LMFDB - Embedded newform 690.2.m.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 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("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0867074 + 0.603063i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0867074 + 0.603063i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(2.32694 - 5.09530i) q^{11} +(0.415415 - 0.909632i) q^{12} +(0.602914 - 4.19336i) q^{13} +(-0.512546 + 0.329393i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.45949 + 2.83841i) q^{17} +(0.841254 + 0.540641i) q^{18} +(1.15764 - 1.33599i) q^{19} +(0.959493 - 0.281733i) q^{20} +(-0.253098 - 0.554206i) q^{21} +5.60149 q^{22} +(-1.17376 + 4.64998i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(4.06487 - 1.19355i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-0.512546 - 0.329393i) q^{28} +(-0.762794 - 0.880311i) q^{29} +(0.142315 + 0.989821i) q^{30} +(8.18849 + 2.40436i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.797176 + 5.54448i) q^{33} +(-1.56019 + 3.41635i) q^{34} +(0.253098 - 0.554206i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(1.99368 - 1.28126i) q^{37} +(1.69616 + 0.498037i) q^{38} +(0.602914 + 4.19336i) q^{39} +(0.654861 + 0.755750i) q^{40} +(-3.48941 - 2.24251i) q^{41} +(0.398983 - 0.460451i) q^{42} +(8.12204 - 2.38485i) q^{43} +(2.32694 + 5.09530i) q^{44} -1.00000 q^{45} +(-4.71737 + 0.863983i) q^{46} +2.90344 q^{47} +(0.415415 + 0.909632i) q^{48} +(6.36028 - 1.86755i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-3.15954 - 2.03051i) q^{51} +(2.77430 + 3.20172i) q^{52} +(-1.78625 - 12.4236i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(-4.71228 + 3.02840i) q^{55} +(0.0867074 - 0.603063i) q^{56} +(-0.734356 + 1.60802i) q^{57} +(0.483883 - 1.05956i) q^{58} +(1.70185 - 11.8366i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(-1.61114 - 0.473074i) q^{61} +(1.21454 + 8.44732i) q^{62} +(0.398983 + 0.460451i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.77430 + 3.20172i) q^{65} +(-5.37459 + 1.57812i) q^{66} +(4.60658 + 10.0870i) q^{67} -3.75575 q^{68} +(-0.183838 - 4.79231i) q^{69} +0.609264 q^{70} +(-5.15445 - 11.2867i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-1.54955 + 1.78827i) q^{73} +(1.99368 + 1.28126i) q^{74} +(-0.654861 - 0.755750i) q^{75} +(0.251579 + 1.74977i) q^{76} +(3.27455 + 0.961494i) q^{77} +(-3.56395 + 2.29041i) q^{78} +(-1.25664 + 8.74014i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.590304 - 4.10565i) q^{82} +(-13.0379 + 8.37893i) q^{83} +(0.584585 + 0.171650i) q^{84} +(-0.534499 - 3.71752i) q^{85} +(5.54335 + 6.39737i) q^{86} +(0.979908 + 0.629749i) q^{87} +(-3.66820 + 4.23333i) q^{88} +(3.57112 - 1.04858i) q^{89} +(-0.415415 - 0.909632i) q^{90} +2.58114 q^{91} +(-2.74557 - 3.93215i) q^{92} -8.53418 q^{93} +(1.20613 + 2.64106i) q^{94} +(-1.69616 + 0.498037i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-2.76448 - 1.77662i) q^{97} +(4.34094 + 5.00971i) q^{98} +(-0.797176 - 5.54448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	$ 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	−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
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	0.0867074	+	0.603063i	0.0327723	+	0.227936i	0.999625	−	0.0274001i	$-0.00872283\pi$
$7$	0.0867074	+	0.603063i	0.0327723	+	0.227936i	−0.966852	+	0.255337i	$0.917814\pi$
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.142315	−	0.989821i	0.0450039	−	0.313009i
$11$	2.32694	−	5.09530i	0.701600	−	1.53629i	−0.136420	−	0.990651i	$-0.543560\pi$
$11$	2.32694	−	5.09530i	0.701600	−	1.53629i	0.838020	−	0.545639i	$-0.183713\pi$
$12$	0.415415	−	0.909632i	0.119920	−	0.262588i
$13$	0.602914	−	4.19336i	0.167218	−	1.16303i	−0.717383	−	0.696679i	$-0.754660\pi$
$13$	0.602914	−	4.19336i	0.167218	−	1.16303i	0.884601	−	0.466349i	$-0.154431\pi$
$14$	−0.512546	+	0.329393i	−0.136984	+	0.0880340i
$15$	0.959493	+	0.281733i	0.247740	+	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	2.45949	+	2.83841i	0.596515	+	0.688415i	0.971071	−	0.238789i	$-0.0767506\pi$
$17$	2.45949	+	2.83841i	0.596515	+	0.688415i	−0.374557	+	0.927204i	$0.622205\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	1.15764	−	1.33599i	0.265581	−	0.306497i	−0.607258	−	0.794504i	$-0.707731\pi$
$19$	1.15764	−	1.33599i	0.265581	−	0.306497i	0.872839	+	0.488008i	$0.162276\pi$
$20$	0.959493	−	0.281733i	0.214549	−	0.0629973i
$21$	−0.253098	−	0.554206i	−0.0552304	−	0.120938i
$22$	5.60149			1.19424
$23$	−1.17376	+	4.64998i	−0.244745	+	0.969587i
$23$	−1.17376	+	4.64998i	−0.244745	+	0.969587i
$24$	1.00000			0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	4.06487	−	1.19355i	0.797187	−	0.234075i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	−0.512546	−	0.329393i	−0.0968621	−	0.0622495i
$29$	−0.762794	−	0.880311i	−0.141647	−	0.163470i	0.680493	−	0.732755i	$-0.261766\pi$
$29$	−0.762794	−	0.880311i	−0.141647	−	0.163470i	−0.822140	+	0.569285i	$0.807220\pi$
$30$	0.142315	+	0.989821i	0.0259830	+	0.180716i
$31$	8.18849	+	2.40436i	1.47070	+	0.431835i	0.916325	−	0.400434i	$-0.131141\pi$
$31$	8.18849	+	2.40436i	1.47070	+	0.431835i	0.554371	+	0.832270i	$0.312959\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	−0.797176	+	5.54448i	−0.138770	+	0.965170i
$34$	−1.56019	+	3.41635i	−0.267571	+	0.585899i
$35$	0.253098	−	0.554206i	0.0427813	−	0.0936780i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	1.99368	−	1.28126i	0.327758	−	0.210638i	−0.366404	−	0.930456i	$-0.619411\pi$
$37$	1.99368	−	1.28126i	0.327758	−	0.210638i	0.694163	+	0.719818i	$0.255775\pi$
$38$	1.69616	+	0.498037i	0.275153	+	0.0807923i
$39$	0.602914	+	4.19336i	0.0965435	+	0.671475i
$40$	0.654861	+	0.755750i	0.103543	+	0.119494i
$41$	−3.48941	−	2.24251i	−0.544955	−	0.350221i	0.239019	−	0.971015i	$-0.423174\pi$
$41$	−3.48941	−	2.24251i	−0.544955	−	0.350221i	−0.783974	+	0.620794i	$0.786810\pi$
$42$	0.398983	−	0.460451i	0.0615645	−	0.0710492i
$43$	8.12204	−	2.38485i	1.23860	−	0.363686i	0.404111	−	0.914710i	$-0.367581\pi$
$43$	8.12204	−	2.38485i	1.23860	−	0.363686i	0.834489	+	0.551024i	$0.185763\pi$
$44$	2.32694	+	5.09530i	0.350800	+	0.768145i
$45$	−1.00000			−0.149071
$46$	−4.71737	+	0.863983i	−0.695538	+	0.127387i
$47$	2.90344			0.423511			0.211755	−	0.977323i	$-0.432082\pi$
$47$	2.90344			0.423511			0.211755	+	0.977323i	$0.432082\pi$
$48$	0.415415	+	0.909632i	0.0599600	+	0.131294i
$49$	6.36028	−	1.86755i	0.908612	−	0.266793i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	−3.15954	−	2.03051i	−0.442424	−	0.284328i
$52$	2.77430	+	3.20172i	0.384727	+	0.443998i
$53$	−1.78625	−	12.4236i	−0.245360	−	1.70652i	−0.624372	−	0.781127i	$-0.714645\pi$
$53$	−1.78625	−	12.4236i	−0.245360	−	1.70652i	0.379012	−	0.925392i	$-0.376264\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	−4.71228	+	3.02840i	−0.635403	+	0.408349i
$56$	0.0867074	−	0.603063i	0.0115868	−	0.0805877i
$57$	−0.734356	+	1.60802i	−0.0972679	+	0.212987i
$58$	0.483883	−	1.05956i	0.0635370	−	0.139127i
$59$	1.70185	−	11.8366i	0.221562	−	1.54100i	−0.510569	−	0.859837i	$-0.670565\pi$
$59$	1.70185	−	11.8366i	0.221562	−	1.54100i	0.732132	−	0.681163i	$-0.238526\pi$
$60$	−0.841254	+	0.540641i	−0.108605	+	0.0697964i
$61$	−1.61114	−	0.473074i	−0.206286	−	0.0605709i	0.176957	−	0.984219i	$-0.443375\pi$
$61$	−1.61114	−	0.473074i	−0.206286	−	0.0605709i	−0.383243	+	0.923648i	$0.625193\pi$
$62$	1.21454	+	8.44732i	0.154247	+	1.07281i
$63$	0.398983	+	0.460451i	0.0502672	+	0.0580114i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−2.77430	+	3.20172i	−0.344110	+	0.397124i
$66$	−5.37459	+	1.57812i	−0.661567	+	0.194254i
$67$	4.60658	+	10.0870i	0.562784	+	1.23232i	0.950551	+	0.310567i	$0.100519\pi$
$67$	4.60658	+	10.0870i	0.562784	+	1.23232i	−0.387768	+	0.921757i	$0.626754\pi$
$68$	−3.75575			−0.455452
$69$	−0.183838	−	4.79231i	−0.0221315	−	0.576926i
$70$	0.609264			0.0728210
$71$	−5.15445	−	11.2867i	−0.611720	−	1.33948i	−0.921391	−	0.388637i	$-0.872946\pi$
$71$	−5.15445	−	11.2867i	−0.611720	−	1.33948i	0.309670	−	0.950844i	$-0.399781\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	−1.54955	+	1.78827i	−0.181361	+	0.209301i	−0.839149	−	0.543901i	$-0.816947\pi$
$73$	−1.54955	+	1.78827i	−0.181361	+	0.209301i	0.657789	+	0.753203i	$0.271492\pi$
$74$	1.99368	+	1.28126i	0.231760	+	0.148943i
$75$	−0.654861	−	0.755750i	−0.0756168	−	0.0872664i
$76$	0.251579	+	1.74977i	0.0288581	+	0.200713i
$77$	3.27455	+	0.961494i	0.373169	+	0.109572i
$78$	−3.56395	+	2.29041i	−0.403538	+	0.259338i
$79$	−1.25664	+	8.74014i	−0.141383	+	0.983343i	0.788381	+	0.615188i	$0.210920\pi$
$79$	−1.25664	+	8.74014i	−0.141383	+	0.983343i	−0.929764	+	0.368156i	$0.879989\pi$
$80$	−0.415415	+	0.909632i	−0.0464448	+	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.590304	−	4.10565i	0.0651882	−	0.453394i
$83$	−13.0379	+	8.37893i	−1.43109	+	0.919707i	−0.431244	+	0.902235i	$0.641925\pi$
$83$	−13.0379	+	8.37893i	−1.43109	+	0.919707i	−0.999847	+	0.0174713i	$0.994438\pi$
$84$	0.584585	+	0.171650i	0.0637835	+	0.0187285i
$85$	−0.534499	−	3.71752i	−0.0579745	−	0.403222i
$86$	5.54335	+	6.39737i	0.597755	+	0.689846i
$87$	0.979908	+	0.629749i	0.105057	+	0.0675161i
$88$	−3.66820	+	4.23333i	−0.391031	+	0.451274i
