LMFDB - Embedded newform 966.2.q.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
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} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.2
Root			$-1.42457 - 0.418291i$ of defining polynomial
Character	$\chi$	$=$	966.127
Dual form			966.2.q.d.715.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.26582 - 0.958931i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.26582 - 0.958931i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(2.22895 - 2.57234i) q^{10} +(0.242354 + 0.155751i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(1.17217 - 1.35276i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.484396 - 3.36905i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.365891 + 0.801189i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(0.787107 - 1.72352i) q^{19} +(0.484396 - 3.36905i) q^{20} +(-0.841254 + 0.540641i) q^{21} +0.288087 q^{22} +(-3.13162 + 3.63221i) q^{23} -1.00000 q^{24} +(5.53977 - 3.56019i) q^{25} +(0.254737 - 1.77174i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-1.76841 - 3.87228i) q^{29} +(-2.22895 - 2.57234i) q^{30} +(0.596135 + 4.14621i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(0.188657 - 0.217721i) q^{33} +(0.740962 + 0.476188i) q^{34} +(-2.86337 - 1.84018i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(2.02679 + 0.595120i) q^{37} +(-0.269651 - 1.87546i) q^{38} +(-1.17217 - 1.35276i) q^{39} +(-1.41395 - 3.09611i) q^{40} +(3.99143 - 1.17199i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(-0.801118 + 5.57190i) q^{43} +(0.242354 - 0.155751i) q^{44} -3.40369 q^{45} +(-0.670770 + 4.74869i) q^{46} +2.61186 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(2.73556 - 5.99005i) q^{50} +(0.845106 - 0.248145i) q^{51} +(-0.743575 - 1.62820i) q^{52} +(-0.982100 - 1.13340i) q^{53} +(0.142315 + 0.989821i) q^{54} +(0.940839 + 0.276255i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(-1.59396 - 1.02438i) q^{57} +(-3.58120 - 2.30150i) q^{58} +(-6.90623 + 7.97021i) q^{59} +(-3.26582 - 0.958931i) q^{60} +(-1.02804 - 7.15019i) q^{61} +(2.74311 + 3.16572i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.53090 - 5.54190i) q^{65} +(0.0409990 - 0.285154i) q^{66} +(-1.45752 + 0.936692i) q^{67} +0.880784 q^{68} +(3.14956 + 3.61667i) q^{69} -3.40369 q^{70} +(1.64501 - 1.05718i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-3.39909 + 7.44297i) q^{73} +(2.02679 - 0.595120i) q^{74} +(-2.73556 - 5.99005i) q^{75} +(-1.24080 - 1.43195i) q^{76} +(-0.0409990 - 0.285154i) q^{77} +(-1.71745 - 0.504289i) q^{78} +(-0.585965 + 0.676240i) q^{79} +(-2.86337 - 1.84018i) q^{80} +(0.841254 + 0.540641i) q^{81} +(2.72418 - 3.14387i) q^{82} +(3.12351 + 0.917145i) q^{83} +(0.142315 + 0.989821i) q^{84} +(1.96322 + 2.26568i) q^{85} +(2.33845 + 5.12049i) q^{86} +(-4.08454 + 1.19933i) q^{87} +(0.119676 - 0.262053i) q^{88} +(-0.0869863 + 0.605003i) q^{89} +(-2.86337 + 1.84018i) q^{90} -1.78996 q^{91} +(2.00305 + 4.35750i) q^{92} +4.18885 q^{93} +(2.19724 - 1.41208i) q^{94} +(0.917808 - 6.38350i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(2.39358 - 0.702818i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-0.188657 - 0.217721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	3.26582	−	0.958931i	1.46052	−	0.428847i	0.547515	−	0.836796i	$-0.315574\pi$
$5$	3.26582	−	0.958931i	1.46052	−	0.428847i	0.913005	+	0.407949i	$0.133756\pi$
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	2.22895	−	2.57234i	0.704854	−	0.813445i
$11$	0.242354	+	0.155751i	0.0730725	+	0.0469608i	0.576667	−	0.816979i	$-0.304353\pi$
$11$	0.242354	+	0.155751i	0.0730725	+	0.0469608i	−0.503594	+	0.863940i	$0.667989\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	1.17217	−	1.35276i	0.325102	−	0.375188i	−0.569546	−	0.821960i	$-0.692881\pi$
$13$	1.17217	−	1.35276i	0.325102	−	0.375188i	0.894648	+	0.446772i	$0.147426\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	−0.484396	−	3.36905i	−0.125071	−	0.869885i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	0.365891	+	0.801189i	0.0887416	+	0.194317i	0.948799	−	0.315880i	$-0.102300\pi$
$17$	0.365891	+	0.801189i	0.0887416	+	0.194317i	−0.860058	+	0.510197i	$0.829572\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	0.787107	−	1.72352i	0.180575	−	0.395403i	−0.797600	−	0.603186i	$-0.793898\pi$
$19$	0.787107	−	1.72352i	0.180575	−	0.395403i	0.978175	+	0.207783i	$0.0666248\pi$
$20$	0.484396	−	3.36905i	0.108314	−	0.753342i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	0.288087			0.0614203
$23$	−3.13162	+	3.63221i	−0.652989	+	0.757368i
$23$	−3.13162	+	3.63221i	−0.652989	+	0.757368i
$24$	−1.00000			−0.204124
$25$	5.53977	−	3.56019i	1.10795	−	0.712038i
$26$	0.254737	−	1.77174i	0.0499581	−	0.347466i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	−1.76841	−	3.87228i	−0.328386	−	0.719065i	0.671371	−	0.741122i	$-0.265706\pi$
$29$	−1.76841	−	3.87228i	−0.328386	−	0.719065i	−0.999757	+	0.0220569i	$0.992979\pi$
$30$	−2.22895	−	2.57234i	−0.406948	−	0.469643i
$31$	0.596135	+	4.14621i	0.107069	+	0.744682i	0.970654	+	0.240479i	$0.0773045\pi$
$31$	0.596135	+	4.14621i	0.107069	+	0.744682i	−0.863585	+	0.504203i	$0.831786\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	0.188657	−	0.217721i	0.0328409	−	0.0379004i
$34$	0.740962	+	0.476188i	0.127074	+	0.0816655i
$35$	−2.86337	−	1.84018i	−0.483998	−	0.311046i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	2.02679	+	0.595120i	0.333203	+	0.0978371i	0.444054	−	0.896000i	$-0.353540\pi$
$37$	2.02679	+	0.595120i	0.333203	+	0.0978371i	−0.110852	+	0.993837i	$0.535358\pi$
$38$	−0.269651	−	1.87546i	−0.0437431	−	0.304240i
$39$	−1.17217	−	1.35276i	−0.187698	−	0.216615i
$40$	−1.41395	−	3.09611i	−0.223564	−	0.489538i
$41$	3.99143	−	1.17199i	0.623357	−	0.183034i	0.0452241	−	0.998977i	$-0.485600\pi$
$41$	3.99143	−	1.17199i	0.623357	−	0.183034i	0.578133	+	0.815943i	$0.303782\pi$
$42$	−0.415415	+	0.909632i	−0.0640999	+	0.140359i
$43$	−0.801118	+	5.57190i	−0.122169	+	0.849706i	0.832921	+	0.553392i	$0.186667\pi$
$43$	−0.801118	+	5.57190i	−0.122169	+	0.849706i	−0.955090	+	0.296314i	$0.904242\pi$
$44$	0.242354	−	0.155751i	0.0365362	−	0.0234804i
$45$	−3.40369			−0.507393
$46$	−0.670770	+	4.74869i	−0.0988997	+	0.700156i
$47$	2.61186			0.380979			0.190490	−	0.981689i	$-0.438992\pi$
$47$	2.61186			0.380979			0.190490	+	0.981689i	$0.438992\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	2.73556	−	5.99005i	0.386867	−	0.847121i
$51$	0.845106	−	0.248145i	0.118338	−	0.0347473i
$52$	−0.743575	−	1.62820i	−0.103115	−	0.225791i
$53$	−0.982100	−	1.13340i	−0.134902	−	0.155685i	0.684279	−	0.729220i	$-0.260117\pi$
$53$	−0.982100	−	1.13340i	−0.134902	−	0.155685i	−0.819181	+	0.573535i	$0.805572\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	0.940839	+	0.276255i	0.126863	+	0.0372503i
$56$	−0.654861	+	0.755750i	−0.0875094	+	0.100991i
$57$	−1.59396	−	1.02438i	−0.211126	−	0.135682i
$58$	−3.58120	−	2.30150i	−0.470234	−	0.302201i
$59$	−6.90623	+	7.97021i	−0.899114	+	1.03763i	0.0999762	+	0.994990i	$0.468123\pi$
$59$	−6.90623	+	7.97021i	−0.899114	+	1.03763i	−0.999090	+	0.0426432i	$0.986422\pi$
$60$	−3.26582	−	0.958931i	−0.421616	−	0.123798i
$61$	−1.02804	−	7.15019i	−0.131627	−	0.915488i	−0.943434	−	0.331562i	$-0.892425\pi$
$61$	−1.02804	−	7.15019i	−0.131627	−	0.915488i	0.811806	−	0.583927i	$-0.198485\pi$
$62$	2.74311	+	3.16572i	0.348376	+	0.402047i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	2.53090	−	5.54190i	0.313920	−	0.687388i
$66$	0.0409990	−	0.285154i	0.00504663	−	0.0351001i
$67$	−1.45752	+	0.936692i	−0.178064	+	0.114435i	−0.626637	−	0.779311i	$-0.715569\pi$
$67$	−1.45752	+	0.936692i	−0.178064	+	0.114435i	0.448572	+	0.893747i	$0.351933\pi$
$68$	0.880784			0.106811
$69$	3.14956	+	3.61667i	0.379162	+	0.435395i
$70$	−3.40369			−0.406819
$71$	1.64501	−	1.05718i	0.195227	−	0.125465i	−0.439376	−	0.898303i	$-0.644800\pi$
$71$	1.64501	−	1.05718i	0.195227	−	0.125465i	0.634602	+	0.772839i	$0.281164\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−3.39909	+	7.44297i	−0.397834	+	0.871134i	0.599652	+	0.800261i	$0.295306\pi$
$73$	−3.39909	+	7.44297i	−0.397834	+	0.871134i	−0.997485	+	0.0708729i	$0.977422\pi$
$74$	2.02679	−	0.595120i	0.235610	−	0.0691813i
$75$	−2.73556	−	5.99005i	−0.315876	−	0.691671i
$76$	−1.24080	−	1.43195i	−0.142329	−	0.164256i
$77$	−0.0409990	−	0.285154i	−0.00467227	−	0.0324964i
$78$	−1.71745	−	0.504289i	−0.194463	−	0.0570995i
$79$	−0.585965	+	0.676240i	−0.0659262	+	0.0760829i	−0.787755	−	0.615989i	$-0.788757\pi$
$79$	−0.585965	+	0.676240i	−0.0659262	+	0.0760829i	0.721828	+	0.692072i	$0.243302\pi$
$80$	−2.86337	−	1.84018i	−0.320134	−	0.205738i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	2.72418	−	3.14387i	0.300835	−	0.347182i
$83$	3.12351	+	0.917145i	0.342849	+	0.100670i	0.448624	−	0.893720i	$-0.351914\pi$
$83$	3.12351	+	0.917145i	0.342849	+	0.100670i	−0.105775	+	0.994390i	$0.533732\pi$
$84$	0.142315	+	0.989821i	0.0155278	+	0.107998i
$85$	1.96322	+	2.26568i	0.212941	+	0.245747i
