LMFDB - Embedded newform 605.2.m.f.112.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.4
Character	$\chi$	$=$	605.112
Dual form			605.2.m.f.578.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.574811 - 1.12813i) q^{2} +(0.355543 - 2.24481i) q^{3} +(0.233302 - 0.321113i) q^{4} +(1.94305 - 1.10660i) q^{5} +(-2.73681 + 0.889243i) q^{6} +(2.53096 - 0.400865i) q^{7} +(-2.99744 - 0.474748i) q^{8} +(-2.05960 - 0.669206i) q^{9} +O(q^{10})$	\(q+(-0.574811 - 1.12813i) q^{2} +(0.355543 - 2.24481i) q^{3} +(0.233302 - 0.321113i) q^{4} +(1.94305 - 1.10660i) q^{5} +(-2.73681 + 0.889243i) q^{6} +(2.53096 - 0.400865i) q^{7} +(-2.99744 - 0.474748i) q^{8} +(-2.05960 - 0.669206i) q^{9} +(-2.36528 - 1.55592i) q^{10} +(-0.637889 - 0.637889i) q^{12} +(-4.43979 + 2.26219i) q^{13} +(-1.90705 - 2.62483i) q^{14} +(-1.79328 - 4.75522i) q^{15} +(0.942076 + 2.89941i) q^{16} +(-0.268136 - 0.136622i) q^{17} +(0.428931 + 2.70816i) q^{18} +(4.92080 - 3.57517i) q^{19} +(0.0979719 - 0.882110i) q^{20} -5.82406i q^{21} +(-5.07364 + 5.07364i) q^{23} +(-2.13144 + 6.55990i) q^{24} +(2.55085 - 4.30037i) q^{25} +(5.10408 + 3.70833i) q^{26} +(0.860962 - 1.68973i) q^{27} +(0.461756 - 0.906248i) q^{28} +(3.22334 + 2.34189i) q^{29} +(-4.33370 + 4.75640i) q^{30} +(2.34668 - 7.22235i) q^{31} +(-1.56247 + 1.56247i) q^{32} +0.381023i q^{34} +(4.47418 - 3.57967i) q^{35} +(-0.695400 + 0.505238i) q^{36} +(1.00949 + 6.37366i) q^{37} +(-6.86178 - 3.49625i) q^{38} +(3.49965 + 10.7708i) q^{39} +(-6.34953 + 2.39453i) q^{40} +(1.42557 + 1.96212i) q^{41} +(-6.57030 + 3.34773i) q^{42} +(-1.43561 - 1.43561i) q^{43} +(-4.74245 + 0.978869i) q^{45} +(8.64010 + 2.80734i) q^{46} +(-3.48845 - 0.552516i) q^{47} +(6.84359 - 1.08392i) q^{48} +(-0.412312 + 0.133968i) q^{49} +(-6.31763 - 0.405797i) q^{50} +(-0.402024 + 0.553339i) q^{51} +(-0.309396 + 1.95345i) q^{52} +(3.98977 + 7.83037i) q^{53} -2.40113 q^{54} -7.77673 q^{56} +(-6.27603 - 12.3174i) q^{57} +(0.789148 - 4.98248i) q^{58} +(0.690471 - 0.950352i) q^{59} +(-1.94534 - 0.533557i) q^{60} +(-0.0884033 + 0.0287240i) q^{61} +(-9.49664 + 1.50412i) q^{62} +(-5.48104 - 0.868112i) q^{63} +(8.45961 + 2.74870i) q^{64} +(-6.12337 + 9.30862i) q^{65} +(7.07364 + 7.07364i) q^{67} +(-0.106428 + 0.0542276i) q^{68} +(9.58547 + 13.1933i) q^{69} +(-6.61014 - 2.98982i) q^{70} +(3.47436 + 10.6930i) q^{71} +(5.85584 + 2.98370i) q^{72} +(-0.620840 - 3.91983i) q^{73} +(6.61005 - 4.80248i) q^{74} +(-8.74658 - 7.25516i) q^{75} -2.41423i q^{76} +(10.1392 - 10.1392i) q^{78} +(-0.728767 + 2.24292i) q^{79} +(5.03900 + 4.59118i) q^{80} +(-8.74303 - 6.35219i) q^{81} +(1.39410 - 2.73607i) q^{82} +(3.76855 - 7.39619i) q^{83} +(-1.87018 - 1.35877i) q^{84} +(-0.672186 + 0.0312574i) q^{85} +(-0.794348 + 2.44475i) q^{86} +(6.40314 - 6.40314i) q^{87} +2.55325i q^{89} +(3.83030 + 4.78743i) q^{90} +(-10.3301 + 7.50527i) q^{91} +(0.445520 + 2.81290i) q^{92} +(-15.3785 - 7.83572i) q^{93} +(1.38189 + 4.25301i) q^{94} +(5.60504 - 12.3921i) q^{95} +(2.95192 + 4.06298i) q^{96} +(6.70847 - 3.41814i) q^{97} +(0.388135 + 0.388135i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^5	$ 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.574811	−	1.12813i	−0.406452	−	0.797708i	0.593522	−	0.804818i	$-0.297737\pi$
$2$	−0.574811	−	1.12813i	−0.406452	−	0.797708i	−0.999975	+	0.00710974i	$0.997737\pi$
$3$	0.355543	−	2.24481i	0.205273	−	1.29604i	−0.642747	−	0.766079i	$-0.722205\pi$
$3$	0.355543	−	2.24481i	0.205273	−	1.29604i	0.848020	−	0.529964i	$-0.177795\pi$
$4$	0.233302	−	0.321113i	0.116651	−	0.160556i
$5$	1.94305	−	1.10660i	0.868956	−	0.494889i
$5$	1.94305	−	1.10660i	0.868956	−	0.494889i
$6$	−2.73681	+	0.889243i	−1.11730	+	0.363032i
$7$	2.53096	−	0.400865i	0.956614	−	0.151513i	0.341440	−	0.939904i	$-0.389085\pi$
$7$	2.53096	−	0.400865i	0.956614	−	0.151513i	0.615175	+	0.788391i	$0.289085\pi$
$8$	−2.99744	−	0.474748i	−1.05976	−	0.167849i
$9$	−2.05960	−	0.669206i	−0.686534	−	0.223069i
$10$	−2.36528	−	1.55592i	−0.747966	−	0.492025i
$11$		0			0
$11$		0			0
$12$	−0.637889	−	0.637889i	−0.184143	−	0.184143i
$13$	−4.43979	+	2.26219i	−1.23138	+	0.627418i	−0.943856	−	0.330357i	$-0.892831\pi$
$13$	−4.43979	+	2.26219i	−1.23138	+	0.627418i	−0.287520	+	0.957774i	$0.592831\pi$
$14$	−1.90705	−	2.62483i	−0.509681	−	0.701516i
$15$	−1.79328	−	4.75522i	−0.463024	−	1.22779i
$16$	0.942076	+	2.89941i	0.235519	+	0.724853i
$17$	−0.268136	−	0.136622i	−0.0650324	−	0.0331357i	0.421172	−	0.906981i	$-0.361619\pi$
$17$	−0.268136	−	0.136622i	−0.0650324	−	0.0331357i	−0.486204	+	0.873845i	$0.661619\pi$
$18$	0.428931	+	2.70816i	0.101100	+	0.638321i
$19$	4.92080	−	3.57517i	1.12891	−	0.820200i	0.143373	−	0.989669i	$-0.454205\pi$
$19$	4.92080	−	3.57517i	1.12891	−	0.820200i	0.985536	+	0.169469i	$0.0542051\pi$
$20$	0.0979719	−	0.882110i	0.0219072	−	0.197246i
$21$		−	5.82406i		−	1.27091i
$22$		0			0
$23$	−5.07364	+	5.07364i	−1.05793	+	1.05793i	−0.0597111	+	0.998216i	$0.519018\pi$
$23$	−5.07364	+	5.07364i	−1.05793	+	1.05793i	−0.998216	+	0.0597111i	$0.980982\pi$
$24$	−2.13144	+	6.55990i	−0.435079	+	1.33903i
$25$	2.55085	−	4.30037i	0.510171	−	0.860073i
$26$	5.10408	+	3.70833i	1.00099	+	0.727263i
$27$	0.860962	−	1.68973i	0.165692	−	0.325189i
$28$	0.461756	−	0.906248i	0.0872637	−	0.171265i
$29$	3.22334	+	2.34189i	0.598559	+	0.434878i	0.845367	−	0.534186i	$-0.179382\pi$
$29$	3.22334	+	2.34189i	0.598559	+	0.434878i	−0.246808	+	0.969064i	$0.579382\pi$
$30$	−4.33370	+	4.75640i	−0.791223	+	0.868397i
$31$	2.34668	−	7.22235i	0.421477	−	1.29717i	−0.484851	−	0.874597i	$-0.661126\pi$
$31$	2.34668	−	7.22235i	0.421477	−	1.29717i	0.906328	−	0.422576i	$-0.138874\pi$
$32$	−1.56247	+	1.56247i	−0.276208	+	0.276208i
$33$		0			0
$34$			0.381023i			0.0653449i
$35$	4.47418	−	3.57967i	0.756274	−	0.605075i
$36$	−0.695400	+	0.505238i	−0.115900	+	0.0842063i
$37$	1.00949	+	6.37366i	0.165959	+	1.04782i	0.920264	+	0.391299i	$0.127974\pi$
$37$	1.00949	+	6.37366i	0.165959	+	1.04782i	−0.754305	+	0.656525i	$0.772026\pi$
$38$	−6.86178	−	3.49625i	−1.11313	−	0.567167i
$39$	3.49965	+	10.7708i	0.560392	+	1.72471i
$40$	−6.34953	+	2.39453i	−1.00395	+	0.378608i
$41$	1.42557	+	1.96212i	0.222636	+	0.306432i	0.905694	−	0.423932i	$-0.139350\pi$
$41$	1.42557	+	1.96212i	0.222636	+	0.306432i	−0.683058	+	0.730364i	$0.739350\pi$
$42$	−6.57030	+	3.34773i	−1.01382	+	0.516566i
$43$	−1.43561	−	1.43561i	−0.218928	−	0.218928i	0.589119	−	0.808047i	$-0.299475\pi$
$43$	−1.43561	−	1.43561i	−0.218928	−	0.218928i	−0.808047	+	0.589119i	$0.799475\pi$
$44$		0			0
$45$	−4.74245	+	0.978869i	−0.706963	+	0.145921i
$46$	8.64010	+	2.80734i	1.27391	+	0.413920i
$47$	−3.48845	−	0.552516i	−0.508842	−	0.0805927i	−0.103266	−	0.994654i	$-0.532929\pi$
$47$	−3.48845	−	0.552516i	−0.508842	−	0.0805927i	−0.405576	+	0.914061i	$0.632929\pi$
$48$	6.84359	−	1.08392i	0.987786	−	0.156450i
$49$	−0.412312	+	0.133968i	−0.0589018	+	0.0191383i
$50$	−6.31763	−	0.405797i	−0.893447	−	0.0573884i
$51$	−0.402024	+	0.553339i	−0.0562947	+	0.0774830i
$52$	−0.309396	+	1.95345i	−0.0429055	+	0.270894i
$53$	3.98977	+	7.83037i	0.548037	+	1.07558i	0.984422	+	0.175824i	$0.0562588\pi$
$53$	3.98977	+	7.83037i	0.548037	+	1.07558i	−0.436384	+	0.899760i	$0.643741\pi$
$54$	−2.40113			−0.326752
$55$		0			0
$56$	−7.77673			−1.03921
$57$	−6.27603	−	12.3174i	−0.831280	−	1.63148i
$58$	0.789148	−	4.98248i	0.103620	−	0.654232i
$59$	0.690471	−	0.950352i	0.0898917	−	0.123725i	−0.761702	−	0.647927i	$-0.775636\pi$
$59$	0.690471	−	0.950352i	0.0898917	−	0.123725i	0.851594	+	0.524202i	$0.175636\pi$
$60$	−1.94534	−	0.533557i	−0.251142	−	0.0688819i
$61$	−0.0884033	+	0.0287240i	−0.0113189	+	0.00367773i	−0.314671	−	0.949201i	$-0.601894\pi$
$61$	−0.0884033	+	0.0287240i	−0.0113189	+	0.00367773i	0.303352	+	0.952879i	$0.401894\pi$
$62$	−9.49664	+	1.50412i	−1.20607	+	0.191023i
$63$	−5.48104	−	0.868112i	−0.690546	−	0.109372i
$64$	8.45961	+	2.74870i	1.05745	+	0.343587i
$65$	−6.12337	+	9.30862i	−0.759511	+	1.15459i
$66$		0			0
$67$	7.07364	+	7.07364i	0.864183	+	0.864183i	0.991821	−	0.127638i	$-0.0407397\pi$
$67$	7.07364	+	7.07364i	0.864183	+	0.864183i	−0.127638	+	0.991821i	$0.540740\pi$
$68$	−0.106428	+	0.0542276i	−0.0129062	+	0.00657606i
$69$	9.58547	+	13.1933i	1.15395	+	1.58828i
$70$	−6.61014	−	2.98982i	−0.790063	−	0.357351i
$71$	3.47436	+	10.6930i	0.412330	+	1.26902i	0.914617	+	0.404321i	$0.132492\pi$
$71$	3.47436	+	10.6930i	0.412330	+	1.26902i	−0.502286	+	0.864701i	$0.667508\pi$
$72$	5.85584	+	2.98370i	0.690117	+	0.351632i
$73$	−0.620840	−	3.91983i	−0.0726639	−	0.458782i	−0.997013	−	0.0772339i	$-0.975391\pi$
$73$	−0.620840	−	3.91983i	−0.0726639	−	0.458782i	0.924349	−	0.381548i	$-0.124609\pi$
$74$	6.61005	−	4.80248i	0.768403	−	0.558277i
$75$	−8.74658	−	7.25516i	−1.00997	−	0.837753i
$76$		−	2.41423i		−	0.276931i
$77$		0			0
$78$	10.1392	−	10.1392i	1.14804	−	1.14804i
$79$	−0.728767	+	2.24292i	−0.0819927	+	0.252348i	−0.983646	−	0.180112i	$-0.942354\pi$
