LMFDB - Embedded newform 140.2.w.b.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809319 + 1.15974i) q^{2} +(-0.551941 - 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(1.08510 - 1.95513i) q^{5} +(0.618214 - 0.520418i) q^{6} +(2.54158 + 0.735093i) q^{7} +(2.73551 + 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +O(q^{10})$	\(q+(-0.809319 + 1.15974i) q^{2} +(-0.551941 - 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(1.08510 - 1.95513i) q^{5} +(0.618214 - 0.520418i) q^{6} +(2.54158 + 0.735093i) q^{7} +(2.73551 + 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +(1.38926 + 2.84077i) q^{10} +(3.42960 - 1.98008i) q^{11} +(0.103218 + 1.13815i) q^{12} +(2.04987 + 2.04987i) q^{13} +(-2.90947 + 2.35266i) q^{14} +(-0.888062 + 0.918641i) q^{15} +(-3.04779 + 2.59056i) q^{16} +(0.580528 + 0.155552i) q^{17} +(3.42410 - 1.60331i) q^{18} +(-1.00269 + 1.73671i) q^{19} +(-4.41891 - 0.687909i) q^{20} +(-1.29409 - 0.781608i) q^{21} +(-0.479259 + 5.57997i) q^{22} +(-0.640717 - 2.39119i) q^{23} +(-1.40350 - 0.801422i) q^{24} +(-2.64510 - 4.24305i) q^{25} +(-4.03632 + 0.718322i) q^{26} +(2.29237 + 2.29237i) q^{27} +(-0.373784 - 5.27828i) q^{28} -7.25964i q^{29} +(-0.346661 - 1.77340i) q^{30} +(-2.83005 + 1.63393i) q^{31} +(-0.537745 - 5.63124i) q^{32} +(-2.18578 + 0.585677i) q^{33} +(-0.650233 + 0.547372i) q^{34} +(4.19508 - 4.17148i) q^{35} +(-0.911768 + 5.26867i) q^{36} +(2.49187 + 9.29977i) q^{37} +(-1.20264 - 2.56841i) q^{38} +(-0.828248 - 1.43457i) q^{39} +(4.37411 - 4.56806i) q^{40} -3.35439 q^{41} +(1.95380 - 0.868240i) q^{42} +(-3.31777 + 3.31777i) q^{43} +(-6.08345 - 5.07179i) q^{44} +(-5.12586 + 3.07624i) q^{45} +(3.29171 + 1.19217i) q^{46} +(-12.1147 + 3.24611i) q^{47} +(2.06532 - 0.979091i) q^{48} +(5.91928 + 3.73660i) q^{49} +(7.06157 + 0.366343i) q^{50} +(-0.297413 - 0.171711i) q^{51} +(2.43360 - 5.26244i) q^{52} +(-0.779134 + 2.90777i) q^{53} +(-4.51381 + 0.803298i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(6.42396 + 3.83832i) q^{56} +(0.810271 - 0.810271i) q^{57} +(8.41932 + 5.87537i) q^{58} +(7.41735 + 12.8472i) q^{59} +(2.33724 + 1.03321i) q^{60} +(-2.11676 + 3.66633i) q^{61} +(0.395476 - 4.60450i) q^{62} +(-4.90192 - 5.09941i) q^{63} +(6.96599 + 3.93382i) q^{64} +(6.23209 - 1.78345i) q^{65} +(1.08976 - 3.00894i) q^{66} +(0.984566 - 3.67445i) q^{67} +(-0.108564 - 1.19710i) q^{68} +1.41455i q^{69} +(1.44268 + 8.24128i) q^{70} -4.86004i q^{71} +(-5.37238 - 5.32145i) q^{72} +(-2.53197 + 9.44944i) q^{73} +(-12.8021 - 4.63656i) q^{74} +(0.832427 + 2.73310i) q^{75} +(3.95201 + 0.683915i) q^{76} +(10.1722 - 2.51146i) q^{77} +(2.33405 + 0.200469i) q^{78} +(3.45719 - 5.98803i) q^{79} +(1.75772 + 8.76986i) q^{80} +(3.08400 + 5.34165i) q^{81} +(2.71477 - 3.89023i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(-0.574310 + 2.96858i) q^{84} +(0.934058 - 0.966221i) q^{85} +(-1.16262 - 6.53289i) q^{86} +(-1.07364 + 4.00690i) q^{87} +(10.8054 - 2.95054i) q^{88} +(3.35292 + 1.93581i) q^{89} +(0.580822 - 8.43434i) q^{90} +(3.70307 + 6.71676i) q^{91} +(-4.04665 + 2.85269i) q^{92} +(1.80367 - 0.483291i) q^{93} +(6.03997 - 16.6770i) q^{94} +(2.30748 + 3.84490i) q^{95} +(-0.536012 + 3.18764i) q^{96} +(1.11914 - 1.11914i) q^{97} +(-9.12407 + 3.84074i) q^{98} -10.5874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.809319	+	1.15974i	−0.572275	+	0.820062i
$2$	−0.809319	+	1.15974i	−0.572275	+	0.820062i
$3$	−0.551941	−	0.147892i	−0.318663	−	0.0853856i	0.0959419	−	0.995387i	$-0.469414\pi$
$3$	−0.551941	−	0.147892i	−0.318663	−	0.0853856i	−0.414605	+	0.910001i	$0.636080\pi$
$4$	−0.690004	−	1.87720i	−0.345002	−	0.938602i
$5$	1.08510	−	1.95513i	0.485273	−	0.874363i
$5$	1.08510	−	1.95513i	0.485273	−	0.874363i
$6$	0.618214	−	0.520418i	0.252385	−	0.212460i
$7$	2.54158	+	0.735093i	0.960628	+	0.277839i
$7$	2.54158	+	0.735093i	0.960628	+	0.277839i
$8$	2.73551	+	0.719030i	0.967148	+	0.254216i
$9$	−2.31531	−	1.33674i	−0.771770	−	0.445581i
$10$	1.38926	+	2.84077i	0.439322	+	0.898330i
$11$	3.42960	−	1.98008i	1.03406	−	0.597017i	0.115917	−	0.993259i	$-0.463019\pi$
$11$	3.42960	−	1.98008i	1.03406	−	0.597017i	0.918146	+	0.396242i	$0.129686\pi$
$12$	0.103218	+	1.13815i	0.0297965	+	0.328556i
$13$	2.04987	+	2.04987i	0.568532	+	0.568532i	0.931717	−	0.363185i	$-0.118311\pi$
$13$	2.04987	+	2.04987i	0.568532	+	0.568532i	−0.363185	+	0.931717i	$0.618311\pi$
$14$	−2.90947	+	2.35266i	−0.777588	+	0.628774i
$15$	−0.888062	+	0.918641i	−0.229297	+	0.237192i
$16$	−3.04779	+	2.59056i	−0.761947	+	0.647639i
$17$	0.580528	+	0.155552i	0.140799	+	0.0377269i	0.328530	−	0.944493i	$-0.393447\pi$
$17$	0.580528	+	0.155552i	0.140799	+	0.0377269i	−0.187731	+	0.982220i	$0.560113\pi$
$18$	3.42410	−	1.60331i	0.807069	−	0.377904i
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	−0.957817	−	0.287377i	$-0.907217\pi$
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	0.727785	+	0.685805i	$0.240550\pi$
$20$	−4.41891	−	0.687909i	−0.988099	−	0.153821i
$21$	−1.29409	−	0.781608i	−0.282393	−	0.170561i
$22$	−0.479259	+	5.57997i	−0.102178	+	1.18965i
$23$	−0.640717	−	2.39119i	−0.133599	−	0.498597i	0.866401	−	0.499349i	$-0.166427\pi$
$23$	−0.640717	−	2.39119i	−0.133599	−	0.498597i	−1.00000		0.000751542i	$0.999761\pi$
$24$	−1.40350	−	0.801422i	−0.286488	−	0.163590i
$25$	−2.64510	−	4.24305i	−0.529020	−	0.848609i
$26$	−4.03632	+	0.718322i	−0.791588	+	0.140874i
$27$	2.29237	+	2.29237i	0.441166	+	0.441166i
$28$	−0.373784	−	5.27828i	−0.0706386	−	0.997502i
$29$		−	7.25964i		−	1.34808i	−0.738694	−	0.674041i	$-0.764557\pi$
$29$		−	7.25964i		−	1.34808i	0.738694	−	0.674041i	$-0.235443\pi$
$30$	−0.346661	−	1.77340i	−0.0632913	−	0.323777i
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	−0.732131	−	0.681164i	$-0.761474\pi$
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	0.223840	+	0.974626i	$0.428141\pi$
$32$	−0.537745	−	5.63124i	−0.0950609	−	0.995471i
$33$	−2.18578	+	0.585677i	−0.380495	+	0.101953i
$34$	−0.650233	+	0.547372i	−0.111514	+	0.0938735i
$35$	4.19508	−	4.17148i	0.709099	−	0.705109i
$36$	−0.911768	+	5.26867i	−0.151961	+	0.878111i
$37$	2.49187	+	9.29977i	0.409660	+	1.52887i	0.795295	+	0.606222i	$0.207316\pi$
$37$	2.49187	+	9.29977i	0.409660	+	1.52887i	−0.385635	+	0.922651i	$0.626018\pi$
$38$	−1.20264	−	2.56841i	−0.195094	−	0.416651i
$39$	−0.828248	−	1.43457i	−0.132626	−	0.229715i
$40$	4.37411	−	4.56806i	0.691607	−	0.722274i
$41$	−3.35439			−0.523868			−0.261934	−	0.965086i	$-0.584360\pi$
$41$	−3.35439			−0.523868			−0.261934	+	0.965086i	$0.584360\pi$
$42$	1.95380	−	0.868240i	0.301477	−	0.133972i
$43$	−3.31777	+	3.31777i	−0.505955	+	0.505955i	−0.913282	−	0.407327i	$-0.866461\pi$
$43$	−3.31777	+	3.31777i	−0.505955	+	0.505955i	0.407327	+	0.913282i	$0.366461\pi$
$44$	−6.08345	−	5.07179i	−0.917115	−	0.764602i
$45$	−5.12586	+	3.07624i	−0.764119	+	0.458578i
$46$	3.29171	+	1.19217i	0.485336	+	0.175776i
$47$	−12.1147	+	3.24611i	−1.76710	+	0.473494i	−0.988137	−	0.153572i	$-0.950922\pi$
$47$	−12.1147	+	3.24611i	−1.76710	+	0.473494i	−0.778966	+	0.627066i	$0.784256\pi$
$48$	2.06532	−	0.979091i	0.298104	−	0.141320i
$49$	5.91928	+	3.73660i	0.845611	+	0.533799i
$50$	7.06157	+	0.366343i	0.998657	+	0.0518087i
$51$	−0.297413	−	0.171711i	−0.0416461	−	0.0240444i
$52$	2.43360	−	5.26244i	0.337480	−	0.729770i
$53$	−0.779134	+	2.90777i	−0.107022	+	0.399413i	−0.998567	−	0.0535205i	$-0.982956\pi$
$53$	−0.779134	+	2.90777i	−0.107022	+	0.399413i	0.891544	+	0.452933i	$0.149622\pi$
$54$	−4.51381	+	0.803298i	−0.614252	+	0.109315i
$55$	−0.149853	−	8.85392i	−0.0202062	−	1.19386i
$56$	6.42396	+	3.83832i	0.858438	+	0.512918i
$57$	0.810271	−	0.810271i	0.107323	−	0.107323i
$58$	8.41932	+	5.87537i	1.10551	+	0.771474i
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.707839	+	0.706374i	$0.249670\pi$
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.257818	+	0.966193i	$0.416996\pi$
$60$	2.33724	+	1.03321i	0.301737	+	0.133387i
$61$	−2.11676	+	3.66633i	−0.271023	+	0.469426i	−0.969124	−	0.246574i	$-0.920695\pi$
$61$	−2.11676	+	3.66633i	−0.271023	+	0.469426i	0.698101	+	0.715999i	$0.254029\pi$
$62$	0.395476	−	4.60450i	0.0502255	−	0.584772i
$63$	−4.90192	−	5.09941i	−0.617584	−	0.642466i
$64$	6.96599	+	3.93382i	0.870749	+	0.491728i
$65$	6.23209	−	1.78345i	0.772996	−	0.221210i
$66$	1.08976	−	3.00894i	0.134140	−	0.370375i
$67$	0.984566	−	3.67445i	0.120284	−	0.448906i	−0.879344	−	0.476187i	$-0.842018\pi$
$67$	0.984566	−	3.67445i	0.120284	−	0.448906i	0.999628	+	0.0272817i	$0.00868511\pi$
$68$	−0.108564	−	1.19710i	−0.0131653	−	0.145170i
$69$			1.41455i			0.170292i
$70$	1.44268	+	8.24128i	0.172434	+	0.985021i
$71$		−	4.86004i		−	0.576781i	−0.957513	−	0.288390i	$-0.906880\pi$
$71$		−	4.86004i		−	0.576781i	0.957513	−	0.288390i	$-0.0931201\pi$
$72$	−5.37238	−	5.32145i	−0.633142	−	0.627139i
$73$	−2.53197	+	9.44944i	−0.296345	+	1.10597i	0.643799	+	0.765195i	$0.277357\pi$
$73$	−2.53197	+	9.44944i	−0.296345	+	1.10597i	−0.940143	+	0.340779i	$0.889309\pi$
$74$	−12.8021	−	4.63656i	−1.48821	−	0.538990i
$75$	0.832427	+	2.73310i	0.0961204	+	0.315591i
$76$	3.95201	+	0.683915i	0.453327	+	0.0784504i
$77$	10.1722	−	2.51146i	1.15922	−	0.286208i
$78$	2.33405	+	0.200469i	0.264279	+	0.0226987i
$79$	3.45719	−	5.98803i	0.388965	−	0.673706i	−0.603346	−	0.797480i	$-0.706166\pi$
$79$	3.45719	−	5.98803i	0.388965	−	0.673706i	0.992311	+	0.123773i	$0.0394995\pi$
$80$	1.75772	+	8.76986i	0.196519	+	0.980500i
$81$	3.08400	+	5.34165i	0.342667	+	0.593517i
$82$	2.71477	−	3.89023i	0.299796	−	0.429604i
