LMFDB - Embedded newform 322.2.i.c.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 41 x^{18} - 119 x^{17} + 245 x^{16} - 404 x^{15} + 623 x^{14} - 898 x^{13} + \cdots + 1 $ x^20 - 9x^19 + 41x^18 - 119x^17 + 245x^16 - 404x^15 + 623x^14 - 898x^13 + 1048x^12 - 693x^11 + 859x^10 - 935x^9 + 620x^8 + 679x^7 + 1220x^6 + 2241x^5 + 1750x^4 + 1079x^3 + 534x^2 + 38*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.1
Root			$0.140215 + 0.975217i$ of defining polynomial
Character	$\chi$	$=$	322.29
Dual form			322.2.i.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(0.0141569 + 0.00415683i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-3.50493 + 2.25248i) q^{5} +(0.00966216 - 0.0111507i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.52358 - 1.62180i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(0.0141569 + 0.00415683i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-3.50493 + 2.25248i) q^{5} +(0.00966216 - 0.0111507i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.52358 - 1.62180i) q^{9} +(0.592928 + 4.12391i) q^{10} +(-0.164338 - 0.359850i) q^{11} +(-0.00612925 - 0.0134212i) q^{12} +(0.524026 + 3.64468i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-0.0589820 + 0.0173187i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.01611 + 5.78890i) q^{17} +(-2.52358 + 1.62180i) q^{18} +(-4.06258 - 4.68846i) q^{19} +(3.99755 + 1.17379i) q^{20} +(-0.00612925 + 0.0134212i) q^{21} -0.395599 q^{22} +(1.99735 + 4.36011i) q^{23} -0.0147545 q^{24} +(5.13377 - 11.2414i) q^{25} +(3.53301 + 1.03738i) q^{26} +(-0.0579709 - 0.0669020i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-0.216787 + 0.250186i) q^{29} +(-0.00874838 + 0.0608463i) q^{30} +(6.68165 - 1.96191i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.000830675 - 0.00577747i) q^{33} +(3.18200 + 6.96761i) q^{34} +(-1.73075 - 3.78981i) q^{35} +(0.426914 + 2.96925i) q^{36} +(-3.66590 - 2.35593i) q^{37} +(-5.95243 + 1.74779i) q^{38} +(-0.00773176 + 0.0537756i) q^{39} +(2.72836 - 3.14869i) q^{40} +(3.16030 - 2.03100i) q^{41} +(0.00966216 + 0.0111507i) q^{42} +(-3.79125 - 1.11321i) q^{43} +(-0.164338 + 0.359850i) q^{44} +12.4980 q^{45} +(4.79583 - 0.00559465i) q^{46} -4.21317 q^{47} +(-0.00612925 + 0.0134212i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-8.09289 - 9.33969i) q^{50} +(-0.0950759 + 0.0611016i) q^{51} +(2.41130 - 2.78279i) q^{52} +(0.444306 - 3.09022i) q^{53} +(-0.0849381 + 0.0249401i) q^{54} +(1.38655 + 0.891079i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-0.0380242 - 0.0832614i) q^{57} +(0.137520 + 0.301127i) q^{58} +(0.721739 + 5.01980i) q^{59} +(0.0517136 + 0.0332343i) q^{60} +(-5.98335 + 1.75687i) q^{61} +(0.991042 - 6.89285i) q^{62} +(1.96444 - 2.26708i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-10.0462 - 11.5940i) q^{65} +(-0.00560044 - 0.00164444i) q^{66} +(-5.49536 + 12.0332i) q^{67} +7.65981 q^{68} +(0.0101519 + 0.0700282i) q^{69} -4.16631 q^{70} +(-1.10479 + 2.41915i) q^{71} +(2.87827 + 0.845136i) q^{72} +(3.11036 + 3.58955i) q^{73} +(-3.66590 + 2.35593i) q^{74} +(0.119407 - 0.137803i) q^{75} +(-0.882882 + 6.14058i) q^{76} +(0.379575 - 0.111453i) q^{77} +(0.0457041 + 0.0293722i) q^{78} +(0.237949 + 1.65497i) q^{79} +(-1.73075 - 3.78981i) q^{80} +(3.73792 + 8.18491i) q^{81} +(-0.534628 - 3.71842i) q^{82} +(3.36177 + 2.16048i) q^{83} +(0.0141569 - 0.00415683i) q^{84} +(4.54172 - 31.5884i) q^{85} +(-2.58756 + 2.98620i) q^{86} +(-0.00410901 + 0.00264070i) q^{87} +(0.259062 + 0.298974i) q^{88} +(-7.84641 - 2.30392i) q^{89} +(5.19187 - 11.3686i) q^{90} -3.68216 q^{91} +(1.98717 - 4.36476i) q^{92} +0.102747 q^{93} +(-1.75022 + 3.83244i) q^{94} +(24.7997 + 7.28185i) q^{95} +(0.00966216 + 0.0111507i) q^{96} +(10.0418 - 6.45349i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-0.168887 + 1.17463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	0.0141569	+	0.00415683i	0.00817347	+	0.00239995i	0.285817	−	0.958284i	$-0.407735\pi$
$3$	0.0141569	+	0.00415683i	0.00817347	+	0.00239995i	−0.277643	+	0.960684i	$0.589553\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−3.50493	+	2.25248i	−1.56745	+	1.00734i	−0.587233	+	0.809418i	$0.699783\pi$
$5$	−3.50493	+	2.25248i	−1.56745	+	1.00734i	−0.980218	+	0.197922i	$0.936581\pi$
$6$	0.00966216	−	0.0111507i	0.00394456	−	0.00455227i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−2.52358	−	1.62180i	−0.841192	−	0.540602i
$10$	0.592928	+	4.12391i	0.187500	+	1.30409i
$11$	−0.164338	−	0.359850i	−0.0495497	−	0.108499i	0.883238	−	0.468925i	$-0.155359\pi$
$11$	−0.164338	−	0.359850i	−0.0495497	−	0.108499i	−0.932788	+	0.360426i	$0.882631\pi$
$12$	−0.00612925	−	0.0134212i	−0.00176936	−	0.00387437i
$13$	0.524026	+	3.64468i	0.145339	+	1.01085i	0.923722	+	0.383064i	$0.125131\pi$
$13$	0.524026	+	3.64468i	0.145339	+	1.01085i	−0.778383	+	0.627789i	$0.783960\pi$
$14$	0.841254	+	0.540641i	0.224834	+	0.144492i
$15$	−0.0589820	+	0.0173187i	−0.0152291	+	0.00447166i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−5.01611	+	5.78890i	−1.21659	+	1.40401i	−0.328395	+	0.944541i	$0.606508\pi$
$17$	−5.01611	+	5.78890i	−1.21659	+	1.40401i	−0.888191	+	0.459474i	$0.848038\pi$
$18$	−2.52358	+	1.62180i	−0.594813	+	0.382263i
$19$	−4.06258	−	4.68846i	−0.932019	−	1.07561i	−0.996975	−	0.0777189i	$-0.975236\pi$
$19$	−4.06258	−	4.68846i	−0.932019	−	1.07561i	0.0649565	−	0.997888i	$-0.479309\pi$
$20$	3.99755	+	1.17379i	0.893879	+	0.262467i
$21$	−0.00612925	+	0.0134212i	−0.00133751	+	0.00292874i
$22$	−0.395599			−0.0843420
$23$	1.99735	+	4.36011i	0.416476	+	0.909147i
$23$	1.99735	+	4.36011i	0.416476	+	0.909147i
$24$	−0.0147545			−0.00301176
$25$	5.13377	−	11.2414i	1.02675	−	2.24828i
$26$	3.53301	+	1.03738i	0.692880	+	0.203448i
$27$	−0.0579709	−	0.0669020i	−0.0111565	−	0.0128753i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	−0.216787	+	0.250186i	−0.0402564	+	0.0464583i	−0.775521	−	0.631322i	$-0.782513\pi$
$29$	−0.216787	+	0.250186i	−0.0402564	+	0.0464583i	0.735264	+	0.677780i	$0.237058\pi$
$30$	−0.00874838	+	0.0608463i	−0.00159723	+	0.0111090i
$31$	6.68165	−	1.96191i	1.20006	−	0.352369i	0.380184	−	0.924911i	$-0.375861\pi$
$31$	6.68165	−	1.96191i	1.20006	−	0.352369i	0.819876	+	0.572542i	$0.194042\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.000830675	−	0.00577747i	−0.000144602	−	0.00100573i
$34$	3.18200	+	6.96761i	0.545709	+	1.19494i
$35$	−1.73075	−	3.78981i	−0.292550	−	0.640595i
$36$	0.426914	+	2.96925i	0.0711523	+	0.494875i
$37$	−3.66590	−	2.35593i	−0.602670	−	0.387312i	0.203432	−	0.979089i	$-0.434790\pi$
$37$	−3.66590	−	2.35593i	−0.602670	−	0.387312i	−0.806102	+	0.591777i	$0.798427\pi$
$38$	−5.95243	+	1.74779i	−0.965612	+	0.283529i
$39$	−0.00773176	+	0.0537756i	−0.00123807	+	0.00861098i
$40$	2.72836	−	3.14869i	0.431391	−	0.497852i
$41$	3.16030	−	2.03100i	0.493556	−	0.317189i	−0.270078	−	0.962838i	$-0.587049\pi$
$41$	3.16030	−	2.03100i	0.493556	−	0.317189i	0.763634	+	0.645649i	$0.223413\pi$
$42$	0.00966216	+	0.0111507i	0.00149090	+	0.00172060i
$43$	−3.79125	−	1.11321i	−0.578161	−	0.169763i	−0.0204388	−	0.999791i	$-0.506506\pi$
$43$	−3.79125	−	1.11321i	−0.578161	−	0.169763i	−0.557722	+	0.830028i	$0.688325\pi$
$44$	−0.164338	+	0.359850i	−0.0247749	+	0.0542494i
$45$	12.4980			1.86310
$46$	4.79583	−	0.00559465i	0.707106	−	0.000824887i
$47$	−4.21317			−0.614555			−0.307277	−	0.951620i	$-0.599418\pi$
$47$	−4.21317			−0.614555			−0.307277	+	0.951620i	$0.599418\pi$
$48$	−0.00612925	+	0.0134212i	−0.000884682	+	0.00193718i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−8.09289	−	9.33969i	−1.14451	−	1.32083i
$51$	−0.0950759	+	0.0611016i	−0.0133133	+	0.00855593i
$52$	2.41130	−	2.78279i	0.334388	−	0.385904i
$53$	0.444306	−	3.09022i	0.0610302	−	0.424474i	−0.936285	−	0.351242i	$-0.885759\pi$
$53$	0.444306	−	3.09022i	0.0610302	−	0.424474i	0.997315	−	0.0732323i	$-0.0233315\pi$
$54$	−0.0849381	+	0.0249401i	−0.0115586	+	0.00339392i
$55$	1.38655	+	0.891079i	0.186962	+	0.120153i
$56$	−0.142315	−	0.989821i	−0.0190176	−	0.132270i
$57$	−0.0380242	−	0.0832614i	−0.00503643	−	0.0110282i
$58$	0.137520	+	0.301127i	0.0180573	+	0.0395400i
$59$	0.721739	+	5.01980i	0.0939624	+	0.653523i	0.981312	+	0.192425i	$0.0616352\pi$
$59$	0.721739	+	5.01980i	0.0939624	+	0.653523i	−0.887349	+	0.461098i	$0.847456\pi$
$60$	0.0517136	+	0.0332343i	0.00667619	+	0.00429053i
$61$	−5.98335	+	1.75687i	−0.766089	+	0.224944i	−0.641353	−	0.767246i	$-0.721627\pi$
$61$	−5.98335	+	1.75687i	−0.766089	+	0.224944i	−0.124736	+	0.992190i	$0.539808\pi$
$62$	0.991042	−	6.89285i	0.125862	−	0.875393i
$63$	1.96444	−	2.26708i	0.247496	−	0.285626i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−10.0462	−	11.5940i	−1.24608	−	1.43806i
$66$	−0.00560044	−	0.00164444i	−0.000689367	−	0.000202416i
$67$	−5.49536	+	12.0332i	−0.671365	+	1.47008i	0.200175	+	0.979760i	$0.435849\pi$
$67$	−5.49536	+	12.0332i	−0.671365	+	1.47008i	−0.871540	+	0.490324i	$0.836878\pi$
$68$	7.65981			0.928889
$69$	0.0101519	+	0.0700282i	0.00122215	+	0.00843041i
$70$	−4.16631			−0.497970
$71$	−1.10479	+	2.41915i	−0.131114	+	0.287101i	−0.963791	−	0.266659i	$-0.914080\pi$
$71$	−1.10479	+	2.41915i	−0.131114	+	0.287101i	0.832676	+	0.553760i	$0.186807\pi$
$72$	2.87827	+	0.845136i	0.339207	+	0.0996003i
$73$	3.11036	+	3.58955i	0.364041	+	0.420125i	0.907989	−	0.418993i	$-0.137617\pi$
$73$	3.11036	+	3.58955i	0.364041	+	0.420125i	−0.543949	+	0.839118i	$0.683071\pi$