$89$	3.57112	−	1.04858i	0.378538	−	0.111149i	−0.0869279	−	0.996215i	$-0.527705\pi$
$89$	3.57112	−	1.04858i	0.378538	−	0.111149i	0.465466	+	0.885066i	$0.345887\pi$
$90$	−0.415415	−	0.909632i	−0.0437886	−	0.0958836i
$91$	2.58114			0.270577
$92$	−2.74557	−	3.93215i	−0.286246	−	0.409955i
$93$	−8.53418			−0.884954
$94$	1.20613	+	2.64106i	0.124403	+	0.272405i
$95$	−1.69616	+	0.498037i	−0.174022	+	0.0510975i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	−2.76448	−	1.77662i	−0.280690	−	0.180389i	0.392719	−	0.919658i	$-0.371534\pi$
$97$	−2.76448	−	1.77662i	−0.280690	−	0.180389i	−0.673409	+	0.739270i	$0.735171\pi$
$98$	4.34094	+	5.00971i	0.438501	+	0.506057i
$99$	−0.797176	−	5.54448i	−0.0801192	−	0.557241i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	−13.5321	+	8.69658i	−1.34650	+	0.865342i	−0.997422	−	0.0717524i	$-0.977141\pi$
$101$	−13.5321	+	8.69658i	−1.34650	+	0.865342i	−0.349076	+	0.937094i	$0.613505\pi$
$102$	0.534499	−	3.71752i	0.0529233	−	0.368089i
$103$	−0.386982	+	0.847373i	−0.0381305	+	0.0834941i	−0.927739	−	0.373230i	$-0.878250\pi$
$103$	−0.386982	+	0.847373i	−0.0381305	+	0.0834941i	0.889608	+	0.456724i	$0.150977\pi$
$104$	−1.75990	+	3.85364i	−0.172572	+	0.377880i
$105$	−0.0867074	+	0.603063i	−0.00846177	+	0.0588529i
$106$	10.5589	−	6.78580i	1.02557	−	0.659095i
$107$	9.62042	+	2.82481i	0.930041	+	0.273085i	0.711454	−	0.702733i	$-0.248037\pi$
$107$	9.62042	+	2.82481i	0.930041	+	0.273085i	0.218587	+	0.975817i	$0.429855\pi$
$108$	−0.142315	−	0.989821i	−0.0136943	−	0.0952456i
$109$	−3.85617	−	4.45025i	−0.369354	−	0.426257i	0.540398	−	0.841410i	$-0.318274\pi$
$109$	−3.85617	−	4.45025i	−0.369354	−	0.426257i	−0.909752	+	0.415153i	$0.863728\pi$
$110$	−4.71228	−	3.02840i	−0.449298	−	0.288746i
$111$	−1.55195	+	1.79104i	−0.147304	+	0.169998i
$112$	0.584585	−	0.171650i	0.0552381	−	0.0162194i
$113$	−4.82841	−	10.5727i	−0.454219	−	0.994600i	−0.988767	−	0.149462i	$-0.952246\pi$
$113$	−4.82841	−	10.5727i	−0.454219	−	0.994600i	0.534549	−	0.845138i	$-0.320482\pi$
$114$	−1.76777			−0.165566
$115$	3.50140	−	3.27723i	0.326507	−	0.305603i
$116$	1.16482			0.108151
$117$	−1.75990	−	3.85364i	−0.162703	−	0.356269i
$118$	11.4740	−	3.36906i	1.05626	−	0.310147i
$119$	−1.49848	+	1.72934i	−0.137366	+	0.158528i
$120$	−0.841254	−	0.540641i	−0.0767956	−	0.0493535i
$121$	−13.3439	−	15.3997i	−1.21308	−	1.39997i
$122$	−0.238969	−	1.66207i	−0.0216353	−	0.150477i
$123$	3.97985	+	1.16859i	0.358851	+	0.105368i
$124$	−7.17941	+	4.61393i	−0.644730	+	0.414343i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	−0.253098	+	0.554206i	−0.0225477	+	0.0493726i
$127$	−3.49824	+	7.66008i	−0.310419	+	0.679722i	−0.998966	−	0.0454695i	$-0.985522\pi$
$127$	−3.49824	+	7.66008i	−0.310419	+	0.679722i	0.688547	+	0.725192i	$0.258249\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	−7.12115	+	4.57649i	−0.626983	+	0.402937i
$130$	−4.06487	−	1.19355i	−0.356513	−	0.104682i
$131$	−1.29569	−	9.01173i	−0.113205	−	0.787358i	−0.964767	−	0.263105i	$-0.915254\pi$
$131$	−1.29569	−	9.01173i	−0.113205	−	0.787358i	0.851562	−	0.524253i	$-0.175656\pi$
$132$	−3.66820	−	4.23333i	−0.319276	−	0.368464i
$133$	0.906061	+	0.582290i	0.0785655	+	0.0504910i
$134$	−7.26182	+	8.38059i	−0.627326	+	0.723973i
$135$	0.959493	−	0.281733i	0.0825800	−	0.0242477i
$136$	−1.56019	−	3.41635i	−0.133786	−	0.292950i
$137$	−4.54001			−0.387879			−0.193940	−	0.981013i	$-0.562127\pi$
$137$	−4.54001			−0.387879			−0.193940	+	0.981013i	$0.562127\pi$
$138$	4.28287	−	2.15802i	0.364582	−	0.183703i
$139$	14.9794			1.27054			0.635270	−	0.772290i	$-0.280889\pi$
$139$	14.9794			1.27054			0.635270	+	0.772290i	$0.280889\pi$
$140$	0.253098	+	0.554206i	0.0213907	+	0.0468390i
$141$	−2.78583	+	0.817994i	−0.234609	+	0.0688876i
$142$	8.12548	−	9.37730i	0.681875	−	0.786926i
$143$	−19.9635	−	12.8297i	−1.66943	−	1.07288i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	0.165771	+	1.15296i	0.0137665	+	0.0957483i
$146$	−2.27037	−	0.666642i	−0.187897	−	0.0551717i
$147$	−5.57650	+	3.58380i	−0.459942	+	0.295587i
$148$	−0.337270	+	2.34577i	−0.0277234	+	0.192821i
$149$	4.29389	−	9.40232i	0.351769	−	0.770268i	−0.648192	−	0.761477i	$-0.724475\pi$
$149$	4.29389	−	9.40232i	0.351769	−	0.770268i	0.999961	−	0.00879070i	$-0.00279820\pi$
$150$	0.415415	−	0.909632i	0.0339185	−	0.0742711i
$151$	2.28160	−	15.8689i	0.185674	−	1.29139i	−0.657379	−	0.753560i	$-0.728335\pi$
$151$	2.28160	−	15.8689i	0.185674	−	1.29139i	0.843053	−	0.537831i	$-0.180756\pi$
$152$	−1.48714	+	0.955726i	−0.120623	+	0.0775196i
$153$	3.60362	+	1.05812i	0.291335	+	0.0855437i
$154$	0.485691	+	3.37805i	0.0391381	+	0.272211i
$155$	−5.58870	−	6.44971i	−0.448895	−	0.518053i
$156$	−3.56395	−	2.29041i	−0.285345	−	0.183380i
$157$	3.35001	−	3.86611i	0.267360	−	0.308549i	−0.606156	−	0.795346i	$-0.707289\pi$
$157$	3.35001	−	3.86611i	0.267360	−	0.308549i	0.873515	+	0.486797i	$0.161835\pi$
$158$	−8.47234	+	2.48770i	−0.674023	+	0.197911i
$159$	5.21404	+	11.4172i	0.413500	+	0.905439i
$160$	−1.00000			−0.0790569
$161$	−2.90600	−	0.304662i	−0.229025	−	0.0240108i
$162$	1.00000			0.0785674
$163$	9.66683	+	21.1674i	0.757165	+	1.65796i	0.753045	+	0.657968i	$0.228584\pi$
$163$	9.66683	+	21.1674i	0.757165	+	1.65796i	0.00411947	+	0.999992i	$0.498689\pi$
$164$	3.97985	−	1.16859i	0.310774	−	0.0912516i
$165$	3.66820	−	4.23333i	0.285569	−	0.329564i
$166$	−13.0379	−	8.37893i	−1.01193	−	0.650331i
$167$	15.6481	+	18.0589i	1.21089	+	1.39744i	0.893450	+	0.449164i	$0.148278\pi$
$167$	15.6481	+	18.0589i	1.21089	+	1.39744i	0.317441	+	0.948278i	$0.397177\pi$
$168$	0.0867074	+	0.603063i	0.00668962	+	0.0465273i
$169$	−4.74733	−	1.39394i	−0.365180	−	0.107226i
$170$	3.15954	−	2.03051i	0.242325	−	0.155733i
$171$	0.251579	−	1.74977i	0.0192388	−	0.133808i
$172$	−3.51646	+	7.69997i	−0.268128	+	0.587117i
$173$	−4.88494	+	10.6965i	−0.371395	+	0.813241i	0.627992	+	0.778220i	$0.283877\pi$
$173$	−4.88494	+	10.6965i	−0.371395	+	0.813241i	−0.999387	+	0.0350212i	$0.988850\pi$
$174$	−0.165771	+	1.15296i	−0.0125671	+	0.0874059i
$175$	−0.512546	+	0.329393i	−0.0387448	+	0.0248998i
$176$	−5.37459	−	1.57812i	−0.405125	−	0.118955i
$177$	1.70185	+	11.8366i	0.127919	+	0.889697i
$178$	2.43731	+	2.81281i	0.182684	+	0.210829i
$179$	−3.19121	−	2.05087i	−0.238523	−	0.153289i	0.415919	−	0.909402i	$-0.363460\pi$
$179$	−3.19121	−	2.05087i	−0.238523	−	0.153289i	−0.654442	+	0.756112i	$0.727096\pi$
$180$	0.654861	−	0.755750i	0.0488104	−	0.0563302i
$181$	−19.2929	+	5.66490i	−1.43403	+	0.421069i	−0.904227	−	0.427052i	$-0.859552\pi$
$181$	−19.2929	+	5.66490i	−1.43403	+	0.421069i	−0.529802	+	0.848121i	$0.677734\pi$
$182$	1.07224	+	2.34788i	0.0794799	+	0.174037i
$183$	1.67916			0.124127
$184$	2.43626	−	4.13094i	0.179604	−	0.304537i
$185$	−2.36989			−0.174238
$186$	−3.54523	−	7.76297i	−0.259949	−	0.569208i
$187$	20.1856	−	5.92703i	1.47612	−	0.433428i
$188$	−1.90135	+	2.19428i	−0.138670	+	0.160034i
$189$	−0.512546	−	0.329393i	−0.0372822	−	0.0239598i
$190$	−1.15764	−	1.33599i	−0.0839841	−	0.0969228i
$191$	2.35998	+	16.4141i	0.170762	+	1.18768i	0.877278	+	0.479982i	$0.159357\pi$
$191$	2.35998	+	16.4141i	0.170762	+	1.18768i	−0.706516	+	0.707697i	$0.749734\pi$
$192$	−0.959493	−	0.281733i	−0.0692454	−	0.0203323i
$193$	8.43564	−	5.42126i	0.607211	−	0.390231i	−0.200599	−	0.979673i	$-0.564289\pi$
$193$	8.43564	−	5.42126i	0.607211	−	0.390231i	0.807810	+	0.589443i	$0.200653\pi$
$194$	0.467666	−	3.25269i	0.0335765	−	0.233530i
$195$	1.75990	−	3.85364i	0.126029	−	0.275965i
$196$	−2.75370	+	6.02977i	−0.196693	+	0.430698i
$197$	−0.408807	+	2.84332i	−0.0291263	+	0.202578i	−0.999188	−	0.0402787i	$-0.987175\pi$
$197$	−0.408807	+	2.84332i	−0.0291263	+	0.202578i	0.970062	+	0.242857i	$0.0780845\pi$
$198$	4.71228	−	3.02840i	0.334887	−	0.215219i
$199$	3.39722	+	0.997514i	0.240823	+	0.0707119i	0.399917	−	0.916552i	$-0.369039\pi$
$199$	3.39722	+	0.997514i	0.240823	+	0.0707119i	−0.159094	+	0.987263i	$0.550857\pi$
$200$	−0.142315	−	0.989821i	−0.0100632	−	0.0699909i
$201$	−7.26182	−	8.38059i	−0.512209	−	0.591121i
$202$	−13.5321	−	8.69658i	−0.952118	−	0.611889i
$203$	0.464743	−	0.536342i	0.0326186	−	0.0376439i
$204$	3.60362	−	1.05812i	0.252304	−	0.0740830i
$205$	1.72309	+	3.77304i	0.120346	+	0.263520i
$206$	−0.931556			−0.0649046
$207$	1.52654	+	4.54639i	0.106102	+	0.315996i
$208$	−4.23648			−0.293747
$209$	−4.11349	−	9.00729i	−0.284536	−	0.623047i
$210$	−0.584585	+	0.171650i	−0.0403402	+	0.0118450i
$211$	12.9067	−	14.8951i	0.888533	−	1.02542i	−0.110968	−	0.993824i	$-0.535395\pi$
$211$	12.9067	−	14.8951i	0.888533	−	1.02542i	0.999501	−	0.0315978i	$-0.0100596\pi$
$212$	10.5589	+	6.78580i	0.725189	+	0.466051i
$213$	8.12548	+	9.37730i	0.556749	+	0.642522i
$214$	1.42693	+	9.92451i	0.0975429	+	0.678426i
$215$	−8.12204	−	2.38485i	−0.553919	−	0.162645i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.739977	+	5.14665i	−0.0502329	+	0.349377i
$218$	2.44618	−	5.35640i	0.165676	−	0.362781i
$219$	0.982964	−	2.15239i	0.0664226	−	0.145445i
$220$	0.797176	−	5.54448i	0.0537456	−	0.373809i
$221$	13.3853	−	8.60222i	0.900394	−	0.578648i
$222$	−2.27389	−	0.667675i	−0.152614	−	0.0448114i
$223$	−1.77962	−	12.3775i	−0.119172	−	0.828860i	−0.958471	−	0.285190i	$-0.907943\pi$
$223$	−1.77962	−	12.3775i	−0.119172	−	0.828860i	0.839299	−	0.543670i	$-0.182966\pi$
