LMFDB - Embedded newform 312.2.bk.b.205.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(205,312)] 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("312.205"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.3
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.b.277.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28706 - 0.586059i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.31307 + 1.50859i) q^{4} +2.83647 q^{5} +(-1.40766 + 0.135990i) q^{6} +(0.691790 + 0.399405i) q^{7} +(-0.805882 - 2.71119i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.65072 - 1.66234i) q^{10} +(0.296401 + 0.513382i) q^{11} +(1.89145 + 0.649944i) q^{12} +(1.09999 + 3.43366i) q^{13} +(-0.656303 - 0.919490i) q^{14} +(2.45646 - 1.41824i) q^{15} +(-0.551696 + 3.96177i) q^{16} +(0.0832632 - 0.144216i) q^{17} +(-1.15107 + 0.821601i) q^{18} +(-2.45002 + 4.24357i) q^{19} +(3.72449 + 4.27908i) q^{20} +0.798810 q^{21} +(-0.0806153 - 0.834464i) q^{22} +(-3.46719 - 6.00535i) q^{23} +(-2.05351 - 1.94502i) q^{24} +3.04557 q^{25} +(0.596570 - 5.06400i) q^{26} -1.00000i q^{27} +(0.305829 + 1.56808i) q^{28} +(8.75998 - 5.05758i) q^{29} +(-3.99279 + 0.385732i) q^{30} -2.98291i q^{31} +(3.03190 - 4.77573i) q^{32} +(0.513382 + 0.296401i) q^{33} +(-0.191684 + 0.136818i) q^{34} +(1.96224 + 1.13290i) q^{35} +(1.96301 - 0.382856i) q^{36} +(-0.561354 - 0.972293i) q^{37} +(5.64032 - 4.02588i) q^{38} +(2.66945 + 2.42364i) q^{39} +(-2.28586 - 7.69022i) q^{40} +(-6.29600 + 3.63500i) q^{41} +(-1.02812 - 0.468150i) q^{42} +(-0.928831 - 0.536261i) q^{43} +(-0.385288 + 1.12125i) q^{44} +(1.41824 - 2.45646i) q^{45} +(0.943008 + 9.76125i) q^{46} -2.38164i q^{47} +(1.50310 + 3.70684i) q^{48} +(-3.18095 - 5.50957i) q^{49} +(-3.91985 - 1.78488i) q^{50} -0.166526i q^{51} +(-3.73563 + 6.16807i) q^{52} -2.56107i q^{53} +(-0.586059 + 1.28706i) q^{54} +(0.840734 + 1.45619i) q^{55} +(0.525362 - 2.19745i) q^{56} +4.90005i q^{57} +(-14.2387 + 1.37556i) q^{58} +(-5.47256 + 9.47875i) q^{59} +(5.36504 + 1.84355i) q^{60} +(11.6003 + 6.69744i) q^{61} +(-1.74816 + 3.83919i) q^{62} +(0.691790 - 0.399405i) q^{63} +(-6.70111 + 4.36980i) q^{64} +(3.12009 + 9.73948i) q^{65} +(-0.487047 - 0.682360i) q^{66} +(-3.39369 - 5.87804i) q^{67} +(0.326894 - 0.0637556i) q^{68} +(-6.00535 - 3.46719i) q^{69} +(-1.86159 - 2.60811i) q^{70} +(-3.04531 - 1.75821i) q^{71} +(-2.75090 - 0.657681i) q^{72} +2.97283i q^{73} +(0.152677 + 1.58039i) q^{74} +(2.63754 - 1.52279i) q^{75} +(-9.61886 + 1.87601i) q^{76} +0.473537i q^{77} +(-2.01536 - 4.68384i) q^{78} -6.54925 q^{79} +(-1.56487 + 11.2375i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.2337 - 0.988648i) q^{82} -14.0561 q^{83} +(1.04889 + 1.20508i) q^{84} +(0.236174 - 0.409065i) q^{85} +(0.881184 + 1.23455i) q^{86} +(5.05758 - 8.75998i) q^{87} +(1.15301 - 1.21733i) q^{88} +(-11.1252 + 6.42312i) q^{89} +(-3.26499 + 2.33045i) q^{90} +(-0.610460 + 2.81471i) q^{91} +(4.50696 - 13.1160i) q^{92} +(-1.49145 - 2.58327i) q^{93} +(-1.39578 + 3.06533i) q^{94} +(-6.94942 + 12.0368i) q^{95} +(0.237838 - 5.65185i) q^{96} +(11.5252 + 6.65406i) q^{97} +(0.865157 + 8.95540i) q^{98} +0.592802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.28706	−	0.586059i	−0.910092	−	0.414406i
$2$	−1.28706	−	0.586059i	−0.910092	−	0.414406i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	1.31307	+	1.50859i	0.656535	+	0.754296i
$5$	2.83647			1.26851			0.634254	−	0.773124i	$-0.281307\pi$
$5$	2.83647			1.26851			0.634254	+	0.773124i	$0.281307\pi$
$6$	−1.40766	+	0.135990i	−0.574675	+	0.0555178i
$7$	0.691790	+	0.399405i	0.261472	+	0.150961i	0.625006	−	0.780620i	$-0.285097\pi$
$7$	0.691790	+	0.399405i	0.261472	+	0.150961i	−0.363534	+	0.931581i	$0.618430\pi$
$8$	−0.805882	−	2.71119i	−0.284922	−	0.958551i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−3.65072	−	1.66234i	−1.15446	−	0.525678i
$11$	0.296401	+	0.513382i	0.0893683	+	0.154790i	0.907244	−	0.420604i	$-0.138182\pi$
$11$	0.296401	+	0.513382i	0.0893683	+	0.154790i	−0.817876	+	0.575395i	$0.804849\pi$
$12$	1.89145	+	0.649944i	0.546014	+	0.187623i
$13$	1.09999	+	3.43366i	0.305082	+	0.952326i
$13$	1.09999	+	3.43366i	0.305082	+	0.952326i
$14$	−0.656303	−	0.919490i	−0.175404	−	0.245744i
$15$	2.45646	−	1.41824i	0.634254	−	0.366187i
$16$	−0.551696	+	3.96177i	−0.137924	+	0.990443i
$17$	0.0832632	−	0.144216i	0.0201943	−	0.0349775i	−0.855752	−	0.517387i	$-0.826905\pi$
$17$	0.0832632	−	0.144216i	0.0201943	−	0.0349775i	0.875946	+	0.482409i	$0.160238\pi$
$18$	−1.15107	+	0.821601i	−0.271311	+	0.193653i
$19$	−2.45002	+	4.24357i	−0.562074	+	0.973541i	0.435241	+	0.900314i	$0.356663\pi$
$19$	−2.45002	+	4.24357i	−0.562074	+	0.973541i	−0.997315	+	0.0732270i	$0.976670\pi$
$20$	3.72449	+	4.27908i	0.832820	+	0.956831i
$21$	0.798810			0.174315
$22$	−0.0806153	−	0.834464i	−0.0171872	−	0.177908i
$23$	−3.46719	−	6.00535i	−0.722959	−	1.25220i	−0.959808	−	0.280656i	$-0.909448\pi$
$23$	−3.46719	−	6.00535i	−0.722959	−	1.25220i	0.236849	−	0.971546i	$-0.423885\pi$
$24$	−2.05351	−	1.94502i	−0.419171	−	0.397025i
$25$	3.04557			0.609114
$26$	0.596570	−	5.06400i	0.116997	−	0.993132i
$27$		−	1.00000i		−	0.192450i
$28$	0.305829	+	1.56808i	0.0577963	+	0.296338i
$29$	8.75998	−	5.05758i	1.62669	−	0.939168i	0.641615	−	0.767027i	$-0.278265\pi$
$29$	8.75998	−	5.05758i	1.62669	−	0.939168i	0.985072	−	0.172141i	$-0.0550686\pi$
$30$	−3.99279	+	0.385732i	−0.728980	+	0.0704248i
$31$		−	2.98291i		−	0.535746i	−0.963454	−	0.267873i	$-0.913679\pi$
$31$		−	2.98291i		−	0.535746i	0.963454	−	0.267873i	$-0.0863207\pi$
$32$	3.03190	−	4.77573i	0.535969	−	0.844238i
$33$	0.513382	+	0.296401i	0.0893683	+	0.0515968i
$34$	−0.191684	+	0.136818i	−0.0328736	+	0.0234641i
$35$	1.96224	+	1.13290i	0.331680	+	0.191495i
$36$	1.96301	−	0.382856i	0.327169	−	0.0638093i
$37$	−0.561354	−	0.972293i	−0.0922860	−	0.159844i	0.816187	−	0.577788i	$-0.196084\pi$
$37$	−0.561354	−	0.972293i	−0.0922860	−	0.159844i	−0.908473	+	0.417944i	$0.862751\pi$
$38$	5.64032	−	4.02588i	0.914981	−	0.653085i
$39$	2.66945	+	2.42364i	0.427454	+	0.388093i
$40$	−2.28586	−	7.69022i	−0.361426	−	1.21593i
$41$	−6.29600	+	3.63500i	−0.983269	+	0.567691i	−0.903256	−	0.429103i	$-0.858830\pi$
$41$	−6.29600	+	3.63500i	−0.983269	+	0.567691i	−0.0800139	+	0.996794i	$0.525496\pi$
$42$	−1.02812	−	0.468150i	−0.158642	−	0.0722371i
$43$	−0.928831	−	0.536261i	−0.141645	−	0.0817790i	0.427503	−	0.904014i	$-0.359393\pi$
$43$	−0.928831	−	0.536261i	−0.141645	−	0.0817790i	−0.569148	+	0.822235i	$0.692727\pi$
$44$	−0.385288	+	1.12125i	−0.0580844	+	0.169035i
$45$	1.41824	−	2.45646i	0.211418	−	0.366187i
$46$	0.943008	+	9.76125i	0.139039	+	1.43922i
$47$		−	2.38164i		−	0.347398i	−0.984799	−	0.173699i	$-0.944428\pi$
$47$		−	2.38164i		−	0.347398i	0.984799	−	0.173699i	$-0.0555720\pi$
$48$	1.50310	+	3.70684i	0.216954	+	0.535037i
$49$	−3.18095	−	5.50957i	−0.454422	−	0.787081i
$50$	−3.91985	−	1.78488i	−0.554350	−	0.252421i
$51$		−	0.166526i		−	0.0233184i
$52$	−3.73563	+	6.16807i	−0.518038	+	0.855357i
$53$		−	2.56107i		−	0.351791i	−0.984409	−	0.175895i	$-0.943718\pi$
$53$		−	2.56107i		−	0.351791i	0.984409	−	0.175895i	$-0.0562820\pi$
$54$	−0.586059	+	1.28706i	−0.0797525	+	0.175147i
$55$	0.840734	+	1.45619i	0.113364	+	0.196353i
$56$	0.525362	−	2.19745i	0.0702045	−	0.293646i
$57$			4.90005i			0.649027i
$58$	−14.2387	+	1.37556i	−1.86963	+	0.180620i
$59$	−5.47256	+	9.47875i	−0.712466	+	1.23403i	0.251462	+	0.967867i	$0.419089\pi$
$59$	−5.47256	+	9.47875i	−0.712466	+	1.23403i	−0.963929	+	0.266161i	$0.914245\pi$
$60$	5.36504	+	1.84355i	0.692623	+	0.238001i
$61$	11.6003	+	6.69744i	1.48527	+	0.857519i	0.999859	−	0.0167691i	$-0.00533802\pi$
$61$	11.6003	+	6.69744i	1.48527	+	0.857519i	0.485407	+	0.874288i	$0.338671\pi$
$62$	−1.74816	+	3.83919i	−0.222016	+	0.487578i
$63$	0.691790	−	0.399405i	0.0871573	−	0.0503203i
$64$	−6.70111	+	4.36980i	−0.837639	+	0.546225i
$65$	3.12009	+	9.73948i	0.387000	+	1.20803i
$66$	−0.487047	−	0.682360i	−0.0599513	−	0.0839926i
$67$	−3.39369	−	5.87804i	−0.414605	−	0.718117i	0.580782	−	0.814059i	$-0.302747\pi$
$67$	−3.39369	−	5.87804i	−0.414605	−	0.718117i	−0.995387	+	0.0959425i	$0.969414\pi$
$68$	0.326894	−	0.0637556i	0.0396417	−	0.00773151i
$69$	−6.00535	−	3.46719i	−0.722959	−	0.417401i
$70$	−1.86159	−	2.60811i	−0.222502	−	0.311728i
$71$	−3.04531	−	1.75821i	−0.361411	−	0.208661i	0.308288	−	0.951293i	$-0.400244\pi$
$71$	−3.04531	−	1.75821i	−0.361411	−	0.208661i	−0.669700	+	0.742632i	$0.733577\pi$
$72$	−2.75090	−	0.657681i	−0.324197	−	0.0775085i
$73$			2.97283i			0.347944i	0.984751	+	0.173972i	$0.0556602\pi$
$73$			2.97283i			0.347944i	−0.984751	+	0.173972i	$0.944340\pi$
$74$	0.152677	+	1.58039i	0.0177484	+	0.183717i
$75$	2.63754	−	1.52279i	0.304557	−	0.175836i
$76$	−9.61886	+	1.87601i	−1.10336	+	0.215193i
$77$			0.473537i			0.0539645i
$78$	−2.01536	−	4.68384i	−0.228194	−	0.530340i
$79$	−6.54925			−0.736848			−0.368424	−	0.929658i	$-0.620103\pi$
