	$0.525894\pi$
$350$		−	1324.73i		−	3.78496i
$351$	144.586	−	361.848i	0.411927	−	1.03091i
$352$	−13.7691			−0.0391167
$353$		−	48.3803i		−	0.137055i	−0.997649	−	0.0685274i	$-0.978170\pi$
$353$		−	48.3803i		−	0.137055i	0.997649	−	0.0685274i	$-0.0218301\pi$
$354$	−64.2792	+	504.560i	−0.181580	+	1.42531i
$355$	389.804			1.09804
$356$		−	661.829i		−	1.85907i
$357$	−508.850	−	64.8257i	−1.42535	−	0.181585i
$358$	−378.400			−1.05698
$359$			58.0570i			0.161719i	0.996726	+	0.0808593i	$0.0257664\pi$
$359$			58.0570i			0.161719i	−0.996726	+	0.0808593i	$0.974234\pi$
$360$	−1162.04	−	300.964i	−3.22788	−	0.836010i
$361$	151.535			0.419763
$362$		−	88.3306i		−	0.244007i
$363$	−45.4189	+	356.516i	−0.125121	+	0.982137i
$364$	948.142			2.60478
$365$			592.575i			1.62349i
$366$	194.237	+	24.7451i	0.530702	+	0.0676096i
$367$	218.105			0.594291			0.297145	−	0.954832i	$-0.403965\pi$
$367$	218.105			0.594291			0.297145	+	0.954832i	$0.403965\pi$
$368$			15.5612i			0.0422858i
$369$	−87.7126	+	338.663i	−0.237704	+	0.917787i
$370$	−948.006			−2.56218
$371$			37.0265i			0.0998018i
$372$	43.8336	−	344.072i	0.117832	−	0.924924i
$373$	631.172			1.69215			0.846075	−	0.533064i	$-0.178960\pi$
$373$	631.172			1.69215			0.846075	+	0.533064i	$0.178960\pi$
$374$			84.6784i			0.226413i
$375$	−590.367	−	75.2108i	−1.57431	−	0.200562i
$376$	−151.429			−0.402736
$377$		−	77.7190i		−	0.206151i
$378$	689.259	+	275.412i	1.82344	+	0.728604i
$379$	−58.4410			−0.154198			−0.0770990	−	0.997023i	$-0.524566\pi$
$379$	−58.4410			−0.154198			−0.0770990	+	0.997023i	$0.524566\pi$
$380$			1631.40i			4.29316i
$381$	−88.9907	+	698.533i	−0.233571	+	1.83342i
$382$	710.234			1.85925
$383$		−	85.3724i		−	0.222905i	−0.993770	−	0.111452i	$-0.964450\pi$
$383$		−	85.3724i		−	0.222905i	0.993770	−	0.111452i	$-0.0355502\pi$
$384$	576.944	+	73.5007i	1.50246	+	0.191408i
$385$	73.1220			0.189927
$386$		−	1096.52i		−	2.84072i
$387$	267.715	+	69.3373i	0.691770	+	0.179166i
$388$	−308.363			−0.794749
$389$		−	253.059i		−	0.650537i	−0.945622	−	0.325269i	$-0.894545\pi$
$389$		−	253.059i		−	0.650537i	0.945622	−	0.325269i	$-0.105455\pi$
$390$	164.987	−	1295.07i	0.423044	−	3.32069i
$391$	16.0482			0.0410439
$392$			184.470i			0.470587i
$393$	−81.2433	−	10.3501i	−0.206726	−	0.0263362i
$394$	573.127			1.45464
$395$			833.561i			2.11028i
$396$	20.8293	−	80.4230i	0.0525992	−	0.203088i
$397$	−755.459			−1.90292			−0.951460	−	0.307773i	$-0.900416\pi$
$397$	−755.459			−1.90292			−0.951460	+	0.307773i	$0.900416\pi$
$398$		−	282.107i		−	0.708811i
$399$	66.9440	−	525.478i	0.167780	−	1.31699i
$400$	−1024.37			−2.56093
$401$		−	738.181i		−	1.84085i	−0.390920	−	0.920425i	$-0.627843\pi$
$401$		−	738.181i		−	1.84085i	0.390920	−	0.920425i	$-0.372157\pi$
$402$	666.064	+	84.8543i	1.65688	+	0.211080i
$403$	198.096			0.491552
$404$		−	1398.58i		−	3.46183i
$405$	336.383	−	605.836i	0.830576	−	1.49589i
$406$	148.041			0.364634
$407$		−	34.4533i		−	0.0846519i
$408$	−129.579	+	1017.13i	−0.317595	+	2.49296i
$409$	418.157			1.02239			0.511194	−	0.859465i	$-0.329203\pi$
$409$	418.157			1.02239			0.511194	+	0.859465i	$0.329203\pi$
$410$			1172.09i			2.85877i
$411$	713.778	+	90.9328i	1.73669	+	0.221248i
$412$	−46.4032			−0.112629
$413$		−	375.178i		−	0.908422i
$414$	−22.4796	−	5.82215i	−0.0542987	−	0.0140632i
$415$	−1041.90			−2.51061
$416$		−	181.332i		−	0.435894i
$417$	−81.0910	+	636.524i	−0.194463	+	1.52644i
$418$	−87.4454			−0.209200
$419$			624.367i			1.49014i	0.666988	+	0.745068i	$0.267583\pi$
$419$			624.367i			1.49014i	−0.666988	+	0.745068i	$0.732417\pi$
$420$	1672.60	+	213.083i	3.98238	+	0.507341i
$421$	90.1457			0.214123			0.107061	−	0.994252i	$-0.465856\pi$
$421$	90.1457			0.214123			0.107061	+	0.994252i	$0.465856\pi$
$422$			791.305i			1.87513i
$423$	21.9176	−	84.6250i	0.0518146	−	0.200059i
$424$	74.0114			0.174555
$425$			1056.43i			2.48572i
$426$	−60.8870	+	477.933i	−0.142927	+	1.12191i
$427$	−144.430			−0.338243
$428$			1303.28i			3.04505i
$429$	47.0666	+	5.99612i	0.109712	+	0.0139770i
$430$	926.547			2.15476
$431$		−	54.3086i		−	0.126006i	−0.998013	−	0.0630030i	$-0.979932\pi$
$431$		−	54.3086i		−	0.126006i	0.998013	−	0.0630030i	$-0.0200678\pi$
$432$	212.967	−	532.981i	0.492979	−	1.23375i
$433$	−666.664			−1.53964			−0.769820	−	0.638261i	$-0.779654\pi$
$433$	−666.664			−1.53964			−0.769820	+	0.638261i	$0.779654\pi$
$434$			377.338i			0.869442i
