LMFDB - Embedded newform 55.2.g.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(16,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("55.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.g (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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.2
Root			$-0.628998 - 0.456994i$ of defining polynomial
Character	$\chi$	$=$	55.16
Dual form			55.2.g.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.697759 + 2.14748i) q^{2} +(-0.628998 - 0.456994i) q^{3} +(-2.50678 + 1.82128i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.542497 - 1.66963i) q^{6} +(-0.100294 + 0.0728678i) q^{7} +(-2.00678 - 1.45801i) q^{8} +(-0.740256 - 2.27827i) q^{9} +O(q^{10})$	\(q+(0.697759 + 2.14748i) q^{2} +(-0.628998 - 0.456994i) q^{3} +(-2.50678 + 1.82128i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.542497 - 1.66963i) q^{6} +(-0.100294 + 0.0728678i) q^{7} +(-2.00678 - 1.45801i) q^{8} +(-0.740256 - 2.27827i) q^{9} +2.25800 q^{10} +(-0.899706 - 3.19226i) q^{11} +2.40907 q^{12} +(1.69776 + 5.22517i) q^{13} +(-0.226463 - 0.164535i) q^{14} +(-0.628998 + 0.456994i) q^{15} +(-0.184207 + 0.566931i) q^{16} +(0.160531 - 0.494063i) q^{17} +(4.37603 - 3.17937i) q^{18} +(-2.55605 - 1.85708i) q^{19} +(0.957503 + 2.94689i) q^{20} +0.0963848 q^{21} +(6.22754 - 4.15953i) q^{22} -7.92856 q^{23} +(0.595957 + 1.83417i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-10.0363 + 7.29181i) q^{26} +(-1.29630 + 3.98962i) q^{27} +(0.118702 - 0.365326i) q^{28} +(3.29805 - 2.39618i) q^{29} +(-1.42027 - 1.03189i) q^{30} +(2.17827 + 6.70403i) q^{31} -6.30703 q^{32} +(-0.892930 + 2.41909i) q^{33} +1.17300 q^{34} +(0.0383089 + 0.117903i) q^{35} +(6.00503 + 4.36291i) q^{36} +(7.10927 - 5.16519i) q^{37} +(2.20454 - 6.78486i) q^{38} +(1.31998 - 4.06248i) q^{39} +(-2.00678 + 1.45801i) q^{40} +(6.10927 + 4.43864i) q^{41} +(0.0672534 + 0.206985i) q^{42} +3.42310 q^{43} +(8.06936 + 6.36367i) q^{44} -2.39552 q^{45} +(-5.53222 - 17.0264i) q^{46} +(-0.369254 - 0.268279i) q^{47} +(0.374949 - 0.272417i) q^{48} +(-2.15837 + 6.64278i) q^{49} +(0.697759 - 2.14748i) q^{50} +(-0.326757 + 0.237403i) q^{51} +(-13.7724 - 10.0062i) q^{52} +(0.0109640 + 0.0337437i) q^{53} -9.47214 q^{54} +(-3.31404 - 0.130791i) q^{55} +0.307509 q^{56} +(0.759076 + 2.33620i) q^{57} +(7.44699 + 5.41056i) q^{58} +(4.42925 - 3.21804i) q^{59} +(0.744444 - 2.29116i) q^{60} +(2.37603 - 7.31267i) q^{61} +(-12.8769 + 9.35559i) q^{62} +(0.240256 + 0.174556i) q^{63} +(-4.03237 - 12.4104i) q^{64} +5.49406 q^{65} +(-5.81799 - 0.229612i) q^{66} -2.53792 q^{67} +(0.497412 + 1.53088i) q^{68} +(4.98705 + 3.62330i) q^{69} +(-0.226463 + 0.164535i) q^{70} +(3.79264 - 11.6725i) q^{71} +(-1.83621 + 5.65128i) q^{72} +(-6.89377 + 5.00862i) q^{73} +(16.0527 + 11.6630i) q^{74} +(0.240256 + 0.739431i) q^{75} +9.78970 q^{76} +(0.322848 + 0.254605i) q^{77} +9.64514 q^{78} +(1.93868 + 5.96665i) q^{79} +(0.482260 + 0.350382i) q^{80} +(-3.17544 + 2.30709i) q^{81} +(-5.26911 + 16.2166i) q^{82} +(0.193571 - 0.595751i) q^{83} +(-0.241615 + 0.175544i) q^{84} +(-0.420275 - 0.305348i) q^{85} +(2.38850 + 7.35105i) q^{86} -3.16951 q^{87} +(-2.84883 + 7.71793i) q^{88} -10.1852 q^{89} +(-1.67149 - 5.14433i) q^{90} +(-0.551021 - 0.400340i) q^{91} +(19.8751 - 14.4401i) q^{92} +(1.69357 - 5.21228i) q^{93} +(0.318473 - 0.980160i) q^{94} +(-2.55605 + 1.85708i) q^{95} +(3.96711 + 2.88227i) q^{96} +(-0.567013 - 1.74509i) q^{97} -15.7713 q^{98} +(-6.60683 + 4.41287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9} + 6 q^{10} - 5 q^{11} - 28 q^{12} + 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} + q^{17} + 14 q^{18} - q^{19} - q^{20} - 12 q^{21} + 33 q^{22} - 18 q^{23} + 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} + 4 q^{28} + 19 q^{29} - 12 q^{30} + 6 q^{31} + 12 q^{32} - 19 q^{33} - 20 q^{34} - 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} + 9 q^{39} - 2 q^{40} - 4 q^{41} + 29 q^{42} + 42 q^{43} - 28 q^{44} - 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} - 4 q^{50} + 13 q^{51} - 26 q^{52} + 3 q^{53} - 40 q^{54} + 5 q^{55} + 30 q^{56} - 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} - 2 q^{61} - 38 q^{62} + q^{63} + 6 q^{64} + 14 q^{65} + 13 q^{66} - 2 q^{67} + 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} - 34 q^{72} - 23 q^{73} + 48 q^{74} + q^{75} + 16 q^{76} - 28 q^{77} + 12 q^{78} + 17 q^{79} + 15 q^{80} + 2 q^{82} - 25 q^{83} - 4 q^{84} - 4 q^{85} - 31 q^{86} + 30 q^{87} + 22 q^{88} - 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} + 33 q^{94} - q^{95} + 23 q^{96} + 12 q^{97} - 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9 + 6 * q^10 - 5 * q^11 - 28 * q^12 + 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 + q^17 + 14 * q^18 - q^19 - q^20 - 12 * q^21 + 33 * q^22 - 18 * q^23 + 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 + 4 * q^28 + 19 * q^29 - 12 * q^30 + 6 * q^31 + 12 * q^32 - 19 * q^33 - 20 * q^34 - 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 + 9 * q^39 - 2 * q^40 - 4 * q^41 + 29 * q^42 + 42 * q^43 - 28 * q^44 - 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 - 4 * q^50 + 13 * q^51 - 26 * q^52 + 3 * q^53 - 40 * q^54 + 5 * q^55 + 30 * q^56 - 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 - 2 * q^61 - 38 * q^62 + q^63 + 6 * q^64 + 14 * q^65 + 13 * q^66 - 2 * q^67 + 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 - 34 * q^72 - 23 * q^73 + 48 * q^74 + q^75 + 16 * q^76 - 28 * q^77 + 12 * q^78 + 17 * q^79 + 15 * q^80 + 2 * q^82 - 25 * q^83 - 4 * q^84 - 4 * q^85 - 31 * q^86 + 30 * q^87 + 22 * q^88 - 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 + 33 * q^94 - q^95 + 23 * q^96 + 12 * q^97 - 84 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.697759	+	2.14748i	0.493390	+	1.51850i	0.819451	+	0.573150i	$0.194279\pi$
$2$	0.697759	+	2.14748i	0.493390	+	1.51850i	−0.326060	+	0.945349i	$0.605721\pi$
$3$	−0.628998	−	0.456994i	−0.363152	−	0.263845i	0.391213	−	0.920300i	$-0.372055\pi$
$3$	−0.628998	−	0.456994i	−0.363152	−	0.263845i	−0.754366	+	0.656454i	$0.772055\pi$
$4$	−2.50678	+	1.82128i	−1.25339	+	0.910640i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	0.542497	−	1.66963i	0.221473	−	0.681625i
$7$	−0.100294	+	0.0728678i	−0.0379075	+	0.0275414i	−0.606578	−	0.795024i	$-0.707458\pi$
$7$	−0.100294	+	0.0728678i	−0.0379075	+	0.0275414i	0.568670	+	0.822566i	$0.307458\pi$
$8$	−2.00678	−	1.45801i	−0.709502	−	0.515484i
$9$	−0.740256	−	2.27827i	−0.246752	−	0.759424i
$10$	2.25800			0.714041
$11$	−0.899706	−	3.19226i	−0.271272	−	0.962503i
$11$	−0.899706	−	3.19226i	−0.271272	−	0.962503i
$12$	2.40907			0.695439
$13$	1.69776	+	5.22517i	0.470874	+	1.44920i	0.851443	+	0.524448i	$0.175728\pi$
$13$	1.69776	+	5.22517i	0.470874	+	1.44920i	−0.380569	+	0.924753i	$0.624272\pi$
$14$	−0.226463	−	0.164535i	−0.0605248	−	0.0439739i
$15$	−0.628998	+	0.456994i	−0.162407	+	0.117995i
$16$	−0.184207	+	0.566931i	−0.0460517	+	0.141733i
$17$	0.160531	−	0.494063i	0.0389344	−	0.119828i	−0.929700	−	0.368317i	$-0.879934\pi$
$17$	0.160531	−	0.494063i	0.0389344	−	0.119828i	0.968635	+	0.248489i	$0.0799341\pi$
$18$	4.37603	−	3.17937i	1.03144	−	0.749385i
$19$	−2.55605	−	1.85708i	−0.586398	−	0.426043i	0.254627	−	0.967039i	$-0.418047\pi$
$19$	−2.55605	−	1.85708i	−0.586398	−	0.426043i	−0.841025	+	0.540996i	$0.818047\pi$
$20$	0.957503	+	2.94689i	0.214104	+	0.658945i
$21$	0.0963848			0.0210329
$22$	6.22754	−	4.15953i	1.32772	−	0.886815i
$23$	−7.92856			−1.65322			−0.826609	−	0.562776i	$-0.809733\pi$
$23$	−7.92856			−1.65322			−0.826609	+	0.562776i	$0.809733\pi$
$24$	0.595957	+	1.83417i	0.121649	+	0.374398i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−10.0363	+	7.29181i	−1.96828	+	1.43004i
$27$	−1.29630	+	3.98962i	−0.249474	+	0.767802i
$28$	0.118702	−	0.365326i	0.0224325	−	0.0690402i
$29$	3.29805	−	2.39618i	0.612433	−	0.444959i	−0.237837	−	0.971305i	$-0.576438\pi$
$29$	3.29805	−	2.39618i	0.612433	−	0.444959i	0.850270	+	0.526346i	$0.176438\pi$
$30$	−1.42027	−	1.03189i	−0.259306	−	0.188396i
$31$	2.17827	+	6.70403i	0.391229	+	1.20408i	0.931860	+	0.362819i	$0.118186\pi$
$31$	2.17827	+	6.70403i	0.391229	+	1.20408i	−0.540631	+	0.841260i	$0.681814\pi$
$32$	−6.30703			−1.11494
$33$	−0.892930	+	2.41909i	−0.155439	+	0.421109i
$34$	1.17300			0.201168
$35$	0.0383089	+	0.117903i	0.00647538	+	0.0199292i
$36$	6.00503	+	4.36291i	1.00084	+	0.727151i
$37$	7.10927	−	5.16519i	1.16876	−	0.849151i	0.177897	−	0.984049i	$-0.443071\pi$
$37$	7.10927	−	5.16519i	1.16876	−	0.849151i	0.990860	+	0.134898i	$0.0430706\pi$
$38$	2.20454	−	6.78486i	0.357623	−	1.10065i
$39$	1.31998	−	4.06248i	0.211366	−	0.650518i
$40$	−2.00678	+	1.45801i	−0.317299	+	0.230531i
$41$	6.10927	+	4.43864i	0.954108	+	0.693200i	0.951775	−	0.306798i	$-0.0992575\pi$
$41$	6.10927	+	4.43864i	0.954108	+	0.693200i	0.00233277	+	0.999997i	$0.499257\pi$
$42$	0.0672534	+	0.206985i	0.0103774	+	0.0319384i
$43$	3.42310			0.522018			0.261009	−	0.965336i	$-0.415945\pi$
$43$	3.42310			0.522018			0.261009	+	0.965336i	$0.415945\pi$
$44$	8.06936	+	6.36367i	1.21650	+	0.959359i
$45$	−2.39552			−0.357103
$46$	−5.53222	−	17.0264i	−0.815682	−	2.51041i
$47$	−0.369254	−	0.268279i	−0.0538612	−	0.0391325i	0.560529	−	0.828135i	$-0.310598\pi$
$47$	−0.369254	−	0.268279i	−0.0538612	−	0.0391325i	−0.614390	+	0.789002i	$0.710598\pi$
$48$	0.374949	−	0.272417i	0.0541193	−	0.0393200i
$49$	−2.15837	+	6.64278i	−0.308339	+	0.948968i
$50$	0.697759	−	2.14748i	0.0986780	−	0.303700i
$51$	−0.326757	+	0.237403i	−0.0457551	+	0.0332431i
$52$	−13.7724	−	10.0062i	−1.90989	−	1.38761i