$74$	−3.66590	+	2.35593i	−0.426152	+	0.273871i
$75$	0.119407	−	0.137803i	0.0137879	−	0.0159121i
$76$	−0.882882	+	6.14058i	−0.101274	+	0.704373i
$77$	0.379575	−	0.111453i	0.0432565	−	0.0127013i
$78$	0.0457041	+	0.0293722i	0.00517497	+	0.00332575i
$79$	0.237949	+	1.65497i	0.0267713	+	0.186199i	0.998819	−	0.0485846i	$-0.0154711\pi$
$79$	0.237949	+	1.65497i	0.0267713	+	0.186199i	−0.972048	+	0.234783i	$0.924562\pi$
$80$	−1.73075	−	3.78981i	−0.193504	−	0.423714i
$81$	3.73792	+	8.18491i	0.415325	+	0.909434i
$82$	−0.534628	−	3.71842i	−0.0590398	−	0.410631i
$83$	3.36177	+	2.16048i	0.369003	+	0.237144i	0.711979	−	0.702200i	$-0.247799\pi$
$83$	3.36177	+	2.16048i	0.369003	+	0.237144i	−0.342977	+	0.939344i	$0.611435\pi$
$84$	0.0141569	−	0.00415683i	0.00154464	−	0.000453548i
$85$	4.54172	−	31.5884i	0.492619	−	3.42624i
$86$	−2.58756	+	2.98620i	−0.279024	+	0.322010i
$87$	−0.00410901	+	0.00264070i	−0.000440532	+	0.000283113i
$88$	0.259062	+	0.298974i	0.0276161	+	0.0318707i
$89$	−7.84641	−	2.30392i	−0.831718	−	0.244215i	−0.161963	−	0.986797i	$-0.551783\pi$
$89$	−7.84641	−	2.30392i	−0.831718	−	0.244215i	−0.669755	+	0.742582i	$0.733601\pi$
$90$	5.19187	−	11.3686i	0.547271	−	1.19836i
$91$	−3.68216			−0.385995
$92$	1.98717	−	4.36476i	0.207177	−	0.455058i
$93$	0.102747			0.0106543
$94$	−1.75022	+	3.83244i	−0.180521	+	0.395286i
$95$	24.7997	+	7.28185i	2.54440	+	0.747102i
$96$	0.00966216	+	0.0111507i	0.000986140	+	0.00113807i
$97$	10.0418	−	6.45349i	1.01959	−	0.655253i	0.0797348	−	0.996816i	$-0.474593\pi$
$97$	10.0418	−	6.45349i	1.01959	−	0.655253i	0.939859	+	0.341563i	$0.110956\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	−0.168887	+	1.17463i	−0.0169737	+	0.118055i
$100$	−11.8576	+	3.48170i	−1.18576	+	0.348170i
$101$	−9.04550	−	5.81319i	−0.900061	−	0.578434i	0.00674768	−	0.999977i	$-0.497852\pi$
$101$	−9.04550	−	5.81319i	−0.900061	−	0.578434i	−0.906808	+	0.421543i	$0.861488\pi$
$102$	0.0160840	+	0.111867i	0.00159255	+	0.0110764i
$103$	6.51486	+	14.2655i	0.641928	+	1.40563i	0.898445	+	0.439086i	$0.144698\pi$
$103$	6.51486	+	14.2655i	0.641928	+	1.40563i	−0.256517	+	0.966540i	$0.582575\pi$
$104$	−1.52962	−	3.34941i	−0.149992	−	0.328437i
$105$	−0.00874838	−	0.0608463i	−0.000853755	−	0.00593799i
$106$	−2.62639	−	1.68788i	−0.255098	−	0.163941i
$107$	3.94370	−	1.15797i	0.381251	−	0.111946i	−0.0854907	−	0.996339i	$-0.527246\pi$
$107$	3.94370	−	1.15797i	0.381251	−	0.111946i	0.466742	+	0.884393i	$0.345428\pi$
$108$	−0.0125983	+	0.0876229i	−0.00121227	+	0.00843152i
$109$	5.23211	−	6.03817i	0.501145	−	0.578352i	−0.447664	−	0.894202i	$-0.647744\pi$
$109$	5.23211	−	6.03817i	0.501145	−	0.578352i	0.948809	+	0.315850i	$0.102290\pi$
$110$	1.38655	−	0.891079i	0.132202	−	0.0849610i
$111$	−0.0421044	−	0.0485911i	−0.00399638	−	0.00461206i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	−6.63784	+	14.5348i	−0.624436	+	1.36732i	0.287813	+	0.957687i	$0.407072\pi$
$113$	−6.63784	+	14.5348i	−0.624436	+	1.36732i	−0.912249	+	0.409637i	$0.865655\pi$
$114$	−0.0915331			−0.00857286
$115$	−16.8216	−	10.7829i	−1.56863	−	1.00551i
$116$	0.331043			0.0307366
$117$	4.58854	−	10.0475i	0.424211	−	0.928892i
$118$	4.86599	+	1.42878i	0.447951	+	0.131530i
$119$	−5.01611	−	5.78890i	−0.459826	−	0.530668i
$120$	0.0517136	−	0.0332343i	0.00472078	−	0.00303386i
$121$	7.10098	−	8.19497i	0.645544	−	0.744997i
$122$	−0.887468	+	6.17247i	−0.0803476	+	0.558830i
$123$	0.0531825	−	0.0156158i	0.00479531	−	0.00140803i
$124$	−5.85826	−	3.76488i	−0.526087	−	0.338096i
$125$	4.36287	+	30.3445i	0.390227	+	2.71409i
$126$	−1.24615	−	2.72870i	−0.111016	−	0.243092i
$127$	−5.15936	−	11.2974i	−0.457819	−	1.00248i	−0.987979	−	0.154586i	$-0.950596\pi$
$127$	−5.15936	−	11.2974i	−0.457819	−	1.00248i	0.530161	−	0.847897i	$-0.322132\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	−0.0490449	−	0.0315192i	−0.00431816	−	0.00277511i
$130$	−14.7196	+	4.32207i	−1.29100	+	0.379071i
$131$	−3.20717	+	22.3064i	−0.280212	+	1.94891i	0.0336156	+	0.999435i	$0.489298\pi$
$131$	−3.20717	+	22.3064i	−0.280212	+	1.94891i	−0.313827	+	0.949480i	$0.601611\pi$
$132$	−0.00382234	+	0.00441122i	−0.000332692	+	0.000383947i
$133$	5.21891	−	3.35399i	0.452536	−	0.290828i
$134$	8.66289	+	9.99751i	0.748360	+	0.863653i
$135$	0.353879	+	0.103908i	0.0304571	+	0.00894300i
$136$	3.18200	−	6.96761i	0.272854	−	0.597468i
$137$	−1.51102			−0.129095			−0.0645475	−	0.997915i	$-0.520560\pi$
$137$	−1.51102			−0.129095			−0.0645475	+	0.997915i	$0.520560\pi$
$138$	0.0679172	+	0.0198563i	0.00578149	+	0.00169028i
$139$	−21.5487			−1.82774			−0.913870	−	0.406007i	$-0.866921\pi$
$139$	−21.5487			−1.82774			−0.913870	+	0.406007i	$0.866921\pi$
$140$	−1.73075	+	3.78981i	−0.146275	+	0.320298i
$141$	−0.0596454	−	0.0175135i	−0.00502305	−	0.00147490i
$142$	1.74159	+	2.00990i	0.146151	+	0.168667i
$143$	1.22542	−	0.787530i	0.102475	−	0.0658565i
$144$	1.96444	−	2.26708i	0.163703	−	0.188924i
$145$	0.196285	−	1.36519i	0.0163006	−	0.113373i
$146$	4.55726	−	1.33813i	0.377162	−	0.110745i
$147$	−0.0124123	−	0.00797690i	−0.00102375	−	0.000657924i
$148$	0.620160	+	4.31331i	0.0509768	+	0.354552i
$149$	4.25362	+	9.31413i	0.348470	+	0.763043i	0.999990	+	0.00441200i	$0.00140439\pi$
$149$	4.25362	+	9.31413i	0.348470	+	0.763043i	−0.651520	+	0.758631i	$0.725868\pi$
$150$	−0.0757464	−	0.165862i	−0.00618467	−	0.0135425i
$151$	2.37286	+	16.5036i	0.193101	+	1.34304i	0.823740	+	0.566968i	$0.191884\pi$
$151$	2.37286	+	16.5036i	0.193101	+	1.34304i	−0.630639	+	0.776076i	$0.717207\pi$
$152$	5.21891	+	3.35399i	0.423309	+	0.272044i
$153$	22.0470	−	6.47359i	1.78240	−	0.523359i
$154$	0.0562996	−	0.391572i	0.00453675	−	0.0315538i
$155$	−18.9995	+	21.9266i	−1.52608	+	1.76119i
$156$	0.0457041	−	0.0293722i	0.00365926	−	0.00235166i
$157$	2.89631	+	3.34252i	0.231151	+	0.266762i	0.859462	−	0.511200i	$-0.170799\pi$
$157$	2.89631	+	3.34252i	0.231151	+	0.266762i	−0.628311	+	0.777962i	$0.716253\pi$
$158$	1.60426	+	0.471053i	0.127628	+	0.0374750i
$159$	0.0191355	−	0.0419009i	0.00151754	−	0.00332296i
$160$	−4.16631			−0.329376
$161$	−4.59999	+	1.35651i	−0.362530	+	0.106908i
$162$	8.99804			0.706953
$163$	−3.15259	+	6.90321i	−0.246930	+	0.540701i	−0.991993	−	0.126293i	$-0.959692\pi$
$163$	−3.15259	+	6.90321i	−0.246930	+	0.540701i	0.745063	+	0.666994i	$0.232419\pi$
$164$	−3.60449	−	1.05837i	−0.281463	−	0.0826451i
$165$	0.0159251	+	0.0183785i	0.00123977	+	0.00143077i
$166$	3.36177	−	2.16048i	0.260924	−	0.167686i
$167$	2.63880	−	3.04534i	0.204196	−	0.235655i	−0.644410	−	0.764680i	$-0.722897\pi$
$167$	2.63880	−	3.04534i	0.204196	−	0.235655i	0.848606	+	0.529025i	$0.177442\pi$
$168$	0.00209979	−	0.0146044i	0.000162002	−	0.00112675i
$169$	−0.535695	+	0.157294i	−0.0412073	+	0.0120995i
$170$	−26.8471	−	17.2536i	−2.05908	−	1.32329i
$171$	2.64845	+	18.4204i	0.202532	+	1.40864i
$172$	1.64143	+	3.59424i	0.125158	+	0.274058i
$173$	−5.77236	−	12.6397i	−0.438865	−	0.960980i	−0.991805	−	0.127759i	$-0.959222\pi$
$173$	−5.77236	−	12.6397i	−0.438865	−	0.960980i	0.552941	−	0.833221i	$-0.313506\pi$
$174$	0.000695121		0.00483467i	5.26970e−5		0.000366515i
$175$	10.3964	+	6.68134i	0.785891	+	0.505062i
$176$	0.379575	−	0.111453i	0.0286115	−	0.00840110i
$177$	−0.0106489	+	0.0740648i	−0.000800421	+	0.00556705i
$178$	−5.35523	+	6.18027i	−0.401392	+	0.463231i
$179$	−6.89903	+	4.43374i	−0.515658	+	0.331393i	−0.772452	−	0.635073i	$-0.780970\pi$
$179$	−6.89903	+	4.43374i	−0.515658	+	0.331393i	0.256794	+	0.966466i	$0.417334\pi$
$180$	−8.18447	−	9.44539i	−0.610035	−	0.704018i
$181$	14.0700	+	4.13131i	1.04581	+	0.307078i	0.759124	−	0.650946i	$-0.225628\pi$
$181$	14.0700	+	4.13131i	1.04581	+	0.307078i	0.286688	+	0.958024i	$0.407446\pi$
$182$	−1.52962	+	3.34941i	−0.113383	+	0.248275i
$183$	−0.0920085			−0.00680146
$184$	−3.14483	−	3.62078i	−0.231840	−	0.266928i
$185$	18.1554			1.33481
$186$	0.0426825	−	0.0934616i	0.00312963	−	0.00685293i
$187$	2.90747	+	0.853710i	0.212615	+	0.0624295i
$188$	2.75904	+	3.18410i	0.201224	+	0.232225i
$189$	0.0744711	−	0.0478597i	0.00541698	−	0.00348128i
$190$	16.9260	−	19.5336i	1.22794	−	1.41712i
$191$	2.42241	−	16.8482i	0.175280	−	1.21910i	−0.692230	−	0.721677i	$-0.743372\pi$
$191$	2.42241	−	16.8482i	0.175280	−	1.21910i	0.867510	−	0.497420i	$-0.165719\pi$
$192$	0.0141569	−	0.00415683i	0.00102168	−	0.000299994i
$193$	−3.61365	−	2.32235i	−0.260116	−	0.167166i	0.404083	−	0.914722i	$-0.367591\pi$
$193$	−3.61365	−	2.32235i	−0.260116	−	0.167166i	−0.664199	+	0.747556i	$0.731227\pi$
$194$	−1.69878	−	11.8153i	−0.121965	−	0.848286i
$195$	−0.0940292	−	0.205895i	−0.00673357	−	0.0147445i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	2.09646	+	14.5812i	0.149367	+	1.03887i	0.917260	+	0.398289i	$0.130396\pi$
$197$	2.09646	+	14.5812i	0.149367	+	1.03887i	−0.767893	+	0.640578i	$0.778695\pi$
$198$	0.998325	+	0.641584i	0.0709479	+	0.0455954i
$199$	16.1128	−	4.73113i	1.14220	−	0.335381i	0.344710	−	0.938709i	$-0.387977\pi$
$199$	16.1128	−	4.73113i	1.14220	−	0.335381i	0.797493	+	0.603328i	$0.206159\pi$
$200$	−1.75875	+	12.2324i	−0.124363	+	0.864961i
$201$	−0.127817	+	0.147509i	−0.00901551	+	0.0104045i
$202$	−9.04550	+	5.81319i	−0.636439	+	0.409014i
$203$	−0.216787	−	0.250186i	−0.0152155	−	0.0175596i
$204$	0.108439	+	0.0318406i	0.00759225	+	0.00222929i
$205$	−6.50184	+	14.2370i	−0.454108	+	0.994358i
$206$	15.6828			1.09267
$207$	2.03079	−	14.2424i	0.141150	−	0.989915i
$208$	−3.68216			−0.255312