$224$	0.398983	+	0.460451i	0.0266582	+	0.0307652i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	7.61151	−	8.78415i	0.506310	−	0.584313i
$227$	−23.3829	+	6.86585i	−1.55198	+	0.455703i	−0.941692	−	0.336476i	$-0.890765\pi$
$227$	−23.3829	+	6.86585i	−1.55198	+	0.455703i	−0.610289	+	0.792179i	$0.708947\pi$
$228$	−0.734356	−	1.60802i	−0.0486339	−	0.106493i
$229$	−16.8754			−1.11516			−0.557579	−	0.830124i	$-0.688270\pi$
$229$	−16.8754			−1.11516			−0.557579	+	0.830124i	$0.688270\pi$
$230$	4.43560	+	1.82357i	0.292475	+	0.120243i
$231$	−3.41279			−0.224545
$232$	0.483883	+	1.05956i	0.0317685	+	0.0695633i
$233$	6.04834	−	1.77595i	0.396240	−	0.116346i	−0.0775413	−	0.996989i	$-0.524707\pi$
$233$	6.04834	−	1.77595i	0.396240	−	0.116346i	0.473781	+	0.880643i	$0.342889\pi$
$234$	2.77430	−	3.20172i	0.181362	−	0.209303i
$235$	−2.44253	−	1.56972i	−0.159333	−	0.102397i
$236$	7.83106	+	9.03753i	0.509759	+	0.588293i
$237$	−1.25664	−	8.74014i	−0.0816277	−	0.567733i
$238$	−2.19555	−	0.644673i	−0.142317	−	0.0417879i
$239$	9.13326	−	5.86959i	0.590781	−	0.379672i	−0.210825	−	0.977524i	$-0.567615\pi$
$239$	9.13326	−	5.86959i	0.590781	−	0.379672i	0.801607	+	0.597852i	$0.203979\pi$
$240$	0.142315	−	0.989821i	0.00918638	−	0.0638927i
$241$	−8.41089	+	18.4173i	−0.541793	+	1.18636i	0.418718	+	0.908117i	$0.362480\pi$
$241$	−8.41089	+	18.4173i	−0.541793	+	1.18636i	−0.960510	+	0.278244i	$0.910248\pi$
$242$	8.46480	−	18.5353i	0.544138	−	1.19150i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	1.41260	−	0.907822i	0.0904324	−	0.0581174i
$245$	−6.36028	−	1.86755i	−0.406344	−	0.119313i
$246$	0.590304	+	4.10565i	0.0376364	+	0.261767i
$247$	−4.90432	−	5.65989i	−0.312054	−	0.360130i
$248$	−7.17941	−	4.61393i	−0.455893	−	0.292985i
$249$	10.1491	−	11.7127i	0.643174	−	0.742263i
$250$	0.959493	−	0.281733i	0.0606837	−	0.0178183i
$251$	9.84563	+	21.5589i	0.621451	+	1.36079i	0.914460	+	0.404677i	$0.132616\pi$
$251$	9.84563	+	21.5589i	0.621451	+	1.36079i	−0.293009	+	0.956110i	$0.594657\pi$
$252$	−0.609264			−0.0383801
$253$	20.9618	+	16.8009i	1.31785	+	1.05626i
$254$	−8.42108			−0.528385
$255$	1.56019	+	3.41635i	0.0977032	+	0.213940i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−11.1726	+	12.8939i	−0.696929	+	0.804299i	−0.988334	−	0.152301i	$-0.951332\pi$
$257$	−11.1726	+	12.8939i	−0.696929	+	0.804299i	0.291405	+	0.956600i	$0.405877\pi$
$258$	−7.12115	−	4.57649i	−0.443344	−	0.284920i
$259$	0.945546	+	1.09122i	0.0587534	+	0.0678050i
$260$	−0.602914	−	4.19336i	−0.0373911	−	0.260061i
$261$	−1.11764	−	0.328167i	−0.0691799	−	0.0203130i
$262$	7.65911	−	4.92221i	0.473181	−	0.304095i
$263$	0.0562281	−	0.391075i	0.00346717	−	0.0241147i	−0.988014	−	0.154362i	$-0.950668\pi$
$263$	0.0562281	−	0.391075i	0.00346717	−	0.0241147i	0.991482	+	0.130247i	$0.0415770\pi$
$264$	2.32694	−	5.09530i	0.143214	−	0.313594i
$265$	−5.21404	+	11.4172i	−0.320296	+	0.701350i
$266$	−0.153278	+	1.06607i	−0.00939810	+	0.0653652i
$267$	−3.13105	+	2.01220i	−0.191617	+	0.123145i
$268$	−10.6399	−	3.12416i	−0.649937	−	0.190839i
$269$	2.19283	+	15.2515i	0.133699	+	0.929898i	0.940674	+	0.339312i	$0.110194\pi$
$269$	2.19283	+	15.2515i	0.133699	+	0.929898i	−0.806975	+	0.590586i	$0.798897\pi$
$270$	0.654861	+	0.755750i	0.0398536	+	0.0459935i
$271$	−6.10424	−	3.92296i	−0.370806	−	0.238303i	0.341944	−	0.939720i	$-0.388915\pi$
$271$	−6.10424	−	3.92296i	−0.370806	−	0.238303i	−0.712751	+	0.701417i	$0.752551\pi$
$272$	2.45949	−	2.83841i	0.149129	−	0.172104i
$273$	−2.47658	+	0.727190i	−0.149890	+	0.0440115i
$274$	−1.88599	−	4.12974i	−0.113937	−	0.249487i
$275$	5.60149			0.337783
$276$	3.74217	+	2.99936i	0.225252	+	0.180540i
$277$	−18.8381			−1.13187			−0.565935	−	0.824450i	$-0.691485\pi$
$277$	−18.8381			−1.13187			−0.565935	+	0.824450i	$0.691485\pi$
$278$	6.22268	+	13.6258i	0.373212	+	0.817220i
$279$	8.18849	−	2.40436i	0.490232	−	0.143945i
$280$	−0.398983	+	0.460451i	−0.0238438	+	0.0275172i
$281$	−2.71600	−	1.74547i	−0.162023	−	0.104126i	0.457117	−	0.889407i	$-0.348882\pi$
$281$	−2.71600	−	1.74547i	−0.162023	−	0.104126i	−0.619140	+	0.785281i	$0.712519\pi$
$282$	−1.90135	−	2.19428i	−0.113224	−	0.130667i
$283$	−0.938471	−	6.52721i	−0.0557863	−	0.388002i	−0.998517	−	0.0544466i	$-0.982661\pi$
$283$	−0.938471	−	6.52721i	−0.0557863	−	0.388002i	0.942730	−	0.333556i	$-0.108249\pi$
$284$	11.9053	+	3.49572i	0.706452	+	0.207433i
$285$	1.48714	−	0.955726i	0.0880905	−	0.0566123i
$286$	3.37722	−	23.4891i	0.199699	−	1.38894i
$287$	1.04982	−	2.29878i	0.0619687	−	0.135693i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	0.411908	−	2.86488i	0.0242299	−	0.168523i
$290$	−0.979908	+	0.629749i	−0.0575422	+	0.0369801i
$291$	3.15303	+	0.925812i	0.184834	+	0.0542721i
$292$	−0.336749	−	2.34214i	−0.0197067	−	0.137063i
$293$	0.908488	+	1.04845i	0.0530744	+	0.0612512i	0.781666	−	0.623697i	$-0.214370\pi$
$293$	0.908488	+	1.04845i	0.0530744	+	0.0612512i	−0.728592	+	0.684948i	$0.759825\pi$
$294$	−5.57650	−	3.58380i	−0.325228	−	0.209011i
$295$	−7.83106	+	9.03753i	−0.455942	+	0.526185i
$296$	−2.27389	+	0.667675i	−0.132167	+	0.0388078i
$297$	2.32694	+	5.09530i	0.135023	+	0.295659i
$298$	10.3364			0.598771
$299$	18.7913	+	7.72552i	1.08673	+	0.446778i
$300$	1.00000			0.0577350
$301$	2.14245	+	4.69132i	0.123489	+	0.270403i
$302$	15.3827	−	4.51676i	0.885172	−	0.259910i
$303$	10.5339	−	12.1568i	0.605156	−	0.698387i
$304$	−1.48714	−	0.955726i	−0.0852933	−	0.0548147i
$305$	1.09962	+	1.26902i	0.0629638	+	0.0726641i
$306$	0.534499	+	3.71752i	0.0305553	+	0.212517i
$307$	20.4685	+	6.01008i	1.16820	+	0.343014i	0.807613	−	0.589713i	$-0.200759\pi$
$307$	20.4685	+	6.01008i	1.16820	+	0.343014i	0.360584	+	0.932727i	$0.382577\pi$
$308$	−2.87102	+	1.84509i	−0.163592	+	0.105134i
$309$	0.132574	−	0.922074i	0.00754188	−	0.0524549i
$310$	3.54523	−	7.76297i	0.201355	−	0.440907i
$311$	−11.6985	+	25.6162i	−0.663364	+	1.45256i	0.215991	+	0.976395i	$0.430702\pi$
$311$	−11.6985	+	25.6162i	−0.663364	+	1.45256i	−0.879354	+	0.476168i	$0.842025\pi$
$312$	0.602914	−	4.19336i	0.0341333	−	0.237402i
$313$	6.51111	−	4.18444i	0.368030	−	0.236518i	−0.343533	−	0.939140i	$-0.611624\pi$
$313$	6.51111	−	4.18444i	0.368030	−	0.236518i	0.711563	+	0.702622i	$0.247987\pi$
$314$	4.90838	+	1.44123i	0.276996	+	0.0813334i
$315$	−0.0867074	−	0.603063i	−0.00488541	−	0.0339788i
$316$	−5.78243	−	6.67328i	−0.325287	−	0.375402i
$317$	6.41293	+	4.12134i	0.360186	+	0.231478i	0.708200	−	0.706012i	$-0.249507\pi$
$317$	6.41293	+	4.12134i	0.360186	+	0.231478i	−0.348014	+	0.937489i	$0.613144\pi$
$318$	−8.21942	+	9.48571i	−0.460922	+	0.531932i
$319$	−6.26043	+	1.83823i	−0.350517	+	0.102921i
$320$	−0.415415	−	0.909632i	−0.0232224	−	0.0508500i
$321$	−10.0266			−0.559628
$322$	−0.930067	−	2.76995i	−0.0518306	−	0.154364i
$323$	6.63929			0.369420
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	4.06487	−	1.19355i	0.225479	−	0.0662065i
$326$	−15.2388	+	17.5865i	−0.844000	+	0.974028i
$327$	4.95375	+	3.18358i	0.273943	+	0.176052i
$328$	2.71628	+	3.13475i	0.149981	+	0.173088i
$329$	0.251750	+	1.75096i	0.0138794	+	0.0965335i
$330$	5.37459	+	1.57812i	0.295862	+	0.0868728i
$331$	−8.83805	+	5.67987i	−0.485783	+	0.312194i	−0.760507	−	0.649329i	$-0.775050\pi$
$331$	−8.83805	+	5.67987i	−0.485783	+	0.312194i	0.274724	+	0.961523i	$0.411413\pi$
$332$	2.20562	−	15.3404i	0.121049	−	0.841913i
$333$	0.984487	−	2.15573i	0.0539496	−	0.118133i
$334$	−9.92650	+	21.7360i	−0.543154	+	1.18934i
$335$	1.57814	−	10.9762i	0.0862233	−	0.599696i
$336$	−0.512546	+	0.329393i	−0.0279617	+	0.0179699i
$337$	−2.63631	−	0.774089i	−0.143609	−	0.0421673i	0.209138	−	0.977886i	$-0.432934\pi$
$337$	−2.63631	−	0.774089i	−0.143609	−	0.0421673i	−0.352747	+	0.935719i	$0.614752\pi$
$338$	−0.704139	−	4.89739i	−0.0383001	−	0.266383i
$339$	7.61151	+	8.78415i	0.413400	+	0.477090i
$340$	3.15954	+	2.03051i	0.171350	+	0.110120i
$341$	31.3051	−	36.1280i	1.69526	−	1.95644i
$342$	1.69616	−	0.498037i	0.0917178	−	0.0269308i
$343$	3.44942	+	7.55317i	0.186251	+	0.407833i
$344$	−8.46493			−0.456398
$345$	−2.43626	+	4.13094i	−0.131164	+	0.222402i
$346$	−11.7592			−0.632177
$347$	9.89053	+	21.6572i	0.530952	+	1.16262i	0.965124	+	0.261792i	$0.0843135\pi$
$347$	9.89053	+	21.6572i	0.530952	+	1.16262i	−0.434173	+	0.900830i	$0.642959\pi$
$348$	−1.11764	+	0.328167i	−0.0599115	+	0.0175916i
$349$	−1.52375	+	1.75851i	−0.0815647	+	0.0941307i	−0.795065	−	0.606524i	$-0.792563\pi$
$349$	−1.52375	+	1.75851i	−0.0815647	+	0.0941307i	0.713500	+	0.700655i	$0.247109\pi$
$350$	−0.512546	−	0.329393i	−0.0273967	−	0.0176068i
$351$	2.77430	+	3.20172i	0.148081	+	0.170895i
$352$	−0.797176	−	5.54448i	−0.0424896	−	0.295522i
$353$	−15.9949	−	4.69653i	−0.851323	−	0.249971i	−0.173170	−	0.984892i	$-0.555401\pi$
$353$	−15.9949	−	4.69653i	−0.851323	−	0.249971i	−0.678153	+	0.734921i	$0.737219\pi$
$354$	−10.0600	+	6.46518i	−0.534684	+	0.343620i
$355$	−1.76584	+	12.2817i	−0.0937208	+	0.651843i
$356$	−1.54613	+	3.38554i	−0.0819445	+	0.179433i
$357$	0.950571	−	2.08146i	0.0503096	−	0.110163i
$358$	0.539858	−	3.75479i	0.0285324	−	0.198447i
$359$	6.06862	−	3.90007i	0.320290	−	0.205838i	−0.370610	−	0.928789i	$-0.620851\pi$
$359$	6.06862	−	3.90007i	0.320290	−	0.205838i	0.690899	+	0.722951i	$0.257215\pi$
