LMFDB - Embedded newform 110.2.g.c.71.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(31,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	110.71
Dual form			110.2.g.c.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.33240 - 1.69459i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.890899 + 2.74191i) q^{6} +(-3.17926 + 2.30987i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.64142 + 5.05178i) q^{9} -1.00000 q^{10} +(-1.42705 - 2.99391i) q^{11} +2.88301 q^{12} +(-1.80113 - 5.54330i) q^{13} +(3.17926 + 2.30987i) q^{14} +(-2.33240 + 1.69459i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.332405 - 1.02304i) q^{17} +(4.29730 - 3.12217i) q^{18} +(-1.22713 - 0.891565i) q^{19} +(0.309017 + 0.951057i) q^{20} +11.3296 q^{21} +(-2.40640 + 2.28238i) q^{22} +5.07230 q^{23} +(-0.890899 - 2.74191i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.71542 + 3.42595i) q^{26} +(2.05954 - 6.33861i) q^{27} +(1.21437 - 3.73745i) q^{28} +(-0.306281 + 0.222526i) q^{29} +(2.33240 + 1.69459i) q^{30} +(-2.02891 - 6.24434i) q^{31} -1.00000 q^{32} +(-1.74500 + 9.40129i) q^{33} -1.07569 q^{34} +(1.21437 + 3.73745i) q^{35} +(-4.29730 - 3.12217i) q^{36} +(0.832405 - 0.604778i) q^{37} +(-0.468724 + 1.44258i) q^{38} +(-5.19267 + 15.9814i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-3.19992 - 2.32488i) q^{41} +(-3.50105 - 10.7751i) q^{42} -0.446609 q^{43} +(2.91429 + 1.58333i) q^{44} +5.31175 q^{45} +(-1.56743 - 4.82405i) q^{46} +(6.14416 + 4.46399i) q^{47} +(-2.33240 + 1.69459i) q^{48} +(2.60910 - 8.02999i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-2.50893 + 1.82285i) q^{51} +(4.71542 + 3.42595i) q^{52} +(1.93362 + 5.95106i) q^{53} -6.66481 q^{54} +(-3.28837 + 0.432036i) q^{55} -3.92979 q^{56} +(1.35134 + 4.15898i) q^{57} +(0.306281 + 0.222526i) q^{58} +(8.89194 - 6.46038i) q^{59} +(0.890899 - 2.74191i) q^{60} +(-3.10121 + 9.54455i) q^{61} +(-5.31175 + 3.85921i) q^{62} +(-16.8875 - 12.2695i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.82857 q^{65} +(9.48039 - 1.24556i) q^{66} -5.98422 q^{67} +(0.332405 + 1.02304i) q^{68} +(-11.8307 - 8.59548i) q^{69} +(3.17926 - 2.30987i) q^{70} +(1.55548 - 4.78728i) q^{71} +(-1.64142 + 5.05178i) q^{72} +(-2.86236 + 2.07963i) q^{73} +(-0.832405 - 0.604778i) q^{74} +(0.890899 + 2.74191i) q^{75} +1.51682 q^{76} +(11.4525 + 6.22214i) q^{77} +16.8038 q^{78} +(0.218201 + 0.671554i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-2.65314 + 1.92762i) q^{81} +(-1.22226 + 3.76173i) q^{82} +(3.62801 - 11.1659i) q^{83} +(-9.16586 + 6.65938i) q^{84} +(-0.870248 - 0.632272i) q^{85} +(0.138010 + 0.424750i) q^{86} +1.09146 q^{87} +(0.605270 - 3.26093i) q^{88} +0.0446858 q^{89} +(-1.64142 - 5.05178i) q^{90} +(18.5306 + 13.4633i) q^{91} +(-4.10358 + 2.98142i) q^{92} +(-5.84937 + 18.0025i) q^{93} +(2.34686 - 7.22289i) q^{94} +(-1.22713 + 0.891565i) q^{95} +(2.33240 + 1.69459i) q^{96} +(-5.05466 - 15.5567i) q^{97} -8.44323 q^{98} +(12.7822 - 12.1234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - q^{6} - q^{7} + 2 q^{8} - 6 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + q^{13} + q^{14} - 4 q^{15} - 2 q^{16} - 12 q^{17} + q^{18} - 7 q^{19} - 2 q^{20} + 32 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - q^6 - q^7 + 2 * q^8 - 6 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + q^13 + q^14 - 4 * q^15 - 2 * q^16 - 12 * q^17 + q^18 - 7 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 26 * q^23 - q^24 - 2 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 22 * q^29 + 4 * q^30 - 26 * q^31 - 8 * q^32 + 19 * q^33 + 2 * q^34 + 4 * q^35 - q^36 - 8 * q^37 - 3 * q^38 - 48 * q^39 + 2 * q^40 - 15 * q^41 - 2 * q^42 + 38 * q^43 + 7 * q^44 + 14 * q^45 - 6 * q^46 + 6 * q^47 - 4 * q^48 + 27 * q^49 + 2 * q^50 - 5 * q^51 + 6 * q^52 - 4 * q^53 - 24 * q^54 - 8 * q^55 + 6 * q^56 + 47 * q^57 + 22 * q^58 + 39 * q^59 + q^60 - 20 * q^61 - 14 * q^62 - 57 * q^63 - 2 * q^64 - 14 * q^65 + 36 * q^66 - 26 * q^67 - 12 * q^68 - 10 * q^69 + q^70 + 2 * q^71 + 6 * q^72 + 8 * q^73 + 8 * q^74 + q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 + 14 * q^79 - 2 * q^80 - 31 * q^81 - 15 * q^82 - 21 * q^83 - 18 * q^84 + 13 * q^85 + 17 * q^86 + 20 * q^87 - 7 * q^88 + 32 * q^89 + 6 * q^90 + 53 * q^91 - 19 * q^92 - 38 * q^93 + 9 * q^94 - 7 * q^95 + 4 * q^96 - 31 * q^97 - 22 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−2.33240	−	1.69459i	−1.34661	−	0.978373i	−0.999173	−	0.0406714i	$-0.987050\pi$
$3$	−2.33240	−	1.69459i	−1.34661	−	0.978373i	−0.347442	−	0.937701i	$-0.612950\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	−0.890899	+	2.74191i	−0.363708	+	1.11938i
$7$	−3.17926	+	2.30987i	−1.20165	+	0.873049i	−0.994446	−	0.105249i	$-0.966436\pi$
$7$	−3.17926	+	2.30987i	−1.20165	+	0.873049i	−0.207203	+	0.978298i	$0.566436\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.64142	+	5.05178i	0.547141	+	1.68393i
$10$	−1.00000			−0.316228
$11$	−1.42705	−	2.99391i	−0.430272	−	0.902699i
$11$	−1.42705	−	2.99391i	−0.430272	−	0.902699i
$12$	2.88301			0.832254
$13$	−1.80113	−	5.54330i	−0.499543	−	1.53744i	−0.809755	−	0.586768i	$-0.800400\pi$
$13$	−1.80113	−	5.54330i	−0.499543	−	1.53744i	0.310212	−	0.950668i	$-0.399600\pi$
$14$	3.17926	+	2.30987i	0.849694	+	0.617339i
$15$	−2.33240	+	1.69459i	−0.602224	+	0.437542i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.332405	−	1.02304i	0.0806201	−	0.248123i	−0.902620	−	0.430438i	$-0.858359\pi$
$17$	0.332405	−	1.02304i	0.0806201	−	0.248123i	0.983240	+	0.182315i	$0.0583591\pi$
$18$	4.29730	−	3.12217i	1.01288	−	0.735903i
$19$	−1.22713	−	0.891565i	−0.281524	−	0.204539i	0.438058	−	0.898947i	$-0.355666\pi$
$19$	−1.22713	−	0.891565i	−0.281524	−	0.204539i	−0.719582	+	0.694408i	$0.755666\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	11.3296			2.47233
$22$	−2.40640	+	2.28238i	−0.513046	+	0.486604i
$23$	5.07230			1.05765			0.528824	−	0.848731i	$-0.322633\pi$
$23$	5.07230			1.05765			0.528824	+	0.848731i	$0.322633\pi$
$24$	−0.890899	−	2.74191i	−0.181854	−	0.559689i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.71542	+	3.42595i	−0.924769	+	0.671884i
$27$	2.05954	−	6.33861i	0.396359	−	1.21987i
$28$	1.21437	−	3.73745i	0.229495	−	0.706312i
$29$	−0.306281	+	0.222526i	−0.0568749	+	0.0413221i	−0.615859	−	0.787856i	$-0.711191\pi$
$29$	−0.306281	+	0.222526i	−0.0568749	+	0.0413221i	0.558985	+	0.829178i	$0.311191\pi$
$30$	2.33240	+	1.69459i	0.425837	+	0.309389i
$31$	−2.02891	−	6.24434i	−0.364403	−	1.12152i	−0.950354	−	0.311170i	$-0.899279\pi$
$31$	−2.02891	−	6.24434i	−0.364403	−	1.12152i	0.585951	−	0.810346i	$-0.300721\pi$
$32$	−1.00000			−0.176777
$33$	−1.74500	+	9.40129i	−0.303766	+	1.63655i
$34$	−1.07569			−0.184478
$35$	1.21437	+	3.73745i	0.205266	+	0.631744i
$36$	−4.29730	−	3.12217i	−0.716216	−	0.520362i
$37$	0.832405	−	0.604778i	0.136847	−	0.0994248i	−0.517256	−	0.855831i	$-0.673046\pi$
$37$	0.832405	−	0.604778i	0.136847	−	0.0994248i	0.654103	+	0.756406i	$0.273046\pi$
$38$	−0.468724	+	1.44258i	−0.0760370	+	0.234018i
$39$	−5.19267	+	15.9814i	−0.831493	+	2.55907i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−3.19992	−	2.32488i	−0.499743	−	0.363085i	0.309176	−	0.951005i	$-0.399947\pi$
$41$	−3.19992	−	2.32488i	−0.499743	−	0.363085i	−0.808919	+	0.587920i	$0.799947\pi$
$42$	−3.50105	−	10.7751i	−0.540223	−	1.66264i
$43$	−0.446609			−0.0681072			−0.0340536	−	0.999420i	$-0.510842\pi$
$43$	−0.446609			−0.0681072			−0.0340536	+	0.999420i	$0.510842\pi$
$44$	2.91429	+	1.58333i	0.439345	+	0.238696i
$45$	5.31175			0.791829
$46$	−1.56743	−	4.82405i	−0.231105	−	0.711267i
$47$	6.14416	+	4.46399i	0.896218	+	0.651140i	0.937492	−	0.348008i	$-0.113142\pi$
$47$	6.14416	+	4.46399i	0.896218	+	0.651140i	−0.0412741	+	0.999148i	$0.513142\pi$
$48$	−2.33240	+	1.69459i	−0.336654	+	0.244593i
$49$	2.60910	−	8.02999i	0.372729	−	1.14714i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−2.50893	+	1.82285i	−0.351321	+	0.255250i
$52$	4.71542	+	3.42595i	0.653911	+	0.475094i
$53$	1.93362	+	5.95106i	0.265603	+	0.817441i	0.991554	+	0.129695i	$0.0413998\pi$
$53$	1.93362	+	5.95106i	0.265603	+	0.817441i	−0.725951	+	0.687746i	$0.758600\pi$
$54$	−6.66481			−0.906966
$55$	−3.28837	+	0.432036i	−0.443403	+	0.0582557i
$56$	−3.92979			−0.525140
$57$	1.35134	+	4.15898i	0.178989	+	0.550871i
$58$	0.306281	+	0.222526i	0.0402166	+	0.0292191i
$59$	8.89194	−	6.46038i	1.15763	−	0.841069i	0.168156	−	0.985760i	$-0.446219\pi$
$59$	8.89194	−	6.46038i	1.15763	−	0.841069i	0.989477	+	0.144691i	$0.0462189\pi$
$60$	0.890899	−	2.74191i	0.115015	−	0.353979i
$61$	−3.10121	+	9.54455i	−0.397070	+	1.22205i	0.530269	+	0.847830i	$0.322091\pi$
$61$	−3.10121	+	9.54455i	−0.397070	+	1.22205i	−0.927338	+	0.374225i	$0.877909\pi$
$62$	−5.31175	+	3.85921i	−0.674593	+	0.490121i
$63$	−16.8875	−	12.2695i	−2.12762	−	1.54581i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−5.82857			−0.722946
$66$	9.48039	−	1.24556i	1.16696	−	0.153318i
$67$	−5.98422			−0.731089			−0.365545	−	0.930794i	$-0.619117\pi$
$67$	−5.98422			−0.731089			−0.365545	+	0.930794i	$0.619117\pi$
$68$	0.332405	+	1.02304i	0.0403100	+	0.124062i
$69$	−11.8307	−	8.59548i	−1.42424	−	1.03477i