$79$	−6.54925			−0.736848			−0.368424	+	0.929658i	$0.620103\pi$
$80$	−1.56487	+	11.2375i	−0.174958	+	1.25639i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.2337	−	0.988648i	1.13012	−	0.109178i
$83$	−14.0561			−1.54286			−0.771428	−	0.636316i	$-0.780457\pi$
$83$	−14.0561			−1.54286			−0.771428	+	0.636316i	$0.780457\pi$
$84$	1.04889	+	1.20508i	0.114444	+	0.131485i
$85$	0.236174	−	0.409065i	0.0256166	−	0.0443693i
$86$	0.881184	+	1.23455i	0.0950206	+	0.133125i
$87$	5.05758	−	8.75998i	0.542229	−	0.939168i
$88$	1.15301	−	1.21733i	0.122911	−	0.129767i
$89$	−11.1252	+	6.42312i	−1.17927	+	0.680849i	−0.955845	−	0.293873i	$-0.905056\pi$
$89$	−11.1252	+	6.42312i	−1.17927	+	0.680849i	−0.223421	+	0.974722i	$0.571723\pi$
$90$	−3.26499	+	2.33045i	−0.344160	+	0.245651i
$91$	−0.610460	+	2.81471i	−0.0639935	+	0.295062i
$92$	4.50696	−	13.1160i	0.469883	−	1.36744i
$93$	−1.49145	−	2.58327i	−0.154656	−	0.267873i
$94$	−1.39578	+	3.06533i	−0.143964	+	0.316164i
$95$	−6.94942	+	12.0368i	−0.712996	+	1.23495i
$96$	0.237838	−	5.65185i	0.0242742	−	0.576840i
$97$	11.5252	+	6.65406i	1.17020	+	0.675617i	0.953728	−	0.300671i	$-0.0972106\pi$
$97$	11.5252	+	6.65406i	1.17020	+	0.675617i	0.216475	+	0.976288i	$0.430544\pi$
$98$	0.865157	+	8.95540i	0.0873940	+	0.904632i
$99$	0.592802			0.0595789
$100$	3.99905	+	4.59452i	0.399905	+	0.459452i
$101$	−13.6064	+	7.85564i	−1.35388	+	0.781666i	−0.988791	−	0.149305i	$-0.952296\pi$
$101$	−13.6064	+	7.85564i	−1.35388	+	0.781666i	−0.365093	+	0.930971i	$0.618963\pi$
$102$	−0.0975943	+	0.214330i	−0.00966328	+	0.0212219i
$103$	−7.80561			−0.769110			−0.384555	−	0.923102i	$-0.625645\pi$
$103$	−7.80561			−0.769110			−0.384555	+	0.923102i	$0.625645\pi$
$104$	8.42285	−	5.74941i	0.825928	−	0.563776i
$105$	2.26580			0.221120
$106$	−1.50094	+	3.29627i	−0.145784	+	0.320162i
$107$	13.5667	−	7.83275i	1.31154	−	0.757220i	0.329192	−	0.944263i	$-0.393224\pi$
$107$	13.5667	−	7.83275i	1.31154	−	0.757220i	0.982352	+	0.187042i	$0.0598902\pi$
$108$	1.50859	−	1.31307i	0.145164	−	0.126350i
$109$	5.91665			0.566713			0.283356	−	0.959015i	$-0.408552\pi$
$109$	5.91665			0.566713			0.283356	+	0.959015i	$0.408552\pi$
$110$	−0.228663	−	2.36693i	−0.0218022	−	0.225678i
$111$	−0.972293	−	0.561354i	−0.0922860	−	0.0532813i
$112$	−1.96401	+	2.52036i	−0.185581	+	0.238152i
$113$	0.578921	−	1.00272i	0.0544603	−	0.0943280i	−0.837510	−	0.546422i	$-0.815990\pi$
$113$	0.578921	−	1.00272i	0.0544603	−	0.0943280i	0.891970	+	0.452094i	$0.149323\pi$
$114$	2.87172	−	6.30668i	0.268961	−	0.590675i
$115$	−9.83459	−	17.0340i	−0.917080	−	1.58843i
$116$	19.1323	+	6.57428i	1.77639	+	0.610406i
$117$	3.52363	+	0.764211i	0.325760	+	0.0706513i
$118$	12.5986	−	8.99252i	1.15980	−	0.827828i
$119$	0.115201	−	0.0665115i	0.0105605	−	0.00609710i
$120$	−5.82472	−	5.51699i	−0.531722	−	0.503630i
$121$	5.32429	−	9.22195i	0.484027	−	0.838359i
$122$	−11.0052	−	15.4185i	−0.996368	−	1.39593i
$123$	−3.63500	+	6.29600i	−0.327756	+	0.567691i
$124$	4.49999	−	3.91676i	0.404111	−	0.351736i
$125$	−5.54368			−0.495842
$126$	−1.12445	+	0.108630i	−0.100174	+	0.00967756i
$127$	0.604776	+	1.04750i	0.0536652	+	0.0929508i	0.891610	−	0.452804i	$-0.149576\pi$
$127$	0.604776	+	1.04750i	0.0536652	+	0.0929508i	−0.837945	+	0.545755i	$0.816243\pi$
$128$	11.1857	−	1.69697i	0.988687	−	0.149992i
$129$	−1.07252			−0.0944302
$130$	1.69215	−	14.3639i	0.148412	−	1.25980i
$131$			8.67176i			0.757655i	0.925467	+	0.378828i	$0.123673\pi$
$131$			8.67176i			0.757655i	−0.925467	+	0.378828i	$0.876327\pi$
$132$	0.226958	+	1.16368i	0.0197542	+	0.101285i
$133$	−3.38980	+	1.95710i	−0.293933	+	0.169702i
$134$	0.923017	+	9.55431i	0.0797365	+	0.825367i
$135$		−	2.83647i		−	0.244125i
$136$	−0.458098	−	0.109521i	−0.0392816	−	0.00939137i
$137$	−4.14351	−	2.39225i	−0.354004	−	0.204384i	0.312444	−	0.949936i	$-0.398852\pi$
$137$	−4.14351	−	2.39225i	−0.354004	−	0.204384i	−0.666447	+	0.745552i	$0.732186\pi$
$138$	5.69730	+	7.98199i	0.484986	+	0.679472i
$139$	−6.10309	−	3.52362i	−0.517658	−	0.298870i	0.218318	−	0.975878i	$-0.429943\pi$
$139$	−6.10309	−	3.52362i	−0.517658	−	0.298870i	−0.735976	+	0.677008i	$0.763276\pi$
$140$	0.867476	+	4.44780i	0.0733151	+	0.375908i
$141$	−1.19082	−	2.06256i	−0.100285	−	0.173699i
$142$	2.88909	+	4.04766i	0.242447	+	0.339672i
$143$	−1.43674	+	1.58246i	−0.120146	+	0.132332i
$144$	3.15515	+	2.45867i	0.262929	+	0.204889i
$145$	24.8474	−	14.3457i	2.06347	−	1.19134i
$146$	1.74226	−	3.82623i	0.144190	−	0.316661i
$147$	−5.50957	−	3.18095i	−0.454422	−	0.262360i
$148$	0.729697	−	2.12354i	0.0599807	−	0.174554i
$149$	−4.32937	+	7.49869i	−0.354676	+	0.614317i	−0.987062	−	0.160336i	$-0.948742\pi$
$149$	−4.32937	+	7.49869i	−0.354676	+	0.614317i	0.632386	+	0.774653i	$0.282076\pi$
$150$	−4.28713	+	0.414168i	−0.350043	+	0.0338167i
$151$			13.6960i			1.11456i	0.830324	+	0.557281i	$0.188155\pi$
$151$			13.6960i			1.11456i	−0.830324	+	0.557281i	$0.811845\pi$
$152$	13.4795	+	3.22267i	1.09334	+	0.261393i
$153$	−0.0832632	−	0.144216i	−0.00673143	−	0.0116592i
$154$	0.277520	−	0.609472i	0.0223632	−	0.0491127i
$155$		−	8.46093i		−	0.679598i
$156$	−0.151113	+	7.20952i	−0.0120987	+	0.577223i
$157$		−	20.3214i		−	1.62182i	−0.585168	−	0.810912i	$-0.698971\pi$
$157$		−	20.3214i		−	1.62182i	0.585168	−	0.810912i	$-0.301029\pi$
$158$	8.42930	+	3.83825i	0.670599	+	0.305354i
$159$	−1.28054	−	2.21796i	−0.101553	−	0.175895i
$160$	8.59990	−	13.5462i	0.679882	−	1.07092i
$161$		−	5.53926i		−	0.436555i
$162$	0.135990	+	1.40766i	0.0106844	+	0.110596i
$163$	−4.53859	+	7.86107i	−0.355490	+	0.615726i	−0.987202	−	0.159477i	$-0.949019\pi$
$163$	−4.53859	+	7.86107i	−0.355490	+	0.615726i	0.631712	+	0.775203i	$0.282353\pi$
$164$	−13.7508	−	4.72508i	−1.07376	−	0.368967i
$165$	1.45619	+	0.840734i	0.113364	+	0.0654510i
$166$	18.0911	+	8.23770i	1.40414	+	0.639369i
$167$	17.0856	−	9.86436i	1.32212	−	0.763327i	0.338055	−	0.941127i	$-0.390231\pi$
$167$	17.0856	−	9.86436i	1.32212	−	0.763327i	0.984067	+	0.177799i	$0.0568978\pi$
$168$	−0.643747	−	2.16573i	−0.0496661	−	0.167089i
$169$	−10.5800	+	7.55398i	−0.813850	+	0.581076i
$170$	−0.543707	+	0.388081i	−0.0417004	+	0.0297645i
$171$	2.45002	+	4.24357i	0.187358	+	0.324514i
$172$	−0.410621	−	2.10537i	−0.0313096	−	0.160533i
$173$	−3.90902	−	2.25687i	−0.297197	−	0.171587i	0.343986	−	0.938975i	$-0.388223\pi$
$173$	−3.90902	−	2.25687i	−0.297197	−	0.171587i	−0.641183	+	0.767388i	$0.721556\pi$
$174$	−11.6433	+	8.31062i	−0.882676	+	0.630026i
$175$	2.10690	+	1.21642i	0.159266	+	0.0919525i
$176$	−2.19743	+	0.891043i	−0.165637	+	0.0671649i
$177$			10.9451i			0.822685i
$178$	18.0831	−	1.74696i	1.35539	−	0.130940i
$179$	5.63214	−	3.25171i	0.420966	−	0.243045i	−0.274525	−	0.961580i	$-0.588521\pi$
$179$	5.63214	−	3.25171i	0.420966	−	0.243045i	0.695490	+	0.718535i	$0.255187\pi$
$180$	5.56803	−	1.08596i	0.415017	−	0.0809427i
$181$			2.12509i			0.157957i	0.996876	+	0.0789783i	$0.0251658\pi$
$181$			2.12509i			0.157957i	−0.996876	+	0.0789783i	$0.974834\pi$
$182$	2.43529	−	3.26495i	0.180516	−	0.242014i
$183$	13.3949			0.990178
$184$	−13.4875	+	14.2398i	−0.994312	+	1.04977i
$185$	−1.59226	−	2.75788i	−0.117066	−	0.202764i
$186$	0.405646	+	4.19892i	0.0297434	+	0.307880i
$187$	0.0987173			0.00721892
$188$	3.59292	−	3.12726i	0.262041	−	0.228079i
$189$	0.399405	−	0.691790i	0.0290524	−	0.0503203i
$190$	15.9986	−	11.4193i	1.16066	−	0.828444i
$191$	7.88826	−	13.6629i	0.570775	−	0.988611i	−0.425712	−	0.904859i	$-0.639976\pi$
$191$	7.88826	−	13.6629i	0.570775	−	0.988611i	0.996487	−	0.0837519i	$-0.0266903\pi$
$192$	−3.61843	+	7.13491i	−0.261138	+	0.514918i
$193$	6.11644	−	3.53133i	0.440271	−	0.254190i	−0.263442	−	0.964675i	$-0.584858\pi$
$193$	6.11644	−	3.53133i	0.440271	−	0.254190i	0.703712	+	0.710485i	$0.251524\pi$
$194$	−10.9340	−	15.3186i	−0.785012	−	1.09981i
$195$	7.57182	+	6.87459i	0.542229	+	0.492300i
$196$	4.13488	−	12.0332i	0.295348	−	0.859515i
$197$	2.63096	+	4.55696i	0.187448	+	0.324670i	0.944399	−	0.328802i	$-0.106645\pi$
$197$	2.63096	+	4.55696i	0.187448	+	0.324670i	−0.756950	+	0.653472i	$0.773312\pi$
$198$	−0.762975	−	0.347417i	−0.0542223	−	0.0246899i
$199$	−11.5333	+	19.9763i	−0.817577	+	1.41608i	0.0898859	+	0.995952i	$0.471350\pi$
$199$	−11.5333	+	19.9763i	−0.817577	+	1.41608i	−0.907463	+	0.420133i	$0.861984\pi$
$200$	−2.45437	−	8.25713i	−0.173550	−	0.583867i
$201$	−5.87804	−	3.39369i	−0.414605	−	0.239372i
$202$	22.1161	−	2.13658i	1.55609	−	0.150329i
$203$	8.08009			0.567111
$204$	0.251220	−	0.218661i	0.0175889	−	0.0153093i
$205$	−17.8584	+	10.3106i	−1.24729	+	0.720121i
$206$	10.0463	+	4.57455i	0.699961	+	0.318724i
$207$	−6.93438			−0.481973
$208$	−14.2102	+	2.46357i	−0.985303	+	0.170818i
$209$	−2.90476			−0.200926
$210$	−2.91623	−	1.32789i	−0.201239	−	0.0916334i
$211$	10.6725	−	6.16178i	0.734726	−	0.424194i	−0.0854227	−	0.996345i	$-0.527224\pi$
$211$	10.6725	−	6.16178i	0.734726	−	0.424194i	0.820149	+	0.572151i	$0.193891\pi$
$212$	3.86362	−	3.36287i	0.265354	−	0.230963i
