LMFDB - Embedded newform 221.2.m.b.69.1

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 = [12] 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 13x^{10} + 57x^{8} + 104x^{6} + 78x^{4} + 19x^{2} + 1 $ x^12 + 13x^10 + 57x^8 + 104x^6 + 78x^4 + 19*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.1
Root			$-2.48782i$ of defining polynomial
Character	$\chi$	$=$	221.69
Dual form			221.2.m.b.205.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.15452 - 1.24391i) q^{2} +(1.53909 - 2.66579i) q^{3} +(2.09463 + 3.62801i) q^{4} +1.33009i q^{5} +(-6.63201 + 3.82899i) q^{6} +(0.686981 - 0.396628i) q^{7} -5.44652i q^{8} +(-3.23761 - 5.60771i) q^{9} +(1.65452 - 2.86571i) q^{10} +(-5.52984 - 3.19266i) q^{11} +12.8953 q^{12} +(-0.414751 - 3.58162i) q^{13} -1.97348 q^{14} +(3.54575 + 2.04714i) q^{15} +(-2.58572 + 4.47860i) q^{16} +(0.500000 + 0.866025i) q^{17} +16.1092i q^{18} +(-0.771327 + 0.445326i) q^{19} +(-4.82560 + 2.78606i) q^{20} -2.44179i q^{21} +(7.94277 + 13.7573i) q^{22} +(-0.384465 + 0.665912i) q^{23} +(-14.5193 - 8.38270i) q^{24} +3.23085 q^{25} +(-3.56163 + 8.23258i) q^{26} -10.6974 q^{27} +(2.87795 + 1.66158i) q^{28} +(3.23415 - 5.60172i) q^{29} +(-5.09292 - 8.82119i) q^{30} -2.46567i q^{31} +(1.70832 - 0.986298i) q^{32} +(-17.0219 + 9.82759i) q^{33} -2.48782i q^{34} +(0.527553 + 0.913748i) q^{35} +(13.5632 - 23.4922i) q^{36} +(9.43182 + 5.44546i) q^{37} +2.21579 q^{38} +(-10.1862 - 4.40680i) q^{39} +7.24437 q^{40} +(7.87397 + 4.54604i) q^{41} +(-3.03737 + 5.26089i) q^{42} +(-0.0438926 - 0.0760242i) q^{43} -26.7498i q^{44} +(7.45878 - 4.30633i) q^{45} +(1.65667 - 0.956481i) q^{46} -1.05200i q^{47} +(7.95932 + 13.7860i) q^{48} +(-3.18537 + 5.51723i) q^{49} +(-6.96093 - 4.01890i) q^{50} +3.07819 q^{51} +(12.1254 - 9.00690i) q^{52} +4.07542 q^{53} +(23.0477 + 13.3066i) q^{54} +(4.24653 - 7.35520i) q^{55} +(-2.16024 - 3.74165i) q^{56} +2.74159i q^{57} +(-13.9361 + 8.04600i) q^{58} +(0.891880 - 0.514927i) q^{59} +17.1520i q^{60} +(1.59965 + 2.77068i) q^{61} +(-3.06708 + 5.31234i) q^{62} +(-4.44836 - 2.56826i) q^{63} +5.43541 q^{64} +(4.76388 - 0.551658i) q^{65} +48.8986 q^{66} +(4.80857 + 2.77623i) q^{67} +(-2.09463 + 3.62801i) q^{68} +(1.18345 + 2.04980i) q^{69} -2.62492i q^{70} +(0.884278 - 0.510538i) q^{71} +(-30.5425 + 17.6337i) q^{72} -8.97575i q^{73} +(-13.5474 - 23.4647i) q^{74} +(4.97258 - 8.61276i) q^{75} +(-3.23130 - 1.86559i) q^{76} -5.06519 q^{77} +(16.4646 + 22.1652i) q^{78} -15.5979 q^{79} +(-5.95695 - 3.43925i) q^{80} +(-6.75144 + 11.6938i) q^{81} +(-11.3097 - 19.5890i) q^{82} -0.771107i q^{83} +(8.85885 - 5.11466i) q^{84} +(-1.15189 + 0.665047i) q^{85} +0.218394i q^{86} +(-9.95532 - 17.2431i) q^{87} +(-17.3889 + 30.1184i) q^{88} +(3.49602 + 2.01843i) q^{89} -21.4268 q^{90} +(-1.70550 - 2.29600i) q^{91} -3.22125 q^{92} +(-6.57296 - 3.79490i) q^{93} +(-1.30860 + 2.26656i) q^{94} +(-0.592325 - 1.02594i) q^{95} -6.07201i q^{96} +(-7.76306 + 4.48201i) q^{97} +(13.7259 - 7.92464i) q^{98} +41.3463i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 4 q^{3} + q^{4} - 12 q^{6} - 4 q^{9} - 3 q^{10} - 24 q^{11} + 20 q^{12} + 7 q^{13} + 10 q^{14} + 9 q^{15} - q^{16} + 6 q^{17} + 15 q^{19} - 18 q^{20} + 11 q^{22} - 12 q^{23} - 42 q^{24}+ \cdots - 30 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 4 * q^3 + q^4 - 12 * q^6 - 4 * q^9 - 3 * q^10 - 24 * q^11 + 20 * q^12 + 7 * q^13 + 10 * q^14 + 9 * q^15 - q^16 + 6 * q^17 + 15 * q^19 - 18 * q^20 + 11 * q^22 - 12 * q^23 - 42 * q^24 + 22 * q^25 - 8 * q^26 - 20 * q^27 - 3 * q^28 + 11 * q^29 - 8 * q^30 + 24 * q^32 - 54 * q^33 + 4 * q^35 + 23 * q^36 - 18 * q^37 + 12 * q^38 - 38 * q^39 + 34 * q^40 + 3 * q^41 + 7 * q^42 - 2 * q^43 + 15 * q^45 + 21 * q^46 + 17 * q^48 - 2 * q^49 - 33 * q^50 + 8 * q^51 + 42 * q^52 + 6 * q^53 + 30 * q^54 + 22 * q^55 - 21 * q^56 - 9 * q^58 - 3 * q^59 + 13 * q^61 - 15 * q^62 - 51 * q^63 - 14 * q^65 + 112 * q^66 - 21 * q^67 - q^68 - 4 * q^69 + 18 * q^71 - 81 * q^72 - 24 * q^74 - 2 * q^75 - 45 * q^76 + 38 * q^77 + 28 * q^78 - 38 * q^79 + 33 * q^80 + 6 * q^81 - 32 * q^82 + 33 * q^84 - 9 * q^85 + 23 * q^87 - 39 * q^88 - 12 * q^89 - 40 * q^90 - 14 * q^91 + 10 * q^92 - 21 * q^93 + 25 * q^94 - 13 * q^95 + 36 * q^97 - 30 * q^98

Character values

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

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

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 $

$2$	−2.15452	−	1.24391i	−1.52347	−	0.879579i	−0.999614	−	0.0277748i	$-0.991158\pi$
$2$	−2.15452	−	1.24391i	−1.52347	−	0.879579i	−0.523861	−	0.851804i	$-0.675509\pi$
$3$	1.53909	−	2.66579i	0.888596	−	1.53909i	0.0470595	−	0.998892i	$-0.485015\pi$
$3$	1.53909	−	2.66579i	0.888596	−	1.53909i	0.841536	−	0.540201i	$-0.181652\pi$
$4$	2.09463	+	3.62801i	1.04732	+	1.81401i
$5$			1.33009i			0.594836i	0.954747	+	0.297418i	$0.0961254\pi$
$5$			1.33009i			0.594836i	−0.954747	+	0.297418i	$0.903875\pi$
$6$	−6.63201	+	3.82899i	−2.70751	+	1.56318i
$7$	0.686981	−	0.396628i	0.259654	−	0.149911i	−0.364523	−	0.931195i	$-0.618768\pi$
$7$	0.686981	−	0.396628i	0.259654	−	0.149911i	0.624177	+	0.781283i	$0.285434\pi$
$8$		−	5.44652i		−	1.92563i
$9$	−3.23761	−	5.60771i	−1.07920	−	1.86924i
$10$	1.65452	−	2.86571i	0.523205	−	0.906217i
$11$	−5.52984	−	3.19266i	−1.66731	−	0.962622i	−0.969079	−	0.246749i	$-0.920638\pi$
$11$	−5.52984	−	3.19266i	−1.66731	−	0.962622i	−0.698230	−	0.715873i	$-0.746029\pi$
$12$	12.8953			3.72257
$13$	−0.414751	−	3.58162i	−0.115031	−	0.993362i
$13$	−0.414751	−	3.58162i	−0.115031	−	0.993362i
$14$	−1.97348			−0.527436
$15$	3.54575	+	2.04714i	0.915507	+	0.528568i
$16$	−2.58572	+	4.47860i	−0.646430	+	1.11965i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$			16.1092i			3.79698i
$19$	−0.771327	+	0.445326i	−0.176955	+	0.102165i	−0.585861	−	0.810412i	$-0.699244\pi$
$19$	−0.771327	+	0.445326i	−0.176955	+	0.102165i	0.408906	+	0.912576i	$0.365910\pi$
$20$	−4.82560	+	2.78606i	−1.07904	+	0.622982i
$21$		−	2.44179i		−	0.532843i
$22$	7.94277	+	13.7573i	1.69340	+	2.93306i
$23$	−0.384465	+	0.665912i	−0.0801664	+	0.138852i	−0.903321	−	0.428965i	$-0.858879\pi$
$23$	−0.384465	+	0.665912i	−0.0801664	+	0.138852i	0.823155	+	0.567817i	$0.192212\pi$
$24$	−14.5193	−	8.38270i	−2.96373	−	1.71111i
$25$	3.23085			0.646170
$26$	−3.56163	+	8.23258i	−0.698493	+	1.61454i
$27$	−10.6974			−2.05871
$28$	2.87795	+	1.66158i	0.543881	+	0.314010i
$29$	3.23415	−	5.60172i	0.600567	−	1.04021i	−0.392168	−	0.919893i	$-0.628275\pi$
$29$	3.23415	−	5.60172i	0.600567	−	1.04021i	0.992735	−	0.120319i	$-0.0383918\pi$
$30$	−5.09292	−	8.82119i	−0.929835	−	1.61052i
$31$		−	2.46567i		−	0.442848i	−0.975178	−	0.221424i	$-0.928930\pi$
$31$		−	2.46567i		−	0.442848i	0.975178	−	0.221424i	$-0.0710705\pi$
$32$	1.70832	−	0.986298i	0.301991	−	0.174354i
$33$	−17.0219	+	9.82759i	−2.96313	+	1.71076i
$34$		−	2.48782i		−	0.426658i
$35$	0.527553	+	0.913748i	0.0891727	+	0.154452i
$36$	13.5632	−	23.4922i	2.26054	−	3.91537i
$37$	9.43182	+	5.44546i	1.55058	+	0.895228i	0.998094	+	0.0617068i	$0.0196544\pi$
$37$	9.43182	+	5.44546i	1.55058	+	0.895228i	0.552487	+	0.833522i	$0.313679\pi$
$38$	2.21579			0.359448
$39$	−10.1862	−	4.40680i	−1.63109	−	0.705653i
$40$	7.24437			1.14544
$41$	7.87397	+	4.54604i	1.22971	+	0.709972i	0.966969	−	0.254896i	$-0.0820411\pi$
$41$	7.87397	+	4.54604i	1.22971	+	0.709972i	0.262738	+	0.964867i	$0.415374\pi$
$42$	−3.03737	+	5.26089i	−0.468677	+	0.811773i
$43$	−0.0438926	−	0.0760242i	−0.00669356	−	0.0115936i	0.862659	−	0.505786i	$-0.168797\pi$
$43$	−0.0438926	−	0.0760242i	−0.00669356	−	0.0115936i	−0.869353	+	0.494192i	$0.835464\pi$
$44$		−	26.7498i		−	4.03268i
$45$	7.45878	−	4.30633i	1.11189	−	0.641949i
$46$	1.65667	−	0.956481i	0.244263	−	0.141025i
$47$		−	1.05200i		−	0.153451i	−0.997052	−	0.0767253i	$-0.975554\pi$
$47$		−	1.05200i		−	0.153451i	0.997052	−	0.0767253i	$-0.0244465\pi$
$48$	7.95932	+	13.7860i	1.14883	+	1.98983i
$49$	−3.18537	+	5.51723i	−0.455053	+	0.788175i
$50$	−6.96093	−	4.01890i	−0.984424	−	0.568358i
$51$	3.07819			0.431032
$52$	12.1254	−	9.00690i	1.68149	−	1.24903i
$53$	4.07542			0.559802			0.279901	−	0.960029i	$-0.409698\pi$
$53$	4.07542			0.559802			0.279901	+	0.960029i	$0.409698\pi$
$54$	23.0477	+	13.3066i	3.13640	+	1.81080i
$55$	4.24653	−	7.35520i	0.572602	−	0.991776i
$56$	−2.16024	−	3.74165i	−0.288675	−	0.499999i
$57$			2.74159i			0.363133i
$58$	−13.9361	+	8.04600i	−1.82990	+	1.05649i
$59$	0.891880	−	0.514927i	0.116113	−	0.0670378i	−0.440819	−	0.897596i	$-0.645312\pi$
$59$	0.891880	−	0.514927i	0.116113	−	0.0670378i	0.556932	+	0.830558i	$0.311979\pi$
$60$			17.1520i			2.21432i
$61$	1.59965	+	2.77068i	0.204815	+	0.354749i	0.950074	−	0.312026i	$-0.101008\pi$