$53$	0.0109640	+	0.0337437i	0.00150602	+	0.00463505i	0.951807	−	0.306699i	$-0.0992243\pi$
$53$	0.0109640	+	0.0337437i	0.00150602	+	0.00463505i	−0.950301	+	0.311334i	$0.899224\pi$
$54$	−9.47214			−1.28899
$55$	−3.31404	−	0.130791i	−0.446866	−	0.0176359i
$56$	0.307509			0.0410926
$57$	0.759076	+	2.33620i	0.100542	+	0.309437i
$58$	7.44699	+	5.41056i	0.977838	+	0.710441i
$59$	4.42925	−	3.21804i	0.576639	−	0.418953i	−0.260872	−	0.965373i	$-0.584010\pi$
$59$	4.42925	−	3.21804i	0.576639	−	0.418953i	0.837511	+	0.546421i	$0.184010\pi$
$60$	0.744444	−	2.29116i	0.0961073	−	0.295788i
$61$	2.37603	−	7.31267i	0.304219	−	0.936291i	−0.675748	−	0.737133i	$-0.736179\pi$
$61$	2.37603	−	7.31267i	0.304219	−	0.936291i	0.979967	−	0.199158i	$-0.0638208\pi$
$62$	−12.8769	+	9.35559i	−1.63536	+	1.18816i
$63$	0.240256	+	0.174556i	0.0302694	+	0.0219920i
$64$	−4.03237	−	12.4104i	−0.504047	−	1.55130i
$65$	5.49406			0.681455
$66$	−5.81799	−	0.229612i	−0.716145	−	0.0282633i
$67$	−2.53792			−0.310056			−0.155028	−	0.987910i	$-0.549547\pi$
$67$	−2.53792			−0.310056			−0.155028	+	0.987910i	$0.549547\pi$
$68$	0.497412	+	1.53088i	0.0603200	+	0.185646i
$69$	4.98705	+	3.62330i	0.600370	+	0.436194i
$70$	−0.226463	+	0.164535i	−0.0270675	+	0.0196657i
$71$	3.79264	−	11.6725i	0.450103	−	1.38527i	−0.426686	−	0.904400i	$-0.640319\pi$
$71$	3.79264	−	11.6725i	0.450103	−	1.38527i	0.876789	−	0.480875i	$-0.159681\pi$
$72$	−1.83621	+	5.65128i	−0.216400	+	0.666010i
$73$	−6.89377	+	5.00862i	−0.806855	+	0.586214i	−0.912917	−	0.408145i	$-0.866176\pi$
$73$	−6.89377	+	5.00862i	−0.806855	+	0.586214i	0.106062	+	0.994359i	$0.466176\pi$
$74$	16.0527	+	11.6630i	1.86609	+	1.35579i
$75$	0.240256	+	0.739431i	0.0277424	+	0.0853822i
$76$	9.78970			1.12296
$77$	0.322848	+	0.254605i	0.0367919	+	0.0290149i
$78$	9.64514			1.09210
$79$	1.93868	+	5.96665i	0.218119	+	0.671301i	0.998917	+	0.0465180i	$0.0148125\pi$
$79$	1.93868	+	5.96665i	0.218119	+	0.671301i	−0.780799	+	0.624783i	$0.785188\pi$
$80$	0.482260	+	0.350382i	0.0539183	+	0.0391739i
$81$	−3.17544	+	2.30709i	−0.352827	+	0.256344i
$82$	−5.26911	+	16.2166i	−0.581876	+	1.79083i
$83$	0.193571	−	0.595751i	0.0212472	−	0.0653922i	−0.939871	−	0.341530i	$-0.889055\pi$
$83$	0.193571	−	0.595751i	0.0212472	−	0.0653922i	0.961118	+	0.276138i	$0.0890548\pi$
$84$	−0.241615	+	0.175544i	−0.0263624	+	0.0191534i
$85$	−0.420275	−	0.305348i	−0.0455852	−	0.0331196i
$86$	2.38850	+	7.35105i	0.257559	+	0.792684i
$87$	−3.16951			−0.339807
$88$	−2.84883	+	7.71793i	−0.303687	+	0.822734i
$89$	−10.1852			−1.07963			−0.539816	−	0.841783i	$-0.681506\pi$
$89$	−10.1852			−1.07963			−0.539816	+	0.841783i	$0.681506\pi$
$90$	−1.67149	−	5.14433i	−0.176191	−	0.542260i
$91$	−0.551021	−	0.400340i	−0.0577627	−	0.0419671i
$92$	19.8751	−	14.4401i	2.07212	−	1.50549i
$93$	1.69357	−	5.21228i	0.175615	−	0.540488i
$94$	0.318473	−	0.980160i	0.0328480	−	0.101096i
$95$	−2.55605	+	1.85708i	−0.262245	+	0.190532i
$96$	3.96711	+	2.88227i	0.404891	+	0.294171i
$97$	−0.567013	−	1.74509i	−0.0575714	−	0.177187i	0.918135	−	0.396267i	$-0.129694\pi$
$97$	−0.567013	−	1.74509i	−0.0575714	−	0.177187i	−0.975707	+	0.219080i	$0.929694\pi$
$98$	−15.7713			−1.59314
$99$	−6.60683	+	4.41287i	−0.664011	+	0.443510i
$100$	3.09855			0.309855
$101$	0.379378	+	1.16760i	0.0377495	+	0.116181i	0.968156	−	0.250350i	$-0.0805455\pi$
$101$	0.379378	+	1.16760i	0.0377495	+	0.116181i	−0.930406	+	0.366531i	$0.880546\pi$
$102$	−0.737816	−	0.536055i	−0.0730547	−	0.0530773i
$103$	1.90756	−	1.38593i	0.187958	−	0.136559i	−0.489827	−	0.871820i	$-0.662940\pi$
$103$	1.90756	−	1.38593i	0.187958	−	0.136559i	0.677785	+	0.735260i	$0.262940\pi$
$104$	4.21131	−	12.9611i	0.412953	−	1.27094i
$105$	0.0297845	−	0.0916674i	0.00290667	−	0.00894582i
$106$	−0.0648137	+	0.0470899i	−0.00629526	+	0.00457378i
$107$	−4.67758	−	3.39846i	−0.452199	−	0.328542i	0.338265	−	0.941051i	$-0.390160\pi$
$107$	−4.67758	−	3.39846i	−0.452199	−	0.328542i	−0.790463	+	0.612509i	$0.790160\pi$
$108$	−4.01666	−	12.3620i	−0.386503	−	1.18953i
$109$	4.21902			0.404109			0.202054	−	0.979374i	$-0.435238\pi$
$109$	4.21902			0.404109			0.202054	+	0.979374i	$0.435238\pi$
$110$	−2.03153	−	7.20811i	−0.193699	−	0.687267i
$111$	−6.83217			−0.648481
$112$	−0.0228361	−	0.0702824i	−0.00215781	−	0.00664106i
$113$	−12.2313	−	8.88652i	−1.15062	−	0.835974i	−0.162056	−	0.986782i	$-0.551813\pi$
$113$	−12.2313	−	8.88652i	−1.15062	−	0.835974i	−0.988563	+	0.150808i	$0.951813\pi$
$114$	−4.48729	+	3.26021i	−0.420273	+	0.305346i
$115$	−2.45006	+	7.54051i	−0.228469	+	0.703156i
$116$	−3.90337	+	12.0134i	−0.362419	+	1.11541i
$117$	10.6476	−	7.73592i	0.984369	−	0.715186i
$118$	10.0012	+	7.26632i	0.920688	+	0.668919i
$119$	0.0199010	+	0.0612490i	0.00182432	+	0.00561469i
$120$	1.92856			0.176053
$121$	−9.38106	+	5.74419i	−0.852823	+	0.522199i
$122$	17.3617			1.57186
$123$	−1.81429	−	5.58380i	−0.163589	−	0.503474i
$124$	−17.6703	−	12.8383i	−1.58684	−	1.15291i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−0.207215	+	0.637743i	−0.0184602	+	0.0568147i
$127$	−3.30954	+	10.1857i	−0.293674	+	0.903835i	0.689990	+	0.723819i	$0.257615\pi$
$127$	−3.30954	+	10.1857i	−0.293674	+	0.903835i	−0.983664	+	0.180016i	$0.942385\pi$
$128$	13.6324	−	9.90454i	1.20495	−	0.875446i
$129$	−2.15313	−	1.56434i	−0.189572	−	0.137732i
$130$	3.83353	+	11.7984i	0.336223	+	1.03479i
$131$	6.56014			0.573163			0.286581	−	0.958056i	$-0.407481\pi$
$131$	6.56014			0.573163			0.286581	+	0.958056i	$0.407481\pi$
$132$	−2.16746	−	7.69038i	−0.188653	−	0.669362i
$133$	0.391677			0.0339627
$134$	−1.77086	−	5.45014i	−0.152979	−	0.470820i
$135$	3.39377	+	2.46572i	0.292089	+	0.212215i
$136$	−1.04250	+	0.757418i	−0.0893934	+	0.0649481i
$137$	2.58810	−	7.96536i	0.221116	−	0.680526i	−0.777546	−	0.628826i	$-0.783536\pi$
$137$	2.58810	−	7.96536i	0.221116	−	0.680526i	0.998663	−	0.0517005i	$-0.0164641\pi$
$138$	−4.30122	+	13.2378i	−0.366144	+	1.12688i
$139$	12.9503	−	9.40892i	1.09843	−	0.798054i	0.117625	−	0.993058i	$-0.462472\pi$
$139$	12.9503	−	9.40892i	1.09843	−	0.798054i	0.980802	+	0.195004i	$0.0624719\pi$
$140$	−0.310765	−	0.225784i	−0.0262645	−	0.0190822i
$141$	0.109658	+	0.337493i	0.00923489	+	0.0284221i
$142$	27.7129			2.32561
$143$	15.1526	−	10.1208i	1.26712	−	0.846344i
$144$	1.42798			0.118999
$145$	−1.25974	−	3.87709i	−0.104616	−	0.321975i
$146$	−15.5661	−	11.3094i	−1.28826	−	0.935976i
$147$	4.39332	−	3.19193i	0.362355	−	0.263266i
$148$	−8.41410	+	25.8959i	−0.691635	+	2.12863i
$149$	−4.29145	+	13.2077i	−0.351569	+	1.08202i	0.606403	+	0.795158i	$0.292612\pi$
$149$	−4.29145	+	13.2077i	−0.351569	+	1.08202i	−0.957972	+	0.286861i	$0.907388\pi$
$150$	−1.42027	+	1.03189i	−0.115965	+	0.0842535i
$151$	−6.67408	−	4.84901i	−0.543129	−	0.394606i	0.282117	−	0.959380i	$-0.408963\pi$
$151$	−6.67408	−	4.84901i	−0.543129	−	0.394606i	−0.825246	+	0.564774i	$0.808963\pi$
$152$	2.42178	+	7.45348i	0.196433	+	0.604557i
$153$	−1.24444			−0.100607
$154$	−0.321489	+	0.870963i	−0.0259063	+	0.0701842i
$155$	7.04903			0.566192
$156$	4.09002	+	12.5878i	0.327464	+	1.00783i
$157$	−8.32082	−	6.04543i	−0.664074	−	0.482478i	0.203962	−	0.978979i	$-0.434618\pi$
$157$	−8.32082	−	6.04543i	−0.664074	−	0.482478i	−0.868036	+	0.496501i	$0.834618\pi$
$158$	−11.4605	+	8.32657i	−0.911752	+	0.662426i
$159$	0.00852432	−	0.0262352i	0.000676023	−	0.00208058i
$160$	−1.94898	+	5.99834i	−0.154080	+	0.474210i
$161$	0.795186	−	0.577736i	0.0626694	−	0.0455320i
$162$	−7.17014	−	5.20941i	−0.563339	−	0.409290i
$163$	−0.645379	−	1.98627i	−0.0505500	−	0.155577i	0.922595	−	0.385770i	$-0.126064\pi$
$163$	−0.645379	−	1.98627i	−0.0505500	−	0.155577i	−0.973145	+	0.230193i	$0.926064\pi$
$164$	−23.3986			−1.82712
$165$	2.02476	+	1.59677i	0.157627	+	0.124308i
$166$	1.41443			0.109781
$167$	5.13836	+	15.8143i	0.397618	+	1.22374i	0.926904	+	0.375300i	$0.122460\pi$
$167$	5.13836	+	15.8143i	0.397618	+	1.22374i	−0.529285	+	0.848444i	$0.677540\pi$
$168$	−0.193423	−	0.140530i	−0.0149229	−	0.0108421i
$169$	−13.9027	+	10.1009i	−1.06944	+	0.776995i
$170$	0.362478	−	1.11559i	0.0278008	−	0.0855620i
$171$	−2.33880	+	7.19809i	−0.178853	+	0.550452i
$172$	−8.58095	+	6.23443i	−0.654292	+	0.475371i
$173$	15.6338	+	11.3586i	1.18861	+	0.863579i	0.993117	−	0.117125i	$-0.0373678\pi$
$173$	15.6338	+	11.3586i	1.18861	+	0.863579i	0.195498	+	0.980704i	$0.437368\pi$
$174$	−2.21155	−	6.80646i	−0.167657	−	0.515996i
$175$	0.123970			0.00937126
$176$	1.97552	+	0.0779656i	0.148911	+	0.00587688i
$177$	−4.25661			−0.319947
$178$	−7.10683	−	21.8726i	−0.532679	−	1.63942i
$179$	2.34694	+	1.70515i	0.175418	+	0.127449i	0.672030	−	0.740524i	$-0.265423\pi$
$179$	2.34694	+	1.70515i	0.175418	+	0.127449i	−0.496612	+	0.867973i	$0.665423\pi$
$180$	6.00503	−	4.36291i	0.447588	−	0.325192i
$181$	3.09544	−	9.52678i	0.230082	−	0.708120i	−0.767654	−	0.640865i	$-0.778576\pi$
$181$	3.09544	−	9.52678i	0.230082	−	0.708120i	0.997736	−	0.0672551i	$-0.0214241\pi$
$182$	0.475243	−	1.46265i	0.0352274	−	0.108419i
$183$	−4.83636	+	3.51382i	−0.357514	+	0.259749i
$184$	15.9108	+	11.5599i	1.17296	+	0.852207i
$185$	−2.71550	−	8.35745i	−0.199647	−	0.614452i
$186$	12.3750			0.907377
$187$	−1.72161	−	0.0679446i	−0.125896	−	0.00496860i
$188$	1.41425			0.103145
$189$	−0.160703	−	0.494593i	−0.0116894	−	0.0359763i
$190$	−5.77155	−	4.19328i	−0.418712	−	0.304212i
$191$	10.9739	−	7.97299i	0.794042	−	0.576906i	−0.115118	−	0.993352i	$-0.536725\pi$
$191$	10.9739	−	7.97299i	0.794042	−	0.576906i	0.909160	+	0.416446i	$0.136725\pi$
$192$	−3.13511	+	9.64887i	−0.226257	+	0.696347i
$193$	4.23121	−	13.0223i	0.304569	−	0.937368i	−0.675268	−	0.737572i	$-0.735972\pi$