$435$	17.4664	−	137.103i	0.0401527	−	0.315179i
$436$	−684.729			−1.57048
$437$			16.5726i			0.0379235i
$438$	−726.547	−	92.5596i	−1.65878	−	0.211323i
$439$	−705.505			−1.60707			−0.803537	−	0.595255i	$-0.797051\pi$
$439$	−705.505			−1.60707			−0.803537	+	0.595255i	$0.797051\pi$
$440$		−	146.162i		−	0.332186i
$441$	−103.090	−	26.6999i	−0.233764	−	0.0605441i
$442$	−1115.17			−2.52302
$443$		−	50.6235i		−	0.114274i	−0.998366	−	0.0571371i	$-0.981803\pi$
$443$		−	50.6235i		−	0.114274i	0.998366	−	0.0571371i	$-0.0181972\pi$
$444$	100.400	−	788.089i	0.226126	−	1.77498i
$445$	672.187			1.51053
$446$		−	205.369i		−	0.460468i
$447$	−294.868	−	37.5652i	−0.659660	−	0.0840384i
$448$	−317.788			−0.709349
$449$			167.027i			0.371998i	0.982550	+	0.185999i	$0.0595522\pi$
$449$			167.027i			0.371998i	−0.982550	+	0.185999i	$0.940448\pi$
$450$	383.266	−	1479.81i	0.851701	−	3.28846i
$451$	−42.5974			−0.0944509
$452$			821.821i			1.81819i
$453$	57.8540	−	454.125i	0.127713	−	1.00248i
$454$	1040.99			2.29293
$455$			962.981i			2.11644i
$456$	−1050.37	−	133.813i	−2.30344	−	0.293450i
$457$	579.789			1.26869			0.634343	−	0.773052i	$-0.281271\pi$
$457$	579.789			1.26869			0.634343	+	0.773052i	$0.281271\pi$
$458$			873.513i			1.90723i
$459$	−549.661	−	219.632i	−1.19752	−	0.478501i
$460$	−52.7506			−0.114675
$461$		−	96.7990i		−	0.209976i	−0.994473	−	0.104988i	$-0.966520\pi$
$461$		−	96.7990i		−	0.209976i	0.994473	−	0.104988i	$-0.0334804\pi$
$462$	−11.4216	+	89.6537i	−0.0247220	+	0.194056i
$463$	−590.112			−1.27454			−0.637270	−	0.770641i	$-0.719936\pi$
$463$	−590.112			−1.27454			−0.637270	+	0.770641i	$0.719936\pi$
$464$		−	114.476i		−	0.246715i
$465$	349.457	+	44.5196i	0.751520	+	0.0957410i
$466$	41.6957			0.0894757
$467$		−	172.742i		−	0.369898i	−0.982748	−	0.184949i	$-0.940788\pi$
$467$		−	172.742i		−	0.369898i	0.982748	−	0.184949i	$-0.0592120\pi$
$468$	1059.13	+	274.312i	2.26310	+	0.586136i
$469$	−495.269			−1.05601
$470$		−	292.882i		−	0.623154i
$471$	−0.220788	+	1.73308i	−0.000468764	+	0.00367957i
$472$	−749.936			−1.58885
$473$			33.6734i			0.0711912i
$474$	−1022.02	−	130.201i	−2.15615	−	0.274686i
$475$	−1090.95			−2.29674
$476$		−	1440.26i		−	3.02576i
$477$	−10.7123	+	41.3608i	−0.0224577	+	0.0867103i
$478$	639.547			1.33796
$479$			118.508i			0.247406i	0.992319	+	0.123703i	$0.0394770\pi$
$479$			118.508i			0.247406i	−0.992319	+	0.123703i	$0.960523\pi$
$480$	40.7522	−	319.884i	0.0849004	−	0.666426i
$481$	453.734			0.943313
$482$		−	1182.13i		−	2.45255i
$483$	16.9911	+	2.16461i	0.0351782	+	0.00448158i
$484$	−1009.09			−2.08490
$485$		−	313.189i		−	0.645750i
$486$	690.263	+	507.065i	1.42029	+	1.04334i
$487$	67.0226			0.137624			0.0688118	−	0.997630i	$-0.478079\pi$
$487$	67.0226			0.137624			0.0688118	+	0.997630i	$0.478079\pi$
$488$			288.698i			0.591594i
$489$	−4.55757	+	35.7747i	−0.00932019	+	0.0731589i
$490$	−356.788			−0.728139
$491$			395.594i			0.805690i	0.915268	+	0.402845i	$0.131979\pi$
$491$			395.594i			0.805690i	−0.915268	+	0.402845i	$0.868021\pi$
$492$	−974.376	−	124.132i	−1.98044	−	0.252301i
$493$	−118.058			−0.239469
$494$		−	1151.61i		−	2.33120i
$495$	81.6817	+	21.1553i	0.165014	+	0.0427379i
$496$	291.783			0.588272
$497$		−	355.379i		−	0.715049i
$498$	162.744	−	1277.46i	0.326795	−	2.56518i
$499$	360.138			0.721720			0.360860	−	0.932620i	$-0.382483\pi$
$499$	360.138			0.721720			0.360860	+	0.932620i	$0.382483\pi$
$500$		−	1670.99i		−	3.34198i
$501$	28.1969	+	3.59219i	0.0562813	+	0.00717004i
$502$	−325.535			−0.648477
$503$			515.352i			1.02456i	0.858819	+	0.512279i	$0.171198\pi$
$503$			515.352i			1.02456i	−0.858819	+	0.512279i	$0.828802\pi$
$504$	−274.385	+	1059.41i	−0.544414	+	2.10201i
$505$	1420.47			2.81281
$506$		−	2.82751i		−	0.00558796i
$507$	−14.8937	+	116.908i	−0.0293762	+	0.230588i
$508$	−1977.15			−3.89202
$509$			21.4267i			0.0420956i	0.999778	+	0.0210478i	$0.00670022\pi$
$509$			21.4267i			0.0420956i	−0.999778	+	0.0210478i	$0.993300\pi$
$510$	−1967.26	−	250.622i	−3.85736	−	0.491415i
$511$	540.243			1.05723
$512$			1058.56i			2.06749i
$513$	226.809	−	567.623i	0.442123	−	1.10648i
$514$	1342.04			2.61097
$515$		−	47.1295i		−	0.0915135i
$516$	−98.1271	+	770.249i	−0.190169	+	1.49273i
$517$	10.6442			0.0205884
$518$			864.285i			1.66850i
$519$	131.369	+	16.7360i	0.253120	+	0.0322467i
$520$	1924.88			3.70170
$521$		−	684.405i		−	1.31364i	−0.754049	−	0.656819i	$-0.771902\pi$