$86$	2.33845	+	5.12049i	0.252162	+	0.552157i
$87$	−4.08454	+	1.19933i	−0.437909	+	0.128582i
$88$	0.119676	−	0.262053i	0.0127575	−	0.0279349i
$89$	−0.0869863	+	0.605003i	−0.00922053	+	0.0641302i	−0.993912	−	0.110175i	$-0.964859\pi$
$89$	−0.0869863	+	0.605003i	−0.00922053	+	0.0641302i	0.984692	+	0.174305i	$0.0557679\pi$
$90$	−2.86337	+	1.84018i	−0.301826	+	0.193972i
$91$	−1.78996			−0.187638
$92$	2.00305	+	4.35750i	0.208832	+	0.454301i
$93$	4.18885			0.434363
$94$	2.19724	−	1.41208i	0.226628	−	0.145645i
$95$	0.917808	−	6.38350i	0.0941652	−	0.654933i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	2.39358	−	0.702818i	0.243031	−	0.0713604i	−0.157948	−	0.987447i	$-0.550488\pi$
$97$	2.39358	−	0.702818i	0.243031	−	0.0713604i	0.400980	+	0.916087i	$0.368670\pi$
$98$	0.415415	+	0.909632i	0.0419633	+	0.0918867i
$99$	−0.188657	−	0.217721i	−0.0189607	−	0.0218818i
$100$	−0.937162	−	6.51810i	−0.0937162	−	0.651810i
$101$	4.74469	+	1.39317i	0.472114	+	0.138625i	0.509130	−	0.860689i	$-0.329967\pi$
$101$	4.74469	+	1.39317i	0.472114	+	0.138625i	−0.0370162	+	0.999315i	$0.511785\pi$
$102$	0.576791	−	0.665652i	0.0571108	−	0.0659094i
$103$	−10.7655	−	6.91855i	−1.06075	−	0.681705i	−0.110720	−	0.993852i	$-0.535316\pi$
$103$	−10.7655	−	6.91855i	−1.06075	−	0.681705i	−0.950034	+	0.312147i	$0.898952\pi$
$104$	−1.50581	−	0.967724i	−0.147657	−	0.0948931i
$105$	−2.22895	+	2.57234i	−0.217523	+	0.251035i
$106$	−1.43896	−	0.422517i	−0.139764	−	0.0410384i
$107$	−0.460999	−	3.20632i	−0.0445665	−	0.309967i	−0.999896	−	0.0144239i	$-0.995409\pi$
$107$	−0.460999	−	3.20632i	−0.0445665	−	0.309967i	0.955329	−	0.295543i	$-0.0955005\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	0.687584	+	1.50560i	0.0658586	+	0.144210i	0.939699	−	0.342003i	$-0.111105\pi$
$109$	0.687584	+	1.50560i	0.0658586	+	0.144210i	−0.873840	+	0.486213i	$0.838378\pi$
$110$	0.940839	−	0.276255i	0.0897055	−	0.0263399i
$111$	0.877505	−	1.92147i	0.0832891	−	0.182378i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	15.4740	−	9.94456i	1.45567	−	0.935505i	0.456729	−	0.889606i	$-0.349021\pi$
$113$	15.4740	−	9.94456i	1.45567	−	0.935505i	0.998946	−	0.0458994i	$-0.0146154\pi$
$114$	−1.89475			−0.177459
$115$	−6.74428	+	14.8651i	−0.628908	+	1.38618i
$116$	−4.25698			−0.395250
$117$	−1.50581	+	0.967724i	−0.139212	+	0.0894661i
$118$	−1.50087	+	10.4388i	−0.138166	+	0.960965i
$119$	0.365891	−	0.801189i	0.0335412	−	0.0734449i
$120$	−3.26582	+	0.958931i	−0.298127	+	0.0875381i
$121$	−4.53509	−	9.93046i	−0.412281	−	0.902769i
$122$	−4.73053	−	5.45932i	−0.428282	−	0.494264i
$123$	−0.592021	−	4.11760i	−0.0533807	−	0.371271i
$124$	4.01917	+	1.18014i	0.360932	+	0.105979i
$125$	3.53317	−	4.07750i	0.316017	−	0.364703i
$126$	0.841254	+	0.540641i	0.0749448	+	0.0481641i
$127$	7.46636	+	4.79834i	0.662532	+	0.425784i	0.828226	−	0.560394i	$-0.189350\pi$
$127$	7.46636	+	4.79834i	0.662532	+	0.425784i	−0.165694	+	0.986177i	$0.552986\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	5.40117	+	1.58593i	0.475547	+	0.139633i
$130$	−0.867048	−	6.03045i	−0.0760451	−	0.528906i
$131$	8.40460	+	9.69943i	0.734313	+	0.847443i	0.992950	−	0.118532i	$-0.0378187\pi$
$131$	8.40460	+	9.69943i	0.734313	+	0.847443i	−0.258637	+	0.965975i	$0.583273\pi$
$132$	−0.119676	−	0.262053i	−0.0104164	−	0.0228088i
$133$	−1.81800	+	0.533812i	−0.157640	+	0.0462874i
$134$	−0.719731	+	1.57599i	−0.0621753	+	0.136145i
$135$	−0.484396	+	3.36905i	−0.0416902	+	0.289962i
$136$	0.740962	−	0.476188i	0.0635370	−	0.0408328i
$137$	10.3311			0.882649			0.441325	−	0.897348i	$-0.354509\pi$
$137$	10.3311			0.882649			0.441325	+	0.897348i	$0.354509\pi$
$138$	4.60490	+	1.33975i	0.391995	+	0.114047i
$139$	−18.0845			−1.53391			−0.766953	−	0.641703i	$-0.778228\pi$
$139$	−18.0845			−1.53391			−0.766953	+	0.641703i	$0.778228\pi$
$140$	−2.86337	+	1.84018i	−0.241999	+	0.155523i
$141$	0.371707	−	2.58528i	0.0313033	−	0.217719i
$142$	0.812314	−	1.77872i	0.0681679	−	0.149267i
$143$	0.494775	−	0.145279i	0.0413751	−	0.0121488i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−9.48857	−	10.9504i	−0.787983	−	0.909380i
$146$	1.16448	+	8.09911i	0.0963728	+	0.670287i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	1.38330	−	1.59641i	0.113707	−	0.131224i
$149$	12.5940	+	8.09369i	1.03174	+	0.663061i	0.942931	−	0.332988i	$-0.108057\pi$
$149$	12.5940	+	8.09369i	1.03174	+	0.663061i	0.0888113	+	0.996048i	$0.471693\pi$
$150$	−5.53977	−	3.56019i	−0.452320	−	0.290688i
$151$	−1.92982	+	2.22713i	−0.157046	+	0.181241i	−0.828820	−	0.559515i	$-0.810987\pi$
$151$	−1.92982	+	2.22713i	−0.157046	+	0.181241i	0.671774	+	0.740756i	$0.265533\pi$
$152$	−1.81800	−	0.533812i	−0.147459	−	0.0432979i
$153$	−0.125349	−	0.871819i	−0.0101338	−	0.0704824i
$154$	−0.188657	−	0.217721i	−0.0152024	−	0.0175445i
$155$	5.92281	+	12.9691i	0.475731	+	1.04171i
$156$	−1.71745	+	0.504289i	−0.137506	+	0.0403754i
$157$	−7.82797	+	17.1409i	−0.624740	+	1.36799i	0.287280	+	0.957847i	$0.407249\pi$
$157$	−7.82797	+	17.1409i	−0.624740	+	1.36799i	−0.912021	+	0.410144i	$0.865478\pi$
$158$	−0.127342	+	0.885686i	−0.0101308	+	0.0704614i
$159$	−1.26163	+	0.810803i	−0.100054	+	0.0643009i
$160$	−3.40369			−0.269086
$161$	4.79582	−	0.0118662i	0.377963	−	0.000935189i
$162$	1.00000			0.0785674
$163$	6.58637	−	4.23280i	0.515884	−	0.331538i	−0.256658	−	0.966502i	$-0.582621\pi$
$163$	6.58637	−	4.23280i	0.515884	−	0.331538i	0.772542	+	0.634964i	$0.218985\pi$
$164$	0.592021	−	4.11760i	0.0462291	−	0.321530i
$165$	0.407339	−	0.891948i	0.0317113	−	0.0694380i
$166$	3.12351	−	0.917145i	0.242431	−	0.0711842i
$167$	1.19542	+	2.61761i	0.0925044	+	0.202556i	0.950228	−	0.311554i	$-0.100849\pi$
$167$	1.19542	+	2.61761i	0.0925044	+	0.202556i	−0.857724	+	0.514110i	$0.828122\pi$
$168$	0.654861	+	0.755750i	0.0505236	+	0.0583073i
$169$	1.39412	+	9.69635i	0.107240	+	0.745873i
$170$	2.87648	+	0.844611i	0.220616	+	0.0647787i
$171$	−1.24080	+	1.43195i	−0.0948860	+	0.109504i
$172$	4.73558	+	3.04337i	0.361084	+	0.232055i
$173$	10.3553	+	6.65493i	0.787297	+	0.505965i	0.871448	−	0.490488i	$-0.163181\pi$
$173$	10.3553	+	6.65493i	0.787297	+	0.505965i	−0.0841509	+	0.996453i	$0.526818\pi$
$174$	−2.78773	+	3.21721i	−0.211337	+	0.243896i
$175$	−6.31839	−	1.85525i	−0.477625	−	0.140243i
$176$	−0.0409990	−	0.285154i	−0.00309042	−	0.0214943i
$177$	6.90623	+	7.97021i	0.519104	+	0.599078i
$178$	0.253912	+	0.555989i	0.0190315	+	0.0416731i
$179$	10.3008	−	3.02460i	0.769921	−	0.226069i	0.126898	−	0.991916i	$-0.459498\pi$
$179$	10.3008	−	3.02460i	0.769921	−	0.226069i	0.643023	+	0.765847i	$0.277680\pi$
$180$	−1.41395	+	3.09611i	−0.105389	+	0.230770i
$181$	−3.10918	+	21.6248i	−0.231104	+	1.60736i	0.462241	+	0.886754i	$0.347046\pi$
$181$	−3.10918	+	21.6248i	−0.231104	+	1.60736i	−0.693344	+	0.720606i	$0.743864\pi$
$182$	−1.50581	+	0.967724i	−0.111618	+	0.0717324i
$183$	−7.22372			−0.533993
$184$	4.04091	+	2.58283i	0.297900	+	0.190409i
$185$	7.18982			0.528606
$186$	3.52388	−	2.26466i	0.258384	−	0.166053i
$187$	−0.0361113	+	0.251159i	−0.00264072	+	0.0183666i
$188$	1.08501	−	2.37583i	0.0791322	−	0.173275i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	−2.67907	−	5.86634i	−0.194360	−	0.425589i
$191$	−1.74904	−	2.01850i	−0.126556	−	0.146053i	0.688935	−	0.724823i	$-0.258079\pi$
$191$	−1.74904	−	2.01850i	−0.126556	−	0.146053i	−0.815491	+	0.578770i	$0.803533\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	6.88928	+	2.02288i	0.495902	+	0.145610i	0.520114	−	0.854097i	$-0.325890\pi$
$193$	6.88928	+	2.02288i	0.495902	+	0.145610i	−0.0242122	+	0.999707i	$0.507708\pi$
$194$	1.63363	−	1.88532i	0.117288	−	0.135358i
$195$	−5.12531	−	3.29383i	−0.367031	−	0.235876i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−6.59680	+	7.61311i	−0.470002	+	0.542412i	−0.940412	−	0.340036i	$-0.889561\pi$
$197$	−6.59680	+	7.61311i	−0.470002	+	0.542412i	0.470410	+	0.882448i	$0.344106\pi$
$198$	−0.276417	−	0.0811634i	−0.0196441	−	0.00576803i
$199$	1.94088	+	13.4991i	0.137585	+	0.956927i	0.935291	+	0.353880i	$0.115138\pi$
$199$	1.94088	+	13.4991i	0.137585	+	0.956927i	−0.797706	+	0.603047i	$0.793953\pi$
$200$	−4.31234	−	4.97671i	−0.304929	−	0.351907i
$201$	0.719731	+	1.57599i	0.0507659	+	0.111162i
$202$	4.74469	−	1.39317i	0.333835	−	0.0980228i
$203$	−1.76841	+	3.87228i	−0.124118	+	0.271781i
$204$	0.125349	−	0.871819i	0.00877616	−	0.0610395i
$205$	11.9114	−	7.65502i	0.831931	−	0.534650i
$206$	−12.7969			−0.891605
$207$	4.02808	−	2.60280i	0.279971	−	0.180907i
$208$	−1.78996			−0.124111
$209$	0.459200	−	0.295110i	0.0317635	−	0.0204132i
$210$	−0.484396	+	3.36905i	−0.0334265	+	0.232486i
$211$	−7.05925	+	15.4576i	−0.485979	+	1.06414i	0.494798	+	0.869008i	$0.335242\pi$
$211$	−7.05925	+	15.4576i	−0.485979	+	1.06414i	−0.980776	+	0.195136i	$0.937485\pi$
$212$	−1.43896	+	0.422517i	−0.0988281	+	0.0290186i
$213$	−0.812314	−	1.77872i	−0.0556589	−	0.121876i
$214$	−2.12129	−	2.44809i	−0.145008	−	0.167348i
$215$	2.72676	+	18.9650i	0.185963	+	1.29340i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	2.74311	−	3.16572i	0.186215	−	0.214903i
$218$	1.39242	+	0.894855i	0.0943067	+	0.0606072i
