LMFDB - Embedded newform 221.2.m.c.205.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [221,2,Mod(69,221)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("221.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(221, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.76469388467$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.1
Character	$\chi$	$=$	221.205
Dual form			221.2.m.c.69.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.39781 + 1.38438i) q^{2} +(-0.0844000 - 0.146185i) q^{3} +(2.83300 - 4.90689i) q^{4} +2.08714i q^{5} +(0.404751 + 0.233683i) q^{6} +(-2.66656 - 1.53954i) q^{7} +10.1502i q^{8} +(1.48575 - 2.57340i) q^{9} +(-2.88938 - 5.00456i) q^{10} +(3.92708 - 2.26730i) q^{11} -0.956420 q^{12} +(2.82003 + 2.24665i) q^{13} +8.52520 q^{14} +(0.305108 - 0.176154i) q^{15} +(-8.38574 - 14.5245i) q^{16} +(-0.500000 + 0.866025i) q^{17} +8.22737i q^{18} +(3.24378 + 1.87280i) q^{19} +(10.2414 + 5.91285i) q^{20} +0.519749i q^{21} +(-6.27759 + 10.8731i) q^{22} +(-0.0409745 - 0.0709699i) q^{23} +(1.48381 - 0.856679i) q^{24} +0.643859 q^{25} +(-9.87210 - 1.48306i) q^{26} -1.00799 q^{27} +(-15.1087 + 8.72301i) q^{28} +(4.56389 + 7.90490i) q^{29} +(-0.487728 + 0.844770i) q^{30} +3.51366i q^{31} +(22.6341 + 13.0678i) q^{32} +(-0.662891 - 0.382720i) q^{33} -2.76875i q^{34} +(3.21323 - 5.56547i) q^{35} +(-8.41826 - 14.5809i) q^{36} +(3.04012 - 1.75522i) q^{37} -10.3706 q^{38} +(0.0904166 - 0.601864i) q^{39} -21.1849 q^{40} +(-1.65470 + 0.955344i) q^{41} +(-0.719528 - 1.24626i) q^{42} +(4.93464 - 8.54705i) q^{43} -25.6930i q^{44} +(5.37104 + 3.10097i) q^{45} +(0.196498 + 0.113448i) q^{46} -7.09195i q^{47} +(-1.41551 + 2.45174i) q^{48} +(1.24036 + 2.14837i) q^{49} +(-1.54385 + 0.891344i) q^{50} +0.168800 q^{51} +(19.0132 - 7.47282i) q^{52} +3.68018 q^{53} +(2.41697 - 1.39544i) q^{54} +(4.73216 + 8.19635i) q^{55} +(15.6267 - 27.0662i) q^{56} -0.632256i q^{57} +(-21.8867 - 12.6363i) q^{58} +(-1.72197 - 0.994179i) q^{59} -1.99618i q^{60} +(-1.25243 + 2.16927i) q^{61} +(-4.86423 - 8.42509i) q^{62} +(-7.92370 + 4.57475i) q^{63} -38.8201 q^{64} +(-4.68907 + 5.88578i) q^{65} +2.11931 q^{66} +(0.382620 - 0.220906i) q^{67} +(2.83300 + 4.90689i) q^{68} +(-0.00691650 + 0.0119797i) q^{69} +17.7933i q^{70} +(-4.24416 - 2.45036i) q^{71} +(26.1206 + 15.0807i) q^{72} -3.35868i q^{73} +(-4.85976 + 8.41735i) q^{74} +(-0.0543418 - 0.0941227i) q^{75} +(18.3792 - 10.6112i) q^{76} -13.9624 q^{77} +(0.616404 + 1.56833i) q^{78} +6.24265 q^{79} +(30.3147 - 17.5022i) q^{80} +(-4.37219 - 7.57285i) q^{81} +(2.64511 - 4.58147i) q^{82} -0.0402860i q^{83} +(2.55035 + 1.47245i) q^{84} +(-1.80751 - 1.04357i) q^{85} +27.3256i q^{86} +(0.770386 - 1.33435i) q^{87} +(23.0136 + 39.8607i) q^{88} +(-10.4257 + 6.01926i) q^{89} -17.1716 q^{90} +(-4.06097 - 10.3324i) q^{91} -0.464322 q^{92} +(0.513645 - 0.296553i) q^{93} +(9.81793 + 17.0052i) q^{94} +(-3.90878 + 6.77021i) q^{95} -4.41169i q^{96} +(-7.93350 - 4.58041i) q^{97} +(-5.94829 - 3.43425i) q^{98} -13.4746i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) $ 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.39781	+	1.38438i	−1.69551	+	0.978902i	−0.745588	+	0.666407i	$0.767831\pi$
$2$	−2.39781	+	1.38438i	−1.69551	+	0.978902i	−0.949919	+	0.312495i	$0.898835\pi$
$3$	−0.0844000	−	0.146185i	−0.0487284	−	0.0844000i	0.840632	−	0.541606i	$-0.182184\pi$
$3$	−0.0844000	−	0.146185i	−0.0487284	−	0.0844000i	−0.889361	+	0.457206i	$0.848850\pi$
$4$	2.83300	−	4.90689i	1.41650	−	2.45345i
$5$			2.08714i			0.933396i	0.884417	+	0.466698i	$0.154556\pi$
$5$			2.08714i			0.933396i	−0.884417	+	0.466698i	$0.845444\pi$
$6$	0.404751	+	0.233683i	0.165239	+	0.0954006i
$7$	−2.66656	−	1.53954i	−1.00786	−	0.581891i	−0.0972990	−	0.995255i	$-0.531020\pi$
$7$	−2.66656	−	1.53954i	−1.00786	−	0.581891i	−0.910566	+	0.413364i	$0.864354\pi$
$8$			10.1502i			3.58865i
$9$	1.48575	−	2.57340i	0.495251	−	0.857800i
$10$	−2.88938	−	5.00456i	−0.913703	−	1.58258i
$11$	3.92708	−	2.26730i	1.18406	−	0.683616i	0.227108	−	0.973870i	$-0.427073\pi$
$11$	3.92708	−	2.26730i	1.18406	−	0.683616i	0.956950	+	0.290253i	$0.0937396\pi$
$12$	−0.956420			−0.276095
$13$	2.82003	+	2.24665i	0.782135	+	0.623109i
$13$	2.82003	+	2.24665i	0.782135	+	0.623109i
$14$	8.52520			2.27846
$15$	0.305108	−	0.176154i	0.0787787	−	0.0454829i
$16$	−8.38574	−	14.5245i	−2.09643	−	3.63113i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$			8.22737i			1.93921i
$19$	3.24378	+	1.87280i	0.744174	+	0.429649i	0.823585	−	0.567193i	$-0.191971\pi$
$19$	3.24378	+	1.87280i	0.744174	+	0.429649i	−0.0794111	+	0.996842i	$0.525304\pi$
$20$	10.2414	+	5.91285i	2.29004	+	1.32215i
$21$			0.519749i			0.113418i
$22$	−6.27759	+	10.8731i	−1.33839	+	2.31815i
$23$	−0.0409745	−	0.0709699i	−0.00854377	−	0.0147983i	0.861722	−	0.507381i	$-0.169386\pi$
$23$	−0.0409745	−	0.0709699i	−0.00854377	−	0.0147983i	−0.870266	+	0.492583i	$0.836053\pi$
$24$	1.48381	−	0.856679i	0.302882	−	0.174869i
$25$	0.643859			0.128772
$26$	−9.87210	−	1.48306i	−1.93608	−	0.290853i
$27$	−1.00799			−0.193988
$28$	−15.1087	+	8.72301i	−2.85528	+	1.64849i
$29$	4.56389	+	7.90490i	0.847494	+	1.46790i	0.883438	+	0.468548i	$0.155223\pi$
$29$	4.56389	+	7.90490i	0.847494	+	1.46790i	−0.0359441	+	0.999354i	$0.511444\pi$
$30$	−0.487728	+	0.844770i	−0.0890466	+	0.154233i
$31$			3.51366i			0.631072i	0.948914	+	0.315536i	$0.102184\pi$
$31$			3.51366i			0.631072i	−0.948914	+	0.315536i	$0.897816\pi$
$32$	22.6341	+	13.0678i	4.00118	+	2.31008i
$33$	−0.662891	−	0.382720i	−0.115394	−	0.0666230i
$34$		−	2.76875i		−	0.474837i
$35$	3.21323	−	5.56547i	0.543135	−	0.940737i
$36$	−8.41826	−	14.5809i	−1.40304	−	2.43014i
$37$	3.04012	−	1.75522i	0.499793	−	0.288556i	−0.228835	−	0.973465i	$-0.573492\pi$
$37$	3.04012	−	1.75522i	0.499793	−	0.288556i	0.728628	+	0.684910i	$0.240158\pi$
$38$	−10.3706			−1.68234
$39$	0.0904166	−	0.601864i	0.0144782	−	0.0963753i
$40$	−21.1849			−3.34963
$41$	−1.65470	+	0.955344i	−0.258421	+	0.149200i	−0.623614	−	0.781732i	$-0.714336\pi$
$41$	−1.65470	+	0.955344i	−0.258421	+	0.149200i	0.365193	+	0.930932i	$0.381003\pi$
$42$	−0.719528	−	1.24626i	−0.111026	−	0.192302i
$43$	4.93464	−	8.54705i	0.752526	−	1.30341i	−0.194070	−	0.980988i	$-0.562169\pi$
$43$	4.93464	−	8.54705i	0.752526	−	1.30341i	0.946595	−	0.322425i	$-0.104498\pi$
$44$		−	25.6930i		−	3.87336i
$45$	5.37104	+	3.10097i	0.800667	+	0.462265i
$46$	0.196498	+	0.113448i	0.0289721	+	0.0167270i
$47$		−	7.09195i		−	1.03447i	−0.855844	−	0.517234i	$-0.826962\pi$
$47$		−	7.09195i		−	1.03447i	0.855844	−	0.517234i	$-0.173038\pi$
$48$	−1.41551	+	2.45174i	−0.204312	+	0.353878i
$49$	1.24036	+	2.14837i	0.177194	+	0.306909i
$50$	−1.54385	+	0.891344i	−0.218334	+	0.126055i
$51$	0.168800			0.0236367
$52$	19.0132	−	7.47282i	2.63666	−	1.03629i
$53$	3.68018			0.505512			0.252756	−	0.967530i	$-0.418663\pi$
$53$	3.68018			0.505512			0.252756	+	0.967530i	$0.418663\pi$
$54$	2.41697	−	1.39544i	0.328908	−	0.189895i
$55$	4.73216	+	8.19635i	0.638085	+	1.10519i
$56$	15.6267	−	27.0662i	2.08820	−	3.61687i
$57$		−	0.632256i		−	0.0837444i
$58$	−21.8867	−	12.6363i	−2.87386	−	1.65923i
$59$	−1.72197	−	0.994179i	−0.224181	−	0.129431i	0.383704	−	0.923456i	$-0.374648\pi$
$59$	−1.72197	−	0.994179i	−0.224181	−	0.129431i	−0.607885	+	0.794025i	$0.707982\pi$
$60$		−	1.99618i		−	0.257706i
$61$	−1.25243	+	2.16927i	−0.160357	+	0.277746i	−0.934997	−	0.354657i	$-0.884598\pi$
$61$	−1.25243	+	2.16927i	−0.160357	+	0.277746i	0.774640	+	0.632403i	$0.217931\pi$
$62$	−4.86423	−	8.42509i	−0.617758	−	1.06999i
$63$	−7.92370	+	4.57475i	−0.998292	+	0.576364i
$64$	−38.8201			−4.85251
$65$	−4.68907	+	5.88578i	−0.581607	+	0.730042i
$66$	2.11931			0.260870
$67$	0.382620	−	0.220906i	0.0467445	−	0.0269880i	−0.476446	−	0.879204i	$-0.658075\pi$
$67$	0.382620	−	0.220906i	0.0467445	−	0.0269880i	0.523190	+	0.852216i	$0.324742\pi$
$68$	2.83300	+	4.90689i	0.343551	+	0.595048i
$69$	−0.00691650	+	0.0119797i	−0.000832649	+	0.00144219i
$70$			17.7933i			2.12670i
$71$	−4.24416	−	2.45036i	−0.503689	−	0.290805i	0.226547	−	0.974000i	$-0.427256\pi$
$71$	−4.24416	−	2.45036i	−0.503689	−	0.290805i	−0.730236	+	0.683195i	$0.760590\pi$
$72$	26.1206	+	15.0807i	3.07834	+	1.77728i
$73$		−	3.35868i		−	0.393104i	−0.980493	−	0.196552i	$-0.937026\pi$
$73$		−	3.35868i		−	0.393104i	0.980493	−	0.196552i	$-0.0629744\pi$
$74$	−4.85976	+	8.41735i	−0.564935	+	0.978497i
$75$	−0.0543418	−	0.0941227i	−0.00627485	−	0.0108684i