$70$	3.17926	−	2.30987i	0.379995	−	0.276082i
$71$	1.55548	−	4.78728i	0.184602	−	0.568146i	−0.815340	−	0.578983i	$-0.803450\pi$
$71$	1.55548	−	4.78728i	0.184602	−	0.568146i	0.999941	+	0.0108375i	$0.00344975\pi$
$72$	−1.64142	+	5.05178i	−0.193443	+	0.595358i
$73$	−2.86236	+	2.07963i	−0.335014	+	0.243402i	−0.742555	−	0.669785i	$-0.766386\pi$
$73$	−2.86236	+	2.07963i	−0.335014	+	0.243402i	0.407541	+	0.913187i	$0.366386\pi$
$74$	−0.832405	−	0.604778i	−0.0967651	−	0.0703040i
$75$	0.890899	+	2.74191i	0.102872	+	0.316608i
$76$	1.51682			0.173991
$77$	11.4525	+	6.22214i	1.30514	+	0.709079i
$78$	16.8038			1.90266
$79$	0.218201	+	0.671554i	0.0245495	+	0.0755557i	0.962581	−	0.270995i	$-0.0873528\pi$
$79$	0.218201	+	0.671554i	0.0245495	+	0.0755557i	−0.938031	+	0.346551i	$0.887353\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	−2.65314	+	1.92762i	−0.294793	+	0.214180i
$82$	−1.22226	+	3.76173i	−0.134976	+	0.415413i
$83$	3.62801	−	11.1659i	0.398226	−	1.22561i	−0.528194	−	0.849123i	$-0.677131\pi$
$83$	3.62801	−	11.1659i	0.398226	−	1.22561i	0.926420	−	0.376490i	$-0.122869\pi$
$84$	−9.16586	+	6.65938i	−1.00008	+	0.726598i
$85$	−0.870248	−	0.632272i	−0.0943916	−	0.0685795i
$86$	0.138010	+	0.424750i	0.0148820	+	0.0458020i
$87$	1.09146			0.117017
$88$	0.605270	−	3.26093i	0.0645220	−	0.347616i
$89$	0.0446858			0.00473668			0.00236834	−	0.999997i	$-0.499246\pi$
$89$	0.0446858			0.00473668			0.00236834	+	0.999997i	$0.499246\pi$
$90$	−1.64142	−	5.05178i	−0.173021	−	0.532504i
$91$	18.5306	+	13.4633i	1.94253	+	1.41133i
$92$	−4.10358	+	2.98142i	−0.427828	+	0.310835i
$93$	−5.84937	+	18.0025i	−0.606551	+	1.86677i
$94$	2.34686	−	7.22289i	0.242060	−	0.744984i
$95$	−1.22713	+	0.891565i	−0.125901	+	0.0914727i
$96$	2.33240	+	1.69459i	0.238050	+	0.172954i
$97$	−5.05466	−	15.5567i	−0.513223	−	1.57954i	−0.786491	−	0.617601i	$-0.788105\pi$
$97$	−5.05466	−	15.5567i	−0.513223	−	1.57954i	0.273268	−	0.961938i	$-0.411895\pi$
$98$	−8.44323			−0.852895
$99$	12.7822	−	12.1234i	1.28466	−	1.21845i
$100$	1.00000			0.100000
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	0.988401	−	0.151865i	$-0.0485280\pi$
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	−0.888897	+	0.458106i	$0.848528\pi$
$102$	2.50893	+	1.82285i	0.248421	+	0.180489i
$103$	9.26324	−	6.73014i	0.912734	−	0.663140i	−0.0289709	−	0.999580i	$-0.509223\pi$
$103$	9.26324	−	6.73014i	0.912734	−	0.663140i	0.941705	+	0.336440i	$0.109223\pi$
$104$	1.80113	−	5.54330i	0.176615	−	0.543566i
$105$	3.50105	−	10.7751i	0.341667	−	1.05154i
$106$	5.06228	−	3.67796i	0.491692	−	0.357235i
$107$	−5.83345	−	4.23825i	−0.563941	−	0.409727i	0.268958	−	0.963152i	$-0.413321\pi$
$107$	−5.83345	−	4.23825i	−0.563941	−	0.409727i	−0.832899	+	0.553425i	$0.813321\pi$
$108$	2.05954	+	6.33861i	0.198179	+	0.609933i
$109$	1.56360			0.149766			0.0748828	−	0.997192i	$-0.476142\pi$
$109$	1.56360			0.149766			0.0748828	+	0.997192i	$0.476142\pi$
$110$	1.42705	+	2.99391i	0.136064	+	0.285459i
$111$	−2.96636			−0.281554
$112$	1.21437	+	3.73745i	0.114747	+	0.353156i
$113$	−5.05954	−	3.67597i	−0.475961	−	0.345806i	0.323799	−	0.946126i	$-0.395040\pi$
$113$	−5.05954	−	3.67597i	−0.475961	−	0.345806i	−0.799760	+	0.600320i	$0.795040\pi$
$114$	3.53784	−	2.57039i	0.331349	−	0.240739i
$115$	1.56743	−	4.82405i	0.146163	−	0.449845i
$116$	0.116989	−	0.360055i	0.0108621	−	0.0334302i
$117$	25.0471	−	18.1978i	2.31561	−	1.68239i
$118$	−8.89194	−	6.46038i	−0.818570	−	0.594726i
$119$	1.30628	+	4.02032i	0.119747	+	0.368542i
$120$	−2.88301			−0.263182
$121$	−6.92705	+	8.54494i	−0.629732	+	0.776813i
$122$	10.0357			0.908593
$123$	3.52379	+	10.8451i	0.317729	+	0.977870i
$124$	5.31175	+	3.85921i	0.477010	+	0.346568i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−6.45044	+	19.8524i	−0.574651	+	1.76859i
$127$	−5.86577	+	18.0530i	−0.520503	+	1.60194i	0.252538	+	0.967587i	$0.418735\pi$
$127$	−5.86577	+	18.0530i	−0.520503	+	1.60194i	−0.773041	+	0.634357i	$0.781265\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	1.04167	+	0.756820i	0.0917142	+	0.0666342i
$130$	1.80113	+	5.54330i	0.157969	+	0.486180i
$131$	−6.34749			−0.554582			−0.277291	−	0.960786i	$-0.589437\pi$
$131$	−6.34749			−0.554582			−0.277291	+	0.960786i	$0.589437\pi$
$132$	−4.11420	−	8.63149i	−0.358095	−	0.751275i
$133$	5.96079			0.516866
$134$	1.84923	+	5.69133i	0.159749	+	0.491656i
$135$	−5.39194	−	3.91748i	−0.464065	−	0.337163i
$136$	0.870248	−	0.632272i	0.0746231	−	0.0542169i
$137$	−1.44767	+	4.45548i	−0.123683	+	0.380657i	−0.993659	−	0.112437i	$-0.964134\pi$
$137$	−1.44767	+	4.45548i	−0.123683	+	0.380657i	0.869976	+	0.493094i	$0.164134\pi$
$138$	−4.51891	+	13.9078i	−0.384675	+	1.18391i
$139$	−6.79392	+	4.93607i	−0.576252	+	0.418672i	−0.837371	−	0.546635i	$-0.815909\pi$
$139$	−6.79392	+	4.93607i	−0.576252	+	0.418672i	0.261119	+	0.965307i	$0.415909\pi$
$140$	−3.17926	−	2.30987i	−0.268697	−	0.195220i
$141$	−6.76602	−	20.8237i	−0.569802	−	1.75367i
$142$	−5.03364			−0.422414
$143$	−14.0259	+	13.3030i	−1.17290	+	1.11245i
$144$	5.31175			0.442646
$145$	0.116989	+	0.360055i	0.00971540	+	0.0299009i
$146$	2.86236	+	2.07963i	0.236891	+	0.172111i
$147$	−19.6930	+	14.3078i	−1.62425	+	1.18009i
$148$	−0.317950	+	0.978551i	−0.0261354	+	0.0804364i
$149$	7.13695	−	21.9653i	0.584681	−	1.79946i	−0.0158647	−	0.999874i	$-0.505050\pi$
$149$	7.13695	−	21.9653i	0.584681	−	1.79946i	0.600546	−	0.799590i	$-0.294950\pi$
$150$	2.33240	−	1.69459i	0.190440	−	0.138363i
$151$	4.67028	+	3.39316i	0.380062	+	0.276131i	0.761371	−	0.648316i	$-0.224527\pi$
$151$	4.67028	+	3.39316i	0.380062	+	0.276131i	−0.381309	+	0.924448i	$0.624527\pi$
$152$	−0.468724	−	1.44258i	−0.0380185	−	0.117009i
$153$	5.71377			0.461931
$154$	2.37858	−	12.8148i	0.191672	−	1.03264i
$155$	−6.56569			−0.527369
$156$	−5.19267	−	15.9814i	−0.415747	−	1.27954i
$157$	−8.73047	−	6.34306i	−0.696767	−	0.506231i	0.182111	−	0.983278i	$-0.441707\pi$
$157$	−8.73047	−	6.34306i	−0.696767	−	0.506231i	−0.878878	+	0.477047i	$0.841707\pi$
$158$	0.571258	−	0.415043i	0.0454468	−	0.0330191i
$159$	5.57464	−	17.1570i	0.442098	−	1.36064i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	−16.1262	+	11.7164i	−1.27092	+	0.923379i
$162$	2.65314	+	1.92762i	0.208450	+	0.151448i
$163$	5.14311	+	15.8289i	0.402840	+	1.23981i	0.922686	+	0.385553i	$0.125989\pi$
$163$	5.14311	+	15.8289i	0.402840	+	1.23981i	−0.519846	+	0.854260i	$0.674011\pi$
$164$	3.95531			0.308858
$165$	8.40192	+	4.56475i	0.654089	+	0.355366i
$166$	−11.7405			−0.911239
$167$	−2.67439	−	8.23092i	−0.206950	−	0.636928i	−0.999628	−	0.0272864i	$-0.991313\pi$
$167$	−2.67439	−	8.23092i	−0.206950	−	0.636928i	0.792677	−	0.609642i	$-0.208687\pi$
$168$	9.16586	+	6.65938i	0.707161	+	0.513783i
$169$	−16.9669	+	12.3272i	−1.30515	+	0.948246i
$170$	−0.332405	+	1.02304i	−0.0254943	+	0.0784634i
$171$	2.48974	−	7.66265i	0.190396	−	0.585977i
$172$	0.361314	−	0.262510i	0.0275499	−	0.0200162i
$173$	10.3196	+	7.49762i	0.784584	+	0.570034i	0.906351	−	0.422525i	$-0.138856\pi$
$173$	10.3196	+	7.49762i	0.784584	+	0.570034i	−0.121767	+	0.992559i	$0.538856\pi$
$174$	−0.337280	−	1.03804i	−0.0255691	−	0.0786937i
$175$	3.92979			0.297064
$176$	−3.28837	+	0.432036i	−0.247870	+	0.0325659i
$177$	−31.6873			−2.38176
$178$	−0.0138087	−	0.0424987i	−0.00103500	−	0.00318541i
$179$	−15.2533	−	11.0822i	−1.14008	−	0.828320i	−0.152953	−	0.988233i	$-0.548878\pi$
$179$	−15.2533	−	11.0822i	−1.14008	−	0.828320i	−0.987131	+	0.159914i	$0.948878\pi$
$180$	−4.29730	+	3.12217i	−0.320302	+	0.232713i
$181$	7.34066	−	22.5922i	0.545627	−	1.67927i	−0.173867	−	0.984769i	$-0.555626\pi$
$181$	7.34066	−	22.5922i	0.545627	−	1.67927i	0.719494	−	0.694498i	$-0.244374\pi$
$182$	7.07805	−	21.7840i	0.524660	−	1.61474i
$183$	23.4074	−	17.0065i	1.73032	−	1.25715i
$184$	4.10358	+	2.98142i	0.302520	+	0.219794i
$185$	−0.317950	−	0.978551i	−0.0233762	−	0.0719445i
$186$	18.9290			1.38794
$187$	−3.53725	+	0.464734i	−0.258669	+	0.0339847i
$188$	−7.59460			−0.553893
$189$	8.09355	+	24.9094i	0.588719	+	1.81189i
$190$	1.22713	+	0.891565i	0.0890257	+	0.0646810i
$191$	5.97109	−	4.33825i	0.432053	−	0.313905i	−0.350416	−	0.936594i	$-0.613960\pi$
$191$	5.97109	−	4.33825i	0.432053	−	0.313905i	0.782469	+	0.622689i	$0.213960\pi$
$192$	0.890899	−	2.74191i	0.0642951	−	0.197880i
$193$	2.14590	−	6.60440i	0.154465	−	0.475395i	−0.843641	−	0.536907i	$-0.819592\pi$
$193$	2.14590	−	6.60440i	0.154465	−	0.475395i	0.998106	+	0.0615126i	$0.0195924\pi$
$194$	−13.2333	+	9.61454i	−0.950094	+	0.690284i
$195$	13.5946	+	9.87705i	0.973529	+	0.707310i
$196$	2.60910	+	8.02999i	0.186364	+	0.573570i
$197$	2.58485			0.184163			0.0920813	−	0.995751i	$-0.470648\pi$
$197$	2.58485			0.184163			0.0920813	+	0.995751i	$0.470648\pi$
$198$	−15.4800	−	8.41025i	−1.10011	−	0.597690i
$199$	−4.44587			−0.315159			−0.157580	−	0.987506i	$-0.550369\pi$
$199$	−4.44587			−0.315159			−0.157580	+	0.987506i	$0.550369\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	13.9576	+	10.1408i	0.984495	+	0.715278i
$202$	2.61803	−	1.90211i	0.184204	−	0.133832i
$203$	0.459741	−	1.41494i	0.0322675	−	0.0993092i
$204$	0.958327	−	2.94943i	0.0670963	−	0.206501i
$205$	−3.19992	+	2.32488i	−0.223492	+	0.162376i
