LMFDB - Embedded newform 294.2.m.b.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.1
Character	$\chi$	$=$	294.163
Dual form			294.2.m.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.549960 + 0.374956i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-0.0527428 + 2.64523i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +O(q^{10})$	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.549960 + 0.374956i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-0.0527428 + 2.64523i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(-0.549960 - 0.374956i) q^{10} +(-0.462801 - 0.0697561i) q^{11} +(-0.733052 - 0.680173i) q^{12} +(-1.08354 + 1.35871i) q^{13} +(-2.48164 + 0.917313i) q^{14} +(-0.415006 - 0.520402i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(0.323899 - 0.0999097i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.817207 + 1.41544i) q^{19} +(0.148114 - 0.648930i) q^{20} +(-2.64177 + 0.145083i) q^{21} +(-0.104146 - 0.456294i) q^{22} +(3.81421 + 1.17653i) q^{23} +(0.365341 - 0.930874i) q^{24} +(-1.66484 + 4.24195i) q^{25} +(-1.66065 - 0.512243i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-1.76055 - 1.97496i) q^{28} +(2.18983 - 9.59427i) q^{29} +(0.332809 - 0.576443i) q^{30} +(2.92157 + 5.06032i) q^{31} +(0.955573 - 0.294755i) q^{32} +(0.0349758 - 0.466720i) q^{33} +(0.211337 + 0.265008i) q^{34} +(-0.962838 - 1.47454i) q^{35} +(0.623490 - 0.781831i) q^{36} +(1.99015 + 1.84659i) q^{37} +(-1.61616 - 0.243597i) q^{38} +(-1.43589 - 0.978971i) q^{39} +(0.658184 - 0.0992053i) q^{40} +(-0.571445 - 0.275194i) q^{41} +(-1.10020 - 2.40615i) q^{42} +(10.8398 - 5.22016i) q^{43} +(0.386703 - 0.263650i) q^{44} +(0.487933 - 0.452736i) q^{45} +(0.298288 + 3.98038i) q^{46} +(0.598023 + 1.52374i) q^{47} +1.00000 q^{48} +(-6.99444 - 0.279033i) q^{49} -4.55695 q^{50} +(0.123835 + 0.315527i) q^{51} +(-0.129870 - 1.73300i) q^{52} +(2.76000 - 2.56091i) q^{53} +(0.826239 - 0.563320i) q^{54} +(0.280678 - 0.135167i) q^{55} +(1.19524 - 2.36038i) q^{56} +(-1.47256 - 0.709146i) q^{57} +(9.73109 - 1.46673i) q^{58} +(7.33883 + 5.00353i) q^{59} +(0.658184 + 0.0992053i) q^{60} +(6.15540 + 5.71138i) q^{61} +(-3.64314 + 4.56836i) q^{62} +(-0.342097 - 2.62354i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.0864441 - 1.15352i) q^{65} +(0.447236 - 0.137954i) q^{66} +(4.09683 + 7.09592i) q^{67} +(-0.169479 + 0.293546i) q^{68} +(-0.888201 + 3.89146i) q^{69} +(1.02085 - 1.43499i) q^{70} +(-1.94436 - 8.51878i) q^{71} +(0.955573 + 0.294755i) q^{72} +(-0.876762 + 2.23395i) q^{73} +(-0.991857 + 2.52721i) q^{74} +(-4.35450 - 1.34319i) q^{75} +(-0.363692 - 1.59344i) q^{76} +(0.208930 - 1.22053i) q^{77} +(0.386710 - 1.69429i) q^{78} +(5.65156 - 9.78878i) q^{79} +(0.332809 + 0.576443i) q^{80} +(0.955573 - 0.294755i) q^{81} +(0.0473981 - 0.632483i) q^{82} +(-3.87463 - 4.85863i) q^{83} +(1.83787 - 1.90321i) q^{84} +(-0.140670 + 0.176394i) q^{85} +(8.81952 + 8.18332i) q^{86} +(9.73109 + 1.46673i) q^{87} +(0.386703 + 0.263650i) q^{88} +(-13.9325 + 2.09998i) q^{89} +(0.599702 + 0.288801i) q^{90} +(-3.53695 - 2.93786i) q^{91} +(-3.59625 + 1.73186i) q^{92} +(-4.82784 + 3.29156i) q^{93} +(-1.19992 + 1.11337i) q^{94} +(-0.0812986 - 1.08486i) q^{95} +(0.365341 + 0.930874i) q^{96} -0.540212 q^{97} +(-2.29561 - 6.61288i) q^{98} +0.468029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{10}{21}\right)$

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 $

$2$	0.365341	+	0.930874i	0.258335	+	0.658227i
$2$	0.365341	+	0.930874i	0.258335	+	0.658227i
$3$	0.0747301	+	0.997204i	0.0431454	+	0.575736i
$3$	0.0747301	+	0.997204i	0.0431454	+	0.575736i
$4$	−0.733052	+	0.680173i	−0.366526	+	0.340086i
$5$	−0.549960	+	0.374956i	−0.245950	+	0.167686i	−0.680020	−	0.733193i	$-0.738029\pi$
$5$	−0.549960	+	0.374956i	−0.245950	+	0.167686i	0.434071	+	0.900879i	$0.357077\pi$
$6$	−0.900969	+	0.433884i	−0.367819	+	0.177132i
$7$	−0.0527428	+	2.64523i	−0.0199349	+	0.999801i
$7$	−0.0527428	+	2.64523i	−0.0199349	+	0.999801i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	−0.988831	+	0.149042i	−0.329610	+	0.0496808i
$10$	−0.549960	−	0.374956i	−0.173913	−	0.118572i
$11$	−0.462801	−	0.0697561i	−0.139540	−	0.0210322i	0.0789009	−	0.996882i	$-0.474859\pi$
$11$	−0.462801	−	0.0697561i	−0.139540	−	0.0210322i	−0.218441	+	0.975850i	$0.570097\pi$
$12$	−0.733052	−	0.680173i	−0.211614	−	0.196349i
$13$	−1.08354	+	1.35871i	−0.300519	+	0.376839i	−0.909047	−	0.416693i	$-0.863189\pi$
$13$	−1.08354	+	1.35871i	−0.300519	+	0.376839i	0.608528	+	0.793532i	$0.291760\pi$
$14$	−2.48164	+	0.917313i	−0.663246	+	0.245162i
$15$	−0.415006	−	0.520402i	−0.107154	−	0.134367i
$16$	0.0747301	−	0.997204i	0.0186825	−	0.249301i
$17$	0.323899	−	0.0999097i	0.0785571	−	0.0242317i	−0.255228	−	0.966881i	$-0.582150\pi$
$17$	0.323899	−	0.0999097i	0.0785571	−	0.0242317i	0.333785	+	0.942649i	$0.391674\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.817207	+	1.41544i	−0.187480	+	0.324725i	−0.944409	−	0.328772i	$-0.893365\pi$
$19$	−0.817207	+	1.41544i	−0.187480	+	0.324725i	0.756929	+	0.653497i	$0.226699\pi$
$20$	0.148114	−	0.648930i	0.0331193	−	0.145105i
$21$	−2.64177	+	0.145083i	−0.576482	+	0.0316596i
$22$	−0.104146	−	0.456294i	−0.0222040	−	0.0972823i
$23$	3.81421	+	1.17653i	0.795317	+	0.245323i	0.665679	−	0.746238i	$-0.268142\pi$
$23$	3.81421	+	1.17653i	0.795317	+	0.245323i	0.129639	+	0.991561i	$0.458618\pi$
$24$	0.365341	−	0.930874i	0.0745749	−	0.190014i
$25$	−1.66484	+	4.24195i	−0.332968	+	0.848389i
$26$	−1.66065	−	0.512243i	−0.325680	−	0.100459i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−1.76055	−	1.97496i	−0.332712	−	0.373233i
$29$	2.18983	−	9.59427i	0.406641	−	1.78161i	−0.192849	−	0.981229i	$-0.561773\pi$
$29$	2.18983	−	9.59427i	0.406641	−	1.78161i	0.599490	−	0.800383i	$-0.295370\pi$
$30$	0.332809	−	0.576443i	0.0607624	−	0.105244i
$31$	2.92157	+	5.06032i	0.524730	+	0.908860i	0.999585	+	0.0287956i	$0.00916718\pi$
$31$	2.92157	+	5.06032i	0.524730	+	0.908860i	−0.474855	+	0.880064i	$0.657499\pi$
$32$	0.955573	−	0.294755i	0.168923	−	0.0521058i
$33$	0.0349758	−	0.466720i	0.00608851	−	0.0812455i
$34$	0.211337	+	0.265008i	0.0362440	+	0.0454485i
$35$	−0.962838	−	1.47454i	−0.162749	−	0.249243i
$36$	0.623490	−	0.781831i	0.103915	−	0.130305i
$37$	1.99015	+	1.84659i	0.327178	+	0.303577i	0.826609	−	0.562777i	$-0.190267\pi$
$37$	1.99015	+	1.84659i	0.327178	+	0.303577i	−0.499431	+	0.866354i	$0.666457\pi$
$38$	−1.61616	−	0.243597i	−0.262176	−	0.0395166i
$39$	−1.43589	−	0.978971i	−0.229926	−	0.156761i
$40$	0.658184	−	0.0992053i	0.104068	−	0.0156857i
$41$	−0.571445	−	0.275194i	−0.0892448	−	0.0429780i	0.388729	−	0.921352i	$-0.372914\pi$
$41$	−0.571445	−	0.275194i	−0.0892448	−	0.0429780i	−0.477974	+	0.878374i	$0.658629\pi$
$42$	−1.10020	−	2.40615i	−0.169765	−	0.371277i
$43$	10.8398	−	5.22016i	1.65305	−	0.796067i	0.653827	−	0.756644i	$-0.273163\pi$
$43$	10.8398	−	5.22016i	1.65305	−	0.796067i	0.999223	−	0.0394221i	$-0.0125517\pi$
$44$	0.386703	−	0.263650i	0.0582977	−	0.0397467i
$45$	0.487933	−	0.452736i	0.0727368	−	0.0674898i
$46$	0.298288	+	3.98038i	0.0439802	+	0.586875i
$47$	0.598023	+	1.52374i	0.0872306	+	0.222260i	0.967832	−	0.251598i	$-0.0809562\pi$
$47$	0.598023	+	1.52374i	0.0872306	+	0.222260i	−0.880601	+	0.473858i	$0.842861\pi$
$48$	1.00000			0.144338
$49$	−6.99444	−	0.279033i	−0.999205	−	0.0398619i
$50$	−4.55695			−0.644450
$51$	0.123835	+	0.315527i	0.0173404	+	0.0441827i
$52$	−0.129870	−	1.73300i	−0.0180098	−	0.240324i
$53$	2.76000	−	2.56091i	0.379116	−	0.351768i	−0.467481	−	0.884003i	$-0.654838\pi$
$53$	2.76000	−	2.56091i	0.379116	−	0.351768i	0.846597	+	0.532235i	$0.178648\pi$
$54$	0.826239	−	0.563320i	0.112437	−	0.0766582i
$55$	0.280678	−	0.135167i	0.0378466	−	0.0182259i
$56$	1.19524	−	2.36038i	0.159721	−	0.315419i
$57$	−1.47256	−	0.709146i	−0.195045	−	0.0939287i
$58$	9.73109	−	1.46673i	1.27775	−	0.192590i
$59$	7.33883	+	5.00353i	0.955434	+	0.651404i	0.937334	−	0.348432i	$-0.113286\pi$
$59$	7.33883	+	5.00353i	0.955434	+	0.651404i	0.0180999	+	0.999836i	$0.494238\pi$
$60$	0.658184	+	0.0992053i	0.0849712	+	0.0128074i
$61$	6.15540	+	5.71138i	0.788119	+	0.731267i	0.967598	−	0.252494i	$-0.0812509\pi$
$61$	6.15540	+	5.71138i	0.788119	+	0.731267i	−0.179480	+	0.983762i	$0.557441\pi$
$62$	−3.64314	+	4.56836i	−0.462680	+	0.580182i
$63$	−0.342097	−	2.62354i	−0.0431001	−	0.330535i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	0.0864441	−	1.15352i	0.0107221	−	0.143076i
$66$	0.447236	−	0.137954i	0.0550509	−	0.0169810i
$67$	4.09683	+	7.09592i	0.500508	+	0.866905i	1.00000		0.000586556i	$0.000186706\pi$
$67$	4.09683	+	7.09592i	0.500508	+	0.866905i	−0.499492	+	0.866319i	$0.666480\pi$
$68$	−0.169479	+	0.293546i	−0.0205524	+	0.0355977i
$69$	−0.888201	+	3.89146i	−0.106927	+	0.468477i
$70$	1.02085	−	1.43499i	0.122015	−	0.171514i
$71$	−1.94436	−	8.51878i	−0.230753	−	1.01099i	−0.949018	−	0.315223i	$-0.897921\pi$
$71$	−1.94436	−	8.51878i	−0.230753	−	1.01099i	0.718265	−	0.695770i	$-0.244937\pi$
$72$	0.955573	+	0.294755i	0.112615	+	0.0347372i
$73$	−0.876762	+	2.23395i	−0.102617	+	0.261465i	−0.972957	−	0.230988i	$-0.925804\pi$
$73$	−0.876762	+	2.23395i	−0.102617	+	0.261465i	0.870339	+	0.492452i	$0.163899\pi$
$74$	−0.991857	+	2.52721i	−0.115301	+	0.293782i
$75$	−4.35450	−	1.34319i	−0.502814	−	0.155098i
$76$	−0.363692	−	1.59344i	−0.0417183	−	0.182780i
$77$	0.208930	−	1.22053i	0.0238098	−	0.139093i