$219$	6.88347	+	4.42374i	0.465142	+	0.298929i
$220$	0.642130	−	0.741057i	0.0432924	−	0.0499621i
$221$	1.51270	+	0.444170i	0.101755	+	0.0298781i
$222$	−0.300620	−	2.09086i	−0.0201763	−	0.140329i
$223$	10.7201	+	12.3717i	0.717871	+	0.828468i	0.991049	−	0.133496i	$-0.0426203\pi$
$223$	10.7201	+	12.3717i	0.717871	+	0.828468i	−0.273178	+	0.961963i	$0.588075\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	−6.31839	+	1.85525i	−0.421226	+	0.123683i
$226$	7.64115	−	16.7318i	0.508282	−	1.11298i
$227$	−2.32643	+	16.1807i	−0.154411	+	1.07395i	0.754302	+	0.656527i	$0.227975\pi$
$227$	−2.32643	+	16.1807i	−0.154411	+	1.07395i	−0.908713	+	0.417422i	$0.862934\pi$
$228$	−1.59396	+	1.02438i	−0.105563	+	0.0678411i
$229$	−28.9402			−1.91242			−0.956210	−	0.292680i	$-0.905453\pi$
$229$	−28.9402			−1.91242			−0.956210	+	0.292680i	$0.905453\pi$
$230$	2.36305	+	16.1516i	0.155815	+	1.06500i
$231$	−0.288087			−0.0189547
$232$	−3.58120	+	2.30150i	−0.235117	+	0.151101i
$233$	2.35308	−	16.3661i	0.154156	−	1.07218i	−0.755002	−	0.655723i	$-0.772364\pi$
$233$	2.35308	−	16.3661i	0.154156	−	1.07218i	0.909157	−	0.416453i	$-0.136727\pi$
$234$	−0.743575	+	1.62820i	−0.0486090	+	0.106439i
$235$	8.52987	−	2.50460i	0.556427	−	0.163382i
$236$	4.38101	+	9.59307i	0.285179	+	0.624456i
$237$	0.585965	+	0.676240i	0.0380625	+	0.0439265i
$238$	−0.125349	−	0.871819i	−0.00812514	−	0.0565116i
$239$	−14.6327	−	4.29655i	−0.946511	−	0.277921i	−0.228177	−	0.973620i	$-0.573277\pi$
$239$	−14.6327	−	4.29655i	−0.946511	−	0.277921i	−0.718333	+	0.695699i	$0.755095\pi$
$240$	−2.22895	+	2.57234i	−0.143878	+	0.166044i
$241$	5.67065	+	3.64431i	0.365279	+	0.234750i	0.710385	−	0.703813i	$-0.248521\pi$
$241$	5.67065	+	3.64431i	0.365279	+	0.234750i	−0.345106	+	0.938564i	$0.612157\pi$
$242$	−9.18397	−	5.90218i	−0.590368	−	0.379406i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−6.93111	−	2.03516i	−0.443719	−	0.130288i
$245$	0.484396	+	3.36905i	0.0309469	+	0.215241i
$246$	−2.72418	−	3.14387i	−0.173687	−	0.200446i
$247$	−1.40889	−	3.08503i	−0.0896453	−	0.196296i
$248$	4.01917	−	1.18014i	0.255218	−	0.0749387i
$249$	1.35233	−	2.96119i	0.0857005	−	0.187658i
$250$	0.767832	−	5.34039i	0.0485619	−	0.337756i
$251$	5.39280	−	3.46574i	0.340391	−	0.218756i	−0.359266	−	0.933235i	$-0.616973\pi$
$251$	5.39280	−	3.46574i	0.340391	−	0.218756i	0.699656	+	0.714480i	$0.253336\pi$
$252$	1.00000			0.0629941
$253$	−1.32468	+	0.392525i	−0.0832821	+	0.0246778i
$254$	8.87528			0.556885
$255$	2.52201	−	1.62080i	0.157934	−	0.101498i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	9.08539	−	19.8942i	0.566731	−	1.24097i	−0.381789	−	0.924250i	$-0.624692\pi$
$257$	9.08539	−	19.8942i	0.566731	−	1.24097i	0.948520	−	0.316718i	$-0.102581\pi$
$258$	5.40117	−	1.58593i	0.336262	−	0.0987355i
$259$	−0.877505	−	1.92147i	−0.0545255	−	0.119394i
$260$	−3.98972	−	4.60438i	−0.247432	−	0.285551i
$261$	0.605831	+	4.21365i	0.0375000	+	0.260818i
$262$	12.3143	+	3.61581i	0.760780	+	0.223385i
$263$	16.0411	−	18.5124i	0.989134	−	1.14152i	−0.000801430	−	1.00000i	$-0.500255\pi$
$263$	16.0411	−	18.5124i	0.989134	−	1.14152i	0.989935	−	0.141522i	$-0.0451994\pi$
$264$	−0.242354	−	0.155751i	−0.0149159	−	0.00958584i
$265$	−4.29422	−	2.75973i	−0.263792	−	0.169529i
$266$	−1.24080	+	1.43195i	−0.0760781	+	0.0877988i
$267$	0.586465	+	0.172202i	0.0358911	+	0.0105386i
$268$	0.246569	+	1.71492i	0.0150616	+	0.104756i
$269$	−12.0857	−	13.9476i	−0.736875	−	0.850399i	0.256353	−	0.966583i	$-0.417479\pi$
$269$	−12.0857	−	13.9476i	−0.736875	−	0.850399i	−0.993228	+	0.116184i	$0.962934\pi$
$270$	1.41395	+	3.09611i	0.0860500	+	0.188423i
$271$	8.03674	−	2.35980i	0.488197	−	0.143348i	−0.0283645	−	0.999598i	$-0.509030\pi$
$271$	8.03674	−	2.35980i	0.488197	−	0.143348i	0.516562	+	0.856250i	$0.327212\pi$
$272$	0.365891	−	0.801189i	0.0221854	−	0.0485792i
$273$	−0.254737	+	1.77174i	−0.0154174	+	0.107230i
$274$	8.69111	−	5.58544i	0.525049	−	0.337429i
$275$	1.89709			0.114399
$276$	4.59821	−	1.36252i	0.276780	−	0.0820143i
$277$	7.07448			0.425064			0.212532	−	0.977154i	$-0.431829\pi$
$277$	7.07448			0.425064			0.212532	+	0.977154i	$0.431829\pi$
$278$	−15.2136	+	9.77721i	−0.912454	+	0.586398i
$279$	0.596135	−	4.14621i	0.0356897	−	0.248227i
$280$	−1.41395	+	3.09611i	−0.0844994	+	0.185028i
$281$	−11.2281	+	3.29686i	−0.669810	+	0.196674i	−0.598919	−	0.800810i	$-0.704403\pi$
$281$	−11.2281	+	3.29686i	−0.669810	+	0.196674i	−0.0708918	+	0.997484i	$0.522584\pi$
$282$	−1.08501	−	2.37583i	−0.0646112	−	0.141479i
$283$	−20.8013	−	24.0060i	−1.23651	−	1.42701i	−0.867391	−	0.497627i	$-0.834205\pi$
$283$	−20.8013	−	24.0060i	−1.23651	−	1.42701i	−0.369119	−	0.929382i	$-0.620340\pi$
$284$	−0.278287	−	1.93553i	−0.0165133	−	0.114852i
$285$	−6.18790	−	1.81693i	−0.366540	−	0.107626i
$286$	0.337687	−	0.389712i	0.0199679	−	0.0230441i
$287$	−3.49956	−	2.24903i	−0.206573	−	0.132756i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	10.6246	−	12.2614i	0.624977	−	0.721262i
$290$	−13.9025	−	4.08215i	−0.816384	−	0.239712i
$291$	−0.355023	−	2.46924i	−0.0208118	−	0.144749i
$292$	5.35833	+	6.18384i	0.313573	+	0.361882i
$293$	−3.30252	−	7.23151i	−0.192935	−	0.422469i	0.788298	−	0.615294i	$-0.210963\pi$
$293$	−3.30252	−	7.23151i	−0.192935	−	0.422469i	−0.981233	+	0.192824i	$0.938235\pi$
$294$	0.959493	−	0.281733i	0.0559588	−	0.0164310i
$295$	−14.9116	+	32.6519i	−0.868188	+	1.90107i
$296$	0.300620	−	2.09086i	0.0174732	−	0.121529i
$297$	−0.242354	+	0.155751i	−0.0140628	+	0.00903761i
$298$	14.9705			0.867220
$299$	1.24270	+	8.49391i	0.0718671	+	0.491215i
$300$	−6.58513			−0.380193
$301$	4.73558	−	3.04337i	0.272954	−	0.175417i
$302$	−0.419389	+	2.91692i	−0.0241331	+	0.167850i
$303$	2.05423	−	4.49813i	0.118012	−	0.258411i
$304$	−1.81800	+	0.533812i	−0.104269	+	0.0306162i
$305$	−10.2139	−	22.3654i	−0.584849	−	1.28064i
$306$	−0.576791	−	0.665652i	−0.0329729	−	0.0380528i
$307$	0.157596	+	1.09611i	0.00899450	+	0.0625581i	0.993824	−	0.110965i	$-0.0353941\pi$
$307$	0.157596	+	1.09611i	0.00899450	+	0.0625581i	−0.984830	+	0.173523i	$0.944485\pi$
$308$	−0.276417	−	0.0811634i	−0.0157503	−	0.00462471i
$309$	−8.38022	+	9.67128i	−0.476734	+	0.550180i
$310$	11.9942	+	7.70822i	0.681226	+	0.437797i
$311$	−3.77407	−	2.42545i	−0.214008	−	0.137535i	0.429245	−	0.903188i	$-0.358780\pi$
$311$	−3.77407	−	2.42545i	−0.214008	−	0.137535i	−0.643254	+	0.765653i	$0.722416\pi$
$312$	−1.17217	+	1.35276i	−0.0663612	+	0.0765849i
$313$	−26.7097	−	7.84269i	−1.50972	−	0.443295i	−0.580949	−	0.813940i	$-0.697318\pi$
$313$	−26.7097	−	7.84269i	−1.50972	−	0.443295i	−0.928775	+	0.370645i	$0.879137\pi$
$314$	2.68174	+	18.6519i	0.151340	+	1.05259i
$315$	2.22895	+	2.57234i	0.125587	+	0.144935i
$316$	0.371711	+	0.813933i	0.0209104	+	0.0457873i
$317$	15.2171	−	4.46814i	0.854678	−	0.250956i	0.175092	−	0.984552i	$-0.443978\pi$
$317$	15.2171	−	4.46814i	0.854678	−	0.250956i	0.679586	+	0.733596i	$0.262160\pi$
$318$	−0.623001	+	1.36418i	−0.0349362	+	0.0764995i
$319$	0.174532	−	1.21390i	0.00977191	−	0.0679651i
$320$	−2.86337	+	1.84018i	−0.160067	+	0.102869i
$321$	−3.23929			−0.180800
$322$	4.02808	−	2.60280i	0.224476	−	0.145048i
$323$	1.66886			0.0928580
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	1.67748	−	11.6671i	0.0930498	−	0.647176i
$326$	3.25238	−	7.12172i	0.180133	−	0.394435i
$327$	1.58813	−	0.466317i	0.0878237	−	0.0257874i
$328$	−1.72810	−	3.78401i	−0.0954184	−	0.208937i
$329$	−1.71040	−	1.97391i	−0.0942977	−	0.108825i
$330$	−0.139548	−	0.970578i	−0.00768187	−	0.0534286i
$331$	−5.71944	−	1.67938i	−0.314369	−	0.0923071i	0.120742	−	0.992684i	$-0.461473\pi$
$331$	−5.71944	−	1.67938i	−0.314369	−	0.0923071i	−0.435111	+	0.900377i	$0.643291\pi$
$332$	2.13182	−	2.46025i	0.116999	−	0.135024i
$333$	−1.77703	−	1.14203i	−0.0973806	−	0.0625827i
$334$	2.42084	+	1.55578i	0.132462	+	0.0851283i
$335$	−3.86178	+	4.45673i	−0.210991	+	0.243497i
$336$	0.959493	+	0.281733i	0.0523446	+	0.0153698i
$337$	−1.73537	−	12.0698i	−0.0945315	−	0.657481i	−0.980902	−	0.194504i	$-0.937690\pi$
$337$	−1.73537	−	12.0698i	−0.0945315	−	0.657481i	0.886370	−	0.462977i	$-0.153219\pi$
$338$	6.41505	+	7.40336i	0.348933	+	0.402690i
$339$	−7.64115	−	16.7318i	−0.415010	−	0.908746i
$340$	2.87648	−	0.844611i	0.155999	−	0.0458055i
$341$	−0.501303	+	1.09770i	−0.0271471	+	0.0594438i
$342$	−0.269651	+	1.87546i	−0.0145810	+	0.101413i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	5.62919			0.303506
$345$	13.7540	+	8.79117i	0.740492	+	0.473301i
$346$	12.3093			0.661754
$347$	27.0634	−	17.3926i	1.45284	−	0.933684i	0.453747	−	0.891131i	$-0.350087\pi$
$347$	27.0634	−	17.3926i	1.45284	−	0.933684i	0.999094	−	0.0425533i	$-0.0135492\pi$
$348$	−0.605831	+	4.21365i	−0.0324759	+	0.225875i
$349$	4.37757	−	9.58555i	0.234326	−	0.513103i	−0.755541	−	0.655102i	$-0.772626\pi$
$349$	4.37757	−	9.58555i	0.234326	−	0.513103i	0.989867	+	0.141999i	$0.0453530\pi$
$350$	−6.31839	+	1.85525i	−0.337732	+	0.0991671i
$351$	0.743575	+	1.62820i	0.0396891	+	0.0869070i
$352$	−0.188657	−	0.217721i	−0.0100554	−	0.0116046i