$521$		−	684.405i		−	1.31364i	0.754049	−	0.656819i	$-0.228098\pi$
$522$	165.371	+	42.8306i	0.316803	+	0.0820509i
$523$	534.714			1.02240			0.511199	−	0.859462i	$-0.329202\pi$
$523$	534.714			1.02240			0.511199	+	0.859462i	$0.329202\pi$
$524$		−	229.953i		−	0.438842i
$525$	−142.493	+	1118.50i	−0.271416	+	2.13048i
$526$	−229.815			−0.436912
$527$		−	300.915i		−	0.570995i
$528$	69.3262	+	8.83193i	0.131300	+	0.0167271i
$529$	528.464			0.998987
$530$			143.147i			0.270089i
$531$	108.545	−	419.097i	0.204416	−	0.789260i
$532$	1487.33			2.79573
$533$		−	560.986i		−	1.05251i
$534$	−104.995	+	824.158i	−0.196620	+	1.54337i
$535$	−1323.68			−2.47416
$536$			989.984i			1.84698i
$537$	319.492	+	40.7021i	0.594956	+	0.0757954i
$538$	−651.449			−1.21087
$539$		−	12.9667i		−	0.0240570i
$540$	1806.75	+	721.935i	3.34583	+	1.33692i
$541$	463.594			0.856921			0.428460	−	0.903561i	$-0.359056\pi$
$541$	463.594			0.856921			0.428460	+	0.903561i	$0.359056\pi$
$542$		−	779.572i		−	1.43832i
$543$	−9.50118	+	74.5796i	−0.0174976	+	0.137347i
$544$	−275.450			−0.506342
$545$		−	695.446i		−	1.27605i
$546$	−1180.70	−	150.417i	−2.16245	−	0.275488i
$547$	−38.9155			−0.0711435			−0.0355717	−	0.999367i	$-0.511325\pi$
$547$	−38.9155			−0.0711435			−0.0355717	+	0.999367i	$0.511325\pi$
$548$			2020.30i			3.68667i
$549$	−161.337	−	41.7857i	−0.293874	−	0.0761124i
$550$	186.132			0.338421
$551$		−	121.916i		−	0.221263i
$552$	4.32679	−	33.9631i	0.00783838	−	0.0615274i
$553$	759.947			1.37423
$554$		−	258.118i		−	0.465917i
$555$	800.423	+	101.971i	1.44220	+	0.183732i
$556$	−1801.64			−3.24035
$557$			871.769i			1.56511i	0.622579	+	0.782557i	$0.286085\pi$
$557$			871.769i			1.56511i	−0.622579	+	0.782557i	$0.713915\pi$
$558$	−109.170	+	421.509i	−0.195644	+	0.755393i
$559$	−443.463			−0.793314
$560$			1418.41i			2.53288i
$561$	9.10833	−	71.4959i	0.0162359	−	0.127444i
$562$	1537.07			2.73500
$563$		−	33.3602i		−	0.0592543i	−0.999561	−	0.0296271i	$-0.990568\pi$
$563$		−	33.3602i		−	0.0592543i	0.999561	−	0.0296271i	$-0.00943199\pi$
$564$	243.477	+	31.0181i	0.431696	+	0.0549966i
$565$	−834.684			−1.47732
$566$			542.672i			0.958785i
$567$	−552.332	−	306.676i	−0.974131	−	0.540875i
$568$	−710.360			−1.25063
$569$			312.601i			0.549386i	0.961532	+	0.274693i	$0.0885763\pi$
$569$			312.601i			0.549386i	−0.961532	+	0.274693i	$0.911424\pi$
$570$	258.811	−	2031.54i	0.454055	−	3.56411i
$571$	−398.378			−0.697685			−0.348843	−	0.937181i	$-0.613425\pi$
$571$	−398.378			−0.697685			−0.348843	+	0.937181i	$0.613425\pi$
$572$			133.218i			0.232899i
$573$	−599.666	−	76.3954i	−1.04654	−	0.133325i
$574$	1068.58			1.86164
$575$		−	35.2755i		−	0.0613487i
$576$	−354.989	−	91.9410i	−0.616300	−	0.159620i
$577$	−1035.10			−1.79394			−0.896970	−	0.442091i	$-0.854237\pi$
$577$	−1035.10			−1.79394			−0.896970	+	0.442091i	$0.854237\pi$
$578$			675.364i			1.16845i
$579$	−117.946	+	925.815i	−0.203706	+	1.59899i
$580$	388.059			0.669068
$581$			949.888i			1.63492i
$582$	383.996	+	48.9198i	0.659787	+	0.0840546i
$583$	−5.20240			−0.00892349
$584$		−	1079.88i		−	1.84911i
$585$	−278.605	+	1075.71i	−0.476247	+	1.83882i
$586$	−1469.93			−2.50841
$587$		−	514.612i		−	0.876681i	−0.898809	−	0.438340i	$-0.855566\pi$
$587$		−	514.612i		−	0.876681i	0.898809	−	0.438340i	$-0.144434\pi$
$588$	37.7861	−	296.602i	0.0642621	−	0.504426i
$589$	310.748			0.527585
$590$		−	1450.47i		−	2.45843i
$591$	−483.904	−	61.6477i	−0.818788	−	0.104311i
$592$	668.323			1.12892
$593$			176.044i			0.296870i	0.988922	+	0.148435i	$0.0474235\pi$
$593$			176.044i			0.296870i	−0.988922	+	0.148435i	$0.952576\pi$
$594$	−38.6967	+	96.8442i	−0.0651460	+	0.163037i
$595$	1462.80			2.45849
$596$		−	834.603i		−	1.40034i
$597$	−30.3445	+	238.189i	−0.0508283	+	0.398977i
$598$	37.2369			0.0622691
$599$		−	501.960i		−	0.837997i	−0.907987	−	0.418999i	$-0.862381\pi$
$599$		−	501.960i		−	0.837997i	0.907987	−	0.418999i	$-0.137619\pi$
$600$	2235.75	+	284.827i	3.72626	+	0.474712i
$601$	921.183			1.53275			0.766375	−	0.642393i	$-0.222058\pi$
$601$	921.183			1.53275			0.766375	+	0.642393i	$0.222058\pi$
$602$		−	844.720i		−	1.40319i
$603$	−553.246	−	143.289i	−0.917489	−	0.237627i
$604$	1285.37			2.12809
$605$		−	1024.89i		−	1.69403i
$606$	−221.876	+	1741.61i	−0.366131	+	2.87395i
$607$	784.016			1.29163			0.645813	−	0.763496i	$-0.276519\pi$
$607$	784.016			1.29163			0.645813	+	0.763496i	$0.276519\pi$
$608$		−	284.451i		−	0.467847i