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	−0.940361	−	0.340179i	$-0.889512\pi$
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	0.340179	+	0.940361i	$0.389512\pi$
$84$	−0.574310	+	2.96858i	−0.0626624	+	0.323899i
$85$	0.934058	−	0.966221i	0.101313	−	0.104801i
$86$	−1.16262	−	6.53289i	−0.125369	−	0.704460i
$87$	−1.07364	+	4.00690i	−0.115107	+	0.429584i
$88$	10.8054	−	2.95054i	1.15186	−	0.314528i
$89$	3.35292	+	1.93581i	0.355409	+	0.205195i	0.667065	−	0.745000i	$-0.267550\pi$
$89$	3.35292	+	1.93581i	0.355409	+	0.205195i	−0.311656	+	0.950195i	$0.600884\pi$
$90$	0.580822	−	8.43434i	0.0612240	−	0.889057i
$91$	3.70307	+	6.71676i	0.388187	+	0.704108i
$92$	−4.04665	+	2.85269i	−0.421893	+	0.297413i
$93$	1.80367	−	0.483291i	0.187031	−	0.0501149i
$94$	6.03997	−	16.6770i	0.622975	−	1.72010i
$95$	2.30748	+	3.84490i	0.236742	+	0.394478i
$96$	−0.536012	+	3.18764i	−0.0547065	+	0.325337i
$97$	1.11914	−	1.11914i	0.113632	−	0.113632i	−0.648005	−	0.761636i	$-0.724396\pi$
$97$	1.11914	−	1.11914i	0.113632	−	0.113632i	0.761636	+	0.648005i	$0.224396\pi$
$98$	−9.12407	+	3.84074i	−0.921671	+	0.387973i
$99$	−10.5874			−1.06408
$100$	−6.13993	+	7.89311i	−0.613993	+	0.789311i
$101$	−8.93266	−	15.4718i	−0.888833	−	1.53950i	−0.841257	−	0.540636i	$-0.818184\pi$
$101$	−8.93266	−	15.4718i	−0.888833	−	1.53950i	−0.0475759	−	0.998868i	$-0.515150\pi$
$102$	0.439843	−	0.205953i	0.0435509	−	0.0203924i
$103$	−2.90309	−	10.8345i	−0.286050	−	1.06755i	−0.948069	−	0.318066i	$-0.896967\pi$
$103$	−2.90309	−	10.8345i	−0.286050	−	1.06755i	0.662019	−	0.749487i	$-0.269700\pi$
$104$	4.13352	+	7.08135i	0.405325	+	0.694384i
$105$	−2.93237	+	1.68199i	−0.286170	+	0.164146i
$106$	−2.74169	−	3.25691i	−0.266297	−	0.316339i
$107$	7.59541	−	2.03518i	0.734276	−	0.196749i	0.127743	−	0.991807i	$-0.459227\pi$
$107$	7.59541	−	2.03518i	0.734276	−	0.196749i	0.606533	+	0.795059i	$0.292560\pi$
$108$	2.72150	−	5.88498i	0.261876	−	0.566283i
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	−0.483138	−	0.875544i	$-0.660503\pi$
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	0.516675	+	0.856182i	$0.327170\pi$
$110$	10.3895	+	6.99186i	0.990604	+	0.666648i
$111$		−	5.50146i		−	0.522175i
$112$	−9.65050	+	4.34371i	−0.911887	+	0.410442i
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	0.518834	−	0.854875i	$-0.326366\pi$
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	−0.854875	+	0.518834i	$0.826366\pi$
$114$	0.283937	+	1.59547i	0.0265932	+	0.149430i
$115$	−5.37034	−	1.34200i	−0.500787	−	0.125142i
$116$	−13.6278	+	5.00919i	−1.26531	+	0.465091i
$117$	−2.00593	−	7.48624i	−0.185448	−	0.692103i
$118$	−20.9025	−	1.79530i	−1.92423	−	0.165270i
$119$	1.36112	+	0.822090i	0.124773	+	0.0753609i
$120$	−3.08983	+	1.87440i	−0.282062	+	0.171109i
$121$	2.34144	−	4.05549i	0.212858	−	0.368681i
$122$	−2.53887	−	5.42213i	−0.229858	−	0.490896i
$123$	1.85143	+	0.496088i	0.166937	+	0.0447308i
$124$	5.01996	+	4.18516i	0.450806	+	0.375838i
$125$	−11.1659	+	0.567387i	−0.998711	+	0.0507486i
$126$	9.88122	−	1.55791i	0.880289	−	0.138789i
$127$	−4.80151	−	4.80151i	−0.426065	−	0.426065i	0.461221	−	0.887286i	$-0.347412\pi$
$127$	−4.80151	−	4.80151i	−0.426065	−	0.426065i	−0.887286	+	0.461221i	$0.847412\pi$
$128$	−10.1999	+	4.89504i	−0.901555	+	0.432664i
$129$	2.32188	−	1.34054i	0.204431	−	0.118028i
$130$	−2.97541	+	8.67100i	−0.260961	+	0.760497i
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.948761	−	0.315996i	$-0.102339\pi$
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.200720	+	0.979649i	$0.435672\pi$
$132$	2.60763	+	3.69903i	0.226965	+	0.321959i
$133$	−3.82506	+	3.67692i	−0.331674	+	0.318829i
$134$	3.46459	+	4.11565i	0.299295	+	0.355538i
$135$	6.96934	−	1.99443i	0.599825	−	0.171653i
$136$	1.47619	+	0.842931i	0.126582	+	0.0722807i
$137$	−4.42171	−	1.18479i	−0.377772	−	0.101224i	0.0649361	−	0.997889i	$-0.479316\pi$
$137$	−4.42171	−	1.18479i	−0.377772	−	0.101224i	−0.442708	+	0.896666i	$0.645982\pi$
$138$	−1.64052	−	1.14483i	−0.139650	−	0.0974540i
$139$	11.1198			0.943167			0.471583	−	0.881821i	$-0.343683\pi$
$139$	11.1198			0.943167			0.471583	+	0.881821i	$0.343683\pi$
$140$	−10.7254	−	4.99669i	−0.906458	−	0.422297i
$141$	7.16665			0.603541
$142$	5.63639	+	3.93332i	0.472996	+	0.330077i
$143$	11.0891	+	2.97133i	0.927321	+	0.248475i
$144$	10.5195	−	1.92383i	0.876624	−	0.160319i
$145$	−14.1936	−	7.87746i	−1.17871	−	0.654188i
$146$	−8.90975	−	10.5841i	−0.737376	−	0.875942i
$147$	−2.71448	−	2.93780i	−0.223887	−	0.242305i
$148$	15.7382	−	11.0946i	1.29367	−	0.911973i
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	0.663580	−	0.748105i	$-0.269036\pi$
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	−0.316088	+	0.948730i	$0.602369\pi$
$150$	−3.84339	−	1.24655i	−0.313812	−	0.101780i
$151$	−12.7632	+	7.36881i	−1.03865	+	0.599666i	−0.919451	−	0.393205i	$-0.871366\pi$
$151$	−12.7632	+	7.36881i	−1.03865	+	0.599666i	−0.119200	+	0.992870i	$0.538033\pi$
$152$	−3.99161	+	4.02981i	−0.323762	+	0.326861i
$153$	−1.13617	−	1.13617i	−0.0918538	−	0.0918538i
$154$	−5.31987	+	13.8297i	−0.428687	+	1.11443i
$155$	0.123656	+	7.30611i	0.00993233	+	0.586841i
$156$	−2.12148	+	2.54465i	−0.169854	+	0.203735i
$157$	−10.7377	−	2.87717i	−0.856964	−	0.229623i	−0.196522	−	0.980499i	$-0.562965\pi$
$157$	−10.7377	−	2.87717i	−0.856964	−	0.229623i	−0.660442	+	0.750877i	$0.729631\pi$
$158$	4.14660	+	8.85568i	0.329886	+	0.704520i
$159$	0.860073	−	1.48969i	0.0682082	−	0.118140i
$160$	−11.5933	−	5.05911i	−0.916534	−	0.399958i
$161$	0.129310	−	6.54839i	0.0101911	−	0.516085i
$162$	−8.69088	−	0.746452i	−0.682820	−	0.0586468i
$163$	4.75254	+	17.7367i	0.372248	+	1.38925i	0.857324	+	0.514776i	$0.172125\pi$
$163$	4.75254	+	17.7367i	0.372248	+	1.38925i	−0.485077	+	0.874472i	$0.661208\pi$
$164$	2.31454	+	6.29687i	0.180735	+	0.491703i
$165$	−1.22672	+	4.90901i	−0.0954997	+	0.382166i
$166$	−1.91608	−	10.7667i	−0.148717	−	0.835655i
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.999878	+	0.0156336i	$0.00497655\pi$
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.0156336	+	0.999878i	$0.495023\pi$
$168$	−2.97799	−	3.06858i	−0.229757	−	0.236746i
$169$		−	4.59606i		−	0.353543i
$170$	0.364616	+	1.86525i	0.0279647	+	0.143058i
$171$	4.64307	−	2.68068i	0.355064	−	0.204996i
$172$	8.51740	+	3.93885i	0.649446	+	0.300335i
$173$	7.49083	−	2.00716i	0.569517	−	0.152602i	0.0374420	−	0.999299i	$-0.488079\pi$
$173$	7.49083	−	2.00716i	0.569517	−	0.152602i	0.532075	+	0.846697i	$0.321412\pi$
$174$	−3.77805	−	4.48801i	−0.286413	−	0.340235i
$175$	−3.60371	−	12.7284i	−0.272415	−	0.962180i
$176$	−5.32318	+	14.9194i	−0.401250	+	1.12460i
$177$	−2.19394	−	8.18789i	−0.164906	−	0.615439i
$178$	−4.95862	+	2.32184i	−0.371665	+	0.174029i
$179$	−2.56434	−	4.44157i	−0.191668	−	0.331979i	0.754135	−	0.656719i	$-0.228056\pi$
$179$	−2.56434	−	4.44157i	−0.191668	−	0.331979i	−0.945803	+	0.324741i	$0.894723\pi$
$180$	9.31159	+	7.49968i	0.694045	+	0.558993i
$181$	18.1294			1.34755			0.673774	−	0.738938i	$-0.264672\pi$
$181$	18.1294			1.34755			0.673774	+	0.738938i	$0.264672\pi$
$182$	−10.7867	−	1.14140i	−0.799561	−	0.0846059i
$183$	1.71055	−	1.71055i	0.126447	−	0.126447i
$184$	−0.0333491	−	7.00181i	−0.00245853	−	0.516180i
$185$	20.8862	+	5.21928i	1.53559	+	0.383729i
$186$	−0.899249	+	2.48292i	−0.0659361	+	0.182057i
$187$	2.29899	−	0.616011i	0.168118	−	0.0450472i
$188$	14.4528	+	20.5018i	1.05408	+	1.49525i
$189$	4.14114	+	7.51134i	0.301223	+	0.546370i
$190$	−6.32658	−	0.435673i	−0.458978	−	0.0316070i
$191$	−13.5825	−	7.84185i	−0.982794	−	0.567416i	−0.0796814	−	0.996820i	$-0.525390\pi$
$191$	−13.5825	−	7.84185i	−0.982794	−	0.567416i	−0.903112	+	0.429404i	$0.858724\pi$
$192$	−3.26304	−	3.20145i	−0.235489	−	0.231045i
$193$	2.00899	−	7.49764i	0.144610	−	0.539692i	−0.855162	−	0.518360i	$-0.826543\pi$
$193$	2.00899	−	7.49764i	0.144610	−	0.539692i	0.999772	−	0.0213318i	$-0.00679064\pi$
$194$	0.392173	+	2.20366i	0.0281564	+	0.158214i
$195$	−3.70351	+	0.0626822i	−0.265214	+	0.00448876i
$196$	2.93002	−	13.6900i	0.209287	−	0.977854i
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	−0.540184	−	0.841547i	$-0.681645\pi$
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	0.841547	+	0.540184i	$0.181645\pi$
$198$	8.56863	−	12.2787i	0.608946	−	0.872610i
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	0.500661	−	0.865643i	$-0.333090\pi$
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	−1.00000		0.000763945i	$0.999757\pi$
$200$	−4.18482	−	13.5088i	−0.295911	−	0.955215i
$201$	−1.08685	+	1.88247i	−0.0766601	+	0.132779i
$202$	25.1727	+	2.16206i	1.77114	+	0.152122i
$203$	5.33651	−	18.4510i	0.374550	−	1.29501i
$204$	−0.117121	+	0.676785i	−0.00820011	+	0.0473845i
$205$	−3.63986	+	6.55828i	−0.254219	+	0.458050i
$206$	14.9147	+	5.40172i	1.03916	+	0.376356i
$207$	−1.71295	+	6.39282i	−0.119058	+	0.444332i
$208$	−11.5579	−	0.937263i	−0.801395	−	0.0649875i
$209$			7.94162i			0.549333i
$210$	0.422544	−	4.76206i	0.0291583	−	0.328614i
$211$		−	17.2435i		−	1.18709i	−0.804799	−	0.593547i	$-0.797727\pi$
$211$		−	17.2435i		−	1.18709i	0.804799	−	0.593547i	$-0.202273\pi$
$212$	5.99608	−	0.543779i	0.411813	−	0.0373469i
$213$	−0.718762	+	2.68246i	−0.0492488	+	0.183799i
$214$	−3.78682	+	10.4558i	−0.258862	+	0.714746i
$215$	2.88656	+	10.0868i	0.196862	+	0.687914i
$216$	4.62250	+	7.91907i	0.314522	+	0.538824i
$217$	−8.39389	+	2.07242i	−0.569814	+	0.140685i
$218$	−0.0489282	+	0.569667i	−0.00331383	+	0.0385827i
$219$	2.79500	−	4.84108i	0.188868	−	0.327130i
