LMFDB - Embedded newform 690.2.r.a.49.11

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			49.11
Character	$\chi$	$=$	690.49
Dual form			690.2.r.a.169.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.73517 - 1.41038i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.79620 + 2.79494i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.73517 - 1.41038i) 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} +(1.51679 - 1.64297i) 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} +(2.16426 - 0.562109i) 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} +(1.26754 - 1.84210i) q^{20} +(0.472819 + 3.28853i) q^{21} -1.95746i q^{22} +(-1.90211 - 4.40250i) q^{23} +1.00000 q^{24} +(1.02166 - 4.89451i) 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} +(2.06224 - 0.864395i) 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} +(7.05863 + 2.31638i) 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} +(0.992477 - 2.00374i) 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} +(0.314697 - 4.99009i) 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} +(-2.24928 - 3.75486i) 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} +(1.91823 - 1.14908i) 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} +(0.837783 + 7.49552i) 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} +(2.96258 - 4.02779i) 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} +(0.697212 - 2.12459i) 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} +(-0.335256 - 0.799841i) 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} +(2.23496 + 0.0704032i) q^{90} -11.2062 q^{91} +(-3.06539 - 3.68828i) q^{92} -3.03765i q^{93} +(-0.798966 - 5.55693i) q^{94} +(-9.00838 + 13.0918i) 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
$5$	1.73517	−	1.41038i	0.775993	−	0.630741i
$5$	1.73517	−	1.41038i	0.775993	−	0.630741i
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	1.79620	+	2.79494i	0.678898	+	1.05639i	0.994216	+	0.107400i	$0.0342526\pi$
$7$	1.79620	+	2.79494i	0.678898	+	1.05639i	−0.315318	+	0.948986i	$0.602111\pi$
$8$	0.909632	−	0.415415i	0.321603	−	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	1.51679	−	1.64297i	0.479652	−	0.519551i
$11$	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	−0.996436	−	0.0843581i	$-0.973116\pi$
$13$	−1.82357	+	2.83753i	−0.505766	+	0.786988i	0.490669	+	0.871346i	$0.336752\pi$
$14$	2.17567	+	2.51086i	0.581473	+	0.671056i
$15$	2.16426	−	0.562109i	0.558810	−	0.145136i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.109270	−	0.372140i	0.0265019	−	0.0902573i	−0.945180	−	0.326549i	$-0.894114\pi$
$17$	0.109270	−	0.372140i	0.0265019	−	0.0902573i	0.971682	+	0.236292i	$0.0759322\pi$
$18$	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	$0.712480\pi$
$20$	1.26754	−	1.84210i	0.283430	−	0.411907i
$21$	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
$25$	1.02166	−	4.89451i	0.204331	−	0.978902i
$26$	−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	$0.493429\pi$
$30$	2.06224	−	0.864395i	0.376511	−	0.157816i
$31$	−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
$35$	7.05863	+	2.31638i	1.19313	+	0.391540i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	0.196483	−	0.170254i	0.0323017	−	0.0279896i	−0.638560	−	0.769572i	$-0.720470\pi$
$37$	0.196483	−	0.170254i	0.0323017	−	0.0279896i	0.670862	+	0.741582i	$0.265924\pi$
$38$	−6.46475	+	2.95235i	−1.04872	+	0.478935i
$39$	−2.83753	+	1.82357i	−0.454368	+	0.292004i
$40$	0.992477	−	2.00374i	0.156924	−	0.316820i
$41$	−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	0.548344	−	0.836253i	$-0.315259\pi$
$43$	1.80615	+	0.824839i	0.275435	+	0.125787i	−0.272909	+	0.962040i	$0.587986\pi$
$44$	−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	$-0.865721\pi$
$47$		−	5.61408i		−	0.818897i	0.912333	−	0.409449i	$-0.134279\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	−1.67744	+	3.67308i	−0.239634	+	0.524726i
$50$	0.314697	−	4.99009i	0.0445048	−	0.705705i
$51$	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	0.975446	−	0.220238i	$-0.0706834\pi$
$53$	2.69288	+	4.19021i	0.369896	+	0.575569i	−0.605550	+	0.795807i	$0.707047\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−2.24928	−	3.75486i	−0.303293	−	0.506305i
$56$	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	$0.797765\pi$
$60$	1.91823	−	1.14908i	0.247642	−	0.148346i
$61$	−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
$65$	0.837783	+	7.49552i	0.103914	+	0.929705i
$66$	0.813158	−	1.78057i	0.100093	−	0.219173i
$67$	10.6750	−	1.53484i	1.30416	−	0.187510i	0.545013	−	0.838428i	$-0.316525\pi$
$67$	10.6750	−	1.53484i	1.30416	−	0.187510i	0.759148	+	0.650918i	$0.225616\pi$
$68$		−	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	$0.127666\pi$
$73$	3.05209	+	10.3945i	0.357220	+	1.21658i	−0.563422	+	0.826169i	$0.690515\pi$
$74$	0.170254	−	0.196483i	0.0197916	−	0.0228407i
$75$	2.96258	−	4.02779i	0.342090	−	0.465089i
$76$	−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	$-0.653432\pi$
$80$	0.697212	−	2.12459i	0.0779507	−	0.237537i
$81$	−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	−0.992557	−	0.121783i	$-0.961139\pi$