$609$	−124.995	−	15.9239i	−0.205246	−	0.0261476i
$610$	−558.378			−0.915374
$611$			140.179i			0.229426i
$612$	416.690	−	1608.86i	0.680865	−	2.62886i
$613$	61.6192			0.100521			0.0502604	−	0.998736i	$-0.483995\pi$
$613$	61.6192			0.100521			0.0502604	+	0.998736i	$0.483995\pi$
$614$			2131.63i			3.47171i
$615$	126.075	−	989.626i	0.205000	−	1.60915i
$616$	−133.254			−0.216321
$617$		−	648.871i		−	1.05165i	−0.850591	−	0.525827i	$-0.823756\pi$
$617$		−	648.871i		−	1.05165i	0.850591	−	0.525827i	$-0.176244\pi$
$618$	57.7847	+	7.36157i	0.0935028	+	0.0119119i
$619$	−459.008			−0.741532			−0.370766	−	0.928726i	$-0.620905\pi$
$619$	−459.008			−0.741532			−0.370766	+	0.928726i	$0.620905\pi$
$620$			989.112i			1.59534i
$621$	18.3538	+	7.33377i	0.0295553	+	0.0118096i
$622$	2000.42			3.21611
$623$		−	612.824i		−	0.983666i
$624$	−116.312	+	912.993i	−0.186398	+	1.46313i
$625$	492.429			0.787886
$626$		−	146.185i		−	0.233522i
$627$	73.8322	+	9.40596i	0.117755	+	0.0150015i
$628$	−4.90535			−0.00781106
$629$		−	689.239i		−	1.09577i
$630$	−2049.04	−	530.694i	−3.25244	−	0.842372i
$631$	641.118			1.01604			0.508018	−	0.861347i	$-0.330378\pi$
$631$	641.118			1.01604			0.508018	+	0.861347i	$0.330378\pi$
$632$		−	1519.04i		−	2.40355i
$633$	85.1158	−	668.117i	0.134464	−	1.05548i
$634$	−778.630			−1.22812
$635$		−	2008.09i		−	3.16235i
$636$	−119.000	−	15.1602i	−0.187107	−	0.0238368i
$637$	170.766			0.268078
$638$			20.8005i			0.0326027i
$639$	102.817	−	396.980i	0.160902	−	0.621252i
$640$	−1658.56			−2.59149
$641$		−	615.175i		−	0.959712i	−0.877347	−	0.479856i	$-0.840689\pi$
$641$		−	615.175i		−	0.959712i	0.877347	−	0.479856i	$-0.159311\pi$
$642$	206.757	−	1622.94i	0.322052	−	2.52795i
$643$	226.450			0.352178			0.176089	−	0.984374i	$-0.443655\pi$
$643$	226.450			0.352178			0.176089	+	0.984374i	$0.443655\pi$
$644$			48.0920i			0.0746771i
$645$	−782.304	−	99.6629i	−1.21288	−	0.154516i
$646$	−1749.34			−2.70796
$647$			839.755i			1.29792i	0.760822	+	0.648960i	$0.224796\pi$
$647$			839.755i			1.29792i	−0.760822	+	0.648960i	$0.775204\pi$
$648$	−613.008	+	1104.05i	−0.946001	+	1.70377i
$649$	52.7144			0.0812240
$650$			2451.26i			3.77117i
$651$	40.5879	−	318.595i	0.0623470	−	0.489393i
$652$	−101.258			−0.155303
$653$		−	522.936i		−	0.800821i	−0.916336	−	0.400410i	$-0.868868\pi$
$653$		−	522.936i		−	0.800821i	0.916336	−	0.400410i	$-0.131132\pi$
$654$	852.675	+	108.628i	1.30378	+	0.166098i
$655$	233.552			0.356568
$656$		−	826.300i		−	1.25960i
$657$	603.484	+	156.300i	0.918545	+	0.237900i
$658$	−267.017			−0.405801
$659$			419.643i			0.636787i	0.947959	+	0.318394i	$0.103143\pi$
$659$			419.643i			0.636787i	−0.947959	+	0.318394i	$0.896857\pi$
$660$	−29.9393	+	235.008i	−0.0453625	+	0.356073i
$661$	153.258			0.231857			0.115929	−	0.993258i	$-0.463016\pi$
$661$	153.258			0.231857			0.115929	+	0.993258i	$0.463016\pi$
$662$			1929.46i			2.91460i
$663$	941.566	+	119.952i	1.42016	+	0.180923i
$664$	1898.71			2.85951
$665$			1510.60i			2.27159i
$666$	−250.051	+	965.459i	−0.375451	+	1.44964i
$667$	3.94210			0.00591019
$668$			79.8094i			0.119475i
$669$	−22.0903	+	173.398i	−0.0330198	+	0.259189i
$670$	−1914.75			−2.85784
$671$		−	20.2931i		−	0.0302431i
$672$	−291.634	−	37.1532i	−0.433980	−	0.0552875i
$673$	1029.11			1.52914			0.764570	−	0.644541i	$-0.222952\pi$
$673$	1029.11			1.52914			0.764570	+	0.644541i	$0.222952\pi$
$674$			1036.14i			1.53731i
$675$	−482.774	+	1208.21i	−0.715220	+	1.78994i
$676$	−330.901			−0.489498
$677$			713.851i			1.05443i	0.849731	+	0.527217i	$0.176764\pi$
$677$			713.851i			1.05443i	−0.849731	+	0.527217i	$0.823236\pi$
$678$	130.377	−	1023.39i	0.192296	−	1.50943i
$679$	−285.530			−0.420516
$680$		−	2923.97i		−	4.29995i
$681$	−878.933	−	111.973i	−1.29065	−	0.164424i
$682$	−53.0178			−0.0777387
$683$			928.178i			1.35897i	0.733688	+	0.679486i	$0.237797\pi$
$683$			928.178i			1.35897i	−0.733688	+	0.679486i	$0.762203\pi$
$684$	1661.43	+	430.306i	2.42900	+	0.629102i
$685$	−2051.92			−2.99550
$686$		−	1021.76i		−	1.48945i
$687$	93.9583	−	737.526i	0.136766	−	1.07355i
$688$	−653.194			−0.949410
$689$		−	68.5130i		−	0.0994383i
$690$	65.6889	+	8.36855i	0.0952014	+	0.0121283i
$691$	366.586			0.530515			0.265258	−	0.964178i	$-0.414543\pi$
$691$	366.586			0.530515			0.265258	+	0.964178i	$0.414543\pi$
$692$			371.832i			0.537329i
$693$	19.2870	−	74.4681i	0.0278311	−	0.107458i