$360$	0.959493	+	0.281733i	0.0505697	+	0.0148486i
$361$	2.25925	+	15.7134i	0.118908	+	0.827022i
$362$	−13.1675	−	15.1961i	−0.692070	−	0.798692i
$363$	17.1420	+	11.0165i	0.899721	+	0.578216i
$364$	−1.69028	+	1.95069i	−0.0885950	+	0.102244i
$365$	2.27037	−	0.666642i	0.118837	−	0.0348936i
$366$	0.697548	+	1.52742i	0.0364614	+	0.0798394i
$367$	−27.3781			−1.42913			−0.714563	−	0.699571i	$-0.753375\pi$
$367$	−27.3781			−1.42913			−0.714563	+	0.699571i	$0.753375\pi$
$368$	4.76969	+	0.500049i	0.248637	+	0.0260669i
$369$	−4.14787			−0.215930
$370$	−0.984487	−	2.15573i	−0.0511811	−	0.112071i
$371$	7.33736	−	2.15444i	0.380937	−	0.111853i
$372$	5.58870	−	6.44971i	0.289761	−	0.334402i
$373$	5.76885	+	3.70742i	0.298700	+	0.191963i	0.681403	−	0.731909i	$-0.261370\pi$
$373$	5.76885	+	3.70742i	0.298700	+	0.191963i	−0.382703	+	0.923872i	$0.625007\pi$
$374$	13.7768	+	15.8993i	0.712383	+	0.822134i
$375$	0.142315	+	0.989821i	0.00734911	+	0.0511142i
$376$	−2.78583	−	0.817994i	−0.143668	−	0.0421848i
$377$	−4.15136	+	2.66792i	−0.213806	+	0.137405i
$378$	0.0867074	−	0.603063i	0.00445975	−	0.0310182i
$379$	−0.597145	+	1.30756i	−0.0306733	+	0.0671651i	−0.924348	−	0.381549i	$-0.875391\pi$
$379$	−0.597145	+	1.30756i	−0.0306733	+	0.0671651i	0.893675	+	0.448714i	$0.148118\pi$
$380$	0.734356	−	1.60802i	0.0376717	−	0.0824895i
$381$	1.19844	−	8.33536i	0.0613981	−	0.427034i
$382$	−13.9504	+	8.96536i	−0.713763	+	0.458708i
$383$	5.77845	+	1.69671i	0.295265	+	0.0866976i	0.426010	−	0.904718i	$-0.359919\pi$
$383$	5.77845	+	1.69671i	0.295265	+	0.0866976i	−0.130745	+	0.991416i	$0.541737\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−2.23490	−	2.57922i	−0.113901	−	0.131449i
$386$	8.43564	+	5.42126i	0.429363	+	0.275935i
$387$	5.54335	−	6.39737i	0.281784	−	0.325196i
$388$	3.15303	−	0.925812i	0.160071	−	0.0470010i
$389$	12.2131	+	26.7430i	0.619231	+	1.35593i	0.916077	+	0.401001i	$0.131338\pi$
$389$	12.2131	+	26.7430i	0.619231	+	1.35593i	−0.296847	+	0.954925i	$0.595935\pi$
$390$	4.23648			0.214522
$391$	−16.0854	+	8.10499i	−0.813472	+	0.409887i
$392$	−6.62880			−0.334805
$393$	3.78210	+	8.28165i	0.190782	+	0.417754i
$394$	−2.75620	+	0.809293i	−0.138855	+	0.0407716i
$395$	5.78243	−	6.67328i	0.290946	−	0.335769i
$396$	4.71228	+	3.02840i	0.236801	+	0.152183i
$397$	7.82783	+	9.03380i	0.392868	+	0.453393i	0.917382	−	0.398008i	$-0.130298\pi$
$397$	7.82783	+	9.03380i	0.392868	+	0.453393i	−0.524514	+	0.851402i	$0.675753\pi$
$398$	0.503886	+	3.50460i	0.0252575	+	0.175670i
$399$	−1.03341	−	0.303436i	−0.0517352	−	0.0151908i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	3.06635	−	21.3269i	0.153126	−	1.06502i	−0.757812	−	0.652473i	$-0.773731\pi$
$401$	3.06635	−	21.3269i	0.153126	−	1.06502i	0.910938	−	0.412543i	$-0.135359\pi$
$402$	4.60658	−	10.0870i	0.229755	−	0.503094i
$403$	15.0193	−	32.8876i	0.748164	−	1.63825i
$404$	2.28923	−	15.9220i	0.113894	−	0.792147i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	0.680936	+	0.199941i	0.0337943	+	0.00992289i
$407$	−1.88922	−	13.1398i	−0.0936450	−	0.651315i
$408$	2.45949	+	2.83841i	0.121763	+	0.140522i
$409$	−19.2287	−	12.3575i	−0.950796	−	0.611039i	−0.0293594	−	0.999569i	$-0.509347\pi$
$409$	−19.2287	−	12.3575i	−0.950796	−	0.611039i	−0.921436	+	0.388530i	$0.872983\pi$
$410$	−2.71628	+	3.13475i	−0.134147	+	0.154814i
$411$	4.35611	−	1.27907i	0.214871	−	0.0630918i
$412$	−0.386982	−	0.847373i	−0.0190652	−	0.0417471i
$413$	7.28580			0.358511
$414$	−3.50140	+	3.27723i	−0.172084	+	0.161067i
$415$	15.4981			0.760774
$416$	−1.75990	−	3.85364i	−0.0862860	−	0.188940i
$417$	−14.3727	+	4.22019i	−0.703832	+	0.206664i
$418$	6.48452	−	7.48353i	0.317168	−	0.366031i
$419$	−11.6106	−	7.46165i	−0.567213	−	0.364526i	0.225385	−	0.974270i	$-0.427636\pi$
$419$	−11.6106	−	7.46165i	−0.567213	−	0.364526i	−0.792598	+	0.609744i	$0.791272\pi$
$420$	−0.398983	−	0.460451i	−0.0194684	−	0.0224677i
$421$	2.48549	+	17.2869i	0.121135	+	0.842514i	0.956274	+	0.292474i	$0.0944784\pi$
$421$	2.48549	+	17.2869i	0.121135	+	0.842514i	−0.835138	+	0.550040i	$0.814612\pi$
$422$	18.9107	+	5.55268i	0.920559	+	0.270300i
$423$	2.44253	−	1.56972i	0.118760	−	0.0763224i
$424$	−1.78625	+	12.4236i	−0.0867480	+	0.603345i
$425$	−1.56019	+	3.41635i	−0.0756806	+	0.165717i
$426$	−5.15445	+	11.2867i	−0.249734	+	0.546841i
$427$	0.145596	−	1.01264i	0.00704586	−	0.0490050i
$428$	−8.43489	+	5.42077i	−0.407716	+	0.262023i
$429$	22.7694	+	6.68568i	1.09931	+	0.322788i
$430$	−1.20469	−	8.37877i	−0.0580951	−	0.404060i
$431$	−12.2651	−	14.1547i	−0.590791	−	0.681809i	0.379098	−	0.925357i	$-0.376234\pi$
$431$	−12.2651	−	14.1547i	−0.590791	−	0.681809i	−0.969889	+	0.243547i	$0.921689\pi$
$432$	0.841254	+	0.540641i	0.0404748	+	0.0260116i
$433$	−5.38698	+	6.21691i	−0.258882	+	0.298765i	−0.870280	−	0.492558i	$-0.836062\pi$
$433$	−5.38698	+	6.21691i	−0.258882	+	0.298765i	0.611398	+	0.791323i	$0.290607\pi$
$434$	−4.98896	+	1.46489i	−0.239478	+	0.0703170i
$435$	−0.483883	−	1.05956i	−0.0232004	−	0.0508018i
$436$	5.88853			0.282009
$437$	4.85353	+	6.95113i	0.232176	+	0.332518i
$438$	2.36622			0.113062
$439$	14.6744	+	32.1324i	0.700369	+	1.53359i	0.839524	+	0.543323i	$0.182834\pi$
$439$	14.6744	+	32.1324i	0.700369	+	1.53359i	−0.139155	+	0.990271i	$0.544439\pi$
$440$	5.37459	−	1.57812i	0.256224	−	0.0752341i
$441$	4.34094	−	5.00971i	0.206711	−	0.238558i
$442$	13.3853	+	8.60222i	0.636674	+	0.409166i
$443$	−21.2940	−	24.5746i	−1.01171	−	1.16757i	−0.985802	−	0.167910i	$-0.946298\pi$
$443$	−21.2940	−	24.5746i	−1.01171	−	1.16757i	−0.0259064	−	0.999664i	$-0.508247\pi$
$444$	−0.337270	−	2.34577i	−0.0160061	−	0.111325i
$445$	−3.57112	−	1.04858i	−0.169287	−	0.0497072i
$446$	10.5197	−	6.76060i	0.498122	−	0.320124i
$447$	−1.47102	+	10.2312i	−0.0695770	+	0.483918i
$448$	−0.253098	+	0.554206i	−0.0119577	+	0.0261838i
$449$	4.62742	−	10.1326i	0.218382	−	0.478189i	−0.768456	−	0.639902i	$-0.778975\pi$
$449$	4.62742	−	10.1326i	0.218382	−	0.478189i	0.986838	+	0.161713i	$0.0517020\pi$
$450$	−0.142315	+	0.989821i	−0.00670879	+	0.0466606i
$451$	−19.5459	+	12.5614i	−0.920381	+	0.591493i
$452$	11.1523	+	3.27461i	0.524559	+	0.154024i
$453$	2.28160	+	15.8689i	0.107199	+	0.745585i
$454$	−15.9590	−	18.4177i	−0.748994	−	0.864385i
$455$	−2.17139	−	1.39547i	−0.101796	−	0.0654205i
$456$	1.15764	−	1.33599i	0.0542115	−	0.0625634i
$457$	−24.6301	+	7.23204i	−1.15215	+	0.338301i	−0.801376	−	0.598161i	$-0.795898\pi$
$457$	−24.6301	+	7.23204i	−1.15215	+	0.338301i	−0.350770	+	0.936462i	$0.614080\pi$
$458$	−7.01030	−	15.3504i	−0.327570	−	0.717277i
$459$	−3.75575			−0.175303
$460$	0.183838	+	4.79231i	0.00857150	+	0.223442i
$461$	26.2745			1.22372			0.611862	−	0.790964i	$-0.290421\pi$
$461$	26.2745			1.22372			0.611862	+	0.790964i	$0.290421\pi$
$462$	−1.41772	−	3.10438i	−0.0659585	−	0.144429i
$463$	35.8938	−	10.5394i	1.66813	−	0.489807i	0.694796	−	0.719207i	$-0.255495\pi$
$463$	35.8938	−	10.5394i	1.66813	−	0.489807i	0.973332	+	0.229400i	$0.0736763\pi$
$464$	−0.762794	+	0.880311i	−0.0354118	+	0.0408674i
$465$	7.17941	+	4.61393i	0.332937	+	0.213966i
$466$	4.12803	+	4.76400i	0.191227	+	0.220688i
$467$	0.504009	+	3.50546i	0.0233228	+	0.162213i	0.998154	−	0.0607296i	$-0.0193427\pi$
$467$	0.504009	+	3.50546i	0.0233228	+	0.162213i	−0.974831	+	0.222943i	$0.928434\pi$
$468$	4.06487	+	1.19355i	0.187899	+	0.0551721i
$469$	−5.68368	+	3.65268i	−0.262448	+	0.168665i
$470$	0.413203	−	2.87389i	0.0190596	−	0.132563i
$471$	−2.12510	+	4.65331i	−0.0979193	+	0.214413i
$472$	−4.96768	+	10.8777i	−0.228656	+	0.500687i
$473$	6.74804	−	46.9336i	0.310275	−	2.15801i
$474$	7.42829	−	4.77387i	0.341193	−	0.219271i
$475$	1.69616	+	0.498037i	0.0778251	+	0.0228515i
$476$	−0.325651	−	2.26495i	−0.0149262	−	0.103814i
$477$	−8.21942	−	9.48571i	−0.376341	−	0.434321i
$478$	9.13326	+	5.86959i	0.417746	+	0.268469i
$479$	−7.66548	+	8.84644i	−0.350245	+	0.404204i	−0.903348	−	0.428909i	$-0.858898\pi$
$479$	−7.66548	+	8.84644i	−0.350245	+	0.404204i	0.553103	+	0.833113i	$0.313444\pi$
$480$	0.959493	−	0.281733i	0.0437947	−	0.0128593i
$481$	−4.17076	−	9.13269i	−0.190170	−	0.416415i
$482$	−20.2469			−0.922223
$483$	2.87412	−	0.526394i	0.130777	−	0.0239518i
$484$	20.3767			0.926215
$485$	1.36511	+	2.98918i	0.0619865	+	0.135732i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	11.5751	−	13.3584i	0.524519	−	0.605328i	−0.430237	−	0.902716i	$-0.641570\pi$
$487$	11.5751	−	13.3584i	0.524519	−	0.605328i	0.954757	+	0.297388i	$0.0961156\pi$
$488$	1.41260	+	0.907822i	0.0639453	+	0.0410952i
$489$	−15.2388	−	17.5865i	−0.689123	−	0.795290i
$490$	−0.943376	−	6.56133i	−0.0426174	−	0.296410i
$491$	28.4624	+	8.35731i	1.28449	+	0.377160i	0.851555	−	0.524265i	$-0.175660\pi$
$491$	28.4624	+	8.35731i	1.28449	+	0.377160i	0.432934	+	0.901425i	$0.357478\pi$
$492$	−3.48941	+	2.24251i	−0.157315	+	0.101100i
$493$	0.622594	−	4.33024i	0.0280402	−	0.195024i
$494$	3.11109	−	6.81233i	0.139974	−	0.306501i
$495$	−2.32694	+	5.09530i	−0.104588	+	0.229017i
$496$	1.21454	−	8.44732i	0.0545345	−	0.379296i
$497$	6.35964	−	4.08709i	0.285269	−	0.183331i
$498$	14.8704	+	4.36633i	0.666357	+	0.195660i
$499$	1.61566	+	11.2372i	0.0723271	+	0.503046i	0.993495	+	0.113879i	$0.0363278\pi$
$499$	1.61566	+	11.2372i	0.0723271	+	0.503046i	−0.921168	+	0.389166i	$0.872763\pi$