$83$	−9.23132	+	7.99898i	−1.01327	+	0.878003i	−0.0207122	+	0.999785i	$0.506593\pi$
$84$	1.38015	+	3.02211i	0.150587	+	0.329740i
$85$	−0.335256	−	0.799841i	−0.0363637	−	0.0867549i
$86$	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	$0.185448\pi$
$90$	2.23496	+	0.0704032i	0.235585	+	0.00742115i
$91$	−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
$95$	−9.00838	+	13.0918i	−0.924241	+	1.34319i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	−0.409330	−	0.354687i	−0.0415612	−	0.0360130i	0.633833	−	0.773470i	$-0.281481\pi$
$97$	−0.409330	−	0.354687i	−0.0415612	−	0.0360130i	−0.675394	+	0.737457i	$0.736026\pi$
$98$	−1.13763	+	3.87442i	−0.114918	+	0.391375i
$99$	1.64672	−	1.05828i	0.165502	−	0.106361i
$100$	−0.398670	−	4.98408i	−0.0398670	−	0.498408i
$101$	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	−0.638512	−	0.769612i	$-0.720450\pi$
$103$	−14.8984	−	2.14207i	−1.46798	−	0.211064i	−0.829472	+	0.558548i	$0.811359\pi$
$104$	−0.480024	+	3.33864i	−0.0470702	+	0.327381i
$105$	5.45850	+	5.03932i	0.532695	+	0.491787i
$106$	3.26180	+	3.76432i	0.316814	+	0.365623i
$107$	5.48818	−	2.50637i	0.530563	−	0.242300i	−0.132075	−	0.991240i	$-0.542164\pi$
$107$	5.48818	−	2.50637i	0.530563	−	0.242300i	0.662638	+	0.748940i	$0.269437\pi$
$108$	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	$0.513293\pi$
$110$	−2.76076	−	3.39653i	−0.263228	−	0.323847i
$111$	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	−0.397202	−	0.917731i	$-0.630019\pi$
$113$	−5.52512	+	0.794393i	−0.519760	+	0.0747302i	−0.122558	+	0.992461i	$0.539110\pi$
$114$	−7.10700			−0.665631
$115$	−9.50969	−	4.95640i	−0.886783	−	0.462186i
$116$	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
$120$	1.73517	−	1.41038i	0.158399	−	0.128749i
$121$	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
$125$	−5.13036	−	9.93375i	−0.458874	−	0.888501i
$126$	−0.472819	+	3.28853i	−0.0421221	+	0.292966i
$127$	−0.896971	−	0.128965i	−0.0795933	−	0.0114438i	0.102403	−	0.994743i	$-0.467347\pi$
$127$	−0.896971	−	0.128965i	−0.0795933	−	0.0114438i	−0.181996	+	0.983299i	$0.558256\pi$
$128$	0.540641	−	0.841254i	0.0477863	−	0.0743570i
$129$	1.30028	+	1.50060i	0.114483	+	0.132121i
$130$	1.89598	+	7.30000i	0.166288	+	0.640252i
$131$	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
$135$	1.84210	+	1.26754i	0.158543	+	0.109092i
$136$	−0.0551970	−	0.383903i	−0.00473310	−	0.0329194i
$137$		−	9.96697i		−	0.851536i	−0.904832	−	0.425768i	$-0.860004\pi$
$137$		−	9.96697i		−	0.851536i	0.904832	−	0.425768i	$-0.139996\pi$
$138$	−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	$0.806616\pi$
$140$	7.42531	+	0.233904i	0.627553	+	0.0197685i
$141$	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
$145$	6.69614	−	2.80671i	0.556084	−	0.233085i
$146$	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	$0.993530\pi$
$150$	2.35922	−	4.40841i	0.192629	−	0.359945i
$151$	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
$155$	−6.08668	−	3.01480i	−0.488894	−	0.242154i
$156$	−2.20883	+	2.54912i	−0.176848	+	0.204093i
$157$	−2.55360	−	8.69677i	−0.203800	−	0.694078i	−0.996434	−	0.0843801i	$-0.973109\pi$
$157$	−2.55360	−	8.69677i	−0.203800	−	0.694078i	0.792634	−	0.609698i	$-0.208709\pi$
$158$	−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	−0.871051	−	0.491192i	$-0.836561\pi$
$163$	−20.0244	+	2.87908i	−1.56843	+	0.225507i	−0.697383	+	0.716699i	$0.745652\pi$
$164$	−1.87640	+	4.10874i	−0.146522	+	0.320839i
$165$	−0.486196	−	4.34993i	−0.0378503	−	0.338641i
$166$	−7.99898	+	9.23132i	−0.620842	+	0.716489i
$167$	−4.95661	+	16.8806i	−0.383554	+	1.30626i	0.511107	+	0.859517i	$0.329236\pi$
$167$	−4.95661	+	16.8806i	−0.383554	+	1.30626i	−0.894660	+	0.446747i	$0.852583\pi$
$168$	1.79620	+	2.79494i	0.138580	+	0.215634i
$169$	0.674242	+	1.47638i	0.0518647	+	0.113568i
$170$	−0.445673	−	0.743988i	−0.0341816	−	0.0570613i
$171$	−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	0.305289	−	0.952260i	$-0.401247\pi$
$173$	4.33953	+	0.623930i	0.329928	+	0.0474365i	0.0246396	+	0.999696i	$0.492156\pi$
$174$	2.73157	+	1.75547i	0.207080	+	0.133082i
$175$	15.5149	−	5.93603i	1.17282	−	0.448722i
$176$	−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	$-0.0465897\pi$
$180$	2.22223	−	0.248381i	0.165635	−	0.0185132i
$181$	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
$190$	−7.05353	+	14.2406i	−0.511717	+	1.03312i
$191$	−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	$0.556034\pi$
$193$	−16.3177	+	14.1394i	−1.17458	+	1.01778i	−0.999448	+	0.0332296i	$0.989421\pi$
$194$	−0.455641	−	0.292823i	−0.0327131	−	0.0210235i
$195$	−2.35168	+	7.16619i	−0.168407	+	0.513182i
$196$	−0.574665	+	3.99688i	−0.0410475	+	0.285492i
$197$	−0.589949	+	0.917979i	−0.0420321	+	0.0654033i	−0.861634	−	0.507531i	$-0.830558\pi$
$197$	−0.589949	+	0.917979i	−0.0420321	+	0.0654033i	0.819602	+	0.572934i	$0.194195\pi$
$198$	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	$0.505231\pi$
$200$	−1.10392	−	4.87661i	−0.0780590	−	0.344829i
$201$	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
$205$	−0.318006	+	10.0951i	−0.0222105	+	0.705076i
$206$	−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