$694$	−132.965			−0.191593
$695$		−	1829.83i		−	2.63285i
$696$	−31.8300	+	249.849i	−0.0457327	+	0.358979i
$697$	−852.160			−1.22261
$698$			199.916i			0.286412i
$699$	−35.2046	−	4.48495i	−0.0503643	−	0.00641623i
$700$	−3165.84			−4.52263
$701$			640.296i			0.913403i	0.889620	+	0.456702i	$0.150969\pi$
$701$			640.296i			0.913403i	−0.889620	+	0.456702i	$0.849031\pi$
$702$	−1275.39	−	509.617i	−1.81680	−	0.725951i
$703$	711.761			1.01246
$704$		−	44.6508i		−	0.0634245i
$705$	−31.5035	+	247.287i	−0.0446859	+	0.350762i
$706$	−170.524			−0.241536
$707$		−	1295.02i		−	1.83171i
$708$	1205.79	+	153.614i	1.70310	+	0.216969i
$709$	527.390			0.743851			0.371925	−	0.928263i	$-0.378698\pi$
$709$	527.390			0.743851			0.371925	+	0.928263i	$0.378698\pi$
$710$		−	1373.93i		−	1.93511i
$711$	848.907	+	219.864i	1.19396	+	0.309232i
$712$	−1224.96			−1.72045
$713$			10.0479i			0.0140924i
$714$	−228.488	+	1793.52i	−0.320012	+	2.51193i
$715$	−135.303			−0.189236
$716$			904.298i			1.26299i
$717$	−539.984	−	68.7921i	−0.753116	−	0.0959444i
$718$	204.631			0.285001
$719$			604.994i			0.841438i	0.907191	+	0.420719i	$0.138222\pi$
$719$			604.994i			0.841438i	−0.907191	+	0.420719i	$0.861778\pi$
$720$	−410.368	+	1584.45i	−0.569956	+	2.20063i
$721$	−42.9673			−0.0595941
$722$		−	534.107i		−	0.739761i
$723$	−127.154	+	998.097i	−0.175870	+	1.38049i
$724$	−211.092			−0.291564
$725$			259.504i			0.357936i
$726$	1256.60	+	160.086i	1.73085	+	0.220504i
$727$	−355.665			−0.489223			−0.244611	−	0.969621i	$-0.578660\pi$
$727$	−355.665			−0.489223			−0.244611	+	0.969621i	$0.578660\pi$
$728$		−	1754.89i		−	2.41056i
$729$	−528.263	−	502.374i	−0.724640	−	0.689127i
$730$	2088.62			2.86113
$731$			673.636i			0.921527i
$732$	59.1357	−	464.186i	0.0807865	−	0.634134i
$733$	−477.496			−0.651427			−0.325713	−	0.945469i	$-0.605604\pi$
$733$	−477.496			−0.651427			−0.325713	+	0.945469i	$0.605604\pi$
$734$		−	768.744i		−	1.04734i
$735$	301.244	+	38.3775i	0.409856	+	0.0522143i
$736$	9.19760			0.0124967
$737$		−	69.5877i		−	0.0944203i
$738$	1193.67	+	309.157i	1.61744	+	0.418912i
$739$	−17.2868			−0.0233921			−0.0116961	−	0.999932i	$-0.503723\pi$
$739$	−17.2868			−0.0233921			−0.0116961	+	0.999932i	$0.503723\pi$
$740$			2265.54i			3.06154i
$741$	−123.872	+	972.334i	−0.167169	+	1.31219i
$742$	130.506			0.175883
$743$		−	582.094i		−	0.783437i	−0.920085	−	0.391719i	$-0.871881\pi$
$743$		−	582.094i		−	0.783437i	0.920085	−	0.391719i	$-0.128119\pi$
$744$	−636.833	−	81.1303i	−0.855958	−	0.109046i
$745$	847.665			1.13781
$746$		−	2224.66i		−	2.98212i
$747$	−274.817	+	1061.08i	−0.367894	+	1.42046i
$748$	202.364			0.270540
$749$			1206.78i			1.61119i
$750$	−265.092	+	2080.84i	−0.353456	+	2.77446i
$751$	447.287			0.595588			0.297794	−	0.954630i	$-0.403749\pi$
$751$	447.287			0.595588			0.297794	+	0.954630i	$0.403749\pi$
$752$			206.475i			0.274568i
$753$	274.857	+	35.0158i	0.365016	+	0.0465017i
$754$	−273.933			−0.363306
$755$			1305.49i			1.72912i
$756$	658.179	−	1647.19i	0.870606	−	2.17882i
$757$	1156.49			1.52772			0.763861	−	0.645381i	$-0.223301\pi$
$757$	1156.49			1.52772			0.763861	+	0.645381i	$0.223301\pi$
$758$			205.985i			0.271747i
$759$	−0.304138	+	2.38733i	−0.000400708	+	0.00314536i
$760$	3019.52			3.97305
$761$			588.653i			0.773525i	0.922179	+	0.386763i	$0.126407\pi$
$761$			588.653i			0.773525i	−0.922179	+	0.386763i	$0.873593\pi$
$762$	2462.09	+	313.662i	3.23109	+	0.411629i
$763$	−634.028			−0.830968
$764$		−	1697.31i		−	2.22161i
$765$	1634.04	+	423.211i	2.13600	+	0.553217i
$766$	−300.909			−0.392831
$767$			694.223i			0.905114i
$768$	197.275	−	1548.51i	0.256869	−	2.01629i
$769$	−1321.91			−1.71899			−0.859497	−	0.511141i	$-0.829223\pi$
$769$	−1321.91			−1.71899			−0.859497	+	0.511141i	$0.829223\pi$
$770$		−	257.730i		−	0.334714i
$771$	−1133.11	−	144.355i	−1.46967	−	0.187231i
$772$	−2620.45			−3.39437
$773$		−	245.810i		−	0.317995i	−0.987279	−	0.158997i	$-0.949174\pi$
$773$		−	245.810i		−	0.317995i	0.987279	−	0.158997i	$-0.0508261\pi$
$774$	244.390	−	943.604i	0.315750	−	1.21913i
$775$	−661.441			−0.853472
$776$			570.740i			0.735490i
$777$	92.9658	−	729.735i	0.119647	−	0.939170i
$778$	−891.946			−1.14646
$779$		−	880.006i		−	1.12966i
$780$	−3094.94	−	394.285i	−3.96788	−	0.505494i
$781$	49.9325			0.0639341
$782$		−	56.5643i		−	0.0723328i
$783$	−135.020	−	53.9508i	−0.172439	−	0.0689027i
$784$	251.528			0.320826
$785$		−	4.98212i		−	0.00634665i