$78$	0.386710	−	1.69429i	0.0437863	−	0.191840i
$79$	5.65156	−	9.78878i	0.635850	−	1.10132i	−0.350485	−	0.936568i	$-0.613983\pi$
$79$	5.65156	−	9.78878i	0.635850	−	1.10132i	0.986334	−	0.164756i	$-0.0526835\pi$
$80$	0.332809	+	0.576443i	0.0372092	+	0.0644482i
$81$	0.955573	−	0.294755i	0.106175	−	0.0327506i
$82$	0.0473981	−	0.632483i	0.00523424	−	0.0698461i
$83$	−3.87463	−	4.85863i	−0.425296	−	0.533304i	0.522306	−	0.852758i	$-0.325072\pi$
$83$	−3.87463	−	4.85863i	−0.425296	−	0.533304i	−0.947602	+	0.319454i	$0.896500\pi$
$84$	1.83787	−	1.90321i	0.200528	−	0.207658i
$85$	−0.140670	+	0.176394i	−0.0152578	+	0.0191327i
$86$	8.81952	+	8.18332i	0.951033	+	0.882430i
$87$	9.73109	+	1.46673i	1.04328	+	0.157249i
$88$	0.386703	+	0.263650i	0.0412227	+	0.0281052i
$89$	−13.9325	+	2.09998i	−1.47684	+	0.222598i	−0.837546	−	0.546367i	$-0.816011\pi$
$89$	−13.9325	+	2.09998i	−1.47684	+	0.222598i	−0.639292	+	0.768964i	$0.720772\pi$
$90$	0.599702	+	0.288801i	0.0632141	+	0.0304423i
$91$	−3.53695	−	2.93786i	−0.370773	−	0.307972i
$92$	−3.59625	+	1.73186i	−0.374935	+	0.180559i
$93$	−4.82784	+	3.29156i	−0.500623	+	0.341319i
$94$	−1.19992	+	1.11337i	−0.123763	+	0.114835i
$95$	−0.0812986	−	1.08486i	−0.00834107	−	0.111304i
$96$	0.365341	+	0.930874i	0.0372875	+	0.0950069i
$97$	−0.540212			−0.0548502			−0.0274251	−	0.999624i	$-0.508731\pi$
$97$	−0.540212			−0.0548502			−0.0274251	+	0.999624i	$0.508731\pi$
$98$	−2.29561	−	6.61288i	−0.231892	−	0.668002i
$99$	0.468029			0.0470387
$100$	−1.66484	−	4.24195i	−0.166484	−	0.424195i
$101$	−0.160552	−	2.14242i	−0.0159755	−	0.213179i	−0.999479	−	0.0322873i	$-0.989721\pi$
$101$	−0.160552	−	2.14242i	−0.0159755	−	0.213179i	0.983503	−	0.180891i	$-0.0578982\pi$
$102$	−0.248474	+	0.230550i	−0.0246026	+	0.0228279i
$103$	4.41183	−	3.00793i	0.434710	−	0.296381i	−0.326124	−	0.945327i	$-0.605743\pi$
$103$	4.41183	−	3.00793i	0.434710	−	0.296381i	0.760834	+	0.648947i	$0.224790\pi$
$104$	1.56576	−	0.754029i	0.153535	−	0.0739386i
$105$	1.39847	−	1.07034i	0.136477	−	0.104454i
$106$	3.39223	+	1.63361i	0.329482	+	0.158670i
$107$	9.61185	−	1.44875i	0.929213	−	0.140056i	0.333040	−	0.942913i	$-0.391925\pi$
$107$	9.61185	−	1.44875i	0.929213	−	0.140056i	0.596173	+	0.802856i	$0.296687\pi$
$108$	0.826239	+	0.563320i	0.0795049	+	0.0542055i
$109$	−7.82492	−	1.17942i	−0.749491	−	0.112968i	−0.236821	−	0.971553i	$-0.576106\pi$
$109$	−7.82492	−	1.17942i	−0.749491	−	0.112968i	−0.512670	+	0.858586i	$0.671344\pi$
$110$	0.228367	+	0.211893i	0.0217739	+	0.0202032i
$111$	−1.69270	+	2.12258i	−0.160664	+	0.201466i
$112$	2.63389	+	0.250273i	0.248879	+	0.0236486i
$113$	−1.92133	−	2.40927i	−0.180743	−	0.226645i	0.683203	−	0.730228i	$-0.260586\pi$
$113$	−1.92133	−	2.40927i	−0.180743	−	0.226645i	−0.863947	+	0.503583i	$0.832015\pi$
$114$	0.122140	−	1.62984i	0.0114395	−	0.152649i
$115$	−2.53881	+	0.783118i	−0.236745	+	0.0730262i
$116$	4.92050	+	8.52256i	0.456857	+	0.791300i
$117$	0.868929	−	1.50503i	0.0803326	−	0.139140i
$118$	−1.97648	+	8.65951i	−0.181950	+	0.797173i
$119$	0.247200	+	0.862056i	0.0226608	+	0.0790246i
$120$	0.148114	+	0.648930i	0.0135209	+	0.0592390i
$121$	−10.3020	−	3.17774i	−0.936544	−	0.288886i
$122$	−3.06775	+	7.81650i	−0.277741	+	0.707673i
$123$	0.231720	−	0.590413i	0.0208935	−	0.0532357i
$124$	−5.58356	−	1.72230i	−0.501418	−	0.154667i
$125$	−1.41552	−	6.20179i	−0.126608	−	0.554705i
$126$	2.31720	−	1.27694i	0.206433	−	0.113759i
$127$	0.863695	−	3.78410i	0.0766405	−	0.335784i	−0.922043	−	0.387089i	$-0.873481\pi$
$127$	0.863695	−	3.78410i	0.0766405	−	0.335784i	0.998683	+	0.0513045i	$0.0163379\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.01562	+	10.4194i	0.529646	+	0.917373i
$130$	1.10536	−	0.340958i	0.0969465	−	0.0299040i
$131$	−1.29139	+	17.2324i	−0.112829	+	1.50560i	0.597580	+	0.801809i	$0.296129\pi$
$131$	−1.29139	+	17.2324i	−0.112829	+	1.50560i	−0.710409	+	0.703789i	$0.751490\pi$
$132$	0.291811	+	0.365920i	0.0253989	+	0.0318492i
$133$	−3.70107	−	2.23635i	−0.320923	−	0.193916i
$134$	−5.10867	+	6.40607i	−0.441322	+	0.553400i
$135$	0.487933	+	0.452736i	0.0419946	+	0.0389653i
$136$	−0.335172	−	0.0505191i	−0.0287408	−	0.00433198i
$137$	−7.87840	−	5.37140i	−0.673097	−	0.458910i	0.177922	−	0.984045i	$-0.443063\pi$
$137$	−7.87840	−	5.37140i	−0.673097	−	0.458910i	−0.851019	+	0.525135i	$0.824015\pi$
$138$	−3.94696	+	0.594908i	−0.335987	+	0.0506420i
$139$	−17.3974	−	8.37814i	−1.47563	−	0.710624i	−0.488798	−	0.872397i	$-0.662565\pi$
$139$	−17.3974	−	8.37814i	−1.47563	−	0.710624i	−0.986828	+	0.161772i	$0.948279\pi$
$140$	1.70875	+	0.426022i	0.144416	+	0.0360054i
$141$	−1.47479	+	0.710220i	−0.124199	+	0.0598113i
$142$	7.21955	−	4.92221i	0.605851	−	0.413063i
$143$	0.596241	−	0.553231i	0.0498602	−	0.0462635i
$144$	0.0747301	+	0.997204i	0.00622751	+	0.0831003i
$145$	2.39311	+	6.09755i	0.198737	+	0.506374i
$146$	−2.39985			−0.198613
$147$	−0.244442	−	6.99573i	−0.0201612	−	0.576998i
$148$	−2.71488			−0.223162
$149$	−1.63030	−	4.15394i	−0.133560	−	0.340304i	0.848411	−	0.529338i	$-0.177560\pi$
$149$	−1.63030	−	4.15394i	−0.133560	−	0.340304i	−0.981971	+	0.189034i	$0.939464\pi$
$150$	−0.340541	−	4.54421i	−0.0278051	−	0.371033i
$151$	−7.01003	+	6.50436i	−0.570468	+	0.529317i	−0.911805	−	0.410624i	$-0.865311\pi$
$151$	−7.01003	+	6.50436i	−0.570468	+	0.529317i	0.341336	+	0.939941i	$0.389120\pi$
$152$	1.35042	−	0.920699i	0.109533	−	0.0746785i
$153$	−0.305391	+	0.147068i	−0.0246894	+	0.0118898i
$154$	1.21249	−	0.251424i	0.0977056	−	0.0202603i
$155$	−3.50415	−	1.68751i	−0.281460	−	0.135544i
$156$	1.71845	−	0.259014i	0.137586	−	0.0207378i
$157$	−1.14380	−	0.779832i	−0.0912855	−	0.0622374i	0.516817	−	0.856096i	$-0.327117\pi$
$157$	−1.14380	−	0.779832i	−0.0912855	−	0.0622374i	−0.608103	+	0.793858i	$0.708069\pi$
$158$	11.1769	+	1.68464i	0.889184	+	0.134023i
$159$	2.76000	+	2.56091i	0.218883	+	0.203093i
$160$	−0.415006	+	0.520402i	−0.0328091	+	0.0411414i
$161$	−3.31335	+	10.0274i	−0.261129	+	0.790269i
$162$	0.623490	+	0.781831i	0.0489860	+	0.0614265i
$163$	0.736363	−	9.82608i	0.0576764	−	0.769638i	−0.891124	−	0.453761i	$-0.850082\pi$
$163$	0.736363	−	9.82608i	0.0576764	−	0.769638i	0.948800	−	0.315878i	$-0.102299\pi$
$164$	0.606078	−	0.186950i	0.0473268	−	0.0145984i
$165$	0.155764	+	0.269792i	0.0121262	+	0.0210033i
$166$	3.10721	−	5.38185i	0.241166	−	0.417712i
$167$	−1.99429	+	8.73757i	−0.154323	+	0.676133i	0.837276	+	0.546781i	$0.184147\pi$
$167$	−1.99429	+	8.73757i	−0.154323	+	0.676133i	−0.991599	+	0.129352i	$0.958710\pi$
$168$	2.44310	+	1.01551i	0.188489	+	0.0783480i
$169$	2.22072	+	9.72963i	0.170825	+	0.748433i
$170$	−0.215593	−	0.0665018i	−0.0165353	−	0.00510045i
$171$	0.597119	−	1.52143i	0.0456628	−	0.116347i
$172$	−4.39550	+	11.1996i	−0.335154	+	0.853959i
$173$	−11.2514	−	3.47059i	−0.855426	−	0.263864i	−0.164133	−	0.986438i	$-0.552483\pi$
$173$	−11.2514	−	3.47059i	−0.855426	−	0.263864i	−0.691293	+	0.722574i	$0.742959\pi$
$174$	2.18983	+	9.59427i	0.166011	+	0.727340i
$175$	−11.1331	−	4.62761i	−0.841583	−	0.349815i
$176$	−0.104146	+	0.456294i	−0.00785031	+	0.0343945i
$177$	−4.44111	+	7.69222i	−0.333814	+	0.578183i
$178$	−7.04492	−	12.2022i	−0.528039	−	0.914590i
$179$	10.0042	−	3.08590i	0.747752	−	0.230651i	0.102618	−	0.994721i	$-0.467278\pi$
$179$	10.0042	−	3.08590i	0.747752	−	0.230651i	0.645133	+	0.764070i	$0.276802\pi$
$180$	−0.0497417	+	0.663757i	−0.00370753	+	0.0494736i
$181$	−8.71344	−	10.9263i	−0.647665	−	0.812146i	0.344273	−	0.938869i	$-0.388125\pi$
$181$	−8.71344	−	10.9263i	−0.647665	−	0.812146i	−0.991938	+	0.126724i	$0.959554\pi$
$182$	1.44259	−	4.36578i	0.106932	−	0.323613i
$183$	−5.23542	+	6.56500i	−0.387013	+	0.485299i
$184$	−2.92601	−	2.71494i	−0.215708	−	0.200148i
$185$	−1.78689	−	0.269331i	−0.131375	−	0.0198016i
$186$	−4.82784	−	3.29156i	−0.353994	−	0.241349i
$187$	−0.156870	+	0.0236444i	−0.0114715	+	0.00172905i
$188$	−1.47479	−	0.710220i	−0.107560	−	0.0517981i
$189$	2.59064	−	0.537198i	0.188441	−	0.0390754i
$190$	0.980161	−	0.472021i	0.0711084	−	0.0342440i
$191$	−7.93231	+	5.40816i	−0.573962	+	0.391321i	−0.815230	−	0.579138i	$-0.803389\pi$
$191$	−7.93231	+	5.40816i	−0.573962	+	0.391321i	0.241267	+	0.970459i	$0.422437\pi$
$192$	−0.733052	+	0.680173i	−0.0529035	+	0.0490872i
$193$	0.402740	+	5.37419i	0.0289898	+	0.386842i	0.992761	+	0.120110i	$0.0383248\pi$
$193$	0.402740	+	5.37419i	0.0289898	+	0.386842i	−0.963771	+	0.266732i	$0.914056\pi$
$194$	−0.197361	−	0.502869i	−0.0141697	−	0.0361039i
$195$	1.15675			0.0828367
$196$	5.31708	−	4.55288i	0.379791	−	0.325206i
$197$	6.34764			0.452251			0.226125	−	0.974098i	$-0.427394\pi$
$197$	6.34764			0.452251			0.226125	+	0.974098i	$0.427394\pi$
$198$	0.170990	+	0.435676i	0.0121517	+	0.0309621i
$199$	−0.141048	−	1.88216i	−0.00999865	−	0.133423i	0.989971	−	0.141274i	$-0.0451199\pi$
$199$	−0.141048	−	1.88216i	−0.00999865	−	0.133423i	−0.999969	+	0.00785134i	$0.997501\pi$
$200$	3.34048	−	3.09951i	0.236208	−	0.219169i
$201$	−6.76993	+	4.61566i	−0.477514	+	0.325563i
$202$	1.93566	−	0.932167i	0.136193	−	0.0655870i
$203$	25.2635	+	6.29862i	1.77315	+	0.442077i
$204$	−0.305391	−	0.147068i	−0.0213816	−	0.0102969i
$205$	0.417458	−	0.0629216i	0.0291565	−	0.00439464i
$206$	4.41183	+	3.00793i	0.307387	+	0.209573i
$207$	−3.94696	−	0.594908i	−0.274333	−	0.0413490i
$208$	1.27394	+	1.18204i	0.0883319	+	0.0819600i
$209$	0.476940	−	0.598064i	0.0329907	−	0.0413690i
