LMFDB - Embedded newform 312.2.bk.b.205.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(205,312)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.49133254306$
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			205.12
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.b.277.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.135990 + 1.40766i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.96301 - 0.382856i) q^{4} -2.83647 q^{5} +(-0.586059 - 1.28706i) q^{6} +(0.691790 + 0.399405i) q^{7} +(0.805882 - 2.71119i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.385732 - 3.99279i) 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} +(3.70684 + 1.50310i) q^{16} +(0.0832632 - 0.144216i) q^{17} +(1.15107 + 0.821601i) q^{18} +(2.45002 - 4.24357i) q^{19} +(5.56803 + 1.08596i) q^{20} -0.798810 q^{21} +(0.762975 - 0.347417i) q^{22} +(-3.46719 - 6.00535i) q^{23} +(0.657681 + 2.75090i) q^{24} +3.04557 q^{25} +(4.98301 - 1.08147i) q^{26} +1.00000i q^{27} +(-1.20508 - 1.04889i) q^{28} +(-8.75998 + 5.05758i) q^{29} +(1.66234 + 3.65072i) q^{30} -2.98291i q^{31} +(-2.61995 + 5.01357i) q^{32} +(0.513382 + 0.296401i) q^{33} +(0.191684 + 0.136818i) q^{34} +(-1.96224 - 1.13290i) q^{35} +(-1.31307 + 1.50859i) 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} +(0.108630 - 1.12445i) q^{42} +(0.928831 + 0.536261i) q^{43} +(0.385288 + 1.12125i) q^{44} +(-1.41824 + 2.45646i) q^{45} +(8.92500 - 4.06396i) q^{46} -2.38164i q^{47} +(-3.96177 + 0.551696i) q^{48} +(-3.18095 - 5.50957i) q^{49} +(-0.414168 + 4.28713i) q^{50} +0.166526i q^{51} +(0.844697 + 7.16146i) q^{52} +2.56107i q^{53} +(-1.40766 - 0.135990i) q^{54} +(0.840734 + 1.45619i) q^{55} +(1.64036 - 1.55370i) q^{56} +4.90005i q^{57} +(-5.92808 - 13.0189i) q^{58} +(5.47256 - 9.47875i) q^{59} +(-5.36504 + 1.84355i) q^{60} +(-11.6003 - 6.69744i) q^{61} +(4.19892 + 0.405646i) 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} +(-0.218661 + 0.251220i) q^{68} +(6.00535 + 3.46719i) q^{69} +(1.86159 - 2.60811i) q^{70} +(-3.04531 - 1.75821i) q^{71} +(-1.94502 - 2.05351i) q^{72} +2.97283i q^{73} +(-1.44500 + 0.657973i) q^{74} +(-2.63754 + 1.52279i) q^{75} +(-6.43410 + 7.39217i) q^{76} -0.473537i q^{77} +(-3.77468 + 3.42809i) q^{78} -6.54925 q^{79} +(-10.5144 - 4.26351i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.26064 - 9.35695i) q^{82} +14.0561 q^{83} +(1.56808 + 0.305829i) q^{84} +(-0.236174 + 0.409065i) q^{85} +(-0.881184 + 1.23455i) q^{86} +(5.05758 - 8.75998i) q^{87} +(-1.63074 + 0.389875i) 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} +(3.35254 + 0.323880i) q^{94} +(-6.94942 + 12.0368i) q^{95} +(-0.237838 - 5.65185i) q^{96} +(11.5252 + 6.65406i) q^{97} +(8.18818 - 3.72845i) 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 $

$2$	−0.135990	+	1.40766i	−0.0961596	+	0.995366i
$2$	−0.135990	+	1.40766i	−0.0961596	+	0.995366i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−1.96301	−	0.382856i	−0.981507	−	0.191428i
$5$	−2.83647			−1.26851			−0.634254	−	0.773124i	$-0.718693\pi$
$5$	−2.83647			−1.26851			−0.634254	+	0.773124i	$0.718693\pi$
$6$	−0.586059	−	1.28706i	−0.239258	−	0.525442i
$7$	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
$10$	0.385732	−	3.99279i	0.121979	−	1.26263i
$11$	−0.296401	−	0.513382i	−0.0893683	−	0.154790i	0.817876	−	0.575395i	$-0.195151\pi$
$11$	−0.296401	−	0.513382i	−0.0893683	−	0.154790i	−0.907244	+	0.420604i	$0.861818\pi$
$12$	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
$16$	3.70684	+	1.50310i	0.926711	+	0.375776i
$17$	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	$-0.643337\pi$
$19$	2.45002	−	4.24357i	0.562074	−	0.973541i	0.997315	−	0.0732270i	$-0.0233298\pi$
$20$	5.56803	+	1.08596i	1.24505	+	0.242828i
$21$	−0.798810			−0.174315
$22$	0.762975	−	0.347417i	0.162667	−	0.0740696i
$23$	−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	$-0.423885\pi$
$24$	0.657681	+	2.75090i	0.134249	+	0.561525i
$25$	3.04557			0.609114
$26$	4.98301	−	1.08147i	0.977249	−	0.212093i
$27$			1.00000i			0.192450i
$28$	−1.20508	−	1.04889i	−0.227738	−	0.198222i
$29$	−8.75998	+	5.05758i	−1.62669	+	0.939168i	−0.641615	+	0.767027i	$0.721735\pi$
$29$	−8.75998	+	5.05758i	−1.62669	+	0.939168i	−0.985072	+	0.172141i	$0.944931\pi$
$30$	1.66234	+	3.65072i	0.303500	+	0.666528i
$31$		−	2.98291i		−	0.535746i	−0.963454	−	0.267873i	$-0.913679\pi$
$31$		−	2.98291i		−	0.535746i	0.963454	−	0.267873i	$-0.0863207\pi$
$32$	−2.61995	+	5.01357i	−0.463147	+	0.886282i
$33$	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
$36$	−1.31307	+	1.50859i	−0.218845	+	0.251432i
$37$	0.561354	+	0.972293i	0.0922860	+	0.159844i	0.908473	−	0.417944i	$-0.137249\pi$
$37$	0.561354	+	0.972293i	0.0922860	+	0.159844i	−0.816187	+	0.577788i	$0.803916\pi$
$38$	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	$0.525496\pi$
$42$	0.108630	−	1.12445i	0.0167620	−	0.173507i
$43$	0.928831	+	0.536261i	0.141645	+	0.0817790i	0.569148	−	0.822235i	$-0.307273\pi$
$43$	0.928831	+	0.536261i	0.141645	+	0.0817790i	−0.427503	+	0.904014i	$0.640607\pi$
$44$	0.385288	+	1.12125i	0.0580844	+	0.169035i
$45$	−1.41824	+	2.45646i	−0.211418	+	0.366187i
$46$	8.92500	−	4.06396i	1.31592	−	0.599198i
$47$		−	2.38164i		−	0.347398i	−0.984799	−	0.173699i	$-0.944428\pi$
$47$		−	2.38164i		−	0.347398i	0.984799	−	0.173699i	$-0.0555720\pi$
$48$	−3.96177	+	0.551696i	−0.571832	+	0.0796304i
$49$	−3.18095	−	5.50957i	−0.454422	−	0.787081i
$50$	−0.414168	+	4.28713i	−0.0585722	+	0.606292i
$51$			0.166526i			0.0233184i
$52$	0.844697	+	7.16146i	0.117138	+	0.993116i
$53$			2.56107i			0.351791i	0.984409	+	0.175895i	$0.0562820\pi$
$53$			2.56107i			0.351791i	−0.984409	+	0.175895i	$0.943718\pi$
$54$	−1.40766	−	0.135990i	−0.191558	−	0.0185059i
$55$	0.840734	+	1.45619i	0.113364	+	0.196353i
$56$	1.64036	−	1.55370i	0.219203	−	0.207622i
$57$			4.90005i			0.649027i
$58$	−5.92808	−	13.0189i	−0.778395	−	1.70946i
$59$	5.47256	−	9.47875i	0.712466	−	1.23403i	−0.251462	−	0.967867i	$-0.580911\pi$
$59$	5.47256	−	9.47875i	0.712466	−	1.23403i	0.963929	−	0.266161i	$-0.0857553\pi$
$60$	−5.36504	+	1.84355i	−0.692623	+	0.238001i
$61$	−11.6003	−	6.69744i	−1.48527	−	0.857519i	−0.485407	−	0.874288i	$-0.661329\pi$
$61$	−11.6003	−	6.69744i	−1.48527	−	0.857519i	−0.999859	+	0.0167691i	$0.994662\pi$
$62$	4.19892	+	0.405646i	0.533263	+	0.0515171i
$63$	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	0.995387	−	0.0959425i	$-0.0305865\pi$
$67$	3.39369	+	5.87804i	0.414605	+	0.718117i	−0.580782	+	0.814059i	$0.697253\pi$
