LMFDB - Embedded newform 690.2.r.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, 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:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	690.49
Dual form			690.2.r.a.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.14908 - 1.91823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-1.79620 - 2.79494i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.14908 - 1.91823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-1.79620 - 2.79494i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-0.864395 + 2.06224i) q^{10} +(0.278576 - 1.93754i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(1.82357 - 2.83753i) q^{13} +(2.17567 + 2.51086i) q^{14} +(-1.84210 + 1.26754i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.109270 + 0.372140i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-6.81911 + 2.00227i) q^{19} +(0.562109 - 2.16426i) q^{20} +(0.472819 + 3.28853i) q^{21} +1.95746i q^{22} +(1.90211 + 4.40250i) q^{23} +1.00000 q^{24} +(-2.35922 - 4.40841i) q^{25} +(-1.40118 + 3.06816i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.51086 - 2.17567i) q^{28} +(3.11550 + 0.914793i) q^{29} +(1.64297 - 1.51679i) q^{30} +(-1.26189 - 2.76315i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(-1.05828 + 1.64672i) q^{33} +(0.0551970 - 0.383903i) q^{34} +(-7.42531 + 0.233904i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.196483 + 0.170254i) q^{37} +(6.46475 - 2.95235i) q^{38} +(-2.83753 + 1.82357i) q^{39} +(-0.248381 + 2.22223i) q^{40} +(-2.95796 + 3.41367i) q^{41} +(-0.936013 - 3.18777i) q^{42} +(-1.80615 - 0.824839i) q^{43} +(-0.278576 - 1.93754i) q^{44} +(2.20219 - 0.387755i) q^{45} +(-2.50929 - 4.08699i) q^{46} +5.61408i q^{47} +(-0.989821 + 0.142315i) q^{48} +(-1.67744 + 3.67308i) q^{49} +(2.96258 + 4.02779i) q^{50} +(0.253988 - 0.293118i) q^{51} +(0.950276 - 3.23634i) q^{52} +(-2.69288 - 4.19021i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-3.39653 - 2.76076i) q^{55} +(2.79494 + 1.79620i) q^{56} +(7.03466 + 1.01143i) q^{57} +(-3.21398 - 0.462100i) q^{58} +(-4.60409 - 2.95887i) q^{59} +(-1.41038 + 1.73517i) q^{60} +(-3.39270 - 7.42897i) q^{61} +(1.64228 + 2.55544i) q^{62} +(0.936013 - 3.18777i) q^{63} +(0.654861 - 0.755750i) q^{64} +(-3.34760 - 6.75857i) q^{65} +(0.813158 - 1.78057i) q^{66} +(-10.6750 + 1.53484i) q^{67} +0.387851i q^{68} +(0.0986422 - 4.79482i) q^{69} +(7.31644 - 1.28825i) q^{70} +(0.136656 + 0.950464i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(-3.05209 - 10.3945i) q^{73} +(0.170254 - 0.196483i) q^{74} +(0.314697 + 4.99009i) q^{75} +(-5.97879 + 3.84233i) q^{76} +(-5.91566 + 2.70159i) q^{77} +(2.54912 - 2.20883i) q^{78} +(-12.9957 - 8.35185i) q^{79} +(-0.0704032 - 2.23496i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.44204 - 3.79988i) q^{82} +(9.23132 - 7.99898i) q^{83} +(1.38015 + 3.02211i) q^{84} +(0.588290 + 0.637226i) q^{85} +(1.90515 + 0.559402i) q^{86} +(-2.45394 - 2.12635i) q^{87} +(0.551480 + 1.87817i) q^{88} +(-1.20387 + 2.63611i) q^{89} +(-2.12459 + 0.697212i) q^{90} -11.2062 q^{91} +(3.06539 + 3.68828i) q^{92} +3.03765i q^{93} +(-0.798966 - 5.55693i) q^{94} +(-3.99491 + 15.3814i) q^{95} +(0.959493 - 0.281733i) q^{96} +(0.409330 + 0.354687i) q^{97} +(1.13763 - 3.87442i) q^{98} +(1.64672 - 1.05828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	1.14908	−	1.91823i	0.513886	−	0.857859i
$5$	1.14908	−	1.91823i	0.513886	−	0.857859i
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	−1.79620	−	2.79494i	−0.678898	−	1.05639i	−0.994216	−	0.107400i	$-0.965747\pi$
$7$	−1.79620	−	2.79494i	−0.678898	−	1.05639i	0.315318	−	0.948986i	$-0.397889\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−0.864395	+	2.06224i	−0.273346	+	0.652137i
$11$	0.278576	−	1.93754i	0.0839937	−	0.584189i	−0.903745	−	0.428072i	$-0.859193\pi$
$11$	0.278576	−	1.93754i	0.0839937	−	0.584189i	0.987739	−	0.156117i	$-0.0498978\pi$
$12$	−0.989821	−	0.142315i	−0.285737	−	0.0410828i
$13$	1.82357	−	2.83753i	0.505766	−	0.786988i	−0.490669	−	0.871346i	$-0.663248\pi$
$13$	1.82357	−	2.83753i	0.505766	−	0.786988i	0.996436	+	0.0843581i	$0.0268840\pi$
$14$	2.17567	+	2.51086i	0.581473	+	0.671056i
$15$	−1.84210	+	1.26754i	−0.475629	+	0.327277i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.109270	+	0.372140i	−0.0265019	+	0.0902573i	−0.971682	−	0.236292i	$-0.924068\pi$
$17$	−0.109270	+	0.372140i	−0.0265019	+	0.0902573i	0.945180	+	0.326549i	$0.105886\pi$
$18$	−0.755750	−	0.654861i	−0.178132	−	0.154352i
$19$	−6.81911	+	2.00227i	−1.56441	+	0.459353i	−0.945369	−	0.326004i	$-0.894298\pi$
$19$	−6.81911	+	2.00227i	−1.56441	+	0.459353i	−0.619044	+	0.785357i	$0.712480\pi$
$20$	0.562109	−	2.16426i	0.125691	−	0.483944i
$21$	0.472819	+	3.28853i	0.103178	+	0.717616i
$22$			1.95746i			0.417332i
$23$	1.90211	+	4.40250i	0.396618	+	0.917984i
$23$	1.90211	+	4.40250i	0.396618	+	0.917984i
$24$	1.00000			0.204124
$25$	−2.35922	−	4.40841i	−0.471843	−	0.881683i
$26$	−1.40118	+	3.06816i	−0.274795	+	0.601716i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−2.51086	−	2.17567i	−0.474508	−	0.411164i
$29$	3.11550	+	0.914793i	0.578534	+	0.169873i	0.557891	−	0.829914i	$-0.311611\pi$
$29$	3.11550	+	0.914793i	0.578534	+	0.169873i	0.0206424	+	0.999787i	$0.493429\pi$
$30$	1.64297	−	1.51679i	0.299963	−	0.276927i
$31$	−1.26189	−	2.76315i	−0.226641	−	0.496276i	0.761812	−	0.647798i	$-0.224310\pi$
$31$	−1.26189	−	2.76315i	−0.226641	−	0.496276i	−0.988454	+	0.151522i	$0.951583\pi$
$32$	−0.755750	+	0.654861i	−0.133599	+	0.115764i
$33$	−1.05828	+	1.64672i	−0.184223	+	0.286657i
$34$	0.0551970	−	0.383903i	0.00946620	−	0.0658389i
$35$	−7.42531	+	0.233904i	−1.25511	+	0.0395370i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−0.196483	+	0.170254i	−0.0323017	+	0.0279896i	−0.670862	−	0.741582i	$-0.734076\pi$
$37$	−0.196483	+	0.170254i	−0.0323017	+	0.0279896i	0.638560	+	0.769572i	$0.279530\pi$
$38$	6.46475	−	2.95235i	1.04872	−	0.478935i
$39$	−2.83753	+	1.82357i	−0.454368	+	0.292004i
$40$	−0.248381	+	2.22223i	−0.0392725	+	0.351365i
$41$	−2.95796	+	3.41367i	−0.461955	+	0.533125i	−0.938157	−	0.346211i	$-0.887468\pi$
$41$	−2.95796	+	3.41367i	−0.461955	+	0.533125i	0.476201	+	0.879336i	$0.342013\pi$
$42$	−0.936013	−	3.18777i	−0.144430	−	0.491883i
$43$	−1.80615	−	0.824839i	−0.275435	−	0.125787i	0.272909	−	0.962040i	$-0.412014\pi$
$43$	−1.80615	−	0.824839i	−0.275435	−	0.125787i	−0.548344	+	0.836253i	$0.684741\pi$
$44$	−0.278576	−	1.93754i	−0.0419968	−	0.292094i
$45$	2.20219	−	0.387755i	0.328283	−	0.0578030i
$46$	−2.50929	−	4.08699i	−0.369975	−	0.602593i
$47$			5.61408i			0.818897i	0.912333	+	0.409449i	$0.134279\pi$
$47$			5.61408i			0.818897i	−0.912333	+	0.409449i	$0.865721\pi$
$48$	−0.989821	+	0.142315i	−0.142868	+	0.0205414i
$49$	−1.67744	+	3.67308i	−0.239634	+	0.524726i
$50$	2.96258	+	4.02779i	0.418973	+	0.569616i
$51$	0.253988	−	0.293118i	0.0355655	−	0.0410448i
$52$	0.950276	−	3.23634i	0.131780	−	0.448800i
$53$	−2.69288	−	4.19021i	−0.369896	−	0.575569i	0.605550	−	0.795807i	$-0.292953\pi$
$53$	−2.69288	−	4.19021i	−0.369896	−	0.575569i	−0.975446	+	0.220238i	$0.929317\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−3.39653	−	2.76076i	−0.457988	−	0.372261i
$56$	2.79494	+	1.79620i	0.373489	+	0.240027i
$57$	7.03466	+	1.01143i	0.931763	+	0.133967i
$58$	−3.21398	−	0.462100i	−0.422016	−	0.0606767i
$59$	−4.60409	−	2.95887i	−0.599401	−	0.385212i	0.205468	−	0.978664i	$-0.434128\pi$
$59$	−4.60409	−	2.95887i	−0.599401	−	0.385212i	−0.804869	+	0.593452i	$0.797765\pi$
$60$	−1.41038	+	1.73517i	−0.182079	+	0.224010i
$61$	−3.39270	−	7.42897i	−0.434390	−	0.951182i	−0.992594	−	0.121478i	$-0.961237\pi$
$61$	−3.39270	−	7.42897i	−0.434390	−	0.951182i	0.558204	−	0.829704i	$-0.311491\pi$
$62$	1.64228	+	2.55544i	0.208570	+	0.324541i
$63$	0.936013	−	3.18777i	0.117927	−	0.401621i
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	−3.34760	−	6.75857i	−0.415218	−	0.838298i
$66$	0.813158	−	1.78057i	0.100093	−	0.219173i
$67$	−10.6750	+	1.53484i	−1.30416	+	0.187510i	−0.759148	−	0.650918i	$-0.774384\pi$
$67$	−10.6750	+	1.53484i	−1.30416	+	0.187510i	−0.545013	+	0.838428i	$0.683475\pi$
$68$			0.387851i			0.0470339i
$69$	0.0986422	−	4.79482i	0.0118751	−	0.577228i
$70$	7.31644	−	1.28825i	0.874482	−	0.153976i
$71$	0.136656	+	0.950464i	0.0162181	+	0.112799i	0.996322	−	0.0856840i	$-0.0273075\pi$
$71$	0.136656	+	0.950464i	0.0162181	+	0.112799i	−0.980104	+	0.198483i	$0.936398\pi$
$72$	−0.909632	−	0.415415i	−0.107201	−	0.0489571i
$73$	−3.05209	−	10.3945i	−0.357220	−	1.21658i	−0.920641	−	0.390409i	$-0.872334\pi$
$73$	−3.05209	−	10.3945i	−0.357220	−	1.21658i	0.563422	−	0.826169i	$-0.309485\pi$
$74$	0.170254	−	0.196483i	0.0197916	−	0.0228407i
$75$	0.314697	+	4.99009i	0.0363381	+	0.576206i
$76$	−5.97879	+	3.84233i	−0.685814	+	0.440746i
$77$	−5.91566	+	2.70159i	−0.674152	+	0.307875i
$78$	2.54912	−	2.20883i	0.288631	−	0.250100i
$79$	−12.9957	−	8.35185i	−1.46213	−	0.939657i	−0.998563	−	0.0535973i	$-0.982931\pi$
$79$	−12.9957	−	8.35185i	−1.46213	−	0.939657i	−0.463572	−	0.886059i	$-0.653432\pi$
$80$	−0.0704032	−	2.23496i	−0.00787132	−	0.249876i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	2.44204	−	3.79988i	0.269678	−	0.419627i
