LMFDB - Embedded newform 230.2.g.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (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:	$1.83655924649$
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} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
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			121.2
Root			$1.92732 - 0.565914i$ of defining polynomial
Character	$\chi$	$=$	230.121
Dual form			230.2.g.b.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.248602 - 0.0729960i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.169672 - 0.195812i) q^{6} +(0.663794 - 4.61679i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.46729 - 1.58563i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.248602 - 0.0729960i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.169672 - 0.195812i) q^{6} +(0.663794 - 4.61679i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.46729 - 1.58563i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-1.30572 - 2.85912i) q^{11} +(0.107633 + 0.235683i) q^{12} +(0.713186 + 4.96032i) q^{13} +(3.92383 + 2.52169i) q^{14} +(-0.248602 + 0.0729960i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.20986 - 4.85844i) q^{17} +(2.46729 - 1.58563i) q^{18} +(3.72757 + 4.30184i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-0.502028 + 1.09929i) q^{21} +3.14316 q^{22} +(-0.267084 - 4.78839i) q^{23} -0.259097 q^{24} +(0.415415 - 0.909632i) q^{25} +(-4.80833 - 1.41185i) q^{26} +(1.00664 + 1.16173i) q^{27} +(-3.92383 + 2.52169i) q^{28} +(-2.62657 + 3.03122i) q^{29} +(0.0368733 - 0.256460i) q^{30} +(-0.120675 + 0.0354335i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.115899 + 0.806093i) q^{33} +(2.67055 + 5.84769i) q^{34} +(-1.93761 - 4.24277i) q^{35} +(0.417391 + 2.90302i) q^{36} +(0.702484 + 0.451459i) q^{37} +(-5.46158 + 1.60367i) q^{38} +(0.184784 - 1.28520i) q^{39} +(0.654861 - 0.755750i) q^{40} +(-9.63443 + 6.19167i) q^{41} +(-0.791397 - 0.913321i) q^{42} +(6.90258 + 2.02678i) q^{43} +(-1.30572 + 2.85912i) q^{44} -2.93287 q^{45} +(4.46662 + 1.74622i) q^{46} +5.35505 q^{47} +(0.107633 - 0.235683i) q^{48} +(-14.1577 - 4.15707i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-1.40123 + 0.900513i) q^{51} +(3.28172 - 3.78731i) q^{52} +(0.381558 - 2.65379i) q^{53} +(-1.47492 + 0.433076i) q^{54} +(-2.64419 - 1.69932i) q^{55} +(-0.663794 - 4.61679i) q^{56} +(-0.612663 - 1.34154i) q^{57} +(-1.66618 - 3.64843i) q^{58} +(0.766966 + 5.33437i) q^{59} +(0.217966 + 0.140078i) q^{60} +(-4.71579 + 1.38468i) q^{61} +(0.0178989 - 0.124490i) q^{62} +(-8.95829 + 10.3384i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.28172 + 3.78731i) q^{65} +(-0.781394 - 0.229438i) q^{66} +(2.96438 - 6.49109i) q^{67} -6.42863 q^{68} +(-0.283136 + 1.20990i) q^{69} +4.66427 q^{70} +(3.63593 - 7.96158i) q^{71} +(-2.81407 - 0.826285i) q^{72} +(10.0614 + 11.6115i) q^{73} +(-0.702484 + 0.451459i) q^{74} +(-0.169672 + 0.195812i) q^{75} +(0.810078 - 5.63422i) q^{76} +(-14.0667 + 4.13035i) q^{77} +(1.09230 + 0.701978i) q^{78} +(-0.735229 - 5.11363i) q^{79} +(0.415415 + 0.909632i) q^{80} +(3.48962 + 7.64120i) q^{81} +(-1.62986 - 11.3359i) q^{82} +(-11.6691 - 7.49925i) q^{83} +(1.15954 - 0.340473i) q^{84} +(0.914890 - 6.36320i) q^{85} +(-4.71106 + 5.43686i) q^{86} +(0.874237 - 0.561838i) q^{87} +(-2.05833 - 2.37544i) q^{88} +(10.8120 + 3.17469i) q^{89} +(1.21836 - 2.66783i) q^{90} +23.3741 q^{91} +(-3.44392 + 3.33758i) q^{92} +0.0325866 q^{93} +(-2.22457 + 4.87113i) q^{94} +(5.46158 + 1.60367i) q^{95} +(0.169672 + 0.195812i) q^{96} +(-1.33215 + 0.856119i) q^{97} +(9.66272 - 11.1514i) q^{98} +(-1.31193 + 9.12464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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
$3$	−0.248602	−	0.0729960i	−0.143530	−	0.0421443i	0.209178	−	0.977878i	$-0.432921\pi$
$3$	−0.248602	−	0.0729960i	−0.143530	−	0.0421443i	−0.352709	+	0.935733i	$0.614739\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	0.169672	−	0.195812i	0.0692685	−	0.0799401i
$7$	0.663794	−	4.61679i	0.250891	−	1.74498i	−0.342000	−	0.939700i	$-0.611104\pi$
$7$	0.663794	−	4.61679i	0.250891	−	1.74498i	0.592891	−	0.805283i	$-0.297987\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−2.46729	−	1.58563i	−0.822429	−	0.528543i
$10$	0.142315	+	0.989821i	0.0450039	+	0.313009i
$11$	−1.30572	−	2.85912i	−0.393688	−	0.862056i	−0.997871	−	0.0652111i	$-0.979228\pi$
$11$	−1.30572	−	2.85912i	−0.393688	−	0.862056i	0.604184	−	0.796845i	$-0.293499\pi$
$12$	0.107633	+	0.235683i	0.0310709	+	0.0680358i
$13$	0.713186	+	4.96032i	0.197802	+	1.37574i	0.810644	+	0.585539i	$0.199117\pi$
$13$	0.713186	+	4.96032i	0.197802	+	1.37574i	−0.612842	+	0.790205i	$0.709974\pi$
$14$	3.92383	+	2.52169i	1.04869	+	0.673951i
$15$	−0.248602	+	0.0729960i	−0.0641887	+	0.0188475i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	4.20986	−	4.85844i	1.02104	−	1.17834i	0.0371985	−	0.999308i	$-0.488157\pi$
$17$	4.20986	−	4.85844i	1.02104	−	1.17834i	0.983842	−	0.179036i	$-0.0572979\pi$
$18$	2.46729	−	1.58563i	0.581545	−	0.373736i
$19$	3.72757	+	4.30184i	0.855163	+	0.986911i	0.999997	−	0.00254515i	$-0.000810148\pi$
$19$	3.72757	+	4.30184i	0.855163	+	0.986911i	−0.144834	+	0.989456i	$0.546265\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	−0.502028	+	1.09929i	−0.109551	+	0.239884i
$22$	3.14316			0.670124
$23$	−0.267084	−	4.78839i	−0.0556908	−	0.998448i
$23$	−0.267084	−	4.78839i	−0.0556908	−	0.998448i
$24$	−0.259097			−0.0528879
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−4.80833	−	1.41185i	−0.942991	−	0.276887i
$27$	1.00664	+	1.16173i	0.193729	+	0.223575i
$28$	−3.92383	+	2.52169i	−0.741534	+	0.476555i
$29$	−2.62657	+	3.03122i	−0.487742	+	0.562884i	−0.945261	−	0.326316i	$-0.894193\pi$
$29$	−2.62657	+	3.03122i	−0.487742	+	0.562884i	0.457519	+	0.889200i	$0.348738\pi$
$30$	0.0368733	−	0.256460i	0.00673212	−	0.0468229i
$31$	−0.120675	+	0.0354335i	−0.0216740	+	0.00636405i	−0.292552	−	0.956250i	$-0.594504\pi$
$31$	−0.120675	+	0.0354335i	−0.0216740	+	0.00636405i	0.270878	+	0.962614i	$0.412686\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.115899	+	0.806093i	0.0201754	+	0.140323i
$34$	2.67055	+	5.84769i	0.457996	+	1.00287i
$35$	−1.93761	−	4.24277i	−0.327515	−	0.717158i
$36$	0.417391	+	2.90302i	0.0695651	+	0.483836i
$37$	0.702484	+	0.451459i	0.115488	+	0.0742195i	0.597110	−	0.802160i	$-0.296316\pi$
$37$	0.702484	+	0.451459i	0.115488	+	0.0742195i	−0.481622	+	0.876379i	$0.659952\pi$
$38$	−5.46158	+	1.60367i	−0.885986	+	0.260149i
$39$	0.184784	−	1.28520i	0.0295892	−	0.205797i
$40$	0.654861	−	0.755750i	0.103543	−	0.119494i
$41$	−9.63443	+	6.19167i	−1.50464	+	0.966976i	−0.510389	+	0.859943i	$0.670499\pi$
$41$	−9.63443	+	6.19167i	−1.50464	+	0.966976i	−0.994255	+	0.107033i	$0.965865\pi$
$42$	−0.791397	−	0.913321i	−0.122115	−	0.140929i
$43$	6.90258	+	2.02678i	1.05263	+	0.309081i	0.761881	−	0.647717i	$-0.224276\pi$
$43$	6.90258	+	2.02678i	1.05263	+	0.309081i	0.290753	+	0.956798i	$0.406094\pi$
$44$	−1.30572	+	2.85912i	−0.196844	+	0.431028i
$45$	−2.93287			−0.437206
$46$	4.46662	+	1.74622i	0.658568	+	0.257466i
$47$	5.35505			0.781115			0.390557	−	0.920579i	$-0.372282\pi$
$47$	5.35505			0.781115			0.390557	+	0.920579i	$0.372282\pi$
$48$	0.107633	−	0.235683i	0.0155355	−	0.0340179i
$49$	−14.1577	−	4.15707i	−2.02253	−	0.593867i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	−1.40123	+	0.900513i	−0.196211	+	0.126097i
$52$	3.28172	−	3.78731i	0.455093	−	0.525205i
$53$	0.381558	−	2.65379i	0.0524110	−	0.364527i	−0.946690	−	0.322145i	$-0.895596\pi$
$53$	0.381558	−	2.65379i	0.0524110	−	0.364527i	0.999101	−	0.0423820i	$-0.0134946\pi$
$54$	−1.47492	+	0.433076i	−0.200711	+	0.0589342i
$55$	−2.64419	−	1.69932i	−0.356543	−	0.229136i
$56$	−0.663794	−	4.61679i	−0.0887032	−	0.616945i
$57$	−0.612663	−	1.34154i	−0.0811491	−	0.177692i
$58$	−1.66618	−	3.64843i	−0.218780	−	0.479062i
$59$	0.766966	+	5.33437i	0.0998505	+	0.694475i	0.976841	+	0.213967i	$0.0686386\pi$
$59$	0.766966	+	5.33437i	0.0998505	+	0.694475i	−0.876990	+	0.480508i	$0.840452\pi$
$60$	0.217966	+	0.140078i	0.0281393	+	0.0180840i
$61$	−4.71579	+	1.38468i	−0.603795	+	0.177290i	−0.569321	−	0.822115i	$-0.692794\pi$
$61$	−4.71579	+	1.38468i	−0.603795	+	0.177290i	−0.0344741	+	0.999406i	$0.510976\pi$
$62$	0.0178989	−	0.124490i	0.00227317	−	0.0158102i
$63$	−8.95829	+	10.3384i	−1.12864	+	1.30252i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	3.28172	+	3.78731i	0.407047	+	0.469757i
$66$	−0.781394	−	0.229438i	−0.0961830	−	0.0282419i
$67$	2.96438	−	6.49109i	0.362157	−	0.793013i	−0.637587	−	0.770378i	$-0.720067\pi$
$67$	2.96438	−	6.49109i	0.362157	−	0.793013i	0.999744	−	0.0226343i	$-0.00720533\pi$
$68$	−6.42863			−0.779586
$69$	−0.283136	+	1.20990i	−0.0340856	+	0.145655i
$70$	4.66427			0.557486
$71$	3.63593	−	7.96158i	0.431506	−	0.944866i	−0.561574	−	0.827426i	$-0.689804\pi$
$71$	3.63593	−	7.96158i	0.431506	−	0.944866i	0.993080	−	0.117440i	$-0.0374687\pi$
$72$	−2.81407	−	0.826285i	−0.331641	−	0.0973786i
$73$	10.0614	+	11.6115i	1.17760	+	1.35902i	0.919589	+	0.392882i	$0.128522\pi$
$73$	10.0614	+	11.6115i	1.17760	+	1.35902i	0.258012	+	0.966142i	$0.416933\pi$
$74$	−0.702484	+	0.451459i	−0.0816621	+	0.0524811i
