LMFDB - Embedded newform 207.2.o.a.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261583 - 0.0124607i) q^{2} +(0.845294 - 1.51178i) q^{3} +(-1.92267 - 0.183593i) q^{4} +(-3.04369 + 2.90215i) q^{5} +(-0.239952 + 0.384923i) q^{6} +(-0.702638 + 3.64563i) q^{7} +(1.01908 + 0.146521i) q^{8} +(-1.57095 - 2.55580i) q^{9} +O(q^{10})$	\(q+(-0.261583 - 0.0124607i) q^{2} +(0.845294 - 1.51178i) q^{3} +(-1.92267 - 0.183593i) q^{4} +(-3.04369 + 2.90215i) q^{5} +(-0.239952 + 0.384923i) q^{6} +(-0.702638 + 3.64563i) q^{7} +(1.01908 + 0.146521i) q^{8} +(-1.57095 - 2.55580i) q^{9} +(0.832339 - 0.721226i) q^{10} +(-3.45977 - 1.78363i) q^{11} +(-1.90278 + 2.75147i) q^{12} +(0.259083 - 0.0499342i) q^{13} +(0.229225 - 0.944880i) q^{14} +(1.81460 + 7.05455i) q^{15} +(3.52828 + 0.680021i) q^{16} +(-1.22006 + 2.67157i) q^{17} +(0.379088 + 0.688128i) q^{18} +(1.48734 - 0.679244i) q^{19} +(6.38483 - 5.02109i) q^{20} +(4.91746 + 4.14387i) q^{21} +(0.882791 + 0.509680i) q^{22} +(-3.98136 + 2.67373i) q^{23} +(1.08293 - 1.41677i) q^{24} +(0.603648 - 12.6721i) q^{25} +(-0.0683940 + 0.00983357i) q^{26} +(-5.19172 + 0.214536i) q^{27} +(2.02026 - 6.88036i) q^{28} +(0.234074 + 2.45134i) q^{29} +(-0.386763 - 1.86796i) q^{30} +(0.601339 + 0.472898i) q^{31} +(-2.91554 - 0.707302i) q^{32} +(-5.62099 + 3.72271i) q^{33} +(0.352437 - 0.683633i) q^{34} +(-8.44156 - 13.1353i) q^{35} +(2.55121 + 5.20238i) q^{36} +(1.05184 + 3.58222i) q^{37} +(-0.397526 + 0.159145i) q^{38} +(0.143512 - 0.433886i) q^{39} +(-3.52698 + 2.51155i) q^{40} +(2.75661 + 2.89105i) q^{41} +(-1.23469 - 1.14524i) q^{42} +(-4.40550 - 5.60205i) q^{43} +(6.32454 + 4.06454i) q^{44} +(12.1988 + 3.21990i) q^{45} +(1.07477 - 0.649790i) q^{46} +(-4.75835 + 2.74724i) q^{47} +(4.01048 - 4.75917i) q^{48} +(-6.29837 - 2.52149i) q^{49} +(-0.315808 + 3.30729i) q^{50} +(3.00751 + 4.10273i) q^{51} +(-0.507300 + 0.0484413i) q^{52} +(1.42625 - 1.64598i) q^{53} +(1.36074 + 0.00857370i) q^{54} +(15.7068 - 4.61194i) q^{55} +(-1.25021 + 3.61224i) q^{56} +(0.230370 - 2.82269i) q^{57} +(-0.0306844 - 0.644144i) q^{58} +(-1.82992 - 9.49452i) q^{59} +(-2.19371 - 13.8967i) q^{60} +(1.51839 + 3.79277i) q^{61} +(-0.151407 - 0.131195i) q^{62} +(10.4213 - 3.93132i) q^{63} +(-6.14149 - 1.80331i) q^{64} +(-0.643652 + 0.903883i) q^{65} +(1.51674 - 0.903756i) q^{66} +(6.13936 + 11.9087i) q^{67} +(2.83626 - 4.91255i) q^{68} +(0.676667 + 8.27902i) q^{69} +(2.04449 + 3.54117i) q^{70} +(-0.327930 + 0.510270i) q^{71} +(-1.22645 - 2.83474i) q^{72} +(6.89379 + 15.0953i) q^{73} +(-0.230505 - 0.950155i) q^{74} +(-18.6472 - 11.6243i) q^{75} +(-2.98437 + 1.03290i) q^{76} +(8.93345 - 11.3598i) q^{77} +(-0.0429469 + 0.111709i) q^{78} +(1.99885 + 0.691809i) q^{79} +(-12.7125 + 8.16984i) q^{80} +(-4.06420 + 8.03008i) q^{81} +(-0.685057 - 0.790598i) q^{82} +(8.75158 + 8.34461i) q^{83} +(-8.69388 - 8.87012i) q^{84} +(-4.03979 - 11.6722i) q^{85} +(1.08260 + 1.52030i) q^{86} +(3.90374 + 1.71823i) q^{87} +(-3.26444 - 2.32459i) q^{88} +(1.15305 + 8.01966i) q^{89} +(-3.15088 - 0.994277i) q^{90} +0.979609i q^{91} +(8.14572 - 4.40975i) q^{92} +(1.22323 - 0.509354i) q^{93} +(1.27894 - 0.659337i) q^{94} +(-2.55572 + 6.38388i) q^{95} +(-3.53377 + 3.80977i) q^{96} +(-5.87423 + 1.42507i) q^{97} +(1.61613 + 0.738060i) q^{98} +(0.876531 + 11.6445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.261583	−	0.0124607i	−0.184967	−	0.00881107i	−0.0451060	−	0.998982i	$-0.514363\pi$
$2$	−0.261583	−	0.0124607i	−0.184967	−	0.00881107i	−0.139861	+	0.990171i	$0.544666\pi$
$3$	0.845294	−	1.51178i	0.488031	−	0.872826i
$3$	0.845294	−	1.51178i	0.488031	−	0.872826i
$4$	−1.92267	−	0.183593i	−0.961337	−	0.0917965i
$5$	−3.04369	+	2.90215i	−1.36118	+	1.29788i	−0.445886	+	0.895090i	$0.647111\pi$
$5$	−3.04369	+	2.90215i	−1.36118	+	1.29788i	−0.915292	+	0.402791i	$0.868040\pi$
$6$	−0.239952	+	0.384923i	−0.0979602	+	0.157144i
$7$	−0.702638	+	3.64563i	−0.265572	+	1.37792i	0.566869	+	0.823808i	$0.308154\pi$
$7$	−0.702638	+	3.64563i	−0.265572	+	1.37792i	−0.832442	+	0.554113i	$0.813058\pi$
$8$	1.01908	+	0.146521i	0.360299	+	0.0518031i
$9$	−1.57095	−	2.55580i	−0.523652	−	0.851933i
$10$	0.832339	−	0.721226i	0.263209	−	0.228072i
$11$	−3.45977	−	1.78363i	−1.04316	−	0.537786i	−0.150543	−	0.988603i	$-0.548102\pi$
$11$	−3.45977	−	1.78363i	−1.04316	−	0.537786i	−0.892616	+	0.450817i	$0.851133\pi$
$12$	−1.90278	+	2.75147i	−0.549285	+	0.794280i
$13$	0.259083	−	0.0499342i	0.0718568	−	0.0138493i	−0.153196	−	0.988196i	$-0.548957\pi$
$13$	0.259083	−	0.0499342i	0.0718568	−	0.0138493i	0.225053	+	0.974347i	$0.427744\pi$
$14$	0.229225	−	0.944880i	0.0612631	−	0.252530i
$15$	1.81460	+	7.05455i	0.468527	+	1.82148i
$16$	3.52828	+	0.680021i	0.882071	+	0.170005i
$17$	−1.22006	+	2.67157i	−0.295909	+	0.647950i	−0.997937	−	0.0641992i	$-0.979551\pi$
$17$	−1.22006	+	2.67157i	−0.295909	+	0.647950i	0.702028	+	0.712149i	$0.252278\pi$
$18$	0.379088	+	0.688128i	0.0893519	+	0.162193i
$19$	1.48734	−	0.679244i	0.341218	−	0.155829i	−0.237434	−	0.971404i	$-0.576306\pi$
$19$	1.48734	−	0.679244i	0.341218	−	0.155829i	0.578652	+	0.815575i	$0.303579\pi$
$20$	6.38483	−	5.02109i	1.42769	−	1.12275i
$21$	4.91746	+	4.14387i	1.07308	+	0.904266i
$22$	0.882791	+	0.509680i	0.188212	+	0.108664i
$23$	−3.98136	+	2.67373i	−0.830170	+	0.557510i
$23$	−3.98136	+	2.67373i	−0.830170	+	0.557510i
$24$	1.08293	−	1.41677i	0.221052	−	0.289197i
$25$	0.603648	−	12.6721i	0.120730	−	2.53443i
$26$	−0.0683940	+	0.00983357i	−0.0134132	+	0.00192852i
$27$	−5.19172	+	0.214536i	−0.999147	+	0.0412875i
$28$	2.02026	−	6.88036i	0.381793	−	1.30027i
$29$	0.234074	+	2.45134i	0.0434665	+	0.455201i	0.990837	+	0.135063i	$0.0431235\pi$
$29$	0.234074	+	2.45134i	0.0434665	+	0.455201i	−0.947371	+	0.320139i	$0.896270\pi$
$30$	−0.386763	−	1.86796i	−0.0706130	−	0.341042i
$31$	0.601339	+	0.472898i	0.108004	+	0.0849350i	0.670700	−	0.741728i	$-0.265994\pi$
$31$	0.601339	+	0.472898i	0.108004	+	0.0849350i	−0.562697	+	0.826663i	$0.690236\pi$
$32$	−2.91554	−	0.707302i	−0.515399	−	0.125035i
$33$	−5.62099	+	3.72271i	−0.978488	+	0.648041i
$34$	0.352437	−	0.683633i	0.0604425	−	0.117242i
$35$	−8.44156	−	13.1353i	−1.42688	−	2.22028i
$36$	2.55121	+	5.20238i	0.425201	+	0.867063i
$37$	1.05184	+	3.58222i	0.172921	+	0.588914i	0.999654	+	0.0263193i	$0.00837867\pi$
$37$	1.05184	+	3.58222i	0.172921	+	0.588914i	−0.826733	+	0.562595i	$0.809803\pi$
$38$	−0.397526	+	0.159145i	−0.0644872	+	0.0258168i
$39$	0.143512	−	0.433886i	0.0229803	−	0.0694774i
$40$	−3.52698	+	2.51155i	−0.557665	+	0.397111i
$41$	2.75661	+	2.89105i	0.430510	+	0.451506i	0.902879	−	0.429895i	$-0.141450\pi$
$41$	2.75661	+	2.89105i	0.430510	+	0.451506i	−0.472369	+	0.881401i	$0.656601\pi$
$42$	−1.23469	−	1.14524i	−0.190516	−	0.176714i
$43$	−4.40550	−	5.60205i	−0.671833	−	0.854305i	0.323947	−	0.946075i	$-0.394990\pi$
$43$	−4.40550	−	5.60205i	−0.671833	−	0.854305i	−0.995780	+	0.0917702i	$0.970747\pi$
$44$	6.32454	+	4.06454i	0.953461	+	0.612752i
$45$	12.1988	+	3.21990i	1.81849	+	0.479995i
$46$	1.07477	−	0.649790i	0.158466	−	0.0958064i
$47$	−4.75835	+	2.74724i	−0.694077	+	0.400726i	−0.805138	−	0.593088i	$-0.797909\pi$
$47$	−4.75835	+	2.74724i	−0.694077	+	0.400726i	0.111061	+	0.993814i	$0.464575\pi$
$48$	4.01048	−	4.75917i	0.578863	−	0.686927i
$49$	−6.29837	−	2.52149i	−0.899767	−	0.360213i
$50$	−0.315808	+	3.30729i	−0.0446620	+	0.467721i
$51$	3.00751	+	4.10273i	0.421135	+	0.574497i
$52$	−0.507300	+	0.0484413i	−0.0703499	+	0.00671760i
$53$	1.42625	−	1.64598i	0.195910	−	0.226092i	−0.649292	−	0.760539i	$-0.724935\pi$
$53$	1.42625	−	1.64598i	0.195910	−	0.226092i	0.845202	+	0.534447i	$0.179480\pi$
$54$	1.36074	+	0.00857370i	0.185173	+	0.00116673i
$55$	15.7068	−	4.61194i	2.11791	−	0.621874i
$56$	−1.25021	+	3.61224i	−0.167066	+	0.482705i
$57$	0.230370	−	2.82269i	0.0305133	−	0.373874i
$58$	−0.0306844	−	0.644144i	−0.00402905	−	0.0845803i
$59$	−1.82992	−	9.49452i	−0.238235	−	1.23608i	−0.882144	−	0.470979i	$-0.843901\pi$
$59$	−1.82992	−	9.49452i	−0.238235	−	1.23608i	0.643909	−	0.765102i	$-0.277311\pi$
$60$	−2.19371	−	13.8967i	−0.283207	−	1.79406i
$61$	1.51839	+	3.79277i	0.194411	+	0.485614i	0.993259	−	0.115919i	$-0.0369812\pi$
$61$	1.51839	+	3.79277i	0.194411	+	0.485614i	−0.798848	+	0.601533i	$0.794557\pi$
$62$	−0.151407	−	0.131195i	−0.0192287	−	0.0166618i
$63$	10.4213	−	3.93132i	1.31296	−	0.495300i
$64$	−6.14149	−	1.80331i	−0.767687	−	0.225413i
$65$	−0.643652	+	0.903883i	−0.0798352	+	0.112113i
$66$	1.51674	−	0.903756i	0.186698	−	0.111245i
$67$	6.13936	+	11.9087i	0.750042	+	1.45488i	0.885766	+	0.464132i	$0.153634\pi$
$67$	6.13936	+	11.9087i	0.750042	+	1.45488i	−0.135724	+	0.990747i	$0.543336\pi$
$68$	2.83626	−	4.91255i	0.343948	−	0.595735i
$69$	0.676667	+	8.27902i	0.0814612	+	0.996677i
$70$	2.04449	+	3.54117i	0.244364	+	0.423250i
$71$	−0.327930	+	0.510270i	−0.0389182	+	0.0605579i	−0.860168	−	0.510012i	$-0.829641\pi$
$71$	−0.327930	+	0.510270i	−0.0389182	+	0.0605579i	0.821249	+	0.570569i	$0.193277\pi$
$72$	−1.22645	−	2.83474i	−0.144538	−	0.334077i
$73$	6.89379	+	15.0953i	0.806857	+	1.76677i	0.620365	+	0.784313i	$0.286984\pi$
$73$	6.89379	+	15.0953i	0.806857	+	1.76677i	0.186492	+	0.982457i	$0.440288\pi$
$74$	−0.230505	−	0.950155i	−0.0267957	−	0.110453i
$75$	−18.6472	−	11.6243i	−2.15319	−	1.34225i
$76$	−2.98437	+	1.03290i	−0.342330	+	0.118482i
$77$	8.93345	−	11.3598i	1.01806	−	1.29457i
$78$	−0.0429469	+	0.111709i	−0.00486278	+	0.0126485i
$79$	1.99885	+	0.691809i	0.224888	+	0.0778346i	0.437189	−	0.899370i	$-0.355974\pi$
