LMFDB - Embedded newform 825.2.n.g.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.g.526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.338464 - 1.04169i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.647481 - 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.570387 + 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.338464 - 1.04169i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.647481 - 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.570387 + 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.31118 + 0.189896i) q^{11} +0.800331 q^{12} +(1.45650 + 4.48264i) q^{13} +(0.624741 + 0.453901i) q^{14} +(-0.543502 + 1.67273i) q^{16} +(2.40431 - 7.39971i) q^{17} +(0.886111 - 0.643798i) q^{18} +(0.970553 + 0.705148i) q^{19} -0.705037 q^{21} +(-0.922906 - 3.51349i) q^{22} +6.89318 q^{23} +(-0.947813 - 2.91707i) q^{24} +(4.17653 - 3.03443i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.174367 + 0.536646i) q^{28} +(-1.07389 + 0.780229i) q^{29} +(-2.37364 - 7.30532i) q^{31} -4.20796 q^{32} +(2.56719 + 2.09989i) q^{33} -8.52195 q^{34} +(0.647481 + 0.470423i) q^{36} +(6.82618 - 4.95951i) q^{37} +(0.406045 - 1.24968i) q^{38} +(-1.45650 + 4.48264i) q^{39} +(0.188421 + 0.136896i) q^{41} +(0.238630 + 0.734428i) q^{42} -7.32892 q^{43} +(2.23326 - 1.43470i) q^{44} +(-2.33310 - 7.18053i) q^{46} +(6.73287 + 4.89171i) q^{47} +(-1.42291 + 1.03380i) q^{48} +(-2.00951 + 6.18465i) q^{49} +(6.29457 - 4.57327i) q^{51} +(3.05179 + 2.21726i) q^{52} +(-2.10852 - 6.48936i) q^{53} +1.09529 q^{54} +2.16248 q^{56} +(0.370718 + 1.14095i) q^{57} +(1.17623 + 0.854580i) q^{58} +(2.86401 - 2.08083i) q^{59} +(-3.35959 + 10.3397i) q^{61} +(-6.80645 + 4.94518i) q^{62} +(-0.570387 - 0.414410i) q^{63} +(2.51125 + 7.72883i) q^{64} +(1.31853 - 3.38494i) q^{66} +2.04036 q^{67} +(-1.92424 - 5.92222i) q^{68} +(5.57670 + 4.05171i) q^{69} +(0.207204 - 0.637709i) q^{71} +(0.947813 - 2.91707i) q^{72} +(-4.04859 + 2.94147i) q^{73} +(-7.47668 - 5.43212i) q^{74} +0.960132 q^{76} +(-1.96735 + 1.26387i) q^{77} +5.16248 q^{78} +(0.704642 + 2.16867i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0788288 - 0.242610i) q^{82} +(0.652022 - 2.00672i) q^{83} +(-0.456498 + 0.331666i) q^{84} +(2.48058 + 7.63443i) q^{86} -1.32741 q^{87} +(-7.87404 - 6.44077i) q^{88} -3.34722 q^{89} +(-2.68842 - 1.95325i) q^{91} +(4.46321 - 3.24271i) q^{92} +(2.37364 - 7.30532i) q^{93} +(2.81680 - 8.66921i) q^{94} +(-3.40431 - 2.47338i) q^{96} +(-1.02664 - 3.15968i) q^{97} +7.12261 q^{98} +(0.842610 + 3.20780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.338464	−	1.04169i	−0.239331	−	0.736584i	−0.996517	−	0.0833853i	$-0.973427\pi$
$2$	−0.338464	−	1.04169i	−0.239331	−	0.736584i	0.757187	−	0.653198i	$-0.226573\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.647481	−	0.470423i	0.323741	−	0.235211i
$5$		0			0
$5$		0			0
$6$	0.338464	−	1.04169i	0.138178	−	0.425267i
$7$	−0.570387	+	0.414410i	−0.215586	+	0.156632i	−0.690337	−	0.723487i	$-0.742538\pi$
$7$	−0.570387	+	0.414410i	−0.215586	+	0.156632i	0.474751	+	0.880120i	$0.342538\pi$
$8$	−2.48141	−	1.80285i	−0.877309	−	0.637403i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	3.31118	+	0.189896i	0.998360	+	0.0572559i
$11$	3.31118	+	0.189896i	0.998360	+	0.0572559i
$12$	0.800331			0.231036
$13$	1.45650	+	4.48264i	0.403960	+	1.24326i	0.921761	+	0.387760i	$0.126751\pi$
$13$	1.45650	+	4.48264i	0.403960	+	1.24326i	−0.517801	+	0.855501i	$0.673249\pi$
$14$	0.624741	+	0.453901i	0.166969	+	0.121310i
$15$		0			0
$16$	−0.543502	+	1.67273i	−0.135875	+	0.418181i
$17$	2.40431	−	7.39971i	0.583131	−	1.79469i	−0.0235184	−	0.999723i	$-0.507487\pi$
$17$	2.40431	−	7.39971i	0.583131	−	1.79469i	0.606649	−	0.794969i	$-0.292513\pi$
$18$	0.886111	−	0.643798i	0.208858	−	0.151745i
$19$	0.970553	+	0.705148i	0.222660	+	0.161772i	0.693523	−	0.720434i	$-0.256057\pi$
$19$	0.970553	+	0.705148i	0.222660	+	0.161772i	−0.470863	+	0.882206i	$0.656057\pi$
$20$		0			0
$21$	−0.705037			−0.153852
$22$	−0.922906	−	3.51349i	−0.196764	−	0.749078i
$23$	6.89318			1.43733			0.718664	−	0.695358i	$-0.244754\pi$
$23$	6.89318			1.43733			0.718664	+	0.695358i	$0.244754\pi$
$24$	−0.947813	−	2.91707i	−0.193471	−	0.595444i
$25$		0			0
$26$	4.17653	−	3.03443i	0.819086	−	0.595101i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.174367	+	0.536646i	−0.0329522	+	0.101417i
$29$	−1.07389	+	0.780229i	−0.199417	+	0.144885i	−0.683013	−	0.730407i	$-0.739331\pi$
$29$	−1.07389	+	0.780229i	−0.199417	+	0.144885i	0.483596	+	0.875292i	$0.339331\pi$
$30$		0			0
$31$	−2.37364	−	7.30532i	−0.426318	−	1.31207i	−0.901726	−	0.432308i	$-0.857699\pi$
$31$	−2.37364	−	7.30532i	−0.426318	−	1.31207i	0.475408	−	0.879766i	$-0.342301\pi$
$32$	−4.20796			−0.743869
$33$	2.56719	+	2.09989i	0.446890	+	0.365545i
$34$	−8.52195			−1.46150
$35$		0			0
$36$	0.647481	+	0.470423i	0.107914	+	0.0784038i
$37$	6.82618	−	4.95951i	1.12222	−	0.815339i	0.137674	−	0.990478i	$-0.456037\pi$
$37$	6.82618	−	4.95951i	1.12222	−	0.815339i	0.984544	+	0.175139i	$0.0560375\pi$
$38$	0.406045	−	1.24968i	0.0658692	−	0.202725i
$39$	−1.45650	+	4.48264i	−0.233226	+	0.717797i
$40$		0			0
$41$	0.188421	+	0.136896i	0.0294264	+	0.0213795i	0.602401	−	0.798193i	$-0.294211\pi$
$41$	0.188421	+	0.136896i	0.0294264	+	0.0213795i	−0.572975	+	0.819573i	$0.694211\pi$
$42$	0.238630	+	0.734428i	0.0368214	+	0.113325i
$43$	−7.32892			−1.11765			−0.558825	−	0.829286i	$-0.688748\pi$
$43$	−7.32892			−1.11765			−0.558825	+	0.829286i	$0.688748\pi$
$44$	2.23326	−	1.43470i	0.336677	−	0.216289i
$45$		0			0
$46$	−2.33310	−	7.18053i	−0.343996	−	1.05871i
$47$	6.73287	+	4.89171i	0.982090	+	0.713530i	0.958175	−	0.286184i	$-0.0923869\pi$
$47$	6.73287	+	4.89171i	0.982090	+	0.713530i	0.0239149	+	0.999714i	$0.492387\pi$
$48$	−1.42291	+	1.03380i	−0.205379	+	0.149216i
$49$	−2.00951	+	6.18465i	−0.287073	+	0.883521i
$50$		0			0
$51$	6.29457	−	4.57327i	0.881416	−	0.640386i
$52$	3.05179	+	2.21726i	0.423207	+	0.307478i
$53$	−2.10852	−	6.48936i	−0.289628	−	0.891382i	−0.984973	−	0.172707i	$-0.944749\pi$
$53$	−2.10852	−	6.48936i	−0.289628	−	0.891382i	0.695346	−	0.718675i	$-0.255251\pi$
$54$	1.09529			0.149051
$55$		0			0
$56$	2.16248			0.288974
$57$	0.370718	+	1.14095i	0.0491028	+	0.151123i
$58$	1.17623	+	0.854580i	0.154446	+	0.112212i
$59$	2.86401	−	2.08083i	0.372862	−	0.270900i	−0.385534	−	0.922693i	$-0.625983\pi$
$59$	2.86401	−	2.08083i	0.372862	−	0.270900i	0.758397	+	0.651793i	$0.225983\pi$
$60$		0			0
$61$	−3.35959	+	10.3397i	−0.430151	+	1.32387i	0.467824	+	0.883822i	$0.345038\pi$
$61$	−3.35959	+	10.3397i	−0.430151	+	1.32387i	−0.897975	+	0.440047i	$0.854962\pi$
$62$	−6.80645	+	4.94518i	−0.864421	+	0.628038i
$63$	−0.570387	−	0.414410i	−0.0718620	−	0.0522108i
$64$	2.51125	+	7.72883i	0.313906	+	0.966103i
$65$		0			0
$66$	1.31853	−	3.38494i	0.162300	−	0.416658i
$67$	2.04036			0.249269			0.124635	−	0.992203i	$-0.460224\pi$
$67$	2.04036			0.249269			0.124635	+	0.992203i	$0.460224\pi$
$68$	−1.92424	−	5.92222i	−0.233349	−	0.718174i
$69$	5.57670	+	4.05171i	0.671356	+	0.487768i
$70$		0			0
$71$	0.207204	−	0.637709i	0.0245906	−	0.0756821i	−0.938008	−	0.346613i	$-0.887332\pi$
$71$	0.207204	−	0.637709i	0.0245906	−	0.0756821i	0.962599	+	0.270931i	$0.0873316\pi$
$72$	0.947813	−	2.91707i	0.111701	−	0.343780i
$73$	−4.04859	+	2.94147i	−0.473852	+	0.344273i	−0.798941	−	0.601410i	$-0.794606\pi$
$73$	−4.04859	+	2.94147i	−0.473852	+	0.344273i	0.325089	+	0.945684i	$0.394606\pi$
$74$	−7.47668	−	5.43212i	−0.869146	−	0.631472i
$75$		0			0
$76$	0.960132			0.110135
$77$	−1.96735	+	1.26387i	−0.224200	+	0.144032i
$78$	5.16248			0.584536
$79$	0.704642	+	2.16867i	0.0792784	+	0.243994i	0.982839	−	0.184467i	$-0.0590559\pi$
$79$	0.704642	+	2.16867i	0.0792784	+	0.243994i	−0.903560	+	0.428461i	$0.859056\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	0.0788288	−	0.242610i	0.00870518	−	0.0267918i
$83$	0.652022	−	2.00672i	0.0715687	−	0.220266i	−0.908874	−	0.417071i	$-0.863057\pi$