$500$	0.654861	+	0.755750i	0.0292863	+	0.0337981i
$501$	−20.1021	−	12.9188i	−0.898095	−	0.577170i
$502$	−15.5207	+	17.9118i	−0.692721	+	0.799443i
$503$	−28.9940	+	8.51341i	−1.29278	+	0.379594i	−0.854597	−	0.519292i	$-0.826196\pi$
$503$	−28.9940	+	8.51341i	−1.29278	+	0.379594i	−0.438182	+	0.898886i	$0.644377\pi$
$504$	−0.253098	−	0.554206i	−0.0112739	−	0.0246863i
$505$	16.0857			0.715804
$506$	−6.57479	+	26.0468i	−0.292285	+	1.15792i
$507$	4.94775			0.219737
$508$	−3.49824	−	7.66008i	−0.155209	−	0.339861i
$509$	10.1390	−	2.97707i	0.449402	−	0.131956i	−0.0491970	−	0.998789i	$-0.515666\pi$
$509$	10.1390	−	2.97707i	0.449402	−	0.131956i	0.498599	+	0.866833i	$0.333848\pi$
$510$	−2.45949	+	2.83841i	−0.108908	+	0.125687i
$511$	−1.21280	−	0.779418i	−0.0536510	−	0.0344794i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	0.251579	+	1.74977i	0.0111075	+	0.0772543i
$514$	−16.3700	−	4.80666i	−0.722048	−	0.212013i
$515$	0.783674	−	0.503637i	0.0345328	−	0.0221929i
$516$	1.20469	−	8.37877i	0.0530333	−	0.368855i
$517$	6.75615	−	14.7939i	0.297135	−	0.650635i
$518$	−0.599813	+	1.31341i	−0.0263543	+	0.0577078i
$519$	1.67350	−	11.6395i	0.0734587	−	0.510916i
$520$	3.56395	−	2.29041i	0.156290	−	0.100441i
$521$	41.7321	+	12.2536i	1.82832	+	0.536842i	0.999735	−	0.0230285i	$-0.00733086\pi$
$521$	41.7321	+	12.2536i	1.82832	+	0.536842i	0.828580	+	0.559870i	$0.189149\pi$
$522$	−0.165771	−	1.15296i	−0.00725560	−	0.0504638i
$523$	−9.43072	−	10.8836i	−0.412376	−	0.475908i	0.511123	−	0.859508i	$-0.329230\pi$
$523$	−9.43072	−	10.8836i	−0.412376	−	0.475908i	−0.923499	+	0.383600i	$0.874684\pi$
$524$	7.65911	+	4.92221i	0.334590	+	0.215028i
$525$	0.398983	−	0.460451i	0.0174131	−	0.0200957i
$526$	0.379092	−	0.111311i	0.0165292	−	0.00485341i
$527$	13.3150	+	29.1558i	0.580010	+	1.27004i
$528$	5.60149			0.243774
$529$	−20.2446	−	10.9159i	−0.880199	−	0.474604i
$530$	−12.5514			−0.545198
$531$	−4.96768	−	10.8777i	−0.215579	−	0.472052i
$532$	−1.03341	+	0.303436i	−0.0448040	+	0.0131556i
$533$	−11.5075	+	13.2803i	−0.498443	+	0.575234i
$534$	−3.13105	−	2.01220i	−0.135494	−	0.0870765i
$535$	−6.56601	−	7.57757i	−0.283873	−	0.327607i
$536$	−1.57814	−	10.9762i	−0.0681655	−	0.474101i
$537$	3.63974	+	1.06873i	0.157067	+	0.0461189i
$538$	−12.9623	+	8.33035i	−0.558844	+	0.359147i
$539$	5.28431	−	36.7532i	0.227612	−	1.58307i
$540$	−0.415415	+	0.909632i	−0.0178766	+	0.0391443i
$541$	2.92157	−	6.39734i	0.125608	−	0.275043i	−0.836372	−	0.548162i	$-0.815328\pi$
$541$	2.92157	−	6.39734i	0.125608	−	0.275043i	0.961980	+	0.273119i	$0.0880551\pi$
$542$	1.03265	−	7.18227i	0.0443563	−	0.308505i
$543$	16.9154	−	10.8709i	0.725910	−	0.466514i
$544$	3.60362	+	1.05812i	0.154504	+	0.0453664i
$545$	0.838025	+	5.82859i	0.0358971	+	0.249669i
$546$	−1.69028	−	1.95069i	−0.0723375	−	0.0834819i
$547$	11.5052	+	7.39395i	0.491927	+	0.316142i	0.762980	−	0.646422i	$-0.223735\pi$
$547$	11.5052	+	7.39395i	0.491927	+	0.316142i	−0.271053	+	0.962564i	$0.587372\pi$
$548$	2.97308	−	3.43111i	0.127003	−	0.146570i
$549$	−1.61114	+	0.473074i	−0.0687619	+	0.0201903i
$550$	2.32694	+	5.09530i	0.0992212	+	0.217264i
$551$	−2.05913			−0.0877217
$552$	−1.17376	+	4.64998i	−0.0499584	+	0.197916i
$553$	−5.37982			−0.228773
$554$	−7.82561	−	17.1357i	−0.332478	−	0.728026i
$555$	2.27389	−	0.667675i	0.0965213	−	0.0283412i
$556$	−9.80944	+	11.3207i	−0.416013	+	0.480105i
$557$	−39.3406	−	25.2827i	−1.66691	−	1.07126i	−0.906891	−	0.421365i	$-0.861551\pi$
$557$	−39.3406	−	25.2827i	−1.66691	−	1.07126i	−0.760023	−	0.649896i	$-0.774813\pi$
$558$	5.58870	+	6.44971i	0.236589	+	0.273038i
$559$	−5.10362	−	35.4965i	−0.215860	−	1.50134i
$560$	−0.584585	−	0.171650i	−0.0247032	−	0.00725352i
$561$	−17.6981	+	11.3739i	−0.747216	+	0.480206i
$562$	0.459465	−	3.19565i	0.0193814	−	0.134800i
$563$	2.79318	−	6.11620i	0.117718	−	0.257767i	−0.841596	−	0.540108i	$-0.818384\pi$
$563$	2.79318	−	6.11620i	0.117718	−	0.257767i	0.959314	+	0.282340i	$0.0911108\pi$
$564$	1.20613	−	2.64106i	0.0507874	−	0.111209i
$565$	−1.65414	+	11.5048i	−0.0695902	+	0.484010i
$566$	5.54750	−	3.56516i	0.233179	−	0.149855i
$567$	0.584585	+	0.171650i	0.0245503	+	0.00720861i
$568$	1.76584	+	12.2817i	0.0740928	+	0.515327i
$569$	10.1295	+	11.6901i	0.424652	+	0.490075i	0.927249	−	0.374446i	$-0.122167\pi$
$569$	10.1295	+	11.6901i	0.424652	+	0.490075i	−0.502596	+	0.864521i	$0.667622\pi$
$570$	1.48714	+	0.955726i	0.0622894	+	0.0400310i
$571$	−12.0810	+	13.9422i	−0.505573	+	0.583462i	−0.949960	−	0.312373i	$-0.898876\pi$
$571$	−12.0810	+	13.9422i	−0.505573	+	0.583462i	0.444387	+	0.895835i	$0.353422\pi$
$572$	22.7694	−	6.68568i	0.952034	−	0.279543i
$573$	−6.88876	−	15.0843i	−0.287782	−	0.630155i
$574$	2.52715			0.105481
$575$	−4.71737	+	0.863983i	−0.196728	+	0.0360306i
$576$	1.00000			0.0416667
$577$	−2.42000	−	5.29906i	−0.100746	−	0.220603i	0.852547	−	0.522651i	$-0.175057\pi$
$577$	−2.42000	−	5.29906i	−0.100746	−	0.220603i	−0.953293	+	0.302048i	$0.902330\pi$
$578$	2.77710	−	0.815431i	0.115512	−	0.0339175i
$579$	−6.56659	+	7.57825i	−0.272898	+	0.314941i
$580$	−0.979908	−	0.629749i	−0.0406885	−	0.0261489i
$581$	−6.18350	−	7.13614i	−0.256535	−	0.296057i
$582$	0.467666	+	3.25269i	0.0193854	+	0.134828i
$583$	−67.4587	−	19.8076i	−2.79385	−	0.820349i
$584$	1.99059	−	1.27928i	0.0823713	−	0.0529368i
$585$	−0.602914	+	4.19336i	−0.0249274	+	0.173374i
$586$	−0.576305	+	1.26193i	−0.0238069	+	0.0521299i
$587$	2.40088	−	5.25720i	0.0990951	−	0.216988i	−0.853591	−	0.520944i	$-0.825580\pi$
$587$	2.40088	−	5.25720i	0.0990951	−	0.216988i	0.952686	+	0.303956i	$0.0983075\pi$
$588$	0.943376	−	6.56133i	0.0389042	−	0.270584i
$589$	12.6915	−	8.15635i	0.522945	−	0.336076i
$590$	−11.4740	−	3.36906i	−0.472376	−	0.138702i
$591$	−0.408807	−	2.84332i	−0.0168161	−	0.116958i
$592$	−1.55195	−	1.79104i	−0.0637846	−	0.0736114i
$593$	40.9223	+	26.2992i	1.68048	+	1.07998i	0.866787	+	0.498679i	$0.166181\pi$
$593$	40.9223	+	26.2992i	1.68048	+	1.07998i	0.813691	+	0.581298i	$0.197455\pi$
$594$	−3.66820	+	4.23333i	−0.150508	+	0.173695i
$595$	2.19555	−	0.644673i	0.0900090	−	0.0264290i
$596$	4.29389	+	9.40232i	0.175885	+	0.385134i
$597$	−3.54064			−0.144909
$598$	0.778827	+	20.3025i	0.0318486	+	0.830231i
$599$	−22.8988			−0.935621			−0.467811	−	0.883829i	$-0.654957\pi$
$599$	−22.8988			−0.935621			−0.467811	+	0.883829i	$0.654957\pi$
$600$	0.415415	+	0.909632i	0.0169592	+	0.0371356i
$601$	18.1344	−	5.32473i	0.739716	−	0.217200i	0.109898	−	0.993943i	$-0.464948\pi$
$601$	18.1344	−	5.32473i	0.739716	−	0.217200i	0.629818	+	0.776743i	$0.283129\pi$
$602$	−3.37737	+	3.89769i	−0.137651	+	0.158858i
$603$	9.32875	+	5.99522i	0.379896	+	0.244144i
$604$	10.4988	+	12.1162i	0.427189	+	0.493002i
$605$	2.89991	+	20.1693i	0.117898	+	0.819999i
$606$	15.4341	+	4.53186i	0.626968	+	0.184094i
$607$	−35.1458	+	22.5868i	−1.42652	+	0.916770i	−0.426599	+	0.904441i	$0.640288\pi$
$607$	−35.1458	+	22.5868i	−1.42652	+	0.916770i	−0.999924	+	0.0123294i	$0.996075\pi$
$608$	0.251579	−	1.74977i	0.0102029	−	0.0709626i
$609$	−0.294813	+	0.645550i	−0.0119464	+	0.0261590i
$610$	−0.697548	+	1.52742i	−0.0282429	+	0.0618433i
$611$	1.75053	−	12.1752i	0.0708187	−	0.492555i
$612$	−3.15954	+	2.03051i	−0.127717	+	0.0820786i
$613$	−12.6021	−	3.70031i	−0.508994	−	0.149454i	0.0171443	−	0.999853i	$-0.494543\pi$
$613$	−12.6021	−	3.70031i	−0.508994	−	0.149454i	−0.526139	+	0.850399i	$0.676361\pi$
$614$	3.03594	+	21.1154i	0.122521	+	0.852150i
$615$	−2.71628	−	3.13475i	−0.109531	−	0.126405i
$616$	−2.87102	−	1.84509i	−0.115677	−	0.0743410i
$617$	26.5481	−	30.6382i	1.06879	−	1.23345i	0.0975762	−	0.995228i	$-0.468891\pi$
$617$	26.5481	−	30.6382i	1.06879	−	1.23345i	0.971212	−	0.238219i	$-0.0765635\pi$
$618$	0.893821	−	0.262450i	0.0359548	−	0.0105573i
$619$	−4.99360	−	10.9345i	−0.200710	−	0.439493i	0.782335	−	0.622858i	$-0.214028\pi$
$619$	−4.99360	−	10.9345i	−0.200710	−	0.439493i	−0.983045	+	0.183364i	$0.941301\pi$
$620$	8.53418			0.342741
$621$	−2.74557	−	3.93215i	−0.110176	−	0.157792i
$622$	−28.1611			−1.12916
$623$	0.942000	+	2.06269i	0.0377404	+	0.0826400i
$624$	4.06487	−	1.19355i	0.162725	−	0.0477804i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	6.51111	+	4.18444i	0.260236	+	0.167244i
$627$	6.48452	+	7.48353i	0.258967	+	0.298863i
$628$	0.728026	+	5.06353i	0.0290514	+	0.202057i
$629$	8.54017	+	2.50762i	0.340519	+	0.0999853i
$630$	0.512546	−	0.329393i	0.0204203	−	0.0131233i
$631$	−6.57958	+	45.7620i	−0.261929	+	1.82175i	0.256397	+	0.966572i	$0.417464\pi$
$631$	−6.57958	+	45.7620i	−0.261929	+	1.82175i	−0.518326	+	0.855183i	$0.673445\pi$
$632$	3.66812	−	8.03207i	0.145910	−	0.319499i
$633$	−8.18744	+	17.9280i	−0.325421	+	0.712574i
$634$	−1.08488	+	7.54547i	−0.0430859	+	0.299669i
$635$	7.08426	−	4.55278i	0.281130	−	0.180671i
$636$	−12.0430	−	3.53614i	−0.477535	−	0.140217i
$637$	−3.99659	−	27.7969i	−0.158351	−	1.10135i
$638$	−4.27279	−	4.93106i	−0.169161	−	0.195222i
$639$	−10.4382	−	6.70824i	−0.412930	−	0.265374i
$640$	0.654861	−	0.755750i	0.0258856	−	0.0298736i
$641$	−21.6267	+	6.35018i	−0.854204	+	0.250817i	−0.679383	−	0.733783i	$-0.737753\pi$
$641$	−21.6267	+	6.35018i	−0.854204	+	0.250817i	−0.174820	+	0.984600i	$0.555934\pi$
$642$	−4.16519	−	9.12049i	−0.164387	−	0.359957i
$643$	−5.85011			−0.230706			−0.115353	−	0.993325i	$-0.536800\pi$