$68$	−0.218661	+	0.251220i	−0.0265165	+	0.0304649i
$69$	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	$0.733577\pi$
$72$	−1.94502	−	2.05351i	−0.229223	−	0.242008i
$73$			2.97283i			0.347944i	0.984751	+	0.173972i	$0.0556602\pi$
$73$			2.97283i			0.347944i	−0.984751	+	0.173972i	$0.944340\pi$
$74$	−1.44500	+	0.657973i	−0.167977	+	0.0764878i
$75$	−2.63754	+	1.52279i	−0.304557	+	0.175836i
$76$	−6.43410	+	7.39217i	−0.738042	+	0.847940i
$77$		−	0.473537i		−	0.0539645i
$78$	−3.77468	+	3.42809i	−0.427399	+	0.388154i
$79$	−6.54925			−0.736848			−0.368424	−	0.929658i	$-0.620103\pi$
$79$	−6.54925			−0.736848			−0.368424	+	0.929658i	$0.620103\pi$
$80$	−10.5144	−	4.26351i	−1.17554	−	0.476675i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.26064	−	9.35695i	−0.470509	−	1.03330i
$83$	14.0561			1.54286			0.771428	−	0.636316i	$-0.219543\pi$
$83$	14.0561			1.54286			0.771428	+	0.636316i	$0.219543\pi$
$84$	1.56808	+	0.305829i	0.171091	+	0.0333687i
$85$	−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
$88$	−1.63074	+	0.389875i	−0.173838	+	0.0415608i
$89$	−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
$94$	3.35254	+	0.323880i	0.345788	+	0.0334057i
$95$	−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	$0.430544\pi$
$98$	8.18818	−	3.72845i	0.827131	−	0.376630i
$99$	−0.592802			−0.0595789
$100$	−5.97850	−	1.16602i	−0.597850	−	0.116602i
$101$	13.6064	−	7.85564i	1.35388	−	0.781666i	0.365093	−	0.930971i	$-0.381037\pi$
$101$	13.6064	−	7.85564i	1.35388	−	0.781666i	0.988791	+	0.149305i	$0.0477037\pi$
$102$	−0.234413	−	0.0226460i	−0.0232103	−	0.00224229i
$103$	−7.80561			−0.769110			−0.384555	−	0.923102i	$-0.625645\pi$
$103$	−7.80561			−0.769110			−0.384555	+	0.923102i	$0.625645\pi$
$104$	−10.1958	+	0.215158i	−0.999777	+	0.0210980i
$105$	2.26580			0.221120
$106$	−3.60512	−	0.348281i	−0.350160	−	0.0338281i
$107$	−13.5667	+	7.83275i	−1.31154	+	0.757220i	−0.982352	−	0.187042i	$-0.940110\pi$
$107$	−13.5667	+	7.83275i	−1.31154	+	0.757220i	−0.329192	+	0.944263i	$0.606776\pi$
$108$	0.382856	−	1.96301i	0.0368403	−	0.188891i
$109$	−5.91665			−0.566713			−0.283356	−	0.959015i	$-0.591448\pi$
$109$	−5.91665			−0.566713			−0.283356	+	0.959015i	$0.591448\pi$
$110$	−2.16416	+	0.985439i	−0.206344	+	0.0939579i
$111$	−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	$0.149323\pi$
$114$	−6.89760	−	0.666359i	−0.646020	−	0.0624102i
$115$	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
$120$	−1.86549	−	7.80285i	−0.170296	−	0.712300i
$121$	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
$124$	−1.14202	+	5.85548i	−0.102557	+	0.525838i
$125$	5.54368			0.495842
$126$	0.468150	+	1.02812i	0.0417061	+	0.0915922i
$127$	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	$0.816243\pi$
$128$	7.06248	−	8.83863i	0.624241	−	0.781232i
$129$	−1.07252			−0.0944302
$130$	−14.1342	+	3.06755i	−1.23965	+	0.269042i
$131$		−	8.67176i		−	0.757655i	−0.925467	−	0.378828i	$-0.876327\pi$
$131$		−	8.67176i		−	0.757655i	0.925467	−	0.378828i	$-0.123673\pi$
$132$	−0.894297	−	0.778391i	−0.0778385	−	0.0677502i
$133$	3.38980	−	1.95710i	0.293933	−	0.169702i
$134$	−8.73579	+	3.97780i	−0.754657	+	0.343630i
$135$		−	2.83647i		−	0.244125i
$136$	−0.323897	−	0.341964i	−0.0277739	−	0.0293231i
$137$	−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	0.735976	−	0.677008i	$-0.236724\pi$
$139$	6.10309	+	3.52362i	0.517658	+	0.298870i	−0.218318	+	0.975878i	$0.570057\pi$
$140$	3.41817	+	2.97516i	0.288888	+	0.251447i
$141$	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
$146$	−4.18474	−	0.404276i	−0.346331	−	0.0334581i
$147$	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	−0.632386	−	0.774653i	$-0.717924\pi$
$149$	4.32937	−	7.49869i	0.354676	−	0.614317i	0.987062	+	0.160336i	$0.0512578\pi$
$150$	−1.78488	−	3.91985i	−0.145735	−	0.320054i
$151$			13.6960i			1.11456i	0.830324	+	0.557281i	$0.188155\pi$
$151$			13.6960i			1.11456i	−0.830324	+	0.557281i	$0.811845\pi$
$152$	−9.53069	−	10.0623i	−0.773041	−	0.816160i
$153$	−0.0832632	−	0.144216i	−0.00673143	−	0.0116592i
$154$	0.666579	+	0.0643964i	0.0537144	+	0.00518921i
$155$			8.46093i			0.679598i
$156$	−4.31226	−	5.77966i	−0.345257	−	0.462743i
$157$			20.3214i			1.62182i	0.585168	+	0.810912i	$0.301029\pi$
$157$			20.3214i			1.62182i	−0.585168	+	0.810912i	$0.698971\pi$
$158$	0.890634	−	9.21911i	0.0708550	−	0.733433i
$159$	−1.28054	−	2.21796i	−0.101553	−	0.175895i
$160$	7.43142	−	14.2208i	0.587505	−	1.12426i
$161$		−	5.53926i		−	0.436555i
$162$	1.28706	−	0.586059i	0.101121	−	0.0460451i
$163$	4.53859	−	7.86107i	0.355490	−	0.615726i	−0.631712	−	0.775203i	$-0.717647\pi$
$163$	4.53859	−	7.86107i	0.355490	−	0.615726i	0.987202	+	0.159477i	$0.0509807\pi$
$164$	13.7508	−	4.72508i	1.07376	−	0.368967i
$165$	−1.45619	−	0.840734i	−0.113364	−	0.0654510i
$166$	−1.91149	+	19.7862i	−0.148360	+	1.53571i
$167$	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
$172$	−1.61800	−	1.40830i	−0.123371	−	0.107381i
$173$	3.90902	+	2.25687i	0.297197	+	0.171587i	0.641183	−	0.767388i	$-0.278444\pi$
$173$	3.90902	+	2.25687i	0.297197	+	0.171587i	−0.343986	+	0.938975i	$0.611777\pi$
$174$	11.6433	+	8.31062i	0.882676	+	0.630026i
$175$	2.10690	+	1.21642i	0.159266	+	0.0919525i
$176$	−0.327047	−	2.34855i	−0.0246521	−	0.177028i
$177$			10.9451i			0.822685i
$178$	−7.52866	−	16.5339i	−0.564297	−	1.23927i
$179$	−5.63214	+	3.25171i	−0.420966	+	0.243045i	−0.695490	−	0.718535i	$-0.744813\pi$
$179$	−5.63214	+	3.25171i	−0.420966	+	0.243045i	0.274525	+	0.961580i	$0.411479\pi$
$180$	3.72449	−	4.27908i	0.277607	−	0.318944i
$181$		−	2.12509i		−	0.157957i	−0.996876	−	0.0789783i	$-0.974834\pi$
$181$		−	2.12509i		−	0.157957i	0.996876	−	0.0789783i	$-0.0251658\pi$
$182$	3.87914	+	1.24209i	0.287541	+	0.0920701i
$183$	13.3949			0.990178
$184$	−19.0758	+	4.56061i	−1.40629	+	0.336213i
$185$	−1.59226	−	2.75788i	−0.117066	−	0.202764i
$186$	−3.83919	+	1.74816i	−0.281503	+	0.128181i
$187$	−0.0987173			−0.00721892
$188$	−0.911826	+	4.67519i	−0.0665017	+	0.340974i
$189$	−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	$-0.0266903\pi$
$192$	7.98823	+	0.433802i	0.576501	+	0.0313069i
$193$	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	0.756950	−	0.653472i	$-0.226688\pi$
$197$	−2.63096	−	4.55696i	−0.187448	−	0.324670i	−0.944399	+	0.328802i	$0.893355\pi$
$198$	0.0806153	−	0.834464i	0.00572908	−	0.0593028i
$199$	−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
$202$	9.20774	+	20.2214i	0.647854	+	1.42278i
$203$	−8.08009			−0.567111