$83$	0.652022	−	2.00672i	0.0715687	−	0.220266i	0.980443	+	0.196805i	$0.0630566\pi$
$84$	−0.456498	+	0.331666i	−0.0498081	+	0.0361877i
$85$		0			0
$86$	2.48058	+	7.63443i	0.267488	+	0.823242i
$87$	−1.32741			−0.142313
$88$	−7.87404	−	6.44077i	−0.839375	−	0.686588i
$89$	−3.34722			−0.354805			−0.177402	−	0.984138i	$-0.556769\pi$
$89$	−3.34722			−0.354805			−0.177402	+	0.984138i	$0.556769\pi$
$90$		0			0
$91$	−2.68842	−	1.95325i	−0.281823	−	0.204756i
$92$	4.46321	−	3.24271i	0.465321	−	0.338076i
$93$	2.37364	−	7.30532i	0.246135	−	0.757526i
$94$	2.81680	−	8.66921i	0.290530	−	0.894160i
$95$		0			0
$96$	−3.40431	−	2.47338i	−0.347451	−	0.252438i
$97$	−1.02664	−	3.15968i	−0.104240	−	0.320817i	0.885312	−	0.464998i	$-0.153945\pi$
$97$	−1.02664	−	3.15968i	−0.104240	−	0.320817i	−0.989551	+	0.144182i	$0.953945\pi$
$98$	7.12261			0.719492
$99$	0.842610	+	3.20780i	0.0846855	+	0.322396i
$100$		0			0
$101$	−5.84715	−	17.9957i	−0.581813	−	1.79064i	−0.611708	−	0.791084i	$-0.709517\pi$
$101$	−5.84715	−	17.9957i	−0.581813	−	1.79064i	0.0298945	−	0.999553i	$-0.490483\pi$
$102$	−6.89440	−	5.00908i	−0.682648	−	0.495972i
$103$	−14.6403	+	10.6368i	−1.44255	+	1.04807i	−0.455049	+	0.890467i	$0.650378\pi$
$103$	−14.6403	+	10.6368i	−1.44255	+	1.04807i	−0.987502	+	0.157608i	$0.949622\pi$
$104$	4.46735	−	13.7491i	0.438060	−	1.34821i
$105$		0			0
$106$	−6.04622	+	4.39283i	−0.587261	+	0.426670i
$107$	−4.95074	−	3.59692i	−0.478606	−	0.347727i	0.322180	−	0.946678i	$-0.395584\pi$
$107$	−4.95074	−	3.59692i	−0.478606	−	0.347727i	−0.800786	+	0.598951i	$0.795584\pi$
$108$	0.247316	+	0.761160i	0.0237980	+	0.0732427i
$109$	9.03128			0.865039			0.432520	−	0.901625i	$-0.357625\pi$
$109$	9.03128			0.865039			0.432520	+	0.901625i	$0.357625\pi$
$110$		0			0
$111$	8.43763			0.800864
$112$	−0.383189	−	1.17933i	−0.0362079	−	0.111437i
$113$	3.16879	+	2.30226i	0.298095	+	0.216579i	0.726771	−	0.686879i	$-0.241020\pi$
$113$	3.16879	+	2.30226i	0.298095	+	0.216579i	−0.428676	+	0.903458i	$0.641020\pi$
$114$	1.06304	−	0.772344i	0.0995629	−	0.0723366i
$115$		0			0
$116$	−0.328288	+	1.01037i	−0.0304808	+	0.0938103i
$117$	−3.81316	+	2.77042i	−0.352527	+	0.256126i
$118$	−3.13693	−	2.27912i	−0.288778	−	0.209810i
$119$	1.69513	+	5.21707i	0.155392	+	0.478248i
$120$		0			0
$121$	10.9279	+	1.25756i	0.993444	+	0.114324i
$122$	11.9079			1.07809
$123$	0.0719704	+	0.221502i	0.00648935	+	0.0199722i
$124$	−4.97348	−	3.61344i	−0.446631	−	0.324497i
$125$		0			0
$126$	−0.238630	+	0.734428i	−0.0212588	+	0.0654280i
$127$	−3.35825	+	10.3356i	−0.297996	+	0.917138i	0.684202	+	0.729292i	$0.260151\pi$
$127$	−3.35825	+	10.3356i	−0.297996	+	0.917138i	−0.982199	+	0.187846i	$0.939849\pi$
$128$	0.392424	−	0.285113i	0.0346857	−	0.0252006i
$129$	−5.92922	−	4.30783i	−0.522039	−	0.379283i
$130$		0			0
$131$	−11.7094			−1.02305			−0.511526	−	0.859268i	$-0.670920\pi$
$131$	−11.7094			−1.02305			−0.511526	+	0.859268i	$0.670920\pi$
$132$	2.65004	+	0.151980i	0.230657	+	0.0132282i
$133$	−0.845811			−0.0733411
$134$	−0.690588	−	2.12541i	−0.0596577	−	0.183608i
$135$		0			0
$136$	−19.3066	+	14.0271i	−1.65553	+	1.20281i
$137$	−6.31328	+	19.4303i	−0.539380	+	1.66004i	0.194611	+	0.980881i	$0.437656\pi$
$137$	−6.31328	+	19.4303i	−0.539380	+	1.66004i	−0.733990	+	0.679160i	$0.762344\pi$
$138$	2.33310	−	7.18053i	0.198606	−	0.611247i
$139$	6.61048	−	4.80280i	0.560694	−	0.407368i	−0.271019	−	0.962574i	$-0.587361\pi$
$139$	6.61048	−	4.80280i	0.560694	−	0.407368i	0.831713	+	0.555206i	$0.187361\pi$
$140$		0			0
$141$	2.57173	+	7.91496i	0.216578	+	0.666560i
$142$	−0.734424			−0.0616315
$143$	3.97150	+	15.1194i	0.332113	+	1.26435i
$144$	−1.75881			−0.146567
$145$		0			0
$146$	4.43440	+	3.22178i	0.366993	+	0.266636i
$147$	−5.26097	+	3.82232i	−0.433918	+	0.315260i
$148$	2.08676	−	6.42238i	0.171531	−	0.527917i
$149$	−2.96723	+	9.13221i	−0.243085	+	0.748140i	0.752860	+	0.658181i	$0.228674\pi$
$149$	−2.96723	+	9.13221i	−0.243085	+	0.748140i	−0.995945	+	0.0899592i	$0.971326\pi$
$150$		0			0
$151$	−5.58850	−	4.06028i	−0.454785	−	0.330421i	0.336697	−	0.941613i	$-0.390690\pi$
$151$	−5.58850	−	4.06028i	−0.454785	−	0.330421i	−0.791482	+	0.611192i	$0.790690\pi$
$152$	−1.13706	−	3.49951i	−0.0922278	−	0.283848i
$153$	7.78051			0.629017
$154$	1.98244	+	1.62159i	0.159750	+	0.130671i
$155$		0			0
$156$	1.16568	+	3.58760i	0.0933292	+	0.287238i
$157$	9.18388	+	6.67248i	0.732953	+	0.532522i	0.890496	−	0.454990i	$-0.150357\pi$
$157$	9.18388	+	6.67248i	0.732953	+	0.532522i	−0.157543	+	0.987512i	$0.550357\pi$
$158$	2.02057	−	1.46803i	0.160748	−	0.116790i
$159$	2.10852	−	6.48936i	0.167217	−	0.514640i
$160$		0			0
$161$	−3.93178	+	2.85661i	−0.309868	+	0.225132i
$162$	0.886111	+	0.643798i	0.0696195	+	0.0505815i
$163$	0.553922	+	1.70480i	0.0433865	+	0.133530i	0.970403	−	0.241490i	$-0.0776360\pi$
$163$	0.553922	+	1.70480i	0.0433865	+	0.133530i	−0.927017	+	0.375020i	$0.877636\pi$
$164$	0.186398			0.0145552
$165$		0			0
$166$	−2.31106			−0.179373
$167$	−1.86167	−	5.72964i	−0.144060	−	0.443373i	0.852829	−	0.522191i	$-0.174885\pi$
$167$	−1.86167	−	5.72964i	−0.144060	−	0.443373i	−0.996889	+	0.0788186i	$0.974885\pi$
$168$	1.74948	+	1.27107i	0.134976	+	0.0980655i
$169$	−7.45546	+	5.41671i	−0.573497	+	0.416670i
$170$		0			0
$171$	−0.370718	+	1.14095i	−0.0283495	+	0.0872509i
$172$	−4.74534	+	3.44769i	−0.361829	+	0.262884i
$173$	3.38715	+	2.46091i	0.257520	+	0.187099i	0.709053	−	0.705155i	$-0.249123\pi$
$173$	3.38715	+	2.46091i	0.257520	+	0.187099i	−0.451533	+	0.892254i	$0.649123\pi$
$174$	0.449279	+	1.38274i	0.0340598	+	0.104825i
$175$		0			0
$176$	−2.11728	+	5.43549i	−0.159596	+	0.409716i
$177$	3.54011			0.266091
$178$	1.13292	+	3.48676i	0.0849156	+	0.261343i
$179$	−3.92507	−	2.85173i	−0.293374	−	0.213148i	0.431356	−	0.902182i	$-0.358035\pi$
$179$	−3.92507	−	2.85173i	−0.293374	−	0.213148i	−0.724730	+	0.689033i	$0.758035\pi$
$180$		0			0
$181$	−7.13450	+	21.9577i	−0.530303	+	1.63211i	0.223281	+	0.974754i	$0.428323\pi$
$181$	−7.13450	+	21.9577i	−0.530303	+	1.63211i	−0.753584	+	0.657351i	$0.771677\pi$
$182$	−1.12474	+	3.46160i	−0.0833714	+	0.256591i
$183$	−8.79551	+	6.39031i	−0.650183	+	0.472386i
$184$	−17.1048	−	12.4273i	−1.26098	−	0.916156i
$185$		0			0
$186$	−8.41324			−0.616889
$187$	9.36629	−	24.0452i	0.684931	−	1.75836i
$188$	6.66058			0.485773
$189$	−0.217868	−	0.670530i	−0.0158476	−	0.0487739i
$190$		0			0
$191$	−5.03670	+	3.65938i	−0.364443	+	0.264783i	−0.754903	−	0.655837i	$-0.772316\pi$
$191$	−5.03670	+	3.65938i	−0.364443	+	0.264783i	0.390460	+	0.920620i	$0.372316\pi$
$192$	−2.51125	+	7.72883i	−0.181234	+	0.557780i
$193$	−5.89815	+	18.1526i	−0.424558	+	1.30666i	0.478858	+	0.877892i	$0.341051\pi$
$193$	−5.89815	+	18.1526i	−0.424558	+	1.30666i	−0.903417	+	0.428764i	$0.858949\pi$
$194$	−2.94391	+	2.13888i	−0.211361	+	0.153562i
$195$		0			0
$196$	1.60828	+	4.94977i	0.114877	+	0.353555i
$197$	−6.80056			−0.484520			−0.242260	−	0.970211i	$-0.577889\pi$
$197$	−6.80056			−0.484520			−0.242260	+	0.970211i	$0.577889\pi$
$198$	3.05633	−	1.96346i	0.217204	−	0.139537i
$199$	21.2972			1.50972			0.754860	−	0.655886i	$-0.227705\pi$
$199$	21.2972			1.50972			0.754860	+	0.655886i	$0.227705\pi$
$200$		0			0
$201$	1.65068	+	1.19929i	0.116430	+	0.0845915i
$202$	−16.7668	+	12.1818i	−1.17971	+	0.857108i
$203$	0.289200	−	0.890065i	0.0202978	−	0.0624703i
$204$	1.92424	−	5.92222i	0.134724	−	0.414638i
$205$		0			0
$206$	16.0354	+	11.6504i	1.11724	+	0.811723i
$207$	2.13011	+	6.55580i	0.148053	+	0.455660i
$208$	−8.28984			−0.574797
$209$	3.07977	+	2.51918i	0.213032	+	0.174255i
$210$		0			0
$211$	−2.74739	−	8.45559i	−0.189138	−	0.582107i	0.810857	−	0.585244i	$-0.199001\pi$
$211$	−2.74739	−	8.45559i	−0.189138	−	0.582107i	−0.999995	+	0.00313734i	$0.999001\pi$
$212$	−4.41797	−	3.20984i	−0.303427	−	0.220453i
$213$	0.542467	−	0.394126i	0.0371692	−	0.0270050i
$214$	−2.07121	+	6.37454i	−0.141585	+	0.435755i
$215$		0			0
$216$	2.48141	−	1.80285i	0.168838	−	0.122668i