$213$	−3.51642			−0.240941
$214$	−22.0517	+	2.13035i	−1.50742	+	0.145628i
$215$	−2.63460	−	1.52109i	−0.179678	−	0.103737i
$216$	−2.71119	+	0.805882i	−0.184473	+	0.0548333i
$217$	1.19139	−	2.06354i	0.0808767	−	0.140083i
$218$	−7.61511	−	3.46751i	−0.515761	−	0.234849i
$219$	1.48642	+	2.57455i	0.100443	+	0.173972i
$220$	−1.09286	+	3.18041i	−0.0736805	+	0.214423i
$221$	0.586778	+	0.127261i	0.0394709	+	0.00856052i
$222$	0.922418	+	1.29232i	0.0619086	+	0.0867348i
$223$	23.4983	−	13.5667i	1.57356	−	0.908496i	0.577833	−	0.816155i	$-0.303898\pi$
$223$	23.4983	−	13.5667i	1.57356	−	0.908496i	0.995727	−	0.0923409i	$-0.0294350\pi$
$224$	4.00489	−	2.09284i	0.267588	−	0.139834i
$225$	1.52279	−	2.63754i	0.101519	−	0.175836i
$226$	−1.33276	+	0.951284i	−0.0886540	+	0.0632785i
$227$	−5.15989	+	8.93719i	−0.342474	+	0.593182i	−0.984891	−	0.173173i	$-0.944598\pi$
$227$	−5.15989	+	8.93719i	−0.342474	+	0.593182i	0.642418	+	0.766355i	$0.277931\pi$
$228$	−7.39217	+	6.43410i	−0.489558	+	0.426109i
$229$	−2.98325			−0.197139			−0.0985694	−	0.995130i	$-0.531427\pi$
$229$	−2.98325			−0.197139			−0.0985694	+	0.995130i	$0.531427\pi$
$230$	2.67482	+	27.6875i	0.176372	+	1.82566i
$231$	0.236768	+	0.410095i	0.0155782	+	0.0269823i
$232$	−20.7716	−	19.6742i	−1.36372	−	1.29167i
$233$	−21.5543			−1.41207			−0.706034	−	0.708178i	$-0.749517\pi$
$233$	−21.5543			−1.41207			−0.706034	+	0.708178i	$0.749517\pi$
$234$	−4.08727	−	3.04864i	−0.267193	−	0.199296i
$235$		−	6.75546i		−	0.440677i
$236$	−21.4854	+	4.19040i	−1.39858	+	0.272772i
$237$	−5.67181	+	3.27462i	−0.368424	+	0.212710i
$238$	−0.187251	+	0.0180898i	−0.0121377	+	0.00117259i
$239$			23.4545i			1.51714i	0.651589	+	0.758572i	$0.274103\pi$
$239$			23.4545i			1.51714i	−0.651589	+	0.758572i	$0.725897\pi$
$240$	4.26351	+	10.5144i	0.275208	+	0.678699i
$241$	−23.2876	−	13.4451i	−1.50008	−	0.866073i	−1.00000		9.58436e-5i	$-0.999969\pi$
$241$	−23.2876	−	13.4451i	−1.50008	−	0.866073i	−0.500083	−	0.865977i	$-0.666697\pi$
$242$	−12.2573	+	8.74889i	−0.787930	+	0.562400i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.12831	+	26.2943i	0.328306	+	1.68332i
$245$	−9.02268	−	15.6277i	−0.576438	−	0.998419i
$246$	8.36830	−	5.97303i	0.533543	−	0.380827i
$247$	−17.2660	−	3.74467i	−1.09861	−	0.238268i
$248$	−8.08723	+	2.40387i	−0.513539	+	0.152646i
$249$	−12.1729	+	7.02805i	−0.771428	+	0.445384i
$250$	7.13507	+	3.24892i	0.451262	+	0.205480i
$251$	25.1888	+	14.5427i	1.58990	+	0.917930i	0.993322	+	0.115376i	$0.0368072\pi$
$251$	25.1888	+	14.5427i	1.58990	+	0.917930i	0.596579	+	0.802554i	$0.296526\pi$
$252$	1.51091	+	0.519182i	0.0951782	+	0.0327054i
$253$	2.05536	−	3.55999i	0.129219	−	0.223814i
$254$	−0.164487	−	1.70264i	−0.0103208	−	0.106833i
$255$		−	0.472348i		−	0.0295795i
$256$	−15.3913	−	4.37139i	−0.961954	−	0.273212i
$257$	−10.4996	−	18.1858i	−0.654944	−	1.13440i	−0.981908	−	0.189360i	$-0.939359\pi$
$257$	−10.4996	−	18.1858i	−0.654944	−	1.13440i	0.326964	−	0.945037i	$-0.393975\pi$
$258$	1.38040	+	0.628561i	0.0859402	+	0.0391325i
$259$		−	0.896830i		−	0.0557263i
$260$	−10.5960	+	17.4956i	−0.657136	+	1.08503i
$261$		−	10.1152i		−	0.626112i
$262$	5.08216	−	11.1611i	0.313977	−	0.689536i
$263$	8.91302	+	15.4378i	0.549601	+	0.951936i	0.998302	+	0.0582544i	$0.0185534\pi$
$263$	8.91302	+	15.4378i	0.549601	+	0.951936i	−0.448701	+	0.893682i	$0.648113\pi$
$264$	0.389875	−	1.63074i	0.0239951	−	0.100365i
$265$		−	7.26442i		−	0.446250i
$266$	5.50987	−	0.532294i	0.337832	−	0.0326370i
$267$	−6.42312	+	11.1252i	−0.393089	+	0.680849i
$268$	4.41141	−	12.8380i	0.269470	−	0.784203i
$269$	−1.69642	−	0.979426i	−0.103432	−	0.0597167i	0.447392	−	0.894338i	$-0.352353\pi$
$269$	−1.69642	−	0.979426i	−0.103432	−	0.0597167i	−0.550824	+	0.834622i	$0.685686\pi$
$270$	−1.66234	+	3.65072i	−0.101167	+	0.222176i
$271$	6.21984	−	3.59102i	0.377828	−	0.218139i	−0.299045	−	0.954239i	$-0.596668\pi$
$271$	6.21984	−	3.59102i	0.377828	−	0.218139i	0.676873	+	0.736100i	$0.263335\pi$
$272$	0.525415	+	0.409433i	0.0318580	+	0.0248255i
$273$	0.878683	+	2.74284i	0.0531803	+	0.166004i
$274$	3.93096	+	5.50732i	0.237478	+	0.332710i
$275$	0.902711	+	1.56354i	0.0544355	+	0.0942851i
$276$	−2.65487	−	13.6123i	−0.159804	−	0.819363i
$277$	18.2247	+	10.5220i	1.09501	+	0.632207i	0.934907	−	0.354893i	$-0.115483\pi$
$277$	18.2247	+	10.5220i	1.09501	+	0.632207i	0.160107	+	0.987100i	$0.448816\pi$
$278$	5.79002	+	8.11190i	0.347263	+	0.486520i
$279$	−2.58327	−	1.49145i	−0.154656	−	0.0892910i
$280$	1.49018	−	6.23300i	0.0890550	−	0.372493i
$281$		−	8.46072i		−	0.504724i	−0.967633	−	0.252362i	$-0.918793\pi$
$281$		−	8.46072i		−	0.504724i	0.967633	−	0.252362i	$-0.0812074\pi$
$282$	0.323880	+	3.35254i	0.0192868	+	0.199641i
$283$	−8.73696	+	5.04429i	−0.519358	+	0.299852i	−0.736672	−	0.676250i	$-0.763604\pi$
$283$	−8.73696	+	5.04429i	−0.519358	+	0.299852i	0.217314	+	0.976102i	$0.430271\pi$
$284$	−1.34628	−	6.90277i	−0.0798871	−	0.409604i
$285$			13.8988i			0.823297i
$286$	2.77659	−	1.19471i	0.164183	−	0.0706446i
$287$	−5.80734			−0.342797
$288$	−2.61995	−	5.01357i	−0.154382	−	0.295427i
$289$	8.48613	+	14.6984i	0.499184	+	0.864613i
$290$	−40.3877	+	3.90174i	−2.37164	+	0.229118i
$291$	13.3081			0.780135
$292$	−4.48479	+	3.90354i	−0.262452	+	0.228437i
$293$	1.52266	−	2.63732i	0.0889545	−	0.154074i	−0.818115	−	0.575055i	$-0.804981\pi$
$293$	1.52266	−	2.63732i	0.0889545	−	0.154074i	0.907069	+	0.420981i	$0.138314\pi$
$294$	5.22695	+	7.32302i	0.304842	+	0.427087i
$295$	−15.5228	+	26.8862i	−0.903770	+	1.56538i
$296$	−2.18369	+	2.30549i	−0.126924	+	0.134004i
$297$	0.513382	−	0.296401i	0.0297894	−	0.0171989i
$298$	9.96686	−	7.11403i	0.577365	−	0.412105i
$299$	16.8065	−	18.5110i	0.971943	−	1.07052i
$300$	5.76054	+	1.97945i	0.332585	+	0.114284i
$301$	−0.428370	−	0.741959i	−0.0246909	−	0.0427658i
$302$	8.02664	−	17.6276i	0.461881	−	1.01435i
$303$	−7.85564	+	13.6064i	−0.451295	+	0.781666i
$304$	−15.4604	−	12.0476i	−0.886713	−	0.690977i
$305$	32.9039	+	18.9971i	1.88407	+	1.08777i
$306$	0.0226460	+	0.234413i	0.00129458	+	0.0134005i
$307$	31.9416			1.82300			0.911502	−	0.411296i	$-0.134924\pi$
$307$	31.9416			1.82300			0.911502	+	0.411296i	$0.134924\pi$
$308$	−0.714373	+	0.621787i	−0.0407052	+	0.0354296i
$309$	−6.75986	+	3.90281i	−0.384555	+	0.222023i
$310$	−4.95860	+	10.8898i	−0.281630	+	0.618497i
$311$	8.48928			0.481383			0.240691	−	0.970602i	$-0.422626\pi$
$311$	8.48928			0.481383			0.240691	+	0.970602i	$0.422626\pi$
$312$	4.41970	−	9.19055i	0.250216	−	0.520313i
$313$	−23.8490			−1.34802			−0.674012	−	0.738720i	$-0.735431\pi$
$313$	−23.8490			−1.34802			−0.674012	+	0.738720i	$0.735431\pi$
$314$	−11.9095	+	26.1549i	−0.672094	+	1.47601i
$315$	1.96224	−	1.13290i	0.110560	−	0.0638318i
$316$	−8.59962	−	9.88014i	−0.483766	−	0.555801i
$317$	0.262717			0.0147556			0.00737782	−	0.999973i	$-0.497652\pi$
$317$	0.262717			0.0147556			0.00737782	+	0.999973i	$0.497652\pi$
$318$	0.348281	+	3.60512i	0.0195306	+	0.202165i
$319$	5.19294	+	2.99814i	0.290749	+	0.167864i
$320$	−19.0075	+	12.3948i	−1.06255	+	0.692891i
$321$	7.83275	−	13.5667i	0.437181	−	0.757220i
$322$	−3.24633	+	7.12938i	−0.180911	+	0.397305i
$323$	0.407994	+	0.706666i	0.0227014	+	0.0393199i
$324$	0.649944	−	1.89145i	0.0361080	−	0.105080i
$325$	3.35010	+	10.4575i	0.185830	+	0.580075i
$326$	10.4485	−	7.45782i	0.578689	−	0.413050i
$327$	5.12397	−	2.95833i	0.283356	−	0.163596i
$328$	14.9290	+	14.1403i	0.824316	+	0.780766i
$329$	0.951240	−	1.64760i	0.0524435	−	0.0908349i
$330$	−1.38150	−	1.93549i	−0.0760488	−	0.106545i
$331$	15.7122	−	27.2144i	0.863622	−	1.49584i	−0.00478625	−	0.999989i	$-0.501524\pi$
$331$	15.7122	−	27.2144i	0.863622	−	1.49584i	0.868409	−	0.495849i	$-0.165143\pi$
$332$	−18.4566	−	21.2049i	−1.01294	−	1.16377i
$333$	−1.12271			−0.0615240
$334$	−27.7713	+	2.68291i	−1.51958	+	0.146802i
$335$	−9.62610	−	16.6729i	−0.525930	−	0.910937i
$336$	−0.440700	+	3.16470i	−0.0240422	+	0.172649i
$337$	28.5717			1.55640			0.778201	−	0.628016i	$-0.216133\pi$
$337$	28.5717			1.55640			0.778201	+	0.628016i	$0.216133\pi$
$338$	18.0443	−	3.52193i	0.981479	−	0.191568i
$339$		−	1.15784i		−	0.0628853i
$340$	0.927224	−	0.180841i	0.0502858	−	0.00980749i
$341$	1.53137	−	0.884137i	0.0829283	−	0.0478787i
$342$	−0.666359	−	6.89760i	−0.0360326	−	0.372980i
$343$		−	10.6736i		−	0.576322i
$344$	−0.705377	+	2.95040i	−0.0380314	+	0.159075i
$345$	−17.0340	−	9.83459i	−0.917080	−	0.529477i
$346$	3.70850	+	5.19566i	0.199370	+	0.279320i
$347$	−13.8663	−	8.00570i	−0.744381	−	0.429769i	0.0792791	−	0.996852i	$-0.474738\pi$
$347$	−13.8663	−	8.00570i	−0.744381	−	0.429769i	−0.823660	+	0.567084i	$0.808072\pi$
$348$	19.8562	−	3.87265i	1.06440	−	0.207596i
$349$	6.12306	+	10.6055i	0.327760	+	0.567697i	0.982067	−	0.188532i	$-0.0603729\pi$
$349$	6.12306	+	10.6055i	0.327760	+	0.567697i	−0.654307	+	0.756229i	$0.727040\pi$
$350$	−1.99882	−	2.80037i	−0.106841	−	0.149686i
$351$	3.43366	−	1.09999i	0.183275	−	0.0587131i