$204$	0.0637556	−	0.326894i	0.00446379	−	0.0228871i
$205$	17.8584	−	10.3106i	1.24729	−	0.720121i
$206$	1.06149	−	10.9877i	0.0739573	−	0.765546i
$207$	−6.93438			−0.481973
$208$	1.08366	−	14.3814i	0.0751380	−	0.997173i
$209$	−2.90476			−0.200926
$210$	−0.308127	+	3.18948i	−0.0212628	+	0.220095i
$211$	−10.6725	+	6.16178i	−0.734726	+	0.424194i	−0.820149	−	0.572151i	$-0.806109\pi$
$211$	−10.6725	+	6.16178i	−0.734726	+	0.424194i	0.0854227	+	0.996345i	$0.472776\pi$
$212$	0.980523	−	5.02742i	0.0673426	−	0.345285i
$213$	3.51642			0.240941
$214$	−9.18091	−	20.1625i	−0.627594	−	1.37828i
$215$	−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
$218$	0.804607	−	8.32864i	0.0544949	−	0.564086i
$219$	−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	$-0.0294350\pi$
$224$	−3.81490	+	2.42191i	−0.254894	+	0.161821i
$225$	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	−0.642418	−	0.766355i	$-0.722069\pi$
$227$	5.15989	−	8.93719i	0.342474	−	0.593182i	0.984891	+	0.173173i	$0.0554019\pi$
$228$	1.87601	−	9.61886i	0.124242	−	0.637025i
$229$	2.98325			0.197139			0.0985694	−	0.995130i	$-0.468573\pi$
$229$	2.98325			0.197139			0.0985694	+	0.995130i	$0.468573\pi$
$230$	−25.3155	+	11.5273i	−1.66926	+	0.760088i
$231$	0.236768	+	0.410095i	0.0155782	+	0.0269823i
$232$	6.65255	+	27.8258i	0.436761	+	1.82685i
$233$	−21.5543			−1.41207			−0.706034	−	0.708178i	$-0.749517\pi$
$233$	−21.5543			−1.41207			−0.706034	+	0.708178i	$0.749517\pi$
$234$	1.55493	−	4.85615i	0.101649	−	0.317456i
$235$			6.75546i			0.440677i
$236$	−14.3717	+	16.5117i	−0.935518	+	1.07482i
$237$	5.67181	−	3.27462i	0.368424	−	0.212710i
$238$	0.0779593	+	0.171209i	0.00505335	+	0.0110978i
$239$			23.4545i			1.51714i	0.651589	+	0.758572i	$0.274103\pi$
$239$			23.4545i			1.51714i	−0.651589	+	0.758572i	$0.725897\pi$
$240$	11.2375	−	1.56487i	0.725374	−	0.101012i
$241$	−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
$244$	20.2074	+	17.5884i	1.29365	+	1.12598i
$245$	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
$250$	−0.753886	+	7.80362i	−0.0476800	+	0.493544i
$251$	−25.1888	−	14.5427i	−1.58990	−	0.917930i	−0.993322	−	0.115376i	$-0.963193\pi$
$251$	−25.1888	−	14.5427i	−1.58990	−	0.917930i	−0.596579	−	0.802554i	$-0.703474\pi$
$252$	−1.51091	+	0.519182i	−0.0951782	+	0.0327054i
$253$	−2.05536	+	3.55999i	−0.129219	+	0.223814i
$254$	−1.55677	+	0.708869i	−0.0976805	+	0.0444784i
$255$		−	0.472348i		−	0.0295795i
$256$	11.4814	+	11.1435i	0.717585	+	0.696471i
$257$	−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	$-0.393975\pi$
$258$	0.145852	−	1.50975i	0.00908037	−	0.0939926i
$259$			0.896830i			0.0557263i
$260$	−2.39596	−	20.3133i	−0.148591	−	1.25978i
$261$			10.1152i			0.626112i
$262$	12.2069	+	1.17927i	0.754144	+	0.0728558i
$263$	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	$0.648113\pi$
$264$	1.21733	−	1.15301i	0.0749212	−	0.0709630i
$265$		−	7.26442i		−	0.446250i
$266$	2.29396	+	5.03784i	0.140652	+	0.308890i
$267$	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	0.550824	−	0.834622i	$-0.314314\pi$
$269$	1.69642	+	0.979426i	0.103432	+	0.0597167i	−0.447392	+	0.894338i	$0.647647\pi$
$270$	3.99279	+	0.385732i	0.242993	+	0.0234749i
$271$	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
$276$	−10.4612	−	9.10533i	−0.629687	−	0.548076i
$277$	−18.2247	−	10.5220i	−1.09501	−	0.632207i	−0.160107	−	0.987100i	$-0.551184\pi$
$277$	−18.2247	−	10.5220i	−1.09501	−	0.632207i	−0.934907	+	0.354893i	$0.884517\pi$
$278$	−5.79002	+	8.11190i	−0.347263	+	0.486520i
$279$	−2.58327	−	1.49145i	−0.154656	−	0.0892910i
$280$	−4.65285	+	4.40703i	−0.278061	+	0.263370i
$281$		−	8.46072i		−	0.504724i	−0.967633	−	0.252362i	$-0.918793\pi$
$281$		−	8.46072i		−	0.504724i	0.967633	−	0.252362i	$-0.0812074\pi$
$282$	−3.06533	+	1.39578i	−0.182537	+	0.0831176i
$283$	8.73696	−	5.04429i	0.519358	−	0.299852i	−0.217314	−	0.976102i	$-0.569729\pi$
$283$	8.73696	−	5.04429i	0.519358	−	0.299852i	0.736672	+	0.676250i	$0.236396\pi$
$284$	5.30484	+	4.61730i	0.314784	+	0.273986i
$285$		−	13.8988i		−	0.823297i
$286$	−2.03218	−	2.23764i	−0.120165	−	0.132314i
$287$	−5.80734			−0.342797
$288$	3.03190	+	4.77573i	0.178656	+	0.281413i
$289$	8.48613	+	14.6984i	0.499184	+	0.864613i
$290$	16.8148	+	36.9276i	0.987400	+	2.16846i
$291$	−13.3081			−0.780135
$292$	1.13817	−	5.83571i	0.0666062	−	0.341509i
$293$	−1.52266	+	2.63732i	−0.0889545	+	0.154074i	−0.907069	−	0.420981i	$-0.861686\pi$
$293$	−1.52266	+	2.63732i	−0.0889545	+	0.154074i	0.818115	+	0.575055i	$0.195019\pi$
$294$	−5.22695	+	7.32302i	−0.304842	+	0.427087i
$295$	−15.5228	+	26.8862i	−0.903770	+	1.56538i
$296$	3.08846	−	0.738384i	0.179513	−	0.0429177i
$297$	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
$302$	−19.2793	−	1.86252i	−1.10940	−	0.107176i
$303$	−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
$306$	0.214330	−	0.0975943i	0.0122524	−	0.00557910i
$307$	−31.9416			−1.82300			−0.911502	−	0.411296i	$-0.865076\pi$
$307$	−31.9416			−1.82300			−0.911502	+	0.411296i	$0.865076\pi$
$308$	−0.181296	+	0.929559i	−0.0103303	+	0.0529665i
$309$	6.75986	−	3.90281i	0.384555	−	0.222023i
$310$	−11.9101	−	1.15060i	−0.676449	−	0.0653499i
$311$	8.48928			0.481383			0.240691	−	0.970602i	$-0.422626\pi$
$311$	8.48928			0.481383			0.240691	+	0.970602i	$0.422626\pi$
$312$	8.72222	−	5.28422i	0.493798	−	0.299160i
$313$	−23.8490			−1.34802			−0.674012	−	0.738720i	$-0.735431\pi$
$313$	−23.8490			−1.34802			−0.674012	+	0.738720i	$0.735431\pi$
$314$	−28.6056	−	2.76351i	−1.61431	−	0.155954i
$315$	−1.96224	+	1.13290i	−0.110560	+	0.0638318i
$316$	12.8563	+	2.50742i	0.723221	+	0.141053i
$317$	−0.262717			−0.0147556			−0.00737782	−	0.999973i	$-0.502348\pi$
$317$	−0.262717			−0.0147556			−0.00737782	+	0.999973i	$0.502348\pi$
$318$	3.29627	−	1.50094i	0.184846	−	0.0841686i
$319$	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
$322$	7.79739	+	0.753285i	0.434532	+	0.0419789i
$323$	−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
$328$	4.78134	+	19.9990i	0.264005	+	1.10426i
$329$	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	$0.498476\pi$
$331$	−15.7122	+	27.2144i	−0.863622	+	1.49584i	−0.868409	+	0.495849i	$0.834857\pi$
$332$	−27.5923	−	5.38146i	−1.51432	−	0.295346i
$333$	1.12271			0.0615240
$334$	11.5622	+	25.3921i	0.632655	+	1.38940i
$335$	−9.62610	−	16.6729i	−0.525930	−	0.910937i
$336$	−2.96106	−	1.20069i	−0.161539	−	0.0655032i
$337$	28.5717			1.55640			0.778201	−	0.628016i	$-0.216133\pi$
$337$	28.5717			1.55640			0.778201	+	0.628016i	$0.216133\pi$