$210$	1.50727	+	0.910759i	0.104011	+	0.0628483i
$211$	13.6616	+	17.1311i	0.940501	+	1.17935i	0.983615	+	0.180281i	$0.0577006\pi$
$211$	13.6616	+	17.1311i	0.940501	+	1.17935i	−0.0431144	+	0.999070i	$0.513728\pi$
$212$	−0.281365	+	3.75456i	−0.0193243	+	0.257864i
$213$	8.34966	−	2.57553i	0.572109	−	0.176472i
$214$	4.86021	+	8.41813i	0.332237	+	0.575452i
$215$	−4.00411	+	6.93532i	−0.273078	+	0.472985i
$216$	−0.222521	+	0.974928i	−0.0151406	+	0.0663354i
$217$	−13.5398	+	7.46133i	−0.919139	+	0.506508i
$218$	−1.76088	−	7.71490i	−0.119262	−	0.522519i
$219$	−2.29323	−	0.707367i	−0.154962	−	0.0477994i
$220$	−0.113814	+	0.289994i	−0.00767335	+	0.0195514i
$221$	−0.215208	+	0.548342i	−0.0144765	+	0.0368855i
$222$	−2.59427	−	0.800225i	−0.174116	−	0.0537076i
$223$	−5.66119	−	24.8033i	−0.379102	−	1.66095i	−0.700230	−	0.713917i	$-0.746919\pi$
$223$	−5.66119	−	24.8033i	−0.379102	−	1.66095i	0.321129	−	0.947036i	$-0.395938\pi$
$224$	0.729294	+	2.54325i	0.0487280	+	0.169928i
$225$	1.01402	−	4.44270i	0.0676011	−	0.296180i
$226$	1.54079	−	2.66872i	0.102492	−	0.177521i
$227$	9.94835	+	17.2311i	0.660295	+	1.14367i	0.980538	+	0.196330i	$0.0629023\pi$
$227$	9.94835	+	17.2311i	0.660295	+	1.14367i	−0.320243	+	0.947336i	$0.603764\pi$
$228$	1.56180	−	0.481752i	0.103433	−	0.0319048i
$229$	0.581855	−	7.76432i	0.0384501	−	0.513081i	−0.944415	−	0.328755i	$-0.893371\pi$
$229$	0.581855	−	7.76432i	0.0384501	−	0.513081i	0.982865	−	0.184325i	$-0.0590100\pi$
$230$	−1.65652	−	2.07720i	−0.109227	−	0.136967i
$231$	1.23274	+	0.117135i	0.0811080	+	0.00770692i
$232$	−6.13577	+	7.69401i	−0.402833	+	0.505136i
$233$	−3.58943	−	3.33051i	−0.235152	−	0.218189i	0.553791	−	0.832656i	$-0.313181\pi$
$233$	−3.58943	−	3.33051i	−0.235152	−	0.218189i	−0.788943	+	0.614467i	$0.789371\pi$
$234$	1.71845	+	0.259014i	0.112338	+	0.0169323i
$235$	−0.900223	−	0.613762i	−0.0587241	−	0.0400374i
$236$	−8.78300	+	1.32382i	−0.571725	+	0.0861737i
$237$	10.1838	+	4.90424i	0.661506	+	0.318564i
$238$	−0.712153	+	0.545057i	−0.0461620	+	0.0353308i
$239$	23.7263	−	11.4260i	1.53473	−	0.739085i	0.540000	−	0.841665i	$-0.318424\pi$
$239$	23.7263	−	11.4260i	1.53473	−	0.739085i	0.994725	+	0.102580i	$0.0327098\pi$
$240$	−0.549960	+	0.374956i	−0.0354998	+	0.0242033i
$241$	11.6546	−	10.8139i	0.750737	−	0.696583i	−0.208864	−	0.977945i	$-0.566977\pi$
$241$	11.6546	−	10.8139i	0.750737	−	0.696583i	0.959602	+	0.281362i	$0.0907862\pi$
$242$	−0.805661	−	10.7508i	−0.0517899	−	0.691088i
$243$	0.365341	+	0.930874i	0.0234366	+	0.0597156i
$244$	−8.39695			−0.537560
$245$	3.95128	−	2.46915i	0.252438	−	0.157748i
$246$	0.634257			0.0404387
$247$	−1.03771	−	2.64404i	−0.0660278	−	0.168236i
$248$	−0.436659	−	5.82681i	−0.0277279	−	0.370003i
$249$	4.55549	−	4.22688i	0.288693	−	0.267868i
$250$	5.25594	−	3.58344i	0.332415	−	0.226637i
$251$	3.54303	−	1.70623i	0.223634	−	0.107697i	−0.318712	−	0.947852i	$-0.603250\pi$
$251$	3.54303	−	1.70623i	0.223634	−	0.107697i	0.542346	+	0.840155i	$0.317536\pi$
$252$	2.03524	+	1.69051i	0.128208	+	0.106492i
$253$	−1.68315	−	0.810562i	−0.105819	−	0.0509596i
$254$	3.83806	−	0.578494i	0.240821	−	0.0362980i
$255$	−0.186413	−	0.127095i	−0.0116737	−	0.00795897i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	22.9524	+	21.2968i	1.43173	+	1.32846i	0.862280	+	0.506432i	$0.169036\pi$
$257$	22.9524	+	21.2968i	1.43173	+	1.32846i	0.569454	+	0.822023i	$0.307155\pi$
$258$	−7.50135	+	9.40640i	−0.467014	+	0.585617i
$259$	−4.98961	+	5.16700i	−0.310039	+	0.321061i
$260$	0.721223	+	0.904385i	0.0447283	+	0.0560875i
$261$	−0.735419	+	9.81349i	−0.0455213	+	0.607440i
$262$	−16.5129	+	5.09357i	−1.02017	+	0.314682i
$263$	−6.55261	−	11.3494i	−0.404051	−	0.699837i	0.590159	−	0.807287i	$-0.299065\pi$
$263$	−6.55261	−	11.3494i	−0.404051	−	0.699837i	−0.994211	+	0.107450i	$0.965732\pi$
$264$	−0.234014	+	0.405325i	−0.0144026	+	0.0249460i
$265$	−0.557663	+	2.44328i	−0.0342569	+	0.150089i
$266$	0.729610	−	4.26226i	0.0447352	−	0.261336i
$267$	−3.13528	−	13.7366i	−0.191876	−	0.840665i
$268$	−7.82965	−	2.41513i	−0.478272	−	0.147527i
$269$	10.7566	−	27.4074i	0.655842	−	1.67106i	−0.0824648	−	0.996594i	$-0.526279\pi$
$269$	10.7566	−	27.4074i	0.655842	−	1.67106i	0.738307	−	0.674465i	$-0.235626\pi$
$270$	−0.243178	+	0.619607i	−0.0147993	+	0.0377081i
$271$	10.5313	+	3.24847i	0.639729	+	0.197330i	0.597616	−	0.801782i	$-0.296115\pi$
$271$	10.5313	+	3.24847i	0.639729	+	0.197330i	0.0421133	+	0.999113i	$0.486591\pi$
$272$	−0.0754253	−	0.330460i	−0.00457333	−	0.0200371i
$273$	2.66533	−	3.74661i	0.161313	−	0.226755i
$274$	2.12180	−	9.29619i	0.128182	−	0.561604i
$275$	1.06639	−	1.84705i	0.0643059	−	0.111381i
$276$	−1.99577	−	3.45678i	−0.120131	−	0.208073i
$277$	18.5637	−	5.72614i	1.11538	−	0.344050i	0.318343	−	0.947976i	$-0.396874\pi$
$277$	18.5637	−	5.72614i	1.11538	−	0.344050i	0.797041	+	0.603925i	$0.206398\pi$
$278$	1.44301	−	19.2556i	0.0865460	−	1.15488i
$279$	−3.64314	−	4.56836i	−0.218109	−	0.273500i
$280$	0.227706	+	1.74628i	0.0136080	+	0.104360i
$281$	−14.9053	+	18.6907i	−0.889178	+	1.11499i	0.103551	+	0.994624i	$0.466980\pi$
$281$	−14.9053	+	18.6907i	−0.889178	+	1.11499i	−0.992729	+	0.120370i	$0.961592\pi$
$282$	−1.19992	−	1.11337i	−0.0714545	−	0.0663001i
$283$	−4.93887	−	0.744415i	−0.293585	−	0.0442509i	0.000598224	−	1.00000i	$-0.499810\pi$
$283$	−4.93887	−	0.744415i	−0.293585	−	0.0442509i	−0.294183	+	0.955749i	$0.595048\pi$
$284$	7.21955	+	4.92221i	0.428402	+	0.292079i
$285$	1.07575	−	0.162143i	0.0637217	−	0.00960450i
$286$	0.732819	+	0.352907i	0.0433325	+	0.0208678i
$287$	0.758089	−	1.49709i	0.0447486	−	0.0883703i
$288$	−0.900969	+	0.433884i	−0.0530901	+	0.0255668i
$289$	−13.9511	+	9.51172i	−0.820655	+	0.559513i
$290$	−4.80175	+	4.45537i	−0.281968	+	0.261629i
$291$	−0.0403701	−	0.538701i	−0.00236654	−	0.0315792i
$292$	−0.876762	−	2.23395i	−0.0513086	−	0.130732i
$293$	32.6371			1.90668			0.953341	−	0.301895i	$-0.0976193\pi$
$293$	32.6371			1.90668			0.953341	+	0.301895i	$0.0976193\pi$
$294$	6.42284	−	2.78337i	0.374587	−	0.162330i
$295$	−5.91216			−0.344220
$296$	−0.991857	−	2.52721i	−0.0576505	−	0.146891i
$297$	0.0349758	+	0.466720i	0.00202950	+	0.0270818i
$298$	3.27118	−	3.03521i	0.189494	−	0.175825i
$299$	−5.73140	+	3.90760i	−0.331455	+	0.225982i
$300$	4.10567	−	1.97719i	0.237041	−	0.114153i
$301$	13.2368	+	28.9490i	0.762955	+	1.66859i
$302$	−8.61579	−	4.14915i	−0.495783	−	0.238757i
$303$	2.12443	−	0.320206i	0.122045	−	0.0183954i
$304$	1.35042	+	0.920699i	0.0774517	+	0.0528057i
$305$	−5.52674	−	0.833022i	−0.316460	−	0.0476987i
$306$	−0.248474	−	0.230550i	−0.0142043	−	0.0131797i
$307$	16.2362	−	20.3596i	0.926650	−	1.16198i	−0.0598476	−	0.998208i	$-0.519061\pi$
$307$	16.2362	−	20.3596i	0.926650	−	1.16198i	0.986498	−	0.163775i	$-0.0523671\pi$
$308$	0.677018	+	1.03682i	0.0385767	+	0.0590785i
$309$	3.32922	+	4.17471i	0.189393	+	0.237491i
$310$	0.290648	−	3.87843i	0.0165077	−	0.220280i
$311$	−0.840555	+	0.259277i	−0.0476635	+	0.0147022i	−0.318495	−	0.947924i	$-0.603177\pi$
$311$	−0.840555	+	0.259277i	−0.0476635	+	0.0147022i	0.270832	+	0.962627i	$0.412701\pi$
$312$	0.868929	+	1.50503i	0.0491934	+	0.0852055i
$313$	12.1463	−	21.0381i	0.686552	−	1.18914i	−0.286394	−	0.958112i	$-0.592457\pi$
$313$	12.1463	−	21.0381i	0.686552	−	1.18914i	0.972946	−	0.231031i	$-0.0742099\pi$
$314$	0.308047	−	1.34964i	0.0173841	−	0.0761647i
$315$	1.17185	+	1.31457i	0.0660264	+	0.0740677i
$316$	2.51518	+	11.0197i	0.141490	+	0.619908i
$317$	−9.73679	−	3.00340i	−0.546873	−	0.168688i	0.00899372	−	0.999960i	$-0.497137\pi$
$317$	−9.73679	−	3.00340i	−0.546873	−	0.168688i	−0.555866	+	0.831272i	$0.687613\pi$
$318$	−1.37554	+	3.50482i	−0.0771365	+	0.196541i
$319$	−1.68271	+	4.28749i	−0.0942139	+	0.240053i
$320$	−0.636047	−	0.196195i	−0.0355561	−	0.0109676i
$321$	2.16300	+	9.47671i	0.120727	+	0.528939i
$322$	−10.5447	+	0.579103i	−0.587635	+	0.0322722i
$323$	−0.123276	+	0.540108i	−0.00685927	+	0.0300524i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−3.95967	−	6.85835i	−0.219643	−	0.380433i
$326$	9.41587	−	2.90441i	0.521497	−	0.160860i
$327$	0.591362	−	7.89117i	0.0327024	−	0.436383i
$328$	0.395452	+	0.495882i	0.0218352	+	0.0273805i
$329$	−4.06217	+	1.50154i	−0.223955	+	0.0827825i
$330$	−0.194235	+	0.243563i	−0.0106923	+	0.0134077i
$331$	4.77944	+	4.43467i	0.262702	+	0.243752i	0.800516	−	0.599312i	$-0.204559\pi$
$331$	4.77944	+	4.43467i	0.262702	+	0.243752i	−0.537814	+	0.843064i	$0.680750\pi$
$332$	6.14501	+	0.926211i	0.337251	+	0.0508325i
$333$	−2.24314	−	1.52935i	−0.122923	−	0.0838077i
$334$	−8.86217	+	1.33576i	−0.484916	+	0.0730894i
$335$	−4.91376	−	2.36634i	−0.268467	−	0.129287i
$336$	−0.0527428	+	2.64523i	−0.00287736	+	0.144309i
$337$	18.5852	−	8.95015i	1.01240	−	0.487546i	0.147271	−	0.989096i	$-0.452951\pi$
$337$	18.5852	−	8.95015i	1.01240	−	0.487546i	0.865129	+	0.501550i	$0.167237\pi$
$338$	−8.24574	+	5.62185i	−0.448509	+	0.305788i
$339$	2.25895	−	2.09600i	0.122689	−	0.113839i
$340$	−0.0168604	−	0.224986i	−0.000914382	−	0.0122016i
$341$	−0.999121	−	2.54572i	−0.0541054	−	0.137858i
$342$	1.63441			0.0883790
$343$	1.10701	−	18.4871i	0.0597730	−	0.998212i
$344$	−12.0312			−0.648681
$345$	−0.970654	−	2.47319i	−0.0522583	−	0.133152i
$346$	−0.879908	−	11.7416i	−0.0473042	−	0.631230i
$347$	−18.8772	+	17.5155i	−1.01338	+	0.940280i	−0.998222	−	0.0596048i	$-0.981016\pi$
$347$	−18.8772	+	17.5155i	−1.01338	+	0.940280i	−0.0151591	+	0.999885i	$0.504825\pi$