$76$	18.3792	−	10.6112i	2.10824	−	1.21719i
$77$	−13.9624			−1.59116
$78$	0.616404	+	1.56833i	0.0697940	+	0.177578i
$79$	6.24265			0.702353			0.351176	−	0.936309i	$-0.385782\pi$
$79$	6.24265			0.702353			0.351176	+	0.936309i	$0.385782\pi$
$80$	30.3147	−	17.5022i	3.38928	−	1.95680i
$81$	−4.37219	−	7.57285i	−0.485798	−	0.841427i
$82$	2.64511	−	4.58147i	0.292104	−	0.505938i
$83$		−	0.0402860i		−	0.00442196i	−0.999998	−	0.00221098i	$-0.999296\pi$
$83$		−	0.0402860i		−	0.00442196i	0.999998	−	0.00221098i	$-0.000703778\pi$
$84$	2.55035	+	1.47245i	0.278266	+	0.160657i
$85$	−1.80751	−	1.04357i	−0.196052	−	0.113191i
$86$			27.3256i			2.94659i
$87$	0.770386	−	1.33435i	0.0825940	−	0.143057i
$88$	23.0136	+	39.8607i	2.45326	+	4.24916i
$89$	−10.4257	+	6.01926i	−1.10512	+	0.638041i	−0.937561	−	0.347821i	$-0.886922\pi$
$89$	−10.4257	+	6.01926i	−1.10512	+	0.638041i	−0.167558	+	0.985862i	$0.553588\pi$
$90$	−17.1716			−1.81005
$91$	−4.06097	−	10.3324i	−0.425705	−	1.08313i
$92$	−0.464322			−0.0484089
$93$	0.513645	−	0.296553i	0.0532625	−	0.0307511i
$94$	9.81793	+	17.0052i	1.01264	+	1.75395i
$95$	−3.90878	+	6.77021i	−0.401033	+	0.694609i
$96$		−	4.41169i		−	0.450267i
$97$	−7.93350	−	4.58041i	−0.805524	−	0.465070i	0.0398748	−	0.999205i	$-0.487304\pi$
$97$	−7.93350	−	4.58041i	−0.805524	−	0.465070i	−0.845399	+	0.534135i	$0.820637\pi$
$98$	−5.94829	−	3.43425i	−0.600868	−	0.346912i
$99$		−	13.4746i		−	1.35425i
$100$	1.82405	−	3.15935i	0.182405	−	0.315935i
$101$	2.86731	+	4.96633i	0.285308	+	0.494168i	0.972684	−	0.232134i	$-0.0745707\pi$
$101$	2.86731	+	4.96633i	0.285308	+	0.494168i	−0.687376	+	0.726302i	$0.741237\pi$
$102$	−0.404751	+	0.233683i	−0.0400763	+	0.0231380i
$103$	−4.96416			−0.489133			−0.244566	−	0.969633i	$-0.578646\pi$
$103$	−4.96416			−0.489133			−0.244566	+	0.969633i	$0.578646\pi$
$104$	−22.8040	+	28.6239i	−2.23612	+	2.80681i
$105$	−1.08479			−0.105864
$106$	−8.82437	+	5.09475i	−0.857099	+	0.494846i
$107$	0.147285	+	0.255105i	0.0142386	+	0.0246620i	0.873057	−	0.487618i	$-0.162134\pi$
$107$	0.147285	+	0.255105i	0.0142386	+	0.0246620i	−0.858818	+	0.512280i	$0.828801\pi$
$108$	−2.85563	+	4.94610i	−0.274783	+	0.475939i
$109$		−	5.64382i		−	0.540580i	−0.962779	−	0.270290i	$-0.912880\pi$
$109$		−	5.64382i		−	0.540580i	0.962779	−	0.270290i	$-0.0871196\pi$
$110$	−22.6937	−	13.1022i	−2.16375	−	1.24924i
$111$	−0.513173	−	0.296281i	−0.0487082	−	0.0281217i
$112$			51.6407i			4.87958i
$113$	3.38339	−	5.86020i	0.318282	−	0.551281i	−0.661847	−	0.749639i	$-0.730227\pi$
$113$	3.38339	−	5.86020i	0.318282	−	0.551281i	0.980130	+	0.198357i	$0.0635606\pi$
$114$	0.875281	+	1.51603i	0.0819775	+	0.141989i
$115$	0.148124	−	0.0855194i	0.0138126	−	0.00797472i
$116$	51.7180			4.80189
$117$	9.97140	−	3.91909i	0.921856	−	0.362320i
$118$	5.50527			0.506801
$119$	2.66656	−	1.53954i	0.244443	−	0.141129i
$120$	1.78801	+	3.09692i	0.163222	+	0.282709i
$121$	4.78128	−	8.28143i	0.434662	−	0.752857i
$122$		−	6.93532i		−	0.627894i
$123$	0.279314	+	0.161262i	0.0251849	+	0.0145405i
$124$	17.2412	+	9.95418i	1.54830	+	0.893912i
$125$			11.7795i			1.05359i
$126$	12.6664	−	21.9388i	1.12841	−	1.95446i
$127$	6.70155	+	11.6074i	0.594667	+	1.02999i	0.993594	+	0.113010i	$0.0360492\pi$
$127$	6.70155	+	11.6074i	0.594667	+	1.02999i	−0.398927	+	0.916983i	$0.630617\pi$
$128$	47.8150	−	27.6060i	4.22629	−	2.44005i
$129$	−1.66594			−0.146677
$130$	3.09536	−	20.6044i	0.271481	−	1.80713i
$131$	−16.2127			−1.41651			−0.708256	−	0.705956i	$-0.750518\pi$
$131$	−16.2127			−1.41651			−0.708256	+	0.705956i	$0.750518\pi$
$132$	−3.75593	+	2.16849i	−0.326912	+	0.188743i
$133$	−5.76649	−	9.98785i	−0.500018	−	0.866056i
$134$	−0.611634	+	1.05938i	−0.0528371	+	0.0915166i
$135$		−	2.10381i		−	0.181068i
$136$	−8.79035	−	5.07511i	−0.753766	−	0.435187i
$137$	5.17925	+	2.99024i	0.442493	+	0.255473i	0.704654	−	0.709551i	$-0.251102\pi$
$137$	5.17925	+	2.99024i	0.442493	+	0.255473i	−0.262162	+	0.965024i	$0.584435\pi$
$138$		−	0.0383001i		−	0.00326033i
$139$	1.82881	−	3.16759i	0.155117	−	0.268671i	−0.777984	−	0.628284i	$-0.783758\pi$
$139$	1.82881	−	3.16759i	0.155117	−	0.268671i	0.933102	+	0.359612i	$0.117091\pi$
$140$	−18.2061	−	31.5339i	−1.53870	−	2.66510i
$141$	−1.03674	+	0.598561i	−0.0873091	+	0.0504079i
$142$	13.5689			1.13868
$143$	16.1683	+	2.42893i	1.35206	+	0.203117i
$144$	−49.8365			−4.15304
$145$	−16.4986	+	9.52547i	−1.37013	+	0.791047i
$146$	4.64968	+	8.05348i	0.384810	+	0.666511i
$147$	0.209373	−	0.362644i	0.0172688	−	0.0299104i
$148$		−	19.8901i		−	1.63495i
$149$	0.299655	+	0.173006i	0.0245487	+	0.0141732i	0.512224	−	0.858852i	$-0.328822\pi$
$149$	0.299655	+	0.173006i	0.0245487	+	0.0141732i	−0.487675	+	0.873025i	$0.662155\pi$
$150$	0.260602	+	0.150459i	0.0212781	+	0.0122849i
$151$		−	14.5703i		−	1.18571i	−0.805308	−	0.592857i	$-0.798000\pi$
$151$		−	14.5703i		−	1.18571i	0.805308	−	0.592857i	$-0.202000\pi$
$152$	−19.0093	+	32.9251i	−1.54186	+	2.67058i
$153$	1.48575	+	2.57340i	0.120116	+	0.208047i
$154$	33.4791	−	19.3292i	2.69782	−	1.55759i
$155$	−7.33349			−0.589040
$156$	−2.69713	−	2.14874i	−0.215943	−	0.172037i
$157$	−3.83355			−0.305950			−0.152975	−	0.988230i	$-0.548885\pi$
$157$	−3.83355			−0.305950			−0.152975	+	0.988230i	$0.548885\pi$
$158$	−14.9687	+	8.64218i	−1.19084	+	0.687535i
$159$	−0.310607	−	0.537988i	−0.0246328	−	0.0426652i
$160$	−27.2743	+	47.2405i	−2.15622	+	3.73469i
$161$			0.252327i			0.0198862i
$162$	20.9673	+	12.1055i	1.64735	+	0.951098i
$163$	13.4773	+	7.78112i	1.05562	+	0.609464i	0.924218	−	0.381864i	$-0.124718\pi$
$163$	13.4773	+	7.78112i	1.05562	+	0.609464i	0.131405	+	0.991329i	$0.458051\pi$
$164$			10.8259i			0.845364i
$165$	0.798789	−	1.38354i	0.0621857	−	0.107709i
$166$	0.0557710	+	0.0965982i	0.00432867	+	0.00749747i
$167$	−16.8412	+	9.72328i	−1.30321	+	0.752410i	−0.980954	−	0.194242i	$-0.937775\pi$
$167$	−16.8412	+	9.72328i	−1.30321	+	0.752410i	−0.322258	+	0.946652i	$0.604442\pi$
$168$	−5.27556			−0.407019
$169$	2.90512	+	12.6712i	0.223470	+	0.974711i
$170$	5.77877			0.443211
$171$	9.63891	−	5.56503i	0.737106	−	0.425568i
$172$	−27.9596	−	48.4275i	−2.13190	−	3.69256i
$173$	−11.6312	+	20.1459i	−0.884306	+	1.53166i	−0.0377987	+	0.999285i	$0.512035\pi$
$173$	−11.6312	+	20.1459i	−0.884306	+	1.53166i	−0.846507	+	0.532377i	$0.821299\pi$
$174$			4.26601i			0.323406i
$175$	−1.71689	−	0.991247i	−0.129785	−	0.0749312i
$176$	−65.8628	−	38.0259i	−4.96460	−	2.86631i
$177$			0.335635i			0.0252279i
$178$	16.6659	−	28.8661i	1.24916	−	2.16361i
$179$	−0.824671	−	1.42837i	−0.0616388	−	0.106762i	0.833559	−	0.552430i	$-0.186299\pi$
$179$	−0.824671	−	1.42837i	−0.0616388	−	0.106762i	−0.895198	+	0.445668i	$0.852966\pi$
$180$	30.4323	−	17.5701i	2.26829	−	1.30960i
$181$	−14.4849			−1.07665			−0.538327	−	0.842736i	$-0.680944\pi$
$181$	−14.4849			−1.07665			−0.538327	+	0.842736i	$0.680944\pi$
$182$	24.0413	+	19.1532i	1.78206	+	1.41973i
$183$	0.422819			0.0312557
$184$	0.720360	−	0.415900i	0.0531057	−	0.0306606i
$185$	3.66338	+	6.34515i	0.269337	+	0.466505i
$186$	−0.821082	+	1.42216i	−0.0602047	+	0.104278i
$187$			4.53460i			0.331603i
$188$	−34.7994	−	20.0915i	−2.53801	−	1.46532i
$189$	2.68787	+	1.55184i	0.195514	+	0.112880i
$190$		−	21.6449i		−	1.57029i
$191$	4.30270	−	7.45249i	0.311332	−	0.539243i	−0.667319	−	0.744772i	$-0.732558\pi$
$191$	4.30270	−	7.45249i	0.311332	−	0.539243i	0.978651	+	0.205529i	$0.0658914\pi$
$192$	3.27642	+	5.67492i	0.236455	+	0.409552i
$193$	−13.5165	+	7.80376i	−0.972939	+	0.561727i	−0.900131	−	0.435619i	$-0.856529\pi$
$193$	−13.5165	+	7.80376i	−0.972939	+	0.561727i	−0.0728080	+	0.997346i	$0.523196\pi$
$194$	25.3640			1.82103
$195$	1.25617	+	0.188712i	0.0899563	+	0.0135139i
$196$	14.0557			1.00398
$197$	−4.26236	+	2.46088i	−0.303681	+	0.175330i	−0.644095	−	0.764945i	$-0.722766\pi$
$197$	−4.26236	+	2.46088i	−0.303681	+	0.175330i	0.340414	+	0.940275i	$0.389433\pi$
$198$	18.6539	+	32.3095i	1.32567	+	2.29614i
$199$	−10.9206	+	18.9150i	−0.774138	+	1.34085i	0.161140	+	0.986932i	$0.448483\pi$
$199$	−10.9206	+	18.9150i	−0.774138	+	1.34085i	−0.935278	+	0.353915i	$0.884850\pi$
$200$			6.53532i			0.462117i
$201$	−0.0645863	−	0.0372889i	−0.00455557	−	0.00263016i
$202$	−13.7505	−	7.93888i	−0.967485	−	0.558577i
$203$		−	28.1052i		−	1.97260i
$204$	0.478210	−	0.828284i	0.0334814	−	0.0579915i
$205$	−1.99393	−	3.45359i	−0.139262	−	0.241209i
$206$	11.9031	−	6.87226i	0.829328	−	0.478813i
$207$	−0.243512			−0.0169253