$217$	4.38129	+	3.18320i	0.297422	+	0.216089i
$218$	−3.05677	−	9.40776i	−0.207030	−	0.637174i
$219$	−5.00433			−0.338162
$220$		0			0
$221$	36.6721			2.46683
$222$	−2.85584	−	8.78936i	−0.191671	−	0.589903i
$223$	4.38261	+	3.18415i	0.293481	+	0.213226i	0.724776	−	0.688985i	$-0.241943\pi$
$223$	4.38261	+	3.18415i	0.293481	+	0.213226i	−0.431295	+	0.902211i	$0.641943\pi$
$224$	2.40017	−	1.74382i	0.160368	−	0.116514i
$225$		0			0
$226$	1.32571	−	4.08012i	0.0881850	−	0.271406i
$227$	−6.82682	+	4.95998i	−0.453112	+	0.329205i	−0.790823	−	0.612045i	$-0.790347\pi$
$227$	−6.82682	+	4.95998i	−0.453112	+	0.329205i	0.337711	+	0.941250i	$0.390347\pi$
$228$	0.776763	+	0.564352i	0.0514424	+	0.0373751i
$229$	−3.46262	−	10.6569i	−0.228817	−	0.704225i	−0.997882	−	0.0650545i	$-0.979278\pi$
$229$	−3.46262	−	10.6569i	−0.228817	−	0.704225i	0.769065	−	0.639170i	$-0.220722\pi$
$230$		0			0
$231$	−2.33451	−	0.133884i	−0.153599	−	0.00880892i
$232$	4.07140			0.267300
$233$	−1.80459	−	5.55397i	−0.118223	−	0.363852i	0.874383	−	0.485237i	$-0.161267\pi$
$233$	−1.80459	−	5.55397i	−0.118223	−	0.363852i	−0.992606	+	0.121384i	$0.961267\pi$
$234$	4.17653	+	3.03443i	0.273029	+	0.198367i
$235$		0			0
$236$	0.875526	−	2.69459i	0.0569919	−	0.175403i
$237$	−0.704642	+	2.16867i	−0.0457714	+	0.140870i
$238$	4.86081	−	3.53158i	0.315079	−	0.228919i
$239$	13.3699	+	9.71382i	0.864829	+	0.628335i	0.929194	−	0.369592i	$-0.120502\pi$
$239$	13.3699	+	9.71382i	0.864829	+	0.628335i	−0.0643656	+	0.997926i	$0.520502\pi$
$240$		0			0
$241$	−3.29180			−0.212043			−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180			−0.212043			−0.106022	+	0.994364i	$0.533811\pi$
$242$	−2.38871	−	11.8091i	−0.153552	−	0.759115i
$243$	−1.00000			−0.0641500
$244$	2.68878	+	8.27522i	0.172132	+	0.529767i
$245$		0			0
$246$	0.206376	−	0.149941i	0.0131581	−	0.00955990i
$247$	−1.74732	+	5.37769i	−0.111179	+	0.342174i
$248$	−7.28040	+	22.4068i	−0.462306	+	1.42283i
$249$	1.70702	−	1.24022i	0.108178	−	0.0785957i
$250$		0			0
$251$	−2.28652	−	7.03719i	−0.144324	−	0.444183i	0.852600	−	0.522565i	$-0.175025\pi$
$251$	−2.28652	−	7.03719i	−0.144324	−	0.444183i	−0.996923	+	0.0783815i	$0.975025\pi$
$252$	−0.564263			−0.0355452
$253$	22.8246	+	1.30899i	1.43497	+	0.0822955i
$254$	11.9031			0.746869
$255$		0			0
$256$	12.7192	+	9.24107i	0.794953	+	0.577567i
$257$	−15.1279	+	10.9911i	−0.943653	+	0.685604i	−0.949297	−	0.314380i	$-0.898203\pi$
$257$	−15.1279	+	10.9911i	−0.943653	+	0.685604i	0.00564422	+	0.999984i	$0.498203\pi$
$258$	−2.48058	+	7.63443i	−0.154434	+	0.475299i
$259$	−1.83829	+	5.65768i	−0.114226	+	0.351551i
$260$		0			0
$261$	−1.07389	−	0.780229i	−0.0664723	−	0.0482950i
$262$	3.96321	+	12.1975i	0.244848	+	0.753564i
$263$	−3.99020			−0.246046			−0.123023	−	0.992404i	$-0.539259\pi$
$263$	−3.99020			−0.246046			−0.123023	+	0.992404i	$0.539259\pi$
$264$	−2.58444	−	9.83893i	−0.159061	−	0.605544i
$265$		0			0
$266$	0.286277	+	0.881070i	0.0175528	+	0.0540219i
$267$	−2.70796	−	1.96745i	−0.165724	−	0.120406i
$268$	1.32109	−	0.959830i	0.0806986	−	0.0586309i
$269$	−3.92915	+	12.0927i	−0.239564	+	0.737303i	0.756919	+	0.653509i	$0.226704\pi$
$269$	−3.92915	+	12.0927i	−0.239564	+	0.737303i	−0.996483	+	0.0837941i	$0.973296\pi$
$270$		0			0
$271$	−19.2773	+	14.0057i	−1.17101	+	0.850788i	−0.991129	−	0.132900i	$-0.957571\pi$
$271$	−19.2773	+	14.0057i	−1.17101	+	0.850788i	−0.179880	+	0.983689i	$0.557571\pi$
$272$	11.0709	+	8.04351i	0.671274	+	0.487709i
$273$	−1.02689	−	3.16043i	−0.0621499	−	0.191278i
$274$	22.3771			1.35185
$275$		0			0
$276$	5.51683			0.332074
$277$	−2.29059	−	7.04973i	−0.137628	−	0.423577i	0.858361	−	0.513046i	$-0.171483\pi$
$277$	−2.29059	−	7.04973i	−0.137628	−	0.423577i	−0.995990	+	0.0894691i	$0.971483\pi$
$278$	−7.24042	−	5.26047i	−0.434252	−	0.315502i
$279$	6.21427	−	4.51493i	0.372039	−	0.270302i
$280$		0			0
$281$	−8.98667	+	27.6581i	−0.536100	+	1.64994i	0.205161	+	0.978728i	$0.434228\pi$
$281$	−8.98667	+	27.6581i	−0.536100	+	1.64994i	−0.741261	+	0.671217i	$0.765772\pi$
$282$	7.37447	−	5.35786i	0.439143	−	0.319056i
$283$	−17.5337	−	12.7390i	−1.04227	−	0.757256i	−0.0715451	−	0.997437i	$-0.522793\pi$
$283$	−17.5337	−	12.7390i	−1.04227	−	0.757256i	−0.970728	+	0.240182i	$0.922793\pi$
$284$	−0.165832	−	0.510378i	−0.00984031	−	0.0302854i
$285$		0			0
$286$	14.4055	−	9.25445i	0.851815	−	0.547227i
$287$	−0.164204			−0.00969265
$288$	−1.30033	−	4.00201i	−0.0766227	−	0.235821i
$289$	−35.2217	−	25.5901i	−2.07186	−	1.50530i
$290$		0			0
$291$	1.02664	−	3.15968i	0.0601828	−	0.185224i
$292$	−1.23765	+	3.80910i	−0.0724281	+	0.222911i
$293$	−6.80561	+	4.94456i	−0.397588	+	0.288865i	−0.768558	−	0.639780i	$-0.779025\pi$
$293$	−6.80561	+	4.94456i	−0.397588	+	0.288865i	0.370970	+	0.928645i	$0.379025\pi$
$294$	5.76231	+	4.18657i	0.336065	+	0.244166i
$295$		0			0
$296$	−25.8798			−1.50423
$297$	−1.20381	+	3.09044i	−0.0698524	+	0.179326i
$298$	10.5172			0.609245
$299$	10.0399	+	30.8997i	0.580623	+	1.78697i
$300$		0			0
$301$	4.18032	−	3.03718i	0.240950	−	0.175060i
$302$	−2.33803	+	7.19572i	−0.134539	+	0.414067i
$303$	5.84715	−	17.9957i	0.335910	−	1.03382i
$304$	−1.70702	+	1.24022i	−0.0979041	+	0.0711315i
$305$		0			0
$306$	−2.63343	−	8.10486i	−0.150543	−	0.463324i
$307$	−23.7431			−1.35509			−0.677545	−	0.735481i	$-0.736956\pi$
$307$	−23.7431			−1.35509			−0.677545	+	0.735481i	$0.736956\pi$
$308$	−0.679268	+	1.74382i	−0.0387049	+	0.0993635i
$309$	−18.0964			−1.02947
$310$		0			0
$311$	−18.6455	−	13.5467i	−1.05729	−	0.768164i	−0.0837029	−	0.996491i	$-0.526675\pi$
$311$	−18.6455	−	13.5467i	−1.05729	−	0.768164i	−0.973585	+	0.228326i	$0.926675\pi$
$312$	11.6957	−	8.49741i	0.662137	−	0.481071i
$313$	5.36571	−	16.5140i	0.303288	−	0.933424i	−0.677023	−	0.735962i	$-0.736730\pi$
$313$	5.36571	−	16.5140i	0.303288	−	0.933424i	0.980311	−	0.197462i	$-0.0632699\pi$
$314$	3.84221	−	11.8251i	0.216829	−	0.667330i
$315$		0			0
$316$	1.47643	+	1.07269i	0.0830558	+	0.0603436i
$317$	1.90075	+	5.84990i	0.106757	+	0.328563i	0.990139	−	0.140090i	$-0.0447393\pi$
$317$	1.90075	+	5.84990i	0.106757	+	0.328563i	−0.883382	+	0.468654i	$0.844739\pi$
$318$	−7.47354			−0.419095
$319$	−3.70402	+	2.37955i	−0.207385	+	0.133229i
$320$		0			0
$321$	−1.89101	−	5.81994i	−0.105546	−	0.324837i
$322$	4.30645	+	3.12882i	0.239989	+	0.174362i
$323$	7.55140	−	5.48641i	0.420171	−	0.305272i
$324$	−0.247316	+	0.761160i	−0.0137398	+	0.0422867i
$325$		0			0
$326$	1.58838	−	1.15403i	0.0879722	−	0.0639156i
$327$	7.30645	+	5.30845i	0.404048	+	0.293558i
$328$	−0.220747	−	0.679388i	−0.0121887	−	0.0375129i
$329$	−5.86752			−0.323487
$330$		0			0
$331$	19.4191			1.06737			0.533685	−	0.845683i	$-0.320807\pi$
$331$	19.4191			1.06737			0.533685	+	0.845683i	$0.320807\pi$
$332$	−0.521833	−	1.60604i	−0.0286393	−	0.0881428i
$333$	6.82618	+	4.95951i	0.374072	+	0.271780i
$334$	−5.33837	+	3.87856i	−0.292103	+	0.212225i
$335$		0			0
$336$	0.383189	−	1.17933i	0.0209047	−	0.0643379i
$337$	25.6352	−	18.6250i	1.39644	−	1.01457i	0.401312	−	0.915941i	$-0.368554\pi$
$337$	25.6352	−	18.6250i	1.39644	−	1.01457i	0.995124	−	0.0986291i	$-0.0314457\pi$
$338$	8.16593	+	5.93289i	0.444168	+	0.322707i
$339$	1.21037	+	3.72514i	0.0657383	+	0.202322i
$340$		0			0
$341$	−6.47231	−	24.6400i	−0.350495	−	1.33433i
$342$	1.31399			0.0710524
$343$	−2.94186	−	9.05412i	−0.158846	−	0.488876i
$344$	18.1860	+	13.2129i	0.980524	+	0.712392i
$345$		0			0
$346$	1.41706	−	4.36127i	0.0761818	−	0.234463i
$347$	8.63499	−	26.5758i	0.463551	−	1.42666i	−0.397246	−	0.917712i	$-0.630034\pi$
$347$	8.63499	−	26.5758i	0.463551	−	1.42666i	0.860796	−	0.508950i	$-0.169966\pi$
$348$	−0.859470	+	0.624442i	−0.0460724	+	0.0334736i
$349$	0.552827	+	0.401652i	0.0295921	+	0.0214999i	0.602483	−	0.798132i	$-0.294178\pi$
$349$	0.552827	+	0.401652i	0.0295921	+	0.0214999i	−0.572891	+	0.819632i	$0.694178\pi$
$350$		0			0
$351$	−4.71333			−0.251579
$352$	−13.9333	−	0.799077i	−0.742649	−	0.0425909i