$83$	9.23132	−	7.99898i	1.01327	−	0.878003i	0.0207122	−	0.999785i	$-0.493407\pi$
$83$	9.23132	−	7.99898i	1.01327	−	0.878003i	0.992557	+	0.121783i	$0.0388612\pi$
$84$	1.38015	+	3.02211i	0.150587	+	0.329740i
$85$	0.588290	+	0.637226i	0.0638091	+	0.0691169i
$86$	1.90515	+	0.559402i	0.205438	+	0.0603219i
$87$	−2.45394	−	2.12635i	−0.263090	−	0.227969i
$88$	0.551480	+	1.87817i	0.0587880	+	0.200213i
$89$	−1.20387	+	2.63611i	−0.127610	+	0.279427i	−0.962643	−	0.270772i	$-0.912721\pi$
$89$	−1.20387	+	2.63611i	−0.127610	+	0.279427i	0.835034	+	0.550199i	$0.185448\pi$
$90$	−2.12459	+	0.697212i	−0.223952	+	0.0734926i
$91$	−11.2062			−1.17473
$92$	3.06539	+	3.68828i	0.319589	+	0.384530i
$93$			3.03765i			0.314990i
$94$	−0.798966	−	5.55693i	−0.0824071	−	0.573154i
$95$	−3.99491	+	15.3814i	−0.409869	+	1.57810i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	0.409330	+	0.354687i	0.0415612	+	0.0360130i	0.675394	−	0.737457i	$-0.263974\pi$
$97$	0.409330	+	0.354687i	0.0415612	+	0.0360130i	−0.633833	+	0.773470i	$0.718519\pi$
$98$	1.13763	−	3.87442i	0.114918	−	0.391375i
$99$	1.64672	−	1.05828i	0.165502	−	0.106361i
$100$	−3.50564	−	3.56517i	−0.350564	−	0.356517i
$101$	7.16014	+	8.26324i	0.712460	+	0.822223i	0.990379	−	0.138382i	$-0.0441900\pi$
$101$	7.16014	+	8.26324i	0.712460	+	0.822223i	−0.277919	+	0.960605i	$0.589645\pi$
$102$	−0.209688	+	0.326281i	−0.0207622	+	0.0323066i
$103$	14.8984	+	2.14207i	1.46798	+	0.211064i	0.829472	−	0.558548i	$-0.188641\pi$
$103$	14.8984	+	2.14207i	1.46798	+	0.211064i	0.638512	+	0.769612i	$0.279550\pi$
$104$	−0.480024	+	3.33864i	−0.0470702	+	0.327381i
$105$	6.85147	+	2.87182i	0.668635	+	0.280261i
$106$	3.26180	+	3.76432i	0.316814	+	0.365623i
$107$	−5.48818	+	2.50637i	−0.530563	+	0.242300i	−0.662638	−	0.748940i	$-0.730563\pi$
$107$	−5.48818	+	2.50637i	−0.530563	+	0.242300i	0.132075	+	0.991240i	$0.457836\pi$
$108$	−0.540641	−	0.841254i	−0.0520232	−	0.0809497i
$109$	4.83695	+	1.42026i	0.463296	+	0.136036i	0.505047	−	0.863092i	$-0.331475\pi$
$109$	4.83695	+	1.42026i	0.463296	+	0.136036i	−0.0417505	+	0.999128i	$0.513293\pi$
$110$	3.75486	+	2.24928i	0.358012	+	0.214461i
$111$	0.249454	−	0.0732462i	0.0236771	−	0.00695222i
$112$	−3.02211	−	1.38015i	−0.285563	−	0.130412i
$113$	5.52512	−	0.794393i	0.519760	−	0.0747302i	0.122558	−	0.992461i	$-0.460890\pi$
$113$	5.52512	−	0.794393i	0.519760	−	0.0747302i	0.397202	+	0.917731i	$0.369981\pi$
$114$	−7.10700			−0.665631
$115$	10.6307	+	1.41015i	0.991317	+	0.131497i
$116$	3.24703			0.301479
$117$	3.33864	−	0.480024i	0.308657	−	0.0443782i
$118$	4.97832	+	2.27352i	0.458291	+	0.209295i
$119$	1.23638	−	0.363034i	0.113339	−	0.0332792i
$120$	1.14908	−	1.91823i	0.104896	−	0.175110i
$121$	6.87798	+	2.01956i	0.625271	+	0.183596i
$122$	4.41542	+	6.87052i	0.399753	+	0.622028i
$123$	4.10874	−	1.87640i	0.370473	−	0.169189i
$124$	−1.98924	−	2.29570i	−0.178639	−	0.206160i
$125$	−11.1673	−	0.540115i	−0.998832	−	0.0483094i
$126$	−0.472819	+	3.28853i	−0.0421221	+	0.292966i
$127$	0.896971	+	0.128965i	0.0795933	+	0.0114438i	0.181996	−	0.983299i	$-0.441744\pi$
$127$	0.896971	+	0.128965i	0.0795933	+	0.0114438i	−0.102403	+	0.994743i	$0.532653\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$	1.30028	+	1.50060i	0.114483	+	0.132121i
$130$	4.27537	+	6.21337i	0.374975	+	0.544948i
$131$	14.9752	−	9.62395i	1.30839	−	0.840848i	0.314287	−	0.949328i	$-0.398235\pi$
$131$	14.9752	−	9.62395i	1.30839	−	0.840848i	0.994099	+	0.108480i	$0.0345983\pi$
$132$	−0.551480	+	1.87817i	−0.0480002	+	0.163474i
$133$	17.8447	+	15.4625i	1.54733	+	1.34077i
$134$	10.3479	−	3.03843i	0.893925	−	0.262480i
$135$	−2.16426	−	0.562109i	−0.186270	−	0.0483787i
$136$	−0.0551970	−	0.383903i	−0.00473310	−	0.0329194i
$137$			9.96697i			0.851536i	0.904832	+	0.425768i	$0.139996\pi$
$137$			9.96697i			0.851536i	−0.904832	+	0.425768i	$0.860004\pi$
$138$	0.584735	+	4.76005i	0.0497760	+	0.405202i
$139$	−19.3603			−1.64212			−0.821058	−	0.570844i	$-0.806616\pi$
$139$	−19.3603			−1.64212			−0.821058	+	0.570844i	$0.806616\pi$
$140$	−7.05863	+	2.31638i	−0.596563	+	0.195770i
$141$	2.33217	−	5.10674i	0.196404	−	0.430065i
$142$	−0.270530	−	0.921342i	−0.0227024	−	0.0773173i
$143$	−4.98981	−	4.32369i	−0.417268	−	0.361565i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	5.33475	−	4.92507i	0.443027	−	0.409005i
$146$	4.50031	+	9.85429i	0.372448	+	0.815547i
$147$	3.05171	−	2.64432i	0.251700	−	0.218100i
$148$	−0.140558	+	0.218713i	−0.0115538	+	0.0179781i
$149$	−0.564246	+	3.92442i	−0.0462249	+	0.321501i	0.953569	+	0.301176i	$0.0973792\pi$
$149$	−0.564246	+	3.92442i	−0.0462249	+	0.321501i	−0.999793	+	0.0203249i	$0.993530\pi$
$150$	−1.02166	−	4.89451i	−0.0834179	−	0.399635i
$151$	5.23526	+	3.36450i	0.426039	+	0.273799i	0.736041	−	0.676937i	$-0.236693\pi$
$151$	5.23526	+	3.36450i	0.426039	+	0.273799i	−0.310002	+	0.950736i	$0.600330\pi$
$152$	5.37111	−	4.65409i	0.435655	−	0.377497i
$153$	−0.352802	+	0.161119i	−0.0285223	+	0.0130257i
$154$	5.47097	−	3.51598i	0.440864	−	0.283326i
$155$	−6.75036	−	0.754496i	−0.542202	−	0.0606026i
$156$	−2.20883	+	2.54912i	−0.176848	+	0.204093i
$157$	2.55360	+	8.69677i	0.203800	+	0.694078i	0.996434	+	0.0843801i	$0.0268910\pi$
$157$	2.55360	+	8.69677i	0.203800	+	0.694078i	−0.792634	+	0.609698i	$0.791291\pi$
$158$	14.0520	+	6.41736i	1.11792	+	0.510537i
$159$	0.708857	+	4.93021i	0.0562160	+	0.390991i
$160$	0.387755	+	2.20219i	0.0306547	+	0.174099i
$161$	8.88813	−	13.2240i	0.700483	−	1.04220i
$162$		−	1.00000i		−	0.0785674i
$163$	20.0244	−	2.87908i	1.56843	−	0.225507i	0.697383	−	0.716699i	$-0.254348\pi$
$163$	20.0244	−	2.87908i	1.56843	−	0.225507i	0.871051	+	0.491192i	$0.163439\pi$
$164$	−1.87640	+	4.10874i	−0.146522	+	0.320839i
$165$	1.94273	+	3.92225i	0.151242	+	0.305347i
$166$	−7.99898	+	9.23132i	−0.620842	+	0.716489i
$167$	4.95661	−	16.8806i	0.383554	−	1.30626i	−0.511107	−	0.859517i	$-0.670764\pi$
$167$	4.95661	−	16.8806i	0.383554	−	1.30626i	0.894660	−	0.446747i	$-0.147417\pi$
$168$	−1.79620	−	2.79494i	−0.138580	−	0.215634i
$169$	0.674242	+	1.47638i	0.0518647	+	0.113568i
$170$	−0.672989	−	0.547017i	−0.0516159	−	0.0419543i
$171$	−5.97879	−	3.84233i	−0.457209	−	0.293831i
$172$	−1.96537	−	0.282577i	−0.149858	−	0.0215463i
$173$	−4.33953	−	0.623930i	−0.329928	−	0.0474365i	−0.0246396	−	0.999696i	$-0.507844\pi$
$173$	−4.33953	−	0.623930i	−0.329928	−	0.0474365i	−0.305289	+	0.952260i	$0.598753\pi$
$174$	2.73157	+	1.75547i	0.207080	+	0.133082i
$175$	−8.08362	+	14.5122i	−0.611064	+	1.09702i
$176$	−0.813158	−	1.78057i	−0.0612941	−	0.134215i
$177$	2.95887	+	4.60409i	0.222402	+	0.346064i
$178$	0.816458	−	2.78060i	0.0611961	−	0.208415i
$179$	13.2837	−	15.3303i	0.992874	−	1.14584i	0.00356615	−	0.999994i	$-0.498865\pi$
$179$	13.2837	−	15.3303i	0.992874	−	1.14584i	0.989308	−	0.145844i	$-0.0465897\pi$
$180$	2.00374	−	0.992477i	0.149350	−	0.0739748i
$181$	5.71645	−	12.5173i	0.424900	−	0.930401i	−0.569227	−	0.822181i	$-0.692757\pi$
$181$	5.71645	−	12.5173i	0.424900	−	0.930401i	0.994127	−	0.108221i	$-0.0345153\pi$
$182$	11.0921	−	1.59481i	0.822203	−	0.118215i
$183$			8.16701i			0.603722i
$184$	−3.55908	−	3.21449i	−0.262379	−	0.236975i
$185$	0.100810	+	0.572536i	0.00741172	+	0.0420937i
$186$	−0.432303	−	3.00673i	−0.0316980	−	0.220464i
$187$	0.690595	+	0.315384i	0.0505013	+	0.0230632i
$188$	1.58167	+	5.38667i	0.115355	+	0.392863i
$189$	−2.17567	+	2.51086i	−0.158257	+	0.182638i
$190$	1.76525	−	15.7934i	0.128064	−	1.14577i
$191$	−18.4371	+	11.8488i	−1.33406	+	0.857348i	−0.996470	−	0.0839451i	$-0.973248\pi$
$191$	−18.4371	+	11.8488i	−1.33406	+	0.857348i	−0.337590	+	0.941293i	$0.609612\pi$
$192$	−0.909632	+	0.415415i	−0.0656470	+	0.0299800i
$193$	16.3177	−	14.1394i	1.17458	−	1.01778i	0.175128	−	0.984546i	$-0.443966\pi$
$193$	16.3177	−	14.1394i	1.17458	−	1.01778i	0.999448	−	0.0332296i	$-0.0105792\pi$
$194$	−0.455641	−	0.292823i	−0.0327131	−	0.0210235i
$195$	0.237468	+	7.53846i	0.0170055	+	0.539840i
$196$	−0.574665	+	3.99688i	−0.0410475	+	0.285492i
$197$	0.589949	−	0.917979i	0.0420321	−	0.0654033i	−0.819602	−	0.572934i	$-0.805805\pi$
$197$	0.589949	−	0.917979i	0.0420321	−	0.0654033i	0.861634	+	0.507531i	$0.169442\pi$
$198$	−1.47935	+	1.28186i	−0.105133	+	0.0910981i
$199$	10.5797	+	23.1663i	0.749976	+	1.64222i	0.766409	+	0.642353i	$0.222042\pi$
$199$	10.5797	+	23.1663i	0.749976	+	1.64222i	−0.0164335	+	0.999865i	$0.505231\pi$
$200$	3.97734	+	3.02998i	0.281240	+	0.214252i
$201$	10.3479	+	3.03843i	0.729887	+	0.214314i
$202$	−8.26324	−	7.16014i	−0.581400	−	0.503786i
$203$	−3.03926	−	10.3508i	−0.213314	−	0.726481i
$204$	0.161119	−	0.352802i	0.0112806	−	0.0247011i
$205$	3.14926	+	9.59663i	0.219954	+	0.670258i
$206$	−15.0516			−1.04870
$207$	−2.08157	+	4.32054i	−0.144679	+	0.300298i
$208$		−	3.37297i		−	0.233874i
$209$	1.97984	+	13.7701i	0.136948	+	0.952495i
$210$	−7.19043	−	1.86752i	−0.496187	−	0.128871i
$211$	2.69963	−	0.792682i	0.185850	−	0.0545705i	−0.187483	−	0.982268i	$-0.560033\pi$
$211$	2.69963	−	0.792682i	0.185850	−	0.0545705i	0.373333	+	0.927697i	$0.378215\pi$
$212$	−3.76432	−	3.26180i	−0.258534	−	0.224021i
$213$	0.270530	−	0.921342i	0.0185364	−	0.0631293i
$214$	5.07563	−	3.26191i	0.346963	−	0.222979i