$643$	−5.85011			−0.230706			−0.115353	+	0.993325i	$0.536800\pi$
$644$	2.13328	−	1.99670i	0.0840628	−	0.0786810i
$645$	8.46493			0.333306
$646$	2.75806	+	6.03931i	0.108514	+	0.237613i
$647$	−25.5912	+	7.51427i	−1.00610	+	0.295416i	−0.742955	−	0.669341i	$-0.766576\pi$
$647$	−25.5912	+	7.51427i	−1.00610	+	0.295416i	−0.263140	+	0.964758i	$0.584758\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	−56.3511	−	36.2147i	−2.21197	−	1.42155i
$650$	2.77430	+	3.20172i	0.108817	+	0.125582i
$651$	−0.739977	−	5.14665i	−0.0290020	−	0.201713i
$652$	−22.3277	−	6.55600i	−0.874420	−	0.256753i
$653$	−28.0369	+	18.0182i	−1.09717	+	0.705107i	−0.958460	−	0.285227i	$-0.907931\pi$
$653$	−28.0369	+	18.0182i	−1.09717	+	0.705107i	−0.138707	+	0.990333i	$0.544295\pi$
$654$	−0.838025	+	5.82859i	−0.0327694	+	0.227916i
$655$	−3.78210	+	8.28165i	−0.147779	+	0.323591i
$656$	−1.72309	+	3.77304i	−0.0672753	+	0.147312i
$657$	−0.336749	+	2.34214i	−0.0131378	+	0.0913755i
$658$	−1.48815	+	0.956375i	−0.0580140	+	0.0372834i
$659$	−43.2299	−	12.6935i	−1.68400	−	0.494467i	−0.706911	−	0.707302i	$-0.749912\pi$
$659$	−43.2299	−	12.6935i	−1.68400	−	0.494467i	−0.977088	+	0.212835i	$0.931730\pi$
$660$	0.797176	+	5.54448i	0.0310300	+	0.215819i
$661$	8.20905	+	9.47375i	0.319295	+	0.368486i	0.892595	−	0.450860i	$-0.148882\pi$
$661$	8.20905	+	9.47375i	0.319295	+	0.368486i	−0.573300	+	0.819346i	$0.694337\pi$
$662$	−8.83805	−	5.67987i	−0.343501	−	0.220754i
$663$	−10.4196	+	12.0248i	−0.404663	+	0.467006i
$664$	14.8704	−	4.36633i	0.577082	−	0.169446i
$665$	−0.447417	−	0.979707i	−0.0173501	−	0.0379914i
$666$	2.36989			0.0918313
$667$	4.98876	−	2.51370i	0.193166	−	0.0973310i
$668$	−23.8954			−0.924540
$669$	5.19468	+	11.3748i	0.200838	+	0.439774i
$670$	10.6399	−	3.12416i	0.411056	−	0.120697i
$671$	−6.15949	+	7.10843i	−0.237784	+	0.274418i
$672$	−0.512546	−	0.329393i	−0.0197719	−	0.0127066i
$673$	5.87941	+	6.78520i	0.226635	+	0.261550i	0.857666	−	0.514207i	$-0.171914\pi$
$673$	5.87941	+	6.78520i	0.226635	+	0.261550i	−0.631032	+	0.775757i	$0.717368\pi$
$674$	−0.391025	−	2.71964i	−0.0150617	−	0.104757i
$675$	−0.959493	−	0.281733i	−0.0369309	−	0.0108439i
$676$	4.16231	−	2.67496i	0.160089	−	0.102883i
$677$	1.57005	−	10.9199i	0.0603418	−	0.419687i	−0.937151	−	0.348923i	$-0.886547\pi$
$677$	1.57005	−	10.9199i	0.0603418	−	0.419687i	0.997493	−	0.0707633i	$-0.0225435\pi$
$678$	−4.82841	+	10.5727i	−0.185434	+	0.406044i
$679$	0.831714	−	1.82120i	0.0319183	−	0.0698912i
$680$	−0.534499	+	3.71752i	−0.0204971	+	0.142560i
$681$	20.5014	−	13.1755i	0.785617	−	0.504885i
$682$	45.8678	+	13.4680i	1.75637	+	0.515716i
$683$	−6.13994	−	42.7043i	−0.234938	−	1.63403i	−0.676245	−	0.736677i	$-0.736394\pi$
$683$	−6.13994	−	42.7043i	−0.234938	−	1.63403i	0.441307	−	0.897356i	$-0.354515\pi$
$684$	1.15764	+	1.33599i	0.0442635	+	0.0510828i
$685$	3.81930	+	2.45452i	0.145928	+	0.0937822i
$686$	−5.43766	+	6.27540i	−0.207611	+	0.239596i
$687$	16.1918	−	4.75435i	0.617757	−	0.181390i
$688$	−3.51646	−	7.69997i	−0.134064	−	0.293559i
$689$	−53.1737			−2.02576
$690$	−4.76969	−	0.500049i	−0.181579	−	0.0190366i
$691$	20.9212			0.795881			0.397941	−	0.917411i	$-0.369725\pi$
$691$	20.9212			0.795881			0.397941	+	0.917411i	$0.369725\pi$
$692$	−4.88494	−	10.6965i	−0.185697	−	0.406621i
$693$	3.27455	−	0.961494i	0.124390	−	0.0365241i
$694$	−15.5915	+	17.9935i	−0.591843	+	0.683024i
$695$	−12.6015	−	8.09849i	−0.478002	−	0.307193i
$696$	−0.762794	−	0.880311i	−0.0289136	−	0.0333681i
$697$	−2.21703	−	15.4198i	−0.0839761	−	0.584067i
$698$	−2.23258	−	0.655546i	−0.0845046	−	0.0248128i
$699$	−5.30299	+	3.40803i	−0.200578	+	0.128903i
$700$	0.0867074	−	0.603063i	0.00327723	−	0.0227936i
$701$	−9.88228	+	21.6392i	−0.373249	+	0.817300i	0.626047	+	0.779785i	$0.284672\pi$
$701$	−9.88228	+	21.6392i	−0.373249	+	0.817300i	−0.999296	+	0.0375155i	$0.988056\pi$
$702$	−1.75990	+	3.85364i	−0.0664230	+	0.145446i
$703$	0.596215	−	4.14677i	0.0224867	−	0.156398i
$704$	4.71228	−	3.02840i	0.177601	−	0.114137i
$705$	2.78583	+	0.817994i	0.104921	+	0.0308075i
$706$	−2.37241	−	16.5005i	−0.0892869	−	0.621004i
$707$	−6.41792	−	7.40668i	−0.241371	−	0.278557i
$708$	−10.0600	−	6.46518i	−0.378078	−	0.242976i
$709$	27.1224	−	31.3009i	1.01860	−	1.17553i	0.0342345	−	0.999414i	$-0.489101\pi$
$709$	27.1224	−	31.3009i	1.01860	−	1.17553i	0.984369	−	0.176117i	$-0.0563538\pi$
$710$	−11.9053	+	3.49572i	−0.446799	+	0.131192i
$711$	3.66812	+	8.03207i	0.137565	+	0.301226i
$712$	−3.72188			−0.139483
$713$	−20.7915	+	35.2542i	−0.778648	+	1.32028i
$714$	2.28824			0.0856354
$715$	9.85805	+	21.5861i	0.368670	+	0.807275i
$716$	3.63974	−	1.06873i	0.136024	−	0.0399401i
$717$	−7.10964	+	8.20497i	−0.265514	+	0.306420i
$718$	6.06862	+	3.90007i	0.226479	+	0.145549i
$719$	17.9003	+	20.6580i	0.667567	+	0.770413i	0.983994	−	0.178204i	$-0.0570286\pi$
$719$	17.9003	+	20.6580i	0.667567	+	0.770413i	−0.316427	+	0.948617i	$0.602483\pi$
$720$	0.142315	+	0.989821i	0.00530376	+	0.0368885i
$721$	−0.544573	−	0.159901i	−0.0202810	−	0.00595503i
$722$	−13.3549	+	8.58267i	−0.497018	+	0.319414i
$723$	2.88144	−	20.0409i	0.107162	−	0.745328i
$724$	8.35291	−	18.2903i	0.310433	−	0.679754i
$725$	0.483883	−	1.05956i	0.0179710	−	0.0393509i
$726$	−2.89991	+	20.1693i	−0.107626	+	0.748554i
$727$	−30.6485	+	19.6966i	−1.13669	+	0.730506i	−0.966946	−	0.254982i	$-0.917930\pi$
$727$	−30.6485	+	19.6966i	−1.13669	+	0.730506i	−0.169744	+	0.985488i	$0.554294\pi$
$728$	−2.47658	−	0.727190i	−0.0917882	−	0.0269515i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	1.54955	+	1.78827i	0.0573513	+	0.0661869i
$731$	26.7453	+	17.1881i	0.989209	+	0.635726i
$732$	−1.09962	+	1.26902i	−0.0406430	+	0.0469045i
$733$	6.27275	−	1.84184i	0.231689	−	0.0680301i	−0.163827	−	0.986489i	$-0.552384\pi$
$733$	6.27275	−	1.84184i	0.231689	−	0.0680301i	0.395516	+	0.918459i	$0.370566\pi$
$734$	−11.3733	−	24.9040i	−0.419796	−	0.919224i
$735$	6.62880			0.244507
$736$	1.52654	+	4.54639i	0.0562690	+	0.167582i
$737$	62.1156			2.28806
$738$	−1.72309	−	3.77304i	−0.0634278	−	0.138887i
$739$	4.27608	−	1.25557i	0.157298	−	0.0461869i	−0.202135	−	0.979358i	$-0.564788\pi$
$739$	4.27608	−	1.25557i	0.157298	−	0.0461869i	0.359433	+	0.933171i	$0.382970\pi$
$740$	1.55195	−	1.79104i	0.0570507	−	0.0658400i
$741$	6.30023	+	4.04891i	0.231445	+	0.148741i
$742$	5.00780	+	5.77931i	0.183842	+	0.212165i
$743$	−4.49380	−	31.2551i	−0.164862	−	1.14664i	−0.889309	−	0.457307i	$-0.848814\pi$
$743$	−4.49380	−	31.2551i	−0.164862	−	1.14664i	0.724447	−	0.689330i	$-0.242095\pi$
$744$	8.18849	+	2.40436i	0.300205	+	0.0881480i
$745$	−8.69553	+	5.58828i	−0.318580	+	0.204739i
$746$	−0.975917	+	6.78765i	−0.0357308	+	0.248514i
$747$	−6.43816	+	14.0976i	−0.235560	+	0.515804i
$748$	−8.73942	+	19.1367i	−0.319545	+	0.699706i
$749$	−0.869377	+	6.04665i	−0.0317664	+	0.220940i
$750$	−0.841254	+	0.540641i	−0.0307182	+	0.0197414i
$751$	41.4660	+	12.1755i	1.51312	+	0.444291i	0.929834	−	0.367978i	$-0.119950\pi$
$751$	41.4660	+	12.1755i	1.51312	+	0.444291i	0.583282	+	0.812269i	$0.301768\pi$
$752$	−0.413203	−	2.87389i	−0.0150680	−	0.104800i
$753$	−15.5207	−	17.9118i	−0.565604	−	0.652742i
$754$	−4.15136	−	2.66792i	−0.151184	−	0.0971598i
$755$	−10.4988	+	12.1162i	−0.382089	+	0.440955i
$756$	0.584585	−	0.171650i	0.0212612	−	0.00624284i
$757$	−9.24653	−	20.2471i	−0.336071	−	0.735892i	0.663858	−	0.747859i	$-0.268918\pi$
$757$	−9.24653	−	20.2471i	−0.336071	−	0.735892i	−0.999928	+	0.0119666i	$0.996191\pi$
$758$	−1.43747			−0.0522111
$759$	−24.8460	−	10.2147i	−0.901853	−	0.370771i
$760$	1.76777			0.0641236
$761$	8.92292	+	19.5385i	0.323456	+	0.708269i	0.999594	−	0.0285058i	$-0.00907492\pi$
$761$	8.92292	+	19.5385i	0.323456	+	0.708269i	−0.676138	+	0.736775i	$0.736348\pi$
$762$	8.07996	−	2.37249i	0.292706	−	0.0859463i
$763$	2.34943	−	2.71138i	0.0850549	−	0.0981586i
$764$	−13.9504	−	8.96536i	−0.504707	−	0.324355i
$765$	−2.45949	−	2.83841i	−0.0889232	−	0.102623i
$766$	0.857077	+	5.96110i	0.0309674	+	0.215383i
$767$	−48.6092	−	14.2730i	−1.75518	−	0.515366i
$768$	0.841254	−	0.540641i	0.0303561	−	0.0195087i
$769$	−0.461655	+	3.21088i	−0.0166477	+	0.115787i	−0.996451	−	0.0841776i	$-0.973174\pi$
$769$	−0.461655	+	3.21088i	−0.0166477	+	0.115787i	0.979803	+	0.199965i	$0.0640828\pi$
$770$	1.41772	−	3.10438i	0.0510912	−	0.111874i
$771$	7.08742	−	15.5193i	0.255247	−	0.558913i
$772$	−1.42706	+	9.92540i	−0.0513609	+	0.357223i
$773$	−7.57241	+	4.86649i	−0.272361	+	0.175036i	−0.669691	−	0.742640i	$-0.733573\pi$
$773$	−7.57241	+	4.86649i	−0.272361	+	0.175036i	0.397330	+	0.917676i	$0.369937\pi$
$774$	8.12204	+	2.38485i	0.291941	+	0.0857215i
$775$	1.21454	+	8.44732i	0.0436276	+	0.303437i
$776$	2.15196	+	2.48350i	0.0772510	+	0.0891524i
$777$	−1.21468	−	0.780625i	−0.0435763	−	0.0280048i
$778$	−19.2528	+	22.2189i	−0.690247	+	0.796587i
$779$	−7.03545	+	2.06579i	−0.252071	+	0.0740148i
$780$	1.75990	+	3.85364i	0.0630144	+	0.137982i
$781$	−69.5030			−2.48701
$782$	−14.0547	−	11.2648i	−0.502594	−	0.402830i
$783$	1.16482			0.0416272
$784$	−2.75370	−	6.02977i	−0.0983465	−	0.215349i
$785$	−4.90838	+	1.44123i	−0.175188	+	0.0514397i
$786$	−5.96211	+	6.88064i	−0.212661	+	0.245424i
$787$	−34.2053	−	21.9824i	−1.21929	−	0.783589i	−0.237099	−	0.971485i	$-0.576197\pi$