$79$	1.99885	+	0.691809i	0.224888	+	0.0778346i	−0.212300	+	0.977205i	$0.568095\pi$
$80$	−12.7125	+	8.16984i	−1.42130	+	0.913415i
$81$	−4.06420	+	8.03008i	−0.451578	+	0.892232i
$82$	−0.685057	−	0.790598i	−0.0756519	−	0.0873069i
$83$	8.75158	+	8.34461i	0.960611	+	0.915940i	0.996515	−	0.0834149i	$-0.0265827\pi$
$83$	8.75158	+	8.34461i	0.960611	+	0.915940i	−0.0359043	+	0.999355i	$0.511431\pi$
$84$	−8.69388	−	8.87012i	−0.948580	−	0.967809i
$85$	−4.03979	−	11.6722i	−0.438177	−	1.26603i
$86$	1.08260	+	1.52030i	0.116740	+	0.163938i
$87$	3.90374	+	1.71823i	0.418525	+	0.184214i
$88$	−3.26444	−	2.32459i	−0.347990	−	0.247803i
$89$	1.15305	+	8.01966i	0.122223	+	0.850082i	0.955028	+	0.296515i	$0.0958246\pi$
$89$	1.15305	+	8.01966i	0.122223	+	0.850082i	−0.832805	+	0.553567i	$0.813266\pi$
$90$	−3.15088	−	0.994277i	−0.332131	−	0.104806i
$91$			0.979609i			0.102691i
$92$	8.14572	−	4.40975i	0.849250	−	0.459749i
$93$	1.22323	−	0.509354i	0.126843	−	0.0528175i
$94$	1.27894	−	0.659337i	0.131912	−	0.0680055i
$95$	−2.55572	+	6.38388i	−0.262211	+	0.654972i
$96$	−3.53377	+	3.80977i	−0.360664	+	0.388833i
$97$	−5.87423	+	1.42507i	−0.596438	+	0.144694i	−0.522603	−	0.852576i	$-0.675039\pi$
$97$	−5.87423	+	1.42507i	−0.596438	+	0.144694i	−0.0738351	+	0.997270i	$0.523524\pi$
$98$	1.61613	+	0.738060i	0.163253	+	0.0745554i
$99$	0.876531	+	11.6445i	0.0880947	+	1.17031i
$100$	−3.48713	+	24.2535i	−0.348713	+	2.42535i
$101$	0.493298	−	0.517356i	0.0490850	−	0.0514789i	−0.698734	−	0.715382i	$-0.746253\pi$
$101$	0.493298	−	0.517356i	0.0490850	−	0.0514789i	0.747819	+	0.663903i	$0.231101\pi$
$102$	−0.735589	−	1.11068i	−0.0728342	−	0.109974i
$103$	−16.2006	+	0.771732i	−1.59630	+	0.0760410i	−0.826758	−	0.562558i	$-0.809817\pi$
$103$	−16.2006	+	0.771732i	−1.59630	+	0.0760410i	−0.769539	+	0.638599i	$0.779514\pi$
$104$	0.271343	−	0.0129257i	0.0266074	−	0.00126746i
$105$	−26.9933	+	1.65856i	−2.63428	+	0.161859i
$106$	−0.393592	+	0.412787i	−0.0382290	+	0.0400934i
$107$	1.68209	−	11.6992i	0.162614	−	1.13100i	−0.731069	−	0.682304i	$-0.760978\pi$
$107$	1.68209	−	11.6992i	0.162614	−	1.13100i	0.893683	−	0.448700i	$-0.148113\pi$
$108$	10.0214	+	0.540681i	0.964307	+	0.0520271i
$109$	−18.0521	−	8.24414i	−1.72908	−	0.789645i	−0.993710	−	0.111981i	$-0.964280\pi$
$109$	−18.0521	−	8.24414i	−1.72908	−	0.789645i	−0.735372	−	0.677664i	$-0.762992\pi$
$110$	−4.16611	+	1.01069i	−0.397223	+	0.0963651i
$111$	6.30465	+	1.43789i	0.598410	+	0.136478i
$112$	−4.95822	+	12.3850i	−0.468507	+	1.17027i
$113$	0.270422	−	0.139412i	0.0254392	−	0.0131148i	−0.445460	−	0.895302i	$-0.646960\pi$
$113$	0.270422	−	0.139412i	0.0254392	−	0.0131148i	0.470899	+	0.882187i	$0.343930\pi$
$114$	−0.0954336	+	0.735496i	−0.00893818	+	0.0688855i
$115$	4.35844	−	19.6925i	0.406427	−	1.83633i
$116$		−	4.75609i		−	0.441592i
$117$	−0.534630	−	0.583720i	−0.0494266	−	0.0539650i
$118$	0.360367	+	2.50641i	0.0331745	+	0.230733i
$119$	−8.88229	−	6.32505i	−0.814238	−	0.579816i
$120$	0.815576	+	7.45502i	0.0744515	+	0.680547i
$121$	2.40802	+	3.38159i	0.218911	+	0.307418i
$122$	−0.349926	−	1.01104i	−0.0316808	−	0.0915356i
$123$	6.70077	−	1.72360i	0.604188	−	0.155412i
$124$	−1.06936	−	1.01963i	−0.0960311	−	0.0915655i
$125$	21.1689	+	24.4302i	1.89340	+	2.18510i
$126$	−2.77503	+	0.898510i	−0.247219	+	0.0800456i
$127$	1.05634	−	0.678868i	0.0937349	−	0.0602398i	−0.492934	−	0.870067i	$-0.664075\pi$
$127$	1.05634	−	0.678868i	0.0937349	−	0.0602398i	0.586669	+	0.809827i	$0.300439\pi$
$128$	7.25425	+	2.51072i	0.641191	+	0.221918i
$129$	−12.1930	+	1.92477i	−1.07354	+	0.169466i
$130$	0.179631	−	0.228420i	0.0157547	−	0.0200338i
$131$	6.63876	−	2.29770i	0.580031	−	0.200751i	−0.0212693	−	0.999774i	$-0.506771\pi$
$131$	6.63876	−	2.29770i	0.580031	−	0.200751i	0.601300	+	0.799023i	$0.294650\pi$
$132$	11.4908	−	6.12558i	1.00014	−	0.533164i
$133$	1.43121	+	5.89955i	0.124102	+	0.511556i
$134$	−1.45756	−	3.19161i	−0.125914	−	0.275713i
$135$	15.1794	−	15.7201i	1.30643	−	1.35297i
$136$	−1.63478	+	2.54377i	−0.140181	+	0.218127i
$137$	0.000589825		0.00102161i	5.03921e−5		8.72817e-5i	0.866051	−	0.499956i	$-0.166651\pi$
$137$	0.000589825		0.00102161i	5.03921e−5		8.72817e-5i	−0.866000	+	0.500044i	$0.833317\pi$
$138$	−0.0738420	−	2.17408i	−0.00628585	−	0.185070i
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	−0.642391	−	0.766377i	$-0.722057\pi$
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	0.984898	+	0.173138i	$0.0553908\pi$
$140$	13.8188	+	26.8048i	1.16790	+	2.26542i
$141$	0.131007	+	9.51580i	0.0110327	+	0.801375i
$142$	0.0921393	−	0.129392i	0.00773216	−	0.0108583i
$143$	−0.985433	−	0.289349i	−0.0824061	−	0.0241966i
$144$	−3.80478	−	10.0859i	−0.317065	−	0.840488i
$145$	−7.82659	−	6.78178i	−0.649963	−	0.563196i
$146$	−1.61520	−	4.03457i	−0.133675	−	0.333903i
$147$	−9.13591	+	7.39035i	−0.753517	+	0.609546i
$148$	−1.36467	−	7.08056i	−0.112175	−	0.582018i
$149$	−0.132687	−	2.78545i	−0.0108702	−	0.228193i	−0.997765	−	0.0668258i	$-0.978713\pi$
$149$	−0.132687	−	2.78545i	−0.0108702	−	0.228193i	0.986895	−	0.161367i	$-0.0515902\pi$
$150$	4.73294	+	3.27307i	0.386443	+	0.267245i
$151$	−3.05152	+	8.81680i	−0.248329	+	0.717501i	0.750092	+	0.661334i	$0.230009\pi$
$151$	−3.05152	+	8.81680i	−0.248329	+	0.717501i	−0.998421	+	0.0561671i	$0.982112\pi$
$152$	1.61524	−	0.474276i	0.131013	−	0.0384689i
$153$	8.74465	−	1.07867i	0.706963	−	0.0872057i
$154$	−2.47839	+	2.86021i	−0.199714	+	0.230482i
$155$	−3.20271	+	0.305821i	−0.257248	+	0.0245642i
$156$	−0.355586	+	0.807874i	−0.0284696	+	0.0646817i
$157$	0.421650	−	4.41572i	0.0336514	−	0.352413i	−0.962927	−	0.269761i	$-0.913055\pi$
$157$	0.421650	−	4.41572i	0.0336514	−	0.352413i	0.996579	−	0.0826514i	$-0.0263388\pi$
$158$	−0.514245	−	0.205873i	−0.0409111	−	0.0163784i
$159$	−1.28276	−	3.54751i	−0.101729	−	0.281335i
$160$	10.9267	−	6.30852i	0.863830	−	0.498732i
$161$	−6.94997	−	16.3932i	−0.547735	−	1.29197i
$162$	1.16319	−	2.04989i	0.0913886	−	0.161055i
$163$	0.905001	+	0.581609i	0.0708852	+	0.0455551i	0.575603	−	0.817729i	$-0.304767\pi$
$163$	0.905001	+	0.581609i	0.0708852	+	0.0455551i	−0.504718	+	0.863284i	$0.668404\pi$
$164$	−4.76928	−	6.06463i	−0.372418	−	0.473568i
$165$	6.30465	−	27.6437i	0.490817	−	2.15206i
$166$	−2.18528	−	2.29186i	−0.169611	−	0.177883i
$167$	12.8153	−	9.12572i	0.991676	−	0.706169i	0.0356238	−	0.999365i	$-0.488658\pi$
$167$	12.8153	−	9.12572i	0.991676	−	0.706169i	0.956052	+	0.293196i	$0.0947188\pi$
$168$	4.40411	+	4.94344i	0.339785	+	0.381395i
$169$	−12.0042	+	4.80574i	−0.923396	+	0.369672i
$170$	0.911296	+	3.10359i	0.0698932	+	0.238035i
$171$	−4.07255	−	2.73427i	−0.311435	−	0.209095i
$172$	7.44184	+	11.5797i	0.567435	+	0.882947i
$173$	−8.04110	+	15.5976i	−0.611353	+	1.18586i	0.356488	+	0.934300i	$0.383974\pi$
$173$	−8.04110	+	15.5976i	−0.611353	+	1.18586i	−0.967842	+	0.251560i	$0.919056\pi$
$174$	−0.999741	−	0.498103i	−0.0757902	−	0.0377611i
$175$	45.7738	+	11.1046i	3.46017	+	0.839429i
$176$	−10.9941	−	8.64589i	−0.828714	−	0.651708i
$177$	−15.9004	−	5.25923i	−1.19515	−	0.395308i
$178$	−0.201688	−	2.11217i	−0.0151172	−	0.158314i
$179$	−4.41110	+	15.0228i	−0.329701	+	1.12286i	0.613239	+	0.789898i	$0.289866\pi$
$179$	−4.41110	+	15.0228i	−0.329701	+	1.12286i	−0.942940	+	0.332962i	$0.891952\pi$
$180$	−22.8632	−	8.43043i	−1.70412	−	0.628367i
$181$	−2.90054	+	0.417035i	−0.215596	+	0.0309980i	−0.249266	−	0.968435i	$-0.580189\pi$
$181$	−2.90054	+	0.417035i	−0.215596	+	0.0309980i	0.0336705	+	0.999433i	$0.489280\pi$
$182$	0.0122066	−	0.256249i	0.000904817	−	0.0189944i
$183$	7.01732	+	0.910526i	0.518735	+	0.0673081i
$184$	−4.44907	+	2.14138i	−0.327990	+	0.157865i
$185$	−13.5976	−	7.85058i	−0.999716	−	0.577186i
$186$	−0.326322	+	0.117996i	−0.0239271	+	0.00865188i
$187$	8.98623	−	7.06685i	0.657139	−	0.516779i
$188$	9.65313	−	4.40844i	0.704027	−	0.321518i
$189$	2.86578	−	19.0779i	0.208455	−	1.38771i
$190$	0.748080	−	1.63807i	0.0542714	−	0.118838i
$191$	−14.4137	−	2.77802i	−1.04294	−	0.201010i	−0.361112	−	0.932522i	$-0.617603\pi$
$191$	−14.4137	−	2.77802i	−1.04294	−	0.201010i	−0.681829	+	0.731512i	$0.738815\pi$
$192$	−7.91757	+	7.76026i	−0.571401	+	0.560049i
$193$	−2.84923	+	11.7447i	−0.205092	+	0.845400i	0.772521	+	0.634989i	$0.218995\pi$
$193$	−2.84923	+	11.7447i	−0.205092	+	0.845400i	−0.977613	+	0.210411i	$0.932520\pi$
$194$	1.55436	−	0.299578i	0.111596	−	0.0215084i
$195$	0.822396	+	1.73711i	0.0588930	+	0.124397i
$196$	11.6468	+	6.00433i	0.831913	+	0.428881i
$197$	3.10535	−	2.69081i	0.221247	−	0.191712i	−0.537184	−	0.843465i	$-0.680512\pi$
$197$	3.10535	−	2.69081i	0.221247	−	0.191712i	0.758431	+	0.651753i	$0.225966\pi$
$198$	−0.0841868	−	3.05692i	−0.00598290	−	0.217246i
$199$	16.4077	+	2.35908i	1.16311	+	0.167230i	0.696717	−	0.717346i	$-0.254643\pi$
$199$	16.4077	+	2.35908i	1.16311	+	0.167230i	0.466396	+	0.884576i	$0.345552\pi$
$200$	2.47190	−	12.8254i	0.174790	−	0.906896i
$201$	23.1929	+	0.784996i	1.63590	+	0.0553693i
$202$	−0.135485	+	0.129185i	−0.00953269	+	0.00908940i
$203$	−9.10114	−	0.869054i	−0.638775	−	0.0609956i
$204$	−5.02922	−	8.44036i	−0.352116	−	0.590943i
$205$	−16.7805	−	0.799353i	−1.17200	−	0.0558293i
$206$	4.24743			0.295932
$207$	13.0880	+	5.97524i	0.909681	+	0.415308i
$208$	0.948076			0.0657373
$209$	−6.35736	−	0.302839i	−0.439748	−	0.0209478i
$210$	7.08166	−	0.0974951i	0.488681	−	0.00672780i
$211$	10.2841	+	0.982017i	0.707990	+	0.0676048i	0.442838	−	0.896602i	$-0.353972\pi$