$338$	−9.19466	−	15.9204i	−0.500123	−	0.865954i
$339$			1.15784i			0.0628853i
$340$	0.620225	−	0.712579i	0.0336364	−	0.0386450i
$341$	−1.53137	+	0.884137i	−0.0829283	+	0.0478787i
$342$	6.30668	−	2.87172i	0.341026	−	0.155285i
$343$		−	10.6736i		−	0.576322i
$344$	2.20243	−	2.08607i	0.118747	−	0.112474i
$345$	−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	0.823660	−	0.567084i	$-0.191928\pi$
$347$	13.8663	+	8.00570i	0.744381	+	0.429769i	−0.0792791	+	0.996852i	$0.525262\pi$
$348$	−13.2819	+	15.2596i	−0.711985	+	0.818002i
$349$	−6.12306	−	10.6055i	−0.327760	−	0.567697i	0.654307	−	0.756229i	$-0.272960\pi$
$349$	−6.12306	−	10.6055i	−0.327760	−	0.567697i	−0.982067	+	0.188532i	$0.939627\pi$
$350$	−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	$0.156832\pi$
$354$	−15.4070	−	1.48843i	−0.818873	−	0.0791091i
$355$	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
$358$	−3.81139	−	8.37033i	−0.201438	−	0.442386i
$359$		−	24.2509i		−	1.27991i	−0.768411	−	0.639957i	$-0.778952\pi$
$359$		−	24.2509i		−	1.27991i	0.768411	−	0.639957i	$-0.221048\pi$
$360$	5.51699	+	5.82472i	0.290771	+	0.306990i
$361$	−2.50524	−	4.33920i	−0.131855	−	0.228379i
$362$	2.99140	+	0.288991i	0.157225	+	0.0151890i
$363$			10.6486i			0.558906i
$364$	−2.27597	+	5.29160i	−0.119293	+	0.277355i
$365$		−	8.43236i		−	0.441370i
$366$	−1.82157	+	18.8554i	−0.0952151	+	0.985589i
$367$	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	$0.652611\pi$
$368$	−3.82567	−	27.4724i	−0.199427	−	1.43210i
$369$			7.26999i			0.378461i
$370$	4.09869	−	1.86632i	0.213081	−	0.0970254i
$371$	−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	0.670379	−	0.742019i	$-0.266132\pi$
$373$	7.00993	+	4.04718i	0.362960	+	0.209555i	−0.307418	+	0.951575i	$0.599465\pi$
$374$	0.0134246	−	0.138960i	0.000694169	−	0.00718547i
$375$	−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	$-0.853409\pi$
$379$	−16.2127	−	28.0812i	−0.832789	−	1.44243i	0.0630282	−	0.998012i	$-0.479924\pi$
$380$	18.2502	−	20.9677i	0.936213	−	1.07562i
$381$	−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	$0.565660\pi$
$384$	−1.69697	+	11.1857i	−0.0865980	+	0.570819i
$385$			1.34317i			0.0684544i
$386$	4.13913	+	9.09009i	0.210676	+	0.462673i
$387$	0.928831	−	0.536261i	0.0472151	−	0.0272597i
$388$	−20.0765	−	17.4745i	−1.01923	−	0.887132i
$389$			21.2746i			1.07867i	0.842093	+	0.539333i	$0.181323\pi$
$389$			21.2746i			1.07867i	−0.842093	+	0.539333i	$0.818677\pi$
$390$	10.7068	−	9.72367i	0.542159	−	0.492377i
$391$	−1.15476			−0.0583986
$392$	−17.5010	+	4.18410i	−0.883932	+	0.211329i
$393$	4.33588	+	7.50996i	0.218716	+	0.378828i
$394$	6.77244	−	3.08380i	0.341191	−	0.155360i
$395$	18.5768			0.934698
$396$	1.16368	+	0.226958i	0.0584771	+	0.0114051i
$397$	2.19056	−	3.79416i	0.109941	−	0.190423i	−0.805805	−	0.592181i	$-0.798267\pi$
$397$	2.19056	−	3.79416i	0.109941	−	0.190423i	0.915746	+	0.401757i	$0.131600\pi$
$398$	−26.5515	−	18.9516i	−1.33090	−	0.949958i
$399$	−1.95710	+	3.38980i	−0.0979778	+	0.169702i
$400$	11.2895	+	4.57781i	0.564473	+	0.228890i
$401$	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
$406$	1.09881	−	11.3740i	0.0545332	−	0.564483i
$407$	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	$0.832020\pi$
$410$	12.0852	+	26.5407i	0.596845	+	1.31075i
$411$	4.78451			0.236002
$412$	15.3225	+	2.98843i	0.754887	+	0.147229i
$413$	7.57172	−	4.37154i	0.372580	−	0.215109i
$414$	0.943008	−	9.76125i	0.0463463	−	0.479739i
$415$	−39.8697			−1.95713
$416$	20.0968	+	3.48115i	0.985327	+	0.170678i
$417$	−7.04725			−0.345105
$418$	0.395019	−	4.08891i	0.0193210	−	0.199995i
$419$	13.4526	−	7.76687i	0.657203	−	0.379436i	−0.134008	−	0.990980i	$-0.542785\pi$
$419$	13.4526	−	7.76687i	0.657203	−	0.379436i	0.791210	+	0.611544i	$0.209451\pi$
$420$	−4.44780	−	0.867476i	−0.217030	−	0.0423285i
$421$	−14.6028			−0.711697			−0.355848	−	0.934544i	$-0.615808\pi$
$421$	−14.6028			−0.711697			−0.355848	+	0.934544i	$0.615808\pi$
$422$	−7.22233	−	15.8612i	−0.351577	−	0.772111i
$423$	−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
$426$	−0.478198	+	4.94992i	−0.0231688	+	0.239824i
$427$	−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	$0.236056\pi$
$432$	−1.50310	+	3.70684i	−0.0723181	+	0.178346i
$433$	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
$436$	11.6145	+	2.26523i	0.556232	+	0.108485i
$437$	−33.9788			−1.62543
$438$	3.82623	−	1.74226i	0.182824	−	0.0832482i
$439$	−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	$-0.336938\pi$
$440$	4.62555	−	1.10587i	0.220514	−	0.0527203i
$441$	−6.36190			−0.302948
$442$	0.258937	−	0.808677i	0.0123164	−	0.0384649i
$443$		−	0.675587i		−	0.0320981i	−0.999871	−	0.0160491i	$-0.994891\pi$
$443$		−	0.675587i		−	0.0320981i	0.999871	−	0.0160491i	$-0.00510880\pi$
$444$	1.69371	+	1.47419i	0.0803798	+	0.0699621i
$445$	31.5562	−	18.2190i	1.49591	−	0.863663i
$446$	15.9018	+	34.9225i	0.752973	+	1.65363i
$447$			8.65875i			0.409545i
$448$	−2.89044	−	5.69944i	−0.136560	−	0.269273i
$449$	−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
$452$	−1.52033	+	1.74671i	−0.0715102	+	0.0821583i
$453$	−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	$0.362525\pi$
$458$	−0.405693	+	4.19940i	−0.0189568	+	0.196225i
$459$	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	$-0.658165\pi$
$461$	11.2282	−	19.4479i	0.522951	−	0.905777i	0.999643	−	0.0267070i	$-0.00850212\pi$
$462$	−0.609472	+	0.277520i	−0.0283552	+	0.0129114i
$463$		−	11.1931i		−	0.520189i	−0.965583	−	0.260095i	$-0.916246\pi$
$463$		−	11.1931i		−	0.520189i	0.965583	−	0.260095i	$-0.0837538\pi$
$464$	−40.0739	+	5.58049i	−1.86038	+	0.259068i
$465$	−4.23046	−	7.32738i	−0.196183	−	0.339799i
$466$	2.93117	−	30.3411i	0.135784	−	1.40552i
$467$		−	16.1230i		−	0.746083i	−0.927815	−	0.373041i	$-0.878315\pi$
$467$		−	16.1230i		−	0.746083i	0.927815	−	0.373041i	$-0.121685\pi$
$468$	6.62435	+	2.84920i	0.306211	+	0.131704i
$469$			5.42182i			0.250357i
$470$	−9.50939	−	0.918676i	−0.438635	−	0.0423754i
$471$	−10.1607	−	17.5988i	−0.468180	−	0.810912i
$472$	−21.2885	−	22.4759i	−0.979881	−	1.03454i
$473$		−	0.635793i		−	0.0292338i
$474$	3.83825	+	8.42930i	0.176296	+	0.387171i
$475$	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
$478$	−33.0159	−	3.18958i	−1.51011	−	0.145888i
$479$	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
$484$	−13.9823	+	16.0644i	−0.635561	+	0.730198i
$485$	−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	$0.653025\pi$
$488$	−27.5065	+	26.0533i	−1.24516	+	1.17938i
$489$			9.07718i			0.410484i