$786$	−36.4806	+	286.355i	−0.0464130	+	0.364319i
$787$	931.681			1.18384			0.591920	−	0.805997i	$-0.298370\pi$
$787$	931.681			1.18384			0.591920	+	0.805997i	$0.298370\pi$
$788$		−	1369.66i		−	1.73814i
$789$	194.038	+	24.7198i	0.245930	+	0.0313306i
$790$	2938.02			3.71901
$791$			760.970i			0.962035i
$792$	−148.853	−	38.5524i	−0.187945	−	0.0486772i
$793$	267.250			0.337012
$794$			2662.73i			3.35357i
$795$	15.3975	−	120.863i	0.0193679	−	0.152028i
$796$	−674.178			−0.846957
$797$			424.426i			0.532530i	0.963900	+	0.266265i	$0.0857896\pi$
$797$			424.426i			0.532530i	−0.963900	+	0.266265i	$0.914210\pi$
$798$	−1852.13	−	235.955i	−2.32096	−	0.295683i
$799$	212.937			0.266505
$800$			605.467i			0.756834i
$801$	177.299	−	684.562i	0.221347	−	0.854634i
$802$	−2601.83			−3.24418
$803$			75.9068i			0.0945290i
$804$	202.784	−	1591.76i	0.252219	−	1.97980i
$805$	−48.8447			−0.0606767
$806$		−	698.219i		−	0.866276i
$807$	550.033	+	70.0723i	0.681577	+	0.0868306i
$808$	−2588.59			−3.20370
$809$		−	1219.50i		−	1.50742i	−0.657206	−	0.753711i	$-0.728262\pi$
$809$		−	1219.50i		−	1.50742i	0.657206	−	0.753711i	$-0.271738\pi$
$810$	−2135.36	−	1185.64i	−2.63625	−	1.46375i
$811$	890.104			1.09754			0.548770	−	0.835974i	$-0.315096\pi$
$811$	890.104			1.09754			0.548770	+	0.835974i	$0.315096\pi$
$812$		−	353.789i		−	0.435700i
$813$	−83.8537	+	658.210i	−0.103141	+	0.809606i
$814$	−121.436			−0.149185
$815$		−	102.843i		−	0.126187i
$816$	1386.87	+	176.683i	1.69960	+	0.216523i
$817$	−695.649			−0.851468
$818$		−	1473.86i		−	1.80178i
$819$	980.709	+	254.000i	1.19745	+	0.310135i
$820$	2801.07			3.41593
$821$			934.673i			1.13846i	0.822180	+	0.569228i	$0.192758\pi$
$821$			934.673i			1.13846i	−0.822180	+	0.569228i	$0.807242\pi$
$822$	320.507	−	2515.82i	0.389911	−	3.06061i
$823$	−1273.42			−1.54729			−0.773645	−	0.633620i	$-0.781568\pi$
$823$	−1273.42			−1.54729			−0.773645	+	0.633620i	$0.781568\pi$
$824$			85.8865i			0.104231i
$825$	−157.155	−	20.0210i	−0.190491	−	0.0242679i
$826$	−1322.38			−1.60094
$827$			620.101i			0.749820i	0.927061	+	0.374910i	$0.122326\pi$
$827$			620.101i			0.749820i	−0.927061	+	0.374910i	$0.877674\pi$
$828$	−13.9137	+	53.7217i	−0.0168040	+	0.0648813i
$829$	−227.025			−0.273854			−0.136927	−	0.990581i	$-0.543723\pi$
$829$	−227.025			−0.273854			−0.136927	+	0.990581i	$0.543723\pi$
$830$			3672.35i			4.42451i
$831$	−27.7641	+	217.935i	−0.0334105	+	0.262256i
$832$	588.030			0.706766
$833$		−	259.399i		−	0.311404i
$834$	2243.53	+	285.818i	2.69008	+	0.342707i
$835$	−81.0585			−0.0970760
$836$			208.977i			0.249972i
$837$	137.513	−	344.147i	0.164293	−	0.411168i
$838$	2200.68			2.62611
$839$		−	810.421i		−	0.965937i	−0.875638	−	0.482969i	$-0.839559\pi$
$839$		−	810.421i		−	0.965937i	0.875638	−	0.482969i	$-0.160441\pi$
$840$	394.390	−	3095.77i	0.469512	−	3.68544i
$841$	−29.0000			−0.0344828
$842$		−	317.733i		−	0.377355i
$843$	−1297.78	−	165.333i	−1.53948	−	0.196125i
$844$	1891.06			2.24059
$845$		−	336.080i		−	0.397727i
$846$	−298.274	−	77.2520i	−0.352570	−	0.0913144i
$847$	−934.374			−1.10316
$848$		−	100.916i		−	0.119004i
$849$	58.3719	−	458.190i	0.0687537	−	0.539682i
$850$	3723.56			4.38066
$851$			23.0145i			0.0270440i
$852$	1142.16	+	145.507i	1.34056	+	0.170783i
$853$	704.282			0.825653			0.412826	−	0.910810i	$-0.364542\pi$
$853$	704.282			0.825653			0.412826	+	0.910810i	$0.364542\pi$
$854$			509.066i			0.596096i
$855$	−437.040	+	1687.44i	−0.511158	+	1.97361i
$856$	2412.21			2.81800
$857$		−	604.936i		−	0.705876i	−0.935647	−	0.352938i	$-0.885183\pi$
$857$		−	604.936i		−	0.705876i	0.935647	−	0.352938i	$-0.114817\pi$
$858$	21.1343	−	165.893i	0.0246320	−	0.193349i
$859$	551.888			0.642478			0.321239	−	0.946998i	$-0.395901\pi$
$859$	551.888			0.642478			0.321239	+	0.946998i	$0.395901\pi$
$860$		−	2214.26i		−	2.57472i
$861$	−902.229	−	114.941i	−1.04788	−	0.133497i
$862$	−191.419			−0.222064
$863$			607.523i			0.703966i	0.936006	+	0.351983i	$0.114493\pi$
$863$			607.523i			0.703966i	−0.936006	+	0.351983i	$0.885507\pi$
$864$	−315.024	−	125.877i	−0.364611	−	0.145690i
$865$	−377.651			−0.436591
$866$			2349.76i			2.71335i
$867$	72.6447	−	570.225i	0.0837886	−	0.657699i
$868$	901.760			1.03889
$869$			106.776i			0.122873i
$870$	−483.240	−	61.5631i	−0.555448	−	0.0707622i
$871$	916.436			1.05217
$872$			1267.35i			1.45338i
$873$	−318.954	−	82.6081i	−0.365354	−	0.0946256i