$193$	4.23121	−	13.0223i	0.304569	−	0.937368i	0.979838	−	0.199796i	$-0.0640279\pi$
$194$	3.35190	−	2.43530i	0.240653	−	0.174844i
$195$	−3.45576	−	2.51075i	−0.247472	−	0.179799i
$196$	−6.68781	−	20.5830i	−0.477701	−	1.47021i
$197$	2.59965			0.185217			0.0926087	−	0.995703i	$-0.470479\pi$
$197$	2.59965			0.185217			0.0926087	+	0.995703i	$0.470479\pi$
$198$	−14.0865	−	11.1089i	−1.00109	−	0.789477i
$199$	17.6907			1.25406			0.627029	−	0.778996i	$-0.284271\pi$
$199$	17.6907			1.25406			0.627029	+	0.778996i	$0.284271\pi$
$200$	0.766520	+	2.35911i	0.0542012	+	0.166814i
$201$	1.59635	+	1.15981i	0.112598	+	0.0818069i
$202$	−2.24270	+	1.62941i	−0.157796	+	0.114645i
$203$	−0.156171	+	0.480644i	−0.0109610	+	0.0337346i
$204$	0.386730	−	1.19023i	0.0270765	−	0.0833329i
$205$	6.10927	−	4.43864i	0.426690	−	0.310008i
$206$	4.30727	+	3.12941i	0.300102	+	0.218037i
$207$	5.86916	+	18.0634i	0.407935	+	1.25549i
$208$	−3.27504			−0.227083
$209$	−3.62859	+	9.83040i	−0.250994	+	0.679983i
$210$	0.217636			0.0150183
$211$	5.67600	+	17.4689i	0.390752	+	1.20261i	0.932221	+	0.361890i	$0.117869\pi$
$211$	5.67600	+	17.4689i	0.390752	+	1.20261i	−0.541468	+	0.840721i	$0.682131\pi$
$212$	−0.0889409	−	0.0646193i	−0.00610849	−	0.00443808i
$213$	−7.71984	+	5.60879i	−0.528954	+	0.384308i
$214$	4.03431	−	12.4163i	0.275780	−	0.848762i
$215$	1.05780	−	3.25556i	0.0721412	−	0.222028i
$216$	8.41829	−	6.11624i	0.572792	−	0.416158i
$217$	−0.706975	−	0.513647i	−0.0479926	−	0.0348687i
$218$	2.94386	+	9.06027i	0.199383	+	0.613639i
$219$	6.62507			0.447681
$220$	8.54578	−	5.70794i	0.576156	−	0.384829i
$221$	2.85410			0.191988
$222$	−4.76721	−	14.6720i	−0.319954	−	0.984718i
$223$	−1.56063	−	1.13386i	−0.104507	−	0.0759290i	0.534304	−	0.845292i	$-0.320574\pi$
$223$	−1.56063	−	1.13386i	−0.104507	−	0.0759290i	−0.638812	+	0.769363i	$0.720574\pi$
$224$	0.632556	−	0.459579i	0.0422645	−	0.0307069i
$225$	−0.740256	+	2.27827i	−0.0493504	+	0.151885i
$226$	10.5492	−	32.4670i	0.701721	−	2.15968i
$227$	−23.7743	+	17.2730i	−1.57796	+	1.14645i	−0.658966	+	0.752173i	$0.729006\pi$
$227$	−23.7743	+	17.2730i	−1.57796	+	1.14645i	−0.918991	+	0.394279i	$0.870994\pi$
$228$	−6.15770	−	4.47383i	−0.407804	−	0.296287i
$229$	−6.06659	−	18.6710i	−0.400891	−	1.23382i	−0.924278	−	0.381721i	$-0.875332\pi$
$229$	−6.06659	−	18.6710i	−0.400891	−	1.23382i	0.523386	−	0.852095i	$-0.324668\pi$
$230$	−17.9027			−1.18047
$231$	−0.0867180	−	0.307685i	−0.00570562	−	0.0202442i
$232$	−10.1121			−0.663892
$233$	1.56617	+	4.82018i	0.102603	+	0.315781i	0.989160	−	0.146838i	$-0.0469097\pi$
$233$	1.56617	+	4.82018i	0.102603	+	0.315781i	−0.886557	+	0.462619i	$0.846910\pi$
$234$	24.0422	+	17.4677i	1.57169	+	1.14190i
$235$	−0.369254	+	0.268279i	−0.0240875	+	0.0175006i
$236$	−5.24219	+	16.1338i	−0.341238	+	1.05022i
$237$	1.50730	−	4.63898i	0.0979094	−	0.301334i
$238$	−0.117645	+	0.0854741i	−0.00762579	+	0.00554046i
$239$	−18.2054	−	13.2270i	−1.17761	−	0.855582i	−0.185708	−	0.982605i	$-0.559458\pi$
$239$	−18.2054	−	13.2270i	−1.17761	−	0.855582i	−0.991900	+	0.127023i	$0.959458\pi$
$240$	−0.143218	−	0.440780i	−0.00924468	−	0.0284522i
$241$	−27.6924			−1.78382			−0.891911	−	0.452212i	$-0.850635\pi$
$241$	−27.6924			−1.78382			−0.891911	+	0.452212i	$0.850635\pi$
$242$	−18.8813	−	16.1376i	−1.21373	−	1.03736i
$243$	15.6365			1.00308
$244$	7.36224	+	22.6586i	0.471319	+	1.45057i
$245$	5.65069	+	4.10546i	0.361009	+	0.262288i
$246$	10.7252	−	7.79229i	0.683812	−	0.496818i
$247$	5.36399	−	16.5086i	0.341302	−	1.05042i
$248$	5.40323	−	16.6294i	0.343105	−	1.05597i
$249$	−0.394010	+	0.286265i	−0.0249694	+	0.0181413i
$250$	−1.82676	−	1.32722i	−0.115534	−	0.0839406i
$251$	−1.35019	−	4.15547i	−0.0852234	−	0.262291i	0.899359	−	0.437210i	$-0.144033\pi$
$251$	−1.35019	−	4.15547i	−0.0852234	−	0.262291i	−0.984583	+	0.174920i	$0.944033\pi$
$252$	−0.920183			−0.0579661
$253$	7.13337	+	25.3100i	0.448471	+	1.59123i
$254$	−24.1829			−1.51737
$255$	0.124810	+	0.384126i	0.00781591	+	0.0240549i
$256$	9.66819	+	7.02435i	0.604262	+	0.439022i
$257$	−14.6132	+	10.6171i	−0.911547	+	0.662278i	−0.941406	−	0.337276i	$-0.890494\pi$
$257$	−14.6132	+	10.6171i	−0.911547	+	0.662278i	0.0298583	+	0.999554i	$0.490494\pi$
$258$	1.85702	−	5.71533i	0.115613	−	0.355821i
$259$	−0.336641	+	1.03607i	−0.0209178	+	0.0643785i
$260$	−13.7724	+	10.0062i	−0.854127	+	0.620560i
$261$	−7.90055	−	5.74008i	−0.489032	−	0.355302i
$262$	4.57740	+	14.0878i	0.282793	+	0.870347i
$263$	13.4340			0.828377			0.414188	−	0.910191i	$-0.364065\pi$
$263$	13.4340			0.828377			0.414188	+	0.910191i	$0.364065\pi$
$264$	5.31896	−	3.55266i	0.327359	−	0.218651i
$265$	0.0354802			0.00217953
$266$	0.273296	+	0.841120i	0.0167569	+	0.0515724i
$267$	6.40648	+	4.65458i	0.392070	+	0.284856i
$268$	6.36200	−	4.62226i	0.388621	−	0.282350i
$269$	−1.31579	+	4.04959i	−0.0802253	+	0.246908i	−0.983123	−	0.182948i	$-0.941436\pi$
$269$	−1.31579	+	4.04959i	−0.0802253	+	0.246908i	0.902897	+	0.429857i	$0.141436\pi$
$270$	−2.92705	+	9.00854i	−0.178135	+	0.548242i
$271$	−10.2348	+	7.43600i	−0.621718	+	0.451705i	−0.853521	−	0.521058i	$-0.825537\pi$
$271$	−10.2348	+	7.43600i	−0.621718	+	0.451705i	0.231803	+	0.972763i	$0.425537\pi$
$272$	0.250528	+	0.182020i	0.0151905	+	0.0110366i
$273$	0.163638	+	0.503626i	0.00990383	+	0.0304809i
$274$	18.9113			1.14248
$275$	−1.14849	+	3.11143i	−0.0692563	+	0.187626i
$276$	−19.1005			−1.14971
$277$	−9.88149	−	30.4121i	−0.593721	−	1.82729i	−0.560993	−	0.827821i	$-0.689580\pi$
$277$	−9.88149	−	30.4121i	−0.593721	−	1.82729i	−0.0327282	−	0.999464i	$-0.510420\pi$
$278$	29.2417	+	21.2453i	1.75380	+	1.27421i
$279$	13.6611	−	9.92539i	0.817870	−	0.594218i
$280$	0.0950256	−	0.292459i	0.00567886	−	0.0174777i
$281$	−8.92530	+	27.4693i	−0.532439	+	1.63868i	0.216680	+	0.976243i	$0.430477\pi$
$281$	−8.92530	+	27.4693i	−0.532439	+	1.63868i	−0.749119	+	0.662436i	$0.769523\pi$
$282$	−0.648246	+	0.470978i	−0.0386025	+	0.0280463i
$283$	3.92558	+	2.85210i	0.233352	+	0.169540i	0.698316	−	0.715789i	$-0.253933\pi$
$283$	3.92558	+	2.85210i	0.233352	+	0.169540i	−0.464965	+	0.885329i	$0.653933\pi$
$284$	11.7517	+	36.1679i	0.697333	+	2.14617i
$285$	2.45642			0.145506
$286$	32.3071	+	25.4781i	1.91036	+	1.50655i
$287$	−0.936157			−0.0552596
$288$	4.66881	+	14.3691i	0.275113	+	0.846709i
$289$	13.5350	+	9.83372i	0.796174	+	0.578454i
$290$	7.44699	−	5.41056i	0.437302	−	0.317719i
$291$	−0.440844	+	1.35678i	−0.0258427	+	0.0795357i
$292$	8.15905	−	25.1110i	0.477472	−	1.46951i
$293$	−3.24221	+	2.35561i	−0.189412	+	0.137616i	−0.678450	−	0.734647i	$-0.737348\pi$
$293$	−3.24221	+	2.35561i	−0.189412	+	0.137616i	0.489038	+	0.872263i	$0.337348\pi$
$294$	9.92010	+	7.20737i	0.578552	+	0.420342i
$295$	−1.69182	−	5.20690i	−0.0985017	−	0.303157i
$296$	−21.7976			−1.26696
$297$	13.9022	+	0.548661i	0.806687	+	0.0318365i
$298$	−31.3577			−1.81651
$299$	−13.4608	−	41.4280i	−0.778457	−	2.39584i
$300$	−1.94898	−	1.41602i	−0.112524	−	0.0817537i
$301$	−0.343316	+	0.249434i	−0.0197884	+	0.0143771i
$302$	5.75625	−	17.7159i	0.331235	−	1.01944i
$303$	0.294960	−	0.907794i	0.0169450	−	0.0521514i
$304$	1.52368	−	1.10702i	0.0873888	−	0.0634917i
$305$	−6.22053	−	4.51948i	−0.356186	−	0.258785i
$306$	−0.868322	−	2.67242i	−0.0496387	−	0.152772i
$307$	3.68515			0.210323			0.105161	−	0.994455i	$-0.466464\pi$
$307$	3.68515			0.210323			0.105161	+	0.994455i	$0.466464\pi$
$308$	−1.27301	−	0.0502405i	−0.0725367	−	0.00286272i
$309$	−1.83321			−0.104288
$310$	4.91853	+	15.1377i	0.279354	+	0.859762i
$311$	8.06391	+	5.85877i	0.457262	+	0.332220i	0.792456	−	0.609929i	$-0.208802\pi$
$311$	8.06391	+	5.85877i	0.457262	+	0.332220i	−0.335194	+	0.942149i	$0.608802\pi$
$312$	−8.57204	+	6.22795i	−0.485296	+	0.352588i
$313$	5.82844	−	17.9381i	0.329443	−	1.01392i	−0.639952	−	0.768415i	$-0.721046\pi$
$313$	5.82844	−	17.9381i	0.329443	−	1.01392i	0.969395	−	0.245506i	$-0.0789541\pi$
$314$	7.17652	−	22.0871i	0.404995	−	1.24645i
$315$	0.240256	−	0.174556i	0.0135369	−	0.00983512i
$316$	−15.7268	−	11.4262i	−0.884701	−	0.642773i
$317$	1.20345	+	3.70385i	0.0675928	+	0.208029i	0.979148	−	0.203149i	$-0.0651175\pi$
$317$	1.20345	+	3.70385i	0.0675928	+	0.208029i	−0.911555	+	0.411178i	$0.865118\pi$
$318$	0.0622875			0.00349291
$319$	−10.6165	−	8.37239i	−0.594410	−	0.468764i
$320$	−13.0490			−0.729463
$321$	1.38911	+	4.27525i	0.0775327	+	0.238621i
$322$	1.79553	+	1.30453i	0.100061	+	0.0726984i
$323$	−1.32784	+	0.964730i	−0.0738829	+	0.0536790i
$324$	3.75826	−	11.5667i	0.208792	−	0.642596i
$325$	1.69776	−	5.22517i	0.0941747	−	0.289840i
$326$	3.81516	−	2.77188i	0.211302	−	0.153520i
$327$	−2.65375	−	1.92807i	−0.146753	−	0.106622i
$328$	−5.78836	−	17.8147i	−0.319609	−	0.983654i
$329$	0.0565828			0.00311951
$330$	−2.01623	+	5.46229i	−0.110990	+	0.300689i
$331$	7.97626			0.438415			0.219207	−	0.975678i	$-0.429653\pi$
$331$	7.97626			0.438415			0.219207	+	0.975678i	$0.429653\pi$
$332$	0.599789	+	1.84596i	0.0329177	+	0.101310i
$333$	−17.0304	−	12.3733i	−0.933259	−	0.678053i
$334$	−30.3755	+	22.0691i	−1.66207	+	1.20757i
$335$	−0.784260	+	2.41371i	−0.0428487	+	0.131875i
$336$	−0.0177547	+	0.0546435i	−0.000968600	+	0.00298105i
$337$	11.1097	−	8.07164i	0.605182	−	0.439690i	−0.242533	−	0.970143i	$-0.577978\pi$
$337$	11.1097	−	8.07164i	0.605182	−	0.439690i	0.847714	+	0.530453i	$0.177978\pi$
$338$	−31.3923	−	22.8079i	−1.70752	−	1.24058i
$339$	3.63235	+	11.1792i	0.197282	+	0.607171i
$340$	1.60966			0.0872960
$341$	19.4412	−	12.9853i	1.05280	−	0.703191i
$342$	−17.0897			−0.924105
$343$	−0.535735	−	1.64882i	−0.0289270	−	0.0890281i
$344$	−6.86940	−	4.99091i	−0.370373	−	0.269092i
$345$	4.98705	−	3.62330i	0.268494	−	0.195072i