$220$	−16.5172	+	6.39055i	−1.11359	+	0.430851i
$221$	0.871146	+	1.50887i	0.0585996	+	0.101498i
$222$	6.38027	+	4.45244i	0.428216	+	0.298828i
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	−0.978540	−	0.206056i	$-0.933937\pi$
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	0.206056	+	0.978540i	$0.433937\pi$
$224$	2.77276	−	14.7075i	0.185263	−	0.982689i
$225$	0.452361	+	13.3598i	0.0301574	+	0.890653i
$226$	7.03382	−	1.25177i	0.467882	−	0.0832664i
$227$	3.12892	−	11.6773i	0.207674	−	0.775049i	−0.780944	−	0.624601i	$-0.785262\pi$
$227$	3.12892	−	11.6773i	0.207674	−	0.775049i	0.988618	−	0.150448i	$-0.0480717\pi$
$228$	−2.08013	−	0.961953i	−0.137760	−	0.0637069i
$229$	−1.89994	−	1.09693i	−0.125552	−	0.0724873i	0.435909	−	0.899991i	$-0.356427\pi$
$229$	−1.89994	−	1.09693i	−0.125552	−	0.0724873i	−0.561460	+	0.827504i	$0.689760\pi$
$230$	5.90269	−	5.14211i	0.389212	−	0.339060i
$231$	−5.98586	−	0.118202i	−0.393840	−	0.00777710i
$232$	5.21990	−	19.8588i	0.342703	−	1.30379i
$233$	−1.08868	+	0.291712i	−0.0713220	+	0.0191107i	−0.294304	−	0.955712i	$-0.595088\pi$
$233$	−1.08868	+	0.291712i	−0.0713220	+	0.0191107i	0.222982	+	0.974823i	$0.428421\pi$
$234$	10.3055	+	3.73239i	0.673694	+	0.243994i
$235$	−6.79907	+	27.2081i	−0.443522	+	1.77486i
$236$	18.9989	−	22.7885i	1.23672	−	1.48341i
$237$	−2.79375	+	2.79375i	−0.181474	+	0.181474i
$238$	−2.05499	+	0.913209i	−0.133205	+	0.0591946i
$239$	−19.8536			−1.28422			−0.642111	−	0.766612i	$-0.721941\pi$
$239$	−19.8536			−1.28422			−0.642111	+	0.766612i	$0.721941\pi$
$240$	0.326833	−	5.10040i	0.0210970	−	0.329229i
$241$	4.32744	+	7.49535i	0.278755	+	0.482818i	0.971076	−	0.238772i	$-0.0767449\pi$
$241$	4.32744	+	7.49535i	0.278755	+	0.482818i	−0.692321	+	0.721590i	$0.743412\pi$
$242$	2.80835	+	5.99765i	0.180528	+	0.385544i
$243$	−3.42939	−	12.7987i	−0.219996	−	0.821035i
$244$	8.34302	+	1.44380i	0.534107	+	0.0924299i
$245$	13.7286	−	7.51839i	0.877087	−	0.480332i
$246$	−2.07373	+	1.74568i	−0.132216	+	0.111301i
$247$	−5.61541	+	1.50464i	−0.357300	+	0.0957382i
$248$	−8.91646	+	2.43473i	−0.566196	+	0.154606i
$249$	3.82663	−	2.20931i	0.242503	−	0.140009i
$250$	8.37878	−	13.4088i	0.529921	−	0.848047i
$251$		−	1.55623i		−	0.0982283i	−0.998793	−	0.0491141i	$-0.984360\pi$
$251$		−	1.55623i		−	0.0982283i	0.998793	−	0.0491141i	$-0.0156398\pi$
$252$	−6.19029	+	12.7205i	−0.389952	+	0.801317i
$253$	−6.93215	−	6.93215i	−0.435821	−	0.435821i
$254$	9.45447	−	1.68256i	0.593226	−	0.105573i
$255$	−0.658442	+	0.395157i	−0.0412332	+	0.0247457i
$256$	2.57802	−	15.7909i	0.161126	−	0.986934i
$257$	4.60489	+	17.1857i	0.287245	+	1.07201i	0.947183	+	0.320693i	$0.103916\pi$
$257$	4.60489	+	17.1857i	0.287245	+	1.07201i	−0.659938	+	0.751320i	$0.729418\pi$
$258$	−0.324464	+	3.77771i	−0.0202003	+	0.235190i
$259$	−0.502910	+	25.4679i	−0.0312493	+	1.58250i
$260$	−7.64807	−	10.4683i	−0.474313	−	0.649218i
$261$	−9.70429	+	16.8083i	−0.600680	+	1.04041i
$262$	−19.4570	+	9.11057i	−1.20206	+	0.562853i
$263$	18.5489	+	4.97016i	1.14377	+	0.306473i	0.780467	−	0.625197i	$-0.214981\pi$
$263$	18.5489	+	4.97016i	1.14377	+	0.306473i	0.363306	+	0.931670i	$0.381648\pi$
$264$	−6.40032	+	0.0304843i	−0.393913	+	0.00187618i
$265$	4.83964	+	4.67854i	0.297297	+	0.287401i
$266$	−1.16858	−	7.41188i	−0.0716504	−	0.454451i
$267$	−1.56432	−	1.56432i	−0.0957350	−	0.0957350i
$268$	−7.57705	+	0.687156i	−0.462842	+	0.0419747i
$269$	−12.4257	+	7.17398i	−0.757608	+	0.437405i	−0.828436	−	0.560083i	$-0.810769\pi$
$269$	−12.4257	+	7.17398i	−0.757608	+	0.437405i	0.0708284	+	0.997489i	$0.477436\pi$
$270$	−3.32740	+	9.69677i	−0.202499	+	0.590127i
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.932962	−	0.359975i	$-0.117215\pi$
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.154733	+	0.987956i	$0.450548\pi$
$272$	−2.17229	+	1.02980i	−0.131715	+	0.0624409i
$273$	−1.05052	−	4.25491i	−0.0635804	−	0.257519i
$274$	4.95263	−	4.16917i	0.299199	−	0.251869i
$275$	−17.4732	−	9.31444i	−1.05367	−	0.561682i
$276$	2.65540	−	0.976048i	0.159837	−	0.0587512i
$277$	−4.70760	−	1.26140i	−0.282853	−	0.0757901i	0.114604	−	0.993411i	$-0.463440\pi$
$277$	−4.70760	−	1.26140i	−0.282853	−	0.0757901i	−0.397456	+	0.917621i	$0.630107\pi$
$278$	−8.99945	+	12.8961i	−0.539751	+	0.773455i
$279$	8.73658			0.523045
$280$	14.4751	−	8.39473i	0.865053	−	0.501681i
$281$	−9.71163			−0.579347			−0.289674	−	0.957125i	$-0.593547\pi$
$281$	−9.71163			−0.579347			−0.289674	+	0.957125i	$0.593547\pi$
$282$	−5.80011	+	8.31147i	−0.345391	+	0.494941i
$283$	−1.36959	−	0.366980i	−0.0814136	−	0.0218147i	0.217882	−	0.975975i	$-0.430085\pi$
$283$	−1.36959	−	0.366980i	−0.0814136	−	0.0218147i	−0.299296	+	0.954160i	$0.596752\pi$
$284$	−9.12328	+	3.35345i	−0.541367	+	0.198991i
$285$	−0.704961	−	2.46342i	−0.0417583	−	0.145920i
$286$	−12.4206	+	10.4558i	−0.734447	+	0.618264i
$287$	−8.52546	−	2.46579i	−0.503242	−	0.145551i
$288$	−6.28248	+	13.7569i	−0.370199	+	0.810632i
$289$	−14.4096	−	8.31940i	−0.847624	−	0.489376i
$290$	20.6230	−	10.0855i	1.21102	−	0.592242i
$291$	−0.783214	+	0.452189i	−0.0459128	+	0.0265078i
$292$	19.4856	−	1.76713i	1.14031	−	0.103414i
$293$	−6.02648	−	6.02648i	−0.352071	−	0.352071i	0.508809	−	0.860880i	$-0.330086\pi$
$293$	−6.02648	−	6.02648i	−0.352071	−	0.352071i	−0.860880	+	0.508809i	$0.830086\pi$
$294$	5.60397	−	0.770482i	0.326830	−	0.0449354i
$295$	33.1667	−	0.561349i	1.93104	−	0.0326830i
$296$	0.129701	+	27.2313i	0.00753870	+	1.58279i
$297$	12.4010	+	3.32283i	0.719578	+	0.192810i
$298$	−6.27302	+	2.93729i	−0.363386	+	0.170153i
$299$	3.58824	−	6.21502i	0.207513	−	0.359424i
$300$	4.55621	−	3.44849i	0.263053	−	0.199099i
$301$	−10.8712	+	5.99351i	−0.626608	+	0.345460i
$302$	1.78355	−	20.7657i	0.102632	−	1.19493i
$303$	2.64214	+	9.86060i	0.151787	+	0.566477i
$304$	−1.44306	−	7.89064i	−0.0827651	−	0.452559i
$305$	4.87127	+	8.11690i	0.278928	+	0.464772i
$306$	2.23719	−	0.398140i	0.127891	−	0.0227601i
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	0.319583	−	0.947558i	$-0.396457\pi$
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	−0.947558	+	0.319583i	$0.896457\pi$
$308$	−11.7334	−	17.3623i	−0.668570	−	0.989308i
$309$			6.40934i			0.364615i
$310$	−8.57328	−	5.76956i	−0.486929	−	0.327689i
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.970561	−	0.240854i	$-0.922572\pi$
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.276695	+	0.960958i	$0.589239\pi$
$312$	−1.23418	−	4.51980i	−0.0698717	−	0.255884i
$313$	25.0624	−	6.71544i	1.41661	−	0.379579i	0.532330	−	0.846537i	$-0.321317\pi$
$313$	25.0624	−	6.71544i	1.41661	−	0.379579i	0.884280	+	0.466958i	$0.154650\pi$
$314$	12.0270	−	10.1245i	0.678724	−	0.571356i
$315$	−15.2891	+	4.05052i	−0.861444	+	0.228221i
$316$	−13.6262	−	2.35809i	−0.766536	−	0.132653i
$317$	0.0554686	+	0.207012i	0.00311543	+	0.0116269i	0.967466	−	0.253001i	$-0.0814176\pi$
$317$	0.0554686	+	0.207012i	0.00311543	+	0.0116269i	−0.964351	+	0.264628i	$0.914751\pi$
$318$	1.03158	+	2.20310i	0.0578483	+	0.123544i
$319$	−14.3747	−	24.8977i	−0.804828	−	1.39400i
$320$	15.2500	−	9.35085i	0.852499	−	0.522728i
$321$	−4.49321			−0.250786
$322$	7.48979	+	5.44971i	0.417390	+	0.303700i
$323$	−0.852238	+	0.852238i	−0.0474198	+	0.0474198i
$324$	7.89939	−	9.47507i	0.438855	−	0.526393i
$325$	3.27558	−	14.1198i	0.181696	−	0.783226i
$326$	−24.4164	−	8.84296i	−1.35230	−	0.489766i
$327$	−0.223149	+	0.0597926i	−0.0123402	+	0.00330654i
$328$	−9.17595	−	2.41191i	−0.506657	−	0.133175i
$329$	−33.1766	−	0.655132i	−1.82908	−	0.0361186i
$330$	−4.70038	−	5.39563i	−0.258747	−	0.297020i
$331$	1.84066	+	1.06270i	0.101172	+	0.0584115i	0.549732	−	0.835341i	$-0.314730\pi$
$331$	1.84066	+	1.06270i	0.101172	+	0.0584115i	−0.448560	+	0.893753i	$0.648063\pi$
$332$	14.0373	+	6.49151i	0.770396	+	0.356268i
$333$	6.66198	−	24.8628i	0.365074	−	1.36248i
$334$	−25.8406	+	4.59871i	−1.41393	+	0.251630i
$335$	−6.11569	−	5.91212i	−0.334136	−	0.323013i
$336$	5.96891	−	0.970238i	0.325631	−	0.0529308i
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.256552	+	0.966530i	$0.582586\pi$
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.966530	+	0.256552i	$0.917414\pi$
$338$	5.33025	+	3.71968i	0.289927	+	0.202324i
$339$	1.44333	+	2.49992i	0.0783909	+	0.135777i
$340$	−2.45830	−	1.08672i	−0.133320	−	0.0589357i
$341$	−6.47062	+	11.2074i	−0.350404	+	0.606917i
$342$	−0.648831	+	7.55429i	−0.0350848	+	0.408489i
$343$	12.2976	+	13.8481i	0.664007	+	0.747726i
$344$	−11.4613	+	6.69020i	−0.617955	+	0.360711i
$345$	2.76564	+	1.53494i	0.148897	+	0.0826382i
$346$	−3.73468	+	10.3119i	−0.200778	+	0.554369i
$347$	4.72717	−	17.6420i	0.253768	−	0.947074i	−0.715004	−	0.699120i	$-0.753575\pi$
$347$	4.72717	−	17.6420i	0.253768	−	0.947074i	0.968772	−	0.247954i	$-0.0797582\pi$
$348$	8.26258	−	0.749326i	0.442921	−	0.0401681i
$349$		−	21.6072i		−	1.15661i	−0.815821	−	0.578304i	$-0.803715\pi$
$349$		−	21.6072i		−	1.15661i	0.815821	−	0.578304i	$-0.196285\pi$
$350$	17.6783	+	6.12200i	0.944943	+	0.327235i
$351$			9.39811i			0.501634i
$352$	−12.9946	−	18.2481i	−0.692612	−	0.972628i
$353$	4.39216	−	16.3918i	0.233771	−	0.872446i	−0.744928	−	0.667145i	$-0.767516\pi$
$353$	4.39216	−	16.3918i	0.233771	−	0.872446i	0.978699	−	0.205301i	$-0.0658173\pi$
$354$	11.2714	+	4.08221i	0.599070	+	0.216967i
$355$	−9.50203	−	5.27365i	−0.504315	−	0.279896i
$356$	1.32038	−	7.62983i	0.0699799	−	0.404380i
$357$	−0.629675	−	0.655044i	−0.0333259	−	0.0346686i
$358$	7.22645	+	0.620673i	0.381930	+	0.0328036i
$359$	−4.43990	+	7.69014i	−0.234329	+	0.405870i	−0.959078	−	0.283144i	$-0.908623\pi$