$787$	−34.2053	−	21.9824i	−1.21929	−	0.783589i	−0.982189	+	0.187897i	$0.939833\pi$
$788$	−1.88112	−	2.17093i	−0.0670123	−	0.0773363i
$789$	0.0562281	+	0.391075i	0.00200177	+	0.0139226i
$790$	8.47234	+	2.48770i	0.301432	+	0.0885086i
$791$	5.95737	−	3.82857i	0.211820	−	0.136128i
$792$	−0.797176	+	5.54448i	−0.0283264	+	0.197014i
$793$	−2.95515	+	6.47087i	−0.104940	+	0.229787i
$794$	−4.96563	+	10.8732i	−0.176224	+	0.385876i
$795$	1.78625	−	12.4236i	0.0633518	−	0.440621i
$796$	−2.97858	+	1.91421i	−0.105573	+	0.0678476i
$797$	−14.2086	−	4.17202i	−0.503295	−	0.147781i	0.0202230	−	0.999795i	$-0.493562\pi$
$797$	−14.2086	−	4.17202i	−0.503295	−	0.147781i	−0.523518	+	0.852015i	$0.675381\pi$
$798$	−0.153278	−	1.06607i	−0.00542599	−	0.0377386i
$799$	7.14100	+	8.24115i	0.252630	+	0.291551i
$800$	0.841254	+	0.540641i	0.0297428	+	0.0191145i
$801$	2.43731	−	2.81281i	0.0861183	−	0.0993858i
$802$	20.6735	−	6.07028i	0.730006	−	0.214349i
$803$	5.50607	+	12.0566i	0.194305	+	0.425468i
$804$	11.0891			0.391083
$805$	2.27997	+	1.82740i	0.0803585	+	0.0644075i
$806$	36.1549			1.27350
$807$	−6.40084	−	14.0159i	−0.225320	−	0.493382i
$808$	15.4341	−	4.53186i	0.542970	−	0.159430i
$809$	5.39738	−	6.22891i	0.189762	−	0.218997i	−0.652894	−	0.757449i	$-0.726445\pi$
$809$	5.39738	−	6.22891i	0.189762	−	0.218997i	0.842656	+	0.538452i	$0.180991\pi$
$810$	−0.841254	−	0.540641i	−0.0295586	−	0.0189962i
$811$	3.13844	+	3.62195i	0.110205	+	0.127184i	0.808172	−	0.588946i	$-0.200457\pi$
$811$	3.13844	+	3.62195i	0.110205	+	0.127184i	−0.697967	+	0.716130i	$0.745912\pi$
$812$	0.100998	+	0.702459i	0.00354435	+	0.0246515i
$813$	6.96220	+	2.04429i	0.244175	+	0.0716963i
$814$	11.1676	−	7.17696i	0.391423	−	0.251552i
$815$	3.31171	−	23.0334i	0.116004	−	0.806827i
$816$	−1.56019	+	3.41635i	−0.0546177	+	0.119596i
$817$	6.21628	−	13.6117i	0.217480	−	0.476215i
$818$	3.25291	−	22.6245i	0.113735	−	0.791047i
$819$	2.17139	−	1.39547i	0.0758745	−	0.0487616i
$820$	−3.97985	−	1.16859i	−0.138983	−	0.0408090i
$821$	2.80075	+	19.4796i	0.0977468	+	0.679844i	0.978497	+	0.206262i	$0.0661300\pi$
$821$	2.80075	+	19.4796i	0.0977468	+	0.679844i	−0.880750	+	0.473582i	$0.842961\pi$
$822$	2.97308	+	3.43111i	0.103698	+	0.119674i
$823$	−2.20468	−	1.41686i	−0.0768502	−	0.0493886i	0.501651	−	0.865070i	$-0.332726\pi$
$823$	−2.20468	−	1.41686i	−0.0768502	−	0.0493886i	−0.578502	+	0.815681i	$0.696362\pi$
$824$	0.610039	−	0.704023i	0.0212517	−	0.0245258i
$825$	−5.37459	+	1.57812i	−0.187119	+	0.0549432i
$826$	3.02663	+	6.62740i	0.105310	+	0.230597i
$827$	35.7017			1.24147			0.620735	−	0.784020i	$-0.286834\pi$
$827$	35.7017			1.24147			0.620735	+	0.784020i	$0.286834\pi$
$828$	−4.43560	−	1.82357i	−0.154148	−	0.0633735i
$829$	−5.55053			−0.192778			−0.0963889	−	0.995344i	$-0.530729\pi$
$829$	−5.55053			−0.192778			−0.0963889	+	0.995344i	$0.530729\pi$
$830$	6.43816	+	14.0976i	0.223472	+	0.489335i
$831$	18.0750	−	5.30729i	0.627014	−	0.184108i
$832$	2.77430	−	3.20172i	0.0961817	−	0.111000i
$833$	20.9439	+	13.4598i	0.725664	+	0.466356i
$834$	−9.80944	−	11.3207i	−0.339673	−	0.392004i
$835$	−3.40067	−	23.6522i	−0.117685	−	0.818517i
$836$	9.50102	+	2.78975i	0.328600	+	0.0964856i
$837$	−7.17941	+	4.61393i	−0.248157	+	0.159481i
$838$	1.96416	−	13.6610i	0.0678507	−	0.471912i
$839$	−6.54549	+	14.3326i	−0.225975	+	0.494817i	−0.988327	−	0.152346i	$-0.951317\pi$
$839$	−6.54549	+	14.3326i	−0.225975	+	0.494817i	0.762352	+	0.647163i	$0.224045\pi$
$840$	0.253098	−	0.554206i	0.00873270	−	0.0191219i
$841$	3.93404	−	27.3618i	0.135656	−	0.943511i
$842$	−14.6922	+	9.44213i	−0.506328	+	0.325397i
$843$	3.09773	+	0.909577i	0.106692	+	0.0313275i
$844$	2.80489	+	19.5084i	0.0965483	+	0.671508i
$845$	3.24009	+	3.73926i	0.111462	+	0.128635i
$846$	2.44253	+	1.56972i	0.0839760	+	0.0539681i
$847$	8.12997	−	9.38249i	0.279349	−	0.322386i
$848$	−12.0430	+	3.53614i	−0.413558	+	0.121431i
$849$	2.73938	+	5.99841i	0.0940154	+	0.205865i
$850$	−3.75575			−0.128821
$851$	3.61773	+	10.7744i	0.124014	+	0.369343i
$852$	−12.4079			−0.425089
$853$	14.8766	+	32.5752i	0.509365	+	1.11535i	0.973311	+	0.229491i	$0.0737060\pi$
$853$	14.8766	+	32.5752i	0.509365	+	1.11535i	−0.463946	+	0.885864i	$0.653567\pi$
$854$	0.981611	−	0.288227i	0.0335901	−	0.00986293i
$855$	−1.15764	+	1.33599i	−0.0395905	+	0.0456898i
$856$	−8.43489	−	5.42077i	−0.288298	−	0.185278i
$857$	15.8881	+	18.3359i	0.542728	+	0.626341i	0.959173	−	0.282820i	$-0.0912698\pi$
$857$	15.8881	+	18.3359i	0.542728	+	0.626341i	−0.416445	+	0.909161i	$0.636724\pi$
$858$	3.37722	+	23.4891i	0.115296	+	0.801903i
$859$	14.9051	+	4.37654i	0.508556	+	0.149326i	0.525937	−	0.850523i	$-0.323715\pi$
$859$	14.9051	+	4.37654i	0.508556	+	0.149326i	−0.0173810	+	0.999849i	$0.505533\pi$
$860$	7.12115	−	4.57649i	0.242829	−	0.156057i
$861$	−0.359651	+	2.50143i	−0.0122569	+	0.0852485i
$862$	7.78047	−	17.0369i	0.265004	−	0.580278i
$863$	11.4911	−	25.1621i	0.391163	−	0.856527i	−0.606927	−	0.794757i	$-0.707598\pi$
$863$	11.4911	−	25.1621i	0.391163	−	0.856527i	0.998090	−	0.0617701i	$-0.0196746\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	9.89244	−	6.35749i	0.336353	−	0.216161i
$866$	−7.89293	−	2.31757i	−0.268213	−	0.0787543i
$867$	0.411908	+	2.86488i	0.0139891	+	0.0972966i
$868$	−3.40500	−	3.92958i	−0.115573	−	0.133379i
$869$	41.6095	+	26.7408i	1.41151	+	0.907119i
$870$	0.762794	−	0.880311i	0.0258611	−	0.0298453i
$871$	45.0758	−	13.2355i	1.52734	−	0.448466i
$872$	2.44618	+	5.35640i	0.0828382	+	0.181390i
$873$	−3.28614			−0.111219
$874$	−4.30674	+	7.30253i	−0.145678	+	0.247012i
$875$	0.609264			0.0205969
$876$	0.982964	+	2.15239i	0.0332113	+	0.0727226i
$877$	−2.12178	+	0.623010i	−0.0716473	+	0.0210376i	−0.317360	−	0.948305i	$-0.602796\pi$
$877$	−2.12178	+	0.623010i	−0.0716473	+	0.0210376i	0.245712	+	0.969343i	$0.420978\pi$
$878$	−23.1327	+	26.6965i	−0.780690	+	0.900964i
$879$	−1.16707	−	0.750031i	−0.0393643	−	0.0252979i
$880$	3.66820	+	4.23333i	0.123655	+	0.142705i
$881$	2.15434	+	14.9838i	0.0725816	+	0.504816i	0.993389	+	0.114798i	$0.0366221\pi$
$881$	2.15434	+	14.9838i	0.0725816	+	0.504816i	−0.920807	+	0.390018i	$0.872469\pi$
$882$	6.36028	+	1.86755i	0.214162	+	0.0628836i
$883$	−38.0888	+	24.4782i	−1.28179	+	0.823758i	−0.991108	−	0.133062i	$-0.957519\pi$
$883$	−38.0888	+	24.4782i	−1.28179	+	0.823758i	−0.290684	+	0.956819i	$0.593883\pi$
$884$	−2.26439	+	15.7492i	−0.0761598	+	0.529703i
$885$	4.96768	−	10.8777i	0.166987	−	0.365650i
$886$	13.5080	−	29.5784i	0.453810	−	0.993705i
$887$	−2.58521	+	17.9805i	−0.0868029	+	0.603727i	0.899268	+	0.437399i	$0.144100\pi$
$887$	−2.58521	+	17.9805i	−0.0868029	+	0.603727i	−0.986070	+	0.166328i	$0.946809\pi$
$888$	1.99368	−	1.28126i	0.0669034	−	0.0429962i
$889$	−4.92283	−	1.44547i	−0.165107	−	0.0484797i
$890$	−0.529679	−	3.68400i	−0.0177549	−	0.123488i
$891$	−3.66820	−	4.23333i	−0.122889	−	0.141822i
$892$	10.5197	+	6.76060i	0.352226	+	0.226362i
$893$	3.36114	−	3.87897i	0.112476	−	0.129805i
$894$	−9.91770	+	2.91210i	−0.331697	+	0.0973952i
$895$	1.57584	+	3.45060i	0.0526744	+	0.115341i
$896$	−0.609264			−0.0203541
$897$	−20.2067	−	2.11845i	−0.674682	−	0.0707329i
$898$	11.1393			0.371723
$899$	−4.12955	−	9.04245i	−0.137728	−	0.301583i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	30.8701	−	35.6260i	1.02843	−	1.18687i
$902$	−19.5459	−	12.5614i	−0.650808	−	0.418249i
$903$	−3.37737	−	3.89769i	−0.112392	−	0.129707i
$904$	1.65414	+	11.5048i	0.0550159	+	0.382644i
$905$	19.2929	+	5.66490i	0.641317	+	0.188308i
$906$	−13.4870	+	8.66759i	−0.448077	+	0.287961i
$907$	6.55828	−	45.6139i	0.217764	−	1.51458i	−0.528500	−	0.848934i	$-0.677245\pi$
$907$	6.55828	−	45.6139i	0.217764	−	1.51458i	0.746264	−	0.665650i	$-0.231846\pi$
$908$	10.1237	−	22.1678i	0.335967	−	0.735665i
$909$	−6.68224	+	14.6321i	−0.221636	+	0.485315i
$910$	0.367334	−	2.55486i	0.0121770	−	0.0846929i
$911$	4.36981	−	2.80830i	0.144778	−	0.0930433i	−0.466246	−	0.884655i	$-0.654394\pi$
$911$	4.36981	−	2.80830i	0.144778	−	0.0930433i	0.611025	+	0.791612i	$0.290758\pi$
$912$	1.69616	+	0.498037i	0.0561654	+	0.0164917i
$913$	12.3547	+	85.9291i	0.408882	+	2.84384i
$914$	−16.8102	−	19.4000i	−0.556032	−	0.641695i
$915$	−1.41260	−	0.907822i	−0.0466991	−	0.0300117i
$916$	11.0510	−	12.7536i	0.365137	−	0.421390i
$917$	5.32229	−	1.56277i	0.175758	−	0.0516071i
$918$	−1.56019	−	3.41635i	−0.0514941	−	0.112756i
$919$	−1.24484			−0.0410636			−0.0205318	−	0.999789i	$-0.506536\pi$
$919$	−1.24484			−0.0410636			−0.0205318	+	0.999789i	$0.506536\pi$
$920$	−4.28287	+	2.15802i	−0.141202	+	0.0711479i
$921$	−21.3326			−0.702932
$922$	10.9148	+	23.9001i	0.359460	+	0.787108i
$923$	−50.4367	+	14.8096i	−1.66014	+	0.487463i
$924$	2.23490	−	2.57922i	0.0735229	−	0.0848499i
$925$	1.99368	+	1.28126i	0.0655517	+	0.0421275i
$926$	24.4978	+	28.2720i	0.805048	+	0.929075i
$927$	0.132574	+	0.922074i	0.00435431	+	0.0302849i
$928$	−1.11764	−	0.328167i	−0.0366882	−	0.0107726i
$929$	37.6568	−	24.2005i	1.23548	−	0.793994i	0.250744	−	0.968053i	$-0.419325\pi$
$929$	37.6568	−	24.2005i	1.23548	−	0.793994i	0.984735	+	0.174059i	$0.0556884\pi$
$930$	−1.21454	+	8.44732i	−0.0398264	+	0.276998i
$931$	4.86790	−	10.6592i	0.159539	−	0.349342i
$932$	−2.61864	+	5.73403i	−0.0857765	+	0.187824i
$933$	4.00774	−	27.8745i	0.131208	−	0.912569i