$211$	10.2841	+	0.982017i	0.707990	+	0.0676048i	0.265152	+	0.964207i	$0.414578\pi$
$212$	−3.04440	+	2.90283i	−0.209090	+	0.199367i
$213$	0.494217	+	0.927086i	0.0338632	+	0.0635229i
$214$	−0.585786	+	3.03935i	−0.0400435	+	0.207766i
$215$	29.6670	+	4.26546i	2.02327	+	0.290902i
$216$	−5.32221	−	0.542069i	−0.362130	−	0.0368831i
$217$	−2.14654	+	1.85998i	−0.145716	+	0.126264i
$218$	4.61941	+	2.38147i	0.312866	+	0.161293i
$219$	28.6480	+	2.33808i	1.93585	+	0.157993i
$220$	−31.0458	+	5.98359i	−2.09311	+	0.403414i
$221$	−0.182696	+	0.753081i	−0.0122894	+	0.0506577i
$222$	−1.63127	−	0.454688i	−0.109484	−	0.0305167i
$223$	−17.6050	−	3.39309i	−1.17892	−	0.227218i	−0.438102	−	0.898925i	$-0.644349\pi$
$223$	−17.6050	−	3.39309i	−1.17892	−	0.227218i	−0.740817	+	0.671707i	$0.765561\pi$
$224$	4.62713	−	10.1320i	0.309163	−	0.676973i
$225$	−33.3357	+	18.3645i	−2.22238	+	1.22430i
$226$	−0.0724749	+	0.0330982i	−0.00482096	+	0.00220166i
$227$	14.9425	−	11.7509i	0.991767	−	0.779935i	0.0162526	−	0.999868i	$-0.494826\pi$
$227$	14.9425	−	11.7509i	0.991767	−	0.779935i	0.975515	+	0.219933i	$0.0705840\pi$
$228$	−0.961152	+	5.38481i	−0.0636539	+	0.356618i
$229$	−13.9991	−	8.08237i	−0.925085	−	0.534098i	−0.0398315	−	0.999206i	$-0.512682\pi$
$229$	−13.9991	−	8.08237i	−0.925085	−	0.534098i	−0.885254	+	0.465108i	$0.846015\pi$
$230$	−1.38548	+	5.09690i	−0.0913557	+	0.336080i
$231$	−9.62212	−	23.1078i	−0.633089	−	1.52038i
$232$	−0.120633	+	2.53240i	−0.00791995	+	0.166260i
$233$	−12.5681	+	1.80702i	−0.823363	+	0.118382i	−0.541103	−	0.840956i	$-0.681993\pi$
$233$	−12.5681	+	1.80702i	−0.823363	+	0.118382i	−0.282260	+	0.959338i	$0.591084\pi$
$234$	0.132577	+	0.159353i	0.00866680	+	0.0104172i
$235$	6.51004	−	22.1712i	0.424668	−	1.44629i
$236$	1.77521	+	18.5908i	0.115556	+	1.21016i
$237$	2.73548	−	2.43704i	0.177689	−	0.158303i
$238$	2.24464	+	1.76520i	0.145498	+	0.114421i
$239$	5.16143	+	1.25215i	0.333865	+	0.0809948i	0.399187	−	0.916869i	$-0.369292\pi$
$239$	5.16143	+	1.25215i	0.333865	+	0.0809948i	−0.0653221	+	0.997864i	$0.520807\pi$
$240$	1.60517	+	26.1244i	0.103614	+	1.68632i
$241$	2.66476	−	5.16892i	0.171653	−	0.332959i	−0.787279	−	0.616597i	$-0.788511\pi$
$241$	2.66476	−	5.16892i	0.171653	−	0.332959i	0.958932	+	0.283637i	$0.0915412\pi$
$242$	−0.587760	−	0.914573i	−0.0377826	−	0.0587910i
$243$	8.70427	+	12.9320i	0.558379	+	0.829586i
$244$	−2.22305	−	7.57102i	−0.142316	−	0.484685i
$245$	26.4880	−	10.6042i	1.69226	−	0.677477i
$246$	−1.77428	+	0.367367i	−0.113124	+	0.0234225i
$247$	0.351427	−	0.250250i	0.0223607	−	0.0159230i
$248$	0.543522	+	0.570029i	0.0345137	+	0.0361969i
$249$	20.0129	−	6.17680i	1.26826	−	0.391439i
$250$	−5.23300	−	6.65431i	−0.330964	−	0.420855i
$251$	−9.76049	−	6.27268i	−0.616076	−	0.395928i	0.195055	−	0.980792i	$-0.437512\pi$
$251$	−9.76049	−	6.27268i	−0.616076	−	0.395928i	−0.811131	+	0.584864i	$0.801148\pi$
$252$	−20.7586	+	5.64537i	−1.30767	+	0.355625i
$253$	18.5435	−	2.14919i	1.16582	−	0.135118i
$254$	−0.284779	+	0.164417i	−0.0178686	+	0.0103165i
$255$	−21.0606	−	3.75918i	−1.31887	−	0.235409i
$256$	10.0182	+	4.01070i	0.626140	+	0.250669i
$257$	−0.105383	+	1.10362i	−0.00657362	+	0.0688421i	−0.998163	−	0.0605782i	$-0.980706\pi$
$257$	−0.105383	+	1.10362i	−0.00657362	+	0.0688421i	0.991590	+	0.129420i	$0.0413116\pi$
$258$	3.21347	−	0.351552i	0.200062	−	0.0218867i
$259$	−13.7985	+	1.31760i	−0.857400	+	0.0818717i
$260$	1.40348	−	1.61970i	0.0870401	−	0.100450i
$261$	5.89740	−	4.44918i	0.365040	−	0.275397i
$262$	−1.76522	+	0.518314i	−0.109055	+	0.0320216i
$263$	4.49143	−	12.9771i	0.276953	−	0.800204i	−0.717646	−	0.696409i	$-0.754780\pi$
$263$	4.49143	−	12.9771i	0.276953	−	0.800204i	0.994599	−	0.103795i	$-0.0330986\pi$
$264$	−6.27368	+	2.97014i	−0.386119	+	0.182800i
$265$	0.435821	+	9.14902i	0.0267723	+	0.562020i
$266$	−0.300869	−	1.56105i	−0.0184474	−	0.0957144i
$267$	13.0986	+	5.03581i	0.801623	+	0.308187i
$268$	−9.61763	−	24.0237i	−0.587490	−	1.46748i
$269$	−9.11016	−	7.89400i	−0.555456	−	0.481305i	0.331311	−	0.943522i	$-0.392509\pi$
$269$	−9.11016	−	7.89400i	−0.555456	−	0.481305i	−0.886767	+	0.462216i	$0.847054\pi$
$270$	−4.16654	+	3.92297i	−0.253568	+	0.238744i
$271$	−16.1529	−	4.74293i	−0.981222	−	0.288113i	−0.248493	−	0.968634i	$-0.579935\pi$
$271$	−16.1529	−	4.74293i	−0.981222	−	0.288113i	−0.732729	+	0.680521i	$0.761754\pi$
$272$	−6.12145	+	8.59637i	−0.371167	+	0.521232i
$273$	1.48095	+	0.828058i	0.0896314	+	0.0501164i
$274$	−0.000141558	0	0.000274584i	−8.55184e−6	0	1.65883e-5i
$275$	−24.6909	+	42.7659i	−1.48892	+	2.57888i
$276$	0.218960	−	16.0421i	0.0131798	−	0.965620i
$277$	14.1883	+	24.5748i	0.852490	+	1.47656i	0.878954	+	0.476907i	$0.158242\pi$
$277$	14.1883	+	24.5748i	0.852490	+	1.47656i	−0.0264633	+	0.999650i	$0.508425\pi$
$278$	−1.14345	+	1.77924i	−0.0685795	+	0.106712i
$279$	0.263956	−	2.27980i	0.0158026	−	0.136488i
$280$	−6.67801	−	14.6228i	−0.399087	−	0.873880i
$281$	0.433611	+	1.78737i	0.0258671	+	0.106625i	0.983282	−	0.182091i	$-0.0582866\pi$
$281$	0.433611	+	1.78737i	0.0258671	+	0.106625i	−0.957415	+	0.288717i	$0.906771\pi$
$282$	0.0843047	−	2.49080i	0.00502027	−	0.148325i
$283$	−11.9314	+	4.12950i	−0.709249	+	0.245473i	−0.657790	−	0.753202i	$-0.728508\pi$
$283$	−11.9314	+	4.12950i	−0.709249	+	0.245473i	−0.0514592	+	0.998675i	$0.516387\pi$
$284$	0.724185	−	0.920876i	0.0429725	−	0.0546439i
$285$	7.49068	+	9.25994i	0.443710	+	0.548511i
$286$	0.254167	+	0.0879681i	0.0150292	+	0.00520166i
$287$	−12.4766	+	8.01822i	−0.736470	+	0.473301i
$288$	2.77246	+	8.56267i	0.163369	+	0.504560i
$289$	5.48392	+	6.32878i	0.322584	+	0.372281i
$290$	1.96280	+	1.87152i	0.115259	+	0.109900i
$291$	−2.81106	+	10.0852i	−0.164787	+	0.591202i
$292$	−10.4831	−	30.2890i	−0.613478	−	1.77253i
$293$	0.137444	+	0.193013i	0.00802954	+	0.0112759i	0.818571	−	0.574405i	$-0.194767\pi$
$293$	0.137444	+	0.193013i	0.00802954	+	0.0112759i	−0.810542	+	0.585681i	$0.800827\pi$
$294$	2.48189	−	1.81935i	0.144747	−	0.106107i
$295$	33.1242	+	23.5876i	1.92857	+	1.37333i
$296$	0.547031	+	3.80469i	0.0317955	+	0.221143i
$297$	18.3448	+	8.51789i	1.06447	+	0.494258i
$298$			0.730278i			0.0423039i
$299$	−0.897993	+	0.891524i	−0.0519323	+	0.0515582i
$300$	33.7183	+	25.7732i	1.94673	+	1.48801i
$301$	23.5185	−	12.1246i	1.35558	−	0.698852i
$302$	0.908090	−	2.26830i	0.0522547	−	0.130526i
$303$	−0.365146	−	1.18308i	−0.0209771	−	0.0679660i
$304$	5.70964	−	1.38514i	0.327471	−	0.0794435i
$305$	−15.6287	−	7.13739i	−0.894896	−	0.408686i
$306$	−2.30089	+	0.173198i	−0.131533	+	0.00990108i
$307$	3.74628	−	26.0559i	0.213811	−	1.48709i	−0.546460	−	0.837485i	$-0.684025\pi$
$307$	3.74628	−	26.0559i	0.213811	−	1.48709i	0.760271	−	0.649606i	$-0.225066\pi$
$308$	−19.2617	+	20.2011i	−1.09754	+	1.15106i
$309$	−12.5276	+	25.1441i	−0.712672	+	1.43040i
$310$	0.841584	−	0.0400896i	0.0477988	−	0.00227694i
$311$	14.1350	−	0.673333i	0.801522	−	0.0381812i	0.357177	−	0.934037i	$-0.383739\pi$
$311$	14.1350	−	0.673333i	0.801522	−	0.0381812i	0.444345	+	0.895856i	$0.353436\pi$
$312$	0.209824	−	0.421137i	0.0118789	−	0.0238422i
$313$	−1.05571	+	1.10720i	−0.0596722	+	0.0625824i	−0.752893	−	0.658143i	$-0.771342\pi$
$313$	−1.05571	+	1.10720i	−0.0596722	+	0.0625824i	0.693221	+	0.720725i	$0.256191\pi$
$314$	−0.165320	+	1.14982i	−0.00932952	+	0.0648883i
$315$	−20.3099	+	42.2099i	−1.14433	+	2.37826i
$316$	−3.71613	−	1.69710i	−0.209049	−	0.0954693i
$317$	18.2374	−	4.42435i	1.02432	−	0.248496i	0.311797	−	0.950149i	$-0.399069\pi$
$317$	18.2374	−	4.42435i	1.02432	−	0.248496i	0.712520	+	0.701652i	$0.247554\pi$
$318$	0.291342	+	0.943951i	0.0163377	+	0.0529341i
$319$	3.56244	−	8.89856i	0.199459	−	0.498223i
$320$	23.9262	−	12.3348i	1.33752	−	0.689538i
$321$	−16.2647	−	12.4322i	−0.907809	−	0.693898i
$322$	1.61372	+	4.37479i	0.0899293	+	0.243797i
$323$			4.80224i			0.267204i
$324$	9.28840	−	14.6931i	0.516022	−	0.816282i
$325$	−0.476378	−	3.31328i	−0.0264247	−	0.183788i
$326$	−0.229486	−	0.163416i	−0.0127100	−	0.00905077i
$327$	−27.7227	+	20.3221i	−1.53307	+	1.12382i
$328$	2.38560	+	3.35011i	0.131723	+	0.184979i
$329$	−6.67202	−	19.2775i	−0.367840	−	1.06280i
$330$	−1.99365	+	7.15256i	−0.109747	+	0.393735i
$331$	−13.7642	−	13.1242i	−0.756552	−	0.721370i	0.210040	−	0.977693i	$-0.432641\pi$
$331$	−13.7642	−	13.1242i	−0.756552	−	0.721370i	−0.966591	+	0.256322i	$0.917489\pi$
$332$	−15.2944	−	17.6507i	−0.839390	−	0.968708i
$333$	7.50305	−	8.31579i	0.411165	−	0.455703i
$334$	−3.46597	+	2.22744i	−0.189650	+	0.121880i
$335$	−53.2471	−	18.4290i	−2.90920	−	1.00688i
$336$	14.5323	+	17.9647i	0.792800	+	0.980056i
$337$	−6.80507	+	8.65335i	−0.370696	+	0.471378i	−0.935235	−	0.354028i	$-0.884812\pi$
$337$	−6.80507	+	8.65335i	−0.370696	+	0.471378i	0.564539	+	0.825407i	$0.309054\pi$
$338$	3.19996	−	1.10752i	0.174055	−	0.0602411i
$339$	0.0178256	−	0.526663i	0.000968156	−	0.0286044i
$340$	5.62426	+	23.1835i	0.305019	+	1.25730i
$341$	−1.23702	−	2.70869i	−0.0669882	−	0.146684i
$342$	1.03124	+	0.765985i	0.0557630	+	0.0414197i
$343$	−0.432867	+	0.673554i	−0.0233726	+	0.0363685i
$344$	−3.66873	−	6.35443i	−0.197805	−	0.342608i
$345$	−26.0865	−	23.2349i	−1.40445	−	1.25093i
$346$	2.29777	−	3.97986i	0.123529	−	0.213958i
$347$	5.98854	+	11.6161i	0.321482	+	0.623588i	0.993095	−	0.117315i	$-0.0374286\pi$
$347$	5.98854	+	11.6161i	0.321482	+	0.623588i	−0.671613	+	0.740902i	$0.734398\pi$
$348$	−7.19016	−	4.02030i	−0.385433	−	0.215511i
$349$	−1.25044	+	1.75600i	−0.0669348	+	0.0939967i	−0.846686	−	0.532092i	$-0.821406\pi$