$353$	−1.55900			−0.0829769			−0.0414885	−	0.999139i	$-0.513210\pi$
$353$	−1.55900			−0.0829769			−0.0414885	+	0.999139i	$0.513210\pi$
$354$	−1.19820	−	3.68769i	−0.0636837	−	0.195998i
$355$		0			0
$356$	−2.16726	+	1.57461i	−0.114865	+	0.0834542i
$357$	−1.69513	+	5.21707i	−0.0897157	+	0.276117i
$358$	−1.64211	+	5.05390i	−0.0867884	+	0.267107i
$359$	−12.8151	+	9.31073i	−0.676356	+	0.491402i	−0.872147	−	0.489244i	$-0.837273\pi$
$359$	−12.8151	+	9.31073i	−0.676356	+	0.491402i	0.195791	+	0.980646i	$0.437273\pi$
$360$		0			0
$361$	−5.42658	−	16.7013i	−0.285610	−	0.879016i
$362$	25.2878			1.32910
$363$	8.10166	+	7.44064i	0.425227	+	0.390532i
$364$	−2.65956			−0.139399
$365$		0			0
$366$	9.63367	+	6.99927i	0.503560	+	0.365858i
$367$	12.7308	−	9.24947i	0.664542	−	0.482818i	−0.203652	−	0.979043i	$-0.565281\pi$
$367$	12.7308	−	9.24947i	0.664542	−	0.482818i	0.868194	+	0.496225i	$0.165281\pi$
$368$	−3.74645	+	11.5304i	−0.195297	+	0.601064i
$369$	−0.0719704	+	0.221502i	−0.00374663	+	0.0115309i
$370$		0			0
$371$	3.89193	+	2.82765i	0.202059	+	0.146804i
$372$	−1.89970	−	5.84667i	−0.0984948	−	0.303136i
$373$	5.27703			0.273234			0.136617	−	0.990624i	$-0.456377\pi$
$373$	5.27703			0.273234			0.136617	+	0.990624i	$0.456377\pi$
$374$	−28.2177	−	1.61829i	−1.45910	−	0.0836797i
$375$		0			0
$376$	−7.88796	−	24.2767i	−0.406791	−	1.25197i
$377$	−5.06161	−	3.67748i	−0.260686	−	0.189400i
$378$	−0.624741	+	0.453901i	−0.0321332	+	0.0233462i
$379$	10.3549	−	31.8692i	0.531897	−	1.63701i	−0.218363	−	0.975868i	$-0.570072\pi$
$379$	10.3549	−	31.8692i	0.531897	−	1.63701i	0.750260	−	0.661143i	$-0.229928\pi$
$380$		0			0
$381$	−8.79201	+	6.38777i	−0.450428	+	0.327255i
$382$	5.51667	+	4.00810i	0.282257	+	0.205072i
$383$	6.25212	+	19.2420i	0.319468	+	0.983222i	0.973876	+	0.227080i	$0.0729180\pi$
$383$	6.25212	+	19.2420i	0.319468	+	0.983222i	−0.654408	+	0.756142i	$0.727082\pi$
$384$	0.485063			0.0247532
$385$		0			0
$386$	20.9057			1.06407
$387$	−2.26476	−	6.97021i	−0.115124	−	0.354316i
$388$	−2.15112	−	1.56288i	−0.109206	−	0.0793430i
$389$	22.3069	−	16.2069i	1.13101	−	0.821724i	0.145165	−	0.989408i	$-0.453629\pi$
$389$	22.3069	−	16.2069i	1.13101	−	0.821724i	0.985841	+	0.167684i	$0.0536288\pi$
$390$		0			0
$391$	16.5733	−	51.0075i	0.838150	−	2.57956i
$392$	16.1364	−	11.7238i	0.815011	−	0.592140i
$393$	−9.47308	−	6.88260i	−0.477854	−	0.347181i
$394$	2.30175	+	7.08406i	0.115960	+	0.356890i
$395$		0			0
$396$	2.05460	+	1.68061i	0.103247	+	0.0844539i
$397$	−11.7601			−0.590222			−0.295111	−	0.955463i	$-0.595357\pi$
$397$	−11.7601			−0.590222			−0.295111	+	0.955463i	$0.595357\pi$
$398$	−7.20835	−	22.1850i	−0.361322	−	1.11204i
$399$	−0.684276	−	0.497155i	−0.0342566	−	0.0248889i
$400$		0			0
$401$	−2.38687	+	7.34602i	−0.119194	+	0.366843i	−0.992799	−	0.119794i	$-0.961777\pi$
$401$	−2.38687	+	7.34602i	−0.119194	+	0.366843i	0.873604	+	0.486637i	$0.161777\pi$
$402$	0.690588	−	2.12541i	0.0344434	−	0.106006i
$403$	29.2899	−	21.2804i	1.45903	−	1.06005i
$404$	−12.2515	−	8.90124i	−0.609535	−	0.442853i
$405$		0			0
$406$	−1.02505			−0.0508725
$407$	23.5445	−	15.1256i	1.16706	−	0.749748i
$408$	−23.8643			−1.18146
$409$	5.17322	+	15.9215i	0.255799	+	0.787269i	0.993671	+	0.112328i	$0.0358307\pi$
$409$	5.17322	+	15.9215i	0.255799	+	0.787269i	−0.737872	+	0.674941i	$0.764169\pi$
$410$		0			0
$411$	−16.5284	+	12.0086i	−0.815285	+	0.592339i
$412$	−4.47553	+	13.7743i	−0.220493	+	0.678609i
$413$	−0.771279	+	2.37375i	−0.0379521	+	0.116805i
$414$	6.10813	−	4.43781i	0.300198	−	0.218107i
$415$		0			0
$416$	−6.12889	−	18.8628i	−0.300493	−	0.924824i
$417$	8.17100			0.400136
$418$	1.58180	−	4.06081i	0.0773684	−	0.198621i
$419$	−38.0968			−1.86115			−0.930576	−	0.366100i	$-0.880693\pi$
$419$	−38.0968			−1.86115			−0.930576	+	0.366100i	$0.880693\pi$
$420$		0			0
$421$	18.3350	+	13.3212i	0.893594	+	0.649234i	0.936813	−	0.349831i	$-0.113761\pi$
$421$	18.3350	+	13.3212i	0.893594	+	0.649234i	−0.0432184	+	0.999066i	$0.513761\pi$
$422$	−7.87818	+	5.72383i	−0.383504	+	0.278632i
$423$	−2.57173	+	7.91496i	−0.125042	+	0.384839i
$424$	−6.46722	+	19.9041i	−0.314076	+	0.966627i
$425$		0			0
$426$	−0.594161	−	0.431683i	−0.0287872	−	0.0209151i
$427$	−2.36863	−	7.28990i	−0.114626	−	0.352783i
$428$	−4.89758			−0.236734
$429$	−5.67397	+	14.5663i	−0.273942	+	0.703266i
$430$		0			0
$431$	−10.4994	−	32.3137i	−0.505736	−	1.55650i	−0.799529	−	0.600627i	$-0.794918\pi$
$431$	−10.4994	−	32.3137i	−0.505736	−	1.55650i	0.293793	−	0.955869i	$-0.405082\pi$
$432$	−1.42291	−	1.03380i	−0.0684596	−	0.0497388i
$433$	−29.6709	+	21.5572i	−1.42589	+	1.03597i	−0.435131	+	0.900367i	$0.643298\pi$
$433$	−29.6709	+	21.5572i	−1.42589	+	1.03597i	−0.990763	+	0.135605i	$0.956702\pi$
$434$	1.83298	−	5.64133i	0.0879858	−	0.270793i
$435$		0			0
$436$	5.84758	−	4.24852i	0.280048	−	0.203467i
$437$	6.69019	+	4.86071i	0.320035	+	0.232519i
$438$	1.69379	+	5.21295i	0.0809324	+	0.249084i
$439$	1.05012			0.0501193			0.0250596	−	0.999686i	$-0.492022\pi$
$439$	1.05012			0.0501193			0.0250596	+	0.999686i	$0.492022\pi$
$440$		0			0
$441$	−6.50292			−0.309663
$442$	−12.4122	−	38.2008i	−0.590388	−	1.81703i
$443$	−24.6917	−	17.9396i	−1.17314	−	0.852334i	−0.181756	−	0.983344i	$-0.558178\pi$
$443$	−24.6917	−	17.9396i	−1.17314	−	0.852334i	−0.991381	+	0.131009i	$0.958178\pi$
$444$	5.46321	−	3.96925i	0.259272	−	0.188372i
$445$		0			0
$446$	1.83353	−	5.64302i	0.0868201	−	0.267205i
$447$	−7.76832	+	5.64402i	−0.367429	+	0.266953i
$448$	−4.63529	−	3.36773i	−0.218997	−	0.159111i
$449$	−11.3006	−	34.7796i	−0.533308	−	1.64135i	−0.747277	−	0.664513i	$-0.768639\pi$
$449$	−11.3006	−	34.7796i	−0.533308	−	1.64135i	0.213969	−	0.976840i	$-0.431361\pi$
$450$		0			0
$451$	0.597901	+	0.489068i	0.0281540	+	0.0230293i
$452$	3.13477			0.147447
$453$	−2.13462	−	6.56967i	−0.100293	−	0.308670i
$454$	7.47738	+	5.43263i	0.350931	+	0.254966i
$455$		0			0
$456$	1.13706	−	3.49951i	0.0532478	−	0.163880i
$457$	0.736724	−	2.26740i	0.0344625	−	0.106065i	−0.932346	−	0.361568i	$-0.882241\pi$
$457$	0.736724	−	2.26740i	0.0344625	−	0.106065i	0.966808	+	0.255504i	$0.0822414\pi$
$458$	−9.92913	+	7.21393i	−0.463958	+	0.337085i
$459$	6.29457	+	4.57327i	0.293805	+	0.213462i
$460$		0			0
$461$	28.5962			1.33186			0.665929	−	0.746015i	$-0.268035\pi$
$461$	28.5962			1.33186			0.665929	+	0.746015i	$0.268035\pi$
$462$	0.650683	+	2.47714i	0.0302725	+	0.115247i
$463$	30.5806			1.42120			0.710600	−	0.703596i	$-0.248423\pi$
$463$	30.5806			1.42120			0.710600	+	0.703596i	$0.248423\pi$
$464$	−0.721447	−	2.22038i	−0.0334923	−	0.103079i
$465$		0			0
$466$	−5.17470	+	3.75964i	−0.239713	+	0.174162i
$467$	1.15640	−	3.55903i	0.0535118	−	0.164692i	−0.920729	−	0.390203i	$-0.872405\pi$
$467$	1.15640	−	3.55903i	0.0535118	−	0.164692i	0.974241	+	0.225510i	$0.0724049\pi$
$468$	−1.16568	+	3.58760i	−0.0538836	+	0.165837i
$469$	−1.16379	+	0.845545i	−0.0537389	+	0.0390436i
$470$		0			0
$471$	3.50793	+	10.7963i	0.161637	+	0.497467i
$472$	−10.8582			−0.499788
$473$	−24.2674	−	1.39174i	−1.11582	−	0.0639920i
$474$	2.49757			0.114717
$475$		0			0
$476$	3.55179	+	2.58053i	0.162796	+	0.118278i
$477$	5.52018	−	4.01064i	0.252752	−	0.183635i
$478$	5.59351	−	17.2151i	0.255841	−	0.787398i
$479$	−0.292006	+	0.898702i	−0.0133421	+	0.0410627i	−0.957506	−	0.288414i	$-0.906872\pi$
$479$	−0.292006	+	0.898702i	−0.0133421	+	0.0410627i	0.944164	+	0.329476i	$0.106872\pi$
$480$		0			0
$481$	32.1740	+	23.3758i	1.46701	+	1.06584i
$482$	1.11416	+	3.42902i	0.0507484	+	0.156188i
$483$	−4.85995			−0.221135
$484$	7.66719	−	4.32647i	0.348508	−	0.196658i
$485$		0			0
$486$	0.338464	+	1.04169i	0.0153531	+	0.0472519i
$487$	−10.8306	−	7.86887i	−0.490780	−	0.356573i	0.314704	−	0.949190i	$-0.398095\pi$
$487$	−10.8306	−	7.86887i	−0.490780	−	0.356573i	−0.805484	+	0.592617i	$0.798095\pi$
$488$	26.9775	−	19.6003i	1.22121	−	0.887263i
$489$	−0.553922	+	1.70480i	−0.0250492	+	0.0770935i
$490$		0			0
$491$	2.25625	−	1.63926i	0.101823	−	0.0739787i	−0.535709	−	0.844403i	$-0.679955\pi$