$209$	−1.01951	+	2.23241i	−0.0705207	+	0.154419i
$210$	−0.0589820	−	0.0173187i	−0.00407014	−	0.00119510i
$211$	−5.62986	−	6.49721i	−0.387576	−	0.447286i	0.528113	−	0.849174i	$-0.322900\pi$
$211$	−5.62986	−	6.49721i	−0.387576	−	0.447286i	−0.915689	+	0.401888i	$0.868354\pi$
$212$	−2.62639	+	1.68788i	−0.180381	+	0.115924i
$213$	−0.0256964	+	0.0296552i	−0.00176069	+	0.00203194i
$214$	0.584941	−	4.06835i	0.0399857	−	0.278107i
$215$	15.7956	−	4.63800i	1.07725	−	0.316309i
$216$	0.0744711	+	0.0478597i	0.00506712	+	0.00325644i
$217$	0.991042	+	6.89285i	0.0672763	+	0.467917i
$218$	−3.31902	−	7.26764i	−0.224792	−	0.492227i
$219$	0.0291119	+	0.0637461i	0.00196720	+	0.00430756i
$220$	−0.234562	−	1.63141i	−0.0158142	−	0.109990i
$221$	−23.7273	−	15.2486i	−1.59607	−	1.02573i
$222$	−0.0616908	+	0.0181141i	−0.00414042	+	0.00121574i
$223$	−3.50704	+	24.3920i	−0.234849	+	1.63341i	0.441808	+	0.897110i	$0.354337\pi$
$223$	−3.50704	+	24.3920i	−0.234849	+	1.63341i	−0.676656	+	0.736299i	$0.736572\pi$
$224$	−0.654861	+	0.755750i	−0.0437547	+	0.0504956i
$225$	−31.1868	+	20.0426i	−2.07912	+	1.33617i
$226$	10.4639	+	12.0760i	0.696049	+	0.803283i
$227$	−12.4584	−	3.65813i	−0.826896	−	0.242798i	−0.159213	−	0.987244i	$-0.550896\pi$
$227$	−12.4584	−	3.65813i	−0.826896	−	0.242798i	−0.667683	+	0.744446i	$0.732714\pi$
$228$	−0.0380242	+	0.0832614i	−0.00251821	+	0.00551412i
$229$	−28.7750			−1.90150			−0.950752	−	0.309953i	$-0.899687\pi$
$229$	−28.7750			−1.90150			−0.950752	+	0.309953i	$0.899687\pi$
$230$	−16.7964	+	10.8221i	−1.10752	+	0.713589i
$231$	0.00583688			0.000384038
$232$	0.137520	−	0.301127i	0.00902865	−	0.0197700i
$233$	1.89442	+	0.556253i	0.124108	+	0.0364413i	0.343197	−	0.939264i	$-0.388490\pi$
$233$	1.89442	+	0.556253i	0.124108	+	0.0364413i	−0.219089	+	0.975705i	$0.570308\pi$
$234$	−7.23338	−	8.34777i	−0.472861	−	0.545711i
$235$	14.7669	−	9.49009i	0.963284	−	0.619065i
$236$	3.32108	−	3.83272i	0.216184	−	0.249489i
$237$	−0.00351082	+	0.0244183i	−0.000228052	+	0.00158614i
$238$	−7.34954	+	2.15802i	−0.476400	+	0.139884i
$239$	10.4142	+	6.69280i	0.673639	+	0.432921i	0.832236	−	0.554422i	$-0.187061\pi$
$239$	10.4142	+	6.69280i	0.673639	+	0.432921i	−0.158597	+	0.987343i	$0.550697\pi$
$240$	−0.00874838	−	0.0608463i	−0.000564706	−	0.00392761i
$241$	−4.59654	−	10.0650i	−0.296089	−	0.648345i	0.701863	−	0.712312i	$-0.252352\pi$
$241$	−4.59654	−	10.0650i	−0.296089	−	0.648345i	−0.997952	+	0.0639671i	$0.979625\pi$
$242$	−4.50455	−	9.86360i	−0.289564	−	0.634056i
$243$	0.0566888	+	0.394279i	0.00363659	+	0.0252930i
$244$	5.24601	+	3.37141i	0.335842	+	0.215832i
$245$	3.99755	−	1.17379i	0.255394	−	0.0749905i
$246$	0.00788819	−	0.0548636i	0.000502933	−	0.00349797i
$247$	14.9591	−	17.2637i	0.951822	−	1.09846i
$248$	−5.85826	+	3.76488i	−0.372000	+	0.239070i
$249$	0.0386114	+	0.0445600i	0.00244690	+	0.00282387i
$250$	29.4147	+	8.63693i	1.86035	+	0.546248i
$251$	1.37383	−	3.00827i	0.0867155	−	0.189880i	−0.861306	−	0.508086i	$-0.830353\pi$
$251$	1.37383	−	3.00827i	0.0867155	−	0.189880i	0.948022	+	0.318206i	$0.103080\pi$
$252$	−2.99978			−0.188969
$253$	1.24075	−	1.43528i	0.0780050	−	0.0902351i
$254$	−12.4198			−0.779285
$255$	0.195604	−	0.428313i	0.0122492	−	0.0268220i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−13.1293	−	15.1520i	−0.818984	−	0.945158i	0.180276	−	0.983616i	$-0.442301\pi$
$257$	−13.1293	−	15.1520i	−0.818984	−	0.945158i	−0.999260	+	0.0384578i	$0.987755\pi$
$258$	−0.0490449	+	0.0315192i	−0.00305340	+	0.00196230i
$259$	2.85366	−	3.29330i	0.177318	−	0.204636i
$260$	−2.18326	+	15.1849i	−0.135400	+	0.941727i
$261$	0.952831	−	0.279777i	0.0589788	−	0.0173177i
$262$	18.9583	+	12.1837i	1.17125	+	0.752714i
$263$	−2.23688	−	15.5579i	−0.137932	−	0.959339i	−0.934797	−	0.355182i	$-0.884419\pi$
$263$	−2.23688	−	15.5579i	−0.137932	−	0.959339i	0.796865	−	0.604157i	$-0.206490\pi$
$264$	0.00242473	+	0.00530941i	0.000149232	+	0.000326772i
$265$	5.40340	+	11.8318i	0.331928	+	0.726821i
$266$	−0.882882	−	6.14058i	−0.0541330	−	0.376503i
$267$	−0.101504	−	0.0652325i	−0.00621192	−	0.00399216i
$268$	12.6927	−	3.72693i	0.775333	−	0.227658i
$269$	2.22693	−	15.4887i	0.135779	−	0.944361i	−0.802049	−	0.597259i	$-0.796257\pi$
$269$	2.22693	−	15.4887i	0.135779	−	0.944361i	0.937827	−	0.347102i	$-0.112834\pi$
$270$	0.241525	−	0.278735i	0.0146987	−	0.0169633i
$271$	−2.24968	+	1.44578i	−0.136658	+	0.0878250i	−0.607184	−	0.794562i	$-0.707701\pi$
$271$	−2.24968	+	1.44578i	−0.136658	+	0.0878250i	0.470525	+	0.882386i	$0.344064\pi$
$272$	−5.01611	−	5.78890i	−0.304146	−	0.351004i
$273$	−0.0521279	−	0.0153061i	−0.00315492	−	0.000926369i
$274$	−0.627700	+	1.37447i	−0.0379207	+	0.0830348i
$275$	−4.88888			−0.294811
$276$	0.0462757	−	0.0535311i	0.00278547	−	0.00322219i
$277$	−6.79789			−0.408446			−0.204223	−	0.978924i	$-0.565467\pi$
$277$	−6.79789			−0.408446			−0.204223	+	0.978924i	$0.565467\pi$
$278$	−8.95167	+	19.6014i	−0.536885	+	1.17561i
$279$	−20.0435	−	5.88530i	−1.19997	−	0.352344i
$280$	2.72836	+	3.14869i	0.163050	+	0.188170i
$281$	−12.7350	+	8.18426i	−0.759704	+	0.488232i	−0.862242	−	0.506497i	$-0.830940\pi$
$281$	−12.7350	+	8.18426i	−0.759704	+	0.488232i	0.102538	+	0.994729i	$0.467304\pi$
$282$	−0.0407084	+	0.0469800i	−0.00242415	+	0.00279762i
$283$	3.12890	−	21.7620i	0.185994	−	1.29362i	−0.656260	−	0.754535i	$-0.727862\pi$
$283$	3.12890	−	21.7620i	0.185994	−	1.29362i	0.842254	−	0.539081i	$-0.181229\pi$
$284$	2.55176	−	0.749263i	0.151419	−	0.0444606i
$285$	0.320817	+	0.206176i	0.0190035	+	0.0122128i
$286$	−0.207304	−	1.44183i	−0.0122582	−	0.0852574i
$287$	1.56057	+	3.41718i	0.0921177	+	0.201710i
$288$	−1.24615	−	2.72870i	−0.0734304	−	0.160790i
$289$	−5.93065	−	41.2486i	−0.348862	−	2.42639i
$290$	−1.16028	−	0.745668i	−0.0681341	−	0.0437871i
$291$	0.168987	−	0.0496191i	0.00990619	−	0.00290872i
$292$	0.675947	−	4.70131i	0.0395568	−	0.275123i
$293$	−1.41122	+	1.62864i	−0.0824444	+	0.0951459i	−0.795473	−	0.605989i	$-0.792778\pi$
$293$	−1.41122	+	1.62864i	−0.0824444	+	0.0951459i	0.713029	+	0.701135i	$0.247323\pi$
$294$	−0.0124123	+	0.00797690i	−0.000723900	+	0.000465222i
$295$	−13.8366	−	15.9683i	−0.805601	−	0.929713i
$296$	4.18114	+	1.22769i	0.243024	+	0.0713583i
$297$	−0.0145478	+	0.0318553i	−0.000844151	+	0.00184843i
$298$	10.2395			0.593155
$299$	−14.8446	+	9.56451i	−0.858484	+	0.553130i
$300$	−0.182339			−0.0105274
$301$	1.64143	−	3.59424i	0.0946107	−	0.207168i
$302$	15.9979	+	4.69742i	0.920578	+	0.270306i
$303$	−0.103891	−	0.119897i	−0.00596841	−	0.00688791i
$304$	5.21891	−	3.35399i	0.299325	−	0.192364i
$305$	17.0139	−	19.6351i	0.974212	−	1.12430i
$306$	3.27008	−	22.7439i	0.186938	−	1.30018i
$307$	7.73611	−	2.27153i	0.441523	−	0.129643i	−0.0534124	−	0.998573i	$-0.517010\pi$
$307$	7.73611	−	2.27153i	0.441523	−	0.129643i	0.494936	+	0.868930i	$0.335192\pi$
$308$	−0.332799	−	0.213877i	−0.0189630	−	0.0121868i
$309$	0.0329305	+	0.229037i	0.00187335	+	0.0130294i
$310$	12.0525	+	26.3912i	0.684534	+	1.49892i
$311$	−5.58092	−	12.2205i	−0.316465	−	0.692962i	0.682827	−	0.730580i	$-0.260750\pi$
$311$	−5.58092	−	12.2205i	−0.316465	−	0.692962i	−0.999292	+	0.0376180i	$0.988023\pi$
$312$	−0.00773176	−	0.0537756i	−0.000437725	−	0.00304444i
$313$	17.1169	+	11.0004i	0.967506	+	0.621778i	0.926066	−	0.377363i	$-0.123169\pi$
$313$	17.1169	+	11.0004i	0.967506	+	0.621778i	0.0414404	+	0.999141i	$0.486805\pi$
$314$	4.24364	−	1.24604i	0.239482	−	0.0703184i
$315$	−1.77866	+	12.3708i	−0.100216	+	0.697017i
$316$	1.09492	−	1.26360i	0.0615940	−	0.0710833i
$317$	3.51952	−	2.26186i	0.197676	−	0.127039i	−0.438058	−	0.898947i	$-0.644334\pi$
$317$	3.51952	−	2.26186i	0.197676	−	0.127039i	0.635734	+	0.771908i	$0.280697\pi$
$318$	−0.0301652	−	0.0348125i	−0.00169158	−	0.00195219i
$319$	0.125656	+	0.0368958i	0.00703536	+	0.00206577i
$320$	−1.73075	+	3.78981i	−0.0967519	+	0.211857i
$321$	0.0606439			0.00338481
$322$	−0.676980	+	4.74781i	−0.0377266	+	0.264585i
$323$	47.5194			2.64405
$324$	3.73792	−	8.18491i	0.207662	−	0.454717i
$325$	43.6615	+	12.8202i	2.42191	+	0.711136i
$326$	4.96975	+	5.73539i	0.275249	+	0.317654i
$327$	0.0991699	−	0.0637326i	0.00548411	−	0.00352442i
$328$	−2.46009	+	2.83909i	−0.135836	+	0.156763i
$329$	0.599597	−	4.17029i	0.0330569	−	0.229916i
$330$	0.0233332	−	0.00685125i	0.00128445	−	0.000377149i
$331$	20.7631	+	13.3437i	1.14125	+	0.733434i	0.967877	−	0.251423i	$-0.0808986\pi$
$331$	20.7631	+	13.3437i	1.14125	+	0.733434i	0.173368	+	0.984857i	$0.444535\pi$
$332$	−0.568711	−	3.95547i	−0.0312121	−	0.217085i
$333$	5.43032	+	11.8907i	0.297580	+	0.651609i
$334$	−1.67394	−	3.66541i	−0.0915938	−	0.200563i
$335$	−7.84361	−	54.5535i	−0.428542	−	2.98058i
$336$	−0.0124123	−	0.00797690i	−0.000677147	−	0.000435176i
$337$	31.4021	−	9.22050i	1.71058	−	0.502273i	0.727605	−	0.685996i	$-0.240633\pi$
$337$	31.4021	−	9.22050i	1.71058	−	0.502273i	0.982978	+	0.183724i	$0.0588152\pi$
$338$	−0.0794558	+	0.552627i	−0.00432183	+	0.0300590i
$339$	−0.154390	+	0.178176i	−0.00838531	+	0.00967717i
$340$	−26.8471	+	17.2536i	−1.45599	+	0.935707i
$341$	−1.80404	−	2.08197i	−0.0976942	−	0.112745i
$342$	17.8560	+	5.24299i	0.965542	+	0.283509i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	3.95131			0.213040
$345$	−0.193319	−	0.222577i	−0.0104079	−	0.0119831i
$346$	−13.8954			−0.747022
$347$	−2.83804	+	6.21443i	−0.152354	+	0.333608i	−0.970384	−	0.241567i	$-0.922339\pi$