$61$	1.59965	+	2.77068i	0.204815	+	0.354749i	−0.745259	+	0.666775i	$0.767674\pi$
$62$	−3.06708	+	5.31234i	−0.389520	+	0.674668i
$63$	−4.44836	−	2.56826i	−0.560440	−	0.323570i
$64$	5.43541			0.679426
$65$	4.76388	−	0.551658i	0.590887	−	0.0684247i
$66$	48.8986			6.01900
$67$	4.80857	+	2.77623i	0.587461	+	0.339171i	0.764093	−	0.645106i	$-0.223187\pi$
$67$	4.80857	+	2.77623i	0.587461	+	0.339171i	−0.176632	+	0.984277i	$0.556520\pi$
$68$	−2.09463	+	3.62801i	−0.254012	+	0.439961i
$69$	1.18345	+	2.04980i	0.142471	+	0.246767i
$70$		−	2.62492i		−	0.313738i
$71$	0.884278	−	0.510538i	0.104944	−	0.0605897i	−0.446609	−	0.894729i	$-0.647369\pi$
$71$	0.884278	−	0.510538i	0.104944	−	0.0605897i	0.551554	+	0.834139i	$0.314035\pi$
$72$	−30.5425	+	17.6337i	−3.59947	+	2.07815i
$73$		−	8.97575i		−	1.05053i	−0.850938	−	0.525266i	$-0.823966\pi$
$73$		−	8.97575i		−	1.05053i	0.850938	−	0.525266i	$-0.176034\pi$
$74$	−13.5474	−	23.4647i	−1.57485	−	2.72772i
$75$	4.97258	−	8.61276i	0.574184	−	0.994516i
$76$	−3.23130	−	1.86559i	−0.370655	−	0.213998i
$77$	−5.06519			−0.577232
$78$	16.4646	+	22.1652i	1.86425	+	2.50972i
$79$	−15.5979			−1.75491			−0.877453	−	0.479663i	$-0.840759\pi$
$79$	−15.5979			−1.75491			−0.877453	+	0.479663i	$0.840759\pi$
$80$	−5.95695	−	3.43925i	−0.666007	−	0.384520i
$81$	−6.75144	+	11.6938i	−0.750160	+	1.29932i
$82$	−11.3097	−	19.5890i	−1.24895	−	2.16325i
$83$		−	0.771107i		−	0.0846400i	−0.999104	−	0.0423200i	$-0.986525\pi$
$83$		−	0.771107i		−	0.0846400i	0.999104	−	0.0423200i	$-0.0134749\pi$
$84$	8.85885	−	5.11466i	0.966580	−	0.558055i
$85$	−1.15189	+	0.665047i	−0.124940	+	0.0721344i
$86$			0.218394i			0.0235500i
$87$	−9.95532	−	17.2431i	−1.06732	−	1.84866i
$88$	−17.3889	+	30.1184i	−1.85366	+	3.21063i
$89$	3.49602	+	2.01843i	0.370577	+	0.213953i	0.673711	−	0.738995i	$-0.264699\pi$
$89$	3.49602	+	2.01843i	0.370577	+	0.213953i	−0.303133	+	0.952948i	$0.598033\pi$
$90$	−21.4268			−2.25858
$91$	−1.70550	−	2.29600i	−0.178785	−	0.240686i
$92$	−3.22125			−0.335839
$93$	−6.57296	−	3.79490i	−0.681584	−	0.393513i
$94$	−1.30860	+	2.26656i	−0.134972	+	0.233778i
$95$	−0.592325	−	1.02594i	−0.0607713	−	0.105259i
$96$		−	6.07201i		−	0.619722i
$97$	−7.76306	+	4.48201i	−0.788219	+	0.455079i	−0.839335	−	0.543614i	$-0.817056\pi$
$97$	−7.76306	+	4.48201i	−0.788219	+	0.455079i	0.0511159	+	0.998693i	$0.483722\pi$
$98$	13.7259	−	7.92464i	1.38652	−	0.800510i
$99$			41.3463i			4.15546i
$100$	6.76745	+	11.7216i	0.676745	+	1.17216i
$101$	6.53079	−	11.3117i	0.649838	−	1.12555i	−0.333323	−	0.942813i	$-0.608170\pi$
$101$	6.53079	−	11.3117i	0.649838	−	1.12555i	0.983161	−	0.182740i	$-0.0584966\pi$
$102$	−6.63201	−	3.82899i	−0.656667	−	0.379127i
$103$	10.2909			1.01400			0.506999	−	0.861947i	$-0.330755\pi$
$103$	10.2909			1.01400			0.506999	+	0.861947i	$0.330755\pi$
$104$	−19.5073	+	2.25895i	−1.91285	+	0.221508i
$105$	3.24781			0.316954
$106$	−8.78057	−	5.06947i	−0.852845	−	0.492390i
$107$	−4.12756	+	7.14914i	−0.399026	+	0.691133i	−0.993606	−	0.112903i	$-0.963985\pi$
$107$	−4.12756	+	7.14914i	−0.399026	+	0.691133i	0.594580	+	0.804036i	$0.297318\pi$
$108$	−22.4071	−	38.8103i	−2.15613	−	3.73452i
$109$		−	12.0657i		−	1.15568i	−0.816150	−	0.577840i	$-0.803896\pi$
$109$		−	12.0657i		−	1.15568i	0.816150	−	0.577840i	$-0.196104\pi$
$110$	−18.2985	+	10.5646i	−1.74469	+	1.00730i
$111$	29.0329	−	16.7621i	2.75568	−	1.59099i
$112$			4.10228i			0.387629i
$113$	6.17273	+	10.6915i	0.580682	+	1.00577i	0.995399	+	0.0958199i	$0.0305473\pi$
$113$	6.17273	+	10.6915i	0.580682	+	1.00577i	−0.414717	+	0.909950i	$0.636119\pi$
$114$	3.41030	−	5.90681i	0.319404	−	0.553224i
$115$	−0.885726	−	0.511374i	−0.0825943	−	0.0476859i
$116$	27.0975			2.51594
$117$	−18.7419	+	13.9217i	−1.73269	+	1.28706i
$118$	−2.56210			−0.235860
$119$	0.686981	+	0.396628i	0.0629754	+	0.0363589i
$120$	11.1498	−	19.3120i	1.01783	−	1.76293i
$121$	14.8861	+	25.7835i	1.35328	+	2.34395i
$122$		−	7.95931i		−	0.720602i
$123$	24.2375	−	13.9935i	2.18542	−	1.26176i
$124$	8.94550	−	5.16469i	0.803330	−	0.463803i
$125$			10.9478i			0.979201i
$126$	6.38938	+	11.0667i	0.569211	+	0.985902i
$127$	−7.47831	+	12.9528i	−0.663592	+	1.14938i	0.316073	+	0.948735i	$0.397636\pi$
$127$	−7.47831	+	12.9528i	−0.663592	+	1.14938i	−0.979665	+	0.200641i	$0.935698\pi$
$128$	−15.1273	−	8.73376i	−1.33708	−	0.771963i
$129$	−0.270219			−0.0237915
$130$	−10.9501	−	4.73730i	−0.960387	−	0.415488i
$131$	−3.78774			−0.330937			−0.165468	−	0.986215i	$-0.552914\pi$
$131$	−3.78774			−0.330937			−0.165468	+	0.986215i	$0.552914\pi$
$132$	−71.3092	−	41.1704i	−6.20667	−	3.58342i
$133$	−0.353258	+	0.611861i	−0.0306313	+	0.0530550i
$134$	−6.90677	−	11.9629i	−0.596654	−	1.03344i
$135$		−	14.2285i		−	1.22460i
$136$	4.71682	−	2.72326i	0.404464	−	0.233517i
$137$	7.42074	−	4.28437i	0.633997	−	0.366038i	−0.148301	−	0.988942i	$-0.547381\pi$
$137$	7.42074	−	4.28437i	0.633997	−	0.366038i	0.782298	+	0.622904i	$0.214047\pi$
$138$		−	5.88845i		−	0.501258i
$139$	−5.08538	−	8.80814i	−0.431337	−	0.747097i	0.565652	−	0.824644i	$-0.308625\pi$
$139$	−5.08538	−	8.80814i	−0.431337	−	0.747097i	−0.996989	+	0.0775471i	$0.975291\pi$
$140$	−2.21006	+	3.82794i	−0.186784	+	0.323520i
$141$	−2.80442	−	1.61913i	−0.236175	−	0.136356i
$142$	−2.54026			−0.213174
$143$	−9.14136	+	21.1299i	−0.764439	+	1.76697i
$144$	33.4862			2.79052
$145$	7.45080	+	4.30172i	0.618756	+	0.357239i
$146$	−11.1650	+	19.3384i	−0.924025	+	1.60046i
$147$	9.80517	+	16.9830i	0.808716	+	1.40074i
$148$			45.6250i			3.75035i
$149$	−1.49236	+	0.861614i	−0.122259	+	0.0705862i	−0.559882	−	0.828572i	$-0.689154\pi$
$149$	−1.49236	+	0.861614i	−0.122259	+	0.0705862i	0.437623	+	0.899158i	$0.355820\pi$
$150$	−21.4270	+	12.3709i	−1.74951	+	1.01008i
$151$		−	15.0927i		−	1.22823i	−0.789218	−	0.614113i	$-0.789514\pi$
$151$		−	15.0927i		−	1.22823i	0.789218	−	0.614113i	$-0.210486\pi$
$152$	2.42548	+	4.20105i	0.196732	+	0.340750i
$153$	3.23761	−	5.60771i	0.261746	−	0.453357i
$154$	10.9131	+	6.30065i	0.879399	+	0.507721i
$155$	3.27958			0.263422
$156$	−5.34836	−	46.1862i	−0.428212	−	3.69786i
$157$	2.23837			0.178641			0.0893205	−	0.996003i	$-0.471530\pi$
$157$	2.23837			0.178641			0.0893205	+	0.996003i	$0.471530\pi$
$158$	33.6061	+	19.4025i	2.67355	+	1.54358i
$159$	6.27245	−	10.8642i	0.497438	−	0.861588i
$160$	1.31187	+	2.27222i	0.103712	+	0.179635i
$161$			0.609959i			0.0480715i
$162$	29.0922	−	16.7964i	2.28570	−	1.31965i
$163$	7.02897	−	4.05818i	0.550552	−	0.317861i	−0.198793	−	0.980042i	$-0.563702\pi$
$163$	7.02897	−	4.05818i	0.550552	−	0.317861i	0.749344	+	0.662180i	$0.230369\pi$
$164$			38.0891i			2.97426i
$165$	−13.0716	−	22.6407i	−1.01762	−	1.76257i
$166$	−0.959189	+	1.66136i	−0.0744475	+	0.128947i
$167$	18.2655	+	10.5456i	1.41343	+	0.816043i	0.995710	−	0.0925329i	$-0.0294963\pi$
$167$	18.2655	+	10.5456i	1.41343	+	0.816043i	0.417719	+	0.908576i	$0.362830\pi$
$168$	−13.2993			−1.02606
$169$	−12.6560	+	2.97096i	−0.973536	+	0.228535i
$170$	3.30904			0.253792
$171$	4.99452	+	2.88359i	0.381940	+	0.220513i
$172$	0.183878	−	0.318486i	0.0140206	−	0.0242843i
$173$	−0.198747	−	0.344241i	−0.0151105	−	0.0261721i	0.858371	−	0.513029i	$-0.171477\pi$
$173$	−0.198747	−	0.344241i	−0.0151105	−	0.0261721i	−0.873482	+	0.486857i	$0.838143\pi$
$174$			49.5342i			3.75518i
$175$	2.21953	−	1.28145i	0.167781	−	0.0968684i
$176$	28.5972	−	16.5106i	2.15560	−	1.24453i
$177$		−	3.17008i		−	0.238278i
$178$	−5.02149	−	8.69748i	−0.376377	−	0.651904i
$179$	−8.19365	+	14.1918i	−0.612422	+	1.06075i	0.378409	+	0.925638i	$0.376471\pi$
$179$	−8.19365	+	14.1918i	−0.612422	+	1.06075i	−0.990831	+	0.135107i	$0.956862\pi$
$180$	31.2468	+	18.0404i	2.32900	+	1.34465i
$181$	−12.6103			−0.937319			−0.468659	−	0.883379i	$-0.655263\pi$
$181$	−12.6103			−0.937319			−0.468659	+	0.883379i	$0.655263\pi$
$182$	0.818505	+	7.06826i	0.0606716	+	0.523935i
$183$	9.84806			0.727989
$184$	3.62690	+	2.09399i	0.267379	+	0.154371i
$185$	−7.24297	+	12.5452i	−0.532514	+	0.922341i
$186$	9.44105	+	16.3524i	0.692251	+	1.19901i
$187$		−	6.38531i		−	0.466940i
$188$	3.81669	−	2.20357i	0.278361	−	0.160712i
$189$	−7.34890	+	4.24289i	−0.534554	+	0.308625i
$190$			2.94720i			0.213812i
$191$	0.604650	+	1.04728i	0.0437509	+	0.0757788i	0.887072	−	0.461632i	$-0.152736\pi$
$191$	0.604650	+	1.04728i	0.0437509	+	0.0757788i	−0.843321	+	0.537411i	$0.819403\pi$
$192$	8.36560	−	14.4896i	0.603735	−	1.04570i
$193$	−14.2861	−	8.24807i	−1.02833	−	0.593709i	−0.111827	−	0.993728i	$-0.535670\pi$
$193$	−14.2861	−	8.24807i	−1.02833	−	0.593709i	−0.916507	+	0.400019i	$0.869004\pi$
$194$	22.3009			1.60111
$195$	5.86146	−	13.5486i	0.419748	−	0.970232i
$196$	−26.6888			−1.90634