$208$	8.98352	−	59.7994i	0.622895	−	4.14634i
$209$	16.9848			1.17486
$210$	2.60111	−	1.50175i	0.179494	−	0.103631i
$211$	5.70214	+	9.87640i	0.392552	+	0.679919i	0.992785	−	0.119905i	$-0.0382591\pi$
$211$	5.70214	+	9.87640i	0.392552	+	0.679919i	−0.600234	+	0.799825i	$0.704926\pi$
$212$	10.4259	−	18.0582i	0.716056	−	1.24025i
$213$			0.827244i			0.0566818i
$214$	−0.706324	−	0.407796i	−0.0482833	−	0.0278764i
$215$	17.8389	+	10.2993i	1.21660	+	0.702404i
$216$		−	10.2313i		−	0.696154i
$217$	5.40942	−	9.36938i	0.367215	−	0.636035i
$218$	7.81318	+	13.5328i	0.529175	+	0.916558i
$219$	−0.490989	+	0.283473i	−0.0331780	+	0.0191553i
$220$	53.6248			3.61538
$221$	−3.35567	+	1.31889i	−0.225727	+	0.0887182i
$222$	1.64066			0.110114
$223$	16.7446	−	9.66752i	1.12130	−	0.647385i	0.179570	−	0.983745i	$-0.442529\pi$
$223$	16.7446	−	9.66752i	1.12130	−	0.647385i	0.941733	+	0.336360i	$0.109196\pi$
$224$	−40.2368	−	69.6922i	−2.68843	−	4.65650i
$225$	0.956616	−	1.65691i	0.0637744	−	0.110461i
$226$			18.7355i			1.24627i
$227$	−11.2762	−	6.51034i	−0.748430	−	0.432107i	0.0766960	−	0.997055i	$-0.475563\pi$
$227$	−11.2762	−	6.51034i	−0.748430	−	0.432107i	−0.825127	+	0.564948i	$0.808896\pi$
$228$	−3.10241	−	1.79118i	−0.205462	−	0.118624i
$229$			21.0616i			1.39179i	0.718145	+	0.695894i	$0.244992\pi$
$229$			21.0616i			1.39179i	−0.718145	+	0.695894i	$0.755008\pi$
$230$	−0.236782	+	0.410119i	−0.0156129	+	0.0270424i
$231$	1.17843	+	2.04109i	0.0775347	+	0.134294i
$232$	−80.2364	+	46.3245i	−5.26778	+	3.04135i
$233$	0.240364			0.0157467			0.00787337	−	0.999969i	$-0.497494\pi$
$233$	0.240364			0.0157467			0.00787337	+	0.999969i	$0.497494\pi$
$234$	−18.4840	+	23.2014i	−1.20834	+	1.51672i
$235$	14.8019			0.965568
$236$	−9.75666	+	5.63301i	−0.635105	+	0.366678i
$237$	−0.526880	−	0.912583i	−0.0342245	−	0.0592786i
$238$	−4.26260	+	7.38304i	−0.276303	+	0.478572i
$239$		−	19.8813i		−	1.28602i	−0.765860	−	0.643008i	$-0.777686\pi$
$239$		−	19.8813i		−	1.28602i	0.765860	−	0.643008i	$-0.222314\pi$
$240$	−5.11712	−	2.95437i	−0.330309	−	0.190704i
$241$	1.69593	+	0.979148i	0.109245	+	0.0630725i	0.553627	−	0.832765i	$-0.313243\pi$
$241$	1.69593	+	0.979148i	0.109245	+	0.0630725i	−0.444382	+	0.895837i	$0.646577\pi$
$242$			26.4764i			1.70197i
$243$	−2.25001	+	3.89713i	−0.144338	+	0.250001i
$244$	7.09623	+	12.2910i	0.454290	+	0.786853i
$245$	−4.48393	+	2.58880i	−0.286468	+	0.165392i
$246$	−0.892990			−0.0569350
$247$	4.94003	+	12.5690i	0.314326	+	0.799745i
$248$	−35.6644			−2.26469
$249$	−0.00588921	+	0.00340014i	−0.000373214	+	0.000215475i
$250$	−16.3073	−	28.2450i	−1.03136	−	1.78637i
$251$	3.87068	−	6.70421i	0.244315	−	0.423166i	−0.717624	−	0.696431i	$-0.754770\pi$
$251$	3.87068	−	6.70421i	0.244315	−	0.423166i	0.961939	+	0.273265i	$0.0881036\pi$
$252$			51.8410i			3.26567i
$253$	−0.321820	−	0.185803i	−0.0202326	−	0.0116813i
$254$	−32.1381	−	18.5549i	−2.01652	−	1.16424i
$255$			0.352309i			0.0220624i
$256$	−37.6141	+	65.1496i	−2.35088	+	4.07185i
$257$	−0.222110	−	0.384707i	−0.0138549	−	0.0239973i	0.859015	−	0.511951i	$-0.171077\pi$
$257$	−0.222110	−	0.384707i	−0.0138549	−	0.0239973i	−0.872870	+	0.487953i	$0.837744\pi$
$258$	3.99460	−	2.30628i	0.248693	−	0.143583i
$259$	−10.8089			−0.671632
$260$	15.5968	+	39.6832i	0.967272	+	2.46104i
$261$	27.1233			1.67889
$262$	38.8750	−	22.4445i	2.40171	−	1.38663i
$263$	−2.56660	−	4.44549i	−0.158264	−	0.274120i	0.775979	−	0.630759i	$-0.217256\pi$
$263$	−2.56660	−	4.44549i	−0.158264	−	0.274120i	−0.934243	+	0.356638i	$0.883923\pi$
$264$	3.88469	−	6.72849i	0.239086	−	0.414110i
$265$			7.68104i			0.471842i
$266$	27.6539	+	15.9660i	1.69557	+	0.978936i
$267$	1.75985	+	1.01605i	0.107701	+	0.0621814i
$268$		−	2.50330i		−	0.152914i
$269$	14.1735	−	24.5493i	0.864176	−	1.49680i	−0.00368634	−	0.999993i	$-0.501173\pi$
$269$	14.1735	−	24.5493i	0.864176	−	1.49680i	0.867863	−	0.496804i	$-0.165493\pi$
$270$	2.91247	+	5.04455i	0.177247	+	0.307001i
$271$	3.58092	−	2.06744i	0.217525	−	0.125588i	−0.387279	−	0.921963i	$-0.626585\pi$
$271$	3.58092	−	2.06744i	0.217525	−	0.125588i	0.604804	+	0.796374i	$0.293252\pi$
$272$	16.7715			1.01692
$273$	−1.16769	+	1.46571i	−0.0706720	+	0.0887085i
$274$	−16.5585			−1.00033
$275$	2.52849	−	1.45982i	0.152473	−	0.0880305i
$276$	0.0391888	+	0.0678770i	0.00235889	+	0.00408572i
$277$	3.39773	−	5.88504i	0.204150	−	0.353598i	−0.745712	−	0.666269i	$-0.767890\pi$
$277$	3.39773	−	5.88504i	0.204150	−	0.353598i	0.949861	+	0.312671i	$0.101224\pi$
$278$			10.1270i			0.607379i
$279$	9.04205	+	5.22043i	0.541334	+	0.312539i
$280$	56.4908	+	32.6150i	3.37597	+	1.94912i
$281$			28.5315i			1.70205i	0.525129	+	0.851023i	$0.324017\pi$
$281$			28.5315i			1.70205i	−0.525129	+	0.851023i	$0.675983\pi$
$282$	1.65727	−	2.87047i	0.0986889	−	0.170934i
$283$	−6.27274	−	10.8647i	−0.372876	−	0.645840i	0.617131	−	0.786860i	$-0.288295\pi$
$283$	−6.27274	−	10.8647i	−0.372876	−	0.645840i	−0.990007	+	0.141021i	$0.954962\pi$
$284$	−24.0474	+	13.8837i	−1.42695	+	0.823849i
$285$	1.31961			0.0781667
$286$	−42.1310	+	16.5589i	−2.49126	+	0.979148i
$287$	5.88316			0.347272
$288$	67.2574	−	38.8311i	3.96318	−	2.28814i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	26.3737	−	45.6805i	1.54872	−	2.68245i
$291$			1.54635i			0.0906484i
$292$	−16.4807	−	9.51513i	−0.964459	−	0.556831i
$293$	−28.2242	−	16.2953i	−1.64888	−	0.951980i	−0.977519	−	0.210847i	$-0.932378\pi$
$293$	−28.2242	−	16.2953i	−1.64888	−	0.951980i	−0.671358	−	0.741133i	$-0.734289\pi$
$294$			1.15940i			0.0676178i
$295$	2.07499	−	3.59399i	0.120810	−	0.209250i
$296$	17.8158	+	30.8579i	1.03552	+	1.79358i
$297$	−3.95846	+	2.28542i	−0.229693	+	0.132613i
$298$	−0.958022			−0.0554967
$299$	0.0438954	−	0.292193i	0.00253854	−	0.0168979i
$300$	−0.615800			−0.0355532
$301$	−26.3170	+	15.1941i	−1.51689	+	0.875776i
$302$	20.1708	+	34.9368i	1.16070	+	2.01039i
$303$	0.484003	−	0.838317i	0.0278052	−	0.0481600i
$304$		−	62.8191i		−	3.60292i
$305$	−4.52755	−	2.61398i	−0.259247	−	0.149676i
$306$	−7.12511	−	4.11368i	−0.407315	−	0.235164i
$307$		−	5.64069i		−	0.321931i	−0.986960	−	0.160966i	$-0.948539\pi$
$307$		−	5.64069i		−	0.321931i	0.986960	−	0.160966i	$-0.0514608\pi$
$308$	−39.5553	+	68.5119i	−2.25388	+	3.90383i
$309$	0.418975	+	0.725686i	0.0238347	+	0.0412828i
$310$	17.5843	−	10.1523i	0.998722	−	0.576612i
$311$	−25.6063			−1.45200			−0.725999	−	0.687696i	$-0.758622\pi$
$311$	−25.6063			−1.45200			−0.725999	+	0.687696i	$0.758622\pi$
$312$	6.10905	+	0.917748i	0.345857	+	0.0519573i
$313$	6.93646			0.392072			0.196036	−	0.980597i	$-0.437193\pi$
$313$	6.93646			0.392072			0.196036	+	0.980597i	$0.437193\pi$
$314$	9.19212	−	5.30707i	0.518741	−	0.299495i
$315$	−9.54813	−	16.5378i	−0.537976	−	0.931802i
$316$	17.6854	−	30.6320i	0.994881	−	1.72319i
$317$		−	33.6205i		−	1.88832i	−0.329492	−	0.944159i	$-0.606877\pi$
$317$		−	33.6205i		−	1.88832i	0.329492	−	0.944159i	$-0.393123\pi$
$318$	1.48955	+	0.859995i	0.0835301	+	0.0482261i
$319$	35.8455	+	20.6954i	2.00696	+	1.15872i
$320$		−	81.0229i		−	4.52932i
$321$	0.0248618	−	0.0430618i	0.00138765	−	0.00240348i
$322$	−0.349316	−	0.605033i	−0.0194666	−	0.0337172i
$323$	−3.24378	+	1.87280i	−0.180489	+	0.104205i
$324$	−49.5455			−2.75253
$325$	1.81570	+	1.44653i	0.100717	+	0.0802389i
$326$	−43.0880			−2.38642
$327$	−0.825043	+	0.476339i	−0.0456250	+	0.0263416i
$328$	−9.69695	−	16.7956i	−0.535425	−	0.927383i
$329$	−10.9183	+	18.9111i	−0.601947	+	1.04260i
$330$			4.42330i			0.243495i
$331$	−23.2676	−	13.4336i	−1.27890	−	0.738375i	−0.302257	−	0.953227i	$-0.597740\pi$
$331$	−23.2676	−	13.4336i	−1.27890	−	0.738375i	−0.976647	+	0.214851i	$0.931073\pi$
$332$	−0.197679	−	0.114130i	−0.0108490	−	0.00626370i
$333$		−	10.4313i		−	0.571630i
$334$	26.9213	−	46.6291i	1.47307	−	2.55143i
$335$	0.461061	+	0.798581i	0.0251904	+	0.0436311i
$336$	7.54910	−	4.35847i	0.411837	−	0.237774i
$337$	25.2191			1.37377			0.686886	−	0.726765i	$-0.258977\pi$
$337$	25.2191			1.37377			0.686886	+	0.726765i	$0.258977\pi$
$338$	−24.5077	−	26.3615i	−1.33304	−	1.43387i
$339$	−1.14223			−0.0620376
$340$	−10.2414	+	5.91285i	−0.555416	+	0.320669i
$341$	7.96652	+	13.7984i	0.431411	+	0.747226i
$342$	−15.4082	+	26.6878i	−0.833179	+	1.44311i
$343$			13.9152i			0.751351i
$344$	86.7544	+	50.0877i	4.67749	+	2.70055i
$345$	−0.0250033	−	0.0144357i	−0.00134613	−	0.000777191i
$346$		−	64.4080i		−	3.46259i
$347$	−7.31851	+	12.6760i	−0.392878	+	0.680485i	−0.992828	−	0.119553i	$-0.961854\pi$