$353$	4.71023	+	32.7604i	0.250700	+	1.74366i	0.594028	+	0.804444i	$0.297537\pi$
$353$	4.71023	+	32.7604i	0.250700	+	1.74366i	−0.343328	+	0.939216i	$0.611554\pi$
$354$	10.1189	+	2.97118i	0.537814	+	0.157916i
$355$	4.35854	−	5.03003i	0.231327	−	0.266966i
$356$	0.514195	+	0.330453i	0.0272523	+	0.0175140i
$357$	−0.740962	−	0.476188i	−0.0392159	−	0.0252025i
$358$	7.03039	−	8.11351i	0.371568	−	0.428812i
$359$	−26.3613	−	7.74037i	−1.39129	−	0.408521i	−0.501609	−	0.865095i	$-0.667258\pi$
$359$	−26.3613	−	7.74037i	−1.39129	−	0.408521i	−0.889686	+	0.456574i	$0.849076\pi$
$360$	0.484396	+	3.36905i	0.0255299	+	0.177564i
$361$	10.0914	+	11.6460i	0.531124	+	0.612950i
$362$	9.07565	+	19.8729i	0.477006	+	1.04450i
$363$	−10.4748	+	3.07568i	−0.549784	+	0.161431i
$364$	−0.743575	+	1.62820i	−0.0389739	+	0.0853410i
$365$	−3.96352	+	27.5669i	−0.207460	+	1.44292i
$366$	−6.07698	+	3.90544i	−0.317649	+	0.204141i
$367$	−12.3652			−0.645461			−0.322730	−	0.946491i	$-0.604601\pi$
$367$	−12.3652			−0.645461			−0.322730	+	0.946491i	$0.604601\pi$
$368$	4.79582	−	0.0118662i	0.249999	−	0.000618569i
$369$	−4.15994			−0.216558
$370$	6.04846	−	3.88711i	0.314445	−	0.202081i
$371$	−0.213431	+	1.48444i	−0.0110808	+	0.0770684i
$372$	1.74011	−	3.81031i	0.0902206	−	0.197555i
$373$	−19.5857	+	5.75087i	−1.01411	+	0.297769i	−0.746233	−	0.665685i	$-0.768139\pi$
$373$	−19.5857	+	5.75087i	−1.01411	+	0.297769i	−0.267874	+	0.963454i	$0.586321\pi$
$374$	0.105408	+	0.230812i	0.00545053	+	0.0119350i
$375$	−3.53317	−	4.07750i	−0.182452	−	0.210561i
$376$	−0.371707	−	2.58528i	−0.0191693	−	0.133325i
$377$	−7.31115	−	2.14675i	−0.376543	−	0.110563i
$378$	0.654861	−	0.755750i	0.0336824	−	0.0388716i
$379$	−22.4834	−	14.4492i	−1.15489	−	0.742205i	−0.184286	−	0.982873i	$-0.558997\pi$
$379$	−22.4834	−	14.4492i	−1.15489	−	0.742205i	−0.970607	+	0.240668i	$0.922633\pi$
$380$	−5.42536	−	3.48667i	−0.278315	−	0.178862i
$381$	5.81207	−	6.70749i	0.297761	−	0.343635i
$382$	−2.56267	−	0.752467i	−0.131118	−	0.0384996i
$383$	1.01894	+	7.08691i	0.0520656	+	0.362124i	0.999153	+	0.0411486i	$0.0131017\pi$
$383$	1.01894	+	7.08691i	0.0520656	+	0.362124i	−0.947087	+	0.320976i	$0.895989\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	−0.407339	−	0.891948i	−0.0207599	−	0.0454579i
$386$	6.88928	−	2.02288i	0.350655	−	0.102962i
$387$	2.33845	−	5.12049i	0.118870	−	0.260289i
$388$	0.355023	−	2.46924i	0.0180236	−	0.125357i
$389$	8.11024	−	5.21213i	0.411205	−	0.264266i	−0.318643	−	0.947875i	$-0.603227\pi$
$389$	8.11024	−	5.21213i	0.411205	−	0.264266i	0.729848	+	0.683609i	$0.239591\pi$
$390$	−6.09246			−0.308504
$391$	−4.05592	−	1.18003i	−0.205117	−	0.0596768i
$392$	1.00000			0.0505076
$393$	10.7968	−	6.93868i	0.544627	−	0.350010i
$394$	−1.43362	+	9.97105i	−0.0722248	+	0.502334i
$395$	−1.26519	+	2.77038i	−0.0636586	+	0.139393i
$396$	−0.276417	+	0.0811634i	−0.0138905	+	0.00407861i
$397$	−13.0348	−	28.5422i	−0.654198	−	1.43249i	−0.887831	−	0.460169i	$-0.847789\pi$
$397$	−13.0348	−	28.5422i	−0.654198	−	1.43249i	0.233634	−	0.972325i	$-0.424938\pi$
$398$	8.93094	+	10.3069i	0.447668	+	0.516636i
$399$	0.269651	+	1.87546i	0.0134994	+	0.0938905i
$400$	−6.31839	−	1.85525i	−0.315919	−	0.0927623i
$401$	−7.91331	+	9.13245i	−0.395172	+	0.456053i	−0.918115	−	0.396315i	$-0.870289\pi$
$401$	−7.91331	+	9.13245i	−0.395172	+	0.456053i	0.522943	+	0.852368i	$0.324834\pi$
$402$	1.45752	+	0.936692i	0.0726945	+	0.0467179i
$403$	6.30760	+	4.05365i	0.314204	+	0.201927i
$404$	3.23828	−	3.73718i	0.161111	−	0.185932i
$405$	3.26582	+	0.958931i	0.162280	+	0.0476497i
$406$	0.605831	+	4.21365i	0.0300669	+	0.209120i
$407$	0.398510	+	0.459906i	0.0197534	+	0.0227967i
$408$	−0.365891	−	0.801189i	−0.0181143	−	0.0396648i
$409$	−3.98986	+	1.17153i	−0.197286	+	0.0579283i	−0.378883	−	0.925445i	$-0.623692\pi$
$409$	−3.98986	+	1.17153i	−0.197286	+	0.0579283i	0.181597	+	0.983373i	$0.441873\pi$
$410$	5.88193	−	12.8796i	0.290488	−	0.636079i
$411$	1.47028	−	10.2260i	0.0725233	−	0.504411i
$412$	−10.7655	+	6.91855i	−0.530377	+	0.340852i
$413$	10.5461			0.518940
$414$	1.98146	−	4.36736i	0.0973835	−	0.214644i
$415$	11.0803			0.543910
$416$	−1.50581	+	0.967724i	−0.0738283	+	0.0474466i
$417$	−2.57369	+	17.9004i	−0.126034	+	0.876587i
$418$	0.226755	−	0.496524i	0.0110909	−	0.0242858i
$419$	−27.6498	+	8.11872i	−1.35078	+	0.396625i	−0.875504	−	0.483210i	$-0.839471\pi$
$419$	−27.6498	+	8.11872i	−1.35078	+	0.396625i	−0.475278	+	0.879836i	$0.657652\pi$
$420$	1.41395	+	3.09611i	0.0689935	+	0.151075i
$421$	−0.906278	−	1.04590i	−0.0441693	−	0.0509741i	0.733235	−	0.679975i	$-0.238010\pi$
$421$	−0.906278	−	1.04590i	−0.0441693	−	0.0509741i	−0.777404	+	0.629001i	$0.783464\pi$
$422$	2.41839	+	16.8203i	0.117725	+	0.818798i
$423$	−2.50606	−	0.735846i	−0.121849	−	0.0357781i
$424$	−0.982100	+	1.13340i	−0.0476950	+	0.0550429i
$425$	4.87934	+	3.13576i	0.236683	+	0.152107i
$426$	−1.64501	−	1.05718i	−0.0797011	−	0.0512208i
$427$	−4.73053	+	5.45932i	−0.228926	+	0.264195i
$428$	−3.10808	−	0.912614i	−0.150235	−	0.0441129i
$429$	−0.0733865	−	0.510414i	−0.00354313	−	0.0246430i
$430$	12.5472	+	14.4802i	0.605078	+	0.698297i
$431$	−10.9357	−	23.9459i	−0.526755	−	1.15343i	−0.966818	−	0.255466i	$-0.917771\pi$
$431$	−10.9357	−	23.9459i	−0.526755	−	1.15343i	0.440063	−	0.897967i	$-0.354956\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	−13.3782	+	29.2941i	−0.642915	+	1.40779i	0.254706	+	0.967018i	$0.418021\pi$
$433$	−13.3782	+	29.2941i	−0.642915	+	1.40779i	−0.897621	+	0.440768i	$0.854706\pi$
$434$	0.596135	−	4.14621i	0.0286154	−	0.199025i
$435$	−12.1893	+	7.83358i	−0.584432	+	0.375592i
$436$	1.65517			0.0792685
$437$	3.79527	+	8.25636i	0.181552	+	0.394955i
$438$	8.18240			0.390970
$439$	10.9229	−	7.01973i	0.521322	−	0.335033i	−0.253373	−	0.967369i	$-0.581540\pi$
$439$	10.9229	−	7.01973i	0.521322	−	0.335033i	0.774695	+	0.632335i	$0.217904\pi$
$440$	0.139548	−	0.970578i	0.00665269	−	0.0462705i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	1.51270	−	0.444170i	0.0719519	−	0.0211270i
$443$	−15.6678	−	34.3076i	−0.744398	−	1.63000i	−0.776182	−	0.630509i	$-0.782846\pi$
$443$	−15.6678	−	34.3076i	−0.744398	−	1.63000i	0.0317840	−	0.999495i	$-0.489881\pi$
$444$	−1.38330	−	1.59641i	−0.0656485	−	0.0757625i
$445$	0.296075	+	2.05924i	0.0140353	+	0.0976175i
$446$	15.7070	+	4.61198i	0.743746	+	0.218383i
$447$	9.80362	−	11.3140i	0.463695	−	0.535133i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−7.81408	−	5.02180i	−0.368769	−	0.236994i	0.343110	−	0.939295i	$-0.388519\pi$
$449$	−7.81408	−	5.02180i	−0.368769	−	0.236994i	−0.711880	+	0.702301i	$0.752156\pi$
$450$	−4.31234	+	4.97671i	−0.203286	+	0.234604i
$451$	1.14988	+	0.337635i	0.0541456	+	0.0158986i
$452$	−2.61774	−	18.2068i	−0.123128	−	0.856376i
$453$	1.92982	+	2.22713i	0.0906707	+	0.104640i
$454$	6.79082	+	14.8698i	0.318709	+	0.697875i
$455$	−5.84568	+	1.71645i	−0.274050	+	0.0804682i
$456$	−0.787107	+	1.72352i	−0.0368596	+	0.0807114i
$457$	1.36981	−	9.52724i	0.0640770	−	0.445665i	−0.932374	−	0.361494i	$-0.882267\pi$
$457$	1.36981	−	9.52724i	0.0640770	−	0.445665i	0.996451	−	0.0841711i	$-0.0268242\pi$
$458$	−24.3460	+	15.6462i	−1.13762	+	0.731101i
$459$	−0.880784			−0.0411115
$460$	10.7201	+	12.3100i	0.499829	+	0.573958i
$461$	−13.9651			−0.650421			−0.325211	−	0.945642i	$-0.605435\pi$
$461$	−13.9651			−0.650421			−0.325211	+	0.945642i	$0.605435\pi$
$462$	−0.242354	+	0.155751i	−0.0112753	+	0.00724621i
$463$	−0.0744451	+	0.517777i	−0.00345976	+	0.0240632i	−0.991478	−	0.130273i	$-0.958415\pi$
$463$	−0.0744451	+	0.517777i	−0.00345976	+	0.0240632i	0.988018	+	0.154336i	$0.0493238\pi$
$464$	−1.76841	+	3.87228i	−0.0820965	+	0.179766i
$465$	13.6800	−	4.01682i	0.634396	−	0.186276i
$466$	−6.86862	−	15.0402i	−0.318183	−	0.696723i
$467$	18.6514	+	21.5249i	0.863085	+	0.996053i	0.999985	+	0.00546805i	$0.00174054\pi$
$467$	18.6514	+	21.5249i	0.863085	+	0.996053i	−0.136900	+	0.990585i	$0.543714\pi$
$468$	0.254737	+	1.77174i	0.0117752	+	0.0818986i
$469$	1.66238	+	0.488118i	0.0767615	+	0.0225392i
$470$	5.82169	−	6.71859i	0.268535	−	0.309906i
$471$	15.8524	+	10.1877i	0.730438	+	0.469424i
$472$	8.87194	+	5.70165i	0.408364	+	0.262440i
$473$	−1.06198	+	1.22560i	−0.0488301	+	0.0563529i
$474$	0.858548	+	0.252093i	0.0394344	+	0.0115790i
$475$	−1.77569	−	12.3502i	−0.0814740	−	0.566664i
$476$	−0.576791	−	0.665652i	−0.0264372	−	0.0305101i
$477$	0.623001	+	1.36418i	0.0285253	+	0.0624616i
$478$	−14.6327	+	4.29655i	−0.669284	+	0.196520i
$479$	3.03789	−	6.65205i	0.138805	−	0.303940i	−0.827445	−	0.561546i	$-0.810207\pi$
$479$	3.03789	−	6.65205i	0.138805	−	0.303940i	0.966250	+	0.257607i	$0.0829339\pi$
$480$	−0.484396	+	3.36905i	−0.0221096	+	0.153775i
$481$	3.18080	−	2.04418i	0.145032	−	0.0932065i
$482$	6.74072			0.307031
$483$	0.670770	−	4.74869i	0.0305211	−	0.216073i
$484$	−10.9170			−0.496228
$485$	7.14305	−	4.59056i	0.324349	−	0.208446i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	3.83449	−	8.39635i	0.173757	−	0.380475i	−0.802638	−	0.596466i	$-0.796571\pi$
$487$	3.83449	−	8.39635i	0.173757	−	0.380475i	0.976395	+	0.215991i	$0.0692982\pi$
