LMFDB - Embedded newform 221.2.m.c.69.8

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			69.8
Character	$\chi$	$=$	221.69
Dual form			221.2.m.c.205.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.720682 + 0.416086i) q^{2} +(-0.251133 + 0.434974i) q^{3} +(-0.653745 - 1.13232i) q^{4} -1.03543i q^{5} +(-0.361974 + 0.208986i) q^{6} +(2.58322 - 1.49142i) q^{7} -2.75240i q^{8} +(1.37386 + 2.37960i) q^{9} +(0.430827 - 0.746214i) q^{10} +(1.81620 + 1.04858i) q^{11} +0.656706 q^{12} +(1.13303 - 3.42290i) q^{13} +2.48224 q^{14} +(0.450384 + 0.260029i) q^{15} +(-0.162253 + 0.281030i) q^{16} +(-0.500000 - 0.866025i) q^{17} +2.28658i q^{18} +(-4.93472 + 2.84906i) q^{19} +(-1.17243 + 0.676904i) q^{20} +1.49818i q^{21} +(0.872603 + 1.51139i) q^{22} +(-0.255486 + 0.442515i) q^{23} +(1.19722 + 0.691217i) q^{24} +3.92789 q^{25} +(2.24077 - 1.99539i) q^{26} -2.88688 q^{27} +(-3.37754 - 1.95002i) q^{28} +(-4.13432 + 7.16085i) q^{29} +(0.216389 + 0.374797i) q^{30} -3.19297i q^{31} +(-5.00116 + 2.88742i) q^{32} +(-0.912215 + 0.526667i) q^{33} -0.832172i q^{34} +(-1.54426 - 2.67474i) q^{35} +(1.79631 - 3.11131i) q^{36} +(-8.44410 - 4.87520i) q^{37} -4.74182 q^{38} +(1.20433 + 1.35244i) q^{39} -2.84991 q^{40} +(6.78916 + 3.91972i) q^{41} +(-0.623372 + 1.07971i) q^{42} +(4.19618 + 7.26799i) q^{43} -2.74203i q^{44} +(2.46390 - 1.42254i) q^{45} +(-0.368249 + 0.212609i) q^{46} -1.15368i q^{47} +(-0.0814940 - 0.141152i) q^{48} +(0.948695 - 1.64319i) q^{49} +(2.83076 + 1.63434i) q^{50} +0.502265 q^{51} +(-4.61652 + 0.954756i) q^{52} +0.563021 q^{53} +(-2.08053 - 1.20119i) q^{54} +(1.08573 - 1.88054i) q^{55} +(-4.10500 - 7.11007i) q^{56} -2.86197i q^{57} +(-5.95906 + 3.44047i) q^{58} +(-5.15910 + 2.97861i) q^{59} -0.679971i q^{60} +(-1.86661 - 3.23307i) q^{61} +(1.32855 - 2.30112i) q^{62} +(7.09800 + 4.09803i) q^{63} -4.15666 q^{64} +(-3.54416 - 1.17317i) q^{65} -0.876556 q^{66} +(12.6635 + 7.31125i) q^{67} +(-0.653745 + 1.13232i) q^{68} +(-0.128322 - 0.222260i) q^{69} -2.57018i q^{70} +(-5.86968 + 3.38886i) q^{71} +(6.54962 - 3.78143i) q^{72} -6.54897i q^{73} +(-4.05701 - 7.02695i) q^{74} +(-0.986421 + 1.70853i) q^{75} +(6.45209 + 3.72512i) q^{76} +6.25554 q^{77} +(0.305211 + 1.47579i) q^{78} -12.5129 q^{79} +(0.290986 + 0.168001i) q^{80} +(-3.39660 + 5.88309i) q^{81} +(3.26189 + 5.64975i) q^{82} +13.0974i q^{83} +(1.69642 - 0.979428i) q^{84} +(-0.896706 + 0.517713i) q^{85} +6.98389i q^{86} +(-2.07652 - 3.59665i) q^{87} +(2.88613 - 4.99892i) q^{88} +(11.6217 + 6.70979i) q^{89} +2.36759 q^{90} +(-2.17814 - 10.5319i) q^{91} +0.668091 q^{92} +(1.38886 + 0.801858i) q^{93} +(0.480028 - 0.831434i) q^{94} +(2.94999 + 5.10954i) q^{95} -2.90050i q^{96} +(6.71621 - 3.87760i) q^{97} +(1.36742 - 0.789477i) q^{98} +5.76246i 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 $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.720682	+	0.416086i	0.509599	+	0.294217i	0.732669	−	0.680585i	$-0.238274\pi$
$2$	0.720682	+	0.416086i	0.509599	+	0.294217i	−0.223070	+	0.974803i	$0.571608\pi$
$3$	−0.251133	+	0.434974i	−0.144991	+	0.251133i	−0.929370	−	0.369150i	$-0.879649\pi$
$3$	−0.251133	+	0.434974i	−0.144991	+	0.251133i	0.784378	+	0.620283i	$0.212982\pi$
$4$	−0.653745	−	1.13232i	−0.326872	−	0.566159i
$5$		−	1.03543i		−	0.463057i	−0.972828	−	0.231528i	$-0.925627\pi$
$5$		−	1.03543i		−	0.463057i	0.972828	−	0.231528i	$-0.0743726\pi$
$6$	−0.361974	+	0.208986i	−0.147775	+	0.0853180i
$7$	2.58322	−	1.49142i	0.976367	−	0.563706i	0.0751954	−	0.997169i	$-0.476042\pi$
$7$	2.58322	−	1.49142i	0.976367	−	0.563706i	0.901171	+	0.433463i	$0.142709\pi$
$8$		−	2.75240i		−	0.973121i
$9$	1.37386	+	2.37960i	0.457955	+	0.793201i
$10$	0.430827	−	0.746214i	0.136239	−	0.235973i
$11$	1.81620	+	1.04858i	0.547606	+	0.316160i	0.748156	−	0.663523i	$-0.230940\pi$
$11$	1.81620	+	1.04858i	0.547606	+	0.316160i	−0.200550	+	0.979683i	$0.564273\pi$
$12$	0.656706			0.189575
$13$	1.13303	−	3.42290i	0.314245	−	0.949342i
$13$	1.13303	−	3.42290i	0.314245	−	0.949342i
$14$	2.48224			0.663408
$15$	0.450384	+	0.260029i	0.116289	+	0.0671393i
$16$	−0.162253	+	0.281030i	−0.0405633	+	0.0702576i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$			2.28658i			0.538953i
$19$	−4.93472	+	2.84906i	−1.13210	+	0.653620i	−0.944463	−	0.328618i	$-0.893417\pi$
$19$	−4.93472	+	2.84906i	−1.13210	+	0.653620i	−0.187640	+	0.982238i	$0.560084\pi$
$20$	−1.17243	+	0.676904i	−0.262164	+	0.151360i
$21$			1.49818i			0.326930i
$22$	0.872603	+	1.51139i	0.186040	+	0.322230i
$23$	−0.255486	+	0.442515i	−0.0532726	+	0.0922708i	−0.891432	−	0.453155i	$-0.850299\pi$
$23$	−0.255486	+	0.442515i	−0.0532726	+	0.0922708i	0.838159	+	0.545425i	$0.183632\pi$
$24$	1.19722	+	0.691217i	0.244382	+	0.141094i
$25$	3.92789			0.785578
$26$	2.24077	−	1.99539i	0.439452	−	0.391328i
$27$	−2.88688			−0.555581
$28$	−3.37754	−	1.95002i	−0.638294	−	0.368519i
$29$	−4.13432	+	7.16085i	−0.767724	+	1.32974i	0.171071	+	0.985259i	$0.445277\pi$
$29$	−4.13432	+	7.16085i	−0.767724	+	1.32974i	−0.938794	+	0.344478i	$0.888056\pi$
$30$	0.216389	+	0.374797i	0.0395071	+	0.0684283i
$31$		−	3.19297i		−	0.573474i	−0.958009	−	0.286737i	$-0.907429\pi$
$31$		−	3.19297i		−	0.573474i	0.958009	−	0.286737i	$-0.0925706\pi$
$32$	−5.00116	+	2.88742i	−0.884089	+	0.510429i
$33$	−0.912215	+	0.526667i	−0.158796	+	0.0916810i
$34$		−	0.832172i		−	0.142716i
$35$	−1.54426	−	2.67474i	−0.261028	−	0.452113i
$36$	1.79631	−	3.11131i	0.299386	−	0.518551i
$37$	−8.44410	−	4.87520i	−1.38820	−	0.801478i	−0.395089	−	0.918643i	$-0.629286\pi$
$37$	−8.44410	−	4.87520i	−1.38820	−	0.801478i	−0.993113	+	0.117165i	$0.962619\pi$
$38$	−4.74182			−0.769225
$39$	1.20433	+	1.35244i	0.192848	+	0.216564i
$40$	−2.84991			−0.450610
$41$	6.78916	+	3.91972i	1.06029	+	0.612158i	0.925512	−	0.378718i	$-0.123635\pi$
$41$	6.78916	+	3.91972i	1.06029	+	0.612158i	0.134777	+	0.990876i	$0.456968\pi$
$42$	−0.623372	+	1.07971i	−0.0961884	+	0.166603i
$43$	4.19618	+	7.26799i	0.639911	+	1.10836i	0.985452	+	0.169955i	$0.0543622\pi$
$43$	4.19618	+	7.26799i	0.639911	+	1.10836i	−0.345541	+	0.938404i	$0.612305\pi$
$44$		−	2.74203i		−	0.413376i
$45$	2.46390	−	1.42254i	0.367297	−	0.212059i
$46$	−0.368249	+	0.212609i	−0.0542954	+	0.0313474i
$47$		−	1.15368i		−	0.168281i	−0.996454	−	0.0841404i	$-0.973186\pi$
$47$		−	1.15368i		−	0.168281i	0.996454	−	0.0841404i	$-0.0268144\pi$
$48$	−0.0814940	−	0.141152i	−0.0117626	−	0.0203735i
$49$	0.948695	−	1.64319i	0.135528	−	0.234741i
$50$	2.83076	+	1.63434i	0.400330	+	0.231131i
$51$	0.502265			0.0703312
$52$	−4.61652	+	0.954756i	−0.640197	+	0.132401i
$53$	0.563021			0.0773369			0.0386685	−	0.999252i	$-0.487688\pi$
$53$	0.563021			0.0773369			0.0386685	+	0.999252i	$0.487688\pi$
$54$	−2.08053	−	1.20119i	−0.283124	−	0.163462i
$55$	1.08573	−	1.88054i	0.146400	−	0.253572i
$56$	−4.10500	−	7.11007i	−0.548554	−	0.950123i
$57$		−	2.86197i		−	0.379077i
$58$	−5.95906	+	3.44047i	−0.782463	+	0.451755i
$59$	−5.15910	+	2.97861i	−0.671657	+	0.387782i	−0.796704	−	0.604369i	$-0.793425\pi$
$59$	−5.15910	+	2.97861i	−0.671657	+	0.387782i	0.125047	+	0.992151i	$0.460092\pi$
$60$		−	0.679971i		−	0.0877838i
$61$	−1.86661	−	3.23307i	−0.238995	−	0.413952i	0.721431	−	0.692486i	$-0.243485\pi$
$61$	−1.86661	−	3.23307i	−0.238995	−	0.413952i	−0.960426	+	0.278534i	$0.910151\pi$
$62$	1.32855	−	2.30112i	0.168726	−	0.292242i
$63$	7.09800	+	4.09803i	0.894264	+	0.516303i
$64$	−4.15666			−0.519582
$65$	−3.54416	−	1.17317i	−0.439599	−	0.145513i
$66$	−0.876556			−0.107897
$67$	12.6635	+	7.31125i	1.54709	+	0.893212i	0.998362	+	0.0572095i	$0.0182203\pi$
$67$	12.6635	+	7.31125i	1.54709	+	0.893212i	0.548726	+	0.836002i	$0.315113\pi$
$68$	−0.653745	+	1.13232i	−0.0792782	+	0.137314i
$69$	−0.128322	−	0.222260i	−0.0154481	−	0.0267570i
$70$		−	2.57018i		−	0.307195i
$71$	−5.86968	+	3.38886i	−0.696603	+	0.402184i	−0.806081	−	0.591805i	$-0.798415\pi$
$71$	−5.86968	+	3.38886i	−0.696603	+	0.402184i	0.109478	+	0.993989i	$0.465082\pi$
$72$	6.54962	−	3.78143i	0.771881	−	0.445645i
$73$		−	6.54897i		−	0.766499i	−0.923645	−	0.383250i	$-0.874805\pi$
$73$		−	6.54897i		−	0.766499i	0.923645	−	0.383250i	$-0.125195\pi$
$74$	−4.05701	−	7.02695i	−0.471618	−	0.816866i
$75$	−0.986421	+	1.70853i	−0.113902	+	0.197284i
$76$	6.45209	+	3.72512i	0.740106	+	0.427300i
$77$	6.25554			0.712885
$78$	0.305211	+	1.47579i	0.0345584	+	0.167100i
$79$	−12.5129			−1.40781			−0.703907	−	0.710293i	$-0.748563\pi$