$347$	−7.31851	+	12.6760i	−0.392878	+	0.680485i	0.599950	+	0.800038i	$0.295187\pi$
$348$	−4.36500	−	7.56040i	−0.233988	−	0.405280i
$349$	−4.02257	+	2.32243i	−0.215323	+	0.124317i	−0.603783	−	0.797149i	$-0.706341\pi$
$349$	−4.02257	+	2.32243i	−0.215323	+	0.124317i	0.388460	+	0.921466i	$0.373007\pi$
$350$	5.48903			0.293401
$351$	−2.84256	−	2.26460i	−0.151725	−	0.120876i
$352$	118.514			6.31684
$353$	14.4116	−	8.32052i	0.767050	−	0.442856i	−0.0647714	−	0.997900i	$-0.520632\pi$
$353$	14.4116	−	8.32052i	0.767050	−	0.442856i	0.831821	+	0.555044i	$0.187298\pi$
$354$	−0.464645	−	0.804789i	−0.0246956	−	0.0427741i
$355$	5.11425	−	8.85814i	0.271436	−	0.470141i
$356$			68.2102i			3.61513i
$357$	−0.450115	−	0.259874i	−0.0238226	−	0.0137540i
$358$	3.95481	+	2.28331i	0.209018	+	0.120677i
$359$		−	23.8773i		−	1.26019i	−0.776516	−	0.630097i	$-0.783015\pi$
$359$		−	23.8773i		−	1.26019i	0.776516	−	0.630097i	$-0.216985\pi$
$360$	−31.4755	+	54.5172i	−1.65891	+	2.87331i
$361$	−2.48527	−	4.30461i	−0.130804	−	0.226558i
$362$	34.7321	−	20.0526i	1.82548	−	1.05394i
$363$	−1.61416			−0.0847215
$364$	−62.2045	−	9.34484i	−3.26040	−	0.489803i
$365$	7.01003			0.366922
$366$	−1.01384	+	0.585341i	−0.0529943	+	0.0305963i
$367$	−7.76942	−	13.4570i	−0.405561	−	0.702452i	0.588826	−	0.808260i	$-0.299590\pi$
$367$	−7.76942	−	13.4570i	−0.405561	−	0.702452i	−0.994387	+	0.105808i	$0.966257\pi$
$368$	−0.687203	+	1.19027i	−0.0358229	+	0.0620471i
$369$			5.67762i			0.295565i
$370$	−17.5682	−	10.1430i	−0.913325	−	0.527308i
$371$	−9.81342	−	5.66578i	−0.509487	−	0.294153i
$372$		−	3.36053i		−	0.174236i
$373$	−12.2261	+	21.1762i	−0.633043	+	1.09646i	0.353884	+	0.935289i	$0.384861\pi$
$373$	−12.2261	+	21.1762i	−0.633043	+	1.09646i	−0.986926	+	0.161172i	$0.948472\pi$
$374$	−6.27759	−	10.8731i	−0.324606	−	0.562235i
$375$	1.72199	−	0.994191i	0.0889231	−	0.0513398i
$376$	71.9849			3.71234
$377$	−4.88924	+	32.5455i	−0.251808	+	1.67618i
$378$	−8.59333			−0.441993
$379$	−22.9129	+	13.2288i	−1.17696	+	0.679517i	−0.955309	−	0.295610i	$-0.904477\pi$
$379$	−22.9129	+	13.2288i	−1.17696	+	0.679517i	−0.221649	+	0.975127i	$0.571144\pi$
$380$	22.1471	+	38.3599i	1.13612	+	1.96782i
$381$	1.13122	−	1.95933i	0.0579543	−	0.100380i
$382$			23.8262i			1.21906i
$383$	−0.0536315	−	0.0309641i	−0.00274044	−	0.00158219i	0.498629	−	0.866815i	$-0.333837\pi$
$383$	−0.0536315	−	0.0309641i	−0.00274044	−	0.00158219i	−0.501370	+	0.865233i	$0.667170\pi$
$384$	−8.07118	−	4.65990i	−0.411881	−	0.237799i
$385$		−	29.1414i		−	1.48518i
$386$	21.6067	−	37.4238i	1.09975	−	1.90482i
$387$	−14.6633	−	25.3976i	−0.745378	−	1.29103i
$388$	−44.9511	+	25.9525i	−2.28205	+	1.31754i
$389$	8.61294			0.436694			0.218347	−	0.975871i	$-0.429934\pi$
$389$	8.61294			0.436694			0.218347	+	0.975871i	$0.429934\pi$
$390$	−3.27331	+	1.28652i	−0.165750	+	0.0651455i
$391$	0.0819490			0.00414434
$392$	−21.8064	+	12.5899i	−1.10139	+	0.635887i
$393$	1.36835	+	2.37006i	0.0690243	+	0.119554i
$394$	6.81356	−	11.8014i	0.343262	−	0.594547i
$395$			13.0293i			0.655573i
$396$	−66.1183	−	38.1734i	−3.32257	−	1.91829i
$397$	25.3072	+	14.6111i	1.27013	+	0.733312i	0.975013	−	0.222148i	$-0.0713067\pi$
$397$	25.3072	+	14.6111i	1.27013	+	0.733312i	0.295121	+	0.955460i	$0.404640\pi$
$398$		−	60.4727i		−	3.03122i
$399$	−0.973383	+	1.68595i	−0.0487301	+	0.0844030i
$400$	−5.39924	−	9.35175i	−0.269962	−	0.467588i
$401$	−15.2466	+	8.80264i	−0.761380	+	0.439583i	−0.829791	−	0.558074i	$-0.811540\pi$
$401$	−15.2466	+	8.80264i	−0.761380	+	0.439583i	0.0684111	+	0.997657i	$0.478207\pi$
$402$	0.206488			0.0102987
$403$	−7.89397	+	9.90862i	−0.393227	+	0.493584i
$404$	32.4923			1.61655
$405$	15.8056	−	9.12535i	0.785385	−	0.453442i
$406$	38.9081	+	67.3908i	1.93098	+	3.34455i
$407$	7.95920	−	13.7857i	0.394523	−	0.683333i
$408$			1.71336i			0.0848239i
$409$	17.8163	+	10.2862i	0.880959	+	0.508622i	0.870974	−	0.491328i	$-0.163488\pi$
$409$	17.8163	+	10.2862i	0.880959	+	0.508622i	0.00998437	+	0.999950i	$0.496822\pi$
$410$	9.56215	+	5.52071i	0.472241	+	0.272648i
$411$		−	1.00951i		−	0.0497952i
$412$	−14.0634	+	24.3586i	−0.692855	+	1.20006i
$413$	3.06116	+	5.30208i	0.150630	+	0.260898i
$414$	0.583895	−	0.337112i	0.0286969	−	0.0165682i
$415$	0.0840824			0.00412744
$416$	34.4700	+	87.7025i	1.69003	+	4.29997i
$417$	−0.617406			−0.0302345
$418$	−40.7262	+	23.5133i	−1.99198	+	1.15007i
$419$	10.9754	+	19.0099i	0.536183	+	0.928696i	0.999105	+	0.0422974i	$0.0134677\pi$
$419$	10.9754	+	19.0099i	0.536183	+	0.928696i	−0.462922	+	0.886399i	$0.653199\pi$
$420$	−3.07320	+	5.32293i	−0.149957	+	0.259732i
$421$		−	1.28415i		−	0.0625857i	−0.999510	−	0.0312928i	$-0.990038\pi$
$421$		−	1.28415i		−	0.0625857i	0.999510	−	0.0312928i	$-0.00996244\pi$
$422$	−27.3453	−	15.7878i	−1.33115	−	0.768539i
$423$	−18.2504	−	10.5369i	−0.887366	−	0.512321i
$424$			37.3546i			1.81410i
$425$	−0.321930	+	0.557599i	−0.0156159	+	0.0270475i
$426$	−1.14522	−	1.98357i	−0.0554859	−	0.0961044i
$427$	6.67934	−	3.85632i	0.323236	−	0.186620i
$428$	1.66903			0.0806758
$429$	−1.00953	−	2.56857i	−0.0487407	−	0.124012i
$430$	−57.0323			−2.75034
$431$	−15.2304	+	8.79327i	−0.733622	+	0.423557i	−0.819746	−	0.572728i	$-0.805885\pi$
$431$	−15.2304	+	8.79327i	−0.733622	+	0.423557i	0.0861237	+	0.996284i	$0.472552\pi$
$432$	8.45274	+	14.6406i	0.406683	+	0.704395i
$433$	18.6883	−	32.3691i	0.898103	−	1.55556i	0.0681855	−	0.997673i	$-0.478279\pi$
$433$	18.6883	−	32.3691i	0.898103	−	1.55556i	0.829917	−	0.557887i	$-0.188388\pi$
$434$			29.9547i			1.43787i
$435$	2.78496	+	1.60790i	0.133529	+	0.0770929i
$436$	−27.6936	−	15.9889i	−1.32628	−	0.765731i
$437$		−	0.306948i		−	0.0146833i
$438$	0.784866	−	1.35943i	0.0375023	−	0.0649560i
$439$	9.83303	+	17.0313i	0.469305	+	0.812860i	0.999384	−	0.0350883i	$-0.0111712\pi$
$439$	9.83303	+	17.0313i	0.469305	+	0.812860i	−0.530079	+	0.847948i	$0.677838\pi$
$440$	−83.1947	+	48.0325i	−3.96615	+	2.28986i
$441$	7.37147			0.351023
$442$	6.22042	−	7.80796i	0.295875	−	0.371387i
$443$	−15.7720			−0.749349			−0.374674	−	0.927156i	$-0.622245\pi$
$443$	−15.7720			−0.749349			−0.374674	+	0.927156i	$0.622245\pi$
$444$	−2.90763	+	1.67872i	−0.137990	+	0.0796687i
$445$	−12.5630	−	21.7598i	−0.595545	−	1.03151i
$446$	−26.7670	+	46.3617i	−1.26745	+	2.19529i
$447$		−	0.0584069i		−	0.00276255i
$448$	103.516	+	59.7651i	4.89068	+	2.82363i
$449$	−9.50776	−	5.48931i	−0.448699	−	0.259056i	0.258582	−	0.965989i	$-0.416745\pi$
$449$	−9.50776	−	5.48931i	−0.448699	−	0.259056i	−0.707281	+	0.706933i	$0.750078\pi$
$450$			5.29727i			0.249716i
$451$	−4.33210	+	7.50342i	−0.203991	+	0.353322i
$452$	−19.1703	−	33.2038i	−0.901693	−	1.56178i
$453$	−2.12996	+	1.22973i	−0.100074	+	0.0577780i
$454$	36.0510			1.69196
$455$	21.5651	−	8.47579i	1.01099	−	0.397351i
$456$	6.41754			0.300529
$457$	−12.2201	+	7.05526i	−0.571630	+	0.330031i	−0.757800	−	0.652487i	$-0.773726\pi$
$457$	−12.2201	+	7.05526i	−0.571630	+	0.330031i	0.186170	+	0.982518i	$0.440393\pi$
$458$	−29.1571	−	50.5016i	−1.36242	−	2.35979i
$459$	0.503995	−	0.872946i	0.0235245	−	0.0407456i
$460$		−	0.969104i		−	0.0451847i
$461$	−26.2077	−	15.1310i	−1.22061	−	0.704722i	−0.255566	−	0.966792i	$-0.582262\pi$
$461$	−26.2077	−	15.1310i	−1.22061	−	0.704722i	−0.965049	+	0.262069i	$0.915595\pi$
$462$	−5.65128	−	3.26277i	−0.262921	−	0.151798i
$463$			39.8682i			1.85283i	0.376500	+	0.926416i	$0.377127\pi$
$463$			39.8682i			1.85283i	−0.376500	+	0.926416i	$0.622873\pi$
$464$	76.5432	−	132.577i	3.55343	−	6.15472i
$465$	0.618947	+	1.07205i	0.0287030	+	0.0497150i
$466$	−0.576346	+	0.332754i	−0.0266987	+	0.0154145i
$467$	−22.7432			−1.05243			−0.526216	−	0.850351i	$-0.676390\pi$
$467$	−22.7432			−1.05243			−0.526216	+	0.850351i	$0.676390\pi$
$468$	9.01837	−	60.0313i	0.416874	−	2.77495i
$469$	−1.36037			−0.0628162
$470$	−35.4921	+	20.4914i	−1.63713	+	0.945196i
$471$	0.323552	+	0.560408i	0.0149085	+	0.0258222i
$472$	10.0911	−	17.4784i	0.464482	−	0.804507i
$473$		−	44.7532i		−	2.05775i
$474$	2.52672	+	1.45880i	0.116056	+	0.0670049i
$475$	2.08854	+	1.20582i	0.0958287	+	0.0553267i
$476$		−	17.4460i		−	0.799637i
$477$	5.46784	−	9.47057i	0.250355	−	0.433628i
$478$	27.5232	+	47.6716i	1.25888	+	2.18045i
$479$	28.9535	−	16.7163i	1.32292	−	0.763788i	0.338726	−	0.940885i	$-0.390004\pi$
$479$	28.9535	−	16.7163i	1.32292	−	0.763788i	0.984193	+	0.177097i	$0.0566707\pi$
$480$	9.20781			0.420277
$481$	12.5166	+	1.88034i	0.570707	+	0.0857360i
$482$	−5.42204			−0.246967