$488$	−6.93111	+	2.03516i	−0.313757	+	0.0921272i
$489$	−3.25238	−	7.12172i	−0.147078	−	0.322055i
$490$	2.22895	+	2.57234i	0.100693	+	0.116206i
$491$	3.15779	+	21.9629i	0.142509	+	0.991174i	0.928074	+	0.372395i	$0.121463\pi$
$491$	3.15779	+	21.9629i	0.142509	+	0.991174i	−0.785565	+	0.618779i	$0.787628\pi$
$492$	−3.99143	−	1.17199i	−0.179948	−	0.0528374i
$493$	2.45538	−	2.83366i	0.110585	−	0.127622i
$494$	−2.85312	−	1.83359i	−0.128368	−	0.0824972i
$495$	−0.824899	−	0.530130i	−0.0370764	−	0.0238276i
$496$	2.74311	−	3.16572i	0.123169	−	0.142145i
$497$	−1.87622	−	0.550908i	−0.0841600	−	0.0247116i
$498$	−0.463288	−	3.22224i	−0.0207604	−	0.144392i
$499$	−5.47520	−	6.31872i	−0.245104	−	0.282865i	0.619846	−	0.784724i	$-0.287195\pi$
$499$	−5.47520	−	6.31872i	−0.245104	−	0.282865i	−0.864949	+	0.501859i	$0.832650\pi$
$500$	−2.24129	−	4.90774i	−0.100234	−	0.219481i
$501$	2.76109	−	0.810729i	0.123356	−	0.0362207i
$502$	2.66299	−	5.83114i	0.118855	−	0.260256i
$503$	2.74492	−	19.0914i	0.122390	−	0.851241i	−0.832446	−	0.554107i	$-0.813060\pi$
$503$	2.74492	−	19.0914i	0.122390	−	0.851241i	0.954836	−	0.297135i	$-0.0960310\pi$
$504$	0.841254	−	0.540641i	0.0374724	−	0.0240821i
$505$	16.8312			0.748981
$506$	−0.902179	+	1.04639i	−0.0401068	+	0.0465177i
$507$	9.79606			0.435058
$508$	7.46636	−	4.79834i	0.331266	−	0.212892i
$509$	5.03955	−	35.0508i	0.223374	−	1.55360i	−0.501769	−	0.865002i	$-0.667317\pi$
$509$	5.03955	−	35.0508i	0.223374	−	1.55360i	0.725143	−	0.688598i	$-0.241774\pi$
$510$	1.24538	−	2.72700i	0.0551464	−	0.120754i
$511$	7.85095	−	2.30525i	0.347306	−	0.101978i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	1.24080	+	1.43195i	0.0547825	+	0.0632223i
$514$	−3.11251	−	21.6480i	−0.137287	−	0.954853i
$515$	−41.7925	−	12.2714i	−1.84160	−	0.540742i
$516$	3.68634	−	4.25426i	0.162282	−	0.187283i
$517$	0.632995	+	0.406801i	0.0278391	+	0.0178911i
$518$	−1.77703	−	1.14203i	−0.0780782	−	0.0501778i
$519$	8.06090	−	9.30278i	0.353834	−	0.408347i
$520$	−5.84568	−	1.71645i	−0.256350	−	0.0752711i
$521$	3.58897	+	24.9619i	0.157236	+	1.09360i	0.903698	+	0.428171i	$0.140842\pi$
$521$	3.58897	+	24.9619i	0.157236	+	1.09360i	−0.746462	+	0.665428i	$0.768249\pi$
$522$	2.78773	+	3.21721i	0.122015	+	0.140813i
$523$	0.571249	+	1.25086i	0.0249790	+	0.0546963i	0.921710	−	0.387879i	$-0.126792\pi$
$523$	0.571249	+	1.25086i	0.0249790	+	0.0546963i	−0.896731	+	0.442575i	$0.854065\pi$
$524$	12.3143	−	3.61581i	0.537953	−	0.157957i
$525$	−2.73556	+	5.99005i	−0.119390	+	0.261427i
$526$	3.48605	−	24.2460i	0.151999	−	1.05718i
$527$	−3.10378	+	1.99468i	−0.135203	+	0.0868896i
$528$	−0.288087			−0.0125374
$529$	−3.38586	−	22.7494i	−0.147211	−	0.989105i
$530$	−5.10455			−0.221727
$531$	8.87194	−	5.70165i	0.385010	−	0.247431i
$532$	−0.269651	+	1.87546i	−0.0116908	+	0.0813116i
$533$	3.09322	−	6.77322i	0.133982	−	0.293381i
$534$	0.586465	−	0.172202i	0.0253788	−	0.00745190i
$535$	−4.58018	−	10.0292i	−0.198019	−	0.433600i
$536$	1.13458	+	1.30938i	0.0490066	+	0.0565566i
$537$	−1.52785	−	10.6264i	−0.0659316	−	0.458564i
$538$	−17.7077	−	5.19946i	−0.763434	−	0.224165i
$539$	−0.188657	+	0.217721i	−0.00812602	+	0.00937792i
$540$	2.86337	+	1.84018i	0.123220	+	0.0791886i
$541$	10.1551	+	6.52628i	0.436601	+	0.280587i	0.740422	−	0.672143i	$-0.234626\pi$
$541$	10.1551	+	6.52628i	0.436601	+	0.280587i	−0.303820	+	0.952729i	$0.598262\pi$
$542$	5.48513	−	6.33018i	0.235606	−	0.271904i
$543$	20.9622	+	6.15507i	0.899576	+	0.264139i
$544$	−0.125349	−	0.871819i	−0.00537428	−	0.0373789i
$545$	3.68929	+	4.25767i	0.158032	+	0.182379i
$546$	0.743575	+	1.62820i	0.0318221	+	0.0696806i
$547$	−29.3490	+	8.61765i	−1.25487	+	0.368464i	−0.840584	−	0.541681i	$-0.817788\pi$
$547$	−29.3490	+	8.61765i	−1.25487	+	0.368464i	−0.414290	+	0.910145i	$0.635970\pi$
$548$	4.29171	−	9.39754i	0.183333	−	0.401443i
$549$	−1.02804	+	7.15019i	−0.0438758	+	0.305163i
$550$	1.59593	−	1.02564i	0.0680508	−	0.0437336i
$551$	−8.06589			−0.343619
$552$	3.13162	−	3.63221i	0.133291	−	0.154597i
$553$	0.894794			0.0380505
$554$	5.95143	−	3.82475i	0.252852	−	0.162498i
$555$	1.02322	−	7.11664i	0.0434332	−	0.302085i
$556$	−7.51257	+	16.4502i	−0.318604	+	0.697645i
$557$	−18.2341	+	5.35400i	−0.772602	+	0.226856i	−0.644191	−	0.764865i	$-0.722806\pi$
$557$	−18.2341	+	5.35400i	−0.772602	+	0.226856i	−0.128411	+	0.991721i	$0.540988\pi$
$558$	−1.74011	−	3.81031i	−0.0736648	−	0.161303i
$559$	6.59838	+	7.61494i	0.279082	+	0.322078i
$560$	0.484396	+	3.36905i	0.0204695	+	0.142368i
$561$	0.243464	+	0.0714874i	0.0102790	+	0.00301820i
$562$	−7.66323	+	8.84384i	−0.323254	+	0.373055i
$563$	−8.09371	−	5.20151i	−0.341109	−	0.219218i	0.358859	−	0.933392i	$-0.383166\pi$
$563$	−8.09371	−	5.20151i	−0.341109	−	0.219218i	−0.699968	+	0.714174i	$0.746802\pi$
$564$	−2.19724	−	1.41208i	−0.0925204	−	0.0594592i
$565$	40.9993	−	47.3157i	1.72485	−	1.99059i
$566$	−30.4778	−	8.94909i	−1.28108	−	0.376158i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−1.28053	−	1.47781i	−0.0537300	−	0.0620077i
$569$	−12.3451	−	27.0320i	−0.517534	−	1.13324i	−0.970365	−	0.241644i	$-0.922313\pi$
$569$	−12.3451	−	27.0320i	−0.517534	−	1.13324i	0.452831	−	0.891596i	$-0.350414\pi$
$570$	−6.18790	+	1.81693i	−0.259183	+	0.0761029i
$571$	−16.4266	+	35.9693i	−0.687434	+	1.50527i	0.167136	+	0.985934i	$0.446548\pi$
$571$	−16.4266	+	35.9693i	−0.687434	+	1.50527i	−0.854570	+	0.519336i	$0.826179\pi$
$572$	0.0733865	−	0.510414i	0.00306844	−	0.0213415i
$573$	−2.24687	+	1.44397i	−0.0938642	+	0.0603229i
$574$	−4.15994			−0.173632
$575$	−4.41711	+	31.2708i	−0.184206	+	1.30408i
$576$	1.00000			0.0416667
$577$	−8.01904	+	5.15353i	−0.333837	+	0.214544i	−0.696810	−	0.717256i	$-0.745398\pi$
$577$	−8.01904	+	5.15353i	−0.333837	+	0.214544i	0.362973	+	0.931800i	$0.381762\pi$
$578$	2.30895	−	16.0591i	0.0960395	−	0.667970i
$579$	2.98273	−	6.53128i	0.123958	−	0.271431i
$580$	−13.9025	+	4.08215i	−0.577271	+	0.169502i
$581$	−1.35233	−	2.96119i	−0.0561041	−	0.122851i
$582$	−1.63363	−	1.88532i	−0.0677163	−	0.0781488i
$583$	−0.0614865	−	0.427648i	−0.00254651	−	0.0177114i
$584$	7.85095	+	2.30525i	0.324875	+	0.0953918i
$585$	−3.98972	+	4.60438i	−0.164954	+	0.190368i
$586$	−6.68791	−	4.29806i	−0.276275	−	0.177551i
$587$	−31.0799	−	19.9739i	−1.28281	−	0.824409i	−0.291575	−	0.956548i	$-0.594179\pi$
$587$	−31.0799	−	19.9739i	−1.28281	−	0.824409i	−0.991231	+	0.132139i	$0.957816\pi$
$588$	0.654861	−	0.755750i	0.0270060	−	0.0311666i
$589$	7.61532	+	2.23606i	0.313784	+	0.0921352i
$590$	5.10849	+	35.5303i	0.210313	+	1.46276i
$591$	6.59680	+	7.61311i	0.271356	+	0.313161i
$592$	−0.877505	−	1.92147i	−0.0360652	−	0.0789719i
$593$	33.3314	−	9.78697i	1.36875	−	0.401903i	0.486914	−	0.873450i	$-0.338123\pi$
$593$	33.3314	−	9.78697i	1.36875	−	0.401903i	0.881841	+	0.471547i	$0.156304\pi$
$594$	−0.119676	+	0.262053i	−0.00491035	+	0.0107522i
$595$	0.426648	−	2.96740i	0.0174909	−	0.121652i
$596$	12.5940	−	8.09369i	0.515871	−	0.331530i
$597$	13.6379			0.558163
$598$	5.63758	+	6.47367i	0.230538	+	0.264728i
$599$	−41.6239			−1.70071			−0.850354	−	0.526212i	$-0.823612\pi$
$599$	−41.6239			−1.70071			−0.850354	+	0.526212i	$0.823612\pi$
$600$	−5.53977	+	3.56019i	−0.226160	+	0.145344i
$601$	2.38672	−	16.6000i	0.0973562	−	0.677127i	−0.881441	−	0.472294i	$-0.843426\pi$
$601$	2.38672	−	16.6000i	0.0973562	−	0.677127i	0.978797	−	0.204833i	$-0.0656650\pi$
$602$	2.33845	−	5.12049i	0.0953081	−	0.208696i
$603$	1.66238	−	0.488118i	0.0676972	−	0.0198777i
$604$	1.22419	+	2.68061i	0.0498117	+	0.109072i
$605$	−24.3334	−	28.0823i	−0.989294	−	1.14171i
$606$	−0.703746	−	4.89466i	−0.0285877	−	0.198832i
$607$	19.5573	+	5.74255i	0.793807	+	0.233083i	0.653402	−	0.757011i	$-0.273341\pi$
$607$	19.5573	+	5.74255i	0.793807	+	0.233083i	0.140406	+	0.990094i	$0.455159\pi$
$608$	−1.24080	+	1.43195i	−0.0503209	+	0.0580734i
$609$	3.58120	+	2.30150i	0.145117	+	0.0932613i
$610$	−20.6842	−	13.2929i	−0.837478	−	0.538214i
$611$	3.06155	−	3.53322i	0.123857	−	0.142939i
$612$	−0.845106	−	0.248145i	−0.0341614	−	0.0100307i
$613$	−2.19995	−	15.3010i	−0.0888551	−	0.618001i	−0.984781	−	0.173798i	$-0.944396\pi$
$613$	−2.19995	−	15.3010i	−0.0888551	−	0.618001i	0.895926	−	0.444203i	$-0.146513\pi$
$614$	0.725179	+	0.836901i	0.0292658	+	0.0337746i
$615$	−5.88193	−	12.8796i	−0.237182	−	0.519356i
$616$	−0.276417	+	0.0811634i	−0.0111372	+	0.00327017i
$617$	−14.1434	+	30.9697i	−0.569392	+	1.24679i	0.377729	+	0.925916i	$0.376705\pi$
$617$	−14.1434	+	30.9697i	−0.569392	+	1.24679i	−0.947121	+	0.320878i	$0.896022\pi$
$618$	−1.82119	+	12.6667i	−0.0732592	+	0.509529i
$619$	−24.7001	+	15.8738i	−0.992781	+	0.638022i	−0.932882	−	0.360183i	$-0.882714\pi$
$619$	−24.7001	+	15.8738i	−0.992781	+	0.638022i	−0.0598994	+	0.998204i	$0.519078\pi$
$620$	14.2576			0.572597
$621$	−2.00305	−	4.35750i	−0.0803796	−	0.174860i
$622$	−4.48625			−0.179882
$623$	0.514195	−	0.330453i	0.0206008	−	0.0132393i
$624$	−0.254737	+	1.77174i	−0.0101977	+	0.0709263i
$625$	−6.04915	+	13.2458i	−0.241966	+	0.529831i
$626$	−26.7097	+	7.84269i	−1.06754	+	0.313457i