$874$	58.4126			0.0668337
$875$		−	1547.26i		−	1.76830i
$876$	−221.198	+	1736.30i	−0.252510	+	1.98208i
$877$	−958.796			−1.09327			−0.546634	−	0.837372i	$-0.684091\pi$
$877$	−958.796			−1.09327			−0.546634	+	0.837372i	$0.684091\pi$
$878$			2486.66i			2.83219i
$879$	1241.09	+	158.111i	1.41194	+	0.179876i
$880$	−199.294			−0.226470
$881$		−	1042.11i		−	1.18287i	−0.806353	−	0.591435i	$-0.798562\pi$
$881$		−	1042.11i		−	1.18287i	0.806353	−	0.591435i	$-0.201438\pi$
$882$	−94.1081	+	363.356i	−0.106699	+	0.411969i
$883$	−988.448			−1.11942			−0.559710	−	0.828688i	$-0.689088\pi$
$883$	−988.448			−1.11942			−0.559710	+	0.828688i	$0.689088\pi$
$884$			2665.03i			3.01474i
$885$	−156.018	+	1224.67i	−0.176292	+	1.38380i
$886$	−178.430			−0.201389
$887$			453.929i			0.511757i	0.966709	+	0.255879i	$0.0823647\pi$
$887$			453.929i			0.511757i	−0.966709	+	0.255879i	$0.917635\pi$
$888$	−1458.65	−	185.827i	−1.64263	−	0.209265i
$889$	−1830.75			−2.05934
$890$		−	2369.23i		−	2.66205i
$891$	43.0895	−	77.6054i	0.0483608	−	0.0870992i
$892$	−490.789			−0.550212
$893$			219.895i			0.246243i
$894$	−132.404	+	1039.31i	−0.148103	+	1.16254i
$895$	−918.451			−1.02620
$896$			1512.08i			1.68759i
$897$	−31.4400	−	4.00534i	−0.0350501	−	0.00446527i
$898$	588.714			0.655583
$899$		−	73.9172i		−	0.0822215i
$900$	−3536.44	−	915.926i	−3.92938	−	1.01770i
$901$	−104.074			−0.115509
$902$			150.141i			0.166454i
$903$	−90.8613	+	713.216i	−0.100622	+	0.789830i
$904$	1521.09			1.68262
$905$		−	214.396i		−	0.236902i
$906$	−1600.64	−	203.916i	−1.76671	−	0.225072i
$907$	243.046			0.267967			0.133984	−	0.990984i	$-0.457223\pi$
$907$	243.046			0.267967			0.133984	+	0.990984i	$0.457223\pi$
$908$		−	2487.76i		−	2.73982i
$909$	374.669	−	1446.62i	0.412177	−	1.59144i
$910$	3394.18			3.72986
$911$		−	1173.35i		−	1.28798i	−0.765032	−	0.643992i	$-0.777277\pi$
$911$		−	1173.35i		−	1.28798i	0.765032	−	0.643992i	$-0.222723\pi$
$912$	−182.456	+	1432.19i	−0.200061	+	1.57038i
$913$	−133.464			−0.146182
$914$		−	2043.56i		−	2.23584i
$915$	471.451	+	60.0613i	0.515247	+	0.0656407i
$916$	2087.52			2.27895
$917$		−	212.926i		−	0.232199i
$918$	−774.128	+	1937.37i	−0.843277	+	2.11042i
$919$	983.929			1.07065			0.535326	−	0.844646i	$-0.320189\pi$
$919$	983.929			1.07065			0.535326	+	0.844646i	$0.320189\pi$
$920$			97.6347i			0.106125i
$921$	229.286	−	1799.78i	0.248954	−	1.95416i
$922$	−341.183			−0.370047
$923$			657.587i			0.712445i
$924$	214.254	+	27.2952i	0.231877	+	0.0295403i
$925$	−1515.02			−1.63786
$926$			2079.94i			2.24616i
$927$	−47.9971	−	12.4311i	−0.0517768	−	0.0134100i
$928$	−67.6620			−0.0729117
$929$		−	1731.92i		−	1.86429i	−0.362091	−	0.932143i	$-0.617937\pi$
$929$		−	1731.92i		−	1.86429i	0.362091	−	0.932143i	$-0.382063\pi$
$930$	156.916	−	1231.72i	0.168727	−	1.32442i
$931$	267.876			0.287729
$932$		−	99.6442i		−	0.106914i
$933$	−1689.00	−	215.173i	−1.81029	−	0.230625i
$934$	−608.858			−0.651882
$935$			205.531i			0.219819i
$936$	507.716	−	1960.32i	0.542431	−	2.09436i
$937$	−1668.20			−1.78037			−0.890183	−	0.455603i	$-0.849424\pi$
$937$	−1668.20			−1.78037			−0.890183	+	0.455603i	$0.849424\pi$
$938$			1745.65i			1.86104i
$939$	−15.7242	+	123.427i	−0.0167457	+	0.131445i
$940$	−699.929			−0.744605
$941$			195.447i			0.207702i	0.994593	+	0.103851i	$0.0331165\pi$
$941$			195.447i			0.207702i	−0.994593	+	0.103851i	$0.966884\pi$
$942$	6.10850	+	0.778202i	0.00648461	+	0.000826117i
$943$	28.4546			0.0301745
$944$			1022.55i			1.08321i
$945$	1672.97	+	668.480i	1.77033	+	0.707386i
$946$	118.687			0.125462
$947$		−	823.578i		−	0.869670i	−0.900510	−	0.434835i	$-0.856807\pi$
$947$		−	823.578i		−	0.869670i	0.900510	−	0.434835i	$-0.143193\pi$
$948$	−311.155	+	2442.41i	−0.328222	+	2.57638i
$949$	−999.655			−1.05338
$950$			3845.24i			4.04762i
$951$	657.415	+	83.7524i	0.691288	+	0.0880677i
$952$	−2665.74			−2.80015
$953$			227.649i			0.238877i	0.992842	+	0.119438i	$0.0381094\pi$
$953$			227.649i			0.238877i	−0.992842	+	0.119438i	$0.961891\pi$
$954$	145.783	+	37.7572i	0.152812	+	0.0395778i
$955$	1723.88			1.80511
$956$		−	1528.39i		−	1.59873i
$957$	2.23738	−	17.5624i	0.00233792	−	0.0183515i
$958$	417.699			0.436011
$959$			1870.70i			1.95068i
$960$	1037.33	+	132.153i	1.08055	+	0.137659i
$961$	−772.595			−0.803949
$962$		−	1599.26i		−	1.66243i
$963$	−349.139	+	1348.05i	−0.362554	+	1.39984i
$964$	−2825.04			−2.93054
$965$		−	2661.46i		−	2.75799i