$352$	3.35043	+	0.140991i	0.178579	+	0.00751484i
$353$	17.1340	−	9.89229i	0.911948	−	0.526514i	0.0308909	−	0.999523i	$-0.490166\pi$
$353$	17.1340	−	9.89229i	0.911948	−	0.526514i	0.881058	+	0.473009i	$0.156832\pi$
$354$	6.41448	−	14.0871i	0.340926	−	0.748719i
$355$	−8.63792	−	4.98711i	−0.458453	−	0.264688i
$356$	−24.2980	−	8.34933i	−1.28779	−	0.442514i
$357$	0.0665115	−	0.115201i	0.00352016	−	0.00609710i
$358$	−9.15462	+	0.884403i	−0.483837	+	0.0467422i
$359$		−	24.2509i		−	1.27991i	−0.768411	−	0.639957i	$-0.778952\pi$
$359$		−	24.2509i		−	1.27991i	0.768411	−	0.639957i	$-0.221048\pi$
$360$	−7.80285	−	1.86549i	−0.411246	−	0.0983202i
$361$	−2.50524	−	4.33920i	−0.131855	−	0.228379i
$362$	1.24543	−	2.73512i	0.0654582	−	0.143755i
$363$		−	10.6486i		−	0.558906i
$364$	−5.04783	+	2.77498i	−0.264578	+	0.145449i
$365$			8.43236i			0.441370i
$366$	−17.2401	−	7.85019i	−0.901153	−	0.410336i
$367$	10.3016	+	17.8429i	0.537741	+	0.931394i	0.999025	+	0.0441419i	$0.0140554\pi$
$367$	10.3016	+	17.8429i	0.537741	+	0.931394i	−0.461285	+	0.887252i	$0.652611\pi$
$368$	25.7047	−	10.4231i	1.33995	−	0.543341i
$369$			7.26999i			0.378461i
$370$	0.433065	+	4.48273i	0.0225140	+	0.233046i
$371$	1.02291	−	1.77173i	0.0531067	−	0.0919834i
$372$	1.93872	−	5.64201i	0.100518	−	0.292525i
$373$	−7.00993	−	4.04718i	−0.362960	−	0.209555i	0.307418	−	0.951575i	$-0.400535\pi$
$373$	−7.00993	−	4.04718i	−0.362960	−	0.209555i	−0.670379	+	0.742019i	$0.733868\pi$
$374$	−0.127055	−	0.0578541i	−0.00656988	−	0.00299157i
$375$	−4.80097	+	2.77184i	−0.247921	+	0.143137i
$376$	−6.45708	+	1.91932i	−0.332999	+	0.0989814i
$377$	27.0019	+	24.5155i	1.39067	+	1.26261i
$378$	−0.919490	+	0.656303i	−0.0472935	+	0.0337566i
$379$	16.2127	+	28.0812i	0.832789	+	1.44243i	0.895818	+	0.444422i	$0.146591\pi$
$379$	16.2127	+	28.0812i	0.832789	+	1.44243i	−0.0630282	+	0.998012i	$0.520076\pi$
$380$	−27.2836	+	5.32126i	−1.39962	+	0.272975i
$381$	1.04750	+	0.604776i	0.0536652	+	0.0309836i
$382$	−18.1599	+	12.9620i	−0.929144	+	0.663194i
$383$	10.5766	+	6.10641i	0.540439	+	0.312023i	0.745257	−	0.666777i	$-0.232327\pi$
$383$	10.5766	+	6.10641i	0.540439	+	0.312023i	−0.204818	+	0.978800i	$0.565660\pi$
$384$	8.83863	−	7.06248i	0.451045	−	0.360405i
$385$			1.34317i			0.0684544i
$386$	−9.94181	+	0.960452i	−0.506025	+	0.0488857i
$387$	−0.928831	+	0.536261i	−0.0472151	+	0.0272597i
$388$	5.09509	+	26.1240i	0.258664	+	1.32625i
$389$		−	21.2746i		−	1.07867i	−0.842093	−	0.539333i	$-0.818677\pi$
$389$		−	21.2746i		−	1.07867i	0.842093	−	0.539333i	$-0.181323\pi$
$390$	−5.71650	−	13.2856i	−0.289466	−	0.672741i
$391$	−1.15476			−0.0583986
$392$	−12.3740	+	13.0642i	−0.624982	+	0.659843i
$393$	4.33588	+	7.50996i	0.218716	+	0.378828i
$394$	−0.715571	−	7.40701i	−0.0360499	−	0.373160i
$395$	−18.5768			−0.934698
$396$	0.778391	+	0.894297i	0.0391156	+	0.0449401i
$397$	−2.19056	+	3.79416i	−0.109941	+	0.190423i	−0.915746	−	0.401757i	$-0.868400\pi$
$397$	−2.19056	+	3.79416i	−0.109941	+	0.190423i	0.805805	+	0.592181i	$0.201733\pi$
$398$	26.5515	−	18.9516i	1.33090	−	0.949958i
$399$	−1.95710	+	3.38980i	−0.0979778	+	0.169702i
$400$	−1.68023	+	12.0659i	−0.0840115	+	0.603293i
$401$	17.8119	−	10.2837i	0.889482	−	0.513542i	0.0157087	−	0.999877i	$-0.495000\pi$
$401$	17.8119	−	10.2837i	0.889482	−	0.513542i	0.873773	+	0.486334i	$0.161666\pi$
$402$	5.57651	+	7.81277i	0.278131	+	0.389666i
$403$	10.2423	−	3.28117i	0.510205	−	0.163447i
$404$	−29.7171	−	10.2114i	−1.47848	−	0.508039i
$405$	−1.41824	−	2.45646i	−0.0704727	−	0.122062i
$406$	−10.3996	−	4.73541i	−0.516123	−	0.235014i
$407$	0.332772	−	0.576378i	0.0164949	−	0.0285700i
$408$	−0.451485	+	0.134201i	−0.0223518	+	0.00664392i
$409$	−17.3890	−	10.0395i	−0.859830	−	0.496423i	0.00412536	−	0.999991i	$-0.498687\pi$
$409$	−17.3890	−	10.0395i	−0.859830	−	0.496423i	−0.863955	+	0.503568i	$0.832020\pi$
$410$	29.0275	−	2.80427i	1.43357	−	0.138493i
$411$	−4.78451			−0.236002
$412$	−10.2493	−	11.7755i	−0.504948	−	0.580136i
$413$	−7.57172	+	4.37154i	−0.372580	+	0.215109i
$414$	8.92500	+	4.06396i	0.438640	+	0.199733i
$415$	−39.8697			−1.95713
$416$	19.7333	+	5.15726i	0.967504	+	0.252856i
$417$	−7.04725			−0.345105
$418$	3.73861	+	1.70236i	0.182862	+	0.0832652i
$419$	−13.4526	+	7.76687i	−0.657203	+	0.379436i	−0.791210	−	0.611544i	$-0.790549\pi$
$419$	−13.4526	+	7.76687i	−0.657203	+	0.379436i	0.134008	+	0.990980i	$0.457215\pi$
$420$	2.97516	+	3.41817i	0.145173	+	0.166790i
$421$	14.6028			0.711697			0.355848	−	0.934544i	$-0.384192\pi$
$421$	14.6028			0.711697			0.355848	+	0.934544i	$0.384192\pi$
$422$	−17.3474	+	1.67588i	−0.844457	+	0.0815807i
$423$	−2.06256	−	1.19082i	−0.100285	−	0.0578997i
$424$	−6.94356	+	2.06392i	−0.337209	+	0.100233i
$425$	0.253584	−	0.439221i	0.0123006	−	0.0213053i
$426$	4.52585	+	2.06083i	0.219278	+	0.0998474i
$427$	5.34998	+	9.26644i	0.258904	+	0.448434i
$428$	29.6305	+	10.1817i	1.43224	+	0.492151i
$429$	−0.453026	+	2.08882i	−0.0218723	+	0.100849i
$430$	2.49945	+	3.50177i	0.120534	+	0.168870i
$431$	10.8188	−	6.24624i	0.521123	−	0.300871i	−0.216271	−	0.976333i	$-0.569389\pi$
$431$	10.8188	−	6.24624i	0.521123	−	0.300871i	0.737394	+	0.675463i	$0.236056\pi$
$432$	3.96177	+	0.551696i	0.190611	+	0.0265435i
$433$	15.1594	−	26.2568i	0.728513	−	1.26182i	−0.228999	−	0.973427i	$-0.573545\pi$
$433$	15.1594	−	26.2568i	0.728513	−	1.26182i	0.957512	−	0.288395i	$-0.0931215\pi$
$434$	−2.74275	+	1.95769i	−0.131656	+	0.0939722i
$435$	14.3457	−	24.8474i	0.687822	−	1.19134i
$436$	7.76898	+	8.92581i	0.372067	+	0.427469i
$437$	33.9788			1.62543
$438$	−0.404276	−	4.18474i	−0.0193171	−	0.199955i
$439$	−10.6810	−	18.5000i	−0.509774	−	0.882955i	−0.999936	−	0.0113236i	$-0.996396\pi$
$439$	−10.6810	−	18.5000i	−0.509774	−	0.882955i	0.490161	−	0.871632i	$-0.336938\pi$
$440$	3.27049	−	3.45291i	0.155914	−	0.164611i
$441$	−6.36190			−0.302948
$442$	−0.680638	−	0.507680i	−0.0323747	−	0.0241479i
$443$			0.675587i			0.0320981i	0.999871	+	0.0160491i	$0.00510880\pi$
$443$			0.675587i			0.0320981i	−0.999871	+	0.0160491i	$0.994891\pi$
$444$	−0.429835	−	2.20389i	−0.0203991	−	0.104592i
$445$	−31.5562	+	18.2190i	−1.49591	+	0.863663i
$446$	−38.1947	+	3.68989i	−1.80857	+	0.174721i
$447$			8.65875i			0.409545i
$448$	−6.38108	+	0.346525i	−0.301478	+	0.0163718i
$449$	−5.72392	−	3.30471i	−0.270129	−	0.155959i	0.358817	−	0.933408i	$-0.383180\pi$
$449$	−5.72392	−	3.30471i	−0.270129	−	0.155959i	−0.628946	+	0.777449i	$0.716513\pi$
$450$	−3.50568	+	2.50224i	−0.165259	+	0.117957i
$451$	−3.73228	−	2.15483i	−0.175746	−	0.101467i
$452$	2.27286	−	0.443287i	0.106906	−	0.0208504i
$453$	6.84798	+	11.8610i	0.321746	+	0.557281i
$454$	11.8788	−	8.47874i	0.557501	−	0.397927i
$455$	−1.73155	+	7.98385i	−0.0811764	+	0.374289i
$456$	13.2850	−	3.94886i	0.622125	−	0.184922i
$457$	−3.39098	+	1.95778i	−0.158623	+	0.0915812i	−0.577210	−	0.816595i	$-0.695859\pi$
$457$	−3.39098	+	1.95778i	−0.158623	+	0.0915812i	0.418587	+	0.908177i	$0.362525\pi$
$458$	3.83964	+	1.74836i	0.179414	+	0.0816956i
$459$	−0.144216	−	0.0832632i	−0.00673143	−	0.00388639i
$460$	12.7839	−	37.2032i	0.596051	−	1.73461i
$461$	−11.2282	+	19.4479i	−0.522951	+	0.905777i	0.476693	+	0.879070i	$0.341835\pi$
$461$	−11.2282	+	19.4479i	−0.522951	+	0.905777i	−0.999643	+	0.0267070i	$0.991498\pi$
$462$	−0.0643964	−	0.666579i	−0.00299599	−	0.0310120i
$463$		−	11.1931i		−	0.520189i	−0.965583	−	0.260095i	$-0.916246\pi$
$463$		−	11.1931i		−	0.520189i	0.965583	−	0.260095i	$-0.0837538\pi$
$464$	15.2041	+	37.4953i	0.705833	+	1.74067i
$465$	−4.23046	−	7.32738i	−0.196183	−	0.339799i
$466$	27.7417	+	12.6321i	1.28511	+	0.585169i
$467$			16.1230i			0.746083i	0.927815	+	0.373041i	$0.121685\pi$
$467$			16.1230i			0.746083i	−0.927815	+	0.373041i	$0.878315\pi$
$468$	3.47389	+	6.31918i	0.160581	+	0.292104i
$469$		−	5.42182i		−	0.250357i
$470$	−3.95910	+	8.69471i	−0.182620	+	0.401057i
$471$	−10.1607	−	17.5988i	−0.468180	−	0.810912i
$472$	30.1089	+	7.19840i	1.38588	+	0.331333i
$473$		−	0.635793i		−	0.0292338i
$474$	9.21911	−	0.890634i	0.423448	−	0.0409082i
$475$	−7.46172	+	12.9241i	−0.342367	+	0.592998i
$476$	0.251606	+	0.0864575i	0.0115323	+	0.00396277i
$477$	−2.21796	−	1.28054i	−0.101553	−	0.0586318i
$478$	13.7457	−	30.1874i	0.628714	−	1.38074i
$479$	15.7769	−	9.10881i	0.720866	−	0.416192i	−0.0942053	−	0.995553i	$-0.530031\pi$
$479$	15.7769	−	9.10881i	0.720866	−	0.416192i	0.815071	+	0.579361i	$0.196698\pi$
$480$	0.674621	−	16.0313i	0.0307921	−	0.731726i
$481$	2.72104	−	2.99701i	0.124069	−	0.136652i
$482$	22.0930	+	30.9526i	1.00631	+	1.40985i
$483$	−2.76963	−	4.79714i	−0.126022	−	0.218277i
$484$	20.9033	−	4.07688i	0.950151	−	0.185313i
$485$	32.6908	+	18.8740i	1.48441	+	0.857026i
$486$	0.821601	+	1.15107i	0.0372686	+	0.0522138i
$487$	1.63767	+	0.945507i	0.0742097	+	0.0428450i	0.536646	−	0.843808i	$-0.319691\pi$
$487$	1.63767	+	0.945507i	0.0742097	+	0.0428450i	−0.462436	+	0.886653i	$0.653025\pi$
$488$	8.80956	−	36.8480i	0.398790	−	1.66803i