$346$	−13.4838	+	41.4988i	−0.724893	+	2.23099i
$347$	0.0503533	−	0.154972i	0.00270311	−	0.00831931i	−0.949696	−	0.313174i	$-0.898608\pi$
$347$	0.0503533	−	0.154972i	0.00270311	−	0.00831931i	0.952399	+	0.304854i	$0.0986078\pi$
$348$	7.94524	−	5.77256i	0.425910	−	0.309441i
$349$	2.21788	+	1.61138i	0.118720	+	0.0862553i	0.645561	−	0.763709i	$-0.276624\pi$
$349$	2.21788	+	1.61138i	0.118720	+	0.0862553i	−0.526841	+	0.849964i	$0.676624\pi$
$350$	0.0865012	+	0.266223i	0.00462369	+	0.0142302i
$351$	−23.0472			−1.23017
$352$	5.67447	+	20.1337i	0.302450	+	1.07313i
$353$	−5.13584			−0.273353			−0.136677	−	0.990616i	$-0.543642\pi$
$353$	−5.13584			−0.273353			−0.136677	+	0.990616i	$0.543642\pi$
$354$	−2.97009	−	9.14100i	−0.157859	−	0.485839i
$355$	−9.92925	−	7.21402i	−0.526990	−	0.382881i
$356$	25.5321	−	18.5501i	1.35320	−	0.983155i
$357$	0.0154727	−	0.0476201i	0.000818903	−	0.00252032i
$358$	−2.02418	+	6.22979i	−0.106981	+	0.329255i
$359$	12.2777	−	8.92024i	0.647990	−	0.470792i	−0.214596	−	0.976703i	$-0.568843\pi$
$359$	12.2777	−	8.92024i	0.647990	−	0.470792i	0.862586	+	0.505911i	$0.168843\pi$
$360$	4.80727	+	3.49269i	0.253365	+	0.184081i
$361$	−2.78668	−	8.57651i	−0.146667	−	0.451395i
$362$	22.6185			1.18880
$363$	8.52573	+	0.673999i	0.447485	+	0.0353758i
$364$	2.11042			0.110616
$365$	2.63319	+	8.10411i	0.137827	+	0.424189i
$366$	−10.9205	−	7.93420i	−0.570823	−	0.414727i
$367$	−16.3133	+	11.8523i	−0.851547	+	0.618685i	−0.925572	−	0.378572i	$-0.876415\pi$
$367$	−16.3133	+	11.8523i	−0.851547	+	0.618685i	0.0740255	+	0.997256i	$0.476415\pi$
$368$	1.46050	−	4.49494i	0.0761336	−	0.234315i
$369$	5.59002	−	17.2043i	0.291005	−	0.895621i
$370$	16.0527	−	11.6630i	0.834540	−	0.606329i
$371$	−0.00355845	−	0.00258536i	−0.000184745	−	0.000134225i
$372$	5.24761	+	16.1505i	0.272076	+	0.837363i
$373$	11.2539			0.582707			0.291354	−	0.956615i	$-0.405894\pi$
$373$	11.2539			0.582707			0.291354	+	0.956615i	$0.405894\pi$
$374$	−1.05536	−	3.74453i	−0.0545712	−	0.193625i
$375$	0.777484			0.0401491
$376$	0.349857	+	1.07675i	0.0180425	+	0.0555292i
$377$	18.1197	+	13.1647i	0.933213	+	0.678019i
$378$	0.949997	−	0.690213i	0.0488626	−	0.0355008i
$379$	−6.47458	+	19.9267i	−0.332577	+	1.02357i	0.635327	+	0.772243i	$0.280865\pi$
$379$	−6.47458	+	19.9267i	−0.332577	+	1.02357i	−0.967903	+	0.251322i	$0.919135\pi$
$380$	3.02518	−	9.31056i	0.155189	−	0.477622i
$381$	6.73650	−	4.89435i	0.345121	−	0.250745i
$382$	24.7790	+	18.0030i	1.26780	+	0.921113i
$383$	5.20102	+	16.0071i	0.265759	+	0.817924i	0.991517	+	0.129973i	$0.0414892\pi$
$383$	5.20102	+	16.0071i	0.265759	+	0.817924i	−0.725758	+	0.687950i	$0.758511\pi$
$384$	−13.1011			−0.668562
$385$	0.341909	−	0.228370i	0.0174253	−	0.0116388i
$386$	30.9176			1.57366
$387$	−2.53397	−	7.79877i	−0.128809	−	0.396434i
$388$	4.59966	+	3.34185i	0.233513	+	0.169657i
$389$	−12.7525	+	9.26524i	−0.646578	+	0.469766i	−0.862104	−	0.506732i	$-0.830853\pi$
$389$	−12.7525	+	9.26524i	−0.646578	+	0.469766i	0.215526	+	0.976498i	$0.430853\pi$
$390$	2.98051	−	9.17307i	0.150924	−	0.464497i
$391$	−1.27278	+	3.91721i	−0.0643671	+	0.198102i
$392$	14.0166	−	10.1836i	0.707945	−	0.514352i
$393$	−4.12632	−	2.99795i	−0.208145	−	0.151226i
$394$	1.81393	+	5.58270i	0.0913844	+	0.281252i
$395$	6.27371			0.315665
$396$	8.52478	−	23.0950i	0.428386	−	1.16056i
$397$	6.85466			0.344025			0.172013	−	0.985095i	$-0.444973\pi$
$397$	6.85466			0.344025			0.172013	+	0.985095i	$0.444973\pi$
$398$	12.3438	+	37.9904i	0.618740	+	1.90429i
$399$	−0.246364	−	0.178994i	−0.0123336	−	0.00896091i
$400$	0.482260	−	0.350382i	0.0241130	−	0.0175191i
$401$	−0.0436009	+	0.134190i	−0.00217732	+	0.00670111i	−0.952139	−	0.305665i	$-0.901121\pi$
$401$	−0.0436009	+	0.134190i	−0.00217732	+	0.00670111i	0.949962	+	0.312366i	$0.101121\pi$
$402$	−1.37681	+	4.23740i	−0.0686692	+	0.211342i
$403$	−31.3315	+	22.7637i	−1.56073	+	1.13394i
$404$	−3.07755	−	2.23597i	−0.153114	−	0.111244i
$405$	1.21291	+	3.73296i	0.0602700	+	0.185492i
$406$	−1.14114			−0.0566340
$407$	−22.8849	−	18.0475i	−1.13436	−	0.894581i
$408$	1.00186			0.0495996
$409$	8.88382	+	27.3416i	0.439277	+	1.35195i	0.888640	+	0.458605i	$0.151651\pi$
$409$	8.88382	+	27.3416i	0.439277	+	1.35195i	−0.449364	+	0.893349i	$0.648349\pi$
$410$	13.7947	+	10.0224i	0.681272	+	0.494973i
$411$	−5.26803	+	3.82745i	−0.259853	+	0.188794i
$412$	−2.25768	+	6.94841i	−0.111228	+	0.342324i
$413$	−0.209735	+	0.645499i	−0.0103204	+	0.0317629i
$414$	−34.6956	+	25.2078i	−1.70520	+	1.23890i
$415$	−0.506776	−	0.368194i	−0.0248767	−	0.0180740i
$416$	−10.7078	−	32.9553i	−0.524994	−	1.61576i
$417$	−12.4455			−0.609459
$418$	−23.6425	−	0.933070i	−1.15639	−	0.0456379i
$419$	−11.0837			−0.541472			−0.270736	−	0.962654i	$-0.587267\pi$
$419$	−11.0837			−0.541472			−0.270736	+	0.962654i	$0.587267\pi$
$420$	0.0922887	+	0.284036i	0.00450323	+	0.0138595i
$421$	2.75336	+	2.00043i	0.134190	+	0.0974950i	0.652856	−	0.757482i	$-0.273571\pi$
$421$	2.75336	+	2.00043i	0.134190	+	0.0974950i	−0.518665	+	0.854977i	$0.673571\pi$
$422$	−33.5538	+	24.3782i	−1.63337	+	1.18671i
$423$	−0.337870	+	1.03986i	−0.0164278	+	0.0505595i
$424$	0.0271963	−	0.0837016i	0.00132077	−	0.00406491i
$425$	−0.420275	+	0.305348i	−0.0203863	+	0.0148115i
$426$	−17.4314	−	12.6646i	−0.844552	−	0.613603i
$427$	0.294557	+	0.906552i	0.0142546	+	0.0438711i
$428$	17.9152			0.865963
$429$	−14.1561	−	0.558682i	−0.683463	−	0.0269734i
$430$	7.72935			0.372743
$431$	−4.22510	−	13.0035i	−0.203516	−	0.626358i	−0.999771	−	0.0213970i	$-0.993189\pi$
$431$	−4.22510	−	13.0035i	−0.203516	−	0.626358i	0.796255	−	0.604961i	$-0.206811\pi$
$432$	−2.02305	−	1.46983i	−0.0973339	−	0.0707172i
$433$	12.4949	−	9.07811i	0.600469	−	0.436266i	−0.245577	−	0.969377i	$-0.578977\pi$
$433$	12.4949	−	9.07811i	0.600469	−	0.436266i	0.846045	+	0.533111i	$0.178977\pi$
$434$	0.609750	−	1.87662i	0.0292689	−	0.0900805i
$435$	−0.979431	+	3.01438i	−0.0469601	+	0.144528i
$436$	−10.5761	+	7.68401i	−0.506505	+	0.367997i
$437$	20.2658	+	14.7240i	0.969444	+	0.704342i
$438$	4.62271	+	14.2272i	0.220881	+	0.679803i
$439$	9.87042			0.471089			0.235545	−	0.971864i	$-0.424313\pi$
$439$	9.87042			0.471089			0.235545	+	0.971864i	$0.424313\pi$
$440$	6.45985	+	5.09437i	0.307961	+	0.242865i
$441$	16.7318			0.796753
$442$	1.99148	+	6.12913i	0.0947248	+	0.291533i
$443$	−25.3222	−	18.3977i	−1.20310	−	0.874100i	−0.208509	−	0.978020i	$-0.566861\pi$
$443$	−25.3222	−	18.3977i	−1.20310	−	0.874100i	−0.994586	+	0.103921i	$0.966861\pi$
$444$	17.1267	−	12.4433i	0.812799	−	0.590533i
$445$	−3.14741	+	9.68672i	−0.149201	+	0.459195i
$446$	1.34600	−	4.14258i	0.0637352	−	0.196157i
$447$	8.73516	−	6.34647i	0.413159	−	0.300177i
$448$	1.30874	+	0.950854i	0.0618321	+	0.0449236i
$449$	−3.93292	−	12.1043i	−0.185606	−	0.571236i	0.814352	−	0.580371i	$-0.197092\pi$
$449$	−3.93292	−	12.1043i	−0.185606	−	0.571236i	−0.999958	+	0.00913449i	$0.997092\pi$
$450$	−5.40907			−0.254986
$451$	8.67276	−	23.4959i	0.408384	−	1.10638i
$452$	46.8459			2.20344
$453$	1.98202	+	6.10003i	0.0931234	+	0.286604i
$454$	−53.6823	−	39.0025i	−2.51943	−	1.83048i
$455$	−0.551021	+	0.400340i	−0.0258323	+	0.0187682i
$456$	1.88290	−	5.79496i	0.0881748	−	0.271374i
$457$	−1.33235	+	4.10054i	−0.0623245	+	0.191815i	−0.977371	−	0.211534i	$-0.932154\pi$
$457$	−1.33235	+	4.10054i	−0.0623245	+	0.191815i	0.915046	+	0.403349i	$0.132154\pi$
$458$	35.8627	−	26.0558i	1.67575	−	1.21751i
$459$	1.76302	+	1.28091i	0.0822909	+	0.0597878i
$460$	−7.59162	−	23.3646i	−0.353961	−	1.08938i
$461$	−17.7315			−0.825837			−0.412918	−	0.910768i	$-0.635491\pi$
$461$	−17.7315			−0.825837			−0.412918	+	0.910768i	$0.635491\pi$
$462$	0.600240	−	0.400916i	0.0279257	−	0.0186523i
$463$	3.43092			0.159448			0.0797242	−	0.996817i	$-0.474596\pi$
$463$	3.43092			0.159448			0.0797242	+	0.996817i	$0.474596\pi$
$464$	0.750941	+	2.31116i	0.0348616	+	0.107293i
$465$	−4.43383	−	3.22136i	−0.205614	−	0.149387i
$466$	−9.25845	+	6.72666i	−0.428889	+	0.311606i
$467$	−4.83245	+	14.8728i	−0.223619	+	0.688229i	0.774810	+	0.632195i	$0.217846\pi$
$467$	−4.83245	+	14.8728i	−0.223619	+	0.688229i	−0.998429	+	0.0560346i	$0.982154\pi$
$468$	−12.6018	+	38.7844i	−0.582520	+	1.79281i
$469$	0.254538	−	0.184933i	0.0117535	−	0.00853939i
$470$	−0.833774	−	0.605772i	−0.0384591	−	0.0279422i
$471$	2.47106	+	7.60513i	0.113860	+	0.350426i
$472$	−13.5804			−0.625090
$473$	−3.07979	−	10.9274i	−0.141609	−	0.502444i
$474$	11.0138			0.505883
$475$	0.976324	+	3.00482i	0.0447968	+	0.137870i
$476$	−0.161439	−	0.117292i	−0.00739954	−	0.00537608i
$477$	0.0687611	−	0.0499579i	0.00314836	−	0.00228742i
$478$	15.7017	−	48.3250i	0.718180	−	2.21033i
$479$	−11.8994	+	36.6227i	−0.543699	+	1.67333i	0.180363	+	0.983600i	$0.442273\pi$
$479$	−11.8994	+	36.6227i	−0.543699	+	1.67333i	−0.724062	+	0.689735i	$0.757727\pi$
$480$	3.96711	−	2.88227i	0.181073	−	0.131557i
$481$	39.0588	+	28.3779i	1.78093	+	1.29392i
$482$	−19.3226	−	59.4688i	−0.880120	−	2.70873i
$483$	−0.764192			−0.0347720
$484$	13.0544	−	31.4849i	0.593383	−	1.43113i
$485$	−1.83489			−0.0833182
$486$	10.9105	+	33.5790i	0.494910	+	1.52318i
$487$	7.29777	+	5.30214i	0.330694	+	0.240263i	0.740725	−	0.671808i	$-0.234482\pi$
$487$	7.29777	+	5.30214i	0.330694	+	0.240263i	−0.410031	+	0.912071i	$0.634482\pi$
$488$	−15.4301	+	11.2106i	−0.698487	+	0.507481i
$489$	−0.501772	+	1.54430i	−0.0226909	+	0.0698354i
$490$	−4.87359	+	14.9994i	−0.220166	+	0.677602i
$491$	3.82721	−	2.78063i	0.172719	−	0.125488i	−0.498067	−	0.867139i	$-0.665957\pi$
$491$	3.82721	−	2.78063i	0.172719	−	0.125488i	0.670787	+	0.741650i	$0.265957\pi$
$492$	14.7177	+	10.6930i	0.663523	+	0.482078i