$348$	−8.13102	+	5.54363i	−0.435868	+	0.297170i
$349$	11.6268	−	5.59916i	0.622367	−	0.299716i	−0.0959990	−	0.995381i	$-0.530605\pi$
$349$	11.6268	−	5.59916i	0.622367	−	0.299716i	0.718366	+	0.695665i	$0.244890\pi$
$350$	0.240346	−	12.0542i	0.0128471	−	0.644322i
$351$	1.56576	+	0.754029i	0.0835739	+	0.0402471i
$352$	−0.462801	+	0.0697561i	−0.0246674	+	0.00371801i
$353$	−26.1125	−	17.8032i	−1.38983	−	0.947568i	−0.999640	−	0.0268326i	$-0.991458\pi$
$353$	−26.1125	−	17.8032i	−1.38983	−	0.947568i	−0.390187	−	0.920736i	$-0.627590\pi$
$354$	−8.78300	−	1.32382i	−0.466811	−	0.0703605i
$355$	4.26349	+	3.95594i	0.226282	+	0.209959i
$356$	8.78487	−	11.0159i	0.465597	−	0.583840i
$357$	−0.841172	+	0.310931i	−0.0445196	+	0.0164562i
$358$	6.52754	+	8.18528i	0.344991	+	0.432605i
$359$	−2.14031	+	28.5605i	−0.112961	+	1.50736i	0.596496	+	0.802616i	$0.296559\pi$
$359$	−2.14031	+	28.5605i	−0.112961	+	1.50736i	−0.709458	+	0.704748i	$0.751060\pi$
$360$	−0.636047	+	0.196195i	−0.0335226	+	0.0103404i
$361$	8.16434	+	14.1411i	0.429702	+	0.744266i
$362$	6.98763	−	12.1029i	0.367262	−	0.636116i
$363$	2.39899	−	10.5106i	0.125914	−	0.551666i
$364$	4.59102	−	0.252133i	0.240635	−	0.0132154i
$365$	−0.355451	−	1.55733i	−0.0186052	−	0.0815145i
$366$	−8.02390	−	2.47505i	−0.419416	−	0.129373i
$367$	−3.49142	+	8.89599i	−0.182251	+	0.464367i	−0.992578	−	0.121611i	$-0.961194\pi$
$367$	−3.49142	+	8.89599i	−0.182251	+	0.464367i	0.810327	+	0.585977i	$0.199289\pi$
$368$	1.45827	−	3.71562i	0.0760178	−	0.193690i
$369$	0.606078	+	0.186950i	0.0315512	+	0.00973225i
$370$	−0.402112	−	1.76177i	−0.0209048	−	0.0915899i
$371$	6.62861	+	7.43590i	0.344141	+	0.386053i
$372$	1.30022	−	5.69665i	0.0674134	−	0.295358i
$373$	7.86394	−	13.6207i	0.407179	−	0.705255i	−0.587393	−	0.809302i	$-0.699846\pi$
$373$	7.86394	−	13.6207i	0.407179	−	0.705255i	0.994572	+	0.104047i	$0.0331791\pi$
$374$	−0.0793211	−	0.137388i	−0.00410160	−	0.00710417i
$375$	6.07867	−	1.87502i	0.313901	−	0.0968257i
$376$	0.122325	−	1.63231i	0.00630842	−	0.0841801i
$377$	10.6631	+	13.3711i	0.549177	+	0.688647i
$378$	1.44653	+	2.21530i	0.0744015	+	0.113943i
$379$	−8.85104	+	11.0989i	−0.454647	+	0.570110i	−0.955338	−	0.295517i	$-0.904508\pi$
$379$	−8.85104	+	11.0989i	−0.454647	+	0.570110i	0.500690	+	0.865627i	$0.333080\pi$
$380$	0.797485	+	0.739958i	0.0409101	+	0.0379590i
$381$	3.83806	+	0.578494i	0.196630	+	0.0296372i
$382$	−7.93231	−	5.40816i	−0.405853	−	0.276706i
$383$	−30.2029	+	4.55236i	−1.54330	+	0.232615i	−0.864848	−	0.502034i	$-0.832585\pi$
$383$	−30.2029	+	4.55236i	−1.54330	+	0.232615i	−0.678448	+	0.734648i	$0.737347\pi$
$384$	−0.900969	−	0.433884i	−0.0459774	−	0.0221415i
$385$	0.342744	+	0.749585i	0.0174679	+	0.0382024i
$386$	−4.85555	+	2.33831i	−0.247141	+	0.119017i
$387$	−9.94067	+	6.77744i	−0.505313	+	0.344516i
$388$	0.396003	−	0.367437i	0.0201040	−	0.0186538i
$389$	−2.49780	−	33.3308i	−0.126643	−	1.68994i	−0.592889	−	0.805284i	$-0.702013\pi$
$389$	−2.49780	−	33.3308i	−0.126643	−	1.68994i	0.466245	−	0.884655i	$-0.345606\pi$
$390$	0.422609	+	1.07679i	0.0213996	+	0.0545253i
$391$	1.35297			0.0684224
$392$	6.18070	+	3.28617i	0.312173	+	0.165977i
$393$	−17.2807			−0.871695
$394$	2.31905	+	5.90885i	0.116832	+	0.297684i
$395$	0.562237	+	7.50252i	0.0282892	+	0.377493i
$396$	−0.343089	+	0.318340i	−0.0172409	+	0.0159972i
$397$	29.9094	−	20.3919i	1.50111	−	1.02344i	0.515031	−	0.857171i	$-0.327780\pi$
$397$	29.9094	−	20.3919i	1.50111	−	1.02344i	0.986080	−	0.166269i	$-0.0531721\pi$
$398$	1.70052	−	0.818928i	0.0852394	−	0.0410491i
$399$	1.95352	−	3.85784i	0.0977982	−	0.193134i
$400$	4.10567	+	1.97719i	0.205284	+	0.0988594i
$401$	−19.6564	+	2.96272i	−0.981592	+	0.147951i	−0.620184	−	0.784457i	$-0.712942\pi$
$401$	−19.6564	+	2.96272i	−0.981592	+	0.147951i	−0.361408	+	0.932408i	$0.617704\pi$
$402$	−6.76993	−	4.61566i	−0.337653	−	0.230208i
$403$	−10.0412	−	1.51346i	−0.500185	−	0.0753908i
$404$	1.57491	+	1.46130i	0.0783546	+	0.0727024i
$405$	−0.415006	+	0.520402i	−0.0206218	+	0.0258590i
$406$	3.36658	+	25.8183i	0.167080	+	1.28134i
$407$	−0.792232	−	0.993428i	−0.0392695	−	0.0492424i
$408$	0.0253304	−	0.338010i	0.00125404	−	0.0167340i
$409$	−29.2528	+	9.02330i	−1.44646	+	0.446173i	−0.915876	−	0.401460i	$-0.868503\pi$
$409$	−29.2528	+	9.02330i	−1.44646	+	0.446173i	−0.530582	+	0.847634i	$0.678027\pi$
$410$	0.211086	+	0.365613i	0.0104248	+	0.0180563i
$411$	4.76763	−	8.25778i	0.235170	−	0.407326i
$412$	−1.18818	+	5.20578i	−0.0585377	+	0.256470i
$413$	−13.6225	+	19.1490i	−0.670321	+	0.942258i
$414$	−0.888201	−	3.89146i	−0.0436527	−	0.191255i
$415$	3.95266	+	1.21924i	0.194029	+	0.0598499i
$416$	−0.634911	+	1.61773i	−0.0311291	+	0.0793156i
$417$	7.05460	−	17.9748i	0.345465	−	0.880231i
$418$	0.730968	+	0.225474i	0.0357528	+	0.0110283i
$419$	7.85289	+	34.4058i	0.383639	+	1.68083i	0.685971	+	0.727629i	$0.259378\pi$
$419$	7.85289	+	34.4058i	0.383639	+	1.68083i	−0.302333	+	0.953202i	$0.597765\pi$
$420$	−0.297135	+	1.73581i	−0.0144987	+	0.0846990i
$421$	−6.22175	+	27.2592i	−0.303229	+	1.32853i	0.561991	+	0.827143i	$0.310035\pi$
$421$	−6.22175	+	27.2592i	−0.303229	+	1.32853i	−0.865221	+	0.501391i	$0.832822\pi$
$422$	−10.9557	+	18.9759i	−0.533316	+	0.923731i
$423$	−0.818445	−	1.41759i	−0.0397941	−	0.0689255i
$424$	−3.59782	+	1.10978i	−0.174725	+	0.0538956i
$425$	−0.115429	+	1.54030i	−0.00559914	+	0.0747154i
$426$	5.44796	+	6.83153i	0.263955	+	0.330989i
$427$	−15.4325	+	15.9812i	−0.746833	+	0.773384i
$428$	−6.06059	+	7.59973i	−0.292949	+	0.367347i
$429$	0.596241	+	0.553231i	0.0287868	+	0.0267102i
$430$	−7.91877	−	1.19356i	−0.381877	−	0.0575587i
$431$	−13.9888	−	9.53741i	−0.673817	−	0.459401i	0.177452	−	0.984129i	$-0.443214\pi$
$431$	−13.9888	−	9.53741i	−0.673817	−	0.459401i	−0.851270	+	0.524729i	$0.824167\pi$
$432$	−0.988831	+	0.149042i	−0.0475751	+	0.00717080i
$433$	20.3906	+	9.81958i	0.979908	+	0.471899i	0.854073	−	0.520152i	$-0.174125\pi$
$433$	20.3906	+	9.81958i	0.979908	+	0.471899i	0.125835	+	0.992051i	$0.459839\pi$
$434$	−11.8922	−	9.87789i	−0.570843	−	0.474154i
$435$	−5.90167	+	2.84209i	−0.282963	+	0.136268i
$436$	6.53828	−	4.45772i	0.313127	−	0.213486i
$437$	−4.78231	+	4.43733i	−0.228769	+	0.212266i
$438$	−0.179341	−	2.39314i	−0.00856923	−	0.114348i
$439$	12.0663	+	30.7445i	0.575895	+	1.46736i	0.860872	+	0.508822i	$0.169919\pi$
$439$	12.0663	+	30.7445i	0.575895	+	1.46736i	−0.284977	+	0.958534i	$0.591986\pi$
$440$	−0.311529			−0.0148515
$441$	6.95790	−	0.766550i	0.331329	−	0.0365024i
$442$	−0.589062			−0.0280188
$443$	−6.11469	−	15.5800i	−0.290518	−	0.740227i	−0.999391	−	0.0348915i	$-0.988891\pi$
$443$	−6.11469	−	15.5800i	−0.290518	−	0.740227i	0.708873	−	0.705336i	$-0.249204\pi$
$444$	−0.202883	−	2.70729i	−0.00962841	−	0.128482i
$445$	6.87489	−	6.37897i	0.325901	−	0.302392i
$446$	21.0205	−	14.3315i	0.995349	−	0.678617i
$447$	4.02049	−	1.93617i	0.190163	−	0.0915776i
$448$	−2.10101	+	1.60804i	−0.0992632	+	0.0759725i
$449$	2.23475	+	1.07620i	0.105464	+	0.0507889i	0.485872	−	0.874030i	$-0.338502\pi$
$449$	2.23475	+	1.07620i	0.105464	+	0.0507889i	−0.380408	+	0.924819i	$0.624216\pi$
$450$	4.50605	−	0.679178i	0.212417	−	0.0320168i
$451$	0.245269	+	0.167222i	0.0115493	+	0.00787416i
$452$	3.04715	+	0.459284i	0.143326	+	0.0216029i
$453$	−7.01003	−	6.50436i	−0.329360	−	0.305602i
$454$	−12.4054	+	15.5559i	−0.582214	+	0.730073i
$455$	3.04675	+	0.289504i	0.142834	+	0.0135722i
$456$	1.01904	+	1.27784i	0.0477210	+	0.0598402i
$457$	−1.89788	+	25.3255i	−0.0887792	+	1.18468i	0.757827	+	0.652456i	$0.226261\pi$
$457$	−1.89788	+	25.3255i	−0.0887792	+	1.18468i	−0.846606	+	0.532220i	$0.821358\pi$
$458$	7.44018	−	2.29499i	0.347657	−	0.107238i
$459$	−0.169479	−	0.293546i	−0.00791061	−	0.0137016i
$460$	1.32842	−	2.30089i	0.0619380	−	0.107280i
$461$	−0.779594	+	3.41562i	−0.0363093	+	0.159081i	−0.989832	−	0.142238i	$-0.954570\pi$
$461$	−0.779594	+	3.41562i	−0.0363093	+	0.159081i	0.953523	+	0.301320i	$0.0974272\pi$
$462$	0.341331	+	1.19031i	0.0158801	+	0.0553785i
$463$	3.96372	+	17.3662i	0.184210	+	0.807076i	0.979597	+	0.200974i	$0.0644105\pi$
$463$	3.96372	+	17.3662i	0.184210	+	0.807076i	−0.795387	+	0.606102i	$0.792732\pi$
$464$	−9.40380	−	2.90069i	−0.436560	−	0.134661i
$465$	1.42092	−	3.62046i	0.0658938	−	0.167895i
$466$	1.78892	−	4.55808i	0.0828699	−	0.211149i
$467$	−26.8793	−	8.29116i	−1.24382	−	0.383669i	−0.398126	−	0.917331i	$-0.630339\pi$
$467$	−26.8793	−	8.29116i	−1.24382	−	0.383669i	−0.845698	+	0.533662i	$0.820816\pi$
$468$	0.386710	+	1.69429i	0.0178757	+	0.0783184i
$469$	−18.9864	+	10.4628i	−0.876710	+	0.483127i
$470$	0.242446	−	1.06223i	0.0111832	−	0.0489969i
$471$	0.692175	−	1.19888i	0.0318937	−	0.0552416i
$472$	−4.44111	−	7.69222i	−0.204418	−	0.354063i
$473$	−5.38080	+	1.65976i	−0.247409	+	0.0763157i
$474$	−0.844683	+	11.2715i	−0.0387976	+	0.517717i
$475$	−4.64372	−	5.82304i	−0.213069	−	0.267179i
$476$	−0.767558	−	0.463793i	−0.0351809	−	0.0212579i
$477$	−2.34749	+	2.94366i	−0.107484	+	0.134781i
$478$	19.3043	+	17.9118i	0.882959	+	0.819266i
$479$	−20.0528	−	3.02248i	−0.916237	−	0.138100i	−0.326036	−	0.945357i	$-0.605713\pi$
$479$	−20.0528	−	3.02248i	−0.916237	−	0.138100i	−0.590200	+	0.807257i	$0.700951\pi$
$480$	−0.549960	−	0.374956i	−0.0251021	−	0.0171143i
$481$	−4.66538	+	0.703193i	−0.212723	+	0.0320628i
$482$	14.3242	+	6.89819i	0.652451	+	0.314204i
$483$	−10.2470	−	2.55474i	−0.466253	−	0.116245i
$484$	9.71330	−	4.67768i	0.441514	−	0.212622i