$206$	−9.26324	−	6.73014i	−0.645400	−	0.468911i
$207$	8.32579	+	25.6241i	0.578682	+	1.78100i
$208$	−5.82857			−0.404139
$209$	−0.918087	+	4.94625i	−0.0635054	+	0.342139i
$210$	−11.3296			−0.781818
$211$	3.39194	+	10.4393i	0.233511	+	0.718673i	0.997315	+	0.0732254i	$0.0233292\pi$
$211$	3.39194	+	10.4393i	0.233511	+	0.718673i	−0.763804	+	0.645448i	$0.776671\pi$
$212$	−5.06228	−	3.67796i	−0.347679	−	0.252603i
$213$	−11.7405	+	8.52997i	−0.804445	+	0.584464i
$214$	−2.22818	+	6.85763i	−0.152315	+	0.468778i
$215$	−0.138010	+	0.424750i	−0.00941219	+	0.0289677i
$216$	5.39194	−	3.91748i	0.366875	−	0.266551i
$217$	20.8741	+	15.1659i	1.41702	+	1.02953i
$218$	−0.483178	−	1.48707i	−0.0327250	−	0.100717i
$219$	10.2003			0.689272
$220$	2.40640	−	2.28238i	0.162239	−	0.153878i
$221$	−6.26971			−0.421746
$222$	0.916655	+	2.82117i	0.0615218	+	0.189345i
$223$	21.6246	+	15.7112i	1.44809	+	1.05210i	0.986273	+	0.165123i	$0.0528020\pi$
$223$	21.6246	+	15.7112i	1.44809	+	1.05210i	0.461816	+	0.886976i	$0.347198\pi$
$224$	3.17926	−	2.30987i	0.212424	−	0.154335i
$225$	1.64142	−	5.05178i	0.109428	−	0.336785i
$226$	−1.93257	+	5.94785i	−0.128553	+	0.395645i
$227$	14.4359	−	10.4883i	0.958147	−	0.696134i	0.00542711	−	0.999985i	$-0.498272\pi$
$227$	14.4359	−	10.4883i	0.958147	−	0.696134i	0.952720	+	0.303851i	$0.0982725\pi$
$228$	−3.53784	−	2.57039i	−0.234299	−	0.170228i
$229$	4.83833	+	14.8908i	0.319726	+	0.984014i	0.973765	+	0.227554i	$0.0730728\pi$
$229$	4.83833	+	14.8908i	0.319726	+	0.984014i	−0.654040	+	0.756460i	$0.726927\pi$
$230$	−5.07230			−0.334458
$231$	−16.1679	−	33.9199i	−1.06377	−	2.23177i
$232$	−0.378584			−0.0248553
$233$	−5.16692	−	15.9021i	−0.338496	−	1.04178i	−0.964974	−	0.262345i	$-0.915504\pi$
$233$	−5.16692	−	15.9021i	−0.338496	−	1.04178i	0.626478	−	0.779439i	$-0.284496\pi$
$234$	−25.0471	−	18.1978i	−1.63738	−	1.18963i
$235$	6.14416	−	4.46399i	0.400801	−	0.291199i
$236$	−3.39642	+	10.4531i	−0.221088	+	0.680439i
$237$	0.629076	−	1.93610i	0.0408629	−	0.125763i
$238$	3.41989	−	2.48469i	0.221678	−	0.161059i
$239$	15.4900	+	11.2541i	1.00196	+	0.727970i	0.962509	−	0.271251i	$-0.0874374\pi$
$239$	15.4900	+	11.2541i	1.00196	+	0.727970i	0.0394564	+	0.999221i	$0.487437\pi$
$240$	0.890899	+	2.74191i	0.0575073	+	0.176989i
$241$	−6.59386			−0.424748			−0.212374	−	0.977188i	$-0.568119\pi$
$241$	−6.59386			−0.424748			−0.212374	+	0.977188i	$0.568119\pi$
$242$	10.2673	+	3.94749i	0.660007	+	0.253754i
$243$	−10.5397			−0.676122
$244$	−3.10121	−	9.54455i	−0.198535	−	0.611027i
$245$	−6.83071	−	4.96280i	−0.436398	−	0.317062i
$246$	9.22539	−	6.70264i	0.588190	−	0.427345i
$247$	−2.73199	+	8.40820i	−0.173832	+	0.535001i
$248$	2.02891	−	6.24434i	0.128836	−	0.396516i
$249$	−27.3836	+	19.8953i	−1.73536	+	1.26082i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	6.30583	+	19.4074i	0.398021	+	1.22498i	0.926584	+	0.376088i	$0.122731\pi$
$251$	6.30583	+	19.4074i	0.398021	+	1.22498i	−0.528563	+	0.848894i	$0.677269\pi$
$252$	20.8741			1.31494
$253$	−7.23844	−	15.1860i	−0.455077	−	0.954738i
$254$	18.9820			1.19104
$255$	0.958327	+	2.94943i	0.0600128	+	0.184700i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	21.0516	−	15.2948i	1.31316	−	0.954066i	0.313169	−	0.949697i	$-0.398609\pi$
$257$	21.0516	−	15.2948i	1.31316	−	0.954066i	0.999990	−	0.00436917i	$-0.00139075\pi$
$258$	0.397884	−	1.22456i	0.0247711	−	0.0762378i
$259$	−1.24948	+	3.84550i	−0.0776388	+	0.238948i
$260$	4.71542	−	3.42595i	0.292438	−	0.212468i
$261$	−1.62689	−	1.18200i	−0.100702	−	0.0731642i
$262$	1.96148	+	6.03682i	0.121181	+	0.372956i
$263$	21.5368			1.32801			0.664007	−	0.747726i	$-0.268854\pi$
$263$	21.5368			1.32801			0.664007	+	0.747726i	$0.268854\pi$
$264$	−6.93768	+	6.58012i	−0.426984	+	0.404978i
$265$	6.25732			0.384384
$266$	−1.84198	−	5.66904i	−0.112939	−	0.347591i
$267$	−0.104225	−	0.0757241i	−0.00637849	−	0.00463424i
$268$	4.84134	−	3.51744i	0.295732	−	0.214862i
$269$	−5.16112	+	15.8843i	−0.314679	+	0.968483i	0.661207	+	0.750203i	$0.270044\pi$
$269$	−5.16112	+	15.8843i	−0.314679	+	0.968483i	−0.975886	+	0.218279i	$0.929956\pi$
$270$	−2.05954	+	6.33861i	−0.125340	+	0.385756i
$271$	10.0233	−	7.28238i	0.608874	−	0.442373i	−0.240143	−	0.970737i	$-0.577194\pi$
$271$	10.0233	−	7.28238i	0.608874	−	0.442373i	0.849018	+	0.528364i	$0.177194\pi$
$272$	−0.870248	−	0.632272i	−0.0527665	−	0.0383371i
$273$	−20.4061	−	62.8035i	−1.23503	−	3.80104i
$274$	4.68477			0.283017
$275$	−0.605270	+	3.26093i	−0.0364992	+	0.196641i
$276$	14.6235			0.880232
$277$	−6.63207	−	20.4114i	−0.398483	−	1.22640i	−0.926216	−	0.376993i	$-0.876958\pi$
$277$	−6.63207	−	20.4114i	−0.398483	−	1.22640i	0.527734	−	0.849410i	$-0.323042\pi$
$278$	6.79392	+	4.93607i	0.407472	+	0.296046i
$279$	28.2147	−	20.4992i	1.68917	−	1.22725i
$280$	−1.21437	+	3.73745i	−0.0725725	+	0.223355i
$281$	0.0891435	−	0.274356i	0.00531786	−	0.0163667i	−0.948362	−	0.317189i	$-0.897261\pi$
$281$	0.0891435	−	0.274356i	0.00531786	−	0.0163667i	0.953680	+	0.300822i	$0.0972611\pi$
$282$	−17.7137	+	12.8697i	−1.05483	+	0.766382i
$283$	−21.8829	−	15.8989i	−1.30080	−	0.945090i	−0.300841	−	0.953674i	$-0.597267\pi$
$283$	−21.8829	−	15.8989i	−1.30080	−	0.945090i	−0.999963	+	0.00858475i	$0.997267\pi$
$284$	1.55548	+	4.78728i	0.0923008	+	0.284073i
$285$	4.37301			0.259035
$286$	16.9861	+	9.22855i	1.00441	+	0.545695i
$287$	15.5435			0.917506
$288$	−1.64142	−	5.05178i	−0.0967217	−	0.297679i
$289$	12.8172	+	9.31222i	0.753952	+	0.547778i
$290$	0.306281	−	0.222526i	0.0179854	−	0.0130672i
$291$	−14.5727	+	44.8500i	−0.854264	+	2.62915i
$292$	1.09332	−	3.36491i	0.0639819	−	0.196916i
$293$	9.88747	−	7.18367i	0.577632	−	0.419674i	−0.260238	−	0.965545i	$-0.583801\pi$
$293$	9.88747	−	7.18367i	0.577632	−	0.419674i	0.837870	+	0.545870i	$0.183801\pi$
$294$	19.6930	+	14.3078i	1.14852	+	0.834449i
$295$	−3.39642	−	10.4531i	−0.197747	−	0.608603i
$296$	1.02891			0.0598041
$297$	−21.9163	+	2.87944i	−1.27171	+	0.167082i
$298$	−23.0956			−1.33789
$299$	−9.13587	−	28.1173i	−0.528341	−	1.62607i
$300$	−2.33240	−	1.69459i	−0.134661	−	0.0978373i
$301$	1.41989	−	1.03161i	0.0818410	−	0.0594609i
$302$	1.78389	−	5.49025i	0.102651	−	0.315928i
$303$	2.88301	−	8.87300i	0.165625	−	0.509740i
$304$	−1.22713	+	0.891565i	−0.0703810	+	0.0511348i
$305$	8.11908	+	5.89886i	0.464897	+	0.337768i
$306$	−1.76565	−	5.43412i	−0.100936	−	0.310648i
$307$	−28.6957			−1.63775			−0.818875	−	0.573971i	$-0.805402\pi$
$307$	−28.6957			−1.63775			−0.818875	+	0.573971i	$0.805402\pi$
$308$	−12.9226	+	1.69781i	−0.736332	+	0.0967416i
$309$	−33.0105			−1.87790
$310$	2.02891	+	6.24434i	0.115234	+	0.354655i
$311$	−21.6936	−	15.7613i	−1.23013	−	0.893744i	−0.233232	−	0.972421i	$-0.574930\pi$
$311$	−21.6936	−	15.7613i	−1.23013	−	0.893744i	−0.996900	+	0.0786775i	$0.974930\pi$
$312$	−13.5946	+	9.87705i	−0.769643	+	0.559178i
$313$	−7.92965	+	24.4049i	−0.448210	+	1.37945i	0.430715	+	0.902488i	$0.358262\pi$
$313$	−7.92965	+	24.4049i	−0.448210	+	1.37945i	−0.878925	+	0.476961i	$0.841738\pi$
$314$	−3.33474	+	10.2633i	−0.188190	+	0.579190i
$315$	−16.8875	+	12.2695i	−0.951501	+	0.691306i
$316$	−0.571258	−	0.415043i	−0.0321358	−	0.0233480i
$317$	4.45573	+	13.7133i	0.250259	+	0.770218i	0.994727	+	0.102559i	$0.0327032\pi$
$317$	4.45573	+	13.7133i	0.250259	+	0.770218i	−0.744468	+	0.667658i	$0.767297\pi$
$318$	−18.0399			−1.01163
$319$	1.10330	+	0.599423i	0.0617731	+	0.0335612i
$320$	1.00000			0.0559017
$321$	6.42387	+	19.7706i	0.358545	+	1.10349i
$322$	16.1262	+	11.7164i	0.898678	+	0.652928i
$323$	−1.32001	+	0.959044i	−0.0734473	+	0.0533626i
$324$	1.01341	−	3.11895i	0.0563005	−	0.173275i
$325$	−1.80113	+	5.54330i	−0.0999086	+	0.307487i
$326$	13.4648	−	9.78278i	0.745749	−	0.541818i
$327$	−3.64694	−	2.64966i	−0.201676	−	0.146526i
$328$	−1.22226	−	3.76173i	−0.0674880	−	0.207707i
$329$	−29.8451			−1.64542
$330$	1.74500	−	9.40129i	0.0960592	−	0.517524i
$331$	19.0365			1.04634			0.523171	−	0.852228i	$-0.324749\pi$
$331$	19.0365			1.04634			0.523171	+	0.852228i	$0.324749\pi$
$332$	3.62801	+	11.1659i	0.199113	+	0.612807i
$333$	4.42153	+	3.21243i	0.242298	+	0.176040i
$334$	−7.00164	+	5.08699i	−0.383113	+	0.278348i
$335$	−1.84923	+	5.69133i	−0.101034	+	0.310951i
$336$	3.50105	−	10.7751i	0.190998	−	0.587830i
$337$	2.45390	−	1.78286i	0.133672	−	0.0971187i	−0.518940	−	0.854811i	$-0.673673\pi$
$337$	2.45390	−	1.78286i	0.133672	−	0.0971187i	0.652612	+	0.757692i	$0.273673\pi$
$338$	16.9669	+	12.3272i	0.922880	+	0.670511i
$339$	5.57163	+	17.1477i	0.302609	+	0.931335i
$340$	1.07569			0.0583372
$341$	−15.7997	+	14.9854i	−0.855600	+	0.811503i
$342$	−8.05698			−0.435672
$343$	1.75261	+	5.39399i	0.0946322	+	0.291248i
$344$	−0.361314	−	0.262510i	−0.0194808	−	0.0141536i
$345$	−11.8307	+	8.59548i	−0.636942	+	0.462765i
$346$	3.94173	−	12.1314i	0.211909	−	0.652189i
$347$	−1.08056	+	3.32562i	−0.0580075	+	0.178529i	−0.975862	−	0.218388i	$-0.929920\pi$
$347$	−1.08056	+	3.32562i	−0.0580075	+	0.178529i	0.917854	+	0.396917i	$0.129920\pi$
$348$	−0.883011	+	0.641545i	−0.0473344	+	0.0343904i
$349$	13.7784	+	10.0106i	0.737542	+	0.535855i	0.891940	−	0.452153i	$-0.149344\pi$
$349$	13.7784	+	10.0106i	0.737542	+	0.535855i	−0.154399	+	0.988009i	$0.549344\pi$