$493$	−0.654422	−	2.01410i	−0.0294737	−	0.0907107i
$494$	39.1948			1.76346
$495$	2.15526	+	7.64712i	0.0968718	+	0.343712i
$496$	−4.20197			−0.188674
$497$	0.470173	+	1.44704i	0.0210902	+	0.0649088i
$498$	−0.889674	−	0.646386i	−0.0398672	−	0.0289652i
$499$	−0.926422	+	0.673085i	−0.0414723	+	0.0301314i	−0.608328	−	0.793685i	$-0.708160\pi$
$499$	−0.926422	+	0.673085i	−0.0414723	+	0.0301314i	0.566856	+	0.823817i	$0.308160\pi$
$500$	0.957503	−	2.94689i	0.0428208	−	0.131789i
$501$	3.99500	−	12.2953i	0.178483	−	0.549315i
$502$	7.98168	−	5.79903i	0.356240	−	0.258823i
$503$	−13.4634	−	9.78171i	−0.600302	−	0.436145i	0.245684	−	0.969350i	$-0.420987\pi$
$503$	−13.4634	−	9.78171i	−0.600302	−	0.436145i	−0.845986	+	0.533205i	$0.820987\pi$
$504$	−0.227635	−	0.700590i	−0.0101397	−	0.0312068i
$505$	1.22769			0.0546316
$506$	−49.3754	+	32.9791i	−2.19501	+	1.46610i
$507$	13.3609			0.593377
$508$	−10.2547	−	31.5609i	−0.454981	−	1.40029i
$509$	23.9289	+	17.3854i	1.06063	+	0.770594i	0.974205	−	0.225664i	$-0.0724552\pi$
$509$	23.9289	+	17.3854i	1.06063	+	0.770594i	0.0864265	+	0.996258i	$0.472455\pi$
$510$	−0.737816	+	0.536055i	−0.0326710	+	0.0237369i
$511$	0.326436	−	1.00467i	0.0144407	−	0.0444439i
$512$	2.07565	−	6.38820i	0.0917318	−	0.282321i
$513$	10.7224	−	7.79031i	0.473408	−	0.343951i
$514$	−32.9966	−	23.9734i	−1.45542	−	1.05742i
$515$	−0.728624	−	2.24247i	−0.0321070	−	0.0988152i
$516$	8.24650			0.363032
$517$	−0.524195	+	1.42013i	−0.0230541	+	0.0624571i
$518$	−2.45984			−0.108079
$519$	−4.64281	−	14.2891i	−0.203797	−	0.627221i
$520$	−11.0254	−	8.01039i	−0.483494	−	0.351279i
$521$	5.35218	−	3.88859i	0.234483	−	0.170362i	−0.464339	−	0.885658i	$-0.653708\pi$
$521$	5.35218	−	3.88859i	0.234483	−	0.170362i	0.698822	+	0.715296i	$0.253708\pi$
$522$	6.81404	−	20.9715i	0.298243	−	0.917896i
$523$	11.2091	−	34.4980i	0.490138	−	1.50849i	−0.334260	−	0.942481i	$-0.608486\pi$
$523$	11.2091	−	34.4980i	0.490138	−	1.50849i	0.824399	−	0.566010i	$-0.191514\pi$
$524$	−16.4448	+	11.9479i	−0.718395	+	0.521945i
$525$	−0.0779769	−	0.0566535i	−0.00340319	−	0.00247256i
$526$	9.37371	+	28.8493i	0.408713	+	1.25789i
$527$	3.66189			0.159514
$528$	−1.20697	−	0.951842i	−0.0525266	−	0.0414236i
$529$	39.8620			1.73313
$530$	0.0247566	+	0.0761931i	0.00107536	+	0.00330962i
$531$	−10.6103	−	7.70887i	−0.460450	−	0.334536i
$532$	−0.981847	+	0.713354i	−0.0425685	+	0.0309278i
$533$	−12.8206	+	39.4577i	−0.555321	+	1.70910i
$534$	−5.52545	+	17.0056i	−0.239110	+	0.735903i
$535$	−4.67758	+	3.39846i	−0.202229	+	0.146928i
$536$	5.09304	+	3.70031i	0.219986	+	0.159829i
$537$	−0.696976	−	2.14507i	−0.0300767	−	0.0925666i
$538$	−9.61454			−0.414512
$539$	23.1474	+	0.913530i	0.997028	+	0.0393485i
$540$	−12.9982			−0.559353
$541$	−2.75148	−	8.46820i	−0.118296	−	0.364076i	0.874325	−	0.485342i	$-0.161305\pi$
$541$	−2.75148	−	8.46820i	−0.118296	−	0.364076i	−0.992620	+	0.121265i	$0.961305\pi$
$542$	−23.1101	−	16.7904i	−0.992663	−	0.721212i
$543$	−6.30070	+	4.57773i	−0.270389	+	0.196449i
$544$	−1.01247	+	3.11607i	−0.0434094	+	0.133600i
$545$	1.30375	−	4.01253i	0.0558465	−	0.171878i
$546$	−0.967348	+	0.702820i	−0.0413987	+	0.0300779i
$547$	−13.8026	−	10.0282i	−0.590158	−	0.428775i	0.252214	−	0.967671i	$-0.418841\pi$
$547$	−13.8026	−	10.0282i	−0.590158	−	0.428775i	−0.842372	+	0.538897i	$0.818841\pi$
$548$	8.01935	+	24.6810i	0.342570	+	1.05432i
$549$	−18.4191			−0.786109
$550$	−7.48310	−	0.295327i	−0.319080	−	0.0125928i
$551$	−12.8799			−0.548701
$552$	−4.72508	−	14.5423i	−0.201113	−	0.618962i
$553$	−0.629215	−	0.457151i	−0.0267569	−	0.0194400i
$554$	58.4145	−	42.4406i	2.48179	−	1.80313i
$555$	−2.11126	+	6.49778i	−0.0896179	+	0.275816i
$556$	−15.3272	+	47.1721i	−0.650016	+	2.00054i
$557$	23.5380	−	17.1013i	0.997335	−	0.724607i	0.0358202	−	0.999358i	$-0.488596\pi$
$557$	23.5380	−	17.1013i	0.997335	−	0.724607i	0.961515	+	0.274752i	$0.0885956\pi$
$558$	30.8468	+	22.4115i	1.30585	+	0.948754i
$559$	5.81161	+	17.8863i	0.245805	+	0.756509i
$560$	−0.0738993			−0.00312282
$561$	1.05184	+	0.829501i	0.0444086	+	0.0350216i
$562$	−65.2174			−2.75103
$563$	−3.41751	−	10.5180i	−0.144031	−	0.443282i	0.852854	−	0.522149i	$-0.174870\pi$
$563$	−3.41751	−	10.5180i	−0.144031	−	0.443282i	−0.996885	+	0.0788673i	$0.974870\pi$
$564$	−0.889558	−	0.646302i	−0.0374572	−	0.0272142i
$565$	−12.2313	+	8.88652i	−0.514573	+	0.373859i
$566$	−3.38573	+	10.4202i	−0.142313	+	0.437993i
$567$	0.150365	−	0.462775i	0.00631472	−	0.0194347i
$568$	−24.6296	+	17.8945i	−1.03344	+	0.750835i
$569$	2.52382	+	1.83367i	0.105804	+	0.0768713i	0.639429	−	0.768850i	$-0.279171\pi$
$569$	2.52382	+	1.83367i	0.105804	+	0.0768713i	−0.533625	+	0.845721i	$0.679171\pi$
$570$	1.71399	+	5.27512i	0.0717912	+	0.220951i
$571$	9.68683			0.405381			0.202691	−	0.979243i	$-0.435031\pi$
$571$	9.68683			0.405381			0.202691	+	0.979243i	$0.435031\pi$
$572$	−19.5514	+	52.9677i	−0.817484	+	2.21469i
$573$	−10.5462			−0.440572
$574$	−0.653212	−	2.01038i	−0.0272645	−	0.0839116i
$575$	6.41434	+	4.66029i	0.267496	+	0.194348i
$576$	−25.2892	+	18.3737i	−1.05372	+	0.765571i
$577$	0.934922	−	2.87739i	0.0389213	−	0.119788i	−0.929708	−	0.368297i	$-0.879941\pi$
$577$	0.934922	−	2.87739i	0.0389213	−	0.119788i	0.968629	+	0.248510i	$0.0799408\pi$
$578$	−11.6736	+	35.9277i	−0.485558	+	1.49439i
$579$	−8.61255	+	6.25738i	−0.357925	+	0.260048i
$580$	10.2192	+	7.42466i	0.424328	+	0.308292i
$581$	0.0239970	+	0.0738553i	0.000995565	+	0.00306403i
$582$	−3.22126			−0.133525
$583$	0.0978542	−	0.0653593i	0.00405271	−	0.00270690i
$584$	21.1369			0.874649
$585$	−4.06701	−	12.5170i	−0.168150	−	0.517513i
$586$	−7.32091	−	5.31895i	−0.302424	−	0.219724i
$587$	35.6212	−	25.8803i	1.47024	−	1.06820i	0.489702	−	0.871890i	$-0.337106\pi$
$587$	35.6212	−	25.8803i	1.47024	−	1.06820i	0.980543	−	0.196306i	$-0.0628945\pi$
$588$	−5.19966	+	16.0029i	−0.214431	+	0.659949i
$589$	6.88214	−	21.1810i	0.283574	−	0.872750i
$590$	10.0012	−	7.26632i	0.411744	−	0.299150i
$591$	−1.63517	−	1.18802i	−0.0672621	−	0.0488688i
$592$	1.61873	+	4.98192i	0.0665292	+	0.204756i
$593$	−6.60880			−0.271391			−0.135696	−	0.990751i	$-0.543327\pi$
$593$	−6.60880			−0.271391			−0.135696	+	0.990751i	$0.543327\pi$
$594$	8.52214	+	30.2375i	0.349668	+	1.24066i
$595$	0.0644010			0.00264018
$596$	−13.2973	−	40.9247i	−0.544677	−	1.67634i
$597$	−11.1274	−	8.08453i	−0.455414	−	0.330878i
$598$	79.5736	−	57.8136i	3.25400	−	2.36417i
$599$	−8.71690	+	26.8279i	−0.356163	+	1.09616i	0.599169	+	0.800622i	$0.295498\pi$
$599$	−8.71690	+	26.8279i	−0.356163	+	1.09616i	−0.955332	+	0.295534i	$0.904502\pi$
$600$	0.595957	−	1.83417i	0.0243299	−	0.0748796i
$601$	−3.37956	+	2.45540i	−0.137855	+	0.100158i	−0.654576	−	0.755996i	$-0.727153\pi$
$601$	−3.37956	+	2.45540i	−0.137855	+	0.100158i	0.516720	+	0.856154i	$0.327153\pi$
$602$	−0.775207	−	0.563221i	−0.0315951	−	0.0229552i
$603$	1.87871	+	5.78207i	0.0765070	+	0.235464i
$604$	25.5618			1.04010
$605$	2.56415	+	10.6970i	0.104247	+	0.434894i
$606$	2.15528			0.0875524
$607$	4.22672	+	13.0085i	0.171557	+	0.527999i	0.999460	−	0.0328735i	$-0.0104659\pi$
$607$	4.22672	+	13.0085i	0.171557	+	0.527999i	−0.827902	+	0.560872i	$0.810466\pi$
$608$	16.1211	+	11.7126i	0.653796	+	0.475010i
$609$	0.317882	−	0.230955i	0.0128812	−	0.00935876i
$610$	5.36507	−	16.5120i	0.217225	−	0.668550i
$611$	0.774896	−	2.38488i	0.0313489	−	0.0964821i
$612$	3.11954	−	2.26648i	0.126100	−	0.0916170i
$613$	26.2215	+	19.0511i	1.05908	+	0.769465i	0.973918	−	0.226902i	$-0.0728597\pi$
$613$	26.2215	+	19.0511i	1.05908	+	0.769465i	0.0851604	+	0.996367i	$0.472860\pi$
$614$	2.57135	+	7.91380i	0.103771	+	0.319375i
$615$	−5.87115			−0.236748
$616$	−0.276668	−	0.981650i	−0.0111473	−	0.0395518i
$617$	−37.0480			−1.49150			−0.745749	−	0.666227i	$-0.767908\pi$
$617$	−37.0480			−1.49150			−0.745749	+	0.666227i	$0.767908\pi$
$618$	−1.27914	−	3.93679i	−0.0514546	−	0.158361i
$619$	−16.0560	−	11.6654i	−0.645346	−	0.468871i	0.216337	−	0.976319i	$-0.430589\pi$
$619$	−16.0560	−	11.6654i	−0.645346	−	0.468871i	−0.861683	+	0.507448i	$0.830589\pi$
$620$	−17.6703	+	12.8383i	−0.709658	+	0.515597i
$621$	10.2778	−	31.6319i	0.412435	−	1.26934i
$622$	−6.95494	+	21.4051i	−0.278868	+	0.858266i
$623$	1.02152	−	0.742174i	0.0409261	−	0.0297346i
$624$	2.06000	+	1.49667i	0.0824659	+	0.0599150i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	42.5886			1.70218
$627$	6.77480	−	4.52506i	0.270560	−	0.180714i
$628$	31.8689			1.27171
$629$	−1.41067	−	4.34160i	−0.0562471	−	0.173111i
$630$	0.542497	+	0.394147i	0.0216136	+	0.0157032i
$631$	37.9144	−	27.5464i	1.50935	−	1.09661i	0.542884	−	0.839807i	$-0.317332\pi$
$631$	37.9144	−	27.5464i	1.50935	−	1.09661i	0.966465	−	0.256799i	$-0.0826678\pi$
$632$	4.80893	−	14.8003i	0.191289	−	0.588726i
$633$	4.41300	−	13.5818i	0.175401	−	0.539829i
$634$	−7.11424	+	5.16879i	−0.282542	+	0.205279i
$635$	8.66448	+	6.29511i	0.343839	+	0.249814i
$636$	0.0264130	+	0.0812909i	0.00104734	+	0.00322339i
$637$	−38.3740			−1.52043
$638$	10.5718	−	28.6406i	0.418542	−	1.13389i
$639$	−29.4007			−1.16308
$640$	−5.20712	−	16.0259i	−0.205830	−	0.633478i
$641$	12.0438	+	8.75035i	0.475703	+	0.345618i	0.799660	−	0.600454i	$-0.205013\pi$
$641$	12.0438	+	8.75035i	0.475703	+	0.345618i	−0.323957	+	0.946072i	$0.605013\pi$
$642$	−8.21175	+	5.96619i	−0.324092	+	0.235467i
$643$	−10.2176	+	31.4464i	−0.402942	+	1.24013i	0.519660	+	0.854373i	$0.326059\pi$
$643$	−10.2176	+	31.4464i	−0.402942	+	1.24013i	−0.922602	+	0.385754i	$0.873941\pi$
$644$	−0.941134	+	2.89651i	−0.0370859	+	0.114139i
$645$	−2.15313	+	1.56434i	−0.0847792	+	0.0615957i
$646$	−2.99825	−	2.17836i	−0.117965	−	0.0857063i