$79$	−0.728767	+	2.24292i	−0.0819927	+	0.252348i	0.901653	+	0.432459i	$0.142354\pi$
$80$	5.03900	+	4.59118i	0.563377	+	0.513310i
$81$	−8.74303	−	6.35219i	−0.971448	−	0.705798i
$82$	1.39410	−	2.73607i	0.153952	−	0.302149i
$83$	3.76855	−	7.39619i	0.413652	−	0.811837i	−0.586347	−	0.810060i	$-0.699434\pi$
$83$	3.76855	−	7.39619i	0.413652	−	0.811837i	0.999998	−	0.00177691i	$-0.000565610\pi$
$84$	−1.87018	−	1.35877i	−0.204054	−	0.148254i
$85$	−0.672186	+	0.0312574i	−0.0729088	+	0.00339034i
$86$	−0.794348	+	2.44475i	−0.0856567	+	0.263624i
$87$	6.40314	−	6.40314i	0.686489	−	0.686489i
$88$		0			0
$89$			2.55325i			0.270644i	0.990802	+	0.135322i	$0.0432069\pi$
$89$			2.55325i			0.270644i	−0.990802	+	0.135322i	$0.956793\pi$
$90$	3.83030	+	4.78743i	0.403749	+	0.504640i
$91$	−10.3301	+	7.50527i	−1.08289	+	0.786766i
$92$	0.445520	+	2.81290i	0.0464487	+	0.293265i
$93$	−15.3785	−	7.83572i	−1.59467	−	0.812527i
$94$	1.38189	+	4.25301i	0.142531	+	0.438664i
$95$	5.60504	−	12.3921i	0.575065	−	1.27140i
$96$	2.95192	+	4.06298i	0.301280	+	0.414676i
$97$	6.70847	−	3.41814i	0.681142	−	0.347059i	−0.0789463	−	0.996879i	$-0.525156\pi$
$97$	6.70847	−	3.41814i	0.681142	−	0.347059i	0.760088	+	0.649820i	$0.225156\pi$
$98$	0.388135	+	0.388135i	0.0392076	+	0.0392076i
$99$		0			0
$100$	−0.785783	−	1.82240i	−0.0785783	−	0.182240i
$101$	−15.2512	−	4.95543i	−1.51756	−	0.493084i	−0.572475	−	0.819922i	$-0.694017\pi$
$101$	−15.2512	−	4.95543i	−1.51756	−	0.493084i	−0.945080	+	0.326838i	$0.894017\pi$
$102$	0.855326	+	0.135470i	0.0846899	+	0.0134136i
$103$	−1.42153	+	0.225148i	−0.140067	+	0.0221845i	−0.226074	−	0.974110i	$-0.572589\pi$
$103$	−1.42153	+	0.225148i	−0.140067	+	0.0221845i	0.0860071	+	0.996295i	$0.472589\pi$
$104$	14.3820	−	4.67299i	1.41027	−	0.458225i
$105$	−6.44493	−	11.3164i	−0.628961	−	1.10437i
$106$	6.54031	−	9.00196i	0.635251	−	0.874347i
$107$	1.74939	−	11.0452i	0.169120	−	1.06778i	−0.746396	−	0.665502i	$-0.768218\pi$
$107$	1.74939	−	11.0452i	0.169120	−	1.06778i	0.915516	−	0.402281i	$-0.131782\pi$
$108$	−0.341731	−	0.670684i	−0.0328830	−	0.0645366i
$109$	16.2607			1.55749			0.778746	−	0.627339i	$-0.215856\pi$
$109$	16.2607			1.55749			0.778746	+	0.627339i	$0.215856\pi$
$110$		0			0
$111$	14.6666			1.39209
$112$	3.54663	+	6.96066i	0.335125	+	0.657721i
$113$	0.300452	−	1.89698i	0.0282641	−	0.178453i	−0.969518	−	0.245021i	$-0.921205\pi$
$113$	0.300452	−	1.89698i	0.0282641	−	0.178453i	0.997782	+	0.0665686i	$0.0212051\pi$
$114$	−10.2881	+	14.1603i	−0.963568	+	1.32624i
$115$	−4.24380	+	15.4728i	−0.395737	+	1.44285i
$116$	1.50402	−	0.488687i	0.139645	−	0.0453734i
$117$	10.6581	−	1.68807i	0.985340	−	0.156062i
$118$	−1.46901	−	0.232668i	−0.135233	−	0.0214189i
$119$	−0.733408	−	0.238299i	−0.0672314	−	0.0218448i
$120$	3.11773	+	15.1049i	0.284608	+	1.37888i
$121$		0			0
$122$	0.0832195	+	0.0832195i	0.00753434	+	0.00753434i
$123$	4.91145	−	2.50251i	0.442850	−	0.225644i
$124$	−1.77170	−	2.43854i	−0.159104	−	0.218987i
$125$	0.197622	−	11.1786i	0.0176758	−	0.999844i
$126$	2.17122	+	6.68232i	0.193428	+	0.595309i
$127$	−2.24556	−	1.14417i	−0.199261	−	0.101529i	0.351513	−	0.936183i	$-0.385667\pi$
$127$	−2.24556	−	1.14417i	−0.199261	−	0.101529i	−0.550774	+	0.834654i	$0.685667\pi$
$128$	−1.07046	−	6.75860i	−0.0946159	−	0.597381i
$129$	−3.73309	+	2.71225i	−0.328680	+	0.238800i
$130$	14.0211	+	1.55726i	1.22973	+	0.136581i
$131$			13.8354i			1.20880i	0.796680	+	0.604401i	$0.206588\pi$
$131$			13.8354i			1.20880i	−0.796680	+	0.604401i	$0.793412\pi$
$132$		0			0
$133$	11.0212	−	11.0212i	0.955659	−	0.955659i
$134$	3.91398	−	12.0460i	0.338116	−	1.04061i
$135$	−0.196977	−	4.23597i	−0.0169531	−	0.364574i
$136$	0.738860	+	0.536813i	0.0633567	+	0.0460314i
$137$	0.890591	−	1.74788i	0.0760883	−	0.149332i	−0.849828	−	0.527060i	$-0.823294\pi$
$137$	0.890591	−	1.74788i	0.0760883	−	0.149332i	0.925917	+	0.377728i	$0.123294\pi$
$138$	9.37388	−	18.3973i	0.797958	−	1.56608i
$139$	7.00922	+	5.09250i	0.594515	+	0.431940i	0.843928	−	0.536457i	$-0.180238\pi$
$139$	7.00922	+	5.09250i	0.594515	+	0.431940i	−0.249413	+	0.968397i	$0.580238\pi$
$140$	−0.105644	−	2.27186i	−0.00892855	−	0.192007i
$141$	−2.48059	+	7.63446i	−0.208903	+	0.642938i
$142$	10.0660	−	10.0660i	0.844717	−	0.844717i
$143$		0			0
$144$		−	6.60208i		−	0.550173i
$145$	8.85464	+	0.983443i	0.735338	+	0.0816705i
$146$	−4.06521	+	2.95355i	−0.336439	+	0.244437i
$147$	0.154139	+	0.973195i	0.0127132	+	0.0802678i
$148$	2.28218	+	1.16283i	0.187594	+	0.0955840i
$149$	−2.63136	−	8.09850i	−0.215569	−	0.663455i	−0.999113	−	0.0421173i	$-0.986590\pi$
$149$	−2.63136	−	8.09850i	−0.215569	−	0.663455i	0.783543	−	0.621337i	$-0.213410\pi$
$150$	−3.15713	+	14.0376i	−0.257778	+	1.14617i
$151$	4.05134	+	5.57618i	0.329693	+	0.453783i	0.941396	−	0.337304i	$-0.109515\pi$
$151$	4.05134	+	5.57618i	0.329693	+	0.453783i	−0.611703	+	0.791088i	$0.709515\pi$
$152$	−16.4471	+	8.38023i	−1.33404	+	0.679726i
$153$	0.460825	+	0.460825i	0.0372555	+	0.0372555i
$154$		0			0
$155$	−3.43257	−	16.6302i	−0.275711	−	1.33577i
$156$	4.27512	+	1.38907i	0.342284	+	0.111215i
$157$	−5.38625	−	0.853099i	−0.429870	−	0.0680847i	−0.0622494	−	0.998061i	$-0.519827\pi$
$157$	−5.38625	−	0.853099i	−0.429870	−	0.0680847i	−0.367620	+	0.929976i	$0.619827\pi$
$158$	2.94920	−	0.467108i	0.234626	−	0.0371611i
$159$	18.9963	−	6.17226i	1.50650	−	0.489492i
$160$	−1.30691	+	4.76498i	−0.103321	+	0.376705i
$161$	−10.8073	+	14.8750i	−0.851738	+	1.17232i
$162$	−2.14050	+	13.5146i	−0.168173	+	1.06181i
$163$	1.01710	+	1.99617i	0.0796654	+	0.156352i	0.927403	−	0.374064i	$-0.122036\pi$
$163$	1.01710	+	1.99617i	0.0796654	+	0.156352i	−0.847738	+	0.530416i	$0.822036\pi$
$164$	0.962651			0.0751704
$165$		0			0
$166$	−10.5101			−0.815738
$167$	3.81934	+	7.49587i	0.295549	+	0.580048i	0.990258	−	0.139243i	$-0.0444669\pi$
$167$	3.81934	+	7.49587i	0.295549	+	0.580048i	−0.694709	+	0.719291i	$0.744467\pi$
$168$	−2.76496	+	17.4573i	−0.213322	+	1.34686i
$169$	6.95305	−	9.57005i	0.534850	−	0.736158i
$170$	0.421642	+	0.740346i	0.0323385	+	0.0567819i
$171$	−12.5274	+	4.07040i	−0.957995	+	0.311272i
$172$	−0.795922	+	0.126062i	−0.0606885	+	0.00961211i
$173$	−13.6375	−	2.15996i	−1.03684	−	0.164219i	−0.385266	−	0.922806i	$-0.625890\pi$
$173$	−13.6375	−	2.15996i	−1.03684	−	0.164219i	−0.651572	+	0.758587i	$0.725890\pi$
$174$	−10.9042	−	3.54298i	−0.826643	−	0.268593i
$175$	4.73225	−	11.9066i	0.357725	−	0.900056i
$176$		0			0
$177$	−1.88787	−	1.88787i	−0.141901	−	0.141901i
$178$	2.88040	−	1.46763i	0.215895	−	0.110004i
$179$	4.04948	+	5.57363i	0.302672	+	0.416593i	0.933079	−	0.359673i	$-0.117112\pi$
$179$	4.04948	+	5.57363i	0.302672	+	0.416593i	−0.630406	+	0.776265i	$0.717112\pi$
$180$	−0.792096	+	1.75123i	−0.0590394	+	0.130529i
$181$	−7.19068	−	22.1306i	−0.534479	−	1.64496i	−0.744773	−	0.667318i	$-0.767442\pi$
$181$	−7.19068	−	22.1306i	−0.534479	−	1.64496i	0.210294	−	0.977638i	$-0.432558\pi$
$182$	14.4048	+	7.33960i	1.06775	+	0.544047i
$183$	0.0330487	+	0.208661i	0.00244303	+	0.0154247i
$184$	17.6166	−	12.7992i	1.29872	−	0.943573i
$185$	9.01461	+	11.2672i	0.662767	+	0.828382i
$186$			21.8530i			1.60234i
$187$		0			0
$188$	−0.991282	+	0.991282i	−0.0722967	+	0.0722967i
$189$	1.50171	−	4.62178i	0.109233	−	0.336185i
$190$	−17.2017	+	0.799899i	−1.24794	+	0.0580308i
$191$	−6.09475	−	4.42809i	−0.441000	−	0.320405i	0.345032	−	0.938591i	$-0.387868\pi$
$191$	−6.09475	−	4.42809i	−0.441000	−	0.320405i	−0.786032	+	0.618185i	$0.787868\pi$
$192$	9.17807	−	18.0130i	0.662370	−	1.29997i
$193$	11.4722	−	22.5154i	0.825787	−	1.62070i	0.0424509	−	0.999099i	$-0.486483\pi$
$193$	11.4722	−	22.5154i	0.825787	−	1.62070i	0.783336	−	0.621599i	$-0.213517\pi$
$194$	−7.71220	−	5.60324i	−0.553704	−	0.402289i
$195$	18.7190	+	17.0554i	1.34050	+	1.22137i
$196$	−0.0531744	+	0.163654i	−0.00379817	+	0.0116896i
$197$	−10.3579	+	10.3579i	−0.737967	+	0.737967i	−0.972184	−	0.234217i	$-0.924747\pi$
$197$	−10.3579	+	10.3579i	−0.737967	+	0.737967i	0.234217	+	0.972184i	$0.424747\pi$
$198$		0			0
$199$			8.62950i			0.611729i	0.952075	+	0.305865i	$0.0989455\pi$
$199$			8.62950i			0.611729i	−0.952075	+	0.305865i	$0.901055\pi$
$200$	−9.68763	+	11.6791i	−0.685019	+	0.825836i
$201$	18.3940	−	13.3640i	1.29741	−	0.942624i
$202$	3.17621	+	20.0538i	0.223477	+	1.41098i
$203$	9.09693	+	4.63512i	0.638479	+	0.325321i
$204$	0.0838912	+	0.258190i	0.00587356	+	0.0180769i
$205$	4.94123	+	2.23496i	0.345111	+	0.156096i
$206$	1.07110	+	1.47425i	0.0746274	+	0.102716i
$207$	13.8450	−	7.05438i	0.962293	−	0.490313i
$208$	−10.7416	−	10.7416i	−0.744798	−	0.744798i
$209$		0			0
$210$	−9.06177	+	13.7755i	−0.625322	+	0.950601i
$211$	16.0838	+	5.22593i	1.10725	+	0.359768i	0.804889	−	0.593425i	$-0.202225\pi$
$211$	16.0838	+	5.22593i	1.10725	+	0.359768i	0.302363	+	0.953193i	$0.402225\pi$
$212$	3.44526	+	0.545675i	0.236621	+	0.0374771i
$213$	25.2390	−	3.99747i	1.72935	−	0.273902i