$75$	−0.169672	+	0.195812i	−0.0195921	+	0.0226105i
$76$	0.810078	−	5.63422i	0.0929224	−	0.646289i
$77$	−14.0667	+	4.13035i	−1.60305	+	0.470697i
$78$	1.09230	+	0.701978i	0.123679	+	0.0794834i
$79$	−0.735229	−	5.11363i	−0.0827197	−	0.575328i	−0.988459	−	0.151492i	$-0.951592\pi$
$79$	−0.735229	−	5.11363i	−0.0827197	−	0.575328i	0.905739	−	0.423836i	$-0.139317\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	3.48962	+	7.64120i	0.387736	+	0.849023i
$82$	−1.62986	−	11.3359i	−0.179987	−	1.25184i
$83$	−11.6691	−	7.49925i	−1.28085	−	0.823150i	−0.289854	−	0.957071i	$-0.593607\pi$
$83$	−11.6691	−	7.49925i	−1.28085	−	0.823150i	−0.990992	+	0.133921i	$0.957243\pi$
$84$	1.15954	−	0.340473i	0.126517	−	0.0371487i
$85$	0.914890	−	6.36320i	0.0992338	−	0.690186i
$86$	−4.71106	+	5.43686i	−0.508007	+	0.586271i
$87$	0.874237	−	0.561838i	0.0937280	−	0.0602353i
$88$	−2.05833	−	2.37544i	−0.219419	−	0.253223i
$89$	10.8120	+	3.17469i	1.14607	+	0.336516i	0.799005	−	0.601325i	$-0.205360\pi$
$89$	10.8120	+	3.17469i	1.14607	+	0.336516i	0.347065	+	0.937841i	$0.387178\pi$
$90$	1.21836	−	2.66783i	0.128426	−	0.281214i
$91$	23.3741			2.45028
$92$	−3.44392	+	3.33758i	−0.359053	+	0.347966i
$93$	0.0325866			0.00337908
$94$	−2.22457	+	4.87113i	−0.229447	+	0.502418i
$95$	5.46158	+	1.60367i	0.560347	+	0.164533i
$96$	0.169672	+	0.195812i	0.0173171	+	0.0199850i
$97$	−1.33215	+	0.856119i	−0.135259	+	0.0869257i	−0.606521	−	0.795068i	$-0.707435\pi$
$97$	−1.33215	+	0.856119i	−0.135259	+	0.0869257i	0.471261	+	0.881994i	$0.343799\pi$
$98$	9.66272	−	11.1514i	0.976082	−	1.12646i
$99$	−1.31193	+	9.12464i	−0.131853	+	0.917061i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	13.6072	+	8.74483i	1.35397	+	0.870144i	0.997929	−	0.0643268i	$-0.0204900\pi$
$101$	13.6072	+	8.74483i	1.35397	+	0.870144i	0.356041	+	0.934470i	$0.384126\pi$
$102$	−0.237045	−	1.64869i	−0.0234710	−	0.163244i
$103$	4.44685	+	9.73725i	0.438161	+	0.959440i	0.991932	+	0.126771i	$0.0404612\pi$
$103$	4.44685	+	9.73725i	0.438161	+	0.959440i	−0.553771	+	0.832669i	$0.686812\pi$
$104$	2.08178	+	4.55846i	0.204135	+	0.446994i
$105$	0.171987	+	1.19620i	0.0167842	+	0.116737i
$106$	2.25547	+	1.44950i	0.219071	+	0.140788i
$107$	−5.42247	+	1.59218i	−0.524210	+	0.153922i	−0.533122	−	0.846038i	$-0.678981\pi$
$107$	−5.42247	+	1.59218i	−0.524210	+	0.153922i	0.00891189	+	0.999960i	$0.497163\pi$
$108$	0.218765	−	1.52154i	0.0210506	−	0.146410i
$109$	2.89083	−	3.33619i	0.276891	−	0.319549i	−0.600222	−	0.799834i	$-0.704921\pi$
$109$	2.89083	−	3.33619i	0.276891	−	0.319549i	0.877113	+	0.480284i	$0.159467\pi$
$110$	2.64419	−	1.69932i	0.252114	−	0.162024i
$111$	−0.141684	−	0.163512i	−0.0134481	−	0.0155199i
$112$	4.47533	+	1.31408i	0.422879	+	0.124168i
$113$	−1.98780	+	4.35268i	−0.186997	+	0.409466i	−0.979791	−	0.200023i	$-0.935898\pi$
$113$	−1.98780	+	4.35268i	−0.186997	+	0.409466i	0.792794	+	0.609489i	$0.208625\pi$
$114$	1.47482			0.138130
$115$	−2.81348	−	3.88385i	−0.262359	−	0.362171i
$116$	4.01088			0.372401
$117$	6.10558	−	13.3694i	0.564462	−	1.23600i
$118$	−5.17092	−	1.51832i	−0.476022	−	0.139773i
$119$	−19.6359	−	22.6610i	−1.80002	−	2.07733i
$120$	−0.217966	+	0.140078i	−0.0198975	+	0.0127873i
$121$	0.733809	−	0.846861i	0.0667100	−	0.0769874i
$122$	0.699460	−	4.86485i	0.0633261	−	0.440443i
$123$	2.84710	−	0.835985i	0.256715	−	0.0753782i
$124$	0.105804	+	0.0679964i	0.00950152	+	0.00610626i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−5.68275	−	12.4435i	−0.506259	−	1.10855i
$127$	7.03877	+	15.4127i	0.624590	+	1.36766i	0.912134	+	0.409893i	$0.134434\pi$
$127$	7.03877	+	15.4127i	0.624590	+	1.36766i	−0.287544	+	0.957767i	$0.592839\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−1.56805	−	1.00772i	−0.138059	−	0.0887250i
$130$	−4.80833	+	1.41185i	−0.421718	+	0.123828i
$131$	0.597142	−	4.15321i	0.0521725	−	0.362868i	−0.946965	−	0.321338i	$-0.895868\pi$
$131$	0.597142	−	4.15321i	0.0521725	−	0.362868i	0.999137	−	0.0415304i	$-0.0132233\pi$
$132$	0.533307	−	0.615469i	0.0464184	−	0.0535697i
$133$	22.3351	−	14.3539i	1.93670	−	1.24464i
$134$	4.67305	+	5.39299i	0.403690	+	0.465883i
$135$	1.47492	+	0.433076i	0.126941	+	0.0372732i
$136$	2.67055	−	5.84769i	0.228998	−	0.501435i
$137$	−11.6712			−0.997137			−0.498568	−	0.866850i	$-0.666141\pi$
$137$	−11.6712			−0.997137			−0.498568	+	0.866850i	$0.666141\pi$
$138$	−0.982943	−	0.760159i	−0.0836736	−	0.0647090i
$139$	5.31325			0.450664			0.225332	−	0.974282i	$-0.427653\pi$
$139$	5.31325			0.450664			0.225332	+	0.974282i	$0.427653\pi$
$140$	−1.93761	+	4.24277i	−0.163758	+	0.358579i
$141$	−1.33128	−	0.390898i	−0.112114	−	0.0329195i
$142$	5.73169	+	6.61472i	0.480993	+	0.555095i
$143$	13.2509	−	8.51584i	1.10810	−	0.712130i
$144$	1.92062	−	2.21651i	0.160052	−	0.184710i
$145$	−0.570808	+	3.97006i	−0.0474030	+	0.329695i
$146$	−14.7419	+	4.32860i	−1.22005	+	0.358238i
$147$	3.21617	+	2.06691i	0.265266	+	0.170476i
$148$	−0.118839	−	0.826545i	−0.00976853	−	0.0679416i
$149$	1.66244	+	3.64023i	0.136192	+	0.298220i	0.965424	−	0.260686i	$-0.0839487\pi$
$149$	1.66244	+	3.64023i	0.136192	+	0.298220i	−0.829231	+	0.558905i	$0.811221\pi$
$150$	−0.107633	−	0.235683i	−0.00878818	−	0.0192434i
$151$	1.16015	+	8.06904i	0.0944119	+	0.656649i	0.980988	+	0.194067i	$0.0621679\pi$
$151$	1.16015	+	8.06904i	0.0944119	+	0.656649i	−0.886576	+	0.462582i	$0.846923\pi$
$152$	4.78855	+	3.07741i	0.388402	+	0.249611i
$153$	−18.0906	+	5.31188i	−1.46254	+	0.429440i
$154$	2.08641	−	14.5113i	0.168128	−	1.16935i
$155$	−0.0823619	+	0.0950507i	−0.00661546	+	0.00763465i
$156$	−1.09230	+	0.701978i	−0.0874539	+	0.0562032i
$157$	11.1637	+	12.8836i	0.890958	+	1.02822i	0.999418	+	0.0341196i	$0.0108627\pi$
$157$	11.1637	+	12.8836i	0.890958	+	1.02822i	−0.108460	+	0.994101i	$0.534592\pi$
$158$	4.95694	+	1.45549i	0.394353	+	0.115793i
$159$	−0.288572	+	0.631885i	−0.0228853	+	0.0501118i
$160$	−1.00000			−0.0790569
$161$	−22.2843	−	1.94544i	−1.75625	−	0.153322i
$162$	−8.40033			−0.659992
$163$	−6.03788	+	13.2211i	−0.472923	+	1.03556i	0.511426	+	0.859327i	$0.329117\pi$
$163$	−6.03788	+	13.2211i	−0.472923	+	1.03556i	−0.984349	+	0.176230i	$0.943610\pi$
$164$	10.9886	+	3.22653i	0.858062	+	0.251950i
$165$	0.533307	+	0.615469i	0.0415179	+	0.0479142i
$166$	11.6691	−	7.49925i	0.905695	−	0.582055i
$167$	8.27694	−	9.55210i	0.640489	−	0.739164i	−0.338972	−	0.940796i	$-0.610079\pi$
$167$	8.27694	−	9.55210i	0.640489	−	0.739164i	0.979461	+	0.201633i	$0.0646247\pi$
$168$	−0.171987	+	1.19620i	−0.0132691	+	0.0922886i
$169$	−11.6227	+	3.41273i	−0.894053	+	0.262518i
$170$	5.40811	+	3.47558i	0.414783	+	0.266565i
$171$	−2.37585	−	16.5244i	−0.181686	−	1.26365i
$172$	−2.98849	−	6.54389i	−0.227870	−	0.498967i
$173$	−1.27558	−	2.79313i	−0.0969804	−	0.212357i	0.854924	−	0.518754i	$-0.173604\pi$
$173$	−1.27558	−	2.79313i	−0.0969804	−	0.212357i	−0.951904	+	0.306397i	$0.900877\pi$
$174$	0.147895	+	1.02863i	0.0112119	+	0.0779802i
$175$	−3.92383	−	2.52169i	−0.296614	−	0.190622i
$176$	3.01584	−	0.885530i	0.227327	−	0.0667493i
$177$	0.198719	−	1.38212i	0.0149366	−	0.103886i
$178$	−7.37927	+	8.51613i	−0.553099	+	0.638311i
$179$	−3.11368	+	2.00104i	−0.232728	+	0.149565i	−0.651808	−	0.758384i	$-0.725989\pi$
$179$	−3.11368	+	2.00104i	−0.232728	+	0.149565i	0.419080	+	0.907949i	$0.362353\pi$
$180$	1.92062	+	2.21651i	0.143155	+	0.165209i
$181$	−4.19045	−	1.23043i	−0.311474	−	0.0914569i	0.122260	−	0.992498i	$-0.460986\pi$
$181$	−4.19045	−	1.23043i	−0.311474	−	0.0914569i	−0.433733	+	0.901041i	$0.642804\pi$
$182$	−9.70997	+	21.2619i	−0.719751	+	1.57603i
$183$	1.27343			0.0941346
$184$	−1.60531	−	4.51918i	−0.118345	−	0.333158i
$185$	0.835045			0.0613937
$186$	−0.0135370	+	0.0296418i	−0.000992579	+	0.00217345i
$187$	−19.3877	−	5.69275i	−1.41777	−	0.416295i
$188$	−3.50681	−	4.04708i	−0.255761	−	0.295164i
$189$	6.03167	−	3.87632i	0.438739	−	0.281961i
$190$	−3.72757	+	4.30184i	−0.270426	+	0.312089i
$191$	0.339423	−	2.36074i	0.0245598	−	0.170817i	−0.973850	−	0.227193i	$-0.927045\pi$
$191$	0.339423	−	2.36074i	0.0245598	−	0.170817i	0.998410	+	0.0563756i	$0.0179544\pi$
$192$	−0.248602	+	0.0729960i	−0.0179413	+	0.00526804i
$193$	−7.90881	−	5.08268i	−0.569288	−	0.365859i	0.224108	−	0.974564i	$-0.428053\pi$
$193$	−7.90881	−	5.08268i	−0.569288	−	0.365859i	−0.793397	+	0.608705i	$0.791689\pi$
$194$	−0.225359	−	1.56741i	−0.0161799	−	0.112533i
$195$	−0.539383	−	1.18108i	−0.0386260	−	0.0845791i
$196$	6.12961	+	13.4220i	0.437829	+	0.958712i
$197$	−0.261682	−	1.82004i	−0.0186441	−	0.129672i	0.978374	−	0.206845i	$-0.0663197\pi$
$197$	−0.261682	−	1.82004i	−0.0186441	−	0.129672i	−0.997018	+	0.0771730i	$0.975411\pi$
$198$	−7.75507	−	4.98388i	−0.551129	−	0.354189i
$199$	−4.67294	+	1.37210i	−0.331256	+	0.0972655i	−0.443131	−	0.896457i	$-0.646132\pi$
$199$	−4.67294	+	1.37210i	−0.331256	+	0.0972655i	0.111875	+	0.993722i	$0.464314\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	−1.21077	+	1.39731i	−0.0854014	+	0.0985585i
$202$	−13.6072	+	8.74483i	−0.957401	+	0.615284i
$203$	12.2510	+	14.1384i	0.859853	+	0.992323i
$204$	1.59817	+	0.469265i	0.111894	+	0.0328551i
$205$	−4.75753	+	10.4175i	−0.332280	+	0.727592i
$206$	−10.7046			−0.745825
$207$	−6.93363	+	12.2378i	−0.481921	+	0.850587i
$208$	−5.01132			−0.347473