$79$	−12.5129			−1.40781			−0.703907	+	0.710293i	$0.748563\pi$
$80$	0.290986	+	0.168001i	0.0325333	+	0.0187831i
$81$	−3.39660	+	5.88309i	−0.377400	+	0.653677i
$82$	3.26189	+	5.64975i	0.360215	+	0.623911i
$83$			13.0974i			1.43763i	0.695202	+	0.718815i	$0.255315\pi$
$83$			13.0974i			1.43763i	−0.695202	+	0.718815i	$0.744685\pi$
$84$	1.69642	−	0.979428i	0.185094	−	0.106864i
$85$	−0.896706	+	0.517713i	−0.0972614	+	0.0561539i
$86$			6.98389i			0.753092i
$87$	−2.07652	−	3.59665i	−0.222627	−	0.385601i
$88$	2.88613	−	4.99892i	0.307662	−	0.532886i
$89$	11.6217	+	6.70979i	1.23190	+	0.711236i	0.967425	−	0.253157i	$-0.0814689\pi$
$89$	11.6217	+	6.70979i	1.23190	+	0.711236i	0.264472	+	0.964393i	$0.414802\pi$
$90$	2.36759			0.249566
$91$	−2.17814	−	10.5319i	−0.228331	−	1.10405i
$92$	0.668091			0.0696533
$93$	1.38886	+	0.801858i	0.144018	+	0.0831488i
$94$	0.480028	−	0.831434i	0.0495112	−	0.0857558i
$95$	2.94999	+	5.10954i	0.302663	+	0.524228i
$96$		−	2.90050i		−	0.296031i
$97$	6.71621	−	3.87760i	0.681927	−	0.393711i	−0.118654	−	0.992936i	$-0.537858\pi$
$97$	6.71621	−	3.87760i	0.681927	−	0.393711i	0.800581	+	0.599225i	$0.204524\pi$
$98$	1.36742	−	0.789477i	0.138130	−	0.0797493i
$99$			5.76246i			0.579149i
$100$	−2.56784	−	4.44763i	−0.256784	−	0.444763i
$101$	7.32803	−	12.6925i	0.729167	−	1.26295i	−0.228069	−	0.973645i	$-0.573241\pi$
$101$	7.32803	−	12.6925i	0.729167	−	1.26295i	0.957236	−	0.289309i	$-0.0934254\pi$
$102$	0.361974	+	0.208986i	0.0358407	+	0.0206927i
$103$	−7.06280			−0.695918			−0.347959	−	0.937510i	$-0.613125\pi$
$103$	−7.06280			−0.695918			−0.347959	+	0.937510i	$0.613125\pi$
$104$	−9.42120	−	3.11854i	−0.923824	−	0.305798i
$105$	1.55126			0.151387
$106$	0.405760	+	0.234265i	0.0394109	+	0.0227539i
$107$	−6.89926	+	11.9499i	−0.666977	+	1.15524i	0.311769	+	0.950158i	$0.399079\pi$
$107$	−6.89926	+	11.9499i	−0.666977	+	1.15524i	−0.978745	+	0.205079i	$0.934255\pi$
$108$	1.88728	+	3.26887i	0.181604	+	0.314547i
$109$		−	11.8898i		−	1.13884i	−0.822048	−	0.569418i	$-0.807169\pi$
$109$		−	11.8898i		−	1.13884i	0.822048	−	0.569418i	$-0.192831\pi$
$110$	1.56494	−	0.903517i	0.149211	−	0.0861469i
$111$	4.24118	−	2.44864i	0.402555	−	0.232415i
$112$			0.967952i			0.0914629i
$113$	−2.51440	−	4.35507i	−0.236535	−	0.409691i	0.723183	−	0.690657i	$-0.242678\pi$
$113$	−2.51440	−	4.35507i	−0.236535	−	0.409691i	−0.959718	+	0.280966i	$0.909345\pi$
$114$	1.19083	−	2.06257i	0.111531	−	0.193177i
$115$	0.458192	+	0.264537i	0.0427266	+	0.0246682i
$116$	10.8112			1.00379
$117$	9.70177	−	2.00645i	0.896929	−	0.185496i
$118$	−4.95743			−0.456368
$119$	−2.58322	−	1.49142i	−0.236804	−	0.136719i
$120$	0.715705	−	1.23964i	0.0653346	−	0.113163i
$121$	−3.30094	−	5.71740i	−0.300085	−	0.519763i
$122$		−	3.10669i		−	0.281266i
$123$	−3.40996	+	1.96874i	−0.307466	+	0.177515i
$124$	−3.61546	+	2.08739i	−0.324678	+	0.187453i
$125$		−	9.24418i		−	0.826824i
$126$	3.41027	+	5.90676i	0.303811	+	0.526216i
$127$	0.316585	−	0.548341i	0.0280924	−	0.0486574i	−0.851637	−	0.524131i	$-0.824390\pi$
$127$	0.316585	−	0.548341i	0.0280924	−	0.0486574i	0.879730	+	0.475474i	$0.157723\pi$
$128$	7.00670	+	4.04532i	0.619311	+	0.357559i
$129$	−4.21519			−0.371126
$130$	−2.06608	−	2.32016i	−0.181207	−	0.203491i
$131$	11.3167			0.988747			0.494373	−	0.869250i	$-0.335398\pi$
$131$	11.3167			0.988747			0.494373	+	0.869250i	$0.335398\pi$
$132$	1.19271	+	0.688612i	0.103812	+	0.0599360i
$133$	−8.49832	+	14.7195i	−0.736898	+	1.27634i
$134$	6.08422	+	10.5382i	0.525597	+	0.910360i
$135$			2.98916i			0.257266i
$136$	−2.38365	+	1.37620i	−0.204396	+	0.118008i
$137$	12.5721	−	7.25850i	1.07411	−	0.620135i	0.144805	−	0.989460i	$-0.453744\pi$
$137$	12.5721	−	7.25850i	1.07411	−	0.620135i	0.929300	+	0.369325i	$0.120411\pi$
$138$		−	0.213572i		−	0.0181804i
$139$	−6.60946	−	11.4479i	−0.560607	−	0.971000i	−0.997444	−	0.0714594i	$-0.977234\pi$
$139$	−6.60946	−	11.4479i	−0.560607	−	0.971000i	0.436836	−	0.899541i	$-0.356099\pi$
$140$	−2.01910	+	3.49719i	−0.170645	+	0.295567i
$141$	0.501819	+	0.289725i	0.0422608	+	0.0243993i
$142$	−5.64023			−0.473318
$143$	5.64701	−	5.02861i	0.472226	−	0.420513i
$144$	−0.891655			−0.0743046
$145$	7.41453	+	4.28078i	0.615744	+	0.355500i
$146$	2.72494	−	4.71973i	0.225517	−	0.390608i
$147$	0.476496	+	0.825315i	0.0393007	+	0.0680709i
$148$			12.7485i			1.04792i
$149$	7.77279	−	4.48762i	0.636772	−	0.367641i	−0.146598	−	0.989196i	$-0.546832\pi$
$149$	7.77279	−	4.48762i	0.636772	−	0.367641i	0.783370	+	0.621556i	$0.213499\pi$
$150$	−1.42179	+	0.820873i	−0.116089	+	0.0670240i
$151$		−	10.6329i		−	0.865293i	−0.901564	−	0.432646i	$-0.857580\pi$
$151$		−	10.6329i		−	0.865293i	0.901564	−	0.432646i	$-0.142420\pi$
$152$	7.84176	+	13.5823i	0.636051	+	1.10167i
$153$	1.37386	−	2.37960i	0.111070	−	0.192380i
$154$	4.50826	+	2.60284i	0.363286	+	0.209743i
$155$	−3.30608			−0.265551
$156$	0.744065	−	2.24784i	0.0595729	−	0.179971i
$157$	−1.02228			−0.0815867			−0.0407933	−	0.999168i	$-0.512989\pi$
$157$	−1.02228			−0.0815867			−0.0407933	+	0.999168i	$0.512989\pi$
$158$	−9.01784	−	5.20645i	−0.717421	−	0.414203i
$159$	−0.141393	+	0.244900i	−0.0112132	+	0.0194218i
$160$	2.98971	+	5.17834i	0.236358	+	0.409384i
$161$			1.52415i			0.120120i
$162$	−4.89575	+	2.82656i	−0.384646	+	0.222076i
$163$	2.65582	−	1.53334i	0.208020	−	0.120100i	−0.392371	−	0.919807i	$-0.628345\pi$
$163$	2.65582	−	1.53334i	0.208020	−	0.120100i	0.600391	+	0.799707i	$0.295012\pi$
$164$		−	10.2500i		−	0.800390i
$165$	0.545325	+	0.944531i	0.0424535	+	0.0735317i
$166$	−5.44966	+	9.43909i	−0.422976	+	0.732615i
$167$	11.2703	+	6.50693i	0.872124	+	0.503521i	0.868054	−	0.496470i	$-0.165371\pi$
$167$	11.2703	+	6.50693i	0.872124	+	0.503521i	0.00407076	+	0.999992i	$0.498704\pi$
$168$	4.12359			0.318142
$169$	−10.4325	−	7.75647i	−0.802500	−	0.596652i
$170$	−0.861653			−0.0660858
$171$	−13.5593	−	7.82845i	−1.03690	−	0.598657i
$172$	5.48646	−	9.50282i	0.418338	−	0.724583i
$173$	−2.55585	−	4.42687i	−0.194318	−	0.336568i	0.752359	−	0.658753i	$-0.228916\pi$
$173$	−2.55585	−	4.42687i	−0.194318	−	0.336568i	−0.946677	+	0.322185i	$0.895583\pi$
$174$		−	3.45605i		−	0.262003i
$175$	10.1466	−	5.85815i	0.767013	−	0.442835i
$176$	−0.589369	+	0.340272i	−0.0444253	+	0.0256490i
$177$		−	2.99210i		−	0.224900i
$178$	5.58370	+	9.67126i	0.418516	+	0.724891i
$179$	−10.1819	+	17.6356i	−0.761032	+	1.31815i	0.181287	+	0.983430i	$0.441974\pi$
$179$	−10.1819	+	17.6356i	−0.761032	+	1.31815i	−0.942319	+	0.334716i	$0.891360\pi$
$180$	−3.22153	−	1.85995i	−0.240119	−	0.138633i
$181$	−20.0831			−1.49276			−0.746381	−	0.665519i	$-0.768210\pi$
$181$	−20.0831			−1.49276			−0.746381	+	0.665519i	$0.768210\pi$
$182$	2.81245	−	8.49648i	0.208473	−	0.629801i
$183$	1.87507			0.138609
$184$	1.21798	+	0.703201i	0.0897906	+	0.0518407i
$185$	−5.04791	+	8.74324i	−0.371130	+	0.642816i
$186$	0.667284	+	1.15577i	0.0489277	+	0.0847452i
$187$		−	2.09717i		−	0.153360i
$188$	−1.30633	+	0.754209i	−0.0952738	+	0.0550063i
$189$	−7.45746	+	4.30557i	−0.542451	+	0.313184i
$190$			4.90981i			0.356195i
$191$	2.43186	+	4.21210i	0.175963	+	0.304777i	0.940494	−	0.339810i	$-0.110363\pi$
$191$	2.43186	+	4.21210i	0.175963	+	0.304777i	−0.764531	+	0.644587i	$0.777029\pi$
$192$	1.04387	−	1.80804i	0.0753349	−	0.130484i
$193$	−14.2799	−	8.24452i	−1.02789	−	0.593454i	−0.111512	−	0.993763i	$-0.535569\pi$
$193$	−14.2799	−	8.24452i	−1.02789	−	0.593454i	−0.916380	+	0.400309i	$0.868903\pi$
$194$	6.45367			0.463346
$195$	1.40035	−	1.24700i	0.100281	−	0.0892995i
$196$	−2.48082			−0.177201
$197$	−16.1857	−	9.34481i	−1.15318	−	0.665790i	−0.203522	−	0.979070i	$-0.565239\pi$
$197$	−16.1857	−	9.34481i	−1.15318	−	0.665790i	−0.949661	+	0.313280i	$0.898572\pi$
$198$	−2.39768	+	4.15290i	−0.170396	+	0.295134i
$199$	−1.90868	−	3.30592i	−0.135302	−	0.234351i	0.790410	−	0.612578i	$-0.209867\pi$
$199$	−1.90868	−	3.30592i	−0.135302	−	0.234351i	−0.925713	+	0.378227i	$0.876534\pi$
$200$		−	10.8111i		−	0.764463i
$201$	−6.36041	+	3.67219i	−0.448629	+	0.259016i
$202$	10.5624	−	6.09819i	0.743166	−	0.429067i
$203$			24.6641i			1.73108i
$204$	−0.328353	−	0.568724i	−0.0229893	−	0.0398187i
$205$	4.05859	−	7.02968i	0.283464	−	0.490974i
$206$	−5.09003	−	2.93873i	−0.354639	−	0.204751i
$207$	−1.40401			−0.0975858
$208$	0.778102	+	0.873791i	0.0539517	+	0.0605865i
$209$	−11.9499			−0.826594
$210$	1.11796	+	0.645456i	0.0771468	+	0.0445407i
$211$	−6.35786	+	11.0121i	−0.437693	+	0.758106i	−0.997511	−	0.0705091i	$-0.977538\pi$