$627$	−0.226755	−	0.496524i	−0.00905572	−	0.0198293i
$628$	12.3400	+	14.2412i	0.492421	+	0.568284i
$629$	0.264781	+	1.84159i	0.0105575	+	0.0734291i
$630$	3.26582	+	0.958931i	0.130113	+	0.0382047i
$631$	28.1428	−	32.4785i	1.12035	−	1.29295i	0.168729	−	0.985662i	$-0.446034\pi$
$631$	28.1428	−	32.4785i	1.12035	−	1.29295i	0.951617	−	0.307286i	$-0.0994209\pi$
$632$	0.752748	+	0.483762i	0.0299427	+	0.0192430i
$633$	14.2956	+	9.18724i	0.568200	+	0.365160i
$634$	10.3858	−	11.9858i	0.412472	−	0.476018i
$635$	28.9851	+	8.51078i	1.15024	+	0.337740i
$636$	0.213431	+	1.48444i	0.00846308	+	0.0588620i
$637$	1.17217	+	1.35276i	0.0464432	+	0.0535983i
$638$	−0.509456	−	1.11555i	−0.0201696	−	0.0441652i
$639$	−1.87622	+	0.550908i	−0.0742221	+	0.0217936i
$640$	−1.41395	+	3.09611i	−0.0558911	+	0.122384i
$641$	−3.65079	+	25.3918i	−0.144198	+	1.00292i	0.781298	+	0.624158i	$0.214558\pi$
$641$	−3.65079	+	25.3918i	−0.144198	+	1.00292i	−0.925496	+	0.378758i	$0.876351\pi$
$642$	−2.72507	+	1.75129i	−0.107550	+	0.0691180i
$643$	−31.7242			−1.25108			−0.625541	−	0.780192i	$-0.715122\pi$
$643$	−31.7242			−1.25108			−0.625541	+	0.780192i	$0.715122\pi$
$644$	1.98146	−	4.36736i	0.0780805	−	0.172098i
$645$	19.1600			0.754426
$646$	1.40394	−	0.902255i	0.0552372	−	0.0354988i
$647$	6.79823	−	47.2827i	0.267266	−	1.85888i	−0.206796	−	0.978384i	$-0.566304\pi$
$647$	6.79823	−	47.2827i	0.267266	−	1.85888i	0.474062	−	0.880491i	$-0.342787\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−2.91512	+	0.855957i	−0.114429	+	0.0335993i
$650$	−4.89654	−	10.7219i	−0.192058	−	0.420548i
$651$	−2.74311	−	3.16572i	−0.107511	−	0.124074i
$652$	−1.11422	−	7.74954i	−0.0436360	−	0.303495i
$653$	2.64976	+	0.778040i	0.103693	+	0.0304471i	0.333168	−	0.942868i	$-0.391883\pi$
$653$	2.64976	+	0.778040i	0.103693	+	0.0304471i	−0.229474	+	0.973315i	$0.573701\pi$
$654$	1.08391	−	1.25090i	0.0423842	−	0.0489140i
$655$	36.7490	+	23.6172i	1.43590	+	0.922798i
$656$	−3.49956	−	2.24903i	−0.136635	−	0.0878099i
$657$	5.35833	−	6.18384i	0.209048	−	0.241255i
$658$	−2.50606	−	0.735846i	−0.0976965	−	0.0286863i
$659$	−4.89405	−	34.0388i	−0.190645	−	1.32596i	−0.830306	−	0.557308i	$-0.811834\pi$
$659$	−4.89405	−	34.0388i	−0.190645	−	1.32596i	0.639661	−	0.768657i	$-0.279075\pi$
$660$	−0.642130	−	0.741057i	−0.0249949	−	0.0288456i
$661$	−11.3787	−	24.9160i	−0.442581	−	0.969118i	−0.991117	−	0.132991i	$-0.957542\pi$
$661$	−11.3787	−	24.9160i	−0.442581	−	0.969118i	0.548536	−	0.836127i	$-0.315185\pi$
$662$	−5.71944	+	1.67938i	−0.222293	+	0.0652710i
$663$	0.654929	−	1.43409i	0.0254353	−	0.0556956i
$664$	0.463288	−	3.22224i	0.0179791	−	0.125047i
$665$	−5.42536	+	3.48667i	−0.210387	+	0.135207i
$666$	−2.11236			−0.0818522
$667$	19.6029	+	5.70329i	0.759029	+	0.220832i
$668$	2.87765			0.111340
$669$	13.7714	−	8.85032i	0.532432	−	0.342173i
$670$	−0.839244	+	5.83707i	−0.0324228	+	0.225506i
$671$	0.864503	−	1.89300i	0.0333738	−	0.0730783i
$672$	0.959493	−	0.281733i	0.0370132	−	0.0108681i
$673$	0.472368	+	1.03434i	0.0182085	+	0.0398710i	0.918518	−	0.395380i	$-0.129387\pi$
$673$	0.472368	+	1.03434i	0.0182085	+	0.0398710i	−0.900309	+	0.435251i	$0.856660\pi$
$674$	−7.98529	−	9.21551i	−0.307582	−	0.354968i
$675$	0.937162	+	6.51810i	0.0360714	+	0.250882i
$676$	9.39925	+	2.75987i	0.361509	+	0.106149i
$677$	7.84058	−	9.04852i	0.301338	−	0.347763i	−0.584805	−	0.811174i	$-0.698829\pi$
$677$	7.84058	−	9.04852i	0.301338	−	0.347763i	0.886144	+	0.463411i	$0.153375\pi$
$678$	−15.4740	−	9.94456i	−0.594277	−	0.381918i
$679$	−2.09862	−	1.34870i	−0.0805375	−	0.0517583i
$680$	1.96322	−	2.26568i	0.0752860	−	0.0868847i
$681$	15.6849	+	4.60550i	0.601047	+	0.176483i
$682$	0.171739	+	1.19447i	0.00657621	+	0.0457386i
$683$	−1.60654	−	1.85404i	−0.0614724	−	0.0709429i	0.724180	−	0.689610i	$-0.242218\pi$
$683$	−1.60654	−	1.85404i	−0.0614724	−	0.0709429i	−0.785653	+	0.618668i	$0.787673\pi$
$684$	0.787107	+	1.72352i	0.0300958	+	0.0659005i
$685$	33.7397	−	9.90686i	1.28913	−	0.378522i
$686$	0.415415	−	0.909632i	0.0158606	−	0.0347299i
$687$	−4.11862	+	28.6456i	−0.157135	+	1.09290i
$688$	4.73558	−	3.04337i	0.180542	−	0.116027i
$689$	−2.68441			−0.102268
$690$	16.3235	−	0.0403890i	0.621425	−	0.00153758i
$691$	11.4700			0.436341			0.218170	−	0.975911i	$-0.429991\pi$
$691$	11.4700			0.436341			0.218170	+	0.975911i	$0.429991\pi$
$692$	10.3553	−	6.65493i	0.393649	−	0.252983i
$693$	−0.0409990	+	0.285154i	−0.00155742	+	0.0108321i
$694$	13.3640	−	29.2632i	0.507292	−	1.11082i
$695$	−59.0607	+	17.3418i	−2.24030	+	0.657811i
$696$	1.76841	+	3.87228i	0.0670315	+	0.146778i
$697$	2.39941	+	2.76907i	0.0908843	+	0.104886i
$698$	−1.49969	−	10.4306i	−0.0567641	−	0.394803i
$699$	−15.8646	−	4.65826i	−0.600054	−	0.176192i
$700$	−4.31234	+	4.97671i	−0.162991	+	0.188102i
$701$	−0.270476	−	0.173824i	−0.0102157	−	0.00656525i	0.535523	−	0.844521i	$-0.320115\pi$
$701$	−0.270476	−	0.173824i	−0.0102157	−	0.00656525i	−0.545739	+	0.837955i	$0.683751\pi$
$702$	1.50581	+	0.967724i	0.0568330	+	0.0365244i
$703$	2.62101	−	3.02480i	0.0988531	−	0.114083i
$704$	−0.276417	−	0.0811634i	−0.0104179	−	0.00305896i
$705$	−1.26518	−	8.79949i	−0.0476493	−	0.331408i
$706$	21.6741	+	25.0132i	0.815716	+	0.941386i
$707$	−2.05423	−	4.49813i	−0.0772571	−	0.169169i
$708$	10.1189	−	2.97118i	0.380292	−	0.111664i
$709$	−13.3237	+	29.1748i	−0.500381	+	1.09568i	0.475964	+	0.879465i	$0.342099\pi$
$709$	−13.3237	+	29.1748i	−0.500381	+	1.09568i	−0.976345	+	0.216217i	$0.930628\pi$
$710$	0.947202	−	6.58793i	0.0355479	−	0.247241i
$711$	0.752748	−	0.483762i	0.0282303	−	0.0181425i
$712$	0.611224			0.0229066
$713$	−16.9268	−	10.8191i	−0.633913	−	0.405178i
$714$	−0.880784			−0.0329625
$715$	1.47653	−	0.948910i	0.0552192	−	0.0354872i
$716$	1.52785	−	10.6264i	0.0570985	−	0.397128i
$717$	−6.33527	+	13.8723i	−0.236595	+	0.518071i
$718$	−26.3613	+	7.74037i	−0.983794	+	0.288868i
$719$	2.75745	+	6.03796i	0.102835	+	0.225178i	0.954055	−	0.299632i	$-0.0968638\pi$
$719$	2.75745	+	6.03796i	0.102835	+	0.225178i	−0.851220	+	0.524810i	$0.824136\pi$
$720$	2.22895	+	2.57234i	0.0830679	+	0.0958655i
$721$	1.82119	+	12.6667i	0.0678248	+	0.471732i
$722$	14.7857	+	4.34148i	0.550268	+	0.161573i
$723$	4.41423	−	5.09429i	0.164167	−	0.189459i
$724$	18.3790	+	11.8115i	0.683051	+	0.438970i
$725$	−23.5826	−	15.1556i	−0.875838	−	0.562867i
$726$	−7.14912	+	8.25052i	−0.265329	+	0.306206i
$727$	13.1744	+	3.86836i	0.488612	+	0.143469i	0.516753	−	0.856135i	$-0.327141\pi$
$727$	13.1744	+	3.86836i	0.488612	+	0.143469i	−0.0281411	+	0.999604i	$0.508959\pi$
$728$	0.254737	+	1.77174i	0.00944120	+	0.0656650i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	11.5695	+	25.3336i	0.428205	+	0.937638i
$731$	−4.75726	+	1.39686i	−0.175954	+	0.0516647i
$732$	−3.00084	+	6.57093i	−0.110914	+	0.242868i
$733$	4.08822	−	28.4342i	0.151002	−	1.05024i	−0.763543	−	0.645757i	$-0.776542\pi$
$733$	4.08822	−	28.4342i	0.151002	−	1.05024i	0.914545	−	0.404484i	$-0.132549\pi$
$734$	−10.4023	+	6.68516i	−0.383956	+	0.246754i
$735$	3.40369			0.125547
$736$	4.02808	−	2.60280i	0.148477	−	0.0959404i
$737$	−0.499127			−0.0183856
$738$	−3.49956	+	2.24903i	−0.128821	+	0.0827880i
$739$	−2.57489	+	17.9088i	−0.0947189	+	0.658784i	0.886047	+	0.463596i	$0.153441\pi$
$739$	−2.57489	+	17.9088i	−0.0947189	+	0.658784i	−0.980766	+	0.195188i	$0.937468\pi$
$740$	2.98676	−	6.54009i	0.109795	−	0.240419i
$741$	−3.25414	+	0.955500i	−0.119544	+	0.0351012i
$742$	0.623001	+	1.36418i	0.0228711	+	0.0500807i
$743$	24.5986	+	28.3883i	0.902435	+	1.04147i	0.998935	+	0.0461326i	$0.0146897\pi$
$743$	24.5986	+	28.3883i	0.902435	+	1.04147i	−0.0965003	+	0.995333i	$0.530765\pi$
$744$	−0.596135	−	4.14621i	−0.0218554	−	0.152008i
$745$	48.8911	+	14.3557i	1.79123	+	0.525953i
$746$	−13.3674	+	15.4267i	−0.489414	+	0.564813i
$747$	−2.73859	−	1.75999i	−0.100200	−	0.0643946i
$748$	0.213461	+	0.137183i	0.00780492	+	0.00501592i
$749$	−2.12129	+	2.44809i	−0.0775101	+	0.0894514i
$750$	−5.17676	−	1.52003i	−0.189028	−	0.0555037i
$751$	3.06530	+	21.3196i	0.111854	+	0.777963i	0.966114	+	0.258117i	$0.0831019\pi$
$751$	3.06530	+	21.3196i	0.111854	+	0.777963i	−0.854259	+	0.519847i	$0.825989\pi$
$752$	−1.71040	−	1.97391i	−0.0623720	−	0.0719812i
$753$	−2.66299	−	5.83114i	−0.0970448	−	0.212498i
$754$	−7.31115	+	2.14675i	−0.266256	+	0.0781799i
$755$	−4.16677	+	9.12396i	−0.151644	+	0.332055i
$756$	0.142315	−	0.989821i	0.00517594	−	0.0359995i
$757$	21.2266	−	13.6415i	0.771493	−	0.495808i	−0.0947076	−	0.995505i	$-0.530192\pi$
$757$	21.2266	−	13.6415i	0.771493	−	0.495808i	0.866200	+	0.499697i	$0.166555\pi$
$758$	−26.7260			−0.970733
$759$	0.200007	+	1.36706i	0.00725981	+	0.0496212i
$760$	−6.44914			−0.233935
$761$	−4.78462	+	3.07489i	−0.173442	+	0.111465i	−0.624482	−	0.781039i	$-0.714690\pi$
$761$	−4.78462	+	3.07489i	−0.173442	+	0.111465i	0.451039	+	0.892504i	$0.351053\pi$
$762$	1.26308	−	8.78494i	0.0457567	−	0.318245i
$763$	0.687584	−	1.50560i	0.0248922	−	0.0545064i
$764$	−2.56267	+	0.752467i	−0.0927141	+	0.0272233i
$765$	−1.24538	−	2.72700i	−0.0450268	−	0.0985950i
$766$	4.68867	+	5.41101i	0.169408	+	0.195508i