$350$	−1.21437	−	3.73745i	−0.0649109	−	0.199775i
$351$	−38.8463			−2.07346
$352$	1.42705	+	2.99391i	0.0760621	+	0.159576i
$353$	17.3965			0.925920			0.462960	−	0.886379i	$-0.346787\pi$
$353$	17.3965			0.925920			0.462960	+	0.886379i	$0.346787\pi$
$354$	9.79192	+	30.1364i	0.520435	+	1.60173i
$355$	−4.07230	−	2.95870i	−0.216135	−	0.157032i
$356$	−0.0361516	+	0.0262656i	−0.00191603	+	0.00139208i
$357$	3.76602	−	11.5906i	0.199319	−	0.613441i
$358$	−5.82624	+	17.9313i	−0.307926	+	0.947700i
$359$	−0.789459	+	0.573576i	−0.0416661	+	0.0302722i	−0.608423	−	0.793613i	$-0.708198\pi$
$359$	−0.789459	+	0.573576i	−0.0416661	+	0.0302722i	0.566757	+	0.823885i	$0.308198\pi$
$360$	4.29730	+	3.12217i	0.226488	+	0.164553i
$361$	−5.16035	−	15.8819i	−0.271598	−	0.835891i
$362$	−23.7549			−1.24853
$363$	30.6369	−	8.19173i	1.60802	−	0.429955i
$364$	−22.9051			−1.20055
$365$	1.09332	+	3.36491i	0.0572272	+	0.176127i
$366$	−23.4074	−	17.0065i	−1.22352	−	0.888942i
$367$	28.1390	−	20.4442i	1.46885	−	1.06718i	0.487899	−	0.872900i	$-0.337763\pi$
$367$	28.1390	−	20.4442i	1.46885	−	1.06718i	0.980946	−	0.194279i	$-0.0622367\pi$
$368$	1.56743	−	4.82405i	0.0817078	−	0.251471i
$369$	6.49234	−	19.9814i	0.337978	−	1.04019i
$370$	−0.832405	+	0.604778i	−0.0432747	+	0.0314409i
$371$	−19.8937	−	14.4536i	−1.03283	−	0.750393i
$372$	−5.84937	−	18.0025i	−0.303276	−	0.933386i
$373$	29.2364			1.51380			0.756902	−	0.653528i	$-0.226712\pi$
$373$	29.2364			1.51380			0.756902	+	0.653528i	$0.226712\pi$
$374$	1.53506	+	3.22051i	0.0793759	+	0.166529i
$375$	2.88301			0.148878
$376$	2.34686	+	7.22289i	0.121030	+	0.372492i
$377$	1.78518	+	1.29701i	0.0919415	+	0.0667994i
$378$	21.1892	−	15.3949i	1.08985	−	0.791826i
$379$	3.90786	−	12.0272i	0.200733	−	0.617794i	−0.799128	−	0.601161i	$-0.794705\pi$
$379$	3.90786	−	12.0272i	0.200733	−	0.617794i	0.999862	−	0.0166333i	$-0.00529479\pi$
$380$	0.468724	−	1.44258i	0.0240450	−	0.0740030i
$381$	44.2738	−	32.1668i	2.26822	−	1.64795i
$382$	−5.97109	−	4.33825i	−0.305508	−	0.221964i
$383$	−0.468306	−	1.44130i	−0.0239293	−	0.0736468i	0.938379	−	0.345609i	$-0.112328\pi$
$383$	−0.468306	−	1.44130i	−0.0239293	−	0.0736468i	−0.962308	+	0.271962i	$0.912328\pi$
$384$	−2.88301			−0.147123
$385$	9.45664	−	8.96925i	0.481955	−	0.457116i
$386$	−6.94427			−0.353454
$387$	−0.733074	−	2.25617i	−0.0372642	−	0.114687i
$388$	13.2333	+	9.61454i	0.671818	+	0.488104i
$389$	−5.53897	+	4.02429i	−0.280837	+	0.204040i	−0.719282	−	0.694718i	$-0.755529\pi$
$389$	−5.53897	+	4.02429i	−0.280837	+	0.204040i	0.438446	+	0.898758i	$0.355529\pi$
$390$	5.19267	−	15.9814i	0.262941	−	0.809250i
$391$	1.68606	−	5.18916i	0.0852677	−	0.262427i
$392$	6.83071	−	4.96280i	0.345003	−	0.250659i
$393$	14.8049	+	10.7564i	0.746809	+	0.542588i
$394$	−0.798762	−	2.45834i	−0.0402410	−	0.123849i
$395$	0.706114			0.0355284
$396$	−3.21505	+	17.3212i	−0.161562	+	0.870425i
$397$	−4.56861			−0.229292			−0.114646	−	0.993406i	$-0.536573\pi$
$397$	−4.56861			−0.229292			−0.114646	+	0.993406i	$0.536573\pi$
$398$	1.37385	+	4.22827i	0.0688649	+	0.211944i
$399$	−13.9030	−	10.1011i	−0.696019	−	0.505687i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−0.155249	+	0.477808i	−0.00775278	+	0.0238606i	−0.954858	−	0.297062i	$-0.903993\pi$
$401$	−0.155249	+	0.477808i	−0.00775278	+	0.0238606i	0.947105	+	0.320923i	$0.103993\pi$
$402$	5.33134	−	16.4082i	0.265903	−	0.818366i
$403$	−30.9600	+	22.4937i	−1.54222	+	1.12049i
$404$	−2.61803	−	1.90211i	−0.130252	−	0.0946337i
$405$	1.01341	+	3.11895i	0.0503567	+	0.154982i
$406$	−1.48775			−0.0738360
$407$	−2.99854	−	1.62910i	−0.148632	−	0.0807515i
$408$	−3.10121			−0.153533
$409$	4.07979	+	12.5563i	0.201733	+	0.620870i	0.999832	+	0.0183432i	$0.00583915\pi$
$409$	4.07979	+	12.5563i	0.201733	+	0.620870i	−0.798099	+	0.602526i	$0.794161\pi$
$410$	3.19992	+	2.32488i	0.158033	+	0.114817i
$411$	10.9268	−	7.93877i	0.538978	−	0.391590i
$412$	−3.53824	+	10.8896i	−0.174317	+	0.536492i
$413$	−13.3472	+	41.0785i	−0.656773	+	2.02134i
$414$	21.7972	−	15.8366i	1.07127	−	0.778326i
$415$	−9.49826	−	6.90089i	−0.466251	−	0.338751i
$416$	1.80113	+	5.54330i	0.0883076	+	0.271783i
$417$	24.2108			1.18561
$418$	4.98786	−	0.655321i	0.243964	−	0.0320528i
$419$	12.6691			0.618925			0.309463	−	0.950912i	$-0.399851\pi$
$419$	12.6691			0.618925			0.309463	+	0.950912i	$0.399851\pi$
$420$	3.50105	+	10.7751i	0.170834	+	0.525771i
$421$	−15.4576	−	11.2306i	−0.753355	−	0.547344i	0.143510	−	0.989649i	$-0.454161\pi$
$421$	−15.4576	−	11.2306i	−0.753355	−	0.547344i	−0.896865	+	0.442304i	$0.854161\pi$
$422$	8.88023	−	6.45186i	0.432283	−	0.314072i
$423$	−12.4659	+	38.3662i	−0.606115	+	1.86543i
$424$	−1.93362	+	5.95106i	−0.0939048	+	0.289009i
$425$	−0.870248	+	0.632272i	−0.0422132	+	0.0306697i
$426$	11.7405	+	8.52997i	0.568829	+	0.413278i
$427$	−12.1871	−	37.5080i	−0.589775	−	1.81514i
$428$	7.21054			0.348535
$429$	55.2572	−	7.25986i	2.66784	−	0.350509i
$430$	0.446609			0.0215374
$431$	4.12720	+	12.7022i	0.198800	+	0.611844i	0.999911	+	0.0133279i	$0.00424254\pi$
$431$	4.12720	+	12.7022i	0.198800	+	0.611844i	−0.801111	+	0.598516i	$0.795757\pi$
$432$	−5.39194	−	3.91748i	−0.259420	−	0.188480i
$433$	6.96927	−	5.06347i	0.334922	−	0.243335i	−0.407594	−	0.913163i	$-0.633632\pi$
$433$	6.96927	−	5.06347i	0.334922	−	0.243335i	0.742516	+	0.669828i	$0.233632\pi$
$434$	7.97318	−	24.5389i	0.382725	−	1.17791i
$435$	0.337280	−	1.03804i	0.0161713	−	0.0497703i
$436$	−1.26498	+	0.919060i	−0.0605814	+	0.0440150i
$437$	−6.22440	−	4.52229i	−0.297753	−	0.216330i
$438$	−3.15207	−	9.70106i	−0.150611	−	0.463535i
$439$	−11.3874			−0.543493			−0.271746	−	0.962369i	$-0.587601\pi$
$439$	−11.3874			−0.543493			−0.271746	+	0.962369i	$0.587601\pi$
$440$	−2.91429	−	1.58333i	−0.138933	−	0.0754822i
$441$	44.8483			2.13564
$442$	1.93745	+	5.96285i	0.0921550	+	0.283624i
$443$	−22.5127	−	16.3565i	−1.06961	−	0.777119i	−0.0937702	−	0.995594i	$-0.529892\pi$
$443$	−22.5127	−	16.3565i	−1.06961	−	0.777119i	−0.975843	+	0.218475i	$0.929892\pi$
$444$	2.39983	−	1.74358i	0.113891	−	0.0827467i
$445$	0.0138087	−	0.0424987i	0.000654593	−	0.00201463i
$446$	8.25986	−	25.4212i	0.391115	−	1.20373i
$447$	−53.8684	+	39.1377i	−2.54789	+	1.85115i
$448$	−3.17926	−	2.30987i	−0.150206	−	0.109131i
$449$	6.64270	+	20.4441i	0.313488	+	0.964817i	0.976372	+	0.216095i	$0.0693322\pi$
$449$	6.64270	+	20.4441i	0.313488	+	0.964817i	−0.662884	+	0.748722i	$0.730668\pi$
$450$	−5.31175			−0.250398
$451$	−2.39403	+	12.8980i	−0.112731	+	0.607343i
$452$	6.25393			0.294160
$453$	−5.14297	−	15.8284i	−0.241638	−	0.743685i
$454$	−14.4359	−	10.4883i	−0.677512	−	0.492241i
$455$	18.5306	−	13.4633i	0.868727	−	0.631167i
$456$	−1.35134	+	4.15898i	−0.0632821	+	0.194762i
$457$	4.29411	−	13.2159i	0.200870	−	0.618215i	−0.798988	−	0.601348i	$-0.794631\pi$
$457$	4.29411	−	13.2159i	0.200870	−	0.618215i	0.999858	−	0.0168673i	$-0.00536929\pi$
$458$	12.6669	−	9.20304i	0.591885	−	0.430030i
$459$	−5.80003	−	4.21397i	−0.270722	−	0.196691i
$460$	1.56743	+	4.82405i	0.0730817	+	0.224922i
$461$	−14.9375			−0.695709			−0.347855	−	0.937549i	$-0.613090\pi$
$461$	−14.9375			−0.695709			−0.347855	+	0.937549i	$0.613090\pi$
$462$	−27.2636	+	25.8585i	−1.26842	+	1.20304i
$463$	−38.5141			−1.78990			−0.894951	−	0.446165i	$-0.852789\pi$
$463$	−38.5141			−1.78990			−0.894951	+	0.446165i	$0.852789\pi$
$464$	0.116989	+	0.360055i	0.00543107	+	0.0167151i
$465$	15.3138	+	11.1262i	0.710162	+	0.515963i
$466$	−13.5272	+	9.82806i	−0.626634	+	0.455276i
$467$	−4.86514	+	14.9734i	−0.225132	+	0.692885i	0.773146	+	0.634228i	$0.218682\pi$
$467$	−4.86514	+	14.9734i	−0.225132	+	0.692885i	−0.998278	+	0.0586572i	$0.981318\pi$
$468$	−9.56715	+	29.4447i	−0.442242	+	1.36108i
$469$	19.0254	−	13.8228i	0.878513	−	0.638277i
$470$	−6.14416	−	4.46399i	−0.283409	−	0.205909i
$471$	9.61410	+	29.5892i	0.442994	+	1.36340i
$472$	10.9910			0.505904
$473$	0.637334	+	1.33711i	0.0293046	+	0.0614803i
$474$	−2.03573			−0.0935043
$475$	0.468724	+	1.44258i	0.0215065	+	0.0661903i
$476$	−3.41989	−	2.48469i	−0.156750	−	0.113886i
$477$	−26.8896	+	19.5364i	−1.23119	+	0.894511i
$478$	5.91665	−	18.2096i	0.270621	−	0.832887i
$479$	−5.01996	+	15.4498i	−0.229368	+	0.705921i	0.768451	+	0.639909i	$0.221028\pi$
$479$	−5.01996	+	15.4498i	−0.229368	+	0.705921i	−0.997819	+	0.0660126i	$0.978972\pi$
$480$	2.33240	−	1.69459i	0.106459	−	0.0773472i
$481$	−4.85173	−	3.52499i	−0.221220	−	0.160726i
$482$	2.03761	+	6.27113i	0.0928108	+	0.285642i
$483$	57.4673			2.61485
$484$	0.581513	−	10.9846i	0.0264324	−	0.499301i
$485$	−16.3572			−0.742744
$486$	3.25695	+	10.0239i	0.147738	+	0.454691i
$487$	8.51344	+	6.18538i	0.385781	+	0.280286i	0.763724	−	0.645542i	$-0.223369\pi$
$487$	8.51344	+	6.18538i	0.385781	+	0.280286i	−0.377944	+	0.925829i	$0.623369\pi$
$488$	−8.11908	+	5.89886i	−0.367533	+	0.267029i
$489$	14.8277	−	45.6348i	0.670530	−	2.06368i
$490$	−2.60910	+	8.02999i	−0.117867	+	0.362758i
$491$	3.44984	−	2.50646i	0.155689	−	0.113115i	−0.507213	−	0.861821i	$-0.669324\pi$
$491$	3.44984	−	2.50646i	0.155689	−	0.113115i	0.662903	+	0.748706i	$0.269324\pi$
$492$	−9.22539	−	6.70264i	−0.415913	−	0.302178i