$209$	7.43233	−	16.2745i	0.514105	−	1.12573i
$210$	−1.15954	−	0.340473i	−0.0800162	−	0.0234949i
$211$	−10.8737	−	12.5489i	−0.748575	−	0.863901i	0.245855	−	0.969307i	$-0.420931\pi$
$211$	−10.8737	−	12.5489i	−0.748575	−	0.863901i	−0.994429	+	0.105405i	$0.966386\pi$
$212$	−2.25547	+	1.44950i	−0.154906	+	0.0995523i
$213$	−1.48506	+	1.71385i	−0.101755	+	0.117431i
$214$	0.804277	−	5.59387i	0.0549793	−	0.382389i
$215$	6.90258	−	2.02678i	0.470752	−	0.138225i
$216$	1.29317	+	0.831067i	0.0879887	+	0.0565469i
$217$	0.0834854	+	0.580654i	0.00566736	+	0.0394174i
$218$	1.83381	+	4.01549i	0.124202	+	0.271964i
$219$	−1.65369	−	3.62108i	−0.111746	−	0.244690i
$220$	0.447318	+	3.11117i	0.0301582	+	0.209755i
$221$	27.1018	+	17.4173i	1.82306	+	1.17161i
$222$	0.207594	−	0.0609550i	0.0139328	−	0.00409103i
$223$	2.45494	−	17.0745i	0.164395	−	1.14339i	−0.725830	−	0.687874i	$-0.758544\pi$
$223$	2.45494	−	17.0745i	0.164395	−	1.14339i	0.890225	−	0.455520i	$-0.150547\pi$
$224$	−3.05444	+	3.52502i	−0.204084	+	0.235525i
$225$	−2.46729	+	1.58563i	−0.164486	+	0.105709i
$226$	−3.13358	−	3.61634i	−0.208442	−	0.240555i
$227$	−0.768131	−	0.225544i	−0.0509827	−	0.0149699i	0.256142	−	0.966639i	$-0.417549\pi$
$227$	−0.768131	−	0.225544i	−0.0509827	−	0.0149699i	−0.307124	+	0.951669i	$0.599367\pi$
$228$	−0.612663	+	1.34154i	−0.0405746	+	0.0888459i
$229$	−2.48769			−0.164391			−0.0821956	−	0.996616i	$-0.526193\pi$
$229$	−2.48769			−0.164391			−0.0821956	+	0.996616i	$0.526193\pi$
$230$	4.70164	−	0.945824i	0.310017	−	0.0623658i
$231$	3.79850			0.249923
$232$	−1.66618	+	3.64843i	−0.109390	+	0.239531i
$233$	−3.57476	−	1.04964i	−0.234190	−	0.0687644i	0.162532	−	0.986703i	$-0.448034\pi$
$233$	−3.57476	−	1.04964i	−0.234190	−	0.0687644i	−0.396722	+	0.917939i	$0.629852\pi$
$234$	9.62485	+	11.1077i	0.629196	+	0.726131i
$235$	4.50496	−	2.89516i	0.293871	−	0.188859i
$236$	3.52919	−	4.07290i	0.229731	−	0.265123i
$237$	−0.190495	+	1.32493i	−0.0123740	+	0.0860631i
$238$	28.7703	−	8.44771i	1.86490	−	0.547584i
$239$	3.69997	+	2.37783i	0.239331	+	0.153809i	0.654809	−	0.755795i	$-0.272749\pi$
$239$	3.69997	+	2.37783i	0.239331	+	0.153809i	−0.415478	+	0.909603i	$0.636386\pi$
$240$	−0.0368733	−	0.256460i	−0.00238016	−	0.0165544i
$241$	1.02437	+	2.24306i	0.0659854	+	0.144488i	0.939751	−	0.341859i	$-0.111056\pi$
$241$	1.02437	+	2.24306i	0.0659854	+	0.144488i	−0.873766	+	0.486347i	$0.838329\pi$
$242$	0.465497	+	1.01930i	0.0299233	+	0.0655228i
$243$	−0.966042	−	6.71897i	−0.0619716	−	0.431022i
$244$	4.13466	+	2.65718i	0.264694	+	0.170109i
$245$	−14.1577	+	4.15707i	−0.904501	+	0.265586i
$246$	−0.422291	+	2.93710i	−0.0269243	+	0.187262i
$247$	−18.6801	+	21.5579i	−1.18858	+	1.37170i
$248$	−0.105804	+	0.0679964i	−0.00671859	+	0.00431778i
$249$	2.35353	+	2.71612i	0.149149	+	0.172127i
$250$	0.959493	+	0.281733i	0.0606837	+	0.0178183i
$251$	−5.07446	+	11.1115i	−0.320297	+	0.701353i	−0.999468	−	0.0326276i	$-0.989612\pi$
$251$	−5.07446	+	11.1115i	−0.320297	+	0.701353i	0.679170	+	0.733981i	$0.262340\pi$
$252$	13.6797			0.861739
$253$	−13.3418	+	7.01589i	−0.838794	+	0.441085i
$254$	−16.9439			−1.06316
$255$	−0.691932	+	1.51512i	−0.0433304	+	0.0948804i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−6.75998	−	7.80143i	−0.421676	−	0.486640i	0.504671	−	0.863312i	$-0.331614\pi$
$257$	−6.75998	−	7.80143i	−0.421676	−	0.486640i	−0.926347	+	0.376672i	$0.877068\pi$
$258$	1.56805	−	1.00772i	0.0976224	−	0.0627381i
$259$	2.55060	−	2.94355i	0.158486	−	0.182903i
$260$	0.713186	−	4.96032i	0.0442299	−	0.307626i
$261$	11.2869	−	3.31413i	0.698641	−	0.205139i
$262$	3.52984	+	2.26849i	0.218074	+	0.140148i
$263$	−0.304343	−	2.11675i	−0.0187666	−	0.130525i	0.978284	−	0.207267i	$-0.0664570\pi$
$263$	−0.304343	−	2.11675i	−0.0187666	−	0.130525i	−0.997051	+	0.0767429i	$0.975548\pi$
$264$	0.338307	+	0.740789i	0.0208213	+	0.0455924i
$265$	−1.11376	−	2.43880i	−0.0684179	−	0.149814i
$266$	3.77842	+	26.2795i	0.231670	+	1.61130i
$267$	−2.45614	−	1.57847i	−0.150313	−	0.0966006i
$268$	−6.84689	+	2.01043i	−0.418241	+	0.122807i
$269$	1.89510	−	13.1807i	0.115546	−	0.803641i	−0.846819	−	0.531881i	$-0.821485\pi$
$269$	1.89510	−	13.1807i	0.115546	−	0.803641i	0.962365	−	0.271760i	$-0.0876056\pi$
$270$	−1.00664	+	1.16173i	−0.0612624	+	0.0707006i
$271$	−10.7836	+	6.93023i	−0.655060	+	0.420981i	−0.825512	−	0.564384i	$-0.809114\pi$
$271$	−10.7836	+	6.93023i	−0.655060	+	0.420981i	0.170452	+	0.985366i	$0.445477\pi$
$272$	4.20986	+	4.85844i	0.255260	+	0.294586i
$273$	−5.81085	−	1.70622i	−0.351689	−	0.103265i
$274$	4.84839	−	10.6165i	0.292902	−	0.641365i
$275$	−3.14316			−0.189540
$276$	1.09979	−	0.578335i	0.0661998	−	0.0348116i
$277$	18.2786			1.09825			0.549126	−	0.835740i	$-0.314961\pi$
$277$	18.2786			1.09825			0.549126	+	0.835740i	$0.314961\pi$
$278$	−2.20721	+	4.83311i	−0.132379	+	0.289870i
$279$	0.353925	+	0.103922i	0.0211890	+	0.00622164i
$280$	−3.05444	−	3.52502i	−0.182538	−	0.210660i
$281$	−15.7751	+	10.1380i	−0.941062	+	0.604784i	−0.918696	−	0.394966i	$-0.870756\pi$
$281$	−15.7751	+	10.1380i	−0.941062	+	0.604784i	−0.0223662	+	0.999750i	$0.507120\pi$
$282$	0.908605	−	1.04859i	0.0541066	−	0.0624424i
$283$	3.14338	−	21.8627i	0.186855	−	1.29960i	−0.653234	−	0.757156i	$-0.726588\pi$
$283$	3.14338	−	21.8627i	0.186855	−	1.29960i	0.840089	−	0.542448i	$-0.182502\pi$
$284$	−8.39799	+	2.46587i	−0.498329	+	0.146323i
$285$	−1.24070	−	0.797348i	−0.0734926	−	0.0472308i
$286$	2.24166	+	15.5911i	0.132552	+	0.921918i
$287$	22.1904	+	48.5901i	1.30986	+	2.86818i
$288$	1.21836	+	2.66783i	0.0717924	+	0.157203i
$289$	−3.46214	−	24.0797i	−0.203655	−	1.41645i
$290$	−3.37417	−	2.16845i	−0.198138	−	0.127336i
$291$	0.393668	−	0.115591i	0.0230772	−	0.00677608i
$292$	2.18656	−	15.2078i	0.127959	−	0.889971i
$293$	19.7896	−	22.8384i	1.15612	−	1.33423i	0.222938	−	0.974833i	$-0.428435\pi$
$293$	19.7896	−	22.8384i	1.15612	−	1.33423i	0.933183	−	0.359402i	$-0.117019\pi$
$294$	−3.21617	+	2.06691i	−0.187571	+	0.120545i
$295$	3.52919	+	4.07290i	0.205477	+	0.237134i
$296$	0.801220	+	0.235259i	0.0465699	+	0.0136742i
$297$	2.00713	−	4.39500i	0.116465	−	0.255024i
$298$	−4.00187			−0.231822
$299$	23.5614	−	4.73983i	1.36259	−	0.274111i
$300$	0.259097			0.0149590
$301$	13.9391	−	30.5224i	0.803438	−	1.75928i
$302$	−7.82180	−	2.29669i	−0.450094	−	0.132160i
$303$	−2.74444	−	3.16725i	−0.157664	−	0.181954i
$304$	−4.78855	+	3.07741i	−0.274642	+	0.176502i
$305$	−3.21856	+	3.71442i	−0.184294	+	0.212687i
$306$	2.68325	−	18.6624i	0.153391	−	1.06686i
$307$	−15.9409	+	4.68068i	−0.909798	+	0.267141i	−0.702956	−	0.711234i	$-0.748137\pi$
$307$	−15.9409	+	4.68068i	−0.909798	+	0.267141i	−0.206842	+	0.978374i	$0.566319\pi$
$308$	12.3332	+	7.92608i	0.702750	+	0.451630i
$309$	−0.394715	−	2.74530i	−0.0224545	−	0.156175i
$310$	−0.0522468	−	0.114404i	−0.00296742	−	0.00649774i
$311$	−4.61366	−	10.1025i	−0.261617	−	0.572861i	0.732550	−	0.680713i	$-0.238330\pi$
$311$	−4.61366	−	10.1025i	−0.261617	−	0.572861i	−0.994167	+	0.107852i	$0.965603\pi$
$312$	−0.184784	−	1.28520i	−0.0104613	−	0.0727603i
$313$	−26.6049	−	17.0979i	−1.50380	−	0.966431i	−0.994375	−	0.105913i	$-0.966223\pi$
$313$	−26.6049	−	17.0979i	−1.50380	−	0.966431i	−0.509421	−	0.860518i	$-0.670140\pi$
$314$	−16.3569	+	4.80281i	−0.923071	+	0.271038i
$315$	−1.94682	+	13.5404i	−0.109691	+	0.762917i
$316$	−3.38315	+	3.90436i	−0.190317	+	0.219638i
$317$	−5.10121	+	3.27835i	−0.286512	+	0.184130i	−0.676000	−	0.736901i	$-0.736288\pi$
$317$	−5.10121	+	3.27835i	−0.286512	+	0.184130i	0.389488	+	0.921031i	$0.372652\pi$
$318$	−0.454906	−	0.524989i	−0.0255099	−	0.0294399i
$319$	12.0962	+	3.55176i	0.677255	+	0.198860i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	1.46426			0.0817270
$322$	11.0269	−	19.4623i	0.614503	−	1.08459i
$323$	36.5928			2.03608
$324$	3.48962	−	7.64120i	0.193868	−	0.424511i
$325$	4.80833	+	1.41185i	0.266718	+	0.0783155i
$326$	−9.51812	−	10.9845i	−0.527160	−	0.608375i
$327$	−0.962193	+	0.618364i	−0.0532094	+	0.0341956i
$328$	−7.49977	+	8.65520i	−0.414106	+	0.477903i
$329$	3.55465	−	24.7232i	0.195974	−	1.36303i
$330$	−0.781394	+	0.229438i	−0.0430143	+	0.0126302i
$331$	−22.5310	−	14.4798i	−1.23841	−	0.795881i	−0.253234	−	0.967405i	$-0.581494\pi$
$331$	−22.5310	−	14.4798i	−1.23841	−	0.795881i	−0.985180	+	0.171524i	$0.945131\pi$
$332$	1.97406	+	13.7299i	0.108340	+	0.753524i
$333$	−1.01738	−	2.22776i	−0.0557523	−	0.122080i
$334$	5.25053	+	11.4971i	0.287296	+	0.629091i
$335$	−1.01555	−	7.06332i	−0.0554855	−	0.385910i
$336$	−1.01665	−	0.653363i	−0.0554629	−	0.0356439i
$337$	29.3108	−	8.60642i	1.59666	−	0.468821i	0.642045	−	0.766667i	$-0.278086\pi$
$337$	29.3108	−	8.60642i	1.59666	−	0.468821i	0.954614	+	0.297846i	$0.0962680\pi$
$338$	1.72391	−	11.9901i	0.0937684	−	0.652174i
$339$	0.811900	−	0.936983i	0.0440964	−	0.0508899i
$340$	−5.40811	+	3.47558i	−0.293296	+	0.188490i
$341$	0.258876	+	0.298759i	0.0140189	+	0.0161787i
$342$	16.0181	+	4.70334i	0.866160	+	0.254328i
$343$	−15.0269	+	32.9043i	−0.811375	+	1.77666i
$344$	7.19399			0.387874
$345$	0.415931	+	1.17091i	0.0223930	+	0.0630394i
$346$	3.07061			0.165077
$347$	1.42862	−	3.12825i	0.0766925	−	0.167933i	−0.867402	−	0.497608i	$-0.834212\pi$
$347$	1.42862	−	3.12825i	0.0766925	−	0.167933i	0.944095	+	0.329675i	$0.106939\pi$