$211$	−6.35786	+	11.0121i	−0.437693	+	0.758106i	0.559818	+	0.828615i	$0.310871\pi$
$212$	−0.368072	−	0.637520i	−0.0252793	−	0.0437850i
$213$		−	3.40421i		−	0.233253i
$214$	−9.94435	+	5.74137i	−0.679782	+	0.392472i
$215$	7.52547	−	4.34483i	0.513233	−	0.296315i
$216$			7.94586i			0.540647i
$217$	−4.76207	−	8.24815i	−0.323270	−	0.559921i
$218$	4.94718	−	8.56877i	0.335065	−	0.580350i
$219$	2.84863	+	1.64466i	0.192493	+	0.111136i
$220$	−2.83917			−0.191417
$221$	−3.53083	+	0.730221i	−0.237509	+	0.0491200i
$222$	4.07539			0.273522
$223$	−5.20996	−	3.00797i	−0.348884	−	0.201429i	0.315309	−	0.948989i	$-0.397892\pi$
$223$	−5.20996	−	3.00797i	−0.348884	−	0.201429i	−0.664194	+	0.747560i	$0.731225\pi$
$224$	−8.61275	+	14.9177i	−0.575464	+	0.996732i
$225$	5.39639	+	9.34683i	0.359760	+	0.623122i
$226$		−	4.18483i		−	0.278371i
$227$	−7.35123	+	4.24423i	−0.487918	+	0.281700i	−0.723710	−	0.690104i	$-0.757565\pi$
$227$	−7.35123	+	4.24423i	−0.487918	+	0.281700i	0.235792	+	0.971803i	$0.424231\pi$
$228$	−3.24066	+	1.87100i	−0.214618	+	0.123910i
$229$			4.98616i			0.329495i	0.986336	+	0.164747i	$0.0526809\pi$
$229$			4.98616i			0.329495i	−0.986336	+	0.164747i	$0.947319\pi$
$230$	0.220141	+	0.381295i	0.0145156	+	0.0251418i
$231$	−1.57097	+	2.72100i	−0.103362	+	0.179029i
$232$	19.7095	+	11.3793i	1.29399	+	0.747088i
$233$	−4.34393			−0.284580			−0.142290	−	0.989825i	$-0.545447\pi$
$233$	−4.34393			−0.284580			−0.142290	+	0.989825i	$0.545447\pi$
$234$	7.82675	+	2.59076i	0.511651	+	0.169363i
$235$	−1.19455			−0.0779236
$236$	6.74546	+	3.89450i	0.439092	+	0.253510i
$237$	3.14240	−	5.44280i	0.204121	−	0.353548i
$238$	−1.24112	−	2.14969i	−0.0804500	−	0.139344i
$239$			15.6959i			1.01528i	0.861569	+	0.507641i	$0.169482\pi$
$239$			15.6959i			1.01528i	−0.861569	+	0.507641i	$0.830518\pi$
$240$	−0.146152	+	0.0843810i	−0.00943409	+	0.00544677i
$241$	16.7326	−	9.66057i	1.07784	−	0.622292i	0.147528	−	0.989058i	$-0.452868\pi$
$241$	16.7326	−	9.66057i	1.07784	−	0.622292i	0.930313	+	0.366766i	$0.119535\pi$
$242$		−	5.49390i		−	0.353161i
$243$	−6.03632	−	10.4552i	−0.387230	−	0.670702i
$244$	−2.44058	+	4.22720i	−0.156242	+	0.270619i
$245$	−1.70140	−	0.982303i	−0.108698	−	0.0627571i
$246$	−3.27666			−0.208912
$247$	4.16089	+	20.1191i	0.264751	+	1.28015i
$248$	−8.78833			−0.558060
$249$	−5.69704	−	3.28919i	−0.361036	−	0.208444i
$250$	3.84637	−	6.66211i	0.243266	−	0.421349i
$251$	−15.6225	−	27.0589i	−0.986081	−	1.70794i	−0.637029	−	0.770840i	$-0.719837\pi$
$251$	−15.6225	−	27.0589i	−0.986081	−	1.70794i	−0.349052	−	0.937103i	$-0.613496\pi$
$252$		−	10.7163i		−	0.675061i
$253$	−0.928030	+	0.535798i	−0.0583447	+	0.0336853i
$254$	0.456315	−	0.263453i	0.0286317	−	0.0165305i
$255$		−	0.520058i		−	0.0325673i
$256$	7.52306	+	13.0303i	0.470191	+	0.814395i
$257$	−0.876628	+	1.51836i	−0.0546825	+	0.0947129i	−0.892071	−	0.451895i	$-0.850748\pi$
$257$	−0.876628	+	1.51836i	−0.0546825	+	0.0947129i	0.837388	+	0.546608i	$0.184081\pi$
$258$	−3.03781	−	1.75388i	−0.189126	−	0.109192i
$259$	−29.0840			−1.80719
$260$	0.988579	+	4.78007i	0.0613091	+	0.296447i
$261$	−22.7200			−1.40633
$262$	8.15576	+	4.70873i	0.503865	+	0.290906i
$263$	7.78024	−	13.4758i	0.479750	−	0.830952i	−0.519980	−	0.854178i	$-0.674061\pi$
$263$	7.78024	−	13.4758i	0.479750	−	0.830952i	0.999730	+	0.0232266i	$0.00739392\pi$
$264$	1.44960	+	2.51078i	0.0892167	+	0.154528i
$265$		−	0.582967i		−	0.0358114i
$266$	−12.2492	+	7.07207i	−0.751045	+	0.433616i
$267$	−5.83717	+	3.37009i	−0.357229	+	0.206246i
$268$		−	19.1188i		−	1.16786i
$269$	−2.24400	−	3.88672i	−0.136819	−	0.236978i	0.789472	−	0.613787i	$-0.210355\pi$
$269$	−2.24400	−	3.88672i	−0.136819	−	0.236978i	−0.926291	+	0.376809i	$0.877021\pi$
$270$	−1.24375	+	2.15423i	−0.0756920	+	0.131102i
$271$	4.87589	+	2.81509i	0.296189	+	0.171005i	0.640730	−	0.767767i	$-0.278632\pi$
$271$	4.87589	+	2.81509i	0.296189	+	0.171005i	−0.344541	+	0.938771i	$0.611965\pi$
$272$	0.324506			0.0196761
$273$	5.12812	+	1.69748i	0.310368	+	0.102736i
$274$	12.0806			0.729818
$275$	7.13385	+	4.11873i	0.430187	+	0.248369i
$276$	−0.167779	+	0.290602i	−0.0100991	+	0.0174922i
$277$	16.5380	+	28.6447i	0.993674	+	1.72109i	0.594098	+	0.804393i	$0.297509\pi$
$277$	16.5380	+	28.6447i	0.993674	+	1.72109i	0.399576	+	0.916700i	$0.369157\pi$
$278$		−	11.0004i		−	0.659762i
$279$	7.59800	−	4.38671i	0.454880	−	0.262625i
$280$	−7.36195	+	4.25042i	−0.439961	+	0.254011i
$281$		−	5.72421i		−	0.341478i	−0.985316	−	0.170739i	$-0.945385\pi$
$281$		−	5.72421i		−	0.341478i	0.985316	−	0.170739i	$-0.0546155\pi$
$282$	0.241101	+	0.417600i	0.0143574	+	0.0248677i
$283$	9.76771	−	16.9182i	0.580630	−	1.00568i	−0.414775	−	0.909924i	$-0.636140\pi$
$283$	9.76771	−	16.9182i	0.580630	−	1.00568i	0.995405	−	0.0957563i	$-0.0305270\pi$
$284$	7.67454	+	4.43090i	0.455400	+	0.262925i
$285$	−2.96336			−0.175534
$286$	6.16203	−	1.27439i	0.364369	−	0.0753560i
$287$	23.3839			1.38031
$288$	−13.7418	−	7.93386i	−0.809746	−	0.467507i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	3.56235	+	6.17017i	0.209188	+	0.362325i
$291$			3.89517i			0.228339i
$292$	−7.41552	+	4.28136i	−0.433961	+	0.250547i
$293$	6.49048	−	3.74728i	0.379178	−	0.218918i	−0.298283	−	0.954478i	$-0.596414\pi$
$293$	6.49048	−	3.74728i	0.379178	−	0.218918i	0.677460	+	0.735559i	$0.263080\pi$
$294$			0.793054i			0.0462518i
$295$	3.08413	+	5.34187i	0.179565	+	0.311016i
$296$	−13.4185	+	23.2415i	−0.779935	+	1.35089i
$297$	−5.24316	−	3.02714i	−0.304239	−	0.175653i
$298$	7.46895			0.432665
$299$	1.22521	+	1.37589i	0.0708559	+	0.0795695i
$300$	2.57947			0.148926
$301$	21.6793	+	12.5166i	1.24958	+	0.721443i
$302$	4.42420	−	7.66294i	0.254584	−	0.440953i
$303$	3.68061	+	6.37501i	0.211446	+	0.366235i
$304$		−	1.84908i		−	0.106052i
$305$	−3.34761	+	1.93274i	−0.191683	+	0.110668i
$306$	1.98024	−	1.14329i	0.113203	−	0.0653577i
$307$		−	11.6373i		−	0.664175i	−0.943249	−	0.332087i	$-0.892247\pi$
$307$		−	11.6373i		−	0.664175i	0.943249	−	0.332087i	$-0.107753\pi$
$308$	−4.08953	−	7.08327i	−0.233022	−	0.403607i
$309$	1.77370	−	3.07213i	0.100902	−	0.174768i
$310$	−2.38264	−	1.37562i	−0.135325	−	0.0781297i
$311$	4.10295			0.232657			0.116329	−	0.993211i	$-0.462887\pi$
$311$	4.10295			0.232657			0.116329	+	0.993211i	$0.462887\pi$
$312$	3.72245	−	3.31481i	0.210742	−	0.187664i
$313$	−1.55217			−0.0877340			−0.0438670	−	0.999037i	$-0.513968\pi$
$313$	−1.55217			−0.0877340			−0.0438670	+	0.999037i	$0.513968\pi$
$314$	−0.736738	−	0.425356i	−0.0415765	−	0.0240042i
$315$	4.24321	−	7.34946i	0.239078	−	0.414095i
$316$	8.18025	+	14.1686i	0.460175	+	0.797047i
$317$			7.46828i			0.419461i	0.977759	+	0.209730i	$0.0672586\pi$
$317$			7.46828i			0.419461i	−0.977759	+	0.209730i	$0.932741\pi$
$318$	−0.203799	+	0.117663i	−0.0114285	+	0.00659823i
$319$	−15.0175	+	8.67037i	−0.840820	+	0.485447i
$320$			4.30391i			0.240596i
$321$	−3.46526	−	6.00200i	−0.193412	−	0.334999i
$322$	−0.634180	+	1.09843i	−0.0353414	+	0.0612132i
$323$	4.93472	+	2.84906i	0.274575	+	0.158526i
$324$	8.88205			0.493447
$325$	4.45041	−	13.4448i	0.246864	−	0.745783i
$326$	2.55200			0.141342
$327$	5.17176	+	2.98591i	0.285999	+	0.165121i
$328$	10.7887	−	18.6865i	0.595704	−	1.03179i
$329$	−1.72062	−	2.98020i	−0.0948609	−	0.164304i
$330$			0.907609i			0.0499623i
$331$	24.1626	−	13.9503i	1.32810	−	0.766777i	0.343092	−	0.939302i	$-0.388526\pi$
$331$	24.1626	−	13.9503i	1.32810	−	0.766777i	0.985005	+	0.172525i	$0.0551925\pi$
$332$	14.8305	−	8.56237i	0.813928	−	0.469921i
$333$		−	26.7915i		−	1.46816i
$334$	5.41489	+	9.37886i	0.296289	+	0.513188i
$335$	7.57026	−	13.1121i	0.413608	−	0.716390i
$336$	−0.421034	−	0.243084i	−0.0229693	−	0.0132613i
$337$	22.9740			1.25147			0.625736	−	0.780035i	$-0.284799\pi$
$337$	22.9740			1.25147			0.625736	+	0.780035i	$0.284799\pi$
$338$	−4.29116	−	9.93077i	−0.233408	−	0.540163i
$339$	2.52579			0.137182
$340$	1.17243	+	0.676904i	0.0635841	+	0.0367103i
$341$	3.34810	−	5.79908i	0.181310	−	0.314038i
$342$	−6.51462	−	11.2837i	−0.352270	−	0.610150i
$343$			15.2203i			0.821820i
$344$	20.0044	−	11.5496i	1.07857	−	0.622711i
$345$	−0.230134	+	0.132868i	−0.0123900	+	0.00715336i
$346$		−	4.25382i		−	0.228687i
$347$	−18.5310	−	32.0967i	−0.994797	−	1.72304i	−0.585628	−	0.810580i	$-0.699152\pi$
$347$	−18.5310	−	32.0967i	−0.994797	−	1.72304i	−0.409169	−	0.912459i	$-0.634181\pi$
$348$	−2.71503	+	4.70257i	−0.145541	+	0.252084i