$197$	−12.0121	−	6.93517i	−0.855824	−	0.494110i	0.00678782	−	0.999977i	$-0.497839\pi$
$197$	−12.0121	−	6.93517i	−0.855824	−	0.494110i	−0.862612	+	0.505867i	$0.831173\pi$
$198$	51.4312	−	89.0815i	3.65506	−	6.33074i
$199$	−3.59146	−	6.22060i	−0.254592	−	0.440967i	0.710192	−	0.704008i	$-0.248608\pi$
$199$	−3.59146	−	6.22060i	−0.254592	−	0.440967i	−0.964785	+	0.263041i	$0.915275\pi$
$200$		−	17.5969i		−	1.24429i
$201$	14.8017	−	8.54575i	1.04403	−	0.602771i
$202$	−28.1414	+	16.2475i	−1.98002	+	1.14317i
$203$		−	5.13103i		−	0.360128i
$204$	6.44767	+	11.1677i	0.451427	+	0.781895i
$205$	−6.04665	+	10.4731i	−0.422316	+	0.731474i
$206$	−22.1720	−	12.8010i	−1.54480	−	0.891890i
$207$	4.97899			0.346064
$208$	17.1130	+	7.40355i	1.18658	+	0.513344i
$209$	5.68709			0.393384
$210$	−6.99747	−	4.03999i	−0.482871	−	0.278786i
$211$	11.4291	−	19.7958i	0.786813	−	1.36280i	−0.141096	−	0.989996i	$-0.545063\pi$
$211$	11.4291	−	19.7958i	0.786813	−	1.36280i	0.927910	−	0.372805i	$-0.121604\pi$
$212$	8.53652	+	14.7857i	0.586291	+	1.01548i
$213$		−	3.14306i		−	0.215359i
$214$	17.7858	−	10.2686i	1.21581	−	0.701950i
$215$	0.101119	−	0.0583813i	0.00689628	−	0.00398157i
$216$			58.2635i			3.96433i
$217$	−0.977957	−	1.69387i	−0.0663880	−	0.114987i
$218$	−15.0086	+	25.9957i	−1.01651	+	1.76065i
$219$	−23.9274	−	13.8145i	−1.61687	−	0.933498i
$220$	35.5797			2.39878
$221$	2.89440	−	2.14999i	0.194698	−	0.144624i
$222$	−83.4025			−5.59761
$223$	7.97925	+	4.60682i	0.534330	+	0.308495i	0.742778	−	0.669538i	$-0.233508\pi$
$223$	7.97925	+	4.60682i	0.534330	+	0.308495i	−0.208448	+	0.978033i	$0.566841\pi$
$224$	0.782387	−	1.35513i	0.0522755	−	0.0905437i
$225$	−10.4603	−	18.1177i	−0.697350	−	1.20785i
$226$		−	30.7133i		−	2.04302i
$227$	20.8394	−	12.0317i	1.38316	−	0.798569i	0.390630	−	0.920548i	$-0.372257\pi$
$227$	20.8394	−	12.0317i	1.38316	−	0.798569i	0.992533	+	0.121979i	$0.0389239\pi$
$228$	−9.94653	+	5.74263i	−0.658725	+	0.380315i
$229$		−	13.0294i		−	0.861006i	−0.902589	−	0.430503i	$-0.858336\pi$
$229$		−	13.0294i		−	0.861006i	0.902589	−	0.430503i	$-0.141664\pi$
$230$	1.27221	+	2.20353i	0.0838869	+	0.145296i
$231$	−7.79580	+	13.5027i	−0.512926	+	0.888414i
$232$	−30.5098	−	17.6149i	−2.00307	−	1.15647i
$233$	4.49811			0.294681			0.147341	−	0.989086i	$-0.452929\pi$
$233$	4.49811			0.294681			0.147341	+	0.989086i	$0.452929\pi$
$234$	57.6971	−	6.68132i	3.77178	−	0.436772i
$235$	1.39926			0.0912780
$236$	3.73633	+	2.15717i	0.243214	+	0.140420i
$237$	−24.0067	+	41.5808i	−1.55940	+	2.70096i
$238$	−0.986742	−	1.70909i	−0.0639610	−	0.110784i
$239$			8.00056i			0.517513i	0.965943	+	0.258757i	$0.0833128\pi$
$239$			8.00056i			0.517513i	−0.965943	+	0.258757i	$0.916687\pi$
$240$	−18.3366	+	10.5866i	−1.18362	+	0.683365i
$241$	−20.3478	+	11.7478i	−1.31072	+	0.756742i	−0.982215	−	0.187762i	$-0.939877\pi$
$241$	−20.3478	+	11.7478i	−1.31072	+	0.756742i	−0.328501	+	0.944504i	$0.606543\pi$
$242$		−	74.0680i		−	4.76127i
$243$	4.73610	+	8.20317i	0.303821	+	0.526233i
$244$	−6.70138	+	11.6071i	−0.429012	+	0.743070i
$245$	−7.33842	−	4.23684i	−0.468835	−	0.270682i
$246$	−69.6270			−4.43925
$247$	1.91490	+	2.57790i	0.121842	+	0.164028i
$248$	−13.4293			−0.852764
$249$	−2.05561	−	1.18680i	−0.130269	−	0.0752107i
$250$	13.6181	−	23.5872i	0.861284	−	1.49179i
$251$	11.3367	+	19.6358i	0.715569	+	1.23940i	0.962740	+	0.270430i	$0.0871659\pi$
$251$	11.3367	+	19.6358i	0.715569	+	1.23940i	−0.247171	+	0.968972i	$0.579501\pi$
$252$		−	21.5183i		−	1.35552i
$253$	4.25206	−	2.45493i	0.267325	−	0.154340i
$254$	32.2243	−	18.6047i	2.02193	−	1.16736i
$255$			4.09427i			0.256393i
$256$	16.2927	+	28.2197i	1.01829	+	1.76373i
$257$	−0.452743	+	0.784173i	−0.0282413	+	0.0489154i	−0.879801	−	0.475343i	$-0.842324\pi$
$257$	−0.452743	+	0.784173i	−0.0282413	+	0.0489154i	0.851559	+	0.524258i	$0.175657\pi$
$258$	0.582192	+	0.336129i	0.0362457	+	0.0209265i
$259$	8.63930			0.536820
$260$	11.9800	+	16.1279i	0.742969	+	1.00021i
$261$	−41.8837			−2.59254
$262$	8.16076	+	4.71162i	0.504174	+	0.291085i
$263$	−0.165492	+	0.286641i	−0.0102047	+	0.0176750i	−0.871083	−	0.491136i	$-0.836582\pi$
$263$	−0.165492	+	0.286641i	−0.0102047	+	0.0176750i	0.860878	+	0.508811i	$0.169915\pi$
$264$	53.5261	+	92.7099i	3.29430	+	5.70590i
$265$			5.42069i			0.332990i
$266$	1.52220	−	0.878844i	0.0933322	−	0.0538854i
$267$	10.7614	−	6.21309i	0.658587	−	0.380235i
$268$			23.2608i			1.42088i
$269$	−7.89636	−	13.6769i	−0.481450	−	0.833895i	0.518324	−	0.855184i	$-0.326556\pi$
$269$	−7.89636	−	13.6769i	−0.481450	−	0.833895i	−0.999773	+	0.0212893i	$0.993223\pi$
$270$	−17.6990	+	30.6556i	−1.07713	+	1.86564i
$271$	0.406746	+	0.234835i	0.0247081	+	0.0142652i	0.512303	−	0.858805i	$-0.328792\pi$
$271$	0.406746	+	0.234835i	0.0247081	+	0.0142652i	−0.487595	+	0.873070i	$0.662126\pi$
$272$	−5.17144			−0.313564
$273$	−8.74556	+	1.01274i	−0.529306	+	0.0612936i
$274$	−21.3175			−1.28784
$275$	−17.8661	−	10.3150i	−1.07737	−	0.622018i
$276$	−4.95781	+	8.58717i	−0.298425	+	0.516887i
$277$	5.59761	+	9.69534i	0.336328	+	0.582537i	0.983739	−	0.179604i	$-0.0574817\pi$
$277$	5.59761	+	9.69534i	0.336328	+	0.582537i	−0.647411	+	0.762141i	$0.724148\pi$
$278$			25.3031i			1.51758i
$279$	−13.8268	+	7.98290i	−0.827788	+	0.477924i
$280$	4.97675	−	2.87333i	0.297417	−	0.171714i
$281$			14.1301i			0.842932i	0.906844	+	0.421466i	$0.138484\pi$
$281$			14.1301i			0.842932i	−0.906844	+	0.421466i	$0.861516\pi$
$282$	4.02812	+	6.97691i	0.239871	+	0.415469i
$283$	−8.88245	+	15.3849i	−0.528007	+	0.914535i	0.471460	+	0.881888i	$0.343727\pi$
$283$	−8.88245	+	15.3849i	−0.528007	+	0.914535i	−0.999467	+	0.0326476i	$0.989606\pi$
$284$	3.70448	+	2.13878i	0.219820	+	0.126913i
$285$	−3.64657			−0.216004
$286$	45.9790	−	34.1538i	2.71880	−	2.01956i
$287$	7.21235			0.425732
$288$	−11.0617	−	6.38650i	−0.651819	−	0.376328i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−10.7019	−	18.5363i	−0.628439	−	1.08849i
$291$			27.5929i			1.61752i
$292$	32.5641	−	18.8009i	1.90567	−	1.10024i
$293$	5.19937	−	3.00186i	0.303751	−	0.175371i	−0.340376	−	0.940289i	$-0.610554\pi$
$293$	5.19937	−	3.00186i	0.303751	−	0.175371i	0.644127	+	0.764919i	$0.277221\pi$
$294$		−	48.7871i		−	2.84532i
$295$	0.684901	+	1.18628i	0.0398765	+	0.0690681i
$296$	29.6588	−	51.3706i	1.72388	−	2.98585i
$297$	59.1549	+	34.1531i	3.43252	+	1.98176i
$298$	4.28709			0.248344
$299$	2.54450	+	1.10082i	0.147152	+	0.0636619i
$300$	41.6630			2.40541
$301$	−0.0603067	−	0.0348181i	−0.00347602	−	0.00200688i
$302$	−18.7740	+	32.5175i	−1.08032	+	1.87117i
$303$	−20.1030	−	34.8194i	−1.15489	−	2.00032i
$304$		−	4.60595i		−	0.264169i
$305$	−3.68526	+	2.12769i	−0.211017	+	0.121831i
$306$	−13.9510	+	8.05461i	−0.797526	+	0.460452i
$307$			4.49286i			0.256421i	0.991747	+	0.128211i	$0.0409233\pi$
$307$			4.49286i			0.256421i	−0.991747	+	0.128211i	$0.959077\pi$
$308$	−10.6097	−	18.3766i	−0.604545	−	1.04710i
$309$	15.8387	−	27.4335i	0.901033	−	1.56064i
$310$	−7.06591	−	4.07950i	−0.401317	−	0.231700i
$311$	−15.2858			−0.866778			−0.433389	−	0.901207i	$-0.642682\pi$
$311$	−15.2858			−0.866778			−0.433389	+	0.901207i	$0.642682\pi$
$312$	−24.0017	+	55.4791i	−1.35883	+	3.14089i
$313$	11.3839			0.643455			0.321727	−	0.946832i	$-0.395737\pi$
$313$	11.3839			0.643455			0.321727	+	0.946832i	$0.395737\pi$
$314$	−4.82260	−	2.78433i	−0.272155	−	0.157129i
$315$	3.41602	−	5.91673i	0.192471	−	0.333370i
$316$	−32.6720	−	56.5895i	−1.83794	−	3.18341i
$317$			10.3281i			0.580082i	0.957014	+	0.290041i	$0.0936689\pi$
$317$			10.3281i			0.580082i	−0.957014	+	0.290041i	$0.906331\pi$
$318$	−27.0282	+	15.6048i	−1.51567	+	0.875071i
$319$	−35.7687	+	20.6511i	−2.00266	+	1.15624i
$320$			7.22960i			0.404147i
$321$	12.7054	+	22.0064i	0.709146	+	1.22828i
$322$	0.758735	−	1.31417i	0.0422826	−	0.0732357i
$323$	−0.771327	−	0.445326i	−0.0429178	−	0.0247786i
$324$	−56.5672			−3.14262
$325$	−1.34000	−	11.5717i	−0.0743298	−	0.641881i
$326$	−20.1921			−1.11834
$327$	−32.1645	−	18.5702i	−1.77870	−	1.02693i
$328$	24.7601	−	42.8857i	1.36715	−	2.36797i
$329$	−0.417255	−	0.722707i	−0.0230040	−	0.0398441i
$330$			65.0397i			3.58032i
$331$	2.35936	−	1.36218i	0.129682	−	0.0748720i	−0.433756	−	0.901031i	$-0.642812\pi$
$331$	2.35936	−	1.36218i	0.129682	−	0.0748720i	0.563438	+	0.826159i	$0.309479\pi$
$332$	2.79759	−	1.61519i	0.153537	−	0.0886449i
$333$		−	70.5212i		−	3.86454i
$334$	−26.2356	−	45.4414i	−1.43555	−	2.48644i
$335$	−3.69264	+	6.39585i	−0.201751	+	0.349443i
$336$	10.9358	+	6.31379i	0.596597	+	0.344445i
$337$	−3.60112			−0.196165			−0.0980827	−	0.995178i	$-0.531271\pi$
$337$	−3.60112			−0.196165			−0.0980827	+	0.995178i	$0.531271\pi$
$338$	30.9631	+	9.34192i	1.68417	+	0.508133i