$210$	6.12011	+	4.21120i	0.422328	+	0.290600i
$211$	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
$215$	4.29732	−	1.11611i	0.293074	−	0.0761183i
$216$	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
$220$	−3.21604	−	2.96906i	−0.216825	−	0.200174i
$221$	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	$0.0654571\pi$
$223$	11.3195	+	17.6135i	0.758009	+	1.17948i	−0.220922	+	0.975292i	$0.570907\pi$
$224$	3.18777	+	0.936013i	0.212992	+	0.0625400i
$225$	4.36807	−	2.43310i	0.291204	−	0.162207i
$226$	−5.35583	+	1.57261i	−0.356265	+	0.104609i
$227$	17.8220	+	8.13904i	1.18289	+	0.540207i	0.907061	−	0.421000i	$-0.138321\pi$
$227$	17.8220	+	8.13904i	1.18289	+	0.540207i	0.275828	+	0.961207i	$0.411048\pi$
$228$	−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	$0.747205\pi$
$230$	−10.1183	−	3.55258i	−0.667178	−	0.234250i
$231$	6.50336			0.427890
$232$	3.21398	−	0.462100i	0.211008	−	0.0303383i
$233$	15.3610	+	7.01512i	1.00633	+	0.459576i	0.849239	−	0.528008i	$-0.177061\pi$
$233$	15.3610	+	7.01512i	1.00633	+	0.459576i	0.157091	+	0.987584i	$0.449788\pi$
$234$	−3.23634	+	0.950276i	−0.211566	+	0.0621215i
$235$	−7.91798	−	9.74140i	−0.516512	−	0.635459i
$236$	−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	$0.608055\pi$
$240$	1.51679	−	1.64297i	0.0979087	−	0.106053i
$241$	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
$245$	2.26979	+	8.73926i	0.145012	+	0.558331i
$246$	−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
$250$	−6.49186	−	9.10251i	−0.410582	−	0.575693i
$251$	−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
$255$	0.0273060	−	0.866831i	0.00170997	−	0.0542831i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−1.40879	−	4.79792i	−0.0878782	−	0.299286i	0.903813	−	0.427928i	$-0.140756\pi$
$257$	−1.40879	−	4.79792i	−0.0878782	−	0.299286i	−0.991691	+	0.128642i	$0.958938\pi$
$258$	1.50060	+	1.30028i	0.0934233	+	0.0809518i
$259$	0.828772	+	0.243349i	0.0514974	+	0.0151210i
$260$	2.91558	+	6.95587i	0.180817	+	0.431385i
$261$	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	−0.998032	−	0.0627076i	$-0.980026\pi$
$263$	−8.53667	+	13.2833i	−0.526394	+	0.819084i	0.471638	+	0.881792i	$0.343663\pi$
$264$	0.278576	−	1.93754i	0.0171451	−	0.119247i
$265$	10.5824	+	3.47275i	0.650072	+	0.213329i
$266$	−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	$-0.0933687\pi$
$270$	2.00374	+	0.992477i	0.121944	+	0.0604002i
$271$	−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	$0.0573304\pi$
$277$			5.96286i			0.358273i	−0.983824	+	0.179137i	$0.942670\pi$
$278$	−19.1632	+	2.75525i	−1.14933	+	0.165249i
$279$	1.26189	−	2.76315i	0.0755472	−	0.165425i
$280$	7.38302	−	0.825209i	0.441220	−	0.0493156i
$281$	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	0.805670	−	0.592365i	$-0.201806\pi$
$283$	−1.14144	−	1.77611i	−0.0678515	−	0.105579i	−0.873521	+	0.486786i	$0.838169\pi$
$284$	0.398897	+	0.873463i	0.0236702	+	0.0518305i
$285$	−13.6329	+	8.16653i	−0.807541	+	0.483744i
$286$	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
$290$	6.22854	−	3.73110i	0.365753	−	0.219098i
$291$	−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	−0.980412	−	0.196958i	$-0.936894\pi$
$293$	−0.841371	+	2.86545i	−0.0491534	+	0.167401i	0.931259	+	0.364359i	$0.118712\pi$
$294$	−2.64432	+	3.05171i	−0.154220	+	0.177979i
$295$	−12.1620	+	1.35936i	−0.708100	+	0.0791452i
$296$	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
$305$	−16.3646	−	8.10556i	−0.937034	−	0.464123i
$306$	0.326281	−	0.209688i	0.0186523	−	0.0119871i
$307$	10.8719	−	4.96502i	0.620491	−	0.283369i	−0.0802608	−	0.996774i	$-0.525575\pi$
$307$	10.8719	−	4.96502i	0.620491	−	0.283369i	0.700752	+	0.713405i	$0.252848\pi$
$308$	4.91491	−	4.25879i	0.280053	−	0.242667i
$309$	−12.6622	−	8.13752i	−0.720329	−	0.462927i
$310$	−6.45377	−	2.11789i	−0.366550	−	0.120288i
$311$	−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	−0.512111	−	0.858919i	$-0.671137\pi$
$313$	4.69158	−	4.06528i	0.265184	−	0.229783i	0.777295	+	0.629136i	$0.216591\pi$
$314$	−3.76529	−	8.24483i	−0.212488	−	0.465283i
$315$	2.87182	+	6.85147i	0.161809	+	0.386036i
$316$	−14.8223	−	4.35222i	−0.833820	−	0.244832i
$317$	22.4379	+	19.4425i	1.26024	+	1.09200i	0.991679	+	0.128738i	$0.0410927\pi$
$317$	22.4379	+	19.4425i	1.26024	+	1.09200i	0.268559	+	0.963263i	$0.413453\pi$
$318$	1.40328	+	4.77915i	0.0786923	+	0.268001i
$319$	2.64035	−	5.78155i	0.147831	−	0.323705i
$320$	0.0704032	−	2.23496i	0.00393566	−	0.124938i
$321$	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
$325$	12.0252	+	11.8244i	0.667040	+	0.655902i
$326$	−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
$330$	−1.10031	−	4.23646i	−0.0605699	−	0.233209i
$331$	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
$335$	16.3583	−	17.7190i	0.893750	−	0.968094i
$336$	2.17567	+	2.51086i	0.118693	+	0.136979i
$337$	19.5452	−	8.92600i	1.06470	−	0.486230i	0.195503	−	0.980703i	$-0.437366\pi$
$337$	19.5452	−	8.92600i	1.06470	−	0.486230i	0.869193	+	0.494473i	$0.164639\pi$
$338$	0.877490	+	1.36540i	0.0477292	+	0.0742680i
$339$	−5.35583	−	1.57261i	−0.290889	−	0.0854127i
$340$	−0.547017	−	0.672989i	−0.0296662	−	0.0364980i