$349$	−2.20851	−	1.27509i	−0.118219	−	0.0682537i	0.439725	−	0.898133i	$-0.355076\pi$
$349$	−2.20851	−	1.27509i	−0.118219	−	0.0682537i	−0.557943	+	0.829879i	$0.688409\pi$
$350$	9.74999			0.521159
$351$	−3.27092	+	9.88152i	−0.174589	+	0.527436i
$352$	−12.1108			−0.645510
$353$	6.85603	+	3.95833i	0.364910	+	0.210681i	0.671232	−	0.741247i	$-0.265765\pi$
$353$	6.85603	+	3.95833i	0.364910	+	0.210681i	−0.306323	+	0.951928i	$0.599099\pi$
$354$	1.24497	−	2.15635i	0.0661695	−	0.114609i
$355$	3.50892	+	6.07762i	0.186234	+	0.322567i
$356$		−	17.5460i		−	0.929934i
$357$	1.29746	−	0.749090i	0.0686690	−	0.0396461i
$358$	−14.6759	+	8.47311i	−0.775643	+	0.447818i
$359$			19.7210i			1.04084i	0.853912	+	0.520418i	$0.174224\pi$
$359$			19.7210i			1.04084i	−0.853912	+	0.520418i	$0.825776\pi$
$360$	−3.91539	−	6.78165i	−0.206359	−	0.357425i
$361$	6.73430	−	11.6642i	0.354437	−	0.613903i
$362$	−14.4735	−	8.35628i	−0.760710	−	0.439196i
$363$	3.31589			0.174039
$364$	−10.5016	+	9.35155i	−0.550432	+	0.490154i
$365$	−6.78098			−0.354933
$366$	1.35133	+	0.780191i	0.0706351	+	0.0407812i
$367$	9.95717	−	17.2463i	0.519760	−	0.900251i	−0.479976	−	0.877282i	$-0.659355\pi$
$367$	9.95717	−	17.2463i	0.519760	−	0.900251i	0.999736	−	0.0229694i	$-0.00731204\pi$
$368$	−0.0829068	−	0.143599i	−0.00432182	−	0.00748561i
$369$			21.5407i			1.12136i
$370$	−7.27589	+	4.20073i	−0.378255	+	0.218386i
$371$	1.45441	−	0.839704i	0.0755092	−	0.0435953i
$372$		−	2.09684i		−	0.108716i
$373$	17.3414	+	30.0362i	0.897903	+	1.55521i	0.830170	+	0.557510i	$0.188243\pi$
$373$	17.3414	+	30.0362i	0.897903	+	1.55521i	0.0677323	+	0.997704i	$0.478424\pi$
$374$	0.872603	−	1.51139i	0.0451212	−	0.0781523i
$375$	4.02098	+	2.32151i	0.207642	+	0.119882i
$376$	−3.17538			−0.163758
$377$	19.8266	+	22.2648i	1.02112	+	1.14670i
$378$	−7.16595			−0.368577
$379$	3.51800	+	2.03112i	0.180707	+	0.104331i	0.587625	−	0.809133i	$-0.300063\pi$
$379$	3.51800	+	2.03112i	0.180707	+	0.104331i	−0.406918	+	0.913465i	$0.633396\pi$
$380$	3.85708	−	6.68067i	0.197864	−	0.342711i
$381$	0.159010	+	0.275413i	0.00814631	+	0.0141098i
$382$			4.04745i			0.207086i
$383$	−13.8332	+	7.98661i	−0.706844	+	0.408097i	−0.809891	−	0.586580i	$-0.800474\pi$
$383$	−13.8332	+	7.98661i	−0.706844	+	0.408097i	0.103047	+	0.994676i	$0.467141\pi$
$384$	−3.51922	+	2.03182i	−0.179589	+	0.103686i
$385$		−	6.47715i		−	0.330106i
$386$	−6.86087	−	11.8834i	−0.349209	−	0.604848i
$387$	−11.5300	+	19.9705i	−0.586101	+	1.01516i
$388$	−8.78136	−	5.06992i	−0.445806	−	0.257386i
$389$	−23.9526			−1.21444			−0.607221	−	0.794533i	$-0.707716\pi$
$389$	−23.9526			−1.21444			−0.607221	+	0.794533i	$0.707716\pi$
$390$	1.52807	−	0.316024i	0.0773767	−	0.0160025i
$391$	0.510973			0.0258410
$392$	−4.52271	−	2.61119i	−0.228431	−	0.131885i
$393$	−2.84200	+	4.92248i	−0.143360	+	0.248306i
$394$	−7.77650	−	13.4693i	−0.391774	−	0.678573i
$395$			12.9562i			0.651897i
$396$	6.52494	−	3.76717i	0.327890	−	0.189308i
$397$	4.16646	−	2.40551i	0.209108	−	0.120729i	−0.391789	−	0.920055i	$-0.628144\pi$
$397$	4.16646	−	2.40551i	0.209108	−	0.120729i	0.600897	+	0.799326i	$0.294810\pi$
$398$		−	3.17670i		−	0.159233i
$399$	−4.26841	−	7.39310i	−0.213688	−	0.370118i
$400$	−0.637312	+	1.10386i	−0.0318656	+	0.0551929i
$401$	12.2085	+	7.04859i	0.609664	+	0.351990i	0.772834	−	0.634608i	$-0.218839\pi$
$401$	12.2085	+	7.04859i	0.609664	+	0.351990i	−0.163170	+	0.986598i	$0.552172\pi$
$402$	−6.11178			−0.304828
$403$	−10.9292	−	3.61772i	−0.544423	−	0.180211i
$404$	−19.1626			−0.953377
$405$	6.09151	+	3.51693i	0.302689	+	0.174758i
$406$	−10.2624	+	17.7750i	−0.509314	+	0.882158i
$407$	−10.2241	−	17.7087i	−0.506791	−	0.877788i
$408$		−	1.38243i		−	0.0684407i
$409$	14.7509	−	8.51645i	0.729386	−	0.421111i	−0.0888114	−	0.996048i	$-0.528307\pi$
$409$	14.7509	−	8.51645i	0.729386	−	0.421111i	0.818198	+	0.574937i	$0.194973\pi$
$410$	5.84990	−	3.37744i	0.288906	−	0.166800i
$411$			7.29138i			0.359657i
$412$	4.61726	+	7.99734i	0.227476	+	0.394000i
$413$	−8.88473	+	15.3888i	−0.437189	+	0.757234i
$414$	−1.01185	−	0.584191i	−0.0497297	−	0.0287114i
$415$	13.5614			0.665704
$416$	4.21691	+	20.3900i	0.206751	+	0.999703i
$417$	6.63940			0.325133
$418$	−8.61211	−	4.97220i	−0.421232	−	0.243198i
$419$	0.336539	−	0.582902i	0.0164410	−	0.0284766i	−0.857688	−	0.514171i	$-0.828100\pi$
$419$	0.336539	−	0.582902i	0.0164410	−	0.0284766i	0.874129	+	0.485694i	$0.161433\pi$
$420$	−1.01413	−	1.75652i	−0.0494842	−	0.0857092i
$421$			26.3883i			1.28609i	0.765830	+	0.643043i	$0.222328\pi$
$421$			26.3883i			1.28609i	−0.765830	+	0.643043i	$0.777672\pi$
$422$	−9.16399	+	5.29083i	−0.446096	+	0.257554i
$423$	2.74529	−	1.58499i	0.133481	−	0.0770651i
$424$		−	1.54966i		−	0.0752582i
$425$	−1.96395	−	3.40165i	−0.0952654	−	0.165004i
$426$	1.41645	−	2.45336i	0.0686270	−	0.118865i
$427$	−9.64376	−	5.56783i	−0.466694	−	0.269446i
$428$	18.0414			0.872065
$429$	0.769167	+	3.71915i	0.0371357	+	0.179562i
$430$	7.23130			0.348724
$431$	4.39553	+	2.53776i	0.211725	+	0.122240i	0.602113	−	0.798411i	$-0.294326\pi$
$431$	4.39553	+	2.53776i	0.211725	+	0.122240i	−0.390388	+	0.920651i	$0.627659\pi$
$432$	0.468406	−	0.811302i	0.0225362	−	0.0390338i
$433$	−13.4448	−	23.2871i	−0.646116	−	1.11911i	−0.984043	−	0.177933i	$-0.943059\pi$
$433$	−13.4448	−	23.2871i	−0.646116	−	1.11911i	0.337927	−	0.941172i	$-0.390274\pi$
$434$		−	7.92573i		−	0.380447i
$435$	−3.72406	+	2.15009i	−0.178555	+	0.103089i
$436$	−13.4630	+	7.77289i	−0.644763	+	0.372254i
$437$		−	2.91158i		−	0.139280i
$438$	1.36864	+	2.37055i	0.0653962	+	0.113269i
$439$	0.180223	−	0.312155i	0.00860157	−	0.0148984i	−0.861693	−	0.507431i	$-0.830595\pi$
$439$	0.180223	−	0.312155i	0.00860157	−	0.0148984i	0.870294	+	0.492532i	$0.163929\pi$
$440$	−5.17601	−	2.98837i	−0.246757	−	0.142465i
$441$	5.21351			0.248263
$442$	−2.84844	−	0.942873i	−0.135487	−	0.0448479i
$443$	0.994914			0.0472698			0.0236349	−	0.999721i	$-0.492476\pi$
$443$	0.994914			0.0472698			0.0236349	+	0.999721i	$0.492476\pi$
$444$	−5.54529	−	3.20157i	−0.263168	−	0.151940i
$445$	6.94749	−	12.0334i	0.329343	−	0.570439i
$446$	−2.50315	−	4.33558i	−0.118528	−	0.205296i
$447$			4.50795i			0.213219i
$448$	−10.7376	+	6.19934i	−0.507303	+	0.292891i
$449$	2.45269	−	1.41606i	0.115750	−	0.0668281i	−0.441007	−	0.897503i	$-0.645379\pi$
$449$	2.45269	−	1.41606i	0.115750	−	0.0668281i	0.556757	+	0.830675i	$0.312045\pi$
$450$			8.98146i			0.423390i
$451$	8.22033	+	14.2380i	0.387080	+	0.670442i
$452$	−3.28755	+	5.69421i	−0.154633	+	0.267833i
$453$	4.62503	+	2.67027i	0.217303	+	0.125460i
$454$	−7.06387			−0.331524
$455$	−10.9050	+	2.25530i	−0.511237	+	0.105730i
$456$	−7.87728			−0.368888
$457$	−4.16639	−	2.40546i	−0.194895	−	0.112523i	0.399377	−	0.916787i	$-0.369226\pi$
$457$	−4.16639	−	2.40546i	−0.194895	−	0.112523i	−0.594272	+	0.804264i	$0.702560\pi$
$458$	−2.07467	+	3.59344i	−0.0969430	+	0.167910i
$459$	1.44344	+	2.50011i	0.0673741	+	0.116695i
$460$		−	0.691759i		−	0.0322534i
$461$	10.2442	−	5.91452i	0.477122	−	0.275466i	−0.242094	−	0.970253i	$-0.577834\pi$
$461$	10.2442	−	5.91452i	0.477122	−	0.275466i	0.719216	+	0.694786i	$0.244501\pi$
$462$	−2.26434	+	1.30732i	−0.105347	+	0.0608219i
$463$		−	4.96811i		−	0.230888i	−0.993314	−	0.115444i	$-0.963171\pi$
$463$		−	4.96811i		−	0.230888i	0.993314	−	0.115444i	$-0.0368291\pi$
$464$	−1.34161	−	2.32374i	−0.0622828	−	0.107877i
$465$	0.830265	−	1.43806i	0.0385026	−	0.0666885i
$466$	−3.13059	−	1.80745i	−0.145022	−	0.0837284i
$467$	−24.2093			−1.12027			−0.560137	−	0.828400i	$-0.689252\pi$
$467$	−24.2093			−1.12027			−0.560137	+	0.828400i	$0.689252\pi$
$468$	−8.61442	−	9.67380i	−0.398202	−	0.447171i
$469$	43.6167			2.01403
$470$	−0.860888	−	0.497034i	−0.0397098	−	0.0229265i
$471$	0.256727	−	0.444665i	0.0118294	−	0.0204891i
$472$	8.19832	+	14.1999i	0.377358	+	0.653604i
$473$			17.6002i			0.809258i
$474$	4.52934	−	2.61502i	0.208040	−	0.120112i
$475$	−19.3830	+	11.1908i	−0.889355	+	0.513469i
$476$			3.90004i			0.178758i
$477$	0.773515	+	1.33977i	0.0354168	+	0.0613438i
$478$	−6.53083	+	11.3117i	−0.298713	+	0.517387i
$479$	−30.9818	−	17.8874i	−1.41560	−	0.817295i	−0.419688	−	0.907668i	$-0.637861\pi$
$479$	−30.9818	−	17.8874i	−1.41560	−	0.817295i	−0.995908	+	0.0903735i	$0.971194\pi$
$480$	−3.00326			−0.137079
$481$	−26.2547	+	23.3796i	−1.19711	+	1.06602i
$482$	16.0785			0.732356
$483$	−0.662968	−	0.382765i	−0.0301661	−	0.0174164i