$349$	−1.25044	+	1.75600i	−0.0669348	+	0.0939967i	0.779752	+	0.626089i	$0.215345\pi$
$350$	−11.8353	−	3.47515i	−0.632622	−	0.185755i
$351$	−1.33438	+	0.314827i	−0.0712237	+	0.0168042i
$352$	8.82552	+	7.64736i	0.470402	+	0.407605i
$353$	8.79217	+	21.9618i	0.467960	+	1.16891i	0.955285	+	0.295687i	$0.0955485\pi$
$353$	8.79217	+	21.9618i	0.467960	+	1.16891i	−0.487325	+	0.873221i	$0.662027\pi$
$354$	4.09375	+	1.57386i	0.217580	+	0.0836495i
$355$	−0.482761	−	2.50480i	−0.0256223	−	0.132941i
$356$	−0.744591	−	15.6309i	−0.0394632	−	0.828435i
$357$	−17.0702	+	8.08153i	−0.903452	+	0.427720i
$358$	1.34106	−	3.87475i	0.0708775	−	0.204787i
$359$	−31.0308	+	9.11147i	−1.63774	+	0.480885i	−0.965707	−	0.259633i	$-0.916398\pi$
$359$	−31.0308	+	9.11147i	−1.63774	+	0.480885i	−0.672037	+	0.740518i	$0.734580\pi$
$360$	11.9598	+	5.06872i	0.630334	+	0.267145i
$361$	−10.6916	+	12.3387i	−0.562714	+	0.649406i
$362$	0.763929	−	0.0729464i	0.0401512	−	0.00383398i
$363$	7.14771	−	0.781956i	0.375157	−	0.0410420i
$364$	0.179849	−	1.88347i	0.00942667	−	0.0987206i
$365$	−64.7913	−	25.9385i	−3.39133	−	1.35768i
$366$	−1.82426	−	0.325619i	−0.0953559	−	0.0170204i
$367$	11.6368	−	6.71851i	0.607436	−	0.350703i	−0.164525	−	0.986373i	$-0.552609\pi$
$367$	11.6368	−	6.71851i	0.607436	−	0.350703i	0.771961	+	0.635670i	$0.219276\pi$
$368$	−15.8655	+	6.72626i	−0.827048	+	0.350631i
$369$	3.05842	−	11.5870i	0.159215	−	0.603197i
$370$	3.45908	+	2.22301i	0.179829	+	0.115569i
$371$	4.99849	+	6.35610i	0.259509	+	0.329992i
$372$	−2.44538	+	0.754745i	−0.126787	+	0.0391317i
$373$	18.5467	+	19.4512i	0.960311	+	1.00714i	0.999969	+	0.00793156i	$0.00252472\pi$
$373$	18.5467	+	19.4512i	0.960311	+	1.00714i	−0.0396578	+	0.999213i	$0.512627\pi$
$374$	−2.43870	+	1.73659i	−0.126102	+	0.0897971i
$375$	54.8270	−	11.3520i	2.83126	−	0.586214i
$376$	−5.25166	+	2.10245i	−0.270834	+	0.108426i
$377$	0.183050	+	0.623412i	0.00942757	+	0.0321074i
$378$	−0.987364	+	4.95473i	−0.0507845	+	0.254844i
$379$	−10.4054	−	16.1911i	−0.534487	−	0.831679i	0.464046	−	0.885811i	$-0.346397\pi$
$379$	−10.4054	−	16.1911i	−0.534487	−	0.831679i	−0.998534	+	0.0541323i	$0.982761\pi$
$380$	6.08585	−	11.8049i	0.312197	−	0.605578i
$381$	−0.133381	−	2.17079i	−0.00683332	−	0.111213i
$382$	3.73577	+	0.906288i	0.191139	+	0.0463697i
$383$	14.9063	+	11.7224i	0.761674	+	0.598987i	0.921600	−	0.388142i	$-0.126883\pi$
$383$	14.9063	+	11.7224i	0.761674	+	0.598987i	−0.159926	+	0.987129i	$0.551125\pi$
$384$	9.92763	−	8.84452i	0.506617	−	0.451345i
$385$	5.77723	+	60.5019i	0.294435	+	3.08346i
$386$	0.891656	−	3.03670i	0.0453841	−	0.154564i
$387$	−7.39687	+	20.0601i	−0.376004	+	1.01971i
$388$	11.5559	−	1.66148i	0.586660	−	0.0843490i
$389$	−1.65809	+	34.8077i	−0.0840687	+	1.76482i	0.426035	+	0.904707i	$0.359910\pi$
$389$	−1.65809	+	34.8077i	−0.0840687	+	1.76482i	−0.510104	+	0.860113i	$0.670393\pi$
$390$	−0.193479	−	0.464645i	−0.00979720	−	0.0235282i
$391$	−2.28553	−	13.8986i	−0.115584	−	0.702881i
$392$	−6.04908	−	3.49244i	−0.305525	−	0.176395i
$393$	2.13809	−	11.9786i	0.107853	−	0.604239i
$394$	−0.845837	+	0.665174i	−0.0426127	+	0.0335110i
$395$	−8.09161	+	3.69532i	−0.407133	+	0.185932i
$396$	0.452563	−	22.5495i	0.0227421	−	1.13315i
$397$	10.4790	−	22.9457i	0.525924	−	1.15161i	−0.441224	−	0.897397i	$-0.645456\pi$
$397$	10.4790	−	22.9457i	0.525924	−	1.15161i	0.967148	−	0.254215i	$-0.0818172\pi$
$398$	−4.26259	−	0.821546i	−0.213664	−	0.0411804i
$399$	10.1286	+	2.82317i	0.507065	+	0.141335i
$400$	10.7472	−	44.3004i	0.537358	−	2.21502i
$401$	28.0713	−	5.41030i	1.40181	−	0.270177i	0.568365	−	0.822776i	$-0.307576\pi$
$401$	28.0713	−	5.41030i	1.40181	−	0.270177i	0.833447	+	0.552599i	$0.186364\pi$
$402$	−6.05708	−	0.494342i	−0.302100	−	0.0246555i
$403$	0.179411	+	0.0924927i	0.00893708	+	0.00460739i
$404$	−1.04343	+	0.904141i	−0.0519128	+	0.0449827i
$405$	−10.9343	−	36.2360i	−0.543332	−	1.80058i
$406$	2.36987	+	0.340736i	0.117615	+	0.0169105i
$407$	2.75027	−	14.2698i	0.136326	−	0.707326i
$408$	2.46375	+	4.62167i	0.121974	+	0.228807i
$409$	21.6521	−	20.6453i	1.07063	−	1.02084i	0.0709013	−	0.997483i	$-0.477412\pi$
$409$	21.6521	−	20.6453i	1.07063	−	1.02084i	0.999727	−	0.0233589i	$-0.00743603\pi$
$410$	4.37953	+	0.418194i	0.216290	+	0.0206532i
$411$	0.00204302		2.81268e-5i	0.000100775		1.38739e-6i
$412$	31.2902	+	1.49054i	1.54156	+	0.0734335i
$413$	35.8993			1.76649
$414$	−3.34915	−	1.72611i	−0.164602	−	0.0848335i
$415$	−50.8544			−2.49634
$416$	−0.790686	−	0.0376650i	−0.0387666	−	0.00184668i
$417$	−7.16028	−	12.0168i	−0.350641	−	0.588468i
$418$	1.65920	+	0.158435i	0.0811543	+	0.00774930i
$419$	9.41010	−	8.97251i	0.459713	−	0.438336i	−0.424494	−	0.905431i	$-0.639548\pi$
$419$	9.41010	−	8.97251i	0.459713	−	0.438336i	0.884207	+	0.467095i	$0.154699\pi$
$420$	52.2039	+	1.76691i	2.54729	+	0.0862165i
$421$	−0.793744	+	4.11834i	−0.0386847	+	0.200715i	−0.996129	−	0.0879025i	$-0.971984\pi$
$421$	−0.793744	+	4.11834i	−0.0386847	+	0.200715i	0.957444	+	0.288618i	$0.0931957\pi$
$422$	−2.67792	−	0.385027i	−0.130359	−	0.0187428i
$423$	14.4965	+	7.84560i	0.704846	+	0.381466i
$424$	1.69463	−	1.46840i	0.0822984	−	0.0713120i
$425$	33.1179	+	17.0735i	1.60646	+	0.828185i
$426$	−0.117727	−	0.248668i	−0.00570387	−	0.0120480i
$427$	−14.8939	+	2.87057i	−0.720768	+	0.138917i
$428$	−5.38200	+	22.1849i	−0.260149	+	1.07235i
$429$	−1.27041	+	1.24517i	−0.0613361	+	0.0601175i
$430$	−7.70722	−	1.48544i	−0.371675	−	0.0716345i
$431$	8.23138	−	18.0242i	0.396491	−	0.868195i	−0.601123	−	0.799157i	$-0.705280\pi$
$431$	8.23138	−	18.0242i	0.396491	−	0.868195i	0.997614	−	0.0690383i	$-0.0219931\pi$
$432$	−18.4638	−	2.77354i	−0.888338	−	0.133442i
$433$	−2.39698	+	1.09467i	−0.115192	+	0.0526063i	−0.472177	−	0.881504i	$-0.656532\pi$
$433$	−2.39698	+	1.09467i	−0.115192	+	0.0526063i	0.356986	+	0.934110i	$0.383805\pi$
$434$	0.584674	−	0.459793i	0.0280653	−	0.0220708i
$435$	−16.8683	+	6.09948i	−0.808774	+	0.292448i
$436$	33.1948	+	19.1650i	1.58974	+	0.917839i
$437$	−4.10550	+	6.68104i	−0.196393	+	0.319598i
$438$	−7.46470	−	0.968576i	−0.356677	−	0.0462804i
$439$	0.281569	−	5.91086i	0.0134386	−	0.282110i	−0.982138	−	0.188160i	$-0.939748\pi$
$439$	0.281569	−	5.91086i	0.0134386	−	0.282110i	0.995577	−	0.0939499i	$-0.0299494\pi$
$440$	16.6822	−	2.39854i	0.795295	−	0.114346i
$441$	3.45005	+	20.0585i	0.164288	+	0.955167i
$442$	0.0571740	−	0.194717i	0.00271949	−	0.00926173i
$443$	−0.906099	−	9.48910i	−0.0430501	−	0.450841i	−0.991138	−	0.132834i	$-0.957592\pi$
$443$	−0.906099	−	9.48910i	−0.0430501	−	0.450841i	0.948088	−	0.318007i	$-0.103014\pi$
$444$	−11.8578	−	3.92208i	−0.562746	−	0.186134i
$445$	−26.7838	−	21.0630i	−1.26967	−	0.998482i
$446$	4.56289	+	1.10695i	0.216059	+	0.0524154i
$447$	−4.32314	−	2.15393i	−0.204477	−	0.101877i
$448$	10.8894	−	21.1226i	0.514478	−	0.997947i
$449$	7.65255	+	11.9076i	0.361146	+	0.561954i	0.973517	−	0.228617i	$-0.0734202\pi$
$449$	7.65255	+	11.9076i	0.361146	+	0.561954i	−0.612370	+	0.790571i	$0.709784\pi$
$450$	8.94888	−	4.38846i	0.421854	−	0.206874i
$451$	−4.38065	−	14.9191i	−0.206277	−	0.702514i
$452$	−0.545528	+	0.218396i	−0.0256595	+	0.0102725i
$453$	10.7496	+	12.0660i	0.505061	+	0.566911i
$454$	−4.05512	+	2.88764i	−0.190316	+	0.135524i
$455$	−2.84297	−	2.98162i	−0.133281	−	0.139781i
$456$	0.648349	−	2.84278i	0.0303617	−	0.133126i
$457$	21.1977	+	26.9551i	0.991586	+	1.26090i	0.965271	+	0.261251i	$0.0841350\pi$
$457$	21.1977	+	26.9551i	0.991586	+	1.26090i	0.0263154	+	0.999654i	$0.491623\pi$
$458$	3.56121	+	2.28865i	0.166404	+	0.106942i
$459$	5.76108	−	14.1318i	0.268904	−	0.659615i
$460$	−11.9953	+	37.0620i	−0.559282	+	1.72803i
$461$	23.9595	−	13.8330i	1.11590	−	0.644267i	0.175551	−	0.984470i	$-0.443829\pi$
$461$	23.9595	−	13.8330i	1.11590	−	0.644267i	0.940352	+	0.340203i	$0.110496\pi$
$462$	2.22904	+	6.16450i	0.103704	+	0.286798i
$463$	0.173922	+	0.0696279i	0.00808285	+	0.00323588i	0.375700	−	0.926741i	$-0.377402\pi$
$463$	0.173922	+	0.0696279i	0.00808285	+	0.00323588i	−0.367618	+	0.929977i	$0.619826\pi$
$464$	−0.841079	+	8.80818i	−0.0390461	+	0.408910i
$465$	−2.24490	+	5.10030i	−0.104105	+	0.236521i
$466$	3.31012	−	0.316078i	0.153338	−	0.0146420i
$467$	18.8588	−	21.7643i	0.872683	−	1.00713i	−0.127201	−	0.991877i	$-0.540599\pi$
$467$	18.8588	−	21.7643i	0.872683	−	1.00713i	0.999884	−	0.0152530i	$-0.00485537\pi$
$468$	0.920752	+	1.22046i	0.0425618	+	0.0564157i
$469$	−47.7285	+	14.0143i	−2.20390	+	0.647122i
$470$	−1.97918	+	5.71848i	−0.0912930	+	0.263774i
$471$	−6.31918	−	4.37003i	−0.291172	−	0.201360i
$472$	−0.473681	−	9.94379i	−0.0218029	−	0.457700i
$473$	5.25000	+	27.2396i	0.241395	+	1.25248i
$474$	−0.745923	+	0.603402i	−0.0342614	+	0.0277152i
$475$	−7.70964	−	19.2577i	−0.353742	−	0.883606i
$476$	15.9165	+	13.7917i	0.729532	+	0.632143i
$477$	−6.44735	−	1.05944i	−0.295204	−	0.0485086i
$478$	−1.33454	−	0.391856i	−0.0610404	−	0.0179231i
$479$	−8.11157	+	11.3911i	−0.370627	+	0.520473i	−0.957201	−	0.289422i	$-0.906537\pi$
$479$	−8.11157	+	11.3911i	−0.370627	+	0.520473i	0.586574	+	0.809895i	$0.300476\pi$
$480$	−0.300833	−	21.8513i	−0.0137311	−	0.997370i
$481$	0.451389	+	0.875572i	0.0205816	+	0.0399227i
$482$	−0.761465	+	1.31890i	−0.0346838	+	0.0600741i
$483$	−30.6577	−	3.35027i	−1.39497	−	0.152443i
$484$	−4.00900	−	6.94379i	−0.182227	−	0.315627i
$485$	13.7436	−	21.3854i	0.624062	−	0.971060i
$486$	−2.11575	−	3.49124i	−0.0959722	−	0.158366i
$487$	5.80138	+	12.7033i	0.262886	+	0.575639i	0.994339	−	0.106252i	$-0.0338850\pi$