$966$	7.62949	−	59.8877i	0.00789802	−	0.0619956i
$967$	−1139.60			−1.17849			−0.589247	−	0.807953i	$-0.700576\pi$
$967$	−1139.60			−1.17849			−0.589247	+	0.807953i	$0.700576\pi$
$968$			1867.70i			1.92944i
$969$	1477.01	+	188.166i	1.52426	+	0.194186i
$970$	−1103.88			−1.13802
$971$		−	1282.21i		−	1.32051i	−0.751043	−	0.660253i	$-0.770449\pi$
$971$		−	1282.21i		−	1.32051i	0.751043	−	0.660253i	$-0.229551\pi$
$972$	1211.78	−	1649.59i	1.24669	−	1.69711i
$973$	−1668.23			−1.71453
$974$		−	236.232i		−	0.242538i
$975$	263.667	−	2069.66i	0.270428	−	2.12272i
$976$	393.644			0.403323
$977$			1473.68i			1.50837i	0.656661	+	0.754186i	$0.271968\pi$
$977$			1473.68i			1.50837i	−0.656661	+	0.754186i	$0.728032\pi$
$978$	126.094	+	16.0639i	0.128930	+	0.0164252i
$979$	86.1047			0.0879517
$980$			852.651i			0.870052i
$981$	−708.248	−	183.434i	−0.721966	−	0.186987i
$982$	1394.33			1.41989
$983$			1792.38i			1.82338i	0.410877	+	0.911691i	$0.365222\pi$
$983$			1792.38i			1.82338i	−0.410877	+	0.911691i	$0.634778\pi$
$984$	−229.753	+	1803.45i	−0.233489	+	1.83277i
$985$	1391.09			1.41228
$986$			416.114i			0.422023i
$987$	225.448	+	28.7214i	0.228418	+	0.0290996i
$988$	−2752.12			−2.78555
$989$		−	22.4935i		−	0.0227437i
$990$	74.5651	−	287.900i	0.0753183	−	0.290808i
$991$	914.570			0.922876			0.461438	−	0.887173i	$-0.347334\pi$
$991$	914.570			0.922876			0.461438	+	0.887173i	$0.347334\pi$
$992$		−	172.462i		−	0.173852i
$993$	207.540	−	1629.09i	0.209004	−	1.64057i
$994$	−1252.59			−1.26015
$995$		−	684.729i		−	0.688170i
$996$	−3052.87	−	388.925i	−3.06513	−	0.390487i
$997$	1317.06			1.32102			0.660512	−	0.750815i	$-0.270339\pi$
$997$	1317.06			1.32102			0.660512	+	0.750815i	$0.270339\pi$
$998$		−	1269.36i		−	1.27191i
$999$	314.972	−	788.262i	0.315287	−	0.789051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.3.b.a.59.2	✓	18
3.2	odd	2	inner	87.3.b.a.59.17	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.3.b.a.59.2	✓	18	1.1	even	1	trivial
87.3.b.a.59.17	yes	18	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.52466i q^{2} +(-0.379125 + 2.97595i) q^{3} -8.42321 q^{4} -8.55504i q^{5} +(10.4892 + 1.33629i) q^{6} -7.79951 q^{7} +15.5903i q^{8} +(-8.71253 - 2.25652i) q^{9} +O(q^{10})\)	\(q-3.52466i q^{2} +(-0.379125 + 2.97595i) q^{3} -8.42321 q^{4} -8.55504i q^{5} +(10.4892 + 1.33629i) q^{6} -7.79951 q^{7} +15.5903i q^{8} +(-8.71253 - 2.25652i) q^{9} -30.1536 q^{10} -1.09587i q^{11} +(3.19345 - 25.0670i) q^{12} +14.4321 q^{13} +27.4906i q^{14} +(25.4593 + 3.24343i) q^{15} +21.2576 q^{16} -21.9228i q^{17} +(-7.95344 + 30.7087i) q^{18} +22.6392 q^{19} +72.0608i q^{20} +(2.95699 - 23.2109i) q^{21} -3.86256 q^{22} +0.732029i q^{23} +(-46.3959 - 5.91067i) q^{24} -48.1886 q^{25} -50.8681i q^{26} +(10.0184 - 25.0725i) q^{27} +65.6969 q^{28} -5.38516i q^{29} +(11.4320 - 89.7354i) q^{30} +13.7261 q^{31} -12.5645i q^{32} +(3.26125 + 0.415472i) q^{33} -77.2705 q^{34} +66.7251i q^{35} +(73.3874 + 19.0071i) q^{36} +31.4393 q^{37} -79.7955i q^{38} +(-5.47156 + 42.9491i) q^{39} +133.375 q^{40} -38.8708i q^{41} +(-81.8106 - 10.4224i) q^{42} -30.7276 q^{43} +9.23073i q^{44} +(-19.3046 + 74.5360i) q^{45} +2.58015 q^{46} +9.71303i q^{47} +(-8.05929 + 63.2614i) q^{48} +11.8324 q^{49} +169.848i q^{50} +(65.2412 + 8.31151i) q^{51} -121.564 q^{52} -4.74728i q^{53} +(-88.3720 - 35.3115i) q^{54} -9.37520 q^{55} -121.597i q^{56} +(-8.58311 + 67.3732i) q^{57} -18.9809 q^{58} +48.1028i q^{59} +(-214.449 - 27.3201i) q^{60} +18.5178 q^{61} -48.3797i q^{62} +(67.9535 + 17.5997i) q^{63} +40.7447 q^{64} -123.467i q^{65} +(1.46440 - 11.4948i) q^{66} +63.5000 q^{67} +184.661i q^{68} +(-2.17848 - 0.277531i) q^{69} +235.183 q^{70} +45.5643i q^{71} +(35.1797 - 135.831i) q^{72} -69.2663 q^{73} -110.813i q^{74} +(18.2695 - 143.407i) q^{75} -190.695 q^{76} +8.54724i q^{77} +(151.381 + 19.2854i) q^{78} -97.4352 q^{79} -181.859i q^{80} +(70.8163 + 39.3199i) q^{81} -137.006 q^{82} -121.788i q^{83} +(-24.9074 + 195.510i) q^{84} -187.551 q^{85} +108.304i q^{86} +(16.0260 + 2.04165i) q^{87} +17.0849 q^{88} +78.5721i q^{89} +(262.714 + 68.0420i) q^{90} -112.563 q^{91} -6.16603i q^{92} +(-5.20390 + 40.8481i) q^{93} +34.2351 q^{94} -193.679i q^{95} +(37.3914 + 4.76353i) q^{96} +36.6087 q^{97} -41.7051i q^{98} +(-2.47285 + 9.54779i) 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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