$484$	−4.31594	+	7.47543i	−0.196179	+	0.339792i
$485$	−4.01497	−	6.95414i	−0.182311	−	0.315771i
$486$		−	10.0465i		−	0.455719i
$487$	17.3039	−	9.99042i	0.784115	−	0.452709i	−0.0537716	−	0.998553i	$-0.517124\pi$
$487$	17.3039	−	9.99042i	0.784115	−	0.452709i	0.837887	+	0.545844i	$0.183791\pi$
$488$	−8.89871	+	5.13767i	−0.402825	+	0.232571i
$489$			1.54028i			0.0696540i
$490$	−0.817446	−	1.41586i	−0.0369284	−	0.0639619i
$491$	−5.93560	+	10.2808i	−0.267870	+	0.463965i	−0.968312	−	0.249745i	$-0.919653\pi$
$491$	−5.93560	+	10.2808i	−0.267870	+	0.463965i	0.700442	+	0.713710i	$0.252986\pi$
$492$	4.45848	+	2.57411i	0.201004	+	0.116050i
$493$	8.26864			0.372401
$494$	−5.37261	+	16.2308i	−0.241725	+	0.730257i
$495$	5.96660			0.268179
$496$	0.897321	+	0.518069i	0.0402909	+	0.0232620i
$497$	−10.1085	+	17.5084i	−0.453426	+	0.785358i
$498$	−2.73717	−	4.74092i	−0.122656	−	0.212446i
$499$			1.40392i			0.0628481i	0.999506	+	0.0314241i	$0.0100042\pi$
$499$			1.40392i			0.0628481i	−0.999506	+	0.0314241i	$0.989996\pi$
$500$	−10.4674	+	6.04333i	−0.468114	+	0.270266i
$501$	−5.66069	+	3.26820i	−0.252901	+	0.146013i
$502$		−	26.0012i		−	1.16049i
$503$	15.8016	+	27.3691i	0.704557	+	1.22033i	0.966851	+	0.255341i	$0.0821877\pi$
$503$	15.8016	+	27.3691i	0.704557	+	1.22033i	−0.262294	+	0.964988i	$0.584479\pi$
$504$	11.2794	−	19.5365i	0.502426	−	0.870227i
$505$	−13.1422	−	7.58764i	−0.584819	−	0.337646i
$506$	−0.891753			−0.0396432
$507$	5.99381	−	2.58997i	0.266194	−	0.115024i
$508$	−0.827863			−0.0367305
$509$	−28.2501	−	16.3102i	−1.25216	−	0.722938i	−0.280626	−	0.959817i	$-0.590542\pi$
$509$	−28.2501	−	16.3102i	−1.25216	−	0.722938i	−0.971539	+	0.236880i	$0.923875\pi$
$510$	0.216389	−	0.374797i	0.00958187	−	0.0165963i
$511$	−9.76730	−	16.9175i	−0.432080	−	0.748384i
$512$		−	3.66031i		−	0.161765i
$513$	14.2460	−	8.22491i	0.628975	−	0.363139i
$514$	−1.26354	+	0.729505i	−0.0557324	+	0.0321771i
$515$			7.31300i			0.322249i
$516$	2.75566	+	4.77293i	0.121311	+	0.210117i
$517$	1.20973	−	2.09531i	0.0532037	−	0.0921515i
$518$	−20.9603	−	12.1014i	−0.920944	−	0.531707i
$519$	2.56743			0.112698
$520$	−3.22902	+	9.75496i	−0.141602	+	0.427783i
$521$	−27.1269			−1.18845			−0.594225	−	0.804299i	$-0.702541\pi$
$521$	−27.1269			−1.18845			−0.594225	+	0.804299i	$0.702541\pi$
$522$	−16.3739	−	9.45347i	−0.716666	−	0.413767i
$523$	−0.115714	+	0.200422i	−0.00505981	+	0.00876385i	−0.868544	−	0.495612i	$-0.834944\pi$
$523$	−0.115714	+	0.200422i	−0.00505981	+	0.00876385i	0.863484	+	0.504376i	$0.168277\pi$
$524$	−7.39825	−	12.8141i	−0.323194	−	0.559788i
$525$			5.88469i			0.256829i
$526$	11.2142	−	6.47450i	0.488961	−	0.282302i
$527$	−2.76519	+	1.59648i	−0.120454	+	0.0695439i
$528$		−	0.341814i		−	0.0148755i
$529$	11.3695	+	19.6925i	0.494324	+	0.856194i
$530$	0.242565	−	0.420134i	0.0105363	−	0.0182495i
$531$	−14.1758	−	8.18441i	−0.615178	−	0.355173i
$532$	22.2229			0.963486
$533$	21.1091	−	18.7975i	0.914338	−	0.814209i
$534$	−5.60900			−0.242725
$535$	12.3732	+	7.14367i	0.534940	+	0.308848i
$536$	20.1235	−	34.8549i	0.869203	−	1.50550i
$537$	−5.11402	−	8.85774i	−0.220686	−	0.382240i
$538$		−	3.73479i		−	0.161018i
$539$	3.44604	−	1.98957i	0.148432	−	0.0856970i
$540$	3.38468	−	1.95414i	0.145653	−	0.0840930i
$541$			6.00529i			0.258188i	0.991632	+	0.129094i	$0.0412068\pi$
$541$			6.00529i			0.258188i	−0.991632	+	0.129094i	$0.958793\pi$
$542$	2.34264	+	4.05758i	0.100625	+	0.174288i
$543$	5.04351	−	8.73561i	0.216438	−	0.374881i
$544$	5.00116	+	2.88742i	0.214423	+	0.123797i
$545$	−12.3110			−0.527346
$546$	2.98945	+	3.35708i	0.127937	+	0.143670i
$547$	13.8580			0.592525			0.296263	−	0.955106i	$-0.404260\pi$
$547$	13.8580			0.592525			0.296263	+	0.955106i	$0.404260\pi$
$548$	−16.4379	−	9.49041i	−0.702191	−	0.405410i
$549$	5.12895	−	8.88360i	0.218898	−	0.379143i
$550$	3.42749	+	5.93659i	0.146149	+	0.253137i
$551$		−	47.1157i		−	2.00720i
$552$	−0.611748	+	0.353193i	−0.0260377	+	0.0150329i
$553$	−32.3237	+	18.6621i	−1.37454	+	0.793592i
$554$			27.5250i			1.16942i
$555$	−2.53539	−	4.39142i	−0.107621	−	0.186406i
$556$	−8.64180	+	14.9680i	−0.366494	+	0.634786i
$557$	0.644073	+	0.371856i	0.0272902	+	0.0157560i	0.513583	−	0.858040i	$-0.328318\pi$
$557$	0.644073	+	0.371856i	0.0272902	+	0.0157560i	−0.486293	+	0.873796i	$0.661651\pi$
$558$	7.30099			0.309076
$559$	29.6320	−	6.12827i	1.25330	−	0.259198i
$560$	1.00224			0.0423525
$561$	0.912215	+	0.526667i	0.0385137	+	0.0222359i
$562$	2.38177	−	4.12534i	0.100469	−	0.174017i
$563$	4.03420	+	6.98743i	0.170021	+	0.294485i	0.938427	−	0.345478i	$-0.112283\pi$
$563$	4.03420	+	6.98743i	0.170021	+	0.294485i	−0.768406	+	0.639963i	$0.778950\pi$
$564$		−	0.757626i		−	0.0319018i
$565$	−4.50936	+	2.60348i	−0.189710	+	0.109529i
$566$	14.0788	−	8.12841i	0.591777	−	0.341663i
$567$			20.2631i			0.850971i
$568$	9.32750	+	16.1557i	0.391373	+	0.677879i
$569$	15.2055	−	26.3367i	0.637447	−	1.10409i	−0.348544	−	0.937292i	$-0.613324\pi$
$569$	15.2055	−	26.3367i	0.637447	−	1.10409i	0.985991	−	0.166798i	$-0.0533429\pi$
$570$	−2.13564	−	1.23301i	−0.0894521	−	0.0516452i
$571$	16.7044			0.699056			0.349528	−	0.936926i	$-0.386342\pi$
$571$	16.7044			0.699056			0.349528	+	0.936926i	$0.386342\pi$
$572$	−9.38569	−	3.10679i	−0.392435	−	0.129901i
$573$	−2.44287			−0.102053
$574$	16.8524	+	9.72971i	0.703404	+	0.406110i
$575$	−1.00352	+	1.73815i	−0.0418498	+	0.0724860i
$576$	−5.71068	−	9.89120i	−0.237945	−	0.412133i
$577$		−	16.4021i		−	0.682829i	−0.939913	−	0.341415i	$-0.889094\pi$
$577$		−	16.4021i		−	0.682829i	0.939913	−	0.341415i	$-0.110906\pi$
$578$	−0.720682	+	0.416086i	−0.0299764	+	0.0173069i
$579$	7.17231	−	4.14094i	0.298071	−	0.172091i
$580$		−	11.1942i		−	0.464812i
$581$	19.5338	+	33.8336i	0.810400	+	1.40365i
$582$	−1.62073	+	2.80718i	−0.0671812	+	0.116361i
$583$	1.02256	+	0.590376i	0.0423501	+	0.0244509i
$584$	−18.0254			−0.745896
$585$	−2.07753	−	10.0455i	−0.0858953	−	0.415329i
$586$	6.23676			0.257638
$587$	−16.3741	−	9.45360i	−0.675832	−	0.390192i	0.122451	−	0.992475i	$-0.460925\pi$
$587$	−16.3741	−	9.45360i	−0.675832	−	0.390192i	−0.798283	+	0.602283i	$0.794258\pi$
$588$	0.623013	−	1.07909i	0.0256926	−	0.0445010i
$589$	9.09696	+	15.7564i	0.374834	+	0.649231i
$590$			5.13305i			0.211324i
$591$	8.12951	−	4.69357i	0.334403	−	0.193068i
$592$	2.74016	−	1.58203i	0.112620	−	0.0650211i
$593$			18.6932i			0.767637i	0.923408	+	0.383819i	$0.125391\pi$
$593$			18.6932i			0.767637i	−0.923408	+	0.383819i	$0.874609\pi$
$594$	−2.51910	−	4.36322i	−0.103360	−	0.179025i
$595$	−1.54426	+	2.67474i	−0.0633085	+	0.109654i
$596$	−10.1628	−	5.86752i	−0.416286	−	0.240343i
$597$	1.91732			0.0784708
$598$	0.310503	+	1.50137i	0.0126974	+	0.0613956i
$599$	24.5524			1.00318			0.501592	−	0.865104i	$-0.332748\pi$
$599$	24.5524			1.00318			0.501592	+	0.865104i	$0.332748\pi$
$600$	4.70257	+	2.71503i	0.191981	+	0.110841i
$601$	−20.1512	+	34.9029i	−0.821983	+	1.42372i	0.0822197	+	0.996614i	$0.473799\pi$
$601$	−20.1512	+	34.9029i	−0.821983	+	1.42372i	−0.904203	+	0.427103i	$0.859534\pi$
$602$	10.4159	+	18.0409i	0.424522	+	0.735294i
$603$			40.1787i			1.63620i
$604$	−12.0398	+	6.95120i	−0.489894	+	0.282840i
$605$	−5.91994	+	3.41788i	−0.240680	+	0.138957i
$606$			6.12581i			0.248844i
$607$	−7.53247	−	13.0466i	−0.305734	−	0.529546i	0.671691	−	0.740832i	$-0.265568\pi$
$607$	−7.53247	−	13.0466i	−0.305734	−	0.529546i	−0.977424	+	0.211286i	$0.932235\pi$
$608$	16.4529	−	28.4973i	0.667253	−	1.15572i
$609$	−10.7283	−	6.19396i	−0.434731	−	0.250992i
$610$	−3.21675			−0.130242
$611$	−3.94892	−	1.30714i	−0.159756	−	0.0528814i
$612$	−3.59263			−0.145223
$613$	1.97876	+	1.14244i	0.0799215	+	0.0461427i	0.539428	−	0.842032i	$-0.318640\pi$
$613$	1.97876	+	1.14244i	0.0799215	+	0.0461427i	−0.459507	+	0.888174i	$0.651974\pi$
$614$	4.84211	−	8.38678i	0.195412	−	0.338463i
$615$	2.03849	+	3.53076i	0.0821997	+	0.142374i
$616$		−	17.2178i		−	0.693723i
$617$	18.2976	−	10.5641i	0.736635	−	0.425296i	−0.0842096	−	0.996448i	$-0.526837\pi$
$617$	18.2976	−	10.5641i	0.736635	−	0.425296i	0.820845	+	0.571152i	$0.193503\pi$
$618$	2.55655	−	1.47602i	0.102839	−	0.0593743i
$619$			7.26002i			0.291805i	0.989299	+	0.145902i	$0.0466086\pi$
$619$			7.26002i			0.291805i	−0.989299	+	0.145902i	$0.953391\pi$
$620$	2.16133	+	3.74354i	0.0868013	+	0.150344i
$621$	0.737559	−	1.27749i	0.0295972	−	0.0512639i
$622$	2.95693	+	1.70718i	0.118562	+	0.0684518i
$623$	40.0286			1.60371