$491$	2.25625	−	1.63926i	0.101823	−	0.0739787i	0.637532	+	0.770424i	$0.279955\pi$
$492$	0.150799	+	0.109562i	0.00679855	+	0.00493944i
$493$	3.19149	+	9.82241i	0.143738	+	0.442379i
$494$	6.19327			0.278648
$495$		0			0
$496$	13.5099			0.606611
$497$	0.146087	+	0.449608i	0.00655288	+	0.0201677i
$498$	−1.86968	−	1.35840i	−0.0837825	−	0.0608716i
$499$	−14.3835	+	10.4503i	−0.643896	+	0.467818i	−0.861187	−	0.508289i	$-0.830278\pi$
$499$	−14.3835	+	10.4503i	−0.643896	+	0.467818i	0.217290	+	0.976107i	$0.430278\pi$
$500$		0			0
$501$	1.86167	−	5.72964i	0.0831733	−	0.255981i
$502$	−6.55664	+	4.76368i	−0.292637	+	0.212613i
$503$	20.8596	+	15.1554i	0.930081	+	0.675744i	0.946013	−	0.324129i	$-0.105071\pi$
$503$	20.8596	+	15.1554i	0.930081	+	0.675744i	−0.0159313	+	0.999873i	$0.505071\pi$
$504$	0.668243	+	2.05664i	0.0297659	+	0.0916100i
$505$		0			0
$506$	−6.36175	−	24.2191i	−0.282814	−	1.07667i
$507$	−9.21546			−0.409273
$508$	2.68771	+	8.27192i	0.119248	+	0.367007i
$509$	22.8386	+	16.5932i	1.01231	+	0.735483i	0.964691	−	0.263383i	$-0.0848383\pi$
$509$	22.8386	+	16.5932i	1.01231	+	0.735483i	0.0476138	+	0.998866i	$0.484838\pi$
$510$		0			0
$511$	1.09029	−	3.35556i	0.0482314	−	0.148441i
$512$	5.62107	−	17.2999i	0.248419	−	0.764554i
$513$	−0.970553	+	0.705148i	−0.0428509	+	0.0311330i
$514$	16.5695	+	12.0385i	0.730850	+	0.530993i
$515$		0			0
$516$	−5.86556			−0.258217
$517$	21.3648	+	17.4759i	0.939625	+	0.768590i
$518$	6.51573			0.286285
$519$	1.29377	+	3.98183i	0.0567904	+	0.174783i
$520$		0			0
$521$	−9.46183	+	6.87442i	−0.414530	+	0.301174i	−0.775433	−	0.631429i	$-0.782469\pi$
$521$	−9.46183	+	6.87442i	−0.414530	+	0.301174i	0.360903	+	0.932603i	$0.382469\pi$
$522$	−0.449279	+	1.38274i	−0.0196644	+	0.0605209i
$523$	6.08365	−	18.7236i	0.266019	−	0.818724i	−0.725437	−	0.688288i	$-0.758362\pi$
$523$	6.08365	−	18.7236i	0.266019	−	0.818724i	0.991457	−	0.130436i	$-0.0416376\pi$
$524$	−7.58160	+	5.50836i	−0.331204	+	0.240634i
$525$		0			0
$526$	1.35054	+	4.15654i	0.0588863	+	0.181234i
$527$	−59.7642			−2.60337
$528$	−4.90782	+	3.15290i	−0.213585	+	0.137212i
$529$	24.5159			1.06591
$530$		0			0
$531$	2.86401	+	2.08083i	0.124287	+	0.0903001i
$532$	−0.547647	+	0.397889i	−0.0237435	+	0.0172507i
$533$	−0.339220	+	1.04401i	−0.0146933	+	0.0452212i
$534$	−1.13292	+	3.48676i	−0.0490261	+	0.150887i
$535$		0			0
$536$	−5.06295	−	3.67845i	−0.218686	−	0.158885i
$537$	−1.49924	−	4.61420i	−0.0646972	−	0.199117i
$538$	13.9266			0.600420
$539$	−7.82831	+	20.0969i	−0.337189	+	0.865635i
$540$		0			0
$541$	−1.68443	−	5.18413i	−0.0724191	−	0.222883i	0.908295	−	0.418330i	$-0.137384\pi$
$541$	−1.68443	−	5.18413i	−0.0724191	−	0.222883i	−0.980714	+	0.195447i	$0.937384\pi$
$542$	21.1143	+	15.3404i	0.906935	+	0.658927i
$543$	−18.6784	+	13.5706i	−0.801565	+	0.582371i
$544$	−10.1172	+	31.1377i	−0.433773	+	1.33502i
$545$		0			0
$546$	−2.94461	+	2.13939i	−0.126018	+	0.0915572i
$547$	10.3467	+	7.51731i	0.442393	+	0.321417i	0.786585	−	0.617482i	$-0.211847\pi$
$547$	10.3467	+	7.51731i	0.442393	+	0.321417i	−0.344192	+	0.938899i	$0.611847\pi$
$548$	5.05271	+	15.5507i	0.215841	+	0.664291i
$549$	−10.8719			−0.463999
$550$		0			0
$551$	−1.59245			−0.0678405
$552$	−6.53344	−	20.1079i	−0.278082	−	0.855848i
$553$	−1.30064	−	0.944967i	−0.0553087	−	0.0401841i
$554$	−6.56832	+	4.77216i	−0.279061	+	0.202750i
$555$		0			0
$556$	2.02082	−	6.21944i	0.0857018	−	0.263763i
$557$	−0.286771	+	0.208351i	−0.0121509	+	0.00882812i	−0.593844	−	0.804580i	$-0.702390\pi$
$557$	−0.286771	+	0.208351i	−0.0121509	+	0.00882812i	0.581693	+	0.813408i	$0.302390\pi$
$558$	−6.80645	−	4.94518i	−0.288140	−	0.209346i
$559$	−10.6746	−	32.8529i	−0.451486	−	1.38953i
$560$		0			0
$561$	21.7109	−	13.9476i	0.916636	−	0.588869i
$562$	31.8528			1.34363
$563$	−10.8409	−	33.3648i	−0.456888	−	1.40616i	−0.868904	−	0.494981i	$-0.835175\pi$
$563$	−10.8409	−	33.3648i	−0.456888	−	1.40616i	0.412015	−	0.911177i	$-0.364825\pi$
$564$	5.38852	+	3.91499i	0.226898	+	0.164851i
$565$		0			0
$566$	−7.33551	+	22.5764i	−0.308334	+	0.948956i
$567$	0.217868	−	0.670530i	0.00914961	−	0.0281596i
$568$	−1.66385	+	1.20886i	−0.0698135	+	0.0507225i
$569$	13.2015	+	9.59145i	0.553436	+	0.402094i	0.829051	−	0.559174i	$-0.188881\pi$
$569$	13.2015	+	9.59145i	0.553436	+	0.402094i	−0.275615	+	0.961268i	$0.588881\pi$
$570$		0			0
$571$	−14.4160			−0.603291			−0.301645	−	0.953420i	$-0.597536\pi$
$571$	−14.4160			−0.603291			−0.301645	+	0.953420i	$0.597536\pi$
$572$	9.68400	+	7.92127i	0.404908	+	0.331205i
$573$	−6.22571			−0.260083
$574$	0.0555772	+	0.171049i	0.00231975	+	0.00713945i
$575$		0			0
$576$	−6.57453	+	4.77668i	−0.273939	+	0.199028i
$577$	−2.75292	+	8.47261i	−0.114605	+	0.352719i	−0.991865	−	0.127298i	$-0.959370\pi$
$577$	−2.75292	+	8.47261i	−0.114605	+	0.352719i	0.877259	+	0.480017i	$0.159370\pi$
$578$	−14.7355	+	45.3513i	−0.612917	+	1.88636i
$579$	−15.4416	+	11.2190i	−0.641730	+	0.466244i
$580$		0			0
$581$	0.459700	+	1.41481i	0.0190716	+	0.0586962i
$582$	−3.63887			−0.150836
$583$	−5.74939	−	21.8879i	−0.238116	−	0.906503i
$584$	15.3492			0.635155
$585$		0			0
$586$	7.45414	+	5.41575i	0.307928	+	0.223723i
$587$	−11.1655	+	8.11225i	−0.460851	+	0.334828i	−0.793865	−	0.608094i	$-0.791934\pi$
$587$	−11.1655	+	8.11225i	−0.460851	+	0.334828i	0.333014	+	0.942922i	$0.391934\pi$
$588$	−1.60828	+	4.94977i	−0.0663242	+	0.204125i
$589$	2.84758	−	8.76396i	0.117333	−	0.361113i
$590$		0			0
$591$	−5.50177	−	3.99727i	−0.226313	−	0.164426i
$592$	4.58586	+	14.1138i	0.188478	+	0.580075i
$593$	16.4676			0.676242			0.338121	−	0.941103i	$-0.390209\pi$
$593$	16.4676			0.676242			0.338121	+	0.941103i	$0.390209\pi$
$594$	3.62672	+	0.207992i	0.148806	+	0.00853403i
$595$		0			0
$596$	2.37477	+	7.30879i	0.0972744	+	0.299380i
$597$	17.2298	+	12.5182i	0.705170	+	0.512336i
$598$	28.7896	−	20.9169i	1.17729	−	0.855354i
$599$	11.6994	−	36.0069i	0.478023	−	1.47120i	−0.363814	−	0.931472i	$-0.618525\pi$
$599$	11.6994	−	36.0069i	0.478023	−	1.47120i	0.841837	−	0.539732i	$-0.181475\pi$
$600$		0			0
$601$	−1.26563	+	0.919535i	−0.0516262	+	0.0375086i	−0.613299	−	0.789851i	$-0.710158\pi$
$601$	−1.26563	+	0.919535i	−0.0516262	+	0.0375086i	0.561673	+	0.827359i	$0.310158\pi$
$602$	−4.57868	−	3.32660i	−0.186613	−	0.135582i
$603$	0.630505	+	1.94049i	0.0256761	+	0.0790230i
$604$	−5.52850			−0.224951
$605$		0			0
$606$	−20.7249			−0.841892
$607$	−5.82568	−	17.9296i	−0.236457	−	0.727740i	−0.996925	−	0.0783641i	$-0.975030\pi$
$607$	−5.82568	−	17.9296i	−0.236457	−	0.727740i	0.760468	−	0.649376i	$-0.224970\pi$
$608$	−4.08405	−	2.96723i	−0.165630	−	0.120337i
$609$	0.757135	−	0.550090i	0.0306806	−	0.0222908i
$610$		0			0
$611$	−12.1214	+	37.3058i	−0.490379	+	1.50923i
$612$	5.03774	−	3.66013i	0.203639	−	0.147952i
$613$	26.4306	+	19.2030i	1.06752	+	0.775601i	0.975465	−	0.220153i	$-0.0706557\pi$
$613$	26.4306	+	19.2030i	1.06752	+	0.775601i	0.0920574	+	0.995754i	$0.470656\pi$
$614$	8.03619	+	24.7329i	0.324314	+	0.998137i
$615$		0			0
$616$	7.16037	+	0.410647i	0.288499	+	0.0165454i
$617$	33.6559			1.35493			0.677467	−	0.735553i	$-0.263078\pi$
$617$	33.6559			1.35493			0.677467	+	0.735553i	$0.263078\pi$
$618$	6.12499	+	18.8508i	0.246383	+	0.758289i
$619$	7.23262	+	5.25480i	0.290703	+	0.211208i	0.723572	−	0.690248i	$-0.242499\pi$
$619$	7.23262	+	5.25480i	0.290703	+	0.211208i	−0.432869	+	0.901457i	$0.642499\pi$
$620$		0			0
$621$	−2.13011	+	6.55580i	−0.0854784	+	0.263075i
$622$	−7.80061	+	24.0078i	−0.312776	+	0.962626i
$623$	1.90921	−	1.38712i	0.0764910	−	0.0555739i
$624$	−6.70662	−	4.87265i	−0.268480	−	0.195062i
$625$		0			0
$626$	−19.0185			−0.760131
$627$	1.01085	+	3.84830i	0.0403696	+	0.153686i
$628$	9.08528			0.362542
$629$	−20.2867	−	62.4360i	−0.808883	−	2.48949i
$630$		0			0
$631$	15.5798	−	11.3194i	0.620224	−	0.450619i	−0.232776	−	0.972530i	$-0.574781\pi$
$631$	15.5798	−	11.3194i	0.620224	−	0.450619i	0.853000	+	0.521912i	$0.174781\pi$
$632$	2.16127	−	6.65170i	0.0859706	−	0.264590i