$489$			9.07718i			0.410484i
$490$	2.45399	+	25.4017i	0.110860	+	1.14753i
$491$	17.8621	−	10.3127i	0.806106	−	0.465406i	−0.0394956	−	0.999220i	$-0.512575\pi$
$491$	17.8621	−	10.3127i	0.806106	−	0.465406i	0.845602	+	0.533814i	$0.179242\pi$
$492$	−14.2711	+	2.78336i	−0.643390	+	0.125484i
$493$		−	1.68444i		−	0.0758634i
$494$	20.0278	+	14.9385i	0.901094	+	0.672115i
$495$	1.68147			0.0755763
$496$	11.8176	+	1.64566i	0.530626	+	0.0738922i
$497$	−1.40447	−	2.43262i	−0.0629993	−	0.109118i
$498$	19.7862	−	1.91149i	0.886641	−	0.0856560i
$499$	−24.6797			−1.10481			−0.552407	−	0.833575i	$-0.686291\pi$
$499$	−24.6797			−1.10481			−0.552407	+	0.833575i	$0.686291\pi$
$500$	−7.27924	−	8.36315i	−0.325537	−	0.374011i
$501$	9.86436	−	17.0856i	0.440707	−	0.763327i
$502$	−23.8967	−	33.4796i	−1.06656	−	1.49427i
$503$	4.27176	−	7.39890i	0.190468	−	0.329901i	−0.754937	−	0.655797i	$-0.772333\pi$
$503$	4.27176	−	7.39890i	0.190468	−	0.329901i	0.945405	+	0.325896i	$0.105666\pi$
$504$	−1.64036	−	1.55370i	−0.0730676	−	0.0692073i
$505$	−38.5941	+	22.2823i	−1.71741	+	0.991550i
$506$	−4.73174	+	3.37737i	−0.210352	+	0.150142i
$507$	−5.38560	+	11.8320i	−0.239183	+	0.525476i
$508$	−0.786141	+	2.28780i	−0.0348793	+	0.101505i
$509$	−13.2450	−	22.9411i	−0.587076	−	1.01685i	−0.994613	−	0.103657i	$-0.966946\pi$
$509$	−13.2450	−	22.9411i	−0.587076	−	1.01685i	0.407537	−	0.913189i	$-0.366388\pi$
$510$	−0.276824	+	0.607942i	−0.0122580	+	0.0269201i
$511$	−1.18736	+	2.05658i	−0.0525259	+	0.0909776i
$512$	17.2477	+	14.6464i	0.762246	+	0.647287i
$513$	4.24357	+	2.45002i	0.187358	+	0.108171i
$514$	2.85567	+	29.5596i	0.125958	+	1.30382i
$515$	−22.1404			−0.975623
$516$	−1.40830	−	1.61800i	−0.0619967	−	0.0712283i
$517$	1.22269	−	0.705921i	0.0537739	−	0.0310464i
$518$	−0.525595	+	1.15428i	−0.0230933	+	0.0507161i
$519$	−4.51375			−0.198131
$520$	23.8912	−	16.3080i	1.04770	−	0.715154i
$521$	−12.0965			−0.529958			−0.264979	−	0.964254i	$-0.585365\pi$
$521$	−12.0965			−0.529958			−0.264979	+	0.964254i	$0.585365\pi$
$522$	−5.92808	+	13.0189i	−0.259465	+	0.569820i
$523$	−31.0173	+	17.9079i	−1.35629	+	0.783057i	−0.989122	−	0.147097i	$-0.953007\pi$
$523$	−31.0173	+	17.9079i	−1.35629	+	0.783057i	−0.367172	+	0.930153i	$0.619674\pi$
$524$	−13.0821	+	11.3866i	−0.571496	+	0.497427i
$525$	2.43283			0.106178
$526$	−2.42417	−	25.0930i	−0.105699	−	1.09411i
$527$	−0.430183	−	0.248366i	−0.0187391	−	0.0108190i
$528$	−1.45750	+	1.87038i	−0.0634297	+	0.0813978i
$529$	−12.5428	+	21.7248i	−0.545341	+	0.944558i
$530$	−4.25738	+	9.34977i	−0.184929	+	0.406128i
$531$	5.47256	+	9.47875i	0.237489	+	0.411343i
$532$	−7.40352	−	2.54401i	−0.320983	−	0.110297i
$533$	−19.4069	−	17.6199i	−0.840605	−	0.763201i
$534$	14.7870	−	10.5545i	0.639895	−	0.456737i
$535$	38.4816	−	22.2174i	1.66371	−	0.960541i
$536$	−13.2016	+	13.9379i	−0.570221	+	0.602027i
$537$	3.25171	−	5.63214i	0.140322	−	0.243045i
$538$	1.60940	+	2.25478i	0.0693860	+	0.0972107i
$539$	1.88568	−	3.26609i	0.0812218	−	0.140680i
$540$	4.27908	−	3.72449i	0.184142	−	0.160276i
$541$	−14.5464			−0.625398			−0.312699	−	0.949852i	$-0.601233\pi$
$541$	−14.5464			−0.625398			−0.312699	+	0.949852i	$0.601233\pi$
$542$	−10.1099	+	0.976688i	−0.434257	+	0.0419524i
$543$	1.06254	+	1.84038i	0.0455981	+	0.0789783i
$544$	−0.436291	−	0.834891i	−0.0187058	−	0.0357957i
$545$	16.7824			0.718880
$546$	0.476546	−	4.04518i	0.0203943	−	0.173118i
$547$			19.0401i			0.814094i	0.913407	+	0.407047i	$0.133441\pi$
$547$			19.0401i			0.814094i	−0.913407	+	0.407047i	$0.866559\pi$
$548$	−1.83178	−	9.39205i	−0.0782497	−	0.401209i
$549$	11.6003	−	6.69744i	0.495089	−	0.285840i
$550$	−0.245520	−	2.54142i	−0.0104690	−	0.108367i
$551$			49.5647i			2.11153i
$552$	−4.56061	+	19.0758i	−0.194113	+	0.811920i
$553$	−4.53070	−	2.61580i	−0.192665	−	0.111235i
$554$	−17.2898	−	24.2232i	−0.734573	−	1.02915i
$555$	−2.75788	−	1.59226i	−0.117066	−	0.0675879i
$556$	−2.69808	−	13.8338i	−0.114424	−	0.586685i
$557$	−10.8055	−	18.7157i	−0.457843	−	0.793008i	0.541004	−	0.841020i	$-0.318045\pi$
$557$	−10.8055	−	18.7157i	−0.457843	−	0.793008i	−0.998847	+	0.0480126i	$0.984711\pi$
$558$	2.45076	+	3.43355i	0.103749	+	0.145354i
$559$	0.819632	−	3.77917i	0.0346668	−	0.159842i
$560$	−5.57086	+	7.14894i	−0.235412	+	0.302098i
$561$	0.0854917	−	0.0493586i	0.00360946	−	0.00208392i
$562$	−4.95848	+	10.8895i	−0.209161	+	0.459346i
$563$	−16.6780	−	9.62908i	−0.702896	−	0.405817i	0.105529	−	0.994416i	$-0.466346\pi$
$563$	−16.6780	−	9.62908i	−0.702896	−	0.405817i	−0.808425	+	0.588599i	$0.799680\pi$
$564$	1.54793	−	4.50475i	0.0651797	−	0.189684i
$565$	1.64209	−	2.84419i	0.0690833	−	0.119656i
$566$	14.2013	−	1.37195i	0.596924	−	0.0576672i
$567$		−	0.798810i		−	0.0335469i
$568$	−2.31268	+	9.67331i	−0.0970379	+	0.405883i
$569$	1.84337	+	3.19281i	0.0772781	+	0.133850i	0.902075	−	0.431580i	$-0.142044\pi$
$569$	1.84337	+	3.19281i	0.0772781	+	0.133850i	−0.824797	+	0.565430i	$0.808710\pi$
$570$	8.14555	−	17.8887i	0.341179	−	0.749276i
$571$			17.9486i			0.751124i	0.926797	+	0.375562i	$0.122550\pi$
$571$			17.9486i			0.751124i	−0.926797	+	0.375562i	$0.877450\pi$
$572$	−4.27382	−	0.0895799i	−0.178697	−	0.00374552i
$573$		−	15.7765i		−	0.659074i
$574$	7.47442	+	3.40345i	0.311976	+	0.142057i
$575$	−10.5596	−	18.2897i	−0.440365	−	0.762735i
$576$	0.433802	+	7.98823i	0.0180751	+	0.332843i
$577$			13.2639i			0.552182i	0.961132	+	0.276091i	$0.0890391\pi$
$577$			13.2639i			0.552182i	−0.961132	+	0.276091i	$0.910961\pi$
$578$	−2.30806	−	23.8912i	−0.0960028	−	0.993742i
$579$	3.53133	−	6.11644i	0.146757	−	0.254190i
$580$	54.2682	+	18.6478i	2.25336	+	0.774306i
$581$	−9.72386	−	5.61407i	−0.403414	−	0.232911i
$582$	−17.1284	−	7.79934i	−0.709995	−	0.323293i
$583$	1.31481	−	0.759106i	0.0544538	−	0.0314389i
$584$	8.05992	−	2.39575i	0.333522	−	0.0991369i
$585$	9.99468	+	2.16766i	0.413229	+	0.0896218i
$586$	−3.50538	+	2.50203i	−0.144806	+	0.103358i
$587$	−18.4456	−	31.9486i	−0.761330	−	1.31866i	−0.942165	−	0.335148i	$-0.891214\pi$
$587$	−18.4456	−	31.9486i	−0.761330	−	1.31866i	0.180836	−	0.983513i	$-0.442120\pi$
$588$	−2.43569	−	12.4885i	−0.100446	−	0.515017i
$589$	12.6582	+	7.30819i	0.521570	+	0.301129i
$590$	35.7357	−	25.5070i	1.47122	−	1.05011i
$591$	4.55696	+	2.63096i	0.187448	+	0.108223i
$592$	4.16170	−	1.68755i	0.171045	−	0.0693577i
$593$			27.8239i			1.14259i	0.820745	+	0.571295i	$0.193559\pi$
$593$			27.8239i			1.14259i	−0.820745	+	0.571295i	$0.806441\pi$
$594$	−0.834464	+	0.0806153i	−0.0342385	+	0.00330769i
$595$	0.326765	−	0.188658i	0.0133961	−	0.00773422i
$596$	−16.9972	+	3.31505i	−0.696234	+	0.135790i
$597$			23.0667i			0.944056i
$598$	−32.4795	+	13.9753i	−1.32819	+	0.571491i
$599$	31.0169			1.26732			0.633658	−	0.773613i	$-0.281553\pi$
$599$	31.0169			1.26732			0.633658	+	0.773613i	$0.281553\pi$
$600$	−6.25411	−	5.92369i	−0.255323	−	0.241834i
$601$	18.1543	+	31.4441i	0.740528	+	1.28263i	0.952255	+	0.305303i	$0.0987577\pi$
$601$	18.1543	+	31.4441i	0.740528	+	1.28263i	−0.211728	+	0.977329i	$0.567909\pi$
$602$	0.116508	+	1.20600i	0.00474853	+	0.0491529i
$603$	−6.78737			−0.276403
$604$	−20.6616	+	17.9838i	−0.840709	+	0.731748i
$605$	15.1022	−	26.1578i	0.613992	−	1.06347i
$606$	18.0849	−	12.9084i	0.734647	−	0.524368i
$607$	15.7207	−	27.2290i	0.638082	−	1.10519i	−0.347771	−	0.937580i	$-0.613061\pi$
$607$	15.7207	−	27.2290i	0.638082	−	1.10519i	0.985853	−	0.167612i	$-0.0536054\pi$
$608$	12.8379	+	24.5667i	0.520645	+	0.996312i
$609$	6.99756	−	4.04004i	0.283555	−	0.163711i
$610$	−31.2161	−	43.7341i	−1.26390	−	1.77074i
$611$	8.17775	−	2.61978i	0.330836	−	0.105985i
$612$	0.108233	−	0.314976i	0.00437505	−	0.0127321i
$613$	−21.8144	−	37.7837i	−0.881077	−	1.52607i	−0.850145	−	0.526549i	$-0.823486\pi$
$613$	−21.8144	−	37.7837i	−0.881077	−	1.52607i	−0.0309319	−	0.999521i	$-0.509848\pi$
$614$	−41.1109	−	18.7197i	−1.65910	−	0.755464i
$615$	−10.3106	+	17.8584i	−0.415762	+	0.720121i
$616$	1.28385	−	0.381615i	0.0517277	−	0.0153757i
$617$	−2.64284	−	1.52584i	−0.106397	−	0.0614281i	0.445857	−	0.895104i	$-0.352899\pi$
$617$	−2.64284	−	1.52584i	−0.106397	−	0.0614281i	−0.552254	+	0.833676i	$0.686232\pi$
$618$	10.9877	−	1.06149i	0.441988	−	0.0426993i
$619$	−22.2751			−0.895311			−0.447655	−	0.894206i	$-0.647741\pi$
$619$	−22.2751			−0.895311			−0.447655	+	0.894206i	$0.647741\pi$
$620$	12.7641	−	11.1098i	0.512618	−	0.446180i
$621$	−6.00535	+	3.46719i	−0.240986	+	0.139134i
$622$	−10.9262	−	4.97522i	−0.438103	−	0.199488i
$623$	−10.2617			−0.411127
$624$	−11.0746	+	9.23863i	−0.443340	+	0.369841i
$625$	−30.9524			−1.23809
$626$	30.6952	+	13.9769i	1.22683	+	0.558630i
$627$	−2.51560	+	1.45238i	−0.100463	+	0.0580025i
$628$	30.6567	−	26.6834i	1.22333	−	1.06478i
$629$	−0.186960			−0.00745460
$630$	−3.18948	+	0.308127i	−0.127072	+	0.0122761i
$631$	15.1490	+	8.74629i	0.603073	+	0.348184i	0.770250	−	0.637743i	$-0.220132\pi$
$631$	15.1490	+	8.74629i	0.603073	+	0.348184i	−0.167177	+	0.985927i	$0.553465\pi$