$214$	−13.4660	+	4.37537i	−0.920518	+	0.299094i
$215$	−4.37810	−	1.20080i	−0.298584	−	0.0818939i
$216$	−3.38288	+	4.65614i	−0.230176	+	0.316810i
$217$	3.04418	−	19.2202i	0.206653	−	1.30475i
$218$	−9.34682	−	18.3442i	−0.633046	−	1.24242i
$219$	−9.02002			−0.609517
$220$		0			0
$221$	1.49953			0.100869
$222$	−8.43051	−	16.5458i	−0.565819	−	1.11048i
$223$	−1.17854	+	7.44099i	−0.0789207	+	0.498286i	0.916289	+	0.400519i	$0.131170\pi$
$223$	−1.17854	+	7.44099i	−0.0789207	+	0.498286i	−0.995209	+	0.0977672i	$0.968830\pi$
$224$	−3.32821	+	4.58089i	−0.222376	+	0.306074i
$225$	−8.13158	+	7.15000i	−0.542105	+	0.476667i
$226$	−2.31274	+	0.751454i	−0.153841	+	0.0499860i
$227$	5.80020	−	0.918662i	0.384973	−	0.0609737i	0.0390515	−	0.999237i	$-0.487566\pi$
$227$	5.80020	−	0.918662i	0.384973	−	0.0609737i	0.345921	+	0.938263i	$0.387566\pi$
$228$	−5.41949	−	0.858362i	−0.358914	−	0.0568464i
$229$	−22.8021	−	7.40885i	−1.50680	−	0.489590i	−0.564810	−	0.825221i	$-0.691051\pi$
$229$	−22.8021	−	7.40885i	−1.50680	−	0.489590i	−0.941994	+	0.335630i	$0.891051\pi$
$230$	19.8947	−	4.10639i	1.31182	−	0.270767i
$231$		0			0
$232$	−8.54996	−	8.54996i	−0.561332	−	0.561332i
$233$	−12.8419	+	6.54328i	−0.841301	+	0.428664i	−0.820862	−	0.571127i	$-0.806507\pi$
$233$	−12.8419	+	6.54328i	−0.841301	+	0.428664i	−0.0204394	+	0.999791i	$0.506507\pi$
$234$	−8.03074	−	11.0534i	−0.524986	−	0.722581i
$235$	−7.38963	+	2.78677i	−0.482046	+	0.181789i
$236$	−0.144082	−	0.443438i	−0.00937893	−	0.0288654i
$237$	4.77582	+	2.43340i	0.310223	+	0.158066i
$238$	0.152739	+	0.964356i	0.00990060	+	0.0625099i
$239$	−12.2305	+	8.88598i	−0.791125	+	0.574786i	−0.908297	−	0.418325i	$-0.862617\pi$
$239$	−12.2305	+	8.88598i	−0.791125	+	0.574786i	0.117172	+	0.993112i	$0.462617\pi$
$240$	12.0979	−	9.67924i	0.780918	−	0.624792i
$241$		−	3.12966i		−	0.201599i	−0.994907	−	0.100800i	$-0.967860\pi$
$241$		−	3.12966i		−	0.201599i	0.994907	−	0.100800i	$-0.0321401\pi$
$242$		0			0
$243$	−13.3451	+	13.3451i	−0.856086	+	0.856086i
$244$	−0.0114010	+	0.0350888i	−0.000729877	+	0.00224633i
$245$	−0.652892	+	0.716573i	−0.0417117	+	0.0457802i
$246$	−5.64631	−	4.10228i	−0.359995	−	0.261552i
$247$	−13.7596	+	27.0048i	−0.875504	+	1.71827i
$248$	−10.4629	+	20.5345i	−0.664392	+	1.30394i
$249$	−15.2632	−	11.0893i	−0.967264	−	0.702759i
$250$	−12.7245	+	6.20263i	−0.804768	+	0.392289i
$251$	−1.91506	+	5.89395i	−0.120878	+	0.372023i	−0.993128	−	0.117037i	$-0.962660\pi$
$251$	−1.91506	+	5.89395i	−0.120878	+	0.372023i	0.872250	+	0.489060i	$0.162660\pi$
$252$	−1.55750	+	1.55750i	−0.0981133	+	0.0981133i
$253$		0			0
$254$			3.19096i			0.200219i
$255$	−0.168824	+	1.52005i	−0.0105722	+	0.0951889i
$256$	7.38309	−	5.36413i	0.461443	−	0.335258i
$257$	0.211882	+	1.33777i	0.0132168	+	0.0834478i	0.993415	−	0.114571i	$-0.0365493\pi$
$257$	0.211882	+	1.33777i	0.0132168	+	0.0834478i	−0.980198	+	0.198019i	$0.936549\pi$
$258$	5.20558	+	2.65238i	0.324085	+	0.165130i
$259$	5.10996	+	15.7268i	0.317517	+	0.977218i
$260$	1.56052	+	4.13802i	0.0967795	+	0.256629i
$261$	−5.07159	−	6.98044i	−0.313923	−	0.432078i
$262$	15.6081	−	7.95272i	0.964271	−	0.491321i
$263$	−6.97161	−	6.97161i	−0.429888	−	0.429888i	0.458702	−	0.888590i	$-0.348314\pi$
$263$	−6.97161	−	6.97161i	−0.429888	−	0.429888i	−0.888590	+	0.458702i	$0.848314\pi$
$264$		0			0
$265$	16.4174	+	10.7997i	1.00851	+	0.663418i
$266$	−18.7684	−	6.09824i	−1.15077	−	0.373907i
$267$	5.73157	+	0.907791i	0.350766	+	0.0555559i
$268$	3.92173	−	0.621141i	0.239558	−	0.0379422i
$269$	−12.8901	+	4.18825i	−0.785924	+	0.255362i	−0.674367	−	0.738396i	$-0.735584\pi$
$269$	−12.8901	+	4.18825i	−0.785924	+	0.255362i	−0.111556	+	0.993758i	$0.535584\pi$
$270$	−4.66550	+	2.65710i	−0.283933	+	0.161706i
$271$	3.16786	−	4.36018i	0.192434	−	0.264862i	−0.701887	−	0.712288i	$-0.747659\pi$
$271$	3.16786	−	4.36018i	0.192434	−	0.264862i	0.894321	+	0.447426i	$0.147659\pi$
$272$	0.143519	−	0.906144i	0.00870212	−	0.0549430i
$273$	13.1751	+	25.8576i	0.797395	+	1.56497i
$274$	−2.48376			−0.150049
$275$		0			0
$276$	6.47284			0.389619
$277$	12.9486	+	25.4130i	0.778005	+	1.52692i	0.848372	+	0.529400i	$0.177583\pi$
$277$	12.9486	+	25.4130i	0.778005	+	1.52692i	−0.0703667	+	0.997521i	$0.522417\pi$
$278$	1.71602	−	10.8345i	0.102920	−	0.649812i
$279$	−9.66648	+	13.3048i	−0.578717	+	0.796535i
$280$	−15.1105	+	8.60576i	−0.903028	+	0.514293i
$281$	−10.8555	+	3.52717i	−0.647586	+	0.210413i	−0.614349	−	0.789034i	$-0.710581\pi$
$281$	−10.8555	+	3.52717i	−0.647586	+	0.210413i	−0.0332364	+	0.999448i	$0.510581\pi$
$282$	10.0385	−	1.58995i	0.597786	−	0.0946800i
$283$	−1.83500	−	0.290635i	−0.109079	−	0.0172765i	0.101656	−	0.994820i	$-0.467586\pi$
$283$	−1.83500	−	0.290635i	−0.109079	−	0.0172765i	−0.210735	+	0.977543i	$0.567586\pi$
$284$	4.24423	+	1.37903i	0.251849	+	0.0818306i
$285$	−25.8251	−	16.9882i	−1.52975	−	1.00629i
$286$		0			0
$287$	4.39460	+	4.39460i	0.259405	+	0.259405i
$288$	4.26368	−	2.17245i	0.251240	−	0.128013i
$289$	−9.93912	−	13.6800i	−0.584654	−	0.804707i
$290$	−3.98029	−	10.5545i	−0.233731	−	0.619780i
$291$	−5.28793	−	16.2746i	−0.309984	−	0.954032i
$292$	−1.40355	−	0.715145i	−0.0821367	−	0.0418507i
$293$	−2.80055	−	17.6820i	−0.163610	−	1.03299i	−0.923684	−	0.383155i	$-0.874837\pi$
$293$	−2.80055	−	17.6820i	−0.163610	−	1.03299i	0.760074	−	0.649836i	$-0.225163\pi$
$294$	1.00929	−	0.733292i	0.0588630	−	0.0427664i
$295$	0.289953	−	2.61066i	0.0168817	−	0.151998i
$296$		−	19.5839i		−	1.13829i
$297$		0			0
$298$	−7.62362	+	7.62362i	−0.441624	+	0.441624i
$299$	11.0484	−	34.0034i	0.638944	−	1.96647i
$300$	−4.37032	+	1.11599i	−0.252320	+	0.0644320i
$301$	−4.20895	−	3.05798i	−0.242600	−	0.176259i
$302$	3.96191	−	7.77568i	0.227982	−	0.447440i
$303$	−16.5465	+	32.4743i	−0.950571	+	1.86560i
$304$	15.0017	+	10.8993i	0.860404	+	0.625120i
$305$	−0.139986	+	0.153639i	−0.00801555	+	0.00879737i
$306$	0.254983	−	0.784757i	0.0145764	−	0.0448616i
$307$	9.10688	−	9.10688i	0.519757	−	0.519757i	−0.397741	−	0.917498i	$-0.630206\pi$
$307$	9.10688	−	9.10688i	0.519757	−	0.519757i	0.917498	+	0.397741i	$0.130206\pi$
$308$		0			0
$309$			3.27111i			0.186087i
$310$	−16.7879	+	13.4316i	−0.953491	+	0.762864i
$311$	15.2532	−	11.0821i	0.864931	−	0.628409i	−0.0642908	−	0.997931i	$-0.520479\pi$
$311$	15.2532	−	11.0821i	0.864931	−	0.628409i	0.929222	+	0.369522i	$0.120479\pi$
$312$	−5.37657	−	33.9463i	−0.304388	−	1.92183i
$313$	8.55186	+	4.35739i	0.483379	+	0.246294i	0.678659	−	0.734453i	$-0.262561\pi$
$313$	8.55186	+	4.35739i	0.483379	+	0.246294i	−0.195280	+	0.980748i	$0.562561\pi$
$314$	2.13367	+	6.56676i	0.120410	+	0.370584i
$315$	−11.6106	+	4.37856i	−0.654182	+	0.246704i
$316$	0.550206	+	0.757294i	0.0309515	+	0.0426011i
$317$	−11.7602	+	5.99214i	−0.660521	+	0.336552i	−0.751913	−	0.659263i	$-0.770868\pi$
$317$	−11.7602	+	5.99214i	−0.660521	+	0.336552i	0.0913917	+	0.995815i	$0.470868\pi$
$318$	−17.8823	−	17.8823i	−1.00279	−	1.00279i
$319$		0			0
$320$	19.4791	−	4.02060i	1.08892	−	0.224759i
$321$	−24.1725	−	7.85412i	−1.34918	−	0.438374i
$322$	22.9931	+	3.64176i	1.28136	+	0.202947i
$323$	−1.80789	+	0.286341i	−0.100594	+	0.0159325i
$324$	−4.07954	+	1.32552i	−0.226641	+	0.0736401i
$325$	−1.59703	+	24.8632i	−0.0885872	+	1.37916i
$326$	1.66730	−	2.29484i	0.0923431	−	0.127099i
$327$	5.78138	−	36.5022i	0.319711	−	2.01858i
$328$	−3.34154	−	6.55814i	−0.184506	−	0.362113i
$329$	−9.05061			−0.498976
$330$		0			0
$331$	−12.7005			−0.698084			−0.349042	−	0.937107i	$-0.613493\pi$
$331$	−12.7005			−0.698084			−0.349042	+	0.937107i	$0.613493\pi$
$332$	−1.49580	−	2.93568i	−0.0820928	−	0.161116i
$333$	2.18614	−	13.8028i	0.119800	−	0.756387i
$334$	6.26091	−	8.61741i	0.342582	−	0.471524i
$335$	21.5721	+	5.91668i	1.17861	+	0.323263i
$336$	16.8864	−	5.48671i	0.921226	−	0.299325i
$337$	−15.4199	+	2.44227i	−0.839976	+	0.133039i	−0.561575	−	0.827426i	$-0.689804\pi$
$337$	−15.4199	+	2.44227i	−0.839976	+	0.133039i	−0.278401	+	0.960465i	$0.589804\pi$
$338$	−14.7929	−	2.34297i	−0.804630	−	0.127441i
$339$	−4.15153	−	1.34891i	−0.225480	−	0.0732630i
$340$	−0.146785	+	0.223140i	−0.00796055	+	0.0121015i
$341$		0			0
$342$	11.7928	+	11.7928i	0.637683	+	0.637683i
$343$	−16.9724	+	8.64784i	−0.916421	+	0.466940i
$344$	3.62160	+	4.98470i	0.195263	+	0.268757i
$345$	33.2247	+	15.0278i	1.78876	+	0.809070i
$346$	5.40224	+	16.6264i	0.290426	+	0.893841i
$347$	−2.12746	−	1.08400i	−0.114208	−	0.0581919i	0.395953	−	0.918271i	$-0.370414\pi$
$347$	−2.12746	−	1.08400i	−0.114208	−	0.0581919i	−0.510161	+	0.860079i	$0.670414\pi$
$348$	−0.562265	−	3.55000i	−0.0301405	−	0.190300i
$349$	−28.5645	+	20.7533i	−1.52902	+	1.11090i	−0.572242	+	0.820085i	$0.693926\pi$
$349$	−28.5645	+	20.7533i	−1.52902	+	1.11090i	−0.956780	+	0.290814i	$0.906074\pi$
$350$	−16.1524	+	1.50546i	−0.863379	+	0.0804702i
$351$			9.44972i			0.504389i
$352$		0			0
$353$	−0.0520523	+	0.0520523i	−0.00277046	+	0.00277046i	−0.708491	−	0.705720i	$-0.750624\pi$