$490$	−23.2255	+	10.5756i	−1.04922	+	0.477759i
$491$	−17.8621	+	10.3127i	−0.806106	+	0.465406i	−0.845602	−	0.533814i	$-0.820758\pi$
$491$	−17.8621	+	10.3127i	−0.806106	+	0.465406i	0.0394956	+	0.999220i	$0.487425\pi$
$492$	−9.54600	+	10.9674i	−0.430367	+	0.494451i
$493$			1.68444i			0.0758634i
$494$	7.61923	−	23.7954i	0.342805	−	1.07060i
$495$	1.68147			0.0755763
$496$	4.48362	−	11.0572i	0.201320	−	0.496481i
$497$	−1.40447	−	2.43262i	−0.0629993	−	0.109118i
$498$	−8.23770	−	18.0911i	−0.369140	−	0.810681i
$499$	24.6797			1.10481			0.552407	−	0.833575i	$-0.313709\pi$
$499$	24.6797			1.10481			0.552407	+	0.833575i	$0.313709\pi$
$500$	−10.8823	−	2.12243i	−0.486672	−	0.0949180i
$501$	−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	$0.105666\pi$
$504$	−0.525362	−	2.19745i	−0.0234015	−	0.0978821i
$505$	−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	$0.0330543\pi$
$509$	13.2450	+	22.9411i	0.587076	+	1.01685i	−0.407537	+	0.913189i	$0.633612\pi$
$510$	0.664905	+	0.0642346i	0.0294425	+	0.00284436i
$511$	−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
$514$	27.0272	−	12.3067i	1.19212	−	0.542826i
$515$	22.1404			0.975623
$516$	2.10537	+	0.410621i	0.0926839	+	0.0180766i
$517$	−1.22269	+	0.705921i	−0.0537739	+	0.0310464i
$518$	−1.26243	−	0.121960i	−0.0554681	−	0.00535862i
$519$	−4.51375			−0.198131
$520$	28.9200	−	0.610289i	1.26823	−	0.0267630i
$521$	−12.0965			−0.529958			−0.264979	−	0.964254i	$-0.585365\pi$
$521$	−12.0965			−0.529958			−0.264979	+	0.964254i	$0.585365\pi$
$522$	−14.2387	−	1.37556i	−0.623211	−	0.0602067i
$523$	31.0173	−	17.9079i	1.35629	−	0.783057i	0.367172	−	0.930153i	$-0.380326\pi$
$523$	31.0173	−	17.9079i	1.35629	−	0.783057i	0.989122	+	0.147097i	$0.0469928\pi$
$524$	−3.32004	+	17.0228i	−0.145036	+	0.743644i
$525$	−2.43283			−0.106178
$526$	−22.9433	+	10.4471i	−1.00037	+	0.455516i
$527$	−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
$530$	10.2258	+	0.987890i	0.444182	+	0.0429112i
$531$	−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
$536$	18.6714	−	4.46393i	0.806481	−	0.192812i
$537$	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
$540$	−1.08596	+	5.56803i	−0.0467323	+	0.239610i
$541$	14.5464			0.625398			0.312699	−	0.949852i	$-0.398767\pi$
$541$	14.5464			0.625398			0.312699	+	0.949852i	$0.398767\pi$
$542$	4.20910	+	9.24376i	0.180797	+	0.397053i
$543$	1.06254	+	1.84038i	0.0455981	+	0.0789783i
$544$	0.504891	+	0.795285i	0.0216470	+	0.0340976i
$545$	16.7824			0.718880
$546$	−3.98048	+	0.863887i	−0.170349	+	0.0369710i
$547$		−	19.0401i		−	0.814094i	−0.913407	−	0.407047i	$-0.866559\pi$
$547$		−	19.0401i		−	0.814094i	0.913407	−	0.407047i	$-0.133441\pi$
$548$	7.21787	+	6.28239i	0.308332	+	0.268371i
$549$	−11.6003	+	6.69744i	−0.495089	+	0.285840i
$550$	2.32369	−	1.05808i	0.0990827	−	0.0451168i
$551$			49.5647i			2.11153i
$552$	14.2398	−	13.4875i	0.606087	−	0.574066i
$553$	−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
$556$	−10.6314	−	9.25352i	−0.450872	−	0.392437i
$557$	10.8055	+	18.7157i	0.457843	+	0.793008i	0.998847	−	0.0480126i	$-0.0152888\pi$
$557$	10.8055	+	18.7157i	0.457843	+	0.793008i	−0.541004	+	0.841020i	$0.681955\pi$
$558$	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
$562$	11.9098	+	1.15058i	0.502385	+	0.0485341i
$563$	16.6780	+	9.62908i	0.702896	+	0.405817i	0.808425	−	0.588599i	$-0.200320\pi$
$563$	16.6780	+	9.62908i	0.702896	+	0.405817i	−0.105529	+	0.994416i	$0.533654\pi$
$564$	−1.54793	−	4.50475i	−0.0651797	−	0.189684i
$565$	−1.64209	+	2.84419i	−0.0690833	+	0.119656i
$566$	5.91250	+	12.9846i	0.248521	+	0.545785i
$567$		−	0.798810i		−	0.0335469i
$568$	−7.22099	+	6.83950i	−0.302986	+	0.286979i
$569$	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	$0.808710\pi$
$570$	19.5649	+	1.89011i	0.819481	+	0.0791679i
$571$		−	17.9486i		−	0.751124i	−0.926797	−	0.375562i	$-0.877450\pi$
$571$		−	17.9486i		−	0.751124i	0.926797	−	0.375562i	$-0.122550\pi$
$572$	3.42619	−	2.55632i	0.143256	−	0.106885i
$573$			15.7765i			0.659074i
$574$	0.789742	−	8.17476i	0.0329632	−	0.341208i
$575$	−10.5596	−	18.2897i	−0.440365	−	0.762735i
$576$	−7.13491	+	3.61843i	−0.297288	+	0.150768i
$577$			13.2639i			0.552182i	0.961132	+	0.276091i	$0.0890391\pi$
$577$			13.2639i			0.552182i	−0.961132	+	0.276091i	$0.910961\pi$
$578$	−21.8444	+	9.94675i	−0.908607	+	0.413730i
$579$	−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
$582$	1.80977	−	18.7333i	0.0750175	−	0.776520i
$583$	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	$0.108786\pi$
$587$	18.4456	+	31.9486i	0.761330	+	1.31866i	−0.180836	+	0.983513i	$0.557880\pi$
$588$	−9.59751	−	8.35362i	−0.395795	−	0.344498i
$589$	−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
$592$	0.619393	+	4.44791i	0.0254569	+	0.182808i
$593$			27.8239i			1.14259i	0.820745	+	0.571295i	$0.193559\pi$
$593$			27.8239i			1.14259i	−0.820745	+	0.571295i	$0.806441\pi$
$594$	0.347417	+	0.762975i	0.0142547	+	0.0313052i
$595$	−0.326765	+	0.188658i	−0.0133961	+	0.00773422i
$596$	−11.3695	+	13.0625i	−0.465714	+	0.535061i
$597$		−	23.0667i		−	0.944056i
$598$	−23.7717	−	26.1751i	−0.972095	−	1.07038i
$599$	31.0169			1.26732			0.633658	−	0.773613i	$-0.281553\pi$
$599$	31.0169			1.26732			0.633658	+	0.773613i	$0.281553\pi$
$600$	2.00302	+	8.37807i	0.0817728	+	0.342033i
$601$	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	$0.567909\pi$
$602$	−1.10268	+	0.502101i	−0.0449419	+	0.0204641i
$603$	6.78737			0.276403
$604$	5.24358	−	26.8854i	0.213358	−	1.09395i
$605$	−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	$-0.0536054\pi$
$608$	14.8565	+	23.4013i	0.602509	+	0.949048i
$609$	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	$0.176514\pi$
$613$	21.8144	+	37.7837i	0.881077	+	1.52607i	0.0309319	+	0.999521i	$0.490152\pi$
$614$	4.34375	−	44.9629i	0.175299	−	1.81456i
$615$	−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	$0.686232\pi$
$618$	4.57455	+	10.0463i	0.184015	+	0.404123i
$619$	22.2751			0.895311			0.447655	−	0.894206i	$-0.352259\pi$
$619$	22.2751			0.895311			0.447655	+	0.894206i	$0.352259\pi$
$620$	3.23932	−	16.6089i	0.130094	−	0.667030i
$621$	6.00535	−	3.46719i	0.240986	−	0.139134i
$622$	−1.15446	+	11.9500i	−0.0462896	+	0.479152i
$623$	−10.2617			−0.411127
$624$	6.25224	+	12.9965i	0.250290	+	0.520277i
$625$	−30.9524			−1.23809
$626$	3.24323	−	33.5713i	0.129626	−	1.34178i
$627$	2.51560	−	1.45238i	0.100463	−	0.0580025i
$628$	7.78017	−	39.8912i	0.310463	−	1.59183i
$629$	0.186960			0.00745460
$630$	−1.32789	−	2.91623i	−0.0529046	−	0.116186i