$347$	−2.83804	+	6.21443i	−0.152354	+	0.333608i	0.818030	+	0.575175i	$0.195066\pi$
$348$	0.00468653	+	0.00137609i	0.000251225	+	7.37662e-5i
$349$	−0.834162	−	0.962674i	−0.0446517	−	0.0515308i	0.732984	−	0.680245i	$-0.238127\pi$
$349$	−0.834162	−	0.962674i	−0.0446517	−	0.0515308i	−0.777636	+	0.628715i	$0.783581\pi$
$350$	10.3964	−	6.68134i	0.555709	−	0.357132i
$351$	0.213458	−	0.246344i	0.0113936	−	0.0131489i
$352$	0.0562996	−	0.391572i	0.00300078	−	0.0208709i
$353$	−31.5333	+	9.25901i	−1.67835	+	0.492807i	−0.975770	−	0.218800i	$-0.929786\pi$
$353$	−31.5333	+	9.25901i	−1.67835	+	0.492807i	−0.702577	+	0.711607i	$0.747967\pi$
$354$	0.0629480	+	0.0404542i	0.00334565	+	0.00215012i
$355$	−1.57688	−	10.9675i	−0.0836923	−	0.582093i
$356$	3.39713	+	7.43867i	0.180047	+	0.394249i
$357$	−0.0469490	−	0.102804i	−0.00248480	−	0.00544096i
$358$	1.16711	+	8.11742i	0.0616837	+	0.429019i
$359$	24.1062	+	15.4921i	1.27228	+	0.817644i	0.989915	−	0.141663i	$-0.0452450\pi$
$359$	24.1062	+	15.4921i	1.27228	+	0.817644i	0.282364	+	0.959307i	$0.408881\pi$
$360$	−11.9918	+	3.52110i	−0.632022	+	0.185578i
$361$	−2.77318	+	19.2879i	−0.145957	+	1.01515i
$362$	9.60284	−	11.0823i	0.504714	−	0.582471i
$363$	0.134593	−	0.0864976i	0.00706429	−	0.00453994i
$364$	2.41130	+	2.78279i	0.126387	+	0.145858i
$365$	−18.9870	−	5.57508i	−0.993824	−	0.291813i
$366$	−0.0382217	+	0.0836939i	−0.00199788	+	0.00437475i
$367$	−18.9964			−0.991605			−0.495803	−	0.868435i	$-0.665126\pi$
$367$	−18.9964			−0.991605			−0.495803	+	0.868435i	$0.665126\pi$
$368$	−4.59999	+	1.35651i	−0.239791	+	0.0707129i
$369$	−11.2692			−0.586649
$370$	7.54202	−	16.5147i	0.392091	−	0.858559i
$371$	2.99553	+	0.879568i	0.155520	+	0.0456649i
$372$	−0.0672847	−	0.0776507i	−0.00348855	−	0.00402600i
$373$	−6.13638	+	3.94361i	−0.317730	+	0.204192i	−0.689778	−	0.724021i	$-0.742292\pi$
$373$	−6.13638	+	3.94361i	−0.317730	+	0.204192i	0.372048	+	0.928213i	$0.378656\pi$
$374$	1.98437	−	2.29008i	0.102609	−	0.118417i
$375$	−0.0643722	+	0.447718i	−0.00332416	+	0.0231201i
$376$	4.04251	−	1.18699i	0.208477	−	0.0612142i
$377$	−1.02545	−	0.659016i	−0.0528133	−	0.0339411i
$378$	−0.0125983	−	0.0876229i	−0.000647985	−	0.00450684i
$379$	−5.16947	−	11.3196i	−0.265538	−	0.581447i	0.729153	−	0.684350i	$-0.239914\pi$
$379$	−5.16947	−	11.3196i	−0.265538	−	0.581447i	−0.994691	+	0.102903i	$0.967187\pi$
$380$	−10.7371	−	23.5110i	−0.550801	−	1.20609i
$381$	−0.0260789	−	0.181383i	−0.00133606	−	0.00929251i
$382$	−14.3194	−	9.20252i	−0.732644	−	0.470842i
$383$	−5.09661	+	1.49650i	−0.260425	+	0.0764676i	−0.409338	−	0.912383i	$-0.634240\pi$
$383$	−5.09661	+	1.49650i	−0.260425	+	0.0764676i	0.148914	+	0.988850i	$0.452422\pi$
$384$	0.00209979	−	0.0146044i	0.000107154	−	0.000745275i
$385$	−1.07934	+	1.24562i	−0.0550080	+	0.0634826i
$386$	−3.61365	+	2.32235i	−0.183930	+	0.118204i
$387$	7.76211	+	8.95795i	0.394570	+	0.455358i
$388$	−11.4532	−	3.36297i	−0.581450	−	0.170729i
$389$	2.04648	−	4.48117i	0.103761	−	0.227204i	−0.850630	−	0.525765i	$-0.823779\pi$
$389$	2.04648	−	4.48117i	0.103761	−	0.227204i	0.954391	+	0.298561i	$0.0965065\pi$
$390$	−0.226350			−0.0114617
$391$	−35.2592	−	10.3084i	−1.78313	−	0.521317i
$392$	1.00000			0.0505076
$393$	−0.138127	+	0.302456i	−0.00696760	+	0.0152569i
$394$	14.1344	+	4.15024i	0.712082	+	0.209086i
$395$	−4.56178	−	5.26457i	−0.229528	−	0.264889i
$396$	0.998325	−	0.641584i	0.0501677	−	0.0322408i
$397$	−5.86434	+	6.76781i	−0.294323	+	0.339666i	−0.883581	−	0.468278i	$-0.844875\pi$
$397$	−5.86434	+	6.76781i	−0.294323	+	0.339666i	0.589258	+	0.807945i	$0.299420\pi$
$398$	2.38989	−	16.6221i	0.119794	−	0.833189i
$399$	0.0878253	−	0.0257878i	0.00439677	−	0.00129101i
$400$	10.3964	+	6.68134i	0.519818	+	0.334067i
$401$	−0.680213	−	4.73099i	−0.0339682	−	0.236254i	0.965763	−	0.259425i	$-0.0835330\pi$
$401$	−0.680213	−	4.73099i	−0.0339682	−	0.236254i	−0.999732	+	0.0231706i	$0.992624\pi$
$402$	0.0810814	+	0.177544i	0.00404397	+	0.00885507i
$403$	10.6519	+	23.3244i	0.530609	+	1.16187i
$404$	1.53023	+	10.6430i	0.0761316	+	0.529507i
$405$	−31.5375	−	20.2679i	−1.56711	−	1.00712i
$406$	−0.317634	+	0.0932656i	−0.0157639	+	0.00462869i
$407$	−0.245335	+	1.70634i	−0.0121608	+	0.0845801i
$408$	0.0740104	−	0.0854125i	0.00366406	−	0.00422855i
$409$	−27.2378	+	17.5046i	−1.34682	+	0.865549i	−0.997445	−	0.0714336i	$-0.977243\pi$
$409$	−27.2378	+	17.5046i	−1.34682	+	0.865549i	−0.349376	+	0.936983i	$0.613606\pi$
$410$	10.2495	+	11.8286i	0.506187	+	0.584171i
$411$	−0.0213913	−	0.00628105i	−0.00105515	−	0.000309821i
$412$	6.51486	−	14.2655i	0.320964	−	0.702813i
$413$	−5.07142			−0.249548
$414$	−12.1117	−	7.76378i	−0.595258	−	0.381569i
$415$	−16.6492			−0.817277
$416$	−1.52962	+	3.34941i	−0.0749960	+	0.164218i
$417$	−0.305063	−	0.0895745i	−0.0149390	−	0.00438648i
$418$	1.60715	+	1.85475i	0.0786083	+	0.0907189i
$419$	0.654944	−	0.420907i	0.0319961	−	0.0205626i	−0.524545	−	0.851383i	$-0.675765\pi$
$419$	0.654944	−	0.420907i	0.0319961	−	0.0205626i	0.556541	+	0.830820i	$0.312128\pi$
$420$	−0.0402556	+	0.0464575i	−0.00196427	+	0.00226689i
$421$	−4.38905	+	30.5265i	−0.213909	+	1.48777i	0.546025	+	0.837769i	$0.316141\pi$
$421$	−4.38905	+	30.5265i	−0.213909	+	1.48777i	−0.759934	+	0.650001i	$0.774769\pi$
$422$	−8.24880	+	2.42207i	−0.401545	+	0.117904i
$423$	10.6323	+	6.83295i	0.516959	+	0.332229i
$424$	0.444306	+	3.09022i	0.0215774	+	0.150074i
$425$	39.3238	+	86.1070i	1.90748	+	4.17680i
$426$	0.0163007	+	0.0356935i	0.000789769	+	0.00172935i
$427$	−0.887468	−	6.17247i	−0.0429476	−	0.298707i
$428$	−3.45771	−	2.22214i	−0.167135	−	0.107411i
$429$	0.0206217	−	0.00605509i	0.000995627	−	0.000292342i
$430$	2.34284	−	16.2948i	0.112982	−	0.785807i
$431$	−15.9850	+	18.4476i	−0.769968	+	0.888591i	−0.996342	−	0.0854496i	$-0.972767\pi$
$431$	−15.9850	+	18.4476i	−0.769968	+	0.888591i	0.226374	+	0.974040i	$0.427313\pi$
$432$	0.0744711	−	0.0478597i	0.00358299	−	0.00230265i
$433$	−16.6887	−	19.2597i	−0.802006	−	0.925564i	0.196483	−	0.980507i	$-0.437048\pi$
$433$	−16.6887	−	19.2597i	−0.802006	−	0.925564i	−0.998490	+	0.0549428i	$0.982502\pi$
$434$	6.68165	+	1.96191i	0.320729	+	0.0941747i
$435$	0.00845365	−	0.0185109i	0.000405321	−	0.000887530i
$436$	−7.98965			−0.382635
$437$	12.3279	−	27.0778i	0.589721	−	1.29531i
$438$	0.0700790			0.00334850
$439$	4.44671	−	9.73693i	0.212230	−	0.464718i	−0.773339	−	0.633992i	$-0.781415\pi$
$439$	4.44671	−	9.73693i	0.212230	−	0.464718i	0.985569	+	0.169274i	$0.0541423\pi$
$440$	−1.58143	−	0.464349i	−0.0753916	−	0.0221370i
$441$	1.96444	+	2.26708i	0.0935447	+	0.107956i
$442$	−23.7273	+	15.2486i	−1.12859	+	0.725302i
$443$	7.39317	−	8.53217i	0.351260	−	0.405376i	−0.552433	−	0.833558i	$-0.686300\pi$
$443$	7.39317	−	8.53217i	0.351260	−	0.405376i	0.903693	+	0.428182i	$0.140846\pi$
$444$	−0.00915017	+	0.0636408i	−0.000434248	+	0.00302026i
$445$	32.6906	−	9.59884i	1.54968	−	0.455028i
$446$	20.7309	+	13.3229i	0.981635	+	0.630858i
$447$	0.0215007	+	0.149541i	0.00101695	+	0.00707303i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	−10.6839	−	23.3944i	−0.504203	−	1.10405i	−0.975080	−	0.221852i	$-0.928790\pi$
$449$	−10.6839	−	23.3944i	−0.504203	−	1.10405i	0.470877	−	0.882199i	$-0.343938\pi$
$450$	5.27587	+	36.6945i	0.248707	+	1.72980i
$451$	−1.25021	−	0.803463i	−0.0588702	−	0.0378336i
$452$	15.3316	−	4.50175i	0.721136	−	0.211745i
$453$	−0.0350104	+	0.243503i	−0.00164493	+	0.0114408i
$454$	−8.50297	+	9.81295i	−0.399064	+	0.460545i
$455$	12.9057	−	8.29399i	0.605029	−	0.388828i
$456$	0.0599414	+	0.0691761i	0.00280701	+	0.00323947i
$457$	9.60529	+	2.82037i	0.449317	+	0.131931i	0.498559	−	0.866856i	$-0.333863\pi$
$457$	9.60529	+	2.82037i	0.449317	+	0.131931i	−0.0492426	+	0.998787i	$0.515681\pi$
$458$	−11.9536	+	26.1746i	−0.558553	+	1.22306i
$459$	0.678077			0.0316499
$460$	2.86665	+	19.7742i	0.133658	+	0.921979i
$461$	7.81147			0.363816			0.181908	−	0.983316i	$-0.441773\pi$
$461$	7.81147			0.363816			0.181908	+	0.983316i	$0.441773\pi$
$462$	0.00242473	−	0.00530941i	0.000112809	−	0.000247016i
$463$	36.5105	+	10.7204i	1.69679	+	0.498221i	0.979987	−	0.199059i	$-0.0637887\pi$
$463$	36.5105	+	10.7204i	1.69679	+	0.498221i	0.716798	+	0.697281i	$0.245607\pi$
$464$	−0.216787	−	0.250186i	−0.0100641	−	0.0116146i
$465$	−0.360119	+	0.231435i	−0.0167001	+	0.0107325i
$466$	1.29296	−	1.49215i	0.0598951	−	0.0691226i
$467$	2.07598	−	14.4388i	0.0960651	−	0.668148i	−0.883708	−	0.468038i	$-0.844961\pi$
$467$	2.07598	−	14.4388i	0.0960651	−	0.668148i	0.979774	−	0.200110i	$-0.0641298\pi$
$468$	−10.5983	+	3.11193i	−0.489904	+	0.143849i
$469$	−11.1286	−	7.15192i	−0.513871	−	0.330245i
$470$	−2.49811	−	17.3747i	−0.115229	−	0.801437i
$471$	0.0271084	+	0.0593592i	0.00124909	+	0.00273513i
$472$	−2.10674	−	4.61313i	−0.0969708	−	0.212336i
$473$	0.222457	+	1.54722i	0.0102286	+	0.0711415i
$474$	0.0207532	+	0.0133373i	0.000953227	+	0.000612602i
$475$	−73.5612	+	21.5995i	−3.37522	+	0.991054i
$476$	−1.09011	+	7.58185i	−0.0499649	+	0.347513i
$477$	−6.13297	+	7.07783i	−0.280810	+	0.324072i
$478$	10.4142	−	6.69280i	0.476335	−	0.306122i
$479$	−11.0839	−	12.7915i	−0.506435	−	0.584457i	0.443747	−	0.896152i	$-0.353649\pi$
$479$	−11.0839	−	12.7915i	−0.506435	−	0.584457i	−0.950182	+	0.311695i	$0.899103\pi$
$480$	−0.0589820	−	0.0173187i	−0.00269215	−	0.000790486i
$481$	6.66559	−	14.5956i	0.303925	−	0.665502i
$482$	−11.0649			−0.503994
$483$	−0.0707602		8.25465e-5i	−0.00321970		3.75600e-6i