$353$	−0.0520523	+	0.0520523i	−0.00277046	+	0.00277046i	0.705720	+	0.708491i	$0.250624\pi$
$354$	−1.04459	+	3.21493i	−0.0555195	+	0.170871i
$355$	18.5837	+	16.9322i	0.986322	+	0.898668i
$356$	0.819881	+	0.595679i	0.0434536	+	0.0315709i
$357$	−0.795695	+	1.56164i	−0.0421126	+	0.0826507i
$358$	3.96009	−	7.77212i	0.209297	−	0.410769i
$359$	13.1252	+	9.53601i	0.692721	+	0.503291i	0.877553	−	0.479479i	$-0.159174\pi$
$359$	13.1252	+	9.53601i	0.692721	+	0.503291i	−0.184832	+	0.982770i	$0.559174\pi$
$360$	14.6799	−	0.682633i	0.773701	−	0.0359779i
$361$	5.56110	−	17.1153i	0.292689	−	0.900805i
$362$	−20.8329	+	20.8329i	−1.09495	+	1.09495i
$363$		0			0
$364$			5.06813i			0.265642i
$365$	−5.54402	−	6.92939i	−0.290187	−	0.362701i
$366$	0.216400	−	0.157224i	0.0113114	−	0.00821823i
$367$	2.05737	+	12.9897i	0.107394	+	0.678056i	0.981376	+	0.192098i	$0.0615292\pi$
$367$	2.05737	+	12.9897i	0.107394	+	0.678056i	−0.873982	+	0.485958i	$0.838471\pi$
$368$	−19.4903	−	9.93081i	−1.01600	−	0.517680i
$369$	−1.62304	−	4.99519i	−0.0844919	−	0.260039i
$370$	7.52918	−	16.6462i	0.391424	−	0.865392i
$371$	13.2369	+	18.2190i	0.687225	+	0.945884i
$372$	−6.10398	+	3.11014i	−0.316477	+	0.161253i
$373$	18.8004	+	18.8004i	0.973446	+	0.973446i	0.999656	−	0.0262108i	$-0.00834413\pi$
$373$	18.8004	+	18.8004i	0.973446	+	0.973446i	−0.0262108	+	0.999656i	$0.508344\pi$
$374$		0			0
$375$	−25.0236	−	4.41810i	−1.29221	−	0.228150i
$376$	10.1941	+	3.31227i	0.525721	+	0.170817i
$377$	−19.6087	−	3.10572i	−1.00990	−	0.159953i
$378$	−6.07716	+	0.962528i	−0.312576	+	0.0495071i
$379$	12.8578	−	4.17775i	0.660460	−	0.214596i	0.0404392	−	0.999182i	$-0.487124\pi$
$379$	12.8578	−	4.17775i	0.660460	−	0.214596i	0.620020	+	0.784586i	$0.287124\pi$
$380$	−2.67159	−	4.69095i	−0.137050	−	0.240641i
$381$	−3.36684	+	4.63406i	−0.172488	+	0.237410i
$382$	−1.49214	+	9.42097i	−0.0763443	+	0.482019i
$383$	−8.29106	−	16.2721i	−0.423653	−	0.831466i	−0.999899	−	0.0141899i	$-0.995483\pi$
$383$	−8.29106	−	16.2721i	−0.423653	−	0.831466i	0.576246	−	0.817276i	$-0.304517\pi$
$384$	−15.5524			−0.793654
$385$		0			0
$386$	−31.9947			−1.62849
$387$	1.99606	+	3.91750i	0.101466	+	0.199138i
$388$	0.467493	−	2.95164i	0.0237334	−	0.149847i
$389$	−10.3849	+	14.2935i	−0.526534	+	0.724712i	−0.986597	−	0.163174i	$-0.947827\pi$
$389$	−10.3849	+	14.2935i	−0.526534	+	0.724712i	0.460063	+	0.887886i	$0.347827\pi$
$390$	8.48087	−	30.9211i	0.429445	−	1.56575i
$391$	2.05359	−	0.667253i	0.103855	−	0.0337444i
$392$	1.29948	−	0.205818i	0.0656338	−	0.0103954i
$393$	31.0578	+	4.91908i	1.56666	+	0.248135i
$394$	17.6388	+	5.73120i	0.888631	+	0.288734i
$395$	1.06599	+	5.16454i	0.0536359	+	0.259856i
$396$		0			0
$397$	−11.7203	−	11.7203i	−0.588223	−	0.588223i	0.348927	−	0.937150i	$-0.386546\pi$
$397$	−11.7203	−	11.7203i	−0.588223	−	0.588223i	−0.937150	+	0.348927i	$0.886546\pi$
$398$	9.73519	−	4.96033i	0.487981	−	0.248639i
$399$	−20.8220	−	28.6590i	−1.04240	−	1.43475i
$400$	14.8716	+	3.34470i	0.743581	+	0.167235i
$401$	−6.75419	−	20.7873i	−0.337288	−	1.03807i	−0.965584	−	0.260092i	$-0.916247\pi$
$401$	−6.75419	−	20.7873i	−0.337288	−	1.03807i	0.628296	−	0.777975i	$-0.283753\pi$
$402$	−25.6494	−	13.0690i	−1.27927	−	0.651823i
$403$	5.91952	+	37.3744i	0.294872	+	1.86175i
$404$	−5.14940	+	3.74126i	−0.256192	+	0.186135i
$405$	−24.0175	−	2.66751i	−1.19344	−	0.132550i
$406$		−	12.9268i		−	0.641548i
$407$		0			0
$408$	1.46774	−	1.46774i	0.0726641	−	0.0726641i
$409$	−6.24074	+	19.2070i	−0.308585	+	0.949727i	0.669730	+	0.742605i	$0.266410\pi$
$409$	−6.24074	+	19.2070i	−0.308585	+	0.949727i	−0.978315	+	0.207122i	$0.933590\pi$
$410$	−0.318952	−	6.85903i	−0.0157519	−	0.338743i
$411$	−3.60703	−	2.62066i	−0.177921	−	0.129268i
$412$	−0.259347	+	0.508998i	−0.0127771	+	0.0250765i
$413$	1.36659	−	2.68209i	0.0672457	−	0.131977i
$414$	−15.9165	−	11.5640i	−0.782253	−	0.568340i
$415$	−0.862196	−	18.5414i	−0.0423236	−	0.910163i
$416$	3.40244	−	10.4716i	0.166818	−	0.513414i
$417$	13.9238	−	13.9238i	0.681851	−	0.681851i
$418$		0			0
$419$			11.1391i			0.544179i	0.962272	+	0.272090i	$0.0877148\pi$
$419$			11.1391i			0.544179i	−0.962272	+	0.272090i	$0.912285\pi$
$420$	−5.13747	−	0.570594i	−0.250683	−	0.0278422i
$421$	−24.1936	+	17.5777i	−1.17912	+	0.856683i	−0.992072	−	0.125667i	$-0.959893\pi$
$421$	−24.1936	+	17.5777i	−1.17912	+	0.856683i	−0.187050	+	0.982350i	$0.559893\pi$
$422$	−3.34959	−	21.1485i	−0.163056	−	1.02949i
$423$	6.81507	+	3.47245i	0.331360	+	0.168836i
$424$	−8.24166	−	25.3652i	−0.400250	−	1.23184i
$425$	−1.27150	+	0.804579i	−0.0616767	+	0.0390278i
$426$	−19.0173	−	26.1751i	−0.921392	−	1.26819i
$427$	−0.212231	+	0.108137i	−0.0102706	+	0.00523312i
$428$	−3.13863	−	3.13863i	−0.151711	−	0.151711i
$429$		0			0
$430$	1.16192	+	5.62929i	0.0560327	+	0.271469i
$431$	36.2199	+	11.7686i	1.74465	+	0.566872i	0.995434	−	0.0954519i	$-0.0304296\pi$
$431$	36.2199	+	11.7686i	1.74465	+	0.566872i	0.749218	+	0.662324i	$0.230430\pi$
$432$	5.71032	+	0.904426i	0.274738	+	0.0435142i
$433$	3.78600	−	0.599643i	0.181943	−	0.0288170i	−0.0647978	−	0.997898i	$-0.520640\pi$
$433$	3.78600	−	0.599643i	0.181943	−	0.0288170i	0.246741	+	0.969081i	$0.420640\pi$
$434$	−23.4327	+	7.61375i	−1.12481	+	0.365472i
$435$	5.35585	−	19.5273i	0.256794	−	0.936265i
$436$	3.79366	−	5.22152i	0.181683	−	0.250065i
$437$	−6.82724	+	43.1055i	−0.326591	+	2.06201i
$438$	5.18480	+	10.1758i	0.247740	+	0.486216i
$439$	17.8832			0.853518			0.426759	−	0.904365i	$-0.359655\pi$
$439$	17.8832			0.853518			0.426759	+	0.904365i	$0.359655\pi$
$440$		0			0
$441$	0.938852			0.0447072
$442$	−0.861946	−	1.69166i	−0.0409986	−	0.0804642i
$443$	0.281666	−	1.77837i	0.0133824	−	0.0844930i	−0.980093	−	0.198538i	$-0.936381\pi$
$443$	0.281666	−	1.77837i	0.0133824	−	0.0844930i	0.993476	+	0.114045i	$0.0363807\pi$
$444$	3.42175	−	4.70963i	0.162389	−	0.223509i
$445$	2.82544	+	4.96108i	0.133939	+	0.235178i
$446$	9.07184	−	2.94762i	0.429564	−	0.139574i
$447$	−19.1152	+	3.02755i	−0.904117	+	0.143198i
$448$	22.5128	+	3.56568i	1.06363	+	0.168463i
$449$	13.7838	+	4.47863i	0.650498	+	0.211360i	0.615634	−	0.788032i	$-0.288900\pi$
$449$	13.7838	+	4.47863i	0.650498	+	0.211360i	0.0348645	+	0.999392i	$0.488900\pi$
$450$	12.7402	+	5.06357i	0.600581	+	0.238699i
$451$		0			0
$452$	−0.539048	−	0.539048i	−0.0253547	−	0.0253547i
$453$	13.9579	−	7.11191i	0.655800	−	0.334147i
$454$	−4.37039	−	6.01532i	−0.205112	−	0.282313i
$455$	−11.7665	+	26.0144i	−0.551623	+	1.21958i
$456$	12.9644	+	39.9002i	0.607112	+	1.86850i
$457$	34.3197	+	17.4868i	1.60541	+	0.817997i	0.999752	+	0.0222709i	$0.00708965\pi$
$457$	34.3197	+	17.4868i	1.60541	+	0.817997i	0.605657	+	0.795726i	$0.292910\pi$
$458$	4.74874	+	29.9824i	0.221894	+	1.40098i
$459$	−0.461709	+	0.335451i	−0.0215507	+	0.0156575i
$460$	3.97843	+	4.97258i	0.185495	+	0.231848i
$461$		−	19.2825i		−	0.898077i	−0.893512	−	0.449038i	$-0.851767\pi$
$461$		−	19.2825i		−	0.898077i	0.893512	−	0.449038i	$-0.148233\pi$
$462$		0			0
$463$	13.7252	−	13.7252i	0.637863	−	0.637863i	−0.312165	−	0.950028i	$-0.601054\pi$
$463$	13.7252	−	13.7252i	0.637863	−	0.637863i	0.950028	+	0.312165i	$0.101054\pi$
$464$	−3.75348	+	11.5520i	−0.174251	+	0.536289i
$465$	−38.5521	+	1.79272i	−1.78781	+	0.0831352i
$466$	14.7633	+	10.7262i	0.683898	+	0.496881i
$467$	16.5025	−	32.3880i	0.763646	−	1.49874i	−0.100192	−	0.994968i	$-0.531946\pi$
$467$	16.5025	−	32.3880i	0.763646	−	1.49874i	0.863837	−	0.503771i	$-0.168054\pi$
$468$	1.94449	−	3.81628i	0.0898841	−	0.176407i
$469$	20.7387	+	15.0675i	0.957624	+	0.695755i
$470$	7.39147	+	6.73459i	0.340943	+	0.310643i
$471$	−3.83009	+	11.7878i	−0.176481	+	0.543154i
$472$	−2.52083	+	2.52083i	−0.116030	+	0.116030i
$473$		0			0
$474$		−	6.78648i		−	0.311713i
$475$	−2.82230	−	30.2810i	−0.129496	−	1.38939i
$476$	−0.247627	+	0.179911i	−0.0113499	+	0.00824622i
$477$	−2.97722	−	18.7974i	−0.136318	−	0.860675i
$478$	17.0548	+	8.68983i	0.780066	+	0.397464i
$479$	−2.63180	−	8.09984i	−0.120250	−	0.370091i	0.872756	−	0.488157i	$-0.162331\pi$
$479$	−2.63180	−	8.09984i	−0.120250	−	0.370091i	−0.993006	+	0.118066i	$0.962331\pi$
$480$	10.2318	+	4.62793i	0.467017	+	0.211235i
$481$	−18.9003	−	26.0141i	−0.861781	−	1.18614i
$482$	−3.53066	+	1.79896i	−0.160817	+	0.0819405i
$483$	29.5492	+	29.5492i	1.34454	+	1.34454i
$484$		0			0
$485$	9.25234	−	14.0652i	0.420127	−	0.638669i
$486$	22.7258	+	7.38407i	1.03086	+	0.334948i
$487$	4.31026	+	0.682678i	0.195317	+	0.0309351i	0.253326	−	0.967381i	$-0.418475\pi$
$487$	4.31026	+	0.682678i	0.195317	+	0.0309351i	−0.0580096	+	0.998316i	$0.518475\pi$
$488$	0.278620	−	0.0441292i	0.0126126	−	0.00199763i
$489$	4.84265	−	1.57347i	0.218992	−	0.0711549i
$490$	1.18368	+	0.324652i	0.0534730	+	0.0146663i
$491$	−10.2343	+	14.0863i	−0.461868	+	0.635707i	−0.974895	−	0.222666i	$-0.928524\pi$
$491$	−10.2343	+	14.0863i	−0.461868	+	0.635707i	0.513027	+	0.858372i	$0.328524\pi$
$492$	0.342264	−	2.16097i	0.0154305	−	0.0974241i