$487$	5.80138	+	12.7033i	0.262886	+	0.575639i	−0.731454	+	0.681891i	$0.761158\pi$
$488$	0.991643	+	4.08761i	0.0448895	+	0.185037i
$489$	1.64426	−	0.876531i	0.0743559	−	0.0396381i
$490$	−7.06094	+	2.44382i	−0.318981	+	0.110400i
$491$	−8.31954	+	10.5792i	−0.375455	+	0.477430i	−0.936657	−	0.350249i	$-0.886097\pi$
$491$	−8.31954	+	10.5792i	−0.375455	+	0.477430i	0.561201	+	0.827679i	$0.310339\pi$
$492$	−13.1998	+	2.08370i	−0.595094	+	0.0939404i
$493$	−6.83449	−	2.36544i	−0.307810	−	0.106534i
$494$	−0.0950455	+	0.0610820i	−0.00427630	+	0.00274821i
$495$	−36.4619	−	32.8983i	−1.63884	−	1.47867i
$496$	1.80011	+	2.07744i	0.0808275	+	0.0932799i
$497$	−1.62984	−	1.55405i	−0.0731083	−	0.0697086i
$498$	−5.31199	+	1.36637i	−0.238036	+	0.0612285i
$499$	−5.22670	−	15.1016i	−0.233979	−	0.676039i	−0.999469	−	0.0325903i	$-0.989624\pi$
$499$	−5.22670	−	15.1016i	−0.233979	−	0.676039i	0.765490	−	0.643448i	$-0.222497\pi$
$500$	−36.2157	−	50.8578i	−1.61961	−	2.27443i
$501$	−2.96339	−	27.0878i	−0.132395	−	1.21019i
$502$	2.47501	+	1.76245i	0.110465	+	0.0786620i
$503$	−1.81756	−	12.6414i	−0.0810410	−	0.563653i	−0.989373	−	0.145402i	$-0.953552\pi$
$503$	−1.81756	−	12.6414i	−0.0810410	−	0.563653i	0.908332	−	0.418251i	$-0.137357\pi$
$504$	11.1962	−	2.47938i	0.498717	−	0.110441i
$505$			3.00630i			0.133778i
$506$	−4.87745	+	0.331126i	−0.216829	+	0.0147203i
$507$	−2.88183	+	22.2099i	−0.127986	+	0.986376i
$508$	−2.15563	+	1.11130i	−0.0956406	+	0.0493062i
$509$	−5.27664	+	13.1804i	−0.233883	+	0.584211i	−0.998157	−	0.0606799i	$-0.980673\pi$
$509$	−5.27664	+	13.1804i	−0.233883	+	0.584211i	0.764274	+	0.644891i	$0.223097\pi$
$510$	5.46226	+	1.24577i	0.241873	+	0.0551635i
$511$	−59.8757	+	14.5257i	−2.64875	+	0.642579i
$512$	−16.5361	−	7.55178i	−0.730799	−	0.333745i
$513$	−7.57611	+	3.84553i	−0.334494	+	0.169784i
$514$	0.0413184	−	0.287376i	0.00182248	−	0.0126756i
$515$	47.0700	−	49.3656i	2.07415	−	2.17531i
$516$	23.7966	−	1.46214i	1.04759	−	0.0643672i
$517$	21.3629	−	1.01764i	0.939538	−	0.0447557i
$518$	3.62588	−	0.172722i	0.159312	−	0.00758897i
$519$	16.7830	+	25.3409i	0.736691	+	1.11234i
$520$	−0.788370	+	0.826819i	−0.0345723	+	0.0362584i
$521$	−5.63432	+	39.1875i	−0.246844	+	1.71684i	0.369390	+	0.929274i	$0.379567\pi$
$521$	−5.63432	+	39.1875i	−0.246844	+	1.71684i	−0.616234	+	0.787563i	$0.711343\pi$
$522$	−1.59810	+	1.09034i	−0.0699469	+	0.0477231i
$523$	10.2065	+	4.66115i	0.446299	+	0.203818i	0.625870	−	0.779927i	$-0.284744\pi$
$523$	10.2065	+	4.66115i	0.446299	+	0.203818i	−0.179572	+	0.983745i	$0.557471\pi$
$524$	−13.1860	+	3.19889i	−0.576033	+	0.139744i
$525$	55.4800	−	59.8132i	2.42135	−	2.61046i
$526$	−1.33658	+	3.33863i	−0.0582779	+	0.145571i
$527$	−1.99705	+	1.02955i	−0.0869928	+	0.0448479i
$528$	−22.3640	+	9.31239i	−0.973266	+	0.405270i
$529$	8.70238	−	21.2901i	0.378364	−	0.925657i
$530$		−	2.39866i		−	0.104191i
$531$	−21.3914	+	19.5924i	−0.928306	+	0.850236i
$532$	−1.66864	−	11.6057i	−0.0723448	−	0.503169i
$533$	0.858553	+	0.611373i	0.0371881	+	0.0264815i
$534$	−3.36363	−	1.48050i	−0.145558	−	0.0640675i
$535$	28.8330	+	40.4903i	1.24656	+	1.75055i
$536$	4.51161	+	13.0354i	0.194872	+	0.563045i
$537$	18.9825	+	19.3673i	0.819157	+	0.835762i
$538$	2.28470	+	2.17845i	0.0985003	+	0.0939198i
$539$	17.2935	+	19.9578i	0.744884	+	0.859642i
$540$	−32.0711	+	27.4379i	−1.38012	+	1.18074i
$541$	−20.8576	+	13.4044i	−0.896739	+	0.576299i	−0.905822	−	0.423659i	$-0.860745\pi$
$541$	−20.8576	+	13.4044i	−0.896739	+	0.576299i	0.00908220	+	0.999959i	$0.497109\pi$
$542$	4.16624	+	1.44195i	0.178955	+	0.0619370i
$543$	−1.82135	+	4.73750i	−0.0781615	+	0.203306i
$544$	5.44674	−	6.92610i	0.233527	−	0.296954i
$545$	78.8708	−	27.2974i	3.37845	−	1.16929i
$546$	−0.377074	−	0.235060i	−0.0161373	−	0.0100596i
$547$	−6.92108	−	28.5291i	−0.295924	−	1.21981i	−0.904553	−	0.426360i	$-0.859796\pi$
$547$	−6.92108	−	28.5291i	−0.295924	−	1.21981i	0.608630	−	0.793455i	$-0.291720\pi$
$548$	−0.000946481	−	0.00207250i	−4.04316e−5	−	8.85330e-5i
$549$	7.30822	−	9.83898i	0.311907	−	0.419917i
$550$	6.99162	−	10.8792i	0.298124	−	0.463889i
$551$	2.01320	+	3.48697i	0.0857652	+	0.148550i
$552$	−0.523476	+	8.53612i	−0.0222806	+	0.363321i
$553$	−3.92655	+	6.80099i	−0.166974	+	0.289208i
$554$	−3.40519	−	6.60514i	−0.144673	−	0.280626i
$555$	−23.3623	+	13.9205i	−0.991676	+	0.590894i
$556$	−9.04802	+	12.7062i	−0.383721	+	0.538861i
$557$	1.53026	+	0.449323i	0.0648390	+	0.0190384i	0.313991	−	0.949426i	$-0.398334\pi$
$557$	1.53026	+	0.449323i	0.0648390	+	0.0190384i	−0.249152	+	0.968464i	$0.580152\pi$
$558$	−0.0974543	+	0.593068i	−0.00412557	+	0.0251066i
$559$	−1.42113	−	1.23141i	−0.0601073	−	0.0520832i
$560$	−20.8519	−	52.0856i	−0.881155	−	2.20102i
$561$	−3.08751	−	19.5588i	−0.130355	−	0.825772i
$562$	−0.0911533	−	0.472948i	−0.00384507	−	0.0199501i
$563$	−1.02486	−	21.5145i	−0.0431928	−	0.906728i	−0.911651	−	0.410966i	$-0.865192\pi$
$563$	−1.02486	−	21.5145i	−0.0431928	−	0.906728i	0.868458	−	0.495763i	$-0.165111\pi$
$564$	1.49515	−	18.3198i	0.0629573	−	0.771404i
$565$	−0.418484	+	1.20913i	−0.0176058	+	0.0508685i
$566$	3.17251	−	0.931533i	0.133351	−	0.0391553i
$567$	−26.4191	−	20.4588i	−1.10950	−	0.859191i
$568$	−0.408952	+	0.471956i	−0.0171593	+	0.0198028i
$569$	−30.3144	+	2.89467i	−1.27084	+	0.121351i	−0.708594	−	0.705616i	$-0.750670\pi$
$569$	−30.3144	+	2.89467i	−1.27084	+	0.121351i	−0.562250	+	0.826967i	$0.690064\pi$
$570$	−1.84405	−	2.51558i	−0.0772387	−	0.105366i
$571$	−2.97623	+	31.1685i	−0.124551	+	1.30436i	0.689805	+	0.723996i	$0.257696\pi$
$571$	−2.97623	+	31.1685i	−0.124551	+	1.30436i	−0.814356	+	0.580366i	$0.802910\pi$
$572$	1.84154	+	0.737243i	0.0769988	+	0.0308257i
$573$	−16.3836	+	19.4421i	−0.684435	+	0.812207i
$574$	3.36358	−	1.94196i	0.140393	−	0.0810559i
$575$	31.4785	+	52.0662i	1.31274	+	2.17131i
$576$	5.03913	+	18.5293i	0.209964	+	0.772055i
$577$	26.1902	+	16.8314i	1.09031	+	0.700701i	0.956917	−	0.290362i	$-0.0937758\pi$
$577$	26.1902	+	16.8314i	1.09031	+	0.700701i	0.133395	+	0.991063i	$0.457412\pi$
$578$	−1.35564	−	1.72384i	−0.0563872	−	0.0717021i
$579$	15.3469	+	14.2351i	0.637796	+	0.591591i
$580$	13.8029	+	14.4761i	0.573134	+	0.601085i
$581$	−36.5706	+	26.0418i	−1.51720	+	1.08040i
$582$	0.860994	−	2.60308i	0.0356893	−	0.107901i
$583$	−7.87031	+	3.15080i	−0.325955	+	0.130493i
$584$	4.81353	+	16.3934i	0.199185	+	0.678363i
$585$	3.32129	+	0.225085i	0.137318	+	0.00930613i
$586$	−0.0335478	−	0.0522014i	−0.00138585	−	0.00215642i
$587$	−10.3454	+	20.0672i	−0.426999	+	0.828262i	0.572963	+	0.819581i	$0.305794\pi$
$587$	−10.3454	+	20.0672i	−0.426999	+	0.828262i	−0.999962	+	0.00868140i	$0.997237\pi$
$588$	18.9222	−	12.5319i	0.780338	−	0.516808i
$589$	1.21561	+	0.294903i	0.0500882	+	0.0121513i
$590$	−8.37081	−	6.58288i	−0.344621	−	0.271013i
$591$	−1.44297	−	6.96913i	−0.0593557	−	0.286672i
$592$	1.27519	+	13.3544i	0.0524099	+	0.548861i
$593$	−0.429753	+	1.46360i	−0.0176478	+	0.0601030i	−0.967846	−	0.251543i	$-0.919062\pi$
$593$	−0.429753	+	1.46360i	−0.0176478	+	0.0601030i	0.950198	+	0.311646i	$0.100880\pi$
$594$	−4.69255	−	2.45672i	−0.192538	−	0.100801i
$595$	45.3911	−	6.52626i	1.86085	−	0.267551i
$596$	−0.256274	+	5.37986i	−0.0104974	+	0.220368i
$597$	17.4358	−	22.8108i	0.713598	−	0.933582i
$598$	0.246009	−	0.222018i	0.0100600	−	0.00907898i
$599$	24.7668	+	14.2991i	1.01195	+	0.584247i	0.911761	−	0.410722i	$-0.134723\pi$
$599$	24.7668	+	14.2991i	1.01195	+	0.584247i	0.100185	+	0.994969i	$0.468057\pi$
$600$	−17.2998	−	14.5783i	−0.706260	−	0.595155i
$601$	−7.53928	+	5.92896i	−0.307534	+	0.241847i	−0.759983	−	0.649943i	$-0.774793\pi$
$601$	−7.53928	+	5.92896i	−0.307534	+	0.241847i	0.452449	+	0.891790i	$0.350550\pi$
$602$	−6.30312	+	2.87854i	−0.256896	+	0.117320i
$603$	20.7916	−	34.3990i	0.846698	−	1.40083i
$604$	7.48578	−	16.3916i	0.304592	−	0.666964i
$605$	−17.1431	−	3.30407i	−0.696968	−	0.134330i
$606$	0.0807741	+	0.314023i	0.00328122	+	0.0127563i
$607$	−9.90570	+	40.8318i	−0.402060	+	1.65731i	0.306657	+	0.951820i	$0.400790\pi$
$607$	−9.90570	+	40.8318i	−0.402060	+	1.65731i	−0.708717	+	0.705493i	$0.750726\pi$
$608$	−4.81682	+	0.928365i	−0.195348	+	0.0376502i
$609$	−9.00696	+	13.0243i	−0.364980	+	0.527772i
$610$	3.99926	+	2.06176i	0.161925	+	0.0834783i
$611$	−1.09563	+	0.949368i	−0.0443244	+	0.0384073i
$612$	−17.0111	+	0.468483i	−0.687634	+	0.0189373i
$613$	−14.7166	−	2.11593i	−0.594399	−	0.0854617i	−0.161451	−	0.986881i	$-0.551618\pi$
$613$	−14.7166	−	2.11593i	−0.594399	−	0.0854617i	−0.432948	+	0.901419i	$0.642527\pi$
$614$	−1.30464	+	6.76911i	−0.0526509	+	0.273179i
$615$	−15.3929	+	24.6927i	−0.620702	+	0.995707i
$616$	10.7683	−	10.2676i	0.433869	−	0.413693i
$617$	−25.8710	−	2.47038i	−1.04153	−	0.0994536i	−0.439751	−	0.898120i	$-0.644933\pi$
$617$	−25.8710	−	2.47038i	−1.04153	−	0.0994536i	−0.601775	+	0.798666i	$0.705539\pi$
$618$	3.59033	−	6.42118i	0.144424	−	0.258298i
$619$	14.9413	+	0.711739i	0.600540	+	0.0286072i	0.345651	−	0.938363i	$-0.387658\pi$
$619$	14.9413	+	0.711739i	0.600540	+	0.0286072i	0.254889	+	0.966970i	$0.417961\pi$
$620$	6.21391			0.249557
$621$	20.0965	−	14.7354i	0.806444	−	0.591311i
$622$	−3.70586			−0.148592
$623$	−30.0469	−	1.43131i	−1.20380	−	0.0573443i
$624$	0.801404	−	1.43328i	0.0320818	−	0.0573772i
$625$	−72.1863	−	6.89296i	−2.88745	−	0.275718i
$626$	0.289952	−	0.276469i	0.0115888	−	0.0110499i
$627$	−5.83167	+	9.35494i	−0.232894	+	0.373600i
$628$	−1.62139	+	8.41258i	−0.0647006	+	0.335698i
$629$	−10.8535	−	1.56049i	−0.432756	−	0.0622209i