$339$	38.0016			2.06397
$340$	−4.82560	−	2.78606i	−0.261705	−	0.151095i
$341$	−7.87205	+	13.6348i	−0.426295	+	0.738365i
$342$	−7.17386	−	12.4255i	−0.387918	−	0.671893i
$343$			10.6064i			0.572694i
$344$	−0.414067	+	0.239062i	−0.0223250	+	0.0128893i
$345$	−2.72643	+	1.57410i	−0.146786	+	0.0847469i
$346$			0.988898i			0.0531635i
$347$	−2.20204	−	3.81404i	−0.118212	−	0.204749i	0.800847	−	0.598868i	$-0.204383\pi$
$347$	−2.20204	−	3.81404i	−0.118212	−	0.204749i	−0.919059	+	0.394120i	$0.871049\pi$
$348$	41.7055	−	72.2361i	2.23565	−	3.87226i
$349$	26.8553	+	15.5049i	1.43753	+	0.829960i	0.997678	−	0.0681085i	$-0.0216964\pi$
$349$	26.8553	+	15.5049i	1.43753	+	0.829960i	0.439855	+	0.898069i	$0.355030\pi$
$350$	−6.37603			−0.340813
$351$	4.43676	+	38.3140i	0.236817	+	2.04505i
$352$	−12.5956			−0.671349
$353$	−12.9669	−	7.48646i	−0.690160	−	0.398464i	0.113512	−	0.993537i	$-0.463790\pi$
$353$	−12.9669	−	7.48646i	−0.690160	−	0.398464i	−0.803672	+	0.595073i	$0.797123\pi$
$354$	−3.94331	+	6.83001i	−0.209584	+	0.363011i
$355$	0.679063	+	1.17617i	0.0360409	+	0.0624247i
$356$			16.9115i			0.896306i
$357$	2.11465	−	1.22090i	0.111919	−	0.0646167i
$358$	35.3067	−	20.3844i	1.86602	−	1.07735i
$359$		−	16.3185i		−	0.861257i	−0.902529	−	0.430629i	$-0.858292\pi$
$359$		−	16.3185i		−	0.861257i	0.902529	−	0.430629i	$-0.141708\pi$
$360$	−23.4545	−	40.6244i	−1.23616	−	2.14109i
$361$	−9.10337	+	15.7675i	−0.479125	+	0.829868i
$362$	27.1692	+	15.6861i	1.42798	+	0.824445i
$363$	91.6443			4.81008
$364$	4.75752	−	10.9968i	0.249362	−	0.576391i
$365$	11.9386			0.624894
$366$	−21.2178	−	12.2501i	−1.10907	−	0.640324i
$367$	3.94506	−	6.83304i	0.205930	−	0.356682i	−0.744498	−	0.667624i	$-0.767311\pi$
$367$	3.94506	−	6.83304i	0.205930	−	0.356682i	0.950429	+	0.310942i	$0.100645\pi$
$368$	−1.98824	−	3.44373i	−0.103644	−	0.179517i
$369$		−	58.8732i		−	3.06482i
$370$	31.2102	−	18.0192i	1.62254	−	0.936776i
$371$	2.79974	−	1.61643i	0.145355	−	0.0839208i
$372$		−	31.7957i		−	1.64853i
$373$	4.98004	+	8.62568i	0.257857	+	0.446621i	0.965668	−	0.259781i	$-0.0836504\pi$
$373$	4.98004	+	8.62568i	0.257857	+	0.446621i	−0.707811	+	0.706402i	$0.750317\pi$
$374$	−7.94277	+	13.7573i	−0.410711	+	0.711372i
$375$	29.1845	+	16.8497i	1.50708	+	0.870114i
$376$	−5.72976			−0.295490
$377$	−21.4046	−	9.26018i	−1.10239	−	0.476923i
$378$	21.1111			1.08584
$379$	−16.5195	−	9.53752i	−0.848548	−	0.489909i	0.0116126	−	0.999933i	$-0.496304\pi$
$379$	−16.5195	−	9.53752i	−0.848548	−	0.489909i	−0.860161	+	0.510023i	$0.829637\pi$
$380$	2.48141	−	4.29793i	0.127294	−	0.220479i
$381$	23.0196	+	39.8711i	1.17933	+	2.04266i
$382$		−	3.00852i		−	0.153929i
$383$	−18.8882	+	10.9051i	−0.965141	+	0.557225i	−0.897752	−	0.440502i	$-0.854800\pi$
$383$	−18.8882	+	10.9051i	−0.965141	+	0.557225i	−0.0673898	+	0.997727i	$0.521467\pi$
$384$	−46.5647	+	26.8841i	−2.37625	+	1.37193i
$385$		−	6.73718i		−	0.343358i
$386$	20.5197	+	35.5412i	1.04443	+	1.80900i
$387$	−0.284215	+	0.492274i	−0.0144474	+	0.0250237i
$388$	−32.5216	−	18.7763i	−1.65103	−	0.953224i
$389$	−16.1722			−0.819961			−0.409980	−	0.912094i	$-0.634464\pi$
$389$	−16.1722			−0.819961			−0.409980	+	0.912094i	$0.634464\pi$
$390$	−29.4818	+	21.8995i	−1.49287	+	1.10892i
$391$	−0.768930			−0.0388864
$392$	30.0497	+	17.3492i	1.51774	+	0.876266i
$393$	−5.82969	+	10.0973i	−0.294069	+	0.509342i
$394$	17.2535	+	29.8839i	0.869217	+	1.50553i
$395$		−	20.7467i		−	1.04388i
$396$	−150.005	+	86.6055i	−7.53804	+	4.35209i
$397$	−2.90146	+	1.67516i	−0.145620	+	0.0840737i	−0.571040	−	0.820922i	$-0.693460\pi$
$397$	−2.90146	+	1.67516i	−0.145620	+	0.0840737i	0.425420	+	0.904996i	$0.360126\pi$
$398$			17.8699i			0.895735i
$399$	1.08739	+	1.88342i	0.0544378	+	0.0942890i
$400$	−8.35408	+	14.4697i	−0.417704	+	0.723484i
$401$	22.3578	+	12.9083i	1.11650	+	0.644609i	0.940504	−	0.339782i	$-0.110353\pi$
$401$	22.3578	+	12.9083i	1.11650	+	0.644609i	0.175992	+	0.984392i	$0.443687\pi$
$402$	−42.5207			−2.12074
$403$	−8.83110	+	1.02264i	−0.439908	+	0.0509414i
$404$	54.7185			2.72235
$405$	−15.5539	−	8.98005i	−0.772879	−	0.446222i
$406$	−6.38255	+	11.0549i	−0.316760	+	0.548645i
$407$	−34.7710	−	60.2251i	−1.72353	−	2.98525i
$408$		−	16.7654i		−	0.830011i
$409$	−24.0849	+	13.9054i	−1.19092	+	0.687579i	−0.958516	−	0.285040i	$-0.907993\pi$
$409$	−24.0849	+	13.9054i	−1.19092	+	0.687579i	−0.232406	+	0.972619i	$0.574660\pi$
$410$	26.0553	−	15.0430i	1.28678	−	0.742921i
$411$		−	26.3762i		−	1.30104i
$412$	21.5558	+	37.3357i	1.06198	+	1.83940i
$413$	0.408470	−	0.707490i	0.0200995	−	0.0348133i
$414$	−10.7273	−	6.19343i	−0.527220	−	0.304390i
$415$	1.02564			0.0503469
$416$	−4.24107	−	5.70947i	−0.207935	−	0.279930i
$417$	−31.3075			−1.53314
$418$	−12.2529	−	7.07424i	−0.599311	−	0.346012i
$419$	9.11979	−	15.7959i	0.445531	−	0.771682i	−0.552558	−	0.833474i	$-0.686348\pi$
$419$	9.11979	−	15.7959i	0.445531	−	0.771682i	0.998089	+	0.0617923i	$0.0196816\pi$
$420$	6.80298	+	11.7831i	0.331951	+	0.574957i
$421$		−	2.78966i		−	0.135960i	−0.997687	−	0.0679799i	$-0.978345\pi$
$421$		−	2.78966i		−	0.135960i	0.997687	−	0.0679799i	$-0.0216554\pi$
$422$	−49.2485	+	28.4337i	−2.39738	+	1.38413i
$423$	−5.89934	+	3.40599i	−0.286836	+	0.165605i
$424$		−	22.1969i		−	1.07797i
$425$	1.61543	+	2.79800i	0.0783597	+	0.135723i
$426$	−3.90969	+	6.77179i	−0.189425	+	0.328094i
$427$	2.19786	+	1.26894i	0.106362	+	0.0614081i
$428$	−34.5829			−1.67163
$429$	42.2585	+	56.8898i	2.04026	+	2.74667i
$430$	−0.290485			−0.0140084
$431$	−0.369291	−	0.213210i	−0.0177881	−	0.0102700i	0.491080	−	0.871115i	$-0.336602\pi$
$431$	−0.369291	−	0.213210i	−0.0177881	−	0.0102700i	−0.508868	+	0.860845i	$0.669936\pi$
$432$	27.6605	−	47.9093i	1.33081	−	2.30504i
$433$	−2.72391	−	4.71794i	−0.130903	−	0.226730i	0.793122	−	0.609063i	$-0.208454\pi$
$433$	−2.72391	−	4.71794i	−0.130903	−	0.226730i	−0.924025	+	0.382333i	$0.875121\pi$
$434$			4.86597i			0.233574i
$435$	22.9350	−	13.2415i	1.09965	−	0.634882i
$436$	43.7744	−	25.2731i	2.09641	−	1.21036i
$437$		−	0.684849i		−	0.0327607i
$438$	34.3681	+	59.5272i	1.64217	+	2.84432i
$439$	−3.92544	+	6.79906i	−0.187351	+	0.324502i	−0.944366	−	0.328896i	$-0.893324\pi$
$439$	−3.92544	+	6.79906i	−0.187351	+	0.324502i	0.757015	+	0.653397i	$0.226657\pi$
$440$	−40.0602	−	23.1288i	−1.90980	−	1.10262i
$441$	41.2520			1.96438
$442$	−8.91043	+	1.03183i	−0.423826	+	0.0490791i
$443$	19.3696			0.920276			0.460138	−	0.887847i	$-0.347800\pi$
$443$	19.3696			0.920276			0.460138	+	0.887847i	$0.347800\pi$
$444$	121.627	+	70.2211i	5.77214	+	3.33255i
$445$	−2.68470	+	4.65003i	−0.127267	+	0.220433i
$446$	−11.4610	−	19.8510i	−0.542692	−	0.939970i
$447$			5.30442i			0.250890i
$448$	3.73402	−	2.15584i	0.176416	−	0.101854i
$449$	−11.4146	+	6.59023i	−0.538689	+	0.311012i	−0.744548	−	0.667569i	$-0.767335\pi$
$449$	−11.4146	+	6.59023i	−0.538689	+	0.311012i	0.205858	+	0.978582i	$0.434001\pi$
$450$			52.0465i			2.45350i
$451$	−29.0279	−	50.2777i	−1.36687	−	2.36749i
$452$	−25.8592	+	44.7895i	−1.21632	+	2.10672i
$453$	−40.2339	−	23.2291i	−1.89035	−	1.09140i
$454$	−59.8653			−2.80962
$455$	3.05389	−	2.26847i	0.143169	−	0.106348i
$456$	14.9321			0.699261
$457$	32.8548	+	18.9687i	1.53688	+	0.887319i	0.999019	+	0.0442870i	$0.0141016\pi$
$457$	32.8548	+	18.9687i	1.53688	+	0.887319i	0.537863	+	0.843032i	$0.319232\pi$
$458$	−16.2074	+	28.0721i	−0.757323	+	1.31172i
$459$	−5.34870	−	9.26422i	−0.249656	−	0.432417i
$460$		−	4.28457i		−	0.199769i
$461$	−10.7755	+	6.22126i	−0.501867	+	0.289753i	−0.729484	−	0.683998i	$-0.760240\pi$
$461$	−10.7755	+	6.22126i	−0.501867	+	0.289753i	0.227617	+	0.973751i	$0.426907\pi$
$462$	33.5924	−	19.3946i	1.56286	−	0.902318i
$463$			24.0900i			1.11956i	0.828642	+	0.559778i	$0.189114\pi$
$463$			24.0900i			1.11956i	−0.828642	+	0.559778i	$0.810886\pi$
$464$	16.7252	+	28.9689i	0.776449	+	1.34485i
$465$	5.04757	−	8.74265i	0.234076	−	0.405431i
$466$	−9.69127	−	5.59526i	−0.448939	−	0.259195i
$467$	7.46481			0.345430			0.172715	−	0.984972i	$-0.444746\pi$
$467$	7.46481			0.345430			0.172715	+	0.984972i	$0.444746\pi$
$468$	−89.7655	−	38.8349i	−4.14941	−	1.79514i
$469$	4.40453			0.203382
$470$	−3.01474	−	1.74056i	−0.139060	−	0.0802861i
$471$	3.44505	−	5.96701i	0.158740	−	0.274945i
$472$	−2.80456	−	4.85764i	−0.129090	−	0.223591i
$473$			0.560536i			0.0257735i
$474$	103.446	−	59.7244i	4.75142	−	2.74323i
$475$	−2.49204	+	1.43878i	−0.114343	+	0.0660159i
$476$			3.32317i			0.152317i
$477$	−13.1946	−	22.8538i	−0.604141	−	1.04640i
$478$	9.95200	−	17.2374i	0.455194	−	0.788419i
$479$	−4.52842	−	2.61449i	−0.206909	−	0.119459i	0.392965	−	0.919553i	$-0.371449\pi$
$479$	−4.52842	−	2.61449i	−0.206909	−	0.119459i	−0.599874	+	0.800094i	$0.704783\pi$