$493$	−0.544338	−	1.06832i	−0.0245157	−	0.0481148i
$494$	38.3740			1.72653
$495$		0			0
$496$	23.1513			1.03953
$497$	13.0799	+	25.6708i	0.586714	+	1.15149i
$498$	−3.73678	+	23.5931i	−0.167449	+	1.05723i
$499$	−4.64582	+	6.39443i	−0.207976	+	0.286254i	−0.900244	−	0.435387i	$-0.856612\pi$
$499$	−4.64582	+	6.39443i	−0.207976	+	0.286254i	0.692268	+	0.721641i	$0.256612\pi$
$500$	−3.54348	−	2.67145i	−0.158469	−	0.119471i
$501$	18.1848	−	5.90859i	0.812435	−	0.263976i
$502$	7.74994	−	1.22747i	0.345897	−	0.0547847i
$503$	37.2597	+	5.90135i	1.66133	+	0.263128i	0.915296	−	0.402782i	$-0.131957\pi$
$503$	37.2597	+	5.90135i	1.66133	+	0.263128i	0.746031	+	0.665911i	$0.231957\pi$
$504$	16.0170	+	5.20423i	0.713453	+	0.231815i
$505$	−35.1176	+	7.24847i	−1.56271	+	0.322553i
$506$		0			0
$507$	−19.0109	−	19.0109i	−0.844302	−	0.844302i
$508$	−0.891301	+	0.454141i	−0.0395451	+	0.0201492i
$509$	24.1207	+	33.1994i	1.06913	+	1.47154i	0.870951	+	0.491371i	$0.163504\pi$
$509$	24.1207	+	33.1994i	1.06913	+	1.47154i	0.198183	+	0.980165i	$0.436496\pi$
$510$	1.81185	−	0.683282i	0.0802300	−	0.0302562i
$511$	−3.14265	−	9.67208i	−0.139023	−	0.427868i
$512$	−22.4893	−	11.4589i	−0.993898	−	0.506416i
$513$	−1.80446	−	11.3929i	−0.0796689	−	0.503010i
$514$	1.38738	−	1.00799i	0.0611949	−	0.0444607i
$515$	−2.51294	+	2.01054i	−0.110733	+	0.0885950i
$516$			1.83152i			0.0806280i
$517$		0			0
$518$	14.8046	−	14.8046i	0.650479	−	0.650479i
$519$	−9.69743	+	29.8456i	−0.425670	+	1.31008i
$520$	22.7737	−	24.9950i	0.998693	−	1.09610i
$521$	28.7332	+	20.8759i	1.25882	+	0.914589i	0.998699	−	0.0509857i	$-0.0162363\pi$
$521$	28.7332	+	20.8759i	1.25882	+	0.914589i	0.260125	+	0.965575i	$0.416236\pi$
$522$	−4.95964	+	9.73384i	−0.217077	+	0.426038i
$523$	−15.2883	+	30.0050i	−0.668512	+	1.31203i	0.268685	+	0.963228i	$0.413411\pi$
$523$	−15.2883	+	30.0050i	−0.668512	+	1.31203i	−0.937197	+	0.348800i	$0.886589\pi$
$524$	4.44272	+	3.22782i	0.194081	+	0.141008i
$525$	−25.0456	−	14.8563i	−1.09308	−	0.648384i
$526$	−3.85752	+	11.8722i	−0.168196	+	0.517654i
$527$	−1.61596	+	1.61596i	−0.0703923	+	0.0703923i
$528$		0			0
$529$		−	28.4836i		−	1.23842i
$530$	2.74651	−	24.7287i	0.119301	−	1.07415i
$531$	−2.05808	+	1.49528i	−0.0893129	+	0.0648897i
$532$	−0.967780	−	6.11032i	−0.0419586	−	0.264916i
$533$	−10.7679	−	5.48652i	−0.466410	−	0.237648i
$534$	−2.27046	−	6.98775i	−0.0982524	−	0.302390i
$535$	−8.82355	−	23.3973i	−0.381475	−	1.01155i
$536$	−17.8446	−	24.5610i	−0.770771	−	1.06087i
$537$	13.9515	−	7.10866i	0.602053	−	0.306761i
$538$	12.1343	+	12.1343i	0.523145	+	0.523145i
$539$		0			0
$540$	−1.40618	−	0.925009i	−0.0605124	−	0.0398061i
$541$	12.2443	+	3.97842i	0.526424	+	0.171046i	0.560159	−	0.828385i	$-0.310740\pi$
$541$	12.2443	+	3.97842i	0.526424	+	0.171046i	−0.0337345	+	0.999431i	$0.510740\pi$
$542$	−6.73977	−	1.06747i	−0.289498	−	0.0458520i
$543$	−52.2357	+	8.27332i	−2.24165	+	0.355042i
$544$	0.632421	−	0.205486i	0.0271148	−	0.00881014i
$545$	31.5953	−	17.9942i	1.35339	−	0.770785i
$546$	21.5975	−	29.7265i	0.924290	−	1.27218i
$547$	−3.38898	+	21.3972i	−0.144902	+	0.914877i	0.802922	+	0.596084i	$0.203278\pi$
$547$	−3.38898	+	21.3972i	−0.144902	+	0.914877i	−0.947824	+	0.318793i	$0.896722\pi$
$548$	−0.353491	−	0.693765i	−0.0151004	−	0.0296362i
$549$	0.201298			0.00859119
$550$		0			0
$551$	24.2340			1.03241
$552$	−22.4684	−	44.0968i	−0.956319	−	1.87688i
$553$	−0.945377	+	5.96887i	−0.0402015	+	0.253822i
$554$	21.2262	−	29.2154i	0.901815	−	1.24124i
$555$	28.4979	−	16.2301i	1.20967	−	0.688930i
$556$	3.27053	−	1.06266i	0.138702	−	0.0450669i
$557$	17.5927	−	2.78641i	0.745427	−	0.118064i	0.227844	−	0.973698i	$-0.426832\pi$
$557$	17.5927	−	2.78641i	0.745427	−	0.118064i	0.517582	+	0.855634i	$0.326832\pi$
$558$	20.5659	+	3.25732i	0.870623	+	0.137893i
$559$	9.62140	+	3.12618i	0.406942	+	0.132223i
$560$	14.5940	+	9.60016i	0.616708	+	0.405681i
$561$		0			0
$562$	10.2190	+	10.2190i	0.431061	+	0.431061i
$563$	−25.0476	+	12.7624i	−1.05563	+	0.537870i	−0.893576	−	0.448912i	$-0.851812\pi$
$563$	−25.0476	+	12.7624i	−1.05563	+	0.537870i	−0.162053	+	0.986782i	$0.551812\pi$
$564$	1.87280	+	2.57769i	0.0788590	+	0.108540i
$565$	−1.51541	−	4.01839i	−0.0637538	−	0.169055i
$566$	0.726902	+	2.23717i	0.0305540	+	0.0940354i
$567$	−24.6747	−	12.5724i	−1.03624	−	0.527990i
$568$	−5.33772	−	33.7010i	−0.223966	−	1.41406i
$569$	21.1690	−	15.3802i	0.887452	−	0.644772i	−0.0477604	−	0.998859i	$-0.515208\pi$
$569$	21.1690	−	15.3802i	0.887452	−	0.644772i	0.935212	+	0.354087i	$0.115208\pi$
$570$	−4.32033	+	38.8990i	−0.180959	+	1.62930i
$571$			27.6158i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$571$			27.6158i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$572$		0			0
$573$	−12.1072	+	12.1072i	−0.505785	+	0.505785i
$574$	2.43162	−	7.48374i	0.101494	−	0.312365i
$575$	8.87639	+	34.7606i	0.370171	+	1.44962i
$576$	−15.5840	−	11.3224i	−0.649334	−	0.471768i
$577$	−13.4271	+	26.3522i	−0.558978	+	1.09706i	0.422657	+	0.906290i	$0.361098\pi$
$577$	−13.4271	+	26.3522i	−0.558978	+	1.09706i	−0.981635	+	0.190767i	$0.938902\pi$
$578$	−9.71972	+	19.0760i	−0.404287	+	0.793458i
$579$	−46.4641	−	33.7581i	−1.93098	−	1.40294i
$580$	2.38160	−	2.61390i	0.0988907	−	0.108536i
$581$	6.57318	−	20.2302i	0.272701	−	0.839288i
$582$	−15.3203	+	15.3203i	−0.635045	+	0.635045i
$583$		0			0
$584$			12.0442i			0.498393i
$585$	18.8411	−	15.0743i	0.778984	−	0.623245i
$586$	−18.3378	+	13.3232i	−0.757526	+	0.550375i
$587$	−1.13068	−	7.13885i	−0.0466683	−	0.294652i	0.953305	−	0.302010i	$-0.0976577\pi$
$587$	−1.13068	−	7.13885i	−0.0466683	−	0.294652i	−0.999973	+	0.00735852i	$0.997658\pi$
$588$	0.348467	+	0.177553i	0.0143705	+	0.00732215i
$589$	−14.2736	−	43.9295i	−0.588132	−	1.81008i
$590$	−3.11182	+	1.17353i	−0.128112	+	0.0483134i
$591$	19.5688	+	26.9341i	0.804952	+	1.10792i
$592$	−17.5289	+	8.93140i	−0.720432	+	0.367078i
$593$	−7.89832	−	7.89832i	−0.324345	−	0.324345i	0.526086	−	0.850431i	$-0.323659\pi$
$593$	−7.89832	−	7.89832i	−0.324345	−	0.324345i	−0.850431	+	0.526086i	$0.823659\pi$
$594$		0			0
$595$	−1.68875	+	0.348567i	−0.0692319	+	0.0142899i
$596$	−3.21443	−	1.04443i	−0.131668	−	0.0427816i
$597$	19.3716	+	3.06816i	0.792827	+	0.125572i
$598$	−44.7110	+	7.08152i	−1.82837	+	0.289585i
$599$	−15.5479	+	5.05183i	−0.635271	+	0.206412i	−0.608909	−	0.793240i	$-0.708392\pi$
$599$	−15.5479	+	5.05183i	−0.635271	+	0.206412i	−0.0263626	+	0.999652i	$0.508392\pi$
$600$	22.7730	+	25.8993i	0.929703	+	1.05734i
$601$	19.1335	−	26.3350i	0.780472	−	1.07423i	−0.214758	−	0.976667i	$-0.568896\pi$
$601$	19.1335	−	26.3350i	0.780472	−	1.07423i	0.995230	−	0.0975599i	$-0.0311037\pi$
$602$	−1.03045	+	6.50600i	−0.0419980	+	0.265165i
$603$	−9.83517	−	19.3026i	−0.400519	−	0.786063i
$604$	2.73577			0.111317
$605$		0			0
$606$	46.1463			1.87457
$607$	−9.60793	−	18.8566i	−0.389974	−	0.765367i	0.609653	−	0.792668i	$-0.291309\pi$
$607$	−9.60793	−	18.8566i	−0.389974	−	0.765367i	−0.999627	+	0.0273011i	$0.991309\pi$
$608$	−2.10250	+	13.2747i	−0.0852678	+	0.538360i
$609$	13.6393	−	18.7729i	0.552693	−	0.760717i
$610$	0.253790	+	0.0696082i	0.0102757	+	0.00281835i
$611$	16.7379	−	5.43846i	0.677142	−	0.220017i
$612$	0.255488	−	0.0404653i	0.0103275	−	0.00163571i
$613$	−29.5896	−	4.68654i	−1.19511	−	0.189287i	−0.473000	−	0.881062i	$-0.656829\pi$
$613$	−29.5896	−	4.68654i	−1.19511	−	0.189287i	−0.722113	+	0.691775i	$0.756829\pi$
$614$	−15.5085	−	5.03901i	−0.625871	−	0.203358i
$615$	6.77388	−	10.2975i	0.273149	−	0.415236i
$616$		0			0
$617$	16.8977	+	16.8977i	0.680276	+	0.680276i	0.960062	−	0.279786i	$-0.0902636\pi$
$617$	16.8977	+	16.8977i	0.680276	+	0.680276i	−0.279786	+	0.960062i	$0.590264\pi$
$618$	3.69024	−	1.88027i	0.148443	−	0.0756355i
$619$	4.10082	+	5.64430i	0.164826	+	0.226863i	0.883438	−	0.468547i	$-0.155222\pi$
$619$	4.10082	+	5.64430i	0.164826	+	0.226863i	−0.718612	+	0.695411i	$0.755222\pi$
$620$	−6.14100	−	2.77762i	−0.246628	−	0.111552i
$621$	4.20488	+	12.9413i	0.168736	+	0.519317i
$622$	−21.2698	−	10.8375i	−0.852840	−	0.434544i
$623$	1.02351	+	6.46218i	0.0410060	+	0.258902i
$624$	−27.9321	+	20.2938i	−1.11818	+	0.812404i
$625$	−11.9863	−	21.9392i	−0.479452	−	0.877568i
$626$		−	12.1523i		−	0.485702i
$627$		0			0
$628$	−1.53057	+	1.53057i	−0.0610762	+	0.0610762i
$629$	0.600102	−	1.84692i	0.0239276	−	0.0736417i
$630$	11.6135	+	10.5814i	0.462691	+	0.421572i
$631$	−14.0517	−	10.2092i	−0.559391	−	0.406421i	0.271845	−	0.962341i	$-0.412366\pi$
$631$	−14.0517	−	10.2092i	−0.559391	−	0.406421i	−0.831236	+	0.555920i	$0.812366\pi$
$632$	3.24926	−	6.37703i	0.129249	−	0.253665i
$633$	17.4497	−	34.2470i	0.693564	−	1.36120i
$634$	13.5198	+	9.82272i	0.536941	+	0.390110i
$635$	−5.62937	+	0.261772i	−0.223395	+	0.0103881i
$636$	2.44988	−	7.53994i	0.0971439	−	0.298978i
$637$	1.52752	−	1.52752i	0.0605225	−	0.0605225i
$638$		0			0
$639$		−	24.3483i		−	0.963206i