$484$	−10.8435			−0.492886
$485$	−20.6595	+	45.2381i	−0.938101	+	2.05415i
$486$	0.382199	+	0.112224i	0.0173369	+	0.00509057i
$487$	−11.0073	−	12.7031i	−0.498789	−	0.575633i	0.449404	−	0.893329i	$-0.351636\pi$
$487$	−11.0073	−	12.7031i	−0.498789	−	0.575633i	−0.948193	+	0.317696i	$0.897091\pi$
$488$	5.24601	−	3.37141i	0.237476	−	0.152616i
$489$	−0.0733263	+	0.0846230i	−0.00331593	+	0.00382679i
$490$	0.592928	−	4.12391i	0.0267858	−	0.186299i
$491$	22.9696	−	6.74449i	1.03661	−	0.304375i	0.281211	−	0.959646i	$-0.409264\pi$
$491$	22.9696	−	6.74449i	1.03661	−	0.304375i	0.755394	+	0.655271i	$0.227446\pi$
$492$	−0.0466288	−	0.0299665i	−0.00210219	−	0.00135099i
$493$	−0.360872	−	2.50992i	−0.0162529	−	0.113041i
$494$	−9.48937	−	20.7788i	−0.426947	−	0.934884i
$495$	−2.05390	−	4.49741i	−0.0923159	−	0.202144i
$496$	0.991042	+	6.89285i	0.0444991	+	0.309498i
$497$	−2.23730	−	1.43783i	−0.100357	−	0.0644953i
$498$	0.0565729	−	0.0166113i	0.00253509	−	0.000744371i
$499$	−1.82017	+	12.6596i	−0.0814821	+	0.566721i	0.907654	+	0.419719i	$0.137871\pi$
$499$	−1.82017	+	12.6596i	−0.0814821	+	0.566721i	−0.989136	+	0.147002i	$0.953038\pi$
$500$	20.0757	−	23.1686i	0.897814	−	1.03613i
$501$	0.0500161	−	0.0321434i	0.00223455	−	0.00143606i
$502$	−2.16571	−	2.49936i	−0.0966604	−	0.111552i
$503$	17.3981	+	5.10854i	0.775743	+	0.227779i	0.645558	−	0.763711i	$-0.276625\pi$
$503$	17.3981	+	5.10854i	0.775743	+	0.227779i	0.130185	+	0.991490i	$0.458443\pi$
$504$	−1.24615	+	2.72870i	−0.0555081	+	0.121546i
$505$	44.7979			1.99348
$506$	−0.790149	−	1.72486i	−0.0351264	−	0.0766793i
$507$	−0.00823761			−0.000365845
$508$	−5.15936	+	11.2974i	−0.228909	+	0.501242i
$509$	−2.00048	−	0.587394i	−0.0886698	−	0.0260358i	0.237097	−	0.971486i	$-0.423804\pi$
$509$	−2.00048	−	0.587394i	−0.0886698	−	0.0260358i	−0.325767	+	0.945450i	$0.605622\pi$
$510$	−0.308351	−	0.355856i	−0.0136540	−	0.0157575i
$511$	−3.99567	+	2.56786i	−0.176758	+	0.113595i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−0.0781562	+	0.543589i	−0.00345068	+	0.0240000i
$514$	−19.2369	+	5.64846i	−0.848503	+	0.249143i
$515$	−54.9669	−	35.3251i	−2.42213	−	1.55661i
$516$	0.00829692	+	0.0577063i	0.000365251	+	0.00254038i
$517$	0.692384	+	1.51611i	0.0304510	+	0.0666784i
$518$	−1.81024	−	3.96387i	−0.0795373	−	0.174162i
$519$	−0.0291774	−	0.202934i	−0.00128075	−	0.00890779i
$520$	12.9057	+	8.29399i	0.565953	+	0.363716i
$521$	22.9854	−	6.74913i	1.00701	−	0.295685i	0.263680	−	0.964610i	$-0.415064\pi$
$521$	22.9854	−	6.74913i	1.00701	−	0.295685i	0.743329	+	0.668926i	$0.233246\pi$
$522$	0.141327	−	0.982949i	0.00618571	−	0.0430225i
$523$	−5.21343	+	6.01662i	−0.227968	+	0.263089i	−0.858197	−	0.513320i	$-0.828415\pi$
$523$	−5.21343	+	6.01662i	−0.227968	+	0.263089i	0.630230	+	0.776409i	$0.282961\pi$
$524$	18.9583	−	12.1837i	0.828196	−	0.532249i
$525$	0.119407	+	0.137803i	0.00521134	+	0.00601420i
$526$	−15.0812	−	4.42823i	−0.657570	−	0.193080i
$527$	−22.1586	+	48.5206i	−0.965244	+	2.11359i
$528$	0.00583688			0.000254018
$529$	−15.0212	+	17.4173i	−0.653096	+	0.757275i
$530$	13.0072			0.564998
$531$	6.31978	−	13.8384i	0.274255	−	0.600534i
$532$	−5.95243	−	1.74779i	−0.258071	−	0.0757764i
$533$	9.05844	+	10.4540i	0.392365	+	0.452813i
$534$	−0.101504	+	0.0652325i	−0.00439249	+	0.00282288i
$535$	−11.2141	+	12.9417i	−0.484826	+	0.559519i
$536$	1.88263	−	13.0940i	0.0813170	−	0.565573i
$537$	−0.116099	+	0.0340898i	−0.00501004	+	0.00147108i
$538$	−13.1639	−	8.45992i	−0.567536	−	0.364733i
$539$	0.0562996	+	0.391572i	0.00242500	+	0.0168662i
$540$	−0.153213	−	0.335489i	−0.00659323	−	0.0144372i
$541$	17.3025	+	37.8872i	0.743892	+	1.62890i	0.777044	+	0.629447i	$0.216718\pi$
$541$	17.3025	+	37.8872i	0.743892	+	1.62890i	−0.0331514	+	0.999450i	$0.510554\pi$
$542$	0.380578	+	2.64698i	0.0163472	+	0.113698i
$543$	0.182013	+	0.116973i	0.00781094	+	0.00501979i
$544$	−7.34954	+	2.15802i	−0.315109	+	0.0925243i
$545$	−4.73729	+	32.9486i	−0.202923	+	1.41136i
$546$	−0.0355776	+	0.0410588i	−0.00152258	+	0.00175715i
$547$	−28.2453	+	18.1522i	−1.20768	+	0.776130i	−0.980269	−	0.197668i	$-0.936663\pi$
$547$	−28.2453	+	18.1522i	−1.20768	+	0.776130i	−0.227413	+	0.973798i	$0.573027\pi$
$548$	0.989507	+	1.14195i	0.0422696	+	0.0487817i
$549$	17.9487	+	5.27023i	0.766033	+	0.224928i
$550$	−2.03092	+	4.44709i	−0.0865985	+	0.189624i
$551$	2.05370			0.0874906
$552$	−0.0294699	−	0.0643315i	−0.00125432	−	0.00273813i
$553$	−1.67199			−0.0711002
$554$	−2.82395	+	6.18358i	−0.119978	+	0.262715i
$555$	0.257023	+	0.0754689i	0.0109100	+	0.00320348i
$556$	14.1114	+	16.2854i	0.598457	+	0.690657i
$557$	4.79393	−	3.08087i	0.203125	−	0.130541i	−0.435124	−	0.900371i	$-0.643295\pi$
$557$	4.79393	−	3.08087i	0.203125	−	0.130541i	0.638249	+	0.769830i	$0.279659\pi$
$558$	−13.6798	+	15.7874i	−0.579113	+	0.668332i
$559$	2.07059	−	14.4013i	0.0875766	−	0.609109i
$560$	3.99755	−	1.17379i	0.168927	−	0.0496015i
$561$	0.0376120	+	0.0241717i	0.00158798	+	0.00102053i
$562$	2.15437	+	14.9840i	0.0908767	+	0.632061i
$563$	4.71331	+	10.3207i	0.198642	+	0.434966i	0.982572	−	0.185884i	$-0.0595148\pi$
$563$	4.71331	+	10.3207i	0.198642	+	0.434966i	−0.783929	+	0.620850i	$0.786788\pi$
$564$	0.0258236	+	0.0565458i	0.00108737	+	0.00238101i
$565$	−9.47430	−	65.8952i	−0.398587	−	2.77223i
$566$	−18.4956	−	11.8864i	−0.777429	−	0.499623i
$567$	−8.63356	+	2.53504i	−0.362575	+	0.106462i
$568$	0.378484	−	2.63242i	0.0158808	−	0.110454i
$569$	26.5539	−	30.6449i	1.11320	−	1.28470i	0.158424	−	0.987371i	$-0.449359\pi$
$569$	26.5539	−	30.6449i	1.11320	−	1.28470i	0.954775	−	0.297329i	$-0.0960958\pi$
$570$	0.320817	−	0.206176i	0.0134375	−	0.00863578i
$571$	−14.3558	−	16.5675i	−0.600773	−	0.693330i	0.371164	−	0.928567i	$-0.378959\pi$
$571$	−14.3558	−	16.5675i	−0.600773	−	0.693330i	−0.971938	+	0.235238i	$0.924413\pi$
$572$	−1.39765	−	0.410388i	−0.0584389	−	0.0171592i
$573$	0.104329	−	0.228449i	0.00435841	−	0.00954359i
$574$	3.75666			0.156800
$575$	59.2677	−	0.0691397i	2.47163	−	0.00288333i
$576$	−2.99978			−0.124991
$577$	−8.00234	+	17.5227i	−0.333142	+	0.729479i	−0.999875	−	0.0158178i	$-0.994965\pi$
$577$	−8.00234	+	17.5227i	−0.333142	+	0.729479i	0.666733	+	0.745297i	$0.267692\pi$
$578$	−39.9847	−	11.7406i	−1.66315	−	0.488344i
$579$	−0.0415043	−	0.0478985i	−0.00172486	−	0.00199059i
$580$	−1.16028	+	0.745668i	−0.0481781	+	0.0309622i
$581$	−2.61692	+	3.02009i	−0.108568	+	0.125294i
$582$	0.0250647	−	0.174329i	0.00103896	−	0.00722615i
$583$	−1.18503	+	0.347956i	−0.0490789	+	0.0144109i
$584$	−3.99567	−	2.56786i	−0.165342	−	0.106259i
$585$	6.54930	+	45.5514i	0.270780	+	1.88332i
$586$	0.895217	+	1.96025i	0.0369811	+	0.0809772i
$587$	−0.672878	−	1.47340i	−0.0277727	−	0.0608136i	0.895237	−	0.445590i	$-0.147006\pi$
$587$	−0.672878	−	1.47340i	−0.0277727	−	0.0608136i	−0.923010	+	0.384776i	$0.874279\pi$
$588$	0.00209979	+	0.0146044i	8.65938e−5	+	0.000602273i
$589$	−36.3430	−	23.3563i	−1.49749	−	0.962378i
$590$	−20.2733	+	5.95277i	−0.834637	+	0.245072i
$591$	−0.0309323	+	0.215139i	−0.00127238	+	0.00884962i
$592$	2.85366	−	3.29330i	0.117285	−	0.135354i
$593$	−6.11927	+	3.93262i	−0.251288	+	0.161493i	−0.660221	−	0.751071i	$-0.729537\pi$
$593$	−6.11927	+	3.93262i	−0.251288	+	0.161493i	0.408933	+	0.912565i	$0.365901\pi$
$594$	0.0229332	+	0.0264664i	0.000940962	+	0.00108593i
$595$	30.6205	+	8.99099i	1.25532	+	0.368595i
$596$	4.25362	−	9.31413i	0.174235	−	0.381522i
$597$	0.247773			0.0101407
$598$	2.53353	+	17.4763i	0.103604	+	0.714661i
$599$	6.90069			0.281954			0.140977	−	0.990013i	$-0.454976\pi$
$599$	6.90069			0.281954			0.140977	+	0.990013i	$0.454976\pi$
$600$	−0.0757464	+	0.165862i	−0.00309233	+	0.00677127i
$601$	−11.7833	−	3.45990i	−0.480652	−	0.141132i	0.0324259	−	0.999474i	$-0.489677\pi$
$601$	−11.7833	−	3.45990i	−0.480652	−	0.141132i	−0.513078	+	0.858342i	$0.671495\pi$
$602$	−2.58756	−	2.98620i	−0.105461	−	0.121708i
$603$	33.3834	−	21.4542i	1.35948	−	0.873683i
$604$	10.9187	−	12.6009i	0.444276	−	0.512721i
$605$	−6.42942	+	44.7176i	−0.261393	+	1.81803i
$606$	−0.152220	+	0.0446959i	−0.00618353	+	0.00181565i
$607$	13.6815	+	8.79258i	0.555316	+	0.356880i	0.788003	−	0.615672i	$-0.211115\pi$
$607$	13.6815	+	8.79258i	0.555316	+	0.356880i	−0.232687	+	0.972552i	$0.574752\pi$
$608$	−0.882882	−	6.14058i	−0.0358056	−	0.249033i
$609$	−0.00202905	−	0.00444299i	−8.22211e−5	−	0.000180039i
$610$	−10.7929	−	23.6331i	−0.436990	−	0.956875i
$611$	−2.20781	−	15.3557i	−0.0893186	−	0.621224i
$612$	−19.3301	−	12.4227i	−0.781374	−	0.502159i
$613$	30.1284	−	8.84650i	1.21687	−	0.357307i	0.390593	−	0.920564i	$-0.372270\pi$
$613$	30.1284	−	8.84650i	1.21687	−	0.357307i	0.826282	+	0.563257i	$0.190452\pi$
$614$	1.14744	−	7.98064i	0.0463070	−	0.322073i
$615$	−0.151227	+	0.174525i	−0.00609805	+	0.00703752i
$616$	−0.332799	+	0.213877i	−0.0134089	+	0.00861735i
$617$	−0.302504	−	0.349109i	−0.0121784	−	0.0140546i	0.749628	−	0.661860i	$-0.230233\pi$
$617$	−0.302504	−	0.349109i	−0.0121784	−	0.0140546i	−0.761806	+	0.647805i	$0.775687\pi$
$618$	0.222019	+	0.0651906i	0.00893091	+	0.00262235i
$619$	−8.66879	+	18.9820i	−0.348428	+	0.762951i	0.651563	+	0.758595i	$0.274114\pi$
$619$	−8.66879	+	18.9820i	−0.348428	+	0.762951i	−0.999991	+	0.00435586i	$0.998613\pi$
$620$	29.0131			1.16519
$621$	0.175912	−	0.386386i	0.00705911	−	0.0155051i
$622$	−13.4346			−0.538677
$623$	3.39713	−	7.43867i	0.136103	−	0.298024i
$624$	−0.0521279	−	0.0153061i	−0.00208679	−	0.000612735i