$633$	2.74739	−	8.45559i	0.109199	−	0.336080i
$634$	5.45043	−	3.95997i	0.216464	−	0.157270i
$635$		0			0
$636$	−1.68751	−	5.19364i	−0.0669143	−	0.205941i
$637$	−30.6504			−1.21441
$638$	3.73243	+	3.05303i	0.147768	+	0.120871i
$639$	0.670527			0.0265256
$640$		0			0
$641$	12.0485	+	8.75375i	0.475887	+	0.345752i	0.799731	−	0.600358i	$-0.204975\pi$
$641$	12.0485	+	8.75375i	0.475887	+	0.345752i	−0.323844	+	0.946110i	$0.604975\pi$
$642$	−5.42251	+	3.93968i	−0.214009	+	0.155487i
$643$	−10.9143	+	33.5907i	−0.430417	+	1.32469i	0.467295	+	0.884102i	$0.345229\pi$
$643$	−10.9143	+	33.5907i	−0.430417	+	1.32469i	−0.897711	+	0.440584i	$0.854771\pi$
$644$	−1.20194	+	3.69920i	−0.0473632	+	0.145769i
$645$		0			0
$646$	−8.27100	−	6.00923i	−0.325418	−	0.236430i
$647$	−9.62366	−	29.6186i	−0.378345	−	1.16443i	−0.941194	−	0.337867i	$-0.890295\pi$
$647$	−9.62366	−	29.6186i	−0.378345	−	1.16443i	0.562849	−	0.826560i	$-0.309705\pi$
$648$	3.06719			0.120490
$649$	9.87841	−	6.34613i	0.387761	−	0.249107i
$650$		0			0
$651$	1.67350	+	5.15052i	0.0655898	+	0.201865i
$652$	1.16063	+	0.843246i	0.0454537	+	0.0330241i
$653$	4.08953	−	2.97122i	0.160036	−	0.116273i	−0.504885	−	0.863186i	$-0.668465\pi$
$653$	4.08953	−	2.97122i	0.160036	−	0.116273i	0.664921	+	0.746914i	$0.268465\pi$
$654$	3.05677	−	9.40776i	0.119529	−	0.367872i
$655$		0			0
$656$	−0.331396	+	0.240774i	−0.0129389	+	0.00940063i
$657$	−4.04859	−	2.94147i	−0.157951	−	0.114758i
$658$	1.98595	+	6.11211i	0.0774202	+	0.238275i
$659$	−14.4486			−0.562837			−0.281419	−	0.959585i	$-0.590805\pi$
$659$	−14.4486			−0.562837			−0.281419	+	0.959585i	$0.590805\pi$
$660$		0			0
$661$	14.8696			0.578361			0.289181	−	0.957275i	$-0.406617\pi$
$661$	14.8696			0.578361			0.289181	+	0.957275i	$0.406617\pi$
$662$	−6.57267	−	20.2286i	−0.255454	−	0.786207i
$663$	29.6684	+	21.5553i	1.15222	+	0.837140i
$664$	−5.23573	+	3.80398i	−0.203186	+	0.147623i
$665$		0			0
$666$	2.85584	−	8.78936i	0.110661	−	0.340581i
$667$	−7.40254	+	5.37826i	−0.286627	+	0.208247i
$668$	−3.90075	−	2.83406i	−0.150925	−	0.109653i
$669$	1.67401	+	5.15206i	0.0647208	+	0.199190i
$670$		0			0
$671$	−13.0877	+	33.5988i	−0.505245	+	1.29707i
$672$	2.96677			0.114446
$673$	12.8598	+	39.5785i	0.495710	+	1.52564i	0.815848	+	0.578267i	$0.196271\pi$
$673$	12.8598	+	39.5785i	0.495710	+	1.52564i	−0.320138	+	0.947371i	$0.603729\pi$
$674$	−28.0780	−	20.3999i	−1.08153	−	0.785774i
$675$		0			0
$676$	−2.27913	+	7.01444i	−0.0876588	+	0.269786i
$677$	−13.6699	+	42.0715i	−0.525376	+	1.61694i	0.238195	+	0.971217i	$0.423444\pi$
$677$	−13.6699	+	42.0715i	−0.525376	+	1.61694i	−0.763571	+	0.645724i	$0.776556\pi$
$678$	3.47076	−	2.52165i	0.133294	−	0.0968435i
$679$	1.89499	+	1.37679i	0.0727229	+	0.0528363i
$680$		0			0
$681$	−8.43842			−0.323361
$682$	−23.4765	+	15.0819i	−0.898962	+	0.577515i
$683$	−24.5318			−0.938683			−0.469342	−	0.883017i	$-0.655509\pi$
$683$	−24.5318			−0.938683			−0.469342	+	0.883017i	$0.655509\pi$
$684$	0.296697	+	0.913140i	0.0113445	+	0.0349148i
$685$		0			0
$686$	−8.43584	+	6.12899i	−0.322082	+	0.234006i
$687$	3.46262	−	10.6569i	0.132107	−	0.406584i
$688$	3.98328	−	12.2593i	0.151861	−	0.467380i
$689$	26.0184	−	18.9035i	0.991222	−	0.720165i
$690$		0			0
$691$	7.34440	+	22.6037i	0.279394	+	0.859887i	0.988023	+	0.154306i	$0.0493141\pi$
$691$	7.34440	+	22.6037i	0.279394	+	0.859887i	−0.708629	+	0.705581i	$0.750686\pi$
$692$	3.35078			0.127378
$693$	−1.80996	−	1.48050i	−0.0687547	−	0.0562397i
$694$	−30.6063			−1.16180
$695$		0			0
$696$	3.29383	+	2.39311i	0.124852	+	0.0907105i
$697$	1.46601	−	1.06512i	0.0555292	−	0.0403443i
$698$	0.231283	−	0.711817i	0.00875420	−	0.0269427i
$699$	1.80459	−	5.55397i	0.0682560	−	0.210070i
$700$		0			0
$701$	26.4499	+	19.2170i	0.998999	+	0.725816i	0.961873	−	0.273495i	$-0.0881797\pi$
$701$	26.4499	+	19.2170i	0.998999	+	0.725816i	0.0371259	+	0.999311i	$0.488180\pi$
$702$	1.59529	+	4.90981i	0.0602105	+	0.185309i
$703$	10.1224			0.381772
$704$	6.84753	+	26.0684i	0.258076	+	0.982491i
$705$		0			0
$706$	0.527664	+	1.62398i	0.0198589	+	0.0611194i
$707$	10.7927	+	7.84138i	0.405903	+	0.294905i
$708$	2.29216	−	1.66535i	0.0861445	−	0.0625877i
$709$	7.36278	−	22.6603i	0.276515	−	0.851025i	−0.712300	−	0.701875i	$-0.752346\pi$
$709$	7.36278	−	22.6603i	0.276515	−	0.851025i	0.988815	−	0.149150i	$-0.0476537\pi$
$710$		0			0
$711$	−1.84478	+	1.34031i	−0.0691845	+	0.0502655i
$712$	8.30582	+	6.03453i	0.311274	+	0.226154i
$713$	−16.3619	−	50.3568i	−0.612759	−	1.88588i
$714$	6.00829			0.224855
$715$		0			0
$716$	−3.88293			−0.145112
$717$	5.10686	+	15.7173i	0.190719	+	0.586973i
$718$	14.0363	+	10.1980i	0.523831	+	0.380586i
$719$	2.30311	−	1.67331i	0.0858914	−	0.0624038i	−0.544011	−	0.839078i	$-0.683095\pi$
$719$	2.30311	−	1.67331i	0.0858914	−	0.0624038i	0.629902	+	0.776674i	$0.283095\pi$
$720$		0			0
$721$	3.94263	−	12.1342i	0.146831	−	0.451900i
$722$	−15.5608	+	11.3056i	−0.579114	+	0.420751i
$723$	−2.66312	−	1.93487i	−0.0990425	−	0.0719586i
$724$	5.70996	+	17.5735i	0.212209	+	0.653112i
$725$		0			0
$726$	5.00869	−	10.9578i	0.185890	−	0.406681i
$727$	13.5192			0.501399			0.250700	−	0.968065i	$-0.419339\pi$
$727$	13.5192			0.501399			0.250700	+	0.968065i	$0.419339\pi$
$728$	3.14965	+	9.69362i	0.116734	+	0.359270i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−17.6210	+	54.2318i	−0.651736	+	2.00584i
$732$	−2.68878	+	8.27522i	−0.0993802	+	0.305861i
$733$	26.5643	−	19.3001i	0.981174	−	0.712864i	0.0232030	−	0.999731i	$-0.492614\pi$
$733$	26.5643	−	19.3001i	0.981174	−	0.712864i	0.957971	+	0.286866i	$0.0926136\pi$
$734$	−13.9440	−	10.1309i	−0.514681	−	0.373938i
$735$		0			0
$736$	−29.0062			−1.06918
$737$	6.75599	+	0.387456i	0.248860	+	0.0142721i
$738$	0.255095			0.00939018
$739$	15.7267	+	48.4018i	0.578516	+	1.78049i	0.623882	+	0.781519i	$0.285555\pi$
$739$	15.7267	+	48.4018i	0.578516	+	1.78049i	−0.0453660	+	0.998970i	$0.514445\pi$
$740$		0			0
$741$	−4.57453	+	3.32359i	−0.168050	+	0.122095i
$742$	1.62825	−	5.01123i	0.0597749	−	0.183968i
$743$	4.78528	−	14.7276i	0.175555	−	0.540302i	−0.824104	−	0.566439i	$-0.808321\pi$
$743$	4.78528	−	14.7276i	0.175555	−	0.540302i	0.999658	+	0.0261370i	$0.00832063\pi$
$744$	−19.0603	+	13.8481i	−0.698786	+	0.507697i
$745$		0			0
$746$	−1.78609	−	5.49702i	−0.0653933	−	0.201260i
$747$	2.10999			0.0772004
$748$	−5.24692	−	19.9750i	−0.191846	−	0.730357i
$749$	4.31444			0.157646
$750$		0			0
$751$	−8.94571	−	6.49944i	−0.326434	−	0.237168i	0.412482	−	0.910966i	$-0.364662\pi$
$751$	−8.94571	−	6.49944i	−0.326434	−	0.237168i	−0.738916	+	0.673798i	$0.764662\pi$
$752$	−11.8418	+	8.60359i	−0.431827	+	0.313740i
$753$	2.28652	−	7.03719i	0.0833255	−	0.256449i
$754$	−2.11760	+	6.51731i	−0.0771185	+	0.237346i
$755$		0			0
$756$	−0.456498	−	0.331666i	−0.0166027	−	0.0120626i
$757$	−2.78203	−	8.56219i	−0.101114	−	0.311198i	0.887684	−	0.460452i	$-0.152313\pi$
$757$	−2.78203	−	8.56219i	−0.101114	−	0.311198i	−0.988799	+	0.149254i	$0.952313\pi$
$758$	−36.7025			−1.33309
$759$	17.6961	+	14.4750i	0.642327	+	0.525407i
$760$		0			0
$761$	2.56374	+	7.89038i	0.0929355	+	0.286026i	0.986710	−	0.162490i	$-0.0519526\pi$
$761$	2.56374	+	7.89038i	0.0929355	+	0.286026i	−0.893775	+	0.448516i	$0.851953\pi$
$762$	9.62983	+	6.99648i	0.348852	+	0.253456i
$763$	−5.15132	+	3.74265i	−0.186490	+	0.135493i
$764$	−1.53972	+	4.73876i	−0.0557050	+	0.171442i
$765$		0			0
$766$	17.9281	−	13.0255i	0.647767	−	0.470630i
$767$	13.4990	+	9.80761i	0.487421	+	0.354132i
$768$	4.85832	+	14.9524i	0.175310	+	0.539547i
$769$	2.89088			0.104248			0.0521239	−	0.998641i	$-0.483401\pi$
$769$	2.89088			0.104248			0.0521239	+	0.998641i	$0.483401\pi$
$770$		0			0
$771$	−18.6991			−0.673432
$772$	4.72047	+	14.5281i	0.169894	+	0.522879i
$773$	−22.5293	−	16.3685i	−0.810322	−	0.588734i	0.103602	−	0.994619i	$-0.466963\pi$
$773$	−22.5293	−	16.3685i	−0.810322	−	0.588734i	−0.913924	+	0.405885i	$0.866963\pi$
$774$	−6.49424	+	4.71834i	−0.233431	+	0.169597i
$775$		0			0