$341$	−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
$345$	−6.59135	−	8.45896i	−0.354866	−	0.455415i
$346$	4.38415			0.235693
$347$	−29.4476	+	4.23393i	−1.58083	+	0.227289i	−0.876080	−	0.482165i	$-0.839850\pi$
$347$	−29.4476	+	4.23393i	−1.58083	+	0.227289i	−0.704751	+	0.709454i	$0.748941\pi$
$348$	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	$0.280690\pi$
$350$	14.5122	−	8.08362i	0.775711	−	0.432088i
$351$	−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	0.510633	−	0.859799i	$-0.329411\pi$
$353$	28.0851	−	12.8260i	1.49482	−	0.682661i	0.984186	+	0.177138i	$0.0566837\pi$
$354$	−3.58398	−	4.13613i	−0.190486	−	0.219833i
$355$	1.57764	+	1.45648i	0.0837323	+	0.0773021i
$356$	−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	$0.873223\pi$
$360$	2.16426	−	0.562109i	0.114067	−	0.0296258i
$361$	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
$365$	19.9560	+	13.7316i	1.04455	+	0.718744i
$366$	−1.16229	−	8.08388i	−0.0607537	−	0.422551i
$367$			21.0177i			1.09711i	0.836113	+	0.548557i	$0.184822\pi$
$367$			21.0177i			1.09711i	−0.836113	+	0.548557i	$0.815178\pi$
$368$	−3.98033	−	2.67526i	−0.207489	−	0.139457i
$369$	−4.51693			−0.235142
$370$	0.0183038	−	0.581056i	0.000951568	−	0.0302076i
$371$	−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	$-0.927886\pi$
$373$	−25.7920	−	22.3489i	−1.33546	−	1.15718i	−0.361012	−	0.932561i	$-0.617569\pi$
$374$	−0.728450	−	0.213892i	−0.0376672	−	0.0110601i
$375$	−0.540115	−	11.1673i	−0.0278914	−	0.576676i
$376$	−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	$-0.0597184\pi$
$380$	−4.95509	+	15.0995i	−0.254191	+	0.774587i
$381$	−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	−0.271644	−	0.962398i	$-0.587567\pi$
$383$	5.43663	−	2.48283i	0.277799	−	0.126867i	0.549443	+	0.835531i	$0.314840\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	6.45443	−	13.0311i	0.328948	−	0.664125i
$386$	−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
$395$	−34.3291	+	3.83701i	−1.72729	+	0.193061i
$396$	1.28186	−	1.47935i	0.0644161	−	0.0743401i
$397$	−6.74754	+	22.9800i	−0.338649	+	1.15333i	0.597541	+	0.801839i	$0.296145\pi$
$397$	−6.74754	+	22.9800i	−0.338649	+	1.15333i	−0.936190	+	0.351495i	$0.885674\pi$
$398$	13.7689	+	21.4249i	0.690174	+	1.07393i
$399$	−9.80874	−	21.4781i	−0.491051	−	1.07525i
$400$	−1.78670	−	4.66987i	−0.0893349	−	0.233494i
$401$	−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
$405$	1.14908	+	1.91823i	0.0570984	+	0.0953176i
$406$	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	$0.366652\pi$
$410$	1.12192	+	10.0377i	0.0554077	+	0.495724i
$411$	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	$0.0210536\pi$
$420$	6.65713	+	3.29735i	0.324835	+	0.160894i
$421$	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
$425$	−1.70981	−	0.915024i	−0.0829379	−	0.0443852i
$426$	−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
$430$	4.09474	−	1.71632i	0.197466	−	0.0827685i
$431$	−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	$0.209425\pi$
$433$	9.49291	+	32.3299i	0.456200	+	1.55368i	−0.335061	+	0.942197i	$0.608757\pi$
$434$	4.19242	−	9.18013i	0.201243	−	0.440660i
$435$	7.25697	+	0.228601i	0.347945	+	0.0109606i
$436$	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	$-0.206983\pi$
$440$	−3.60585	−	2.48115i	−0.171902	−	0.118284i
$441$	−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	$-0.625633\pi$
$443$	9.21952	−	31.3988i	0.438033	−	1.49180i	0.822554	−	0.568687i	$-0.192548\pi$
$444$	0.218713	−	0.140558i	0.0103797	−	0.00667061i
$445$	1.62899	+	6.27201i	0.0772214	+	0.297322i
$446$	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	$0.0289877\pi$
$450$	3.97734	−	3.02998i	0.187494	−	0.142835i
$451$	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
$455$	−19.4447	+	15.8050i	−0.911581	+	0.740949i
$456$	−6.81911	+	2.00227i	−0.319334	+	0.0937650i
$457$	−1.90013	−	0.867760i	−0.0888844	−	0.0405921i	0.370477	−	0.928842i	$-0.379194\pi$
$457$	−1.90013	−	0.867760i	−0.0888844	−	0.0405921i	−0.459361	+	0.888250i	$0.651922\pi$
$458$	−20.9963	+	3.01881i	−0.981092	+	0.141060i
$459$	0.387851			0.0181033
$460$	−10.5209	−	2.07644i	−0.490537	−	0.0968146i
$461$	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	0.249294	−	0.968428i	$-0.419801\pi$
$463$	−6.87141	−	3.13807i	−0.319342	−	0.145838i	−0.568636	+	0.822589i	$0.692529\pi$
$464$	3.11550	−	0.914793i	0.144633	−	0.0424682i
$465$	−4.28424	−	5.27085i	−0.198677	−	0.244430i
$466$	16.2030	+	4.75762i	0.750588	+	0.220393i
$467$	−13.1017	−	20.3866i	−0.606274	−	0.943380i	−0.999711	−	0.0240288i	$-0.992351\pi$
$467$	−13.1017	−	20.3866i	−0.606274	−	0.943380i	0.393438	−	0.919351i	$-0.371286\pi$
$468$	−3.06816	+	1.40118i	−0.141826	+	0.0647697i
$469$	23.4642	+	27.0791i	1.08348	+	1.25040i
$470$	−9.22373	−	8.51540i	−0.425459	−	0.392786i
$471$	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
$475$	2.83335	+	35.4219i	0.130003	+	1.62527i
$476$	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	$0.555403\pi$
$480$	1.26754	−	1.84210i	0.0578549	−	0.0840802i
$481$	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