$631$	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
$634$	0.0357269	−	0.369816i	0.00141890	−	0.0146873i
$635$	−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
$640$	−20.0325	+	25.0705i	−0.791855	+	0.991000i
$641$	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	−0.983272	−	0.182141i	$-0.941697\pi$
$643$	−8.46678	+	14.6649i	−0.333897	+	0.578327i	0.649375	+	0.760468i	$0.275030\pi$
$644$	−2.12074	+	10.8736i	−0.0835688	+	0.428481i
$645$	3.04218			0.119786
$646$	1.05023	−	0.478217i	0.0413207	−	0.0188152i
$647$	−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	$0.995000\pi$
$648$	−2.75090	+	0.657681i	−0.108066	+	0.0258362i
$649$	−6.48829			−0.254688
$650$	15.1761	−	3.29369i	0.595257	−	0.129189i
$651$			2.38278i			0.0933884i
$652$	−11.9190	+	13.6938i	−0.466783	+	0.536289i
$653$	−14.4460	+	8.34043i	−0.565317	+	0.326386i	−0.755277	−	0.655406i	$-0.772498\pi$
$653$	−14.4460	+	8.34043i	−0.565317	+	0.326386i	0.189960	+	0.981792i	$0.439164\pi$
$654$	3.46751	+	7.61511i	0.135590	+	0.297775i
$655$			24.5972i			0.961092i
$656$	−28.8020	+	4.01082i	−1.12453	+	0.156596i
$657$	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	0.546844	−	0.837234i	$-0.315829\pi$
$659$	2.44389	+	1.41098i	0.0952006	+	0.0549641i	−0.451644	+	0.892198i	$0.649162\pi$
$660$	2.53665	+	2.20788i	0.0987388	+	0.0859418i
$661$	−6.31822	−	10.9435i	−0.245750	−	0.425652i	0.716592	−	0.697492i	$-0.245701\pi$
$661$	−6.31822	−	10.9435i	−0.245750	−	0.425652i	−0.962342	+	0.271841i	$0.912368\pi$
$662$	−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
$666$	−0.152677	+	1.58039i	−0.00591612	+	0.0612389i
$667$	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
$670$	24.7788	−	11.2829i	0.957289	−	0.435897i
$671$			7.94051i			0.306540i
$672$	2.09284	−	4.00489i	0.0807332	−	0.154492i
$673$	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	$0.474422\pi$
$674$	−3.88548	+	40.2193i	−0.149663	+	1.54919i
$675$			3.04557i			0.117224i
$676$	23.6609	−	10.7779i	0.910033	−	0.414536i
$677$		−	40.9956i		−	1.57559i	−0.615938	−	0.787795i	$-0.711223\pi$
$677$		−	40.9956i		−	1.57559i	0.615938	−	0.787795i	$-0.288777\pi$
$678$	−1.62985	−	0.157455i	−0.0625939	−	0.00604703i
$679$	5.31533	+	9.20642i	0.203984	+	0.353310i
$680$	0.918725	+	0.969970i	0.0352315	+	0.0371967i
$681$			10.3198i			0.395455i
$682$	−1.03631	−	2.27588i	−0.0396825	−	0.0871480i
$683$	−0.260068	+	0.450451i	−0.00995123	+	0.0172360i	−0.870958	−	0.491357i	$-0.836501\pi$
$683$	−0.260068	+	0.450451i	−0.00995123	+	0.0172360i	0.861007	+	0.508593i	$0.169834\pi$
$684$	3.18476	+	9.26818i	0.121772	+	0.354378i
$685$	11.7529	+	6.78556i	0.449057	+	0.259263i
$686$	15.0248	+	1.45151i	0.573651	+	0.0554189i
$687$	−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	$-0.982160\pi$
$691$	−14.3980	−	24.9381i	−0.547727	−	0.948691i	0.450703	−	0.892674i	$-0.351173\pi$
$692$	−6.80940	−	5.92686i	−0.258855	−	0.225306i
$693$	−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
$696$	−19.6742	−	20.7716i	−0.745747	−	0.787344i
$697$			1.21065i			0.0458565i
$698$	15.7615	−	7.17695i	0.596583	−	0.271652i
$699$	18.6665	−	10.7771i	0.706034	−	0.407629i
$700$	−3.67015	−	3.19448i	−0.138719	−	0.120740i
$701$		−	31.8042i		−	1.20123i	−0.799539	−	0.600614i	$-0.794923\pi$
$701$		−	31.8042i		−	1.20123i	0.799539	−	0.600614i	$-0.205077\pi$
$702$	1.08147	+	4.98301i	0.0408174	+	0.188072i
$703$	5.50132			0.207486
$704$	−0.257159	+	4.73544i	−0.00969203	+	0.178474i
$705$	−3.37773	−	5.85040i	−0.127213	−	0.220339i
$706$	11.5949	+	25.4640i	0.436381	+	0.958352i
$707$	12.5503			0.472004
$708$	4.19040	−	21.4854i	0.157485	−	0.807471i
$709$	−0.0624691	+	0.108200i	−0.00234608	+	0.00406352i	−0.867196	−	0.497967i	$-0.834080\pi$
$709$	−0.0624691	+	0.108200i	−0.00234608	+	0.00406352i	0.864850	+	0.502030i	$0.167413\pi$
$710$	−8.19483	+	11.4811i	−0.307546	+	0.430877i
$711$	−3.27462	+	5.67181i	−0.122808	+	0.212710i
$712$	8.44873	+	35.3387i	0.316630	+	1.32438i
$713$	−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
$718$	34.1370	+	3.29789i	1.27398	+	0.123076i
$719$	−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
$722$	6.44880	−	2.93643i	0.240000	−	0.109283i
$723$	26.8901			1.00006
$724$	−0.813603	+	4.17158i	−0.0302373	+	0.155035i
$725$	−26.6791	+	15.4032i	−0.990838	+	0.572061i
$726$	−14.9896	−	1.44810i	−0.556316	−	0.0537442i
$727$	−26.0065			−0.964526			−0.482263	−	0.876026i	$-0.660185\pi$
$727$	−26.0065			−0.964526			−0.482263	+	0.876026i	$0.660185\pi$
$728$	−7.13927	−	3.92340i	−0.264599	−	0.145411i
$729$	−1.00000			−0.0370370
$730$	11.8699	+	1.14672i	0.439324	+	0.0424419i
$731$	0.154675	−	0.0893016i	0.00572086	−	0.00330294i
$732$	−26.2943	−	5.12831i	−0.971866	−	0.189548i
$733$	−5.53151			−0.204311			−0.102155	−	0.994768i	$-0.532574\pi$
$733$	−5.53151			−0.204311			−0.102155	+	0.994768i	$0.532574\pi$
$734$	−26.5177	+	12.0747i	−0.978787	+	0.445686i
$735$	−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
$738$	−10.2337	−	0.988648i	−0.376707	−	0.0363926i
$739$	−11.3146	−	19.5975i	−0.416215	−	0.720906i	0.579340	−	0.815086i	$-0.303310\pi$
$739$	−11.3146	−	19.5975i	−0.416215	−	0.720906i	−0.995555	+	0.0941803i	$0.969977\pi$
$740$	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	$0.617873\pi$
$744$	8.20568	−	1.96180i	0.300835	−	0.0719231i
$745$	−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
$748$	0.193783	+	0.0377945i	0.00708542	+	0.00138190i
$749$	−12.5138			−0.457243
$750$	−3.24892	−	7.13507i	−0.118634	−	0.260536i
$751$	−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	$-0.433634\pi$
$752$	3.57985	−	8.82837i	0.130544	−	0.321937i
$753$	29.0855			1.05993
$754$	−38.1815	+	34.6756i	−1.39049	+	1.26281i
$755$		−	38.8482i		−	1.41383i
$756$	1.04889	−	1.20508i	0.0381479	−	0.0438283i
$757$	−17.0025	+	9.81641i	−0.617967	+	0.356783i	−0.776077	−	0.630638i	$-0.782793\pi$
$757$	−17.0025	+	9.81641i	−0.617967	+	0.356783i	0.158110	+	0.987421i	$0.449460\pi$
$758$	41.7335	−	19.0032i	1.51583	−	0.690226i
$759$		−	4.11072i		−	0.149210i
$760$	27.0335	+	28.5414i	0.980609	+	1.03531i
$761$	−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
$764$	−20.7157	+	23.8003i	−0.749467	+	0.861066i
$765$	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	$0.244053\pi$
$770$	−1.89073	−	0.182658i	−0.0681372	−	0.00658255i
$771$	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	$-0.446770\pi$
$773$	26.0560	−	45.1303i	0.937169	−	1.62322i	0.770719	−	0.637175i	$-0.219897\pi$
$774$	0.628561	+	1.38040i	0.0225931	+	0.0496176i