$624$	−0.575483	+	0.119017i	−0.0230378	+	0.00476450i
$625$	10.0678			0.402712
$626$	−1.11862	−	0.645838i	−0.0447092	−	0.0258129i
$627$	3.00102	−	5.19791i	0.119849	−	0.207585i
$628$	0.668309	+	1.15754i	0.0266684	+	0.0461911i
$629$			9.75041i			0.388774i
$630$	6.11601	−	3.53108i	0.243668	−	0.140682i
$631$	−23.9479	+	13.8263i	−0.953350	+	0.550417i	−0.894120	−	0.447827i	$-0.852198\pi$
$631$	−23.9479	+	13.8263i	−0.953350	+	0.550417i	−0.0592302	+	0.998244i	$0.518865\pi$
$632$			34.4406i			1.36997i
$633$	−3.19333	−	5.53101i	−0.126923	−	0.219838i
$634$	−3.10745	+	5.38226i	−0.123413	+	0.213757i
$635$	−0.567767	−	0.327800i	−0.0225311	−	0.0130084i
$636$	0.369740			0.0146611
$637$	−4.54957	−	5.10906i	−0.180261	−	0.202428i
$638$	−14.4305			−0.571308
$639$	−16.1283	−	9.31167i	−0.638025	−	0.368364i
$640$	4.18863	−	7.25492i	0.165570	−	0.286776i
$641$	−12.2703	−	21.2527i	−0.484646	−	0.839432i	0.515198	−	0.857071i	$-0.327718\pi$
$641$	−12.2703	−	21.2527i	−0.484646	−	0.839432i	−0.999844	+	0.0176394i	$0.994385\pi$
$642$		−	5.76738i		−	0.227620i
$643$	16.9580	−	9.79070i	0.668758	−	0.386108i	−0.126848	−	0.991922i	$-0.540486\pi$
$643$	16.9580	−	9.79070i	0.668758	−	0.386108i	0.795606	+	0.605815i	$0.207153\pi$
$644$	1.72583	−	0.996408i	0.0680072	−	0.0392640i
$645$			4.36452i			0.171853i
$646$	2.37091	+	4.10654i	0.0932822	+	0.161570i
$647$	−8.34215	+	14.4490i	−0.327964	+	0.568050i	−0.982108	−	0.188320i	$-0.939696\pi$
$647$	−8.34215	+	14.4490i	−0.327964	+	0.568050i	0.654144	+	0.756370i	$0.273029\pi$
$648$	16.1926	+	9.34882i	0.636106	+	0.367256i
$649$	−12.4933			−0.490404
$650$	8.80152	−	7.83767i	0.345224	−	0.307419i
$651$	4.78364			0.187486
$652$	−3.47245	−	2.00482i	−0.135992	−	0.0785148i
$653$	12.3418	−	21.3766i	0.482971	−	0.836530i	−0.516838	−	0.856083i	$-0.672891\pi$
$653$	12.3418	−	21.3766i	0.482971	−	0.836530i	0.999809	+	0.0195533i	$0.00622441\pi$
$654$	2.48480	+	4.30379i	0.0971632	+	0.168292i
$655$		−	11.7176i		−	0.457846i
$656$	−2.20312	+	1.27197i	−0.0860175	+	0.0496622i
$657$	15.5840	−	8.99740i	0.607988	−	0.351022i
$658$		−	2.86370i		−	0.111639i
$659$	−8.30332	−	14.3818i	−0.323452	−	0.560235i	0.657746	−	0.753240i	$-0.271510\pi$
$659$	−8.30332	−	14.3818i	−0.323452	−	0.560235i	−0.981198	+	0.193005i	$0.938177\pi$
$660$	0.713007	−	1.23496i	0.0277538	−	0.0480709i
$661$	−29.4159	−	16.9833i	−1.14414	−	0.660572i	−0.196691	−	0.980465i	$-0.563020\pi$
$661$	−29.4159	−	16.9833i	−1.14414	−	0.660572i	−0.947454	+	0.319893i	$0.896353\pi$
$662$	23.2181			0.902397
$663$	0.569080	−	1.71920i	0.0221012	−	0.0667683i
$664$	36.0494			1.39899
$665$	15.2410	+	8.79939i	0.591020	+	0.341226i
$666$	11.1476	−	19.3081i	0.431959	−	0.748176i
$667$	−2.11252	−	3.65900i	−0.0817973	−	0.141677i
$668$		−	17.0155i		−	0.658349i
$669$	2.61678	−	1.51080i	0.101170	−	0.0584108i
$670$	10.9115	−	6.29977i	0.421549	−	0.243381i
$671$		−	7.82921i		−	0.302243i
$672$	−4.32588	−	7.49265i	−0.166875	−	0.289035i
$673$	−21.5417	+	37.3113i	−0.830371	+	1.43825i	0.0673729	+	0.997728i	$0.478538\pi$
$673$	−21.5417	+	37.3113i	−0.830371	+	1.43825i	−0.897744	+	0.440517i	$0.854795\pi$
$674$	16.5569	+	9.55916i	0.637750	+	0.368205i
$675$	−11.3394			−0.436452
$676$	−1.96261	+	16.8837i	−0.0754850	+	0.649372i
$677$	1.42508			0.0547703			0.0273851	−	0.999625i	$-0.491282\pi$
$677$	1.42508			0.0547703			0.0273851	+	0.999625i	$0.491282\pi$
$678$	1.82029	+	1.05095i	0.0699080	+	0.0403614i
$679$	11.5663	−	20.0334i	0.443874	−	0.768812i
$680$	1.42495	+	2.46809i	0.0546445	+	0.0946471i
$681$		−	4.26346i		−	0.163376i
$682$	4.82583	−	2.78620i	0.184791	−	0.106689i
$683$	−16.0945	+	9.29216i	−0.615839	+	0.355555i	−0.775247	−	0.631658i	$-0.782375\pi$
$683$	−16.0945	+	9.29216i	−0.615839	+	0.355555i	0.159408	+	0.987213i	$0.449041\pi$
$684$			20.4712i			0.782737i
$685$	−7.51564	−	13.0175i	−0.287158	−	0.497372i
$686$	−6.33296	+	10.9690i	−0.241794	+	0.418799i
$687$	−2.16885	−	1.25219i	−0.0827468	−	0.0477739i
$688$	−2.72337			−0.103827
$689$	0.637918	−	1.92717i	0.0243027	−	0.0734192i
$690$	−0.221138			−0.00841857
$691$	33.6477	+	19.4265i	1.28002	+	0.739019i	0.976852	−	0.213918i	$-0.0686226\pi$
$691$	33.6477	+	19.4265i	1.28002	+	0.739019i	0.303167	+	0.952937i	$0.401956\pi$
$692$	−3.34175	+	5.78808i	−0.127034	+	0.220030i
$693$	8.59427	+	14.8857i	0.326469	+	0.565461i
$694$		−	30.8420i		−	1.17075i
$695$	−11.8535	+	6.84361i	−0.449628	+	0.259593i
$696$	−9.89941	+	5.71543i	−0.375236	+	0.216643i
$697$		−	7.83945i		−	0.296940i
$698$	−1.06109	−	1.83786i	−0.0401629	−	0.0695641i
$699$	1.09090	−	1.88950i	0.0412617	−	0.0714673i
$700$	−13.2666	−	7.65947i	−0.501430	−	0.289501i
$701$	−20.6141			−0.778585			−0.389292	−	0.921114i	$-0.627280\pi$
$701$	−20.6141			−0.778585			−0.389292	+	0.921114i	$0.627280\pi$
$702$	−6.46885	+	5.76045i	−0.244151	+	0.217414i
$703$	55.5590			2.09545
$704$	−7.54933	−	4.35861i	−0.284526	−	0.164271i
$705$	0.299989	−	0.519597i	0.0112983	−	0.0195691i
$706$	3.29401	+	5.70540i	0.123972	+	0.214725i
$707$		−	43.7168i		−	1.64414i
$708$	−3.38801	+	1.95607i	−0.127329	+	0.0735136i
$709$	15.6127	−	9.01402i	0.586349	−	0.338529i	−0.177304	−	0.984156i	$-0.556737\pi$
$709$	15.6127	−	9.01402i	0.586349	−	0.338529i	0.763653	+	0.645627i	$0.223404\pi$
$710$			5.84005i			0.219173i
$711$	−17.1911	−	29.7758i	−0.644715	−	1.11668i
$712$	18.4680	−	31.9876i	0.692119	−	1.19879i
$713$	1.41294	+	0.815760i	0.0529149	+	0.0305504i
$714$	1.24674			0.0466582
$715$	−5.20675	−	5.84706i	−0.194721	−	0.218668i
$716$	26.6255			0.995041
$717$	−6.82730	−	3.94174i	−0.254970	−	0.147207i
$718$	−8.20565	+	14.2126i	−0.306232	+	0.530409i
$719$	−9.95396	−	17.2408i	−0.371220	−	0.642972i	0.618533	−	0.785758i	$-0.287727\pi$
$719$	−9.95396	−	17.2408i	−0.371220	−	0.642972i	−0.989754	+	0.142786i	$0.954394\pi$
$720$			0.923243i			0.0344072i
$721$	−18.2448	+	10.5336i	−0.679471	+	0.392293i
$722$	9.70659	−	5.60410i	0.361242	−	0.208563i
$723$			9.70433i			0.360908i
$724$	13.1292	+	22.7404i	0.487942	+	0.845141i
$725$	−16.2392	+	28.1271i	−0.603107	+	1.04461i
$726$	2.38971	+	1.37970i	0.0886903	+	0.0512054i
$727$	41.3159			1.53232			0.766161	−	0.642649i	$-0.222165\pi$
$727$	41.3159			1.53232			0.766161	+	0.642649i	$0.222165\pi$
$728$	−28.9881	+	5.99511i	−1.07437	+	0.222194i
$729$	−14.3160			−0.530221
$730$	−4.88693	−	2.82147i	−0.180873	−	0.104427i
$731$	4.19618	−	7.26799i	0.155201	−	0.268816i
$732$	−1.22582	−	2.12318i	−0.0453075	−	0.0784749i
$733$			46.4139i			1.71434i	0.515037	+	0.857168i	$0.327778\pi$
$733$			46.4139i			1.71434i	−0.515037	+	0.857168i	$0.672222\pi$
$734$	14.3519	−	8.28608i	0.529739	−	0.305845i
$735$	0.854553	−	0.493377i	0.0315207	−	0.0181985i
$736$		−	2.95079i		−	0.108768i
$737$	15.3329	+	26.5574i	0.564796	+	0.978255i
$738$	−8.96278	+	15.5240i	−0.329925	+	0.571446i
$739$	−28.6968	−	16.5681i	−1.05563	−	0.609467i	−0.131409	−	0.991328i	$-0.541950\pi$
$739$	−28.6968	−	16.5681i	−1.05563	−	0.609467i	−0.924220	+	0.381861i	$0.875283\pi$
$740$	13.2002			0.485248
$741$	−9.79623	−	3.24269i	−0.359874	−	0.119123i
$742$	1.39756			0.0513059
$743$	16.3200	+	9.42234i	0.598722	+	0.345672i	0.768539	−	0.639803i	$-0.220984\pi$
$743$	16.3200	+	9.42234i	0.598722	+	0.345672i	−0.169817	+	0.985476i	$0.554318\pi$
$744$	2.20704	−	3.82270i	0.0809138	−	0.140147i
$745$	−4.64661	−	8.04816i	−0.170238	−	0.294862i
$746$			28.8620i			1.05671i
$747$	−31.1667	+	17.9941i	−1.14033	+	0.658370i
$748$	−2.37466	+	1.37101i	−0.0868263	+	0.0501292i
$749$			41.1589i			1.50391i
$750$	1.93190	+	3.34615i	0.0705430	+	0.122184i
$751$	13.4365	−	23.2727i	0.490304	−	0.849232i	−0.509633	−	0.860392i	$-0.670219\pi$
$751$	13.4365	−	23.2727i	0.490304	−	0.849232i	0.999938	+	0.0111597i	$0.00355232\pi$
$752$	0.324218	+	0.187187i	0.0118230	+	0.00682602i
$753$	15.6932			0.571893
$754$	5.02460	+	24.2954i	0.182985	+	0.884787i
$755$	−11.0096			−0.400680
$756$	9.75055	+	5.62948i	0.354624	+	0.204742i
$757$	−4.32514	+	7.49136i	−0.157200	+	0.272278i	−0.933858	−	0.357644i	$-0.883580\pi$
$757$	−4.32514	+	7.49136i	−0.157200	+	0.272278i	0.776658	+	0.629922i	$0.216913\pi$
$758$	1.69024	+	2.92758i	0.0613922	+	0.106334i
$759$		−	0.538225i		−	0.0195363i
$760$	14.0635	−	8.11957i	0.510137	−	0.294528i
$761$	7.08126	−	4.08837i	0.256696	−	0.148203i	−0.366131	−	0.930563i	$-0.619318\pi$
$761$	7.08126	−	4.08837i	0.256696	−	0.148203i	0.622826	+	0.782360i	$0.285984\pi$
$762$			0.264647i			0.00958714i
$763$	−17.7327	−	30.7140i	−0.641968	−	1.11192i
$764$	3.17963	−	5.50728i	0.115035	−	0.199246i