$767$	2.68649	+	18.6849i	0.0970034	+	0.674673i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	−20.5934	+	23.7660i	−0.742616	+	0.857024i	−0.993831	−	0.110907i	$-0.964624\pi$
$769$	−20.5934	+	23.7660i	−0.742616	+	0.857024i	0.251215	+	0.967931i	$0.419170\pi$
$770$	−0.824899	−	0.530130i	−0.0297273	−	0.0191046i
$771$	−18.3987	−	11.8242i	−0.662614	−	0.425836i
$772$	4.70199	−	5.42638i	0.169228	−	0.195300i
$773$	13.9893	+	4.10763i	0.503161	+	0.147741i	0.523456	−	0.852053i	$-0.324642\pi$
$773$	13.9893	+	4.10763i	0.503161	+	0.147741i	−0.0202952	+	0.999794i	$0.506461\pi$
$774$	−0.801118	−	5.57190i	−0.0287956	−	0.200278i
$775$	18.0638	+	20.8467i	0.648869	+	0.748835i
$776$	−1.03631	−	2.26919i	−0.0372012	−	0.0814593i
$777$	−2.02679	+	0.595120i	−0.0727108	+	0.0213498i
$778$	4.00487	−	8.76945i	0.143582	−	0.314400i
$779$	1.12173	−	7.80180i	0.0401901	−	0.279529i
$780$	−5.12531	+	3.29383i	−0.183515	+	0.117938i
$781$	0.563333			0.0201576
$782$	−4.05003	+	1.20009i	−0.144829	+	0.0429151i
$783$	4.25698			0.152132
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−9.12784	+	63.4855i	−0.325786	+	2.26589i
$786$	5.33151	−	11.6744i	0.190169	−	0.416411i
$787$	−13.7857	+	4.04786i	−0.491408	+	0.144290i	−0.518043	−	0.855355i	$-0.673339\pi$
$787$	−13.7857	+	4.04786i	−0.491408	+	0.144290i	0.0266344	+	0.999645i	$0.491521\pi$
$788$	4.18472	+	9.16326i	0.149074	+	0.326428i
$789$	−16.0411	−	18.5124i	−0.571077	−	0.659058i
$790$	0.433435	+	3.01460i	0.0154209	+	0.107255i
$791$	−17.6489	−	5.18219i	−0.627524	−	0.184258i
$792$	−0.188657	+	0.217721i	−0.00670362	+	0.00773639i
$793$	−10.8775	−	6.99057i	−0.386272	−	0.248242i
$794$	−26.3967	−	16.9641i	−0.936783	−	0.602034i
$795$	−3.34277	+	3.85776i	−0.118556	+	0.136821i
$796$	13.0855	+	3.84225i	0.463803	+	0.136185i
$797$	4.09813	+	28.5031i	0.145163	+	1.00963i	0.923996	+	0.382401i	$0.124903\pi$
$797$	4.09813	+	28.5031i	0.145163	+	1.00963i	−0.778833	+	0.627231i	$0.784188\pi$
$798$	1.24080	+	1.43195i	0.0439237	+	0.0506906i
$799$	0.955656	+	2.09259i	0.0338087	+	0.0740307i
$800$	−6.31839	+	1.85525i	−0.223389	+	0.0655929i
$801$	0.253912	−	0.555989i	0.00897153	−	0.0196449i
$802$	−1.71973	+	11.9610i	−0.0607257	+	0.422356i
$803$	−1.98304	+	1.27442i	−0.0699798	+	0.0449733i
$804$	1.73256			0.0611026
$805$	15.6509	−	4.63761i	0.551622	−	0.163454i
$806$	7.49786			0.264101
$807$	−15.5256	+	9.97769i	−0.546527	+	0.351231i
$808$	0.703746	−	4.89466i	0.0247577	−	0.172194i
$809$	2.50322	−	5.48130i	0.0880087	−	0.192712i	−0.860510	−	0.509434i	$-0.829855\pi$
$809$	2.50322	−	5.48130i	0.0880087	−	0.192712i	0.948519	+	0.316722i	$0.102582\pi$
$810$	3.26582	−	0.958931i	0.114749	−	0.0336934i
$811$	17.6855	+	38.7259i	0.621022	+	1.35985i	0.914774	+	0.403967i	$0.132369\pi$
$811$	17.6855	+	38.7259i	0.621022	+	1.35985i	−0.293751	+	0.955882i	$0.594904\pi$
$812$	2.78773	+	3.21721i	0.0978300	+	0.112902i
$813$	−1.19203	−	8.29077i	−0.0418064	−	0.290770i
$814$	0.583892	+	0.171446i	0.0204654	+	0.00600919i
$815$	17.4509	−	20.1394i	0.611279	−	0.705454i
$816$	−0.740962	−	0.476188i	−0.0259389	−	0.0166699i
$817$	8.97272	+	5.76642i	0.313916	+	0.201741i
$818$	−2.72311	+	3.14263i	−0.0952111	+	0.109880i
$819$	1.71745	+	0.504289i	0.0600126	+	0.0176213i
$820$	−2.01506	−	14.0150i	−0.0703689	−	0.489426i
$821$	−28.1843	−	32.5264i	−0.983639	−	1.13518i	−0.990818	−	0.135206i	$-0.956830\pi$
$821$	−28.1843	−	32.5264i	−0.983639	−	1.13518i	0.00717846	−	0.999974i	$-0.497715\pi$
$822$	−4.29171	−	9.39754i	−0.149691	−	0.327777i
$823$	−14.1848	+	4.16502i	−0.494449	+	0.145183i	−0.519445	−	0.854504i	$-0.673861\pi$
$823$	−14.1848	+	4.16502i	−0.494449	+	0.145183i	0.0249952	+	0.999688i	$0.492043\pi$
$824$	−5.31604	+	11.6405i	−0.185193	+	0.405516i
$825$	0.269984	−	1.87778i	0.00939963	−	0.0653759i
$826$	8.87194	−	5.70165i	0.308694	−	0.198386i
$827$	41.0400			1.42710			0.713550	−	0.700604i	$-0.247086\pi$
$827$	41.0400			1.42710			0.713550	+	0.700604i	$0.247086\pi$
$828$	−0.694261	−	4.74531i	−0.0241272	−	0.164911i
$829$	34.2629			1.19000			0.595000	−	0.803726i	$-0.297152\pi$
$829$	34.2629			1.19000			0.595000	+	0.803726i	$0.297152\pi$
$830$	9.32134	−	5.99046i	0.323548	−	0.207932i
$831$	1.00680	−	7.00247i	0.0349256	−	0.242913i
$832$	−0.743575	+	1.62820i	−0.0257788	+	0.0564477i
$833$	−0.845106	+	0.248145i	−0.0292812	+	0.00859773i
$834$	7.51257	+	16.4502i	0.260139	+	0.569625i
$835$	6.41413	+	7.40230i	0.221970	+	0.256167i
$836$	−0.0776828	−	0.540296i	−0.00268671	−	0.0186865i
$837$	−4.01917	−	1.18014i	−0.138923	−	0.0407914i
$838$	−18.8712	+	21.7785i	−0.651895	+	0.752327i
$839$	−22.5201	−	14.4728i	−0.777481	−	0.499657i	0.0907154	−	0.995877i	$-0.471085\pi$
$839$	−22.5201	−	14.4728i	−0.777481	−	0.499657i	−0.868197	+	0.496220i	$0.834721\pi$
$840$	2.86337	+	1.84018i	0.0987956	+	0.0634921i
$841$	7.12368	−	8.22116i	0.245644	−	0.283488i
$842$	−1.32787	−	0.389897i	−0.0457613	−	0.0134367i
$843$	1.66538	+	11.5830i	0.0573587	+	0.398939i
$844$	11.1282	+	12.8426i	0.383049	+	0.442062i
$845$	13.8511	+	30.3297i	0.476492	+	1.04337i
$846$	−2.50606	+	0.735846i	−0.0861602	+	0.0252989i
$847$	−4.53509	+	9.93046i	−0.155827	+	0.341215i
$848$	−0.213431	+	1.48444i	−0.00732924	+	0.0509760i
$849$	−26.7220	+	17.1732i	−0.917096	+	0.589382i
$850$	5.80008			0.198941
$851$	−8.50875	+	5.49804i	−0.291676	+	0.188470i
$852$	−1.95543			−0.0669919
$853$	2.74828	−	1.76621i	0.0940993	−	0.0604739i	−0.492745	−	0.870174i	$-0.664006\pi$
$853$	2.74828	−	1.76621i	0.0940993	−	0.0604739i	0.586844	+	0.809700i	$0.300370\pi$
$854$	−1.02804	+	7.15019i	−0.0351789	+	0.244675i
$855$	−2.67907	+	5.86634i	−0.0916223	+	0.200625i
$856$	−3.10808	+	0.912614i	−0.106232	+	0.0311925i
$857$	19.1113	+	41.8478i	0.652828	+	1.42949i	0.889057	+	0.457797i	$0.151361\pi$
$857$	19.1113	+	41.8478i	0.652828	+	1.42949i	−0.236229	+	0.971697i	$0.575912\pi$
$858$	−0.337687	−	0.389712i	−0.0115285	−	0.0133045i
$859$	−3.08837	−	21.4801i	−0.105374	−	0.732890i	−0.972178	−	0.234242i	$-0.924739\pi$
$859$	−3.08837	−	21.4801i	−0.105374	−	0.732890i	0.866805	−	0.498648i	$-0.166170\pi$
$860$	18.3839	+	5.39801i	0.626887	+	0.184071i
$861$	−2.72418	+	3.14387i	−0.0928398	+	0.107143i
$862$	−22.1459	−	14.2323i	−0.754291	−	0.484753i
$863$	−41.2071	−	26.4822i	−1.40271	−	0.901465i	−0.402803	−	0.915287i	$-0.631964\pi$
$863$	−41.2071	−	26.4822i	−1.40271	−	0.901465i	−0.999904	+	0.0138214i	$0.995600\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	40.2001	+	11.8038i	1.36684	+	0.401342i
$866$	4.58316	+	31.8766i	0.155742	+	1.08321i
$867$	−10.6246	−	12.2614i	−0.360830	−	0.416421i
$868$	−1.74011	−	3.81031i	−0.0590632	−	0.129330i
$869$	−0.247336	+	0.0726245i	−0.00839031	+	0.00246362i
$870$	−6.01913	+	13.1801i	−0.204068	+	0.446846i
$871$	−0.441347	+	3.06964i	−0.0149545	+	0.104011i
$872$	1.39242	−	0.894855i	0.0471533	−	0.0303036i
$873$	−2.49463			−0.0844304
$874$	7.65651	+	4.89381i	0.258985	+	0.165536i
$875$	−5.39530			−0.182395
$876$	6.88347	−	4.42374i	0.232571	−	0.149464i
$877$	6.79728	−	47.2761i	0.229528	−	1.59640i	−0.470575	−	0.882360i	$-0.655954\pi$
$877$	6.79728	−	47.2761i	0.229528	−	1.59640i	0.700103	−	0.714042i	$-0.253137\pi$
$878$	5.39378	−	11.8107i	0.182031	−	0.398593i
$879$	−7.62790	+	2.23975i	−0.257283	+	0.0755450i
$880$	−0.407339	−	0.891948i	−0.0137314	−	0.0300676i
$881$	17.0616	+	19.6902i	0.574821	+	0.663379i	0.966483	−	0.256731i	$-0.0826453\pi$
$881$	17.0616	+	19.6902i	0.574821	+	0.663379i	−0.391662	+	0.920109i	$0.628100\pi$
$882$	−0.142315	−	0.989821i	−0.00479199	−	0.0333290i
$883$	29.1397	+	8.55620i	0.980630	+	0.287939i	0.732484	−	0.680784i	$-0.238361\pi$
$883$	29.1397	+	8.55620i	0.980630	+	0.287939i	0.248146	+	0.968723i	$0.420179\pi$
$884$	1.03243	−	1.19149i	0.0347244	−	0.0400741i
$885$	30.1974	+	19.4067i	1.01507	+	0.652348i
$886$	−31.7287	−	20.3908i	−1.06595	−	0.685041i
$887$	26.4958	−	30.5777i	0.889641	−	1.02670i	−0.109823	−	0.993951i	$-0.535028\pi$
$887$	26.4958	−	30.5777i	0.889641	−	1.02670i	0.999464	−	0.0327488i	$-0.0104261\pi$
$888$	−2.02679	−	0.595120i	−0.0680147	−	0.0199709i
$889$	−1.26308	−	8.78494i	−0.0423625	−	0.294637i
$890$	1.36239	+	1.57228i	0.0456673	+	0.0527028i
$891$	0.119676	+	0.262053i	0.00400928	+	0.00877910i
$892$	15.7070	−	4.61198i	0.525908	−	0.154420i
$893$	2.05581	−	4.50160i	0.0687951	−	0.150640i
$894$	2.13053	−	14.8182i	0.0712556	−	0.495594i
$895$	30.7403	−	19.7556i	1.02753	−	0.660357i
$896$	1.00000			0.0334077
$897$	8.58430	−	0.0212400i	0.286622	−	0.000709184i
$898$	−9.28862			−0.309965
$899$	15.0011	−	9.64062i	0.500314	−	0.321533i
$900$	−0.937162	+	6.51810i	−0.0312387	+	0.217270i
$901$	0.548729	−	1.20155i	0.0182808	−	0.0400294i
$902$	1.14988	−	0.337635i	0.0382868	−	0.0112420i
$903$	−2.33845	−	5.12049i	−0.0778188	−	0.170399i
$904$	−12.0455	−	13.9013i	−0.400628	−	0.462350i
$905$	10.5827	+	73.6043i	0.351781	+	2.44669i
$906$	2.82754	+	0.830241i	0.0939388	+	0.0275829i
$907$	−8.28018	+	9.55584i	−0.274939	+	0.317296i	−0.876380	−	0.481621i	$-0.840048\pi$
$907$	−8.28018	+	9.55584i	−0.274939	+	0.317296i	0.601441	+	0.798917i	$0.294594\pi$
$908$	13.7520	+	8.83789i	0.456377	+	0.293296i
$909$	−4.15999	−	2.67347i	−0.137978	−	0.0886733i