$483$	0.0368865	−	0.0212964i	0.00167839	−	0.000969021i
$484$	−27.0907	−	46.9225i	−1.23140	−	2.13284i
$485$	9.55993	−	16.5583i	0.434094	−	0.751873i
$486$		−	12.4595i		−	0.565172i
$487$	−13.0360	−	7.52631i	−0.590715	−	0.341050i	0.174665	−	0.984628i	$-0.444116\pi$
$487$	−13.0360	−	7.52631i	−0.590715	−	0.341050i	−0.765380	+	0.643578i	$0.777449\pi$
$488$	−22.0185	−	12.7124i	−0.996732	−	0.575463i
$489$		−	2.62691i		−	0.118793i
$490$	7.16775	−	12.4149i	0.323806	−	0.560848i
$491$	10.8799	+	18.8445i	0.491002	+	0.850440i	0.999946	−	0.0103591i	$-0.00329746\pi$
$491$	10.8799	+	18.8445i	0.491002	+	0.850440i	−0.508944	+	0.860799i	$0.669964\pi$
$492$	1.58259	−	0.913710i	0.0713487	−	0.0411932i
$493$	−9.12779			−0.411095
$494$	−29.2454	−	23.2992i	−1.31581	−	1.04828i
$495$	28.1233			1.26405
$496$	51.0342	−	29.4646i	2.29150	−	1.32300i
$497$	7.54486	+	13.0681i	0.338433	+	0.586184i
$498$	0.00941414	−	0.0163058i	0.000421858	−	0.000730679i
$499$			15.6160i			0.699068i	0.936924	+	0.349534i	$0.113660\pi$
$499$			15.6160i			0.699068i	−0.936924	+	0.349534i	$0.886340\pi$
$500$	57.8008	+	33.3713i	2.58493	+	1.49241i
$501$	2.84280	+	1.64129i	0.127007	+	0.0733274i
$502$			21.4339i			0.956641i
$503$	−1.75277	+	3.03588i	−0.0781520	+	0.135363i	−0.902453	−	0.430789i	$-0.858235\pi$
$503$	−1.75277	+	3.03588i	−0.0781520	+	0.135363i	0.824301	+	0.566152i	$0.191569\pi$
$504$	−46.4347	−	80.4273i	−2.06837	−	3.58252i
$505$	−10.3654	+	5.98447i	−0.461255	+	0.266306i
$506$	1.02888			0.0457395
$507$	1.60716	−	1.49414i	0.0713763	−	0.0663570i
$508$	75.9419			3.36938
$509$	10.7906	−	6.22994i	0.478284	−	0.276137i	−0.241417	−	0.970421i	$-0.577612\pi$
$509$	10.7906	−	6.22994i	0.478284	−	0.276137i	0.719701	+	0.694284i	$0.244279\pi$
$510$	−0.487728	−	0.844770i	−0.0215970	−	0.0374070i
$511$	−5.17082	+	8.95612i	−0.228744	+	0.396195i
$512$		−	97.8644i		−	4.32503i
$513$	−3.26970	−	1.88776i	−0.144361	−	0.0833467i
$514$	1.06516	+	0.614969i	0.0469821	+	0.0271251i
$515$		−	10.3609i		−	0.456555i
$516$	−4.71959	+	8.17457i	−0.207768	+	0.359865i
$517$	−16.0796	−	27.8506i	−0.707179	−	1.22487i
$518$	25.9177	−	14.9636i	1.13876	−	0.657462i
$519$	3.92670			0.172363
$520$	−59.7420	−	47.5951i	−2.61986	−	2.08718i
$521$	23.9174			1.04784			0.523919	−	0.851768i	$-0.324469\pi$
$521$	23.9174			1.04784			0.523919	+	0.851768i	$0.324469\pi$
$522$	−65.0365	+	37.5488i	−2.84657	+	1.64347i
$523$	1.66894	+	2.89069i	0.0729776	+	0.126401i	0.900205	−	0.435466i	$-0.143417\pi$
$523$	1.66894	+	2.89069i	0.0729776	+	0.126401i	−0.827227	+	0.561867i	$0.810083\pi$
$524$	−45.9306	+	79.5541i	−2.00649	+	3.47534i
$525$			0.334645i			0.0146051i
$526$	12.3085	+	7.10629i	0.536674	+	0.309849i
$527$	−3.04292	−	1.75683i	−0.132552	−	0.0765287i
$528$			12.8376i			0.558683i
$529$	11.4966	−	19.9128i	0.499854	−	0.865773i
$530$	−10.6334	−	18.4177i	−0.461887	−	0.800013i
$531$	−5.11684	+	2.95421i	−0.222052	+	0.128202i
$532$	−65.3457			−2.83310
$533$	−6.81264	−	1.02345i	−0.295088	−	0.0443304i
$534$	−5.62640			−0.243478
$535$	−0.532440	+	0.307404i	−0.0230194	+	0.0132902i
$536$	2.24224	+	3.88368i	0.0968502	+	0.167749i
$537$	−0.139205	+	0.241109i	−0.00600712	+	0.0104046i
$538$			78.4861i			3.38378i
$539$	9.74197	+	5.62453i	0.419616	+	0.242266i
$540$	−10.3232	−	5.96010i	−0.444239	−	0.256482i
$541$			19.0350i			0.818380i	0.912449	+	0.409190i	$0.134189\pi$
$541$			19.0350i			0.818380i	−0.912449	+	0.409190i	$0.865811\pi$
$542$	−5.72424	+	9.91468i	−0.245877	+	0.425872i
$543$	1.22253	+	2.11748i	0.0524637	+	0.0908697i
$544$	−22.6341	+	13.0678i	−0.970429	+	0.560278i
$545$	11.7794			0.504575
$546$	0.770820	−	5.13101i	0.0329880	−	0.219587i
$547$	−2.60831			−0.111523			−0.0557617	−	0.998444i	$-0.517759\pi$
$547$	−2.60831			−0.111523			−0.0557617	+	0.998444i	$0.517759\pi$
$548$	29.3456	−	16.9427i	1.25358	−	0.723755i
$549$	3.72159	+	6.44599i	0.158834	+	0.275108i
$550$	−4.04188	+	7.00075i	−0.172347	+	0.298513i
$551$			34.1890i			1.45650i
$552$	−0.121597	−	0.0702040i	−0.00517551	−	0.00298808i
$553$	−16.6464	−	9.61080i	−0.707877	−	0.408693i
$554$			18.8149i			0.799370i
$555$	0.618378	−	1.07106i	0.0262487	−	0.0454641i
$556$	−10.3620	−	17.9475i	−0.439447	−	0.761145i
$557$	7.93014	−	4.57847i	0.336011	−	0.193996i	−0.322496	−	0.946571i	$-0.604522\pi$
$557$	7.93014	−	4.57847i	0.336011	−	0.193996i	0.658507	+	0.752575i	$0.271188\pi$
$558$	−28.9082			−1.22378
$559$	33.1181	−	13.0165i	1.40074	−	0.550539i
$560$	−107.781			−4.55458
$561$	0.662891	−	0.382720i	0.0279873	−	0.0161585i
$562$	−39.4983	−	68.4131i	−1.66614	−	2.88583i
$563$	−8.22457	+	14.2454i	−0.346624	+	0.600371i	−0.985648	−	0.168816i	$-0.946006\pi$
$563$	−8.22457	+	14.2454i	−0.346624	+	0.600371i	0.639023	+	0.769188i	$0.279339\pi$
$564$			6.78288i			0.285611i
$565$	12.2310	+	7.06160i	0.514564	+	0.297084i
$566$	30.0817	+	17.3677i	1.26443	+	0.730017i
$567$			26.9246i			1.13073i
$568$	24.8717	−	43.0791i	1.04360	−	1.80756i
$569$	13.7152	+	23.7555i	0.574973	+	0.995883i	0.996045	+	0.0888552i	$0.0283208\pi$
$569$	13.7152	+	23.7555i	0.574973	+	0.995883i	−0.421071	+	0.907027i	$0.638346\pi$
$570$	−3.16416	+	1.82683i	−0.132532	+	0.0765175i
$571$	−41.0478			−1.71780			−0.858899	−	0.512145i	$-0.828851\pi$
$571$	−41.0478			−1.71780			−0.858899	+	0.512145i	$0.828851\pi$
$572$	57.7232	−	72.4549i	2.41353	−	3.02949i
$573$	−1.45259			−0.0606829
$574$	−14.1067	+	8.14450i	−0.588802	+	0.339945i
$575$	−0.0263818	−	0.0456947i	−0.00110020	−	0.00190560i
$576$	−57.6771	+	99.8997i	−2.40321	+	4.16249i
$577$		−	21.2467i		−	0.884514i	−0.896888	−	0.442257i	$-0.854178\pi$
$577$		−	21.2467i		−	0.884514i	0.896888	−	0.442257i	$-0.145822\pi$
$578$	2.39781	+	1.38438i	0.0997358	+	0.0575825i
$579$	2.28159	+	1.31727i	0.0948195	+	0.0547441i
$580$			107.942i			4.48207i
$581$	−0.0620218	+	0.107425i	−0.00257310	+	0.00445674i
$582$	−2.14072	−	3.70784i	−0.0887359	−	0.153695i
$583$	14.4523	−	8.34406i	0.598555	−	0.345576i
$584$	34.0914			1.41071
$585$	8.17968	+	20.8117i	0.338188	+	0.860457i
$586$	90.2351			3.72758
$587$	40.3705	−	23.3079i	1.66627	−	0.962020i	0.696643	−	0.717418i	$-0.254676\pi$
$587$	40.3705	−	23.3079i	1.66627	−	0.962020i	0.969624	−	0.244602i	$-0.0786573\pi$
$588$	−1.18630	−	2.05474i	−0.0489224	−	0.0847360i
$589$	−6.58037	+	11.3975i	−0.271139	+	0.469627i
$590$			11.4903i			0.473046i
$591$	0.719487	+	0.415396i	0.0295957	+	0.0170871i
$592$	−50.9873	−	29.4376i	−2.09557	−	1.20988i
$593$		−	26.7997i		−	1.10053i	−0.834990	−	0.550265i	$-0.814527\pi$
$593$		−	26.7997i		−	1.10053i	0.834990	−	0.550265i	$-0.185473\pi$
$594$	6.32775	−	10.9600i	0.259631	−	0.449694i
$595$	3.21323	+	5.56547i	0.131730	+	0.228162i
$596$	1.69784	−	0.980251i	0.0695464	−	0.0401526i
$597$	3.68678			0.150890
$598$	0.299252	+	0.761390i	0.0122373	+	0.0311356i
$599$	−1.63638			−0.0668605			−0.0334303	−	0.999441i	$-0.510643\pi$
$599$	−1.63638			−0.0668605			−0.0334303	+	0.999441i	$0.510643\pi$
$600$	0.955366	−	0.551581i	0.0390027	−	0.0225182i
$601$	−17.7801	−	30.7961i	−0.725266	−	1.25620i	−0.958865	−	0.283864i	$-0.908384\pi$
$601$	−17.7801	−	30.7961i	−0.725266	−	1.25620i	0.233599	−	0.972333i	$-0.424950\pi$
$602$	42.0688	−	72.8653i	1.71460	−	2.96977i
$603$		−	1.31285i		−	0.0534633i
$604$	−71.4949	−	41.2776i	−2.90909	−	1.67956i
$605$	17.2845	+	9.97919i	0.702714	+	0.405712i
$606$			2.68017i			0.108874i
$607$	−23.4217	+	40.5675i	−0.950656	+	1.64658i	−0.206646	+	0.978416i	$0.566255\pi$
$607$	−23.4217	+	40.5675i	−0.950656	+	1.64658i	−0.744010	+	0.668168i	$0.767079\pi$
$608$	48.9467	+	84.7781i	1.98505	+	3.43821i
$609$	−4.10856	+	2.37208i	−0.166487	+	0.0961214i
$610$	14.4750			0.586074
$611$	15.9331	−	19.9995i	0.644586	−	0.809093i
$612$	16.8365			0.680576
$613$	−8.11887	+	4.68743i	−0.327918	+	0.189324i	−0.654916	−	0.755701i	$-0.727296\pi$
$613$	−8.11887	+	4.68743i	−0.327918	+	0.189324i	0.326998	+	0.945025i	$0.393963\pi$
$614$	7.80884	+	13.5253i	0.315139	+	0.545837i
$615$	−0.336576	+	0.582967i	−0.0135721	+	0.0235075i
$616$		−	141.721i		−	5.71011i
$617$	−21.1584	−	12.2158i	−0.851807	−	0.491791i	0.00945324	−	0.999955i	$-0.496991\pi$
$617$	−21.1584	−	12.2158i	−0.851807	−	0.491791i	−0.861260	+	0.508164i	$0.830324\pi$
$618$	−2.00924	−	1.16004i	−0.0808237	−	0.0466636i
$619$		−	11.5324i		−	0.463528i	−0.972772	−	0.231764i	$-0.925550\pi$
$619$		−	11.5324i		−	0.463528i	0.972772	−	0.231764i	$-0.0744497\pi$
$620$	−20.7757	+	35.9846i	−0.834374	+	1.44518i
$621$	0.0413019	+	0.0715370i	0.00165739	+	0.00287068i
$622$	61.3990	−	35.4487i	2.46187	−	1.42136i