$640$	−9.55904	−	11.9477i	−0.377854	−	0.472274i
$641$	22.5577	−	16.3891i	0.890976	−	0.647332i	−0.0451563	−	0.998980i	$-0.514379\pi$
$641$	22.5577	−	16.3891i	0.890976	−	0.647332i	0.936132	+	0.351648i	$0.114379\pi$
$642$	5.03414	+	31.7843i	0.198682	+	1.25443i
$643$	−14.8744	−	7.57888i	−0.586588	−	0.298882i	0.135395	−	0.990792i	$-0.456770\pi$
$643$	−14.8744	−	7.57888i	−0.586588	−	0.298882i	−0.721984	+	0.691910i	$0.756770\pi$
$644$	2.25519	+	6.94076i	0.0888669	+	0.273504i
$645$	−4.25218	+	9.40107i	−0.167429	+	0.370167i
$646$	1.36222	+	1.87494i	0.0535959	+	0.0737685i
$647$	17.6973	−	9.01724i	0.695754	−	0.354504i	−0.0700812	−	0.997541i	$-0.522326\pi$
$647$	17.6973	−	9.01724i	0.695754	−	0.354504i	0.765835	+	0.643037i	$0.222326\pi$
$648$	23.1911	+	23.1911i	0.911031	+	0.911031i
$649$		0			0
$650$	28.9669	−	12.4900i	1.13618	−	0.489898i
$651$	−42.0634	−	13.6672i	−1.64860	−	0.535661i
$652$	0.878288	+	0.139107i	0.0343964	+	0.00544786i
$653$	−36.6267	+	5.80109i	−1.43331	+	0.227014i	−0.824303	−	0.566149i	$-0.808433\pi$
$653$	−36.6267	+	5.80109i	−1.43331	+	0.227014i	−0.609009	+	0.793163i	$0.708433\pi$
$654$	−44.5024	+	14.4597i	−1.74018	+	0.565419i
$655$	15.3103	+	26.8828i	0.598222	+	1.05040i
$656$	−4.34601	+	5.98177i	−0.169683	+	0.233549i
$657$	−1.34449	+	8.48877i	−0.0524535	+	0.331178i
$658$	5.20239	+	10.2103i	0.202810	+	0.398037i
$659$	−25.1740			−0.980641			−0.490320	−	0.871542i	$-0.663120\pi$
$659$	−25.1740			−0.980641			−0.490320	+	0.871542i	$0.663120\pi$
$660$		0			0
$661$	−25.7739			−1.00249			−0.501244	−	0.865306i	$-0.667124\pi$
$661$	−25.7739			−1.00249			−0.501244	+	0.865306i	$0.667124\pi$
$662$	7.30040	+	14.3278i	0.283738	+	0.556867i
$663$	0.533148	−	3.36616i	0.0207058	−	0.130731i
$664$	−14.8073	+	20.3805i	−0.574636	+	0.790918i
$665$	9.21859	−	33.6108i	0.357482	−	1.30337i
$666$	−16.8279	+	5.46773i	−0.652069	+	0.211870i
$667$	−28.2360	+	4.47214i	−1.09330	+	0.173162i
$668$	3.29808	+	0.522365i	0.127607	+	0.0202109i
$669$	16.2846	+	5.29119i	0.629600	+	0.204569i
$670$	−5.72510	−	27.7371i	−0.221180	−	1.07158i
$671$		0			0
$672$	9.09992	+	9.09992i	0.351037	+	0.351037i
$673$	20.1607	−	10.2724i	0.777138	−	0.395971i	−0.0199762	−	0.999800i	$-0.506359\pi$
$673$	20.1607	−	10.2724i	0.777138	−	0.395971i	0.797114	+	0.603829i	$0.206359\pi$
$674$	11.6187	+	15.9918i	0.447537	+	0.615981i
$675$	−5.07028	−	8.01271i	−0.195155	−	0.308409i
$676$	−1.45091	−	4.46543i	−0.0558041	−	0.171747i
$677$	24.9613	+	12.7184i	0.959339	+	0.488808i	0.862258	−	0.506469i	$-0.169050\pi$
$677$	24.9613	+	12.7184i	0.959339	+	0.488808i	0.0970807	+	0.995277i	$0.469050\pi$
$678$	0.864595	+	5.45884i	0.0332046	+	0.209645i
$679$	15.6087	−	11.3404i	0.599006	−	0.435204i
$680$	2.02968	+	0.225427i	0.0778346	+	0.00864473i
$681$		−	13.3470i		−	0.511458i
$682$		0			0
$683$	−27.8670	+	27.8670i	−1.06630	+	1.06630i	−0.0686610	+	0.997640i	$0.521873\pi$
$683$	−27.8670	+	27.8670i	−1.06630	+	1.06630i	−0.997640	+	0.0686610i	$0.978127\pi$
$684$	−1.61561	+	4.97235i	−0.0617745	+	0.190123i
$685$	−0.203756	−	4.38175i	−0.00778512	−	0.167418i
$686$	19.5118	+	14.1761i	0.744963	+	0.541247i
$687$	−24.7386	+	48.5522i	−0.943837	+	1.85238i
$688$	2.80996	−	5.51486i	0.107129	−	0.210252i
$689$	−35.4275	−	25.7396i	−1.34968	−	0.980601i
$690$	−2.14463	−	46.1199i	−0.0816446	−	1.75576i
$691$	−14.4480	+	44.4664i	−0.549628	+	1.69158i	0.160096	+	0.987101i	$0.448820\pi$
$691$	−14.4480	+	44.4664i	−0.549628	+	1.69158i	−0.709724	+	0.704480i	$0.751180\pi$
$692$	−3.87524	+	3.87524i	−0.147315	+	0.147315i
$693$		0			0
$694$			3.02314i			0.114757i
$695$	19.2546	+	2.13852i	0.730370	+	0.0811187i
$696$	−22.2329	+	16.1532i	−0.842737	+	0.612285i
$697$	−0.114176	−	0.720879i	−0.00432472	−	0.0273052i
$698$	39.8316	+	20.2952i	1.50765	+	0.768185i
$699$	10.1226	+	31.1541i	0.382871	+	1.17836i
$700$	−2.71932	−	4.29743i	−0.102781	−	0.162427i
$701$	13.5043	+	18.5870i	0.510049	+	0.702023i	0.983928	−	0.178568i	$-0.0571464\pi$
$701$	13.5043	+	18.5870i	0.510049	+	0.702023i	−0.473878	+	0.880590i	$0.657146\pi$
$702$	10.6605	−	5.43180i	0.402355	−	0.205010i
$703$	27.7544	+	27.7544i	1.04678	+	1.04678i
$704$		0			0
$705$	3.62844	+	17.5791i	0.136655	+	0.662069i
$706$	0.0886419	+	0.0288015i	0.00333608	+	0.00108396i
$707$	−40.5868	−	6.42832i	−1.52642	−	0.241762i
$708$	−1.04666	+	0.165775i	−0.0393360	+	0.00623021i
$709$	−10.3999	+	3.37912i	−0.390575	+	0.126906i	−0.497720	−	0.867338i	$-0.665829\pi$
$709$	−10.3999	+	3.37912i	−0.390575	+	0.126906i	0.107145	+	0.994243i	$0.465829\pi$
$710$	8.41959	−	30.6977i	0.315981	−	1.15206i
$711$	3.00194	−	4.13182i	0.112582	−	0.154955i
$712$	1.21215	−	7.65322i	0.0454273	−	0.286817i
$713$	24.7374	+	48.5498i	0.926422	+	1.81821i
$714$	2.21910			0.0830479
$715$		0			0
$716$	2.73452			0.102194
$717$	15.5989	+	30.6145i	0.582551	+	1.14332i
$718$	3.21335	−	20.2883i	0.119921	−	0.757153i
$719$	26.9002	−	37.0249i	1.00321	−	1.38080i	0.0798709	−	0.996805i	$-0.474549\pi$
$719$	26.9002	−	37.0249i	1.00321	−	1.38080i	0.923337	−	0.383991i	$-0.125451\pi$
$720$	−7.30589	−	12.8281i	−0.272274	−	0.478077i
$721$	−3.50758	+	1.13968i	−0.130629	+	0.0424440i
$722$	−22.5049	+	3.56442i	−0.837544	+	0.132654i
$723$	−7.02551	−	1.11273i	−0.261281	−	0.0413829i
$724$	−8.78403	−	2.85410i	−0.326456	−	0.106072i
$725$	18.2932	−	7.88770i	0.679394	−	0.292942i
$726$		0			0
$727$	−36.0611	−	36.0611i	−1.33743	−	1.33743i	−0.898539	−	0.438893i	$-0.855371\pi$
$727$	−36.0611	−	36.0611i	−1.33743	−	1.33743i	−0.438893	−	0.898539i	$-0.644629\pi$
$728$	34.5271	−	17.5924i	1.27966	−	0.652018i
$729$	6.15585	+	8.47280i	0.227994	+	0.313807i
$730$	−4.63048	+	10.2375i	−0.171382	+	0.378905i
$731$	0.188802	+	0.581072i	0.00698309	+	0.0214917i
$732$	0.0747142	+	0.0380688i	0.00276152	+	0.00140706i
$733$	−0.620840	−	3.91983i	−0.0229313	−	0.144782i	0.973566	−	0.228405i	$-0.0733510\pi$
$733$	−0.620840	−	3.91983i	−0.0229313	−	0.144782i	−0.996497	+	0.0836226i	$0.973351\pi$
$734$	13.4715	−	9.78759i	0.497240	−	0.361266i
$735$	1.37644	+	1.72039i	0.0507708	+	0.0634576i
$736$		−	15.8548i		−	0.584416i
$737$		0			0
$738$	−4.70228	+	4.70228i	−0.173093	+	0.173093i
$739$	−0.485939	+	1.49557i	−0.0178755	+	0.0550153i	−0.959596	−	0.281380i	$-0.909208\pi$
$739$	−0.485939	+	1.49557i	−0.0178755	+	0.0550153i	0.941721	+	0.336395i	$0.109208\pi$
$740$	5.72117	−	0.266041i	0.210315	−	0.00977986i
$741$	55.7285	+	40.4891i	2.04724	+	1.48741i
$742$	12.9447	−	25.4054i	0.475215	−	0.932662i
$743$	−19.3660	+	38.0080i	−0.710471	+	1.39438i	0.199580	+	0.979882i	$0.436042\pi$
$743$	−19.3660	+	38.0080i	−0.710471	+	1.39438i	−0.910051	+	0.414497i	$0.863958\pi$
$744$	42.3761	+	30.7880i	1.55358	+	1.12874i
$745$	−14.0747	−	12.8239i	−0.515657	−	0.469830i
$746$	10.4026	−	32.0159i	0.380866	−	1.17218i
$747$	−12.7113	+	12.7113i	−0.465081	+	0.465081i
$748$		0			0
$749$		−	28.6563i		−	1.04708i
$750$	9.39963	+	30.7694i	0.343226	+	1.12354i
$751$	−31.8399	+	23.1330i	−1.16185	+	0.844137i	−0.990011	−	0.140987i	$-0.954972\pi$
$751$	−31.8399	+	23.1330i	−1.16185	+	0.844137i	−0.171843	+	0.985124i	$0.554972\pi$
$752$	−1.68441	−	10.6350i	−0.0614241	−	0.387817i
$753$	12.5499	+	6.39451i	0.457345	+	0.233029i
$754$	7.76766	+	23.9064i	0.282881	+	0.870619i
$755$	14.0426	+	6.35156i	0.511061	+	0.231157i
$756$	−1.13376	−	1.56049i	−0.0412345	−	0.0567544i
$757$	13.6741	−	6.96731i	0.496994	−	0.253231i	−0.187480	−	0.982268i	$-0.560032\pi$
$757$	13.6741	−	6.96731i	0.496994	−	0.253231i	0.684474	+	0.729037i	$0.260032\pi$
$758$	−12.1038	−	12.1038i	−0.439631	−	0.439631i
$759$		0			0
$760$	−22.6839	+	34.4836i	−0.822832	+	1.25085i
$761$	−3.79798	−	1.23404i	−0.137677	−	0.0447338i	0.239368	−	0.970929i	$-0.423060\pi$
$761$	−3.79798	−	1.23404i	−0.137677	−	0.0447338i	−0.377045	+	0.926195i	$0.623060\pi$
$762$	7.16311	+	1.13453i	0.259492	+	0.0410995i
$763$	41.1552	−	6.51835i	1.48992	−	0.235980i
$764$	−2.84383	+	0.924018i	−0.102886	+	0.0334298i
$765$	1.40535	+	0.385453i	0.0508107	+	0.0139361i
$766$	−13.5913	+	18.7068i	−0.491072	+	0.675903i
$767$	−0.915674	+	5.78134i	−0.0330631	+	0.208752i
$768$	−9.41646	−	18.4808i	−0.339787	−	0.666870i
$769$	−43.6566			−1.57430			−0.787148	−	0.616764i	$-0.788443\pi$
$769$	−43.6566			−1.57430			−0.787148	+	0.616764i	$0.788443\pi$
$770$		0			0
$771$	3.07838			0.110865
$772$	−4.55351	−	8.93677i	−0.163885	−	0.321641i
$773$	0.787235	−	4.97041i	0.0283149	−	0.178773i	−0.969478	−	0.245179i	$-0.921153\pi$
$773$	0.787235	−	4.97041i	0.0283149	−	0.178773i	0.997793	+	0.0664060i	$0.0211532\pi$
$774$	3.27208	−	4.50364i	0.117613	−	0.161880i
$775$	−25.0727	−	28.5148i	−0.900638	−	1.02428i
$776$	−21.7310	+	7.06084i	−0.780098	+	0.253469i
$777$	37.1206	−	5.87933i	1.33169	−	0.210920i
$778$	22.0943	+	3.49939i	0.792119	+	0.125459i
$779$	14.0298	+	4.55857i	0.502671	+	0.163328i
$780$	9.84390	−	2.03184i	0.352468	−	0.0727515i
$781$		0			0
$782$	−1.93317	−	1.93317i	−0.0691302	−	0.0691302i
$783$	6.73234	−	3.43030i	0.240594	−	0.122589i
$784$	−0.776859	−	1.06925i	−0.0277450	−	0.0381877i