$485$	0.297095	−	0.202556i	0.0134904	−	0.00919758i
$486$	−0.733052	+	0.680173i	−0.0332519	+	0.0308533i
$487$	0.522975	+	6.97861i	0.0236982	+	0.316231i	0.996438	+	0.0843308i	$0.0268753\pi$
$487$	0.522975	+	6.97861i	0.0236982	+	0.316231i	−0.972740	+	0.231900i	$0.925506\pi$
$488$	−3.06775	−	7.81650i	−0.138871	−	0.353837i
$489$	9.85364			0.445597
$490$	3.74203	+	2.77607i	0.169048	+	0.125410i
$491$	1.85994			0.0839378			0.0419689	−	0.999119i	$-0.486637\pi$
$491$	1.85994			0.0839378			0.0419689	+	0.999119i	$0.486637\pi$
$492$	0.231720	+	0.590413i	0.0104467	+	0.0266179i
$493$	−0.249276	−	3.32636i	−0.0112268	−	0.149812i
$494$	2.08215	−	1.93195i	0.0936803	−	0.0869226i
$495$	−0.257397	+	0.175490i	−0.0115691	+	0.00788770i
$496$	5.26450	−	2.53525i	0.236383	−	0.113836i
$497$	22.6366	−	4.69395i	1.01539	−	0.210553i
$498$	5.59900	+	2.69634i	0.250897	+	0.120826i
$499$	8.03005	−	1.21033i	0.359474	−	0.0541820i	0.0331777	−	0.999449i	$-0.489437\pi$
$499$	8.03005	−	1.21033i	0.359474	−	0.0541820i	0.326297	+	0.945267i	$0.394199\pi$
$500$	5.25594	+	3.58344i	0.235053	+	0.160256i
$501$	−8.86217	−	1.33576i	−0.395932	−	0.0596772i
$502$	2.88270	+	2.67476i	0.128661	+	0.119380i
$503$	−24.9251	+	31.2551i	−1.11136	+	1.39360i	−0.201088	+	0.979573i	$0.564448\pi$
$503$	−24.9251	+	31.2551i	−1.11136	+	1.39360i	−0.910267	+	0.414022i	$0.864124\pi$
$504$	−0.830093	+	2.51216i	−0.0369753	+	0.111900i
$505$	0.891610	+	1.11804i	0.0396761	+	0.0497523i
$506$	0.139607	−	1.86293i	0.00620631	−	0.0828174i
$507$	−9.53647	+	2.94161i	−0.423530	+	0.130642i
$508$	1.94071	+	3.36140i	0.0861049	+	0.149138i
$509$	17.9923	−	31.1636i	0.797496	−	1.38130i	−0.123746	−	0.992314i	$-0.539491\pi$
$509$	17.9923	−	31.1636i	0.797496	−	1.38130i	0.921242	−	0.388990i	$-0.127176\pi$
$510$	0.0502045	−	0.219960i	0.00222309	−	0.00974000i
$511$	−5.86307	−	2.43706i	−0.259367	−	0.107809i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	1.56180	+	0.481752i	0.0689553	+	0.0212699i
$514$	−11.4391	+	29.1464i	−0.504558	+	1.28559i
$515$	−1.29849	+	3.30849i	−0.0572181	+	0.145789i
$516$	−11.4967	−	3.54627i	−0.506115	−	0.156116i
$517$	−0.170476	−	0.746903i	−0.00749752	−	0.0328488i
$518$	−6.63273	−	2.75698i	−0.291425	−	0.121135i
$519$	2.62007	−	11.4793i	0.115008	−	0.503884i
$520$	−0.578376	+	1.00178i	−0.0253634	+	0.0439308i
$521$	−6.20029	−	10.7392i	−0.271639	−	0.470493i	0.697642	−	0.716446i	$-0.254232\pi$
$521$	−6.20029	−	10.7392i	−0.271639	−	0.470493i	−0.969282	+	0.245953i	$0.920899\pi$
$522$	−9.40380	+	2.90069i	−0.411593	+	0.126960i
$523$	2.95322	−	39.4080i	0.129135	−	1.72319i	−0.437495	−	0.899221i	$-0.644134\pi$
$523$	2.95322	−	39.4080i	0.129135	−	1.72319i	0.566631	−	0.823972i	$-0.308247\pi$
$524$	−10.7743	−	13.5106i	−0.470679	−	0.590212i
$525$	3.78270	−	11.4478i	0.165090	−	0.499622i
$526$	8.17097	−	10.2461i	0.356271	−	0.446750i
$527$	1.45187	+	1.34714i	0.0632445	+	0.0586823i
$528$	−0.462801	−	0.0697561i	−0.0201408	−	0.00303574i
$529$	−5.83953	−	3.98132i	−0.253892	−	0.173101i
$530$	−2.47812	+	0.373517i	−0.107643	+	0.0162245i
$531$	−8.00259	−	3.85385i	−0.347283	−	0.167243i
$532$	4.23418	−	0.878004i	0.183575	−	0.0380663i
$533$	0.993091	−	0.478248i	0.0430156	−	0.0207152i
$534$	11.6416	−	7.93709i	0.503780	−	0.343471i
$535$	−4.74292	+	4.40078i	−0.205054	+	0.190262i
$536$	−0.612314	−	8.17076i	−0.0264479	−	0.352923i
$537$	3.82489	+	9.74565i	0.165056	+	0.420556i
$538$	29.4427			1.26936
$539$	3.21757	+	0.617041i	0.138591	+	0.0265778i
$540$	−0.665619			−0.0286437
$541$	−0.686027	−	1.74797i	−0.0294946	−	0.0751510i	0.915368	−	0.402619i	$-0.131900\pi$
$541$	−0.686027	−	1.74797i	−0.0294946	−	0.0751510i	−0.944862	+	0.327468i	$0.893805\pi$
$542$	0.823593	+	10.9901i	0.0353763	+	0.472065i
$543$	10.2446	−	9.50560i	0.439638	−	0.407924i
$544$	0.280060	−	0.190942i	0.0120075	−	0.00818657i
$545$	4.74562	−	2.28537i	0.203280	−	0.0978945i
$546$	4.46138	+	1.11230i	0.190929	+	0.0476019i
$547$	−35.2787	−	16.9893i	−1.50841	−	0.726410i	−0.516849	−	0.856077i	$-0.672895\pi$
$547$	−35.2787	−	16.9893i	−1.50841	−	0.726410i	−0.991558	+	0.129666i	$0.958609\pi$
$548$	9.42876	−	1.42116i	0.402777	−	0.0607088i
$549$	−6.93789	−	4.73017i	−0.296102	−	0.201879i
$550$	2.10896	+	0.317875i	0.0899265	+	0.0135542i
$551$	11.7906	+	10.9401i	0.502297	+	0.466064i
$552$	2.48868	−	3.12071i	0.105925	−	0.132826i
$553$	25.5955	+	15.4659i	1.08843	+	0.657678i
$554$	12.1124	+	15.1885i	0.514606	+	0.645295i
$555$	0.135043	−	1.80202i	0.00573225	−	0.0764916i
$556$	18.4518	−	5.69162i	0.782529	−	0.241378i
$557$	−10.1007	−	17.4949i	−0.427979	−	0.741281i	0.568714	−	0.822535i	$-0.307441\pi$
$557$	−10.1007	−	17.4949i	−0.427979	−	0.741281i	−0.996693	+	0.0812537i	$0.974108\pi$
$558$	2.92157	−	5.06032i	0.123680	−	0.214220i
$559$	−4.65260	+	20.3844i	−0.196784	+	0.862167i
$560$	−1.54237	+	0.849953i	−0.0651772	+	0.0359170i
$561$	−0.0353012	−	0.154665i	−0.00149042	−	0.00652995i
$562$	−22.8442	−	7.04651i	−0.963626	−	0.297239i
$563$	2.84391	−	7.24617i	0.119857	−	0.305389i	−0.858337	−	0.513087i	$-0.828502\pi$
$563$	2.84391	−	7.24617i	0.119857	−	0.305389i	0.978193	+	0.207698i	$0.0665970\pi$
$564$	0.598023	−	1.52374i	0.0251813	−	0.0641609i
$565$	1.96002	+	0.604588i	0.0824589	+	0.0254352i
$566$	−1.11142	−	4.86943i	−0.0467163	−	0.204677i
$567$	0.729294	+	2.54325i	0.0306275	+	0.106807i
$568$	−1.94436	+	8.51878i	−0.0815833	+	0.357440i
$569$	17.7965	−	30.8245i	0.746069	−	1.29223i	−0.203625	−	0.979049i	$-0.565272\pi$
$569$	17.7965	−	30.8245i	0.746069	−	1.29223i	0.949694	−	0.313180i	$-0.101394\pi$
$570$	0.543949	+	0.942146i	0.0227835	+	0.0394622i
$571$	14.2777	−	4.40408i	0.597502	−	0.184305i	0.0187715	−	0.999824i	$-0.494024\pi$
$571$	14.2777	−	4.40408i	0.597502	−	0.184305i	0.578731	+	0.815519i	$0.303548\pi$
$572$	−0.0607831	+	0.811094i	−0.00254147	+	0.0339135i
$573$	−5.98582	−	7.50598i	−0.250061	−	0.313567i
$574$	1.67056	+	0.158737i	0.0697278	+	0.00662557i
$575$	−11.3408	+	14.2209i	−0.472945	+	0.593054i
$576$	−0.733052	−	0.680173i	−0.0305438	−	0.0283405i
$577$	−11.5868	−	1.74643i	−0.482364	−	0.0727047i	−0.0966412	−	0.995319i	$-0.530810\pi$
$577$	−11.5868	−	1.74643i	−0.482364	−	0.0727047i	−0.385723	+	0.922615i	$0.626048\pi$
$578$	−13.9511	−	9.51172i	−0.580291	−	0.395635i
$579$	−5.32906	+	0.803227i	−0.221468	+	0.0333810i
$580$	−5.90167	−	2.84209i	−0.245053	−	0.118011i
$581$	13.0565	−	9.99301i	0.541676	−	0.414580i
$582$	0.486714	−	0.234389i	0.0201749	−	0.00971574i
$583$	−1.45597	+	0.992665i	−0.0603002	+	0.0411120i
$584$	1.75921	−	1.63231i	0.0727967	−	0.0675455i
$585$	0.0864441	+	1.15352i	0.00357402	+	0.0476920i
$586$	11.9237	+	30.3811i	0.492563	+	1.25503i
$587$	3.99682			0.164966			0.0824831	−	0.996592i	$-0.473715\pi$
$587$	3.99682			0.164966			0.0824831	+	0.996592i	$0.473715\pi$
$588$	4.93749	+	4.96197i	0.203619	+	0.204628i
$589$	−9.55013			−0.393506
$590$	−2.15996	−	5.50348i	−0.0889240	−	0.226575i
$591$	0.474360	+	6.32989i	0.0195126	+	0.260377i
$592$	1.99015	−	1.84659i	0.0817946	−	0.0758943i
$593$	28.4921	−	19.4256i	1.17003	−	0.797714i	0.187219	−	0.982318i	$-0.440053\pi$
$593$	28.4921	−	19.4256i	1.17003	−	0.797714i	0.982813	+	0.184604i	$0.0591003\pi$
$594$	−0.421679	+	0.203070i	−0.0173017	+	0.00833207i
$595$	−0.459184	−	0.381407i	−0.0188247	−	0.0156362i
$596$	4.02049	+	1.93617i	0.164686	+	0.0793085i
$597$	1.86636	−	0.281308i	0.0763848	−	0.0115132i
$598$	−5.73140	−	3.90760i	−0.234374	−	0.159794i
$599$	−1.43753	−	0.216672i	−0.0587358	−	0.00885299i	0.119609	−	0.992821i	$-0.461836\pi$
$599$	−1.43753	−	0.216672i	−0.0587358	−	0.00885299i	−0.178344	+	0.983968i	$0.557074\pi$
$600$	3.34048	+	3.09951i	0.136375	+	0.126537i
$601$	11.3341	−	14.2125i	0.462326	−	0.579738i	−0.494947	−	0.868923i	$-0.664813\pi$
$601$	11.3341	−	14.2125i	0.462326	−	0.579738i	0.957273	+	0.289185i	$0.0933841\pi$
$602$	−22.1119	+	22.8980i	−0.901213	+	0.933253i
$603$	−5.10867	−	6.40607i	−0.208041	−	0.260875i
$604$	0.714629	−	9.53607i	0.0290779	−	0.388017i
$605$	6.85719	−	2.11516i	0.278784	−	0.0859936i
$606$	1.07421	+	1.86059i	0.0436369	+	0.0755813i
$607$	16.0976	−	27.8819i	0.653383	−	1.13169i	−0.328913	−	0.944360i	$-0.606682\pi$
$607$	16.0976	−	27.8819i	0.653383	−	1.13169i	0.982297	−	0.187333i	$-0.0599843\pi$
$608$	−0.363692	+	1.59344i	−0.0147496	+	0.0646224i
$609$	−4.39306	+	25.6636i	−0.178016	+	1.03994i
$610$	−1.24371	−	5.44904i	−0.0503562	−	0.220625i
$611$	−2.71830	−	0.838485i	−0.109971	−	0.0339215i
$612$	0.123835	−	0.315527i	0.00500575	−	0.0127544i
$613$	10.7575	−	27.4097i	0.434492	−	1.10707i	−0.531170	−	0.847265i	$-0.678247\pi$
$613$	10.7575	−	27.4097i	0.434492	−	1.10707i	0.965662	−	0.259802i	$-0.0836574\pi$
$614$	24.8840	+	7.67568i	1.00423	+	0.309765i
$615$	0.0939423	+	0.411588i	0.00378812	+	0.0165968i
$616$	−0.717809	+	1.00901i	−0.0289214	+	0.0406543i
$617$	3.02651	−	13.2600i	0.121843	−	0.533828i	−0.876757	−	0.480933i	$-0.840298\pi$
$617$	3.02651	−	13.2600i	0.121843	−	0.533828i	0.998600	−	0.0528948i	$-0.0168448\pi$
$618$	−2.66983	+	4.62428i	−0.107396	+	0.186016i
$619$	−4.68702	−	8.11815i	−0.188387	−	0.326296i	0.756326	−	0.654195i	$-0.226993\pi$
$619$	−4.68702	−	8.11815i	−0.188387	−	0.326296i	−0.944713	+	0.327899i	$0.893659\pi$
$620$	3.71652	−	1.14639i	0.149259	−	0.0460403i
$621$	0.298288	−	3.98038i	0.0119699	−	0.159727i
$622$	−0.548443	−	0.687726i	−0.0219906	−	0.0275753i
$623$	−4.82009	−	36.9653i	−0.193113	−	1.48098i
$624$	−1.08354	+	1.35871i	−0.0433762	+	0.0543920i