$623$	37.0676			1.48508
$624$	−9.49999	+	3.73381i	−0.380304	+	0.149472i
$625$	−21.3661			−0.854646
$626$	−16.6323	+	9.60268i	−0.664761	+	0.383800i
$627$	−1.43351	−	2.48292i	−0.0572490	−	0.0991582i
$628$	−10.8604	+	18.8108i	−0.433378	+	0.750633i
$629$			3.51043i			0.139970i
$630$	45.7892	+	26.4364i	1.82429	+	1.05325i
$631$	−27.1666	−	15.6846i	−1.08148	−	0.624396i	−0.150188	−	0.988657i	$-0.547988\pi$
$631$	−27.1666	−	15.6846i	−1.08148	−	0.624396i	−0.931297	+	0.364262i	$0.881321\pi$
$632$			63.3643i			2.52050i
$633$	0.962522	−	1.66714i	0.0382568	−	0.0662627i
$634$	46.5435	+	80.6156i	1.84848	+	3.20166i
$635$	−24.2263	+	13.9871i	−0.961391	+	0.555059i
$636$	−3.51980			−0.139569
$637$	−1.32878	+	8.84511i	−0.0526482	+	0.350456i
$638$	−114.601			−4.53710
$639$	−12.6115	+	7.28128i	−0.498905	+	0.288043i
$640$	57.6175	+	99.7965i	2.27753	+	3.94480i
$641$	11.5854	−	20.0664i	0.457594	−	0.792577i	−0.541239	−	0.840869i	$-0.682044\pi$
$641$	11.5854	−	20.0664i	0.457594	−	0.792577i	0.998833	+	0.0482920i	$0.0153778\pi$
$642$			0.137672i			0.00543348i
$643$	21.5598	+	12.4476i	0.850235	+	0.490884i	0.860730	−	0.509061i	$-0.170007\pi$
$643$	21.5598	+	12.4476i	0.850235	+	0.490884i	−0.0104950	+	0.999945i	$0.503341\pi$
$644$	1.23814	+	0.714842i	0.0487897	+	0.0281687i
$645$		−	3.47704i		−	0.136908i
$646$	5.18531	−	8.98122i	0.204013	−	0.353361i
$647$	18.0753	+	31.3074i	0.710615	+	1.23082i	0.964627	+	0.263620i	$0.0849166\pi$
$647$	18.0753	+	31.3074i	0.710615	+	1.23082i	−0.254012	+	0.967201i	$0.581750\pi$
$648$	76.8661	−	44.3787i	3.01958	−	1.74336i
$649$	−9.01640			−0.353925
$650$	−6.35625	−	0.954884i	−0.249313	−	0.0374536i
$651$	−1.82622			−0.0715752
$652$	76.3622	−	44.0878i	2.99058	−	1.72661i
$653$	−2.83043	−	4.90245i	−0.110763	−	0.191848i	0.805315	−	0.592847i	$-0.201996\pi$
$653$	−2.83043	−	4.90245i	−0.110763	−	0.191848i	−0.916078	+	0.401000i	$0.868663\pi$
$654$	1.31886	−	2.28434i	0.0515717	−	0.0893248i
$655$		−	33.8382i		−	1.32217i
$656$	27.7518	+	16.0225i	1.08353	+	0.625574i
$657$	−8.64323	−	4.99017i	−0.337204	−	0.194685i
$658$		−	60.4603i		−	2.35699i
$659$	9.60895	−	16.6432i	0.374312	−	0.648327i	−0.615912	−	0.787815i	$-0.711212\pi$
$659$	9.60895	−	16.6432i	0.374312	−	0.648327i	0.990224	+	0.139488i	$0.0445457\pi$
$660$	−4.52593	−	7.83915i	−0.176172	−	0.305138i
$661$	23.1553	−	13.3687i	0.900637	−	0.519983i	0.0232301	−	0.999730i	$-0.492605\pi$
$661$	23.1553	−	13.3687i	0.900637	−	0.519983i	0.877407	+	0.479747i	$0.159272\pi$
$662$	74.3884			2.89119
$663$	0.476021	+	0.379235i	0.0184871	+	0.0147283i
$664$	0.408912			0.0158689
$665$	20.8460	−	12.0354i	0.808373	−	0.466715i
$666$	14.4408	+	25.0122i	0.559570	+	0.969203i
$667$	0.374006	−	0.647798i	0.0144816	−	0.0250828i
$668$			110.184i			4.26315i
$669$	−2.82650	−	1.63188i	−0.109279	−	0.0630920i
$670$	−2.21107	−	1.27656i	−0.0854212	−	0.0493180i
$671$			11.3585i			0.438490i
$672$	−6.79197	+	11.7640i	−0.262006	+	0.453808i
$673$	10.9790	+	19.0161i	0.423208	+	0.733018i	0.996251	−	0.0865072i	$-0.0275706\pi$
$673$	10.9790	+	19.0161i	0.423208	+	0.733018i	−0.573043	+	0.819525i	$0.694237\pi$
$674$	−60.4706	+	34.9127i	−2.32924	+	1.34479i
$675$	−0.649004			−0.0249802
$676$	70.4066	+	21.6425i	2.70795	+	0.832403i
$677$	−29.5457			−1.13554			−0.567768	−	0.823189i	$-0.692193\pi$
$677$	−29.5457			−1.13554			−0.567768	+	0.823189i	$0.692193\pi$
$678$	2.73886	−	1.58128i	0.105185	−	0.0607287i
$679$	14.1034	+	24.4278i	0.541240	+	0.937455i
$680$	10.5925	−	18.3467i	0.406202	−	0.703562i
$681$			2.19789i			0.0842234i
$682$	−38.2044	−	22.0573i	−1.46292	−	0.844618i
$683$	−9.37686	−	5.41373i	−0.358796	−	0.207151i	0.309757	−	0.950816i	$-0.399752\pi$
$683$	−9.37686	−	5.41373i	−0.358796	−	0.207151i	−0.668552	+	0.743665i	$0.733086\pi$
$684$		−	63.0628i		−	2.41127i
$685$	−6.24104	+	10.8098i	−0.238458	+	0.413021i
$686$	−19.2639	−	33.3660i	−0.735499	−	1.27392i
$687$	3.07889	−	1.77760i	0.117467	−	0.0678196i
$688$	−165.522			−6.31048
$689$	10.3782	+	8.26808i	0.395378	+	0.314989i
$690$	0.0799377			0.00304317
$691$	12.3357	−	7.12202i	0.469272	−	0.270934i	−0.246663	−	0.969101i	$-0.579334\pi$
$691$	12.3357	−	7.12202i	0.469272	−	0.270934i	0.715935	+	0.698167i	$0.246001\pi$
$692$	65.9024	+	114.146i	2.50523	+	4.33919i
$693$	−20.7446	+	35.9308i	−0.788024	+	1.36490i
$694$		−	40.5263i		−	1.53836i
$695$	6.61119	+	3.81697i	0.250777	+	0.144786i
$696$	13.5439	+	7.81958i	0.513381	+	0.296401i
$697$		−	1.91069i		−	0.0723725i
$698$	6.43024	−	11.1375i	0.243388	−	0.421560i
$699$	−0.0202867	−	0.0351376i	−0.000767313	−	0.00132903i
$700$	−9.72788	+	5.61639i	−0.367679	+	0.212280i
$701$	−40.6705			−1.53610			−0.768051	−	0.640389i	$-0.778773\pi$
$701$	−40.6705			−1.53610			−0.768051	+	0.640389i	$0.778773\pi$
$702$	9.95099	+	1.49491i	0.375576	+	0.0564219i
$703$	13.1486			0.495911
$704$	−152.449	+	88.0168i	−5.74566	+	3.31726i
$705$	−1.24928	−	2.16381i	−0.0470506	−	0.0814940i
$706$	−23.0375	+	39.9020i	−0.867026	+	1.50173i
$707$		−	17.6574i		−	0.664073i
$708$	1.64693	+	0.950853i	0.0618952	+	0.0357352i
$709$	31.3581	+	18.1046i	1.17768	+	0.679933i	0.955477	−	0.295067i	$-0.0953420\pi$
$709$	31.3581	+	18.1046i	1.17768	+	0.679933i	0.222203	+	0.975001i	$0.428675\pi$
$710$			28.3202i			1.06284i
$711$	9.27504	−	16.0648i	0.347841	−	0.602478i
$712$	−61.0969	−	105.823i	−2.28970	−	3.96588i
$713$	0.249364	−	0.143970i	0.00933876	−	0.00539174i
$714$	1.43906			0.0538553
$715$	−5.06950	+	33.7454i	−0.189589	+	1.26201i
$716$	−9.34516			−0.349245
$717$	−2.90635	+	1.67798i	−0.108540	+	0.0626654i
$718$	33.0551	+	57.2532i	1.23361	+	2.13667i
$719$	−6.27711	+	10.8723i	−0.234097	+	0.405467i	−0.959010	−	0.283373i	$-0.908547\pi$
$719$	−6.27711	+	10.8723i	−0.234097	+	0.405467i	0.724913	+	0.688840i	$0.241880\pi$
$720$		−	104.016i		−	3.87644i
$721$	13.2372	+	7.64251i	0.492980	+	0.284622i
$722$	11.9184	+	6.88109i	0.443557	+	0.256088i
$723$		−	0.330560i		−	0.0122937i
$724$	−41.0357	+	71.0759i	−1.52508	+	2.64151i
$725$	2.93851	+	5.08964i	0.109133	+	0.189025i
$726$	3.87045	−	2.23461i	0.143646	−	0.0829341i
$727$	−29.3190			−1.08738			−0.543691	−	0.839285i	$-0.682974\pi$
$727$	−29.3190			−1.08738			−0.543691	+	0.839285i	$0.682974\pi$
$728$	104.876	−	41.2197i	3.88696	−	1.52770i
$729$	−25.4735			−0.943463
$730$	−16.8087	+	9.70451i	−0.622118	+	0.359180i
$731$	4.93464	+	8.54705i	0.182514	+	0.316124i
$732$	1.19784	−	2.07473i	0.0442736	−	0.0766842i
$733$		−	11.0117i		−	0.406728i	−0.979103	−	0.203364i	$-0.934813\pi$
$733$		−	11.0117i		−	0.406728i	0.979103	−	0.203364i	$-0.0651875\pi$
$734$	37.2592	+	21.5116i	1.37526	+	0.794008i
$735$	0.756888	+	0.436990i	0.0279182	+	0.0161186i
$736$		−	2.14179i		−	0.0789473i
$737$	1.00172	−	1.73503i	0.0368988	−	0.0639106i
$738$	−7.85996	−	13.6139i	−0.289329	−	0.501133i
$739$	−3.59769	+	2.07713i	−0.132343	+	0.0764084i	−0.564710	−	0.825289i	$-0.691012\pi$
$739$	−3.59769	+	2.07713i	−0.132343	+	0.0764084i	0.432367	+	0.901698i	$0.357679\pi$
$740$	41.5133			1.52606
$741$	1.42046	−	1.78298i	0.0521819	−	0.0654994i
$742$	31.3743			1.15179
$743$	27.7334	−	16.0119i	1.01744	−	0.587419i	0.104078	−	0.994569i	$-0.466811\pi$
$743$	27.7334	−	16.0119i	1.01744	−	0.587419i	0.913361	+	0.407150i	$0.133477\pi$
$744$	3.01008	+	5.21361i	0.110355	+	0.191140i
$745$	−0.361087	+	0.625422i	−0.0132292	+	0.0229137i
$746$		−	67.7020i		−	2.47875i
$747$	−0.103672	−	0.0598550i	−0.00379316	−	0.00218998i
$748$	22.2508	+	12.8465i	0.813569	+	0.469714i
$749$		−	0.907005i		−	0.0331412i
$750$	−2.75267	+	4.76776i	−0.100513	+	0.174094i
$751$	−4.69277	−	8.12811i	−0.171242	−	0.296599i	0.767613	−	0.640914i	$-0.221445\pi$
$751$	−4.69277	−	8.12811i	−0.171242	−	0.296599i	−0.938854	+	0.344315i	$0.888111\pi$
$752$	−103.007	+	59.4712i	−3.75629	+	2.16869i
$753$	−1.30674			−0.0476203
$754$	−33.3318	−	84.8065i	−1.21387	−	3.08847i
$755$	30.4102			1.10674
$756$	15.2294	−	8.79272i	0.553889	−	0.319788i
$757$	3.50430	+	6.06963i	0.127366	+	0.220604i	0.922655	−	0.385626i	$-0.126014\pi$
$757$	3.50430	+	6.06963i	0.127366	+	0.220604i	−0.795289	+	0.606230i	$0.792681\pi$
$758$	36.6272	−	63.4402i	1.33036	−	2.30425i
$759$			0.0627271i			0.00227685i
$760$	−68.7191	−	39.6750i	−2.49270	−	1.43916i
$761$	27.6990	+	15.9920i	1.00409	+	0.579711i	0.909455	−	0.415802i	$-0.136499\pi$
$761$	27.6990	+	15.9920i	1.00409	+	0.579711i	0.0946330	+	0.995512i	$0.469832\pi$
$762$			6.26415i			0.226926i
$763$	−8.68889	+	15.0496i	−0.314559	+	0.544832i
$764$	−24.3791	−	42.2258i	−0.882003	−	1.52767i