$348$	−0.997112	−	0.292778i	−0.0534508	−	0.0156946i
$349$	15.6360	+	18.0449i	0.836976	+	0.965921i	0.999785	−	0.0207361i	$-0.00660099\pi$
$349$	15.6360	+	18.0449i	0.836976	+	0.965921i	−0.162809	+	0.986658i	$0.552056\pi$
$350$	3.92383	−	2.52169i	0.209738	−	0.134790i
$351$	−5.04462	+	5.82180i	−0.269262	+	0.310745i
$352$	−0.447318	+	3.11117i	−0.0238421	+	0.165826i
$353$	3.93792	−	1.15628i	0.209594	−	0.0615424i	−0.175250	−	0.984524i	$-0.556073\pi$
$353$	3.93792	−	1.15628i	0.209594	−	0.0615424i	0.384844	+	0.922982i	$0.374255\pi$
$354$	1.17467	+	0.754914i	0.0624329	+	0.0401232i
$355$	−1.24562	−	8.66344i	−0.0661104	−	0.459808i
$356$	−4.68108	−	10.2501i	−0.248097	−	0.543257i
$357$	3.22735	+	7.06692i	0.170810	+	0.374021i
$358$	−0.526742	−	3.66357i	−0.0278392	−	0.193626i
$359$	1.46944	+	0.944353i	0.0775542	+	0.0498411i	0.578843	−	0.815439i	$-0.303504\pi$
$359$	1.46944	+	0.944353i	0.0775542	+	0.0498411i	−0.501289	+	0.865280i	$0.667141\pi$
$360$	−2.81407	+	0.826285i	−0.148314	+	0.0435490i
$361$	−1.90711	+	13.2642i	−0.100374	+	0.698118i
$362$	2.86001	−	3.30063i	0.150319	−	0.173477i
$363$	−0.244244	+	0.156966i	−0.0128195	+	0.00823858i
$364$	−15.3068	−	17.6650i	−0.802295	−	0.925898i
$365$	14.7419	+	4.32860i	0.771624	+	0.226569i
$366$	−0.529002	+	1.15835i	−0.0276514	+	0.0605481i
$367$	−2.76843			−0.144511			−0.0722554	−	0.997386i	$-0.523020\pi$
$367$	−2.76843			−0.144511			−0.0722554	+	0.997386i	$0.523020\pi$
$368$	4.77766	+	0.417094i	0.249053	+	0.0217425i
$369$	33.5886			1.74855
$370$	−0.346890	+	0.759583i	−0.0180340	+	0.0394889i
$371$	−11.9987	−	3.52315i	−0.622943	−	0.182913i
$372$	−0.0213397	−	0.0246273i	−0.00110641	−	0.00127687i
$373$	−10.4434	+	6.71158i	−0.540740	+	0.347512i	−0.782328	−	0.622867i	$-0.785968\pi$
$373$	−10.4434	+	6.71158i	−0.540740	+	0.347512i	0.241589	+	0.970379i	$0.422332\pi$
$374$	13.2323	−	15.2708i	0.684224	−	0.789636i
$375$	−0.0368733	+	0.256460i	−0.00190413	+	0.0132435i
$376$	5.13814	−	1.50869i	0.264979	−	0.0778049i
$377$	−16.9090	−	10.8668i	−0.870860	−	0.559668i
$378$	1.02038	+	7.09688i	0.0524825	+	0.365024i
$379$	3.85452	+	8.44022i	0.197993	+	0.433545i	0.982422	−	0.186674i	$-0.0597709\pi$
$379$	3.85452	+	8.44022i	0.197993	+	0.433545i	−0.784429	+	0.620219i	$0.787044\pi$
$380$	−2.36461	−	5.17777i	−0.121302	−	0.265614i
$381$	−0.624780	−	4.34544i	−0.0320084	−	0.222624i
$382$	2.00640	+	1.28944i	0.102656	+	0.0659733i
$383$	10.9382	−	3.21174i	0.558915	−	0.164112i	0.00993950	−	0.999951i	$-0.496836\pi$
$383$	10.9382	−	3.21174i	0.558915	−	0.164112i	0.548976	+	0.835838i	$0.315018\pi$
$384$	0.0368733	−	0.256460i	0.00188168	−	0.0130874i
$385$	−9.60060	+	11.0797i	−0.489292	+	0.564673i
$386$	7.90881	−	5.08268i	0.402548	−	0.258702i
$387$	−13.8169	−	15.9456i	−0.702354	−	0.810560i
$388$	1.51938	+	0.446131i	0.0771350	+	0.0226489i
$389$	−9.35144	+	20.4768i	−0.474137	+	1.03821i	0.509897	+	0.860235i	$0.329683\pi$
$389$	−9.35144	+	20.4768i	−0.474137	+	1.03821i	−0.984034	+	0.177980i	$0.943044\pi$
$390$	1.29842			0.0657480
$391$	−24.3885	−	18.8608i	−1.23338	−	0.953833i
$392$	−14.7554			−0.745259
$393$	−0.451619	+	0.988907i	−0.0227812	+	0.0498838i
$394$	1.76427	+	0.518037i	0.0888828	+	0.0260983i
$395$	−3.38315	−	3.90436i	−0.170225	−	0.196450i
$396$	7.75507	−	4.98388i	0.389707	−	0.250449i
$397$	12.4035	−	14.3144i	0.622512	−	0.718417i	−0.353670	−	0.935370i	$-0.615066\pi$
$397$	12.4035	−	14.3144i	0.622512	−	0.718417i	0.976182	+	0.216953i	$0.0696118\pi$
$398$	0.693104	−	4.82065i	0.0347422	−	0.241637i
$399$	−6.60031	+	1.93803i	−0.330429	+	0.0970226i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−0.735081	−	5.11260i	−0.0367082	−	0.255311i	0.963201	−	0.268782i	$-0.0866211\pi$
$401$	−0.735081	−	5.11260i	−0.0367082	−	0.255311i	−0.999909	+	0.0134708i	$0.995712\pi$
$402$	−0.768062	−	1.68182i	−0.0383074	−	0.0838816i
$403$	−0.261825	−	0.573318i	−0.0130425	−	0.0285590i
$404$	−2.30193	−	16.0103i	−0.114526	−	0.796542i
$405$	7.06680	+	4.54156i	0.351152	+	0.225672i
$406$	−17.9500	+	5.27060i	−0.890844	+	0.261576i
$407$	0.373531	−	2.59796i	0.0185152	−	0.128776i
$408$	−1.09076	+	1.25881i	−0.0540008	+	0.0623202i
$409$	1.94689	−	1.25119i	0.0962674	−	0.0618673i	−0.491621	−	0.870809i	$-0.663596\pi$
$409$	1.94689	−	1.25119i	0.0962674	−	0.0618673i	0.587889	+	0.808942i	$0.299959\pi$
$410$	−7.49977	−	8.65520i	−0.370387	−	0.427450i
$411$	2.90148	+	0.851950i	0.143119	+	0.0420236i
$412$	4.44685	−	9.73725i	0.219081	−	0.479720i
$413$	25.1368			1.23690
$414$	−8.25158	−	11.3908i	−0.405543	−	0.559829i
$415$	−13.8710			−0.680903
$416$	2.08178	−	4.55846i	0.102068	−	0.223497i
$417$	−1.32088	−	0.387847i	−0.0646840	−	0.0189929i
$418$	11.7163	+	13.5214i	0.573065	+	0.661352i
$419$	−25.3586	+	16.2970i	−1.23885	+	0.796161i	−0.985246	−	0.171147i	$-0.945253\pi$
$419$	−25.3586	+	16.2970i	−1.23885	+	0.796161i	−0.253605	+	0.967308i	$0.581616\pi$
$420$	0.791397	−	0.913321i	0.0386162	−	0.0445655i
$421$	−3.16698	+	22.0269i	−0.154349	+	1.07352i	0.754470	+	0.656334i	$0.227894\pi$
$421$	−3.16698	+	22.0269i	−0.154349	+	1.07352i	−0.908820	+	0.417189i	$0.863015\pi$
$422$	15.9320	−	4.67805i	0.775556	−	0.227724i
$423$	−13.2124	−	8.49112i	−0.642411	−	0.412853i
$424$	−0.381558	−	2.65379i	−0.0185301	−	0.128880i
$425$	−2.67055	−	5.84769i	−0.129541	−	0.283655i
$426$	−0.942059	−	2.06282i	−0.0456429	−	0.0999441i
$427$	3.26247	+	22.6910i	0.157882	+	1.09809i
$428$	4.75426	+	3.05537i	0.229806	+	0.147687i
$429$	−3.91582	+	1.14979i	−0.189058	+	0.0555123i
$430$	−1.02381	+	7.12077i	−0.0493726	+	0.343394i
$431$	6.42857	−	7.41897i	0.309653	−	0.357359i	−0.579497	−	0.814975i	$-0.696751\pi$
$431$	6.42857	−	7.41897i	0.309653	−	0.357359i	0.889150	+	0.457615i	$0.151296\pi$
$432$	−1.29317	+	0.831067i	−0.0622174	+	0.0399847i
$433$	17.6868	+	20.4117i	0.849975	+	0.980923i	0.999970	−	0.00776381i	$-0.00247132\pi$
$433$	17.6868	+	20.4117i	0.849975	+	0.980923i	−0.149995	+	0.988687i	$0.547926\pi$
$434$	−0.562863	−	0.165271i	−0.0270183	−	0.00793328i
$435$	0.431702	−	0.945296i	0.0206985	−	0.0453235i
$436$	−4.41441			−0.211412
$437$	19.6033	−	18.9980i	0.937755	−	0.908798i
$438$	3.98082			0.190211
$439$	−12.7223	+	27.8579i	−0.607201	+	1.32958i	0.317271	+	0.948335i	$0.397233\pi$
$439$	−12.7223	+	27.8579i	−0.607201	+	1.32958i	−0.924472	+	0.381249i	$0.875494\pi$
$440$	−3.01584	−	0.885530i	−0.143774	−	0.0422160i
$441$	28.3395	+	32.7055i	1.34950	+	1.55741i
$442$	−27.1018	+	17.4173i	−1.28910	+	0.828455i
$443$	−22.8193	+	26.3349i	−1.08418	+	1.25121i	−0.118089	+	0.993003i	$0.537677\pi$
$443$	−22.8193	+	26.3349i	−1.08418	+	1.25121i	−0.966090	+	0.258206i	$0.916869\pi$
$444$	−0.0307909	+	0.214155i	−0.00146127	+	0.0101634i
$445$	10.8120	−	3.17469i	0.512538	−	0.150495i
$446$	14.5117	+	9.32611i	0.687149	+	0.441604i
$447$	−0.147562	−	1.02632i	−0.00697947	−	0.0485432i
$448$	−1.93761	−	4.24277i	−0.0915433	−	0.200452i
$449$	14.0662	+	30.8006i	0.663824	+	1.45357i	0.878916	+	0.476977i	$0.158268\pi$
$449$	14.0662	+	30.8006i	0.663824	+	1.45357i	−0.215092	+	0.976594i	$0.569005\pi$
$450$	−0.417391	−	2.90302i	−0.0196760	−	0.136850i
$451$	30.2825	+	19.4614i	1.42595	+	0.916401i
$452$	4.59127	−	1.34812i	0.215955	−	0.0634102i
$453$	0.300592	−	2.09066i	0.0141230	−	0.0982280i
$454$	0.524255	−	0.605023i	0.0246045	−	0.0283951i
$455$	19.6636	−	12.6370i	0.921843	−	0.592433i
$456$	−0.965802	−	1.11459i	−0.0452278	−	0.0521957i
$457$	−10.4920	−	3.08074i	−0.490796	−	0.144111i	0.0269642	−	0.999636i	$-0.491416\pi$
$457$	−10.4920	−	3.08074i	−0.490796	−	0.144111i	−0.517761	+	0.855526i	$0.673234\pi$
$458$	1.03342	−	2.26288i	0.0482887	−	0.105738i
$459$	9.88202			0.461253
$460$	−1.09278	+	4.66967i	−0.0509511	+	0.217725i
$461$	10.7264			0.499580			0.249790	−	0.968300i	$-0.419638\pi$
$461$	10.7264			0.499580			0.249790	+	0.968300i	$0.419638\pi$
$462$	−1.57795	+	3.45524i	−0.0734130	+	0.160752i
$463$	−14.8284	−	4.35402i	−0.689136	−	0.202349i	−0.0816289	−	0.996663i	$-0.526012\pi$
$463$	−14.8284	−	4.35402i	−0.689136	−	0.202349i	−0.607507	+	0.794314i	$0.707830\pi$
$464$	−2.62657	−	3.03122i	−0.121935	−	0.140721i
$465$	0.0274136	−	0.0176177i	0.00127128	−	0.000817000i
$466$	2.43980	−	2.81567i	0.113021	−	0.130434i
$467$	−2.08242	+	14.4835i	−0.0963628	+	0.670218i	0.883188	+	0.469020i	$0.155393\pi$
$467$	−2.08242	+	14.4835i	−0.0963628	+	0.670218i	−0.979551	+	0.201198i	$0.935516\pi$
$468$	−14.1022	+	4.14078i	−0.651874	+	0.191408i
$469$	−28.0003	−	17.9947i	−1.29293	−	0.830917i
$470$	0.762103	+	5.30055i	0.0351532	+	0.244496i
$471$	−1.83486	−	4.01778i	−0.0845458	−	0.185130i
$472$	2.23876	+	4.90221i	0.103047	+	0.225642i
$473$	−3.21800	−	22.3817i	−0.147964	−	1.02911i
$474$	−1.12606	−	0.723675i	−0.0517216	−	0.0332395i
$475$	5.46158	−	1.60367i	0.250595	−	0.0735812i
$476$	−4.26729	+	29.6797i	−0.195591	+	1.36036i
$477$	−5.14934	+	5.94266i	−0.235772	+	0.272096i
$478$	−3.69997	+	2.37783i	−0.169233	+	0.108759i
$479$	−7.61284	−	8.78569i	−0.347840	−	0.401428i	0.554689	−	0.832058i	$-0.312837\pi$
$479$	−7.61284	−	8.78569i	−0.347840	−	0.401428i	−0.902529	+	0.430629i	$0.858292\pi$
$480$	0.248602	+	0.0729960i	0.0113471	+	0.00333180i
$481$	−1.73838	+	3.80652i	−0.0792632	+	0.173562i
$482$	−2.46589			−0.112318
$483$	5.39790	+	2.11030i	0.245613	+	0.0960221i
$484$	−1.12056			−0.0509345