$632$	5.27792	+	17.7563i	0.209944	+	0.706306i
$633$	6.16178	−	10.6725i	0.244909	−	0.424194i
$634$	−0.338133	−	0.153967i	−0.0134290	−	0.00611483i
$635$	1.71543	+	2.97121i	0.0680748	+	0.117909i
$636$	1.66455	−	4.84414i	0.0660039	−	0.192083i
$637$	15.4190	−	16.9828i	0.610922	−	0.672882i
$638$	−4.92655	−	6.90217i	−0.195044	−	0.273260i
$639$	−3.04531	+	1.75821i	−0.120470	+	0.0695536i
$640$	31.7280	−	4.81340i	1.25416	−	0.190266i
$641$	6.95443	−	12.0454i	0.274683	−	0.475766i	−0.695372	−	0.718650i	$-0.744760\pi$
$641$	6.95443	−	12.0454i	0.274683	−	0.475766i	0.970055	+	0.242885i	$0.0780936\pi$
$642$	−18.0322	+	12.8708i	−0.711672	+	0.507970i
$643$	8.46678	−	14.6649i	0.333897	−	0.578327i	−0.649375	−	0.760468i	$-0.724970\pi$
$643$	8.46678	−	14.6649i	0.333897	−	0.578327i	0.983272	+	0.182141i	$0.0583029\pi$
$644$	8.35647	−	7.27343i	0.329291	−	0.286613i
$645$	−3.04218			−0.119786
$646$	−0.110966	−	1.14863i	−0.00436591	−	0.0451924i
$647$	−12.3705	−	21.4264i	−0.486335	−	0.842358i	0.513541	−	0.858065i	$-0.328333\pi$
$647$	−12.3705	−	21.4264i	−0.486335	−	0.842358i	−0.999877	+	0.0157072i	$0.995000\pi$
$648$	−1.94502	+	2.05351i	−0.0764076	+	0.0806695i
$649$	−6.48829			−0.254688
$650$	1.81690	−	15.4228i	0.0712645	−	0.604931i
$651$		−	2.38278i		−	0.0933884i
$652$	−17.8186	+	3.47525i	−0.697831	+	0.136101i
$653$	14.4460	−	8.34043i	0.565317	−	0.326386i	−0.189960	−	0.981792i	$-0.560836\pi$
$653$	14.4460	−	8.34043i	0.565317	−	0.326386i	0.755277	+	0.655406i	$0.227502\pi$
$654$	−8.32864	+	0.804607i	−0.325675	+	0.0314626i
$655$			24.5972i			0.961092i
$656$	−10.9275	−	26.9487i	−0.426649	−	1.05217i
$657$	2.57455	+	1.48642i	0.100443	+	0.0579906i
$658$	−2.18989	+	1.56308i	−0.0853710	+	0.0609352i
$659$	−2.44389	−	1.41098i	−0.0952006	−	0.0549641i	0.451644	−	0.892198i	$-0.350838\pi$
$659$	−2.44389	−	1.41098i	−0.0952006	−	0.0549641i	−0.546844	+	0.837234i	$0.684171\pi$
$660$	0.643760	+	3.30074i	0.0250583	+	0.128481i
$661$	6.31822	+	10.9435i	0.245750	+	0.425652i	0.962342	−	0.271841i	$-0.0876324\pi$
$661$	6.31822	+	10.9435i	0.245750	+	0.425652i	−0.716592	+	0.697492i	$0.754299\pi$
$662$	−36.1719	+	25.8184i	−1.40586	+	1.00346i
$663$	0.571795	−	0.183177i	0.0222067	−	0.00711402i
$664$	11.3275	+	38.1087i	0.439594	+	1.47891i
$665$	−9.61508	+	5.55127i	−0.372857	+	0.215269i
$666$	1.44500	+	0.657973i	0.0559925	+	0.0254959i
$667$	−60.7451	−	35.0712i	−2.35206	−	1.35796i
$668$	37.3158	+	12.8226i	1.44379	+	0.496120i
$669$	13.5667	−	23.4983i	0.524520	−	0.908496i
$670$	2.61811	+	27.1005i	0.101146	+	1.04699i
$671$			7.94051i			0.306540i
$672$	2.42191	−	3.81490i	0.0934273	−	0.147163i
$673$	23.4353	+	40.5912i	0.903365	+	1.56467i	0.823097	+	0.567901i	$0.192244\pi$
$673$	23.4353	+	40.5912i	0.903365	+	1.56467i	0.0802681	+	0.996773i	$0.474422\pi$
$674$	−36.7737	−	16.7447i	−1.41647	−	0.644982i
$675$		−	3.04557i		−	0.117224i
$676$	−25.2882	−	6.04206i	−0.972623	−	0.232387i
$677$			40.9956i			1.57559i	0.615938	+	0.787795i	$0.288777\pi$
$677$			40.9956i			1.57559i	−0.615938	+	0.787795i	$0.711223\pi$
$678$	−0.678563	+	1.49022i	−0.0260601	+	0.0572314i
$679$	5.31533	+	9.20642i	0.203984	+	0.353310i
$680$	−1.29938	−	0.310654i	−0.0498290	−	0.0119130i
$681$			10.3198i			0.395455i
$682$	−2.48913	+	0.240468i	−0.0953137	+	0.00920800i
$683$	0.260068	−	0.450451i	0.00995123	−	0.0172360i	−0.861007	−	0.508593i	$-0.830166\pi$
$683$	0.260068	−	0.450451i	0.00995123	−	0.0172360i	0.870958	+	0.491357i	$0.163499\pi$
$684$	−3.18476	+	9.26818i	−0.121772	+	0.354378i
$685$	−11.7529	−	6.78556i	−0.449057	−	0.259263i
$686$	−6.25537	+	13.7376i	−0.238831	+	0.524506i
$687$	−2.58357	+	1.49163i	−0.0985694	+	0.0569091i
$688$	2.63697	−	3.38396i	0.100534	−	0.129012i
$689$	8.79386	−	2.81716i	0.335019	−	0.107325i
$690$	16.1602	+	22.6407i	0.615209	+	0.861916i
$691$	14.3980	+	24.9381i	0.547727	+	0.948691i	0.998430	+	0.0560166i	$0.0178400\pi$
$691$	14.3980	+	24.9381i	0.547727	+	0.948691i	−0.450703	+	0.892674i	$0.648827\pi$
$692$	−1.72812	−	8.86055i	−0.0656931	−	0.336827i
$693$	0.410095	+	0.236768i	0.0155782	+	0.00899408i
$694$	13.1550	+	18.4303i	0.499356	+	0.699605i
$695$	−17.3113	−	9.99466i	−0.656653	−	0.379119i
$696$	−27.8258	−	6.65255i	−1.05473	−	0.252164i
$697$			1.21065i			0.0458565i
$698$	−1.66535	−	17.2384i	−0.0630345	−	0.652482i
$699$	−18.6665	+	10.7771i	−0.706034	+	0.407629i
$700$	0.931425	+	4.77569i	0.0352046	+	0.180504i
$701$			31.8042i			1.20123i	0.799539	+	0.600614i	$0.205077\pi$
$701$			31.8042i			1.20123i	−0.799539	+	0.600614i	$0.794923\pi$
$702$	−5.06400	−	0.596570i	−0.191128	−	0.0225161i
$703$	5.50132			0.207486
$704$	−4.22959	−	2.14501i	−0.159409	−	0.0808433i
$705$	−3.37773	−	5.85040i	−0.127213	−	0.220339i
$706$	−27.8500	+	2.69051i	−1.04815	+	0.101259i
$707$	−12.5503			−0.472004
$708$	−16.5117	+	14.3717i	−0.620548	+	0.540122i
$709$	0.0624691	−	0.108200i	0.00234608	−	0.00406352i	−0.864850	−	0.502030i	$-0.832587\pi$
$709$	0.0624691	−	0.108200i	0.00234608	−	0.00406352i	0.867196	+	0.497967i	$0.165920\pi$
$710$	8.19483	+	11.4811i	0.307546	+	0.430877i
$711$	−3.27462	+	5.67181i	−0.122808	+	0.212710i
$712$	26.3799	+	24.9862i	0.988628	+	0.936397i
$713$	−17.9134	+	10.3423i	−0.670862	+	0.387322i
$714$	−0.153119	+	0.109292i	−0.00573035	+	0.00409014i
$715$	−4.07527	+	4.48859i	−0.152407	+	0.167864i
$716$	12.3009	+	4.22686i	0.459706	+	0.157965i
$717$	11.7272	+	20.3122i	0.437962	+	0.758572i
$718$	−14.2125	+	31.2125i	−0.530404	+	1.16484i
$719$	−4.28487	+	7.42161i	−0.159799	+	0.276779i	−0.934796	−	0.355185i	$-0.884418\pi$
$719$	−4.28487	+	7.42161i	−0.159799	+	0.276779i	0.774997	+	0.631965i	$0.217751\pi$
$720$	8.94948	+	6.97394i	0.333528	+	0.259904i
$721$	−5.39985	−	3.11760i	−0.201101	−	0.116106i
$722$	0.681375	+	7.05304i	0.0253582	+	0.262487i
$723$	−26.8901			−1.00006
$724$	−3.20589	+	2.79039i	−0.119146	+	0.103704i
$725$	26.6791	−	15.4032i	0.990838	−	0.572061i
$726$	−6.24070	+	13.7054i	−0.231614	+	0.508656i
$727$	−26.0065			−0.964526			−0.482263	−	0.876026i	$-0.660185\pi$
$727$	−26.0065			−0.964526			−0.482263	+	0.876026i	$0.660185\pi$
$728$	8.12318	−	0.613254i	0.301065	−	0.0227287i
$729$	−1.00000			−0.0370370
$730$	4.94186	−	10.8530i	0.182906	−	0.401687i
$731$	−0.154675	+	0.0893016i	−0.00572086	+	0.00330294i
$732$	17.5884	+	20.2074i	0.650086	+	0.746887i
$733$	5.53151			0.204311			0.102155	−	0.994768i	$-0.467426\pi$
$733$	5.53151			0.204311			0.102155	+	0.994768i	$0.467426\pi$
$734$	−2.80184	−	29.0024i	−0.103418	−	1.07050i
$735$	−15.6277	−	9.02268i	−0.576438	−	0.332806i
$736$	−39.1921	−	1.64926i	−1.44464	−	0.0607925i
$737$	2.01179	−	3.48451i	0.0741051	−	0.128354i
$738$	4.26064	−	9.35695i	0.156836	−	0.344434i
$739$	11.3146	+	19.5975i	0.416215	+	0.720906i	0.995555	−	0.0941803i	$-0.0300230\pi$
$739$	11.3146	+	19.5975i	0.416215	+	0.720906i	−0.579340	+	0.815086i	$0.696690\pi$
$740$	2.06976	−	6.02337i	0.0760860	−	0.221423i
$741$	−16.8251	+	5.39000i	−0.618086	+	0.198007i
$742$	−2.35488	+	1.68084i	−0.0864505	+	0.0617056i
$743$	−36.8032	+	21.2483i	−1.35018	+	0.779526i	−0.988274	−	0.152689i	$-0.951207\pi$
$743$	−36.8032	+	21.2483i	−1.35018	+	0.779526i	−0.361904	+	0.932215i	$0.617873\pi$
$744$	−5.80181	+	6.12543i	−0.212705	+	0.224569i
$745$	−12.2801	+	21.2698i	−0.449910	+	0.779266i
$746$	6.65034	+	9.31722i	0.243486	+	0.341128i
$747$	−7.02805	+	12.1729i	−0.257143	+	0.445384i
$748$	0.129623	+	0.148924i	0.00473947	+	0.00544520i
$749$	12.5138			0.457243
$750$	7.80362	−	0.753886i	0.284948	−	0.0275280i
$751$	−20.3828	−	35.3040i	−0.743777	−	1.28826i	−0.950764	−	0.309916i	$-0.899699\pi$
$751$	−20.3828	−	35.3040i	−0.743777	−	1.28826i	0.206987	−	0.978344i	$-0.433634\pi$
$752$	9.43552	+	1.31394i	0.344078	+	0.0479145i
$753$	29.0855			1.05993
$754$	−20.3856	−	47.3777i	−0.742401	−	1.72540i
$755$			38.8482i			1.41383i
$756$	1.56808	−	0.305829i	0.0570303	−	0.0111229i
$757$	17.0025	−	9.81641i	0.617967	−	0.356783i	−0.158110	−	0.987421i	$-0.550540\pi$
$757$	17.0025	−	9.81641i	0.617967	−	0.356783i	0.776077	+	0.630638i	$0.217207\pi$
$758$	−4.40953	−	45.6439i	−0.160161	−	1.65786i
$759$		−	4.11072i		−	0.149210i
$760$	38.2344	+	9.14101i	1.38691	+	0.331579i
$761$	−38.0835	−	21.9875i	−1.38053	−	0.797047i	−0.388304	−	0.921531i	$-0.626939\pi$
$761$	−38.0835	−	21.9875i	−1.38053	−	0.797047i	−0.992222	+	0.124484i	$0.960272\pi$
$762$	−0.993769	−	1.39228i	−0.0360005	−	0.0504371i
$763$	4.09308	+	2.36314i	0.148180	+	0.0855515i
$764$	30.9695	−	6.04014i	1.12044	−	0.218524i
$765$	−0.236174	−	0.409065i	−0.00853888	−	0.0147898i
$766$	−10.0341	−	14.0579i	−0.362545	−	0.507931i
$767$	−38.5666	−	8.36438i	−1.39256	−	0.302020i
$768$	−15.5149	+	3.90990i	−0.559846	+	0.141086i
$769$	13.2959	−	7.67640i	0.479463	−	0.276818i	−0.240730	−	0.970592i	$-0.577387\pi$
$769$	13.2959	−	7.67640i	0.479463	−	0.276818i	0.720193	+	0.693774i	$0.244053\pi$
$770$	0.787179	−	1.72875i	0.0283680	−	0.0622998i
$771$	−18.1858	−	10.4996i	−0.654944	−	0.378132i
$772$	13.3586	+	4.59033i	0.480788	+	0.165209i