$765$	−5.37104	+	3.10097i	−0.194190	+	0.112116i
$766$	0.171464			0.00619525
$767$	−2.62243	−	6.67228i	−0.0946903	−	0.240922i
$768$	12.6985			0.458219
$769$	38.7544	−	22.3748i	1.39752	−	0.806858i	0.403386	−	0.915030i	$-0.367833\pi$
$769$	38.7544	−	22.3748i	1.39752	−	0.806858i	0.994132	+	0.108172i	$0.0344998\pi$
$770$	40.3426	+	69.8755i	1.45385	+	2.51814i
$771$	−0.0374923	+	0.0649385i	−0.00135025	+	0.00233870i
$772$			88.4320i			3.18274i
$773$	15.6875	+	9.05716i	0.564239	+	0.325763i	0.754845	−	0.655903i	$-0.227712\pi$
$773$	15.6875	+	9.05716i	0.564239	+	0.325763i	−0.190606	+	0.981667i	$0.561045\pi$
$774$	70.3197	+	40.5991i	2.52759	+	1.45930i
$775$			2.26230i			0.0812643i
$776$	46.4921	−	80.5267i	1.66897	−	2.89074i
$777$	0.912271	+	1.58010i	0.0327275	+	0.0566858i
$778$	−20.6522	+	11.9236i	−0.740417	+	0.427480i
$779$	−7.15666			−0.256414
$780$	4.48472	−	5.62928i	0.160579	−	0.201561i
$781$	−22.2228			−0.795195
$782$	−0.196498	+	0.113448i	−0.00702676	+	0.00405690i
$783$	−4.60036	−	7.96806i	−0.164404	−	0.284755i
$784$	20.8027	−	36.0313i	0.742952	−	1.28683i
$785$		−	8.00114i		−	0.285573i
$786$	−6.56211	−	3.78863i	−0.234063	−	0.135136i
$787$	−35.1518	−	20.2949i	−1.25303	−	0.723436i	−0.281318	−	0.959615i	$-0.590771\pi$
$787$	−35.1518	−	20.2949i	−1.25303	−	0.723436i	−0.971710	+	0.236179i	$0.924105\pi$
$788$			27.8866i			0.993419i
$789$	−0.433243	+	0.750399i	−0.0154239	+	0.0267149i
$790$	−18.0374	−	31.2417i	−0.641742	−	1.11153i
$791$	−18.0440	+	10.4177i	−0.641571	+	0.370411i
$792$	136.770			4.85991
$793$	−8.40546	+	3.30362i	−0.298487	+	0.117315i
$794$	−80.9093			−2.87136
$795$	1.12285	−	0.648280i	0.0398235	−	0.0229921i
$796$	61.8758	+	107.172i	2.19313	+	3.79861i
$797$	4.19343	−	7.26324i	0.148539	−	0.257277i	−0.782149	−	0.623092i	$-0.785876\pi$
$797$	4.19343	−	7.26324i	0.148539	−	0.257277i	0.930688	+	0.365815i	$0.119210\pi$
$798$		−	5.39011i		−	0.190808i
$799$	6.14181	+	3.54598i	0.217282	+	0.125448i
$800$	14.5732	+	8.41383i	0.515240	+	0.297474i
$801$			35.7726i			1.26396i
$802$	24.3723	−	42.2141i	0.860617	−	1.49063i
$803$	−7.61513	−	13.1898i	−0.268732	−	0.465458i
$804$	−0.365946	+	0.211279i	−0.0129059	+	0.00745123i
$805$	−0.526642			−0.0185617
$806$	5.21098	−	34.6872i	0.183549	−	1.22180i
$807$	−4.78499			−0.168440
$808$	−50.4094	+	29.1039i	−1.77339	+	1.02387i
$809$	−6.31255	−	10.9337i	−0.221938	−	0.384407i	0.733459	−	0.679734i	$-0.237905\pi$
$809$	−6.31255	−	10.9337i	−0.221938	−	0.384407i	−0.955396	+	0.295327i	$0.904571\pi$
$810$	−25.2658	+	43.7617i	−0.887751	+	1.53763i
$811$		−	8.02110i		−	0.281659i	−0.990034	−	0.140829i	$-0.955023\pi$
$811$		−	8.02110i		−	0.281659i	0.990034	−	0.140829i	$-0.0449769\pi$
$812$	−137.909	−	79.6218i	−4.83966	−	2.79418i
$813$	−0.604459	−	0.348985i	−0.0211993	−	0.0122394i
$814$			44.0741i			1.54480i
$815$	−16.2403	+	28.1290i	−0.568872	+	0.985314i
$816$	−1.41551	−	2.45174i	−0.0495529	−	0.0858281i
$817$	32.0138	−	18.4832i	1.12002	−	0.646644i
$818$	−56.9601			−1.99156
$819$	−32.6229	−	4.90087i	−1.13994	−	0.171250i
$820$	−22.5952			−0.789059
$821$	39.5104	−	22.8113i	1.37892	−	0.796121i	0.386893	−	0.922125i	$-0.373548\pi$
$821$	39.5104	−	22.8113i	1.37892	−	0.796121i	0.992030	+	0.126003i	$0.0402150\pi$
$822$	1.39754	+	2.42060i	0.0487446	+	0.0844282i
$823$	−26.3091	+	45.5688i	−0.917079	+	1.58843i	−0.113250	+	0.993567i	$0.536126\pi$
$823$	−26.3091	+	45.5688i	−0.917079	+	1.58843i	−0.803829	+	0.594861i	$0.797207\pi$
$824$		−	50.3873i		−	1.75532i
$825$	−0.426808	−	0.246418i	−0.0148596	−	0.00857917i
$826$	−14.6801	−	8.47558i	−0.510787	−	0.294903i
$827$		−	5.96244i		−	0.207334i	−0.994612	−	0.103667i	$-0.966942\pi$
$827$		−	5.96244i		−	0.207334i	0.994612	−	0.103667i	$-0.0330577\pi$
$828$	−0.689868	+	1.19489i	−0.0239746	+	0.0415252i
$829$	−26.8943	−	46.5823i	−0.934077	−	1.61787i	−0.776271	−	0.630400i	$-0.782891\pi$
$829$	−26.8943	−	46.5823i	−0.934077	−	1.61787i	−0.157807	−	0.987470i	$-0.550442\pi$
$830$	−0.201614	+	0.116402i	−0.00699811	+	0.00404036i
$831$	−1.14707			−0.0397915
$832$	−109.474	−	87.2152i	−3.79532	−	3.02364i
$833$	−2.48072			−0.0859518
$834$	1.48042	−	0.854722i	0.0512628	−	0.0295966i
$835$	−20.2938	−	35.1499i	−0.702296	−	1.21641i
$836$	48.1177	−	83.3423i	1.66419	−	2.88246i
$837$		−	3.54174i		−	0.122420i
$838$	−52.6338	−	30.3882i	−1.81821	−	1.04974i
$839$	11.3151	+	6.53276i	0.390640	+	0.225536i	0.682437	−	0.730944i	$-0.260920\pi$
$839$	11.3151	+	6.53276i	0.390640	+	0.225536i	−0.291798	+	0.956480i	$0.594253\pi$
$840$		−	11.0108i		−	0.379909i
$841$	−27.1582	+	47.0395i	−0.936491	+	1.62205i
$842$	1.77775	+	3.07915i	0.0612652	+	0.106114i
$843$	4.17088	−	2.40806i	0.143653	−	0.0829379i
$844$	64.6166			2.22419
$845$	−26.4466	+	6.06338i	−0.909791	+	0.208586i
$846$	58.3481			2.00605
$847$	−25.4992	+	14.7219i	−0.876161	+	0.505852i
$848$	−30.8610	−	53.4528i	−1.05977	−	1.83558i
$849$	−1.05884	+	1.83396i	−0.0363393	+	0.0629414i
$850$		−	1.78269i		−	0.0611457i
$851$	−0.249135	−	0.143838i	−0.00854024	−	0.00493071i
$852$	4.05919	+	2.34358i	0.139066	+	0.0802896i
$853$		−	0.787657i		−	0.0269689i	−0.999909	−	0.0134844i	$-0.995708\pi$
$853$		−	0.787657i		−	0.0269689i	0.999909	−	0.0134844i	$-0.00429236\pi$
$854$	−10.6772	+	18.4934i	−0.365366	+	0.632832i
$855$	11.6150	+	20.1177i	0.397224	+	0.688012i
$856$	−2.58938	+	1.49498i	−0.0885031	+	0.0510973i
$857$	−19.3791			−0.661977			−0.330988	−	0.943635i	$-0.607382\pi$
$857$	−19.3791			−0.661977			−0.330988	+	0.943635i	$0.607382\pi$
$858$	5.97653	+	4.76136i	0.204035	+	0.162550i
$859$	22.1171			0.754624			0.377312	−	0.926086i	$-0.376848\pi$
$859$	22.1171			0.754624			0.377312	+	0.926086i	$0.376848\pi$
$860$	101.075	−	58.3556i	3.44662	−	1.98991i
$861$	−0.496539	−	0.860030i	−0.0169220	−	0.0293097i
$862$	24.3464	−	42.1692i	0.829241	−	1.43629i
$863$			17.2929i			0.588656i	0.955704	+	0.294328i	$0.0950959\pi$
$863$			17.2929i			0.588656i	−0.955704	+	0.294328i	$0.904904\pi$
$864$	−22.8150	−	13.1722i	−0.776181	−	0.448128i
$865$	−42.0472	−	24.2760i	−1.42965	−	0.825408i
$866$			103.487i			3.51662i
$867$	−0.0844000	+	0.146185i	−0.00286638	+	0.00496471i
$868$	−30.6497	−	53.0868i	−1.04032	−	1.80188i
$869$	24.5154	−	14.1539i	0.831627	−	0.480140i
$870$	−8.90376			−0.301866
$871$	1.57530	+	0.236653i	0.0533770	+	0.00801870i
$872$	57.2861			1.93995
$873$	−23.5744	+	13.6107i	−0.797874	+	0.460653i
$874$	0.424931	+	0.736002i	0.0143735	+	0.0248956i
$875$	18.1350	−	31.4108i	0.613075	−	1.06188i
$876$			3.21231i			0.108534i
$877$	37.3731	+	21.5774i	1.26200	+	0.728616i	0.973461	−	0.228852i	$-0.0734973\pi$
$877$	37.3731	+	21.5774i	1.26200	+	0.728616i	0.288539	+	0.957468i	$0.406831\pi$
$878$	−47.1555	−	27.2252i	−1.59142	−	0.918807i
$879$			5.50129i			0.185554i
$880$	79.3653	−	137.465i	2.67540	−	4.63394i
$881$	11.2820	+	19.5410i	0.380101	+	0.658354i	0.991076	−	0.133295i	$-0.0425559\pi$
$881$	11.2820	+	19.5410i	0.380101	+	0.658354i	−0.610975	+	0.791650i	$0.709223\pi$
$882$	−17.6754	+	10.2049i	−0.595161	+	0.343617i
$883$	−40.6625			−1.36840			−0.684201	−	0.729294i	$-0.739849\pi$
$883$	−40.6625			−1.36840			−0.684201	+	0.729294i	$0.739849\pi$
$884$	−3.03495	+	20.2023i	−0.102076	+	0.679478i
$885$	−0.700516			−0.0235476
$886$	37.8182	−	21.8343i	1.27053	−	0.733539i
$887$	10.5679	+	18.3042i	0.354836	+	0.614594i	0.987090	−	0.160168i	$-0.0512035\pi$
$887$	10.5679	+	18.3042i	0.354836	+	0.614594i	−0.632254	+	0.774761i	$0.717870\pi$
$888$	3.00731	−	5.20882i	0.100919	−	0.174797i
$889$		−	41.2692i		−	1.38412i
$890$	60.2475	+	34.7839i	2.01950	+	1.16596i
$891$	−34.3398	−	19.8261i	−1.15043	−	0.664199i
$892$		−	109.552i		−	3.66808i
$893$	13.2818	−	23.0047i	0.444458	−	0.769824i
$894$	0.0808571	+	0.140049i	0.00270427	+	0.00468393i
$895$	2.98121	−	1.72120i	0.0996508	−	0.0575334i
$896$	−170.002			−5.67937
$897$	−0.0464190	+	0.0182442i	−0.00154989	+	0.000609156i
$898$	30.3971			1.01436
$899$	−27.7751	+	16.0360i	−0.926352	+	0.534830i
$900$	−5.42018	−	9.38803i	−0.180673	−	0.312934i
$901$	−1.84009	+	3.18713i	−0.0613023	+	0.106179i
$902$		−	23.9890i		−	0.798747i
$903$	4.44232	+	2.56477i	0.147831	+	0.0853503i
$904$	59.4823	+	34.3421i	1.97835	+	1.14220i
$905$		−	30.2320i		−	1.00495i
$906$	3.40483	−	5.89734i	0.113118	−	0.195926i
$907$	−13.7288	−	23.7790i	−0.455857	−	0.789567i	0.542880	−	0.839810i	$-0.317334\pi$
$907$	−13.7288	−	23.7790i	−0.455857	−	0.789567i	−0.998737	+	0.0502429i	$0.984000\pi$
$908$	−63.8911	+	36.8875i	−2.12030	+	1.22416i
$909$	17.0405			0.565197