$215$	−3.65764	+	2.51680i	−0.249449	+	0.171644i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−5.45622	+	8.49004i	−0.370392	+	0.576342i
$218$	−4.98984	−	0.717431i	−0.337955	−	0.0485906i
$219$	−1.54174	+	10.7230i	−0.104181	+	0.724594i
$220$	−4.03675	−	1.69202i	−0.272157	−	0.114076i
$221$	0.856696	+	0.988680i	0.0576276	+	0.0665058i
$222$	−0.236491	+	0.108002i	−0.0158722	+	0.00724859i
$223$	−11.3195	−	17.6135i	−0.758009	−	1.17948i	−0.978931	−	0.204193i	$-0.934543\pi$
$223$	−11.3195	−	17.6135i	−0.758009	−	1.17948i	0.220922	−	0.975292i	$-0.429093\pi$
$224$	3.18777	+	0.936013i	0.212992	+	0.0625400i
$225$	1.78670	−	4.66987i	0.119113	−	0.311325i
$226$	−5.35583	+	1.57261i	−0.356265	+	0.104609i
$227$	−17.8220	−	8.13904i	−1.18289	−	0.540207i	−0.275828	−	0.961207i	$-0.588952\pi$
$227$	−17.8220	−	8.13904i	−1.18289	−	0.540207i	−0.907061	+	0.421000i	$0.861679\pi$
$228$	7.03466	−	1.01143i	0.465882	−	0.0669837i
$229$	−21.2122			−1.40174			−0.700870	−	0.713289i	$-0.747205\pi$
$229$	−21.2122			−1.40174			−0.700870	+	0.713289i	$0.747205\pi$
$230$	−10.7232	+	0.117109i	−0.707065	+	0.00772196i
$231$	6.50336			0.427890
$232$	−3.21398	+	0.462100i	−0.211008	+	0.0303383i
$233$	−15.3610	−	7.01512i	−1.00633	−	0.459576i	−0.157091	−	0.987584i	$-0.550212\pi$
$233$	−15.3610	−	7.01512i	−1.00633	−	0.459576i	−0.849239	+	0.528008i	$0.822939\pi$
$234$	−3.23634	+	0.950276i	−0.211566	+	0.0621215i
$235$	10.7691	+	6.45104i	0.702498	+	0.420820i
$236$	−5.25120	−	1.54189i	−0.341824	−	0.100369i
$237$	8.35185	+	12.9957i	0.542511	+	0.844164i
$238$	−1.17213	+	0.535294i	−0.0759779	+	0.0346979i
$239$	10.0138	+	11.5566i	0.647741	+	0.747533i	0.980724	−	0.195400i	$-0.0626005\pi$
$239$	10.0138	+	11.5566i	0.647741	+	0.747533i	−0.332983	+	0.942933i	$0.608055\pi$
$240$	−0.864395	+	2.06224i	−0.0557964	+	0.133117i
$241$	2.73712	−	19.0371i	0.176313	−	1.22629i	−0.688890	−	0.724866i	$-0.741902\pi$
$241$	2.73712	−	19.0371i	0.176313	−	1.22629i	0.865203	−	0.501421i	$-0.167189\pi$
$242$	−7.09539	−	1.02016i	−0.456109	−	0.0655785i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	−5.34825	−	6.17221i	−0.342387	−	0.395135i
$245$	5.11830	+	7.43839i	0.326996	+	0.475221i
$246$	−3.79988	+	2.44204i	−0.242272	+	0.155698i
$247$	−6.75361	+	23.0007i	−0.429722	+	1.46350i
$248$	2.29570	+	1.98924i	0.145777	+	0.126317i
$249$	−11.7200	+	3.44130i	−0.742725	+	0.218084i
$250$	11.1305	−	1.05465i	0.703954	−	0.0667021i
$251$	−2.44981	−	17.0388i	−0.154631	−	1.07548i	−0.908328	−	0.418259i	$-0.862640\pi$
$251$	−2.44981	−	17.0388i	−0.154631	−	1.07548i	0.753697	−	0.657222i	$-0.228269\pi$
$252$		−	3.32235i		−	0.209288i
$253$	9.05988	−	2.45898i	0.569589	−	0.154595i
$254$	−0.906195			−0.0568597
$255$	−0.270415	−	0.824026i	−0.0169340	−	0.0516025i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	1.40879	+	4.79792i	0.0878782	+	0.299286i	0.991691	−	0.128642i	$-0.0410619\pi$
$257$	1.40879	+	4.79792i	0.0878782	+	0.299286i	−0.903813	+	0.427928i	$0.859244\pi$
$258$	−1.50060	−	1.30028i	−0.0934233	−	0.0809518i
$259$	0.828772	+	0.243349i	0.0514974	+	0.0151210i
$260$	−5.11611	−	5.54168i	−0.317287	−	0.343680i
$261$	1.34886	+	2.95360i	0.0834925	+	0.182823i
$262$	−13.4531	+	11.6572i	−0.831135	+	0.720183i
$263$	8.53667	−	13.2833i	0.526394	−	0.819084i	−0.471638	−	0.881792i	$-0.656337\pi$
$263$	8.53667	−	13.2833i	0.526394	−	0.819084i	0.998032	+	0.0627076i	$0.0199736\pi$
$264$	0.278576	−	1.93754i	0.0171451	−	0.119247i
$265$	−11.1321	+	0.350672i	−0.683841	+	0.0215416i
$266$	−19.8636	−	12.7656i	−1.21792	−	0.782707i
$267$	2.19016	−	1.89778i	0.134035	−	0.116142i
$268$	−9.81019	+	4.48016i	−0.599253	+	0.273670i
$269$	26.5367	−	17.0541i	1.61797	−	1.03981i	0.660681	−	0.750667i	$-0.270268\pi$
$269$	26.5367	−	17.0541i	1.61797	−	1.03981i	0.957287	−	0.289138i	$-0.0933687\pi$
$270$	2.22223	+	0.248381i	0.135241	+	0.0151160i
$271$	−0.172054	+	0.198561i	−0.0104515	+	0.0120617i	−0.760951	−	0.648809i	$-0.775267\pi$
$271$	−0.172054	+	0.198561i	−0.0104515	+	0.0120617i	0.750500	+	0.660871i	$0.229813\pi$
$272$	0.109270	+	0.372140i	0.00662548	+	0.0225643i
$273$	10.1935	+	4.65522i	0.616939	+	0.281747i
$274$	−1.41845	−	9.86552i	−0.0856916	−	0.595998i
$275$	−9.19868	+	3.34299i	−0.554701	+	0.201590i
$276$	−1.25621	−	4.62838i	−0.0756149	−	0.278596i
$277$		−	5.96286i		−	0.358273i	−0.983824	−	0.179137i	$-0.942670\pi$
$277$		−	5.96286i		−	0.358273i	0.983824	−	0.179137i	$-0.0573304\pi$
$278$	19.1632	−	2.75525i	1.14933	−	0.165249i
$279$	1.26189	−	2.76315i	0.0755472	−	0.165425i
$280$	6.65713	−	3.29735i	0.397840	−	0.197054i
$281$	15.8547	−	18.2973i	0.945812	−	1.09153i	−0.0498752	−	0.998755i	$-0.515882\pi$
$281$	15.8547	−	18.2973i	0.945812	−	1.09153i	0.995688	−	0.0927702i	$-0.0295722\pi$
$282$	−1.58167	+	5.38667i	−0.0941870	+	0.320771i
$283$	1.14144	+	1.77611i	0.0678515	+	0.105579i	0.873521	−	0.486786i	$-0.161831\pi$
$283$	1.14144	+	1.77611i	0.0678515	+	0.105579i	−0.805670	+	0.592365i	$0.798194\pi$
$284$	0.398897	+	0.873463i	0.0236702	+	0.0518305i
$285$	10.0236	−	12.3319i	0.593745	−	0.730477i
$286$	5.55434	+	3.56956i	0.328435	+	0.211072i
$287$	14.8540	+	2.13569i	0.876807	+	0.126066i
$288$	−0.989821	−	0.142315i	−0.0583258	−	0.00838598i
$289$	14.1748	+	9.10957i	0.833810	+	0.535857i
$290$	−4.57954	+	5.63415i	−0.268920	+	0.330849i
$291$	−0.224998	−	0.492676i	−0.0131896	−	0.0288812i
$292$	−5.85691	−	9.11353i	−0.342750	−	0.533329i
$293$	0.841371	−	2.86545i	0.0491534	−	0.167401i	−0.931259	−	0.364359i	$-0.881288\pi$
$293$	0.841371	−	2.86545i	0.0491534	−	0.167401i	0.980412	+	0.196958i	$0.0631062\pi$
$294$	−2.64432	+	3.05171i	−0.154220	+	0.177979i
$295$	−10.9663	+	5.43172i	−0.638481	+	0.316247i
$296$	0.108002	−	0.236491i	0.00627747	−	0.0137457i
$297$	−1.93754	+	0.278576i	−0.112427	+	0.0161646i
$298$		−	3.96477i		−	0.229673i
$299$	15.9608	+	2.63096i	0.923038	+	0.152152i
$300$	1.70782	+	4.69929i	0.0986010	+	0.271314i
$301$	0.938820	+	6.52964i	0.0541127	+	0.376362i
$302$	−5.66079	−	2.58519i	−0.325742	−	0.148761i
$303$	−3.08042	−	10.4909i	−0.176965	−	0.602689i
$304$	−4.65409	+	5.37111i	−0.266931	+	0.308054i
$305$	−18.1490	−	2.02853i	−1.03921	−	0.116153i
$306$	0.326281	−	0.209688i	0.0186523	−	0.0119871i
$307$	−10.8719	+	4.96502i	−0.620491	+	0.283369i	−0.700752	−	0.713405i	$-0.747152\pi$
$307$	−10.8719	+	4.96502i	−0.620491	+	0.283369i	0.0802608	+	0.996774i	$0.474425\pi$
$308$	−4.91491	+	4.25879i	−0.280053	+	0.242667i
$309$	−12.6622	−	8.13752i	−0.720329	−	0.462927i
$310$	6.78903	−	0.213861i	0.385591	−	0.0121465i
$311$	−1.51960	+	10.5690i	−0.0861685	+	0.599315i	0.900288	+	0.435294i	$0.143356\pi$
$311$	−1.51960	+	10.5690i	−0.0861685	+	0.599315i	−0.986457	+	0.164021i	$0.947554\pi$
$312$	1.82357	−	2.83753i	0.103239	−	0.160643i
$313$	−4.69158	+	4.06528i	−0.265184	+	0.229783i	−0.777295	−	0.629136i	$-0.783409\pi$
$313$	−4.69158	+	4.06528i	−0.265184	+	0.229783i	0.512111	+	0.858919i	$0.328863\pi$
$314$	−3.76529	−	8.24483i	−0.212488	−	0.465283i
$315$	−5.03932	−	5.45850i	−0.283933	−	0.307552i
$316$	−14.8223	−	4.35222i	−0.833820	−	0.244832i
$317$	−22.4379	−	19.4425i	−1.26024	−	1.09200i	−0.991679	−	0.128738i	$-0.958907\pi$
$317$	−22.4379	−	19.4425i	−1.26024	−	1.09200i	−0.268559	−	0.963263i	$-0.586547\pi$
$318$	−1.40328	−	4.77915i	−0.0786923	−	0.268001i
$319$	2.64035	−	5.78155i	0.147831	−	0.323705i
$320$	−0.697212	−	2.12459i	−0.0389753	−	0.118768i
$321$	6.03341			0.336752
$322$	−6.91569	+	14.3543i	−0.385396	+	0.799936i
$323$		−	2.75646i		−	0.153373i
$324$	0.142315	+	0.989821i	0.00790638	+	0.0549901i
$325$	−16.8112	−	1.34470i	−0.932516	−	0.0745907i
$326$	−19.4109	+	5.69955i	−1.07507	+	0.315669i
$327$	−3.80985	−	3.30125i	−0.210685	−	0.182560i
$328$	1.27257	−	4.33396i	0.0702657	−	0.239303i
$329$	15.6910	−	10.0840i	0.865072	−	0.555948i
$330$	−2.48115	−	3.60585i	−0.136583	−	0.198495i
$331$	14.7520	+	17.0247i	0.810841	+	0.935761i	0.998923	−	0.0463927i	$-0.0147726\pi$
$331$	14.7520	+	17.0247i	0.810841	+	0.935761i	−0.188082	+	0.982153i	$0.560227\pi$
$332$	6.60381	−	10.2757i	0.362431	−	0.563954i
$333$	−0.257339	−	0.0369997i	−0.0141021	−	0.00202757i
$334$	−2.50379	+	17.4142i	−0.137001	+	0.952864i
$335$	−9.32231	+	22.2408i	−0.509332	+	1.21514i
$336$	2.17567	+	2.51086i	0.118693	+	0.136979i
$337$	−19.5452	+	8.92600i	−1.06470	+	0.486230i	−0.869193	−	0.494473i	$-0.835361\pi$
$337$	−19.5452	+	8.92600i	−1.06470	+	0.486230i	−0.195503	+	0.980703i	$0.562634\pi$
$338$	−0.877490	−	1.36540i	−0.0477292	−	0.0742680i
$339$	−5.35583	−	1.57261i	−0.290889	−	0.0854127i
$340$	0.743988	+	0.445673i	0.0403484	+	0.0241700i
$341$	−5.70522	+	1.67520i	−0.308955	+	0.0907174i
$342$	6.46475	+	2.95235i	0.349574	+	0.159645i
$343$	−9.74067	+	1.40050i	−0.525947	+	0.0756197i
$344$	1.98558			0.107055
$345$	−9.08422	−	5.69886i	−0.489078	−	0.306816i
$346$	4.38415			0.235693
$347$	29.4476	−	4.23393i	1.58083	−	0.227289i	0.704751	−	0.709454i	$-0.251059\pi$
$347$	29.4476	−	4.23393i	1.58083	−	0.227289i	0.876080	+	0.482165i	$0.160150\pi$
$348$	−2.95360	−	1.34886i	−0.158329	−	0.0723067i
$349$	14.0722	−	4.13196i	0.753265	−	0.221179i	0.117512	−	0.993071i	$-0.462508\pi$
$349$	14.0722	−	4.13196i	0.753265	−	0.221179i	0.635753	+	0.771893i	$0.280690\pi$
$350$	5.93603	−	15.5149i	0.317294	−	0.829308i