$359$	−4.43990	+	7.69014i	−0.234329	+	0.405870i	0.724748	+	0.689014i	$0.241956\pi$
$360$	−16.2337	+	4.72941i	−0.855593	+	0.249262i
$361$	7.48923	+	12.9717i	0.394170	+	0.682723i
$362$	−14.6725	+	21.0254i	−0.771168	+	1.10507i
$363$	−1.89211	+	1.89211i	−0.0993101	+	0.0993101i
$364$	10.0536	−	11.5860i	0.526951	−	0.607272i
$365$	15.7275	+	15.2040i	0.823214	+	0.795812i
$366$	0.599415	+	3.36817i	0.0313319	+	0.176057i
$367$	5.62655	−	20.9986i	0.293704	−	1.09612i	−0.648538	−	0.761182i	$-0.724619\pi$
$367$	5.62655	−	20.9986i	0.293704	−	1.09612i	0.942241	−	0.334934i	$-0.108714\pi$
$368$	8.14728	+	5.62802i	0.424707	+	0.293381i
$369$	7.76645	+	4.48396i	0.404305	+	0.233426i
$370$	−22.9567	+	19.9986i	−1.19346	+	1.03968i
$371$	−4.11771	+	6.81760i	−0.213781	+	0.353952i
$372$	−2.15177	−	3.05237i	−0.111564	−	0.158258i
$373$	0.472145	−	0.126511i	0.0244467	−	0.00655048i	−0.246575	−	0.969124i	$-0.579305\pi$
$373$	0.472145	−	0.126511i	0.0244467	−	0.00655048i	0.271022	+	0.962573i	$0.412638\pi$
$374$	−1.14620	+	3.16478i	−0.0592686	+	0.163647i
$375$	6.24685	+	1.33819i	0.322586	+	0.0691039i
$376$	−35.4738	+	0.168959i	−1.82942	+	0.00871339i
$377$	14.8813	−	14.8813i	0.766427	−	0.766427i
$378$	−12.0627	−	1.27642i	−0.620440	−	0.0656521i
$379$	27.8315			1.42961			0.714805	−	0.699324i	$-0.246516\pi$
$379$	27.8315			1.42961			0.714805	+	0.699324i	$0.246516\pi$
$380$	5.62549	−	6.98460i	0.288581	−	0.358302i
$381$	1.94004	+	3.36026i	0.0993915	+	0.172151i
$382$	20.0871	−	9.40562i	1.02774	−	0.481233i
$383$	−1.33854	−	4.99551i	−0.0683964	−	0.255259i	0.923259	−	0.384179i	$-0.125516\pi$
$383$	−1.33854	−	4.99551i	−0.0683964	−	0.255259i	−0.991655	+	0.128920i	$0.958849\pi$
$384$	6.35370	−	1.19328i	0.324236	−	0.0608944i
$385$	6.12759	−	22.6131i	0.312291	−	1.15247i
$386$	7.06942	+	8.39789i	0.359824	+	0.427441i
$387$	12.1167	−	3.24665i	0.615925	−	0.165037i
$388$	−2.87307	−	1.32865i	−0.145858	−	0.0674518i
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	−0.743780	−	0.668424i	$-0.766969\pi$
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	0.206982	+	0.978345i	$0.433636\pi$
$390$	2.92463	−	4.34584i	0.148094	−	0.220060i
$391$		−	1.48782i		−	0.0752422i
$392$	13.5055	+	14.4776i	0.682131	+	0.731230i
$393$	−6.13820	−	6.13820i	−0.309631	−	0.309631i
$394$	1.48223	+	8.32880i	0.0746737	+	0.419599i
$395$	−7.95600	−	13.2569i	−0.400310	−	0.667028i
$396$	7.30538	+	19.8748i	0.367109	+	0.998746i
$397$	−4.52602	−	16.8913i	−0.227154	−	0.847751i	−0.981530	−	0.191308i	$-0.938727\pi$
$397$	−4.52602	−	16.8913i	−0.227154	−	0.847751i	0.754376	−	0.656443i	$-0.227940\pi$
$398$	19.8505	+	1.70494i	0.995013	+	0.0854608i
$399$	2.65499	−	1.46375i	0.132916	−	0.0732789i
$400$	19.0536	+	6.07962i	0.952678	+	0.303981i
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	−0.156524	−	0.987674i	$-0.550029\pi$
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	0.933613	−	0.358284i	$-0.116638\pi$
$402$	−1.30358	−	2.78398i	−0.0650165	−	0.138852i
$403$	−9.15057	−	2.45189i	−0.455823	−	0.122137i
$404$	−22.8802	+	27.4440i	−1.13833	+	1.36539i
$405$	13.7901	−	0.233399i	0.685236	−	0.0115977i
$406$	17.0794	+	21.1217i	0.847639	+	1.04825i
$407$	26.9604	+	26.9604i	1.33638	+	1.33638i
$408$	−0.690108	−	0.683566i	−0.0341655	−	0.0338415i
$409$	−4.43457	+	2.56030i	−0.219275	+	0.126599i	−0.605615	−	0.795758i	$-0.707073\pi$
$409$	−4.43457	+	2.56030i	−0.219275	+	0.126599i	0.386339	+	0.922357i	$0.373739\pi$
$410$	−4.66011	−	9.52904i	−0.230146	−	0.470606i
$411$	2.26530	+	1.30787i	0.111739	+	0.0645126i
$412$	−18.3354	+	12.9255i	−0.903319	+	0.636795i
$413$	9.40791	+	38.1047i	0.462933	+	1.87501i
$414$	−6.02770	−	7.16041i	−0.296245	−	0.351915i
$415$	4.75726	+	16.6238i	0.233525	+	0.816028i
$416$	10.4410	−	12.6456i	0.511912	−	0.620002i
$417$	−6.13746	−	1.64453i	−0.300553	−	0.0805329i
$418$	−9.21023	−	6.42730i	−0.450487	−	0.314370i
$419$	−14.0529			−0.686531			−0.343266	−	0.939238i	$-0.611533\pi$
$419$	−14.0529			−0.686531			−0.343266	+	0.939238i	$0.611533\pi$
$420$	5.18079	+	4.34407i	0.252797	+	0.211969i
$421$	37.5305			1.82913			0.914563	−	0.404443i	$-0.132535\pi$
$421$	37.5305			1.82913			0.914563	+	0.404443i	$0.132535\pi$
$422$	19.9981	+	13.9555i	0.973491	+	0.679345i
$423$	32.3884	+	8.67844i	1.57478	+	0.421960i
$424$	−4.22210	+	7.39400i	−0.205043	+	0.359084i
$425$	−0.875542	−	2.87466i	−0.0424700	−	0.139441i
$426$	−2.52925	−	3.00454i	−0.122543	−	0.145571i
$427$	−8.07501	+	7.76227i	−0.390777	+	0.375643i
$428$	−9.06132	−	12.8538i	−0.437995	−	0.621314i
$429$	−5.68112	−	3.28000i	−0.274287	−	0.158360i
$430$	−14.0342	−	4.81578i	−0.676791	−	0.232237i
$431$	21.0173	−	12.1344i	1.01237	−	0.584492i	0.100485	−	0.994939i	$-0.467961\pi$
$431$	21.0173	−	12.1344i	1.01237	−	0.584492i	0.911885	+	0.410447i	$0.134627\pi$
$432$	−12.9252	−	1.04814i	−0.621862	−	0.0504287i
$433$	0.0253628	+	0.0253628i	0.00121886	+	0.00121886i	0.707716	−	0.706497i	$-0.249726\pi$
$433$	0.0253628	+	0.0253628i	0.00121886	+	0.00121886i	−0.706497	+	0.707716i	$0.749726\pi$
$434$	4.38987	−	11.4120i	0.210720	−	0.547793i
$435$	6.66901	+	6.44702i	0.319754	+	0.309111i
$436$	−0.621068	−	0.517787i	−0.0297438	−	0.0247975i
$437$	4.79524	+	1.28488i	0.229387	+	0.0614641i
$438$	3.35236	+	7.15946i	0.160182	+	0.342092i
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	−0.624500	−	0.781024i	$-0.714697\pi$
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	0.988637	+	0.150321i	$0.0480307\pi$
$440$	5.95631	−	24.3277i	0.283956	−	1.15978i
$441$	−8.71009	−	16.5639i	−0.414766	−	0.788759i
$442$	−2.45494	−	0.210852i	−0.116769	−	0.0100292i
$443$	−3.09446	−	11.5487i	−0.147022	−	0.548695i	−0.999657	−	0.0261872i	$-0.991663\pi$
$443$	−3.09446	−	11.5487i	−0.147022	−	0.548695i	0.852635	−	0.522507i	$-0.175003\pi$
$444$	−10.3274	+	3.79603i	−0.490115	+	0.180152i
$445$	7.42303	−	4.45486i	0.351885	−	0.211180i
$446$	−4.04235	−	22.7144i	−0.191411	−	1.07556i
$447$	−1.97898	−	1.97898i	−0.0936027	−	0.0936027i
$448$	14.8129	+	15.1188i	0.699844	+	0.714295i
$449$			13.7142i			0.647213i	0.946192	+	0.323607i	$0.104895\pi$
$449$			13.7142i			0.647213i	−0.946192	+	0.323607i	$0.895105\pi$
$450$	−15.8600	−	10.2877i	−0.747648	−	0.484967i
$451$	−11.5042	+	6.64196i	−0.541712	+	0.312758i
$452$	−4.24087	+	9.17049i	−0.199474	+	0.431344i
$453$	8.13430	−	2.17958i	0.382183	−	0.102406i
$454$	11.0104	+	13.0794i	0.516741	+	0.613847i
$455$	17.1504	+	0.0483779i	0.804022	+	0.00226799i
$456$	2.79911	−	1.63389i	0.131080	−	0.0765140i
$457$	−3.61073	−	13.4754i	−0.168903	−	0.630354i	−0.997510	−	0.0705235i	$-0.977533\pi$
$457$	−3.61073	−	13.4754i	−0.168903	−	0.630354i	0.828607	−	0.559830i	$-0.189134\pi$
$458$	2.80982	−	1.31567i	0.131294	−	0.0614774i
$459$	0.974202	+	1.68737i	0.0454718	+	0.0787595i
$460$	1.18635	+	11.0072i	0.0553140	+	0.513214i
$461$	−27.6588			−1.28820			−0.644100	−	0.764941i	$-0.722768\pi$
$461$	−27.6588			−1.28820			−0.644100	+	0.764941i	$0.722768\pi$
$462$	4.98155	−	6.84639i	0.231763	−	0.318523i
$463$	4.03783	−	4.03783i	0.187654	−	0.187654i	−0.607027	−	0.794681i	$-0.707638\pi$
$463$	4.03783	−	4.03783i	0.187654	−	0.187654i	0.794681	+	0.607027i	$0.207638\pi$
$464$	18.8065	+	22.1259i	0.873071	+	1.02717i
$465$	1.01226	−	4.05083i	0.0469427	−	0.187853i
$466$	0.542782	−	1.49868i	0.0251439	−	0.0694250i
$467$	−11.8626	+	3.17857i	−0.548935	+	0.147087i	−0.522618	−	0.852567i	$-0.675045\pi$
$467$	−11.8626	+	3.17857i	−0.548935	+	0.147087i	−0.0263172	+	0.999654i	$0.508378\pi$
$468$	−12.6691	+	8.93108i	−0.585629	+	0.412839i
$469$	5.20342	−	8.61517i	0.240271	−	0.397812i
$470$	−26.0518	−	29.9052i	−1.20168	−	1.37943i
$471$	5.50108	+	3.17605i	0.253477	+	0.146345i
$472$	11.0527	+	40.4770i	0.508740	+	1.86310i
$473$	−4.80917	+	17.9481i	−0.221126	+	0.825253i
$474$	−0.978994	−	5.50107i	−0.0449667	−	0.252672i
$475$	10.0211	−	0.339315i	0.459802	−	0.0155688i
$476$	0.604056	−	3.12234i	0.0276869	−	0.143112i
$477$	5.69088	−	5.69088i	0.260568	−	0.260568i
$478$	16.0679	−	23.0250i	0.734928	−	1.05314i
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	−0.998258	−	0.0589981i	$-0.981209\pi$
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	0.448035	−	0.894016i	$-0.352124\pi$
$480$	5.65064	+	4.50689i	0.257915	+	0.205711i
$481$	−13.9553	+	24.1713i	−0.636308	+	1.10212i
$482$	−12.1950	−	1.04741i	−0.555465	−	0.0477084i
$483$	−1.03983	+	3.59520i	−0.0473138	+	0.163587i
$484$	−9.22859	−	1.59705i	−0.419481	−	0.0725932i
$485$	−0.973689	−	3.40246i	−0.0442130	−	0.154498i
$486$	17.6186	+	6.38100i	0.799198	+	0.289448i
$487$	0.888247	−	3.31498i	0.0402503	−	0.150216i	−0.942876	−	0.333144i	$-0.891891\pi$
$487$	0.888247	−	3.31498i	0.0402503	−	0.150216i	0.983126	+	0.182927i	$0.0585573\pi$
$488$	−8.42661	+	8.50726i	−0.381455	+	0.385106i
$489$		−	10.4925i		−	0.474487i
$490$	−2.39140	+	22.0064i	−0.108033	+	0.994147i
$491$		−	3.54370i		−	0.159925i	−0.996798	−	0.0799626i	$-0.974520\pi$
$491$		−	3.54370i		−	0.159925i	0.996798	−	0.0799626i	$-0.0254801\pi$
$492$	−0.346234	−	3.81781i	−0.0156094	−	0.172120i
$493$	1.12925	−	4.21443i	0.0508590	−	0.189808i
$494$	2.79966	−	7.73016i	0.125963	−	0.347796i
$495$	−11.4885	+	20.6999i	−0.516368	+	0.930391i
$496$	4.39260	−	12.3113i	0.197234	−	0.552792i
$497$	3.57258	−	12.3522i	0.160252	−	0.554071i
$498$	−0.534740	+	6.22594i	−0.0239623	+	0.278991i
$499$	−15.1647	+	26.2660i	−0.678864	+	1.17583i	0.296460	+	0.955045i	$0.404194\pi$
$499$	−15.1647	+	26.2660i	−0.678864	+	1.17583i	−0.975323	+	0.220781i	$0.929139\pi$
$500$	8.76964	+	20.5692i	0.392190	+	0.919884i
$501$	−5.30246	−	9.18412i	−0.236896	−	0.410316i