$625$	−13.5985	−	12.6176i	−0.543941	−	0.504704i
$626$	24.0214	+	3.62064i	0.960087	+	0.144710i
$627$	0.632034	+	0.430913i	0.0252410	+	0.0172090i
$628$	1.36889	−	0.206327i	0.0546246	−	0.00823333i
$629$	0.829099	+	0.399273i	0.0330584	+	0.0159201i
$630$	−0.795574	+	1.57111i	−0.0316964	+	0.0625947i
$631$	41.9404	−	20.1974i	1.66962	−	0.804046i	0.671615	−	0.740901i	$-0.265601\pi$
$631$	41.9404	−	20.1974i	1.66962	−	0.804046i	0.998004	−	0.0631456i	$-0.0201132\pi$
$632$	−9.33907	+	6.36727i	−0.371488	+	0.253276i
$633$	−16.0622	+	14.9036i	−0.638416	+	0.592364i
$634$	−0.761461	−	10.1610i	−0.0302415	−	0.403544i
$635$	0.943873	+	2.40495i	0.0374564	+	0.0954375i
$636$	−3.76509			−0.149295
$637$	7.95786	−	9.20109i	0.315302	−	0.364560i
$638$	−4.60587			−0.182348
$639$	3.19230	+	8.13384i	0.126285	+	0.321770i
$640$	−0.0497417	−	0.663757i	−0.00196622	−	0.0262373i
$641$	−22.2062	+	20.6044i	−0.877093	+	0.813823i	−0.983577	−	0.180491i	$-0.942231\pi$
$641$	−22.2062	+	20.6044i	−0.877093	+	0.813823i	0.106484	+	0.994314i	$0.466041\pi$
$642$	−8.03139	+	5.47571i	−0.316974	+	0.216109i
$643$	−14.4115	+	6.94021i	−0.568334	+	0.273695i	−0.695905	−	0.718134i	$-0.744996\pi$
$643$	−14.4115	+	6.94021i	−0.568334	+	0.273695i	0.127571	+	0.991830i	$0.459282\pi$
$644$	−4.39150	−	9.60425i	−0.173049	−	0.378460i
$645$	−7.21515	−	3.47463i	−0.284096	−	0.136814i
$646$	−0.547811	+	0.0825692i	−0.0215533	+	0.00324864i
$647$	15.0902	+	10.2883i	0.593257	+	0.404476i	0.822394	−	0.568918i	$-0.192638\pi$
$647$	15.0902	+	10.2883i	0.593257	+	0.404476i	−0.229137	+	0.973394i	$0.573590\pi$
$648$	−0.988831	−	0.149042i	−0.0388449	−	0.00585493i
$649$	−3.04739	−	2.82757i	−0.119621	−	0.110992i
$650$	4.93763	−	6.19159i	0.193670	−	0.242854i
$651$	−8.45229	−	12.9443i	−0.331272	−	0.507328i
$652$	6.14364	+	7.70388i	0.240604	+	0.301707i
$653$	−0.351094	+	4.68502i	−0.0137394	+	0.183339i	0.986112	+	0.166083i	$0.0531120\pi$
$653$	−0.351094	+	4.68502i	−0.0137394	+	0.183339i	−0.999851	+	0.0172558i	$0.994507\pi$
$654$	7.56174	−	2.33249i	0.295687	−	0.0912074i
$655$	−5.75117	−	9.96132i	−0.224717	−	0.389221i
$656$	−0.317128	+	0.549282i	−0.0123818	+	0.0214459i
$657$	0.534016	−	2.33968i	0.0208340	−	0.0912795i
$658$	−2.88182	−	3.23279i	−0.112345	−	0.126027i
$659$	−3.92738	−	17.2070i	−0.152989	−	0.670288i	−0.992007	−	0.126184i	$-0.959727\pi$
$659$	−3.92738	−	17.2070i	−0.152989	−	0.670288i	0.839018	−	0.544104i	$-0.183130\pi$
$660$	−0.297688	−	0.0918247i	−0.0115875	−	0.00357427i
$661$	−2.15028	+	5.47881i	−0.0836361	+	0.213101i	−0.966574	−	0.256389i	$-0.917467\pi$
$661$	−2.15028	+	5.47881i	−0.0836361	+	0.213101i	0.882938	+	0.469490i	$0.155562\pi$
$662$	−2.38200	+	6.06922i	−0.0925789	+	0.235887i
$663$	−0.562891	−	0.173629i	−0.0218609	−	0.00674319i
$664$	1.38284	+	6.05861i	0.0536645	+	0.235120i
$665$	2.87397	−	0.157835i	0.111448	−	0.00612058i
$666$	0.604118	−	2.64681i	0.0234091	−	0.102562i
$667$	19.6404	−	34.0181i	0.760479	−	1.31719i
$668$	−4.48113	−	7.76155i	−0.173380	−	0.300303i
$669$	24.3109	−	7.49892i	0.939913	−	0.289925i
$670$	0.407567	−	5.43861i	0.0157457	−	0.210112i
$671$	−2.45032	−	3.07261i	−0.0945937	−	0.118617i
$672$	−2.48164	+	0.917313i	−0.0957313	+	0.0353861i
$673$	−16.8508	+	21.1303i	−0.649551	+	0.814512i	−0.992161	−	0.124966i	$-0.960118\pi$
$673$	−16.8508	+	21.1303i	−0.649551	+	0.814512i	0.342610	+	0.939478i	$0.388689\pi$
$674$	15.1214	+	14.0306i	0.582454	+	0.540439i
$675$	4.50605	+	0.679178i	0.173438	+	0.0261416i
$676$	−8.24574	−	5.62185i	−0.317144	−	0.216225i
$677$	7.93640	−	1.19622i	0.305021	−	0.0459744i	0.00525136	−	0.999986i	$-0.498328\pi$
$677$	7.93640	−	1.19622i	0.305021	−	0.0459744i	0.299769	+	0.954012i	$0.403090\pi$
$678$	2.77640	+	1.33704i	0.106627	+	0.0513489i
$679$	0.0284923	−	1.42898i	0.00109343	−	0.0548393i
$680$	0.203274	−	0.0978915i	0.00779519	−	0.00375397i
$681$	−16.4394	+	11.2082i	−0.629960	+	0.429500i
$682$	2.00472	−	1.86011i	0.0767648	−	0.0712273i
$683$	0.260550	+	3.47679i	0.00996965	+	0.133036i	0.999968	−	0.00804578i	$-0.00256108\pi$
$683$	0.260550	+	3.47679i	0.00996965	+	0.133036i	−0.989998	+	0.141082i	$0.954942\pi$
$684$	0.597119	+	1.52143i	0.0228314	+	0.0581735i
$685$	6.34685			0.242501
$686$	17.6136	−	5.72362i	0.672492	−	0.218529i
$687$	7.78609			0.297058
$688$	−4.39550	−	11.1996i	−0.167577	−	0.426979i
$689$	0.488973	+	6.52490i	0.0186284	+	0.248579i
$690$	1.94760	−	1.80711i	0.0741440	−	0.0687956i
$691$	−40.0673	+	27.3174i	−1.52423	+	1.03920i	−0.544529	+	0.838742i	$0.683291\pi$
$691$	−40.0673	+	27.3174i	−1.52423	+	1.03920i	−0.979702	+	0.200460i	$0.935756\pi$
$692$	10.6084	−	5.10876i	0.403272	−	0.194206i
$693$	−0.0246851	+	1.23804i	−0.000937711	+	0.0470293i
$694$	−23.2013	−	11.1732i	−0.880710	−	0.424128i
$695$	12.7093	−	1.91562i	0.482091	−	0.0726635i
$696$	−8.13102	−	5.54363i	−0.308205	−	0.210131i
$697$	−0.212585	−	0.0320421i	−0.00805224	−	0.00121368i
$698$	9.45985	+	8.77746i	0.358061	+	0.332232i
$699$	3.05296	−	3.82829i	0.115473	−	0.144799i
$700$	11.3087	−	4.18015i	0.427429	−	0.157995i
$701$	31.5902	+	39.6128i	1.19314	+	1.49615i	0.823818	+	0.566855i	$0.191840\pi$
$701$	31.5902	+	39.6128i	1.19314	+	1.49615i	0.369326	+	0.929300i	$0.379589\pi$
$702$	−0.129870	+	1.73300i	−0.00490164	+	0.0654078i
$703$	−4.24011	+	1.30790i	−0.159919	+	0.0493284i
$704$	−0.234014	−	0.405325i	−0.00881975	−	0.0152763i
$705$	0.544772	−	0.943573i	0.0205173	−	0.0355370i
$706$	7.03256	−	30.8117i	0.264674	−	1.15961i
$707$	5.67565	−	0.311699i	0.213455	−	0.0117227i
$708$	−1.97648	−	8.65951i	−0.0742806	−	0.325444i
$709$	6.05621	+	1.86809i	0.227446	+	0.0701577i	0.406383	−	0.913703i	$-0.366790\pi$
$709$	6.05621	+	1.86809i	0.227446	+	0.0701577i	−0.178938	+	0.983860i	$0.557266\pi$
$710$	−2.12485	+	5.41403i	−0.0797443	+	0.203185i
$711$	−4.12949	+	10.5218i	−0.154868	+	0.394597i
$712$	13.4639	+	4.15305i	0.504580	+	0.155642i
$713$	5.18989	+	22.7384i	0.194363	+	0.851560i
$714$	−0.596752	−	0.669430i	−0.0223329	−	0.0250528i
$715$	−0.120471	+	0.527819i	−0.00450537	+	0.0197393i
$716$	−5.23468	+	9.06673i	−0.195629	+	0.338840i
$717$	13.1671	+	22.8061i	0.491734	+	0.851708i
$718$	−27.3681	+	8.44195i	−1.02137	+	0.315051i
$719$	2.35789	−	31.4639i	0.0879345	−	1.17340i	−0.762380	−	0.647129i	$-0.775969\pi$
$719$	2.35789	−	31.4639i	0.0879345	−	1.17340i	0.850315	−	0.526275i	$-0.176412\pi$
$720$	−0.415006	−	0.520402i	−0.0154664	−	0.0193942i
$721$	7.72397	+	11.8289i	0.287656	+	0.440532i
$722$	−10.1808	+	12.7663i	−0.378889	+	0.475112i
$723$	11.6546	+	10.8139i	0.433438	+	0.402172i
$724$	13.8192	+	2.08291i	0.513586	+	0.0774106i
$725$	37.0527	+	25.2621i	1.37610	+	0.938210i
$726$	10.6605	−	1.60682i	0.395650	−	0.0596346i
$727$	−18.4265	−	8.87376i	−0.683403	−	0.329109i	0.0597671	−	0.998212i	$-0.480964\pi$
$727$	−18.4265	−	8.87376i	−0.683403	−	0.329109i	−0.743170	+	0.669103i	$0.766678\pi$
$728$	1.91199	+	4.18155i	0.0708632	+	0.154979i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	1.31982	−	0.899838i	0.0488487	−	0.0333045i
$731$	2.98945	−	2.77380i	0.110569	−	0.102593i
$732$	−0.627505	−	8.37348i	−0.0231933	−	0.309493i
$733$	2.46176	+	6.27246i	0.0909272	+	0.231679i	0.969102	−	0.246662i	$-0.0793337\pi$
$733$	2.46176	+	6.27246i	0.0909272	+	0.231679i	−0.878174	+	0.478341i	$0.841238\pi$
$734$	−9.55660			−0.352740
$735$	2.75753	+	3.75572i	0.101713	+	0.138532i
$736$	3.99154			0.147130
$737$	−1.40104	−	3.56978i	−0.0516078	−	0.131495i
$738$	0.0473981	+	0.632483i	0.00174475	+	0.0232820i
$739$	−16.4342	+	15.2487i	−0.604542	+	0.560933i	−0.921927	−	0.387364i	$-0.873386\pi$
$739$	−16.4342	+	15.2487i	−0.604542	+	0.560933i	0.317385	+	0.948297i	$0.397195\pi$
$740$	1.49308	−	1.01796i	0.0548865	−	0.0374210i
$741$	2.55910	−	1.23240i	0.0940107	−	0.0452732i
$742$	−4.50018	+	8.88704i	−0.165207	+	0.326254i
$743$	4.26256	+	2.05274i	0.156378	+	0.0753078i	0.510436	−	0.859916i	$-0.329484\pi$
$743$	4.26256	+	2.05274i	0.156378	+	0.0753078i	−0.354058	+	0.935224i	$0.615198\pi$
$744$	5.77789	−	0.870876i	0.211828	−	0.0319279i
$745$	2.45415	+	1.67321i	0.0899130	+	0.0613017i
$746$	15.5522	+	2.34412i	0.569407	+	0.0858243i
$747$	4.55549	+	4.22688i	0.166677	+	0.154653i
$748$	0.0989118	−	0.124031i	0.00361657	−	0.00453504i
$749$	3.32532	+	25.5019i	0.121505	+	0.931820i
$750$	3.96620	+	4.97345i	0.144825	+	0.181605i
$751$	−2.92031	+	38.9688i	−0.106564	+	1.42199i	0.645932	+	0.763395i	$0.276469\pi$
$751$	−2.92031	+	38.9688i	−0.106564	+	1.42199i	−0.752495	+	0.658597i	$0.771150\pi$
$752$	1.56417	−	0.482482i	0.0570393	−	0.0175943i
$753$	1.96623	+	3.40562i	0.0716536	+	0.124108i
$754$	−8.55114	+	14.8110i	−0.311414	+	0.539385i
$755$	1.41639	−	6.20559i	0.0515476	−	0.225845i
$756$	−1.53369	+	2.15588i	−0.0557796	+	0.0784085i
$757$	−2.83132	−	12.4048i	−0.102906	−	0.450860i	−0.999960	−	0.00893957i	$-0.997154\pi$
$757$	−2.83132	−	12.4048i	−0.102906	−	0.450860i	0.897054	−	0.441921i	$-0.145703\pi$
$758$	−13.5653	−	4.18433i	−0.492713	−	0.151982i
$759$	0.682514	−	1.73902i	0.0247737	−	0.0631223i
$760$	−0.397453	+	1.01269i	−0.0144172	+	0.0367343i
$761$	2.56973	+	0.792655i	0.0931525	+	0.0287337i	0.340981	−	0.940070i	$-0.389241\pi$
$761$	2.56973	+	0.792655i	0.0931525	+	0.0287337i	−0.247829	+	0.968804i	$0.579717\pi$
$762$	0.863695	+	3.78410i	0.0312884	+	0.137083i
$763$	3.53253	−	20.6365i	0.127886	−	0.747090i
$764$	2.13631	−	9.35981i	0.0772892	−	0.338626i
$765$	0.112808	−	0.195390i	0.00407860	−	0.00706434i
$766$	−15.2720	−	26.4519i	−0.551801	−	0.955747i
$767$	−14.7502	+	4.54985i	−0.532601	+	0.164286i