$647$	−13.5568	−	41.7234i	−0.532971	−	1.64032i	−0.747993	−	0.663707i	$-0.768982\pi$
$647$	−13.5568	−	41.7234i	−0.532971	−	1.64032i	0.215022	−	0.976609i	$-0.431018\pi$
$648$	9.73616			0.382473
$649$	−14.2578	−	11.2440i	−0.559669	−	0.441367i
$650$	12.4056			0.486587
$651$	0.209952	+	0.646166i	0.00822867	+	0.0253253i
$652$	5.23538	+	3.80372i	0.205033	+	0.148965i
$653$	−27.6105	+	20.0602i	−1.08048	+	0.785016i	−0.977767	−	0.209694i	$-0.932753\pi$
$653$	−27.6105	+	20.0602i	−1.08048	+	0.785016i	−0.102715	+	0.994711i	$0.532753\pi$
$654$	2.28880	−	7.04421i	0.0894993	−	0.275451i
$655$	2.02720	−	6.23907i	0.0792091	−	0.243781i
$656$	−3.64177	+	2.64590i	−0.142187	+	0.103305i
$657$	16.5142	+	11.9982i	0.644278	+	0.468096i
$658$	0.0394811	+	0.121510i	0.00153914	+	0.00473697i
$659$	10.4408			0.406716			0.203358	−	0.979104i	$-0.434815\pi$
$659$	10.4408			0.406716			0.203358	+	0.979104i	$0.434815\pi$
$660$	−7.98377	−	0.315086i	−0.310768	−	0.0122647i
$661$	−45.6827			−1.77685			−0.888426	−	0.459020i	$-0.848201\pi$
$661$	−45.6827			−1.77685			−0.888426	+	0.459020i	$0.848201\pi$
$662$	5.56551	+	17.1289i	0.216310	+	0.665732i
$663$	−1.79522	−	1.30431i	−0.0697207	−	0.0506551i
$664$	−1.25706	+	0.913311i	−0.0487835	+	0.0354433i
$665$	0.121035	−	0.372507i	0.00469353	−	0.0144452i
$666$	14.6883	−	45.2060i	0.569161	−	1.75170i
$667$	−26.1488	+	18.9982i	−1.01249	+	0.735614i
$668$	−41.6829	−	30.2844i	−1.61276	−	1.17174i
$669$	0.463463	+	1.42639i	0.0179185	+	0.0551475i
$670$	−5.73061			−0.221393
$671$	−25.4817	−	1.00565i	−0.983709	−	0.0388229i
$672$	−0.607902			−0.0234503
$673$	−8.99702	−	27.6900i	−0.346810	−	1.06737i	−0.960608	−	0.277908i	$-0.910359\pi$
$673$	−8.99702	−	27.6900i	−0.346810	−	1.06737i	0.613798	−	0.789463i	$-0.289641\pi$
$674$	25.0856	+	18.2257i	0.966260	+	0.702029i
$675$	3.39377	−	2.46572i	0.130626	−	0.0949055i
$676$	16.4544	−	50.6416i	0.632863	−	1.94775i
$677$	−9.96120	+	30.6574i	−0.382840	+	1.17826i	0.555195	+	0.831720i	$0.312643\pi$
$677$	−9.96120	+	30.6574i	−0.382840	+	1.17826i	−0.938035	+	0.346540i	$0.887357\pi$
$678$	−21.4726	+	15.6008i	−0.824652	+	0.599145i
$679$	0.184029	+	0.133705i	0.00706237	+	0.00513111i
$680$	0.398198	+	1.22553i	0.0152702	+	0.0469969i
$681$	22.8477			0.875524
$682$	41.4509	+	32.6890i	1.58724	+	1.25173i
$683$	−11.0364			−0.422295			−0.211148	−	0.977454i	$-0.567720\pi$
$683$	−11.0364			−0.422295			−0.211148	+	0.977454i	$0.567720\pi$
$684$	−7.24688	−	22.3036i	−0.277092	−	0.852800i
$685$	−6.77574	−	4.92286i	−0.258888	−	0.188093i
$686$	3.16700	−	2.30096i	0.120917	−	0.0878512i
$687$	−4.71667	+	14.5164i	−0.179952	+	0.553836i
$688$	−0.630559	+	1.94066i	−0.0240398	+	0.0739870i
$689$	−0.157702	+	0.114577i	−0.00600797	+	0.00436505i
$690$	11.2607	+	8.18140i	0.428689	+	0.311461i
$691$	11.1744	+	34.3912i	0.425093	+	1.30830i	0.902905	+	0.429840i	$0.141430\pi$
$691$	11.1744	+	34.3912i	0.425093	+	1.30830i	−0.477812	+	0.878462i	$0.658570\pi$
$692$	−59.8776			−2.27620
$693$	0.341069	−	0.924008i	0.0129561	−	0.0351002i
$694$	0.367933			0.0139665
$695$	−4.94656	−	15.2240i	−0.187634	−	0.577478i
$696$	6.36049	+	4.62117i	0.241094	+	0.175165i
$697$	3.17369	−	2.30582i	0.120212	−	0.0873393i
$698$	−1.91287	+	5.88721i	−0.0724032	+	0.222834i
$699$	1.21767	−	3.74762i	0.0460567	−	0.141748i
$700$	−0.310765	+	0.225784i	−0.0117458	+	0.00853384i
$701$	−11.4452	−	8.31544i	−0.432280	−	0.314070i	0.350280	−	0.936645i	$-0.386086\pi$
$701$	−11.4452	−	8.31544i	−0.432280	−	0.314070i	−0.782560	+	0.622575i	$0.786086\pi$
$702$	−16.0814	−	49.4935i	−0.606954	−	1.86801i
$703$	−27.7638			−1.04713
$704$	−35.9892	+	24.0381i	−1.35639	+	0.905969i
$705$	0.354862			0.0133649
$706$	−3.58358	−	11.0291i	−0.134870	−	0.415087i
$707$	−0.123130	−	0.0894592i	−0.00463078	−	0.00336446i
$708$	10.6704	−	7.75248i	0.401017	−	0.291356i
$709$	5.30360	−	16.3228i	0.199181	−	0.613016i	−0.800721	−	0.599037i	$-0.795550\pi$
$709$	5.30360	−	16.3228i	0.199181	−	0.613016i	0.999902	−	0.0139788i	$-0.00444974\pi$
$710$	8.56376	−	26.3565i	0.321392	−	0.989143i
$711$	12.1585	−	8.83370i	0.455981	−	0.331290i
$712$	20.4395	+	14.8501i	0.766001	+	0.556532i
$713$	−17.2705	−	53.1533i	−0.646787	−	1.99061i
$714$	0.113060			0.00423115
$715$	−4.94304	−	17.5385i	−0.184859	−	0.655902i
$716$	−8.98880			−0.335927
$717$	5.40650	+	16.6395i	0.201909	+	0.621413i
$718$	27.7229	+	20.1419i	1.03461	+	0.751688i
$719$	14.8493	−	10.7886i	0.553785	−	0.402348i	−0.275394	−	0.961331i	$-0.588808\pi$
$719$	14.8493	−	10.7886i	0.553785	−	0.402348i	0.829179	+	0.558983i	$0.188808\pi$
$720$	0.441271	−	1.35809i	0.0164452	−	0.0506131i
$721$	−0.0903276	+	0.278000i	−0.00336397	+	0.0103533i
$722$	16.4735	−	11.9687i	0.613079	−	0.445428i
$723$	17.4184	+	12.6552i	0.647799	+	0.470653i
$724$	9.59136	+	29.5192i	0.356460	+	1.09707i
$725$	−4.07662			−0.151402
$726$	4.50150	+	18.7791i	0.167066	+	0.696959i
$727$	47.2976			1.75417			0.877085	−	0.480336i	$-0.159485\pi$
$727$	47.2976			1.75417			0.877085	+	0.480336i	$0.159485\pi$
$728$	0.522077	+	1.60679i	0.0193494	+	0.0595515i
$729$	−0.308979	−	0.224486i	−0.0114437	−	0.00831430i
$730$	−15.5661	+	11.3094i	−0.576127	+	0.418581i
$731$	0.549513	−	1.69123i	0.0203245	−	0.0625523i
$732$	5.72402	−	17.6167i	0.211566	−	0.651133i
$733$	−23.2568	+	16.8970i	−0.859009	+	0.624107i	−0.927615	−	0.373537i	$-0.878145\pi$
$733$	−23.2568	+	16.8970i	−0.859009	+	0.624107i	0.0686062	+	0.997644i	$0.478145\pi$
$734$	−36.8353	−	26.7624i	−1.35962	−	0.987820i
$735$	−1.67810	−	5.16466i	−0.0618976	−	0.190501i
$736$	50.0056			1.84323
$737$	2.28338	+	8.10170i	0.0841095	+	0.298430i
$738$	40.8464			1.50358
$739$	10.6365	+	32.7358i	0.391271	+	1.20421i	0.931828	+	0.362900i	$0.118213\pi$
$739$	10.6365	+	32.7358i	0.391271	+	1.20421i	−0.540557	+	0.841307i	$0.681787\pi$
$740$	22.0284	+	16.0046i	0.809780	+	0.588340i
$741$	−10.9183	+	7.93260i	−0.401093	+	0.291411i
$742$	0.00306908	−	0.00944566i	0.000112670	−	0.000346761i
$743$	3.76476	−	11.5867i	0.138116	−	0.425076i	−0.857946	−	0.513740i	$-0.828260\pi$
$743$	3.76476	−	11.5867i	0.138116	−	0.425076i	0.996062	+	0.0886638i	$0.0282597\pi$
$744$	−10.9982	+	7.99063i	−0.403212	+	0.292951i
$745$	11.2352	+	8.16282i	0.411624	+	0.299063i
$746$	7.85254	+	24.1676i	0.287502	+	0.884840i
$747$	−1.50058			−0.0549032
$748$	4.43943	−	2.96521i	0.162322	−	0.108419i
$749$	0.716771			0.0261902
$750$	0.542497	+	1.66963i	0.0198092	+	0.0609664i
$751$	41.7345	+	30.3219i	1.52292	+	1.10646i	0.960019	+	0.279935i	$0.0903130\pi$
$751$	41.7345	+	30.3219i	1.52292	+	1.10646i	0.562896	+	0.826527i	$0.309687\pi$
$752$	0.220114	−	0.159922i	0.00802675	−	0.00583177i
$753$	−1.04975	+	3.23081i	−0.0382552	+	0.117737i
$754$	−15.6278	+	48.0976i	−0.569133	+	1.75161i
$755$	−6.67408	+	4.84901i	−0.242895	+	0.176473i
$756$	1.30364	+	0.947149i	0.0474129	+	0.0344475i
$757$	3.42444	+	10.5393i	0.124463	+	0.383059i	0.993803	−	0.111156i	$-0.0354555\pi$
$757$	3.42444	+	10.5393i	0.124463	+	0.383059i	−0.869340	+	0.494215i	$0.835455\pi$
$758$	−47.3099			−1.71837
$759$	7.07965	−	19.1799i	0.256975	−	0.696185i
$760$	7.83705			0.284280
$761$	0.400855	+	1.23370i	0.0145310	+	0.0447217i	0.958059	−	0.286571i	$-0.0925153\pi$
$761$	0.400855	+	1.23370i	0.0145310	+	0.0447217i	−0.943528	+	0.331292i	$0.892515\pi$
$762$	15.2110	+	11.0514i	0.551036	+	0.400351i
$763$	−0.423142	+	0.307431i	−0.0153188	+	0.0111297i
$764$	−12.9880	+	39.9730i	−0.469890	+	1.44617i
$765$	−0.384554	+	1.18354i	−0.0139036	+	0.0427908i
$766$	−30.7459	+	22.3382i	−1.11089	+	0.807111i
$767$	24.3346	+	17.6801i	0.878671	+	0.638392i
$768$	−2.87119	−	8.83660i	−0.103605	−	0.318863i
$769$	−24.2693			−0.875173			−0.437587	−	0.899176i	$-0.644167\pi$
$769$	−24.2693			−0.875173			−0.437587	+	0.899176i	$0.644167\pi$
$770$	0.728989	+	0.574896i	0.0262710	+	0.0207178i
$771$	14.0436			0.505769
$772$	13.1106	+	40.3503i	0.471861	+	1.45224i
$773$	21.5005	+	15.6211i	0.773321	+	0.561850i	0.902967	−	0.429710i	$-0.141384\pi$
$773$	21.5005	+	15.6211i	0.773321	+	0.561850i	−0.129646	+	0.991560i	$0.541384\pi$
$774$	14.9796	−	10.8833i	0.538431	−	0.391193i
$775$	2.17827	−	6.70403i	0.0782458	−	0.240816i
$776$	−1.40648	+	4.32871i	−0.0504898	+	0.155392i
$777$	0.685225	−	0.497845i	0.0245823	−	0.0178601i
$778$	−28.7951	−	20.9209i	−1.03235	−	0.750050i
$779$	−7.37268	−	22.6908i	−0.264154	−	0.812982i
$780$	13.2356			0.473910
$781$	−40.6740	−	1.60523i	−1.45543	−	0.0574398i
$782$	−9.30022			−0.332575
$783$	5.28454	+	16.2641i	0.188854	+	0.581233i
$784$	−3.36841	−	2.44729i	−0.120300	−	0.0874033i
$785$	−8.32082	+	6.04543i	−0.296983	+	0.215771i
$786$	3.55886	−	10.9530i	0.126940	−	0.390682i
$787$	16.7746	−	51.6268i	0.597949	−	1.84030i	0.0584840	−	0.998288i	$-0.481373\pi$
$787$	16.7746	−	51.6268i	0.597949	−	1.84030i	0.539465	−	0.842008i	$-0.318627\pi$
$788$	−6.51674	+	4.73469i	−0.232149	+	0.168666i
$789$	−8.44997	−	6.13926i	−0.300827	−	0.218563i
$790$	4.37754	+	13.4727i	0.155746	+	0.479336i
$791$	1.87426			0.0666410
$792$	19.6924	+	0.777177i	0.699740	+	0.0276158i
$793$	42.2438			1.50012
$794$	4.78290	+	14.7203i	0.169739	+	0.522402i
$795$	−0.0223170	−	0.0162142i	−0.000791501	−	0.000575059i
$796$	−44.3466	+	32.2197i	−1.57182	+	1.14200i
$797$	2.34830	−	7.22732i	0.0831810	−	0.256005i	−0.900813	−	0.434208i	$-0.857028\pi$
$797$	2.34830	−	7.22732i	0.0831810	−	0.256005i	0.983994	+	0.178203i	$0.0570283\pi$
$798$	0.212484	−	0.653957i	0.00752184	−	0.0231498i
$799$	−0.191823	+	0.139368i	−0.00678621	+	0.00493047i
$800$	5.10249	+	3.70718i	0.180400	+	0.131069i
$801$	7.53967	+	23.2047i	0.266401	+	0.819898i
$802$	−0.318593			−0.0112499
$803$	22.1912	+	17.5004i	0.783110	+	0.617577i
$804$	−6.11403			−0.215625