$485$	−1.21050	−	0.0381319i	−0.0549661	−	0.00173148i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	6.28026	+	21.3886i	0.284586	+	0.969210i	0.970414	+	0.241447i	$0.0776219\pi$
$487$	6.28026	+	21.3886i	0.284586	+	0.969210i	−0.685828	+	0.727763i	$0.740560\pi$
$488$	−6.17221	−	5.34825i	−0.279403	−	0.242104i
$489$	−19.4109	−	5.69955i	−0.877790	−	0.257742i
$490$	3.49041	+	8.32728i	0.157681	+	0.376188i
$491$	−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
$495$	1.36476	−	4.15881i	0.0613416	−	0.186924i
$496$	−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	$0.176718\pi$
$500$	−7.72121	−	8.08597i	−0.345303	−	0.361616i
$501$	−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	0.489249	−	0.872144i	$-0.337271\pi$
$503$	3.37573	+	1.54165i	0.150517	+	0.0687386i	−0.338733	+	0.940883i	$0.609998\pi$
$504$	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	$0.0247544\pi$
$510$	−0.0963349	−	0.861894i	−0.00426578	−	0.0381653i
$511$	−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
$515$	−28.8725	+	17.2956i	−1.27227	+	0.762133i
$516$	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
$520$	3.87583	+	6.47014i	0.169966	+	0.283734i
$521$	−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	−0.872984	−	0.487748i	$-0.837818\pi$
$523$	2.86125	−	9.74451i	0.125114	−	0.426097i	0.998098	+	0.0616509i	$0.0196365\pi$
$524$	11.6572	−	13.4531i	0.509246	−	0.587701i
$525$	16.5788	+	1.04553i	0.723558	+	0.0456307i
$526$	−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
$535$	5.98802	−	12.0894i	0.258885	−	0.522671i
$536$	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
$540$	2.12459	+	0.697212i	0.0914279	+	0.0300032i
$541$	−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
$545$	10.3961	−	4.35755i	0.445318	−	0.186657i
$546$	−10.7523	−	3.15715i	−0.460154	−	0.135113i
$547$	29.9197	+	25.9255i	1.27927	+	1.10850i	0.988422	+	0.151727i	$0.0484833\pi$
$547$	29.9197	+	25.9255i	1.27927	+	1.10850i	0.290849	+	0.956769i	$0.406062\pi$
$548$	−2.80802	−	9.56324i	−0.119953	−	0.408521i
$549$	3.39270	−	7.42897i	0.144797	−	0.317061i
$550$	−9.58080	−	1.99985i	−0.408527	−	0.0852740i
$551$	−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
$555$	0.329541	−	0.478919i	0.0139882	−	0.0203290i
$556$	−18.5760	+	5.45442i	−0.787800	+	0.231319i
$557$	−4.30625	−	3.73138i	−0.182461	−	0.158104i	0.558841	−	0.829275i	$-0.311246\pi$
$557$	−4.30625	−	3.73138i	−0.182461	−	0.158104i	−0.741303	+	0.671171i	$0.765792\pi$
$558$	0.855805	−	2.91461i	0.0362291	−	0.123385i
$559$	−5.63413	+	3.62084i	−0.238298	+	0.153145i
$560$	7.19043	−	1.86752i	0.303851	−	0.0789172i
$561$	−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	−0.543209	−	0.839598i	$-0.682791\pi$
$563$	−30.8686	−	4.43823i	−1.30096	−	0.187049i	−0.757747	+	0.652549i	$0.773700\pi$
$564$	0.798966	−	5.55693i	0.0336426	−	0.233989i
$565$	−8.46666	+	9.17094i	−0.356195	+	0.385824i
$566$	−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	$0.701320\pi$
$570$	−12.3319	+	10.0236i	−0.516526	+	0.419841i
$571$	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
$575$	−23.4914	+	4.81206i	−0.979658	+	0.200677i
$576$	1.00000			0.0416667
$577$	−21.3541	+	3.07026i	−0.888983	+	0.127816i	−0.571650	−	0.820498i	$-0.693696\pi$
$577$	−21.3541	+	3.07026i	−0.888983	+	0.127816i	−0.317333	+	0.948314i	$0.602787\pi$
$578$	15.3269	+	6.99956i	0.637515	+	0.291144i
$579$	−20.7168	+	6.08301i	−0.860962	+	0.252801i
$580$	5.63415	−	4.57954i	0.233946	−	0.190155i
$581$	−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
$585$	−5.11611	+	5.54168i	−0.211525	+	0.229120i
$586$	−0.425012	+	2.95602i	−0.0175571	+	0.122112i
$587$	−36.7517	−	5.28409i	−1.51690	−	0.218098i	−0.667009	−	0.745050i	$-0.732426\pi$
$587$	−36.7517	−	5.28409i	−1.51690	−	0.218098i	−0.849895	+	0.526952i	$0.823335\pi$
$588$	−2.18310	+	3.39697i	−0.0900295	+	0.140089i
$589$	14.1375	+	16.3156i	0.582526	+	0.672271i
$590$	−11.8448	+	3.07636i	−0.487642	+	0.126652i
$591$	−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	0.817626	−	0.575749i	$-0.195290\pi$
$593$	8.86636	+	7.68275i	0.364098	+	0.315493i	−0.453528	+	0.891242i	$0.649835\pi$
$594$	1.87817	−	0.551480i	0.0770622	−	0.0226275i
$595$	1.63332	−	2.37369i	0.0669595	−	0.0973119i
$596$	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	$0.359852\pi$
$600$	1.02166	−	4.89451i	0.0417090	−	0.199817i
$601$	−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
$605$	14.7828	−	6.19628i	0.601008	−	0.251915i
$606$	4.54208	+	9.94576i	0.184509	+	0.404019i
$607$	−2.02885	+	1.75801i	−0.0823484	+	0.0713553i	−0.695062	−	0.718949i	$-0.744623\pi$
$607$	−2.02885	+	1.75801i	−0.0823484	+	0.0713553i	0.612714	+	0.790305i	$0.290078\pi$
$608$	−3.84233	+	5.97879i	−0.155827	+	0.242472i
$609$	−1.53526	+	10.6779i	−0.0622117	+	0.432692i
$610$	−17.3516	−	5.69414i	−0.702544	−	0.230549i
$611$	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	−0.384865	−	0.922973i	$-0.625752\pi$
$613$	1.50132	−	0.685630i	0.0606377	−	0.0276923i	0.445503	+	0.895280i	$0.353025\pi$
$614$	10.0546	−	6.46171i	0.405772	−	0.260774i
$615$	−4.48294	+	9.05077i	−0.180770	+	0.364962i
$616$	4.25879	−	4.91491i	0.171592	−	0.198027i
$617$	−8.89495	−	30.2934i	−0.358097	−	1.21957i	−0.919853	−	0.392264i	$-0.871692\pi$