$480$	8.07634			0.368633
$481$	15.5917	−	36.0397i	0.710920	−	1.64327i
$482$	58.4529			2.66246
$483$	1.62602	+	0.938783i	0.0739865	+	0.0427161i
$484$	−62.3619	+	108.014i	−2.83463	+	4.90972i
$485$	−5.96148	−	10.3256i	−0.270697	−	0.468861i
$486$		−	23.5652i		−	1.06894i
$487$	22.4064	−	12.9364i	1.01533	−	0.586203i	0.102584	−	0.994724i	$-0.467289\pi$
$487$	22.4064	−	12.9364i	1.01533	−	0.586203i	0.912749	+	0.408521i	$0.133955\pi$
$488$	15.0906	−	8.71254i	0.683117	−	0.394398i
$489$		−	24.9837i		−	1.12980i
$490$	10.5405	+	18.2567i	0.476172	+	0.824754i
$491$	10.8913	−	18.8642i	0.491516	−	0.851331i	−0.508436	−	0.861100i	$-0.669776\pi$
$491$	10.8913	−	18.8642i	0.491516	−	0.851331i	0.999952	+	0.00976875i	$0.00310954\pi$
$492$	101.538	+	58.6227i	4.57767	+	2.64292i
$493$	6.46830			0.291318
$494$	−0.919000	−	7.93610i	−0.0413477	−	0.357062i
$495$	−54.9945			−2.47182
$496$	11.0428	+	6.37554i	0.495835	+	0.286270i
$497$	0.404988	−	0.701460i	0.0181662	−	0.0314648i
$498$	2.95256	+	5.11399i	0.132307	+	0.229163i
$499$			8.93237i			0.399868i	0.979809	+	0.199934i	$0.0640728\pi$
$499$			8.93237i			0.399868i	−0.979809	+	0.199934i	$0.935927\pi$
$500$	−39.7188	+	22.9316i	−1.77628	+	1.02553i
$501$	56.2247	−	32.4613i	2.51193	−	1.45027i
$502$		−	56.4077i		−	2.51760i
$503$	0.385756	+	0.668149i	0.0172000	+	0.0297913i	0.874497	−	0.485030i	$-0.161191\pi$
$503$	0.385756	+	0.668149i	0.0172000	+	0.0297913i	−0.857297	+	0.514822i	$0.827858\pi$
$504$	−13.9881	+	24.2280i	−0.623078	+	1.07920i
$505$	15.0456	+	8.68656i	0.669519	+	0.386547i
$506$	−12.2149			−0.543016
$507$	−11.5588	+	38.3107i	−0.513342	+	1.70144i
$508$	−62.6573			−2.77997
$509$	−5.23115	−	3.02021i	−0.231867	−	0.133868i	0.379566	−	0.925165i	$-0.376073\pi$
$509$	−5.23115	−	3.02021i	−0.231867	−	0.133868i	−0.611433	+	0.791296i	$0.709407\pi$
$510$	5.09292	−	8.82119i	0.225518	−	0.390609i
$511$	−3.56004	−	6.16617i	−0.157487	−	0.272775i
$512$		−	46.1315i		−	2.03874i
$513$	8.25119	−	4.76383i	0.364299	−	0.210328i
$514$	1.95089	−	1.12634i	0.0860499	−	0.0496809i
$515$			13.6879i			0.603162i
$516$	−0.566010	−	0.980359i	−0.0249172	−	0.0431579i
$517$	−3.35869	+	5.81742i	−0.147715	+	0.255850i
$518$	−18.6135	−	10.7465i	−0.817832	−	0.472175i
$519$	−1.22356			−0.0537085
$520$	−3.00461	−	25.9466i	−0.131761	−	1.13783i
$521$	24.2443			1.06216			0.531081	−	0.847321i	$-0.321786\pi$
$521$	24.2443			1.06216			0.531081	+	0.847321i	$0.321786\pi$
$522$	90.2393	+	52.0997i	3.94967	+	2.28034i
$523$	−16.9882	+	29.4244i	−0.742843	+	1.28664i	0.208353	+	0.978054i	$0.433190\pi$
$523$	−16.9882	+	29.4244i	−0.742843	+	1.28664i	−0.951196	+	0.308587i	$0.900144\pi$
$524$	−7.93394	−	13.7420i	−0.346596	−	0.600321i
$525$		−	7.88907i		−	0.344307i
$526$	0.713112	−	0.411715i	0.0310931	−	0.0179516i
$527$	2.13534	−	1.23284i	0.0930167	−	0.0537032i
$528$		−	101.646i		−	4.42355i
$529$	11.2044	+	19.4065i	0.487147	+	0.843763i
$530$	6.74286	−	11.6790i	0.292891	−	0.507302i
$531$	−5.77513	−	3.33427i	−0.250619	−	0.144695i
$532$	−2.95978			−0.128323
$533$	13.0164	−	30.0870i	0.563804	−	1.30321i
$534$	−30.9142			−1.33779
$535$	−9.50902	−	5.49004i	−0.411111	−	0.237355i
$536$	15.1208	−	26.1900i	0.653118	−	1.13123i
$537$	25.2216	+	43.6850i	1.08839	+	1.88515i
$538$			39.2895i			1.69389i
$539$	35.2292	−	20.3396i	1.51743	−	0.876088i
$540$	51.6213	−	29.8036i	2.22143	−	1.28254i
$541$		−	23.4816i		−	1.00955i	−0.863251	−	0.504775i	$-0.831575\pi$
$541$		−	23.4816i		−	1.00955i	0.863251	−	0.504775i	$-0.168425\pi$
$542$	−0.584228	−	1.01191i	−0.0250947	−	0.0434654i
$543$	−19.4085	+	33.6165i	−0.832897	+	1.44262i
$544$	1.70832	+	0.986298i	0.0732435	+	0.0422872i
$545$	16.0485			0.687440
$546$	20.1022	+	8.69675i	0.860296	+	0.372187i
$547$	−33.7599			−1.44347			−0.721735	−	0.692169i	$-0.756655\pi$
$547$	−33.7599			−1.44347			−0.721735	+	0.692169i	$0.756655\pi$
$548$	31.0875	+	17.9484i	1.32799	+	0.766717i
$549$	10.3581	−	17.9408i	0.442074	−	0.765694i
$550$	25.6619	+	44.4477i	1.09423	+	1.89526i
$551$			5.76101i			0.245427i
$552$	11.1643	−	6.44570i	0.475183	−	0.274347i
$553$	−10.7155	+	6.18659i	−0.455669	+	0.263080i
$554$		−	27.8517i		−	1.18331i
$555$	22.2952	+	38.6164i	0.946379	+	1.63918i
$556$	21.3040	−	36.8997i	0.903493	−	1.56489i
$557$	1.91321	+	1.10459i	0.0810655	+	0.0468032i	0.539985	−	0.841675i	$-0.318430\pi$
$557$	1.91321	+	1.10459i	0.0810655	+	0.0468032i	−0.458919	+	0.888478i	$0.651763\pi$
$558$	39.7201			1.68149
$559$	−0.254085	+	0.188738i	−0.0107467	+	0.00798275i
$560$	−5.45641			−0.230576
$561$	−17.0219	−	9.82759i	−0.718664	−	0.414921i
$562$	17.5766	−	30.4436i	0.741425	−	1.28419i
$563$	0.214382	+	0.371320i	0.00903511	+	0.0156493i	0.870508	−	0.492155i	$-0.163791\pi$
$563$	0.214382	+	0.371320i	0.00903511	+	0.0156493i	−0.861472	+	0.507804i	$0.830457\pi$
$564$		−	13.5660i		−	0.571230i
$565$	−14.2207	+	8.21031i	−0.598268	+	0.345410i
$566$	38.2748	−	22.0980i	1.60881	−	0.928848i
$567$			10.7113i			0.449830i
$568$	−2.78065	−	4.81624i	−0.116674	−	0.202085i
$569$	−12.7152	+	22.0234i	−0.533049	+	0.923267i	0.466206	+	0.884676i	$0.345620\pi$
$569$	−12.7152	+	22.0234i	−0.533049	+	0.923267i	−0.999255	+	0.0385913i	$0.987713\pi$
$570$	7.85661	+	4.53602i	0.329077	+	0.189993i
$571$	−37.9815			−1.58947			−0.794737	−	0.606953i	$-0.792391\pi$
$571$	−37.9815			−1.58947			−0.794737	+	0.606953i	$0.792391\pi$
$572$	−95.8075	+	11.0945i	−4.00591	+	0.463885i
$573$	3.72245			0.155507
$574$	−15.5391	−	8.97153i	−0.648591	−	0.374464i
$575$	−1.24215	+	2.15146i	−0.0518012	+	0.0897223i
$576$	−17.5977	−	30.4802i	−0.733239	−	1.27001i
$577$			0.0973434i			0.00405246i	0.999998	+	0.00202623i	$0.000644969\pi$
$577$			0.0973434i			0.00405246i	−0.999998	+	0.00202623i	$0.999355\pi$
$578$	2.15452	−	1.24391i	0.0896162	−	0.0517399i
$579$	−43.9752	+	25.3891i	−1.82755	+	1.05513i
$580$			36.0422i			1.49657i
$581$	−0.305843	−	0.529735i	−0.0126885	−	0.0219771i
$582$	34.3231	−	59.4494i	1.42274	−	2.46426i
$583$	−22.5364	−	13.0114i	−0.933364	−	0.538878i
$584$	−48.8866			−2.02294
$585$	−18.5172	−	24.9284i	−0.765590	−	1.03066i
$586$	−14.9362			−0.617009
$587$	20.6494	+	11.9219i	0.852291	+	0.492071i	0.861423	−	0.507888i	$-0.169574\pi$
$587$	20.6494	+	11.9219i	0.852291	+	0.492071i	−0.00913201	+	0.999958i	$0.502907\pi$
$588$	−41.0765	+	71.1465i	−1.69397	+	2.93403i
$589$	1.09803	+	1.90184i	0.0452435	+	0.0783640i
$590$		−	3.40783i		−	0.140298i
$591$	−36.9753	+	21.3477i	−1.52096	+	0.878128i
$592$	−48.7761	+	28.1609i	−2.00468	+	1.15740i
$593$			31.8718i			1.30882i	0.756140	+	0.654410i	$0.227083\pi$
$593$			31.8718i			1.30882i	−0.756140	+	0.654410i	$0.772917\pi$
$594$	−84.9669	−	147.167i	−3.48623	−	6.03833i
$595$	−0.527553	+	0.913748i	−0.0216276	+	0.0374600i
$596$	−6.25190	−	3.60953i	−0.256088	−	0.147852i
$597$	−22.1104			−0.904918
$598$	−4.11285	−	5.53687i	−0.168187	−	0.226419i
$599$	−10.6187			−0.433868			−0.216934	−	0.976186i	$-0.569606\pi$
$599$	−10.6187			−0.433868			−0.216934	+	0.976186i	$0.569606\pi$
$600$	−46.9096	−	27.0832i	−1.91507	−	1.10567i
$601$	8.69880	−	15.0668i	0.354831	−	0.614586i	−0.632258	−	0.774758i	$-0.717872\pi$
$601$	8.69880	−	15.0668i	0.354831	−	0.614586i	0.987089	+	0.160172i	$0.0512050\pi$
$602$	0.0866213	+	0.150033i	0.00353042	+	0.00611487i
$603$		−	35.9534i		−	1.46414i
$604$	54.7565	−	31.6137i	2.22801	−	1.28634i
$605$	−34.2944	+	19.7999i	−1.39427	+	0.804980i
$606$			100.025i			4.06325i
$607$	19.3919	+	33.5878i	0.787094	+	1.36329i	0.927740	+	0.373227i	$0.121749\pi$
$607$	19.3919	+	33.5878i	0.787094	+	1.36329i	−0.140646	+	0.990060i	$0.544918\pi$
$608$	−0.878448	+	1.52152i	−0.0356258	+	0.0617056i
$609$	−13.6782	−	7.89713i	−0.554270	−	0.320008i
$610$	10.5866			0.428640
$611$	−3.76788	+	0.436320i	−0.152432	+	0.0176516i
$612$	27.1265			1.09652
$613$	16.3344	+	9.43069i	0.659742	+	0.380902i	0.792179	−	0.610289i	$-0.208947\pi$
$613$	16.3344	+	9.43069i	0.659742	+	0.380902i	−0.132437	+	0.991191i	$0.542280\pi$
$614$	5.58873	−	9.67996i	0.225543	−	0.390651i
$615$	18.6127	+	32.2382i	0.750537	+	1.29997i
$616$			27.5877i			1.11154i
$617$	−20.8164	+	12.0183i	−0.838035	+	0.483840i	−0.856596	−	0.515988i	$-0.827425\pi$
$617$	−20.8164	+	12.0183i	−0.838035	+	0.483840i	0.0185610	+	0.999828i	$0.494092\pi$
$618$	−68.2497	+	39.4040i	−2.74540	+	1.58506i
$619$			4.55127i			0.182931i	0.995808	+	0.0914654i	$0.0291551\pi$
$619$			4.55127i			0.182931i	−0.995808	+	0.0914654i	$0.970845\pi$
$620$	6.86951	+	11.8983i	0.275886	+	0.477849i
$621$	4.11277	−	7.12353i	0.165040	−	0.285857i
$622$	32.9335	+	19.0142i	1.32051	+	0.762400i
$623$	3.20226			0.128296
$624$	46.0749	−	34.2250i	1.84447	−	1.37010i
$625$	1.59267			0.0637067
$626$	−24.5268	−	14.1605i	−0.980287	−	0.565969i
$627$	8.75296	−	15.1606i	0.349559	−	0.605455i