$934$	−2.97931	+	1.91468i	−0.0974859	+	0.0626504i
$935$	−20.1856	−	5.92703i	−0.660141	−	0.193835i
$936$	0.602914	+	4.19336i	0.0197069	+	0.137064i
$937$	−35.5961	−	41.0801i	−1.16287	−	1.34203i	−0.929140	−	0.369729i	$-0.879451\pi$
$937$	−35.5961	−	41.0801i	−1.16287	−	1.34203i	−0.233735	−	0.972300i	$-0.575095\pi$
$938$	−5.68368	−	3.65268i	−0.185579	−	0.119264i
$939$	−5.06848	+	5.84933i	−0.165403	+	0.190886i
$940$	2.78583	−	0.817994i	0.0908639	−	0.0266800i
$941$	−4.66630	−	10.2178i	−0.152117	−	0.333090i	0.818197	−	0.574938i	$-0.194974\pi$
$941$	−4.66630	−	10.2178i	−0.152117	−	0.333090i	−0.970314	+	0.241848i	$0.922246\pi$
$942$	−5.11560			−0.166675
$943$	14.5233	−	13.5935i	0.472945	−	0.442666i
$944$	−11.9584			−0.389212
$945$	0.253098	+	0.554206i	0.00823327	+	0.0180283i
$946$	45.4956	−	13.3587i	1.47919	−	0.434329i
$947$	5.62115	−	6.48715i	0.182663	−	0.210804i	−0.657032	−	0.753863i	$-0.728188\pi$
$947$	5.62115	−	6.48715i	0.182663	−	0.210804i	0.839695	+	0.543058i	$0.182734\pi$
$948$	7.42829	+	4.77387i	0.241260	+	0.155048i
$949$	6.56462	+	7.57597i	0.213097	+	0.245927i
$950$	0.251579	+	1.74977i	0.00816231	+	0.0567701i
$951$	−7.31428	−	2.14767i	−0.237182	−	0.0696428i
$952$	1.92499	−	1.23712i	0.0623894	−	0.0400952i
$953$	3.36195	−	23.3829i	0.108904	−	0.757447i	−0.860050	−	0.510209i	$-0.829568\pi$
$953$	3.36195	−	23.3829i	0.108904	−	0.757447i	0.968955	−	0.247238i	$-0.0795228\pi$
$954$	5.21404	−	11.4172i	0.168811	−	0.369644i
$955$	6.88876	−	15.0843i	0.222915	−	0.488116i
$956$	−1.54507	+	10.7462i	−0.0499712	+	0.347558i
$957$	5.48895	−	3.52753i	0.177432	−	0.114029i
$958$	−11.2314	−	3.29782i	−0.362869	−	0.106548i
$959$	−0.393652	−	2.73791i	−0.0127117	−	0.0884118i
$960$	0.654861	+	0.755750i	0.0211355	+	0.0243917i
$961$	35.1916	+	22.6162i	1.13521	+	0.729556i
$962$	6.57479	−	7.58771i	0.211980	−	0.244638i
$963$	9.62042	−	2.82481i	0.310014	−	0.0910282i
$964$	−8.41089	−	18.4173i	−0.270896	−	0.593180i
$965$	−10.0275			−0.322796
$966$	1.67278	+	2.39572i	0.0538208	+	0.0770811i
$967$	22.5137			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$967$	22.5137			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$968$	8.46480	+	18.5353i	0.272069	+	0.595748i
$969$	−6.37035	+	1.87050i	−0.204645	+	0.0600892i
$970$	−2.15196	+	2.48350i	−0.0690954	+	0.0797403i
$971$	35.4938	+	22.8105i	1.13905	+	0.732023i	0.967430	−	0.253140i	$-0.0814635\pi$
$971$	35.4938	+	22.8105i	1.13905	+	0.732023i	0.171620	+	0.985163i	$0.445100\pi$
$972$	−0.654861	−	0.755750i	−0.0210047	−	0.0242407i
$973$	1.29883	+	9.03354i	0.0416385	+	0.289602i
$974$	16.9597	+	4.97983i	0.543425	+	0.159564i
$975$	−3.56395	+	2.29041i	−0.114138	+	0.0733519i
$976$	−0.238969	+	1.66207i	−0.00764922	+	0.0532015i
$977$	−17.6479	+	38.6436i	−0.564608	+	1.23632i	0.385011	+	0.922912i	$0.374197\pi$
$977$	−17.6479	+	38.6436i	−0.564608	+	1.23632i	−0.949619	+	0.313406i	$0.898530\pi$
$978$	9.66683	−	21.1674i	0.309111	−	0.676859i
$979$	2.96699	−	20.6359i	0.0948255	−	0.659526i
$980$	5.57650	−	3.58380i	0.178135	−	0.114480i
$981$	−5.65000	−	1.65899i	−0.180391	−	0.0529675i
$982$	4.22163	+	29.3620i	0.134717	+	0.936981i
$983$	21.9115	+	25.2872i	0.698869	+	0.806537i	0.988599	−	0.150571i	$-0.0481111\pi$
$983$	21.9115	+	25.2872i	0.698869	+	0.806537i	−0.289731	+	0.957108i	$0.593566\pi$
$984$	−3.48941	−	2.24251i	−0.111238	−	0.0714886i
$985$	1.88112	−	2.17093i	0.0599376	−	0.0691717i
$986$	4.19756	−	1.23251i	0.133677	−	0.0392513i
$987$	−0.734854	−	1.60911i	−0.0233907	−	0.0512184i
$988$	7.48910			0.238260
$989$	1.55618	+	40.5665i	0.0494836	+	1.28994i
$990$	−5.60149			−0.178027
$991$	−2.71219	−	5.93888i	−0.0861557	−	0.188655i	0.861650	−	0.507503i	$-0.169431\pi$
$991$	−2.71219	−	5.93888i	−0.0861557	−	0.188655i	−0.947806	+	0.318848i	$0.896704\pi$
$992$	8.18849	−	2.40436i	0.259985	−	0.0763384i
$993$	6.87984	−	7.93976i	0.218325	−	0.251961i
$994$	6.35964	+	4.08709i	0.201716	+	0.129635i
$995$	−2.31863	−	2.67584i	−0.0735054	−	0.0848298i
$996$	2.20562	+	15.3404i	0.0698876	+	0.486079i
$997$	−16.6912	−	4.90099i	−0.528616	−	0.155216i	0.00652433	−	0.999979i	$-0.497923\pi$
$997$	−16.6912	−	4.90099i	−0.528616	−	0.155216i	−0.535141	+	0.844763i	$0.679741\pi$
$998$	−9.55054	+	6.13776i	−0.302317	+	0.194287i
$999$	−0.337270	+	2.34577i	−0.0106708	+	0.0742168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.a.211.1	yes	10
23.6	even	11	inner	690.2.m.a.121.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.a.121.1	✓	10	23.6	even	11	inner
690.2.m.a.211.1	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0867074 + 0.603063i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.0867074 + 0.603063i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(2.32694 - 5.09530i) q^{11} +(0.415415 - 0.909632i) q^{12} +(0.602914 - 4.19336i) q^{13} +(-0.512546 + 0.329393i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.45949 + 2.83841i) q^{17} +(0.841254 + 0.540641i) q^{18} +(1.15764 - 1.33599i) q^{19} +(0.959493 - 0.281733i) q^{20} +(-0.253098 - 0.554206i) q^{21} +5.60149 q^{22} +(-1.17376 + 4.64998i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(4.06487 - 1.19355i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-0.512546 - 0.329393i) q^{28} +(-0.762794 - 0.880311i) q^{29} +(0.142315 + 0.989821i) q^{30} +(8.18849 + 2.40436i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.797176 + 5.54448i) q^{33} +(-1.56019 + 3.41635i) q^{34} +(0.253098 - 0.554206i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(1.99368 - 1.28126i) q^{37} +(1.69616 + 0.498037i) q^{38} +(0.602914 + 4.19336i) q^{39} +(0.654861 + 0.755750i) q^{40} +(-3.48941 - 2.24251i) q^{41} +(0.398983 - 0.460451i) q^{42} +(8.12204 - 2.38485i) q^{43} +(2.32694 + 5.09530i) q^{44} -1.00000 q^{45} +(-4.71737 + 0.863983i) q^{46} +2.90344 q^{47} +(0.415415 + 0.909632i) q^{48} +(6.36028 - 1.86755i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-3.15954 - 2.03051i) q^{51} +(2.77430 + 3.20172i) q^{52} +(-1.78625 - 12.4236i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(-4.71228 + 3.02840i) q^{55} +(0.0867074 - 0.603063i) q^{56} +(-0.734356 + 1.60802i) q^{57} +(0.483883 - 1.05956i) q^{58} +(1.70185 - 11.8366i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(-1.61114 - 0.473074i) q^{61} +(1.21454 + 8.44732i) q^{62} +(0.398983 + 0.460451i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.77430 + 3.20172i) q^{65} +(-5.37459 + 1.57812i) q^{66} +(4.60658 + 10.0870i) q^{67} -3.75575 q^{68} +(-0.183838 - 4.79231i) q^{69} +0.609264 q^{70} +(-5.15445 - 11.2867i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-1.54955 + 1.78827i) q^{73} +(1.99368 + 1.28126i) q^{74} +(-0.654861 - 0.755750i) q^{75} +(0.251579 + 1.74977i) q^{76} +(3.27455 + 0.961494i) q^{77} +(-3.56395 + 2.29041i) q^{78} +(-1.25664 + 8.74014i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.590304 - 4.10565i) q^{82} +(-13.0379 + 8.37893i) q^{83} +(0.584585 + 0.171650i) q^{84} +(-0.534499 - 3.71752i) q^{85} +(5.54335 + 6.39737i) q^{86} +(0.979908 + 0.629749i) q^{87} +(-3.66820 + 4.23333i) q^{88} +(3.57112 - 1.04858i) q^{89} +(-0.415415 - 0.909632i) q^{90} +2.58114 q^{91} +(-2.74557 - 3.93215i) q^{92} -8.53418 q^{93} +(1.20613 + 2.64106i) q^{94} +(-1.69616 + 0.498037i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-2.76448 - 1.77662i) q^{97} +(4.34094 + 5.00971i) q^{98} +(-0.797176 - 5.54448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{8} - q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 16 q^{17} - q^{18} + 18 q^{19} + q^{20} + 20 q^{22} - q^{23} + 10 q^{24} - q^{25} + 11 q^{26} - q^{27} + 22 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 16 q^{37} - 4 q^{38} + q^{40} - 9 q^{41} - 11 q^{42} + 2 q^{43} - 2 q^{44} - 10 q^{45} - q^{46} - 48 q^{47} - q^{48} + 7 q^{49} - q^{50} - 17 q^{51} + 2 q^{53} - q^{54} - 9 q^{55} - 15 q^{57} + 22 q^{58} - 22 q^{59} + q^{60} + 13 q^{61} + 8 q^{62} - 11 q^{63} - q^{64} - 13 q^{66} + 2 q^{67} - 6 q^{68} - q^{69} - 45 q^{71} - q^{72} + 21 q^{73} - 16 q^{74} - q^{75} - 4 q^{76} + 22 q^{77} + 11 q^{78} + 66 q^{79} + q^{80} - q^{81} + 57 q^{82} + 15 q^{83} + 11 q^{84} - 5 q^{85} + 24 q^{86} - 2 q^{88} + 29 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 58 q^{93} + 7 q^{94} + 4 q^{95} - q^{96} - 27 q^{97} + 7 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + q^5 - q^6 - q^8 - q^9 + q^10 - 2 * q^11 - q^12 + q^15 - q^16 + 16 * q^17 - q^18 + 18 * q^19 + q^20 + 20 * q^22 - q^23 + 10 * q^24 - q^25 + 11 * q^26 - q^27 + 22 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 5 * q^34 - q^36 - 16 * q^37 - 4 * q^38 + q^40 - 9 * q^41 - 11 * q^42 + 2 * q^43 - 2 * q^44 - 10 * q^45 - q^46 - 48 * q^47 - q^48 + 7 * q^49 - q^50 - 17 * q^51 + 2 * q^53 - q^54 - 9 * q^55 - 15 * q^57 + 22 * q^58 - 22 * q^59 + q^60 + 13 * q^61 + 8 * q^62 - 11 * q^63 - q^64 - 13 * q^66 + 2 * q^67 - 6 * q^68 - q^69 - 45 * q^71 - q^72 + 21 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 22 * q^77 + 11 * q^78 + 66 * q^79 + q^80 - q^81 + 57 * q^82 + 15 * q^83 + 11 * q^84 - 5 * q^85 + 24 * q^86 - 2 * q^88 + 29 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 58 * q^93 + 7 * q^94 + 4 * q^95 - q^96 - 27 * q^97 + 7 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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