$630$	5.83870	−	10.7883i	0.232619	−	0.429817i
$631$	1.81259	−	1.57062i	0.0721583	−	0.0625255i	−0.618035	−	0.786151i	$-0.712071\pi$
$631$	1.81259	−	1.57062i	0.0721583	−	0.0625255i	0.690193	+	0.723625i	$0.257526\pi$
$632$	1.93562	+	0.997883i	0.0769949	+	0.0396937i
$633$	10.1777	−	14.7173i	0.404528	−	0.584959i
$634$	−4.82573	+	0.930084i	−0.191654	+	0.0369383i
$635$	−1.24499	+	5.13191i	−0.0494059	+	0.203654i
$636$	1.81502	+	7.05620i	0.0719703	+	0.279797i
$637$	−1.75771	−	0.338771i	−0.0696431	−	0.0134226i
$638$	−1.04276	+	2.28332i	−0.0412831	+	0.0903975i
$639$	1.81931	+	0.0365131i	0.0719708	+	0.00144444i
$640$	−29.3661	+	13.4111i	−1.16080	+	0.530119i
$641$	−0.957930	+	0.753324i	−0.0378360	+	0.0297545i	−0.636898	−	0.770948i	$-0.719783\pi$
$641$	−0.957930	+	0.753324i	−0.0378360	+	0.0297545i	0.599062	+	0.800703i	$0.295540\pi$
$642$	4.09966	+	3.45472i	0.161801	+	0.136347i
$643$	14.1568	+	8.17341i	0.558288	+	0.322328i	0.752458	−	0.658640i	$-0.228868\pi$
$643$	14.1568	+	8.17341i	0.558288	+	0.322328i	−0.194170	+	0.980968i	$0.562201\pi$
$644$	10.3528	+	32.7948i	0.407959	+	1.29230i
$645$	31.5258	−	41.2443i	1.24133	−	1.62399i
$646$	0.0598394	−	1.25618i	0.00235435	−	0.0494239i
$647$	−15.7972	+	2.27130i	−0.621053	+	0.0892939i	−0.445657	−	0.895204i	$-0.647030\pi$
$647$	−15.7972	+	2.27130i	−0.621053	+	0.0892939i	−0.175396	+	0.984498i	$0.556121\pi$
$648$	−5.31832	+	7.58780i	−0.208923	+	0.298077i
$649$	−10.6037	+	36.1128i	−0.416230	+	1.41755i
$650$	0.0833264	+	0.872634i	0.00326833	+	0.0342275i
$651$	0.997431	+	4.81733i	0.0390924	+	0.188806i
$652$	−1.63324	−	1.28440i	−0.0639627	−	0.0503008i
$653$	30.0751	+	7.29613i	1.17693	+	0.285520i	0.776086	−	0.630627i	$-0.217202\pi$
$653$	30.0751	+	7.29613i	1.17693	+	0.285520i	0.400843	+	0.916147i	$0.368717\pi$
$654$	7.50501	−	4.97048i	0.293469	−	0.194361i
$655$	−13.5380	+	26.2601i	−0.528975	+	1.02607i
$656$	7.76012	+	12.0750i	0.302982	+	0.471449i
$657$	27.7507	−	41.3331i	1.08266	−	1.61256i
$658$	1.50507	+	5.12581i	0.0586739	+	0.199825i
$659$	−7.82109	+	3.13109i	−0.304666	+	0.121970i	−0.518958	−	0.854800i	$-0.673680\pi$
$659$	−7.82109	+	3.13109i	−0.304666	+	0.121970i	0.214292	+	0.976770i	$0.431256\pi$
$660$	−17.1970	+	51.9923i	−0.669392	+	2.02380i
$661$	9.30455	−	6.62574i	0.361905	−	0.257712i	−0.384611	−	0.923079i	$-0.625664\pi$
$661$	9.30455	−	6.62574i	0.361905	−	0.257712i	0.746516	+	0.665367i	$0.231725\pi$
$662$	3.43696	+	3.60458i	0.133581	+	0.140096i
$663$	0.984061	+	0.912771i	0.0382178	+	0.0354491i
$664$	7.69588	+	9.78611i	0.298658	+	0.379775i
$665$	−21.4775	−	13.8028i	−0.832863	−	0.535249i
$666$	−2.06629	+	2.08178i	−0.0800672	+	0.0806672i
$667$	−7.48613	−	9.13379i	−0.289864	−	0.353662i
$668$	−26.3150	+	15.1930i	−1.01816	+	0.587834i
$669$	−20.0110	+	23.7467i	−0.773671	+	0.918102i
$670$	13.6989	+	5.48421i	0.529234	+	0.211873i
$671$	1.51162	−	15.8304i	0.0583553	−	0.611124i
$672$	−11.4061	−	15.5597i	−0.439999	−	0.600230i
$673$	−18.6263	+	1.77859i	−0.717990	+	0.0685598i	−0.447655	−	0.894206i	$-0.647741\pi$
$673$	−18.6263	+	1.77859i	−0.717990	+	0.0685598i	−0.270335	+	0.962766i	$0.587135\pi$
$674$	1.88792	−	2.17877i	0.0727199	−	0.0839232i
$675$	−0.415344	+	65.9197i	−0.0159866	+	2.53725i
$676$	23.9624	−	7.03599i	0.921629	−	0.270615i
$677$	14.1329	−	40.8342i	0.543170	−	1.56939i	−0.254992	−	0.966943i	$-0.582073\pi$
$677$	14.1329	−	40.8342i	0.543170	−	1.56939i	0.798162	−	0.602443i	$-0.205806\pi$
$678$	−0.0112255	+	0.137544i	−0.000431112	+	0.00528234i
$679$	−1.06784	−	22.4166i	−0.0409798	−	0.860271i
$680$	−2.40664	−	12.4868i	−0.0922903	−	0.478848i
$681$	−5.13397	−	32.5227i	−0.196734	−	1.24627i
$682$	0.289830	+	0.723960i	0.0110982	+	0.0277219i
$683$	21.8205	+	18.9076i	0.834940	+	0.723479i	0.963352	−	0.268241i	$-0.0864425\pi$
$683$	21.8205	+	18.9076i	0.834940	+	0.723479i	−0.128412	+	0.991721i	$0.540988\pi$
$684$	7.32819	+	6.00480i	0.280200	+	0.229599i
$685$	−0.00476010	−	0.00139769i	−0.000181874	−	5.34030e-5i
$686$	0.121624	−	0.170796i	0.00464361	−	0.00652104i
$687$	−24.0521	+	14.3315i	−0.917645	+	0.546782i
$688$	−11.7343	−	22.7615i	−0.447368	−	0.867773i
$689$	0.287326	−	0.497664i	0.0109463	−	0.0189595i
$690$	6.53426	+	6.40292i	0.248755	+	0.243755i
$691$	7.76050	+	13.4416i	0.295223	+	0.511342i	0.975037	−	0.222043i	$-0.0712726\pi$
$691$	7.76050	+	13.4416i	0.295223	+	0.511342i	−0.679813	+	0.733385i	$0.737939\pi$
$692$	18.3240	−	28.5127i	0.696574	−	1.08389i
$693$	−43.0674	−	4.98635i	−1.63599	−	0.189416i
$694$	−1.42175	−	3.11321i	−0.0539691	−	0.118176i
$695$	8.00747	+	33.0072i	0.303741	+	1.25204i
$696$	3.72646	+	2.32299i	0.141251	+	0.0880529i
$697$	−11.0869	+	3.83720i	−0.419945	+	0.145344i
$698$	0.348976	−	0.443759i	0.0132089	−	0.0167965i
$699$	−7.89193	+	20.5277i	−0.298500	+	0.776427i
$700$	−85.9693	−	29.7543i	−3.24933	−	1.12461i
$701$	−9.56055	+	6.14419i	−0.361097	+	0.232063i	−0.708591	−	0.705619i	$-0.750669\pi$
$701$	−9.56055	+	6.14419i	−0.361097	+	0.232063i	0.347494	+	0.937682i	$0.387033\pi$
$702$	0.352973	−	0.0657262i	0.0133221	−	0.00248067i
$703$	3.99764	+	4.61352i	0.150774	+	0.174002i
$704$	18.0317	+	17.1932i	0.679596	+	0.647993i
$705$	−28.0150	−	28.5829i	−1.05511	−	1.07649i
$706$	−2.02622	−	5.85438i	−0.0762578	−	0.220333i
$707$	1.53948	+	2.16190i	0.0578982	+	0.0813066i
$708$	29.6058	+	13.0310i	1.11265	+	0.489735i
$709$	−12.2578	−	8.72875i	−0.460352	−	0.327815i	0.326242	−	0.945286i	$-0.394218\pi$
$709$	−12.2578	−	8.72875i	−0.460352	−	0.327815i	−0.786593	+	0.617471i	$0.788157\pi$
$710$	0.0950704	+	0.661229i	0.00356793	+	0.0248155i
$711$	−1.37198	−	6.19546i	−0.0514533	−	0.232348i
$712$			8.34161i			0.312615i
$713$	−3.65854	−	0.274960i	−0.137014	−	0.0102973i
$714$	4.56598	−	1.90128i	0.170878	−	0.0711537i
$715$	3.83908	−	1.97919i	0.143574	−	0.0740173i
$716$	11.2392	−	28.0742i	0.420029	−	1.04918i
$717$	6.25590	−	6.74451i	0.233631	−	0.251878i
$718$	8.23067	−	1.99674i	0.307166	−	0.0745176i
$719$	−16.0632	−	7.33582i	−0.599057	−	0.273580i	0.0927192	−	0.995692i	$-0.470444\pi$
$719$	−16.0632	−	7.33582i	−0.599057	−	0.273580i	−0.691776	+	0.722112i	$0.743171\pi$
$720$	40.8512	+	19.6562i	1.52244	+	0.732542i
$721$	8.56974	−	59.6039i	0.319154	−	2.21976i
$722$	2.95048	−	3.09437i	0.109805	−	0.115161i
$723$	−5.56176	−	8.39779i	−0.206844	−	0.312317i
$724$	5.65336	−	0.269303i	0.210106	−	0.0100086i
$725$	31.2049	−	1.48647i	1.15892	−	0.0552063i
$726$	−1.87946	+	0.115481i	−0.0697534	+	0.00428589i
$727$	27.1060	−	28.4280i	1.00531	−	1.05433i	0.00678467	−	0.999977i	$-0.497840\pi$
$727$	27.1060	−	28.4280i	1.00531	−	1.05433i	0.998522	−	0.0543578i	$-0.0173112\pi$
$728$	−0.143534	+	0.998299i	−0.00531971	+	0.0369994i
$729$	26.9079	−	2.22762i	0.996591	−	0.0825045i
$730$	16.6251	+	7.59242i	0.615322	+	0.281008i
$731$	20.3412	−	4.93473i	0.752348	−	0.182518i
$732$	−13.3248	−	3.03898i	−0.492501	−	0.112324i
$733$	−7.02712	+	17.5529i	−0.259553	+	0.648331i	−0.999709	−	0.0241032i	$-0.992327\pi$
$733$	−7.02712	+	17.5529i	−0.259553	+	0.648331i	0.740157	+	0.672434i	$0.234751\pi$
$734$	−3.12770	+	1.61244i	−0.115446	+	0.0595164i
$735$	6.35895	−	49.0077i	0.234553	−	1.80768i
$736$	13.4989	−	4.97933i	0.497577	−	0.183541i
$737$		−	52.1517i		−	1.92103i
$738$	−0.944414	+	2.99286i	−0.0347644	+	0.110169i
$739$	4.87676	+	33.9186i	0.179394	+	1.24772i	0.858169	+	0.513368i	$0.171602\pi$
$739$	4.87676	+	33.9186i	0.179394	+	1.24772i	−0.678774	+	0.734347i	$0.737488\pi$
$740$	24.7024	+	17.5905i	0.908080	+	0.646641i
$741$	−0.0812635	−	0.742814i	−0.00298529	−	0.0272880i
$742$	−1.22832	−	1.72493i	−0.0450930	−	0.0633243i
$743$	−15.0299	−	43.4262i	−0.551395	−	1.59315i	−0.784120	−	0.620609i	$-0.786886\pi$
$743$	−15.0299	−	43.4262i	−0.551395	−	1.59315i	0.232725	−	0.972542i	$-0.425236\pi$
$744$	1.32119	−	0.339843i	0.0484374	−	0.0124592i
$745$	8.48764	+	8.09294i	0.310963	+	0.296503i
$746$	−4.60912	−	5.31921i	−0.168752	−	0.194750i
$747$	7.57881	−	35.4763i	0.277294	−	1.29801i
$748$	−18.5750	+	11.9374i	−0.679170	+	0.436476i
$749$	41.4691	+	14.3526i	1.51525	+	0.524432i
$750$	−14.4833	+	2.28630i	−0.528854	+	0.0834839i
$751$	−18.5579	+	23.5982i	−0.677186	+	0.861112i	−0.996241	−	0.0866245i	$-0.972392\pi$
$751$	−18.5579	+	23.5982i	−0.677186	+	0.861112i	0.319055	+	0.947736i	$0.396634\pi$
$752$	−18.6570	+	6.45725i	−0.680351	+	0.235472i
$753$	−17.7334	+	9.45344i	−0.646241	+	0.344502i
$754$	−0.0401147	−	0.165355i	−0.00146089	−	0.00602187i
$755$	−16.2998	−	35.6915i	−0.593210	−	1.29895i
$756$	−9.01253	+	36.1544i	−0.327782	+	1.31492i
$757$	−5.75878	+	8.96084i	−0.209306	+	0.325687i	−0.929995	−	0.367572i	$-0.880189\pi$
$757$	−5.75878	+	8.96084i	−0.209306	+	0.325687i	0.720689	+	0.693259i	$0.243826\pi$
$758$	2.52011	+	4.36496i	0.0915346	+	0.158543i
$759$	12.4256	−	29.8504i	0.451022	−	1.08350i
$760$	−3.53985	+	6.13121i	−0.128404	+	0.222402i
$761$	15.4051	+	29.8818i	0.558435	+	1.08321i	0.983981	+	0.178276i	$0.0570519\pi$
$761$	15.4051	+	29.8818i	0.558435	+	1.08321i	−0.425545	+	0.904937i	$0.639918\pi$
$762$	0.00784053	+	0.569505i	0.000284032	+	0.0206310i
$763$	42.7392	−	60.0189i	1.54726	−	2.17283i
$764$	27.2029	+	7.98749i	0.984166	+	0.288977i
$765$	−23.4855	+	28.6614i	−0.849119	+	1.03626i
$766$	−3.75315	−	3.25212i	−0.135607	−	0.117504i
$767$	−0.948203	−	2.36850i	−0.0342376	−	0.0855215i
$768$	14.5316	−	11.7551i	0.524366	−	0.424177i
$769$	−3.75589	−	19.4874i	−0.135441	−	0.702734i	−0.984631	−	0.174647i	$-0.944122\pi$
$769$	−3.75589	−	19.4874i	−0.135441	−	0.702734i	0.849190	−	0.528087i	$-0.177091\pi$
$770$	−0.757327	−	15.8982i	−0.0272922	−	0.572933i