$617$	−8.89495	−	30.2934i	−0.358097	−	1.21957i	0.561756	−	0.827303i	$-0.310126\pi$
$618$	−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
$625$	−22.9124	−	10.0010i	−0.916497	−	0.400041i
$626$	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
$630$	3.81765	+	6.37303i	0.152099	+	0.253907i
$631$	−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
$635$	−1.73829	+	1.04129i	−0.0689819	+	0.0413225i
$636$	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
$640$	−0.248381	−	2.22223i	−0.00981813	−	0.0878414i
$641$	−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	$0.289203\pi$
$643$			39.9947i			1.57724i	−0.614883	+	0.788619i	$0.710797\pi$
$644$	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	−0.259468	−	0.965752i	$-0.583547\pi$
$647$	−29.4869	−	13.4662i	−1.15925	−	0.529411i	−0.899782	+	0.436340i	$0.856274\pi$
$648$	0.281733	+	0.959493i	0.0110675	+	0.0376924i
$649$	−7.01550	+	8.09632i	−0.275382	+	0.317808i
$650$	13.5856	+	9.99272i	0.532872	+	0.391947i
$651$	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	0.0468618	−	0.998901i	$-0.485078\pi$
$653$	26.6339	−	23.0784i	1.04226	−	0.903128i	0.995403	+	0.0957737i	$0.0305325\pi$
$654$	4.24089	+	2.72545i	0.165832	+	0.106574i
$655$	12.4111	−	37.8199i	0.484941	−	1.47775i
$656$	−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	$0.554702\pi$
$660$	−1.69202	−	4.03675i	−0.0658617	−	0.157130i
$661$	−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
$665$	−52.7717	−	1.66235i	−2.04640	−	0.0644634i
$666$	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
$670$	13.6701	−	19.8667i	0.528123	−	0.767518i
$671$	−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	−0.881525	−	0.472137i	$-0.843483\pi$
$673$	2.99159	−	10.1884i	0.115317	−	0.392735i	0.996843	+	0.0794020i	$0.0253011\pi$
$674$	18.0760	−	11.6167i	0.696260	−	0.447459i
$675$	4.98408	−	0.398670i	0.191837	−	0.0153448i
$676$	1.06288	+	1.22662i	0.0408798	+	0.0471778i
$677$	−15.1662	+	23.5991i	−0.582884	+	0.906985i	−0.999998	−	0.00186877i	$-0.999405\pi$
$677$	−15.1662	+	23.5991i	−0.582884	+	0.906985i	0.417114	+	0.908854i	$0.363042\pi$
$678$	−5.52512	−	0.794393i	−0.212191	−	0.0305085i
$679$	0.256089	−	1.78114i	0.00982780	−	0.0683538i
$680$	−0.637226	−	0.588290i	−0.0244365	−	0.0225599i
$681$	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	0.532245	−	0.846590i	$-0.321349\pi$
$683$	−11.9942	−	18.6633i	−0.458943	−	0.714130i	−0.991188	+	0.132461i	$0.957712\pi$
$684$	−6.81911	−	2.00227i	−0.260735	−	0.0765588i
$685$	−14.0572	−	17.2944i	−0.537099	−	0.660786i
$686$	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
$690$	−7.72810	−	7.43482i	−0.294204	−	0.283039i
$691$	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
$695$	−33.5934	+	27.3053i	−1.27427	+	1.03575i
$696$	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
$700$	13.2141	−	10.0666i	0.499446	−	0.380483i
$701$	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
$705$	−3.15573	−	12.1503i	−0.118851	−	0.457608i
$706$	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	$0.792495\pi$
$710$	1.76886	+	1.21714i	0.0663841	+	0.0456784i
$711$	−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
$715$	14.7562	+	0.464834i	0.551852	+	0.0173838i
$716$	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	$0.704198\pi$
$720$	2.06224	−	0.864395i	0.0768550	−	0.0322141i
$721$	−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
$725$	7.66043	−	14.3142i	0.284501	−	0.531617i
$726$	6.03040	+	3.87550i	0.223809	+	0.143833i
$727$	−23.0552	+	19.9774i	−0.855070	+	0.740922i	−0.967536	−	0.252734i	$-0.918670\pi$
$727$	−23.0552	+	19.9774i	−0.855070	+	0.740922i	0.112466	+	0.993656i	$0.464125\pi$
$728$	−10.1935	+	4.65522i	−0.377796	+	0.172534i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	21.7071	+	10.7518i	0.803416	+	0.397941i
$731$	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	0.406855	−	0.913493i	$-0.366625\pi$
$733$	−0.462523	−	0.211227i	−0.0170837	−	0.00780185i	−0.423939	+	0.905691i	$0.639353\pi$
$734$	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	$-0.0983885\pi$
$740$	−0.0645754	−	0.577746i	−0.00237384	−	0.0212384i
$741$	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	0.894762	−	0.446544i	$-0.147345\pi$
$743$	3.18575	+	4.95712i	0.116874	+	0.181859i	−0.777888	+	0.628403i	$0.783709\pi$
$744$	−1.26189	−	2.76315i	−0.0462630	−	0.101302i
$745$	4.55586	+	7.60535i	0.166914	+	0.278638i
$746$	−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
$750$	−2.12389	−	10.9768i	−0.0775534	−	0.400814i
$751$	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
$755$	13.8293	−	1.54572i	0.503300	−	0.0562544i
$756$	−1.38015	+	3.02211i	−0.0501957	+	0.109913i
$757$	−2.16830	+	0.311755i	−0.0788082	+	0.0113309i	−0.181606	−	0.983371i	$-0.558130\pi$
$757$	−2.16830	+	0.311755i	−0.0788082	+	0.0113309i	0.102798	+	0.994702i	$0.467221\pi$
$758$		−	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
$765$	0.384933	−	0.777154i	0.0139173	−	0.0280981i
$766$	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	$0.817897\pi$
$770$	4.53422	−	13.8170i	0.163402	−	0.497930i
$771$	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	−0.681100	−	0.732191i	$-0.738498\pi$