$765$	−2.46390	−	1.42254i	−0.0890827	−	0.0514319i
$766$	−13.2925			−0.480276
$767$	4.35008	+	21.0339i	0.157072	+	0.759491i
$768$	−7.55714			−0.272695
$769$	2.78841	+	1.60989i	0.100553	+	0.0580542i	0.549433	−	0.835538i	$-0.314844\pi$
$769$	2.78841	+	1.60989i	0.100553	+	0.0580542i	−0.448880	+	0.893592i	$0.648177\pi$
$770$	2.69505	−	4.66797i	0.0971230	−	0.168222i
$771$	−0.440299	−	0.762621i	−0.0158570	−	0.0274651i
$772$			21.5593i			0.775934i
$773$	30.8689	−	17.8222i	1.11028	−	0.641019i	0.171376	−	0.985206i	$-0.445179\pi$
$773$	30.8689	−	17.8222i	1.11028	−	0.641019i	0.938901	+	0.344187i	$0.111845\pi$
$774$	−16.6189	+	9.59492i	−0.597353	+	0.344882i
$775$		−	12.5416i		−	0.450509i
$776$	−10.6727	−	18.4857i	−0.383128	−	0.663598i
$777$	7.30393	−	12.6508i	0.262027	−	0.453844i
$778$	−17.2622	−	9.96633i	−0.618879	−	0.357310i
$779$	−44.6701			−1.60047
$780$	−2.32747	−	0.770425i	−0.0833369	−	0.0275856i
$781$	−14.2140			−0.508618
$782$	0.368249	+	0.212609i	0.0131686	+	0.00760287i
$783$	11.9353	−	20.6725i	0.426533	−	0.738776i
$784$	0.307857	+	0.533224i	0.0109949	+	0.0190437i
$785$			1.05849i			0.0377793i
$786$	−4.09636	+	2.36503i	−0.146112	+	0.0843579i
$787$	−26.2033	+	15.1285i	−0.934045	+	0.539271i	−0.888089	−	0.459672i	$-0.847967\pi$
$787$	−26.2033	+	15.1285i	−0.934045	+	0.539271i	−0.0459565	+	0.998943i	$0.514634\pi$
$788$			24.4365i			0.870514i
$789$	3.90774	+	6.76841i	0.139119	+	0.240962i
$790$	−5.39090	+	9.33731i	−0.191800	+	0.332207i
$791$	−12.9905	−	7.50008i	−0.461890	−	0.266672i
$792$	15.8606			0.563582
$793$	−13.1814	+	2.72608i	−0.468085	+	0.0968060i
$794$	4.00359			0.142082
$795$	0.253576	+	0.146402i	0.00899341	+	0.00519235i
$796$	−2.49557	+	4.32246i	−0.0884532	+	0.153206i
$797$	−23.3367	−	40.4204i	−0.826628	−	1.43176i	−0.900668	−	0.434507i	$-0.856923\pi$
$797$	−23.3367	−	40.4204i	−0.826628	−	1.43176i	0.0740399	−	0.997255i	$-0.476411\pi$
$798$		−	7.10410i		−	0.251483i
$799$	−0.999112	+	0.576838i	−0.0353461	+	0.0204071i
$800$	−19.6440	+	11.3415i	−0.694521	+	0.400982i
$801$			36.8734i			1.30286i
$802$	5.86564	+	10.1596i	0.207123	+	0.358748i
$803$	6.86715	−	11.8943i	0.242337	−	0.419739i
$804$	8.31617	+	4.80134i	0.293289	+	0.169330i
$805$	1.57815			0.0556225
$806$	−6.37121	−	7.15472i	−0.224416	−	0.252014i
$807$	2.25417			0.0793504
$808$	−34.9349	−	20.1697i	−1.22901	−	0.709567i
$809$	17.2190	−	29.8241i	0.605387	−	1.04856i	−0.386604	−	0.922246i	$-0.626352\pi$
$809$	17.2190	−	29.8241i	0.605387	−	1.04856i	0.991990	−	0.126314i	$-0.0403148\pi$
$810$	2.92670	+	5.06919i	0.102834	+	0.178113i
$811$		−	23.9086i		−	0.839545i	−0.907629	−	0.419773i	$-0.862110\pi$
$811$		−	23.9086i		−	0.839545i	0.907629	−	0.419773i	$-0.137890\pi$
$812$	27.9276	−	16.1240i	0.980068	−	0.565842i
$813$	−2.44899	+	1.41392i	−0.0858897	+	0.0495885i
$814$		−	17.0165i		−	0.596427i
$815$	−1.58766	−	2.74990i	−0.0556132	−	0.0963249i
$816$	−0.0814940	+	0.141152i	−0.00285286	+	0.00494130i
$817$	−41.4139	−	23.9103i	−1.44889	−	0.836517i
$818$	14.1743			0.495593
$819$	22.0694	−	19.6526i	0.771166	−	0.686716i
$820$	−10.6131			−0.370626
$821$	24.9242	+	14.3900i	0.869861	+	0.502215i	0.867302	−	0.497782i	$-0.165852\pi$
$821$	24.9242	+	14.3900i	0.869861	+	0.502215i	0.00255929	+	0.999997i	$0.499185\pi$
$822$	−3.03384	+	5.25477i	−0.105817	+	0.183281i
$823$	−5.08232	−	8.80283i	−0.177158	−	0.306847i	0.763748	−	0.645515i	$-0.223357\pi$
$823$	−5.08232	−	8.80283i	−0.177158	−	0.306847i	−0.940906	+	0.338667i	$0.890024\pi$
$824$			19.4396i			0.677212i
$825$	−3.58308	+	2.06869i	−0.124747	+	0.0720226i
$826$	−12.8061	+	7.39363i	−0.445583	+	0.257257i
$827$			8.84039i			0.307411i	0.988117	+	0.153705i	$0.0491206\pi$
$827$			8.84039i			0.307411i	−0.988117	+	0.153705i	$0.950879\pi$
$828$	0.917867	+	1.58979i	0.0318981	+	0.0552491i
$829$	−0.632302	+	1.09518i	−0.0219607	+	0.0380371i	−0.876797	−	0.480861i	$-0.840324\pi$
$829$	−0.632302	+	1.09518i	−0.0219607	+	0.0380371i	0.854836	+	0.518898i	$0.173658\pi$
$830$	9.77348	+	5.64272i	0.339242	+	0.195862i
$831$	−16.6129			−0.576297
$832$	−4.70960	+	14.2278i	−0.163276	+	0.493261i
$833$	−1.89739			−0.0657406
$834$	4.78490	+	2.76256i	0.165688	+	0.0956598i
$835$	6.73745	−	11.6696i	0.233159	−	0.403843i
$836$	7.81220	+	13.5311i	0.270191	+	0.467984i
$837$			9.21773i			0.318611i
$838$	0.485075	−	0.280058i	0.0167566	−	0.00967445i
$839$	27.3612	−	15.7970i	0.944614	−	0.545373i	0.0532105	−	0.998583i	$-0.483055\pi$
$839$	27.3612	−	15.7970i	0.944614	−	0.545373i	0.891404	+	0.453210i	$0.149721\pi$
$840$		−	4.26968i		−	0.147318i
$841$	−19.6852	−	34.0958i	−0.678800	−	1.17572i
$842$	−10.9798	+	19.0176i	−0.378389	+	0.655388i
$843$	2.48989	+	1.43754i	0.0857562	+	0.0495114i
$844$	16.6257			0.572279
$845$	−8.03126	+	10.8021i	−0.276284	+	0.371603i
$846$	2.63798			0.0906955
$847$	−17.0541	−	9.84621i	−0.585987	−	0.338320i
$848$	−0.0913519	+	0.158226i	−0.00313704	+	0.00543351i
$849$	4.90598	+	8.49740i	0.168373	+	0.291630i
$850$		−	3.26868i		−	0.112115i
$851$	4.31470	−	2.49110i	0.147906	−	0.0853936i
$852$	−3.85465	+	2.22549i	−0.132058	+	0.0762439i
$853$		−	39.5184i		−	1.35309i	−0.736403	−	0.676543i	$-0.763477\pi$
$853$		−	39.5184i		−	1.35309i	0.736403	−	0.676543i	$-0.236523\pi$
$854$	−4.63339	−	8.02527i	−0.158551	−	0.274619i
$855$	−8.10579	+	14.0396i	−0.277212	+	0.480145i
$856$	32.8908	+	18.9895i	1.12419	+	0.649049i
$857$	24.4044			0.833637			0.416819	−	0.908990i	$-0.363145\pi$
$857$	24.4044			0.833637			0.416819	+	0.908990i	$0.363145\pi$
$858$	−0.993161	+	3.00037i	−0.0339060	+	0.102431i
$859$	−9.75141			−0.332714			−0.166357	−	0.986066i	$-0.553200\pi$
$859$	−9.75141			−0.332714			−0.166357	+	0.986066i	$0.553200\pi$
$860$	−9.83947	−	5.68082i	−0.335523	−	0.193714i
$861$	−5.87246	+	10.1714i	−0.200133	+	0.346640i
$862$	2.11185	+	3.65784i	0.0719301	+	0.124587i
$863$			35.9459i			1.22361i	0.791008	+	0.611806i	$0.209557\pi$
$863$			35.9459i			1.22361i	−0.791008	+	0.611806i	$0.790443\pi$
$864$	14.4378	−	8.33566i	0.491183	−	0.283585i
$865$	−4.58369	+	2.64640i	−0.155850	+	0.0899802i
$866$		−	22.3768i		−	0.760394i
$867$	−0.251133	−	0.434974i	−0.00852891	−	0.0147725i
$868$	−6.22636	+	10.7844i	−0.211336	+	0.366045i
$869$	−22.7260	−	13.1209i	−0.770926	−	0.445094i
$870$	−3.57849			−0.121322
$871$	39.3737	−	35.0619i	1.33413	−	1.18803i
$872$	−32.7255			−1.10822
$873$	18.4543	+	10.6546i	0.624584	+	0.360604i
$874$	1.21147	−	2.09833i	0.0409786	−	0.0709770i
$875$	−13.7870	−	23.8798i	−0.466085	−	0.807284i
$876$		−	4.30075i		−	0.145309i
$877$	−32.8469	+	18.9642i	−1.10916	+	0.640374i	−0.938612	−	0.344975i	$-0.887887\pi$
$877$	−32.8469	+	18.9642i	−1.10916	+	0.640374i	−0.170549	+	0.985349i	$0.554554\pi$
$878$	0.259767	−	0.149976i	0.00876671	−	0.00506146i
$879$			3.76425i			0.126965i
$880$	0.352327	+	0.610248i	0.0118769	+	0.0205714i
$881$	−26.2097	+	45.3965i	−0.883027	+	1.52945i	−0.0350681	+	0.999385i	$0.511165\pi$
$881$	−26.2097	+	45.3965i	−0.883027	+	1.52945i	−0.847959	+	0.530062i	$0.822169\pi$
$882$	3.75729	+	2.16927i	0.126514	+	0.0730431i
$883$	−26.5657			−0.894007			−0.447003	−	0.894532i	$-0.647509\pi$
$883$	−26.5657			−0.894007			−0.447003	+	0.894532i	$0.647509\pi$
$884$	3.13511	+	3.52065i	0.105445	+	0.118412i
$885$	−3.09810			−0.104141
$886$	0.717017	+	0.413970i	0.0240887	+	0.0139076i
$887$	−26.0932	+	45.1948i	−0.876124	+	1.51749i	−0.0205641	+	0.999789i	$0.506546\pi$
$887$	−26.0932	+	45.1948i	−0.876124	+	1.51749i	−0.855560	+	0.517703i	$0.826787\pi$
$888$	−6.73965	−	11.6734i	−0.226168	−	0.391734i
$889$		−	1.88865i		−	0.0633433i
$890$	10.0139	−	5.78151i	0.335666	−	0.193797i
$891$	−12.3378	+	7.12326i	−0.413333	+	0.238638i
$892$			7.86577i			0.263366i
$893$	3.28689	+	5.69306i	0.109992	+	0.190511i
$894$	−1.87570	+	3.24880i	−0.0627327	+	0.108656i
$895$	18.2604	+	10.5426i	0.610377	+	0.352401i
$896$	24.1332			0.806232
$897$	−0.906166	+	0.187407i	−0.0302560	+	0.00625732i
$898$	2.35681			0.0786479
$899$	22.8644	+	13.2008i	0.762570	+	0.440270i
$900$	7.05573	−	12.2209i	0.235191	−	0.407362i
$901$	−0.281511	−	0.487591i	−0.00937848	−	0.0162440i
$902$			13.6815i			0.455543i
$903$	−10.8888	+	6.28663i	−0.362355	+	0.209206i
$904$	−11.9869	+	6.92064i	−0.398678	+	0.230177i
$905$			20.7945i			0.691233i
$906$	2.22212	+	3.84883i	0.0738250	+	0.127869i
$907$	15.9066	−	27.5511i	0.528171	−	0.914819i	−0.471290	−	0.881978i	$-0.656211\pi$
$907$	15.9066	−	27.5511i	0.528171	−	0.914819i	0.999461	−	0.0328401i	$-0.0104552\pi$
$908$	9.61165	+	5.54929i	0.318974	+	0.184160i