$805$	−0.303734	−	0.934797i	−0.0107052	−	0.0329473i
$806$	−70.7463	−	51.4002i	−2.49193	−	1.81050i
$807$	2.67827	−	1.94588i	0.0942796	−	0.0684981i
$808$	0.941051	−	2.89626i	0.0331061	−	0.101890i
$809$	16.2438	−	49.9932i	0.571101	−	1.75767i	−0.0779854	−	0.996955i	$-0.524849\pi$
$809$	16.2438	−	49.9932i	0.571101	−	1.75767i	0.649087	−	0.760714i	$-0.275151\pi$
$810$	−7.17014	+	5.20941i	−0.251933	+	0.183040i
$811$	−21.4543	−	15.5874i	−0.753361	−	0.547349i	0.143506	−	0.989649i	$-0.454162\pi$
$811$	−21.4543	−	15.5874i	−0.753361	−	0.547349i	−0.896867	+	0.442301i	$0.854162\pi$
$812$	−0.483902	−	1.48930i	−0.0169816	−	0.0522640i
$813$	9.83585			0.344958
$814$	22.7885	−	61.7377i	0.798738	−	2.16390i
$815$	−2.08849			−0.0731566
$816$	−0.0744001	−	0.228980i	−0.00260452	−	0.00801590i
$817$	−8.74962	−	6.35697i	−0.306110	−	0.222402i
$818$	−52.5168	+	38.1557i	−1.83621	+	1.33408i
$819$	−0.504188	+	1.55173i	−0.0176177	+	0.0542219i
$820$	−7.23056	+	22.2534i	−0.252502	+	0.777121i
$821$	24.5948	−	17.8692i	0.858364	−	0.623638i	−0.0690756	−	0.997611i	$-0.522005\pi$
$821$	24.5948	−	17.8692i	0.858364	−	0.623638i	0.927439	+	0.373974i	$0.122005\pi$
$822$	−11.8952	−	8.64236i	−0.414892	−	0.301437i
$823$	7.60476	+	23.4050i	0.265085	+	0.815849i	0.991674	+	0.128776i	$0.0411047\pi$
$823$	7.60476	+	23.4050i	0.265085	+	0.815849i	−0.726588	+	0.687073i	$0.758895\pi$
$824$	−5.84874			−0.203751
$825$	2.14430	−	1.43223i	0.0746549	−	0.0498639i
$826$	−1.53254			−0.0533240
$827$	4.94739	+	15.2265i	0.172038	+	0.529477i	0.999486	−	0.0320649i	$-0.0102083\pi$
$827$	4.94739	+	15.2265i	0.172038	+	0.529477i	−0.827448	+	0.561542i	$0.810208\pi$
$828$	−47.6112	−	34.5916i	−1.65460	−	1.20214i
$829$	13.4671	−	9.78440i	0.467731	−	0.339826i	−0.328826	−	0.944391i	$-0.606653\pi$
$829$	13.4671	−	9.78440i	0.467731	−	0.339826i	0.796556	+	0.604564i	$0.206653\pi$
$830$	0.437083	−	1.34520i	0.0151714	−	0.0466927i
$831$	−7.68270	+	23.6449i	−0.266510	+	0.820233i
$832$	58.0002	−	42.1396i	2.01080	−	1.46093i
$833$	2.93547	+	2.13274i	0.101708	+	0.0738951i
$834$	−8.68397	−	26.7265i	−0.300701	−	0.925463i
$835$	16.6281			0.575439
$836$	−8.80785	−	31.2513i	−0.304626	−	1.08085i
$837$	−29.5702			−1.02210
$838$	−7.73372	−	23.8020i	−0.267157	−	0.822225i
$839$	−1.65638	−	1.20343i	−0.0571846	−	0.0415471i	0.558826	−	0.829285i	$-0.311252\pi$
$839$	−1.65638	−	1.20343i	−0.0571846	−	0.0415471i	−0.616010	+	0.787738i	$0.711252\pi$
$840$	−0.193423	+	0.140530i	−0.00667372	+	0.00484874i
$841$	−3.82600	+	11.7752i	−0.131931	+	0.406042i
$842$	−2.37471	+	7.30860i	−0.0818379	+	0.251871i
$843$	18.1673	−	13.1993i	0.625714	−	0.454608i
$844$	−46.0443	−	33.4531i	−1.58491	−	1.15150i
$845$	5.31038	+	16.3437i	0.182682	+	0.562239i
$846$	−2.46882			−0.0848799
$847$	0.522296	−	1.25968i	0.0179463	−	0.0432833i
$848$	−0.0211500			−0.000726293
$849$	−1.16579	−	3.58793i	−0.0400098	−	0.123138i
$850$	−0.948979	−	0.689474i	−0.0325497	−	0.0236487i
$851$	−56.3663	+	40.9525i	−1.93221	+	1.40383i
$852$	9.13673	−	28.1200i	0.313019	−	0.963374i
$853$	−10.8792	+	33.4826i	−0.372495	+	1.14642i	0.572658	+	0.819795i	$0.305912\pi$
$853$	−10.8792	+	33.4826i	−0.372495	+	1.14642i	−0.945153	+	0.326628i	$0.894088\pi$
$854$	−1.74127	+	1.26511i	−0.0595852	+	0.0432912i
$855$	6.12306	+	4.44866i	0.209404	+	0.152141i
$856$	4.43187	+	13.6399i	0.151478	+	0.466202i
$857$	21.9827			0.750915			0.375458	−	0.926840i	$-0.377486\pi$
$857$	21.9827			0.750915			0.375458	+	0.926840i	$0.377486\pi$
$858$	−8.67779	−	30.7898i	−0.296255	−	1.05115i
$859$	−13.4218			−0.457945			−0.228972	−	0.973433i	$-0.573537\pi$
$859$	−13.4218			−0.457945			−0.228972	+	0.973433i	$0.573537\pi$
$860$	3.27763	+	10.0875i	0.111766	+	0.343981i
$861$	0.588841	+	0.427818i	0.0200676	+	0.0145800i
$862$	24.9767	−	18.1467i	0.850711	−	0.618078i
$863$	−4.96951	+	15.2946i	−0.169164	+	0.520633i	−0.999319	−	0.0368995i	$-0.988252\pi$
$863$	−4.96951	+	15.2946i	−0.169164	+	0.520633i	0.830155	+	0.557533i	$0.188252\pi$
$864$	8.17583	−	25.1626i	0.278147	−	0.856050i
$865$	15.6338	−	11.3586i	0.531565	−	0.386204i
$866$	28.2135	+	20.4983i	0.958735	+	0.696562i
$867$	−4.01951	−	12.3708i	−0.136510	−	0.420134i
$868$	2.70772			0.0919061
$869$	17.3029	−	11.5570i	0.586959	−	0.392045i
$870$	−7.15673			−0.242636
$871$	−4.30878	−	13.2611i	−0.145997	−	0.449334i
$872$	−8.46663	−	6.15136i	−0.286716	−	0.208311i
$873$	−3.55605	+	2.58362i	−0.120354	+	0.0874423i
$874$	−17.4788	+	53.7942i	−0.591229	+	1.81962i
$875$	0.0383089	−	0.117903i	0.00129508	−	0.00398583i
$876$	−16.6076	+	12.0661i	−0.561118	+	0.407676i
$877$	−27.7819	−	20.1847i	−0.938127	−	0.681589i	0.00984245	−	0.999952i	$-0.496867\pi$
$877$	−27.7819	−	20.1847i	−0.938127	−	0.681589i	−0.947969	+	0.318363i	$0.896867\pi$
$878$	6.88718	+	21.1965i	0.232431	+	0.715349i
$879$	3.11584			0.105095
$880$	0.684620	−	1.85474i	0.0230785	−	0.0625233i
$881$	6.08507			0.205011			0.102506	−	0.994732i	$-0.467314\pi$
$881$	6.08507			0.205011			0.102506	+	0.994732i	$0.467314\pi$
$882$	11.6748	+	35.9313i	0.393110	+	1.20987i
$883$	−3.76784	−	2.73750i	−0.126798	−	0.0921241i	0.522579	−	0.852591i	$-0.324970\pi$
$883$	−3.76784	−	2.73750i	−0.126798	−	0.0921241i	−0.649377	+	0.760467i	$0.724970\pi$
$884$	−7.15459	+	5.19812i	−0.240635	+	0.174832i
$885$	−1.31537	+	4.04828i	−0.0442155	+	0.136081i
$886$	21.8399	−	67.2162i	0.733724	−	2.25817i
$887$	17.9163	−	13.0169i	0.601569	−	0.437066i	−0.244866	−	0.969557i	$-0.578744\pi$
$887$	17.9163	−	13.0169i	0.601569	−	0.437066i	0.846435	+	0.532491i	$0.178744\pi$
$888$	13.7106	+	9.96137i	0.460099	+	0.334282i
$889$	−0.410283	−	1.26272i	−0.0137605	−	0.0423504i
$890$	−22.9982			−0.770901
$891$	10.2218	+	8.06113i	0.342444	+	0.270058i
$892$	5.97722			0.200132
$893$	0.445616	+	1.37147i	0.0149120	+	0.0458944i
$894$	19.7240	+	14.3303i	0.659668	+	0.479277i
$895$	2.34694	−	1.70515i	0.0784494	−	0.0569969i
$896$	−0.645527	+	1.98673i	−0.0215656	+	0.0663720i
$897$	−10.4655	+	32.2096i	−0.349434	+	1.07545i
$898$	23.2495	−	16.8917i	0.775846	−	0.563685i
$899$	23.2481	+	16.8907i	0.775367	+	0.563337i
$900$	−2.29372	−	7.05933i	−0.0764572	−	0.235311i
$901$	0.0184315			0.000614044
$902$	56.5084	+	2.23015i	1.88152	+	0.0742559i
$903$	0.329935			0.0109796
$904$	11.5888	+	35.6665i	0.385436	+	1.18625i
$905$	−8.10396	−	5.88787i	−0.269385	−	0.195720i
$906$	−11.7167	+	8.51270i	−0.389262	+	0.282816i
$907$	11.3906	−	35.0566i	0.378218	−	1.16404i	−0.563063	−	0.826414i	$-0.690377\pi$
$907$	11.3906	−	35.0566i	0.378218	−	1.16404i	0.941281	−	0.337623i	$-0.109623\pi$
$908$	28.1378	−	86.5993i	0.933787	−	2.87390i
$909$	2.37929	−	1.72865i	0.0789159	−	0.0573358i
$910$	−1.24420	−	0.903967i	−0.0412449	−	0.0299662i
$911$	5.14788	+	15.8435i	0.170557	+	0.524920i	0.999403	−	0.0345572i	$-0.0110021\pi$
$911$	5.14788	+	15.8435i	0.170557	+	0.524920i	−0.828846	+	0.559477i	$0.811002\pi$
$912$	−1.46429			−0.0484874
$913$	−2.07595	−	0.0819291i	−0.0687039	−	0.00271146i
$914$	−9.73549			−0.322021
$915$	1.84733	+	5.68548i	0.0610707	+	0.187956i
$916$	49.2127	+	35.7551i	1.62603	+	1.18138i
$917$	−0.657942	+	0.478023i	−0.0217272	+	0.0157857i
$918$	−1.52057	+	4.67983i	−0.0501862	+	0.154457i
$919$	−15.5426	+	47.8353i	−0.512704	+	1.57794i	0.274718	+	0.961525i	$0.411415\pi$
$919$	−15.5426	+	47.8353i	−0.512704	+	1.57794i	−0.787422	+	0.616415i	$0.788585\pi$
$920$	15.9108	−	11.5599i	0.524565	−	0.381119i
$921$	−2.31795	−	1.68409i	−0.0763792	−	0.0554927i
$922$	−12.3723	−	38.0780i	−0.407460	−	1.25403i
$923$	67.4299			2.21948
$924$	0.777764	+	0.613361i	0.0255865	+	0.0201781i
$925$	−8.78754			−0.288933
$926$	2.39396	+	7.36784i	0.0786703	+	0.242122i
$927$	−4.56960	−	3.32001i	−0.150085	−	0.109043i
$928$	−20.8009	+	15.1127i	−0.682823	+	0.496100i
$929$	11.9754	−	36.8566i	0.392901	−	1.20923i	−0.537682	−	0.843147i	$-0.680700\pi$
$929$	11.9754	−	36.8566i	0.392901	−	1.20923i	0.930584	−	0.366079i	$-0.119300\pi$
$930$	3.82408	−	11.7693i	0.125396	−	0.385931i
$931$	17.8531	−	12.9710i	0.585110	−	0.425108i
$932$	−12.7049	−	9.23068i	−0.416164	−	0.302361i
$933$	−2.39476	−	7.37031i	−0.0784009	−	0.241293i
$934$	−35.3109			−1.15541
$935$	−0.596625	+	1.61635i	−0.0195117	+	0.0528603i
$936$	−32.6463			−1.06708
$937$	4.84312	+	14.9056i	0.158218	+	0.486944i	0.998473	−	0.0552472i	$-0.0175947\pi$
$937$	4.84312	+	14.9056i	0.158218	+	0.486944i	−0.840255	+	0.542192i	$0.817595\pi$
$938$	0.574745	+	0.417577i	0.0187661	+	0.0136344i
$939$	−11.8637	+	8.61946i	−0.387156	+	0.281285i
$940$	0.437026	−	1.34503i	0.0142542	−	0.0438700i
$941$	−8.75099	+	26.9328i	−0.285274	+	0.877984i	0.701042	+	0.713120i	$0.252719\pi$
$941$	−8.75099	+	26.9328i	−0.285274	+	0.877984i	−0.986316	+	0.164864i	$0.947281\pi$
$942$	−14.6077	+	10.6131i	−0.475944	+	0.345793i
$943$	−48.4377	−	35.1920i	−1.57735	−	1.14601i
$944$	1.00851	+	3.10386i	0.0328241	+	0.101022i
$945$	−0.520046			−0.0169171
$946$	21.3175	−	14.2385i	0.693093	−	0.462934i
$947$	10.1955			0.331309			0.165654	−	0.986184i	$-0.447026\pi$
$947$	10.1955			0.331309			0.165654	+	0.986184i	$0.447026\pi$
$948$	4.67042	+	14.3741i	0.151688	+	0.466849i
$949$	−37.8748	−	27.5177i	−1.22947	−	0.893261i
$950$	−5.77155	+	4.19328i	−0.187254	+	0.136048i
$951$	0.935667	−	2.87969i	0.0303411	−	0.0933803i
$952$	0.0493647	−	0.151929i	0.00159992	−	0.00492404i
$953$	−3.75591	+	2.72883i	−0.121666	+	0.0883953i	−0.646954	−	0.762529i	$-0.723957\pi$
$953$	−3.75591	+	2.72883i	−0.121666	+	0.0883953i	0.525288	+	0.850924i	$0.323957\pi$
$954$	0.155262	+	0.112805i	0.00502681	+	0.00365219i
$955$	−4.19165	−	12.9006i	−0.135639	−	0.417453i
$956$	69.7268			2.25513
$957$	2.85162	+	10.1179i	0.0921799	+	0.327065i
$958$	−86.9496			−2.80921
$959$	0.320847	+	0.987466i	0.0103607	+	0.0318869i