$502$	1.80482	+	1.25949i	0.0805532	+	0.0562136i
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	−0.843162	−	0.537659i	$-0.819309\pi$
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	0.537659	+	0.843162i	$0.319309\pi$
$504$	−9.74260	−	17.4741i	−0.433970	−	0.778358i
$505$	−39.9423	+	0.676027i	−1.77741	+	0.0300828i
$506$	13.6498	−	2.42919i	0.606809	−	0.107990i
$507$	−0.679722	+	2.53676i	−0.0301875	+	0.112661i
$508$	−5.70035	+	12.3265i	−0.252912	+	0.546899i
$509$	8.23953	+	4.75709i	0.365211	+	0.210854i	0.671364	−	0.741128i	$-0.265709\pi$
$509$	8.23953	+	4.75709i	0.365211	+	0.210854i	−0.306153	+	0.951982i	$0.599042\pi$
$510$	0.0746093	−	1.08343i	0.00330376	−	0.0479751i
$511$	−13.3814	+	22.1553i	−0.591960	+	0.980093i
$512$	16.2270	+	15.7698i	0.717138	+	0.696931i
$513$	−6.27970	+	1.68264i	−0.277256	+	0.0742904i
$514$	−23.6578	−	8.56822i	−1.04350	−	0.377928i
$515$	−24.3330	−	6.08060i	−1.07224	−	0.267943i
$516$	−4.11858	−	3.43367i	−0.181310	−	0.151159i
$517$	−35.1209	+	35.1209i	−1.54461	+	1.54461i
$518$	−29.1292	−	21.1949i	−1.27986	−	0.931251i
$519$	−4.43134			−0.194514
$520$	18.3303	−	0.397579i	0.803836	−	0.0174350i
$521$	2.30406	+	3.99075i	0.100943	+	0.174838i	0.912073	−	0.410027i	$-0.134481\pi$
$521$	2.30406	+	3.99075i	0.100943	+	0.174838i	−0.811131	+	0.584865i	$0.801147\pi$
$522$	−11.6395	−	24.8578i	−0.509445	−	1.08800i
$523$	−8.89583	−	33.1997i	−0.388987	−	1.45172i	−0.831784	−	0.555099i	$-0.812680\pi$
$523$	−8.89583	−	33.1997i	−0.388987	−	1.45172i	0.442797	−	0.896622i	$-0.353986\pi$
$524$	5.18099	−	29.9384i	0.226333	−	1.30787i
$525$	0.106599	+	7.55831i	0.00465238	+	0.329872i
$526$	−20.7761	+	17.4895i	−0.905880	+	0.762578i
$527$	−1.89708	+	0.508322i	−0.0826383	+	0.0221429i
$528$	5.14455	−	7.44740i	0.223888	−	0.324106i
$529$	14.6113	−	8.43585i	0.635275	−	0.366776i
$530$	−9.34272	+	1.82630i	−0.405822	+	0.0793293i
$531$		−	39.6604i		−	1.72112i
$532$	9.54163	+	4.64332i	0.413682	+	0.201314i
$533$	−6.87606	−	6.87606i	−0.297835	−	0.297835i
$534$	3.08025	−	0.548175i	0.133295	−	0.0237218i
$535$	4.26275	−	17.0584i	0.184295	−	0.737500i
$536$	5.33533	−	9.34355i	0.230451	−	0.403580i
$537$	0.758493	+	2.83073i	0.0327314	+	0.122155i
$538$	1.73639	−	20.2166i	0.0748610	−	0.871601i
$539$	27.6995	+	1.09438i	1.19310	+	0.0471384i
$540$	−8.55283	−	11.7067i	−0.368055	−	0.503777i
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	−0.648677	−	0.761064i	$-0.724677\pi$
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	0.983439	+	0.181239i	$0.0580107\pi$
$542$	−26.4807	+	12.3994i	−1.13744	+	0.532599i
$543$	−10.0064	−	2.68120i	−0.429414	−	0.115061i
$544$	0.563774	−	3.35274i	0.0241716	−	0.143748i
$545$	−0.0152987	−	0.903909i	−0.000655326	−	0.0387192i
$546$	5.78481	+	2.22525i	0.247567	+	0.0952318i
$547$	6.09970	+	6.09970i	0.260804	+	0.260804i	0.825381	−	0.564577i	$-0.190961\pi$
$547$	6.09970	+	6.09970i	0.260804	+	0.260804i	−0.564577	+	0.825381i	$0.690961\pi$
$548$	0.826900	+	9.11797i	0.0353234	+	0.389500i
$549$	9.80190	−	5.65913i	0.418335	−	0.241526i
$550$	24.9438	−	12.7261i	1.06361	−	0.542642i
$551$	12.6079	+	7.27916i	0.537114	+	0.310103i
$552$	−1.01711	+	3.86952i	−0.0432909	+	0.164698i
$553$	13.1885	−	12.6777i	0.560832	−	0.539112i
$554$	5.27285	−	4.43873i	0.224022	−	0.188584i
$555$	−10.7561	−	5.96965i	−0.456570	−	0.253397i
$556$	−7.67269	−	20.8741i	−0.325395	−	0.885258i
$557$	12.5982	+	3.37568i	0.533804	+	0.143032i	0.515644	−	0.856803i	$-0.327553\pi$
$557$	12.5982	+	3.37568i	0.533804	+	0.143032i	0.0181595	+	0.999835i	$0.494219\pi$
$558$	−7.07068	+	10.1322i	−0.299326	+	0.428930i
$559$	−13.6020			−0.575303
$560$	−1.97926	+	23.5814i	−0.0836389	+	0.996496i
$561$	−1.36001			−0.0574196
$562$	7.85981	−	11.2630i	0.331546	−	0.475100i
$563$	−20.1494	−	5.39902i	−0.849197	−	0.227542i	−0.192126	−	0.981370i	$-0.561538\pi$
$563$	−20.1494	−	5.39902i	−0.849197	−	0.227542i	−0.657071	+	0.753829i	$0.728205\pi$
$564$	−4.94502	−	13.4533i	−0.208223	−	0.566485i
$565$	−10.8602	+	3.10790i	−0.456894	+	0.130750i
$566$	1.53404	−	1.29137i	0.0644804	−	0.0542801i
$567$	3.91164	+	15.8433i	0.164274	+	0.665355i
$568$	3.49451	−	13.2947i	0.146627	−	0.557832i
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	0.638132	−	0.769927i	$-0.279707\pi$
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	−0.347710	+	0.937602i	$0.613041\pi$
$570$	3.42747	+	1.17612i	0.143561	+	0.0492621i
$571$	28.4622	−	16.4326i	1.19110	−	0.687684i	0.232547	−	0.972585i	$-0.425294\pi$
$571$	28.4622	−	16.4326i	1.19110	−	0.687684i	0.958557	+	0.284901i	$0.0919607\pi$
$572$	−2.07377	−	22.8668i	−0.0867087	−	0.956109i
$573$	6.33698	+	6.33698i	0.264731	+	0.264731i
$574$	9.75949	−	7.89172i	0.407353	−	0.329394i
$575$	−8.45116	+	9.04353i	−0.352438	+	0.377141i
$576$	−10.8699	−	18.4198i	−0.452913	−	0.767490i
$577$	37.4537	+	10.0357i	1.55922	+	0.417791i	0.932416	−	0.361387i	$-0.117697\pi$
$577$	37.4537	+	10.0357i	1.55922	+	0.417791i	0.626802	+	0.779178i	$0.284363\pi$
$578$	21.3103	−	9.97839i	0.886393	−	0.415046i
$579$	−2.21768	+	3.84114i	−0.0921638	+	0.159632i
$580$	−4.99397	+	32.0797i	−0.207363	+	1.33204i
$581$	−17.9166	+	9.87773i	−0.743305	+	0.409797i
$582$	0.109448	−	1.27429i	0.00453675	−	0.0528211i
$583$	3.08550	+	11.5152i	0.127788	+	0.476912i
$584$	−13.7207	+	24.0285i	−0.567765	+	0.994304i
$585$	−16.8132	−	4.20147i	−0.695142	−	0.173710i
$586$	11.8665	−	2.11182i	0.490201	−	0.0872383i
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	0.821854	−	0.569699i	$-0.192940\pi$
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	−0.569699	+	0.821854i	$0.692940\pi$
$588$	−3.64184	+	7.12272i	−0.150187	+	0.293736i
$589$		−	6.55329i		−	0.270023i
$590$	−26.1914	+	38.9191i	−1.07828	+	1.60227i
$591$	−2.96018	+	1.70906i	−0.121765	+	0.0703013i
$592$	−31.6863	−	21.8884i	−1.30230	−	0.899608i
$593$	−41.4359	+	11.1027i	−1.70157	+	0.455934i	−0.973334	−	0.229392i	$-0.926326\pi$
$593$	−41.4359	+	11.1027i	−1.70157	+	0.455934i	−0.728236	+	0.685327i	$0.759659\pi$
$594$	−13.8900	+	11.6927i	−0.569913	+	0.479757i
$595$	3.08425	−	1.76911i	0.126442	−	0.0725264i
$596$	1.67038	−	9.65229i	0.0684212	−	0.395373i
$597$	2.08351	+	7.77578i	0.0852726	+	0.318242i
$598$	4.30378	+	9.19137i	0.175995	+	0.375863i
$599$	5.01596	+	8.68789i	0.204946	+	0.354978i	0.950116	−	0.311898i	$-0.100965\pi$
$599$	5.01596	+	8.68789i	0.204946	+	0.354978i	−0.745169	+	0.666875i	$0.767631\pi$
$600$	0.311928	+	8.07496i	0.0127344	+	0.329659i
$601$	24.3587			0.993613			0.496806	−	0.867861i	$-0.334506\pi$
$601$	24.3587			0.993613			0.496806	+	0.867861i	$0.334506\pi$
$602$	1.84738	−	17.4585i	0.0752935	−	0.711556i
$603$	−7.19138	+	7.19138i	−0.292855	+	0.292855i
$604$	22.6394	+	18.8745i	0.921184	+	0.767994i
$605$	−5.38833	−	8.97845i	−0.219067	−	0.365026i
$606$	−13.5741	−	4.91618i	−0.551410	−	0.199706i
$607$	−24.1790	+	6.47873i	−0.981394	+	0.262964i	−0.713632	−	0.700521i	$-0.752951\pi$
$607$	−24.1790	+	6.47873i	−0.981394	+	0.262964i	−0.267762	+	0.963485i	$0.586284\pi$
$608$	10.3190	+	4.71247i	0.418491	+	0.191116i
$609$	−5.67420	+	9.39463i	−0.229930	+	0.380690i
$610$	−13.3559	−	0.919741i	−0.540765	−	0.0372392i
$611$	−31.4876	−	18.1794i	−1.27385	−	0.735458i
$612$	−1.34886	+	2.91678i	−0.0545244	+	0.117904i
$613$	−2.42522	+	9.05103i	−0.0979535	+	0.365568i	−0.997451	−	0.0713590i	$-0.977266\pi$
$613$	−2.42522	+	9.05103i	−0.0979535	+	0.365568i	0.899497	+	0.436927i	$0.143933\pi$
$614$	21.6656	−	3.85571i	0.874353	−	0.155604i
$615$	2.97891	−	3.08148i	0.120121	−	0.124257i
$616$	29.6318	+	0.443959i	1.19390	+	0.0178876i
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	−0.958169	−	0.286204i	$-0.907606\pi$
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	0.286204	+	0.958169i	$0.407606\pi$
$618$	−7.43318	−	5.18720i	−0.299006	−	0.208660i
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	0.993031	+	0.117857i	$0.0376023\pi$
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	−0.394448	+	0.918918i	$0.629064\pi$
$620$	13.6297	−	5.27337i	0.547383	−	0.211784i
$621$	4.01273	−	6.95024i	0.161025	−	0.278904i
$622$	3.07371	−	35.7869i	0.123244	−	1.43492i
$623$	7.09872	+	7.38472i	0.284404	+	0.295863i
$624$	6.24065	+	2.22663i	0.249826	+	0.0891367i
$625$	−11.0069	+	22.4466i	−0.440275	+	0.897863i
$626$	−12.4953	+	34.5008i	−0.499412	+	1.37893i
$627$	1.17450	−	4.38331i	0.0469051	−	0.175052i
$628$	2.00805	+	22.1422i	0.0801301	+	0.883569i
$629$			5.78640i			0.230719i
$630$	7.67623	−	21.0096i	0.305828	−	0.837043i
$631$		−	9.29850i		−	0.370167i	−0.982723	−	0.185084i	$-0.940744\pi$
$631$		−	9.29850i		−	0.370167i	0.982723	−	0.185084i	$-0.0592556\pi$
$632$	13.7627	−	13.8945i	0.547453	−	0.552693i
$633$	−2.55019	+	9.51742i	−0.101361	+	0.378284i
$634$	−0.284972	−	0.103209i	−0.0113177	−	0.00409896i
$635$	−14.5977	+	4.17746i	−0.579293	+	0.165778i
$636$	−3.38991	−	0.586639i	−0.134418	−	0.0232618i
$637$	4.47422	+	19.7933i	0.177275	+	0.784239i
$638$	40.5086	+	3.47925i	1.60375	+	0.137745i
$639$	−6.49663	+	11.2525i	−0.257003	+	0.445142i
$640$	−1.49753	+	25.2539i	−0.0591950	+	0.998246i
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	0.891844	−	0.452344i	$-0.149412\pi$
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	−0.837663	+	0.546187i	$0.816079\pi$
$642$	3.63644	−	5.21096i	0.143519	−	0.205660i
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	−0.613782	−	0.789475i	$-0.710353\pi$
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	0.789475	+	0.613782i	$0.210353\pi$
$644$	−12.3819	+	4.27568i	−0.487915	+	0.168485i
$645$	−0.101453	−	5.99422i	−0.00399470	−	0.236022i