$351$	−3.23634	−	0.950276i	−0.172743	−	0.0507220i
$352$	1.05828	+	1.64672i	0.0564067	+	0.0877705i
$353$	−28.0851	+	12.8260i	−1.49482	+	0.682661i	−0.984186	−	0.177138i	$-0.943316\pi$
$353$	−28.0851	+	12.8260i	−1.49482	+	0.682661i	−0.510633	+	0.859799i	$0.670589\pi$
$354$	−3.58398	−	4.13613i	−0.190486	−	0.219833i
$355$	1.98024	+	0.830025i	0.105100	+	0.0440531i
$356$	−0.412427	+	2.86849i	−0.0218586	+	0.152030i
$357$	−1.27546	−	0.183383i	−0.0675045	−	0.00970568i
$358$	−10.9668	+	17.0647i	−0.579614	+	0.901897i
$359$	−7.70519	−	8.89226i	−0.406664	−	0.469315i	0.515064	−	0.857152i	$-0.327768\pi$
$359$	−7.70519	−	8.89226i	−0.406664	−	0.469315i	−0.921728	+	0.387836i	$0.873223\pi$
$360$	−1.84210	+	1.26754i	−0.0970874	+	0.0668051i
$361$	26.5074	−	17.0353i	1.39513	−	0.896594i
$362$	−3.87687	+	13.2034i	−0.203764	+	0.693955i
$363$	−5.41748	−	4.69427i	−0.284344	−	0.246385i
$364$	−10.7523	+	3.15715i	−0.563571	+	0.165479i
$365$	−23.4461	−	6.08949i	−1.22722	−	0.318738i
$366$	−1.16229	−	8.08388i	−0.0607537	−	0.422551i
$367$		−	21.0177i		−	1.09711i	−0.836113	−	0.548557i	$-0.815178\pi$
$367$		−	21.0177i		−	1.09711i	0.836113	−	0.548557i	$-0.184822\pi$
$368$	3.98033	+	2.67526i	0.207489	+	0.139457i
$369$	−4.51693			−0.235142
$370$	−0.181265	−	0.552362i	−0.00942350	−	0.0287159i
$371$	−6.87441	+	15.0529i	−0.356902	+	0.781506i
$372$	0.855805	+	2.91461i	0.0443714	+	0.151115i
$373$	25.7920	+	22.3489i	1.33546	+	1.15718i	0.974447	+	0.224620i	$0.0721140\pi$
$373$	25.7920	+	22.3489i	1.33546	+	1.15718i	0.361012	+	0.932561i	$0.382431\pi$
$374$	−0.728450	−	0.213892i	−0.0376672	−	0.0110601i
$375$	9.93375	+	5.13036i	0.512977	+	0.264931i
$376$	−2.33217	−	5.10674i	−0.120273	−	0.263360i
$377$	8.27707	−	7.17212i	0.426291	−	0.369383i
$378$	1.79620	−	2.79494i	0.0923864	−	0.143756i
$379$	1.79772	−	12.5034i	0.0923428	−	0.642259i	−0.890110	−	0.455746i	$-0.849372\pi$
$379$	1.79772	−	12.5034i	0.0923428	−	0.642259i	0.982453	−	0.186512i	$-0.0597184\pi$
$380$	0.500356	+	15.8839i	0.0256677	+	0.814824i
$381$	−0.762340	−	0.489926i	−0.0390558	−	0.0250997i
$382$	16.5632	−	14.3521i	0.847445	−	0.734315i
$383$	−5.43663	+	2.48283i	−0.277799	+	0.126867i	−0.549443	−	0.835531i	$-0.685160\pi$
$383$	−5.43663	+	2.48283i	−0.277799	+	0.126867i	0.271644	+	0.962398i	$0.412433\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	−1.61531	+	14.4520i	−0.0823239	+	0.736540i
$386$	−14.1394	+	16.3177i	−0.719676	+	0.830550i
$387$	−0.559402	−	1.90515i	−0.0284360	−	0.0968442i
$388$	0.492676	+	0.224998i	0.0250119	+	0.0114225i
$389$	0.940472	+	6.54113i	0.0476838	+	0.331648i	0.999674	+	0.0255207i	$0.00812437\pi$
$389$	0.940472	+	6.54113i	0.0476838	+	0.331648i	−0.951990	+	0.306128i	$0.900967\pi$
$390$	−1.30789	−	7.42793i	−0.0662274	−	0.376128i
$391$	−1.84619	+	0.226790i	−0.0933659	+	0.0114693i
$392$		−	4.03799i		−	0.203949i
$393$	−17.6198	+	2.53335i	−0.888802	+	0.127790i
$394$	−0.453302	+	0.992593i	−0.0228370	+	0.0500061i
$395$	−30.9540	+	15.3318i	−1.55746	+	0.771429i
$396$	1.28186	−	1.47935i	0.0644161	−	0.0743401i
$397$	6.74754	−	22.9800i	0.338649	−	1.15333i	−0.597541	−	0.801839i	$-0.703855\pi$
$397$	6.74754	−	22.9800i	0.338649	−	1.15333i	0.936190	−	0.351495i	$-0.114326\pi$
$398$	−13.7689	−	21.4249i	−0.690174	−	1.07393i
$399$	−9.80874	−	21.4781i	−0.491051	−	1.07525i
$400$	−4.36807	−	2.43310i	−0.218403	−	0.121655i
$401$	−5.48862	−	3.52732i	−0.274088	−	0.176146i	0.396375	−	0.918089i	$-0.370268\pi$
$401$	−5.48862	−	3.52732i	−0.274088	−	0.176146i	−0.670463	+	0.741943i	$0.733905\pi$
$402$	−10.6750	−	1.53484i	−0.532421	−	0.0765506i
$403$	−10.1416	−	1.45815i	−0.505190	−	0.0726354i
$404$	9.19813	+	5.91128i	0.457624	+	0.294097i
$405$	1.73517	+	1.41038i	0.0862215	+	0.0700823i
$406$	4.48139	+	9.81288i	0.222408	+	0.487005i
$407$	0.275138	+	0.428122i	0.0136381	+	0.0212212i
$408$	−0.109270	+	0.372140i	−0.00540969	+	0.0184237i
$409$	−11.2310	+	12.9613i	−0.555339	+	0.640895i	−0.962119	−	0.272631i	$-0.912106\pi$
$409$	−11.2310	+	12.9613i	−0.555339	+	0.640895i	0.406780	+	0.913526i	$0.366652\pi$
$410$	−4.48294	−	9.05077i	−0.221397	−	0.446985i
$411$	4.14043	−	9.06628i	0.204232	−	0.447207i
$412$	14.8984	−	2.14207i	0.733992	−	0.105532i
$413$			18.1828i			0.894719i
$414$	1.44550	−	4.57280i	0.0710426	−	0.224741i
$415$	−4.73634	−	26.8993i	−0.232498	−	1.32043i
$416$	0.480024	+	3.33864i	0.0235351	+	0.163690i
$417$	17.6107	+	8.04255i	0.862401	+	0.393845i
$418$	−3.91937	−	13.3481i	−0.191703	−	0.652879i
$419$	16.1789	−	18.6714i	0.790389	−	0.912157i	−0.207425	−	0.978251i	$-0.566508\pi$
$419$	16.1789	−	18.6714i	0.790389	−	0.912157i	0.997813	+	0.0660937i	$0.0210536\pi$
$420$	7.38302	+	0.825209i	0.360254	+	0.0402661i
$421$	25.6974	−	16.5147i	1.25241	−	0.804877i	0.265186	−	0.964197i	$-0.414567\pi$
$421$	25.6974	−	16.5147i	1.25241	−	0.804877i	0.987227	+	0.159321i	$0.0509303\pi$
$422$	−2.55934	+	1.16881i	−0.124587	+	0.0568968i
$423$	−4.24284	+	3.67644i	−0.206294	+	0.178755i
$424$	4.19021	+	2.69288i	0.203494	+	0.130778i
$425$	1.89834	−	0.396251i	0.0920831	−	0.0192210i
$426$	−0.136656	+	0.950464i	−0.00662101	+	0.0460501i
$427$	−14.6695	+	22.8263i	−0.709909	+	1.10464i
$428$	−4.55975	+	3.95104i	−0.220404	+	0.190981i
$429$	2.74276	+	6.00581i	0.132422	+	0.289963i
$430$	3.26224	−	3.01172i	0.157319	−	0.145238i
$431$	−22.1571	−	6.50590i	−1.06727	−	0.313378i	−0.299493	−	0.954098i	$-0.596818\pi$
$431$	−22.1571	−	6.50590i	−1.06727	−	0.313378i	−0.767774	+	0.640720i	$0.778636\pi$
$432$	−0.755750	−	0.654861i	−0.0363610	−	0.0315070i
$433$	−9.49291	−	32.3299i	−0.456200	−	1.55368i	−0.791261	−	0.611479i	$-0.790575\pi$
$433$	−9.49291	−	32.3299i	−0.456200	−	1.55368i	0.335061	−	0.942197i	$-0.391243\pi$
$434$	4.19242	−	9.18013i	0.201243	−	0.440660i
$435$	−6.89861	+	2.26387i	−0.330763	+	0.108544i
$436$	5.04116			0.241428
$437$	−21.7857	−	26.2126i	−1.04215	−	1.25392i
$438$		−	10.8333i		−	0.517634i
$439$	−2.89808	−	20.1566i	−0.138318	−	0.962021i	−0.934246	−	0.356630i	$-0.883926\pi$
$439$	−2.89808	−	20.1566i	−0.138318	−	0.962021i	0.795928	−	0.605391i	$-0.206983\pi$
$440$	4.23646	+	1.10031i	0.201965	+	0.0524551i
$441$	−3.87442	+	1.13763i	−0.184496	+	0.0541730i
$442$	−0.988680	−	0.856696i	−0.0470267	−	0.0407489i
$443$	−9.21952	+	31.3988i	−0.438033	+	1.49180i	0.384521	+	0.923116i	$0.374367\pi$
$443$	−9.21952	+	31.3988i	−0.438033	+	1.49180i	−0.822554	+	0.568687i	$0.807452\pi$
$444$	0.218713	−	0.140558i	0.0103797	−	0.00667061i
$445$	3.67331	+	5.33840i	0.174132	+	0.253065i
$446$	13.7109	+	15.8233i	0.649231	+	0.749253i
$447$	2.14352	−	3.33538i	0.101385	−	0.157758i
$448$	−3.28853	−	0.472819i	−0.155368	−	0.0223386i
$449$	0.311867	−	2.16908i	0.0147179	−	0.102365i	−0.981138	−	0.193307i	$-0.938079\pi$
$449$	0.311867	−	2.16908i	0.0147179	−	0.102365i	0.995856	+	0.0909418i	$0.0289877\pi$
$450$	−1.10392	+	4.87661i	−0.0520393	+	0.229886i
$451$	5.79008	+	6.68211i	0.272644	+	0.314648i
$452$	5.07751	−	2.31882i	0.238826	−	0.109068i
$453$	−3.36450	−	5.23526i	−0.158078	−	0.245974i
$454$	18.7989	+	5.51986i	0.882277	+	0.259060i
$455$	−12.8768	+	21.4960i	−0.603675	+	1.00775i
$456$	−6.81911	+	2.00227i	−0.319334	+	0.0937650i
$457$	1.90013	+	0.867760i	0.0888844	+	0.0405921i	0.459361	−	0.888250i	$-0.348078\pi$
$457$	1.90013	+	0.867760i	0.0888844	+	0.0405921i	−0.370477	+	0.928842i	$0.620806\pi$
$458$	20.9963	−	3.01881i	0.981092	−	0.141060i
$459$	0.387851			0.0181033
$460$	10.5974	−	1.64198i	0.494104	−	0.0765578i
$461$	26.5960			1.23870			0.619349	−	0.785115i	$-0.287396\pi$
$461$	26.5960			1.23870			0.619349	+	0.785115i	$0.287396\pi$
$462$	−6.43716	+	0.925525i	−0.299484	+	0.0430593i
$463$	6.87141	+	3.13807i	0.319342	+	0.145838i	0.568636	−	0.822589i	$-0.307471\pi$
$463$	6.87141	+	3.13807i	0.319342	+	0.145838i	−0.249294	+	0.968428i	$0.580199\pi$
$464$	3.11550	−	0.914793i	0.144633	−	0.0424682i
$465$	5.82692	+	3.49052i	0.270217	+	0.161869i
$466$	16.2030	+	4.75762i	0.750588	+	0.220393i
$467$	13.1017	+	20.3866i	0.606274	+	0.943380i	0.999711	+	0.0240288i	$0.00764933\pi$
$467$	13.1017	+	20.3866i	0.606274	+	0.943380i	−0.393438	+	0.919351i	$0.628714\pi$
$468$	3.06816	−	1.40118i	0.141826	−	0.0647697i
$469$	23.4642	+	27.0791i	1.08348	+	1.25040i
$470$	−11.5776	−	4.85278i	−0.534033	−	0.223842i
$471$	1.28993	−	8.97167i	0.0594369	−	0.413393i
$472$	5.41718	+	0.778873i	0.249346	+	0.0358506i
$473$	−2.10130	+	3.26969i	−0.0966181	+	0.150341i
$474$	−10.1163	−	11.6749i	−0.464658	−	0.536244i
$475$	24.9146	+	25.3377i	1.14316	+	1.16257i
$476$	1.08402	−	0.696657i	0.0496859	−	0.0319312i
$477$	1.40328	−	4.77915i	0.0642520	−	0.218822i
$478$	−11.5566	−	10.0138i	−0.528586	−	0.458022i
$479$	−18.6323	+	5.47094i	−0.851331	+	0.249973i	−0.678156	−	0.734918i	$-0.737221\pi$
$479$	−18.6323	+	5.47094i	−0.851331	+	0.249973i	−0.173175	+	0.984891i	$0.555403\pi$
$480$	0.562109	−	2.16426i	0.0256567	−	0.0987846i
$481$	0.124799	+	0.867996i	0.00569034	+	0.0395772i
$482$			19.2329i			0.876033i
$483$	−13.5784	+	8.33673i	−0.617838	+	0.379334i
$484$	7.16835			0.325834
$485$	1.15073	−	0.377625i	0.0522518	−	0.0171471i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	−6.28026	−	21.3886i	−0.284586	−	0.969210i	−0.970414	−	0.241447i	$-0.922378\pi$
$487$	−6.28026	−	21.3886i	−0.284586	−	0.969210i	0.685828	−	0.727763i	$-0.259440\pi$