$625$	−43.1774	−	49.8294i	−1.72710	−	1.99317i
$626$	17.1169	−	11.0004i	0.684130	−	0.439664i
$627$	−0.0237128	+	0.0273660i	−0.000946997	+	0.00109289i
$628$	0.629429	−	4.37778i	0.0251170	−	0.174692i
$629$	32.0268	−	9.40392i	1.27699	−	0.374959i
$630$	10.5140	+	6.75695i	0.418889	+	0.269203i
$631$	5.88595	+	40.9377i	0.234316	+	1.62970i	0.679086	+	0.734058i	$0.262376\pi$
$631$	5.88595	+	40.9377i	0.234316	+	1.62970i	−0.444770	+	0.895645i	$0.646715\pi$
$632$	−0.694569	−	1.52089i	−0.0276285	−	0.0604979i
$633$	−0.0526934	−	0.115383i	−0.00209438	−	0.00458604i
$634$	−0.595398	−	4.14108i	−0.0236463	−	0.164463i
$635$	43.5304	+	27.9753i	1.72745	+	1.11016i
$636$	−0.0441977	+	0.0129776i	−0.00175255	+	0.000514596i
$637$	0.524026	−	3.64468i	0.0207627	−	0.144408i
$638$	0.0857608	−	0.0989732i	0.00339530	−	0.00391839i
$639$	6.71142	−	4.31317i	0.265500	−	0.170626i
$640$	2.72836	+	3.14869i	0.107848	+	0.124463i
$641$	−17.9344	−	5.26601i	−0.708365	−	0.207995i	−0.0923472	−	0.995727i	$-0.529437\pi$
$641$	−17.9344	−	5.26601i	−0.708365	−	0.207995i	−0.616018	+	0.787732i	$0.711255\pi$
$642$	0.0251924	−	0.0551636i	0.000994264	−	0.00217713i
$643$	35.2690			1.39087			0.695436	−	0.718588i	$-0.255211\pi$
$643$	35.2690			1.39087			0.695436	+	0.718588i	$0.255211\pi$
$644$	4.03753	+	2.58811i	0.159101	+	0.101986i
$645$	0.242895			0.00956398
$646$	19.7403	−	43.2252i	0.776670	−	1.70067i
$647$	16.4685	+	4.83560i	0.647445	+	0.190107i	0.588936	−	0.808180i	$-0.299547\pi$
$647$	16.4685	+	4.83560i	0.647445	+	0.190107i	0.0585094	+	0.998287i	$0.481365\pi$
$648$	−5.89246	−	6.80027i	−0.231478	−	0.267140i
$649$	1.68776	−	1.08466i	0.0662506	−	0.0425766i
$650$	29.7993	−	34.3902i	1.16883	−	1.34890i
$651$	−0.0146224	+	0.101701i	−0.000573096	+	0.00398597i
$652$	7.28160	−	2.13807i	0.285170	−	0.0837333i
$653$	13.5754	+	8.72440i	0.531247	+	0.341412i	0.778607	−	0.627512i	$-0.215927\pi$
$653$	13.5754	+	8.72440i	0.531247	+	0.341412i	−0.247360	+	0.968924i	$0.579563\pi$
$654$	−0.0167766	−	0.116684i	−0.000656016	−	0.00456269i
$655$	−39.0037	−	85.4062i	−1.52400	−	3.33710i
$656$	1.56057	+	3.41718i	0.0609301	+	0.133418i
$657$	−2.02769	−	14.1029i	−0.0791078	−	0.550207i
$658$	−3.54435	−	2.27781i	−0.138173	−	0.0887984i
$659$	−23.9721	+	7.03884i	−0.933820	+	0.274194i	−0.713035	−	0.701128i	$-0.752680\pi$
$659$	−23.9721	+	7.03884i	−0.933820	+	0.274194i	−0.220785	+	0.975323i	$0.570862\pi$
$660$	0.00346085	−	0.0240708i	0.000134713	−	0.000936953i
$661$	−10.8159	+	12.4823i	−0.420691	+	0.485504i	−0.926047	−	0.377407i	$-0.876816\pi$
$661$	−10.8159	+	12.4823i	−0.420691	+	0.485504i	0.505356	+	0.862911i	$0.331361\pi$
$662$	20.7631	−	13.3437i	0.806982	−	0.518616i
$663$	−0.272518	−	0.314503i	−0.0105837	−	0.0122143i
$664$	−3.83428	−	1.12584i	−0.148799	−	0.0436913i
$665$	−10.7371	+	23.5110i	−0.416367	+	0.911716i
$666$	13.0720			0.506531
$667$	−1.52384	−	0.445509i	−0.0590032	−	0.0172502i
$668$	−4.02956			−0.155908
$669$	−0.151042	+	0.330736i	−0.00583963	+	0.0127870i
$670$	−52.8820	−	15.5276i	−2.04301	−	0.599882i
$671$	1.61550	+	1.86438i	0.0623656	+	0.0719738i
$672$	−0.0124123	+	0.00797690i	−0.000478815	+	0.000307716i
$673$	10.0433	−	11.5906i	0.387142	−	0.446786i	−0.528408	−	0.848991i	$-0.677211\pi$
$673$	10.0433	−	11.5906i	0.387142	−	0.446786i	0.915550	+	0.402205i	$0.131756\pi$
$674$	4.65766	−	32.3947i	0.179406	−	1.24780i
$675$	−1.04968	+	0.308214i	−0.0404022	+	0.0118632i
$676$	0.469680	+	0.301845i	0.0180646	+	0.0116094i
$677$	5.61770	+	39.0720i	0.215906	+	1.50166i	0.752936	+	0.658094i	$0.228637\pi$
$677$	5.61770	+	39.0720i	0.215906	+	1.50166i	−0.537030	+	0.843563i	$0.680454\pi$
$678$	0.0979383	+	0.214455i	0.00376130	+	0.00823609i
$679$	4.95870	+	10.8580i	0.190298	+	0.416694i
$680$	4.54172	+	31.5884i	0.174167	+	1.21136i
$681$	−0.161166	−	0.103575i	−0.00617591	−	0.00396901i
$682$	−2.64325	+	0.776129i	−0.101215	+	0.0297195i
$683$	5.86810	−	40.8136i	0.224537	−	1.56169i	−0.496032	−	0.868304i	$-0.665210\pi$
$683$	5.86810	−	40.8136i	0.224537	−	1.56169i	0.720569	−	0.693383i	$-0.243881\pi$
$684$	12.1868	−	14.0644i	0.465976	−	0.537764i
$685$	5.29601	−	3.40354i	0.202350	−	0.130043i
$686$	−0.654861	−	0.755750i	−0.0250027	−	0.0288547i
$687$	−0.407364	−	0.119613i	−0.0155419	−	0.00456351i
$688$	1.64143	−	3.59424i	0.0625791	−	0.137029i
$689$	11.4957			0.437951
$690$	−0.282771	+	0.0833874i	−0.0107649	+	0.00317450i
$691$	−8.82128			−0.335577			−0.167789	−	0.985823i	$-0.553663\pi$
$691$	−8.82128			−0.335577			−0.167789	+	0.985823i	$0.553663\pi$
$692$	−5.77236	+	12.6397i	−0.219432	+	0.480490i
$693$	−1.13864	−	0.334335i	−0.0432534	−	0.0127003i
$694$	4.47388	+	5.16314i	0.169826	+	0.195990i
$695$	75.5267	−	48.5381i	2.86489	−	1.84115i
$696$	0.00319859	−	0.00369137i	0.000121242	−	0.000139921i
$697$	−4.09515	+	28.4824i	−0.155115	+	1.07885i
$698$	−1.22220	+	0.358871i	−0.0462611	+	0.0135835i
$699$	0.0245069	+	0.0157496i	0.000926934	+	0.000595705i
$700$	−1.75875	−	12.2324i	−0.0664746	−	0.462341i
$701$	−15.3050	−	33.5132i	−0.578061	−	1.26578i	−0.942393	−	0.334508i	$-0.891430\pi$
$701$	−15.3050	−	33.5132i	−0.578061	−	1.26578i	0.364332	−	0.931269i	$-0.381297\pi$
$702$	−0.135408	−	0.296503i	−0.00511066	−	0.0111908i
$703$	3.84730	+	26.7586i	0.145104	+	1.00922i
$704$	−0.332799	−	0.213877i	−0.0125428	−	0.00806079i
$705$	0.248501	−	0.0729666i	0.00935910	−	0.00274808i
$706$	−4.67711	+	32.5300i	−0.176025	+	1.22428i
$707$	7.04133	−	8.12612i	0.264816	−	0.305614i
$708$	0.0629480	−	0.0404542i	0.00236573	−	0.00152036i
$709$	21.0514	+	24.2946i	0.790601	+	0.912402i	0.997827	−	0.0658909i	$-0.0209889\pi$
$709$	21.0514	+	24.2946i	0.790601	+	0.912402i	−0.207226	+	0.978293i	$0.566443\pi$
$710$	−10.6314	−	3.12167i	−0.398990	−	0.117154i
$711$	2.08356	−	4.56235i	0.0781394	−	0.171102i
$712$	8.17767			0.306471
$713$	21.8997	+	25.2141i	0.820151	+	0.944277i
$714$	−0.113017			−0.00422955
$715$	−2.52111	+	5.52047i	−0.0942843	+	0.206454i
$716$	7.86870	+	2.31046i	0.294067	+	0.0863459i
$717$	0.119612	+	0.138039i	0.00446698	+	0.00515517i
$718$	24.1062	−	15.4921i	0.899637	−	0.578162i
$719$	0.622614	−	0.718534i	0.0232196	−	0.0267968i	−0.744021	−	0.668156i	$-0.767084\pi$
$719$	0.622614	−	0.718534i	0.0232196	−	0.0267968i	0.767241	+	0.641359i	$0.221629\pi$
$720$	−1.77866	+	12.3708i	−0.0662866	+	0.461033i
$721$	−15.0475	+	4.41835i	−0.560398	+	0.164548i
$722$	16.3928	+	10.5350i	0.610078	+	0.392073i
$723$	−0.0232340	−	0.161596i	−0.000864083	−	0.00600983i
$724$	−6.09162	−	13.3388i	−0.226393	−	0.495732i
$725$	1.69950	+	3.72139i	0.0631179	+	0.138209i
$726$	−0.0227691	−	0.158362i	−0.000845039	−	0.00587738i
$727$	18.9497	+	12.1783i	0.702807	+	0.451666i	0.842618	−	0.538512i	$-0.181013\pi$
$727$	18.9497	+	12.1783i	0.702807	+	0.451666i	−0.139811	+	0.990178i	$0.544650\pi$
$728$	3.53301	−	1.03738i	0.130942	−	0.0384480i
$729$	3.84083	−	26.7135i	0.142253	−	0.989391i
$730$	−12.9588	+	14.9552i	−0.479625	+	0.553517i
$731$	25.4616	−	16.3632i	0.941733	−	0.605215i
$732$	0.0602527	+	0.0695354i	0.00222701	+	0.00257010i
$733$	14.2302	+	4.17837i	0.525606	+	0.154332i	0.533762	−	0.845635i	$-0.320778\pi$
$733$	14.2302	+	4.17837i	0.525606	+	0.154332i	−0.00815598	+	0.999967i	$0.502596\pi$
$734$	−7.89140	+	17.2798i	−0.291277	+	0.637807i
$735$	0.0614720			0.00226743
$736$	−0.676980	+	4.74781i	−0.0249538	+	0.175007i
$737$	5.23322			0.192768
$738$	−4.68138	+	10.2508i	−0.172324	+	0.377337i
$739$	8.59412	+	2.52346i	0.316140	+	0.0928270i	0.435953	−	0.899969i	$-0.356411\pi$
$739$	8.59412	+	2.52346i	0.316140	+	0.0928270i	−0.119813	+	0.992796i	$0.538230\pi$
$740$	−11.8893	−	13.7209i	−0.437058	−	0.504391i
$741$	0.283536	−	0.182217i	0.0104159	−	0.00669392i
$742$	2.04447	−	2.35945i	0.0750550	−	0.0866181i
$743$	−3.96119	+	27.5507i	−0.145322	+	1.01074i	0.778426	+	0.627736i	$0.216018\pi$
$743$	−3.96119	+	27.5507i	−0.145322	+	1.01074i	−0.923748	+	0.383000i	$0.874891\pi$
$744$	−0.0985846	+	0.0289471i	−0.00361429	+	0.00106125i
$745$	−35.8885	−	23.0642i	−1.31485	−	0.845005i
$746$	1.03809	+	7.22008i	0.0380072	+	0.264346i
$747$	−4.97982	−	10.9043i	−0.182202	−	0.398967i
$748$	−1.25880	−	2.75638i	−0.0460262	−	0.100783i
$749$	0.584941	+	4.06835i	0.0213733	+	0.148654i
$750$	0.380518	+	0.244544i	0.0138945	+	0.00892948i
$751$	−9.64699	+	2.83261i	−0.352024	+	0.103364i	−0.452964	−	0.891529i	$-0.649633\pi$
$751$	−9.64699	+	2.83261i	−0.352024	+	0.103364i	0.100940	+	0.994893i	$0.467815\pi$
$752$	0.599597	−	4.17029i	0.0218651	−	0.152075i
$753$	0.0319540	−	0.0368769i	0.00116447	−	0.00134387i
$754$	−1.02545	+	0.659016i	−0.0373447	+	0.0240000i
$755$	−45.4907	−	52.4991i	−1.65558	−	1.91064i
$756$	−0.0849381	−	0.0249401i	−0.00308917	−	0.000907062i
$757$	−8.72838	+	19.1125i	−0.317238	+	0.694655i	−0.999330	−	0.0366121i	$-0.988343\pi$
$757$	−8.72838	+	19.1125i	−0.317238	+	0.694655i	0.682091	+	0.731267i	$0.261071\pi$
$758$	−12.4441			−0.451991
$759$	0.0235313	−	0.0151615i	0.000854131	−	0.000550326i
$760$	−25.8467			−0.937557
$761$	6.08615	−	13.3268i	0.220623	−	0.483097i	−0.766663	−	0.642049i	$-0.778084\pi$
$761$	6.08615	−	13.3268i	0.220623	−	0.483097i	0.987286	+	0.158953i	$0.0508117\pi$
$762$	−0.175825	−	0.0516269i	−0.00636947	−	0.00187024i
$763$	5.23211	+	6.03817i	0.189415	+	0.218597i
$764$	−14.3194	+	9.20252i	−0.518058	+	0.332935i
$765$	−62.6916	+	72.3499i	−2.26662	+	2.61582i
$766$	−0.755944	+	5.25771i	−0.0273134	+	0.189969i
$767$	−17.9174	+	5.26102i	−0.646959	+	0.189964i
$768$	−0.0124123	−	0.00797690i	−0.000447890	−	0.000287842i