$485$	−0.657821	+	1.44043i	−0.0298701	+	0.0654064i
$486$	6.51310	+	1.91242i	0.295440	+	0.0867491i
$487$	−12.7961	−	14.7674i	−0.579845	−	0.669177i	0.387726	−	0.921775i	$-0.373261\pi$
$487$	−12.7961	−	14.7674i	−0.579845	−	0.669177i	−0.967571	+	0.252598i	$0.918715\pi$
$488$	−4.13466	+	2.65718i	−0.187167	+	0.120285i
$489$	2.46612	−	2.84605i	0.111522	−	0.128703i
$490$	2.09991	−	14.6052i	0.0948643	−	0.659795i
$491$	−10.1242	+	2.97275i	−0.456901	+	0.134158i	−0.502081	−	0.864821i	$-0.667432\pi$
$491$	−10.1242	+	2.97275i	−0.456901	+	0.134158i	0.0451801	+	0.998979i	$0.485614\pi$
$492$	−2.49625	−	1.60424i	−0.112540	−	0.0723249i
$493$	3.66951	+	25.5220i	0.165267	+	1.14945i
$494$	−11.8498	−	25.9475i	−0.533148	−	1.16743i
$495$	3.82949	+	8.38542i	0.172123	+	0.376896i
$496$	−0.0178989	−	0.124490i	−0.000803686	−	0.00558976i
$497$	−34.3435	−	22.0712i	−1.54051	−	0.990029i
$498$	−3.44836	+	1.01253i	−0.154525	+	0.0453726i
$499$	−3.90235	+	27.1414i	−0.174693	+	1.21502i	0.694113	+	0.719866i	$0.255797\pi$
$499$	−3.90235	+	27.1414i	−0.174693	+	1.21502i	−0.868806	+	0.495152i	$0.835112\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	−2.75493	+	1.77048i	−0.123081	+	0.0790994i
$502$	−7.99939	−	9.23179i	−0.357030	−	0.412035i
$503$	−9.21099	−	2.70459i	−0.410698	−	0.120592i	0.0698558	−	0.997557i	$-0.477746\pi$
$503$	−9.21099	−	2.70459i	−0.410698	−	0.120592i	−0.480554	+	0.876965i	$0.659564\pi$
$504$	−5.68275	+	12.4435i	−0.253130	+	0.554276i
$505$	16.1749			0.719776
$506$	−0.839486	−	15.0507i	−0.0373197	−	0.669084i
$507$	3.13854			0.139387
$508$	7.03877	−	15.4127i	0.312295	−	0.683830i
$509$	−9.23880	−	2.71276i	−0.409503	−	0.120241i	0.0704918	−	0.997512i	$-0.477543\pi$
$509$	−9.23880	−	2.71276i	−0.409503	−	0.120241i	−0.479994	+	0.877272i	$0.659361\pi$
$510$	−1.09076	−	1.25881i	−0.0482997	−	0.0557409i
$511$	60.2866	−	38.7438i	2.66692	−	1.71393i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−1.24524	+	8.66085i	−0.0549788	+	0.382386i
$514$	9.90462	−	2.90826i	0.436874	−	0.128278i
$515$	9.00529	+	5.78735i	0.396820	+	0.255021i
$516$	0.265267	+	1.84497i	0.0116777	+	0.0812202i
$517$	−6.99217	−	15.3107i	−0.307515	−	0.673365i
$518$	1.61799	+	3.54290i	0.0710903	+	0.155666i
$519$	0.113224	+	0.787488i	0.00496997	+	0.0345669i
$520$	4.21579	+	2.70933i	0.184875	+	0.118812i
$521$	−24.7696	+	7.27301i	−1.08518	+	0.318636i	−0.774948	−	0.632026i	$-0.782224\pi$
$521$	−24.7696	+	7.27301i	−1.08518	+	0.318636i	−0.310229	+	0.950662i	$0.600406\pi$
$522$	−1.67410	+	11.6437i	−0.0732736	+	0.509629i
$523$	−18.8236	+	21.7236i	−0.823099	+	0.949907i	−0.999407	−	0.0344279i	$-0.989039\pi$
$523$	−18.8236	+	21.7236i	−0.823099	+	0.949907i	0.176308	+	0.984335i	$0.443585\pi$
$524$	−3.52984	+	2.26849i	−0.154202	+	0.0990993i
$525$	0.791397	+	0.913321i	0.0345394	+	0.0398606i
$526$	2.05190	+	0.602491i	0.0894669	+	0.0262698i
$527$	−0.335875	+	0.735464i	−0.0146310	+	0.0320373i
$528$	−0.814383			−0.0354415
$529$	−22.8573	+	2.55780i	−0.993797	+	0.111209i
$530$	2.68108			0.116459
$531$	6.56600	−	14.3775i	0.284940	−	0.623932i
$532$	−25.4743	−	7.47992i	−1.10445	−	0.324296i
$533$	−37.5838	−	43.3740i	−1.62793	−	1.87874i
$534$	2.45614	−	1.57847i	0.106288	−	0.0683069i
$535$	−3.70088	+	4.27104i	−0.160003	+	0.184653i
$536$	1.01555	−	7.06332i	0.0438651	−	0.305089i
$537$	0.920135	−	0.270176i	0.0397068	−	0.0116590i
$538$	11.2023	+	7.19930i	0.482966	+	0.310384i
$539$	6.60035	+	45.9064i	0.284297	+	1.97733i
$540$	−0.638571	−	1.39828i	−0.0274797	−	0.0601722i
$541$	−10.9023	−	23.8728i	−0.468728	−	1.02637i	−0.985411	−	0.170194i	$-0.945560\pi$
$541$	−10.9023	−	23.8728i	−0.468728	−	1.02637i	0.516682	−	0.856177i	$-0.327167\pi$
$542$	−1.82427	−	12.6881i	−0.0783591	−	0.544999i
$543$	0.951936	+	0.611772i	0.0408515	+	0.0262537i
$544$	−6.16823	+	1.81116i	−0.264461	+	0.0776526i
$545$	0.628237	−	4.36948i	0.0269107	−	0.187168i
$546$	3.96595	−	4.57695i	0.169727	−	0.195875i
$547$	3.61542	−	2.32349i	0.154584	−	0.0993453i	−0.461062	−	0.887368i	$-0.652531\pi$
$547$	3.61542	−	2.32349i	0.154584	−	0.0993453i	0.615646	+	0.788023i	$0.288895\pi$
$548$	7.64300	+	8.82049i	0.326493	+	0.376793i
$549$	13.8308	+	4.06109i	0.590284	+	0.173323i
$550$	1.30572	−	2.85912i	0.0556759	−	0.121913i
$551$	−22.8306			−0.972615
$552$	0.0692006	+	1.24066i	0.00294537	+	0.0528059i
$553$	−24.0966			−1.02469
$554$	−7.59318	+	16.6268i	−0.322603	+	0.706403i
$555$	−0.207594	−	0.0609550i	−0.00881186	−	0.00258739i
$556$	−3.47944	−	4.01549i	−0.147561	−	0.170295i
$557$	15.8854	−	10.2089i	0.673086	−	0.432566i	−0.158951	−	0.987286i	$-0.550811\pi$
$557$	15.8854	−	10.2089i	0.673086	−	0.432566i	0.832037	+	0.554721i	$0.187175\pi$
$558$	−0.241557	+	0.278771i	−0.0102259	+	0.0118013i
$559$	−5.13065	+	35.6845i	−0.217003	+	1.50929i
$560$	4.47533	−	1.31408i	0.189117	−	0.0555298i
$561$	4.40427	+	2.83045i	0.185948	+	0.119502i
$562$	−2.66867	−	18.5610i	−0.112571	−	0.782948i
$563$	−1.81216	−	3.96809i	−0.0763736	−	0.167235i	0.867594	−	0.497274i	$-0.165665\pi$
$563$	−1.81216	−	3.96809i	−0.0763736	−	0.167235i	−0.943967	+	0.330039i	$0.892938\pi$
$564$	0.576379	+	1.26209i	0.0242699	+	0.0531438i
$565$	0.680991	+	4.73640i	0.0286495	+	0.199262i
$566$	18.5812	+	11.9414i	0.781027	+	0.501936i
$567$	37.5942	−	11.0387i	1.57881	−	0.463580i
$568$	1.24562	−	8.66344i	0.0522649	−	0.363510i
$569$	−14.0833	+	16.2530i	−0.590403	+	0.681362i	−0.969808	−	0.243869i	$-0.921583\pi$
$569$	−14.0833	+	16.2530i	−0.590403	+	0.681362i	0.379405	+	0.925231i	$0.376129\pi$
$570$	1.24070	−	0.797348i	0.0519671	−	0.0333972i
$571$	−1.69244	−	1.95318i	−0.0708265	−	0.0817381i	0.719230	−	0.694772i	$-0.244495\pi$
$571$	−1.69244	−	1.95318i	−0.0708265	−	0.0817381i	−0.790057	+	0.613033i	$0.789949\pi$
$572$	−15.1133	−	4.43768i	−0.631920	−	0.185549i
$573$	−0.256706	+	0.562107i	−0.0107240	+	0.0234824i
$574$	−53.4174			−2.22960
$575$	−4.46662	−	1.74622i	−0.186271	−	0.0728224i
$576$	−2.93287			−0.122203
$577$	−2.82782	+	6.19207i	−0.117724	+	0.257779i	−0.959316	−	0.282334i	$-0.908891\pi$
$577$	−2.82782	+	6.19207i	−0.117724	+	0.257779i	0.841592	+	0.540113i	$0.181619\pi$
$578$	23.3419	+	6.85380i	0.970895	+	0.285081i
$579$	1.59513	+	1.84088i	0.0662912	+	0.0765042i
$580$	3.37417	−	2.16845i	0.140105	−	0.0900398i
$581$	−42.3683	+	48.8957i	−1.75773	+	2.02853i
$582$	−0.0583899	+	0.406111i	−0.00242034	+	0.0168338i
$583$	−8.08571	+	2.37418i	−0.334876	+	0.0983285i
$584$	12.9252	+	8.30652i	0.534849	+	0.343726i
$585$	−2.09168	−	14.5480i	−0.0864803	−	0.601484i
$586$	12.5537	+	27.4887i	0.518587	+	1.13555i
$587$	−0.560566	−	1.22747i	−0.0231371	−	0.0506631i	0.897711	−	0.440585i	$-0.145229\pi$
$587$	−0.560566	−	1.22747i	−0.0231371	−	0.0506631i	−0.920848	+	0.389922i	$0.872502\pi$
$588$	−0.544080	−	3.78416i	−0.0224375	−	0.156056i
$589$	−0.602256	−	0.387046i	−0.0248155	−	0.0159480i
$590$	−5.17092	+	1.51832i	−0.212883	+	0.0625082i
$591$	−0.0678011	+	0.471567i	−0.00278896	+	0.0193977i
$592$	−0.546838	+	0.631085i	−0.0224749	+	0.0259374i
$593$	5.48826	−	3.52709i	0.225376	−	0.144840i	−0.423081	−	0.906092i	$-0.639051\pi$
$593$	5.48826	−	3.52709i	0.225376	−	0.144840i	0.648456	+	0.761252i	$0.275415\pi$
$594$	3.16404	+	3.65150i	0.129822	+	0.149823i
$595$	−28.7703	−	8.44771i	−1.17947	−	0.346322i
$596$	1.66244	−	3.64023i	0.0680961	−	0.149110i
$597$	1.26186			0.0516444
$598$	−5.47627	+	23.4012i	−0.223942	+	0.956948i
$599$	29.7565			1.21582			0.607910	−	0.794006i	$-0.292008\pi$
$599$	29.7565			1.21582			0.607910	+	0.794006i	$0.292008\pi$
$600$	−0.107633	+	0.235683i	−0.00439409	+	0.00962171i
$601$	7.06797	+	2.07534i	0.288308	+	0.0846550i	0.422689	−	0.906275i	$-0.361086\pi$
$601$	7.06797	+	2.07534i	0.288308	+	0.0846550i	−0.134381	+	0.990930i	$0.542904\pi$
$602$	21.9737	+	25.3589i	0.895579	+	1.03355i
$603$	−17.6064	+	11.3150i	−0.716989	+	0.460781i
$604$	5.33844	−	6.16088i	0.217218	−	0.250683i
$605$	0.159472	−	1.10915i	0.00648346	−	0.0450935i
$606$	4.02112	−	1.18071i	0.163347	−	0.0479629i
$607$	15.6415	+	10.0522i	0.634868	+	0.408005i	0.818109	−	0.575063i	$-0.195022\pi$
$607$	15.6415	+	10.0522i	0.634868	+	0.408005i	−0.183241	+	0.983068i	$0.558659\pi$
$608$	−0.810078	−	5.63422i	−0.0328530	−	0.228498i
$609$	−2.01357	−	4.40911i	−0.0815941	−	0.178666i
$610$	−2.04171	−	4.47073i	−0.0826666	−	0.181015i
$611$	3.81915	+	26.5627i	0.154506	+	1.07461i
$612$	15.8613	+	10.1934i	0.641154	+	0.412045i
$613$	36.0811	−	10.5944i	1.45730	−	0.427902i	0.545352	−	0.838207i	$-0.316396\pi$
$613$	36.0811	−	10.5944i	1.45730	−	0.427902i	0.911948	+	0.410305i	$0.134578\pi$
$614$	2.36441	−	16.4448i	0.0954197	−	0.663659i
$615$	1.94317	−	2.24253i	0.0783561	−	0.0904277i
$616$	−12.3332	+	7.92608i	−0.496920	+	0.319351i
$617$	−0.461390	−	0.532472i	−0.0185749	−	0.0214365i	0.746386	−	0.665513i	$-0.231787\pi$
$617$	−0.461390	−	0.532472i	−0.0185749	−	0.0214365i	−0.764961	+	0.644077i	$0.777242\pi$
$618$	2.66118	+	0.781394i	0.107048	+	0.0314323i
$619$	19.5104	−	42.7218i	0.784188	−	1.71713i	0.0916050	−	0.995795i	$-0.470800\pi$
$619$	19.5104	−	42.7218i	0.784188	−	1.71713i	0.692583	−	0.721338i	$-0.256472\pi$
$620$	0.125770			0.00505105
$621$	5.29395	−	5.13048i	0.212439	−	0.205879i
$622$	11.1062			0.445316
$623$	21.8338	−	47.8094i	0.874754	−	1.91544i
$624$	1.24582	+	0.365807i	0.0498729	+	0.0146440i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	26.6049	−	17.0979i	1.06334	−	0.683370i