$488$	6.17221	+	5.34825i	0.279403	+	0.242104i
$489$	−19.4109	−	5.69955i	−0.877790	−	0.257742i
$490$	−6.12479	−	6.63427i	−0.276690	−	0.299706i
$491$	−6.36938	−	13.9470i	−0.287446	−	0.629419i	0.709733	−	0.704470i	$-0.248815\pi$
$491$	−6.36938	−	13.9470i	−0.287446	−	0.629419i	−0.997180	+	0.0750508i	$0.976088\pi$
$492$	3.41367	−	2.95796i	0.153900	−	0.133355i
$493$	−0.680863	+	1.05944i	−0.0306645	+	0.0477149i
$494$	3.41153	−	23.7277i	0.153492	−	1.06756i
$495$	−0.137812	−	4.37484i	−0.00619417	−	0.196635i
$496$	−2.55544	−	1.64228i	−0.114742	−	0.0737405i
$497$	2.41102	−	2.08916i	0.108149	−	0.0937119i
$498$	11.1110	−	5.07421i	0.497894	−	0.227381i
$499$	16.1589	−	10.3847i	0.723371	−	0.464882i	−0.126437	−	0.991975i	$-0.540354\pi$
$499$	16.1589	−	10.3847i	0.723371	−	0.464882i	0.849808	+	0.527092i	$0.176718\pi$
$500$	−10.8671	+	2.62795i	−0.485992	+	0.117526i
$501$	−11.5212	+	13.2961i	−0.514728	+	0.594027i
$502$	4.84976	+	16.5168i	0.216455	+	0.737179i
$503$	−3.37573	−	1.54165i	−0.150517	−	0.0687386i	0.338733	−	0.940883i	$-0.390002\pi$
$503$	−3.37573	−	1.54165i	−0.150517	−	0.0687386i	−0.489249	+	0.872144i	$0.662729\pi$
$504$	0.472819	+	3.28853i	0.0210610	+	0.146483i
$505$	24.0784	−	4.23964i	1.07147	−	0.188662i
$506$	−8.61771	+	3.72331i	−0.383104	+	0.165521i
$507$		−	1.62306i		−	0.0720824i
$508$	0.896971	−	0.128965i	0.0397967	−	0.00572189i
$509$	6.43851	−	14.0984i	0.285382	−	0.624899i	−0.711596	−	0.702589i	$-0.752027\pi$
$509$	6.43851	−	14.0984i	0.285382	−	0.624899i	0.996978	+	0.0776900i	$0.0247544\pi$
$510$	0.384933	+	0.777154i	0.0170451	+	0.0344130i
$511$	−23.5697	+	27.2009i	−1.04266	+	1.20330i
$512$	−0.281733	+	0.959493i	−0.0124509	+	0.0424040i
$513$	3.84233	+	5.97879i	0.169643	+	0.263970i
$514$	−2.07727	−	4.54859i	−0.0916245	−	0.200630i
$515$	21.2285	−	26.1172i	0.935439	−	1.15086i
$516$	1.67038	+	1.07349i	0.0735342	+	0.0472575i
$517$	10.8775	+	1.56394i	0.478391	+	0.0687822i
$518$	−0.854968	−	0.122926i	−0.0375651	−	0.00540105i
$519$	3.68818	+	2.37025i	0.161893	+	0.104042i
$520$	5.85269	+	4.75717i	0.256658	+	0.208616i
$521$	−0.488272	−	1.06917i	−0.0213916	−	0.0468410i	0.898635	−	0.438698i	$-0.144560\pi$
$521$	−0.488272	−	1.06917i	−0.0213916	−	0.0468410i	−0.920026	+	0.391857i	$0.871833\pi$
$522$	−1.75547	−	2.73157i	−0.0768350	−	0.119558i
$523$	−2.86125	+	9.74451i	−0.125114	+	0.426097i	−0.998098	−	0.0616509i	$-0.980363\pi$
$523$	−2.86125	+	9.74451i	−0.125114	+	0.426097i	0.872984	+	0.487748i	$0.162182\pi$
$524$	11.6572	−	13.4531i	0.509246	−	0.587701i
$525$	13.3817	−	9.84273i	0.584026	−	0.429572i
$526$	−6.55937	+	14.3630i	−0.286002	+	0.626257i
$527$	1.16616	−	0.167669i	0.0507989	−	0.00730378i
$528$			1.95746i			0.0851875i
$529$	−15.7639	+	16.7481i	−0.685389	+	0.728177i
$530$	10.9689	−	1.93137i	0.476459	−	0.0838933i
$531$	−0.778873	−	5.41718i	−0.0338002	−	0.235086i
$532$	21.4781	+	9.80874i	0.931196	+	0.425263i
$533$	4.29233	+	14.6183i	0.185921	+	0.633190i
$534$	−1.89778	+	2.19016i	−0.0821250	+	0.0947773i
$535$	−1.49859	+	13.4076i	−0.0647895	+	0.579662i
$536$	9.07274	−	5.83070i	0.391883	−	0.251848i
$537$	−18.4517	+	8.42663i	−0.796251	+	0.363636i
$538$	−23.8395	+	20.6570i	−1.02779	+	0.890588i
$539$	6.64943	+	4.27333i	0.286411	+	0.184065i
$540$	−2.23496	+	0.0704032i	−0.0961773	+	0.00302967i
$541$	−3.08930	+	21.4865i	−0.132819	+	0.923778i	0.809036	+	0.587759i	$0.199990\pi$
$541$	−3.08930	+	21.4865i	−0.132819	+	0.923778i	−0.941855	+	0.336019i	$0.890919\pi$
$542$	0.142045	−	0.221026i	0.00610134	−	0.00949388i
$543$	−10.3997	+	9.01141i	−0.446295	+	0.386717i
$544$	−0.161119	−	0.352802i	−0.00690793	−	0.0151263i
$545$	8.28244	−	7.64640i	0.354781	−	0.327536i
$546$	−10.7523	−	3.15715i	−0.460154	−	0.135113i
$547$	−29.9197	−	25.9255i	−1.27927	−	1.10850i	−0.988422	−	0.151727i	$-0.951517\pi$
$547$	−29.9197	−	25.9255i	−1.27927	−	1.10850i	−0.290849	−	0.956769i	$-0.593938\pi$
$548$	2.80802	+	9.56324i	0.119953	+	0.408521i
$549$	3.39270	−	7.42897i	0.144797	−	0.317061i
$550$	8.62929	−	4.61807i	0.367954	−	0.196915i
$551$	−23.0766			−0.983096
$552$	1.90211	+	4.40250i	0.0809592	+	0.187383i
$553$			51.3238i			2.18251i
$554$	0.848603	+	5.90216i	0.0360537	+	0.250759i
$555$	0.146140	−	0.562676i	0.00620330	−	0.0238843i
$556$	−18.5760	+	5.45442i	−0.787800	+	0.231319i
$557$	4.30625	+	3.73138i	0.182461	+	0.158104i	0.741303	−	0.671171i	$-0.234208\pi$
$557$	4.30625	+	3.73138i	0.182461	+	0.158104i	−0.558841	+	0.829275i	$0.688754\pi$
$558$	−0.855805	+	2.91461i	−0.0362291	+	0.123385i
$559$	−5.63413	+	3.62084i	−0.238298	+	0.153145i
$560$	−6.12011	+	4.21120i	−0.258622	+	0.177956i
$561$	−0.497172	−	0.573767i	−0.0209906	−	0.0242245i
$562$	−13.0893	+	20.3674i	−0.552141	+	0.859148i
$563$	30.8686	+	4.43823i	1.30096	+	0.187049i	0.757747	−	0.652549i	$-0.226300\pi$
$563$	30.8686	+	4.43823i	1.30096	+	0.187049i	0.543209	+	0.839598i	$0.317209\pi$
$564$	0.798966	−	5.55693i	0.0336426	−	0.233989i
$565$	4.82500	−	11.5113i	0.202989	−	0.484283i
$566$	−1.38259	−	1.59559i	−0.0581145	−	0.0670677i
$567$	3.02211	−	1.38015i	0.126917	−	0.0579610i
$568$	−0.519144	−	0.807804i	−0.0217828	−	0.0338947i
$569$	−15.5613	−	4.56920i	−0.652362	−	0.191551i	−0.0612278	−	0.998124i	$-0.519502\pi$
$569$	−15.5613	−	4.56920i	−0.652362	−	0.191551i	−0.591135	+	0.806573i	$0.701320\pi$
$570$	−8.16653	+	13.6329i	−0.342058	+	0.571018i
$571$	43.7774	−	12.8542i	1.83203	−	0.537931i	0.832164	−	0.554529i	$-0.187102\pi$
$571$	43.7774	−	12.8542i	1.83203	−	0.537931i	0.999862	+	0.0165979i	$0.00528353\pi$
$572$	−6.00581	−	2.74276i	−0.251115	−	0.114681i
$573$	21.6931	−	3.11900i	0.906243	−	0.130298i
$574$	−15.0068			−0.626372
$575$	14.9205	−	18.7717i	0.622229	−	0.782835i
$576$	1.00000			0.0416667
$577$	21.3541	−	3.07026i	0.888983	−	0.127816i	0.317333	−	0.948314i	$-0.397213\pi$
$577$	21.3541	−	3.07026i	0.888983	−	0.127816i	0.571650	+	0.820498i	$0.306304\pi$
$578$	−15.3269	−	6.99956i	−0.637515	−	0.291144i
$579$	−20.7168	+	6.08301i	−0.860962	+	0.252801i
$580$	3.73110	−	6.22854i	0.154926	−	0.258626i
$581$	−38.9379	−	11.4332i	−1.61542	−	0.474329i
$582$	0.292823	+	0.455641i	0.0121379	+	0.0188869i
$583$	−8.86885	+	4.05027i	−0.367310	+	0.167745i
$584$	7.09429	+	8.18724i	0.293564	+	0.338791i
$585$	2.91558	−	6.95587i	0.120544	−	0.287590i
$586$	−0.425012	+	2.95602i	−0.0175571	+	0.122112i
$587$	36.7517	+	5.28409i	1.51690	+	0.218098i	0.849895	−	0.526952i	$-0.176665\pi$
$587$	36.7517	+	5.28409i	1.51690	+	0.218098i	0.667009	+	0.745050i	$0.267574\pi$
$588$	2.18310	−	3.39697i	0.0900295	−	0.140089i
$589$	14.1375	+	16.3156i	0.582526	+	0.672271i
$590$	10.0816	−	6.93709i	0.415054	−	0.285596i
$591$	−0.917979	+	0.589949i	−0.0377606	+	0.0242673i
$592$	−0.0732462	+	0.249454i	−0.00301040	+	0.0102525i
$593$	−8.86636	−	7.68275i	−0.364098	−	0.315493i	0.453528	−	0.891242i	$-0.350165\pi$
$593$	−8.86636	−	7.68275i	−0.364098	−	0.315493i	−0.817626	+	0.575749i	$0.804710\pi$
$594$	1.87817	−	0.551480i	0.0770622	−	0.0226275i
$595$	0.724321	−	2.78882i	0.0296942	−	0.114330i
$596$	0.564246	+	3.92442i	0.0231124	+	0.160750i
$597$		−	25.4678i		−	1.04233i
$598$	−16.1728	−	0.332718i	−0.661354	−	0.0136058i
$599$	20.8620			0.852400			0.426200	−	0.904629i	$-0.359852\pi$
$599$	20.8620			0.852400			0.426200	+	0.904629i	$0.359852\pi$
$600$	−2.35922	−	4.40841i	−0.0963146	−	0.179973i
$601$	−14.8547	+	32.5272i	−0.605935	+	1.32681i	0.319386	+	0.947625i	$0.396523\pi$
$601$	−14.8547	+	32.5272i	−0.605935	+	1.32681i	−0.925320	+	0.379187i	$0.876204\pi$
$602$	−1.85853	−	6.32957i	−0.0757480	−	0.257974i
$603$	−8.15060	−	7.06254i	−0.331918	−	0.287609i
$604$	5.97108	+	1.75327i	0.242960	+	0.0713394i
$605$	11.7774	−	10.8729i	0.478817	−	0.442047i
$606$	4.54208	+	9.94576i	0.184509	+	0.404019i
$607$	2.02885	−	1.75801i	0.0823484	−	0.0713553i	−0.612714	−	0.790305i	$-0.709922\pi$
$607$	2.02885	−	1.75801i	0.0823484	−	0.0713553i	0.695062	+	0.718949i	$0.255377\pi$
$608$	3.84233	−	5.97879i	0.155827	−	0.242472i
$609$	−1.53526	+	10.6779i	−0.0622117	+	0.432692i
$610$	18.2529	−	0.574984i	0.739039	−	0.0232804i
$611$	15.9301	+	10.2376i	0.644462	+	0.414171i
$612$	−0.293118	+	0.253988i	−0.0118486	+	0.0102669i
$613$	−1.50132	+	0.685630i	−0.0606377	+	0.0276923i	−0.445503	−	0.895280i	$-0.646975\pi$
$613$	−1.50132	+	0.685630i	−0.0606377	+	0.0276923i	0.384865	+	0.922973i	$0.374248\pi$
$614$	10.0546	−	6.46171i	0.405772	−	0.260774i
$615$	1.12192	−	10.0377i	0.0452402	−	0.404757i
$616$	4.25879	−	4.91491i	0.171592	−	0.198027i
$617$	8.89495	+	30.2934i	0.358097	+	1.21957i	0.919853	+	0.392264i	$0.128308\pi$
$617$	8.89495	+	30.2934i	0.358097	+	1.21957i	−0.561756	+	0.827303i	$0.689874\pi$
$618$	13.6914	+	6.25267i	0.550750	+	0.251519i
$619$	−5.04260	−	35.0721i	−0.202679	−	1.40967i	−0.796291	−	0.604914i	$-0.793208\pi$
$619$	−5.04260	−	35.0721i	−0.202679	−	1.40967i	0.593612	−	0.804752i	$-0.297701\pi$
$620$	−6.68949	+	1.17786i	−0.268656	+	0.0473041i
$621$	3.68828	−	3.06539i	0.148005	−	0.123010i
$622$		−	10.6777i		−	0.428137i
$623$	9.53013	−	1.37023i	0.381817	−	0.0548969i
$624$	−1.40118	+	3.06816i	−0.0560922	+	0.122825i
$625$	−13.8682	+	20.8008i	−0.554728	+	0.832032i
$626$	4.06528	−	4.69158i	0.162481	−	0.187513i
$627$	3.91937	−	13.3481i	0.156524	−	0.533073i
$628$	4.90033	+	7.62506i	0.195544	+	0.304273i