$628$	4.68856	+	8.12082i	0.187094	+	0.324056i
$629$			10.8909i			0.434250i
$630$	−14.7198	+	8.49847i	−0.586450	+	0.338587i
$631$	−3.78903	+	2.18759i	−0.150839	+	0.0870868i	−0.573520	−	0.819192i	$-0.694422\pi$
$631$	−3.78903	+	2.18759i	−0.150839	+	0.0870868i	0.422681	+	0.906279i	$0.361089\pi$
$632$			84.9545i			3.37931i
$633$	−35.1810	−	60.9352i	−1.39832	−	2.42196i
$634$	12.8472	−	22.2520i	0.510227	−	0.883740i
$635$	−17.2284	−	9.94684i	−0.683690	−	0.394728i
$636$	52.5540			2.08390
$637$	21.0817	+	9.12051i	0.835288	+	0.361368i
$638$	102.752			4.06801
$639$	−5.72590	−	3.30585i	−0.226513	−	0.130777i
$640$	11.6167	−	20.1207i	0.459191	−	0.795342i
$641$	−13.5030	−	23.3879i	−0.533336	−	0.923765i	−0.999242	−	0.0389305i	$-0.987605\pi$
$641$	−13.5030	−	23.3879i	−0.533336	−	0.923765i	0.465906	−	0.884834i	$-0.345728\pi$
$642$		−	63.2175i		−	2.49500i
$643$	−21.1003	+	12.1822i	−0.832113	+	0.480421i	−0.854576	−	0.519327i	$-0.826183\pi$
$643$	−21.1003	+	12.1822i	−0.832113	+	0.480421i	0.0224623	+	0.999748i	$0.492849\pi$
$644$	−2.21294	+	1.27764i	−0.0872020	+	0.0503461i
$645$		−	0.359417i		−	0.0141520i
$646$	1.10789	+	1.91893i	0.0435895	+	0.0754992i
$647$	18.3037	−	31.7030i	0.719594	−	1.24637i	−0.241567	−	0.970384i	$-0.577661\pi$
$647$	18.3037	−	31.7030i	0.719594	−	1.24637i	0.961161	−	0.275989i	$-0.0890052\pi$
$648$	63.6907	+	36.7718i	2.50201	+	1.44453i
$649$	−6.57594			−0.258128
$650$	−11.5071	+	26.5982i	−0.451345	+	1.04327i
$651$	−6.02066			−0.235968
$652$	29.4463	+	17.0008i	1.15320	+	0.665803i
$653$	5.88800	−	10.1983i	0.230415	−	0.399091i	−0.727515	−	0.686092i	$-0.759325\pi$
$653$	5.88800	−	10.1983i	0.230415	−	0.399091i	0.957930	+	0.287001i	$0.0926583\pi$
$654$	46.1993	+	80.0196i	1.80654	+	3.12901i
$655$		−	5.03805i		−	0.196853i
$656$	−40.7197	+	23.5095i	−1.58984	+	0.917893i
$657$	−50.3334	+	29.0600i	−1.96369	+	1.13374i
$658$			2.07611i			0.0809354i
$659$	20.1176	+	34.8447i	0.783670	+	1.35736i	0.929791	+	0.368089i	$0.119988\pi$
$659$	20.1176	+	34.8447i	0.783670	+	1.35736i	−0.146121	+	0.989267i	$0.546679\pi$
$660$	54.7605	−	94.8479i	2.13155	−	3.69195i
$661$	37.4892	+	21.6444i	1.45816	+	0.841869i	0.998921	−	0.0464431i	$-0.0147886\pi$
$661$	37.4892	+	21.6444i	1.45816	+	0.841869i	0.459240	+	0.888312i	$0.348122\pi$
$662$	−6.77771			−0.263423
$663$	−1.27668	−	11.0249i	−0.0495822	−	0.428171i
$664$	−4.19985			−0.162986
$665$	−0.813832	−	0.469866i	−0.0315590	−	0.0182206i
$666$	−87.7222	+	151.939i	−3.39917	+	5.88753i
$667$	2.48684	+	4.30732i	0.0962906	+	0.166780i
$668$			88.3568i			3.41863i
$669$	24.5616	−	14.1806i	0.949606	−	0.548255i
$670$	15.9117	−	9.18665i	0.614724	−	0.354911i
$671$		−	20.4286i		−	0.788636i
$672$	−2.40833	−	4.17136i	−0.0929035	−	0.160914i
$673$	9.46586	−	16.3953i	0.364882	−	0.631994i	−0.623875	−	0.781524i	$-0.714443\pi$
$673$	9.46586	−	16.3953i	0.364882	−	0.631994i	0.988757	+	0.149530i	$0.0477760\pi$
$674$	7.75867	+	4.47947i	0.298853	+	0.172543i
$675$	−34.5617			−1.33028
$676$	−37.2883	−	39.6929i	−1.43417	−	1.52665i
$677$	9.29656			0.357296			0.178648	−	0.983913i	$-0.442828\pi$
$677$	9.29656			0.357296			0.178648	+	0.983913i	$0.442828\pi$
$678$	−81.8752	−	47.2707i	−3.14440	−	1.81542i
$679$	−3.55538	+	6.15810i	−0.136443	+	0.236326i
$680$	3.62219	+	6.27381i	0.138905	+	0.240590i
$681$		−	74.0714i		−	2.83842i
$682$	33.9210	−	19.5843i	1.29890	−	0.749920i
$683$	3.49740	−	2.01922i	0.133824	−	0.0772634i	−0.431593	−	0.902068i	$-0.642048\pi$
$683$	3.49740	−	2.01922i	0.133824	−	0.0772634i	0.565417	+	0.824805i	$0.308715\pi$
$684$			24.1602i			0.923790i
$685$	5.69861	+	9.87028i	0.217733	+	0.377124i
$686$	13.1935	−	22.8518i	0.503729	−	0.872484i
$687$	−34.7336	−	20.0534i	−1.32517	−	0.765086i
$688$	0.453976			0.0173077
$689$	−1.69029	−	14.5966i	−0.0643948	−	0.556086i
$690$	7.83219			0.298166
$691$	−3.14023	−	1.81301i	−0.119460	−	0.0689702i	0.439079	−	0.898448i	$-0.355305\pi$
$691$	−3.14023	−	1.81301i	−0.119460	−	0.0689702i	−0.558539	+	0.829478i	$0.688638\pi$
$692$	0.832607	−	1.44212i	0.0316510	−	0.0548211i
$693$	16.3991	+	28.4041i	0.622952	+	1.07898i
$694$			10.9566i			0.415906i
$695$	11.7156	−	6.76403i	0.444400	−	0.256574i
$696$	−93.9150	+	54.2218i	−3.55984	+	2.05527i
$697$			9.09207i			0.344387i
$698$	−38.5736	−	66.8114i	−1.46003	−	2.52885i
$699$	6.92301	−	11.9910i	0.261852	−	0.453542i
$700$	9.29822	+	5.36833i	0.351440	+	0.202904i
$701$	−7.70896			−0.291163			−0.145582	−	0.989346i	$-0.546505\pi$
$701$	−7.70896			−0.291163			−0.145582	+	0.989346i	$0.546505\pi$
$702$	38.1001	−	88.0671i	1.43800	−	3.32388i
$703$	−9.70002			−0.365843
$704$	−30.0569	−	17.3534i	−1.13281	−	0.654030i
$705$	2.15360	−	3.73014i	0.0811092	−	0.140485i
$706$	18.6250	+	32.2594i	0.700961	+	1.21410i
$707$		−	10.3612i		−	0.389673i
$708$	11.5011	−	6.64017i	0.432238	−	0.249553i
$709$	37.8845	−	21.8726i	1.42278	−	0.821444i	0.426247	−	0.904607i	$-0.359835\pi$
$709$	37.8845	−	21.8726i	1.42278	−	0.821444i	0.996536	+	0.0831622i	$0.0265020\pi$
$710$		−	3.37878i		−	0.126803i
$711$	50.5001	+	87.4687i	1.89390	+	3.28033i
$712$	10.9934	−	19.0411i	0.411995	−	0.713596i
$713$	1.64192	+	0.947965i	0.0614905	+	0.0355016i
$714$	−6.07475			−0.227342
$715$	−28.1048	−	12.1589i	−1.05106	−	0.454716i
$716$	−68.6508			−2.56560
$717$	21.3278	+	12.3136i	0.796501	+	0.459860i
$718$	−20.2988	+	35.1585i	−0.757543	+	1.31210i
$719$	−11.7762	−	20.3970i	−0.439178	−	0.760679i	0.558448	−	0.829540i	$-0.311397\pi$
$719$	−11.7762	−	20.3970i	−0.439178	−	0.760679i	−0.997626	+	0.0688602i	$0.978064\pi$
$720$			44.5398i			1.65990i
$721$	7.06968	−	4.08168i	0.263289	−	0.152010i
$722$	39.2268	−	22.6476i	1.45987	−	0.842856i
$723$			72.3238i			2.68975i
$724$	−26.4140	−	45.7505i	−0.981670	−	1.70030i
$725$	10.4491	−	18.0983i	0.388069	−	0.672155i
$726$	−197.449	−	113.998i	−7.32804	−	4.23084i
$727$	9.77642			0.362587			0.181294	−	0.983429i	$-0.441972\pi$
$727$	9.77642			0.362587			0.181294	+	0.983429i	$0.441972\pi$
$728$	−12.5052	+	9.28902i	−0.463474	+	0.344274i
$729$	−11.3515			−0.420424
$730$	−25.7219	−	14.8505i	−0.952010	−	0.549643i
$731$	0.0438926	−	0.0760242i	0.00162343	−	0.00281186i
$732$	20.6281	+	35.7289i	0.762436	+	1.32058i
$733$			31.9989i			1.18191i	0.806706	+	0.590953i	$0.201248\pi$
$733$			31.9989i			1.18191i	−0.806706	+	0.590953i	$0.798752\pi$
$734$	−16.9994	+	9.81461i	−0.627460	+	0.362264i
$735$	−22.5890	+	13.0418i	−0.833209	+	0.481053i
$736$			1.51679i			0.0559095i
$737$	−17.7271	−	30.7042i	−0.652986	−	1.13100i
$738$	−73.2331	+	126.843i	−2.69575	+	4.66917i
$739$	−23.7679	−	13.7224i	−0.874315	−	0.504786i	−0.00553550	−	0.999985i	$-0.501762\pi$
$739$	−23.7679	−	13.7224i	−0.874315	−	0.504786i	−0.868780	+	0.495198i	$0.835095\pi$
$740$	−60.6855			−2.23084
$741$	9.81933	−	1.13708i	0.360722	−	0.0417716i
$742$	−8.04278			−0.295260
$743$	−3.67170	−	2.11986i	−0.134702	−	0.0777700i	0.431135	−	0.902287i	$-0.358113\pi$
$743$	−3.67170	−	2.11986i	−0.134702	−	0.0777700i	−0.565836	+	0.824517i	$0.691447\pi$
$744$	−20.6690	+	35.7997i	−0.757762	+	1.31248i
$745$	−1.14603	−	1.98498i	−0.0419872	−	0.0727240i
$746$		−	24.7789i		−	0.907221i
$747$	−4.32414	+	2.49655i	−0.158212	+	0.0913438i
$748$	23.1660	−	13.3749i	0.847033	−	0.489035i
$749$			6.54843i			0.239274i
$750$	−41.9190	−	72.6059i	−1.53067	−	2.65119i
$751$	12.8158	−	22.1976i	0.467656	−	0.810003i	−0.531661	−	0.846957i	$-0.678432\pi$
$751$	12.8158	−	22.1976i	0.467656	−	0.810003i	0.999317	+	0.0369536i	$0.0117654\pi$
$752$	4.71151	+	2.72019i	0.171811	+	0.0991951i
$753$	69.7932			2.54341
$754$	34.5977	+	46.5766i	1.25997	+	1.69622i
$755$	20.0747			0.730593
$756$	−30.7865	−	17.7746i	−1.11970	−	0.646456i
$757$	15.7482	−	27.2766i	0.572376	−	0.991385i	−0.423945	−	0.905688i	$-0.639355\pi$
$757$	15.7482	−	27.2766i	0.572376	−	0.991385i	0.996321	−	0.0856970i	$-0.0273117\pi$
$758$	23.7277	+	41.0975i	0.861828	+	1.49273i
$759$		−	15.1134i		−	0.548583i
$760$	−5.58778	+	3.22611i	−0.202690	+	0.117023i
$761$	−6.97556	+	4.02734i	−0.252864	+	0.145991i	−0.621075	−	0.783751i	$-0.713304\pi$
$761$	−6.97556	+	4.02734i	−0.252864	+	0.145991i	0.368211	+	0.929742i	$0.379970\pi$
$762$		−	114.538i		−	4.14926i
$763$	−4.78558	−	8.28887i	−0.173250	−	0.300077i
$764$	−2.53304	+	4.38735i	−0.0916422	+	0.158729i
$765$	7.45878	+	4.30633i	0.269673	+	0.155696i
$766$	54.2599			1.96049
$767$	−2.21418	−	2.98081i	−0.0799495	−	0.107631i
$768$	100.304			3.61940
$769$	−20.9627	−	12.1028i	−0.755933	−	0.436438i	0.0719009	−	0.997412i	$-0.477093\pi$
$769$	−20.9627	−	12.1028i	−0.755933	−	0.436438i	−0.827833	+	0.560974i	$0.810427\pi$
$770$	−8.38046	+	14.5154i	−0.302011	+	0.523098i
$771$	1.39363	+	2.41383i	0.0501902	+	0.0869320i
$772$		−	69.1068i		−	2.48721i
$773$	−5.92989	+	3.42362i	−0.213283	+	0.123139i	−0.602836	−	0.797865i	$-0.705963\pi$