$769$	−4.35205	−	30.2692i	−0.156939	−	1.09153i	−0.904232	−	0.427041i	$-0.859556\pi$
$769$	−4.35205	−	30.2692i	−0.156939	−	1.09153i	0.747293	−	0.664494i	$-0.231353\pi$
$770$	0.684683	+	1.49925i	0.0246743	+	0.0540291i
$771$	−0.122886	−	0.269082i	−0.00442562	−	0.00969075i
$772$	0.611320	+	4.25183i	0.0220019	+	0.153027i
$773$	−31.8972	−	20.4991i	−1.14726	−	0.737301i	−0.178171	−	0.984000i	$-0.557018\pi$
$773$	−31.8972	−	20.4991i	−1.14726	−	0.737301i	−0.969092	+	0.246698i	$0.920654\pi$
$774$	11.3729	−	3.33940i	0.408792	−	0.120032i
$775$	12.2475	−	85.1831i	0.439942	−	3.05987i
$776$	−7.81691	+	9.02119i	−0.280611	+	0.323842i
$777$	0.0540886	−	0.0347606i	0.00194042	−	0.00124703i
$778$	−3.22608	−	3.72309i	−0.115660	−	0.133479i
$779$	−22.3613	−	6.56586i	−0.801175	−	0.235246i
$780$	−0.0940292	+	0.205895i	−0.00336678	+	0.00737223i
$781$	1.05209			0.0376467
$782$	−24.0240	+	27.7906i	−0.859097	+	0.993791i
$783$	0.0293053			0.00104728
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−17.6803	−	5.19142i	−0.631038	−	0.185290i
$786$	0.217744	+	0.251290i	0.00776667	+	0.00896321i
$787$	−19.6267	+	12.6133i	−0.699617	+	0.449617i	−0.841493	−	0.540268i	$-0.818323\pi$
$787$	−19.6267	+	12.6133i	−0.699617	+	0.449617i	0.141876	+	0.989884i	$0.454687\pi$
$788$	9.64684	−	11.1330i	0.343654	−	0.396598i
$789$	0.0330042	−	0.229549i	0.00117498	−	0.00817216i
$790$	−6.68386	+	1.96256i	−0.237801	+	0.0698246i
$791$	−13.4422	−	8.63880i	−0.477951	−	0.307161i
$792$	−0.168887	−	1.17463i	−0.00600112	−	0.0417387i
$793$	−9.53866	−	20.8868i	−0.338728	−	0.741710i
$794$	3.72008	+	8.14584i	0.132021	+	0.289085i
$795$	0.0273124	+	0.189962i	0.000968672	+	0.00673726i
$796$	−14.1272	−	9.07898i	−0.500724	−	0.321796i
$797$	17.2619	−	5.06857i	0.611450	−	0.179538i	0.0386765	−	0.999252i	$-0.487686\pi$
$797$	17.2619	−	5.06857i	0.611450	−	0.179538i	0.572773	+	0.819714i	$0.305868\pi$
$798$	0.0130265	−	0.0906014i	0.000461134	−	0.00320725i
$799$	21.1338	−	24.3897i	0.747658	−	0.862844i
$800$	10.3964	−	6.68134i	0.367567	−	0.236221i
$801$	16.0645	+	18.5395i	0.567612	+	0.655060i
$802$	−4.58603	−	1.34658i	−0.161938	−	0.0475494i
$803$	0.780548	−	1.70916i	0.0275449	−	0.0603150i
$804$	0.195182			0.00688353
$805$	13.0671	−	15.1158i	0.460555	−	0.532763i
$806$	25.6416			0.903186
$807$	0.0959102	−	0.210014i	0.00337620	−	0.00739285i
$808$	10.3169	+	3.02930i	0.362946	+	0.106570i
$809$	0.805280	+	0.929343i	0.0283121	+	0.0326739i	0.769729	−	0.638371i	$-0.220391\pi$
$809$	0.805280	+	0.929343i	0.0283121	+	0.0326739i	−0.741417	+	0.671045i	$0.765846\pi$
$810$	−31.5375	+	20.2679i	−1.10811	+	0.712142i
$811$	−18.8486	+	21.7524i	−0.661863	+	0.763831i	−0.983080	−	0.183175i	$-0.941363\pi$
$811$	−18.8486	+	21.7524i	−0.661863	+	0.763831i	0.321217	+	0.947006i	$0.395908\pi$
$812$	−0.0471123	+	0.327674i	−0.00165332	+	0.0114991i
$813$	−0.0378583	+	0.0111162i	−0.00132775	+	0.000389862i
$814$	1.45023	+	0.932003i	0.0508304	+	0.0326667i
$815$	−4.49974	−	31.2964i	−0.157619	−	1.09626i
$816$	−0.0469490	−	0.102804i	−0.00164354	−	0.00359886i
$817$	10.1830	+	22.2977i	0.356258	+	0.780097i
$818$	4.60781	+	32.0480i	0.161108	+	1.12053i
$819$	9.29222	+	5.97175i	0.324696	+	0.208670i
$820$	15.0174	−	4.40952i	0.524432	−	0.153987i
$821$	−0.944653	+	6.57021i	−0.0329686	+	0.229302i	−0.999643	−	0.0267061i	$-0.991498\pi$
$821$	−0.944653	+	6.57021i	−0.0329686	+	0.229302i	0.966675	+	0.256008i	$0.0824073\pi$
$822$	−0.0145997	+	0.0168490i	−0.000509223	+	0.000587675i
$823$	−7.90771	+	5.08198i	−0.275646	+	0.177147i	−0.671159	−	0.741314i	$-0.734203\pi$
$823$	−7.90771	+	5.08198i	−0.275646	+	0.177147i	0.395513	+	0.918460i	$0.370567\pi$
$824$	−10.2700	−	11.8522i	−0.357773	−	0.412892i
$825$	−0.0692113	−	0.0203223i	−0.00240963	−	0.000707531i
$826$	−2.10674	+	4.61313i	−0.0733030	+	0.160511i
$827$	−27.0794			−0.941643			−0.470821	−	0.882229i	$-0.656042\pi$
$827$	−27.0794			−0.941643			−0.470821	+	0.882229i	$0.656042\pi$
$828$	−12.0936	+	7.79202i	−0.420281	+	0.270791i
$829$	−19.4994			−0.677242			−0.338621	−	0.940923i	$-0.609960\pi$
$829$	−19.4994			−0.677242			−0.338621	+	0.940923i	$0.609960\pi$
$830$	−6.91633	+	15.1447i	−0.240069	+	0.525679i
$831$	−0.0962368	−	0.0282577i	−0.00333842	−	0.000980248i
$832$	2.41130	+	2.78279i	0.0835969	+	0.0964759i
$833$	6.44385	−	4.14121i	0.223266	−	0.143484i
$834$	−0.208207	+	0.240284i	−0.00720963	+	0.00832036i
$835$	−2.38924	+	16.6175i	−0.0826830	+	0.575073i
$836$	2.35478	−	0.691425i	0.0814416	−	0.0239134i
$837$	−0.518597	−	0.333282i	−0.0179253	−	0.0115199i
$838$	−0.110797	−	0.770609i	−0.00382741	−	0.0266202i
$839$	17.5635	+	38.4587i	0.606359	+	1.32774i	0.925036	+	0.379878i	$0.124034\pi$
$839$	17.5635	+	38.4587i	0.606359	+	1.32774i	−0.318677	+	0.947863i	$0.603239\pi$
$840$	0.0255364	+	0.0559169i	0.000881090	+	0.00192932i
$841$	4.11153	+	28.5963i	0.141777	+	0.986081i
$842$	25.9446	+	16.6736i	0.894110	+	0.574609i
$843$	−0.214308	+	0.0629264i	−0.00738115	+	0.00216730i
$844$	−1.22349	+	8.50954i	−0.0421141	+	0.292910i
$845$	1.52327	−	1.75795i	0.0524020	−	0.0604752i
$846$	10.6323	−	6.83295i	0.365545	−	0.234922i
$847$	7.10098	+	8.19497i	0.243993	+	0.281583i
$848$	2.99553	+	0.879568i	0.102867	+	0.0302045i
$849$	0.134756	−	0.295075i	0.00462483	−	0.0101270i
$850$	94.6614			3.24686
$851$	2.95005	−	20.6893i	0.101126	−	0.709222i
$852$	0.0392395			0.00134432
$853$	11.1576	−	24.4318i	0.382030	−	0.836528i	−0.616751	−	0.787158i	$-0.711551\pi$
$853$	11.1576	−	24.4318i	0.382030	−	0.836528i	0.998781	−	0.0493699i	$-0.0157213\pi$
$854$	−5.98335	−	1.75687i	−0.204746	−	0.0601188i
$855$	−50.7742	−	58.5966i	−1.73644	−	2.00396i
$856$	−3.45771	+	2.22214i	−0.118182	+	0.0759510i
$857$	16.5754	−	19.1290i	0.566205	−	0.653435i	−0.398376	−	0.917222i	$-0.630426\pi$
$857$	16.5754	−	19.1290i	0.566205	−	0.653435i	0.964581	+	0.263787i	$0.0849716\pi$
$858$	0.00305868	−	0.0212736i	0.000104422	−	0.000726268i
$859$	27.1213	−	7.96353i	0.925367	−	0.271712i	0.215871	−	0.976422i	$-0.430741\pi$
$859$	27.1213	−	7.96353i	0.925367	−	0.271712i	0.709496	+	0.704710i	$0.248923\pi$
$860$	−13.8491	−	8.90025i	−0.472249	−	0.303496i
$861$	0.00788819	+	0.0548636i	0.000268829	+	0.00186975i
$862$	10.1402	+	22.2038i	0.345375	+	0.756266i
$863$	−6.82917	−	14.9538i	−0.232468	−	0.509033i	0.757066	−	0.653339i	$-0.226632\pi$
$863$	−6.82917	−	14.9538i	−0.232468	−	0.509033i	−0.989533	+	0.144306i	$0.953905\pi$
$864$	−0.0125983	−	0.0876229i	−0.000428602	−	0.00298099i
$865$	48.7024	+	31.2991i	1.65593	+	1.06420i
$866$	−24.4520	+	7.17976i	−0.830913	+	0.243978i
$867$	0.0875040	−	0.608604i	0.00297179	−	0.0206693i
$868$	4.56027	−	5.26284i	0.154786	−	0.178632i
$869$	0.556436	−	0.357600i	0.0188758	−	0.0121307i
$870$	−0.0133263	−	0.0153794i	−0.000451805	−	0.000521411i
$871$	−46.7367	−	13.7231i	−1.58361	−	0.464991i
$872$	−3.31902	+	7.26764i	−0.112396	+	0.246113i
$873$	−35.8076			−1.21191
$874$	−19.5096	−	22.4623i	−0.659924	−	0.759800i
$875$	−30.6565			−1.03638
$876$	0.0291119	−	0.0637461i	0.000983598	−	0.00215378i
$877$	−28.0979	−	8.25027i	−0.948797	−	0.278592i	−0.229511	−	0.973306i	$-0.573713\pi$
$877$	−28.0979	−	8.25027i	−0.948797	−	0.278592i	−0.719286	+	0.694714i	$0.755531\pi$
$878$	−7.00979	−	8.08973i	−0.236569	−	0.273015i
$879$	−0.0267484	+	0.0171902i	−0.000902202	+	0.000579810i
$880$	−1.07934	+	1.24562i	−0.0363844	+	0.0419898i
$881$	−3.56857	+	24.8199i	−0.120228	+	0.836204i	0.837069	+	0.547098i	$0.184267\pi$
$881$	−3.56857	+	24.8199i	−0.120228	+	0.836204i	−0.957297	+	0.289107i	$0.906642\pi$
$882$	2.87827	−	0.845136i	0.0969164	−	0.0284572i
$883$	32.1058	+	20.6331i	1.08045	+	0.694360i	0.954660	−	0.297698i	$-0.0962187\pi$
$883$	32.1058	+	20.6331i	1.08045	+	0.694360i	0.125785	+	0.992058i	$0.459855\pi$
$884$	4.01394	+	27.9176i	0.135004	+	0.938970i
$885$	−0.129506	−	0.283578i	−0.00435329	−	0.00953238i
$886$	−4.68990	−	10.2695i	−0.157560	−	0.345009i
$887$	1.95447	+	13.5936i	0.0656246	+	0.456429i	0.995966	+	0.0897339i	$0.0286016\pi$
$887$	1.95447	+	13.5936i	0.0656246	+	0.456429i	−0.930341	+	0.366695i	$0.880489\pi$
$888$	0.0540886	+	0.0347606i	0.00181509	+	0.00116649i
$889$	11.9167	−	3.49905i	0.399672	−	0.117354i
$890$	4.84877	−	33.7239i	0.162531	−	1.13043i
$891$	2.33105	−	2.69018i	0.0780932	−	0.0901244i
$892$	20.7309	−	13.3229i	0.694121	−	0.446084i
$893$	17.1163	+	19.7533i	0.572776	+	0.661019i
$894$	0.144959	+	0.0425637i	0.00484814	+	0.00142354i
$895$	14.1937	−	31.0799i	0.474443	−	1.03889i
$896$	1.00000			0.0334077
$897$	−0.249911	+	0.0736972i	−0.00834428	+	0.00246068i
$898$	−25.7186			−0.858240
$899$	−0.957654	+	2.09697i	−0.0319395	+	0.0699379i
$900$	35.5702	+	10.4443i	1.18567	+	0.348145i
$901$	15.6603	+	18.0729i	0.521720	+	0.602097i
$902$	−1.25021	+	0.803463i	−0.0416275	+	0.0267524i
$903$	0.0381782	−	0.0440600i	0.00127049	−	0.00146623i
$904$	2.27402	−	15.8162i	0.0756329	−	0.526038i
$905$	−58.6199	+	17.2123i	−1.94859	+	0.572158i
$906$	0.206954	+	0.133001i	0.00687560	+	0.00441868i
$907$	6.65031	+	46.2540i	0.220820	+	1.53584i	0.734948	+	0.678124i	$0.237207\pi$
$907$	6.65031	+	46.2540i	0.220820	+	1.53584i	−0.514128	+	0.857714i	$0.671884\pi$
$908$	5.39391	+	11.8110i	0.179003	+	0.391963i
$909$	13.3992	+	29.3401i	0.444422	+	0.973148i
$910$	−2.18326	−	15.1849i	−0.0723743	−	0.503374i
$911$	22.9361	+	14.7401i	0.759907	+	0.488363i	0.862310	−	0.506380i	$-0.169017\pi$
$911$	22.9361	+	14.7401i	0.759907	+	0.488363i	−0.102403	+	0.994743i	$0.532653\pi$