$960$	8.20781	+	5.96333i	0.264906	+	0.192466i
$961$	−15.1196	+	10.9850i	−0.487729	+	0.354356i
$962$	−33.6873	+	103.679i	−1.08612	+	3.34274i
$963$	−4.28002	+	13.1725i	−0.137922	+	0.424479i
$964$	69.4185	−	50.4355i	2.23582	−	1.62442i
$965$	−11.0775	−	8.04824i	−0.356596	−	0.259082i
$966$	−0.533222	−	1.64109i	−0.0171561	−	0.0528012i
$967$	−38.0543			−1.22374			−0.611872	−	0.790957i	$-0.709583\pi$
$967$	−38.0543			−1.22374			−0.611872	+	0.790957i	$0.709583\pi$
$968$	27.2008	+	2.15035i	0.874266	+	0.0691149i
$969$	1.27608			0.0409937
$970$	−1.28031	−	3.94040i	−0.0411084	−	0.126519i
$971$	−25.6327	−	18.6233i	−0.822594	−	0.597650i	0.0948604	−	0.995491i	$-0.469760\pi$
$971$	−25.6327	−	18.6233i	−0.822594	−	0.597650i	−0.917454	+	0.397841i	$0.869760\pi$
$972$	−39.1971	+	28.4784i	−1.25725	+	0.913444i
$973$	−0.613226	+	1.88731i	−0.0196591	+	0.0605045i
$974$	−6.29417	+	19.3715i	−0.201678	+	0.620701i
$975$	−3.45576	+	2.51075i	−0.110673	+	0.0804084i
$976$	3.70809	+	2.69409i	0.118693	+	0.0862356i
$977$	12.5207	+	38.5349i	0.400574	+	1.23284i	0.924535	+	0.381098i	$0.124454\pi$
$977$	12.5207	+	38.5349i	0.400574	+	1.23284i	−0.523961	+	0.851742i	$0.675546\pi$
$978$	−3.66646			−0.117241
$979$	9.16370	+	32.5139i	0.292873	+	1.03915i
$980$	−21.6422			−0.691335
$981$	−3.12315	−	9.61208i	−0.0997146	−	0.306890i
$982$	8.64182	+	6.27865i	0.275772	+	0.200360i
$983$	15.2402	−	11.0726i	0.486086	−	0.353163i	−0.317591	−	0.948228i	$-0.602874\pi$
$983$	15.2402	−	11.0726i	0.486086	−	0.353163i	0.803677	+	0.595065i	$0.202874\pi$
$984$	−4.50036	+	13.8507i	−0.143466	+	0.441543i
$985$	0.803336	−	2.47241i	0.0255964	−	0.0787777i
$986$	3.86862	−	2.81072i	0.123202	−	0.0895116i
$987$	−0.0355904	−	0.0258580i	−0.00113286	−	0.000823068i
$988$	16.6206	+	51.1528i	0.528770	+	1.62739i
$989$	−27.1403			−0.863011
$990$	−14.9182	+	9.96423i	−0.474131	+	0.316684i
$991$	4.63565			0.147256			0.0736281	−	0.997286i	$-0.476542\pi$
$991$	4.63565			0.147256			0.0736281	+	0.997286i	$0.476542\pi$
$992$	−13.7384	−	42.2825i	−0.436195	−	1.34247i
$993$	−5.01705	−	3.64510i	−0.159211	−	0.115674i
$994$	−2.77943	+	2.01938i	−0.0881583	+	0.0640508i
$995$	5.46672	−	16.8248i	0.173307	−	0.533383i
$996$	0.466327	−	1.43521i	0.0147761	−	0.0454763i
$997$	−16.3373	+	11.8697i	−0.517406	+	0.375918i	−0.815626	−	0.578580i	$-0.803607\pi$
$997$	−16.3373	+	11.8697i	−0.517406	+	0.375918i	0.298220	+	0.954497i	$0.403607\pi$
$998$	−2.09186	−	1.51982i	−0.0662165	−	0.0481091i
$999$	11.3913	+	35.0589i	0.360406	+	1.10921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.g.a.16.2	✓	8
3.2	odd	2		495.2.n.f.181.1		8
4.3	odd	2		880.2.bo.e.401.2		8
5.2	odd	4		275.2.z.b.49.1		16
5.3	odd	4		275.2.z.b.49.4		16
5.4	even	2		275.2.h.b.126.1		8
11.2	odd	10		605.2.g.n.251.1		8
11.3	even	5		605.2.a.l.1.3		4
11.4	even	5		605.2.g.j.366.1		8
11.5	even	5		605.2.g.j.81.1		8
11.6	odd	10		605.2.g.g.81.2		8
11.7	odd	10		605.2.g.g.366.2		8
11.8	odd	10		605.2.a.i.1.2		4
11.9	even	5	inner	55.2.g.a.31.2	yes	8
11.10	odd	2		605.2.g.n.511.1		8
33.8	even	10		5445.2.a.bu.1.3		4
33.14	odd	10		5445.2.a.bg.1.2		4
33.20	odd	10		495.2.n.f.361.1		8
44.3	odd	10		9680.2.a.cs.1.2		4
44.19	even	10		9680.2.a.cv.1.2		4
44.31	odd	10		880.2.bo.e.801.2		8
55.9	even	10		275.2.h.b.251.1		8
55.14	even	10		3025.2.a.v.1.2		4
55.19	odd	10		3025.2.a.be.1.3		4
55.42	odd	20		275.2.z.b.174.4		16
55.53	odd	20		275.2.z.b.174.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.2	✓	8	1.1	even	1	trivial
55.2.g.a.31.2	yes	8	11.9	even	5	inner
275.2.h.b.126.1		8	5.4	even	2
275.2.h.b.251.1		8	55.9	even	10
275.2.z.b.49.1		16	5.2	odd	4
275.2.z.b.49.4		16	5.3	odd	4
275.2.z.b.174.1		16	55.53	odd	20
275.2.z.b.174.4		16	55.42	odd	20
495.2.n.f.181.1		8	3.2	odd	2
495.2.n.f.361.1		8	33.20	odd	10
605.2.a.i.1.2		4	11.8	odd	10
605.2.a.l.1.3		4	11.3	even	5
605.2.g.g.81.2		8	11.6	odd	10
605.2.g.g.366.2		8	11.7	odd	10
605.2.g.j.81.1		8	11.5	even	5
605.2.g.j.366.1		8	11.4	even	5
605.2.g.n.251.1		8	11.2	odd	10
605.2.g.n.511.1		8	11.10	odd	2
880.2.bo.e.401.2		8	4.3	odd	2
880.2.bo.e.801.2		8	44.31	odd	10
3025.2.a.v.1.2		4	55.14	even	10
3025.2.a.be.1.3		4	55.19	odd	10
5445.2.a.bg.1.2		4	33.14	odd	10
5445.2.a.bu.1.3		4	33.8	even	10
9680.2.a.cs.1.2		4	44.3	odd	10
9680.2.a.cv.1.2		4	44.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.697759 + 2.14748i) q^{2} +(-0.628998 - 0.456994i) q^{3} +(-2.50678 + 1.82128i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.542497 - 1.66963i) q^{6} +(-0.100294 + 0.0728678i) q^{7} +(-2.00678 - 1.45801i) q^{8} +(-0.740256 - 2.27827i) q^{9} +O(q^{10})\)	\(q+(0.697759 + 2.14748i) q^{2} +(-0.628998 - 0.456994i) q^{3} +(-2.50678 + 1.82128i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.542497 - 1.66963i) q^{6} +(-0.100294 + 0.0728678i) q^{7} +(-2.00678 - 1.45801i) q^{8} +(-0.740256 - 2.27827i) q^{9} +2.25800 q^{10} +(-0.899706 - 3.19226i) q^{11} +2.40907 q^{12} +(1.69776 + 5.22517i) q^{13} +(-0.226463 - 0.164535i) q^{14} +(-0.628998 + 0.456994i) q^{15} +(-0.184207 + 0.566931i) q^{16} +(0.160531 - 0.494063i) q^{17} +(4.37603 - 3.17937i) q^{18} +(-2.55605 - 1.85708i) q^{19} +(0.957503 + 2.94689i) q^{20} +0.0963848 q^{21} +(6.22754 - 4.15953i) q^{22} -7.92856 q^{23} +(0.595957 + 1.83417i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-10.0363 + 7.29181i) q^{26} +(-1.29630 + 3.98962i) q^{27} +(0.118702 - 0.365326i) q^{28} +(3.29805 - 2.39618i) q^{29} +(-1.42027 - 1.03189i) q^{30} +(2.17827 + 6.70403i) q^{31} -6.30703 q^{32} +(-0.892930 + 2.41909i) q^{33} +1.17300 q^{34} +(0.0383089 + 0.117903i) q^{35} +(6.00503 + 4.36291i) q^{36} +(7.10927 - 5.16519i) q^{37} +(2.20454 - 6.78486i) q^{38} +(1.31998 - 4.06248i) q^{39} +(-2.00678 + 1.45801i) q^{40} +(6.10927 + 4.43864i) q^{41} +(0.0672534 + 0.206985i) q^{42} +3.42310 q^{43} +(8.06936 + 6.36367i) q^{44} -2.39552 q^{45} +(-5.53222 - 17.0264i) q^{46} +(-0.369254 - 0.268279i) q^{47} +(0.374949 - 0.272417i) q^{48} +(-2.15837 + 6.64278i) q^{49} +(0.697759 - 2.14748i) q^{50} +(-0.326757 + 0.237403i) q^{51} +(-13.7724 - 10.0062i) q^{52} +(0.0109640 + 0.0337437i) q^{53} -9.47214 q^{54} +(-3.31404 - 0.130791i) q^{55} +0.307509 q^{56} +(0.759076 + 2.33620i) q^{57} +(7.44699 + 5.41056i) q^{58} +(4.42925 - 3.21804i) q^{59} +(0.744444 - 2.29116i) q^{60} +(2.37603 - 7.31267i) q^{61} +(-12.8769 + 9.35559i) q^{62} +(0.240256 + 0.174556i) q^{63} +(-4.03237 - 12.4104i) q^{64} +5.49406 q^{65} +(-5.81799 - 0.229612i) q^{66} -2.53792 q^{67} +(0.497412 + 1.53088i) q^{68} +(4.98705 + 3.62330i) q^{69} +(-0.226463 + 0.164535i) q^{70} +(3.79264 - 11.6725i) q^{71} +(-1.83621 + 5.65128i) q^{72} +(-6.89377 + 5.00862i) q^{73} +(16.0527 + 11.6630i) q^{74} +(0.240256 + 0.739431i) q^{75} +9.78970 q^{76} +(0.322848 + 0.254605i) q^{77} +9.64514 q^{78} +(1.93868 + 5.96665i) q^{79} +(0.482260 + 0.350382i) q^{80} +(-3.17544 + 2.30709i) q^{81} +(-5.26911 + 16.2166i) q^{82} +(0.193571 - 0.595751i) q^{83} +(-0.241615 + 0.175544i) q^{84} +(-0.420275 - 0.305348i) q^{85} +(2.38850 + 7.35105i) q^{86} -3.16951 q^{87} +(-2.84883 + 7.71793i) q^{88} -10.1852 q^{89} +(-1.67149 - 5.14433i) q^{90} +(-0.551021 - 0.400340i) q^{91} +(19.8751 - 14.4401i) q^{92} +(1.69357 - 5.21228i) q^{93} +(0.318473 - 0.980160i) q^{94} +(-2.55605 + 1.85708i) q^{95} +(3.96711 + 2.88227i) q^{96} +(-0.567013 - 1.74509i) q^{97} -15.7713 q^{98} +(-6.60683 + 4.41287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9} + 6 q^{10} - 5 q^{11} - 28 q^{12} + 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} + q^{17} + 14 q^{18} - q^{19} - q^{20} - 12 q^{21} + 33 q^{22} - 18 q^{23} + 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} + 4 q^{28} + 19 q^{29} - 12 q^{30} + 6 q^{31} + 12 q^{32} - 19 q^{33} - 20 q^{34} - 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} + 9 q^{39} - 2 q^{40} - 4 q^{41} + 29 q^{42} + 42 q^{43} - 28 q^{44} - 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} - 4 q^{50} + 13 q^{51} - 26 q^{52} + 3 q^{53} - 40 q^{54} + 5 q^{55} + 30 q^{56} - 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} - 2 q^{61} - 38 q^{62} + q^{63} + 6 q^{64} + 14 q^{65} + 13 q^{66} - 2 q^{67} + 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} - 34 q^{72} - 23 q^{73} + 48 q^{74} + q^{75} + 16 q^{76} - 28 q^{77} + 12 q^{78} + 17 q^{79} + 15 q^{80} + 2 q^{82} - 25 q^{83} - 4 q^{84} - 4 q^{85} - 31 q^{86} + 30 q^{87} + 22 q^{88} - 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} + 33 q^{94} - q^{95} + 23 q^{96} + 12 q^{97} - 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9 + 6 * q^10 - 5 * q^11 - 28 * q^12 + 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 + q^17 + 14 * q^18 - q^19 - q^20 - 12 * q^21 + 33 * q^22 - 18 * q^23 + 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 + 4 * q^28 + 19 * q^29 - 12 * q^30 + 6 * q^31 + 12 * q^32 - 19 * q^33 - 20 * q^34 - 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 + 9 * q^39 - 2 * q^40 - 4 * q^41 + 29 * q^42 + 42 * q^43 - 28 * q^44 - 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 - 4 * q^50 + 13 * q^51 - 26 * q^52 + 3 * q^53 - 40 * q^54 + 5 * q^55 + 30 * q^56 - 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 - 2 * q^61 - 38 * q^62 + q^63 + 6 * q^64 + 14 * q^65 + 13 * q^66 - 2 * q^67 + 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 - 34 * q^72 - 23 * q^73 + 48 * q^74 + q^75 + 16 * q^76 - 28 * q^77 + 12 * q^78 + 17 * q^79 + 15 * q^80 + 2 * q^82 - 25 * q^83 - 4 * q^84 - 4 * q^85 - 31 * q^86 + 30 * q^87 + 22 * q^88 - 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 + 33 * q^94 - q^95 + 23 * q^96 + 12 * q^97 - 84 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more