$773$	−1.48167	+	1.28388i	−0.0532921	+	0.0461779i	0.627808	+	0.778369i	$0.283952\pi$
$774$	0.824839	+	1.80615i	0.0296482	+	0.0649206i
$775$	−14.8135	+	3.35333i	−0.532115	+	0.120455i
$776$	−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
$780$	−0.237468	+	7.53846i	−0.00850273	+	0.269920i
$781$	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
$785$	−16.6967	−	11.4889i	−0.595931	−	0.410055i
$786$	17.0799	−	5.01512i	0.609221	−	0.178883i
$787$	−16.3565	−	14.1730i	−0.583045	−	0.505212i	0.312657	−	0.949866i	$-0.398781\pi$
$787$	−16.3565	−	14.1730i	−0.583045	−	0.505212i	−0.895702	+	0.444654i	$0.853326\pi$
$788$	−0.307427	+	1.04700i	−0.0109517	+	0.0372979i
$789$	−13.2833	+	8.53667i	−0.472899	+	0.303913i
$790$	−33.4337	+	8.68350i	−1.18952	+	0.308945i
$791$	−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
$795$	8.18346	+	7.55501i	0.290237	+	0.267949i
$796$	16.6779	+	19.2473i	0.591131	+	0.682202i
$797$	24.4488	−	11.1654i	0.866023	−	0.395499i	0.0676831	−	0.997707i	$-0.478439\pi$
$797$	24.4488	−	11.1654i	0.866023	−	0.395499i	0.798340	+	0.602208i	$0.205712\pi$
$798$	−12.7656	−	19.8636i	−0.451896	−	0.703164i
$799$	−2.08922	−	0.613452i	−0.0739115	−	0.0217024i
$800$	−2.43310	−	4.36807i	−0.0860232	−	0.154434i
$801$	−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
$805$	−3.22845	−	35.4816i	−0.113788	−	1.25056i
$806$	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	$0.413963\pi$
$810$	1.41038	+	1.73517i	0.0495557	+	0.0609678i
$811$	−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
$815$	−30.6853	+	33.2378i	−1.07486	+	1.16427i
$816$	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
$820$	2.53901	+	9.77582i	0.0886660	+	0.341386i
$821$	−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	$-0.924471\pi$
$823$	−38.5272	−	33.3840i	−1.34298	−	1.16369i	−0.370994	−	0.928635i	$-0.620983\pi$
$824$	−14.4419	+	4.24053i	−0.503108	+	0.147726i
$825$	−6.97868	−	6.86216i	−0.242967	−	0.238910i
$826$	−2.58769	−	17.9978i	−0.0900372	−	0.626222i
$827$		−	36.1272i		−	1.25627i	−0.778106	−	0.628133i	$-0.783819\pi$
$827$		−	36.1272i		−	1.25627i	0.778106	−	0.628133i	$-0.216181\pi$
$828$	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	$0.745700\pi$
$830$	−0.859961	+	27.2996i	−0.0298497	+	0.947581i
$831$	−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
$835$	15.2076	+	36.2816i	0.526279	+	1.25558i
$836$	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	$0.767822\pi$
$840$	7.05863	+	2.31638i	0.243546	+	0.0799227i
$841$	−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
$845$	3.25219	+	1.61084i	0.111879	+	0.0554147i
$846$	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	−0.282675	−	0.959216i	$-0.591222\pi$
$853$	−8.28455	+	1.19114i	−0.283658	+	0.0407838i	−0.000982526		1.00000i	$0.500313\pi$
$854$	11.2717	−	24.6816i	0.385710	−	0.844587i
$855$	−15.7934	+	1.76525i	−0.540122	+	0.0603701i
$856$	3.95104	−	4.55975i	0.135044	−	0.155849i
$857$	−3.98660	+	13.5771i	−0.136180	+	0.463786i	−0.999139	−	0.0414878i	$-0.986790\pi$
$857$	−3.98660	+	13.5771i	−0.136180	+	0.463786i	0.862959	+	0.505274i	$0.168608\pi$
$858$	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	$0.825235\pi$
$860$	3.80880	−	2.28160i	0.129879	−	0.0778018i
$861$	−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	0.911838	−	0.410549i	$-0.134663\pi$
$863$	49.0910	+	7.05822i	1.67108	+	0.240264i	0.759237	+	0.650814i	$0.225572\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	8.40981	−	5.03776i	0.285942	−	0.171289i
$866$	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
$870$	7.21564	−	0.806500i	0.244633	−	0.0273429i
$871$	−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	0.317563	−	0.948237i	$-0.397136\pi$
$877$	−5.65949	−	2.58460i	−0.191107	−	0.0872758i	−0.508670	+	0.860961i	$0.669863\pi$
$878$	−5.73716	−	19.5390i	−0.193620	−	0.659408i
$879$	−1.95569	+	2.25698i	−0.0659637	+	0.0761262i
$880$	−3.92225	−	1.94273i	−0.132219	−	0.0654895i
$881$	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	−0.884363	−	0.466799i	$-0.845407\pi$
$883$	−16.2891	+	14.1146i	−0.548173	+	0.474995i	0.336190	+	0.941794i	$0.390862\pi$
$884$	1.10054	+	0.707272i	0.0370151	+	0.0237881i
$885$	−11.6277	−	3.81577i	−0.390860	−	0.128266i
$886$	4.65717	−	32.3913i	0.156461	−	1.08821i
$887$	10.4674	−	16.2877i	0.351462	−	0.546886i	−0.619842	−	0.784727i	$-0.712803\pi$
$887$	10.4674	−	16.2877i	0.351462	−	0.546886i	0.971304	+	0.237841i	$0.0764396\pi$
$888$	0.196483	−	0.170254i	0.00659355	−	0.00571335i
$889$	−1.25069	−	2.73862i	−0.0419467	−	0.0918505i
$890$	2.50501	+	5.97634i	0.0839680	+	0.200328i
$891$	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
$895$	1.42812	−	45.3358i	0.0477367	−	1.51541i
$896$	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
$900$	3.50564	−	3.56517i	0.116855	−	0.118839i
$901$	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
$905$	−7.73508	−	29.7820i	−0.257123	−	0.989987i
$906$	4.07530	+	4.70315i	0.135393	+	0.156252i
$907$	19.8024	−	30.8131i	0.657528	−	1.02313i	−0.339074	−	0.940760i	$-0.610114\pi$
$907$	19.8024	−	30.8131i	0.657528	−	1.02313i	0.996602	−	0.0823734i	$-0.0262500\pi$
$908$	19.3931	+	2.78831i	0.643583	+	0.0925333i
$909$	−1.55605	+	10.8225i	−0.0516108	+	0.358961i