$646$	−0.298644	−	1.67811i	−0.0117500	−	0.0660243i
$647$	−5.58856	+	20.8568i	−0.219709	+	0.819964i	0.764747	+	0.644331i	$0.222864\pi$
$647$	−5.58856	+	20.8568i	−0.219709	+	0.819964i	−0.984456	+	0.175633i	$0.943803\pi$
$648$	4.59551	+	16.8296i	0.180528	+	0.661130i
$649$	50.8771	+	29.3739i	1.99710	+	1.15303i
$650$	13.7244	+	15.2263i	0.538313	+	0.597223i
$651$	4.93943	+	0.0975380i	0.193591	+	0.00382282i
$652$	30.0162	−	21.1599i	1.17552	−	0.828686i
$653$	−28.1634	+	7.54635i	−1.10212	+	0.295311i	−0.763627	−	0.645658i	$-0.776583\pi$
$653$	−28.1634	+	7.54635i	−1.10212	+	0.295311i	−0.338491	+	0.940970i	$0.609916\pi$
$654$	0.111255	−	0.307187i	0.00435041	−	0.0120119i
$655$	29.1270	−	17.4803i	1.13809	−	0.683010i
$656$	10.2235	−	8.68974i	0.399159	−	0.339277i
$657$	18.4938	−	18.4938i	0.721511	−	0.721511i
$658$	27.6102	−	37.9461i	1.07636	−	1.47929i
$659$	−8.28576			−0.322768			−0.161384	−	0.986892i	$-0.551596\pi$
$659$	−8.28576			−0.322768			−0.161384	+	0.986892i	$0.551596\pi$
$660$	10.0616	−	1.08444i	0.391649	−	0.0422118i
$661$	−10.4781	−	18.1487i	−0.407553	−	0.705902i	0.587062	−	0.809542i	$-0.300284\pi$
$661$	−10.4781	−	18.1487i	−0.407553	−	0.705902i	−0.994615	+	0.103640i	$0.966951\pi$
$662$	−2.72214	+	1.27462i	−0.105799	+	0.0495396i
$663$	−0.257671	−	0.961643i	−0.0100071	−	0.0373471i
$664$	−18.8891	+	11.0259i	−0.733040	+	0.427889i
$665$	3.03828	+	11.4683i	0.117820	+	0.444723i
$666$	23.4428	+	27.8482i	0.908391	+	1.07909i
$667$	−17.3592	+	4.65138i	−0.672150	+	0.180102i
$668$	15.5800	−	33.6902i	0.602807	−	1.30351i
$669$	8.07303	−	4.66096i	0.312121	−	0.180203i
$670$	11.8061	−	2.30783i	0.456109	−	0.0891593i
$671$			16.7654i			0.647221i
$672$	−3.70553	+	7.70763i	−0.142944	+	0.297328i
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.991758	+	0.128125i	$0.0408958\pi$
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.128125	+	0.991758i	$0.459104\pi$
$674$	−7.86798	−	44.2110i	−0.303063	−	1.70294i
$675$	3.66307	−	15.7902i	0.140992	−	0.607764i
$676$	−8.62775	+	3.17130i	−0.331836	+	0.121973i
$677$	−10.1358	−	37.8274i	−0.389551	−	1.45383i	−0.830866	−	0.556473i	$-0.812154\pi$
$677$	−10.1358	−	37.8274i	−0.389551	−	1.45383i	0.441314	−	0.897353i	$-0.354512\pi$
$678$	−4.06738	−	0.349344i	−0.156207	−	0.0134165i
$679$	3.66707	−	2.02172i	0.140729	−	0.0775865i
$680$	3.24986	−	1.97149i	0.124627	−	0.0756031i
$681$	−3.45396	+	5.98243i	−0.132356	+	0.229247i
$682$	−7.76095	−	16.5747i	−0.297182	−	0.634676i
$683$	−11.4729	−	3.07415i	−0.438998	−	0.117629i	0.0325489	−	0.999470i	$-0.489638\pi$
$683$	−11.4729	−	3.07415i	−0.438998	−	0.117629i	−0.471547	+	0.881841i	$0.656304\pi$
$684$	−8.23591	−	6.86631i	−0.314908	−	0.262540i
$685$	−7.11444	+	7.35942i	−0.271829	+	0.281189i
$686$	−26.0129	+	3.05451i	−0.993176	+	0.116622i
$687$	0.886428	+	0.886428i	0.0338193	+	0.0338193i
$688$	1.51698	−	18.7067i	0.0578345	−	0.713187i
$689$	−7.55767	+	4.36343i	−0.287924	+	0.166233i
$690$	−4.01842	+	1.96518i	−0.152979	+	0.0748130i
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	0.364054	−	0.931378i	$-0.381392\pi$
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	−0.624570	+	0.780969i	$0.714726\pi$
$692$	−8.93656	−	12.6769i	−0.339717	−	0.481902i
$693$	−26.9089	−	7.78275i	−1.02218	−	0.295642i
$694$	16.6344	+	19.7603i	0.631434	+	0.750092i
$695$	12.0661	−	21.7407i	0.457693	−	0.824670i
$696$	−5.81804	+	10.1889i	−0.220532	+	0.386210i
$697$	−1.94732	−	0.521782i	−0.0737599	−	0.0197639i
$698$	25.0588	+	17.4871i	0.948490	+	0.661898i
$699$	0.644031			0.0243595
$700$	−21.4073	+	15.5476i	−0.809120	+	0.587643i
$701$	29.1974			1.10277			0.551386	−	0.834250i	$-0.314099\pi$
$701$	29.1974			1.10277			0.551386	+	0.834250i	$0.314099\pi$
$702$	−10.8994	−	7.60607i	−0.411371	−	0.287073i
$703$	−18.6496	−	4.99713i	−0.703381	−	0.188470i
$704$	31.6799	−	0.301784i	1.19398	−	0.0113739i
$705$	7.77656	−	14.0118i	0.292882	−	0.527714i
$706$	15.4556	+	18.3600i	0.581678	+	0.690986i
$707$	−11.3299	−	45.8892i	−0.426103	−	1.72584i
$708$	−13.8565	+	9.76814i	−0.520759	+	0.367109i
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.872900	−	0.487900i	$-0.162237\pi$
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.0139163	+	0.999903i	$0.495570\pi$
$710$	13.8062	−	6.75184i	0.518139	−	0.253392i
$711$	−16.0089	+	9.24277i	−0.600382	+	0.346631i
$712$	7.78003	+	7.70627i	0.291569	+	0.288805i
$713$	5.72029	+	5.72029i	0.214227	+	0.214227i
$714$	1.26929	−	0.200121i	0.0475020	−	0.00748933i
$715$	17.8422	−	18.4566i	0.667261	−	0.690237i
$716$	−6.56833	+	7.87850i	−0.245470	+	0.294433i
$717$	10.9580	+	2.93619i	0.409234	+	0.109654i
$718$	−5.32528	−	11.3729i	−0.198738	−	0.424434i
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	−0.307474	−	0.951557i	$-0.599484\pi$
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	0.977809	−	0.209498i	$-0.0671831\pi$
$720$	7.65338	−	22.6546i	0.285225	−	0.844286i
$721$	0.585904	−	29.6708i	0.0218202	−	1.10500i
$722$	−21.1050	−	1.81269i	−0.785448	−	0.0674615i
$723$	−1.27999	−	4.77699i	−0.0476033	−	0.177658i
$724$	−12.5094	−	34.0326i	−0.464907	−	1.26481i
$725$	−30.8030	+	19.2025i	−1.14399	+	0.713163i
$726$	−0.663039	−	3.72568i	−0.0246077	−	0.138273i
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	0.594739	−	0.803919i	$-0.297256\pi$
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	−0.803919	+	0.594739i	$0.797256\pi$
$728$	5.30022	+	21.0364i	0.196439	+	0.779659i
$729$		−	10.9327i		−	0.404916i
$730$	−30.3612	+	5.93496i	−1.12372	+	0.219663i
$731$	−2.44214	+	1.40997i	−0.0903260	+	0.0521497i
$732$	−4.39133	−	2.03076i	−0.162308	−	0.0750591i
$733$	15.5419	−	4.16444i	0.574053	−	0.153817i	0.0398983	−	0.999204i	$-0.487297\pi$
$733$	15.5419	−	4.16444i	0.574053	−	0.153817i	0.534155	+	0.845387i	$0.320630\pi$
$734$	19.7993	+	23.5199i	0.730804	+	0.868136i
$735$	−8.68928	+	2.11936i	−0.320509	+	0.0781738i
$736$	−13.1208	+	4.89388i	−0.483640	+	0.180391i
$737$	−3.89904	−	14.5514i	−0.143623	−	0.536008i
$738$	−11.4858	+	5.37812i	−0.422797	+	0.197971i
$739$	11.4543	+	19.8395i	0.421355	+	0.729808i	0.996072	−	0.0885439i	$-0.0282214\pi$
$739$	11.4543	+	19.8395i	0.421355	+	0.729808i	−0.574717	+	0.818352i	$0.694888\pi$
$740$	−4.61395	−	42.8091i	−0.169612	−	1.57369i
$741$	3.32190			0.122033
$742$	−4.57411	−	10.2931i	−0.167921	−	0.377872i
$743$	−21.3493	+	21.3493i	−0.783229	+	0.783229i	−0.980374	−	0.197145i	$-0.936833\pi$
$743$	−21.3493	+	21.3493i	−0.783229	+	0.783229i	0.197145	+	0.980374i	$0.436833\pi$
$744$	5.28144	−	0.0251551i	0.193627	−	0.000922230i
$745$	9.39067	−	5.63572i	0.344048	−	0.206477i
$746$	−0.235396	+	0.649954i	−0.00861846	+	0.0237965i
$747$	19.9691	−	5.35071i	0.730632	−	0.195772i
$748$	−2.74269	−	3.89061i	−0.100283	−	0.142255i
$749$	20.8004	+	0.410742i	0.760030	+	0.0150082i
$750$	−6.60765	+	6.16171i	−0.241277	+	0.224994i
$751$	31.7774	+	18.3467i	1.15958	+	0.669481i	0.951202	−	0.308568i	$-0.0998498\pi$
$751$	31.7774	+	18.3467i	1.15958	+	0.669481i	0.208373	+	0.978049i	$0.433183\pi$
$752$	28.5137	−	41.2772i	1.03979	−	1.50522i
$753$	−0.230154	+	0.858946i	−0.00838728	+	0.0313017i
$754$	5.21476	+	29.3023i	0.189910	+	1.06713i
$755$	0.557675	+	32.9496i	0.0202959	+	1.19916i
$756$	11.2429	−	12.9566i	0.408901	−	0.471228i
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	−0.143191	−	0.989695i	$-0.545736\pi$
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	0.989695	+	0.143191i	$0.0457363\pi$
$758$	−22.5246	+	32.2774i	−0.818130	+	1.17237i
$759$	2.80093	+	4.85135i	0.101667	+	0.176093i
$760$	3.54752	+	12.1769i	0.128682	+	0.441702i
$761$	−3.80960	+	6.59842i	−0.138098	+	0.239192i	−0.926777	−	0.375613i	$-0.877432\pi$
$761$	−3.80960	+	6.59842i	−0.138098	+	0.239192i	0.788679	+	0.614806i	$0.210766\pi$
$762$	−5.46715	−	0.469568i	−0.198054	−	0.0170107i
$763$	1.03849	−	0.256399i	0.0375958	−	0.00928226i
$764$	−5.34878	+	30.9080i	−0.193512	+	1.11821i
$765$	−3.45422	+	0.988503i	−0.124888	+	0.0357394i
$766$	6.87682	+	2.49060i	0.248470	+	0.0899890i
$767$	−11.1305	+	41.5398i	−0.401901	+	1.49991i
$768$	−3.75827	+	8.33440i	−0.135615	+	0.300742i
$769$		−	30.3461i		−	1.09431i	−0.837031	−	0.547155i	$-0.815711\pi$
$769$		−	30.3461i		−	1.09431i	0.837031	−	0.547155i	$-0.184289\pi$
$770$	21.2662	+	25.4077i	0.766381	+	0.915629i
$771$		−	10.1665i		−	0.366138i
$772$	−15.4608	+	1.40213i	−0.556447	+	0.0504637i
$773$	−6.78186	+	25.3103i	−0.243927	+	0.910347i	0.729993	+	0.683454i	$0.239523\pi$
$773$	−6.78186	+	25.3103i	−0.243927	+	0.910347i	−0.973920	+	0.226892i	$0.927143\pi$
$774$	−6.04097	+	16.6798i	−0.217138	+	0.599543i
$775$	14.4186	+	7.68611i	0.517931	+	0.276093i
$776$	3.86612	−	2.25673i	0.138786	−	0.0810117i
$777$	4.04408	−	13.9824i	0.145081	−	0.501616i
$778$	1.47949	−	17.2256i	0.0530423	−	0.617568i
$779$	3.36341	−	5.82559i	0.120507	−	0.208724i
$780$	2.67310	+	6.90899i	0.0957125	+	0.247381i
$781$	−9.62327	−	16.6680i	−0.344348	−	0.596428i
$782$	1.72549	+	1.20412i	0.0617032	+	0.0430592i
$783$	16.6418	−	16.6418i	0.594728	−	0.594728i
$784$	−27.7206	+	3.94588i	−0.990020	+	0.140924i
$785$	−17.2768	+	17.8717i	−0.616635	+	0.637868i
$786$	12.0865	−	2.15096i	0.431111	−	0.0767224i
$787$	2.88594	−	10.7705i	0.102873	−	0.383926i	−0.895222	−	0.445619i	$-0.852983\pi$
$787$	2.88594	−	10.7705i	0.102873	−	0.383926i	0.998095	+	0.0616935i	$0.0196501\pi$
$788$	−10.8589	−	5.02166i	−0.386831	−	0.178889i
$789$	−9.50285	−	5.48647i	−0.338310	−	0.195324i
$790$	21.8135	+	1.50217i	0.776091	+	0.0534447i
$791$	−6.45308	−	11.7048i	−0.229445	−	0.416176i
$792$	−28.9620	−	7.61269i	−1.02912	−	0.270505i