$785$	−11.4098	+	4.30284i	−0.407233	+	0.153575i
$786$	−12.3030	−	37.8648i	−0.438834	−	1.35059i
$787$	−37.7720	−	19.2458i	−1.34643	−	0.686039i	−0.375816	−	0.926694i	$-0.622638\pi$
$787$	−37.7720	−	19.2458i	−1.34643	−	0.686039i	−0.970611	+	0.240656i	$0.922638\pi$
$788$	0.909531	+	5.74255i	0.0324007	+	0.204570i
$789$	−18.1287	+	13.1712i	−0.645397	+	0.468909i
$790$	5.21353	−	4.17121i	0.185489	−	0.148405i
$791$		−	4.92162i		−	0.174993i
$792$		0			0
$793$	0.327513	−	0.327513i	0.0116303	−	0.0116303i
$794$	−6.48504	+	19.9589i	−0.230145	+	0.708315i
$795$	30.0803	−	33.0143i	1.06684	−	1.17090i
$796$	2.77104	+	2.01328i	0.0982171	+	0.0713589i
$797$	−20.7338	+	40.6924i	−0.734429	+	1.44140i	0.156699	+	0.987646i	$0.449915\pi$
$797$	−20.7338	+	40.6924i	−0.734429	+	1.44140i	−0.891128	+	0.453752i	$0.850085\pi$
$798$	−20.3624	+	39.9634i	−0.720821	+	1.41469i
$799$	0.859891	+	0.624747i	0.0304207	+	0.0221020i
$800$	2.73356	+	10.7048i	0.0966459	+	0.378472i
$801$	1.70865	−	5.25868i	0.0603721	−	0.185806i
$802$	−19.5683	+	19.5683i	−0.690982	+	0.690982i
$803$		0			0
$804$		−	9.02440i		−	0.318266i
$805$	−4.53839	+	40.8623i	−0.159957	+	1.44021i
$806$	38.7605	−	28.1612i	1.36528	−	0.991935i
$807$	4.81884	+	30.4250i	0.169631	+	1.07101i
$808$	43.3622	+	22.0941i	1.52548	+	0.777269i
$809$	−9.83541	−	30.2703i	−0.345794	−	1.06425i	−0.961157	−	0.276002i	$-0.910990\pi$
$809$	−9.83541	−	30.2703i	−0.345794	−	1.06425i	0.615363	−	0.788244i	$-0.289010\pi$
$810$	10.7962	+	28.6281i	0.379340	+	1.00589i
$811$	18.6330	+	25.6461i	0.654292	+	0.900556i	0.999276	−	0.0380531i	$-0.0121156\pi$
$811$	18.6330	+	25.6461i	0.654292	+	0.900556i	−0.344984	+	0.938609i	$0.612116\pi$
$812$	3.61073	−	1.83976i	0.126712	−	0.0645629i
$813$	−8.66148	−	8.66148i	−0.303772	−	0.303772i
$814$		0			0
$815$	4.18524	+	2.75312i	0.146603	+	0.0964377i
$816$	−1.98310	−	0.644347i	−0.0694222	−	0.0225566i
$817$	−12.1969	−	1.93179i	−0.426714	−	0.0675849i
$818$	25.2553	−	4.00004i	0.883029	−	0.139858i
$819$	26.2985	−	8.54490i	0.918944	−	0.298583i
$820$	1.87047	−	1.06527i	0.0653198	−	0.0372010i
$821$	−18.2365	+	25.1003i	−0.636457	+	0.876007i	−0.998420	−	0.0561848i	$-0.982106\pi$
$821$	−18.2365	+	25.1003i	−0.636457	+	0.876007i	0.361964	+	0.932192i	$0.382106\pi$
$822$	−0.883084	+	5.57557i	−0.0308011	+	0.194470i
$823$	−18.2430	−	35.8038i	−0.635910	−	1.24804i	−0.953950	−	0.299966i	$-0.903025\pi$
$823$	−18.2430	−	35.8038i	−0.635910	−	1.24804i	0.318040	−	0.948077i	$-0.396975\pi$
$824$	4.36783			0.152161
$825$		0			0
$826$	−3.81128			−0.132611
$827$	−1.27735	−	2.50695i	−0.0444180	−	0.0871752i	0.867731	−	0.497035i	$-0.165578\pi$
$827$	−1.27735	−	2.50695i	−0.0444180	−	0.0871752i	−0.912149	+	0.409859i	$0.865578\pi$
$828$	0.964816	−	6.09161i	0.0335297	−	0.211698i
$829$	16.4001	−	22.5729i	0.569600	−	0.783988i	−0.422907	−	0.906173i	$-0.638990\pi$
$829$	16.4001	−	22.5729i	0.569600	−	0.783988i	0.992507	+	0.122185i	$0.0389903\pi$
$830$	−20.4215	+	11.6305i	−0.708841	+	0.403700i
$831$	61.6513	−	20.0317i	2.13866	−	0.694893i
$832$	−43.7770	+	6.93359i	−1.51769	+	0.240379i
$833$	0.128859	+	0.0204092i	0.00446469	+	0.000707137i
$834$	−23.7114	−	7.70429i	−0.821058	−	0.266778i
$835$	15.7161	+	10.3383i	0.543878	+	0.357772i
$836$		0			0
$837$	−10.1834	−	10.1834i	−0.351991	−	0.351991i
$838$	12.5663	−	6.40286i	0.434096	−	0.221183i
$839$	−25.3711	−	34.9203i	−0.875906	−	1.20558i	−0.977538	−	0.210759i	$-0.932406\pi$
$839$	−25.3711	−	34.9203i	−0.875906	−	1.20558i	0.101632	−	0.994822i	$-0.467594\pi$
$840$	13.9459	+	36.9801i	0.481178	+	1.27593i
$841$	−4.05605	−	12.4832i	−0.139864	−	0.430456i
$842$	33.7366	+	17.1897i	1.16264	+	0.592395i
$843$	4.05823	+	25.6227i	0.139773	+	0.882491i
$844$	5.43049	−	3.94548i	0.186925	−	0.135809i
$845$	2.91983	−	26.2893i	0.100445	−	0.904380i
$846$		−	9.68428i		−	0.332952i
$847$		0			0
$848$	−18.9448	+	18.9448i	−0.650567	+	0.650567i
$849$	−1.30484	+	4.01589i	−0.0447821	+	0.137825i
$850$	1.63854	+	0.971935i	0.0562014	+	0.0333371i
$851$	−37.4594	−	27.2159i	−1.28409	−	0.932948i
$852$	4.60468	−	9.03719i	0.157754	−	0.309609i
$853$	−2.97986	+	5.84830i	−0.102028	+	0.200242i	−0.936378	−	0.350994i	$-0.885844\pi$
$853$	−2.97986	+	5.84830i	−0.102028	+	0.200242i	0.834349	+	0.551236i	$0.185844\pi$
$854$	0.243985	+	0.177266i	0.00834901	+	0.00606591i
$855$	−19.8370	+	21.7719i	−0.678412	+	0.744582i
$856$	−10.4874	+	32.2769i	−0.358452	+	1.10320i
$857$	16.3855	−	16.3855i	0.559717	−	0.559717i	−0.369510	−	0.929227i	$-0.620474\pi$
$857$	16.3855	−	16.3855i	0.559717	−	0.559717i	0.929227	+	0.369510i	$0.120474\pi$
$858$		0			0
$859$			44.6723i			1.52420i	0.647461	+	0.762099i	$0.275831\pi$
$859$			44.6723i			1.52420i	−0.647461	+	0.762099i	$0.724169\pi$
$860$	−1.40701	+	1.12571i	−0.0479787	+	0.0383865i
$861$	11.4275	−	8.30259i	0.389449	−	0.282951i
$862$	−7.54313	−	47.6254i	−0.256920	−	1.62213i
$863$	−10.6275	−	5.41499i	−0.361765	−	0.184328i	0.263655	−	0.964617i	$-0.415072\pi$
$863$	−10.6275	−	5.41499i	−0.361765	−	0.184328i	−0.625419	+	0.780289i	$0.715072\pi$
$864$	1.29493	+	3.98538i	0.0440544	+	0.135585i
$865$	−28.8885	+	10.8944i	−0.982237	+	0.370420i
$866$	−2.85271	−	3.92641i	−0.0969389	−	0.133425i
$867$	−34.2429	+	17.4476i	−1.16295	+	0.592552i
$868$	−5.46164	−	5.46164i	−0.185380	−	0.185380i
$869$		0			0
$870$	−25.1080	+	5.18243i	−0.851240	+	0.175701i
$871$	−47.4074	−	15.4036i	−1.60634	−	0.521931i
$872$	−48.7405	−	7.71974i	−1.65056	−	0.261423i
$873$	−16.1042	+	2.55066i	−0.545046	+	0.0863267i
$874$	52.5529	−	17.0755i	1.77763	−	0.577587i
$875$	−3.98094	−	28.3718i	−0.134580	−	0.959143i
$876$	−2.10439	+	2.89645i	−0.0711008	+	0.0978618i
$877$	−2.49182	+	15.7327i	−0.0841426	+	0.531256i	0.909228	+	0.416299i	$0.136673\pi$
$877$	−2.49182	+	15.7327i	−0.0841426	+	0.531256i	−0.993370	+	0.114957i	$0.963327\pi$
$878$	−10.2794	−	20.1745i	−0.346914	−	0.680858i
$879$	−40.6884			−1.37239
$880$		0			0
$881$	−35.9869			−1.21243			−0.606214	−	0.795301i	$-0.707313\pi$
$881$	−35.9869			−1.21243			−0.606214	+	0.795301i	$0.707313\pi$
$882$	−0.539662	−	1.05915i	−0.0181714	−	0.0356633i
$883$	2.54338	−	16.0583i	0.0855915	−	0.540404i	−0.907214	−	0.420669i	$-0.861796\pi$
$883$	2.54338	−	16.0583i	0.0855915	−	0.540404i	0.992806	−	0.119735i	$-0.0382045\pi$
$884$	0.349844	−	0.481518i	0.0117665	−	0.0161952i
$885$	−5.75734	−	1.57909i	−0.193531	−	0.0530806i
$886$	−2.16814	+	0.704470i	−0.0728400	+	0.0236671i
$887$	30.7795	−	4.87499i	1.03347	−	0.163686i	0.383420	−	0.923574i	$-0.374746\pi$
$887$	30.7795	−	4.87499i	1.03347	−	0.163686i	0.650054	+	0.759888i	$0.274746\pi$
$888$	−43.9623	−	6.96294i	−1.47528	−	0.233661i
$889$	−6.14209	−	1.99568i	−0.205999	−	0.0669331i
$890$	3.97265	−	6.03914i	0.133163	−	0.202432i
$891$		0			0
$892$	2.11444	+	2.11444i	0.0707968	+	0.0707968i
$893$	−19.1413	+	9.75297i	−0.640538	+	0.326371i
$894$	14.4031	+	19.8241i	0.481711	+	0.663018i
$895$	14.0361	+	6.34865i	0.469176	+	0.212212i
$896$	−5.41857	−	16.6767i	−0.181022	−	0.557128i
$897$	−72.4031	−	36.8912i	−2.41747	−	1.23176i
$898$	−2.87061	−	18.1243i	−0.0957933	−	0.604815i
$899$	24.4781	−	17.7844i	0.816391	−	0.593143i
$900$	0.398843	+	4.27926i	0.0132948	+	0.142642i
$901$		−	2.64469i		−	0.0881074i
$902$		0			0
$903$	−8.36106	+	8.36106i	−0.278239	+	0.278239i
$904$	−1.80117	+	5.54344i	−0.0599061	+	0.184372i
$905$	−38.4617	−	35.0436i	−1.27851	−	1.16489i
$906$	−16.0463	−	11.6583i	−0.533103	−	0.387322i
$907$	15.7217	−	30.8556i	0.522030	−	1.02454i	−0.468005	−	0.883726i	$-0.655027\pi$
$907$	15.7217	−	30.8556i	0.522030	−	1.02454i	0.990036	−	0.140817i	$-0.0449728\pi$
$908$	1.05821	−	2.07685i	0.0351178	−	0.0689225i
$909$	28.0953	+	20.4124i	0.931863	+	0.677038i
$910$	36.1112	−	1.67921i	1.19707	−	0.0556652i
$911$	−9.48160	+	29.1814i	−0.314140	+	0.966822i	0.661968	+	0.749532i	$0.269722\pi$
$911$	−9.48160	+	29.1814i	−0.314140	+	0.966822i	−0.976107	+	0.217290i	$0.930278\pi$
$912$	29.8007	−	29.8007i	0.986800	−	0.986800i
$913$		0			0
$914$		−	48.7687i		−	1.61312i
$915$	0.295121	+	0.368867i	0.00975639	+	0.0121944i
$916$	−7.69885	+	5.59354i	−0.254377	+	0.184816i
$917$	5.54612	+	35.0168i	0.183149	+	1.15636i
$918$	0.643827	+	0.328046i	0.0212495	+	0.0108271i
$919$	−8.27877	−	25.4794i	−0.273091	−	0.840489i	−0.989718	−	0.143032i	$-0.954315\pi$
$919$	−8.27877	−	25.4794i	−0.273091	−	0.840489i	0.716627	−	0.697457i	$-0.245685\pi$
$920$	20.0663	−	44.3642i	0.661565	−	1.46264i
$921$	−17.2053	−	23.6811i	−0.566935	−	0.780320i
$922$	−21.7532	+	11.0838i	−0.716403	+	0.365026i
$923$	−39.6149	−	39.6149i	−1.30394	−	1.30394i
$924$		0			0
$925$	29.9841	+	11.9171i	0.985872	+	0.391832i
$926$	−23.3732	−	7.59440i	−0.768090	−	0.249568i
$927$	3.07845	+	0.487579i	0.101110	+	0.0160142i
$928$	−8.69549	+	1.37723i	−0.285444	+	0.0452098i
$929$	24.2075	−	7.86549i	0.794222	−	0.258058i	0.116321	−	0.993212i	$-0.462890\pi$
$929$	24.2075	−	7.86549i	0.794222	−	0.258058i	0.677901	+	0.735153i	$0.262890\pi$
$930$	24.1826	+	42.4613i	0.792978	+	1.39236i