$493$	0.125843	+	0.387306i	0.00566769	+	0.0174434i
$494$	8.84091			0.397771
$495$	−7.58014	−	15.9029i	−0.340702	−	0.714784i
$496$	−6.56569			−0.294808
$497$	6.11271	+	18.8130i	0.274193	+	0.843878i
$498$	27.3836	+	19.8953i	1.22709	+	0.891532i
$499$	−0.884781	+	0.642831i	−0.0396082	+	0.0287771i	−0.607413	−	0.794386i	$-0.707793\pi$
$499$	−0.884781	+	0.642831i	−0.0396082	+	0.0287771i	0.567805	+	0.823163i	$0.307793\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−7.71029	+	23.7298i	−0.344471	+	1.06017i
$502$	16.5089	−	11.9944i	0.736828	−	0.535337i
$503$	−13.7746	−	10.0078i	−0.614178	−	0.446227i	0.236705	−	0.971582i	$-0.423933\pi$
$503$	−13.7746	−	10.0078i	−0.614178	−	0.446227i	−0.850883	+	0.525355i	$0.823933\pi$
$504$	−6.45044	−	19.8524i	−0.287325	−	0.884297i
$505$	3.23607			0.144003
$506$	−12.2060	+	11.5769i	−0.542622	+	0.514656i
$507$	60.4633			2.68527
$508$	−5.86577	−	18.0530i	−0.260252	−	0.800972i
$509$	19.9574	+	14.4999i	0.884596	+	0.642697i	0.934463	−	0.356059i	$-0.115880\pi$
$509$	19.9574	+	14.4999i	0.884596	+	0.642697i	−0.0498671	+	0.998756i	$0.515880\pi$
$510$	2.50893	−	1.82285i	0.111097	−	0.0807170i
$511$	4.29653	−	13.2234i	0.190067	−	0.584967i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−8.17862	+	5.94211i	−0.361095	+	0.262351i
$514$	−21.0516	−	15.2948i	−0.928544	−	0.674627i
$515$	−3.53824	−	10.8896i	−0.155914	−	0.479853i
$516$	−1.28758			−0.0566825
$517$	4.59679	−	24.7654i	0.202166	−	1.08918i
$518$	4.04339			0.177657
$519$	−11.3641	−	34.9750i	−0.498827	−	1.53523i
$520$	−4.71542	−	3.42595i	−0.206785	−	0.150238i
$521$	−10.7212	+	7.78944i	−0.469706	+	0.341262i	−0.797327	−	0.603548i	$-0.793753\pi$
$521$	−10.7212	+	7.78944i	−0.469706	+	0.341262i	0.327621	+	0.944809i	$0.393753\pi$
$522$	−0.621416	+	1.91252i	−0.0271986	+	0.0837088i
$523$	0.300114	−	0.923655i	0.0131231	−	0.0403886i	−0.944281	−	0.329142i	$-0.893241\pi$
$523$	0.300114	−	0.923655i	0.0131231	−	0.0403886i	0.957404	+	0.288753i	$0.0932406\pi$
$524$	5.13522	−	3.73096i	0.224333	−	0.162988i
$525$	−9.16586	−	6.65938i	−0.400031	−	0.290639i
$526$	−6.65523	−	20.4827i	−0.290182	−	0.893088i
$527$	−7.06261			−0.307652
$528$	8.40192	+	4.56475i	0.365647	+	0.198655i
$529$	2.72826			0.118620
$530$	−1.93362	−	5.95106i	−0.0839910	−	0.258498i
$531$	47.2318	+	34.3159i	2.04969	+	1.48918i
$532$	−4.82238	+	3.50366i	−0.209077	+	0.151903i
$533$	−7.12403	+	21.9255i	−0.308576	+	0.949699i
$534$	−0.0398105	+	0.122524i	−0.00172277	+	0.00530214i
$535$	−5.83345	+	4.23825i	−0.252202	+	0.183236i
$536$	−4.84134	−	3.51744i	−0.209114	−	0.151930i
$537$	16.7971	+	51.6962i	0.724849	+	2.23086i
$538$	16.7017			0.720063
$539$	−27.7644	+	3.64777i	−1.19590	+	0.157121i
$540$	6.66481			0.286808
$541$	−11.1569	−	34.3374i	−0.479673	−	1.47628i	−0.839551	−	0.543281i	$-0.817182\pi$
$541$	−11.1569	−	34.3374i	−0.479673	−	1.47628i	0.359878	−	0.932999i	$-0.382818\pi$
$542$	−10.0233	−	7.28238i	−0.430539	−	0.312805i
$543$	−55.4060	+	40.2548i	−2.37770	+	1.72750i
$544$	−0.332405	+	1.02304i	−0.0142517	+	0.0438624i
$545$	0.483178	−	1.48707i	0.0206971	−	0.0636991i
$546$	−53.4239	+	38.8147i	−2.28633	+	1.66112i
$547$	−15.7856	−	11.4689i	−0.674944	−	0.490375i	0.196733	−	0.980457i	$-0.436967\pi$
$547$	−15.7856	−	11.4689i	−0.674944	−	0.490375i	−0.871677	+	0.490082i	$0.836967\pi$
$548$	−1.44767	−	4.45548i	−0.0618415	−	0.190329i
$549$	−53.3073			−2.27510
$550$	3.28837	−	0.432036i	0.140216	−	0.0184221i
$551$	0.574244			0.0244636
$552$	−4.51891	−	13.9078i	−0.192338	−	0.591954i
$553$	−2.24492	−	1.63103i	−0.0954638	−	0.0693585i
$554$	−17.3630	+	12.6149i	−0.737683	+	0.535958i
$555$	−0.916655	+	2.82117i	−0.0389098	+	0.119752i
$556$	2.59505	−	7.98673i	0.110054	−	0.338713i
$557$	16.9694	−	12.3290i	0.719014	−	0.522395i	−0.167055	−	0.985948i	$-0.553426\pi$
$557$	16.9694	−	12.3290i	0.719014	−	0.522395i	0.886069	+	0.463553i	$0.153426\pi$
$558$	−28.2147	−	20.4992i	−1.19442	−	0.867800i
$559$	0.804400	+	2.47569i	0.0340225	+	0.104710i
$560$	3.92979			0.166064
$561$	9.03782	+	4.91024i	0.381577	+	0.207310i
$562$	−0.288474			−0.0121686
$563$	−6.88278	−	21.1830i	−0.290075	−	0.892758i	−0.984832	−	0.173513i	$-0.944488\pi$
$563$	−6.88278	−	21.1830i	−0.290075	−	0.892758i	0.694757	−	0.719245i	$-0.255512\pi$
$564$	17.7137	+	12.8697i	0.745880	+	0.541914i
$565$	−5.05954	+	3.67597i	−0.212856	+	0.154649i
$566$	−8.35853	+	25.7249i	−0.351335	+	1.08130i
$567$	3.98248	−	12.2568i	0.167249	−	0.514738i
$568$	4.07230	−	2.95870i	0.170870	−	0.124144i
$569$	0.161029	+	0.116994i	0.00675068	+	0.00490465i	0.591155	−	0.806558i	$-0.298672\pi$
$569$	0.161029	+	0.116994i	0.00675068	+	0.00490465i	−0.584405	+	0.811462i	$0.698672\pi$
$570$	−1.35134	−	4.15898i	−0.0566012	−	0.174201i
$571$	32.7720			1.37146			0.685732	−	0.727854i	$-0.259482\pi$
$571$	32.7720			1.37146			0.685732	+	0.727854i	$0.259482\pi$
$572$	3.52786	−	19.0066i	0.147507	−	0.794704i
$573$	−21.2786			−0.888925
$574$	−4.80322	−	14.7828i	−0.200482	−	0.617022i
$575$	−4.10358	−	2.98142i	−0.171131	−	0.124334i
$576$	−4.29730	+	3.12217i	−0.179054	+	0.130090i
$577$	2.15889	−	6.64438i	0.0898758	−	0.276609i	−0.896009	−	0.444037i	$-0.853546\pi$
$577$	2.15889	−	6.64438i	0.0898758	−	0.276609i	0.985884	+	0.167427i	$0.0535460\pi$
$578$	4.89573	−	15.0675i	0.203635	−	0.626725i
$579$	−16.1969	+	11.7677i	−0.673118	+	0.489049i
$580$	−0.306281	−	0.222526i	−0.0127176	−	0.00923989i
$581$	14.2573	+	43.8795i	0.591493	+	1.82043i
$582$	47.1581			1.95477
$583$	15.0576	−	14.2816i	0.623622	−	0.591482i
$584$	−3.53807			−0.146406
$585$	−9.56715	−	29.4447i	−0.395553	−	1.21739i
$586$	−9.88747	−	7.18367i	−0.408448	−	0.296755i
$587$	−18.9135	+	13.7415i	−0.780645	+	0.567172i	−0.905173	−	0.425044i	$-0.860259\pi$
$587$	−18.9135	+	13.7415i	−0.780645	+	0.567172i	0.124527	+	0.992216i	$0.460259\pi$
$588$	7.52207	−	23.1505i	0.310205	−	0.954712i
$589$	−3.07749	+	9.47155i	−0.126806	+	0.390268i
$590$	−8.89194	+	6.46038i	−0.366076	+	0.265969i
$591$	−6.02891	−	4.38026i	−0.247996	−	0.180180i
$592$	−0.317950	−	0.978551i	−0.0130677	−	0.0402182i
$593$	−30.7990			−1.26476			−0.632382	−	0.774657i	$-0.717923\pi$
$593$	−30.7990			−1.26476			−0.632382	+	0.774657i	$0.717923\pi$
$594$	9.51102	+	19.9539i	0.390242	+	0.818717i
$595$	4.22721			0.173299
$596$	7.13695	+	21.9653i	0.292341	+	0.899732i
$597$	10.3696	+	7.53393i	0.424398	+	0.308343i
$598$	−23.9180	+	17.3775i	−0.978081	+	0.710617i
$599$	7.32833	−	22.5543i	0.299427	−	0.921543i	−0.682271	−	0.731100i	$-0.739008\pi$
$599$	7.32833	−	22.5543i	0.299427	−	0.921543i	0.981698	−	0.190443i	$-0.0609925\pi$
$600$	−0.890899	+	2.74191i	−0.0363708	+	0.111938i
$601$	−6.68382	+	4.85608i	−0.272639	+	0.198084i	−0.715700	−	0.698408i	$-0.753892\pi$
$601$	−6.68382	+	4.85608i	−0.272639	+	0.198084i	0.443062	+	0.896491i	$0.353892\pi$
$602$	−1.41989	−	1.03161i	−0.0578703	−	0.0420452i
$603$	−9.82264	−	30.2310i	−0.400009	−	1.23110i
$604$	−5.77279			−0.234891
$605$	5.98614	+	9.22855i	0.243371	+	0.375194i
$606$	−9.32962			−0.378990
$607$	12.8809	+	39.6433i	0.522819	+	1.60907i	0.768589	+	0.639743i	$0.220959\pi$
$607$	12.8809	+	39.6433i	0.522819	+	1.60907i	−0.245770	+	0.969328i	$0.579041\pi$
$608$	1.22713	+	0.891565i	0.0497669	+	0.0361578i
$609$	−3.47005	+	2.52114i	−0.140613	+	0.102162i
$610$	3.10121	−	9.54455i	0.125564	−	0.386448i
$611$	13.6788	−	42.0992i	0.553387	−	1.70315i
$612$	−4.62254	+	3.35847i	−0.186855	+	0.135758i
$613$	26.7817	+	19.4580i	1.08170	+	0.785903i	0.977979	−	0.208703i	$-0.0669242\pi$
$613$	26.7817	+	19.4580i	1.08170	+	0.785903i	0.103724	+	0.994606i	$0.466924\pi$
$614$	8.86746	+	27.2912i	0.357862	+	1.10138i
$615$	11.4032			0.459822
$616$	5.60801	+	11.7654i	0.225953	+	0.474043i
$617$	30.3874			1.22335			0.611675	−	0.791109i	$-0.290496\pi$
$617$	30.3874			1.22335			0.611675	+	0.791109i	$0.290496\pi$
$618$	10.2008	+	31.3948i	0.410336	+	1.26288i
$619$	−32.8059	−	23.8349i	−1.31858	−	0.958004i	−0.999949	−	0.0101243i	$-0.996777\pi$
$619$	−32.8059	−	23.8349i	−1.31858	−	0.958004i	−0.318630	−	0.947879i	$-0.603223\pi$
$620$	5.31175	−	3.85921i	0.213325	−	0.154990i
$621$	10.4466	−	32.1514i	0.419208	−	1.29019i
$622$	−8.28623	+	25.5024i	−0.332247	+	1.02255i
$623$	−0.142068	+	0.103218i	−0.00569183	+	0.00413536i
$624$	13.5946	+	9.87705i	0.544219	+	0.395399i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	25.6609			1.02561
$627$	10.5232	−	9.98086i	0.420257	−	0.398597i
$628$	10.7915			0.430626
$629$	−0.342015	−	1.05261i	−0.0136370	−	0.0419704i
$630$	16.8875	+	12.2695i	0.672813	+	0.488827i
$631$	−13.1880	+	9.58164i	−0.525006	+	0.381439i	−0.818486	−	0.574526i	$-0.805186\pi$
$631$	−13.1880	+	9.58164i	−0.525006	+	0.381439i	0.293480	+	0.955965i	$0.405186\pi$
$632$	−0.218201	+	0.671554i	−0.00867958	+	0.0267130i
$633$	9.77901	−	30.0967i	0.388681	−	1.19624i
$634$	11.6653	−	8.47531i	0.463287	−	0.336597i
$635$	15.3568	+	11.1574i	0.609416	+	0.442766i
$636$	5.57464	+	17.1570i	0.221049	+	0.680318i
$637$	−49.2120			−1.94985
$638$	0.229146	−	1.23453i	0.00907196	−	0.0488757i
$639$	26.7375			1.05772
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	18.1070	+	13.1555i	0.715183	+	0.519611i	0.884842	−	0.465892i	$-0.154266\pi$
$641$	18.1070	+	13.1555i	0.715183	+	0.519611i	−0.169658	+	0.985503i	$0.554266\pi$