$771$	1.57935	+	1.09220i	0.0568791	+	0.0393347i
$772$	7.63437	−	22.0581i	0.274767	−	0.793887i
$773$	−3.36480	+	0.987993i	−0.121023	+	0.0355357i	−0.341683	−	0.939815i	$-0.610997\pi$
$773$	−3.36480	+	0.987993i	−0.121023	+	0.0355357i	0.220660	+	0.975351i	$0.429179\pi$
$774$	2.18486	−	5.15522i	0.0785331	−	0.185301i
$775$	6.35562	−	7.33478i	0.228301	−	0.263473i
$776$	−6.19511	+	0.591561i	−0.222392	+	0.0212358i
$777$	−9.67191	+	21.9741i	−0.346978	+	0.788317i
$778$	0.867458	−	9.08443i	0.0310999	−	0.325693i
$779$	6.06373	+	2.42755i	0.217256	+	0.0869760i
$780$	−1.26228	−	3.49088i	−0.0451968	−	0.124993i
$781$	2.04470	−	1.18051i	0.0731650	−	0.0422419i
$782$	0.424669	+	3.66411i	0.0151861	+	0.131028i
$783$	−1.74115	−	12.6764i	−0.0622235	−	0.453019i
$784$	−20.5078	−	13.1795i	−0.732421	−	0.470698i
$785$	11.5317	+	14.6638i	0.411584	+	0.523372i
$786$	−0.708551	+	3.10675i	−0.0252732	+	0.110814i
$787$	24.9445	+	26.1610i	0.889174	+	0.932539i	0.998106	−	0.0615100i	$-0.0195916\pi$
$787$	24.9445	+	26.1610i	0.889174	+	0.932539i	−0.108932	+	0.994049i	$0.534743\pi$
$788$	−6.46460	+	4.60342i	−0.230292	+	0.163990i
$789$	−15.8220	−	17.7595i	−0.563277	−	0.632256i
$790$	2.16267	−	0.865804i	0.0769445	−	0.0308039i
$791$	0.318237	+	1.08382i	0.0113152	+	0.0385360i
$792$	−0.812911	+	11.9951i	−0.0288855	+	0.426226i
$793$	0.582780	+	0.906823i	0.0206951	+	0.0322022i
$794$	−3.02704	+	5.87163i	−0.107425	+	0.208376i
$795$	14.1997	+	7.07475i	0.503611	+	0.250915i
$796$	−31.1136	−	7.54808i	−1.10279	−	0.267534i
$797$	22.7868	+	17.9197i	0.807149	+	0.634749i	0.934040	−	0.357168i	$-0.116258\pi$
$797$	22.7868	+	17.9197i	0.807149	+	0.634749i	−0.126892	+	0.991917i	$0.540500\pi$
$798$	−2.61429	−	0.864704i	−0.0925450	−	0.0306102i
$799$	−1.53393	−	16.0641i	−0.0542666	−	0.568305i
$800$	−10.7230	+	36.5191i	−0.379115	+	1.29115i
$801$	18.6852	−	15.5455i	0.660210	−	0.549273i
$802$	−7.41038	+	1.06545i	−0.261670	+	0.0376224i
$803$	3.07357	−	64.5222i	0.108464	−	2.27694i
$804$	−44.4482	−	5.76734i	−1.56757	−	0.203399i
$805$	68.7291	+	29.7260i	2.42238	+	1.04770i
$806$	−0.0457783	−	0.0264301i	−0.00161247	−	0.000930960i
$807$	−19.6347	+	7.09980i	−0.691176	+	0.249925i
$808$	0.578514	−	0.454948i	0.0203520	−	0.0160050i
$809$	31.5971	−	14.4299i	1.11089	−	0.507328i	0.226473	−	0.974017i	$-0.427281\pi$
$809$	31.5971	−	14.4299i	1.11089	−	0.507328i	0.884422	+	0.466689i	$0.154553\pi$
$810$	2.40871	+	9.61496i	0.0846335	+	0.337835i
$811$	−2.55975	+	5.60508i	−0.0898851	+	0.196821i	−0.949236	−	0.314566i	$-0.898141\pi$
$811$	−2.55975	+	5.60508i	−0.0898851	+	0.196821i	0.859350	+	0.511387i	$0.170868\pi$
$812$	17.3390	+	3.34181i	0.608479	+	0.117275i
$813$	−20.8243	+	20.4105i	−0.730339	+	0.715828i
$814$	−0.897236	+	3.69846i	−0.0314481	+	0.129631i
$815$	−4.44246	+	0.856213i	−0.155612	+	0.0299918i
$816$	7.82139	+	16.5207i	0.273804	+	0.578342i
$817$	−10.3576	−	5.33973i	−0.362367	−	0.186813i
$818$	−5.92108	+	5.13064i	−0.207026	+	0.179389i
$819$	2.50368	−	1.53892i	0.0874857	−	0.0537743i
$820$	32.1167	+	4.61768i	1.12156	+	0.161256i
$821$	−3.65776	+	18.9783i	−0.127657	+	0.662346i	0.860568	+	0.509336i	$0.170109\pi$
$821$	−3.65776	+	18.9783i	−0.127657	+	0.662346i	−0.988225	+	0.153010i	$0.951103\pi$
$822$	−0.000534769	0	1.81000e-5i	−1.86522e−5	0	6.31311e-7i
$823$	4.72951	−	4.50958i	0.164860	−	0.157194i	−0.603158	−	0.797622i	$-0.706091\pi$
$823$	4.72951	−	4.50958i	0.164860	−	0.157194i	0.768019	+	0.640427i	$0.221243\pi$
$824$	−16.6228	−	1.58729i	−0.579083	−	0.0552957i
$825$	43.7816	+	73.4770i	1.52428	+	2.55814i
$826$	−9.39065	−	0.447332i	−0.326742	−	0.0155647i
$827$	−53.0645			−1.84523			−0.922616	−	0.385719i	$-0.873954\pi$
$827$	−53.0645			−1.84523			−0.922616	+	0.385719i	$0.873954\pi$
$828$	−24.0670	−	13.8913i	−0.836386	−	0.482756i
$829$	50.4138			1.75094			0.875472	−	0.483269i	$-0.160551\pi$
$829$	50.4138			1.75094			0.875472	+	0.483269i	$0.160551\pi$
$830$	13.3026	+	0.633683i	0.461741	+	0.0219954i
$831$	49.1449	−	0.676592i	1.70482	−	0.0234707i
$832$	−1.68121	−	0.160536i	−0.0582853	−	0.00556557i
$833$	14.4207	−	13.7501i	0.499649	−	0.476414i
$834$	1.72327	+	3.23262i	0.0596719	+	0.111937i
$835$	−12.5215	+	64.9677i	−0.433324	+	2.24830i
$836$	12.1675	+	1.74943i	0.420823	+	0.0605052i
$837$	−3.22344	−	2.32615i	−0.111418	−	0.0804034i
$838$	−2.57333	+	2.22980i	−0.0888941	+	0.0770271i
$839$	16.6000	+	8.55787i	0.573094	+	0.295451i	0.720308	−	0.693654i	$-0.244000\pi$
$839$	16.6000	+	8.55787i	0.573094	+	0.295451i	−0.147214	+	0.989105i	$0.547031\pi$
$840$	−27.7513	−	2.26489i	−0.957512	−	0.0781463i
$841$	22.5217	−	4.34070i	0.776610	−	0.149679i
$842$	0.258947	−	1.06740i	0.00892392	−	0.0367849i
$843$	3.06864	+	0.855328i	0.105689	+	0.0294591i
$844$	−19.5928	−	3.77620i	−0.674411	−	0.129982i
$845$	22.5899	−	49.4650i	0.777116	−	1.70165i
$846$	−3.69428	−	2.23291i	−0.127012	−	0.0767691i
$847$	−14.0200	+	6.40273i	−0.481734	+	0.220000i
$848$	6.15150	−	4.83759i	0.211243	−	0.166124i
$849$	−3.84266	+	21.5283i	−0.131880	+	0.738850i
$850$	−8.45034	−	4.87880i	−0.289844	−	0.167342i
$851$	−13.7656	−	11.4498i	−0.471879	−	0.392494i
$852$	−0.780012	−	1.87322i	−0.0267228	−	0.0641754i
$853$	0.578891	−	12.1524i	0.0198208	−	0.416091i	−0.967051	−	0.254584i	$-0.918062\pi$
$853$	0.578891	−	12.1524i	0.0198208	−	0.416091i	0.986872	−	0.161507i	$-0.0516354\pi$
$854$	3.93177	−	0.565303i	0.134542	−	0.0193443i
$855$	20.3308	−	3.49688i	0.695299	−	0.119591i
$856$	3.42836	−	11.6759i	0.117179	−	0.399075i
$857$	−2.51343	−	26.3218i	−0.0858570	−	0.899136i	−0.931103	−	0.364758i	$-0.881152\pi$
$857$	−2.51343	−	26.3218i	−0.0858570	−	0.899136i	0.845245	−	0.534378i	$-0.179454\pi$
$858$	0.347834	−	0.309886i	0.0118749	−	0.0105793i
$859$	−17.6671	−	13.8936i	−0.602794	−	0.474042i	0.269516	−	0.962996i	$-0.413136\pi$
$859$	−17.6671	−	13.8936i	−0.602794	−	0.474042i	−0.872310	+	0.488954i	$0.837379\pi$
$860$	−56.2568	−	13.6477i	−1.91834	−	0.465384i
$861$	1.57539	+	25.6396i	0.0536890	+	0.873796i
$862$	−2.37778	+	4.61225i	−0.0809876	+	0.157094i
$863$	−23.1000	−	35.9442i	−0.786332	−	1.22356i	−0.970604	−	0.240681i	$-0.922629\pi$
$863$	−23.1000	−	35.9442i	−0.786332	−	1.22356i	0.184273	−	0.982875i	$-0.441007\pi$
$864$	15.2884	+	3.04663i	0.520122	+	0.103648i
$865$	−20.7918	−	70.8105i	−0.706944	−	2.40763i
$866$	0.640651	−	0.256478i	0.0217702	−	0.00871547i
$867$	14.2033	−	2.94080i	0.482368	−	0.0998747i
$868$	4.46857	−	3.18205i	0.151673	−	0.108006i
$869$	−5.68163	−	5.95872i	−0.192736	−	0.202136i
$870$	4.48847	−	1.38533i	0.152173	−	0.0469670i
$871$	2.18526	+	2.77878i	0.0740446	+	0.0941554i
$872$	−17.1886	−	11.0465i	−0.582080	−	0.374080i
$873$	12.8704	+	12.7746i	0.435596	+	0.432356i
$874$	1.15718	−	1.69649i	0.0391422	−	0.0573846i
$875$	−103.938	+	60.0084i	−3.51374	+	2.02866i
$876$	−54.6515	−	9.75494i	−1.84650	−	0.329589i
$877$	−34.4711	−	13.8001i	−1.16401	−	0.465998i	−0.292444	−	0.956283i	$-0.594469\pi$
$877$	−34.4711	−	13.8001i	−1.16401	−	0.465998i	−0.871562	+	0.490285i	$0.836893\pi$
$878$	−0.147307	+	1.54267i	−0.00497138	+	0.0520627i
$879$	0.407973	−	0.0446320i	0.0137606	−	0.00150540i
$880$	58.5544	−	5.59126i	1.97387	−	0.188481i
$881$	−25.1322	+	29.0041i	−0.846726	+	0.977174i	−0.999939	−	0.0110188i	$-0.996493\pi$
$881$	−25.1322	+	29.0041i	−0.846726	+	0.977174i	0.153213	+	0.988193i	$0.451038\pi$
$882$	−0.652529	−	5.28995i	−0.0219718	−	0.178122i
$883$	8.16884	−	2.39859i	0.274903	−	0.0807189i	−0.141375	−	0.989956i	$-0.545152\pi$
$883$	8.16884	−	2.39859i	0.274903	−	0.0807189i	0.416278	+	0.909237i	$0.363334\pi$
$884$	0.489524	−	1.41439i	0.0164645	−	0.0475710i
$885$	63.6590	−	30.1380i	2.13987	−	1.01308i
$886$	0.118779	+	2.49348i	0.00399046	+	0.0837700i
$887$	−1.60270	−	8.31561i	−0.0538135	−	0.279211i	0.945047	−	0.326934i	$-0.106016\pi$
$887$	−1.60270	−	8.31561i	−0.0538135	−	0.279211i	−0.998861	+	0.0477233i	$0.984803\pi$
$888$	6.21425	+	2.38909i	0.208537	+	0.0801726i
$889$	1.73268	+	4.32802i	0.0581122	+	0.145157i
$890$	6.74372	+	5.84347i	0.226050	+	0.195873i
$891$	28.3839	−	20.5332i	0.950898	−	0.687888i
$892$	33.2258	+	9.75596i	1.11248	+	0.326654i
$893$	−5.21123	+	7.31814i	−0.174387	+	0.244892i
$894$	1.10402	+	0.617300i	0.0369239	+	0.0206456i
$895$	−30.1725	−	58.5265i	−1.00856	−	1.95632i
$896$	−14.2503	+	24.6822i	−0.476068	+	0.824574i
$897$	0.588720	+	2.11117i	0.0196568	+	0.0704898i
$898$	−1.85340	−	3.21018i	−0.0618487	−	0.107125i
$899$	−1.01847	+	1.58478i	−0.0339680	+	0.0528552i
$900$	67.4653	−	29.1888i	2.24884	−	0.972960i
$901$	2.65722	+	5.81851i	0.0885249	+	0.193843i
$902$	0.960001	+	3.95718i	0.0319645	+	0.131760i
$903$	1.55029	−	45.8037i	0.0515904	−	1.52425i
$904$	0.296008	−	0.102449i	0.00984508	−	0.00340742i
$905$	7.61805	−	9.68713i	0.253232	−	0.322011i
$906$	−2.66156	−	3.29021i	−0.0884246	−	0.109310i
$907$	42.5015	+	14.7099i	1.41124	+	0.488435i	0.923178	−	0.384373i	$-0.125582\pi$
$907$	42.5015	+	14.7099i	1.41124	+	0.488435i	0.488063	+	0.872808i	$0.337704\pi$
$908$	−30.8869	+	19.8498i	−1.02502	+	0.658739i
$909$	−2.09721	−	0.448027i	−0.0695600	−	0.0148601i
$910$	0.706520	+	0.815367i	0.0234209	+	0.0270292i
$911$	25.6804	+	24.4862i	0.850829	+	0.811264i	0.983690	−	0.179871i	$-0.0575679\pi$
$911$	25.6804	+	24.4862i	0.850829	+	0.811264i	−0.132861	+	0.991135i	$0.542416\pi$
$912$	2.73230	−	9.80258i	0.0904754	−	0.324596i
$913$	−15.3947	−	44.4801i	−0.509490	−	1.47207i
$914$	−5.20907	−	7.31512i	−0.172301	−	0.241963i
$915$	−24.0010	+	17.5939i	−0.793449	+	0.581638i
$916$	25.4318	+	18.1099i	0.840290	+	0.598368i