$627$	−3.03567	+	3.50335i	−0.121233	+	0.139910i
$628$	2.42610	−	16.8739i	0.0968118	−	0.673341i
$629$	5.15075	−	1.51240i	0.205374	−	0.0603032i
$630$	−11.5081	−	7.39579i	−0.458493	−	0.294655i
$631$	−6.47365	−	45.0252i	−0.257712	−	1.79243i	−0.549033	−	0.835801i	$-0.685004\pi$
$631$	−6.47365	−	45.0252i	−0.257712	−	1.79243i	0.291321	−	0.956625i	$-0.405905\pi$
$632$	−2.14612	−	4.69935i	−0.0853681	−	0.186930i
$633$	1.78720	+	3.91341i	0.0710346	+	0.155544i
$634$	−0.862971	−	6.00210i	−0.0342730	−	0.238374i
$635$	14.2541	+	9.16058i	0.565659	+	0.363527i
$636$	0.666522	−	0.195708i	0.0264293	−	0.00776035i
$637$	10.5233	−	73.1913i	0.416949	−	2.89995i
$638$	−8.25572	+	9.52761i	−0.326847	+	0.377202i
$639$	−21.5950	+	13.8783i	−0.854285	+	0.549016i
$640$	0.654861	+	0.755750i	0.0258856	+	0.0298736i
$641$	−32.5156	−	9.54744i	−1.28429	−	0.377101i	−0.432808	−	0.901486i	$-0.642477\pi$
$641$	−32.5156	−	9.54744i	−1.28429	−	0.377101i	−0.851481	+	0.524385i	$0.824295\pi$
$642$	−0.608275	+	1.33194i	−0.0240067	+	0.0525674i
$643$	−43.7168			−1.72402			−0.862011	−	0.506890i	$-0.830795\pi$
$643$	−43.7168			−1.72402			−0.862011	+	0.506890i	$0.830795\pi$
$644$	13.1228	+	18.1153i	0.517112	+	0.713844i
$645$	−1.86394			−0.0733926
$646$	−15.2012	+	33.2860i	−0.598083	+	1.30962i
$647$	−12.2349	−	3.59248i	−0.481003	−	0.141235i	0.0322374	−	0.999480i	$-0.489737\pi$
$647$	−12.2349	−	3.59248i	−0.481003	−	0.141235i	−0.513240	+	0.858245i	$0.671555\pi$
$648$	5.50104	+	6.34854i	0.216101	+	0.249394i
$649$	14.2501	−	9.15801i	0.559367	−	0.359483i
$650$	−3.28172	+	3.78731i	−0.128720	+	0.148550i
$651$	0.0216308	−	0.150446i	0.000847779	−	0.00589643i
$652$	13.9458	−	4.09486i	0.546160	−	0.160367i
$653$	27.3978	+	17.6075i	1.07216	+	0.689034i	0.952733	−	0.303809i	$-0.0982586\pi$
$653$	27.3978	+	17.6075i	1.07216	+	0.689034i	0.119425	+	0.992843i	$0.461895\pi$
$654$	−0.162774	−	1.13212i	−0.00636498	−	0.0442694i
$655$	−1.74305	−	3.81675i	−0.0681066	−	0.149133i
$656$	−4.75753	−	10.4175i	−0.185750	−	0.406736i
$657$	−6.41288	−	44.6026i	−0.250190	−	1.74011i
$658$	21.0123	+	13.5038i	0.819146	+	0.526433i
$659$	13.0915	−	3.84400i	0.509971	−	0.149741i	−0.0166162	−	0.999862i	$-0.505289\pi$
$659$	13.0915	−	3.84400i	0.509971	−	0.149741i	0.526588	+	0.850121i	$0.323471\pi$
$660$	0.115899	−	0.806093i	0.00451135	−	0.0313771i
$661$	18.7615	−	21.6519i	0.729736	−	0.842160i	−0.262706	−	0.964876i	$-0.584615\pi$
$661$	18.7615	−	21.6519i	0.729736	−	0.842160i	0.992442	+	0.122716i	$0.0391604\pi$
$662$	22.5310	−	14.4798i	0.875691	−	0.562773i
$663$	−5.46616	−	6.30829i	−0.212288	−	0.244994i
$664$	−13.3092	−	3.90792i	−0.516496	−	0.151657i
$665$	11.0292	−	24.1505i	0.427692	−	0.936516i
$666$	2.44908			0.0948998
$667$	15.2162	+	11.7674i	0.589173	+	0.455637i
$668$	−12.6392			−0.489027
$669$	−1.85668	+	4.06555i	−0.0717832	+	0.157183i
$670$	6.84689	+	2.01043i	0.264519	+	0.0776697i
$671$	10.1164	+	11.6750i	0.390541	+	0.450708i
$672$	1.01665	−	0.653363i	0.0392182	−	0.0252040i
$673$	3.20086	−	3.69399i	0.123384	−	0.142393i	−0.690697	−	0.723145i	$-0.742696\pi$
$673$	3.20086	−	3.69399i	0.123384	−	0.142393i	0.814081	+	0.580752i	$0.197241\pi$
$674$	−4.34746	+	30.2372i	−0.167458	+	1.16470i
$675$	1.47492	−	0.433076i	0.0567697	−	0.0166691i
$676$	10.1904	+	6.54898i	0.391939	+	0.251884i
$677$	0.829400	+	5.76860i	0.0318764	+	0.221705i	0.999533	−	0.0305669i	$-0.00973125\pi$
$677$	0.829400	+	5.76860i	0.0318764	+	0.221705i	−0.967656	+	0.252272i	$0.918822\pi$
$678$	0.515034	+	1.12777i	0.0197798	+	0.0433116i
$679$	3.06825	+	6.71853i	0.117749	+	0.257834i
$680$	−0.914890	−	6.36320i	−0.0350844	−	0.244018i
$681$	0.174495	+	0.112141i	0.00668666	+	0.00429726i
$682$	−0.379302	+	0.111373i	−0.0145242	+	0.00426470i
$683$	−2.19559	+	15.2707i	−0.0840119	+	0.584315i	0.903716	+	0.428132i	$0.140828\pi$
$683$	−2.19559	+	15.2707i	−0.0840119	+	0.584315i	−0.987728	+	0.156183i	$0.950081\pi$
$684$	−10.9325	+	12.6167i	−0.418014	+	0.482413i
$685$	−9.81842	+	6.30992i	−0.375143	+	0.241090i
$686$	−23.6884	−	27.3379i	−0.904427	−	1.04376i
$687$	0.618444	+	0.181592i	0.0235951	+	0.00692815i
$688$	−2.98849	+	6.54389i	−0.113935	+	0.249483i
$689$	13.4358			0.511862
$690$	−1.23788	−	0.108068i	−0.0471252	−	0.00411407i
$691$	0.453717			0.0172602			0.00863011	−	0.999963i	$-0.497253\pi$
$691$	0.453717			0.0172602			0.00863011	+	0.999963i	$0.497253\pi$
$692$	−1.27558	+	2.79313i	−0.0484902	+	0.106179i
$693$	41.2557	+	12.1138i	1.56717	+	0.460164i
$694$	2.25208	+	2.59904i	0.0854879	+	0.0986583i
$695$	4.46979	−	2.87256i	0.169549	−	0.108963i
$696$	0.680536	−	0.785380i	0.0257956	−	0.0297698i
$697$	−10.4777	+	72.8743i	−0.396873	+	2.76031i
$698$	−22.9096	+	6.72688i	−0.867143	+	0.254616i
$699$	0.812071	+	0.521886i	0.0307153	+	0.0197395i
$700$	0.663794	+	4.61679i	0.0250891	+	0.174498i
$701$	−2.24480	−	4.91543i	−0.0847850	−	0.185653i	0.862491	−	0.506073i	$-0.168903\pi$
$701$	−2.24480	−	4.91543i	−0.0847850	−	0.185653i	−0.947276	+	0.320420i	$0.896176\pi$
$702$	−3.20009	−	7.00721i	−0.120779	−	0.264470i
$703$	0.676452	+	4.70482i	0.0255129	+	0.177446i
$704$	−2.64419	−	1.69932i	−0.0996568	−	0.0640455i
$705$	−1.33128	+	0.390898i	−0.0501387	+	0.0147221i
$706$	−0.584084	+	4.06239i	−0.0219823	+	0.152890i
$707$	49.4055	−	57.0170i	1.85808	−	2.14434i
$708$	−1.17467	+	0.754914i	−0.0441467	+	0.0283714i
$709$	8.12574	+	9.37761i	0.305169	+	0.352183i	0.887533	−	0.460745i	$-0.152418\pi$
$709$	8.12574	+	9.37761i	0.305169	+	0.352183i	−0.582364	+	0.812928i	$0.697872\pi$
$710$	8.39799	+	2.46587i	0.315171	+	0.0925426i
$711$	−6.29429	+	13.7826i	−0.236054	+	0.516887i
$712$	11.2685			0.422303
$713$	0.201900	+	0.568377i	0.00756121	+	0.0212859i
$714$	−7.76899			−0.290747
$715$	6.54336	−	14.3280i	0.244708	−	0.535835i
$716$	3.55132	+	1.04276i	0.132719	+	0.0389698i
$717$	−0.746247	−	0.861215i	−0.0278691	−	0.0321627i
$718$	−1.46944	+	0.944353i	−0.0548391	+	0.0352430i
$719$	17.3719	−	20.0483i	0.647864	−	0.747675i	−0.332881	−	0.942969i	$-0.608021\pi$
$719$	17.3719	−	20.0483i	0.647864	−	0.747675i	0.980745	+	0.195294i	$0.0625662\pi$
$720$	0.417391	−	2.90302i	0.0155552	−	0.108189i
$721$	47.9066	−	14.0667i	1.78414	−	0.523870i
$722$	−11.2733	−	7.24494i	−0.419550	−	0.269629i
$723$	−0.0909258	−	0.632403i	−0.00338157	−	0.0235193i
$724$	1.81427	+	3.97269i	0.0674266	+	0.147644i
$725$	1.66618	+	3.64843i	0.0618804	+	0.135499i
$726$	−0.0413187	−	0.287378i	−0.00153348	−	0.0106656i
$727$	−29.9977	−	19.2784i	−1.11255	−	0.714996i	−0.150707	−	0.988579i	$-0.548155\pi$
$727$	−29.9977	−	19.2784i	−1.11255	−	0.714996i	−0.961848	+	0.273583i	$0.911791\pi$
$728$	22.4273	−	6.58526i	0.831212	−	0.244066i
$729$	3.33617	−	23.2036i	0.123562	−	0.859393i
$730$	−10.0614	+	11.6115i	−0.372390	+	0.429761i
$731$	38.9059	−	25.0033i	1.43899	−	0.924781i
$732$	−0.833919	−	0.962394i	−0.0308225	−	0.0355711i
$733$	3.03857	+	0.892206i	0.112232	+	0.0329544i	0.337366	−	0.941373i	$-0.390464\pi$
$733$	3.03857	+	0.892206i	0.112232	+	0.0329544i	−0.225134	+	0.974328i	$0.572282\pi$
$734$	1.15005	−	2.51825i	0.0424490	−	0.0929504i
$735$	3.82307			0.141016
$736$	−2.36411	+	4.17265i	−0.0871424	+	0.153806i
$737$	−22.4294			−0.826198
$738$	−13.9532	+	30.5532i	−0.513624	+	1.12468i
$739$	−1.76399	−	0.517953i	−0.0648893	−	0.0190532i	0.249127	−	0.968471i	$-0.419856\pi$
$739$	−1.76399	−	0.517953i	−0.0648893	−	0.0190532i	−0.314016	+	0.949418i	$0.601675\pi$
$740$	−0.546838	−	0.631085i	−0.0201022	−	0.0231991i
$741$	6.21754	−	3.99577i	0.228407	−	0.146788i
$742$	8.18922	−	9.45087i	0.300636	−	0.346952i
$743$	3.47168	−	24.1461i	0.127364	−	0.885834i	−0.821514	−	0.570189i	$-0.806870\pi$
$743$	3.47168	−	24.1461i	0.127364	−	0.885834i	0.948877	−	0.315645i	$-0.102221\pi$
$744$	0.0312666	−	0.00918072i	0.00114629	−	0.000336581i
$745$	3.36659	+	2.16358i	0.123342	+	0.0792673i
$746$	−1.76671	−	12.2878i	−0.0646839	−	0.449887i
$747$	16.8999	+	37.0056i	0.618335	+	1.35396i
$748$	8.39396	+	18.3802i	0.306914	+	0.672047i
$749$	3.75136	+	26.0913i	0.137072	+	0.953356i
$750$	−0.217966	−	0.140078i	−0.00795900	−	0.00511494i
$751$	−27.2678	+	8.00656i	−0.995017	+	0.292163i	−0.738410	−	0.674352i	$-0.764423\pi$
$751$	−27.2678	+	8.00656i	−0.995017	+	0.292163i	−0.256607	+	0.966516i	$0.582605\pi$
$752$	−0.762103	+	5.30055i	−0.0277911	+	0.193291i
$753$	2.07262	−	2.39193i	0.0755304	−	0.0871667i
$754$	16.9090	−	10.8668i	0.615791	−	0.395745i
$755$	5.33844	+	6.16088i	0.194286	+	0.224217i
$756$	−6.87943	−	2.01998i	−0.250202	−	0.0734660i
$757$	−2.98280	+	6.53142i	−0.108412	+	0.237388i	−0.956061	−	0.293169i	$-0.905290\pi$
$757$	−2.98280	+	6.53142i	−0.108412	+	0.237388i	0.847649	+	0.530557i	$0.178017\pi$
$758$	−9.27872			−0.337018
$759$	3.82893	−	0.770263i	0.138981	−	0.0279588i
$760$	5.69216			0.206476
$761$	−6.58205	+	14.4127i	−0.238599	+	0.522459i	−0.990614	−	0.136686i	$-0.956355\pi$
$761$	−6.58205	+	14.4127i	−0.238599	+	0.522459i	0.752015	+	0.659146i	$0.229082\pi$
$762$	4.21229	+	1.23684i	0.152595	+	0.0448060i
$763$	−13.4836	−	15.5609i	−0.488139	−	0.563342i
$764$	−2.00640	+	1.28944i	−0.0725890	+	0.0466501i
$765$	−12.3470	+	14.2492i	−0.446406	+	0.515179i
$766$	−1.62238	+	11.2839i	−0.0586191	+	0.407705i
$767$	−25.9132	+	7.60879i	−0.935670	+	0.274737i