$773$	−5.92989	+	3.42362i	−0.213283	+	0.123139i	0.389553	+	0.921004i	$0.372629\pi$
$774$	1.22469	−	0.707076i	0.0440206	−	0.0254153i
$775$		−	7.96623i		−	0.286155i
$776$	24.4113	+	42.2816i	0.876315	+	1.51782i
$777$	13.2967	−	23.0305i	0.477016	−	0.826216i
$778$	34.8432	+	20.1167i	1.24919	+	0.721220i
$779$	−8.09787			−0.290136
$780$	61.4319	−	7.11382i	2.19962	−	0.254716i
$781$	−6.51989			−0.233300
$782$	1.65667	+	0.956481i	0.0592425	+	0.0342037i
$783$	−34.5970	+	59.9238i	−1.23640	+	2.14150i
$784$	−16.4730	−	28.5320i	−0.588320	−	1.01900i
$785$			2.97724i			0.106262i
$786$	25.1203	−	14.5032i	0.896013	−	0.517313i
$787$	19.6592	−	11.3503i	0.700776	−	0.404593i	−0.106860	−	0.994274i	$-0.534080\pi$
$787$	19.6592	−	11.3503i	0.700776	−	0.404593i	0.807636	+	0.589681i	$0.200746\pi$
$788$		−	58.1065i		−	2.06996i
$789$	0.509415	+	0.882333i	0.0181357	+	0.0314119i
$790$	−25.8071	+	44.6992i	−0.918175	+	1.59033i
$791$	8.48110	+	4.89656i	0.301553	+	0.174102i
$792$	225.194			8.00190
$793$	9.26006	−	6.87849i	0.328834	−	0.244262i
$794$	8.33499			0.295798
$795$	14.4504	+	8.34295i	0.512503	+	0.295894i
$796$	15.0456	−	26.0598i	0.533278	−	0.923664i
$797$	−19.8702	−	34.4161i	−0.703838	−	1.21908i	−0.967109	−	0.254361i	$-0.918135\pi$
$797$	−19.8702	−	34.4161i	−0.703838	−	1.21908i	0.263272	−	0.964722i	$-0.415198\pi$
$798$		−	5.41049i		−	0.191529i
$799$	0.911063	−	0.526002i	0.0322311	−	0.0186086i
$800$	5.51932	−	3.18658i	0.195137	−	0.112663i
$801$		−	26.1395i		−	0.923596i
$802$	−32.1136	−	55.6223i	−1.13397	−	1.96409i
$803$	−28.6565	+	49.6345i	−1.01126	+	1.75156i
$804$	62.0082	+	35.8005i	2.18686	+	1.26258i
$805$	−0.811302			−0.0285946
$806$	20.2988	+	8.78181i	0.714996	+	0.309326i
$807$	−48.6129			−1.71126
$808$	−61.6091	−	35.5701i	−2.16740	−	1.25135i
$809$	23.6831	−	41.0203i	0.832653	−	1.44220i	−0.0632733	−	0.997996i	$-0.520154\pi$
$809$	23.6831	−	41.0203i	0.832653	−	1.44220i	0.895927	−	0.444202i	$-0.146513\pi$
$810$	22.3408	+	38.6954i	0.784975	+	1.35962i
$811$			34.1230i			1.19822i	0.800667	+	0.599110i	$0.204479\pi$
$811$			34.1230i			1.19822i	−0.800667	+	0.599110i	$0.795521\pi$
$812$	18.6154	−	10.7476i	0.653274	−	0.377168i
$813$	1.25204	−	0.722865i	0.0439109	−	0.0253520i
$814$			173.008i			6.06393i
$815$	5.39776	+	9.34919i	0.189075	+	0.327488i
$816$	−7.95932	+	13.7860i	−0.278632	+	0.482605i
$817$	0.0677111	+	0.0390930i	0.00236891	+	0.00136769i
$818$	69.1885			2.41912
$819$	−7.35356	+	16.9975i	−0.256954	+	0.593941i
$820$	−50.6621			−1.76920
$821$	26.7853	+	15.4645i	0.934813	+	0.539715i	0.888331	−	0.459204i	$-0.151865\pi$
$821$	26.7853	+	15.4645i	0.934813	+	0.539715i	0.0464826	+	0.998919i	$0.485199\pi$
$822$	−32.8096	+	56.8279i	−1.14437	+	1.98210i
$823$	−22.7078	−	39.3311i	−0.791544	−	1.37099i	−0.925011	−	0.379941i	$-0.875944\pi$
$823$	−22.7078	−	39.3311i	−0.791544	−	1.37099i	0.133467	−	0.991053i	$-0.457389\pi$
$824$		−	56.0498i		−	1.95259i
$825$	−54.9952	+	31.7515i	−1.91469	+	1.10544i
$826$	−1.76011	+	1.01620i	−0.0612421	+	0.0353582i
$827$		−	49.5757i		−	1.72391i	−0.506981	−	0.861957i	$-0.669239\pi$
$827$		−	49.5757i		−	1.72391i	0.506981	−	0.861957i	$-0.330761\pi$
$828$	10.4292	+	18.0639i	0.362439	+	0.627762i
$829$	14.0926	−	24.4091i	0.489455	−	0.847762i	−0.510471	−	0.859895i	$-0.670529\pi$
$829$	14.0926	−	24.4091i	0.489455	−	0.847762i	0.999926	+	0.0121334i	$0.00386229\pi$
$830$	−2.20977	−	1.27581i	−0.0767022	−	0.0442840i
$831$	34.4609			1.19544
$832$	−2.25434	−	19.4675i	−0.0781552	−	0.674916i
$833$	−6.37074			−0.220733
$834$	67.4526	+	38.9438i	2.33569	+	1.34851i
$835$	−14.0266	+	24.2948i	−0.485412	+	0.840758i
$836$	11.9124	+	20.6328i	0.411998	+	0.713602i
$837$			26.3763i			0.911698i
$838$	−39.2975	+	22.6884i	−1.35751	+	0.783759i
$839$	−35.2393	+	20.3454i	−1.21660	+	0.702402i	−0.964188	−	0.265218i	$-0.914556\pi$
$839$	−35.2393	+	20.3454i	−1.21660	+	0.702402i	−0.252408	+	0.967621i	$0.581223\pi$
$840$		−	17.6893i		−	0.610337i
$841$	−6.41948	−	11.1189i	−0.221361	−	0.383409i
$842$	−3.47009	+	6.01038i	−0.119587	+	0.207131i
$843$	37.6679	+	21.7476i	1.29735	+	0.749026i
$844$	95.7594			3.29617
$845$	−3.95165	−	16.8336i	−0.135941	−	0.579094i
$846$	16.9470			0.582649
$847$	20.4529	+	11.8085i	0.702771	+	0.405745i
$848$	−10.5379	+	18.2522i	−0.361873	+	0.626782i
$849$	27.3418	+	47.3575i	0.938370	+	1.62530i
$850$		−	8.03779i		−	0.275694i
$851$	−7.25240	+	4.18718i	−0.248609	+	0.143535i
$852$	11.4031	−	6.58357i	0.390663	−	0.225549i
$853$			26.8764i			0.920230i	0.887859	+	0.460115i	$0.152192\pi$
$853$			26.8764i			0.920230i	−0.887859	+	0.460115i	$0.847808\pi$
$854$	−3.15689	−	5.46789i	−0.108027	−	0.187107i
$855$	−3.83544	+	6.64318i	−0.131169	+	0.227192i
$856$	38.9379	+	22.4808i	1.33087	+	0.768378i
$857$	10.6979			0.365432			0.182716	−	0.983166i	$-0.441511\pi$
$857$	10.6979			0.365432			0.182716	+	0.983166i	$0.441511\pi$
$858$	−20.2808	−	175.136i	−0.692374	−	5.97905i
$859$	32.7273			1.11664			0.558321	−	0.829625i	$-0.311446\pi$
$859$	32.7273			1.11664			0.558321	+	0.829625i	$0.311446\pi$
$860$	0.423616	+	0.244575i	0.0144452	+	0.00833993i
$861$	11.1005	−	19.2266i	0.378303	−	0.655240i
$862$	0.530429	+	0.918730i	0.0180665	+	0.0312921i
$863$			8.94887i			0.304623i	0.988333	+	0.152312i	$0.0486717\pi$
$863$			8.94887i			0.304623i	−0.988333	+	0.152312i	$0.951328\pi$
$864$	−18.2745	+	10.5508i	−0.621713	+	0.358946i
$865$	0.457872	−	0.264353i	0.0155681	−	0.00898826i
$866$			13.5532i			0.460556i
$867$	1.53909	+	2.66579i	0.0522703	+	0.0905349i
$868$	4.09692	−	7.09608i	0.139059	−	0.240857i
$869$	86.2541	+	49.7989i	2.92597	+	1.68931i
$870$	−65.8851			−2.23371
$871$	7.94903	−	18.3739i	0.269343	−	0.622576i
$872$	−65.7158			−2.22542
$873$	50.2676	+	29.0220i	1.70130	+	0.982246i
$874$	−0.851891	+	1.47552i	−0.0288157	+	0.0499102i
$875$	4.34221	+	7.52093i	0.146793	+	0.254254i
$876$		−	115.745i		−	3.91067i
$877$	9.86013	−	5.69275i	0.332953	−	0.192231i	−0.324198	−	0.945989i	$-0.605095\pi$
$877$	9.86013	−	5.69275i	0.332953	−	0.192231i	0.657151	+	0.753759i	$0.271761\pi$
$878$	16.9149	−	9.76581i	0.570849	−	0.329580i
$879$		−	18.4806i		−	0.623334i
$880$	21.9607	+	38.0370i	0.740294	+	1.28223i
$881$	−27.7955	+	48.1432i	−0.936455	+	1.62199i	−0.164436	+	0.986388i	$0.552580\pi$
$881$	−27.7955	+	48.1432i	−0.936455	+	1.62199i	−0.772019	+	0.635599i	$0.780753\pi$
$882$	−88.8782	−	51.3139i	−2.99269	−	1.72783i
$883$	13.4034			0.451061			0.225531	−	0.974236i	$-0.427588\pi$
$883$	13.4034			0.451061			0.225531	+	0.974236i	$0.427588\pi$
$884$	13.8629	+	5.99746i	0.466260	+	0.201716i
$885$	4.21651			0.141736
$886$	−41.7321	−	24.0940i	−1.40202	−	0.809455i
$887$	28.6063	−	49.5476i	0.960506	−	1.66365i	0.239274	−	0.970952i	$-0.423090\pi$
$887$	28.6063	−	49.5476i	0.960506	−	1.66365i	0.721232	−	0.692694i	$-0.243576\pi$
$888$	−91.2953	−	158.128i	−3.06367	−	5.30643i
$889$			11.8644i			0.397920i
$890$	11.5685	−	6.67905i	0.387776	−	0.223882i
$891$	74.6688	−	43.1101i	2.50150	−	1.44424i
$892$			38.5984i			1.29237i
$893$	0.468485	+	0.811440i	0.0156773	+	0.0271538i
$894$	6.59823	−	11.4285i	0.220678	−	0.382225i
$895$	−18.8764	−	10.8983i	−0.630969	−	0.364290i
$896$	−13.8562			−0.462904
$897$	6.85077	−	5.08884i	0.228740	−	0.169911i
$898$	32.7907			1.09424
$899$	−13.8120	−	7.97437i	−0.460656	−	0.265960i
$900$	43.8208	−	75.8999i	1.46069	−	2.53000i
$901$	2.03771	+	3.52942i	0.0678860	+	0.117582i
$902$			144.432i			4.80907i
$903$	−0.185635	+	0.107177i	−0.00617756	+	0.00356661i
$904$	58.2314	−	33.6199i	1.93675	−	1.11818i
$905$		−	16.7729i		−	0.557551i
$906$	57.7898	+	100.095i	1.91994	+	3.32543i
$907$	−14.5656	+	25.2283i	−0.483642	+	0.837692i	−0.999824	−	0.0187868i	$-0.994020\pi$
$907$	−14.5656	+	25.2283i	−0.483642	+	0.837692i	0.516182	+	0.856479i	$0.327353\pi$
$908$	87.3020	+	50.4039i	2.89722	+	1.67271i
$909$	−84.5767			−2.80523
$910$	−9.40145	+	1.08869i	−0.311655	+	0.0360896i
$911$	26.4466			0.876216			0.438108	−	0.898922i	$-0.355649\pi$
$911$	26.4466			0.876216			0.438108	+	0.898922i	$0.355649\pi$
$912$	−12.2785	−	7.08899i	−0.406581	−	0.234740i
$913$	−2.46188	+	4.26410i	−0.0814763	+	0.141121i
$914$	−47.1908	−	81.7369i	−1.56093	−	2.70362i
$915$			13.0988i			0.433034i
$916$	47.2708	−	27.2918i	1.56187	−	0.901747i
$917$	−2.60211	+	1.50233i	−0.0859291	+	0.0496112i
$918$			26.6132i			0.878368i
$919$	10.5488	+	18.2711i	0.347974	+	0.602709i	0.985889	−	0.167397i	$-0.0535363\pi$
$919$	10.5488	+	18.2711i	0.347974	+	0.602709i	−0.637915	+	0.770107i	$0.720203\pi$
$920$	−2.78521	+	4.82412i	−0.0918255	+	0.159047i
$921$	11.9770	+	6.91493i	0.394656	+	0.227855i
$922$	30.9548			1.01944
$923$	−2.19531	−	2.95540i	−0.0722594	−	0.0972781i
$924$	−65.3174			−2.14879