$775$		−	9.08465i		−	0.326330i
$776$	27.3283	−	25.8845i	0.981030	−	0.929201i
$777$	−0.448415	−	0.776678i	−0.0160868	−	0.0278632i
$778$	−29.9474	−	2.89314i	−1.07367	−	0.103724i
$779$			35.6233i			1.27634i
$780$	12.2316	+	16.3938i	0.437961	+	0.586993i
$781$			2.08454i			0.0745907i
$782$	0.157036	−	1.62551i	0.00561559	−	0.0581280i
$783$	−5.05758	−	8.75998i	−0.180743	−	0.313056i
$784$	−3.50984	−	25.2044i	−0.125351	−	0.900157i
$785$		−	57.6411i		−	2.05730i
$786$	−11.1611	+	5.08216i	−0.398104	+	0.181275i
$787$	−9.95043	+	17.2346i	−0.354694	+	0.614349i	−0.987066	−	0.160317i	$-0.948748\pi$
$787$	−9.95043	+	17.2346i	−0.354694	+	0.614349i	0.632371	+	0.774666i	$0.282082\pi$
$788$	3.41996	+	9.95266i	0.121831	+	0.354549i
$789$	−15.4378	−	8.91302i	−0.549601	−	0.317312i
$790$	−2.52626	+	26.1498i	−0.0898802	+	0.930367i
$791$	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
$796$	30.2882	−	34.7982i	1.07354	−	1.23339i
$797$	−39.5306	−	22.8230i	−1.40025	−	0.808433i	−0.405829	−	0.913949i	$-0.633017\pi$
$797$	−39.5306	−	22.8230i	−1.40025	−	0.808433i	−0.994418	+	0.105516i	$0.966351\pi$
$798$	−4.50554	−	3.21592i	−0.159495	−	0.113842i
$799$	−0.343471	−	0.198303i	−0.0121511	−	0.00701546i
$800$	−7.97925	+	15.2692i	−0.282109	+	0.539847i
$801$			12.8462i			0.453900i
$802$	12.0537	+	26.4715i	0.425630	+	0.934742i
$803$	1.52620	−	0.881151i	0.0538584	−	0.0310952i
$804$	10.2394	+	8.91229i	0.361115	+	0.314312i
$805$			15.7119i			0.553773i
$806$	−3.22592	−	14.8639i	−0.113628	−	0.523557i
$807$	−1.95885			−0.0689549
$808$	−10.3330	−	43.2202i	−0.363514	−	1.52048i
$809$	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	$0.798391\pi$
$810$	−3.65072	+	1.66234i	−0.128273	+	0.0584087i
$811$	−49.5256			−1.73908			−0.869539	−	0.493865i	$-0.835584\pi$
$811$	−49.5256			−1.73908			−0.869539	+	0.493865i	$0.835584\pi$
$812$	15.8613	+	3.09351i	0.556623	+	0.108561i
$813$	−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
$816$	−0.250306	+	0.617287i	−0.00876248	+	0.0216094i
$817$	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	0.997225	−	0.0744410i	$-0.0237172\pi$
$821$	12.4396	+	21.5460i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$822$	−0.650646	+	6.73496i	−0.0226939	+	0.234909i
$823$	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
$826$	5.12396	+	11.2529i	0.178285	+	0.391538i
$827$	−17.8051			−0.619145			−0.309573	−	0.950876i	$-0.600186\pi$
$827$	−17.8051			−0.619145			−0.309573	+	0.950876i	$0.600186\pi$
$828$	13.6123	+	2.65487i	0.473060	+	0.0922631i
$829$	−41.4103	+	23.9082i	−1.43824	+	0.830367i	−0.997727	−	0.0673800i	$-0.978536\pi$
$829$	−41.4103	+	23.9082i	−1.43824	+	0.830367i	−0.440511	+	0.897747i	$0.645203\pi$
$830$	5.42189	−	56.1230i	0.188197	−	1.94806i
$831$	21.0440			0.730009
$832$	−7.63325	+	27.8161i	−0.264635	+	0.964349i
$833$	−1.05942			−0.0367069
$834$	0.958357	−	9.92013i	0.0331852	−	0.343506i
$835$	−48.4627	+	27.9800i	−1.67712	+	0.968287i
$836$	5.70208	+	1.11210i	0.197211	+	0.0384630i
$837$	2.98291			0.103104
$838$	9.10368	+	19.9929i	0.314482	+	0.690644i
$839$	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
$842$	1.98584	−	20.5558i	0.0684365	−	0.708399i
$843$	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
$848$	−3.84956	+	9.49350i	−0.132194	+	0.326008i
$849$	−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
$852$	−6.90277	−	1.34628i	−0.236485	−	0.0461228i
$853$	44.3484			1.51846			0.759230	−	0.650823i	$-0.225576\pi$
$853$	44.3484			1.51846			0.759230	+	0.650823i	$0.225576\pi$
$854$	13.7715	−	6.27081i	0.471253	−	0.214583i
$855$	6.94942	+	12.0368i	0.237665	+	0.411648i
$856$	10.3029	+	43.0942i	0.352146	+	1.47293i
$857$	−25.5122			−0.871481			−0.435740	−	0.900072i	$-0.643513\pi$
$857$	−25.5122			−0.871481			−0.435740	+	0.900072i	$0.643513\pi$
$858$	2.87874	+	0.921765i	0.0982785	+	0.0314686i
$859$		−	39.0387i		−	1.33198i	−0.745959	−	0.665992i	$-0.768008\pi$
$859$		−	39.0387i		−	1.33198i	0.745959	−	0.665992i	$-0.231992\pi$
$860$	4.58940	+	3.99459i	0.156497	+	0.136214i
$861$	5.02931	−	2.90367i	0.171398	−	0.0989569i
$862$	7.32132	+	16.0786i	0.249365	+	0.547640i
$863$			16.7250i			0.569324i	0.958628	+	0.284662i	$0.0918814\pi$
$863$			16.7250i			0.569324i	−0.958628	+	0.284662i	$0.908119\pi$
$864$	−5.01357	−	2.61995i	−0.170565	−	0.0891326i
$865$	−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
$868$	−3.12875	+	3.59464i	−0.106197	+	0.122010i
$869$	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
$874$	4.62079	−	47.8306i	0.156300	−	1.61789i
$875$	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	$0.334290\pi$
$877$	−14.8841	+	25.7800i	−0.502601	+	0.870530i	−0.999995	+	0.00300555i	$0.999043\pi$
$878$	27.4942	−	12.5193i	0.927883	−	0.422507i
$879$		−	3.04531i		−	0.102716i
$880$	0.927659	+	6.66159i	0.0312714	+	0.224562i
$881$	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	$0.567532\pi$
$882$	0.865157	−	8.95540i	0.0291313	−	0.301544i
$883$		−	11.8178i		−	0.397702i	−0.980030	−	0.198851i	$-0.936279\pi$
$883$		−	11.8178i		−	0.397702i	0.980030	−	0.198851i	$-0.0637210\pi$
$884$	1.10313	+	0.474467i	0.0371023	+	0.0159581i
$885$		−	31.0455i		−	1.04358i
$886$	0.950997	+	0.0918733i	0.0319494	+	0.00308654i
$887$	−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	$-0.443194\pi$
$888$	−2.30549	+	2.18369i	−0.0773672	+	0.0732798i
$889$			0.966203i			0.0324054i
$890$	21.3548	+	46.8981i	0.715815	+	1.57203i
$891$	−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
$894$	−12.1886	−	1.17750i	−0.407647	−	0.0393817i
$895$	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
$900$	−3.99905	+	4.59452i	−0.133302	+	0.153151i
$901$	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
$904$	−2.25202	−	2.37764i	−0.0749012	−	0.0790791i
$905$			6.02775i			0.200369i
$906$	17.6276	−	8.02664i	0.585637	−	0.266667i
$907$	6.77932	−	3.91404i	0.225104	−	0.129964i	−0.383208	−	0.923662i	$-0.625181\pi$
$907$	6.77932	−	3.91404i	0.225104	−	0.129964i	0.608311	+	0.793699i	$0.291847\pi$
$908$	−13.5506	+	15.5683i	−0.449692	+	0.516653i
$909$		−	15.7113i		−	0.521110i
$910$	−11.0031	−	3.52316i	−0.364748	−	0.116792i
$911$	13.0076			0.430963			0.215481	−	0.976508i	$-0.430868\pi$
$911$	13.0076			0.430963			0.215481	+	0.976508i	$0.430868\pi$
$912$	−7.36528	+	18.1637i	−0.243889	+	0.601460i
$913$	−4.16624	−	7.21614i	−0.137882	−	0.238819i
$914$	−2.29475	−	5.03958i	−0.0759036	−	0.166695i
$915$	−37.9942			−1.25605
$916$	−5.85616	−	1.14216i	−0.193493	−	0.0377379i
$917$	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	$-0.0431760\pi$