$910$	−3.98972	+	4.60438i	−0.132258	+	0.152634i
$911$	−15.0727	−	4.42575i	−0.499382	−	0.146632i	0.0223348	−	0.999751i	$-0.492890\pi$
$911$	−15.0727	−	4.42575i	−0.499382	−	0.146632i	−0.521717	+	0.853119i	$0.674708\pi$
$912$	0.269651	+	1.87546i	0.00892903	+	0.0621027i
$913$	0.614148	+	0.708764i	0.0203253	+	0.0234567i
$914$	−3.99846	−	8.75540i	−0.132257	−	0.289603i
$915$	−23.5914	+	6.92705i	−0.779907	+	0.229001i
$916$	−12.0222	+	26.3249i	−0.397224	+	0.869799i
$917$	1.82649	−	12.7035i	0.0603162	−	0.419508i
$918$	−0.740962	+	0.476188i	−0.0244554	+	0.0157165i
$919$	−34.7828			−1.14738			−0.573689	−	0.819073i	$-0.694488\pi$
$919$	−34.7828			−1.14738			−0.573689	+	0.819073i	$0.694488\pi$
$920$	15.6737	+	4.56011i	0.516745	+	0.150342i
$921$	1.10738			0.0364894
$922$	−11.7482	+	7.55012i	−0.386907	+	0.248650i
$923$	0.498121	−	3.46451i	0.0163958	−	0.114036i
$924$	−0.119676	+	0.262053i	−0.00393704	+	0.00862091i
$925$	13.3467	−	3.91894i	0.438837	−	0.128854i
$926$	0.217304	+	0.475830i	0.00714106	+	0.0156367i
$927$	8.38022	+	9.67128i	0.275242	+	0.317647i
$928$	0.605831	+	4.21365i	0.0198874	+	0.138320i
$929$	−35.3937	−	10.3925i	−1.16123	−	0.340968i	−0.356319	−	0.934364i	$-0.615968\pi$
$929$	−35.3937	−	10.3925i	−1.16123	−	0.340968i	−0.804910	+	0.593397i	$0.797786\pi$
$930$	9.33672	−	10.7751i	0.306163	−	0.353331i
$931$	1.59396	+	1.02438i	0.0522400	+	0.0335726i
$932$	−13.9096	−	8.93914i	−0.455623	−	0.292811i
$933$	−2.93787	+	3.39048i	−0.0961815	+	0.110999i
$934$	27.3278	+	8.02417i	0.894193	+	0.262559i
$935$	0.122912	+	0.854870i	0.00401964	+	0.0279572i
$936$	1.17217	+	1.35276i	0.0383137	+	0.0442163i
$937$	8.93346	+	19.5616i	0.291844	+	0.639048i	0.997588	−	0.0694186i	$-0.0221144\pi$
$937$	8.93346	+	19.5616i	0.291844	+	0.639048i	−0.705744	+	0.708467i	$0.749387\pi$
$938$	1.66238	−	0.488118i	0.0542785	−	0.0159376i
$939$	−11.5641	+	25.3217i	−0.377379	+	0.826344i
$940$	1.26518	−	8.79949i	0.0412655	−	0.287008i
$941$	0.721025	−	0.463375i	0.0235047	−	0.0151056i	−0.528836	−	0.848724i	$-0.677371\pi$
$941$	0.721025	−	0.463375i	0.0235047	−	0.0151056i	0.552340	+	0.833619i	$0.313735\pi$
$942$	18.8437			0.613962
$943$	−8.24275	+	18.1679i	−0.268421	+	0.591629i
$944$	10.5461			0.343246
$945$	2.86337	−	1.84018i	0.0931454	−	0.0598609i
$946$	−0.230791	+	1.60519i	−0.00750367	+	0.0521892i
$947$	2.10128	−	4.60117i	0.0682825	−	0.149518i	−0.872413	−	0.488769i	$-0.837446\pi$
$947$	2.10128	−	4.60117i	0.0682825	−	0.149518i	0.940696	+	0.339251i	$0.110173\pi$
$948$	0.858548	−	0.252093i	0.0278844	−	0.00818758i
$949$	6.08423	+	13.3226i	0.197502	+	0.432470i
$950$	−8.17080	−	9.42961i	−0.265096	−	0.305937i
$951$	−2.25705	−	15.6981i	−0.0731897	−	0.509046i
$952$	−0.845106	−	0.248145i	−0.0273900	−	0.00804244i
$953$	−21.7370	+	25.0858i	−0.704130	+	0.812610i	−0.989304	−	0.145866i	$-0.953403\pi$
$953$	−21.7370	+	25.0858i	−0.704130	+	0.812610i	0.285174	+	0.958476i	$0.407949\pi$
$954$	1.26163	+	0.810803i	0.0408469	+	0.0262507i
$955$	−7.64765	−	4.91485i	−0.247472	−	0.159041i
$956$	−9.98692	+	11.5255i	−0.323000	+	0.372762i
$957$	−1.17670	−	0.345511i	−0.0380374	−	0.0111688i
$958$	−1.04073	−	7.23847i	−0.0336246	−	0.233864i
$959$	−6.76546	−	7.80776i	−0.218468	−	0.252126i
$960$	1.41395	+	3.09611i	0.0456349	+	0.0999265i
$961$	12.9086	−	3.79030i	0.416406	−	0.122268i
$962$	1.57070	−	3.43935i	0.0506413	−	0.110889i
$963$	−0.460999	+	3.20632i	−0.0148555	+	0.103322i
$964$	5.67065	−	3.64431i	0.182639	−	0.117375i
$965$	24.4390			0.786718
$966$	−2.00305	−	4.35750i	−0.0644470	−	0.140200i
$967$	−25.8921			−0.832634			−0.416317	−	0.909220i	$-0.636679\pi$
$967$	−25.8921			−0.832634			−0.416317	+	0.909220i	$0.636679\pi$
$968$	−9.18397	+	5.90218i	−0.295184	+	0.189703i
$969$	0.237504	−	1.65188i	0.00762973	−	0.0530659i
$970$	3.52727	−	7.72364i	0.113254	−	0.247991i
$971$	−16.1980	+	4.75616i	−0.519819	+	0.152633i	−0.531109	−	0.847304i	$-0.678224\pi$
$971$	−16.1980	+	4.75616i	−0.519819	+	0.152633i	0.0112899	+	0.999936i	$0.496406\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	11.8428	+	13.6673i	0.379663	+	0.438155i
$974$	−1.31364	−	9.13654i	−0.0420916	−	0.292754i
$975$	−11.3096	−	3.32081i	−0.362198	−	0.106351i
$976$	−4.73053	+	5.45932i	−0.151421	+	0.174749i
$977$	1.63316	+	1.04957i	0.0522493	+	0.0335786i	0.566505	−	0.824059i	$-0.308295\pi$
$977$	1.63316	+	1.04957i	0.0522493	+	0.0335786i	−0.514255	+	0.857637i	$0.671932\pi$
$978$	−6.58637	−	4.23280i	−0.210609	−	0.135350i
$979$	−0.115312	+	0.133077i	−0.00368537	+	0.00425315i
$980$	3.26582	+	0.958931i	0.104323	+	0.0306319i
$981$	−0.235556	−	1.63833i	−0.00752072	−	0.0523078i
$982$	14.5306	+	16.7692i	0.463689	+	0.535126i
$983$	−14.1874	−	31.0662i	−0.452509	−	0.990857i	−0.989131	−	0.147035i	$-0.953027\pi$
$983$	−14.1874	−	31.0662i	−0.452509	−	0.990857i	0.536622	−	0.843823i	$-0.319700\pi$
$984$	−3.99143	+	1.17199i	−0.127242	+	0.0373617i
$985$	−14.2435	+	31.1889i	−0.453836	+	0.993762i
$986$	0.533606	−	3.71131i	0.0169935	−	0.118192i
$987$	−2.19724	+	1.41208i	−0.0699388	+	0.0449470i
$988$	−3.39152			−0.107898
$989$	−17.7295	−	20.3589i	−0.563765	−	0.647376i
$990$	−0.980559			−0.0311642
$991$	24.0776	−	15.4737i	0.764850	−	0.491539i	−0.0991242	−	0.995075i	$-0.531604\pi$
$991$	24.0776	−	15.4737i	0.764850	−	0.491539i	0.863974	+	0.503536i	$0.167968\pi$
$992$	0.596135	−	4.14621i	0.0189273	−	0.131642i
$993$	−2.47625	+	5.42223i	−0.0785814	+	0.172069i
$994$	−1.87622	+	0.550908i	−0.0595101	+	0.0174737i
$995$	19.2833	+	42.2245i	0.611321	+	1.33861i
$996$	−2.13182	−	2.46025i	−0.0675492	−	0.0779559i
$997$	4.51674	+	31.4146i	0.143046	+	0.994910i	0.927260	+	0.374419i	$0.122158\pi$
$997$	4.51674	+	31.4146i	0.143046	+	0.994910i	−0.784213	+	0.620491i	$0.786933\pi$
$998$	−8.02219	−	2.35553i	−0.253938	−	0.0745629i
$999$	−1.38330	+	1.59641i	−0.0437657	+	0.0505083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.127.2	✓	20
23.2	even	11	inner	966.2.q.d.715.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.127.2	✓	20	1.1	even	1	trivial
966.2.q.d.715.2	yes	20	23.2	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.26582 - 0.958931i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.26582 - 0.958931i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(2.22895 - 2.57234i) q^{10} +(0.242354 + 0.155751i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(1.17217 - 1.35276i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.484396 - 3.36905i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.365891 + 0.801189i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(0.787107 - 1.72352i) q^{19} +(0.484396 - 3.36905i) q^{20} +(-0.841254 + 0.540641i) q^{21} +0.288087 q^{22} +(-3.13162 + 3.63221i) q^{23} -1.00000 q^{24} +(5.53977 - 3.56019i) q^{25} +(0.254737 - 1.77174i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-1.76841 - 3.87228i) q^{29} +(-2.22895 - 2.57234i) q^{30} +(0.596135 + 4.14621i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(0.188657 - 0.217721i) q^{33} +(0.740962 + 0.476188i) q^{34} +(-2.86337 - 1.84018i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(2.02679 + 0.595120i) q^{37} +(-0.269651 - 1.87546i) q^{38} +(-1.17217 - 1.35276i) q^{39} +(-1.41395 - 3.09611i) q^{40} +(3.99143 - 1.17199i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(-0.801118 + 5.57190i) q^{43} +(0.242354 - 0.155751i) q^{44} -3.40369 q^{45} +(-0.670770 + 4.74869i) q^{46} +2.61186 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(2.73556 - 5.99005i) q^{50} +(0.845106 - 0.248145i) q^{51} +(-0.743575 - 1.62820i) q^{52} +(-0.982100 - 1.13340i) q^{53} +(0.142315 + 0.989821i) q^{54} +(0.940839 + 0.276255i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(-1.59396 - 1.02438i) q^{57} +(-3.58120 - 2.30150i) q^{58} +(-6.90623 + 7.97021i) q^{59} +(-3.26582 - 0.958931i) q^{60} +(-1.02804 - 7.15019i) q^{61} +(2.74311 + 3.16572i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.53090 - 5.54190i) q^{65} +(0.0409990 - 0.285154i) q^{66} +(-1.45752 + 0.936692i) q^{67} +0.880784 q^{68} +(3.14956 + 3.61667i) q^{69} -3.40369 q^{70} +(1.64501 - 1.05718i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-3.39909 + 7.44297i) q^{73} +(2.02679 - 0.595120i) q^{74} +(-2.73556 - 5.99005i) q^{75} +(-1.24080 - 1.43195i) q^{76} +(-0.0409990 - 0.285154i) q^{77} +(-1.71745 - 0.504289i) q^{78} +(-0.585965 + 0.676240i) q^{79} +(-2.86337 - 1.84018i) q^{80} +(0.841254 + 0.540641i) q^{81} +(2.72418 - 3.14387i) q^{82} +(3.12351 + 0.917145i) q^{83} +(0.142315 + 0.989821i) q^{84} +(1.96322 + 2.26568i) q^{85} +(2.33845 + 5.12049i) q^{86} +(-4.08454 + 1.19933i) q^{87} +(0.119676 - 0.262053i) q^{88} +(-0.0869863 + 0.605003i) q^{89} +(-2.86337 + 1.84018i) q^{90} -1.78996 q^{91} +(2.00305 + 4.35750i) q^{92} +4.18885 q^{93} +(2.19724 - 1.41208i) q^{94} +(0.917808 - 6.38350i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(2.39358 - 0.702818i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-0.188657 - 0.217721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

L-functions

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