$768$	0.217966	+	0.140078i	0.00786518	+	0.00505464i
$769$	1.17691	+	8.18561i	0.0424406	+	0.295181i	0.999976	+	0.00686641i	$0.00218566\pi$
$769$	1.17691	+	8.18561i	0.0424406	+	0.295181i	−0.957536	+	0.288314i	$0.906905\pi$
$770$	−6.09020	−	13.3357i	−0.219476	−	0.480585i
$771$	1.11107	+	2.43290i	0.0400141	+	0.0876187i
$772$	1.33793	+	9.30553i	0.0481533	+	0.334913i
$773$	11.4633	+	7.36702i	0.412306	+	0.264973i	0.730309	−	0.683116i	$-0.239376\pi$
$773$	11.4633	+	7.36702i	0.412306	+	0.264973i	−0.318003	+	0.948090i	$0.603012\pi$
$774$	20.2444	−	5.94428i	0.727669	−	0.213663i
$775$	−0.0178989	+	0.124490i	−0.000642949	+	0.00447181i
$776$	−1.03699	+	1.19675i	−0.0372258	+	0.0429608i
$777$	−0.848950	+	0.545587i	−0.0304559	+	0.0195728i
$778$	−14.7416	−	17.0127i	−0.528513	−	0.609936i
$779$	−62.5486	−	18.3659i	−2.24104	−	0.658028i
$780$	−0.539383	+	1.18108i	−0.0193130	+	0.0422896i
$781$	−27.5106			−0.984406
$782$	27.2878	−	14.3495i	0.975808	−	0.513136i
$783$	−6.16548			−0.220336
$784$	6.12961	−	13.4220i	0.218915	−	0.479356i
$785$	16.3569	+	4.80281i	0.583801	+	0.171420i
$786$	−0.711932	−	0.821614i	−0.0253938	−	0.0293060i
$787$	6.99269	−	4.49393i	0.249262	−	0.160191i	−0.410044	−	0.912066i	$-0.634487\pi$
$787$	6.99269	−	4.49393i	0.249262	−	0.160191i	0.659306	+	0.751875i	$0.270850\pi$
$788$	−1.20413	+	1.38964i	−0.0428953	+	0.0495038i
$789$	−0.0788544	+	0.548444i	−0.00280729	+	0.0195251i
$790$	4.95694	−	1.45549i	0.176360	−	0.0517840i
$791$	18.7759	+	12.0666i	0.667595	+	0.429038i
$792$	1.31193	+	9.12464i	0.0466172	+	0.324230i
$793$	−10.2317	−	22.4043i	−0.363338	−	0.795599i
$794$	7.86822	+	17.2290i	0.279233	+	0.611434i
$795$	0.0988605	+	0.687590i	0.00350622	+	0.0243863i
$796$	4.09709	+	2.63304i	0.145217	+	0.0933256i
$797$	−18.9806	+	5.57322i	−0.672329	+	0.197414i	−0.600040	−	0.799970i	$-0.704849\pi$
$797$	−18.9806	+	5.57322i	−0.672329	+	0.197414i	−0.0722891	+	0.997384i	$0.523030\pi$
$798$	0.978977	−	6.80894i	0.0346554	−	0.241034i
$799$	22.5440	−	26.0172i	0.797550	−	0.920422i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	−21.6424	−	24.9767i	−0.764697	−	0.882508i
$802$	4.95595	+	1.45520i	0.175001	+	0.0513848i
$803$	20.0613	−	43.9281i	0.707948	−	1.55019i
$804$	1.84890			0.0652058
$805$	−19.7985	+	10.4112i	−0.697806	+	0.366946i
$806$	0.630274			0.0222005
$807$	−1.43326	+	3.13841i	−0.0504532	+	0.110477i
$808$	15.5197	+	4.55701i	0.545983	+	0.160315i
$809$	13.1747	+	15.2044i	0.463198	+	0.534558i	0.938507	−	0.345260i	$-0.112209\pi$
$809$	13.1747	+	15.2044i	0.463198	+	0.534558i	−0.475309	+	0.879819i	$0.657664\pi$
$810$	−7.06680	+	4.54156i	−0.248302	+	0.159574i
$811$	−11.3321	+	13.0780i	−0.397925	+	0.459230i	−0.918986	−	0.394289i	$-0.870991\pi$
$811$	−11.3321	+	13.0780i	−0.397925	+	0.459230i	0.521061	+	0.853519i	$0.325536\pi$
$812$	2.66240	−	18.5174i	0.0934319	−	0.649833i
$813$	3.18671	−	0.935703i	0.111763	−	0.0328165i
$814$	2.20802	+	1.41901i	0.0773910	+	0.0497362i
$815$	2.06848	+	14.3866i	0.0724559	+	0.503942i
$816$	−0.691932	−	1.51512i	−0.0242225	−	0.0530398i
$817$	17.0110	+	37.2488i	0.595138	+	1.30317i
$818$	0.329355	+	2.29071i	0.0115156	+	0.0800929i
$819$	−57.6707	−	37.0627i	−2.01518	−	1.29508i
$820$	10.9886	−	3.22653i	0.383737	−	0.112675i
$821$	−6.56167	+	45.6374i	−0.229004	+	1.59276i	0.473314	+	0.880894i	$0.343058\pi$
$821$	−6.56167	+	45.6374i	−0.229004	+	1.59276i	−0.702318	+	0.711863i	$0.747852\pi$
$822$	−1.98028	+	2.28536i	−0.0690701	+	0.0797112i
$823$	−7.93127	+	5.09712i	−0.276467	+	0.177674i	−0.671525	−	0.740982i	$-0.734361\pi$
$823$	−7.93127	+	5.09712i	−0.276467	+	0.177674i	0.395059	+	0.918656i	$0.370724\pi$
$824$	7.01002	+	8.09000i	0.244206	+	0.281829i
$825$	0.781394	+	0.229438i	0.0272047	+	0.00798801i
$826$	−10.4422	+	22.8652i	−0.363330	+	0.795582i
$827$	−44.5622			−1.54958			−0.774790	−	0.632218i	$-0.782145\pi$
$827$	−44.5622			−1.54958			−0.774790	+	0.632218i	$0.782145\pi$
$828$	13.7893	−	2.77398i	0.479211	−	0.0964024i
$829$	−40.8816			−1.41988			−0.709939	−	0.704264i	$-0.751277\pi$
$829$	−40.8816			−1.41988			−0.709939	+	0.704264i	$0.751277\pi$
$830$	5.76224	−	12.6175i	0.200010	−	0.437961i
$831$	−4.54408	−	1.33426i	−0.157632	−	0.0462850i
$832$	3.28172	+	3.78731i	0.113773	+	0.131301i
$833$	−79.7987	+	51.2835i	−2.76486	+	1.77687i
$834$	0.901513	−	1.04040i	0.0312168	−	0.0360261i
$835$	1.79875	−	12.5106i	0.0622484	−	0.432947i
$836$	−17.1666	+	5.04057i	−0.593720	+	0.174332i
$837$	−0.162641	−	0.104523i	−0.00562171	−	0.00361285i
$838$	−4.28992	−	29.8371i	−0.148193	−	1.03070i
$839$	10.9480	+	23.9728i	0.377967	+	0.827632i	0.999037	+	0.0438767i	$0.0139709\pi$
$839$	10.9480	+	23.9728i	0.377967	+	0.827632i	−0.621070	+	0.783755i	$0.713302\pi$
$840$	0.502028	+	1.09929i	0.0173216	+	0.0379290i
$841$	1.83769	+	12.7814i	0.0633686	+	0.440738i
$842$	−18.7207	−	12.0311i	−0.645159	−	0.414618i
$843$	4.66175	−	1.36881i	0.160559	−	0.0471444i
$844$	−2.36308	+	16.4356i	−0.0813404	+	0.565735i
$845$	−7.93257	+	9.15467i	−0.272889	+	0.314930i
$846$	13.2124	−	8.49112i	0.454253	−	0.291931i
$847$	−3.42268	−	3.94999i	−0.117605	−	0.135723i
$848$	2.57248	+	0.755348i	0.0883393	+	0.0259388i
$849$	−2.37734	+	5.20565i	−0.0815902	+	0.178658i
$850$	6.42863			0.220500
$851$	1.97414	−	3.48435i	0.0676727	−	0.119442i
$852$	2.26775			0.0776920
$853$	7.76301	−	16.9986i	0.265800	−	0.582022i	−0.728925	−	0.684593i	$-0.759980\pi$
$853$	7.76301	−	16.9986i	0.265800	−	0.582022i	0.994726	+	0.102572i	$0.0327071\pi$
$854$	−21.9957	−	6.45852i	−0.752677	−	0.221006i
$855$	−10.9325	−	12.6167i	−0.373883	−	0.431484i
$856$	−4.75426	+	3.05537i	−0.162497	+	0.104431i
$857$	30.5432	−	35.2488i	1.04334	−	1.20408i	0.0648225	−	0.997897i	$-0.479352\pi$
$857$	30.5432	−	35.2488i	1.04334	−	1.20408i	0.978514	−	0.206178i	$-0.0661027\pi$
$858$	0.580806	−	4.03959i	0.0198284	−	0.137909i
$859$	20.1758	−	5.92414i	0.688388	−	0.202129i	0.0812129	−	0.996697i	$-0.474121\pi$
$859$	20.1758	−	5.92414i	0.688388	−	0.202129i	0.607176	+	0.794568i	$0.292302\pi$
$860$	−6.05197	−	3.88937i	−0.206371	−	0.132626i
$861$	−1.96968	−	13.6994i	−0.0671264	−	0.466874i
$862$	4.07801	+	8.92959i	0.138897	+	0.304143i
$863$	12.6425	+	27.6832i	0.430355	+	0.942345i	0.993269	+	0.115830i	$0.0369528\pi$
$863$	12.6425	+	27.6832i	0.430355	+	0.942345i	−0.562914	+	0.826515i	$0.690320\pi$
$864$	−0.218765	−	1.52154i	−0.00744253	−	0.0517639i
$865$	−2.58316	−	1.66010i	−0.0878302	−	0.0564450i
$866$	−25.9145	+	7.60918i	−0.880610	+	0.258571i
$867$	−0.897030	+	6.23898i	−0.0304647	+	0.211887i
$868$	0.384158	−	0.443342i	0.0130392	−	0.0150480i
$869$	−13.6605	+	8.77904i	−0.463399	+	0.297809i
$870$	0.680536	+	0.785380i	0.0230723	+	0.0266269i
$871$	34.3120	+	10.0749i	1.16262	+	0.341375i
$872$	1.83381	−	4.01549i	0.0621008	−	0.135982i
$873$	4.64428			0.157185
$874$	9.13767	+	25.7239i	0.309086	+	0.870123i
$875$	−4.66427			−0.157681
$876$	−1.65369	+	3.62108i	−0.0558731	+	0.122345i
$877$	33.6355	+	9.87628i	1.13579	+	0.333498i	0.794981	−	0.606634i	$-0.207481\pi$
$877$	33.6355	+	9.87628i	1.13579	+	0.333498i	0.340810	+	0.940132i	$0.389299\pi$
$878$	−20.0554	−	23.1452i	−0.676837	−	0.781112i
$879$	−6.58684	+	4.23311i	−0.222169	+	0.142779i
$880$	2.05833	−	2.37544i	0.0693863	−	0.0800761i
$881$	−8.39385	+	58.3805i	−0.282796	+	1.96689i	−0.0292283	+	0.999573i	$0.509305\pi$
$881$	−8.39385	+	58.3805i	−0.282796	+	1.96689i	−0.253568	+	0.967318i	$0.581604\pi$
$882$	−41.5226	+	12.1921i	−1.39814	+	0.410531i
$883$	−19.2293	−	12.3579i	−0.647119	−	0.415878i	0.175494	−	0.984481i	$-0.443848\pi$
$883$	−19.2293	−	12.3579i	−0.647119	−	0.415878i	−0.822612	+	0.568603i	$0.807484\pi$
$884$	−4.58481	−	31.8881i	−0.154204	−	1.07251i
$885$	−0.580057	−	1.27015i	−0.0194984	−	0.0426955i
$886$	−14.4756	−	31.6971i	−0.486317	−	1.06489i
$887$	−2.85635	−	19.8663i	−0.0959068	−	0.667047i	−0.979892	−	0.199531i	$-0.936058\pi$
$887$	−2.85635	−	19.8663i	−0.0959068	−	0.667047i	0.883985	−	0.467516i	$-0.154851\pi$
$888$	−0.182012	−	0.116972i	−0.00610791	−	0.00392531i
$889$	75.8297	−	22.2656i	2.54325	−	0.746765i
$890$	−1.60367	+	11.1538i	−0.0537551	+	0.373875i
$891$	17.2906	−	19.9545i	0.579259	−	0.668500i
$892$	−14.5117	+	9.32611i	−0.485888	+	0.312261i
$893$	19.9613	+	23.0366i	0.667980	+	0.770891i
$894$	0.994873	+	0.292121i	0.0332735	+	0.00976999i
$895$	−1.53755	+	3.36677i	−0.0513947	+	0.112539i
$896$	4.66427			0.155822
$897$	−6.20340	−	0.541562i	−0.207126	−	0.0180822i
$898$	−33.8605			−1.12994
$899$	0.209556	−	0.458863i	0.00698907	−	0.0153039i
$900$	2.81407	+	0.826285i	0.0938022	+	0.0275428i
$901$	−11.2870	−	13.0259i	−0.376024	−	0.433955i
$902$	−30.2825	+	19.4614i	−1.00830	+	0.647994i
$903$	−5.69331	+	6.57043i	−0.189461	+	0.218650i
$904$	−0.680991	+	4.73640i	−0.0226494	+	0.157530i
$905$	−4.19045	+	1.23043i	−0.139295	+	0.0409008i
$906$	1.77686	+	1.14192i	0.0590324	+	0.0379378i
$907$	5.81198	+	40.4232i	0.192984	+	1.34223i	0.824056	+	0.566508i	$0.191706\pi$
$907$	5.81198	+	40.4232i	0.192984	+	1.34223i	−0.631073	+	0.775724i	$0.717385\pi$
$908$	0.332565	+	0.728215i	0.0110365	+	0.0241667i
$909$	−19.7069	−	43.1520i	−0.653635	−	1.43126i
$910$	3.32649	+	23.1362i	0.110272	+	0.766959i
$911$	−19.2070	−	12.3436i	−0.636356	−	0.408961i	0.182302	−	0.983243i	$-0.441645\pi$
$911$	−19.2070	−	12.3436i	−0.636356	−	0.408961i	−0.818658	+	0.574282i	$0.805281\pi$