$931$	−1.54995	+	2.13332i	−0.0507974	+	0.0699167i
$932$	−0.894914	+	5.65026i	−0.0293139	+	0.185081i
$933$	−19.4541	−	38.1808i	−0.636899	−	1.24998i
$934$	−46.0237			−1.50594
$935$		0			0
$936$	−32.7484			−1.07041
$937$	−17.9534	−	35.2355i	−0.586511	−	1.15109i	−0.973431	−	0.228980i	$-0.926461\pi$
$937$	−17.9534	−	35.2355i	−0.586511	−	1.15109i	0.386920	−	0.922113i	$-0.373539\pi$
$938$	5.07732	−	32.0569i	0.165780	−	1.04670i
$939$	12.8221	−	17.6481i	0.418433	−	0.575923i
$940$	−0.829149	+	3.02306i	−0.0270439	+	0.0986014i
$941$	−39.0022	+	12.6726i	−1.27144	+	0.413115i	−0.865556	−	0.500812i	$-0.833035\pi$
$941$	−39.0022	+	12.6726i	−1.27144	+	0.413115i	−0.405880	+	0.913926i	$0.633035\pi$
$942$	15.4998	−	2.45492i	0.505009	−	0.0799856i
$943$	−17.1879	−	2.72230i	−0.559715	−	0.0886502i
$944$	3.40594	+	1.10666i	0.110854	+	0.0360186i
$945$	−2.19660	−	10.6421i	−0.0714553	−	0.346188i
$946$		0			0
$947$	42.9022	+	42.9022i	1.39413	+	1.39413i	0.815799	+	0.578336i	$0.196298\pi$
$947$	42.9022	+	42.9022i	1.39413	+	1.39413i	0.578336	+	0.815799i	$0.303702\pi$
$948$	1.89560	−	0.965859i	0.0615664	−	0.0313696i
$949$	11.6238	+	15.9988i	0.377324	+	0.519342i
$950$	−32.5386	+	20.5897i	−1.05569	+	0.668019i
$951$	9.26996	+	28.5300i	0.300599	+	0.925149i
$952$	2.08522	+	1.06247i	0.0675823	+	0.0344349i
$953$	−0.713548	−	4.50516i	−0.0231141	−	0.145937i	0.973432	−	0.228975i	$-0.0735375\pi$
$953$	−0.713548	−	4.50516i	−0.0231141	−	0.145937i	−0.996546	+	0.0830387i	$0.973537\pi$
$954$	−19.4946	+	14.1637i	−0.631161	+	0.458565i
$955$	−16.7425	−	1.85951i	−0.541775	−	0.0601724i
$956$			6.00049i			0.194070i
$957$		0			0
$958$	−7.62489	+	7.62489i	−0.246349	+	0.246349i
$959$	1.55339	−	4.78083i	0.0501615	−	0.154381i
$960$	−2.09983	−	45.1565i	−0.0677716	−	1.45742i
$961$	−21.5759	−	15.6758i	−0.695997	−	0.505671i
$962$	−18.4831	+	36.2752i	−0.595920	+	1.16956i
$963$	−10.9946	+	21.5781i	−0.354296	+	0.695344i
$964$	−1.00497	−	0.730157i	−0.0323681	−	0.0235168i
$965$	−2.62470	−	56.4437i	−0.0844919	−	1.81699i
$966$	16.3501	−	50.3205i	0.526057	−	1.61904i
$967$	27.0023	−	27.0023i	0.868336	−	0.868336i	−0.123952	−	0.992288i	$-0.539557\pi$
$967$	27.0023	−	27.0023i	0.868336	−	0.868336i	0.992288	+	0.123952i	$0.0395569\pi$
$968$		0			0
$969$			4.16018i			0.133644i
$970$	−21.1857	−	2.35300i	−0.680233	−	0.0755503i
$971$	32.0812	−	23.3084i	1.02953	−	0.748001i	0.0613191	−	0.998118i	$-0.480469\pi$
$971$	32.0812	−	23.3084i	1.02953	−	0.748001i	0.968215	+	0.250118i	$0.0804693\pi$
$972$	1.17184	+	7.39870i	0.0375868	+	0.237313i
$973$	19.7815	+	10.0792i	0.634166	+	0.323124i
$974$	−1.70743	−	5.25494i	−0.0547097	−	0.168379i
$975$	55.2455	+	12.4250i	1.76927	+	0.397918i
$976$	−0.166565	−	0.229257i	−0.00533162	−	0.00733835i
$977$	−5.66438	+	2.88615i	−0.181220	+	0.0923360i	−0.542247	−	0.840219i	$-0.682426\pi$
$977$	−5.66438	+	2.88615i	−0.181220	+	0.0923360i	0.361027	+	0.932555i	$0.382426\pi$
$978$	−4.55869	−	4.55869i	−0.145771	−	0.145771i
$979$		0			0
$980$	0.0777799	+	0.376830i	0.00248459	+	0.0120374i
$981$	−33.4906	−	10.8817i	−1.06927	−	0.347427i
$982$	21.7740	+	3.44866i	0.694835	+	0.110051i
$983$	−1.18524	+	0.187724i	−0.0378033	+	0.00598745i	−0.175307	−	0.984514i	$-0.556092\pi$
$983$	−1.18524	+	0.187724i	−0.0378033	+	0.00598745i	0.137504	+	0.990501i	$0.456092\pi$
$984$	−15.9099	+	5.16942i	−0.507188	+	0.164795i
$985$	−8.66374	+	31.5879i	−0.276050	+	1.00647i
$986$	−0.892315	+	1.22817i	−0.0284171	+	0.0391128i
$987$	−3.21789	+	20.3169i	−0.102426	+	0.646695i
$988$	5.46143	+	10.7187i	0.173751	+	0.341006i
$989$	14.5675			0.463220
$990$		0			0
$991$	9.57879			0.304280			0.152140	−	0.988359i	$-0.451383\pi$
$991$	9.57879			0.304280			0.152140	+	0.988359i	$0.451383\pi$
$992$	7.61808	+	14.9513i	0.241874	+	0.474705i
$993$	−4.51559	+	28.5103i	−0.143298	+	0.904747i
$994$	21.4415	−	29.5117i	0.680083	−	0.936053i
$995$	9.54944	+	16.7675i	0.302738	+	0.531566i
$996$	−7.12186	+	2.31403i	−0.225665	+	0.0733230i
$997$	16.6563	−	2.63811i	0.527512	−	0.0835496i	0.113002	−	0.993595i	$-0.463953\pi$
$997$	16.6563	−	2.63811i	0.527512	−	0.0835496i	0.414509	+	0.910045i	$0.363953\pi$
$998$	9.88421	+	1.56550i	0.312879	+	0.0495552i
$999$	11.6389	+	3.78171i	0.368239	+	0.119648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.f.112.4		80
5.3	odd	4	inner	605.2.m.f.233.4		80
11.2	odd	10	inner	605.2.m.f.602.7		80
11.3	even	5	inner	605.2.m.f.282.4		80
11.4	even	5		605.2.e.a.362.7	yes	20
11.5	even	5	inner	605.2.m.f.457.7		80
11.6	odd	10	inner	605.2.m.f.457.4		80
11.7	odd	10		605.2.e.a.362.4	✓	20
11.8	odd	10	inner	605.2.m.f.282.7		80
11.9	even	5	inner	605.2.m.f.602.4		80
11.10	odd	2	inner	605.2.m.f.112.7		80
55.3	odd	20	inner	605.2.m.f.403.7		80
55.8	even	20	inner	605.2.m.f.403.4		80
55.13	even	20	inner	605.2.m.f.118.4		80
55.18	even	20		605.2.e.a.483.7	yes	20
55.28	even	20	inner	605.2.m.f.578.4		80
55.38	odd	20	inner	605.2.m.f.578.7		80
55.43	even	4	inner	605.2.m.f.233.7		80
55.48	odd	20		605.2.e.a.483.4	yes	20
55.53	odd	20	inner	605.2.m.f.118.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.4	✓	20	11.7	odd	10
605.2.e.a.362.7	yes	20	11.4	even	5
605.2.e.a.483.4	yes	20	55.48	odd	20
605.2.e.a.483.7	yes	20	55.18	even	20
605.2.m.f.112.4		80	1.1	even	1	trivial
605.2.m.f.112.7		80	11.10	odd	2	inner
605.2.m.f.118.4		80	55.13	even	20	inner
605.2.m.f.118.7		80	55.53	odd	20	inner
605.2.m.f.233.4		80	5.3	odd	4	inner
605.2.m.f.233.7		80	55.43	even	4	inner
605.2.m.f.282.4		80	11.3	even	5	inner
605.2.m.f.282.7		80	11.8	odd	10	inner
605.2.m.f.403.4		80	55.8	even	20	inner
605.2.m.f.403.7		80	55.3	odd	20	inner
605.2.m.f.457.4		80	11.6	odd	10	inner
605.2.m.f.457.7		80	11.5	even	5	inner
605.2.m.f.578.4		80	55.28	even	20	inner
605.2.m.f.578.7		80	55.38	odd	20	inner
605.2.m.f.602.4		80	11.9	even	5	inner
605.2.m.f.602.7		80	11.2	odd	10	inner

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.574811 - 1.12813i) q^{2} +(0.355543 - 2.24481i) q^{3} +(0.233302 - 0.321113i) q^{4} +(1.94305 - 1.10660i) q^{5} +(-2.73681 + 0.889243i) q^{6} +(2.53096 - 0.400865i) q^{7} +(-2.99744 - 0.474748i) q^{8} +(-2.05960 - 0.669206i) q^{9} +O(q^{10})\)	\(q+(-0.574811 - 1.12813i) q^{2} +(0.355543 - 2.24481i) q^{3} +(0.233302 - 0.321113i) q^{4} +(1.94305 - 1.10660i) q^{5} +(-2.73681 + 0.889243i) q^{6} +(2.53096 - 0.400865i) q^{7} +(-2.99744 - 0.474748i) q^{8} +(-2.05960 - 0.669206i) q^{9} +(-2.36528 - 1.55592i) q^{10} +(-0.637889 - 0.637889i) q^{12} +(-4.43979 + 2.26219i) q^{13} +(-1.90705 - 2.62483i) q^{14} +(-1.79328 - 4.75522i) q^{15} +(0.942076 + 2.89941i) q^{16} +(-0.268136 - 0.136622i) q^{17} +(0.428931 + 2.70816i) q^{18} +(4.92080 - 3.57517i) q^{19} +(0.0979719 - 0.882110i) q^{20} -5.82406i q^{21} +(-5.07364 + 5.07364i) q^{23} +(-2.13144 + 6.55990i) q^{24} +(2.55085 - 4.30037i) q^{25} +(5.10408 + 3.70833i) q^{26} +(0.860962 - 1.68973i) q^{27} +(0.461756 - 0.906248i) q^{28} +(3.22334 + 2.34189i) q^{29} +(-4.33370 + 4.75640i) q^{30} +(2.34668 - 7.22235i) q^{31} +(-1.56247 + 1.56247i) q^{32} +0.381023i q^{34} +(4.47418 - 3.57967i) q^{35} +(-0.695400 + 0.505238i) q^{36} +(1.00949 + 6.37366i) q^{37} +(-6.86178 - 3.49625i) q^{38} +(3.49965 + 10.7708i) q^{39} +(-6.34953 + 2.39453i) q^{40} +(1.42557 + 1.96212i) q^{41} +(-6.57030 + 3.34773i) q^{42} +(-1.43561 - 1.43561i) q^{43} +(-4.74245 + 0.978869i) q^{45} +(8.64010 + 2.80734i) q^{46} +(-3.48845 - 0.552516i) q^{47} +(6.84359 - 1.08392i) q^{48} +(-0.412312 + 0.133968i) q^{49} +(-6.31763 - 0.405797i) q^{50} +(-0.402024 + 0.553339i) q^{51} +(-0.309396 + 1.95345i) q^{52} +(3.98977 + 7.83037i) q^{53} -2.40113 q^{54} -7.77673 q^{56} +(-6.27603 - 12.3174i) q^{57} +(0.789148 - 4.98248i) q^{58} +(0.690471 - 0.950352i) q^{59} +(-1.94534 - 0.533557i) q^{60} +(-0.0884033 + 0.0287240i) q^{61} +(-9.49664 + 1.50412i) q^{62} +(-5.48104 - 0.868112i) q^{63} +(8.45961 + 2.74870i) q^{64} +(-6.12337 + 9.30862i) q^{65} +(7.07364 + 7.07364i) q^{67} +(-0.106428 + 0.0542276i) q^{68} +(9.58547 + 13.1933i) q^{69} +(-6.61014 - 2.98982i) q^{70} +(3.47436 + 10.6930i) q^{71} +(5.85584 + 2.98370i) q^{72} +(-0.620840 - 3.91983i) q^{73} +(6.61005 - 4.80248i) q^{74} +(-8.74658 - 7.25516i) q^{75} -2.41423i q^{76} +(10.1392 - 10.1392i) q^{78} +(-0.728767 + 2.24292i) q^{79} +(5.03900 + 4.59118i) q^{80} +(-8.74303 - 6.35219i) q^{81} +(1.39410 - 2.73607i) q^{82} +(3.76855 - 7.39619i) q^{83} +(-1.87018 - 1.35877i) q^{84} +(-0.672186 + 0.0312574i) q^{85} +(-0.794348 + 2.44475i) q^{86} +(6.40314 - 6.40314i) q^{87} +2.55325i q^{89} +(3.83030 + 4.78743i) q^{90} +(-10.3301 + 7.50527i) q^{91} +(0.445520 + 2.81290i) q^{92} +(-15.3785 - 7.83572i) q^{93} +(1.38189 + 4.25301i) q^{94} +(5.60504 - 12.3921i) q^{95} +(2.95192 + 4.06298i) q^{96} +(6.70847 - 3.41814i) q^{97} +(0.388135 + 0.388135i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^5	\( 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Introduction

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