$917$	3.71192	+	25.8169i	0.122578	+	0.852550i
$918$	−1.68309	+	3.62484i	−0.0555503	+	0.119638i
$919$			34.2932i			1.13123i	0.824670	+	0.565614i	$0.191361\pi$
$919$			34.2932i			1.13123i	−0.824670	+	0.565614i	$0.808639\pi$
$920$	7.32697	−	19.4296i	0.241563	−	0.640574i
$921$	−36.2241	−	27.6885i	−1.19363	−	0.912367i
$922$	−6.43975	+	3.31992i	−0.212082	+	0.109336i
$923$	−0.0594814	+	0.148577i	−0.00195785	+	0.00489048i
$924$	14.2578	+	46.1953i	0.469046	+	1.51971i
$925$	46.0293	−	11.1666i	1.51344	−	0.367155i
$926$	−0.0446274	−	0.0203807i	−0.00146655	−	0.000669750i
$927$	27.4229	+	40.1932i	0.900685	+	1.32012i
$928$	1.05138	−	7.31252i	0.0345133	−	0.240045i
$929$	−27.1433	+	28.4671i	−0.890543	+	0.933974i	−0.998185	−	0.0602154i	$-0.980821\pi$
$929$	−27.1433	+	28.4671i	−0.890543	+	0.933974i	0.107643	+	0.994190i	$0.465670\pi$
$930$	0.650780	−	1.30618i	0.0213399	−	0.0428312i
$931$	−11.0805	+	0.527829i	−0.363149	+	0.0172989i
$932$	24.4961	−	1.16689i	0.802396	−	0.0382228i
$933$	10.9303	−	21.9382i	0.357842	−	0.718223i
$934$	−5.20435	+	5.45816i	−0.170292	+	0.178597i
$935$	−6.84222	+	47.5887i	−0.223764	+	1.55632i
$936$	−0.459303	−	0.673192i	−0.0150128	−	0.0220040i
$937$	31.2252	+	14.2601i	1.02008	+	0.465856i	0.854009	−	0.520258i	$-0.174164\pi$
$937$	31.2252	+	14.2601i	1.02008	+	0.465856i	0.166072	+	0.986114i	$0.446891\pi$
$938$	12.6596	−	3.07118i	0.413350	−	0.100278i
$939$	0.781451	+	2.53191i	0.0255017	+	0.0826256i
$940$	−16.5872	+	41.4327i	−0.541014	+	1.35139i
$941$	−19.2162	+	9.90662i	−0.626429	+	0.322947i	−0.742048	−	0.670347i	$-0.766145\pi$
$941$	−19.2162	+	9.90662i	−0.626429	+	0.322947i	0.115619	+	0.993294i	$0.463115\pi$
$942$	1.59854	+	1.22187i	0.0520831	+	0.0398105i
$943$	−18.7049	−	4.13987i	−0.609115	−	0.134813i
$944$		−	34.7437i		−	1.13081i
$945$	46.6442	+	66.3839i	1.51734	+	2.15947i
$946$	−1.03389	−	7.19084i	−0.0336145	−	0.233794i
$947$	−4.94905	−	3.52420i	−0.160822	−	0.114521i	0.496813	−	0.867858i	$-0.334504\pi$
$947$	−4.94905	−	3.52420i	−0.160822	−	0.114521i	−0.657635	+	0.753337i	$0.728443\pi$
$948$	−5.70686	+	4.18342i	−0.185350	+	0.135871i
$949$	2.53984	+	3.56670i	0.0824466	+	0.115780i
$950$	1.77674	+	5.13356i	0.0576452	+	0.166555i
$951$	8.72735	−	31.3109i	0.283004	−	1.01532i
$952$	−8.12500	−	7.74717i	−0.263333	−	0.251087i
$953$	−30.1429	−	34.7868i	−0.976424	−	1.12685i	−0.991906	−	0.126973i	$-0.959474\pi$
$953$	−30.1429	−	34.7868i	−0.976424	−	1.12685i	0.0154819	−	0.999880i	$-0.495072\pi$
$954$	1.67332	+	0.357471i	0.0541756	+	0.0115736i
$955$	51.9331	−	33.3754i	1.68052	−	1.08000i
$956$	−9.69386	−	3.35508i	−0.313522	−	0.108511i
$957$	−10.4413	−	12.9075i	−0.337521	−	0.417241i
$958$	2.26379	−	2.87864i	0.0731397	−	0.0930047i
$959$	−0.00413884	+	0.00143247i	−0.000133650	+	4.62567e-5i
$960$	1.57717	−	46.5978i	0.0509028	−	1.50394i
$961$	−7.17055	−	29.5574i	−0.231308	−	0.953465i
$962$	−0.107165	−	0.234659i	−0.00345515	−	0.00756572i
$963$	−32.5433	+	14.0798i	−1.04869	+	0.453716i
$964$	−6.07245	+	9.44891i	−0.195580	+	0.304329i
$965$	−25.4126	−	44.0160i	−0.818062	−	1.41692i
$966$	7.97779	+	1.25839i	0.256681	+	0.0404881i
$967$	−21.3193	+	36.9261i	−0.685583	+	1.18746i	0.287670	+	0.957729i	$0.407119\pi$
$967$	−21.3193	+	36.9261i	−0.685583	+	1.18746i	−0.973253	+	0.229735i	$0.926214\pi$
$968$	1.95849	+	3.79894i	0.0629482	+	0.122102i
$969$	7.25992	+	4.05930i	0.233222	+	0.130404i
$970$	−3.86156	+	5.42280i	−0.123987	+	0.174115i
$971$	−37.9374	−	11.1394i	−1.21747	−	0.357481i	−0.390962	−	0.920407i	$-0.627858\pi$
$971$	−37.9374	−	11.1394i	−1.21747	−	0.357481i	−0.826508	+	0.562925i	$0.809676\pi$
$972$	−14.3613	−	26.4620i	−0.460637	−	0.848769i
$973$	22.6609	+	19.6358i	0.726475	+	0.629494i
$974$	−1.35925	−	3.39524i	−0.0435532	−	0.108791i
$975$	−5.41163	−	2.08052i	−0.173311	−	0.0666299i
$976$	2.77817	+	14.4145i	0.0889270	+	0.461397i
$977$	1.66021	+	34.8522i	0.0531149	+	1.11502i	0.855363	+	0.518029i	$0.173334\pi$
$977$	1.66021	+	34.8522i	0.0531149	+	1.11502i	−0.802248	+	0.596991i	$0.796363\pi$
$978$	−0.441032	+	0.208797i	−0.0141026	+	0.00667659i
$979$	10.3148	−	29.8028i	0.329664	−	0.952502i
$980$	−52.8746	+	15.5254i	−1.68902	+	0.495940i
$981$	7.28876	+	59.0888i	0.232712	+	1.88656i
$982$	2.30807	−	2.66366i	0.0736536	−	0.0850007i
$983$	6.80522	−	0.649820i	0.217053	−	0.0207260i	0.0140370	−	0.999901i	$-0.495532\pi$
$983$	6.80522	−	0.649820i	0.217053	−	0.0207260i	0.203016	+	0.979175i	$0.434926\pi$
$984$	7.08116	−	0.774675i	0.225739	−	0.0246957i
$985$	−1.64261	+	17.2022i	−0.0523378	+	0.548107i
$986$	1.75831	+	0.703921i	0.0559960	+	0.0224174i
$987$	−34.7832	−	6.20857i	−1.10716	−	0.197621i
$988$	−0.721623	+	0.416629i	−0.0229579	+	0.0132547i
$989$	32.5182	+	10.5247i	1.03402	+	0.334664i
$990$	9.12787	+	9.05998i	0.290103	+	0.287945i
$991$	−24.3623	−	15.6567i	−0.773895	−	0.497352i	0.0931073	−	0.995656i	$-0.470320\pi$
$991$	−24.3623	−	15.6567i	−0.773895	−	0.497352i	−0.867002	+	0.498304i	$0.833956\pi$
$992$	−1.41874	−	1.80408i	−0.0450452	−	0.0572796i
$993$	−31.4757	+	9.71471i	−0.998852	+	0.308287i
$994$	0.406974	+	0.426822i	0.0129084	+	0.0135380i
$995$	−56.7864	+	40.4374i	−1.80025	+	1.28195i
$996$	−39.6122	+	8.20175i	−1.25516	+	0.259882i
$997$	−25.2766	+	10.1192i	−0.800517	+	0.320479i	−0.735604	−	0.677412i	$-0.763101\pi$
$997$	−25.2766	+	10.1192i	−0.800517	+	0.320479i	−0.0649137	+	0.997891i	$0.520677\pi$
$998$	1.17904	+	4.01544i	0.0373218	+	0.127106i
$999$	−6.22936	−	18.3723i	−0.197088	−	0.581272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.12	yes	440
3.2	odd	2		621.2.s.a.44.11		440
9.2	odd	6	inner	207.2.o.a.182.12	yes	440
9.7	even	3		621.2.s.a.251.11		440
23.11	odd	22	inner	207.2.o.a.149.12	yes	440
69.11	even	22		621.2.s.a.287.11		440
207.11	even	66	inner	207.2.o.a.11.12	✓	440
207.34	odd	66		621.2.s.a.494.11		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.12	✓	440	207.11	even	66	inner
207.2.o.a.113.12	yes	440	1.1	even	1	trivial
207.2.o.a.149.12	yes	440	23.11	odd	22	inner
207.2.o.a.182.12	yes	440	9.2	odd	6	inner
621.2.s.a.44.11		440	3.2	odd	2
621.2.s.a.251.11		440	9.7	even	3
621.2.s.a.287.11		440	69.11	even	22
621.2.s.a.494.11		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261583 - 0.0124607i) q^{2} +(0.845294 - 1.51178i) q^{3} +(-1.92267 - 0.183593i) q^{4} +(-3.04369 + 2.90215i) q^{5} +(-0.239952 + 0.384923i) q^{6} +(-0.702638 + 3.64563i) q^{7} +(1.01908 + 0.146521i) q^{8} +(-1.57095 - 2.55580i) q^{9} +O(q^{10})\)	\(q+(-0.261583 - 0.0124607i) q^{2} +(0.845294 - 1.51178i) q^{3} +(-1.92267 - 0.183593i) q^{4} +(-3.04369 + 2.90215i) q^{5} +(-0.239952 + 0.384923i) q^{6} +(-0.702638 + 3.64563i) q^{7} +(1.01908 + 0.146521i) q^{8} +(-1.57095 - 2.55580i) q^{9} +(0.832339 - 0.721226i) q^{10} +(-3.45977 - 1.78363i) q^{11} +(-1.90278 + 2.75147i) q^{12} +(0.259083 - 0.0499342i) q^{13} +(0.229225 - 0.944880i) q^{14} +(1.81460 + 7.05455i) q^{15} +(3.52828 + 0.680021i) q^{16} +(-1.22006 + 2.67157i) q^{17} +(0.379088 + 0.688128i) q^{18} +(1.48734 - 0.679244i) q^{19} +(6.38483 - 5.02109i) q^{20} +(4.91746 + 4.14387i) q^{21} +(0.882791 + 0.509680i) q^{22} +(-3.98136 + 2.67373i) q^{23} +(1.08293 - 1.41677i) q^{24} +(0.603648 - 12.6721i) q^{25} +(-0.0683940 + 0.00983357i) q^{26} +(-5.19172 + 0.214536i) q^{27} +(2.02026 - 6.88036i) q^{28} +(0.234074 + 2.45134i) q^{29} +(-0.386763 - 1.86796i) q^{30} +(0.601339 + 0.472898i) q^{31} +(-2.91554 - 0.707302i) q^{32} +(-5.62099 + 3.72271i) q^{33} +(0.352437 - 0.683633i) q^{34} +(-8.44156 - 13.1353i) q^{35} +(2.55121 + 5.20238i) q^{36} +(1.05184 + 3.58222i) q^{37} +(-0.397526 + 0.159145i) q^{38} +(0.143512 - 0.433886i) q^{39} +(-3.52698 + 2.51155i) q^{40} +(2.75661 + 2.89105i) q^{41} +(-1.23469 - 1.14524i) q^{42} +(-4.40550 - 5.60205i) q^{43} +(6.32454 + 4.06454i) q^{44} +(12.1988 + 3.21990i) q^{45} +(1.07477 - 0.649790i) q^{46} +(-4.75835 + 2.74724i) q^{47} +(4.01048 - 4.75917i) q^{48} +(-6.29837 - 2.52149i) q^{49} +(-0.315808 + 3.30729i) q^{50} +(3.00751 + 4.10273i) q^{51} +(-0.507300 + 0.0484413i) q^{52} +(1.42625 - 1.64598i) q^{53} +(1.36074 + 0.00857370i) q^{54} +(15.7068 - 4.61194i) q^{55} +(-1.25021 + 3.61224i) q^{56} +(0.230370 - 2.82269i) q^{57} +(-0.0306844 - 0.644144i) q^{58} +(-1.82992 - 9.49452i) q^{59} +(-2.19371 - 13.8967i) q^{60} +(1.51839 + 3.79277i) q^{61} +(-0.151407 - 0.131195i) q^{62} +(10.4213 - 3.93132i) q^{63} +(-6.14149 - 1.80331i) q^{64} +(-0.643652 + 0.903883i) q^{65} +(1.51674 - 0.903756i) q^{66} +(6.13936 + 11.9087i) q^{67} +(2.83626 - 4.91255i) q^{68} +(0.676667 + 8.27902i) q^{69} +(2.04449 + 3.54117i) q^{70} +(-0.327930 + 0.510270i) q^{71} +(-1.22645 - 2.83474i) q^{72} +(6.89379 + 15.0953i) q^{73} +(-0.230505 - 0.950155i) q^{74} +(-18.6472 - 11.6243i) q^{75} +(-2.98437 + 1.03290i) q^{76} +(8.93345 - 11.3598i) q^{77} +(-0.0429469 + 0.111709i) q^{78} +(1.99885 + 0.691809i) q^{79} +(-12.7125 + 8.16984i) q^{80} +(-4.06420 + 8.03008i) q^{81} +(-0.685057 - 0.790598i) q^{82} +(8.75158 + 8.34461i) q^{83} +(-8.69388 - 8.87012i) q^{84} +(-4.03979 - 11.6722i) q^{85} +(1.08260 + 1.52030i) q^{86} +(3.90374 + 1.71823i) q^{87} +(-3.26444 - 2.32459i) q^{88} +(1.15305 + 8.01966i) q^{89} +(-3.15088 - 0.994277i) q^{90} +0.979609i q^{91} +(8.14572 - 4.40975i) q^{92} +(1.22323 - 0.509354i) q^{93} +(1.27894 - 0.659337i) q^{94} +(-2.55572 + 6.38388i) q^{95} +(-3.53377 + 3.80977i) q^{96} +(-5.87423 + 1.42507i) q^{97} +(1.61613 + 0.738060i) q^{98} +(0.876531 + 11.6445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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