$909$	40.2709			1.33570
$910$	−8.79748	−	2.91208i	−0.291634	−	0.0965346i
$911$	−33.1223			−1.09739			−0.548695	−	0.836023i	$-0.684875\pi$
$911$	−33.1223			−1.09739			−0.548695	+	0.836023i	$0.684875\pi$
$912$	0.804300	+	0.464363i	0.0266330	+	0.0153766i
$913$	−13.7338	+	23.7876i	−0.454521	+	0.787254i
$914$	−2.00176	−	3.46715i	−0.0662124	−	0.114683i
$915$		−	1.94150i		−	0.0641839i
$916$	5.64592	−	3.25967i	0.186546	−	0.107703i
$917$	29.2336	−	16.8780i	0.965379	−	0.557362i
$918$			2.40238i			0.0792905i
$919$	−18.0704	−	31.2988i	−0.596087	−	1.03245i	−0.993392	−	0.114767i	$-0.963388\pi$
$919$	−18.0704	−	31.2988i	−0.596087	−	1.03245i	0.397305	−	0.917687i	$-0.369946\pi$
$920$	0.728113	−	1.26113i	0.0240052	−	0.0415782i
$921$	5.06192	+	2.92250i	0.166796	+	0.0962996i
$922$	9.84379			0.324188
$923$	4.94923	+	23.9310i	0.162906	+	0.787698i
$924$	4.10805			0.135145
$925$	−33.1675	−	19.1493i	−1.09054	−	0.629624i
$926$	2.06716	−	3.58043i	0.0679312	−	0.117660i
$927$	−9.70333	−	16.8067i	−0.318699	−	0.552003i
$928$		−	47.7501i		−	1.56747i
$929$	−28.3351	+	16.3593i	−0.929643	+	0.536730i	−0.886699	−	0.462348i	$-0.847007\pi$
$929$	−28.3351	+	16.3593i	−0.929643	+	0.536730i	−0.0429445	+	0.999077i	$0.513674\pi$
$930$	1.19672	−	0.690924i	0.0392418	−	0.0226563i
$931$			10.8116i			0.354334i
$932$	2.83982	+	4.91871i	0.0930213	+	0.161118i
$933$	−1.03038	+	1.78468i	−0.0337333	+	0.0584278i
$934$	−17.4472	−	10.0732i	−0.570891	−	0.329604i
$935$	−2.17146			−0.0710145
$936$	−5.52255	−	26.7032i	−0.180510	−	0.872821i
$937$	20.7407			0.677570			0.338785	−	0.940864i	$-0.389984\pi$
$937$	20.7407			0.677570			0.338785	+	0.940864i	$0.389984\pi$
$938$	31.4338	+	18.1483i	1.02635	+	0.592564i
$939$	0.389801	−	0.675155i	0.0127207	−	0.0220329i
$940$	0.780928	+	1.35261i	0.0254711	+	0.0441172i
$941$			29.2570i			0.953751i	0.878971	+	0.476875i	$0.158231\pi$
$941$			29.2570i			0.953751i	−0.878971	+	0.476875i	$0.841769\pi$
$942$	0.370038	−	0.213641i	0.0120565	−	0.00696081i
$943$	−3.46908	+	2.00287i	−0.112969	+	0.0652225i
$944$		−	1.93315i		−	0.0629187i
$945$	4.45810	+	7.72166i	0.145022	+	0.251185i
$946$	−7.32320	+	12.6841i	−0.238098	+	0.412397i
$947$	−31.2651	−	18.0509i	−1.01598	−	0.586575i	−0.103042	−	0.994677i	$-0.532858\pi$
$947$	−31.2651	−	18.0509i	−1.01598	−	0.586575i	−0.912937	+	0.408102i	$0.866191\pi$
$948$	−8.21731			−0.266886
$949$	−22.4165	−	7.42016i	−0.727670	−	0.240869i
$950$	−18.6254			−0.604286
$951$	−3.24851	−	1.87553i	−0.105340	−	0.0608182i
$952$	−4.10500	+	7.11007i	−0.133044	+	0.230439i
$953$	11.5018	+	19.9217i	0.372579	+	0.645326i	0.989962	−	0.141337i	$-0.0451402\pi$
$953$	11.5018	+	19.9217i	0.372579	+	0.645326i	−0.617382	+	0.786663i	$0.711807\pi$
$954$			1.28740i			0.0416810i
$955$	4.36132	−	2.51801i	0.141129	−	0.0814809i
$956$	17.7727	−	10.2611i	0.574811	−	0.331867i
$957$		−	8.70965i		−	0.281543i
$958$	−14.8854	−	25.7822i	−0.480925	−	0.832986i
$959$	21.6510	−	37.5006i	0.699147	−	1.21096i
$960$	−1.87209	−	1.08085i	−0.0604215	−	0.0348844i
$961$	20.8050			0.671127
$962$	−28.6492	+	5.92503i	−0.923688	+	0.191030i
$963$	−37.9146			−1.22178
$964$	−21.8777	−	12.6311i	−0.704633	−	0.406820i
$965$	−8.53660	+	14.7858i	−0.274803	+	0.475972i
$966$	−0.318526	−	0.551704i	−0.0102484	−	0.0177508i
$967$			9.16533i			0.294737i	0.989082	+	0.147369i	$0.0470803\pi$
$967$			9.16533i			0.294737i	−0.989082	+	0.147369i	$0.952920\pi$
$968$	−15.7366	+	9.08551i	−0.505792	+	0.292019i
$969$	−2.47854	+	1.43098i	−0.0796221	+	0.0459698i
$970$		−	6.68230i		−	0.214556i
$971$	21.0701	+	36.4945i	0.676172	+	1.17116i	0.976125	+	0.217210i	$0.0696955\pi$
$971$	21.0701	+	36.4945i	0.676172	+	1.17116i	−0.299953	+	0.953954i	$0.596971\pi$
$972$	−7.89242	+	13.6701i	−0.253150	+	0.438468i
$973$	−34.1474	−	19.7150i	−1.09472	−	0.632035i
$974$	16.6275			0.532779
$975$	4.73049	+	5.31223i	0.151497	+	0.170128i
$976$	1.21145			0.0387777
$977$	3.14988	+	1.81858i	0.100774	+	0.0581816i	0.549540	−	0.835468i	$-0.314803\pi$
$977$	3.14988	+	1.81858i	0.100774	+	0.0581816i	−0.448766	+	0.893649i	$0.648136\pi$
$978$	−0.640890	+	1.11005i	−0.0204934	+	0.0354956i
$979$	14.0716	+	24.3727i	0.449729	+	0.778954i
$980$			2.56870i			0.0820542i
$981$	28.2930	−	16.3350i	0.903326	−	0.521536i
$982$	−8.55537	+	4.93945i	−0.273013	+	0.157624i
$983$		−	49.4027i		−	1.57570i	−0.615865	−	0.787851i	$-0.711193\pi$
$983$		−	49.4027i		−	1.57570i	0.615865	−	0.787851i	$-0.288807\pi$
$984$	5.41876	+	9.38557i	0.172744	+	0.299201i
$985$	−9.67587	+	16.7591i	−0.308299	+	0.533989i
$986$	5.95906	+	3.44047i	0.189775	+	0.109567i
$987$	1.72841			0.0550160
$988$	20.0611	−	17.8642i	0.638229	−	0.568336i
$989$	−4.28826			−0.136359
$990$	4.30002	+	2.48262i	0.136664	+	0.0789028i
$991$	−14.2688	+	24.7143i	−0.453264	+	0.785076i	−0.998587	−	0.0531502i	$-0.983074\pi$
$991$	−14.2688	+	24.7143i	−0.453264	+	0.785076i	0.545323	+	0.838226i	$0.316407\pi$
$992$	9.21945	+	15.9686i	0.292718	+	0.507002i
$993$			14.0135i			0.444704i
$994$	−14.5700	+	8.41198i	−0.462132	+	0.266812i
$995$	−3.42304	+	1.97629i	−0.108518	+	0.0626527i
$996$			8.60116i			0.272538i
$997$	15.4618	+	26.7807i	0.489681	+	0.848152i	0.999929	−	0.0118748i	$-0.00377995\pi$
$997$	15.4618	+	26.7807i	0.489681	+	0.848152i	−0.510249	+	0.860027i	$0.670447\pi$
$998$	−0.584152	+	1.01178i	−0.0184910	+	0.0320274i
$999$	24.3771	+	14.0741i	0.771258	+	0.445286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.c.69.8	✓	22
13.6	odd	12		2873.2.a.x.1.8		22
13.7	odd	12		2873.2.a.x.1.15		22
13.10	even	6	inner	221.2.m.c.205.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.c.69.8	✓	22	1.1	even	1	trivial
221.2.m.c.205.8	yes	22	13.10	even	6	inner
2873.2.a.x.1.8		22	13.6	odd	12
2873.2.a.x.1.15		22	13.7	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+(0.720682 + 0.416086i) q^{2} +(-0.251133 + 0.434974i) q^{3} +(-0.653745 - 1.13232i) q^{4} -1.03543i q^{5} +(-0.361974 + 0.208986i) q^{6} +(2.58322 - 1.49142i) q^{7} -2.75240i q^{8} +(1.37386 + 2.37960i) q^{9} +(0.430827 - 0.746214i) q^{10} +(1.81620 + 1.04858i) q^{11} +0.656706 q^{12} +(1.13303 - 3.42290i) q^{13} +2.48224 q^{14} +(0.450384 + 0.260029i) q^{15} +(-0.162253 + 0.281030i) q^{16} +(-0.500000 - 0.866025i) q^{17} +2.28658i q^{18} +(-4.93472 + 2.84906i) q^{19} +(-1.17243 + 0.676904i) q^{20} +1.49818i q^{21} +(0.872603 + 1.51139i) q^{22} +(-0.255486 + 0.442515i) q^{23} +(1.19722 + 0.691217i) q^{24} +3.92789 q^{25} +(2.24077 - 1.99539i) q^{26} -2.88688 q^{27} +(-3.37754 - 1.95002i) q^{28} +(-4.13432 + 7.16085i) q^{29} +(0.216389 + 0.374797i) q^{30} -3.19297i q^{31} +(-5.00116 + 2.88742i) q^{32} +(-0.912215 + 0.526667i) q^{33} -0.832172i q^{34} +(-1.54426 - 2.67474i) q^{35} +(1.79631 - 3.11131i) q^{36} +(-8.44410 - 4.87520i) q^{37} -4.74182 q^{38} +(1.20433 + 1.35244i) q^{39} -2.84991 q^{40} +(6.78916 + 3.91972i) q^{41} +(-0.623372 + 1.07971i) q^{42} +(4.19618 + 7.26799i) q^{43} -2.74203i q^{44} +(2.46390 - 1.42254i) q^{45} +(-0.368249 + 0.212609i) q^{46} -1.15368i q^{47} +(-0.0814940 - 0.141152i) q^{48} +(0.948695 - 1.64319i) q^{49} +(2.83076 + 1.63434i) q^{50} +0.502265 q^{51} +(-4.61652 + 0.954756i) q^{52} +0.563021 q^{53} +(-2.08053 - 1.20119i) q^{54} +(1.08573 - 1.88054i) q^{55} +(-4.10500 - 7.11007i) q^{56} -2.86197i q^{57} +(-5.95906 + 3.44047i) q^{58} +(-5.15910 + 2.97861i) q^{59} -0.679971i q^{60} +(-1.86661 - 3.23307i) q^{61} +(1.32855 - 2.30112i) q^{62} +(7.09800 + 4.09803i) q^{63} -4.15666 q^{64} +(-3.54416 - 1.17317i) q^{65} -0.876556 q^{66} +(12.6635 + 7.31125i) q^{67} +(-0.653745 + 1.13232i) q^{68} +(-0.128322 - 0.222260i) q^{69} -2.57018i q^{70} +(-5.86968 + 3.38886i) q^{71} +(6.54962 - 3.78143i) q^{72} -6.54897i q^{73} +(-4.05701 - 7.02695i) q^{74} +(-0.986421 + 1.70853i) q^{75} +(6.45209 + 3.72512i) q^{76} +6.25554 q^{77} +(0.305211 + 1.47579i) q^{78} -12.5129 q^{79} +(0.290986 + 0.168001i) q^{80} +(-3.39660 + 5.88309i) q^{81} +(3.26189 + 5.64975i) q^{82} +13.0974i q^{83} +(1.69642 - 0.979428i) q^{84} +(-0.896706 + 0.517713i) q^{85} +6.98389i q^{86} +(-2.07652 - 3.59665i) q^{87} +(2.88613 - 4.99892i) q^{88} +(11.6217 + 6.70979i) q^{89} +2.36759 q^{90} +(-2.17814 - 10.5319i) q^{91} +0.668091 q^{92} +(1.38886 + 0.801858i) q^{93} +(0.480028 - 0.831434i) q^{94} +(2.94999 + 5.10954i) q^{95} -2.90050i q^{96} +(6.71621 - 3.87760i) q^{97} +(1.36742 - 0.789477i) q^{98} +5.76246i 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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