$793$	−11.8546	+	3.17643i	−0.420969	+	0.112798i
$794$	23.2526	+	8.42146i	0.825203	+	0.298866i
$795$	−1.97928	−	3.29803i	−0.0701977	−	0.116969i
$796$	−18.0426	+	21.6416i	−0.639504	+	0.767065i
$797$	9.45111	−	9.45111i	0.334775	−	0.334775i	−0.519621	−	0.854397i	$-0.673927\pi$
$797$	9.45111	−	9.45111i	0.334775	−	0.334775i	0.854397	+	0.519621i	$0.173927\pi$
$798$	−0.451170	+	4.26374i	−0.0159712	+	0.150935i
$799$	−7.53784			−0.266670
$800$	−22.4712	+	17.1769i	−0.794477	+	0.607294i
$801$	−5.17536	−	8.96399i	−0.182863	−	0.316727i
$802$	18.6643	+	39.8604i	0.659060	+	1.40752i
$803$	10.0270	+	37.4213i	0.353846	+	1.32057i
$804$	4.28371	+	0.741317i	0.151075	+	0.0261442i
$805$	−12.6627	−	7.35850i	−0.446300	−	0.259353i
$806$	10.2493	−	8.62795i	0.361016	−	0.303906i
$807$	7.91923	−	2.12195i	0.278770	−	0.0746962i
$808$	−13.3106	−	48.7461i	−0.468267	−	1.71488i
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.0875707	−	0.996158i	$-0.472090\pi$
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.906484	+	0.422241i	$0.138756\pi$
$810$	−10.8899	+	16.1819i	−0.382633	+	0.568573i
$811$			38.0037i			1.33449i	0.744838	+	0.667245i	$0.232527\pi$
$811$			38.0037i			1.33449i	−0.744838	+	0.667245i	$0.767473\pi$
$812$	−38.3185	+	2.71354i	−1.34471	+	0.0952266i
$813$	−8.35402	−	8.35402i	−0.292988	−	0.292988i
$814$	−53.0867	+	9.44755i	−1.86069	+	0.331136i
$815$	39.8347	+	9.95433i	1.39535	+	0.348685i
$816$	1.35128	−	0.247125i	0.0473042	−	0.00865110i
$817$	−2.43530	−	9.08868i	−0.0852005	−	0.317973i
$818$	0.619695	−	7.21506i	0.0216671	−	0.252269i
$819$	0.404838	−	20.5014i	0.0141462	−	0.716378i
$820$	14.8228	+	2.30751i	0.517633	+	0.0805819i
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	−0.747144	−	0.664662i	$-0.768576\pi$
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	0.949186	+	0.314715i	$0.101909\pi$
$822$	−3.35015	+	1.56868i	−0.116850	+	0.0547140i
$823$	−32.4334	−	8.69051i	−1.13056	−	0.302932i	−0.355409	−	0.934711i	$-0.615659\pi$
$823$	−32.4334	−	8.69051i	−1.13056	−	0.302932i	−0.775149	+	0.631779i	$0.782325\pi$
$824$	−0.151105	−	31.7252i	−0.00526398	−	1.10520i
$825$	8.26665	+	7.72517i	0.287808	+	0.268956i
$826$	−51.8057	−	19.9282i	−1.80255	−	0.693389i
$827$	−4.77258	−	4.77258i	−0.165959	−	0.165959i	0.619242	−	0.785200i	$-0.287440\pi$
$827$	−4.77258	−	4.77258i	−0.165959	−	0.165959i	−0.785200	+	0.619242i	$0.787440\pi$
$828$	13.1826	−	1.19552i	0.458126	−	0.0415470i
$829$	−29.2731	+	16.9008i	−1.01670	+	0.586989i	−0.913145	−	0.407635i	$-0.866354\pi$
$829$	−29.2731	+	16.9008i	−1.01670	+	0.586989i	−0.103550	+	0.994624i	$0.533020\pi$
$830$	−23.1294	−	7.93674i	−0.802834	−	0.275488i
$831$	2.41177	+	1.39244i	0.0836634	+	0.0483031i
$832$	6.21555	+	22.3432i	0.215485	+	0.774611i
$833$	2.85507	+	3.08996i	0.0989224	+	0.107061i
$834$	6.87439	−	5.78693i	0.238041	−	0.200385i
$835$	39.8980	−	11.4177i	1.38073	−	0.395125i
$836$	14.9080	−	5.47975i	0.515605	−	0.189521i
$837$	−10.2331	−	2.74194i	−0.353707	−	0.0947755i
$838$	11.3733	−	16.2978i	0.392885	−	0.562998i
$839$	−3.12360			−0.107839			−0.0539193	−	0.998545i	$-0.517171\pi$
$839$	−3.12360			−0.107839			−0.0539193	+	0.998545i	$0.517171\pi$
$840$	−9.23092	+	2.49264i	−0.318497	+	0.0860043i
$841$	−23.7024			−0.817325
$842$	−30.3742	+	43.5258i	−1.04676	+	1.50000i
$843$	5.36025	+	1.43627i	0.184617	+	0.0494679i
$844$	−32.3696	+	11.8981i	−1.11421	+	0.409550i
$845$	−8.98592	−	4.98720i	−0.309125	−	0.171565i
$846$	−36.2773	+	30.5386i	−1.24724	+	1.04994i
$847$	8.93212	−	8.58619i	0.306911	−	0.295025i
$848$	−5.15811	−	10.8807i	−0.177130	−	0.373643i
$849$	0.701659	+	0.405103i	0.0240809	+	0.0139031i
$850$	4.04246	+	1.31111i	0.138655	+	0.0449709i
$851$	20.6409	−	11.9171i	0.707562	−	0.408511i
$852$	5.53147	−	0.501644i	0.189505	−	0.0171860i
$853$	−3.22775	−	3.22775i	−0.110516	−	0.110516i	0.649686	−	0.760202i	$-0.274900\pi$
$853$	−3.22775	−	3.22775i	−0.110516	−	0.110516i	−0.760202	+	0.649686i	$0.774900\pi$
$854$	−2.46697	−	15.6471i	−0.0844181	−	0.535432i
$855$	−0.202875	−	11.9866i	−0.00693817	−	0.409934i
$856$	22.2406	−	0.105930i	0.760170	−	0.00362063i
$857$	−37.2336	−	9.97671i	−1.27187	−	0.340798i	−0.441126	−	0.897445i	$-0.645421\pi$
$857$	−37.2336	−	9.97671i	−1.27187	−	0.340798i	−0.830749	+	0.556647i	$0.812087\pi$
$858$	8.40179	−	3.93407i	0.286832	−	0.134307i
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	−0.960182	−	0.279374i	$-0.909873\pi$
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	0.722036	+	0.691855i	$0.243206\pi$
$860$	16.9432	−	12.3786i	0.577760	−	0.422107i
$861$	4.34088	+	2.62182i	0.147937	+	0.0893513i
$862$	−2.93700	+	34.1953i	−0.100035	+	1.16470i
$863$	−10.7069	−	39.9587i	−0.364467	−	1.36021i	−0.868142	−	0.496316i	$-0.834686\pi$
$863$	−10.7069	−	39.9587i	−0.364467	−	1.36021i	0.503675	−	0.863893i	$-0.331981\pi$
$864$	11.6762	−	14.1416i	0.397231	−	0.481106i
$865$	4.20405	−	16.8236i	0.142942	−	0.572018i
$866$	−0.0499409	+	0.00888771i	−0.00169706	+	0.000302017i
$867$	6.72289	+	6.72289i	0.228321	+	0.228321i
$868$	9.68217	+	14.3271i	0.328634	+	0.486292i
$869$		−	27.3821i		−	0.928873i
$870$	−12.8742	+	2.51663i	−0.436477	+	0.0853219i
$871$	9.55038	−	5.51391i	0.323602	−	0.186832i
$872$	1.10314	−	0.301224i	0.0373571	−	0.0102007i
$873$	−4.08717	+	1.09515i	−0.138330	+	0.0370653i
$874$	−5.37101	+	4.52136i	−0.181677	+	0.152937i
$875$	−28.7962	−	6.76593i	−0.973490	−	0.228730i
$876$	−11.0163	−	1.90642i	−0.372205	−	0.0644118i
$877$	8.94885	+	33.3976i	0.302181	+	1.12776i	0.935345	+	0.353737i	$0.115089\pi$
$877$	8.94885	+	33.3976i	0.302181	+	1.12776i	−0.633164	+	0.774018i	$0.718244\pi$
$878$	9.15094	+	19.5432i	0.308829	+	0.659550i
$879$	2.43499	+	4.21753i	0.0821303	+	0.142254i
$880$	23.3933	+	26.5967i	0.788589	+	0.896574i
$881$	−9.22163			−0.310685			−0.155342	−	0.987861i	$-0.549648\pi$
$881$	−9.22163			−0.310685			−0.155342	+	0.987861i	$0.549648\pi$
$882$	26.2591	+	3.30406i	0.884191	+	0.111253i
$883$	−18.1891	+	18.1891i	−0.612111	+	0.612111i	−0.943496	−	0.331385i	$-0.892484\pi$
$883$	−18.1891	+	18.1891i	−0.612111	+	0.612111i	0.331385	+	0.943496i	$0.392484\pi$
$884$	2.23136	−	2.67645i	0.0750488	−	0.0900186i
$885$	−18.3891	−	4.59526i	−0.618142	−	0.154468i
$886$	15.8979	+	5.75780i	0.534101	+	0.193437i
$887$	19.5218	−	5.23085i	0.655477	−	0.175635i	0.0842733	−	0.996443i	$-0.473143\pi$
$887$	19.5218	−	5.23085i	0.655477	−	0.175635i	0.571204	+	0.820808i	$0.306476\pi$
$888$	3.95571	−	15.0493i	0.132745	−	0.505020i
$889$	−8.67387	−	15.7330i	−0.290912	−	0.527667i
$890$	−0.841118	+	12.2142i	−0.0281943	+	0.409421i
$891$	21.1538	+	12.2132i	0.708679	+	0.409156i
$892$	29.6144	+	13.6951i	0.991563	+	0.458546i
$893$	6.50968	−	24.2944i	0.217838	−	0.812983i
$894$	3.89674	−	0.693481i	0.130326	−	0.0231935i
$895$	−11.4664	+	0.194071i	−0.383281	+	0.00648706i
$896$	−29.5223	+	4.94324i	−0.986270	+	0.165142i
$897$	−2.89965	+	2.89965i	−0.0968165	+	0.0968165i
$898$	−15.9049	−	11.0992i	−0.530755	−	0.370384i
$899$	11.8617	+	20.5451i	0.395611	+	0.685219i
$900$	24.7669	−	10.0675i	0.825564	−	0.335583i
$901$	−0.904619	+	1.56685i	−0.0301372	+	0.0521992i
$902$	1.60762	−	18.7174i	0.0535279	−	0.623221i
$903$	6.88668	−	1.70029i	0.229174	−	0.0565822i
$904$	−7.20319	−	12.3402i	−0.239574	−	0.410428i
$905$	19.6723	−	35.4454i	0.653928	−	1.17825i
$906$	−4.05550	+	11.1977i	−0.134735	+	0.372018i
$907$	−10.9408	+	40.8315i	−0.363282	+	1.35579i	0.506452	+	0.862268i	$0.330957\pi$
$907$	−10.9408	+	40.8315i	−0.363282	+	1.35579i	−0.869734	+	0.493520i	$0.835710\pi$
$908$	−24.0796	+	2.18376i	−0.799110	+	0.0724706i
$909$			47.7627i			1.58419i
$910$	−13.9362	+	19.8509i	−0.461982	+	0.658050i
$911$		−	47.4291i		−	1.57140i	−0.618610	−	0.785698i	$-0.712304\pi$
$911$		−	47.4291i		−	1.57140i	0.618610	−	0.785698i	$-0.287696\pi$
$912$	−0.370480	+	4.56859i	−0.0122678	+	0.151281i
$913$	−7.92585	+	29.5797i	−0.262307	+	0.978945i
$914$	18.5503	+	6.71841i	0.613588	+	0.222225i
$915$	−1.48823	−	5.20047i	−0.0491994	−	0.171922i
$916$	−0.748196	+	4.32346i	−0.0247211	+	0.142851i
$917$	27.8544	+	28.9767i	0.919834	+	0.956894i
$918$	−2.74535	−	0.235796i	−0.0906101	−	0.00778242i
$919$	15.8502	−	27.4533i	0.522849	−	0.905601i	−0.476797	−	0.879013i	$-0.658202\pi$
$919$	15.8502	−	27.4533i	0.522849	−	0.905601i	0.999646	−	0.0265881i	$-0.00846425\pi$
$920$	−13.7257	−	7.53248i	−0.452522	−	0.248339i
$921$	4.44575	+	7.70027i	0.146493	+	0.253733i
$922$	22.3848	−	32.0771i	0.737205	−	1.05640i
$923$	9.96245	−	9.96245i	0.327918	−	0.327918i
$924$	3.90838	+	11.3182i	0.128576	+	0.372342i
$925$	32.8681	−	35.1720i	1.08070	−	1.15645i
$926$	1.41495	+	7.95074i	0.0464981	+	0.261278i
$927$	−7.76138	+	28.9659i	−0.254917	+	0.951364i
$928$	−40.8808	+	3.90384i	−1.34198	+	0.128150i
$929$	−37.2981	−	21.5341i	−1.22371	−	0.706509i	−0.258003	−	0.966144i	$-0.583065\pi$
$929$	−37.2981	−	21.5341i	−1.22371	−	0.706509i	−0.965707	+	0.259635i	$0.916398\pi$
$930$	3.87867	+	4.45238i	0.127187	+	0.145999i
$931$	−12.4246	+	6.53341i	−0.407199	+	0.214124i
$932$	1.29880	+	1.84240i	0.0425436	+	0.0603498i
$933$	14.0184	−	3.75622i	0.458941	−	0.122973i
$934$	5.91430	−	16.3300i	0.193522	−	0.534335i
$935$	1.29025	−	5.16326i	0.0421958	−	0.168857i
$936$	−0.104408	−	21.9210i	−0.00341268	−	0.716509i
$937$	−11.9105	+	11.9105i	−0.389100	+	0.389100i	−0.874366	−	0.485266i	$-0.838723\pi$
$937$	−11.9105	+	11.9105i	−0.389100	+	0.389100i	0.485266	+	0.874366i	$0.338723\pi$
$938$	5.78015	+	13.0070i	0.188729	+	0.424695i
$939$	−14.8261			−0.483832
$940$	55.7666	−	6.01051i	1.81891	−	0.196041i
$941$	−14.1264	−	24.4676i	−0.460507	−	0.797622i	0.538479	−	0.842639i	$-0.318999\pi$