$910$	−39.9753	+	50.1775i	−1.32517	+	1.66337i
$911$	−17.0854			−0.566066			−0.283033	−	0.959110i	$-0.591341\pi$
$911$	−17.0854			−0.566066			−0.283033	+	0.959110i	$0.591341\pi$
$912$	−9.18322	+	5.30193i	−0.304087	+	0.175565i
$913$	−0.0913404	−	0.158206i	−0.00302292	−	0.00523586i
$914$	19.5343	−	33.8343i	0.646136	−	1.11914i
$915$			0.882482i			0.0291739i
$916$	103.347	+	59.6673i	3.41468	+	1.97146i
$917$	43.2322	+	24.9601i	1.42765	+	0.824256i
$918$			2.79088i			0.0921127i
$919$	5.61587	−	9.72698i	0.185251	−	0.320863i	−0.758410	−	0.651777i	$-0.774024\pi$
$919$	5.61587	−	9.72698i	0.185251	−	0.320863i	0.943661	+	0.330914i	$0.107357\pi$
$920$	0.868041	+	1.50349i	0.0286185	+	0.0495686i
$921$	−0.824586	+	0.476075i	−0.0271710	+	0.0156872i
$922$	83.7882			2.75942
$923$	−6.46352	−	16.4452i	−0.212750	−	0.541302i
$924$	13.3539			0.439311
$925$	1.95741	−	1.13011i	0.0643593	−	0.0371579i
$926$	−55.1926	−	95.5964i	−1.81374	−	3.14149i
$927$	−7.37551	+	12.7748i	−0.242244	+	0.419578i
$928$			238.560i			7.83113i
$929$	−0.0374602	−	0.0216276i	−0.00122903	−	0.000709579i	0.499385	−	0.866380i	$-0.333559\pi$
$929$	−0.0374602	−	0.0216276i	−0.00122903	−	0.000709579i	−0.500614	+	0.865670i	$0.666893\pi$
$930$	−2.96823	−	1.71371i	−0.0973322	−	0.0561948i
$931$			9.29176i			0.304525i
$932$	0.680949	−	1.17944i	0.0223052	−	0.0386338i
$933$	2.16117	+	3.74326i	0.0707535	+	0.122549i
$934$	54.5340	−	31.4852i	1.78441	−	1.03023i
$935$	−9.46432			−0.309516
$936$	39.7796	+	101.212i	1.30024	+	3.30821i
$937$	−54.9392			−1.79479			−0.897393	−	0.441233i	$-0.854541\pi$
$937$	−54.9392			−1.79479			−0.897393	+	0.441233i	$0.854541\pi$
$938$	3.26192	−	1.88327i	0.106505	−	0.0614909i
$939$	−0.585438	−	1.01401i	−0.0191050	−	0.0330909i
$940$	41.9337	−	72.6312i	1.36772	−	2.36897i
$941$		−	56.3882i		−	1.83820i	−0.394021	−	0.919102i	$-0.628916\pi$
$941$		−	56.3882i		−	1.83820i	0.394021	−	0.919102i	$-0.371084\pi$
$942$	−1.55163	−	0.895834i	−0.0505548	−	0.0291879i
$943$	0.135601	+	0.0782895i	0.00441579	+	0.00254946i
$944$			33.3477i			1.08538i
$945$	−3.23890	+	5.60995i	−0.105362	+	0.182492i
$946$	61.9553	+	107.310i	2.01434	+	3.48894i
$947$	−15.0727	+	8.70223i	−0.489797	+	0.282785i	−0.724490	−	0.689285i	$-0.757925\pi$
$947$	−15.0727	+	8.70223i	−0.489797	+	0.282785i	0.234693	+	0.972070i	$0.424591\pi$
$948$	−5.97059			−0.193916
$949$	7.54578	−	9.47157i	0.244947	−	0.307460i
$950$	−6.67722			−0.216638
$951$	−4.91482	+	2.83757i	−0.159374	+	0.0920146i
$952$	15.6267	+	27.0662i	0.506463	+	0.877220i
$953$	5.81119	−	10.0653i	0.188243	−	0.326046i	−0.756422	−	0.654084i	$-0.773054\pi$
$953$	5.81119	−	10.0653i	0.188243	−	0.326046i	0.944665	+	0.328038i	$0.106387\pi$
$954$			30.2782i			0.980292i
$955$	15.5544	+	8.98032i	0.503328	+	0.290596i
$956$	−97.5555	−	56.3237i	−3.15517	−	1.82164i
$957$		−	6.98678i		−	0.225850i
$958$	−46.2833	+	80.1651i	−1.49535	+	2.59002i
$959$	−9.20718	−	15.9473i	−0.297315	−	0.514965i
$960$	−11.8443	+	6.83833i	−0.382274	+	0.220706i
$961$	18.6542			0.601748
$962$	−32.6155	+	12.8190i	−1.05157	+	0.413300i
$963$	0.875318			0.0282067
$964$	9.60915	−	5.54784i	0.309490	−	0.178684i
$965$	−16.2875	−	28.2108i	−0.524313	−	0.908137i
$966$	−0.0589646	+	0.102130i	−0.00189715	+	0.00328597i
$967$			24.8655i			0.799620i	0.916598	+	0.399810i	$0.130924\pi$
$967$			24.8655i			0.799620i	−0.916598	+	0.399810i	$0.869076\pi$
$968$	84.0583	+	48.5311i	2.70174	+	1.55985i
$969$	0.547550	+	0.316128i	0.0175898	+	0.0101555i
$970$			52.9382i			1.69974i
$971$	−26.3429	+	45.6273i	−0.845384	+	1.46425i	0.0399028	+	0.999204i	$0.487295\pi$
$971$	−26.3429	+	45.6273i	−0.845384	+	1.46425i	−0.885287	+	0.465045i	$0.846038\pi$
$972$	12.7485	+	22.0811i	0.408910	+	0.708252i
$973$	−9.75325	+	5.63104i	−0.312675	+	0.180523i
$974$	41.6770			1.33542
$975$	0.0582156	−	0.387516i	0.00186439	−	0.0124104i
$976$	42.0101			1.34471
$977$	−22.5459	+	13.0169i	−0.721306	+	0.416446i	−0.815233	−	0.579133i	$-0.803391\pi$
$977$	−22.5459	+	13.0169i	−0.721306	+	0.416446i	0.0939270	+	0.995579i	$0.470058\pi$
$978$	3.63663	+	6.29883i	0.116287	+	0.201414i
$979$	−27.2949	+	47.2762i	−0.872350	+	1.51095i
$980$			29.3362i			0.937112i
$981$	−14.5238	−	8.38533i	−0.463710	−	0.267723i
$982$	−52.1758	−	30.1237i	−1.66500	−	0.961285i
$983$		−	7.27554i		−	0.232054i	−0.993246	−	0.116027i	$-0.962984\pi$
$983$		−	7.27554i		−	0.232054i	0.993246	−	0.116027i	$-0.0370159\pi$
$984$	−1.63685	+	2.83510i	−0.0521808	+	0.0903797i
$985$	−5.13619	−	8.89613i	−0.163652	−	0.283454i
$986$	21.8867	−	12.6363i	0.697014	−	0.402422i
$987$	3.68603			0.117328
$988$	75.6697	+	11.3677i	2.40737	+	0.361654i
$989$	−0.808778			−0.0257176
$990$	−67.4343	+	38.9332i	−2.14320	+	1.23738i
$991$	−23.1920	−	40.1697i	−0.736718	−	1.27603i	−0.953966	−	0.299916i	$-0.903041\pi$
$991$	−23.1920	−	40.1697i	−0.736718	−	1.27603i	0.217248	−	0.976116i	$-0.430292\pi$
$992$	−45.9158	+	79.5286i	−1.45783	+	2.52503i
$993$			4.53517i			0.143919i
$994$	−36.1823	−	20.8899i	−1.14763	−	0.662586i
$995$	−39.4781	−	22.7927i	−1.25154	−	0.722577i
$996$			0.0385303i			0.00122088i
$997$	−13.5467	+	23.4635i	−0.429027	+	0.743097i	−0.996787	−	0.0800972i	$-0.974477\pi$
$997$	−13.5467	+	23.4635i	−0.429027	+	0.743097i	0.567760	+	0.823194i	$0.307810\pi$
$998$	−21.6184	−	37.4442i	−0.684319	−	1.18528i
$999$	−3.06442	+	1.76924i	−0.0969538	+	0.0559763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.c.205.1	yes	22
13.2	odd	12		2873.2.a.x.1.1		22
13.4	even	6	inner	221.2.m.c.69.1	✓	22
13.11	odd	12		2873.2.a.x.1.22		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.c.69.1	✓	22	13.4	even	6	inner
221.2.m.c.205.1	yes	22	1.1	even	1	trivial
2873.2.a.x.1.1		22	13.2	odd	12
2873.2.a.x.1.22		22	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39781 + 1.38438i) q^{2} +(-0.0844000 - 0.146185i) q^{3} +(2.83300 - 4.90689i) q^{4} +2.08714i q^{5} +(0.404751 + 0.233683i) q^{6} +(-2.66656 - 1.53954i) q^{7} +10.1502i q^{8} +(1.48575 - 2.57340i) q^{9} +(-2.88938 - 5.00456i) q^{10} +(3.92708 - 2.26730i) q^{11} -0.956420 q^{12} +(2.82003 + 2.24665i) q^{13} +8.52520 q^{14} +(0.305108 - 0.176154i) q^{15} +(-8.38574 - 14.5245i) q^{16} +(-0.500000 + 0.866025i) q^{17} +8.22737i q^{18} +(3.24378 + 1.87280i) q^{19} +(10.2414 + 5.91285i) q^{20} +0.519749i q^{21} +(-6.27759 + 10.8731i) q^{22} +(-0.0409745 - 0.0709699i) q^{23} +(1.48381 - 0.856679i) q^{24} +0.643859 q^{25} +(-9.87210 - 1.48306i) q^{26} -1.00799 q^{27} +(-15.1087 + 8.72301i) q^{28} +(4.56389 + 7.90490i) q^{29} +(-0.487728 + 0.844770i) q^{30} +3.51366i q^{31} +(22.6341 + 13.0678i) q^{32} +(-0.662891 - 0.382720i) q^{33} -2.76875i q^{34} +(3.21323 - 5.56547i) q^{35} +(-8.41826 - 14.5809i) q^{36} +(3.04012 - 1.75522i) q^{37} -10.3706 q^{38} +(0.0904166 - 0.601864i) q^{39} -21.1849 q^{40} +(-1.65470 + 0.955344i) q^{41} +(-0.719528 - 1.24626i) q^{42} +(4.93464 - 8.54705i) q^{43} -25.6930i q^{44} +(5.37104 + 3.10097i) q^{45} +(0.196498 + 0.113448i) q^{46} -7.09195i q^{47} +(-1.41551 + 2.45174i) q^{48} +(1.24036 + 2.14837i) q^{49} +(-1.54385 + 0.891344i) q^{50} +0.168800 q^{51} +(19.0132 - 7.47282i) q^{52} +3.68018 q^{53} +(2.41697 - 1.39544i) q^{54} +(4.73216 + 8.19635i) q^{55} +(15.6267 - 27.0662i) q^{56} -0.632256i q^{57} +(-21.8867 - 12.6363i) q^{58} +(-1.72197 - 0.994179i) q^{59} -1.99618i q^{60} +(-1.25243 + 2.16927i) q^{61} +(-4.86423 - 8.42509i) q^{62} +(-7.92370 + 4.57475i) q^{63} -38.8201 q^{64} +(-4.68907 + 5.88578i) q^{65} +2.11931 q^{66} +(0.382620 - 0.220906i) q^{67} +(2.83300 + 4.90689i) q^{68} +(-0.00691650 + 0.0119797i) q^{69} +17.7933i q^{70} +(-4.24416 - 2.45036i) q^{71} +(26.1206 + 15.0807i) q^{72} -3.35868i q^{73} +(-4.85976 + 8.41735i) q^{74} +(-0.0543418 - 0.0941227i) q^{75} +(18.3792 - 10.6112i) q^{76} -13.9624 q^{77} +(0.616404 + 1.56833i) q^{78} +6.24265 q^{79} +(30.3147 - 17.5022i) q^{80} +(-4.37219 - 7.57285i) q^{81} +(2.64511 - 4.58147i) q^{82} -0.0402860i q^{83} +(2.55035 + 1.47245i) q^{84} +(-1.80751 - 1.04357i) q^{85} +27.3256i q^{86} +(0.770386 - 1.33435i) q^{87} +(23.0136 + 39.8607i) q^{88} +(-10.4257 + 6.01926i) q^{89} -17.1716 q^{90} +(-4.06097 - 10.3324i) q^{91} -0.464322 q^{92} +(0.513645 - 0.296553i) q^{93} +(9.81793 + 17.0052i) q^{94} +(-3.90878 + 6.77021i) q^{95} -4.41169i q^{96} +(-7.93350 - 4.58041i) q^{97} +(-5.94829 - 3.43425i) q^{98} -13.4746i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) \) 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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