$910$	−16.9975	+	18.4114i	−0.563461	+	0.610331i
$911$	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
$915$	−11.5186	−	14.1712i	−0.380793	−	0.468485i
$916$	−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	$0.818852\pi$
$920$	−10.7093	−	0.558032i	−0.353074	−	0.0183978i
$921$	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
$925$	−0.632571	−	1.13563i	−0.0207988	−	0.0373393i
$926$	−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	$0.564925\pi$
$930$	−4.99076	−	4.60749i	−0.163653	−	0.151086i
$931$	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
$935$	−1.64311	+	0.426755i	−0.0537356	+	0.0139564i
$936$	−2.83753	+	1.82357i	−0.0927474	+	0.0596051i
$937$	−10.0320	+	34.1658i	−0.327730	+	1.11615i	0.616635	+	0.787249i	$0.288495\pi$
$937$	−10.0320	+	34.1658i	−0.327730	+	1.11615i	−0.944365	+	0.328898i	$0.893323\pi$
$938$	27.0791	+	23.4642i	0.884165	+	0.766133i
$939$	5.95639	−	1.74895i	0.194380	−	0.0570750i
$940$	−10.3417	−	7.11605i	−0.337310	−	0.232100i
$941$	−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
$945$	−0.233904	+	7.42531i	−0.00760890	+	0.241545i
$946$	1.61459	−	3.53546i	0.0524948	−	0.114948i
$947$	−5.28872	−	18.0117i	−0.171860	−	0.585302i	−0.999704	−	0.0243429i	$-0.992251\pi$
$947$	−5.28872	−	18.0117i	−0.171860	−	0.585302i	0.827843	−	0.560959i	$-0.189568\pi$
$948$	−11.6749	−	10.1163i	−0.379182	−	0.328563i
$949$	−35.0602	−	10.2946i	−1.13810	−	0.334177i
$950$	7.84556	+	34.6581i	0.254544	+	1.12446i
$951$	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	−0.846204	−	0.532859i	$-0.821117\pi$
$953$	−0.307841	+	0.479010i	−0.00997195	+	0.0155167i	0.836232	+	0.548376i	$0.184754\pi$
$954$	−0.708857	+	4.93021i	−0.0229501	+	0.159621i
$955$	−15.2802	+	46.5630i	−0.494457	+	1.50674i
$956$	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
$960$	0.992477	−	2.00374i	0.0320320	−	0.0646706i
$961$	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	$-0.895963\pi$
$967$		−	19.9674i		−	0.642110i	0.947061	−	0.321055i	$-0.104037\pi$
$968$	7.09539	−	1.02016i	0.228054	−	0.0327893i
$969$	−1.14507	+	2.50736i	−0.0367851	+	0.0805481i
$970$	−1.20361	+	0.134529i	−0.0386455	+	0.00431946i
$971$	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
$975$	6.02649	+	15.7514i	0.193002	+	0.504447i
$976$	−6.87052	−	4.41542i	−0.219920	−	0.141334i
$977$	38.1918	+	5.49115i	1.22186	+	0.175677i	0.722904	−	0.690948i	$-0.242807\pi$
$977$	38.1918	+	5.49115i	1.22186	+	0.175677i	0.498959	+	0.866626i	$0.333716\pi$
$978$	−20.0244	−	2.87908i	−0.640311	−	0.0920628i
$979$	4.77218	+	3.06689i	0.152520	+	0.0980183i
$980$	4.63998	+	7.74579i	0.148219	+	0.247430i
$981$	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	$0.207890\pi$
$983$	−6.34726	+	21.6168i	−0.202446	+	0.689469i	−0.996648	+	0.0818141i	$0.973929\pi$
$984$	−2.95796	+	3.41367i	−0.0942963	+	0.108824i
$985$	0.271034	+	2.42490i	0.00863588	+	0.0772639i
$986$	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
$995$	51.0310	+	25.2762i	1.61779	+	0.801310i
$996$	−10.2757	+	6.60381i	−0.325599	+	0.209250i
$997$	−41.1013	+	18.7704i	−1.30169	+	0.594463i	−0.941058	−	0.338244i	$-0.890167\pi$
$997$	−41.1013	+	18.7704i	−1.30169	+	0.594463i	−0.360634	+	0.932707i	$0.617440\pi$
$998$	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.49.11	yes	120
5.4	even	2	inner	690.2.r.a.49.4	✓	120
23.8	even	11	inner	690.2.r.a.169.4	yes	120
115.54	even	22	inner	690.2.r.a.169.11	yes	120

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

\(f(q)\)	\(=\)	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.73517 - 1.41038i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.79620 + 2.79494i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(1.73517 - 1.41038i) 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} +(1.51679 - 1.64297i) 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} +(2.16426 - 0.562109i) 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} +(1.26754 - 1.84210i) q^{20} +(0.472819 + 3.28853i) q^{21} -1.95746i q^{22} +(-1.90211 - 4.40250i) q^{23} +1.00000 q^{24} +(1.02166 - 4.89451i) 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} +(2.06224 - 0.864395i) 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} +(7.05863 + 2.31638i) 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} +(0.992477 - 2.00374i) 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} +(0.314697 - 4.99009i) 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} +(-2.24928 - 3.75486i) 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} +(1.91823 - 1.14908i) 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} +(0.837783 + 7.49552i) 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} +(2.96258 - 4.02779i) 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} +(0.697212 - 2.12459i) 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} +(-0.335256 - 0.799841i) 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} +(2.23496 + 0.0704032i) q^{90} -11.2062 q^{91} +(-3.06539 - 3.68828i) q^{92} -3.03765i q^{93} +(-0.798966 - 5.55693i) q^{94} +(-9.00838 + 13.0918i) 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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