$629$	−0.0418886	−	0.0917231i	−0.00167021	−	0.00365724i
$630$	5.76485	+	4.68577i	0.229677	+	0.186686i
$631$	−13.7213	−	8.81813i	−0.546236	−	0.351044i	0.238238	−	0.971207i	$-0.423430\pi$
$631$	−13.7213	−	8.81813i	−0.546236	−	0.351044i	−0.784473	+	0.620163i	$0.787067\pi$
$632$	15.2908	+	2.19849i	0.608236	+	0.0874512i
$633$	−2.78496	−	0.400417i	−0.110692	−	0.0159151i
$634$	24.9765	+	16.0514i	0.991942	+	0.637482i
$635$	1.27808	−	1.57241i	0.0507190	−	0.0623990i
$636$	2.06914	+	4.53079i	0.0820469	+	0.179658i
$637$	7.36354	+	11.4579i	0.291754	+	0.453978i
$638$	−1.79067	+	6.09846i	−0.0708933	+	0.241440i
$639$	−0.628822	+	0.725699i	−0.0248758	+	0.0287082i
$640$	0.992477	+	2.00374i	0.0392311	+	0.0792049i
$641$	−18.7035	+	40.9549i	−0.738744	+	1.61762i	0.0468664	+	0.998901i	$0.485076\pi$
$641$	−18.7035	+	40.9549i	−0.738744	+	1.61762i	−0.785610	+	0.618722i	$0.787651\pi$
$642$	−5.97200	+	0.858644i	−0.235696	+	0.0338880i
$643$		−	39.9947i		−	1.57724i	−0.614883	−	0.788619i	$-0.710797\pi$
$643$		−	39.9947i		−	1.57724i	0.614883	−	0.788619i	$-0.289203\pi$
$644$	4.80246	−	15.1924i	0.189243	−	0.598666i
$645$	4.37263	−	0.769917i	0.172172	−	0.0303155i
$646$	0.392285	+	2.72840i	0.0154342	+	0.107347i
$647$	29.4869	+	13.4662i	1.15925	+	0.529411i	0.899782	−	0.436340i	$-0.143726\pi$
$647$	29.4869	+	13.4662i	1.15925	+	0.529411i	0.259468	+	0.965752i	$0.416453\pi$
$648$	−0.281733	−	0.959493i	−0.0110675	−	0.0376924i
$649$	−7.01550	+	8.09632i	−0.275382	+	0.317808i
$650$	16.8314	−	1.06146i	0.660183	−	0.0416340i
$651$	8.49004	−	5.45622i	0.332751	−	0.213846i
$652$	18.4022	−	8.40399i	0.720685	−	0.329126i
$653$	−26.6339	+	23.0784i	−1.04226	+	0.903128i	−0.995403	−	0.0957737i	$-0.969467\pi$
$653$	−26.6339	+	23.0784i	−1.04226	+	0.903128i	−0.0468618	+	0.998901i	$0.514922\pi$
$654$	4.24089	+	2.72545i	0.165832	+	0.106574i
$655$	−1.25325	−	39.7845i	−0.0489685	−	1.55451i
$656$	−0.642826	+	4.47095i	−0.0250981	+	0.174561i
$657$	5.85691	−	9.11353i	0.228500	−	0.355553i
$658$	−14.0962	+	12.2144i	−0.549526	+	0.476167i
$659$	17.5999	+	38.5385i	0.685597	+	1.50125i	0.856602	+	0.515977i	$0.172571\pi$
$659$	17.5999	+	38.5385i	0.685597	+	1.50125i	−0.171006	+	0.985270i	$0.554702\pi$
$660$	2.96906	+	3.21604i	0.115571	+	0.125184i
$661$	−6.78123	−	1.99115i	−0.263759	−	0.0774467i	0.147179	−	0.989110i	$-0.452981\pi$
$661$	−6.78123	−	1.99115i	−0.263759	−	0.0774467i	−0.410938	+	0.911663i	$0.634799\pi$
$662$	−17.0247	−	14.7520i	−0.661683	−	0.573351i
$663$	−0.368566	−	1.25522i	−0.0143139	−	0.0487487i
$664$	−5.07421	+	11.1110i	−0.196917	+	0.431189i
$665$	50.1657	−	16.4625i	1.94534	−	0.638389i
$666$	0.259985			0.0100742
$667$	1.89865	+	15.4560i	0.0735161	+	0.598459i
$668$		−	17.5933i		−	0.680705i
$669$	2.97967	+	20.7241i	0.115201	+	0.801238i
$670$	6.06223	−	23.3411i	0.234204	−	0.901746i
$671$	−15.3390	+	4.50394i	−0.592156	+	0.173873i
$672$	−2.51086	−	2.17567i	−0.0968586	−	0.0839285i
$673$	−2.99159	+	10.1884i	−0.115317	+	0.392735i	−0.996843	−	0.0794020i	$-0.974699\pi$
$673$	−2.99159	+	10.1884i	−0.115317	+	0.392735i	0.881525	+	0.472137i	$0.156517\pi$
$674$	18.0760	−	11.6167i	0.696260	−	0.447459i
$675$	−3.56517	+	3.50564i	−0.137224	+	0.134932i
$676$	1.06288	+	1.22662i	0.0408798	+	0.0471778i
$677$	15.1662	−	23.5991i	0.582884	−	0.906985i	−0.417114	−	0.908854i	$-0.636958\pi$
$677$	15.1662	−	23.5991i	0.582884	−	0.906985i	0.999998	+	0.00186877i	$0.000594848\pi$
$678$	5.52512	+	0.794393i	0.212191	+	0.0305085i
$679$	0.256089	−	1.78114i	0.00982780	−	0.0683538i
$680$	−0.799841	−	0.335256i	−0.0306725	−	0.0128565i
$681$	12.8304	+	14.8071i	0.491662	+	0.567408i
$682$	5.40875	−	2.47009i	0.207112	−	0.0945847i
$683$	11.9942	+	18.6633i	0.458943	+	0.714130i	0.991188	−	0.132461i	$-0.0422878\pi$
$683$	11.9942	+	18.6633i	0.458943	+	0.714130i	−0.532245	+	0.846590i	$0.678651\pi$
$684$	−6.81911	−	2.00227i	−0.260735	−	0.0765588i
$685$	19.1190	+	11.4529i	0.730498	+	0.437592i
$686$	9.44221	−	2.77248i	0.360505	−	0.105854i
$687$	19.2953	+	8.81186i	0.736161	+	0.336193i
$688$	−1.96537	+	0.282577i	−0.0749290	+	0.0107732i
$689$	−16.8005			−0.640047
$690$	9.80278	+	4.34804i	0.373186	+	0.165527i
$691$	5.35871			0.203855			0.101927	−	0.994792i	$-0.467499\pi$
$691$	5.35871			0.203855			0.101927	+	0.994792i	$0.467499\pi$
$692$	−4.33953	+	0.623930i	−0.164964	+	0.0237183i
$693$	−5.91566	−	2.70159i	−0.224717	−	0.102625i
$694$	−28.5453	+	8.38167i	−1.08357	+	0.318164i
$695$	−22.2466	+	37.1375i	−0.843860	+	1.40870i
$696$	3.11550	+	0.914793i	0.118093	+	0.0346751i
$697$	−0.947146	−	1.47379i	−0.0358757	−	0.0558237i
$698$	−13.3409	+	6.09258i	−0.504960	+	0.230607i
$699$	11.0586	+	12.7624i	0.418276	+	0.482717i
$700$	−3.66761	+	16.2018i	−0.138622	+	0.612370i
$701$	6.98586	−	48.5877i	0.263852	−	1.83513i	−0.239313	−	0.970942i	$-0.576922\pi$
$701$	6.98586	−	48.5877i	0.263852	−	1.83513i	0.503165	−	0.864190i	$-0.332169\pi$
$702$	3.33864	+	0.480024i	0.126009	+	0.0181173i
$703$	0.998949	−	1.55439i	0.0376761	−	0.0586251i
$704$	−1.28186	−	1.47935i	−0.0483121	−	0.0557551i
$705$	−7.11605	−	10.3417i	−0.268006	−	0.389492i
$706$	25.9739	−	16.6924i	0.977541	−	0.628227i
$707$	10.2342	−	34.8545i	0.384897	−	1.31084i
$708$	4.13613	+	3.58398i	0.155445	+	0.134694i
$709$	−47.7072	+	14.0081i	−1.79168	+	0.526085i	−0.996746	−	0.0806094i	$-0.974313\pi$
$709$	−47.7072	+	14.0081i	−1.79168	+	0.526085i	−0.794935	+	0.606694i	$0.792495\pi$
$710$	−2.07821	−	0.539759i	−0.0779937	−	0.0202568i
$711$	−2.19849	−	15.2908i	−0.0824497	−	0.573451i
$712$		−	2.89799i		−	0.108607i
$713$	9.76449	−	10.8113i	0.365683	−	0.404885i
$714$	1.28858			0.0482237
$715$	−14.0275	+	4.60331i	−0.524600	+	0.172154i
$716$	8.42663	−	18.4517i	0.314918	−	0.689574i
$717$	−4.30813	−	14.6721i	−0.160890	−	0.547941i
$718$	8.89226	+	7.70519i	0.331856	+	0.287555i
$719$	−17.9294	−	5.26455i	−0.668655	−	0.196335i	−0.0702509	−	0.997529i	$-0.522380\pi$
$719$	−17.9294	−	5.26455i	−0.668655	−	0.196335i	−0.598404	+	0.801195i	$0.704198\pi$
$720$	1.64297	−	1.51679i	0.0612297	−	0.0565276i
$721$	−20.7735	−	45.4877i	−0.773646	−	1.69405i
$722$	−23.8132	+	20.6343i	−0.886237	+	0.767929i
$723$	−10.3981	+	16.1797i	−0.386708	+	0.601730i
$724$	1.95837	−	13.6207i	0.0727821	−	0.506211i
$725$	−3.31735	−	15.8926i	−0.123203	−	0.590236i
$726$	6.03040	+	3.87550i	0.223809	+	0.143833i
$727$	23.0552	−	19.9774i	0.855070	−	0.740922i	−0.112466	−	0.993656i	$-0.535875\pi$
$727$	23.0552	−	19.9774i	0.855070	−	0.740922i	0.967536	+	0.252734i	$0.0813296\pi$
$728$	10.1935	−	4.65522i	0.377796	−	0.172534i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	24.0740	+	2.69078i	0.891020	+	0.0995903i
$731$	0.504314	−	0.582010i	0.0186527	−	0.0215264i
$732$	2.30091	+	7.83618i	0.0850441	+	0.289634i
$733$	0.462523	+	0.211227i	0.0170837	+	0.00780185i	0.423939	−	0.905691i	$-0.360647\pi$
$733$	0.462523	+	0.211227i	0.0170837	+	0.00780185i	−0.406855	+	0.913493i	$0.633375\pi$
$734$	2.99113	+	20.8037i	0.110404	+	0.767880i
$735$	−1.56575	−	8.89242i	−0.0577535	−	0.328002i
$736$	−4.32054	−	2.08157i	−0.159257	−	0.0767276i
$737$			21.1108i			0.777626i
$738$	4.47095	−	0.642826i	0.164578	−	0.0236627i
$739$	15.1875	−	33.2559i	0.558680	−	1.22334i	−0.393928	−	0.919141i	$-0.628884\pi$
$739$	15.1875	−	33.2559i	0.558680	−	1.22334i	0.952609	−	0.304198i	$-0.0983885\pi$
$740$	0.258029	+	0.520943i	0.00948533	+	0.0191503i
$741$	15.6981	−	18.1166i	0.576685	−	0.665530i
$742$	4.66220	−	15.8780i	0.171155	−	0.582899i
$743$	−3.18575	−	4.95712i	−0.116874	−	0.181859i	0.777888	−	0.628403i	$-0.216291\pi$
$743$	−3.18575	−	4.95712i	−0.116874	−	0.181859i	−0.894762	+	0.446544i	$0.852655\pi$
$744$	−1.26189	−	2.76315i	−0.0462630	−	0.101302i
$745$	6.87957	+	5.59184i	0.252048	+	0.204869i
$746$	−28.7100	−	18.4508i	−1.05115	−	0.675532i
$747$	12.0905	+	1.73835i	0.442367	+	0.0636027i
$748$	0.751475	+	0.108046i	0.0274767	+	0.00395055i
$749$	16.8630	+	10.8372i	0.616160	+	0.395982i
$750$	−10.5628	−	3.66442i	−0.385698	−	0.133806i
$751$	18.8594	+	41.2964i	0.688191	+	1.50693i	0.853725	+	0.520724i	$0.174338\pi$
$751$	18.8594	+	41.2964i	0.688191	+	1.50693i	−0.165534	+	0.986204i	$0.552935\pi$
$752$	3.03520	+	4.72286i	0.110682	+	0.172225i
$753$	−4.84976	+	16.5168i	−0.176735	+	0.601904i
$754$	−7.17212	+	8.27707i	−0.261193	+	0.301433i
$755$	12.4696	−	6.17634i	0.453816	−	0.224780i
$756$	−1.38015	+	3.02211i	−0.0501957	+	0.109913i
$757$	2.16830	−	0.311755i	0.0788082	−	0.0113309i	−0.102798	−	0.994702i	$-0.532779\pi$
$757$	2.16830	−	0.311755i	0.0788082	−	0.0113309i	0.181606	+	0.983371i	$0.441870\pi$
$758$			12.6320i			0.458815i
$759$	−9.26265	−	1.52684i	−0.336213	−	0.0554208i
$760$	−2.75577	−	15.6510i	−0.0999623	−	0.567720i
$761$	1.83337	+	12.7514i	0.0664596	+	0.462236i	0.995691	+	0.0927372i	$0.0295617\pi$
$761$	1.83337	+	12.7514i	0.0664596	+	0.462236i	−0.929231	+	0.369499i	$0.879529\pi$
$762$	0.824304	+	0.376447i	0.0298614	+	0.0136372i
$763$	−4.71859	−	16.0700i	−0.170824	−	0.581774i
$764$	−14.3521	+	16.5632i	−0.519239	+	0.599234i
$765$	−0.0963349	+	0.861894i	−0.00348300	+	0.0311619i
$766$	5.02795	−	3.23127i	0.181667	−	0.116751i
$767$	−16.7917	+	7.66852i	−0.606314	+	0.276894i
$768$	−0.755750	+	0.654861i	−0.0272708	+	0.0236303i
$769$	−19.3442	−	12.4318i	−0.697570	−	0.448301i	0.143200	−	0.989694i	$-0.454261\pi$