$642$	16.8179	−	12.2189i	0.663750	−	0.482242i
$643$	−0.722400	+	2.22332i	−0.0284887	+	0.0876792i	−0.964290	−	0.264849i	$-0.914678\pi$
$643$	−0.722400	+	2.22332i	−0.0284887	+	0.0876792i	0.935801	+	0.352528i	$0.114678\pi$
$644$	6.15966	−	18.9575i	0.242725	−	0.747029i
$645$	1.04167	−	0.756820i	0.0410158	−	0.0297997i
$646$	1.32001	+	0.959044i	0.0519351	+	0.0377331i
$647$	2.18034	+	6.71040i	0.0857180	+	0.263813i	0.984724	−	0.174124i	$-0.0557093\pi$
$647$	2.18034	+	6.71040i	0.0857180	+	0.263813i	−0.899006	+	0.437937i	$0.855709\pi$
$648$	−3.27946			−0.128829
$649$	−32.0311	−	17.4024i	−1.25733	−	0.683105i
$650$	5.82857			0.228616
$651$	−22.9868	−	70.7460i	−0.900923	−	2.77275i
$652$	−13.4648	−	9.78278i	−0.527324	−	0.383123i
$653$	−11.7511	+	8.53771i	−0.459858	+	0.334106i	−0.793476	−	0.608602i	$-0.791731\pi$
$653$	−11.7511	+	8.53771i	−0.459858	+	0.334106i	0.333618	+	0.942709i	$0.391731\pi$
$654$	−1.39301	+	4.28724i	−0.0544709	+	0.167644i
$655$	−1.96148	+	6.03682i	−0.0766414	+	0.235878i
$656$	−3.19992	+	2.32488i	−0.124936	+	0.0907711i
$657$	−15.2041	−	11.0465i	−0.593170	−	0.430963i
$658$	9.22266	+	28.3844i	0.359537	+	1.10654i
$659$	28.5069			1.11047			0.555235	−	0.831693i	$-0.312628\pi$
$659$	28.5069			1.11047			0.555235	+	0.831693i	$0.312628\pi$
$660$	−9.48039	+	1.24556i	−0.369024	+	0.0484835i
$661$	2.00856			0.0781238			0.0390619	−	0.999237i	$-0.487563\pi$
$661$	2.00856			0.0781238			0.0390619	+	0.999237i	$0.487563\pi$
$662$	−5.88261	−	18.1048i	−0.228634	−	0.703664i
$663$	14.6235	+	10.6246i	0.567930	+	0.412625i
$664$	9.49826	−	6.90089i	0.368604	−	0.267806i
$665$	1.84198	−	5.66904i	0.0714291	−	0.219836i
$666$	1.68887	−	5.19782i	0.0654425	−	0.201411i
$667$	−1.55355	+	1.12872i	−0.0601537	+	0.0437042i
$668$	7.00164	+	5.08699i	0.270902	+	0.196822i
$669$	−23.8133	−	73.2897i	−0.920674	−	2.83354i
$670$	5.98422			0.231191
$671$	33.0012	−	4.33579i	1.27400	−	0.167381i
$672$	−11.3296			−0.437050
$673$	5.28692	+	16.2715i	0.203796	+	0.627219i	0.999761	+	0.0218762i	$0.00696397\pi$
$673$	5.28692	+	16.2715i	0.203796	+	0.627219i	−0.795965	+	0.605343i	$0.793036\pi$
$674$	−2.45390	−	1.78286i	−0.0945207	−	0.0686733i
$675$	−5.39194	+	3.91748i	−0.207536	+	0.150784i
$676$	6.48079	−	19.9458i	0.249261	−	0.767147i
$677$	−7.28887	+	22.4328i	−0.280134	+	0.862164i	0.707681	+	0.706532i	$0.249741\pi$
$677$	−7.28887	+	22.4328i	−0.280134	+	0.862164i	−0.987815	+	0.155632i	$0.950259\pi$
$678$	14.5867	−	10.5979i	0.560199	−	0.407009i
$679$	52.0040	+	37.7831i	1.99573	+	1.44998i
$680$	−0.332405	−	1.02304i	−0.0127471	−	0.0392317i
$681$	−51.4439			−1.97133
$682$	19.1343	+	10.3956i	0.732690	+	0.398070i
$683$	31.7728			1.21575			0.607876	−	0.794032i	$-0.292022\pi$
$683$	31.7728			1.21575			0.607876	+	0.794032i	$0.292022\pi$
$684$	2.48974	+	7.66265i	0.0951978	+	0.292989i
$685$	3.79006	+	2.75364i	0.144811	+	0.105211i
$686$	4.58840	−	3.33367i	0.175186	−	0.127280i
$687$	13.9489	−	42.9304i	0.532185	−	1.63790i
$688$	−0.138010	+	0.424750i	−0.00526157	+	0.0161935i
$689$	29.5059	−	21.4373i	1.12408	−	0.816694i
$690$	11.8307	+	8.59548i	0.450386	+	0.327224i
$691$	−6.50338	−	20.0154i	−0.247400	−	0.761420i	−0.995232	−	0.0975319i	$-0.968905\pi$
$691$	−6.50338	−	20.0154i	−0.247400	−	0.761420i	0.747832	−	0.663888i	$-0.231095\pi$
$692$	−12.7557			−0.484900
$693$	−12.6345	+	68.0688i	−0.479943	+	2.58572i
$694$	3.49677			0.132735
$695$	2.59505	+	7.98673i	0.0984357	+	0.302954i
$696$	0.883011	+	0.641545i	0.0334705	+	0.0243177i
$697$	−3.44210	+	2.50083i	−0.130379	+	0.0947258i
$698$	5.26289	−	16.1975i	0.199203	−	0.613084i
$699$	−14.8963	+	45.8460i	−0.563429	+	1.73406i
$700$	−3.17926	+	2.30987i	−0.120165	+	0.0873049i
$701$	7.98896	+	5.80432i	0.301739	+	0.219226i	0.728344	−	0.685212i	$-0.240290\pi$
$701$	7.98896	+	5.80432i	0.301739	+	0.219226i	−0.426605	+	0.904438i	$0.640290\pi$
$702$	12.0042	+	36.9451i	0.453069	+	1.39440i
$703$	−1.56067			−0.0588619
$704$	2.40640	−	2.28238i	0.0906946	−	0.0860203i
$705$	−21.8953			−0.824625
$706$	−5.37580	−	16.5450i	−0.202321	−	0.622680i
$707$	−10.2883	−	7.47490i	−0.386932	−	0.281123i
$708$	25.6356	−	18.6253i	0.963444	−	0.699983i
$709$	2.09620	−	6.45143i	0.0787243	−	0.242288i	−0.903947	−	0.427644i	$-0.859344\pi$
$709$	2.09620	−	6.45143i	0.0787243	−	0.242288i	0.982672	+	0.185356i	$0.0593437\pi$
$710$	−1.55548	+	4.78728i	−0.0583762	+	0.179663i
$711$	−3.03438	+	2.20461i	−0.113798	+	0.0826792i
$712$	0.0361516	+	0.0262656i	0.00135484	+	0.000984346i
$713$	−10.2912	−	31.6732i	−0.385410	−	1.18617i
$714$	−12.1871			−0.456091
$715$	8.31767	+	17.4503i	0.311063	+	0.652603i
$716$	18.8541			0.704611
$717$	−17.0578	−	52.4985i	−0.637035	−	1.96059i
$718$	0.789459	+	0.573576i	0.0294624	+	0.0214057i
$719$	−37.9662	+	27.5840i	−1.41590	+	1.02871i	−0.423467	+	0.905911i	$0.639187\pi$
$719$	−37.9662	+	27.5840i	−1.41590	+	1.02871i	−0.992432	+	0.122799i	$0.960813\pi$
$720$	1.64142	−	5.05178i	0.0611722	−	0.188269i
$721$	−13.9045	+	42.7938i	−0.517832	+	1.59372i
$722$	−13.5100	+	9.81557i	−0.502789	+	0.365298i
$723$	15.3795	+	11.1739i	0.571972	+	0.415562i
$724$	7.34066	+	22.5922i	0.272814	+	0.839634i
$725$	0.378584			0.0140603
$726$	−17.2581	−	26.6060i	−0.640509	−	0.987442i
$727$	1.32849			0.0492708			0.0246354	−	0.999697i	$-0.492158\pi$
$727$	1.32849			0.0492708			0.0246354	+	0.999697i	$0.492158\pi$
$728$	7.07805	+	21.7840i	0.262330	+	0.807369i
$729$	32.5423	+	23.6434i	1.20527	+	0.875680i
$730$	2.86236	−	2.07963i	0.105941	−	0.0769704i
$731$	−0.148455	+	0.456898i	−0.00549081	+	0.0168990i
$732$	−8.94083	+	27.5170i	−0.330463	+	1.01706i
$733$	−14.9732	+	10.8787i	−0.553047	+	0.401812i	−0.828908	−	0.559385i	$-0.811037\pi$
$733$	−14.9732	+	10.8787i	−0.553047	+	0.401812i	0.275861	+	0.961198i	$0.411037\pi$
$734$	−28.1390	−	20.4442i	−1.03863	−	0.754609i
$735$	7.52207	+	23.1505i	0.277456	+	0.853920i
$736$	−5.07230			−0.186968
$737$	8.53979	+	17.9163i	0.314567	+	0.659954i
$738$	−21.0097			−0.773376
$739$	7.54121	+	23.2094i	0.277408	+	0.853773i	0.988572	+	0.150748i	$0.0481681\pi$
$739$	7.54121	+	23.2094i	0.277408	+	0.853773i	−0.711165	+	0.703026i	$0.751832\pi$
$740$	0.832405	+	0.604778i	0.0305998	+	0.0222321i
$741$	20.6206	−	14.9817i	0.757516	−	0.550368i
$742$	−7.59870	+	23.3864i	−0.278957	+	0.858542i
$743$	5.92122	−	18.2236i	0.217229	−	0.668561i	−0.781759	−	0.623580i	$-0.785677\pi$
$743$	5.92122	−	18.2236i	0.217229	−	0.668561i	0.998988	−	0.0449805i	$-0.0143226\pi$
$744$	−15.3138	+	11.1262i	−0.561433	+	0.407905i
$745$	−18.6848	−	13.5753i	−0.684557	−	0.497360i
$746$	−9.03455	−	27.8055i	−0.330778	−	1.01803i
$747$	62.3626			2.28173
$748$	2.58853	−	2.45512i	0.0946460	−	0.0897680i
$749$	28.3359			1.03537
$750$	−0.890899	−	2.74191i	−0.0325310	−	0.100120i
$751$	−0.131474	−	0.0955212i	−0.00479754	−	0.00348562i	0.585384	−	0.810756i	$-0.300944\pi$
$751$	−0.131474	−	0.0955212i	−0.00479754	−	0.00348562i	−0.590181	+	0.807271i	$0.700944\pi$
$752$	6.14416	−	4.46399i	0.224054	−	0.162785i
$753$	18.1798	−	55.9516i	0.662508	−	2.03899i
$754$	0.681878	−	2.09861i	0.0248325	−	0.0764267i
$755$	4.67028	−	3.39316i	0.169969	−	0.123490i
$756$	−21.1892	−	15.3949i	−0.770644	−	0.559905i
$757$	0.747984	+	2.30206i	0.0271860	+	0.0836698i	0.963729	−	0.266883i	$-0.0859937\pi$
$757$	0.747984	+	2.30206i	0.0271860	+	0.0836698i	−0.936543	+	0.350553i	$0.885994\pi$
$758$	−12.6461			−0.459327
$759$	−8.85118	+	47.6862i	−0.321277	+	1.73090i
$760$	−1.51682			−0.0550209
$761$	−1.83739	−	5.65489i	−0.0666052	−	0.204990i	0.912215	−	0.409712i	$-0.134371\pi$
$761$	−1.83739	−	5.65489i	−0.0666052	−	0.204990i	−0.978820	+	0.204722i	$0.934371\pi$
$762$	−44.2738	−	32.1668i	−1.60387	−	1.16528i
$763$	−4.97109	+	3.61171i	−0.179966	+	0.130753i
$764$	−2.28075	+	7.01944i	−0.0825148	+	0.253954i
$765$	1.76565	−	5.43412i	0.0638373	−	0.196471i
$766$	−1.22604	+	0.890771i	−0.0442986	+	0.0321849i
$767$	−51.8274	−	37.6548i	−1.87138	−	1.35964i
$768$	0.890899	+	2.74191i	0.0321476	+	0.0989400i
$769$	46.4619			1.67546			0.837730	−	0.546085i	$-0.183882\pi$
$769$	46.4619			1.67546			0.837730	+	0.546085i	$0.183882\pi$
$770$	−11.4525	−	6.22214i	−0.412721	−	0.224230i
$771$	−75.0193			−2.70175
$772$	2.14590	+	6.60440i	0.0772326	+	0.237697i
$773$	−24.5256	−	17.8189i	−0.882123	−	0.640900i	0.0516893	−	0.998663i	$-0.483539\pi$
$773$	−24.5256	−	17.8189i	−0.882123	−	0.640900i	−0.933812	+	0.357763i	$0.883539\pi$
$774$	−1.91921	+	1.39439i	−0.0689846	+	0.0501203i
$775$	−2.02891	+	6.24434i	−0.0728806	+	0.224303i
$776$	5.05466	−	15.5567i	0.181452	−	0.558451i
$777$	9.43083	−	6.85190i	0.338329	−	0.245811i
$778$	5.53897	+	4.02429i	0.198582	+	0.144278i
$779$	1.85395	+	5.70587i	0.0664246	+	0.204434i
$780$	−16.8038			−0.601674
$781$	−16.5525	+	2.17471i	−0.592294	+	0.0778174i
$782$	−5.45620			−0.195113
$783$	0.779709	+	2.39970i	0.0278645	+	0.0857582i
$784$	−6.83071	−	4.96280i	−0.243954	−	0.177243i
$785$	−8.73047	+	6.34306i	−0.311604	+	0.226393i
$786$	5.65497	−	17.4042i	0.201706	−	0.620788i
$787$	14.0130	−	43.1276i	0.499509	−	1.53733i	−0.310300	−	0.950639i	$-0.600430\pi$
$787$	14.0130	−	43.1276i	0.499509	−	1.53733i	0.809810	−	0.586693i	$-0.199570\pi$
$788$	−2.09118	+	1.51933i	−0.0744954	+	0.0541241i
$789$	−50.2325	−	36.4960i	−1.78832	−	1.29929i