$773$	−26.0560	+	45.1303i	−0.937169	+	1.62322i	−0.166450	+	0.986050i	$0.553230\pi$
$773$	−26.0560	+	45.1303i	−0.937169	+	1.62322i	−0.770719	+	0.637175i	$0.780103\pi$
$774$	1.50975	−	0.145852i	0.0542667	−	0.00524256i
$775$		−	9.08465i		−	0.326330i
$776$	8.75250	−	36.6093i	0.314196	−	1.31420i
$777$	−0.448415	−	0.776678i	−0.0160868	−	0.0278632i
$778$	−12.4682	+	27.3818i	−0.447006	+	0.981685i
$779$		−	35.6233i		−	1.27634i
$780$	−0.428627	+	20.4496i	−0.0153473	+	0.732213i
$781$		−	2.08454i		−	0.0745907i
$782$	1.48625	+	0.676756i	0.0531481	+	0.0242008i
$783$	−5.05758	−	8.75998i	−0.180743	−	0.313056i
$784$	23.5826	−	9.56259i	0.842235	−	0.341521i
$785$		−	57.6411i		−	2.05730i
$786$	−1.17927	−	12.2069i	−0.0420633	−	0.435405i
$787$	9.95043	−	17.2346i	0.354694	−	0.614349i	−0.632371	−	0.774666i	$-0.717918\pi$
$787$	9.95043	−	17.2346i	0.354694	−	0.614349i	0.987066	+	0.160317i	$0.0512516\pi$
$788$	−3.41996	+	9.95266i	−0.121831	+	0.354549i
$789$	15.4378	+	8.91302i	0.549601	+	0.317312i
$790$	23.9095	+	10.8871i	0.850661	+	0.387345i
$791$	0.800983	−	0.462448i	0.0284797	−	0.0164428i
$792$	−0.477729	−	1.60720i	−0.0169753	−	0.0571094i
$793$	−10.2365	+	47.1986i	−0.363509	+	1.67607i
$794$	5.04299	−	3.59953i	0.178969	−	0.127743i
$795$	−3.63221	−	6.29117i	−0.128821	−	0.223125i
$796$	−45.2802	+	8.83122i	−1.60491	+	0.313014i
$797$	39.5306	+	22.8230i	1.40025	+	0.808433i	0.994418	−	0.105516i	$-0.0336494\pi$
$797$	39.5306	+	22.8230i	1.40025	+	0.808433i	0.405829	+	0.913949i	$0.366983\pi$
$798$	4.50554	−	3.21592i	0.159495	−	0.113842i
$799$	−0.343471	−	0.198303i	−0.0121511	−	0.00701546i
$800$	9.23387	−	14.5448i	0.326467	−	0.514237i
$801$			12.8462i			0.453900i
$802$	−28.9518	+	2.79696i	−1.02233	+	0.0987641i
$803$	−1.52620	+	0.881151i	−0.0538584	+	0.0310952i
$804$	−2.59859	−	13.3237i	−0.0916451	−	0.469891i
$805$		−	15.7119i		−	0.553773i
$806$	−15.1054	−	1.77951i	−0.532066	−	0.0626806i
$807$	−1.95885			−0.0689549
$808$	32.2633	+	30.5587i	1.13502	+	1.07505i
$809$	3.11603	+	5.39713i	0.109554	+	0.189753i	0.915590	−	0.402114i	$-0.131724\pi$
$809$	3.11603	+	5.39713i	0.109554	+	0.189753i	−0.806036	+	0.591867i	$0.798391\pi$
$810$	0.385732	+	3.99279i	0.0135533	+	0.140292i
$811$	49.5256			1.73908			0.869539	−	0.493865i	$-0.164416\pi$
$811$	49.5256			1.73908			0.869539	+	0.493865i	$0.164416\pi$
$812$	10.6097	+	12.1895i	0.372328	+	0.427769i
$813$	3.59102	−	6.21984i	0.125943	−	0.218139i
$814$	−0.766090	+	0.546811i	−0.0268514	+	0.0191657i
$815$	−12.8736	+	22.2977i	−0.450942	+	0.781054i
$816$	0.659740	+	0.0918719i	0.0230955	+	0.00321616i
$817$	4.55131	−	2.62770i	0.159230	−	0.0919317i
$818$	16.4970	+	23.1125i	0.576804	+	0.808110i
$819$	2.13238	+	1.93603i	0.0745115	+	0.0676504i
$820$	−39.0038	−	13.4026i	−1.36207	−	0.468038i
$821$	−12.4396	−	21.5460i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$821$	−12.4396	−	21.5460i	−0.434145	−	0.751961i	−0.997225	+	0.0744410i	$0.976283\pi$
$822$	6.15797	+	2.80400i	0.214784	+	0.0978009i
$823$	20.9071	−	36.2122i	0.728777	−	1.26228i	−0.228624	−	0.973515i	$-0.573423\pi$
$823$	20.9071	−	36.2122i	0.728777	−	1.26228i	0.957401	−	0.288763i	$-0.0932440\pi$
$824$	6.29040	+	21.1625i	0.219137	+	0.737231i
$825$	1.56354	+	0.902711i	0.0544355	+	0.0314284i
$826$	12.3073	−	1.18897i	0.428225	−	0.0413696i
$827$	17.8051			0.619145			0.309573	−	0.950876i	$-0.399814\pi$
$827$	17.8051			0.619145			0.309573	+	0.950876i	$0.399814\pi$
$828$	−9.10533	−	10.4612i	−0.316432	−	0.363550i
$829$	41.4103	−	23.9082i	1.43824	−	0.830367i	0.440511	−	0.897747i	$-0.354797\pi$
$829$	41.4103	−	23.9082i	1.43824	−	0.830367i	0.997727	+	0.0673800i	$0.0214640\pi$
$830$	51.3149	+	23.3660i	1.78117	+	0.811046i
$831$	21.0440			0.730009
$832$	−22.3756	−	18.2026i	−0.775733	−	0.631062i
$833$	−1.05942			−0.0367069
$834$	9.07026	+	4.13010i	0.314077	+	0.143014i
$835$	48.4627	−	27.9800i	1.67712	−	0.968287i
$836$	−3.81415	−	4.38210i	−0.131915	−	0.151558i
$837$	−2.98291			−0.103104
$838$	21.8662	−	2.11244i	0.755356	−	0.0729729i
$839$	26.5231	+	15.3131i	0.915678	+	0.528667i	0.882254	−	0.470775i	$-0.156025\pi$
$839$	26.5231	+	15.3131i	0.915678	+	0.528667i	0.0334240	+	0.999441i	$0.489359\pi$
$840$	−1.82597	−	6.14302i	−0.0630019	−	0.211954i
$841$	36.6582	−	63.4938i	1.26407	−	2.18944i
$842$	−18.7947	−	8.55810i	−0.647709	−	0.294932i
$843$	−4.23036	−	7.32720i	−0.145701	−	0.252362i
$844$	23.3093	+	8.00961i	0.802341	+	0.275702i
$845$	−30.0100	+	21.4267i	−1.03238	+	0.737099i
$846$	1.95676	+	2.74145i	0.0672747	+	0.0942528i
$847$	7.36658	−	4.25310i	0.253119	−	0.146138i
$848$	10.1464	+	1.41293i	0.348429	+	0.0485204i
$849$	−5.04429	+	8.73696i	−0.173119	+	0.299852i
$850$	−0.583788	+	0.416690i	−0.0200238	+	0.0142923i
$851$	−3.89264	+	6.74226i	−0.133438	+	0.231122i
$852$	−4.61730	−	5.30484i	−0.158186	−	0.181741i
$853$	−44.3484			−1.51846			−0.759230	−	0.650823i	$-0.774424\pi$
$853$	−44.3484			−1.51846			−0.759230	+	0.650823i	$0.774424\pi$
$854$	−1.45509	−	15.0619i	−0.0497922	−	0.515408i
$855$	6.94942	+	12.0368i	0.237665	+	0.411648i
$856$	−32.1692	−	30.4697i	−1.09952	−	1.04143i
$857$	−25.5122			−0.871481			−0.435740	−	0.900072i	$-0.643513\pi$
$857$	−25.5122			−0.871481			−0.435740	+	0.900072i	$0.643513\pi$
$858$	1.80724	−	2.42294i	0.0616983	−	0.0827179i
$859$			39.0387i			1.33198i	0.745959	+	0.665992i	$0.231992\pi$
$859$			39.0387i			1.33198i	−0.745959	+	0.665992i	$0.768008\pi$
$860$	−1.16472	−	5.97183i	−0.0397165	−	0.203638i
$861$	−5.02931	+	2.90367i	−0.171398	+	0.0989569i
$862$	−17.5852	+	1.69885i	−0.598953	+	0.0578632i
$863$			16.7250i			0.569324i	0.958628	+	0.284662i	$0.0918814\pi$
$863$			16.7250i			0.569324i	−0.958628	+	0.284662i	$0.908119\pi$
$864$	−4.77573	−	3.03190i	−0.162474	−	0.103147i
$865$	−11.0878	−	6.40156i	−0.376997	−	0.217659i
$866$	−34.8991	+	24.9099i	−1.18592	+	0.846473i
$867$	14.6984	+	8.48613i	0.499184	+	0.288204i
$868$	4.67742	−	0.912260i	0.158762	−	0.0309641i
$869$	−1.94120	−	3.36227i	−0.0658509	−	0.114057i
$870$	−33.0259	+	23.5728i	−1.11968	+	0.799194i
$871$	16.4502	−	18.1185i	0.557393	−	0.613924i
$872$	−4.76812	−	16.0412i	−0.161469	−	0.543223i
$873$	11.5252	−	6.65406i	0.390068	−	0.225206i
$874$	−43.7329	−	19.9136i	−1.47929	−	0.673587i
$875$	−3.83506	−	2.21417i	−0.129649	−	0.0748528i
$876$	−1.93217	+	5.62296i	−0.0652821	+	0.189982i
$877$	14.8841	−	25.7800i	0.502601	−	0.870530i	−0.497395	−	0.867524i	$-0.665710\pi$
$877$	14.8841	−	25.7800i	0.502601	−	0.870530i	0.999995	−	0.00300555i	$-0.000956697\pi$
$878$	2.90501	+	30.0703i	0.0980394	+	1.01482i
$879$		−	3.04531i		−	0.102716i
$880$	−6.23293	+	2.52742i	−0.210112	+	0.0851993i
$881$	22.0037	+	38.1115i	0.741323	+	1.28401i	0.951893	+	0.306431i	$0.0991349\pi$
$881$	22.0037	+	38.1115i	0.741323	+	1.28401i	−0.210569	+	0.977579i	$0.567532\pi$
$882$	8.18818	+	3.72845i	0.275710	+	0.125543i
$883$			11.8178i			0.397702i	0.980030	+	0.198851i	$0.0637210\pi$
$883$			11.8178i			0.397702i	−0.980030	+	0.198851i	$0.936279\pi$
$884$	0.578495	+	1.05231i	0.0194569	+	0.0353930i
$885$			31.0455i			1.04358i
$886$	0.395934	−	0.869525i	0.0133017	−	0.0292123i
$887$	−22.7394	−	39.3857i	−0.763513	−	1.32244i	−0.941029	−	0.338325i	$-0.890140\pi$
$887$	−22.7394	−	39.3857i	−0.763513	−	1.32244i	0.177516	−	0.984118i	$-0.443194\pi$
$888$	−0.738384	+	3.08846i	−0.0247785	+	0.103642i
$889$			0.966203i			0.0324054i
$890$	51.2923	−	4.95521i	1.71932	−	0.166099i
$891$	0.296401	−	0.513382i	0.00992981	−	0.0171989i
$892$	51.3215	+	17.6352i	1.71837	+	0.590471i
$893$	10.1067	+	5.83508i	0.338206	+	0.195263i
$894$	5.07454	−	11.1444i	0.169718	−	0.372723i
$895$	15.9754	−	9.22340i	0.533998	−	0.308304i
$896$	8.41594	+	3.29369i	0.281157	+	0.110034i
$897$	5.29933	−	24.4342i	0.176940	−	0.815835i
$898$	5.43030	+	7.60793i	0.181212	+	0.253880i
$899$	−15.0863	−	26.1302i	−0.503155	−	0.871491i
$900$	5.97850	−	1.16602i	0.199283	−	0.0388672i
$901$	−0.369348	−	0.213243i	−0.0123048	−	0.00710417i
$902$	3.54083	+	4.96075i	0.117897	+	0.165175i
$903$	−0.741959	−	0.428370i	−0.0246909	−	0.0142553i
$904$	−3.18511	−	0.761491i	−0.105935	−	0.0253268i
$905$			6.02775i			0.200369i
$906$	−1.86252	−	19.2793i	−0.0618780	−	0.640510i
$907$	−6.77932	+	3.91404i	−0.225104	+	0.129964i	−0.608311	−	0.793699i	$-0.708153\pi$
$907$	−6.77932	+	3.91404i	−0.225104	+	0.129964i	0.383208	+	0.923662i	$0.374819\pi$
$908$	−20.2579	+	3.95099i	−0.672280	+	0.131118i
$909$			15.7113i			0.521110i
$910$	6.90763	−	9.26094i	0.228986	−	0.306997i
$911$	13.0076			0.430963			0.215481	−	0.976508i	$-0.430868\pi$
$911$	13.0076			0.430963			0.215481	+	0.976508i	$0.430868\pi$
$912$	−19.4129	−	2.70334i	−0.642824	−	0.0895164i
$913$	−4.16624	−	7.21614i	−0.137882	−	0.238819i
$914$	5.51178	−	0.532479i	0.182314	−	0.0176128i
$915$	37.9942			1.25605
$916$	−3.91722	−	4.50051i	−0.129428	−	0.148701i
$917$	−3.46355	+	5.99904i	−0.114376	+	0.198106i
$918$	0.136818	+	0.191684i	0.00451568	+	0.00632652i
$919$	18.5684	−	32.1615i	0.612516	−	1.06091i	−0.378298	−	0.925684i	$-0.623491\pi$