$769$	−19.3442	−	12.4318i	−0.697570	−	0.448301i	−0.840770	+	0.541393i	$0.817897\pi$
$770$	−0.457858	−	14.5347i	−0.0165000	−	0.523796i
$771$	0.711641	−	4.94957i	0.0256291	−	0.178254i
$772$	11.6732	−	18.1639i	0.420128	−	0.653732i
$773$	1.48167	−	1.28388i	0.0532921	−	0.0461779i	−0.627808	−	0.778369i	$-0.716048\pi$
$773$	1.48167	−	1.28388i	0.0532921	−	0.0461779i	0.681100	+	0.732191i	$0.261502\pi$
$774$	0.824839	+	1.80615i	0.0296482	+	0.0649206i
$775$	−9.20402	+	12.0818i	−0.330618	+	0.433990i
$776$	−0.519682	−	0.152592i	−0.0186555	−	0.00547775i
$777$	−0.652786	−	0.565642i	−0.0234186	−	0.0202923i
$778$	−1.86180	−	6.34071i	−0.0667487	−	0.227325i
$779$	13.3356	−	29.2008i	0.477796	−	1.04623i
$780$	2.35168	+	7.16619i	0.0842036	+	0.256591i
$781$	1.87963			0.0672583
$782$	1.79512	−	0.487222i	0.0641935	−	0.0174230i
$783$		−	3.24703i		−	0.116039i
$784$	0.574665	+	3.99688i	0.0205238	+	0.142746i
$785$	19.6167	+	5.09492i	0.700150	+	0.181845i
$786$	17.0799	−	5.01512i	0.609221	−	0.178883i
$787$	16.3565	+	14.1730i	0.583045	+	0.505212i	0.895702	−	0.444654i	$-0.146674\pi$
$787$	16.3565	+	14.1730i	0.583045	+	0.505212i	−0.312657	+	0.949866i	$0.601219\pi$
$788$	0.307427	−	1.04700i	0.0109517	−	0.0372979i
$789$	−13.2833	+	8.53667i	−0.472899	+	0.303913i
$790$	28.4569	−	19.5810i	1.01245	−	0.696660i
$791$	−12.1445	−	14.0155i	−0.431808	−	0.498333i
$792$	−1.05828	+	1.64672i	−0.0376044	+	0.0585136i
$793$	−27.2667	−	3.92036i	−0.968269	−	0.139216i
$794$	−3.40846	+	23.7064i	−0.120962	+	0.841308i
$795$	10.2718	+	4.30547i	0.364304	+	0.152699i
$796$	16.6779	+	19.2473i	0.591131	+	0.682202i
$797$	−24.4488	+	11.1654i	−0.866023	+	0.395499i	−0.798340	−	0.602208i	$-0.794288\pi$
$797$	−24.4488	+	11.1654i	−0.866023	+	0.395499i	−0.0676831	+	0.997707i	$0.521561\pi$
$798$	12.7656	+	19.8636i	0.451896	+	0.703164i
$799$	−2.08922	−	0.613452i	−0.0739115	−	0.0217024i
$800$	4.66987	+	1.78670i	0.165105	+	0.0631693i
$801$	−2.78060	+	0.816458i	−0.0982477	+	0.0288481i
$802$	5.93474	+	2.71030i	0.209563	+	0.0957042i
$803$	−20.9899	+	3.01789i	−0.740716	+	0.106499i
$804$	10.7848			0.380350
$805$	−15.1535	−	32.2450i	−0.534091	−	1.13649i
$806$	10.2459			0.360897
$807$	−31.2231	+	4.48920i	−1.09911	+	0.158027i
$808$	−9.94576	−	4.54208i	−0.349891	−	0.159790i
$809$	−0.835334	+	0.245276i	−0.0293688	+	0.00862345i	−0.296384	−	0.955069i	$-0.595781\pi$
$809$	−0.835334	+	0.245276i	−0.0293688	+	0.00862345i	0.267015	+	0.963692i	$0.413963\pi$
$810$	−1.91823	−	1.14908i	−0.0673997	−	0.0403747i
$811$	−24.8854	−	7.30700i	−0.873843	−	0.256583i	−0.186094	−	0.982532i	$-0.559583\pi$
$811$	−24.8854	−	7.30700i	−0.873843	−	0.256583i	−0.687749	+	0.725948i	$0.741401\pi$
$812$	−5.83229	−	9.07523i	−0.204673	−	0.318478i
$813$	0.238991	−	0.109144i	0.00838179	−	0.00382784i
$814$	−0.333265	−	0.384609i	−0.0116809	−	0.0134805i
$815$	17.4870	−	41.7198i	0.612543	−	1.46138i
$816$	0.0551970	−	0.383903i	0.00193228	−	0.0134393i
$817$	13.9679	+	2.00828i	0.488674	+	0.0702607i
$818$	9.27213	−	14.4277i	0.324193	−	0.504454i
$819$	−7.33849	−	8.46907i	−0.256428	−	0.295933i
$820$	5.72537	+	8.32065i	0.199939	+	0.290570i
$821$	−37.1714	+	23.8886i	−1.29729	+	0.833719i	−0.992914	−	0.118832i	$-0.962085\pi$
$821$	−37.1714	+	23.8886i	−1.29729	+	0.833719i	−0.304378	+	0.952551i	$0.598449\pi$
$822$	−2.80802	+	9.56324i	−0.0979410	+	0.333556i
$823$	38.5272	+	33.3840i	1.34298	+	1.16369i	0.971981	+	0.235060i	$0.0755285\pi$
$823$	38.5272	+	33.3840i	1.34298	+	1.16369i	0.370994	+	0.928635i	$0.379017\pi$
$824$	−14.4419	+	4.24053i	−0.503108	+	0.147726i
$825$	9.75614	+	0.780380i	0.339665	+	0.0271693i
$826$	−2.58769	−	17.9978i	−0.0900372	−	0.626222i
$827$			36.1272i			1.25627i	0.778106	+	0.628133i	$0.216181\pi$
$827$			36.1272i			1.25627i	−0.778106	+	0.628133i	$0.783819\pi$
$828$	−0.780012	+	4.73197i	−0.0271073	+	0.164447i
$829$	−40.1648			−1.39498			−0.697491	−	0.716594i	$-0.745700\pi$
$829$	−40.1648			−1.39498			−0.697491	+	0.716594i	$0.745700\pi$
$830$	8.51630	+	25.9514i	0.295605	+	0.900788i
$831$	−2.47706	+	5.42401i	−0.0859283	+	0.188157i
$832$	−0.950276	−	3.23634i	−0.0329449	−	0.112200i
$833$	−1.18361	−	1.02560i	−0.0410096	−	0.0355350i
$834$	−18.5760	−	5.45442i	−0.643236	−	0.188871i
$835$	−26.6854	−	28.9052i	−0.923487	−	1.00031i
$836$	5.77911	+	12.6545i	0.199875	+	0.437665i
$837$	−2.29570	+	1.98924i	−0.0793511	+	0.0687582i
$838$	−13.3570	+	20.7838i	−0.461409	+	0.717966i
$839$	−6.31318	+	43.9092i	−0.217955	+	1.51591i	0.527614	+	0.849484i	$0.323087\pi$
$839$	−6.31318	+	43.9092i	−0.217955	+	1.51591i	−0.745569	+	0.666428i	$0.767822\pi$
$840$	−7.42531	+	0.233904i	−0.256198	+	0.00807045i
$841$	−15.5269	−	9.97851i	−0.535409	−	0.344087i
$842$	−23.0855	+	20.0037i	−0.795579	+	0.689373i
$843$	−22.0229	+	10.0575i	−0.758510	+	0.346400i
$844$	2.36695	−	1.52115i	0.0814738	−	0.0523600i
$845$	3.60680	+	0.403137i	0.124078	+	0.0138683i
$846$	3.67644	−	4.24284i	0.126399	−	0.145872i
$847$	−6.70967	−	22.8510i	−0.230547	−	0.785171i
$848$	−4.53079	−	2.06914i	−0.155588	−	0.0710547i
$849$	−0.300465	−	2.08978i	−0.0103119	−	0.0717211i
$850$	−1.82263	+	0.662380i	−0.0625156	+	0.0227194i
$851$	−1.12328	−	0.541176i	−0.0385054	−	0.0185513i
$852$		−	0.960238i		−	0.0328972i
$853$	8.28455	−	1.19114i	0.283658	−	0.0407838i	0.000982526	−	1.00000i	$-0.499687\pi$
$853$	8.28455	−	1.19114i	0.283658	−	0.0407838i	0.282675	+	0.959216i	$0.408778\pi$
$854$	11.2717	−	24.6816i	0.385710	−	0.844587i
$855$	−14.2406	+	7.05353i	−0.487018	+	0.241226i
$856$	3.95104	−	4.55975i	0.135044	−	0.155849i
$857$	3.98660	−	13.5771i	0.136180	−	0.463786i	−0.862959	−	0.505274i	$-0.831392\pi$
$857$	3.98660	−	13.5771i	0.136180	−	0.463786i	0.999139	+	0.0414878i	$0.0132098\pi$
$858$	−3.56956	−	5.55434i	−0.121863	−	0.189622i
$859$	2.93057	+	6.41706i	0.0999898	+	0.218947i	0.953015	−	0.302922i	$-0.0979622\pi$
$859$	2.93057	+	6.41706i	0.0999898	+	0.218947i	−0.853026	+	0.521869i	$0.825235\pi$
$860$	−2.80042	+	3.44533i	−0.0954936	+	0.117485i
$861$	−12.6245	−	8.11329i	−0.430243	−	0.276500i
$862$	22.8574	+	3.28640i	0.778527	+	0.111935i
$863$	−49.0910	−	7.05822i	−1.67108	−	0.240264i	−0.759237	−	0.650814i	$-0.774428\pi$
$863$	−49.0910	−	7.05822i	−1.67108	−	0.240264i	−0.911838	+	0.410549i	$0.865337\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−6.18332	+	7.60727i	−0.210239	+	0.258655i
$866$	13.9973	+	30.6498i	0.475648	+	1.04152i
$867$	−9.10957	−	14.1748i	−0.309377	−	0.481400i
$868$	−2.84328	+	9.68333i	−0.0965073	+	0.328674i
$869$	−19.8023	+	22.8531i	−0.671747	+	0.775238i
$870$	6.50621	−	3.22260i	0.220581	−	0.109256i
$871$	−15.1115	+	33.0895i	−0.512033	+	1.12119i
$872$	−4.98984	+	0.717431i	−0.168977	+	0.0242953i
$873$			0.541622i			0.0183311i
$874$	25.2944	+	22.8453i	0.855596	+	0.772755i
$875$	18.5490	+	32.1820i	0.627072	+	1.08795i
$876$	1.54174	+	10.7230i	0.0520904	+	0.362297i
$877$	5.65949	+	2.58460i	0.191107	+	0.0872758i	0.508670	−	0.860961i	$-0.330137\pi$
$877$	5.65949	+	2.58460i	0.191107	+	0.0872758i	−0.317563	+	0.948237i	$0.602864\pi$
$878$	5.73716	+	19.5390i	0.193620	+	0.659408i
$879$	−1.95569	+	2.25698i	−0.0659637	+	0.0761262i
$880$	−4.34993	−	0.486196i	−0.146636	−	0.0163897i
$881$	25.3293	−	16.2781i	0.853364	−	0.548424i	−0.0392581	−	0.999229i	$-0.512499\pi$
$881$	25.3293	−	16.2781i	0.853364	−	0.548424i	0.892622	+	0.450805i	$0.148863\pi$
$882$	3.67308	−	1.67744i	0.123679	−	0.0564823i
$883$	16.2891	−	14.1146i	0.548173	−	0.474995i	−0.336190	−	0.941794i	$-0.609138\pi$
$883$	16.2891	−	14.1146i	0.548173	−	0.474995i	0.884363	+	0.466799i	$0.154593\pi$
$884$	1.10054	+	0.707272i	0.0370151	+	0.0237881i
$885$	12.2317	−	0.385309i	0.411164	−	0.0129520i
$886$	4.65717	−	32.3913i	0.156461	−	1.08821i
$887$	−10.4674	+	16.2877i	−0.351462	+	0.546886i	−0.971304	−	0.237841i	$-0.923560\pi$
$887$	−10.4674	+	16.2877i	−0.351462	+	0.546886i	0.619842	+	0.784727i	$0.287197\pi$
$888$	−0.196483	+	0.170254i	−0.00659355	+	0.00571335i
$889$	−1.25069	−	2.73862i	−0.0419467	−	0.0918505i
$890$	−4.39566	−	4.76130i	−0.147343	−	0.159599i
$891$	1.87817	+	0.551480i	0.0629210	+	0.0184753i
$892$	−15.8233	−	13.7109i	−0.529802	−	0.459076i
$893$	−11.2409	−	38.2830i	−0.376163	−	1.28109i
$894$	−1.64703	+	3.60649i	−0.0550848	+	0.120619i
$895$	−14.1428	−	43.0970i	−0.472743	−	1.44057i
$896$	3.32235			0.110992
$897$	−13.4255	−	9.02357i	−0.448266	−	0.301288i
$898$			2.19139i			0.0731275i
$899$	−1.40370	−	9.76294i	−0.0468160	−	0.325612i
$900$	0.398670	−	4.98408i	0.0132890	−	0.166136i
$901$	1.85360	−	0.544265i	0.0617523	−	0.0181321i
$902$	−6.68211	−	5.79008i	−0.222490	−	0.192789i
$903$	1.85853	−	6.32957i	0.0618479	−	0.210635i
$904$	−4.69583	+	3.01783i	−0.156181	+	0.100371i
$905$	−17.4423	−	25.3488i	−0.579803	−	0.842624i
$906$	4.07530	+	4.70315i	0.135393	+	0.156252i
$907$	−19.8024	+	30.8131i	−0.657528	+	1.02313i	0.339074	+	0.940760i	$0.389886\pi$
$907$	−19.8024	+	30.8131i	−0.657528	+	1.02313i	−0.996602	+	0.0823734i	$0.973750\pi$
$908$	−19.3931	−	2.78831i	−0.643583	−	0.0925333i
$909$	−1.55605	+	10.8225i	−0.0516108	+	0.358961i
$910$	9.68656	−	23.1098i	0.321107	−	0.766083i
$911$	33.4972	+	38.6578i	1.10981	+	1.28079i	0.956218	+	0.292656i	$0.0945389\pi$
$911$	33.4972	+	38.6578i	1.10981	+	1.28079i	0.153593	+	0.988134i	$0.450916\pi$