$925$	30.4728	+	17.5935i	1.00194	+	0.578470i
$926$	29.9658	−	51.9024i	0.984738	−	1.70562i
$927$	−33.3181	−	57.7087i	−1.09431	−	1.89540i
$928$		−	12.7593i		−	0.418846i
$929$	−44.8440	+	25.8907i	−1.47128	+	0.849446i	−0.999480	−	0.0322576i	$-0.989730\pi$
$929$	−44.8440	+	25.8907i	−1.47128	+	0.849446i	−0.471804	+	0.881704i	$0.656397\pi$
$930$	−21.7502	+	12.5575i	−0.713216	+	0.411776i
$931$		−	5.67411i		−	0.185962i
$932$	9.42190	+	16.3192i	0.308625	+	0.534554i
$933$	−23.5263	+	40.7487i	−0.770215	+	1.33405i
$934$	−16.0831	−	9.28556i	−0.526254	−	0.303833i
$935$	8.49306			0.277753
$936$	75.8248	+	102.078i	2.47841	+	3.33652i
$937$	−53.3897			−1.74417			−0.872083	−	0.489358i	$-0.837231\pi$
$937$	−53.3897			−1.74417			−0.872083	+	0.489358i	$0.837231\pi$
$938$	−9.48964	−	5.47885i	−0.309848	−	0.178891i
$939$	17.5208	−	30.3470i	0.571771	−	0.990337i
$940$	2.93095	+	5.07655i	0.0955970	+	0.165579i
$941$		−	33.8292i		−	1.10280i	−0.834241	−	0.551401i	$-0.814094\pi$
$941$		−	33.8292i		−	1.10280i	0.834241	−	0.551401i	$-0.185906\pi$
$942$	−14.8449	+	8.57069i	−0.483672	+	0.279248i
$943$	−6.05452	+	3.49558i	−0.197162	+	0.113832i
$944$			5.32583i			0.173341i
$945$	−5.64344	−	9.77473i	−0.183581	−	0.317972i
$946$	0.697257	−	1.20769i	0.0226698	−	0.0392652i
$947$	28.8092	+	16.6330i	0.936173	+	0.540500i	0.888759	−	0.458376i	$-0.151569\pi$
$947$	28.8092	+	16.6330i	0.936173	+	0.540500i	0.0474143	+	0.998875i	$0.484902\pi$
$948$	−201.141			−6.53275
$949$	−32.1477	+	3.72270i	−1.04356	+	0.120844i
$950$	7.15888			0.232265
$951$	27.5324	+	15.8958i	0.892800	+	0.515458i
$952$	2.16024	−	3.74165i	0.0700139	−	0.121268i
$953$	−1.56838	−	2.71651i	−0.0508047	−	0.0879963i	0.839505	−	0.543352i	$-0.182845\pi$
$953$	−1.56838	−	2.71651i	−0.0508047	−	0.0879963i	−0.890309	+	0.455356i	$0.849512\pi$
$954$			65.6519i			2.12556i
$955$	−1.39299	+	0.804240i	−0.0450759	+	0.0260246i
$956$	−29.0261	+	16.7583i	−0.938773	+	0.542001i
$957$			127.136i			4.10971i
$958$	6.50438	+	11.2659i	0.210147	+	0.363985i
$959$	3.39861	−	5.88656i	0.109747	−	0.190087i
$960$	19.2726	+	11.1270i	0.622019	+	0.359123i
$961$	24.9205			0.803886
$962$	−78.4228	+	58.2534i	−2.52845	+	1.87817i
$963$	53.4537			1.72252
$964$	−85.2423	−	49.2147i	−2.74547	−	1.58510i
$965$	10.9707	−	19.0018i	0.353159	−	0.611690i
$966$	−2.33553	−	4.04525i	−0.0751444	−	0.130154i
$967$			25.1328i			0.808217i	0.914711	+	0.404108i	$0.132418\pi$
$967$			25.1328i			0.808217i	−0.914711	+	0.404108i	$0.867582\pi$
$968$	140.430	−	81.0774i	4.51360	−	2.60593i
$969$	−2.37429	+	1.37080i	−0.0762731	+	0.0440363i
$970$			29.6622i			0.952397i
$971$	9.13405	+	15.8206i	0.293126	+	0.507708i	0.974547	−	0.224183i	$-0.0719713\pi$
$971$	9.13405	+	15.8206i	0.293126	+	0.507708i	−0.681422	+	0.731891i	$0.738638\pi$
$972$	−19.8408	+	34.3653i	−0.636394	+	1.10227i
$973$	−6.98712	−	4.03402i	−0.223997	−	0.129325i
$974$	−64.3668			−2.06245
$975$	−32.9100	−	14.2377i	−1.05396	−	0.455972i
$976$	−16.5450			−0.529593
$977$	−7.87009	−	4.54380i	−0.251787	−	0.145369i	0.368795	−	0.929511i	$-0.379770\pi$
$977$	−7.87009	−	4.54380i	−0.251787	−	0.145369i	−0.620582	+	0.784142i	$0.713104\pi$
$978$	−31.0775	+	53.8278i	−0.993748	+	1.72122i
$979$	−12.8883	−	22.3232i	−0.411911	−	0.713451i
$980$		−	35.4985i		−	1.13396i
$981$	−67.6607	+	39.0639i	−2.16024	+	1.24722i
$982$	−46.9309	+	27.0956i	−1.49763	+	0.864654i
$983$		−	28.9896i		−	0.924626i	−0.886717	−	0.462313i	$-0.847020\pi$
$983$		−	28.9896i		−	0.924626i	0.886717	−	0.462313i	$-0.152980\pi$
$984$	−76.2161	−	132.010i	−2.42968	−	4.20833i
$985$	9.22442	−	15.9772i	0.293914	−	0.509075i
$986$	−13.9361	−	8.04600i	−0.443815	−	0.256237i
$987$	−2.56878			−0.0817651
$988$	−5.34165	+	12.3470i	−0.169940	+	0.392811i
$989$	0.0675006			0.00214640
$990$	118.487	+	68.4083i	3.76575	+	2.17416i
$991$	7.91122	−	13.7026i	0.251308	−	0.435279i	−0.712578	−	0.701593i	$-0.752473\pi$
$991$	7.91122	−	13.7026i	0.251308	−	0.435279i	0.963886	+	0.266314i	$0.0858059\pi$
$992$	−2.43189	−	4.21215i	−0.0772125	−	0.133736i
$993$		−	8.38606i		−	0.266124i
$994$	−1.74511	+	1.00754i	−0.0553515	+	0.0319572i
$995$	8.27398	−	4.77698i	0.262303	−	0.151441i
$996$		−	9.94369i		−	0.315078i
$997$	8.45874	+	14.6510i	0.267891	+	0.464001i	0.968317	−	0.249724i	$-0.0803400\pi$
$997$	8.45874	+	14.6510i	0.267891	+	0.464001i	−0.700426	+	0.713725i	$0.747007\pi$
$998$	11.1111	−	19.2450i	0.351715	−	0.609189i
$999$	−100.896	−	58.2523i	−3.19220	−	1.84302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.b.69.1	✓	12
13.6	odd	12		2873.2.a.u.1.12		12
13.7	odd	12		2873.2.a.u.1.1		12
13.10	even	6	inner	221.2.m.b.205.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.b.69.1	✓	12	1.1	even	1	trivial
221.2.m.b.205.1	yes	12	13.10	even	6	inner
2873.2.a.u.1.1		12	13.7	odd	12
2873.2.a.u.1.12		12	13.6	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+(-2.15452 - 1.24391i) q^{2} +(1.53909 - 2.66579i) q^{3} +(2.09463 + 3.62801i) q^{4} +1.33009i q^{5} +(-6.63201 + 3.82899i) q^{6} +(0.686981 - 0.396628i) q^{7} -5.44652i q^{8} +(-3.23761 - 5.60771i) q^{9} +(1.65452 - 2.86571i) q^{10} +(-5.52984 - 3.19266i) q^{11} +12.8953 q^{12} +(-0.414751 - 3.58162i) q^{13} -1.97348 q^{14} +(3.54575 + 2.04714i) q^{15} +(-2.58572 + 4.47860i) q^{16} +(0.500000 + 0.866025i) q^{17} +16.1092i q^{18} +(-0.771327 + 0.445326i) q^{19} +(-4.82560 + 2.78606i) q^{20} -2.44179i q^{21} +(7.94277 + 13.7573i) q^{22} +(-0.384465 + 0.665912i) q^{23} +(-14.5193 - 8.38270i) q^{24} +3.23085 q^{25} +(-3.56163 + 8.23258i) q^{26} -10.6974 q^{27} +(2.87795 + 1.66158i) q^{28} +(3.23415 - 5.60172i) q^{29} +(-5.09292 - 8.82119i) q^{30} -2.46567i q^{31} +(1.70832 - 0.986298i) q^{32} +(-17.0219 + 9.82759i) q^{33} -2.48782i q^{34} +(0.527553 + 0.913748i) q^{35} +(13.5632 - 23.4922i) q^{36} +(9.43182 + 5.44546i) q^{37} +2.21579 q^{38} +(-10.1862 - 4.40680i) q^{39} +7.24437 q^{40} +(7.87397 + 4.54604i) q^{41} +(-3.03737 + 5.26089i) q^{42} +(-0.0438926 - 0.0760242i) q^{43} -26.7498i q^{44} +(7.45878 - 4.30633i) q^{45} +(1.65667 - 0.956481i) q^{46} -1.05200i q^{47} +(7.95932 + 13.7860i) q^{48} +(-3.18537 + 5.51723i) q^{49} +(-6.96093 - 4.01890i) q^{50} +3.07819 q^{51} +(12.1254 - 9.00690i) q^{52} +4.07542 q^{53} +(23.0477 + 13.3066i) q^{54} +(4.24653 - 7.35520i) q^{55} +(-2.16024 - 3.74165i) q^{56} +2.74159i q^{57} +(-13.9361 + 8.04600i) q^{58} +(0.891880 - 0.514927i) q^{59} +17.1520i q^{60} +(1.59965 + 2.77068i) q^{61} +(-3.06708 + 5.31234i) q^{62} +(-4.44836 - 2.56826i) q^{63} +5.43541 q^{64} +(4.76388 - 0.551658i) q^{65} +48.8986 q^{66} +(4.80857 + 2.77623i) q^{67} +(-2.09463 + 3.62801i) q^{68} +(1.18345 + 2.04980i) q^{69} -2.62492i q^{70} +(0.884278 - 0.510538i) q^{71} +(-30.5425 + 17.6337i) q^{72} -8.97575i q^{73} +(-13.5474 - 23.4647i) q^{74} +(4.97258 - 8.61276i) q^{75} +(-3.23130 - 1.86559i) q^{76} -5.06519 q^{77} +(16.4646 + 22.1652i) q^{78} -15.5979 q^{79} +(-5.95695 - 3.43925i) q^{80} +(-6.75144 + 11.6938i) q^{81} +(-11.3097 - 19.5890i) q^{82} -0.771107i q^{83} +(8.85885 - 5.11466i) q^{84} +(-1.15189 + 0.665047i) q^{85} +0.218394i q^{86} +(-9.95532 - 17.2431i) q^{87} +(-17.3889 + 30.1184i) q^{88} +(3.49602 + 2.01843i) q^{89} -21.4268 q^{90} +(-1.70550 - 2.29600i) q^{91} -3.22125 q^{92} +(-6.57296 - 3.79490i) q^{93} +(-1.30860 + 2.26656i) q^{94} +(-0.592325 - 1.02594i) q^{95} -6.07201i q^{96} +(-7.76306 + 4.48201i) q^{97} +(13.7259 - 7.92464i) q^{98} +41.3463i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 4 q^{3} + q^{4} - 12 q^{6} - 4 q^{9} - 3 q^{10} - 24 q^{11} + 20 q^{12} + 7 q^{13} + 10 q^{14} + 9 q^{15} - q^{16} + 6 q^{17} + 15 q^{19} - 18 q^{20} + 11 q^{22} - 12 q^{23} - 42 q^{24}+ \cdots - 30 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 4 * q^3 + q^4 - 12 * q^6 - 4 * q^9 - 3 * q^10 - 24 * q^11 + 20 * q^12 + 7 * q^13 + 10 * q^14 + 9 * q^15 - q^16 + 6 * q^17 + 15 * q^19 - 18 * q^20 + 11 * q^22 - 12 * q^23 - 42 * q^24 + 22 * q^25 - 8 * q^26 - 20 * q^27 - 3 * q^28 + 11 * q^29 - 8 * q^30 + 24 * q^32 - 54 * q^33 + 4 * q^35 + 23 * q^36 - 18 * q^37 + 12 * q^38 - 38 * q^39 + 34 * q^40 + 3 * q^41 + 7 * q^42 - 2 * q^43 + 15 * q^45 + 21 * q^46 + 17 * q^48 - 2 * q^49 - 33 * q^50 + 8 * q^51 + 42 * q^52 + 6 * q^53 + 30 * q^54 + 22 * q^55 - 21 * q^56 - 9 * q^58 - 3 * q^59 + 13 * q^61 - 15 * q^62 - 51 * q^63 - 14 * q^65 + 112 * q^66 - 21 * q^67 - q^68 - 4 * q^69 + 18 * q^71 - 81 * q^72 - 24 * q^74 - 2 * q^75 - 45 * q^76 + 38 * q^77 + 28 * q^78 - 38 * q^79 + 33 * q^80 + 6 * q^81 - 32 * q^82 + 33 * q^84 - 9 * q^85 + 23 * q^87 - 39 * q^88 - 12 * q^89 - 40 * q^90 - 14 * q^91 + 10 * q^92 - 21 * q^93 + 25 * q^94 - 13 * q^95 + 36 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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