$768$	0.0747301	−	0.997204i	0.00269659	−	0.0359835i
$769$	16.6820	+	20.9186i	0.601570	+	0.754345i	0.985622	−	0.168967i	$-0.0540430\pi$
$769$	16.6820	+	20.9186i	0.601570	+	0.754345i	−0.384052	+	0.923312i	$0.625472\pi$
$770$	−0.572550	+	0.592905i	−0.0206333	+	0.0213668i
$771$	−19.5220	+	24.4798i	−0.703066	+	0.881617i
$772$	−3.95060	−	3.66562i	−0.142185	−	0.131929i
$773$	−27.4331	−	4.13488i	−0.986702	−	0.148721i	−0.364184	−	0.931327i	$-0.618652\pi$
$773$	−27.4331	−	4.13488i	−0.986702	−	0.148721i	−0.622518	+	0.782606i	$0.713890\pi$
$774$	−9.94067	−	6.77744i	−0.357310	−	0.243610i
$775$	−26.3296	+	3.96854i	−0.945785	+	0.142554i
$776$	0.486714	+	0.234389i	0.0174720	+	0.00841408i
$777$	−5.52542	−	4.58952i	−0.198223	−	0.164648i
$778$	30.1142	−	14.5023i	1.07965	−	0.519931i
$779$	0.856511	−	0.583959i	0.0306877	−	0.0209225i
$780$	−0.847959	+	0.786791i	−0.0303618	+	0.0281716i
$781$	0.305614	+	4.07813i	0.0109357	+	0.145927i
$782$	0.494294	+	1.25944i	0.0176759	+	0.0450375i
$783$	−9.84100			−0.351689
$784$	−0.800948	+	6.95403i	−0.0286053	+	0.248358i
$785$	0.921449			0.0328879
$786$	−6.31334	−	16.0861i	−0.225189	−	0.573773i
$787$	3.36186	+	44.8608i	0.119837	+	1.59912i	0.655840	+	0.754900i	$0.272315\pi$
$787$	3.36186	+	44.8608i	0.119837	+	1.59912i	−0.536003	+	0.844216i	$0.680066\pi$
$788$	−4.65315	+	4.31749i	−0.165762	+	0.153804i
$789$	10.8280	−	7.38243i	0.385488	−	0.262821i
$790$	−6.77850	+	3.26435i	−0.241168	+	0.116140i
$791$	6.47440	−	4.95528i	0.230203	−	0.176189i
$792$	−0.421679	−	0.203070i	−0.0149837	−	0.00721578i
$793$	−14.4297	+	2.17493i	−0.512415	+	0.0772341i
$794$	29.9094	+	20.3919i	1.06145	+	0.723682i
$795$	−2.47812	−	0.373517i	−0.0878899	−	0.0132473i
$796$	1.38359	+	1.28378i	0.0490400	+	0.0455025i
$797$	−9.84392	+	12.3439i	−0.348689	+	0.437243i	−0.924988	−	0.379997i	$-0.875925\pi$
$797$	−9.84392	+	12.3439i	−0.348689	+	0.437243i	0.576299	+	0.817239i	$0.304497\pi$
$798$	4.30487	+	0.409050i	0.152391	+	0.0144802i
$799$	0.345935	+	0.433789i	0.0122383	+	0.0153464i
$800$	−0.340541	+	4.54421i	−0.0120400	+	0.160662i
$801$	13.4639	−	4.15305i	0.475722	−	0.146741i
$802$	−9.93919	−	17.2152i	−0.350965	−	0.607889i
$803$	0.561599	−	0.972717i	0.0198184	−	0.0343264i
$804$	1.82326	−	7.98823i	0.0643015	−	0.281723i
$805$	−1.93762	−	6.75702i	−0.0682922	−	0.238154i
$806$	−2.25960	−	9.89997i	−0.0795912	−	0.348712i
$807$	28.1346	+	8.67838i	0.990385	+	0.305493i
$808$	−0.784908	+	1.99991i	−0.0276130	+	0.0703567i
$809$	0.778829	−	1.98442i	0.0273822	−	0.0697686i	−0.916529	−	0.399969i	$-0.869021\pi$
$809$	0.778829	−	1.98442i	0.0273822	−	0.0697686i	0.943911	+	0.330200i	$0.107116\pi$
$810$	−0.636047	−	0.196195i	−0.0223484	−	0.00689357i
$811$	−9.98773	−	43.7591i	−0.350717	−	1.53659i	−0.775531	−	0.631310i	$-0.782518\pi$
$811$	−9.98773	−	43.7591i	−0.350717	−	1.53659i	0.424814	−	0.905281i	$-0.360339\pi$
$812$	−22.8036	+	12.5663i	−0.800250	+	0.440992i
$813$	−2.45238	+	10.7446i	−0.0860088	+	0.376829i
$814$	0.635321	−	1.10041i	0.0222680	−	0.0385693i
$815$	3.27938	+	5.68006i	0.114872	+	0.198964i
$816$	0.323899	−	0.0999097i	0.0113387	−	0.00349754i
$817$	−1.46949	+	19.6090i	−0.0514111	+	0.686034i
$818$	−19.0868	−	23.9341i	−0.667354	−	0.836836i
$819$	3.93531	+	2.37789i	0.137511	+	0.0830903i
$820$	−0.263221	+	0.330068i	−0.00919206	+	0.0115265i
$821$	−18.7708	−	17.4168i	−0.655107	−	0.607850i	0.280940	−	0.959725i	$-0.409354\pi$
$821$	−18.7708	−	17.4168i	−0.655107	−	0.607850i	−0.936047	+	0.351875i	$0.885544\pi$
$822$	9.42876	+	1.42116i	0.328866	+	0.0495686i
$823$	29.7848	+	20.3069i	1.03823	+	0.707856i	0.957369	−	0.288869i	$-0.0932793\pi$
$823$	29.7848	+	20.3069i	1.03823	+	0.707856i	0.0808652	+	0.996725i	$0.474232\pi$
$824$	−5.28001	+	0.795834i	−0.183938	+	0.0277242i
$825$	1.92157	+	0.925380i	0.0669006	+	0.0322176i
$826$	−22.8021	−	5.68496i	−0.793387	−	0.197805i
$827$	17.8091	−	8.57643i	0.619285	−	0.298232i	−0.0978126	−	0.995205i	$-0.531185\pi$
$827$	17.8091	−	8.57643i	0.619285	−	0.298232i	0.717097	+	0.696973i	$0.245470\pi$
$828$	3.29797	−	2.24851i	0.114612	−	0.0781413i
$829$	39.0976	−	36.2773i	1.35792	−	1.25996i	0.422525	−	0.906351i	$-0.361144\pi$
$829$	39.0976	−	36.2773i	1.35792	−	1.25996i	0.935392	−	0.353612i	$-0.115047\pi$
$830$	0.309116	+	4.12487i	0.0107296	+	0.143176i
$831$	7.09739	+	18.0839i	0.246206	+	0.627322i
$832$	−1.73786			−0.0602494
$833$	−2.29337	+	0.608433i	−0.0794606	+	0.0210810i
$834$	19.3096			0.668638
$835$	−2.17942	−	5.55308i	−0.0754221	−	0.192172i
$836$	0.0571650	+	0.762814i	0.00197709	+	0.0263825i
$837$	4.28333	−	3.97435i	0.148054	−	0.137374i
$838$	−29.1584	+	19.8799i	−1.00726	+	0.686739i
$839$	−13.4998	+	6.50118i	−0.466066	+	0.224446i	−0.652153	−	0.758088i	$-0.726134\pi$
$839$	−13.4998	+	6.50118i	−0.466066	+	0.224446i	0.186086	+	0.982533i	$0.440420\pi$
$840$	−1.72438	+	0.357569i	−0.0594967	+	0.0123373i
$841$	−61.1266	−	29.4370i	−2.10781	−	1.01507i
$842$	−27.6480	+	4.16726i	−0.952812	+	0.143613i
$843$	−19.7523	−	13.4669i	−0.680306	−	0.463825i
$844$	−21.6667	−	3.26573i	−0.745799	−	0.112411i
$845$	−4.86950	−	4.51823i	−0.167516	−	0.155432i
$846$	1.02058	−	1.27977i	0.0350884	−	0.0439994i
$847$	8.94920	−	27.0835i	0.307498	−	0.930599i
$848$	−2.34749	−	2.94366i	−0.0806133	−	0.101086i
$849$	0.373251	−	4.98069i	0.0128099	−	0.170937i
$850$	−1.47599	+	0.455284i	−0.0506262	+	0.0156161i
$851$	5.41828	+	9.38473i	0.185736	+	0.321704i
$852$	−4.36893	+	7.56720i	−0.149677	+	0.259248i
$853$	−9.16432	+	40.1515i	−0.313780	+	1.37476i	0.534480	+	0.845181i	$0.320508\pi$
$853$	−9.16432	+	40.1515i	−0.313780	+	1.37476i	−0.848260	+	0.529580i	$0.822350\pi$
$854$	−20.5146	−	8.52716i	−0.701996	−	0.291793i
$855$	0.242080	+	1.06062i	0.00827896	+	0.0362725i
$856$	−9.28857	−	2.86515i	−0.317477	−	0.0979286i
$857$	7.48120	−	19.0618i	0.255553	−	0.651138i	−0.744308	−	0.667837i	$-0.767220\pi$
$857$	7.48120	−	19.0618i	0.255553	−	0.651138i	0.999861	+	0.0166989i	$0.00531566\pi$
$858$	−0.297157	+	0.757143i	−0.0101448	+	0.0258484i
$859$	−38.3926	−	11.8426i	−1.30994	−	0.404063i	−0.440345	−	0.897829i	$-0.645144\pi$
$859$	−38.3926	−	11.8426i	−1.30994	−	0.404063i	−0.869595	+	0.493766i	$0.835620\pi$
$860$	−1.78200	−	7.80743i	−0.0607655	−	0.266231i
$861$	1.54955	+	0.644092i	0.0528086	+	0.0219506i
$862$	3.76744	−	16.5062i	0.128319	−	0.562204i
$863$	11.5601	−	20.0226i	0.393509	−	0.681578i	−0.599401	−	0.800449i	$-0.704594\pi$
$863$	11.5601	−	20.0226i	0.393509	−	0.681578i	0.992910	+	0.118872i	$0.0379277\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	7.48913	−	2.31009i	0.254638	−	0.0785454i
$866$	−1.69128	+	22.5685i	−0.0574720	+	0.766910i
$867$	−10.5277	−	13.2013i	−0.357539	−	0.448340i
$868$	4.85036	−	14.6789i	0.164632	−	0.498235i
$869$	−3.29837	+	4.13603i	−0.111890	+	0.140305i
$870$	−4.80175	−	4.45537i	−0.162795	−	0.151051i
$871$	−14.0804	−	2.12228i	−0.477096	−	0.0719106i
$872$	6.53828	+	4.45772i	0.221414	+	0.150958i
$873$	0.534178	−	0.0805144i	0.0180792	−	0.00272500i
$874$	−5.87777	−	2.83059i	−0.198819	−	0.0957460i
$875$	16.4798	−	3.41727i	0.557119	−	0.115525i
$876$	2.16219	−	1.04125i	0.0730535	−	0.0351807i
$877$	−8.80528	+	6.00334i	−0.297333	+	0.202718i	−0.702793	−	0.711395i	$-0.748064\pi$
$877$	−8.80528	+	6.00334i	−0.297333	+	0.202718i	0.405460	+	0.914113i	$0.367112\pi$
$878$	−24.2109	+	22.4645i	−0.817080	+	0.758139i
$879$	2.43898	+	32.5459i	0.0822646	+	1.09775i
$880$	−0.113814	−	0.289994i	−0.00383668	−	0.00977569i
$881$	−38.6901			−1.30350			−0.651751	−	0.758433i	$-0.725965\pi$
$881$	−38.6901			−1.30350			−0.651751	+	0.758433i	$0.725965\pi$
$882$	3.25557	+	6.19688i	0.109621	+	0.208660i
$883$	−12.5913			−0.423733			−0.211866	−	0.977299i	$-0.567954\pi$
$883$	−12.5913			−0.423733			−0.211866	+	0.977299i	$0.567954\pi$
$884$	−0.215208	−	0.548342i	−0.00723824	−	0.0184427i
$885$	−0.441817	−	5.89563i	−0.0148515	−	0.198180i
$886$	12.2691	−	11.3840i	0.412187	−	0.382453i
$887$	−9.92581	+	6.76731i	−0.333276	+	0.227224i	−0.718382	−	0.695648i	$-0.755117\pi$
$887$	−9.92581	+	6.76731i	−0.333276	+	0.227224i	0.385106	+	0.922872i	$0.374165\pi$
$888$	2.44602	−	1.17794i	0.0820831	−	0.0395292i
$889$	9.96423	+	2.48425i	0.334190	+	0.0833191i
$890$	8.44970	+	4.06916i	0.283234	+	0.136399i
$891$	−0.462801	+	0.0697561i	−0.0155044	+	0.00233692i
$892$	21.0205	+	14.3315i	0.703818	+	0.479855i
$893$	−2.64547	−	0.398741i	−0.0885274	−	0.0133434i
$894$	3.27118	+	3.03521i	0.109405	+	0.101513i
$895$	−4.34485	+	5.44827i	−0.145232	+	0.182116i
$896$	−2.26446	−	1.36829i	−0.0756503	−	0.0457113i
$897$	−4.32498	−	5.42336i	−0.144407	−	0.181081i
$898$	−0.185359	+	2.47345i	−0.00618552	+	0.0825401i
$899$	54.9478	−	16.9491i	1.83261	−	0.565286i
$900$	2.27848	+	3.94644i	0.0759492	+	0.131548i
$901$	0.638104	−	1.10523i	0.0212583	−	0.0368205i
$902$	−0.0660554	+	0.289408i	−0.00219940	+	0.00963622i
$903$	−27.8788	+	15.3631i	−0.927749	+	0.511253i
$904$	0.685714	+	3.00431i	0.0228065	+	0.0999219i
$905$	8.88893	+	2.74187i	0.295478	+	0.0911429i
$906$	3.49369	−	8.90177i	0.116070	−	0.295741i
$907$	−1.93177	+	4.92207i	−0.0641434	+	0.163435i	−0.959352	−	0.282213i	$-0.908931\pi$
$907$	−1.93177	+	4.92207i	−0.0641434	+	0.163435i	0.895208	+	0.445648i	$0.147027\pi$
$908$	−19.0128	−	5.86466i	−0.630960	−	0.194625i
$909$	0.478070	+	2.09456i	0.0158566	+	0.0694722i
$910$	0.843612	+	2.94191i	0.0279655	+	0.0975234i
$911$	4.77858	−	20.9363i	0.158321	−	0.693651i	−0.831990	−	0.554790i	$-0.812799\pi$