$912$	6.46475	−	2.95235i	0.214069	−	0.0977622i
$913$	−12.9267	−	20.1143i	−0.427811	−	0.665687i
$914$	−2.00429	−	0.588511i	−0.0662959	−	0.0194662i
$915$	15.6662	+	9.38457i	0.517909	+	0.310244i
$916$	−20.3529	+	5.97616i	−0.672480	+	0.197458i
$917$	−53.7966	−	24.5681i	−1.77652	−	0.811310i
$918$	−0.383903	+	0.0551970i	−0.0126707	+	0.00182177i
$919$	−51.0741			−1.68478			−0.842390	−	0.538868i	$-0.818852\pi$
$919$	−51.0741			−1.68478			−0.842390	+	0.538868i	$0.818852\pi$
$920$	−10.2558	+	3.13343i	−0.338124	+	0.103306i
$921$	11.9520			0.393830
$922$	−26.3253	+	3.78500i	−0.866977	+	0.124652i
$923$	2.94617	+	1.34547i	0.0969743	+	0.0442867i
$924$	6.23993	−	1.83221i	0.205279	−	0.0602752i
$925$	1.21410	+	0.464515i	0.0399192	+	0.0152731i
$926$	−7.24807	−	2.12822i	−0.238186	−	0.0699378i
$927$	8.13752	+	12.6622i	0.267271	+	0.415882i
$928$	−2.95360	+	1.34886i	−0.0969566	+	0.0442786i
$929$	24.2487	+	27.9845i	0.795573	+	0.918140i	0.998130	−	0.0611304i	$-0.0194706\pi$
$929$	24.2487	+	27.9845i	0.795573	+	0.918140i	−0.202557	+	0.979271i	$0.564925\pi$
$930$	−6.26436	−	2.62573i	−0.205416	−	0.0861011i
$931$	4.08415	−	28.4059i	0.133852	−	0.930964i
$932$	−16.7151	−	2.40327i	−0.547522	−	0.0787218i
$933$	5.77281	−	8.98267i	0.188993	−	0.294079i
$934$	−15.8696	−	18.3145i	−0.519271	−	0.599270i
$935$	1.39853	−	0.962318i	0.0457369	−	0.0314712i
$936$	−2.83753	+	1.82357i	−0.0927474	+	0.0596051i
$937$	10.0320	−	34.1658i	0.327730	−	1.11615i	−0.616635	−	0.787249i	$-0.711505\pi$
$937$	10.0320	−	34.1658i	0.327730	−	1.11615i	0.944365	−	0.328898i	$-0.106677\pi$
$938$	−27.0791	−	23.4642i	−0.884165	−	0.766133i
$939$	5.95639	−	1.74895i	0.194380	−	0.0570750i
$940$	12.1503	+	3.15573i	0.396300	+	0.102928i
$941$	−2.56188	−	17.8183i	−0.0835150	−	0.580860i	−0.988012	−	0.154379i	$-0.950662\pi$
$941$	−2.56188	−	17.8183i	−0.0835150	−	0.580860i	0.904497	−	0.426481i	$-0.140247\pi$
$942$			9.06392i			0.295319i
$943$	−20.6550	−	6.52923i	−0.672620	−	0.212621i
$944$	−5.47289			−0.178127
$945$	2.31638	+	7.05863i	0.0753519	+	0.229617i
$946$	1.61459	−	3.53546i	0.0524948	−	0.114948i
$947$	5.28872	+	18.0117i	0.171860	+	0.585302i	0.999704	+	0.0243429i	$0.00774936\pi$
$947$	5.28872	+	18.0117i	0.171860	+	0.585302i	−0.827843	+	0.560959i	$0.810432\pi$
$948$	11.6749	+	10.1163i	0.379182	+	0.328563i
$949$	−35.0602	−	10.2946i	−1.13810	−	0.334177i
$950$	−28.2669	−	21.5341i	−0.917101	−	0.698657i
$951$	12.3335	+	27.0066i	0.399941	+	0.875749i
$952$	−0.973841	+	0.843838i	−0.0315624	+	0.0273489i
$953$	0.307841	−	0.479010i	0.00997195	−	0.0155167i	−0.836232	−	0.548376i	$-0.815246\pi$
$953$	0.307841	−	0.479010i	0.00997195	−	0.0155167i	0.846204	+	0.532859i	$0.178883\pi$
$954$	−0.708857	+	4.93021i	−0.0229501	+	0.159621i
$955$	1.54297	+	48.9818i	0.0499294	+	1.58501i
$956$	12.8641	+	8.26724i	0.416054	+	0.267382i
$957$	−4.80349	+	4.16224i	−0.155275	+	0.134546i
$958$	17.6641	−	8.06690i	0.570700	−	0.260630i
$959$	27.8570	−	17.9026i	0.899551	−	0.578106i
$960$	−0.248381	+	2.22223i	−0.00801647	+	0.0717222i
$961$	14.2581	−	16.4547i	0.459938	−	0.530796i
$962$	−0.247057	−	0.841400i	−0.00796545	−	0.0271278i
$963$	−5.48818	−	2.50637i	−0.176854	−	0.0807666i
$964$	−2.73712	−	19.0371i	−0.0881567	−	0.613143i
$965$	−8.37218	−	47.5485i	−0.269510	−	1.53064i
$966$	12.2537	−	10.1843i	0.394258	−	0.327674i
$967$			19.9674i			0.642110i	0.947061	+	0.321055i	$0.104037\pi$
$967$			19.9674i			0.642110i	−0.947061	+	0.321055i	$0.895963\pi$
$968$	−7.09539	+	1.02016i	−0.228054	+	0.0327893i
$969$	−1.14507	+	2.50736i	−0.0367851	+	0.0805481i
$970$	−1.08527	+	0.537547i	−0.0348460	+	0.0172596i
$971$	33.2339	−	38.3540i	1.06653	−	1.23084i	0.0946094	−	0.995514i	$-0.469840\pi$
$971$	33.2339	−	38.3540i	1.06653	−	1.23084i	0.971917	−	0.235323i	$-0.0756147\pi$
$972$	0.281733	−	0.959493i	0.00903658	−	0.0307758i
$973$	34.7748	+	54.1107i	1.11483	+	1.73471i
$974$	9.26025	+	20.2771i	0.296718	+	0.649721i
$975$	14.7334	+	8.20680i	0.471845	+	0.262828i
$976$	−6.87052	−	4.41542i	−0.219920	−	0.141334i
$977$	−38.1918	−	5.49115i	−1.22186	−	0.175677i	−0.498959	−	0.866626i	$-0.666284\pi$
$977$	−38.1918	−	5.49115i	−1.22186	−	0.175677i	−0.722904	+	0.690948i	$0.757193\pi$
$978$	20.0244	+	2.87908i	0.640311	+	0.0920628i
$979$	4.77218	+	3.06689i	0.152520	+	0.0980183i
$980$	7.00661	+	5.69509i	0.223818	+	0.181923i
$981$	2.09417	+	4.58560i	0.0668618	+	0.146407i
$982$	8.28942	+	12.8986i	0.264526	+	0.411610i
$983$	6.34726	−	21.6168i	0.202446	−	0.689469i	−0.794201	−	0.607655i	$-0.792110\pi$
$983$	6.34726	−	21.6168i	0.202446	−	0.689469i	0.996648	−	0.0818141i	$-0.0260714\pi$
$984$	−2.95796	+	3.41367i	−0.0942963	+	0.108824i
$985$	−1.08299	−	2.18649i	−0.0345071	−	0.0696674i
$986$	0.523158	−	1.14556i	0.0166607	−	0.0364819i
$987$	−18.4621	+	2.65444i	−0.587654	+	0.0844919i
$988$			23.9717i			0.762642i
$989$	0.195862	−	9.52049i	0.00622805	−	0.302734i
$990$	0.759014	+	4.31070i	0.0241230	+	0.137003i
$991$	−2.05811	−	14.3145i	−0.0653781	−	0.454715i	−0.996045	−	0.0888477i	$-0.971682\pi$
$991$	−2.05811	−	14.3145i	−0.0653781	−	0.454715i	0.930667	−	0.365867i	$-0.119228\pi$
$992$	2.76315	+	1.26189i	0.0877300	+	0.0400649i
$993$	−6.34655	−	21.6144i	−0.201402	−	0.685911i
$994$	−2.08916	+	2.41102i	−0.0662643	+	0.0764731i
$995$	56.5953	+	6.32573i	1.79419	+	0.200539i
$996$	−10.2757	+	6.60381i	−0.325599	+	0.209250i
$997$	41.1013	−	18.7704i	1.30169	−	0.594463i	0.360634	−	0.932707i	$-0.382560\pi$
$997$	41.1013	−	18.7704i	1.30169	−	0.594463i	0.941058	+	0.338244i	$0.109833\pi$
$998$	−14.5165	+	12.5786i	−0.459512	+	0.398170i
$999$	0.218713	+	0.140558i	0.00691978	+	0.00444707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.a.49.4	✓	120
5.4	even	2	inner	690.2.r.a.49.11	yes	120
23.8	even	11	inner	690.2.r.a.169.11	yes	120
115.54	even	22	inner	690.2.r.a.169.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.a.49.4	✓	120	1.1	even	1	trivial
690.2.r.a.49.11	yes	120	5.4	even	2	inner
690.2.r.a.169.4	yes	120	115.54	even	22	inner
690.2.r.a.169.11	yes	120	23.8	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.14908 - 1.91823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-1.79620 - 2.79494i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.14908 - 1.91823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-1.79620 - 2.79494i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-0.864395 + 2.06224i) q^{10} +(0.278576 - 1.93754i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(1.82357 - 2.83753i) q^{13} +(2.17567 + 2.51086i) q^{14} +(-1.84210 + 1.26754i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.109270 + 0.372140i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-6.81911 + 2.00227i) q^{19} +(0.562109 - 2.16426i) q^{20} +(0.472819 + 3.28853i) q^{21} +1.95746i q^{22} +(1.90211 + 4.40250i) q^{23} +1.00000 q^{24} +(-2.35922 - 4.40841i) q^{25} +(-1.40118 + 3.06816i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.51086 - 2.17567i) q^{28} +(3.11550 + 0.914793i) q^{29} +(1.64297 - 1.51679i) q^{30} +(-1.26189 - 2.76315i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(-1.05828 + 1.64672i) q^{33} +(0.0551970 - 0.383903i) q^{34} +(-7.42531 + 0.233904i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.196483 + 0.170254i) q^{37} +(6.46475 - 2.95235i) q^{38} +(-2.83753 + 1.82357i) q^{39} +(-0.248381 + 2.22223i) q^{40} +(-2.95796 + 3.41367i) q^{41} +(-0.936013 - 3.18777i) q^{42} +(-1.80615 - 0.824839i) q^{43} +(-0.278576 - 1.93754i) q^{44} +(2.20219 - 0.387755i) q^{45} +(-2.50929 - 4.08699i) q^{46} +5.61408i q^{47} +(-0.989821 + 0.142315i) q^{48} +(-1.67744 + 3.67308i) q^{49} +(2.96258 + 4.02779i) q^{50} +(0.253988 - 0.293118i) q^{51} +(0.950276 - 3.23634i) q^{52} +(-2.69288 - 4.19021i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-3.39653 - 2.76076i) q^{55} +(2.79494 + 1.79620i) q^{56} +(7.03466 + 1.01143i) q^{57} +(-3.21398 - 0.462100i) q^{58} +(-4.60409 - 2.95887i) q^{59} +(-1.41038 + 1.73517i) q^{60} +(-3.39270 - 7.42897i) q^{61} +(1.64228 + 2.55544i) q^{62} +(0.936013 - 3.18777i) q^{63} +(0.654861 - 0.755750i) q^{64} +(-3.34760 - 6.75857i) q^{65} +(0.813158 - 1.78057i) q^{66} +(-10.6750 + 1.53484i) q^{67} +0.387851i q^{68} +(0.0986422 - 4.79482i) q^{69} +(7.31644 - 1.28825i) q^{70} +(0.136656 + 0.950464i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(-3.05209 - 10.3945i) q^{73} +(0.170254 - 0.196483i) q^{74} +(0.314697 + 4.99009i) q^{75} +(-5.97879 + 3.84233i) q^{76} +(-5.91566 + 2.70159i) q^{77} +(2.54912 - 2.20883i) q^{78} +(-12.9957 - 8.35185i) q^{79} +(-0.0704032 - 2.23496i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.44204 - 3.79988i) q^{82} +(9.23132 - 7.99898i) q^{83} +(1.38015 + 3.02211i) q^{84} +(0.588290 + 0.637226i) q^{85} +(1.90515 + 0.559402i) q^{86} +(-2.45394 - 2.12635i) q^{87} +(0.551480 + 1.87817i) q^{88} +(-1.20387 + 2.63611i) q^{89} +(-2.12459 + 0.697212i) q^{90} -11.2062 q^{91} +(3.06539 + 3.68828i) q^{92} +3.03765i q^{93} +(-0.798966 - 5.55693i) q^{94} +(-3.99491 + 15.3814i) q^{95} +(0.959493 - 0.281733i) q^{96} +(0.409330 + 0.354687i) q^{97} +(1.13763 - 3.87442i) q^{98} +(1.64672 - 1.05828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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