$912$	0.0878253	−	0.0257878i	0.00290819	−	0.000853921i
$913$	0.224982	−	1.56478i	0.00744580	−	0.0517867i
$914$	6.55568	−	7.56566i	0.216843	−	0.250250i
$915$	0.322483	−	0.207247i	0.0106610	−	0.00685138i
$916$	18.8436	+	21.7467i	0.622610	+	0.718530i
$917$	−21.6229	−	6.34905i	−0.714050	−	0.209664i
$918$	0.281684	−	0.616801i	0.00929694	−	0.0203575i
$919$	45.7818			1.51020			0.755102	−	0.655608i	$-0.227588\pi$
$919$	45.7818			1.51020			0.755102	+	0.655608i	$0.227588\pi$
$920$	19.1781	+	5.60691i	0.632284	+	0.184854i
$921$	0.118962			0.00391992
$922$	3.24500	−	7.10556i	0.106868	−	0.234009i
$923$	−9.39598	−	2.75891i	−0.309272	−	0.0908106i
$924$	−0.00382234	−	0.00441122i	−0.000125746	−	0.000145118i
$925$	−45.3038	+	29.1150i	−1.48958	+	0.957295i
$926$	24.9187	−	28.7577i	0.818878	−	0.945035i
$927$	6.69518	−	46.5660i	0.219899	−	1.52943i
$928$	−0.317634	+	0.0932656i	−0.0104268	+	0.00306159i
$929$	1.21847	+	0.783064i	0.0399767	+	0.0256915i	0.560477	−	0.828170i	$-0.310618\pi$
$929$	1.21847	+	0.783064i	0.0399767	+	0.0256915i	−0.520500	+	0.853862i	$0.674254\pi$
$930$	0.0609214	+	0.423717i	0.00199769	+	0.0138942i
$931$	2.57712	+	5.64311i	0.0844617	+	0.184945i
$932$	−0.820195	−	1.79598i	−0.0268664	−	0.0588292i
$933$	−0.0282098	−	0.196203i	−0.000923546	−	0.00642341i
$934$	−12.2716	−	7.88647i	−0.401539	−	0.258053i
$935$	−12.1134	+	3.55683i	−0.396152	+	0.116321i
$936$	−1.57196	+	10.9333i	−0.0513813	+	0.357365i
$937$	−4.07246	+	4.69987i	−0.133042	+	0.153538i	−0.818361	−	0.574704i	$-0.805117\pi$
$937$	−4.07246	+	4.69987i	−0.133042	+	0.153538i	0.685320	+	0.728242i	$0.259663\pi$
$938$	−11.1286	+	7.15192i	−0.363362	+	0.233518i
$939$	0.196595	+	0.226883i	0.00641565	+	0.00740405i
$940$	−16.8424	−	4.94537i	−0.549338	−	0.161300i
$941$	22.2106	−	48.6345i	0.724045	−	1.58544i	−0.0841017	−	0.996457i	$-0.526802\pi$
$941$	22.2106	−	48.6345i	0.724045	−	1.58544i	0.808147	−	0.588981i	$-0.200471\pi$
$942$	0.0652563			0.00212616
$943$	15.1676	+	9.72266i	0.493926	+	0.316613i
$944$	−5.07142			−0.165061
$945$	−0.153213	+	0.335489i	−0.00498401	+	0.0109135i
$946$	1.49982	+	0.440386i	0.0487633	+	0.0143182i
$947$	26.9009	+	31.0453i	0.874162	+	1.00884i	0.999859	+	0.0167684i	$0.00533780\pi$
$947$	26.9009	+	31.0453i	0.874162	+	1.00884i	−0.125697	+	0.992069i	$0.540117\pi$
$948$	0.0207532	−	0.0133373i	0.000674033	−	0.000433175i
$949$	−11.4529	+	13.2173i	−0.371776	+	0.429052i
$950$	−10.9108	+	75.8864i	−0.353994	+	2.46208i
$951$	0.0592276	−	0.0173908i	0.00192059	−	0.000563935i
$952$	6.44385	+	4.14121i	0.208846	+	0.134217i
$953$	−6.55745	−	45.6080i	−0.212416	−	1.47739i	−0.765053	−	0.643967i	$-0.777287\pi$
$953$	−6.55745	−	45.6080i	−0.212416	−	1.47739i	0.552637	−	0.833422i	$-0.313622\pi$
$954$	3.89049	+	8.51899i	0.125959	+	0.275812i
$955$	29.4600	+	64.5083i	0.953302	+	2.08744i
$956$	−1.76177	−	12.2534i	−0.0569797	−	0.396303i
$957$	0.00162552	+	0.00104466i	5.25456e−5	+	3.37690e-5i
$958$	−16.2399	+	4.76848i	−0.524689	+	0.154063i
$959$	0.215040	−	1.49564i	0.00694401	−	0.0482967i
$960$	−0.0402556	+	0.0464575i	−0.00129924	+	0.00149941i
$961$	14.7165	−	9.45772i	0.474726	−	0.305088i
$962$	−10.5076	−	12.1265i	−0.338780	−	0.390973i
$963$	−11.8302	−	3.47367i	−0.381224	−	0.111937i
$964$	−4.59654	+	10.0650i	−0.148045	+	0.324173i
$965$	17.8966			0.576112
$966$	−0.0293198	+	0.0644000i	−0.000943348	+	0.00207204i
$967$	−25.6216			−0.823934			−0.411967	−	0.911199i	$-0.635158\pi$
$967$	−25.6216			−0.823934			−0.411967	+	0.911199i	$0.635158\pi$
$968$	−4.50455	+	9.86360i	−0.144782	+	0.317028i
$969$	0.672726	+	0.197530i	0.0216111	+	0.00634558i
$970$	32.5677	+	37.5851i	1.04569	+	1.20679i
$971$	−11.5661	+	7.43307i	−0.371173	+	0.238539i	−0.712908	−	0.701258i	$-0.752622\pi$
$971$	−11.5661	+	7.43307i	−0.371173	+	0.238539i	0.341734	+	0.939797i	$0.388986\pi$
$972$	0.260853	−	0.301041i	0.00836687	−	0.00965588i
$973$	3.06670	−	21.3294i	0.0983140	−	0.683789i
$974$	−16.1278	+	4.73554i	−0.516767	+	0.151736i
$975$	0.564819	+	0.362987i	0.0180887	+	0.0116249i
$976$	−0.887468	−	6.17247i	−0.0284071	−	0.197576i
$977$	15.7472	+	34.4815i	0.503796	+	1.10316i	0.975217	+	0.221251i	$0.0710141\pi$
$977$	15.7472	+	34.4815i	0.503796	+	1.10316i	−0.471421	+	0.881908i	$0.656259\pi$
$978$	0.0465150	+	0.101854i	0.00148738	+	0.00325692i
$979$	0.460400	+	3.20215i	0.0147144	+	0.102341i
$980$	−3.50493	−	2.25248i	−0.111961	−	0.0719528i
$981$	−22.9964	+	6.75234i	−0.734217	+	0.215586i
$982$	3.40692	−	23.6957i	0.108719	−	0.756159i
$983$	−24.6182	+	28.4109i	−0.785198	+	0.906167i	−0.997473	−	0.0710433i	$-0.977367\pi$
$983$	−24.6182	+	28.4109i	−0.785198	+	0.906167i	0.212275	+	0.977210i	$0.431913\pi$
$984$	−0.0466288	+	0.0299665i	−0.00148647	+	0.000955297i
$985$	−40.1918	−	46.3838i	−1.28062	−	1.47791i
$986$	−2.43301	−	0.714397i	−0.0774830	−	0.0227510i
$987$	0.0258236	−	0.0565458i	0.000821975	−	0.00179987i
$988$	−22.8431			−0.726736
$989$	−2.71872	−	18.7538i	−0.0864503	−	0.596336i
$990$	−4.94421			−0.157137
$991$	−15.7288	+	34.4414i	−0.499643	+	1.09407i	0.476942	+	0.878935i	$0.341745\pi$
$991$	−15.7288	+	34.4414i	−0.499643	+	1.09407i	−0.976585	+	0.215131i	$0.930982\pi$
$992$	6.68165	+	1.96191i	0.212143	+	0.0622907i
$993$	0.238474	+	0.275213i	0.00756773	+	0.00873363i
$994$	−2.23730	+	1.43783i	−0.0709629	+	0.0456051i
$995$	−45.8173	+	52.8759i	−1.45250	+	1.67628i
$996$	0.00839107	−	0.0583611i	0.000265881	−	0.00184924i
$997$	20.8133	−	6.11135i	0.659165	−	0.193548i	0.0649924	−	0.997886i	$-0.479298\pi$
$997$	20.8133	−	6.11135i	0.659165	−	0.193548i	0.594173	+	0.804337i	$0.297480\pi$
$998$	10.7594	+	6.91467i	0.340584	+	0.218880i
$999$	0.0548990	+	0.381831i	0.00173693	+	0.0120806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.c.29.1	✓	20
23.2	even	11		7406.2.a.bp.1.7		10
23.4	even	11	inner	322.2.i.c.211.1	yes	20
23.21	odd	22		7406.2.a.bo.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.c.29.1	✓	20	1.1	even	1	trivial
322.2.i.c.211.1	yes	20	23.4	even	11	inner
7406.2.a.bo.1.7		10	23.21	odd	22
7406.2.a.bp.1.7		10	23.2	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.0141569 + 0.00415683i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-3.50493 + 2.25248i) q^{5} +(0.00966216 - 0.0111507i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.52358 - 1.62180i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.0141569 + 0.00415683i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-3.50493 + 2.25248i) q^{5} +(0.00966216 - 0.0111507i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.52358 - 1.62180i) q^{9} +(0.592928 + 4.12391i) q^{10} +(-0.164338 - 0.359850i) q^{11} +(-0.00612925 - 0.0134212i) q^{12} +(0.524026 + 3.64468i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-0.0589820 + 0.0173187i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.01611 + 5.78890i) q^{17} +(-2.52358 + 1.62180i) q^{18} +(-4.06258 - 4.68846i) q^{19} +(3.99755 + 1.17379i) q^{20} +(-0.00612925 + 0.0134212i) q^{21} -0.395599 q^{22} +(1.99735 + 4.36011i) q^{23} -0.0147545 q^{24} +(5.13377 - 11.2414i) q^{25} +(3.53301 + 1.03738i) q^{26} +(-0.0579709 - 0.0669020i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-0.216787 + 0.250186i) q^{29} +(-0.00874838 + 0.0608463i) q^{30} +(6.68165 - 1.96191i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.000830675 - 0.00577747i) q^{33} +(3.18200 + 6.96761i) q^{34} +(-1.73075 - 3.78981i) q^{35} +(0.426914 + 2.96925i) q^{36} +(-3.66590 - 2.35593i) q^{37} +(-5.95243 + 1.74779i) q^{38} +(-0.00773176 + 0.0537756i) q^{39} +(2.72836 - 3.14869i) q^{40} +(3.16030 - 2.03100i) q^{41} +(0.00966216 + 0.0111507i) q^{42} +(-3.79125 - 1.11321i) q^{43} +(-0.164338 + 0.359850i) q^{44} +12.4980 q^{45} +(4.79583 - 0.00559465i) q^{46} -4.21317 q^{47} +(-0.00612925 + 0.0134212i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-8.09289 - 9.33969i) q^{50} +(-0.0950759 + 0.0611016i) q^{51} +(2.41130 - 2.78279i) q^{52} +(0.444306 - 3.09022i) q^{53} +(-0.0849381 + 0.0249401i) q^{54} +(1.38655 + 0.891079i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-0.0380242 - 0.0832614i) q^{57} +(0.137520 + 0.301127i) q^{58} +(0.721739 + 5.01980i) q^{59} +(0.0517136 + 0.0332343i) q^{60} +(-5.98335 + 1.75687i) q^{61} +(0.991042 - 6.89285i) q^{62} +(1.96444 - 2.26708i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-10.0462 - 11.5940i) q^{65} +(-0.00560044 - 0.00164444i) q^{66} +(-5.49536 + 12.0332i) q^{67} +7.65981 q^{68} +(0.0101519 + 0.0700282i) q^{69} -4.16631 q^{70} +(-1.10479 + 2.41915i) q^{71} +(2.87827 + 0.845136i) q^{72} +(3.11036 + 3.58955i) q^{73} +(-3.66590 + 2.35593i) q^{74} +(0.119407 - 0.137803i) q^{75} +(-0.882882 + 6.14058i) q^{76} +(0.379575 - 0.111453i) q^{77} +(0.0457041 + 0.0293722i) q^{78} +(0.237949 + 1.65497i) q^{79} +(-1.73075 - 3.78981i) q^{80} +(3.73792 + 8.18491i) q^{81} +(-0.534628 - 3.71842i) q^{82} +(3.36177 + 2.16048i) q^{83} +(0.0141569 - 0.00415683i) q^{84} +(4.54172 - 31.5884i) q^{85} +(-2.58756 + 2.98620i) q^{86} +(-0.00410901 + 0.00264070i) q^{87} +(0.259062 + 0.298974i) q^{88} +(-7.84641 - 2.30392i) q^{89} +(5.19187 - 11.3686i) q^{90} -3.68216 q^{91} +(1.98717 - 4.36476i) q^{92} +0.102747 q^{93} +(-1.75022 + 3.83244i) q^{94} +(24.7997 + 7.28185i) q^{95} +(0.00966216 + 0.0111507i) q^{96} +(10.0418 - 6.45349i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-0.168887 + 1.17463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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