$776$	−3.14890	+	9.69132i	−0.113039	+	0.347898i
$777$	−4.81271	+	3.49664i	−0.172655	+	0.125441i
$778$	−24.4326	−	17.7513i	−0.875952	−	0.636417i
$779$	0.0863407	+	0.265729i	0.00309348	+	0.00952074i
$780$		0			0
$781$	0.807189	−	2.07222i	0.0288835	−	0.0741500i
$782$	−58.7433			−2.10066
$783$	−0.410191	−	1.26244i	−0.0146590	−	0.0451158i
$784$	−9.25304	−	6.72273i	−0.330466	−	0.240098i
$785$		0			0
$786$	−3.96321	+	12.1975i	−0.141363	+	0.435070i
$787$	7.67461	−	23.6200i	0.273570	−	0.841963i	−0.716024	−	0.698076i	$-0.754040\pi$
$787$	7.67461	−	23.6200i	0.273570	−	0.841963i	0.989594	−	0.143887i	$-0.0459602\pi$
$788$	−4.40324	+	3.19914i	−0.156859	+	0.113965i
$789$	−3.22814	−	2.34538i	−0.114925	−	0.0834977i
$790$		0			0
$791$	−2.76152			−0.0981883
$792$	3.69232	−	9.47896i	0.131201	−	0.336820i
$793$	−51.2426			−1.81968
$794$	3.98037	+	12.2503i	0.141258	+	0.434748i
$795$		0			0
$796$	13.7896	−	10.0187i	0.488758	−	0.355103i
$797$	0.868668	−	2.67348i	0.0307698	−	0.0946997i	−0.934492	−	0.355984i	$-0.884146\pi$
$797$	0.868668	−	2.67348i	0.0307698	−	0.0946997i	0.965262	+	0.261284i	$0.0841459\pi$
$798$	−0.286277	+	0.881070i	−0.0101341	+	0.0311895i
$799$	52.3852	−	38.0600i	1.85325	−	1.34647i
$800$		0			0
$801$	−1.03435	−	3.18340i	−0.0365469	−	0.112480i
$802$	8.46012			0.298737
$803$	−13.9642	+	8.97095i	−0.492786	+	0.316578i
$804$	1.63296			0.0575901
$805$		0			0
$806$	−32.0811	−	23.3083i	−1.13001	−	0.820998i
$807$	−10.2866	+	7.47368i	−0.362107	+	0.263086i
$808$	−17.9343	+	55.1961i	−0.630926	+	1.94179i
$809$	3.60825	−	11.1051i	0.126859	−	0.390433i	−0.867376	−	0.497654i	$-0.834195\pi$
$809$	3.60825	−	11.1051i	0.126859	−	0.390433i	0.994235	+	0.107220i	$0.0341950\pi$
$810$		0			0
$811$	−19.4722	−	14.1474i	−0.683761	−	0.496782i	0.190842	−	0.981621i	$-0.438878\pi$
$811$	−19.4722	−	14.1474i	−0.683761	−	0.496782i	−0.874603	+	0.484839i	$0.838878\pi$
$812$	−0.231455	−	0.712347i	−0.00812250	−	0.0249985i
$813$	−23.8280			−0.835684
$814$	−23.7251	−	19.4066i	−0.831565	−	0.680199i
$815$		0			0
$816$	4.22872	+	13.0147i	0.148035	+	0.455604i
$817$	−7.11310	−	5.16797i	−0.248856	−	0.180804i
$818$	14.8343	−	10.7777i	0.518669	−	0.376835i
$819$	1.02689	−	3.16043i	0.0358823	−	0.110434i
$820$		0			0
$821$	−3.92827	+	2.85406i	−0.137098	+	0.0996073i	−0.654220	−	0.756304i	$-0.727003\pi$
$821$	−3.92827	+	2.85406i	−0.137098	+	0.0996073i	0.517123	+	0.855911i	$0.327003\pi$
$822$	18.1034	+	13.1529i	0.631430	+	0.458761i
$823$	−8.05300	−	24.7846i	−0.280710	−	0.863937i	−0.987652	−	0.156665i	$-0.949926\pi$
$823$	−8.05300	−	24.7846i	−0.280710	−	0.863937i	0.706942	−	0.707272i	$-0.250074\pi$
$824$	55.5050			1.93361
$825$		0			0
$826$	2.73376			0.0951195
$827$	5.03212	+	15.4873i	0.174984	+	0.538546i	0.999633	−	0.0270996i	$-0.00862714\pi$
$827$	5.03212	+	15.4873i	0.174984	+	0.538546i	−0.824649	+	0.565645i	$0.808627\pi$
$828$	4.46321	+	3.24271i	0.155107	+	0.112692i
$829$	8.10161	−	5.88616i	0.281380	−	0.204435i	−0.438139	−	0.898907i	$-0.644362\pi$
$829$	8.10161	−	5.88616i	0.281380	−	0.204435i	0.719519	+	0.694472i	$0.244362\pi$
$830$		0			0
$831$	2.29059	−	7.04973i	0.0794598	−	0.244552i
$832$	−30.9879	+	22.5140i	−1.07431	+	0.780534i
$833$	40.9331	+	29.7396i	1.41825	+	1.03042i
$834$	−2.76559	−	8.51162i	−0.0957647	−	0.294733i
$835$		0			0
$836$	3.17917	+	0.182326i	0.109954	+	0.00630587i
$837$	7.68126			0.265503
$838$	12.8944	+	39.6849i	0.445430	+	1.37089i
$839$	−9.50855	−	6.90837i	−0.328272	−	0.238503i	0.411425	−	0.911444i	$-0.365031\pi$
$839$	−9.50855	−	6.90837i	−0.328272	−	0.238503i	−0.739697	+	0.672940i	$0.765031\pi$
$840$		0			0
$841$	−8.41700	+	25.9049i	−0.290242	+	0.893271i
$842$	7.67073	−	23.6081i	0.264351	−	0.813588i
$843$	−23.5274	+	17.0937i	−0.810327	+	0.588737i
$844$	−5.75659	−	4.18240i	−0.198150	−	0.143964i
$845$		0			0
$846$	9.11534			0.313392
$847$	−6.75427	+	3.81133i	−0.232079	+	0.130959i
$848$	12.0009			0.412113
$849$	−6.69730	−	20.6122i	−0.229851	−	0.707407i
$850$		0			0
$851$	47.0541	−	34.1868i	1.61299	−	1.17191i
$852$	0.165832	−	0.510378i	0.00568131	−	0.0174853i
$853$	14.1021	−	43.4018i	0.482847	−	1.48605i	−0.352229	−	0.935914i	$-0.614576\pi$
$853$	14.1021	−	43.4018i	0.482847	−	1.48605i	0.835076	−	0.550135i	$-0.185424\pi$
$854$	−6.79210	+	4.93475i	−0.232421	+	0.168864i
$855$		0			0
$856$	5.80009	+	17.8508i	0.198243	+	0.610129i
$857$	8.41558			0.287471			0.143735	−	0.989616i	$-0.454089\pi$
$857$	8.41558			0.287471			0.143735	+	0.989616i	$0.454089\pi$
$858$	17.0939	+	0.980336i	0.583577	+	0.0334681i
$859$	−45.3009			−1.54565			−0.772823	−	0.634622i	$-0.781156\pi$
$859$	−45.3009			−1.54565			−0.772823	+	0.634622i	$0.781156\pi$
$860$		0			0
$861$	−0.132844	−	0.0965167i	−0.00452730	−	0.00328928i
$862$	−30.1071	+	21.8741i	−1.02545	+	0.745034i
$863$	3.72644	−	11.4688i	0.126849	−	0.390402i	−0.867384	−	0.497639i	$-0.834200\pi$
$863$	3.72644	−	11.4688i	0.126849	−	0.390402i	0.994233	+	0.107237i	$0.0342003\pi$
$864$	1.30033	−	4.00201i	0.0442382	−	0.136151i
$865$		0			0
$866$	32.4984	+	23.6115i	1.10434	+	0.802350i
$867$	−13.4535	−	41.4056i	−0.456904	−	1.40621i
$868$	4.33425			0.147114
$869$	1.92138	+	7.31466i	0.0651783	+	0.248133i
$870$		0			0
$871$	2.97178	+	9.14618i	0.100695	+	0.309907i
$872$	−22.4103	−	16.2820i	−0.758907	−	0.551378i
$873$	2.68778	−	1.95279i	0.0909676	−	0.0660919i
$874$	2.79894	−	8.61426i	0.0946757	−	0.291382i
$875$		0			0
$876$	−3.24021	+	2.35415i	−0.109477	+	0.0795395i
$877$	−17.1058	−	12.4281i	−0.577621	−	0.419666i	0.260245	−	0.965543i	$-0.416197\pi$
$877$	−17.1058	−	12.4281i	−0.577621	−	0.419666i	−0.837866	+	0.545876i	$0.816197\pi$
$878$	−0.355427	−	1.09389i	−0.0119951	−	0.0369170i
$879$	−8.41220			−0.283736
$880$		0			0
$881$	−13.1669			−0.443605			−0.221803	−	0.975092i	$-0.571194\pi$
$881$	−13.1669			−0.443605			−0.221803	+	0.975092i	$0.571194\pi$
$882$	2.20101	+	6.77401i	0.0741118	+	0.228093i
$883$	−28.1293	−	20.4371i	−0.946627	−	0.687765i	0.00337992	−	0.999994i	$-0.498924\pi$
$883$	−28.1293	−	20.4371i	−0.946627	−	0.687765i	−0.950007	+	0.312230i	$0.898924\pi$
$884$	23.7445	−	17.2514i	0.798614	−	0.580227i
$885$		0			0
$886$	−10.3301	+	31.7929i	−0.347048	+	1.06810i
$887$	−16.9542	+	12.3179i	−0.569266	+	0.413596i	−0.834838	−	0.550495i	$-0.814439\pi$
$887$	−16.9542	+	12.3179i	−0.569266	+	0.413596i	0.265573	+	0.964091i	$0.414439\pi$
$888$	−20.9372	−	15.2117i	−0.702605	−	0.510473i
$889$	−2.36769	−	7.28700i	−0.0794097	−	0.244398i
$890$		0			0
$891$	−2.79042	+	1.79264i	−0.0934827	+	0.0600556i
$892$	4.33555			0.145165
$893$	3.08522	+	9.49533i	0.103243	+	0.317749i
$894$	8.50860	+	6.18186i	0.284570	+	0.206752i
$895$		0			0
$896$	−0.105680	+	0.325249i	−0.00353052	+	0.0108658i
$897$	−10.0399	+	30.8997i	−0.335223	+	1.03171i
$898$	−32.4046	+	23.5433i	−1.08136	+	0.785652i
$899$	8.24886	+	5.99314i	0.275115	+	0.199883i
$900$		0			0
$901$	−53.0889			−1.76865
$902$	0.307087	−	0.788357i	0.0102249	−	0.0262494i
$903$	5.16716			0.171952
$904$	−3.71243	−	11.4257i	−0.123474	−	0.380013i
$905$		0			0
$906$	−6.12105	+	4.44720i	−0.203358	+	0.147748i
$907$	−8.10886	+	24.9565i	−0.269250	+	0.828667i	0.721433	+	0.692484i	$0.243484\pi$
$907$	−8.10886	+	24.9565i	−0.269250	+	0.828667i	−0.990684	+	0.136183i	$0.956516\pi$
$908$	−2.08695	+	6.42299i	−0.0692580	+	0.213154i
$909$	15.3080	−	11.1219i	0.507736	−	0.368891i
$910$		0			0
$911$	−12.2556	−	37.7188i	−0.406045	−	1.24968i	−0.920019	−	0.391873i	$-0.871827\pi$
$911$	−12.2556	−	37.7188i	−0.406045	−	1.24968i	0.513974	−	0.857806i	$-0.328173\pi$
$912$	−2.10999			−0.0698687
$913$	2.54003	−	6.52079i	0.0840628	−	0.215807i
$914$	−2.61128			−0.0863734
$915$		0			0
$916$	−7.25521	−	5.27122i	−0.239719	−	0.174166i
$917$	6.67887	−	4.85249i	0.220556	−	0.160243i
$918$	2.63343	−	8.10486i	0.0869161	−	0.267500i
$919$	4.62777	−	14.2428i	0.152656	−	0.469827i	−0.845260	−	0.534356i	$-0.820554\pi$
$919$	4.62777	−	14.2428i	0.152656	−	0.469827i	0.997916	+	0.0645285i	$0.0205543\pi$
$920$		0			0
$921$	−19.2086	−	13.9558i	−0.632944	−	0.459861i