$790$	−0.218201	−	0.671554i	−0.00776325	−	0.0238928i
$791$	24.5766			0.873844
$792$	17.4670	−	2.29487i	0.620662	−	0.0815445i
$793$	58.4940			2.07718
$794$	1.41178	+	4.34501i	0.0501022	+	0.154199i
$795$	−14.5946	−	10.6036i	−0.517617	−	0.376071i
$796$	3.59679	−	2.61322i	0.127485	−	0.0926230i
$797$	−13.3783	+	41.1742i	−0.473884	+	1.45847i	0.373572	+	0.927601i	$0.378133\pi$
$797$	−13.3783	+	41.1742i	−0.473884	+	1.45847i	−0.847457	+	0.530865i	$0.821867\pi$
$798$	−5.31046	+	16.3439i	−0.187988	+	0.578568i
$799$	6.60918	−	4.80185i	0.233816	−	0.169877i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	0.0733482	+	0.225743i	0.00259163	+	0.00797622i
$802$	0.502397			0.0177403
$803$	10.3110	+	5.60193i	0.363866	+	0.197688i
$804$	−17.2526			−0.608452
$805$	6.15966	+	18.9575i	0.217099	+	0.668163i
$806$	30.9600	+	22.4937i	1.09052	+	0.792308i
$807$	38.9552	−	28.3026i	1.37129	−	0.996299i
$808$	−1.00000	+	3.07768i	−0.0351799	+	0.108273i
$809$	15.2113	−	46.8156i	0.534801	−	1.64595i	−0.209277	−	0.977856i	$-0.567111\pi$
$809$	15.2113	−	46.8156i	0.534801	−	1.64595i	0.744078	−	0.668092i	$-0.232889\pi$
$810$	2.65314	−	1.92762i	0.0932219	−	0.0677296i
$811$	1.47255	+	1.06987i	0.0517084	+	0.0375683i	0.613339	−	0.789820i	$-0.289826\pi$
$811$	1.47255	+	1.06987i	0.0517084	+	0.0375683i	−0.561631	+	0.827388i	$0.689826\pi$
$812$	0.459741	+	1.41494i	0.0161338	+	0.0496546i
$813$	−35.7191			−1.25273
$814$	−0.622768	+	3.35520i	−0.0218280	+	0.117600i
$815$	16.6435			0.582995
$816$	0.958327	+	2.94943i	0.0335482	+	0.103251i
$817$	0.548049	+	0.398181i	0.0191738	+	0.0139306i
$818$	10.6810	−	7.76023i	0.373454	−	0.271330i
$819$	−37.5969	+	115.711i	−1.31374	+	4.04328i
$820$	1.22226	−	3.76173i	0.0426831	−	0.131365i
$821$	22.5912	−	16.4135i	0.788439	−	0.572834i	−0.119061	−	0.992887i	$-0.537988\pi$
$821$	22.5912	−	16.4135i	0.788439	−	0.572834i	0.907500	+	0.420053i	$0.137988\pi$
$822$	−10.9268	−	7.93877i	−0.381115	−	0.276896i
$823$	−5.48381	−	16.8774i	−0.191153	−	0.588310i	−1.00000		0.000289980i	$-0.999908\pi$
$823$	−5.48381	−	16.8774i	−0.191153	−	0.588310i	0.808847	−	0.588020i	$-0.200092\pi$
$824$	11.4500			0.398879
$825$	6.93768	−	6.58012i	0.241539	−	0.229090i
$826$	43.1925			1.50286
$827$	10.4642	+	32.2054i	0.363875	+	1.11989i	0.950683	+	0.310165i	$0.100384\pi$
$827$	10.4642	+	32.2054i	0.363875	+	1.11989i	−0.586808	+	0.809726i	$0.699616\pi$
$828$	−21.7972	−	15.8366i	−0.757505	−	0.550360i
$829$	−20.3888	+	14.8133i	−0.708132	+	0.514488i	−0.882571	−	0.470180i	$-0.844189\pi$
$829$	−20.3888	+	14.8133i	−0.708132	+	0.514488i	0.174439	+	0.984668i	$0.444189\pi$
$830$	−3.62801	+	11.1659i	−0.125930	+	0.387573i
$831$	−19.1203	+	58.8463i	−0.663277	+	2.04136i
$832$	4.71542	−	3.42595i	0.163478	−	0.118773i
$833$	−7.34770	−	5.33841i	−0.254583	−	0.184965i
$834$	−7.48154	−	23.0258i	−0.259065	−	0.797319i
$835$	−8.65451			−0.299502
$836$	−2.16458	−	4.54123i	−0.0748636	−	0.157062i
$837$	−43.7591			−1.51253
$838$	−3.91496	−	12.0490i	−0.135240	−	0.416226i
$839$	6.84982	+	4.97669i	0.236482	+	0.171814i	0.699715	−	0.714422i	$-0.253310\pi$
$839$	6.84982	+	4.97669i	0.236482	+	0.171814i	−0.463232	+	0.886237i	$0.653310\pi$
$840$	9.16586	−	6.65938i	0.316252	−	0.229771i
$841$	−8.91720	+	27.4443i	−0.307490	+	0.946356i
$842$	−5.90426	+	18.1714i	−0.203474	+	0.626229i
$843$	−0.672839	+	0.488846i	−0.0231738	+	0.0168368i
$844$	−8.88023	−	6.45186i	−0.305670	−	0.222082i
$845$	6.48079	+	19.9458i	0.222946	+	0.686157i
$846$	40.3406			1.38694
$847$	2.28522	−	43.1672i	0.0785212	−	1.48324i
$848$	6.25732			0.214877
$849$	24.0977	+	74.1652i	0.827032	+	2.54534i
$850$	0.870248	+	0.632272i	0.0298492	+	0.0216867i
$851$	4.22221	−	3.06762i	0.144736	−	0.105157i
$852$	4.48447	−	13.8018i	0.153635	−	0.472841i
$853$	−1.53299	+	4.71805i	−0.0524884	+	0.161543i	−0.973865	−	0.227129i	$-0.927066\pi$
$853$	−1.53299	+	4.71805i	−0.0524884	+	0.161543i	0.921376	+	0.388672i	$0.127066\pi$
$854$	−31.9063	+	23.1812i	−1.09181	+	0.793246i
$855$	−6.51824	−	4.73578i	−0.222919	−	0.161960i
$856$	−2.22818	−	6.85763i	−0.0761576	−	0.234389i
$857$	−49.4733			−1.68998			−0.844988	−	0.534786i	$-0.820392\pi$
$857$	−49.4733			−1.68998			−0.844988	+	0.534786i	$0.820392\pi$
$858$	−23.9799	−	50.3093i	−0.818662	−	1.71753i
$859$	21.9002			0.747224			0.373612	−	0.927585i	$-0.378119\pi$
$859$	21.9002			0.747224			0.373612	+	0.927585i	$0.378119\pi$
$860$	−0.138010	−	0.424750i	−0.00470609	−	0.0144839i
$861$	−36.2538	−	26.3400i	−1.23553	−	0.897663i
$862$	10.8051	−	7.85039i	0.368024	−	0.267385i
$863$	7.22276	−	22.2294i	0.245866	−	0.756697i	−0.749627	−	0.661860i	$-0.769767\pi$
$863$	7.22276	−	22.2294i	0.245866	−	0.756697i	0.995493	−	0.0948366i	$-0.0302329\pi$
$864$	−2.05954	+	6.33861i	−0.0700670	+	0.215644i
$865$	10.3196	−	7.49762i	0.350877	−	0.254927i
$866$	−6.96927	−	5.06347i	−0.236825	−	0.172064i
$867$	−14.1144	−	43.4398i	−0.479351	−	1.47529i
$868$	−25.8018			−0.875769
$869$	1.69919	−	1.61162i	0.0576411	−	0.0546704i
$870$	−1.09146			−0.0370040
$871$	10.7784	+	33.1724i	0.365211	+	1.12400i
$872$	1.26498	+	0.919060i	0.0428375	+	0.0311233i
$873$	70.2919	−	51.0701i	2.37902	−	1.72846i
$874$	−2.37751	+	7.31722i	−0.0804204	+	0.247509i
$875$	1.21437	−	3.73745i	0.0410532	−	0.126349i
$876$	−8.25221	+	5.99558i	−0.278816	+	0.202572i
$877$	34.6618	+	25.1833i	1.17045	+	0.850378i	0.991062	−	0.133401i	$-0.0425899\pi$
$877$	34.6618	+	25.1833i	1.17045	+	0.850378i	0.179383	+	0.983779i	$0.442590\pi$
$878$	3.51891	+	10.8301i	0.118758	+	0.365498i
$879$	−35.2350			−1.18845
$880$	−0.605270	+	3.26093i	−0.0204037	+	0.109926i
$881$	−5.99014			−0.201813			−0.100906	−	0.994896i	$-0.532174\pi$
$881$	−5.99014			−0.201813			−0.100906	+	0.994896i	$0.532174\pi$
$882$	−13.8589	−	42.6533i	−0.466653	−	1.43621i
$883$	−7.45841	−	5.41885i	−0.250995	−	0.182359i	0.455172	−	0.890403i	$-0.349578\pi$
$883$	−7.45841	−	5.41885i	−0.250995	−	0.182359i	−0.706168	+	0.708044i	$0.749578\pi$
$884$	5.07230	−	3.68524i	0.170600	−	0.123948i
$885$	−9.79192	+	30.1364i	−0.329152	+	1.01302i
$886$	−8.59910	+	26.4653i	−0.288893	+	0.889120i
$887$	−9.95768	+	7.23468i	−0.334346	+	0.242917i	−0.742273	−	0.670098i	$-0.766252\pi$
$887$	−9.95768	+	7.23468i	−0.334346	+	0.242917i	0.407926	+	0.913015i	$0.366252\pi$
$888$	−2.39983	−	1.74358i	−0.0805331	−	0.0585107i
$889$	−23.0512	−	70.9444i	−0.773114	−	2.37940i
$890$	−0.0446858			−0.00149787
$891$	9.55729	+	5.19247i	0.320181	+	0.173954i
$892$	−26.7295			−0.894968
$893$	−3.55977	−	10.9558i	−0.119123	−	0.366623i
$894$	53.8684	+	39.1377i	1.80163	+	1.30896i
$895$	−15.2533	+	11.0822i	−0.509861	+	0.370436i
$896$	−1.21437	+	3.73745i	−0.0405693	+	0.124859i
$897$	−26.3388	+	81.0625i	−0.879427	+	2.70660i
$898$	17.3908	−	12.6352i	0.580339	−	0.421641i
$899$	2.01094	+	1.46104i	0.0670688	+	0.0487283i
$900$	1.64142	+	5.05178i	0.0547141	+	0.168393i
$901$	6.73090			0.224239
$902$	13.0065	−	1.70884i	0.433070	−	0.0568980i
$903$	−5.05991			−0.168383
$904$	−1.93257	−	5.94785i	−0.0642764	−	0.197822i
$905$	−19.2181	−	13.9628i	−0.638831	−	0.464138i
$906$	−13.4645	+	9.78251i	−0.447327	+	0.325002i
$907$	−7.98882	+	24.5870i	−0.265264	+	0.816400i	0.726368	+	0.687306i	$0.241207\pi$
$907$	−7.98882	+	24.5870i	−0.265264	+	0.816400i	−0.991632	+	0.129094i	$0.958793\pi$
$908$	−5.51404	+	16.9705i	−0.182990	+	0.563184i
$909$	−13.9064	+	10.1036i	−0.461245	+	0.335114i
$910$	−18.5306	−	13.4633i	−0.614283	−	0.446303i
$911$	2.70009	+	8.31002i	0.0894579	+	0.275323i	0.985770	−	0.168101i	$-0.0537635\pi$
$911$	2.70009	+	8.31002i	0.0894579	+	0.275323i	−0.896312	+	0.443424i	$0.853764\pi$
$912$	4.37301			0.144805
$913$	−38.6070	+	5.07231i	−1.27771	+	0.167869i
$914$	−13.8960			−0.459640
$915$	−8.94083	−	27.5170i	−0.295575	−	0.909685i
$916$	−12.6669	−	9.20304i	−0.418526	−	0.304077i
$917$	20.1803	−	14.6619i	0.666414	−	0.484178i
$918$	−2.21542	+	6.81835i	−0.0731196	+	0.225039i
$919$	−2.39854	+	7.38195i	−0.0791206	+	0.243508i	−0.982791	−	0.184720i	$-0.940862\pi$
$919$	−2.39854	+	7.38195i	−0.0791206	+	0.243508i	0.903671	+	0.428228i	$0.140862\pi$
$920$	4.10358	−	2.98142i	0.135291	−	0.0982947i
$921$	66.9300	+	48.6275i	2.20542	+	1.60233i
$922$	4.61594	+	14.2064i	0.152018	+	0.467863i
$923$	−29.3390			−0.965704
$924$	33.0178	+	17.9385i	1.08620	+	0.590134i
$925$	−1.02891			−0.0338303
$926$	11.9015	+	36.6291i	0.391108	+	1.20371i
$927$	49.2040	+	35.7488i	1.61607	+	1.17415i
$928$	0.306281	−	0.222526i	0.0100542	−	0.00730478i
$929$	7.01463	−	21.5888i	0.230143	−	0.708306i	−0.767586	−	0.640946i	$-0.778542\pi$
$929$	7.01463	−	21.5888i	0.230143	−	0.708306i	0.997729	−	0.0673604i	$-0.0214577\pi$
$930$	5.84937	−	18.0025i	0.191808	−	0.590325i
$931$	−10.3610	+	7.52769i	−0.339567	+	0.246710i
$932$	13.5272	+	9.82806i	0.443097	+	0.321929i
$933$	23.8893	+	73.5236i	0.782100	+	2.40706i
$934$	15.7439			0.515157
$935$	−0.651080	+	3.50773i	−0.0212926	+	0.114715i
$936$	30.9600			1.01196
$937$	9.35316	+	28.7861i	0.305554	+	0.940400i	0.979470	+	0.201591i	$0.0646113\pi$
$937$	9.35316	+	28.7861i	0.305554	+	0.940400i	−0.673915	+	0.738809i	$0.735389\pi$
$938$	−19.0254	−	13.8228i	−0.621202	−	0.451330i
$939$	59.8516	−	43.4847i	1.95318	−	1.41907i
$940$	−2.34686	+	7.22289i	−0.0765461	+	0.235585i