$919$	18.5684	−	32.1615i	0.612516	−	1.06091i	0.990815	−	0.135226i	$-0.0431760\pi$
$920$	−38.2569	+	40.3909i	−1.26129	+	1.33165i
$921$	27.6622	−	15.9708i	0.911502	−	0.526256i
$922$	25.8490	−	18.4502i	0.851293	−	0.607626i
$923$	2.68728	−	12.3906i	0.0884530	−	0.407840i
$924$	−0.307772	+	0.895670i	−0.0101250	+	0.0294654i
$925$	−1.70964	−	2.96119i	−0.0562127	−	0.0973633i
$926$	−6.55984	+	14.4063i	−0.215570	+	0.473420i
$927$	−3.90281	+	6.75986i	−0.128185	+	0.222023i
$928$	2.40577	−	57.1693i	0.0789732	−	1.87668i
$929$	38.6967	+	22.3415i	1.26960	+	0.733002i	0.974912	−	0.222592i	$-0.0714519\pi$
$929$	38.6967	+	22.3415i	1.26960	+	0.733002i	0.294685	+	0.955594i	$0.404785\pi$
$930$	1.15060	+	11.9101i	0.0377298	+	0.390548i
$931$	31.1736			1.02167
$932$	−28.3023	−	32.5166i	−0.927071	−	1.06512i
$933$	7.35193	−	4.24464i	0.240691	−	0.138963i
$934$	9.44902	−	20.7513i	0.309181	−	0.679004i
$935$	0.280009			0.00915726
$936$	−0.767709	−	10.1691i	−0.0250934	−	0.332387i
$937$	0.432775			0.0141382			0.00706908	−	0.999975i	$-0.497750\pi$
$937$	0.432775			0.0141382			0.00706908	+	0.999975i	$0.497750\pi$
$938$	−3.17751	+	6.97824i	−0.103749	+	0.227847i
$939$	−20.6538	+	11.9245i	−0.674012	+	0.389141i
$940$	10.1912	−	8.87039i	0.332401	−	0.289320i
$941$	9.49891			0.309656			0.154828	−	0.987941i	$-0.450518\pi$
$941$	9.49891			0.309656			0.154828	+	0.987941i	$0.450518\pi$
$942$	2.76351	+	28.6056i	0.0900401	+	0.932021i
$943$	43.6589	+	25.2065i	1.42173	+	0.820835i
$944$	−34.5334	−	26.9104i	−1.12397	−	0.875859i
$945$	1.13290	−	1.96224i	0.0368533	−	0.0638318i
$946$	−0.372612	+	0.818307i	−0.0121147	+	0.0266054i
$947$	26.2258	+	45.4244i	0.852224	+	1.47609i	0.879197	+	0.476458i	$0.158080\pi$
$947$	26.2258	+	45.4244i	0.852224	+	1.47609i	−0.0269736	+	0.999636i	$0.508587\pi$
$948$	−12.3876	−	4.25664i	−0.402329	−	0.138249i
$949$	−10.2077	+	3.27009i	−0.331356	+	0.106151i
$950$	17.1780	−	12.2611i	0.557328	−	0.397803i
$951$	0.227519	−	0.131358i	0.00737782	−	0.00425959i
$952$	−0.273164	−	0.258732i	−0.00885330	−	0.00838556i
$953$	17.4435	−	30.2131i	0.565051	−	0.978697i	−0.431994	−	0.901877i	$-0.642190\pi$
$953$	17.4435	−	30.2131i	0.565051	−	0.978697i	0.997045	−	0.0768206i	$-0.0244769\pi$
$954$	2.10418	+	2.94799i	0.0681254	+	0.0954446i
$955$	22.3748	−	38.7543i	0.724032	−	1.25406i
$956$	−35.3832	+	30.7974i	−1.14438	+	0.996059i
$957$	5.99629			0.193832
$958$	−25.6442	+	2.47742i	−0.828527	+	0.0800418i
$959$	−1.91096	−	3.30988i	−0.0617080	−	0.106881i
$960$	−10.2636	+	20.2380i	−0.331256	+	0.653178i
$961$	22.1023			0.712976
$962$	−5.25858	+	2.26266i	−0.169543	+	0.0729509i
$963$		−	15.6655i		−	0.504814i
$964$	−10.2951	−	52.7857i	−0.331581	−	1.70011i
$965$	17.3491	−	10.0165i	0.558487	−	0.322443i
$966$	0.753285	+	7.79739i	0.0242365	+	0.250877i
$967$		−	23.1920i		−	0.745805i	−0.927871	−	0.372902i	$-0.878363\pi$
$967$		−	23.1920i		−	0.745805i	0.927871	−	0.372902i	$-0.121637\pi$
$968$	−29.2932	−	7.00337i	−0.941519	−	0.225097i
$969$	0.706666	+	0.407994i	0.0227014	+	0.0131066i
$970$	−31.0139	−	43.4508i	−0.995795	−	1.39512i
$971$	24.6859	+	14.2524i	0.792209	+	0.457382i	0.840740	−	0.541439i	$-0.182120\pi$
$971$	24.6859	+	14.2524i	0.792209	+	0.457382i	−0.0485305	+	0.998822i	$0.515454\pi$
$972$	−0.382856	−	1.96301i	−0.0122801	−	0.0629637i
$973$	−2.81471	−	4.87521i	−0.0902353	−	0.156292i
$974$	−1.55366	−	2.17670i	−0.0497824	−	0.0697459i
$975$	8.13000	+	7.38138i	0.260368	+	0.236393i
$976$	−32.9336	+	42.2628i	−1.05418	+	1.35280i
$977$	−33.7853	+	19.5060i	−1.08089	+	0.624051i	−0.931136	−	0.364673i	$-0.881181\pi$
$977$	−33.7853	+	19.5060i	−1.08089	+	0.624051i	−0.149752	+	0.988724i	$0.547848\pi$
$978$	5.31976	−	11.6829i	0.170107	−	0.373578i
$979$	−6.59503	−	3.80764i	−0.210778	−	0.121693i
$980$	11.7285	−	34.1318i	0.374652	−	1.09030i
$981$	2.95833	−	5.12397i	0.0944521	−	0.163596i
$982$	−29.0336	+	2.80485i	−0.926498	+	0.0895065i
$983$			1.48214i			0.0472730i	0.999721	+	0.0236365i	$0.00752443\pi$
$983$			1.48214i			0.0472730i	−0.999721	+	0.0236365i	$0.992476\pi$
$984$	19.9990	+	4.78134i	0.637546	+	0.152423i
$985$	7.46266	+	12.9257i	0.237780	+	0.411847i
$986$	−0.987181	+	2.16798i	−0.0314383	+	0.0690426i
$987$		−	1.90248i		−	0.0605566i
$988$	−17.0222	−	30.9643i	−0.541550	−	0.985106i
$989$			7.43727i			0.236492i
$990$	−2.16416	−	0.985439i	−0.0687814	−	0.0313193i
$991$	12.0632	+	20.8941i	0.383200	+	0.663722i	0.991518	−	0.129972i	$-0.0414886\pi$
$991$	12.0632	+	20.8941i	0.383200	+	0.663722i	−0.608318	+	0.793694i	$0.708155\pi$
$992$	−14.2456	−	9.04387i	−0.452297	−	0.287143i
$993$		−	31.4245i		−	0.997225i
$994$	0.381990	+	3.95405i	0.0121160	+	0.125415i
$995$	−32.7140	+	56.6623i	−1.03710	+	1.79632i
$996$	−26.5864	−	9.13567i	−0.842421	−	0.289475i
$997$	14.7133	+	8.49471i	0.465974	+	0.269030i	0.714553	−	0.699581i	$-0.246630\pi$
$997$	14.7133	+	8.49471i	0.465974	+	0.269030i	−0.248579	+	0.968612i	$0.579964\pi$
$998$	31.7643	+	14.4637i	1.00548	+	0.457842i
$999$	−0.972293	+	0.561354i	−0.0307620	+	0.0177604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bk.b.205.3	✓	48
3.2	odd	2		936.2.dg.e.829.22		48
4.3	odd	2		1248.2.ca.b.49.11		48
8.3	odd	2		1248.2.ca.b.49.14		48
8.5	even	2	inner	312.2.bk.b.205.12	yes	48
13.4	even	6	inner	312.2.bk.b.277.12	yes	48
24.5	odd	2		936.2.dg.e.829.13		48
39.17	odd	6		936.2.dg.e.901.13		48
52.43	odd	6		1248.2.ca.b.433.14		48
104.43	odd	6		1248.2.ca.b.433.11		48
104.69	even	6	inner	312.2.bk.b.277.3	yes	48
312.173	odd	6		936.2.dg.e.901.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.3	✓	48	1.1	even	1	trivial
312.2.bk.b.205.12	yes	48	8.5	even	2	inner
312.2.bk.b.277.3	yes	48	104.69	even	6	inner
312.2.bk.b.277.12	yes	48	13.4	even	6	inner
936.2.dg.e.829.13		48	24.5	odd	2
936.2.dg.e.829.22		48	3.2	odd	2
936.2.dg.e.901.13		48	39.17	odd	6
936.2.dg.e.901.22		48	312.173	odd	6
1248.2.ca.b.49.11		48	4.3	odd	2
1248.2.ca.b.49.14		48	8.3	odd	2
1248.2.ca.b.433.11		48	104.43	odd	6
1248.2.ca.b.433.14		48	52.43	odd	6

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28706 - 0.586059i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.31307 + 1.50859i) q^{4} +2.83647 q^{5} +(-1.40766 + 0.135990i) q^{6} +(0.691790 + 0.399405i) q^{7} +(-0.805882 - 2.71119i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.65072 - 1.66234i) q^{10} +(0.296401 + 0.513382i) q^{11} +(1.89145 + 0.649944i) q^{12} +(1.09999 + 3.43366i) q^{13} +(-0.656303 - 0.919490i) q^{14} +(2.45646 - 1.41824i) q^{15} +(-0.551696 + 3.96177i) q^{16} +(0.0832632 - 0.144216i) q^{17} +(-1.15107 + 0.821601i) q^{18} +(-2.45002 + 4.24357i) q^{19} +(3.72449 + 4.27908i) q^{20} +0.798810 q^{21} +(-0.0806153 - 0.834464i) q^{22} +(-3.46719 - 6.00535i) q^{23} +(-2.05351 - 1.94502i) q^{24} +3.04557 q^{25} +(0.596570 - 5.06400i) q^{26} -1.00000i q^{27} +(0.305829 + 1.56808i) q^{28} +(8.75998 - 5.05758i) q^{29} +(-3.99279 + 0.385732i) q^{30} -2.98291i q^{31} +(3.03190 - 4.77573i) q^{32} +(0.513382 + 0.296401i) q^{33} +(-0.191684 + 0.136818i) q^{34} +(1.96224 + 1.13290i) q^{35} +(1.96301 - 0.382856i) q^{36} +(-0.561354 - 0.972293i) q^{37} +(5.64032 - 4.02588i) q^{38} +(2.66945 + 2.42364i) q^{39} +(-2.28586 - 7.69022i) q^{40} +(-6.29600 + 3.63500i) q^{41} +(-1.02812 - 0.468150i) q^{42} +(-0.928831 - 0.536261i) q^{43} +(-0.385288 + 1.12125i) q^{44} +(1.41824 - 2.45646i) q^{45} +(0.943008 + 9.76125i) q^{46} -2.38164i q^{47} +(1.50310 + 3.70684i) q^{48} +(-3.18095 - 5.50957i) q^{49} +(-3.91985 - 1.78488i) q^{50} -0.166526i q^{51} +(-3.73563 + 6.16807i) q^{52} -2.56107i q^{53} +(-0.586059 + 1.28706i) q^{54} +(0.840734 + 1.45619i) q^{55} +(0.525362 - 2.19745i) q^{56} +4.90005i q^{57} +(-14.2387 + 1.37556i) q^{58} +(-5.47256 + 9.47875i) q^{59} +(5.36504 + 1.84355i) q^{60} +(11.6003 + 6.69744i) q^{61} +(-1.74816 + 3.83919i) q^{62} +(0.691790 - 0.399405i) q^{63} +(-6.70111 + 4.36980i) q^{64} +(3.12009 + 9.73948i) q^{65} +(-0.487047 - 0.682360i) q^{66} +(-3.39369 - 5.87804i) q^{67} +(0.326894 - 0.0637556i) q^{68} +(-6.00535 - 3.46719i) q^{69} +(-1.86159 - 2.60811i) q^{70} +(-3.04531 - 1.75821i) q^{71} +(-2.75090 - 0.657681i) q^{72} +2.97283i q^{73} +(0.152677 + 1.58039i) q^{74} +(2.63754 - 1.52279i) q^{75} +(-9.61886 + 1.87601i) q^{76} +0.473537i q^{77} +(-2.01536 - 4.68384i) q^{78} -6.54925 q^{79} +(-1.56487 + 11.2375i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.2337 - 0.988648i) q^{82} -14.0561 q^{83} +(1.04889 + 1.20508i) q^{84} +(0.236174 - 0.409065i) q^{85} +(0.881184 + 1.23455i) q^{86} +(5.05758 - 8.75998i) q^{87} +(1.15301 - 1.21733i) q^{88} +(-11.1252 + 6.42312i) q^{89} +(-3.26499 + 2.33045i) q^{90} +(-0.610460 + 2.81471i) q^{91} +(4.50696 - 13.1160i) q^{92} +(-1.49145 - 2.58327i) q^{93} +(-1.39578 + 3.06533i) q^{94} +(-6.94942 + 12.0368i) q^{95} +(0.237838 - 5.65185i) q^{96} +(11.5252 + 6.65406i) q^{97} +(0.865157 + 8.95540i) q^{98} +0.592802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

Introduction

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