$920$	54.1080	−	12.9361i	1.78389	−	0.426489i
$921$	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
$926$	15.7561	+	1.52216i	0.517779	+	0.0500212i
$927$	−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	$0.404785\pi$
$930$	10.8898	−	4.95860i	0.357089	−	0.162599i
$931$	−31.1736			−1.02167
$932$	42.3113	+	8.25218i	1.38595	+	0.270309i
$933$	−7.35193	+	4.24464i	−0.240691	+	0.138963i
$934$	22.6957	+	2.19257i	0.742625	+	0.0717430i
$935$	0.280009			0.00915726
$936$	−4.91155	+	8.93737i	−0.160539	+	0.292127i
$937$	0.432775			0.0141382			0.00706908	−	0.999975i	$-0.497750\pi$
$937$	0.432775			0.0141382			0.00706908	+	0.999975i	$0.497750\pi$
$938$	−7.63208	−	0.737315i	−0.249196	−	0.0240742i
$939$	20.6538	−	11.9245i	0.674012	−	0.389141i
$940$	2.58637	−	13.2611i	0.0843580	−	0.432528i
$941$	−9.49891			−0.309656			−0.154828	−	0.987941i	$-0.549482\pi$
$941$	−9.49891			−0.309656			−0.154828	+	0.987941i	$0.549482\pi$
$942$	26.1549	−	11.9095i	0.852174	−	0.388034i
$943$	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
$946$	0.894981	+	0.0864617i	0.0290983	+	0.00281111i
$947$	−26.2258	−	45.4244i	−0.852224	−	1.47609i	−0.879197	−	0.476458i	$-0.841920\pi$
$947$	−26.2258	−	45.4244i	−0.852224	−	1.47609i	0.0269736	−	0.999636i	$-0.491413\pi$
$948$	−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
$952$	−0.0874867	−	0.365933i	−0.00283546	−	0.0118600i
$953$	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
$956$	8.97969	−	46.0415i	0.290424	−	1.48909i
$957$	−5.99629			−0.193832
$958$	10.6766	+	23.4473i	0.344945	+	0.757546i
$959$	−1.91096	−	3.30988i	−0.0617080	−	0.106881i
$960$	−22.6584	−	1.23047i	−0.731296	−	0.0397131i
$961$	22.1023			0.712976
$962$	3.84874	+	4.23787i	0.124088	+	0.136634i
$963$			15.6655i			0.504814i
$964$	40.5662	+	35.3086i	1.30655	+	1.13721i
$965$	−17.3491	+	10.0165i	−0.558487	+	0.322443i
$966$	−7.12938	+	3.24633i	−0.229384	+	0.104449i
$967$		−	23.1920i		−	0.745805i	−0.927871	−	0.372902i	$-0.878363\pi$
$967$		−	23.1920i		−	0.745805i	0.927871	−	0.372902i	$-0.121637\pi$
$968$	−20.7117	−	21.8670i	−0.665699	−	0.702831i
$969$	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	0.0485305	−	0.998822i	$-0.484546\pi$
$971$	−24.6859	−	14.2524i	−0.792209	−	0.457382i	−0.840740	+	0.541439i	$0.817880\pi$
$972$	−1.50859	−	1.31307i	−0.0483881	−	0.0421167i
$973$	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	$0.547848\pi$
$978$	−12.7776	−	1.23441i	−0.408582	−	0.0394720i
$979$	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
$982$	−12.0877	−	26.5462i	−0.385734	−	0.847124i
$983$			1.48214i			0.0472730i	0.999721	+	0.0236365i	$0.00752443\pi$
$983$			1.48214i			0.0472730i	−0.999721	+	0.0236365i	$0.992476\pi$
$984$	−14.1403	−	14.9290i	−0.450775	−	0.475919i
$985$	7.46266	+	12.9257i	0.237780	+	0.411847i
$986$	−2.37112	−	0.229067i	−0.0755118	−	0.00729499i
$987$			1.90248i			0.0605566i
$988$	32.4597	+	13.9612i	1.03268	+	0.444166i
$989$		−	7.43727i		−	0.236492i
$990$	−0.228663	+	2.36693i	−0.00726739	+	0.0752261i
$991$	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	$0.708155\pi$
$992$	14.9550	+	7.81507i	0.474822	+	0.248129i
$993$		−	31.4245i		−	0.997225i
$994$	3.61530	−	1.64621i	0.114670	−	0.0522146i
$995$	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	0.248579	−	0.968612i	$-0.420036\pi$
$997$	−14.7133	−	8.49471i	−0.465974	−	0.269030i	−0.714553	+	0.699581i	$0.753370\pi$
$998$	−3.35619	+	34.7406i	−0.106238	+	1.09969i
$999$	−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.205.12	yes	48
3.2	odd	2		936.2.dg.e.829.13		48
4.3	odd	2		1248.2.ca.b.49.14		48
8.3	odd	2		1248.2.ca.b.49.11		48
8.5	even	2	inner	312.2.bk.b.205.3	✓	48
13.4	even	6	inner	312.2.bk.b.277.3	yes	48
24.5	odd	2		936.2.dg.e.829.22		48
39.17	odd	6		936.2.dg.e.901.22		48
52.43	odd	6		1248.2.ca.b.433.11		48
104.43	odd	6		1248.2.ca.b.433.14		48
104.69	even	6	inner	312.2.bk.b.277.12	yes	48
312.173	odd	6		936.2.dg.e.901.13		48

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

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+(-0.135990 + 1.40766i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.96301 - 0.382856i) q^{4} -2.83647 q^{5} +(-0.586059 - 1.28706i) q^{6} +(0.691790 + 0.399405i) q^{7} +(0.805882 - 2.71119i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.385732 - 3.99279i) 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} +(3.70684 + 1.50310i) q^{16} +(0.0832632 - 0.144216i) q^{17} +(1.15107 + 0.821601i) q^{18} +(2.45002 - 4.24357i) q^{19} +(5.56803 + 1.08596i) q^{20} -0.798810 q^{21} +(0.762975 - 0.347417i) q^{22} +(-3.46719 - 6.00535i) q^{23} +(0.657681 + 2.75090i) q^{24} +3.04557 q^{25} +(4.98301 - 1.08147i) q^{26} +1.00000i q^{27} +(-1.20508 - 1.04889i) q^{28} +(-8.75998 + 5.05758i) q^{29} +(1.66234 + 3.65072i) q^{30} -2.98291i q^{31} +(-2.61995 + 5.01357i) q^{32} +(0.513382 + 0.296401i) q^{33} +(0.191684 + 0.136818i) q^{34} +(-1.96224 - 1.13290i) q^{35} +(-1.31307 + 1.50859i) 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} +(0.108630 - 1.12445i) q^{42} +(0.928831 + 0.536261i) q^{43} +(0.385288 + 1.12125i) q^{44} +(-1.41824 + 2.45646i) q^{45} +(8.92500 - 4.06396i) q^{46} -2.38164i q^{47} +(-3.96177 + 0.551696i) q^{48} +(-3.18095 - 5.50957i) q^{49} +(-0.414168 + 4.28713i) q^{50} +0.166526i q^{51} +(0.844697 + 7.16146i) q^{52} +2.56107i q^{53} +(-1.40766 - 0.135990i) q^{54} +(0.840734 + 1.45619i) q^{55} +(1.64036 - 1.55370i) q^{56} +4.90005i q^{57} +(-5.92808 - 13.0189i) q^{58} +(5.47256 - 9.47875i) q^{59} +(-5.36504 + 1.84355i) q^{60} +(-11.6003 - 6.69744i) q^{61} +(4.19892 + 0.405646i) 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} +(-0.218661 + 0.251220i) q^{68} +(6.00535 + 3.46719i) q^{69} +(1.86159 - 2.60811i) q^{70} +(-3.04531 - 1.75821i) q^{71} +(-1.94502 - 2.05351i) q^{72} +2.97283i q^{73} +(-1.44500 + 0.657973i) q^{74} +(-2.63754 + 1.52279i) q^{75} +(-6.43410 + 7.39217i) q^{76} -0.473537i q^{77} +(-3.77468 + 3.42809i) q^{78} -6.54925 q^{79} +(-10.5144 - 4.26351i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.26064 - 9.35695i) q^{82} +14.0561 q^{83} +(1.56808 + 0.305829i) q^{84} +(-0.236174 + 0.409065i) q^{85} +(-0.881184 + 1.23455i) q^{86} +(5.05758 - 8.75998i) q^{87} +(-1.63074 + 0.389875i) 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} +(3.35254 + 0.323880i) q^{94} +(-6.94942 + 12.0368i) q^{95} +(-0.237838 - 5.65185i) q^{96} +(11.5252 + 6.65406i) q^{97} +(8.18818 - 3.72845i) 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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