$922$	−9.67881	−	29.7883i	−0.318754	−	0.981025i
$923$	3.16041			0.104026
$924$	−1.57453	+	1.01152i	−0.0517983	+	0.0332765i
$925$		0			0
$926$	−10.3504	−	31.8554i	−0.340137	−	1.04683i
$927$	−14.6403	−	10.6368i	−0.480850	−	0.349358i
$928$	4.51890	−	3.28317i	0.148340	−	0.107775i
$929$	−15.3415	+	47.2162i	−0.503338	+	1.54911i	0.300210	+	0.953873i	$0.402943\pi$
$929$	−15.3415	+	47.2162i	−0.503338	+	1.54911i	−0.803547	+	0.595241i	$0.797057\pi$
$930$		0			0
$931$	−6.31143	+	4.58552i	−0.206849	+	0.150284i
$932$	−3.78115	−	2.74717i	−0.123856	−	0.0899865i
$933$	−7.12194	−	21.9191i	−0.233162	−	0.717598i
$934$	−4.09880			−0.134117
$935$		0			0
$936$	14.4567			0.472530
$937$	16.7770	+	51.6342i	0.548079	+	1.68682i	0.713553	+	0.700601i	$0.247085\pi$
$937$	16.7770	+	51.6342i	0.548079	+	1.68682i	−0.165474	+	0.986214i	$0.552915\pi$
$938$	1.27469	+	0.926120i	0.0416203	+	0.0302389i
$939$	14.0476	−	10.2062i	0.458427	−	0.333066i
$940$		0			0
$941$	2.05826	−	6.33466i	0.0670972	−	0.206504i	−0.911886	−	0.410442i	$-0.865374\pi$
$941$	2.05826	−	6.33466i	0.0670972	−	0.206504i	0.978984	+	0.203938i	$0.0653743\pi$
$942$	10.0590	−	7.30833i	0.327742	−	0.238118i
$943$	1.29882	+	0.943648i	0.0422954	+	0.0307294i
$944$	1.92406	+	5.92164i	0.0626227	+	0.192733i
$945$		0			0
$946$	6.76390	+	25.7501i	0.219913	+	0.837207i
$947$	42.6250			1.38513			0.692563	−	0.721358i	$-0.256482\pi$
$947$	42.6250			1.38513			0.692563	+	0.721358i	$0.256482\pi$
$948$	0.563947	+	1.73565i	0.0183161	+	0.0563713i
$949$	−19.0823	−	13.8641i	−0.619439	−	0.450049i
$950$		0			0
$951$	−1.90075	+	5.84990i	−0.0616360	+	0.189696i
$952$	5.19927	−	16.0017i	0.168509	−	0.518619i
$953$	−13.5542	+	9.84772i	−0.439064	+	0.318999i	−0.785263	−	0.619162i	$-0.787472\pi$
$953$	−13.5542	+	9.84772i	−0.439064	+	0.318999i	0.346199	+	0.938161i	$0.387472\pi$
$954$	−6.04622	−	4.39283i	−0.195754	−	0.142223i
$955$		0			0
$956$	13.2264			0.427772
$957$	−4.39528	−	0.252069i	−0.142079	−	0.00814825i
$958$	1.03500			0.0334393
$959$	−4.45110	−	13.6991i	−0.143733	−	0.442366i
$960$		0			0
$961$	−22.6539	+	16.4590i	−0.730772	+	0.530937i
$962$	13.4605	−	41.4271i	0.433984	−	1.33566i
$963$	1.89101	−	5.81994i	0.0609370	−	0.187545i
$964$	−2.13138	+	1.54854i	−0.0686470	+	0.0498750i
$965$		0			0
$966$	1.64492	+	5.06254i	0.0529244	+	0.162885i
$967$	50.1233			1.61186			0.805928	−	0.592014i	$-0.201667\pi$
$967$	50.1233			1.61186			0.805928	+	0.592014i	$0.201667\pi$
$968$	−24.8493	−	22.8218i	−0.798687	−	0.733521i
$969$	9.33404			0.299853
$970$		0			0
$971$	−32.4602	−	23.5837i	−1.04170	−	0.756837i	−0.0710811	−	0.997471i	$-0.522645\pi$
$971$	−32.4602	−	23.5837i	−1.04170	−	0.756837i	−0.970616	+	0.240633i	$0.922645\pi$
$972$	−0.647481	+	0.470423i	−0.0207680	+	0.0150888i
$973$	−1.78020	+	5.47890i	−0.0570707	+	0.175646i
$974$	−4.53113	+	13.9454i	−0.145187	+	0.446839i
$975$		0			0
$976$	−15.4696	−	11.2393i	−0.495170	−	0.359762i
$977$	7.46838	+	22.9853i	0.238935	+	0.735365i	0.996575	+	0.0826930i	$0.0263521\pi$
$977$	7.46838	+	22.9853i	0.238935	+	0.735365i	−0.757640	+	0.652672i	$0.773648\pi$
$978$	1.96335			0.0627809
$979$	−11.0833	−	0.635626i	−0.354223	−	0.0203147i
$980$		0			0
$981$	2.79082	+	8.58925i	0.0891039	+	0.274234i
$982$	−2.47125	−	1.79547i	−0.0788608	−	0.0572958i
$983$	18.8518	−	13.6966i	0.601278	−	0.436854i	−0.245055	−	0.969509i	$-0.578806\pi$
$983$	18.8518	−	13.6966i	0.601278	−	0.436854i	0.846332	+	0.532656i	$0.178806\pi$
$984$	0.220747	−	0.679388i	0.00703715	−	0.0216581i
$985$		0			0
$986$	9.15166	−	6.64907i	0.291448	−	0.211750i
$987$	−4.74692	−	3.44884i	−0.151096	−	0.109778i
$988$	1.39843	+	4.30393i	0.0444900	+	0.136926i
$989$	−50.5195			−1.60643
$990$		0			0
$991$	−54.0689			−1.71756			−0.858778	−	0.512348i	$-0.828776\pi$
$991$	−54.0689			−1.71756			−0.858778	+	0.512348i	$0.828776\pi$
$992$	9.98818	+	30.7405i	0.317125	+	0.976011i
$993$	15.7104	+	11.4143i	0.498554	+	0.362220i
$994$	0.418906	−	0.304353i	0.0132869	−	0.00965348i
$995$		0			0
$996$	0.521833	−	1.60604i	0.0165349	−	0.0508893i
$997$	41.0260	−	29.8071i	1.29931	−	0.944001i	0.299357	−	0.954141i	$-0.403228\pi$
$997$	41.0260	−	29.8071i	1.29931	−	0.944001i	0.999949	+	0.0101405i	$0.00322786\pi$
$998$	15.7542	+	11.4461i	0.498691	+	0.362320i
$999$	2.60737	+	8.02466i	0.0824935	+	0.253889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.g.676.1		8
5.2	odd	4		825.2.bx.f.49.3		16
5.3	odd	4		825.2.bx.f.49.2		16
5.4	even	2		165.2.m.d.16.2	✓	8
11.3	even	5		9075.2.a.di.1.1		4
11.8	odd	10		9075.2.a.cm.1.4		4
11.9	even	5	inner	825.2.n.g.526.1		8
15.14	odd	2		495.2.n.a.181.1		8
55.9	even	10		165.2.m.d.31.2	yes	8
55.14	even	10		1815.2.a.p.1.4		4
55.19	odd	10		1815.2.a.w.1.1		4
55.42	odd	20		825.2.bx.f.724.2		16
55.53	odd	20		825.2.bx.f.724.3		16
165.14	odd	10		5445.2.a.bt.1.1		4
165.74	even	10		5445.2.a.bf.1.4		4
165.119	odd	10		495.2.n.a.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.2	✓	8	5.4	even	2
165.2.m.d.31.2	yes	8	55.9	even	10
495.2.n.a.181.1		8	15.14	odd	2
495.2.n.a.361.1		8	165.119	odd	10
825.2.n.g.526.1		8	11.9	even	5	inner
825.2.n.g.676.1		8	1.1	even	1	trivial
825.2.bx.f.49.2		16	5.3	odd	4
825.2.bx.f.49.3		16	5.2	odd	4
825.2.bx.f.724.2		16	55.42	odd	20
825.2.bx.f.724.3		16	55.53	odd	20
1815.2.a.p.1.4		4	55.14	even	10
1815.2.a.w.1.1		4	55.19	odd	10
5445.2.a.bf.1.4		4	165.74	even	10
5445.2.a.bt.1.1		4	165.14	odd	10
9075.2.a.cm.1.4		4	11.8	odd	10
9075.2.a.di.1.1		4	11.3	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.338464 - 1.04169i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.647481 - 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.570387 + 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.338464 - 1.04169i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.647481 - 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.570387 + 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.31118 + 0.189896i) q^{11} +0.800331 q^{12} +(1.45650 + 4.48264i) q^{13} +(0.624741 + 0.453901i) q^{14} +(-0.543502 + 1.67273i) q^{16} +(2.40431 - 7.39971i) q^{17} +(0.886111 - 0.643798i) q^{18} +(0.970553 + 0.705148i) q^{19} -0.705037 q^{21} +(-0.922906 - 3.51349i) q^{22} +6.89318 q^{23} +(-0.947813 - 2.91707i) q^{24} +(4.17653 - 3.03443i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.174367 + 0.536646i) q^{28} +(-1.07389 + 0.780229i) q^{29} +(-2.37364 - 7.30532i) q^{31} -4.20796 q^{32} +(2.56719 + 2.09989i) q^{33} -8.52195 q^{34} +(0.647481 + 0.470423i) q^{36} +(6.82618 - 4.95951i) q^{37} +(0.406045 - 1.24968i) q^{38} +(-1.45650 + 4.48264i) q^{39} +(0.188421 + 0.136896i) q^{41} +(0.238630 + 0.734428i) q^{42} -7.32892 q^{43} +(2.23326 - 1.43470i) q^{44} +(-2.33310 - 7.18053i) q^{46} +(6.73287 + 4.89171i) q^{47} +(-1.42291 + 1.03380i) q^{48} +(-2.00951 + 6.18465i) q^{49} +(6.29457 - 4.57327i) q^{51} +(3.05179 + 2.21726i) q^{52} +(-2.10852 - 6.48936i) q^{53} +1.09529 q^{54} +2.16248 q^{56} +(0.370718 + 1.14095i) q^{57} +(1.17623 + 0.854580i) q^{58} +(2.86401 - 2.08083i) q^{59} +(-3.35959 + 10.3397i) q^{61} +(-6.80645 + 4.94518i) q^{62} +(-0.570387 - 0.414410i) q^{63} +(2.51125 + 7.72883i) q^{64} +(1.31853 - 3.38494i) q^{66} +2.04036 q^{67} +(-1.92424 - 5.92222i) q^{68} +(5.57670 + 4.05171i) q^{69} +(0.207204 - 0.637709i) q^{71} +(0.947813 - 2.91707i) q^{72} +(-4.04859 + 2.94147i) q^{73} +(-7.47668 - 5.43212i) q^{74} +0.960132 q^{76} +(-1.96735 + 1.26387i) q^{77} +5.16248 q^{78} +(0.704642 + 2.16867i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0788288 - 0.242610i) q^{82} +(0.652022 - 2.00672i) q^{83} +(-0.456498 + 0.331666i) q^{84} +(2.48058 + 7.63443i) q^{86} -1.32741 q^{87} +(-7.87404 - 6.44077i) q^{88} -3.34722 q^{89} +(-2.68842 - 1.95325i) q^{91} +(4.46321 - 3.24271i) q^{92} +(2.37364 - 7.30532i) q^{93} +(2.81680 - 8.66921i) q^{94} +(-3.40431 - 2.47338i) q^{96} +(-1.02664 - 3.15968i) q^{97} +7.12261 q^{98} +(0.842610 + 3.20780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

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