$912$	1.41508	−	0.415505i	0.0468580	−	0.0137587i
$913$	−6.20477	+	43.1551i	−0.205348	+	1.42823i
$914$	7.16088	−	8.26410i	0.236861	−	0.273352i
$915$	1.07128	−	0.688468i	0.0354153	−	0.0227601i
$916$	1.62909	+	1.88007i	0.0538267	+	0.0621193i
$917$	−18.7781	−	5.51376i	−0.620109	−	0.182080i
$918$	−4.10514	+	8.98900i	−0.135490	+	0.296681i
$919$	23.3350			0.769750			0.384875	−	0.922969i	$-0.374245\pi$
$919$	23.3350			0.769750			0.384875	+	0.922969i	$0.374245\pi$
$920$	−3.79373	−	2.93388i	−0.125075	−	0.0967271i
$921$	4.30462			0.141842
$922$	−4.45592	+	9.75711i	−0.146748	+	0.321333i
$923$	42.0851	+	12.3573i	1.38525	+	0.406745i
$924$	−2.48749	−	2.87071i	−0.0818323	−	0.0944395i
$925$	0.702484	−	0.451459i	0.0230975	−	0.0148439i
$926$	10.1205	−	11.6797i	0.332581	−	0.383819i
$927$	4.46800	−	31.0756i	0.146748	−	1.02066i
$928$	3.84841	−	1.13000i	0.126330	−	0.0370939i
$929$	−26.7304	−	17.1786i	−0.876997	−	0.563612i	0.0228886	−	0.999738i	$-0.492714\pi$
$929$	−26.7304	−	17.1786i	−0.876997	−	0.563612i	−0.899885	+	0.436126i	$0.856350\pi$
$930$	0.00463756	+	0.0322550i	0.000152072	+	0.00105768i
$931$	−34.8907	−	76.3999i	−1.14350	−	2.50391i
$932$	1.54770	+	3.38899i	0.0506966	+	0.111010i
$933$	0.409521	+	2.84828i	0.0134071	+	0.0932486i
$934$	−12.3096	−	7.91091i	−0.402783	−	0.258853i
$935$	−19.3877	+	5.69275i	−0.634046	+	0.186173i
$936$	2.09168	−	14.5480i	0.0683687	−	0.475515i
$937$	−4.62754	+	5.34047i	−0.151175	+	0.174465i	−0.826286	−	0.563251i	$-0.809550\pi$
$937$	−4.62754	+	5.34047i	−0.151175	+	0.174465i	0.675111	+	0.737716i	$0.264096\pi$
$938$	28.0003	−	17.9947i	0.914241	−	0.587547i
$939$	5.36594	+	6.19262i	0.175111	+	0.202088i
$940$	−5.13814	−	1.50869i	−0.167587	−	0.0492081i
$941$	1.05406	−	2.30807i	0.0343614	−	0.0752410i	−0.891673	−	0.452680i	$-0.850468\pi$
$941$	1.05406	−	2.30807i	0.0343614	−	0.0752410i	0.926034	+	0.377439i	$0.123195\pi$
$942$	4.41693			0.143911
$943$	32.2213	+	44.4797i	1.04927	+	1.44846i
$944$	−5.38922			−0.175404
$945$	2.97847	−	6.52193i	0.0968895	−	0.212158i
$946$	21.6959	+	6.37050i	0.705395	+	0.207123i
$947$	37.0217	+	42.7253i	1.20304	+	1.38839i	0.900275	+	0.435322i	$0.143366\pi$
$947$	37.0217	+	42.7253i	1.20304	+	1.38839i	0.302769	+	0.953064i	$0.402089\pi$
$948$	1.12606	−	0.723675i	0.0365727	−	0.0235039i
$949$	−50.4210	+	58.1890i	−1.63674	+	1.88889i
$950$	−0.810078	+	5.63422i	−0.0262824	+	0.182798i
$951$	1.50748	−	0.442635i	0.0488832	−	0.0143534i
$952$	−25.2249	−	16.2110i	−0.817543	−	0.525403i
$953$	−1.00214	−	6.97004i	−0.0324625	−	0.225782i	0.967131	−	0.254277i	$-0.0818375\pi$
$953$	−1.00214	−	6.97004i	−0.0324625	−	0.225782i	−0.999594	+	0.0284953i	$0.990928\pi$
$954$	−3.26652	−	7.15268i	−0.105757	−	0.231577i
$955$	−0.990770	−	2.16948i	−0.0320606	−	0.0702029i
$956$	−0.625924	−	4.35340i	−0.0202438	−	0.140799i
$957$	−2.74786	−	1.76594i	−0.0888258	−	0.0570849i
$958$	11.1542	−	3.27518i	0.360377	−	0.105816i
$959$	−7.74727	+	53.8834i	−0.250172	+	1.73999i
$960$	−0.169672	+	0.195812i	−0.00547615	+	0.00631982i
$961$	−26.0656	+	16.7513i	−0.840824	+	0.540365i
$962$	−2.74038	−	3.16257i	−0.0883535	−	0.101965i
$963$	15.9034	+	4.66966i	0.512480	+	0.150478i
$964$	1.02437	−	2.24306i	0.0329927	−	0.0722440i
$965$	−9.40122			−0.302636
$966$	−4.16197	+	4.03345i	−0.133909	+	0.129774i
$967$	0.315127			0.0101338			0.00506690	−	0.999987i	$-0.498387\pi$
$967$	0.315127			0.0101338			0.00506690	+	0.999987i	$0.498387\pi$
$968$	0.465497	−	1.01930i	0.0149616	−	0.0327614i
$969$	−9.09703	−	2.67113i	−0.292239	−	0.0858090i
$970$	−1.03699	−	1.19675i	−0.0332957	−	0.0384253i
$971$	13.7395	−	8.82985i	0.440922	−	0.283363i	−0.301285	−	0.953534i	$-0.597416\pi$
$971$	13.7395	−	8.82985i	0.440922	−	0.283363i	0.742207	+	0.670171i	$0.233779\pi$
$972$	−4.44524	+	5.13008i	−0.142581	+	0.164547i
$973$	3.52691	−	24.5302i	0.113067	−	0.786402i
$974$	18.7486	−	5.50509i	0.600744	−	0.176394i
$975$	−1.09230	−	0.701978i	−0.0349816	−	0.0224813i
$976$	−0.699460	−	4.86485i	−0.0223892	−	0.155720i
$977$	15.6332	+	34.2319i	0.500150	+	1.09518i	0.976420	+	0.215878i	$0.0692612\pi$
$977$	15.6332	+	34.2319i	0.500150	+	1.09518i	−0.476270	+	0.879299i	$0.658012\pi$
$978$	1.56440	+	3.42555i	0.0500239	+	0.109537i
$979$	−5.04058	−	35.0580i	−0.161098	−	1.12046i
$980$	12.4130	+	7.97736i	0.396519	+	0.254827i
$981$	−12.4225	+	3.64756i	−0.396619	+	0.116458i
$982$	1.50166	−	10.4443i	0.0479198	−	0.333290i
$983$	−20.9128	+	24.1346i	−0.667014	+	0.769775i	−0.983906	−	0.178687i	$-0.942815\pi$
$983$	−20.9128	+	24.1346i	−0.667014	+	0.769775i	0.316892	+	0.948461i	$0.397361\pi$
$984$	2.49625	−	1.60424i	0.0795776	−	0.0511414i
$985$	−1.20413	−	1.38964i	−0.0383667	−	0.0442776i
$986$	−24.7400	−	7.26433i	−0.787883	−	0.231343i
$987$	−2.68839	+	5.88674i	−0.0855723	+	0.187377i
$988$	28.5252			0.907509
$989$	7.86145	−	33.5936i	0.249980	−	1.06821i
$990$	−9.21847			−0.292982
$991$	−22.5494	+	49.3762i	−0.716304	+	1.56849i	0.102708	+	0.994712i	$0.467249\pi$
$991$	−22.5494	+	49.3762i	−0.716304	+	1.56849i	−0.819012	+	0.573776i	$0.805478\pi$
$992$	0.120675	+	0.0354335i	0.00383145	+	0.00112502i
$993$	4.54427	+	5.24437i	0.144208	+	0.166425i
$994$	34.3435	−	22.0712i	1.08931	−	0.700056i
$995$	−3.18931	+	3.68066i	−0.101108	+	0.116685i
$996$	0.511472	−	3.55736i	0.0162066	−	0.112719i
$997$	−19.8893	+	5.84003i	−0.629900	+	0.184955i	−0.581073	−	0.813852i	$-0.697367\pi$
$997$	−19.8893	+	5.84003i	−0.629900	+	0.184955i	−0.0488279	+	0.998807i	$0.515549\pi$
$998$	−23.0676	−	14.8247i	−0.730193	−	0.469267i
$999$	0.182678	+	1.27056i	0.00577969	+	0.0401986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.121.2	✓	20
23.2	even	11		5290.2.a.bj.1.5		10
23.4	even	11	inner	230.2.g.b.211.2	yes	20
23.21	odd	22		5290.2.a.bi.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.121.2	✓	20	1.1	even	1	trivial
230.2.g.b.211.2	yes	20	23.4	even	11	inner
5290.2.a.bi.1.5		10	23.21	odd	22
5290.2.a.bj.1.5		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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.248602 - 0.0729960i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.169672 - 0.195812i) q^{6} +(0.663794 - 4.61679i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.46729 - 1.58563i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.248602 - 0.0729960i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.169672 - 0.195812i) q^{6} +(0.663794 - 4.61679i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.46729 - 1.58563i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-1.30572 - 2.85912i) q^{11} +(0.107633 + 0.235683i) q^{12} +(0.713186 + 4.96032i) q^{13} +(3.92383 + 2.52169i) q^{14} +(-0.248602 + 0.0729960i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.20986 - 4.85844i) q^{17} +(2.46729 - 1.58563i) q^{18} +(3.72757 + 4.30184i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-0.502028 + 1.09929i) q^{21} +3.14316 q^{22} +(-0.267084 - 4.78839i) q^{23} -0.259097 q^{24} +(0.415415 - 0.909632i) q^{25} +(-4.80833 - 1.41185i) q^{26} +(1.00664 + 1.16173i) q^{27} +(-3.92383 + 2.52169i) q^{28} +(-2.62657 + 3.03122i) q^{29} +(0.0368733 - 0.256460i) q^{30} +(-0.120675 + 0.0354335i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.115899 + 0.806093i) q^{33} +(2.67055 + 5.84769i) q^{34} +(-1.93761 - 4.24277i) q^{35} +(0.417391 + 2.90302i) q^{36} +(0.702484 + 0.451459i) q^{37} +(-5.46158 + 1.60367i) q^{38} +(0.184784 - 1.28520i) q^{39} +(0.654861 - 0.755750i) q^{40} +(-9.63443 + 6.19167i) q^{41} +(-0.791397 - 0.913321i) q^{42} +(6.90258 + 2.02678i) q^{43} +(-1.30572 + 2.85912i) q^{44} -2.93287 q^{45} +(4.46662 + 1.74622i) q^{46} +5.35505 q^{47} +(0.107633 - 0.235683i) q^{48} +(-14.1577 - 4.15707i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-1.40123 + 0.900513i) q^{51} +(3.28172 - 3.78731i) q^{52} +(0.381558 - 2.65379i) q^{53} +(-1.47492 + 0.433076i) q^{54} +(-2.64419 - 1.69932i) q^{55} +(-0.663794 - 4.61679i) q^{56} +(-0.612663 - 1.34154i) q^{57} +(-1.66618 - 3.64843i) q^{58} +(0.766966 + 5.33437i) q^{59} +(0.217966 + 0.140078i) q^{60} +(-4.71579 + 1.38468i) q^{61} +(0.0178989 - 0.124490i) q^{62} +(-8.95829 + 10.3384i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.28172 + 3.78731i) q^{65} +(-0.781394 - 0.229438i) q^{66} +(2.96438 - 6.49109i) q^{67} -6.42863 q^{68} +(-0.283136 + 1.20990i) q^{69} +4.66427 q^{70} +(3.63593 - 7.96158i) q^{71} +(-2.81407 - 0.826285i) q^{72} +(10.0614 + 11.6115i) q^{73} +(-0.702484 + 0.451459i) q^{74} +(-0.169672 + 0.195812i) q^{75} +(0.810078 - 5.63422i) q^{76} +(-14.0667 + 4.13035i) q^{77} +(1.09230 + 0.701978i) q^{78} +(-0.735229 - 5.11363i) q^{79} +(0.415415 + 0.909632i) q^{80} +(3.48962 + 7.64120i) q^{81} +(-1.62986 - 11.3359i) q^{82} +(-11.6691 - 7.49925i) q^{83} +(1.15954 - 0.340473i) q^{84} +(0.914890 - 6.36320i) q^{85} +(-4.71106 + 5.43686i) q^{86} +(0.874237 - 0.561838i) q^{87} +(-2.05833 - 2.37544i) q^{88} +(10.8120 + 3.17469i) q^{89} +(1.21836 - 2.66783i) q^{90} +23.3741 q^{91} +(-3.44392 + 3.33758i) q^{92} +0.0325866 q^{93} +(-2.22457 + 4.87113i) q^{94} +(5.46158 + 1.60367i) q^{95} +(0.169672 + 0.195812i) q^{96} +(-1.33215 + 0.856119i) q^{97} +(9.66272 - 11.1514i) q^{98} +(-1.31193 + 9.12464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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