$941$	−14.1264	−	24.4676i	−0.460507	−	0.797622i	−0.998986	+	0.0450169i	$0.985666\pi$
$942$	−8.13554	+	3.80940i	−0.265070	+	0.124117i
$943$	2.14922	+	8.02098i	0.0699881	+	0.261199i
$944$	−55.8880	−	19.9406i	−1.81900	−	0.649010i
$945$	19.1792	+	0.0541009i	0.623901	+	0.00175990i
$946$	−16.9230	−	20.1031i	−0.550213	−	0.653609i
$947$	23.9653	−	6.42148i	0.778767	−	0.208670i	0.152526	−	0.988299i	$-0.451259\pi$
$947$	23.9653	−	6.42148i	0.778767	−	0.208670i	0.626241	+	0.779629i	$0.284592\pi$
$948$	7.17214	+	3.31674i	0.232940	+	0.107723i
$949$	−24.5603	+	14.1799i	−0.797263	+	0.460300i
$950$	−7.71679	+	11.8966i	−0.250366	+	0.385975i
$951$		−	0.122462i		−	0.00397109i
$952$	3.13223	+	3.22752i	0.101516	+	0.104604i
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	0.318425	−	0.947948i	$-0.396846\pi$
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	−0.947948	+	0.318425i	$0.896846\pi$
$954$	1.99422	+	11.2057i	0.0645651	+	0.362798i
$955$	−30.0703	+	18.0464i	−0.973051	+	0.583967i
$956$	13.6991	+	37.2692i	0.443059	+	1.20537i
$957$	4.25181	+	15.8680i	0.137441	+	0.512938i
$958$	33.9356	+	2.91470i	1.09641	+	0.0941696i
$959$	−10.3672	−	6.26162i	−0.334775	−	0.202198i
$960$	−9.80001	+	2.90576i	−0.316294	+	0.0937832i
$961$	−10.1606	+	17.5986i	−0.327760	+	0.567697i
$962$	−16.7382	−	35.7469i	−0.539661	−	1.15253i
$963$	−20.3062	−	5.44104i	−0.654359	−	0.175335i
$964$	11.0843	−	13.2953i	0.357003	−	0.428213i
$965$	−12.4789	−	12.0636i	−0.401711	−	0.388339i
$966$	−3.32796	−	4.11560i	−0.107075	−	0.132417i
$967$	−34.9483	−	34.9483i	−1.12386	−	1.12386i	−0.991155	−	0.132706i	$-0.957633\pi$
$967$	−34.9483	−	34.9483i	−1.12386	−	1.12386i	−0.132706	−	0.991155i	$-0.542367\pi$
$968$	9.32104	−	9.41026i	0.299590	−	0.302457i
$969$	0.596424	−	0.344346i	0.0191599	−	0.0110620i
$970$	4.73400	+	1.62445i	0.152000	+	0.0521579i
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.988965	−	0.148150i	$-0.0473320\pi$
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.366180	+	0.930544i	$0.380665\pi$
$972$	−21.6594	+	15.2688i	−0.694726	+	0.489747i
$973$	28.2618	+	8.17406i	0.906032	+	0.262048i
$974$	3.12565	+	3.71302i	0.100152	+	0.118973i
$975$	−3.89614	+	7.30887i	−0.124776	+	0.234071i
$976$	−3.04642	−	16.6578i	−0.0975134	−	0.533203i
$977$	42.7841	+	11.4640i	1.36879	+	0.366765i	0.867035	−	0.498248i	$-0.166023\pi$
$977$	42.7841	+	11.4640i	1.36879	+	0.366765i	0.501750	+	0.865012i	$0.332690\pi$
$978$	12.1686	+	8.49178i	0.389109	+	0.271537i
$979$	15.3322			0.490020
$980$	−23.5863	−	20.5836i	−0.753438	−	0.657519i
$981$	−1.08089			−0.0345101
$982$	4.10978	+	2.86799i	0.131148	+	0.0915212i
$983$	−6.04477	−	1.61969i	−0.192798	−	0.0516601i	0.161128	−	0.986934i	$-0.448487\pi$
$983$	−6.04477	−	1.61969i	−0.192798	−	0.0516601i	−0.353926	+	0.935273i	$0.615154\pi$
$984$	4.70789	+	2.68828i	0.150082	+	0.0856993i
$985$	−3.68009	−	12.8597i	−0.117257	−	0.409744i
$986$	3.97373	+	4.72046i	0.126549	+	0.150330i
$987$	18.2146	+	5.26815i	0.579778	+	0.167687i
$988$	6.69918	+	9.50305i	0.213129	+	0.302332i
$989$	10.0592	+	5.80766i	0.319863	+	0.184673i
$990$	−14.7087	−	30.0765i	−0.467473	−	0.955893i
$991$	−23.9504	+	13.8278i	−0.760809	+	0.439253i	−0.829586	−	0.558379i	$-0.811424\pi$
$991$	−23.9504	+	13.8278i	−0.760809	+	0.439253i	0.0687769	+	0.997632i	$0.478090\pi$
$992$	10.7229	+	15.0580i	0.340452	+	0.478093i
$993$	−0.858769	−	0.858769i	−0.0272522	−	0.0272522i
$994$	11.4340	+	14.1401i	0.362664	+	0.448498i
$995$	−31.4974	+	0.533095i	−0.998534	+	0.0169003i
$996$	−6.78771	−	5.65893i	−0.215077	−	0.179310i
$997$	−8.67546	−	2.32458i	−0.274755	−	0.0736203i	0.118811	−	0.992917i	$-0.462092\pi$
$997$	−8.67546	−	2.32458i	−0.274755	−	0.0736203i	−0.393565	+	0.919297i	$0.628758\pi$
$998$	−18.1887	−	38.8447i	−0.575753	−	1.22961i
$999$	−15.6062	+	27.0308i	−0.493759	+	0.855216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.6	✓	72
4.3	odd	2	inner	140.2.w.b.23.17	yes	72
5.2	odd	4	inner	140.2.w.b.107.3	yes	72
5.3	odd	4		700.2.be.e.107.16		72
5.4	even	2		700.2.be.e.443.13		72
7.2	even	3		980.2.k.k.883.17		36
7.3	odd	6		980.2.x.m.263.7		72
7.4	even	3	inner	140.2.w.b.123.7	yes	72
7.5	odd	6		980.2.k.j.883.17		36
7.6	odd	2		980.2.x.m.863.6		72
20.3	even	4		700.2.be.e.107.12		72
20.7	even	4	inner	140.2.w.b.107.7	yes	72
20.19	odd	2		700.2.be.e.443.2		72
28.3	even	6		980.2.x.m.263.3		72
28.11	odd	6	inner	140.2.w.b.123.3	yes	72
28.19	even	6		980.2.k.j.883.9		36
28.23	odd	6		980.2.k.k.883.9		36
28.27	even	2		980.2.x.m.863.17		72
35.2	odd	12		980.2.k.k.687.9		36
35.4	even	6		700.2.be.e.543.12		72
35.12	even	12		980.2.k.j.687.9		36
35.17	even	12		980.2.x.m.67.17		72
35.18	odd	12		700.2.be.e.207.2		72
35.27	even	4		980.2.x.m.667.3		72
35.32	odd	12	inner	140.2.w.b.67.17	yes	72
140.27	odd	4		980.2.x.m.667.7		72
140.39	odd	6		700.2.be.e.543.16		72
140.47	odd	12		980.2.k.j.687.17		36
140.67	even	12	inner	140.2.w.b.67.6	yes	72
140.87	odd	12		980.2.x.m.67.6		72
140.107	even	12		980.2.k.k.687.17		36
140.123	even	12		700.2.be.e.207.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	1.1	even	1	trivial
140.2.w.b.23.17	yes	72	4.3	odd	2	inner
140.2.w.b.67.6	yes	72	140.67	even	12	inner
140.2.w.b.67.17	yes	72	35.32	odd	12	inner
140.2.w.b.107.3	yes	72	5.2	odd	4	inner
140.2.w.b.107.7	yes	72	20.7	even	4	inner
140.2.w.b.123.3	yes	72	28.11	odd	6	inner
140.2.w.b.123.7	yes	72	7.4	even	3	inner
700.2.be.e.107.12		72	20.3	even	4
700.2.be.e.107.16		72	5.3	odd	4
700.2.be.e.207.2		72	35.18	odd	12
700.2.be.e.207.13		72	140.123	even	12
700.2.be.e.443.2		72	20.19	odd	2
700.2.be.e.443.13		72	5.4	even	2
700.2.be.e.543.12		72	35.4	even	6
700.2.be.e.543.16		72	140.39	odd	6
980.2.k.j.687.9		36	35.12	even	12
980.2.k.j.687.17		36	140.47	odd	12
980.2.k.j.883.9		36	28.19	even	6
980.2.k.j.883.17		36	7.5	odd	6
980.2.k.k.687.9		36	35.2	odd	12
980.2.k.k.687.17		36	140.107	even	12
980.2.k.k.883.9		36	28.23	odd	6
980.2.k.k.883.17		36	7.2	even	3
980.2.x.m.67.6		72	140.87	odd	12
980.2.x.m.67.17		72	35.17	even	12
980.2.x.m.263.3		72	28.3	even	6
980.2.x.m.263.7		72	7.3	odd	6
980.2.x.m.667.3		72	35.27	even	4
980.2.x.m.667.7		72	140.27	odd	4
980.2.x.m.863.6		72	7.6	odd	2
980.2.x.m.863.17		72	28.27	even	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809319 + 1.15974i) q^{2} +(-0.551941 - 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(1.08510 - 1.95513i) q^{5} +(0.618214 - 0.520418i) q^{6} +(2.54158 + 0.735093i) q^{7} +(2.73551 + 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +O(q^{10})\)	\(q+(-0.809319 + 1.15974i) q^{2} +(-0.551941 - 0.147892i) q^{3} +(-0.690004 - 1.87720i) q^{4} +(1.08510 - 1.95513i) q^{5} +(0.618214 - 0.520418i) q^{6} +(2.54158 + 0.735093i) q^{7} +(2.73551 + 0.719030i) q^{8} +(-2.31531 - 1.33674i) q^{9} +(1.38926 + 2.84077i) q^{10} +(3.42960 - 1.98008i) q^{11} +(0.103218 + 1.13815i) q^{12} +(2.04987 + 2.04987i) q^{13} +(-2.90947 + 2.35266i) q^{14} +(-0.888062 + 0.918641i) q^{15} +(-3.04779 + 2.59056i) q^{16} +(0.580528 + 0.155552i) q^{17} +(3.42410 - 1.60331i) q^{18} +(-1.00269 + 1.73671i) q^{19} +(-4.41891 - 0.687909i) q^{20} +(-1.29409 - 0.781608i) q^{21} +(-0.479259 + 5.57997i) q^{22} +(-0.640717 - 2.39119i) q^{23} +(-1.40350 - 0.801422i) q^{24} +(-2.64510 - 4.24305i) q^{25} +(-4.03632 + 0.718322i) q^{26} +(2.29237 + 2.29237i) q^{27} +(-0.373784 - 5.27828i) q^{28} -7.25964i q^{29} +(-0.346661 - 1.77340i) q^{30} +(-2.83005 + 1.63393i) q^{31} +(-0.537745 - 5.63124i) q^{32} +(-2.18578 + 0.585677i) q^{33} +(-0.650233 + 0.547372i) q^{34} +(4.19508 - 4.17148i) q^{35} +(-0.911768 + 5.26867i) q^{36} +(2.49187 + 9.29977i) q^{37} +(-1.20264 - 2.56841i) q^{38} +(-0.828248 - 1.43457i) q^{39} +(4.37411 - 4.56806i) q^{40} -3.35439 q^{41} +(1.95380 - 0.868240i) q^{42} +(-3.31777 + 3.31777i) q^{43} +(-6.08345 - 5.07179i) q^{44} +(-5.12586 + 3.07624i) q^{45} +(3.29171 + 1.19217i) q^{46} +(-12.1147 + 3.24611i) q^{47} +(2.06532 - 0.979091i) q^{48} +(5.91928 + 3.73660i) q^{49} +(7.06157 + 0.366343i) q^{50} +(-0.297413 - 0.171711i) q^{51} +(2.43360 - 5.26244i) q^{52} +(-0.779134 + 2.90777i) q^{53} +(-4.51381 + 0.803298i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(6.42396 + 3.83832i) q^{56} +(0.810271 - 0.810271i) q^{57} +(8.41932 + 5.87537i) q^{58} +(7.41735 + 12.8472i) q^{59} +(2.33724 + 1.03321i) q^{60} +(-2.11676 + 3.66633i) q^{61} +(0.395476 - 4.60450i) q^{62} +(-4.90192 - 5.09941i) q^{63} +(6.96599 + 3.93382i) q^{64} +(6.23209 - 1.78345i) q^{65} +(1.08976 - 3.00894i) q^{66} +(0.984566 - 3.67445i) q^{67} +(-0.108564 - 1.19710i) q^{68} +1.41455i q^{69} +(1.44268 + 8.24128i) q^{70} -4.86004i q^{71} +(-5.37238 - 5.32145i) q^{72} +(-2.53197 + 9.44944i) q^{73} +(-12.8021 - 4.63656i) q^{74} +(0.832427 + 2.73310i) q^{75} +(3.95201 + 0.683915i) q^{76} +(10.1722 - 2.51146i) q^{77} +(2.33405 + 0.200469i) q^{78} +(3.45719 - 5.98803i) q^{79} +(1.75772 + 8.76986i) q^{80} +(3.08400 + 5.34165i) q^{81} +(2.71477 - 3.89023i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(-0.574310 + 2.96858i) q^{84} +(0.934058 - 0.966221i) q^{85} +(-1.16262 - 6.53289i) q^{86} +(-1.07364 + 4.00690i) q^{87} +(10.8054 - 2.95054i) q^{88} +(3.35292 + 1.93581i) q^{89} +(0.580822 - 8.43434i) q^{90} +(3.70307 + 6.71676i) q^{91} +(-4.04665 + 2.85269i) q^{92} +(1.80367 - 0.483291i) q^{93} +(6.03997 - 16.6770i) q^{94} +(2.30748 + 3.84490i) q^{95} +(-0.536012 + 3.18764i) q^{96} +(1.11914 - 1.11914i) q^{97} +(-9.12407 + 3.84074i) q^{98} -10.5874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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