$911$	4.77858	−	20.9363i	0.158321	−	0.693651i	0.990312	−	0.138861i	$-0.0443442\pi$
$912$	−0.817207	+	1.41544i	−0.0270604	+	0.0468701i
$913$	1.45426	+	2.51886i	0.0481291	+	0.0833621i
$914$	−24.2682	+	7.48575i	−0.802721	+	0.247607i
$915$	0.417679	−	5.57354i	0.0138080	−	0.184256i
$916$	4.85455	+	6.08741i	0.160399	+	0.201134i
$917$	−45.5154	−	4.32489i	−1.50305	−	0.142820i
$918$	0.211337	−	0.265008i	0.00697516	−	0.00874657i
$919$	20.9780	+	19.4647i	0.691999	+	0.642081i	0.945639	−	0.325217i	$-0.105437\pi$
$919$	20.9780	+	19.4647i	0.691999	+	0.642081i	−0.253640	+	0.967299i	$0.581628\pi$
$920$	2.62717	+	0.395982i	0.0866152	+	0.0130551i
$921$	21.5160	+	14.6693i	0.708976	+	0.483371i
$922$	−3.46433	+	0.522164i	−0.114092	+	0.0171966i
$923$	13.6814	+	6.58859i	0.450327	+	0.216866i
$924$	−0.983331	+	0.752607i	−0.0323492	+	0.0247589i
$925$	−11.1464	+	5.36783i	−0.366492	+	0.176493i
$926$	−14.7176	+	10.0343i	−0.483651	+	0.329748i
$927$	−3.91424	+	3.63189i	−0.128561	+	0.119287i
$928$	−0.735419	−	9.81349i	−0.0241413	−	0.322143i
$929$	6.18328	+	15.7547i	0.202867	+	0.516896i	0.995710	−	0.0925297i	$-0.0294953\pi$
$929$	6.18328	+	15.7547i	0.202867	+	0.516896i	−0.792843	+	0.609426i	$0.791400\pi$
$930$	3.88931			0.127535
$931$	6.11086	−	9.67221i	0.200275	−	0.316994i
$932$	4.89656			0.160392
$933$	−0.321367	−	0.818829i	−0.0105211	−	0.0268072i
$934$	−2.10208	−	28.0503i	−0.0687822	−	0.917834i
$935$	0.0774068	−	0.0718230i	0.00253147	−	0.00234886i
$936$	−1.43589	+	0.978971i	−0.0469334	+	0.0319987i
$937$	−19.6324	+	9.45446i	−0.641362	+	0.308864i	−0.726151	−	0.687535i	$-0.758693\pi$
$937$	−19.6324	+	9.45446i	−0.641362	+	0.308864i	0.0847891	+	0.996399i	$0.472978\pi$
$938$	−16.6760	−	13.8515i	−0.544492	−	0.452266i
$939$	21.8870	+	10.5402i	0.714254	+	0.343966i
$940$	1.07737	−	0.162388i	0.0351401	−	0.00529652i
$941$	−37.4186	−	25.5116i	−1.21981	−	0.831653i	−0.229882	−	0.973218i	$-0.573834\pi$
$941$	−37.4186	−	25.5116i	−1.21981	−	0.831653i	−0.989929	+	0.141565i	$0.954786\pi$
$942$	1.36889	+	0.206327i	0.0446008	+	0.00672249i
$943$	−1.85584	−	1.72197i	−0.0604344	−	0.0560750i
$944$	5.53797	−	6.94439i	0.180245	−	0.226021i
$945$	−1.22332	+	1.26681i	−0.0397947	+	0.0412095i
$946$	−3.51085	−	4.40246i	−0.114148	−	0.143136i
$947$	−2.23048	+	29.7637i	−0.0724810	+	0.967191i	0.835855	+	0.548950i	$0.184972\pi$
$947$	−2.23048	+	29.7637i	−0.0724810	+	0.967191i	−0.908336	+	0.418241i	$0.862647\pi$
$948$	−10.8009	+	3.33165i	−0.350798	+	0.108207i
$949$	−2.08530	−	3.61184i	−0.0676916	−	0.117245i
$950$	3.72398	−	6.45011i	0.120822	−	0.209269i
$951$	2.26737	−	9.93401i	0.0735246	−	0.322132i
$952$	0.151312	−	0.883942i	0.00490406	−	0.0286487i
$953$	6.46595	+	28.3292i	0.209453	+	0.917672i	0.964932	+	0.262500i	$0.0845468\pi$
$953$	6.46595	+	28.3292i	0.209453	+	0.917672i	−0.755480	+	0.655172i	$0.772596\pi$
$954$	−3.59782	−	1.10978i	−0.116484	−	0.0359304i
$955$	2.33463	−	5.94854i	0.0755469	−	0.192490i
$956$	−9.62095	+	24.5138i	−0.311164	+	0.792833i
$957$	−4.40125	−	1.35760i	−0.142272	−	0.0438851i
$958$	−4.51257	−	19.7709i	−0.145795	−	0.638768i
$959$	14.6241	−	20.5569i	0.472237	−	0.663815i
$960$	0.148114	−	0.648930i	0.00478036	−	0.0209441i
$961$	−1.57120	+	2.72140i	−0.0506839	+	0.0877870i
$962$	−2.35904	−	4.08598i	−0.0760585	−	0.131737i
$963$	−9.28857	+	2.86515i	−0.299320	+	0.0923280i
$964$	−1.18811	+	15.8543i	−0.0382665	+	0.510631i
$965$	−2.23658	−	2.80458i	−0.0719979	−	0.0902825i
$966$	−1.36549	−	10.4720i	−0.0439340	−	0.336930i
$967$	25.4521	−	31.9159i	0.818484	−	1.02635i	−0.180600	−	0.983557i	$-0.557804\pi$
$967$	25.4521	−	31.9159i	0.818484	−	1.02635i	0.999084	−	0.0427898i	$-0.0136246\pi$
$968$	7.90299	+	7.33291i	0.254012	+	0.235689i
$969$	−0.547811	−	0.0825692i	−0.0175982	−	0.00265250i
$970$	0.297095	+	0.202556i	0.00953914	+	0.00650367i
$971$	−46.4140	+	6.99579i	−1.48950	+	0.224506i	−0.842794	−	0.538236i	$-0.819091\pi$
$971$	−46.4140	+	6.99579i	−1.48950	+	0.224506i	−0.646703	+	0.762742i	$0.723853\pi$
$972$	−0.900969	−	0.433884i	−0.0288986	−	0.0139168i
$973$	23.0796	−	45.5781i	0.739900	−	1.46117i
$974$	−6.30514	+	3.03640i	−0.202030	+	0.0972924i
$975$	6.54327	−	4.46112i	0.209552	−	0.142870i
$976$	6.15540	−	5.71138i	0.197030	−	0.182817i
$977$	1.71960	+	22.9464i	0.0550148	+	0.734121i	0.954698	+	0.297577i	$0.0961785\pi$
$977$	1.71960	+	22.9464i	0.0550148	+	0.734121i	−0.899683	+	0.436544i	$0.856202\pi$
$978$	3.59994	+	9.17249i	0.115113	+	0.293304i
$979$	6.59445			0.210759
$980$	−1.21705	+	4.49757i	−0.0388772	+	0.143670i
$981$	7.91330			0.252652
$982$	0.679511	+	1.73137i	0.0216841	+	0.0552501i
$983$	2.16267	+	28.8588i	0.0689784	+	0.920452i	0.919140	+	0.393931i	$0.128885\pi$
$983$	2.16267	+	28.8588i	0.0689784	+	0.920452i	−0.850162	+	0.526522i	$0.823496\pi$
$984$	−0.464943	+	0.431404i	−0.0148218	+	0.0137527i
$985$	−3.49095	+	2.38009i	−0.111231	+	0.0758359i
$986$	3.00535	−	1.44730i	0.0957099	−	0.0460915i
$987$	−1.80091	−	3.93860i	−0.0573235	−	0.125367i
$988$	2.55910	+	1.23240i	0.0814157	+	0.0392077i
$989$	47.4868	−	7.15748i	1.50999	−	0.227595i
$990$	−0.257397	−	0.175490i	−0.00818062	−	0.00557745i
$991$	16.5264	+	2.49095i	0.524977	+	0.0791276i	0.406184	−	0.913791i	$-0.366859\pi$
$991$	16.5264	+	2.49095i	0.524977	+	0.0791276i	0.118793	+	0.992919i	$0.462097\pi$
$992$	4.28333	+	3.97435i	0.135996	+	0.126186i
$993$	−4.06511	+	5.09748i	−0.129002	+	0.161764i
$994$	12.6396	+	19.3570i	0.400903	+	0.613965i
$995$	0.783298	+	0.982225i	0.0248322	+	0.0311386i
$996$	−0.464404	+	6.19704i	−0.0147152	+	0.196361i
$997$	−19.2889	+	5.94985i	−0.610887	+	0.188434i	−0.584735	−	0.811224i	$-0.698801\pi$
$997$	−19.2889	+	5.94985i	−0.610887	+	0.188434i	−0.0261517	+	0.999658i	$0.508325\pi$
$998$	4.06037	+	7.03277i	0.128529	+	0.222619i
$999$	1.35744	−	2.35116i	0.0429475	−	0.0743873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.163.1	✓	24
3.2	odd	2		882.2.z.a.163.2		24
49.46	even	21	inner	294.2.m.b.193.1	yes	24
147.95	odd	42		882.2.z.a.487.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.163.1	✓	24	1.1	even	1	trivial
294.2.m.b.193.1	yes	24	49.46	even	21	inner
882.2.z.a.163.2		24	3.2	odd	2
882.2.z.a.487.2		24	147.95	odd	42

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.549960 + 0.374956i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-0.0527428 + 2.64523i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +O(q^{10})\)	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.549960 + 0.374956i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-0.0527428 + 2.64523i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(-0.549960 - 0.374956i) q^{10} +(-0.462801 - 0.0697561i) q^{11} +(-0.733052 - 0.680173i) q^{12} +(-1.08354 + 1.35871i) q^{13} +(-2.48164 + 0.917313i) q^{14} +(-0.415006 - 0.520402i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(0.323899 - 0.0999097i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.817207 + 1.41544i) q^{19} +(0.148114 - 0.648930i) q^{20} +(-2.64177 + 0.145083i) q^{21} +(-0.104146 - 0.456294i) q^{22} +(3.81421 + 1.17653i) q^{23} +(0.365341 - 0.930874i) q^{24} +(-1.66484 + 4.24195i) q^{25} +(-1.66065 - 0.512243i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-1.76055 - 1.97496i) q^{28} +(2.18983 - 9.59427i) q^{29} +(0.332809 - 0.576443i) q^{30} +(2.92157 + 5.06032i) q^{31} +(0.955573 - 0.294755i) q^{32} +(0.0349758 - 0.466720i) q^{33} +(0.211337 + 0.265008i) q^{34} +(-0.962838 - 1.47454i) q^{35} +(0.623490 - 0.781831i) q^{36} +(1.99015 + 1.84659i) q^{37} +(-1.61616 - 0.243597i) q^{38} +(-1.43589 - 0.978971i) q^{39} +(0.658184 - 0.0992053i) q^{40} +(-0.571445 - 0.275194i) q^{41} +(-1.10020 - 2.40615i) q^{42} +(10.8398 - 5.22016i) q^{43} +(0.386703 - 0.263650i) q^{44} +(0.487933 - 0.452736i) q^{45} +(0.298288 + 3.98038i) q^{46} +(0.598023 + 1.52374i) q^{47} +1.00000 q^{48} +(-6.99444 - 0.279033i) q^{49} -4.55695 q^{50} +(0.123835 + 0.315527i) q^{51} +(-0.129870 - 1.73300i) q^{52} +(2.76000 - 2.56091i) q^{53} +(0.826239 - 0.563320i) q^{54} +(0.280678 - 0.135167i) q^{55} +(1.19524 - 2.36038i) q^{56} +(-1.47256 - 0.709146i) q^{57} +(9.73109 - 1.46673i) q^{58} +(7.33883 + 5.00353i) q^{59} +(0.658184 + 0.0992053i) q^{60} +(6.15540 + 5.71138i) q^{61} +(-3.64314 + 4.56836i) q^{62} +(-0.342097 - 2.62354i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.0864441 - 1.15352i) q^{65} +(0.447236 - 0.137954i) q^{66} +(4.09683 + 7.09592i) q^{67} +(-0.169479 + 0.293546i) q^{68} +(-0.888201 + 3.89146i) q^{69} +(1.02085 - 1.43499i) q^{70} +(-1.94436 - 8.51878i) q^{71} +(0.955573 + 0.294755i) q^{72} +(-0.876762 + 2.23395i) q^{73} +(-0.991857 + 2.52721i) q^{74} +(-4.35450 - 1.34319i) q^{75} +(-0.363692 - 1.59344i) q^{76} +(0.208930 - 1.22053i) q^{77} +(0.386710 - 1.69429i) q^{78} +(5.65156 - 9.78878i) q^{79} +(0.332809 + 0.576443i) q^{80} +(0.955573 - 0.294755i) q^{81} +(0.0473981 - 0.632483i) q^{82} +(-3.87463 - 4.85863i) q^{83} +(1.83787 - 1.90321i) q^{84} +(-0.140670 + 0.176394i) q^{85} +(8.81952 + 8.18332i) q^{86} +(9.73109 + 1.46673i) q^{87} +(0.386703 + 0.263650i) q^{88} +(-13.9325 + 2.09998i) q^{89} +(0.599702 + 0.288801i) q^{90} +(-3.53695 - 2.93786i) q^{91} +(-3.59625 + 1.73186i) q^{92} +(-4.82784 + 3.29156i) q^{93} +(-1.19992 + 1.11337i) q^{94} +(-0.0812986 - 1.08486i) q^{95} +(0.365341 + 0.930874i) q^{96} -0.540212 q^{97} +(-2.29561 - 6.61288i) q^{98} +0.468029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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