$941$	5.67714	−	17.4725i	0.185070	−	0.569586i	−0.814880	−	0.579630i	$-0.803197\pi$
$941$	5.67714	−	17.4725i	0.185070	−	0.569586i	0.999950	+	0.0100441i	$0.00319718\pi$
$942$	25.1700	−	18.2871i	0.820084	−	0.595826i
$943$	−16.2309	−	11.7925i	−0.528552	−	0.384016i
$944$	−3.39642	−	10.4531i	−0.110544	−	0.340220i
$945$	26.1913			0.852003
$946$	1.07472	−	1.01933i	0.0349421	−	0.0331413i
$947$	−34.5692			−1.12335			−0.561674	−	0.827358i	$-0.689843\pi$
$947$	−34.5692			−1.12335			−0.561674	+	0.827358i	$0.689843\pi$
$948$	0.629076	+	1.93610i	0.0204314	+	0.0628815i
$949$	16.6835	+	12.1213i	0.541569	+	0.393473i
$950$	1.22713	−	0.891565i	0.0398135	−	0.0289262i
$951$	12.8459	−	39.5357i	0.416558	−	1.28203i
$952$	−1.30628	+	4.02032i	−0.0423368	+	0.130299i
$953$	14.2979	−	10.3881i	0.463155	−	0.336502i	−0.331612	−	0.943416i	$-0.607593\pi$
$953$	14.2979	−	10.3881i	0.463155	−	0.336502i	0.794768	+	0.606914i	$0.207593\pi$
$954$	26.8896	+	19.5364i	0.870582	+	0.632515i
$955$	−2.28075	−	7.01944i	−0.0738035	−	0.227144i
$956$	−19.1467			−0.619248
$957$	−1.55757	−	3.26774i	−0.0503491	−	0.105631i
$958$	16.2449			0.524850
$959$	−5.68905	−	17.5091i	−0.183709	−	0.565398i
$960$	−2.33240	−	1.69459i	−0.0752780	−	0.0546927i
$961$	−9.79579	+	7.11706i	−0.315993	+	0.229582i
$962$	−1.85320	+	5.70356i	−0.0597495	+	0.183890i
$963$	11.8355	−	36.4260i	0.381395	−	1.17381i
$964$	5.33454	−	3.87577i	0.171814	−	0.124830i
$965$	−5.61803	−	4.08174i	−0.180851	−	0.131396i
$966$	−17.7584	−	54.6546i	−0.571366	−	1.75848i
$967$	17.1334			0.550973			0.275487	−	0.961305i	$-0.411161\pi$
$967$	17.1334			0.550973			0.275487	+	0.961305i	$0.411161\pi$
$968$	−10.6267	+	2.84138i	−0.341555	+	0.0913255i
$969$	4.70399			0.151114
$970$	5.05466	+	15.5567i	0.162295	+	0.499494i
$971$	−44.0566	−	32.0090i	−1.41384	−	1.02722i	−0.992750	−	0.120201i	$-0.961646\pi$
$971$	−44.0566	−	32.0090i	−1.41384	−	1.02722i	−0.421094	−	0.907017i	$-0.638354\pi$
$972$	8.52680	−	6.19508i	0.273497	−	0.198707i
$973$	10.1980	−	31.3861i	0.326932	−	1.00619i
$974$	3.25184	−	10.0081i	0.104196	−	0.320682i
$975$	13.5946	−	9.87705i	0.435376	−	0.316319i
$976$	8.11908	+	5.89886i	0.259885	+	0.188818i
$977$	−17.3469	−	53.3884i	−0.554978	−	1.70805i	−0.696003	−	0.718039i	$-0.745040\pi$
$977$	−17.3469	−	53.3884i	−0.554978	−	1.70805i	0.141025	−	0.990006i	$-0.454960\pi$
$978$	−47.9833			−1.53434
$979$	−0.0637689	−	0.133785i	−0.00203806	−	0.00427580i
$980$	8.44323			0.269709
$981$	2.56652	+	7.89895i	0.0819428	+	0.252194i
$982$	−3.44984	−	2.50646i	−0.110089	−	0.0799843i
$983$	26.5241	−	19.2709i	0.845988	−	0.614646i	−0.0780492	−	0.996950i	$-0.524869\pi$
$983$	26.5241	−	19.2709i	0.845988	−	0.614646i	0.924037	+	0.382304i	$0.124869\pi$
$984$	−3.52379	+	10.8451i	−0.112334	+	0.345729i
$985$	0.798762	−	2.45834i	0.0254507	−	0.0783291i
$986$	0.329462	−	0.239368i	0.0104922	−	0.00762303i
$987$	69.6110	+	50.5753i	2.21574	+	1.60983i
$988$	−2.73199	−	8.40820i	−0.0869162	−	0.267501i
$989$	−2.26534			−0.0720335
$990$	−12.7822	+	12.1234i	−0.406245	+	0.385308i
$991$	−9.43591			−0.299742			−0.149871	−	0.988706i	$-0.547886\pi$
$991$	−9.43591			−0.299742			−0.149871	+	0.988706i	$0.547886\pi$
$992$	2.02891	+	6.24434i	0.0644179	+	0.198258i
$993$	−44.4009	−	32.2591i	−1.40902	−	1.02371i
$994$	16.0033	−	11.6271i	0.507593	−	0.368788i
$995$	−1.37385	+	4.22827i	−0.0435540	+	0.134045i
$996$	10.4596	−	32.1913i	0.331425	−	1.02002i
$997$	−27.1877	+	19.7531i	−0.861044	+	0.625585i	−0.928169	−	0.372159i	$-0.878618\pi$
$997$	−27.1877	+	19.7531i	−0.861044	+	0.625585i	0.0671244	+	0.997745i	$0.478618\pi$
$998$	0.884781	+	0.642831i	0.0280073	+	0.0203485i
$999$	−2.11908	−	6.52185i	−0.0670447	−	0.206342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.g.c.71.1	yes	8
3.2	odd	2		990.2.n.j.181.1		8
4.3	odd	2		880.2.bo.g.401.2		8
5.2	odd	4		550.2.ba.f.49.3		16
5.3	odd	4		550.2.ba.f.49.2		16
5.4	even	2		550.2.h.l.401.2		8
11.3	even	5		1210.2.a.u.1.4		4
11.8	odd	10		1210.2.a.v.1.4		4
11.9	even	5	inner	110.2.g.c.31.1	✓	8
33.20	odd	10		990.2.n.j.361.1		8
44.3	odd	10		9680.2.a.cj.1.1		4
44.19	even	10		9680.2.a.ci.1.1		4
44.31	odd	10		880.2.bo.g.801.2		8
55.9	even	10		550.2.h.l.251.2		8
55.14	even	10		6050.2.a.dh.1.1		4
55.19	odd	10		6050.2.a.cy.1.1		4
55.42	odd	20		550.2.ba.f.449.2		16
55.53	odd	20		550.2.ba.f.449.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.1	✓	8	11.9	even	5	inner
110.2.g.c.71.1	yes	8	1.1	even	1	trivial
550.2.h.l.251.2		8	55.9	even	10
550.2.h.l.401.2		8	5.4	even	2
550.2.ba.f.49.2		16	5.3	odd	4
550.2.ba.f.49.3		16	5.2	odd	4
550.2.ba.f.449.2		16	55.42	odd	20
550.2.ba.f.449.3		16	55.53	odd	20
880.2.bo.g.401.2		8	4.3	odd	2
880.2.bo.g.801.2		8	44.31	odd	10
990.2.n.j.181.1		8	3.2	odd	2
990.2.n.j.361.1		8	33.20	odd	10
1210.2.a.u.1.4		4	11.3	even	5
1210.2.a.v.1.4		4	11.8	odd	10
6050.2.a.cy.1.1		4	55.19	odd	10
6050.2.a.dh.1.1		4	55.14	even	10
9680.2.a.ci.1.1		4	44.19	even	10
9680.2.a.cj.1.1		4	44.3	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.33240 - 1.69459i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.890899 + 2.74191i) q^{6} +(-3.17926 + 2.30987i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.64142 + 5.05178i) q^{9} -1.00000 q^{10} +(-1.42705 - 2.99391i) q^{11} +2.88301 q^{12} +(-1.80113 - 5.54330i) q^{13} +(3.17926 + 2.30987i) q^{14} +(-2.33240 + 1.69459i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.332405 - 1.02304i) q^{17} +(4.29730 - 3.12217i) q^{18} +(-1.22713 - 0.891565i) q^{19} +(0.309017 + 0.951057i) q^{20} +11.3296 q^{21} +(-2.40640 + 2.28238i) q^{22} +5.07230 q^{23} +(-0.890899 - 2.74191i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.71542 + 3.42595i) q^{26} +(2.05954 - 6.33861i) q^{27} +(1.21437 - 3.73745i) q^{28} +(-0.306281 + 0.222526i) q^{29} +(2.33240 + 1.69459i) q^{30} +(-2.02891 - 6.24434i) q^{31} -1.00000 q^{32} +(-1.74500 + 9.40129i) q^{33} -1.07569 q^{34} +(1.21437 + 3.73745i) q^{35} +(-4.29730 - 3.12217i) q^{36} +(0.832405 - 0.604778i) q^{37} +(-0.468724 + 1.44258i) q^{38} +(-5.19267 + 15.9814i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-3.19992 - 2.32488i) q^{41} +(-3.50105 - 10.7751i) q^{42} -0.446609 q^{43} +(2.91429 + 1.58333i) q^{44} +5.31175 q^{45} +(-1.56743 - 4.82405i) q^{46} +(6.14416 + 4.46399i) q^{47} +(-2.33240 + 1.69459i) q^{48} +(2.60910 - 8.02999i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-2.50893 + 1.82285i) q^{51} +(4.71542 + 3.42595i) q^{52} +(1.93362 + 5.95106i) q^{53} -6.66481 q^{54} +(-3.28837 + 0.432036i) q^{55} -3.92979 q^{56} +(1.35134 + 4.15898i) q^{57} +(0.306281 + 0.222526i) q^{58} +(8.89194 - 6.46038i) q^{59} +(0.890899 - 2.74191i) q^{60} +(-3.10121 + 9.54455i) q^{61} +(-5.31175 + 3.85921i) q^{62} +(-16.8875 - 12.2695i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.82857 q^{65} +(9.48039 - 1.24556i) q^{66} -5.98422 q^{67} +(0.332405 + 1.02304i) q^{68} +(-11.8307 - 8.59548i) q^{69} +(3.17926 - 2.30987i) q^{70} +(1.55548 - 4.78728i) q^{71} +(-1.64142 + 5.05178i) q^{72} +(-2.86236 + 2.07963i) q^{73} +(-0.832405 - 0.604778i) q^{74} +(0.890899 + 2.74191i) q^{75} +1.51682 q^{76} +(11.4525 + 6.22214i) q^{77} +16.8038 q^{78} +(0.218201 + 0.671554i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-2.65314 + 1.92762i) q^{81} +(-1.22226 + 3.76173i) q^{82} +(3.62801 - 11.1659i) q^{83} +(-9.16586 + 6.65938i) q^{84} +(-0.870248 - 0.632272i) q^{85} +(0.138010 + 0.424750i) q^{86} +1.09146 q^{87} +(0.605270 - 3.26093i) q^{88} +0.0446858 q^{89} +(-1.64142 - 5.05178i) q^{90} +(18.5306 + 13.4633i) q^{91} +(-4.10358 + 2.98142i) q^{92} +(-5.84937 + 18.0025i) q^{93} +(2.34686 - 7.22289i) q^{94} +(-1.22713 + 0.891565i) q^{95} +(2.33240 + 1.69459i) q^{96} +(-5.05466 - 15.5567i) q^{97} -8.44323 q^{98} +(12.7822 - 12.1234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - q^{6} - q^{7} + 2 q^{8} - 6 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + q^{13} + q^{14} - 4 q^{15} - 2 q^{16} - 12 q^{17} + q^{18} - 7 q^{19} - 2 q^{20} + 32 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - q^6 - q^7 + 2 * q^8 - 6 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + q^13 + q^14 - 4 * q^15 - 2 * q^16 - 12 * q^17 + q^18 - 7 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 26 * q^23 - q^24 - 2 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 22 * q^29 + 4 * q^30 - 26 * q^31 - 8 * q^32 + 19 * q^33 + 2 * q^34 + 4 * q^35 - q^36 - 8 * q^37 - 3 * q^38 - 48 * q^39 + 2 * q^40 - 15 * q^41 - 2 * q^42 + 38 * q^43 + 7 * q^44 + 14 * q^45 - 6 * q^46 + 6 * q^47 - 4 * q^48 + 27 * q^49 + 2 * q^50 - 5 * q^51 + 6 * q^52 - 4 * q^53 - 24 * q^54 - 8 * q^55 + 6 * q^56 + 47 * q^57 + 22 * q^58 + 39 * q^59 + q^60 - 20 * q^61 - 14 * q^62 - 57 * q^63 - 2 * q^64 - 14 * q^65 + 36 * q^66 - 26 * q^67 - 12 * q^68 - 10 * q^69 + q^70 + 2 * q^71 + 6 * q^72 + 8 * q^73 + 8 * q^74 + q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 + 14 * q^79 - 2 * q^80 - 31 * q^81 - 15 * q^82 - 21 * q^83 - 18 * q^84 + 13 * q^85 + 17 * q^86 + 20 * q^87 - 7 * q^88 + 32 * q^89 + 6 * q^90 + 53 * q^91 - 19 * q^92 - 38 * q^93 + 9 * q^94 - 7 * q^95 + 4 * q^96 - 31 * q^97 - 22 * q^98 + 36 * q^99

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